LMFDB - Embedded newform 731.2.v.a.36.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(36,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([21, 8]))

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

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

chi := DirichletCharacter("731.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.v (of order $24$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			36.10
Character	$\chi$	$=$	731.36
Dual form			731.2.v.a.264.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55278 - 1.55278i) q^{2} +(-0.793419 - 0.608812i) q^{3} +2.82227i q^{4} +(-1.19124 + 1.55246i) q^{5} +(0.286655 + 2.17736i) q^{6} +(-0.933104 - 1.21604i) q^{7} +(1.27681 - 1.27681i) q^{8} +(-0.517595 - 1.93169i) q^{9} +O(q^{10})$	\(q+(-1.55278 - 1.55278i) q^{2} +(-0.793419 - 0.608812i) q^{3} +2.82227i q^{4} +(-1.19124 + 1.55246i) q^{5} +(0.286655 + 2.17736i) q^{6} +(-0.933104 - 1.21604i) q^{7} +(1.27681 - 1.27681i) q^{8} +(-0.517595 - 1.93169i) q^{9} +(4.26037 - 0.560889i) q^{10} +(3.97385 + 1.64602i) q^{11} +(1.71823 - 2.23925i) q^{12} +(0.237870 + 0.137335i) q^{13} +(-0.439346 + 3.33716i) q^{14} +(1.89031 - 0.506507i) q^{15} +1.67932 q^{16} +(3.92298 + 1.26894i) q^{17} +(-2.19579 + 3.80321i) q^{18} +(0.514028 - 1.91838i) q^{19} +(-4.38146 - 3.36201i) q^{20} +1.53292i q^{21} +(-3.61461 - 8.72645i) q^{22} +(-0.205519 - 1.56107i) q^{23} +(-1.79039 + 0.235709i) q^{24} +(0.303030 + 1.13092i) q^{25} +(-0.156111 - 0.582612i) q^{26} +(-1.91351 + 4.61963i) q^{27} +(3.43201 - 2.63348i) q^{28} +(-0.954412 - 0.125651i) q^{29} +(-3.72174 - 2.14875i) q^{30} +(-0.624662 - 0.479320i) q^{31} +(-5.16124 - 5.16124i) q^{32} +(-2.15081 - 3.72531i) q^{33} +(-4.12115 - 8.06194i) q^{34} +2.99941 q^{35} +(5.45176 - 1.46080i) q^{36} +(-8.35002 - 6.40720i) q^{37} +(-3.77700 + 2.18065i) q^{38} +(-0.105120 - 0.253782i) q^{39} +(0.461204 + 3.50319i) q^{40} +(4.62445 - 11.1644i) q^{41} +(2.38029 - 2.38029i) q^{42} +(-6.23175 - 2.04092i) q^{43} +(-4.64553 + 11.2153i) q^{44} +(3.61545 + 1.49757i) q^{45} +(-2.10488 + 2.74313i) q^{46} +1.18120i q^{47} +(-1.33240 - 1.02239i) q^{48} +(1.20365 - 4.49209i) q^{49} +(1.28554 - 2.22662i) q^{50} +(-2.34002 - 3.39516i) q^{51} +(-0.387596 + 0.671336i) q^{52} +(-1.44495 + 5.39263i) q^{53} +(10.1446 - 4.20201i) q^{54} +(-7.28920 + 4.20842i) q^{55} +(-2.74406 - 0.361263i) q^{56} +(-1.57577 + 1.20913i) q^{57} +(1.28689 + 1.67710i) q^{58} +(6.79794 - 6.79794i) q^{59} +(1.42950 + 5.33497i) q^{60} +(-3.89532 - 5.07648i) q^{61} +(0.225685 + 1.71424i) q^{62} +(-1.86605 + 2.43189i) q^{63} +12.6700i q^{64} +(-0.496567 + 0.205685i) q^{65} +(-2.44486 + 9.12435i) q^{66} +(-3.35093 - 5.80398i) q^{67} +(-3.58131 + 11.0717i) q^{68} +(-0.787335 + 1.36370i) q^{69} +(-4.65744 - 4.65744i) q^{70} +(-0.170270 + 1.29333i) q^{71} +(-3.12728 - 1.80554i) q^{72} +(1.57427 + 0.207256i) q^{73} +(3.01679 + 22.9148i) q^{74} +(0.448090 - 1.08179i) q^{75} +(5.41419 + 1.45073i) q^{76} +(-1.70638 - 6.36829i) q^{77} +(-0.230840 + 0.557298i) q^{78} +(-8.28003 + 6.35349i) q^{79} +(-2.00047 + 2.60707i) q^{80} +(-0.865017 + 0.499418i) q^{81} +(-24.5167 + 10.1551i) q^{82} +(-3.27056 + 12.2059i) q^{83} -4.32632 q^{84} +(-6.64320 + 4.57864i) q^{85} +(6.50745 + 12.8457i) q^{86} +(0.680751 + 0.680751i) q^{87} +(7.17553 - 2.97220i) q^{88} +(7.69475 - 4.44256i) q^{89} +(-3.28861 - 7.93941i) q^{90} +(-0.0549529 - 0.417409i) q^{91} +(4.40576 - 0.580030i) q^{92} +(0.203803 + 0.760603i) q^{93} +(1.83415 - 1.83415i) q^{94} +(2.36587 + 3.08326i) q^{95} +(0.952803 + 7.23726i) q^{96} +(-4.12163 - 9.95050i) q^{97} +(-8.84425 + 5.10623i) q^{98} +(1.12276 - 8.52822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q - 16 q^{2} - 4 q^{3} - 12 q^{5} - 4 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{9}+O(q^{10}) $ 512 * q - 16 * q^2 - 4 * q^3 - 12 * q^5 - 4 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^9	\( 512 q - 16 q^{2} - 4 q^{3} - 12 q^{5} - 4 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{9} - 4 q^{10} - 16 q^{11} + 32 q^{12} + 12 q^{14} - 4 q^{15} - 496 q^{16} - 4 q^{17} - 32 q^{18} - 4 q^{19} + 12 q^{20} - 16 q^{22} + 36 q^{24} + 4 q^{25} + 36 q^{26} - 112 q^{27} + 28 q^{28} - 4 q^{29} - 12 q^{31} + 16 q^{32} + 32 q^{33} + 12 q^{34} - 96 q^{35} - 52 q^{36} + 28 q^{37} - 40 q^{39} + 40 q^{40} - 32 q^{41} + 32 q^{42} + 44 q^{43} + 112 q^{44} + 16 q^{45} - 20 q^{46} - 104 q^{48} + 16 q^{49} - 16 q^{50} - 16 q^{51} + 88 q^{52} - 8 q^{53} - 104 q^{54} - 44 q^{56} - 40 q^{57} - 32 q^{58} - 40 q^{59} - 32 q^{60} - 8 q^{61} + 16 q^{62} + 8 q^{63} - 56 q^{65} - 100 q^{66} - 72 q^{67} + 12 q^{68} - 80 q^{69} - 48 q^{70} + 44 q^{71} + 52 q^{73} - 68 q^{74} + 96 q^{75} - 8 q^{76} + 36 q^{77} + 40 q^{78} + 60 q^{79} + 76 q^{80} - 136 q^{82} - 24 q^{83} + 96 q^{84} - 56 q^{85} - 40 q^{86} - 56 q^{87} - 24 q^{88} + 96 q^{90} - 44 q^{91} - 44 q^{92} - 4 q^{93} + 88 q^{94} - 20 q^{95} + 40 q^{96} - 152 q^{97} - 88 q^{99}+O(q^{100}) \) 512 * q - 16 * q^2 - 4 * q^3 - 12 * q^5 - 4 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^9 - 4 * q^10 - 16 * q^11 + 32 * q^12 + 12 * q^14 - 4 * q^15 - 496 * q^16 - 4 * q^17 - 32 * q^18 - 4 * q^19 + 12 * q^20 - 16 * q^22 + 36 * q^24 + 4 * q^25 + 36 * q^26 - 112 * q^27 + 28 * q^28 - 4 * q^29 - 12 * q^31 + 16 * q^32 + 32 * q^33 + 12 * q^34 - 96 * q^35 - 52 * q^36 + 28 * q^37 - 40 * q^39 + 40 * q^40 - 32 * q^41 + 32 * q^42 + 44 * q^43 + 112 * q^44 + 16 * q^45 - 20 * q^46 - 104 * q^48 + 16 * q^49 - 16 * q^50 - 16 * q^51 + 88 * q^52 - 8 * q^53 - 104 * q^54 - 44 * q^56 - 40 * q^57 - 32 * q^58 - 40 * q^59 - 32 * q^60 - 8 * q^61 + 16 * q^62 + 8 * q^63 - 56 * q^65 - 100 * q^66 - 72 * q^67 + 12 * q^68 - 80 * q^69 - 48 * q^70 + 44 * q^71 + 52 * q^73 - 68 * q^74 + 96 * q^75 - 8 * q^76 + 36 * q^77 + 40 * q^78 + 60 * q^79 + 76 * q^80 - 136 * q^82 - 24 * q^83 + 96 * q^84 - 56 * q^85 - 40 * q^86 - 56 * q^87 - 24 * q^88 + 96 * q^90 - 44 * q^91 - 44 * q^92 - 4 * q^93 + 88 * q^94 - 20 * q^95 + 40 * q^96 - 152 * q^97 - 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.55278	−	1.55278i	−1.09798	−	1.09798i	−0.994646	−	0.103338i	$-0.967048\pi$
$2$	−1.55278	−	1.55278i	−1.09798	−	1.09798i	−0.103338	−	0.994646i	$-0.532952\pi$
$3$	−0.793419	−	0.608812i	−0.458081	−	0.351498i	0.353800	−	0.935321i	$-0.384889\pi$
$3$	−0.793419	−	0.608812i	−0.458081	−	0.351498i	−0.811881	+	0.583823i	$0.801556\pi$
$4$			2.82227i			1.41114i
$5$	−1.19124	+	1.55246i	−0.532740	+	0.694280i	−0.979745	−	0.200252i	$-0.935824\pi$
$5$	−1.19124	+	1.55246i	−0.532740	+	0.694280i	0.447005	+	0.894532i	$0.352491\pi$
$6$	0.286655	+	2.17736i	0.117026	+	0.888904i
$7$	−0.933104	−	1.21604i	−0.352680	−	0.459622i	0.582999	−	0.812473i	$-0.301879\pi$
$7$	−0.933104	−	1.21604i	−0.352680	−	0.459622i	−0.935680	+	0.352851i	$0.885212\pi$
$8$	1.27681	−	1.27681i	0.451422	−	0.451422i
$9$	−0.517595	−	1.93169i	−0.172532	−	0.643897i
$10$	4.26037	−	0.560889i	1.34725	−	0.177369i
$11$	3.97385	+	1.64602i	1.19816	+	0.496294i	0.890404	−	0.455171i	$-0.150422\pi$
$11$	3.97385	+	1.64602i	1.19816	+	0.496294i	0.307757	+	0.951465i	$0.400422\pi$
$12$	1.71823	−	2.23925i	0.496012	−	0.646415i
$13$	0.237870	+	0.137335i	0.0659734	+	0.0380898i	0.532624	−	0.846352i	$-0.321206\pi$
$13$	0.237870	+	0.137335i	0.0659734	+	0.0380898i	−0.466650	+	0.884442i	$0.654539\pi$
$14$	−0.439346	+	3.33716i	−0.117420	+	0.891894i
$15$	1.89031	−	0.506507i	0.488076	−	0.130780i
$16$	1.67932			0.419829
$17$	3.92298	+	1.26894i	0.951463	+	0.307764i
$17$	3.92298	+	1.26894i	0.951463	+	0.307764i
$18$	−2.19579	+	3.80321i	−0.517551	+	0.896425i
$19$	0.514028	−	1.91838i	0.117926	−	0.440106i	−0.881563	−	0.472066i	$-0.843508\pi$
$19$	0.514028	−	1.91838i	0.117926	−	0.440106i	0.999489	+	0.0319601i	$0.0101750\pi$
$20$	−4.38146	−	3.36201i	−0.979724	−	0.751769i
$21$			1.53292i			0.334510i
$22$	−3.61461	−	8.72645i	−0.770638	−	1.86048i
$23$	−0.205519	−	1.56107i	−0.0428536	−	0.325505i	−0.999422	−	0.0339971i	$-0.989176\pi$
$23$	−0.205519	−	1.56107i	−0.0428536	−	0.325505i	0.956568	−	0.291508i	$-0.0941570\pi$
$24$	−1.79039	+	0.235709i	−0.365462	+	0.0481139i
$25$	0.303030	+	1.13092i	0.0606060	+	0.226185i
$26$	−0.156111	−	0.582612i	−0.0306158	−	0.114260i
$27$	−1.91351	+	4.61963i	−0.368256	+	0.889048i
$28$	3.43201	−	2.63348i	0.648589	−	0.497680i
$29$	−0.954412	−	0.125651i	−0.177230	−	0.0233327i	0.0413889	−	0.999143i	$-0.486822\pi$
$29$	−0.954412	−	0.125651i	−0.177230	−	0.0233327i	−0.218619	+	0.975810i	$0.570155\pi$
$30$	−3.72174	−	2.14875i	−0.679493	−	0.392306i
$31$	−0.624662	−	0.479320i	−0.112193	−	0.0860884i	0.551141	−	0.834412i	$-0.314192\pi$
$31$	−0.624662	−	0.479320i	−0.112193	−	0.0860884i	−0.663334	+	0.748323i	$0.730859\pi$
$32$	−5.16124	−	5.16124i	−0.912388	−	0.912388i
$33$	−2.15081	−	3.72531i	−0.374408	−	0.648494i
$34$	−4.12115	−	8.06194i	−0.706771	−	1.38261i
$35$	2.99941			0.506993
$36$	5.45176	−	1.46080i	0.908627	−	0.243466i
$37$	−8.35002	−	6.40720i	−1.37273	−	1.05334i	−0.991672	−	0.128787i	$-0.958892\pi$
$37$	−8.35002	−	6.40720i	−1.37273	−	1.05334i	−0.381062	−	0.924549i	$-0.624442\pi$
$38$	−3.77700	+	2.18065i	−0.612710	+	0.353749i
$39$	−0.105120	−	0.253782i	−0.0168327	−	0.0406377i
$40$	0.461204	+	3.50319i	0.0729228	+	0.553904i
$41$	4.62445	−	11.1644i	0.722217	−	1.74359i	0.0552813	−	0.998471i	$-0.482394\pi$
$41$	4.62445	−	11.1644i	0.722217	−	1.74359i	0.666936	−	0.745115i	$-0.267606\pi$
$42$	2.38029	−	2.38029i	0.367287	−	0.367287i
$43$	−6.23175	−	2.04092i	−0.950332	−	0.311237i
$43$	−6.23175	−	2.04092i	−0.950332	−	0.311237i
$44$	−4.64553	+	11.2153i	−0.700339	+	1.69077i
$45$	3.61545	+	1.49757i	0.538959	+	0.223244i
$46$	−2.10488	+	2.74313i	−0.310347	+	0.404452i
$47$			1.18120i			0.172296i	0.996282	+	0.0861482i	$0.0274558\pi$
$47$			1.18120i			0.172296i	−0.996282	+	0.0861482i	$0.972544\pi$
$48$	−1.33240	−	1.02239i	−0.192316	−	0.147569i
