LMFDB - Embedded newform 684.3.g.d.343.11

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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.11
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07034 - 1.68949i) q^{2} +(-1.70873 + 3.61666i) q^{4} -6.66582 q^{5} +12.1510i q^{7} +(7.93923 - 0.984190i) q^{8} +O(q^{10})$	\(q+(-1.07034 - 1.68949i) q^{2} +(-1.70873 + 3.61666i) q^{4} -6.66582 q^{5} +12.1510i q^{7} +(7.93923 - 0.984190i) q^{8} +(7.13471 + 11.2618i) q^{10} -4.93767i q^{11} +11.2570 q^{13} +(20.5290 - 13.0058i) q^{14} +(-10.1605 - 12.3598i) q^{16} +17.2061 q^{17} +4.35890i q^{19} +(11.3901 - 24.1080i) q^{20} +(-8.34214 + 5.28501i) q^{22} +16.0420i q^{23} +19.4331 q^{25} +(-12.0488 - 19.0185i) q^{26} +(-43.9461 - 20.7628i) q^{28} -50.3944 q^{29} -6.35866i q^{31} +(-10.0065 + 30.3952i) q^{32} +(-18.4164 - 29.0695i) q^{34} -80.9965i q^{35} -36.0832 q^{37} +(7.36430 - 4.66552i) q^{38} +(-52.9215 + 6.56043i) q^{40} +11.8766 q^{41} +59.2181i q^{43} +(17.8579 + 8.43716i) q^{44} +(27.1028 - 17.1705i) q^{46} +35.3518i q^{47} -98.6473 q^{49} +(-20.8001 - 32.8320i) q^{50} +(-19.2352 + 40.7127i) q^{52} -38.6046 q^{53} +32.9136i q^{55} +(11.9589 + 96.4697i) q^{56} +(53.9393 + 85.1406i) q^{58} -89.8121i q^{59} -85.8862 q^{61} +(-10.7429 + 6.80595i) q^{62} +(62.0627 - 15.6274i) q^{64} -75.0370 q^{65} -103.436i q^{67} +(-29.4006 + 62.2286i) q^{68} +(-136.842 + 86.6940i) q^{70} -67.2102i q^{71} +109.478 q^{73} +(38.6214 + 60.9620i) q^{74} +(-15.7647 - 7.44819i) q^{76} +59.9978 q^{77} -66.3475i q^{79} +(67.7279 + 82.3882i) q^{80} +(-12.7120 - 20.0654i) q^{82} +4.01466i q^{83} -114.693 q^{85} +(100.048 - 63.3836i) q^{86} +(-4.85961 - 39.2013i) q^{88} -53.9336 q^{89} +136.784i q^{91} +(-58.0186 - 27.4115i) q^{92} +(59.7263 - 37.8385i) q^{94} -29.0556i q^{95} -62.8736 q^{97} +(105.586 + 166.663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

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 $

$2$	−1.07034	−	1.68949i	−0.535172	−	0.844743i
$2$	−1.07034	−	1.68949i	−0.535172	−	0.844743i
$3$		0			0
$3$		0			0
$4$	−1.70873	+	3.61666i	−0.427183	+	0.904165i
$5$	−6.66582			−1.33316			−0.666582	−	0.745432i	$-0.732243\pi$
$5$	−6.66582			−1.33316			−0.666582	+	0.745432i	$0.732243\pi$
$6$		0			0
$7$			12.1510i			1.73586i	0.496687	+	0.867930i	$0.334550\pi$
$7$			12.1510i			1.73586i	−0.496687	+	0.867930i	$0.665450\pi$
$8$	7.93923	−	0.984190i	0.992404	−	0.123024i
$9$		0			0
$10$	7.13471	+	11.2618i	0.713471	+	1.12618i
$11$		−	4.93767i		−	0.448880i	−0.974488	−	0.224440i	$-0.927945\pi$
$11$		−	4.93767i		−	0.448880i	0.974488	−	0.224440i	$-0.0720552\pi$
$12$		0			0
$13$	11.2570			0.865922			0.432961	−	0.901413i	$-0.357469\pi$
$13$	11.2570			0.865922			0.432961	+	0.901413i	$0.357469\pi$
$14$	20.5290	−	13.0058i	1.46636	−	0.928983i
$15$		0			0
$16$	−10.1605	−	12.3598i	−0.635030	−	0.772488i
$17$	17.2061			1.01212			0.506062	−	0.862497i	$-0.331101\pi$
$17$	17.2061			1.01212			0.506062	+	0.862497i	$0.331101\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	11.3901	−	24.1080i	0.569505	−	1.20540i
$21$		0			0
$22$	−8.34214	+	5.28501i	−0.379188	+	0.240228i
$23$			16.0420i			0.697480i	0.937220	+	0.348740i	$0.113390\pi$
$23$			16.0420i			0.697480i	−0.937220	+	0.348740i	$0.886610\pi$
$24$		0			0
$25$	19.4331			0.777325
$26$	−12.0488	−	19.0185i	−0.463417	−	0.731482i
$27$		0			0
$28$	−43.9461	−	20.7628i	−1.56950	−	0.741529i
$29$	−50.3944			−1.73774			−0.868869	−	0.495043i	$-0.835152\pi$
$29$	−50.3944			−1.73774			−0.868869	+	0.495043i	$0.835152\pi$
$30$		0			0
$31$		−	6.35866i		−	0.205118i	−0.994727	−	0.102559i	$-0.967297\pi$
$31$		−	6.35866i		−	0.205118i	0.994727	−	0.102559i	$-0.0327031\pi$
$32$	−10.0065	+	30.3952i	−0.312704	+	0.949851i
$33$		0			0
$34$	−18.4164	−	29.0695i	−0.541660	−	0.854985i
$35$		−	80.9965i		−	2.31419i
$36$		0			0
$37$	−36.0832			−0.975221			−0.487610	−	0.873061i	$-0.662131\pi$
$37$	−36.0832			−0.975221			−0.487610	+	0.873061i	$0.662131\pi$
$38$	7.36430	−	4.66552i	0.193797	−	0.122777i
$39$		0			0
$40$	−52.9215	+	6.56043i	−1.32304	+	0.164011i
$41$	11.8766			0.289673			0.144837	−	0.989456i	$-0.453734\pi$
$41$	11.8766			0.289673			0.144837	+	0.989456i	$0.453734\pi$
$42$		0			0
$43$			59.2181i			1.37716i	0.725158	+	0.688582i	$0.241767\pi$
$43$			59.2181i			1.37716i	−0.725158	+	0.688582i	$0.758233\pi$
$44$	17.8579	+	8.43716i	0.405861	+	0.191754i
$45$		0			0
$46$	27.1028	−	17.1705i	0.589192	−	0.373271i
$47$			35.3518i			0.752165i	0.926586	+	0.376083i	$0.122729\pi$
$47$			35.3518i			0.752165i	−0.926586	+	0.376083i	$0.877271\pi$
$48$		0			0
$49$	−98.6473			−2.01321
$50$	−20.8001	−	32.8320i	−0.416002	−	0.656640i
$51$		0			0
$52$	−19.2352	+	40.7127i	−0.369907	+	0.782937i
$53$	−38.6046			−0.728388			−0.364194	−	0.931323i	$-0.618655\pi$
$53$	−38.6046			−0.728388			−0.364194	+	0.931323i	$0.618655\pi$
$54$		0			0
$55$			32.9136i			0.598430i
$56$	11.9589	+	96.4697i	0.213552	+	1.72267i
$57$		0			0
$58$	53.9393	+	85.1406i	0.929988	+	1.46794i
$59$		−	89.8121i		−	1.52224i	−0.648612	−	0.761119i	$-0.724650\pi$
$59$		−	89.8121i		−	1.52224i	0.648612	−	0.761119i	$-0.275350\pi$
$60$		0			0
$61$	−85.8862			−1.40797			−0.703985	−	0.710215i	$-0.748598\pi$
$61$	−85.8862			−1.40797			−0.703985	+	0.710215i	$0.748598\pi$
$62$	−10.7429	+	6.80595i	−0.173272	+	0.109773i
$63$		0			0
$64$	62.0627	−	15.6274i	0.969730	−	0.244178i
$65$	−75.0370			−1.15442
$66$		0			0
$67$		−	103.436i		−	1.54383i	−0.635729	−	0.771913i	$-0.719300\pi$
$67$		−	103.436i		−	1.54383i	0.635729	−	0.771913i	$-0.280700\pi$
$68$	−29.4006	+	62.2286i	−0.432362	+	0.915127i
$69$		0			0
$70$	−136.842	+	86.6940i	−1.95489	+	1.23849i
$71$		−	67.2102i		−	0.946623i	−0.880895	−	0.473311i	$-0.843059\pi$
$71$		−	67.2102i		−	0.946623i	0.880895	−	0.473311i	$-0.156941\pi$
$72$		0			0
$73$	109.478			1.49970			0.749848	−	0.661610i	$-0.230126\pi$
$73$	109.478			1.49970			0.749848	+	0.661610i	$0.230126\pi$
$74$	38.6214	+	60.9620i	0.521910	+	0.823811i
$75$		0			0
$76$	−15.7647	−	7.44819i	−0.207430	−	0.0980025i
$77$	59.9978			0.779192
$78$		0			0
$79$		−	66.3475i		−	0.839841i	−0.907561	−	0.419921i	$-0.862058\pi$
$79$		−	66.3475i		−	0.839841i	0.907561	−	0.419921i	$-0.137942\pi$
$80$	67.7279	+	82.3882i	0.846599	+	1.02985i
$81$		0			0
$82$	−12.7120	−	20.0654i	−0.155025	−	0.244700i
