LMFDB - Embedded newform 168.4.c.b.85.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(85,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("168.85");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.c (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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 5 x^{18} - 26 x^{17} + 122 x^{16} + 124 x^{15} - 276 x^{14} - 1376 x^{13} + \cdots + 1073741824 $ x^20 - 2x^19 - 5x^18 - 26x^17 + 122x^16 + 124x^15 - 276x^14 - 1376x^13 - 3344x^12 + 15424x^11 - 1920x^10 + 123392x^9 - 214016x^8 - 704512x^7 - 1130496x^6 + 4063232x^5 + 31981568x^4 - 54525952x^3 - 83886080x^2 - 268435456*x + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			85.8
Root			$2.78865 - 0.472666i$ of defining polynomial
Character	$\chi$	$=$	168.85
Dual form			168.4.c.b.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.472666 + 2.78865i) q^{2} -3.00000i q^{3} +(-7.55317 - 2.63620i) q^{4} -8.98099i q^{5} +(8.36596 + 1.41800i) q^{6} -7.00000 q^{7} +(10.9216 - 19.8171i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-0.472666 + 2.78865i) q^{2} -3.00000i q^{3} +(-7.55317 - 2.63620i) q^{4} -8.98099i q^{5} +(8.36596 + 1.41800i) q^{6} -7.00000 q^{7} +(10.9216 - 19.8171i) q^{8} -9.00000 q^{9} +(25.0449 + 4.24501i) q^{10} +58.9468i q^{11} +(-7.90861 + 22.6595i) q^{12} +54.8428i q^{13} +(3.30866 - 19.5206i) q^{14} -26.9430 q^{15} +(50.1009 + 39.8234i) q^{16} -111.971 q^{17} +(4.25399 - 25.0979i) q^{18} +38.6067i q^{19} +(-23.6757 + 67.8350i) q^{20} +21.0000i q^{21} +(-164.382 - 27.8621i) q^{22} +112.146 q^{23} +(-59.4514 - 32.7647i) q^{24} +44.3418 q^{25} +(-152.937 - 25.9223i) q^{26} +27.0000i q^{27} +(52.8722 + 18.4534i) q^{28} +234.402i q^{29} +(12.7350 - 75.1346i) q^{30} -180.033 q^{31} +(-134.735 + 120.891i) q^{32} +176.840 q^{33} +(52.9249 - 312.248i) q^{34} +62.8669i q^{35} +(67.9786 + 23.7258i) q^{36} -131.345i q^{37} +(-107.661 - 18.2480i) q^{38} +164.528 q^{39} +(-177.978 - 98.0866i) q^{40} -500.500 q^{41} +(-58.5617 - 9.92598i) q^{42} -495.083i q^{43} +(155.396 - 445.235i) q^{44} +80.8289i q^{45} +(-53.0077 + 312.737i) q^{46} +111.705 q^{47} +(119.470 - 150.303i) q^{48} +49.0000 q^{49} +(-20.9588 + 123.654i) q^{50} +335.913i q^{51} +(144.577 - 414.237i) q^{52} +696.410i q^{53} +(-75.2936 - 12.7620i) q^{54} +529.400 q^{55} +(-76.4511 + 138.720i) q^{56} +115.820 q^{57} +(-653.666 - 110.794i) q^{58} +407.787i q^{59} +(203.505 + 71.0271i) q^{60} +124.411i q^{61} +(85.0952 - 502.048i) q^{62} +63.0000 q^{63} +(-273.438 - 432.869i) q^{64} +492.542 q^{65} +(-83.5864 + 493.146i) q^{66} +143.848i q^{67} +(845.736 + 295.178i) q^{68} -336.439i q^{69} +(-175.314 - 29.7151i) q^{70} +251.341 q^{71} +(-98.2942 + 178.354i) q^{72} -709.691 q^{73} +(366.276 + 62.0823i) q^{74} -133.025i q^{75} +(101.775 - 291.603i) q^{76} -412.627i q^{77} +(-77.7669 + 458.812i) q^{78} +865.909 q^{79} +(357.654 - 449.956i) q^{80} +81.0000 q^{81} +(236.569 - 1395.72i) q^{82} -57.3886i q^{83} +(55.3603 - 158.617i) q^{84} +1005.61i q^{85} +(1380.61 + 234.009i) q^{86} +703.206 q^{87} +(1168.16 + 643.792i) q^{88} -765.447 q^{89} +(-225.404 - 38.2051i) q^{90} -383.899i q^{91} +(-847.060 - 295.640i) q^{92} +540.098i q^{93} +(-52.7990 + 311.506i) q^{94} +346.726 q^{95} +(362.672 + 404.204i) q^{96} +370.748 q^{97} +(-23.1606 + 136.644i) q^{98} -530.521i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 14 q^{4} + 6 q^{6} - 140 q^{7} + 10 q^{8} - 180 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 - 14 * q^4 + 6 * q^6 - 140 * q^7 + 10 * q^8 - 180 * q^9	$ 20 q + 4 q^{2} - 14 q^{4} + 6 q^{6} - 140 q^{7} + 10 q^{8} - 180 q^{9} - 84 q^{10} + 12 q^{12} - 28 q^{14} + 60 q^{15} - 134 q^{16} - 52 q^{17} - 36 q^{18} - 8 q^{20} + 8 q^{22} - 244 q^{23} - 348 q^{24} - 844 q^{25} - 332 q^{26} + 98 q^{28} + 60 q^{30} + 264 q^{31} - 46 q^{32} + 396 q^{33} - 612 q^{34} + 126 q^{36} + 884 q^{38} - 312 q^{39} - 964 q^{40} - 236 q^{41} - 42 q^{42} + 576 q^{44} + 1356 q^{46} - 432 q^{48} + 980 q^{49} - 2456 q^{50} + 1492 q^{52} - 54 q^{54} + 72 q^{55} - 70 q^{56} - 912 q^{57} - 1404 q^{58} + 684 q^{60} + 4964 q^{62} + 1260 q^{63} - 1670 q^{64} + 1744 q^{65} + 792 q^{66} + 3408 q^{68} + 588 q^{70} - 636 q^{71} - 90 q^{72} - 2784 q^{73} - 4916 q^{74} + 2664 q^{76} - 888 q^{78} + 2872 q^{79} - 1764 q^{80} + 1620 q^{81} + 2628 q^{82} - 84 q^{84} + 3328 q^{86} - 2348 q^{88} + 220 q^{89} + 756 q^{90} + 2580 q^{92} - 1704 q^{94} - 1240 q^{95} - 564 q^{96} + 4400 q^{97} + 196 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 14 * q^4 + 6 * q^6 - 140 * q^7 + 10 * q^8 - 180 * q^9 - 84 * q^10 + 12 * q^12 - 28 * q^14 + 60 * q^15 - 134 * q^16 - 52 * q^17 - 36 * q^18 - 8 * q^20 + 8 * q^22 - 244 * q^23 - 348 * q^24 - 844 * q^25 - 332 * q^26 + 98 * q^28 + 60 * q^30 + 264 * q^31 - 46 * q^32 + 396 * q^33 - 612 * q^34 + 126 * q^36 + 884 * q^38 - 312 * q^39 - 964 * q^40 - 236 * q^41 - 42 * q^42 + 576 * q^44 + 1356 * q^46 - 432 * q^48 + 980 * q^49 - 2456 * q^50 + 1492 * q^52 - 54 * q^54 + 72 * q^55 - 70 * q^56 - 912 * q^57 - 1404 * q^58 + 684 * q^60 + 4964 * q^62 + 1260 * q^63 - 1670 * q^64 + 1744 * q^65 + 792 * q^66 + 3408 * q^68 + 588 * q^70 - 636 * q^71 - 90 * q^72 - 2784 * q^73 - 4916 * q^74 + 2664 * q^76 - 888 * q^78 + 2872 * q^79 - 1764 * q^80 + 1620 * q^81 + 2628 * q^82 - 84 * q^84 + 3328 * q^86 - 2348 * q^88 + 220 * q^89 + 756 * q^90 + 2580 * q^92 - 1704 * q^94 - 1240 * q^95 - 564 * q^96 + 4400 * q^97 + 196 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−0.472666	+	2.78865i	−0.167113	+	0.985938i
$2$	−0.472666	+	2.78865i	−0.167113	+	0.985938i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	−7.55317	−	2.63620i	−0.944147	−	0.329525i
$5$		−	8.98099i		−	0.803284i	−0.915797	−	0.401642i	$-0.868440\pi$
$5$		−	8.98099i		−	0.803284i	0.915797	−	0.401642i	$-0.131560\pi$
$6$	8.36596	+	1.41800i	0.569231	+	0.0964825i
$7$	−7.00000			−0.377964
$7$	−7.00000			−0.377964
$8$	10.9216	−	19.8171i	0.482670	−	0.875802i
$9$	−9.00000			−0.333333
$10$	25.0449	+	4.24501i	0.791988	+	0.134239i
$11$			58.9468i			1.61574i	0.589362	+	0.807869i	$0.299379\pi$
$11$			58.9468i			1.61574i	−0.589362	+	0.807869i	$0.700621\pi$
$12$	−7.90861	+	22.6595i	−0.190252	+	0.545103i
$13$			54.8428i			1.17005i	0.811015	+	0.585025i	$0.198915\pi$
$13$			54.8428i			1.17005i	−0.811015	+	0.585025i	$0.801085\pi$
$14$	3.30866	−	19.5206i	0.0631626	−	0.372649i
$15$	−26.9430			−0.463776
$16$	50.1009	+	39.8234i	0.782826	+	0.622240i
$17$	−111.971			−1.59747			−0.798734	−	0.601684i	$-0.794497\pi$
$17$	−111.971			−1.59747			−0.798734	+	0.601684i	$0.794497\pi$
$18$	4.25399	−	25.0979i	0.0557042	−	0.328646i
$19$			38.6067i			0.466157i	0.972458	+	0.233078i	$0.0748798\pi$
$19$			38.6067i			0.466157i	−0.972458	+	0.233078i	$0.925120\pi$
$20$	−23.6757	+	67.8350i	−0.264703	+	0.758418i
$21$			21.0000i			0.218218i
$22$	−164.382	−	27.8621i	−1.59302	−	0.270010i
$23$	112.146			1.01670			0.508350	−	0.861151i	$-0.330256\pi$
$23$	112.146			1.01670			0.508350	+	0.861151i	$0.330256\pi$
$24$	−59.4514	−	32.7647i	−0.505645	−	0.278670i
$25$	44.3418			0.354734
$26$	−152.937	−	25.9223i	−1.15360	−	0.195530i
$27$			27.0000i			0.192450i
$28$	52.8722	+	18.4534i	0.356854	+	0.124549i
$29$			234.402i			1.50094i	0.660902	+	0.750472i	$0.270174\pi$
$29$			234.402i			1.50094i	−0.660902	+	0.750472i	$0.729826\pi$
$30$	12.7350	−	75.1346i	0.0775029	−	0.457255i
$31$	−180.033			−1.04306			−0.521529	−	0.853234i	$-0.674638\pi$
$31$	−180.033			−1.04306			−0.521529	+	0.853234i	$0.674638\pi$
$32$	−134.735	+	120.891i	−0.744311	+	0.667834i
$33$	176.840			0.932847
$34$	52.9249	−	312.248i	0.266957	−	1.57500i
$35$			62.8669i			0.303613i
$36$	67.9786	+	23.7258i	0.314716	+	0.109842i
$37$		−	131.345i		−	0.583594i	−0.956480	−	0.291797i	$-0.905747\pi$
$37$		−	131.345i		−	0.583594i	0.956480	−	0.291797i	$-0.0942532\pi$
$38$	−107.661	−	18.2480i	−0.459601	−	0.0779006i
$39$	164.528			0.675528
$40$	−177.978	−	98.0866i	−0.703518	−	0.387721i
$41$	−500.500			−1.90646			−0.953231	−	0.302242i	$-0.902265\pi$
$41$	−500.500			−1.90646			−0.953231	+	0.302242i	$0.902265\pi$
$42$	−58.5617	−	9.92598i	−0.215149	−	0.0364670i
$43$		−	495.083i		−	1.75580i	−0.478844	−	0.877900i	$-0.658944\pi$
$43$		−	495.083i		−	1.75580i	0.478844	−	0.877900i	$-0.341056\pi$