$49$	1.20365	−	4.49209i	0.171950	−	0.641727i
$50$	1.28554	−	2.22662i	0.181803	−	0.314892i
$51$	−2.34002	−	3.39516i	−0.327669	−	0.475418i
$52$	−0.387596	+	0.671336i	−0.0537499	+	0.0930975i
$53$	−1.44495	+	5.39263i	−0.198479	+	0.740735i	0.792859	+	0.609405i	$0.208591\pi$
$53$	−1.44495	+	5.39263i	−0.198479	+	0.740735i	−0.991339	+	0.131330i	$0.958075\pi$
$54$	10.1446	−	4.20201i	1.38050	−	0.571821i
$55$	−7.28920	+	4.20842i	−0.982875	+	0.567463i
$56$	−2.74406	−	0.361263i	−0.366691	−	0.0482758i
$57$	−1.57577	+	1.20913i	−0.208716	+	0.160153i
$58$	1.28689	+	1.67710i	0.168976	+	0.220214i
$59$	6.79794	−	6.79794i	0.885016	−	0.885016i	−0.109023	−	0.994039i	$-0.534772\pi$
$59$	6.79794	−	6.79794i	0.885016	−	0.885016i	0.994039	+	0.109023i	$0.0347723\pi$
$60$	1.42950	+	5.33497i	0.184548	+	0.688742i
$61$	−3.89532	−	5.07648i	−0.498745	−	0.649977i	0.474363	−	0.880330i	$-0.342679\pi$
$61$	−3.89532	−	5.07648i	−0.498745	−	0.649977i	−0.973107	+	0.230353i	$0.926012\pi$
$62$	0.225685	+	1.71424i	0.0286620	+	0.217709i
$63$	−1.86605	+	2.43189i	−0.235101	+	0.306389i
$64$			12.6700i			1.58374i
$65$	−0.496567	+	0.205685i	−0.0615916	+	0.0255121i
$66$	−2.44486	+	9.12435i	−0.300942	+	1.12313i
$67$	−3.35093	−	5.80398i	−0.409381	−	0.709068i	0.585440	−	0.810716i	$-0.300922\pi$
$67$	−3.35093	−	5.80398i	−0.409381	−	0.709068i	−0.994820	+	0.101648i	$0.967589\pi$
$68$	−3.58131	+	11.0717i	−0.434297	+	1.34264i
$69$	−0.787335	+	1.36370i	−0.0947840	+	0.164171i
$70$	−4.65744	−	4.65744i	−0.556670	−	0.556670i
$71$	−0.170270	+	1.29333i	−0.0202073	+	0.153490i	−0.998574	−	0.0533896i	$-0.982997\pi$
$71$	−0.170270	+	1.29333i	−0.0202073	+	0.153490i	0.978366	+	0.206880i	$0.0663308\pi$
$72$	−3.12728	−	1.80554i	−0.368554	−	0.212785i
$73$	1.57427	+	0.207256i	0.184254	+	0.0242575i	0.222089	−	0.975027i	$-0.428713\pi$
$73$	1.57427	+	0.207256i	0.184254	+	0.0242575i	−0.0378344	+	0.999284i	$0.512046\pi$
$74$	3.01679	+	22.9148i	0.350694	+	2.66379i
$75$	0.448090	−	1.08179i	0.0517410	−	0.124914i
$76$	5.41419	+	1.45073i	0.621050	+	0.166410i
$77$	−1.70638	−	6.36829i	−0.194460	−	0.725734i
$78$	−0.230840	+	0.557298i	−0.0261375	+	0.0631016i
$79$	−8.28003	+	6.35349i	−0.931576	+	0.714823i	−0.958583	−	0.284812i	$-0.908069\pi$
$79$	−8.28003	+	6.35349i	−0.931576	+	0.714823i	0.0270074	+	0.999635i	$0.491402\pi$
$80$	−2.00047	+	2.60707i	−0.223660	+	0.291479i
$81$	−0.865017	+	0.499418i	−0.0961130	+	0.0554909i
$82$	−24.5167	+	10.1551i	−2.70741	+	1.12145i
$83$	−3.27056	+	12.2059i	−0.358991	+	1.33977i	0.516396	+	0.856350i	$0.327273\pi$
$83$	−3.27056	+	12.2059i	−0.358991	+	1.33977i	−0.875387	+	0.483422i	$0.839394\pi$
$84$	−4.32632			−0.472040
$85$	−6.64320	+	4.57864i	−0.720556	+	0.496623i
$86$	6.50745	+	12.8457i	0.701717	+	1.38518i
$87$	0.680751	+	0.680751i	0.0729842	+	0.0729842i
$88$	7.17553	−	2.97220i	0.764914	−	0.316838i
$89$	7.69475	−	4.44256i	0.815642	−	0.470911i	−0.0332695	−	0.999446i	$-0.510592\pi$
$89$	7.69475	−	4.44256i	0.815642	−	0.470911i	0.848911	+	0.528535i	$0.177259\pi$
$90$	−3.28861	−	7.93941i	−0.346650	−	0.836887i
$91$	−0.0549529	−	0.417409i	−0.00576063	−	0.0437563i
$92$	4.40576	−	0.580030i	0.459332	−	0.0604723i
$93$	0.203803	+	0.760603i	0.0211334	+	0.0788709i
$94$	1.83415	−	1.83415i	0.189179	−	0.189179i
$95$	2.36587	+	3.08326i	0.242733	+	0.316336i
$96$	0.952803	+	7.23726i	0.0972451	+	0.738650i
$97$	−4.12163	−	9.95050i	−0.418488	−	1.01032i	−0.982786	−	0.184749i	$-0.940853\pi$
$97$	−4.12163	−	9.95050i	−0.418488	−	1.01032i	0.564298	−	0.825572i	$-0.309147\pi$
$98$	−8.84425	+	5.10623i	−0.893404	+	0.515807i
$99$	1.12276	−	8.52822i	0.112842	−	0.857119i
$100$	−3.19178	+	0.855234i	−0.319178	+	0.0855234i
$101$	3.39891	−	5.88709i	0.338205	−	0.585788i	−0.645890	−	0.763430i	$-0.723514\pi$
$101$	3.39891	−	5.88709i	0.338205	−	0.585788i	0.984095	+	0.177643i	$0.0568471\pi$
$102$	−1.63841	+	8.90550i	−0.162226	+	0.881776i
$103$	7.18459	−	12.4441i	0.707919	−	1.22615i	−0.257709	−	0.966222i	$-0.582968\pi$
$103$	7.18459	−	12.4441i	0.707919	−	1.22615i	0.965628	−	0.259928i	$-0.0836990\pi$
$104$	0.479067	−	0.128366i	0.0469764	−	0.0125873i
$105$	−2.37979	−	1.82608i	−0.232244	−	0.178207i
$106$	10.6173	−	6.12989i	1.03124	−	0.595388i
$107$	−6.00275	−	14.4919i	−0.580308	−	1.40099i	−0.892534	−	0.450980i	$-0.851075\pi$
$107$	−6.00275	−	14.4919i	−0.580308	−	1.40099i	0.312226	−	0.950008i	$-0.398925\pi$
$108$	−13.0379	−	5.40046i	−1.25457	−	0.519659i
$109$	8.63344	−	1.13661i	0.826933	−	0.108868i	0.294833	−	0.955549i	$-0.404736\pi$
$109$	8.63344	−	1.13661i	0.826933	−	0.108868i	0.532101	+	0.846681i	$0.321403\pi$
$110$	17.8533	+	4.78378i	1.70225	+	0.456116i
$111$	2.72429	+	10.1672i	0.258578	+	0.965026i
$112$	−1.56698	−	2.04212i	−0.148065	−	0.192963i
$113$	12.5605	+	5.20274i	1.18159	+	0.489433i	0.885009	−	0.465574i	$-0.154152\pi$
$113$	12.5605	+	5.20274i	1.18159	+	0.489433i	0.296586	+	0.955006i	$0.404152\pi$
$114$	4.32435	+	0.569312i	0.405013	+	0.0533209i
$115$	2.66831	+	1.54055i	0.248822	+	0.143657i
$116$	0.354621	−	2.69361i	0.0329257	−	0.250096i
$117$	0.142167	−	0.530576i	0.0131434	−	0.0490518i
$118$	−21.1114			−1.94347
$119$	−2.11746	−	5.95458i	−0.194107	−	0.545855i
$120$	1.76686	−	3.06029i	0.161291	−	0.279365i
$121$	5.30392	+	5.30392i	0.482174	+	0.482174i
$122$	−1.83409	+	13.9313i	−0.166050	+	1.26128i
$123$	−10.4661	+	6.04263i	−0.943700	+	0.544846i
$124$	1.35277	−	1.76297i	0.121482	−	0.158319i
$125$	−11.1561	−	4.62099i	−0.997829	−	0.413314i
$126$	6.67377	−	0.878619i	0.594547	−	0.0782736i
$127$	10.1695	−	10.1695i	0.902396	−	0.902396i	−0.0932473	−	0.995643i	$-0.529725\pi$
$127$	10.1695	−	10.1695i	0.902396	−	0.902396i	0.995643	+	0.0932473i	$0.0297247\pi$
$128$	9.35121	−	9.35121i	0.826538	−	0.826538i
$129$	3.70185	+	5.41326i	0.325930	+	0.476611i
$130$	1.09045	+	0.451678i	0.0956385	+	0.0396147i
$131$	3.81894	+	9.21975i	0.333663	+	0.805533i	0.998295	+	0.0583629i	$0.0185881\pi$
$131$	3.81894	+	9.21975i	0.333663	+	0.805533i	−0.664633	+	0.747170i	$0.731412\pi$
$132$	10.5139	−	6.07018i	0.915114	−	0.528341i
$133$	−2.81248	+	1.16497i	−0.243873	+	0.101015i
$134$	−3.80905	+	14.2156i	−0.329052	+	1.22804i
$135$	−4.89232	−	8.47374i	−0.421064	−	0.729304i
$136$	6.62912	−	3.38871i	0.568443	−	0.290580i
$137$	7.83415			0.669316			0.334658	−	0.942340i	$-0.391379\pi$
$137$	7.83415			0.669316			0.334658	+	0.942340i	$0.391379\pi$
$138$	3.34010	−	0.894976i	0.284328	−	0.0761854i
$139$	−16.0912	−	12.3472i	−1.36483	−	1.04727i	−0.992892	−	0.119019i	$-0.962025\pi$
$139$	−16.0912	−	12.3472i	−1.36483	−	1.04727i	−0.371943	−	0.928256i	$-0.621308\pi$
$140$			8.46516i			0.715437i
$141$	0.719131	−	0.937190i	0.0605618	−	0.0789257i
$142$	2.27265	−	1.74387i	0.190717	−	0.146342i
$143$	0.719206	+	0.937287i	0.0601430	+	0.0783799i
$144$	−0.869206	−	3.24392i	−0.0724338	−	0.270327i
$145$	1.33200	−	1.33200i	0.110617	−	0.110617i
$146$	−2.12267	−	2.76632i	−0.175674	−	0.228942i
$147$	−3.68984	+	2.83131i	−0.304333	+	0.233523i
$148$	18.0829	−	23.5660i	1.48640	−	1.93712i
$149$	15.8332	−	9.14128i	1.29710	−	0.748883i	0.317200	−	0.948359i	$-0.397257\pi$
$149$	15.8332	−	9.14128i	1.29710	−	0.748883i	0.979903	+	0.199476i	$0.0639240\pi$
$150$	−2.37556	+	0.983991i	−0.193964	+	0.0803425i
$151$	9.67234	+	9.67234i	0.787124	+	0.787124i	0.981022	−	0.193898i	$-0.0621130\pi$
$151$	9.67234	+	9.67234i	0.787124	+	0.787124i	−0.193898	+	0.981022i	$0.562113\pi$
$152$	−1.79309	−	3.10573i	−0.145439	−	0.251908i
$153$	0.420691	−	8.23479i	0.0340108	−	0.665743i
$154$	−7.23894	+	12.5382i	−0.583330	+	1.01036i
$155$	1.48825	−	0.398775i	0.119539	−	0.0320303i
$156$	0.716243	−	0.296678i	0.0573454	−	0.0237532i
$157$	3.87143	+	2.23517i	0.308974	+	0.178386i	0.646467	−	0.762942i	$-0.276246\pi$
$157$	3.87143	+	2.23517i	0.308974	+	0.178386i	−0.337493	+	0.941328i	$0.609579\pi$
$158$	22.7227	+	2.99150i	1.80772	+	0.237991i
$159$	4.42955	−	3.39891i	0.351286	−	0.269551i
$160$	14.1609	−	1.86432i	1.11952	−	0.147387i
$161$	−1.70656	+	1.70656i	−0.134496	+	0.134496i
$162$	2.11867	+	0.567696i	0.166459	+	0.0446024i
$163$	−6.50855	−	8.48211i	−0.509789	−	0.664370i	0.465566	−	0.885013i	$-0.345851\pi$
$163$	−6.50855	−	8.48211i	−0.509789	−	0.664370i	−0.975355	+	0.220644i	$0.929184\pi$
$164$	31.5090	+	13.0515i	2.46044	+	1.01915i
$165$	8.34553	+	1.09871i	0.649698	+	0.0855344i
$166$	24.0316	−	13.8747i	1.86521	−	1.07688i
$167$	2.88154	+	2.21108i	0.222980	+	0.171099i	0.714210	−	0.699931i	$-0.246786\pi$
$167$	2.88154	+	2.21108i	0.222980	+	0.171099i	−0.491230	+	0.871030i	$0.663453\pi$
$168$	1.95725	+	1.95725i	0.151005	+	0.151005i
$169$	−6.46228	−	11.1930i	−0.497098	−	0.861000i
$170$	17.4251	+	3.20582i	1.33644	+	0.245875i
$171$	−3.97177			−0.303729
$172$	5.76003	−	17.5877i	0.439198	−	1.34105i
$173$	−15.9407	+	6.60285i	−1.21195	+	0.502005i	−0.894841	−	0.446385i	$-0.852711\pi$
$173$	−15.9407	+	6.60285i	−1.21195	+	0.502005i	−0.317106	+	0.948390i	$0.602711\pi$
$174$		−	2.11412i		−	0.160271i
$175$	1.09250	−	1.42377i	0.0825849	−	0.107627i
$176$	6.67335	+	2.76419i	0.503023	+	0.208359i
$177$	−9.53228	+	1.25495i	−0.716490	+	0.0943277i
$178$	−18.8466	−	5.04994i	−1.41261	−	0.378509i
$179$	−3.66142	−	13.6646i	−0.273667	−	1.02134i	−0.956729	−	0.290980i	$-0.906019\pi$
$179$	−3.66142	−	13.6646i	−0.273667	−	1.02134i	0.683062	−	0.730360i	$-0.260648\pi$
$180$	−4.22655	+	10.2038i	−0.315028	+	0.760545i
$181$	−5.75144	+	4.41323i	−0.427501	+	0.328033i	−0.800000	−	0.599999i	$-0.795167\pi$
$181$	−5.75144	+	4.41323i	−0.427501	+	0.328033i	0.372500	+	0.928032i	$0.378501\pi$
$182$	−0.562815	+	0.733475i	−0.0417186	+	0.0543688i
$183$			6.39930i			0.473050i
$184$	−2.25560	−	1.73078i	−0.166285	−	0.127595i
$185$	19.8938	−	5.33053i	1.46262	−	0.391908i
$186$	0.864590	−	1.49751i	0.0633948	−	0.109803i
$187$	13.5006	+	11.4999i	0.987264	+	0.840956i
$188$	−3.33368			−0.243134
$189$	7.40318	−	1.98368i	0.538502	−	0.144291i
$190$	1.11395	−	8.46132i	0.0808147	−	0.613849i
