LMFDB - Embedded newform 19.3.f.a.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,3,Mod(2,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, 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:	$0.517712502285$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.1
Root			$-2.57727i$ of defining polynomial
Character	$\chi$	$=$	19.14
Dual form			19.3.f.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.881480 - 2.42185i) q^{2} +(-0.384565 - 0.0678091i) q^{3} +(-2.02415 + 1.69847i) q^{4} +(1.73199 + 1.45331i) q^{5} +(0.174763 + 0.991129i) q^{6} +(5.72163 + 9.91015i) q^{7} +(-3.03027 - 1.74952i) q^{8} +(-8.31394 - 3.02603i) q^{9} +O(q^{10})$	\(q+(-0.881480 - 2.42185i) q^{2} +(-0.384565 - 0.0678091i) q^{3} +(-2.02415 + 1.69847i) q^{4} +(1.73199 + 1.45331i) q^{5} +(0.174763 + 0.991129i) q^{6} +(5.72163 + 9.91015i) q^{7} +(-3.03027 - 1.74952i) q^{8} +(-8.31394 - 3.02603i) q^{9} +(1.99298 - 5.47566i) q^{10} +(3.88672 - 6.73200i) q^{11} +(0.893589 - 0.515914i) q^{12} +(-13.5844 + 2.39530i) q^{13} +(18.9574 - 22.5925i) q^{14} +(-0.567513 - 0.676335i) q^{15} +(-3.40132 + 19.2898i) q^{16} +(2.79442 - 1.01709i) q^{17} +22.8025i q^{18} +(17.7595 - 6.75283i) q^{19} -5.97420 q^{20} +(-1.52834 - 4.19907i) q^{21} +(-19.7299 - 3.47892i) q^{22} +(-20.9616 + 17.5889i) q^{23} +(1.04670 + 0.878285i) q^{24} +(-3.45354 - 19.5860i) q^{25} +(17.7754 + 30.7880i) q^{26} +(6.03568 + 3.48470i) q^{27} +(-28.4135 - 10.3417i) q^{28} +(6.50458 - 17.8712i) q^{29} +(-1.13773 + 1.97060i) q^{30} +(28.8085 - 16.6326i) q^{31} +(35.9316 - 6.33571i) q^{32} +(-1.95119 + 2.32533i) q^{33} +(-4.92645 - 5.87112i) q^{34} +(-4.49273 + 25.4795i) q^{35} +(21.9683 - 7.99581i) q^{36} +2.53007i q^{37} +(-32.0089 - 37.0583i) q^{38} +5.38651 q^{39} +(-2.70578 - 7.43406i) q^{40} +(-52.5957 - 9.27403i) q^{41} +(-8.82230 + 7.40279i) q^{42} +(-3.40715 - 2.85894i) q^{43} +(3.56675 + 20.2281i) q^{44} +(-10.0019 - 17.3238i) q^{45} +(61.0747 + 35.2615i) q^{46} +(20.0556 + 7.29965i) q^{47} +(2.61605 - 7.18754i) q^{48} +(-40.9740 + 70.9691i) q^{49} +(-44.3900 + 25.6286i) q^{50} +(-1.14360 + 0.201648i) q^{51} +(23.4286 - 27.9211i) q^{52} +(47.6606 + 56.7997i) q^{53} +(3.11908 - 17.6892i) q^{54} +(16.5154 - 6.01112i) q^{55} -40.0405i q^{56} +(-7.28757 + 1.39264i) q^{57} -49.0150 q^{58} +(18.5831 + 51.0568i) q^{59} +(2.29747 + 0.405105i) q^{60} +(81.0659 - 68.0224i) q^{61} +(-65.6757 - 55.1084i) q^{62} +(-17.5809 - 99.7062i) q^{63} +(-7.84230 - 13.5833i) q^{64} +(-27.0091 - 15.5937i) q^{65} +(7.35153 + 2.67574i) q^{66} +(-10.5574 + 29.0062i) q^{67} +(-3.92885 + 6.80497i) q^{68} +(9.25377 - 5.34267i) q^{69} +(65.6677 - 11.5790i) q^{70} +(-49.1865 + 58.6182i) q^{71} +(19.8993 + 23.7151i) q^{72} +(3.15964 - 17.9192i) q^{73} +(6.12745 - 2.23021i) q^{74} +7.76625i q^{75} +(-24.4785 + 43.8327i) q^{76} +88.9535 q^{77} +(-4.74810 - 13.0453i) q^{78} +(-30.0440 - 5.29757i) q^{79} +(-33.9251 + 28.4665i) q^{80} +(58.9135 + 49.4343i) q^{81} +(23.9017 + 135.553i) q^{82} +(-41.2527 - 71.4518i) q^{83} +(10.2256 + 5.90373i) q^{84} +(6.31804 + 2.29958i) q^{85} +(-3.92058 + 10.7717i) q^{86} +(-3.71326 + 6.43156i) q^{87} +(-23.5556 + 13.5998i) q^{88} +(-86.5010 + 15.2525i) q^{89} +(-33.1390 + 39.4935i) q^{90} +(-101.463 - 120.919i) q^{91} +(12.5554 - 71.2051i) q^{92} +(-12.2066 + 4.44283i) q^{93} -55.0062i q^{94} +(40.5731 + 14.1142i) q^{95} -14.2476 q^{96} +(-18.6025 - 51.1100i) q^{97} +(207.994 + 36.6750i) q^{98} +(-52.6852 + 44.2081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22} - 102 q^{23} - 12 q^{24} - 156 q^{25} + 21 q^{26} - 27 q^{27} + 12 q^{28} + 147 q^{29} + 24 q^{30} + 99 q^{31} + 165 q^{32} + 84 q^{33} + 132 q^{34} + 96 q^{35} + 63 q^{36} + 72 q^{38} - 108 q^{39} - 138 q^{40} - 144 q^{41} - 237 q^{42} - 27 q^{43} - 123 q^{44} - 3 q^{45} - 54 q^{46} - 99 q^{47} - 51 q^{48} - 24 q^{49} + 72 q^{50} - 42 q^{51} + 93 q^{52} + 111 q^{53} + 21 q^{54} + 162 q^{55} - 168 q^{57} - 132 q^{58} + 3 q^{59} - 30 q^{60} + 150 q^{61} + 108 q^{62} + 234 q^{63} + 27 q^{64} + 126 q^{65} + 168 q^{66} + 135 q^{67} - 30 q^{68} + 72 q^{69} + 225 q^{70} - 168 q^{71} - 102 q^{72} - 90 q^{73} - 231 q^{74} + 42 q^{76} + 246 q^{77} - 189 q^{78} - 75 q^{79} + 21 q^{80} - 159 q^{81} - 117 q^{82} - 156 q^{83} + 99 q^{84} - 300 q^{85} - 144 q^{86} + 69 q^{87} - 405 q^{88} - 558 q^{89} - 66 q^{90} - 453 q^{91} + 48 q^{92} - 57 q^{93} - 69 q^{95} + 558 q^{96} + 465 q^{97} + 777 q^{98} + 462 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9 + 51 * q^10 - 18 * q^11 + 63 * q^12 + 21 * q^13 + 9 * q^14 + 63 * q^15 - 12 * q^16 - 3 * q^17 - 24 * q^19 - 90 * q^20 + 30 * q^21 - 78 * q^22 - 102 * q^23 - 12 * q^24 - 156 * q^25 + 21 * q^26 - 27 * q^27 + 12 * q^28 + 147 * q^29 + 24 * q^30 + 99 * q^31 + 165 * q^32 + 84 * q^33 + 132 * q^34 + 96 * q^35 + 63 * q^36 + 72 * q^38 - 108 * q^39 - 138 * q^40 - 144 * q^41 - 237 * q^42 - 27 * q^43 - 123 * q^44 - 3 * q^45 - 54 * q^46 - 99 * q^47 - 51 * q^48 - 24 * q^49 + 72 * q^50 - 42 * q^51 + 93 * q^52 + 111 * q^53 + 21 * q^54 + 162 * q^55 - 168 * q^57 - 132 * q^58 + 3 * q^59 - 30 * q^60 + 150 * q^61 + 108 * q^62 + 234 * q^63 + 27 * q^64 + 126 * q^65 + 168 * q^66 + 135 * q^67 - 30 * q^68 + 72 * q^69 + 225 * q^70 - 168 * q^71 - 102 * q^72 - 90 * q^73 - 231 * q^74 + 42 * q^76 + 246 * q^77 - 189 * q^78 - 75 * q^79 + 21 * q^80 - 159 * q^81 - 117 * q^82 - 156 * q^83 + 99 * q^84 - 300 * q^85 - 144 * q^86 + 69 * q^87 - 405 * q^88 - 558 * q^89 - 66 * q^90 - 453 * q^91 + 48 * q^92 - 57 * q^93 - 69 * q^95 + 558 * q^96 + 465 * q^97 + 777 * q^98 + 462 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−0.881480	−	2.42185i	−0.440740	−	1.21092i	−0.939007	−	0.343899i	$-0.888252\pi$
$2$	−0.881480	−	2.42185i	−0.440740	−	1.21092i	0.498267	−	0.867024i	$-0.333970\pi$
$3$	−0.384565	−	0.0678091i	−0.128188	−	0.0226030i	0.109186	−	0.994021i	$-0.465176\pi$
$3$	−0.384565	−	0.0678091i	−0.128188	−	0.0226030i	−0.237374	+	0.971418i	$0.576287\pi$
$4$	−2.02415	+	1.69847i	−0.506038	+	0.424617i
$5$	1.73199	+	1.45331i	0.346397	+	0.290662i	0.799341	−	0.600877i	$-0.205182\pi$
$5$	1.73199	+	1.45331i	0.346397	+	0.290662i	−0.452944	+	0.891539i	$0.649626\pi$
$6$	0.174763	+	0.991129i	0.0291271	+	0.165188i
$7$	5.72163	+	9.91015i	0.817375	+	1.41574i	0.907610	+	0.419815i	$0.137905\pi$
$7$	5.72163	+	9.91015i	0.817375	+	1.41574i	−0.0902345	+	0.995921i	$0.528762\pi$
$8$	−3.03027	−	1.74952i	−0.378783	−	0.218691i
$9$	−8.31394	−	3.02603i	−0.923771	−	0.336225i
$10$	1.99298	−	5.47566i	0.199298	−	0.547566i
$11$	3.88672	−	6.73200i	0.353338	−	0.612000i	−0.633494	−	0.773748i	$-0.718380\pi$
$11$	3.88672	−	6.73200i	0.353338	−	0.612000i	0.986832	+	0.161748i	$0.0517131\pi$
$12$	0.893589	−	0.515914i	0.0744658	−	0.0429928i
$13$	−13.5844	+	2.39530i	−1.04496	+	0.184254i	−0.669673	−	0.742656i	$-0.733566\pi$
$13$	−13.5844	+	2.39530i	−1.04496	+	0.184254i	−0.375283	+	0.926910i	$0.622454\pi$
$14$	18.9574	−	22.5925i	1.35410	−	1.61375i
$15$	−0.567513	−	0.676335i	−0.0378342	−	0.0450890i
$16$	−3.40132	+	19.2898i	−0.212582	+	1.20561i
$17$	2.79442	−	1.01709i	0.164378	−	0.0598286i	−0.258521	−	0.966006i	$-0.583235\pi$
$17$	2.79442	−	1.01709i	0.164378	−	0.0598286i	0.422898	+	0.906177i	$0.361013\pi$
$18$			22.8025i			1.26680i
$19$	17.7595	−	6.75283i	0.934710	−	0.355412i
$19$	17.7595	−	6.75283i	0.934710	−	0.355412i
$20$	−5.97420			−0.298710
$21$	−1.52834	−	4.19907i	−0.0727779	−	0.199956i
$22$	−19.7299	−	3.47892i	−0.896815	−	0.158133i
$23$	−20.9616	+	17.5889i	−0.911373	+	0.764733i	−0.972380	−	0.233404i	$-0.925013\pi$
$23$	−20.9616	+	17.5889i	−0.911373	+	0.764733i	0.0610065	+	0.998137i	$0.480569\pi$
$24$	1.04670	+	0.878285i	0.0436125	+	0.0365952i
$25$	−3.45354	−	19.5860i	−0.138141	−	0.783439i
$26$	17.7754	+	30.7880i	0.683671	+	1.18415i
$27$	6.03568	+	3.48470i	0.223544	+	0.129063i
$28$	−28.4135	−	10.3417i	−1.01477	−	0.369345i
$29$	6.50458	−	17.8712i	0.224296	−	0.616248i	−0.775592	−	0.631235i	$-0.782548\pi$
$29$	6.50458	−	17.8712i	0.224296	−	0.616248i	0.999888	+	0.0149867i	$0.00477060\pi$
$30$	−1.13773	+	1.97060i	−0.0379243	+	0.0656868i
$31$	28.8085	−	16.6326i	0.929306	−	0.536535i	0.0427142	−	0.999087i	$-0.486400\pi$
$31$	28.8085	−	16.6326i	0.929306	−	0.536535i	0.886592	+	0.462552i	$0.153066\pi$
$32$	35.9316	−	6.33571i	1.12286	−	0.197991i
$33$	−1.95119	+	2.32533i	−0.0591269	+	0.0704646i
$34$	−4.92645	−	5.87112i	−0.144896	−	0.172680i
$35$	−4.49273	+	25.4795i	−0.128364	+	0.727986i
$36$	21.9683	−	7.99581i	0.610231	−	0.222106i
$37$			2.53007i			0.0683803i	0.999415	+	0.0341902i	$0.0108852\pi$
$37$			2.53007i			0.0683803i	−0.999415	+	0.0341902i	$0.989115\pi$
$38$	−32.0089	−	37.0583i	−0.842341	−	0.975217i
$39$	5.38651			0.138116
$40$	−2.70578	−	7.43406i	−0.0676444	−	0.185852i
$41$	−52.5957	−	9.27403i	−1.28282	−	0.226196i	−0.509643	−	0.860386i	$-0.670223\pi$
$41$	−52.5957	−	9.27403i	−1.28282	−	0.226196i	−0.773177	+	0.634190i	$0.781334\pi$
$42$	−8.82230	+	7.40279i	−0.210055	+	0.176257i
$43$	−3.40715	−	2.85894i	−0.0792361	−	0.0664870i	0.602309	−	0.798263i	$-0.294247\pi$
$43$	−3.40715	−	2.85894i	−0.0792361	−	0.0664870i	−0.681545	+	0.731776i	$0.738692\pi$
$44$	3.56675	+	20.2281i	0.0810626	+	0.459729i
$45$	−10.0019	−	17.3238i	−0.222264	−	0.384972i
$46$	61.0747	+	35.2615i	1.32771	+	0.766554i
$47$	20.0556	+	7.29965i	0.426716	+	0.155312i	0.546445	−	0.837495i	$-0.315981\pi$
$47$	20.0556	+	7.29965i	0.426716	+	0.155312i	−0.119730	+	0.992807i	$0.538203\pi$
$48$	2.61605	−	7.18754i	0.0545011	−	0.149740i
$49$	−40.9740	+	70.9691i	−0.836205	+	1.44835i
$50$	−44.3900	+	25.6286i	−0.887800	+	0.512572i
$51$	−1.14360	+	0.201648i	−0.0224236	+	0.00395389i
$52$	23.4286	−	27.9211i	0.450550	−	0.536945i
$53$	47.6606	+	56.7997i	0.899256	+	1.07169i	0.997071	+	0.0764869i	$0.0243703\pi$
$53$	47.6606	+	56.7997i	0.899256	+	1.07169i	−0.0978146	+	0.995205i	$0.531185\pi$