$44$	155.396	−	445.235i	0.532426	−	1.52549i
$45$			80.8289i			0.267761i
$46$	−53.0077	+	312.737i	−0.169903	+	1.00240i
$47$	111.705			0.346677			0.173338	−	0.984862i	$-0.444545\pi$
$47$	111.705			0.346677			0.173338	+	0.984862i	$0.444545\pi$
$48$	119.470	−	150.303i	0.359251	−	0.451965i
$49$	49.0000			0.142857
$50$	−20.9588	+	123.654i	−0.0592806	+	0.349746i
$51$			335.913i			0.922299i
$52$	144.577	−	414.237i	0.385561	−	1.10470i
$53$			696.410i			1.80489i	0.430804	+	0.902445i	$0.358230\pi$
$53$			696.410i			1.80489i	−0.430804	+	0.902445i	$0.641770\pi$
$54$	−75.2936	−	12.7620i	−0.189744	−	0.0321608i
$55$	529.400			1.29790
$56$	−76.4511	+	138.720i	−0.182432	+	0.331022i
$57$	115.820			0.269136
$58$	−653.666	−	110.794i	−1.47984	−	0.250827i
$59$			407.787i			0.899819i	0.893074	+	0.449909i	$0.148544\pi$
$59$			407.787i			0.899819i	−0.893074	+	0.449909i	$0.851456\pi$
$60$	203.505	+	71.0271i	0.437873	+	0.152826i
$61$			124.411i			0.261134i	0.991440	+	0.130567i	$0.0416797\pi$
$61$			124.411i			0.261134i	−0.991440	+	0.130567i	$0.958320\pi$
$62$	85.0952	−	502.048i	0.174308	−	1.02839i
$63$	63.0000			0.125988
$64$	−273.438	−	432.869i	−0.534059	−	0.845447i
$65$	492.542			0.939882
$66$	−83.5864	+	493.146i	−0.155890	+	0.919729i
$67$			143.848i			0.262296i	0.991363	+	0.131148i	$0.0418663\pi$
$67$			143.848i			0.262296i	−0.991363	+	0.131148i	$0.958134\pi$
$68$	845.736	+	295.178i	1.50824	+	0.526406i
$69$		−	336.439i		−	0.586992i
$70$	−175.314	−	29.7151i	−0.299343	−	0.0507376i
$71$	251.341			0.420122			0.210061	−	0.977688i	$-0.432634\pi$
$71$	251.341			0.420122			0.210061	+	0.977688i	$0.432634\pi$
$72$	−98.2942	+	178.354i	−0.160890	+	0.291934i
$73$	−709.691			−1.13785			−0.568925	−	0.822390i	$-0.692640\pi$
$73$	−709.691			−1.13785			−0.568925	+	0.822390i	$0.692640\pi$
$74$	366.276	+	62.0823i	0.575387	+	0.0975259i
$75$		−	133.025i		−	0.204806i
$76$	101.775	−	291.603i	0.153610	−	0.440120i
$77$		−	412.627i		−	0.610691i
$78$	−77.7669	+	458.812i	−0.112889	+	0.666029i
$79$	865.909			1.23319			0.616597	−	0.787279i	$-0.288511\pi$
$79$	865.909			1.23319			0.616597	+	0.787279i	$0.288511\pi$
$80$	357.654	−	449.956i	0.499836	−	0.628832i
$81$	81.0000			0.111111
$82$	236.569	−	1395.72i	0.318594	−	1.87965i
$83$		−	57.3886i		−	0.0758942i	−0.999280	−	0.0379471i	$-0.987918\pi$
$83$		−	57.3886i		−	0.0758942i	0.999280	−	0.0379471i	$-0.0120818\pi$
$84$	55.3603	−	158.617i	0.0719083	−	0.206030i
$85$			1005.61i			1.28322i
$86$	1380.61	+	234.009i	1.73111	+	0.293416i
$87$	703.206			0.866570
$88$	1168.16	+	643.792i	1.41507	+	0.779869i
$89$	−765.447			−0.911654			−0.455827	−	0.890068i	$-0.650656\pi$
$89$	−765.447			−0.911654			−0.455827	+	0.890068i	$0.650656\pi$
$90$	−225.404	−	38.2051i	−0.263996	−	0.0447463i
$91$		−	383.899i		−	0.442237i
$92$	−847.060	−	295.640i	−0.959914	−	0.335028i
$93$			540.098i			0.602210i
$94$	−52.7990	+	311.506i	−0.0579340	+	0.341802i
$95$	346.726			0.374456
$96$	362.672	+	404.204i	0.385574	+	0.429728i
$97$	370.748			0.388080			0.194040	−	0.980994i	$-0.437841\pi$
$97$	370.748			0.388080			0.194040	+	0.980994i	$0.437841\pi$
$98$	−23.1606	+	136.644i	−0.0238732	+	0.140848i
$99$		−	530.521i		−	0.538579i
$100$	−334.921	−	116.894i	−0.334921	−	0.116894i
$101$		−	621.424i		−	0.612218i	−0.951997	−	0.306109i	$-0.900973\pi$
$101$		−	621.424i		−	0.612218i	0.951997	−	0.306109i	$-0.0990272\pi$
$102$	−936.745	−	158.775i	−0.909329	−	0.154128i
$103$	433.871			0.415054			0.207527	−	0.978229i	$-0.433458\pi$
$103$	433.871			0.415054			0.207527	+	0.978229i	$0.433458\pi$
$104$	1086.83	+	598.970i	1.02473	+	0.564748i
$105$	188.601			0.175291
$106$	−1942.04	−	329.169i	−1.77951	−	0.301620i
$107$			926.967i			0.837508i	0.908100	+	0.418754i	$0.137533\pi$
$107$			926.967i			0.837508i	−0.908100	+	0.418754i	$0.862467\pi$
$108$	71.1775	−	203.936i	0.0634172	−	0.181701i
$109$		−	1423.90i		−	1.25123i	−0.780131	−	0.625617i	$-0.784847\pi$
$109$		−	1423.90i		−	1.25123i	0.780131	−	0.625617i	$-0.215153\pi$
$110$	−250.229	+	1476.31i	−0.216895	+	1.27965i
$111$	−394.035			−0.336938
$112$	−350.706	−	278.764i	−0.295880	−	0.235185i
$113$	−2027.39			−1.68779			−0.843897	−	0.536505i	$-0.819744\pi$
$113$	−2027.39			−1.68779			−0.843897	+	0.536505i	$0.819744\pi$
$114$	−54.7441	+	322.982i	−0.0449760	+	0.265351i
$115$		−	1007.18i		−	0.816699i
$116$	617.931	−	1770.48i	0.494599	−	1.41711i
$117$		−	493.585i		−	0.390016i
$118$	−1137.18	−	192.747i	−0.887165	−	0.150371i
$119$	783.797			0.603786
$120$	−294.260	+	533.933i	−0.223851	+	0.406176i
$121$	−2143.72			−1.61061
$122$	−346.938	−	58.8047i	−0.257461	−	0.0436387i
$123$			1501.50i			1.10070i
$124$	1359.82	+	474.602i	0.984800	+	0.343714i
$125$		−	1520.86i		−	1.08824i
$126$	−29.7779	+	175.685i	−0.0210542	+	0.124216i
$127$	−482.735			−0.337290			−0.168645	−	0.985677i	$-0.553939\pi$
$127$	−482.735			−0.337290			−0.168645	+	0.985677i	$0.553939\pi$
$128$	1336.37	−	557.922i	0.922806	−	0.385264i
$129$	−1485.25			−1.01371
$130$	−232.808	+	1373.53i	−0.157066	+	0.926666i
$131$		−	1448.68i		−	0.966193i	−0.875567	−	0.483097i	$-0.839512\pi$
$131$		−	1448.68i		−	0.966193i	0.875567	−	0.483097i	$-0.160488\pi$
$132$	−1335.71	−	466.187i	−0.880744	−	0.307397i
$133$		−	270.247i		−	0.176191i
$134$	−401.142	−	67.9920i	−0.258608	−	0.0438330i
$135$	242.487			0.154592
$136$	−1222.90	+	2218.94i	−0.771050	+	1.39907i
$137$	−1043.62			−0.650823			−0.325412	−	0.945572i	$-0.605503\pi$
$137$	−1043.62			−0.650823			−0.325412	+	0.945572i	$0.605503\pi$
$138$	938.211	+	159.023i	0.578738	+	0.0980938i
$139$			630.925i			0.384995i	0.981297	+	0.192498i	$0.0616588\pi$
$139$			630.925i			0.384995i	−0.981297	+	0.192498i	$0.938341\pi$
$140$	165.730	−	474.845i	0.100048	−	0.286655i
$141$		−	335.114i		−	0.200154i
$142$	−118.800	+	700.903i	−0.0702077	+	0.414214i
$143$	−3232.80			−1.89049
$144$	−450.908	−	358.411i	−0.260942	−	0.207413i
$145$	2105.16			1.20568
$146$	335.447	−	1979.08i	0.190149	−	1.12185i
$147$		−	147.000i		−	0.0824786i
$148$	−346.252	+	992.071i	−0.192309	+	0.550998i
$149$			562.011i			0.309005i	0.987992	+	0.154502i	$0.0493775\pi$
$149$			562.011i			0.309005i	−0.987992	+	0.154502i	$0.950623\pi$
$150$	370.962	+	62.8765i	0.201926	+	0.0342256i
$151$	−466.027			−0.251157			−0.125579	−	0.992084i	$-0.540079\pi$
$151$	−466.027			−0.251157			−0.125579	+	0.992084i	$0.540079\pi$
$152$	765.074	+	421.646i	0.408261	+	0.225000i
$153$	1007.74			0.532489
$154$	1150.67	+	195.035i	0.602104	+	0.102054i
$155$			1616.87i			0.837872i
$156$	−1242.71	−	433.730i	−0.637798	−	0.222604i
$157$		−	314.250i		−	0.159745i	−0.996805	−	0.0798723i	$-0.974549\pi$
$157$		−	314.250i		−	0.159745i	0.996805	−	0.0798723i	$-0.0254513\pi$
$158$	−409.285	+	2414.72i	−0.206082	+	1.21585i
$159$	2089.23			1.04205
$160$	1085.72	+	1210.05i	0.536460	+	0.597893i
$161$	−785.023			−0.384276
$162$	−38.2859	+	225.881i	−0.0185681	+	0.109549i
$163$		−	1926.67i		−	0.925820i	−0.886405	−	0.462910i	$-0.846805\pi$
$163$		−	1926.67i		−	0.925820i	0.886405	−	0.462910i	$-0.153195\pi$
$164$	3780.36	+	1319.42i	1.79998	+	0.628228i
$165$		−	1588.20i		−	0.749341i
$166$	160.037	+	27.1256i	0.0748270	+	0.0126829i
$167$	1454.39			0.673917			0.336958	−	0.941520i	$-0.390602\pi$
$167$	1454.39			0.673917			0.336958	+	0.941520i	$0.390602\pi$
$168$	416.160	+	229.353i	0.191116	+	0.105327i
$169$	−810.727			−0.369016
$170$	−2804.30	−	475.318i	−1.26518	−	0.214442i
$171$		−	347.460i		−	0.155386i
$172$	−1305.14	+	3739.45i	−0.578581	+	1.65773i
$173$			3142.64i			1.38110i	0.723284	+	0.690550i	$0.242632\pi$
$173$			3142.64i			1.38110i	−0.723284	+	0.690550i	$0.757368\pi$
$174$	−332.382	+	1961.00i	−0.144815	+	0.854384i
$175$	−310.392			−0.134077
$176$	−2347.46	+	2953.28i	−1.00538	+	1.26484i
$177$	1223.36			0.519511
$178$	361.801	−	2134.57i	0.152349	−	0.898834i
$179$		−	608.194i		−	0.253958i	−0.991905	−	0.126979i	$-0.959472\pi$
$179$		−	608.194i		−	0.253958i	0.991905	−	0.126979i	$-0.0405281\pi$
$180$	213.081	−	610.515i	0.0882342	−	0.252806i
$181$			3075.47i			1.26297i	0.775387	+	0.631486i	$0.217555\pi$
$181$			3075.47i			1.26297i	−0.775387	+	0.631486i	$0.782445\pi$
$182$	1070.56	+	181.456i	0.436018	+	0.0739034i
$183$	373.232			0.150766
$184$	1224.81	−	2222.42i	0.490731	−	0.890428i
