LMFDB - Embedded newform 124.4.d.c.123.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,4,Mod(123,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("124.123");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	124.d (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:	$7.31623684071$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			123.11
Character	$\chi$	$=$	124.123
Dual form			124.4.d.c.123.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77211 + 2.20446i) q^{2} -7.49955 q^{3} +(-1.71925 - 7.81308i) q^{4} -18.0979 q^{5} +(13.2900 - 16.5324i) q^{6} -21.7591i q^{7} +(20.2703 + 10.0556i) q^{8} +29.2432 q^{9} +O(q^{10})$	\(q+(-1.77211 + 2.20446i) q^{2} -7.49955 q^{3} +(-1.71925 - 7.81308i) q^{4} -18.0979 q^{5} +(13.2900 - 16.5324i) q^{6} -21.7591i q^{7} +(20.2703 + 10.0556i) q^{8} +29.2432 q^{9} +(32.0715 - 39.8960i) q^{10} -59.2463 q^{11} +(12.8936 + 58.5946i) q^{12} +62.3397i q^{13} +(47.9671 + 38.5596i) q^{14} +135.726 q^{15} +(-58.0883 + 26.8653i) q^{16} -0.447075i q^{17} +(-51.8222 + 64.4654i) q^{18} -93.8857i q^{19} +(31.1149 + 141.400i) q^{20} +163.184i q^{21} +(104.991 - 130.606i) q^{22} -46.9150 q^{23} +(-152.018 - 75.4126i) q^{24} +202.534 q^{25} +(-137.425 - 110.473i) q^{26} -16.8232 q^{27} +(-170.006 + 37.4095i) q^{28} +207.134i q^{29} +(-240.521 + 299.202i) q^{30} +(125.578 + 118.411i) q^{31} +(43.7155 - 175.661i) q^{32} +444.320 q^{33} +(0.985558 + 0.792267i) q^{34} +393.795i q^{35} +(-50.2765 - 228.480i) q^{36} -353.884i q^{37} +(206.967 + 166.376i) q^{38} -467.519i q^{39} +(-366.850 - 181.985i) q^{40} -59.8605 q^{41} +(-359.731 - 289.180i) q^{42} +5.12750 q^{43} +(101.859 + 462.896i) q^{44} -529.241 q^{45} +(83.1385 - 103.422i) q^{46} -321.775i q^{47} +(435.636 - 201.478i) q^{48} -130.460 q^{49} +(-358.912 + 446.477i) q^{50} +3.35286i q^{51} +(487.065 - 107.178i) q^{52} -494.516i q^{53} +(29.8126 - 37.0861i) q^{54} +1072.23 q^{55} +(218.802 - 441.064i) q^{56} +704.100i q^{57} +(-456.618 - 367.064i) q^{58} +225.940i q^{59} +(-233.347 - 1060.44i) q^{60} +177.805i q^{61} +(-483.570 + 66.9947i) q^{62} -636.308i q^{63} +(309.769 + 407.660i) q^{64} -1128.22i q^{65} +(-787.385 + 979.485i) q^{66} +50.0548i q^{67} +(-3.49303 + 0.768636i) q^{68} +351.841 q^{69} +(-868.103 - 697.848i) q^{70} +451.582i q^{71} +(592.769 + 294.059i) q^{72} +687.915i q^{73} +(780.122 + 627.121i) q^{74} -1518.91 q^{75} +(-733.536 + 161.413i) q^{76} +1289.15i q^{77} +(1030.63 + 828.496i) q^{78} -1039.27 q^{79} +(1051.28 - 486.206i) q^{80} -663.401 q^{81} +(106.079 - 131.960i) q^{82} +75.5716 q^{83} +(1274.97 - 280.554i) q^{84} +8.09112i q^{85} +(-9.08649 + 11.3033i) q^{86} -1553.41i q^{87} +(-1200.94 - 595.758i) q^{88} -95.8451i q^{89} +(937.873 - 1166.69i) q^{90} +1356.46 q^{91} +(80.6588 + 366.551i) q^{92} +(-941.780 - 888.028i) q^{93} +(709.339 + 570.221i) q^{94} +1699.13i q^{95} +(-327.847 + 1317.38i) q^{96} +389.327 q^{97} +(231.190 - 287.594i) q^{98} -1732.55 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	$ 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.77211	+	2.20446i	−0.626535	+	0.779393i
$2$	−1.77211	+	2.20446i	−0.626535	+	0.779393i
$3$	−7.49955			−1.44329			−0.721644	−	0.692264i	$-0.756613\pi$
$3$	−7.49955			−1.44329			−0.721644	+	0.692264i	$0.756613\pi$
$4$	−1.71925	−	7.81308i	−0.214907	−	0.976635i
$5$	−18.0979			−1.61872			−0.809362	−	0.587309i	$-0.800187\pi$
$5$	−18.0979			−1.61872			−0.809362	+	0.587309i	$0.800187\pi$
$6$	13.2900	−	16.5324i	0.904272	−	1.12489i
$7$		−	21.7591i		−	1.17488i	−0.809266	−	0.587442i	$-0.800135\pi$
$7$		−	21.7591i		−	1.17488i	0.809266	−	0.587442i	$-0.199865\pi$
$8$	20.2703	+	10.0556i	0.895829	+	0.444400i
$9$	29.2432			1.08308
$10$	32.0715	−	39.8960i	1.01419	−	1.26162i
$11$	−59.2463			−1.62395			−0.811974	−	0.583694i	$-0.801607\pi$
$11$	−59.2463			−1.62395			−0.811974	+	0.583694i	$0.801607\pi$
$12$	12.8936	+	58.5946i	0.310172	+	1.40957i
$13$			62.3397i			1.32999i	0.746846	+	0.664997i	$0.231567\pi$
$13$			62.3397i			1.32999i	−0.746846	+	0.664997i	$0.768433\pi$
$14$	47.9671	+	38.5596i	0.915696	+	0.736106i
$15$	135.726			2.33629
$16$	−58.0883	+	26.8653i	−0.907630	+	0.419770i
$17$		−	0.447075i		−	0.00637834i	−0.999995	−	0.00318917i	$-0.998985\pi$
$17$		−	0.447075i		−	0.00637834i	0.999995	−	0.00318917i	$-0.00101515\pi$
$18$	−51.8222	+	64.4654i	−0.678590	+	0.844147i
$19$		−	93.8857i		−	1.13362i	−0.823847	−	0.566812i	$-0.808177\pi$
$19$		−	93.8857i		−	1.13362i	0.823847	−	0.566812i	$-0.191823\pi$
$20$	31.1149	+	141.400i	0.347875	+	1.58090i
$21$			163.184i			1.69570i
$22$	104.991	−	130.606i	1.01746	−	1.26569i
$23$	−46.9150			−0.425324			−0.212662	−	0.977126i	$-0.568213\pi$
$23$	−46.9150			−0.425324			−0.212662	+	0.977126i	$0.568213\pi$
$24$	−152.018	−	75.4126i	−1.29294	−	0.641397i
$25$	202.534			1.62027
$26$	−137.425	−	110.473i	−1.03659	−	0.833288i
$27$	−16.8232			−0.119912
$28$	−170.006	+	37.4095i	−1.14743	+	0.252490i
$29$			207.134i			1.32634i	0.748469	+	0.663170i	$0.230789\pi$
$29$			207.134i			1.32634i	−0.748469	+	0.663170i	$0.769211\pi$
$30$	−240.521	+	299.202i	−1.46377	+	1.82089i
$31$	125.578	+	118.411i	0.727565	+	0.686039i
$31$	125.578	+	118.411i	0.727565	+	0.686039i
$32$	43.7155	−	175.661i	0.241496	−	0.970402i
$33$	444.320			2.34383
$34$	0.985558	+	0.792267i	0.00497123	+	0.00399625i
$35$			393.795i			1.90181i
$36$	−50.2765	−	228.480i	−0.232762	−	1.05778i
$37$		−	353.884i		−	1.57238i	−0.617983	−	0.786191i	$-0.712050\pi$
$37$		−	353.884i		−	1.57238i	0.617983	−	0.786191i	$-0.287950\pi$
$38$	206.967	+	166.376i	0.883539	+	0.710256i
$39$		−	467.519i		−	1.91956i
$40$	−366.850	−	181.985i	−1.45010	−	0.719361i
$41$	−59.8605			−0.228015			−0.114008	−	0.993480i	$-0.536369\pi$
$41$	−59.8605			−0.228015			−0.114008	+	0.993480i	$0.536369\pi$
$42$	−359.731	−	289.180i	−1.32161	−	1.06241i
$43$	5.12750			0.0181846			0.00909228	−	0.999959i	$-0.497106\pi$
$43$	5.12750			0.0181846			0.00909228	+	0.999959i	$0.497106\pi$
$44$	101.859	+	462.896i	0.348997	+	1.58600i
$45$	−529.241			−1.75321
$46$	83.1385	−	103.422i	0.266481	−	0.331495i
$47$		−	321.775i		−	0.998632i	−0.866420	−	0.499316i	$-0.833585\pi$
$47$		−	321.775i		−	0.998632i	0.866420	−	0.499316i	$-0.166415\pi$
$48$	435.636	−	201.478i	1.30997	−	0.605850i
$49$	−130.460			−0.380351
$50$	−358.912	+	446.477i	−1.01516	+	1.26283i
$51$			3.35286i			0.00920578i
$52$	487.065	−	107.178i	1.29892	−	0.285824i
$53$		−	494.516i		−	1.28164i	−0.767691	−	0.640821i	$-0.778594\pi$
$53$		−	494.516i		−	1.28164i	0.767691	−	0.640821i	$-0.221406\pi$
$54$	29.8126	−	37.0861i	0.0751293	−	0.0934588i
$55$	1072.23			2.62873
$56$	218.802	−	441.064i	0.522118	−	1.05249i
$57$			704.100i			1.63615i
$58$	−456.618	−	367.064i	−1.03374	−	0.830999i
$59$			225.940i			0.498557i	0.968432	+	0.249278i	$0.0801934\pi$
$59$			225.940i			0.498557i	−0.968432	+	0.249278i	$0.919807\pi$
$60$	−233.347	−	1060.44i	−0.502084	−	2.28170i
$61$			177.805i			0.373206i	0.982435	+	0.186603i	$0.0597479\pi$
$61$			177.805i			0.373206i	−0.982435	+	0.186603i	$0.940252\pi$
$62$	−483.570	+	66.9947i	−0.990539	+	0.137231i
$63$		−	636.308i		−	1.27250i
$64$	309.769	+	407.660i	0.605018	+	0.796212i
$65$		−	1128.22i		−	2.15289i
$66$	−787.385	+	979.485i	−1.46849	+	1.82676i
$67$			50.0548i			0.0912711i	0.998958	+	0.0456356i	$0.0145313\pi$
$67$			50.0548i			0.0912711i	−0.998958	+	0.0456356i	$0.985469\pi$
$68$	−3.49303	+	0.768636i	−0.00622930	+	0.00137075i
$69$	351.841			0.613866
$70$	−868.103	−	697.848i	−1.48226	−	1.19155i
$71$			451.582i			0.754830i	0.926044	+	0.377415i	$0.123187\pi$
$71$			451.582i			0.754830i	−0.926044	+	0.377415i	$0.876813\pi$
$72$	592.769	+	294.059i	0.970257	+	0.481321i
$73$			687.915i			1.10294i	0.834196	+	0.551469i	$0.185932\pi$
$73$			687.915i			1.10294i	−0.834196	+	0.551469i	$0.814068\pi$
$74$	780.122	+	627.121i	1.22550	+	0.985154i