$54$	3.11908	−	17.6892i	0.0577607	−	0.327577i
$55$	16.5154	−	6.01112i	0.300280	−	0.109293i
$56$		−	40.0405i		−	0.715009i
$57$	−7.28757	+	1.39264i	−0.127852	+	0.0244324i
$58$	−49.0150			−0.845085
$59$	18.5831	+	51.0568i	0.314969	+	0.865369i	0.991634	+	0.129079i	$0.0412020\pi$
$59$	18.5831	+	51.0568i	0.314969	+	0.865369i	−0.676666	+	0.736290i	$0.736576\pi$
$60$	2.29747	+	0.405105i	0.0382911	+	0.00675175i
$61$	81.0659	−	68.0224i	1.32895	−	1.11512i	0.344628	−	0.938739i	$-0.388005\pi$
$61$	81.0659	−	68.0224i	1.32895	−	1.11512i	0.984322	−	0.176382i	$-0.0564393\pi$
$62$	−65.6757	−	55.1084i	−1.05929	−	0.888846i
$63$	−17.5809	−	99.7062i	−0.279062	−	1.58264i
$64$	−7.84230	−	13.5833i	−0.122536	−	0.212238i
$65$	−27.0091	−	15.5937i	−0.415525	−	0.239903i
$66$	7.35153	+	2.67574i	0.111387	+	0.0405415i
$67$	−10.5574	+	29.0062i	−0.157573	+	0.432929i	−0.993207	−	0.116357i	$-0.962878\pi$
$67$	−10.5574	+	29.0062i	−0.157573	+	0.432929i	0.835634	+	0.549286i	$0.185100\pi$
$68$	−3.92885	+	6.80497i	−0.0577773	+	0.100073i
$69$	9.25377	−	5.34267i	0.134113	−	0.0774299i
$70$	65.6677	−	11.5790i	0.938110	−	0.165414i
$71$	−49.1865	+	58.6182i	−0.692768	+	0.825608i	−0.991687	−	0.128670i	$-0.958929\pi$
$71$	−49.1865	+	58.6182i	−0.692768	+	0.825608i	0.298920	+	0.954278i	$0.403374\pi$
$72$	19.8993	+	23.7151i	0.276380	+	0.329377i
$73$	3.15964	−	17.9192i	0.0432827	−	0.245469i	−0.955488	−	0.295029i	$-0.904671\pi$
$73$	3.15964	−	17.9192i	0.0432827	−	0.245469i	0.998771	+	0.0495601i	$0.0157819\pi$
$74$	6.12745	−	2.23021i	0.0828033	−	0.0301379i
$75$			7.76625i			0.103550i
$76$	−24.4785	+	43.8327i	−0.322085	+	0.576745i
$77$	88.9535			1.15524
$78$	−4.74810	−	13.0453i	−0.0608731	−	0.167247i
$79$	−30.0440	−	5.29757i	−0.380304	−	0.0670578i	−0.0197715	−	0.999805i	$-0.506294\pi$
$79$	−30.0440	−	5.29757i	−0.380304	−	0.0670578i	−0.360532	+	0.932747i	$0.617405\pi$
$80$	−33.9251	+	28.4665i	−0.424063	+	0.355832i
$81$	58.9135	+	49.4343i	0.727327	+	0.610300i
$82$	23.9017	+	135.553i	0.291485	+	1.65309i
$83$	−41.2527	−	71.4518i	−0.497020	−	0.860865i	0.502974	−	0.864302i	$-0.332239\pi$
$83$	−41.2527	−	71.4518i	−0.497020	−	0.860865i	−0.999994	+	0.00343715i	$0.998906\pi$
$84$	10.2256	+	5.90373i	0.121733	+	0.0702826i
$85$	6.31804	+	2.29958i	0.0743299	+	0.0270539i
$86$	−3.92058	+	10.7717i	−0.0455881	+	0.125252i
$87$	−3.71326	+	6.43156i	−0.0426812	+	0.0739260i
$88$	−23.5556	+	13.5998i	−0.267677	+	0.154544i
$89$	−86.5010	+	15.2525i	−0.971921	+	0.171376i	−0.636995	−	0.770868i	$-0.719823\pi$
$89$	−86.5010	+	15.2525i	−0.971921	+	0.171376i	−0.334927	+	0.942244i	$0.608712\pi$
$90$	−33.1390	+	39.4935i	−0.368211	+	0.438817i
$91$	−101.463	−	120.919i	−1.11498	−	1.32878i
$92$	12.5554	−	71.2051i	0.136472	−	0.773969i
$93$	−12.2066	+	4.44283i	−0.131253	+	0.0477723i
$94$		−	55.0062i		−	0.585172i
$95$	40.5731	+	14.1142i	0.427085	+	0.148571i
$96$	−14.2476			−0.148413
$97$	−18.6025	−	51.1100i	−0.191779	−	0.526907i	0.806116	−	0.591757i	$-0.201565\pi$
$97$	−18.6025	−	51.1100i	−0.191779	−	0.526907i	−0.997895	+	0.0648495i	$0.979343\pi$
$98$	207.994	+	36.6750i	2.12239	+	0.374234i
$99$	−52.6852	+	44.2081i	−0.532174	+	0.446547i
$100$	40.2566	+	33.7793i	0.402566	+	0.337793i
$101$	−0.783333	−	4.44250i	−0.00775577	−	0.0439852i	0.980684	−	0.195597i	$-0.0626646\pi$
$101$	−0.783333	−	4.44250i	−0.00775577	−	0.0439852i	−0.988440	+	0.151612i	$0.951553\pi$
$102$	1.49642	+	2.59188i	0.0146708	+	0.0254106i
$103$	−32.2256	−	18.6055i	−0.312870	−	0.180636i	0.335340	−	0.942097i	$-0.391149\pi$
$103$	−32.2256	−	18.6055i	−0.312870	−	0.180636i	−0.648210	+	0.761462i	$0.724482\pi$
$104$	45.3550	+	16.5079i	0.436106	+	0.158730i
$105$	3.45549	−	9.49387i	0.0329094	−	0.0904178i
$106$	95.5482	−	165.494i	0.901398	−	1.56127i
$107$	135.019	−	77.9530i	1.26186	−	0.728533i	0.288422	−	0.957503i	$-0.406869\pi$
$107$	135.019	−	77.9530i	1.26186	−	0.728533i	0.973433	+	0.228971i	$0.0735360\pi$
$108$	−18.1358	+	3.19783i	−0.167924	+	0.0296095i
$109$	−35.9660	+	42.8627i	−0.329964	+	0.393235i	−0.905364	−	0.424637i	$-0.860402\pi$
$109$	−35.9660	+	42.8627i	−0.329964	+	0.393235i	0.575400	+	0.817872i	$0.304846\pi$
$110$	−29.1160	−	34.6991i	−0.264691	−	0.315446i
$111$	0.171562	−	0.972976i	0.00154560	−	0.00876555i
$112$	−210.626	+	76.6616i	−1.88059	+	0.684479i
$113$			78.1077i			0.691219i	0.938378	+	0.345609i	$0.112328\pi$
$113$			78.1077i			0.691219i	−0.938378	+	0.345609i	$0.887672\pi$
$114$	9.79662	+	16.4218i	0.0859352	+	0.144051i
$115$	−61.8672			−0.537976
$116$	17.1874	+	47.2219i	0.148167	+	0.407085i
$117$	120.188	+	21.1924i	1.02725	+	0.181132i
$118$	107.271	−	90.0110i	0.909076	−	0.762805i
$119$	26.0681	+	21.8738i	0.219060	+	0.183813i
$120$	0.536449	+	3.04235i	0.00447041	+	0.0253529i
$121$	30.2868	+	52.4583i	0.250304	+	0.433539i
$122$	−236.198	−	136.369i	−1.93605	−	1.11778i
$123$	19.5976	+	7.13293i	0.159330	+	0.0579913i
$124$	−30.0629	+	82.5972i	−0.242443	+	0.666106i
$125$	50.7448	−	87.8926i	0.405959	−	0.703141i
$126$	−225.976	+	130.467i	−1.79346	+	1.03545i
$127$	−124.961	+	22.0339i	−0.983942	+	0.173496i	−0.642399	−	0.766371i	$-0.722061\pi$
$127$	−124.961	+	22.0339i	−0.983942	+	0.173496i	−0.341543	+	0.939866i	$0.610950\pi$
$128$	67.8270	−	80.8331i	0.529898	−	0.631508i
$129$	1.11641	+	1.33048i	0.00865432	+	0.0103138i
$130$	−13.9576	+	79.1575i	−0.107366	+	0.608904i
$131$	47.5418	−	17.3038i	0.362914	−	0.132090i	−0.154126	−	0.988051i	$-0.549256\pi$
$131$	47.5418	−	17.3038i	0.362914	−	0.132090i	0.517040	+	0.855961i	$0.327034\pi$
$132$		−	8.02086i		−	0.0607641i
$133$	168.535	+	137.362i	1.26718	+	1.03280i
$134$	79.5548			0.593692
$135$	5.38936	+	14.8072i	0.0399212	+	0.109683i
$136$	−10.2473	−	1.80687i	−0.0753475	−	0.0132858i
$137$	−84.7583	+	71.1207i	−0.618674	+	0.519129i	−0.897386	−	0.441246i	$-0.854537\pi$
$137$	−84.7583	+	71.1207i	−0.618674	+	0.519129i	0.278713	+	0.960375i	$0.410092\pi$
$138$	−21.0961	−	17.7017i	−0.152870	−	0.128274i
$139$	13.1317	+	74.4737i	0.0944728	+	0.535782i	0.994908	+	0.100791i	$0.0321373\pi$
$139$	13.1317	+	74.4737i	0.0944728	+	0.535782i	−0.900435	+	0.434991i	$0.856752\pi$
$140$	−34.1821	−	59.2052i	−0.244158	−	0.422894i
$141$	−7.21770	−	4.16714i	−0.0511894	−	0.0295542i
$142$	185.321	+	67.4514i	1.30508	+	0.475010i
$143$	−36.6737	+	100.760i	−0.256459	+	0.704617i
$144$	86.6498	−	150.082i	0.601735	−	1.04224i
$145$	37.2382	−	21.4995i	0.256815	−	0.148272i
$146$	−46.1827	+	8.14326i	−0.316320	+	0.0557757i
$147$	20.5695	−	24.5138i	0.139929	−	0.166760i
$148$	−4.29724	−	5.12126i	−0.0290354	−	0.0346031i
$149$	35.5609	−	201.676i	0.238664	−	1.35353i	−0.596096	−	0.802913i	$-0.703282\pi$
$149$	35.5609	−	201.676i	0.238664	−	1.35353i	0.834759	−	0.550615i	$-0.185607\pi$
$150$	18.8087	−	6.84580i	0.125391	−	0.0456386i
$151$		−	45.8135i		−	0.303400i	−0.988427	−	0.151700i	$-0.951525\pi$
$151$		−	45.8135i		−	0.303400i	0.988427	−	0.151700i	$-0.0484748\pi$
$152$	−65.6302	−	10.6078i	−0.431778	−	0.0697881i
$153$	−26.3104			−0.171963
$154$	−78.4107	−	215.432i	−0.509160	−	1.39891i
$155$	74.0682	+	13.0602i	0.477859	+	0.0842595i
$156$	−10.9031	+	9.14881i	−0.0698918	+	0.0586462i
$157$	−7.88720	−	6.61815i	−0.0502369	−	0.0421538i	0.617323	−	0.786709i	$-0.288217\pi$
$157$	−7.88720	−	6.61815i	−0.0502369	−	0.0421538i	−0.667560	+	0.744556i	$0.732661\pi$
$158$	13.6533	+	77.4317i	0.0864132	+	0.490074i
$159$	−14.4770	−	25.0750i	−0.0910505	−	0.157704i
$160$	71.4407	+	41.2463i	0.446505	+	0.257790i
$161$	−294.243	−	107.096i	−1.82759	−	0.665190i
$162$	67.7912	−	186.255i	0.418464	−	1.14972i
$163$	−45.0765	+	78.0748i	−0.276543	+	0.478986i	−0.970523	−	0.241008i	$-0.922522\pi$
$163$	−45.0765	+	78.0748i	−0.276543	+	0.478986i	0.693980	+	0.719994i	$0.255855\pi$
$164$	122.213	−	70.5599i	0.745203	−	0.430243i
$165$	−6.75885	+	1.19177i	−0.0409627	+	0.00722284i
$166$	−136.682	+	162.891i	−0.823384	+	0.981271i
$167$	45.9221	+	54.7278i	0.274983	+	0.327712i	0.885806	−	0.464055i	$-0.153606\pi$
$167$	45.9221	+	54.7278i	0.274983	+	0.327712i	−0.610824	+	0.791767i	$0.709162\pi$
$168$	−2.71511	+	15.3982i	−0.0161614	+	0.0916557i
$169$	19.9910	−	7.27612i	0.118290	−	0.0430540i
$170$		−	17.3284i		−	0.101931i
$171$	−168.086	+	2.40195i	−0.982957	+	0.0140465i
$172$	11.7524			0.0683280
$173$	55.7647	+	153.212i	0.322339	+	0.885620i	0.989989	+	0.141144i	$0.0450781\pi$
$173$	55.7647	+	153.212i	0.322339	+	0.885620i	−0.667650	+	0.744475i	$0.732700\pi$
$174$	18.8494	+	3.32366i	0.108330	+	0.0191015i
$175$	174.340	−	146.289i	0.996229	−	0.835935i
$176$	116.639	+	97.8718i	0.662722	+	0.556090i
$177$	−3.68431	−	20.8947i	−0.0208153	−	0.118049i
$178$	113.188	+	196.047i	0.635887	+	1.10139i
$179$	7.43009	+	4.28977i	0.0415089	+	0.0239652i	0.520611	−	0.853794i	$-0.325704\pi$
$179$	7.43009	+	4.28977i	0.0415089	+	0.0239652i	−0.479102	+	0.877759i	$0.659038\pi$
$180$	49.6692	+	18.0781i	0.275940	+	0.100434i
$181$	−7.79509	+	21.4168i	−0.0430668	+	0.118325i	−0.959362	−	0.282179i	$-0.908943\pi$
$181$	−7.79509	+	21.4168i	−0.0430668	+	0.118325i	0.916295	+	0.400504i	$0.131165\pi$
$182$	−203.409	+	352.315i	−1.11763	+	1.93579i
$183$	−35.7876	+	20.6620i	−0.195561	+	0.112907i
$184$	94.2913	−	16.6261i	0.512453	−	0.0903593i
$185$	−3.67698	+	4.38205i	−0.0198755	+	0.0236868i
$186$	21.5197	+	25.6462i	0.115697	+	0.137883i
$187$	4.01412	−	22.7652i	0.0214659	−	0.121739i
$188$	−52.9939	+	19.2882i	−0.281882	+	0.102597i
$189$			79.7526i			0.421972i
$190$	−1.58195	−	110.703i	−0.00832608	−	0.582648i
$191$	84.5822			0.442839			0.221419	−	0.975179i	$-0.428931\pi$
$191$	84.5822			0.442839			0.221419	+	0.975179i	$0.428931\pi$
$192$	2.09480	+	5.75542i	0.0109104	+	0.0299761i
$193$	−298.867	−	52.6983i	−1.54853	−	0.273048i	−0.666960	−	0.745094i	$-0.732405\pi$
$193$	−298.867	−	52.6983i	−1.54853	−	0.273048i	−0.881574	+	0.472045i	$0.843516\pi$
$194$	−107.383	+	90.1049i	−0.553520	+	0.464458i
$195$	9.32936	+	7.82826i	0.0478429	+	0.0401449i
$196$	−37.6009	−	213.245i	−0.191841	−	1.08799i