$185$	−1179.61			−0.468792
$186$	−1506.14	−	255.286i	−0.593741	−	0.100637i
$187$		−	6600.33i		−	2.58109i
$188$	−843.725	−	294.476i	−0.327314	−	0.114239i
$189$		−	189.000i		−	0.0727393i
$190$	−163.886	+	966.899i	−0.0625764	+	0.369191i
$191$	−222.395			−0.0842509			−0.0421255	−	0.999112i	$-0.513413\pi$
$191$	−222.395			−0.0842509			−0.0421255	+	0.999112i	$0.513413\pi$
$192$	−1298.61	+	820.314i	−0.488119	+	0.308339i
$193$	2275.04			0.848502			0.424251	−	0.905545i	$-0.360537\pi$
$193$	2275.04			0.848502			0.424251	+	0.905545i	$0.360537\pi$
$194$	−175.240	+	1033.89i	−0.0648531	+	0.382623i
$195$		−	1477.63i		−	0.542641i
$196$	−370.106	−	129.174i	−0.134878	−	0.0470750i
$197$			140.119i			0.0506754i	0.999679	+	0.0253377i	$0.00806610\pi$
$197$			140.119i			0.0506754i	−0.999679	+	0.0253377i	$0.991934\pi$
$198$	1479.44	+	250.759i	0.531006	+	0.0900034i
$199$	1003.14			0.357342			0.178671	−	0.983909i	$-0.442820\pi$
$199$	1003.14			0.357342			0.178671	+	0.983909i	$0.442820\pi$
$200$	484.282	−	878.727i	0.171220	−	0.310677i
$201$	431.544			0.151437
$202$	1732.94	+	293.726i	0.603609	+	0.102309i
$203$		−	1640.81i		−	0.567303i
$204$	885.535	−	2537.21i	0.303921	−	0.870785i
$205$			4494.99i			1.53143i
$206$	−205.076	+	1209.92i	−0.0693608	+	0.409218i
$207$	−1009.32			−0.338900
$208$	−2184.02	+	2747.67i	−0.728052	+	0.915945i
$209$	−2275.74			−0.753187
$210$	−89.1452	+	525.942i	−0.0292933	+	0.172826i
$211$			2462.02i			0.803283i	0.915797	+	0.401641i	$0.131560\pi$
$211$			2462.02i			0.803283i	−0.915797	+	0.401641i	$0.868440\pi$
$212$	1835.88	−	5260.10i	0.594757	−	1.70408i
$213$		−	754.023i		−	0.242558i
$214$	−2584.99	−	438.146i	−0.825730	−	0.139958i
$215$	−4446.33			−1.41041
$216$	535.063	+	294.883i	0.168548	+	0.0928899i
$217$	1260.23			0.394239
$218$	3970.75	+	673.027i	1.23364	+	0.209097i
$219$			2129.07i			0.656938i
$220$	−3998.65	−	1395.61i	−1.22541	−	0.427690i
$221$		−	6140.80i		−	1.86912i
$222$	186.247	−	1098.83i	0.0563066	−	0.332200i
$223$	6458.67			1.93948			0.969741	−	0.244138i	$-0.0785050\pi$
$223$	6458.67			1.93948			0.969741	+	0.244138i	$0.0785050\pi$
$224$	943.142	−	846.236i	0.281323	−	0.252417i
$225$	−399.076			−0.118245
$226$	958.278	−	5653.69i	0.282052	−	1.66406i
$227$			1776.16i			0.519329i	0.965699	+	0.259664i	$0.0836120\pi$
$227$			1776.16i			0.519329i	−0.965699	+	0.259664i	$0.916388\pi$
$228$	−874.808	−	305.325i	−0.254104	−	0.0886870i
$229$		−	2046.20i		−	0.590466i	−0.955425	−	0.295233i	$-0.904603\pi$
$229$		−	2046.20i		−	0.590466i	0.955425	−	0.295233i	$-0.0953972\pi$
$230$	2808.69	+	476.062i	0.805215	+	0.136481i
$231$	−1237.88			−0.352583
$232$	4645.18	+	2560.04i	1.31453	+	0.724461i
$233$	5827.32			1.63846			0.819229	−	0.573467i	$-0.194402\pi$
$233$	5827.32			1.63846			0.819229	+	0.573467i	$0.194402\pi$
$234$	1376.44	+	233.301i	0.384532	+	0.0651767i
$235$		−	1003.22i		−	0.278480i
$236$	1075.01	−	3080.08i	0.296513	−	0.849561i
$237$		−	2597.73i		−	0.711985i
$238$	−370.474	+	2185.74i	−0.100900	+	0.595296i
$239$	−5894.12			−1.59523			−0.797613	−	0.603169i	$-0.793904\pi$
$239$	−5894.12			−1.59523			−0.797613	+	0.603169i	$0.793904\pi$
$240$	−1349.87	−	1072.96i	−0.363056	−	0.288580i
$241$	−2057.48			−0.549934			−0.274967	−	0.961454i	$-0.588667\pi$
$241$	−2057.48			−0.549934			−0.274967	+	0.961454i	$0.588667\pi$
$242$	1013.26	−	5978.09i	0.269153	−	1.58796i
$243$		−	243.000i		−	0.0641500i
$244$	327.972	−	939.695i	0.0860501	−	0.246548i
$245$		−	440.069i		−	0.114755i
$246$	−4187.16	−	709.708i	−1.08522	−	0.183940i
$247$	−2117.30			−0.545426
$248$	−1966.24	+	3567.73i	−0.503453	+	0.913512i
$249$	−172.166			−0.0438175
$250$	4241.14	+	718.857i	1.07293	+	0.181858i
$251$			5593.16i			1.40652i	0.710932	+	0.703261i	$0.248273\pi$
$251$			5593.16i			1.40652i	−0.710932	+	0.703261i	$0.751727\pi$
$252$	−475.850	−	166.081i	−0.118951	−	0.0415163i
$253$			6610.65i			1.64272i
$254$	228.172	−	1346.18i	0.0563654	−	0.332547i
$255$	3016.83			0.740868
$256$	924.195	+	3990.37i	0.225634	+	0.974212i
$257$	1528.67			0.371035			0.185517	−	0.982641i	$-0.440604\pi$
$257$	1528.67			0.371035			0.185517	+	0.982641i	$0.440604\pi$
$258$	702.026	−	4141.84i	0.169404	−	0.999457i
$259$			919.415i			0.220578i
$260$	−3720.26	−	1298.44i	−0.887387	−	0.309715i
$261$		−	2109.62i		−	0.500315i
$262$	4039.85	+	684.739i	0.952607	+	0.161463i
$263$	−2983.60			−0.699530			−0.349765	−	0.936837i	$-0.613739\pi$
$263$	−2983.60			−0.699530			−0.349765	+	0.936837i	$0.613739\pi$
$264$	1931.38	−	3504.47i	0.450257	−	0.816989i
$265$	6254.45			1.44984
$266$	753.624	+	127.736i	0.173713	+	0.0294437i
$267$			2296.34i			0.526344i
$268$	379.212	−	1086.51i	0.0864332	−	0.247646i
$269$		−	5552.68i		−	1.25856i	−0.777178	−	0.629281i	$-0.783350\pi$
$269$		−	5552.68i		−	1.25856i	0.777178	−	0.629281i	$-0.216650\pi$
$270$	−114.615	+	676.212i	−0.0258343	+	0.152418i
$271$	−4238.12			−0.949990			−0.474995	−	0.879988i	$-0.657550\pi$
$271$	−4238.12			−0.949990			−0.474995	+	0.879988i	$0.657550\pi$
$272$	−5609.84	−	4459.06i	−1.25054	−	0.994009i
$273$	−1151.70			−0.255326
$274$	493.285	−	2910.30i	0.108761	−	0.641671i
$275$			2613.80i			0.573157i
$276$	−886.920	+	2541.18i	−0.193429	+	0.554207i
$277$			3761.88i			0.815990i	0.912984	+	0.407995i	$0.133772\pi$
$277$			3761.88i			0.815990i	−0.912984	+	0.407995i	$0.866228\pi$
$278$	−1759.43	−	298.217i	−0.379582	−	0.0643376i
$279$	1620.29			0.347686
$280$	1245.84	+	686.606i	0.265905	+	0.146545i
$281$	1343.51			0.285221			0.142610	−	0.989779i	$-0.454450\pi$
$281$	1343.51			0.285221			0.142610	+	0.989779i	$0.454450\pi$
$282$	934.517	+	158.397i	0.197339	+	0.0334482i
$283$		−	2863.45i		−	0.601463i	−0.953709	−	0.300732i	$-0.902769\pi$
$283$		−	2863.45i		−	0.601463i	0.953709	−	0.300732i	$-0.0972309\pi$
$284$	−1898.42	−	662.586i	−0.396657	−	0.138441i
$285$		−	1040.18i		−	0.216192i
$286$	1528.04	−	9015.16i	0.315925	−	1.86391i
$287$	3503.50			0.720575
$288$	1212.61	−	1088.02i	0.248104	−	0.222611i
$289$	7624.50			1.55190
$290$	−995.039	+	5870.57i	−0.201485	+	1.18873i
$291$		−	1112.24i		−	0.224058i
$292$	5360.42	+	1870.89i	1.07430	+	0.374950i
$293$			3539.23i			0.705680i	0.935684	+	0.352840i	$0.114784\pi$
$293$			3539.23i			0.705680i	−0.935684	+	0.352840i	$0.885216\pi$
$294$	409.932	+	69.4819i	0.0813188	+	0.0137832i
$295$	3662.33			0.722810
$296$	−2602.88	−	1434.49i	−0.511113	−	0.281683i
$297$	−1591.56			−0.310949
$298$	−1567.25	−	265.643i	−0.304660	−	0.0516386i
$299$			6150.41i			1.18959i
$300$	−350.682	+	1004.76i	−0.0674887	+	0.193367i
$301$			3465.58i			0.663630i
$302$	220.275	−	1299.59i	0.0419716	−	0.247626i
$303$	−1864.27			−0.353464
$304$	−1537.45	+	1934.23i	−0.290061	+	0.364920i
$305$	1117.33			0.209765
$306$	−476.324	+	2810.23i	−0.0889857	+	0.525001i
$307$			3008.84i			0.559360i	0.960093	+	0.279680i	$0.0902283\pi$
$307$			3008.84i			0.559360i	−0.960093	+	0.279680i	$0.909772\pi$
$308$	−1087.77	+	3116.65i	−0.201238	+	0.576582i
$309$		−	1301.61i		−	0.239632i
$310$	−4508.89	−	764.240i	−0.826090	−	0.140019i
$311$	3951.63			0.720503			0.360252	−	0.932855i	$-0.382691\pi$
$311$	3951.63			0.720503			0.360252	+	0.932855i	$0.382691\pi$
$312$	1796.91	−	3260.48i	0.326057	−	0.591629i
$313$	−262.745			−0.0474479			−0.0237240	−	0.999719i	$-0.507552\pi$
$313$	−262.745			−0.0474479			−0.0237240	+	0.999719i	$0.507552\pi$
$314$	876.336	+	148.535i	0.157498	+	0.0266954i
$315$		−	565.803i		−	0.101204i
$316$	−6540.36	−	2282.71i	−1.16432	−	0.406369i
$317$			5155.26i			0.913401i	0.889621	+	0.456700i	$0.150969\pi$
$317$			5155.26i			0.913401i	−0.889621	+	0.456700i	$0.849031\pi$
$318$	−987.507	+	5826.13i	−0.174140	+	1.02740i
$319$	−13817.2			−2.42513
$320$	−3887.59	+	2455.75i	−0.679135	+	0.429001i
$321$	2780.90			0.483535
$322$	371.054	−	2189.16i	0.0642174	−	0.378873i
$323$		−	4322.83i		−	0.744670i
$324$	−611.807	−	213.532i	−0.104905	−	0.0366139i
$325$			2431.83i			0.415057i
$326$	5372.82	+	910.673i	0.912801	+	0.154716i
$327$	−4271.69			−0.722400
$328$	−5466.25	+	9918.48i	−0.920193	+	1.66968i
$329$	−781.933			−0.131031
$330$	4428.94	+	750.688i	0.738804	+	0.125224i
$331$			6802.50i			1.12961i	0.825226	+	0.564803i	$0.191048\pi$
$331$			6802.50i			1.12961i	−0.825226	+	0.564803i	$0.808952\pi$
$332$	−151.288	+	433.466i	−0.0250091	+	0.0716553i
$333$			1182.10i			0.194531i
