LMFDB - Embedded newform 169.4.e.c.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.4.e.c.147.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.46410 - 2.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(4.00000 - 6.92820i) q^{4} +17.0000i q^{5} +(-6.92820 - 4.00000i) q^{6} +(17.3205 + 10.0000i) q^{7} +(11.5000 - 19.9186i) q^{9} +O(q^{10})$	\(q+(3.46410 - 2.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(4.00000 - 6.92820i) q^{4} +17.0000i q^{5} +(-6.92820 - 4.00000i) q^{6} +(17.3205 + 10.0000i) q^{7} +(11.5000 - 19.9186i) q^{9} +(34.0000 + 58.8897i) q^{10} +(27.7128 - 16.0000i) q^{11} -16.0000 q^{12} +80.0000 q^{14} +(29.4449 - 17.0000i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-6.50000 + 11.2583i) q^{17} -92.0000i q^{18} +(-25.9808 - 15.0000i) q^{19} +(117.779 + 68.0000i) q^{20} -40.0000i q^{21} +(64.0000 - 110.851i) q^{22} +(39.0000 + 67.5500i) q^{23} -164.000 q^{25} -100.000 q^{27} +(138.564 - 80.0000i) q^{28} +(-98.5000 - 170.607i) q^{29} +(68.0000 - 117.779i) q^{30} -74.0000i q^{31} +(221.703 + 128.000i) q^{32} +(-55.4256 - 32.0000i) q^{33} +52.0000i q^{34} +(-170.000 + 294.449i) q^{35} +(-92.0000 - 159.349i) q^{36} +(196.588 - 113.500i) q^{37} -120.000 q^{38} +(-142.894 + 82.5000i) q^{41} +(-80.0000 - 138.564i) q^{42} +(-78.0000 + 135.100i) q^{43} -256.000i q^{44} +(338.616 + 195.500i) q^{45} +(270.200 + 156.000i) q^{46} +162.000i q^{47} +(64.0000 - 110.851i) q^{48} +(28.5000 + 49.3634i) q^{49} +(-568.113 + 328.000i) q^{50} +26.0000 q^{51} +93.0000 q^{53} +(-346.410 + 200.000i) q^{54} +(272.000 + 471.118i) q^{55} +60.0000i q^{57} +(-682.428 - 394.000i) q^{58} +(-748.246 - 432.000i) q^{59} -272.000i q^{60} +(-72.5000 + 125.574i) q^{61} +(-148.000 - 256.344i) q^{62} +(398.372 - 230.000i) q^{63} +512.000 q^{64} -256.000 q^{66} +(746.514 - 431.000i) q^{67} +(52.0000 + 90.0666i) q^{68} +(78.0000 - 135.100i) q^{69} +1360.00i q^{70} +(-566.381 - 327.000i) q^{71} -215.000i q^{73} +(454.000 - 786.351i) q^{74} +(164.000 + 284.056i) q^{75} +(-207.846 + 120.000i) q^{76} +640.000 q^{77} -76.0000 q^{79} +(-942.236 + 544.000i) q^{80} +(-210.500 - 364.597i) q^{81} +(-330.000 + 571.577i) q^{82} +628.000i q^{83} +(-277.128 - 160.000i) q^{84} +(-191.392 - 110.500i) q^{85} +624.000i q^{86} +(-197.000 + 341.214i) q^{87} +(230.363 - 133.000i) q^{89} +1564.00 q^{90} +624.000 q^{92} +(-128.172 + 74.0000i) q^{93} +(324.000 + 561.184i) q^{94} +(255.000 - 441.673i) q^{95} -512.000i q^{96} +(-206.114 - 119.000i) q^{97} +(197.454 + 114.000i) q^{98} -736.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 16 * q^4 + 46 * q^9	$ 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9} + 136 q^{10} - 64 q^{12} + 320 q^{14} + 128 q^{16} - 26 q^{17} + 256 q^{22} + 156 q^{23} - 656 q^{25} - 400 q^{27} - 394 q^{29} + 272 q^{30} - 680 q^{35} - 368 q^{36} - 480 q^{38} - 320 q^{42} - 312 q^{43} + 256 q^{48} + 114 q^{49} + 104 q^{51} + 372 q^{53} + 1088 q^{55} - 290 q^{61} - 592 q^{62} + 2048 q^{64} - 1024 q^{66} + 208 q^{68} + 312 q^{69} + 1816 q^{74} + 656 q^{75} + 2560 q^{77} - 304 q^{79} - 842 q^{81} - 1320 q^{82} - 788 q^{87} + 6256 q^{90} + 2496 q^{92} + 1296 q^{94} + 1020 q^{95}+O(q^{100}) $ 4 * q - 4 * q^3 + 16 * q^4 + 46 * q^9 + 136 * q^10 - 64 * q^12 + 320 * q^14 + 128 * q^16 - 26 * q^17 + 256 * q^22 + 156 * q^23 - 656 * q^25 - 400 * q^27 - 394 * q^29 + 272 * q^30 - 680 * q^35 - 368 * q^36 - 480 * q^38 - 320 * q^42 - 312 * q^43 + 256 * q^48 + 114 * q^49 + 104 * q^51 + 372 * q^53 + 1088 * q^55 - 290 * q^61 - 592 * q^62 + 2048 * q^64 - 1024 * q^66 + 208 * q^68 + 312 * q^69 + 1816 * q^74 + 656 * q^75 + 2560 * q^77 - 304 * q^79 - 842 * q^81 - 1320 * q^82 - 788 * q^87 + 6256 * q^90 + 2496 * q^92 + 1296 * q^94 + 1020 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.46410	−	2.00000i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$2$	3.46410	−	2.00000i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$3$	−1.00000	−	1.73205i	−0.192450	−	0.333333i	0.753612	−	0.657320i	$-0.228310\pi$
$3$	−1.00000	−	1.73205i	−0.192450	−	0.333333i	−0.946062	+	0.323987i	$0.894977\pi$
$4$	4.00000	−	6.92820i	0.500000	−	0.866025i
$5$			17.0000i			1.52053i	0.649615	+	0.760263i	$0.274930\pi$
$5$			17.0000i			1.52053i	−0.649615	+	0.760263i	$0.725070\pi$
$6$	−6.92820	−	4.00000i	−0.471405	−	0.272166i
$7$	17.3205	+	10.0000i	0.935220	+	0.539949i	0.888459	−	0.458957i	$-0.151777\pi$
$7$	17.3205	+	10.0000i	0.935220	+	0.539949i	0.0467610	+	0.998906i	$0.485110\pi$
$8$		0			0
$9$	11.5000	−	19.9186i	0.425926	−	0.737725i
$10$	34.0000	+	58.8897i	1.07517	+	1.86226i
$11$	27.7128	−	16.0000i	0.759612	−	0.438562i	−0.0695447	−	0.997579i	$-0.522155\pi$
$11$	27.7128	−	16.0000i	0.759612	−	0.438562i	0.829156	+	0.559017i	$0.188821\pi$
$12$	−16.0000			−0.384900
$13$		0			0
$13$		0			0
$14$	80.0000			1.52721
$15$	29.4449	−	17.0000i	0.506842	−	0.292625i
$16$	32.0000	+	55.4256i	0.500000	+	0.866025i
$17$	−6.50000	+	11.2583i	−0.0927342	+	0.160620i	−0.908661	−	0.417535i	$-0.862894\pi$
$17$	−6.50000	+	11.2583i	−0.0927342	+	0.160620i	0.815927	+	0.578156i	$0.196227\pi$
$18$		−	92.0000i		−	1.20470i
$19$	−25.9808	−	15.0000i	−0.313705	−	0.181118i	0.334878	−	0.942261i	$-0.391305\pi$
$19$	−25.9808	−	15.0000i	−0.313705	−	0.181118i	−0.648583	+	0.761144i	$0.724638\pi$
$20$	117.779	+	68.0000i	1.31681	+	0.760263i
$21$		−	40.0000i		−	0.415653i
$22$	64.0000	−	110.851i	0.620220	−	1.07425i
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	0.986872	−	0.161506i	$-0.0516350\pi$
$23$	39.0000	+	67.5500i	0.353568	+	0.612398i	−0.633304	+	0.773903i	$0.718302\pi$
$24$		0			0
$25$	−164.000			−1.31200
$26$		0			0
$27$	−100.000			−0.712778
$28$	138.564	−	80.0000i	0.935220	−	0.539949i
$29$	−98.5000	−	170.607i	−0.630724	−	1.09245i	−0.987404	−	0.158219i	$-0.949425\pi$
$29$	−98.5000	−	170.607i	−0.630724	−	1.09245i	0.356680	−	0.934227i	$-0.383909\pi$
$30$	68.0000	−	117.779i	0.413835	−	0.716783i
$31$		−	74.0000i		−	0.428735i	−0.976753	−	0.214368i	$-0.931231\pi$
$31$		−	74.0000i		−	0.428735i	0.976753	−	0.214368i	$-0.0687691\pi$
$32$	221.703	+	128.000i	1.22474	+	0.707107i
$33$	−55.4256	−	32.0000i	−0.292375	−	0.168803i
$34$			52.0000i			0.262292i
$35$	−170.000	+	294.449i	−0.821007	+	1.42203i
$36$	−92.0000	−	159.349i	−0.425926	−	0.737725i
$37$	196.588	−	113.500i	0.873482	−	0.504305i	0.00497814	−	0.999988i	$-0.498415\pi$
$37$	196.588	−	113.500i	0.873482	−	0.504305i	0.868504	+	0.495683i	$0.165082\pi$
$38$	−120.000			−0.512278
$39$		0			0
