LMFDB - Embedded newform 684.3.g.b.343.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.3
Root			$1.57398 + 1.23393i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.b.343.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57398 - 1.23393i) q^{2} +(0.954817 + 3.88437i) q^{4} -3.66290 q^{5} -1.93414i q^{7} +(3.29019 - 7.29209i) q^{8} +O(q^{10})$	\(q+(-1.57398 - 1.23393i) q^{2} +(0.954817 + 3.88437i) q^{4} -3.66290 q^{5} -1.93414i q^{7} +(3.29019 - 7.29209i) q^{8} +(5.76533 + 4.51977i) q^{10} +0.752428i q^{11} -13.0118 q^{13} +(-2.38660 + 3.04430i) q^{14} +(-14.1766 + 7.41772i) q^{16} +23.9304 q^{17} +4.35890i q^{19} +(-3.49740 - 14.2281i) q^{20} +(0.928446 - 1.18431i) q^{22} -6.26712i q^{23} -11.5832 q^{25} +(20.4803 + 16.0557i) q^{26} +(7.51293 - 1.84675i) q^{28} -33.1165 q^{29} -17.5328i q^{31} +(31.4667 + 5.81771i) q^{32} +(-37.6660 - 29.5285i) q^{34} +7.08457i q^{35} +41.5073 q^{37} +(5.37859 - 6.86081i) q^{38} +(-12.0516 + 26.7102i) q^{40} +5.51661 q^{41} +84.5402i q^{43} +(-2.92271 + 0.718431i) q^{44} +(-7.73320 + 9.86431i) q^{46} +18.3582i q^{47} +45.2591 q^{49} +(18.2316 + 14.2929i) q^{50} +(-12.4239 - 50.5426i) q^{52} +41.2010 q^{53} -2.75607i q^{55} +(-14.1040 - 6.36370i) q^{56} +(52.1246 + 40.8635i) q^{58} +69.5279i q^{59} +87.6461 q^{61} +(-21.6343 + 27.5962i) q^{62} +(-42.3493 - 47.9848i) q^{64} +47.6609 q^{65} +105.121i q^{67} +(22.8492 + 92.9546i) q^{68} +(8.74189 - 11.1510i) q^{70} +74.9540i q^{71} +48.7353 q^{73} +(-65.3316 - 51.2173i) q^{74} +(-16.9316 + 4.16195i) q^{76} +1.45530 q^{77} -95.9473i q^{79} +(51.9277 - 27.1704i) q^{80} +(-8.68302 - 6.80713i) q^{82} -65.8722i q^{83} -87.6548 q^{85} +(104.317 - 133.064i) q^{86} +(5.48677 + 2.47563i) q^{88} -3.38934 q^{89} +25.1667i q^{91} +(24.3438 - 5.98395i) q^{92} +(22.6528 - 28.8954i) q^{94} -15.9662i q^{95} -23.5177 q^{97} +(-71.2368 - 55.8467i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.57398	−	1.23393i	−0.786989	−	0.616967i
$2$	−1.57398	−	1.23393i	−0.786989	−	0.616967i
$3$		0			0
$3$		0			0
$4$	0.954817	+	3.88437i	0.238704	+	0.971092i
$5$	−3.66290			−0.732580			−0.366290	−	0.930501i	$-0.619372\pi$
$5$	−3.66290			−0.732580			−0.366290	+	0.930501i	$0.619372\pi$
$6$		0			0
$7$		−	1.93414i		−	0.276306i	−0.990411	−	0.138153i	$-0.955883\pi$
$7$		−	1.93414i		−	0.276306i	0.990411	−	0.138153i	$-0.0441166\pi$
$8$	3.29019	−	7.29209i	0.411274	−	0.911512i
$9$		0			0
$10$	5.76533	+	4.51977i	0.576533	+	0.451977i
$11$			0.752428i			0.0684025i	0.999415	+	0.0342013i	$0.0108887\pi$
$11$			0.752428i			0.0684025i	−0.999415	+	0.0342013i	$0.989111\pi$
$12$		0			0
$13$	−13.0118			−1.00091			−0.500453	−	0.865763i	$-0.666833\pi$
$13$	−13.0118			−1.00091			−0.500453	+	0.865763i	$0.666833\pi$
$14$	−2.38660	+	3.04430i	−0.170472	+	0.217450i
$15$		0			0
$16$	−14.1766	+	7.41772i	−0.886041	+	0.463608i
$17$	23.9304			1.40767			0.703836	−	0.710363i	$-0.251469\pi$
$17$	23.9304			1.40767			0.703836	+	0.710363i	$0.251469\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−3.49740	−	14.2281i	−0.174870	−	0.711403i
$21$		0			0
$22$	0.928446	−	1.18431i	0.0422021	−	0.0538321i
$23$		−	6.26712i		−	0.272483i	−0.990676	−	0.136242i	$-0.956498\pi$
$23$		−	6.26712i		−	0.272483i	0.990676	−	0.136242i	$-0.0435024\pi$
$24$		0			0
$25$	−11.5832			−0.463326
$26$	20.4803	+	16.0557i	0.787703	+	0.617526i
$27$		0			0
$28$	7.51293	−	1.84675i	0.268319	−	0.0659554i
$29$	−33.1165			−1.14195			−0.570974	−	0.820968i	$-0.693434\pi$
$29$	−33.1165			−1.14195			−0.570974	+	0.820968i	$0.693434\pi$
$30$		0			0
$31$		−	17.5328i		−	0.565574i	−0.959183	−	0.282787i	$-0.908741\pi$
$31$		−	17.5328i		−	0.565574i	0.959183	−	0.282787i	$-0.0912589\pi$
$32$	31.4667	+	5.81771i	0.983335	+	0.181803i
$33$		0			0
$34$	−37.6660	−	29.5285i	−1.10782	−	0.868487i
$35$			7.08457i			0.202416i
$36$		0			0
$37$	41.5073			1.12182			0.560910	−	0.827877i	$-0.310451\pi$
$37$	41.5073			1.12182			0.560910	+	0.827877i	$0.310451\pi$
$38$	5.37859	−	6.86081i	0.141542	−	0.180548i
$39$		0			0
$40$	−12.0516	+	26.7102i	−0.301291	+	0.667755i
$41$	5.51661			0.134551			0.0672757	−	0.997734i	$-0.478569\pi$
$41$	5.51661			0.134551			0.0672757	+	0.997734i	$0.478569\pi$
$42$		0			0
$43$			84.5402i			1.96605i	0.183468	+	0.983026i	$0.441267\pi$
$43$			84.5402i			1.96605i	−0.183468	+	0.983026i	$0.558733\pi$
$44$	−2.92271	+	0.718431i	−0.0664252	+	0.0163280i
$45$		0			0
$46$	−7.73320	+	9.86431i	−0.168113	+	0.214441i
$47$			18.3582i			0.390599i	0.980744	+	0.195300i	$0.0625679\pi$
$47$			18.3582i			0.390599i	−0.980744	+	0.195300i	$0.937432\pi$
$48$		0			0
$49$	45.2591			0.923655
$50$	18.2316	+	14.2929i	0.364633	+	0.285857i
$51$		0			0
$52$	−12.4239	−	50.5426i	−0.238921	−	0.971973i
$53$	41.2010			0.777377			0.388688	−	0.921369i	$-0.372928\pi$
$53$	41.2010			0.777377			0.388688	+	0.921369i	$0.372928\pi$
$54$		0			0
$55$		−	2.75607i		−	0.0501103i
$56$	−14.1040	−	6.36370i	−0.251856	−	0.113638i
$57$		0			0
$58$	52.1246	+	40.8635i	0.898701	+	0.704544i
$59$			69.5279i			1.17844i	0.807973	+	0.589219i	$0.200565\pi$
$59$			69.5279i			1.17844i	−0.807973	+	0.589219i	$0.799435\pi$
$60$		0			0
$61$	87.6461			1.43682			0.718411	−	0.695619i	$-0.244870\pi$
$61$	87.6461			1.43682			0.718411	+	0.695619i	$0.244870\pi$
$62$	−21.6343	+	27.5962i	−0.348940	+	0.445100i
$63$		0			0
$64$	−42.3493	−	47.9848i	−0.661707	−	0.749762i
$65$	47.6609			0.733244
$66$		0			0
$67$			105.121i			1.56897i	0.620145	+	0.784487i	$0.287074\pi$
$67$			105.121i			1.56897i	−0.620145	+	0.784487i	$0.712926\pi$
$68$	22.8492	+	92.9546i	0.336017	+	1.36698i
$69$		0			0
$70$	8.74189	−	11.1510i	0.124884	−	0.159300i
$71$			74.9540i			1.05569i	0.849341	+	0.527845i	$0.177000\pi$
$71$			74.9540i			1.05569i	−0.849341	+	0.527845i	$0.823000\pi$
$72$		0			0
$73$	48.7353			0.667607			0.333803	−	0.942643i	$-0.391668\pi$
$73$	48.7353			0.667607			0.333803	+	0.942643i	$0.391668\pi$
$74$	−65.3316	−	51.2173i	−0.882860	−	0.692125i
$75$		0			0
$76$	−16.9316	+	4.16195i	−0.222784	+	0.0547625i
$77$	1.45530			0.0189000
$78$		0			0
$79$		−	95.9473i		−	1.21452i	−0.794502	−	0.607261i	$-0.792268\pi$
$79$		−	95.9473i		−	1.21452i	0.794502	−	0.607261i	$-0.207732\pi$
$80$	51.9277	−	27.1704i	0.649096	−	0.339630i
$81$		0			0
$82$	−8.68302	−	6.80713i	−0.105890	−	0.0830137i
$83$		−	65.8722i		−	0.793641i	−0.917896	−	0.396821i	$-0.870114\pi$
$83$		−	65.8722i		−	0.793641i	0.917896	−	0.396821i	$-0.129886\pi$
