LMFDB - Embedded newform 46.4.c.b.9.2

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			9.2
Character	$\chi$	$=$	46.9
Dual form			46.4.c.b.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91899 - 0.563465i) q^{2} +(1.58551 + 1.82978i) q^{3} +(3.36501 - 2.16256i) q^{4} +(2.65345 + 18.4552i) q^{5} +(4.07359 + 2.61794i) q^{6} +(8.33333 - 18.2475i) q^{7} +(5.23889 - 6.04600i) q^{8} +(3.00826 - 20.9229i) q^{9} +O(q^{10})$	\(q+(1.91899 - 0.563465i) q^{2} +(1.58551 + 1.82978i) q^{3} +(3.36501 - 2.16256i) q^{4} +(2.65345 + 18.4552i) q^{5} +(4.07359 + 2.61794i) q^{6} +(8.33333 - 18.2475i) q^{7} +(5.23889 - 6.04600i) q^{8} +(3.00826 - 20.9229i) q^{9} +(15.4908 + 33.9201i) q^{10} +(-45.9721 - 13.4986i) q^{11} +(9.29229 + 2.72846i) q^{12} +(24.8832 + 54.4866i) q^{13} +(5.70974 - 39.7121i) q^{14} +(-29.5618 + 34.1161i) q^{15} +(6.64664 - 14.5541i) q^{16} +(-100.372 - 64.5049i) q^{17} +(-6.01652 - 41.8458i) q^{18} +(52.8641 - 33.9737i) q^{19} +(48.8393 + 56.3636i) q^{20} +(46.6014 - 13.6834i) q^{21} -95.8258 q^{22} +(-82.6425 + 73.0563i) q^{23} +19.3692 q^{24} +(-213.615 + 62.7231i) q^{25} +(78.4519 + 90.5383i) q^{26} +(98.0474 - 63.0113i) q^{27} +(-11.4195 - 79.4243i) q^{28} +(3.38129 + 2.17302i) q^{29} +(-37.5054 + 82.1254i) q^{30} +(115.632 - 133.446i) q^{31} +(4.55407 - 31.6743i) q^{32} +(-48.1898 - 105.521i) q^{33} +(-228.958 - 67.2281i) q^{34} +(358.872 + 105.374i) q^{35} +(-35.1243 - 76.9114i) q^{36} +(11.8414 - 82.3584i) q^{37} +(82.3025 - 94.9822i) q^{38} +(-60.2459 + 131.920i) q^{39} +(125.481 + 80.6417i) q^{40} +(38.2455 + 266.004i) q^{41} +(81.7173 - 52.5165i) q^{42} +(175.794 + 202.877i) q^{43} +(-183.888 + 53.9945i) q^{44} +394.118 q^{45} +(-117.425 + 186.760i) q^{46} +95.9140 q^{47} +(37.1691 - 10.9138i) q^{48} +(-38.9079 - 44.9021i) q^{49} +(-374.582 + 240.729i) q^{50} +(-41.1107 - 285.931i) q^{51} +(201.563 + 129.537i) q^{52} +(-80.6994 + 176.707i) q^{53} +(152.647 - 176.164i) q^{54} +(127.135 - 884.240i) q^{55} +(-66.6667 - 145.980i) q^{56} +(145.981 + 42.8639i) q^{57} +(7.71307 + 2.26476i) q^{58} +(-44.3023 - 97.0086i) q^{59} +(-25.6976 + 178.730i) q^{60} +(-475.382 + 548.620i) q^{61} +(146.704 - 321.236i) q^{62} +(-356.721 - 229.251i) q^{63} +(-9.10815 - 63.3486i) q^{64} +(-939.533 + 603.801i) q^{65} +(-151.933 - 175.340i) q^{66} +(-289.466 + 84.9949i) q^{67} -477.247 q^{68} +(-264.708 - 35.3859i) q^{69} +748.044 q^{70} +(684.999 - 201.134i) q^{71} +(-110.740 - 127.801i) q^{72} +(252.050 - 161.983i) q^{73} +(-23.6827 - 164.717i) q^{74} +(-453.459 - 291.420i) q^{75} +(104.418 - 228.644i) q^{76} +(-629.416 + 726.385i) q^{77} +(-41.2786 + 287.099i) q^{78} +(-21.8570 - 47.8601i) q^{79} +(286.235 + 84.0461i) q^{80} +(-276.857 - 81.2925i) q^{81} +(223.276 + 488.907i) q^{82} +(-138.349 + 962.240i) q^{83} +(127.223 - 146.823i) q^{84} +(924.116 - 2023.53i) q^{85} +(451.659 + 290.264i) q^{86} +(1.38493 + 9.63238i) q^{87} +(-322.455 + 207.229i) q^{88} +(-306.357 - 353.555i) q^{89} +(756.306 - 222.072i) q^{90} +1201.60 q^{91} +(-120.104 + 424.555i) q^{92} +427.514 q^{93} +(184.058 - 54.0442i) q^{94} +(767.262 + 885.468i) q^{95} +(65.1775 - 41.8870i) q^{96} +(45.1172 + 313.797i) q^{97} +(-99.9644 - 64.2432i) q^{98} +(-420.726 + 921.262i) 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 $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.91899	−	0.563465i	0.678464	−	0.199215i
$2$	1.91899	−	0.563465i	0.678464	−	0.199215i
$3$	1.58551	+	1.82978i	0.305132	+	0.352141i	0.887519	−	0.460770i	$-0.152427\pi$
$3$	1.58551	+	1.82978i	0.305132	+	0.352141i	−0.582387	+	0.812911i	$0.697881\pi$
$4$	3.36501	−	2.16256i	0.420627	−	0.270320i
$5$	2.65345	+	18.4552i	0.237332	+	1.65068i	0.665073	+	0.746778i	$0.268400\pi$
$5$	2.65345	+	18.4552i	0.237332	+	1.65068i	−0.427742	+	0.903901i	$0.640691\pi$
$6$	4.07359	+	2.61794i	0.277173	+	0.178128i
$7$	8.33333	−	18.2475i	0.449958	−	0.985270i	−0.539705	−	0.841854i	$-0.681464\pi$
$7$	8.33333	−	18.2475i	0.449958	−	0.985270i	0.989663	−	0.143416i	$-0.0458085\pi$
$8$	5.23889	−	6.04600i	0.231528	−	0.267198i
$9$	3.00826	−	20.9229i	0.111417	−	0.774922i
$10$	15.4908	+	33.9201i	0.489861	+	1.07265i
$11$	−45.9721	−	13.4986i	−1.26010	−	0.369999i	−0.417569	−	0.908645i	$-0.637118\pi$
$11$	−45.9721	−	13.4986i	−1.26010	−	0.369999i	−0.842532	+	0.538646i	$0.818936\pi$
$12$	9.29229	+	2.72846i	0.223538	+	0.0656366i
$13$	24.8832	+	54.4866i	0.530874	+	1.16245i	0.965156	+	0.261675i	$0.0842749\pi$
$13$	24.8832	+	54.4866i	0.530874	+	1.16245i	−0.434282	+	0.900777i	$0.642998\pi$
$14$	5.70974	−	39.7121i	0.109000	−	0.758108i
$15$	−29.5618	+	34.1161i	−0.508855	+	0.587249i
$16$	6.64664	−	14.5541i	0.103854	−	0.227408i
$17$	−100.372	−	64.5049i	−1.43198	−	0.920278i	−0.999829	−	0.0184770i	$-0.994118\pi$
$17$	−100.372	−	64.5049i	−1.43198	−	0.920278i	−0.432151	−	0.901801i	$-0.642245\pi$
$18$	−6.01652	−	41.8458i	−0.0787837	−	0.547953i
$19$	52.8641	−	33.9737i	0.638308	−	0.410216i	−0.181069	−	0.983470i	$-0.557956\pi$
$19$	52.8641	−	33.9737i	0.638308	−	0.410216i	0.819377	+	0.573254i	$0.194319\pi$
$20$	48.8393	+	56.3636i	0.546040	+	0.630164i
$21$	46.6014	−	13.6834i	0.484251	−	0.142189i
$22$	−95.8258			−0.928642
$23$	−82.6425	+	73.0563i	−0.749224	+	0.662317i
$23$	−82.6425	+	73.0563i	−0.749224	+	0.662317i
$24$	19.3692			0.164738
$25$	−213.615	+	62.7231i	−1.70892	+	0.501785i
$26$	78.4519	+	90.5383i	0.591757	+	0.682924i
$27$	98.0474	−	63.0113i	0.698861	−	0.449130i
$28$	−11.4195	−	79.4243i	−0.0770743	−	0.536064i
$29$	3.38129	+	2.17302i	0.0216514	+	0.0139145i	0.551422	−	0.834227i	$-0.314086\pi$
$29$	3.38129	+	2.17302i	0.0216514	+	0.0139145i	−0.529770	+	0.848141i	$0.677722\pi$
$30$	−37.5054	+	82.1254i	−0.228251	+	0.499799i
$31$	115.632	−	133.446i	0.669939	−	0.773151i	−0.314427	−	0.949282i	$-0.601813\pi$
$31$	115.632	−	133.446i	0.669939	−	0.773151i	0.984367	+	0.176130i	$0.0563580\pi$
$32$	4.55407	−	31.6743i	0.0251579	−	0.174977i
$33$	−48.1898	−	105.521i	−0.254205	−	0.556632i
$34$	−228.958	−	67.2281i	−1.15488	−	0.339104i
$35$	358.872	+	105.374i	1.73315	+	0.508900i
$36$	−35.1243	−	76.9114i	−0.162612	−	0.356071i
$37$	11.8414	−	82.3584i	0.0526137	−	0.365936i	−0.946457	−	0.322830i	$-0.895366\pi$
$37$	11.8414	−	82.3584i	0.0526137	−	0.365936i	0.999071	−	0.0431059i	$-0.0137253\pi$
$38$	82.3025	−	94.9822i	0.351348	−	0.405477i
$39$	−60.2459	+	131.920i	−0.247361	+	0.541644i
$40$	125.481	+	80.6417i	0.496007	+	0.318764i
$41$	38.2455	+	266.004i	0.145682	+	1.01324i	0.923184	+	0.384358i	$0.125577\pi$
$41$	38.2455	+	266.004i	0.145682	+	1.01324i	−0.777502	+	0.628880i	$0.783514\pi$
$42$	81.7173	−	52.5165i	0.300220	−	0.192940i
$43$	175.794	+	202.877i	0.623448	+	0.719497i	0.976358	−	0.216160i	$-0.0693533\pi$
$43$	175.794	+	202.877i	0.623448	+	0.719497i	−0.352910	+	0.935657i	$0.614808\pi$
$44$	−183.888	+	53.9945i	−0.630050	+	0.184999i
$45$	394.118			1.30559
$46$	−117.425	+	186.760i	−0.376378	+	0.598615i
$47$	95.9140			0.297670			0.148835	−	0.988862i	$-0.452448\pi$
$47$	95.9140			0.297670			0.148835	+	0.988862i	$0.452448\pi$
$48$	37.1691	−	10.9138i	0.111769	−	0.0328183i
$49$	−38.9079	−	44.9021i	−0.113434	−	0.130910i
$50$	−374.582	+	240.729i	−1.05948	+	0.680886i
$51$	−41.1107	−	285.931i	−0.112875	−	0.785066i
$52$	201.563	+	129.537i	0.537534	+	0.345452i
$53$	−80.6994	+	176.707i	−0.209149	+	0.457973i	−0.984913	−	0.173050i	$-0.944638\pi$
$53$	−80.6994	+	176.707i	−0.209149	+	0.457973i	0.775764	+	0.631024i	$0.217365\pi$
$54$	152.647	−	176.164i	0.384678	−	0.443942i
$55$	127.135	−	884.240i	0.311688	−	2.16783i
$56$	−66.6667	−	145.980i	−0.159084	−	0.348345i
$57$	145.981	+	42.8639i	0.339222	+	0.0996047i
$58$	7.71307	+	2.26476i	0.0174617	+	0.00512721i
$59$	−44.3023	−	97.0086i	−0.0977572	−	0.214058i	0.854435	−	0.519559i	$-0.173904\pi$
$59$	−44.3023	−	97.0086i	−0.0977572	−	0.214058i	−0.952192	+	0.305500i	$0.901176\pi$
$60$	−25.6976	+	178.730i	−0.0552923	+	0.384567i
$61$	−475.382	+	548.620i	−0.997811	+	1.15154i	−0.00936580	+	0.999956i	$0.502981\pi$
$61$	−475.382	+	548.620i	−0.997811	+	1.15154i	−0.988445	+	0.151579i	$0.951564\pi$
$62$	146.704	−	321.236i	0.300506	−	0.658017i
$63$	−356.721	−	229.251i	−0.713375	−	0.458458i
$64$	−9.10815	−	63.3486i	−0.0177894	−	0.123728i
$65$	−939.533	+	603.801i	−1.79284	+	1.15219i
$66$	−151.933	−	175.340i	−0.283359	−	0.327013i
$67$	−289.466	+	84.9949i	−0.527819	+	0.154982i	−0.534776	−	0.844994i	$-0.679604\pi$
$67$	−289.466	+	84.9949i	−0.527819	+	0.154982i	0.00695639	+	0.999976i	$0.497786\pi$
$68$	−477.247			−0.851099
$69$	−264.708	−	35.3859i	−0.461841	−	0.0617386i
$70$	748.044			1.27726
$71$	684.999	−	201.134i	1.14499	−	0.336200i	0.346408	−	0.938084i	$-0.387401\pi$
$71$	684.999	−	201.134i	1.14499	−	0.336200i	0.798583	+	0.601884i	$0.205583\pi$
$72$	−110.740	−	127.801i	−0.181261	−	0.209187i
$73$	252.050	−	161.983i	0.404112	−	0.259707i	−0.322759	−	0.946481i	$-0.604610\pi$
$73$	252.050	−	161.983i	0.404112	−	0.259707i	0.726871	+	0.686774i	$0.240974\pi$
$74$	−23.6827	−	164.717i	−0.0372035	−	0.258756i
$75$	−453.459	−	291.420i	−0.698146	−	0.448671i
$76$	104.418	−	228.644i	0.157600	−	0.345096i
$77$	−629.416	+	726.385i	−0.931541	+	1.07506i