$40$		0			0
$41$	−142.894	+	82.5000i	−0.544301	+	0.314252i	−0.746820	−	0.665026i	$-0.768420\pi$
$41$	−142.894	+	82.5000i	−0.544301	+	0.314252i	0.202520	+	0.979278i	$0.435087\pi$
$42$	−80.0000	−	138.564i	−0.293911	−	0.509069i
$43$	−78.0000	+	135.100i	−0.276625	+	0.479129i	−0.970544	−	0.240924i	$-0.922549\pi$
$43$	−78.0000	+	135.100i	−0.276625	+	0.479129i	0.693919	+	0.720053i	$0.255883\pi$
$44$		−	256.000i		−	0.877124i
$45$	338.616	+	195.500i	1.12173	+	0.647632i
$46$	270.200	+	156.000i	0.866061	+	0.500021i
$47$			162.000i			0.502769i	0.967887	+	0.251384i	$0.0808858\pi$
$47$			162.000i			0.502769i	−0.967887	+	0.251384i	$0.919114\pi$
$48$	64.0000	−	110.851i	0.192450	−	0.333333i
$49$	28.5000	+	49.3634i	0.0830904	+	0.143917i
$50$	−568.113	+	328.000i	−1.60687	+	0.927724i
$51$	26.0000			0.0713868
$52$		0			0
$53$	93.0000			0.241029			0.120514	−	0.992712i	$-0.461546\pi$
$53$	93.0000			0.241029			0.120514	+	0.992712i	$0.461546\pi$
$54$	−346.410	+	200.000i	−0.872971	+	0.504010i
$55$	272.000	+	471.118i	0.666845	+	1.15501i
$56$		0			0
$57$			60.0000i			0.139424i
$58$	−682.428	−	394.000i	−1.54495	−	0.891978i
$59$	−748.246	−	432.000i	−1.65107	−	0.953248i	−0.976632	−	0.214919i	$-0.931051\pi$
$59$	−748.246	−	432.000i	−1.65107	−	0.953248i	−0.674442	−	0.738328i	$-0.735616\pi$
$60$		−	272.000i		−	0.585251i
$61$	−72.5000	+	125.574i	−0.152175	+	0.263575i	−0.932027	−	0.362389i	$-0.881961\pi$
$61$	−72.5000	+	125.574i	−0.152175	+	0.263575i	0.779852	+	0.625964i	$0.215294\pi$
$62$	−148.000	−	256.344i	−0.303162	−	0.525091i
$63$	398.372	−	230.000i	0.796668	−	0.459957i
$64$	512.000			1.00000
$65$		0			0
$66$	−256.000			−0.477446
$67$	746.514	−	431.000i	1.36121	−	0.785896i	0.371427	−	0.928462i	$-0.378869\pi$
$67$	746.514	−	431.000i	1.36121	−	0.785896i	0.989785	+	0.142566i	$0.0455354\pi$
$68$	52.0000	+	90.0666i	0.0927342	+	0.160620i
$69$	78.0000	−	135.100i	0.136088	−	0.235712i
$70$			1360.00i			2.32216i
$71$	−566.381	−	327.000i	−0.946718	−	0.546588i	−0.0546585	−	0.998505i	$-0.517407\pi$
$71$	−566.381	−	327.000i	−0.946718	−	0.546588i	−0.892060	+	0.451917i	$0.850740\pi$
$72$		0			0
$73$		−	215.000i		−	0.344710i	−0.985035	−	0.172355i	$-0.944862\pi$
$73$		−	215.000i		−	0.344710i	0.985035	−	0.172355i	$-0.0551377\pi$
$74$	454.000	−	786.351i	0.713195	−	1.23529i
$75$	164.000	+	284.056i	0.252495	+	0.437333i
$76$	−207.846	+	120.000i	−0.313705	+	0.181118i
$77$	640.000			0.947205
$78$		0			0
$79$	−76.0000			−0.108236			−0.0541182	−	0.998535i	$-0.517235\pi$
$79$	−76.0000			−0.108236			−0.0541182	+	0.998535i	$0.517235\pi$
$80$	−942.236	+	544.000i	−1.31681	+	0.760263i
$81$	−210.500	−	364.597i	−0.288752	−	0.500133i
$82$	−330.000	+	571.577i	−0.444420	+	0.769757i
$83$			628.000i			0.830505i	0.909706	+	0.415253i	$0.136307\pi$
$83$			628.000i			0.830505i	−0.909706	+	0.415253i	$0.863693\pi$
$84$	−277.128	−	160.000i	−0.359966	−	0.207827i
$85$	−191.392	−	110.500i	−0.244227	−	0.141005i
$86$			624.000i			0.782415i
$87$	−197.000	+	341.214i	−0.242766	+	0.420483i
$88$		0			0
$89$	230.363	−	133.000i	0.274364	−	0.158404i	−0.356505	−	0.934293i	$-0.616032\pi$
$89$	230.363	−	133.000i	0.274364	−	0.158404i	0.630869	+	0.775889i	$0.282698\pi$
$90$	1564.00			1.83178
$91$		0			0
$92$	624.000			0.707136
$93$	−128.172	+	74.0000i	−0.142912	+	0.0825101i
$94$	324.000	+	561.184i	0.355511	+	0.615763i
$95$	255.000	−	441.673i	0.275394	−	0.476997i
$96$		−	512.000i		−	0.544331i
$97$	−206.114	−	119.000i	−0.215750	−	0.124563i	0.388231	−	0.921562i	$-0.373086\pi$
$97$	−206.114	−	119.000i	−0.215750	−	0.124563i	−0.603981	+	0.796999i	$0.706420\pi$
$98$	197.454	+	114.000i	0.203529	+	0.117508i
$99$		−	736.000i		−	0.747180i
$100$	−656.000	+	1136.23i	−0.656000	+	1.13623i
$101$	−409.500	−	709.275i	−0.403433	−	0.698767i	0.590704	−	0.806888i	$-0.298850\pi$
$101$	−409.500	−	709.275i	−0.403433	−	0.698767i	−0.994138	+	0.108121i	$0.965517\pi$
$102$	90.0666	−	52.0000i	0.0874307	−	0.0504781i
$103$	−1638.00			−1.56696			−0.783480	−	0.621417i	$-0.786557\pi$
$103$	−1638.00			−1.56696			−0.783480	+	0.621417i	$0.786557\pi$
$104$		0			0
$105$	680.000			0.632011
$106$	322.161	−	186.000i	0.295199	−	0.170433i
$107$	−261.000	−	452.065i	−0.235811	−	0.408437i	0.723697	−	0.690118i	$-0.242441\pi$
$107$	−261.000	−	452.065i	−0.235811	−	0.408437i	−0.959508	+	0.281681i	$0.909108\pi$
$108$	−400.000	+	692.820i	−0.356389	+	0.617284i
$109$		−	1634.00i		−	1.43586i	−0.696115	−	0.717930i	$-0.745090\pi$
$109$		−	1634.00i		−	1.43586i	0.696115	−	0.717930i	$-0.254910\pi$
$110$	1884.47	+	1088.00i	1.63343	+	0.943061i
$111$	−393.176	−	227.000i	−0.336203	−	0.194107i
$112$			1280.00i			1.07990i
$113$	−163.500	+	283.190i	−0.136113	+	0.235755i	−0.926022	−	0.377469i	$-0.876794\pi$
$113$	−163.500	+	283.190i	−0.136113	+	0.235755i	0.789909	+	0.613224i	$0.210128\pi$
$114$	120.000	+	207.846i	0.0985880	+	0.170759i
$115$	−1148.35	+	663.000i	−0.931167	+	0.537609i
$116$	−1576.00			−1.26145
$117$		0			0
$118$	−3456.00			−2.69619
$119$	−225.167	+	130.000i	−0.173454	+	0.100144i
$120$		0			0
$121$	−153.500	+	265.870i	−0.115327	+	0.199752i
$122$			580.000i			0.430416i
$123$	285.788	+	165.000i	0.209501	+	0.120956i
$124$	−512.687	−	296.000i	−0.371296	−	0.214368i
$125$		−	663.000i		−	0.474404i
$126$	920.000	−	1593.49i	0.650477	−	1.12666i
$127$	−1079.00	−	1868.88i	−0.753904	−	1.30580i	−0.945918	−	0.324407i	$-0.894835\pi$
$127$	−1079.00	−	1868.88i	−0.753904	−	1.30580i	0.192014	−	0.981392i	$-0.438498\pi$
$128$		0			0
$129$	312.000			0.212946
$130$		0			0
$131$	730.000			0.486873			0.243437	−	0.969917i	$-0.421725\pi$
$131$	730.000			0.486873			0.243437	+	0.969917i	$0.421725\pi$
$132$	−443.405	+	256.000i	−0.292375	+	0.168803i
$133$	−300.000	−	519.615i	−0.195589	−	0.338770i
$134$	1724.00	−	2986.06i	1.11142	−	1.92504i
$135$		−	1700.00i		−	1.08380i
$136$		0			0
$137$	1447.13	+	835.500i	0.902456	+	0.521033i	0.877996	−	0.478667i	$-0.158880\pi$
$137$	1447.13	+	835.500i	0.902456	+	0.521033i	0.0244601	+	0.999701i	$0.492213\pi$
$138$		−	624.000i		−	0.384916i
$139$	−456.000	+	789.815i	−0.278255	+	0.481951i	−0.970951	−	0.239278i	$-0.923089\pi$
$139$	−456.000	+	789.815i	−0.278255	+	0.481951i	0.692696	+	0.721229i	$0.256423\pi$
$140$	1360.00	+	2355.59i	0.821007	+	1.42203i
$141$	280.592	−	162.000i	0.167590	−	0.0967579i
$142$	−2616.00			−1.54598
$143$		0			0
$144$	1472.00			0.851852
$145$	2900.32	−	1674.50i	1.66109	−	0.959032i
$146$	−430.000	−	744.782i	−0.243747	−	0.422182i
$147$	57.0000	−	98.7269i	0.0319815	−	0.0553936i
