LMFDB - Embedded newform 17.3.e.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,3,Mod(3,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(16))

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("17.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	17.e (of order $16$, degree $8$, 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:	$0.463216449413$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			7.1
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	17.7
Dual form			17.3.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841487 + 2.03153i) q^{2} +(0.0897902 - 0.134381i) q^{3} +(-0.590587 - 0.590587i) q^{4} +(-1.04667 - 5.26197i) q^{5} +(0.197441 + 0.295491i) q^{6} +(1.21824 - 6.12453i) q^{7} +(-6.42935 + 2.66313i) q^{8} +(3.43416 + 8.29078i) q^{9} +O(q^{10})$	\(q+(-0.841487 + 2.03153i) q^{2} +(0.0897902 - 0.134381i) q^{3} +(-0.590587 - 0.590587i) q^{4} +(-1.04667 - 5.26197i) q^{5} +(0.197441 + 0.295491i) q^{6} +(1.21824 - 6.12453i) q^{7} +(-6.42935 + 2.66313i) q^{8} +(3.43416 + 8.29078i) q^{9} +(11.5706 + 2.30154i) q^{10} +(-12.1433 + 8.11392i) q^{11} +(-0.132392 + 0.0263345i) q^{12} +(4.79884 - 4.79884i) q^{13} +(11.4170 + 7.62861i) q^{14} +(-0.801088 - 0.331821i) q^{15} -18.6433i q^{16} +(6.50562 - 15.7060i) q^{17} -19.7328 q^{18} +(-9.56175 + 23.0841i) q^{19} +(-2.48950 + 3.72580i) q^{20} +(-0.713631 - 0.713631i) q^{21} +(-6.26521 - 31.4973i) q^{22} +(7.27639 + 10.8899i) q^{23} +(-0.219421 + 1.10310i) q^{24} +(-3.49585 + 1.44803i) q^{25} +(5.71082 + 13.7871i) q^{26} +(2.84909 + 0.566719i) q^{27} +(-4.33654 + 2.89759i) q^{28} +(32.3980 - 6.44436i) q^{29} +(1.34821 - 1.34821i) q^{30} +(-1.00960 - 0.674593i) q^{31} +(12.1570 + 5.03558i) q^{32} +2.36038i q^{33} +(26.4327 + 26.4327i) q^{34} -33.5022 q^{35} +(2.86826 - 6.92459i) q^{36} +(-25.8238 + 38.6481i) q^{37} +(-38.8500 - 38.8500i) q^{38} +(-0.213982 - 1.07576i) q^{39} +(20.7427 + 31.0437i) q^{40} +(6.13577 - 30.8466i) q^{41} +(2.05027 - 0.849251i) q^{42} +(-27.8948 - 67.3441i) q^{43} +(11.9637 + 2.37972i) q^{44} +(40.0314 - 26.7482i) q^{45} +(-28.2461 + 5.61851i) q^{46} +(-10.4882 + 10.4882i) q^{47} +(-2.50529 - 1.67398i) q^{48} +(9.24438 + 3.82915i) q^{49} -8.32041i q^{50} +(-1.52643 - 2.28447i) q^{51} -5.66826 q^{52} +(-1.97838 + 4.77624i) q^{53} +(-3.54878 + 5.31112i) q^{54} +(55.4053 + 55.4053i) q^{55} +(8.47786 + 42.6211i) q^{56} +(2.24350 + 3.35764i) q^{57} +(-14.1706 + 71.2404i) q^{58} +(26.1013 - 10.8115i) q^{59} +(0.277142 + 0.669081i) q^{60} +(-81.0541 - 16.1227i) q^{61} +(2.22002 - 1.48337i) q^{62} +(54.9608 - 10.9324i) q^{63} +(32.2713 - 32.2713i) q^{64} +(-30.2741 - 20.2285i) q^{65} +(-4.79518 - 1.98623i) q^{66} +44.5324i q^{67} +(-13.1179 + 5.43359i) q^{68} +2.11674 q^{69} +(28.1917 - 68.0607i) q^{70} +(32.1978 - 48.1875i) q^{71} +(-44.1588 - 44.1588i) q^{72} +(-0.262865 - 1.32151i) q^{73} +(-56.7843 - 84.9838i) q^{74} +(-0.119306 + 0.599792i) q^{75} +(19.2802 - 7.98612i) q^{76} +(34.9004 + 84.2570i) q^{77} +(2.36550 + 0.470527i) q^{78} +(-24.7128 + 16.5125i) q^{79} +(-98.1004 + 19.5134i) q^{80} +(-56.7774 + 56.7774i) q^{81} +(57.5026 + 38.4220i) q^{82} +(-62.2748 - 25.7951i) q^{83} +0.842922i q^{84} +(-89.4535 - 17.7934i) q^{85} +160.285 q^{86} +(2.04303 - 4.93230i) q^{87} +(56.4655 - 84.5065i) q^{88} +(90.1397 + 90.1397i) q^{89} +(20.6537 + 103.833i) q^{90} +(-23.5444 - 35.2368i) q^{91} +(2.13408 - 10.7288i) q^{92} +(-0.181304 + 0.0750988i) q^{93} +(-12.4814 - 30.1327i) q^{94} +(131.476 + 26.1522i) q^{95} +(1.76826 - 1.18151i) q^{96} +(-66.3366 + 13.1952i) q^{97} +(-15.5581 + 15.5581i) q^{98} +(-108.973 - 72.8134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{11} + 48 q^{12} + 16 q^{13} + 8 q^{14} - 16 q^{15} + 56 q^{18} - 80 q^{20} - 64 q^{21} - 104 q^{22} - 56 q^{23} - 80 q^{24} + 64 q^{25} + 176 q^{26} + 40 q^{27} + 152 q^{28} + 48 q^{29} + 16 q^{30} + 24 q^{31} + 88 q^{32} - 136 q^{34} - 160 q^{35} - 128 q^{36} + 32 q^{37} - 120 q^{38} + 48 q^{39} + 64 q^{40} + 48 q^{41} + 16 q^{42} - 232 q^{43} + 120 q^{44} - 88 q^{46} + 192 q^{47} + 136 q^{48} + 16 q^{49} + 136 q^{51} - 384 q^{52} - 32 q^{53} + 8 q^{54} + 224 q^{55} - 120 q^{56} + 24 q^{57} + 240 q^{58} - 48 q^{59} + 64 q^{60} - 160 q^{61} - 168 q^{62} + 56 q^{63} - 64 q^{64} - 96 q^{65} - 8 q^{66} + 272 q^{68} + 240 q^{69} + 224 q^{70} + 40 q^{71} + 40 q^{72} + 48 q^{73} - 160 q^{74} - 296 q^{75} + 80 q^{76} - 48 q^{77} - 400 q^{78} - 136 q^{79} - 240 q^{80} - 424 q^{81} - 64 q^{82} - 264 q^{83} - 272 q^{85} + 832 q^{86} + 208 q^{87} + 264 q^{88} + 160 q^{89} + 448 q^{90} + 320 q^{91} + 24 q^{92} - 64 q^{93} + 32 q^{94} + 272 q^{95} - 56 q^{96} + 48 q^{97} - 120 q^{98} - 224 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^11 + 48 * q^12 + 16 * q^13 + 8 * q^14 - 16 * q^15 + 56 * q^18 - 80 * q^20 - 64 * q^21 - 104 * q^22 - 56 * q^23 - 80 * q^24 + 64 * q^25 + 176 * q^26 + 40 * q^27 + 152 * q^28 + 48 * q^29 + 16 * q^30 + 24 * q^31 + 88 * q^32 - 136 * q^34 - 160 * q^35 - 128 * q^36 + 32 * q^37 - 120 * q^38 + 48 * q^39 + 64 * q^40 + 48 * q^41 + 16 * q^42 - 232 * q^43 + 120 * q^44 - 88 * q^46 + 192 * q^47 + 136 * q^48 + 16 * q^49 + 136 * q^51 - 384 * q^52 - 32 * q^53 + 8 * q^54 + 224 * q^55 - 120 * q^56 + 24 * q^57 + 240 * q^58 - 48 * q^59 + 64 * q^60 - 160 * q^61 - 168 * q^62 + 56 * q^63 - 64 * q^64 - 96 * q^65 - 8 * q^66 + 272 * q^68 + 240 * q^69 + 224 * q^70 + 40 * q^71 + 40 * q^72 + 48 * q^73 - 160 * q^74 - 296 * q^75 + 80 * q^76 - 48 * q^77 - 400 * q^78 - 136 * q^79 - 240 * q^80 - 424 * q^81 - 64 * q^82 - 264 * q^83 - 272 * q^85 + 832 * q^86 + 208 * q^87 + 264 * q^88 + 160 * q^89 + 448 * q^90 + 320 * q^91 + 24 * q^92 - 64 * q^93 + 32 * q^94 + 272 * q^95 - 56 * q^96 + 48 * q^97 - 120 * q^98 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−0.841487	+	2.03153i	−0.420744	+	1.01577i	0.561385	+	0.827555i	$0.310269\pi$
$2$	−0.841487	+	2.03153i	−0.420744	+	1.01577i	−0.982129	+	0.188210i	$0.939731\pi$
$3$	0.0897902	−	0.134381i	0.0299301	−	0.0447935i	−0.816203	−	0.577765i	$-0.803925\pi$
$3$	0.0897902	−	0.134381i	0.0299301	−	0.0447935i	0.846133	+	0.532972i	$0.178925\pi$
$4$	−0.590587	−	0.590587i	−0.147647	−	0.147647i
$5$	−1.04667	−	5.26197i	−0.209334	−	1.05239i	−0.932348	−	0.361561i	$-0.882244\pi$
$5$	−1.04667	−	5.26197i	−0.209334	−	1.05239i	0.723014	−	0.690833i	$-0.242756\pi$
$6$	0.197441	+	0.295491i	0.0329068	+	0.0492485i
$7$	1.21824	−	6.12453i	0.174035	−	0.874933i	−0.790800	−	0.612075i	$-0.790335\pi$
$7$	1.21824	−	6.12453i	0.174035	−	0.874933i	0.964835	−	0.262858i	$-0.0846649\pi$
$8$	−6.42935	+	2.66313i	−0.803669	+	0.332891i
$9$	3.43416	+	8.29078i	0.381573	+	0.921198i
$10$	11.5706	+	2.30154i	1.15706	+	0.230154i
$11$	−12.1433	+	8.11392i	−1.10394	+	0.737629i	−0.967463	−	0.253014i	$-0.918578\pi$
$11$	−12.1433	+	8.11392i	−1.10394	+	0.737629i	−0.136478	+	0.990643i	$0.543578\pi$
$12$	−0.132392	+	0.0263345i	−0.0110327	+	0.00219454i
$13$	4.79884	−	4.79884i	0.369141	−	0.369141i	−0.498023	−	0.867164i	$-0.665940\pi$
$13$	4.79884	−	4.79884i	0.369141	−	0.369141i	0.867164	+	0.498023i	$0.165940\pi$
$14$	11.4170	+	7.62861i	0.815502	+	0.544901i
$15$	−0.801088	−	0.331821i	−0.0534058	−	0.0221214i
$16$		−	18.6433i		−	1.16520i
$17$	6.50562	−	15.7060i	0.382683	−	0.923880i
$17$	6.50562	−	15.7060i	0.382683	−	0.923880i
$18$	−19.7328			−1.09627
$19$	−9.56175	+	23.0841i	−0.503250	+	1.21495i	0.444454	+	0.895802i	$0.353398\pi$
$19$	−9.56175	+	23.0841i	−0.503250	+	1.21495i	−0.947704	+	0.319151i	$0.896602\pi$
$20$	−2.48950	+	3.72580i	−0.124475	+	0.186290i
$21$	−0.713631	−	0.713631i	−0.0339824	−	0.0339824i
$22$	−6.26521	−	31.4973i	−0.284782	−	1.43170i
$23$	7.27639	+	10.8899i	0.316365	+	0.473474i	0.955238	−	0.295839i	$-0.0955991\pi$
$23$	7.27639	+	10.8899i	0.316365	+	0.473474i	−0.638873	+	0.769312i	$0.720599\pi$
$24$	−0.219421	+	1.10310i	−0.00914253	+	0.0459626i
$25$	−3.49585	+	1.44803i	−0.139834	+	0.0579211i
$26$	5.71082	+	13.7871i	0.219647	+	0.530274i
$27$	2.84909	+	0.566719i	0.105522	+	0.0209896i
$28$	−4.33654	+	2.89759i	−0.154877	+	0.103485i
$29$	32.3980	−	6.44436i	1.11717	−	0.222219i	0.398228	−	0.917287i	$-0.369625\pi$
$29$	32.3980	−	6.44436i	1.11717	−	0.222219i	0.718945	+	0.695067i	$0.244625\pi$
$30$	1.34821	−	1.34821i	0.0449403	−	0.0449403i
$31$	−1.00960	−	0.674593i	−0.0325678	−	0.0217611i	0.539180	−	0.842191i	$-0.318734\pi$
$31$	−1.00960	−	0.674593i	−0.0325678	−	0.0217611i	−0.571748	+	0.820430i	$0.693734\pi$
$32$	12.1570	+	5.03558i	0.379905	+	0.157362i
$33$			2.36038i			0.0715267i
$34$	26.4327	+	26.4327i	0.777433	+	0.777433i
$35$	−33.5022			−0.957206
$36$	2.86826	−	6.92459i	0.0796739	−	0.192350i
$37$	−25.8238	+	38.6481i	−0.697941	+	1.04454i	0.298002	+	0.954565i	$0.403680\pi$
$37$	−25.8238	+	38.6481i	−0.697941	+	1.04454i	−0.995944	+	0.0899781i	$0.971320\pi$
$38$	−38.8500	−	38.8500i	−1.02237	−	1.02237i
$39$	−0.213982	−	1.07576i	−0.00548671	−	0.0275836i
$40$	20.7427	+	31.0437i	0.518568	+	0.776092i
$41$	6.13577	−	30.8466i	0.149653	−	0.752356i	−0.830949	−	0.556348i	$-0.812202\pi$
$41$	6.13577	−	30.8466i	0.149653	−	0.752356i	0.980602	−	0.196008i	$-0.0627979\pi$
$42$	2.05027	−	0.849251i	0.0488161	−	0.0202203i
$43$	−27.8948	−	67.3441i	−0.648717	−	1.56614i	−0.814617	−	0.579999i	$-0.803053\pi$
$43$	−27.8948	−	67.3441i	−0.648717	−	1.56614i	0.165901	−	0.986142i	$-0.446947\pi$
$44$	11.9637	+	2.37972i	0.271902	+	0.0540846i
$45$	40.0314	−	26.7482i	0.889588	−	0.594403i
$46$	−28.2461	+	5.61851i	−0.614047	+	0.122141i
$47$	−10.4882	+	10.4882i	−0.223153	+	0.223153i	−0.809825	−	0.586672i	$-0.800438\pi$
$47$	−10.4882	+	10.4882i	−0.223153	+	0.223153i	0.586672	+	0.809825i	$0.300438\pi$
$48$	−2.50529	−	1.67398i	−0.0521936	−	0.0348747i
$49$	9.24438	+	3.82915i	0.188661	+	0.0781458i
$50$		−	8.32041i		−	0.166408i
$51$	−1.52643	−	2.28447i	−0.0299301	−	0.0447935i
$52$	−5.66826			−0.109005