$83$			4.01466i			0.0483694i	0.999708	+	0.0241847i	$0.00769898\pi$
$83$			4.01466i			0.0483694i	−0.999708	+	0.0241847i	$0.992301\pi$
$84$		0			0
$85$	−114.693			−1.34933
$86$	100.048	−	63.3836i	1.16335	−	0.737019i
$87$		0			0
$88$	−4.85961	−	39.2013i	−0.0552228	−	0.445470i
$89$	−53.9336			−0.605996			−0.302998	−	0.952991i	$-0.597988\pi$
$89$	−53.9336			−0.605996			−0.302998	+	0.952991i	$0.597988\pi$
$90$		0			0
$91$			136.784i			1.50312i
$92$	−58.0186	−	27.4115i	−0.630637	−	0.297951i
$93$		0			0
$94$	59.7263	−	37.8385i	0.635386	−	0.402537i
$95$		−	29.0556i		−	0.305849i
$96$		0			0
$97$	−62.8736			−0.648181			−0.324090	−	0.946026i	$-0.605058\pi$
$97$	−62.8736			−0.648181			−0.324090	+	0.946026i	$0.605058\pi$
$98$	105.586	+	166.663i	1.07741	+	1.70065i
$99$		0			0
$100$	−33.2060	+	70.2830i	−0.332060	+	0.702830i
$101$	−73.2286			−0.725036			−0.362518	−	0.931977i	$-0.618083\pi$
$101$	−73.2286			−0.725036			−0.362518	+	0.931977i	$0.618083\pi$
$102$		0			0
$103$			53.3144i			0.517615i	0.965929	+	0.258808i	$0.0833296\pi$
$103$			53.3144i			0.517615i	−0.965929	+	0.258808i	$0.916670\pi$
$104$	89.3718	−	11.0790i	0.859344	−	0.106529i
$105$		0			0
$106$	41.3201	+	65.2219i	0.389813	+	0.615301i
$107$		−	54.1071i		−	0.505673i	−0.967509	−	0.252837i	$-0.918636\pi$
$107$		−	54.1071i		−	0.505673i	0.967509	−	0.252837i	$-0.0813635\pi$
$108$		0			0
$109$	−114.140			−1.04716			−0.523578	−	0.851978i	$-0.675403\pi$
$109$	−114.140			−1.04716			−0.523578	+	0.851978i	$0.675403\pi$
$110$	55.6072	−	35.2289i	0.505520	−	0.320263i
$111$		0			0
$112$	150.184	−	123.460i	1.34093	−	1.10232i
$113$	−55.4302			−0.490533			−0.245266	−	0.969456i	$-0.578875\pi$
$113$	−55.4302			−0.490533			−0.245266	+	0.969456i	$0.578875\pi$
$114$		0			0
$115$		−	106.933i		−	0.929855i
$116$	86.1104	−	182.259i	0.742331	−	1.57120i
$117$		0			0
$118$	−151.736	+	96.1297i	−1.28590	+	0.814659i
$119$			209.072i			1.75690i
$120$		0			0
$121$	96.6194			0.798507
$122$	91.9277	+	145.104i	0.753505	+	1.18937i
$123$		0			0
$124$	22.9971	+	10.8652i	0.185461	+	0.0876229i
$125$	37.1077			0.296862
$126$		0			0
$127$		−	39.6329i		−	0.312070i	−0.987752	−	0.156035i	$-0.950129\pi$
$127$		−	39.6329i		−	0.312070i	0.987752	−	0.156035i	$-0.0498712\pi$
$128$	−92.8307	−	88.1275i	−0.725240	−	0.688496i
$129$		0			0
$130$	80.3154	+	126.774i	0.617811	+	0.975185i
$131$			166.297i			1.26944i	0.772743	+	0.634720i	$0.218884\pi$
$131$			166.297i			1.26944i	−0.772743	+	0.634720i	$0.781116\pi$
$132$		0			0
$133$	−52.9651			−0.398234
$134$	−174.754	+	110.712i	−1.30414	+	0.826211i
$135$		0			0
$136$	136.603	−	16.9341i	1.00444	−	0.124515i
$137$	−167.858			−1.22524			−0.612621	−	0.790377i	$-0.709885\pi$
$137$	−167.858			−1.22524			−0.612621	+	0.790377i	$0.709885\pi$
$138$		0			0
$139$		−	11.0197i		−	0.0792785i	−0.999214	−	0.0396393i	$-0.987379\pi$
$139$		−	11.0197i		−	0.0792785i	0.999214	−	0.0396393i	$-0.0126209\pi$
$140$	292.937	+	138.401i	2.09241	+	0.988580i
$141$		0			0
$142$	−113.551	+	71.9380i	−0.799653	+	0.506606i
$143$		−	55.5833i		−	0.388695i
$144$		0			0
$145$	335.920			2.31669
$146$	−117.179	−	184.961i	−0.802595	−	1.26686i
$147$		0			0
$148$	61.6564	−	130.501i	0.416598	−	0.881761i
$149$	−243.481			−1.63410			−0.817051	−	0.576565i	$-0.804393\pi$
$149$	−243.481			−1.63410			−0.817051	+	0.576565i	$0.804393\pi$
$150$		0			0
$151$		−	116.761i		−	0.773250i	−0.922237	−	0.386625i	$-0.873641\pi$
$151$		−	116.761i		−	0.773250i	0.922237	−	0.386625i	$-0.126359\pi$
$152$	4.28998	+	34.6063i	0.0282236	+	0.227673i
$153$		0			0
$154$	−64.2182	−	101.365i	−0.417001	−	0.658217i
$155$			42.3857i			0.273456i
$156$		0			0
$157$	−41.8235			−0.266392			−0.133196	−	0.991090i	$-0.542524\pi$
$157$	−41.8235			−0.266392			−0.133196	+	0.991090i	$0.542524\pi$
$158$	−112.093	+	71.0145i	−0.709450	+	0.449459i
$159$		0			0
$160$	66.7017	−	202.609i	0.416886	−	1.26631i
$161$	−194.927			−1.21073
$162$		0			0
$163$			285.363i			1.75069i	0.483497	+	0.875346i	$0.339366\pi$
$163$			285.363i			1.75069i	−0.483497	+	0.875346i	$0.660634\pi$
$164$	−20.2939	+	42.9536i	−0.123743	+	0.261912i
$165$		0			0
$166$	6.78271	−	4.29706i	0.0408597	−	0.0258859i
$167$			67.9780i			0.407054i	0.979069	+	0.203527i	$0.0652405\pi$
$167$			67.9780i			0.407054i	−0.979069	+	0.203527i	$0.934760\pi$
$168$		0			0
$169$	−42.2802			−0.250179
$170$	122.761	+	193.772i	0.722121	+	1.13983i
$171$		0			0
$172$	−214.172	−	101.188i	−1.24518	−	0.588301i
$173$	−323.430			−1.86954			−0.934768	−	0.355259i	$-0.884393\pi$
$173$	−323.430			−1.86954			−0.934768	+	0.355259i	$0.884393\pi$
$174$		0			0
$175$			236.132i			1.34933i
$176$	−61.0287	+	50.1691i	−0.346754	+	0.285052i
$177$		0			0
$178$	57.7275	+	91.1201i	0.324312	+	0.511911i
$179$		−	281.726i		−	1.57389i	−0.617024	−	0.786944i	$-0.711662\pi$
$179$		−	281.726i		−	1.57389i	0.617024	−	0.786944i	$-0.288338\pi$
$180$		0			0
$181$	278.611			1.53929			0.769645	−	0.638473i	$-0.220433\pi$
$181$	278.611			1.53929			0.769645	+	0.638473i	$0.220433\pi$
$182$	231.095	−	146.406i	1.26975	−	0.804427i
$183$		0			0
$184$	15.7884	+	127.361i	0.0858066	+	0.692182i
$185$	240.524			1.30013
$186$		0			0
$187$		−	84.9581i		−	0.454321i
$188$	−127.855	−	60.4067i	−0.680082	−	0.321312i
$189$		0			0
$190$	−49.0891	+	31.0995i	−0.258364	+	0.163682i
$191$			99.7898i			0.522459i	0.965277	+	0.261230i	$0.0841280\pi$
$191$			99.7898i			0.522459i	−0.965277	+	0.261230i	$0.915872\pi$
$192$		0			0
$193$	252.868			1.31020			0.655100	−	0.755543i	$-0.272627\pi$
$193$	252.868			1.31020			0.655100	+	0.755543i	$0.272627\pi$
$194$	67.2963	+	106.224i	0.346888	+	0.547547i
$195$		0			0
$196$	168.562	−	356.774i	0.860009	−	1.82027i
$197$	12.7366			0.0646529			0.0323265	−	0.999477i	$-0.489708\pi$
$197$	12.7366			0.0646529			0.0323265	+	0.999477i	$0.489708\pi$
$198$		0			0
$199$		−	248.822i		−	1.25036i	−0.780480	−	0.625181i	$-0.785025\pi$
$199$		−	248.822i		−	1.25036i	0.780480	−	0.625181i	$-0.214975\pi$
$200$	154.284	−	19.1259i	0.771420	−	0.0956294i
$201$		0			0
$202$	78.3797	+	123.719i	0.388018	+	0.612469i
$203$		−	612.343i		−	3.01647i
$204$		0			0
$205$	−79.1673			−0.386182
$206$	90.0739	−	57.0647i	0.437252	−	0.277013i
$207$		0			0
$208$	−114.376	−	139.134i	−0.549886	−	0.668914i
$209$	21.5228			0.102980
$210$		0			0
$211$		−	262.582i		−	1.24446i	−0.782833	−	0.622232i	$-0.786226\pi$
$211$		−	262.582i		−	1.24446i	0.782833	−	0.622232i	$-0.213774\pi$