$148$		−	1816.00i		−	1.00861i
$149$	1831.64	+	1057.50i	1.00707	+	0.581435i	0.910334	−	0.413875i	$-0.135825\pi$
$149$	1831.64	+	1057.50i	1.00707	+	0.581435i	0.0967407	+	0.995310i	$0.469158\pi$
$150$	1136.23	+	656.000i	0.618483	+	0.357081i
$151$		−	514.000i		−	0.277011i	−0.990362	−	0.138506i	$-0.955770\pi$
$151$		−	514.000i		−	0.277011i	0.990362	−	0.138506i	$-0.0442299\pi$
$152$		0			0
$153$	149.500	+	258.942i	0.0789958	+	0.136825i
$154$	2217.03	−	1280.00i	1.16008	−	0.669775i
$155$	1258.00			0.651903
$156$		0			0
$157$	2901.00			1.47468			0.737341	−	0.675521i	$-0.236081\pi$
$157$	2901.00			1.47468			0.737341	+	0.675521i	$0.236081\pi$
$158$	−263.272	+	152.000i	−0.132562	+	0.0765346i
$159$	−93.0000	−	161.081i	−0.0463860	−	0.0803430i
$160$	−2176.00	+	3768.94i	−1.07517	+	1.86226i
$161$			1560.00i			0.763635i
$162$	−1458.39	−	842.000i	−0.707294	−	0.408357i
$163$	2043.82	+	1180.00i	0.982112	+	0.567023i	0.902907	−	0.429835i	$-0.141428\pi$
$163$	2043.82	+	1180.00i	0.982112	+	0.567023i	0.0792052	+	0.996858i	$0.474762\pi$
$164$			1320.00i			0.628504i
$165$	544.000	−	942.236i	0.256669	−	0.444563i
$166$	1256.00	+	2175.46i	0.587256	+	1.01716i
$167$	−242.487	+	140.000i	−0.112361	+	0.0648714i	−0.555127	−	0.831766i	$-0.687330\pi$
$167$	−242.487	+	140.000i	−0.112361	+	0.0648714i	0.442767	+	0.896637i	$0.353997\pi$
$168$		0			0
$169$		0			0
$170$	−884.000			−0.398822
$171$	−597.558	+	345.000i	−0.267230	+	0.154285i
$172$	624.000	+	1080.80i	0.276625	+	0.479129i
$173$	663.000	−	1148.35i	0.291370	−	0.504667i	−0.682764	−	0.730639i	$-0.739222\pi$
$173$	663.000	−	1148.35i	0.291370	−	0.504667i	0.974134	+	0.225972i	$0.0725557\pi$
$174$			1576.00i			0.686645i
$175$	−2840.56	−	1640.00i	−1.22701	−	0.708413i
$176$	1773.62	+	1024.00i	0.759612	+	0.438562i
$177$			1728.00i			0.733810i
$178$	532.000	−	921.451i	0.224017	−	0.388009i
$179$	2132.00	+	3692.73i	0.890241	+	1.54194i	0.839586	+	0.543227i	$0.182798\pi$
$179$	2132.00	+	3692.73i	0.890241	+	1.54194i	0.0506550	+	0.998716i	$0.483869\pi$
$180$	2708.93	−	1564.00i	1.12173	−	0.647632i
$181$	403.000			0.165496			0.0827479	−	0.996571i	$-0.473630\pi$
$181$	403.000			0.165496			0.0827479	+	0.996571i	$0.473630\pi$
$182$		0			0
$183$	290.000			0.117144
$184$		0			0
$185$	1929.50	+	3341.99i	0.766809	+	1.32815i
$186$	−296.000	+	512.687i	−0.116687	+	0.202108i
$187$			416.000i			0.162679i
$188$	1122.37	+	648.000i	0.435410	+	0.251384i
$189$	−1732.05	−	1000.00i	−0.666604	−	0.384864i
$190$		−	2040.00i		−	0.778932i
$191$	623.000	−	1079.07i	0.236014	−	0.408788i	−0.723553	−	0.690269i	$-0.757492\pi$
$191$	623.000	−	1079.07i	0.236014	−	0.408788i	0.959567	+	0.281481i	$0.0908255\pi$
$192$	−512.000	−	886.810i	−0.192450	−	0.333333i
$193$	−231.229	+	133.500i	−0.0862394	+	0.0497904i	−0.542500	−	0.840056i	$-0.682522\pi$
$193$	−231.229	+	133.500i	−0.0862394	+	0.0497904i	0.456260	+	0.889846i	$0.349189\pi$
$194$	−952.000			−0.352318
$195$		0			0
$196$	456.000			0.166181
$197$	1106.78	−	639.000i	0.400278	−	0.231101i	−0.286326	−	0.958132i	$-0.592434\pi$
$197$	1106.78	−	639.000i	0.400278	−	0.231101i	0.686604	+	0.727032i	$0.259101\pi$
$198$	−1472.00	−	2549.58i	−0.528336	−	0.915104i
$199$	2119.00	−	3670.22i	0.754834	−	1.30741i	−0.190623	−	0.981663i	$-0.561051\pi$
$199$	2119.00	−	3670.22i	0.754834	−	1.30741i	0.945457	−	0.325747i	$-0.105616\pi$
$200$		0			0
$201$	−1493.03	−	862.000i	−0.523931	−	0.302492i
$202$	−2837.10	−	1638.00i	−0.988206	−	0.570541i
$203$		−	3940.00i		−	1.36224i
$204$	104.000	−	180.133i	0.0356934	−	0.0618228i
$205$	−1402.50	−	2429.20i	−0.477829	−	0.827623i
$206$	−5674.20	+	3276.00i	−1.91913	+	1.10801i
$207$	1794.00			0.602375
$208$		0			0
$209$	−960.000			−0.317725
$210$	2355.59	−	1360.00i	0.774053	−	0.446900i
$211$	−1535.00	−	2658.70i	−0.500823	−	0.867452i	−1.00000		0.000951154i	$-0.999697\pi$
$211$	−1535.00	−	2658.70i	−0.500823	−	0.867452i	0.499176	−	0.866501i	$-0.333636\pi$
$212$	372.000	−	644.323i	0.120514	−	0.208737i
$213$			1308.00i			0.420764i
$214$	−1808.26	−	1044.00i	−0.577618	−	0.333488i
$215$	−2296.70	−	1326.00i	−0.728528	−	0.420616i
$216$		0			0
$217$	740.000	−	1281.72i	0.231495	−	0.400962i
$218$	−3268.00	−	5660.34i	−1.01531	−	1.75856i
$219$	−372.391	+	215.000i	−0.114903	+	0.0663395i
$220$	4352.00			1.33369
$221$		0			0
$222$	−1816.00			−0.549018
$223$	−4657.48	+	2689.00i	−1.39860	+	0.807483i	−0.994246	−	0.107119i	$-0.965838\pi$
$223$	−4657.48	+	2689.00i	−1.39860	+	0.807483i	−0.404356	+	0.914602i	$0.632504\pi$
$224$	2560.00	+	4434.05i	0.763604	+	1.32260i
$225$	−1886.00	+	3266.65i	−0.558815	+	0.967896i
$226$			1308.00i			0.384986i
$227$	3441.58	+	1987.00i	1.00628	+	0.580977i	0.910101	−	0.414387i	$-0.136004\pi$
$227$	3441.58	+	1987.00i	1.00628	+	0.580977i	0.0961811	+	0.995364i	$0.469337\pi$
$228$	415.692	+	240.000i	0.120745	+	0.0697122i
$229$			6298.00i			1.81740i	0.417455	+	0.908698i	$0.362922\pi$
$229$			6298.00i			1.81740i	−0.417455	+	0.908698i	$0.637078\pi$
$230$	−2652.00	+	4593.40i	−0.760294	+	1.31687i
$231$	−640.000	−	1108.51i	−0.182290	−	0.315735i
$232$		0			0
$233$	−4030.00			−1.13311			−0.566554	−	0.824025i	$-0.691724\pi$
$233$	−4030.00			−1.13311			−0.566554	+	0.824025i	$0.691724\pi$
$234$		0			0
$235$	−2754.00			−0.764473
$236$	−5985.97	+	3456.00i	−1.65107	+	0.953248i
$237$	76.0000	+	131.636i	0.0208301	+	0.0360788i
$238$	−520.000	+	900.666i	−0.141624	+	0.245301i
$239$		−	984.000i		−	0.266317i	−0.991095	−	0.133158i	$-0.957488\pi$
$239$		−	984.000i		−	0.266317i	0.991095	−	0.133158i	$-0.0425119\pi$
$240$	1884.47	+	1088.00i	0.506842	+	0.292625i
$241$	816.662	+	471.500i	0.218281	+	0.126025i	0.605154	−	0.796108i	$-0.293111\pi$
$241$	816.662	+	471.500i	0.218281	+	0.126025i	−0.386873	+	0.922133i	$0.626445\pi$
$242$			1228.00i			0.326194i
$243$	−1771.00	+	3067.46i	−0.467530	+	0.809785i
$244$	580.000	+	1004.59i	0.152175	+	0.263575i
$245$	−839.179	+	484.500i	−0.218829	+	0.126341i
$246$	1320.00			0.342114
$247$		0			0
$248$		0			0
$249$	1087.73	−	628.000i	0.276835	−	0.159831i
$250$	−1326.00	−	2296.70i	−0.335454	−	0.581024i
$251$	−1365.00	+	2364.25i	−0.343259	+	0.594542i	−0.985036	−	0.172349i	$-0.944864\pi$
$251$	−1365.00	+	2364.25i	−0.343259	+	0.594542i	0.641777	+	0.766891i	$0.278198\pi$
$252$		−	3680.00i		−	0.919914i
$253$	2161.60	+	1248.00i	0.537149	+	0.310123i
$254$	−7475.53	−	4316.00i	−1.84668	−	1.06618i
$255$			442.000i			0.108546i
$256$	−2048.00	+	3547.24i	−0.500000	+	0.866025i
$257$	−942.500	−	1632.46i	−0.228761	−	0.396225i	0.728680	−	0.684854i	$-0.240134\pi$