$53$	−1.97838	+	4.77624i	−0.0373280	+	0.0901178i	−0.941444	−	0.337169i	$-0.890531\pi$
$53$	−1.97838	+	4.77624i	−0.0373280	+	0.0901178i	0.904116	+	0.427287i	$0.140531\pi$
$54$	−3.54878	+	5.31112i	−0.0657181	+	0.0983541i
$55$	55.4053	+	55.4053i	1.00737	+	1.00737i
$56$	8.47786	+	42.6211i	0.151390	+	0.761091i
$57$	2.24350	+	3.35764i	0.0393597	+	0.0589059i
$58$	−14.1706	+	71.2404i	−0.244321	+	1.22828i
$59$	26.1013	−	10.8115i	0.442394	−	0.183246i	−0.150356	−	0.988632i	$-0.548042\pi$
$59$	26.1013	−	10.8115i	0.442394	−	0.183246i	0.592751	+	0.805386i	$0.298042\pi$
$60$	0.277142	+	0.669081i	0.00461904	+	0.0111513i
$61$	−81.0541	−	16.1227i	−1.32876	−	0.264306i	−0.520866	−	0.853639i	$-0.674391\pi$
$61$	−81.0541	−	16.1227i	−1.32876	−	0.264306i	−0.807891	+	0.589332i	$0.799391\pi$
$62$	2.22002	−	1.48337i	0.0358068	−	0.0239254i
$63$	54.9608	−	10.9324i	0.872393	−	0.173530i
$64$	32.2713	−	32.2713i	0.504239	−	0.504239i
$65$	−30.2741	−	20.2285i	−0.465756	−	0.311208i
$66$	−4.79518	−	1.98623i	−0.0726543	−	0.0300944i
$67$			44.5324i			0.664663i	0.943163	+	0.332332i	$0.107835\pi$
$67$			44.5324i			0.664663i	−0.943163	+	0.332332i	$0.892165\pi$
$68$	−13.1179	+	5.43359i	−0.192910	+	0.0799058i
$69$	2.11674			0.0306774
$70$	28.1917	−	68.0607i	0.402738	−	0.972296i
$71$	32.1978	−	48.1875i	0.453491	−	0.678697i	−0.532323	−	0.846541i	$-0.678681\pi$
$71$	32.1978	−	48.1875i	0.453491	−	0.678697i	0.985813	+	0.167845i	$0.0536807\pi$
$72$	−44.1588	−	44.1588i	−0.613317	−	0.613317i
$73$	−0.262865	−	1.32151i	−0.00360089	−	0.0181029i	0.978943	−	0.204133i	$-0.0654377\pi$
$73$	−0.262865	−	1.32151i	−0.00360089	−	0.0181029i	−0.982544	+	0.186031i	$0.940438\pi$
$74$	−56.7843	−	84.9838i	−0.767356	−	1.14843i
$75$	−0.119306	+	0.599792i	−0.00159075	+	0.00799723i
$76$	19.2802	−	7.98612i	0.253687	−	0.105081i
$77$	34.9004	+	84.2570i	0.453252	+	1.09425i
$78$	2.36550	+	0.470527i	0.0303269	+	0.00603240i
$79$	−24.7128	+	16.5125i	−0.312820	+	0.209020i	−0.702062	−	0.712116i	$-0.747737\pi$
$79$	−24.7128	+	16.5125i	−0.312820	+	0.209020i	0.389242	+	0.921136i	$0.372737\pi$
$80$	−98.1004	+	19.5134i	−1.22626	+	0.243917i
$81$	−56.7774	+	56.7774i	−0.700956	+	0.700956i
$82$	57.5026	+	38.4220i	0.701252	+	0.468561i
$83$	−62.2748	−	25.7951i	−0.750298	−	0.310784i	−0.0254351	−	0.999676i	$-0.508097\pi$
$83$	−62.2748	−	25.7951i	−0.750298	−	0.310784i	−0.724863	+	0.688893i	$0.758097\pi$
$84$			0.842922i			0.0100348i
$85$	−89.4535	−	17.7934i	−1.05239	−	0.209334i
$86$	160.285			1.86377
$87$	2.04303	−	4.93230i	0.0234831	−	0.0566931i
$88$	56.4655	−	84.5065i	0.641653	−	0.960302i
$89$	90.1397	+	90.1397i	1.01281	+	1.01281i	0.999917	+	0.0128890i	$0.00410281\pi$
$89$	90.1397	+	90.1397i	1.01281	+	1.01281i	0.0128890	+	0.999917i	$0.495897\pi$
$90$	20.6537	+	103.833i	0.229486	+	1.15370i
$91$	−23.5444	−	35.2368i	−0.258730	−	0.387217i
$92$	2.13408	−	10.7288i	0.0231966	−	0.116617i
$93$	−0.181304	+	0.0750988i	−0.00194951	+	0.000807514i
$94$	−12.4814	−	30.1327i	−0.132781	−	0.320561i
$95$	131.476	+	26.1522i	1.38396	+	0.275286i
$96$	1.76826	−	1.18151i	0.0184194	−	0.0123074i
$97$	−66.3366	+	13.1952i	−0.683882	+	0.136033i	−0.524791	−	0.851231i	$-0.675856\pi$
$97$	−66.3366	+	13.1952i	−0.683882	+	0.136033i	−0.159091	+	0.987264i	$0.550856\pi$
$98$	−15.5581	+	15.5581i	−0.158756	+	0.158756i
$99$	−108.973	−	72.8134i	−1.10074	−	0.735489i
$100$	2.91979	+	1.20941i	0.0291979	+	0.0120941i
$101$			34.6405i			0.342975i	0.985186	+	0.171488i	$0.0548573\pi$
$101$			34.6405i			0.342975i	−0.985186	+	0.171488i	$0.945143\pi$
$102$	5.92544	−	1.17864i	0.0580926	−	0.0115553i
$103$	151.166			1.46763			0.733817	−	0.679347i	$-0.237737\pi$
$103$	151.166			1.46763			0.733817	+	0.679347i	$0.237737\pi$
$104$	−18.0735	+	43.6333i	−0.173784	+	0.419551i
$105$	−3.00817	+	4.50204i	−0.0286492	+	0.0428766i
$106$	−8.03830	−	8.03830i	−0.0758330	−	0.0758330i
$107$	−1.86075	−	9.35463i	−0.0173902	−	0.0874264i	0.971116	−	0.238610i	$-0.0766917\pi$
$107$	−1.86075	−	9.35463i	−0.0173902	−	0.0874264i	−0.988506	+	0.151183i	$0.951692\pi$
$108$	−1.34794	−	2.01733i	−0.0124809	−	0.0186790i
$109$	22.6951	−	114.096i	0.208212	−	1.04675i	−0.725362	−	0.688368i	$-0.758327\pi$
$109$	22.6951	−	114.096i	0.208212	−	1.04675i	0.933574	−	0.358385i	$-0.116673\pi$
$110$	−159.180	+	65.9347i	−1.44710	+	0.599406i
$111$	2.87483	+	6.94044i	0.0258993	+	0.0625265i
$112$	−114.181	−	22.7121i	−1.01948	−	0.202786i
$113$	−54.8360	+	36.6403i	−0.485274	+	0.324250i	−0.774026	−	0.633154i	$-0.781760\pi$
$113$	−54.8360	+	36.6403i	−0.485274	+	0.324250i	0.288751	+	0.957404i	$0.406760\pi$
$114$	−8.70902	+	1.73233i	−0.0763949	+	0.0151959i
$115$	49.6863	−	49.6863i	0.432055	−	0.432055i
$116$	−22.9398	−	15.3279i	−0.197757	−	0.132137i
$117$	56.2660	+	23.3062i	0.480906	+	0.199198i
$118$			62.1233i			0.526468i
$119$	−88.2661	−	58.9775i	−0.741732	−	0.495609i
$120$	6.03416			0.0502847
$121$	35.3203	−	85.2709i	0.291904	−	0.704718i
$122$	100.960	−	151.097i	0.827539	−	1.23850i
$123$	−3.59425	−	3.59425i	−0.0292216	−	0.0292216i
$124$	0.197851	+	0.994662i	0.00159557	+	0.00802147i
$125$	−63.2382	−	94.6427i	−0.505906	−	0.757141i
$126$	−24.0393	+	120.854i	−0.190788	+	0.959158i
$127$	88.2580	−	36.5576i	0.694945	−	0.287855i	−0.00711395	−	0.999975i	$-0.502264\pi$
$127$	88.2580	−	36.5576i	0.694945	−	0.287855i	0.702059	+	0.712119i	$0.252264\pi$
$128$	58.5465	+	141.344i	0.457395	+	1.10425i
$129$	−11.5544	−	2.29832i	−0.0895691	−	0.0178164i
$130$	66.5702	−	44.4808i	0.512078	−	0.342160i
$131$	42.0736	−	8.36897i	0.321173	−	0.0638852i	−0.0318711	−	0.999492i	$-0.510147\pi$
$131$	42.0736	−	8.36897i	0.321173	−	0.0638852i	0.353044	+	0.935607i	$0.385147\pi$
$132$	1.39401	−	1.39401i	0.0105607	−	0.0105607i
$133$	129.731	+	86.6833i	0.975419	+	0.651754i
$134$	−90.4690	−	37.4735i	−0.675142	−	0.279653i
$135$		−	15.5850i		−	0.115444i
$136$			118.304i			0.869885i
$137$	−63.8232			−0.465863			−0.232931	−	0.972493i	$-0.574832\pi$
$137$	−63.8232			−0.465863			−0.232931	+	0.972493i	$0.574832\pi$
$138$	−1.78121	+	4.30022i	−0.0129073	+	0.0311610i
$139$	−145.186	+	217.286i	−1.04450	+	1.56321i	−0.238632	+	0.971110i	$0.576699\pi$
$139$	−145.186	+	217.286i	−1.04450	+	1.56321i	−0.805868	+	0.592095i	$0.798301\pi$
$140$	19.7860	+	19.7860i	0.141328	+	0.141328i
$141$	0.467671	+	2.35114i	0.00331682	+	0.0166748i
$142$	70.8002	+	105.960i	0.498593	+	0.746197i
$143$	−19.3365	+	97.2113i	−0.135220	+	0.679799i
$144$	154.567	−	64.0239i	1.07338	−	0.444610i
$145$	−67.8201	−	163.732i	−0.467725	−	1.12919i
$146$	2.90589	+	0.578017i	0.0199033	+	0.00395902i
$147$	1.34462	−	0.898445i	0.00914706	−	0.00611187i
$148$	38.0763	−	7.57384i	0.257272	−	0.0511746i
$149$	−83.6010	+	83.6010i	−0.561080	+	0.561080i	−0.929614	−	0.368534i	$-0.879860\pi$
$149$	−83.6010	+	83.6010i	−0.561080	+	0.561080i	0.368534	+	0.929614i	$0.379860\pi$
$150$	−1.11810	−	0.747092i	−0.00745401	−	0.00498061i
$151$	25.5851	+	10.5977i	0.169437	+	0.0701833i	0.465790	−	0.884895i	$-0.345770\pi$
$151$	25.5851	+	10.5977i	0.169437	+	0.0701833i	−0.296352	+	0.955079i	$0.595770\pi$
$152$		−	173.880i		−	1.14395i
$153$	152.556			0.997098
$154$	−200.539			−1.30220
$155$	−2.49297	+	6.01857i	−0.0160837	+	0.0388295i
$156$	−0.508954	+	0.761703i	−0.00326252	+	0.00488271i
$157$	−55.8958	−	55.8958i	−0.356024	−	0.356024i	0.506321	−	0.862345i	$-0.331005\pi$
$157$	−55.8958	−	55.8958i	−0.356024	−	0.356024i	−0.862345	+	0.506321i	$0.831005\pi$
$158$	−12.7503	−	64.0998i	−0.0806978	−	0.405695i
$159$	0.464195	+	0.694716i	0.00291946	+	0.00436929i
$160$	13.7727	−	69.2402i	0.0860796	−	0.432751i
$161$	75.5599	−	31.2979i	0.469316	−	0.194397i
$162$	−67.5676	−	163.123i	−0.417084	−	1.00693i
$163$	−54.4489	−	10.8306i	−0.334042	−	0.0664451i	0.0252196	−	0.999682i	$-0.491971\pi$
$163$	−54.4489	−	10.8306i	−0.334042	−	0.0664451i	−0.359262	+	0.933237i	$0.616971\pi$
$164$	−21.8413	+	14.5939i	−0.133179	+	0.0889871i
$165$	12.4203	−	2.47054i	0.0752743	−	0.0149730i
$166$	104.807	−	104.807i	0.631367	−	0.631367i
$167$	−42.9537	−	28.7008i	−0.257208	−	0.171861i	0.420281	−	0.907394i	$-0.361932\pi$
$167$	−42.9537	−	28.7008i	−0.257208	−	0.171861i	−0.677489	+	0.735533i	$0.736932\pi$
$168$	6.48868	+	2.68770i	0.0386231	+	0.0159982i
$169$			122.942i			0.727470i
$170$	111.422	−	166.755i	0.655423	−	0.980910i
$171$	−224.222			−1.31124
$172$	−23.2982	+	56.2468i	−0.135455	+	0.327016i
$173$	−10.2620	+	15.3581i	−0.0593178	+	0.0887754i	−0.859943	−	0.510390i	$-0.829501\pi$
$173$	−10.2620	+	15.3581i	−0.0593178	+	0.0887754i	0.800625	+	0.599166i	$0.204501\pi$
$174$	8.30094	+	8.30094i	0.0477066	+	0.0477066i
$175$	4.60969	+	23.1745i	0.0263411	+	0.132425i
$176$	151.270	+	226.392i	0.859489	+	1.28632i
$177$	0.890783	−	4.47827i	0.00503267	−	0.0253010i
$178$	−258.973	+	107.270i	−1.45490	+	0.602641i
$179$	23.9825	+	57.8989i	0.133980	+	0.323457i	0.976604	−	0.215046i	$-0.0689900\pi$
$179$	23.9825	+	57.8989i	0.133980	+	0.323457i	−0.842624	+	0.538503i	$0.818990\pi$
$180$	−39.4391	−	7.84493i	−0.219106	−	0.0435830i
$181$	86.9711	−	58.1122i	0.480503	−	0.321062i	−0.291621	−	0.956534i	$-0.594194\pi$
$181$	86.9711	−	58.1122i	0.480503	−	0.321062i	0.772124	+	0.635472i	$0.219194\pi$
$182$	91.3969	−	18.1800i	0.502181	−	0.0998899i
$183$	−9.44444	+	9.44444i	−0.0516090	+	0.0516090i
$184$	−75.7837	−	50.6370i	−0.411868	−	0.275201i
$185$	230.394	+	95.4324i	1.24537	+	0.515851i
$186$		−	0.431520i		−	0.00232000i
$187$	48.4369	+	243.509i	0.259021	+	1.30219i
$188$	12.3883			0.0658954
$189$	6.94177	−	16.7589i	0.0367289	−	0.0886715i
$190$	−163.764	+	245.091i	−0.861917	+	1.28995i
$191$	−137.930	−	137.930i	−0.722145	−	0.722145i	0.246897	−	0.969042i	$-0.420589\pi$
$191$	−137.930	−	137.930i	−0.722145	−	0.722145i	−0.969042	+	0.246897i	$0.920589\pi$
$192$	−1.43899	−	7.23428i	−0.00749473	−	0.0376785i
$193$	49.1142	+	73.5045i	0.254478	+	0.380853i	0.936609	−	0.350377i	$-0.113947\pi$
$193$	49.1142	+	73.5045i	0.254478	+	0.380853i	−0.682131	+	0.731230i	$0.738947\pi$
$194$	29.0150	−	145.868i	0.149562	−	0.751899i