$78$	−41.2786	+	287.099i	−0.0599216	+	0.416764i
$79$	−21.8570	−	47.8601i	−0.0311279	−	0.0681605i	0.893429	−	0.449204i	$-0.148292\pi$
$79$	−21.8570	−	47.8601i	−0.0311279	−	0.0681605i	−0.924557	+	0.381043i	$0.875565\pi$
$80$	286.235	+	84.0461i	0.400025	+	0.117458i
$81$	−276.857	−	81.2925i	−0.379776	−	0.111512i
$82$	223.276	+	488.907i	0.300692	+	0.658424i
$83$	−138.349	+	962.240i	−0.182961	+	1.27252i	0.666752	+	0.745280i	$0.267684\pi$
$83$	−138.349	+	962.240i	−0.182961	+	1.27252i	−0.849713	+	0.527245i	$0.823225\pi$
$84$	127.223	−	146.823i	0.165252	−	0.190711i
$85$	924.116	−	2023.53i	1.17923	−	2.58215i
$86$	451.659	+	290.264i	0.566322	+	0.363953i
$87$	1.38493	+	9.63238i	0.00170666	+	0.0118701i
$88$	−322.455	+	207.229i	−0.390612	+	0.251031i
$89$	−306.357	−	353.555i	−0.364874	−	0.421087i	0.543393	−	0.839479i	$-0.317139\pi$
$89$	−306.357	−	353.555i	−0.364874	−	0.421087i	−0.908267	+	0.418391i	$0.862594\pi$
$90$	756.306	−	222.072i	0.885796	−	0.260093i
$91$	1201.60			1.38420
$92$	−120.104	+	424.555i	−0.136106	+	0.481119i
$93$	427.514			0.476678
$94$	184.058	−	54.0442i	0.201958	−	0.0593003i
$95$	767.262	+	885.468i	0.828626	+	0.956285i
$96$	65.1775	−	41.8870i	0.0692932	−	0.0445321i
$97$	45.1172	+	313.797i	0.0472264	+	0.328467i	0.999715	+	0.0238912i	$0.00760553\pi$
$97$	45.1172	+	313.797i	0.0472264	+	0.328467i	−0.952488	+	0.304576i	$0.901485\pi$
$98$	−99.9644	−	64.2432i	−0.103040	−	0.0662199i
$99$	−420.726	+	921.262i	−0.427117	+	0.935256i
$100$	−583.176	+	673.021i	−0.583176	+	0.673021i
$101$	−30.0943	+	209.311i	−0.0296485	+	0.206210i	−0.999261	−	0.0384358i	$-0.987763\pi$
$101$	−30.0943	+	209.311i	−0.0296485	+	0.206210i	0.969613	+	0.244646i	$0.0786716\pi$
$102$	−240.003	−	525.533i	−0.232979	−	0.510152i
$103$	−212.219	−	62.3132i	−0.203015	−	0.0596107i	0.178644	−	0.983914i	$-0.442829\pi$
$103$	−212.219	−	62.3132i	−0.203015	−	0.0596107i	−0.381659	+	0.924303i	$0.624647\pi$
$104$	459.786	+	135.005i	0.433517	+	0.127292i
$105$	376.184	+	823.728i	0.349636	+	0.765596i
$106$	−55.2928	+	384.570i	−0.0506652	+	0.352384i
$107$	830.708	−	958.689i	0.750539	−	0.866168i	−0.244082	−	0.969755i	$-0.578487\pi$
$107$	830.708	−	958.689i	0.750539	−	0.866168i	0.994620	+	0.103587i	$0.0330320\pi$
$108$	193.665	−	424.068i	0.172550	−	0.377833i
$109$	−596.050	−	383.058i	−0.523773	−	0.336609i	0.251890	−	0.967756i	$-0.418948\pi$
$109$	−596.050	−	383.058i	−0.523773	−	0.336609i	−0.775663	+	0.631147i	$0.782584\pi$
$110$	−254.269	−	1768.48i	−0.220396	−	1.53289i
$111$	169.472	−	108.913i	0.144915	−	0.0931315i
$112$	−210.187	−	242.569i	−0.177328	−	0.204648i
$113$	−144.451	+	42.4147i	−0.120255	+	0.0353101i	−0.341306	−	0.939952i	$-0.610869\pi$
$113$	−144.451	+	42.4147i	−0.120255	+	0.0353101i	0.221051	+	0.975262i	$0.429051\pi$
$114$	304.288			0.249993
$115$	−1567.55	−	1331.33i	−1.27109	−	1.07954i
$116$	16.0774			0.0128685
$117$	1214.87	−	356.719i	0.959958	−	0.281869i
$118$	−139.677	−	161.195i	−0.108968	−	0.125756i
$119$	−2013.48	+	1293.98i	−1.55105	+	0.996801i
$120$	51.3951	+	357.461i	0.0390976	+	0.271930i
$121$	811.512	+	521.527i	0.609701	+	0.391831i
$122$	−603.123	+	1320.66i	−0.447576	+	0.980054i
$123$	−426.089	+	491.733i	−0.312351	+	0.360472i
$124$	100.517	−	699.111i	0.0727959	−	0.506306i
$125$	−756.209	−	1655.87i	−0.541099	−	1.18484i
$126$	−813.717	−	238.929i	−0.575331	−	0.168932i
$127$	488.284	+	143.373i	0.341167	+	0.100176i	0.447828	−	0.894120i	$-0.352198\pi$
$127$	488.284	+	143.373i	0.341167	+	0.100176i	−0.106661	+	0.994295i	$0.534016\pi$
$128$	−53.1731	−	116.433i	−0.0367178	−	0.0804009i
$129$	−92.4964	+	643.327i	−0.0631307	+	0.439083i
$130$	−1462.73	+	1688.08i	−0.986845	+	1.13888i
$131$	−25.6367	+	56.1366i	−0.0170984	+	0.0374403i	−0.917989	−	0.396607i	$-0.870188\pi$
$131$	−25.6367	+	56.1366i	−0.0170984	+	0.0374403i	0.900890	+	0.434047i	$0.142915\pi$
$132$	−390.355	−	250.866i	−0.257394	−	0.165417i
$133$	−179.399	−	1247.75i	−0.116962	−	0.813486i
$134$	−507.589	+	326.208i	−0.327232	+	0.210299i
$135$	1423.05	+	1642.28i	0.907232	+	1.04700i
$136$	−915.831	+	268.912i	−0.577440	+	0.169552i
$137$	3017.09			1.88152			0.940758	−	0.339079i	$-0.110115\pi$
$137$	3017.09			1.88152			0.940758	+	0.339079i	$0.110115\pi$
$138$	−527.909	+	81.2484i	−0.325642	+	0.0501183i
$139$	−275.424			−0.168066			−0.0840331	−	0.996463i	$-0.526780\pi$
$139$	−275.424			−0.168066			−0.0840331	+	0.996463i	$0.526780\pi$
$140$	1435.49	−	421.497i	0.866577	−	0.254450i
$141$	152.073	+	175.501i	0.0908287	+	0.104822i
$142$	1201.17	−	771.946i	0.709859	−	0.456199i
$143$	−408.439	−	2840.75i	−0.238849	−	1.66123i
$144$	−284.519	−	182.850i	−0.164652	−	0.105816i
$145$	−31.1314	+	68.1683i	−0.0178298	+	0.0390418i
$146$	392.409	−	452.864i	0.222438	−	0.256707i
$147$	20.4720	−	142.386i	0.0114864	−	0.0798896i
$148$	−138.259	−	302.745i	−0.0767893	−	0.168145i
$149$	−3370.44	−	989.651i	−1.85314	−	0.544130i	−0.999738	−	0.0228700i	$-0.992720\pi$
$149$	−3370.44	−	989.651i	−1.85314	−	0.544130i	−0.853398	−	0.521260i	$-0.825462\pi$
$150$	−1034.39	−	303.723i	−0.563049	−	0.165326i
$151$	−59.2757	−	129.796i	−0.0319456	−	0.0699511i	0.892987	−	0.450083i	$-0.148606\pi$
$151$	−59.2757	−	129.796i	−0.0319456	−	0.0699511i	−0.924932	+	0.380132i	$0.875878\pi$
$152$	71.5442	−	497.601i	0.0381776	−	0.265531i
$153$	−1651.57	+	1906.02i	−0.872691	+	1.00714i
$154$	−798.548	+	1748.58i	−0.417850	+	0.914963i
$155$	2769.60	+	1779.91i	1.43522	+	0.922362i
$156$	82.5573	+	574.198i	0.0423710	+	0.294697i
$157$	2620.16	−	1683.88i	1.33192	−	0.855975i	0.335629	−	0.941994i	$-0.391051\pi$
$157$	2620.16	−	1683.88i	1.33192	−	0.855975i	0.996293	+	0.0860195i	$0.0274147\pi$
$158$	−68.9107	−	79.5272i	−0.0346977	−	0.0400433i
$159$	−451.285	+	132.509i	−0.225089	+	0.0660922i
$160$	596.638			0.294802
$161$	644.403	+	2116.82i	0.315442	+	1.03620i
$162$	−577.090			−0.279879
$163$	−2553.82	+	749.870i	−1.22718	+	0.360333i	−0.830186	−	0.557486i	$-0.811766\pi$
$163$	−2553.82	+	749.870i	−1.22718	+	0.360333i	−0.396997	+	0.917820i	$0.629948\pi$
$164$	703.946	+	812.398i	0.335177	+	0.386815i
$165$	1819.54	−	1169.35i	0.858490	−	0.551718i
$166$	276.698	+	1924.48i	0.129373	+	0.899811i
$167$	−2844.89	−	1828.30i	−1.31823	−	0.847173i	−0.323157	−	0.946345i	$-0.604744\pi$
$167$	−2844.89	−	1828.30i	−1.31823	−	0.847173i	−0.995070	+	0.0991725i	$0.968380\pi$
$168$	161.410	−	353.438i	0.0741251	−	0.162311i
$169$	−910.891	+	1051.22i	−0.414607	+	0.478482i
$170$	633.176	−	4403.84i	0.285661	−	1.98682i
$171$	−551.800	−	1208.27i	−0.246767	−	0.540344i
$172$	1030.28	+	302.518i	0.456734	+	0.134109i
$173$	4096.18	+	1202.75i	1.80015	+	0.528573i	0.997678	−	0.0681114i	$-0.0216973\pi$
$173$	4096.18	+	1202.75i	1.80015	+	0.528573i	0.802476	+	0.596684i	$0.203516\pi$
$174$	8.08516	+	17.7040i	0.00352261	+	0.00771345i
$175$	−635.590	+	4420.63i	−0.274549	+	1.90953i
$176$	−502.020	+	579.362i	−0.215007	+	0.248131i
$177$	107.262	−	234.872i	0.0455499	−	0.0997404i
$178$	−787.111	−	505.846i	−0.331441	−	0.213004i
$179$	−502.238	−	3493.14i	−0.209715	−	1.45860i	−0.774086	−	0.633081i	$-0.781790\pi$
$179$	−502.238	−	3493.14i	−0.209715	−	1.45860i	0.564370	−	0.825522i	$-0.309119\pi$
$180$	1326.21	−	852.304i	0.549166	−	0.352928i
$181$	−124.391	−	143.555i	−0.0510823	−	0.0589521i	0.729633	−	0.683839i	$-0.239691\pi$
$181$	−124.391	−	143.555i	−0.0510823	−	0.0589521i	−0.780716	+	0.624886i	$0.785145\pi$
$182$	2305.86	−	677.061i	0.939130	−	0.275753i
$183$	−1757.58			−0.709967
$184$	8.74330	+	882.390i	0.00350307	+	0.353536i
$185$	1551.36			0.616530
$186$	820.393	−	240.889i	0.323409	−	0.0949615i
$187$	3743.56	+	4320.30i	1.46394	+	1.68947i
$188$	322.752	−	207.420i	0.125208	−	0.0804663i
$189$	−332.733	−	2314.21i	−0.128057	−	0.890656i
$190$	1971.30	+	1266.87i	0.752699	+	0.483730i
$191$	1635.24	−	3580.69i	0.619488	−	1.35649i	−0.296404	−	0.955063i	$-0.595787\pi$
$191$	1635.24	−	3580.69i	0.619488	−	1.35649i	0.915891	−	0.401426i	$-0.131485\pi$
$192$	101.473	−	117.106i	0.0381415	−	0.0440176i
$193$	173.332	−	1205.55i	0.0646463	−	0.449625i	−0.931630	−	0.363408i	$-0.881613\pi$
$193$	173.332	−	1205.55i	0.0646463	−	0.449625i	0.996276	−	0.0862169i	$-0.0274778\pi$
$194$	263.393	+	576.750i	0.0974769	+	0.213445i
$195$	−2594.46	−	761.803i	−0.952787	−	0.279763i
$196$	−228.029	−	66.9554i	−0.0831010	−	0.0244007i
$197$	516.237	+	1130.40i	0.186702	+	0.408821i	0.979718	−	0.200380i	$-0.0642176\pi$
$197$	516.237	+	1130.40i	0.186702	+	0.408821i	−0.793016	+	0.609201i	$0.791490\pi$
$198$	−288.269	+	2004.95i	−0.103467	+	0.719626i
$199$	−353.424	+	407.873i	−0.125897	+	0.145293i	−0.815199	−	0.579182i	$-0.803372\pi$
$199$	−353.424	+	407.873i	−0.125897	+	0.145293i	0.689301	+	0.724475i	$0.257918\pi$
$200$	−739.882	+	1620.12i	−0.261588	+	0.572798i
$201$	−614.474	−	394.898i	−0.215630	−	0.138577i
$202$	60.1887	+	418.621i	0.0209646	+	0.145812i
$203$	67.8296	−	43.5914i	0.0234517	−	0.0150715i
$204$	−756.682	−	873.257i	−0.259698	−	0.299707i
$205$	−4807.66	+	1411.65i	−1.63796	+	0.480948i
$206$	−442.357			−0.149614
$207$	1279.94	+	1948.89i	0.429768	+	0.654384i
$208$	958.394			0.319484
$209$	−2888.87	+	848.249i	−0.956112	+	0.280740i
$210$	1186.03	+	1368.76i	0.389734	+	0.449777i
