LMFDB - Embedded newform 84.4.e.a.71.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, 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:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.12
Character	$\chi$	$=$	84.71
Dual form			84.4.e.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69169 + 2.26676i) q^{2} +(4.63286 - 2.35300i) q^{3} +(-2.27640 - 7.66929i) q^{4} +6.19268i q^{5} +(-2.50367 + 14.4821i) q^{6} +7.00000i q^{7} +(21.2354 + 7.81399i) q^{8} +(15.9268 - 21.8022i) q^{9} +(-14.0373 - 10.4761i) q^{10} +68.7622 q^{11} +(-28.5920 - 30.1744i) q^{12} +21.0411 q^{13} +(-15.8673 - 11.8418i) q^{14} +(14.5713 + 28.6898i) q^{15} +(-53.6360 + 34.9167i) q^{16} +112.772i q^{17} +(22.4772 + 72.9848i) q^{18} -57.7920i q^{19} +(47.4934 - 14.0970i) q^{20} +(16.4710 + 32.4300i) q^{21} +(-116.324 + 155.867i) q^{22} -106.466 q^{23} +(116.767 - 13.7657i) q^{24} +86.6508 q^{25} +(-35.5949 + 47.6950i) q^{26} +(22.4862 - 138.482i) q^{27} +(53.6850 - 15.9348i) q^{28} +14.4004i q^{29} +(-89.6830 - 15.5044i) q^{30} -117.828i q^{31} +(11.5876 - 180.648i) q^{32} +(318.566 - 161.797i) q^{33} +(-255.627 - 190.775i) q^{34} -43.3487 q^{35} +(-203.463 - 72.5168i) q^{36} -335.143 q^{37} +(131.000 + 97.7659i) q^{38} +(97.4803 - 49.5095i) q^{39} +(-48.3895 + 131.504i) q^{40} +105.821i q^{41} +(-101.375 - 17.5257i) q^{42} -287.527i q^{43} +(-156.530 - 527.357i) q^{44} +(135.014 + 98.6296i) q^{45} +(180.106 - 241.332i) q^{46} -355.416 q^{47} +(-166.329 + 287.970i) q^{48} -49.0000 q^{49} +(-146.586 + 196.416i) q^{50} +(265.353 + 522.458i) q^{51} +(-47.8978 - 161.370i) q^{52} -246.326i q^{53} +(275.867 + 285.239i) q^{54} +425.822i q^{55} +(-54.6979 + 148.648i) q^{56} +(-135.984 - 267.742i) q^{57} +(-32.6422 - 24.3610i) q^{58} +4.99979 q^{59} +(186.860 - 177.061i) q^{60} +476.146 q^{61} +(267.087 + 199.327i) q^{62} +(152.616 + 111.488i) q^{63} +(389.883 + 331.866i) q^{64} +130.300i q^{65} +(-172.158 + 995.822i) q^{66} +392.103i q^{67} +(864.883 - 256.714i) q^{68} +(-493.241 + 250.513i) q^{69} +(73.3324 - 98.2611i) q^{70} -346.845 q^{71} +(508.574 - 338.527i) q^{72} -1017.15 q^{73} +(566.956 - 759.688i) q^{74} +(401.441 - 203.889i) q^{75} +(-443.223 + 131.557i) q^{76} +481.335i q^{77} +(-52.6798 + 304.719i) q^{78} -164.386i q^{79} +(-216.228 - 332.151i) q^{80} +(-221.673 - 694.480i) q^{81} +(-239.870 - 179.015i) q^{82} -533.141 q^{83} +(211.221 - 200.144i) q^{84} -698.362 q^{85} +(651.754 + 486.405i) q^{86} +(33.8841 + 66.7151i) q^{87} +(1460.19 + 537.307i) q^{88} -506.353i q^{89} +(-451.971 + 139.194i) q^{90} +147.287i q^{91} +(242.358 + 816.516i) q^{92} +(-277.248 - 545.879i) q^{93} +(601.252 - 805.642i) q^{94} +357.887 q^{95} +(-371.381 - 864.183i) q^{96} +652.469 q^{97} +(82.8926 - 111.071i) q^{98} +(1095.16 - 1499.17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) $ 36 * q + 12 * q^4 + 30 * q^6 + 20 * q^9 - 132 * q^10 - 78 * q^12 + 324 * q^16 + 424 * q^18 - 240 * q^22 - 382 * q^24 - 900 * q^25 + 168 * q^28 + 476 * q^30 + 848 * q^33 - 576 * q^34 + 412 * q^36 + 528 * q^37 - 1068 * q^40 + 70 * q^42 - 984 * q^45 + 288 * q^46 + 526 * q^48 - 1764 * q^49 + 468 * q^52 - 1826 * q^54 + 1840 * q^57 + 1536 * q^58 + 652 * q^60 + 2448 * q^61 - 2604 * q^64 - 1188 * q^66 - 744 * q^69 + 252 * q^70 + 1888 * q^72 - 1656 * q^73 - 972 * q^76 - 1348 * q^78 + 2452 * q^81 + 888 * q^82 + 490 * q^84 + 2904 * q^85 + 4008 * q^88 + 3184 * q^90 - 6744 * q^93 + 3264 * q^94 - 1330 * q^96 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.69169	+	2.26676i	−0.598101	+	0.801420i
$2$	−1.69169	+	2.26676i	−0.598101	+	0.801420i
$3$	4.63286	−	2.35300i	0.891595	−	0.452834i
$3$	4.63286	−	2.35300i	0.891595	−	0.452834i
$4$	−2.27640	−	7.66929i	−0.284550	−	0.958661i
$5$			6.19268i			0.553890i	0.960886	+	0.276945i	$0.0893219\pi$
$5$			6.19268i			0.553890i	−0.960886	+	0.276945i	$0.910678\pi$
$6$	−2.50367	+	14.4821i	−0.170353	+	0.985383i
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	21.2354	+	7.81399i	0.938480	+	0.345333i
$9$	15.9268	−	21.8022i	0.589882	−	0.807490i
$10$	−14.0373	−	10.4761i	−0.443899	−	0.331282i
$11$	68.7622			1.88478			0.942390	−	0.334515i	$-0.108573\pi$
$11$	68.7622			1.88478			0.942390	+	0.334515i	$0.108573\pi$
$12$	−28.5920	−	30.1744i	−0.687818	−	0.725883i
$13$	21.0411			0.448903			0.224451	−	0.974485i	$-0.427941\pi$
$13$	21.0411			0.448903			0.224451	+	0.974485i	$0.427941\pi$
$14$	−15.8673	−	11.8418i	−0.302908	−	0.226061i
$15$	14.5713	+	28.6898i	0.250820	+	0.493845i
$16$	−53.6360	+	34.9167i	−0.838063	+	0.545573i
$17$			112.772i			1.60890i	0.594021	+	0.804449i	$0.297539\pi$
$17$			112.772i			1.60890i	−0.594021	+	0.804449i	$0.702461\pi$
$18$	22.4772	+	72.9848i	0.294330	+	0.955704i
$19$		−	57.7920i		−	0.697810i	−0.937158	−	0.348905i	$-0.886554\pi$
$19$		−	57.7920i		−	0.697810i	0.937158	−	0.348905i	$-0.113446\pi$
$20$	47.4934	−	14.0970i	0.530993	−	0.157609i
$21$	16.4710	+	32.4300i	0.171155	+	0.336991i
$22$	−116.324	+	155.867i	−1.12729	+	1.51050i
$23$	−106.466			−0.965201			−0.482600	−	0.875841i	$-0.660308\pi$
$23$	−106.466			−0.965201			−0.482600	+	0.875841i	$0.660308\pi$
$24$	116.767	−	13.7657i	0.993123	−	0.117079i
$25$	86.6508			0.693206
$26$	−35.5949	+	47.6950i	−0.268489	+	0.359760i
$27$	22.4862	−	138.482i	0.160276	−	0.987072i
$28$	53.6850	−	15.9348i	0.362340	−	0.107550i
$29$			14.4004i			0.0922099i	0.998937	+	0.0461050i	$0.0146809\pi$
$29$			14.4004i			0.0922099i	−0.998937	+	0.0461050i	$0.985319\pi$
$30$	−89.6830	−	15.5044i	−0.545794	−	0.0943568i
$31$		−	117.828i		−	0.682661i	−0.939943	−	0.341330i	$-0.889123\pi$
$31$		−	117.828i		−	0.682661i	0.939943	−	0.341330i	$-0.110877\pi$
$32$	11.5876	−	180.648i	0.0640129	−	0.997949i
$33$	318.566	−	161.797i	1.68046	−	0.853494i
$34$	−255.627	−	190.775i	−1.28940	−	0.962284i
$35$	−43.3487			−0.209351
$36$	−203.463	−	72.5168i	−0.941960	−	0.335726i
$37$	−335.143			−1.48911			−0.744556	−	0.667561i	$-0.767339\pi$
$37$	−335.143			−1.48911			−0.744556	+	0.667561i	$0.767339\pi$
$38$	131.000	+	97.7659i	0.559239	+	0.417361i
$39$	97.4803	−	49.5095i	0.400239	−	0.203279i
$40$	−48.3895	+	131.504i	−0.191276	+	0.519815i
$41$			105.821i			0.403083i	0.979480	+	0.201541i	$0.0645951\pi$
$41$			105.821i			0.403083i	−0.979480	+	0.201541i	$0.935405\pi$
$42$	−101.375	−	17.5257i	−0.372440	−	0.0643874i
$43$		−	287.527i		−	1.01971i	−0.860261	−	0.509854i	$-0.829700\pi$
$43$		−	287.527i		−	1.01971i	0.860261	−	0.509854i	$-0.170300\pi$
$44$	−156.530	−	527.357i	−0.536314	−	1.80687i
$45$	135.014	+	98.6296i	0.447260	+	0.326730i
$46$	180.106	−	241.332i	0.577288	−	0.773532i
$47$	−355.416			−1.10304			−0.551519	−	0.834163i	$-0.685951\pi$
$47$	−355.416			−1.10304			−0.551519	+	0.834163i	$0.685951\pi$
$48$	−166.329	+	287.970i	−0.500158	+	0.865934i
$49$	−49.0000			−0.142857
$50$	−146.586	+	196.416i	−0.414607	+	0.555550i
$51$	265.353	+	522.458i	0.728565	+	1.43449i
$52$	−47.8978	−	161.370i	−0.127735	−	0.430346i
$53$		−	246.326i		−	0.638404i	−0.947687	−	0.319202i	$-0.896585\pi$
$53$		−	246.326i		−	0.638404i	0.947687	−	0.319202i	$-0.103415\pi$
$54$	275.867	+	285.239i	0.695198	+	0.718818i
$55$			425.822i			1.04396i
$56$	−54.6979	+	148.648i	−0.130523	+	0.354712i
$57$	−135.984	−	267.742i	−0.315992	−	0.622163i
$58$	−32.6422	−	24.3610i	−0.0738989	−	0.0551509i
$59$	4.99979			0.0110325			0.00551625	−	0.999985i	$-0.498244\pi$
$59$	4.99979			0.0110325			0.00551625	+	0.999985i	$0.498244\pi$
$60$	186.860	−	177.061i	0.402059	−	0.380975i
$61$	476.146			0.999413			0.499707	−	0.866195i	$-0.333441\pi$
$61$	476.146			0.999413			0.499707	+	0.866195i	$0.333441\pi$
$62$	267.087	+	199.327i	0.547098	+	0.408300i
$63$	152.616	+	111.488i	0.305202	+	0.222954i
$64$	389.883	+	331.866i	0.761491	+	0.648176i
$65$			130.300i			0.248643i
$66$	−172.158	+	995.822i	−0.321078	+	1.85723i
$67$			392.103i			0.714970i	0.933919	+	0.357485i	$0.116366\pi$
$67$			392.103i			0.714970i	−0.933919	+	0.357485i	$0.883634\pi$
$68$	864.883	−	256.714i	1.54239	−	0.457811i
$69$	−493.241	+	250.513i	−0.860568	+	0.437076i
$70$	73.3324	−	98.2611i	0.125213	−	0.167778i
$71$	−346.845			−0.579760			−0.289880	−	0.957063i	$-0.593615\pi$
$71$	−346.845			−0.579760			−0.289880	+	0.957063i	$0.593615\pi$
$72$	508.574	−	338.527i	0.832445	−	0.554108i
