LMFDB - Embedded newform 40.4.d.a.21.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,4,Mod(21,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.21"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.36007640023$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.11
Root			$1.71681 - 1.02595i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.4.d.a.21.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.74276 - 0.690860i) q^{2} -4.24443i q^{3} +(7.04543 - 3.78972i) q^{4} +5.00000i q^{5} +(-2.93231 - 11.6414i) q^{6} -14.6308 q^{7} +(16.7057 - 15.2617i) q^{8} +8.98481 q^{9} +(3.45430 + 13.7138i) q^{10} +14.9969i q^{11} +(-16.0852 - 29.9038i) q^{12} +85.6955i q^{13} +(-40.1288 + 10.1078i) q^{14} +21.2222 q^{15} +(35.2761 - 53.4004i) q^{16} -91.9247 q^{17} +(24.6432 - 6.20724i) q^{18} -60.3737i q^{19} +(18.9486 + 35.2271i) q^{20} +62.0995i q^{21} +(10.3608 + 41.1330i) q^{22} +1.33730 q^{23} +(-64.7771 - 70.9063i) q^{24} -25.0000 q^{25} +(59.2035 + 235.042i) q^{26} -152.735i q^{27} +(-103.080 + 55.4467i) q^{28} +25.5118i q^{29} +(58.2072 - 14.6615i) q^{30} +73.4354 q^{31} +(59.8615 - 170.835i) q^{32} +63.6535 q^{33} +(-252.127 + 63.5070i) q^{34} -73.1541i q^{35} +(63.3018 - 34.0499i) q^{36} -211.259i q^{37} +(-41.7098 - 165.590i) q^{38} +363.728 q^{39} +(76.3084 + 83.5286i) q^{40} +330.839 q^{41} +(42.9020 + 170.324i) q^{42} -388.500i q^{43} +(56.8342 + 105.660i) q^{44} +44.9241i q^{45} +(3.66788 - 0.923883i) q^{46} -550.348 q^{47} +(-226.654 - 149.727i) q^{48} -128.939 q^{49} +(-68.5689 + 17.2715i) q^{50} +390.168i q^{51} +(324.762 + 603.761i) q^{52} +187.705i q^{53} +(-105.518 - 418.915i) q^{54} -74.9847 q^{55} +(-244.419 + 223.291i) q^{56} -256.252 q^{57} +(17.6251 + 69.9727i) q^{58} +779.090i q^{59} +(149.519 - 80.4260i) q^{60} -358.850i q^{61} +(201.415 - 50.7335i) q^{62} -131.455 q^{63} +(46.1625 - 509.915i) q^{64} -428.477 q^{65} +(174.586 - 43.9756i) q^{66} +283.674i q^{67} +(-647.648 + 348.369i) q^{68} -5.67606i q^{69} +(-50.5392 - 200.644i) q^{70} -534.811 q^{71} +(150.098 - 137.123i) q^{72} +1016.16 q^{73} +(-145.950 - 579.431i) q^{74} +106.111i q^{75} +(-228.799 - 425.359i) q^{76} -219.418i q^{77} +(997.618 - 251.285i) q^{78} +1119.59 q^{79} +(267.002 + 176.380i) q^{80} -405.683 q^{81} +(907.411 - 228.563i) q^{82} +1190.49i q^{83} +(235.340 + 437.518i) q^{84} -459.623i q^{85} +(-268.399 - 1065.56i) q^{86} +108.283 q^{87} +(228.879 + 250.535i) q^{88} -398.940 q^{89} +(31.0362 + 123.216i) q^{90} -1253.80i q^{91} +(9.42182 - 5.06797i) q^{92} -311.691i q^{93} +(-1509.47 + 380.213i) q^{94} +301.869 q^{95} +(-725.097 - 254.078i) q^{96} +278.022 q^{97} +(-353.648 + 89.0787i) q^{98} +134.745i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	2.74276	−	0.690860i	0.969711	−	0.244256i
$2$	2.74276	−	0.690860i	0.969711	−	0.244256i
$3$		−	4.24443i		−	0.816841i	−0.912794	−	0.408420i	$-0.866080\pi$
$3$		−	4.24443i		−	0.816841i	0.912794	−	0.408420i	$-0.133920\pi$
$4$	7.04543	−	3.78972i	0.880678	−	0.473715i
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	−2.93231	−	11.6414i	−0.199518	−	0.792100i
$7$	−14.6308			−0.789990			−0.394995	−	0.918683i	$-0.629254\pi$
$7$	−14.6308			−0.789990			−0.394995	+	0.918683i	$0.629254\pi$
$8$	16.7057	−	15.2617i	0.738296	−	0.674477i
$9$	8.98481			0.332771
$10$	3.45430	+	13.7138i	0.109234	+	0.433668i
$11$			14.9969i			0.411068i	0.978650	+	0.205534i	$0.0658931\pi$
$11$			14.9969i			0.411068i	−0.978650	+	0.205534i	$0.934107\pi$
$12$	−16.0852	−	29.9038i	−0.386950	−	0.719374i
$13$			85.6955i			1.82828i	0.405398	+	0.914140i	$0.367133\pi$
$13$			85.6955i			1.82828i	−0.405398	+	0.914140i	$0.632867\pi$
$14$	−40.1288	+	10.1078i	−0.766062	+	0.192960i
$15$	21.2222			0.365302
$16$	35.2761	−	53.4004i	0.551188	−	0.834381i
$17$	−91.9247			−1.31147			−0.655735	−	0.754991i	$-0.727641\pi$
$17$	−91.9247			−1.31147			−0.655735	+	0.754991i	$0.727641\pi$
$18$	24.6432	−	6.20724i	0.322691	−	0.0812812i
$19$		−	60.3737i		−	0.728983i	−0.931207	−	0.364492i	$-0.881243\pi$
$19$		−	60.3737i		−	0.728983i	0.931207	−	0.364492i	$-0.118757\pi$
$20$	18.9486	+	35.2271i	0.211852	+	0.393851i
$21$			62.0995i			0.645296i
$22$	10.3608	+	41.1330i	0.100406	+	0.398617i
$23$	1.33730			0.0121237			0.00606186	−	0.999982i	$-0.498070\pi$
$23$	1.33730			0.0121237			0.00606186	+	0.999982i	$0.498070\pi$
$24$	−64.7771	−	70.9063i	−0.550941	−	0.603070i
$25$	−25.0000			−0.200000
$26$	59.2035	+	235.042i	0.446568	+	1.77290i
$27$		−	152.735i		−	1.08866i
$28$	−103.080	+	55.4467i	−0.695727	+	0.374230i
$29$			25.5118i			0.163360i	0.996659	+	0.0816798i	$0.0260285\pi$
$29$			25.5118i			0.163360i	−0.996659	+	0.0816798i	$0.973972\pi$
$30$	58.2072	−	14.6615i	0.354238	−	0.0892272i
$31$	73.4354			0.425464			0.212732	−	0.977111i	$-0.431764\pi$
$31$	73.4354			0.425464			0.212732	+	0.977111i	$0.431764\pi$
$32$	59.8615	−	170.835i	0.330691	−	0.943739i
$33$	63.6535			0.335777
$34$	−252.127	+	63.5070i	−1.27175	+	0.320334i
$35$		−	73.1541i		−	0.353294i
$36$	63.3018	−	34.0499i	0.293064	−	0.157638i
$37$		−	211.259i		−	0.938668i	−0.883021	−	0.469334i	$-0.844494\pi$
$37$		−	211.259i		−	0.938668i	0.883021	−	0.469334i	$-0.155506\pi$
$38$	−41.7098	−	165.590i	−0.178058	−	0.706903i
$39$	363.728			1.49341
$40$	76.3084	+	83.5286i	0.301635	+	0.330176i
$41$	330.839			1.26020			0.630102	−	0.776512i	$-0.283013\pi$
$41$	330.839			1.26020			0.630102	+	0.776512i	$0.283013\pi$
$42$	42.9020	+	170.324i	0.157617	+	0.625751i
$43$		−	388.500i		−	1.37781i	−0.724853	−	0.688904i	$-0.758092\pi$
$43$		−	388.500i		−	1.37781i	0.724853	−	0.688904i	$-0.241908\pi$
$44$	56.8342	+	105.660i	0.194729	+	0.362019i
$45$			44.9241i			0.148820i
$46$	3.66788	−	0.923883i	0.0117565	−	0.00296129i
$47$	−550.348			−1.70801			−0.854005	−	0.520265i	$-0.825833\pi$
$47$	−550.348			−1.70801			−0.854005	+	0.520265i	$0.825833\pi$
$48$	−226.654	−	149.727i	−0.681556	−	0.450233i
$49$	−128.939			−0.375915
$50$	−68.5689	+	17.2715i	−0.193942	+	0.0488511i
$51$			390.168i			1.07126i
$52$	324.762	+	603.761i	0.866084	+	1.61013i
$53$			187.705i			0.486477i	0.969966	+	0.243239i	$0.0782098\pi$
$53$			187.705i			0.486477i	−0.969966	+	0.243239i	$0.921790\pi$
$54$	−105.518	−	418.915i	−0.265912	−	1.05569i
$55$	−74.9847			−0.183835
$56$	−244.419	+	223.291i	−0.583246	+	0.532830i
$57$	−256.252			−0.595463
$58$	17.6251	+	69.9727i	0.0399015	+	0.158412i
$59$			779.090i			1.71913i	0.511023	+	0.859567i	$0.329267\pi$
$59$			779.090i			1.71913i	−0.511023	+	0.859567i	$0.670733\pi$
$60$	149.519	−	80.4260i	0.321714	−	0.173049i
$61$		−	358.850i		−	0.753215i	−0.926373	−	0.376607i	$-0.877091\pi$
$61$		−	358.850i		−	0.753215i	0.926373	−	0.376607i	$-0.122909\pi$
$62$	201.415	−	50.7335i	0.412577	−	0.103922i
$63$	−131.455			−0.262886
$64$	46.1625	−	509.915i	0.0901611	−	0.995927i
$65$	−428.477			−0.817632
$66$	174.586	−	43.9756i	0.325607	−	0.0820155i
$67$			283.674i			0.517258i	0.965977	+	0.258629i	$0.0832706\pi$
$67$			283.674i			0.517258i	−0.965977	+	0.258629i	$0.916729\pi$
$68$	−647.648	+	348.369i	−1.15498	+	0.621263i
$69$		−	5.67606i		−	0.00990315i
$70$	−50.5392	−	200.644i	−0.0862942	−	0.342593i
$71$	−534.811			−0.893949			−0.446975	−	0.894547i	$-0.647499\pi$
$71$	−534.811			−0.893949			−0.446975	+	0.894547i	$0.647499\pi$
$72$	150.098	−	137.123i	0.245683	−	0.224446i
$73$	1016.16			1.62921			0.814607	−	0.580014i	$-0.196953\pi$
$73$	1016.16			1.62921			0.814607	+	0.580014i	$0.196953\pi$
$74$	−145.950	−	579.431i	−0.229275	−	0.910237i
$75$			106.111i			0.163368i
$76$	−228.799	−	425.359i	−0.345330	−	0.642000i
$77$		−	219.418i		−	0.324740i
$78$	997.618	−	251.285i	1.44818	−	0.364775i
$79$	1119.59			1.59447			0.797237	−	0.603666i	$-0.206294\pi$
$79$	1119.59			1.59447			0.797237	+	0.603666i	$0.206294\pi$
$80$	267.002	+	176.380i	0.373146	+	0.246499i
$81$	−405.683			−0.556493
$82$	907.411	−	228.563i	1.22203	−	0.307812i
$83$			1190.49i			1.57437i	0.616716	+	0.787186i	$0.288463\pi$