$257$	−942.500	−	1632.46i	−0.228761	−	0.396225i	−0.957441	+	0.288629i	$0.906801\pi$
$258$	1080.80	−	624.000i	0.260805	−	0.150576i
$259$	4540.00			1.08920
$260$		0			0
$261$	−4531.00			−1.07457
$262$	2528.79	−	1460.00i	0.596296	−	0.344271i
$263$	−2016.00	−	3491.81i	−0.472669	−	0.818686i	0.526842	−	0.849963i	$-0.323376\pi$
$263$	−2016.00	−	3491.81i	−0.472669	−	0.818686i	−0.999511	+	0.0312769i	$0.990043\pi$
$264$		0			0
$265$			1581.00i			0.366491i
$266$	−2078.46	−	1200.00i	−0.479093	−	0.276604i
$267$	−460.726	−	266.000i	−0.105603	−	0.0609698i
$268$		−	6896.00i		−	1.57179i
$269$	−2003.00	+	3469.30i	−0.453997	+	0.786345i	−0.998630	−	0.0523292i	$-0.983335\pi$
$269$	−2003.00	+	3469.30i	−0.453997	+	0.786345i	0.544633	+	0.838674i	$0.316669\pi$
$270$	−3400.00	−	5888.97i	−0.766361	−	1.32738i
$271$	3720.45	−	2148.00i	0.833952	−	0.481482i	−0.0212520	−	0.999774i	$-0.506765\pi$
$271$	3720.45	−	2148.00i	0.833952	−	0.481482i	0.855204	+	0.518292i	$0.173432\pi$
$272$	−832.000			−0.185468
$273$		0			0
$274$	6684.00			1.47371
$275$	−4544.90	+	2624.00i	−0.996610	+	0.575393i
$276$	−624.000	−	1080.80i	−0.136088	−	0.235712i
$277$	−2775.50	+	4807.31i	−0.602035	+	1.04275i	0.390478	+	0.920612i	$0.372310\pi$
$277$	−2775.50	+	4807.31i	−0.602035	+	1.04275i	−0.992513	+	0.122142i	$0.961024\pi$
$278$			3648.00i			0.787023i
$279$	−1473.98	−	851.000i	−0.316289	−	0.182609i
$280$		0			0
$281$			5557.00i			1.17973i	0.807504	+	0.589863i	$0.200818\pi$
$281$			5557.00i			1.17973i	−0.807504	+	0.589863i	$0.799182\pi$
$282$	648.000	−	1122.37i	0.136836	−	0.237007i
$283$	1560.00	+	2702.00i	0.327676	+	0.567552i	0.982050	−	0.188619i	$-0.0604012\pi$
$283$	1560.00	+	2702.00i	0.327676	+	0.567552i	−0.654374	+	0.756171i	$0.727068\pi$
$284$	−4531.04	+	2616.00i	−0.946718	+	0.546588i
$285$	−1020.00			−0.211999
$286$		0			0
$287$	−3300.00			−0.678721
$288$	5099.16	−	2944.00i	1.04330	−	0.602350i
$289$	2372.00	+	4108.42i	0.482801	+	0.836235i
$290$	6698.00	−	11601.3i	1.35628	−	2.34914i
$291$			476.000i			0.0958887i
$292$	−1489.56	−	860.000i	−0.298528	−	0.172355i
$293$	7188.88	+	4150.50i	1.43337	+	0.827559i	0.997376	−	0.0723887i	$-0.0230622\pi$
$293$	7188.88	+	4150.50i	1.43337	+	0.827559i	0.435998	+	0.899948i	$0.356396\pi$
$294$		−	456.000i		−	0.0904573i
$295$	7344.00	−	12720.2i	1.44944	−	2.51050i
$296$		0			0
$297$	−2771.28	+	1600.00i	−0.541435	+	0.312597i
$298$	8460.00			1.64455
$299$		0			0
$300$	2624.00			0.504989
$301$	−2702.00	+	1560.00i	−0.517411	+	0.298727i
$302$	−1028.00	−	1780.55i	−0.195877	−	0.339268i
$303$	−819.000	+	1418.55i	−0.155282	+	0.268956i
$304$		−	1920.00i		−	0.362235i
$305$	−2134.75	−	1232.50i	−0.400772	−	0.231386i
$306$	1035.77	+	598.000i	0.193499	+	0.111717i
$307$		−	8678.00i		−	1.61329i	−0.591037	−	0.806644i	$-0.701281\pi$
$307$		−	8678.00i		−	1.61329i	0.591037	−	0.806644i	$-0.298719\pi$
$308$	2560.00	−	4434.05i	0.473602	−	0.820303i
$309$	1638.00	+	2837.10i	0.301562	+	0.522320i
$310$	4357.84	−	2516.00i	0.798415	−	0.460965i
$311$	−8658.00			−1.57862			−0.789309	−	0.613996i	$-0.789561\pi$
$311$	−8658.00			−1.57862			−0.789309	+	0.613996i	$0.789561\pi$
$312$		0			0
$313$	−5250.00			−0.948075			−0.474038	−	0.880505i	$-0.657204\pi$
$313$	−5250.00			−0.948075			−0.474038	+	0.880505i	$0.657204\pi$
$314$	10049.4	−	5802.00i	1.80611	−	1.04276i
$315$	3910.00	+	6772.32i	0.699376	+	1.21136i
$316$	−304.000	+	526.543i	−0.0541182	+	0.0937354i
$317$			6413.00i			1.13625i	0.822944	+	0.568123i	$0.192330\pi$
$317$			6413.00i			1.13625i	−0.822944	+	0.568123i	$0.807670\pi$
$318$	−644.323	−	372.000i	−0.113622	−	0.0655998i
$319$	−5459.42	−	3152.00i	−0.958210	−	0.553223i
$320$			8704.00i			1.52053i
$321$	−522.000	+	904.131i	−0.0907639	+	0.157208i
$322$	3120.00	+	5404.00i	0.539971	+	0.935258i
$323$	337.750	−	195.000i	0.0581824	−	0.0335916i
$324$	−3368.00			−0.577503
$325$		0			0
$326$	9440.00			1.60378
$327$	−2830.17	+	1634.00i	−0.478620	+	0.276332i
$328$		0			0
$329$	−1620.00	+	2805.92i	−0.271470	+	0.470199i
$330$		−	4352.00i		−	0.725969i
$331$	−3020.70	−	1744.00i	−0.501609	−	0.289604i	0.227769	−	0.973715i	$-0.426857\pi$
$331$	−3020.70	−	1744.00i	−0.501609	−	0.289604i	−0.729378	+	0.684111i	$0.760190\pi$
$332$	4350.91	+	2512.00i	0.719239	+	0.415253i
$333$		−	5221.00i		−	0.859186i
$334$	−560.000	+	969.948i	−0.0917420	+	0.158902i
$335$	7327.00	+	12690.7i	1.19498	+	2.06976i
$336$	2217.03	−	1280.00i	0.359966	−	0.207827i
$337$	1833.00			0.296290			0.148145	−	0.988966i	$-0.452670\pi$
$337$	1833.00			0.296290			0.148145	+	0.988966i	$0.452670\pi$
$338$		0			0
$339$	654.000			0.104780
$340$	−1531.13	+	884.000i	−0.244227	+	0.141005i
$341$	−1184.00	−	2050.75i	−0.188027	−	0.325672i
$342$	−1380.00	+	2390.23i	−0.218193	+	0.377921i
$343$		−	5720.00i		−	0.900440i
$344$		0			0
$345$	2296.70	+	1326.00i	0.358406	+	0.206926i
$346$		−	5304.00i		−	0.824118i
$347$	−3615.00	+	6261.36i	−0.559260	+	0.968667i	0.438298	+	0.898830i	$0.355581\pi$
$347$	−3615.00	+	6261.36i	−0.559260	+	0.968667i	−0.997558	+	0.0698377i	$0.977752\pi$
$348$	1576.00	+	2729.71i	0.242766	+	0.420483i
$349$	4553.56	−	2629.00i	0.698414	−	0.403230i	−0.108342	−	0.994114i	$-0.534554\pi$
$349$	4553.56	−	2629.00i	0.698414	−	0.403230i	0.806757	+	0.590884i	$0.201221\pi$
$350$	−13120.0			−2.00370
$351$		0			0
$352$	8192.00			1.24044
$353$	2739.24	−	1581.50i	0.413017	−	0.238455i	−0.279068	−	0.960271i	$-0.590026\pi$
$353$	2739.24	−	1581.50i	0.413017	−	0.238455i	0.692085	+	0.721816i	$0.256692\pi$
$354$	3456.00	+	5985.97i	0.518882	+	0.898730i
$355$	5559.00	−	9628.47i	0.831102	−	1.43951i
$356$		−	2128.00i		−	0.316808i
$357$	450.333	+	260.000i	0.0667624	+	0.0385453i
$358$	14770.9	+	8528.00i	2.18064	+	1.25899i
$359$			10068.0i			1.48014i	0.672532	+	0.740068i	$0.265207\pi$
$359$			10068.0i			1.48014i	−0.672532	+	0.740068i	$0.734793\pi$
$360$		0			0
$361$	−2979.50	−	5160.65i	−0.434393	−	0.752390i
$362$	1396.03	−	806.000i	0.202690	−	0.117023i
$363$	614.000			0.0887786
$364$		0			0
$365$	3655.00			0.524141
$366$	1004.59	−	580.000i	0.143472	−	0.0828336i
$367$	−3719.00	−	6441.50i	−0.528965	−	0.916195i	−0.999429	−	0.0337755i	$-0.989247\pi$
$367$	−3719.00	−	6441.50i	−0.528965	−	0.916195i	0.470464	−	0.882419i	$-0.344086\pi$
$368$	−2496.00	+	4323.20i	−0.353568	+	0.612398i
$369$			3795.00i			0.535392i
$370$	13368.0	+	7718.00i	1.87829	+	1.08443i
$371$	1610.81	+	930.000i	0.225415	+	0.130143i
$372$			1184.00i			0.165020i
$373$	4841.50	−	8385.72i	0.672073	−	1.16407i	−0.305242	−	0.952275i	$-0.598737\pi$