$211$	−2728.91	+	1753.76i	−0.890359	+	0.572199i	−0.903916	−	0.427709i	$-0.859321\pi$
$211$	−2728.91	+	1753.76i	−0.890359	+	0.572199i	0.0135576	+	0.999908i	$0.495684\pi$
$212$	110.586	+	769.139i	0.0358257	+	0.249173i
$213$	1454.10	+	934.496i	0.467763	+	0.300613i
$214$	1053.93	−	2307.79i	0.336660	−	0.737182i
$215$	−3277.66	+	3782.62i	−1.03969	+	1.19987i
$216$	132.693	−	922.903i	0.0417993	−	0.290720i
$217$	−1471.46	−	3222.04i	−0.460318	−	1.00796i
$218$	−1359.65	−	399.230i	−0.422419	−	0.124033i
$219$	696.021	+	204.370i	0.214761	+	0.0630596i
$220$	−1484.42	−	3250.42i	−0.454906	−	0.996105i
$221$	1017.09	−	7074.00i	0.309578	−	2.15316i
$222$	263.846	−	304.495i	0.0797667	−	0.0920557i
$223$	2478.92	−	5428.09i	0.744399	−	1.63001i	−0.0317800	−	0.999495i	$-0.510118\pi$
$223$	2478.92	−	5428.09i	0.744399	−	1.63001i	0.776179	−	0.630512i	$-0.217155\pi$
$224$	−540.024	−	347.053i	−0.161080	−	0.103520i
$225$	669.739	+	4658.14i	0.198441	+	1.38019i
$226$	−253.301	+	162.786i	−0.0745545	+	0.0479132i
$227$	−350.342	−	404.316i	−0.102436	−	0.118218i	0.702216	−	0.711964i	$-0.252194\pi$
$227$	−350.342	−	404.316i	−0.102436	−	0.118218i	−0.804653	+	0.593746i	$0.797648\pi$
$228$	583.924	−	171.456i	0.169611	−	0.0498023i
$229$	1746.54			0.503993			0.251997	−	0.967728i	$-0.418913\pi$
$229$	1746.54			0.503993			0.251997	+	0.967728i	$0.418913\pi$
$230$	−3758.27	−	1671.54i	−1.07745	−	0.479209i
$231$	−2327.07			−0.662814
$232$	30.8523	−	9.05905i	0.00873083	−	0.00256360i
$233$	520.909	+	601.161i	0.146463	+	0.169027i	0.824241	−	0.566239i	$-0.191602\pi$
$233$	520.909	+	601.161i	0.146463	+	0.169027i	−0.677778	+	0.735267i	$0.737057\pi$
$234$	2130.33	−	1369.08i	0.595145	−	0.382476i
$235$	254.503	+	1770.11i	0.0706466	+	0.491358i
$236$	−358.865	−	230.629i	−0.0989836	−	0.0636129i
$237$	52.9189	−	115.876i	0.0145040	−	0.0317594i
$238$	−3134.72	+	3617.66i	−0.853756	+	0.985287i
$239$	−489.727	+	3406.12i	−0.132543	+	0.921857i	0.809680	+	0.586871i	$0.199641\pi$
$239$	−489.727	+	3406.12i	−0.132543	+	0.921857i	−0.942223	+	0.334986i	$0.891268\pi$
$240$	300.043	+	657.003i	0.0806988	+	0.176706i
$241$	−6482.03	−	1903.30i	−1.73255	−	0.508723i	−0.745140	−	0.666908i	$-0.767618\pi$
$241$	−6482.03	−	1903.30i	−1.73255	−	0.508723i	−0.987409	+	0.158185i	$0.949436\pi$
$242$	1851.14	+	543.544i	0.491719	+	0.144382i
$243$	−1597.45	−	3497.93i	−0.421715	−	0.923426i
$244$	−413.242	+	2874.16i	−0.108423	+	0.754095i
$245$	725.435	−	837.196i	0.189169	−	0.218312i
$246$	−540.585	+	1183.72i	−0.140107	+	0.306792i
$247$	3166.54	+	2035.01i	0.815718	+	0.524230i
$248$	−201.034	−	1398.22i	−0.0514745	−	0.358013i
$249$	−1980.04	+	1272.50i	−0.503936	+	0.323860i
$250$	−2384.18	−	2751.49i	−0.603154	−	0.696077i
$251$	282.716	−	83.0128i	0.0710951	−	0.0208754i	−0.245992	−	0.969272i	$-0.579114\pi$
$251$	282.716	−	83.0128i	0.0710951	−	0.0208754i	0.317087	+	0.948397i	$0.397295\pi$
$252$	−1696.14			−0.423995
$253$	4785.41	−	2242.99i	1.18915	−	0.557374i
$254$	1017.80			0.251426
$255$	5167.82	−	1517.41i	1.26910	−	0.372642i
$256$	−167.644	−	193.472i	−0.0409288	−	0.0472343i
$257$	4152.24	−	2668.48i	1.00782	−	0.647686i	0.0709907	−	0.997477i	$-0.477384\pi$
$257$	4152.24	−	2668.48i	1.00782	−	0.647686i	0.936828	+	0.349791i	$0.113748\pi$
$258$	184.993	+	1286.65i	0.0446401	+	0.310479i
$259$	−1404.15	−	902.395i	−0.336872	−	0.216495i
$260$	−1855.78	+	4063.60i	−0.442657	+	0.969284i
$261$	55.6378	−	64.2094i	0.0131950	−	0.0152278i
$262$	−17.5655	+	122.171i	−0.00414198	+	0.0288081i
$263$	1002.38	+	2194.91i	0.235017	+	0.514615i	0.989989	−	0.141141i	$-0.0450772\pi$
$263$	1002.38	+	2194.91i	0.235017	+	0.514615i	−0.754973	+	0.655756i	$0.772350\pi$
$264$	−890.441	−	261.457i	−0.207587	−	0.0609529i
$265$	−3475.29	−	1020.44i	−0.805605	−	0.236547i
$266$	−1047.33	−	2293.33i	−0.241413	−	0.528620i
$267$	161.194	−	1121.13i	0.0369473	−	0.256974i
$268$	−790.250	+	911.997i	−0.180120	+	0.207870i
$269$	−1585.99	+	3472.84i	−0.359478	+	0.787147i	0.640340	+	0.768091i	$0.278793\pi$
$269$	−1585.99	+	3472.84i	−0.359478	+	0.787147i	−0.999818	+	0.0190559i	$0.993934\pi$
$270$	3656.18	+	2349.68i	0.824103	+	0.529619i
$271$	166.544	+	1158.34i	0.0373314	+	0.259645i	0.999937	−	0.0112628i	$-0.00358513\pi$
$271$	166.544	+	1158.34i	0.0373314	+	0.259645i	−0.962605	+	0.270908i	$0.912676\pi$
$272$	−1605.94	+	1032.08i	−0.357995	+	0.230070i
$273$	1905.16	+	2198.67i	0.422364	+	0.487434i
$274$	5789.76	−	1700.03i	1.27654	−	0.374826i
$275$	10667.0			2.33907
$276$	−967.269	+	453.373i	−0.210952	+	0.0988762i
$277$	3313.81			0.718799			0.359400	−	0.933184i	$-0.382982\pi$
$277$	3313.81			0.718799			0.359400	+	0.933184i	$0.382982\pi$
$278$	−528.536	+	155.192i	−0.114027	+	0.0334813i
$279$	−2444.24	−	2820.80i	−0.524490	−	0.605293i
$280$	2517.18	−	1617.69i	0.537251	−	0.345270i
$281$	649.741	+	4519.05i	0.137937	+	0.959372i	0.934790	+	0.355200i	$0.115587\pi$
$281$	649.741	+	4519.05i	0.137937	+	0.959372i	−0.796853	+	0.604173i	$0.793504\pi$
$282$	390.715	+	251.097i	0.0825061	+	0.0530234i
$283$	611.470	−	1338.93i	0.128439	−	0.281241i	−0.834478	−	0.551042i	$-0.814230\pi$
$283$	611.470	−	1338.93i	0.128439	−	0.281241i	0.962916	+	0.269800i	$0.0869577\pi$
$284$	1870.07	−	2158.17i	0.390732	−	0.450929i
$285$	−403.707	+	2807.84i	−0.0839071	+	0.583587i
$286$	−2384.45	−	5221.23i	−0.492992	−	1.07950i
$287$	5172.60	+	1518.81i	1.06386	+	0.312379i
$288$	−649.018	−	190.569i	−0.132791	−	0.0389909i
$289$	3872.63	+	8479.88i	0.788242	+	1.72601i
$290$	−21.3303	+	148.355i	−0.00431916	+	0.0300404i
$291$	−502.646	+	580.084i	−0.101256	+	0.116856i
$292$	497.854	−	1090.15i	0.0997763	−	0.218480i
$293$	4150.96	+	2667.66i	0.827650	+	0.531898i	0.884530	−	0.466483i	$-0.154479\pi$
$293$	4150.96	+	2667.66i	0.827650	+	0.531898i	−0.0568803	+	0.998381i	$0.518115\pi$
$294$	−40.9439	−	284.771i	−0.00812210	−	0.0564905i
$295$	1672.75	−	1075.01i	0.330141	−	0.212169i
$296$	−435.903	−	503.059i	−0.0855958	−	0.0987829i
$297$	−5358.01	+	1573.25i	−1.04681	+	0.307372i
$298$	−7025.46			−1.36569
$299$	−6037.00	−	2685.04i	−1.16765	−	0.519330i
$300$	−2156.11			−0.414944
$301$	5166.93	−	1517.15i	0.989424	−	0.290521i
$302$	−186.885	−	215.676i	−0.0356093	−	0.0410953i
$303$	−430.707	+	276.799i	−0.0816617	+	0.0524808i
$304$	−143.088	−	995.201i	−0.0269957	−	0.187759i
$305$	−11386.3	−	7317.52i	−2.13763	−	1.37377i
$306$	−2095.37	+	4588.22i	−0.391452	+	0.857161i
$307$	3906.07	−	4507.85i	0.726160	−	0.838034i	−0.265873	−	0.964008i	$-0.585660\pi$
$307$	3906.07	−	4507.85i	0.726160	−	0.838034i	0.992034	+	0.125974i	$0.0402057\pi$
$308$	−547.141	+	3805.45i	−0.101222	+	0.704011i
$309$	−222.457	−	487.113i	−0.0409551	−	0.0896792i
$310$	6317.74	+	1855.06i	1.15750	+	0.339871i
$311$	−3874.40	−	1137.63i	−0.706421	−	0.207424i	−0.0912620	−	0.995827i	$-0.529090\pi$
$311$	−3874.40	−	1137.63i	−0.706421	−	0.207424i	−0.615159	+	0.788403i	$0.710908\pi$
$312$	481.967	+	1055.36i	0.0874552	+	0.191500i
$313$	−1037.71	+	7217.41i	−0.187395	+	1.30336i	0.651325	+	0.758799i	$0.274213\pi$
$313$	−1037.71	+	7217.41i	−0.187395	+	1.30336i	−0.838720	+	0.544562i	$0.816696\pi$
$314$	4079.25	−	4707.71i	0.733139	−	0.846087i
$315$	3284.31	−	7191.64i	0.587461	−	1.28636i
$316$	−177.049	−	113.783i	−0.0315184	−	0.0202556i
$317$	237.904	+	1654.66i	0.0421516	+	0.293170i	0.999983	+	0.00583964i	$0.00185882\pi$
$317$	237.904	+	1654.66i	0.0421516	+	0.293170i	−0.957831	+	0.287331i	$0.907232\pi$
$318$	−791.345	+	508.567i	−0.139549	+	0.0896824i
$319$	−126.112	−	145.541i	−0.0221346	−	0.0255447i
$320$	1144.94	−	336.185i	0.200013	−	0.0587290i
$321$	3071.29			0.534027
$322$	2429.35	+	3699.04i	0.420443	+	0.640185i
$323$	−7497.52			−1.29156
$324$	−1107.43	+	325.170i	−0.189888	+	0.0557562i
$325$	−8733.01	−	10078.4i	−1.49052	−	1.72016i
$326$	−4478.22	+	2877.98i	−0.760816	+	0.488947i
$327$	−244.133	−	1697.98i	−0.0412862	−	0.287152i
$328$	1808.62	+	1162.33i	0.304465	+	0.195668i
$329$	799.283	−	1750.19i	0.133939	−	0.293285i
$330$	2832.78	−	3269.20i	0.472544	−	0.545345i
$331$	−237.702	+	1653.25i	−0.0394722	+	0.274535i	−0.999993	−	0.00367228i	$-0.998831\pi$
$331$	−237.702	+	1653.25i	−0.0394722	+	0.274535i	0.960521	+	0.278207i	$0.0897402\pi$
$332$	1615.36	+	3537.14i	0.267031	+	0.584716i
$333$	−1687.56	−	495.511i	−0.277710	−	0.0815431i
$334$	−6489.48	−	1905.48i	−1.06314	−	0.312166i
$335$	−2336.68	−	5116.61i	−0.381093	−	0.834478i
$336$	110.593	−	769.191i	0.0179564	−	0.124889i
$337$	−1618.39	+	1867.72i	−0.261600	+	0.301902i	−0.871321	−	0.490714i	$-0.836736\pi$
$337$	−1618.39	+	1867.72i	−0.261600	+	0.301902i	0.609721	+	0.792616i	$0.291282\pi$
$338$	−1155.66	+	2530.54i	−0.185975	+	0.407228i
$339$	−306.639	−	197.065i	−0.0491278	−	0.0315725i
$340$	−1266.35	−	8807.67i	−0.201993	−	1.40489i
$341$	−7117.19	+	4573.94i	−1.13026	+	0.726372i
$342$	−1739.72	−	2007.74i	−0.275067	−	0.317445i
$343$	5458.37	−	1602.72i	0.859255	−	0.252300i
$344$	2147.55			0.336594
$345$	−49.3363	−	4979.11i	−0.00769907	−	0.777004i
$346$	8538.21			1.32664
$347$	−11217.6	+	3293.78i	−1.73542	+	0.509566i	−0.987956	−	0.154735i	$-0.950547\pi$
$347$	−11217.6	+	3293.78i	−1.73542	+	0.509566i	−0.747465	+	0.664301i	$0.768729\pi$