$195$	−5.43664	+	2.25193i	−0.0278802	+	0.0115484i
$196$	−3.19816	−	7.72105i	−0.0163172	−	0.0393931i
$197$	252.430	+	50.2114i	1.28137	+	0.254880i	0.788398	−	0.615165i	$-0.210911\pi$
$197$	252.430	+	50.2114i	1.28137	+	0.254880i	0.492972	+	0.870045i	$0.335911\pi$
$198$	239.622	−	160.110i	1.21021	−	0.808637i
$199$	223.079	−	44.3732i	1.12100	−	0.222981i	0.400406	−	0.916338i	$-0.368869\pi$
$199$	223.079	−	44.3732i	1.12100	−	0.222981i	0.720594	+	0.693357i	$0.243869\pi$
$200$	18.6198	−	18.6198i	0.0930988	−	0.0930988i
$201$	5.98429	+	3.99858i	0.0297726	+	0.0198934i
$202$	−70.3732	−	29.1495i	−0.348382	−	0.144305i
$203$		−	206.273i		−	1.01612i
$204$	−0.447686	+	2.25067i	−0.00219454	+	0.0110327i
$205$	−168.736			−0.823103
$206$	−127.204	+	307.099i	−0.617498	+	1.49077i
$207$	−65.2975	+	97.7246i	−0.315447	+	0.472100i
$208$	−89.4660	−	89.4660i	−0.430125	−	0.430125i
$209$	−71.1910	−	357.901i	−0.340627	−	1.71245i
$210$	−6.61470	−	9.89960i	−0.0314986	−	0.0471410i
$211$	1.57784	−	7.93236i	0.00747794	−	0.0375941i	−0.976866	−	0.213852i	$-0.931399\pi$
$211$	1.57784	−	7.93236i	0.00747794	−	0.0375941i	0.984344	+	0.176257i	$0.0563991\pi$
$212$	3.98919	−	1.65238i	0.0188169	−	0.00779423i
$213$	−3.58441	−	8.65353i	−0.0168282	−	0.0406269i
$214$	20.5700	+	4.09163i	0.0961215	+	0.0191198i
$215$	−325.166	+	217.269i	−1.51240	+	1.01055i
$216$	−19.8270	+	3.94384i	−0.0917918	+	0.0182585i
$217$	−5.36151	+	5.36151i	−0.0247074	+	0.0247074i
$218$	212.692	+	142.116i	0.975651	+	0.651909i
$219$	−0.201188	−	0.0833348i	−0.000918667	−	0.000380524i
$220$		−	65.4433i		−	0.297469i
$221$	−44.1509	−	106.590i	−0.199778	−	0.482306i
$222$	−16.5188			−0.0744092
$223$	18.7769	−	45.3315i	0.0842014	−	0.203280i	−0.876171	−	0.482001i	$-0.839910\pi$
$223$	18.7769	−	45.3315i	0.0842014	−	0.203280i	0.960372	+	0.278720i	$0.0899103\pi$
$224$	45.6507	−	68.3211i	0.203798	−	0.305005i
$225$	−24.0106	−	24.0106i	−0.106714	−	0.106714i
$226$	−28.2920	−	142.233i	−0.125186	−	0.629351i
$227$	−93.3694	−	139.737i	−0.411319	−	0.615582i	0.566743	−	0.823894i	$-0.308203\pi$
$227$	−93.3694	−	139.737i	−0.411319	−	0.615582i	−0.978062	+	0.208312i	$0.933203\pi$
$228$	0.657994	−	3.30796i	0.00288594	−	0.0145086i
$229$	114.723	−	47.5197i	0.500972	−	0.207510i	−0.117864	−	0.993030i	$-0.537605\pi$
$229$	114.723	−	47.5197i	0.500972	−	0.207510i	0.618836	+	0.785520i	$0.287605\pi$
$230$	59.1289	+	142.750i	0.257082	+	0.620651i
$231$	14.4562	+	2.87552i	0.0625810	+	0.0124481i
$232$	−191.136	+	127.713i	−0.823863	+	0.550487i
$233$	−346.291	+	68.8815i	−1.48623	+	0.295629i	−0.870436	−	0.492281i	$-0.836163\pi$
$233$	−346.291	+	68.8815i	−1.48623	+	0.295629i	−0.615791	+	0.787910i	$0.711163\pi$
$234$	−94.6943	+	94.6943i	−0.404677	+	0.404677i
$235$	66.1661	+	44.2108i	0.281558	+	0.188131i
$236$	−21.8002	−	9.02993i	−0.0923737	−	0.0382624i
$237$			4.80358i			0.0202683i
$238$	194.089	−	129.686i	0.815502	−	0.544901i
$239$	206.527			0.864131			0.432066	−	0.901842i	$-0.357785\pi$
$239$	206.527			0.864131			0.432066	+	0.901842i	$0.357785\pi$
$240$	−6.18624	+	14.9349i	−0.0257760	+	0.0622287i
$241$	160.021	−	239.488i	0.663988	−	0.993728i	−0.334691	−	0.942328i	$-0.608632\pi$
$241$	160.021	−	239.488i	0.663988	−	0.993728i	0.998678	−	0.0513996i	$-0.0163682\pi$
$242$	143.509	+	143.509i	0.593011	+	0.593011i
$243$	7.63219	+	38.3696i	0.0314082	+	0.157900i
$244$	38.3477	+	57.3913i	0.157163	+	0.235210i
$245$	10.4730	−	52.6515i	0.0427471	−	0.214904i
$246$	10.3263	−	4.27731i	0.0419770	−	0.0173875i
$247$	64.8915	+	156.662i	0.262719	+	0.634259i
$248$	8.28761	+	1.64851i	0.0334178	+	0.00664721i
$249$	−9.05802	+	6.05237i	−0.0363776	+	0.0243067i
$250$	245.484	−	48.8297i	0.981935	−	0.195319i
$251$	191.096	−	191.096i	0.761337	−	0.761337i	−0.215227	−	0.976564i	$-0.569049\pi$
$251$	191.096	−	191.096i	0.761337	−	0.761337i	0.976564	+	0.215227i	$0.0690490\pi$
$252$	−38.9156	−	26.0026i	−0.154427	−	0.103185i
$253$	−176.720	−	73.1996i	−0.698496	−	0.289327i
$254$			210.062i			0.827014i
$255$	−10.4231	+	10.4231i	−0.0408751	+	0.0408751i
$256$	−153.856			−0.601002
$257$	−20.2061	+	48.7819i	−0.0786230	+	0.189813i	−0.958303	−	0.285753i	$-0.907756\pi$
$257$	−20.2061	+	48.7819i	−0.0786230	+	0.189813i	0.879680	+	0.475565i	$0.157756\pi$
$258$	14.3920	−	21.5391i	0.0557829	−	0.0834850i
$259$	205.242	+	205.242i	0.792439	+	0.792439i
$260$	5.93280	+	29.8262i	0.0228185	+	0.114716i
$261$	164.689	+	246.474i	0.630991	+	0.944345i
$262$	−18.4026	+	92.5162i	−0.0702390	+	0.353115i
$263$	−468.907	+	194.228i	−1.78292	+	0.738509i	−0.790970	+	0.611854i	$0.790424\pi$
$263$	−468.907	+	194.228i	−1.78292	+	0.738509i	−0.991947	+	0.126654i	$0.959576\pi$
$264$	−6.28599	−	15.1757i	−0.0238106	−	0.0574838i
$265$	27.2032	+	5.41105i	0.102654	+	0.0204191i
$266$	−285.266	+	190.609i	−1.07243	+	0.716575i
$267$	20.2067	−	4.01936i	0.0756805	−	0.0150538i
$268$	26.3003	−	26.3003i	0.0981353	−	0.0981353i
$269$	146.551	+	97.9225i	0.544801	+	0.364024i	0.797310	−	0.603570i	$-0.206256\pi$
$269$	146.551	+	97.9225i	0.544801	+	0.364024i	−0.252509	+	0.967595i	$0.581256\pi$
$270$	31.6614	+	13.1146i	0.117264	+	0.0485725i
$271$		−	464.255i		−	1.71312i	−0.516050	−	0.856559i	$-0.672598\pi$
$271$		−	464.255i		−	1.71312i	0.516050	−	0.856559i	$-0.327402\pi$
$272$	−292.810	−	121.286i	−1.07651	−	0.445905i
$273$	−6.84919			−0.0250886
$274$	53.7064	−	129.659i	0.196009	−	0.473207i
$275$	30.7021	−	45.9489i	0.111644	−	0.167087i
$276$	−1.25012	−	1.25012i	−0.00452941	−	0.00452941i
$277$	34.4498	+	173.191i	0.124368	+	0.625238i	0.991812	+	0.127704i	$0.0407609\pi$
$277$	34.4498	+	173.191i	0.124368	+	0.625238i	−0.867445	+	0.497534i	$0.834239\pi$
$278$	−319.250	−	477.792i	−1.14838	−	1.71868i
$279$	2.12578	−	10.6870i	0.00761930	−	0.0383048i
$280$	215.398	−	89.2206i	0.769277	−	0.318645i
$281$	152.875	+	369.073i	0.544040	+	1.31343i	0.921851	+	0.387545i	$0.126677\pi$
$281$	152.875	+	369.073i	0.544040	+	1.31343i	−0.377811	+	0.925883i	$0.623323\pi$
$282$	−5.16995	−	1.02837i	−0.0183332	−	0.00364669i
$283$	297.348	−	198.682i	1.05070	−	0.702055i	0.0947249	−	0.995503i	$-0.469803\pi$
$283$	297.348	−	198.682i	1.05070	−	0.702055i	0.955975	+	0.293448i	$0.0948029\pi$
$284$	−47.4745	+	9.44326i	−0.167164	+	0.0332509i
$285$	15.3196	−	15.3196i	0.0537530	−	0.0537530i
$286$	−181.216	−	121.085i	−0.633623	−	0.423373i
$287$	−181.446	−	75.1574i	−0.632216	−	0.261872i
$288$			118.084i			0.410013i
$289$	−204.354	−	204.354i	−0.707107	−	0.707107i
$290$	389.697			1.34378
$291$	−4.18320	+	10.0991i	−0.0143753	+	0.0347050i
$292$	−0.625222	+	0.935711i	−0.00214117	+	0.00320449i
$293$	−169.002	−	169.002i	−0.576800	−	0.576800i	0.357220	−	0.934020i	$-0.383725\pi$
$293$	−169.002	−	169.002i	−0.576800	−	0.576800i	−0.934020	+	0.357220i	$0.883725\pi$
$294$	0.693739	+	3.48766i	0.00235966	+	0.0118628i
$295$	−84.2093	−	126.028i	−0.285455	−	0.427214i
$296$	63.1058	−	317.254i	0.213195	−	1.07181i
$297$	−39.1958	+	16.2354i	−0.131972	+	0.0546647i
$298$	−99.4888	−	240.187i	−0.333855	−	0.805997i
$299$	87.1770	+	17.3406i	0.291562	+	0.0579953i
$300$	0.424690	−	0.283769i	0.00141563	−	0.000945896i
$301$	−446.433	+	88.8011i	−1.48317	+	0.295020i
$302$	−43.0590	+	43.0590i	−0.142579	+	0.142579i
$303$	4.65501	+	3.11038i	0.0153631	+	0.0102653i
$304$	430.363	+	178.262i	1.41567	+	0.586389i
$305$			443.380i			1.45370i
$306$	−128.374	+	309.922i	−0.419523	+	1.01282i
$307$	409.955			1.33536			0.667679	−	0.744450i	$-0.267288\pi$
$307$	409.955			1.33536			0.667679	+	0.744450i	$0.267288\pi$
$308$	29.1493	−	70.3727i	0.0946407	−	0.228483i
$309$	13.5733	−	20.3138i	0.0439264	−	0.0657405i
$310$	−10.1291	−	10.1291i	−0.0326745	−	0.0326745i
$311$	42.2576	+	212.443i	0.135877	+	0.683098i	0.987332	+	0.158670i	$0.0507207\pi$
$311$	42.2576	+	212.443i	0.135877	+	0.683098i	−0.851455	+	0.524428i	$0.824279\pi$
$312$	4.24064	+	6.34657i	0.0135918	+	0.0203416i
$313$	−92.3584	+	464.317i	−0.295075	+	1.48344i	0.494171	+	0.869365i	$0.335472\pi$
$313$	−92.3584	+	464.317i	−0.295075	+	1.48344i	−0.789246	+	0.614077i	$0.789528\pi$
$314$	160.590	−	66.5184i	0.511432	−	0.211842i
$315$	−115.052	−	277.759i	−0.365244	−	0.881776i
$316$	24.3471	+	4.84294i	0.0770479	+	0.0153258i
$317$	213.145	−	142.419i	0.672383	−	0.449272i	−0.171939	−	0.985108i	$-0.555003\pi$
$317$	213.145	−	142.419i	0.672383	−	0.449272i	0.844322	+	0.535836i	$0.180003\pi$
$318$	−1.80195	+	0.358430i	−0.00566651	+	0.00112714i
$319$	−341.131	+	341.131i	−1.06938	+	1.06938i
$320$	−203.588	−	136.033i	−0.636213	−	0.425104i
$321$	−1.42416	−	0.589905i	−0.00443663	−	0.00183771i
$322$			179.839i			0.558506i
$323$	300.353	+	300.353i	0.929884	+	0.929884i
$324$	67.0640			0.206988
$325$	−9.82715	+	23.7248i	−0.0302374	+	0.0729995i
$326$	67.8206	−	101.501i	0.208039	−	0.311352i
$327$	−13.2945	−	13.2945i	−0.0406560	−	0.0406560i
$328$	42.6993	+	214.664i	0.130181	+	0.654464i
$329$	51.4579	+	77.0122i	0.156407	+	0.234080i
$330$	−5.43251	+	27.3111i	−0.0164621	+	0.0827608i
$331$	208.580	−	86.3966i	0.630151	−	0.261017i	−0.0446663	−	0.999002i	$-0.514222\pi$
$331$	208.580	−	86.3966i	0.630151	−	0.261017i	0.674817	+	0.737985i	$0.264222\pi$
$332$	21.5444	+	52.0129i	0.0648929	+	0.156665i
$333$	−409.106	−	81.3763i	−1.22855	−	0.244373i
$334$	94.4515	−	63.1105i	0.282789	−	0.188954i
$335$	234.328	−	46.6108i	0.699488	−	0.139137i
$336$	−13.3044	+	13.3044i	−0.0395965	+	0.0395965i
$337$	−300.276	−	200.638i	−0.891027	−	0.595365i	0.0235742	−	0.999722i	$-0.492495\pi$
$337$	−300.276	−	200.638i	−0.891027	−	0.595365i	−0.914601	+	0.404357i	$0.867495\pi$
$338$	−249.761	−	103.454i	−0.738938	−	0.306078i
$339$			10.6588i			0.0314420i
$340$	42.3215	+	63.3386i	0.124475	+	0.186290i
$341$	17.7335			0.0520045
$342$	188.680	−	455.513i	0.551695	−	1.33191i
$343$	204.708	−	306.367i	0.596815	−	0.893197i
$344$	358.691	+	358.691i	1.04271	+	1.04271i
$345$	−2.21553	−	11.1382i	−0.00642183	−	0.0322847i
$346$	−22.5652	−	33.7712i	−0.0652173	−	0.0976046i