$73$	−1017.15			−1.63080			−0.815402	−	0.578896i	$-0.803484\pi$
$73$	−1017.15			−1.63080			−0.815402	+	0.578896i	$0.803484\pi$
$74$	566.956	−	759.688i	0.890639	−	1.19340i
$75$	401.441	−	203.889i	0.618059	−	0.313908i
$76$	−443.223	+	131.557i	−0.668963	+	0.198562i
$77$			481.335i			0.712380i
$78$	−52.6798	+	304.719i	−0.0764720	+	0.442341i
$79$		−	164.386i		−	0.234113i	−0.993125	−	0.117056i	$-0.962654\pi$
$79$		−	164.386i		−	0.234113i	0.993125	−	0.117056i	$-0.0373458\pi$
$80$	−216.228	−	332.151i	−0.302188	−	0.464195i
$81$	−221.673	−	694.480i	−0.304079	−	0.952647i
$82$	−239.870	−	179.015i	−0.323039	−	0.241084i
$83$	−533.141			−0.705058			−0.352529	−	0.935801i	$-0.614678\pi$
$83$	−533.141			−0.705058			−0.352529	+	0.935801i	$0.614678\pi$
$84$	211.221	−	200.144i	0.274358	−	0.259971i
$85$	−698.362			−0.891152
$86$	651.754	+	486.405i	0.817214	+	0.609888i
$87$	33.8841	+	66.7151i	0.0417558	+	0.0822139i
$88$	1460.19	+	537.307i	1.76883	+	0.650876i
$89$		−	506.353i		−	0.603071i	−0.953455	−	0.301536i	$-0.902501\pi$
$89$		−	506.353i		−	0.603071i	0.953455	−	0.301536i	$-0.0974992\pi$
$90$	−451.971	+	139.194i	−0.529355	+	0.163026i
$91$			147.287i			0.169669i
$92$	242.358	+	816.516i	0.274648	+	0.925301i
$93$	−277.248	−	545.879i	−0.309132	−	0.608656i
$94$	601.252	−	805.642i	0.659728	−	0.883997i
$95$	357.887			0.386510
$96$	−371.381	−	864.183i	−0.394832	−	0.918753i
$97$	652.469			0.682971			0.341485	−	0.939887i	$-0.389070\pi$
$97$	652.469			0.682971			0.341485	+	0.939887i	$0.389070\pi$
$98$	82.8926	−	111.071i	0.0854430	−	0.114489i
$99$	1095.16	−	1499.17i	1.11180	−	1.52194i
$100$	−197.252	−	664.550i	−0.197252	−	0.664550i
$101$			949.009i			0.934950i	0.884006	+	0.467475i	$0.154836\pi$
$101$			949.009i			0.934950i	−0.884006	+	0.467475i	$0.845164\pi$
$102$	−1633.18	−	282.344i	−1.58538	−	0.274081i
$103$			1582.09i			1.51348i	0.653719	+	0.756738i	$0.273208\pi$
$103$			1582.09i			1.51348i	−0.653719	+	0.756738i	$0.726792\pi$
$104$	446.815	+	164.414i	0.421287	+	0.155021i
$105$	−200.829	+	101.999i	−0.186656	+	0.0948012i
$106$	558.361	+	416.705i	0.511630	+	0.381830i
$107$	−503.414			−0.454830			−0.227415	−	0.973798i	$-0.573027\pi$
$107$	−503.414			−0.454830			−0.227415	+	0.973798i	$0.573027\pi$
$108$	−1113.25	+	142.788i	−0.991875	+	0.127220i
$109$	267.700			0.235239			0.117619	−	0.993059i	$-0.462474\pi$
$109$	267.700			0.235239			0.117619	+	0.993059i	$0.462474\pi$
$110$	−965.236	−	720.357i	−0.836652	−	0.624394i
$111$	−1552.67	+	788.590i	−1.32768	+	0.674321i
$112$	−244.417	−	375.452i	−0.206207	−	0.316758i
$113$			347.219i			0.289058i	0.989501	+	0.144529i	$0.0461668\pi$
$113$			347.219i			0.289058i	−0.989501	+	0.144529i	$0.953833\pi$
$114$	836.950	+	144.692i	0.687610	+	0.118874i
$115$		−	659.307i		−	0.534615i
$116$	110.441	−	32.7810i	0.0883981	−	0.0262383i
$117$	335.117	−	458.742i	0.264800	−	0.362484i
$118$	−8.45807	+	11.3333i	−0.00659855	+	0.00884167i
$119$	−789.405			−0.608106
$120$	85.2464	+	723.100i	0.0648491	+	0.550080i
$121$	3397.24			2.55240
$122$	−805.489	+	1079.31i	−0.597750	+	0.800950i
$123$	248.995	+	490.252i	0.182530	+	0.359386i
$124$	−903.655	+	268.223i	−0.654440	+	0.194251i
$125$			1310.68i			0.937850i
$126$	−510.893	+	157.341i	−0.361222	+	0.111246i
$127$		−	1122.08i		−	0.784007i	−0.919964	−	0.392003i	$-0.871782\pi$
$127$		−	1122.08i		−	0.784007i	0.919964	−	0.392003i	$-0.128218\pi$
$128$	−1411.82	+	322.358i	−0.974910	+	0.222599i
$129$	−676.550	−	1332.07i	−0.461759	−	0.909166i
$130$	−295.360	−	220.427i	−0.199267	−	0.148714i
$131$	−770.765			−0.514061			−0.257031	−	0.966403i	$-0.582744\pi$
$131$	−770.765			−0.514061			−0.257031	+	0.966403i	$0.582744\pi$
$132$	−1966.05	−	2074.86i	−1.29639	−	1.36813i
$133$	404.544			0.263747
$134$	−888.803	−	663.315i	−0.572992	−	0.427624i
$135$	857.577	+	139.250i	0.546729	+	0.0887755i
$136$	−881.200	+	2394.76i	−0.555605	+	1.50992i
$137$		−	2713.01i		−	1.69188i	−0.533277	−	0.845941i	$-0.679040\pi$
$137$		−	2713.01i		−	1.69188i	0.533277	−	0.845941i	$-0.320960\pi$
$138$	266.555	−	1541.85i	0.164425	−	0.951093i
$139$		−	389.470i		−	0.237658i	−0.992915	−	0.118829i	$-0.962086\pi$
$139$		−	389.470i		−	0.237658i	0.992915	−	0.118829i	$-0.0379140\pi$
$140$	98.6789	+	332.454i	0.0595707	+	0.200696i
$141$	−1646.59	+	836.293i	−0.983462	+	0.499493i
$142$	586.753	−	786.215i	0.346755	−	0.464632i
$143$	1446.83			0.846083
$144$	−92.9895	+	1725.50i	−0.0538134	+	0.998551i
$145$	−89.1770			−0.0510741
$146$	1720.70	−	2305.64i	0.975386	−	1.30696i
$147$	−227.010	+	115.297i	−0.127371	+	0.0646906i
$148$	762.918	+	2570.31i	0.423726	+	1.42755i
$149$			1762.16i			0.968874i	0.874826	+	0.484437i	$0.160975\pi$
$149$			1762.16i			0.968874i	−0.874826	+	0.484437i	$0.839025\pi$
$150$	−216.945	+	1254.89i	−0.118090	+	0.683074i
$151$		−	3600.16i		−	1.94025i	−0.242615	−	0.970123i	$-0.578005\pi$
$151$		−	3600.16i		−	1.94025i	0.242615	−	0.970123i	$-0.421995\pi$
$152$	451.586	−	1227.23i	0.240977	−	0.654881i
$153$	2458.68	+	1796.10i	1.29917	+	0.949060i
$154$	−1091.07	−	814.268i	−0.570916	−	0.426075i
$155$	729.669			0.378119
$156$	−601.607	−	634.901i	−0.308763	−	0.325851i
$157$	135.955			0.0691107			0.0345554	−	0.999403i	$-0.488998\pi$
$157$	135.955			0.0691107			0.0345554	+	0.999403i	$0.488998\pi$
$158$	372.624	+	278.090i	0.187623	+	0.140023i
$159$	−579.603	−	1141.19i	−0.289091	−	0.569198i
$160$	1118.70	+	71.7580i	0.552754	+	0.0354561i
$161$		−	745.259i		−	0.364812i
$162$	1949.22	+	672.361i	0.945341	+	0.326085i
$163$			209.411i			0.100628i	0.998733	+	0.0503139i	$0.0160222\pi$
$163$			209.411i			0.100628i	−0.998733	+	0.0503139i	$0.983978\pi$
$164$	811.569	−	240.890i	0.386420	−	0.114697i
$165$	1001.96	+	1972.77i	0.472741	+	0.930790i
$166$	901.907	−	1208.50i	0.421696	−	0.565048i
$167$	3285.32			1.52231			0.761155	−	0.648570i	$-0.224633\pi$
$167$	3285.32			1.52231			0.761155	+	0.648570i	$0.224633\pi$
$168$	96.3597	+	817.368i	0.0442519	+	0.375365i
$169$	−1754.27			−0.798486
$170$	1181.41	−	1583.02i	0.532999	−	0.714188i
$171$	−1259.99	−	920.442i	−0.563474	−	0.411625i
$172$	−2205.13	+	654.525i	−0.977554	+	0.290157i
$173$			3187.70i			1.40091i	0.713699	+	0.700453i	$0.247019\pi$
$173$			3187.70i			1.40091i	−0.713699	+	0.700453i	$0.752981\pi$
$174$	−208.548	−	36.0538i	−0.0908621	−	0.0157082i
$175$			606.555i			0.262007i
$176$	−3688.13	+	2400.95i	−1.57956	+	1.02829i
$177$	23.1633	−	11.7645i	0.00983651	−	0.00499589i
$178$	1147.78	+	856.591i	0.483314	+	0.360698i
$179$	514.995			0.215042			0.107521	−	0.994203i	$-0.465709\pi$
$179$	514.995			0.215042			0.107521	+	0.994203i	$0.465709\pi$
$180$	449.073	−	1259.98i	0.185955	−	0.521742i
$181$	−564.937			−0.231997			−0.115998	−	0.993249i	$-0.537007\pi$
$181$	−564.937			−0.231997			−0.115998	+	0.993249i	$0.537007\pi$
$182$	−333.865	−	249.164i	−0.135976	−	0.101479i
$183$	2205.92	−	1120.37i	0.891071	−	0.452569i
$184$	−2260.84	−	831.921i	−0.905822	−	0.333315i
$185$		−	2075.43i		−	0.824803i
$186$	1706.39	+	295.002i	0.672682	+	0.116293i
$187$			7754.47i			3.03242i
$188$	809.068	+	2725.79i	0.313869	+	1.05744i
$189$	969.377	+	157.403i	0.373078	+	0.0605788i
$190$	−605.432	+	811.244i	−0.231172	+	0.309757i
$191$	−1865.70			−0.706793			−0.353396	−	0.935474i	$-0.614973\pi$
$191$	−1865.70			−0.706793			−0.353396	+	0.935474i	$0.614973\pi$
$192$	2587.15	+	620.095i	0.972457	+	0.233081i
$193$	−1068.54			−0.398524			−0.199262	−	0.979946i	$-0.563855\pi$
$193$	−1068.54			−0.398524			−0.199262	+	0.979946i	$0.563855\pi$
$194$	−1103.77	+	1478.99i	−0.408486	+	0.547347i
$195$	306.596	+	603.664i	0.112594	+	0.221689i
$196$	111.543	+	375.795i	0.0406499	+	0.136952i
$197$		−	4223.90i		−	1.52761i	−0.645444	−	0.763807i	$-0.723328\pi$
$197$		−	4223.90i		−	1.52761i	0.645444	−	0.763807i	$-0.276672\pi$
$198$	1545.58	+	5018.59i	0.554747	+	1.80129i
$199$		−	4084.37i		−	1.45494i	−0.686138	−	0.727471i	$-0.740696\pi$
$199$		−	4084.37i		−	1.45494i	0.686138	−	0.727471i	$-0.259304\pi$
$200$	1840.06	+	677.088i	0.650560	+	0.239387i
$201$	922.617	+	1816.56i	0.323763	+	0.637463i
$202$	−2151.18	−	1605.43i	−0.749288	−	0.559195i
$203$	−100.803			−0.0348521
$204$	3402.83	−	3224.39i	1.16787	−	1.10663i
$205$	−655.312			−0.223263
$206$	−3586.22	−	2676.40i	−1.21293	−	0.905212i
$207$	−1695.66	+	2321.19i	−0.569355	+	0.779390i