$373$	4841.50	−	8385.72i	0.672073	−	1.16407i	0.977315	−	0.211790i	$-0.0679294\pi$
$374$	832.000	+	1441.07i	0.115031	+	0.199240i
$375$	−1148.35	+	663.000i	−0.158135	+	0.0912991i
$376$		0			0
$377$		0			0
$378$	−8000.00			−1.08856
$379$	−919.719	+	531.000i	−0.124651	+	0.0719674i	−0.561029	−	0.827796i	$-0.689594\pi$
$379$	−919.719	+	531.000i	−0.124651	+	0.0719674i	0.436378	+	0.899763i	$0.356261\pi$
$380$	−2040.00	−	3533.38i	−0.275394	−	0.476997i
$381$	−2158.00	+	3737.77i	−0.290178	+	0.502602i
$382$		−	4984.00i		−	0.667549i
$383$	3058.80	+	1766.00i	0.408087	+	0.235609i	0.689968	−	0.723840i	$-0.257625\pi$
$383$	3058.80	+	1766.00i	0.408087	+	0.235609i	−0.281880	+	0.959450i	$0.590958\pi$
$384$		0			0
$385$			10880.0i			1.44025i
$386$	−534.000	+	924.915i	−0.0704142	+	0.121961i
$387$	1794.00	+	3107.30i	0.235644	+	0.408147i
$388$	−1648.91	+	952.000i	−0.215750	+	0.124563i
$389$	11063.0			1.44194			0.720972	−	0.692964i	$-0.243696\pi$
$389$	11063.0			1.44194			0.720972	+	0.692964i	$0.243696\pi$
$390$		0			0
$391$	−1014.00			−0.131151
$392$		0			0
$393$	−730.000	−	1264.40i	−0.0936988	−	0.162291i
$394$	2556.00	−	4427.12i	0.326826	−	0.566079i
$395$		−	1292.00i		−	0.164576i
$396$	−5099.16	−	2944.00i	−0.647077	−	0.373590i
$397$	−5184.03	−	2993.00i	−0.655362	−	0.378374i	0.135145	−	0.990826i	$-0.456850\pi$
$397$	−5184.03	−	2993.00i	−0.655362	−	0.378374i	−0.790508	+	0.612452i	$0.790183\pi$
$398$		−	16952.0i		−	2.13499i
$399$	−600.000	+	1039.23i	−0.0752821	+	0.130392i
$400$	−5248.00	−	9089.80i	−0.656000	−	1.13623i
$401$	−5139.86	+	2967.50i	−0.640081	+	0.369551i	−0.784646	−	0.619945i	$-0.787155\pi$
$401$	−5139.86	+	2967.50i	−0.640081	+	0.369551i	0.144565	+	0.989495i	$0.453822\pi$
$402$	−6896.00			−0.855575
$403$		0			0
$404$	−6552.00			−0.806867
$405$	6198.14	−	3578.50i	0.760465	−	0.439055i
$406$	−7880.00	−	13648.6i	−0.963246	−	1.66839i
$407$	3632.00	−	6290.81i	0.442338	−	0.766152i
$408$		0			0
$409$	13067.5	+	7544.50i	1.57981	+	0.912106i	0.994884	+	0.101023i	$0.0322116\pi$
$409$	13067.5	+	7544.50i	1.57981	+	0.912106i	0.584931	+	0.811083i	$0.301122\pi$
$410$	−9716.81	−	5610.00i	−1.17044	−	0.675752i
$411$		−	3342.00i		−	0.401092i
$412$	−6552.00	+	11348.4i	−0.783480	+	1.35703i
$413$	−8640.00	−	14964.9i	−1.02941	−	1.78299i
$414$	6214.60	−	3588.00i	0.737756	−	0.425943i
$415$	−10676.0			−1.26281
$416$		0			0
$417$	1824.00			0.214201
$418$	−3325.54	+	1920.00i	−0.389132	+	0.224666i
$419$	5407.00	+	9365.20i	0.630428	+	1.09193i	0.987464	+	0.157843i	$0.0504538\pi$
$419$	5407.00	+	9365.20i	0.630428	+	1.09193i	−0.357037	+	0.934090i	$0.616213\pi$
$420$	2720.00	−	4711.18i	0.316006	−	0.547338i
$421$		−	6535.00i		−	0.756524i	−0.925699	−	0.378262i	$-0.876522\pi$
$421$		−	6535.00i		−	0.756524i	0.925699	−	0.378262i	$-0.123478\pi$
$422$	−10634.8	−	6140.00i	−1.22676	−	0.708271i
$423$	3226.81	+	1863.00i	0.370905	+	0.214142i
$424$		0			0
$425$	1066.00	−	1846.37i	0.121667	−	0.210734i
$426$	2616.00	+	4531.04i	0.297525	+	0.515328i
$427$	−2511.47	+	1450.00i	−0.284634	+	0.164334i
$428$	−4176.00			−0.471623
$429$		0			0
$430$	−10608.0			−1.18968
$431$	1714.73	−	990.000i	0.191637	−	0.110642i	−0.401112	−	0.916029i	$-0.631376\pi$
$431$	1714.73	−	990.000i	0.191637	−	0.110642i	0.592749	+	0.805387i	$0.298043\pi$
$432$	−3200.00	−	5542.56i	−0.356389	−	0.617284i
$433$	−3464.50	+	6000.69i	−0.384511	+	0.665993i	−0.991701	−	0.128564i	$-0.958963\pi$
$433$	−3464.50	+	6000.69i	−0.384511	+	0.665993i	0.607190	+	0.794556i	$0.292297\pi$
$434$		−	5920.00i		−	0.654767i
$435$	−5800.64	−	3349.00i	−0.639355	−	0.369132i
$436$	−11320.7	−	6536.00i	−1.24349	−	0.717930i
$437$		−	2340.00i		−	0.256150i
$438$	−860.000	+	1489.56i	−0.0938182	+	0.162498i
$439$	−2288.00	−	3962.93i	−0.248748	−	0.430844i	0.714431	−	0.699706i	$-0.246686\pi$
$439$	−2288.00	−	3962.93i	−0.248748	−	0.430844i	−0.963179	+	0.268862i	$0.913352\pi$
$440$		0			0
$441$	1311.00			0.141561
$442$		0			0
$443$	−8812.00			−0.945081			−0.472540	−	0.881309i	$-0.656663\pi$
$443$	−8812.00			−0.945081			−0.472540	+	0.881309i	$0.656663\pi$
$444$	−3145.40	+	1816.00i	−0.336203	+	0.194107i
$445$	2261.00	+	3916.17i	0.240858	+	0.417178i
$446$	−10756.0	+	18629.9i	−1.14195	+	1.97792i
$447$		−	4230.00i		−	0.447589i
$448$	8868.10	+	5120.00i	0.935220	+	0.539949i
$449$	1661.04	+	959.000i	0.174586	+	0.100797i	0.584747	−	0.811216i	$-0.301194\pi$
$449$	1661.04	+	959.000i	0.174586	+	0.100797i	−0.410160	+	0.912013i	$0.634527\pi$
$450$			15088.0i			1.58057i
$451$	−2640.00	+	4572.61i	−0.275638	+	0.477419i
$452$	1308.00	+	2265.52i	0.136113	+	0.235755i
$453$	−890.274	+	514.000i	−0.0923371	+	0.0533109i
$454$	15896.0			1.64325
$455$		0			0
$456$		0			0
$457$	−10185.3	+	5880.50i	−1.04256	+	0.601922i	−0.920557	−	0.390608i	$-0.872265\pi$
$457$	−10185.3	+	5880.50i	−1.04256	+	0.601922i	−0.122002	+	0.992530i	$0.538931\pi$
$458$	12596.0	+	21816.9i	1.28509	+	2.22585i
$459$	650.000	−	1125.83i	0.0660989	−	0.114487i
$460$			10608.0i			1.07522i
$461$	−780.289	−	450.500i	−0.0788323	−	0.0455138i	0.460066	−	0.887885i	$-0.347826\pi$
$461$	−780.289	−	450.500i	−0.0788323	−	0.0455138i	−0.538898	+	0.842371i	$0.681159\pi$
$462$	−4434.05	−	2560.00i	−0.446517	−	0.257796i
$463$		−	1372.00i		−	0.137715i	−0.997626	−	0.0688577i	$-0.978065\pi$
$463$		−	1372.00i		−	0.137715i	0.997626	−	0.0688577i	$-0.0219354\pi$
$464$	6304.00	−	10918.8i	0.630724	−	1.09245i
$465$	−1258.00	−	2178.92i	−0.125459	−	0.217301i
$466$	−13960.3	+	8060.00i	−1.38777	+	0.801228i
$467$	6396.00			0.633772			0.316886	−	0.948464i	$-0.397363\pi$
$467$	6396.00			0.633772			0.316886	+	0.948464i	$0.397363\pi$
$468$		0			0
$469$	17240.0			1.69738
$470$	−9540.14	+	5508.00i	−0.936284	+	0.540564i
$471$	−2901.00	−	5024.68i	−0.283803	−	0.491561i
$472$		0			0
$473$			4992.00i			0.485269i
$474$	526.543	+	304.000i	0.0510231	+	0.0294582i
$475$	4260.84	+	2460.00i	0.411581	+	0.237626i
$476$			2080.00i			0.200287i
$477$	1069.50	−	1852.43i	0.102660	−	0.177813i
$478$	−1968.00	−	3408.68i	−0.188314	−	0.326170i
$479$	−2831.90	+	1635.00i	−0.270131	+	0.155960i	−0.628947	−	0.777448i	$-0.716514\pi$
$479$	−2831.90	+	1635.00i	−0.270131	+	0.155960i	0.358816	+	0.933408i	$0.383181\pi$
$480$	8704.00			0.827670
$481$		0			0
$482$	3772.00			0.356452
$483$	2702.00	−	1560.00i	0.254545	−	0.146962i
$484$	1228.00	+	2126.96i	0.115327	+	0.199752i
$485$	2023.00	−	3503.94i	0.189401	−	0.328053i
$486$			14168.0i			1.32237i
$487$	−17251.2	−	9960.00i	−1.60519	−	0.926757i	−0.990426	−	0.138046i	$-0.955918\pi$
