LMFDB - Embedded newform 46.4.c.b.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,4,Mod(3,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("46.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, 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:	$2.71408786026$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	46.3
Dual form			46.4.c.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.284630 + 1.97964i) q^{2} +(2.60327 - 5.70036i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(6.82565 - 7.87722i) q^{5} +(12.0256 + 3.53105i) q^{6} +(9.96901 - 6.40669i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-8.03584 - 9.27386i) q^{9} +O(q^{10})$	\(q+(0.284630 + 1.97964i) q^{2} +(2.60327 - 5.70036i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(6.82565 - 7.87722i) q^{5} +(12.0256 + 3.53105i) q^{6} +(9.96901 - 6.40669i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-8.03584 - 9.27386i) q^{9} +(17.5369 + 11.2703i) q^{10} +(-5.03629 + 35.0282i) q^{11} +(-3.56736 + 24.8115i) q^{12} +(3.24703 + 2.08674i) q^{13} +(15.5204 + 17.9115i) q^{14} +(-27.1340 - 59.4152i) q^{15} +(13.4601 - 8.65025i) q^{16} +(29.6669 + 8.71100i) q^{17} +(16.0717 - 18.5477i) q^{18} +(-128.737 + 37.8006i) q^{19} +(-17.3196 + 37.9246i) q^{20} +(-10.5685 - 73.5052i) q^{21} -70.7768 q^{22} +(-94.6684 - 56.6118i) q^{23} -50.1333 q^{24} +(2.32826 + 16.1934i) q^{25} +(-3.20680 + 7.02191i) q^{26} +(88.5624 - 26.0043i) q^{27} +(-31.0409 + 35.8231i) q^{28} +(-60.1958 - 17.6751i) q^{29} +(109.898 - 70.6269i) q^{30} +(107.495 + 235.381i) q^{31} +(20.9555 + 24.1840i) q^{32} +(186.562 + 119.896i) q^{33} +(-8.80057 + 61.2093i) q^{34} +(17.5780 - 122.258i) q^{35} +(41.2923 + 26.5370i) q^{36} +(214.264 + 247.274i) q^{37} +(-111.474 - 244.094i) q^{38} +(20.3480 - 13.0769i) q^{39} +(-80.0068 - 23.4921i) q^{40} +(45.2881 - 52.2653i) q^{41} +(142.506 - 41.8435i) q^{42} +(123.622 - 270.695i) q^{43} +(-20.1452 - 140.113i) q^{44} -127.902 q^{45} +(85.1257 - 203.523i) q^{46} -502.104 q^{47} +(-14.2694 - 99.2460i) q^{48} +(-84.1520 + 184.267i) q^{49} +(-31.3944 + 9.21823i) q^{50} +(126.887 - 146.435i) q^{51} +(-14.8136 - 4.34967i) q^{52} +(485.770 - 312.185i) q^{53} +(76.6866 + 167.920i) q^{54} +(241.549 + 278.762i) q^{55} +(-79.7520 - 51.2535i) q^{56} +(-119.660 + 832.253i) q^{57} +(17.8569 - 124.197i) q^{58} +(-376.047 - 241.671i) q^{59} +(171.096 + 197.456i) q^{60} +(147.131 + 322.171i) q^{61} +(-435.374 + 279.798i) q^{62} +(-139.524 - 40.9680i) q^{63} +(-41.9111 + 48.3680i) q^{64} +(38.6008 - 11.3342i) q^{65} +(-184.251 + 403.453i) q^{66} +(-143.214 - 996.079i) q^{67} -123.678 q^{68} +(-569.154 + 392.268i) q^{69} +247.030 q^{70} +(-107.399 - 746.978i) q^{71} +(-40.7807 + 89.2973i) q^{72} +(-679.053 + 199.388i) q^{73} +(-428.528 + 494.548i) q^{74} +(98.3691 + 28.8838i) q^{75} +(451.491 - 290.155i) q^{76} +(174.208 + 381.462i) q^{77} +(31.6792 + 36.5598i) q^{78} +(96.0377 + 61.7197i) q^{79} +(23.7337 - 165.071i) q^{80} +(129.469 - 900.480i) q^{81} +(116.357 + 74.7780i) q^{82} +(-169.463 - 195.571i) q^{83} +(123.397 + 270.201i) q^{84} +(271.114 - 174.235i) q^{85} +(571.066 + 167.680i) q^{86} +(-257.460 + 297.125i) q^{87} +(271.639 - 79.7605i) q^{88} +(141.598 - 310.057i) q^{89} +(-36.4047 - 253.200i) q^{90} +45.7388 q^{91} +(427.132 + 110.590i) q^{92} +1621.59 q^{93} +(-142.914 - 993.986i) q^{94} +(-580.951 + 1272.10i) q^{95} +(192.410 - 56.4967i) q^{96} +(412.119 - 475.611i) q^{97} +(-388.735 - 114.143i) q^{98} +(365.317 - 234.775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 2 * q^3 - 12 * q^4 - 4 * q^6 - 115 * q^7 + 24 * q^8 - 83 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9} - 30 q^{11} + 52 q^{12} + 104 q^{13} - 56 q^{14} + 492 q^{15} - 48 q^{16} + 274 q^{17} + 166 q^{18} - 381 q^{19} - 176 q^{20} - 546 q^{21} + 60 q^{22} - 461 q^{23} - 16 q^{24} - 363 q^{25} - 318 q^{26} + 929 q^{27} + 112 q^{28} - 41 q^{29} + 776 q^{30} + 416 q^{31} + 96 q^{32} - 960 q^{33} - 416 q^{34} + 1671 q^{35} - 420 q^{36} + 1338 q^{37} - 118 q^{38} - 1642 q^{39} - 263 q^{41} - 8 q^{42} - 561 q^{43} - 120 q^{44} - 48 q^{45} - 1322 q^{46} - 1508 q^{47} + 208 q^{48} - 304 q^{49} + 1298 q^{50} - 1313 q^{51} - 24 q^{52} + 337 q^{53} + 1222 q^{54} + 4597 q^{55} + 920 q^{56} + 3446 q^{57} + 500 q^{58} + 1507 q^{59} + 516 q^{60} - 1291 q^{61} - 590 q^{62} + 1108 q^{63} - 192 q^{64} - 2522 q^{65} - 1204 q^{66} - 5093 q^{67} - 576 q^{68} - 5786 q^{69} - 2000 q^{70} + 850 q^{71} - 1800 q^{72} + 2452 q^{73} - 2676 q^{74} + 1267 q^{75} - 512 q^{76} - 6123 q^{77} + 2272 q^{78} + 536 q^{79} + 704 q^{80} + 3083 q^{81} - 1542 q^{82} + 7180 q^{83} + 2612 q^{84} + 1126 q^{85} + 6182 q^{86} - 7541 q^{87} + 856 q^{88} + 3457 q^{89} - 300 q^{90} + 4134 q^{91} + 92 q^{92} + 4930 q^{93} + 1542 q^{94} - 9721 q^{95} - 64 q^{96} + 4159 q^{97} + 2192 q^{98} + 7587 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 - 12 * q^4 - 4 * q^6 - 115 * q^7 + 24 * q^8 - 83 * q^9 - 30 * q^11 + 52 * q^12 + 104 * q^13 - 56 * q^14 + 492 * q^15 - 48 * q^16 + 274 * q^17 + 166 * q^18 - 381 * q^19 - 176 * q^20 - 546 * q^21 + 60 * q^22 - 461 * q^23 - 16 * q^24 - 363 * q^25 - 318 * q^26 + 929 * q^27 + 112 * q^28 - 41 * q^29 + 776 * q^30 + 416 * q^31 + 96 * q^32 - 960 * q^33 - 416 * q^34 + 1671 * q^35 - 420 * q^36 + 1338 * q^37 - 118 * q^38 - 1642 * q^39 - 263 * q^41 - 8 * q^42 - 561 * q^43 - 120 * q^44 - 48 * q^45 - 1322 * q^46 - 1508 * q^47 + 208 * q^48 - 304 * q^49 + 1298 * q^50 - 1313 * q^51 - 24 * q^52 + 337 * q^53 + 1222 * q^54 + 4597 * q^55 + 920 * q^56 + 3446 * q^57 + 500 * q^58 + 1507 * q^59 + 516 * q^60 - 1291 * q^61 - 590 * q^62 + 1108 * q^63 - 192 * q^64 - 2522 * q^65 - 1204 * q^66 - 5093 * q^67 - 576 * q^68 - 5786 * q^69 - 2000 * q^70 + 850 * q^71 - 1800 * q^72 + 2452 * q^73 - 2676 * q^74 + 1267 * q^75 - 512 * q^76 - 6123 * q^77 + 2272 * q^78 + 536 * q^79 + 704 * q^80 + 3083 * q^81 - 1542 * q^82 + 7180 * q^83 + 2612 * q^84 + 1126 * q^85 + 6182 * q^86 - 7541 * q^87 + 856 * q^88 + 3457 * q^89 - 300 * q^90 + 4134 * q^91 + 92 * q^92 + 4930 * q^93 + 1542 * q^94 - 9721 * q^95 - 64 * q^96 + 4159 * q^97 + 2192 * q^98 + 7587 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.284630	+	1.97964i	0.100632	+	0.699909i
$2$	0.284630	+	1.97964i	0.100632	+	0.699909i
$3$	2.60327	−	5.70036i	0.500999	−	1.09703i	−0.475145	−	0.879908i	$-0.657604\pi$
$3$	2.60327	−	5.70036i	0.500999	−	1.09703i	0.976143	−	0.217127i	$-0.0696685\pi$
$4$	−3.83797	+	1.12693i	−0.479746	+	0.140866i
$5$	6.82565	−	7.87722i	0.610505	−	0.704560i	−0.363370	−	0.931645i	$-0.618374\pi$
$5$	6.82565	−	7.87722i	0.610505	−	0.704560i	0.973875	+	0.227085i	$0.0729195\pi$
$6$	12.0256	+	3.53105i	0.818241	+	0.240257i
$7$	9.96901	−	6.40669i	0.538276	−	0.345929i	−0.243088	−	0.970004i	$-0.578161\pi$
$7$	9.96901	−	6.40669i	0.538276	−	0.345929i	0.781364	+	0.624075i	$0.214524\pi$
$8$	−3.32332	−	7.27706i	−0.146871	−	0.321603i
$9$	−8.03584	−	9.27386i	−0.297624	−	0.343476i
$10$	17.5369	+	11.2703i	0.554564	+	0.356397i
$11$	−5.03629	+	35.0282i	−0.138045	+	0.960127i	0.796590	+	0.604520i	$0.206635\pi$
$11$	−5.03629	+	35.0282i	−0.138045	+	0.960127i	−0.934636	+	0.355607i	$0.884274\pi$
$12$	−3.56736	+	24.8115i	−0.0858173	+	0.596872i
$13$	3.24703	+	2.08674i	0.0692742	+	0.0445198i	0.574819	−	0.818280i	$-0.305072\pi$
$13$	3.24703	+	2.08674i	0.0692742	+	0.0445198i	−0.505545	+	0.862800i	$0.668709\pi$
$14$	15.5204	+	17.9115i	0.296286	+	0.341933i
$15$	−27.1340	−	59.4152i	−0.467064	−	1.02273i
$16$	13.4601	−	8.65025i	0.210313	−	0.135160i
$17$	29.6669	+	8.71100i	0.423252	+	0.124278i	0.486420	−	0.873725i	$-0.338302\pi$
$17$	29.6669	+	8.71100i	0.423252	+	0.124278i	−0.0631684	+	0.998003i	$0.520121\pi$
$18$	16.0717	−	18.5477i	0.210452	−	0.242874i
$19$	−128.737	+	37.8006i	−1.55444	+	0.456424i	−0.942423	−	0.334422i	$-0.891459\pi$
$19$	−128.737	+	37.8006i	−1.55444	+	0.456424i	−0.612014	+	0.790847i	$0.709641\pi$
$20$	−17.3196	+	37.9246i	−0.193639	+	0.424010i
$21$	−10.5685	−	73.5052i	−0.109820	−	0.763817i
$22$	−70.7768			−0.685894
$23$	−94.6684	−	56.6118i	−0.858249	−	0.513233i
$23$	−94.6684	−	56.6118i	−0.858249	−	0.513233i
$24$	−50.1333			−0.426392
$25$	2.32826	+	16.1934i	0.0186260	+	0.129547i
$26$	−3.20680	+	7.02191i	−0.0241886	+	0.0529657i
$27$	88.5624	−	26.0043i	0.631253	−	0.185353i
$28$	−31.0409	+	35.8231i	−0.209506	+	0.241783i
$29$	−60.1958	−	17.6751i	−0.385451	−	0.113179i	0.0832651	−	0.996527i	$-0.473465\pi$
$29$	−60.1958	−	17.6751i	−0.385451	−	0.113179i	−0.468716	+	0.883349i	$0.655283\pi$
$30$	109.898	−	70.6269i	0.668816	−	0.429822i
$31$	107.495	+	235.381i	0.622796	+	1.36373i	0.913468	+	0.406910i	$0.133394\pi$
$31$	107.495	+	235.381i	0.622796	+	1.36373i	−0.290673	+	0.956822i	$0.593879\pi$
$32$	20.9555	+	24.1840i	0.115764	+	0.133599i
$33$	186.562	+	119.896i	0.984132	+	0.632463i
$34$	−8.80057	+	61.2093i	−0.0443908	+	0.308744i
$35$	17.5780	−	122.258i	0.0848923	−	0.590439i
$36$	41.2923	+	26.5370i	0.191168	+	0.122856i
$37$	214.264	+	247.274i	0.952022	+	1.09869i	0.995026	+	0.0996170i	$0.0317618\pi$
$37$	214.264	+	247.274i	0.952022	+	1.09869i	−0.0430039	+	0.999075i	$0.513693\pi$
$38$	−111.474	−	244.094i	−0.475881	−	1.04203i
$39$	20.3480	−	13.0769i	0.0835460	−	0.0536918i
$40$	−80.0068	−	23.4921i	−0.316255	−	0.0928607i
$41$	45.2881	−	52.2653i	0.172508	−	0.199084i	−0.662912	−	0.748698i	$-0.730679\pi$
$41$	45.2881	−	52.2653i	0.172508	−	0.199084i	0.835419	+	0.549613i	$0.185225\pi$
$42$	142.506	−	41.8435i	0.523551	−	0.153729i
$43$	123.622	−	270.695i	0.438424	−	0.960014i	−0.553461	−	0.832875i	$-0.686693\pi$
$43$	123.622	−	270.695i	0.438424	−	0.960014i	0.991885	−	0.127139i	$-0.0405795\pi$
$44$	−20.1452	−	140.113i	−0.0690227	−	0.480063i
$45$	−127.902			−0.423700
$46$	85.1257	−	203.523i	0.272850	−	0.652344i
$47$	−502.104			−1.55828			−0.779142	−	0.626847i	$-0.784345\pi$
