LMFDB - Embedded newform 135.4.q.a.113.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$52$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.26
Character	$\chi$	$=$	135.113
Dual form			135.4.q.a.92.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.474611 - 0.0415231i) q^{2} +(-2.87247 - 4.33000i) q^{3} +(-7.65493 - 1.34977i) q^{4} +(4.26878 + 10.3333i) q^{5} +(1.18351 + 2.17434i) q^{6} +(11.2028 + 7.84429i) q^{7} +(7.25858 + 1.94493i) q^{8} +(-10.4978 + 24.8756i) q^{9} +O(q^{10})$	\(q+(-0.474611 - 0.0415231i) q^{2} +(-2.87247 - 4.33000i) q^{3} +(-7.65493 - 1.34977i) q^{4} +(4.26878 + 10.3333i) q^{5} +(1.18351 + 2.17434i) q^{6} +(11.2028 + 7.84429i) q^{7} +(7.25858 + 1.94493i) q^{8} +(-10.4978 + 24.8756i) q^{9} +(-1.59694 - 5.08156i) q^{10} +(1.54807 - 4.25327i) q^{11} +(16.1441 + 37.0230i) q^{12} +(-6.42210 - 73.4049i) q^{13} +(-4.99125 - 4.18816i) q^{14} +(32.4813 - 48.1660i) q^{15} +(55.0698 + 20.0438i) q^{16} +(89.2214 - 23.9068i) q^{17} +(6.01527 - 11.3703i) q^{18} +(58.1927 - 33.5976i) q^{19} +(-18.7296 - 84.8627i) q^{20} +(1.78599 - 71.0407i) q^{21} +(-0.911337 + 1.95437i) q^{22} +(31.3040 + 44.7068i) q^{23} +(-12.4285 - 37.0164i) q^{24} +(-88.5550 + 88.2214i) q^{25} +35.1054i q^{26} +(137.866 - 25.9992i) q^{27} +(-75.1687 - 75.1687i) q^{28} +(91.1138 - 76.4535i) q^{29} +(-17.4160 + 21.5114i) q^{30} +(-8.07498 + 45.7955i) q^{31} +(-79.7890 - 37.2062i) q^{32} +(-22.8635 + 5.51430i) q^{33} +(-43.3381 + 7.64167i) q^{34} +(-33.2352 + 149.248i) q^{35} +(113.936 - 176.252i) q^{36} +(105.000 + 391.864i) q^{37} +(-29.0139 + 13.5294i) q^{38} +(-299.396 + 238.662i) q^{39} +(10.8877 + 83.3078i) q^{40} +(303.621 - 361.842i) q^{41} +(-3.79748 + 33.6425i) q^{42} +(204.990 + 439.602i) q^{43} +(-17.5913 + 30.4690i) q^{44} +(-301.861 - 2.28835i) q^{45} +(-13.0009 - 22.5182i) q^{46} +(186.441 - 266.266i) q^{47} +(-71.3970 - 296.027i) q^{48} +(-53.3429 - 146.558i) q^{49} +(45.6924 - 38.1937i) q^{50} +(-359.802 - 317.657i) q^{51} +(-49.9191 + 570.578i) q^{52} +(-5.76362 + 5.76362i) q^{53} +(-66.5123 + 6.61489i) q^{54} +(50.5588 - 2.15964i) q^{55} +(66.0599 + 78.7272i) q^{56} +(-312.634 - 155.466i) q^{57} +(-46.4182 + 32.5023i) q^{58} +(-54.6402 + 19.8874i) q^{59} +(-313.655 + 324.865i) q^{60} +(-12.3447 - 70.0102i) q^{61} +(5.73404 - 21.3997i) q^{62} +(-312.736 + 196.329i) q^{63} +(-369.697 - 213.444i) q^{64} +(731.102 - 379.711i) q^{65} +(11.0802 - 1.66779i) q^{66} +(-517.127 + 45.2427i) q^{67} +(-715.252 + 62.5764i) q^{68} +(103.660 - 263.966i) q^{69} +(21.9710 - 69.4546i) q^{70} +(482.639 + 278.652i) q^{71} +(-124.580 + 160.144i) q^{72} +(32.1510 - 119.989i) q^{73} +(-33.5626 - 190.343i) q^{74} +(636.370 + 130.030i) q^{75} +(-490.810 + 178.640i) q^{76} +(50.7066 - 35.5052i) q^{77} +(152.006 - 100.839i) q^{78} +(52.0505 + 62.0314i) q^{79} +(27.9622 + 654.616i) q^{80} +(-508.593 - 522.278i) q^{81} +(-159.127 + 159.127i) q^{82} +(-118.961 + 1359.73i) q^{83} +(-109.560 + 541.401i) q^{84} +(627.903 + 819.900i) q^{85} +(-79.0368 - 217.152i) q^{86} +(-592.766 - 174.912i) q^{87} +(19.5091 - 27.8619i) q^{88} +(-522.117 - 904.334i) q^{89} +(143.171 + 13.6202i) q^{90} +(503.864 - 872.719i) q^{91} +(-179.286 - 384.481i) q^{92} +(221.490 - 96.5817i) q^{93} +(-99.5431 + 118.631i) q^{94} +(595.586 + 457.903i) q^{95} +(68.0890 + 452.360i) q^{96} +(941.041 - 438.815i) q^{97} +(19.2315 + 71.7731i) q^{98} +(89.5516 + 83.1590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 624 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 18 * q^8	$ 624 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} + 702 q^{18} + 756 q^{20} - 24 q^{21} - 12 q^{22} - 324 q^{23} + 420 q^{25} - 900 q^{27} - 24 q^{28} - 1020 q^{30} - 24 q^{31} + 1752 q^{32} + 516 q^{33} + 2466 q^{35} + 984 q^{36} - 6 q^{37} - 132 q^{38} - 396 q^{40} + 1680 q^{41} - 2256 q^{42} - 12 q^{43} - 1332 q^{45} - 12 q^{46} - 3480 q^{47} - 3228 q^{48} - 684 q^{50} - 6840 q^{51} + 84 q^{52} - 24 q^{55} - 4752 q^{56} + 1842 q^{57} - 12 q^{58} - 2376 q^{60} - 132 q^{61} - 18 q^{62} + 2592 q^{63} + 2076 q^{65} + 9864 q^{66} + 3660 q^{67} + 2676 q^{68} - 12 q^{70} - 36 q^{71} + 1908 q^{72} - 6 q^{73} + 9300 q^{75} - 792 q^{76} - 3324 q^{77} - 606 q^{78} - 3336 q^{81} - 24 q^{82} - 2832 q^{83} - 12 q^{85} - 12516 q^{86} - 8640 q^{87} - 3036 q^{88} - 14532 q^{90} - 12 q^{91} - 1938 q^{92} + 6804 q^{93} - 4302 q^{95} + 3732 q^{96} + 6900 q^{97} - 5832 q^{98}+O(q^{100}) $ 624 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 + 702 * q^18 + 756 * q^20 - 24 * q^21 - 12 * q^22 - 324 * q^23 + 420 * q^25 - 900 * q^27 - 24 * q^28 - 1020 * q^30 - 24 * q^31 + 1752 * q^32 + 516 * q^33 + 2466 * q^35 + 984 * q^36 - 6 * q^37 - 132 * q^38 - 396 * q^40 + 1680 * q^41 - 2256 * q^42 - 12 * q^43 - 1332 * q^45 - 12 * q^46 - 3480 * q^47 - 3228 * q^48 - 684 * q^50 - 6840 * q^51 + 84 * q^52 - 24 * q^55 - 4752 * q^56 + 1842 * q^57 - 12 * q^58 - 2376 * q^60 - 132 * q^61 - 18 * q^62 + 2592 * q^63 + 2076 * q^65 + 9864 * q^66 + 3660 * q^67 + 2676 * q^68 - 12 * q^70 - 36 * q^71 + 1908 * q^72 - 6 * q^73 + 9300 * q^75 - 792 * q^76 - 3324 * q^77 - 606 * q^78 - 3336 * q^81 - 24 * q^82 - 2832 * q^83 - 12 * q^85 - 12516 * q^86 - 8640 * q^87 - 3036 * q^88 - 14532 * q^90 - 12 * q^91 - 1938 * q^92 + 6804 * q^93 - 4302 * q^95 + 3732 * q^96 + 6900 * q^97 - 5832 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.474611	−	0.0415231i	−0.167800	−	0.0146806i	0.00294599	−	0.999996i	$-0.499062\pi$
$2$	−0.474611	−	0.0415231i	−0.167800	−	0.0146806i	−0.170746	+	0.985315i	$0.554618\pi$
$3$	−2.87247	−	4.33000i	−0.552808	−	0.833309i
$3$	−2.87247	−	4.33000i	−0.552808	−	0.833309i
$4$	−7.65493	−	1.34977i	−0.956866	−	0.168721i
$5$	4.26878	+	10.3333i	0.381811	+	0.924240i
$5$	4.26878	+	10.3333i	0.381811	+	0.924240i
$6$	1.18351	+	2.17434i	0.0805278	+	0.147945i
$7$	11.2028	+	7.84429i	0.604895	+	0.423552i	0.835496	−	0.549496i	$-0.185180\pi$
$7$	11.2028	+	7.84429i	0.604895	+	0.423552i	−0.230601	+	0.973048i	$0.574069\pi$
$8$	7.25858	+	1.94493i	0.320787	+	0.0859547i
$9$	−10.4978	+	24.8756i	−0.388807	+	0.921319i
$10$	−1.59694	−	5.08156i	−0.0504996	−	0.160693i
$11$	1.54807	−	4.25327i	0.0424327	−	0.116583i	−0.916667	−	0.399653i	$-0.869131\pi$
$11$	1.54807	−	4.25327i	0.0424327	−	0.116583i	0.959099	+	0.283070i	$0.0913529\pi$
$12$	16.1441	+	37.0230i	0.388366	+	0.890636i
$13$	−6.42210	−	73.4049i	−0.137013	−	1.56607i	−0.684350	−	0.729154i	$-0.739914\pi$
$13$	−6.42210	−	73.4049i	−0.137013	−	1.56607i	0.547336	−	0.836913i	$-0.315642\pi$
$14$	−4.99125	−	4.18816i	−0.0952835	−	0.0799523i
$15$	32.4813	−	48.1660i	0.559109	−	0.829094i
$16$	55.0698	+	20.0438i	0.860465	+	0.313184i
$17$	89.2214	−	23.9068i	1.27290	−	0.341073i	0.441761	−	0.897133i	$-0.354354\pi$
$17$	89.2214	−	23.9068i	1.27290	−	0.341073i	0.831143	+	0.556059i	$0.187687\pi$
$18$	6.01527	−	11.3703i	0.0787674	−	0.148890i
$19$	58.1927	−	33.5976i	0.702648	−	0.405674i	−0.105685	−	0.994400i	$-0.533703\pi$
$19$	58.1927	−	33.5976i	0.702648	−	0.405674i	0.808333	+	0.588726i	$0.200370\pi$
$20$	−18.7296	−	84.8627i	−0.209403	−	0.948794i
$21$	1.78599	−	71.0407i	0.0185588	−	0.738207i
$22$	−0.911337	+	1.95437i	−0.00883172	+	0.0189397i
$23$	31.3040	+	44.7068i	0.283797	+	0.405305i	0.935588	−	0.353095i	$-0.114871\pi$
$23$	31.3040	+	44.7068i	0.283797	+	0.405305i	−0.651790	+	0.758399i	$0.725982\pi$
$24$	−12.4285	−	37.0164i	−0.105707	−	0.314831i
$25$	−88.5550	+	88.2214i	−0.708440	+	0.705771i
$26$			35.1054i			0.264798i
$27$	137.866	−	25.9992i	0.982679	−	0.185317i
$28$	−75.1687	−	75.1687i	−0.507341	−	0.507341i
$29$	91.1138	−	76.4535i	0.583428	−	0.489554i	−0.302643	−	0.953104i	$-0.597869\pi$
$29$	91.1138	−	76.4535i	0.583428	−	0.489554i	0.886071	+	0.463550i	$0.153425\pi$
$30$	−17.4160	+	21.5114i	−0.105990	+	0.130914i
$31$	−8.07498	+	45.7955i	−0.0467842	+	0.265326i	−0.999223	−	0.0394023i	$-0.987455\pi$
$31$	−8.07498	+	45.7955i	−0.0467842	+	0.265326i	0.952439	+	0.304728i	$0.0985657\pi$
$32$	−79.7890	−	37.2062i	−0.440776	−	0.205537i
$33$	−22.8635	+	5.51430i	−0.120607	+	0.0290884i
$34$	−43.3381	+	7.64167i	−0.218601	+	0.0385452i
$35$	−33.2352	+	149.248i	−0.160508	+	0.720785i
$36$	113.936	−	176.252i	0.527482	−	0.815980i
$37$	105.000	+	391.864i	0.466537	+	1.74114i	0.651744	+	0.758439i	$0.274038\pi$
$37$	105.000	+	391.864i	0.466537	+	1.74114i	−0.185208	+	0.982699i	$0.559296\pi$
$38$	−29.0139	+	13.5294i	−0.123860	+	0.0577569i
$39$	−299.396	+	238.662i	−1.22928	+	0.979908i
$40$	10.8877	+	83.3078i	0.0430374	+	0.329303i
$41$	303.621	−	361.842i	1.15653	−	1.37830i	0.243751	−	0.969838i	$-0.421622\pi$
$41$	303.621	−	361.842i	1.15653	−	1.37830i	0.912777	−	0.408459i	$-0.133934\pi$
$42$	−3.79748	+	33.6425i	−0.0139515	+	0.123599i
$43$	204.990	+	439.602i	0.726993	+	1.55904i	0.825819	+	0.563936i	$0.190714\pi$
$43$	204.990	+	439.602i	0.726993	+	1.55904i	−0.0988260	+	0.995105i	$0.531509\pi$
$44$	−17.5913	+	30.4690i	−0.0602724	+	0.104395i
$45$	−301.861	−	2.28835i	−0.999971	−	0.00758060i
$46$	−13.0009	−	22.5182i	−0.0416711	−	0.0721765i
$47$	186.441	−	266.266i	0.578622	−	0.826358i	−0.418003	−	0.908446i	$-0.637270\pi$
$47$	186.441	−	266.266i	0.578622	−	0.826358i	0.996625	+	0.0820877i	$0.0261588\pi$
$48$	−71.3970	−	296.027i	−0.214693	−	0.890163i
$49$	−53.3429	−	146.558i	−0.155519	−	0.427284i
$50$	45.6924	−	38.1937i	0.129238	−	0.108028i
$51$	−359.802	−	317.657i	−0.987891	−	0.872173i
$52$	−49.9191	+	570.578i	−0.133126	+	1.52163i
$53$	−5.76362	+	5.76362i	−0.0149376	+	0.0149376i	−0.714536	−	0.699599i	$-0.753362\pi$
$53$	−5.76362	+	5.76362i	−0.0149376	+	0.0149376i	0.699599	+	0.714536i	$0.253362\pi$
$54$	−66.5123	+	6.61489i	−0.167614	+	0.0166698i
$55$	50.5588	−	2.15964i	0.123952	−	0.00529466i
$56$	66.0599	+	78.7272i	0.157636	+	0.187864i
$57$	−312.634	−	155.466i	−0.726481	−	0.361263i
$58$	−46.4182	+	32.5023i	−0.105086	+	0.0735822i