$191$	0.203321	−	0.117388i	0.0147118	−	0.00849386i	−0.492626	−	0.870241i	$-0.663963\pi$
$191$	0.203321	−	0.117388i	0.0147118	−	0.00849386i	0.507338	+	0.861747i	$0.330630\pi$
$192$	7.71362	−	10.0526i	0.556683	−	0.725483i
$193$	7.52695	+	3.11776i	0.541802	+	0.224422i	0.636763	−	0.771059i	$-0.280273\pi$
$193$	7.52695	+	3.11776i	0.541802	+	0.224422i	−0.0949616	+	0.995481i	$0.530273\pi$
$194$	−9.05097	+	21.8510i	−0.649822	+	1.56881i
$195$	0.519210	+	0.139122i	0.0371814	+	0.00996272i
$196$	12.6779	+	3.39703i	0.905565	+	0.242645i
$197$	1.75394	+	2.28579i	0.124963	+	0.162855i	0.851645	−	0.524119i	$-0.175605\pi$
$197$	1.75394	+	2.28579i	0.124963	+	0.162855i	−0.726682	+	0.686974i	$0.758939\pi$
$198$	−14.9859	+	11.4991i	−1.06500	+	0.817204i
$199$	−5.84037	−	14.0999i	−0.414013	−	0.999516i	−0.984049	−	0.177896i	$-0.943071\pi$
$199$	−5.84037	−	14.0999i	−0.414013	−	0.999516i	0.570036	−	0.821620i	$-0.306929\pi$
$200$	1.83089	+	1.05707i	0.129464	+	0.0747459i
$201$	−0.874840	+	6.64507i	−0.0617065	+	0.468707i
$202$	−14.4192	+	3.86360i	−1.01453	+	0.271842i
$203$	0.737768	+	1.27785i	0.0517812	+	0.0896876i
$204$	9.58208	−	6.60418i	0.670880	−	0.462385i
$205$	11.8234	+	20.4788i	0.825783	+	1.43030i
$206$	−30.4791	+	8.16684i	−2.12358	+	0.569011i
$207$	−2.90913	+	1.20500i	−0.202198	+	0.0837532i
$208$	0.399460	+	0.230628i	0.0276976	+	0.0159912i
$209$	5.20036	−	6.77725i	0.359717	−	0.468792i
$210$	0.859796	+	6.53080i	0.0593316	+	0.450668i
$211$	1.54732	−	3.73557i	0.106522	−	0.257167i	−0.861627	−	0.507543i	$-0.830554\pi$
$211$	1.54732	−	3.73557i	0.106522	−	0.257167i	0.968149	+	0.250375i	$0.0805540\pi$
$212$	−15.2195	−	4.07805i	−1.04528	−	0.280081i
$213$	0.922490	−	0.922490i	0.0632080	−	0.0632080i
$214$	−13.1819	+	31.8238i	−0.901093	+	2.17543i
$215$	10.5920	−	7.24329i	0.722365	−	0.493989i
$216$	3.45521	+	8.34161i	0.235097	+	0.567574i
$217$			1.20687i			0.0819278i
$218$	−15.1708	−	11.6409i	−1.02749	−	0.788424i
$219$	−1.12287	−	1.12287i	−0.0758768	−	0.0758768i
$220$	−11.8773	−	20.5721i	−0.800768	−	1.38697i
$221$	0.758892	+	0.840605i	0.0510486	+	0.0565452i
$222$	11.5572	−	20.0177i	0.775669	−	1.34350i
$223$	−7.95379	−	7.95379i	−0.532625	−	0.532625i	0.388727	−	0.921353i	$-0.372915\pi$
$223$	−7.95379	−	7.95379i	−0.532625	−	0.532625i	−0.921353	+	0.388727i	$0.872915\pi$
$224$	−1.46033	+	11.0923i	−0.0975722	+	0.741134i
$225$	2.02775	−	1.17072i	0.135183	−	0.0780481i
$226$	−11.4250	−	27.5825i	−0.759983	−	1.83476i
$227$	1.24939	+	9.49002i	0.0829246	+	0.629875i	0.981557	+	0.191172i	$0.0612287\pi$
$227$	1.24939	+	9.49002i	0.0829246	+	0.629875i	−0.898632	+	0.438703i	$0.855438\pi$
$228$	−3.41250	−	4.44726i	−0.225998	−	0.294527i
$229$	3.01880	+	11.2663i	0.199488	+	0.744499i	0.991059	+	0.133422i	$0.0425966\pi$
$229$	3.01880	+	11.2663i	0.199488	+	0.744499i	−0.791571	+	0.611077i	$0.790737\pi$
$230$	−1.75117	−	6.53546i	−0.115469	−	0.430935i
$231$	−2.52322	+	6.09159i	−0.166016	+	0.400797i
$232$	−1.37904	+	1.05817i	−0.0905383	+	0.0694725i
$233$	2.14018	+	0.281761i	0.140208	+	0.0184588i	0.200304	−	0.979734i	$-0.435807\pi$
$233$	2.14018	+	0.281761i	0.140208	+	0.0184588i	−0.0600954	+	0.998193i	$0.519140\pi$
$234$	−1.04462	+	0.603114i	−0.0682893	+	0.0394268i
$235$	−1.83377	−	1.40710i	−0.119622	−	0.0917891i
$236$	19.1856	+	19.1856i	1.24888	+	1.24888i
$237$	10.4376			0.677996
$238$	−5.95822	+	12.5341i	−0.386214	+	0.812467i
$239$	9.03384	+	15.6471i	0.584350	+	1.01212i	0.994956	+	0.100312i	$0.0319840\pi$
$239$	9.03384	+	15.6471i	0.584350	+	1.01212i	−0.410606	+	0.911813i	$0.634683\pi$
$240$	3.17443	−	0.850585i	0.204908	−	0.0549050i
$241$	−1.32725	+	10.0815i	−0.0854958	+	0.649405i	0.894018	+	0.448030i	$0.147874\pi$
$241$	−1.32725	+	10.0815i	−0.0854958	+	0.649405i	−0.979514	+	0.201375i	$0.935459\pi$
$242$		−	16.4717i		−	1.05884i
$243$	15.8628	+	2.08838i	1.01760	+	0.133969i
$244$	14.3272	−	10.9937i	0.917206	−	0.703797i
$245$	5.53993	+	7.21978i	0.353933	+	0.461255i
$246$	25.6346	+	6.86876i	1.63440	+	0.437936i
$247$	0.385732	−	0.385732i	0.0245435	−	0.0245435i
$248$	−1.40958	+	0.185575i	−0.0895084	+	0.0117840i
$249$	10.0260	−	7.69324i	0.635374	−	0.487539i
$250$	10.1476	+	24.4984i	0.641788	+	1.54941i
$251$	−20.1479	−	11.6324i	−1.27172	−	0.734230i	−0.296412	−	0.955060i	$-0.595790\pi$
$251$	−20.1479	−	11.6324i	−1.27172	−	0.734230i	−0.975312	+	0.220830i	$0.929123\pi$
$252$	−6.86345	−	5.26651i	−0.432357	−	0.331759i
$253$	1.75285	−	6.54174i	0.110201	−	0.411276i
$254$	−31.5820			−1.98163
$255$	8.05838	+	0.411679i	0.504635	+	0.0257803i
$256$	−3.70091			−0.231307
$257$	−15.8447	−	15.8447i	−0.988364	−	0.988364i	0.0115692	−	0.999933i	$-0.496317\pi$
$257$	−15.8447	−	15.8447i	−0.988364	−	0.988364i	−0.999933	+	0.0115692i	$0.996317\pi$
$258$	2.65745	−	14.1538i	0.165446	−	0.881178i
$259$			16.1326i			1.00243i
$260$	−0.580499	−	1.40145i	−0.0360010	−	0.0869142i
$261$	0.251280	+	1.90866i	0.0155539	+	0.118143i
$262$	8.38628	−	20.2463i	0.518106	−	1.25082i
$263$	−16.0375	−	4.29724i	−0.988915	−	0.264979i	−0.272120	−	0.962263i	$-0.587725\pi$
$263$	−16.0375	−	4.29724i	−0.988915	−	0.264979i	−0.716795	+	0.697284i	$0.754392\pi$
$264$	−7.50272	−	2.01035i	−0.461760	−	0.123728i
$265$	−6.65054	−	8.66715i	−0.408539	−	0.532419i
$266$	6.17611	+	2.55823i	0.378681	+	0.156855i
$267$	−8.80985	−	1.15984i	−0.539154	−	0.0709810i
$268$	16.3804	−	9.45723i	1.00059	−	0.577693i
$269$	6.19317	−	2.56529i	0.377604	−	0.156409i	−0.185805	−	0.982587i	$-0.559489\pi$
$269$	6.19317	−	2.56529i	0.377604	−	0.156409i	0.563409	+	0.826178i	$0.309489\pi$
$270$	−5.56118	+	20.7546i	−0.338443	+	1.26308i
$271$	−5.99327	+	10.3806i	−0.364065	+	0.630579i	−0.988626	−	0.150397i	$-0.951945\pi$
$271$	−5.99327	+	10.3806i	−0.364065	+	0.630579i	0.624561	+	0.780976i	$0.285278\pi$
$272$	6.58793	+	2.13096i	0.399452	+	0.129208i
$273$	−0.210523	+	0.364636i	−0.0127414	+	0.0220688i
$274$	−12.1647	−	12.1647i	−0.734898	−	0.734898i
$275$	−0.657330	+	4.99291i	−0.0396385	+	0.301084i
$276$	−3.84875	−	2.22207i	−0.231667	−	0.133753i
$277$	14.8002	−	19.2880i	0.889259	−	1.15891i	−0.0972599	−	0.995259i	$-0.531008\pi$
$277$	14.8002	−	19.2880i	0.889259	−	1.15891i	0.986519	−	0.163646i	$-0.0523255\pi$
$278$	5.81359	+	44.1586i	0.348676	+	2.64846i
$279$	−0.602576	+	1.45475i	−0.0360753	+	0.0870934i
$280$	3.82969	−	3.82969i	0.228868	−	0.228868i
$281$	27.5721	+	7.38792i	1.64481	+	0.440726i	0.958154	−	0.286253i	$-0.0924097\pi$
$281$	27.5721	+	7.38792i	1.64481	+	0.440726i	0.686660	+	0.726979i	$0.259076\pi$
$282$	−2.57191	+	0.338598i	−0.153155	+	0.0201632i
$283$	−18.0382	+	13.8412i	−1.07226	+	0.822772i	−0.984851	−	0.173401i	$-0.944524\pi$
$283$	−18.0382	+	13.8412i	−1.07226	+	0.822772i	−0.0874061	+	0.996173i	$0.527858\pi$
$284$	−3.65013	−	0.480549i	−0.216595	−	0.0285153i
$285$		−	3.88669i		−	0.230227i
$286$	0.338633	−	2.57218i	0.0200238	−	0.152096i
$287$	−17.8915	+	4.79401i	−1.05610	+	0.282982i
$288$	−7.29849	+	12.6414i	−0.430068	+	0.744899i
$289$	13.7796	+	9.95608i	0.810563	+	0.585652i
$290$	−4.13662			−0.242911
$291$	−2.78780	+	10.4042i	−0.163424	+	0.609906i
$292$	−0.584934	+	4.44302i	−0.0342307	+	0.260008i
$293$		−	24.9909i		−	1.45999i	−0.683455	−	0.729993i	$-0.739523\pi$
$293$		−	24.9909i		−	1.45999i	0.683455	−	0.729993i	$-0.260477\pi$
$294$	10.1259	+	1.33310i	0.590557	+	0.0777482i
$295$	2.45552	+	18.6515i	0.142966	+	1.08593i
$296$	−18.8422	+	2.48063i	−1.09518	+	0.144183i
$297$	−15.2080	+	15.2080i	−0.882459	+	0.882459i
$298$	−38.7799	−	10.3910i	−2.24646	−	0.601937i
$299$	0.165502	−	0.399557i	0.00957122	−	0.0231070i
$300$	3.05309	+	1.26463i	0.176270	+	0.0730136i
$301$	3.33302	+	9.48247i	0.192112	+	0.546560i
$302$		−	30.0381i		−	1.72850i
$303$	−6.28090	+	2.60163i	−0.360828	+	0.149460i
$304$	0.863216	−	3.22156i	0.0495088	−	0.184769i
$305$	12.5213			0.716967
$306$	−13.4401	+	12.1336i	−0.768318	+	0.693632i
$307$	−5.09643	−	8.82727i	−0.290868	−	0.503799i	0.683147	−	0.730281i	$-0.260611\pi$
$307$	−5.09643	−	8.82727i	−0.290868	−	0.503799i	−0.974015	+	0.226482i	$0.927278\pi$
$308$	17.9731	−	4.81587i	1.02411	−	0.274409i
$309$	−13.2765	+	5.49930i	−0.755273	+	0.312844i
$310$	−2.93014	−	1.69171i	−0.166421	−	0.0960829i
$311$	−11.7262	+	15.2819i	−0.664931	+	0.866555i	−0.997056	−	0.0766801i	$-0.975568\pi$
$311$	−11.7262	+	15.2819i	−0.664931	+	0.866555i	0.332124	+	0.943236i	$0.392235\pi$
$312$	−0.458252	−	0.189814i	−0.0259434	−	0.0107461i
$313$	26.8119	−	3.52985i	1.51550	−	0.199519i	0.673575	−	0.739119i	$-0.264758\pi$
$313$	26.8119	−	3.52985i	1.51550	−	0.199519i	0.841922	+	0.539600i	$0.181424\pi$
$314$	−2.54076	−	9.48223i	−0.143383	−	0.535113i
$315$	−1.55248	−	5.79393i	−0.0874723	−	0.326451i
$316$	−17.9313	−	23.3685i	−1.00871	−	1.31458i
$317$	−3.89038	−	1.61145i	−0.218505	−	0.0905078i	0.270746	−	0.962651i	$-0.412730\pi$
$317$	−3.89038	−	1.61145i	−0.218505	−	0.0905078i	−0.489251	+	0.872143i	$0.662730\pi$
$318$	−12.1559	−	1.60036i	−0.681670	−	0.0897435i
$319$	−3.58586	−	2.07030i	−0.200770	−	0.115915i
$320$	−19.6696	−	15.0930i	−1.09956	−	0.843724i
$321$	−4.06016	+	15.1527i	−0.226616	+	0.845743i
$322$	5.29983			0.295348
$323$	4.45084	−	6.87349i	0.247651	−	0.382451i
$324$	−1.40949	−	2.44131i	−0.0783052	−	0.135629i
$325$	−0.0832330	+	0.310630i	−0.00461694	+	0.0172306i
$326$	−3.06451	+	23.2772i	−0.169727	+	1.28921i
$327$	−7.54192	−	4.35433i	−0.417069	−	0.240795i
$328$	−8.35030	−	20.1594i	−0.461068	−	1.11312i
$329$	1.43640	−	1.10219i	0.0791911	−	0.0607655i
$330$	−11.2527	−	14.6649i	−0.619443	−	0.807274i
$331$	−0.242311	−	0.904319i	−0.0133186	−	0.0497059i	0.958947	−	0.283586i	$-0.0915242\pi$
$331$	−0.242311	−	0.904319i	−0.0133186	−	0.0497059i	−0.972265	+	0.233880i	$0.924858\pi$
$332$	−34.4484	−	9.23042i	−1.89060	−	0.506585i
$333$	−8.05479	+	19.4460i	−0.441400	+	1.06563i
$334$	−1.04107	−	7.90774i	−0.0569651	−	0.432693i
$335$	13.0022	+	1.71177i	0.710385	+	0.0935240i
$336$			2.57426i			0.140437i