$212$	65.9648	−	139.620i	0.311155	−	0.658583i
$213$		0			0
$214$	−91.4132	+	57.9131i	−0.427164	+	0.270622i
$215$		−	394.737i		−	1.83599i
$216$		0			0
$217$	77.2642			0.356056
$218$	122.169	+	192.838i	0.560408	+	0.884578i
$219$		0			0
$220$	−119.037	−	56.2406i	−0.541079	−	0.255639i
$221$	193.689			0.876420
$222$		0			0
$223$			297.653i			1.33477i	0.744714	+	0.667384i	$0.232586\pi$
$223$			297.653i			1.33477i	−0.744714	+	0.667384i	$0.767414\pi$
$224$	−369.333	−	121.590i	−1.64881	−	0.542810i
$225$		0			0
$226$	59.3293	+	93.6486i	0.262519	+	0.414374i
$227$			70.5415i			0.310756i	0.987855	+	0.155378i	$0.0496595\pi$
$227$			70.5415i			0.310756i	−0.987855	+	0.155378i	$0.950340\pi$
$228$		0			0
$229$	332.538			1.45213			0.726064	−	0.687627i	$-0.241347\pi$
$229$	332.538			1.45213			0.726064	+	0.687627i	$0.241347\pi$
$230$	−180.662	+	114.455i	−0.785489	+	0.497632i
$231$		0			0
$232$	−400.093	+	49.5976i	−1.72454	+	0.213783i
$233$	421.259			1.80798			0.903989	−	0.427555i	$-0.140625\pi$
$233$	421.259			1.80798			0.903989	+	0.427555i	$0.140625\pi$
$234$		0			0
$235$		−	235.648i		−	1.00276i
$236$	324.820	+	153.465i	1.37636	+	0.650274i
$237$		0			0
$238$	353.224	−	223.778i	1.48413	−	0.940245i
$239$			234.793i			0.982396i	0.871048	+	0.491198i	$0.163441\pi$
$239$			234.793i			0.982396i	−0.871048	+	0.491198i	$0.836559\pi$
$240$		0			0
$241$	−264.431			−1.09722			−0.548612	−	0.836077i	$-0.684844\pi$
$241$	−264.431			−1.09722			−0.548612	+	0.836077i	$0.684844\pi$
$242$	−103.416	−	163.237i	−0.427338	−	0.674534i
$243$		0			0
$244$	146.756	−	310.621i	0.601460	−	1.27304i
$245$	657.565			2.68394
$246$		0			0
$247$			49.0681i			0.198656i
$248$	−6.25813	−	50.4829i	−0.0252344	−	0.203560i
$249$		0			0
$250$	−39.7180	−	62.6930i	−0.158872	−	0.250772i
$251$		−	141.609i		−	0.564178i	−0.959388	−	0.282089i	$-0.908973\pi$
$251$		−	141.609i		−	0.564178i	0.959388	−	0.282089i	$-0.0910274\pi$
$252$		0			0
$253$	79.2104			0.313084
$254$	−66.9592	+	42.4208i	−0.263619	+	0.167011i
$255$		0			0
$256$	−49.5295	+	251.163i	−0.193474	+	0.981105i
$257$	−403.482			−1.56997			−0.784985	−	0.619515i	$-0.787329\pi$
$257$	−403.482			−1.56997			−0.784985	+	0.619515i	$0.787329\pi$
$258$		0			0
$259$		−	438.447i		−	1.69285i
$260$	128.218	−	271.384i	0.493147	−	1.04378i
$261$		0			0
$262$	280.956	−	177.994i	1.07235	−	0.679368i
$263$		−	329.342i		−	1.25225i	−0.779722	−	0.626126i	$-0.784640\pi$
$263$		−	329.342i		−	1.25225i	0.779722	−	0.626126i	$-0.215360\pi$
$264$		0			0
$265$	257.331			0.971060
$266$	56.6908	+	89.4838i	0.213123	+	0.336405i
$267$		0			0
$268$	374.094	+	176.745i	1.39587	+	0.659495i
$269$	−251.084			−0.933397			−0.466698	−	0.884417i	$-0.654557\pi$
$269$	−251.084			−0.933397			−0.466698	+	0.884417i	$0.654557\pi$
$270$		0			0
$271$			150.264i			0.554479i	0.960801	+	0.277240i	$0.0894196\pi$
$271$			150.264i			0.554479i	−0.960801	+	0.277240i	$0.910580\pi$
$272$	−174.822	−	212.664i	−0.642729	−	0.781853i
$273$		0			0
$274$	179.666	+	283.594i	0.655715	+	1.03502i
$275$		−	95.9545i		−	0.348925i
$276$		0			0
$277$	−177.410			−0.640469			−0.320235	−	0.947338i	$-0.603762\pi$
$277$	−177.410			−0.640469			−0.320235	+	0.947338i	$0.603762\pi$
$278$	−18.6177	+	11.7949i	−0.0669700	+	0.0424276i
$279$		0			0
$280$	−79.7159	−	643.050i	−0.284700	−	2.29661i
$281$	−152.887			−0.544083			−0.272042	−	0.962285i	$-0.587699\pi$
$281$	−152.887			−0.544083			−0.272042	+	0.962285i	$0.587699\pi$
$282$		0			0
$283$		−	351.150i		−	1.24081i	−0.784280	−	0.620407i	$-0.786967\pi$
$283$		−	351.150i		−	1.24081i	0.784280	−	0.620407i	$-0.213033\pi$
$284$	243.077	+	114.844i	0.855903	+	0.404381i
$285$		0			0
$286$	−93.9073	+	59.4933i	−0.328347	+	0.208018i
$287$			144.313i			0.502832i
$288$		0			0
$289$	7.04985			0.0243940
$290$	−359.549	−	567.532i	−1.23983	−	1.95701i
$291$		0			0
$292$	−187.068	+	395.944i	−0.640645	+	1.35597i
$293$	−141.826			−0.484049			−0.242025	−	0.970270i	$-0.577811\pi$
$293$	−141.826			−0.484049			−0.242025	+	0.970270i	$0.577811\pi$
$294$		0			0
$295$			598.671i			2.02939i
$296$	−286.473	+	35.5127i	−0.967813	+	0.119975i
$297$		0			0
$298$	260.608	+	411.358i	0.874525	+	1.38040i
$299$			180.585i			0.603963i
$300$		0			0
$301$	−719.560			−2.39056
$302$	−197.266	+	124.974i	−0.653197	+	0.413821i
$303$		0			0
$304$	53.8751	−	44.2885i	0.177221	−	0.145686i
$305$	572.501			1.87705
$306$		0			0
$307$		−	367.051i		−	1.19561i	−0.801643	−	0.597804i	$-0.796040\pi$
$307$		−	367.051i		−	1.19561i	0.801643	−	0.597804i	$-0.203960\pi$
$308$	−102.520	+	216.992i	−0.332857	+	0.704518i
$309$		0			0
$310$	71.6100	−	45.3672i	0.231000	−	0.146346i
$311$			365.139i			1.17408i	0.809558	+	0.587040i	$0.199707\pi$
$311$			365.139i			1.17408i	−0.809558	+	0.587040i	$0.800293\pi$
$312$		0			0
$313$	422.596			1.35015			0.675073	−	0.737751i	$-0.264112\pi$
$313$	422.596			1.35015			0.675073	+	0.737751i	$0.264112\pi$
$314$	44.7655	+	70.6602i	0.142565	+	0.225032i
$315$		0			0
$316$	239.956	+	113.370i	0.759355	+	0.358766i
$317$	141.440			0.446182			0.223091	−	0.974798i	$-0.428385\pi$
$317$	141.440			0.446182			0.223091	+	0.974798i	$0.428385\pi$
$318$		0			0
$319$			248.831i			0.780035i
$320$	−413.699	+	104.170i	−1.29281	+	0.325530i
$321$		0			0
$322$	208.639	+	329.327i	0.647947	+	1.02275i
$323$			74.9996i			0.232197i
$324$		0			0
$325$	218.759			0.673103
$326$	482.117	−	305.436i	1.47889	−	0.936921i
$327$		0			0
$328$	94.2911	−	11.6888i	0.287473	−	0.0356367i
$329$	−429.560			−1.30565
$330$		0			0
$331$			276.637i			0.835760i	0.908502	+	0.417880i	$0.137227\pi$
$331$			276.637i			0.835760i	−0.908502	+	0.417880i	$0.862773\pi$
$332$	−14.5197	−	6.85997i	−0.0437339	−	0.0206626i
$333$		0			0
$334$	114.848	−	72.7598i	0.343856	−	0.217844i
$335$			689.487i			2.05817i
$336$		0			0
$337$	−380.293			−1.12847			−0.564234	−	0.825615i	$-0.690828\pi$
$337$	−380.293			−1.12847			−0.564234	+	0.825615i	$0.690828\pi$
$338$	45.2543	+	71.4318i	0.133889	+	0.211337i
$339$		0			0
$340$	195.979	−	414.805i	0.576409	−	1.22001i
$341$	−31.3970			−0.0920733
$342$		0			0
$343$		−	603.265i		−	1.75879i
$344$	58.2818	+	470.146i	0.169424	+	1.36670i
$345$		0			0
$346$	346.181	+	546.430i	1.00052	+	1.57928i
$347$			537.101i			1.54784i	0.633283	+	0.773920i	$0.281707\pi$
$347$			537.101i			1.54784i	−0.633283	+	0.773920i	$0.718293\pi$
$348$		0			0