$59$	−54.6402	+	19.8874i	−0.120569	+	0.0438834i	−0.401600	−	0.915815i	$-0.631546\pi$
$59$	−54.6402	+	19.8874i	−0.120569	+	0.0438834i	0.281031	+	0.959699i	$0.409324\pi$
$60$	−313.655	+	324.865i	−0.674879	+	0.698999i
$61$	−12.3447	−	70.0102i	−0.0259111	−	0.146949i	0.969108	−	0.246639i	$-0.0793261\pi$
$61$	−12.3447	−	70.0102i	−0.0259111	−	0.146949i	−0.995019	+	0.0996897i	$0.968215\pi$
$62$	5.73404	−	21.3997i	0.0117455	−	0.0438350i
$63$	−312.736	+	196.329i	−0.625414	+	0.392622i
$64$	−369.697	−	213.444i	−0.722064	−	0.416884i
$65$	731.102	−	379.711i	1.39511	−	0.724575i
$66$	11.0802	−	1.66779i	0.0206648	−	0.00311046i
$67$	−517.127	+	45.2427i	−0.942941	+	0.0824967i	−0.548248	−	0.836316i	$-0.684705\pi$
$67$	−517.127	+	45.2427i	−0.942941	+	0.0824967i	−0.394694	+	0.918813i	$0.629149\pi$
$68$	−715.252	+	62.5764i	−1.27554	+	0.111596i
$69$	103.660	−	263.966i	0.180858	−	0.460547i
$70$	21.9710	−	69.4546i	0.0375149	−	0.118592i
$71$	482.639	+	278.652i	0.806742	+	0.465773i	0.845823	−	0.533463i	$-0.179110\pi$
$71$	482.639	+	278.652i	0.806742	+	0.465773i	−0.0390813	+	0.999236i	$0.512443\pi$
$72$	−124.580	+	160.144i	−0.203916	+	0.262128i
$73$	32.1510	−	119.989i	0.0515479	−	0.192379i	−0.935351	−	0.353722i	$-0.884916\pi$
$73$	32.1510	−	119.989i	0.0515479	−	0.192379i	0.986898	+	0.161343i	$0.0515825\pi$
$74$	−33.5626	−	190.343i	−0.0527239	−	0.299012i
$75$	636.370	+	130.030i	0.979756	+	0.200194i
$76$	−490.810	+	178.640i	−0.740786	+	0.269624i
$77$	50.7066	−	35.5052i	0.0750462	−	0.0525479i
$78$	152.006	−	100.839i	0.220658	−	0.146382i
$79$	52.0505	+	62.0314i	0.0741284	+	0.0883428i	0.801834	−	0.597547i	$-0.203858\pi$
$79$	52.0505	+	62.0314i	0.0741284	+	0.0883428i	−0.727706	+	0.685890i	$0.759413\pi$
$80$	27.9622	+	654.616i	0.0390784	+	0.914853i
$81$	−508.593	−	522.278i	−0.697659	−	0.716430i
$82$	−159.127	+	159.127i	−0.214300	+	0.214300i
$83$	−118.961	+	1359.73i	−0.157321	+	1.79819i	0.350332	+	0.936626i	$0.386069\pi$
$83$	−118.961	+	1359.73i	−0.157321	+	1.79819i	−0.507653	+	0.861562i	$0.669487\pi$
$84$	−109.560	+	541.401i	−0.142310	+	0.703234i
$85$	627.903	+	819.900i	0.801243	+	1.04624i
$86$	−79.0368	−	217.152i	−0.0991018	−	0.272280i
$87$	−592.766	−	174.912i	−0.730473	−	0.215546i
$88$	19.5091	−	27.8619i	0.0236327	−	0.0337510i
$89$	−522.117	−	904.334i	−0.621847	−	1.07707i	−0.989142	−	0.146965i	$-0.953049\pi$
$89$	−522.117	−	904.334i	−0.621847	−	1.07707i	0.367295	−	0.930104i	$-0.380284\pi$
$90$	143.171	+	13.6202i	0.167684	+	0.0159522i
$91$	503.864	−	872.719i	0.580432	−	1.00534i
$92$	−179.286	−	384.481i	−0.203173	−	0.435705i
$93$	221.490	−	96.5817i	0.246961	−	0.107689i
$94$	−99.5431	+	118.631i	−0.109224	+	0.130169i
$95$	595.586	+	457.903i	0.643219	+	0.494525i
$96$	68.0890	+	452.360i	0.0723886	+	0.480925i
$97$	941.041	−	438.815i	0.985033	−	0.459329i	0.137749	−	0.990467i	$-0.456013\pi$
$97$	941.041	−	438.815i	0.985033	−	0.459329i	0.847285	+	0.531139i	$0.178236\pi$
$98$	19.2315	+	71.7731i	0.0198233	+	0.0739814i
$99$	89.5516	+	83.1590i	0.0909119	+	0.0844222i
$100$	796.961	−	555.799i	0.796961	−	0.555799i
$101$	826.510	−	145.736i	0.814265	−	0.143577i	0.249018	−	0.968499i	$-0.419892\pi$
$101$	826.510	−	145.736i	0.814265	−	0.143577i	0.565247	+	0.824922i	$0.308781\pi$
$102$	157.576	+	165.703i	0.152964	+	0.160854i
$103$	−1014.70	−	473.163i	−0.970693	−	0.452642i	−0.128436	−	0.991718i	$-0.540996\pi$
$103$	−1014.70	−	473.163i	−0.970693	−	0.452642i	−0.842257	+	0.539076i	$0.818774\pi$
$104$	96.1522	−	545.306i	0.0906587	−	0.514151i
$105$	741.710	−	284.802i	0.689367	−	0.264703i
$106$	2.97480	−	2.49615i	0.00272583	−	0.00228724i
$107$	−232.192	−	232.192i	−0.209784	−	0.209784i	0.594392	−	0.804176i	$-0.297393\pi$
$107$	−232.192	−	232.192i	−0.209784	−	0.209784i	−0.804176	+	0.594392i	$0.797393\pi$
$108$	−1090.45	+	12.9346i	−0.971559	+	0.0115244i
$109$			409.812i			0.360118i	0.983656	+	0.180059i	$0.0576289\pi$
$109$			409.812i			0.360118i	−0.983656	+	0.180059i	$0.942371\pi$
$110$	−24.0854	−	1.07437i	−0.0208769	−	0.000931244i
$111$	1395.16	−	1580.27i	1.19300	−	1.35128i
$112$	459.707	+	656.530i	0.387841	+	0.553895i
$113$	381.783	−	818.737i	0.317833	−	0.681595i	−0.680875	−	0.732399i	$-0.738401\pi$
$113$	381.783	−	818.737i	0.317833	−	0.681595i	0.998709	+	0.0508037i	$0.0161783\pi$
$114$	141.924	+	86.7674i	0.116600	+	0.0712852i
$115$	−328.340	+	514.318i	−0.266242	+	0.417047i
$116$	−800.664	+	462.264i	−0.640861	+	0.370001i
$117$	1893.41	+	610.835i	1.49612	+	0.482664i
$118$	26.7586	−	7.16995i	0.0208757	−	0.00559362i
$119$	1187.06	+	432.055i	0.914435	+	0.332827i
$120$	329.448	−	286.443i	0.250619	−	0.217905i
$121$	1003.91	+	842.382i	0.754253	+	0.632894i
$122$	2.95188	+	33.7402i	0.00219058	+	0.0250385i
$123$	−2438.92	−	275.298i	−1.78788	−	0.201812i
$124$	123.627	−	339.662i	0.0895324	−	0.245988i
$125$	−1289.64	−	538.470i	−0.922792	−	0.385298i
$126$	156.580	−	80.1942i	0.110709	−	0.0567005i
$127$	−1470.67	−	394.064i	−1.02756	−	0.275335i	−0.294612	−	0.955617i	$-0.595191\pi$
$127$	−1470.67	−	394.064i	−1.02756	−	0.275335i	−0.732950	+	0.680282i	$0.761857\pi$
$128$	743.528	+	520.624i	0.513431	+	0.359508i
$129$	1314.65	−	2150.35i	0.897275	−	1.46766i
$130$	−362.756	+	149.857i	−0.244737	+	0.101103i
$131$	−1800.13	−	317.411i	−1.20059	−	0.211697i	−0.462639	−	0.886547i	$-0.653097\pi$
$131$	−1800.13	−	317.411i	−1.20059	−	0.211697i	−0.737956	+	0.674849i	$0.764209\pi$
$132$	182.461	−	11.3512i	0.120312	−	0.00748480i
$133$	915.471	+	80.0933i	0.596852	+	0.0522178i
$134$	247.312			0.159437
$135$	857.178	+	1313.63i	0.546475	+	0.837475i
$136$	694.118			0.437648
$137$	1349.07	+	118.028i	0.841305	+	0.0736046i	0.499657	−	0.866223i	$-0.333459\pi$
$137$	1349.07	+	118.028i	0.841305	+	0.0736046i	0.341648	+	0.939828i	$0.389015\pi$
$138$	−60.1589	+	120.977i	−0.0371092	+	0.0746247i
$139$	−1163.99	−	205.242i	−0.710275	−	0.125241i	−0.193173	−	0.981165i	$-0.561878\pi$
$139$	−1163.99	−	205.242i	−0.710275	−	0.125241i	−0.517101	+	0.855924i	$0.672989\pi$
$140$	455.864	−	1097.62i	0.275197	−	0.662614i
$141$	−1688.48	−	42.4490i	−1.00848	−	0.0253535i
$142$	−217.495	−	152.292i	−0.128534	−	0.0900002i
$143$	−322.153	−	86.3207i	−0.188390	−	0.0504790i
$144$	−1076.71	+	1159.48i	−0.623097	+	0.670995i
$145$	1178.96	+	615.144i	0.675225	+	0.352310i
$146$	−20.2415	+	55.6132i	−0.0114740	+	0.0315245i
$147$	−481.371	+	651.960i	−0.270087	+	0.365801i
$148$	−274.839	−	3141.42i	−0.152646	−	1.74475i
$149$	−491.665	−	412.556i	−0.270328	−	0.226832i	0.497539	−	0.867442i	$-0.334237\pi$
$149$	−491.665	−	412.556i	−0.270328	−	0.226832i	−0.767866	+	0.640610i	$0.778682\pi$
$150$	−296.629	−	88.1374i	−0.161464	−	0.0479759i
$151$	1913.02	+	696.282i	1.03099	+	0.375249i	0.801457	−	0.598052i	$-0.204059\pi$
$151$	1913.02	+	696.282i	1.03099	+	0.375249i	0.229531	+	0.973301i	$0.426281\pi$
$152$	487.741	−	130.690i	0.260270	−	0.0697391i
$153$	−341.930	+	2470.41i	−0.180676	+	1.30536i
$154$	−25.5402	+	14.7456i	−0.0133642	+	0.00771582i
$155$	−507.690	+	112.050i	−0.263088	+	0.0580647i
$156$	2613.99	−	1422.82i	1.34158	−	0.730236i
$157$	−140.137	+	300.525i	−0.0712367	+	0.152768i	−0.938702	−	0.344731i	$-0.887970\pi$
$157$	−140.137	+	300.525i	−0.0712367	+	0.152768i	0.867465	+	0.497498i	$0.165748\pi$
$158$	−22.1280	−	31.6021i	−0.0111418	−	0.0159122i
$159$	41.5123	+	8.40061i	0.0207053	+	0.00419001i
$160$	43.8621	−	983.311i	0.0216725	−	0.485860i
$161$			746.400i			0.365370i
$162$	219.697	+	268.997i	0.106550	+	0.130459i
$163$	1470.79	+	1470.79i	0.706756	+	0.706756i	0.965852	−	0.259096i	$-0.0834245\pi$
$163$	1470.79	+	1470.79i	0.706756	+	0.706756i	−0.259096	+	0.965852i	$0.583425\pi$
$164$	−2812.60	+	2360.05i	−1.33919	+	1.12371i
$165$	−154.580	−	212.716i	−0.0729336	−	0.100363i
$166$	112.920	−	640.402i	0.0527970	−	0.299427i
$167$	953.679	+	444.708i	0.441904	+	0.206063i	0.630819	−	0.775930i	$-0.282719\pi$
$167$	953.679	+	444.708i	0.441904	+	0.206063i	−0.188915	+	0.981993i	$0.560497\pi$
$168$	151.133	−	512.181i	0.0694058	−	0.235212i
$169$	−3183.42	+	561.323i	−1.44898	+	0.255495i
$170$	−263.965	−	415.206i	−0.119089	−	0.187323i
$171$	224.866	+	1800.28i	0.100561	+	0.805092i
$172$	−975.822	−	3641.82i	−0.432591	−	1.61445i
$173$	1744.89	−	813.654i	0.766828	−	0.357578i	0.000476842	−	1.00000i	$-0.499848\pi$
$173$	1744.89	−	813.654i	0.766828	−	0.357578i	0.766351	+	0.642422i	$0.222070\pi$
$174$	274.070	+	107.628i	0.119409	+	0.0468925i
$175$	−1684.10	+	293.676i	−0.727463	+	0.126856i
$176$	170.503	−	203.198i	0.0730236	−	0.0870262i
$177$	243.065	+	179.466i	0.103220	+	0.0762118i
$178$	210.252	+	450.886i	0.0885339	+	0.189862i
$179$	223.485	−	387.088i	0.0933188	−	0.161633i	−0.815587	−	0.578635i	$-0.803586\pi$
$179$	223.485	−	387.088i	0.0933188	−	0.161633i	0.908906	+	0.417002i	$0.136919\pi$
$180$	2307.63	+	424.960i	0.955560	+	0.175970i
$181$	−2201.67	−	3813.41i	−0.904139	−	1.56601i	−0.822069	−	0.569388i	$-0.807180\pi$
$181$	−2201.67	−	3813.41i	−0.904139	−	1.56601i	−0.0820703	−	0.996627i	$-0.526153\pi$
$182$	−275.377	+	393.280i	−0.112156	+	0.160175i
$183$	−267.684	+	254.555i	−0.108130	+	0.102826i
$184$	140.271	+	385.392i	0.0562007	+	0.154410i
$185$	−3601.04	+	2757.78i	−1.43110	+	1.09598i
$186$	−109.132	+	36.6418i	−0.0430211	+	0.0144447i
$187$	36.4383	−	416.492i	0.0142494	−	0.162871i
$188$	−1786.59	+	1786.59i	−0.693088	+	0.693088i
$189$	1748.43	+	790.197i	0.672909	+	0.304118i
$190$	−263.658	−	242.056i	−0.100672	−	0.0924242i
$191$	−1075.45	−	1281.67i	−0.407418	−	0.485542i	0.522849	−	0.852425i	$-0.324869\pi$
$191$	−1075.45	−	1281.67i	−0.407418	−	0.485542i	−0.930267	+	0.366884i	$0.880425\pi$
$192$	137.730	+	2213.90i	0.0517698	+	0.832159i
$193$	−1533.78	+	1073.97i	−0.572042	+	0.400548i	−0.823497	−	0.567321i	$-0.807980\pi$
$193$	−1533.78	+	1073.97i	−0.572042	+	0.400548i	0.251455	+	0.967869i	$0.419091\pi$
$194$	−464.849	+	169.191i	−0.172032	+	0.0626145i