$208$	−1128.56	+	734.684i	−0.376209	+	0.244909i
$209$		−	3973.90i		−	1.31522i
$210$	108.531	−	627.781i	0.0356635	−	0.206291i
$211$		−	1912.31i		−	0.623927i	−0.950094	−	0.311964i	$-0.899013\pi$
$211$		−	1912.31i		−	0.623927i	0.950094	−	0.311964i	$-0.100987\pi$
$212$	−1889.14	+	560.735i	−0.612013	+	0.181658i
$213$	−1606.89	+	816.126i	−0.516911	+	0.262535i
$214$	851.618	−	1141.12i	0.272035	−	0.364510i
$215$	1780.56			0.564805
$216$	1559.60	−	2765.02i	0.491285	−	0.870999i
$217$	824.794			0.258021
$218$	−452.865	+	606.812i	−0.140697	+	0.188525i
$219$	−4712.32	+	2393.36i	−1.45402	+	0.738484i
$220$	3265.75	−	969.340i	1.00080	−	0.297059i
$221$			2372.85i			0.722239i
$222$	839.086	−	4853.57i	0.253675	−	1.46734i
$223$			5284.04i			1.58675i	0.608732	+	0.793376i	$0.291678\pi$
$223$			5284.04i			1.58675i	−0.608732	+	0.793376i	$0.708322\pi$
$224$	1264.54	+	81.1130i	0.377189	+	0.0241946i
$225$	1380.07	−	1889.18i	0.408910	−	0.559757i
$226$	−787.062	−	587.385i	−0.231657	−	0.172886i
$227$	2286.43			0.668527			0.334264	−	0.942480i	$-0.391512\pi$
$227$	2286.43			0.668527			0.334264	+	0.942480i	$0.391512\pi$
$228$	−1743.84	+	1652.39i	−0.506529	+	0.479966i
$229$	−3378.21			−0.974841			−0.487420	−	0.873167i	$-0.662062\pi$
$229$	−3378.21			−0.974841			−0.487420	+	0.873167i	$0.662062\pi$
$230$	1494.49	+	1115.34i	0.428451	+	0.319754i
$231$	1132.58	+	2229.96i	0.322590	+	0.635154i
$232$	−112.525	+	305.798i	−0.0318431	+	0.0865372i
$233$		−	3279.45i		−	0.922077i	−0.887380	−	0.461038i	$-0.847477\pi$
$233$		−	3279.45i		−	0.922077i	0.887380	−	0.461038i	$-0.152523\pi$
$234$	472.944	+	1535.68i	0.132125	+	0.429018i
$235$		−	2200.98i		−	0.610961i
$236$	−11.3815	−	38.3448i	−0.00313929	−	0.0105764i
$237$	−386.801	−	761.580i	−0.106014	−	0.208734i
$238$	1335.43	−	1789.39i	0.363709	−	0.487349i
$239$	540.789			0.146363			0.0731814	−	0.997319i	$-0.476685\pi$
$239$	540.789			0.146363			0.0731814	+	0.997319i	$0.476685\pi$
$240$	−1783.30	−	1030.02i	−0.479632	−	0.277032i
$241$	2219.30			0.593186			0.296593	−	0.955004i	$-0.404150\pi$
$241$	2219.30			0.593186			0.296593	+	0.955004i	$0.404150\pi$
$242$	−5747.07	+	7700.73i	−1.52659	+	2.04554i
$243$	−2661.09	−	2695.83i	−0.702506	−	0.711678i
$244$	−1083.90	−	3651.70i	−0.284383	−	0.958099i
$245$		−	303.441i		−	0.0791271i
$246$	−1532.51	−	264.940i	−0.397191	−	0.0686664i
$247$		−	1216.00i		−	0.313249i
$248$	920.704	−	2502.12i	0.235745	−	0.640663i
$249$	−2469.97	+	1254.48i	−0.628626	+	0.319275i
$250$	−2971.01	−	2217.27i	−0.751612	−	0.560929i
$251$	−5036.94			−1.26665			−0.633325	−	0.773886i	$-0.718310\pi$
$251$	−5036.94			−1.26665			−0.633325	+	0.773886i	$0.718310\pi$
$252$	507.618	−	1424.24i	0.126893	−	0.356027i
$253$	−7320.81			−1.81919
$254$	2543.49	+	1898.21i	0.628319	+	0.468915i
$255$	−3235.41	+	1643.24i	−0.794547	+	0.403545i
$256$	1657.65	−	3745.59i	0.404699	−	0.914450i
$257$			2752.40i			0.668054i	0.942563	+	0.334027i	$0.108408\pi$
$257$			2752.40i			0.668054i	−0.942563	+	0.334027i	$0.891592\pi$
$258$	4164.00	+	719.872i	1.00480	+	0.173710i
$259$		−	2346.00i		−	0.562831i
$260$	999.312	−	296.615i	0.238364	−	0.0707512i
$261$	313.961	+	229.352i	0.0744585	+	0.0543930i
$262$	1303.89	−	1747.14i	0.307461	−	0.411979i
$263$	−1457.14			−0.341640			−0.170820	−	0.985302i	$-0.554642\pi$
$263$	−1457.14			−0.341640			−0.170820	+	0.985302i	$0.554642\pi$
$264$	8029.15	−	946.558i	1.87182	−	0.220669i
$265$	1525.41			0.353605
$266$	−684.361	+	917.003i	−0.157748	+	0.211372i
$267$	−1191.45	−	2345.86i	−0.273091	−	0.537695i
$268$	3007.15	−	892.582i	0.685414	−	0.203444i
$269$			1797.48i			0.407415i	0.979032	+	0.203707i	$0.0652991\pi$
$269$			1797.48i			0.407415i	−0.979032	+	0.203707i	$0.934701\pi$
$270$	−1766.40	+	1708.35i	−0.398146	+	0.385063i
$271$		−	2553.52i		−	0.572381i	−0.958173	−	0.286191i	$-0.907611\pi$
$271$		−	2553.52i		−	0.572381i	0.958173	−	0.286191i	$-0.0923891\pi$
$272$	−3937.63	−	6048.65i	−0.877772	−	1.34836i
$273$	346.567	+	682.362i	0.0768321	+	0.151276i
$274$	6149.73	+	4589.56i	1.35591	+	1.01192i
$275$	5958.30			1.30654
$276$	3044.07	+	3212.54i	0.663882	+	0.700623i
$277$	−1669.52			−0.362136			−0.181068	−	0.983471i	$-0.557955\pi$
$277$	−1669.52			−0.362136			−0.181068	+	0.983471i	$0.557955\pi$
$278$	882.835	+	658.861i	0.190464	+	0.142143i
$279$	−2568.90	−	1876.62i	−0.551241	−	0.402689i
$280$	−920.527	−	338.726i	−0.196471	−	0.0722956i
$281$		−	3317.21i		−	0.704229i	−0.935957	−	0.352114i	$-0.885463\pi$
$281$		−	3317.21i		−	0.704229i	0.935957	−	0.352114i	$-0.114537\pi$
$282$	889.844	−	5147.17i	0.187906	−	1.08691i
$283$			3255.20i			0.683751i	0.939745	+	0.341876i	$0.111062\pi$
$283$			3255.20i			0.683751i	−0.939745	+	0.341876i	$0.888938\pi$
$284$	789.558	+	2660.06i	0.164971	+	0.555794i
$285$	1658.04	−	842.107i	0.344610	−	0.175025i
$286$	−2447.58	+	3279.61i	−0.506044	+	0.678069i
$287$	−740.744			−0.152351
$288$	−3753.98	−	3129.78i	−0.768073	−	0.640362i
$289$	−7804.57			−1.58855
$290$	150.860	−	202.143i	0.0305475	−	0.0409319i
$291$	3022.80	−	1535.26i	0.608933	−	0.309273i
$292$	2315.44	+	7800.83i	0.464044	+	1.56339i
$293$		−	3355.38i		−	0.669021i	−0.942392	−	0.334510i	$-0.891429\pi$
$293$		−	3355.38i		−	0.669021i	0.942392	−	0.334510i	$-0.108571\pi$
$294$	122.680	−	709.624i	0.0243362	−	0.140769i
$295$			30.9621i			0.00611079i
$296$	−7116.88	−	2618.80i	−1.39750	−	0.514239i
$297$	1546.20	−	9522.36i	0.302086	−	1.86041i
$298$	−3994.40	−	2981.03i	−0.776475	−	0.579485i
$299$	−2240.15			−0.433281
$300$	−2477.52	−	2614.64i	−0.476799	−	0.503187i
$301$	2012.69			0.385413
$302$	8160.70	+	6090.34i	1.55495	+	1.16046i
$303$	2233.02	+	4396.63i	0.423378	+	0.833596i
$304$	2017.90	+	3099.73i	0.380706	+	0.584809i
$305$			2948.62i			0.553565i
$306$	−8230.65	+	2534.81i	−1.53763	+	0.473546i
$307$			5173.42i			0.961768i	0.876784	+	0.480884i	$0.159684\pi$
$307$			5173.42i			0.961768i	−0.876784	+	0.480884i	$0.840316\pi$
$308$	3691.50	−	1095.71i	0.682931	−	0.202707i
$309$	3722.65	+	7329.60i	0.685354	+	1.34941i
$310$	−1234.37	+	1653.98i	−0.226153	+	0.303032i
$311$	6703.69			1.22229			0.611144	−	0.791520i	$-0.290710\pi$
$311$	6703.69			1.22229			0.611144	+	0.791520i	$0.290710\pi$
$312$	2456.90	−	289.644i	0.445816	−	0.0525573i
$313$	10677.3			1.92817			0.964085	−	0.265594i	$-0.0855680\pi$
$313$	10677.3			1.92817			0.964085	+	0.265594i	$0.0855680\pi$
$314$	−229.993	+	308.177i	−0.0413352	+	0.0553867i
$315$	−690.407	+	945.098i	−0.123492	+	0.169048i
$316$	−1260.73	+	374.209i	−0.224435	+	0.0666167i
$317$			10683.1i			1.89282i	0.322969	+	0.946410i	$0.395319\pi$
$317$			10683.1i			1.89282i	−0.322969	+	0.946410i	$0.604681\pi$
$318$	3567.31	+	616.718i	0.629072	+	0.108754i
$319$			990.203i			0.173795i
$320$	−2055.14	+	2414.42i	−0.359018	+	0.421782i
$321$	−2332.25	+	1184.53i	−0.405524	+	0.205963i
$322$	1689.32	+	1260.75i	0.292368	+	0.218194i
$323$	6517.33			1.12271
$324$	−4821.55	+	3280.99i	−0.826740	+	0.562584i
$325$	1823.22			0.311182
$326$	−474.684	−	354.257i	−0.0806451	−	0.0601856i
$327$	1240.22	−	629.898i	0.209738	−	0.106524i
$328$	−826.880	+	2247.14i	−0.139198	+	0.378285i
$329$		−	2487.91i		−	0.416909i
$330$	−6166.80	−	1066.12i	−1.02870	−	0.177842i
$331$		−	1250.05i		−	0.207579i	−0.994599	−	0.103790i	$-0.966903\pi$
$331$		−	1250.05i		−	0.207579i	0.994599	−	0.103790i	$-0.0330969\pi$
$332$	1213.64	+	4088.81i	0.200624	+	0.675912i
$333$	−5337.75	+	7306.85i	−0.878400	+	1.20244i
$334$	−5557.73	+	7447.03i	−0.910495	+	1.22001i
$335$	−2428.17			−0.396015
$336$	−2015.79	−	1164.31i	−0.327292	−	0.189042i
$337$	7570.90			1.22378			0.611889	−	0.790944i	$-0.290410\pi$
$337$	7570.90			1.22378			0.611889	+	0.790944i	$0.290410\pi$
$338$	2967.68	−	3976.52i	0.477576	−	0.639923i
$339$	817.005	+	1608.62i	0.130896	+	0.257723i
$340$	1589.75	+	5355.94i	0.253577	+	0.854313i
$341$		−	8102.09i		−	1.28667i
$342$	4217.93	−	1299.00i	0.666900	−	0.205386i
$343$		−	343.000i		−	0.0539949i
$344$	2246.73	−	6105.74i	0.352138	−	0.956975i
$345$	−1551.35	−	3054.48i	−0.242092	−	0.476660i
$346$	−7225.76	−	5392.59i	−1.12271	−	0.837883i
$347$	−5145.12			−0.795979			−0.397989	−	0.917390i	$-0.630292\pi$
$347$	−5145.12			−0.795979			−0.397989	+	0.917390i	$0.630292\pi$
$348$	434.524	−	411.737i	0.0669336	−	0.0634236i