$47$	−502.104			−1.55828			−0.779142	+	0.626847i	$0.784345\pi$
$48$	−14.2694	−	99.2460i	−0.0429086	−	0.298436i
$49$	−84.1520	+	184.267i	−0.245341	+	0.537222i
$50$	−31.3944	+	9.21823i	−0.0887968	+	0.0260731i
$51$	126.887	−	146.435i	0.348386	−	0.402059i
$52$	−14.8136	−	4.34967i	−0.0395054	−	0.0115998i
$53$	485.770	−	312.185i	1.25897	−	0.809093i	0.270831	−	0.962627i	$-0.412702\pi$
$53$	485.770	−	312.185i	1.25897	−	0.809093i	0.988143	+	0.153534i	$0.0490653\pi$
$54$	76.6866	+	167.920i	0.193254	+	0.423168i
$55$	241.549	+	278.762i	0.592190	+	0.683423i
$56$	−79.7520	−	51.2535i	−0.190309	−	0.122304i
$57$	−119.660	+	832.253i	−0.278059	+	1.93394i
$58$	17.8569	−	124.197i	0.0404262	−	0.281170i
$59$	−376.047	−	241.671i	−0.829783	−	0.533269i	0.0554258	−	0.998463i	$-0.482348\pi$
$59$	−376.047	−	241.671i	−0.829783	−	0.533269i	−0.885209	+	0.465194i	$0.845985\pi$
$60$	171.096	+	197.456i	0.368140	+	0.424857i
$61$	147.131	+	322.171i	0.308822	+	0.676227i	0.998869	−	0.0475379i	$-0.0151375\pi$
$61$	147.131	+	322.171i	0.308822	+	0.676227i	−0.690047	+	0.723764i	$0.742410\pi$
$62$	−435.374	+	279.798i	−0.891816	+	0.573135i
$63$	−139.524	−	40.9680i	−0.279022	−	0.0819283i
$64$	−41.9111	+	48.3680i	−0.0818576	+	0.0944687i
$65$	38.6008	−	11.3342i	0.0736591	−	0.0216283i
$66$	−184.251	+	403.453i	−0.343632	+	0.752449i
$67$	−143.214	−	996.079i	−0.261141	−	1.81627i	−0.524313	−	0.851525i	$-0.675678\pi$
$67$	−143.214	−	996.079i	−0.261141	−	1.81627i	0.263173	−	0.964749i	$-0.415231\pi$
$68$	−123.678			−0.220560
$69$	−569.154	+	392.268i	−0.993017	+	0.684399i
$70$	247.030			0.421796
$71$	−107.399	−	746.978i	−0.179520	−	1.24859i	−0.857876	−	0.513857i	$-0.828216\pi$
$71$	−107.399	−	746.978i	−0.179520	−	1.24859i	0.678355	−	0.734734i	$-0.262693\pi$
$72$	−40.7807	+	89.2973i	−0.0667507	+	0.146164i
$73$	−679.053	+	199.388i	−1.08873	+	0.319680i	−0.776365	−	0.630283i	$-0.782939\pi$
$73$	−679.053	+	199.388i	−1.08873	+	0.319680i	−0.312363	+	0.949963i	$0.601121\pi$
$74$	−428.528	+	494.548i	−0.673181	+	0.776892i
$75$	98.3691	+	28.8838i	0.151449	+	0.0444695i
$76$	451.491	−	290.155i	0.681441	−	0.437936i
$77$	174.208	+	381.462i	0.257829	+	0.564567i
$78$	31.6792	+	36.5598i	0.0459868	+	0.0530715i
$79$	96.0377	+	61.7197i	0.136773	+	0.0878989i	0.607238	−	0.794520i	$-0.292277\pi$
$79$	96.0377	+	61.7197i	0.136773	+	0.0878989i	−0.470465	+	0.882419i	$0.655914\pi$
$80$	23.7337	−	165.071i	0.0331688	−	0.230694i
$81$	129.469	−	900.480i	0.177599	−	1.23523i
$82$	116.357	+	74.7780i	0.156701	+	0.100706i
$83$	−169.463	−	195.571i	−0.224108	−	0.258635i	0.632549	−	0.774520i	$-0.282009\pi$
$83$	−169.463	−	195.571i	−0.224108	−	0.258635i	−0.856658	+	0.515885i	$0.827463\pi$
$84$	123.397	+	270.201i	0.160282	+	0.350968i
$85$	271.114	−	174.235i	0.345959	−	0.222334i
$86$	571.066	+	167.680i	0.716043	+	0.210249i
$87$	−257.460	+	297.125i	−0.317272	+	0.366151i
$88$	271.639	−	79.7605i	0.329055	−	0.0966193i
$89$	141.598	−	310.057i	0.168645	−	0.369280i	−0.806373	−	0.591407i	$-0.798573\pi$
$89$	141.598	−	310.057i	0.168645	−	0.369280i	0.975018	+	0.222127i	$0.0712999\pi$
$90$	−36.4047	−	253.200i	−0.0426377	−	0.296552i
$91$	45.7388			0.0526893
$92$	427.132	+	110.590i	0.484039	+	0.125324i
$93$	1621.59			1.80808
$94$	−142.914	−	993.986i	−0.156813	−	1.09066i
$95$	−580.951	+	1272.10i	−0.627413	+	1.37384i
$96$	192.410	−	56.4967i	0.204560	−	0.0600643i
$97$	412.119	−	475.611i	0.431385	−	0.497845i	−0.497886	−	0.867242i	$-0.665890\pi$
$97$	412.119	−	475.611i	0.431385	−	0.497845i	0.929272	+	0.369397i	$0.120436\pi$
$98$	−388.735	−	114.143i	−0.400696	−	0.117655i
$99$	365.317	−	234.775i	0.370866	−	0.238341i
$100$	−27.1846	−	59.5259i	−0.0271846	−	0.0595259i
$101$	−739.345	−	853.250i	−0.728392	−	0.840609i	0.263898	−	0.964551i	$-0.414992\pi$
$101$	−739.345	−	853.250i	−0.728392	−	0.840609i	−0.992290	+	0.123942i	$0.960446\pi$
$102$	326.005	+	209.511i	0.316464	+	0.203379i
$103$	−158.077	+	1099.45i	−0.151221	+	1.05177i	0.762955	+	0.646451i	$0.223748\pi$
$103$	−158.077	+	1099.45i	−0.151221	+	1.05177i	−0.914177	+	0.405316i	$0.867162\pi$
$104$	4.39440	−	30.5637i	0.00414333	−	0.0288175i
$105$	−651.153	−	418.471i	−0.605201	−	0.388939i
$106$	756.280	+	872.794i	0.692985	+	0.799747i
$107$	182.845	+	400.375i	0.165199	+	0.361736i	0.974069	−	0.226252i	$-0.0726474\pi$
$107$	182.845	+	400.375i	0.165199	+	0.361736i	−0.808870	+	0.587988i	$0.799920\pi$
$108$	−310.595	+	199.607i	−0.276732	+	0.177845i
$109$	515.605	+	151.395i	0.453083	+	0.133037i	0.500309	−	0.865847i	$-0.333220\pi$
$109$	515.605	+	151.395i	0.453083	+	0.133037i	−0.0472259	+	0.998884i	$0.515038\pi$
$110$	−483.098	+	557.524i	−0.418741	+	0.483253i
$111$	1967.34	−	577.662i	1.68226	−	0.493957i
$112$	78.7639	−	172.469i	0.0664508	−	0.145507i
$113$	−122.218	−	850.042i	−0.101746	−	0.707657i	−0.975293	−	0.220917i	$-0.929095\pi$
$113$	−122.218	−	850.042i	−0.101746	−	0.707657i	0.873547	−	0.486740i	$-0.161814\pi$
$114$	−1681.62			−1.38156
$115$	−1092.12	+	359.312i	−0.885569	+	0.291356i
$116$	250.949			0.200862
$117$	−6.74050	−	46.8812i	−0.00532615	−	0.0370442i
$118$	371.388	−	813.226i	0.289738	−	0.634437i
$119$	351.558	−	103.227i	0.270818	−	0.0795193i
$120$	−342.192	+	394.911i	−0.260315	+	0.300419i
$121$	75.4754	+	22.1616i	0.0567058	+	0.0166503i
$122$	−595.907	+	382.966i	−0.442220	+	0.284198i
$123$	−180.034	−	394.219i	−0.131976	−	0.288988i
$124$	−677.821	−	782.247i	−0.490888	−	0.566515i
$125$	1239.50	+	796.581i	0.886917	+	0.569987i
$126$	41.3893	−	287.869i	0.0292639	−	0.203535i
$127$	−370.646	+	2577.90i	−0.258972	+	1.80119i	0.281211	+	0.959646i	$0.409264\pi$
$127$	−370.646	+	2577.90i	−0.258972	+	1.80119i	−0.540184	+	0.841547i	$0.681645\pi$
$128$	−107.680	−	69.2020i	−0.0743570	−	0.0477863i
$129$	−1221.24	−	1409.38i	−0.833519	−	0.961932i
$130$	33.4246	+	73.1897i	0.0225503	+	0.0493782i
$131$	−1287.46	+	827.403i	−0.858674	+	0.551836i	−0.894269	−	0.447530i	$-0.852304\pi$
$131$	−1287.46	+	827.403i	−0.858674	+	0.551836i	0.0355952	+	0.999366i	$0.488667\pi$
$132$	−851.136	−	249.916i	−0.561226	−	0.164791i
$133$	−1041.20	+	1201.61i	−0.678826	+	0.783407i
$134$	1931.12	−	567.027i	1.24495	−	0.365550i
$135$	399.655	−	875.121i	0.254791	−	0.557914i
$136$	−35.2023	−	244.837i	−0.0221954	−	0.154372i
$137$	−436.585			−0.272262			−0.136131	−	0.990691i	$-0.543467\pi$
$137$	−436.585			−0.272262			−0.136131	+	0.990691i	$0.543467\pi$
$138$	−938.549	−	1015.07i	−0.578947	−	0.626149i
$139$	842.549			0.514130			0.257065	−	0.966394i	$-0.417245\pi$
$139$	842.549			0.514130			0.257065	+	0.966394i	$0.417245\pi$
$140$	70.3121	+	489.032i	0.0424461	+	0.295219i
$141$	−1307.11	+	2862.17i	−0.780698	+	1.70949i
$142$	1448.18	−	425.224i	0.855835	−	0.251296i
$143$	−89.4477	+	103.228i	−0.0523076	+	0.0603662i
$144$	−188.384	−	55.3146i	−0.109019	−	0.0320107i
$145$	−550.106	+	353.532i	−0.315061	+	0.202477i
$146$	−587.996	−	1287.53i	−0.333307	−	0.729842i
$147$	831.318	+	959.393i	0.466435	+	0.538295i
$148$	−1101.00	−	707.570i	−0.611498	−	0.392986i
$149$	296.308	−	2060.87i	0.162916	−	1.13311i	−0.730184	−	0.683251i	$-0.760566\pi$
$149$	296.308	−	2060.87i	0.162916	−	1.13311i	0.893100	−	0.449857i	$-0.148525\pi$
$150$	−29.1808	+	202.957i	−0.0158840	+	0.110476i
$151$	−1163.86	−	747.969i	−0.627244	−	0.403105i	0.188045	−	0.982161i	$-0.439785\pi$
$151$	−1163.86	−	747.969i	−0.627244	−	0.403105i	−0.815288	+	0.579056i	$0.803421\pi$
$152$	702.912	+	811.204i	0.375090	+	0.432877i
$153$	−157.614	−	345.127i	−0.0832834	−	0.182365i
$154$	−705.574	+	453.445i	−0.369200	+	0.237270i
$155$	2587.87	+	759.868i	1.34105	+	0.393768i
$156$	−63.3585	+	73.1196i	−0.0325175	+	0.0375273i
$157$	15.3806	−	4.51615i	0.00781850	−	0.00229572i	−0.277821	−	0.960633i	$-0.589612\pi$
$157$	15.3806	−	4.51615i	0.00781850	−	0.00229572i	0.285639	+	0.958337i	$0.407794\pi$
$158$	−94.8478	+	207.688i	−0.0477575	+	0.104574i
$159$	−514.980	−	3581.76i	−0.256859	−	1.78649i
$160$	333.538			0.164803
$161$	−1306.44	+	42.1482i	−0.639517	+	0.0206319i
$162$	1819.48			0.882419
$163$	105.404	+	733.098i	0.0506494	+	0.352274i	0.999348	+	0.0360936i	$0.0114915\pi$
$163$	105.404	+	733.098i	0.0506494	+	0.352274i	−0.948699	+	0.316181i	$0.897599\pi$
$164$	−114.915	+	251.629i	−0.0547156	+	0.119811i
$165$	2217.86	−	651.222i	1.04643	−	0.307258i
$166$	338.926	−	391.142i	0.158469	−	0.182883i
$167$	178.438	+	52.3940i	0.0826821	+	0.0242777i	0.322812	−	0.946463i	$-0.395372\pi$
$167$	178.438	+	52.3940i	0.0826821	+	0.0242777i	−0.240130	+	0.970741i	$0.577190\pi$
$168$	−499.779	+	321.189i	−0.229517	+	0.147501i
$169$	−906.478	−	1984.91i	−0.412598	−	0.903464i
$170$	422.090	+	487.118i	0.190428	+	0.219766i
$171$	1385.07	+	890.130i	0.619409	+	0.398070i
$172$	−169.404	+	1178.23i	−0.0750987	+	0.522323i
$173$	−627.519	+	4364.49i	−0.275777	+	1.91807i	0.107060	+	0.994253i	$0.465856\pi$
$173$	−627.519	+	4364.49i	−0.275777	+	1.91807i	−0.382837	+	0.923816i	$0.625053\pi$
$174$	−661.482	−	425.109i	−0.288200	−	0.185215i
$175$	126.956	+	146.515i	0.0548400	+	0.0632887i
$176$	235.214	+	515.047i	0.100738	+	0.220586i
$177$	−2356.56	+	1514.47i	−1.00074	+	0.643133i
$178$	654.105	+	192.062i	0.275434	+	0.0808747i
$179$	2006.25	−	2315.33i	0.837731	−	0.966793i	−0.162069	−	0.986779i	$-0.551817\pi$
$179$	2006.25	−	2315.33i	0.837731	−	0.966793i	0.999800	+	0.0199861i	$0.00636220\pi$
$180$	490.885	−	144.137i	0.203269	−	0.0596851i
$181$	1321.00	−	2892.58i	0.542481	−	1.18787i	−0.417725	−	0.908574i	$-0.637172\pi$
$181$	1321.00	−	2892.58i	0.542481	−	1.18787i	0.960206	−	0.279294i	$-0.0901003\pi$
$182$	13.0186	+	90.5464i	0.00530222	+	0.0368777i
$183$	2219.51			0.896563
$184$	−97.3536	+	877.046i	−0.0390054	+	0.351395i
$185$	3410.32			1.35531
$186$	461.554	+	3210.18i	0.181950	+	1.26549i
$187$	−454.542	+	995.308i	−0.177751	+	0.389220i
$188$	1927.06	−	565.836i	0.747581	−	0.219510i
$189$	716.278	−	826.628i	0.275669	−	0.318140i