$195$	−3744.22	−	2074.96i	−1.37502	−	0.762005i
$196$	210.516	+	1193.89i	0.0767186	+	0.435093i
$197$	−1315.56	+	4909.73i	−0.475785	+	1.77565i	0.142604	+	0.989780i	$0.454452\pi$
$197$	−1315.56	+	4909.73i	−0.475785	+	1.77565i	−0.618389	+	0.785872i	$0.712214\pi$
$198$	−39.0491	−	43.1866i	−0.0140157	−	0.0155007i
$199$	−1780.01	−	1027.69i	−0.634080	−	0.366086i	0.148251	−	0.988950i	$-0.452636\pi$
$199$	−1780.01	−	1027.69i	−0.634080	−	0.366086i	−0.782330	+	0.622864i	$0.785969\pi$
$200$	−814.369	+	468.129i	−0.287923	+	0.165508i
$201$	1681.33	+	2109.20i	0.590011	+	0.740156i
$202$	−398.322	+	34.8486i	−0.138742	+	0.0121383i
$203$	1620.45	−	141.771i	0.560264	−	0.0490168i
$204$	2325.50	+	2917.29i	0.798125	+	1.00123i
$205$	5035.12	+	1592.79i	1.71545	+	0.542661i
$206$	461.941	+	266.702i	0.156238	+	0.0902038i
$207$	−1440.73	+	309.385i	−0.483757	+	0.103883i
$208$	1117.65	−	4171.12i	0.372572	−	1.39046i
$209$	−52.8136	−	299.521i	−0.0174794	−	0.0991305i
$210$	−363.849	+	104.372i	−0.119562	+	0.0342969i
$211$	−1689.68	+	614.994i	−0.551292	+	0.200654i	−0.602620	−	0.798028i	$-0.705877\pi$
$211$	−1689.68	+	614.994i	−0.551292	+	0.200654i	0.0513285	+	0.998682i	$0.483654\pi$
$212$	51.8996	−	36.3405i	0.0168136	−	0.0117730i
$213$	−179.806	−	2890.24i	−0.0578410	−	0.929748i
$214$	100.560	+	119.842i	0.0321220	+	0.0382816i
$215$	−3667.50	+	3994.79i	−1.16335	+	1.26718i
$216$	1051.28	+	79.4225i	0.331160	+	0.0250186i
$217$	−449.696	+	449.696i	−0.140679	+	0.140679i
$218$	17.0166	−	194.501i	0.00528675	−	0.0604279i
$219$	−611.907	+	205.452i	−0.188807	+	0.0633935i
$220$	−389.939	−	51.7109i	−0.119499	−	0.0158470i
$221$	−2327.87	−	6395.76i	−0.708548	−	1.94672i
$222$	−727.777	+	692.081i	−0.220023	+	0.209232i
$223$	1833.66	−	2618.74i	0.550633	−	0.786386i	−0.443300	−	0.896373i	$-0.646192\pi$
$223$	1833.66	−	2618.74i	0.550633	−	0.786386i	0.993933	+	0.109988i	$0.0350811\pi$
$224$	−602.005	−	1042.70i	−0.179568	−	0.311020i
$225$	−1264.93	−	3128.99i	−0.374794	−	0.927108i
$226$	−215.195	+	372.728i	−0.0633387	+	0.109706i
$227$	−1536.66	−	3295.39i	−0.449304	−	0.963535i	−0.992307	−	0.123804i	$-0.960490\pi$
$227$	−1536.66	−	3295.39i	−0.449304	−	0.963535i	0.543003	−	0.839731i	$-0.317287\pi$
$228$	2183.35	+	1612.07i	0.634193	+	0.468253i
$229$	872.352	−	1039.63i	0.251732	−	0.300002i	−0.625349	−	0.780345i	$-0.715043\pi$
$229$	872.352	−	1039.63i	0.251732	−	0.300002i	0.877081	+	0.480343i	$0.159488\pi$
$230$	177.189	−	230.467i	0.0507980	−	0.0660720i
$231$	−299.391	−	117.572i	−0.0852747	−	0.0334877i
$232$	810.054	−	377.734i	0.229236	−	0.106894i
$233$	279.422	+	1042.82i	0.0785645	+	0.293207i	0.994018	−	0.109217i	$-0.0348345\pi$
$233$	279.422	+	1042.82i	0.0785645	+	0.293207i	−0.915453	+	0.402424i	$0.868168\pi$
$234$	−873.269	−	368.529i	−0.243963	−	0.102955i
$235$	3547.28	+	789.927i	0.984678	+	0.219273i
$236$	445.110	−	78.4850i	0.122772	−	0.0216480i
$237$	119.082	−	403.562i	0.0326380	−	0.110608i
$238$	−545.452	−	254.348i	−0.148556	−	0.0692729i
$239$	750.047	−	4253.73i	0.202998	−	1.15126i	−0.697562	−	0.716525i	$-0.745732\pi$
$239$	750.047	−	4253.73i	0.202998	−	1.15126i	0.900559	−	0.434733i	$-0.143157\pi$
$240$	2754.17	−	2001.44i	0.740752	−	0.538303i
$241$	−3634.32	+	3049.56i	−0.971400	+	0.815101i	−0.982770	−	0.184834i	$-0.940825\pi$
$241$	−3634.32	+	3049.56i	−0.971400	+	0.815101i	0.0113699	+	0.999935i	$0.496381\pi$
$242$	−441.489	−	441.489i	−0.117273	−	0.117273i
$243$	−800.541	+	3702.44i	−0.211336	+	0.977413i
$244$			552.586i			0.144982i
$245$	1286.72	−	1176.83i	0.335534	−	0.306878i
$246$	1146.11	+	231.931i	0.297045	+	0.0601113i
$247$	−2839.95	−	4055.86i	−0.731585	−	1.04481i
$248$	−147.682	+	316.705i	−0.0378138	+	0.0810919i
$249$	6229.33	−	3390.68i	1.58541	−	0.862955i
$250$	589.719	+	309.113i	0.149188	+	0.0782002i
$251$	−1848.54	+	1067.25i	−0.464855	+	0.268384i	−0.714083	−	0.700061i	$-0.753156\pi$
$251$	−1848.54	+	1067.25i	−0.464855	+	0.268384i	0.249229	+	0.968445i	$0.419823\pi$
$252$	2658.97	−	1080.76i	0.664681	−	0.270166i
$253$	238.611	−	63.9356i	0.0592938	−	0.0158877i
$254$	681.631	+	248.093i	0.168383	+	0.0612865i
$255$	1746.53	−	5073.96i	0.428910	−	1.24605i
$256$	2284.86	+	1917.22i	0.557827	+	0.468072i
$257$	47.7245	+	545.493i	0.0115835	+	0.132401i	0.999784	−	0.0207628i	$-0.00660949\pi$
$257$	47.7245	+	545.493i	0.0115835	+	0.132401i	−0.988201	+	0.153163i	$0.951054\pi$
$258$	−713.236	+	965.992i	−0.172109	+	0.233101i
$259$	−1897.61	+	5213.63i	−0.455257	+	1.25081i
$260$	−6109.06	+	1919.84i	−1.45718	+	0.457937i
$261$	945.337	+	3069.10i	0.224195	+	0.727865i
$262$	841.180	+	225.394i	0.198352	+	0.0531483i
$263$	5328.99	+	3731.40i	1.24943	+	0.874858i	0.995720	−	0.0924228i	$-0.0294611\pi$
$263$	5328.99	+	3731.40i	1.24943	+	0.874858i	0.253707	+	0.967281i	$0.418350\pi$
$264$	−176.681	−	4.44183i	−0.0411893	−	0.00103551i
$265$	−84.1609	−	34.9537i	−0.0195093	−	0.00810259i
$266$	−431.166	−	76.0263i	−0.0993854	−	0.0175243i
$267$	−2416.00	+	4858.44i	−0.553770	+	1.11360i
$268$	4019.64	+	351.673i	0.916188	+	0.0801560i
$269$	7500.71			1.70010			0.850049	−	0.526704i	$-0.176572\pi$
$269$	7500.71			1.70010			0.850049	+	0.526704i	$0.176572\pi$
$270$	−352.280	−	659.055i	−0.0794040	−	0.148551i
$271$	101.474			0.0227458			0.0113729	−	0.999935i	$-0.496380\pi$
$271$	101.474			0.0227458			0.0113729	+	0.999935i	$0.496380\pi$
$272$	5392.58	+	471.790i	1.20211	+	0.105171i
$273$	−5226.21	+	325.130i	−1.15862	+	0.0720797i
$274$	−635.382	−	112.035i	−0.140091	−	0.0247018i
$275$	238.141	+	513.221i	0.0522197	+	0.112540i
$276$	−1149.81	+	1880.72i	−0.250761	+	0.410167i
$277$	−2124.32	−	1487.47i	−0.460787	−	0.322647i	0.320029	−	0.947408i	$-0.396307\pi$
$277$	−2124.32	−	1487.47i	−0.460787	−	0.322647i	−0.780816	+	0.624761i	$0.785196\pi$
$278$	543.919	+	145.743i	0.117346	+	0.0314427i
$279$	−1054.42	−	681.621i	−0.226260	−	0.146264i
$280$	−531.518	+	1018.69i	−0.113444	+	0.217422i
$281$	−1728.57	+	4749.22i	−0.366968	+	1.00824i	0.609540	+	0.792755i	$0.291354\pi$
$281$	−1728.57	+	4749.22i	−0.366968	+	1.00824i	−0.976508	+	0.215481i	$0.930868\pi$
$282$	799.607	+	90.2574i	0.168851	+	0.0190594i
$283$	−223.152	−	2550.64i	−0.0468728	−	0.535759i	−0.982939	−	0.183934i	$-0.941117\pi$
$283$	−223.152	−	2550.64i	−0.0468728	−	0.535759i	0.936066	−	0.351825i	$-0.114439\pi$
$284$	−3318.45	−	2784.51i	−0.693358	−	0.581797i
$285$	271.913	−	3894.20i	0.0565149	−	0.809377i
$286$	149.313	+	54.3455i	0.0308709	+	0.0112361i
$287$	6239.80	−	1671.95i	1.28336	−	0.343875i
$288$	1763.14	−	1594.22i	0.360742	−	0.326181i
$289$	3134.13	−	1809.49i	0.637927	−	0.368307i
$290$	−534.006	−	340.908i	−0.108131	−	0.0690304i
$291$	−4603.18	−	2814.22i	−0.927297	−	0.566916i
$292$	−408.072	+	875.113i	−0.0817829	+	0.175384i
$293$	2306.88	+	3294.57i	0.459964	+	0.656897i	0.980403	−	0.197002i	$-0.0631206\pi$
$293$	2306.88	+	3294.57i	0.459964	+	0.656897i	−0.520439	+	0.853899i	$0.674232\pi$
$294$	255.535	−	289.439i	0.0506909	−	0.0574164i
$295$	−438.750	−	479.720i	−0.0865933	−	0.0946792i
$296$			3048.60i			0.598636i
$297$	102.844	−	626.631i	0.0200929	−	0.122427i
$298$	216.219	+	216.219i	0.0420310	+	0.0420310i
$299$	3080.66	−	2584.98i	0.595850	−	0.499978i
$300$	−4695.86	−	1854.32i	−0.903719	−	0.356864i
$301$	−1151.91	+	6532.78i	−0.220581	+	1.25097i
$302$	−879.027	−	409.897i	−0.167491	−	0.0781024i
$303$	−3005.16	−	3160.16i	−0.569776	−	0.599164i
$304$	3878.08	−	683.810i	0.731655	−	0.129010i
$305$	670.741	−	426.420i	0.125923	−	0.0800548i
$306$	264.862	−	1158.28i	0.0494810	−	0.216388i
$307$	15.4248	+	57.5661i	0.00286756	+	0.0107019i	0.967345	−	0.253464i	$-0.0815700\pi$
$307$	15.4248	+	57.5661i	0.00286756	+	0.0107019i	−0.964477	+	0.264166i	$0.914903\pi$
$308$	−436.079	+	203.347i	−0.0806751	+	0.0376194i
$309$	865.908	+	5752.80i	0.159417	+	1.05911i
$310$	245.608	−	32.0991i	0.0449986	−	0.00588098i
$311$	−668.298	+	796.447i	−0.121851	+	0.145217i	−0.823521	−	0.567285i	$-0.807994\pi$
$311$	−668.298	+	796.447i	−0.121851	+	0.145217i	0.701670	+	0.712502i	$0.252438\pi$
$312$	−2637.37	+	1150.04i	−0.478563	+	0.208680i
$313$	−414.528	−	888.958i	−0.0748579	−	0.160533i	0.865317	−	0.501224i	$-0.167117\pi$
$313$	−414.528	−	888.958i	−0.0748579	−	0.160533i	−0.940175	+	0.340691i	$0.889339\pi$
$314$	78.9893	−	136.813i	0.0141963	−	0.0245886i
$315$	−3363.74	−	2393.52i	−0.601667	−	0.428125i
$316$	−314.715	−	545.102i	−0.0560256	−	0.0970393i
$317$	5390.08	−	7697.83i	0.955007	−	1.36389i	0.0236746	−	0.999720i	$-0.492463\pi$
$317$	5390.08	−	7697.83i	0.955007	−	1.36389i	0.931332	−	0.364171i	$-0.118648\pi$
$318$	−19.3534	−	5.71074i	−0.00341284	−	0.00100705i
$319$	−184.128	−	505.887i	−0.0323172	−	0.0887907i
$320$	627.436	−	4731.34i	0.109609	−	0.826531i
$321$	−338.426	+	1672.36i	−0.0588446	+	0.290785i
$322$	30.9928	−	354.249i	0.00536385	−	0.0613091i
$323$	4388.82	−	4388.82i	0.756038	−	0.756038i
$324$	3188.29	+	4684.48i	0.546689	+	0.803238i
$325$	7044.59	+	5933.81i	1.20235	+	1.01276i
$326$	−636.981	−	759.125i	−0.108218	−	0.128969i
$327$	1774.48	−	1177.17i	0.300089	−	0.199076i
$328$	2907.62	−	2035.94i	0.489470	−	0.342731i
$329$	4177.33	−	1520.42i	0.700011	−	0.254783i
$330$	64.5327	+	107.376i	0.0107649	+	0.0179117i
$331$	1765.15	+	10010.7i	0.293116	+	1.66234i	0.674763	+	0.738035i	$0.264246\pi$
$331$	1765.15	+	10010.7i	0.293116	+	1.66234i	−0.381647	+	0.924308i	$0.624643\pi$
$332$	2745.96	−	10248.1i	0.453928	−	1.69408i
$333$	−10850.1	−	1501.77i	−1.78554	−	0.247137i
$334$	−434.161	−	250.663i	−0.0711264	−	0.0410648i
$335$	−2675.01	−	5150.50i	−0.436272	−	0.840006i
$336$	1522.28	−	3876.40i	0.247164	−	0.629389i
$337$	−1167.60	+	102.152i	−0.188733	+	0.0165120i	−0.181130	−	0.983459i	$-0.557976\pi$
$337$	−1167.60	+	102.152i	−0.188733	+	0.0165120i	−0.00760276	+	0.999971i	$0.502420\pi$
$338$	1534.19	−	134.224i	0.246891	−	0.0216001i
$339$	−4641.79	+	698.680i	−0.743680	+	0.111938i