$197$	−168.617	−	292.053i	−0.855923	−	1.48250i	−0.875786	−	0.482700i	$-0.839656\pi$
$197$	−168.617	−	292.053i	−0.855923	−	1.48250i	0.0198628	−	0.999803i	$-0.493677\pi$
$198$	153.506	+	88.6269i	0.775284	+	0.447610i
$199$	11.1776	+	4.06832i	0.0561689	+	0.0204438i	0.369952	−	0.929051i	$-0.379374\pi$
$199$	11.1776	+	4.06832i	0.0561689	+	0.0204438i	−0.313783	+	0.949495i	$0.601596\pi$
$200$	−23.8010	+	65.3928i	−0.119005	+	0.326964i
$201$	6.02689	−	10.4389i	0.0299845	−	0.0519347i
$202$	−10.0686	+	5.81309i	−0.0498444	+	0.0287777i
$203$	214.323	−	37.7909i	1.05578	−	0.186162i
$204$	1.97234	−	2.35054i	0.00966832	−	0.0115223i
$205$	−77.6169	−	92.5002i	−0.378619	−	0.451220i
$206$	−16.6533	+	94.4458i	−0.0808415	+	0.458475i
$207$	227.498	−	82.8024i	1.09902	−	0.400012i
$208$		−	270.188i		−	1.29898i
$209$	23.5661	−	145.803i	0.112757	−	0.697623i
$210$	−26.0386			−0.123994
$211$	37.7556	+	103.733i	0.178937	+	0.491624i	0.996441	−	0.0842986i	$-0.0268650\pi$
$211$	37.7556	+	103.733i	0.178937	+	0.491624i	−0.817504	+	0.575923i	$0.804643\pi$
$212$	−192.945	−	34.0213i	−0.910116	−	0.160478i
$213$	22.8902	−	19.2072i	0.107466	−	0.0901746i
$214$	−307.806	−	258.280i	−1.43835	−	1.20692i
$215$	−1.74622	−	9.90329i	−0.00812194	−	0.0460618i
$216$	−12.1931	−	21.1191i	−0.0564497	−	0.0977738i
$217$	329.663	+	190.331i	1.51918	+	0.877101i
$218$	135.510	+	49.3217i	0.621606	+	0.226246i
$219$	−2.43017	+	6.67684i	−0.0110967	+	0.0304878i
$220$	−23.2201	+	40.2183i	−0.105546	+	0.182811i
$221$	−35.5244	+	20.5100i	−0.160744	+	0.0928055i
$222$	−2.50763	+	0.442162i	−0.0112956	+	0.00199172i
$223$	171.538	−	204.430i	0.769227	−	0.916729i	−0.229167	−	0.973387i	$-0.573600\pi$
$223$	171.538	−	204.430i	0.769227	−	0.916729i	0.998394	+	0.0566585i	$0.0180446\pi$
$224$	268.375	+	319.837i	1.19810	+	1.42784i
$225$	−30.5552	+	173.287i	−0.135801	+	0.770165i
$226$	189.165	−	68.8504i	0.837013	−	0.304648i
$227$			277.497i			1.22245i	0.791455	+	0.611227i	$0.209324\pi$
$227$			277.497i			1.22245i	−0.791455	+	0.611227i	$0.790676\pi$
$228$	12.3858	−	15.1966i	0.0543237	−	0.0666519i
$229$	−222.383			−0.971104			−0.485552	−	0.874208i	$-0.661381\pi$
$229$	−222.383			−0.971104			−0.485552	+	0.874208i	$0.661381\pi$
$230$	54.5347	+	149.833i	0.237107	+	0.651447i
$231$	−34.2084	−	6.03186i	−0.148088	−	0.0261119i
$232$	−50.9767	+	42.7746i	−0.219727	+	0.184373i
$233$	−270.748	−	227.185i	−1.16201	−	0.975042i	−0.162079	−	0.986778i	$-0.551820\pi$
$233$	−270.748	−	227.185i	−1.16201	−	0.975042i	−0.999931	+	0.0117359i	$0.996264\pi$
$234$	−54.6188	−	309.758i	−0.233413	−	1.32375i
$235$	24.1274	+	41.7899i	0.102670	+	0.177829i
$236$	−124.333	−	71.7839i	−0.526836	−	0.304169i
$237$	11.1946	+	4.07452i	0.0472348	+	0.0171920i
$238$	29.9963	−	82.4143i	0.126035	−	0.346278i
$239$	−156.376	+	270.851i	−0.654292	+	1.13327i	0.327778	+	0.944755i	$0.393700\pi$
$239$	−156.376	+	270.851i	−0.654292	+	1.13327i	−0.982071	+	0.188513i	$0.939633\pi$
$240$	14.9767	−	8.64679i	0.0624028	−	0.0360283i
$241$	374.608	−	66.0535i	1.55439	−	0.274081i	0.670547	−	0.741867i	$-0.266059\pi$
$241$	374.608	−	66.0535i	1.55439	−	0.274081i	0.883842	+	0.467786i	$0.154948\pi$
$242$	100.349	−	119.591i	0.414664	−	0.494177i
$243$	−59.6225	−	71.0554i	−0.245360	−	0.292409i
$244$	−48.5561	+	275.376i	−0.199001	+	1.12859i
$245$	−174.106	+	63.3695i	−0.710638	+	0.258651i
$246$		−	53.7498i		−	0.218495i
$247$	−225.077	+	134.273i	−0.911244	+	0.543614i
$248$	−116.397			−0.469341
$249$	11.0192	+	30.2751i	0.0442540	+	0.121587i
$250$	−257.593	−	45.4206i	−1.03037	−	0.181682i
$251$	−30.6486	+	25.7173i	−0.122106	+	0.102459i	−0.701796	−	0.712378i	$-0.747618\pi$
$251$	−30.6486	+	25.7173i	−0.122106	+	0.102459i	0.579690	+	0.814837i	$0.303174\pi$
$252$	204.934	+	171.960i	0.813230	+	0.682381i
$253$	36.9363	+	209.476i	0.145993	+	0.827970i
$254$	163.513	+	283.213i	0.643752	+	1.11501i
$255$	−2.27376	−	1.31276i	−0.00891671	−	0.00514807i
$256$	−314.508	−	114.472i	−1.22855	−	0.447155i
$257$	123.982	−	340.638i	0.482420	−	1.32544i	−0.424992	−	0.905197i	$-0.639723\pi$
$257$	123.982	−	340.638i	0.482420	−	1.32544i	0.907412	−	0.420241i	$-0.138055\pi$
$258$	2.23813	−	3.87656i	0.00867494	−	0.0150254i
$259$	−25.0734	+	14.4761i	−0.0968085	+	0.0558924i
$260$	81.1560	−	14.3100i	0.312139	−	0.0550385i
$261$	−108.157	+	128.897i	−0.414396	+	0.493858i
$262$	−83.8142	−	99.8859i	−0.319902	−	0.381244i
$263$	9.78136	−	55.4728i	0.0371915	−	0.210923i	−0.960549	−	0.278111i	$-0.910292\pi$
$263$	9.78136	−	55.4728i	0.0371915	−	0.210923i	0.997740	+	0.0671879i	$0.0214027\pi$
$264$	9.98084	−	3.63273i	0.0378062	−	0.0137603i
$265$			167.642i			0.632610i
$266$	184.110	−	529.247i	0.692141	−	1.98965i
$267$	34.2995			0.128462
$268$	−27.8963	−	76.6445i	−0.104091	−	0.285987i
$269$	154.339	+	27.2140i	0.573749	+	0.101167i	0.452992	−	0.891515i	$-0.350357\pi$
$269$	154.339	+	27.2140i	0.573749	+	0.101167i	0.120757	+	0.992682i	$0.461468\pi$
$270$	31.1100	−	26.1044i	0.115222	−	0.0966830i
$271$	302.405	+	253.748i	1.11589	+	0.936339i	0.998389	−	0.0567338i	$-0.0180686\pi$
$271$	302.405	+	253.748i	1.11589	+	0.936339i	0.117497	+	0.993073i	$0.462513\pi$
$272$	10.1147	+	57.3633i	0.0371864	+	0.210895i
$273$	30.8196	+	53.3811i	0.112892	+	0.195535i
$274$	246.956	+	142.580i	0.901299	+	0.520365i
$275$	−145.276	−	52.8760i	−0.528275	−	0.192276i
$276$	−9.65671	+	26.5316i	−0.0349881	+	0.0961290i
$277$	94.7607	−	164.130i	0.342097	−	0.592529i	−0.642725	−	0.766097i	$-0.722196\pi$
$277$	94.7607	−	164.130i	0.342097	−	0.592529i	0.984822	+	0.173568i	$0.0555297\pi$
$278$	168.788	−	97.4500i	0.607153	−	0.350540i
$279$	−289.843	+	51.1071i	−1.03886	+	0.183180i
$280$	58.1912	−	69.3496i	0.207826	−	0.247677i
$281$	103.971	+	123.908i	0.370005	+	0.440955i	0.918633	−	0.395112i	$-0.129294\pi$
$281$	103.971	+	123.908i	0.370005	+	0.440955i	−0.548628	+	0.836067i	$0.684850\pi$
$282$	−3.72992	+	21.1534i	−0.0132267	+	0.0750121i
$283$	223.599	−	81.3834i	0.790103	−	0.287574i	0.0847242	−	0.996404i	$-0.472999\pi$
$283$	223.599	−	81.3834i	0.790103	−	0.287574i	0.705379	+	0.708830i	$0.250777\pi$
$284$		−	202.194i		−	0.711950i
$285$	−14.6459	−	8.17905i	−0.0513892	−	0.0286984i
$286$	276.353			0.966268
$287$	−209.026	−	574.293i	−0.728312	−	2.00102i
$288$	−317.905	−	56.0553i	−1.10384	−	0.194636i
$289$	−214.613	+	180.081i	−0.742604	+	0.623119i
$290$	−84.8932	−	71.2338i	−0.292735	−	0.245634i
$291$	3.68815	+	20.9165i	0.0126740	+	0.0718781i
$292$	24.0396	+	41.6378i	0.0823273	+	0.142595i
$293$	−137.822	−	79.5714i	−0.470381	−	0.271575i	0.246018	−	0.969265i	$-0.420878\pi$
$293$	−137.822	−	79.5714i	−0.470381	−	0.271575i	−0.716399	+	0.697690i	$0.754211\pi$
$294$	−77.5002	−	28.2078i	−0.263606	−	0.0959448i
$295$	−42.0155	+	115.437i	−0.142425	+	0.391311i
$296$	4.42643	−	7.66679i	0.0149541	−	0.0259013i
$297$	46.9180	−	27.0881i	0.157973	−	0.0912058i
$298$	−519.774	+	91.6501i	−1.74421	+	0.307551i
$299$	242.620	−	289.144i	0.811439	−	0.967036i
$300$	−13.1907	−	15.7201i	−0.0439691	−	0.0524003i
$301$	8.83807	−	50.1232i	0.0293624	−	0.166522i
$302$	−110.953	+	40.3836i	−0.367395	+	0.133721i
$303$			1.76155i			0.00581368i
$304$	69.8553	+	365.546i	0.229787	+	1.20245i
$305$	239.263			0.784467
$306$	23.1921	+	63.7197i	0.0757911	+	0.208234i
$307$	39.0433	+	6.88439i	0.127177	+	0.0224247i	0.236874	−	0.971540i	$-0.423877\pi$
$307$	39.0433	+	6.88439i	0.127177	+	0.0224247i	−0.109697	+	0.993965i	$0.534988\pi$
$308$	−180.056	+	151.085i	−0.584596	+	0.490534i
$309$	11.1312	+	9.34019i	0.0360233	+	0.0302272i
$310$	−33.6598	−	190.894i	−0.108580	−	0.615787i
$311$	291.271	+	504.495i	0.936561	+	1.62217i	0.771826	+	0.635834i	$0.219344\pi$
$311$	291.271	+	504.495i	0.936561	+	1.62217i	0.164735	+	0.986338i	$0.447323\pi$
$312$	−16.3226	−	9.42383i	−0.0523159	−	0.0302046i
$313$	−116.689	−	42.4713i	−0.372808	−	0.135691i	0.148820	−	0.988864i	$-0.452453\pi$
$313$	−116.689	−	42.4713i	−0.372808	−	0.135691i	−0.521627	+	0.853173i	$0.674675\pi$
$314$	−9.07572	+	24.9353i	−0.0289036	+	0.0794119i
$315$	114.454	−	198.240i	0.363346	−	0.629334i
$316$	69.8114	−	40.3057i	0.220922	−	0.127550i
$317$	18.1720	−	3.20421i	0.0573248	−	0.0101079i	−0.144912	−	0.989445i	$-0.546290\pi$
$317$	18.1720	−	3.20421i	0.0573248	−	0.0101079i	0.202237	+	0.979337i	$0.435179\pi$
$318$	−47.9665	+	57.1642i	−0.150838	+	0.179762i
$319$	−95.0274	−	113.249i	−0.297892	−	0.355013i
$320$	6.15792	−	34.9233i	0.0192435	−	0.109135i
$321$	−57.2093	+	20.8225i	−0.178222	+	0.0648675i
$322$			807.013i			2.50625i
$323$	42.7593	−	36.9332i	0.132382	−	0.114344i
$324$	−203.212			−0.627199
$325$	93.8286	+	257.792i	0.288703	+	0.793206i
$326$	228.819	+	40.3470i	0.701899	+	0.123764i
$327$	16.7377	−	14.0446i	0.0511858	−	0.0429500i
$328$	143.154	+	120.120i	0.436444	+	0.366220i
$329$	42.4102	+	240.520i	0.128906	+	0.731064i
$330$	8.84407	+	15.3184i	0.0268002	+	0.0464193i
$331$	−432.302	−	249.589i	−1.30605	−	0.754047i	−0.324613	−	0.945847i	$-0.605234\pi$
$331$	−432.302	−	249.589i	−1.30605	−	0.754047i	−0.981434	+	0.191800i	$0.938567\pi$
$332$	204.860	+	74.5630i	0.617049	+	0.224587i
$333$	7.65607	−	21.0349i	0.0229912	−	0.0631678i
$334$	92.0630	−	159.458i	0.275638	−	0.477418i
$335$	−60.4403	+	34.8952i	−0.180419	+	0.104165i
$336$	86.1977	−	15.1990i	0.256541	−	0.0452350i
$337$	93.6673	−	111.628i	0.277945	−	0.331241i	−0.608954	−	0.793205i	$-0.708411\pi$
$337$	93.6673	−	111.628i	0.277945	−	0.331241i	0.886899	+	0.461964i	$0.152855\pi$
$338$	−35.2433	−	42.0013i	−0.104270	−	0.124264i
$339$	5.29642	−	30.0375i	0.0156236	−	0.0886061i
$340$	−16.6944	+	6.07628i	−0.0491013	+	0.0178714i
$341$		−	258.585i		−	0.758314i
$342$	153.981	+	404.960i	0.450237	+	1.18409i
$343$	−377.033			−1.09922
$344$	5.32279	+	14.6242i	0.0154732	+	0.0425124i
$345$	23.7919	+	4.19516i	0.0689621	+	0.0121599i
$346$	321.901	−	270.107i	0.930349	−	0.780656i
$347$	−178.944	−	150.152i	−0.515689	−	0.432715i	0.347437	−	0.937703i	$-0.387052\pi$