$190$	−2683.67	−	787.996i	−1.02470	−	0.300880i
$191$	934.957	−	600.860i	0.354194	−	0.227627i	−0.351428	−	0.936215i	$-0.614304\pi$
$191$	934.957	−	600.860i	0.354194	−	0.227627i	0.705622	+	0.708588i	$0.250668\pi$
$192$	166.609	+	364.823i	0.0626249	+	0.137129i
$193$	−2511.07	−	2897.93i	−0.936531	−	1.08081i	−0.996581	−	0.0826193i	$-0.973671\pi$
$193$	−2511.07	−	2897.93i	−0.936531	−	1.08081i	0.0600500	−	0.998195i	$-0.480874\pi$
$194$	1058.84	+	680.476i	0.391857	+	0.251832i
$195$	35.8791	−	249.544i	0.0131762	−	0.0916423i
$196$	115.317	−	802.045i	0.0420250	−	0.292291i
$197$	2905.88	+	1867.50i	1.05094	+	0.675399i	0.947669	−	0.319254i	$-0.103432\pi$
$197$	2905.88	+	1867.50i	1.05094	+	0.675399i	0.103272	+	0.994653i	$0.467069\pi$
$198$	568.751	+	656.374i	0.204138	+	0.235588i
$199$	−398.876	−	873.418i	−0.142088	−	0.311130i	0.825187	−	0.564860i	$-0.191070\pi$
$199$	−398.876	−	873.418i	−0.142088	−	0.311130i	−0.967275	+	0.253730i	$0.918343\pi$
$200$	110.103	−	70.7586i	0.0389271	−	0.0250169i
$201$	−6050.83	−	1776.68i	−2.12335	−	0.623471i
$202$	1478.69	−	1706.50i	0.515051	−	0.594400i
$203$	−713.332	+	209.453i	−0.246631	+	0.0724173i
$204$	−321.965	+	705.006i	−0.110500	+	0.241962i
$205$	−102.584	−	713.489i	−0.0349502	−	0.243084i
$206$	−2221.51			−0.751359
$207$	235.731	+	1332.86i	0.0791519	+	0.447539i
$208$	61.7560			0.0205866
$209$	−675.730	−	4699.80i	−0.223642	−	1.55546i
$210$	643.085	−	1408.16i	0.211320	−	0.462725i
$211$	−3300.10	+	968.995i	−1.07672	+	0.316154i	−0.771566	−	0.636149i	$-0.780526\pi$
$211$	−3300.10	+	968.995i	−1.07672	+	0.316154i	−0.305154	+	0.952303i	$0.598708\pi$
$212$	−1512.56	+	1745.59i	−0.490014	+	0.565507i
$213$	−4537.63	−	1332.37i	−1.45969	−	0.428603i
$214$	−740.556	+	475.927i	−0.236558	+	0.152027i
$215$	−1288.52	−	2821.47i	−0.408728	−	0.894989i
$216$	−483.556	−	558.053i	−0.152323	−	0.175790i
$217$	2579.63	+	1657.83i	0.806990	+	0.518621i
$218$	−152.952	+	1063.81i	−0.0475194	+	0.330505i
$219$	−631.173	+	4389.91i	−0.194752	+	1.35453i
$220$	−1241.20	−	797.673i	−0.380372	−	0.244450i
$221$	78.1518	+	90.1920i	0.0237876	+	0.0274524i
$222$	1703.53	+	3730.21i	0.515015	+	1.12773i
$223$	−1741.73	+	1119.34i	−0.523027	+	0.336129i	−0.775368	−	0.631509i	$-0.782436\pi$
$223$	−1741.73	+	1119.34i	−0.523027	+	0.336129i	0.252342	+	0.967638i	$0.418799\pi$
$224$	363.845	+	106.835i	0.108529	+	0.0318669i
$225$	131.466	−	151.719i	0.0389528	−	0.0449539i
$226$	1647.99	−	483.895i	0.485057	−	0.142426i
$227$	279.223	−	611.413i	0.0816418	−	0.178771i	−0.864409	−	0.502790i	$-0.832307\pi$
$227$	279.223	−	611.413i	0.0816418	−	0.178771i	0.946050	+	0.324019i	$0.105034\pi$
$228$	−478.639	−	3329.01i	−0.139029	−	0.966970i
$229$	1899.18			0.548042			0.274021	−	0.961724i	$-0.411646\pi$
$229$	1899.18			0.548042			0.274021	+	0.961724i	$0.411646\pi$
$230$	−1022.16	−	2059.73i	−0.293040	−	0.590498i
$231$	2627.98			0.748521
$232$	71.4274	+	496.789i	0.0202131	+	0.140585i
$233$	−986.970	+	2161.16i	−0.277504	+	0.607650i	−0.996144	−	0.0877328i	$-0.972038\pi$
$233$	−986.970	+	2161.16i	−0.277504	+	0.607650i	0.718640	+	0.695383i	$0.244765\pi$
$234$	90.8895	−	26.6876i	0.0253916	−	0.00745564i
$235$	−3427.18	+	3955.18i	−0.951340	+	1.09790i
$236$	1715.61	+	503.747i	0.473205	+	0.138946i
$237$	601.836	−	386.777i	0.164951	−	0.106008i
$238$	304.416	+	666.579i	0.0829091	+	0.181546i
$239$	2078.05	+	2398.20i	0.562418	+	0.649065i	0.963731	−	0.266876i	$-0.0859913\pi$
$239$	2078.05	+	2398.20i	0.562418	+	0.649065i	−0.401313	+	0.915941i	$0.631446\pi$
$240$	−879.181	−	565.015i	−0.236462	−	0.151965i
$241$	−942.137	+	6552.71i	−0.251819	+	1.75144i	0.335459	+	0.942055i	$0.391109\pi$
$241$	−942.137	+	6552.71i	−0.251819	+	1.75144i	−0.587278	+	0.809385i	$0.699800\pi$
$242$	−22.3895	+	155.722i	−0.00594731	+	0.0413644i
$243$	−2699.50	−	1734.86i	−0.712646	−	0.457990i
$244$	−927.748	−	1070.68i	−0.243414	−	0.280915i
$245$	877.121	+	1920.63i	0.228723	+	0.500834i
$246$	729.169	−	468.609i	0.188984	−	0.121453i
$247$	−496.893	−	145.901i	−0.128002	−	0.0375849i
$248$	1355.64	−	1564.49i	0.347110	−	0.400586i
$249$	−1555.98	+	456.878i	−0.396009	+	0.116279i
$250$	−1224.15	+	2680.51i	−0.309687	+	0.678121i
$251$	506.196	+	3520.67i	0.127294	+	0.885349i	0.948964	+	0.315385i	$0.102134\pi$
$251$	506.196	+	3520.67i	0.127294	+	0.885349i	−0.821670	+	0.569964i	$0.806957\pi$
$252$	581.658			0.145401
$253$	2459.79	−	3030.95i	0.611247	−	0.753178i
$254$	−5208.82			−1.28673
$255$	−287.417	−	1999.03i	−0.0705833	−	0.490918i
$256$	106.346	−	232.866i	0.0259634	−	0.0568520i
$257$	4466.97	−	1311.62i	1.08421	−	0.318353i	0.309649	−	0.950851i	$-0.399788\pi$
$257$	4466.97	−	1311.62i	1.08421	−	0.318353i	0.774562	+	0.632498i	$0.217970\pi$
$258$	2442.47	−	2818.77i	0.589387	−	0.680189i
$259$	3720.21	+	1092.35i	0.892519	+	0.262067i
$260$	−135.376	+	87.0008i	−0.0322910	+	0.0207522i
$261$	319.808	+	700.282i	0.0758453	+	0.166078i
$262$	−2004.41	−	2313.22i	−0.472645	−	0.545461i
$263$	−1293.66	−	831.383i	−0.303309	−	0.194925i	0.380129	−	0.924934i	$-0.375880\pi$
$263$	−1293.66	−	831.383i	−0.303309	−	0.194925i	−0.683438	+	0.730009i	$0.739516\pi$
$264$	252.486	−	1756.08i	0.0588615	−	0.409391i
$265$	856.542	−	5957.38i	0.198555	−	1.38098i
$266$	−2675.12	−	1719.20i	−0.616625	−	0.396281i
$267$	−1398.82	−	1614.32i	−0.320622	−	0.370018i
$268$	1672.16	+	3661.53i	0.381133	+	0.834565i
$269$	2372.42	−	1524.66i	0.537728	−	0.345577i	−0.243421	−	0.969921i	$-0.578270\pi$
$269$	2372.42	−	1524.66i	0.537728	−	0.345577i	0.781150	+	0.624344i	$0.214633\pi$
$270$	1846.18	+	542.088i	0.416130	+	0.122187i
$271$	1841.37	−	2125.06i	0.412751	−	0.476340i	−0.510864	−	0.859661i	$-0.670675\pi$
$271$	1841.37	−	2125.06i	0.412751	−	0.476340i	0.923615	+	0.383322i	$0.125220\pi$
$272$	474.671	−	139.376i	0.105813	−	0.0310695i
$273$	119.070	−	260.727i	0.0263973	−	0.0578019i
$274$	−124.265	−	864.282i	−0.0273983	−	0.190559i
$275$	−578.950			−0.126953
$276$	1742.34	−	2146.91i	0.379987	−	0.468221i
$277$	4489.62			0.973845			0.486923	−	0.873445i	$-0.338119\pi$
$277$	4489.62			0.973845			0.486923	+	0.873445i	$0.338119\pi$
$278$	239.815	+	1667.95i	0.0517379	+	0.359845i
$279$	1319.08	−	2888.38i	0.283051	−	0.619795i
$280$	−948.095	+	278.386i	−0.202355	+	0.0594169i
$281$	−4339.88	+	5008.49i	−0.921336	+	1.06328i	0.0764697	+	0.997072i	$0.475635\pi$
$281$	−4339.88	+	5008.49i	−0.921336	+	1.06328i	−0.997806	+	0.0662068i	$0.978910\pi$
$282$	−6038.12	−	1772.95i	−1.27505	−	0.374389i
$283$	6808.26	−	4375.40i	1.43007	−	0.919049i	0.430201	−	0.902733i	$-0.358443\pi$
$283$	6808.26	−	4375.40i	1.43007	−	0.919049i	0.999867	−	0.0163152i	$-0.00519352\pi$
$284$	1253.99	+	2745.85i	0.262009	+	0.573719i
$285$	5739.08	+	6623.25i	1.19282	+	1.37659i
$286$	−229.814	−	147.693i	−0.0475147	−	0.0305358i
$287$	116.630	−	811.179i	0.0239876	−	0.166838i
$288$	55.8834	−	388.677i	0.0114339	−	0.0795244i
$289$	−3328.83	−	2139.31i	−0.677556	−	0.435439i
$290$	−856.444	−	988.389i	−0.173421	−	0.200139i
$291$	−1638.30	−	3587.37i	−0.330030	−	0.722664i
$292$	2381.49	−	1530.49i	0.477282	−	0.306730i
$293$	−521.758	−	153.202i	−0.104032	−	0.0305466i	0.229302	−	0.973355i	$-0.426356\pi$
$293$	−521.758	−	153.202i	−0.104032	−	0.0305466i	−0.333334	+	0.942809i	$0.608174\pi$
$294$	−1662.64	+	1918.79i	−0.329820	+	0.380632i
$295$	−4470.46	+	1312.65i	−0.882307	+	0.259069i
$296$	1087.36	−	2380.98i	0.213518	−	0.467540i
$297$	464.856	+	3233.14i	0.0908205	+	0.631670i
$298$	4164.13			0.809468
$299$	−189.257	−	381.368i	−0.0366054	−	0.0737629i
$300$	−410.088			−0.0789214
$301$	−501.868	−	3490.57i	−0.0961037	−	0.668416i
$302$	1149.44	−	2516.93i	0.219016	−	0.479579i
$303$	−6788.54	+	1993.30i	−1.28710	+	0.377927i
$304$	−1405.82	+	1622.41i	−0.265229	+	0.306090i
$305$	3542.08	+	1040.05i	0.664980	+	0.195256i
$306$	638.367	−	410.253i	0.119258	−	0.0766426i
$307$	2264.60	+	4958.78i	0.421001	+	0.921865i	0.994702	+	0.102800i	$0.0327800\pi$
$307$	2264.60	+	4958.78i	0.421001	+	0.921865i	−0.573701	+	0.819065i	$0.694493\pi$
$308$	−1098.49	−	1267.72i	−0.203221	−	0.234530i
$309$	5855.74	+	3763.26i	1.07806	+	0.692829i
$310$	−767.682	+	5339.34i	−0.140650	+	0.978240i
$311$	25.6978	−	178.732i	0.00468549	−	0.0325883i	−0.987345	−	0.158590i	$-0.949305\pi$
$311$	25.6978	−	178.732i	0.00468549	−	0.0325883i	0.992030	+	0.126001i	$0.0402144\pi$
$312$	−162.784	−	104.615i	−0.0295380	−	0.0189829i
$313$	2355.28	+	2718.14i	0.425331	+	0.490858i	0.927453	−	0.373939i	$-0.121993\pi$
$313$	2355.28	+	2718.14i	0.425331	+	0.490858i	−0.502123	+	0.864796i	$0.667447\pi$
$314$	13.3181	+	29.1626i	0.00239358	+	0.00524122i
$315$	−1275.06	+	819.429i	−0.228068	+	0.146570i
$316$	−438.144	−	128.651i	−0.0779985	−	0.0229024i
$317$	−5712.89	+	6593.03i	−1.01220	+	1.16814i	−0.0264994	+	0.999649i	$0.508436\pi$
$317$	−5712.89	+	6593.03i	−1.01220	+	1.16814i	−0.985703	+	0.168495i	$0.946109\pi$
$318$	6944.03	−	2038.95i	1.22453	−	0.359556i
$319$	922.290	−	2019.53i	0.161876	−	0.354458i
$320$	94.9348	+	660.286i	0.0165844	+	0.115347i
$321$	2758.28			0.479601
$322$	−455.291	−	2574.30i	−0.0787962	−	0.445528i
$323$	−4148.52			−0.714643
$324$	517.878	+	3601.92i	0.0887994	+	0.617613i
$325$	−26.2314	+	57.4388i	−0.00447710	+	0.00980349i
$326$	−1421.27	+	417.323i	−0.241463	+	0.0709000i
$327$	2205.27	−	2545.01i	0.372940	−	0.430396i
$328$	−530.844	−	155.870i	−0.0893627	−	0.0262392i
$329$	−5005.47	+	3216.82i	−0.838786	+	0.539055i
$330$	1920.46	+	4205.21i	0.320357	+	0.701483i
$331$	1461.72	+	1686.91i	0.242729	+	0.280124i	0.864022	−	0.503455i	$-0.167938\pi$
$331$	1461.72	+	1686.91i	0.242729	+	0.280124i	−0.621293	+	0.783578i	$0.713392\pi$
$332$	870.790	+	559.623i	0.143948	+	0.0925099i
$333$	571.391	−	3974.11i	0.0940301	−	0.653994i
$334$	−52.9328	+	368.156i	−0.00867172	+	0.0603131i
$335$	−8823.86	−	5670.75i	−1.43910	−	0.924855i
$336$	−778.091	−	897.965i	−0.126334	−	0.145798i