$75$	−1518.91			−2.33852
$76$	−733.536	+	161.413i	−1.10714	+	0.243623i
$77$			1289.15i			1.90795i
$78$	1030.63	+	828.496i	1.49610	+	1.20268i
$79$	−1039.27			−1.48009			−0.740045	−	0.672557i	$-0.765196\pi$
$79$	−1039.27			−1.48009			−0.740045	+	0.672557i	$0.765196\pi$
$80$	1051.28	−	486.206i	1.46920	−	0.679493i
$81$	−663.401			−0.910015
$82$	106.079	−	131.960i	0.142860	−	0.177714i
$83$	75.5716			0.0999405			0.0499702	−	0.998751i	$-0.484087\pi$
$83$	75.5716			0.0999405			0.0499702	+	0.998751i	$0.484087\pi$
$84$	1274.97	−	280.554i	1.65608	−	0.364416i
$85$			8.09112i			0.0103248i
$86$	−9.08649	+	11.3033i	−0.0113933	+	0.0141729i
$87$		−	1553.41i		−	1.91429i
$88$	−1200.94	−	595.758i	−1.45478	−	0.721682i
$89$		−	95.8451i		−	0.114152i	−0.998370	−	0.0570762i	$-0.981822\pi$
$89$		−	95.8451i		−	0.114152i	0.998370	−	0.0570762i	$-0.0181778\pi$
$90$	937.873	−	1166.69i	1.09845	−	1.36644i
$91$	1356.46			1.56259
$92$	80.6588	+	366.551i	0.0914050	+	0.415386i
$93$	−941.780	−	888.028i	−1.05009	−	0.990152i
$94$	709.339	+	570.221i	0.778327	+	0.625678i
$95$			1699.13i			1.83503i
$96$	−327.847	+	1317.38i	−0.348549	+	1.40057i
$97$	389.327			0.407527			0.203764	−	0.979020i	$-0.434683\pi$
$97$	389.327			0.407527			0.203764	+	0.979020i	$0.434683\pi$
$98$	231.190	−	287.594i	0.238303	−	0.296443i
$99$	−1732.55			−1.75887
$100$	−348.207	−	1582.41i	−0.348207	−	1.58241i
$101$	1008.39			0.993452			0.496726	−	0.867908i	$-0.334535\pi$
$101$	1008.39			0.993452			0.496726	+	0.867908i	$0.334535\pi$
$102$	−7.39124	−	5.94164i	−0.00717492	−	0.00576775i
$103$		−	534.871i		−	0.511673i	−0.966720	−	0.255837i	$-0.917649\pi$
$103$		−	534.871i		−	0.511673i	0.966720	−	0.255837i	$-0.0823509\pi$
$104$	−626.864	+	1263.64i	−0.591049	+	1.19145i
$105$		−	2953.28i		−	2.74487i
$106$	1090.14	+	876.337i	0.998902	+	0.802994i
$107$			1251.25i			1.13049i	0.824922	+	0.565246i	$0.191219\pi$
$107$			1251.25i			1.13049i	−0.824922	+	0.565246i	$0.808781\pi$
$108$	28.9234	+	131.441i	0.0257700	+	0.117111i
$109$	−934.713			−0.821370			−0.410685	−	0.911777i	$-0.634710\pi$
$109$	−934.713			−0.821370			−0.410685	+	0.911777i	$0.634710\pi$
$110$	−1900.12	+	2363.69i	−1.64699	+	2.04881i
$111$			2653.97i			2.26940i
$112$	584.566	+	1263.95i	0.493181	+	1.06636i
$113$	437.738			0.364415			0.182208	−	0.983260i	$-0.441676\pi$
$113$	437.738			0.364415			0.182208	+	0.983260i	$0.441676\pi$
$114$	−1552.16	−	1247.74i	−1.27520	−	1.02510i
$115$	849.063			0.688483
$116$	1618.35	−	356.116i	1.29535	−	0.285039i
$117$			1823.01i			1.44049i
$118$	−498.074	−	400.390i	−0.388572	−	0.312363i
$119$	−9.72798			−0.00749380
$120$	2751.21	+	1364.81i	2.09291	+	1.03825i
$121$	2179.12			1.63721
$122$	−391.963	−	315.090i	−0.290874	−	0.233827i
$123$	448.926			0.329092
$124$	709.252	−	1184.73i	0.513651	−	0.857999i
$125$	−1403.20			−1.00405
$126$	1402.71	+	1127.61i	0.991774	+	0.797264i
$127$	221.459			0.154735			0.0773675	−	0.997003i	$-0.475349\pi$
$127$	221.459			0.154735			0.0773675	+	0.997003i	$0.475349\pi$
$128$	−1447.61	−	39.5462i	−0.999627	−	0.0273080i
$129$	−38.4539			−0.0262456
$130$	2487.10	+	1999.32i	1.67795	+	1.34886i
$131$			1063.99i			0.709629i	0.934937	+	0.354814i	$0.115456\pi$
$131$			1063.99i			0.709629i	−0.934937	+	0.354814i	$0.884544\pi$
$132$	−763.899	−	3471.51i	−0.503704	−	2.28906i
$133$	−2042.87			−1.33188
$134$	−110.344	−	88.7026i	−0.0711361	−	0.0571846i
$135$	304.465			0.194105
$136$	4.49562	−	9.06235i	0.00283453	−	0.00571390i
$137$		−	432.482i		−	0.269704i	−0.990866	−	0.134852i	$-0.956944\pi$
$137$		−	432.482i		−	0.269704i	0.990866	−	0.134852i	$-0.0430559\pi$
$138$	−623.502	+	775.619i	−0.384609	+	0.478442i
$139$	−693.276			−0.423042			−0.211521	−	0.977373i	$-0.567842\pi$
$139$	−693.276			−0.423042			−0.211521	+	0.977373i	$0.567842\pi$
$140$	3076.75	−	677.033i	1.85738	−	0.408712i
$141$			2413.17i			1.44131i
$142$	−995.493	−	800.253i	−0.588309	−	0.472928i
$143$		−	3693.39i		−	2.15984i
$144$	−1698.69	+	785.629i	−0.983039	+	0.454646i
$145$		−	3748.69i		−	2.14698i
$146$	−1516.48	−	1219.06i	−0.859621	−	0.691029i
$147$	978.394			0.548956
$148$	−2764.92	+	608.416i	−1.53564	+	0.337915i
$149$	2001.51			1.10047			0.550236	−	0.835010i	$-0.314538\pi$
$149$	2001.51			1.10047			0.550236	+	0.835010i	$0.314538\pi$
$150$	2691.68	−	3348.38i	1.46516	−	1.82262i
$151$	606.260			0.326733			0.163367	−	0.986565i	$-0.447765\pi$
$151$	606.260			0.326733			0.163367	+	0.986565i	$0.447765\pi$
$152$	944.078	−	1903.09i	0.503782	−	1.01553i
$153$		−	13.0739i		−	0.00690827i
$154$	−2841.87	−	2284.51i	−1.48704	−	1.19540i
$155$	−2272.70	−	2142.99i	−1.17773	−	1.11051i
$156$	−3652.77	+	803.784i	−1.87471	+	0.412527i
$157$	3322.44			1.68891			0.844456	−	0.535625i	$-0.179924\pi$
$157$	3322.44			1.68891			0.844456	+	0.535625i	$0.179924\pi$
$158$	1841.70	−	2291.03i	0.927329	−	1.15357i
$159$			3708.65i			1.84978i
$160$	−791.159	+	3179.10i	−0.390916	+	1.57081i
$161$			1020.83i			0.499706i
$162$	1175.62	−	1462.44i	0.570156	−	0.709259i
$163$		−	594.006i		−	0.285436i	−0.989763	−	0.142718i	$-0.954416\pi$
$163$		−	594.006i		−	0.285436i	0.989763	−	0.142718i	$-0.0455843\pi$
$164$	102.915	+	467.694i	0.0490020	+	0.222688i
$165$	−8041.26			−3.79401
$166$	−133.921	+	166.594i	−0.0626162	+	0.0778929i
$167$	525.927			0.243697			0.121849	−	0.992549i	$-0.461118\pi$
$167$	525.927			0.243697			0.121849	+	0.992549i	$0.461118\pi$
$168$	−1640.91	+	3307.78i	−0.753567	+	1.51905i
$169$	−1689.24			−0.768883
$170$	−17.8365	−	14.3384i	−0.00804705	−	0.00646884i
$171$		−	2745.52i		−	1.22781i
$172$	−8.81547	−	40.0616i	−0.00390798	−	0.0177597i
$173$	3914.73			1.72041			0.860205	−	0.509948i	$-0.170335\pi$
$173$	3914.73			1.72041			0.860205	+	0.509948i	$0.170335\pi$
$174$	3424.43	+	2752.82i	1.49198	+	1.19937i
$175$		−	4406.96i		−	1.90363i
$176$	3441.52	−	1591.67i	1.47394	−	0.681685i
$177$		−	1694.45i		−	0.719561i
$178$	211.286	+	169.848i	0.0889695	+	0.0715205i
$179$	−3265.87			−1.36370			−0.681851	−	0.731492i	$-0.738825\pi$
$179$	−3265.87			−1.36370			−0.681851	+	0.731492i	$0.738825\pi$
$180$	909.899	+	4135.00i	0.376777	+	1.71225i
$181$		−	1032.56i		−	0.424030i	−0.977266	−	0.212015i	$-0.931997\pi$
$181$		−	1032.56i		−	0.424030i	0.977266	−	0.212015i	$-0.0680025\pi$
$182$	−2403.79	+	2990.25i	−0.979016	+	1.21787i
$183$		−	1333.46i		−	0.538645i
$184$	−950.981	−	471.759i	−0.381018	−	0.189014i
$185$			6404.56i			2.54526i
$186$	3626.56	−	502.430i	1.42963	−	0.198064i
$187$			26.4876i			0.0103581i
$188$	−2514.05	+	553.213i	−0.975299	+	0.214613i
$189$			366.059i			0.140883i
$190$	−3745.67	−	3011.05i	−1.43021	−	1.14971i
$191$			2797.75i			1.05988i	0.848034	+	0.529942i	$0.177786\pi$
$191$			2797.75i			1.05988i	−0.848034	+	0.529942i	$0.822214\pi$
$192$	−2323.13	−	3057.27i	−0.873216	−	1.14916i
$193$	−4145.68			−1.54618			−0.773089	−	0.634298i	$-0.781289\pi$
$193$	−4145.68			−1.54618			−0.773089	+	0.634298i	$0.781289\pi$
$194$	−689.930	+	858.254i	−0.255330	+	0.317624i
$195$			8461.12i			3.10725i
$196$	224.294	+	1019.30i	0.0817400	+	0.371464i
$197$		−	4324.68i		−	1.56406i	−0.623239	−	0.782031i	$-0.714184\pi$
$197$		−	4324.68i		−	1.56406i	0.623239	−	0.782031i	$-0.285816\pi$
$198$	3070.27	−	3819.34i	1.10199	−	1.37085i
$199$	77.6287			0.0276530			0.0138265	−	0.999904i	$-0.495599\pi$
$199$	77.6287			0.0276530			0.0138265	+	0.999904i	$0.495599\pi$
$200$	4105.42	+	2036.60i	1.45148	+	0.720047i
$201$		−	375.388i		−	0.131731i
$202$	−1786.98	+	2222.95i	−0.622433	+	0.774289i
$203$	4507.06			1.55829
$204$	26.1962	−	5.76442i	0.00899069	−	0.00197838i
$205$	1083.35			0.369094
$206$	1179.10	+	947.849i	0.398795	+	0.320582i
$207$	−1371.95			−0.460661
$208$	−1674.77	−	3621.21i	−0.558292	−	1.20714i
$209$			5562.38i			1.84095i
$210$	6510.38	+	5233.54i	2.13933	+	1.71976i
$211$			777.870i			0.253795i	0.991916	+	0.126898i	$0.0405020\pi$