$337$	2.28296	−	17.3408i	0.124361	−	0.944612i	−0.809536	−	0.587070i	$-0.800281\pi$
$337$	2.28296	−	17.3408i	0.124361	−	0.944612i	0.933897	−	0.357542i	$-0.116385\pi$
$338$	−7.34578	+	27.4148i	−0.399558	+	1.49117i
$339$	−6.79827	−	11.7750i	−0.369231	−	0.639528i
$340$	−12.9222	−	18.7489i	−0.700804	−	1.01680i
$341$	−1.69334	−	2.93295i	−0.0916995	−	0.158828i
$342$	6.16730	+	6.16730i	0.333490	+	0.333490i
$343$	−16.4985	+	6.83391i	−0.890836	+	0.368996i
$344$	−10.5627	+	5.35091i	−0.569500	+	0.288502i
$345$	−1.17919	−	2.84681i	−0.0634852	−	0.153267i
$346$	35.0052	+	14.4996i	1.88189	+	0.779505i
$347$	10.5649	−	1.39090i	0.567155	−	0.0746673i	0.158504	−	0.987358i	$-0.449333\pi$
$347$	10.5649	−	1.39090i	0.567155	−	0.0746673i	0.408650	+	0.912691i	$0.366000\pi$
$348$	−1.92127	+	1.92127i	−0.102991	+	0.102991i
$349$	−6.23438	−	1.67050i	−0.333719	−	0.0894197i	0.0880687	−	0.996114i	$-0.471930\pi$
$349$	−6.23438	−	1.67050i	−0.333719	−	0.0894197i	−0.421787	+	0.906695i	$0.638597\pi$
$350$	−3.90721	+	0.514394i	−0.208849	+	0.0274955i
$351$	−1.08960	+	0.836082i	−0.0581587	+	0.0446267i
$352$	−12.0145	−	29.0055i	−0.640374	−	1.54600i
$353$	−6.61212	−	3.81751i	−0.351928	−	0.203185i	0.313606	−	0.949553i	$-0.398463\pi$
$353$	−6.61212	−	3.81751i	−0.351928	−	0.203185i	−0.665534	+	0.746368i	$0.731796\pi$
$354$	16.7502	+	12.8529i	0.890265	+	0.683124i
$355$	−1.80501	−	1.80501i	−0.0957998	−	0.0957998i
$356$	12.5381	+	21.7167i	0.664520	+	1.15098i
$357$	−1.94519	+	6.01361i	−0.102950	+	0.318274i
$358$	−15.5328	+	26.9036i	−0.820933	+	1.42190i
$359$	−17.6818	+	4.73782i	−0.933208	+	0.250052i	−0.693222	−	0.720724i	$-0.743810\pi$
$359$	−17.6818	+	4.73782i	−0.933208	+	0.250052i	−0.239986	+	0.970776i	$0.577143\pi$
$360$	6.52837	−	2.70414i	0.344075	−	0.142521i
$361$	13.0385	+	7.52780i	0.686239	+	0.396200i
$362$	15.7835	+	2.07794i	0.829564	+	0.109214i
$363$	−0.979141	−	7.43732i	−0.0513916	−	0.390358i
$364$	1.17804	−	0.155092i	0.0617462	−	0.00812904i
$365$	−2.19709	+	2.19709i	−0.115001	+	0.115001i
$366$	9.93672	−	9.93672i	0.519401	−	0.519401i
$367$	−14.6718	+	1.93158i	−0.765863	+	0.100828i	−0.503329	−	0.864095i	$-0.667892\pi$
$367$	−14.6718	+	1.93158i	−0.765863	+	0.100828i	−0.262534	+	0.964923i	$0.584558\pi$
$368$	−0.345131	−	2.62153i	−0.0179912	−	0.136657i
$369$	−23.9598	−	3.15436i	−1.24730	−	0.164210i
$370$	−39.1679	−	22.6136i	−2.03624	−	1.17563i
$371$	7.90597	−	3.27476i	0.410457	−	0.170017i
$372$	−2.14663	+	0.575188i	−0.111298	+	0.0298221i
$373$	−3.44313	+	5.96368i	−0.178279	+	0.308788i	−0.941291	−	0.337596i	$-0.890386\pi$
$373$	−3.44313	+	5.96368i	−0.178279	+	0.308788i	0.763012	+	0.646384i	$0.223720\pi$
$374$	−3.10669	−	38.8204i	−0.160643	−	2.00736i
$375$	6.03812	+	10.4583i	0.311807	+	0.540066i
$376$	1.50818	+	1.50818i	0.0777783	+	0.0777783i
$377$	−0.209770	−	0.160962i	−0.0108037	−	0.00828998i
$378$	−14.5758	−	8.41532i	−0.749696	−	0.432837i
$379$	5.99756	+	14.4794i	0.308074	+	0.743756i	0.999767	+	0.0215648i	$0.00686482\pi$
$379$	5.99756	+	14.4794i	0.308074	+	0.743756i	−0.691694	+	0.722191i	$0.743135\pi$
$380$	−8.70181	+	6.67713i	−0.446393	+	0.342530i
$381$	−14.2600	+	1.87736i	−0.730560	+	0.0961801i
$382$	−0.497991	−	0.133436i	−0.0254794	−	0.00682720i
$383$	−20.8688	+	20.8688i	−1.06635	+	1.06635i	−0.0687116	+	0.997637i	$0.521889\pi$
$383$	−20.8688	+	20.8688i	−1.06635	+	1.06635i	−0.997637	+	0.0687116i	$0.978111\pi$
$384$	−13.1126	+	1.72630i	−0.669148	+	0.0880950i
$385$	11.9192	+	4.93710i	0.607459	+	0.251618i
$386$	−6.84651	−	16.5289i	−0.348478	−	0.841301i
$387$	−0.716899	+	13.0942i	−0.0364420	+	0.665614i
$388$	28.0830	−	11.6324i	1.42570	−	0.590544i
$389$	7.62205	+	7.62205i	0.386453	+	0.386453i	0.873420	−	0.486967i	$-0.161897\pi$
$389$	7.62205	+	7.62205i	0.386453	+	0.386453i	−0.486967	+	0.873420i	$0.661897\pi$
$390$	−0.590194	−	1.02225i	−0.0298857	−	0.0517635i
$391$	1.17466	−	6.38483i	0.0594052	−	0.322895i
$392$	−4.19872	−	7.27240i	−0.212068	−	0.367312i
$393$	2.58307	−	9.64015i	0.130299	−	0.486281i
$394$	0.825833	−	6.27283i	0.0416049	−	0.316020i
$395$		−	20.4229i		−	1.02759i
$396$	24.0690	+	3.16874i	1.20951	+	0.159235i
$397$	3.49210	+	26.5251i	0.175263	+	1.33126i	0.822411	+	0.568893i	$0.192628\pi$
$397$	3.49210	+	26.5251i	0.175263	+	1.33126i	−0.647148	+	0.762364i	$0.724038\pi$
$398$	−12.8253	+	30.9629i	−0.642873	+	1.55203i
$399$	2.94072	+	0.787963i	0.147220	+	0.0394475i
$400$	0.508883	+	1.89918i	0.0254442	+	0.0949589i
$401$	18.5974	+	24.2366i	0.928710	+	1.21032i	0.977377	+	0.211504i	$0.0678360\pi$
$401$	18.5974	+	24.2366i	0.928710	+	1.21032i	−0.0486671	+	0.998815i	$0.515497\pi$
$402$	11.6768	−	8.95992i	0.582386	−	0.446880i
$403$	−0.0827614	−	0.199804i	−0.00412264	−	0.00995293i
$404$	16.6150	+	9.59267i	0.826627	+	0.477253i
$405$	0.255120	−	1.93783i	0.0126770	−	0.0962915i
$406$	0.838634	−	3.12982i	0.0416207	−	0.155331i
$407$	−22.6353	−	39.2055i	−1.12199	−	1.94335i
$408$	−7.32276	−	1.34722i	−0.362531	−	0.0666973i
$409$	32.8893			1.62627			0.813137	−	0.582073i	$-0.197758\pi$
$409$	32.8893			1.62627			0.813137	+	0.582073i	$0.197758\pi$
$410$	13.4399	−	50.1583i	0.663748	−	2.47714i
$411$	−6.21576	−	4.76952i	−0.306601	−	0.235263i
$412$	35.1206	+	20.2769i	1.73027	+	0.998970i
$413$	−14.6098	−	1.92341i	−0.718900	−	0.0946450i
$414$	6.38835	+	2.64614i	0.313970	+	0.130051i
$415$	−15.0531	−	19.6176i	−0.738928	−	0.962990i
$416$	−0.518890	−	1.93652i	−0.0254407	−	0.0949459i
$417$	5.24993	+	19.5930i	0.257090	+	0.959473i
$418$	−18.5986	+	2.44856i	−0.909689	+	0.119763i
$419$	1.01278	+	0.419508i	0.0494776	+	0.0204943i	0.407285	−	0.913301i	$-0.366476\pi$
$419$	1.01278	+	0.419508i	0.0494776	+	0.0204943i	−0.357807	+	0.933795i	$0.616476\pi$
$420$	5.15369	−	6.71642i	0.251474	−	0.327728i
$421$	−7.49273	−	4.32593i	−0.365173	−	0.210833i	0.306174	−	0.951975i	$-0.400951\pi$
$421$	−7.49273	−	4.32593i	−0.365173	−	0.210833i	−0.671348	+	0.741143i	$0.734284\pi$
$422$	−8.20319	+	3.39787i	−0.399325	+	0.165406i
$423$	2.28172	−	0.611385i	0.110941	−	0.0297266i
$424$	5.04045	+	8.73032i	0.244786	+	0.423982i
$425$	−0.246297	+	4.82112i	−0.0119471	+	0.233859i
$426$	−2.86486			−0.138803
$427$	−2.53849	+	9.47377i	−0.122846	+	0.458468i
$428$	40.9002	−	16.9414i	1.97699	−	0.818894i
$429$		−	1.18152i		−	0.0570445i
$430$	−27.6943	−	5.19975i	−1.33554	−	0.250754i
$431$	1.24038	+	0.513782i	0.0597469	+	0.0247480i	0.412357	−	0.911022i	$-0.364706\pi$
$431$	1.24038	+	0.513782i	0.0597469	+	0.0247480i	−0.352610	+	0.935770i	$0.614706\pi$
$432$	−3.21339	+	7.75782i	−0.154604	+	0.373248i
$433$	2.76274	+	0.740274i	0.132769	+	0.0355753i	0.324591	−	0.945854i	$-0.394773\pi$
$433$	2.76274	+	0.740274i	0.132769	+	0.0355753i	−0.191823	+	0.981430i	$0.561440\pi$
$434$	1.87401	−	1.87401i	0.0899554	−	0.0899554i
$435$	−1.86778	+	0.245897i	−0.0895530	+	0.0117899i
$436$	3.20784	+	24.3659i	0.153627	+	1.16692i
$437$	−3.10036	−	0.408170i	−0.148310	−	0.0195254i
$438$			3.48716i			0.166623i
$439$	2.07081	−	15.7293i	0.0988342	−	0.750720i	−0.868225	−	0.496170i	$-0.834739\pi$
$439$	2.07081	−	15.7293i	0.0988342	−	0.750720i	0.967060	−	0.254550i	$-0.0819274\pi$
$440$	−3.93358	+	14.6803i	−0.187526	+	0.699857i
$441$	−9.30033			−0.442873
$442$	0.126883	−	2.48367i	0.00603523	−	0.118136i
$443$	1.39135	−	2.40989i	0.0661050	−	0.114497i	−0.831079	−	0.556155i	$-0.812276\pi$
$443$	1.39135	−	2.40989i	0.0661050	−	0.114497i	0.897184	+	0.441658i	$0.145609\pi$
$444$	−28.6946	+	7.68869i	−1.36178	+	0.364889i
$445$	−2.26942	+	17.2379i	−0.107581	+	0.817157i
$446$			24.7010i			1.16963i
$447$	−18.1277	−	2.38655i	−0.857409	−	0.112880i
$448$	15.4072	−	11.8224i	0.727923	−	0.558555i
$449$	−21.2887	+	2.80271i	−1.00468	+	0.132268i	−0.614870	−	0.788628i	$-0.710792\pi$
$449$	−21.2887	+	2.80271i	−1.00468	+	0.132268i	−0.389807	+	0.920897i	$0.627458\pi$
$450$	−4.96653	−	1.33078i	−0.234124	−	0.0627335i
$451$	36.7537	−	36.7537i	1.73066	−	1.73066i
$452$	−14.6836	+	35.4492i	−0.690656	+	1.66739i
$453$	−1.78558	−	13.5629i	−0.0838941	−	0.637239i
$454$	12.7959	−	16.6760i	0.600543	−	0.782642i
$455$	0.713471	+	0.411923i	0.0334480	+	0.0193112i
$456$	−0.468131	+	3.55580i	−0.0219222	+	0.166516i
$457$	−1.46028	−	1.46028i	−0.0683088	−	0.0683088i	0.672127	−	0.740436i	$-0.265381\pi$
$457$	−1.46028	−	1.46028i	−0.0683088	−	0.0683088i	−0.740436	+	0.672127i	$0.765381\pi$
$458$	12.8066	−	22.1817i	0.598413	−	1.03648i
$459$	−13.3687	+	15.6946i	−0.623998	+	0.732560i
$460$	−4.34786	+	7.53071i	−0.202720	+	0.351121i
$461$	−1.53091	+	5.71343i	−0.0713016	+	0.266101i	−0.992369	−	0.123301i	$-0.960652\pi$
$461$	−1.53091	+	5.71343i	−0.0713016	+	0.266101i	0.921068	+	0.389403i	$0.127318\pi$
$462$	13.3769	−	5.54091i	0.622351	−	0.257786i
$463$	33.4170	−	19.2933i	1.55302	−	0.896636i	0.555126	−	0.831766i	$-0.312670\pi$
$463$	33.4170	−	19.2933i	1.55302	−	0.896636i	0.997894	−	0.0648698i	$-0.0206632\pi$
$464$	−1.60276	−	0.211007i	−0.0744062	−	0.00979576i
$465$	−1.42358	−	0.589667i	−0.0660171	−	0.0273452i
$466$	−2.88573	−	3.76076i	−0.133679	−	0.174214i
$467$	13.5429	+	3.62880i	0.626690	+	0.167921i	0.558167	−	0.829729i	$-0.311505\pi$
$467$	13.5429	+	3.62880i	0.626690	+	0.167921i	0.0685225	+	0.997650i	$0.478171\pi$
$468$	1.49743	+	0.401235i	0.0692188	+	0.0185471i
$469$	−3.93113	+	9.49059i	−0.181523	+	0.438235i
$470$	0.662524	+	5.03237i	0.0305600	+	0.232126i
$471$	−1.71087	−	4.13040i	−0.0788326	−	0.190319i
$472$		−	17.3594i		−	0.799031i
$473$	−21.4046	−	18.3679i	−0.984186	−	0.844556i
$474$	−16.2074	−	16.2074i	−0.744429	−	0.744429i
$475$	2.32531			0.106692
$476$	16.8054	−	5.97605i	0.770277	−	0.273912i
$477$	11.1648			0.511201
$478$	10.2689	−	38.3241i	0.469689	−	1.75290i
$479$	−13.6330	−	10.4609i	−0.622907	−	0.477973i	0.248436	−	0.968648i	$-0.420083\pi$
$479$	−13.6330	−	10.4609i	−0.622907	−	0.477973i	−0.871342	+	0.490675i	$0.836750\pi$
$480$	−12.3706	−	7.14214i	−0.564636	−	0.325993i
$481$	−1.10629	−	2.67083i	−0.0504426	−	0.121779i
$482$	17.7153	−	13.5934i	0.806909	−	0.619163i