$84$		0			0
$85$	−87.6548			−1.03123
$86$	104.317	−	133.064i	1.21299	−	1.54726i
$87$		0			0
$88$	5.48677	+	2.47563i	0.0623497	+	0.0281322i
$89$	−3.38934			−0.0380825			−0.0190412	−	0.999819i	$-0.506061\pi$
$89$	−3.38934			−0.0380825			−0.0190412	+	0.999819i	$0.506061\pi$
$90$		0			0
$91$			25.1667i			0.276557i
$92$	24.3438	−	5.98395i	0.264606	−	0.0650429i
$93$		0			0
$94$	22.6528	−	28.8954i	0.240987	−	0.307397i
$95$		−	15.9662i		−	0.168065i
$96$		0			0
$97$	−23.5177			−0.242451			−0.121225	−	0.992625i	$-0.538682\pi$
$97$	−23.5177			−0.242451			−0.121225	+	0.992625i	$0.538682\pi$
$98$	−71.2368	−	55.8467i	−0.726906	−	0.569864i
$99$		0			0
$100$	−11.0598	−	44.9933i	−0.110598	−	0.449933i
$101$	153.325			1.51807			0.759035	−	0.651050i	$-0.225671\pi$
$101$	153.325			1.51807			0.759035	+	0.651050i	$0.225671\pi$
$102$		0			0
$103$		−	114.566i		−	1.11229i	−0.831084	−	0.556147i	$-0.812279\pi$
$103$		−	114.566i		−	1.11229i	0.831084	−	0.556147i	$-0.187721\pi$
$104$	−42.8113	+	94.8832i	−0.411647	+	0.912338i
$105$		0			0
$106$	−64.8494	−	50.8392i	−0.611787	−	0.479616i
$107$			161.991i			1.51393i	0.653454	+	0.756966i	$0.273319\pi$
$107$			161.991i			1.51393i	−0.653454	+	0.756966i	$0.726681\pi$
$108$		0			0
$109$	120.924			1.10939			0.554696	−	0.832053i	$-0.312834\pi$
$109$	120.924			1.10939			0.554696	+	0.832053i	$0.312834\pi$
$110$	−3.40080	+	4.33799i	−0.0309164	+	0.0394363i
$111$		0			0
$112$	14.3469	+	27.4197i	0.128098	+	0.244818i
$113$	91.1817			0.806918			0.403459	−	0.914998i	$-0.367808\pi$
$113$	91.1817			0.806918			0.403459	+	0.914998i	$0.367808\pi$
$114$		0			0
$115$			22.9558i			0.199616i
$116$	−31.6202	−	128.637i	−0.272588	−	1.10894i
$117$		0			0
$118$	85.7928	−	109.435i	0.727057	−	0.927418i
$119$		−	46.2849i		−	0.388948i
$120$		0			0
$121$	120.434			0.995321
$122$	−137.953	−	108.149i	−1.13076	−	0.886471i
$123$		0			0
$124$	68.1038	−	16.7406i	0.549224	−	0.135005i
$125$	134.000			1.07200
$126$		0			0
$127$			191.974i			1.51160i	0.654800	+	0.755802i	$0.272753\pi$
$127$			191.974i			1.51160i	−0.654800	+	0.755802i	$0.727247\pi$
$128$	7.44683	+	127.783i	0.0581783	+	0.998306i
$129$		0			0
$130$	−75.0172	−	58.8104i	−0.577055	−	0.452387i
$131$		−	92.3292i		−	0.704803i	−0.935849	−	0.352401i	$-0.885365\pi$
$131$		−	92.3292i		−	0.704803i	0.935849	−	0.352401i	$-0.114635\pi$
$132$		0			0
$133$	8.43073			0.0633890
$134$	129.713	−	165.459i	0.968005	−	1.23477i
$135$		0			0
$136$	78.7357	−	174.503i	0.578939	−	1.28311i
$137$	2.46732			0.0180097			0.00900483	−	0.999959i	$-0.497134\pi$
$137$	2.46732			0.0180097			0.00900483	+	0.999959i	$0.497134\pi$
$138$		0			0
$139$			245.321i			1.76490i	0.470409	+	0.882448i	$0.344106\pi$
$139$			245.321i			1.76490i	−0.470409	+	0.882448i	$0.655894\pi$
$140$	−27.5191	+	6.76447i	−0.196565	+	0.0483176i
$141$		0			0
$142$	92.4883	−	117.976i	0.651326	−	0.830817i
$143$		−	9.79043i		−	0.0684646i
$144$		0			0
$145$	121.302			0.836568
$146$	−76.7083	−	60.1361i	−0.525399	−	0.411891i
$147$		0			0
$148$	39.6319	+	161.230i	0.267783	+	1.08939i
$149$	−52.3645			−0.351439			−0.175720	−	0.984440i	$-0.556225\pi$
$149$	−52.3645			−0.351439			−0.175720	+	0.984440i	$0.556225\pi$
$150$		0			0
$151$		−	25.3459i		−	0.167853i	−0.996472	−	0.0839267i	$-0.973254\pi$
$151$		−	25.3459i		−	0.167853i	0.996472	−	0.0839267i	$-0.0267461\pi$
$152$	31.7855	+	14.3416i	0.209115	+	0.0943527i
$153$		0			0
$154$	−2.29062	−	1.79575i	−0.0148741	−	0.0116607i
$155$			64.2208i			0.414328i
$156$		0			0
$157$	−54.8571			−0.349408			−0.174704	−	0.984621i	$-0.555897\pi$
$157$	−54.8571			−0.349408			−0.174704	+	0.984621i	$0.555897\pi$
$158$	−118.393	+	151.019i	−0.749320	+	0.955816i
$159$		0			0
$160$	−115.259	−	21.3097i	−0.720372	−	0.133185i
$161$	−12.1215			−0.0752888
$162$		0			0
$163$		−	26.8048i		−	0.164446i	−0.996614	−	0.0822232i	$-0.973798\pi$
$163$		−	26.8048i		−	0.164446i	0.996614	−	0.0822232i	$-0.0262020\pi$
$164$	5.26735	+	21.4285i	0.0321180	+	0.130662i
$165$		0			0
$166$	−81.2819	+	103.681i	−0.489650	+	0.624587i
$167$			62.7282i			0.375618i	0.982206	+	0.187809i	$0.0601386\pi$
$167$			62.7282i			0.375618i	−0.982206	+	0.187809i	$0.939861\pi$
$168$		0			0
$169$	0.306683			0.00181469
$170$	137.967	+	108.160i	0.811569	+	0.636236i
$171$		0			0
$172$	−328.385	+	80.7204i	−1.90922	+	0.469305i
$173$	−328.974			−1.90159			−0.950793	−	0.309827i	$-0.899729\pi$
$173$	−328.974			−1.90159			−0.950793	+	0.309827i	$0.899729\pi$
$174$		0			0
$175$			22.4035i			0.128020i
$176$	−5.58130	−	10.6669i	−0.0317119	−	0.0606074i
$177$		0			0
$178$	5.33475	+	4.18222i	0.0299705	+	0.0234956i
$179$		−	335.845i		−	1.87623i	−0.346327	−	0.938114i	$-0.612571\pi$
$179$		−	335.845i		−	1.87623i	0.346327	−	0.938114i	$-0.387429\pi$
$180$		0			0
$181$	−58.9250			−0.325552			−0.162776	−	0.986663i	$-0.552045\pi$
$181$	−58.9250			−0.325552			−0.162776	+	0.986663i	$0.552045\pi$
$182$	31.0540	−	39.6118i	0.170626	−	0.217647i
$183$		0			0
$184$	−45.7004	−	20.6200i	−0.248372	−	0.112065i
$185$	−152.037			−0.821823
$186$		0			0
$187$			18.0059i			0.0962883i
$188$	−71.3099	+	17.5287i	−0.379308	+	0.0932377i
$189$		0			0
$190$	−19.7012	+	25.1305i	−0.103691	+	0.132266i
$191$			98.6857i			0.516679i	0.966054	+	0.258339i	$0.0831753\pi$
$191$			98.6857i			0.516679i	−0.966054	+	0.258339i	$0.916825\pi$
$192$		0			0
$193$	−278.391			−1.44244			−0.721220	−	0.692706i	$-0.756418\pi$
$193$	−278.391			−1.44244			−0.721220	+	0.692706i	$0.756418\pi$
$194$	37.0164	+	29.0193i	0.190806	+	0.149584i
$195$		0			0
$196$	43.2141	+	175.803i	0.220480	+	0.896954i
$197$	47.3378			0.240293			0.120147	−	0.992756i	$-0.461664\pi$
$197$	47.3378			0.240293			0.120147	+	0.992756i	$0.461664\pi$
$198$		0			0
$199$			251.355i			1.26309i	0.775340	+	0.631545i	$0.217579\pi$
$199$			251.355i			1.26309i	−0.775340	+	0.631545i	$0.782421\pi$
$200$	−38.1108	+	84.4655i	−0.190554	+	0.422328i
$201$		0			0
$202$	−241.330	−	189.193i	−1.19470	−	0.936598i
$203$			64.0520i			0.315527i
$204$		0			0
$205$	−20.2068			−0.0985697
$206$	−141.367	+	180.325i	−0.686249	+	0.875364i
$207$		0			0
$208$	184.464	−	96.5178i	0.886844	−	0.464028i
$209$	−3.27976			−0.0156926
$210$		0			0
$211$			38.9936i			0.184804i	0.995722	+	0.0924019i	$0.0294544\pi$
$211$			38.9936i			0.184804i	−0.995722	+	0.0924019i	$0.970546\pi$
$212$	39.3394	+	160.040i	0.185563	+	0.754905i
$213$		0			0
$214$	199.886	−	254.970i	0.934046	−	1.19145i