$347$	3.09377	−	15.5534i	0.00891575	−	0.0448225i	−0.976071	−	0.217451i	$-0.930226\pi$
$347$	3.09377	−	15.5534i	0.00891575	−	0.0448225i	0.984987	+	0.172628i	$0.0552259\pi$
$348$	−4.11954	+	1.70637i	−0.0118377	+	0.00490336i
$349$	−121.062	−	292.270i	−0.346883	−	0.837448i	−0.996984	−	0.0776015i	$-0.975274\pi$
$349$	−121.062	−	292.270i	−0.346883	−	0.837448i	0.650102	−	0.759847i	$-0.274726\pi$
$350$	−50.9586	−	10.1363i	−0.145596	−	0.0289608i
$351$	16.3919	−	10.9527i	0.0467005	−	0.0312043i
$352$	−188.484	+	37.4919i	−0.535467	+	0.106511i
$353$	191.613	−	191.613i	0.542812	−	0.542812i	−0.381540	−	0.924352i	$-0.624606\pi$
$353$	191.613	−	191.613i	0.542812	−	0.542812i	0.924352	+	0.381540i	$0.124606\pi$
$354$	8.34816	+	5.57806i	0.0235824	+	0.0157572i
$355$	−287.262	−	118.988i	−0.809188	−	0.335177i
$356$		−	106.471i		−	0.299075i
$357$	−15.8509	+	6.56564i	−0.0444002	+	0.0183912i
$358$	−137.804			−0.384928
$359$	60.5865	−	146.269i	0.168765	−	0.407434i	−0.816757	−	0.576981i	$-0.804231\pi$
$359$	60.5865	−	146.269i	0.168765	−	0.407434i	0.985522	+	0.169547i	$0.0542305\pi$
$360$	−186.143	+	278.582i	−0.517063	+	0.773839i
$361$	−186.183	−	186.183i	−0.515743	−	0.515743i
$362$	44.8717	+	225.585i	0.123955	+	0.623163i
$363$	−8.28732	−	12.4029i	−0.0228301	−	0.0341676i
$364$	−6.90532	+	34.7154i	−0.0189707	+	0.0953719i
$365$	−6.67862	+	2.76638i	−0.0182976	+	0.00757911i
$366$	−11.2393	−	27.1340i	−0.0307084	−	0.0741367i
$367$	−479.595	−	95.3974i	−1.30680	−	0.259938i	−0.507906	−	0.861413i	$-0.669580\pi$
$367$	−479.595	−	95.3974i	−1.30680	−	0.259938i	−0.798892	+	0.601474i	$0.794580\pi$
$368$	203.023	−	135.656i	0.551694	−	0.368630i
$369$	276.814	−	55.0617i	0.750173	−	0.149219i
$370$	−387.748	+	387.748i	−1.04797	+	1.04797i
$371$	26.8421	+	17.9353i	0.0723506	+	0.0483431i
$372$	0.151428	+	0.0627237i	0.000407065	+	0.000168612i
$373$			573.453i			1.53741i	0.639605	+	0.768704i	$0.279098\pi$
$373$			573.453i			1.53741i	−0.639605	+	0.768704i	$0.720902\pi$
$374$	−535.455	−	106.509i	−1.43170	−	0.284782i
$375$	−18.3963			−0.0490568
$376$	39.5008	−	95.3635i	0.105055	−	0.253626i
$377$	124.547	−	186.398i	0.330364	−	0.494425i
$378$	28.2048	+	28.2048i	0.0746159	+	0.0746159i
$379$	136.954	+	688.516i	0.361357	+	1.81666i	0.550641	+	0.834742i	$0.314383\pi$
$379$	136.954	+	688.516i	0.361357	+	1.81666i	−0.189284	+	0.981922i	$0.560617\pi$
$380$	−62.2028	−	93.0930i	−0.163692	−	0.244982i
$381$	3.01206	−	15.1427i	0.00790568	−	0.0397445i
$382$	396.274	−	164.142i	1.03737	−	0.429692i
$383$	−118.024	−	284.935i	−0.308157	−	0.743956i	−0.999765	−	0.0216830i	$-0.993098\pi$
$383$	−118.024	−	284.935i	−0.308157	−	0.743956i	0.691608	−	0.722273i	$-0.256902\pi$
$384$	24.2508	+	4.82378i	0.0631530	+	0.0125619i
$385$	406.829	−	271.834i	1.05670	−	0.706063i
$386$	−190.656	+	37.9238i	−0.493927	+	0.0982481i
$387$	462.540	−	462.540i	1.19519	−	1.19519i
$388$	46.9704	+	31.3846i	0.121058	+	0.0808882i
$389$	263.382	+	109.097i	0.677076	+	0.280454i	0.694604	−	0.719392i	$-0.255580\pi$
$389$	263.382	+	109.097i	0.677076	+	0.280454i	−0.0175282	+	0.999846i	$0.505580\pi$
$390$		−	12.9397i		−	0.0331787i
$391$	218.374	−	43.4372i	0.558500	−	0.111093i
$392$	−69.6329			−0.177635
$393$	2.65317	−	6.40533i	0.00675108	−	0.0162986i
$394$	−314.423	+	470.567i	−0.798027	+	1.19433i
$395$	112.755	+	112.755i	0.285455	+	0.285455i
$396$	21.3553	+	107.361i	0.0539276	+	0.271112i
$397$	69.0841	+	103.392i	0.174015	+	0.260432i	0.908217	−	0.418499i	$-0.137444\pi$
$397$	69.0841	+	103.392i	0.174015	+	0.260432i	−0.734202	+	0.678931i	$0.762444\pi$
$398$	−97.5727	+	490.531i	−0.245158	+	1.23249i
$399$	23.2971	−	9.64997i	0.0583887	−	0.0241854i
$400$	26.9960	+	65.1740i	0.0674899	+	0.162935i
$401$	−418.770	−	83.2986i	−1.04432	−	0.207727i	−0.357014	−	0.934099i	$-0.616205\pi$
$401$	−418.770	−	83.2986i	−1.04432	−	0.207727i	−0.687302	+	0.726372i	$0.741205\pi$
$402$	−13.1589	+	8.79252i	−0.0327337	+	0.0218719i
$403$	−8.08217	+	1.60764i	−0.0200550	+	0.00398919i
$404$	20.4582	−	20.4582i	0.0506391	−	0.0506391i
$405$	358.189	+	239.334i	0.884417	+	0.590948i
$406$	419.050	+	173.576i	1.03214	+	0.427528i
$407$		−	678.850i		−	1.66794i
$408$	15.8978	+	10.6226i	0.0389652	+	0.0260357i
$409$	−215.550			−0.527018			−0.263509	−	0.964657i	$-0.584880\pi$
$409$	−215.550			−0.527018			−0.263509	+	0.964657i	$0.584880\pi$
$410$	141.989	−	342.793i	0.346315	−	0.836079i
$411$	−5.73070	+	8.57659i	−0.0139433	+	0.0208676i
$412$	−89.2768	−	89.2768i	−0.216691	−	0.216691i
$413$	−34.4176	−	173.029i	−0.0833356	−	0.418956i
$414$	−143.583	−	214.888i	−0.346820	−	0.519053i
$415$	−70.5517	+	354.687i	−0.170004	+	0.854668i
$416$	82.5042	−	34.1743i	0.198327	−	0.0821499i
$417$	16.1627	+	39.0202i	0.0387595	+	0.0935737i
$418$	786.994	+	156.543i	1.88276	+	0.374504i
$419$	−517.326	+	345.666i	−1.23467	+	0.824979i	−0.989504	−	0.144503i	$-0.953842\pi$
$419$	−517.326	+	345.666i	−1.23467	+	0.824979i	−0.245164	+	0.969482i	$0.578842\pi$
$420$	4.43543	−	0.882262i	0.0105606	−	0.00210062i
$421$	−36.3708	+	36.3708i	−0.0863916	+	0.0863916i	−0.748982	−	0.662590i	$-0.769457\pi$
$421$	−36.3708	+	36.3708i	−0.0863916	+	0.0863916i	0.662590	+	0.748982i	$0.269457\pi$
$422$	14.7871	+	9.88042i	0.0350405	+	0.0234133i
$423$	−122.973	−	50.9371i	−0.290717	−	0.120419i
$424$		−	35.9769i		−	0.0848511i
$425$			64.3259i			0.151355i
$426$	20.5961			0.0483477
$427$	−197.488	+	476.777i	−0.462500	+	1.11657i
$428$	−4.42578	+	6.62365i	−0.0103406	+	0.0154758i
$429$	11.3271	+	11.3271i	0.0264034	+	0.0264034i
$430$	−167.765	−	843.413i	−0.390152	−	1.96143i
$431$	261.460	+	391.302i	0.606635	+	0.907893i	0.999934	−	0.0115175i	$-0.00366621\pi$
$431$	261.460	+	391.302i	0.606635	+	0.907893i	−0.393299	+	0.919411i	$0.628666\pi$
$432$	10.5655	−	53.1163i	0.0244572	−	0.122954i
$433$	−594.595	+	246.289i	−1.37320	+	0.568798i	−0.942654	−	0.333772i	$-0.891679\pi$
$433$	−594.595	+	246.289i	−1.37320	+	0.568798i	−0.430545	+	0.902569i	$0.641679\pi$
$434$	−6.38042	−	15.4037i	−0.0147014	−	0.0354924i
$435$	−28.0920	−	5.58785i	−0.0645794	−	0.0128456i
$436$	−80.7871	+	53.9802i	−0.185291	+	0.123808i
$437$	−320.958	+	63.8426i	−0.734459	+	0.146093i
$438$	0.338594	−	0.338594i	0.000773047	−	0.000773047i
$439$	−688.000	−	459.707i	−1.56720	−	1.04717i	−0.969389	−	0.245530i	$-0.921038\pi$
$439$	−688.000	−	459.707i	−1.56720	−	1.04717i	−0.597809	−	0.801638i	$-0.703962\pi$
$440$	−503.772	−	208.669i	−1.14494	−	0.474248i
$441$			89.7930i			0.203612i
$442$	253.693			0.573965
$443$	354.430			0.800068			0.400034	−	0.916500i	$-0.368998\pi$
$443$	354.430			0.800068			0.400034	+	0.916500i	$0.368998\pi$
$444$	2.40110	−	5.79677i	0.00540788	−	0.0130558i
$445$	379.966	−	568.659i	0.853856	−	1.27789i
$446$	76.2917	+	76.2917i	0.171058	+	0.171058i
$447$	3.72780	+	18.7409i	0.00833959	+	0.0419259i
$448$	−158.332	−	236.961i	−0.353420	−	0.528930i
$449$	153.330	−	770.842i	0.341492	−	1.71680i	−0.303692	−	0.952770i	$-0.598220\pi$
$449$	153.330	−	770.842i	0.341492	−	1.71680i	0.645185	−	0.764027i	$-0.276780\pi$
$450$	68.9828	−	28.5736i	0.153295	−	0.0634969i
$451$	175.778	+	424.366i	0.389752	+	0.940945i
$452$	54.0247	+	10.7462i	0.119524	+	0.0237747i
$453$	3.72141	−	2.48657i	0.00821503	−	0.00548911i
$454$	362.450	−	72.0957i	0.798347	−	0.158801i
$455$	−160.772	+	160.772i	−0.353344	+	0.353344i
$456$	−23.3661	−	15.6127i	−0.0512414	−	0.0342384i
$457$	300.390	+	124.426i	0.657309	+	0.272266i	0.686306	−	0.727313i	$-0.259231\pi$
$457$	300.390	+	124.426i	0.657309	+	0.272266i	−0.0289968	+	0.999580i	$0.509231\pi$
$458$			273.050i			0.596178i
$459$	27.4359	−	41.0608i	0.0597733	−	0.0894570i
$460$	−58.6882			−0.127583
$461$	−94.2242	+	227.477i	−0.204391	+	0.493444i	−0.992522	−	0.122064i	$-0.961049\pi$
$461$	−94.2242	+	227.477i	−0.204391	+	0.493444i	0.788131	+	0.615507i	$0.211049\pi$
$462$	−18.0064	+	26.9485i	−0.0389749	+	0.0583301i
$463$	−248.069	−	248.069i	−0.535786	−	0.535786i	0.386503	−	0.922288i	$-0.373683\pi$
$463$	−248.069	−	248.069i	−0.535786	−	0.535786i	−0.922288	+	0.386503i	$0.873683\pi$
$464$	−120.144	−	604.005i	−0.258931	−	1.30174i
$465$	0.584934	+	0.875415i	0.00125792	+	0.00188261i
$466$	151.464	−	761.463i	0.325031	−	1.63404i
$467$	−202.212	+	83.7591i	−0.433003	+	0.179356i	−0.588529	−	0.808476i	$-0.700293\pi$
$467$	−202.212	+	83.7591i	−0.433003	+	0.179356i	0.155526	+	0.987832i	$0.450293\pi$
$468$	−19.4657	−	46.9943i	−0.0415933	−	0.100415i
$469$	272.740	+	54.2514i	0.581536	+	0.115675i
$470$	−145.493	+	97.2156i	−0.309561	+	0.206842i
$471$	−12.5302	+	2.49241i	−0.0266034	+	0.00529174i
$472$	−139.022	+	139.022i	−0.294538	+	0.294538i
$473$	885.161	+	591.446i	1.87138	+	1.25041i
$474$	−9.75862	−	4.04215i	−0.0205878	−	0.00852775i
$475$		−	94.5441i		−	0.199040i
$476$	17.2974	+	86.9601i	0.0363392	+	0.182689i
$477$	−46.3929			−0.0972597
$478$	−173.790	+	419.566i	−0.363578	+	0.877754i
$479$	−279.157	+	417.789i	−0.582792	+	0.872210i	−0.999318	−	0.0369135i	$-0.988247\pi$
$479$	−279.157	+	417.789i	−0.582792	+	0.872210i	0.416526	+	0.909124i	$0.363247\pi$
$480$	−8.06788	−	8.06788i	−0.0168081	−	0.0168081i
$481$	61.5415	+	309.390i	0.127945	+	0.643223i
$482$	351.872	+	526.614i	0.730025	+	1.09256i
$483$	2.57871	−	12.9640i	0.00533893	−	0.0268406i
$484$	−71.2196	+	29.5001i	−0.147148	+	0.0609506i
$485$	138.865	+	335.250i	0.286320	+	0.691238i
$486$	−84.3715	−	16.7825i	−0.173604	−	0.0345319i
$487$	−209.352	+	139.885i	−0.429882	+	0.287238i	−0.751627	−	0.659589i	$-0.770731\pi$
$487$	−209.352	+	139.885i	−0.429882	+	0.287238i	0.321745	+	0.946826i	$0.395731\pi$
$488$	564.063	−	112.199i	1.15587	−	0.229916i
$489$	−6.34439	+	6.34439i	−0.0129742	+	0.0129742i
$490$	98.1502	+	65.5819i	0.200307	+	0.133841i
$491$	−209.123	−	86.6215i	−0.425912	−	0.176418i	0.159423	−	0.987210i	$-0.449037\pi$
$491$	−209.123	−	86.6215i	−0.425912	−	0.176418i	−0.585334	+	0.810792i	$0.699037\pi$
$492$			4.24543i			0.00862893i
$493$	109.554	−	550.766i	0.222219	−	1.11717i