$340$	−3699.88	−	7123.80i	−0.590159	−	1.13630i
$341$	182.280	+	105.240i	0.0289473	+	0.0167127i
$342$	−31.9708	−	863.769i	−0.00505492	−	0.136571i
$343$	1766.15	−	6591.37i	0.278027	−	1.03761i
$344$	632.940	+	3589.58i	0.0992031	+	0.562609i
$345$	3170.14	−	55.6557i	0.494710	−	0.00868523i
$346$	−861.927	+	313.716i	−0.133923	+	0.0487441i
$347$	−5083.77	+	3559.69i	−0.786487	+	0.550704i	−0.896405	−	0.443236i	$-0.853830\pi$
$347$	−5083.77	+	3559.69i	−0.786487	+	0.550704i	0.109918	+	0.993941i	$0.464941\pi$
$348$	4301.49	+	2139.04i	0.662598	+	0.329495i
$349$	−2297.32	−	2737.84i	−0.352357	−	0.419923i	0.560530	−	0.828134i	$-0.310597\pi$
$349$	−2297.32	−	2737.84i	−0.352357	−	0.419923i	−0.912888	+	0.408211i	$0.866153\pi$
$350$	811.486	−	69.4527i	0.123931	−	0.0106069i
$351$	−2793.86	−	9953.08i	−0.424858	−	1.51355i
$352$	−281.767	+	281.767i	−0.0426654	+	0.0426654i
$353$	−455.616	+	5207.72i	−0.0686969	+	0.785209i	0.881220	+	0.472706i	$0.156723\pi$
$353$	−455.616	+	5207.72i	−0.0686969	+	0.785209i	−0.949917	+	0.312503i	$0.898833\pi$
$354$	−107.909	−	95.2693i	−0.0162015	−	0.0143037i
$355$	−819.117	+	6176.76i	−0.122463	+	0.923461i
$356$	2776.13	+	7627.35i	0.413299	+	1.13553i
$357$	−1539.01	−	6381.04i	−0.228159	−	0.945996i
$358$	−122.142	+	174.436i	−0.0180318	+	0.0257521i
$359$	2391.30	+	4141.85i	0.351554	+	0.608909i	0.986522	−	0.163629i	$-0.0523202\pi$
$359$	2391.30	+	4141.85i	0.351554	+	0.608909i	−0.634968	+	0.772538i	$0.718987\pi$
$360$	−2186.63	−	603.708i	−0.320126	−	0.0883839i
$361$	−1171.91	+	2029.81i	−0.170857	+	0.295933i
$362$	886.594	+	1901.31i	0.128725	+	0.276051i
$363$	763.802	−	6766.65i	0.110439	−	0.978395i
$364$	−5035.02	+	6000.50i	−0.725018	+	0.864043i
$365$	1377.13	−	179.981i	0.197486	−	0.0258100i
$366$	137.616	−	109.699i	0.0196538	−	0.0156669i
$367$	−7410.13	+	3455.40i	−1.05397	+	0.491472i	−0.870814	−	0.491612i	$-0.836408\pi$
$367$	−7410.13	+	3455.40i	−1.05397	+	0.491472i	−0.183152	+	0.983085i	$0.558630\pi$
$368$	827.814	+	3089.44i	0.117263	+	0.437631i
$369$	5813.69	+	11351.3i	0.820185	+	1.60142i
$370$	1823.60	−	1159.35i	0.256229	−	0.162896i
$371$	−109.780	+	19.3572i	−0.0153625	+	0.00270883i
$372$	−1825.85	+	440.366i	−0.254478	+	0.0613761i
$373$	−1551.51	−	723.482i	−0.215373	−	0.100430i	0.311938	−	0.950103i	$-0.399022\pi$
$373$	−1551.51	−	723.482i	−0.215373	−	0.100430i	−0.527311	+	0.849672i	$0.676800\pi$
$374$	−34.5881	+	196.159i	−0.00478210	+	0.0271206i
$375$	1372.89	+	7130.89i	0.189055	+	0.981966i
$376$	1871.17	−	1570.10i	0.256644	−	0.215350i
$377$	−6197.21	−	6197.21i	−0.846611	−	0.846611i
$378$	−797.013	−	447.636i	−0.108450	−	0.0609099i
$379$			11212.5i			1.51964i	0.650131	+	0.759822i	$0.274714\pi$
$379$			11212.5i			1.51964i	−0.650131	+	0.759822i	$0.725286\pi$
$380$	−3941.11	−	4309.12i	−0.532038	−	0.581719i
$381$	2518.15	+	7499.92i	0.338606	+	1.00848i
$382$	457.201	+	652.951i	0.0612368	+	0.0874551i
$383$	−2253.70	+	4833.08i	−0.300675	+	0.644801i	−0.997363	−	0.0725740i	$-0.976879\pi$
$383$	−2253.70	+	4833.08i	−0.300675	+	0.644801i	0.696688	+	0.717375i	$0.254656\pi$
$384$	118.536	−	4714.95i	0.0157526	−	0.626586i
$385$	583.342	+	372.404i	0.0772204	+	0.0492973i
$386$	772.544	−	446.029i	0.101869	−	0.0588141i
$387$	−13087.3	+	484.404i	−1.71903	+	0.0636269i
$388$	−7795.90	+	2088.91i	−1.02004	+	0.273320i
$389$	−9092.18	−	3309.28i	−1.18507	−	0.431330i	−0.327080	−	0.944997i	$-0.606064\pi$
$389$	−9092.18	−	3309.28i	−1.18507	−	0.431330i	−0.857990	+	0.513667i	$0.828287\pi$
$390$	1690.89	+	1140.27i	0.219542	+	0.148051i
$391$	3861.78	+	3240.42i	0.499485	+	0.419118i
$392$	−102.148	−	1167.55i	−0.0131613	−	0.150435i
$393$	3796.43	+	8706.31i	0.487289	+	1.11749i
$394$	828.244	−	2275.58i	0.105904	−	0.290970i
$395$	−418.798	+	802.653i	−0.0533469	+	0.102243i
$396$	−573.266	−	757.451i	−0.0727467	−	0.0961195i
$397$	547.042	+	146.580i	0.0691569	+	0.0185305i	0.293232	−	0.956041i	$-0.405269\pi$
$397$	547.042	+	146.580i	0.0691569	+	0.0185305i	−0.224075	+	0.974572i	$0.571936\pi$
$398$	802.141	+	561.665i	0.101024	+	0.0707380i
$399$	−2282.86	−	4194.05i	−0.286431	−	0.526229i
$400$	−6644.99	+	3083.35i	−0.830624	+	0.385419i
$401$	3828.77	+	675.115i	0.476807	+	0.0840739i	0.406887	−	0.913479i	$-0.366614\pi$
$401$	3828.77	+	675.115i	0.476807	+	0.0840739i	0.0699202	+	0.997553i	$0.477726\pi$
$402$	−710.399	−	1070.86i	−0.0881380	−	0.132860i
$403$	3413.47	+	298.640i	0.421929	+	0.0369140i
$404$	−6523.58			−0.803367
$405$	3225.79	−	7484.95i	0.395780	−	0.918345i
$406$	−774.972			−0.0947320
$407$	1829.25	+	160.039i	0.222783	+	0.0194910i
$408$	−1993.84	−	3005.53i	−0.241935	−	0.364696i
$409$	7951.09	+	1401.99i	0.961262	+	0.169496i	0.632194	−	0.774810i	$-0.282154\pi$
$409$	7951.09	+	1401.99i	0.961262	+	0.169496i	0.329068	+	0.944306i	$0.393266\pi$
$410$	−2323.58	−	965.030i	−0.279887	−	0.116242i
$411$	−3364.11	−	6180.50i	−0.403745	−	0.741756i
$412$	7128.80	+	4991.64i	0.852454	+	0.596894i
$413$	−768.127	−	205.819i	−0.0915183	−	0.0245222i
$414$	696.633	−	87.0139i	0.0826997	−	0.0103297i
$415$	−14558.3	+	4575.12i	−1.72202	+	0.541166i
$416$	−2218.71	+	6095.85i	−0.261493	+	0.718446i
$417$	2454.83	+	5629.62i	0.288281	+	0.661112i
$418$	12.6289	+	144.349i	0.00147775	+	0.0168907i
$419$	−5080.25	−	4262.84i	−0.592331	−	0.497024i	0.296640	−	0.954990i	$-0.404134\pi$
$419$	−5080.25	−	4262.84i	−0.592331	−	0.497024i	−0.888970	+	0.457965i	$0.848578\pi$
$420$	−6062.16	+	1179.00i	−0.704293	+	0.136975i
$421$	−13126.5	−	4777.64i	−1.51958	−	0.553083i	−0.558540	−	0.829478i	$-0.688638\pi$
$421$	−13126.5	−	4777.64i	−1.51958	−	0.553083i	−0.961044	+	0.276394i	$0.910860\pi$
$422$	827.478	−	221.722i	0.0954526	−	0.0255764i
$423$	4666.30	+	7433.04i	0.536367	+	0.854389i
$424$	−53.0455	+	30.6259i	−0.00607575	+	0.00350784i
$425$	−5791.91	+	9988.30i	−0.661056	+	1.14001i
$426$	−34.6738	+	1379.21i	−0.00394355	+	0.156861i
$427$	410.885	−	881.146i	0.0465670	−	0.0998633i
$428$	1464.01	+	2090.82i	0.165340	+	0.236130i
$429$	551.608	+	1642.88i	0.0620790	+	0.184892i
$430$	1906.51	−	1743.69i	0.213814	−	0.195554i
$431$		−	9308.84i		−	1.04035i	−0.854060	−	0.520175i	$-0.825867\pi$
$431$		−	9308.84i		−	1.04035i	0.854060	−	0.520175i	$-0.174133\pi$
$432$	8113.37	+	1331.58i	0.903599	+	0.148300i
$433$	5827.12	+	5827.12i	0.646728	+	0.646728i	0.952201	−	0.305473i	$-0.0988144\pi$
$433$	5827.12	+	5827.12i	0.646728	+	0.646728i	−0.305473	+	0.952201i	$0.598814\pi$
$434$	232.103	−	194.758i	0.0256712	−	0.0215407i
$435$	−722.968	−	6871.90i	−0.0796866	−	0.757431i
$436$	553.152	−	3137.08i	0.0607596	−	0.344585i
$437$	3323.70	+	1549.87i	0.363831	+	0.169657i
$438$	298.948	−	72.1016i	0.0326126	−	0.00786563i
$439$	−7810.41	+	1377.19i	−0.849135	+	0.149725i	−0.581250	−	0.813725i	$-0.697436\pi$
$439$	−7810.41	+	1377.19i	−0.849135	+	0.149725i	−0.267886	+	0.963451i	$0.586325\pi$
$440$	371.186	+	82.6575i	0.0402172	+	0.00895577i
$441$	4205.71	+	211.600i	0.454131	+	0.0228485i
$442$	839.258	+	3132.15i	0.0903155	+	0.337062i
$443$	5082.80	−	2370.15i	0.545127	−	0.254197i	−0.130490	−	0.991450i	$-0.541655\pi$
$443$	5082.80	−	2370.15i	0.545127	−	0.254197i	0.675617	+	0.737253i	$0.263877\pi$
$444$	−12812.9	+	10213.7i	−1.36953	+	1.09171i
$445$	7115.97	−	9255.61i	0.758043	−	0.985973i
$446$	−979.015	+	1166.74i	−0.103941	+	0.123872i
$447$	−374.072	+	3313.97i	−0.0395816	+	0.350661i
$448$	−2467.32	−	5291.19i	−0.260201	−	0.558002i
$449$	8530.18	−	14774.7i	0.896579	−	1.55292i	0.0647409	−	0.997902i	$-0.479378\pi$
$449$	8530.18	−	14774.7i	0.896579	−	1.55292i	0.831838	−	0.555018i	$-0.187289\pi$
$450$	470.424	+	1537.58i	0.0492800	+	0.161071i
$451$	−1068.99	−	1851.54i	−0.111611	−	0.193316i
$452$	−4027.63	+	5752.05i	−0.419124	+	0.598571i
$453$	−2480.20	−	10283.4i	−0.257240	−	1.06657i
$454$	592.483	+	1627.83i	0.0612480	+	0.168277i
$455$	11169.0	+	1481.15i	1.15079	+	0.152609i
$456$	−1966.91	−	1736.52i	−0.201994	−	0.178333i
$457$	437.775	−	5003.79i	0.0448101	−	0.512182i	−0.940310	−	0.340318i	$-0.889465\pi$
$457$	437.775	−	5003.79i	0.0448101	−	0.512182i	0.985121	−	0.171864i	$-0.0549791\pi$
$458$	−457.196	+	457.196i	−0.0466449	+	0.0466449i
$459$	11679.0	−	5615.62i	1.18765	−	0.571056i
$460$	3207.63	−	3493.89i	0.325123	−	0.354138i
$461$	−4170.41	−	4970.10i	−0.421335	−	0.502128i	0.513067	−	0.858349i	$-0.328509\pi$
$461$	−4170.41	−	4970.10i	−0.421335	−	0.502128i	−0.934402	+	0.356221i	$0.884065\pi$
$462$	137.212	+	68.2325i	0.0138175	+	0.00687113i
$463$	10647.2	−	7455.27i	1.06872	−	0.748328i	0.0996304	−	0.995025i	$-0.468234\pi$
$463$	10647.2	−	7455.27i	1.06872	−	0.748328i	0.969093	+	0.246696i	$0.0793451\pi$
$464$	6550.03	−	2384.02i	0.655339	−	0.238524i
$465$	1943.50	+	1876.44i	0.193823	+	0.187135i
$466$	−89.3156	−	506.534i	−0.00887868	−	0.0503535i
$467$	−706.333	+	2636.07i	−0.0699897	+	0.261205i	−0.992051	−	0.125840i	$-0.959837\pi$
$467$	−706.333	+	2636.07i	−0.0699897	+	0.261205i	0.922061	+	0.387045i	$0.126504\pi$
$468$	−13669.4	−	7231.57i	−1.35015	−	0.714273i
$469$	−6148.17	−	3549.65i	−0.605322	−	0.349483i
$470$	−1650.78	−	522.202i	−0.162010	−	0.0512497i
$471$	1703.81	−	256.457i	0.166683	−	0.0250890i
$472$	−435.290	+	38.0830i	−0.0424488	+	0.00371379i
$473$	2187.09	−	191.345i	0.212606	−	0.0186006i
$474$	−73.2748	+	186.590i	−0.00710047	+	0.0180810i
$475$	−2189.23	+	8109.07i	−0.211471	+	0.783304i
$476$	−8503.70	−	4909.61i	−0.818837	−	0.472756i
$477$	−82.8684	−	203.879i	−0.00795447	−	0.0195702i
$478$	−532.608	+	1987.72i	−0.0509643	+	0.190201i
$479$	−964.443	−	5469.63i	−0.0919969	−	0.521740i	−0.995626	−	0.0934251i	$-0.970218\pi$
$479$	−964.443	−	5469.63i	−0.0919969	−	0.521740i	0.903629	−	0.428315i	$-0.140893\pi$
$480$	−4383.73	+	2634.61i	−0.416852	+	0.250527i
$481$	28090.5	−	10224.1i	2.66282	−	0.969186i
$482$	1851.52	−	1296.45i	0.174967	−	0.122513i
$483$	3231.91	−	2144.01i	0.304466	−	0.201979i
$484$	−6547.85	−	7803.42i	−0.614937	−	0.732853i
$485$	8551.51	+	7850.88i	0.800627	+	0.735031i