$349$	117.919			0.337877			0.168938	−	0.985627i	$-0.445966\pi$
$349$	117.919			0.337877			0.168938	+	0.985627i	$0.445966\pi$
$350$	398.942	−	252.743i	1.13984	−	0.722122i
$351$		0			0
$352$	150.082	+	49.4090i	0.426368	+	0.140366i
$353$	384.382			1.08890			0.544451	−	0.838793i	$-0.316738\pi$
$353$	384.382			1.08890			0.544451	+	0.838793i	$0.316738\pi$
$354$		0			0
$355$			448.011i			1.26200i
$356$	92.1581	−	195.060i	0.258871	−	0.547920i
$357$		0			0
$358$	−475.972	+	301.543i	−1.32953	+	0.842300i
$359$			222.659i			0.620221i	0.950701	+	0.310110i	$0.100366\pi$
$359$			222.659i			0.620221i	−0.950701	+	0.310110i	$0.899634\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−298.210	−	470.710i	−0.823784	−	1.30030i
$363$		0			0
$364$	−494.701	−	233.727i	−1.35907	−	0.642107i
$365$	−729.759			−1.99934
$366$		0			0
$367$			70.5386i			0.192203i	0.995372	+	0.0961016i	$0.0306374\pi$
$367$			70.5386i			0.192203i	−0.995372	+	0.0961016i	$0.969363\pi$
$368$	198.276	−	162.995i	0.538795	−	0.442920i
$369$		0			0
$370$	−257.443	−	406.362i	−0.695792	−	1.09828i
$371$		−	469.085i		−	1.26438i
$372$		0			0
$373$	256.364			0.687302			0.343651	−	0.939097i	$-0.388336\pi$
$373$	256.364			0.687302			0.343651	+	0.939097i	$0.388336\pi$
$374$	−143.536	+	90.9343i	−0.383785	+	0.243140i
$375$		0			0
$376$	34.7928	+	280.666i	0.0925342	+	0.746451i
$377$	−567.289			−1.50475
$378$		0			0
$379$			337.173i			0.889638i	0.895620	+	0.444819i	$0.146732\pi$
$379$			337.173i			0.889638i	−0.895620	+	0.444819i	$0.853268\pi$
$380$	105.084	+	49.6483i	0.276538	+	0.130653i
$381$		0			0
$382$	168.593	−	106.809i	0.441344	−	0.279605i
$383$			53.8050i			0.140483i	0.997530	+	0.0702415i	$0.0223770\pi$
$383$			53.8050i			0.140483i	−0.997530	+	0.0702415i	$0.977623\pi$
$384$		0			0
$385$	−399.934			−1.03879
$386$	−270.656	−	427.218i	−0.701181	−	1.10678i
$387$		0			0
$388$	107.434	−	227.392i	0.276892	−	0.586063i
$389$	768.174			1.97474			0.987370	−	0.158434i	$-0.0506445\pi$
$389$	768.174			1.97474			0.987370	+	0.158434i	$0.0506445\pi$
$390$		0			0
$391$			276.021i			0.705936i
$392$	−783.183	+	97.0876i	−1.99792	+	0.247673i
$393$		0			0
$394$	−13.6326	−	21.5184i	−0.0346004	−	0.0546151i
$395$			442.260i			1.11965i
$396$		0			0
$397$	132.666			0.334172			0.167086	−	0.985942i	$-0.446564\pi$
$397$	132.666			0.334172			0.167086	+	0.985942i	$0.446564\pi$
$398$	−420.381	+	266.325i	−1.05623	+	0.669158i
$399$		0			0
$400$	−197.450	−	240.190i	−0.493625	−	0.600474i
$401$	112.782			0.281253			0.140626	−	0.990063i	$-0.455088\pi$
$401$	112.782			0.281253			0.140626	+	0.990063i	$0.455088\pi$
$402$		0			0
$403$		−	71.5794i		−	0.177616i
$404$	125.128	−	264.843i	0.309723	−	0.655552i
$405$		0			0
$406$	−1034.55	+	655.417i	−2.54814	+	1.61433i
$407$			178.167i			0.437757i
$408$		0			0
$409$	−808.855			−1.97764			−0.988820	−	0.149112i	$-0.952358\pi$
$409$	−808.855			−1.97764			−0.988820	+	0.149112i	$0.952358\pi$
$410$	84.7361	+	133.752i	0.206673	+	0.326224i
$411$		0			0
$412$	−192.820	−	91.0999i	−0.468010	−	0.221116i
$413$	1091.31			2.64239
$414$		0			0
$415$		−	26.7610i		−	0.0644843i
$416$	−112.643	+	342.159i	−0.270777	+	0.822497i
$417$		0			0
$418$	−23.0368	−	36.3625i	−0.0551120	−	0.0869917i
$419$			566.901i			1.35299i	0.736449	+	0.676493i	$0.236501\pi$
$419$			566.901i			1.35299i	−0.736449	+	0.676493i	$0.763499\pi$
$420$		0			0
$421$	−300.257			−0.713199			−0.356599	−	0.934257i	$-0.616064\pi$
$421$	−300.257			−0.713199			−0.356599	+	0.934257i	$0.616064\pi$
$422$	−443.629	+	281.053i	−1.05125	+	0.666002i
$423$		0			0
$424$	−306.491	+	37.9942i	−0.722855	+	0.0896090i
$425$	334.368			0.786749
$426$		0			0
$427$		−	1043.60i		−	2.44404i
$428$	195.687	+	92.4544i	0.457212	+	0.216015i
$429$		0			0
$430$	−666.903	+	422.504i	−1.55094	+	0.982567i
$431$			756.625i			1.75551i	0.479110	+	0.877755i	$0.340959\pi$
$431$			756.625i			1.75551i	−0.479110	+	0.877755i	$0.659041\pi$
$432$		0			0
$433$	−707.649			−1.63429			−0.817146	−	0.576430i	$-0.804445\pi$
$433$	−707.649			−1.63429			−0.817146	+	0.576430i	$0.804445\pi$
$434$	−82.6992	−	130.537i	−0.190551	−	0.300776i
$435$		0			0
$436$	195.035	−	412.806i	0.447327	−	0.946802i
$437$	−69.9256			−0.160013
$438$		0			0
$439$		−	230.253i		−	0.524495i	−0.965001	−	0.262247i	$-0.915536\pi$
$439$		−	230.253i		−	0.524495i	0.965001	−	0.262247i	$-0.0844636\pi$
$440$	32.3933	+	261.309i	0.0736211	+	0.593884i
$441$		0			0
$442$	−207.314	−	327.235i	−0.469035	−	0.740350i
$443$			63.6893i			0.143768i	0.997413	+	0.0718841i	$0.0229012\pi$
$443$			63.6893i			0.143768i	−0.997413	+	0.0718841i	$0.977099\pi$
$444$		0			0
$445$	359.512			0.807891
$446$	502.881	−	318.591i	1.12754	−	0.714330i
$447$		0			0
$448$	189.889	+	754.126i	0.423860	+	1.68332i
$449$	212.618			0.473536			0.236768	−	0.971566i	$-0.423912\pi$
$449$	212.618			0.473536			0.236768	+	0.971566i	$0.423912\pi$
$450$		0			0
$451$		−	58.6428i		−	0.130028i
$452$	94.7153	−	200.472i	0.209547	−	0.443523i
$453$		0			0
$454$	119.179	−	75.5037i	0.262509	−	0.166308i
$455$		−	911.777i		−	2.00390i
$456$		0			0
$457$	−436.548			−0.955247			−0.477624	−	0.878565i	$-0.658502\pi$
$457$	−436.548			−0.955247			−0.477624	+	0.878565i	$0.658502\pi$
$458$	−355.929	−	561.818i	−0.777138	−	1.22668i
$459$		0			0
$460$	386.742	+	182.720i	0.840742	+	0.397218i
$461$	101.372			0.219895			0.109948	−	0.993937i	$-0.464932\pi$
$461$	101.372			0.219895			0.109948	+	0.993937i	$0.464932\pi$
$462$		0			0
$463$		−	527.038i		−	1.13831i	−0.822230	−	0.569155i	$-0.807270\pi$
$463$		−	527.038i		−	1.13831i	0.822230	−	0.569155i	$-0.192730\pi$
$464$	512.031	+	622.865i	1.10351	+	1.34238i
$465$		0			0
$466$	−450.892	−	711.712i	−0.967579	−	1.52728i
$467$		−	460.432i		−	0.985936i	−0.870048	−	0.492968i	$-0.835912\pi$
$467$		−	460.432i		−	0.985936i	0.870048	−	0.492968i	$-0.164088\pi$
$468$		0			0
$469$	1256.86			2.67986
$470$	−398.125	+	252.225i	−0.847074	+	0.536648i
$471$		0			0
$472$	−88.3921	−	713.039i	−0.187271	−	1.51068i
$473$	292.400			0.618181
$474$		0			0
$475$			84.7070i			0.178331i
$476$	−756.141	−	357.247i	−1.58853	−	0.750519i
$477$		0			0
$478$	396.679	−	251.309i	0.829872	−	0.525750i
$479$		−	175.329i		−	0.366031i	−0.983110	−	0.183016i	$-0.941414\pi$
$479$		−	175.329i		−	0.366031i	0.983110	−	0.183016i	$-0.0585859\pi$
$480$		0			0
$481$	−406.188			−0.844465