$349$	6454.15			0.989923			0.494961	−	0.868915i	$-0.335182\pi$
$349$	6454.15			0.989923			0.494961	+	0.868915i	$0.335182\pi$
$350$	−1374.92	−	1026.10i	−0.209978	−	0.156707i
$351$	473.133	−	2913.82i	0.0719486	−	0.443100i
$352$	796.787	−	12421.8i	0.120650	−	1.88092i
$353$			10310.8i			1.55464i	0.629106	+	0.777319i	$0.283421\pi$
$353$			10310.8i			1.55464i	−0.629106	+	0.777319i	$0.716579\pi$
$354$	−12.5178	+	72.4075i	−0.00187942	+	0.0108712i
$355$		−	2147.90i		−	0.321123i
$356$	−3883.37	+	1152.66i	−0.578141	+	0.171604i
$357$	−3657.21	+	1857.47i	−0.542184	+	0.275372i
$358$	−871.210	+	1167.37i	−0.128617	+	0.172339i
$359$	953.991			0.140250			0.0701250	−	0.997538i	$-0.477660\pi$
$359$	953.991			0.140250			0.0701250	+	0.997538i	$0.477660\pi$
$360$	2096.39	+	3149.44i	0.306915	+	0.461083i
$361$	3519.09			0.513062
$362$	955.696	−	1280.58i	0.138758	−	0.185927i
$363$	15739.0	−	7993.70i	2.27570	−	1.15581i
$364$	1129.59	−	335.285i	0.162655	−	0.0482793i
$365$		−	6298.89i		−	0.903285i
$366$	−1192.11	+	6895.60i	−0.170253	+	0.984805i
$367$		−	6462.48i		−	0.919179i	−0.888132	−	0.459589i	$-0.847997\pi$
$367$		−	6462.48i		−	0.919179i	0.888132	−	0.459589i	$-0.152003\pi$
$368$	5710.39	−	3717.43i	0.808899	−	0.526588i
$369$	2307.12	+	1685.38i	0.325485	+	0.237771i
$370$	4704.50	+	3510.98i	0.661014	+	0.493316i
$371$	1724.28			0.241294
$372$	−3555.38	+	3368.93i	−0.495532	+	0.469546i
$373$	10213.6			1.41781			0.708904	−	0.705305i	$-0.249190\pi$
$373$	10213.6			1.41781			0.708904	+	0.705305i	$0.249190\pi$
$374$	−17577.5	−	13118.1i	−2.43024	−	1.81369i
$375$	3084.04	+	6072.22i	0.424691	+	0.836182i
$376$	−7547.39	−	2777.22i	−1.03518	−	0.380915i
$377$			303.000i			0.0413933i
$378$	−1996.68	+	1931.07i	−0.271688	+	0.262760i
$379$			7942.35i			1.07644i	0.842804	+	0.538220i	$0.180903\pi$
$379$			7942.35i			1.07644i	−0.842804	+	0.538220i	$0.819097\pi$
$380$	−814.693	−	2744.74i	−0.109981	−	0.370532i
$381$	−2640.26	−	5198.46i	−0.355025	−	0.699016i
$382$	3156.18	−	4229.10i	0.422734	−	0.566438i
$383$	−781.367			−0.104245			−0.0521227	−	0.998641i	$-0.516599\pi$
$383$	−781.367			−0.104245			−0.0521227	+	0.998641i	$0.516599\pi$
$384$	−5782.26	+	4815.45i	−0.768424	+	0.639941i
$385$	−2980.75			−0.394580
$386$	1807.63	−	2422.12i	0.238358	−	0.319386i
$387$	−6268.72	−	4579.38i	−0.823403	−	0.601507i
$388$	−1485.28	−	5003.97i	−0.194339	−	0.654738i
$389$		−	885.114i		−	0.115365i	−0.998335	−	0.0576826i	$-0.981629\pi$
$389$		−	885.114i		−	0.115365i	0.998335	−	0.0576826i	$-0.0183711\pi$
$390$	−1887.03	−	326.229i	−0.245008	−	0.0423571i
$391$		−	12006.4i		−	1.55291i
$392$	−1040.53	−	382.885i	−0.134069	−	0.0493332i
$393$	−3570.85	+	1813.61i	−0.458334	+	0.232785i
$394$	9574.56	+	7145.51i	1.22426	+	0.913669i
$395$	1017.99			0.129673
$396$	−13990.6	−	4986.42i	−1.77539	−	0.632770i
$397$	−11540.6			−1.45895			−0.729476	−	0.684006i	$-0.760236\pi$
$397$	−11540.6			−1.45895			−0.729476	+	0.684006i	$0.760236\pi$
$398$	9258.29	+	6909.47i	1.16602	+	0.870203i
$399$	1874.20	−	951.890i	0.235156	−	0.119434i
$400$	−4647.60	+	3025.56i	−0.580950	+	0.378195i
$401$		−	3491.51i		−	0.434807i	−0.976082	−	0.217403i	$-0.930241\pi$
$401$		−	3491.51i		−	0.434807i	0.976082	−	0.217403i	$-0.0697587\pi$
$402$	−5678.48	−	981.696i	−0.704519	−	0.121797i
$403$		−	2479.22i		−	0.306448i
$404$	7278.23	−	2160.32i	0.896300	−	0.266040i
$405$	4300.69	−	1372.75i	0.527661	−	0.168426i
$406$	170.527	−	228.496i	0.0208451	−	0.0279312i
$407$	−23045.1			−2.80665
$408$	1552.39	+	13168.1i	0.188369	+	1.59783i
$409$	−5670.80			−0.685582			−0.342791	−	0.939412i	$-0.611372\pi$
$409$	−5670.80			−0.685582			−0.342791	+	0.939412i	$0.611372\pi$
$410$	1108.58	−	1485.44i	0.133534	−	0.178928i
$411$	−6383.70	−	12569.0i	−0.766142	−	1.50847i
$412$	12133.5	−	3601.47i	1.45091	−	0.430659i
$413$			34.9985i			0.00416989i
$414$	−2393.05	−	7770.37i	−0.284087	−	0.922446i
$415$		−	3301.57i		−	0.390525i
$416$	243.815	−	3801.03i	0.0287356	−	0.447982i
$417$	−916.422	−	1804.36i	−0.107620	−	0.211894i
$418$	9007.88	+	6722.60i	1.05404	+	0.786634i
$419$	−8420.94			−0.981838			−0.490919	−	0.871205i	$-0.663339\pi$
$419$	−8420.94			−0.981838			−0.490919	+	0.871205i	$0.663339\pi$
$420$	1239.43	+	1308.02i	0.143995	+	0.151964i
$421$	15207.5			1.76050			0.880249	−	0.474513i	$-0.157376\pi$
$421$	15207.5			1.76050			0.880249	+	0.474513i	$0.157376\pi$
$422$	4334.74	+	3235.02i	0.500028	+	0.373172i
$423$	−5660.64	+	7748.86i	−0.650662	+	0.890691i
$424$	1924.78	−	5230.82i	0.220462	−	0.599130i
$425$			9771.80i			1.11530i
$426$	868.386	−	5023.05i	0.0987639	−	0.571286i
$427$			3333.02i			0.377743i
$428$	1145.97	+	3860.83i	0.129422	+	0.436028i
$429$	6702.96	−	3404.38i	0.754363	−	0.383136i
$430$	−3012.15	+	4036.10i	−0.337811	+	0.452647i
$431$	−4941.26			−0.552232			−0.276116	−	0.961124i	$-0.589047\pi$
$431$	−4941.26			−0.552232			−0.276116	+	0.961124i	$0.589047\pi$
$432$	3629.28	+	8212.79i	0.404199	+	0.914671i
$433$	−9130.50			−1.01336			−0.506679	−	0.862135i	$-0.669127\pi$
$433$	−9130.50			−1.01336			−0.506679	+	0.862135i	$0.669127\pi$
$434$	−1395.29	+	1869.61i	−0.154323	+	0.206784i
$435$	−413.145	+	209.833i	−0.0455374	+	0.0231281i
$436$	−609.392	−	2053.07i	−0.0669371	−	0.225514i
$437$			6152.86i			0.673527i
$438$	2546.61	−	14730.5i	0.277812	−	1.60697i
$439$			9920.43i			1.07853i	0.842135	+	0.539267i	$0.181299\pi$
$439$			9920.43i			1.07853i	−0.842135	+	0.539267i	$0.818701\pi$
$440$	−3327.37	+	9042.50i	−0.360514	+	0.979737i
$441$	−780.414	+	1068.31i	−0.0842688	+	0.115356i
$442$	−5378.67	−	4014.11i	−0.578817	−	0.431972i
$443$	3266.60			0.350341			0.175170	−	0.984538i	$-0.443952\pi$
$443$	3266.60			0.350341			0.175170	+	0.984538i	$0.443952\pi$
$444$	9582.41	+	10112.7i	1.02424	+	1.08092i
$445$	3135.68			0.334035
$446$	−11977.7	−	8938.94i	−1.27166	−	0.949038i
$447$	4146.37	+	8163.86i	0.438739	+	0.863842i
$448$	−2323.06	+	2729.18i	−0.244987	+	0.287816i
$449$			10028.7i			1.05408i	0.849839	+	0.527042i	$0.176699\pi$
$449$			10028.7i			1.05408i	−0.849839	+	0.527042i	$0.823301\pi$
$450$	1947.67	+	6324.18i	0.204031	+	0.662500i
$451$			7276.46i			0.759723i
$452$	2662.92	−	790.408i	0.277109	−	0.0822515i
$453$	−8471.17	−	16679.1i	−0.878610	−	1.72991i
$454$	−3867.92	+	5182.79i	−0.399847	+	0.535772i
$455$	−912.103			−0.0939781
$456$	−795.546	−	6748.19i	−0.0816992	−	0.693011i
$457$	−8195.67			−0.838900			−0.419450	−	0.907778i	$-0.637777\pi$
$457$	−8195.67			−0.838900			−0.419450	+	0.907778i	$0.637777\pi$
$458$	5714.87	−	7657.59i	0.583054	−	0.781257i
$459$	15617.0	+	2535.81i	1.58810	+	0.257869i
$460$	−5056.42	+	1500.84i	−0.512515	+	0.152124i
$461$			10349.1i			1.04557i	0.852465	+	0.522784i	$0.175106\pi$
$461$			10349.1i			1.04557i	−0.852465	+	0.522784i	$0.824894\pi$
$462$	−6970.76	−	1205.10i	−0.701967	−	0.121356i
$463$			8166.03i			0.819671i	0.912159	+	0.409836i	$0.134414\pi$
$463$			8166.03i			0.819671i	−0.912159	+	0.409836i	$0.865586\pi$
$464$	−502.815	−	772.380i	−0.0503073	−	0.0772777i
$465$	3380.45	−	1716.91i	0.337129	−	0.171225i
$466$	7433.72	+	5547.80i	0.738971	+	0.551495i
$467$	14477.3			1.43454			0.717268	−	0.696797i	$-0.245392\pi$
$467$	14477.3			1.43454			0.717268	+	0.696797i	$0.245392\pi$
$468$	−4281.08	−	1525.83i	−0.422848	−	0.150708i
$469$	−2744.72			−0.270233
$470$	4989.08	+	3723.36i	0.489637	+	0.365417i
$471$	629.860	−	319.901i	0.0616187	−	0.0312957i
$472$	106.172	+	39.0683i	0.0103538	+	0.00380988i
$473$		−	19771.0i		−	1.92192i
$474$	2380.66	+	411.569i	0.230691	+	0.0398819i
$475$		−	5007.72i		−	0.483726i
$476$	1797.00	+	6054.18i	0.173036	+	0.582968i
$477$	−5370.44	−	3923.18i	−0.515505	−	0.376583i
$478$	−914.845	+	1225.84i	−0.0875398	+	0.117298i
$479$	−9837.43			−0.938379			−0.469190	−	0.883097i	$-0.655454\pi$
$479$	−9837.43			−0.938379			−0.469190	+	0.883097i	$0.655454\pi$
$480$	5351.61	−	2299.84i	0.508888	−	0.218694i
$481$	−7051.75			−0.668466
$482$	−3754.36	+	5030.62i	−0.354785	+	0.475391i
$483$	−1753.59	−	3452.68i	−0.165199	−	0.325264i
$484$	−7733.47	−	26054.4i	−0.726284	−	2.44689i
$485$			4040.53i			0.378291i
$486$	10612.5	−	1471.55i	0.990523	−	0.137348i
$487$			2247.96i			0.209168i	0.994516	+	0.104584i	$0.0333510\pi$
$487$			2247.96i			0.209168i	−0.994516	+	0.104584i	$0.966649\pi$
$488$	10111.1	+	3720.60i	0.937930	+	0.345130i