$215$		−	309.662i		−	1.44029i
$216$		0			0
$217$	−33.9109			−0.156272
$218$	−190.331	−	149.212i	−0.873080	−	0.684458i
$219$		0			0
$220$	10.7056	−	2.63154i	0.0486618	−	0.0119615i
$221$	−311.378			−1.40895
$222$		0			0
$223$		−	189.466i		−	0.849622i	−0.905282	−	0.424811i	$-0.860340\pi$
$223$		−	189.466i		−	0.849622i	0.905282	−	0.424811i	$-0.139660\pi$
$224$	11.2523	−	60.8611i	0.0502334	−	0.271702i
$225$		0			0
$226$	−143.518	−	112.512i	−0.635035	−	0.497841i
$227$			167.625i			0.738438i	0.929342	+	0.369219i	$0.120375\pi$
$227$			167.625i			0.738438i	−0.929342	+	0.369219i	$0.879625\pi$
$228$		0			0
$229$	203.355			0.888013			0.444006	−	0.896024i	$-0.353557\pi$
$229$	203.355			0.888013			0.444006	+	0.896024i	$0.353557\pi$
$230$	28.3260	−	36.1320i	0.123156	−	0.157096i
$231$		0			0
$232$	−108.960	+	241.489i	−0.469653	+	1.04090i
$233$	200.769			0.861671			0.430836	−	0.902430i	$-0.358219\pi$
$233$	200.769			0.861671			0.430836	+	0.902430i	$0.358219\pi$
$234$		0			0
$235$		−	67.2441i		−	0.286145i
$236$	−270.072	+	66.3864i	−1.14437	+	0.281298i
$237$		0			0
$238$	−57.1124	+	72.8514i	−0.239968	+	0.306098i
$239$		−	165.710i		−	0.693349i	−0.937986	−	0.346674i	$-0.887311\pi$
$239$		−	165.710i		−	0.693349i	0.937986	−	0.346674i	$-0.112689\pi$
$240$		0			0
$241$	−396.818			−1.64655			−0.823273	−	0.567646i	$-0.807854\pi$
$241$	−396.818			−1.64655			−0.823273	+	0.567646i	$0.807854\pi$
$242$	−189.560	−	148.607i	−0.783307	−	0.614080i
$243$		0			0
$244$	83.6860	+	340.450i	0.342975	+	1.39529i
$245$	−165.780			−0.676651
$246$		0			0
$247$		−	56.7171i		−	0.229624i
$248$	−127.851	−	57.6862i	−0.515527	−	0.232606i
$249$		0			0
$250$	−210.914	−	165.348i	−0.843655	−	0.661391i
$251$			249.643i			0.994592i	0.867581	+	0.497296i	$0.165674\pi$
$251$			249.643i			0.994592i	−0.867581	+	0.497296i	$0.834326\pi$
$252$		0			0
$253$	4.71555			0.0186385
$254$	236.883	−	302.163i	0.932610	−	1.18962i
$255$		0			0
$256$	145.955	−	210.317i	0.570136	−	0.821550i
$257$	−24.5770			−0.0956302			−0.0478151	−	0.998856i	$-0.515226\pi$
$257$	−24.5770			−0.0956302			−0.0478151	+	0.998856i	$0.515226\pi$
$258$		0			0
$259$		−	80.2811i		−	0.309966i
$260$	45.5074	+	185.132i	0.175029	+	0.712048i
$261$		0			0
$262$	−113.928	+	145.324i	−0.434840	+	0.554672i
$263$			343.809i			1.30726i	0.756816	+	0.653628i	$0.226754\pi$
$263$			343.809i			1.30726i	−0.756816	+	0.653628i	$0.773246\pi$
$264$		0			0
$265$	−150.915			−0.569491
$266$	−13.2698	−	10.4030i	−0.0498864	−	0.0391089i
$267$		0			0
$268$	−408.330	+	100.372i	−1.52362	+	0.374521i
$269$	−64.7826			−0.240828			−0.120414	−	0.992724i	$-0.538422\pi$
$269$	−64.7826			−0.240828			−0.120414	+	0.992724i	$0.538422\pi$
$270$		0			0
$271$		−	113.329i		−	0.418189i	−0.977895	−	0.209095i	$-0.932948\pi$
$271$		−	113.329i		−	0.418189i	0.977895	−	0.209095i	$-0.0670517\pi$
$272$	−339.253	+	177.509i	−1.24725	+	0.652607i
$273$		0			0
$274$	−3.88352	−	3.04451i	−0.0141734	−	0.0111114i
$275$		−	8.71549i		−	0.0316927i
$276$		0			0
$277$	−42.8037			−0.154526			−0.0772629	−	0.997011i	$-0.524618\pi$
$277$	−42.8037			−0.154526			−0.0772629	+	0.997011i	$0.524618\pi$
$278$	302.709	−	386.129i	1.08888	−	1.38895i
$279$		0			0
$280$	51.6614	+	23.3096i	0.184505	+	0.0832486i
$281$	202.018			0.718924			0.359462	−	0.933160i	$-0.382960\pi$
$281$	202.018			0.718924			0.359462	+	0.933160i	$0.382960\pi$
$282$		0			0
$283$		−	77.5872i		−	0.274160i	−0.990560	−	0.137080i	$-0.956228\pi$
$283$		−	77.5872i		−	0.274160i	0.990560	−	0.137080i	$-0.0437717\pi$
$284$	−291.149	+	71.5674i	−1.02517	+	0.251998i
$285$		0			0
$286$	−12.0807	+	15.4099i	−0.0422404	+	0.0538809i
$287$		−	10.6699i		−	0.0371774i
$288$		0			0
$289$	283.665			0.981540
$290$	−190.927	−	149.679i	−0.658370	−	0.516135i
$291$		0			0
$292$	46.5333	+	189.306i	0.159360	+	0.648308i
$293$	−327.131			−1.11649			−0.558243	−	0.829677i	$-0.688524\pi$
$293$	−327.131			−1.11649			−0.558243	+	0.829677i	$0.688524\pi$
$294$		0			0
$295$		−	254.674i		−	0.863300i
$296$	136.567	−	302.675i	0.461375	−	1.02255i
$297$		0			0
$298$	82.4206	+	64.6143i	0.276579	+	0.216826i
$299$			81.5464i			0.272730i
$300$		0			0
$301$	163.513			0.543232
$302$	−31.2751	+	39.8938i	−0.103560	+	0.132099i
$303$		0			0
$304$	−32.3331	−	61.7946i	−0.106359	−	0.203272i
$305$	−321.039			−1.05259
$306$		0			0
$307$			268.290i			0.873910i	0.899483	+	0.436955i	$0.143943\pi$
$307$			268.290i			0.873910i	−0.899483	+	0.436955i	$0.856057\pi$
$308$	1.38955	+	5.65294i	0.00451152	+	0.0183537i
$309$		0			0
$310$	79.2442	−	101.082i	0.255627	−	0.326072i
$311$			449.497i			1.44533i	0.691199	+	0.722664i	$0.257083\pi$
$311$			449.497i			1.44533i	−0.691199	+	0.722664i	$0.742917\pi$
$312$		0			0
$313$	−283.901			−0.907032			−0.453516	−	0.891248i	$-0.649830\pi$
$313$	−283.901			−0.907032			−0.453516	+	0.891248i	$0.649830\pi$
$314$	86.3439	+	67.6900i	0.274981	+	0.215573i
$315$		0			0
$316$	372.695	−	91.6121i	1.17941	−	0.289912i
$317$	553.100			1.74480			0.872398	−	0.488797i	$-0.162564\pi$
$317$	553.100			1.74480			0.872398	+	0.488797i	$0.162564\pi$
$318$		0			0
$319$		−	24.9178i		−	0.0781121i
$320$	155.121	+	175.763i	0.484754	+	0.549261i
$321$		0			0
$322$	19.0790	+	14.9571i	0.0592515	+	0.0464507i
$323$			104.310i			0.322942i
$324$		0			0
$325$	150.718			0.463747
$326$	−33.0753	+	42.1901i	−0.101458	+	0.129418i
$327$		0			0
$328$	18.1507	−	40.2276i	0.0553375	−	0.122645i
$329$	35.5073			0.107925
$330$		0			0
$331$		−	280.828i		−	0.848422i	−0.905563	−	0.424211i	$-0.860552\pi$
$331$		−	280.828i		−	0.848422i	0.905563	−	0.424211i	$-0.139448\pi$
$332$	255.872	−	62.8959i	0.770699	−	0.189445i
$333$		0			0
$334$	77.4024	−	98.7328i	0.231744	−	0.295607i
$335$		−	385.049i		−	1.14940i
$336$		0			0
$337$	93.1413			0.276384			0.138192	−	0.990405i	$-0.455871\pi$
$337$	93.1413			0.276384			0.138192	+	0.990405i	$0.455871\pi$
$338$	−0.482713	−	0.378427i	−0.00142814	−	0.00111961i
$339$		0			0
$340$	−83.6942	−	340.483i	−0.246159	−	1.00142i
$341$	13.1922			0.0386867
$342$		0			0
$343$		−	182.311i		−	0.531518i
$344$	616.475	+	278.153i	1.79208	+	0.808586i
$345$		0			0
$346$	517.799	+	405.932i	1.49653	+	1.17322i
$347$		−	221.251i		−	0.637612i	−0.947820	−	0.318806i	$-0.896718\pi$
$347$		−	221.251i		−	0.637612i	0.947820	−	0.318806i	$-0.103282\pi$
$348$		0			0
$349$	−227.761			−0.652611			−0.326306	−	0.945264i	$-0.605804\pi$