$494$	−372.869			−0.754796
$495$	−269.083	+	649.624i	−0.543602	+	1.31237i
$496$	−12.5766	+	18.8223i	−0.0253561	+	0.0379481i
$497$	−255.901	−	255.901i	−0.514891	−	0.514891i
$498$	−4.67337	−	23.4946i	−0.00938428	−	0.0471780i
$499$	−119.919	−	179.471i	−0.240318	−	0.359662i	0.691631	−	0.722251i	$-0.256893\pi$
$499$	−119.919	−	179.471i	−0.240318	−	0.359662i	−0.931949	+	0.362590i	$0.881893\pi$
$500$	−18.5471	+	93.2423i	−0.0370941	+	0.186485i
$501$	−7.71365	+	3.19510i	−0.0153965	+	0.00637744i
$502$	227.412	+	549.021i	0.453012	+	1.09367i
$503$	865.523	+	172.163i	1.72072	+	0.342273i	0.954023	−	0.299735i	$-0.0968982\pi$
$503$	865.523	+	172.163i	1.72072	+	0.342273i	0.766698	+	0.642008i	$0.221898\pi$
$504$	−324.248	+	216.656i	−0.643349	+	0.429872i
$505$	182.277	−	36.2572i	0.360945	−	0.0717964i
$506$	297.414	−	297.414i	0.587776	−	0.587776i
$507$	16.5211	+	11.0390i	0.0325859	+	0.0217732i
$508$	−73.7144	−	30.5335i	−0.145107	−	0.0601053i
$509$		−	459.446i		−	0.902645i	−0.892361	−	0.451323i	$-0.850952\pi$
$509$		−	459.446i		−	0.902645i	0.892361	−	0.451323i	$-0.149048\pi$
$510$	−12.4040	−	29.9459i	−0.0243215	−	0.0587174i
$511$	−8.41386			−0.0164655
$512$	−104.718	+	252.811i	−0.204527	+	0.493772i
$513$	−40.3244	+	60.3498i	−0.0786052	+	0.117641i
$514$	−82.0986	−	82.0986i	−0.159725	−	0.159725i
$515$	−158.221	−	795.433i	−0.307226	−	1.54453i
$516$	5.46653	+	8.18124i	0.0105940	+	0.0158551i
$517$	42.2612	−	212.462i	0.0817432	−	0.410951i
$518$	−589.663	+	244.246i	−1.13835	+	0.471518i
$519$	1.14241	+	2.75802i	0.00220117	+	0.00531411i
$520$	248.514	+	49.4326i	0.477912	+	0.0950626i
$521$	84.0959	−	56.1911i	0.161412	−	0.107852i	−0.472241	−	0.881470i	$-0.656555\pi$
$521$	84.0959	−	56.1911i	0.161412	−	0.107852i	0.633653	+	0.773617i	$0.281555\pi$
$522$	−639.303	+	127.165i	−1.22472	+	0.243611i
$523$	395.099	−	395.099i	0.755448	−	0.755448i	−0.220042	−	0.975490i	$-0.570620\pi$
$523$	395.099	−	395.099i	0.755448	−	0.755448i	0.975490	+	0.220042i	$0.0706196\pi$
$524$	−29.7907	−	19.9055i	−0.0568525	−	0.0379876i
$525$	3.52810	+	1.46139i	0.00672019	+	0.00278360i
$526$		−	1116.04i		−	2.12175i
$527$	−17.1632	+	11.4681i	−0.0325678	+	0.0217611i
$528$	44.0052			0.0833432
$529$	136.796	−	330.254i	0.258593	−	0.624299i
$530$	−33.8838	+	50.7108i	−0.0639318	+	0.0956807i
$531$	179.272	+	179.272i	0.337611	+	0.337611i
$532$	−25.4232	−	127.811i	−0.0477880	−	0.240247i
$533$	−118.583	−	177.472i	−0.222483	−	0.332969i
$534$	−8.83822	+	44.4327i	−0.0165510	+	0.0832074i
$535$	−47.2762	+	19.5824i	−0.0883667	+	0.0366027i
$536$	−118.596	−	286.315i	−0.221260	−	0.534170i
$537$	9.93388	+	1.97597i	0.0184988	+	0.00367965i
$538$	−322.254	+	215.323i	−0.598985	+	0.400229i
$539$	−143.327	+	28.5095i	−0.265913	+	0.0528934i
$540$	−9.20429	+	9.20429i	−0.0170450	+	0.0170450i
$541$	−33.9436	−	22.6804i	−0.0627423	−	0.0419230i	0.523804	−	0.851839i	$-0.324513\pi$
$541$	−33.9436	−	22.6804i	−0.0627423	−	0.0419230i	−0.586546	+	0.809916i	$0.699513\pi$
$542$	943.148	+	390.665i	1.74012	+	0.720783i
$543$		−	16.9051i		−	0.0311328i
$544$	158.177	−	158.177i	0.290767	−	0.290767i
$545$	−624.125			−1.14518
$546$	5.76351	−	13.9143i	0.0105559	−	0.0254841i
$547$	−37.8284	+	56.6142i	−0.0691562	+	0.103500i	−0.864436	−	0.502743i	$-0.832324\pi$
$547$	−37.8284	+	56.6142i	−0.0691562	+	0.103500i	0.795280	+	0.606243i	$0.207324\pi$
$548$	37.6931	+	37.6931i	0.0687830	+	0.0687830i
$549$	−144.683	−	727.370i	−0.263539	−	1.32490i
$550$	67.5112	+	101.038i	0.122748	+	0.183705i
$551$	−161.019	+	809.498i	−0.292231	+	1.46914i
$552$	−13.6093	+	5.63714i	−0.0246545	+	0.0102122i
$553$	71.0254	+	171.470i	0.128436	+	0.310073i
$554$	−380.832	−	75.7521i	−0.687422	−	0.136737i
$555$	33.5114	−	22.3916i	0.0603809	−	0.0403453i
$556$	214.071	−	42.5813i	0.385019	−	0.0765850i
$557$	−208.814	+	208.814i	−0.374890	+	0.374890i	−0.869255	−	0.494365i	$-0.835401\pi$
$557$	−208.814	+	208.814i	−0.374890	+	0.374890i	0.494365	+	0.869255i	$0.335401\pi$
$558$	19.9222	+	13.3116i	0.0357029	+	0.0238559i
$559$	−457.036	−	189.310i	−0.817595	−	0.338659i
$560$			624.591i			1.11534i
$561$	37.0720	+	15.3557i	0.0660820	+	0.0273721i
$562$	−878.426			−1.56304
$563$	169.121	−	408.295i	0.300393	−	0.725212i	−0.699551	−	0.714583i	$-0.746616\pi$
$563$	169.121	−	408.295i	0.300393	−	0.725212i	0.999944	−	0.0106294i	$-0.00338352\pi$
$564$	1.11235	−	1.66475i	0.00197226	−	0.00295169i
$565$	250.195	+	250.195i	0.442824	+	0.442824i
$566$	153.413	+	771.260i	0.271048	+	1.36265i
$567$	278.566	+	416.904i	0.491298	+	0.735280i
$568$	−78.6820	+	395.561i	−0.138525	+	0.696411i
$569$	595.479	−	246.656i	1.04654	−	0.433490i	0.207882	−	0.978154i	$-0.433343\pi$
$569$	595.479	−	246.656i	1.04654	−	0.433490i	0.838654	+	0.544664i	$0.183343\pi$
$570$	18.2310	+	44.0135i	0.0319842	+	0.0772166i
$571$	−117.482	−	23.3687i	−0.205748	−	0.0409259i	0.0911400	−	0.995838i	$-0.470949\pi$
$571$	−117.482	−	23.3687i	−0.205748	−	0.0409259i	−0.296888	+	0.954912i	$0.595949\pi$
$572$	68.8316	−	45.9918i	0.120335	−	0.0804052i
$573$	−30.9198	+	6.15033i	−0.0539613	+	0.0107336i
$574$	305.369	−	305.369i	0.532002	−	0.532002i
$575$	−41.2060	−	27.5330i	−0.0716626	−	0.0478834i
$576$	378.379	+	156.730i	0.656908	+	0.272100i
$577$			177.008i			0.306773i	0.988166	+	0.153387i	$0.0490180\pi$
$577$			177.008i			0.306773i	−0.988166	+	0.153387i	$0.950982\pi$
$578$	587.112	−	243.190i	1.01577	−	0.420744i
$579$	14.2876			0.0246763
$580$	−56.6444	+	136.752i	−0.0976628	+	0.235779i
$581$	−233.848	+	349.979i	−0.402493	+	0.602373i
$582$	−16.9966	−	16.9966i	−0.0292038	−	0.0292038i
$583$	−14.7299	−	74.0520i	−0.0252656	−	0.127019i
$584$	5.20940	+	7.79642i	0.00892021	+	0.0133500i
$585$	63.7443	−	320.464i	0.108965	−	0.547802i
$586$	485.547	−	201.120i	0.828578	−	0.343208i
$587$	−239.200	−	577.480i	−0.407496	−	0.983781i	−0.985794	−	0.167956i	$-0.946283\pi$
$587$	−239.200	−	577.480i	−0.407496	−	0.983781i	0.578299	−	0.815825i	$-0.303717\pi$
$588$	−1.32472	−	0.263504i	−0.00225293	−	0.000448135i
$589$	25.2259	−	16.8554i	0.0428284	−	0.0286170i
$590$	326.891	−	65.0226i	0.554052	−	0.110208i
$591$	29.4132	−	29.4132i	0.0497685	−	0.0497685i
$592$	720.527	+	481.441i	1.21711	+	0.813245i
$593$	−138.551	−	57.3899i	−0.233645	−	0.0967789i	0.262789	−	0.964853i	$-0.415358\pi$
$593$	−138.551	−	57.3899i	−0.233645	−	0.0967789i	−0.496434	+	0.868074i	$0.665358\pi$
$594$		−	93.2893i		−	0.157053i
$595$	−217.953	+	526.184i	−0.366307	+	0.884343i
$596$	98.7472			0.165683
$597$	14.0674	−	33.9618i	0.0235635	−	0.0568874i
$598$	−108.586	+	162.511i	−0.181582	+	0.271757i
$599$	−217.159	−	217.159i	−0.362536	−	0.362536i	0.502210	−	0.864746i	$-0.332520\pi$
$599$	−217.159	−	217.159i	−0.362536	−	0.362536i	−0.864746	+	0.502210i	$0.832520\pi$
$600$	−0.830261	−	4.17401i	−0.00138377	−	0.00695668i
$601$	225.714	+	337.804i	0.375564	+	0.562071i	0.970317	−	0.241838i	$-0.0777502\pi$
$601$	225.714	+	337.804i	0.375564	+	0.562071i	−0.594753	+	0.803908i	$0.702750\pi$
$602$	195.266	−	981.668i	0.324362	−	1.63068i
$603$	−369.209	+	152.931i	−0.612287	+	0.253617i
$604$	−8.85135	−	21.3690i	−0.0146545	−	0.0353792i
$605$	−485.662	−	96.6041i	−0.802747	−	0.159676i
$606$	−10.2360	+	6.83945i	−0.0168910	+	0.0112862i
$607$	1017.17	−	202.327i	1.67573	−	0.333323i	0.736452	−	0.676490i	$-0.236500\pi$
$607$	1017.17	−	202.327i	1.67573	−	0.333323i	0.939274	+	0.343167i	$0.111500\pi$
$608$	−232.484	+	232.484i	−0.382374	+	0.382374i
$609$	−27.7191	−	18.5213i	−0.0455158	−	0.0304127i
$610$	−900.740	−	373.099i	−1.47662	−	0.611637i
$611$			100.662i			0.164750i
$612$	−90.0975	−	90.0975i	−0.147218	−	0.147218i
$613$	132.402			0.215991			0.107995	−	0.994151i	$-0.465557\pi$
$613$	132.402			0.215991			0.107995	+	0.994151i	$0.465557\pi$
$614$	−344.972	+	832.835i	−0.561843	+	1.35641i
$615$	−15.1509	+	22.6749i	−0.0246355	+	0.0368697i
$616$	−448.774	−	448.774i	−0.728529	−	0.728529i
$617$	49.9956	+	251.345i	0.0810302	+	0.407366i	0.999917	+	0.0128460i	$0.00408913\pi$
$617$	49.9956	+	251.345i	0.0810302	+	0.407366i	−0.918887	+	0.394520i	$0.870911\pi$
$618$	29.8464	+	44.6683i	0.0482951	+	0.0722788i
$619$	−17.9310	+	90.1450i	−0.0289676	+	0.145630i	−0.992562	−	0.121737i	$-0.961154\pi$
$619$	−17.9310	+	90.1450i	−0.0289676	+	0.145630i	0.963595	+	0.267367i	$0.0861536\pi$
$620$	5.02680	−	2.08217i	0.00810774	−	0.00335834i
$621$	14.5596	+	35.1499i	0.0234454	+	0.0566021i
$622$	−467.145	−	92.9208i	−0.751036	−	0.149390i
$623$	661.875	−	442.251i	1.06240	−	0.709873i
$624$	−20.0557	+	3.98932i	−0.0321405	+	0.00639314i
$625$	−498.708	+	498.708i	−0.797932	+	0.797932i
$626$	−865.556	−	578.346i	−1.38268	−	0.923875i
$627$	−54.4872	−	22.5694i	−0.0869015	−	0.0359958i
$628$			66.0226i			0.105131i
$629$	439.005	+	657.018i	0.697941	+	1.04454i
$630$	661.091			1.04935
$631$	219.866	−	530.804i	0.348441	−	0.841210i	−0.648364	−	0.761331i	$-0.724546\pi$
$631$	219.866	−	530.804i	0.348441	−	0.841210i	0.996805	−	0.0798795i	$-0.0254536\pi$
$632$	114.912	−	171.978i	0.181823	−	0.272117i
$633$	−0.924280	−	0.924280i	−0.00146016	−	0.00146016i
$634$	109.970	+	552.855i	0.173454	+	0.872012i
$635$	−284.742	−	426.147i	−0.448413	−	0.671098i
$636$	0.136143	−	0.684437i	0.000214061	−	0.00107616i
$637$	62.7377	−	25.9868i	0.0984893	−	0.0407956i
$638$	−405.961	−	980.076i	−0.636302	−	1.53617i
$639$	510.084	+	101.462i	0.798254	+	0.158783i
$640$	682.468	−	456.011i	1.06636	−	0.712517i
$641$	−966.275	+	192.204i	−1.50745	+	0.299850i	−0.878555	−	0.477641i	$-0.841492\pi$
$641$	−966.275	+	192.204i	−1.50745	+	0.299850i	−0.628894	+	0.777491i	$0.716492\pi$
$642$	2.39682	−	2.39682i	0.00373337	−	0.00373337i
$643$	−29.4169	−	19.6558i	−0.0457495	−	0.0305688i	0.532485	−	0.846439i	$-0.321258\pi$
$643$	−29.4169	−	19.6558i	−0.0457495	−	0.0305688i	−0.578235	+	0.815870i	$0.696258\pi$
$644$	−63.1088	−	26.1405i	−0.0979950	−	0.0405909i
$645$			63.2046i			0.0979916i
$646$	−862.919	+	357.433i	−1.33579	+	0.553301i
$647$	−472.176			−0.729793			−0.364897	−	0.931048i	$-0.618896\pi$