$83$			1190.49i			1.57437i	−0.616716	+	0.787186i	$0.711537\pi$
$84$	235.340	+	437.518i	0.305687	+	0.568299i
$85$		−	459.623i		−	0.586508i
$86$	−268.399	−	1065.56i	−0.336537	−	1.33607i
$87$	108.283			0.133439
$88$	228.879	+	250.535i	0.277256	+	0.303490i
$89$	−398.940			−0.475141			−0.237571	−	0.971370i	$-0.576351\pi$
$89$	−398.940			−0.475141			−0.237571	+	0.971370i	$0.576351\pi$
$90$	31.0362	+	123.216i	0.0363501	+	0.144312i
$91$		−	1253.80i		−	1.44432i
$92$	9.42182	−	5.06797i	0.0106771	−	0.00574318i
$93$		−	311.691i		−	0.347536i
$94$	−1509.47	+	380.213i	−1.65628	+	0.417191i
$95$	301.869			0.326011
$96$	−725.097	−	254.078i	−0.770885	−	0.270122i
$97$	278.022			0.291019			0.145510	−	0.989357i	$-0.453518\pi$
$97$	278.022			0.291019			0.145510	+	0.989357i	$0.453518\pi$
$98$	−353.648	+	89.0787i	−0.364529	+	0.0918195i
$99$			134.745i			0.136791i
$100$	−176.136	+	94.7430i	−0.176136	+	0.0947430i
$101$			116.836i			0.115105i	0.998342	+	0.0575523i	$0.0183296\pi$
$101$			116.836i			0.115105i	−0.998342	+	0.0575523i	$0.981670\pi$
$102$	269.551	+	1070.14i	0.261662	+	1.03882i
$103$	−1458.02			−1.39478			−0.697391	−	0.716691i	$-0.745656\pi$
$103$	−1458.02			−1.39478			−0.697391	+	0.716691i	$0.745656\pi$
$104$	1307.86	+	1431.60i	1.23313	+	1.34981i
$105$	−310.498			−0.288585
$106$	129.678	+	514.830i	0.118825	+	0.471742i
$107$		−	695.124i		−	0.628039i	−0.949417	−	0.314020i	$-0.898324\pi$
$107$		−	695.124i		−	0.628039i	0.949417	−	0.314020i	$-0.101676\pi$
$108$	−578.823	−	1076.08i	−0.515715	−	0.958761i
$109$		−	191.775i		−	0.168520i	−0.996444	−	0.0842602i	$-0.973147\pi$
$109$		−	191.775i		−	0.168520i	0.996444	−	0.0842602i	$-0.0268527\pi$
$110$	−205.665	+	51.8039i	−0.178267	+	0.0449028i
$111$	−896.673			−0.766743
$112$	−516.118	+	781.292i	−0.435434	+	0.659153i
$113$	1234.25			1.02751			0.513753	−	0.857938i	$-0.328255\pi$
$113$	1234.25			1.02751			0.513753	+	0.857938i	$0.328255\pi$
$114$	−702.837	+	177.034i	−0.577427	+	0.145445i
$115$			6.68648i			0.00542189i
$116$	96.6827	+	179.742i	0.0773859	+	0.143867i
$117$			769.958i			0.608398i
$118$	538.242	+	2136.85i	0.419908	+	1.66706i
$119$	1344.93			1.03605
$120$	354.531	−	323.886i	0.269701	−	0.246388i
$121$	1106.09			0.831023
$122$	−247.915	−	984.239i	−0.183977	−	0.730400i
$123$		−	1404.22i		−	1.02939i
$124$	517.384	−	278.299i	0.374697	−	0.201549i
$125$		−	125.000i		−	0.0894427i
$126$	−360.550	+	90.8171i	−0.254923	+	0.0642114i
$127$	786.958			0.549852			0.274926	−	0.961465i	$-0.411347\pi$
$127$	786.958			0.549852			0.274926	+	0.961465i	$0.411347\pi$
$128$	−225.667	−	1430.46i	−0.155831	−	0.987784i
$129$	−1648.96			−1.12545
$130$	−1175.21	+	296.018i	−0.792866	+	0.199711i
$131$			28.0441i			0.0187040i	0.999956	+	0.00935201i	$0.00297688\pi$
$131$			28.0441i			0.0187040i	−0.999956	+	0.00935201i	$0.997023\pi$
$132$	448.466	−	241.229i	0.295712	−	0.159063i
$133$			883.317i			0.575890i
$134$	195.979	+	778.048i	0.126343	+	0.501590i
$135$	763.675			0.486864
$136$	−1535.67	+	1402.92i	−0.968253	+	0.884557i
$137$	−71.4326			−0.0445467			−0.0222733	−	0.999752i	$-0.507090\pi$
$137$	−71.4326			−0.0445467			−0.0222733	+	0.999752i	$0.507090\pi$
$138$	−3.92136	−	15.5680i	−0.00241890	−	0.00960319i
$139$		−	2343.99i		−	1.43032i	−0.698961	−	0.715160i	$-0.746354\pi$
$139$		−	2343.99i		−	1.43032i	0.698961	−	0.715160i	$-0.253646\pi$
$140$	−277.234	−	515.402i	−0.167361	−	0.311139i
$141$			2335.91i			1.39517i
$142$	−1466.86	+	369.479i	−0.866872	+	0.218352i
$143$	−1285.17			−0.751548
$144$	316.949	−	479.792i	0.183419	−	0.277658i
$145$	−127.559			−0.0730566
$146$	2787.08	−	702.024i	1.57987	−	0.397945i
$147$			547.272i			0.307063i
$148$	−800.611	−	1488.41i	−0.444661	−	0.826665i
$149$		−	1417.40i		−	0.779315i	−0.920960	−	0.389657i	$-0.872593\pi$
$149$		−	1417.40i		−	0.779315i	0.920960	−	0.389657i	$-0.127407\pi$
$150$	73.3076	+	291.036i	0.0399036	+	0.158420i
$151$	1296.61			0.698786			0.349393	−	0.936976i	$-0.386388\pi$
$151$	1296.61			0.698786			0.349393	+	0.936976i	$0.386388\pi$
$152$	−921.404	−	1008.59i	−0.491683	−	0.538205i
$153$	−825.926			−0.436419
$154$	−151.587	−	601.809i	−0.0793196	−	0.314904i
$155$			367.177i			0.190273i
$156$	2562.62	−	1378.43i	1.31522	−	0.707453i
$157$			2002.41i			1.01790i	0.860797	+	0.508948i	$0.169966\pi$
$157$			2002.41i			1.01790i	−0.860797	+	0.508948i	$0.830034\pi$
$158$	3070.76	−	773.478i	1.54618	−	0.389459i
$159$	796.702			0.397375
$160$	854.175	+	299.307i	0.422053	+	0.147890i
$161$	−19.5657			−0.00957762
$162$	−1112.69	+	280.270i	−0.539637	+	0.135927i
$163$		−	163.315i		−	0.0784774i	−0.999230	−	0.0392387i	$-0.987507\pi$
$163$		−	163.315i		−	0.0784774i	0.999230	−	0.0392387i	$-0.0124933\pi$
$164$	2330.90	−	1253.79i	1.10983	−	0.596977i
$165$			318.267i			0.150164i
$166$	822.459	+	3265.21i	0.384549	+	1.52669i
$167$	−243.412			−0.112789			−0.0563945	−	0.998409i	$-0.517960\pi$
$167$	−243.412			−0.112789			−0.0563945	+	0.998409i	$0.517960\pi$
$168$	947.743	+	1037.42i	0.435238	+	0.476420i
$169$	−5146.71			−2.34261
$170$	−317.535	−	1260.63i	−0.143258	−	0.568743i
$171$		−	542.447i		−	0.242584i
$172$	−1472.31	−	2737.15i	−0.652688	−	1.21341i
$173$		−	1955.73i		−	0.859490i	−0.902950	−	0.429745i	$-0.858604\pi$
$173$		−	1955.73i		−	0.859490i	0.902950	−	0.429745i	$-0.141396\pi$
$174$	296.994	−	74.8085i	0.129397	−	0.0325932i
$175$	365.771			0.157998
$176$	800.842	+	529.033i	0.342987	+	0.226576i
$177$	3306.79			1.40426
$178$	−1094.20	+	275.611i	−0.460749	+	0.116056i
$179$			3978.28i			1.66118i	0.556887	+	0.830588i	$0.311995\pi$
$179$			3978.28i			1.66118i	−0.556887	+	0.830588i	$0.688005\pi$
$180$	170.250	+	316.509i	0.0704981	+	0.131062i
$181$			964.412i			0.396045i	0.980197	+	0.198022i	$0.0634519\pi$
$181$			964.412i			0.396045i	−0.980197	+	0.198022i	$0.936548\pi$
$182$	−866.197	−	3438.86i	−0.352784	−	1.40058i
$183$	−1523.12			−0.615256
$184$	22.3405	−	20.4094i	0.00895089	−	0.00817717i
$185$	1056.29			0.419785
$186$	−215.335	−	854.894i	−0.0848878	−	0.337010i
$187$		−	1378.59i		−	0.539104i
$188$	−3877.43	+	2085.66i	−1.50421	+	0.809110i
$189$			2234.64i			0.860032i
$190$	827.952	−	208.549i	0.316137	−	0.0796301i
$191$	−908.237			−0.344072			−0.172036	−	0.985091i	$-0.555035\pi$
$191$	−908.237			−0.344072			−0.172036	+	0.985091i	$0.555035\pi$
$192$	−2164.30	−	195.933i	−0.813514	−	0.0736473i
$193$	1243.86			0.463910			0.231955	−	0.972727i	$-0.425488\pi$
$193$	1243.86			0.463910			0.231955	+	0.972727i	$0.425488\pi$
$194$	762.547	−	192.074i	0.282205	−	0.0710831i
$195$			1818.64i			0.667875i
$196$	−908.430	+	488.642i	−0.331060	+	0.178077i
$197$		−	1884.72i		−	0.681627i	−0.940131	−	0.340813i	$-0.889298\pi$
$197$		−	1884.72i		−	0.681627i	0.940131	−	0.340813i	$-0.110702\pi$
$198$	93.0897	+	369.572i	0.0334121	+	0.132648i
$199$	−3886.45			−1.38444			−0.692219	−	0.721688i	$-0.743367\pi$
$199$	−3886.45			−1.38444			−0.692219	+	0.721688i	$0.743367\pi$
$200$	−417.643	+	381.542i	−0.147659	+	0.134895i
$201$	1204.03			0.422517
$202$	80.7170	+	320.452i	0.0281150	+	0.111618i
$203$		−	373.259i		−	0.129052i
$204$	1478.63	+	2748.90i	0.507473	+	0.943438i
$205$			1654.20i			0.563580i
$206$	−3998.98	+	1007.28i	−1.35254	+	0.340684i
$207$	12.0154			0.00403442
$208$	4576.17	+	3023.00i	1.52548	+	1.00773i
$209$	905.421			0.299662
$210$	−851.619	+	214.510i	−0.279844	+	0.0704886i
$211$			3282.65i			1.07103i	0.844527	+	0.535514i	$0.179882\pi$
$211$			3282.65i			1.07103i	−0.844527	+	0.535514i	$0.820118\pi$
$212$	711.350	+	1322.46i	0.230451	+	0.428430i
$213$			2269.97i			0.730214i
$214$	−480.233	−	1906.56i	−0.153402	−	0.609016i
$215$	1942.50			0.616174
$216$	−2330.99	−	2551.55i	−0.734278	−	0.803754i
$217$	−1074.42			−0.336112
$218$	−132.490	−	525.992i	−0.0411621	−	0.163416i
$219$		−	4313.02i		−	1.33081i
$220$	−528.299	+	284.171i	−0.161900	+	0.0870855i
$221$		−	7877.53i		−	2.39774i
$222$	−2459.36	+	619.475i	−0.743519	+	0.187281i
$223$	1453.07			0.436343			0.218171	−	0.975910i	$-0.429991\pi$