$487$	−17251.2	−	9960.00i	−1.60519	−	0.926757i	−0.614765	−	0.788711i	$-0.710749\pi$
$488$		0			0
$489$		−	4720.00i		−	0.436494i
$490$	−1938.00	+	3356.71i	−0.178673	+	0.309471i
$491$	3276.00	+	5674.20i	0.301108	+	0.521534i	0.976387	−	0.216028i	$-0.0693103\pi$
$491$	3276.00	+	5674.20i	0.301108	+	0.521534i	−0.675280	+	0.737562i	$0.735977\pi$
$492$	2286.31	−	1320.00i	0.209501	−	0.120956i
$493$	2561.00			0.233959
$494$		0			0
$495$	12512.0			1.13611
$496$	4101.50	−	2368.00i	0.371296	−	0.214368i
$497$	−6540.00	−	11327.6i	−0.590260	−	1.02236i
$498$	2512.00	−	4350.91i	0.226035	−	0.391504i
$499$			1746.00i			0.156637i	0.996928	+	0.0783183i	$0.0249551\pi$
$499$			1746.00i			0.156637i	−0.996928	+	0.0783183i	$0.975045\pi$
$500$	−4593.40	−	2652.00i	−0.410846	−	0.237202i
$501$	484.974	+	280.000i	0.0432476	+	0.0249690i
$502$			10920.0i			0.970883i
$503$	−7346.00	+	12723.6i	−0.651177	+	1.12787i	0.331661	+	0.943399i	$0.392391\pi$
$503$	−7346.00	+	12723.6i	−0.651177	+	1.12787i	−0.982838	+	0.184473i	$0.940942\pi$
$504$		0			0
$505$	12057.7	−	6961.50i	1.06249	−	0.613431i
$506$	9984.00			0.877160
$507$		0			0
$508$	−17264.0			−1.50781
$509$	6994.89	−	4038.50i	0.609122	−	0.351677i	−0.163500	−	0.986543i	$-0.552278\pi$
$509$	6994.89	−	4038.50i	0.609122	−	0.351677i	0.772622	+	0.634867i	$0.218945\pi$
$510$	884.000	+	1531.13i	0.0767533	+	0.132941i
$511$	2150.00	−	3723.91i	0.186126	−	0.322380i
$512$			16384.0i			1.41421i
$513$	2598.08	+	1500.00i	0.223602	+	0.129097i
$514$	−6529.83	−	3770.00i	−0.560347	−	0.323517i
$515$		−	27846.0i		−	2.38260i
$516$	1248.00	−	2161.60i	0.106473	−	0.184417i
$517$	2592.00	+	4489.48i	0.220495	+	0.381909i
$518$	15727.0	−	9080.00i	1.33399	−	0.770178i
$519$	−2652.00			−0.224296
$520$		0			0
$521$	11247.0			0.945758			0.472879	−	0.881127i	$-0.343215\pi$
$521$	11247.0			0.945758			0.472879	+	0.881127i	$0.343215\pi$
$522$	−15695.8	+	9062.00i	−1.31607	+	0.759833i
$523$	−1366.00	−	2365.98i	−0.114208	−	0.197815i	0.803255	−	0.595636i	$-0.203100\pi$
$523$	−1366.00	−	2365.98i	−0.114208	−	0.197815i	−0.917463	+	0.397821i	$0.869767\pi$
$524$	2920.00	−	5057.59i	0.243437	−	0.421645i
$525$			6560.00i			0.545337i
$526$	−13967.3	−	8064.00i	−1.15780	−	0.668455i
$527$	833.116	+	481.000i	0.0688636	+	0.0397584i
$528$		−	4096.00i		−	0.337605i
$529$	3041.50	−	5268.03i	0.249979	−	0.432977i
$530$	3162.00	+	5476.74i	0.259148	+	0.448858i
$531$	−17209.7	+	9936.00i	−1.40647	+	0.812026i
$532$	−4800.00			−0.391177
$533$		0			0
$534$	−2128.00			−0.172449
$535$	7685.11	−	4437.00i	0.621040	−	0.358557i
$536$		0			0
$537$	4264.00	−	7385.46i	0.342654	−	0.593494i
$538$			16024.0i			1.28410i
$539$	1579.63	+	912.000i	0.126233	+	0.0728806i
$540$	−11777.9	−	6800.00i	−0.938596	−	0.541899i
$541$			18375.0i			1.46026i	0.683306	+	0.730132i	$0.260542\pi$
$541$			18375.0i			1.46026i	−0.683306	+	0.730132i	$0.739458\pi$
$542$	8592.00	−	14881.8i	0.680919	−	1.17939i
$543$	−403.000	−	698.016i	−0.0318497	−	0.0551653i
$544$	−2882.13	+	1664.00i	−0.227151	+	0.131146i
$545$	27778.0			2.18326
$546$		0			0
$547$	−10346.0			−0.808708			−0.404354	−	0.914603i	$-0.632504\pi$
$547$	−10346.0			−0.808708			−0.404354	+	0.914603i	$0.632504\pi$
$548$	11577.0	−	6684.00i	0.902456	−	0.521033i
$549$	1667.50	+	2888.19i	0.129631	+	0.224527i
$550$	−10496.0	+	18179.6i	−0.813729	+	1.40942i
$551$			5910.00i			0.456941i
$552$		0			0
$553$	−1316.36	−	760.000i	−0.101225	−	0.0584421i
$554$			22204.0i			1.70281i
$555$	3859.00	−	6683.98i	0.295145	−	0.511206i
$556$	3648.00	+	6318.52i	0.278255	+	0.481951i
$557$	−298.779	+	172.500i	−0.0227283	+	0.0131222i	−0.511321	−	0.859390i	$-0.670844\pi$
$557$	−298.779	+	172.500i	−0.0227283	+	0.0131222i	0.488593	+	0.872512i	$0.337510\pi$
$558$	−6808.00			−0.516498
$559$		0			0
$560$	−21760.0			−1.64201
$561$	720.533	−	416.000i	0.0542263	−	0.0313075i
$562$	11114.0	+	19250.0i	0.834192	+	1.44486i
$563$	−4290.00	+	7430.50i	−0.321140	+	0.556231i	−0.980724	−	0.195400i	$-0.937399\pi$
$563$	−4290.00	+	7430.50i	−0.321140	+	0.556231i	0.659583	+	0.751631i	$0.270733\pi$
$564$		−	2592.00i		−	0.193516i
$565$	−4814.24	−	2779.50i	−0.358472	−	0.206964i
$566$	10808.0	+	6240.00i	0.802640	+	0.463404i
$567$		−	8420.00i		−	0.623645i
$568$		0			0
$569$	−9841.00	−	17045.1i	−0.725055	−	1.25583i	−0.958951	−	0.283570i	$-0.908481\pi$
$569$	−9841.00	−	17045.1i	−0.725055	−	1.25583i	0.233897	−	0.972261i	$-0.424852\pi$
$570$	−3533.38	+	2040.00i	−0.259644	+	0.149906i
$571$	−26624.0			−1.95128			−0.975639	−	0.219382i	$-0.929596\pi$
$571$	−26624.0			−1.95128			−0.975639	+	0.219382i	$0.929596\pi$
$572$		0			0
$573$	−2492.00			−0.181684
$574$	−11431.5	+	6600.00i	−0.831260	+	0.479928i
$575$	−6396.00	−	11078.2i	−0.463881	−	0.803466i
$576$	5888.00	−	10198.3i	0.425926	−	0.737725i
$577$		−	14101.0i		−	1.01739i	−0.860948	−	0.508694i	$-0.830129\pi$
$577$		−	14101.0i		−	1.01739i	0.860948	−	0.508694i	$-0.169871\pi$
$578$	16433.7	+	9488.00i	1.18262	+	0.682783i
$579$	462.458	+	267.000i	0.0331936	+	0.0191643i
$580$		−	26792.0i		−	1.91806i
$581$	−6280.00	+	10877.3i	−0.448431	+	0.776705i
$582$	952.000	+	1648.91i	0.0678036	+	0.117439i
$583$	2577.29	−	1488.00i	0.183088	−	0.105706i
$584$		0			0
$585$		0			0
$586$	33204.0			2.34069
$587$	1219.36	−	704.000i	0.0857386	−	0.0495012i	−0.456518	−	0.889714i	$-0.650904\pi$
$587$	1219.36	−	704.000i	0.0857386	−	0.0495012i	0.542256	+	0.840213i	$0.317570\pi$
$588$	−456.000	−	789.815i	−0.0319815	−	0.0553936i
$589$	−1110.00	+	1922.58i	−0.0776515	+	0.134496i
$590$		−	58752.0i		−	4.09963i
$591$	−2213.56	−	1278.00i	−0.154067	−	0.0889508i
$592$	12581.6	+	7264.00i	0.873482	+	0.504305i
$593$			1241.00i			0.0859389i	0.999076	+	0.0429694i	$0.0136818\pi$
$593$			1241.00i			0.0859389i	−0.999076	+	0.0429694i	$0.986318\pi$
$594$	−6400.00	+	11085.1i	−0.442079	+	0.765704i
$595$	−2210.00	−	3827.83i	−0.152271	−	0.263741i
$596$	14653.1	−	8460.00i	1.00707	−	0.581435i
$597$	−8476.00			−0.581071
$598$		0			0
$599$	11078.0			0.755651			0.377825	−	0.925877i	$-0.376672\pi$
$599$	11078.0			0.755651			0.377825	+	0.925877i	$0.376672\pi$
$600$		0			0
$601$	6908.50	+	11965.9i	0.468891	+	0.812143i	0.999368	−	0.0355563i	$-0.0113203\pi$
$601$	6908.50	+	11965.9i	0.468891	+	0.812143i	−0.530477	+	0.847700i	$0.677987\pi$
$602$	−6240.00	+	10808.0i	−0.422464	+	0.731729i
$603$		−	19826.0i		−	1.33893i
$604$	−3561.10	−	2056.00i	−0.239899	−	0.138506i
$605$	−4519.79	−	2609.50i	−0.303728	−	0.175357i
$606$			6552.00i			0.439203i