$486$	533.682	−	1723.98i	0.0498113	−	0.160908i
$487$	−6204.36	+	6204.36i	−0.577303	+	0.577303i	−0.934159	−	0.356856i	$-0.883849\pi$
$487$	−6204.36	+	6204.36i	−0.577303	+	0.577303i	0.356856	+	0.934159i	$0.383849\pi$
$488$	46.5601	−	532.184i	0.00431901	−	0.0493665i
$489$	2143.71	−	10593.3i	0.198246	−	0.979646i
$490$	−659.559	+	505.109i	−0.0608078	+	0.0465684i
$491$	1670.96	+	4590.91i	0.153583	+	0.421965i	0.992493	−	0.122305i	$-0.0390287\pi$
$491$	1670.96	+	4590.91i	0.153583	+	0.421965i	−0.838910	+	0.544271i	$0.816806\pi$
$492$	18298.2	+	5399.37i	1.67672	+	0.494761i
$493$	6301.54	−	8999.53i	0.575673	−	0.822147i
$494$	1179.46	+	2042.88i	0.107422	+	0.186060i
$495$	−477.033	+	1280.35i	−0.0433152	+	0.116258i
$496$	−1362.60	+	2360.09i	−0.123352	+	0.213652i
$497$	3221.09	+	6907.64i	0.290715	+	0.623441i
$498$	−3097.30	+	1350.59i	−0.278701	+	0.121529i
$499$	−8318.88	+	9914.06i	−0.746301	+	0.889407i	−0.996900	−	0.0786841i	$-0.974928\pi$
$499$	−8318.88	+	9914.06i	−0.746301	+	0.889407i	0.250599	+	0.968091i	$0.419373\pi$
$500$	9145.31	+	5862.67i	0.817981	+	0.524373i
$501$	−813.834	−	5406.84i	−0.0725737	−	0.482155i
$502$	921.650	−	429.773i	0.0819428	−	0.0382105i
$503$	4954.47	+	18490.3i	0.439183	+	1.63905i	0.730854	+	0.682534i	$0.239122\pi$
$503$	4954.47	+	18490.3i	0.439183	+	1.63905i	−0.291671	+	0.956519i	$0.594211\pi$
$504$	−2651.87	+	816.821i	−0.234372	+	0.0721907i
$505$	5034.12	+	7918.47i	0.443595	+	0.697757i
$506$	−115.902	+	20.4367i	−0.0101828	+	0.00179550i
$507$	11574.8	+	12171.8i	1.01392	+	1.06621i
$508$	10725.9	+	5001.59i	0.936785	+	0.436830i
$509$	1146.17	−	6500.28i	0.0998100	−	0.566051i	−0.893357	−	0.449348i	$-0.851656\pi$
$509$	1146.17	−	6500.28i	0.0998100	−	0.566051i	0.993167	−	0.116703i	$-0.0372325\pi$
$510$	−1039.61	+	2335.63i	−0.0902640	+	0.202791i
$511$	1301.41	−	1092.02i	0.112664	−	0.0945360i
$512$	−6139.42	−	6139.42i	−0.529935	−	0.529935i
$513$	7149.28	−	6144.92i	0.615299	−	0.528860i
$514$		−	260.879i		−	0.0223869i
$515$	557.807	−	12505.1i	0.0477280	−	1.06998i
$516$	−12966.0	+	14686.3i	−1.10620	+	1.25296i
$517$	−843.877	−	1205.18i	−0.0717866	−	0.102522i
$518$	1117.11	−	2395.65i	0.0947548	−	0.203202i
$519$	−8535.26	−	5218.15i	−0.721881	−	0.441332i
$520$	6045.28	−	1334.22i	0.509814	−	0.112518i
$521$	12184.8	−	7034.90i	1.02462	−	0.591564i	0.109180	−	0.994022i	$-0.465178\pi$
$521$	12184.8	−	7034.90i	1.02462	−	0.591564i	0.915438	+	0.402458i	$0.131844\pi$
$522$	−321.228	−	1495.88i	−0.0269345	−	0.125427i
$523$	−21800.5	+	5841.43i	−1.82270	+	0.488390i	−0.997116	−	0.0758958i	$-0.975818\pi$
$523$	−21800.5	+	5841.43i	−1.82270	+	0.488390i	−0.825580	+	0.564286i	$0.809152\pi$
$524$	13351.4	+	4859.52i	1.11309	+	0.405132i
$525$	6109.15	+	6448.57i	0.507857	+	0.536074i
$526$	−2374.25	−	1992.24i	−0.196811	−	0.165144i
$527$	374.362	+	4278.98i	0.0309440	+	0.353691i
$528$	−1369.61	−	154.598i	−0.112888	−	0.0127425i
$529$	3142.60	−	8634.24i	0.258289	−	0.709644i
$530$	38.4923	+	20.0840i	0.00315471	+	0.00164603i
$531$	78.8892	−	1567.98i	0.00644727	−	0.128144i
$532$	−6899.76	−	1848.78i	−0.562298	−	0.150667i
$533$	−28510.8	−	19963.5i	−2.31696	−	1.62236i
$534$	1348.39	−	2205.55i	0.109271	−	0.178733i
$535$	1408.14	−	3390.50i	0.113793	−	0.273989i
$536$	−3841.60	−	677.378i	−0.309574	−	0.0545863i
$537$	−2318.05	+	144.209i	−0.186278	+	0.0115886i
$538$	−3559.92	−	311.452i	−0.285277	−	0.0249585i
$539$	−705.931			−0.0564130
$540$	−4788.54	−	11212.7i	−0.381604	−	0.893554i
$541$	2526.30			0.200765			0.100383	−	0.994949i	$-0.467993\pi$
$541$	2526.30			0.200765			0.100383	+	0.994949i	$0.467993\pi$
$542$	−48.1606	−	4.21351i	−0.00381674	−	0.000333922i
$543$	−10187.8	+	20487.2i	−0.805158	+	1.61913i
$544$	−8008.37	−	1412.09i	−0.631169	−	0.111292i
$545$	−4234.72	+	1749.40i	−0.332835	+	0.137497i
$546$	2493.91	+	62.6980i	0.195476	+	0.00491433i
$547$	−3095.87	−	2167.75i	−0.241992	−	0.169445i	0.446289	−	0.894889i	$-0.352745\pi$
$547$	−3095.87	−	2167.75i	−0.241992	−	0.169445i	−0.688281	+	0.725444i	$0.741634\pi$
$548$	−10167.7	−	2724.43i	−0.792598	−	0.212376i
$549$	1871.14	+	427.870i	0.145461	+	0.0332624i
$550$	−91.7136	−	253.469i	−0.00711033	−	0.0196508i
$551$	2733.50	−	7510.24i	0.211345	−	0.580666i
$552$	1265.82	−	1714.40i	0.0976032	−	0.132192i
$553$	96.5197	+	1103.23i	0.00742213	+	0.0848353i
$554$	946.461	+	794.175i	0.0725835	+	0.0609048i
$555$	22285.1	+	7670.85i	1.70441	+	0.586683i
$556$	8633.22	+	3142.23i	0.658507	+	0.239677i
$557$	−5939.74	+	1591.55i	−0.451840	+	0.121070i	−0.477560	−	0.878599i	$-0.658479\pi$
$557$	−5939.74	+	1591.55i	−0.451840	+	0.121070i	0.0257203	+	0.999669i	$0.491812\pi$
$558$	472.137	+	367.287i	0.0358193	+	0.0278647i
$559$	30952.5	−	17870.4i	2.34195	−	1.35213i
$560$	−4821.74	+	7552.88i	−0.363850	+	0.569942i
$561$	−1908.08	+	1038.59i	−0.143599	+	0.0781624i
$562$	1017.60	−	2182.25i	0.0763789	−	0.163795i
$563$	10503.2	+	15000.2i	0.786250	+	1.12288i	0.989610	+	0.143778i	$0.0459250\pi$
$563$	10503.2	+	15000.2i	0.786250	+	1.12288i	−0.203360	+	0.979104i	$0.565186\pi$
$564$	12867.9	+	2604.00i	0.960701	+	0.194412i
$565$	10090.0	+	450.081i	0.751310	+	0.0335133i
$566$			1219.83i			0.0905885i
$567$	−1600.77	−	9840.53i	−0.118565	−	0.728860i
$568$	2961.31	+	2961.31i	0.218757	+	0.218757i
$569$	−19351.9	+	16238.2i	−1.42579	+	1.19638i	−0.477640	+	0.878556i	$0.658508\pi$
$569$	−19351.9	+	16238.2i	−1.42579	+	1.19638i	−0.948150	+	0.317824i	$0.897048\pi$
$570$	−290.752	+	1836.94i	−0.0213654	+	0.134984i
$571$	2166.21	−	12285.2i	0.158762	−	0.900385i	−0.796503	−	0.604635i	$-0.793319\pi$
$571$	2166.21	−	12285.2i	0.158762	−	0.900385i	0.955265	−	0.295751i	$-0.0955698\pi$
$572$	2349.55	+	1095.61i	0.171747	+	0.0800871i
$573$	−2460.43	+	8338.26i	−0.179382	+	0.607916i
$574$	−3030.90	+	534.430i	−0.220396	+	0.0388618i
$575$	−6716.22	−	1197.33i	−0.487106	−	0.0868382i
$576$	9190.56	−	6955.74i	0.664826	−	0.503164i
$577$	−5306.60	−	19804.5i	−0.382871	−	1.42890i	−0.841495	−	0.540265i	$-0.818324\pi$
$577$	−5306.60	−	19804.5i	−0.382871	−	1.42890i	0.458624	−	0.888631i	$-0.348343\pi$
$578$	−1562.63	+	728.666i	−0.112451	+	0.0524368i
$579$	9056.03	+	3556.34i	0.650010	+	0.255261i
$580$	−8194.58	−	6300.22i	−0.586658	−	0.451039i
$581$	−11998.8	+	14299.6i	−0.856789	+	1.02108i
$582$	2067.86	+	1526.80i	0.147278	+	0.108742i
$583$	15.5918	+	33.4367i	0.00110763	+	0.00237531i
$584$	466.742	−	808.421i	0.0330718	−	0.0572820i
$585$	1770.60	+	22172.7i	0.125137	+	1.56706i
$586$	−958.070	−	1659.43i	−0.0675384	−	0.116980i
$587$	122.617	−	175.116i	0.00862173	−	0.0123131i	−0.814818	−	0.579717i	$-0.803163\pi$
$587$	122.617	−	175.116i	0.00862173	−	0.0123131i	0.823440	+	0.567404i	$0.192052\pi$
$588$	4564.86	−	4340.96i	0.320156	−	0.304453i
$589$	1068.71	+	2936.26i	0.0747631	+	0.205410i
$590$	188.316	+	245.898i	0.0131404	+	0.0171584i
$591$	25038.0	−	8406.70i	1.74268	−	0.585119i
$592$	−2072.12	+	23684.5i	−0.143858	+	1.64430i
$593$	10281.3	−	10281.3i	0.711976	−	0.711976i	−0.254972	−	0.966948i	$-0.582066\pi$
$593$	10281.3	−	10281.3i	0.711976	−	0.711976i	0.966948	+	0.254972i	$0.0820664\pi$
$594$	−74.8304	+	293.135i	−0.00516890	+	0.0202483i
$595$	602.742	+	14110.6i	0.0415295	+	0.972235i
$596$	3206.81	+	3821.73i	0.220396	+	0.262658i
$597$	663.142	+	10659.5i	0.0454616	+	0.730760i
$598$	−1569.45	+	1098.94i	−0.107324	+	0.0751489i
$599$	−23451.9	+	8535.79i	−1.59970	+	0.582242i	−0.979365	−	0.202098i	$-0.935224\pi$
$599$	−23451.9	+	8535.79i	−1.59970	+	0.582242i	−0.620331	+	0.784340i	$0.713002\pi$
$600$	4366.25	+	2181.53i	0.297086	+	0.148434i
$601$	−3477.82	−	19723.7i	−0.236046	−	1.33868i	−0.840401	−	0.541966i	$-0.817680\pi$
$601$	−3477.82	−	19723.7i	−0.236046	−	1.33868i	0.604355	−	0.796715i	$-0.293431\pi$
$602$	817.968	−	3052.70i	0.0553786	−	0.206676i
$603$	4303.24	−	13338.8i	0.290616	−	0.900825i
$604$	−13704.2	−	7912.12i	−0.923205	−	0.533013i
$605$	−4419.12	+	13969.7i	−0.296963	+	0.938757i
$606$	1295.06	+	1624.63i	0.0868125	+	0.108904i
$607$	22773.6	−	1992.44i	1.52282	−	0.133230i	0.705210	−	0.708998i	$-0.250853\pi$
$607$	22773.6	−	1992.44i	1.52282	−	0.133230i	0.817613	+	0.575768i	$0.195297\pi$
$608$	−5893.17	+	515.586i	−0.393092	+	0.0343911i
$609$	−5268.58	−	6609.33i	−0.350565	−	0.439776i
$610$	−336.047	+	174.532i	−0.0223052	+	0.0115846i
$611$	−20742.6	−	11975.7i	−1.37341	−	0.792939i
$612$	5951.93	−	18449.3i	0.393125	−	1.21857i
$613$	2259.52	−	8432.66i	0.148877	−	0.555615i	−0.850676	−	0.525691i	$-0.823807\pi$
$613$	2259.52	−	8432.66i	0.148877	−	0.555615i	0.999552	−	0.0299238i	$-0.00952648\pi$
$614$	−4.93045	−	27.9620i	−0.000324066	−	0.00183787i
$615$	−7566.46	−	26377.3i	−0.496112	−	1.72949i
$616$	437.113	−	159.096i	0.0285906	−	0.0104061i
$617$	−19442.0	+	13613.4i	−1.26857	+	0.888260i	−0.997241	−	0.0742283i	$-0.976351\pi$
$617$	−19442.0	+	13613.4i	−1.26857	+	0.888260i	−0.271325	+	0.962488i	$0.587462\pi$
$618$	−172.095	−	2766.30i	−0.0112018	−	0.180059i
$619$	−9450.86	−	11263.1i	−0.613670	−	0.731344i	0.366298	−	0.930498i	$-0.380625\pi$
$619$	−9450.86	−	11263.1i	−0.613670	−	0.731344i	−0.979968	+	0.199154i	$0.936181\pi$
$620$	4037.57	−	172.467i	0.261537	−	0.0111717i
$621$	5478.10	+	5349.67i	0.353991	+	0.345692i
$622$	350.252	−	350.252i	0.0225785	−	0.0225785i
$623$	1244.68	−	14226.7i	0.0800432	−	0.914898i
$624$	−21271.3	+	7142.01i	−1.36464	+	0.458188i
$625$	58.9832	−	15624.9i	0.00377492	−	0.999993i
$626$	159.827	+	439.121i	0.0102044	+	0.0280365i
$627$	−1145.22	+	1089.05i	−0.0729436	+	0.0693658i
$628$	1478.38	−	2111.35i	0.0939391	−	0.134159i
$629$	18736.4	+	32452.5i	1.18771	+	2.05718i
$630$	1497.08	+	1275.66i	0.0946747	+	0.0806724i
$631$	−11113.4	+	19249.0i	−0.701137	+	1.21440i	0.266931	+	0.963716i	$0.413990\pi$
$631$	−11113.4	+	19249.0i	−0.701137	+	1.21440i	−0.968068	+	0.250689i	$0.919343\pi$
$632$	257.166	+	551.495i	0.0161860	+	0.0347109i