$334$	−687.440	+	4055.79i	−0.112620	+	0.664440i
$335$	1291.90			0.210698
$336$	−836.291	+	1052.12i	−0.135784	+	0.170827i
$337$	433.772			0.0701159			0.0350580	−	0.999385i	$-0.488838\pi$
$337$	433.772			0.0701159			0.0350580	+	0.999385i	$0.488838\pi$
$338$	383.203	−	2260.84i	0.0616672	−	0.363826i
$339$			6082.17i			0.974449i
$340$	2650.99	−	7595.55i	0.422854	−	1.21155i
$341$		−	10612.3i		−	1.68531i
$342$	968.945	+	164.232i	0.153200	+	0.0259669i
$343$	−343.000			−0.0539949
$344$	−9811.12	−	5407.09i	−1.53773	−	0.847473i
$345$	−3021.55			−0.471521
$346$	−8763.73	−	1485.42i	−1.36168	−	0.230799i
$347$			4388.13i			0.678867i	0.940630	+	0.339434i	$0.110235\pi$
$347$			4388.13i			0.678867i	−0.940630	+	0.339434i	$0.889765\pi$
$348$	−5311.44	−	1853.79i	−0.818169	−	0.285557i
$349$		−	1270.81i		−	0.194914i	−0.995240	−	0.0974571i	$-0.968929\pi$
$349$		−	1270.81i		−	0.194914i	0.995240	−	0.0974571i	$-0.0310709\pi$
$350$	146.712	−	865.577i	0.0224059	−	0.132192i
$351$	−1480.75			−0.225176
$352$	−7126.12	−	7942.17i	−1.07904	−	1.20261i
$353$	12777.9			1.92663			0.963315	−	0.268375i	$-0.0864865\pi$
$353$	12777.9			1.92663			0.963315	+	0.268375i	$0.0864865\pi$
$354$	−578.241	+	3411.53i	−0.0868168	+	0.512205i
$355$		−	2257.29i		−	0.337478i
$356$	5781.55	+	2017.87i	0.860735	+	0.300413i
$357$		−	2351.39i		−	0.348596i
$358$	1696.04	+	287.472i	0.250387	+	0.0424396i
$359$	6124.58			0.900399			0.450199	−	0.892928i	$-0.351353\pi$
$359$	6124.58			0.900399			0.450199	+	0.892928i	$0.351353\pi$
$360$	1601.80	+	882.780i	0.234506	+	0.129240i
$361$	5368.53			0.782698
$362$	−8576.43	−	1453.67i	−1.24521	−	0.211059i
$363$			6431.16i			0.929885i
$364$	−1012.04	+	2899.66i	−0.145728	+	0.417537i
$365$			6373.73i			0.914017i
$366$	−176.414	+	1040.81i	−0.0251948	+	0.148645i
$367$	−3190.01			−0.453725			−0.226863	−	0.973927i	$-0.572847\pi$
$367$	−3190.01			−0.453725			−0.226863	+	0.973927i	$0.572847\pi$
$368$	5618.62	+	4466.04i	0.795899	+	0.632632i
$369$	4504.50			0.635488
$370$	557.560	−	3289.52i	0.0783410	−	0.462200i
$371$		−	4874.87i		−	0.682185i
$372$	1423.81	−	4079.45i	0.198443	−	0.568574i
$373$			8037.61i			1.11574i	0.829928	+	0.557871i	$0.188382\pi$
$373$			8037.61i			1.11574i	−0.829928	+	0.557871i	$0.811618\pi$
$374$	18406.0	+	3119.75i	2.54479	+	0.431333i
$375$	−4562.57			−0.628294
$376$	1219.99	−	2213.67i	0.167331	−	0.303620i
$377$	−12855.3			−1.75618
$378$	527.055	+	89.3338i	0.0717164	+	0.0121557i
$379$		−	3762.31i		−	0.509913i	−0.966953	−	0.254956i	$-0.917939\pi$
$379$		−	3762.31i		−	0.509913i	0.966953	−	0.254956i	$-0.0820611\pi$
$380$	−2618.88	−	914.040i	−0.353542	−	0.123393i
$381$			1448.21i			0.194734i
$382$	105.118	−	620.182i	0.0140794	−	0.0830662i
$383$	9479.32			1.26468			0.632338	−	0.774693i	$-0.282096\pi$
$383$	9479.32			1.26468			0.632338	+	0.774693i	$0.282096\pi$
$384$	−1673.76	−	4009.10i	−0.222432	−	0.532783i
$385$	−3705.80			−0.490559
$386$	−1075.33	+	6344.30i	−0.141795	+	0.836571i
$387$			4455.74i			0.585267i
$388$	−2800.33	−	977.367i	−0.366405	−	0.127882i
$389$		−	6672.27i		−	0.869660i	−0.900513	−	0.434830i	$-0.856808\pi$
$389$		−	6672.27i		−	0.869660i	0.900513	−	0.434830i	$-0.143192\pi$
$390$	4120.59	+	698.424i	0.535011	+	0.0906822i
$391$	−12557.1			−1.62415
$392$	535.158	−	971.040i	0.0689529	−	0.125115i
$393$	−4346.03			−0.557832
$394$	−390.743	−	66.2294i	−0.0499628	−	0.00846850i
$395$		−	7776.72i		−	0.990606i
$396$	−1398.56	+	4007.12i	−0.177475	+	0.508498i
$397$		−	13824.8i		−	1.74772i	−0.486178	−	0.873860i	$-0.661609\pi$
$397$		−	13824.8i		−	1.74772i	0.486178	−	0.873860i	$-0.338391\pi$
$398$	−474.152	+	2797.42i	−0.0597163	+	0.352317i
$399$	−810.740			−0.101724
$400$	2221.56	+	1765.84i	0.277695	+	0.220730i
$401$	−137.695			−0.0171475			−0.00857377	−	0.999963i	$-0.502729\pi$
$401$	−137.695			−0.0171475			−0.00857377	+	0.999963i	$0.502729\pi$
$402$	−203.976	+	1203.43i	−0.0253070	+	0.149307i
$403$		−	9873.48i		−	1.22043i
$404$	−1638.20	+	4693.72i	−0.201741	+	0.578023i
$405$		−	727.460i		−	0.0892538i
$406$	4575.66	+	775.557i	0.559326	+	0.0948036i
$407$	7742.36			0.942935
$408$	6656.83	+	3668.70i	0.807751	+	0.445166i
$409$	−12325.1			−1.49007			−0.745034	−	0.667027i	$-0.767567\pi$
$409$	−12325.1			−1.49007			−0.745034	+	0.667027i	$0.767567\pi$
$410$	−12535.0	−	2124.63i	−1.50990	−	0.255922i
$411$			3130.87i			0.375753i
$412$	−3277.10	−	1143.77i	−0.391872	−	0.136771i
$413$		−	2854.51i		−	0.340100i
$414$	477.069	−	2814.63i	0.0566345	−	0.334134i
$415$	−515.407			−0.0609646
$416$	−6629.98	−	7389.22i	−0.781398	−	0.870880i
$417$	1892.78			0.222277
$418$	1075.66	−	6346.24i	0.125867	−	0.742595i
$419$			3339.25i			0.389339i	0.980869	+	0.194670i	$0.0623635\pi$
$419$			3339.25i			0.389339i	−0.980869	+	0.194670i	$0.937637\pi$
$420$	−1424.53	−	497.190i	−0.165500	−	0.0577628i
$421$			3287.17i			0.380539i	0.981732	+	0.190270i	$0.0609362\pi$
$421$			3287.17i			0.380539i	−0.981732	+	0.190270i	$0.939064\pi$
$422$	−6865.73	−	1163.71i	−0.791987	−	0.134239i
$423$	−1005.34			−0.115559
$424$	13800.8	+	7605.89i	1.58073	+	0.871167i
$425$	−4964.99			−0.566677
$426$	2102.71	+	356.401i	0.239147	+	0.0405345i
$427$		−	870.874i		−	0.0986992i
$428$	2443.67	−	7001.55i	0.275980	−	0.790730i
$429$			9698.41i			1.09148i
$430$	2101.63	−	12399.3i	0.235697	−	1.39057i
$431$	−12701.9			−1.41955			−0.709776	−	0.704427i	$-0.751204\pi$
$431$	−12701.9			−1.41955			−0.709776	+	0.704427i	$0.751204\pi$
$432$	−1075.23	+	1352.72i	−0.119750	+	0.150655i
$433$	−11643.1			−1.29222			−0.646108	−	0.763246i	$-0.723604\pi$
$433$	−11643.1			−1.29222			−0.646108	+	0.763246i	$0.723604\pi$
$434$	−595.667	+	3514.34i	−0.0658823	+	0.388695i
$435$		−	6315.49i		−	0.696102i
$436$	−3753.68	+	10754.9i	−0.412313	+	1.18135i
$437$			4329.59i			0.473941i
$438$	−5937.24	−	1006.34i	−0.647700	−	0.109783i
$439$	−11073.2			−1.20386			−0.601930	−	0.798549i	$-0.705601\pi$
$439$	−11073.2			−1.20386			−0.601930	+	0.798549i	$0.705601\pi$
$440$	5781.89	−	10491.2i	0.626456	−	1.13670i
$441$	−441.000			−0.0476190
$442$	17124.6	+	2902.55i	1.84283	+	0.312353i
$443$			7274.35i			0.780168i	0.920779	+	0.390084i	$0.127554\pi$
$443$			7274.35i			0.780168i	−0.920779	+	0.390084i	$0.872446\pi$
$444$	2976.21	+	1038.76i	0.318119	+	0.111030i
$445$			6874.47i			0.732318i
$446$	−3052.79	+	18011.0i	−0.324112	+	1.91221i
$447$	1686.03			0.178404
$448$	1914.07	+	3030.08i	0.201855	+	0.319549i
$449$	9735.36			1.02325			0.511626	−	0.859208i	$-0.329043\pi$
$449$	9735.36			1.02325			0.511626	+	0.859208i	$0.329043\pi$
$450$	188.630	−	1112.88i	0.0197602	−	0.116582i
$451$		−	29502.8i		−	3.08034i
$452$	15313.2	+	5344.61i	1.59353	+	0.556171i
$453$			1398.08i			0.145006i
$454$	−4953.09	−	839.529i	−0.512026	−	0.0867864i
$455$	−3447.80			−0.355242
$456$	1264.94	−	2295.22i	0.129904	−	0.235710i
$457$	2155.33			0.220617			0.110309	−	0.993897i	$-0.464816\pi$
$457$	2155.33			0.220617			0.110309	+	0.993897i	$0.464816\pi$
$458$	5706.14	+	967.168i	0.582162	+	0.0986742i
$459$		−	3023.22i		−	0.307433i
$460$	−2655.14	+	7607.44i	−0.269123	+	0.771084i
$461$			3606.81i			0.364395i	0.983262	+	0.182197i	$0.0583209\pi$
$461$			3606.81i			0.364395i	−0.983262	+	0.182197i	$0.941679\pi$
$462$	585.104	−	3452.02i	0.0589210	−	0.347625i
$463$	8719.74			0.875250			0.437625	−	0.899158i	$-0.355820\pi$
$463$	8719.74			0.875250			0.437625	+	0.899158i	$0.355820\pi$
$464$	−9334.68	+	11743.7i	−0.933948	+	1.17498i
$465$	4850.61			0.483746
$466$	−2754.38	+	16250.4i	−0.273807	+	1.61542i
$467$		−	9661.28i		−	0.957325i	−0.877999	−	0.478662i	$-0.841122\pi$
$467$		−	9661.28i		−	0.957325i	0.877999	−	0.478662i	$-0.158878\pi$
$468$	−1301.19	+	3728.13i	−0.128520	+	0.368233i
$469$		−	1006.94i		−	0.0991386i
$470$	2797.63	+	474.187i	0.274564	+	0.0465375i
$471$	−942.751			−0.0922286
$472$	8081.17	+	4453.68i	0.788063	+	0.434316i
$473$	29183.5			2.83691
$474$	7244.16	+	1227.86i	0.701973	+	0.118982i
$475$			1711.89i			0.165362i
$476$	−5920.15	−	2066.25i	−0.570063	−	0.198963i
$477$		−	6267.69i		−	0.601630i
$478$	2785.95	−	16436.7i	0.266582	−	1.57279i
$479$	7341.60			0.700306			0.350153	−	0.936693i	$-0.386130\pi$
$479$	7341.60			0.700306			0.350153	+	0.936693i	$0.386130\pi$
$480$	3630.15	−	3257.16i	0.345194	−	0.309726i
$481$	7203.32			0.682834