$211$			777.870i			0.253795i	−0.991916	+	0.126898i	$0.959498\pi$
$212$	−3863.69	+	850.198i	−1.25170	+	0.275433i
$213$		−	3386.66i		−	1.08944i
$214$	−2758.32	−	2217.35i	−0.881097	−	0.708293i
$215$	−92.7970			−0.0294358
$216$	−341.012	−	169.168i	−0.107421	−	0.0532890i
$217$	2576.52	−	2732.47i	0.806016	−	0.854804i
$218$	1656.41	−	2060.53i	0.514617	−	0.640170i
$219$		−	5159.05i		−	1.59186i
$220$	−1843.44	−	8377.44i	−0.564930	−	2.56730i
$221$	27.8705			0.00848315
$222$	−5850.56	−	4703.13i	−1.76876	−	1.42186i
$223$	2953.81			0.887003			0.443502	−	0.896274i	$-0.353736\pi$
$223$	2953.81			0.887003			0.443502	+	0.896274i	$0.353736\pi$
$224$	−3822.24	−	951.212i	−1.14011	−	0.283730i
$225$	5922.74			1.75489
$226$	−775.720	+	964.975i	−0.228319	+	0.284023i
$227$		−	2490.21i		−	0.728110i	−0.931377	−	0.364055i	$-0.881392\pi$
$227$		−	2490.21i		−	0.728110i	0.931377	−	0.364055i	$-0.118608\pi$
$228$	5501.19	−	1210.53i	1.59792	−	0.351619i
$229$			5917.80i			1.70768i	0.520534	+	0.853841i	$0.325733\pi$
$229$			5917.80i			1.70768i	−0.520534	+	0.853841i	$0.674267\pi$
$230$	−1504.63	+	1871.72i	−0.431359	+	0.536599i
$231$		−	9668.03i		−	2.75372i
$232$	−2082.86	+	4198.67i	−0.589425	+	1.18817i
$233$	−2373.68			−0.667404			−0.333702	−	0.942679i	$-0.608298\pi$
$233$	−2373.68			−0.667404			−0.333702	+	0.942679i	$0.608298\pi$
$234$	−4018.75	−	3230.58i	−1.12271	−	0.902520i
$235$			5823.45i			1.61651i
$236$	1765.28	−	388.448i	0.486908	−	0.107143i
$237$	7794.07			2.13620
$238$	17.2390	−	21.4449i	0.00469513	−	0.00584062i
$239$	3189.65			0.863268			0.431634	−	0.902049i	$-0.357937\pi$
$239$	3189.65			0.863268			0.431634	+	0.902049i	$0.357937\pi$
$240$	−7884.10	+	3646.32i	−2.12049	+	0.980705i
$241$			1574.07i			0.420725i	0.977623	+	0.210362i	$0.0674644\pi$
$241$			1574.07i			0.420725i	−0.977623	+	0.210362i	$0.932536\pi$
$242$	−3861.65	+	4803.78i	−1.02577	+	1.27603i
$243$	5429.43			1.43333
$244$	1389.20	−	305.692i	0.364486	−	0.0802045i
$245$	2361.06			0.615684
$246$	−795.547	+	989.639i	−0.206188	+	0.256492i
$247$	5852.80			1.50771
$248$	1354.81	+	3662.99i	0.346898	+	0.937903i
$249$	−566.753			−0.144243
$250$	2486.62	−	3093.29i	0.629071	−	0.782547i
$251$	4004.47			1.00701			0.503506	−	0.863992i	$-0.332043\pi$
$251$	4004.47			1.00701			0.503506	+	0.863992i	$0.332043\pi$
$252$	−4971.52	+	1093.97i	−1.24276	+	0.273468i
$253$	2779.54			0.690704
$254$	−392.450	+	488.197i	−0.0969469	+	0.120599i
$255$		−	60.6798i		−	0.0149016i
$256$	2652.51	−	3121.12i	0.647585	−	0.761993i
$257$	5592.64			1.35743			0.678715	−	0.734402i	$-0.262537\pi$
$257$	5592.64			1.35743			0.678715	+	0.734402i	$0.262537\pi$
$258$	68.1446	−	84.7700i	0.0164438	−	0.0204556i
$259$	−7700.21			−1.84737
$260$	−8814.85	+	1939.69i	−2.10259	+	0.462671i
$261$			6057.27i			1.43654i
$262$	−2345.52	−	1885.51i	−0.553080	−	0.444608i
$263$	2255.96			0.528929			0.264465	−	0.964395i	$-0.414805\pi$
$263$	2255.96			0.528929			0.264465	+	0.964395i	$0.414805\pi$
$264$	9006.50	+	4467.91i	2.09967	+	1.04160i
$265$			8949.70i			2.07462i
$266$	3620.19	−	4503.42i	0.834468	−	1.03805i
$267$			718.795i			0.164755i
$268$	391.082	−	86.0568i	0.0891385	−	0.0196148i
$269$		−	5120.23i		−	1.16054i	−0.814423	−	0.580271i	$-0.802947\pi$
$269$		−	5120.23i		−	1.16054i	0.814423	−	0.580271i	$-0.197053\pi$
$270$	−539.546	+	671.180i	−0.121614	+	0.151284i
$271$	−4652.29			−1.04283			−0.521415	−	0.853303i	$-0.674596\pi$
$271$	−4652.29			−1.04283			−0.521415	+	0.853303i	$0.674596\pi$
$272$	12.0108	+	25.9699i	0.00267744	+	0.00578917i
$273$	−10172.8			−2.25527
$274$	953.387	+	766.405i	0.210205	+	0.168979i
$275$	−11999.4			−2.63124
$276$	−604.904	−	2748.96i	−0.131924	−	0.599522i
$277$		−	1902.16i		−	0.412599i	−0.978489	−	0.206299i	$-0.933858\pi$
$277$		−	1902.16i		−	0.412599i	0.978489	−	0.206299i	$-0.0661421\pi$
$278$	1228.56	−	1528.30i	0.265051	−	0.329716i
$279$	3672.31	+	3462.71i	0.788013	+	0.743037i
$280$	−3959.85	+	7982.33i	−0.845165	+	1.70370i
$281$	−2034.82			−0.431982			−0.215991	−	0.976395i	$-0.569298\pi$
$281$	−2034.82			−0.431982			−0.215991	+	0.976395i	$0.569298\pi$
$282$	−5319.72	−	4276.40i	−1.12335	−	0.903035i
$283$			1507.02i			0.316547i	0.987395	+	0.158274i	$0.0505928\pi$
$283$			1507.02i			0.316547i	−0.987395	+	0.158274i	$0.949407\pi$
$284$	3528.25	−	776.384i	0.737193	−	0.162218i
$285$		−	12742.7i		−	2.64847i
$286$	8141.93	+	6545.10i	1.68336	+	1.35322i
$287$			1302.51i			0.267892i
$288$	1278.38	−	5136.91i	0.261561	−	1.05103i
$289$	4912.80			0.999959
$290$	8263.83	+	6643.09i	1.67334	+	1.34516i
$291$	−2919.78			−0.588180
$292$	5374.74	−	1182.70i	1.07717	−	0.237028i
$293$	−8905.93			−1.77573			−0.887867	−	0.460100i	$-0.847814\pi$
$293$	−8905.93			−1.77573			−0.887867	+	0.460100i	$0.847814\pi$
$294$	−1733.82	+	2156.83i	−0.343941	+	0.427853i
$295$		−	4089.03i		−	0.807026i
$296$	3558.52	−	7173.33i	0.698766	−	1.40859i
$297$	996.714			0.194731
$298$	−3546.90	+	4412.24i	−0.689484	+	0.857699i
$299$		−	2924.67i		−	0.565678i
$300$	2611.39	+	11867.4i	0.502563	+	2.28388i
$301$		−	111.570i		−	0.0213647i
$302$	−1074.36	+	1336.47i	−0.204710	+	0.254654i
$303$	−7562.47			−1.43384
$304$	2522.27	+	5453.66i	0.475862	+	1.02891i
$305$		−	3217.90i		−	0.604119i
$306$	28.8209	+	23.1684i	0.00538425	+	0.00432827i
$307$			7624.78i			1.41749i	0.705465	+	0.708744i	$0.250738\pi$
$307$			7624.78i			1.41749i	−0.705465	+	0.708744i	$0.749262\pi$
$308$	10072.2	−	2216.37i	1.86337	−	0.410031i
$309$			4011.29i			0.738492i
$310$	8751.59	−	1212.46i	1.60341	−	0.222140i
$311$			8368.76i			1.52588i	0.646469	+	0.762940i	$0.276245\pi$
$311$			8368.76i			1.52588i	−0.646469	+	0.762940i	$0.723755\pi$
$312$	4701.20	−	9476.76i	0.853054	−	1.71960i
$313$			9969.49i			1.80035i	0.435531	+	0.900174i	$0.356561\pi$
$313$			9969.49i			1.80035i	−0.435531	+	0.900174i	$0.643439\pi$
$314$	−5887.72	+	7324.16i	−1.05816	+	1.31633i
$315$			11515.8i			2.05982i
$316$	1786.77	+	8119.91i	0.318081	+	1.44551i
$317$	−943.552			−0.167177			−0.0835886	−	0.996500i	$-0.526638\pi$
$317$	−943.552			−0.167177			−0.0835886	+	0.996500i	$0.526638\pi$
$318$	−8175.55	−	6572.13i	−1.44170	−	1.15895i
$319$		−	12271.9i		−	2.15391i
$320$	−5606.17	−	7377.79i	−0.979358	−	1.28885i
$321$		−	9383.79i		−	1.63163i
$322$	−2250.38	−	1809.02i	−0.389467	−	0.313084i
$323$	−41.9740			−0.00723064
$324$	1140.55	+	5183.20i	0.195568	+	0.888752i
$325$			12625.9i			2.15495i
$326$	1309.46	+	1052.64i	0.222467	+	0.178836i
$327$	7009.93			1.18547
$328$	−1213.39	−	601.934i	−0.204263	−	0.101330i
$329$	−7001.55			−1.17328
$330$	14250.0	−	17726.6i	2.37708	−	2.95702i
$331$	529.386			0.0879084			0.0439542	−	0.999034i	$-0.486004\pi$
$331$	529.386			0.0879084			0.0439542	+	0.999034i	$0.486004\pi$
$332$	−129.927	−	590.447i	−0.0214779	−	0.0976053i
$333$		−	10348.7i		−	1.70302i
$334$	−932.001	+	1159.38i	−0.152685	+	0.189936i
$335$		−	905.886i		−	0.147743i
$336$	−4383.98	−	9479.07i	−0.711803	−	1.53907i
$337$			4784.71i			0.773412i	0.922203	+	0.386706i	$0.126387\pi$
$337$			4784.71i			0.773412i	−0.922203	+	0.386706i	$0.873613\pi$
$338$	2993.51	−	3723.85i	0.481732	−	0.599262i
$339$	−3282.84			−0.525957
$340$	63.2166	−	13.9107i	0.0100835	−	0.00221886i
$341$	−7440.04	−	7015.40i	−1.18153	−	1.11409i
$342$	6052.38	+	4865.37i	0.956945	+	0.769266i
$343$		−	4624.68i		−	0.728015i
$344$	103.936	+	51.5602i	0.0162903	+	0.00808121i
$345$	−6367.59			−0.993679
$346$	−6937.32	+	8629.84i	−1.07790	+	1.34088i
$347$	−2912.00			−0.450502			−0.225251	−	0.974301i	$-0.572320\pi$
$347$	−2912.00			−0.450502			−0.225251	+	0.974301i	$0.572320\pi$
$348$	−12136.9	+	2670.71i	−1.86956	+	0.411394i
$349$	9508.98			1.45846			0.729232	−	0.684266i	$-0.239877\pi$
$349$	9508.98			1.45846			0.729232	+	0.684266i	$0.239877\pi$
$350$	9714.96	+	7809.62i	1.48367	+	1.19269i
$351$		−	1048.76i		−	0.159483i
$352$	−2589.98	+	10407.3i	−0.392178	+	1.57588i