$337$	−3400.95	−	7447.04i	−0.549737	−	1.20376i	−0.956904	−	0.290403i	$-0.906211\pi$
$337$	−3400.95	−	7447.04i	−0.549737	−	1.20376i	0.407167	−	0.913354i	$-0.366517\pi$
$338$	3671.40	−	2359.47i	0.590822	−	0.379699i
$339$	−5163.71	−	1516.20i	−0.827299	−	0.242917i
$340$	−844.179	+	974.235i	−0.134653	+	0.155398i
$341$	−8786.35	+	2579.90i	−1.39533	+	0.409706i
$342$	−1367.91	+	2995.30i	−0.216281	+	0.473588i
$343$	920.085	+	6399.34i	0.144839	+	1.00738i
$344$	−2380.70			−0.373136
$345$	−794.865	+	7160.84i	−0.124041	+	1.11747i
$346$	−8818.74			−1.37023
$347$	−1740.02	−	12102.1i	−0.269191	−	1.87226i	−0.456161	−	0.889897i	$-0.650776\pi$
$347$	−1740.02	−	12102.1i	−0.269191	−	1.87226i	0.186970	−	0.982366i	$-0.440133\pi$
$348$	653.286	−	1430.50i	0.100632	−	0.220352i
$349$	−2337.49	+	686.350i	−0.358519	+	0.105271i	−0.456032	−	0.889964i	$-0.650730\pi$
$349$	−2337.49	+	686.350i	−0.358519	+	0.105271i	0.0975124	+	0.995234i	$0.468911\pi$
$350$	−253.913	+	293.031i	−0.0387777	+	0.0447519i
$351$	341.829	+	100.370i	0.0519814	+	0.0152631i
$352$	−952.660	+	612.237i	−0.144253	+	0.0927055i
$353$	−4886.02	−	10698.9i	−0.736704	−	1.61316i	−0.788902	−	0.614519i	$-0.789350\pi$
$353$	−4886.02	−	10698.9i	−0.736704	−	1.61316i	0.0521981	−	0.998637i	$-0.483377\pi$
$354$	−3668.86	−	4234.09i	−0.550841	−	0.635704i
$355$	−6617.18	−	4252.60i	−0.989305	−	0.635788i
$356$	−194.038	+	1349.56i	−0.0288875	+	0.200917i
$357$	326.770	−	2272.74i	0.0484440	−	0.336935i
$358$	5154.57	+	3312.64i	0.760970	+	0.489046i
$359$	6863.44	+	7920.83i	1.00902	+	1.16447i	0.986339	+	0.164729i	$0.0526749\pi$
$359$	6863.44	+	7920.83i	1.00902	+	1.16447i	0.0226816	+	0.999743i	$0.492780\pi$
$360$	425.060	+	930.751i	0.0622295	+	0.136264i
$361$	9374.20	−	6024.43i	1.36670	−	0.878325i
$362$	6102.28	+	1791.79i	0.885990	+	0.260150i
$363$	322.811	−	372.544i	0.0466755	−	0.0538664i
$364$	−175.544	+	51.5444i	−0.0252775	+	0.00742214i
$365$	−3064.36	+	6710.01i	−0.439441	+	0.962241i
$366$	631.739	+	4393.84i	0.0902228	+	0.627513i
$367$	3780.54			0.537718			0.268859	−	0.963180i	$-0.413353\pi$
$367$	3780.54			0.537718			0.268859	+	0.963180i	$0.413353\pi$
$368$	−1763.95	+	56.9081i	−0.249870	+	0.00806124i
$369$	−848.629			−0.119723
$370$	970.679	+	6751.22i	0.136387	+	0.948593i
$371$	2842.57	−	6224.35i	0.397786	−	0.871031i
$372$	−6223.63	+	1827.42i	−0.867420	+	0.254698i
$373$	2792.15	−	3222.31i	0.387592	−	0.447305i	−0.528102	−	0.849181i	$-0.677096\pi$
$373$	2792.15	−	3222.31i	0.387592	−	0.447305i	0.915694	+	0.401876i	$0.131642\pi$
$374$	−2099.73	−	616.536i	−0.290306	−	0.0852415i
$375$	7767.56	−	4991.91i	1.06964	−	0.687416i
$376$	1668.65	+	3653.84i	0.228867	+	0.501150i
$377$	−158.574	−	183.005i	−0.0216631	−	0.0250006i
$378$	1840.30	+	1182.69i	0.250410	+	0.160929i
$379$	895.224	−	6226.42i	0.121331	−	0.843878i	−0.834719	−	0.550676i	$-0.814370\pi$
$379$	895.224	−	6226.42i	0.121331	−	0.843878i	0.956050	−	0.293202i	$-0.0947209\pi$
$380$	796.099	−	5536.99i	0.107471	−	0.747478i
$381$	13730.1	+	8823.77i	1.84623	+	1.18650i
$382$	1455.60	+	1679.86i	0.194961	+	0.224997i
$383$	−2361.58	−	5171.14i	−0.315068	−	0.689904i	0.684154	−	0.729338i	$-0.260172\pi$
$383$	−2361.58	−	5171.14i	−0.315068	−	0.689904i	−0.999222	+	0.0394341i	$0.987444\pi$
$384$	−674.797	+	433.666i	−0.0896760	+	0.0576313i
$385$	4193.94	+	1231.45i	0.555177	+	0.163015i
$386$	5022.13	−	5795.85i	0.662228	−	0.764251i
$387$	−3503.80	+	1028.81i	−0.460228	+	0.135135i
$388$	−1045.72	+	2289.81i	−0.136826	+	0.299607i
$389$	91.8868	+	639.087i	0.0119765	+	0.0832982i	0.994933	−	0.100540i	$-0.0320569\pi$
$389$	91.8868	+	639.087i	0.0119765	+	0.0832982i	−0.982957	+	0.183838i	$0.941148\pi$
$390$	504.221			0.0654672
$391$	−2315.38	−	2504.15i	−0.299472	−	0.323889i
$392$	1620.59			0.208806
$393$	1364.88	+	9492.95i	0.175189	+	1.21846i
$394$	−2869.88	+	6284.15i	−0.366960	+	0.803530i
$395$	1141.70	−	335.233i	0.145431	−	0.0427023i
$396$	−1137.50	+	1312.75i	−0.144348	+	0.166586i
$397$	7541.44	+	2214.37i	0.953385	+	0.279939i	0.721196	−	0.692731i	$-0.243593\pi$
$397$	7541.44	+	2214.37i	0.953385	+	0.279939i	0.232190	+	0.972671i	$0.425411\pi$
$398$	1615.52	−	1038.23i	0.203464	−	0.130759i
$399$	4139.10	+	9063.35i	0.519333	+	1.13718i
$400$	171.415	+	197.824i	0.0214269	+	0.0247280i
$401$	−2283.05	−	1467.23i	−0.284314	−	0.182718i	0.390709	−	0.920514i	$-0.372230\pi$
$401$	−2283.05	−	1467.23i	−0.284314	−	0.182718i	−0.675023	+	0.737797i	$0.735866\pi$
$402$	1794.95	−	12484.2i	0.222697	−	1.54889i
$403$	−142.140	+	988.603i	−0.0175694	+	0.122198i
$404$	3799.14	+	2441.56i	0.467857	+	0.300673i
$405$	−6209.57	−	7166.22i	−0.761866	−	0.879240i
$406$	−617.678	−	1352.53i	−0.0755045	−	0.165332i
$407$	−9740.66	+	6259.94i	−1.18631	+	0.762393i
$408$	−1487.30	−	436.711i	−0.180472	−	0.0529912i
$409$	−3314.28	+	3824.89i	−0.400686	+	0.462417i	−0.919857	−	0.392254i	$-0.871695\pi$
$409$	−3314.28	+	3824.89i	−0.400686	+	0.462417i	0.519171	+	0.854671i	$0.326241\pi$
$410$	1383.25	−	406.160i	0.166620	−	0.0489239i
$411$	−1136.55	+	2488.69i	−0.136403	+	0.298681i
$412$	−632.308	−	4397.80i	−0.0756106	−	0.525884i
$413$	−5297.13			−0.631125
$414$	−2571.50	+	846.036i	−0.305271	+	0.100436i
$415$	−2697.25			−0.319043
$416$	17.5776	+	122.255i	0.00207167	+	0.0144087i
$417$	2193.38	−	4802.83i	0.257579	−	0.564019i
$418$	9111.60	−	2675.41i	1.06618	−	0.313058i
$419$	9992.46	−	11531.9i	1.16507	−	1.34456i	0.237286	−	0.971440i	$-0.423742\pi$
$419$	9992.46	−	11531.9i	1.16507	−	1.34456i	0.927783	−	0.373121i	$-0.121712\pi$
$420$	2970.70	+	872.275i	0.345131	+	0.101340i
$421$	−1838.51	+	1181.54i	−0.212835	+	0.136781i	−0.642715	−	0.766105i	$-0.722192\pi$
$421$	−1838.51	+	1181.54i	−0.212835	+	0.136781i	0.429880	+	0.902886i	$0.358556\pi$
$422$	−2857.57	−	6257.21i	−0.329631	−	0.721791i
$423$	4034.83	+	4656.44i	0.463782	+	0.535234i
$424$	−3886.16	−	2497.48i	−0.445115	−	0.286058i
$425$	−71.9882	+	500.689i	−0.00821633	+	0.0571459i
$426$	1346.07	−	9362.12i	0.153092	−	1.06478i
$427$	3530.80	+	2269.11i	0.400158	+	0.257166i
$428$	−1152.95	−	1330.57i	−0.130210	−	0.150270i
$429$	355.581	+	778.614i	0.0400178	+	0.0876267i
$430$	5218.75	−	3353.89i	0.585280	−	0.376137i
$431$	40.2650	+	11.8229i	0.00449999	+	0.00132132i	0.283982	−	0.958830i	$-0.408344\pi$
$431$	40.2650	+	11.8229i	0.00449999	+	0.00132132i	−0.279482	+	0.960151i	$0.590163\pi$
$432$	967.111	−	1116.11i	0.107709	−	0.124302i
$433$	−11851.4	+	3479.89i	−1.31534	+	0.386219i	−0.862810	−	0.505529i	$-0.831297\pi$
$433$	−11851.4	+	3479.89i	−1.31534	+	0.386219i	−0.452532	+	0.891748i	$0.649479\pi$
$434$	−2547.67	+	5578.62i	−0.281779	+	0.617010i
$435$	583.185	+	4056.14i	0.0642795	+	0.447074i
$436$	−2149.49			−0.236105
$437$	14327.3	+	3709.51i	1.56835	+	0.406064i
$438$	−8870.10			−0.967648
$439$	1456.15	+	10127.7i	0.158310	+	1.10107i	0.901746	+	0.432265i	$0.142286\pi$
$439$	1456.15	+	10127.7i	0.158310	+	1.10107i	−0.743436	+	0.668807i	$0.766805\pi$
$440$	1225.82	−	2684.18i	0.132816	−	0.290826i
$441$	2385.10	−	700.328i	0.257542	−	0.0756212i
$442$	−156.304	+	180.384i	−0.0168204	+	0.0194117i
$443$	14566.0	+	4276.97i	1.56219	+	0.458702i	0.944717	−	0.327887i	$-0.106336\pi$
$443$	14566.0	+	4276.97i	1.56219	+	0.458702i	0.617478	+	0.786588i	$0.288155\pi$
$444$	−6899.60	+	4434.10i	−0.737479	+	0.473949i
$445$	−1475.89	−	3231.74i	−0.157222	−	0.344268i
$446$	−2711.65	−	3129.41i	−0.287893	−	0.332246i
$447$	−10976.3	−	7054.06i	−1.16144	−	0.746411i
$448$	−107.933	+	750.692i	−0.0113825	+	0.0791671i
$449$	536.866	−	3733.98i	0.0564282	−	0.392467i	−0.941961	−	0.335723i	$-0.891019\pi$
$449$	536.866	−	3733.98i	0.0564282	−	0.392467i	0.998389	−	0.0567432i	$-0.0180716\pi$
$450$	337.769	+	217.071i	0.0353835	+	0.0227396i
$451$	1602.67	+	1849.58i	0.167332	+	0.193112i
$452$	1427.01	+	3124.71i	0.148497	+	0.325163i
$453$	−7293.53	+	4687.27i	−0.756468	+	0.486153i
$454$	1289.85	+	378.735i	0.133339	+	0.0391518i
$455$	312.197	−	360.294i	0.0321671	−	0.0371228i
$456$	6454.02	−	1895.07i	0.662801	−	0.194616i
$457$	2317.25	−	5074.07i	0.237191	−	0.519376i	−0.753180	−	0.657815i	$-0.771481\pi$
$457$	2317.25	−	5074.07i	0.237191	−	0.519376i	0.990371	+	0.138439i	$0.0442083\pi$
$458$	540.564	+	3759.70i	0.0551504	+	0.383579i
$459$	2853.90			0.290215
$460$	3786.59	−	2609.77i	0.383806	−	0.264524i
$461$	−5688.78			−0.574735			−0.287367	−	0.957820i	$-0.592780\pi$
$461$	−5688.78			−0.574735			−0.287367	+	0.957820i	$0.592780\pi$
$462$	748.001	+	5202.46i	0.0753250	+	0.523897i
$463$	−5588.40	+	12236.9i	−0.560940	+	1.22829i	0.390543	+	0.920585i	$0.372287\pi$
$463$	−5588.40	+	12236.9i	−0.560940	+	1.22829i	−0.951483	+	0.307702i	$0.900440\pi$
$464$	−963.134	+	282.802i	−0.0963628	+	0.0282947i
$465$	11068.4	−	12773.7i	1.10384	−	1.27390i
$466$	−4559.25	−	1338.72i	−0.453226	−	0.133079i
$467$	−16845.3	+	10825.8i	−1.66918	+	1.07272i	−0.766671	+	0.642040i	$0.778088\pi$
$467$	−16845.3	+	10825.8i	−1.66918	+	1.07272i	−0.902507	+	0.430675i	$0.858275\pi$
$468$	78.7017	+	172.333i	0.00777348	+	0.0170215i
$469$	−7809.27	−	9012.38i	−0.768867	−	0.887320i
$470$	−8805.32	−	5658.84i	−0.864169	−	0.555368i
$471$	14.2961	−	99.4316i	0.00139858	−	0.00972731i
$472$	−508.927	+	3539.67i	−0.0496298	+	0.345183i
$473$	8859.36	+	5693.57i	0.861213	+	0.553468i
$474$	936.980	+	1081.33i	0.0907952	+	0.104783i
$475$	−911.853	−	1996.68i	−0.0880814	−	0.192871i
$476$	−1232.94	+	792.364i	−0.118722	+	0.0762982i
$477$	−6798.73	−	1996.29i	−0.652605	−	0.191622i
$478$	−4156.10	+	4796.40i	−0.397690	+	0.458959i
$479$	2706.81	−	794.791i	0.258199	−	0.0758141i	−0.150071	−	0.988675i	$-0.547950\pi$
$479$	2706.81	−	794.791i	0.258199	−	0.0758141i	0.408270	+	0.912861i	$0.366132\pi$
$480$	868.288	−	1901.28i	0.0825661	−	0.180795i
$481$	179.726	+	1250.02i	0.0170370	+	0.118495i
$482$	−13240.2			−1.25119
$483$	−3160.76	+	7556.92i	−0.297763	+	0.711909i
$484$	−314.647			−0.0295499