$349$	−227.761			−0.652611			−0.326306	+	0.945264i	$0.605804\pi$
$350$	27.6444	−	35.2626i	0.0789841	−	0.100750i
$351$		0			0
$352$	−4.37740	+	23.6764i	−0.0124358	+	0.0672626i
$353$	169.824			0.481089			0.240545	−	0.970638i	$-0.422674\pi$
$353$	169.824			0.481089			0.240545	+	0.970638i	$0.422674\pi$
$354$		0			0
$355$		−	274.549i		−	0.773378i
$356$	−3.23620	−	13.1654i	−0.00909045	−	0.0369816i
$357$		0			0
$358$	−414.410	+	528.612i	−1.15757	+	1.47657i
$359$		−	585.928i		−	1.63211i	−0.577972	−	0.816056i	$-0.696156\pi$
$359$		−	585.928i		−	1.63211i	0.577972	−	0.816056i	$-0.303844\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	92.7466	+	72.7095i	0.256206	+	0.200855i
$363$		0			0
$364$	−97.7566	+	24.0296i	−0.268562	+	0.0660153i
$365$	−178.512			−0.489075
$366$		0			0
$367$			428.832i			1.16848i	0.811581	+	0.584239i	$0.198607\pi$
$367$			428.832i			1.16848i	−0.811581	+	0.584239i	$0.801393\pi$
$368$	46.4877	+	88.8467i	0.126325	+	0.241431i
$369$		0			0
$370$	239.303	+	187.604i	0.646766	+	0.507037i
$371$		−	79.6886i		−	0.214794i
$372$		0			0
$373$	−127.502			−0.341830			−0.170915	−	0.985286i	$-0.554672\pi$
$373$	−127.502			−0.341830			−0.170915	+	0.985286i	$0.554672\pi$
$374$	22.2181	−	28.3409i	0.0594067	−	0.0757779i
$375$		0			0
$376$	133.869	+	60.4019i	0.356036	+	0.160643i
$377$	430.905			1.14298
$378$		0			0
$379$		−	244.665i		−	0.645555i	−0.946475	−	0.322777i	$-0.895384\pi$
$379$		−	244.665i		−	0.645555i	0.946475	−	0.322777i	$-0.104616\pi$
$380$	62.0187	−	15.2448i	0.163207	−	0.0401179i
$381$		0			0
$382$	121.772	−	155.329i	0.318774	−	0.406621i
$383$		−	685.025i		−	1.78858i	−0.447491	−	0.894288i	$-0.647682\pi$
$383$		−	685.025i		−	1.78858i	0.447491	−	0.894288i	$-0.352318\pi$
$384$		0			0
$385$	−5.33063			−0.0138458
$386$	438.181	+	343.516i	1.13518	+	0.889937i
$387$		0			0
$388$	−22.4551	−	91.3515i	−0.0578740	−	0.235442i
$389$	−290.167			−0.745931			−0.372966	−	0.927845i	$-0.621659\pi$
$389$	−290.167			−0.745931			−0.372966	+	0.927845i	$0.621659\pi$
$390$		0			0
$391$		−	149.975i		−	0.383567i
$392$	148.911	−	330.034i	0.379875	−	0.841922i
$393$		0			0
$394$	−74.5086	−	58.4117i	−0.189108	−	0.148253i
$395$			351.445i			0.889735i
$396$		0			0
$397$	317.752			0.800384			0.400192	−	0.916431i	$-0.368943\pi$
$397$	317.752			0.800384			0.400192	+	0.916431i	$0.368943\pi$
$398$	310.155	−	395.627i	0.779284	−	0.994038i
$399$		0			0
$400$	164.210	−	85.9207i	0.410526	−	0.214802i
$401$	−445.424			−1.11078			−0.555392	−	0.831589i	$-0.687432\pi$
$401$	−445.424			−1.11078			−0.555392	+	0.831589i	$0.687432\pi$
$402$		0			0
$403$			228.133i			0.566087i
$404$	146.397	+	595.571i	0.362369	+	1.47419i
$405$		0			0
$406$	79.0359	−	100.817i	0.194670	−	0.248317i
$407$			31.2313i			0.0767353i
$408$		0			0
$409$	571.233			1.39666			0.698328	−	0.715778i	$-0.253928\pi$
$409$	571.233			1.39666			0.698328	+	0.715778i	$0.253928\pi$
$410$	31.8050	+	24.9338i	0.0775733	+	0.0608142i
$411$		0			0
$412$	445.018	−	109.390i	1.08014	−	0.265509i
$413$	134.477			0.325610
$414$		0			0
$415$			241.283i			0.581406i
$416$	−409.438	−	75.6988i	−0.984227	−	0.181968i
$417$		0			0
$418$	5.16227	+	4.04700i	0.0123499	+	0.00968182i
$419$			308.595i			0.736502i	0.929726	+	0.368251i	$0.120043\pi$
$419$			308.595i			0.736502i	−0.929726	+	0.368251i	$0.879957\pi$
$420$		0			0
$421$	38.8298			0.0922324			0.0461162	−	0.998936i	$-0.485316\pi$
$421$	38.8298			0.0922324			0.0461162	+	0.998936i	$0.485316\pi$
$422$	48.1155	−	61.3751i	0.114018	−	0.145439i
$423$		0			0
$424$	135.559	−	300.441i	0.319715	−	0.708588i
$425$	−277.190			−0.652212
$426$		0			0
$427$		−	169.520i		−	0.397003i
$428$	−629.232	+	154.672i	−1.47017	+	0.361382i
$429$		0			0
$430$	−382.103	+	487.402i	−0.888611	+	1.13349i
$431$		−	479.659i		−	1.11290i	−0.830881	−	0.556450i	$-0.812163\pi$
$431$		−	479.659i		−	1.11290i	0.830881	−	0.556450i	$-0.187837\pi$
$432$		0			0
$433$	434.901			1.00439			0.502195	−	0.864754i	$-0.332526\pi$
$433$	434.901			1.00439			0.502195	+	0.864754i	$0.332526\pi$
$434$	53.3751	+	41.8438i	0.122984	+	0.0964143i
$435$		0			0
$436$	115.460	+	469.713i	0.264817	+	1.07732i
$437$	27.3177			0.0625120
$438$		0			0
$439$		−	25.4779i		−	0.0580363i	−0.999579	−	0.0290182i	$-0.990762\pi$
$439$		−	25.4779i		−	0.0580363i	0.999579	−	0.0290182i	$-0.00923807\pi$
$440$	−20.0975	−	9.06799i	−0.0456762	−	0.0206091i
$441$		0			0
$442$	490.102	+	384.219i	1.10883	+	0.869274i
$443$			805.631i			1.81858i	0.416164	+	0.909290i	$0.363374\pi$
$443$			805.631i			1.81858i	−0.416164	+	0.909290i	$0.636626\pi$
$444$		0			0
$445$	12.4148			0.0278985
$446$	−233.788	+	298.215i	−0.524189	+	0.668644i
$447$		0			0
$448$	−92.8094	+	81.9096i	−0.207164	+	0.182834i
$449$	106.288			0.236721			0.118360	−	0.992971i	$-0.462236\pi$
$449$	106.288			0.236721			0.118360	+	0.992971i	$0.462236\pi$
$450$		0			0
$451$			4.15085i			0.00920366i
$452$	87.0618	+	354.183i	0.192615	+	0.783591i
$453$		0			0
$454$	206.839	−	263.839i	0.455592	−	0.581143i
$455$		−	92.1830i		−	0.202600i
$456$		0			0
$457$	−730.620			−1.59873			−0.799365	−	0.600846i	$-0.794831\pi$
$457$	−730.620			−1.59873			−0.799365	+	0.600846i	$0.794831\pi$
$458$	−320.076	−	250.926i	−0.698856	−	0.547874i
$459$		0			0
$460$	−89.1689	+	21.9186i	−0.193845	+	0.0476491i
$461$	854.696			1.85401			0.927003	−	0.375055i	$-0.122376\pi$
$461$	854.696			1.85401			0.927003	+	0.375055i	$0.122376\pi$
$462$		0			0
$463$		−	769.128i		−	1.66118i	−0.556882	−	0.830591i	$-0.688003\pi$
$463$		−	769.128i		−	1.66118i	0.556882	−	0.830591i	$-0.311997\pi$
$464$	469.481	−	245.649i	1.01181	−	0.529416i
$465$		0			0
$466$	−316.007	−	247.736i	−0.678126	−	0.531622i
$467$			54.2556i			0.116179i	0.998311	+	0.0580895i	$0.0185009\pi$
$467$			54.2556i			0.116179i	−0.998311	+	0.0580895i	$0.981499\pi$
$468$		0			0
$469$	203.320			0.433517
$470$	−82.9748	+	105.841i	−0.176542	+	0.225193i
$471$		0			0
$472$	507.004	+	228.760i	1.07416	+	0.484661i
$473$	−63.6104			−0.134483
$474$		0			0
$475$		−	50.4898i		−	0.106294i
$476$	179.788	−	44.1936i	0.377705	−	0.0928436i
$477$		0			0
$478$	−204.475	+	260.824i	−0.427773	+	0.545658i
$479$		−	512.359i		−	1.06964i	−0.844965	−	0.534821i	$-0.820379\pi$
$479$		−	512.359i		−	1.06964i	0.844965	−	0.534821i	$-0.179621\pi$
$480$		0			0
$481$	−540.085			−1.12284
$482$	624.582	+	489.646i	1.29581	+	1.01586i
$483$		0			0
$484$	114.992	+	467.810i	0.237587	+	0.966549i
$485$	86.1431			0.177615