$347$	−178.944	−	150.152i	−0.515689	−	0.432715i	−0.863126	+	0.504989i	$0.831497\pi$
$348$	−3.40758	−	19.3253i	−0.00979188	−	0.0555325i
$349$	−73.2661	−	126.901i	−0.209932	−	0.363612i	0.741761	−	0.670664i	$-0.233991\pi$
$349$	−73.2661	−	126.901i	−0.209932	−	0.363612i	−0.951693	+	0.307052i	$0.900657\pi$
$350$	−507.966	−	293.274i	−1.45133	−	0.837927i
$351$	−90.3381	−	32.8804i	−0.257374	−	0.0936763i
$352$	97.0041	−	266.517i	0.275580	−	0.757149i
$353$	180.912	−	313.349i	0.512499	−	0.887674i	−0.487396	−	0.873181i	$-0.662053\pi$
$353$	180.912	−	313.349i	0.512499	−	0.887674i	0.999895	−	0.0144932i	$-0.00461350\pi$
$354$	−47.3562	+	27.3411i	−0.133775	+	0.0772348i
$355$	−170.381	+	30.0427i	−0.479945	+	0.0846273i
$356$	149.185	−	177.792i	0.419060	−	0.499417i
$357$	−8.54164	−	10.1795i	−0.0239262	−	0.0285141i
$358$	3.83968	−	21.7759i	0.0107254	−	0.0608265i
$359$	−152.232	+	55.4079i	−0.424045	+	0.154340i	−0.545223	−	0.838291i	$-0.683555\pi$
$359$	−152.232	+	55.4079i	−0.424045	+	0.154340i	0.121178	+	0.992631i	$0.461333\pi$
$360$			69.9941i			0.194428i
$361$	269.799	−	239.854i	0.747364	−	0.664414i
$362$	58.7395			0.162264
$363$	−8.09008	−	22.2273i	−0.0222867	−	0.0612323i
$364$	410.752	+	72.4267i	1.12844	+	0.198975i
$365$	31.5146	−	26.4439i	0.0863413	−	0.0724490i
$366$	81.5862	+	68.4590i	0.222913	+	0.187046i
$367$	−62.6679	−	355.407i	−0.170757	−	0.968412i	−0.942928	−	0.332997i	$-0.891940\pi$
$367$	−62.6679	−	355.407i	−0.170757	−	0.968412i	0.772171	−	0.635415i	$-0.219171\pi$
$368$	−267.989	−	464.170i	−0.728231	−	1.26133i
$369$	409.214	+	236.260i	1.10898	+	0.640270i
$370$	13.8538	+	5.04238i	0.0374428	+	0.0136281i
$371$	−290.197	+	797.310i	−0.782202	+	2.14908i
$372$	17.1620	−	29.7254i	0.0461343	−	0.0799070i
$373$	−362.340	+	209.197i	−0.971422	+	0.560851i	−0.899669	−	0.436572i	$-0.856192\pi$
$373$	−362.340	+	209.197i	−0.971422	+	0.560851i	−0.0717523	+	0.997422i	$0.522859\pi$
$374$	−58.6721	+	10.3455i	−0.156877	+	0.0276617i
$375$	−25.4746	+	30.3594i	−0.0679322	+	0.0809585i
$376$	−48.0030	−	57.2077i	−0.127668	−	0.152148i
$377$	−45.5541	+	258.350i	−0.120833	+	0.685279i
$378$	193.149	−	70.3003i	0.510975	−	0.185980i
$379$		−	653.197i		−	1.72347i	−0.507355	−	0.861737i	$-0.669377\pi$
$379$		−	653.197i		−	1.72347i	0.507355	−	0.861737i	$-0.330623\pi$
$380$	−106.099	+	40.3428i	−0.279207	+	0.106165i
$381$	49.5495			0.130051
$382$	−74.5575	−	204.845i	−0.195177	−	0.536244i
$383$	469.379	+	82.7642i	1.22553	+	0.216095i	0.748706	−	0.662902i	$-0.230676\pi$
$383$	469.379	+	82.7642i	1.22553	+	0.216095i	0.476827	+	0.878997i	$0.341787\pi$
$384$	−31.5651	+	26.4862i	−0.0822007	+	0.0689746i
$385$	154.066	+	129.277i	0.400172	+	0.335784i
$386$	135.818	+	770.263i	0.351860	+	1.99550i
$387$	19.6756	+	34.0792i	0.0508414	+	0.0880599i
$388$	124.463	+	71.8588i	0.320781	+	0.185203i
$389$	367.599	+	133.795i	0.944984	+	0.343946i	0.768132	−	0.640292i	$-0.221186\pi$
$389$	367.599	+	133.795i	0.944984	+	0.343946i	0.176852	+	0.984237i	$0.443409\pi$
$390$	10.7352	−	29.4947i	0.0275262	−	0.0756275i
$391$	−40.6861	+	70.4705i	−0.104057	+	0.180231i
$392$	248.324	−	143.370i	0.633481	−	0.365740i
$393$	−19.4562	+	3.43066i	−0.0495070	+	0.00872941i
$394$	−558.675	+	665.803i	−1.41796	+	1.68986i
$395$	−44.3368	−	52.8385i	−0.112245	−	0.133768i
$396$	31.5569	−	178.968i	0.0796891	−	0.451940i
$397$	−446.951	+	162.677i	−1.12582	+	0.409765i	−0.836773	−	0.547550i	$-0.815561\pi$
$397$	−446.951	+	162.677i	−1.12582	+	0.409765i	−0.289047	+	0.957315i	$0.593338\pi$
$398$		−	30.6566i		−	0.0770266i
$399$	−55.4981	−	64.2527i	−0.139093	−	0.161034i
$400$	389.556			0.973891
$401$	77.4625	+	212.827i	0.193173	+	0.530740i	0.998031	−	0.0627289i	$-0.0199804\pi$
$401$	77.4625	+	212.827i	0.193173	+	0.530740i	−0.804857	+	0.593469i	$0.797758\pi$
$402$	−30.5940	−	5.39454i	−0.0761044	−	0.0134193i
$403$	−351.507	+	294.949i	−0.872225	+	0.731884i
$404$	9.13102	+	7.66184i	0.0226015	+	0.0189649i
$405$	30.1940	+	171.239i	0.0745532	+	0.422812i
$406$	−280.445	−	485.745i	−0.690752	−	1.19642i
$407$	17.0324	+	9.83369i	0.0418488	+	0.0241614i
$408$	3.81821	+	1.38972i	0.00935836	+	0.00340617i
$409$	262.474	−	721.141i	0.641746	−	1.76318i	−0.00442700	−	0.999990i	$-0.501409\pi$
$409$	262.474	−	721.141i	0.641746	−	1.76318i	0.646173	−	0.763191i	$-0.276369\pi$
$410$	−155.603	+	269.513i	−0.379521	+	0.657349i
$411$	37.4177	−	21.6031i	0.0910406	−	0.0525623i
$412$	96.8303	−	17.0738i	0.235025	−	0.0414413i
$413$	−399.654	+	476.290i	−0.967686	+	1.15324i
$414$	−401.069	−	477.976i	−0.968767	−	1.15453i
$415$	32.3924	−	183.706i	0.0780539	−	0.442666i
$416$	−472.934	+	172.134i	−1.13686	+	0.413783i
$417$		−	29.5304i		−	0.0708163i
$418$	−373.886	+	71.4491i	−0.894464	+	0.170931i
$419$	−108.615			−0.259224			−0.129612	−	0.991565i	$-0.541373\pi$
$419$	−108.615			−0.259224			−0.129612	+	0.991565i	$0.541373\pi$
$420$	9.13059	+	25.0861i	0.0217395	+	0.0597288i
$421$	15.3964	+	2.71481i	0.0365711	+	0.00644847i	0.191904	−	0.981414i	$-0.438534\pi$
$421$	15.3964	+	2.71481i	0.0365711	+	0.00644847i	−0.155333	+	0.987862i	$0.549645\pi$
$422$	217.944	−	182.877i	0.516455	−	0.433357i
$423$	−144.652	−	121.378i	−0.341968	−	0.286945i
$424$	−45.0518	−	255.501i	−0.106254	−	0.602598i
$425$	−29.5713	−	51.2190i	−0.0695795	−	0.120515i
$426$	−66.6941	−	38.5059i	−0.156559	−	0.0903894i
$427$	1137.94	+	414.177i	2.66497	+	0.969969i
$428$	−140.898	+	387.113i	−0.329200	+	0.904470i
$429$	20.9359	−	36.2620i	0.0488016	−	0.0845268i
$430$	−22.4450	+	12.9586i	−0.0521976	+	0.0301363i
$431$	529.294	−	93.3289i	1.22806	−	0.216540i	0.478269	−	0.878213i	$-0.341264\pi$
$431$	529.294	−	93.3289i	1.22806	−	0.216540i	0.749792	+	0.661673i	$0.230153\pi$
$432$	−87.7485	+	104.575i	−0.203121	+	0.242071i
$433$	424.707	+	506.146i	0.980847	+	1.16893i	0.985626	+	0.168940i	$0.0540344\pi$
$433$	424.707	+	506.146i	0.980847	+	1.16893i	−0.00477897	+	0.999989i	$0.501521\pi$
$434$	170.361	−	966.166i	0.392537	−	2.22619i
$435$	−15.7784	+	5.74285i	−0.0362721	+	0.0132020i
$436$		−	147.848i		−	0.339100i
$437$	−253.492	+	453.919i	−0.580074	+	1.03872i
$438$	18.3124			0.0418092
$439$	30.9280	+	84.9740i	0.0704510	+	0.193563i	0.969921	−	0.243420i	$-0.0782693\pi$
$439$	30.9280	+	84.9740i	0.0704510	+	0.193563i	−0.899470	+	0.436983i	$0.856047\pi$
$440$	−60.5627	−	10.6788i	−0.137643	−	0.0242701i
$441$	555.410	−	466.044i	1.25943	−	1.05679i
$442$	80.9861	+	67.9554i	0.183227	+	0.153745i
$443$	−43.7840	−	248.311i	−0.0988351	−	0.560522i	−0.993504	−	0.113793i	$-0.963700\pi$
$443$	−43.7840	−	248.311i	−0.0988351	−	0.560522i	0.894669	−	0.446729i	$-0.147411\pi$
$444$	1.30530	+	2.26085i	0.00293987	+	0.00509200i
$445$	−171.985	−	99.2956i	−0.386483	−	0.223136i
$446$	−646.306	−	235.236i	−1.44912	−	0.527435i
$447$	−27.3509	+	75.1460i	−0.0611877	+	0.168112i
$448$	89.7414	−	155.437i	0.200316	−	0.346957i
$449$	26.6751	−	15.4009i	0.0594101	−	0.0343005i	−0.470001	−	0.882666i	$-0.655746\pi$
$449$	26.6751	−	15.4009i	0.0594101	−	0.0343005i	0.529411	+	0.848366i	$0.322413\pi$
$450$	446.609	−	78.7491i	0.992464	−	0.174998i
$451$	−266.857	+	318.028i	−0.591702	+	0.705163i
$452$	−132.663	−	158.102i	−0.293503	−	0.349783i
$453$	−3.10657	+	17.6182i	−0.00685777	+	0.0388924i
$454$	672.055	−	244.608i	1.48030	−	0.538784i
$455$		−	356.886i		−	0.784365i
$456$	24.5197	+	8.52971i	0.0537714	+	0.0187055i
$457$	289.618			0.633738			0.316869	−	0.948469i	$-0.397368\pi$
$457$	289.618			0.633738			0.316869	+	0.948469i	$0.397368\pi$
$458$	196.026	+	538.577i	0.428004	+	1.17593i
$459$	20.4105	+	3.59892i	0.0444673	+	0.00784078i
$460$	125.229	−	105.079i	0.272236	−	0.228433i
$461$	−443.364	−	372.027i	−0.961745	−	0.807000i	0.0194910	−	0.999810i	$-0.493795\pi$
$461$	−443.364	−	372.027i	−0.961745	−	0.807000i	−0.981236	+	0.192810i	$0.938240\pi$
$462$	15.5458	+	88.1643i	0.0336488	+	0.190832i
$463$	−153.233	−	265.407i	−0.330957	−	0.573234i	0.651743	−	0.758440i	$-0.274038\pi$
$463$	−153.233	−	265.407i	−0.330957	−	0.573234i	−0.982700	+	0.185206i	$0.940705\pi$
$464$	322.608	+	186.258i	0.695276	+	0.401418i
$465$	−27.5984	−	10.0450i	−0.0593514	−	0.0216021i
$466$	−311.547	+	855.969i	−0.668557	+	1.83684i
$467$	−288.992	+	500.549i	−0.618827	+	1.07184i	0.370873	+	0.928684i	$0.379058\pi$
$467$	−288.992	+	500.549i	−0.618827	+	1.07184i	−0.989700	+	0.143156i	$0.954275\pi$
$468$	−279.274	+	161.239i	−0.596740	+	0.344528i
$469$	−347.862	+	61.3374i	−0.741709	+	0.130783i
$470$	79.9409	−	95.2699i	0.170087	−	0.202702i
$471$	2.58437	+	3.07993i	0.00548698	+	0.00653913i
$472$	33.0132	−	187.227i	0.0699433	−	0.396668i
$473$	−32.4890	+	11.8250i	−0.0686872	+	0.0250001i
$474$		−	30.7033i		−	0.0647749i
$475$	−193.594	−	324.516i	−0.407566	−	0.683191i
$476$	−89.9177			−0.188903
$477$	−224.370	−	616.451i	−0.470377	−	1.29235i
$478$	793.801	+	139.969i	1.66067	+	0.292821i
$479$	137.695	−	115.540i	0.287464	−	0.241211i	−0.487640	−	0.873045i	$-0.662142\pi$
$479$	137.695	−	115.540i	0.287464	−	0.241211i	0.775104	+	0.631834i	$0.217698\pi$
$480$	−24.6767	−	20.7062i	−0.0514098	−	0.0431379i
$481$	−6.06028	−	34.3696i	−0.0125993	−	0.0714544i
$482$	−490.181	−	849.018i	−1.01697	−	1.76145i
$483$	105.893	+	61.1375i	0.219241	+	0.126579i
$484$	−150.404	−	54.7425i	−0.310751	−	0.113104i
$485$	42.0593	−	115.557i	0.0867202	−	0.238262i
$486$	−119.529	+	207.031i	−0.245945	+	0.425989i
$487$	−597.122	+	344.748i	−1.22612	+	0.707902i	−0.966217	−	0.257731i	$-0.917025\pi$
$487$	−597.122	+	344.748i	−1.22612	+	0.707902i	−0.259906	+	0.965634i	$0.583692\pi$
$488$	−364.658	+	64.2991i	−0.747250	+	0.131760i
$489$	22.6290	−	26.9682i	0.0462761	−	0.0551497i
$490$	306.943	+	365.800i	0.626413	+	0.746530i
$491$	−75.1146	+	425.996i	−0.152983	+	0.867609i	0.807624	+	0.589698i	$0.200753\pi$
$491$	−75.1146	+	425.996i	−0.152983	+	0.867609i	−0.960607	+	0.277911i	$0.910358\pi$
$492$	−51.7835	+	18.8477i	−0.105251	+	0.0383082i