$353$			1060.41i			0.159886i	0.996799	+	0.0799432i	$0.0254739\pi$
$353$			1060.41i			0.159886i	−0.996799	+	0.0799432i	$0.974526\pi$
$354$	3735.33	+	3002.74i	0.560821	+	0.450831i
$355$		−	8172.68i		−	1.22186i
$356$	−748.845	+	164.782i	−0.111485	+	0.0245321i
$357$	72.9555			0.0108157
$358$	5787.48	−	7199.46i	0.854407	−	1.06286i
$359$		−	4173.08i		−	0.613500i	−0.951790	−	0.306750i	$-0.900758\pi$
$359$		−	4173.08i		−	0.613500i	0.951790	−	0.306750i	$-0.0992416\pi$
$360$	−10727.9	−	5321.84i	−1.57058	−	0.779127i
$361$	−1955.53			−0.285104
$362$	2276.23	+	1829.80i	0.330486	+	0.265670i
$363$	−16342.4			−2.36296
$364$	−2332.09	−	10598.1i	−0.335810	−	1.52608i
$365$		−	12449.8i		−	1.78535i
$366$	2939.55	+	2363.03i	0.419816	+	0.337480i
$367$	11897.0			1.69214			0.846072	−	0.533068i	$-0.178961\pi$
$367$	11897.0			1.69214			0.846072	+	0.533068i	$0.178961\pi$
$368$	2725.21	−	1260.39i	0.386037	−	0.178538i
$369$	−1750.51			−0.246960
$370$	−14118.6	−	11349.6i	−1.98375	−	1.59469i
$371$	−10760.2			−1.50578
$372$	−5319.07	+	8884.94i	−0.741347	+	1.23834i
$373$	4362.45			0.605574			0.302787	−	0.953058i	$-0.402083\pi$
$373$	4362.45			0.605574			0.302787	+	0.953058i	$0.402083\pi$
$374$	−58.3907	−	46.9389i	−0.00807302	−	0.00648971i
$375$	10523.4			1.44913
$376$	3235.65	−	6522.47i	0.443792	−	0.894603i
$377$	−12912.7			−1.76402
$378$	−806.961	−	648.697i	−0.109803	−	0.0882682i
$379$		−	103.713i		−	0.0140564i	−0.999975	−	0.00702819i	$-0.997763\pi$
$379$		−	103.713i		−	0.0140564i	0.999975	−	0.00702819i	$-0.00223716\pi$
$380$	13275.5	−	2921.24i	1.79215	−	0.394359i
$381$	−1660.85			−0.223327
$382$	−6167.51	−	4957.91i	−0.826066	−	0.664055i
$383$	−5441.82			−0.726016			−0.363008	−	0.931786i	$-0.618250\pi$
$383$	−5441.82			−0.726016			−0.363008	+	0.931786i	$0.618250\pi$
$384$	10856.5	+	296.579i	1.44275	+	0.0394134i
$385$		−	23330.9i		−	3.08845i
$386$	7346.59	−	9138.96i	0.968735	−	1.20508i
$387$	149.945			0.0196954
$388$	−669.351	−	3041.84i	−0.0875803	−	0.398005i
$389$			1331.04i			0.173487i	0.996231	+	0.0867437i	$0.0276461\pi$
$389$			1331.04i			0.173487i	−0.996231	+	0.0867437i	$0.972354\pi$
$390$	−18652.2	−	14994.0i	−2.42177	−	1.94680i
$391$			20.9745i			0.00271286i
$392$	−2644.47	−	1311.86i	−0.340729	−	0.169028i
$393$		−	7979.46i		−	1.02420i
$394$	9533.56	+	7663.80i	1.21902	+	0.979941i
$395$	18808.6			2.39586
$396$	2978.70	+	13536.6i	0.377993	+	1.71777i
$397$	−8247.85			−1.04269			−0.521345	−	0.853346i	$-0.674569\pi$
$397$	−8247.85			−1.04269			−0.521345	+	0.853346i	$0.674569\pi$
$398$	−137.567	+	171.129i	−0.0173256	+	0.0215526i
$399$	15320.6			1.92228
$400$	−11764.9	+	5441.13i	−1.47061	+	0.680142i
$401$			5158.51i			0.642404i	0.947011	+	0.321202i	$0.104087\pi$
$401$			5158.51i			0.642404i	−0.947011	+	0.321202i	$0.895913\pi$
$402$	827.527	+	665.229i	0.102670	+	0.0825339i
$403$	−7381.69	+	7828.51i	−0.912427	+	0.967657i
$404$	−1733.68	−	7878.63i	−0.213499	−	0.970239i
$405$	12006.2			1.47306
$406$	−7987.01	+	9935.62i	−0.976327	+	1.21452i
$407$			20966.3i			2.55347i
$408$	−33.7151	+	67.9635i	−0.00409105	+	0.00824680i
$409$			633.606i			0.0766009i	0.999266	+	0.0383005i	$0.0121944\pi$
$409$			633.606i			0.0766009i	−0.999266	+	0.0383005i	$0.987806\pi$
$410$	−1919.81	+	2388.19i	−0.231251	+	0.287669i
$411$			3243.42i			0.389261i
$412$	−4178.98	+	919.578i	−0.499718	+	0.109962i
$413$	4916.26			0.585746
$414$	2431.24	−	3024.40i	0.288621	−	0.359036i
$415$	−1367.69			−0.161776
$416$	10950.7	+	2725.21i	1.29063	+	0.321189i
$417$	5199.26			0.610572
$418$	−12262.0	−	9857.15i	−1.43482	−	1.15342i
$419$			7622.65i			0.888760i	0.895838	+	0.444380i	$0.146576\pi$
$419$			7622.65i			0.888760i	−0.895838	+	0.444380i	$0.853424\pi$
$420$	−23074.2	+	5077.44i	−2.68073	+	0.589890i
$421$	3158.23			0.365612			0.182806	−	0.983149i	$-0.441482\pi$
$421$	3158.23			0.365612			0.182806	+	0.983149i	$0.441482\pi$
$422$	−1714.78	−	1378.47i	−0.197806	−	0.159012i
$423$		−	9409.74i		−	1.08160i
$424$	4972.66	−	10024.0i	0.569561	−	1.14813i
$425$		−	90.5479i		−	0.0103346i
$426$	7465.75	+	6001.54i	0.849100	+	0.682571i
$427$	3868.88			0.438474
$428$	9776.09	−	2151.21i	1.10408	−	0.242950i
$429$			27698.8i			3.11727i
$430$	164.446	−	204.567i	0.0184426	−	0.0229421i
$431$		−	14627.0i		−	1.63470i	−0.576140	−	0.817351i	$-0.695442\pi$
$431$		−	14627.0i		−	1.63470i	0.576140	−	0.817351i	$-0.304558\pi$
$432$	977.234	−	451.961i	0.108836	−	0.0503357i
$433$		−	11858.5i		−	1.31613i	−0.752963	−	0.658063i	$-0.771376\pi$
$433$		−	11858.5i		−	1.31613i	0.752963	−	0.658063i	$-0.228624\pi$
$434$	1457.75	+	10522.1i	0.161231	+	1.16377i
$435$			28113.5i			3.09871i
$436$	1607.01	+	7302.99i	0.176518	+	0.802178i
$437$			4404.65i			0.482158i
$438$	11372.9	+	9142.41i	1.24068	+	0.997355i
$439$			283.581i			0.0308305i	0.999881	+	0.0154152i	$0.00490702\pi$
$439$			283.581i			0.0308305i	−0.999881	+	0.0154152i	$0.995093\pi$
$440$	21734.5	+	10782.0i	2.35489	+	1.16820i
$441$	−3815.08			−0.411952
$442$	−49.3897	+	61.4394i	−0.00531499	+	0.00661170i
$443$		−	2691.07i		−	0.288616i	−0.989533	−	0.144308i	$-0.953904\pi$
$443$		−	2691.07i		−	0.288616i	0.989533	−	0.144308i	$-0.0460956\pi$
$444$	20735.7	−	4562.85i	2.21638	−	0.487710i
$445$			1734.59i			0.184781i
$446$	−5234.47	+	6511.54i	−0.555739	+	0.691324i
$447$	−15010.4			−1.58830
$448$	8870.34	−	6740.31i	0.935456	−	0.710826i
$449$		−	4115.21i		−	0.432536i	−0.976334	−	0.216268i	$-0.930612\pi$
$449$		−	4115.21i		−	0.432536i	0.976334	−	0.216268i	$-0.0693885\pi$
$450$	−10495.8	+	13056.4i	−1.09950	+	1.36775i
$451$	3546.51			0.370285
$452$	−752.583	−	3420.08i	−0.0783153	−	0.355901i
$453$	−4546.67			−0.471570
$454$	5489.56	+	4412.92i	0.567484	+	0.456187i
$455$	−24549.0			−2.52940
$456$	−7080.16	+	14272.3i	−0.727103	+	1.46571i
$457$			17986.0i			1.84103i	0.390708	+	0.920515i	$0.372230\pi$
$457$			17986.0i			1.84103i	−0.390708	+	0.920515i	$0.627770\pi$
$458$	−13045.5	−	10487.0i	−1.33095	−	1.06992i
$459$			7.52125i			0.000764841i
$460$	−1459.75	−	6633.79i	−0.147959	−	0.672396i
$461$		−	376.809i		−	0.0380688i	−0.999819	−	0.0190344i	$-0.993941\pi$
$461$		−	376.809i		−	0.0380688i	0.999819	−	0.0190344i	$-0.00605921\pi$
$462$	21312.8	+	17132.8i	2.14623	+	1.72530i
$463$	16598.9			1.66613			0.833065	−	0.553175i	$-0.186584\pi$
$463$	16598.9			1.66613			0.833065	+	0.553175i	$0.186584\pi$
$464$	−5564.72	−	12032.1i	−0.556758	−	1.20383i
$465$	17044.2	+	16071.4i	1.69980	+	1.60278i
$466$	4206.43	−	5232.68i	0.418152	−	0.520170i
$467$		−	837.839i		−	0.0830204i	−0.999138	−	0.0415102i	$-0.986783\pi$
$467$		−	837.839i		−	0.0830204i	0.999138	−	0.0415102i	$-0.0132169\pi$
$468$	14243.3	−	3134.22i	1.40684	−	0.309571i
$469$	1089.15			0.107233
$470$	−12837.5	−	10319.8i	−1.25990	−	1.01280i
$471$	−24916.8			−2.43759
$472$	−2271.96	+	4579.86i	−0.221558	+	0.446621i
$473$	−303.785			−0.0295308
$474$	−13811.9	+	17181.7i	−1.33840	+	1.66494i
$475$		−	19015.0i		−	1.83678i
$476$	16.7249	+	76.0055i	0.00161047	+	0.00731871i
$477$		−	14461.2i		−	1.38812i
$478$	−5652.40	+	7031.43i	−0.540868	+	0.672825i
$479$		−	15221.6i		−	1.45196i	−0.687714	−	0.725982i	$-0.741386\pi$
$479$		−	15221.6i		−	1.45196i	0.687714	−	0.725982i	$-0.258614\pi$
$480$	5933.34	−	23841.8i	0.564205	−	2.26714i
$481$	22061.0			2.09126
$482$	−3469.96	−	2789.42i	−0.327910	−	0.263599i
$483$		−	7655.77i		−	0.721220i
$484$	−3746.46	−	17025.7i	−0.351847	−	1.59895i
$485$	−7045.99			−0.659675
$486$	−9621.55	+	11968.9i	−0.898030	+	1.11712i
$487$	12700.4			1.18174			0.590871	−	0.806766i	$-0.298784\pi$
$487$	12700.4			1.18174			0.590871	+	0.806766i	$0.298784\pi$
$488$	−1787.94	+	3604.16i	−0.165853	+	0.334329i
$489$			4454.78i			0.411967i
$490$	−4184.06	+	5204.85i	−0.385748	+	0.479860i
$491$	−8409.12			−0.772909			−0.386455	−	0.922308i	$-0.626300\pi$
$491$	−8409.12			−0.772909			−0.386455	+	0.922308i	$0.626300\pi$