$489$	492.743	+	970.171i	0.0455677	+	0.0897191i
$490$	687.828	+	513.327i	0.0634141	+	0.0473260i
$491$	2477.43			0.227708			0.113854	−	0.993497i	$-0.463680\pi$
$491$	2477.43			0.227708			0.113854	+	0.993497i	$0.463680\pi$
$492$	3193.07	−	3025.63i	0.292591	−	0.277248i
$493$	−1623.96			−0.148356
$494$	2756.39	+	2057.10i	0.251044	+	0.187355i
$495$	9283.87	+	6781.99i	0.842987	+	0.615814i
$496$	4114.15	+	6319.81i	0.372441	+	0.572113i
$497$		−	2427.92i		−	0.219129i
$498$	1334.81	−	7721.01i	0.120109	−	0.694753i
$499$			4193.13i			0.376173i	0.982152	+	0.188087i	$0.0602285\pi$
$499$			4193.13i			0.376173i	−0.982152	+	0.188087i	$0.939771\pi$
$500$	10052.0	−	2983.64i	0.899080	−	0.266865i
$501$	15220.4	−	7730.35i	1.35728	−	0.689354i
$502$	8520.93	−	11417.5i	0.757585	−	1.01512i
$503$	6856.04			0.607745			0.303872	−	0.952713i	$-0.401720\pi$
$503$	6856.04			0.607745			0.303872	+	0.952713i	$0.401720\pi$
$504$	2369.69	+	3560.02i	0.209433	+	0.314635i
$505$	−5876.91			−0.517859
$506$	12384.5	−	16594.5i	1.08806	−	1.45794i
$507$	−8127.31	+	4127.80i	−0.711926	+	0.361582i
$508$	−8605.59	+	2554.31i	−0.751597	+	0.223089i
$509$		−	13595.9i		−	1.18395i	−0.805958	−	0.591973i	$-0.798349\pi$
$509$		−	13595.9i		−	1.18395i	0.805958	−	0.591973i	$-0.201651\pi$
$510$	1748.47	−	10113.8i	0.151811	−	0.878126i
$511$		−	7120.06i		−	0.616386i
$512$	5686.12	+	10093.8i	0.490808	+	0.871268i
$513$	−8003.17	−	1299.52i	−0.688789	−	0.111842i
$514$	−6239.03	−	4656.20i	−0.535393	−	0.399564i
$515$	−9797.37			−0.838299
$516$	−8675.95	+	8220.98i	−0.740189	+	0.701373i
$517$	−24439.2			−2.07898
$518$	5317.81	+	3968.69i	0.451064	+	0.336630i
$519$	7500.66	+	14768.2i	0.634378	+	1.24904i
$520$	−1018.17	+	2766.98i	−0.0858645	+	0.233346i
$521$			18084.7i			1.52074i	0.649491	+	0.760369i	$0.274982\pi$
$521$			18084.7i			1.52074i	−0.649491	+	0.760369i	$0.725018\pi$
$522$	−1051.01	+	323.681i	−0.0881254	+	0.0271401i
$523$		−	11204.7i		−	0.936799i	−0.883517	−	0.468400i	$-0.844831\pi$
$523$		−	11204.7i		−	0.936799i	0.883517	−	0.468400i	$-0.155169\pi$
$524$	1754.57	+	5911.22i	0.146276	+	0.492811i
$525$	1427.22	+	2810.09i	0.118646	+	0.233604i
$526$	2465.03	−	3302.99i	0.204335	−	0.273797i
$527$	13287.7			1.09833
$528$	−11437.2	+	19801.4i	−0.942688	+	1.63210i
$529$	−832.068			−0.0683873
$530$	−2580.52	+	3457.75i	−0.211492	+	0.283387i
$531$	79.6307	−	109.007i	0.00650787	−	0.00890862i
$532$	−920.902	−	3102.56i	−0.0750492	−	0.252844i
$533$			2226.58i			0.180945i
$534$	7333.07	+	1267.74i	0.594256	+	0.102735i
$535$		−	3117.48i		−	0.251926i
$536$	−3063.89	+	8326.45i	−0.246902	+	0.670985i
$537$	2385.90	−	1211.78i	0.191730	−	0.0973785i
$538$	−4074.46	−	3040.78i	−0.326510	−	0.243675i
$539$	−3369.35			−0.269254
$540$	−884.240	−	6893.99i	−0.0704660	−	0.549389i
$541$	5192.99			0.412688			0.206344	−	0.978480i	$-0.433843\pi$
$541$	5192.99			0.412688			0.206344	+	0.978480i	$0.433843\pi$
$542$	5788.22	+	4319.76i	0.458718	+	0.342342i
$543$	−2617.27	+	1329.29i	−0.206847	+	0.105056i
$544$	20372.1	+	1306.75i	1.60560	+	0.102990i
$545$			1657.78i			0.130296i
$546$	−2133.03	−	368.759i	−0.167189	−	0.0289037i
$547$			21828.6i			1.70626i	0.521700	+	0.853129i	$0.325298\pi$
$547$			21828.6i			1.70626i	−0.521700	+	0.853129i	$0.674702\pi$
$548$	−20806.8	+	6175.88i	−1.62194	+	0.481424i
$549$	7583.48	−	10381.0i	0.589536	−	0.807016i
$550$	−10079.6	+	13506.0i	−0.781444	+	1.04709i
$551$	832.227			0.0643450
$552$	−12431.7	+	1465.57i	−0.958563	+	0.113005i
$553$	1150.70			0.0884864
$554$	2824.30	−	3784.40i	0.216594	−	0.290223i
$555$	−4883.48	−	9615.18i	−0.373499	−	0.735390i
$556$	−2986.96	+	886.589i	−0.227833	+	0.0676254i
$557$		−	14606.0i		−	1.11109i	−0.831486	−	0.555545i	$-0.812510\pi$
$557$		−	14606.0i		−	1.11109i	0.831486	−	0.555545i	$-0.187490\pi$
$558$	8599.62	−	2648.44i	0.652421	−	0.200927i
$559$		−	6049.86i		−	0.457750i
$560$	2325.05	−	1513.59i	0.175449	−	0.114216i
$561$	18246.2	+	35925.4i	1.37318	+	2.70369i
$562$	7519.32	+	5611.68i	0.564383	+	0.421200i
$563$	3200.54			0.239585			0.119793	−	0.992799i	$-0.461777\pi$
$563$	3200.54			0.239585			0.119793	+	0.992799i	$0.461777\pi$
$564$	10162.1	+	10724.5i	0.758689	+	0.800676i
$565$	−2150.21			−0.160107
$566$	−7378.76	−	5506.78i	−0.547972	−	0.408953i
$567$	4861.36	−	1551.71i	0.360067	−	0.114931i
$568$	−7365.40	−	2710.25i	−0.544094	−	0.200210i
$569$		−	5357.36i		−	0.394714i	−0.980332	−	0.197357i	$-0.936764\pi$
$569$		−	5357.36i		−	0.394714i	0.980332	−	0.197357i	$-0.0632358\pi$
$570$	−896.030	+	5182.96i	−0.0658431	+	0.380860i
$571$			13530.9i			0.991684i	0.868413	+	0.495842i	$0.165141\pi$
$571$			13530.9i			0.991684i	−0.868413	+	0.495842i	$0.834859\pi$
$572$	−3293.56	−	11096.2i	−0.240753	−	0.811107i
$573$	−8643.54	+	4389.99i	−0.630173	+	0.320060i
$574$	1253.11	−	1679.09i	0.0911213	−	0.122097i
$575$	−9225.33			−0.669083
$576$	13445.0	−	3214.75i	0.972585	−	0.232549i
$577$	3337.75			0.240818			0.120409	−	0.992724i	$-0.461579\pi$
$577$	3337.75			0.240818			0.120409	+	0.992724i	$0.461579\pi$
$578$	13202.9	−	17691.1i	0.950116	−	1.27310i
$579$	−4950.40	+	2514.27i	−0.355322	+	0.180466i
$580$	203.002	+	683.924i	0.0145331	+	0.0489628i
$581$		−	3731.99i		−	0.266487i
$582$	−1633.57	+	9449.13i	−0.116346	+	0.672988i
$583$		−	16937.9i		−	1.20325i
$584$	−21599.6	−	7948.01i	−1.53048	−	0.563170i
$585$	2840.84	+	2075.27i	0.200776	+	0.146670i
$586$	7605.83	+	5676.24i	0.536167	+	0.400142i
$587$	−21998.8			−1.54683			−0.773414	−	0.633901i	$-0.781453\pi$
$587$	−21998.8			−1.54683			−0.773414	+	0.633901i	$0.781453\pi$
$588$	1401.01	+	1478.55i	0.0982597	+	0.103698i
$589$	−6809.49			−0.476367
$590$	−70.1836	−	52.3781i	−0.00489731	−	0.00365487i
$591$	−9938.81	−	19568.7i	−0.691757	−	1.36201i
$592$	17975.7	−	11702.1i	1.24797	−	0.812419i
$593$			19174.5i			1.32783i	0.747808	+	0.663915i	$0.231106\pi$
$593$			19174.5i			1.32783i	−0.747808	+	0.663915i	$0.768894\pi$
$594$	18969.2	+	19613.7i	1.31030	+	1.35481i
$595$		−	4888.53i		−	0.336824i
$596$	13514.6	−	4011.39i	0.928822	−	0.275693i
$597$	−9610.51	−	18922.3i	−0.658848	−	1.29722i
$598$	3789.63	−	5077.88i	0.259146	−	0.347241i
$599$	8533.09			0.582058			0.291029	−	0.956714i	$-0.406002\pi$
$599$	8533.09			0.582058			0.291029	+	0.956714i	$0.406002\pi$
$600$	10117.9	−	1192.81i	0.688439	−	0.0811602i
$601$	10157.4			0.689396			0.344698	−	0.938714i	$-0.387981\pi$
$601$	10157.4			0.689396			0.344698	+	0.938714i	$0.387981\pi$
$602$	−3404.83	+	4562.28i	−0.230516	+	0.308878i
$603$	8548.71	+	6244.95i	0.577331	+	0.421748i
$604$	−27610.7	+	8195.40i	−1.86004	+	0.552096i
$605$			21038.0i			1.41375i
$606$	−13743.7	−	2376.00i	−0.921284	−	0.159272i
$607$		−	21312.8i		−	1.42514i	−0.701602	−	0.712569i	$-0.747532\pi$
$607$		−	21312.8i		−	1.42514i	0.701602	−	0.712569i	$-0.252468\pi$
$608$	−10440.0	−	669.668i	−0.696379	−	0.0446688i
$609$	−467.005	+	237.189i	−0.0310739	+	0.0157822i
$610$	−6683.80	−	4988.13i	−0.443638	−	0.331088i
$611$	−7478.32			−0.495157
$612$	8177.88	−	22945.0i	0.540149	−	1.51552i
$613$	19403.1			1.27844			0.639221	−	0.769023i	$-0.279257\pi$
$613$	19403.1			1.27844			0.639221	+	0.769023i	$0.279257\pi$
$614$	−11726.9	−	8751.81i	−0.770781	−	0.575235i
$615$	−3035.97	+	1541.95i	−0.199060	+	0.101101i
$616$	−3761.15	+	10221.3i	−0.246008	+	0.668555i
$617$		−	9621.86i		−	0.627814i	−0.949454	−	0.313907i	$-0.898362\pi$
$617$		−	9621.86i		−	0.627814i	0.949454	−	0.313907i	$-0.101638\pi$
$618$	−22912.0	−	3961.03i	−1.49135	−	0.257825i
$619$			20617.5i			1.33875i	0.742924	+	0.669376i	$0.233439\pi$
$619$			20617.5i			1.33875i	−0.742924	+	0.669376i	$0.766561\pi$
$620$	−1661.02	−	5596.04i	−0.107594	−	0.362488i
$621$	−2394.00	+	14743.6i	−0.154699	+	0.952723i
$622$	−11340.5	+	15195.7i	−0.731052	+	0.979566i
$623$	3544.47			0.227939
$624$	−3499.75	+	6059.18i	−0.224522	+	0.388720i
$625$	2714.70			0.173741
$626$	−18062.7	+	24202.9i	−1.15324	+	1.54528i
$627$	−9350.58	−	18410.5i	−0.595576	−	1.17264i
$628$	−309.487	−	1042.68i	−0.0196654	−	0.0662538i
$629$		−	37794.8i		−	2.39583i
$630$	−974.359	−	3163.80i	−0.0616181	−	0.200077i
$631$		−	23614.1i		−	1.48980i	−0.667178	−	0.744898i	$-0.732498\pi$
$631$		−	23614.1i		−	1.48980i	0.667178	−	0.744898i	$-0.267502\pi$
$632$	1284.51	−	3490.81i	0.0808468	−	0.219710i