$486$		0			0
$487$			445.189i			0.914146i	0.889429	+	0.457073i	$0.151102\pi$
$487$			445.189i			0.914146i	−0.889429	+	0.457073i	$0.848898\pi$
$488$	288.373	−	639.124i	0.590927	−	1.30968i
$489$		0			0
$490$	260.933	+	204.561i	0.532517	+	0.417471i
$491$		−	219.288i		−	0.446615i	−0.974748	−	0.223308i	$-0.928315\pi$
$491$		−	219.288i		−	0.446615i	0.974748	−	0.223308i	$-0.0716855\pi$
$492$		0			0
$493$	−792.492			−1.60749
$494$	−69.9851	+	89.2715i	−0.141670	+	0.180711i
$495$		0			0
$496$	130.053	+	248.556i	0.262204	+	0.501121i
$497$	144.972			0.291694
$498$		0			0
$499$			277.168i			0.555446i	0.960661	+	0.277723i	$0.0895798\pi$
$499$			277.168i			0.555446i	−0.960661	+	0.277723i	$0.910420\pi$
$500$	127.946	+	520.507i	0.255892	+	1.04101i
$501$		0			0
$502$	308.042	−	392.932i	0.613630	−	0.782733i
$503$			328.913i			0.653903i	0.945041	+	0.326951i	$0.106021\pi$
$503$			328.913i			0.653903i	−0.945041	+	0.326951i	$0.893979\pi$
$504$		0			0
$505$	−561.614			−1.11211
$506$	−7.42218	−	5.81868i	−0.0146683	−	0.0114994i
$507$		0			0
$508$	−745.697	+	183.300i	−1.46791	+	0.360826i
$509$	371.573			0.730006			0.365003	−	0.931006i	$-0.381068\pi$
$509$	371.573			0.730006			0.365003	+	0.931006i	$0.381068\pi$
$510$		0			0
$511$		−	94.2610i		−	0.184464i
$512$	−489.247	+	150.936i	−0.955560	+	0.294796i
$513$		0			0
$514$	38.6836	+	30.3263i	0.0752599	+	0.0590006i
$515$			419.645i			0.814845i
$516$		0			0
$517$	−13.8132			−0.0267180
$518$	−99.0616	+	126.361i	−0.191239	+	0.243940i
$519$		0			0
$520$	156.813	−	347.548i	0.301564	−	0.668361i
$521$	607.799			1.16660			0.583300	−	0.812256i	$-0.301761\pi$
$521$	607.799			1.16660			0.583300	+	0.812256i	$0.301761\pi$
$522$		0			0
$523$		−	384.474i		−	0.735131i	−0.929998	−	0.367566i	$-0.880191\pi$
$523$		−	384.474i		−	0.735131i	0.929998	−	0.367566i	$-0.119809\pi$
$524$	358.641	−	88.1574i	0.684429	−	0.168239i
$525$		0			0
$526$	424.237	−	541.147i	0.806534	−	1.02880i
$527$		−	419.567i		−	0.796142i
$528$		0			0
$529$	489.723			0.925753
$530$	237.537	+	186.219i	0.448183	+	0.351357i
$531$		0			0
$532$	8.04981	+	32.7481i	0.0151312	+	0.0615566i
$533$	−71.7809			−0.134673
$534$		0			0
$535$		−	593.356i		−	1.10908i
$536$	766.554	+	345.869i	1.43014	+	0.645278i
$537$		0			0
$538$	101.966	+	79.9375i	0.189529	+	0.148583i
$539$			34.0542i			0.0631803i
$540$		0			0
$541$	−382.676			−0.707350			−0.353675	−	0.935368i	$-0.615068\pi$
$541$	−382.676			−0.707350			−0.353675	+	0.935368i	$0.615068\pi$
$542$	−139.841	+	178.378i	−0.258009	+	0.329111i
$543$		0			0
$544$	753.012	+	139.220i	1.38421	+	0.255919i
$545$	−442.932			−0.812719
$546$		0			0
$547$		−	179.104i		−	0.327430i	−0.986508	−	0.163715i	$-0.947652\pi$
$547$		−	179.104i		−	0.327430i	0.986508	−	0.163715i	$-0.0523477\pi$
$548$	2.35584	+	9.58400i	0.00429898	+	0.0174891i
$549$		0			0
$550$	−10.7543	+	13.7180i	−0.0195533	+	0.0249418i
$551$		−	144.351i		−	0.261981i
$552$		0			0
$553$	−185.576			−0.335580
$554$	67.3720	+	52.8169i	0.121610	+	0.0953373i
$555$		0			0
$556$	−952.916	+	234.236i	−1.71388	+	0.421288i
$557$	−720.325			−1.29322			−0.646612	−	0.762819i	$-0.723815\pi$
$557$	−720.325			−1.29322			−0.646612	+	0.762819i	$0.723815\pi$
$558$		0			0
$559$		−	1100.02i		−	1.96783i
$560$	−52.5514	−	100.436i	−0.0938418	−	0.179349i
$561$		0			0
$562$	−317.971	−	249.276i	−0.565785	−	0.443552i
$563$		−	175.948i		−	0.312519i	−0.987716	−	0.156260i	$-0.950056\pi$
$563$		−	175.948i		−	0.312519i	0.987716	−	0.156260i	$-0.0499436\pi$
$564$		0			0
$565$	−333.989			−0.591132
$566$	−95.7374	+	122.121i	−0.169147	+	0.215761i
$567$		0			0
$568$	546.572	+	246.613i	0.962274	+	0.434178i
$569$	547.930			0.962971			0.481485	−	0.876454i	$-0.340097\pi$
$569$	547.930			0.962971			0.481485	+	0.876454i	$0.340097\pi$
$570$		0			0
$571$		−	376.007i		−	0.658507i	−0.944242	−	0.329253i	$-0.893203\pi$
$571$		−	376.007i		−	0.658507i	0.944242	−	0.329253i	$-0.106797\pi$
$572$	38.0297	−	9.34807i	0.0664854	−	0.0163428i
$573$		0			0
$574$	−13.1660	+	16.7942i	−0.0229372	+	0.0292582i
$575$			72.5930i			0.126249i
$576$		0			0
$577$	458.453			0.794546			0.397273	−	0.917700i	$-0.369957\pi$
$577$	458.453			0.794546			0.397273	+	0.917700i	$0.369957\pi$
$578$	−446.483	−	350.024i	−0.772462	−	0.605578i
$579$		0			0
$580$	115.822	+	471.183i	0.199692	+	0.812385i
$581$	−127.406			−0.219288
$582$		0			0
$583$			31.0008i			0.0531745i
$584$	160.348	−	355.382i	0.274569	−	0.608531i
$585$		0			0
$586$	514.896	+	403.657i	0.878663	+	0.688835i
$587$			335.174i			0.570995i	0.958379	+	0.285497i	$0.0921588\pi$
$587$			335.174i			0.570995i	−0.958379	+	0.285497i	$0.907841\pi$
$588$		0			0
$589$	76.4236			0.129752
$590$	−314.250	+	400.851i	−0.532628	+	0.679408i
$591$		0			0
$592$	−588.435	+	307.890i	−0.993978	+	0.520084i
$593$	280.543			0.473092			0.236546	−	0.971620i	$-0.423985\pi$
$593$	280.543			0.473092			0.236546	+	0.971620i	$0.423985\pi$
$594$		0			0
$595$			169.537i			0.284936i
$596$	−49.9985	−	203.403i	−0.0838901	−	0.341280i
$597$		0			0
$598$	100.623	−	128.352i	0.168266	−	0.214636i
$599$		−	677.612i		−	1.13124i	−0.824667	−	0.565619i	$-0.808637\pi$
$599$		−	677.612i		−	1.13124i	0.824667	−	0.565619i	$-0.191363\pi$
$600$		0			0
$601$	177.699			0.295672			0.147836	−	0.989012i	$-0.452769\pi$
$601$	177.699			0.295672			0.147836	+	0.989012i	$0.452769\pi$
$602$	−257.366	−	201.764i	−0.427518	−	0.335156i
$603$		0			0
$604$	98.4527	−	24.2006i	0.163001	−	0.0400673i
$605$	−441.137			−0.729152
$606$		0			0
$607$			826.068i			1.36090i	0.732793	+	0.680451i	$0.238216\pi$
$607$			826.068i			1.36090i	−0.732793	+	0.680451i	$0.761784\pi$
$608$	−25.3588	+	137.160i	−0.0417085	+	0.225593i
$609$		0			0
$610$	505.308	+	396.141i	0.828374	+	0.649411i
$611$		−	238.873i		−	0.390954i
$612$		0			0
$613$	839.090			1.36883			0.684413	−	0.729095i	$-0.260059\pi$
$613$	839.090			1.36883			0.684413	+	0.729095i	$0.260059\pi$
$614$	331.052	−	422.283i	0.539173	−	0.687758i
$615$		0			0
$616$	4.78823	−	10.6122i	0.00777310	−	0.0172276i
$617$	−615.452			−0.997491			−0.498746	−	0.866748i	$-0.666206\pi$
$617$	−615.452			−0.997491			−0.498746	+	0.866748i	$0.666206\pi$
$618$		0			0
$619$		−	118.351i		−	0.191197i	−0.995420	−	0.0955984i	$-0.969524\pi$
$619$		−	118.351i		−	0.191197i	0.995420	−	0.0955984i	$-0.0304765\pi$
$620$	−249.457	+	61.3191i	−0.402351	+	0.0989018i
$621$		0			0
$622$	554.650	−	707.499i	0.891720	−	1.13746i
$623$			6.55547i			0.0105224i