$483$	2.39299	−	0.315043i	0.108885	−	0.0143350i
$484$	−14.9691	+	14.9691i	−0.680414	+	0.680414i
$485$	20.3576	+	5.45480i	0.924390	+	0.247690i
$486$	−21.3887	−	27.8743i	−0.970210	−	1.26440i
$487$	7.79802	−	5.98363i	0.353362	−	0.271144i	−0.416792	−	0.909002i	$-0.636846\pi$
$487$	7.79802	−	5.98363i	0.353362	−	0.271144i	0.770154	+	0.637858i	$0.220179\pi$
$488$	−11.4553	−	1.50812i	−0.518558	−	0.0682695i
$489$			10.6923i			0.483525i
$490$	2.60844	−	19.8131i	0.117837	−	0.895064i
$491$	8.57155	−	2.29674i	0.386829	−	0.103650i	−0.0601630	−	0.998189i	$-0.519162\pi$
$491$	8.57155	−	2.29674i	0.386829	−	0.103650i	0.446992	+	0.894538i	$0.352495\pi$
$492$	−17.0540	−	29.5383i	−0.768852	−	1.33169i
$493$	−3.58470	−	1.70402i	−0.161447	−	0.0767452i
$494$	−1.19792			−0.0538968
$495$	11.9022	+	11.9022i	0.534965	+	0.534965i
$496$	−1.04900	−	0.804930i	−0.0471017	−	0.0361424i
$497$	1.73163	−	0.999755i	0.0776741	−	0.0448451i
$498$	−27.5142	−	3.62231i	−1.23294	−	0.162320i
$499$	−13.3662	+	10.2563i	−0.598354	+	0.459133i	−0.862994	−	0.505214i	$-0.831414\pi$
$499$	−13.3662	+	10.2563i	−0.598354	+	0.459133i	0.264640	+	0.964347i	$0.414747\pi$
$500$	13.0417	−	31.4855i	0.583243	−	1.40807i
$501$	−0.940136	−	3.50863i	−0.0420022	−	0.156754i
$502$	13.2227	+	49.3479i	0.590160	+	2.20251i
$503$	3.45163	+	4.49826i	0.153901	+	0.200567i	0.863940	−	0.503595i	$-0.167990\pi$
$503$	3.45163	+	4.49826i	0.153901	+	0.200567i	−0.710039	+	0.704162i	$0.751323\pi$
$504$	0.722465	+	5.48767i	0.0321812	+	0.244440i
$505$	5.09053	+	12.2896i	0.226526	+	0.546881i
$506$	−12.8797	+	7.43610i	−0.572573	+	0.330575i
$507$	−1.68713	+	12.8151i	−0.0749282	+	0.569136i
$508$	28.7011	+	28.7011i	1.27340	+	1.27340i
$509$	−9.39242	+	16.2682i	−0.416312	+	0.721073i	−0.995565	−	0.0940743i	$-0.970011\pi$
$509$	−9.39242	+	16.2682i	−0.416312	+	0.721073i	0.579253	+	0.815148i	$0.303344\pi$
$510$	−11.8737	−	13.1522i	−0.525775	−	0.582388i
$511$	−1.21692	−	2.10777i	−0.0538335	−	0.0932423i
$512$	−12.9557	−	12.9557i	−0.572567	−	0.572567i
$513$	7.87860	+	6.04546i	0.347849	+	0.266914i
$514$			49.2067i			2.17042i
$515$	10.7603	+	25.9777i	0.474156	+	1.14471i
$516$	−15.2777	+	10.4476i	−0.672564	+	0.459932i
$517$	−1.94429	+	4.69393i	−0.0855097	+	0.206439i
$518$	25.0504	−	25.0504i	1.10065	−	1.10065i
$519$	16.6675	+	4.46605i	0.731624	+	0.196038i
$520$	−0.371403	+	0.896646i	−0.0162871	+	0.0393205i
$521$	−1.84397	−	14.0063i	−0.0807858	−	0.613629i	−0.983170	−	0.182696i	$-0.941518\pi$
$521$	−1.84397	−	14.0063i	−0.0807858	−	0.613629i	0.902384	−	0.430933i	$-0.141816\pi$
$522$	2.57356	−	3.35393i	0.112642	−	0.146797i
$523$	23.6117	+	13.6322i	1.03247	+	0.596097i	0.917691	−	0.397295i	$-0.130051\pi$
$523$	23.6117	+	13.6322i	1.03247	+	0.596097i	0.114778	+	0.993391i	$0.463384\pi$
$524$	−26.0207	+	10.7781i	−1.13672	+	0.470844i
$525$	−1.73361	+	0.464520i	−0.0756611	+	0.0202733i
$526$	18.2301	+	31.5755i	0.794870	+	1.37676i
$527$	−1.84231	−	2.67302i	−0.0802521	−	0.116439i
$528$	−3.61189	−	6.25598i	−0.157187	−	0.272257i
$529$	19.8216	−	5.31118i	0.861809	−	0.230921i
$530$	−3.13136	+	23.7851i	−0.136018	+	1.03316i
$531$	−16.6501	−	9.61293i	−0.722552	−	0.417166i
$532$	−3.28785	−	7.93758i	−0.142546	−	0.344138i
$533$	2.63328	−	2.02058i	0.114060	−	0.0875212i
$534$	11.8788	+	15.4808i	0.514046	+	0.669918i
$535$	29.6488	+	7.94438i	1.28183	+	0.343466i
$536$	−11.6891	−	3.13209i	−0.504893	−	0.135286i
$537$	−5.41413	+	13.0709i	−0.233637	+	0.564050i
$538$	−13.6000	−	5.63330i	−0.586338	−	0.242869i
$539$	12.1772	−	15.8696i	0.524509	−	0.683554i
$540$	23.9152	−	13.8075i	1.02915	−	0.594179i
$541$	−4.94164	+	37.5355i	−0.212458	+	1.61378i	0.469873	+	0.882734i	$0.344300\pi$
$541$	−4.94164	+	37.5355i	−0.212458	+	1.61378i	−0.682331	+	0.731044i	$0.739034\pi$
$542$	25.4251	−	6.81265i	1.09210	−	0.292628i
$543$	7.25013			0.311133
$544$	−13.6981	−	26.7968i	−0.587303	−	1.14890i
$545$	−8.51997	+	14.7570i	−0.364956	+	0.632122i
$546$	0.893097	−	0.239305i	0.0382210	−	0.0102413i
$547$	17.0301	+	13.0677i	0.728154	+	0.558732i	0.904951	−	0.425515i	$-0.139907\pi$
$547$	17.0301	+	13.0677i	0.728154	+	0.558732i	−0.176797	+	0.984247i	$0.556574\pi$
$548$			22.1101i			0.944497i
$549$	−7.78999	+	10.1521i	−0.332469	+	0.433282i
$550$	8.77361	−	6.73223i	0.374108	−	0.287063i
$551$	−0.731640	+	1.76633i	−0.0311689	+	0.0752484i
$552$	0.735916	+	2.74648i	0.0313227	+	0.116898i
$553$	15.4523	+	4.14042i	0.657097	+	0.176069i
$554$	−52.9317	+	6.96859i	−2.24885	+	0.296067i
$555$	−19.0294	−	7.88224i	−0.807753	−	0.334582i
$556$	34.8471	−	45.4137i	1.47785	−	1.92597i
$557$		−	1.48483i		−	0.0629142i	−0.999505	−	0.0314571i	$-0.989985\pi$
$557$		−	1.48483i		−	0.0629142i	0.999505	−	0.0314571i	$-0.0100148\pi$
$558$	3.19458	−	1.32324i	0.135237	−	0.0560171i
$559$	−1.20206	−	1.34131i	−0.0508417	−	0.0567313i
$560$	5.03696			0.212850
$561$	−3.71038	−	17.3436i	−0.156652	−	0.732247i
$562$	−31.3417	−	54.2854i	−1.32207	−	2.28989i
$563$	3.51714	+	3.51714i	0.148230	+	0.148230i	0.777327	−	0.629097i	$-0.216575\pi$
$563$	3.51714	+	3.51714i	0.148230	+	0.148230i	−0.629097	+	0.777327i	$0.716575\pi$
$564$	2.64501	+	2.02959i	0.111375	+	0.0854610i
$565$	−23.0397	+	13.3020i	−0.969286	+	0.559617i
$566$	49.5017	+	6.51702i	2.08071	+	0.273931i
$567$	1.41446	+	0.585891i	0.0594019	+	0.0246051i
$568$	1.43394	+	1.86874i	0.0601667	+	0.0784108i
$569$	4.55860	+	1.22147i	0.191107	+	0.0512069i	0.353103	−	0.935585i	$-0.385127\pi$
$569$	4.55860	+	1.22147i	0.191107	+	0.0512069i	−0.161996	+	0.986791i	$0.551793\pi$
$570$	−6.03518	+	6.03518i	−0.252786	+	0.252786i
$571$	−34.6680	+	4.56412i	−1.45081	+	0.191003i	−0.814380	−	0.580332i	$-0.802923\pi$
$571$	−34.6680	+	4.56412i	−1.45081	+	0.191003i	−0.636429	+	0.771335i	$0.719589\pi$
$572$	−2.64528	+	2.02980i	−0.110605	+	0.0848700i
$573$	−0.232786	−	0.0306468i	−0.00972477	−	0.00128029i
$574$	35.2257	+	20.3376i	1.47029	+	0.848873i
$575$	1.70317	−	0.705476i	0.0710271	−	0.0294204i
$576$	24.4744	−	6.55791i	1.01977	−	0.273246i
$577$	−6.67493	+	11.5613i	−0.277881	+	0.481304i	−0.970858	−	0.239656i	$-0.922965\pi$
$577$	−6.67493	+	11.5613i	−0.277881	+	0.481304i	0.692977	+	0.720960i	$0.256299\pi$
$578$	−5.93704	−	36.8563i	−0.246948	−	1.53302i
$579$	−4.07389	−	7.05619i	−0.169305	−	0.293245i
$580$	3.75928	+	3.75928i	0.156095	+	0.156095i
$581$	17.8947	−	7.41223i	0.742397	−	0.307511i
$582$	20.4844	−	11.8266i	0.849104	−	0.490230i
$583$	−14.6184	+	19.0511i	−0.605433	+	0.789015i
$584$	2.27467	−	1.74542i	0.0941267	−	0.0722260i
$585$	0.654341	+	0.852753i	0.0270537	+	0.0352570i
$586$	−38.8055	+	38.8055i	−1.60304	+	1.60304i
$587$	−0.585236	−	2.18413i	−0.0241553	−	0.0901487i	0.952796	−	0.303611i	$-0.0981925\pi$
$587$	−0.585236	−	2.18413i	−0.0241553	−	0.0901487i	−0.976951	+	0.213463i	$0.931526\pi$
$588$	−7.99074	−	10.4137i	−0.329533	−	0.429455i
$589$	−1.24061	+	0.951954i	−0.0511185	+	0.0392246i
$590$	25.1488	−	32.7746i	1.03536	−	1.34931i
$591$		−	2.88141i		−	0.118525i
$592$	−14.0223	−	10.7597i	−0.576314	−	0.442221i
$593$	−24.3339	+	6.52024i	−0.999273	+	0.267754i	−0.721141	−	0.692789i	$-0.756382\pi$
$593$	−24.3339	+	6.52024i	−0.999273	+	0.267754i	−0.278132	+	0.960543i	$0.589715\pi$
$594$	47.2295			1.93785
$595$	11.7666	+	3.80608i	0.482385	+	0.156034i
$596$	25.7992	+	44.6855i	1.05678	+	1.83039i
$597$	−3.95033	+	14.7428i	−0.161676	+	0.603384i
$598$	−0.877414	+	0.363437i	−0.0358801	+	0.0148620i
$599$	37.2599	−	21.5120i	1.52240	−	0.878958i	0.522750	−	0.852486i	$-0.324906\pi$
$599$	37.2599	−	21.5120i	1.52240	−	0.878958i	0.999650	−	0.0264715i	$-0.00842711\pi$
$600$	−0.809111	−	1.95337i	−0.0330318	−	0.0797458i
$601$	−16.1400	−	6.68541i	−0.658365	−	0.272704i	0.0283855	−	0.999597i	$-0.490963\pi$
$601$	−16.1400	−	6.68541i	−0.658365	−	0.272704i	−0.686750	+	0.726893i	$0.740963\pi$
$602$	9.54876	−	19.8997i	0.389179	−	0.811051i
$603$	−9.47706	+	9.47706i	−0.385936	+	0.385936i
$604$	−27.2980	+	27.2980i	−1.11074	+	1.11074i
$605$	−14.5524	+	1.91585i	−0.591637	+	0.0778905i
$606$	13.7926	+	5.71310i	0.560288	+	0.232079i
$607$	0.414174	−	0.539762i	0.0168108	−	0.0219083i	−0.784872	−	0.619658i	$-0.787272\pi$
$607$	0.414174	−	0.539762i	0.0168108	−	0.0219083i	0.801683	+	0.597749i	$0.203938\pi$
$608$	−12.5542	+	7.24819i	−0.509142	+	0.293953i
$609$	0.192612	−	1.46304i	0.00780504	−	0.0592852i
$610$	−19.4429	−	19.4429i	−0.787218	−	0.787218i
$611$	−0.162220	+	0.280974i	−0.00656273	+	0.0113670i
$612$	23.2408	+	1.18731i	0.939455	+	0.0479940i
$613$	28.5609			1.15357			0.576783	−	0.816898i	$-0.304308\pi$
$613$	28.5609			1.15357			0.576783	+	0.816898i	$0.304308\pi$
$614$	−5.79319	+	21.6205i	−0.233794	+	0.872532i
$615$	3.08679	−	23.4465i	0.124471	−	0.945453i
$616$	−10.3098	−	5.95239i	−0.415396	−	0.239829i
$617$	39.8715	+	5.24918i	1.60517	+	0.211324i	0.879216	−	0.476424i	$-0.158067\pi$
$617$	39.8715	+	5.24918i	1.60517	+	0.211324i	0.725950	+	0.687748i	$0.241400\pi$
$618$	29.1547	+	12.0763i	1.17278	+	0.485780i
$619$	−5.82021	−	7.58505i	−0.233934	−	0.304869i	0.661604	−	0.749853i	$-0.269876\pi$
$619$	−5.82021	−	7.58505i	−0.233934	−	0.304869i	−0.895538	+	0.444984i	$0.853209\pi$
$620$	1.12545	+	4.20024i	0.0451992	+	0.168686i
$621$	7.60482	+	2.03770i	0.305171	+	0.0817703i
$622$	41.9377	−	5.52120i	1.68155	−	0.221380i
$623$	−12.5824	−	5.21178i	−0.504102	−	0.208806i
$624$	−0.176530	−	0.426181i	−0.00706685	−	0.0170609i
$625$	15.3937	−	8.88755i	0.615747	−	0.355502i
$626$	−47.1141	−	36.1520i	−1.88306	−	1.44492i
$627$	−8.25214	+	2.21115i	−0.329559	+	0.0883050i
$628$	−6.30826	+	10.9262i	−0.251727	+	0.436004i
$629$	−24.6266	−	35.7310i	−0.981927	−	1.42469i
$630$	−6.58606	+	11.4074i	−0.262395	+	0.454481i
$631$	41.0874	−	11.0093i	1.63566	−	0.438275i	0.680115	−	0.733106i	$-0.261930\pi$
$631$	41.0874	−	11.0093i	1.63566	−	0.438275i	0.955550	+	0.294831i	$0.0952632\pi$
$632$	−2.45983	+	18.6843i	−0.0978469	+	0.743221i
$633$	−3.50194	+	2.02184i	−0.139189	+	0.0803611i