$492$	−771.818	−	3507.50i	−0.0707241	−	0.321403i
$493$	92.6046			0.00845984
$494$	−10371.8	+	12902.3i	−0.944636	+	1.17510i
$495$	31355.6			2.84713
$496$	−10475.8	−	3504.59i	−0.948339	−	0.317259i
$497$	9826.04			0.886837
$498$	1004.35	−	1249.38i	0.0903733	−	0.112422i
$499$	−9824.90			−0.881409			−0.440704	−	0.897652i	$-0.645271\pi$
$499$	−9824.90			−0.881409			−0.440704	+	0.897652i	$0.645271\pi$
$500$	2412.45	+	10963.3i	0.215776	+	0.980587i
$501$	−3944.22			−0.351726
$502$	−7096.37	+	8827.69i	−0.630929	+	0.784858i
$503$		−	7369.26i		−	0.653239i	−0.945156	−	0.326620i	$-0.894090\pi$
$503$		−	7369.26i		−	0.653239i	0.945156	−	0.326620i	$-0.105910\pi$
$504$	6398.46	−	12898.1i	0.565497	−	1.13994i
$505$	−18249.7			−1.60812
$506$	−4925.65	+	6127.37i	−0.432751	+	0.538330i
$507$	12668.5			1.10972
$508$	−380.745	−	1730.28i	−0.0332536	−	0.151120i
$509$		−	10893.6i		−	0.948624i	−0.880357	−	0.474312i	$-0.842697\pi$
$509$		−	10893.6i		−	0.948624i	0.880357	−	0.474312i	$-0.157303\pi$
$510$	133.766	+	107.531i	0.0116142	+	0.00933640i
$511$	14968.5			1.29582
$512$	2179.84	+	11378.3i	0.188157	+	0.982139i
$513$			1579.46i			0.135936i
$514$	−9910.77	+	12328.7i	−0.850478	+	1.05797i
$515$			9680.03i			0.828258i
$516$	66.1120	+	300.444i	0.00564035	+	0.0256323i
$517$			19064.0i			1.62173i
$518$	13645.6	−	16974.8i	1.15744	−	1.43982i
$519$	−29358.7			−2.48305
$520$	11344.9	−	22869.3i	0.956745	−	1.92862i
$521$	−3431.80			−0.288579			−0.144290	−	0.989536i	$-0.546090\pi$
$521$	−3431.80			−0.288579			−0.144290	+	0.989536i	$0.546090\pi$
$522$	−13353.0	−	10734.2i	−1.11963	−	0.900040i
$523$	1221.16			0.102099			0.0510495	−	0.998696i	$-0.483743\pi$
$523$	1221.16			0.102099			0.0510495	+	0.998696i	$0.483743\pi$
$524$	8313.05	−	1829.27i	0.693048	−	0.152504i
$525$			33050.2i			2.74749i
$526$	−3997.81	+	4973.16i	−0.331393	+	0.412244i
$527$	52.9386	−	56.1429i	0.00437579	−	0.00464065i
$528$	−25809.8	+	11936.8i	−2.12733	+	0.983869i
$529$	−9965.98			−0.819099
$530$	−19729.2	−	15859.8i	−1.61695	−	1.29983i
$531$			6607.21i			0.539978i
$532$	3512.21	+	15961.1i	0.286229	+	1.30076i
$533$		−	3731.68i		−	0.303259i
$534$	−1584.55	−	1273.78i	−0.128409	−	0.103225i
$535$		−	22644.9i		−	1.82996i
$536$	−503.332	+	1014.63i	−0.0405608	+	0.0817633i
$537$	24492.5			1.96821
$538$	11287.3	+	9073.61i	0.904518	+	0.727121i
$539$	7729.30			0.617670
$540$	−523.453	−	2378.81i	−0.0417145	−	0.189570i
$541$	168.625			0.0134007			0.00670034	−	0.999978i	$-0.497867\pi$
$541$	168.625			0.0134007			0.00670034	+	0.999978i	$0.497867\pi$
$542$	8244.38	−	10255.8i	0.653370	−	0.812774i
$543$			7743.71i			0.611997i
$544$	−78.5339	−	19.5441i	−0.00618955	−	0.00154035i
$545$	16916.3			1.32957
$546$	18027.4	−	22425.5i	1.41300	−	1.75774i
$547$		−	12655.9i		−	0.989260i	−0.869104	−	0.494630i	$-0.835304\pi$
$547$		−	12655.9i		−	0.989260i	0.869104	−	0.494630i	$-0.164696\pi$
$548$	−3379.01	+	743.546i	−0.263402	+	0.0579611i
$549$			5199.59i			0.404213i
$550$	21264.2	−	26452.1i	1.64856	−	2.05077i
$551$	19446.9			1.50357
$552$	7131.93	+	3537.98i	0.549918	+	0.272802i
$553$			22613.7i			1.73893i
$554$	4193.24	+	3370.84i	0.321577	+	0.258508i
$555$		−	48031.3i		−	3.67354i
$556$	1191.92	+	5416.62i	0.0909146	+	0.413158i
$557$			12192.7i			0.927510i	0.885964	+	0.463755i	$0.153498\pi$
$557$			12192.7i			0.927510i	−0.885964	+	0.463755i	$0.846502\pi$
$558$	−14141.1	+	1959.14i	−1.07284	+	0.148633i
$559$			319.647i			0.0241854i
$560$	−10579.4	−	22874.9i	−0.798325	−	1.72614i
$561$		−	198.645i		−	0.0149497i
$562$	3605.92	−	4485.67i	0.270652	−	0.336684i
$563$			2374.89i			0.177779i	0.996041	+	0.0888895i	$0.0283318\pi$
$563$			2374.89i			0.177779i	−0.996041	+	0.0888895i	$0.971668\pi$
$564$	18854.3	−	4148.85i	1.40764	−	0.309748i
$565$	−7922.14			−0.589888
$566$	−3322.15	−	2670.60i	−0.246715	−	0.198328i
$567$			14435.0i			1.06916i
$568$	−4540.93	+	9153.70i	−0.335446	+	0.676198i
$569$		−	20773.6i		−	1.53053i	−0.643714	−	0.765266i	$-0.722607\pi$
$569$		−	20773.6i		−	1.53053i	0.643714	−	0.765266i	$-0.277393\pi$
$570$	28090.8	+	22581.5i	2.06420	+	1.65936i
$571$	−11697.2			−0.857292			−0.428646	−	0.903473i	$-0.641009\pi$
$571$	−11697.2			−0.857292			−0.428646	+	0.903473i	$0.641009\pi$
$572$	−28856.8	+	6349.88i	−2.10938	+	0.464164i
$573$		−	20981.8i		−	1.52972i
$574$	−2871.33	−	2308.20i	−0.208793	−	0.167844i
$575$	−9501.87			−0.689140
$576$	9058.66	+	11921.3i	0.655285	+	0.862363i
$577$	17261.2			1.24540			0.622698	−	0.782462i	$-0.286037\pi$
$577$	17261.2			1.24540			0.622698	+	0.782462i	$0.286037\pi$
$578$	−8706.02	+	10830.1i	−0.626510	+	0.779361i
$579$	31090.7			2.23158
$580$	−29288.8	+	6444.95i	−2.09681	+	0.461400i
$581$		−	1644.37i		−	0.117418i
$582$	5174.16	−	6436.52i	0.368515	−	0.458423i
$583$			29298.2i			2.08132i
$584$	−6917.41	+	13944.2i	−0.490145	+	0.988043i
$585$		−	32992.7i		−	2.33176i
$586$	15782.3	−	19632.7i	1.11256	−	1.38399i
$587$	12730.7			0.895147			0.447574	−	0.894247i	$-0.352288\pi$
$587$	12730.7			0.895147			0.447574	+	0.894247i	$0.352288\pi$
$588$	−1682.11	−	7644.27i	−0.117974	−	0.536130i
$589$	11117.1	−	11790.0i	0.777710	−	0.824785i
$590$	9014.09	+	7246.22i	0.628991	+	0.505631i
$591$			32433.1i			2.25739i
$592$	9507.20	+	20556.5i	0.660040	+	1.42714i
$593$	−8548.38			−0.591973			−0.295986	−	0.955192i	$-0.595648\pi$
$593$	−8548.38			−0.591973			−0.295986	+	0.955192i	$0.595648\pi$
$594$	−1766.29	+	2197.21i	−0.122006	+	0.151772i
$595$	176.056			0.0121304
$596$	−3441.10	−	15638.0i	−0.236499	−	1.07476i
$597$	−582.180			−0.0399113
$598$	6447.30	+	5182.83i	0.440886	+	0.354418i
$599$			20995.3i			1.43213i	0.698033	+	0.716065i	$0.254059\pi$
$599$			20995.3i			1.43213i	−0.698033	+	0.716065i	$0.745941\pi$
$600$	−30788.8	−	15273.6i	−2.09491	−	1.03924i
$601$		−	11219.0i		−	0.761453i	−0.924688	−	0.380727i	$-0.875674\pi$
$601$		−	11219.0i		−	0.761453i	0.924688	−	0.380727i	$-0.124326\pi$
$602$	245.951	+	197.714i	0.0166515	+	0.0133858i
$603$			1463.76i			0.0988542i
$604$	−1042.31	−	4736.75i	−0.0702171	−	0.319099i
$605$	−39437.5			−2.65019
$606$	13401.5	−	16671.1i	0.898350	−	1.11752i
$607$			17490.1i			1.16952i	0.811206	+	0.584761i	$0.198812\pi$
$607$			17490.1i			1.16952i	−0.811206	+	0.584761i	$0.801188\pi$
$608$	−16492.1	−	4104.26i	−1.10007	−	0.273766i
$609$	−33800.9			−2.24907
$610$	7093.71	+	5702.46i	0.470846	+	0.378502i
$611$	20059.4			1.32817
$612$	−102.148	+	22.4774i	−0.00674685	+	0.00148463i
$613$		−	17915.1i		−	1.18040i	−0.807258	−	0.590199i	$-0.799049\pi$
$613$		−	17915.1i		−	1.18040i	0.807258	−	0.590199i	$-0.200951\pi$
$614$	−16808.5	−	13511.9i	−1.10478	−	0.888107i
$615$	−8124.62			−0.532710
$616$	−12963.2	+	26131.4i	−0.847892	+	1.70920i
$617$	−981.672			−0.0640529			−0.0320264	−	0.999487i	$-0.510196\pi$
$617$	−981.672			−0.0640529			−0.0320264	+	0.999487i	$0.510196\pi$
$618$	−8842.71	−	7108.44i	−0.575576	−	0.462692i
$619$	−19717.5			−1.28031			−0.640155	−	0.768246i	$-0.721130\pi$
$619$	−19717.5			−1.28031			−0.640155	+	0.768246i	$0.721130\pi$
$620$	−12836.0	+	21441.1i	−0.831459	+	1.38886i
$621$	789.262			0.0510016
$622$	−18448.6	−	14830.4i	−1.18926	−	0.956018i
$623$	−2085.51			−0.134116
$624$	12560.1	+	27157.4i	0.805777	+	1.74226i
$625$	78.2148			0.00500574
$626$	−21977.3	−	17667.0i	−1.40318	−	1.12798i
$627$		−	41715.3i		−	2.65702i
$628$	−5712.11	−	25958.4i	−0.362958	−	1.64945i
$629$	−158.213			−0.0100292
$630$	−25386.1	−	20407.3i	−1.60541	−	1.29055i
$631$	−25176.0			−1.58833			−0.794167	−	0.607699i	$-0.792093\pi$
$631$	−25176.0			−1.58833			−0.794167	+	0.607699i	$0.792093\pi$
$632$	−21066.3	−	10450.5i	−1.32591	−	0.657752i
$633$		−	5833.68i		−	0.366300i
$634$	1672.08	−	2080.02i	0.104742	−	0.130297i
$635$	−4007.95			−0.250473
$636$	28975.9	−	6376.10i	1.80656	−	0.397530i
$637$		−	8132.86i		−	0.505865i
$638$	27052.9	+	21747.2i	1.67874	+	1.34950i