$482$	283.032	+	446.753i	0.587204	+	0.926873i
$483$		0			0
$484$	−165.097	+	349.440i	−0.341109	+	0.721982i
$485$	419.104			0.864131
$486$		0			0
$487$			726.060i			1.49088i	0.666571	+	0.745441i	$0.267761\pi$
$487$			726.060i			1.49088i	−0.666571	+	0.745441i	$0.732239\pi$
$488$	−681.870	+	84.5283i	−1.39727	+	0.173214i
$489$		0			0
$490$	−703.820	−	1110.95i	−1.43637	−	2.26724i
$491$			812.931i			1.65566i	0.560976	+	0.827832i	$0.310426\pi$
$491$			812.931i			1.65566i	−0.560976	+	0.827832i	$0.689574\pi$
$492$		0			0
$493$	−867.091			−1.75880
$494$	82.8999	−	52.5197i	0.167813	−	0.106315i
$495$		0			0
$496$	−78.5918	+	64.6070i	−0.158451	+	0.130256i
$497$	816.672			1.64320
$498$		0			0
$499$			454.585i			0.910993i	0.890238	+	0.455496i	$0.150538\pi$
$499$			454.585i			0.910993i	−0.890238	+	0.455496i	$0.849462\pi$
$500$	−63.4072	+	134.206i	−0.126814	+	0.268412i
$501$		0			0
$502$	−239.246	+	151.570i	−0.476586	+	0.301932i
$503$		−	709.318i		−	1.41018i	−0.709120	−	0.705088i	$-0.750908\pi$
$503$		−	709.318i		−	1.41018i	0.709120	−	0.705088i	$-0.249092\pi$
$504$		0			0
$505$	488.128			0.966591
$506$	−84.7823	−	133.825i	−0.167554	−	0.264476i
$507$		0			0
$508$	143.339	+	67.7219i	0.282163	+	0.133311i
$509$	112.989			0.221983			0.110991	−	0.993821i	$-0.464597\pi$
$509$	112.989			0.221983			0.110991	+	0.993821i	$0.464597\pi$
$510$		0			0
$511$			1330.27i			2.60326i
$512$	477.350	−	185.151i	0.932324	−	0.361623i
$513$		0			0
$514$	431.864	+	681.678i	0.840203	+	1.32622i
$515$		−	355.384i		−	0.690066i
$516$		0			0
$517$	174.555			0.337631
$518$	−740.751	+	469.289i	−1.43002	+	0.905963i
$519$		0			0
$520$	−595.736	+	73.8507i	−1.14565	+	0.142021i
$521$	−194.174			−0.372694			−0.186347	−	0.982484i	$-0.559665\pi$
$521$	−194.174			−0.372694			−0.186347	+	0.982484i	$0.559665\pi$
$522$		0			0
$523$			448.356i			0.857278i	0.903476	+	0.428639i	$0.141007\pi$
$523$			448.356i			0.857278i	−0.903476	+	0.428639i	$0.858993\pi$
$524$	−601.438	−	284.156i	−1.14778	−	0.542283i
$525$		0			0
$526$	−556.419	+	352.509i	−1.05783	+	0.670170i
$527$		−	109.408i		−	0.207605i
$528$		0			0
$529$	271.653			0.513522
$530$	−275.432	−	434.757i	−0.519684	−	0.820297i
$531$		0			0
$532$	90.5031	−	191.557i	0.170119	−	0.360069i
$533$	133.695			0.250834
$534$		0			0
$535$			360.668i			0.674145i
$536$	−101.801	−	821.204i	−0.189927	−	1.53210i
$537$		0			0
$538$	268.746	+	424.203i	0.499527	+	0.788481i
$539$			487.088i			0.903689i
$540$		0			0
$541$	260.593			0.481687			0.240844	−	0.970564i	$-0.422576\pi$
$541$	260.593			0.481687			0.240844	+	0.970564i	$0.422576\pi$
$542$	253.869	−	160.834i	0.468393	−	0.296741i
$543$		0			0
$544$	−172.173	+	522.983i	−0.316495	+	0.961366i
$545$	760.837			1.39603
$546$		0			0
$547$			698.050i			1.27614i	0.769978	+	0.638071i	$0.220267\pi$
$547$			698.050i			1.27614i	−0.769978	+	0.638071i	$0.779733\pi$
$548$	286.825	−	607.086i	0.523403	−	1.10782i
$549$		0			0
$550$	−162.114	+	102.704i	−0.294752	+	0.186735i
$551$		−	219.664i		−	0.398664i
$552$		0			0
$553$	806.189			1.45785
$554$	189.890	+	299.732i	0.342761	+	0.541032i
$555$		0			0
$556$	39.8546	+	18.8297i	0.0716809	+	0.0338664i
$557$	−344.964			−0.619324			−0.309662	−	0.950847i	$-0.600216\pi$
$557$	−344.964			−0.619324			−0.309662	+	0.950847i	$0.600216\pi$
$558$		0			0
$559$			666.617i			1.19252i
$560$	−1001.10	+	822.963i	−1.78768	+	1.46958i
$561$		0			0
$562$	163.642	+	258.301i	0.291178	+	0.459611i
$563$		−	1075.78i		−	1.91080i	−0.295314	−	0.955400i	$-0.595424\pi$
$563$		−	1075.78i		−	1.91080i	0.295314	−	0.955400i	$-0.404576\pi$
$564$		0			0
$565$	369.488			0.653960
$566$	−593.264	+	375.851i	−1.04817	+	0.664048i
$567$		0			0
$568$	−66.1476	−	533.597i	−0.116457	−	0.939432i
$569$	−206.716			−0.363298			−0.181649	−	0.983363i	$-0.558143\pi$
$569$	−206.716			−0.363298			−0.181649	+	0.983363i	$0.558143\pi$
$570$		0			0
$571$		−	908.816i		−	1.59162i	−0.605545	−	0.795811i	$-0.707045\pi$
$571$		−	908.816i		−	1.59162i	0.605545	−	0.795811i	$-0.292955\pi$
$572$	201.026	+	94.9770i	0.351444	+	0.166044i
$573$		0			0
$574$	243.815	−	154.464i	0.424764	−	0.269101i
$575$			311.747i			0.542169i
$576$		0			0
$577$	−766.400			−1.32825			−0.664125	−	0.747622i	$-0.731196\pi$
$577$	−766.400			−1.32825			−0.664125	+	0.747622i	$0.731196\pi$
$578$	−7.54576	−	11.9106i	−0.0130550	−	0.0206066i
$579$		0			0
$580$	−573.997	+	1214.91i	−0.989649	+	2.09467i
$581$	−48.7822			−0.0839625
$582$		0			0
$583$			190.617i			0.326958i
$584$	869.170	−	107.747i	1.48830	−	0.184498i
$585$		0			0
$586$	151.803	+	239.614i	0.259049	+	0.408897i
$587$			730.808i			1.24499i	0.782625	+	0.622494i	$0.213880\pi$
$587$			730.808i			1.24499i	−0.782625	+	0.622494i	$0.786120\pi$
$588$		0			0
$589$	27.7168			0.0470573
$590$	1011.45	−	640.783i	1.71432	−	1.08607i
$591$		0			0
$592$	366.622	+	445.981i	0.619294	+	0.753346i
$593$	−770.478			−1.29929			−0.649644	−	0.760239i	$-0.725082\pi$
$593$	−770.478			−1.29929			−0.649644	+	0.760239i	$0.725082\pi$
$594$		0			0
$595$		−	1393.63i		−	2.34224i
$596$	416.044	−	880.589i	0.698060	−	1.47750i
$597$		0			0
$598$	305.096	−	193.288i	0.510194	−	0.323224i
$599$			312.936i			0.522430i	0.965281	+	0.261215i	$0.0841232\pi$
$599$			312.936i			0.522430i	−0.965281	+	0.261215i	$0.915877\pi$
$600$		0			0
$601$	70.1694			0.116754			0.0583772	−	0.998295i	$-0.481407\pi$
$601$	70.1694			0.116754			0.0583772	+	0.998295i	$0.481407\pi$
$602$	770.176	+	1215.69i	1.27936	+	2.01941i
$603$		0			0
$604$	422.284	+	199.513i	0.699145	+	0.330319i
$605$	−644.047			−1.06454
$606$		0			0
$607$			128.626i			0.211904i	0.994371	+	0.105952i	$0.0337889\pi$
$607$			128.626i			0.211904i	−0.994371	+	0.105952i	$0.966211\pi$
$608$	−132.490	−	43.6174i	−0.217911	−	0.0717392i
$609$		0			0
$610$	−612.773	−	967.234i	−1.00455	−	1.58563i
$611$			397.954i			0.651316i
$612$		0			0
$613$	113.004			0.184346			0.0921731	−	0.995743i	$-0.470619\pi$
$613$	113.004			0.184346			0.0921731	+	0.995743i	$0.470619\pi$
$614$	−620.129	+	392.871i	−1.00998	+	0.639855i
$615$		0			0
$616$	476.336	−	59.0492i	0.773273	−	0.0958591i
$617$	−335.800			−0.544246			−0.272123	−	0.962262i	$-0.587726\pi$
$617$	−335.800			−0.544246			−0.272123	+	0.962262i	$0.587726\pi$
$618$		0			0
$619$			173.951i			0.281019i	0.990079	+	0.140510i	$0.0448741\pi$
$619$			173.951i			0.281019i	−0.990079	+	0.140510i	$0.955126\pi$