$482$	972.502	−	5737.61i	0.0919010	−	0.542201i
$483$			2355.07i			0.221862i
$484$	16191.9	+	5651.28i	1.52065	+	0.530736i
$485$		−	3329.69i		−	0.311739i
$486$	677.643	+	114.858i	0.0632479	+	0.0107203i
$487$	14785.8			1.37579			0.687894	−	0.725811i	$-0.258535\pi$
$487$	14785.8			1.37579			0.687894	+	0.725811i	$0.258535\pi$
$488$	2465.46	+	1358.76i	0.228701	+	0.126041i
$489$	−5780.02			−0.534523
$490$	1227.20	+	208.005i	0.113141	+	0.0191770i
$491$			7352.33i			0.675776i	0.941186	+	0.337888i	$0.109712\pi$
$491$			7352.33i			0.675776i	−0.941186	+	0.337888i	$0.890288\pi$
$492$	3958.26	−	11341.1i	0.362707	−	1.03922i
$493$		−	26246.2i		−	2.39771i
$494$	1000.77	−	5904.40i	0.0911476	−	0.537756i
$495$	−4764.60			−0.432632
$496$	−9019.79	−	7169.51i	−0.816533	−	0.649033i
$497$	−1759.39			−0.158791
$498$	81.3769	−	480.111i	0.00732246	−	0.0432014i
$499$		−	16803.9i		−	1.50751i	−0.657157	−	0.753754i	$-0.728241\pi$
$499$		−	16803.9i		−	1.50751i	0.657157	−	0.753754i	$-0.271759\pi$
$500$	−4009.29	+	11487.3i	−0.358602	+	1.02746i
$501$		−	4363.17i		−	0.389086i
$502$	−15597.4	−	2643.69i	−1.38674	−	0.235047i
$503$	3372.87			0.298984			0.149492	−	0.988763i	$-0.452236\pi$
$503$	3372.87			0.298984			0.149492	+	0.988763i	$0.452236\pi$
$504$	688.060	−	1248.48i	0.0608107	−	0.110341i
$505$	−5581.00			−0.491785
$506$	−18434.8	−	3124.63i	−1.61962	−	0.274519i
$507$			2432.18i			0.213051i
$508$	3646.18	+	1272.59i	0.318451	+	0.111146i
$509$			1413.69i			0.123106i	0.998104	+	0.0615530i	$0.0196053\pi$
$509$			1413.69i			0.123106i	−0.998104	+	0.0615530i	$0.980395\pi$
$510$	−1425.95	+	8412.90i	−0.123808	+	0.730450i
$511$	4967.83			0.430067
$512$	−11564.6	+	691.147i	−0.998219	+	0.0596575i
$513$	−1042.38			−0.0897119
$514$	−722.551	+	4262.93i	−0.0620046	+	0.365817i
$515$		−	3896.59i		−	0.333407i
$516$	11218.3	+	3915.41i	0.957093	+	0.334044i
$517$			6584.63i			0.560139i
$518$	−2563.93	−	434.576i	−0.217476	−	0.0368613i
$519$	9427.92			0.797379
$520$	5379.34	−	9760.78i	0.453653	−	0.823151i
$521$	−20868.7			−1.75484			−0.877422	−	0.479720i	$-0.840738\pi$
$521$	−20868.7			−1.75484			−0.877422	+	0.479720i	$0.840738\pi$
$522$	5882.99	+	997.145i	0.493279	+	0.0836089i
$523$			17290.7i			1.44564i	0.691035	+	0.722821i	$0.257155\pi$
$523$			17290.7i			1.44564i	−0.691035	+	0.722821i	$0.742845\pi$
$524$	−3819.00	+	10942.1i	−0.318385	+	0.912228i
$525$			931.177i			0.0774094i
$526$	1410.24	−	8320.21i	0.116900	−	0.689693i
$527$	20158.4			1.66625
$528$	8859.85	+	7042.38i	0.730257	+	0.580455i
$529$	409.770			0.0336788
$530$	−2956.26	+	17441.5i	−0.242287	+	1.42945i
$531$		−	3670.08i		−	0.299940i
$532$	−712.425	+	2041.22i	−0.0580593	+	0.166350i
$533$		−	27448.8i		−	2.23066i
$534$	−6403.70	−	1085.40i	−0.518942	−	0.0879587i
$535$	8325.09			0.672757
$536$	2850.66	+	1571.05i	0.229719	+	0.126602i
$537$	−1824.58			−0.146623
$538$	15484.5	+	2624.56i	1.24086	+	0.210321i
$539$			2888.39i			0.230820i
$540$	−1831.54	−	639.244i	−0.145958	−	0.0509420i
$541$			4714.93i			0.374696i	0.982294	+	0.187348i	$0.0599892\pi$
$541$			4714.93i			0.374696i	−0.982294	+	0.187348i	$0.940011\pi$
$542$	2003.21	−	11818.6i	0.158755	−	0.936631i
$543$	9226.42			0.729178
$544$	15086.4	−	13536.3i	1.18901	−	1.06684i
$545$	−12788.0			−1.00510
$546$	544.368	−	3211.69i	0.0426681	−	0.251735i
$547$			11384.3i			0.889868i	0.895563	+	0.444934i	$0.146773\pi$
$547$			11384.3i			0.889868i	−0.895563	+	0.444934i	$0.853227\pi$
$548$	7882.67	+	2751.20i	0.614473	+	0.214463i
$549$		−	1119.70i		−	0.0870445i
$550$	−7288.99	−	1235.46i	−0.565098	−	0.0957818i
$551$	−9049.48			−0.699675
$552$	−6667.25	−	3674.44i	−0.514089	−	0.283324i
$553$	−6061.36			−0.466104
$554$	−10490.6	−	1778.11i	−0.804515	−	0.136362i
$555$			3538.82i			0.270657i
$556$	1663.25	−	4765.49i	0.126866	−	0.363492i
$557$		−	1616.13i		−	0.122940i	−0.998109	−	0.0614699i	$-0.980421\pi$
$557$		−	1616.13i		−	0.122940i	0.998109	−	0.0614699i	$-0.0195788\pi$
$558$	−765.857	+	4518.43i	−0.0581027	+	0.342797i
$559$	27151.7			2.05437
$560$	−2503.57	+	3149.69i	−0.188920	+	0.237676i
$561$	−19801.0			−1.49019
$562$	−635.031	+	3746.58i	−0.0476640	+	0.281210i
$563$		−	2529.62i		−	0.189362i	−0.995508	−	0.0946811i	$-0.969817\pi$
$563$		−	2529.62i		−	0.189362i	0.995508	−	0.0946811i	$-0.0301831\pi$
$564$	−883.429	+	2531.18i	−0.0659558	+	0.188975i
$565$			18208.0i			1.35578i
$566$	7985.16	+	1353.45i	0.593006	+	0.100512i
$567$	−567.000			−0.0419961
$568$	2745.04	−	4980.86i	0.202781	−	0.367944i
$569$	5697.25			0.419756			0.209878	−	0.977728i	$-0.432693\pi$
$569$	5697.25			0.419756			0.209878	+	0.977728i	$0.432693\pi$
$570$	2900.70	+	491.657i	0.213152	+	0.0361285i
$571$			15930.1i			1.16752i	0.811926	+	0.583760i	$0.198419\pi$
$571$			15930.1i			1.16752i	−0.811926	+	0.583760i	$0.801581\pi$
$572$	24417.9	+	8522.32i	1.78490	+	0.622965i
$573$			667.184i			0.0486423i
$574$	−1655.98	+	9770.05i	−0.120417	+	0.710442i
$575$	4972.76			0.360658
$576$	2460.94	+	3895.82i	0.178020	+	0.281816i
$577$	−9446.91			−0.681595			−0.340797	−	0.940137i	$-0.610697\pi$
$577$	−9446.91			−0.681595			−0.340797	+	0.940137i	$0.610697\pi$
$578$	−3603.84	+	21262.1i	−0.259343	+	1.53008i
$579$		−	6825.12i		−	0.489883i
$580$	−15900.7	−	5549.64i	−1.13834	−	0.397304i
$581$			401.720i			0.0286853i
$582$	3101.67	+	525.720i	0.220907	+	0.0374430i
$583$	−41051.1			−2.91623
$584$	−7750.94	+	14064.0i	−0.549206	+	0.996531i
$585$	−4432.88			−0.313294
$586$	−9869.69	−	1672.87i	−0.695756	−	0.117928i
$587$		−	17574.2i		−	1.23571i	−0.786290	−	0.617857i	$-0.788001\pi$
$587$		−	17574.2i		−	1.23571i	0.786290	−	0.617857i	$-0.211999\pi$
$588$	−387.522	+	1110.32i	−0.0271788	+	0.0778719i
$589$		−	6950.45i		−	0.486228i
$590$	−1731.06	+	10213.0i	−0.120791	+	0.712646i
$591$	420.356			0.0292575
$592$	5230.60	−	6580.50i	0.363136	−	0.456853i
$593$	6137.13			0.424995			0.212497	−	0.977162i	$-0.431840\pi$
$593$	6137.13			0.424995			0.212497	+	0.977162i	$0.431840\pi$
$594$	752.277	−	4438.32i	0.0519635	−	0.306576i
$595$		−	7039.27i		−	0.485012i
$596$	1481.57	−	4244.97i	0.101825	−	0.291746i
$597$		−	3009.43i		−	0.206311i
$598$	−17151.3	−	2907.09i	−1.17286	−	0.198795i
$599$	−26532.1			−1.80980			−0.904901	−	0.425622i	$-0.860055\pi$
$599$	−26532.1			−1.80980			−0.904901	+	0.425622i	$0.860055\pi$
$600$	−2636.18	−	1452.85i	−0.179369	−	0.0988537i
$601$	−6237.94			−0.423379			−0.211690	−	0.977337i	$-0.567897\pi$
$601$	−6237.94			−0.423379			−0.211690	+	0.977337i	$0.567897\pi$
$602$	−9664.30	−	1638.06i	−0.654298	−	0.110901i
$603$		−	1294.63i		−	0.0874320i
$604$	3519.99	+	1228.54i	0.237130	+	0.0827627i
$605$			19252.7i			1.29378i
$606$	881.178	−	5198.81i	0.0590683	−	0.348494i
$607$	2650.63			0.177242			0.0886209	−	0.996065i	$-0.471754\pi$
$607$	2650.63			0.177242			0.0886209	+	0.996065i	$0.471754\pi$
$608$	−4667.19	−	5201.65i	−0.311315	−	0.346965i
$609$	−4922.44			−0.327533
$610$	−528.124	+	3115.85i	−0.0350543	+	0.206815i
$611$			6126.19i			0.405629i
$612$	−7611.63	−	2656.60i	−0.502748	−	0.175469i
$613$			2531.31i			0.166784i	0.996517	+	0.0833921i	$0.0265754\pi$
$613$			2531.31i			0.166784i	−0.996517	+	0.0833921i	$0.973425\pi$
$614$	−8390.60	−	1422.17i	−0.551494	−	0.0934760i
$615$	13485.0			0.884172
$616$	−8177.09	−	4506.54i	−0.534845	−	0.294763i
$617$	22390.8			1.46097			0.730485	−	0.682928i	$-0.239294\pi$
$617$	22390.8			1.46097			0.730485	+	0.682928i	$0.239294\pi$
$618$	3629.75	+	615.228i	0.236262	+	0.0400455i
$619$		−	4854.99i		−	0.315248i	−0.987499	−	0.157624i	$-0.949617\pi$
$619$		−	4854.99i		−	0.315248i	0.987499	−	0.157624i	$-0.0503834\pi$
$620$	4262.40	−	12212.5i	0.276100	−	0.791074i
$621$			3027.95i			0.195664i
$622$	−1867.80	+	11019.7i	−0.120405	+	0.710371i
$623$	5358.13			0.344573
$624$	8243.01	+	6552.07i	0.528821	+	0.420341i
$625$	−8116.08			−0.519429
$626$	124.190	−	732.704i	0.00792915	−	0.0467807i
$627$			6827.21i			0.434853i
$628$	−828.428	+	2373.59i	−0.0526399	+	0.150822i
$629$			14706.8i			0.932273i
$630$	1577.83	+	267.436i	0.0997812	+	0.0169125i
$631$	23946.3			1.51076			0.755379	−	0.655289i	$-0.227453\pi$
$631$	23946.3			1.51076			0.755379	+	0.655289i	$0.227453\pi$
$632$	9457.09	−	17159.8i	0.595226	−	1.08003i
$633$	7386.07			0.463776
$634$	−14376.2	−	2436.71i	−0.900556	−	0.152641i
$635$			4335.44i			0.270940i