$639$			13205.7i			0.817543i
$640$	26198.8	+	715.704i	1.61812	+	0.0442042i
$641$			9348.42i			0.576038i	0.957625	+	0.288019i	$0.0929966\pi$
$641$			9348.42i			0.576038i	−0.957625	+	0.288019i	$0.907003\pi$
$642$	20686.2	+	16629.1i	1.27168	+	1.02227i
$643$	30127.8			1.84778			0.923892	−	0.382653i	$-0.124990\pi$
$643$	30127.8			1.84778			0.923892	+	0.382653i	$0.124990\pi$
$644$	7975.83	−	1755.07i	0.488030	−	0.107390i
$645$	695.935			0.0424844
$646$	74.3825	−	92.5298i	0.00453025	−	0.00563551i
$647$	−17671.8			−1.07380			−0.536902	−	0.843644i	$-0.680406\pi$
$647$	−17671.8			−1.07380			−0.536902	+	0.843644i	$0.680406\pi$
$648$	−13447.3	−	6670.90i	−0.815217	−	0.404410i
$649$		−	13386.1i		−	0.809630i
$650$	−27833.2	−	22374.5i	−1.67955	−	1.35015i
$651$	−19322.7	+	20492.3i	−1.16331	+	1.23373i
$652$	−4641.01	+	1021.25i	−0.278767	+	0.0613422i
$653$	−2285.60			−0.136972			−0.0684859	−	0.997652i	$-0.521817\pi$
$653$	−2285.60			−0.136972			−0.0684859	+	0.997652i	$0.521817\pi$
$654$	−12422.4	+	15453.1i	−0.742741	+	0.923950i
$655$		−	19256.0i		−	1.14869i
$656$	3477.19	−	1608.17i	0.206954	−	0.0957141i
$657$			20116.9i			1.19457i
$658$	12407.5	−	15434.6i	0.735099	−	0.914443i
$659$			5582.36i			0.329981i	0.986295	+	0.164991i	$0.0527594\pi$
$659$			5582.36i			0.329981i	−0.986295	+	0.164991i	$0.947241\pi$
$660$	13825.0	+	62827.0i	0.815358	+	3.70536i
$661$	23796.0			1.40023			0.700117	−	0.714028i	$-0.253131\pi$
$661$	23796.0			1.40023			0.700117	+	0.714028i	$0.253131\pi$
$662$	−938.130	+	1167.01i	−0.0550777	+	0.0685152i
$663$	−209.016			−0.0122436
$664$	1531.86	+	759.919i	0.0895295	+	0.0444135i
$665$	36971.7			2.15594
$666$	22813.3	+	18339.1i	1.32732	+	1.06700i
$667$		−	9717.70i		−	0.564124i
$668$	−904.202	−	4109.11i	−0.0523722	−	0.238003i
$669$	−22152.2			−1.28020
$670$	1996.99	+	1605.33i	0.115150	+	0.0925661i
$671$		−	10534.3i		−	0.606068i
$672$	28665.1	+	7133.66i	1.64551	+	0.409505i
$673$			19002.6i			1.08840i	0.838954	+	0.544202i	$0.183168\pi$
$673$			19002.6i			1.08840i	−0.838954	+	0.544202i	$0.816832\pi$
$674$	−10547.7	−	8479.03i	−0.602792	−	0.484570i
$675$	−3407.27			−0.194290
$676$	2904.22	+	13198.1i	0.165238	+	0.750918i
$677$		−	19970.6i		−	1.13373i	−0.823812	−	0.566863i	$-0.808157\pi$
$677$		−	19970.6i		−	1.13373i	0.823812	−	0.566863i	$-0.191843\pi$
$678$	5817.55	−	7236.87i	0.329531	−	0.409927i
$679$		−	8471.42i		−	0.478797i
$680$	−81.3612	+	164.009i	−0.00458832	+	0.00924923i
$681$			18675.4i			1.05087i
$682$	28649.7	−	3969.19i	1.60858	−	0.222856i
$683$			7899.44i			0.442553i	0.975211	+	0.221276i	$0.0710223\pi$
$683$			7899.44i			0.442553i	−0.975211	+	0.221276i	$0.928978\pi$
$684$	−21451.0	+	4720.25i	−1.19912	+	0.263864i
$685$			7827.01i			0.436576i
$686$	10194.9	+	8195.44i	0.567410	+	0.456127i
$687$		−	44380.8i		−	2.46468i
$688$	−297.848	+	137.752i	−0.0165049	+	0.00763334i
$689$	30828.0			1.70457
$690$	11284.1	−	14037.1i	0.622575	−	0.774467i
$691$			12053.9i			0.663604i	0.943349	+	0.331802i	$0.107657\pi$
$691$			12053.9i			0.663604i	−0.943349	+	0.331802i	$0.892343\pi$
$692$	−6730.40	−	30586.0i	−0.369728	−	1.68021i
$693$			37698.9i			2.06647i
$694$	5160.38	−	6419.37i	0.282256	−	0.351118i
$695$	12546.8			0.684789
$696$	15620.5	−	31488.1i	0.850710	−	1.71488i
$697$			26.7621i			0.00145436i
$698$	−16851.0	+	20962.1i	−0.913780	+	1.13672i
$699$	17801.6			0.963257
$700$	−34431.9	+	7576.68i	−1.85915	+	0.409102i
$701$	2880.20			0.155184			0.0775918	−	0.996985i	$-0.475277\pi$
$701$	2880.20			0.155184			0.0775918	+	0.996985i	$0.475277\pi$
$702$	2311.93	+	1858.51i	0.124300	+	0.0999215i
$703$	−33224.6			−1.78249
$704$	−18352.7	−	24152.4i	−0.982518	−	1.29301i
$705$		−	43673.2i		−	2.33309i
$706$	−2337.63	−	1879.16i	−0.124614	−	0.100175i
$707$		−	21941.7i		−	1.16719i
$708$	−13238.8	+	2913.18i	−0.702749	+	0.154639i
$709$		−	238.354i		−	0.0126256i	−0.999980	−	0.00631281i	$-0.997991\pi$
$709$		−	238.354i		−	0.0126256i	0.999980	−	0.00631281i	$-0.00200944\pi$
$710$	18016.3	+	14482.9i	0.952311	+	0.765540i
$711$	−30391.7			−1.60306
$712$	963.781	−	1942.81i	0.0507293	−	0.102261i
$713$	−5891.50	−	5555.24i	−0.309451	−	0.291789i
$714$	−129.285	+	160.827i	−0.00677643	+	0.00842970i
$715$			66842.7i			3.49619i
$716$	5614.85	+	25516.5i	0.293068	+	1.33184i
$717$	−23920.9			−1.24595
$718$	9199.36	+	7395.15i	0.478158	+	0.384380i
$719$	27737.9			1.43873			0.719366	−	0.694632i	$-0.244433\pi$
$719$	27737.9			1.43873			0.719366	+	0.694632i	$0.244433\pi$
$720$	30742.7	−	14218.2i	1.59127	−	0.735947i
$721$	−11638.3			−0.601157
$722$	3465.41	−	4310.87i	0.178628	−	0.222208i
$723$		−	11804.8i		−	0.607227i
$724$	−8067.45	+	1775.23i	−0.414122	+	0.0911268i
$725$			41951.7i			2.14903i
$726$	28960.6	−	36026.2i	1.48048	−	1.84168i
$727$			26855.5i			1.37003i	0.728528	+	0.685016i	$0.240205\pi$
$727$			26855.5i			1.37003i	−0.728528	+	0.685016i	$0.759795\pi$
$728$	27495.8	+	13640.0i	1.39981	+	0.694413i
$729$	−22806.5			−1.15869
$730$	27445.1	+	22062.4i	1.39149	+	1.11859i
$731$		−	2.29238i		−	0.000115987i
$732$	−10418.4	+	2292.55i	−0.526059	+	0.115758i
$733$	10357.5			0.521912			0.260956	−	0.965351i	$-0.415962\pi$
$733$	10357.5			0.521912			0.260956	+	0.965351i	$0.415962\pi$
$734$	−21082.7	+	26226.4i	−1.06019	+	1.31885i
$735$	−17706.9			−0.888610
$736$	−2050.91	+	8241.16i	−0.102714	+	0.412735i
$737$		−	2965.56i		−	0.148220i
$738$	3102.10	−	3858.93i	0.154729	−	0.192479i
$739$	3200.30			0.159303			0.0796514	−	0.996823i	$-0.474619\pi$
$739$	3200.30			0.159303			0.0796514	+	0.996823i	$0.474619\pi$
$740$	50039.3	−	11011.1i	2.48578	−	0.546992i
$741$	−43893.4			−2.17607
$742$	19068.3	−	23720.5i	0.943424	−	1.17359i
$743$	32627.2			1.61100			0.805502	−	0.592593i	$-0.201896\pi$
$743$	32627.2			1.61100			0.805502	+	0.592593i	$0.201896\pi$
$744$	−10160.5	−	27470.7i	−0.500674	−	1.35366i
$745$	−36223.1			−1.78136
$746$	−7730.74	+	9616.83i	−0.379414	+	0.471980i
$747$	2209.96			0.108244
$748$	206.949	−	45.5388i	0.0101161	−	0.00222602i
$749$	27226.1			1.32820
$750$	−18648.5	+	23198.3i	−0.907931	+	1.12944i
$751$		−	9972.90i		−	0.484576i	−0.970204	−	0.242288i	$-0.922102\pi$
$751$		−	9972.90i		−	0.484576i	0.970204	−	0.242288i	$-0.0778978\pi$
$752$	8644.59	+	18691.4i	0.419196	+	0.906389i
$753$	−30031.7			−1.45341
$754$	22882.7	−	28465.4i	1.10522	−	1.37487i
$755$	−10972.0			−0.528891
$756$	2860.05	−	629.348i	0.137591	−	0.0302767i
$757$		−	3556.38i		−	0.170751i	−0.996349	−	0.0853756i	$-0.972791\pi$
$757$		−	3556.38i		−	0.170751i	0.996349	−	0.0853756i	$-0.0272090\pi$
$758$	228.630	+	183.790i	0.0109554	+	0.00880682i
$759$	−20845.3			−0.996886
$760$	−17085.8	+	34441.9i	−0.815484	+	1.64387i
$761$		−	27982.6i		−	1.33294i	−0.745532	−	0.666470i	$-0.767804\pi$
$761$		−	27982.6i		−	1.33294i	0.745532	−	0.666470i	$-0.232196\pi$
$762$	2943.20	−	3661.26i	0.139922	−	0.174060i
$763$			20338.6i			0.965014i
$764$	21859.0	−	4810.03i	1.03512	−	0.227776i
$765$			236.611i			0.0111826i
$766$	9643.50	−	11996.3i	0.454875	−	0.565852i
$767$	−14085.0			−0.663077
$768$	−19892.6	+	23407.0i	−0.934653	+	1.09978i
$769$	37379.9			1.75287			0.876433	−	0.481523i	$-0.159916\pi$
$769$	37379.9			1.75287			0.876433	+	0.481523i	$0.159916\pi$
$770$	51431.9	+	41344.9i	2.40711	+	1.93502i
$771$	−41942.3			−1.95916
$772$	7127.47	+	32390.5i	0.332284	+	1.51005i
$773$		−	31894.5i		−	1.48405i	−0.670375	−	0.742023i	$-0.733867\pi$
$773$		−	31894.5i		−	1.48405i	0.670375	−	0.742023i	$-0.266133\pi$
$774$	−265.718	+	330.546i	−0.0123399	+	0.0153504i
$775$	25433.8	+	23982.2i	1.17885	+	1.11157i
$776$	7891.77	+	3914.92i	0.365075	+	0.181105i
$777$	57748.1			2.66628
$778$	−2934.23	−	2358.76i	−0.135215	−	0.108696i
$779$			5620.04i			0.258484i
$780$	66107.4	−	14546.8i	3.03465	−	0.667768i
$781$		−	26754.6i		−	1.22580i
$782$	−46.2375	−	37.1692i	−0.00211438	−	0.00169970i
$783$		−	3484.67i		−	0.159044i