$633$	−4499.65	−	8859.46i	−0.282536	−	0.556290i
$634$	−24216.1	−	18072.5i	−1.51694	−	1.13210i
$635$	6948.70			0.434253
$636$	−7432.73	+	7042.95i	−0.463407	+	0.439106i
$637$	−1031.01			−0.0641290
$638$	−2244.55	−	1675.11i	−0.139283	−	0.103947i
$639$	−5524.14	+	7562.00i	−0.341990	+	0.468150i
$640$	−1996.26	−	8742.95i	−0.123296	−	0.539993i
$641$			8435.00i			0.519754i	0.965642	+	0.259877i	$0.0836821\pi$
$641$			8435.00i			0.519754i	−0.965642	+	0.259877i	$0.916318\pi$
$642$	1260.38	−	7290.50i	0.0774818	−	0.448182i
$643$			360.416i			0.0221048i	0.999939	+	0.0110524i	$0.00351816\pi$
$643$			360.416i			0.0221048i	−0.999939	+	0.0110524i	$0.996482\pi$
$644$	−5715.61	+	1696.51i	−0.349731	+	0.103807i
$645$	8249.09	−	4189.65i	0.503578	−	0.255763i
$646$	−11025.3	+	14773.2i	−0.671491	+	0.899759i
$647$	16899.2			1.02685			0.513427	−	0.858133i	$-0.328376\pi$
$647$	16899.2			1.02685			0.513427	+	0.858133i	$0.328376\pi$
$648$	719.335	−	16479.7i	0.0436083	−	0.999049i
$649$	343.797			0.0207938
$650$	−3084.32	+	4132.81i	−0.186119	+	0.249388i
$651$	3821.16	−	1940.74i	0.230051	−	0.116841i
$652$	1606.03	−	476.702i	0.0964679	−	0.0286336i
$653$		−	6321.58i		−	0.378840i	−0.981896	−	0.189420i	$-0.939339\pi$
$653$		−	6321.58i		−	0.378840i	0.981896	−	0.189420i	$-0.0606608\pi$
$654$	−670.233	+	3876.87i	−0.0400737	+	0.231800i
$655$		−	4773.09i		−	0.284733i
$656$	−3694.90	−	5675.79i	−0.219911	−	0.337809i
$657$	−16200.0	+	22176.2i	−0.961981	+	1.31686i
$658$	5639.50	+	4208.77i	0.334119	+	0.249354i
$659$	−3683.45			−0.217734			−0.108867	−	0.994056i	$-0.534722\pi$
$659$	−3683.45			−0.217734			−0.108867	+	0.994056i	$0.534722\pi$
$660$	12848.9	−	12175.1i	0.757794	−	0.718055i
$661$	32127.2			1.89047			0.945236	−	0.326388i	$-0.105832\pi$
$661$	32127.2			1.89047			0.945236	+	0.326388i	$0.105832\pi$
$662$	2833.56	+	2114.69i	0.166358	+	0.124154i
$663$	5583.30	+	10993.1i	0.327055	+	0.643945i
$664$	−11321.5	−	4165.96i	−0.661683	−	0.243480i
$665$			2505.21i			0.146087i
$666$	−7533.07	−	24460.3i	−0.438289	−	1.42315i
$667$		−	1533.15i		−	0.0890011i
$668$	−7478.69	−	25196.1i	−0.433173	−	1.45938i
$669$	12433.3	+	24480.2i	0.718536	+	1.41474i
$670$	4107.69	−	5504.07i	0.236857	−	0.317374i
$671$	32740.8			1.88367
$672$	6049.28	−	2599.67i	0.347256	−	0.149233i
$673$	8788.04			0.503349			0.251675	−	0.967812i	$-0.419019\pi$
$673$	8788.04			0.503349			0.251675	+	0.967812i	$0.419019\pi$
$674$	−12807.6	+	17161.4i	−0.731943	+	0.980761i
$675$	1948.44	−	11999.6i	0.111105	−	0.684244i
$676$	3993.42	+	13454.0i	0.227209	+	0.765478i
$677$		−	10657.5i		−	0.605024i	−0.953146	−	0.302512i	$-0.902175\pi$
$677$		−	10657.5i		−	0.605024i	0.953146	−	0.302512i	$-0.0978252\pi$
$678$	−5028.46	−	869.321i	−0.284833	−	0.0492420i
$679$			4567.28i			0.258139i
$680$	−14830.0	−	5456.99i	−0.836329	−	0.307744i
$681$	10592.7	−	5379.96i	0.596055	−	0.302732i
$682$	18365.5	+	13706.2i	1.03116	+	0.769556i
$683$	−5438.86			−0.304703			−0.152352	−	0.988326i	$-0.548685\pi$
$683$	−5438.86			−0.304703			−0.152352	+	0.988326i	$0.548685\pi$
$684$	−4190.89	+	11758.5i	−0.234273	+	0.657309i
$685$	16800.8			0.937116
$686$	777.499	+	580.248i	0.0432726	+	0.0322944i
$687$	−15650.8	+	7948.92i	−0.869163	+	0.441441i
$688$	10039.5	+	15421.8i	0.556325	+	0.854579i
$689$		−	5182.95i		−	0.286581i
$690$	9548.16	+	1650.69i	0.526800	+	0.0910733i
$691$		−	5741.11i		−	0.316067i	−0.987434	−	0.158033i	$-0.949485\pi$
$691$		−	5741.11i		−	0.316067i	0.987434	−	0.158033i	$-0.0505154\pi$
$692$	24447.4	−	7256.48i	1.34299	−	0.398627i
$693$	10494.2	+	7666.14i	0.575239	+	0.420220i
$694$	8703.93	−	11662.8i	0.476076	−	0.637914i
$695$	2411.86			0.131636
$696$	198.231	+	1681.49i	0.0107959	+	0.0915757i
$697$	−11933.6			−0.648519
$698$	−10918.4	+	14630.0i	−0.592074	+	0.793344i
$699$	−7716.53	−	15193.2i	−0.417548	−	0.822119i
$700$	4651.85	−	1380.76i	0.251176	−	0.0745541i
$701$		−	9324.02i		−	0.502373i	−0.967939	−	0.251187i	$-0.919179\pi$
$701$		−	9324.02i		−	0.502373i	0.967939	−	0.251187i	$-0.0808207\pi$
$702$	5804.53	+	6001.74i	0.312077	+	0.322679i
$703$			19368.6i			1.03912i
$704$	26809.2	+	22819.8i	1.43524	+	1.22167i
$705$	−5178.89	−	10196.8i	−0.276664	−	0.544730i
$706$	−23372.1	−	17442.6i	−1.24592	−	0.929832i
$707$	−6643.06			−0.353378
$708$	−142.954	−	150.866i	−0.00758835	−	0.00800830i
$709$	−17467.3			−0.925246			−0.462623	−	0.886555i	$-0.653092\pi$
$709$	−17467.3			−0.925246			−0.462623	+	0.886555i	$0.653092\pi$
$710$	4868.78	+	3633.57i	0.257355	+	0.192064i
$711$	−3583.99	−	2618.15i	−0.189044	−	0.138099i
$712$	3956.64	−	10752.6i	0.208260	−	0.565970i
$713$			12544.6i			0.658905i
$714$	1976.41	−	11432.3i	0.103593	−	0.599218i
$715$			8959.74i			0.468637i
$716$	−1172.33	−	3949.65i	−0.0611902	−	0.206153i
$717$	2505.40	−	1272.47i	0.130496	−	0.0662781i
$718$	−1613.85	+	2162.47i	−0.0838837	+	0.112399i
$719$	27087.0			1.40497			0.702487	−	0.711697i	$-0.252073\pi$
$719$	27087.0			1.40497			0.702487	+	0.711697i	$0.252073\pi$
$720$	−10685.4	−	575.854i	−0.553087	−	0.0298067i
$721$	−11074.6			−0.572040
$722$	−5953.19	+	7976.93i	−0.306863	+	0.411178i
$723$	10281.7	−	5222.01i	0.528881	−	0.268615i
$724$	1286.02	+	4332.66i	0.0660146	+	0.222406i
$725$			1247.81i			0.0639205i
$726$	−8505.57	+	49199.2i	−0.434809	+	2.51509i
$727$		−	2617.94i		−	0.133554i	−0.997768	−	0.0667771i	$-0.978728\pi$
$727$		−	2617.94i		−	0.133554i	0.997768	−	0.0667771i	$-0.0212716\pi$
$728$	−1150.90	+	3127.70i	−0.0585924	+	0.159231i
$729$	−18671.7	−	6227.88i	−0.948623	−	0.316409i
$730$	14278.1	+	10655.7i	0.723911	+	0.540256i
$731$	32425.0			1.64061
$732$	−13614.0	−	14367.4i	−0.687414	−	0.725457i
$733$	18373.1			0.925820			0.462910	−	0.886405i	$-0.346805\pi$
$733$	18373.1			0.925820			0.462910	+	0.886405i	$0.346805\pi$
$734$	14648.9	+	10932.5i	0.736649	+	0.549762i
$735$	−713.996	−	1405.80i	−0.0358315	−	0.0705493i
$736$	−1233.68	+	19232.8i	−0.0617853	+	0.963221i
$737$			26961.9i			1.34756i
$738$	−7723.29	+	2378.55i	−0.385228	+	0.118639i
$739$			15553.3i			0.774204i	0.922037	+	0.387102i	$0.126524\pi$
$739$			15553.3i			0.774204i	−0.922037	+	0.387102i	$0.873476\pi$
$740$	−15917.1	+	4724.50i	−0.790707	+	0.234698i
$741$	−2861.25	−	5633.58i	−0.141850	−	0.279291i
$742$	−2916.94	+	3908.52i	−0.144318	+	0.193378i
$743$	−23983.4			−1.18421			−0.592104	−	0.805862i	$-0.701703\pi$
$743$	−23983.4			−1.18421			−0.592104	+	0.805862i	$0.701703\pi$
$744$	−1621.98	−	13758.4i	−0.0799255	−	0.677966i
$745$	−10912.5			−0.536649
$746$	−17278.3	+	23151.9i	−0.847992	+	1.13626i
$747$	−8491.24	+	11623.7i	−0.415901	+	0.569327i
$748$	59471.2	−	17652.2i	2.90706	−	0.862874i
$749$		−	3523.90i		−	0.171910i
$750$	−18981.5	−	3281.52i	−0.924141	−	0.159766i
$751$			27368.4i			1.32981i	0.746928	+	0.664905i	$0.231528\pi$
$751$			27368.4i			1.32981i	−0.746928	+	0.664905i	$0.768472\pi$
$752$	19063.1	−	12410.0i	0.924415	−	0.601788i
$753$	−23335.5	+	11851.9i	−1.12934	+	0.573583i
$754$	−686.827	−	512.580i	−0.0331734	−	0.0247574i
$755$	22294.6			1.07468
$756$	−999.516	−	7792.74i	−0.0480847	−	0.374893i
$757$	9225.71			0.442951			0.221476	−	0.975166i	$-0.428913\pi$
$757$	9225.71			0.442951			0.221476	+	0.975166i	$0.428913\pi$
$758$	−18003.4	−	13436.0i	−0.862682	−	0.643821i
$759$	−33916.3	+	17225.8i	−1.62198	+	0.823793i
$760$	7599.87	+	2796.52i	0.362732	+	0.133474i
$761$		−	373.231i		−	0.0177787i	−0.999960	−	0.00888936i	$-0.997170\pi$
$761$		−	373.231i		−	0.0177787i	0.999960	−	0.00888936i	$-0.00282961\pi$
$762$	16250.1	+	2809.33i	0.772547	+	0.133558i
$763$			1873.90i			0.0889119i
$764$	4247.08	+	14308.6i	0.201118	+	0.677575i
$765$	−11122.7	+	15225.8i	−0.525675	+	0.719596i
$766$	1321.83	−	1771.17i	0.0623493	−	0.0835444i
$767$	105.201			0.00495252
$768$	−1133.70	−	21253.2i	−0.0532667	−	0.998580i
$769$	665.625			0.0312133			0.0156067	−	0.999878i	$-0.495032\pi$
$769$	665.625			0.0312133			0.0156067	+	0.999878i	$0.495032\pi$
$770$	5042.50	−	6756.65i	0.235999	−	0.316225i
$771$	6476.39	+	12751.5i	0.302518	+	0.595634i
$772$	2432.42	+	8194.94i	0.113400	+	0.382050i
$773$		−	17982.1i		−	0.836705i	−0.908285	−	0.418352i	$-0.862608\pi$
$773$		−	17982.1i		−	0.836705i	0.908285	−	0.418352i	$-0.137392\pi$
$774$	20985.1	−	6462.80i	0.974538	−	0.300130i
$775$		−	10209.9i		−	0.473224i