$348$	25.4909	+	29.4181i	0.00392660	+	0.00453154i
$349$	−2673.91	+	1718.42i	−0.410119	+	0.263567i	−0.729393	−	0.684095i	$-0.760197\pi$
$349$	−2673.91	+	1718.42i	−0.410119	+	0.263567i	0.319274	+	0.947662i	$0.396561\pi$
$350$	1271.18	+	8841.25i	0.194136	+	1.35024i
$351$	5873.01	+	3774.35i	0.893100	+	0.573960i
$352$	−636.920	+	1394.66i	−0.0964430	+	0.211181i
$353$	−862.532	+	995.415i	−0.130051	+	0.150087i	−0.817040	−	0.576581i	$-0.804387\pi$
$353$	−862.532	+	995.415i	−0.130051	+	0.150087i	0.686989	+	0.726668i	$0.258932\pi$
$354$	73.4929	−	511.154i	0.0110342	−	0.0767445i
$355$	5529.57	+	12108.1i	0.826701	+	1.81022i
$356$	−1795.48	−	527.201i	−0.267304	−	0.0784876i
$357$	−5560.10	−	1632.59i	−0.824291	−	0.242034i
$358$	−2932.05	−	6420.30i	−0.432860	−	0.947831i
$359$	−396.267	+	2756.10i	−0.0582568	+	0.405185i	0.939738	+	0.341895i	$0.111069\pi$
$359$	−396.267	+	2756.10i	−0.0582568	+	0.405185i	−0.997995	+	0.0632905i	$0.979841\pi$
$360$	2064.74	−	2382.83i	0.302281	−	0.348851i
$361$	−1208.93	+	2647.19i	−0.176254	+	0.385943i
$362$	−319.592	−	205.390i	−0.0464017	−	0.0298205i
$363$	332.383	+	2311.78i	0.0480595	+	0.334261i
$364$	4043.41	−	2598.54i	0.582231	−	0.374177i
$365$	3658.22	+	4221.81i	0.524602	+	0.605423i
$366$	−3372.77	+	990.334i	−0.481687	+	0.141436i
$367$	−7439.41			−1.05813			−0.529065	−	0.848581i	$-0.677457\pi$
$367$	−7439.41			−1.05813			−0.529065	+	0.848581i	$0.677457\pi$
$368$	513.974	+	1688.37i	0.0728064	+	0.239164i
$369$	5680.62			0.801413
$370$	2977.03	−	874.136i	0.418294	−	0.122822i
$371$	2551.96	+	2945.12i	0.357119	+	0.412137i
$372$	1438.59	−	924.525i	0.200504	−	0.128856i
$373$	−559.637	−	3892.36i	−0.0776861	−	0.540319i	−0.991083	−	0.133248i	$-0.957459\pi$
$373$	−559.637	−	3892.36i	−0.0776861	−	0.540319i	0.913397	−	0.407071i	$-0.133450\pi$
$374$	9618.18	+	6181.23i	1.32980	+	0.854609i
$375$	1830.89	−	4009.09i	0.252125	−	0.552076i
$376$	502.482	−	579.896i	0.0689190	−	0.0795368i
$377$	−34.2634	+	238.307i	−0.00468078	+	0.0325555i
$378$	−1942.49	−	4253.45i	−0.264314	−	0.578767i
$379$	141.072	+	41.4223i	0.0191197	+	0.00561405i	0.291278	−	0.956638i	$-0.405919\pi$
$379$	141.072	+	41.4223i	0.0191197	+	0.00561405i	−0.272159	+	0.962252i	$0.587738\pi$
$380$	4496.73	+	1320.36i	0.607046	+	0.178245i
$381$	511.840	+	1120.77i	0.0688250	+	0.150706i
$382$	1120.42	−	7792.69i	0.150067	−	1.04374i
$383$	4604.73	−	5314.14i	0.614335	−	0.708981i	−0.360286	−	0.932842i	$-0.617321\pi$
$383$	4604.73	−	5314.14i	0.614335	−	0.708981i	0.974621	+	0.223861i	$0.0718662\pi$
$384$	128.740	−	281.901i	0.0171087	−	0.0374627i
$385$	−15075.7	−	9688.55i	−1.99566	−	1.28253i
$386$	−346.665	−	2411.11i	−0.0457118	−	0.317933i
$387$	4773.60	−	3067.81i	0.627017	−	0.402959i
$388$	830.426	+	958.363i	0.108656	+	0.125396i
$389$	559.145	−	164.180i	0.0728786	−	0.0213991i	−0.245090	−	0.969500i	$-0.578818\pi$
$389$	559.145	−	164.180i	0.0728786	−	0.0213991i	0.317969	+	0.948101i	$0.396999\pi$
$390$	−5407.99			−0.702165
$391$	13007.4	−	2001.93i	1.68239	−	0.258930i
$392$	−475.312			−0.0612420
$393$	−143.365	+	42.0957i	−0.0184015	+	0.00540318i
$394$	1627.59	+	1878.34i	0.208114	+	0.240176i
$395$	825.269	−	530.368i	0.105123	−	0.0675588i
$396$	576.538	+	4009.91i	0.0731619	+	0.508852i
$397$	−3693.44	−	2373.63i	−0.466923	−	0.300073i	0.285944	−	0.958246i	$-0.407693\pi$
$397$	−3693.44	−	2373.63i	−0.466923	−	0.300073i	−0.752866	+	0.658173i	$0.771329\pi$
$398$	−448.394	+	981.845i	−0.0564722	+	0.123657i
$399$	1998.67	−	2306.58i	0.250773	−	0.289408i
$400$	−506.945	+	3525.88i	−0.0633681	+	0.440735i
$401$	4039.72	+	8845.76i	0.503078	+	1.10159i	0.975457	+	0.220191i	$0.0706681\pi$
$401$	4039.72	+	8845.76i	0.503078	+	1.10159i	−0.472379	+	0.881396i	$0.656605\pi$
$402$	−1401.68	−	411.570i	−0.173904	−	0.0510628i
$403$	10148.3	+	2979.82i	1.25440	+	0.368326i
$404$	351.380	+	769.414i	0.0432718	+	0.0947519i
$405$	765.640	−	5325.14i	0.0939381	−	0.653354i
$406$	105.602	−	121.871i	0.0129087	−	0.0148974i
$407$	−1656.10	+	3626.35i	−0.201695	+	0.441650i
$408$	−1944.11	−	1249.40i	−0.235902	−	0.151605i
$409$	1421.35	+	9885.67i	0.171836	+	1.19515i	0.875001	+	0.484120i	$0.160860\pi$
$409$	1421.35	+	9885.67i	0.171836	+	1.19515i	−0.703165	+	0.711026i	$0.748231\pi$
$410$	−8430.40	+	5417.89i	−1.01548	+	0.652611i
$411$	4783.64	+	5520.61i	0.574111	+	0.662559i
$412$	−848.877	+	249.253i	−0.101508	+	0.0298053i
$413$	−2139.35			−0.254892
$414$	3554.32	+	3018.70i	0.421945	+	0.358360i
$415$	−18125.4			−2.14395
$416$	1839.15	−	540.022i	0.216758	−	0.0636460i
$417$	−436.689	−	503.966i	−0.0512824	−	0.0591830i
$418$	−5065.75	+	3255.56i	−0.592760	+	0.380944i
$419$	−2287.85	−	15912.3i	−0.266751	−	1.85529i	−0.478655	−	0.878003i	$-0.658876\pi$
$419$	−2287.85	−	15912.3i	−0.266751	−	1.85529i	0.211904	−	0.977290i	$-0.432033\pi$
$420$	3047.23	+	1958.33i	0.354023	+	0.227517i
$421$	−505.727	+	1107.39i	−0.0585454	+	0.128197i	−0.936644	−	0.350284i	$-0.886085\pi$
$421$	−505.727	+	1107.39i	−0.0585454	+	0.128197i	0.878098	+	0.478481i	$0.158812\pi$
$422$	−4248.55	+	4903.09i	−0.490086	+	0.565589i
$423$	288.534	−	2006.80i	0.0331655	−	0.230671i
$424$	645.595	+	1413.66i	0.0739455	+	0.161918i
$425$	25486.8	+	7483.61i	2.90892	+	0.854137i
$426$	3316.96	+	973.948i	0.377247	+	0.110770i
$427$	6049.41	+	13246.4i	0.685600	+	1.50126i
$428$	722.121	−	5022.46i	0.0815538	−	0.567219i
$429$	4550.37	−	5251.40i	0.512107	−	0.591003i
$430$	−4158.41	+	9105.64i	−0.466363	+	1.02119i
$431$	−14297.7	−	9188.54i	−1.59790	−	1.02691i	−0.968237	−	0.250036i	$-0.919558\pi$
$431$	−14297.7	−	9188.54i	−1.59790	−	1.02691i	−0.629661	−	0.776870i	$-0.716806\pi$
$432$	−265.387	−	1845.81i	−0.0295566	−	0.205570i
$433$	7763.14	−	4989.07i	0.861600	−	0.553716i	−0.0335729	−	0.999436i	$-0.510689\pi$
$433$	7763.14	−	4989.07i	0.861600	−	0.553716i	0.895173	+	0.445720i	$0.147052\pi$
$434$	−4639.22	−	5353.94i	−0.513109	−	0.592160i
$435$	−174.092	+	51.1181i	−0.0191887	+	0.00563431i
$436$	−2834.11			−0.311305
$437$	−1886.83	+	6669.73i	−0.206543	+	0.730106i
$438$	1450.81			0.158270
$439$	−3083.25	+	905.323i	−0.335206	+	0.0984253i	−0.445004	−	0.895529i	$-0.646798\pi$
$439$	−3083.25	+	905.323i	−0.335206	+	0.0984253i	0.109798	+	0.993954i	$0.464980\pi$
$440$	−4680.07	−	5401.09i	−0.507076	−	0.585197i
$441$	−1056.53	+	678.988i	−0.114083	+	0.0733170i
$442$	−2034.17	−	14148.0i	−0.218905	−	1.52251i
$443$	−695.973	−	447.275i	−0.0746426	−	0.0479699i	0.502787	−	0.864410i	$-0.332308\pi$
$443$	−695.973	−	447.275i	−0.0746426	−	0.0479699i	−0.577430	+	0.816440i	$0.695944\pi$
$444$	334.745	−	732.989i	0.0357800	−	0.0783472i
$445$	5712.01	−	6592.01i	0.608484	−	0.702228i
$446$	1698.48	−	11813.2i	0.180326	−	1.25420i
$447$	−3533.04	−	7736.27i	−0.373841	−	0.818597i
$448$	−1231.85	−	361.704i	−0.129910	−	0.0381449i
$449$	8613.80	+	2529.24i	0.905368	+	0.265840i	0.701090	−	0.713073i	$-0.252697\pi$
$449$	8613.80	+	2529.24i	0.905368	+	0.265840i	0.204278	+	0.978913i	$0.434515\pi$
$450$	3909.92	+	8561.53i	0.409590	+	0.896876i
$451$	1832.46	−	12745.0i	0.191324	−	1.33068i
$452$	−394.356	+	455.111i	−0.0410375	+	0.0473598i
$453$	143.515	−	314.254i	0.0148850	−	0.0325937i
$454$	−900.120	−	578.472i	−0.0930500	−	0.0597996i
$455$	3188.39	+	22175.8i	0.328515	+	2.28487i
$456$	1023.93	−	658.042i	0.105154	−	0.0675782i
$457$	−98.1231	−	113.240i	−0.0100438	−	0.0115911i	0.750705	−	0.660637i	$-0.229714\pi$
$457$	−98.1231	−	113.240i	−0.0100438	−	0.0115911i	−0.760749	+	0.649046i	$0.775168\pi$
$458$	3351.58	−	984.113i	0.341941	−	0.100403i
$459$	−13905.7			−1.41408
$460$	−8153.92	−	1090.01i	−0.826475	−	0.110482i
$461$	−1766.24			−0.178442			−0.0892212	−	0.996012i	$-0.528438\pi$
$461$	−1766.24			−0.178442			−0.0892212	+	0.996012i	$0.528438\pi$
$462$	−4465.62	+	1311.22i	−0.449696	+	0.132043i
$463$	−719.827	−	830.725i	−0.0722531	−	0.0833846i	0.718472	−	0.695556i	$-0.244842\pi$
$463$	−719.827	−	830.725i	−0.0722531	−	0.0833846i	−0.790725	+	0.612171i	$0.790296\pi$
$464$	54.1007	−	34.7684i	0.00541285	−	0.00347862i
$465$	1134.39	+	7889.83i	0.113131	+	0.786843i
$466$	1338.35	+	860.106i	0.133043	+	0.0855014i
$467$	1239.38	−	2713.87i	0.122809	−	0.268914i	−0.838235	−	0.545309i	$-0.816412\pi$
$467$	1239.38	−	2713.87i	0.122809	−	0.268914i	0.961044	+	0.276395i	$0.0891397\pi$
$468$	3316.64	−	3827.61i	0.327589	−	0.378058i
$469$	−861.276	+	5990.31i	−0.0847975	+	0.589780i
$470$	1485.78	+	3253.41i	0.145817	+	0.319295i
$471$	7235.43	+	2124.51i	0.707836	+	0.207839i
$472$	−818.609	−	240.365i	−0.0798295	−	0.0234400i
$473$	−5343.04	−	11699.6i	−0.519394	−	1.13731i
$474$	36.2584	−	252.183i	0.00351351	−	0.0244370i
$475$	−9161.65	+	10573.1i	−0.884979	+	1.02132i
$476$	−3977.06	+	8708.55i	−0.382959	+	0.838562i
$477$	3454.46	+	2220.05i	0.331591	+	0.213101i
$478$	979.454	+	6812.25i	0.0937221	+	0.651852i
$479$	10600.5	−	6812.55i	1.01117	−	0.649840i	0.0734748	−	0.997297i	$-0.476591\pi$
$479$	10600.5	−	6812.55i	1.01117	−	0.649840i	0.937696	+	0.347457i	$0.112955\pi$
$480$	945.977	+	1091.72i	0.0899536	+	0.103812i
$481$	4782.09	−	1404.15i	0.453315	−	0.133105i
$482$	−13511.4			−1.27682
$483$	−2851.60	+	4535.36i	−0.268638	+	0.427259i
$484$	3858.58			0.362376
$485$	−5671.46	+	1665.29i	−0.530985	+	0.155911i