$633$	7516.50	+	5549.77i	0.471965	+	0.348473i
$634$	−2877.83	+	3429.66i	−0.180273	+	0.214841i
$635$	−2205.96	−	16879.0i	−0.137860	−	1.05484i
$636$	−306.435	−	120.338i	−0.0191052	−	0.00750270i
$637$	−10415.5	+	4856.84i	−0.647847	+	0.302096i
$638$	66.3830	+	247.745i	0.00411933	+	0.0153735i
$639$	−11998.3	+	9080.71i	−0.742792	+	0.562171i
$640$	−2205.81	+	9905.54i	−0.136238	+	0.611798i
$641$	−1420.37	+	250.450i	−0.0875217	+	0.0154324i	−0.217237	−	0.976119i	$-0.569705\pi$
$641$	−1420.37	+	250.450i	−0.0875217	+	0.0154324i	0.129716	+	0.991551i	$0.458593\pi$
$642$	230.062	−	779.667i	0.0141430	−	0.0479299i
$643$	−18058.8	−	8420.98i	−1.10758	−	0.516471i	−0.219243	−	0.975670i	$-0.570359\pi$
$643$	−18058.8	−	8420.98i	−1.10758	−	0.516471i	−0.888333	+	0.459199i	$0.848136\pi$
$644$	1007.47	−	5713.64i	0.0616457	−	0.349610i
$645$	27832.2	+	4405.31i	1.69906	+	0.268928i
$646$	−2265.22	+	1900.74i	−0.137963	+	0.115764i
$647$	6740.82	+	6740.82i	0.409597	+	0.409597i	0.881598	−	0.472001i	$-0.156468\pi$
$647$	6740.82	+	6740.82i	0.409597	+	0.409597i	−0.472001	+	0.881598i	$0.656468\pi$
$648$	−2675.87	−	4780.18i	−0.162219	−	0.289789i
$649$			263.187i			0.0159183i
$650$	−3097.05	−	3108.76i	−0.186887	−	0.187593i
$651$	3238.92	+	655.442i	0.194997	+	0.0394605i
$652$	−9273.57	−	13244.0i	−0.557026	−	0.795516i
$653$	−9754.19	+	20917.9i	−0.584550	+	1.25357i	0.362350	+	0.932042i	$0.381974\pi$
$653$	−9754.19	+	20917.9i	−0.584550	+	1.25357i	−0.946900	+	0.321529i	$0.895803\pi$
$654$	−891.069	+	485.017i	−0.0532776	+	0.0289995i
$655$	−4404.44	−	19956.3i	−0.262742	−	1.19047i
$656$	23973.0	−	13840.8i	1.42681	−	0.823770i
$657$	2647.29	+	2059.40i	0.157201	+	0.122290i
$658$	−2045.74	+	548.154i	−0.121202	+	0.0324761i
$659$	−11486.5	−	4180.76i	−0.678986	−	0.247131i	−0.0205741	−	0.999788i	$-0.506549\pi$
$659$	−11486.5	−	4180.76i	−0.678986	−	0.247131i	−0.658412	+	0.752657i	$0.728772\pi$
$660$	896.182	+	1836.97i	0.0528543	+	0.108340i
$661$	−5118.77	−	4295.16i	−0.301206	−	0.252742i	0.479640	−	0.877465i	$-0.340767\pi$
$661$	−5118.77	−	4295.16i	−0.301206	−	0.252742i	−0.780846	+	0.624723i	$0.785212\pi$
$662$	−422.085	−	4824.46i	−0.0247807	−	0.283245i
$663$	−21006.9	+	28451.3i	−1.23053	+	1.66660i
$664$	−3508.07	+	9638.33i	−0.205029	+	0.563313i
$665$	3080.31	+	9801.75i	0.179623	+	0.571572i
$666$	5087.23	+	1163.29i	0.295985	+	0.0676824i
$667$	6270.22	+	1680.10i	0.363994	+	0.0975319i
$668$	−6700.09	−	4691.46i	−0.388076	−	0.271733i
$669$	−16606.3	−	417.489i	−0.959697	−	0.0241271i
$670$	1055.72	+	2555.56i	0.0608748	+	0.147358i
$671$	−316.883	−	55.8750i	−0.0182312	−	0.00321465i
$672$	−2785.66	+	5601.82i	−0.159909	+	0.321570i
$673$	−17408.2	−	1523.02i	−0.997083	−	0.0872335i	−0.423085	−	0.906090i	$-0.639053\pi$
$673$	−17408.2	−	1523.02i	−0.997083	−	0.0872335i	−0.573998	+	0.818857i	$0.694608\pi$
$674$	558.396			0.0319119
$675$	−9915.04	+	14465.1i	−0.565378	+	0.824832i
$676$	25126.5			1.42959
$677$	−936.692	−	81.9499i	−0.0531758	−	0.00465228i	0.0605368	−	0.998166i	$-0.480719\pi$
$677$	−936.692	−	81.9499i	−0.0531758	−	0.00465228i	−0.113713	+	0.993514i	$0.536274\pi$
$678$	2232.06	−	138.859i	0.126433	−	0.00786558i
$679$	13984.5	+	2465.84i	0.790391	+	0.139367i
$680$	2963.04	+	7172.54i	0.167099	+	0.404492i
$681$	−9854.99	+	16119.7i	−0.554544	+	0.907059i
$682$	−82.1422	−	57.5166i	−0.00461201	−	0.00322936i
$683$	−19833.0	−	5314.24i	−1.11111	−	0.297721i	−0.343830	−	0.939032i	$-0.611724\pi$
$683$	−19833.0	−	5314.24i	−1.11111	−	0.297721i	−0.767281	+	0.641311i	$0.778391\pi$
$684$	708.629	−	14084.5i	0.0396127	−	0.787332i
$685$	4539.26	+	14444.2i	0.253191	+	0.805671i
$686$	−1111.93	+	3055.00i	−0.0618857	+	0.170030i
$687$	−7007.40	−	790.976i	−0.389154	−	0.0439267i
$688$	2477.47	+	28317.6i	0.137286	+	1.56918i
$689$	460.092	+	386.063i	0.0254400	+	0.0213467i
$690$	−1506.89	−	105.219i	−0.0831399	−	0.00580526i
$691$	−9514.96	−	3463.16i	−0.523829	−	0.190658i	0.0665516	−	0.997783i	$-0.478800\pi$
$691$	−9514.96	−	3463.16i	−0.523829	−	0.190658i	−0.590381	+	0.807125i	$0.701023\pi$
$692$	−14455.2	+	3873.27i	−0.794083	+	0.212774i
$693$	350.906	+	1634.08i	0.0192349	+	0.0895725i
$694$	2560.62	−	1478.37i	0.140057	−	0.0808622i
$695$	−2847.97	−	12904.0i	−0.155439	−	0.704283i
$696$	−3962.45	−	2422.50i	−0.215799	−	0.131932i
$697$	18439.0	−	39542.6i	1.00205	−	2.14890i
$698$	976.649	+	1394.80i	0.0529609	+	0.0756360i
$699$	3712.76	−	4205.36i	0.200901	−	0.227555i
$700$	13288.1	+	25.0808i	0.717488	+	0.00135424i
$701$		−	28194.0i		−	1.51908i	−0.650461	−	0.759539i	$-0.725424\pi$
$701$		−	28194.0i		−	1.51908i	0.650461	−	0.759539i	$-0.274576\pi$
$702$	912.714	+	4839.85i	0.0490714	+	0.260211i
$703$	19275.9	+	19275.9i	1.03415	+	1.03415i
$704$	−1480.15	+	1242.00i	−0.0792406	+	0.0664907i
$705$	−6769.10	−	17628.8i	−0.361616	−	0.941756i
$706$	432.481	−	2452.72i	0.0230547	−	0.130750i
$707$	10402.4	+	4850.73i	0.553357	+	0.258035i
$708$	−1618.41	−	1701.88i	−0.0859089	−	0.0903399i
$709$	−21691.8	+	3824.85i	−1.14902	+	0.202603i	−0.715546	−	0.698565i	$-0.753822\pi$
$709$	−21691.8	+	3824.85i	−1.14902	+	0.202603i	−0.433470	+	0.901168i	$0.642711\pi$
$710$	645.240	−	2897.54i	0.0341062	−	0.153159i
$711$	−2089.48	+	643.597i	−0.110214	+	0.0339477i
$712$	−2030.97	−	7579.67i	−0.106901	−	0.398961i
$713$	−2300.15	+	1072.58i	−0.120815	+	0.0563370i
$714$	465.468	+	3092.42i	0.0243974	+	0.162088i
$715$	−483.222	−	3697.40i	−0.0252748	−	0.193391i
$716$	−2233.24	+	2661.48i	−0.116565	+	0.138916i
$717$	−20573.1	+	8971.02i	−1.07157	+	0.467265i
$718$	−962.952	−	2065.06i	−0.0500516	−	0.107336i
$719$	6138.24	−	10631.8i	0.318384	−	0.551457i	−0.661767	−	0.749709i	$-0.730193\pi$
$719$	6138.24	−	10631.8i	0.318384	−	0.551457i	0.980151	+	0.198253i	$0.0635266\pi$
$720$	−16577.5	−	6176.44i	−0.858066	−	0.319697i
$721$	−7655.87	−	13260.4i	−0.395450	−	0.684940i
$722$	640.484	−	914.706i	0.0330143	−	0.0471494i
$723$	23644.1	+	6976.83i	1.21623	+	0.358881i
$724$	11706.4	+	32163.2i	0.600920	+	1.65101i
$725$	−1323.75	+	14808.5i	−0.0678107	+	0.758586i
$726$	−643.481	+	3179.81i	−0.0328951	+	0.162554i
$727$	−1976.25	+	22588.6i	−0.100818	+	1.15236i	0.762254	+	0.647278i	$0.224093\pi$
$727$	−1976.25	+	22588.6i	−0.100818	+	1.15236i	−0.863072	+	0.505081i	$0.831463\pi$
$728$	5354.72	−	5354.72i	0.272609	−	0.272609i
$729$	18331.1	−	7168.82i	0.931315	−	0.364214i
$730$	−661.076	+	28.2381i	−0.0335171	+	0.00143170i
$731$	28799.0	+	34321.3i	1.45714	+	1.73655i
$732$	2392.69	−	1587.29i	0.120815	−	0.0801473i
$733$	−30528.0	+	21375.9i	−1.53830	+	1.07713i	−0.571828	+	0.820374i	$0.693765\pi$
$733$	−30528.0	+	21375.9i	−1.53830	+	1.07713i	−0.966476	+	0.256758i	$0.917346\pi$
$734$	3660.40	−	1332.28i	0.184071	−	0.0669963i
$735$	−8791.78	−	2191.09i	−0.441210	−	0.109959i
$736$	−834.347	−	4731.82i	−0.0417859	−	0.236980i
$737$	−608.116	+	2269.52i	−0.0303938	+	0.113431i
$738$	−2287.90	−	5628.85i	−0.114117	−	0.280760i
$739$	18496.9	+	10679.2i	0.920731	+	0.531584i	0.883868	−	0.467736i	$-0.154930\pi$
$739$	18496.9	+	10679.2i	0.920731	+	0.531584i	0.0368629	+	0.999320i	$0.488264\pi$
$740$	31288.1	−	16250.0i	1.55429	−	0.807247i
$741$	−9404.21	+	23947.3i	−0.466224	+	1.18722i
$742$	52.9066	−	4.62873i	0.00261761	−	0.000229011i
$743$	17756.7	−	1553.51i	0.876755	−	0.0767061i	0.360114	−	0.932908i	$-0.382738\pi$
$743$	17756.7	−	1553.51i	0.876755	−	0.0767061i	0.516641	+	0.856202i	$0.327182\pi$
$744$	1795.55	−	270.264i	0.0884783	−	0.0133177i
$745$	2164.26	−	6841.65i	0.106433	−	0.336454i
$746$	706.323	+	407.796i	0.0346653	+	0.0200140i
$747$	−32575.3	−	17233.4i	−1.59554	−	0.844090i
$748$	−841.102	+	3139.04i	−0.0411146	+	0.153442i
$749$	−779.822	−	4422.59i	−0.0380428	−	0.215752i
$750$	−355.492	−	3441.40i	−0.0173076	−	0.167550i
$751$	−24314.7	+	8849.83i	−1.18143	+	0.430006i	−0.856708	−	0.515802i	$-0.827494\pi$
$751$	−24314.7	+	8849.83i	−1.18143	+	0.430006i	−0.324725	+	0.945808i	$0.605272\pi$
$752$	15604.2	−	10926.2i	0.756686	−	0.529837i
$753$	9931.07	+	4938.50i	0.480622	+	0.239003i
$754$	2683.93	+	3198.59i	0.129633	+	0.154490i
$755$	971.354	+	22740.1i	0.0468228	+	1.09615i
$756$	−12317.5	−	8408.89i	−0.592572	−	0.404535i
$757$	805.837	−	805.837i	0.0386904	−	0.0386904i	−0.687497	−	0.726187i	$-0.741291\pi$
$757$	805.837	−	805.837i	0.0386904	−	0.0386904i	0.726187	+	0.687497i	$0.241291\pi$
$758$	465.575	−	5321.55i	0.0223093	−	0.254997i
$759$	−962.245	−	849.532i	−0.0460175	−	0.0406272i
$760$	3432.52	+	4482.10i	0.163830	+	0.213925i
$761$	−6402.68	−	17591.2i	−0.304989	−	0.837952i	−0.993614	−	0.112833i	$-0.964007\pi$
$761$	−6402.68	−	17591.2i	−0.304989	−	0.837952i	0.688625	−	0.725118i	$-0.258215\pi$
$762$	−883.723	−	3664.10i	−0.0420130	−	0.174195i
$763$	−3214.68	+	4591.04i	−0.152529	+	0.217834i
$764$	6502.53	+	11262.7i	0.307923	+	0.533339i
$765$	−26987.1	+	7012.35i	−1.27545	+	0.331414i
$766$	1270.31	−	2200.25i	0.0599195	−	0.103784i
$767$	1810.74	+	3883.14i	0.0852438	+	0.182806i
$768$	1738.38	−	15400.6i	0.0816776	−	0.723596i
$769$	1320.34	−	1573.52i	0.0619150	−	0.0737875i	−0.734198	−	0.678935i	$-0.762442\pi$
$769$	1320.34	−	1573.52i	0.0619150	−	0.0737875i	0.796113	+	0.605148i	$0.206886\pi$
$770$	−261.397	−	200.969i	−0.0122339	−	0.00940574i
$771$	2224.90	−	1773.56i	0.103927	−	0.0828447i
$772$	13190.6	−	6150.88i	0.614949	−	0.286755i
$773$	−1690.05	−	6307.34i	−0.0786375	−	0.293479i	0.915396	−	0.402555i	$-0.131878\pi$
$773$	−1690.05	−	6307.34i	−0.0786375	−	0.293479i	−0.994033	+	0.109076i	$0.965211\pi$
$774$	6231.50	+	313.523i	0.289388	+	0.0145599i
$775$	−3325.06	−	4767.81i	−0.154116	−	0.220987i
$776$	7684.09	−	1354.91i	0.355468	−	0.0626785i
$777$	28025.8	−	6759.39i	1.29398	−	0.312087i
$778$	4177.83	+	1948.16i	0.192523	+	0.0897748i
$779$	5511.53	−	31257.5i	0.253493	−	1.43763i
$780$	25861.0	+	20937.5i	1.18715	+	0.961133i
$781$	1932.34	−	1621.42i	0.0885333	−	0.0742882i
$782$	−1698.29	−	1698.29i	−0.0776608	−	0.0776608i