$634$	3.53868	+	8.54314i	0.140539	+	0.339291i
$635$	3.67337	+	27.9020i	0.145773	+	1.10726i
$636$	9.59267	+	12.5014i	0.380374	+	0.495713i
$637$	0.903232	−	0.903232i	0.0357874	−	0.0357874i
$638$	2.35334	+	8.78280i	0.0931698	+	0.347714i
$639$	2.58644	−	0.340512i	0.102318	−	0.0134704i
$640$	3.37780	+	25.6569i	0.133519	+	1.01418i
$641$	5.11094	+	12.3389i	0.201870	+	0.487358i	0.992099	−	0.125454i	$-0.0400386\pi$
$641$	5.11094	+	12.3389i	0.201870	+	0.487358i	−0.790229	+	0.612811i	$0.790039\pi$
$642$	29.8335	−	17.2244i	1.17743	−	0.679791i
$643$	36.5433	−	15.1367i	1.44113	−	0.596934i	0.481055	−	0.876690i	$-0.340254\pi$
$643$	36.5433	−	15.1367i	1.44113	−	0.596934i	0.960071	+	0.279756i	$0.0902536\pi$
$644$	−4.81638	−	4.81638i	−0.189792	−	0.189792i
$645$	−12.8137	−	0.701541i	−0.504538	−	0.0276232i
$646$	−17.5842	+	3.76186i	−0.691842	+	0.148008i
$647$	−40.1496			−1.57844			−0.789222	−	0.614108i	$-0.789516\pi$
$647$	−40.1496			−1.57844			−0.789222	+	0.614108i	$0.789516\pi$
$648$	−0.466802	+	1.74213i	−0.0183377	+	0.0684373i
$649$	38.2035	−	15.8244i	1.49962	−	0.621163i
$650$	0.611584	−	0.353098i	0.0239883	−	0.0138496i
$651$	0.734758	−	0.957555i	0.0287974	−	0.0375296i
$652$	23.9388	−	18.3689i	0.937517	−	0.719382i
$653$	0.591523	−	1.42806i	0.0231481	−	0.0558844i	−0.911883	−	0.410451i	$-0.865371\pi$
$653$	0.591523	−	1.42806i	0.0231481	−	0.0558844i	0.935031	+	0.354566i	$0.115371\pi$
$654$	4.94964	+	18.4723i	0.193546	+	0.722324i
$655$	−18.8626	−	5.05421i	−0.737021	−	0.197484i
$656$	7.76591	−	18.7486i	0.303208	−	0.732008i
$657$	−0.414478	−	3.14827i	−0.0161703	−	0.122826i
$658$	−3.94187	−	0.518957i	−0.153670	−	0.0202311i
$659$	−13.2980	−	7.67760i	−0.518016	−	0.299077i	0.218106	−	0.975925i	$-0.430012\pi$
$659$	−13.2980	−	7.67760i	−0.518016	−	0.299077i	−0.736123	+	0.676848i	$0.763345\pi$
$660$	−3.10086	+	23.5534i	−0.120701	+	0.916813i
$661$	−5.09161	−	5.09161i	−0.198041	−	0.198041i	0.601119	−	0.799160i	$-0.294722\pi$
$661$	−5.09161	−	5.09161i	−0.198041	−	0.198041i	−0.799160	+	0.601119i	$0.794722\pi$
$662$	−1.02795	+	1.78047i	−0.0399526	+	0.0691999i
$663$	−0.0903487	−	1.12897i	−0.00350885	−	0.0438458i
$664$	11.4088	+	19.7606i	0.442746	+	0.766859i
$665$	1.54178	−	5.75400i	0.0597877	−	0.223131i
$666$	42.7028	−	17.6881i	1.65470	−	0.685399i
$667$			1.51572i			0.0586891i
$668$	−6.24029	+	8.13250i	−0.241444	+	0.314656i
$669$	1.46833	+	11.1531i	0.0567689	+	0.431202i
$670$	−17.5316	−	22.8476i	−0.677304	−	0.882680i
$671$	−7.12342	−	26.5850i	−0.274996	−	1.02630i
$672$	7.91176	−	7.91176i	0.305203	−	0.305203i
$673$	2.63139	+	3.42930i	0.101433	+	0.132190i	0.841312	−	0.540550i	$-0.181784\pi$
$673$	2.63139	+	3.42930i	0.101433	+	0.132190i	−0.739879	+	0.672740i	$0.765117\pi$
$674$	−30.4714	+	23.3815i	−1.17371	+	0.900623i
$675$	−5.80430	−	0.764150i	−0.223408	−	0.0294122i
$676$	31.5897	−	18.2383i	1.21499	−	0.701474i
$677$	−21.1624	+	8.76573i	−0.813335	+	0.336894i	−0.750284	−	0.661116i	$-0.770083\pi$
$677$	−21.1624	+	8.76573i	−0.813335	+	0.336894i	−0.0630514	+	0.998010i	$0.520083\pi$
$678$	−7.72771	+	28.8402i	−0.296781	+	1.10760i
$679$	−8.25434	+	14.2969i	−0.316773	+	0.548666i
$680$	−2.63606	+	14.3282i	−0.101088	+	0.549462i
$681$	4.78635	−	8.29021i	0.183413	−	0.317681i
$682$	−1.92485	+	7.18363i	−0.0737062	+	0.275075i
$683$	3.35039	+	2.57084i	0.128199	+	0.0983706i	0.670871	−	0.741574i	$-0.265921\pi$
$683$	3.35039	+	2.57084i	0.128199	+	0.0983706i	−0.542672	+	0.839945i	$0.682587\pi$
$684$		−	11.2094i		−	0.428603i
$685$	−9.33237	+	12.1622i	−0.356571	+	0.464693i
$686$	36.2302	+	15.0070i	1.38328	+	0.572971i
$687$	4.46389	−	10.7768i	0.170308	−	0.411160i
$688$	−10.4651	−	3.42734i	−0.398977	−	0.130666i
$689$	−1.08431	+	1.08431i	−0.0413088	+	0.0413088i
$690$	−2.58945	+	6.25149i	−0.0985788	+	0.237990i
$691$	−4.44652	−	33.7746i	−0.169153	−	1.28485i	−0.839729	−	0.543006i	$-0.817286\pi$
$691$	−4.44652	−	33.7746i	−0.169153	−	1.28485i	0.670575	−	0.741842i	$-0.266047\pi$
$692$	−18.6350	−	44.9890i	−0.708398	−	1.71022i
$693$	−11.4184	+	6.59239i	−0.433747	+	0.250424i
$694$	−18.5648	−	14.2453i	−0.704710	−	0.540743i
$695$	38.3370	−	10.2724i	1.45420	−	0.389653i
$696$	1.73838			0.0658933
$697$	32.3086	−	37.9296i	1.22378	−	1.43668i
$698$	7.08672	+	12.2746i	0.268236	+	0.464599i
$699$	−1.52652	−	1.52652i	−0.0577385	−	0.0577385i
$700$	4.01826	+	3.08332i	0.151876	+	0.116539i
$701$	−21.9988	−	12.7010i	−0.830884	−	0.479711i	0.0232711	−	0.999729i	$-0.492592\pi$
$701$	−21.9988	−	12.7010i	−0.830884	−	0.479711i	−0.854155	+	0.520018i	$0.825925\pi$
$702$	2.99017	+	0.393664i	0.112857	+	0.0148579i
$703$	−16.5836	+	12.7250i	−0.625461	+	0.479933i
$704$	−20.8550	+	50.3485i	−0.786004	+	1.89758i
$705$	0.598288	+	2.23284i	0.0225328	+	0.0840937i
$706$	4.33942	+	16.1950i	0.163316	+	0.609505i
$707$	−10.3305	+	1.36004i	−0.388519	+	0.0511495i
$708$	−3.54181	−	26.9027i	−0.133109	−	1.01107i
$709$	11.4397	+	27.6179i	0.429627	+	1.03721i	0.979406	+	0.201901i	$0.0647119\pi$
$709$	11.4397	+	27.6179i	0.429627	+	1.03721i	−0.549779	+	0.835310i	$0.685288\pi$
$710$			5.60557i			0.210373i
$711$	16.5587	+	12.7059i	0.620999	+	0.476509i
$712$	4.15243	−	15.4971i	0.155619	−	0.580778i
$713$	−0.619871	+	1.07365i	−0.0232144	+	0.0402084i
$714$	12.3583	−	6.31738i	0.462497	−	0.236422i
$715$	−2.31185			−0.0864582
$716$	38.5652	−	10.3335i	1.44125	−	0.386182i
$717$	2.35850	−	17.9146i	0.0880799	−	0.669033i
$718$	34.8128	+	20.0992i	1.29920	+	0.750094i
$719$	−27.2887	+	35.5634i	−1.01770	+	1.32629i	−0.0733636	+	0.997305i	$0.523373\pi$
$719$	−27.2887	+	35.5634i	−1.01770	+	1.32629i	−0.944335	+	0.328985i	$0.893293\pi$
$720$	6.07148	+	2.51489i	0.226271	+	0.0937244i
$721$	−21.8365	+	2.87483i	−0.813234	+	0.107064i
$722$	−8.55697	−	31.9351i	−0.318458	−	1.18850i
$723$	7.19079	−	7.19079i	0.267428	−	0.267428i
$724$	−12.4554	−	16.2321i	−0.462900	−	0.603262i
$725$	−0.147114	−	1.11744i	−0.00546368	−	0.0415008i
$726$	−10.0281	+	13.0689i	−0.372180	+	0.485034i
$727$		−	52.0675i		−	1.93108i	−0.260262	−	0.965538i	$-0.583809\pi$
$727$		−	52.0675i		−	1.93108i	0.260262	−	0.965538i	$-0.416191\pi$
$728$	−0.603118	−	0.462789i	−0.0223530	−	0.0171521i
$729$	−9.19556	−	9.19556i	−0.340576	−	0.340576i
$730$	6.82321			0.252538
$731$	−21.8572	−	15.9142i	−0.808418	−	0.588608i
$732$	−18.0606			−0.667538
$733$	8.27376	+	8.27376i	0.305598	+	0.305598i	0.843199	−	0.537601i	$-0.180669\pi$
$733$	8.27376	+	8.27376i	0.305598	+	0.305598i	−0.537601	+	0.843199i	$0.680669\pi$
$734$	25.7815	+	19.7828i	0.951613	+	0.730198i
$735$		−	9.10109i		−	0.335699i
$736$	−6.99632	+	9.11778i	−0.257888	+	0.336086i
$737$	−3.76261	−	28.5798i	−0.138597	−	1.05275i
$738$	32.3063	+	42.1024i	1.18921	+	1.54981i
$739$	−12.1465	+	12.1465i	−0.446818	+	0.446818i	−0.894295	−	0.447477i	$-0.852322\pi$
$739$	−12.1465	+	12.1465i	−0.446818	+	0.446818i	0.447477	+	0.894295i	$0.352322\pi$
$740$	15.0442	+	56.1457i	0.553036	+	2.06396i
$741$	−0.540885	+	0.0712089i	−0.0198699	+	0.00261592i
$742$	−17.3613	−	7.19127i	−0.637352	−	0.264000i
$743$	−19.4658	+	25.3683i	−0.714130	+	0.930672i	−0.999616	−	0.0277105i	$-0.991178\pi$
$743$	−19.4658	+	25.3683i	−0.714130	+	0.930672i	0.285486	+	0.958383i	$0.407845\pi$
$744$	1.23137	+	0.710930i	0.0451441	+	0.0260640i
$745$	−4.66969	+	35.4698i	−0.171084	+	1.29951i
$746$	14.6067	−	3.91387i	0.534791	−	0.143297i
$747$	25.2709			0.924612
$748$	−32.4559	+	38.1025i	−1.18670	+	1.39316i
$749$	−12.0216	+	20.8221i	−0.439261	+	0.760823i
$750$	6.86363	−	25.6154i	0.250624	−	0.935343i
$751$	−31.5819	−	24.2336i	−1.15244	−	0.884298i	−0.157777	−	0.987475i	$-0.550433\pi$
$751$	−31.5819	−	24.2336i	−1.15244	−	0.884298i	−0.994663	+	0.103176i	$0.967099\pi$
$752$			1.98362i			0.0723350i
$753$	8.90379	+	21.4956i	0.324472	+	0.783345i
$754$	0.0757880	+	0.575667i	0.00276004	+	0.0209646i
$755$	−26.5380	+	3.49379i	−0.965817	+	0.127152i
$756$	5.59848	+	20.8938i	0.203615	+	0.759900i
$757$	9.20546	+	34.3552i	0.334578	+	1.24866i	0.904326	+	0.426843i	$0.140374\pi$
$757$	9.20546	+	34.3552i	0.334578	+	1.24866i	−0.569748	+	0.821820i	$0.692959\pi$
$758$	13.1704	−	31.7963i	0.478372	−	1.15489i
$759$	−5.37344	+	4.12318i	−0.195043	+	0.149662i
$760$	6.95752	+	0.915975i	0.252376	+	0.0332259i
$761$	18.4155	+	10.6322i	0.667563	+	0.385418i	0.795153	−	0.606409i	$-0.207391\pi$
$761$	18.4155	+	10.6322i	0.667563	+	0.385418i	−0.127590	+	0.991827i	$0.540724\pi$
$762$	25.0578	+	19.2275i	0.907748	+	0.696539i
$763$	−9.43807	−	9.43807i	−0.341681	−	0.341681i
$764$	0.331300	+	0.573828i	0.0119860	+	0.0207604i
$765$	12.2830	+	10.4627i	0.444093	+	0.378281i
$766$	64.8096			2.34167
$767$	2.55062	−	0.683437i	0.0920975	−	0.0246775i
$768$	2.93638	+	2.25316i	0.105957	+	0.0813039i
$769$	−1.29150	+	0.745646i	−0.0465726	+	0.0268887i	−0.523106	−	0.852268i	$-0.675227\pi$
$769$	−1.29150	+	0.745646i	−0.0465726	+	0.0268887i	0.476533	+	0.879157i	$0.341893\pi$
$770$	−10.8417	−	26.1742i	−0.390708	−	0.943252i
$771$	2.92504	+	22.2179i	0.105343	+	0.800158i
$772$	−8.79919	+	21.2431i	−0.316690	+	0.764556i
$773$	37.2720	−	37.2720i	1.34058	−	1.34058i	0.445099	−	0.895482i	$-0.353169\pi$
$773$	37.2720	−	37.2720i	1.34058	−	1.34058i	0.895482	−	0.445099i	$-0.146831\pi$
$774$	21.4456	−	19.2192i	0.770847	−	0.690821i
$775$	0.352783	−	0.851693i	0.0126723	−	0.0305937i
$776$	−17.9675	−	7.44238i	−0.644995	−	0.267166i
$777$	9.82171	−	12.7999i	0.352352	−	0.459194i
$778$		−	23.6708i		−	0.848639i
$779$	−19.0404	−	14.6102i	−0.682195	−	0.523466i
$780$	−0.392640	+	1.46535i	−0.0140588	+	0.0524680i
$781$	−2.80548	+	4.85923i	−0.100388	+	0.173877i
$782$	−11.7383	+	8.09027i	−0.419759	+	0.289307i
$783$	2.40674	−	4.16859i	0.0860098	−	0.148973i
$784$	2.02131	−	7.54364i	0.0721897	−	0.269416i
$785$	−8.08182	+	3.34760i	−0.288452	+	0.119481i
$786$	−18.9800	+	10.9581i	−0.676995	+	0.390863i
$787$	−26.5189	−	3.49129i	−0.945298	−	0.124451i	−0.357910	−	0.933756i	$-0.616511\pi$