$636$	−15780.3	−	5507.63i	−0.983852	−	0.343383i
$637$			2687.29i			0.167150i
$638$	6530.94	−	38531.5i	0.405270	−	2.39103i
$639$	−2262.07			−0.140041
$640$	−5010.69	−	12001.9i	−0.309476	−	0.741276i
$641$	−17358.0			−1.06958			−0.534790	−	0.844985i	$-0.679609\pi$
$641$	−17358.0			−1.06958			−0.534790	+	0.844985i	$0.679609\pi$
$642$	−1314.44	+	7754.97i	−0.0808048	+	0.476736i
$643$		−	11744.3i		−	0.720293i	−0.932896	−	0.360146i	$-0.882727\pi$
$643$		−	11744.3i		−	0.720293i	0.932896	−	0.360146i	$-0.117273\pi$
$644$	5929.42	+	2069.48i	0.362813	+	0.126629i
$645$			13339.0i			0.814299i
$646$	12054.9	+	2043.25i	0.734199	+	0.124444i
$647$	23793.4			1.44577			0.722887	−	0.690967i	$-0.242815\pi$
$647$	23793.4			1.44577			0.722887	+	0.690967i	$0.242815\pi$
$648$	884.648	−	1605.19i	0.0536300	−	0.0973113i
$649$	−24037.7			−1.45387
$650$	−6781.52	−	1149.44i	−0.409220	−	0.0693612i
$651$		−	3780.68i		−	0.227614i
$652$	−5079.10	+	14552.5i	−0.305081	+	0.874110i
$653$			7027.81i			0.421163i	0.977576	+	0.210582i	$0.0675358\pi$
$653$			7027.81i			0.421163i	−0.977576	+	0.210582i	$0.932464\pi$
$654$	2019.08	−	11912.3i	0.120722	−	0.712241i
$655$	−13010.5			−0.776128
$656$	−25075.5	−	19931.6i	−1.49243	−	1.18628i
$657$	6387.22			0.379283
$658$	369.593	−	2180.54i	0.0218970	−	0.129189i
$659$		−	16588.1i		−	0.980547i	−0.871569	−	0.490273i	$-0.836897\pi$
$659$		−	16588.1i		−	0.980547i	0.871569	−	0.490273i	$-0.163103\pi$
$660$	−4186.82	+	11996.0i	−0.246927	+	0.707488i
$661$			5341.60i			0.314318i	0.987573	+	0.157159i	$0.0502335\pi$
$661$			5341.60i			0.314318i	−0.987573	+	0.157159i	$0.949766\pi$
$662$	−18969.8	−	3215.31i	−1.11372	−	0.188771i
$663$	−18422.4			−1.07913
$664$	−1137.28	−	626.774i	−0.0664683	−	0.0366319i
$665$	−2427.08			−0.141531
$666$	−3296.48	−	558.740i	−0.191796	−	0.0325086i
$667$			26287.3i			1.52601i
$668$	−10985.3	−	3834.07i	−0.636276	−	0.222073i
$669$		−	19376.0i		−	1.11976i
$670$	−610.636	+	3602.66i	−0.0352103	+	0.207735i
$671$	−7333.60			−0.421923
$672$	−2538.71	−	2829.43i	−0.145733	−	0.162422i
$673$	−10396.5			−0.595477			−0.297738	−	0.954648i	$-0.596232\pi$
$673$	−10396.5			−0.595477			−0.297738	+	0.954648i	$0.596232\pi$
$674$	−205.029	+	1209.64i	−0.0117173	+	0.0691300i
$675$			1197.23i			0.0682686i
$676$	6123.56	+	2137.24i	0.348405	+	0.121600i
$677$			7689.12i			0.436510i	0.975892	+	0.218255i	$0.0700364\pi$
$677$			7689.12i			0.436510i	−0.975892	+	0.218255i	$0.929964\pi$
$678$	−16961.1	−	2874.83i	−0.960746	−	0.162843i
$679$	−2595.24			−0.146681
$680$	19928.3	+	10982.9i	1.12385	+	0.619373i
$681$	5328.47			0.299835
$682$	29594.1	+	5016.09i	1.66161	+	0.281636i
$683$			1703.19i			0.0954182i	0.998861	+	0.0477091i	$0.0151920\pi$
$683$			1703.19i			0.0954182i	−0.998861	+	0.0477091i	$0.984808\pi$
$684$	−915.975	+	2624.43i	−0.0512035	+	0.146707i
$685$			9372.78i			0.522796i
$686$	162.124	−	956.508i	0.00902323	−	0.0532356i
$687$	−6138.60			−0.340905
$688$	19715.9	−	24804.1i	1.09253	−	1.37449i
$689$	−38193.0			−2.11181
$690$	1428.18	−	8426.06i	0.0787972	−	0.464891i
$691$			19314.7i			1.06334i	0.846952	+	0.531669i	$0.178435\pi$
$691$			19314.7i			1.06334i	−0.846952	+	0.531669i	$0.821565\pi$
$692$	8284.63	−	23736.9i	0.455108	−	1.30396i
$693$			3713.65i			0.203564i
$694$	−12237.0	−	2074.12i	−0.669321	−	0.113447i
$695$	5666.33			0.309261
$696$	7680.12	−	13935.5i	0.418268	−	0.758944i
$697$	56041.5			3.04551
$698$	3543.86	+	600.670i	0.192173	+	0.0325726i
$699$		−	17482.0i		−	0.945964i
$700$	2344.45	+	818.257i	0.126588	+	0.0441817i
$701$		−	8776.10i		−	0.472851i	−0.971650	−	0.236426i	$-0.924024\pi$
$701$		−	8776.10i		−	0.472851i	0.971650	−	0.236426i	$-0.0759760\pi$
$702$	699.902	−	4129.31i	0.0376298	−	0.222010i
$703$	5070.79			0.272046
$704$	25516.2	−	16118.3i	1.36602	−	0.862899i
$705$	−3009.66			−0.160780
$706$	−6039.69	+	35633.2i	−0.321964	+	1.89954i
$707$			4349.97i			0.231397i
$708$	−9240.25	−	3225.03i	−0.490494	−	0.171192i
$709$		−	15446.1i		−	0.818180i	−0.912494	−	0.409090i	$-0.865846\pi$
$709$		−	15446.1i		−	0.818180i	0.912494	−	0.409090i	$-0.134154\pi$
$710$	6294.80	+	1066.94i	0.332732	+	0.0563968i
$711$	−7793.18			−0.411065
$712$	−8359.89	+	15169.0i	−0.440028	+	0.798429i
$713$	−20190.0			−1.06048
$714$	6557.21	+	1111.42i	0.343694	+	0.0582548i
$715$			29033.8i			1.51860i
$716$	−1603.32	+	4593.79i	−0.0836857	+	0.239774i
$717$			17682.4i			0.921004i
$718$	−2894.88	+	17079.3i	−0.150468	+	0.887737i
$719$	1510.03			0.0783237			0.0391618	−	0.999233i	$-0.487531\pi$
$719$	1510.03			0.0783237			0.0391618	+	0.999233i	$0.487531\pi$
$720$	−3218.88	+	4049.60i	−0.166612	+	0.209611i
$721$	−3037.10			−0.156876
$722$	−2537.52	+	14971.0i	−0.130799	+	0.771692i
$723$			6172.45i			0.317505i
$724$	8107.57	−	23229.6i	0.416181	−	1.19243i
$725$			10393.8i			0.532436i
$726$	−17934.3	−	3039.79i	−0.916809	−	0.155396i
$727$	32352.4			1.65046			0.825231	−	0.564795i	$-0.191045\pi$
$727$	32352.4			1.65046			0.825231	+	0.564795i	$0.191045\pi$
$728$	−7607.79	−	4192.79i	−0.387312	−	0.213455i
$729$	−729.000			−0.0370370
$730$	−17774.1	−	3012.64i	−0.901164	−	0.152744i
$731$			55434.9i			2.80483i
$732$	−2819.09	−	983.915i	−0.142345	−	0.0496811i
$733$		−	11397.7i		−	0.574327i	−0.957882	−	0.287164i	$-0.907288\pi$
$733$		−	11397.7i		−	0.574327i	0.957882	−	0.287164i	$-0.0927123\pi$
$734$	1507.81	−	8895.84i	0.0758232	−	0.447345i
$735$	−1320.21			−0.0662538
$736$	−15110.0	+	13557.4i	−0.756740	+	0.678986i
$737$	−8479.37			−0.423802
$738$	−2129.12	+	12561.5i	−0.106198	+	0.626551i
$739$		−	5146.85i		−	0.256198i	−0.991761	−	0.128099i	$-0.959113\pi$
$739$		−	5146.85i		−	0.256198i	0.991761	−	0.128099i	$-0.0408875\pi$
$740$	8909.78	+	3109.69i	0.442608	+	0.154479i
$741$			6351.89i			0.314902i
$742$	13594.3	+	2304.18i	0.672592	+	0.114002i
$743$	22350.2			1.10357			0.551783	−	0.833988i	$-0.313948\pi$
$743$	22350.2			1.10357			0.551783	+	0.833988i	$0.313948\pi$
$744$	10703.2	+	5898.72i	0.527417	+	0.290669i
$745$	5047.42			0.248219
$746$	−22414.1	−	3799.11i	−1.10005	−	0.186455i
$747$			516.498i			0.0252981i
$748$	−17399.8	+	49853.4i	−0.850534	+	2.43693i
$749$		−	6488.77i		−	0.316548i
$750$	2156.57	−	12723.4i	0.104996	−	0.619459i
$751$	12773.8			0.620670			0.310335	−	0.950627i	$-0.399559\pi$
$751$	12773.8			0.620670			0.310335	+	0.950627i	$0.399559\pi$
$752$	5596.50	+	4448.46i	0.271388	+	0.215716i
$753$	16779.5			0.812055
$754$	6076.24	−	35848.8i	0.293480	−	1.73148i
$755$			4185.39i			0.201751i
$756$	−498.242	+	1427.55i	−0.0239694	+	0.0686766i
$757$			1662.37i			0.0798149i	0.999203	+	0.0399075i	$0.0127063\pi$
$757$			1662.37i			0.0798149i	−0.999203	+	0.0399075i	$0.987294\pi$
$758$	10491.8	+	1778.32i	0.502742	+	0.0852129i
$759$	19832.0			0.948425
$760$	3786.80	−	6871.12i	0.180739	−	0.327950i
$761$	36358.5			1.73192			0.865962	−	0.500109i	$-0.166707\pi$
$761$	36358.5			1.73192			0.865962	+	0.500109i	$0.166707\pi$
$762$	−4038.54	−	684.517i	−0.191996	−	0.0325426i
$763$			9967.27i			0.472922i
$764$	1679.79	+	586.278i	0.0795452	+	0.0277628i
$765$		−	9050.50i		−	0.427740i
$766$	−4480.55	+	26434.5i	−0.211343	+	1.24689i
$767$	−22364.1			−1.05283
$768$	11971.1	−	2772.59i	0.562462	−	0.130270i
$769$	17531.9			0.822127			0.411063	−	0.911607i	$-0.365158\pi$
$769$	17531.9			0.822127			0.411063	+	0.911607i	$0.365158\pi$
$770$	1751.61	−	10334.2i	0.0819786	−	0.483661i
$771$		−	4586.01i		−	0.214217i
$772$	−17183.8	−	5997.47i	−0.801111	−	0.279603i
$773$		−	17860.7i		−	0.831054i	−0.909581	−	0.415527i	$-0.863597\pi$
$773$		−	17860.7i		−	0.831054i	0.909581	−	0.415527i	$-0.136403\pi$
$774$	−12425.5	−	2106.08i	−0.577037	−	0.0978054i
$775$	−7982.96			−0.370008
$776$	4049.16	−	7347.17i	0.187315	−	0.339882i
$777$	2758.24			0.127351
$778$	18606.7	+	3153.76i	0.857431	+	0.145331i
$779$		−	19322.6i		−	0.888710i
$780$	−3895.32	+	11160.8i	−0.178814	+	0.512333i
$781$			14815.7i			0.678807i
$782$	5935.32	−	35017.5i	0.271415	−	1.60131i
$783$	−6328.86			−0.288857
$784$	2454.94	+	1951.35i	0.111832	+	0.0888915i
$785$	−2822.28			−0.128320
$786$	2054.22	−	12119.6i	0.0932208	−	0.549988i
$787$			11778.6i			0.533496i	0.963766	+	0.266748i	$0.0859492\pi$
$787$			11778.6i			0.533496i	−0.963766	+	0.266748i	$0.914051\pi$
$788$	369.382	−	1058.34i	0.0166988	−	0.0478450i