$493$		−	56.5554i		−	0.114717i
$494$	523.589	+	426.744i	1.05990	+	0.863854i
$495$	−155.498			−0.314137
$496$	222.853	+	612.283i	0.449300	+	1.23444i
$497$	−862.342	−	152.054i	−1.73509	−	0.305944i
$498$	63.6084	−	53.3738i	0.127728	−	0.107176i
$499$	218.993	+	183.757i	0.438865	+	0.368251i	0.835284	−	0.549818i	$-0.185303\pi$
$499$	218.993	+	183.757i	0.438865	+	0.368251i	−0.396420	+	0.918069i	$0.629747\pi$
$500$	46.5673	+	264.097i	0.0931347	+	0.528193i
$501$	−13.9490	−	24.1603i	−0.0278423	−	0.0482242i
$502$	89.2994	+	51.5570i	0.177887	+	0.102703i
$503$	514.811	+	187.376i	1.02348	+	0.372517i	0.798595	−	0.601868i	$-0.205577\pi$
$503$	514.811	+	187.376i	1.02348	+	0.372517i	0.224886	+	0.974385i	$0.427799\pi$
$504$	−121.164	+	332.895i	−0.240404	+	0.660505i
$505$	5.09960	−	8.83277i	0.0100982	−	0.0174906i
$506$	474.761	−	274.103i	0.938263	−	0.541706i
$507$	−8.18121	+	1.44257i	−0.0161365	+	0.00284530i
$508$	215.516	−	256.842i	0.424243	−	0.505594i
$509$	327.430	+	390.216i	0.643281	+	0.766633i	0.984885	−	0.173211i	$-0.0554144\pi$
$509$	327.430	+	390.216i	0.643281	+	0.766633i	−0.341603	+	0.939844i	$0.610970\pi$
$510$	−1.17502	+	6.66387i	−0.00230396	+	0.0130664i
$511$	195.660	−	71.2145i	0.382897	−	0.139363i
$512$			440.514i			0.860380i
$513$	130.722	+	21.1286i	0.254819	+	0.0411863i
$514$	−934.260			−1.81763
$515$	−28.7748	−	79.0581i	−0.0558734	−	0.153511i
$516$	−4.51956	−	0.796921i	−0.00875884	−	0.00154442i
$517$	127.092	−	106.643i	0.245826	−	0.206272i
$518$	57.1607	+	47.9635i	0.110349	+	0.0925936i
$519$	−11.0559	−	62.7013i	−0.0213024	−	0.120812i
$520$	54.5632	+	94.5063i	0.104929	+	0.181743i
$521$	−581.410	−	335.677i	−1.11595	−	0.644294i	−0.175586	−	0.984464i	$-0.556182\pi$
$521$	−581.410	−	335.677i	−1.11595	−	0.644294i	−0.940364	+	0.340170i	$0.889515\pi$
$522$	407.507	+	148.321i	0.780666	+	0.284139i
$523$	178.253	−	489.745i	0.340827	−	0.936415i	−0.644328	−	0.764749i	$-0.722863\pi$
$523$	178.253	−	489.745i	0.340827	−	0.936415i	0.985155	−	0.171666i	$-0.0549149\pi$
$524$	−66.8420	+	115.774i	−0.127561	+	0.220942i
$525$	−76.9647	+	44.4356i	−0.146599	+	0.0846392i
$526$	−142.969	+	25.2092i	−0.271804	+	0.0479263i
$527$	63.5863	−	75.7792i	0.120657	−	0.143794i
$528$	−38.2187	−	45.5472i	−0.0723838	−	0.0862637i
$529$	38.1602	−	216.417i	0.0721365	−	0.409107i
$530$	406.002	−	147.773i	0.766042	−	0.278817i
$531$		−	480.716i		−	0.905303i
$532$	−574.445	+	8.20884i	−1.07978	+	0.0154302i
$533$	736.696			1.38217
$534$	−30.2343	−	83.0680i	−0.0566185	−	0.155558i
$535$	347.140	+	61.2101i	0.648860	+	0.114411i
$536$	82.7389	−	69.4262i	0.154364	−	0.129526i
$537$	−2.56647	−	2.15352i	−0.00477927	−	0.00401028i
$538$	−70.1381	−	397.773i	−0.130368	−	0.739355i
$539$	318.509	+	551.674i	0.590926	+	1.02351i
$540$	−36.0584	−	20.8183i	−0.0667747	−	0.0385524i
$541$	−603.970	−	219.827i	−1.11640	−	0.406335i	−0.283060	−	0.959102i	$-0.591350\pi$
$541$	−603.970	−	219.827i	−1.11640	−	0.406335i	−0.833335	+	0.552768i	$0.813572\pi$
$542$	347.975	−	956.052i	0.642020	−	1.76393i
$543$	4.44997	−	7.70758i	0.00819516	−	0.0141944i
$544$	93.9641	−	54.2502i	0.172728	−	0.0997246i
$545$	−124.585	+	21.9678i	−0.228597	+	0.0403078i
$546$	102.114	−	121.695i	0.187022	−	0.222884i
$547$	−250.734	−	298.813i	−0.458380	−	0.546275i	0.486506	−	0.873677i	$-0.338271\pi$
$547$	−250.734	−	298.813i	−0.458380	−	0.546275i	−0.944885	+	0.327402i	$0.893827\pi$
$548$	50.7678	−	287.918i	0.0926419	−	0.525398i
$549$	−879.815	+	320.226i	−1.60258	+	0.583291i
$550$			398.445i			0.724445i
$551$	−5.16310	−	361.308i	−0.00937042	−	0.655731i
$552$	−37.3885			−0.0677328
$553$	−119.401	−	328.051i	−0.215915	−	0.593221i
$554$	−481.028	−	84.8183i	−0.868282	−	0.153102i
$555$	1.71118	−	1.43585i	0.00308320	−	0.00258711i
$556$	−153.072	−	128.442i	−0.275309	−	0.231011i
$557$	38.9770	+	221.049i	0.0699766	+	0.396857i	0.999598	+	0.0283418i	$0.00902267\pi$
$557$	38.9770	+	221.049i	0.0699766	+	0.396857i	−0.929622	+	0.368515i	$0.879866\pi$
$558$	379.264	+	656.905i	0.679685	+	1.17725i
$559$	53.1322	+	30.6759i	0.0950487	+	0.0548764i
$560$	−476.214	−	173.328i	−0.850382	−	0.309514i
$561$	−3.08737	+	8.48249i	−0.00550334	+	0.0151203i
$562$	208.438	−	361.026i	0.370886	−	0.642394i
$563$	816.176	−	471.220i	1.44969	−	0.836980i	0.451229	−	0.892408i	$-0.350986\pi$
$563$	816.176	−	471.220i	1.44969	−	0.836980i	0.998463	+	0.0554288i	$0.0176526\pi$
$564$	21.6875	−	3.82409i	0.0384530	−	0.00678030i
$565$	−113.515	+	135.281i	−0.200911	+	0.239436i
$566$	−394.196	−	469.785i	−0.696460	−	0.830009i
$567$	−152.820	+	866.686i	−0.269524	+	1.52855i
$568$	251.602	−	91.5757i	0.442962	−	0.161225i
$569$		−	4.69641i		−	0.00825379i	−0.999991	−	0.00412690i	$-0.998686\pi$
$569$		−	4.69641i		−	0.00825379i	0.999991	−	0.00412690i	$-0.00131364\pi$
$570$	−6.89832	+	42.6798i	−0.0121023	+	0.0748769i
$571$	220.091			0.385449			0.192724	−	0.981253i	$-0.438268\pi$
$571$	220.091			0.385449			0.192724	+	0.981253i	$0.438268\pi$
$572$	−96.9046	−	266.243i	−0.169414	−	0.465460i
$573$	−32.5273	−	5.73544i	−0.0567667	−	0.0100095i
$574$	−1206.60	+	1012.46i	−2.10209	+	1.76386i
$575$	416.887	+	349.809i	0.725020	+	0.608364i
$576$	24.0971	+	136.661i	0.0418352	+	0.237259i
$577$	242.783	+	420.513i	0.420768	+	0.728792i	0.996015	−	0.0891883i	$-0.0284273\pi$
$577$	242.783	+	420.513i	0.420768	+	0.728792i	−0.575247	+	0.817980i	$0.695094\pi$
$578$	625.306	+	361.020i	1.08184	+	0.624603i
$579$	111.360	+	40.5318i	0.192332	+	0.0700031i
$580$	−38.8597	+	106.766i	−0.0669995	+	0.184080i
$581$	472.065	−	817.641i	0.812504	−	1.40730i
$582$	47.4056	−	27.3696i	0.0814529	−	0.0470268i
$583$	567.619	−	100.086i	0.973617	−	0.171675i
$584$	−40.9246	+	48.7721i	−0.0700764	+	0.0835138i
$585$	177.365	+	211.376i	0.303188	+	0.361326i
$586$	−71.2226	+	403.924i	−0.121540	+	0.689289i
$587$	−76.8141	+	27.9581i	−0.130859	+	0.0476287i	−0.406619	−	0.913598i	$-0.633293\pi$
$587$	−76.8141	+	27.9581i	−0.130859	+	0.0476287i	0.275761	+	0.961226i	$0.411070\pi$
$588$			84.5563i			0.143803i
$589$	399.307	−	489.925i	0.677940	−	0.831791i
$590$	316.606			0.536620
$591$	45.0402	+	123.747i	0.0762102	+	0.209386i
$592$	−48.8046	−	8.60557i	−0.0824403	−	0.0145364i
$593$	−404.876	+	339.732i	−0.682759	+	0.572903i	−0.916811	−	0.399321i	$-0.869246\pi$
$593$	−404.876	+	339.732i	−0.682759	+	0.572903i	0.234052	+	0.972224i	$0.424801\pi$
$594$	−106.961	−	89.7506i	−0.180068	−	0.151095i
$595$	13.3603	+	75.7700i	0.0224543	+	0.127345i
$596$	270.559	+	468.622i	0.453958	+	0.786278i
$597$	−4.02265	−	2.32248i	−0.00673810	−	0.00389024i
$598$	−914.127	−	332.715i	−1.52864	−	0.556379i
$599$	−308.310	+	847.074i	−0.514708	+	1.41415i	0.361572	+	0.932344i	$0.382240\pi$
$599$	−308.310	+	847.074i	−0.514708	+	1.41415i	−0.876279	+	0.481803i	$0.839982\pi$
$600$	13.5873	−	23.5338i	0.0226454	−	0.0392230i
$601$	−805.467	+	465.037i	−1.34021	+	0.773772i	−0.986838	−	0.161710i	$-0.948299\pi$
$601$	−805.467	+	465.037i	−1.34021	+	0.773772i	−0.353374	+	0.935482i	$0.614966\pi$
$602$	−129.181	+	22.7781i	−0.214587	+	0.0378374i
$603$	175.547	−	209.209i	0.291123	−	0.346947i
$604$	77.8126	+	92.7335i	0.128829	+	0.153532i
$605$	−23.7817	+	134.873i	−0.0393087	+	0.222931i
$606$	4.26619	−	1.55277i	0.00703992	−	0.00256232i
$607$			893.795i			1.47248i	0.676721	+	0.736240i	$0.263400\pi$
$607$			893.795i			1.47248i	−0.676721	+	0.736240i	$0.736600\pi$
$608$	595.343	−	355.159i	0.979182	−	0.584143i
$609$	−84.9836			−0.139546
$610$	−210.905	−	579.457i	−0.345746	−	0.949929i
$611$	−289.929	−	51.1223i	−0.474516	−	0.0836699i
$612$	53.2563	−	44.6873i	0.0870201	−	0.0730185i
$613$	142.362	+	119.456i	0.232238	+	0.194871i	0.751479	−	0.659757i	$-0.229341\pi$
$613$	142.362	+	119.456i	0.232238	+	0.194871i	−0.519241	+	0.854628i	$0.673785\pi$
$614$	−17.7430	−	100.625i	−0.0288973	−	0.163885i
$615$	23.5763	+	40.8354i	0.0383355	+	0.0663991i
$616$	−269.553	−	155.626i	−0.437586	−	0.252640i
$617$	53.8998	+	19.6179i	0.0873579	+	0.0317957i	0.385329	−	0.922779i	$-0.374088\pi$
$617$	53.8998	+	19.6179i	0.0873579	+	0.0317957i	−0.297972	+	0.954575i	$0.596310\pi$
$618$	12.8086	−	35.1913i	0.0207258	−	0.0569438i
$619$	64.5910	−	111.875i	0.104347	−	0.180735i	−0.809124	−	0.587638i	$-0.800058\pi$
$619$	64.5910	−	111.875i	0.104347	−	0.180735i	0.913471	+	0.406903i	$0.133391\pi$
$620$	−172.108	+	99.3664i	−0.277593	+	0.160268i
$621$	−187.809	+	33.1158i	−0.302430	+	0.0533266i
$622$	965.061	−	1150.11i	1.55154	−	1.84906i
$623$	−646.080	−	769.969i	−1.03705	−	1.23590i
$624$	−18.3212	+	103.905i	−0.0293609	+	0.166514i
$625$	−251.594	+	91.5726i	−0.402550	+	0.146516i
$626$			320.040i			0.511246i
$627$	−18.9495	+	54.4728i	−0.0302225	+	0.0868784i
$628$	27.2056			0.0433210
$629$	2.57330	+	7.07009i	0.00409110	+	0.0112402i
$630$	−580.996	−	102.445i	−0.922216	−	0.162612i
$631$	−524.183	+	439.842i	−0.830718	+	0.697055i	−0.955456	−	0.295135i	$-0.904635\pi$
$631$	−524.183	+	439.842i	−0.830718	+	0.697055i	0.124738	+	0.992190i	$0.460191\pi$
$632$	81.7731	+	68.6158i	0.129388	+	0.108569i
$633$	−7.48545	−	42.4521i	−0.0118254	−	0.0670650i
$634$	−23.7783	−	41.1852i	−0.0375052	−	0.0649609i
$635$	−248.452	−	143.444i	−0.391263	−	0.225896i
$636$	71.8927	+	26.1668i	0.113039	+	0.0411428i
$637$	386.616	−	1062.22i	0.606933	−	1.66753i
$638$	−190.507	+	329.969i	−0.298601	+	0.517192i
$639$	586.314	−	338.508i	0.917549	−	0.529747i
$640$	234.951	−	41.4281i	0.367110	−	0.0647315i
$641$	413.266	−	492.512i	0.644721	−	0.768349i	−0.340387	−	0.940285i	$-0.610558\pi$
$641$	413.266	−	492.512i	0.644721	−	0.768349i	0.985108	+	0.171937i	$0.0550025\pi$
$642$	100.858	+	120.197i	0.157099	+	0.187223i
$643$	−25.5425	+	144.859i	−0.0397240	+	0.225286i	−0.998206	−	0.0598656i	$-0.980933\pi$
$643$	−25.5425	+	144.859i	−0.0397240	+	0.225286i	0.958482	+	0.285151i	$0.0920439\pi$
$644$	777.490	−	282.983i	1.20728	−	0.439415i
$645$			3.92686i			0.00608816i
$646$	−127.138	−	71.0006i	−0.196808	−	0.109908i