$784$	7578.23	−	3504.86i	0.345218	−	0.159660i
$785$	−60129.1			−2.73388
$786$	17590.4	+	14140.5i	0.798254	+	0.641697i
$787$	−15479.9			−0.701144			−0.350572	−	0.936536i	$-0.614013\pi$
$787$	−15479.9			−0.701144			−0.350572	+	0.936536i	$0.614013\pi$
$788$	−33789.0	+	7435.21i	−1.52752	+	0.336127i
$789$	−16918.7			−0.763398
$790$	−33330.9	+	41462.8i	−1.50109	+	1.86732i
$791$		−	9524.81i		−	0.428146i
$792$	−35119.4	−	17421.9i	−1.57565	−	0.781641i
$793$	−11084.3			−0.496362
$794$	14616.1	−	18182.0i	0.653282	−	0.812664i
$795$		−	67118.7i		−	2.99428i
$796$	−133.463	−	606.519i	−0.00594282	−	0.0270069i
$797$			44659.1i			1.98482i	0.122953	+	0.992412i	$0.460763\pi$
$797$			44659.1i			1.98482i	−0.122953	+	0.992412i	$0.539237\pi$
$798$	−27149.8	+	33773.6i	−1.20438	+	1.49821i
$799$	−143.858			−0.00636961
$800$	8853.87	−	35577.4i	0.391290	−	1.57231i
$801$		−	2802.82i		−	0.123636i
$802$	−11371.7	−	9141.45i	−0.500685	−	0.402489i
$803$		−	40756.4i		−	1.79111i
$804$	−2932.94	+	645.388i	−0.128653	+	0.0283098i
$805$		−	18474.9i		−	0.808887i
$806$	−4176.43	−	30145.6i	−0.182517	−	1.31741i
$807$			38399.4i			1.67500i
$808$	20440.4	+	10140.0i	0.889963	+	0.441489i
$809$			26622.4i			1.15698i	0.815691	+	0.578488i	$0.196357\pi$
$809$			26622.4i			1.15698i	−0.815691	+	0.578488i	$0.803643\pi$
$810$	−21276.2	+	26467.0i	−0.922926	+	1.14810i
$811$			32032.1i			1.38693i	0.720492	+	0.693464i	$0.243916\pi$
$811$			32032.1i			1.38693i	−0.720492	+	0.693464i	$0.756084\pi$
$812$	−7748.78	−	35214.0i	−0.334888	−	1.52188i
$813$	34890.1			1.50510
$814$	−46219.3	−	37154.6i	−1.99016	−	1.59984i
$815$			10750.3i			0.462043i
$816$	−90.0757	−	194.762i	−0.00386432	−	0.00835545i
$817$		−	481.399i		−	0.0206145i
$818$	−1396.76	−	1122.82i	−0.0597022	−	0.0479932i
$819$	39667.2			1.69241
$820$	−1862.55	−	8464.28i	−0.0793208	−	0.360470i
$821$		−	4836.25i		−	0.205586i	−0.994703	−	0.102793i	$-0.967222\pi$
$821$		−	4836.25i		−	0.205586i	0.994703	−	0.102793i	$-0.0327779\pi$
$822$	−7149.98	−	5747.70i	−0.303387	−	0.243886i
$823$	−30655.7			−1.29841			−0.649204	−	0.760615i	$-0.724898\pi$
$823$	−30655.7			−1.29841			−0.649204	+	0.760615i	$0.724898\pi$
$824$	5378.45	−	10842.0i	0.227387	−	0.458372i
$825$	89989.9			3.79763
$826$	−8712.15	+	10837.7i	−0.366991	+	0.456526i
$827$	28520.9			1.19924			0.599618	−	0.800286i	$-0.295319\pi$
$827$	28520.9			1.19924			0.599618	+	0.800286i	$0.295319\pi$
$828$	2358.72	+	10719.1i	0.0989991	+	0.449898i
$829$			2561.91i			0.107333i	0.998559	+	0.0536664i	$0.0170907\pi$
$829$			2561.91i			0.107333i	−0.998559	+	0.0536664i	$0.982909\pi$
$830$	2423.69	−	3015.00i	0.101358	−	0.126087i
$831$			14265.4i			0.595499i
$832$	−25413.4	+	19310.9i	−1.05896	+	0.804670i
$833$			58.3256i			0.00242601i
$834$	−9213.65	+	11461.5i	−0.382545	+	0.475876i
$835$	−9518.17			−0.394479
$836$	43459.3	−	9563.14i	1.79793	−	0.395632i
$837$	−2112.63	−	1992.05i	−0.0872440	−	0.0822645i
$838$	−16803.8	−	13508.2i	−0.692693	−	0.556840i
$839$		−	34169.1i		−	1.40602i	−0.711182	−	0.703008i	$-0.751840\pi$
$839$		−	34169.1i		−	1.40602i	0.711182	−	0.703008i	$-0.248160\pi$
$840$	29697.1	−	59863.9i	1.21982	−	2.45893i
$841$	−18515.6			−0.759176
$842$	−5596.73	+	6962.18i	−0.229069	+	0.284955i
$843$	15260.2			0.623475
$844$	6077.56	−	1337.36i	0.247865	−	0.0545423i
$845$	30571.6			1.24461
$846$	20743.4	+	16675.1i	0.842992	+	0.677661i
$847$		−	47415.9i		−	1.92353i
$848$	13285.3	+	28725.6i	0.537995	+	1.16326i
$849$		−	11301.9i		−	0.456869i
$850$	199.609	+	160.461i	0.00805474	+	0.00647501i
$851$			16602.5i			0.668772i
$852$	−26460.2	+	5822.53i	−1.06398	+	0.234127i
$853$	−9529.04			−0.382495			−0.191247	−	0.981542i	$-0.561253\pi$
$853$	−9529.04			−0.382495			−0.191247	+	0.981542i	$0.561253\pi$
$854$	−6856.09	+	8528.78i	−0.274720	+	0.341744i
$855$			49688.2i			1.98748i
$856$	−12582.1	+	25363.1i	−0.502390	+	1.01273i
$857$	−30026.9			−1.19685			−0.598424	−	0.801180i	$-0.704206\pi$
$857$	−30026.9			−1.19685			−0.598424	+	0.801180i	$0.704206\pi$
$858$	−61060.8	−	49085.3i	−2.42958	−	1.95308i
$859$	−7926.93			−0.314858			−0.157429	−	0.987530i	$-0.550321\pi$
$859$	−7926.93			−0.314858			−0.157429	+	0.987530i	$0.550321\pi$
$860$	159.541	+	725.030i	0.00632595	+	0.0287480i
$861$		−	9768.26i		−	0.386645i
$862$	32244.5	+	25920.6i	1.27407	+	1.02420i
$863$	−6139.74			−0.242177			−0.121089	−	0.992642i	$-0.538639\pi$
$863$	−6139.74			−0.242177			−0.121089	+	0.992642i	$0.538639\pi$
$864$	−735.437	+	2955.19i	−0.0289584	+	0.116363i
$865$	−70848.3			−2.78487
$866$	26141.5	+	21014.5i	1.02578	+	0.824599i
$867$	−36843.8			−1.44323
$868$	−25778.7	−	15432.7i	−1.00805	−	0.603480i
$869$	61573.0			2.40359
$870$	−61975.0	−	49820.2i	−2.41511	−	1.94145i
$871$	−3120.40			−0.121390
$872$	−18946.9	−	9399.11i	−0.735806	−	0.365016i
$873$	11385.2			0.441386
$874$	−9709.85	−	7805.52i	−0.375790	−	0.302089i
$875$			30532.4i			1.17964i
$876$	−40308.1	+	8869.72i	−1.55466	+	0.342101i
$877$	29078.6			1.11963			0.559814	−	0.828618i	$-0.310872\pi$
$877$	29078.6			1.11963			0.559814	+	0.828618i	$0.310872\pi$
$878$	−625.142	−	502.536i	−0.0240290	−	0.0193164i
$879$	66790.5			2.56290
$880$	−62284.2	+	28805.9i	−2.38591	+	1.10346i
$881$			50235.5i			1.92109i	0.278131	+	0.960543i	$0.410285\pi$
$881$			50235.5i			1.92109i	−0.278131	+	0.960543i	$0.589715\pi$
$882$	6760.75	−	8410.19i	0.258102	−	0.321072i
$883$	12225.8			0.465945			0.232972	−	0.972483i	$-0.425155\pi$
$883$	12225.8			0.465945			0.232972	+	0.972483i	$0.425155\pi$
$884$	−47.9165	−	217.755i	−0.00182308	−	0.00828493i
$885$			30665.9i			1.16477i
$886$	5932.35	+	4768.88i	0.224945	+	0.180828i
$887$		−	424.407i		−	0.0160656i	−0.999968	−	0.00803280i	$-0.997443\pi$
$887$		−	424.407i		−	0.0160656i	0.999968	−	0.00803280i	$-0.00255695\pi$
$888$	−26687.3	+	53796.7i	−1.00852	+	2.03300i
$889$		−	4818.77i		−	0.181796i
$890$	−3823.84	−	3073.89i	−0.144017	−	0.115772i
$891$	39304.0			1.47782
$892$	−5078.34	−	23078.3i	−0.190623	−	0.866278i
$893$	−30210.1			−1.13207
$894$	26600.1	−	33089.8i	0.995125	−	1.23791i
$895$	59105.3			2.20746
$896$	−860.492	+	31498.9i	−0.0320837	+	1.17445i
$897$			21933.7i			0.816437i
$898$	9071.80	+	7292.60i	0.337116	+	0.270999i
$899$	−24526.9	+	26011.5i	−0.909920	+	0.964998i
$900$	−10182.7	−	46274.8i	−0.377137	−	1.71388i
$901$	−221.086			−0.00817474
$902$	−6284.81	+	7818.13i	−0.231997	+	0.288598i
$903$			836.725i			0.0308355i
$904$	8873.08	+	4401.73i	0.326454	+	0.161946i
$905$			18687.1i			0.686387i
$906$	8057.21	−	10022.9i	0.295456	−	0.367539i
$907$		−	49770.1i		−	1.82204i	−0.412365	−	0.911019i	$-0.635297\pi$
$907$		−	49770.1i		−	1.82204i	0.412365	−	0.911019i	$-0.364703\pi$
$908$	−19456.2	+	4281.30i	−0.711098	+	0.156476i
$909$	29488.6			1.07599
$910$	43503.6	−	54117.3i	1.58476	−	1.97140i
$911$	−11228.3			−0.408353			−0.204176	−	0.978934i	$-0.565452\pi$
$911$	−11228.3			−0.408353			−0.204176	+	0.978934i	$0.565452\pi$
$912$	−18915.9	−	40900.0i	−0.686806	−	1.48502i
$913$	−4477.34			−0.162298
$914$	−39649.4	−	31873.2i	−1.43489	−	1.15347i
$915$			24132.8i			0.871918i
$916$	46236.2	−	10174.2i	1.66778	−	0.366992i
$917$	23151.5			0.833731
$918$	−16.5803	−	13.3285i	−0.000596112	−	0.000479200i
$919$			17129.4i			0.614851i	0.951572	+	0.307425i	$0.0994675\pi$
$919$			17129.4i			0.614851i	−0.951572	+	0.307425i	$0.900533\pi$
$920$	17210.7	+	8537.85i	0.616763	+	0.305961i
$921$		−	57182.4i		−	2.04585i
$922$	830.658	+	667.747i	0.0296706	+	0.0238515i
$923$	−28151.5			−1.00392
$924$	−75537.1	+	16621.8i	−2.68938	+	0.591793i
$925$		−	71673.5i		−	2.54769i
$926$	−29415.2	+	36591.6i	−1.04389	+	1.29857i
$927$		−	15641.3i		−	0.554185i
$928$	36385.5	+	9054.98i	1.28708	+	0.320306i
$929$		−	10729.4i		−	0.378924i	−0.981888	−	0.189462i	$-0.939326\pi$
$929$		−	10729.4i		−	0.378924i	0.981888	−	0.189462i	$-0.0606744\pi$
$930$	−65633.0	+	9092.92i	−2.31418	+	0.320612i