$620$	−153.295	−	72.4257i	−0.247249	−	0.116816i
$621$		0			0
$622$	616.897	−	390.824i	0.991796	−	0.628334i
$623$		−	655.348i		−	1.05192i
$624$		0			0
$625$	−733.182			−1.17309
$626$	−452.322	−	713.970i	−0.722560	−	1.14053i
$627$		0			0
$628$	71.4651	−	151.261i	0.113798	−	0.240862i
$629$	−620.851			−0.987044
$630$		0			0
$631$		−	32.0362i		−	0.0507705i	−0.999678	−	0.0253852i	$-0.991919\pi$
$631$		−	32.0362i		−	0.0507705i	0.999678	−	0.0253852i	$-0.00808124\pi$
$632$	−65.2985	−	526.748i	−0.103320	−	0.833462i
$633$		0			0
$634$	−151.389	−	238.961i	−0.238784	−	0.376909i
$635$			264.186i			0.416040i
$636$		0			0
$637$	−1110.47			−1.74328
$638$	420.397	−	266.335i	0.658929	−	0.417452i
$639$		0			0
$640$	618.793	+	587.442i	0.966864	+	0.917878i
$641$	711.508			1.11000			0.554999	−	0.831851i	$-0.312719\pi$
$641$	711.508			1.11000			0.554999	+	0.831851i	$0.312719\pi$
$642$		0			0
$643$		−	261.269i		−	0.406329i	−0.979145	−	0.203164i	$-0.934877\pi$
$643$		−	261.269i		−	0.406329i	0.979145	−	0.203164i	$-0.0651226\pi$
$644$	333.078	−	704.985i	0.517202	−	1.09470i
$645$		0			0
$646$	126.711	−	80.2754i	0.196147	−	0.124265i
$647$		−	658.867i		−	1.01834i	−0.860666	−	0.509170i	$-0.829952\pi$
$647$		−	658.867i		−	1.01834i	0.860666	−	0.509170i	$-0.170048\pi$
$648$		0			0
$649$	−443.463			−0.683302
$650$	−234.147	−	369.590i	−0.360226	−	0.568599i
$651$		0			0
$652$	−1032.06	−	487.608i	−1.58292	−	0.747866i
$653$	89.8604			0.137612			0.0688058	−	0.997630i	$-0.478081\pi$
$653$	89.8604			0.137612			0.0688058	+	0.997630i	$0.478081\pi$
$654$		0			0
$655$		−	1108.50i		−	1.69237i
$656$	−120.672	−	146.792i	−0.183951	−	0.223769i
$657$		0			0
$658$	459.777	+	725.736i	0.698748	+	1.10294i
$659$			317.095i			0.481176i	0.970627	+	0.240588i	$0.0773403\pi$
$659$			317.095i			0.481176i	−0.970627	+	0.240588i	$0.922660\pi$
$660$		0			0
$661$	−338.063			−0.511442			−0.255721	−	0.966751i	$-0.582313\pi$
$661$	−338.063			−0.511442			−0.255721	+	0.966751i	$0.582313\pi$
$662$	467.374	−	296.096i	0.706003	−	0.447275i
$663$		0			0
$664$	3.95119	+	31.8733i	0.00595058	+	0.0480019i
$665$	353.055			0.530911
$666$		0			0
$667$		−	808.429i		−	1.21204i
$668$	−245.853	−	116.156i	−0.368044	−	0.173886i
$669$		0			0
$670$	1164.88	−	737.988i	1.73863	−	1.10147i
$671$			424.078i			0.632009i
$672$		0			0
$673$	300.946			0.447170			0.223585	−	0.974684i	$-0.428224\pi$
$673$	300.946			0.447170			0.223585	+	0.974684i	$0.428224\pi$
$674$	407.045	+	642.501i	0.603924	+	0.953265i
$675$		0			0
$676$	72.2455	−	152.913i	0.106872	−	0.226203i
$677$	366.287			0.541044			0.270522	−	0.962714i	$-0.412804\pi$
$677$	366.287			0.541044			0.270522	+	0.962714i	$0.412804\pi$
$678$		0			0
$679$		−	763.978i		−	1.12515i
$680$	−910.572	+	112.879i	−1.33908	+	0.165999i
$681$		0			0
$682$	33.6056	+	53.0448i	0.0492750	+	0.0777783i
$683$		−	157.941i		−	0.231247i	−0.993293	−	0.115623i	$-0.963113\pi$
$683$		−	157.941i		−	0.231247i	0.993293	−	0.115623i	$-0.0368866\pi$
$684$		0			0
$685$	1118.91			1.63345
$686$	−1019.21	+	645.701i	−1.48573	+	0.941254i
$687$		0			0
$688$	731.924	−	601.684i	1.06384	−	0.874540i
$689$	−434.571			−0.630727
$690$		0			0
$691$		−	340.395i		−	0.492613i	−0.969192	−	0.246306i	$-0.920783\pi$
$691$		−	340.395i		−	0.492613i	0.969192	−	0.246306i	$-0.0792170\pi$
$692$	552.654	−	1169.74i	0.798633	−	1.69037i
$693$		0			0
$694$	907.424	−	574.882i	1.30753	−	0.828360i
$695$			73.4554i			0.105691i
$696$		0			0
$697$	204.350			0.293185
$698$	−126.214	−	199.223i	−0.180822	−	0.285419i
$699$		0			0
$700$	−854.011	−	403.487i	−1.22002	−	0.576410i
$701$	−68.5225			−0.0977496			−0.0488748	−	0.998805i	$-0.515564\pi$
$701$	−68.5225			−0.0977496			−0.0488748	+	0.998805i	$0.515564\pi$
$702$		0			0
$703$		−	157.283i		−	0.223731i
$704$	−77.1631	−	306.446i	−0.109607	−	0.435292i
$705$		0			0
$706$	−411.421	−	649.409i	−0.582749	−	0.919843i
$707$		−	889.802i		−	1.25856i
$708$		0			0
$709$	−508.634			−0.717396			−0.358698	−	0.933454i	$-0.616779\pi$
$709$	−508.634			−0.717396			−0.358698	+	0.933454i	$0.616779\pi$
$710$	756.909	−	479.525i	1.06607	−	0.675388i
$711$		0			0
$712$	−428.191	+	53.0809i	−0.601392	+	0.0745519i
$713$	102.006			0.143066
$714$		0			0
$715$			370.508i			0.518194i
$716$	1018.91	+	481.394i	1.42305	+	0.672338i
$717$		0			0
$718$	376.180	−	238.322i	0.523927	−	0.331925i
$719$			1118.37i			1.55545i	0.628605	+	0.777725i	$0.283626\pi$
$719$			1118.37i			1.55545i	−0.628605	+	0.777725i	$0.716374\pi$
$720$		0			0
$721$	−647.824			−0.898508
$722$	20.3365	+	32.1002i	0.0281669	+	0.0444602i
$723$		0			0
$724$	−476.072	+	1007.64i	−0.657558	+	1.39177i
$725$	−979.320			−1.35079
$726$		0			0
$727$			421.983i			0.580444i	0.956959	+	0.290222i	$0.0937291\pi$
$727$			421.983i			0.580444i	−0.956959	+	0.290222i	$0.906271\pi$
$728$	134.621	+	1085.96i	0.184919	+	1.49170i
$729$		0			0
$730$	781.093	+	1232.92i	1.06999	+	1.68893i
$731$			1018.91i			1.39386i
$732$		0			0
$733$	484.508			0.660994			0.330497	−	0.943807i	$-0.392784\pi$
$733$	484.508			0.660994			0.330497	+	0.943807i	$0.392784\pi$
$734$	119.174	−	75.5005i	0.162362	−	0.102862i
$735$		0			0
$736$	−487.601	−	160.525i	−0.662502	−	0.218105i
$737$	−510.735			−0.692991
$738$		0			0
$739$			523.500i			0.708390i	0.935172	+	0.354195i	$0.115245\pi$
$739$			523.500i			0.708390i	−0.935172	+	0.354195i	$0.884755\pi$
$740$	−410.991	+	869.893i	−0.555393	+	1.17553i
$741$		0			0
$742$	−792.513	+	502.082i	−1.06808	+	0.676660i
$743$		−	1021.39i		−	1.37468i	−0.726336	−	0.687340i	$-0.758778\pi$
$743$		−	1021.39i		−	1.37468i	0.726336	−	0.687340i	$-0.241222\pi$
$744$		0			0
$745$	1623.00			2.17853
$746$	−274.397	−	433.123i	−0.367824	−	0.580594i
$747$		0			0
$748$	307.265	+	145.171i	0.410782	+	0.194078i
$749$	657.456			0.877778
$750$		0			0
$751$			263.896i			0.351393i	0.984444	+	0.175697i	$0.0562177\pi$
$751$			263.896i			0.351393i	−0.984444	+	0.175697i	$0.943782\pi$
$752$	436.941	−	359.191i	0.581038	−	0.477647i
$753$		0			0
$754$	607.194	+	958.427i	0.805297	+	1.27112i
$755$			778.305i			1.03087i
$756$		0			0
$757$	233.092			0.307916			0.153958	−	0.988077i	$-0.450798\pi$
$757$	233.092			0.307916			0.153958	+	0.988077i	$0.450798\pi$
$758$	569.649	−	360.891i	0.751516	−	0.476109i
$759$		0			0
$760$	−28.5963	−	230.679i	−0.0376266	−	0.303525i
$761$	−835.785			−1.09827			−0.549136	−	0.835733i	$-0.685043\pi$