$647$	−854.914			−1.32135			−0.660675	−	0.750672i	$-0.729730\pi$
$647$	−854.914			−1.32135			−0.660675	+	0.750672i	$0.729730\pi$
$648$	−92.0370	−	252.870i	−0.142032	−	0.390231i
$649$	415.942	+	73.3417i	0.640896	+	0.113007i
$650$	541.624	−	454.477i	0.833268	−	0.699195i
$651$	−113.870	−	95.5487i	−0.174916	−	0.146772i
$652$	−41.3656	−	234.596i	−0.0634442	−	0.359810i
$653$	381.801	+	661.299i	0.584688	+	1.01271i	0.994914	+	0.100726i	$0.0321164\pi$
$653$	381.801	+	661.299i	0.584688	+	1.01271i	−0.410226	+	0.911984i	$0.634550\pi$
$654$	−48.7679	−	28.1562i	−0.0745687	−	0.0430523i
$655$	107.489	+	39.1229i	0.164106	+	0.0597297i
$656$	357.789	−	983.017i	0.545410	−	1.49850i
$657$	−80.4931	+	139.418i	−0.122516	+	0.212204i
$658$	545.119	−	314.725i	0.828449	−	0.478305i
$659$	−651.850	+	114.939i	−0.989150	+	0.174414i	−0.644737	−	0.764405i	$-0.723033\pi$
$659$	−651.850	+	114.939i	−0.989150	+	0.174414i	−0.344413	+	0.938818i	$0.611922\pi$
$660$	11.6568	−	13.8920i	0.0176618	−	0.0210485i
$661$	548.030	+	653.116i	0.829092	+	0.988073i	0.999996	+	0.00278525i	$0.000886574\pi$
$661$	548.030	+	653.116i	0.829092	+	0.988073i	−0.170905	+	0.985288i	$0.554669\pi$
$662$	−223.402	+	1266.98i	−0.337465	+	1.91386i
$663$	15.0522	−	5.47855i	0.0227031	−	0.00826327i
$664$			288.690i			0.434775i
$665$	92.2704	+	482.842i	0.138752	+	0.726078i
$666$	−57.6919			−0.0866245
$667$	177.988	+	489.017i	0.266848	+	0.733159i
$668$	−185.907	−	32.7804i	−0.278304	−	0.0490724i
$669$	−79.8295	+	66.9849i	−0.119327	+	0.100127i
$670$	137.788	+	115.618i	0.205653	+	0.172564i
$671$	−142.846	−	810.120i	−0.212885	−	1.20733i
$672$	−81.5197	−	141.196i	−0.121309	−	0.210113i
$673$	443.932	+	256.304i	0.659631	+	0.380838i	0.792136	−	0.610344i	$-0.208969\pi$
$673$	443.932	+	256.304i	0.659631	+	0.380838i	−0.132505	+	0.991182i	$0.542302\pi$
$674$	−352.913	−	128.450i	−0.523609	−	0.190578i
$675$	47.4068	−	130.249i	0.0702323	−	0.192962i
$676$	−28.1066	+	48.6820i	−0.0415777	+	0.0720148i
$677$	75.6633	−	43.6842i	0.111763	−	0.0645261i	−0.443077	−	0.896484i	$-0.646113\pi$
$677$	75.6633	−	43.6842i	0.111763	−	0.0645261i	0.554839	+	0.831958i	$0.312780\pi$
$678$	−77.4148	+	13.6503i	−0.114181	+	0.0201332i
$679$	400.071	−	476.786i	0.589206	−	0.702189i
$680$	−15.1222	−	18.0219i	−0.0222385	−	0.0265028i
$681$	18.8168	−	106.716i	0.0276312	−	0.156704i
$682$	−626.253	+	227.937i	−0.918260	+	0.334219i
$683$		−	387.459i		−	0.567289i	−0.958929	−	0.283645i	$-0.908456\pi$
$683$		−	387.459i		−	0.567289i	0.958929	−	0.283645i	$-0.0915436\pi$
$684$	336.151	−	290.350i	0.491449	−	0.424488i
$685$	−250.160			−0.365198
$686$	332.347	+	913.116i	0.484471	+	1.33107i
$687$	85.5206	+	15.0796i	0.124484	+	0.0219499i
$688$	66.7372	−	55.9992i	0.0970018	−	0.0813942i
$689$	−783.493	−	657.429i	−1.13715	−	0.954179i
$690$	−10.8121	−	61.3183i	−0.0156697	−	0.0888672i
$691$	82.9844	+	143.733i	0.120093	+	0.208008i	0.919804	−	0.392378i	$-0.128347\pi$
$691$	82.9844	+	143.733i	0.120093	+	0.208008i	−0.799711	+	0.600385i	$0.795014\pi$
$692$	−373.102	−	215.411i	−0.539165	−	0.311287i
$693$	−739.554	−	269.176i	−1.06718	−	0.388421i
$694$	−205.909	+	565.731i	−0.296699	+	0.815175i
$695$	−85.4893	+	148.072i	−0.123006	+	0.213053i
$696$	22.5043	−	12.9929i	0.0323338	−	0.0186679i
$697$	−156.407	+	27.5788i	−0.224400	+	0.0395678i
$698$	−242.751	+	289.300i	−0.347781	+	0.414469i
$699$	88.7150	+	105.726i	0.126917	+	0.151254i
$700$	−104.425	+	592.222i	−0.149178	+	0.846031i
$701$	1016.97	−	370.147i	1.45074	−	0.528027i	0.507944	−	0.861390i	$-0.330406\pi$
$701$	1016.97	−	370.147i	1.45074	−	0.528027i	0.942798	+	0.333363i	$0.108184\pi$
$702$			247.768i			0.352946i
$703$	17.0852	+	44.9328i	0.0243032	+	0.0639158i
$704$	−121.923			−0.173187
$705$	−6.44481	−	17.7070i	−0.00914158	−	0.0251163i
$706$	−918.354	−	161.931i	−1.30078	−	0.229363i
$707$	39.5439	−	33.1813i	0.0559320	−	0.0469325i
$708$	42.9466	+	36.0365i	0.0606590	+	0.0508990i
$709$	6.71442	+	38.0794i	0.00947027	+	0.0537086i	0.989177	−	0.146729i	$-0.0468746\pi$
$709$	6.71442	+	38.0794i	0.00947027	+	0.0537086i	−0.979706	+	0.200438i	$0.935764\pi$
$710$	222.946	+	386.154i	0.314008	+	0.543878i
$711$	233.754	+	134.958i	0.328767	+	0.189814i
$712$	288.806	+	105.117i	0.405626	+	0.147636i
$713$	−311.323	+	855.354i	−0.436639	+	1.19965i
$714$	−17.1240	+	29.6596i	−0.0239831	+	0.0415400i
$715$	−209.954	+	121.217i	−0.293642	+	0.169534i
$716$	−22.3257	+	3.93662i	−0.0311811	+	0.00549807i
$717$	78.5028	−	93.5560i	0.109488	−	0.130483i
$718$	268.379	+	319.842i	0.373787	+	0.445462i
$719$	85.6403	−	485.690i	0.119110	−	0.675508i	−0.865522	−	0.500870i	$-0.833013\pi$
$719$	85.6403	−	485.690i	0.119110	−	0.675508i	0.984633	−	0.174638i	$-0.0558755\pi$
$720$	368.192	−	134.011i	0.511377	−	0.186126i
$721$		−	425.814i		−	0.590588i
$722$	−818.710	−	441.985i	−1.13395	−	0.612167i
$723$	−148.540			−0.205449
$724$	−20.5973	−	56.5907i	−0.0284493	−	0.0781639i
$725$	−372.489	−	65.6798i	−0.513778	−	0.0905928i
$726$	−46.6999	+	39.1858i	−0.0643249	+	0.0539750i
$727$	157.405	+	132.079i	0.216514	+	0.181677i	0.744593	−	0.667518i	$-0.232643\pi$
$727$	157.405	+	132.079i	0.216514	+	0.181677i	−0.528080	+	0.849195i	$0.677088\pi$
$728$	95.9090	+	543.927i	0.131743	+	0.747153i
$729$	−327.967	−	568.055i	−0.449886	−	0.779225i
$730$	−91.8224	−	53.0137i	−0.125784	−	0.0726215i
$731$	−12.4288	−	4.52372i	−0.0170025	−	0.00618840i
$732$	37.3459	−	102.607i	0.0510190	−	0.140174i
$733$	−458.497	+	794.140i	−0.625507	+	1.08341i	0.362935	+	0.931814i	$0.381775\pi$
$733$	−458.497	+	794.140i	−0.625507	+	1.08341i	−0.988443	+	0.151596i	$0.951559\pi$
$734$	−805.501	+	465.056i	−1.09741	+	0.633592i
$735$	71.2522	−	12.5637i	0.0969417	−	0.0170934i
$736$	−641.745	+	764.802i	−0.871936	+	1.03913i
$737$	154.236	+	183.812i	0.209276	+	0.249405i
$738$	211.471	−	1199.31i	0.286546	−	1.62508i
$739$	1021.54	−	371.811i	1.38233	−	0.503127i	0.459446	−	0.888206i	$-0.348048\pi$
$739$	1021.54	−	371.811i	1.38233	−	0.503127i	0.922884	+	0.385079i	$0.125826\pi$
$740$		−	15.1152i		−	0.0204259i
$741$	95.6616	−	36.3742i	0.129098	−	0.0490880i
$742$	2186.76			2.94712
$743$	−443.888	−	1219.57i	−0.597427	−	1.64142i	−0.756381	−	0.654131i	$-0.773034\pi$
$743$	−443.888	−	1219.57i	−0.597427	−	1.64142i	0.158954	−	0.987286i	$-0.449188\pi$
$744$	44.7620	+	7.89275i	0.0601640	+	0.0106085i
$745$	354.688	−	297.619i	0.476091	−	0.399488i
$746$	826.039	+	693.129i	1.10729	+	0.929128i
$747$	126.758	+	718.878i	0.169689	+	0.962353i
$748$	30.5407	+	52.8981i	0.0408298	+	0.0707194i
$749$	1545.05	+	892.036i	2.06282	+	1.19097i
$750$	95.9812	+	34.9343i	0.127975	+	0.0465791i
$751$	−14.6260	+	40.1847i	−0.0194754	+	0.0535082i	−0.949049	−	0.315127i	$-0.897953\pi$
$751$	−14.6260	+	40.1847i	−0.0194754	+	0.0535082i	0.929574	+	0.368636i	$0.120175\pi$
$752$	−209.025	+	362.041i	−0.277958	+	0.481438i
$753$	13.5302	−	7.81169i	0.0179684	−	0.0103741i
$754$	665.840	−	117.406i	0.883077	−	0.155710i
$755$	66.5811	−	79.3483i	0.0881869	−	0.105097i
$756$	−135.457	−	161.432i	−0.179176	−	0.213534i
$757$	149.235	−	846.352i	0.197140	−	1.11803i	−0.712199	−	0.701977i	$-0.752301\pi$
$757$	149.235	−	846.352i	0.197140	−	1.11803i	0.909339	−	0.416057i	$-0.136588\pi$
$758$	−1581.94	+	575.780i	−2.08699	+	0.759604i
$759$		−	83.0618i		−	0.109436i
$760$	−98.2542	−	113.753i	−0.129282	−	0.149676i
$761$	−296.354			−0.389427			−0.194713	−	0.980860i	$-0.562378\pi$
$761$	−296.354			−0.389427			−0.194713	+	0.980860i	$0.562378\pi$
$762$	−43.6769	−	120.001i	−0.0573188	−	0.157482i
$763$	−630.560	−	111.185i	−0.826422	−	0.145720i
$764$	−171.207	+	143.660i	−0.224093	+	0.188037i
$765$	−45.5692	−	38.2371i	−0.0595676	−	0.0499832i
$766$	−213.306	−	1209.72i	−0.278468	−	1.57927i
$767$	−374.738	−	649.064i	−0.488576	−	0.846238i
$768$	113.186	+	65.3482i	0.147378	+	0.0850889i
$769$	−340.363	−	123.882i	−0.442605	−	0.161095i	0.111098	−	0.993809i	$-0.464563\pi$
$769$	−340.363	−	123.882i	−0.442605	−	0.161095i	−0.553703	+	0.832714i	$0.686786\pi$
$770$	177.282	−	487.079i	0.230237	−	0.632571i
$771$	−70.7774	+	122.590i	−0.0917995	+	0.159001i
$772$	694.459	−	400.946i	0.899559	−	0.519360i
$773$	1501.64	−	264.780i	1.94262	−	0.342536i	0.942655	−	0.333769i	$-0.108320\pi$
$773$	1501.64	−	264.780i	1.94262	−	0.342536i	0.999962	−	0.00876702i	$-0.00279067\pi$
$774$	65.1909	−	77.6915i	0.0842260	−	0.100377i
$775$	−425.257	−	506.801i	−0.548718	−	0.653937i
$776$	−33.0477	+	187.423i	−0.0425872	+	0.241524i
$777$	10.6240	−	3.86680i	0.0136730	−	0.00497658i
$778$		−	1008.21i		−	1.29589i
$779$	−996.698	+	190.467i	−1.27946	+	0.244503i
$780$	−32.1801			−0.0412565
$781$	203.443	+	558.956i	0.260491	+	0.715693i
$782$	206.533	+	36.4173i	0.264108	+	0.0465694i
$783$	101.535	−	85.1983i	0.129675	−	0.108810i
$784$	−1229.62	−	1031.77i	−1.56839	−	1.31603i
$785$	−4.04231	−	22.9251i	−0.00514944	−	0.0292039i
$786$	25.4588	+	44.0960i	0.0323903	+	0.0561017i
$787$	−1175.65	−	678.760i	−1.49383	−	0.862465i	−0.493858	−	0.869542i	$-0.664414\pi$
$787$	−1175.65	−	678.760i	−1.49383	−	0.862465i	−0.999975	+	0.00707738i	$0.997747\pi$
$788$	837.349	+	304.770i	1.06263	+	0.386764i
$789$	−7.52313	+	20.6696i	−0.00953502	+	0.0261972i
$790$	−88.8848	+	153.953i	−0.112512	+	0.194877i
$791$	−774.059	+	446.903i	−0.978583	+	0.564985i
$792$	236.993	−	41.7883i	0.299234	−	0.0527630i
$793$	−938.300	+	1118.22i	−1.18323	+	1.41012i
$794$	787.956	+	939.049i	0.992388	+	1.18268i
$795$	11.3676	−	64.4690i	0.0142989	−	0.0810931i
$796$	−29.5351	+	10.7499i	−0.0371044	+	0.0135049i
$797$			857.375i			1.07575i	0.843024	+	0.537876i	$0.180773\pi$
$797$			857.375i			1.07575i	−0.843024	+	0.537876i	$0.819227\pi$
$798$	−106.690	+	191.045i	−0.133696	+	0.239405i
$799$	63.4683			0.0794347
$800$	−248.182	−	681.875i	−0.310228	−	0.852343i
$801$	765.318	+	134.946i	0.955454	+	0.168472i
$802$	447.152	−	375.205i	0.557546	−	0.467836i
$803$	−108.351	−	90.9176i	−0.134933	−	0.113222i