$783$	10573.8	−	12909.2i	0.482600	−	0.589193i
$784$		−	9140.12i		−	0.416369i
$785$	−3703.64	−	165.206i	−0.168393	−	0.00751142i
$786$	−1440.31	−	4289.75i	−0.0653617	−	0.194669i
$787$	13140.0	+	18765.9i	0.595160	+	0.849977i	0.997862	−	0.0653543i	$-0.0208178\pi$
$787$	13140.0	+	18765.9i	0.595160	+	0.849977i	−0.402702	+	0.915331i	$0.631929\pi$
$788$	16697.5	−	35807.9i	0.754853	−	1.61879i
$789$	849.565	−	33792.8i	0.0383337	−	1.52479i
$790$	232.095	−	363.558i	0.0104526	−	0.0163732i
$791$	10699.5	−	6177.33i	0.480947	−	0.277675i
$792$	488.279	+	777.789i	0.0219069	+	0.0348959i
$793$	−5059.81	+	1355.77i	−0.226582	+	0.0607124i
$794$	−253.546	−	92.2831i	−0.0113325	−	0.00412469i
$795$	90.4007	+	464.820i	0.00403293	+	0.0207364i
$796$	12238.7	+	10269.5i	0.544963	+	0.457278i
$797$	1650.35	+	18863.6i	0.0733481	+	0.838372i	0.940381	+	0.340122i	$0.110468\pi$
$797$	1650.35	+	18863.6i	0.0733481	+	0.838372i	−0.867033	+	0.498250i	$0.833976\pi$
$798$	909.321	+	2085.33i	0.0403379	+	0.0925063i
$799$	10269.0	−	28213.8i	0.454681	−	1.24923i
$800$	10348.1	−	3744.30i	0.457326	−	0.165476i
$801$	27976.9	−	3494.50i	1.23410	−	0.154147i
$802$	−1789.14	−	479.399i	−0.0787740	−	0.0211074i
$803$	−460.576	−	322.498i	−0.0202408	−	0.0141728i
$804$	−10023.6	−	18415.2i	−0.439681	−	0.807778i
$805$	−7712.79	+	3186.22i	−0.337689	+	0.139502i
$806$	−1607.67	−	283.476i	−0.0702578	−	0.0123883i
$807$	−21545.6	−	32478.1i	−0.939827	−	1.41671i
$808$	6282.74	+	549.668i	0.273547	+	0.0239323i
$809$	−18113.8			−0.787201			−0.393600	−	0.919282i	$-0.628771\pi$
$809$	−18113.8			−0.787201			−0.393600	+	0.919282i	$0.628771\pi$
$810$	−1841.79	+	3418.49i	−0.0798938	+	0.148288i
$811$	−36277.5			−1.57075			−0.785373	−	0.619023i	$-0.787529\pi$
$811$	−36277.5			−1.57075			−0.785373	+	0.619023i	$0.787529\pi$
$812$	−12595.8	−	1101.99i	−0.544368	−	0.0476260i
$813$	−291.481	−	439.382i	−0.0125740	−	0.0189542i
$814$	−861.538	−	151.912i	−0.0370969	−	0.00654119i
$815$	−8919.67	+	21476.6i	−0.383365	+	0.923060i
$816$	−13447.2	−	24705.1i	−0.576895	−	1.05987i
$817$	26698.5	+	18694.5i	1.14328	+	0.800535i
$818$	−3715.46	−	995.554i	−0.158812	−	0.0425535i
$819$	16420.0	+	21695.5i	0.700561	+	0.925646i
$820$	−36393.6	−	18989.0i	−1.54990	−	0.808687i
$821$	1250.62	−	3436.05i	0.0531632	−	0.146065i	−0.910269	−	0.414018i	$-0.864125\pi$
$821$	1250.62	−	3436.05i	0.0531632	−	0.146065i	0.963432	+	0.267953i	$0.0863473\pi$
$822$	1340.01	+	3073.02i	0.0568590	+	0.130394i
$823$	−3342.40	−	38203.8i	−0.141566	−	1.61810i	−0.652021	−	0.758201i	$-0.726079\pi$
$823$	−3342.40	−	38203.8i	−0.141566	−	1.61810i	0.510456	−	0.859904i	$-0.329477\pi$
$824$	−6445.02	−	5408.01i	−0.272479	−	0.228637i
$825$	1538.19	−	2505.36i	0.0649128	−	0.105728i
$826$	356.015	+	129.579i	0.0149968	+	0.00545838i
$827$	37938.6	−	10165.6i	1.59523	−	0.427440i	0.651631	−	0.758536i	$-0.274085\pi$
$827$	37938.6	−	10165.6i	1.59523	−	0.427440i	0.943597	+	0.331097i	$0.107419\pi$
$828$	11446.3	−	423.664i	0.480419	−	0.0177818i
$829$	31788.0	−	18352.8i	1.33178	−	0.768901i	0.346204	−	0.938159i	$-0.387471\pi$
$829$	31788.0	−	18352.8i	1.33178	−	0.768901i	0.985572	+	0.169258i	$0.0541373\pi$
$830$	7099.51	−	1566.90i	0.296901	−	0.0655274i
$831$	−338.666	+	13471.0i	−0.0141374	+	0.562340i
$832$	−13293.7	+	28508.3i	−0.553936	+	1.18792i
$833$	−8263.06	−	11800.9i	−0.343695	−	0.490848i
$834$	−931.328	−	2773.81i	−0.0386681	−	0.115167i
$835$	−524.262	+	11753.0i	−0.0217279	+	0.487102i
$836$			2364.10i			0.0978038i
$837$	77.3812	+	6523.58i	0.00319556	+	0.269400i
$838$	2234.14	+	2234.14i	0.0920966	+	0.0920966i
$839$	−12177.6	+	10218.2i	−0.501093	+	0.420467i	−0.857982	−	0.513680i	$-0.828282\pi$
$839$	−12177.6	+	10218.2i	−0.501093	+	0.420467i	0.356889	+	0.934147i	$0.383838\pi$
$840$	5937.69	−	624.683i	0.243892	−	0.0256591i
$841$	−1778.53	+	10086.5i	−0.0729234	+	0.413569i
$842$	6031.58	+	2812.57i	0.246867	+	0.115116i
$843$	25529.4	−	6157.28i	1.04304	−	0.251564i
$844$	13764.5	−	2427.05i	0.561367	−	0.0989842i
$845$	−19389.6	−	30499.1i	−0.789378	−	1.24166i
$846$	−1906.03	−	3721.56i	−0.0774596	−	0.151241i
$847$	4638.74	+	17312.0i	0.188181	+	0.702300i
$848$	−432.925	+	201.876i	−0.0175315	+	0.00817508i
$849$	−10403.3	+	8292.89i	−0.420541	+	0.335231i
$850$	3163.65	−	4500.05i	0.127661	−	0.181589i
$851$	−14232.1	+	16961.1i	−0.573290	+	0.683220i
$852$	−2524.76	+	22367.3i	−0.101522	+	0.899403i
$853$	3077.12	+	6598.92i	0.123516	+	0.264880i	0.958337	−	0.285642i	$-0.0922067\pi$
$853$	3077.12	+	6598.92i	0.123516	+	0.264880i	−0.834821	+	0.550521i	$0.814429\pi$
$854$	−231.598	+	401.140i	−0.00928002	+	0.0160735i
$855$	−17643.0	+	10008.6i	−0.705703	+	0.400336i
$856$	−1233.79	−	2136.99i	−0.0492641	−	0.0853279i
$857$	3611.09	−	5157.17i	0.143935	−	0.205561i	−0.740711	−	0.671824i	$-0.765511\pi$
$857$	3611.09	−	5157.17i	0.143935	−	0.205561i	0.884646	+	0.466263i	$0.154400\pi$
$858$	−193.582	−	802.631i	−0.00770254	−	0.0319363i
$859$	9721.33	+	26709.1i	0.386132	+	1.06089i	0.968728	+	0.248127i	$0.0798150\pi$
$859$	9721.33	+	26709.1i	0.386132	+	1.06089i	−0.582596	+	0.812762i	$0.697963\pi$
$860$	33466.5	−	25629.6i	1.32697	−	1.01623i
$861$	−25163.2	−	22215.7i	−0.996005	−	0.879337i
$862$	−386.531	+	4418.07i	−0.0152730	+	0.174571i
$863$	−12184.8	+	12184.8i	−0.480619	+	0.480619i	−0.905329	−	0.424710i	$-0.860376\pi$
$863$	−12184.8	+	12184.8i	−0.480619	+	0.480619i	0.424710	+	0.905329i	$0.360376\pi$
$864$	−11967.5	−	3055.02i	−0.471231	−	0.120294i
$865$	15856.3	+	14557.2i	0.623271	+	0.572206i
$866$	−2523.65	−	3007.57i	−0.0990268	−	0.118016i
$867$	−16837.8	−	8373.07i	−0.659564	−	0.327987i
$868$	4049.38	−	2835.40i	0.158346	−	0.110875i
$869$	344.414	−	125.357i	0.0134447	−	0.00489347i
$870$	57.7862	+	3291.50i	0.00225188	+	0.128267i
$871$	6642.08	+	37669.1i	0.258391	+	1.46541i
$872$	−797.056	+	2974.65i	−0.0309538	+	0.115521i
$873$	1036.95	+	28015.6i	0.0402008	+	1.08612i
$874$	−1513.11	−	873.594i	−0.0585603	−	0.0338098i
$875$	−10223.7	−	16148.7i	−0.394999	−	0.623915i
$876$	4961.42	−	746.789i	0.191359	−	0.0288033i
$877$	17151.6	−	1500.57i	0.660396	−	0.0577772i	0.247969	−	0.968768i	$-0.420237\pi$
$877$	17151.6	−	1500.57i	0.660396	−	0.0577772i	0.412427	+	0.910991i	$0.364681\pi$
$878$	3764.09	−	329.315i	0.144683	−	0.0126581i
$879$	7639.02	−	19452.4i	0.293126	−	0.746430i
$880$	2827.55	+	894.457i	0.108314	+	0.0342638i
$881$	11967.7	+	6909.58i	0.457666	+	0.264233i	0.711062	−	0.703129i	$-0.248214\pi$
$881$	11967.7	+	6909.58i	0.457666	+	0.264233i	−0.253397	+	0.967362i	$0.581548\pi$
$882$	−1987.29	−	275.062i	−0.0758679	−	0.0105009i
$883$	−4284.58	+	15990.3i	−0.163293	+	0.609418i	0.834959	+	0.550313i	$0.185491\pi$
$883$	−4284.58	+	15990.3i	−0.163293	+	0.609418i	−0.998252	+	0.0591053i	$0.981175\pi$
$884$	9186.84	+	52101.2i	0.349533	+	1.98230i
$885$	−816.888	+	3277.77i	−0.0310276	+	0.124498i
$886$	−2510.77	+	913.845i	−0.0952042	+	0.0346515i
$887$	−31695.9	+	22193.7i	−1.19983	+	0.840127i	−0.990472	−	0.137713i	$-0.956025\pi$
$887$	−31695.9	+	22193.7i	−1.19983	+	0.840127i	−0.209353	+	0.977840i	$0.567136\pi$
$888$	13200.4	−	8757.02i	0.498848	−	0.330931i
$889$	−13384.4	−	15951.0i	−0.504949	−	0.601775i
$890$	−3761.64	+	4097.33i	−0.141674	+	0.154318i
$891$	−3008.73	+	1354.67i	−0.113127	+	0.0509349i
$892$	−17571.3	+	17571.3i	−0.659563	+	0.659563i
$893$	1903.64	−	21758.7i	0.0713357	−	0.815371i
$894$	315.145	−	1557.31i	0.0117897	−	0.0582598i
$895$	4953.91	+	656.952i	0.185018	+	0.0245357i
$896$	4245.67	+	11664.9i	0.158301	+	0.434929i
$897$	−20042.1	−	5913.97i	−0.746027	−	0.220136i
$898$	−4662.00	+	6658.03i	−0.173244	+	0.247418i
$899$	2765.48	+	4789.96i	0.102596	+	0.177702i
$900$	5459.53	+	25659.6i	0.202205	+	0.950354i
$901$	−376.448	+	652.027i	−0.0139193	+	0.0241090i
$902$	430.471	+	923.147i	0.0158904	+	0.0340770i
$903$	31595.8	−	13777.5i	1.16439	−	0.507737i
$904$	4363.59	−	5200.33i	0.160543	−	0.191328i
$905$	30006.7	−	39029.2i	1.10216	−	1.43356i
$906$	750.129	+	4983.60i	0.0275070	+	0.182747i
$907$	23998.2	−	11190.6i	0.878553	−	0.409676i	0.0696180	−	0.997574i	$-0.477822\pi$
$907$	23998.2	−	11190.6i	0.878553	−	0.409676i	0.808935	+	0.587898i	$0.200044\pi$
$908$	7315.04	+	27300.1i	0.267355	+	0.997782i
$909$	−5051.24	+	22089.8i	−0.184312	+	0.806022i
$910$	−5239.41	−	1166.74i	−0.190862	−	0.0425022i
$911$	47637.6	−	8399.79i	1.73250	−	0.305486i	0.783645	−	0.621209i	$-0.213358\pi$
$911$	47637.6	−	8399.79i	1.73250	−	0.305486i	0.948851	+	0.315723i	$0.102247\pi$
$912$	−14100.6	−	14827.8i	−0.511970	−	0.538376i
$913$	5599.14	+	2610.92i	0.202962	+	0.0946428i
$914$	−415.545	+	2356.67i	−0.0150383	+	0.0852864i
$915$	−3773.08	−	1679.43i	−0.136322	−	0.0606778i
$916$	−8081.05	+	6780.81i	−0.291491	+	0.244590i
$917$	−17676.6	−	17676.6i	−0.636569	−	0.636569i
$918$	−5776.17	+	2180.28i	−0.207671	+	0.0783879i
$919$			13418.9i			0.481665i	0.970567	+	0.240833i	$0.0774205\pi$
$919$			13418.9i			0.481665i	−0.970567	+	0.240833i	$0.922580\pi$
$920$	−3383.59	+	3094.62i	−0.121254	+	0.110899i
$921$	204.954	−	232.147i	0.00733275	−	0.00830563i
$922$	1772.95	+	2532.03i	0.0633286	+	0.0904426i
$923$	17354.8	−	37217.6i	0.618897	−	1.32723i
$924$	2133.12	+	1304.11i	0.0759464	+	0.0464310i
$925$	−43869.1	−	25438.3i	−1.55936	−	0.904224i
$926$	−5362.86	+	3096.25i	−0.190318	+	0.109880i
$927$	22422.3	−	20274.2i	0.794440	−	0.718329i
$928$	−10114.4	+	2710.15i	−0.357783	+	0.0958676i
$929$	−20923.0	−	7615.36i	−0.738926	−	0.268947i	−0.0549876	−	0.998487i	$-0.517512\pi$
$929$	−20923.0	−	7615.36i	−0.738926	−	0.268947i	−0.683938	+	0.729540i	$0.739734\pi$
$930$	−844.491	−	971.277i	−0.0297763	−	0.0342467i
$931$	−8028.16	−	6736.43i	−0.282613	−	0.237140i
$932$	−731.391	−	8359.84i	−0.0257055	−	0.293815i
$933$	5368.28	+	605.957i	0.188371	+	0.0212628i
$934$	444.691	−	1221.78i	0.0155789	−	0.0428028i
$935$	4459.29	−	1401.38i	0.155973	−	0.0490162i
$936$	12555.5	+	8116.35i	0.438449	+	0.283431i