$624$		0			0
$625$	−201.251			−0.322002
$626$	446.854	+	350.315i	0.713824	+	0.559608i
$627$		0			0
$628$	−52.3785	−	213.085i	−0.0834053	−	0.339308i
$629$	993.288			1.57915
$630$		0			0
$631$			665.915i			1.05533i	0.849452	+	0.527667i	$0.176933\pi$
$631$			665.915i			1.05533i	−0.849452	+	0.527667i	$0.823067\pi$
$632$	−699.657	−	315.685i	−1.10705	−	0.499501i
$633$		0			0
$634$	−870.568	−	682.489i	−1.37313	−	1.07648i
$635$		−	703.181i		−	1.10737i
$636$		0			0
$637$	−588.902			−0.924493
$638$	−30.7469	+	39.2200i	−0.0481926	+	0.0614734i
$639$		0			0
$640$	−27.2770	−	468.057i	−0.0426203	−	0.731339i
$641$	−396.009			−0.617798			−0.308899	−	0.951095i	$-0.599961\pi$
$641$	−396.009			−0.617798			−0.308899	+	0.951095i	$0.599961\pi$
$642$		0			0
$643$			890.406i			1.38477i	0.721529	+	0.692384i	$0.243440\pi$
$643$			890.406i			1.38477i	−0.721529	+	0.692384i	$0.756560\pi$
$644$	−11.5738	−	47.0844i	−0.0179718	−	0.0731124i
$645$		0			0
$646$	128.712	−	164.182i	0.199245	−	0.254152i
$647$			1022.42i			1.58025i	0.612945	+	0.790126i	$0.289985\pi$
$647$			1022.42i			1.58025i	−0.612945	+	0.790126i	$0.710015\pi$
$648$		0			0
$649$	−52.3147			−0.0806082
$650$	−237.226	−	185.976i	−0.364964	−	0.286116i
$651$		0			0
$652$	104.120	−	25.5936i	0.159693	−	0.0392541i
$653$	−298.828			−0.457623			−0.228811	−	0.973471i	$-0.573484\pi$
$653$	−298.828			−0.457623			−0.228811	+	0.973471i	$0.573484\pi$
$654$		0			0
$655$			338.193i			0.516324i
$656$	−78.2070	+	40.9207i	−0.119218	+	0.0623790i
$657$		0			0
$658$	−55.8878	−	43.8137i	−0.0849358	−	0.0665861i
$659$		−	76.0870i		−	0.115458i	−0.998332	−	0.0577292i	$-0.981614\pi$
$659$		−	76.0870i		−	0.115458i	0.998332	−	0.0577292i	$-0.0183860\pi$
$660$		0			0
$661$	−63.4958			−0.0960602			−0.0480301	−	0.998846i	$-0.515294\pi$
$661$	−63.4958			−0.0960602			−0.0480301	+	0.998846i	$0.515294\pi$
$662$	−346.523	+	442.017i	−0.523448	+	0.667699i
$663$		0			0
$664$	−480.346	−	216.732i	−0.723413	−	0.326404i
$665$	−30.8809			−0.0464375
$666$		0			0
$667$			207.545i			0.311162i
$668$	−243.659	+	59.8939i	−0.364760	+	0.0896616i
$669$		0			0
$670$	−475.124	+	606.058i	−0.709141	+	0.904565i
$671$			65.9474i			0.0982822i
$672$		0			0
$673$	−814.516			−1.21028			−0.605138	−	0.796120i	$-0.706882\pi$
$673$	−814.516			−1.21028			−0.605138	+	0.796120i	$0.706882\pi$
$674$	−146.602	−	114.930i	−0.217511	−	0.170520i
$675$		0			0
$676$	0.292826	+	1.19127i	0.000433175	+	0.00176224i
$677$	−127.732			−0.188673			−0.0943365	−	0.995540i	$-0.530073\pi$
$677$	−127.732			−0.188673			−0.0943365	+	0.995540i	$0.530073\pi$
$678$		0			0
$679$			45.4866i			0.0669906i
$680$	−288.401	+	639.187i	−0.424119	+	0.939980i
$681$		0			0
$682$	−20.7642	−	16.2782i	−0.0304460	−	0.0238684i
$683$			518.648i			0.759367i	0.925116	+	0.379684i	$0.123967\pi$
$683$			518.648i			0.759367i	−0.925116	+	0.379684i	$0.876033\pi$
$684$		0			0
$685$	−9.03756			−0.0131935
$686$	−224.959	+	286.953i	−0.327929	+	0.418299i
$687$		0			0
$688$	−627.096	−	1198.50i	−0.911476	−	1.74200i
$689$	−536.098			−0.778082
$690$		0			0
$691$			1279.00i			1.85094i	0.378823	+	0.925469i	$0.376329\pi$
$691$			1279.00i			1.85094i	−0.378823	+	0.925469i	$0.623671\pi$
$692$	−314.110	−	1277.86i	−0.453916	−	1.84662i
$693$		0			0
$694$	−273.009	+	348.245i	−0.393385	+	0.501793i
$695$		−	898.585i		−	1.29293i
$696$		0			0
$697$	132.015			0.189404
$698$	358.491	+	281.042i	0.513598	+	0.402639i
$699$		0			0
$700$	−87.0234	+	21.3912i	−0.124319	+	0.0305589i
$701$	−189.067			−0.269710			−0.134855	−	0.990865i	$-0.543057\pi$
$701$	−189.067			−0.269710			−0.134855	+	0.990865i	$0.543057\pi$
$702$		0			0
$703$			180.926i			0.257363i
$704$	36.1051	−	31.8648i	0.0512856	−	0.0452625i
$705$		0			0
$706$	−267.300	−	209.552i	−0.378612	−	0.296816i
$707$		−	296.552i		−	0.419452i
$708$		0			0
$709$	722.894			1.01960			0.509798	−	0.860294i	$-0.329720\pi$
$709$	722.894			1.01960			0.509798	+	0.860294i	$0.329720\pi$
$710$	−338.775	+	432.134i	−0.477148	+	0.608640i
$711$		0			0
$712$	−11.1516	+	24.7154i	−0.0156623	+	0.0347126i
$713$	−109.880			−0.154109
$714$		0			0
$715$			35.8614i			0.0501558i
$716$	1304.55	−	320.670i	1.82199	−	0.447863i
$717$		0			0
$718$	−722.997	+	922.239i	−1.00696	+	1.28446i
$719$			768.781i			1.06924i	0.845094	+	0.534618i	$0.179545\pi$
$719$			768.781i			1.06924i	−0.845094	+	0.534618i	$0.820455\pi$
$720$		0			0
$721$	−221.588			−0.307334
$722$	29.9056	+	23.4447i	0.0414205	+	0.0324719i
$723$		0			0
$724$	−56.2625	−	228.886i	−0.0777107	−	0.316141i
$725$	383.594			0.529095
$726$		0			0
$727$		−	1092.23i		−	1.50238i	−0.660085	−	0.751191i	$-0.729480\pi$
$727$		−	1092.23i		−	1.50238i	0.660085	−	0.751191i	$-0.270520\pi$
$728$	183.518	+	82.8032i	0.252085	+	0.113741i
$729$		0			0
$730$	280.975	+	220.273i	0.384897	+	0.301743i
$731$			2023.08i			2.76756i
$732$		0			0
$733$	571.768			0.780038			0.390019	−	0.920807i	$-0.372468\pi$
$733$	571.768			0.780038			0.390019	+	0.920807i	$0.372468\pi$
$734$	529.150	−	674.972i	0.720912	−	0.919580i
$735$		0			0
$736$	36.4602	−	197.206i	0.0495384	−	0.267942i
$737$	−79.0961			−0.107322
$738$		0			0
$739$			299.431i			0.405184i	0.979263	+	0.202592i	$0.0649365\pi$
$739$			299.431i			0.405184i	−0.979263	+	0.202592i	$0.935063\pi$
$740$	−145.168	−	590.569i	−0.196173	−	0.798066i
$741$		0			0
$742$	−98.3304	+	125.428i	−0.132521	+	0.169041i
$743$		−	16.0943i		−	0.0216612i	−0.999941	−	0.0108306i	$-0.996552\pi$
$743$		−	16.0943i		−	0.0216612i	0.999941	−	0.0108306i	$-0.00344755\pi$
$744$		0			0
$745$	191.806			0.257458
$746$	200.686	+	157.330i	0.269016	+	0.210898i
$747$		0			0
$748$	−69.9416	+	17.1924i	−0.0935049	+	0.0229844i
$749$	313.313			0.418309
$750$		0			0
$751$		−	699.482i		−	0.931401i	−0.884942	−	0.465701i	$-0.845802\pi$
$751$		−	699.482i		−	0.931401i	0.884942	−	0.465701i	$-0.154198\pi$
$752$	−136.176	−	260.257i	−0.181085	−	0.346087i
$753$		0			0
$754$	−678.235	−	531.708i	−0.899516	−	0.705183i
$755$			92.8393i			0.122966i
$756$		0			0
$757$	11.5679			0.0152812			0.00764062	−	0.999971i	$-0.497568\pi$
$757$	11.5679			0.0152812			0.00764062	+	0.999971i	$0.497568\pi$
$758$	−301.901	+	385.098i	−0.398286	+	0.508045i
$759$		0			0
$760$	−116.427	−	52.5319i	−0.153194	−	0.0691209i
$761$	354.338			0.465622			0.232811	−	0.972522i	$-0.425208\pi$
$761$	354.338			0.465622			0.232811	+	0.972522i	$0.425208\pi$
$762$		0			0
$763$		−	233.884i		−	0.306532i