$804$	5.53074	+	31.3664i	0.00687903	+	0.0390129i
$805$	−353.981	−	613.113i	−0.439728	−	0.761631i
$806$	1024.17	+	591.303i	1.27068	+	0.733627i
$807$	−57.5078	−	20.9311i	−0.0712612	−	0.0259370i
$808$	−5.39856	+	14.8324i	−0.00668138	+	0.0183570i
$809$	274.303	−	475.106i	0.339064	−	0.587276i	−0.645193	−	0.764020i	$-0.723223\pi$
$809$	274.303	−	475.106i	0.339064	−	0.587276i	0.984257	+	0.176744i	$0.0565564\pi$
$810$	388.099	−	224.069i	0.479134	−	0.276628i
$811$	−292.785	+	51.6259i	−0.361017	+	0.0636571i	−0.351215	−	0.936295i	$-0.614231\pi$
$811$	−292.785	+	51.6259i	−0.361017	+	0.0636571i	−0.00980232	+	0.999952i	$0.503120\pi$
$812$	−369.636	+	440.515i	−0.455217	+	0.542506i
$813$	−99.0879	−	118.088i	−0.121879	−	0.145250i
$814$	8.80192	−	49.9182i	0.0108132	−	0.0613245i
$815$	−191.538	+	69.7143i	−0.235017	+	0.0855390i
$816$		−	22.7458i		−	0.0278747i
$817$	−79.8152	−	27.7654i	−0.0976930	−	0.0339846i
$818$	−1977.86			−2.41792
$819$	477.652	+	1312.34i	0.583214	+	1.60237i
$820$	314.217	+	55.4049i	0.383191	+	0.0675670i
$821$	292.255	−	245.231i	0.355975	−	0.298698i	−0.447209	−	0.894429i	$-0.647582\pi$
$821$	292.255	−	245.231i	0.355975	−	0.298698i	0.803184	+	0.595731i	$0.203138\pi$
$822$	−85.3023	−	71.5771i	−0.103774	−	0.0870768i
$823$	119.883	+	679.892i	0.145666	+	0.826114i	0.966830	+	0.255421i	$0.0822141\pi$
$823$	119.883	+	679.892i	0.145666	+	0.826114i	−0.821164	+	0.570693i	$0.806675\pi$
$824$	65.1014	+	112.759i	0.0790066	+	0.136843i
$825$	52.2824	+	30.1853i	0.0633726	+	0.0365882i
$826$	1505.79	+	548.062i	1.82299	+	0.663513i
$827$	−113.265	+	311.194i	−0.136959	+	0.376292i	−0.989144	−	0.146948i	$-0.953055\pi$
$827$	−113.265	+	311.194i	−0.136959	+	0.376292i	0.852185	+	0.523241i	$0.175277\pi$
$828$	−319.853	+	554.002i	−0.386296	+	0.669085i
$829$	745.368	−	430.338i	0.899117	−	0.519105i	0.0222033	−	0.999753i	$-0.492932\pi$
$829$	745.368	−	430.338i	0.899117	−	0.519105i	0.876914	+	0.480648i	$0.159599\pi$
$830$	−473.462	+	83.4840i	−0.570436	+	0.100583i
$831$	−47.5712	+	56.6931i	−0.0572457	+	0.0682227i
$832$	139.069	+	165.736i	0.167150	+	0.199202i
$833$	−42.3170	+	239.992i	−0.0508007	+	0.288105i
$834$	−71.5181	+	26.0304i	−0.0857531	+	0.0312116i
$835$			161.527i			0.193445i
$836$	199.940	+	335.154i	0.239163	+	0.400902i
$837$	231.838			0.276987
$838$	95.7417	+	263.048i	0.114250	+	0.313900i
$839$	844.603	+	148.926i	1.00668	+	0.177505i	0.652593	−	0.757708i	$-0.273681\pi$
$839$	844.603	+	148.926i	1.00668	+	0.177505i	0.354085	+	0.935213i	$0.384792\pi$
$840$	−27.0808	+	22.7235i	−0.0322391	+	0.0270518i
$841$	367.173	+	308.095i	0.436591	+	0.366344i
$842$	−6.99680	−	39.6808i	−0.00830974	−	0.0471269i
$843$	−31.5816	−	54.7010i	−0.0374634	−	0.0648885i
$844$	−252.610	−	145.844i	−0.299301	−	0.172801i
$845$	45.1985	+	16.4509i	0.0534894	+	0.0194685i
$846$	−166.450	+	457.318i	−0.196750	+	0.540565i
$847$	−346.579	+	600.293i	−0.409185	+	0.708729i
$848$	−1257.76	+	726.170i	−1.48321	+	0.856333i
$849$	−91.5069	+	16.1351i	−0.107782	+	0.0190049i
$850$	−97.9779	+	116.766i	−0.115268	+	0.137371i
$851$	−44.5011	−	53.0343i	−0.0522927	−	0.0623200i
$852$	−13.7106	+	77.7566i	−0.0160922	+	0.0912636i
$853$	−33.4869	+	12.1882i	−0.0392578	+	0.0142887i	−0.361574	−	0.932343i	$-0.617761\pi$
$853$	−33.4869	+	12.1882i	−0.0392578	+	0.0142887i	0.322317	+	0.946632i	$0.395538\pi$
$854$		−	3121.01i		−	3.65457i
$855$	−294.613	−	240.120i	−0.344576	−	0.280842i
$856$	−545.523			−0.637293
$857$	310.321	+	852.601i	0.362102	+	0.994867i	0.978285	+	0.207264i	$0.0664560\pi$
$857$	310.321	+	852.601i	0.362102	+	0.994867i	−0.616183	+	0.787603i	$0.711322\pi$
$858$	−106.275	−	18.7392i	−0.123864	−	0.0218406i
$859$	333.193	−	279.582i	0.387885	−	0.325474i	−0.427904	−	0.903824i	$-0.640748\pi$
$859$	333.193	−	279.582i	0.387885	−	0.325474i	0.815789	+	0.578350i	$0.196303\pi$
$860$	20.3550	+	17.0799i	0.0236686	+	0.0198603i
$861$	41.4415	+	235.027i	0.0481319	+	0.272969i
$862$	−692.591	−	1199.60i	−0.803469	−	1.39165i
$863$	−225.876	−	130.410i	−0.261733	−	0.151112i	0.363392	−	0.931636i	$-0.381619\pi$
$863$	−225.876	−	130.410i	−0.261733	−	0.151112i	−0.625125	+	0.780525i	$0.714952\pi$
$864$	238.950	+	86.9705i	0.276562	+	0.100660i
$865$	−126.081	+	346.405i	−0.145758	+	0.400468i
$866$	851.437	−	1474.73i	0.983184	−	1.70292i
$867$	94.7435	−	54.7002i	0.109277	−	0.0630913i
$868$	−990.559	+	174.662i	−1.14120	+	0.201224i
$869$	−152.436	+	181.666i	−0.175415	+	0.209052i
$870$	27.8166	+	33.1505i	0.0319731	+	0.0381041i
$871$	73.9376	−	419.321i	0.0848882	−	0.481425i
$872$	183.976	−	66.9618i	0.210982	−	0.0767910i
$873$			481.217i			0.551223i
$874$	1322.77	+	213.799i	1.51347	+	0.244621i
$875$	1161.37			1.32728
$876$	−6.42135	−	17.6425i	−0.00733031	−	0.0201399i
$877$	−398.570	−	70.2786i	−0.454469	−	0.0801352i	−0.0582724	−	0.998301i	$-0.518559\pi$
$877$	−398.570	−	70.2786i	−0.454469	−	0.0801352i	−0.396197	+	0.918165i	$0.629670\pi$
$878$	178.531	−	149.806i	0.203339	−	0.170621i
$879$	47.6057	+	39.9459i	0.0541589	+	0.0454447i
$880$	59.7793	+	339.025i	0.0679310	+	0.385256i
$881$	−825.678	−	1430.12i	−0.937205	−	1.62329i	−0.770653	−	0.637255i	$-0.780070\pi$
$881$	−825.678	−	1430.12i	−0.937205	−	1.62329i	−0.166552	−	0.986033i	$-0.553263\pi$
$882$	−1618.27	−	934.309i	−1.83477	−	1.05931i
$883$	−276.411	−	100.605i	−0.313037	−	0.113936i	0.180724	−	0.983534i	$-0.442156\pi$
$883$	−276.411	−	100.605i	−0.313037	−	0.113936i	−0.493761	+	0.869598i	$0.664378\pi$
$884$	37.0712	−	101.852i	0.0419358	−	0.115218i
$885$	23.9853	−	41.5438i	0.0271021	−	0.0469422i
$886$	−562.777	+	324.919i	−0.635188	+	0.366726i
$887$	878.140	−	154.840i	0.990011	−	0.174566i	0.344888	−	0.938644i	$-0.387917\pi$
$887$	878.140	−	154.840i	0.990011	−	0.174566i	0.645124	+	0.764078i	$0.276806\pi$
$888$	−2.22212	+	2.64823i	−0.00250239	+	0.00298224i
$889$	−933.338	−	1112.31i	−1.04987	−	1.25119i
$890$	−88.8773	+	504.048i	−0.0998621	+	0.566346i
$891$	561.772	−	204.468i	0.630496	−	0.229482i
$892$			705.150i			0.790526i
$893$	405.471	−	5.79420i	0.454055	−	0.00648847i
$894$	206.101			0.230538
$895$	6.63446	+	18.2280i	0.00741281	+	0.0203665i
$896$	1189.15	+	209.679i	1.32717	+	0.234017i
$897$	−112.910	+	94.7426i	−0.125875	+	0.105622i
$898$	−60.8122	−	51.0275i	−0.0677196	−	0.0568235i
$899$	−109.857	−	623.030i	−0.122199	−	0.693026i
$900$	−232.474	−	402.657i	−0.258304	−	0.447396i
$901$	190.954	+	110.247i	0.211936	+	0.122361i
$902$	1005.45	+	365.952i	1.11468	+	0.405712i
$903$	−6.79762	+	18.6763i	−0.00752781	+	0.0206825i
$904$	136.651	−	236.687i	0.151163	−	0.261822i
$905$	−44.6262	+	25.7650i	−0.0493108	+	0.0284696i
$906$	45.4070	−	8.00649i	0.0501181	−	0.00883718i
$907$	686.143	−	817.714i	0.756498	−	0.901559i	−0.241123	−	0.970494i	$-0.577516\pi$
$907$	686.143	−	817.714i	0.756498	−	0.901559i	0.997621	+	0.0689355i	$0.0219603\pi$
$908$	−471.320	−	561.697i	−0.519074	−	0.618609i
$909$	−6.93055	+	39.3051i	−0.00762436	+	0.0432399i
$910$	−864.323	+	314.588i	−0.949805	+	0.345701i
$911$			1495.34i			1.64143i	0.571338	+	0.820715i	$0.306425\pi$
$911$			1495.34i			1.64143i	−0.571338	+	0.820715i	$0.693575\pi$
$912$	−2.07653	−	145.313i	−0.00227689	−	0.159334i
$913$	−641.351			−0.702465
$914$	−255.293	−	701.411i	−0.279314	−	0.767408i
$915$	−92.0119	−	16.2242i	−0.100559	−	0.0177313i
$916$	450.137	−	377.710i	0.491416	−	0.412347i
$917$	443.499	+	372.140i	0.483642	+	0.405824i
$918$	−9.27540	−	52.6034i	−0.0101039	−	0.0573022i
$919$	399.126	+	691.307i	0.434305	+	0.752238i	0.997239	−	0.0742639i	$-0.0236607\pi$
$919$	399.126	+	691.307i	0.434305	+	0.752238i	−0.562934	+	0.826502i	$0.690327\pi$
$920$	187.474	+	108.238i	0.203776	+	0.117650i
$921$	−14.5478	−	5.29498i	−0.0157957	−	0.00574917i
$922$	−510.175	+	1401.69i	−0.553335	+	1.52028i
$923$	527.762	−	914.110i	0.571790	−	0.990369i
$924$	79.4879	−	45.8923i	0.0860258	−	0.0496670i
$925$	49.5539	−	8.73770i	0.0535718	−	0.00944616i
$926$	−507.704	+	605.058i	−0.548276	+	0.653410i
$927$	211.621	+	252.200i	0.228286	+	0.272061i
$928$	120.493	−	683.352i	0.129842	−	0.736370i
$929$	−1028.73	+	374.429i	−1.10736	+	0.403045i	−0.830023	−	0.557729i	$-0.811673\pi$
$929$	−1028.73	+	374.429i	−1.10736	+	0.403045i	−0.277334	+	0.960774i	$0.589451\pi$
$930$			75.6935i			0.0813909i
$931$	−248.435	+	1537.07i	−0.266848	+	1.65098i
$932$	933.902			1.00204
$933$	−77.8029	−	213.762i	−0.0833901	−	0.229112i
$934$	1466.99	+	258.671i	1.57066	+	0.276949i
$935$	40.0372	−	33.5952i	0.0428206	−	0.0359307i
$936$	−327.126	−	274.491i	−0.349493	−	0.293260i
$937$	212.273	+	1203.86i	0.226546	+	1.28480i	0.859708	+	0.510786i	$0.170645\pi$
$937$	212.273	+	1203.86i	0.226546	+	1.28480i	−0.633162	+	0.774019i	$0.718243\pi$
$938$	455.183	+	788.400i	0.485270	+	0.840511i
$939$	41.9945	+	24.2455i	0.0447225	+	0.0258206i
$940$	−119.816	−	43.6096i	−0.127464	−	0.0463932i
$941$	319.934	−	879.011i	0.339993	−	0.934124i	−0.645402	−	0.763843i	$-0.723310\pi$
$941$	319.934	−	879.011i	0.339993	−	0.934124i	0.985396	−	0.170281i	$-0.0544676\pi$
$942$	5.18104	−	8.97383i	0.00550005	−	0.00952636i
$943$	1265.61	−	730.699i	1.34211	−	0.774866i
$944$	−1048.08	+	184.805i	−1.11026	+	0.195768i
$945$	−115.905	+	138.130i	−0.122651	+	0.146170i
$946$	57.2769	+	68.2599i	0.0605464	+	0.0721564i
$947$	214.396	−	1215.90i	0.226395	−	1.28395i	−0.633605	−	0.773657i	$-0.718426\pi$
$947$	214.396	−	1215.90i	0.226395	−	1.28395i	0.860000	−	0.510294i	$-0.170463\pi$
$948$	−29.5801	+	10.7663i	−0.0312026	+	0.0113568i
$949$			250.990i			0.264479i
$950$	−615.278	+	754.908i	−0.647661	+	0.794640i
$951$	−7.20556			−0.00757683
$952$	−40.7247	−	111.890i	−0.0427780	−	0.117532i
$953$	741.991	+	130.833i	0.778585	+	0.137285i	0.548797	−	0.835955i	$-0.315086\pi$
$953$	741.991	+	130.833i	0.778585	+	0.137285i	0.229787	+	0.973241i	$0.426197\pi$
$954$	−1295.17	+	1086.78i	−1.35762	+	1.13918i
$955$	146.495	+	122.924i	0.153398	+	0.128716i
$956$	−143.502	−	813.843i	−0.150107	−	0.851300i