$789$			8950.79i			0.403874i
$790$	21686.6	+	3675.79i	0.976675	+	0.165543i
$791$	14191.7			0.637926
$792$	−10513.4	−	5794.13i	−0.471689	−	0.259956i
$793$	−6823.02			−0.305539
$794$	38552.5	+	6534.49i	1.72314	+	0.292066i
$795$		−	18763.3i		−	0.837066i
$796$	−7576.93	−	2644.49i	−0.337383	−	0.117753i
$797$			9149.34i			0.406633i	0.979113	+	0.203316i	$0.0651720\pi$
$797$			9149.34i			0.406633i	−0.979113	+	0.203316i	$0.934828\pi$
$798$	383.209	−	2260.87i	0.0169993	−	0.100293i
$799$	−12507.7			−0.553805
$800$	−5974.37	+	5360.51i	−0.264032	+	0.236903i
$801$	6889.02			0.303885
$802$	65.0838	−	383.984i	0.00286557	−	0.0169064i
$803$		−	41834.0i		−	1.83847i
$804$	−3259.53	−	1137.64i	−0.142978	−	0.0499022i
$805$			7050.29i			0.308683i
$806$	27533.7	+	4666.86i	1.20327	+	0.203949i
$807$	−16658.0			−0.726631
$808$	−12314.8	−	6786.93i	−0.536182	−	0.295499i
$809$	11885.2			0.516514			0.258257	−	0.966076i	$-0.416852\pi$
$809$	11885.2			0.516514			0.258257	+	0.966076i	$0.416852\pi$
$810$	2028.63	+	343.846i	0.0879987	+	0.0149154i
$811$			22554.1i			0.976549i	0.872690	+	0.488274i	$0.162374\pi$
$811$			22554.1i			0.976549i	−0.872690	+	0.488274i	$0.837626\pi$
$812$	−4325.52	+	12393.4i	−0.186941	+	0.535618i
$813$			12714.4i			0.548477i
$814$	−3659.55	+	21590.8i	−0.157576	+	0.929675i
$815$	−17303.4			−0.743697
$816$	−13377.2	+	16829.5i	−0.573891	+	0.721999i
$817$	19113.5			0.818478
$818$	5825.66	−	34370.5i	0.249009	−	1.46911i
$819$			3455.09i			0.147412i
$820$	11849.7	−	33951.4i	0.504645	−	1.44590i
$821$		−	9016.04i		−	0.383267i	−0.981467	−	0.191633i	$-0.938622\pi$
$821$		−	9016.04i		−	0.383267i	0.981467	−	0.191633i	$-0.0613784\pi$
$822$	−8730.91	−	1479.86i	−0.370469	−	0.0627931i
$823$	8909.42			0.377355			0.188677	−	0.982039i	$-0.439580\pi$
$823$	8909.42			0.377355			0.188677	+	0.982039i	$0.439580\pi$
$824$	4738.56	−	8598.08i	0.200334	−	0.363505i
$825$	7841.41			0.330913
$826$	7960.23	+	1349.23i	0.335317	+	0.0568349i
$827$		−	24206.8i		−	1.01784i	−0.860814	−	0.508920i	$-0.830045\pi$
$827$		−	24206.8i		−	1.01784i	0.860814	−	0.508920i	$-0.169955\pi$
$828$	7623.54	+	2660.76i	0.319971	+	0.111676i
$829$		−	498.801i		−	0.0208976i	−0.999945	−	0.0104488i	$-0.996674\pi$
$829$		−	498.801i		−	0.0208976i	0.999945	−	0.0104488i	$-0.00332601\pi$
$830$	243.615	−	1437.29i	0.0101880	−	0.0601073i
$831$	11285.6			0.471112
$832$	23739.7	−	14996.1i	0.989215	−	0.624875i
$833$	−5486.58			−0.228210
$834$	−894.650	+	5278.29i	−0.0371453	+	0.219152i
$835$		−	13061.9i		−	0.541347i
$836$	17189.0	+	5999.30i	0.711119	+	0.248194i
$837$		−	4860.88i		−	0.200737i
$838$	−9312.02	−	1578.35i	−0.383864	−	0.0650635i
$839$	−23273.2			−0.957666			−0.478833	−	0.877906i	$-0.658940\pi$
$839$	−23273.2			−0.957666			−0.478833	+	0.877906i	$0.658940\pi$
$840$	2059.82	−	3737.53i	0.0846078	−	0.153520i
$841$	−30555.3			−1.25283
$842$	−9166.79	−	1553.74i	−0.375188	−	0.0635929i
$843$		−	4030.53i		−	0.164672i
$844$	6490.39	−	18596.1i	0.264702	−	0.758417i
$845$			7281.14i			0.296424i
$846$	475.191	−	2803.55i	0.0193113	−	0.113934i
$847$	15006.0			0.608753
$848$	−27733.4	+	34890.7i	−1.12308	+	1.41292i
$849$	−8590.34			−0.347255
$850$	2346.78	−	13845.6i	0.0946988	−	0.558708i
$851$		−	14729.8i		−	0.593340i
$852$	−1987.76	+	5695.27i	−0.0799289	+	0.229010i
$853$		−	17701.4i		−	0.710531i	−0.934765	−	0.355266i	$-0.884390\pi$
$853$		−	17701.4i		−	0.710531i	0.934765	−	0.355266i	$-0.115610\pi$
$854$	2428.57	+	411.633i	0.0973113	+	0.0164939i
$855$	−3120.53			−0.124819
$856$	18369.8	+	10123.9i	0.733491	+	0.404240i
$857$	13312.4			0.530620			0.265310	−	0.964163i	$-0.414526\pi$
$857$	13312.4			0.530620			0.265310	+	0.964163i	$0.414526\pi$
$858$	−27045.5	−	4584.11i	−1.07613	−	0.182400i
$859$			6535.20i			0.259579i	0.991542	+	0.129789i	$0.0414301\pi$
$859$			6535.20i			0.259579i	−0.991542	+	0.129789i	$0.958570\pi$
$860$	33583.9	+	11721.4i	1.33163	+	0.464765i
$861$		−	10510.5i		−	0.416024i
$862$	6003.74	−	35421.1i	0.237225	−	1.39959i
$863$	−32795.4			−1.29359			−0.646795	−	0.762664i	$-0.723891\pi$
$863$	−32795.4			−1.29359			−0.646795	+	0.762664i	$0.723891\pi$
$864$	−3264.05	−	3637.83i	−0.128525	−	0.143243i
$865$	28224.0			1.10942
$866$	5503.28	−	32468.4i	0.215946	−	1.27404i
$867$		−	22873.5i		−	0.895992i
$868$	−9518.72	−	3322.22i	−0.372219	−	0.129912i
$869$			51042.5i			1.99252i
$870$	17611.7	+	2985.12i	0.686314	+	0.116327i
$871$	−7889.02			−0.306899
$872$	−28217.5	−	15551.2i	−1.09583	−	0.603933i
$873$	−3336.73			−0.129360
$874$	−12073.7	−	2046.45i	−0.467277	−	0.0792016i
$875$			10646.0i			0.411315i
$876$	5612.66	−	16081.2i	0.216478	−	0.620246i
$877$		−	47714.2i		−	1.83716i	−0.395231	−	0.918582i	$-0.629335\pi$
$877$		−	47714.2i		−	1.83716i	0.395231	−	0.918582i	$-0.370665\pi$
$878$	5233.92	−	30879.3i	0.201180	−	1.18693i
$879$	10617.7			0.407424
$880$	26523.4	+	21082.5i	1.01603	+	0.807604i
$881$	−26128.4			−0.999191			−0.499595	−	0.866259i	$-0.666518\pi$
$881$	−26128.4			−0.999191			−0.499595	+	0.866259i	$0.666518\pi$
$882$	208.446	−	1229.80i	0.00795774	−	0.0469494i
$883$		−	26426.3i		−	1.00715i	−0.863950	−	0.503577i	$-0.832017\pi$
$883$		−	26426.3i		−	1.00715i	0.863950	−	0.503577i	$-0.167983\pi$
$884$	−16188.4	+	46382.5i	−0.615921	+	1.76472i
$885$		−	10987.0i		−	0.417315i
$886$	−20285.6	−	3438.34i	−0.769198	−	0.130376i
$887$	11595.6			0.438944			0.219472	−	0.975619i	$-0.429567\pi$
$887$	11595.6			0.438944			0.219472	+	0.975619i	$0.429567\pi$
$888$	−4303.48	+	7808.64i	−0.162630	+	0.295091i
$889$	3379.15			0.127484
$890$	−19170.5	−	3249.33i	−0.722020	−	0.122379i
$891$			4774.69i			0.179526i
$892$	−48783.4	−	17026.4i	−1.83115	−	0.639108i
$893$			4312.55i			0.161606i
$894$	−796.930	+	4701.76i	−0.0298136	+	0.175895i
$895$	−5462.18			−0.204001
$896$	−9354.57	+	3905.45i	−0.348788	+	0.145616i
$897$	18451.2			0.686810
$898$	−4601.57	+	27148.5i	−0.170998	+	1.00886i
$899$		−	42200.0i		−	1.56557i
$900$	3014.29	+	1052.05i	0.111640	+	0.0389646i
$901$		−	77977.7i		−	2.88326i
$902$	82273.2	+	13945.0i	3.03703	+	0.514764i
$903$	10396.7			0.383147
$904$	−22142.3	+	40177.1i	−0.814648	+	1.47817i
$905$	27620.8			1.01453
$906$	−3898.77	−	660.826i	−0.142967	−	0.0242323i
$907$			42382.2i			1.55158i	0.630994	+	0.775788i	$0.282647\pi$
$907$			42382.2i			1.55158i	−0.630994	+	0.775788i	$0.717353\pi$
$908$	4682.31	−	13415.6i	0.171132	−	0.490323i
$909$			5592.82i			0.204073i
$910$	1629.66	−	9614.71i	0.0593654	−	0.350247i
$911$	−8454.22			−0.307465			−0.153733	−	0.988112i	$-0.549129\pi$
$911$	−8454.22			−0.307465			−0.153733	+	0.988112i	$0.549129\pi$
$912$	5802.68	+	4612.34i	0.210686	+	0.167467i
$913$	3382.87			0.122625
$914$	−1018.75	+	6010.47i	−0.0368680	+	0.217515i
$915$		−	3351.99i		−	0.121108i
$916$	−5394.19	+	15455.3i	−0.194573	+	0.557486i
$917$			10140.7i			0.365187i
$918$	8430.70	+	1428.97i	0.303110	+	0.0513759i
$919$	36015.8			1.29277			0.646383	−	0.763014i	$-0.276281\pi$
$919$	36015.8			1.29277			0.646383	+	0.763014i	$0.276281\pi$
$920$	−19959.5	−	11000.0i	−0.715267	−	0.394196i
$921$	9026.51			0.322946
$922$	−10058.1	−	1704.82i	−0.359270	−	0.0608949i
$923$			13784.2i			0.491564i
$924$	9349.94	+	3263.31i	0.332890	+	0.116185i
$925$		−	5824.07i		−	0.207021i
$926$	−4121.53	+	24316.3i	−0.146265	+	0.862942i
$927$	−3904.84			−0.138351
$928$	−28337.1	−	31582.1i	−1.00238	−	1.11717i
$929$	19664.5			0.694481			0.347240	−	0.937776i	$-0.387119\pi$
$929$	19664.5			0.694481			0.347240	+	0.937776i	$0.387119\pi$
$930$	−2292.72	+	13526.7i	−0.0808400	+	0.476943i
$931$			1891.73i			0.0665938i
$932$	−44014.8	−	15362.0i	−1.54694	−	0.539913i
$933$		−	11854.9i		−	0.415983i
$934$	26942.0	+	4566.56i	0.943863	+	0.159981i
$935$	−59277.5			−2.07335
$936$	−9781.44	−	5390.73i	−0.341577	−	0.188249i
$937$	20967.0			0.731017			0.365509	−	0.930808i	$-0.380895\pi$
$937$	20967.0			0.731017			0.365509	+	0.930808i	$0.380895\pi$
$938$	2808.00	+	475.944i	0.0977445	+	0.0165673i
$939$			788.234i			0.0273941i
$940$	−2644.69	+	7577.49i	−0.0917662	+	0.262926i
$941$			37124.0i			1.28609i	0.765829	+	0.643044i	$0.222329\pi$
$941$			37124.0i			1.28609i	−0.765829	+	0.643044i	$0.777671\pi$
$942$	445.606	−	2629.01i	0.0154126	−	0.0909317i
$943$	−56129.2			−1.93830
$944$	−16239.5	+	20430.5i	−0.559904	+	0.704402i
$945$	−1697.41			−0.0584303