$486$	−5036.45	−	5812.38i	−0.470078	−	0.542499i
$487$	−10430.2	+	6703.06i	−0.970505	+	0.623706i	−0.926886	−	0.375342i	$-0.877525\pi$
$487$	−10430.2	+	6703.06i	−0.970505	+	0.623706i	−0.0436189	+	0.999048i	$0.513889\pi$
$488$	826.484	+	5748.32i	0.0766663	+	0.533226i
$489$	−5421.22	−	3484.00i	−0.501341	−	0.322192i
$490$	920.368	−	2015.32i	0.0848530	−	0.185802i
$491$	6311.17	−	7283.48i	0.580080	−	0.669448i	−0.387542	−	0.921852i	$-0.626676\pi$
$491$	6311.17	−	7283.48i	0.580080	−	0.669448i	0.967622	+	0.252404i	$0.0812213\pi$
$492$	−370.392	+	2576.13i	−0.0339402	+	0.236059i
$493$	−199.215	−	436.220i	−0.0181992	−	0.0398506i
$494$	7223.21	+	2120.93i	0.657870	+	0.193168i
$495$	−18118.4	−	5320.05i	−1.64518	−	0.483067i
$496$	−1173.63	−	2569.89i	−0.106245	−	0.232644i
$497$	2038.14	−	14175.6i	0.183950	−	1.27940i
$498$	−3082.66	+	3557.58i	−0.277385	+	0.320119i
$499$	−4284.70	+	9382.18i	−0.384388	+	0.841692i	0.614230	+	0.789127i	$0.289467\pi$
$499$	−4284.70	+	9382.18i	−0.384388	+	0.841692i	−0.998618	+	0.0525645i	$0.983260\pi$
$500$	−6125.57	−	3936.66i	−0.547888	−	0.352106i
$501$	−1165.22	−	8104.30i	−0.103909	−	0.722702i
$502$	495.753	−	318.601i	0.0440768	−	0.0283264i
$503$	1732.98	+	1999.96i	0.153618	+	0.177284i	0.827342	−	0.561699i	$-0.189852\pi$
$503$	1732.98	+	1999.96i	0.153618	+	0.177284i	−0.673724	+	0.738983i	$0.735306\pi$
$504$	−3254.87	+	955.715i	−0.287665	+	0.0844662i
$505$	−3942.71			−0.347423
$506$	7919.28	−	7000.67i	0.695761	−	0.615055i
$507$	−3367.74			−0.295003
$508$	1953.14	−	573.493i	0.170584	−	0.0500878i
$509$	−1502.30	−	1733.74i	−0.130822	−	0.150976i	0.686559	−	0.727074i	$-0.259120\pi$
$509$	−1502.30	−	1733.74i	−0.130822	−	0.150976i	−0.817381	+	0.576098i	$0.804575\pi$
$510$	9061.96	−	5823.77i	0.786805	−	0.505649i
$511$	−855.355	−	5949.12i	−0.0740483	−	0.515017i
$512$	−430.722	−	276.808i	−0.0371785	−	0.0238932i
$513$	3042.47	−	6662.07i	0.261848	−	0.573368i
$514$	6464.49	−	7460.41i	0.554740	−	0.640204i
$515$	586.886	−	4081.88i	0.0502161	−	0.349261i
$516$	1079.98	+	2364.83i	0.0921387	+	0.201756i
$517$	−4409.37	−	1294.71i	−0.375094	−	0.110138i
$518$	−3203.02	−	940.491i	−0.271685	−	0.0797738i
$519$	4293.78	+	9402.07i	0.363152	+	0.795193i
$520$	−1271.53	+	8843.66i	−0.107231	+	0.745808i
$521$	8707.34	−	10048.8i	0.732198	−	0.845002i	−0.260519	−	0.965469i	$-0.583894\pi$
$521$	8707.34	−	10048.8i	0.732198	−	0.845002i	0.992717	+	0.120467i	$0.0384391\pi$
$522$	70.5883	−	154.567i	0.00591871	−	0.0129602i
$523$	18878.2	+	12132.3i	1.57837	+	1.01436i	0.976435	+	0.215810i	$0.0692392\pi$
$523$	18878.2	+	12132.3i	1.57837	+	1.01436i	0.601934	+	0.798546i	$0.294397\pi$
$524$	35.1310	+	244.341i	0.00292883	+	0.0203704i
$525$	−9096.51	+	5845.97i	−0.756198	+	0.485979i
$526$	3160.31	+	3647.19i	0.261969	+	0.302329i
$527$	−20214.1	+	5935.40i	−1.67085	+	0.490607i
$528$	−1856.07			−0.152983
$529$	1492.57	−	12075.1i	0.122673	−	0.992447i
$530$	−7244.01			−0.593697
$531$	−2162.97	+	635.107i	−0.176770	+	0.0519045i
$532$	−3302.02	−	3810.73i	−0.269099	−	0.310557i
$533$	−13542.0	+	8702.90i	−1.10050	+	0.707250i
$534$	−322.389	−	2242.26i	−0.0261257	−	0.181708i
$535$	19897.0	+	12787.0i	1.60789	+	1.03333i
$536$	−1002.60	+	2195.39i	−0.0807943	+	0.176915i
$537$	5595.38	−	6457.41i	0.449643	−	0.518916i
$538$	−1086.67	+	7557.98i	−0.0870814	+	0.605665i
$539$	1182.56	+	2589.44i	0.0945018	+	0.206930i
$540$	8340.11	+	2448.88i	0.664632	+	0.195154i
$541$	11487.5	+	3373.04i	0.912916	+	0.268056i	0.704268	−	0.709934i	$-0.251275\pi$
$541$	11487.5	+	3373.04i	0.912916	+	0.268056i	0.208648	+	0.977991i	$0.433094\pi$
$542$	972.277	+	2128.99i	0.0770532	+	0.168723i
$543$	65.4501	−	455.216i	0.00517262	−	0.0359764i
$544$	−2500.24	+	2885.44i	−0.197054	+	0.227412i
$545$	5487.81	−	12016.6i	0.431325	−	0.944469i
$546$	4894.84	+	3145.72i	0.383663	+	0.246565i
$547$	−1701.08	−	11831.3i	−0.132967	−	0.924807i	−0.941658	−	0.336573i	$-0.890732\pi$
$547$	−1701.08	−	11831.3i	−0.132967	−	0.924807i	0.808690	−	0.588235i	$-0.200177\pi$
$548$	10152.6	−	6524.65i	0.791416	−	0.508612i
$549$	10048.7	+	11596.8i	0.781177	+	0.901527i
$550$	20469.9	−	6010.49i	1.58698	−	0.465979i
$551$	252.575			0.0195282
$552$	−1600.72	+	1415.04i	−0.123426	+	0.109109i
$553$	−1055.47			−0.0811627
$554$	6359.15	−	1867.21i	0.487679	−	0.143196i
$555$	2459.70	+	2838.64i	0.188123	+	0.217106i
$556$	−926.807	+	595.623i	−0.0706931	+	0.0454317i
$557$	403.872	+	2808.99i	0.0307228	+	0.213682i	0.999400	−	0.0346424i	$-0.0110292\pi$
$557$	403.872	+	2808.99i	0.0307228	+	0.213682i	−0.968677	+	0.248324i	$0.920120\pi$
$558$	−6279.88	−	4035.83i	−0.476431	−	0.306183i
$559$	−6679.75	+	14626.6i	−0.505409	+	1.10669i
$560$	3918.92	−	4522.67i	0.295722	−	0.341282i
$561$	−1969.73	+	13699.8i	−0.148239	+	1.03103i
$562$	3793.17	+	8305.88i	0.284707	+	0.623420i
$563$	7487.12	+	2198.42i	0.560470	+	0.164569i	0.549683	−	0.835373i	$-0.314748\pi$
$563$	7487.12	+	2198.42i	0.560470	+	0.164569i	0.0107862	+	0.999942i	$0.496567\pi$
$564$	891.260	+	261.698i	0.0665405	+	0.0195380i
$565$	−1166.06	−	2553.32i	−0.0868260	−	0.190122i
$566$	418.961	−	2913.94i	0.0311135	−	0.216399i
$567$	−3790.52	+	4374.50i	−0.280753	+	0.324006i
$568$	2372.58	−	5195.22i	0.175266	−	0.383779i
$569$	−7025.63	−	4515.10i	−0.517627	−	0.332658i	0.255606	−	0.966781i	$-0.417725\pi$
$569$	−7025.63	−	4515.10i	−0.517627	−	0.332658i	−0.773232	+	0.634123i	$0.781361\pi$
$570$	807.413	+	5615.68i	0.0593313	+	0.412658i
$571$	−17793.4	+	11435.1i	−1.30408	+	0.838084i	−0.993650	−	0.112512i	$-0.964110\pi$
$571$	−17793.4	+	11435.1i	−1.30408	+	0.838084i	−0.310433	+	0.950595i	$0.600474\pi$
$572$	−7517.71	−	8675.90i	−0.549530	−	0.634192i
$573$	9144.57	−	2685.09i	0.666701	−	0.195761i
$574$	10781.9			0.784024
$575$	13071.4	−	20789.5i	0.948025	−	1.50780i
$576$	−1352.84			−0.0978614
$577$	−7753.25	+	2276.56i	−0.559397	+	0.164254i	−0.549195	−	0.835694i	$-0.685066\pi$
$577$	−7753.25	+	2276.56i	−0.559397	+	0.164254i	−0.0102019	+	0.999948i	$0.503247\pi$
$578$	12209.6	+	14090.7i	0.878640	+	1.01401i
$579$	2480.72	−	1594.26i	0.178057	−	0.114430i
$580$	42.6606	+	296.711i	0.00305411	+	0.0212418i
$581$	16405.5	+	10543.2i	1.17146	+	0.752849i
$582$	−637.713	+	1396.40i	−0.0454193	+	0.0994545i
$583$	6095.22	−	7034.26i	0.432999	−	0.499707i
$584$	341.114	−	2372.50i	0.0241702	−	0.168108i
$585$	9806.91	+	21474.1i	0.693104	+	1.51769i
$586$	9468.76	+	2780.28i	0.667493	+	0.195994i
$587$	−12463.3	−	3659.56i	−0.876348	−	0.257319i	−0.187535	−	0.982258i	$-0.560050\pi$
$587$	−12463.3	−	3659.56i	−0.876348	−	0.257319i	−0.688813	+	0.724939i	$0.741868\pi$
$588$	−239.029	−	523.402i	−0.0167643	−	0.0367087i
$589$	1579.11	−	10983.0i	0.110469	−	0.768329i
$590$	2604.26	−	3005.48i	0.181721	−	0.209718i
$591$	−1249.88	+	2736.86i	−0.0869938	+	0.190490i
$592$	−1119.95	−	719.747i	−0.0777527	−	0.0499686i
$593$	−2212.71	−	15389.8i	−0.153230	−	1.06574i	−0.910760	−	0.412936i	$-0.864503\pi$
$593$	−2212.71	−	15389.8i	−0.153230	−	1.06574i	0.757530	−	0.652800i	$-0.226406\pi$
$594$	−9395.47	+	6038.10i	−0.648992	+	0.417082i
$595$	−29223.3	−	33725.5i	−2.01351	−	2.32372i
$596$	−13481.8	+	3958.60i	−0.926568	+	0.272065i
$597$	−1306.68			−0.0895791
$598$	−13097.8	−	1750.91i	−0.895670	−	0.119732i
$599$	22302.7			1.52131			0.760653	−	0.649158i	$-0.224879\pi$
$599$	22302.7			1.52131			0.760653	+	0.649158i	$0.224879\pi$
$600$	−4137.55	+	1214.89i	−0.281524	+	0.0826630i
$601$	−14108.9	−	16282.6i	−0.957595	−	1.10512i	−0.994387	−	0.105801i	$-0.966259\pi$
$601$	−14108.9	−	16282.6i	−0.957595	−	1.10512i	0.0367919	−	0.999323i	$-0.488286\pi$
$602$	9060.40	−	5822.76i	0.613412	−	0.394216i
$603$	907.551	+	6312.15i	0.0612907	+	0.426287i
$604$	−480.155	−	308.577i	−0.0323464	−	0.0207878i
$605$	−7471.55	+	16360.4i	−0.502086	+	1.09941i
$606$	−670.555	+	773.861i	−0.0449495	+	0.0518745i
$607$	−3051.27	+	21222.0i	−0.204032	+	1.41907i	0.588133	+	0.808764i	$0.299863\pi$
$607$	−3051.27	+	21222.0i	−0.204032	+	1.41907i	−0.792165	+	0.610307i	$0.791046\pi$
$608$	−835.346	−	1829.15i	−0.0557200	−	0.122010i
$609$	187.307	+	54.9984i	0.0124632	+	0.00365952i
$610$	−25973.3	−	7626.44i	−1.72398	−	0.506206i
$611$	2386.65	+	5226.03i	0.158025	+	0.346027i
$612$	−1435.68	+	9985.40i	−0.0948269	+	0.659536i
$613$	16561.8	−	19113.3i	1.09123	−	1.25934i	0.127679	−	0.991816i	$-0.459247\pi$
$613$	16561.8	−	19113.3i	1.09123	−	1.25934i	0.963550	−	0.267529i	$-0.0862071\pi$
$614$	4955.68	−	10851.4i	0.325725	−	0.713238i
$615$	−10205.6	−	6558.75i	−0.669155	−	0.430040i
$616$	1094.28	+	7610.90i	0.0715745	+	0.497811i
$617$	−9220.77	+	5925.83i	−0.601643	+	0.386653i	−0.805715	−	0.592303i	$-0.798219\pi$
$617$	−9220.77	+	5925.83i	−0.601643	+	0.386653i	0.204072	+	0.978956i	$0.434582\pi$
$618$	−701.363	−	809.416i	−0.0456520	−	0.0526852i
$619$	−14424.1	+	4235.30i	−0.936598	+	0.275010i	−0.714197	−	0.699945i	$-0.753208\pi$
$619$	−14424.1	+	4235.30i	−0.936598	+	0.275010i	−0.222402	+	0.974955i	$0.571390\pi$
$620$	13168.9			0.853026
$621$	−3499.52	+	12370.4i	−0.226137	+	0.799366i
$622$	−8075.93			−0.520603
$623$	−9004.46	+	2643.95i	−0.579063	+	0.170028i
$624$	1519.55	+	1753.65i	0.0974849	+	0.112504i