$223$	1453.07			0.436343			0.218171	+	0.975910i	$0.429991\pi$
$224$	−875.823	+	2499.46i	−0.261243	+	0.745545i
$225$	−224.620			−0.0665542
$226$	3385.24	−	852.691i	0.996383	−	0.250974i
$227$			4750.20i			1.38891i	0.719537	+	0.694454i	$0.244354\pi$
$227$			4750.20i			1.38891i	−0.719537	+	0.694454i	$0.755646\pi$
$228$	−1805.40	+	971.123i	−0.524412	+	0.282080i
$229$		−	6475.51i		−	1.86862i	−0.356462	−	0.934310i	$-0.616017\pi$
$229$		−	6475.51i		−	1.86862i	0.356462	−	0.934310i	$-0.383983\pi$
$230$	4.61942	+	18.3394i	0.00132433	+	0.00525767i
$231$	−931.303			−0.265261
$232$	389.353	+	426.194i	0.110182	+	0.120608i
$233$	257.988			0.0725379			0.0362690	−	0.999342i	$-0.488453\pi$
$233$	257.988			0.0725379			0.0362690	+	0.999342i	$0.488453\pi$
$234$	531.933	+	2111.81i	0.148605	+	0.589971i
$235$		−	2751.74i		−	0.763845i
$236$	2952.53	+	5489.02i	0.814379	+	1.51400i
$237$		−	4752.01i		−	1.30243i
$238$	3688.83	−	929.160i	1.00467	−	0.253061i
$239$	−257.014			−0.0695600			−0.0347800	−	0.999395i	$-0.511073\pi$
$239$	−257.014			−0.0695600			−0.0347800	+	0.999395i	$0.511073\pi$
$240$	748.634	−	1133.27i	0.201350	−	0.304801i
$241$	1194.01			0.319140			0.159570	−	0.987187i	$-0.448989\pi$
$241$	1194.01			0.319140			0.159570	+	0.987187i	$0.448989\pi$
$242$	3033.74	−	764.154i	0.805852	−	0.202982i
$243$		−	2401.95i		−	0.634096i
$244$	−1359.94	−	2528.25i	−0.356809	−	0.663340i
$245$		−	644.695i		−	0.168114i
$246$	−970.121	−	3851.44i	−0.251434	−	0.998207i
$247$	5173.75			1.33279
$248$	1226.79	−	1120.75i	0.314118	−	0.286966i
$249$	5052.94			1.28601
$250$	−86.3574	−	342.845i	−0.0218469	−	0.0867336i
$251$			587.080i			0.147634i	0.997272	+	0.0738171i	$0.0235181\pi$
$251$			587.080i			0.147634i	−0.997272	+	0.0738171i	$0.976482\pi$
$252$	−926.158	+	498.178i	−0.231518	+	0.124533i
$253$			20.0553i			0.00498367i
$254$	2158.43	−	543.677i	0.533198	−	0.134305i
$255$	−1950.84			−0.479083
$256$	−1607.20	−	3767.51i	−0.392383	−	0.919802i
$257$	−791.436			−0.192095			−0.0960475	−	0.995377i	$-0.530620\pi$
$257$	−791.436			−0.192095			−0.0960475	+	0.995377i	$0.530620\pi$
$258$	−4522.70	+	1139.20i	−1.09136	+	0.274898i
$259$			3090.89i			0.741539i
$260$	−3018.81	+	1623.81i	−0.720071	+	0.387324i
$261$			229.219i			0.0543613i
$262$	19.3746	+	76.9182i	0.00456856	+	0.0181375i
$263$	2705.80			0.634398			0.317199	−	0.948359i	$-0.397258\pi$
$263$	2705.80			0.634398			0.317199	+	0.948359i	$0.397258\pi$
$264$	1063.38	−	971.459i	0.247903	−	0.226474i
$265$	−938.526			−0.217559
$266$	610.248	+	2422.72i	0.140664	+	0.558446i
$267$			1693.27i			0.388115i
$268$	1075.04	+	1998.60i	0.245033	+	0.455538i
$269$			2767.26i			0.627222i	0.949552	+	0.313611i	$0.101539\pi$
$269$			2767.26i			0.627222i	−0.949552	+	0.313611i	$0.898461\pi$
$270$	2094.57	−	527.592i	0.472118	−	0.118919i
$271$	400.361			0.0897423			0.0448712	−	0.998993i	$-0.485712\pi$
$271$	400.361			0.0897423			0.0448712	+	0.998993i	$0.485712\pi$
$272$	−3242.74	+	4908.81i	−0.722868	+	1.09427i
$273$	−5321.65			−1.17978
$274$	−195.922	+	49.3499i	−0.0431974	+	0.0108808i
$275$		−	374.924i		−	0.0822136i
$276$	−21.5107	−	39.9902i	−0.00469127	−	0.00872149i
$277$			6743.86i			1.46281i	0.681942	+	0.731407i	$0.261136\pi$
$277$			6743.86i			1.46281i	−0.681942	+	0.731407i	$0.738864\pi$
$278$	−1619.37	−	6428.99i	−0.349364	−	1.38700i
$279$	659.803			0.141582
$280$	−1116.45	−	1222.09i	−0.238289	−	0.260836i
$281$	−6373.81			−1.35313			−0.676565	−	0.736382i	$-0.736532\pi$
$281$	−6373.81			−1.35313			−0.676565	+	0.736382i	$0.736532\pi$
$282$	1613.79	+	6406.84i	0.340779	+	1.35291i
$283$			2383.90i			0.500736i	0.968151	+	0.250368i	$0.0805516\pi$
$283$			2383.90i			0.500736i	−0.968151	+	0.250368i	$0.919448\pi$
$284$	−3767.97	+	2026.78i	−0.787281	+	0.423477i
$285$		−	1281.26i		−	0.266299i
$286$	−3524.91	+	887.872i	−0.728784	+	0.183570i
$287$	−4840.45			−0.995549
$288$	537.844	−	1534.92i	0.110044	−	0.314049i
$289$	3537.14			0.719956
$290$	−349.864	+	88.1255i	−0.0708438	+	0.0178445i
$291$		−	1180.05i		−	0.237717i
$292$	7159.28	−	3850.96i	1.43481	−	0.771783i
$293$			748.528i			0.149247i	0.997212	+	0.0746237i	$0.0237756\pi$
$293$			748.528i			0.149247i	−0.997212	+	0.0746237i	$0.976224\pi$
$294$	378.088	+	1501.03i	0.0750019	+	0.297762i
$295$	−3895.45			−0.768820
$296$	−3224.16	−	3529.23i	−0.633110	−	0.693015i
$297$	2290.56			0.447514
$298$	−979.224	−	3887.58i	−0.190352	−	0.755710i
$299$			114.600i			0.0221655i
$300$	402.130	+	747.595i	0.0773899	+	0.143875i
$301$			5684.08i			1.08845i
$302$	3556.29	−	895.776i	0.677621	−	0.170683i
$303$	495.900			0.0940222
$304$	−3223.98	−	2129.75i	−0.608250	−	0.401807i
$305$	1794.25			0.336848
$306$	−2265.31	+	570.599i	−0.423200	+	0.106598i
$307$		−	2639.75i		−	0.490745i	−0.969429	−	0.245372i	$-0.921090\pi$
$307$		−	2639.75i		−	0.490745i	0.969429	−	0.245372i	$-0.0789102\pi$
$308$	−831.531	−	1545.89i	−0.153834	−	0.285991i
$309$			6188.45i			1.13932i
$310$	253.668	+	1007.08i	0.0464753	+	0.184510i
$311$	−2880.46			−0.525196			−0.262598	−	0.964905i	$-0.584579\pi$
$311$	−2880.46			−0.525196			−0.262598	+	0.964905i	$0.584579\pi$
$312$	6076.35	−	5551.11i	1.10258	−	1.00727i
$313$	−3620.24			−0.653763			−0.326882	−	0.945065i	$-0.605998\pi$
$313$	−3620.24			−0.653763			−0.326882	+	0.945065i	$0.605998\pi$
$314$	1383.38	+	5492.12i	0.248627	+	0.987065i
$315$		−	657.276i		−	0.117566i
$316$	7887.97	−	4242.92i	1.40422	−	0.755326i
$317$			2066.64i			0.366164i	0.983098	+	0.183082i	$0.0586073\pi$
$317$			2066.64i			0.366164i	−0.983098	+	0.183082i	$0.941393\pi$
$318$	2185.16	−	550.409i	0.385338	−	0.0970610i
$319$	−382.599			−0.0671519
$320$	2549.57	+	230.812i	0.445392	+	0.0403213i
$321$	−2950.41			−0.513008
$322$	−53.6641	+	13.5172i	−0.00928752	+	0.00233939i
$323$			5549.83i			0.956040i
$324$	−2858.21	+	1537.43i	−0.490091	+	0.263619i
$325$		−	2142.39i		−	0.365656i
$326$	−112.828	−	447.933i	−0.0191686	−	0.0761004i
$327$	−813.976			−0.137654
$328$	5526.91	−	5049.16i	0.930403	−	0.849979i
$329$	8052.04			1.34931
$330$	219.878	+	872.930i	0.0366785	+	0.145616i
$331$		−	3193.53i		−	0.530309i	−0.964206	−	0.265155i	$-0.914577\pi$
$331$		−	3193.53i		−	0.530309i	0.964206	−	0.265155i	$-0.0854230\pi$
$332$	4511.61	+	8387.48i	0.745803	+	1.38651i
$333$		−	1898.12i		−	0.312361i
$334$	−667.619	+	168.163i	−0.109373	+	0.0275493i
$335$	−1418.37			−0.231325
$336$	3316.14	+	2190.63i	0.538423	+	0.355680i
$337$	−7803.01			−1.26130			−0.630649	−	0.776068i	$-0.717211\pi$
$337$	−7803.01			−1.26130			−0.630649	+	0.776068i	$0.717211\pi$
$338$	−14116.2	+	3555.66i	−2.27165	+	0.572196i
$339$		−	5238.67i		−	0.839309i
$340$	−1741.84	−	3238.24i	−0.277837	−	0.516524i
$341$			1101.31i			0.174895i
$342$	−374.754	−	1487.80i	−0.0592526	−	0.235237i
$343$	6904.86			1.08696
$344$	−5929.16	−	6490.18i	−0.929300	−	1.01723i
$345$	28.3803			0.00442882
$346$	−1351.14	−	5364.10i	−0.209935	−	0.833456i
$347$		−	9098.25i		−	1.40755i	−0.710423	−	0.703775i	$-0.751496\pi$
$347$		−	9098.25i		−	1.40755i	0.710423	−	0.703775i	$-0.248504\pi$
$348$	762.901	−	410.363i	0.117517	−	0.0632119i
$349$			8700.89i			1.33452i	0.744824	+	0.667261i	$0.232533\pi$
$349$			8700.89i			1.33452i	−0.744824	+	0.667261i	$0.767467\pi$
$350$	1003.22	−	252.696i	0.153212	−	0.0385919i
$351$	13088.7			1.99038
$352$	2562.00	+	897.739i	0.387941	+	0.135937i
$353$	1182.38			0.178276			0.0891382	−	0.996019i	$-0.471589\pi$
$353$	1182.38			0.178276			0.0891382	+	0.996019i	$0.471589\pi$
$354$	9069.73	−	2284.53i	1.36172	−	0.342998i
$355$		−	2674.05i		−	0.399786i
$356$	−2810.70	+	1511.87i	−0.418446	+	0.225081i
$357$		−	5708.48i		−	0.846288i
$358$	2748.43	+	10911.4i	0.405752	+	1.61086i
$359$	−7514.20			−1.10469			−0.552346	−	0.833615i	$-0.686267\pi$
$359$	−7514.20			−1.10469			−0.552346	+	0.833615i	$0.686267\pi$
$360$	685.617	+	750.489i	0.100375	+	0.109873i
$361$	3214.01			0.468584
$362$	666.273	+	2645.15i	0.0967363	+	0.384049i
$363$		−	4694.73i		−	0.678814i