$647$	−472.176			−0.729793			−0.364897	+	0.931048i	$0.618896\pi$
$648$	213.837	−	516.248i	0.329995	−	0.796679i
$649$	−229.233	+	343.071i	−0.353210	+	0.528615i
$650$	−39.9283	−	39.9283i	−0.0614281	−	0.0614281i
$651$	0.239071	+	1.20189i	0.000367237	+	0.00184623i
$652$	25.7604	+	38.5532i	0.0395098	+	0.0591306i
$653$	−124.126	+	624.023i	−0.190086	+	0.955625i	0.761482	+	0.648186i	$0.224472\pi$
$653$	−124.126	+	624.023i	−0.190086	+	0.955625i	−0.951568	+	0.307439i	$0.900528\pi$
$654$	38.1953	−	15.8210i	0.0584026	−	0.0241912i
$655$	−88.0746	−	212.631i	−0.134465	−	0.324627i
$656$	−575.082	−	114.391i	−0.876649	−	0.174376i
$657$	10.0536	−	6.71763i	0.0153023	−	0.0102247i
$658$	−199.754	+	39.7335i	−0.303577	+	0.0603853i
$659$	128.530	−	128.530i	0.195037	−	0.195037i	−0.602831	−	0.797869i	$-0.705961\pi$
$659$	128.530	−	128.530i	0.195037	−	0.195037i	0.797869	+	0.602831i	$0.205961\pi$
$660$	−8.79431	−	5.87617i	−0.0133247	−	0.00890328i
$661$	1075.49	+	445.481i	1.62706	+	0.673950i	0.994898	−	0.100887i	$-0.0321681\pi$
$661$	1075.49	+	445.481i	1.62706	+	0.673950i	0.632161	+	0.774837i	$0.282168\pi$
$662$			496.438i			0.749906i
$663$	−18.2879	−	3.63769i	−0.0275836	−	0.00548671i
$664$	469.082			0.706449
$665$	320.340	−	773.368i	0.481714	−	1.16296i
$666$	509.576	−	762.634i	0.765129	−	1.14510i
$667$	305.919	+	305.919i	0.458649	+	0.458649i
$668$	8.41761	+	42.3182i	0.0126012	+	0.0633506i
$669$	−4.40568	−	6.59357i	−0.00658548	−	0.00985586i
$670$	−102.493	+	515.268i	−0.152975	+	0.769056i
$671$	1115.09	−	461.884i	1.66183	−	0.688352i
$672$	−5.08204	−	12.2691i	−0.00756256	−	0.0182576i
$673$	105.260	+	20.9375i	0.156404	+	0.0311106i	0.272671	−	0.962107i	$-0.412093\pi$
$673$	105.260	+	20.9375i	0.156404	+	0.0311106i	−0.116267	+	0.993218i	$0.537093\pi$
$674$	660.281	−	441.186i	0.979645	−	0.654578i
$675$	−10.7806	+	2.14439i	−0.0159713	+	0.00317688i
$676$	72.6081	−	72.6081i	0.107408	−	0.107408i
$677$	−876.782	−	585.847i	−1.29510	−	0.865358i	−0.299057	−	0.954235i	$-0.596672\pi$
$677$	−876.782	−	585.847i	−1.29510	−	0.865358i	−0.996043	+	0.0888773i	$0.971672\pi$
$678$	−21.6537	−	8.96927i	−0.0319377	−	0.0132290i
$679$			422.355i			0.622025i
$680$	622.515	−	123.826i	0.915463	−	0.182097i
$681$	−27.1616			−0.0398849
$682$	−14.9225	+	36.0262i	−0.0218805	+	0.0528243i
$683$	−339.367	+	507.899i	−0.496877	+	0.743629i	−0.992143	−	0.125113i	$-0.960071\pi$
$683$	−339.367	+	507.899i	−0.496877	+	0.743629i	0.495265	+	0.868742i	$0.335071\pi$
$684$	132.422	+	132.422i	0.193600	+	0.193600i
$685$	66.8019	+	335.836i	0.0975210	+	0.490271i
$686$	450.134	+	673.673i	0.656172	+	0.982031i
$687$	3.91525	−	19.6833i	0.00569906	−	0.0286511i
$688$	−1255.51	+	520.051i	−1.82488	+	0.755888i
$689$	13.4265	+	32.4143i	0.0194869	+	0.0470455i
$690$	24.4920	+	4.87176i	0.0354956	+	0.00706052i
$691$	−815.612	+	544.975i	−1.18034	+	0.788675i	−0.981520	−	0.191362i	$-0.938710\pi$
$691$	−815.612	+	544.975i	−1.18034	+	0.788675i	−0.198816	+	0.980037i	$0.563710\pi$
$692$	15.1309	−	3.00972i	0.0218655	−	0.00434931i
$693$	−578.703	+	578.703i	−0.835069	+	0.835069i
$694$	28.9939	+	19.3731i	0.0417779	+	0.0279151i
$695$	1295.31	+	536.536i	1.86376	+	0.771994i
$696$			37.1524i			0.0533798i
$697$	−444.558	−	297.044i	−0.637817	−	0.426176i
$698$	695.626			0.996600
$699$	−21.8372	+	52.7196i	−0.0312406	+	0.0754215i
$700$	10.9641	−	16.4089i	0.0156630	−	0.0234413i
$701$	52.7814	+	52.7814i	0.0752944	+	0.0752944i	0.743751	−	0.668457i	$-0.233045\pi$
$701$	52.7814	+	52.7814i	0.0752944	+	0.0752944i	−0.668457	+	0.743751i	$0.733045\pi$
$702$	8.45719	+	42.5172i	0.0120473	+	0.0605658i
$703$	−645.236	−	965.663i	−0.917832	−	1.37363i
$704$	−130.035	+	653.728i	−0.184708	+	0.928591i
$705$	11.8821	−	4.92174i	0.0168541	−	0.00698120i
$706$	228.027	+	550.507i	0.322985	+	0.779755i
$707$	212.157	+	42.2006i	0.300080	+	0.0596896i
$708$	−3.17089	+	2.11872i	−0.00447866	+	0.00299254i
$709$	−752.626	+	149.707i	−1.06153	+	0.211152i	−0.694821	−	0.719183i	$-0.744516\pi$
$709$	−752.626	+	149.707i	−1.06153	+	0.211152i	−0.366711	+	0.930335i	$0.619516\pi$
$710$	483.454	−	483.454i	0.680921	−	0.680921i
$711$	−221.769	−	148.182i	−0.311912	−	0.208413i
$712$	−819.594	−	339.487i	−1.15111	−	0.476807i
$713$		−	15.9030i		−	0.0223044i
$714$		−	37.7264i		−	0.0528381i
$715$	531.762			0.743723
$716$	20.0306	−	48.3580i	0.0279756	−	0.0675392i
$717$	18.5441	−	27.7533i	0.0258635	−	0.0387075i
$718$	246.167	+	246.167i	0.342851	+	0.342851i
$719$	224.919	+	1130.74i	0.312822	+	1.57266i	0.742606	+	0.669729i	$0.233590\pi$
$719$	224.919	+	1130.74i	0.312822	+	1.57266i	−0.429785	+	0.902931i	$0.641410\pi$
$720$	−498.673	−	746.317i	−0.692602	−	1.03655i
$721$	184.157	−	925.822i	0.255419	−	1.28408i
$722$	534.907	−	221.566i	0.740869	−	0.306878i
$723$	−17.8143	−	43.0074i	−0.0246394	−	0.0594847i
$724$	−85.6842	−	17.0437i	−0.118348	−	0.0235410i
$725$	−103.927	+	69.4417i	−0.143347	+	0.0957817i
$726$	32.1705	−	6.39910i	0.0443119	−	0.00881419i
$727$	195.955	−	195.955i	0.269539	−	0.269539i	−0.559376	−	0.828914i	$-0.688959\pi$
$727$	195.955	−	195.955i	0.269539	−	0.269539i	0.828914	+	0.559376i	$0.188959\pi$
$728$	245.216	+	163.848i	0.336834	+	0.225066i
$729$	−661.808	−	274.130i	−0.907830	−	0.376036i
$730$		−	15.8957i		−	0.0217749i
$731$	−1239.18			−1.69518
$732$	11.1555			0.0152398
$733$	169.675	−	409.632i	0.231480	−	0.558843i	−0.764871	−	0.644183i	$-0.777198\pi$
$733$	169.675	−	409.632i	0.231480	−	0.558843i	0.996352	+	0.0853397i	$0.0271976\pi$
$734$	597.376	−	894.036i	0.813863	−	1.21803i
$735$	−6.13496	−	6.13496i	−0.00834689	−	0.00834689i
$736$	33.6219	+	169.029i	0.0456820	+	0.229659i
$737$	−361.333	−	540.773i	−0.490275	−	0.733749i
$738$	−121.076	+	608.689i	−0.164059	+	0.824782i
$739$	98.1432	−	40.6523i	0.132805	−	0.0550098i	−0.315291	−	0.948995i	$-0.602102\pi$
$739$	98.1432	−	40.6523i	0.132805	−	0.0550098i	0.448096	+	0.893985i	$0.352102\pi$
$740$	−79.7067	−	192.429i	−0.107712	−	0.260039i
$741$	26.8790	+	5.34656i	0.0362739	+	0.00721533i
$742$	−59.0234	+	39.4382i	−0.0795463	+	0.0531512i
$743$	905.734	−	180.162i	1.21902	−	0.242479i	0.456668	−	0.889637i	$-0.349043\pi$
$743$	905.734	−	180.162i	1.21902	−	0.242479i	0.762355	+	0.647159i	$0.224043\pi$
$744$	0.965673	−	0.965673i	0.00129795	−	0.00129795i
$745$	527.409	+	352.403i	0.707931	+	0.473025i
$746$	−1164.99	−	482.554i	−1.56165	−	0.646855i
$747$		−	604.891i		−	0.809760i
$748$	115.207	−	172.419i	0.154020	−	0.230507i
$749$	−59.5595			−0.0795187
$750$	15.4803	−	37.3727i	0.0206403	−	0.0498302i
$751$	636.671	−	952.846i	0.847765	−	1.26877i	−0.113610	−	0.993525i	$-0.536241\pi$
$751$	636.671	−	952.846i	0.847765	−	1.26877i	0.961374	−	0.275244i	$-0.0887587\pi$
$752$	195.534	+	195.534i	0.260018	+	0.260018i
$753$	−8.52102	−	42.8381i	−0.0113161	−	0.0568899i
$754$	273.869	+	409.873i	0.363221	+	0.543598i
$755$	28.9855	−	145.720i	0.0383914	−	0.193007i
$756$	−13.9973	+	5.79787i	−0.0185150	+	0.00766915i
$757$	24.5973	+	59.3832i	0.0324932	+	0.0784455i	0.939293	−	0.343116i	$-0.111482\pi$
$757$	24.5973	+	59.3832i	0.0324932	+	0.0784455i	−0.906800	+	0.421561i	$0.861482\pi$
$758$	−1513.99	−	301.151i	−1.99734	−	0.397296i
$759$	−25.7043	+	17.1751i	−0.0338660	+	0.0226285i
$760$	−914.952	+	181.995i	−1.20388	+	0.239467i
$761$	−173.164	+	173.164i	−0.227548	+	0.227548i	−0.811668	−	0.584120i	$-0.801440\pi$
$761$	−173.164	+	173.164i	−0.227548	+	0.227548i	0.584120	+	0.811668i	$0.301440\pi$
$762$	28.2282	+	18.8615i	0.0370449	+	0.0247526i
$763$	−671.137	−	277.994i	−0.879602	−	0.364343i
$764$			162.919i			0.213245i
$765$	−159.676	−	802.745i	−0.208727	−	1.04934i
$766$	678.170			0.885339
$767$	73.3731	−	177.138i	0.0956624	−	0.230950i
$768$	−13.8148	+	20.6753i	−0.0179880	+	0.0269210i
$769$	550.339	+	550.339i	0.715655	+	0.715655i	0.967712	−	0.252057i	$-0.0811072\pi$
$769$	550.339	+	550.339i	0.715655	+	0.715655i	−0.252057	+	0.967712i	$0.581107\pi$
$770$	209.898	+	1055.23i	0.272595	+	1.37043i
$771$	4.74102	+	7.09544i	0.00614919	+	0.00920291i
$772$	14.4046	−	72.4170i	0.0186588	−	0.0938044i
$773$	399.534	−	165.492i	0.516861	−	0.214091i	−0.108976	−	0.994044i	$-0.534757\pi$
$773$	399.534	−	165.492i	0.516861	−	0.214091i	0.625837	+	0.779953i	$0.284757\pi$
$774$	550.442	+	1328.89i	0.711166	+	1.71691i
$775$	4.50624	+	0.896346i	0.00581450	+	0.00115658i
$776$	391.361	−	261.499i	0.504331	−	0.336983i
$777$	46.0092	−	9.15179i	0.0592139	−	0.0117784i
$778$	−443.266	+	443.266i	−0.569751	+	0.569751i
$779$	653.397	+	436.586i	0.838764	+	0.560444i
$780$	4.54077	+	1.88085i	0.00582150	+	0.00241134i
$781$			846.408i			1.08375i
$782$	−95.5146	+	480.184i	−0.122141	+	0.614047i
$783$	95.9569			0.122550
$784$	71.3878	−	172.345i	0.0910559	−	0.219828i
$785$	−235.617	+	352.626i	−0.300150	+	0.449206i
$786$	10.7800	+	10.7800i	0.0137150	+	0.0137150i
$787$	−222.286	−	1117.51i	−0.282447	−	1.41996i	−0.817884	−	0.575383i	$-0.804853\pi$
$787$	−222.286	−	1117.51i	−0.282447	−	1.41996i	0.535437	−	0.844575i	$-0.320147\pi$
$788$	−119.428	−	178.736i	−0.151558	−	0.226822i
$789$	−16.0029	+	80.4518i	−0.0202824	+	0.101967i
$790$	−323.946	+	134.183i	−0.410059	+	0.169852i
$791$	157.601	+	380.481i	0.199242	+	0.481013i
$792$	894.537	+	177.934i	1.12947	+	0.224665i
$793$	−466.336	+	311.595i	−0.588065	+	0.392932i
$794$	−268.177	+	53.3436i	−0.337754	+	0.0671834i
$795$	3.16972	−	3.16972i	0.00398707	−	0.00398707i
$796$	−157.954	−	105.541i	−0.198434	−	0.132590i
$797$	104.084	+	43.1132i	0.130595	+	0.0540943i	0.447024	−	0.894522i	$-0.352484\pi$
$797$	104.084	+	43.1132i	0.130595	+	0.0540943i	−0.316429	+	0.948616i	$0.602484\pi$
$798$			55.4491i			0.0694850i
$799$	96.4946	+	232.959i	0.120769	+	0.291563i
$800$	−49.7905			−0.0622381
$801$	−437.775	+	1056.88i	−0.546536	+	1.31945i
$802$	521.614	−	780.650i	0.650391	−	0.973379i
$803$	13.9147	+	13.9147i	0.0173284	+	0.0173284i
$804$	−1.17274	−	5.89575i	−0.00145863	−	0.00733302i
$805$	−243.775	−	364.835i	−0.302826	−	0.453212i