$625$	5141.30	−	3304.12i	0.329044	−	0.211463i
$626$	2075.41	+	14434.8i	0.132508	+	0.921615i
$627$	−6132.45	−	3941.09i	−0.390601	−	0.251024i
$628$	5175.40	−	11332.5i	0.328855	−	0.720092i
$629$	−6501.05	+	7502.62i	−0.412105	+	0.475594i
$630$	2250.31	−	15651.3i	0.142309	−	0.989779i
$631$	−1702.58	−	3728.12i	−0.107414	−	0.235205i	0.848291	−	0.529531i	$-0.177632\pi$
$631$	−1702.58	−	3728.12i	−0.107414	−	0.235205i	−0.955705	+	0.294326i	$0.904905\pi$
$632$	−403.868	−	118.586i	−0.0254193	−	0.00746378i
$633$	−7535.71	−	2212.69i	−0.473172	−	0.138936i
$634$	1388.88	+	3041.22i	0.0870023	+	0.190508i
$635$	−1350.34	+	9391.79i	−0.0843881	+	0.586932i
$636$	−1232.02	+	1421.83i	−0.0768126	+	0.0886464i
$637$	1478.41	−	3237.27i	0.0919572	−	0.201358i
$638$	−324.015	−	208.232i	−0.0201064	−	0.0129216i
$639$	−2147.65	−	14937.2i	−0.132957	−	0.924738i
$640$	2007.69	−	1290.27i	0.124002	−	0.0796911i
$641$	−5511.26	−	6360.34i	−0.339597	−	0.391916i	0.560104	−	0.828422i	$-0.310761\pi$
$641$	−5511.26	−	6360.34i	−0.339597	−	0.391916i	−0.899701	+	0.436506i	$0.856216\pi$
$642$	5893.76	−	1730.56i	0.362318	−	0.106386i
$643$	17449.4			1.07020			0.535098	−	0.844790i	$-0.320275\pi$
$643$	17449.4			1.07020			0.535098	+	0.844790i	$0.320275\pi$
$644$	6746.18	+	5729.56i	0.412790	+	0.350584i
$645$	−12118.1			−0.739769
$646$	−14387.6	+	4224.59i	−0.876276	+	0.257298i
$647$	−13674.8	−	15781.5i	−0.830929	−	0.958943i	0.168714	−	0.985665i	$-0.446038\pi$
$647$	−13674.8	−	15781.5i	−0.830929	−	0.958943i	−0.999643	+	0.0267223i	$0.991493\pi$
$648$	−1941.92	+	1247.99i	−0.117725	+	0.0756571i
$649$	727.189	+	5057.71i	0.0439825	+	0.305905i
$650$	−22437.4	−	14419.6i	−1.35395	−	0.870129i
$651$	3562.61	−	7801.03i	0.214485	−	0.469657i
$652$	−6972.01	+	8046.13i	−0.418781	+	0.483299i
$653$	−3495.65	+	24312.8i	−0.209488	+	1.45702i	0.565346	+	0.824854i	$0.308743\pi$
$653$	−3495.65	+	24312.8i	−0.209488	+	1.45702i	−0.774834	+	0.632165i	$0.782166\pi$
$654$	−1425.24	−	3120.85i	−0.0852163	−	0.186598i
$655$	−1104.03	−	324.174i	−0.0658599	−	0.0193382i
$656$	4125.65	+	1211.40i	0.245548	+	0.0720995i
$657$	−2630.91	−	5760.90i	−0.156228	−	0.342091i
$658$	547.644	−	3808.95i	0.0324459	−	0.225666i
$659$	4080.29	−	4708.90i	0.241192	−	0.278350i	−0.622228	−	0.782836i	$-0.713772\pi$
$659$	4080.29	−	4708.90i	0.241192	−	0.278350i	0.863420	+	0.504486i	$0.168318\pi$
$660$	3593.98	−	7869.73i	0.211963	−	0.464135i
$661$	22921.3	+	14730.7i	1.34877	+	0.866802i	0.997582	−	0.0695033i	$-0.0221414\pi$
$661$	22921.3	+	14730.7i	1.34877	+	0.866802i	0.351188	+	0.936305i	$0.385778\pi$
$662$	475.404	+	3306.51i	0.0279110	+	0.194125i
$663$	14556.5	−	9354.87i	0.852679	−	0.547983i
$664$	5092.90	+	5877.52i	0.297655	+	0.343512i
$665$	22551.4	−	6621.68i	1.31505	−	0.386132i
$666$	−3517.60			−0.204661
$667$	−438.191	+	67.4404i	−0.0254375	+	0.00391500i
$668$	−13526.9			−0.783490
$669$	13862.6	−	4070.42i	0.801133	−	0.235234i
$670$	−7367.08	−	8502.06i	−0.424799	−	0.490244i
$671$	29259.9	−	18804.2i	1.68341	−	1.08186i
$672$	−221.186	−	1538.38i	−0.0126971	−	0.0883101i
$673$	−12528.9	−	8051.81i	−0.717611	−	0.461180i	0.130194	−	0.991489i	$-0.458440\pi$
$673$	−12528.9	−	8051.81i	−0.717611	−	0.461180i	−0.847805	+	0.530308i	$0.822076\pi$
$674$	−2053.27	+	4496.03i	−0.117343	+	0.256944i
$675$	−16992.2	+	19610.0i	−0.968932	+	1.11821i
$676$	−791.822	+	5507.24i	−0.0450513	+	0.313339i
$677$	−4680.11	−	10248.0i	−0.265689	−	0.581777i	0.729022	−	0.684490i	$-0.239975\pi$
$677$	−4680.11	−	10248.0i	−0.265689	−	0.581777i	−0.994711	+	0.102713i	$0.967248\pi$
$678$	−699.475	−	205.384i	−0.0396212	−	0.0116338i
$679$	6101.98	+	1791.70i	0.344878	+	0.101265i
$680$	−7392.93	−	16188.3i	−0.416920	−	0.912928i
$681$	184.338	−	1282.10i	0.0103727	−	0.0721440i
$682$	−11080.5	+	12787.6i	−0.622134	+	0.717981i
$683$	−4927.99	+	10790.8i	−0.276083	+	0.604536i	−0.995983	−	0.0895407i	$-0.971460\pi$
$683$	−4927.99	+	10790.8i	−0.276083	+	0.604536i	0.719901	+	0.694077i	$0.244187\pi$
$684$	−4469.78	−	2872.55i	−0.249863	−	0.160577i
$685$	8005.71	+	55680.9i	0.446544	+	3.10578i
$686$	9571.46	−	6151.20i	0.532712	−	0.342353i
$687$	2769.16	+	3195.78i	0.153784	+	0.177477i
$688$	4121.12	−	1210.07i	0.228367	−	0.0670545i
$689$	−11636.2			−0.643404
$690$	−2900.23	−	9527.05i	−0.160014	−	0.525636i
$691$	14493.5			0.797913			0.398956	−	0.916970i	$-0.369372\pi$
$691$	14493.5			0.797913			0.398956	+	0.916970i	$0.369372\pi$
$692$	16384.7	−	4810.98i	0.900077	−	0.264286i
$693$	13304.6	+	15354.4i	0.729295	+	0.841651i
$694$	−19670.4	+	12641.4i	−1.07591	+	0.691444i
$695$	−730.825	−	5083.00i	−0.0398874	−	0.277423i
$696$	65.4928	+	42.0897i	0.00356681	+	0.00229225i
$697$	13319.8	−	29166.2i	0.723848	−	1.58501i
$698$	−4162.93	+	4804.28i	−0.225744	+	0.260523i
$699$	−274.084	+	1906.30i	−0.0148309	+	0.103151i
$700$	7421.12	+	16250.0i	0.400703	+	0.877416i
$701$	−31302.0	−	9191.09i	−1.68653	−	0.495211i	−0.708861	−	0.705348i	$-0.750791\pi$
$701$	−31302.0	−	9191.09i	−1.68653	−	0.495211i	−0.977672	+	0.210137i	$0.932609\pi$
$702$	13396.9	+	3933.70i	0.720277	+	0.211493i
$703$	−2172.04	−	4756.10i	−0.116529	−	0.255163i
$704$	−436.398	+	3035.21i	−0.0233627	+	0.162491i
$705$	−2835.39	+	3272.21i	−0.151471	+	0.174807i
$706$	−1094.31	+	2396.19i	−0.0583353	+	0.127736i
$707$	3568.60	+	2293.40i	0.189832	+	0.121997i
$708$	−146.986	−	1022.31i	−0.00780235	−	0.0542666i
$709$	7795.79	−	5010.05i	0.412943	−	0.265383i	−0.317633	−	0.948214i	$-0.602888\pi$
$709$	7795.79	−	5010.05i	0.412943	−	0.265383i	0.730576	+	0.682831i	$0.239252\pi$
$710$	17433.6	+	20119.5i	0.921510	+	1.06348i
$711$	−1067.12	+	313.336i	−0.0562873	+	0.0165274i
$712$	−3742.56			−0.196992
$713$	192.981	+	19476.0i	0.0101363	+	1.02298i
$714$	−11589.7			−0.607468
$715$	51342.8	−	15075.6i	2.68547	−	0.788525i
$716$	−9244.18	−	10668.4i	−0.482502	−	0.556837i
$717$	−7008.92	+	4504.36i	−0.365067	+	0.234614i
$718$	792.535	+	5512.20i	0.0411938	+	0.286509i
$719$	24040.5	+	15449.9i	1.24695	+	0.801367i	0.986443	−	0.164105i	$-0.0524736\pi$
$719$	24040.5	+	15449.9i	1.24695	+	0.801367i	0.260508	+	0.965472i	$0.416110\pi$
$720$	2619.56	−	5736.03i	0.135591	−	0.296902i
$721$	−2905.55	+	3353.18i	−0.150081	+	0.173203i
$722$	−828.321	+	5761.10i	−0.0426966	+	0.296961i
$723$	−6794.73	−	14878.4i	−0.349514	−	0.765330i
$724$	−729.023	−	214.060i	−0.0374226	−	0.0109883i
$725$	−858.594	−	252.106i	−0.0439826	−	0.0129145i
$726$	1940.44	+	4248.98i	0.0991964	+	0.217210i
$727$	−1919.02	+	13347.1i	−0.0978991	+	0.680903i	0.880480	+	0.474083i	$0.157221\pi$
$727$	−1919.02	+	13347.1i	−0.0978991	+	0.680903i	−0.978379	+	0.206820i	$0.933689\pi$
$728$	6295.06	−	7264.89i	0.320481	−	0.369855i
$729$	631.285	−	1382.32i	0.0320726	−	0.0702292i
$730$	9398.90	+	6040.31i	0.476533	+	0.306249i
$731$	−4558.14	−	31702.6i	−0.230628	−	1.60405i
$732$	−5914.28	+	3800.88i	−0.298631	+	0.191919i
$733$	−370.328	−	427.381i	−0.0186608	−	0.0215357i	0.746342	−	0.665562i	$-0.231808\pi$
$733$	−370.328	−	427.381i	−0.0186608	−	0.0215357i	−0.765003	+	0.644026i	$0.777263\pi$
$734$	−14276.1	+	4191.85i	−0.717903	+	0.210795i
$735$	2682.07			0.134598
$736$	1937.64	+	2950.35i	0.0970415	+	0.147760i
$737$	14454.7			0.722448
$738$	10901.0	−	3200.83i	0.543730	−	0.159653i
$739$	−15.4675	−	17.8504i	−0.000769933	−	0.000888550i	0.755364	−	0.655305i	$-0.227460\pi$
$739$	−15.4675	−	17.8504i	−0.000769933	−	0.000888550i	−0.756134	+	0.654416i	$0.772914\pi$
$740$	5220.34	−	3354.91i	0.259329	−	0.166661i
$741$	1296.97	+	9020.61i	0.0642987	+	0.447207i
$742$	6556.64	+	4213.70i	0.324396	+	0.208477i
$743$	−15308.9	+	33521.9i	−0.755895	+	1.65518i	−0.000421751		1.00000i	$0.500134\pi$
$743$	−15308.9	+	33521.9i	−0.755895	+	1.65518i	−0.755473	+	0.655179i	$0.772593\pi$
$744$	2239.69	−	2584.75i	0.110365	−	0.127367i
$745$	9320.86	−	64828.0i	0.458376	−	3.18807i
$746$	−3267.15	−	7154.05i	−0.160347	−	0.351110i
$747$	19716.7	+	5789.33i	0.965723	+	0.283562i
$748$	21940.1	+	6442.18i	1.07247	+	0.314906i
$749$	−10571.1	−	23147.4i	−0.515698	−	1.12922i
$750$	1254.47	−	8725.04i	0.0610757	−	0.424791i
$751$	−9441.07	+	10895.6i	−0.458734	+	0.529407i	−0.937244	−	0.348675i	$-0.886632\pi$
$751$	−9441.07	+	10895.6i	−0.458734	+	0.529407i	0.478510	+	0.878082i	$0.341177\pi$
$752$	637.506	−	1395.94i	0.0309142	−	0.0676926i
$753$	600.145	+	385.690i	0.0290445	+	0.0186657i
$754$	68.5268	+	476.614i	0.00330981	+	0.0230202i
$755$	2238.11	−	1438.35i	0.107885	−	0.0693336i
$756$	−6124.28	−	7067.79i	−0.294627	−	0.340017i
$757$	5196.61	−	1525.86i	0.249503	−	0.0732608i	−0.154589	−	0.987979i	$-0.549405\pi$
$757$	5196.61	−	1525.86i	0.249503	−	0.0732608i	0.404093	+	0.914718i	$0.367587\pi$
$758$	294.054			0.0140904
$759$	11691.5	+	5199.95i	0.559123	+	0.248678i
$760$	9373.14			0.447368
$761$	−29401.6	+	8633.09i	−1.40054	+	0.411234i	−0.892868	−	0.450319i	$-0.851310\pi$
$761$	−29401.6	+	8633.09i	−1.40054	+	0.411234i	−0.507668	+	0.861553i	$0.669492\pi$
$762$	1613.73	+	1862.34i	0.0767182	+	0.0885375i
$763$	−11956.9	+	7684.25i	−0.567326	+	0.364598i
$764$	−2240.84	−	15585.4i	−0.106114	−	0.738036i
$765$	−39558.2	−	25422.5i	−1.86958	−	1.20151i
$766$	5842.07	−	12792.4i	0.275565	−	0.603403i
$767$	4183.29	−	4827.77i	0.196936	−	0.227276i