$485$	−933.510	−	6492.71i	−0.0873990	−	0.607873i
$486$	2666.05	−	5837.84i	0.248836	−	0.544876i
$487$	−3831.14	+	1124.92i	−0.356480	+	0.104672i	−0.455069	−	0.890456i	$-0.650385\pi$
$487$	−3831.14	+	1124.92i	−0.356480	+	0.104672i	0.0985891	+	0.995128i	$0.468567\pi$
$488$	1855.50	−	2141.36i	0.172120	−	0.198637i
$489$	4453.32	+	1307.61i	0.411832	+	0.120925i
$490$	−3552.50	+	2283.05i	−0.327522	+	0.210485i
$491$	1548.49	+	3390.72i	0.142327	+	0.311652i	0.967349	−	0.253448i	$-0.0815648\pi$
$491$	1548.49	+	3390.72i	0.142327	+	0.311652i	−0.825022	+	0.565100i	$0.808837\pi$
$492$	1135.22	+	1310.12i	0.104024	+	0.120050i
$493$	−1631.86	−	1048.73i	−0.149077	−	0.0958063i
$494$	147.401	−	1025.20i	0.0134249	−	0.0933722i
$495$	644.152	−	4480.18i	0.0584899	−	0.406806i
$496$	3482.99	+	2238.38i	0.315305	+	0.202634i
$497$	−5856.32	−	6758.55i	−0.528555	−	0.609985i
$498$	−1347.33	−	2950.25i	−0.121236	−	0.265469i
$499$	11100.4	−	7133.81i	0.995838	−	0.639986i	0.0621472	−	0.998067i	$-0.480205\pi$
$499$	11100.4	−	7133.81i	0.995838	−	0.639986i	0.933691	+	0.358081i	$0.116569\pi$
$500$	−5654.88	−	1660.42i	−0.505787	−	0.148513i
$501$	763.185	−	880.763i	0.0680571	−	0.0785421i
$502$	−6825.59	+	2004.17i	−0.606855	+	0.178189i
$503$	2682.00	−	5872.77i	0.237743	−	0.520584i	−0.752724	−	0.658336i	$-0.771260\pi$
$503$	2682.00	−	5872.77i	0.237743	−	0.520584i	0.990467	+	0.137752i	$0.0439877\pi$
$504$	165.557	+	1151.47i	0.0146319	+	0.101767i
$505$	−11767.7			−1.03695
$506$	6700.33	+	4006.80i	0.588668	+	0.352024i
$507$	−13674.5			−1.19784
$508$	−1482.58	−	10311.6i	−0.129486	−	0.900596i
$509$	−3414.14	+	7475.92i	−0.297306	+	0.651010i	−0.998051	−	0.0624019i	$-0.980124\pi$
$509$	−3414.14	+	7475.92i	−0.297306	+	0.651010i	0.700745	+	0.713412i	$0.252851\pi$
$510$	3875.56	−	1137.97i	0.336495	−	0.0988039i
$511$	−5492.07	+	6338.19i	−0.475450	+	0.548698i
$512$	491.260	+	144.247i	0.0424040	+	0.0124509i
$513$	−10418.3	+	6695.43i	−0.896644	+	0.576238i
$514$	3867.98	+	8469.69i	0.331924	+	0.726813i
$515$	7581.63	+	8749.67i	0.648712	+	0.748653i
$516$	6275.35	+	4032.92i	0.535382	+	0.344069i
$517$	2528.74	−	17587.8i	0.215114	−	1.49615i
$518$	−1103.58	+	7675.60i	−0.0936076	+	0.651055i
$519$	23245.5	+	14939.0i	1.96602	+	1.26349i
$520$	−210.763	−	243.233i	−0.0177741	−	0.0205124i
$521$	−343.340	−	751.810i	−0.0288714	−	0.0632195i	0.894647	−	0.446774i	$-0.147427\pi$
$521$	−343.340	−	751.810i	−0.0288714	−	0.0632195i	−0.923518	+	0.383554i	$0.874700\pi$
$522$	−1295.28	+	832.427i	−0.108607	+	0.0697976i
$523$	9346.92	+	2744.50i	0.781477	+	0.229462i	0.648052	−	0.761597i	$-0.275584\pi$
$523$	9346.92	+	2744.50i	0.781477	+	0.229462i	0.133425	+	0.991059i	$0.457402\pi$
$524$	4008.82	−	4626.43i	0.334211	−	0.385700i
$525$	1165.69	−	342.278i	0.0969047	−	0.0284538i
$526$	1277.63	−	2797.61i	0.105907	−	0.231905i
$527$	1138.64	+	7919.42i	0.0941176	+	0.654602i
$528$	3548.27			0.292460
$529$	5757.21	+	10718.7i	0.473183	+	0.880964i
$530$	12037.3			0.986541
$531$	780.636	+	5429.44i	0.0637979	+	0.443724i
$532$	2641.98	−	5785.12i	0.215309	−	0.471460i
$533$	256.116	−	75.2024i	0.0208135	−	0.00611140i
$534$	2797.63	−	3228.64i	0.226714	−	0.261642i
$535$	4401.88	+	1292.51i	0.355719	+	0.104449i
$536$	−6772.57	+	4352.47i	−0.545766	+	0.350742i
$537$	−7975.43	−	17463.7i	−0.640903	−	1.40338i
$538$	3693.55	+	4262.58i	0.295985	+	0.341585i
$539$	−6030.73	−	3875.71i	−0.481933	−	0.309720i
$540$	−547.662	+	3809.07i	−0.0436438	+	0.303549i
$541$	847.793	−	5896.53i	0.0673743	−	0.468598i	−0.928004	−	0.372570i	$-0.878477\pi$
$541$	847.793	−	5896.53i	0.0673743	−	0.468598i	0.995379	−	0.0960288i	$-0.0306141\pi$
$542$	4730.96	+	3040.41i	0.374930	+	0.240953i
$543$	−13049.8	−	15060.3i	−1.03135	−	1.19024i
$544$	411.020	+	900.008i	0.0323940	+	0.0709330i
$545$	4711.92	−	3028.16i	0.370342	−	0.238004i
$546$	550.038	+	161.506i	0.0431125	+	0.0126590i
$547$	6019.22	−	6946.55i	0.470500	−	0.542986i	−0.470051	−	0.882639i	$-0.655764\pi$
$547$	6019.22	−	6946.55i	0.470500	−	0.542986i	0.940551	+	0.339654i	$0.110310\pi$
$548$	1675.60	−	492.001i	0.130617	−	0.0383526i
$549$	1805.45	−	3953.39i	0.140355	−	0.307334i
$550$	−164.786	−	1146.12i	−0.0127755	−	0.0888555i
$551$	8417.57			0.650818
$552$	4746.04	+	2838.14i	0.365951	+	0.218839i
$553$	1352.82			0.104028
$554$	1277.88	+	8887.84i	0.0979998	+	0.681604i
$555$	8877.98	−	19440.1i	0.679008	−	1.48682i
$556$	−3233.68	+	949.494i	−0.246652	+	0.0724236i
$557$	−4625.59	+	5338.22i	−0.351872	+	0.406082i	−0.903900	−	0.427744i	$-0.859309\pi$
$557$	−4625.59	+	5338.22i	−0.351872	+	0.406082i	0.552028	+	0.833826i	$0.313854\pi$
$558$	6093.41	+	1789.19i	0.462284	+	0.135739i
$559$	966.276	−	620.988i	0.0731111	−	0.0469856i
$560$	−820.960	−	1797.65i	−0.0619498	−	0.135651i
$561$	4490.32	+	5182.10i	0.337935	+	0.389997i
$562$	−11150.3	−	7165.85i	−0.836915	−	0.537852i
$563$	13.6442	−	94.8978i	0.00102138	−	0.00710384i	−0.989304	−	0.145866i	$-0.953403\pi$
$563$	13.6442	−	94.8978i	0.00102138	−	0.00710384i	0.990326	+	0.138762i	$0.0443123\pi$
$564$	1791.18	−	12458.0i	0.133728	−	0.930096i
$565$	−7530.19	−	4839.36i	−0.560703	−	0.360342i
$566$	10599.6	+	12232.6i	0.787161	+	0.908432i
$567$	−4478.41	−	9806.36i	−0.331703	−	0.726329i
$568$	−5078.88	+	3264.00i	−0.375185	+	0.241117i
$569$	21553.8	+	6328.78i	1.58802	+	0.466285i	0.952181	−	0.305536i	$-0.0988355\pi$
$569$	21553.8	+	6328.78i	1.58802	+	0.466285i	0.635840	+	0.771821i	$0.280654\pi$
$570$	−11478.2	+	13246.5i	−0.843451	+	0.973395i
$571$	−820.198	+	240.832i	−0.0601125	+	0.0176506i	−0.311651	−	0.950197i	$-0.600882\pi$
$571$	−820.198	+	240.832i	−0.0601125	+	0.0176506i	0.251538	+	0.967847i	$0.419064\pi$
$572$	226.967	−	496.988i	0.0165908	−	0.0363289i
$573$	−991.177	−	6893.79i	−0.0722635	−	0.502604i
$574$	1639.04			0.119185
$575$	696.323	−	1664.81i	0.0505021	−	0.120743i
$576$	785.349			0.0568105
$577$	1281.00	+	8909.55i	0.0924242	+	0.642824i	0.982396	+	0.186809i	$0.0598146\pi$
$577$	1281.00	+	8909.55i	0.0924242	+	0.642824i	−0.889972	+	0.456015i	$0.849276\pi$
$578$	3287.59	−	7198.81i	0.236584	−	0.518047i
$579$	−23056.2	+	6769.91i	−1.65489	+	0.485920i
$580$	1712.89	−	1976.78i	0.122627	−	0.141519i
$581$	−2942.34	−	863.949i	−0.210101	−	0.0616913i
$582$	6635.40	−	4264.31i	0.472588	−	0.303714i
$583$	8488.81	+	18587.9i	0.603037	+	1.32047i
$584$	3707.67	+	4278.88i	0.262713	+	0.303187i
$585$	−415.302	−	266.898i	−0.0293515	−	0.0188631i
$586$	154.777	−	1076.50i	0.0109109	−	0.0758870i
$587$	451.029	−	3136.97i	0.0317137	−	0.220574i	−0.967801	−	0.251716i	$-0.919005\pi$
$587$	451.029	−	3136.97i	0.0317137	−	0.220574i	0.999515	+	0.0311418i	$0.00991435\pi$
$588$	−4271.75	−	2745.28i	−0.299598	−	0.192540i
$589$	−22736.1	−	26238.9i	−1.59054	−	1.83558i
$590$	−3871.00	−	8476.30i	−0.270113	−	0.591464i
$591$	18210.2	−	11703.0i	1.26746	−	0.814545i
$592$	5022.99	+	1474.88i	0.348722	+	0.102394i
$593$	−107.216	+	123.734i	−0.00742466	+	0.00856852i	−0.759450	−	0.650566i	$-0.774532\pi$
$593$	−107.216	+	123.734i	−0.00742466	+	0.00856852i	0.752025	+	0.659134i	$0.229077\pi$
$594$	−6268.16	+	1840.50i	−0.432973	+	0.127132i
$595$	1586.47	−	3473.89i	0.109309	−	0.239354i
$596$	1185.23	+	8243.48i	0.0814582	+	0.566554i
$597$	−6017.17			−0.412507
$598$	701.105	−	483.210i	0.0479437	−	0.0330434i
$599$	12468.7			0.850510			0.425255	−	0.905074i	$-0.360184\pi$
$599$	12468.7			0.850510			0.425255	+	0.905074i	$0.360184\pi$
$600$	−116.723	−	811.828i	−0.00794201	−	0.0552379i
$601$	−2566.40	+	5619.63i	−0.174186	+	0.381413i	−0.976509	−	0.215476i	$-0.930870\pi$
$601$	−2566.40	+	5619.63i	−0.174186	+	0.381413i	0.802323	+	0.596889i	$0.203597\pi$
$602$	6767.24	−	1987.04i	0.458160	−	0.134528i
$603$	−8086.64	+	9332.48i	−0.546125	+	0.630262i
$604$	5309.78	+	1559.09i	0.357702	+	0.105031i
$605$	689.740	−	443.269i	0.0463503	−	0.0297875i
$606$	−5878.23	−	12871.5i	−0.394038	−	0.862822i
$607$	−9537.08	−	11006.4i	−0.637723	−	0.735972i	0.341247	−	0.939974i	$-0.389151\pi$
$607$	−9537.08	−	11006.4i	−0.637723	−	0.735972i	−0.978971	+	0.204002i	$0.934605\pi$
$608$	−3611.93	−	2321.24i	−0.240926	−	0.154834i
$609$	−663.035	+	4611.51i	−0.0441174	+	0.306844i
$610$	−1050.74	+	7308.08i	−0.0697432	+	0.485075i
$611$	−1630.35	−	1047.76i	−0.107949	−	0.0693745i
$612$	993.853	+	1146.97i	0.0656440	+	0.0757572i
$613$	4931.12	+	10797.7i	0.324904	+	0.711441i	0.999646	−	0.0266132i	$-0.00847225\pi$
$613$	4931.12	+	10797.7i	0.324904	+	0.711441i	−0.674742	+	0.738054i	$0.735745\pi$
$614$	−9172.04	+	5894.51i	−0.602856	+	0.387432i
$615$	−4334.19	−	1272.63i	−0.284181	−	0.0834432i
$616$	2196.97	−	2535.44i	0.143699	−	0.165837i
$617$	3754.65	−	1102.47i	0.244986	−	0.0719345i	−0.156934	−	0.987609i	$-0.550161\pi$
$617$	3754.65	−	1102.47i	0.244986	−	0.0719345i	0.401920	+	0.915675i	$0.368343\pi$
$618$	−5783.19	+	12663.4i	−0.376430	+	0.824267i
$619$	1277.74	+	8886.90i	0.0829674	+	0.577051i	0.988320	+	0.152391i	$0.0486973\pi$
$619$	1277.74	+	8886.90i	0.0829674	+	0.577051i	−0.905353	+	0.424660i	$0.860394\pi$
$620$	−10788.5			−0.698833
$621$	−9856.21	−	2551.89i	−0.636902	−	0.164902i
$622$	361.140			0.0232804
$623$	−574.845	−	3998.13i	−0.0369674	−	0.257114i
$624$	160.767	−	352.031i	0.0103139	−	0.0225842i
$625$	12773.1	−	3750.53i	0.817480	−	0.240034i
$626$	−4710.57	+	5436.28i	−0.300754	+	0.347089i
$627$	−28549.7	−	8382.94i	−1.81844	−	0.533943i
$628$	−53.9409	+	34.6657i	−0.00342751	+	0.00220273i
$629$	4202.56	+	9202.31i	0.266402	+	0.583339i
$630$	−1985.10	−	2290.92i	−0.125537	−	0.144877i
$631$	−1304.17	−	838.141i	−0.0822794	−	0.0528777i	0.498854	−	0.866686i	$-0.333754\pi$
$631$	−1304.17	−	838.141i	−0.0822794	−	0.0528777i	−0.581134	+	0.813808i	$0.697391\pi$
$632$	129.974	−	903.986i	0.00818050	−	0.0568966i
$633$	−3067.41	+	21334.3i	−0.192604	+	1.33959i
$634$	−14677.9	−	9432.92i	−0.919454	−	0.590897i
$635$	17776.8	+	20515.5i	1.11094	+	1.28210i
$636$	6012.88	+	13166.4i	0.374884	+	0.820881i