$806$	3.53507	−	17.7720i	0.00438594	−	0.0220496i
$807$	26.3178	−	10.9012i	0.0326119	−	0.0135083i
$808$	−92.2520	−	222.716i	−0.114173	−	0.275639i
$809$	638.126	+	126.931i	0.788783	+	0.156899i	0.573014	−	0.819546i	$-0.305774\pi$
$809$	638.126	+	126.931i	0.788783	+	0.156899i	0.215769	+	0.976444i	$0.430774\pi$
$810$	−787.626	+	526.275i	−0.972377	+	0.649722i
$811$	−631.322	+	125.578i	−0.778449	+	0.154843i	−0.568294	−	0.822825i	$-0.692397\pi$
$811$	−631.322	+	125.578i	−0.778449	+	0.154843i	−0.210154	+	0.977668i	$0.567397\pi$
$812$	−121.822	+	121.822i	−0.150027	+	0.150027i
$813$	−62.3868	−	41.6855i	−0.0767366	−	0.0512737i
$814$	1379.10	+	571.243i	1.69423	+	0.701773i
$815$			297.845i			0.365453i
$816$	−42.5900	+	28.4577i	−0.0521936	+	0.0348747i
$817$	1821.30			2.22925
$818$	181.383	−	437.897i	0.221739	−	0.535326i
$819$	211.285	−	316.210i	0.257979	−	0.386093i
$820$	99.6533	+	99.6533i	0.121528	+	0.121528i
$821$	−174.401	−	876.775i	−0.212426	−	1.06794i	−0.928902	−	0.370325i	$-0.879246\pi$
$821$	−174.401	−	876.775i	−0.212426	−	1.06794i	0.716477	−	0.697611i	$-0.245754\pi$
$822$	−12.6013	−	18.8592i	−0.0153300	−	0.0229430i
$823$	180.424	−	907.053i	0.219227	−	1.10213i	−0.701723	−	0.712450i	$-0.747586\pi$
$823$	180.424	−	907.053i	0.219227	−	1.10213i	0.920950	−	0.389680i	$-0.127414\pi$
$824$	−971.901	+	402.575i	−1.17949	+	0.488562i
$825$	−3.41789	−	8.25153i	−0.00414290	−	0.0100018i
$826$	380.476	+	75.6813i	0.460624	+	0.0916239i
$827$	−704.948	+	471.032i	−0.852417	+	0.569567i	−0.903237	−	0.429141i	$-0.858816\pi$
$827$	−704.948	+	471.032i	−0.852417	+	0.569567i	0.0508208	+	0.998708i	$0.483816\pi$
$828$	96.2787	−	19.1510i	0.116279	−	0.0231292i
$829$	862.801	−	862.801i	1.04077	−	1.04077i	0.0416400	−	0.999133i	$-0.486742\pi$
$829$	862.801	−	862.801i	1.04077	−	1.04077i	0.999133	−	0.0416400i	$-0.0132583\pi$
$830$	−661.189	−	441.793i	−0.796614	−	0.532280i
$831$	26.3667	+	10.9215i	0.0317289	+	0.0131426i
$832$		−	309.729i		−	0.372271i
$833$	120.281	−	120.281i	0.144395	−	0.144395i
$834$	−92.8715			−0.111357
$835$	−106.064	+	256.062i	−0.127023	+	0.306661i
$836$	−169.327	+	253.416i	−0.202545	+	0.303129i
$837$	−2.49414	−	2.49414i	−0.00297985	−	0.00297985i
$838$	−266.908	−	1341.84i	−0.318506	−	1.60124i
$839$	−213.563	−	319.620i	−0.254545	−	0.380954i	0.682085	−	0.731273i	$-0.261073\pi$
$839$	−213.563	−	319.620i	−0.254545	−	0.380954i	−0.936631	+	0.350319i	$0.886073\pi$
$840$	7.35108	−	36.9564i	0.00875129	−	0.0439957i
$841$	231.119	−	95.7324i	0.274814	−	0.113832i
$842$	−43.2829	−	104.494i	−0.0514048	−	0.124102i
$843$	63.3230	+	12.5957i	0.0751162	+	0.0149415i
$844$	−5.61660	+	3.75289i	−0.00665474	+	0.00444655i
$845$	646.919	−	128.680i	0.765585	−	0.152284i
$846$	206.961	−	206.961i	0.244634	−	0.244634i
$847$	−479.215	−	320.201i	−0.565779	−	0.378042i
$848$	89.0448	+	36.8836i	0.105006	+	0.0434948i
$849$		−	57.7975i		−	0.0680771i
$850$	−130.680	−	54.1294i	−0.153741	−	0.0636817i
$851$	−608.778			−0.715368
$852$	−2.99375	+	7.22756i	−0.00351380	+	0.00848305i
$853$	−485.458	+	726.539i	−0.569118	+	0.851745i	−0.998684	−	0.0512903i	$-0.983667\pi$
$853$	−485.458	+	726.539i	−0.569118	+	0.851745i	0.429566	+	0.903036i	$0.358667\pi$
$854$	−802.404	−	802.404i	−0.939583	−	0.939583i
$855$	234.687	+	1179.85i	0.274487	+	1.37994i
$856$	36.8760	+	55.1888i	0.0430794	+	0.0644729i
$857$	−262.053	+	1317.43i	−0.305779	+	1.53726i	0.456332	+	0.889810i	$0.349163\pi$
$857$	−262.053	+	1317.43i	−0.305779	+	1.53726i	−0.762111	+	0.647446i	$0.775837\pi$
$858$	−32.5429	+	13.4797i	−0.0379288	+	0.0157106i
$859$	−97.9655	−	236.510i	−0.114046	−	0.275331i	0.856542	−	0.516077i	$-0.172608\pi$
$859$	−97.9655	−	236.510i	−0.114046	−	0.275331i	−0.970588	+	0.240745i	$0.922608\pi$
$860$	320.355	+	63.7225i	0.372506	+	0.0740960i
$861$	−26.3918	+	17.6344i	−0.0306525	+	0.0204813i
$862$	−1014.96	+	201.887i	−1.17744	+	0.234208i
$863$	−1137.90	+	1137.90i	−1.31854	+	1.31854i	−0.403612	+	0.914930i	$0.632245\pi$
$863$	−1137.90	+	1137.90i	−1.31854	+	1.31854i	−0.914930	+	0.403612i	$0.867755\pi$
$864$	31.7825	+	21.2364i	0.0367853	+	0.0245791i
$865$	91.5550	+	37.9233i	0.105844	+	0.0438420i
$866$		−	1415.19i		−	1.63417i
$867$	−45.8102	+	9.11221i	−0.0528376	+	0.0105100i
$868$	6.33287			0.00729593
$869$	166.114	−	401.035i	0.191156	−	0.461490i
$870$	34.9910	−	52.3677i	0.0402195	−	0.0601927i
$871$	213.704	+	213.704i	0.245355	+	0.245355i
$872$	157.937	+	794.004i	0.181121	+	0.910555i
$873$	−337.208	−	504.668i	−0.386264	−	0.578085i
$874$	140.384	−	705.760i	0.160623	−	0.807505i
$875$	−656.681	+	272.006i	−0.750493	+	0.310864i
$876$	0.0696025	+	0.168035i	7.94550e−5	+	0.000191821i
$877$	−483.538	−	96.1816i	−0.551354	−	0.109671i	−0.0884519	−	0.996080i	$-0.528192\pi$
$877$	−483.538	−	96.1816i	−0.551354	−	0.109671i	−0.462902	+	0.886409i	$0.653192\pi$
$878$	1512.85	−	1010.86i	1.72307	−	1.15132i
$879$	−37.8854	+	7.53588i	−0.0431006	+	0.00857324i
$880$	1032.94	−	1032.94i	1.17379	−	1.17379i
$881$	−334.347	−	223.404i	−0.379508	−	0.253579i	0.351155	−	0.936317i	$-0.385789\pi$
$881$	−334.347	−	223.404i	−0.379508	−	0.253579i	−0.730663	+	0.682738i	$0.760789\pi$
$882$	−182.417	−	75.5597i	−0.206822	−	0.0856686i
$883$			907.327i			1.02755i	0.857925	+	0.513775i	$0.171754\pi$
$883$			907.327i			1.02755i	−0.857925	+	0.513775i	$0.828246\pi$
$884$	−36.8755	+	89.0253i	−0.0417144	+	0.100707i
$885$	−24.4969			−0.0276801
$886$	−298.248	+	720.035i	−0.336624	+	0.812681i
$887$	−705.933	+	1056.50i	−0.795866	+	1.19110i	0.182294	+	0.983244i	$0.441648\pi$
$887$	−705.933	+	1056.50i	−0.795866	+	1.19110i	−0.978160	+	0.207854i	$0.933352\pi$
$888$	−36.9665	−	36.9665i	−0.0416290	−	0.0416290i
$889$	−116.379	−	585.074i	−0.130910	−	0.658127i
$890$	835.512	+	1250.43i	0.938778	+	1.40498i
$891$	228.780	−	1150.16i	0.256768	−	1.29086i
$892$	−37.8615	+	15.6828i	−0.0424457	+	0.0175816i
$893$	−141.825	−	342.395i	−0.158818	−	0.383421i
$894$	−41.2096	−	8.19710i	−0.0460957	−	0.00916901i
$895$	279.561	−	186.796i	0.312358	−	0.208711i
$896$	936.988	−	186.379i	1.04575	−	0.208012i
$897$	10.1579	−	10.1579i	0.0113243	−	0.0113243i
$898$	1436.96	+	960.148i	1.60018	+	1.06921i
$899$	−37.0564	−	15.3493i	−0.0412195	−	0.0170737i
$900$			28.3606i			0.0315118i
$901$	62.1448	+	62.1448i	0.0689732	+	0.0689732i
$902$	−1010.03			−1.11976
$903$	−28.1522	+	67.9654i	−0.0311763	+	0.0752663i
$904$	254.983	−	381.608i	0.282060	−	0.422133i
$905$	−396.815	−	396.815i	−0.438470	−	0.438470i
$906$	1.92002	+	9.65257i	0.00211922	+	0.0106541i
$907$	852.359	+	1275.64i	0.939756	+	1.40644i	0.913522	+	0.406788i	$0.133351\pi$
$907$	852.359	+	1275.64i	0.939756	+	1.40644i	0.0262336	+	0.999656i	$0.491649\pi$
$908$	−27.3842	+	137.670i	−0.0301588	+	0.151619i
$909$	−287.197	+	118.961i	−0.315948	+	0.130870i
$910$	−191.325	−	461.899i	−0.210247	−	0.507582i
$911$	359.228	+	71.4549i	0.394323	+	0.0784357i	0.388269	−	0.921546i	$-0.373073\pi$
$911$	359.228	+	71.4549i	0.394323	+	0.0784357i	0.00605352	+	0.999982i	$0.498073\pi$
$912$	62.5974	−	41.8262i	0.0686375	−	0.0458621i
$913$	965.523	−	192.054i	1.05753	−	0.210355i
$914$	−505.549	+	505.549i	−0.553117	+	0.553117i
$915$	59.5816	+	39.8112i	0.0651165	+	0.0435095i
$916$	−95.8181	−	39.6892i	−0.104605	−	0.0433288i
$917$		−	267.877i		−	0.292123i
$918$	60.3292	+	90.2891i	0.0657181	+	0.0983541i
$919$	−944.655			−1.02792			−0.513958	−	0.857815i	$-0.671821\pi$
$919$	−944.655			−1.02792			−0.513958	+	0.857815i	$0.671821\pi$
$920$	−187.130	+	451.772i	−0.203402	+	0.491057i
$921$	36.8099	−	55.0899i	0.0399673	−	0.0598153i
$922$	−382.839	−	382.839i	−0.415226	−	0.415226i
$923$	−76.7316	−	385.756i	−0.0831328	−	0.417937i
$924$	−6.83940	−	10.2359i	−0.00740195	−	0.0110778i
$925$	34.3127	−	172.501i	0.0370948	−	0.186488i
$926$	712.706	−	295.212i	0.769661	−	0.318804i
$927$	519.128	+	1253.29i	0.560009	+	1.35198i
$928$	426.312	+	84.7988i	0.459388	+	0.0913780i
$929$	807.914	−	539.831i	0.869660	−	0.581088i	−0.0387126	−	0.999250i	$-0.512326\pi$
$929$	807.914	−	539.831i	0.869660	−	0.581088i	0.908372	+	0.418162i	$0.137326\pi$
$930$	−2.27065	+	0.451660i	−0.00244156	+	0.000485656i
$931$	−176.785	+	176.785i	−0.189887	+	0.189887i
$932$	245.195	+	163.834i	0.263085	+	0.175788i
$933$	32.3426	+	13.3967i	0.0346652	+	0.0143588i
$934$		−	481.282i		−	0.515292i
$935$	1230.64	−	509.748i	1.31619	−	0.545184i
$936$	−423.822			−0.452801
$937$	−229.656	+	554.438i	−0.245097	+	0.591716i	−0.997775	−	0.0666728i	$-0.978762\pi$
$937$	−229.656	+	554.438i	−0.245097	+	0.591716i	0.752678	+	0.658389i	$0.228762\pi$
$938$	−339.721	+	508.428i	−0.362176	+	0.542034i
$939$	54.1023	+	54.1023i	0.0576170	+	0.0576170i
$940$	−12.9665	−	65.1871i	−0.0137942	−	0.0693480i
$941$	602.514	+	901.726i	0.640291	+	0.958263i	0.999686	+	0.0250777i	$0.00798332\pi$
$941$	602.514	+	901.726i	0.640291	+	0.958263i	−0.359394	+	0.933186i	$0.617017\pi$
$942$	5.48059	−	27.5528i	0.00581804	−	0.0292493i
$943$	380.563	−	157.634i	0.403566	−	0.167162i
$944$	−201.562	−	486.613i	−0.213519	−	0.515480i
$945$	−95.4507	−	18.9863i	−0.101006	−	0.0200913i
$946$	−1946.39	+	1300.54i	−2.05750	+	1.37478i
$947$	683.372	−	135.931i	0.721618	−	0.143539i	0.179400	−	0.983776i	$-0.442584\pi$
$947$	683.372	−	135.931i	0.721618	−	0.143539i	0.542219	+	0.840237i	$0.317584\pi$
$948$	2.83693	−	2.83693i	0.00299254	−	0.00299254i
$949$	−7.60316	−	5.08027i	−0.00801176	−	0.00535329i
$950$	192.069	+	79.5577i	0.202178	+	0.0837449i
$951$		−	41.4305i		−	0.0435651i
$952$	724.559	+	144.124i	0.761091	+	0.151390i
$953$	−1779.95			−1.86774			−0.933868	−	0.357618i	$-0.883589\pi$
$953$	−1779.95			−1.86774			−0.933868	+	0.357618i	$0.883589\pi$
$954$	39.0390	−	94.2485i	0.0409214	−	0.0987930i
$955$	−581.415	+	870.149i	−0.608812	+	0.911151i
$956$	−121.972	−	121.972i	−0.127586	−	0.127586i
$957$	15.2111	+	76.4716i	0.0158946	+	0.0799076i
$958$	−613.843	−	918.681i	−0.640754	−	0.958957i
$959$	−77.7522	+	390.887i	−0.0810763	+	0.407598i