$787$	−26.5189	−	3.49129i	−0.945298	−	0.124451i	−0.587388	+	0.809305i	$0.699844\pi$
$788$	−6.45111	+	4.95011i	−0.229811	+	0.176340i
$789$	10.1083	+	13.1733i	0.359864	+	0.468983i
$790$	−31.7124	+	31.7124i	−1.12828	+	1.12828i
$791$	−5.39351	−	20.1289i	−0.191771	−	0.715700i
$792$	−9.45540	−	12.3225i	−0.335983	−	0.437861i
$793$	−0.229405	−	1.74251i	−0.00814642	−	0.0618782i
$794$	35.7653	−	46.6103i	1.26926	−	1.65414i
$795$			10.9256i			0.387492i
$796$	39.7938	−	16.4831i	1.41045	−	0.584229i
$797$	7.59687	−	28.3519i	0.269095	−	1.00428i	−0.690601	−	0.723236i	$-0.742654\pi$
$797$	7.59687	−	28.3519i	0.269095	−	1.00428i	0.959696	−	0.281040i	$-0.0906793\pi$
$798$	−3.34276	−	5.78983i	−0.118333	−	0.204958i
$799$	−1.49888	+	4.63384i	−0.0530266	+	0.163934i
$800$	4.27296	−	7.40098i	0.151072	−	0.261664i
$801$	−12.5644	−	12.5644i	−0.443942	−	0.443942i
$802$	8.75647	−	66.5120i	0.309202	−	2.34862i
$803$	5.91475	+	3.41488i	0.208727	+	0.120509i
$804$	−18.7542	−	2.46904i	−0.661410	−	0.0870763i
$805$	−0.616434	−	4.68228i	−0.0217265	−	0.165029i
$806$	−0.181741	+	0.438762i	−0.00640157	+	0.0154547i
$807$	−6.47556	−	1.73512i	−0.227951	−	0.0610792i
$808$	−3.17694	−	11.8565i	−0.111764	−	0.417110i
$809$	7.53725	−	18.1965i	0.264996	−	0.639756i	−0.734238	−	0.678892i	$-0.762461\pi$
$809$	7.53725	−	18.1965i	0.264996	−	0.639756i	0.999234	+	0.0391359i	$0.0124605\pi$
$810$	−3.40518	+	2.61288i	−0.119646	+	0.0918074i
$811$	−21.8272	+	28.4457i	−0.766455	+	0.998864i	0.233195	+	0.972430i	$0.425082\pi$
$811$	−21.8272	+	28.4457i	−0.766455	+	0.998864i	−0.999651	+	0.0264340i	$0.991585\pi$
$812$	−3.60645	+	2.08218i	−0.126562	+	0.0730704i
$813$	11.0750	−	4.58743i	0.388418	−	0.160888i
$814$	−25.7300	+	96.0255i	−0.901835	+	3.36569i
$815$	20.9214			0.732843
$816$	−3.92964	−	5.70155i	−0.137565	−	0.199594i
$817$	−7.11854	+	10.9058i	−0.249046	+	0.381544i
$818$	−51.0700	−	51.0700i	−1.78562	−	1.78562i
$819$	−0.777861	+	0.322201i	−0.0271807	+	0.0112586i
$820$	−57.7967	+	33.3689i	−2.01835	+	1.16529i
$821$	2.96522	+	7.15867i	0.103487	+	0.249839i	0.967139	−	0.254249i	$-0.0818284\pi$
$821$	2.96522	+	7.15867i	0.103487	+	0.249839i	−0.863652	+	0.504089i	$0.831828\pi$
$822$	2.24570	+	17.0578i	0.0783277	+	0.594958i
$823$	12.8214	−	1.68797i	0.446927	−	0.0588390i	0.0962960	−	0.995353i	$-0.469300\pi$
$823$	12.8214	−	1.68797i	0.446927	−	0.0588390i	0.350631	+	0.936514i	$0.385967\pi$
$824$	−6.71538	−	25.0621i	−0.233941	−	0.873081i
$825$	3.56128	−	3.56128i	0.123988	−	0.123988i
$826$	19.6992	+	25.6725i	0.685422	+	0.893259i
$827$	3.15302	+	23.9495i	0.109641	+	0.832807i	0.954582	+	0.297948i	$0.0963021\pi$
$827$	3.15302	+	23.9495i	0.109641	+	0.832807i	−0.844941	+	0.534859i	$0.820365\pi$
$828$	−3.40084	−	8.21035i	−0.118187	−	0.285329i
$829$	−21.6895	+	12.5225i	−0.753309	+	0.434923i	−0.826888	−	0.562366i	$-0.809891\pi$
$829$	−21.6895	+	12.5225i	−0.753309	+	0.434923i	0.0735792	+	0.997289i	$0.476558\pi$
$830$	−7.08766	+	53.8361i	−0.246016	+	1.86868i
$831$	−23.4856	+	6.29294i	−0.814705	+	0.218300i
$832$	−1.74002	+	3.01381i	−0.0603245	+	0.104485i
$833$	10.4221	−	16.0950i	0.361105	−	0.557659i
$834$	22.2717	−	38.5757i	0.771205	−	1.33577i
$835$	−6.86523	+	1.83953i	−0.237581	+	0.0636596i
$836$	19.1272	+	14.6769i	0.661530	+	0.507610i
$837$	3.40958	−	1.96852i	0.117852	−	0.0680420i
$838$	−0.921226	−	2.22404i	−0.0318232	−	0.0768280i
$839$	−20.3573	−	8.43228i	−0.702813	−	0.291115i	0.00251403	−	0.999997i	$-0.499200\pi$
$839$	−20.3573	−	8.43228i	−0.702813	−	0.291115i	−0.705327	+	0.708882i	$0.749200\pi$
$840$	−5.37011	+	0.706989i	−0.185286	+	0.0243934i
$841$	−27.1167	−	7.26591i	−0.935060	−	0.250549i
$842$	4.91735	+	18.3518i	0.169463	+	0.632445i
$843$	−17.3784	−	22.6479i	−0.598543	−	0.780037i
$844$	10.5428	+	4.36697i	0.362898	+	0.150317i
$845$	25.0748	+	3.30116i	0.862599	+	0.113563i
$846$	−4.49237	−	2.59367i	−0.154451	−	0.0891722i
$847$	1.50069	−	11.3989i	0.0515645	−	0.391671i
$848$	−2.42653	+	9.05593i	−0.0833274	+	0.310982i
$849$	22.7385			0.780383
$850$	7.86860	−	7.10371i	0.269891	−	0.243655i
$851$	−8.28598	+	14.3517i	−0.284040	+	0.491971i
$852$	2.60352	+	2.60352i	0.0891951	+	0.0891951i
$853$	−6.08965	+	46.2555i	−0.208506	+	1.58376i	0.492313	+	0.870418i	$0.336152\pi$
$853$	−6.08965	+	46.2555i	−0.208506	+	1.58376i	−0.700819	+	0.713340i	$0.747182\pi$
$854$	18.6524	−	10.7690i	0.638273	−	0.368507i
$855$	4.73134	−	6.16601i	0.161809	−	0.210873i
$856$	−26.1679	−	10.8391i	−0.894400	−	0.370473i
$857$	12.7335	−	1.67640i	0.434969	−	0.0572648i	0.0901377	−	0.995929i	$-0.471269\pi$
$857$	12.7335	−	1.67640i	0.434969	−	0.0572648i	0.344832	+	0.938664i	$0.387936\pi$
$858$	−1.83465	+	1.83465i	−0.0626339	+	0.0626339i
$859$	5.34670	−	5.34670i	0.182427	−	0.182427i	−0.609986	−	0.792413i	$-0.708825\pi$
$859$	5.34670	−	5.34670i	0.182427	−	0.182427i	0.792413	+	0.609986i	$0.208825\pi$
$860$	20.4426	+	29.8934i	0.697086	+	1.01936i
$861$	17.1141	+	7.08890i	0.583247	+	0.241589i
$862$	−1.12825	−	2.72383i	−0.0384283	−	0.0927741i
$863$	28.3350	−	16.3592i	0.964535	−	0.556875i	0.0669695	−	0.997755i	$-0.478667\pi$
$863$	28.3350	−	16.3592i	0.964535	−	0.556875i	0.897566	+	0.440880i	$0.145334\pi$
$864$	33.7191	−	13.9669i	1.14715	−	0.475164i
$865$	8.73858	−	32.6128i	0.297121	−	1.10887i
$866$	−3.14045	−	5.43942i	−0.106717	−	0.184839i
$867$	−4.87159	−	16.2885i	−0.165448	−	0.553187i
$868$	−3.40612			−0.115611
$869$	−43.3616	+	11.6187i	−1.47094	+	0.394137i
$870$	3.28208	+	2.51843i	0.111273	+	0.0853827i
$871$		−	1.84079i		−	0.0623729i
$872$	9.57205	−	12.4745i	0.324151	−	0.422441i
$873$	−17.0880	+	13.1120i	−0.578340	+	0.443776i
$874$	4.18039	+	5.44799i	0.141404	+	0.184281i
$875$	4.79043	+	17.8781i	0.161946	+	0.604392i
$876$	3.16906	−	3.16906i	0.107073	−	0.107073i
$877$	−24.5905	−	32.0470i	−0.830362	−	1.08215i	−0.995395	−	0.0958612i	$-0.969440\pi$
$877$	−24.5905	−	32.0470i	−0.830362	−	1.08215i	0.165032	−	0.986288i	$-0.447227\pi$
$878$	−27.6398	+	21.2087i	−0.932797	+	0.715761i
$879$	−15.2148	+	19.8283i	−0.513182	+	0.668792i
$880$	−12.2409	+	7.06727i	−0.412640	+	0.238238i
$881$	−37.4786	+	15.5241i	−1.26268	+	0.523021i	−0.910733	−	0.412997i	$-0.864482\pi$
$881$	−37.4786	+	15.5241i	−1.26268	+	0.523021i	−0.351952	+	0.936018i	$0.614482\pi$
$882$	14.4414	+	14.4414i	0.486267	+	0.486267i
$883$	14.9760	+	25.9393i	0.503984	+	0.872926i	0.999989	+	0.00460620i	$0.00146620\pi$
$883$	14.9760	+	25.9393i	0.503984	+	0.872926i	−0.496006	+	0.868319i	$0.665200\pi$
$884$	−2.37242	+	2.14180i	−0.0797931	+	0.0720365i
$885$	9.40700	−	16.2934i	0.316213	−	0.547697i
$886$	−5.90250	+	1.58157i	−0.198298	+	0.0531339i
$887$	−15.9985	+	6.62679i	−0.537176	+	0.222506i	−0.634743	−	0.772723i	$-0.718894\pi$
$887$	−15.9985	+	6.62679i	−0.537176	+	0.222506i	0.0975667	+	0.995229i	$0.468894\pi$
$888$	16.4600	+	9.50319i	0.552362	+	0.318906i
$889$	−21.8557	−	2.87736i	−0.733018	−	0.0965036i
$890$	30.2907	−	23.2429i	1.01535	−	0.779103i
$891$	−4.25950	+	0.560774i	−0.142699	+	0.0187866i
$892$	22.4478	−	22.4478i	0.751608	−	0.751608i
$893$	2.26600	+	0.607172i	0.0758287	+	0.0203182i
$894$	24.4425	+	31.8541i	0.817480	+	1.06536i
$895$	25.5753	+	10.5937i	0.854889	+	0.354107i
$896$	−20.0971	−	2.64584i	−0.671399	−	0.0883913i
$897$	−0.374567	+	0.216257i	−0.0125064	+	0.00722060i
$898$	37.4088	+	28.7048i	1.24835	+	0.957891i
$899$	0.535957	+	0.535957i	0.0178752	+	0.0178752i
$900$	3.30410	+	5.72286i	0.110137	+	0.190762i
$901$	−12.5115	+	19.3216i	−0.416817	+	0.643697i
$902$	−114.141			−3.80048
$903$	3.12856	−	9.55276i	0.104112	−	0.317896i
$904$	22.6804	−	9.39452i	0.754338	−	0.312457i
$905$		−	14.1861i		−	0.471562i
$906$	−18.2876	+	23.8328i	−0.607564	+	0.791792i
$907$	7.99974	+	3.31360i	0.265627	+	0.110026i	0.511522	−	0.859270i	$-0.329082\pi$
$907$	7.99974	+	3.31360i	0.265627	+	0.110026i	−0.245895	+	0.969296i	$0.579082\pi$
$908$	−26.7834	+	3.52611i	−0.888840	+	0.117018i
$909$	−13.1313	−	3.51852i	−0.435538	−	0.116702i
$910$	−0.468239	−	1.74749i	−0.0155220	−	0.0579288i
$911$	−9.93445	+	23.9839i	−0.329143	+	0.794622i	0.669513	+	0.742800i	$0.266503\pi$
$911$	−9.93445	+	23.9839i	−0.329143	+	0.794622i	−0.998656	+	0.0518216i	$0.983497\pi$
$912$	−2.64622	+	2.03052i	−0.0876251	+	0.0672371i
$913$	−33.0879	+	43.1210i	−1.09505	+	1.42710i
$914$			4.53498i			0.150004i
$915$	−9.93463	−	7.62311i	−0.328429	−	0.252012i
$916$	−31.7966	+	8.51988i	−1.05059	+	0.281505i
$917$	7.64815	−	13.2470i	0.252564	−	0.437454i
$918$	45.1290	−	3.61155i	1.48948	−	0.119199i
$919$	−6.46373			−0.213219			−0.106609	−	0.994301i	$-0.533999\pi$
$919$	−6.46373			−0.213219			−0.106609	+	0.994301i	$0.533999\pi$
$920$	5.37394	−	1.43994i	0.177174	−	0.0474735i
$921$	−1.33054	+	10.1065i	−0.0438429	+	0.333020i
$922$	11.2489	−	6.49455i	0.370463	−	0.213887i
$923$	−0.218121	+	0.284261i	−0.00717954	+	0.00935656i
$924$	−17.1921	−	7.12121i	−0.565580	−	0.234271i
$925$	4.71574	−	11.3848i	0.155053	−	0.374330i
$926$	−81.8477	−	21.9310i	−2.68968	−	0.720698i
$927$	−27.7568	−	7.43741i	−0.911653	−	0.244277i
$928$	4.27744	+	5.57446i	0.140414	+	0.182991i
$929$	45.5935	−	34.9851i	1.49587	−	1.14782i	0.544920	−	0.838488i	$-0.316560\pi$
$929$	45.5935	−	34.9851i	1.49587	−	1.14782i	0.950953	−	0.309336i	$-0.100107\pi$
$930$	1.29489	+	3.12614i	0.0424611	+	0.102510i
$931$	−7.99881	−	4.61812i	−0.262151	−	0.151353i
$932$	−0.795206	+	6.04019i	−0.0260478	+	0.197853i
$933$	18.6076	−	4.98589i	0.609185	−	0.163231i
$934$	−15.3944	−	26.6639i	−0.503721	−	0.872470i
$935$	−33.9356	+	7.25997i	−1.10981	+	0.237427i
$936$	−0.495926	−	0.858968i	−0.0162098	−	0.0280763i
$937$	−14.3859	+	3.85470i	−0.469968	+	0.125927i	−0.486027	−	0.873944i	$-0.661554\pi$
$937$	−14.3859	+	3.85470i	−0.469968	+	0.125927i	0.0160598	+	0.999871i	$0.494888\pi$
$938$	20.8410	−	8.63264i	0.680484	−	0.281866i
$939$	−23.4221	−	13.5227i	−0.764351	−	0.441298i
$940$	3.97122	−	5.17540i	0.129527	−	0.168803i
$941$	−1.76256	−	13.3879i	−0.0574577	−	0.436435i	−0.995861	−	0.0908919i	$-0.971028\pi$