$637$	−657.761	+	422.718i	−0.0409128	+	0.0262931i
$638$	4260.47	+	1250.99i	0.264379	+	0.0776286i
$639$	−6064.32	+	6998.60i	−0.375432	+	0.433271i
$640$	−1280.11	+	375.874i	−0.0790637	+	0.0232152i
$641$	−11739.5	+	25705.9i	−0.723373	+	1.58397i	0.0857440	+	0.996317i	$0.472673\pi$
$641$	−11739.5	+	25705.9i	−0.723373	+	1.58397i	−0.809117	+	0.587648i	$0.800054\pi$
$642$	785.087	+	5460.40i	0.0482631	+	0.335677i
$643$	17966.4			1.10191			0.550953	−	0.834537i	$-0.314265\pi$
$643$	17966.4			1.10191			0.550953	+	0.834537i	$0.314265\pi$
$644$	4966.60	−	1634.03i	0.303900	−	0.0999845i
$645$	−19437.8			−1.18661
$646$	−1180.79	−	8212.58i	−0.0719158	−	0.500185i
$647$	4224.28	−	9249.88i	0.256682	−	0.562056i	−0.736791	−	0.676121i	$-0.763660\pi$
$647$	4224.28	−	9249.88i	0.256682	−	0.562056i	0.993473	+	0.114065i	$0.0363871\pi$
$648$	−6983.11	+	2050.43i	−0.423337	+	0.124303i
$649$	10359.2	−	11955.1i	0.626554	−	0.723082i
$650$	−121.175	−	35.5801i	−0.00731209	−	0.00214702i
$651$	16165.7	−	10389.1i	0.973246	−	0.625467i
$652$	−1230.69	−	2694.83i	−0.0739224	−	0.161868i
$653$	−9873.83	−	11395.0i	−0.591719	−	0.682881i	0.378363	−	0.925657i	$-0.376487\pi$
$653$	−9873.83	−	11395.0i	−0.591719	−	0.682881i	−0.970082	+	0.242777i	$0.921942\pi$
$654$	5665.90	+	3641.25i	0.338768	+	0.217713i
$655$	−2270.14	+	15789.2i	−0.135423	+	0.941885i
$656$	157.473	−	1095.25i	0.00937237	−	0.0651863i
$657$	7305.86	+	4695.19i	0.433834	+	0.278808i
$658$	−7792.87	−	8993.45i	−0.461698	−	0.532828i
$659$	−4104.91	−	8988.50i	−0.242647	−	0.531324i	0.748650	−	0.662965i	$-0.230702\pi$
$659$	−4104.91	−	8988.50i	−0.242647	−	0.531324i	−0.991297	+	0.131642i	$0.957975\pi$
$660$	−7778.20	+	4998.75i	−0.458736	+	0.294812i
$661$	−18994.6	−	5577.32i	−1.11771	−	0.328189i	−0.329842	−	0.944036i	$-0.606996\pi$
$661$	−18994.6	−	5577.32i	−1.11771	−	0.328189i	−0.787866	+	0.615847i	$0.788814\pi$
$662$	−2923.43	+	3373.82i	−0.171635	+	0.198077i
$663$	717.577	−	210.700i	0.0420337	−	0.0123422i
$664$	−860.000	+	1883.14i	−0.0502628	+	0.110060i
$665$	2358.48	+	16403.6i	0.137531	+	0.956547i
$666$	8029.96			0.467199
$667$	4698.03	+	5081.07i	0.272726	+	0.294962i
$668$	−743.883			−0.0430864
$669$	1846.46	+	12842.4i	0.106709	+	0.742178i
$670$	8714.53	−	19082.2i	0.502495	−	1.10031i
$671$	−12026.1	+	3531.17i	−0.691895	+	0.203159i
$672$	1556.18	−	1795.93i	0.0893319	−	0.103094i
$673$	10048.4	+	2950.46i	0.575536	+	0.168993i	0.556531	−	0.830827i	$-0.312132\pi$
$673$	10048.4	+	2950.46i	0.575536	+	0.168993i	0.0190048	+	0.999819i	$0.493950\pi$
$674$	13774.5	−	8852.31i	0.787200	−	0.505902i
$675$	627.293	+	1373.58i	0.0357696	+	0.0783246i
$676$	5715.89	+	6596.49i	0.325210	+	0.375312i
$677$	11535.9	+	7413.69i	0.654891	+	0.420873i	0.825451	−	0.564474i	$-0.190921\pi$
$677$	11535.9	+	7413.69i	0.654891	+	0.420873i	−0.170559	+	0.985347i	$0.554557\pi$
$678$	1531.79	−	10653.9i	0.0867672	−	0.603479i
$679$	1061.33	−	7381.69i	0.0599852	−	0.417206i
$680$	−2168.92	−	1393.88i	−0.122315	−	0.0786070i
$681$	−2758.38	−	3183.34i	−0.155215	−	0.179128i
$682$	−7608.15	−	16659.5i	−0.427172	−	0.935375i
$683$	9936.96	−	6386.10i	0.556702	−	0.357770i	−0.231838	−	0.972754i	$-0.574474\pi$
$683$	9936.96	−	6386.10i	0.556702	−	0.357770i	0.788540	+	0.614984i	$0.210838\pi$
$684$	−6318.97	−	1855.42i	−0.353234	−	0.103719i
$685$	−2979.97	+	3439.07i	−0.166217	+	0.191825i
$686$	−12406.5	+	3642.88i	−0.690500	+	0.202749i
$687$	4944.08	−	10826.0i	0.274568	−	0.601220i
$688$	−677.618	−	4712.94i	−0.0375493	−	0.261161i
$689$	2228.76			0.123235
$690$	−14402.1	+	464.639i	−0.794609	+	0.0256355i
$691$	−32460.7			−1.78707			−0.893533	−	0.448998i	$-0.851781\pi$
$691$	−32460.7			−1.78707			−0.893533	+	0.448998i	$0.851781\pi$
$692$	−2510.07	−	17457.9i	−0.137888	−	0.959034i
$693$	2137.72	−	4680.95i	0.117179	−	0.256587i
$694$	23462.6	−	6889.24i	1.28333	−	0.376818i
$695$	5750.95	−	6636.95i	0.313879	−	0.362236i
$696$	3017.82	+	886.111i	0.164354	+	0.0482585i
$697$	1798.84	−	1156.04i	0.0977560	−	0.0628240i
$698$	−2024.05	−	4432.05i	−0.109758	−	0.240337i
$699$	9750.05	+	11252.2i	0.527583	+	0.608864i
$700$	−652.368	−	419.251i	−0.0352245	−	0.0226374i
$701$	1604.54	−	11159.8i	0.0864516	−	0.601284i	−0.899834	−	0.436233i	$-0.856312\pi$
$701$	1604.54	−	11159.8i	0.0864516	−	0.601284i	0.986285	−	0.165050i	$-0.0527787\pi$
$702$	−101.402	+	705.267i	−0.00545182	+	0.0379182i
$703$	−36930.9	−	23734.0i	−1.98133	−	1.27332i
$704$	−1483.17	−	1711.66i	−0.0794019	−	0.0916346i
$705$	13624.1	+	29832.6i	0.727819	+	1.59370i
$706$	19789.3	−	12717.8i	1.05493	−	0.677961i
$707$	−12837.0	−	3769.30i	−0.682866	−	0.200508i
$708$	7337.72	−	8468.18i	0.389503	−	0.449511i
$709$	15339.1	−	4503.96i	0.812512	−	0.238575i	0.151023	−	0.988530i	$-0.451743\pi$
$709$	15339.1	−	4503.96i	0.812512	−	0.238575i	0.661489	+	0.749955i	$0.269925\pi$
$710$	6535.19	−	14310.1i	0.345438	−	0.756405i
$711$	−199.364	−	1386.61i	−0.0105158	−	0.0731392i
$712$	−2726.88			−0.143531
$713$	3148.97	−	28368.6i	0.165399	−	1.49006i
$714$	4592.21			0.240699
$715$	202.612	+	1409.20i	0.0105976	+	0.0737077i
$716$	−5090.70	+	11147.1i	−0.265710	+	0.581824i
$717$	19080.3	−	5602.49i	0.993818	−	0.291811i
$718$	−13726.9	+	15841.7i	−0.713485	+	0.823406i
$719$	−32202.8	−	9455.60i	−1.67032	−	0.490451i	−0.696462	−	0.717594i	$-0.745243\pi$
$719$	−32202.8	−	9455.60i	−1.67032	−	0.490451i	−0.973861	+	0.227143i	$0.927062\pi$
$720$	−1721.57	+	1106.39i	−0.0891099	+	0.0572674i
$721$	5467.96	+	11973.2i	0.282438	+	0.618452i
$722$	14594.4	+	16842.8i	0.752281	+	0.868179i
$723$	34900.2	+	22429.0i	1.79523	+	1.15372i
$724$	−1810.22	+	12590.3i	−0.0929228	+	0.646292i
$725$	146.068	−	1015.93i	0.00748253	−	0.0520421i
$726$	829.386	+	533.014i	0.0423986	+	0.0272479i
$727$	25328.5	+	29230.7i	1.29214	+	1.49120i	0.769497	+	0.638650i	$0.220507\pi$
$727$	25328.5	+	29230.7i	1.29214	+	1.49120i	0.522639	+	0.852554i	$0.324948\pi$
$728$	−152.005	−	332.843i	−0.00773855	−	0.0169451i
$729$	3746.84	−	2407.95i	0.190359	−	0.122336i
$730$	−14155.6	−	4156.47i	−0.717703	−	0.210737i
$731$	6025.52	−	6953.82i	0.304873	−	0.351842i
$732$	−8518.43	+	2501.24i	−0.430123	+	0.126296i
$733$	−325.893	+	713.607i	−0.0164218	+	0.0359586i	−0.917665	−	0.397355i	$-0.869928\pi$
$733$	−325.893	+	713.607i	−0.0164218	+	0.0359586i	0.901243	+	0.433313i	$0.142656\pi$
$734$	1076.05	+	7484.12i	0.0541115	+	0.376354i
$735$	13231.6			0.664022
$736$	−614.730	−	3475.79i	−0.0307870	−	0.174075i
$737$	35612.1			1.77990
$738$	−241.545	−	1679.98i	−0.0120480	−	0.0837954i
$739$	−15946.6	+	34918.1i	−0.793781	+	1.73814i	−0.128284	+	0.991737i	$0.540947\pi$
$739$	−15946.6	+	34918.1i	−0.793781	+	1.73814i	−0.665497	+	0.746400i	$0.731780\pi$
$740$	−13088.7	+	3843.20i	−0.650204	+	0.190917i
$741$	−2125.23	+	2452.65i	−0.105361	+	0.121593i
$742$	13131.1	+	3855.63i	0.649673	+	0.190761i
$743$	11079.0	−	7120.02i	0.547036	−	0.351559i	−0.237749	−	0.971327i	$-0.576410\pi$
$743$	11079.0	−	7120.02i	0.547036	−	0.351559i	0.784785	+	0.619768i	$0.212773\pi$
$744$	−5389.08	−	11800.4i	−0.265555	−	0.581485i
$745$	−14211.4	−	16400.9i	−0.698881	−	0.806552i
$746$	7173.75	+	4610.29i	0.352077	+	0.226266i
$747$	−451.917	+	3143.16i	−0.0221349	+	0.153952i
$748$	622.876	−	4332.20i	0.0304473	−	0.211766i
$749$	4387.86	+	2819.91i	0.214057	+	0.137566i
$750$	12093.1	+	13956.1i	0.588769	+	0.679475i
$751$	2742.58	+	6005.41i	0.133260	+	0.291798i	0.964485	−	0.264138i	$-0.0850873\pi$
$751$	2742.58	+	6005.41i	0.133260	+	0.291798i	−0.831225	+	0.555936i	$0.812360\pi$
$752$	−6758.34	+	4343.32i	−0.327728	+	0.210618i
$753$	21386.8	+	6279.74i	1.03503	+	0.303913i
$754$	317.149	−	366.009i	0.0153181	−	0.0176781i
$755$	−13836.0	+	4062.63i	−0.666947	+	0.195833i
$756$	−1817.50	+	3979.77i	−0.0874363	+	0.191459i
$757$	−680.509	−	4733.04i	−0.0326731	−	0.227246i	0.966942	−	0.254997i	$-0.0820746\pi$
$757$	−680.509	−	4733.04i	−0.0326731	−	0.227246i	−0.999615	+	0.0277509i	$0.991165\pi$
$758$	12580.9			0.602848
$759$	−10874.0	−	21912.0i	−0.520029	−	1.04790i
$760$	11187.9			0.533982
$761$	−993.184	−	6907.74i	−0.0473100	−	0.329048i	−0.999707	−	0.0241888i	$-0.992300\pi$
$761$	−993.184	−	6907.74i	−0.0473100	−	0.329048i	0.952397	−	0.304859i	$-0.0986094\pi$
$762$	−13559.9	+	29692.1i	−0.644652	+	1.41159i
$763$	6110.01	−	1794.06i	0.289905	−	0.0851237i
$764$	−2911.21	+	3359.72i	−0.137858	+	0.159097i
$765$	−3794.46	−	1114.15i	−0.179332	−	0.0526567i
$766$	9564.84	−	6146.95i	0.451164	−	0.289946i
$767$	−716.733	−	1569.43i	−0.0337415	−	0.0738836i
$768$	−1050.57	−	1212.42i	−0.0493609	−	0.0569656i
$769$	−14306.6	−	9194.29i	−0.670883	−	0.431150i	0.160361	−	0.987058i	$-0.448734\pi$
$769$	−14306.6	−	9194.29i	−0.670883	−	0.431150i	−0.831244	+	0.555908i	$0.812371\pi$
$770$	−1244.12	+	8653.02i	−0.0582271	+	0.404978i
$771$	4152.01	−	28877.9i	0.193944	−	1.34891i
$772$	12903.2	+	8292.36i	0.601548	+	0.386591i
$773$	−1310.11	−	1511.95i	−0.0609592	−	0.0703506i	0.724451	−	0.689326i	$-0.242093\pi$
$773$	−1310.11	−	1511.95i	−0.0609592	−	0.0703506i	−0.785410	+	0.618976i	$0.787548\pi$
$774$	−3033.96	−	6643.44i	−0.140896	−	0.308519i
$775$	−3561.34	+	2288.73i	−0.165067	+	0.106082i
$776$	−4830.65	−	1418.41i	−0.223467	−	0.0656158i
$777$	15911.5	−	18362.8i	0.734648	−	0.847829i
$778$	−1239.01	+	363.806i	−0.0570960	+	0.0167649i
$779$	−3854.60	+	8440.40i	−0.177285	+	0.388201i
$780$	143.516	+	998.177i	0.00658808	+	0.0458211i
$781$	26706.2			1.22359
$782$	4298.30	−	5296.37i	0.196556	−	0.242197i
$783$	−5790.72			−0.264295
$784$	461.267	+	3208.18i	0.0210125	+	0.146145i
$785$	69.4078	−	151.982i	0.00315576	−	0.00691015i
$786$	−18404.2	+	5403.95i	−0.835185	+	0.245232i
$787$	−26371.4	+	30434.2i	−1.19446	+	1.37848i	−0.287219	+	0.957865i	$0.592731\pi$
$787$	−26371.4	+	30434.2i	−1.19446	+	1.37848i	−0.907240	+	0.420614i	$0.861815\pi$
$788$	−13257.2	−	3892.67i	−0.599326	−	0.175978i
$789$	−8106.91	+	5210.00i	−0.365797	+	0.235083i