$364$	−4751.53	−	8833.52i	−0.684198	−	1.27198i
$365$			5080.80i			0.728606i
$366$	−4177.53	+	1052.26i	−0.596621	+	0.150280i
$367$	−7217.04			−1.02650			−0.513251	−	0.858238i	$-0.671559\pi$
$367$	−7217.04			−1.02650			−0.513251	+	0.858238i	$0.671559\pi$
$368$	47.1745	−	71.4121i	0.00668245	−	0.0101158i
$369$	2972.53			0.419359
$370$	2897.16	−	729.751i	0.407070	−	0.102535i
$371$		−	2746.28i		−	0.384312i
$372$	−1181.22	−	2196.00i	−0.164633	−	0.306068i
$373$			2350.20i			0.326244i	0.986606	+	0.163122i	$0.0521564\pi$
$373$			2350.20i			0.326244i	−0.986606	+	0.163122i	$0.947844\pi$
$374$	−952.411	−	3781.13i	−0.131679	−	0.522775i
$375$	−530.554			−0.0730605
$376$	−9193.96	+	8399.23i	−1.26102	+	1.15201i
$377$	−2186.25			−0.298667
$378$	1543.82	+	6129.07i	0.210068	+	0.833983i
$379$			3493.78i			0.473518i	0.971568	+	0.236759i	$0.0760852\pi$
$379$			3493.78i			0.473518i	−0.971568	+	0.236759i	$0.923915\pi$
$380$	2126.79	−	1144.00i	0.287111	−	0.154436i
$381$		−	3340.19i		−	0.449142i
$382$	−2491.07	+	627.464i	−0.333650	+	0.0840415i
$383$	14241.7			1.90004			0.950019	−	0.312191i	$-0.101063\pi$
$383$	14241.7			1.90004			0.950019	+	0.312191i	$0.101063\pi$
$384$	−6071.50	+	957.828i	−0.806862	+	0.127289i
$385$	1097.09			0.145228
$386$	3411.59	−	859.329i	0.449859	−	0.113313i
$387$		−	3490.60i		−	0.458494i
$388$	1958.78	−	1053.63i	0.256294	−	0.137860i
$389$		−	7518.81i		−	0.979997i	−0.871723	−	0.489998i	$-0.836997\pi$
$389$		−	7518.81i		−	0.979997i	0.871723	−	0.489998i	$-0.163003\pi$
$390$	1256.43	+	4988.09i	0.163132	+	0.647646i
$391$	−122.930			−0.0158999
$392$	−2154.02	+	1967.82i	−0.277537	+	0.253546i
$393$	119.031			0.0152782
$394$	−1302.07	−	5169.32i	−0.166491	−	0.660981i
$395$			5597.94i			0.713071i
$396$	510.645	+	949.334i	0.0648002	+	0.120469i
$397$		−	4665.28i		−	0.589782i	−0.955531	−	0.294891i	$-0.904717\pi$
$397$		−	4665.28i		−	0.589782i	0.955531	−	0.294891i	$-0.0952834\pi$
$398$	−10659.6	+	2684.99i	−1.34250	+	0.338157i
$399$	3749.18			0.470410
$400$	−881.901	+	1335.01i	−0.110238	+	0.166876i
$401$	−3094.11			−0.385318			−0.192659	−	0.981266i	$-0.561711\pi$
$401$	−3094.11			−0.385318			−0.192659	+	0.981266i	$0.561711\pi$
$402$	3302.37	−	831.818i	0.409720	−	0.103202i
$403$			6293.08i			0.777867i
$404$	442.774	+	823.156i	0.0545268	+	0.101370i
$405$		−	2028.42i		−	0.248871i
$406$	−257.870	−	1023.76i	−0.0315218	−	0.125144i
$407$	3168.24			0.385857
$408$	5954.61	+	6518.04i	0.722543	+	0.790909i
$409$	7341.17			0.887525			0.443762	−	0.896144i	$-0.353643\pi$
$409$	7341.17			0.887525			0.443762	+	0.896144i	$0.353643\pi$
$410$	1142.82	+	4537.05i	0.137658	+	0.546510i
$411$			303.191i			0.0363876i
$412$	−10272.3	+	5525.47i	−1.22835	+	0.660729i
$413$		−	11398.7i		−	1.35810i
$414$	32.9552	−	8.30092i	0.00391222	−	0.000985430i
$415$	−5952.43			−0.704080
$416$	14639.8	+	5129.86i	1.72542	+	0.604596i
$417$	−9948.90			−1.16834
$418$	2483.35	−	625.519i	0.290585	−	0.0731941i
$419$		−	6193.33i		−	0.722110i	−0.932544	−	0.361055i	$-0.882417\pi$
$419$		−	6193.33i		−	0.722110i	0.932544	−	0.361055i	$-0.117583\pi$
$420$	−2187.59	+	1176.70i	−0.254151	+	0.136707i
$421$			4266.62i			0.493925i	0.969025	+	0.246962i	$0.0794324\pi$
$421$			4266.62i			0.493925i	−0.969025	+	0.246962i	$0.920568\pi$
$422$	2267.85	+	9003.50i	0.261605	+	1.03859i
$423$	−4944.77			−0.568376
$424$	2864.70	+	3135.75i	0.328118	+	0.359164i
$425$	2298.12			0.262294
$426$	1568.23	+	6225.97i	0.178359	+	0.708097i
$427$			5250.28i			0.595032i
$428$	−2634.33	−	4897.45i	−0.297511	−	0.553100i
$429$			5454.81i			0.613895i
$430$	5327.81	−	1342.00i	0.597511	−	0.150504i
$431$	−328.807			−0.0367473			−0.0183736	−	0.999831i	$-0.505849\pi$
$431$	−328.807			−0.0367473			−0.0183736	+	0.999831i	$0.505849\pi$
$432$	−8156.11	−	5387.89i	−0.908359	−	0.600058i
$433$	−6914.22			−0.767382			−0.383691	−	0.923462i	$-0.625347\pi$
$433$	−6914.22			−0.767382			−0.383691	+	0.923462i	$0.625347\pi$
$434$	−2946.87	+	742.274i	−0.325932	+	0.0820974i
$435$			541.416i			0.0596756i
$436$	−726.774	−	1351.14i	−0.0798306	−	0.148412i
$437$		−	80.7375i		−	0.00883798i
$438$	−2979.69	−	11829.6i	−0.325058	−	1.29050i
$439$	−11922.4			−1.29619			−0.648093	−	0.761562i	$-0.724433\pi$
$439$	−11922.4			−1.29619			−0.648093	+	0.761562i	$0.724433\pi$
$440$	−1252.67	+	1144.39i	−0.135725	+	0.123993i
$441$	−1158.49			−0.125094
$442$	−5442.26	−	21606.1i	−0.585661	−	2.32511i
$443$			6687.54i			0.717234i	0.933485	+	0.358617i	$0.116752\pi$
$443$			6687.54i			0.717234i	−0.933485	+	0.358617i	$0.883248\pi$
$444$	−6317.44	+	3398.14i	−0.675254	+	0.363217i
$445$		−	1994.70i		−	0.212490i
$446$	3985.41	−	1003.86i	0.423126	−	0.106579i
$447$	−6016.05			−0.636576
$448$	−675.395	+	7460.47i	−0.0712264	+	0.786773i
$449$	3761.85			0.395396			0.197698	−	0.980263i	$-0.436653\pi$
$449$	3761.85			0.395396			0.197698	+	0.980263i	$0.436653\pi$
$450$	−616.079	+	155.181i	−0.0645383	+	0.0162562i
$451$			4961.57i			0.518030i
$452$	8695.79	−	4677.45i	0.904902	−	0.486745i
$453$		−	5503.38i		−	0.570797i
$454$	3281.72	+	13028.7i	0.339249	+	1.34684i
$455$	6268.98			0.645921
$456$	−4280.88	+	3910.84i	−0.439628	+	0.401626i
$457$	957.270			0.0979852			0.0489926	−	0.998799i	$-0.484399\pi$
$457$	957.270			0.0979852			0.0489926	+	0.998799i	$0.484399\pi$
$458$	−4473.67	−	17760.8i	−0.456421	−	1.81202i
$459$			14040.1i			1.42775i
$460$	25.3399	+	47.1091i	0.00256843	+	0.00477494i
$461$			2903.76i			0.293365i	0.989184	+	0.146683i	$0.0468596\pi$
$461$			2903.76i			0.293365i	−0.989184	+	0.146683i	$0.953140\pi$
$462$	−2554.34	+	643.400i	−0.257226	+	0.0647915i
$463$	−6265.25			−0.628879			−0.314440	−	0.949278i	$-0.601817\pi$
$463$	−6265.25			−0.628879			−0.314440	+	0.949278i	$0.601817\pi$
$464$	1362.34	+	899.957i	0.136304	+	0.0900419i
$465$	1558.46			0.155423
$466$	707.597	−	178.233i	0.0703408	−	0.0177178i
$467$		−	4895.67i		−	0.485107i	−0.970138	−	0.242553i	$-0.922015\pi$
$467$		−	4895.67i		−	0.485107i	0.970138	−	0.242553i	$-0.0779849\pi$
$468$	2917.92	+	5424.68i	0.288207	+	0.535803i
$469$		−	4150.38i		−	0.408629i
$470$	−1901.06	−	7547.35i	−0.186574	−	0.740709i
$471$	8499.09			0.831460
$472$	11890.2	+	13015.3i	1.15952	+	1.26923i
$473$	5826.32			0.566373
$474$	−3282.97	−	13033.6i	−0.318126	−	1.26298i
$475$			1509.34i			0.145797i
$476$	9475.63	−	5096.92i	0.912426	−	0.490792i
$477$			1686.50i			0.161885i
$478$	−704.926	+	177.560i	−0.0674531	+	0.0169904i
$479$	−5684.05			−0.542194			−0.271097	−	0.962552i	$-0.587386\pi$
$479$	−5684.05			−0.542194			−0.271097	+	0.962552i	$0.587386\pi$
$480$	1270.39	−	3625.49i	0.120802	−	0.344750i
$481$	18103.9			1.71615
$482$	3274.87	−	824.892i	0.309474	−	0.0779518i
$483$			83.0454i			0.00782339i
$484$	7792.89	−	4191.78i	0.731864	−	0.393668i
$485$			1390.11i			0.130148i
$486$	−1659.41	−	6587.97i	−0.154882	−	0.614890i
$487$	16399.6			1.52595			0.762973	−	0.646430i	$-0.223739\pi$
$487$	16399.6			1.52595			0.762973	+	0.646430i	$0.223739\pi$
$488$	−5476.66	−	5994.86i	−0.508026	−	0.556095i
$489$	−693.179			−0.0641036
$490$	−445.393	−	1768.24i	−0.0410629	−	0.163022i
$491$			10721.8i			0.985472i	0.870179	+	0.492736i	$0.164003\pi$
$491$			10721.8i			0.985472i	−0.870179	+	0.492736i	$0.835997\pi$
$492$	−5321.61	−	9893.35i	−0.487636	−	0.906558i
$493$		−	2345.17i		−	0.214241i
$494$	14190.3	−	3574.34i	1.29242	−	0.325541i
$495$	−673.724			−0.0611750
$496$	2590.51	−	3921.48i	0.234511	−	0.354999i
$497$	7824.73			0.706211
$498$	13859.0	−	3490.87i	1.24706	−	0.314116i
$499$		−	11116.5i		−	0.997281i	−0.866809	−	0.498640i	$-0.833833\pi$
$499$		−	11116.5i		−	0.997281i	0.866809	−	0.498640i	$-0.166167\pi$
$500$	−473.715	−	880.678i	−0.0423703	−	0.0787703i
$501$			1033.14i			0.0921306i
$502$	405.590	+	1610.22i	0.0360605	+	0.143162i
$503$	−6432.33			−0.570186			−0.285093	−	0.958500i	$-0.592024\pi$
$503$	−6432.33			−0.570186			−0.285093	+	0.958500i	$0.592024\pi$
$504$	−2196.05	+	2006.23i	−0.194087	+	0.177310i
$505$	−584.178			−0.0514764