$937$	−33362.4	−	8939.43i	−1.16318	−	0.311674i	−0.374947	−	0.927046i	$-0.622339\pi$
$937$	−33362.4	−	8939.43i	−1.16318	−	0.311674i	−0.788237	+	0.615372i	$0.789006\pi$
$938$	2770.59	+	1939.99i	0.0964425	+	0.0675298i
$939$	−2658.47	+	4348.42i	−0.0923917	+	0.151124i
$940$	−26088.0	−	10834.9i	−0.905209	−	0.375951i
$941$	15101.9	+	2662.87i	0.523175	+	0.0922499i	0.428998	−	0.903306i	$-0.358867\pi$
$941$	15101.9	+	2662.87i	0.523175	+	0.0922499i	0.0941774	+	0.995555i	$0.469978\pi$
$942$	−819.297	+	50.9696i	−0.0283377	+	0.00176293i
$943$	25681.3	+	2246.83i	0.886850	+	0.0775893i
$944$	−3407.64			−0.117489
$945$	−701.686	+	21440.3i	−0.0241543	+	0.738045i
$946$	−1045.96			−0.0359483
$947$	46585.5	+	4075.70i	1.59855	+	0.139855i	0.851296	−	0.524685i	$-0.175817\pi$
$947$	46585.5	+	4075.70i	1.59855	+	0.139855i	0.747253	+	0.664540i	$0.231373\pi$
$948$	−1456.28	+	2928.51i	−0.0498922	+	0.100331i
$949$	−9014.28	−	1589.46i	−0.308341	−	0.0543689i
$950$	1375.75	−	3757.75i	0.0469843	−	0.128334i
$951$	−48814.5	−	1227.21i	−1.66448	−	0.0418456i
$952$	7776.07	+	5444.86i	0.264731	+	0.185367i
$953$	−17008.0	−	4557.28i	−0.578114	−	0.154905i	−0.0420990	−	0.999113i	$-0.513404\pi$
$953$	−17008.0	−	4557.28i	−0.578114	−	0.154905i	−0.536015	+	0.844208i	$0.680071\pi$
$954$	30.8645	+	100.204i	0.00104746	+	0.00340065i
$955$	8653.06	−	16584.1i	0.293200	−	0.561937i
$956$	−11483.1	+	31549.6i	−0.388484	+	1.06735i
$957$	−1661.59	+	2250.42i	−0.0561249	+	0.0760144i
$958$	230.619	+	2635.99i	0.00777763	+	0.0888987i
$959$	14187.5	+	11904.7i	0.477726	+	0.400859i
$960$	−22289.0	+	10873.9i	−0.749348	+	0.365575i
$961$	25962.4	+	9449.53i	0.871483	+	0.317194i
$962$	−13756.6	+	3686.06i	−0.461049	+	0.123538i
$963$	8213.44	−	3338.43i	0.274843	−	0.111713i
$964$	31936.7	−	18438.7i	1.06702	−	0.616047i
$965$	−17645.0	−	11264.5i	−0.588615	−	0.375770i
$966$	−1622.92	+	883.373i	−0.0540546	+	0.0294224i
$967$	11485.5	−	24630.7i	0.381953	−	0.819101i	−0.617517	−	0.786557i	$-0.711861\pi$
$967$	11485.5	−	24630.7i	0.381953	−	0.819101i	0.999470	−	0.0325435i	$-0.0103607\pi$
$968$	5648.60	+	8067.04i	0.187555	+	0.267856i
$969$	−31610.4	−	6396.81i	−1.04796	−	0.212069i
$970$	−3732.65	−	4081.19i	−0.123555	−	0.135092i
$971$			43303.9i			1.43119i	0.698513	+	0.715597i	$0.253845\pi$
$971$			43303.9i			1.43119i	−0.698513	+	0.715597i	$0.746155\pi$
$972$	11125.5	−	27261.4i	0.367131	−	0.899597i
$973$	−11430.0	−	11430.0i	−0.376596	−	0.376596i
$974$	3202.28	−	2687.03i	0.105347	−	0.0883964i
$975$	5457.98	−	47547.8i	0.179277	−	1.56179i
$976$	723.448	−	4102.88i	0.0237264	−	0.134559i
$977$	−33824.1	−	15772.5i	−1.10760	−	0.516485i	−0.219262	−	0.975666i	$-0.570365\pi$
$977$	−33824.1	−	15772.5i	−1.10760	−	0.516485i	−0.888343	+	0.459181i	$0.848143\pi$
$978$	−1457.30	+	4938.69i	−0.0476474	+	0.161474i
$979$	−4654.65	+	820.741i	−0.151954	+	0.0267937i
$980$	−11438.2	+	7271.80i	−0.372838	+	0.237030i
$981$	−10194.3	−	4302.11i	−0.331784	−	0.140016i
$982$	−602.425	−	2248.28i	−0.0195765	−	0.0730606i
$983$	−3438.50	+	1603.40i	−0.111568	+	0.0520249i	−0.477601	−	0.878577i	$-0.658493\pi$
$983$	−3438.50	+	1603.40i	−0.111568	+	0.0520249i	0.366033	+	0.930602i	$0.380716\pi$
$984$	−17167.7	−	6741.81i	−0.556184	−	0.218416i
$985$	−56349.6	+	7364.47i	−1.82279	+	0.238225i
$986$	−3364.46	+	4009.61i	−0.108668	+	0.129505i
$987$	−18582.7	−	13720.5i	−0.599285	−	0.442479i
$988$	16265.1	+	34880.6i	0.523747	+	1.12318i
$989$	−13236.2	+	22925.8i	−0.425568	+	0.737105i
$990$	279.569	−	587.861i	0.00897504	−	0.0188722i
$991$	−11798.0	−	20434.7i	−0.378178	−	0.655024i	0.612619	−	0.790378i	$-0.290116\pi$
$991$	−11798.0	−	20434.7i	−0.378178	−	0.655024i	−0.990797	+	0.135354i	$0.956783\pi$
$992$	2348.17	−	3353.54i	0.0751558	−	0.107334i
$993$	38275.8	−	36398.5i	1.22321	−	1.16321i
$994$	−1241.94	−	3412.19i	−0.0396296	−	0.108881i
$995$	3020.98	−	22780.5i	0.0962527	−	0.725818i
$996$	−52261.8	+	17547.3i	−1.66263	+	0.558240i
$997$	−192.541	+	2200.76i	−0.00611619	+	0.0699084i	−0.998639	−	0.0521479i	$-0.983393\pi$
$997$	−192.541	+	2200.76i	−0.00611619	+	0.0699084i	0.992523	+	0.122056i	$0.0389488\pi$
$998$	4359.89	−	4359.89i	0.138287	−	0.138287i
$999$	24664.1	+	51294.9i	0.781118	+	1.62452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.q.a.113.26	yes	624
5.2	odd	4	inner	135.4.q.a.32.27	✓	624
27.11	odd	18	inner	135.4.q.a.38.27	yes	624
135.92	even	36	inner	135.4.q.a.92.26	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.q.a.32.27	✓	624	5.2	odd	4	inner
135.4.q.a.38.27	yes	624	27.11	odd	18	inner
135.4.q.a.92.26	yes	624	135.92	even	36	inner
135.4.q.a.113.26	yes	624	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.474611 - 0.0415231i) q^{2} +(-2.87247 - 4.33000i) q^{3} +(-7.65493 - 1.34977i) q^{4} +(4.26878 + 10.3333i) q^{5} +(1.18351 + 2.17434i) q^{6} +(11.2028 + 7.84429i) q^{7} +(7.25858 + 1.94493i) q^{8} +(-10.4978 + 24.8756i) q^{9} +O(q^{10})\)	\(q+(-0.474611 - 0.0415231i) q^{2} +(-2.87247 - 4.33000i) q^{3} +(-7.65493 - 1.34977i) q^{4} +(4.26878 + 10.3333i) q^{5} +(1.18351 + 2.17434i) q^{6} +(11.2028 + 7.84429i) q^{7} +(7.25858 + 1.94493i) q^{8} +(-10.4978 + 24.8756i) q^{9} +(-1.59694 - 5.08156i) q^{10} +(1.54807 - 4.25327i) q^{11} +(16.1441 + 37.0230i) q^{12} +(-6.42210 - 73.4049i) q^{13} +(-4.99125 - 4.18816i) q^{14} +(32.4813 - 48.1660i) q^{15} +(55.0698 + 20.0438i) q^{16} +(89.2214 - 23.9068i) q^{17} +(6.01527 - 11.3703i) q^{18} +(58.1927 - 33.5976i) q^{19} +(-18.7296 - 84.8627i) q^{20} +(1.78599 - 71.0407i) q^{21} +(-0.911337 + 1.95437i) q^{22} +(31.3040 + 44.7068i) q^{23} +(-12.4285 - 37.0164i) q^{24} +(-88.5550 + 88.2214i) q^{25} +35.1054i q^{26} +(137.866 - 25.9992i) q^{27} +(-75.1687 - 75.1687i) q^{28} +(91.1138 - 76.4535i) q^{29} +(-17.4160 + 21.5114i) q^{30} +(-8.07498 + 45.7955i) q^{31} +(-79.7890 - 37.2062i) q^{32} +(-22.8635 + 5.51430i) q^{33} +(-43.3381 + 7.64167i) q^{34} +(-33.2352 + 149.248i) q^{35} +(113.936 - 176.252i) q^{36} +(105.000 + 391.864i) q^{37} +(-29.0139 + 13.5294i) q^{38} +(-299.396 + 238.662i) q^{39} +(10.8877 + 83.3078i) q^{40} +(303.621 - 361.842i) q^{41} +(-3.79748 + 33.6425i) q^{42} +(204.990 + 439.602i) q^{43} +(-17.5913 + 30.4690i) q^{44} +(-301.861 - 2.28835i) q^{45} +(-13.0009 - 22.5182i) q^{46} +(186.441 - 266.266i) q^{47} +(-71.3970 - 296.027i) q^{48} +(-53.3429 - 146.558i) q^{49} +(45.6924 - 38.1937i) q^{50} +(-359.802 - 317.657i) q^{51} +(-49.9191 + 570.578i) q^{52} +(-5.76362 + 5.76362i) q^{53} +(-66.5123 + 6.61489i) q^{54} +(50.5588 - 2.15964i) q^{55} +(66.0599 + 78.7272i) q^{56} +(-312.634 - 155.466i) q^{57} +(-46.4182 + 32.5023i) q^{58} +(-54.6402 + 19.8874i) q^{59} +(-313.655 + 324.865i) q^{60} +(-12.3447 - 70.0102i) q^{61} +(5.73404 - 21.3997i) q^{62} +(-312.736 + 196.329i) q^{63} +(-369.697 - 213.444i) q^{64} +(731.102 - 379.711i) q^{65} +(11.0802 - 1.66779i) q^{66} +(-517.127 + 45.2427i) q^{67} +(-715.252 + 62.5764i) q^{68} +(103.660 - 263.966i) q^{69} +(21.9710 - 69.4546i) q^{70} +(482.639 + 278.652i) q^{71} +(-124.580 + 160.144i) q^{72} +(32.1510 - 119.989i) q^{73} +(-33.5626 - 190.343i) q^{74} +(636.370 + 130.030i) q^{75} +(-490.810 + 178.640i) q^{76} +(50.7066 - 35.5052i) q^{77} +(152.006 - 100.839i) q^{78} +(52.0505 + 62.0314i) q^{79} +(27.9622 + 654.616i) q^{80} +(-508.593 - 522.278i) q^{81} +(-159.127 + 159.127i) q^{82} +(-118.961 + 1359.73i) q^{83} +(-109.560 + 541.401i) q^{84} +(627.903 + 819.900i) q^{85} +(-79.0368 - 217.152i) q^{86} +(-592.766 - 174.912i) q^{87} +(19.5091 - 27.8619i) q^{88} +(-522.117 - 904.334i) q^{89} +(143.171 + 13.6202i) q^{90} +(503.864 - 872.719i) q^{91} +(-179.286 - 384.481i) q^{92} +(221.490 - 96.5817i) q^{93} +(-99.5431 + 118.631i) q^{94} +(595.586 + 457.903i) q^{95} +(68.0890 + 452.360i) q^{96} +(941.041 - 438.815i) q^{97} +(19.2315 + 71.7731i) q^{98} +(89.5516 + 83.1590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 624 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 18 * q^8	\( 624 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} + 702 q^{18} + 756 q^{20} - 24 q^{21} - 12 q^{22} - 324 q^{23} + 420 q^{25} - 900 q^{27} - 24 q^{28} - 1020 q^{30} - 24 q^{31} + 1752 q^{32} + 516 q^{33} + 2466 q^{35} + 984 q^{36} - 6 q^{37} - 132 q^{38} - 396 q^{40} + 1680 q^{41} - 2256 q^{42} - 12 q^{43} - 1332 q^{45} - 12 q^{46} - 3480 q^{47} - 3228 q^{48} - 684 q^{50} - 6840 q^{51} + 84 q^{52} - 24 q^{55} - 4752 q^{56} + 1842 q^{57} - 12 q^{58} - 2376 q^{60} - 132 q^{61} - 18 q^{62} + 2592 q^{63} + 2076 q^{65} + 9864 q^{66} + 3660 q^{67} + 2676 q^{68} - 12 q^{70} - 36 q^{71} + 1908 q^{72} - 6 q^{73} + 9300 q^{75} - 792 q^{76} - 3324 q^{77} - 606 q^{78} - 3336 q^{81} - 24 q^{82} - 2832 q^{83} - 12 q^{85} - 12516 q^{86} - 8640 q^{87} - 3036 q^{88} - 14532 q^{90} - 12 q^{91} - 1938 q^{92} + 6804 q^{93} - 4302 q^{95} + 3732 q^{96} + 6900 q^{97} - 5832 q^{98}+O(q^{100}) \) 624 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 + 702 * q^18 + 756 * q^20 - 24 * q^21 - 12 * q^22 - 324 * q^23 + 420 * q^25 - 900 * q^27 - 24 * q^28 - 1020 * q^30 - 24 * q^31 + 1752 * q^32 + 516 * q^33 + 2466 * q^35 + 984 * q^36 - 6 * q^37 - 132 * q^38 - 396 * q^40 + 1680 * q^41 - 2256 * q^42 - 12 * q^43 - 1332 * q^45 - 12 * q^46 - 3480 * q^47 - 3228 * q^48 - 684 * q^50 - 6840 * q^51 + 84 * q^52 - 24 * q^55 - 4752 * q^56 + 1842 * q^57 - 12 * q^58 - 2376 * q^60 - 132 * q^61 - 18 * q^62 + 2592 * q^63 + 2076 * q^65 + 9864 * q^66 + 3660 * q^67 + 2676 * q^68 - 12 * q^70 - 36 * q^71 + 1908 * q^72 - 6 * q^73 + 9300 * q^75 - 792 * q^76 - 3324 * q^77 - 606 * q^78 - 3336 * q^81 - 24 * q^82 - 2832 * q^83 - 12 * q^85 - 12516 * q^86 - 8640 * q^87 - 3036 * q^88 - 14532 * q^90 - 12 * q^91 - 1938 * q^92 + 6804 * q^93 - 4302 * q^95 + 3732 * q^96 + 6900 * q^97 - 5832 * q^98

Introduction

L-functions

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