$768$	88.2086	−	613.504i	0.00414447	−	0.0288254i
$769$	−2106.01	−	4611.51i	−0.0987575	−	0.216249i	0.853804	−	0.520594i	$-0.174290\pi$
$769$	−2106.01	−	4611.51i	−0.0987575	−	0.216249i	−0.952562	+	0.304345i	$0.901562\pi$
$770$	−34389.2	−	10097.6i	−1.60948	−	0.472586i
$771$	11466.2	+	3366.77i	0.535594	+	0.157265i
$772$	−2023.82	−	4431.55i	−0.0943508	−	0.206599i
$773$	−3060.74	+	21287.9i	−0.142415	+	0.990521i	0.785801	+	0.618480i	$0.212251\pi$
$773$	−3060.74	+	21287.9i	−0.142415	+	0.990521i	−0.928216	+	0.372041i	$0.878658\pi$
$774$	7431.87	−	8576.83i	0.345133	−	0.398305i
$775$	−16330.6	+	35759.0i	−0.756919	+	1.65742i
$776$	2133.58	+	1371.17i	0.0986999	+	0.0634305i
$777$	−575.120	−	4000.05i	−0.0265538	−	0.184686i
$778$	980.481	−	630.117i	0.0451825	−	0.0290370i
$779$	11058.9	+	12762.7i	0.508637	+	0.586998i
$780$	−10377.9	+	3047.21i	−0.476393	+	0.139882i
$781$	−34205.9			−1.56720
$782$	23833.1	−	11170.9i	1.08986	−	0.510832i
$783$	468.452			0.0213807
$784$	−912.116	+	267.822i	−0.0415505	+	0.0122003i
$785$	38028.7	+	43887.4i	1.72905	+	1.99543i
$786$	−251.396	+	161.562i	−0.0114084	+	0.00733172i
$787$	2221.86	+	15453.3i	0.100636	+	0.699939i	0.976206	+	0.216847i	$0.0695773\pi$
$787$	2221.86	+	15453.3i	0.100636	+	0.699939i	−0.875570	+	0.483092i	$0.839514\pi$
$788$	4181.71	+	2687.42i	0.189045	+	0.121492i
$789$	−2426.91	+	5314.19i	−0.109506	+	0.239785i
$790$	1284.84	−	1482.78i	0.0578638	−	0.0667784i
$791$	−429.800	+	2989.32i	−0.0193197	+	0.134372i
$792$	3365.81	+	7370.10i	0.151009	+	0.330663i
$793$	−41721.5	−	12250.5i	−1.86832	−	0.548587i
$794$	−8425.11	−	2473.84i	−0.376569	−	0.110571i
$795$	−3642.94	−	7976.92i	−0.162518	−	0.355865i
$796$	−307.226	+	2136.80i	−0.0136801	+	0.0951469i
$797$	7427.05	−	8571.27i	0.330087	−	0.380941i	−0.566310	−	0.824192i	$-0.691630\pi$
$797$	7427.05	−	8571.27i	0.330087	−	0.380941i	0.896397	+	0.443251i	$0.146175\pi$
$798$	2535.73	−	5552.48i	0.112486	−	0.246310i
$799$	−9627.03	−	6186.92i	−0.426258	−	0.273939i
$800$	1013.89	+	7051.76i	0.0448080	+	0.311647i
$801$	−8319.00	+	5346.30i	−0.366963	+	0.235833i
$802$	12736.5	+	14698.6i	0.560773	+	0.647166i
$803$	−13773.8	+	4044.35i	−0.605314	+	0.177736i
$804$	−2921.71			−0.128160
$805$	−37356.3	+	17509.4i	−1.63557	+	0.766617i
$806$	21153.6			0.924445
$807$	−8869.14	+	2604.21i	−0.386875	+	0.113597i
$808$	1107.83	+	1278.50i	0.0482343	+	0.0556654i
$809$	22304.7	−	14334.4i	0.969336	−	0.622955i	0.0427695	−	0.999085i	$-0.486382\pi$
$809$	22304.7	−	14334.4i	0.969336	−	0.622955i	0.926567	+	0.376130i	$0.122746\pi$
$810$	−1531.28	−	10650.3i	−0.0664243	−	0.461991i
$811$	−23834.1	−	15317.3i	−1.03197	−	0.663208i	−0.0889838	−	0.996033i	$-0.528362\pi$
$811$	−23834.1	−	15317.3i	−1.03197	−	0.663208i	−0.942989	+	0.332825i	$0.891998\pi$
$812$	133.978	−	293.372i	0.00579029	−	0.0126790i
$813$	−1855.44	+	2141.29i	−0.0800408	+	0.0923720i
$814$	−1134.71	+	7892.06i	−0.0488593	+	0.339824i
$815$	−20615.4	−	45141.5i	−0.886045	−	1.94017i
$816$	−4434.72	−	1302.15i	−0.190253	−	0.0558632i
$817$	16185.6	+	4752.53i	0.693101	+	0.203513i
$818$	8297.77	+	18169.6i	0.354676	+	0.776632i
$819$	3614.73	−	25141.0i	0.154223	−	1.07265i
$820$	−13125.0	+	15147.1i	−0.558959	+	0.645073i
$821$	−1910.25	+	4182.87i	−0.0812038	+	0.177811i	−0.945879	−	0.324520i	$-0.894797\pi$
$821$	−1910.25	+	4182.87i	−0.0812038	+	0.177811i	0.864675	+	0.502332i	$0.167524\pi$
$822$	12290.4	+	7898.57i	0.521505	+	0.335151i
$823$	−3241.19	−	22543.0i	−0.137279	−	0.954798i	−0.935725	−	0.352731i	$-0.885253\pi$
$823$	−3241.19	−	22543.0i	−0.137279	−	0.954798i	0.798446	−	0.602067i	$-0.205656\pi$
$824$	−1488.54	+	956.625i	−0.0629316	+	0.0404437i
$825$	16912.7	+	19518.3i	0.713726	+	0.823684i
$826$	−4105.37	+	1205.45i	−0.172935	+	0.0507783i
$827$	29552.9			1.24263			0.621315	−	0.783561i	$-0.286599\pi$
$827$	29552.9			1.24263			0.621315	+	0.783561i	$0.286599\pi$
$828$	8521.62	+	3790.10i	0.357665	+	0.159076i
$829$	−2188.73			−0.0916981			−0.0458490	−	0.998948i	$-0.514599\pi$
$829$	−2188.73			−0.0916981			−0.0458490	+	0.998948i	$0.514599\pi$
$830$	−34782.4	+	10213.0i	−1.45459	+	0.427107i
$831$	5254.08	+	6063.54i	0.219329	+	0.253119i
$832$	3225.01	−	2072.59i	0.134384	−	0.0863631i
$833$	1008.84	+	7016.64i	0.0419619	+	0.291851i
$834$	−1121.97	−	721.044i	−0.0465834	−	0.0299373i
$835$	26192.7	−	57354.1i	1.08555	−	2.37703i
$836$	−7886.70	+	9101.74i	−0.326277	+	0.376543i
$837$	2928.79	−	20370.2i	0.120948	−	0.841215i
$838$	−13356.4	−	29246.4i	−0.550583	−	1.20561i
$839$	−3061.91	−	899.057i	−0.125994	−	0.0369951i	0.218128	−	0.975920i	$-0.430005\pi$
$839$	−3061.91	−	899.057i	−0.125994	−	0.0369951i	−0.344122	+	0.938925i	$0.611823\pi$
$840$	6951.04	+	2041.01i	0.285516	+	0.0838352i
$841$	−10124.8	−	22170.3i	−0.415140	−	0.909029i
$842$	−346.509	+	2410.02i	−0.0141823	+	0.0986399i
$843$	−7238.68	+	8353.89i	−0.295746	+	0.341309i
$844$	−5390.19	+	11802.9i	−0.219832	+	0.481364i
$845$	−21817.5	−	14021.3i	−0.888219	−	0.570824i
$846$	−577.068	−	4013.60i	−0.0234516	−	0.163109i
$847$	16279.1	−	10462.0i	0.660399	−	0.424413i
$848$	2035.43	+	2349.02i	0.0824258	+	0.0951245i
$849$	3419.45	−	1004.04i	0.138227	−	0.0405872i
$850$	53125.6			2.14376
$851$	5038.20	+	7671.39i	0.202946	+	0.309015i
$852$	6913.99			0.278016
$853$	−23437.9	+	6882.00i	−0.940797	+	0.276243i	−0.715950	−	0.698151i	$-0.754006\pi$
$853$	−23437.9	+	6882.00i	−0.940797	+	0.276243i	−0.224847	+	0.974394i	$0.572188\pi$
$854$	19072.6	+	22010.9i	0.764228	+	0.881966i
$855$	20834.7	−	13389.6i	0.833370	−	0.535574i
$856$	−1444.24	−	10044.9i	−0.0576672	−	0.401085i
$857$	38740.6	+	24897.1i	1.54417	+	0.992379i	0.986768	+	0.162136i	$0.0518384\pi$
$857$	38740.6	+	24897.1i	1.54417	+	0.992379i	0.557403	+	0.830242i	$0.311798\pi$
$858$	5773.11	−	12641.3i	0.229709	−	0.502993i
$859$	−25320.5	+	29221.4i	−1.00573	+	1.16068i	−0.0187541	+	0.999824i	$0.505970\pi$
$859$	−25320.5	+	29221.4i	−1.00573	+	1.16068i	−0.986978	+	0.160853i	$0.948575\pi$
$860$	−2849.21	+	19816.7i	−0.112974	+	0.785749i
$861$	5422.13	+	11872.8i	0.214618	+	0.469947i
$862$	−32614.4	−	9576.46i	−1.28869	−	0.378394i
$863$	−37050.8	−	10879.1i	−1.46144	−	0.429118i	−0.548134	−	0.836390i	$-0.684662\pi$
$863$	−37050.8	−	10879.1i	−1.46144	−	0.429118i	−0.913307	+	0.407273i	$0.866480\pi$
$864$	−1549.32	−	3392.54i	−0.0610058	−	0.133584i
$865$	−11327.9	+	78787.0i	−0.445270	+	3.09692i
$866$	12086.2	−	13948.2i	0.474256	−	0.547320i
$867$	−9376.20	+	20531.0i	−0.367281	+	0.804233i
$868$	−11919.3	−	7660.10i	−0.466093	−	0.299540i
$869$	358.765	+	2495.27i	0.0140049	+	0.0974064i
$870$	−305.277	+	196.190i	−0.0118964	+	0.00764535i
$871$	−11833.9	−	13657.1i	−0.460364	−	0.531289i
$872$	−5438.61	+	1596.92i	−0.211209	+	0.0620167i
$873$	6701.27			0.259798
$874$	137.357	+	13862.3i	0.00531597	+	0.536497i
$875$	−36517.1			−1.41086
$876$	2784.08	−	817.480i	0.107381	−	0.0315298i
$877$	−14313.6	−	16518.8i	−0.551125	−	0.636032i	0.410020	−	0.912077i	$-0.365522\pi$
$877$	−14313.6	−	16518.8i	−0.551125	−	0.636032i	−0.961145	+	0.276044i	$0.910976\pi$
$878$	−5406.59	+	3474.60i	−0.207817	+	0.133556i
$879$	1700.17	+	11824.9i	0.0652393	+	0.453749i
$880$	−12024.3	−	7727.55i	−0.460613	−	0.296018i
$881$	−20239.7	+	44318.8i	−0.774000	+	1.69482i	−0.0563585	+	0.998411i	$0.517949\pi$
$881$	−20239.7	+	44318.8i	−0.774000	+	1.69482i	−0.717641	+	0.696413i	$0.754778\pi$
$882$	−1644.87	+	1898.29i	−0.0627957	+	0.0724701i
$883$	7256.48	−	50469.9i	0.276557	−	1.92350i	−0.0957872	−	0.995402i	$-0.530537\pi$
$883$	7256.48	−	50469.9i	0.276557	−	1.92350i	0.372344	−	0.928095i	$-0.378554\pi$
$884$	−11875.5	−	26003.6i	−0.451827	−	0.989362i
$885$	4619.21	+	1356.32i	0.175450	+	0.0515167i
$886$	−1587.59	−	466.158i	−0.0601987	−	0.0176759i
$887$	12666.3	+	27735.3i	0.479473	+	1.04990i	0.982608	+	0.185692i	$0.0594528\pi$
$887$	12666.3	+	27735.3i	0.479473	+	1.04990i	−0.503134	+	0.864208i	$0.667820\pi$
$888$	229.357	−	1595.21i	0.00866748	−	0.0602836i
$889$	6685.23	−	7715.17i	0.252211	−	0.291067i
$890$	7246.90	−	15868.5i	0.272940	−	0.597655i
$891$	11630.4	+	7474.37i	0.437297	+	0.281034i
$892$	−3396.97	−	23626.4i	−0.127510	−	0.886851i
$893$	5070.41	−	3258.55i	0.190005	−	0.122109i
$894$	−11139.0	−	12855.0i	−0.416714	−	0.480914i
$895$	63133.9	−	18537.8i	2.35791	−	0.692346i
$896$	−2567.71			−0.0957380
$897$	−4658.72	−	15303.5i	−0.173411	−	0.569644i
$898$	17954.9			0.667219
$899$	680.968	−	199.950i	0.0252631	−	0.00741792i
$900$	12327.2	+	14226.3i	0.456563	+	0.526902i
$901$	19498.4	−	12530.9i	0.720961	−	0.463333i
$902$	−3664.91	−	25490.0i	−0.135286	−	0.940936i
$903$	10968.3	+	7048.88i	0.404209	+	0.259770i
$904$	−500.324	+	1095.56i	−0.0184077	+	0.0403072i
$905$	2319.26	−	2676.57i	0.0851876	−	0.0983117i
$906$	98.3321	−	683.915i	0.00360581	−	0.0250790i
$907$	12163.7	+	26634.9i	0.445303	+	0.975078i	0.990594	+	0.136832i	$0.0436919\pi$
$907$	12163.7	+	26634.9i	0.445303	+	0.975078i	−0.545291	+	0.838247i	$0.683581\pi$
$908$	−2053.27	−	602.893i	−0.0750441	−	0.0220349i
$909$	4288.85	+	1259.32i	0.156493	+	0.0459506i
$910$	18613.7	+	40758.4i	0.678066	+	1.48476i
$911$	1783.16	−	12402.2i	0.0648506	−	0.451046i	−0.931362	−	0.364095i	$-0.881378\pi$