$506$	13.8554	+	55.0069i	0.00121729	+	0.00483272i
$507$			21844.9i			1.91354i
$508$	5544.45	−	2982.35i	0.484243	−	0.260473i
$509$		−	9622.35i		−	0.837924i	−0.908004	−	0.418962i	$-0.862394\pi$
$509$		−	9622.35i		−	0.837924i	0.908004	−	0.418962i	$-0.137606\pi$
$510$	−5350.68	+	1347.76i	−0.464572	+	0.117019i
$511$	−14867.3			−1.28706
$512$	−7010.98	−	9223.01i	−0.605165	−	0.796100i
$513$	−9221.18			−0.793616
$514$	−2170.72	+	546.771i	−0.186277	+	0.0469203i
$515$		−	7290.08i		−	0.623766i
$516$	−11617.6	+	6249.10i	−0.991159	+	0.533142i
$517$		−	8253.53i		−	0.702108i
$518$	2135.37	+	8477.56i	0.181125	+	0.719078i
$519$	−8300.98			−0.702066
$520$	−7158.02	+	6539.28i	−0.603654	+	0.551474i
$521$	−19725.1			−1.65868			−0.829338	−	0.558747i	$-0.811282\pi$
$521$	−19725.1			−1.65868			−0.829338	+	0.558747i	$0.811282\pi$
$522$	158.358	+	628.692i	0.0132781	+	0.0527147i
$523$		−	4068.08i		−	0.340123i	−0.985433	−	0.170062i	$-0.945603\pi$
$523$		−	4068.08i		−	0.340123i	0.985433	−	0.170062i	$-0.0543967\pi$
$524$	106.279	+	197.583i	0.00886037	+	0.0164722i
$525$		−	1552.49i		−	0.129059i
$526$	7421.35	−	1869.33i	0.615183	−	0.154955i
$527$	−6750.52			−0.557984
$528$	2245.44	−	3399.12i	0.185077	−	0.280166i
$529$	−12165.2			−0.999853
$530$	−2574.15	+	648.390i	−0.210970	+	0.0531401i
$531$			6999.98i			0.572078i
$532$	3347.52	+	6223.35i	0.272808	+	0.507174i
$533$			28351.4i			2.30401i
$534$	1169.81	+	4644.23i	0.0947992	+	0.376359i
$535$	3475.62			0.280868
$536$	4329.34	+	4738.98i	0.348878	+	0.381889i
$537$	16885.5			1.35692
$538$	1911.79	+	7589.92i	0.153203	+	0.608224i
$539$		−	1933.69i		−	0.154527i
$540$	5380.42	−	2894.11i	0.428771	−	0.230635i
$541$		−	13192.1i		−	1.04837i	−0.851603	−	0.524187i	$-0.824369\pi$
$541$		−	13192.1i		−	1.04837i	0.851603	−	0.524187i	$-0.175631\pi$
$542$	1098.09	−	276.593i	0.0870241	−	0.0219201i
$543$	4093.38			0.323506
$544$	−5502.75	+	15704.0i	−0.433692	+	1.23769i
$545$	958.875			0.0753646
$546$	−14596.0	+	3676.51i	−1.14405	+	0.288169i
$547$			2125.25i			0.166123i	0.996544	+	0.0830614i	$0.0264697\pi$
$547$			2125.25i			0.166123i	−0.996544	+	0.0830614i	$0.973530\pi$
$548$	−503.273	+	270.709i	−0.0392313	+	0.0211024i
$549$		−	3224.20i		−	0.250648i
$550$	−259.020	−	1028.32i	−0.0200811	−	0.0797234i
$551$	1540.24			0.119086
$552$	−86.6262	−	94.8227i	−0.00667945	−	0.00731145i
$553$	−16380.5			−1.25962
$554$	4659.06	+	18496.8i	0.357301	+	1.41851i
$555$		−	4483.37i		−	0.342898i
$556$	−8883.06	−	16514.4i	−0.677564	−	1.25965i
$557$			18387.1i			1.39872i	0.714769	+	0.699360i	$0.246532\pi$
$557$			18387.1i			1.39872i	−0.714769	+	0.699360i	$0.753468\pi$
$558$	1809.68	−	455.831i	0.137294	−	0.0345822i
$559$	33292.7			2.51902
$560$	−3906.46	−	2580.59i	−0.294782	−	0.194732i
$561$	−5851.32			−0.440362
$562$	−17481.8	+	4403.41i	−1.31215	+	0.330510i
$563$		−	22098.7i		−	1.65426i	−0.562008	−	0.827132i	$-0.689971\pi$
$563$		−	22098.7i		−	1.65426i	0.562008	−	0.827132i	$-0.310029\pi$
$564$	8852.45	+	16457.5i	0.660914	+	1.22870i
$565$			6171.23i			0.459515i
$566$	1646.94	+	6538.46i	0.122308	+	0.485569i
$567$	5935.48			0.439624
$568$	−8934.40	+	8162.11i	−0.659999	+	0.602948i
$569$	−19489.2			−1.43591			−0.717954	−	0.696091i	$-0.754921\pi$
$569$	−19489.2			−1.43591			−0.717954	+	0.696091i	$0.754921\pi$
$570$	−885.171	−	3514.18i	−0.0650451	−	0.258233i
$571$		−	1501.40i		−	0.110038i	−0.998485	−	0.0550189i	$-0.982478\pi$
$571$		−	1501.40i		−	0.110038i	0.998485	−	0.0550189i	$-0.0175219\pi$
$572$	−9054.57	+	4870.43i	−0.661872	+	0.356019i
$573$			3854.95i			0.281052i
$574$	−13276.2	+	3344.07i	−0.965395	+	0.243169i
$575$	−33.4324			−0.00242474
$576$	414.761	−	4581.49i	0.0300030	−	0.331416i
$577$	15875.8			1.14544			0.572718	−	0.819753i	$-0.305889\pi$
$577$	15875.8			1.14544			0.572718	+	0.819753i	$0.305889\pi$
$578$	9701.52	−	2443.67i	0.698149	−	0.175853i
$579$		−	5279.46i		−	0.378941i
$580$	−898.709	+	483.413i	−0.0643394	+	0.0346080i
$581$		−	17417.8i		−	1.24374i
$582$	−815.246	−	3236.58i	−0.0580636	−	0.230516i
$583$	−2815.00			−0.199975
$584$	16975.7	−	15508.3i	1.20284	−	1.09887i
$585$	−3849.79			−0.272084
$586$	517.128	+	2053.03i	0.0364545	+	0.144727i
$587$		−	5444.12i		−	0.382799i	−0.981512	−	0.191399i	$-0.938697\pi$
$587$		−	5444.12i		−	0.382799i	0.981512	−	0.191399i	$-0.0613025\pi$
$588$	2074.01	+	3855.77i	0.145460	+	0.270424i
$589$		−	4433.57i		−	0.310156i
$590$	−10684.3	+	2691.21i	−0.745533	+	0.187789i
$591$	−7999.55			−0.556781
$592$	−11281.3	−	7452.38i	−0.783207	−	0.517383i
$593$	28383.8			1.96557			0.982787	−	0.184744i	$-0.0591456\pi$
$593$	28383.8			1.96557			0.982787	+	0.184744i	$0.0591456\pi$
$594$	6282.45	−	1582.45i	0.433959	−	0.109308i
$595$			6724.67i			0.463335i
$596$	−5371.55	−	9986.18i	−0.369173	−	0.686326i
$597$			16495.8i			1.13087i
$598$	79.1726	+	314.320i	0.00541406	+	0.0214942i
$599$	−2045.77			−0.139546			−0.0697729	−	0.997563i	$-0.522227\pi$
$599$	−2045.77			−0.139546			−0.0697729	+	0.997563i	$0.522227\pi$
$600$	1619.43	+	1772.66i	0.110188	+	0.120614i
$601$	13847.5			0.939851			0.469926	−	0.882706i	$-0.344281\pi$
$601$	13847.5			0.939851			0.469926	+	0.882706i	$0.344281\pi$
$602$	3926.90	+	15590.0i	0.265861	+	1.05549i
$603$			2548.76i			0.172128i
$604$	9135.18	−	4913.79i	0.615406	−	0.331025i
$605$			5530.46i			0.371645i
$606$	1360.13	−	342.598i	0.0911744	−	0.0229655i
$607$	11611.0			0.776405			0.388202	−	0.921574i	$-0.373096\pi$
$607$	11611.0			0.776405			0.388202	+	0.921574i	$0.373096\pi$
$608$	−10313.9	−	3614.06i	−0.687970	−	0.241068i
$609$	−1584.27			−0.105415
$610$	4921.20	−	1239.58i	0.326645	−	0.0822770i
$611$		−	47162.3i		−	3.12272i
$612$	−5819.00	+	3130.03i	−0.384345	+	0.206738i
$613$		−	21644.9i		−	1.42615i	−0.701087	−	0.713076i	$-0.747301\pi$
$613$		−	21644.9i		−	1.42615i	0.701087	−	0.713076i	$-0.252699\pi$
$614$	−1823.70	−	7240.20i	−0.119867	−	0.475881i
$615$	7021.12			0.460356
$616$	−3348.68	−	3665.53i	−0.219030	−	0.239754i
$617$	−3432.62			−0.223974			−0.111987	−	0.993710i	$-0.535722\pi$
$617$	−3432.62			−0.223974			−0.111987	+	0.993710i	$0.535722\pi$
$618$	4275.35	+	16973.4i	0.278284	+	1.10481i
$619$			2936.25i			0.190659i	0.995446	+	0.0953295i	$0.0303905\pi$
$619$			2936.25i			0.190659i	−0.995446	+	0.0953295i	$0.969610\pi$
$620$	1391.50	+	2586.92i	0.0901353	+	0.167570i
$621$		−	204.252i		−	0.0131986i
$622$	−7900.40	+	1989.99i	−0.509288	+	0.128282i
$623$	5836.82			0.375357
$624$	12830.9	−	19423.2i	0.823153	−	1.24608i
$625$	625.000			0.0400000
$626$	−9929.43	+	2501.08i	−0.633961	+	0.159685i
$627$		−	3843.00i		−	0.244776i
$628$	7588.57	+	14107.8i	0.482193	+	0.896439i
$629$			19419.9i			1.23104i
$630$	−454.086	−	1802.75i	−0.0287162	−	0.114005i
$631$	−18455.3			−1.16433			−0.582167	−	0.813069i	$-0.697795\pi$
$631$	−18455.3			−1.16433			−0.582167	+	0.813069i	$0.697795\pi$
$632$	18703.5	−	17086.8i	1.17719	−	1.07544i
$633$	13933.0			0.874859
$634$	1427.76	+	5668.28i	0.0894376	+	0.355073i
$635$			3934.79i			0.245901i
$636$	5613.10	−	3019.28i	0.349959	−	0.188242i
$637$		−	11049.5i		−	0.687278i
$638$	−1049.38	+	264.323i	−0.0651179	+	0.0164022i
$639$	−4805.18			−0.297480
$640$	7152.32	−	1128.34i	0.441750	−	0.0696896i
$641$	−14764.4			−0.909761			−0.454880	−	0.890552i	$-0.650318\pi$
$641$	−14764.4			−0.909761			−0.454880	+	0.890552i	$0.650318\pi$
$642$	−8092.25	+	2038.32i	−0.497470	+	0.125305i
$643$		−	21285.4i		−	1.30547i	−0.757588	−	0.652733i	$-0.773622\pi$
$643$		−	21285.4i		−	1.30547i	0.757588	−	0.652733i	$-0.226378\pi$
$644$	−137.849	+	74.1487i	−0.00843480	+	0.00453706i
$645$		−	8244.81i		−	0.503316i
$646$	3834.16	+	15221.8i	0.233518	+	0.927083i
$647$	18831.7			1.14428			0.572140	−	0.820156i	$-0.306113\pi$
$647$	18831.7			1.14428			0.572140	+	0.820156i	$0.306113\pi$
$648$	−6777.23	+	6191.41i	−0.410856	+	0.375342i
$649$	−11684.0			−0.706681
$650$	−1480.09	−	5876.04i	−0.0893136	−	0.354581i
$651$			4560.30i			0.274550i