$941$	−1.76256	−	13.3879i	−0.0574577	−	0.436435i	0.938403	−	0.345543i	$-0.112305\pi$
$942$	−3.75701	+	9.07022i	−0.122410	+	0.295524i
$943$	−18.3788	−	4.92458i	−0.598496	−	0.160366i
$944$	11.4159	−	11.4159i	0.371555	−	0.371555i
$945$	−5.73941	+	13.8562i	−0.186703	+	0.450741i
$946$	4.71540	+	61.7581i	0.153311	+	2.00793i
$947$	20.0202	+	48.3331i	0.650569	+	1.57061i	0.811954	+	0.583722i	$0.198404\pi$
$947$	20.0202	+	48.3331i	0.650569	+	1.57061i	−0.161384	+	0.986892i	$0.551596\pi$
$948$			29.4578i			0.956745i
$949$	0.346008	+	0.265502i	0.0112319	+	0.00861855i
$950$	−3.61070	−	3.61070i	−0.117146	−	0.117146i
$951$	2.10563	+	3.64706i	0.0682798	+	0.118264i
$952$	−10.3065	−	4.89929i	−0.334035	−	0.158787i
$953$	9.82126	−	17.0109i	0.318142	−	0.551038i	−0.661959	−	0.749540i	$-0.730275\pi$
$953$	9.82126	−	17.0109i	0.318142	−	0.551038i	0.980100	+	0.198503i	$0.0636079\pi$
$954$	−17.3365	−	17.3365i	−0.561290	−	0.561290i
$955$	−0.0599657	+	0.455484i	−0.00194044	+	0.0147391i
$956$	−44.1603	+	25.4960i	−1.42825	+	0.824599i
$957$	1.58467	+	3.82573i	0.0512251	+	0.123668i
$958$	4.92547	+	37.4127i	0.159135	+	1.20875i
$959$	−7.31007	−	9.52667i	−0.236055	−	0.307632i
$960$	6.41742	+	23.9501i	0.207121	+	0.772987i
$961$	−7.86294	−	29.3449i	−0.253643	−	0.946609i
$962$	−2.42939	+	5.86505i	−0.0783265	+	0.189097i
$963$	−24.8869	+	19.0964i	−0.801970	+	0.615373i
$964$	−28.4527	−	3.74587i	−0.916399	−	0.120646i
$965$	−13.8066	+	7.97125i	−0.444451	+	0.256604i
$966$	−4.20499	−	3.22660i	−0.135293	−	0.103814i
$967$	3.31882	+	3.31882i	0.106726	+	0.106726i	0.758453	−	0.651727i	$-0.225955\pi$
$967$	3.31882	+	3.31882i	0.106726	+	0.106726i	−0.651727	+	0.758453i	$0.725955\pi$
$968$	13.5442			0.435328
$969$	−7.71604	+	2.74384i	−0.247875	+	0.0881448i
$970$	−23.1408	−	40.0811i	−0.743006	−	1.28692i
$971$	3.75165	−	1.00525i	0.120396	−	0.0322601i	−0.198118	−	0.980178i	$-0.563483\pi$
$971$	3.75165	−	1.00525i	0.120396	−	0.0322601i	0.318514	+	0.947918i	$0.396816\pi$
$972$	−5.89397	+	44.7691i	−0.189049	+	1.43597i
$973$			31.0888i			0.996661i
$974$	−21.3999	−	2.81735i	−0.685698	−	0.0902738i
$975$	0.255154	−	0.195786i	0.00817146	−	0.00627019i
$976$	−6.54148	−	8.52502i	−0.209388	−	0.272879i
$977$	−35.8203	−	9.59801i	−1.14599	−	0.307068i	−0.364634	−	0.931151i	$-0.618806\pi$
$977$	−35.8203	−	9.59801i	−1.14599	−	0.307068i	−0.781358	+	0.624083i	$0.785473\pi$
$978$	16.6029	−	16.6029i	0.530902	−	0.530902i
$979$	37.8903	−	4.98836i	1.21098	−	0.159429i
$980$	−20.3762	+	15.6352i	−0.650894	+	0.499449i
$981$	−6.66421	−	16.0888i	−0.212772	−	0.513677i
$982$	−16.8761	−	9.74342i	−0.538538	−	0.310925i
$983$	38.4310	+	29.4891i	1.22576	+	0.940557i	0.999439	−	0.0334967i	$-0.0106643\pi$
$983$	38.4310	+	29.4891i	1.22576	+	0.940557i	0.226318	+	0.974053i	$0.427331\pi$
$984$	−5.64800	+	21.0786i	−0.180052	+	0.671962i
$985$	−5.63796			−0.179640
$986$	2.92028	+	8.21223i	0.0930007	+	0.261531i
$987$	−1.81069			−0.0576349
$988$	1.08864	+	1.08864i	0.0346343	+	0.0346343i
$989$	−1.90527	+	10.1476i	−0.0605841	+	0.322676i
$990$		−	36.9631i		−	1.17477i
$991$	−14.4874	−	34.9757i	−0.460207	−	1.11104i	−0.968312	−	0.249744i	$-0.919654\pi$
$991$	−14.4874	−	34.9757i	−0.460207	−	1.11104i	0.508105	−	0.861295i	$-0.330346\pi$
$992$	0.750145	+	5.69792i	0.0238171	+	0.180909i
$993$	−0.358306	+	0.865026i	−0.0113705	+	0.0274508i
$994$	−4.24124	−	1.13644i	−0.134524	−	0.0360456i
$995$	28.8468	+	7.72948i	0.914505	+	0.245041i
$996$	21.7124	+	28.2962i	0.687985	+	0.896599i
$997$	−39.7002	−	16.4443i	−1.25732	−	0.520798i	−0.348232	−	0.937408i	$-0.613218\pi$
$997$	−39.7002	−	16.4443i	−1.25732	−	0.520798i	−0.909085	+	0.416611i	$0.863218\pi$
$998$	36.6806	+	4.82909i	1.16110	+	0.152862i
$999$	45.5767	−	26.3137i	1.44198	−	0.832530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.v.a.36.10	✓	512
17.9	even	8	inner	731.2.v.a.638.10	yes	512
43.6	even	3	inner	731.2.v.a.393.10	yes	512
731.264	even	24	inner	731.2.v.a.264.10	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.v.a.36.10	✓	512	1.1	even	1	trivial
731.2.v.a.264.10	yes	512	731.264	even	24	inner
731.2.v.a.393.10	yes	512	43.6	even	3	inner
731.2.v.a.638.10	yes	512	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.v (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55278 - 1.55278i) q^{2} +(-0.793419 - 0.608812i) q^{3} +2.82227i q^{4} +(-1.19124 + 1.55246i) q^{5} +(0.286655 + 2.17736i) q^{6} +(-0.933104 - 1.21604i) q^{7} +(1.27681 - 1.27681i) q^{8} +(-0.517595 - 1.93169i) q^{9} +O(q^{10})\)	\(q+(-1.55278 - 1.55278i) q^{2} +(-0.793419 - 0.608812i) q^{3} +2.82227i q^{4} +(-1.19124 + 1.55246i) q^{5} +(0.286655 + 2.17736i) q^{6} +(-0.933104 - 1.21604i) q^{7} +(1.27681 - 1.27681i) q^{8} +(-0.517595 - 1.93169i) q^{9} +(4.26037 - 0.560889i) q^{10} +(3.97385 + 1.64602i) q^{11} +(1.71823 - 2.23925i) q^{12} +(0.237870 + 0.137335i) q^{13} +(-0.439346 + 3.33716i) q^{14} +(1.89031 - 0.506507i) q^{15} +1.67932 q^{16} +(3.92298 + 1.26894i) q^{17} +(-2.19579 + 3.80321i) q^{18} +(0.514028 - 1.91838i) q^{19} +(-4.38146 - 3.36201i) q^{20} +1.53292i q^{21} +(-3.61461 - 8.72645i) q^{22} +(-0.205519 - 1.56107i) q^{23} +(-1.79039 + 0.235709i) q^{24} +(0.303030 + 1.13092i) q^{25} +(-0.156111 - 0.582612i) q^{26} +(-1.91351 + 4.61963i) q^{27} +(3.43201 - 2.63348i) q^{28} +(-0.954412 - 0.125651i) q^{29} +(-3.72174 - 2.14875i) q^{30} +(-0.624662 - 0.479320i) q^{31} +(-5.16124 - 5.16124i) q^{32} +(-2.15081 - 3.72531i) q^{33} +(-4.12115 - 8.06194i) q^{34} +2.99941 q^{35} +(5.45176 - 1.46080i) q^{36} +(-8.35002 - 6.40720i) q^{37} +(-3.77700 + 2.18065i) q^{38} +(-0.105120 - 0.253782i) q^{39} +(0.461204 + 3.50319i) q^{40} +(4.62445 - 11.1644i) q^{41} +(2.38029 - 2.38029i) q^{42} +(-6.23175 - 2.04092i) q^{43} +(-4.64553 + 11.2153i) q^{44} +(3.61545 + 1.49757i) q^{45} +(-2.10488 + 2.74313i) q^{46} +1.18120i q^{47} +(-1.33240 - 1.02239i) q^{48} +(1.20365 - 4.49209i) q^{49} +(1.28554 - 2.22662i) q^{50} +(-2.34002 - 3.39516i) q^{51} +(-0.387596 + 0.671336i) q^{52} +(-1.44495 + 5.39263i) q^{53} +(10.1446 - 4.20201i) q^{54} +(-7.28920 + 4.20842i) q^{55} +(-2.74406 - 0.361263i) q^{56} +(-1.57577 + 1.20913i) q^{57} +(1.28689 + 1.67710i) q^{58} +(6.79794 - 6.79794i) q^{59} +(1.42950 + 5.33497i) q^{60} +(-3.89532 - 5.07648i) q^{61} +(0.225685 + 1.71424i) q^{62} +(-1.86605 + 2.43189i) q^{63} +12.6700i q^{64} +(-0.496567 + 0.205685i) q^{65} +(-2.44486 + 9.12435i) q^{66} +(-3.35093 - 5.80398i) q^{67} +(-3.58131 + 11.0717i) q^{68} +(-0.787335 + 1.36370i) q^{69} +(-4.65744 - 4.65744i) q^{70} +(-0.170270 + 1.29333i) q^{71} +(-3.12728 - 1.80554i) q^{72} +(1.57427 + 0.207256i) q^{73} +(3.01679 + 22.9148i) q^{74} +(0.448090 - 1.08179i) q^{75} +(5.41419 + 1.45073i) q^{76} +(-1.70638 - 6.36829i) q^{77} +(-0.230840 + 0.557298i) q^{78} +(-8.28003 + 6.35349i) q^{79} +(-2.00047 + 2.60707i) q^{80} +(-0.865017 + 0.499418i) q^{81} +(-24.5167 + 10.1551i) q^{82} +(-3.27056 + 12.2059i) q^{83} -4.32632 q^{84} +(-6.64320 + 4.57864i) q^{85} +(6.50745 + 12.8457i) q^{86} +(0.680751 + 0.680751i) q^{87} +(7.17553 - 2.97220i) q^{88} +(7.69475 - 4.44256i) q^{89} +(-3.28861 - 7.93941i) q^{90} +(-0.0549529 - 0.417409i) q^{91} +(4.40576 - 0.580030i) q^{92} +(0.203803 + 0.760603i) q^{93} +(1.83415 - 1.83415i) q^{94} +(2.36587 + 3.08326i) q^{95} +(0.952803 + 7.23726i) q^{96} +(-4.12163 - 9.95050i) q^{97} +(-8.84425 + 5.10623i) q^{98} +(1.12276 - 8.52822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 16 q^{2} - 4 q^{3} - 12 q^{5} - 4 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{9}+O(q^{10}) \) 512 * q - 16 * q^2 - 4 * q^3 - 12 * q^5 - 4 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^9	\( 512 q - 16 q^{2} - 4 q^{3} - 12 q^{5} - 4 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{9} - 4 q^{10} - 16 q^{11} + 32 q^{12} + 12 q^{14} - 4 q^{15} - 496 q^{16} - 4 q^{17} - 32 q^{18} - 4 q^{19} + 12 q^{20} - 16 q^{22} + 36 q^{24} + 4 q^{25} + 36 q^{26} - 112 q^{27} + 28 q^{28} - 4 q^{29} - 12 q^{31} + 16 q^{32} + 32 q^{33} + 12 q^{34} - 96 q^{35} - 52 q^{36} + 28 q^{37} - 40 q^{39} + 40 q^{40} - 32 q^{41} + 32 q^{42} + 44 q^{43} + 112 q^{44} + 16 q^{45} - 20 q^{46} - 104 q^{48} + 16 q^{49} - 16 q^{50} - 16 q^{51} + 88 q^{52} - 8 q^{53} - 104 q^{54} - 44 q^{56} - 40 q^{57} - 32 q^{58} - 40 q^{59} - 32 q^{60} - 8 q^{61} + 16 q^{62} + 8 q^{63} - 56 q^{65} - 100 q^{66} - 72 q^{67} + 12 q^{68} - 80 q^{69} - 48 q^{70} + 44 q^{71} + 52 q^{73} - 68 q^{74} + 96 q^{75} - 8 q^{76} + 36 q^{77} + 40 q^{78} + 60 q^{79} + 76 q^{80} - 136 q^{82} - 24 q^{83} + 96 q^{84} - 56 q^{85} - 40 q^{86} - 56 q^{87} - 24 q^{88} + 96 q^{90} - 44 q^{91} - 44 q^{92} - 4 q^{93} + 88 q^{94} - 20 q^{95} + 40 q^{96} - 152 q^{97} - 88 q^{99}+O(q^{100}) \) 512 * q - 16 * q^2 - 4 * q^3 - 12 * q^5 - 4 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^9 - 4 * q^10 - 16 * q^11 + 32 * q^12 + 12 * q^14 - 4 * q^15 - 496 * q^16 - 4 * q^17 - 32 * q^18 - 4 * q^19 + 12 * q^20 - 16 * q^22 + 36 * q^24 + 4 * q^25 + 36 * q^26 - 112 * q^27 + 28 * q^28 - 4 * q^29 - 12 * q^31 + 16 * q^32 + 32 * q^33 + 12 * q^34 - 96 * q^35 - 52 * q^36 + 28 * q^37 - 40 * q^39 + 40 * q^40 - 32 * q^41 + 32 * q^42 + 44 * q^43 + 112 * q^44 + 16 * q^45 - 20 * q^46 - 104 * q^48 + 16 * q^49 - 16 * q^50 - 16 * q^51 + 88 * q^52 - 8 * q^53 - 104 * q^54 - 44 * q^56 - 40 * q^57 - 32 * q^58 - 40 * q^59 - 32 * q^60 - 8 * q^61 + 16 * q^62 + 8 * q^63 - 56 * q^65 - 100 * q^66 - 72 * q^67 + 12 * q^68 - 80 * q^69 - 48 * q^70 + 44 * q^71 + 52 * q^73 - 68 * q^74 + 96 * q^75 - 8 * q^76 + 36 * q^77 + 40 * q^78 + 60 * q^79 + 76 * q^80 - 136 * q^82 - 24 * q^83 + 96 * q^84 - 56 * q^85 - 40 * q^86 - 56 * q^87 - 24 * q^88 + 96 * q^90 - 44 * q^91 - 44 * q^92 - 4 * q^93 + 88 * q^94 - 20 * q^95 + 40 * q^96 - 152 * q^97 - 88 * q^99

Introduction

L-functions

Modular forms

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