$790$	988.604	+	2164.74i	0.0445227	+	0.0974912i
$791$	−6664.35	−	7691.07i	−0.299566	−	0.345718i
$792$	−2922.54	−	1878.20i	−0.131121	−	0.0842664i
$793$	−194.550	+	1353.12i	−0.00871206	+	0.0605937i
$794$	−2237.14	+	15559.6i	−0.0999912	+	0.695454i
$795$	−31729.4	−	20391.3i	−1.41550	−	0.909690i
$796$	2515.16	+	2902.65i	0.111994	+	0.129248i
$797$	−9626.50	−	21079.1i	−0.427839	−	0.936838i	−0.993672	−	0.112318i	$-0.964173\pi$
$797$	−9626.50	−	21079.1i	−0.427839	−	0.936838i	0.565833	−	0.824520i	$-0.308555\pi$
$798$	−16764.1	+	10773.6i	−0.743662	+	0.477923i
$799$	−14895.9	−	4373.82i	−0.659547	−	0.193660i
$800$	−342.831	+	395.647i	−0.0151511	+	0.0174853i
$801$	−4013.28	+	1178.41i	−0.177032	+	0.0519812i
$802$	2254.76	−	4937.24i	0.0992747	−	0.217381i
$803$	−3564.29	−	24790.2i	−0.156639	−	1.08945i
$804$	25225.1			1.10649
$805$	−8585.32	+	10578.8i	−0.375892	+	0.463174i
$806$	−1997.54			−0.0872957
$807$	−2515.08	−	17492.7i	−0.109709	−	0.763040i
$808$	−3752.07	+	8215.88i	−0.163363	+	0.357715i
$809$	−20504.5	+	6020.66i	−0.891099	+	0.261650i	−0.695065	−	0.718947i	$-0.744624\pi$
$809$	−20504.5	+	6020.66i	−0.891099	+	0.261650i	−0.196034	+	0.980597i	$0.562806\pi$
$810$	12419.1	−	14332.4i	0.538721	−	0.621717i
$811$	4527.07	+	1329.27i	0.196014	+	0.0575548i	0.378266	−	0.925697i	$-0.376521\pi$
$811$	4527.07	+	1329.27i	0.196014	+	0.0575548i	−0.182252	+	0.983252i	$0.558339\pi$
$812$	2501.71	−	1607.75i	0.108119	−	0.0694839i
$813$	−7320.00	−	16028.6i	−0.315773	−	0.691447i
$814$	−15164.9	−	17501.3i	−0.652986	−	0.753586i
$815$	6494.23	+	4173.59i	0.279120	+	0.179380i
$816$	441.202	−	3068.63i	0.0189279	−	0.131646i
$817$	−5682.34	+	39521.5i	−0.243329	+	1.69239i
$818$	−8515.25	−	5472.42i	−0.363972	−	0.233910i
$819$	−367.549	−	424.175i	−0.0156816	−	0.0180975i
$820$	1197.77	+	2622.74i	0.0510096	+	0.111695i
$821$	−30958.8	+	19896.0i	−1.31604	+	0.845767i	−0.994861	−	0.101251i	$-0.967715\pi$
$821$	−30958.8	+	19896.0i	−1.31604	+	0.845767i	−0.321179	+	0.947019i	$0.604079\pi$
$822$	−5250.21	−	1541.60i	−0.222776	−	0.0654130i
$823$	12737.2	−	14699.5i	0.539477	−	0.622590i	−0.418922	−	0.908022i	$-0.637592\pi$
$823$	12737.2	−	14699.5i	0.539477	−	0.622590i	0.958399	+	0.285433i	$0.0921373\pi$
$824$	8526.10	−	2503.49i	0.360462	−	0.105841i
$825$	−1507.16	+	3300.22i	−0.0636032	+	0.139272i
$826$	−1507.72	−	10486.4i	−0.0635113	−	0.441731i
$827$	−22924.2			−0.963909			−0.481954	−	0.876196i	$-0.660073\pi$
$827$	−22924.2			−0.963909			−0.481954	+	0.876196i	$0.660073\pi$
$828$	−2406.77	−	4849.85i	−0.101016	−	0.203555i
$829$	−4044.07			−0.169429			−0.0847143	−	0.996405i	$-0.526998\pi$
$829$	−4044.07			−0.169429			−0.0847143	+	0.996405i	$0.526998\pi$
$830$	−767.718	−	5339.60i	−0.0321059	−	0.223301i
$831$	11687.7	−	25592.4i	0.487895	−	1.06834i
$832$	−237.018	+	69.5947i	−0.00987634	+	0.00289996i
$833$	−4101.68	+	4733.59i	−0.170606	+	0.196890i
$834$	10132.2	+	2975.08i	0.420683	+	0.123524i
$835$	1630.67	−	1047.97i	0.0675829	−	0.0434329i
$836$	7889.78	+	17276.2i	0.326404	+	0.714725i
$837$	15640.9	+	18050.6i	0.645913	+	0.745423i
$838$	25673.2	+	16499.2i	1.05831	+	0.680137i
$839$	−3950.77	+	27478.2i	−0.162569	+	1.13070i	0.731198	+	0.682165i	$0.238962\pi$
$839$	−3950.77	+	27478.2i	−0.162569	+	1.13070i	−0.893768	+	0.448530i	$0.851948\pi$
$840$	−881.245	+	6129.19i	−0.0361974	+	0.251759i
$841$	−17206.2	−	11057.8i	−0.705490	−	0.453391i
$842$	−2862.32	−	3303.29i	−0.117152	−	0.135201i
$843$	17252.3	+	37777.3i	0.704865	+	1.54344i
$844$	11573.7	−	7437.95i	0.472017	−	0.303347i
$845$	−21822.9	−	6407.77i	−0.888438	−	0.260869i
$846$	−8069.65	+	9312.88i	−0.327944	+	0.378467i
$847$	894.397	−	262.619i	0.0362832	−	0.0106537i
$848$	3838.01	−	8404.06i	0.155422	−	0.340326i
$849$	−7217.65	−	50199.9i	−0.291766	−	2.02928i
$850$	−1011.68			−0.0408237
$851$	−6285.43	−	35538.9i	−0.253186	−	1.43156i
$852$	18916.8			0.760655
$853$	5487.98	+	38169.8i	0.220287	+	1.53213i	0.736953	+	0.675944i	$0.236264\pi$
$853$	5487.98	+	38169.8i	0.220287	+	1.53213i	−0.516666	+	0.856187i	$0.672827\pi$
$854$	−3487.05	+	7635.58i	−0.139724	+	0.305953i
$855$	16465.7	−	4834.78i	0.658616	−	0.193387i
$856$	2305.90	−	2661.15i	0.0920724	−	0.106257i
$857$	20149.8	+	5916.51i	0.803154	+	0.235827i	0.657447	−	0.753500i	$-0.271636\pi$
$857$	20149.8	+	5916.51i	0.803154	+	0.235827i	0.145707	+	0.989328i	$0.453454\pi$
$858$	−1440.17	+	925.540i	−0.0573037	+	0.0368268i
$859$	774.044	+	1694.92i	0.0307451	+	0.0673224i	0.924382	−	0.381469i	$-0.124582\pi$
$859$	774.044	+	1694.92i	0.0307451	+	0.0673224i	−0.893636	+	0.448792i	$0.851855\pi$
$860$	8124.91	+	9376.65i	0.322160	+	0.371792i
$861$	−4320.39	−	2776.55i	−0.171009	−	0.109901i
$862$	−11.9444	+	83.0754i	−0.000471960	+	0.00328255i
$863$	679.649	−	4727.06i	0.0268082	−	0.186455i	−0.972017	−	0.234910i	$-0.924521\pi$
$863$	679.649	−	4727.06i	0.0268082	−	0.186455i	0.998825	+	0.0484545i	$0.0154296\pi$
$864$	2484.76	+	1596.86i	0.0978394	+	0.0628776i
$865$	30096.8	+	34733.6i	1.18303	+	1.36529i
$866$	−10262.2	−	22471.1i	−0.402684	−	0.881754i
$867$	−20860.7	+	13406.3i	−0.817146	+	0.525148i
$868$	−11768.8	−	3455.63i	−0.460207	−	0.135129i
$869$	−2645.60	+	3053.19i	−0.103275	+	0.119186i
$870$	−7863.72	+	2309.00i	−0.306443	+	0.0899797i
$871$	1613.53	−	3533.15i	0.0627698	−	0.137447i
$872$	−611.809	−	4255.22i	−0.0237597	−	0.165252i
$873$	−7722.47			−0.299388
$874$	−3265.53	+	29418.8i	−0.126382	+	1.13856i
$875$	17460.1			0.674581
$876$	−2524.69	−	17559.6i	−0.0973761	−	0.677266i
$877$	9577.68	−	20972.2i	0.368775	−	0.807504i	−0.630729	−	0.776003i	$-0.717244\pi$
$877$	9577.68	−	20972.2i	0.368775	−	0.807504i	0.999504	−	0.0315005i	$-0.0100286\pi$
$878$	−19634.8	+	5765.31i	−0.754720	+	0.221606i
$879$	−2231.58	+	2575.38i	−0.0856307	+	0.0988230i
$880$	5662.62	+	1662.70i	0.216917	+	0.0636926i
$881$	−21591.7	+	13876.2i	−0.825702	+	0.530646i	−0.883909	−	0.467658i	$-0.845098\pi$
$881$	−21591.7	+	13876.2i	−0.825702	+	0.530646i	0.0582075	+	0.998305i	$0.481462\pi$
$882$	2065.27	+	4522.31i	0.0788450	+	0.172646i
$883$	−8131.38	−	9384.11i	−0.309901	−	0.357645i	0.579338	−	0.815087i	$-0.303311\pi$
$883$	−8131.38	−	9384.11i	−0.309901	−	0.357645i	−0.889239	+	0.457442i	$0.848766\pi$
$884$	−401.585	−	258.083i	−0.0152791	−	0.00981930i
$885$	−4155.25	+	28900.4i	−0.157827	+	1.09771i
$886$	−4320.95	+	30052.9i	−0.163843	+	1.13955i
$887$	7580.97	+	4871.99i	0.286972	+	0.184426i	0.676205	−	0.736714i	$-0.263623\pi$
$887$	7580.97	+	4871.99i	0.286972	+	0.184426i	−0.389233	+	0.921139i	$0.627260\pi$
$888$	−10741.8	−	12396.7i	−0.405935	−	0.468474i
$889$	12820.8	+	28073.7i	0.483686	+	1.05912i
$890$	5977.61	−	3841.58i	0.225135	−	0.144685i
$891$	30890.1	+	9070.16i	1.16146	+	0.341035i
$892$	5423.29	−	6258.82i	0.203571	−	0.234933i
$893$	64639.4	−	18979.8i	2.42226	−	0.711238i
$894$	10840.3	−	23737.0i	0.405542	−	0.888014i
$895$	−4544.44	−	31607.3i	−0.169725	−	1.18046i
$896$	−1516.82			−0.0565552
$897$	−2666.62	+	86.0299i	−0.0992597	+	0.00320229i
$898$	7544.76			0.280370
$899$	−2310.37	−	16068.9i	−0.0857119	−	0.596139i
$900$	−333.584	+	730.447i	−0.0123550	+	0.0270536i
$901$	17130.7	−	5030.04i	0.633416	−	0.185988i
$902$	−3205.35	+	3699.17i	−0.118322	+	0.136551i
$903$	−21204.0	−	6226.06i	−0.781423	−	0.229447i
$904$	−5779.64	+	3714.35i	−0.212641	+	0.136656i
$905$	−13768.8	−	30149.6i	−0.505737	−	1.10741i
$906$	−11355.1	−	13104.5i	−0.416388	−	0.480537i
$907$	6578.96	+	4228.04i	0.240850	+	0.154785i	0.655498	−	0.755197i	$-0.272459\pi$
$907$	6578.96	+	4228.04i	0.240850	+	0.154785i	−0.414648	+	0.909982i	$0.636095\pi$
$908$	−382.630	+	2661.25i	−0.0139846	+	0.0972651i
$909$	−1971.65	+	13713.2i	−0.0719424	+	0.500371i
$910$	802.114	+	515.488i	0.0292196	+	0.0187783i
$911$	7244.16	+	8360.21i	0.263457	+	0.304046i	0.872030	−	0.489452i	$-0.162803\pi$
$911$	7244.16	+	8360.21i	0.263457	+	0.304046i	−0.608573	+	0.793498i	$0.708258\pi$
$912$	5588.57	+	12237.3i	0.202912	+	0.444316i
$913$	7703.96	−	4951.04i	0.279259	−	0.179469i
$914$	10704.4	+	3143.09i	0.387385	+	0.113747i
$915$	15149.6	−	17483.6i	0.547356	−	0.631683i
$916$	−7289.01	+	2140.25i	−0.262921	+	0.0772006i
$917$	−7533.82	+	16496.8i	−0.271307	+	0.594080i
$918$	812.304	+	5649.70i	0.0292048	+	0.203124i
$919$	−33508.3			−1.20276			−0.601381	−	0.798962i	$-0.705383\pi$
$919$	−33508.3			−1.20276			−0.601381	+	0.798962i	$0.705383\pi$
$920$	6244.19	+	6753.29i	0.223766	+	0.242010i
$921$	34162.2			1.22224
$922$	−1619.19	−	11261.7i	−0.0578366	−	0.402262i
$923$	1210.02	−	2649.57i	0.0431509	−	0.0944873i
$924$	−10086.1	+	2961.55i	−0.359100	+	0.105441i
$925$	−3505.34	+	4045.38i	−0.124600	+	0.143796i
$926$	−25815.3	−	7580.06i	−0.916138	−	0.269002i
$927$	11466.4	−	7369.02i	0.406264	−	0.261090i
$928$	−833.982	−	1826.17i	−0.0295009	−	0.0645979i
$929$	−6728.16	−	7764.71i	−0.237614	−	0.274222i	0.624401	−	0.781104i	$-0.285343\pi$
$929$	−6728.16	−	7764.71i	−0.237614	−	0.274222i	−0.862015	+	0.506883i	$0.830798\pi$
$930$	28437.7	+	18275.8i	1.00270	+	0.644394i
$931$	3868.07	−	26903.0i	0.136166	−	0.947058i
$932$	1352.48	−	9406.72i	0.0475344	−	0.330609i
$933$	−951.939	−	611.774i	−0.0334031	−	0.0214669i
$934$	−26225.9	−	30266.3i	−0.918776	−	1.06032i
$935$	4737.71	+	10374.1i	0.165711	+	0.362857i
$936$	−318.756	+	204.852i	−0.0111313	+	0.00715364i
$937$	19439.4	+	5707.92i	0.677756	+	0.199007i	0.602454	−	0.798154i	$-0.294190\pi$
$937$	19439.4	+	5707.92i	0.677756	+	0.199007i	0.0753020	+	0.997161i	$0.476008\pi$
$938$	15618.5	−	18024.8i	0.543671	−	0.627430i
$939$	21625.8	−	6349.91i	0.751578	−	0.220683i
$940$	8696.22	−	19042.1i	0.301744	−	0.660728i
$941$	3409.92	+	23716.5i	0.118130	+	0.821610i	0.959612	+	0.281326i	$0.0907742\pi$
$941$	3409.92	+	23716.5i	0.118130	+	0.821610i	−0.841483	+	0.540284i	$0.818317\pi$
$942$	200.908			0.00694898
$943$	−7246.18	+	2384.03i	−0.250231	+	0.0823273i
$944$	−7152.14			−0.246591