$764$	−383.332	+	94.2267i	−0.501743	+	0.123333i
$765$		0			0
$766$	−845.275	+	1078.21i	−1.10349	+	1.40759i
$767$		−	904.682i		−	1.17951i
$768$		0			0
$769$	847.602			1.10221			0.551106	−	0.834435i	$-0.314206\pi$
$769$	847.602			1.10221			0.551106	+	0.834435i	$0.314206\pi$
$770$	8.39030	+	6.57764i	0.0108965	+	0.00854239i
$771$		0			0
$772$	−265.812	−	1081.37i	−0.344316	−	1.40074i
$773$	−712.408			−0.921615			−0.460807	−	0.887500i	$-0.652440\pi$
$773$	−712.408			−0.921615			−0.460807	+	0.887500i	$0.652440\pi$
$774$		0			0
$775$			203.085i			0.262045i
$776$	−77.3778	+	171.493i	−0.0997137	+	0.220997i
$777$		0			0
$778$	456.717	+	358.047i	0.587040	+	0.460215i
$779$			24.0463i			0.0308682i
$780$		0			0
$781$	−56.3975			−0.0722119
$782$	−185.059	+	236.057i	−0.236648	+	0.301863i
$783$		0			0
$784$	−641.622	+	335.719i	−0.818396	+	0.428213i
$785$	200.936			0.255970
$786$		0			0
$787$		−	514.229i		−	0.653404i	−0.945127	−	0.326702i	$-0.894063\pi$
$787$		−	514.229i		−	0.653404i	0.945127	−	0.326702i	$-0.105937\pi$
$788$	45.1989	+	183.877i	0.0573590	+	0.233347i
$789$		0			0
$790$	433.660	−	553.167i	0.548937	−	0.700212i
$791$		−	176.358i		−	0.222956i
$792$		0			0
$793$	−1140.43			−1.43812
$794$	−500.135	−	392.085i	−0.629894	−	0.493810i
$795$		0			0
$796$	−976.355	+	239.998i	−1.22658	+	0.301505i
$797$	−934.459			−1.17247			−0.586235	−	0.810141i	$-0.699391\pi$
$797$	−934.459			−1.17247			−0.586235	+	0.810141i	$0.699391\pi$
$798$		0			0
$799$			439.319i			0.549836i
$800$	−364.484	−	67.3874i	−0.455605	−	0.0842343i
$801$		0			0
$802$	701.088	+	549.624i	0.874175	+	0.685316i
$803$			36.6698i			0.0456660i
$804$		0			0
$805$	44.3998			0.0551551
$806$	281.501	−	359.076i	0.349257	−	0.445504i
$807$		0			0
$808$	504.469	−	1118.06i	0.624342	−	1.38374i
$809$	−1126.44			−1.39239			−0.696195	−	0.717853i	$-0.745125\pi$
$809$	−1126.44			−1.39239			−0.696195	+	0.717853i	$0.745125\pi$
$810$		0			0
$811$		−	938.339i		−	1.15702i	−0.815677	−	0.578508i	$-0.803635\pi$
$811$		−	938.339i		−	1.15702i	0.815677	−	0.578508i	$-0.196365\pi$
$812$	−248.802	+	61.1580i	−0.306406	+	0.0753177i
$813$		0			0
$814$	38.5373	−	49.1573i	0.0473431	−	0.0603899i
$815$			98.1832i			0.120470i
$816$		0			0
$817$	−368.502			−0.451043
$818$	−899.108	−	704.863i	−1.09915	−	0.861691i
$819$		0			0
$820$	−19.2938	−	78.4906i	−0.0235290	−	0.0957202i
$821$	−509.877			−0.621044			−0.310522	−	0.950566i	$-0.600504\pi$
$821$	−509.877			−0.621044			−0.310522	+	0.950566i	$0.600504\pi$
$822$		0			0
$823$			791.322i			0.961509i	0.876855	+	0.480754i	$0.159637\pi$
$823$			791.322i			0.961509i	−0.876855	+	0.480754i	$0.840363\pi$
$824$	−835.429	−	376.945i	−1.01387	−	0.457458i
$825$		0			0
$826$	−211.664	−	165.935i	−0.256251	−	0.200890i
$827$		−	725.787i		−	0.877615i	−0.898581	−	0.438807i	$-0.855401\pi$
$827$		−	725.787i		−	0.877615i	0.898581	−	0.438807i	$-0.144599\pi$
$828$		0			0
$829$	−987.501			−1.19120			−0.595598	−	0.803283i	$-0.703085\pi$
$829$	−987.501			−1.19120			−0.595598	+	0.803283i	$0.703085\pi$
$830$	297.728	−	379.775i	0.358708	−	0.457560i
$831$		0			0
$832$	551.040	+	624.368i	0.662308	+	0.750442i
$833$	1083.07			1.30020
$834$		0			0
$835$		−	229.767i		−	0.275170i
$836$	−3.13157	−	12.7398i	−0.00374589	−	0.0152390i
$837$		0			0
$838$	380.785	−	485.721i	0.454397	−	0.579620i
$839$			1549.38i			1.84670i	0.383959	+	0.923350i	$0.374561\pi$
$839$			1549.38i			1.84670i	−0.383959	+	0.923350i	$0.625439\pi$
$840$		0			0
$841$	255.702			0.304045
$842$	−61.1173	−	47.9134i	−0.0725859	−	0.0569043i
$843$		0			0
$844$	−151.466	+	37.2317i	−0.179462	+	0.0441134i
$845$	−1.12335			−0.00132941
$846$		0			0
$847$		−	232.936i		−	0.275013i
$848$	−584.092	+	305.617i	−0.688787	+	0.360398i
$849$		0			0
$850$	436.291	+	342.034i	0.513284	+	0.402393i
$851$		−	260.131i		−	0.305677i
$852$		0			0
$853$	−108.740			−0.127480			−0.0637399	−	0.997967i	$-0.520303\pi$
$853$	−108.740			−0.127480			−0.0637399	+	0.997967i	$0.520303\pi$
$854$	−209.177	+	266.821i	−0.244937	+	0.312437i
$855$		0			0
$856$	1181.25	+	532.981i	1.37997	+	0.622641i
$857$	958.909			1.11891			0.559457	−	0.828860i	$-0.311010\pi$
$857$	958.909			1.11891			0.559457	+	0.828860i	$0.311010\pi$
$858$		0			0
$859$			1060.62i			1.23471i	0.786684	+	0.617356i	$0.211796\pi$
$859$			1060.62i			1.23471i	−0.786684	+	0.617356i	$0.788204\pi$
$860$	1202.84	−	295.671i	1.39865	−	0.343803i
$861$		0			0
$862$	−591.868	+	754.974i	−0.686622	+	0.875840i
$863$		−	838.621i		−	0.971751i	−0.874028	−	0.485875i	$-0.838501\pi$
$863$		−	838.621i		−	0.971751i	0.874028	−	0.485875i	$-0.161499\pi$
$864$		0			0
$865$	1205.00			1.39306
$866$	−684.525	−	536.639i	−0.790444	−	0.619675i
$867$		0			0
$868$	−32.3787	−	131.723i	−0.0373027	−	0.151754i
$869$	72.1934			0.0830764
$870$		0			0
$871$		−	1367.82i		−	1.57040i
$872$	397.862	−	881.788i	0.456264	−	1.01122i
$873$		0			0
$874$	−42.9975	−	33.7083i	−0.0491962	−	0.0385678i
$875$		−	259.176i		−	0.296201i
$876$		0			0
$877$	1453.86			1.65776			0.828882	−	0.559424i	$-0.188978\pi$
$877$	1453.86			1.65776			0.828882	+	0.559424i	$0.188978\pi$
$878$	−31.4381	+	40.1017i	−0.0358065	+	0.0456740i
$879$		0			0
$880$	20.4437	+	39.0718i	0.0232315	+	0.0443998i
$881$	−156.229			−0.177332			−0.0886659	−	0.996061i	$-0.528260\pi$
$881$	−156.229			−0.177332			−0.0886659	+	0.996061i	$0.528260\pi$
$882$		0			0
$883$			37.1369i			0.0420577i	0.999779	+	0.0210288i	$0.00669418\pi$
$883$			37.1369i			0.0420577i	−0.999779	+	0.0210288i	$0.993306\pi$
$884$	−297.309	−	1209.51i	−0.336322	−	1.36822i
$885$		0			0
$886$	994.094	−	1268.05i	1.12200	−	1.43120i
$887$		−	490.932i		−	0.553474i	−0.960946	−	0.276737i	$-0.910747\pi$
$887$		−	490.932i		−	0.553474i	0.960946	−	0.276737i	$-0.0892532\pi$
$888$		0			0
$889$	371.305			0.417666
$890$	−19.5407	−	15.3191i	−0.0219558	−	0.0172124i
$891$		0			0
$892$	735.955	−	180.905i	0.825062	−	0.202808i
$893$	−80.0214			−0.0896096
$894$		0			0
$895$			1230.17i			1.37449i
$896$	247.151	−	14.4032i	0.275838	−	0.0160750i
$897$		0			0
$898$	−167.294	−	131.152i	−0.186297	−	0.146049i
$899$			580.624i			0.645856i
$900$		0			0
$901$	985.957			1.09429
$902$	5.12187	−	6.53335i	0.00567835	−	0.00724318i
$903$		0			0
$904$	300.005	−	664.905i	0.331864	−	0.735515i
$905$	215.836			0.238493
$906$		0			0
$907$			167.806i			0.185012i	0.995712	+	0.0925060i	$0.0294877\pi$
$907$			167.806i			0.185012i	−0.995712	+	0.0925060i	$0.970512\pi$