$652$	−618.918	−	1150.62i	−0.0371759	−	0.0691134i
$653$			26184.9i			1.56921i	0.619996	+	0.784605i	$0.287134\pi$
$653$			26184.9i			1.56921i	−0.619996	+	0.784605i	$0.712866\pi$
$654$	−2232.54	+	562.343i	−0.133485	+	0.0336229i
$655$	−140.221			−0.00836469
$656$	11670.7	−	17666.9i	0.694610	−	1.05149i
$657$	9130.01			0.542155
$658$	22084.8	−	5562.83i	1.30844	−	0.329577i
$659$			5338.89i			0.315590i	0.987472	+	0.157795i	$0.0504385\pi$
$659$			5338.89i			0.315590i	−0.987472	+	0.157795i	$0.949561\pi$
$660$	1206.14	+	2242.33i	0.0711350	+	0.132246i
$661$			23161.9i			1.36293i	0.731852	+	0.681464i	$0.238656\pi$
$661$			23161.9i			1.36293i	−0.731852	+	0.681464i	$0.761344\pi$
$662$	−2206.28	−	8759.08i	−0.129531	−	0.514247i
$663$	−33435.6			−1.95857
$664$	18168.8	+	19887.9i	1.06188	+	1.16235i
$665$	−4416.59			−0.257546
$666$	−1311.33	−	5206.08i	−0.0762961	−	0.302900i
$667$			34.1169i			0.00198052i
$668$	−1714.94	+	922.461i	−0.0993308	+	0.0534298i
$669$		−	6167.44i		−	0.356423i
$670$	−3890.24	+	979.894i	−0.224318	+	0.0565024i
$671$	5381.66			0.309622
$672$	10608.8	+	3717.37i	0.608991	+	0.213394i
$673$	3571.25			0.204549			0.102275	−	0.994756i	$-0.467388\pi$
$673$	3571.25			0.204549			0.102275	+	0.994756i	$0.467388\pi$
$674$	−21401.8	+	5390.79i	−1.22309	+	0.308079i
$675$			3818.38i			0.217732i
$676$	−36260.8	+	19504.6i	−2.06308	+	1.10973i
$677$		−	1010.61i		−	0.0573721i	−0.999588	−	0.0286861i	$-0.990868\pi$
$677$		−	1010.61i		−	0.0573721i	0.999588	−	0.0286861i	$-0.00913231\pi$
$678$	−3619.19	−	14368.4i	−0.205006	−	0.813887i
$679$	−4067.69			−0.229902
$680$	−7014.62	−	7678.34i	−0.395586	−	0.433016i
$681$	20161.9			1.13452
$682$	760.848	+	3020.62i	0.0427190	+	0.169597i
$683$			24805.2i			1.38967i	0.719168	+	0.694836i	$0.244523\pi$
$683$			24805.2i			1.38967i	−0.719168	+	0.694836i	$0.755477\pi$
$684$	−2055.72	−	3821.77i	−0.114916	−	0.213639i
$685$		−	357.163i		−	0.0199219i
$686$	18938.3	−	4770.29i	1.05404	−	0.265496i
$687$	−27484.9			−1.52637
$688$	−20746.1	−	13704.8i	−1.14962	−	0.759431i
$689$	−16085.5			−0.889417
$690$	77.8402	−	19.6068i	0.00429468	−	0.00108177i
$691$			12948.4i			0.712854i	0.934323	+	0.356427i	$0.116005\pi$
$691$			12948.4i			0.712854i	−0.934323	+	0.356427i	$0.883995\pi$
$692$	−7411.68	−	13779.0i	−0.407153	−	0.756934i
$693$		−	1971.43i		−	0.108064i
$694$	−6285.61	−	24954.3i	−0.343802	−	1.36492i
$695$	11719.9			0.639659
$696$	1808.95	−	1652.58i	0.0985173	−	0.0900014i
$697$	−30412.3			−1.65272
$698$	6011.09	+	23864.4i	0.325965	+	1.29410i
$699$		−	1095.01i		−	0.0592519i
$700$	2577.01	−	1386.17i	0.139145	−	0.0748460i
$701$			27490.7i			1.48118i	0.671954	+	0.740592i	$0.265455\pi$
$701$			27490.7i			1.48118i	−0.671954	+	0.740592i	$0.734545\pi$
$702$	35899.1	−	9042.45i	1.93009	−	0.486161i
$703$	−12754.5			−0.684273
$704$	7647.16	+	692.296i	0.409394	+	0.0370623i
$705$	−11679.6			−0.623940
$706$	3242.97	−	816.856i	0.172877	−	0.0435450i
$707$		−	1709.40i		−	0.0909316i
$708$	23297.8	−	12531.8i	1.23670	−	0.665218i
$709$		−	11490.7i		−	0.608663i	−0.952566	−	0.304332i	$-0.901567\pi$
$709$		−	11490.7i		−	0.608663i	0.952566	−	0.304332i	$-0.0984331\pi$
$710$	−1847.40	−	7334.28i	−0.0976501	−	0.387677i
$711$	10059.3			0.530595
$712$	−6664.58	+	6088.49i	−0.350795	+	0.320472i
$713$	98.2048			0.00515820
$714$	−3943.76	−	15657.0i	−0.206711	−	0.820654i
$715$		−	6425.85i		−	0.336102i
$716$	15076.6	+	28028.7i	0.786924	+	1.46296i
$717$			1090.88i			0.0568195i
$718$	−20609.6	+	5191.26i	−1.07123	+	0.269827i
$719$	30178.1			1.56530			0.782652	−	0.622459i	$-0.213866\pi$
$719$	30178.1			1.56530			0.782652	+	0.622459i	$0.213866\pi$
$720$	2398.96	+	1584.74i	0.124172	+	0.0820277i
$721$	21332.0			1.10186
$722$	8815.26	−	2220.43i	0.454391	−	0.114454i
$723$		−	5067.88i		−	0.260687i
$724$	3654.85	+	6794.69i	0.187612	+	0.348788i
$725$		−	637.796i		−	0.0326719i
$726$	−3243.40	−	12876.5i	−0.165804	−	0.658253i
$727$	24019.3			1.22535			0.612674	−	0.790336i	$-0.290094\pi$
$727$	24019.3			1.22535			0.612674	+	0.790336i	$0.290094\pi$
$728$	−19135.0	−	20945.6i	−0.974163	−	1.06634i
$729$	−21148.4			−1.07445
$730$	3510.12	+	13935.4i	0.177966	+	0.706538i
$731$			35712.7i			1.80695i
$732$	−10731.0	+	5772.18i	−0.541843	+	0.291456i
$733$		−	14231.8i		−	0.717142i	−0.933502	−	0.358571i	$-0.883264\pi$
$733$		−	14231.8i		−	0.717142i	0.933502	−	0.358571i	$-0.116736\pi$
$734$	−19794.6	+	4985.96i	−0.995411	+	0.250729i
$735$	−2736.36			−0.137323
$736$	80.0525	−	228.457i	0.00400920	−	0.0114416i
$737$	−4254.24			−0.212628
$738$	8152.92	−	2053.60i	0.406657	−	0.102431i
$739$			34171.8i			1.70099i	0.525985	+	0.850494i	$0.323697\pi$
$739$			34171.8i			1.70099i	−0.525985	+	0.850494i	$0.676303\pi$
$740$	7442.04	−	4003.06i	0.369696	−	0.198859i
$741$		−	21959.6i		−	1.08867i
$742$	−1897.30	−	7532.38i	−0.0938705	−	0.372672i
$743$	−1648.56			−0.0813994			−0.0406997	−	0.999171i	$-0.512959\pi$
$743$	−1648.56			−0.0813994			−0.0406997	+	0.999171i	$0.512959\pi$
$744$	−4756.93	−	5207.03i	−0.234405	−	0.256585i
$745$	7087.00			0.348520
$746$	1623.66	+	6446.04i	0.0796870	+	0.316362i
$747$			10696.3i			0.523905i
$748$	−5224.47	−	9712.75i	−0.255382	−	0.474777i
$749$			10170.2i			0.496145i
$750$	−1455.18	+	366.538i	−0.0708475	+	0.0178454i
$751$	7622.18			0.370356			0.185178	−	0.982705i	$-0.440714\pi$
$751$	7622.18			0.370356			0.185178	+	0.982705i	$0.440714\pi$
$752$	−19414.1	+	29388.8i	−0.941435	+	1.42513i
$753$	2491.82			0.120594
$754$	−5996.35	+	1510.39i	−0.289621	+	0.0729512i
$755$			6483.06i			0.312507i
$756$	8468.66	+	15744.0i	0.407410	+	0.757412i
$757$		−	1436.99i		−	0.0689939i	−0.999405	−	0.0344970i	$-0.989017\pi$
$757$		−	1436.99i		−	0.0689939i	0.999405	−	0.0344970i	$-0.0109829\pi$
$758$	2413.71	+	9582.59i	0.115660	+	0.459176i
$759$	85.1235			0.00407087
$760$	5042.93	−	4607.02i	0.240693	−	0.219887i
$761$	−4491.30			−0.213942			−0.106971	−	0.994262i	$-0.534115\pi$
$761$	−4491.30			−0.213942			−0.106971	+	0.994262i	$0.534115\pi$
$762$	−2307.60	−	9161.32i	−0.109705	−	0.435538i
$763$			2805.83i			0.133129i
$764$	−6398.92	+	3441.96i	−0.303017	+	0.162992i
$765$		−	4129.63i		−	0.195173i
$766$	39061.4	−	9838.99i	1.84249	−	0.464095i
$767$	−66764.5			−3.14306
$768$	−15990.9	+	6821.64i	−0.751332	+	0.320514i
$769$	7977.22			0.374078			0.187039	−	0.982353i	$-0.440111\pi$
$769$	7977.22			0.374078			0.187039	+	0.982353i	$0.440111\pi$
$770$	3009.05	−	757.934i	0.140829	−	0.0354728i
$771$			3359.19i			0.156911i
$772$	8763.49	−	4713.86i	0.408556	−	0.219761i
$773$		−	21972.3i		−	1.02237i	−0.859472	−	0.511183i	$-0.829208\pi$
$773$		−	21972.3i		−	1.02237i	0.859472	−	0.511183i	$-0.170792\pi$
$774$	−2411.52	−	9573.87i	−0.111990	−	0.444607i
$775$	−1835.88			−0.0850928
$776$	4644.56	−	4243.08i	0.214858	−	0.196286i
$777$	13119.1			0.605719
$778$	−5194.44	−	20622.3i	−0.239370	−	0.950314i
$779$		−	19974.0i		−	0.918668i
$780$	6892.14	+	12813.1i	0.316382	+	0.588183i
$781$		−	8020.53i		−	0.367474i
$782$	−337.168	+	84.9277i	−0.0154183	+	0.00388364i
$783$	3896.55			0.177843
$784$	−4548.46	+	6885.39i	−0.207200	+	0.313656i
$785$	−10012.1			−0.455217
$786$	326.474	−	82.2339i	0.0148154	−	0.00373179i
$787$		−	14770.5i		−	0.669010i	−0.942394	−	0.334505i	$-0.891431\pi$
$787$		−	14770.5i		−	0.669010i	0.942394	−	0.334505i	$-0.108569\pi$
$788$	−7142.54	−	13278.6i	−0.322897	−	0.600294i
$789$		−	11484.6i		−	0.518203i
$790$	3867.39	+	15353.8i	0.174172	+	0.691472i
$791$	−18058.0			−0.811720
$792$	2056.43	+	2251.01i	0.0922627	+	0.100993i
$793$	30751.8			1.37709
$794$	−3223.05	−	12795.7i	−0.144058	−	0.571918i
$795$			3983.51i			0.177711i
$796$	−27381.7	+	14728.5i	−1.21924	+	0.655829i
$797$		−	33342.5i		−	1.48187i	−0.671576	−	0.740936i	$-0.734382\pi$
$797$		−	33342.5i		−	1.48187i	0.671576	−	0.740936i	$-0.265618\pi$
$798$	10283.1	−	2590.16i	0.456162	−	0.114900i
$799$	50590.5			2.24001
$800$	−1496.54	+	4270.88i	−0.0661382	+	0.188748i
$801$	−3584.40			−0.158113
$802$	−8486.39	+	2137.60i	−0.373647	+	0.0941161i