$945$	−1622.47	−	11284.6i	−0.0558509	−	0.388451i
$946$	−8749.59	+	19158.9i	−0.300712	+	0.658468i
$947$	37782.3	−	11093.9i	1.29647	−	0.380678i	0.440524	−	0.897741i	$-0.354793\pi$
$947$	37782.3	−	11093.9i	1.29647	−	0.380678i	0.855948	+	0.517062i	$0.172974\pi$
$948$	−1873.96	+	2162.67i	−0.0642019	+	0.0740929i
$949$	−2620.98	−	769.588i	−0.0896528	−	0.0263244i
$950$	3693.17	−	2373.46i	0.126129	−	0.0810580i
$951$	22710.4	+	49728.9i	0.774381	+	1.69566i
$952$	−1919.53	−	2215.25i	−0.0653490	−	0.0754168i
$953$	−26598.0	−	17093.5i	−0.904086	−	0.581021i	0.00391318	−	0.999992i	$-0.498754\pi$
$953$	−26598.0	−	17093.5i	−0.904086	−	0.581021i	−0.907999	+	0.418971i	$0.862391\pi$
$954$	2016.82	−	14027.3i	0.0684453	−	0.476048i
$955$	1648.58	−	11466.1i	0.0558605	−	0.388518i
$956$	−10678.1	−	6862.40i	−0.361250	−	0.232161i
$957$	−9111.10	−	10514.8i	−0.307753	−	0.355166i
$958$	2343.84	+	5132.30i	0.0790460	+	0.173087i
$959$	−4352.32	+	2797.06i	−0.146552	+	0.0941834i
$960$	4011.01	+	1177.74i	0.134849	+	0.0395951i
$961$	−24340.1	+	28090.0i	−0.817030	+	0.942903i
$962$	−2423.44	+	711.585i	−0.0812212	+	0.0238487i
$963$	2243.71	−	4913.03i	0.0750804	−	0.164403i
$964$	−3768.55	−	26210.8i	−0.125910	−	0.875720i
$965$	−39967.3			−1.33326
$966$	−15859.7	−	4106.26i	−0.528236	−	0.136767i
$967$	43574.2			1.44907			0.724535	−	0.689238i	$-0.242055\pi$
$967$	43574.2			1.44907			0.724535	+	0.689238i	$0.242055\pi$
$968$	−89.5578	−	622.888i	−0.00297365	−	0.0206822i
$969$	−10799.7	+	23648.0i	−0.358035	+	0.783987i
$970$	12587.5	−	3696.03i	0.416661	−	0.122343i
$971$	−3107.51	+	3586.26i	−0.102703	+	0.118526i	−0.804774	−	0.593581i	$-0.797714\pi$
$971$	−3107.51	+	3586.26i	−0.102703	+	0.118526i	0.702071	+	0.712107i	$0.252259\pi$
$972$	12315.7	+	3616.21i	0.406405	+	0.119331i
$973$	8399.38	−	5397.95i	0.276744	−	0.177852i
$974$	−3317.40	−	7264.10i	−0.109134	−	0.238970i
$975$	259.135	+	299.057i	0.00851174	+	0.00982307i
$976$	4767.25	+	3063.73i	0.156348	+	0.100479i
$977$	−505.988	+	3519.23i	−0.0165691	+	0.115241i	−0.996427	−	0.0844532i	$-0.973086\pi$
$977$	−505.988	+	3519.23i	−0.0165691	+	0.115241i	0.979858	+	0.199694i	$0.0639947\pi$
$978$	−1321.06	+	9188.16i	−0.0431930	+	0.300414i
$979$	10147.6	+	6521.47i	0.331275	+	0.212898i
$980$	−5530.78	−	6382.86i	−0.180280	−	0.208054i
$981$	−2739.30	−	5998.24i	−0.0891532	−	0.195218i
$982$	−6271.67	+	4030.56i	−0.203806	+	0.130978i
$983$	−35384.3	−	10389.8i	−1.14810	−	0.337113i	−0.348303	−	0.937382i	$-0.613242\pi$
$983$	−35384.3	−	10389.8i	−1.14810	−	0.337113i	−0.799798	+	0.600270i	$0.795060\pi$
$984$	−2270.44	+	2620.23i	−0.0735560	+	0.0848881i
$985$	34545.2	−	10143.4i	1.11746	−	0.328117i
$986$	1611.64	−	3529.00i	0.0520538	−	0.113982i
$987$	5306.46	+	36907.2i	0.171131	+	1.19024i
$988$	2071.48			0.0667031
$989$	−27027.7	+	18627.8i	−0.868988	+	0.598918i
$990$	9052.50			0.290613
$991$	5905.02	+	41070.3i	0.189283	+	1.31649i	0.833871	+	0.551960i	$0.186120\pi$
$991$	5905.02	+	41070.3i	0.189283	+	1.31649i	−0.644588	+	0.764530i	$0.722971\pi$
$992$	−3439.84	+	7532.19i	−0.110096	+	0.241076i
$993$	13421.2	−	3940.83i	0.428912	−	0.125940i
$994$	11712.6	−	13517.1i	0.373745	−	0.431325i
$995$	−9602.69	−	2819.61i	−0.305956	−	0.0898367i
$996$	5456.95	−	3506.97i	0.173604	−	0.111569i
$997$	−22649.7	−	49596.0i	−0.719482	−	1.57545i	−0.814629	−	0.579983i	$-0.803059\pi$
$997$	−22649.7	−	49596.0i	−0.719482	−	1.57545i	0.0951468	−	0.995463i	$-0.469668\pi$
$998$	17281.9	+	19944.4i	0.548145	+	0.632593i
$999$	25405.9	+	16327.4i	0.804612	+	0.517093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.3.3	✓	30
23.8	even	11	inner	46.4.c.b.31.3	yes	30
23.10	odd	22		1058.4.a.t.1.13		15
23.13	even	11		1058.4.a.u.1.13		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.3.3	✓	30	1.1	even	1	trivial
46.4.c.b.31.3	yes	30	23.8	even	11	inner
1058.4.a.t.1.13		15	23.10	odd	22
1058.4.a.u.1.13		15	23.13	even	11

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.284630 + 1.97964i) q^{2} +(2.60327 - 5.70036i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(6.82565 - 7.87722i) q^{5} +(12.0256 + 3.53105i) q^{6} +(9.96901 - 6.40669i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-8.03584 - 9.27386i) q^{9} +O(q^{10})\)	\(q+(0.284630 + 1.97964i) q^{2} +(2.60327 - 5.70036i) q^{3} +(-3.83797 + 1.12693i) q^{4} +(6.82565 - 7.87722i) q^{5} +(12.0256 + 3.53105i) q^{6} +(9.96901 - 6.40669i) q^{7} +(-3.32332 - 7.27706i) q^{8} +(-8.03584 - 9.27386i) q^{9} +(17.5369 + 11.2703i) q^{10} +(-5.03629 + 35.0282i) q^{11} +(-3.56736 + 24.8115i) q^{12} +(3.24703 + 2.08674i) q^{13} +(15.5204 + 17.9115i) q^{14} +(-27.1340 - 59.4152i) q^{15} +(13.4601 - 8.65025i) q^{16} +(29.6669 + 8.71100i) q^{17} +(16.0717 - 18.5477i) q^{18} +(-128.737 + 37.8006i) q^{19} +(-17.3196 + 37.9246i) q^{20} +(-10.5685 - 73.5052i) q^{21} -70.7768 q^{22} +(-94.6684 - 56.6118i) q^{23} -50.1333 q^{24} +(2.32826 + 16.1934i) q^{25} +(-3.20680 + 7.02191i) q^{26} +(88.5624 - 26.0043i) q^{27} +(-31.0409 + 35.8231i) q^{28} +(-60.1958 - 17.6751i) q^{29} +(109.898 - 70.6269i) q^{30} +(107.495 + 235.381i) q^{31} +(20.9555 + 24.1840i) q^{32} +(186.562 + 119.896i) q^{33} +(-8.80057 + 61.2093i) q^{34} +(17.5780 - 122.258i) q^{35} +(41.2923 + 26.5370i) q^{36} +(214.264 + 247.274i) q^{37} +(-111.474 - 244.094i) q^{38} +(20.3480 - 13.0769i) q^{39} +(-80.0068 - 23.4921i) q^{40} +(45.2881 - 52.2653i) q^{41} +(142.506 - 41.8435i) q^{42} +(123.622 - 270.695i) q^{43} +(-20.1452 - 140.113i) q^{44} -127.902 q^{45} +(85.1257 - 203.523i) q^{46} -502.104 q^{47} +(-14.2694 - 99.2460i) q^{48} +(-84.1520 + 184.267i) q^{49} +(-31.3944 + 9.21823i) q^{50} +(126.887 - 146.435i) q^{51} +(-14.8136 - 4.34967i) q^{52} +(485.770 - 312.185i) q^{53} +(76.6866 + 167.920i) q^{54} +(241.549 + 278.762i) q^{55} +(-79.7520 - 51.2535i) q^{56} +(-119.660 + 832.253i) q^{57} +(17.8569 - 124.197i) q^{58} +(-376.047 - 241.671i) q^{59} +(171.096 + 197.456i) q^{60} +(147.131 + 322.171i) q^{61} +(-435.374 + 279.798i) q^{62} +(-139.524 - 40.9680i) q^{63} +(-41.9111 + 48.3680i) q^{64} +(38.6008 - 11.3342i) q^{65} +(-184.251 + 403.453i) q^{66} +(-143.214 - 996.079i) q^{67} -123.678 q^{68} +(-569.154 + 392.268i) q^{69} +247.030 q^{70} +(-107.399 - 746.978i) q^{71} +(-40.7807 + 89.2973i) q^{72} +(-679.053 + 199.388i) q^{73} +(-428.528 + 494.548i) q^{74} +(98.3691 + 28.8838i) q^{75} +(451.491 - 290.155i) q^{76} +(174.208 + 381.462i) q^{77} +(31.6792 + 36.5598i) q^{78} +(96.0377 + 61.7197i) q^{79} +(23.7337 - 165.071i) q^{80} +(129.469 - 900.480i) q^{81} +(116.357 + 74.7780i) q^{82} +(-169.463 - 195.571i) q^{83} +(123.397 + 270.201i) q^{84} +(271.114 - 174.235i) q^{85} +(571.066 + 167.680i) q^{86} +(-257.460 + 297.125i) q^{87} +(271.639 - 79.7605i) q^{88} +(141.598 - 310.057i) q^{89} +(-36.4047 - 253.200i) q^{90} +45.7388 q^{91} +(427.132 + 110.590i) q^{92} +1621.59 q^{93} +(-142.914 - 993.986i) q^{94} +(-580.951 + 1272.10i) q^{95} +(192.410 - 56.4967i) q^{96} +(412.119 - 475.611i) q^{97} +(-388.735 - 114.143i) q^{98} +(365.317 - 234.775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 2 * q^3 - 12 * q^4 - 4 * q^6 - 115 * q^7 + 24 * q^8 - 83 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} - 12 q^{4} - 4 q^{6} - 115 q^{7} + 24 q^{8} - 83 q^{9} - 30 q^{11} + 52 q^{12} + 104 q^{13} - 56 q^{14} + 492 q^{15} - 48 q^{16} + 274 q^{17} + 166 q^{18} - 381 q^{19} - 176 q^{20} - 546 q^{21} + 60 q^{22} - 461 q^{23} - 16 q^{24} - 363 q^{25} - 318 q^{26} + 929 q^{27} + 112 q^{28} - 41 q^{29} + 776 q^{30} + 416 q^{31} + 96 q^{32} - 960 q^{33} - 416 q^{34} + 1671 q^{35} - 420 q^{36} + 1338 q^{37} - 118 q^{38} - 1642 q^{39} - 263 q^{41} - 8 q^{42} - 561 q^{43} - 120 q^{44} - 48 q^{45} - 1322 q^{46} - 1508 q^{47} + 208 q^{48} - 304 q^{49} + 1298 q^{50} - 1313 q^{51} - 24 q^{52} + 337 q^{53} + 1222 q^{54} + 4597 q^{55} + 920 q^{56} + 3446 q^{57} + 500 q^{58} + 1507 q^{59} + 516 q^{60} - 1291 q^{61} - 590 q^{62} + 1108 q^{63} - 192 q^{64} - 2522 q^{65} - 1204 q^{66} - 5093 q^{67} - 576 q^{68} - 5786 q^{69} - 2000 q^{70} + 850 q^{71} - 1800 q^{72} + 2452 q^{73} - 2676 q^{74} + 1267 q^{75} - 512 q^{76} - 6123 q^{77} + 2272 q^{78} + 536 q^{79} + 704 q^{80} + 3083 q^{81} - 1542 q^{82} + 7180 q^{83} + 2612 q^{84} + 1126 q^{85} + 6182 q^{86} - 7541 q^{87} + 856 q^{88} + 3457 q^{89} - 300 q^{90} + 4134 q^{91} + 92 q^{92} + 4930 q^{93} + 1542 q^{94} - 9721 q^{95} - 64 q^{96} + 4159 q^{97} + 2192 q^{98} + 7587 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 - 12 * q^4 - 4 * q^6 - 115 * q^7 + 24 * q^8 - 83 * q^9 - 30 * q^11 + 52 * q^12 + 104 * q^13 - 56 * q^14 + 492 * q^15 - 48 * q^16 + 274 * q^17 + 166 * q^18 - 381 * q^19 - 176 * q^20 - 546 * q^21 + 60 * q^22 - 461 * q^23 - 16 * q^24 - 363 * q^25 - 318 * q^26 + 929 * q^27 + 112 * q^28 - 41 * q^29 + 776 * q^30 + 416 * q^31 + 96 * q^32 - 960 * q^33 - 416 * q^34 + 1671 * q^35 - 420 * q^36 + 1338 * q^37 - 118 * q^38 - 1642 * q^39 - 263 * q^41 - 8 * q^42 - 561 * q^43 - 120 * q^44 - 48 * q^45 - 1322 * q^46 - 1508 * q^47 + 208 * q^48 - 304 * q^49 + 1298 * q^50 - 1313 * q^51 - 24 * q^52 + 337 * q^53 + 1222 * q^54 + 4597 * q^55 + 920 * q^56 + 3446 * q^57 + 500 * q^58 + 1507 * q^59 + 516 * q^60 - 1291 * q^61 - 590 * q^62 + 1108 * q^63 - 192 * q^64 - 2522 * q^65 - 1204 * q^66 - 5093 * q^67 - 576 * q^68 - 5786 * q^69 - 2000 * q^70 + 850 * q^71 - 1800 * q^72 + 2452 * q^73 - 2676 * q^74 + 1267 * q^75 - 512 * q^76 - 6123 * q^77 + 2272 * q^78 + 536 * q^79 + 704 * q^80 + 3083 * q^81 - 1542 * q^82 + 7180 * q^83 + 2612 * q^84 + 1126 * q^85 + 6182 * q^86 - 7541 * q^87 + 856 * q^88 + 3457 * q^89 - 300 * q^90 + 4134 * q^91 + 92 * q^92 + 4930 * q^93 + 1542 * q^94 - 9721 * q^95 - 64 * q^96 + 4159 * q^97 + 2192 * q^98 + 7587 * q^99

Introduction

L-functions

Modular forms

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