$776$	13855.4	+	5098.38i	0.640955	+	0.235852i
$777$	−5520.13	−	10868.7i	−0.254869	−	0.501817i
$778$	2006.34	+	1497.33i	0.0924560	+	0.0690000i
$779$	6115.58			0.281275
$780$	3931.74	−	3725.56i	0.180486	−	0.171021i
$781$	−23849.9			−1.09272
$782$	27215.5	+	20311.0i	1.24453	+	0.928798i
$783$	1994.20	+	323.810i	0.0910178	+	0.0147791i
$784$	2628.17	−	1710.92i	0.119723	−	0.0779391i
$785$			841.925i			0.0382797i
$786$	1929.74	−	11162.3i	0.0875719	−	0.506547i
$787$		−	21745.1i		−	0.984916i	−0.870336	−	0.492458i	$-0.836099\pi$
$787$		−	21745.1i		−	0.984916i	0.870336	−	0.492458i	$-0.163901\pi$
$788$	−32394.3	+	9615.27i	−1.46447	+	0.434682i
$789$	−6750.74	+	3428.65i	−0.304604	+	0.154706i
$790$	−1722.12	+	2307.54i	−0.0775574	+	0.103922i
$791$	−2430.53			−0.109254
$792$	34970.7	−	23277.8i	1.56898	−	1.04437i
$793$	10018.6			0.448639
$794$	19523.0	−	26159.7i	0.872601	−	1.16923i
$795$	7067.03	−	3589.29i	0.315273	−	0.160125i
$796$	−31324.2	+	9297.65i	−1.39480	+	0.414003i
$797$		−	2949.59i		−	0.131091i	−0.997850	−	0.0655457i	$-0.979121\pi$
$797$		−	2949.59i		−	0.131091i	0.997850	−	0.0655457i	$-0.0208788\pi$
$798$	−1012.84	+	5858.65i	−0.0449302	+	0.259892i
$799$		−	40081.0i		−	1.77467i
$800$	1004.07	−	15653.3i	0.0443741	−	0.691784i
$801$	−11039.6	−	8064.59i	−0.486974	−	0.355741i
$802$	7914.41	+	5906.53i	0.348463	+	0.260059i
$803$	−69941.6			−3.07371
$804$	11831.5	−	11211.0i	0.518985	−	0.491769i
$805$	4615.15			0.202065
$806$	5619.79	+	4194.06i	0.245594	+	0.183287i
$807$	4229.47	+	8327.49i	0.184491	+	0.363249i
$808$	−7415.55	+	20152.6i	−0.322869	+	0.877432i
$809$		−	40.7406i		−	0.00177054i	−1.00000		0.000885269i	$-0.999718\pi$
$809$		−	40.7406i		−	0.00177054i	1.00000		0.000885269i	$-0.000281790\pi$
$810$	−4163.72	+	12070.9i	−0.180615	+	0.523615i
$811$			8505.84i			0.368287i	0.982899	+	0.184143i	$0.0589511\pi$
$811$			8505.84i			0.368287i	−0.982899	+	0.184143i	$0.941049\pi$
$812$	229.467	+	773.086i	0.00991714	+	0.0334113i
$813$	−6008.43	−	11830.1i	−0.259194	−	0.510332i
$814$	38985.2	−	52237.8i	1.67866	−	2.24930i
$815$	−1296.81			−0.0557367
$816$	−32475.0	−	18757.3i	−1.39320	−	0.804703i
$817$	−16616.7			−0.711562
$818$	9593.22	−	12854.3i	0.410048	−	0.549440i
$819$	3211.19	+	2345.82i	0.137006	+	0.100085i
$820$	1491.75	+	5025.78i	0.0635295	+	0.214034i
$821$			5980.54i			0.254229i	0.991888	+	0.127115i	$0.0405716\pi$
$821$			5980.54i			0.254229i	−0.991888	+	0.127115i	$0.959428\pi$
$822$	39290.1	+	6792.47i	1.66715	+	0.288217i
$823$		−	1221.64i		−	0.0517418i	−0.999665	−	0.0258709i	$-0.991764\pi$
$823$		−	1221.64i		−	0.0517418i	0.999665	−	0.0258709i	$-0.00823589\pi$
$824$	−12362.4	+	33596.3i	−0.522653	+	1.42037i
$825$	27604.0	−	14019.9i	1.16491	−	0.591647i
$826$	−79.3332	−	59.2065i	−0.00334184	−	0.00249402i
$827$	27111.0			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$827$	27111.0			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$828$	21661.8	+	7720.55i	0.909180	+	0.324043i
$829$	−24655.1			−1.03294			−0.516470	−	0.856305i	$-0.672754\pi$
$829$	−24655.1			−1.03294			−0.516470	+	0.856305i	$0.672754\pi$
$830$	7483.87	+	5585.22i	0.312974	+	0.233573i
$831$	−7734.65	+	3928.37i	−0.322879	+	0.163988i
$832$	8203.55	+	6982.81i	0.341835	+	0.290968i
$833$		−	5525.84i		−	0.229843i
$834$	5640.35	+	975.104i	0.234184	+	0.0404857i
$835$			20344.9i			0.843192i
$836$	−30477.0	+	9046.18i	−1.26085	+	0.374245i
$837$	−16317.1	−	2649.49i	−0.673835	−	0.109414i
$838$	14245.6	−	19088.3i	0.587238	−	0.786865i
$839$	−12923.5			−0.531787			−0.265894	−	0.964002i	$-0.585667\pi$
$839$	−12923.5			−0.531787			−0.265894	+	0.964002i	$0.585667\pi$
$840$	−5061.70	+	596.725i	−0.207911	+	0.0245107i
$841$	24181.6			0.991497
$842$	−25726.4	+	34471.8i	−1.05296	+	1.41090i
$843$	−7805.39	−	15368.2i	−0.318899	−	0.627887i
$844$	−14666.0	+	4353.17i	−0.598135	+	0.177538i
$845$		−	10863.7i		−	0.442273i
$846$	−7988.76	−	25939.9i	−0.324656	−	1.05418i
$847$			23780.7i			0.964716i
$848$	8600.87	+	13211.9i	0.348296	+	0.535023i
$849$	7659.48	+	15080.9i	0.309626	+	0.609629i
$850$	−22150.3	−	16530.8i	−0.893823	−	0.667061i
$851$	35681.2			1.43729
$852$	9917.02	+	10465.9i	0.398769	+	0.420838i
$853$	6459.47			0.259283			0.129641	−	0.991561i	$-0.458617\pi$
$853$	6459.47			0.259283			0.129641	+	0.991561i	$0.458617\pi$
$854$	−7555.15	−	5638.42i	−0.302731	−	0.225928i
$855$	5700.00	−	7802.73i	0.227995	−	0.312103i
$856$	−10690.2	−	3933.67i	−0.426849	−	0.157068i
$857$		−	15756.3i		−	0.628034i	−0.949417	−	0.314017i	$-0.898325\pi$
$857$		−	15756.3i		−	0.628034i	0.949417	−	0.314017i	$-0.101675\pi$
$858$	−3622.38	+	20953.1i	−0.144133	+	0.833716i
$859$		−	6531.69i		−	0.259439i	−0.991551	−	0.129720i	$-0.958592\pi$
$859$		−	6531.69i		−	0.259439i	0.991551	−	0.129720i	$-0.0414077\pi$
$860$	−4053.26	−	13655.6i	−0.160715	−	0.541457i
$861$	−3431.76	+	1742.97i	−0.135835	+	0.0689898i
$862$	8359.06	−	11200.6i	0.330291	−	0.442570i
$863$	−11849.5			−0.467396			−0.233698	−	0.972309i	$-0.575083\pi$
$863$	−11849.5			−0.467396			−0.233698	+	0.972309i	$0.575083\pi$
$864$	−24756.0	−	5666.76i	−0.974788	−	0.223133i
$865$	−19740.4			−0.775947
$866$	15445.9	−	20696.6i	0.606090	−	0.812125i
$867$	−36157.5	+	18364.1i	−1.41635	+	0.719352i
$868$	−1877.56	−	6325.58i	−0.0734199	−	0.247355i
$869$		−	11303.6i		−	0.441251i
$870$	223.270	−	1291.47i	0.00870064	−	0.0503276i
$871$			8250.26i			0.320952i
$872$	5684.72	+	2091.81i	0.220767	+	0.0812357i
$873$	10391.7	−	14225.3i	0.402872	−	0.551492i
$874$	−13947.0	−	10408.7i	−0.539778	−	0.402837i
$875$	−9174.79			−0.354474
$876$	29082.5	+	30692.0i	1.12170	+	1.18377i
$877$	−14641.4			−0.563744			−0.281872	−	0.959452i	$-0.590955\pi$
$877$	−14641.4			−0.563744			−0.281872	+	0.959452i	$0.590955\pi$
$878$	−22487.2	−	16782.3i	−0.864359	−	0.645072i
$879$	−7895.19	−	15545.0i	−0.302956	−	0.596495i
$880$	−14868.3	−	22839.4i	−0.569557	−	0.874905i
$881$		−	33527.2i		−	1.28213i	−0.767485	−	0.641066i	$-0.778492\pi$
$881$		−	33527.2i		−	1.28213i	0.767485	−	0.641066i	$-0.221508\pi$
$882$	−1101.38	−	3576.25i	−0.0420471	−	0.136529i
$883$			11725.5i			0.446880i	0.974718	+	0.223440i	$0.0717286\pi$
$883$			11725.5i			0.446880i	−0.974718	+	0.223440i	$0.928271\pi$
$884$	18198.0	−	5401.54i	0.692383	−	0.205513i
$885$	72.8537	+	143.443i	0.00276717	+	0.00544834i
$886$	−5526.07	+	7404.60i	−0.209539	+	0.280770i
$887$	−1850.93			−0.0700655			−0.0350327	−	0.999386i	$-0.511154\pi$
$887$	−1850.93			−0.0700655			−0.0350327	+	0.999386i	$0.511154\pi$
$888$	−39133.6	+	4613.47i	−1.47887	+	0.174344i
$889$	7854.59			0.296327
$890$	−5304.59	+	7107.84i	−0.199787	+	0.267702i
$891$	−15242.7	−	47754.0i	−0.573122	−	1.79553i
$892$	40524.8	−	12028.6i	1.52116	−	0.451510i
$893$			20540.2i			0.769710i
$894$	−25519.9	−	4411.88i	−0.954712	−	0.165051i
$895$			3189.20i			0.119110i
$896$	−2256.51	−	9882.74i	−0.0841347	−	0.368481i
$897$	−10378.3	+	5271.06i	−0.386311	+	0.196205i
$898$	−22732.7	−	16965.4i	−0.844765	−	0.630449i
$899$	1696.77			0.0629481
$900$	−17630.2	−	6283.64i	−0.652972	−	0.232727i
$901$	27778.7			1.02713
$902$	−16494.0	−	12309.5i	−0.608857	−	0.454391i
$903$	9324.50	−	4735.85i	0.343632	−	0.174528i
$904$	−2713.16	+	7373.33i	−0.0998213	+	0.271276i
$905$		−	3498.47i		−	0.128501i
$906$	52138.0	+	9013.61i	1.91188	+	0.330527i
$907$			33119.9i			1.21249i	0.795278	+	0.606245i	$0.207325\pi$
$907$			33119.9i			1.21249i	−0.795278	+	0.606245i	$0.792675\pi$
$908$	−5204.82	−	17535.3i	−0.190229	−	0.640891i
$909$	20690.5	+	15114.7i	0.754962	+	0.551510i
$910$	1542.99	−	2067.52i	0.0562084	−	0.0753160i
$911$	2299.09			0.0836139			0.0418069	−	0.999126i	$-0.486689\pi$
$911$	2299.09			0.0836139			0.0418069	+	0.999126i	$0.486689\pi$
$912$	16642.3	+	9612.50i	0.604257	+	0.349015i
$913$	−36660.0			−1.32888
$914$	13864.5	−	18577.6i	0.501747	−	0.672312i
$915$	6938.08	+	13660.5i	0.250673	+	0.493555i
$916$	7690.15	+	25908.5i	0.277391	+	0.934542i
$917$		−	5395.35i		−	0.194297i
$918$	−32167.1	+	31110.1i	−1.15651	+	1.11850i
$919$		−	2936.36i		−	0.105399i	−0.998610	−	0.0526994i	$-0.983217\pi$
$919$		−	2936.36i		−	0.105399i	0.998610	−	0.0526994i	$-0.0167825\pi$
$920$	5151.82	−	14000.6i	0.184620	−	0.501726i
$921$	12173.1	+	23967.8i	0.435522	+	0.857508i
$922$	−23459.0	−	17507.5i	−0.837939	−	0.625355i