$957$	28.8648	+	49.9954i	0.0301618	+	0.0522418i
$958$	−401.196	−	231.631i	−0.418785	−	0.241786i
$959$	−1189.77	−	433.042i	−1.24064	−	0.451555i
$960$	−4.73623	+	13.0127i	−0.00493358	+	0.0135549i
$961$	72.7862	−	126.069i	0.0757401	−	0.131186i
$962$	−77.8958	+	44.9732i	−0.0809728	+	0.0467496i
$963$	−1358.42	+	239.527i	−1.41062	+	0.248730i
$964$	−646.074	+	769.961i	−0.670201	+	0.798715i
$965$	−441.046	−	525.619i	−0.457043	−	0.544683i
$966$	54.7228	−	310.348i	0.0566489	−	0.321272i
$967$	−684.162	+	249.015i	−0.707510	+	0.257513i	−0.670614	−	0.741807i	$-0.733969\pi$
$967$	−684.162	+	249.015i	−0.707510	+	0.257513i	−0.0368960	+	0.999319i	$0.511747\pi$
$968$		−	211.950i		−	0.218957i
$969$	−18.9481	+	11.3037i	−0.0195543	+	0.0116654i
$970$	−316.936			−0.326738
$971$	−554.573	−	1523.68i	−0.571136	−	1.56918i	−0.802713	−	0.596366i	$-0.796611\pi$
$971$	−554.573	−	1523.68i	−0.571136	−	1.56918i	0.231577	−	0.972817i	$-0.425611\pi$
$972$	241.370	+	42.5601i	0.248323	+	0.0437861i
$973$	−662.910	+	556.248i	−0.681306	+	0.571683i
$974$	1361.28	+	1142.25i	1.39762	+	1.17274i
$975$	−18.6025	−	105.500i	−0.0190795	−	0.108205i
$976$	1036.41	+	1795.11i	1.06189	+	1.83925i
$977$	−1082.21	−	624.813i	−1.10768	−	0.639522i	−0.169456	−	0.985538i	$-0.554201\pi$
$977$	−1082.21	−	624.813i	−1.10768	−	0.639522i	−0.938229	+	0.346016i	$0.887534\pi$
$978$	−85.2598	−	31.0320i	−0.0871777	−	0.0317301i
$979$	−233.526	+	641.607i	−0.238535	+	0.655369i
$980$	244.787	−	423.984i	0.249783	−	0.432636i
$981$	428.723	−	247.523i	0.437027	−	0.252318i
$982$	1097.91	−	193.591i	1.11803	−	0.197140i
$983$	−365.271	+	435.313i	−0.371588	+	0.442841i	−0.919140	−	0.393930i	$-0.871115\pi$
$983$	−365.271	+	435.313i	−0.371588	+	0.442841i	0.547553	+	0.836771i	$0.315560\pi$
$984$	−46.9066	−	55.9011i	−0.0476693	−	0.0568101i
$985$	132.401	−	750.884i	0.134417	−	0.762319i
$986$	−136.968	+	49.8525i	−0.138913	+	0.0505603i
$987$		−	95.3713i		−	0.0966275i
$988$	227.533	−	654.075i	0.230297	−	0.662019i
$989$	121.705			0.123058
$990$	137.068	+	376.592i	0.138453	+	0.380396i
$991$	−251.477	−	44.3421i	−0.253760	−	0.0447448i	0.0453208	−	0.998972i	$-0.485569\pi$
$991$	−251.477	−	44.3421i	−0.253760	−	0.0447448i	−0.299081	+	0.954228i	$0.596680\pi$
$992$	929.756	−	780.158i	0.937254	−	0.786449i
$993$	149.323	+	125.297i	0.150376	+	0.126180i
$994$	391.885	+	2222.49i	0.394251	+	2.23591i
$995$	13.4469	+	23.2908i	0.0135145	+	0.0234078i
$996$	−73.7259	−	42.5657i	−0.0740220	−	0.0427366i
$997$	−682.929	−	248.566i	−0.684984	−	0.249314i	−0.0239977	−	0.999712i	$-0.507639\pi$
$997$	−682.929	−	248.566i	−0.684984	−	0.249314i	−0.660986	+	0.750398i	$0.729862\pi$
$998$	251.994	−	692.347i	0.252499	−	0.693734i
$999$	−8.81655	+	15.2707i	−0.00882537	+	0.0152860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.3.f.a.14.1	✓	12
3.2	odd	2		171.3.ba.b.109.2		12
4.3	odd	2		304.3.z.a.33.1		12
19.2	odd	18		361.3.b.c.360.2		12
19.3	odd	18		361.3.d.f.69.1		12
19.4	even	9		361.3.f.g.262.2		12
19.5	even	9		361.3.d.f.293.1		12
19.6	even	9		361.3.f.b.333.1		12
19.7	even	3		361.3.f.f.116.2		12
19.8	odd	6		361.3.f.c.307.2		12
19.9	even	9		361.3.f.c.127.2		12
19.10	odd	18		361.3.f.e.127.1		12
19.11	even	3		361.3.f.e.307.1		12
19.12	odd	6		361.3.f.b.116.1		12
19.13	odd	18		361.3.f.f.333.2		12
19.14	odd	18		361.3.d.d.293.6		12
19.15	odd	18	inner	19.3.f.a.15.1	yes	12
19.16	even	9		361.3.d.d.69.6		12
19.17	even	9		361.3.b.c.360.11		12
19.18	odd	2		361.3.f.g.299.2		12
57.53	even	18		171.3.ba.b.91.2		12
76.15	even	18		304.3.z.a.129.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.1	✓	12	1.1	even	1	trivial
19.3.f.a.15.1	yes	12	19.15	odd	18	inner
171.3.ba.b.91.2		12	57.53	even	18
171.3.ba.b.109.2		12	3.2	odd	2
304.3.z.a.33.1		12	4.3	odd	2
304.3.z.a.129.1		12	76.15	even	18
361.3.b.c.360.2		12	19.2	odd	18
361.3.b.c.360.11		12	19.17	even	9
361.3.d.d.69.6		12	19.16	even	9
361.3.d.d.293.6		12	19.14	odd	18
361.3.d.f.69.1		12	19.3	odd	18
361.3.d.f.293.1		12	19.5	even	9
361.3.f.b.116.1		12	19.12	odd	6
361.3.f.b.333.1		12	19.6	even	9
361.3.f.c.127.2		12	19.9	even	9
361.3.f.c.307.2		12	19.8	odd	6
361.3.f.e.127.1		12	19.10	odd	18
361.3.f.e.307.1		12	19.11	even	3
361.3.f.f.116.2		12	19.7	even	3
361.3.f.f.333.2		12	19.13	odd	18
361.3.f.g.262.2		12	19.4	even	9
361.3.f.g.299.2		12	19.18	odd	2

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.881480 - 2.42185i) q^{2} +(-0.384565 - 0.0678091i) q^{3} +(-2.02415 + 1.69847i) q^{4} +(1.73199 + 1.45331i) q^{5} +(0.174763 + 0.991129i) q^{6} +(5.72163 + 9.91015i) q^{7} +(-3.03027 - 1.74952i) q^{8} +(-8.31394 - 3.02603i) q^{9} +O(q^{10})\)	\(q+(-0.881480 - 2.42185i) q^{2} +(-0.384565 - 0.0678091i) q^{3} +(-2.02415 + 1.69847i) q^{4} +(1.73199 + 1.45331i) q^{5} +(0.174763 + 0.991129i) q^{6} +(5.72163 + 9.91015i) q^{7} +(-3.03027 - 1.74952i) q^{8} +(-8.31394 - 3.02603i) q^{9} +(1.99298 - 5.47566i) q^{10} +(3.88672 - 6.73200i) q^{11} +(0.893589 - 0.515914i) q^{12} +(-13.5844 + 2.39530i) q^{13} +(18.9574 - 22.5925i) q^{14} +(-0.567513 - 0.676335i) q^{15} +(-3.40132 + 19.2898i) q^{16} +(2.79442 - 1.01709i) q^{17} +22.8025i q^{18} +(17.7595 - 6.75283i) q^{19} -5.97420 q^{20} +(-1.52834 - 4.19907i) q^{21} +(-19.7299 - 3.47892i) q^{22} +(-20.9616 + 17.5889i) q^{23} +(1.04670 + 0.878285i) q^{24} +(-3.45354 - 19.5860i) q^{25} +(17.7754 + 30.7880i) q^{26} +(6.03568 + 3.48470i) q^{27} +(-28.4135 - 10.3417i) q^{28} +(6.50458 - 17.8712i) q^{29} +(-1.13773 + 1.97060i) q^{30} +(28.8085 - 16.6326i) q^{31} +(35.9316 - 6.33571i) q^{32} +(-1.95119 + 2.32533i) q^{33} +(-4.92645 - 5.87112i) q^{34} +(-4.49273 + 25.4795i) q^{35} +(21.9683 - 7.99581i) q^{36} +2.53007i q^{37} +(-32.0089 - 37.0583i) q^{38} +5.38651 q^{39} +(-2.70578 - 7.43406i) q^{40} +(-52.5957 - 9.27403i) q^{41} +(-8.82230 + 7.40279i) q^{42} +(-3.40715 - 2.85894i) q^{43} +(3.56675 + 20.2281i) q^{44} +(-10.0019 - 17.3238i) q^{45} +(61.0747 + 35.2615i) q^{46} +(20.0556 + 7.29965i) q^{47} +(2.61605 - 7.18754i) q^{48} +(-40.9740 + 70.9691i) q^{49} +(-44.3900 + 25.6286i) q^{50} +(-1.14360 + 0.201648i) q^{51} +(23.4286 - 27.9211i) q^{52} +(47.6606 + 56.7997i) q^{53} +(3.11908 - 17.6892i) q^{54} +(16.5154 - 6.01112i) q^{55} -40.0405i q^{56} +(-7.28757 + 1.39264i) q^{57} -49.0150 q^{58} +(18.5831 + 51.0568i) q^{59} +(2.29747 + 0.405105i) q^{60} +(81.0659 - 68.0224i) q^{61} +(-65.6757 - 55.1084i) q^{62} +(-17.5809 - 99.7062i) q^{63} +(-7.84230 - 13.5833i) q^{64} +(-27.0091 - 15.5937i) q^{65} +(7.35153 + 2.67574i) q^{66} +(-10.5574 + 29.0062i) q^{67} +(-3.92885 + 6.80497i) q^{68} +(9.25377 - 5.34267i) q^{69} +(65.6677 - 11.5790i) q^{70} +(-49.1865 + 58.6182i) q^{71} +(19.8993 + 23.7151i) q^{72} +(3.15964 - 17.9192i) q^{73} +(6.12745 - 2.23021i) q^{74} +7.76625i q^{75} +(-24.4785 + 43.8327i) q^{76} +88.9535 q^{77} +(-4.74810 - 13.0453i) q^{78} +(-30.0440 - 5.29757i) q^{79} +(-33.9251 + 28.4665i) q^{80} +(58.9135 + 49.4343i) q^{81} +(23.9017 + 135.553i) q^{82} +(-41.2527 - 71.4518i) q^{83} +(10.2256 + 5.90373i) q^{84} +(6.31804 + 2.29958i) q^{85} +(-3.92058 + 10.7717i) q^{86} +(-3.71326 + 6.43156i) q^{87} +(-23.5556 + 13.5998i) q^{88} +(-86.5010 + 15.2525i) q^{89} +(-33.1390 + 39.4935i) q^{90} +(-101.463 - 120.919i) q^{91} +(12.5554 - 71.2051i) q^{92} +(-12.2066 + 4.44283i) q^{93} -55.0062i q^{94} +(40.5731 + 14.1142i) q^{95} -14.2476 q^{96} +(-18.6025 - 51.1100i) q^{97} +(207.994 + 36.6750i) q^{98} +(-52.6852 + 44.2081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9	\( 12 q - 6 q^{2} - 6 q^{5} - 36 q^{6} + 6 q^{7} - 9 q^{8} - 24 q^{9} + 51 q^{10} - 18 q^{11} + 63 q^{12} + 21 q^{13} + 9 q^{14} + 63 q^{15} - 12 q^{16} - 3 q^{17} - 24 q^{19} - 90 q^{20} + 30 q^{21} - 78 q^{22} - 102 q^{23} - 12 q^{24} - 156 q^{25} + 21 q^{26} - 27 q^{27} + 12 q^{28} + 147 q^{29} + 24 q^{30} + 99 q^{31} + 165 q^{32} + 84 q^{33} + 132 q^{34} + 96 q^{35} + 63 q^{36} + 72 q^{38} - 108 q^{39} - 138 q^{40} - 144 q^{41} - 237 q^{42} - 27 q^{43} - 123 q^{44} - 3 q^{45} - 54 q^{46} - 99 q^{47} - 51 q^{48} - 24 q^{49} + 72 q^{50} - 42 q^{51} + 93 q^{52} + 111 q^{53} + 21 q^{54} + 162 q^{55} - 168 q^{57} - 132 q^{58} + 3 q^{59} - 30 q^{60} + 150 q^{61} + 108 q^{62} + 234 q^{63} + 27 q^{64} + 126 q^{65} + 168 q^{66} + 135 q^{67} - 30 q^{68} + 72 q^{69} + 225 q^{70} - 168 q^{71} - 102 q^{72} - 90 q^{73} - 231 q^{74} + 42 q^{76} + 246 q^{77} - 189 q^{78} - 75 q^{79} + 21 q^{80} - 159 q^{81} - 117 q^{82} - 156 q^{83} + 99 q^{84} - 300 q^{85} - 144 q^{86} + 69 q^{87} - 405 q^{88} - 558 q^{89} - 66 q^{90} - 453 q^{91} + 48 q^{92} - 57 q^{93} - 69 q^{95} + 558 q^{96} + 465 q^{97} + 777 q^{98} + 462 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^5 - 36 * q^6 + 6 * q^7 - 9 * q^8 - 24 * q^9 + 51 * q^10 - 18 * q^11 + 63 * q^12 + 21 * q^13 + 9 * q^14 + 63 * q^15 - 12 * q^16 - 3 * q^17 - 24 * q^19 - 90 * q^20 + 30 * q^21 - 78 * q^22 - 102 * q^23 - 12 * q^24 - 156 * q^25 + 21 * q^26 - 27 * q^27 + 12 * q^28 + 147 * q^29 + 24 * q^30 + 99 * q^31 + 165 * q^32 + 84 * q^33 + 132 * q^34 + 96 * q^35 + 63 * q^36 + 72 * q^38 - 108 * q^39 - 138 * q^40 - 144 * q^41 - 237 * q^42 - 27 * q^43 - 123 * q^44 - 3 * q^45 - 54 * q^46 - 99 * q^47 - 51 * q^48 - 24 * q^49 + 72 * q^50 - 42 * q^51 + 93 * q^52 + 111 * q^53 + 21 * q^54 + 162 * q^55 - 168 * q^57 - 132 * q^58 + 3 * q^59 - 30 * q^60 + 150 * q^61 + 108 * q^62 + 234 * q^63 + 27 * q^64 + 126 * q^65 + 168 * q^66 + 135 * q^67 - 30 * q^68 + 72 * q^69 + 225 * q^70 - 168 * q^71 - 102 * q^72 - 90 * q^73 - 231 * q^74 + 42 * q^76 + 246 * q^77 - 189 * q^78 - 75 * q^79 + 21 * q^80 - 159 * q^81 - 117 * q^82 - 156 * q^83 + 99 * q^84 - 300 * q^85 - 144 * q^86 + 69 * q^87 - 405 * q^88 - 558 * q^89 - 66 * q^90 - 453 * q^91 + 48 * q^92 - 57 * q^93 - 69 * q^95 + 558 * q^96 + 465 * q^97 + 777 * q^98 + 462 * q^99

Introduction

L-functions

Modular forms

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