$761$	−835.785			−1.09827			−0.549136	+	0.835733i	$0.685043\pi$
$762$		0			0
$763$		−	1386.92i		−	1.81772i
$764$	−360.906	−	170.514i	−0.472390	−	0.223186i
$765$		0			0
$766$	90.9029	−	57.5898i	0.118672	−	0.0751826i
$767$		−	1011.01i		−	1.31814i
$768$		0			0
$769$	−467.786			−0.608304			−0.304152	−	0.952623i	$-0.598373\pi$
$769$	−467.786			−0.608304			−0.304152	+	0.952623i	$0.598373\pi$
$770$	428.067	+	675.684i	0.555931	+	0.877511i
$771$		0			0
$772$	−432.084	+	914.539i	−0.559695	+	1.18464i
$773$	85.5085			0.110619			0.0553095	−	0.998469i	$-0.482385\pi$
$773$	85.5085			0.110619			0.0553095	+	0.998469i	$0.482385\pi$
$774$		0			0
$775$		−	123.569i		−	0.159443i
$776$	−499.168	+	61.8795i	−0.643257	+	0.0797416i
$777$		0			0
$778$	−822.209	−	1297.82i	−1.05682	−	1.66815i
$779$			51.7689i			0.0664556i
$780$		0			0
$781$	−331.862			−0.424919
$782$	466.334	−	295.437i	0.596335	−	0.377797i
$783$		0			0
$784$	1002.30	+	1219.26i	1.27845	+	1.55518i
$785$	278.788			0.355144
$786$		0			0
$787$		−	19.7664i		−	0.0251162i	−0.999921	−	0.0125581i	$-0.996003\pi$
$787$		−	19.7664i		−	0.0251162i	0.999921	−	0.0125581i	$-0.00399747\pi$
$788$	−21.7635	+	46.0641i	−0.0276186	+	0.0584569i
$789$		0			0
$790$	747.193	−	473.370i	0.945813	−	0.599203i
$791$		−	673.533i		−	0.851496i
$792$		0			0
$793$	−966.819			−1.21919
$794$	−141.999	−	224.138i	−0.178839	−	0.282290i
$795$		0			0
$796$	899.905	+	425.170i	1.13053	+	0.534133i
$797$	462.093			0.579791			0.289895	−	0.957058i	$-0.406380\pi$
$797$	462.093			0.579791			0.289895	+	0.957058i	$0.406380\pi$
$798$		0			0
$799$			608.266i			0.761284i
$800$	−194.458	+	590.674i	−0.243073	+	0.738343i
$801$		0			0
$802$	−120.716	−	190.544i	−0.150519	−	0.237586i
$803$		−	540.566i		−	0.673183i
$804$		0			0
$805$	1299.35			1.61410
$806$	−120.932	+	76.6145i	−0.150040	+	0.0950552i
$807$		0			0
$808$	−581.379	+	72.0708i	−0.719528	+	0.0891966i
$809$	1230.01			1.52041			0.760206	−	0.649682i	$-0.225098\pi$
$809$	1230.01			1.52041			0.760206	+	0.649682i	$0.225098\pi$
$810$		0			0
$811$		−	512.789i		−	0.632292i	−0.948711	−	0.316146i	$-0.897611\pi$
$811$		−	512.789i		−	0.632292i	0.948711	−	0.316146i	$-0.102389\pi$
$812$	2214.64	+	1046.33i	2.72739	+	1.28858i
$813$		0			0
$814$	301.011	−	190.700i	0.369792	−	0.234275i
$815$		−	1902.18i		−	2.33396i
$816$		0			0
$817$	−258.126			−0.315943
$818$	865.752	+	1366.55i	1.05838	+	1.67060i
$819$		0			0
$820$	135.276	−	286.321i	0.164970	−	0.349172i
$821$	−289.781			−0.352961			−0.176481	−	0.984304i	$-0.556471\pi$
$821$	−289.781			−0.352961			−0.176481	+	0.984304i	$0.556471\pi$
$822$		0			0
$823$			1455.81i			1.76891i	0.466629	+	0.884453i	$0.345468\pi$
$823$			1455.81i			1.76891i	−0.466629	+	0.884453i	$0.654532\pi$
$824$	52.4715	+	423.275i	0.0636790	+	0.513683i
$825$		0			0
$826$	−1168.07	−	1843.75i	−1.41413	−	2.23214i
$827$			453.430i			0.548282i	0.961689	+	0.274141i	$0.0883936\pi$
$827$			453.430i			0.548282i	−0.961689	+	0.274141i	$0.911606\pi$
$828$		0			0
$829$	−1194.07			−1.44038			−0.720190	−	0.693777i	$-0.755945\pi$
$829$	−1194.07			−1.44038			−0.720190	+	0.693777i	$0.755945\pi$
$830$	−45.2123	+	28.6434i	−0.0544727	+	0.0345102i
$831$		0			0
$832$	698.640	−	175.918i	0.839711	−	0.211440i
$833$	−1697.33			−2.03762
$834$		0			0
$835$		−	453.129i		−	0.542670i
$836$	−36.7767	+	77.8408i	−0.0439913	+	0.0931110i
$837$		0			0
$838$	957.773	−	606.779i	1.14293	−	0.724080i
$839$			139.199i			0.165911i	0.996553	+	0.0829554i	$0.0264359\pi$
$839$			139.199i			0.165911i	−0.996553	+	0.0829554i	$0.973564\pi$
$840$		0			0
$841$	1698.59			2.01973
$842$	321.378	+	507.280i	0.381684	+	0.602470i
$843$		0			0
$844$	949.670	+	448.682i	1.12520	+	0.531614i
$845$	281.832			0.333529
$846$		0			0
$847$			1174.02i			1.38610i
$848$	392.241	+	477.145i	0.462548	+	0.562671i
$849$		0			0
$850$	−357.889	−	564.911i	−0.421046	−	0.664601i
$851$		−	578.848i		−	0.680197i
$852$		0			0
$853$	389.779			0.456951			0.228476	−	0.973550i	$-0.426626\pi$
$853$	389.779			0.456951			0.228476	+	0.973550i	$0.426626\pi$
$854$	−1763.16	+	1117.01i	−2.06459	+	1.30798i
$855$		0			0
$856$	−53.2516	−	429.568i	−0.0622098	−	0.501832i
$857$	1341.14			1.56493			0.782464	−	0.622696i	$-0.213963\pi$
$857$	1341.14			1.56493			0.782464	+	0.622696i	$0.213963\pi$
$858$		0			0
$859$			551.747i			0.642313i	0.947026	+	0.321157i	$0.104072\pi$
$859$			551.747i			0.642313i	−0.947026	+	0.321157i	$0.895928\pi$
$860$	1427.63	+	674.499i	1.66003	+	0.784301i
$861$		0			0
$862$	1278.31	−	809.848i	1.48296	−	0.939499i
$863$			1298.16i			1.50425i	0.659023	+	0.752123i	$0.270970\pi$
$863$			1298.16i			1.50425i	−0.659023	+	0.752123i	$0.729030\pi$
$864$		0			0
$865$	2155.92			2.49240
$866$	757.427	+	1195.56i	0.874627	+	1.38056i
$867$		0			0
$868$	−132.024	+	279.438i	−0.152101	+	0.321934i
$869$	−327.602			−0.376987
$870$		0			0
$871$		−	1164.38i		−	1.33683i
$872$	−906.184	+	112.335i	−1.03920	+	0.128825i
$873$		0			0
$874$	74.8444	+	118.138i	0.0856343	+	0.135170i
$875$			450.897i			0.515311i
$876$		0			0
$877$	943.666			1.07602			0.538008	−	0.842940i	$-0.319177\pi$
$877$	943.666			1.07602			0.538008	+	0.842940i	$0.319177\pi$
$878$	−389.010	+	246.450i	−0.443063	+	0.280695i
$879$		0			0
$880$	406.806	−	334.418i	0.462280	−	0.380021i
$881$	−1220.11			−1.38492			−0.692460	−	0.721456i	$-0.743473\pi$
$881$	−1220.11			−1.38492			−0.692460	+	0.721456i	$0.743473\pi$
$882$		0			0
$883$		−	1315.99i		−	1.49036i	−0.666862	−	0.745181i	$-0.732363\pi$
$883$		−	1315.99i		−	1.49036i	0.666862	−	0.745181i	$-0.267637\pi$
$884$	−330.962	+	700.507i	−0.374392	+	0.792429i
$885$		0			0
$886$	107.602	−	68.1695i	0.121447	−	0.0769407i
$887$		−	588.646i		−	0.663637i	−0.943343	−	0.331819i	$-0.892338\pi$
$887$		−	588.646i		−	0.663637i	0.943343	−	0.331819i	$-0.107662\pi$
$888$		0			0
$889$	481.580			0.541710
$890$	−384.801	−	607.390i	−0.432361	−	0.682461i
$891$		0			0
$892$	−1076.51	−	508.609i	−1.20685	−	0.570190i
$893$	−154.095			−0.172559
$894$		0			0
$895$			1877.93i			2.09825i
$896$	1070.84	−	1127.99i	1.19513	−	1.25892i
$897$		0			0
$898$	−227.574	−	359.215i	−0.253423	−	0.400016i
$899$			320.441i			0.356441i
$900$		0			0
$901$	−664.234			−0.737219
$902$	−99.0762	+	62.7679i	−0.109841	+	0.0695875i
$903$		0			0
$904$	−440.073	+	54.5538i	−0.486807	+	0.0603472i
$905$	−1857.17			−2.05212
$906$		0			0