$803$			15239.3i			0.669718i
$804$	8482.93	−	4562.95i	0.372102	−	0.200153i
$805$		−	97.8287i		−	0.00428324i
$806$	4347.63	+	17260.4i	0.189999	+	0.754307i
$807$	11745.4			0.512341
$808$	1783.11	+	1951.82i	0.0776355	+	0.0849813i
$809$	27061.3			1.17605			0.588026	−	0.808842i	$-0.299905\pi$
$809$	27061.3			1.17605			0.588026	+	0.808842i	$0.299905\pi$
$810$	−1401.35	−	5563.45i	−0.0607882	−	0.241333i
$811$		−	36672.2i		−	1.58784i	−0.608025	−	0.793918i	$-0.708038\pi$
$811$		−	36672.2i		−	1.58784i	0.608025	−	0.793918i	$-0.291962\pi$
$812$	−1414.55	−	2629.77i	−0.0611341	−	0.113654i
$813$		−	1699.30i		−	0.0733052i
$814$	8689.70	−	2188.81i	0.374169	−	0.0942477i
$815$	816.575			0.0350962
$816$	20835.1	+	13763.6i	0.893841	+	0.590468i
$817$	−23455.2			−1.00440
$818$	20135.0	−	5071.72i	0.860642	−	0.216783i
$819$		−	11265.1i		−	0.480629i
$820$	6268.93	+	11654.5i	0.266976	+	0.496333i
$821$			24984.9i			1.06209i	0.847342	+	0.531047i	$0.178201\pi$
$821$			24984.9i			1.06209i	−0.847342	+	0.531047i	$0.821799\pi$
$822$	209.462	+	831.578i	0.00888787	+	0.0352854i
$823$	−30397.5			−1.28747			−0.643737	−	0.765247i	$-0.722617\pi$
$823$	−30397.5			−1.28747			−0.643737	+	0.765247i	$0.722617\pi$
$824$	−24357.2	+	22251.8i	−1.02976	+	0.940749i
$825$	−1591.34			−0.0671555
$826$	−7874.92	−	31263.9i	−0.331723	−	1.31696i
$827$		−	21641.5i		−	0.909972i	−0.890498	−	0.454986i	$-0.849644\pi$
$827$		−	21641.5i		−	0.909972i	0.890498	−	0.454986i	$-0.150356\pi$
$828$	84.6533	−	45.5348i	0.00355302	−	0.00191116i
$829$		−	36955.2i		−	1.54826i	−0.633028	−	0.774129i	$-0.718188\pi$
$829$		−	36955.2i		−	1.54826i	0.633028	−	0.774129i	$-0.281812\pi$
$830$	−16326.1	+	4112.29i	−0.682754	+	0.171976i
$831$	28623.8			1.19489
$832$	43697.4	+	3955.91i	1.82083	+	0.164840i
$833$	11852.7			0.493002
$834$	−27287.4	+	6873.29i	−1.13296	+	0.285375i
$835$		−	1217.06i		−	0.0504407i
$836$	6379.08	−	3431.29i	0.263906	−	0.141954i
$837$		−	11216.2i		−	0.463186i
$838$	−4278.72	−	16986.8i	−0.176380	−	0.700238i
$839$	−4786.98			−0.196978			−0.0984891	−	0.995138i	$-0.531401\pi$
$839$	−4786.98			−0.196978			−0.0984891	+	0.995138i	$0.531401\pi$
$840$	−5187.09	+	4738.71i	−0.213061	+	0.194644i
$841$	23738.1			0.973314
$842$	2947.63	+	11702.3i	0.120644	+	0.478964i
$843$			27053.2i			1.10529i
$844$	12440.3	+	23127.6i	0.507362	+	0.943230i
$845$		−	25733.6i		−	1.04765i
$846$	−13562.3	+	3416.14i	−0.551160	+	0.138829i
$847$	−16183.0			−0.656500
$848$	10023.5	+	6621.50i	0.405907	+	0.268141i
$849$	10118.3			0.409021
$850$	6303.17	−	1587.68i	0.254349	−	0.0640669i
$851$		−	282.515i		−	0.0113801i
$852$	8602.54	+	15992.9i	0.345913	+	0.643084i
$853$		−	4074.67i		−	0.163557i	−0.996651	−	0.0817785i	$-0.973940\pi$
$853$		−	4074.67i		−	0.163557i	0.996651	−	0.0817785i	$-0.0260600\pi$
$854$	3627.20	+	14400.2i	0.145340	+	0.577009i
$855$	2712.23			0.108487
$856$	−10608.8	−	11612.6i	−0.423598	−	0.463679i
$857$	−6011.57			−0.239616			−0.119808	−	0.992797i	$-0.538228\pi$
$857$	−6011.57			−0.239616			−0.119808	+	0.992797i	$0.538228\pi$
$858$	3768.51	+	14961.2i	0.149947	+	0.595301i
$859$			16761.1i			0.665752i	0.942971	+	0.332876i	$0.108019\pi$
$859$			16761.1i			0.665752i	−0.942971	+	0.332876i	$0.891981\pi$
$860$	13685.7	−	7361.53i	0.542651	−	0.291891i
$861$			20544.9i			0.813205i
$862$	−901.837	+	227.159i	−0.0356342	+	0.00897573i
$863$	25926.9			1.02267			0.511334	−	0.859382i	$-0.329152\pi$
$863$	25926.9			1.02267			0.511334	+	0.859382i	$0.329152\pi$
$864$	−26092.5	−	9142.95i	−1.02741	−	0.360011i
$865$	9778.67			0.384375
$866$	−18964.0	+	4776.76i	−0.744138	+	0.187437i
$867$		−	15013.2i		−	0.588089i
$868$	−7569.75	+	4071.75i	−0.296007	+	0.159221i
$869$			16790.4i			0.655438i
$870$	374.042	+	1484.97i	0.0145761	+	0.0578681i
$871$	−24309.6			−0.945692
$872$	−2926.81	−	3203.74i	−0.113663	−	0.124418i
$873$	2497.98			0.0968427
$874$	−55.7783	−	221.443i	−0.00215873	−	0.00857029i
$875$			1828.85i			0.0706589i
$876$	−16345.1	−	30387.1i	−0.630424	−	1.17201i
$877$			26838.9i			1.03339i	0.856169	+	0.516697i	$0.172839\pi$
$877$			26838.9i			1.03339i	−0.856169	+	0.516697i	$0.827161\pi$
$878$	−32700.3	+	8236.71i	−1.25692	+	0.316601i
$879$	3177.08			0.121911
$880$	−2645.17	+	4004.21i	−0.101328	+	0.153389i
$881$	−16191.5			−0.619190			−0.309595	−	0.950869i	$-0.600193\pi$
$881$	−16191.5			−0.619190			−0.309595	+	0.950869i	$0.600193\pi$
$882$	−3177.46	+	800.355i	−0.121305	+	0.0305548i
$883$			22021.1i			0.839263i	0.907695	+	0.419631i	$0.137841\pi$
$883$			22021.1i			0.839263i	−0.907695	+	0.419631i	$0.862159\pi$
$884$	−29853.6	−	55500.5i	−1.13584	−	2.11163i
$885$			16534.0i			0.628004i
$886$	4620.15	+	18342.3i	0.175189	+	0.695510i
$887$	−8897.22			−0.336797			−0.168399	−	0.985719i	$-0.553860\pi$
$887$	−8897.22			−0.336797			−0.168399	+	0.985719i	$0.553860\pi$
$888$	−14979.6	+	13684.7i	−0.566083	+	0.517151i
$889$	−11513.8			−0.434378
$890$	−1378.06	−	5470.98i	−0.0519018	−	0.206053i
$891$		−	6084.01i		−	0.228756i
$892$	10237.5	−	5506.71i	0.384278	−	0.206702i
$893$			33226.5i			1.24511i
$894$	−16500.6	+	4156.25i	−0.617295	+	0.155487i
$895$	−19891.4			−0.742900
$896$	3301.70	+	20928.9i	0.123105	+	0.780340i
$897$	486.412			0.0181057
$898$	10317.8	−	2598.91i	0.383420	−	0.0965777i
$899$			1873.47i			0.0695036i
$900$	−1582.55	+	851.248i	−0.0586128	+	0.0315277i
$901$		−	17254.7i		−	0.638001i
$902$	3427.75	+	13608.4i	0.126532	+	0.502339i
$903$	24125.7			0.889094
$904$	20619.0	−	18836.7i	0.758603	−	0.693029i
$905$	−4822.06			−0.177117
$906$	−3802.06	−	15094.4i	−0.139420	−	0.553508i
$907$			15822.5i			0.579246i	0.957141	+	0.289623i	$0.0935299\pi$
$907$			15822.5i			0.579246i	−0.957141	+	0.289623i	$0.906470\pi$
$908$	18001.9	+	33467.2i	0.657946	+	1.22318i
$909$			1049.75i			0.0383035i
$910$	17194.3	−	4330.98i	0.626357	−	0.157770i
$911$	4136.51			0.150438			0.0752188	−	0.997167i	$-0.476034\pi$
$911$	4136.51			0.150438			0.0752188	+	0.997167i	$0.476034\pi$
$912$	−9039.56	+	13684.0i	−0.328212	+	0.496843i
$913$	−17853.7			−0.647174
$914$	2625.56	−	661.339i	0.0950173	−	0.0239334i
$915$		−	7615.58i		−	0.275151i
$916$	−24540.4	−	45622.7i	−0.885193	−	1.64565i
$917$		−	410.309i		−	0.0147760i
$918$	9699.75	+	38508.6i	0.348736	+	1.38450i
$919$	−8655.85			−0.310697			−0.155348	−	0.987860i	$-0.549650\pi$
$919$	−8655.85			−0.310697			−0.155348	+	0.987860i	$0.549650\pi$
$920$	102.047	+	111.702i	0.00365694	+	0.00400296i
$921$	−11204.2			−0.400860
$922$	2006.09	+	7964.30i	0.0716562	+	0.284480i
$923$		−	45830.9i		−	1.63439i
$924$	−6561.43	+	3529.38i	−0.233609	+	0.125658i
$925$			5281.47i			0.187734i
$926$	−17184.1	+	4328.41i	−0.609831	+	0.153607i
$927$	−13100.0			−0.464143
$928$	4358.31	+	1527.18i	0.154169	+	0.0540216i
$929$	−19787.3			−0.698817			−0.349409	−	0.936970i	$-0.613618\pi$
$929$	−19787.3			−0.698817			−0.349409	+	0.936970i	$0.613618\pi$
$930$	4274.47	−	1076.67i	0.150715	−	0.0379630i
$931$			7784.52i			0.274036i
$932$	1817.63	−	977.701i	0.0638826	−	0.0343623i
$933$			12225.9i			0.429002i
$934$	−3382.22	−	13427.6i	−0.118490	−	0.470413i
$935$	6892.95			0.241095
$936$	11750.8	+	12862.7i	0.410351	+	0.449178i
$937$	−21427.2			−0.747061			−0.373531	−	0.927618i	$-0.621853\pi$
$937$	−21427.2			−0.747061			−0.373531	+	0.927618i	$0.621853\pi$
$938$	−2867.33	−	11383.5i	−0.0998099	−	0.396252i
$939$			15365.8i			0.534021i
$940$	−10428.3	−	19387.2i	−0.361845	−	0.672702i
$941$		−	40905.9i		−	1.41710i	−0.705659	−	0.708552i	$-0.749349\pi$
$941$		−	40905.9i		−	1.41710i	0.705659	−	0.708552i	$-0.250651\pi$
$942$	23310.9	−	5871.68i	0.806275	−	0.203089i
$943$	442.430			0.0152784
$944$	41603.7	+	27483.2i	1.43441	+	0.947567i
$945$	−11173.2			−0.384618
$946$	15980.2	−	4025.17i	0.549218	−	0.138340i
$947$			4430.18i			0.152019i	0.997107	+	0.0760093i	$0.0242179\pi$
$947$			4430.18i			0.152019i	−0.997107	+	0.0760093i	$0.975782\pi$
$948$	−18008.8	−	33480.0i	−0.616981	−	1.14702i
$949$			87080.3i			2.97866i