$607$	−4135.00	+	7162.03i	−0.276498	+	0.478909i	−0.970512	−	0.241053i	$-0.922507\pi$
$607$	−4135.00	+	7162.03i	−0.276498	+	0.478909i	0.694014	+	0.719962i	$0.255841\pi$
$608$	−3840.00	−	6651.08i	−0.256139	−	0.443646i
$609$	−6824.28	+	3940.00i	−0.454078	+	0.262162i
$610$	−9860.00			−0.654459
$611$		0			0
$612$	2392.00			0.157992
$613$	19289.0	−	11136.5i	1.27092	−	0.733767i	0.295760	−	0.955262i	$-0.404427\pi$
$613$	19289.0	−	11136.5i	1.27092	−	0.733767i	0.975161	+	0.221496i	$0.0710938\pi$
$614$	−17356.0	−	30061.5i	−1.14077	−	1.97587i
$615$	−2805.00	+	4858.40i	−0.183916	+	0.318552i
$616$		0			0
$617$	16445.0	+	9494.50i	1.07301	+	0.619504i	0.929003	−	0.370072i	$-0.120667\pi$
$617$	16445.0	+	9494.50i	1.07301	+	0.619504i	0.144010	+	0.989576i	$0.454000\pi$
$618$	11348.4	+	6552.00i	0.738672	+	0.426473i
$619$		−	72.0000i		−	0.00467516i	−0.999997	−	0.00233758i	$-0.999256\pi$
$619$		−	72.0000i		−	0.00467516i	0.999997	−	0.00233758i	$-0.000744076\pi$
$620$	5032.00	−	8715.68i	0.325952	−	0.564565i
$621$	−3900.00	−	6755.00i	−0.252015	−	0.436504i
$622$	−29992.2	+	17316.0i	−1.93340	+	1.11625i
$623$	5320.00			0.342121
$624$		0			0
$625$	−9229.00			−0.590656
$626$	−18186.5	+	10500.0i	−1.16115	+	0.670390i
$627$	960.000	+	1662.77i	0.0611463	+	0.105908i
$628$	11604.0	−	20098.7i	0.737341	−	1.27711i
$629$			2951.00i			0.187065i
$630$	27089.3	+	15640.0i	1.71312	+	0.989067i
$631$	−20247.7	−	11690.0i	−1.27741	−	0.737514i	−0.301040	−	0.953611i	$-0.597334\pi$
$631$	−20247.7	−	11690.0i	−1.27741	−	0.737514i	−0.976372	+	0.216097i	$0.930667\pi$
$632$		0			0
$633$	−3070.00	+	5317.40i	−0.192767	+	0.333882i
$634$	12826.0	+	22215.3i	0.803447	+	1.39161i
$635$	31771.0	−	18343.0i	1.98550	−	1.14633i
$636$	−1488.00			−0.0927721
$637$		0			0
$638$	−25216.0			−1.56475
$639$	−13026.8	+	7521.00i	−0.806464	+	0.465612i
$640$		0			0
$641$	3191.50	−	5527.84i	0.196656	−	0.340619i	−0.750786	−	0.660546i	$-0.770325\pi$
$641$	3191.50	−	5527.84i	0.196656	−	0.340619i	0.947442	+	0.319927i	$0.103658\pi$
$642$			4176.00i			0.256719i
$643$	14812.5	+	8552.00i	0.908473	+	0.524507i	0.879939	−	0.475086i	$-0.157583\pi$
$643$	14812.5	+	8552.00i	0.908473	+	0.524507i	0.0285332	+	0.999593i	$0.490916\pi$
$644$	10808.0	+	6240.00i	0.661327	+	0.381817i
$645$			5304.00i			0.323790i
$646$	780.000	−	1351.00i	0.0475057	−	0.0822823i
$647$	3497.00	+	6056.98i	0.212490	+	0.368044i	0.952493	−	0.304560i	$-0.0985093\pi$
$647$	3497.00	+	6056.98i	0.212490	+	0.368044i	−0.740003	+	0.672604i	$0.765176\pi$
$648$		0			0
$649$	−27648.0			−1.67223
$650$		0			0
$651$	−2960.00			−0.178205
$652$	16350.6	−	9440.00i	0.982112	−	0.567023i
$653$	2625.00	+	4546.63i	0.157311	+	0.272471i	0.933898	−	0.357539i	$-0.116384\pi$
$653$	2625.00	+	4546.63i	0.157311	+	0.272471i	−0.776587	+	0.630010i	$0.783051\pi$
$654$	−6536.00	+	11320.7i	−0.390792	+	0.676871i
$655$			12410.0i			0.740304i
$656$	−9145.23	−	5280.00i	−0.544301	−	0.314252i
$657$	−4282.50	−	2472.50i	−0.254301	−	0.146821i
$658$			12960.0i			0.767832i
$659$	2170.00	−	3758.55i	0.128272	−	0.222173i	−0.794735	−	0.606956i	$-0.792390\pi$
$659$	2170.00	−	3758.55i	0.128272	−	0.222173i	0.923007	+	0.384783i	$0.125724\pi$
$660$	−4352.00	−	7537.89i	−0.256669	−	0.444563i
$661$	3619.12	−	2089.50i	0.212961	−	0.122953i	−0.389726	−	0.920931i	$-0.627430\pi$
$661$	3619.12	−	2089.50i	0.212961	−	0.122953i	0.602687	+	0.797978i	$0.294097\pi$
$662$	−13952.0			−0.819124
$663$		0			0
$664$		0			0
$665$	8833.46	−	5100.00i	0.515108	−	0.297398i
$666$	−10442.0	−	18086.1i	−0.607536	−	1.05228i
$667$	7683.00	−	13307.3i	0.446007	−	0.772508i
$668$			2240.00i			0.129743i
$669$	9314.97	+	5378.00i	0.538322	+	0.310800i
$670$	50762.9	+	29308.0i	2.92708	+	1.68995i
$671$			4640.00i			0.266953i
$672$	5120.00	−	8868.10i	0.293911	−	0.509069i
$673$	11433.5	+	19803.4i	0.654872	+	1.13427i	0.981926	+	0.189266i	$0.0606109\pi$
$673$	11433.5	+	19803.4i	0.654872	+	1.13427i	−0.327054	+	0.945006i	$0.606056\pi$
$674$	6349.70	−	3666.00i	0.362880	−	0.209509i
$675$	16400.0			0.935165
$676$		0			0
$677$	5410.00			0.307124			0.153562	−	0.988139i	$-0.450925\pi$
$677$	5410.00			0.307124			0.153562	+	0.988139i	$0.450925\pi$
$678$	2265.52	−	1308.00i	0.128329	−	0.0740906i
$679$	−2380.00	−	4122.28i	−0.134515	−	0.232988i
$680$		0			0
$681$		−	7948.00i		−	0.447236i
$682$	−8202.99	−	4736.00i	−0.460570	−	0.265910i
$683$	−11758.9	−	6789.00i	−0.658772	−	0.380342i	0.133037	−	0.991111i	$-0.457527\pi$
$683$	−11758.9	−	6789.00i	−0.658772	−	0.380342i	−0.791809	+	0.610769i	$0.790861\pi$
$684$			5520.00i			0.308571i
$685$	−14203.5	+	24601.2i	−0.792245	+	1.37221i
$686$	−11440.0	−	19814.7i	−0.636707	−	1.10281i
$687$	10908.5	−	6298.00i	0.605798	−	0.349758i
$688$	−9984.00			−0.553251
$689$		0			0
$690$	10608.0			0.585275
$691$	11036.6	−	6372.00i	0.607602	−	0.350799i	−0.164424	−	0.986390i	$-0.552577\pi$
$691$	11036.6	−	6372.00i	0.607602	−	0.350799i	0.772026	+	0.635590i	$0.219243\pi$
$692$	−5304.00	−	9186.80i	−0.291370	−	0.504667i
$693$	7360.00	−	12747.9i	0.403439	−	0.698777i
$694$			28920.0i			1.58183i
$695$	−13426.9	−	7752.00i	−0.732820	−	0.423094i
$696$		0			0
$697$		−	2145.00i		−	0.116568i
$698$	10516.0	−	18214.2i	0.570253	−	0.987707i
$699$	4030.00	+	6980.16i	0.218067	+	0.377703i
$700$	−22724.5	+	13120.0i	−1.22701	+	0.708413i
$701$	−16406.0			−0.883946			−0.441973	−	0.897028i	$-0.645721\pi$
$701$	−16406.0			−0.883946			−0.441973	+	0.897028i	$0.645721\pi$
$702$		0			0
$703$	−6810.00			−0.365354
$704$	14189.0	−	8192.00i	0.759612	−	0.438562i
$705$	2754.00	+	4770.07i	0.147123	+	0.254824i
$706$	6326.00	−	10957.0i	0.337227	−	0.584094i
$707$		−	16380.0i		−	0.871334i
$708$	11971.9	+	6912.00i	0.635498	+	0.366905i
$709$	614.012	+	354.500i	0.0325243	+	0.0187779i	0.516174	−	0.856484i	$-0.327356\pi$
$709$	614.012	+	354.500i	0.0325243	+	0.0187779i	−0.483650	+	0.875262i	$0.660689\pi$
$710$		−	44472.0i		−	2.35071i
$711$	−874.000	+	1513.81i	−0.0461006	+	0.0798487i
$712$		0			0
$713$	4998.70	−	2886.00i	0.262556	−	0.151587i
$714$	2080.00			0.109022
$715$		0			0
$716$	34112.0			1.78048
$717$	−1704.34	+	984.000i	−0.0887722	+	0.0512527i
$718$	20136.0	+	34876.6i	1.04661	+	1.81279i
$719$	−3822.00	+	6619.90i	−0.198243	+	0.343367i	−0.947959	−	0.318393i	$-0.896857\pi$
$719$	−3822.00	+	6619.90i	−0.198243	+	0.343367i	0.749716	+	0.661760i	$0.230190\pi$
$720$			25024.0i			1.29526i
$721$	−28371.0	−	16380.0i	−1.46545	−	0.846079i
$722$	−20642.6	−	11918.0i	−1.06404	−	0.614324i
$723$		−	1886.00i		−	0.0970140i