$923$	−7297.99			−0.260256
$924$	14524.0	−	13762.4i	0.517105	−	0.489988i
$925$	−29040.4			−1.03226
$926$	−18510.4	−	13814.4i	−0.656901	−	0.490246i
$927$	34493.1	+	25197.7i	1.22212	+	0.892772i
$928$	2601.40	+	166.866i	0.0920208	+	0.00590262i
$929$			39893.8i			1.40891i	0.709751	+	0.704453i	$0.248808\pi$
$929$			39893.8i			1.40891i	−0.709751	+	0.704453i	$0.751192\pi$
$930$	−1826.85	+	10567.1i	−0.0644137	+	0.372592i
$931$			2831.81i			0.0996871i
$932$	−25151.1	+	7465.33i	−0.883959	+	0.262377i
$933$	31057.3	−	15773.8i	1.08978	−	0.553494i
$934$	−24491.0	+	32816.5i	−0.857998	+	1.14967i
$935$	−48020.9			−1.67963
$936$	10700.9	−	7122.96i	0.373687	−	0.248740i
$937$	21761.5			0.758715			0.379358	−	0.925250i	$-0.376145\pi$
$937$	21761.5			0.758715			0.379358	+	0.925250i	$0.376145\pi$
$938$	4643.20	−	6221.62i	0.161627	−	0.216570i
$939$	49466.5	−	25123.7i	1.71915	−	0.873142i
$940$	−16879.9	+	5010.29i	−0.585705	+	0.173849i
$941$			27826.5i			0.963995i	0.876173	+	0.481997i	$0.160088\pi$
$941$			27826.5i			0.963995i	−0.876173	+	0.481997i	$0.839912\pi$
$942$	−340.386	+	1968.91i	−0.0117732	+	0.0681005i
$943$		−	11266.3i		−	0.389056i
$944$	−268.169	+	174.576i	−0.00924593	+	0.00601904i
$945$	−974.747	+	6003.04i	−0.0335540	+	0.206644i
$946$	44816.0	+	33446.3i	1.54027	+	1.14951i
$947$	−22725.4			−0.779806			−0.389903	−	0.920856i	$-0.627492\pi$
$947$	−22725.4			−0.779806			−0.389903	+	0.920856i	$0.627492\pi$
$948$	−4960.26	+	4700.14i	−0.169939	+	0.161027i
$949$	−21401.9			−0.732072
$950$	11351.3	+	8471.49i	0.387668	+	0.289317i
$951$	25137.3	+	49493.4i	0.857134	+	1.68763i
$952$	−16763.3	−	6168.40i	−0.570696	−	0.209999i
$953$		−	52835.7i		−	1.79592i	−0.440073	−	0.897962i	$-0.645048\pi$
$953$		−	52835.7i		−	1.79592i	0.440073	−	0.897962i	$-0.354952\pi$
$954$	17978.0	−	5536.71i	0.610125	−	0.187901i
$955$		−	11553.7i		−	0.391485i
$956$	−1231.05	−	4147.47i	−0.0416475	−	0.140312i
$957$	2329.95	+	4587.48i	0.0787006	+	0.154955i
$958$	16641.8	−	22299.1i	0.561246	−	0.752036i
$959$	18991.0			0.639471
$960$	−3840.05	+	16021.4i	−0.129101	+	0.538634i
$961$	15907.6			0.533975
$962$	11929.4	−	15984.6i	0.399811	−	0.535723i
$963$	−8017.78	+	10975.5i	−0.268296	+	0.367271i
$964$	−5052.01	−	17020.5i	−0.168791	−	0.568664i
$965$		−	6617.12i		−	0.220739i
$966$	10792.9	+	1865.88i	0.359479	+	0.0621468i
$967$		−	21593.3i		−	0.718090i	−0.933320	−	0.359045i	$-0.883102\pi$
$967$		−	21593.3i		−	0.718090i	0.933320	−	0.359045i	$-0.116898\pi$
$968$	72141.7	+	26546.0i	2.39538	+	0.881426i
$969$	30193.9	−	15335.2i	1.00100	−	0.508400i
$970$	−9158.91	−	6835.30i	−0.303170	−	0.226256i
$971$	18183.5			0.600966			0.300483	−	0.953787i	$-0.402852\pi$
$971$	18183.5			0.600966			0.300483	+	0.953787i	$0.402852\pi$
$972$	−14617.4	+	26545.5i	−0.482360	+	0.875973i
$973$	2726.29			0.0898262
$974$	−5095.57	−	3802.83i	−0.167631	−	0.125103i
$975$	8446.74	−	4290.04i	0.277448	−	0.140914i
$976$	−25538.6	+	16625.4i	−0.837571	+	0.545253i
$977$			6264.44i			0.205135i	0.994726	+	0.102568i	$0.0327058\pi$
$977$			6264.44i			0.205135i	−0.994726	+	0.102568i	$0.967294\pi$
$978$	−3032.71	−	524.295i	−0.0991569	−	0.0171422i
$979$		−	34818.0i		−	1.13666i
$980$	−2327.18	+	690.752i	−0.0758561	+	0.0225156i
$981$	4263.61	−	5836.46i	0.138763	−	0.189953i
$982$	−4191.03	+	5615.73i	−0.136193	+	0.182490i
$983$	−34226.0			−1.11052			−0.555259	−	0.831678i	$-0.687381\pi$
$983$	−34226.0			−1.11052			−0.555259	+	0.831678i	$0.687381\pi$
$984$	1456.69	+	12356.3i	0.0471927	+	0.400311i
$985$	26157.2			0.846130
$986$	2747.24	−	3681.14i	0.0887321	−	0.118896i
$987$	−5854.05	−	11526.1i	−0.188791	−	0.371714i
$988$	−9325.89	+	2768.11i	−0.300300	+	0.0891348i
$989$			30611.7i			0.984222i
$990$	−31078.5	+	9571.30i	−0.997717	+	0.307268i
$991$		−	33737.5i		−	1.08144i	−0.841203	−	0.540720i	$-0.818152\pi$
$991$		−	33737.5i		−	1.08144i	0.841203	−	0.540720i	$-0.181848\pi$
$992$	−21285.3	−	1365.34i	−0.681260	−	0.0436990i
$993$	−2941.36	−	5791.29i	−0.0939991	−	0.185077i
$994$	5503.51	+	4107.27i	0.175614	+	0.131061i
$995$	25293.2			0.805877
$996$	15243.6	+	16087.2i	0.484952	+	0.511790i
$997$	−5923.27			−0.188156			−0.0940782	−	0.995565i	$-0.529990\pi$
$997$	−5923.27			−0.188156			−0.0940782	+	0.995565i	$0.529990\pi$
$998$	−9504.82	−	7093.46i	−0.301473	−	0.224990i
$999$	−7536.07	+	46411.4i	−0.238669	+	1.46986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.e.a.71.12	yes	36
3.2	odd	2	inner	84.4.e.a.71.25	yes	36
4.3	odd	2	inner	84.4.e.a.71.26	yes	36
12.11	even	2	inner	84.4.e.a.71.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.e.a.71.11	✓	36	12.11	even	2	inner
84.4.e.a.71.12	yes	36	1.1	even	1	trivial
84.4.e.a.71.25	yes	36	3.2	odd	2	inner
84.4.e.a.71.26	yes	36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69169 + 2.26676i) q^{2} +(4.63286 - 2.35300i) q^{3} +(-2.27640 - 7.66929i) q^{4} +6.19268i q^{5} +(-2.50367 + 14.4821i) q^{6} +7.00000i q^{7} +(21.2354 + 7.81399i) q^{8} +(15.9268 - 21.8022i) q^{9} +(-14.0373 - 10.4761i) q^{10} +68.7622 q^{11} +(-28.5920 - 30.1744i) q^{12} +21.0411 q^{13} +(-15.8673 - 11.8418i) q^{14} +(14.5713 + 28.6898i) q^{15} +(-53.6360 + 34.9167i) q^{16} +112.772i q^{17} +(22.4772 + 72.9848i) q^{18} -57.7920i q^{19} +(47.4934 - 14.0970i) q^{20} +(16.4710 + 32.4300i) q^{21} +(-116.324 + 155.867i) q^{22} -106.466 q^{23} +(116.767 - 13.7657i) q^{24} +86.6508 q^{25} +(-35.5949 + 47.6950i) q^{26} +(22.4862 - 138.482i) q^{27} +(53.6850 - 15.9348i) q^{28} +14.4004i q^{29} +(-89.6830 - 15.5044i) q^{30} -117.828i q^{31} +(11.5876 - 180.648i) q^{32} +(318.566 - 161.797i) q^{33} +(-255.627 - 190.775i) q^{34} -43.3487 q^{35} +(-203.463 - 72.5168i) q^{36} -335.143 q^{37} +(131.000 + 97.7659i) q^{38} +(97.4803 - 49.5095i) q^{39} +(-48.3895 + 131.504i) q^{40} +105.821i q^{41} +(-101.375 - 17.5257i) q^{42} -287.527i q^{43} +(-156.530 - 527.357i) q^{44} +(135.014 + 98.6296i) q^{45} +(180.106 - 241.332i) q^{46} -355.416 q^{47} +(-166.329 + 287.970i) q^{48} -49.0000 q^{49} +(-146.586 + 196.416i) q^{50} +(265.353 + 522.458i) q^{51} +(-47.8978 - 161.370i) q^{52} -246.326i q^{53} +(275.867 + 285.239i) q^{54} +425.822i q^{55} +(-54.6979 + 148.648i) q^{56} +(-135.984 - 267.742i) q^{57} +(-32.6422 - 24.3610i) q^{58} +4.99979 q^{59} +(186.860 - 177.061i) q^{60} +476.146 q^{61} +(267.087 + 199.327i) q^{62} +(152.616 + 111.488i) q^{63} +(389.883 + 331.866i) q^{64} +130.300i q^{65} +(-172.158 + 995.822i) q^{66} +392.103i q^{67} +(864.883 - 256.714i) q^{68} +(-493.241 + 250.513i) q^{69} +(73.3324 - 98.2611i) q^{70} -346.845 q^{71} +(508.574 - 338.527i) q^{72} -1017.15 q^{73} +(566.956 - 759.688i) q^{74} +(401.441 - 203.889i) q^{75} +(-443.223 + 131.557i) q^{76} +481.335i q^{77} +(-52.6798 + 304.719i) q^{78} -164.386i q^{79} +(-216.228 - 332.151i) q^{80} +(-221.673 - 694.480i) q^{81} +(-239.870 - 179.015i) q^{82} -533.141 q^{83} +(211.221 - 200.144i) q^{84} -698.362 q^{85} +(651.754 + 486.405i) q^{86} +(33.8841 + 66.7151i) q^{87} +(1460.19 + 537.307i) q^{88} -506.353i q^{89} +(-451.971 + 139.194i) q^{90} +147.287i q^{91} +(242.358 + 816.516i) q^{92} +(-277.248 - 545.879i) q^{93} +(601.252 - 805.642i) q^{94} +357.887 q^{95} +(-371.381 - 864.183i) q^{96} +652.469 q^{97} +(82.8926 - 111.071i) q^{98} +(1095.16 - 1499.17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{4} + 30 q^{6} + 20 q^{9} - 132 q^{10} - 78 q^{12} + 324 q^{16} + 424 q^{18} - 240 q^{22} - 382 q^{24} - 900 q^{25} + 168 q^{28} + 476 q^{30} + 848 q^{33} - 576 q^{34} + 412 q^{36} + 528 q^{37}+ \cdots - 72 q^{97}+O(q^{100}) \) 36 * q + 12 * q^4 + 30 * q^6 + 20 * q^9 - 132 * q^10 - 78 * q^12 + 324 * q^16 + 424 * q^18 - 240 * q^22 - 382 * q^24 - 900 * q^25 + 168 * q^28 + 476 * q^30 + 848 * q^33 - 576 * q^34 + 412 * q^36 + 528 * q^37 - 1068 * q^40 + 70 * q^42 - 984 * q^45 + 288 * q^46 + 526 * q^48 - 1764 * q^49 + 468 * q^52 - 1826 * q^54 + 1840 * q^57 + 1536 * q^58 + 652 * q^60 + 2448 * q^61 - 2604 * q^64 - 1188 * q^66 - 744 * q^69 + 252 * q^70 + 1888 * q^72 - 1656 * q^73 - 972 * q^76 - 1348 * q^78 + 2452 * q^81 + 888 * q^82 + 490 * q^84 + 2904 * q^85 + 4008 * q^88 + 3184 * q^90 - 6744 * q^93 + 3264 * q^94 - 1330 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

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