$950$	1042.74	+	4139.76i	0.0356117	+	0.141381i
$951$	8771.69			0.299097
$952$	22468.1	−	20525.9i	0.764911	−	0.698792i
$953$	−12381.1			−0.420844			−0.210422	−	0.977611i	$-0.567484\pi$
$953$	−12381.1			−0.420844			−0.210422	+	0.977611i	$0.567484\pi$
$954$	1165.13	+	4625.65i	0.0395414	+	0.156982i
$955$		−	4541.19i		−	0.153874i
$956$	−1810.77	+	974.010i	−0.0612600	+	0.0329516i
$957$			1623.92i			0.0548524i
$958$	−15590.0	+	3926.88i	−0.525771	+	0.132434i
$959$	1045.12			0.0351915
$960$	979.667	−	10821.5i	0.0329361	−	0.363815i
$961$	−24398.2			−0.818980
$962$	49654.6	−	12507.3i	1.66417	−	0.419179i
$963$		−	6245.56i		−	0.208993i
$964$	8412.29	−	4524.95i	0.281060	−	0.151181i
$965$			6219.28i			0.207467i
$966$	57.3727	+	227.773i	0.00191091	+	0.00758643i
$967$	51294.8			1.70582			0.852911	−	0.522056i	$-0.174835\pi$
$967$	51294.8			1.70582			0.852911	+	0.522056i	$0.174835\pi$
$968$	18478.1	−	16880.8i	0.613541	−	0.560506i
$969$	23555.9			0.780933
$970$	960.371	+	3812.74i	0.0317893	+	0.126206i
$971$		−	11036.3i		−	0.364750i	−0.983229	−	0.182375i	$-0.941621\pi$
$971$		−	11036.3i		−	0.364750i	0.983229	−	0.182375i	$-0.0583785\pi$
$972$	−9102.72	−	16922.8i	−0.300381	−	0.558434i
$973$			34294.5i			1.12994i
$974$	44980.1	−	11329.8i	1.47973	−	0.372721i
$975$	−9093.21			−0.298683
$976$	−19162.7	−	12658.8i	−0.628468	−	0.415163i
$977$	24788.2			0.811713			0.405857	−	0.913937i	$-0.366973\pi$
$977$	24788.2			0.811713			0.405857	+	0.913937i	$0.366973\pi$
$978$	−1901.22	+	478.890i	−0.0621619	+	0.0156577i
$979$		−	5982.88i		−	0.195315i
$980$	−2443.21	−	4542.15i	−0.0796383	−	0.148055i
$981$		−	1723.06i		−	0.0560787i
$982$	7407.24	+	29407.2i	0.240707	+	0.955623i
$983$	28853.0			0.936183			0.468091	−	0.883680i	$-0.344942\pi$
$983$	28853.0			0.936183			0.468091	+	0.883680i	$0.344942\pi$
$984$	−21430.8	−	23458.6i	−0.694298	−	0.759992i
$985$	9423.58			0.304833
$986$	−1620.18	−	6432.22i	−0.0523297	−	0.207752i
$987$		−	34176.3i		−	1.10217i
$988$	36451.3	−	19607.1i	1.17376	−	0.631360i
$989$		−	519.540i		−	0.0167041i
$990$	−1847.86	+	465.448i	−0.0593221	+	0.0149423i
$991$	−50061.0			−1.60468			−0.802342	−	0.596865i	$-0.796413\pi$
$991$	−50061.0			−1.60468			−0.802342	+	0.596865i	$0.796413\pi$
$992$	4395.95	−	12545.3i	0.140697	−	0.401527i
$993$	−13554.7			−0.433178
$994$	21461.3	−	5405.79i	0.684821	−	0.172496i
$995$		−	19432.2i		−	0.619139i
$996$	35600.1	−	19149.2i	1.13256	−	0.609203i
$997$		−	7718.06i		−	0.245169i	−0.992458	−	0.122584i	$-0.960882\pi$
$997$		−	7718.06i		−	0.245169i	0.992458	−	0.122584i	$-0.0391182\pi$
$998$	−7679.94	−	30489.9i	−0.243592	−	0.967074i
$999$	−32266.6			−1.02189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.4.d.a.21.11	✓	12
3.2	odd	2		360.4.k.c.181.2		12
4.3	odd	2		160.4.d.a.81.9		12
5.2	odd	4		200.4.f.c.149.6		12
5.3	odd	4		200.4.f.b.149.7		12
5.4	even	2		200.4.d.b.101.2		12
8.3	odd	2		160.4.d.a.81.4		12
8.5	even	2	inner	40.4.d.a.21.12	yes	12
12.11	even	2		1440.4.k.c.721.5		12
16.3	odd	4		1280.4.a.bd.1.2		6
16.5	even	4		1280.4.a.bc.1.2		6
16.11	odd	4		1280.4.a.ba.1.5		6
16.13	even	4		1280.4.a.bb.1.5		6
20.3	even	4		800.4.f.c.49.3		12
20.7	even	4		800.4.f.b.49.10		12
20.19	odd	2		800.4.d.d.401.4		12
24.5	odd	2		360.4.k.c.181.1		12
24.11	even	2		1440.4.k.c.721.11		12
40.3	even	4		800.4.f.b.49.9		12
40.13	odd	4		200.4.f.c.149.5		12
40.19	odd	2		800.4.d.d.401.9		12
40.27	even	4		800.4.f.c.49.4		12
40.29	even	2		200.4.d.b.101.1		12
40.37	odd	4		200.4.f.b.149.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.11	✓	12	1.1	even	1	trivial
40.4.d.a.21.12	yes	12	8.5	even	2	inner
160.4.d.a.81.4		12	8.3	odd	2
160.4.d.a.81.9		12	4.3	odd	2
200.4.d.b.101.1		12	40.29	even	2
200.4.d.b.101.2		12	5.4	even	2
200.4.f.b.149.7		12	5.3	odd	4
200.4.f.b.149.8		12	40.37	odd	4
200.4.f.c.149.5		12	40.13	odd	4
200.4.f.c.149.6		12	5.2	odd	4
360.4.k.c.181.1		12	24.5	odd	2
360.4.k.c.181.2		12	3.2	odd	2
800.4.d.d.401.4		12	20.19	odd	2
800.4.d.d.401.9		12	40.19	odd	2
800.4.f.b.49.9		12	40.3	even	4
800.4.f.b.49.10		12	20.7	even	4
800.4.f.c.49.3		12	20.3	even	4
800.4.f.c.49.4		12	40.27	even	4
1280.4.a.ba.1.5		6	16.11	odd	4
1280.4.a.bb.1.5		6	16.13	even	4
1280.4.a.bc.1.2		6	16.5	even	4
1280.4.a.bd.1.2		6	16.3	odd	4
1440.4.k.c.721.5		12	12.11	even	2
1440.4.k.c.721.11		12	24.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.74276 - 0.690860i) q^{2} -4.24443i q^{3} +(7.04543 - 3.78972i) q^{4} +5.00000i q^{5} +(-2.93231 - 11.6414i) q^{6} -14.6308 q^{7} +(16.7057 - 15.2617i) q^{8} +8.98481 q^{9} +(3.45430 + 13.7138i) q^{10} +14.9969i q^{11} +(-16.0852 - 29.9038i) q^{12} +85.6955i q^{13} +(-40.1288 + 10.1078i) q^{14} +21.2222 q^{15} +(35.2761 - 53.4004i) q^{16} -91.9247 q^{17} +(24.6432 - 6.20724i) q^{18} -60.3737i q^{19} +(18.9486 + 35.2271i) q^{20} +62.0995i q^{21} +(10.3608 + 41.1330i) q^{22} +1.33730 q^{23} +(-64.7771 - 70.9063i) q^{24} -25.0000 q^{25} +(59.2035 + 235.042i) q^{26} -152.735i q^{27} +(-103.080 + 55.4467i) q^{28} +25.5118i q^{29} +(58.2072 - 14.6615i) q^{30} +73.4354 q^{31} +(59.8615 - 170.835i) q^{32} +63.6535 q^{33} +(-252.127 + 63.5070i) q^{34} -73.1541i q^{35} +(63.3018 - 34.0499i) q^{36} -211.259i q^{37} +(-41.7098 - 165.590i) q^{38} +363.728 q^{39} +(76.3084 + 83.5286i) q^{40} +330.839 q^{41} +(42.9020 + 170.324i) q^{42} -388.500i q^{43} +(56.8342 + 105.660i) q^{44} +44.9241i q^{45} +(3.66788 - 0.923883i) q^{46} -550.348 q^{47} +(-226.654 - 149.727i) q^{48} -128.939 q^{49} +(-68.5689 + 17.2715i) q^{50} +390.168i q^{51} +(324.762 + 603.761i) q^{52} +187.705i q^{53} +(-105.518 - 418.915i) q^{54} -74.9847 q^{55} +(-244.419 + 223.291i) q^{56} -256.252 q^{57} +(17.6251 + 69.9727i) q^{58} +779.090i q^{59} +(149.519 - 80.4260i) q^{60} -358.850i q^{61} +(201.415 - 50.7335i) q^{62} -131.455 q^{63} +(46.1625 - 509.915i) q^{64} -428.477 q^{65} +(174.586 - 43.9756i) q^{66} +283.674i q^{67} +(-647.648 + 348.369i) q^{68} -5.67606i q^{69} +(-50.5392 - 200.644i) q^{70} -534.811 q^{71} +(150.098 - 137.123i) q^{72} +1016.16 q^{73} +(-145.950 - 579.431i) q^{74} +106.111i q^{75} +(-228.799 - 425.359i) q^{76} -219.418i q^{77} +(997.618 - 251.285i) q^{78} +1119.59 q^{79} +(267.002 + 176.380i) q^{80} -405.683 q^{81} +(907.411 - 228.563i) q^{82} +1190.49i q^{83} +(235.340 + 437.518i) q^{84} -459.623i q^{85} +(-268.399 - 1065.56i) q^{86} +108.283 q^{87} +(228.879 + 250.535i) q^{88} -398.940 q^{89} +(31.0362 + 123.216i) q^{90} -1253.80i q^{91} +(9.42182 - 5.06797i) q^{92} -311.691i q^{93} +(-1509.47 + 380.213i) q^{94} +301.869 q^{95} +(-725.097 - 254.078i) q^{96} +278.022 q^{97} +(-353.648 + 89.0787i) q^{98} +134.745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 16 q^{4} - 36 q^{6} + 28 q^{7} - 40 q^{8} - 108 q^{9} + 30 q^{10} + 188 q^{12} + 68 q^{14} - 60 q^{15} - 56 q^{16} - 206 q^{18} + 20 q^{20} - 164 q^{22} + 604 q^{23} + 360 q^{24} - 300 q^{25}+ \cdots - 7266 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 + 16 * q^4 - 36 * q^6 + 28 * q^7 - 40 * q^8 - 108 * q^9 + 30 * q^10 + 188 * q^12 + 68 * q^14 - 60 * q^15 - 56 * q^16 - 206 * q^18 + 20 * q^20 - 164 * q^22 + 604 * q^23 + 360 * q^24 - 300 * q^25 - 308 * q^26 - 436 * q^28 + 40 * q^30 - 264 * q^31 + 72 * q^32 - 232 * q^33 - 180 * q^34 + 440 * q^36 + 820 * q^38 + 600 * q^39 + 120 * q^40 + 40 * q^41 + 884 * q^42 - 472 * q^44 - 1268 * q^46 - 940 * q^47 + 424 * q^48 + 1308 * q^49 - 50 * q^50 + 1024 * q^52 - 1512 * q^54 + 440 * q^55 - 728 * q^56 - 680 * q^57 - 360 * q^58 - 820 * q^60 + 592 * q^62 - 1300 * q^63 - 2048 * q^64 + 2928 * q^66 - 2344 * q^68 + 1160 * q^70 - 1592 * q^71 - 152 * q^72 + 432 * q^73 - 420 * q^74 + 2256 * q^76 + 3320 * q^78 + 2016 * q^79 + 1600 * q^80 + 2508 * q^81 + 88 * q^82 + 1048 * q^84 - 244 * q^86 - 1968 * q^87 + 4080 * q^88 - 424 * q^89 - 2250 * q^90 - 900 * q^92 + 292 * q^94 - 1520 * q^95 - 5920 * q^96 - 1584 * q^97 - 7266 * q^98

Introduction

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