$908$	−651.119	+	160.052i	−0.717091	+	0.176268i
$909$		0			0
$910$	−113.748	+	145.094i	−0.124997	+	0.159444i
$911$			1217.97i			1.33696i	0.743730	+	0.668481i	$0.233055\pi$
$911$			1217.97i			1.33696i	−0.743730	+	0.668481i	$0.766945\pi$
$912$		0			0
$913$	49.5641			0.0542871
$914$	1149.98	+	901.536i	1.25818	+	0.986363i
$915$		0			0
$916$	194.167	+	789.906i	0.211972	+	0.862342i
$917$	−178.578			−0.194741
$918$		0			0
$919$		−	1037.14i		−	1.12855i	−0.825585	−	0.564277i	$-0.809155\pi$
$919$		−	1037.14i		−	1.12855i	0.825585	−	0.564277i	$-0.190845\pi$
$920$	167.396	+	75.5291i	0.181952	+	0.0820968i
$921$		0			0
$922$	−1345.27	−	1054.64i	−1.45908	−	1.14386i
$923$		−	975.286i		−	1.05665i
$924$		0			0
$925$	−480.786			−0.519769
$926$	−949.052	+	1210.59i	−1.02489	+	1.30733i
$927$		0			0
$928$	−1042.07	−	192.662i	−1.12292	−	0.207610i
$929$	98.9780			0.106543			0.0532713	−	0.998580i	$-0.483035\pi$
$929$	98.9780			0.106543			0.0532713	+	0.998580i	$0.483035\pi$
$930$		0			0
$931$			197.280i			0.211901i
$932$	191.698	+	779.862i	0.205685	+	0.836762i
$933$		0			0
$934$	66.9478	−	85.3971i	0.0716786	−	0.0914316i
$935$		−	65.9539i		−	0.0705389i
$936$		0			0
$937$	1744.65			1.86195			0.930974	−	0.365084i	$-0.118960\pi$
$937$	1744.65			1.86195			0.930974	+	0.365084i	$0.118960\pi$
$938$	−320.021	−	250.883i	−0.341173	−	0.267466i
$939$		0			0
$940$	261.201	−	64.2058i	0.277873	−	0.0683041i
$941$	723.767			0.769147			0.384574	−	0.923094i	$-0.374348\pi$
$941$	723.767			0.769147			0.384574	+	0.923094i	$0.374348\pi$
$942$		0			0
$943$		−	34.5732i		−	0.0366630i
$944$	−515.738	−	985.672i	−0.546333	−	1.04414i
$945$		0			0
$946$	100.121	+	78.4910i	0.105837	+	0.0829715i
$947$			819.583i			0.865452i	0.901526	+	0.432726i	$0.142448\pi$
$947$			819.583i			0.865452i	−0.901526	+	0.432726i	$0.857552\pi$
$948$		0			0
$949$	−634.133			−0.668212
$950$	−62.3011	+	79.4699i	−0.0655801	+	0.0836525i
$951$		0			0
$952$	−337.514	−	152.286i	−0.354531	−	0.159964i
$953$	−1777.86			−1.86554			−0.932771	−	0.360470i	$-0.882616\pi$
$953$	−1777.86			−1.86554			−0.932771	+	0.360470i	$0.882616\pi$
$954$		0			0
$955$		−	361.476i		−	0.378509i
$956$	643.680	−	158.223i	0.673306	−	0.165505i
$957$		0			0
$958$	−632.216	+	806.441i	−0.659934	+	0.841797i
$959$		−	4.77216i		−	0.00497618i
$960$		0			0
$961$	653.601			0.680126
$962$	850.082	+	666.428i	0.883661	+	0.692753i
$963$		0			0
$964$	−378.888	−	1541.39i	−0.393037	−	1.59895i
$965$	1019.72			1.05670
$966$		0			0
$967$			1306.29i			1.35087i	0.737421	+	0.675433i	$0.236043\pi$
$967$			1306.29i			1.35087i	−0.737421	+	0.675433i	$0.763957\pi$
$968$	396.250	−	878.215i	0.409350	−	0.907247i
$969$		0			0
$970$	−135.587	−	106.295i	−0.139781	−	0.109582i
$971$		−	940.020i		−	0.968094i	−0.875042	−	0.484047i	$-0.839166\pi$
$971$		−	940.020i		−	0.968094i	0.875042	−	0.484047i	$-0.160834\pi$
$972$		0			0
$973$	474.485			0.487652
$974$	549.334	−	700.718i	0.563998	−	0.719423i
$975$		0			0
$976$	−1242.53	+	650.134i	−1.27308	+	0.666121i
$977$	549.002			0.561927			0.280963	−	0.959719i	$-0.409346\pi$
$977$	549.002			0.561927			0.280963	+	0.959719i	$0.409346\pi$
$978$		0			0
$979$		−	2.55023i		−	0.00260494i
$980$	−158.289	−	643.949i	−0.161519	−	0.657091i
$981$		0			0
$982$	−270.587	+	345.155i	−0.275547	+	0.351482i
$983$			506.118i			0.514871i	0.966295	+	0.257436i	$0.0828775\pi$
$983$			506.118i			0.514871i	−0.966295	+	0.257436i	$0.917122\pi$
$984$		0			0
$985$	−173.394			−0.176034
$986$	1247.36	+	977.882i	1.26508	+	0.991767i
$987$		0			0
$988$	220.310	−	54.1544i	0.222986	−	0.0548122i
$989$	529.823			0.535716
$990$		0			0
$991$		−	213.024i		−	0.214959i	−0.994207	−	0.107479i	$-0.965722\pi$
$991$		−	213.024i		−	0.214959i	0.994207	−	0.107479i	$-0.0342780\pi$
$992$	102.001	−	551.699i	0.102823	−	0.556148i
$993$		0			0
$994$	−228.183	−	178.886i	−0.229560	−	0.179965i
$995$		−	920.687i		−	0.925314i
$996$		0			0
$997$	−940.041			−0.942870			−0.471435	−	0.881901i	$-0.656264\pi$
$997$	−940.041			−0.942870			−0.471435	+	0.881901i	$0.656264\pi$
$998$	342.007	−	436.256i	0.342692	−	0.437130i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.b.343.3		14
3.2	odd	2		76.3.b.b.39.12	yes	14
4.3	odd	2	inner	684.3.g.b.343.4		14
12.11	even	2		76.3.b.b.39.11	✓	14
24.5	odd	2		1216.3.d.d.191.10		14
24.11	even	2		1216.3.d.d.191.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.11	✓	14	12.11	even	2
76.3.b.b.39.12	yes	14	3.2	odd	2
684.3.g.b.343.3		14	1.1	even	1	trivial
684.3.g.b.343.4		14	4.3	odd	2	inner
1216.3.d.d.191.5		14	24.11	even	2
1216.3.d.d.191.10		14	24.5	odd	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57398 - 1.23393i) q^{2} +(0.954817 + 3.88437i) q^{4} -3.66290 q^{5} -1.93414i q^{7} +(3.29019 - 7.29209i) q^{8} +O(q^{10})\)	\(q+(-1.57398 - 1.23393i) q^{2} +(0.954817 + 3.88437i) q^{4} -3.66290 q^{5} -1.93414i q^{7} +(3.29019 - 7.29209i) q^{8} +(5.76533 + 4.51977i) q^{10} +0.752428i q^{11} -13.0118 q^{13} +(-2.38660 + 3.04430i) q^{14} +(-14.1766 + 7.41772i) q^{16} +23.9304 q^{17} +4.35890i q^{19} +(-3.49740 - 14.2281i) q^{20} +(0.928446 - 1.18431i) q^{22} -6.26712i q^{23} -11.5832 q^{25} +(20.4803 + 16.0557i) q^{26} +(7.51293 - 1.84675i) q^{28} -33.1165 q^{29} -17.5328i q^{31} +(31.4667 + 5.81771i) q^{32} +(-37.6660 - 29.5285i) q^{34} +7.08457i q^{35} +41.5073 q^{37} +(5.37859 - 6.86081i) q^{38} +(-12.0516 + 26.7102i) q^{40} +5.51661 q^{41} +84.5402i q^{43} +(-2.92271 + 0.718431i) q^{44} +(-7.73320 + 9.86431i) q^{46} +18.3582i q^{47} +45.2591 q^{49} +(18.2316 + 14.2929i) q^{50} +(-12.4239 - 50.5426i) q^{52} +41.2010 q^{53} -2.75607i q^{55} +(-14.1040 - 6.36370i) q^{56} +(52.1246 + 40.8635i) q^{58} +69.5279i q^{59} +87.6461 q^{61} +(-21.6343 + 27.5962i) q^{62} +(-42.3493 - 47.9848i) q^{64} +47.6609 q^{65} +105.121i q^{67} +(22.8492 + 92.9546i) q^{68} +(8.74189 - 11.1510i) q^{70} +74.9540i q^{71} +48.7353 q^{73} +(-65.3316 - 51.2173i) q^{74} +(-16.9316 + 4.16195i) q^{76} +1.45530 q^{77} -95.9473i q^{79} +(51.9277 - 27.1704i) q^{80} +(-8.68302 - 6.80713i) q^{82} -65.8722i q^{83} -87.6548 q^{85} +(104.317 - 133.064i) q^{86} +(5.48677 + 2.47563i) q^{88} -3.38934 q^{89} +25.1667i q^{91} +(24.3438 - 5.98395i) q^{92} +(22.6528 - 28.8954i) q^{94} -15.9662i q^{95} -23.5177 q^{97} +(-71.2368 - 55.8467i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Introduction

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