$724$	1612.00	−	2792.07i	0.0827479	−	0.143324i
$725$	16154.0	+	27979.5i	0.827510	+	1.43329i
$726$	2126.96	−	1228.00i	0.108731	−	0.0627760i
$727$	15808.0			0.806446			0.403223	−	0.915102i	$-0.367890\pi$
$727$	15808.0			0.806446			0.403223	+	0.915102i	$0.367890\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	12661.3	−	7310.00i	0.641939	−	0.370624i
$731$	−1014.00	−	1756.30i	−0.0513053	−	0.0888633i
$732$	1160.00	−	2009.18i	0.0585722	−	0.101450i
$733$		−	2583.00i		−	0.130157i	−0.997880	−	0.0650786i	$-0.979270\pi$
$733$		−	2583.00i		−	0.130157i	0.997880	−	0.0650786i	$-0.0207298\pi$
$734$	−25766.0	−	14876.0i	−1.29569	−	0.748070i
$735$	1678.36	+	969.000i	0.0842274	+	0.0486287i
$736$			19968.0i			1.00004i
$737$	13792.0	−	23888.4i	0.689328	−	1.19395i
$738$	7590.00	+	13146.3i	0.378580	+	0.655719i
$739$	−3529.92	+	2038.00i	−0.175711	+	0.101447i	−0.585276	−	0.810834i	$-0.699014\pi$
$739$	−3529.92	+	2038.00i	−0.175711	+	0.101447i	0.409565	+	0.912281i	$0.365680\pi$
$740$	30872.0			1.53362
$741$		0			0
$742$	7440.00			0.368101
$743$	−29493.4	+	17028.0i	−1.45627	+	0.840776i	−0.998825	−	0.0484632i	$-0.984568\pi$
$743$	−29493.4	+	17028.0i	−1.45627	+	0.840776i	−0.457442	+	0.889239i	$0.651234\pi$
$744$		0			0
$745$	−17977.5	+	31137.9i	−0.884087	+	1.53128i
$746$		−	38732.0i		−	1.90091i
$747$	12508.9	+	7222.00i	0.612685	+	0.353734i
$748$	2882.13	+	1664.00i	0.140884	+	0.0813394i
$749$		−	10440.0i		−	0.509305i
$750$	−2652.00	+	4593.40i	−0.129116	+	0.223636i
$751$	−182.000	−	315.233i	−0.00884324	−	0.0153169i	0.861570	−	0.507639i	$-0.169482\pi$
$751$	−182.000	−	315.233i	−0.00884324	−	0.0153169i	−0.870413	+	0.492322i	$0.836148\pi$
$752$	−8978.95	+	5184.00i	−0.435410	+	0.251384i
$753$	5460.00			0.264241
$754$		0			0
$755$	8738.00			0.421203
$756$	−13856.4	+	8000.00i	−0.666604	+	0.384864i
$757$	3457.00	+	5987.70i	0.165980	+	0.287486i	0.937003	−	0.349322i	$-0.113588\pi$
$757$	3457.00	+	5987.70i	0.165980	+	0.287486i	−0.771023	+	0.636807i	$0.780255\pi$
$758$	−2124.00	+	3678.88i	−0.101777	+	0.176283i
$759$		−	4992.00i		−	0.238733i
$760$		0			0
$761$	12108.8	+	6991.00i	0.576797	+	0.333014i	0.759859	−	0.650087i	$-0.225268\pi$
$761$	12108.8	+	6991.00i	0.576797	+	0.333014i	−0.183062	+	0.983101i	$0.558601\pi$
$762$			17264.0i			0.820746i
$763$	16340.0	−	28301.7i	0.775292	−	1.34284i
$764$	−4984.00	−	8632.54i	−0.236014	−	0.408788i
$765$	−4402.01	+	2541.50i	−0.208046	+	0.120115i
$766$	14128.0			0.666404
$767$		0			0
$768$	8192.00			0.384900
$769$	−15645.6	+	9033.00i	−0.733674	+	0.423587i	−0.819765	−	0.572700i	$-0.805896\pi$
$769$	−15645.6	+	9033.00i	−0.733674	+	0.423587i	0.0860907	+	0.996287i	$0.472563\pi$
$770$	21760.0	+	37689.4i	1.01841	+	1.76394i
$771$	−1885.00	+	3264.92i	−0.0880501

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.46410 - 2.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(4.00000 - 6.92820i) q^{4} +17.0000i q^{5} +(-6.92820 - 4.00000i) q^{6} +(17.3205 + 10.0000i) q^{7} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\)	\(q+(3.46410 - 2.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(4.00000 - 6.92820i) q^{4} +17.0000i q^{5} +(-6.92820 - 4.00000i) q^{6} +(17.3205 + 10.0000i) q^{7} +(11.5000 - 19.9186i) q^{9} +(34.0000 + 58.8897i) q^{10} +(27.7128 - 16.0000i) q^{11} -16.0000 q^{12} +80.0000 q^{14} +(29.4449 - 17.0000i) q^{15} +(32.0000 + 55.4256i) q^{16} +(-6.50000 + 11.2583i) q^{17} -92.0000i q^{18} +(-25.9808 - 15.0000i) q^{19} +(117.779 + 68.0000i) q^{20} -40.0000i q^{21} +(64.0000 - 110.851i) q^{22} +(39.0000 + 67.5500i) q^{23} -164.000 q^{25} -100.000 q^{27} +(138.564 - 80.0000i) q^{28} +(-98.5000 - 170.607i) q^{29} +(68.0000 - 117.779i) q^{30} -74.0000i q^{31} +(221.703 + 128.000i) q^{32} +(-55.4256 - 32.0000i) q^{33} +52.0000i q^{34} +(-170.000 + 294.449i) q^{35} +(-92.0000 - 159.349i) q^{36} +(196.588 - 113.500i) q^{37} -120.000 q^{38} +(-142.894 + 82.5000i) q^{41} +(-80.0000 - 138.564i) q^{42} +(-78.0000 + 135.100i) q^{43} -256.000i q^{44} +(338.616 + 195.500i) q^{45} +(270.200 + 156.000i) q^{46} +162.000i q^{47} +(64.0000 - 110.851i) q^{48} +(28.5000 + 49.3634i) q^{49} +(-568.113 + 328.000i) q^{50} +26.0000 q^{51} +93.0000 q^{53} +(-346.410 + 200.000i) q^{54} +(272.000 + 471.118i) q^{55} +60.0000i q^{57} +(-682.428 - 394.000i) q^{58} +(-748.246 - 432.000i) q^{59} -272.000i q^{60} +(-72.5000 + 125.574i) q^{61} +(-148.000 - 256.344i) q^{62} +(398.372 - 230.000i) q^{63} +512.000 q^{64} -256.000 q^{66} +(746.514 - 431.000i) q^{67} +(52.0000 + 90.0666i) q^{68} +(78.0000 - 135.100i) q^{69} +1360.00i q^{70} +(-566.381 - 327.000i) q^{71} -215.000i q^{73} +(454.000 - 786.351i) q^{74} +(164.000 + 284.056i) q^{75} +(-207.846 + 120.000i) q^{76} +640.000 q^{77} -76.0000 q^{79} +(-942.236 + 544.000i) q^{80} +(-210.500 - 364.597i) q^{81} +(-330.000 + 571.577i) q^{82} +628.000i q^{83} +(-277.128 - 160.000i) q^{84} +(-191.392 - 110.500i) q^{85} +624.000i q^{86} +(-197.000 + 341.214i) q^{87} +(230.363 - 133.000i) q^{89} +1564.00 q^{90} +624.000 q^{92} +(-128.172 + 74.0000i) q^{93} +(324.000 + 561.184i) q^{94} +(255.000 - 441.673i) q^{95} -512.000i q^{96} +(-206.114 - 119.000i) q^{97} +(197.454 + 114.000i) q^{98} -736.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 16 * q^4 + 46 * q^9	\( 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9} + 136 q^{10} - 64 q^{12} + 320 q^{14} + 128 q^{16} - 26 q^{17} + 256 q^{22} + 156 q^{23} - 656 q^{25} - 400 q^{27} - 394 q^{29} + 272 q^{30} - 680 q^{35} - 368 q^{36} - 480 q^{38} - 320 q^{42} - 312 q^{43} + 256 q^{48} + 114 q^{49} + 104 q^{51} + 372 q^{53} + 1088 q^{55} - 290 q^{61} - 592 q^{62} + 2048 q^{64} - 1024 q^{66} + 208 q^{68} + 312 q^{69} + 1816 q^{74} + 656 q^{75} + 2560 q^{77} - 304 q^{79} - 842 q^{81} - 1320 q^{82} - 788 q^{87} + 6256 q^{90} + 2496 q^{92} + 1296 q^{94} + 1020 q^{95}+O(q^{100}) \) 4 * q - 4 * q^3 + 16 * q^4 + 46 * q^9 + 136 * q^10 - 64 * q^12 + 320 * q^14 + 128 * q^16 - 26 * q^17 + 256 * q^22 + 156 * q^23 - 656 * q^25 - 400 * q^27 - 394 * q^29 + 272 * q^30 - 680 * q^35 - 368 * q^36 - 480 * q^38 - 320 * q^42 - 312 * q^43 + 256 * q^48 + 114 * q^49 + 104 * q^51 + 372 * q^53 + 1088 * q^55 - 290 * q^61 - 592 * q^62 + 2048 * q^64 - 1024 * q^66 + 208 * q^68 + 312 * q^69 + 1816 * q^74 + 656 * q^75 + 2560 * q^77 - 304 * q^79 - 842 * q^81 - 1320 * q^82 - 788 * q^87 + 6256 * q^90 + 2496 * q^92 + 1296 * q^94 + 1020 * q^95

Introduction

L-functions

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