$907$		−	446.540i		−	0.492326i	−0.969228	−	0.246163i	$-0.920830\pi$
$907$		−	446.540i		−	0.492326i	0.969228	−	0.246163i	$-0.0791699\pi$
$908$	−255.125	−	120.537i	−0.280975	−	0.132749i
$909$		0			0
$910$	−1540.43	+	975.914i	−1.69278	+	1.07243i
$911$		−	1089.84i		−	1.19632i	−0.801378	−	0.598158i	$-0.795900\pi$
$911$		−	1089.84i		−	1.19632i	0.801378	−	0.598158i	$-0.204100\pi$
$912$		0			0
$913$	19.8231			0.0217120
$914$	467.256	+	737.542i	0.511221	+	0.806939i
$915$		0			0
$916$	−568.217	+	1202.68i	−0.620324	+	1.31296i
$917$	−2020.67			−2.20357
$918$		0			0
$919$		−	1127.18i		−	1.22653i	−0.789879	−	0.613263i	$-0.789856\pi$
$919$		−	1127.18i		−	1.22653i	0.789879	−	0.613263i	$-0.210144\pi$
$920$	−105.243	−	848.968i	−0.114394	−	0.922791i
$921$		0			0
$922$	−108.503	−	171.266i	−0.117682	−	0.185755i
$923$		−	756.585i		−	0.819702i
$924$		0			0
$925$	−701.209			−0.758064
$926$	−890.423	+	564.111i	−0.961580	+	0.609192i
$927$		0			0
$928$	504.273	−	1531.75i	0.543397	−	1.65059i
$929$	−1581.94			−1.70284			−0.851421	−	0.524482i	$-0.824259\pi$
$929$	−1581.94			−1.70284			−0.851421	+	0.524482i	$0.824259\pi$
$930$		0			0
$931$		−	429.993i		−	0.461862i
$932$	−719.818	+	1523.55i	−0.772337	+	1.63471i
$933$		0			0
$934$	−777.894	+	492.820i	−0.832863	+	0.527645i
$935$			566.315i			0.605685i
$936$		0			0
$937$	176.071			0.187909			0.0939547	−	0.995576i	$-0.470049\pi$
$937$	176.071			0.187909			0.0939547	+	0.995576i	$0.470049\pi$
$938$	−1345.27	−	2123.44i	−1.43419	−	2.26380i
$939$		0			0
$940$	852.260	+	402.660i	0.906660	+	0.428361i
$941$	1629.91			1.73210			0.866052	−	0.499954i	$-0.166650\pi$
$941$	1629.91			1.73210			0.866052	+	0.499954i	$0.166650\pi$
$942$		0			0
$943$			190.525i			0.202041i
$944$	−1110.06	+	912.533i	−1.17591	+	0.966667i
$945$		0			0
$946$	−312.968	−	494.005i	−0.330833	−	0.522204i
$947$			1141.57i			1.20546i	0.797945	+	0.602731i	$0.205921\pi$
$947$			1141.57i			1.20546i	−0.797945	+	0.602731i	$0.794079\pi$
$948$		0			0
$949$	1232.39			1.29862
$950$	143.111	−	90.6656i	0.150644	−	0.0954375i
$951$		0			0
$952$	205.766	+	1659.87i	0.216141	+	1.74356i
$953$	824.746			0.865421			0.432711	−	0.901533i	$-0.357557\pi$
$953$	824.746			0.865421			0.432711	+	0.901533i	$0.357557\pi$
$954$		0			0
$955$		−	665.180i		−	0.696524i
$956$	−849.165	−	401.197i	−0.888248	−	0.419663i
$957$		0			0
$958$	−296.216	+	187.662i	−0.309203	+	0.195890i
$959$		−	2039.65i		−	2.12685i
$960$		0			0
$961$	920.567			0.957927
$962$	434.760	+	686.249i	0.451934	+	0.713357i
$963$		0			0
$964$	451.842	−	956.358i	0.468716	−	0.992073i
$965$	−1685.57			−1.74671
$966$		0			0
$967$		−	286.436i		−	0.296211i	−0.988972	−	0.148105i	$-0.952683\pi$
$967$		−	286.436i		−	0.296211i	0.988972	−	0.148105i	$-0.0473175\pi$
$968$	767.083	−	95.0918i	0.792442	−	0.0982353i
$969$		0			0
$970$	−448.585	−	708.070i	−0.462458	−	0.729969i
$971$			509.431i			0.524646i	0.964980	+	0.262323i	$0.0844886\pi$
$971$			509.431i			0.524646i	−0.964980	+	0.262323i	$0.915511\pi$
$972$		0			0
$973$	133.901			0.137616
$974$	1226.67	−	777.133i	1.25941	−	0.797878i
$975$		0			0
$976$	872.644	+	1061.54i	0.894103	+	1.08764i
$977$	−92.0031			−0.0941690			−0.0470845	−	0.998891i	$-0.514993\pi$
$977$	−92.0031			−0.0941690			−0.0470845	+	0.998891i	$0.514993\pi$
$978$		0			0
$979$			266.307i			0.272019i
$980$	−1123.60	+	2378.19i	−1.14653	+	2.42672i
$981$		0			0
$982$	1373.44	−	870.115i	1.39861	−	0.886065i
$983$			699.319i			0.711413i	0.934598	+	0.355706i	$0.115760\pi$
$983$			699.319i			0.711413i	−0.934598	+	0.355706i	$0.884240\pi$
$984$		0			0
$985$	−84.9000			−0.0861929
$986$	928.085	+	1464.94i	0.941262	+	1.48574i
$987$		0			0
$988$	−177.463	−	83.8441i	−0.179618	−	0.0848625i
$989$	−949.978			−0.960544
$990$		0			0
$991$			1338.85i			1.35101i	0.737356	+	0.675505i	$0.236074\pi$
$991$			1338.85i			1.35101i	−0.737356	+	0.675505i	$0.763926\pi$
$992$	193.273	+	63.6281i	0.194832	+	0.0641412i
$993$		0			0
$994$	−874.120	−	1379.76i	−0.879396	−	1.38809i
$995$			1658.60i			1.66694i
$996$		0			0
$997$	−1147.47			−1.15092			−0.575461	−	0.817829i	$-0.695177\pi$
$997$	−1147.47			−1.15092			−0.575461	+	0.817829i	$0.695177\pi$
$998$	768.016	−	486.562i	0.769555	−	0.487538i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.11	✓	36
3.2	odd	2	inner	684.3.g.d.343.26	yes	36
4.3	odd	2	inner	684.3.g.d.343.12	yes	36
12.11	even	2	inner	684.3.g.d.343.25	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.11	✓	36	1.1	even	1	trivial
684.3.g.d.343.12	yes	36	4.3	odd	2	inner
684.3.g.d.343.25	yes	36	12.11	even	2	inner
684.3.g.d.343.26	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07034 - 1.68949i) q^{2} +(-1.70873 + 3.61666i) q^{4} -6.66582 q^{5} +12.1510i q^{7} +(7.93923 - 0.984190i) q^{8} +O(q^{10})\)	\(q+(-1.07034 - 1.68949i) q^{2} +(-1.70873 + 3.61666i) q^{4} -6.66582 q^{5} +12.1510i q^{7} +(7.93923 - 0.984190i) q^{8} +(7.13471 + 11.2618i) q^{10} -4.93767i q^{11} +11.2570 q^{13} +(20.5290 - 13.0058i) q^{14} +(-10.1605 - 12.3598i) q^{16} +17.2061 q^{17} +4.35890i q^{19} +(11.3901 - 24.1080i) q^{20} +(-8.34214 + 5.28501i) q^{22} +16.0420i q^{23} +19.4331 q^{25} +(-12.0488 - 19.0185i) q^{26} +(-43.9461 - 20.7628i) q^{28} -50.3944 q^{29} -6.35866i q^{31} +(-10.0065 + 30.3952i) q^{32} +(-18.4164 - 29.0695i) q^{34} -80.9965i q^{35} -36.0832 q^{37} +(7.36430 - 4.66552i) q^{38} +(-52.9215 + 6.56043i) q^{40} +11.8766 q^{41} +59.2181i q^{43} +(17.8579 + 8.43716i) q^{44} +(27.1028 - 17.1705i) q^{46} +35.3518i q^{47} -98.6473 q^{49} +(-20.8001 - 32.8320i) q^{50} +(-19.2352 + 40.7127i) q^{52} -38.6046 q^{53} +32.9136i q^{55} +(11.9589 + 96.4697i) q^{56} +(53.9393 + 85.1406i) q^{58} -89.8121i q^{59} -85.8862 q^{61} +(-10.7429 + 6.80595i) q^{62} +(62.0627 - 15.6274i) q^{64} -75.0370 q^{65} -103.436i q^{67} +(-29.4006 + 62.2286i) q^{68} +(-136.842 + 86.6940i) q^{70} -67.2102i q^{71} +109.478 q^{73} +(38.6214 + 60.9620i) q^{74} +(-15.7647 - 7.44819i) q^{76} +59.9978 q^{77} -66.3475i q^{79} +(67.7279 + 82.3882i) q^{80} +(-12.7120 - 20.0654i) q^{82} +4.01466i q^{83} -114.693 q^{85} +(100.048 - 63.3836i) q^{86} +(-4.85961 - 39.2013i) q^{88} -53.9336 q^{89} +136.784i q^{91} +(-58.0186 - 27.4115i) q^{92} +(59.7263 - 37.8385i) q^{94} -29.0556i q^{95} -62.8736 q^{97} +(105.586 + 166.663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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