$946$	−13794.1	+	81382.7i	−0.474084	+	2.79702i
$947$			28450.0i			0.976240i	0.872776	+	0.488120i	$0.162317\pi$
$947$			28450.0i			0.976240i	−0.872776	+	0.488120i	$0.837683\pi$
$948$	−6848.13	+	19621.1i	−0.234617	+	0.672218i
$949$		−	38921.4i		−	1.33134i
$950$	−4773.86	−	809.151i	−0.163036	−	0.0276340i
$951$	15465.8			0.527352
$952$	8560.30	−	15532.6i	0.291430	−	0.528797i
$953$	−36489.4			−1.24030			−0.620151	−	0.784483i	$-0.712929\pi$
$953$	−36489.4			−1.24030			−0.620151	+	0.784483i	$0.712929\pi$
$954$	17478.4	+	2962.52i	0.593170	+	0.100540i
$955$			1997.33i			0.0676774i
$956$	44519.3	+	15538.1i	1.50613	+	0.525667i
$957$			41451.7i			1.40015i
$958$	−3470.13	+	20473.2i	−0.117030	+	0.690458i
$959$	7305.37			0.245988
$960$	7367.24	+	11662.8i	0.247684	+	0.392099i
$961$	2620.72			0.0879700
$962$	−3404.76	+	20087.6i	−0.114110	+	0.673232i
$963$		−	8342.71i		−	0.279169i
$964$	15540.5	+	5423.94i	0.519219	+	0.181217i
$965$		−	20432.1i		−	0.681589i
$966$	−6567.47	−	1113.16i	−0.218742	−	0.0370760i
$967$	−39597.5			−1.31682			−0.658412	−	0.752658i	$-0.728772\pi$
$967$	−39597.5			−1.31682			−0.658412	+	0.752658i	$0.728772\pi$
$968$	−23412.8	+	42482.4i	−0.777393	+	1.41057i
$969$	−12968.5			−0.429936
$970$	9285.34	+	1573.83i	0.307355	+	0.0520955i
$971$			6633.40i			0.219234i	0.993974	+	0.109617i	$0.0349624\pi$
$971$			6633.40i			0.219234i	−0.993974	+	0.109617i	$0.965038\pi$
$972$	−640.597	+	1835.42i	−0.0211391	+	0.0605670i
$973$		−	4416.48i		−	0.145515i
$974$	−6988.75	+	41232.5i	−0.229912	+	1.35644i
$975$	7295.48			0.239633
$976$	−4954.45	+	6233.08i	−0.162488	+	0.204422i
$977$	−24844.2			−0.813549			−0.406774	−	0.913529i	$-0.633346\pi$
$977$	−24844.2			−0.813549			−0.406774	+	0.913529i	$0.633346\pi$
$978$	2732.02	−	16118.5i	0.0893255	−	0.527006i
$979$		−	45120.6i		−	1.47299i
$980$	−1160.11	+	3323.91i	−0.0378146	+	0.108345i
$981$			12815.1i			0.417078i
$982$	−20503.1	−	3475.19i	−0.666273	−	0.112931i
$983$	−7133.71			−0.231465			−0.115732	−	0.993280i	$-0.536922\pi$
$983$	−7133.71			−0.231465			−0.115732	+	0.993280i	$0.536922\pi$
$984$	29755.4	+	16398.8i	0.963992	+	0.531274i
$985$	1258.41			0.0407068
$986$	73191.6	+	12405.7i	2.36399	+	0.400688i
$987$			2345.80i			0.0756511i
$988$	15992.3	+	5581.62i	0.514962	+	0.179732i
$989$		−	55521.6i		−	1.78512i
$990$	2252.07	−	13286.8i	0.0722983	−	0.426549i
$991$	−56431.1			−1.80887			−0.904436	−	0.426609i	$-0.859708\pi$
$991$	−56431.1			−1.80887			−0.904436	+	0.426609i	$0.859708\pi$
$992$	24256.6	−	21764.3i	0.776359	−	0.696589i
$993$	20407.5			0.652178
$994$	831.602	−	4906.32i	0.0265360	−	0.156558i
$995$		−	9009.23i		−	0.287047i
$996$	1300.40	+	453.864i	0.0413702	+	0.0144390i
$997$			55825.3i			1.77333i	0.462417	+	0.886663i	$0.346982\pi$
$997$			55825.3i			1.77333i	−0.462417	+	0.886663i	$0.653018\pi$
$998$	46860.3	+	7942.63i	1.48631	+	0.251923i
$999$	3546.31			0.112313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.c.b.85.8	yes	20
3.2	odd	2		504.4.c.e.253.13		20
4.3	odd	2		672.4.c.b.337.14		20
8.3	odd	2		672.4.c.b.337.7		20
8.5	even	2	inner	168.4.c.b.85.7	✓	20
12.11	even	2		2016.4.c.f.1009.15		20
24.5	odd	2		504.4.c.e.253.14		20
24.11	even	2		2016.4.c.f.1009.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.c.b.85.7	✓	20	8.5	even	2	inner
168.4.c.b.85.8	yes	20	1.1	even	1	trivial
504.4.c.e.253.13		20	3.2	odd	2
504.4.c.e.253.14		20	24.5	odd	2
672.4.c.b.337.7		20	8.3	odd	2
672.4.c.b.337.14		20	4.3	odd	2
2016.4.c.f.1009.6		20	24.11	even	2
2016.4.c.f.1009.15		20	12.11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.472666 + 2.78865i) q^{2} -3.00000i q^{3} +(-7.55317 - 2.63620i) q^{4} -8.98099i q^{5} +(8.36596 + 1.41800i) q^{6} -7.00000 q^{7} +(10.9216 - 19.8171i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-0.472666 + 2.78865i) q^{2} -3.00000i q^{3} +(-7.55317 - 2.63620i) q^{4} -8.98099i q^{5} +(8.36596 + 1.41800i) q^{6} -7.00000 q^{7} +(10.9216 - 19.8171i) q^{8} -9.00000 q^{9} +(25.0449 + 4.24501i) q^{10} +58.9468i q^{11} +(-7.90861 + 22.6595i) q^{12} +54.8428i q^{13} +(3.30866 - 19.5206i) q^{14} -26.9430 q^{15} +(50.1009 + 39.8234i) q^{16} -111.971 q^{17} +(4.25399 - 25.0979i) q^{18} +38.6067i q^{19} +(-23.6757 + 67.8350i) q^{20} +21.0000i q^{21} +(-164.382 - 27.8621i) q^{22} +112.146 q^{23} +(-59.4514 - 32.7647i) q^{24} +44.3418 q^{25} +(-152.937 - 25.9223i) q^{26} +27.0000i q^{27} +(52.8722 + 18.4534i) q^{28} +234.402i q^{29} +(12.7350 - 75.1346i) q^{30} -180.033 q^{31} +(-134.735 + 120.891i) q^{32} +176.840 q^{33} +(52.9249 - 312.248i) q^{34} +62.8669i q^{35} +(67.9786 + 23.7258i) q^{36} -131.345i q^{37} +(-107.661 - 18.2480i) q^{38} +164.528 q^{39} +(-177.978 - 98.0866i) q^{40} -500.500 q^{41} +(-58.5617 - 9.92598i) q^{42} -495.083i q^{43} +(155.396 - 445.235i) q^{44} +80.8289i q^{45} +(-53.0077 + 312.737i) q^{46} +111.705 q^{47} +(119.470 - 150.303i) q^{48} +49.0000 q^{49} +(-20.9588 + 123.654i) q^{50} +335.913i q^{51} +(144.577 - 414.237i) q^{52} +696.410i q^{53} +(-75.2936 - 12.7620i) q^{54} +529.400 q^{55} +(-76.4511 + 138.720i) q^{56} +115.820 q^{57} +(-653.666 - 110.794i) q^{58} +407.787i q^{59} +(203.505 + 71.0271i) q^{60} +124.411i q^{61} +(85.0952 - 502.048i) q^{62} +63.0000 q^{63} +(-273.438 - 432.869i) q^{64} +492.542 q^{65} +(-83.5864 + 493.146i) q^{66} +143.848i q^{67} +(845.736 + 295.178i) q^{68} -336.439i q^{69} +(-175.314 - 29.7151i) q^{70} +251.341 q^{71} +(-98.2942 + 178.354i) q^{72} -709.691 q^{73} +(366.276 + 62.0823i) q^{74} -133.025i q^{75} +(101.775 - 291.603i) q^{76} -412.627i q^{77} +(-77.7669 + 458.812i) q^{78} +865.909 q^{79} +(357.654 - 449.956i) q^{80} +81.0000 q^{81} +(236.569 - 1395.72i) q^{82} -57.3886i q^{83} +(55.3603 - 158.617i) q^{84} +1005.61i q^{85} +(1380.61 + 234.009i) q^{86} +703.206 q^{87} +(1168.16 + 643.792i) q^{88} -765.447 q^{89} +(-225.404 - 38.2051i) q^{90} -383.899i q^{91} +(-847.060 - 295.640i) q^{92} +540.098i q^{93} +(-52.7990 + 311.506i) q^{94} +346.726 q^{95} +(362.672 + 404.204i) q^{96} +370.748 q^{97} +(-23.1606 + 136.644i) q^{98} -530.521i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 14 q^{4} + 6 q^{6} - 140 q^{7} + 10 q^{8} - 180 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 - 14 * q^4 + 6 * q^6 - 140 * q^7 + 10 * q^8 - 180 * q^9	\( 20 q + 4 q^{2} - 14 q^{4} + 6 q^{6} - 140 q^{7} + 10 q^{8} - 180 q^{9} - 84 q^{10} + 12 q^{12} - 28 q^{14} + 60 q^{15} - 134 q^{16} - 52 q^{17} - 36 q^{18} - 8 q^{20} + 8 q^{22} - 244 q^{23} - 348 q^{24} - 844 q^{25} - 332 q^{26} + 98 q^{28} + 60 q^{30} + 264 q^{31} - 46 q^{32} + 396 q^{33} - 612 q^{34} + 126 q^{36} + 884 q^{38} - 312 q^{39} - 964 q^{40} - 236 q^{41} - 42 q^{42} + 576 q^{44} + 1356 q^{46} - 432 q^{48} + 980 q^{49} - 2456 q^{50} + 1492 q^{52} - 54 q^{54} + 72 q^{55} - 70 q^{56} - 912 q^{57} - 1404 q^{58} + 684 q^{60} + 4964 q^{62} + 1260 q^{63} - 1670 q^{64} + 1744 q^{65} + 792 q^{66} + 3408 q^{68} + 588 q^{70} - 636 q^{71} - 90 q^{72} - 2784 q^{73} - 4916 q^{74} + 2664 q^{76} - 888 q^{78} + 2872 q^{79} - 1764 q^{80} + 1620 q^{81} + 2628 q^{82} - 84 q^{84} + 3328 q^{86} - 2348 q^{88} + 220 q^{89} + 756 q^{90} + 2580 q^{92} - 1704 q^{94} - 1240 q^{95} - 564 q^{96} + 4400 q^{97} + 196 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 14 * q^4 + 6 * q^6 - 140 * q^7 + 10 * q^8 - 180 * q^9 - 84 * q^10 + 12 * q^12 - 28 * q^14 + 60 * q^15 - 134 * q^16 - 52 * q^17 - 36 * q^18 - 8 * q^20 + 8 * q^22 - 244 * q^23 - 348 * q^24 - 844 * q^25 - 332 * q^26 + 98 * q^28 + 60 * q^30 + 264 * q^31 - 46 * q^32 + 396 * q^33 - 612 * q^34 + 126 * q^36 + 884 * q^38 - 312 * q^39 - 964 * q^40 - 236 * q^41 - 42 * q^42 + 576 * q^44 + 1356 * q^46 - 432 * q^48 + 980 * q^49 - 2456 * q^50 + 1492 * q^52 - 54 * q^54 + 72 * q^55 - 70 * q^56 - 912 * q^57 - 1404 * q^58 + 684 * q^60 + 4964 * q^62 + 1260 * q^63 - 1670 * q^64 + 1744 * q^65 + 792 * q^66 + 3408 * q^68 + 588 * q^70 - 636 * q^71 - 90 * q^72 - 2784 * q^73 - 4916 * q^74 + 2664 * q^76 - 888 * q^78 + 2872 * q^79 - 1764 * q^80 + 1620 * q^81 + 2628 * q^82 - 84 * q^84 + 3328 * q^86 - 2348 * q^88 + 220 * q^89 + 756 * q^90 + 2580 * q^92 - 1704 * q^94 - 1240 * q^95 - 564 * q^96 + 4400 * q^97 + 196 * q^98

Introduction

L-functions

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