$960$	−36.5604	+	15.1438i	−0.0380838	+	0.0157748i
$961$	−367.195	−	886.486i	−0.382096	−	0.922462i
$962$	−680.322	−	135.324i	−0.707195	−	0.140670i
$963$	71.1671	−	47.5523i	0.0739015	−	0.0493794i
$964$	−235.945	+	46.9324i	−0.244756	+	0.0486850i
$965$	335.373	−	335.373i	0.347536	−	0.347536i
$966$	24.1669	+	16.1478i	0.0250175	+	0.0167161i
$967$	−558.012	−	231.136i	−0.577055	−	0.239024i	0.0750154	−	0.997182i	$-0.476099\pi$
$967$	−558.012	−	231.136i	−0.577055	−	0.239024i	−0.652071	+	0.758158i	$0.726099\pi$
$968$			642.299i			0.663532i
$969$	67.3303	−	13.3928i	0.0694843	−	0.0138213i
$970$	−797.924			−0.822602
$971$	421.281	−	1017.06i	0.433863	−	1.04744i	−0.544168	−	0.838976i	$-0.683155\pi$
$971$	421.281	−	1017.06i	0.433863	−	1.04744i	0.978031	−	0.208461i	$-0.0668454\pi$
$972$	18.1531	−	27.1681i	0.0186760	−	0.0279507i
$973$	1153.90	+	1153.90i	1.18592	+	1.18592i
$974$	−108.013	−	543.017i	−0.110896	−	0.557512i
$975$	2.30577	+	3.45084i	0.00236490	+	0.00353932i
$976$	−300.579	+	1511.11i	−0.307971	+	1.54827i
$977$	1012.20	−	419.266i	1.03603	−	0.429136i	0.201142	−	0.979562i	$-0.435535\pi$
$977$	1012.20	−	419.266i	1.03603	−	0.429136i	0.834884	+	0.550426i	$0.185535\pi$
$978$	−7.55010	−	18.2276i	−0.00771994	−	0.0186376i
$979$	−1825.98	−	363.211i	−1.86515	−	0.371002i
$980$	−37.2805	+	24.9100i	−0.0380413	+	0.0254184i
$981$	1023.88	−	203.663i	1.04372	−	0.207608i
$982$	351.948	−	351.948i	0.358399	−	0.358399i
$983$	−1021.98	−	682.863i	−1.03965	−	0.694673i	−0.0862178	−	0.996276i	$-0.527478\pi$
$983$	−1021.98	−	682.863i	−1.03965	−	0.694673i	−0.953433	+	0.301604i	$0.902478\pi$
$984$	32.6807	+	13.5368i	0.0332121	+	0.0137569i
$985$		−	1380.83i		−	1.40186i
$986$	1026.71	+	686.025i	1.04129	+	0.695766i
$987$	14.9694			0.0151665
$988$	54.1984	−	130.847i	0.0548567	−	0.132436i
$989$	530.396	−	793.794i	0.536295	−	0.802623i
$990$	−1093.30	−	1093.30i	−1.10434	−	1.10434i
$991$	−143.735	−	722.604i	−0.145040	−	0.729167i	−0.983025	−	0.183473i	$-0.941266\pi$
$991$	−143.735	−	722.604i	−0.145040	−	0.729167i	0.837985	−	0.545694i	$-0.183734\pi$
$992$	−8.87670	−	13.2849i	−0.00894829	−	0.0133921i
$993$	7.11841	−	35.7867i	0.00716859	−	0.0360389i
$994$	735.207	−	304.533i	0.739645	−	0.306371i
$995$	−466.981	−	1127.39i	−0.469328	−	1.13306i
$996$	8.92400	+	1.77509i	0.00895984	+	0.00178222i
$997$	145.149	−	96.9855i	0.145586	−	0.0972774i	−0.480644	−	0.876916i	$-0.659597\pi$
$997$	145.149	−	96.9855i	0.145586	−	0.0972774i	0.626230	+	0.779638i	$0.284597\pi$
$998$	465.511	−	92.5960i	0.466444	−	0.0927815i
$999$	−95.4770	+	95.4770i	−0.0955725	+	0.0955725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.3.e.a.7.1	yes	8
3.2	odd	2		153.3.p.b.109.1		8
4.3	odd	2		272.3.bh.c.177.1		8
5.2	odd	4		425.3.t.a.24.1		8
5.3	odd	4		425.3.t.c.24.1		8
5.4	even	2		425.3.u.b.126.1		8
17.2	even	8		289.3.e.d.249.1		8
17.3	odd	16		289.3.e.m.131.1		8
17.4	even	4		289.3.e.i.214.1		8
17.5	odd	16	inner	17.3.e.a.5.1	✓	8
17.6	odd	16		289.3.e.b.65.1		8
17.7	odd	16		289.3.e.l.224.1		8
17.8	even	8		289.3.e.l.40.1		8
17.9	even	8		289.3.e.k.40.1		8
17.10	odd	16		289.3.e.k.224.1		8
17.11	odd	16		289.3.e.d.65.1		8
17.12	odd	16		289.3.e.c.158.1		8
17.13	even	4		289.3.e.m.214.1		8
17.14	odd	16		289.3.e.i.131.1		8
17.15	even	8		289.3.e.b.249.1		8
17.16	even	2		289.3.e.c.75.1		8
51.5	even	16		153.3.p.b.73.1		8
68.39	even	16		272.3.bh.c.209.1		8
85.22	even	16		425.3.t.c.124.1		8
85.39	odd	16		425.3.u.b.226.1		8
85.73	even	16		425.3.t.a.124.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	17.5	odd	16	inner
17.3.e.a.7.1	yes	8	1.1	even	1	trivial
153.3.p.b.73.1		8	51.5	even	16
153.3.p.b.109.1		8	3.2	odd	2
272.3.bh.c.177.1		8	4.3	odd	2
272.3.bh.c.209.1		8	68.39	even	16
289.3.e.b.65.1		8	17.6	odd	16
289.3.e.b.249.1		8	17.15	even	8
289.3.e.c.75.1		8	17.16	even	2
289.3.e.c.158.1		8	17.12	odd	16
289.3.e.d.65.1		8	17.11	odd	16
289.3.e.d.249.1		8	17.2	even	8
289.3.e.i.131.1		8	17.14	odd	16
289.3.e.i.214.1		8	17.4	even	4
289.3.e.k.40.1		8	17.9	even	8
289.3.e.k.224.1		8	17.10	odd	16
289.3.e.l.40.1		8	17.8	even	8
289.3.e.l.224.1		8	17.7	odd	16
289.3.e.m.131.1		8	17.3	odd	16
289.3.e.m.214.1		8	17.13	even	4
425.3.t.a.24.1		8	5.2	odd	4
425.3.t.a.124.1		8	85.73	even	16
425.3.t.c.24.1		8	5.3	odd	4
425.3.t.c.124.1		8	85.22	even	16
425.3.u.b.126.1		8	5.4	even	2
425.3.u.b.226.1		8	85.39	odd	16

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	17.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841487 + 2.03153i) q^{2} +(0.0897902 - 0.134381i) q^{3} +(-0.590587 - 0.590587i) q^{4} +(-1.04667 - 5.26197i) q^{5} +(0.197441 + 0.295491i) q^{6} +(1.21824 - 6.12453i) q^{7} +(-6.42935 + 2.66313i) q^{8} +(3.43416 + 8.29078i) q^{9} +O(q^{10})\)	\(q+(-0.841487 + 2.03153i) q^{2} +(0.0897902 - 0.134381i) q^{3} +(-0.590587 - 0.590587i) q^{4} +(-1.04667 - 5.26197i) q^{5} +(0.197441 + 0.295491i) q^{6} +(1.21824 - 6.12453i) q^{7} +(-6.42935 + 2.66313i) q^{8} +(3.43416 + 8.29078i) q^{9} +(11.5706 + 2.30154i) q^{10} +(-12.1433 + 8.11392i) q^{11} +(-0.132392 + 0.0263345i) q^{12} +(4.79884 - 4.79884i) q^{13} +(11.4170 + 7.62861i) q^{14} +(-0.801088 - 0.331821i) q^{15} -18.6433i q^{16} +(6.50562 - 15.7060i) q^{17} -19.7328 q^{18} +(-9.56175 + 23.0841i) q^{19} +(-2.48950 + 3.72580i) q^{20} +(-0.713631 - 0.713631i) q^{21} +(-6.26521 - 31.4973i) q^{22} +(7.27639 + 10.8899i) q^{23} +(-0.219421 + 1.10310i) q^{24} +(-3.49585 + 1.44803i) q^{25} +(5.71082 + 13.7871i) q^{26} +(2.84909 + 0.566719i) q^{27} +(-4.33654 + 2.89759i) q^{28} +(32.3980 - 6.44436i) q^{29} +(1.34821 - 1.34821i) q^{30} +(-1.00960 - 0.674593i) q^{31} +(12.1570 + 5.03558i) q^{32} +2.36038i q^{33} +(26.4327 + 26.4327i) q^{34} -33.5022 q^{35} +(2.86826 - 6.92459i) q^{36} +(-25.8238 + 38.6481i) q^{37} +(-38.8500 - 38.8500i) q^{38} +(-0.213982 - 1.07576i) q^{39} +(20.7427 + 31.0437i) q^{40} +(6.13577 - 30.8466i) q^{41} +(2.05027 - 0.849251i) q^{42} +(-27.8948 - 67.3441i) q^{43} +(11.9637 + 2.37972i) q^{44} +(40.0314 - 26.7482i) q^{45} +(-28.2461 + 5.61851i) q^{46} +(-10.4882 + 10.4882i) q^{47} +(-2.50529 - 1.67398i) q^{48} +(9.24438 + 3.82915i) q^{49} -8.32041i q^{50} +(-1.52643 - 2.28447i) q^{51} -5.66826 q^{52} +(-1.97838 + 4.77624i) q^{53} +(-3.54878 + 5.31112i) q^{54} +(55.4053 + 55.4053i) q^{55} +(8.47786 + 42.6211i) q^{56} +(2.24350 + 3.35764i) q^{57} +(-14.1706 + 71.2404i) q^{58} +(26.1013 - 10.8115i) q^{59} +(0.277142 + 0.669081i) q^{60} +(-81.0541 - 16.1227i) q^{61} +(2.22002 - 1.48337i) q^{62} +(54.9608 - 10.9324i) q^{63} +(32.2713 - 32.2713i) q^{64} +(-30.2741 - 20.2285i) q^{65} +(-4.79518 - 1.98623i) q^{66} +44.5324i q^{67} +(-13.1179 + 5.43359i) q^{68} +2.11674 q^{69} +(28.1917 - 68.0607i) q^{70} +(32.1978 - 48.1875i) q^{71} +(-44.1588 - 44.1588i) q^{72} +(-0.262865 - 1.32151i) q^{73} +(-56.7843 - 84.9838i) q^{74} +(-0.119306 + 0.599792i) q^{75} +(19.2802 - 7.98612i) q^{76} +(34.9004 + 84.2570i) q^{77} +(2.36550 + 0.470527i) q^{78} +(-24.7128 + 16.5125i) q^{79} +(-98.1004 + 19.5134i) q^{80} +(-56.7774 + 56.7774i) q^{81} +(57.5026 + 38.4220i) q^{82} +(-62.2748 - 25.7951i) q^{83} +0.842922i q^{84} +(-89.4535 - 17.7934i) q^{85} +160.285 q^{86} +(2.04303 - 4.93230i) q^{87} +(56.4655 - 84.5065i) q^{88} +(90.1397 + 90.1397i) q^{89} +(20.6537 + 103.833i) q^{90} +(-23.5444 - 35.2368i) q^{91} +(2.13408 - 10.7288i) q^{92} +(-0.181304 + 0.0750988i) q^{93} +(-12.4814 - 30.1327i) q^{94} +(131.476 + 26.1522i) q^{95} +(1.76826 - 1.18151i) q^{96} +(-66.3366 + 13.1952i) q^{97} +(-15.5581 + 15.5581i) q^{98} +(-108.973 - 72.8134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9	\( 8 q - 8 q^{2} - 8 q^{3} + 16 q^{5} - 8 q^{6} + 8 q^{7} - 24 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{11} + 48 q^{12} + 16 q^{13} + 8 q^{14} - 16 q^{15} + 56 q^{18} - 80 q^{20} - 64 q^{21} - 104 q^{22} - 56 q^{23} - 80 q^{24} + 64 q^{25} + 176 q^{26} + 40 q^{27} + 152 q^{28} + 48 q^{29} + 16 q^{30} + 24 q^{31} + 88 q^{32} - 136 q^{34} - 160 q^{35} - 128 q^{36} + 32 q^{37} - 120 q^{38} + 48 q^{39} + 64 q^{40} + 48 q^{41} + 16 q^{42} - 232 q^{43} + 120 q^{44} - 88 q^{46} + 192 q^{47} + 136 q^{48} + 16 q^{49} + 136 q^{51} - 384 q^{52} - 32 q^{53} + 8 q^{54} + 224 q^{55} - 120 q^{56} + 24 q^{57} + 240 q^{58} - 48 q^{59} + 64 q^{60} - 160 q^{61} - 168 q^{62} + 56 q^{63} - 64 q^{64} - 96 q^{65} - 8 q^{66} + 272 q^{68} + 240 q^{69} + 224 q^{70} + 40 q^{71} + 40 q^{72} + 48 q^{73} - 160 q^{74} - 296 q^{75} + 80 q^{76} - 48 q^{77} - 400 q^{78} - 136 q^{79} - 240 q^{80} - 424 q^{81} - 64 q^{82} - 264 q^{83} - 272 q^{85} + 832 q^{86} + 208 q^{87} + 264 q^{88} + 160 q^{89} + 448 q^{90} + 320 q^{91} + 24 q^{92} - 64 q^{93} + 32 q^{94} + 272 q^{95} - 56 q^{96} + 48 q^{97} - 120 q^{98} - 224 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 16 * q^5 - 8 * q^6 + 8 * q^7 - 24 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^11 + 48 * q^12 + 16 * q^13 + 8 * q^14 - 16 * q^15 + 56 * q^18 - 80 * q^20 - 64 * q^21 - 104 * q^22 - 56 * q^23 - 80 * q^24 + 64 * q^25 + 176 * q^26 + 40 * q^27 + 152 * q^28 + 48 * q^29 + 16 * q^30 + 24 * q^31 + 88 * q^32 - 136 * q^34 - 160 * q^35 - 128 * q^36 + 32 * q^37 - 120 * q^38 + 48 * q^39 + 64 * q^40 + 48 * q^41 + 16 * q^42 - 232 * q^43 + 120 * q^44 - 88 * q^46 + 192 * q^47 + 136 * q^48 + 16 * q^49 + 136 * q^51 - 384 * q^52 - 32 * q^53 + 8 * q^54 + 224 * q^55 - 120 * q^56 + 24 * q^57 + 240 * q^58 - 48 * q^59 + 64 * q^60 - 160 * q^61 - 168 * q^62 + 56 * q^63 - 64 * q^64 - 96 * q^65 - 8 * q^66 + 272 * q^68 + 240 * q^69 + 224 * q^70 + 40 * q^71 + 40 * q^72 + 48 * q^73 - 160 * q^74 - 296 * q^75 + 80 * q^76 - 48 * q^77 - 400 * q^78 - 136 * q^79 - 240 * q^80 - 424 * q^81 - 64 * q^82 - 264 * q^83 - 272 * q^85 + 832 * q^86 + 208 * q^87 + 264 * q^88 + 160 * q^89 + 448 * q^90 + 320 * q^91 + 24 * q^92 - 64 * q^93 + 32 * q^94 + 272 * q^95 - 56 * q^96 + 48 * q^97 - 120 * q^98 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more