$931$			12248.4i			0.431175i
$932$	4080.96	+	18545.8i	0.143430	+	0.651810i
$933$		−	62761.9i		−	2.20229i
$934$	1846.98	+	1484.74i	0.0647055	+	0.0520153i
$935$		−	479.369i		−	0.0167669i
$936$	−18331.5	+	36953.0i	−0.640154	+	1.29044i
$937$	−48810.3			−1.70177			−0.850887	−	0.525349i	$-0.823935\pi$
$937$	−48810.3			−1.70177			−0.850887	+	0.525349i	$0.823935\pi$
$938$	−1930.09	+	2400.98i	−0.0671852	+	0.0835766i
$939$		−	74766.6i		−	2.59842i
$940$	45499.1	−	10012.0i	1.57874	−	0.347399i
$941$		−	33331.3i		−	1.15470i	−0.816498	−	0.577349i	$-0.804087\pi$
$941$		−	33331.3i		−	1.15470i	0.816498	−	0.577349i	$-0.195913\pi$
$942$	44155.3	−	54927.9i	1.52724	−	1.89984i
$943$	2808.35			0.0969805
$944$	−6069.94	−	13124.5i	−0.209279	−	0.452505i
$945$		−	6624.90i		−	0.228051i
$946$	538.341	−	669.681i	0.0185021	−	0.0230161i
$947$	17278.2			0.592890			0.296445	−	0.955050i	$-0.404199\pi$
$947$	17278.2			0.592890			0.296445	+	0.955050i	$0.404199\pi$
$948$	−13400.0	−	60895.6i	−0.459083	−	2.08629i
$949$	−42884.4			−1.46690
$950$	41917.8	+	33696.7i	1.43157	+	1.15081i
$951$	7076.21			0.241285
$952$	−197.189	−	97.8208i	−0.00671316	−	0.00333024i
$953$			53900.2i			1.83211i	0.401054	+	0.916055i	$0.368644\pi$
$953$			53900.2i			1.83211i	−0.401054	+	0.916055i	$0.631356\pi$
$954$	31879.2	+	25626.9i	1.08189	+	0.869709i
$955$		−	50633.3i		−	1.71566i
$956$	−5483.81	−	24920.9i	−0.185522	−	0.843097i
$957$			92033.9i			3.10871i
$958$	33555.2	+	26974.3i	1.13165	+	0.909707i
$959$	−9410.44			−0.316871
$960$	42043.8	+	55330.1i	1.41350	+	1.86018i
$961$	1748.77	+	29739.6i	0.0587013	+	0.998276i
$962$	−39094.5	+	48632.5i	−1.31025	+	1.62991i
$963$			36590.5i			1.22442i
$964$	12298.3	−	2706.22i	0.410894	−	0.0904165i
$965$	75028.0			2.50284
$966$	16876.8	+	13566.9i	0.562114	+	0.451870i
$967$	12222.3			0.406455			0.203227	−	0.979132i	$-0.434857\pi$
$967$	12222.3			0.406455			0.203227	+	0.979132i	$0.434857\pi$
$968$	44171.5	+	21912.4i	1.46666	+	0.727574i
$969$	314.786			0.0104359
$970$	12486.3	−	15532.6i	0.413309	−	0.514146i
$971$			5717.01i			0.188947i	0.995527	+	0.0944735i	$0.0301168\pi$
$971$			5717.01i			0.188947i	−0.995527	+	0.0944735i	$0.969883\pi$
$972$	−9334.57	−	42420.6i	−0.308031	−	1.39984i
$973$			15085.1i			0.497025i
$974$	−22506.4	+	27997.4i	−0.740403	+	0.921041i
$975$		−	94688.5i		−	3.11021i
$976$	−4776.79	−	10328.4i	−0.156661	−	0.338733i
$977$	−16786.8			−0.549699			−0.274849	−	0.961487i	$-0.588628\pi$
$977$	−16786.8			−0.549699			−0.274849	+	0.961487i	$0.588628\pi$
$978$	−9820.36	−	7894.35i	−0.321084	−	0.258112i
$979$			5678.47i			0.185377i
$980$	−4059.26	−	18447.1i	−0.132315	−	0.601298i
$981$	−27334.0			−0.889611
$982$	14901.9	−	18537.5i	0.484255	−	0.602400i
$983$	−17140.0			−0.556136			−0.278068	−	0.960561i	$-0.589694\pi$
$983$	−17140.0			−0.556136			−0.278068	+	0.960561i	$0.589694\pi$
$984$	9099.87	+	4514.23i	0.294810	+	0.146248i
$985$			78267.5i			2.53179i
$986$	−164.106	+	204.143i	−0.00530039	+	0.00659354i
$987$	52508.5			1.69338
$988$	−10062.5	−	45728.4i	−0.324017	−	1.47248i
$989$	−240.557			−0.00773433
$990$	−55565.5	+	69122.0i	−1.78383	+	2.21903i
$991$	−25337.6			−0.812185			−0.406092	−	0.913832i	$-0.633109\pi$
$991$	−25337.6			−0.812185			−0.406092	+	0.913832i	$0.633109\pi$
$992$	26289.9	−	16882.9i	0.841438	−	0.540354i
$993$	−3970.16			−0.126877
$994$	−17412.8	+	21661.1i	−0.555635	+	0.691195i
$995$	−1404.92			−0.0447626
$996$	974.391	+	4428.08i	0.0309988	+	0.140873i
$997$	8402.02			0.266895			0.133448	−	0.991056i	$-0.457395\pi$
$997$	8402.02			0.266895			0.133448	+	0.991056i	$0.457395\pi$
$998$	17410.8	−	21658.6i	0.552234	−	0.686964i
$999$			5953.47i			0.188548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.4.d.c.123.11	yes	40
4.3	odd	2	inner	124.4.d.c.123.10	yes	40
31.30	odd	2	inner	124.4.d.c.123.12	yes	40
124.123	even	2	inner	124.4.d.c.123.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.4.d.c.123.9	✓	40	124.123	even	2	inner
124.4.d.c.123.10	yes	40	4.3	odd	2	inner
124.4.d.c.123.11	yes	40	1.1	even	1	trivial
124.4.d.c.123.12	yes	40	31.30	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77211 + 2.20446i) q^{2} -7.49955 q^{3} +(-1.71925 - 7.81308i) q^{4} -18.0979 q^{5} +(13.2900 - 16.5324i) q^{6} -21.7591i q^{7} +(20.2703 + 10.0556i) q^{8} +29.2432 q^{9} +O(q^{10})\)	\(q+(-1.77211 + 2.20446i) q^{2} -7.49955 q^{3} +(-1.71925 - 7.81308i) q^{4} -18.0979 q^{5} +(13.2900 - 16.5324i) q^{6} -21.7591i q^{7} +(20.2703 + 10.0556i) q^{8} +29.2432 q^{9} +(32.0715 - 39.8960i) q^{10} -59.2463 q^{11} +(12.8936 + 58.5946i) q^{12} +62.3397i q^{13} +(47.9671 + 38.5596i) q^{14} +135.726 q^{15} +(-58.0883 + 26.8653i) q^{16} -0.447075i q^{17} +(-51.8222 + 64.4654i) q^{18} -93.8857i q^{19} +(31.1149 + 141.400i) q^{20} +163.184i q^{21} +(104.991 - 130.606i) q^{22} -46.9150 q^{23} +(-152.018 - 75.4126i) q^{24} +202.534 q^{25} +(-137.425 - 110.473i) q^{26} -16.8232 q^{27} +(-170.006 + 37.4095i) q^{28} +207.134i q^{29} +(-240.521 + 299.202i) q^{30} +(125.578 + 118.411i) q^{31} +(43.7155 - 175.661i) q^{32} +444.320 q^{33} +(0.985558 + 0.792267i) q^{34} +393.795i q^{35} +(-50.2765 - 228.480i) q^{36} -353.884i q^{37} +(206.967 + 166.376i) q^{38} -467.519i q^{39} +(-366.850 - 181.985i) q^{40} -59.8605 q^{41} +(-359.731 - 289.180i) q^{42} +5.12750 q^{43} +(101.859 + 462.896i) q^{44} -529.241 q^{45} +(83.1385 - 103.422i) q^{46} -321.775i q^{47} +(435.636 - 201.478i) q^{48} -130.460 q^{49} +(-358.912 + 446.477i) q^{50} +3.35286i q^{51} +(487.065 - 107.178i) q^{52} -494.516i q^{53} +(29.8126 - 37.0861i) q^{54} +1072.23 q^{55} +(218.802 - 441.064i) q^{56} +704.100i q^{57} +(-456.618 - 367.064i) q^{58} +225.940i q^{59} +(-233.347 - 1060.44i) q^{60} +177.805i q^{61} +(-483.570 + 66.9947i) q^{62} -636.308i q^{63} +(309.769 + 407.660i) q^{64} -1128.22i q^{65} +(-787.385 + 979.485i) q^{66} +50.0548i q^{67} +(-3.49303 + 0.768636i) q^{68} +351.841 q^{69} +(-868.103 - 697.848i) q^{70} +451.582i q^{71} +(592.769 + 294.059i) q^{72} +687.915i q^{73} +(780.122 + 627.121i) q^{74} -1518.91 q^{75} +(-733.536 + 161.413i) q^{76} +1289.15i q^{77} +(1030.63 + 828.496i) q^{78} -1039.27 q^{79} +(1051.28 - 486.206i) q^{80} -663.401 q^{81} +(106.079 - 131.960i) q^{82} +75.5716 q^{83} +(1274.97 - 280.554i) q^{84} +8.09112i q^{85} +(-9.08649 + 11.3033i) q^{86} -1553.41i q^{87} +(-1200.94 - 595.758i) q^{88} -95.8451i q^{89} +(937.873 - 1166.69i) q^{90} +1356.46 q^{91} +(80.6588 + 366.551i) q^{92} +(-941.780 - 888.028i) q^{93} +(709.339 + 570.221i) q^{94} +1699.13i q^{95} +(-327.847 + 1317.38i) q^{96} +389.327 q^{97} +(231.190 - 287.594i) q^{98} -1732.55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9	\( 40 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 94 q^{8} + 536 q^{9} + 228 q^{10} - 104 q^{14} - 78 q^{16} + 114 q^{18} - 44 q^{20} + 28 q^{25} + 48 q^{28} - 602 q^{32} - 136 q^{33} - 482 q^{36} + 420 q^{38} - 516 q^{40} - 4 q^{41} - 1596 q^{45} + 1876 q^{49} - 662 q^{50} + 1576 q^{56} - 838 q^{62} - 302 q^{64} - 3900 q^{66} - 872 q^{69} - 912 q^{70} - 2166 q^{72} + 3220 q^{76} - 476 q^{78} + 572 q^{80} - 2056 q^{81} + 3096 q^{82} - 6220 q^{90} - 2904 q^{93} + 6408 q^{94} - 1836 q^{97} - 1358 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 + 10 * q^4 - 4 * q^5 + 94 * q^8 + 536 * q^9 + 228 * q^10 - 104 * q^14 - 78 * q^16 + 114 * q^18 - 44 * q^20 + 28 * q^25 + 48 * q^28 - 602 * q^32 - 136 * q^33 - 482 * q^36 + 420 * q^38 - 516 * q^40 - 4 * q^41 - 1596 * q^45 + 1876 * q^49 - 662 * q^50 + 1576 * q^56 - 838 * q^62 - 302 * q^64 - 3900 * q^66 - 872 * q^69 - 912 * q^70 - 2166 * q^72 + 3220 * q^76 - 476 * q^78 + 572 * q^80 - 2056 * q^81 + 3096 * q^82 - 6220 * q^90 - 2904 * q^93 + 6408 * q^94 - 1836 * q^97 - 1358 * q^98

Introduction

L-functions

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