$911$	1783.16	−	12402.2i	0.0648506	−	0.451046i	0.996213	−	0.0869512i	$-0.0277124\pi$
$912$	1594.13	−	1839.72i	0.0578804	−	0.0667976i
$913$	19349.1	−	42368.7i	0.701383	−	1.53581i
$914$	−252.104	−	162.017i	−0.00912347	−	0.00586330i
$915$	−4663.65	−	32436.4i	−0.168498	−	1.17193i
$916$	5877.12	−	3777.00i	0.211993	−	0.136240i
$917$	810.710	+	935.610i	0.0291952	+	0.0336931i
$918$	−26684.8	+	7835.38i	−0.959402	+	0.281706i
$919$	5971.67			0.214350			0.107175	−	0.994240i	$-0.465820\pi$
$919$	5971.67			0.214350			0.107175	+	0.994240i	$0.465820\pi$
$920$	−16261.4	+	2502.74i	−0.582743	+	0.0896878i
$921$	14441.5			0.516681
$922$	−3389.39	+	995.214i	−0.121067	+	0.0355484i
$923$	28004.1	+	32318.4i	0.998662	+	1.15252i
$924$	−7830.63	+	5032.44i	−0.278797	+	0.179172i
$925$	2636.28	+	18335.7i	0.0937086	+	0.651757i
$926$	−1849.42	−	1188.55i	−0.0656326	−	0.0421795i
$927$	−1942.18	+	4252.79i	−0.0688130	+	0.150679i
$928$	84.2276	−	97.2039i	0.00297943	−	0.00343844i
$929$	3000.16	−	20866.6i	0.105955	−	0.736932i	−0.865706	−	0.500553i	$-0.833130\pi$
$929$	3000.16	−	20866.6i	0.105955	−	0.736932i	0.971661	−	0.236379i	$-0.0759607\pi$
$930$	6622.51	+	14501.3i	0.233506	+	0.511307i
$931$	−3582.32	−	1051.86i	−0.126107	−	0.0370284i
$932$	3052.92	+	896.417i	0.107298	+	0.0315055i
$933$	−4061.30	−	8893.02i	−0.142509	−	0.312052i
$934$	849.187	−	5906.23i	0.0297497	−	0.206914i
$935$	−69798.5	+	80551.7i	−2.44134	+	2.81746i
$936$	4207.86	−	9213.93i	0.146943	−	0.321759i
$937$	26686.4	+	17150.3i	0.930422	+	0.597946i	0.915664	−	0.401945i	$-0.131666\pi$
$937$	26686.4	+	17150.3i	0.930422	+	0.597946i	0.0147585	+	0.999891i	$0.495302\pi$
$938$	1722.55	+	11980.6i	0.0599609	+	0.417037i
$939$	−14851.6	+	9544.52i	−0.516147	+	0.331708i
$940$	4684.38	+	5406.06i	0.162540	+	0.187581i
$941$	25118.7	−	7375.52i	0.870188	−	0.255510i	0.183993	−	0.982928i	$-0.441098\pi$
$941$	25118.7	−	7375.52i	0.870188	−	0.255510i	0.686195	+	0.727417i	$0.259279\pi$
$942$	15081.8			0.521646
$943$	−22593.9	−	19189.1i	−0.780233	−	0.662655i
$944$	−1706.34			−0.0588310
$945$	41826.2	−	12281.3i	1.43980	−	0.422762i
$946$	−16845.6	−	19440.8i	−0.578960	−	0.668155i
$947$	−24706.4	+	15877.8i	−0.847783	+	0.544837i	−0.890882	−	0.454234i	$-0.849913\pi$
$947$	−24706.4	+	15877.8i	−0.847783	+	0.544837i	0.0430997	+	0.999071i	$0.486277\pi$
$948$	−72.5168	−	504.365i	−0.00248443	−	0.0172796i
$949$	15097.7	+	9702.70i	0.516430	+	0.331889i
$950$	−11623.5	+	25451.9i	−0.396964	+	0.869230i
$951$	−2650.46	+	3058.80i	−0.0903756	+	0.104299i
$952$	−2724.96	+	18952.5i	−0.0927694	+	0.645226i
$953$	6670.97	+	14607.4i	0.226751	+	0.496516i	0.988475	−	0.151386i	$-0.0483738\pi$
$953$	6670.97	+	14607.4i	0.226751	+	0.496516i	−0.761724	+	0.647902i	$0.775647\pi$
$954$	7879.98	+	2313.77i	0.267425	+	0.0785231i
$955$	70421.2	+	20677.5i	2.38615	+	0.700637i
$956$	5718.02	+	12520.7i	0.193446	+	0.423587i
$957$	66.3558	−	461.515i	0.00224136	−	0.0155890i
$958$	16503.6	−	19046.2i	0.556585	−	0.642333i
$959$	25142.4	−	55054.3i	0.846602	−	1.85380i
$960$	2430.46	+	1561.96i	0.0817112	+	0.0525126i
$961$	−197.493	−	1373.59i	−0.00662928	−	0.0461077i
$962$	8385.57	−	5389.08i	0.281041	−	0.180614i
$963$	−17559.6	−	20264.8i	−0.587590	−	0.678115i
$964$	−25928.1	+	7613.19i	−0.866275	+	0.254361i
$965$	22708.6			0.757529
$966$	−2916.66	+	10310.1i	−0.0971450	+	0.343396i
$967$	−571.927			−0.0190196			−0.00950979	−	0.999955i	$-0.503027\pi$
$967$	−571.927			−0.0190196			−0.00950979	+	0.999955i	$0.503027\pi$
$968$	7404.57	−	2174.18i	0.245859	−	0.0721908i
$969$	−11887.4	−	13718.8i	−0.394096	−	0.454811i
$970$	−9945.12	+	6391.34i	−0.329194	+	0.211560i
$971$	−1730.18	−	12033.7i	−0.0571825	−	0.397713i	−0.998232	−	0.0594431i	$-0.981068\pi$
$971$	−1730.18	−	12033.7i	−0.0571825	−	0.397713i	0.941049	−	0.338270i	$-0.109842\pi$
$972$	−12940.0	−	8316.00i	−0.427005	−	0.274420i
$973$	−2295.20	+	5025.79i	−0.0756226	+	0.165590i
$974$	−16238.4	+	18740.1i	−0.534201	+	0.616501i
$975$	4595.00	−	31958.9i	0.150931	−	1.04975i
$976$	4824.99	+	10565.2i	0.158242	+	0.346501i
$977$	−32576.2	−	9565.24i	−1.06674	−	0.313223i	−0.299178	−	0.954197i	$-0.596713\pi$
$977$	−32576.2	−	9565.24i	−1.06674	−	0.313223i	−0.767563	+	0.640974i	$0.778531\pi$
$978$	−12366.4	−	3631.09i	−0.404328	−	0.118721i
$979$	9311.38	+	20389.1i	0.303976	+	0.665615i
$980$	630.608	−	4385.97i	0.0205551	−	0.142964i
$981$	−9807.77	+	11318.8i	−0.319203	+	0.368380i
$982$	8007.06	−	17533.0i	0.260199	−	0.569757i
$983$	28997.5	+	18635.5i	0.940870	+	0.604660i	0.918641	−	0.395093i	$-0.129287\pi$
$983$	28997.5	+	18635.5i	0.940870	+	0.604660i	0.0222285	+	0.999753i	$0.492924\pi$
$984$	740.784	+	5152.27i	0.0239993	+	0.166919i
$985$	−19491.9	+	12526.7i	−0.630522	+	0.405212i
$986$	−628.085	−	724.849i	−0.0202863	−	0.0234116i
$987$	4469.73	−	1312.43i	0.144147	−	0.0423254i
$988$	15056.3			0.484823
$989$	−29349.4	−	3923.41i	−0.943637	−	0.126145i
$990$	−37766.6			−1.21243
$991$	39400.9	−	11569.1i	1.26298	−	0.370844i	0.419376	−	0.907813i	$-0.362249\pi$
$991$	39400.9	−	11569.1i	1.26298	−	0.370844i	0.843602	+	0.536969i	$0.180431\pi$
$992$	−3700.22	−	4270.29i	−0.118430	−	0.136675i
$993$	−3401.97	+	2186.31i	−0.108719	+	0.0698696i
$994$	−4076.29	−	28351.2i	−0.130072	−	0.904673i
$995$	−8465.16	−	5440.23i	−0.269712	−	0.173333i
$996$	−3911.01	+	8563.93i	−0.124423	+	0.272448i
$997$	20047.4	−	23135.9i	0.636818	−	0.734928i	−0.341991	−	0.939703i	$-0.611101\pi$
$997$	20047.4	−	23135.9i	0.636818	−	0.734928i	0.978809	+	0.204776i	$0.0656465\pi$
$998$	−2935.74	+	20418.6i	−0.0931156	+	0.647633i
$999$	−4028.49	−	8821.17i	−0.127584	−	0.279369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.b.9.2	✓	30
23.8	even	11		1058.4.a.u.1.6		15
23.15	odd	22		1058.4.a.t.1.6		15
23.18	even	11	inner	46.4.c.b.41.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.9.2	✓	30	1.1	even	1	trivial
46.4.c.b.41.2	yes	30	23.18	even	11	inner
1058.4.a.t.1.6		15	23.15	odd	22
1058.4.a.u.1.6		15	23.8	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)

\(f(q)\)	\(=\)	\(q+(1.91899 - 0.563465i) q^{2} +(1.58551 + 1.82978i) q^{3} +(3.36501 - 2.16256i) q^{4} +(2.65345 + 18.4552i) q^{5} +(4.07359 + 2.61794i) q^{6} +(8.33333 - 18.2475i) q^{7} +(5.23889 - 6.04600i) q^{8} +(3.00826 - 20.9229i) q^{9} +O(q^{10})\)	\(q+(1.91899 - 0.563465i) q^{2} +(1.58551 + 1.82978i) q^{3} +(3.36501 - 2.16256i) q^{4} +(2.65345 + 18.4552i) q^{5} +(4.07359 + 2.61794i) q^{6} +(8.33333 - 18.2475i) q^{7} +(5.23889 - 6.04600i) q^{8} +(3.00826 - 20.9229i) q^{9} +(15.4908 + 33.9201i) q^{10} +(-45.9721 - 13.4986i) q^{11} +(9.29229 + 2.72846i) q^{12} +(24.8832 + 54.4866i) q^{13} +(5.70974 - 39.7121i) q^{14} +(-29.5618 + 34.1161i) q^{15} +(6.64664 - 14.5541i) q^{16} +(-100.372 - 64.5049i) q^{17} +(-6.01652 - 41.8458i) q^{18} +(52.8641 - 33.9737i) q^{19} +(48.8393 + 56.3636i) q^{20} +(46.6014 - 13.6834i) q^{21} -95.8258 q^{22} +(-82.6425 + 73.0563i) q^{23} +19.3692 q^{24} +(-213.615 + 62.7231i) q^{25} +(78.4519 + 90.5383i) q^{26} +(98.0474 - 63.0113i) q^{27} +(-11.4195 - 79.4243i) q^{28} +(3.38129 + 2.17302i) q^{29} +(-37.5054 + 82.1254i) q^{30} +(115.632 - 133.446i) q^{31} +(4.55407 - 31.6743i) q^{32} +(-48.1898 - 105.521i) q^{33} +(-228.958 - 67.2281i) q^{34} +(358.872 + 105.374i) q^{35} +(-35.1243 - 76.9114i) q^{36} +(11.8414 - 82.3584i) q^{37} +(82.3025 - 94.9822i) q^{38} +(-60.2459 + 131.920i) q^{39} +(125.481 + 80.6417i) q^{40} +(38.2455 + 266.004i) q^{41} +(81.7173 - 52.5165i) q^{42} +(175.794 + 202.877i) q^{43} +(-183.888 + 53.9945i) q^{44} +394.118 q^{45} +(-117.425 + 186.760i) q^{46} +95.9140 q^{47} +(37.1691 - 10.9138i) q^{48} +(-38.9079 - 44.9021i) q^{49} +(-374.582 + 240.729i) q^{50} +(-41.1107 - 285.931i) q^{51} +(201.563 + 129.537i) q^{52} +(-80.6994 + 176.707i) q^{53} +(152.647 - 176.164i) q^{54} +(127.135 - 884.240i) q^{55} +(-66.6667 - 145.980i) q^{56} +(145.981 + 42.8639i) q^{57} +(7.71307 + 2.26476i) q^{58} +(-44.3023 - 97.0086i) q^{59} +(-25.6976 + 178.730i) q^{60} +(-475.382 + 548.620i) q^{61} +(146.704 - 321.236i) q^{62} +(-356.721 - 229.251i) q^{63} +(-9.10815 - 63.3486i) q^{64} +(-939.533 + 603.801i) q^{65} +(-151.933 - 175.340i) q^{66} +(-289.466 + 84.9949i) q^{67} -477.247 q^{68} +(-264.708 - 35.3859i) q^{69} +748.044 q^{70} +(684.999 - 201.134i) q^{71} +(-110.740 - 127.801i) q^{72} +(252.050 - 161.983i) q^{73} +(-23.6827 - 164.717i) q^{74} +(-453.459 - 291.420i) q^{75} +(104.418 - 228.644i) q^{76} +(-629.416 + 726.385i) q^{77} +(-41.2786 + 287.099i) q^{78} +(-21.8570 - 47.8601i) q^{79} +(286.235 + 84.0461i) q^{80} +(-276.857 - 81.2925i) q^{81} +(223.276 + 488.907i) q^{82} +(-138.349 + 962.240i) q^{83} +(127.223 - 146.823i) q^{84} +(924.116 - 2023.53i) q^{85} +(451.659 + 290.264i) q^{86} +(1.38493 + 9.63238i) q^{87} +(-322.455 + 207.229i) q^{88} +(-306.357 - 353.555i) q^{89} +(756.306 - 222.072i) q^{90} +1201.60 q^{91} +(-120.104 + 424.555i) q^{92} +427.514 q^{93} +(184.058 - 54.0442i) q^{94} +(767.262 + 885.468i) q^{95} +(65.1775 - 41.8870i) q^{96} +(45.1172 + 313.797i) q^{97} +(-99.9644 - 64.2432i) q^{98} +(-420.726 + 921.262i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more