LMFDB - Embedded newform 684.2.c.b.647.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(647,684)]

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, 1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("684.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			647.29
Character	$\chi$	$=$	684.647
Dual form			684.2.c.b.647.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37167 - 0.344287i) q^{2} +(1.76293 - 0.944493i) q^{4} +2.95253i q^{5} -2.52587i q^{7} +(2.09298 - 1.90248i) q^{8} +O(q^{10})$	\(q+(1.37167 - 0.344287i) q^{2} +(1.76293 - 0.944493i) q^{4} +2.95253i q^{5} -2.52587i q^{7} +(2.09298 - 1.90248i) q^{8} +(1.01652 + 4.04988i) q^{10} +0.275662 q^{11} +3.94244 q^{13} +(-0.869623 - 3.46464i) q^{14} +(2.21587 - 3.33016i) q^{16} +2.91003i q^{17} -1.00000i q^{19} +(2.78864 + 5.20511i) q^{20} +(0.378116 - 0.0949068i) q^{22} +5.02883 q^{23} -3.71743 q^{25} +(5.40771 - 1.35733i) q^{26} +(-2.38566 - 4.45293i) q^{28} +0.0951342i q^{29} +6.84831i q^{31} +(1.89290 - 5.33075i) q^{32} +(1.00188 + 3.99158i) q^{34} +7.45769 q^{35} -11.9077 q^{37} +(-0.344287 - 1.37167i) q^{38} +(5.61714 + 6.17958i) q^{40} +4.10951i q^{41} -8.64895i q^{43} +(0.485974 - 0.260361i) q^{44} +(6.89787 - 1.73136i) q^{46} -5.81949 q^{47} +0.620000 q^{49} +(-5.09906 + 1.27986i) q^{50} +(6.95026 - 3.72361i) q^{52} -0.551324i q^{53} +0.813900i q^{55} +(-4.80542 - 5.28658i) q^{56} +(0.0327535 + 0.130492i) q^{58} -5.80992 q^{59} -13.7963 q^{61} +(2.35778 + 9.39359i) q^{62} +(0.761114 - 7.96371i) q^{64} +11.6402i q^{65} -6.79844i q^{67} +(2.74850 + 5.13018i) q^{68} +(10.2295 - 2.56759i) q^{70} +8.34706 q^{71} -3.65376 q^{73} +(-16.3334 + 4.09967i) q^{74} +(-0.944493 - 1.76293i) q^{76} -0.696285i q^{77} -9.13640i q^{79} +(9.83238 + 6.54241i) q^{80} +(1.41485 + 5.63688i) q^{82} -13.3249 q^{83} -8.59193 q^{85} +(-2.97772 - 11.8635i) q^{86} +(0.576954 - 0.524442i) q^{88} -6.30522i q^{89} -9.95808i q^{91} +(8.86549 - 4.74970i) q^{92} +(-7.98239 + 2.00357i) q^{94} +2.95253 q^{95} +0.763637 q^{97} +(0.850433 - 0.213458i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * 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 $

$2$	1.37167	−	0.344287i	0.969914	−	0.243448i
$2$	1.37167	−	0.344287i	0.969914	−	0.243448i
$3$		0			0
$3$		0			0
$4$	1.76293	−	0.944493i	0.881467	−	0.472246i
$5$			2.95253i			1.32041i	0.751085	+	0.660205i	$0.229531\pi$
$5$			2.95253i			1.32041i	−0.751085	+	0.660205i	$0.770469\pi$
$6$		0			0
$7$		−	2.52587i		−	0.954688i	−0.878717	−	0.477344i	$-0.841600\pi$
$7$		−	2.52587i		−	0.954688i	0.878717	−	0.477344i	$-0.158400\pi$
$8$	2.09298	−	1.90248i	0.739979	−	0.672629i
$9$		0			0
$10$	1.01652	+	4.04988i	0.321451	+	1.28069i
$11$	0.275662			0.0831152			0.0415576	−	0.999136i	$-0.486768\pi$
$11$	0.275662			0.0831152			0.0415576	+	0.999136i	$0.486768\pi$
$12$		0			0
$13$	3.94244			1.09344			0.546718	−	0.837317i	$-0.315877\pi$
$13$	3.94244			1.09344			0.546718	+	0.837317i	$0.315877\pi$
$14$	−0.869623	−	3.46464i	−0.232416	−	0.925965i
$15$		0			0
$16$	2.21587	−	3.33016i	0.553966	−	0.832539i
$17$			2.91003i			0.705785i	0.935664	+	0.352892i	$0.114802\pi$
$17$			2.91003i			0.705785i	−0.935664	+	0.352892i	$0.885198\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.78864	+	5.20511i	0.623559	+	1.16390i
$21$		0			0
$22$	0.378116	−	0.0949068i	0.0806146	−	0.0202342i
$23$	5.02883			1.04858			0.524292	−	0.851539i	$-0.324330\pi$
$23$	5.02883			1.04858			0.524292	+	0.851539i	$0.324330\pi$
$24$		0			0
$25$	−3.71743			−0.743485
$26$	5.40771	−	1.35733i	1.06054	−	0.266194i
$27$		0			0
$28$	−2.38566	−	4.45293i	−0.450848	−	0.841525i
$29$			0.0951342i			0.0176660i	0.999961	+	0.00883299i	$0.00281166\pi$
$29$			0.0951342i			0.0176660i	−0.999961	+	0.00883299i	$0.997188\pi$
$30$		0			0
$31$			6.84831i			1.22999i	0.788530	+	0.614996i	$0.210842\pi$
$31$			6.84831i			1.22999i	−0.788530	+	0.614996i	$0.789158\pi$
$32$	1.89290	−	5.33075i	0.334620	−	0.942353i
$33$		0			0
$34$	1.00188	+	3.99158i	0.171822	+	0.684551i
$35$	7.45769			1.26058
$36$		0			0
$37$	−11.9077			−1.95762			−0.978809	−	0.204774i	$-0.934354\pi$
$37$	−11.9077			−1.95762			−0.978809	+	0.204774i	$0.934354\pi$
$38$	−0.344287	−	1.37167i	−0.0558507	−	0.222514i
$39$		0			0
$40$	5.61714	+	6.17958i	0.888147	+	0.977077i
$41$			4.10951i			0.641798i	0.947113	+	0.320899i	$0.103985\pi$
$41$			4.10951i			0.641798i	−0.947113	+	0.320899i	$0.896015\pi$
$42$		0			0
$43$		−	8.64895i		−	1.31895i	−0.751725	−	0.659476i	$-0.770778\pi$
$43$		−	8.64895i		−	1.31895i	0.751725	−	0.659476i	$-0.229222\pi$
$44$	0.485974	−	0.260361i	0.0732633	−	0.0392509i
$45$		0			0
$46$	6.89787	−	1.73136i	1.01704	−	0.255275i
$47$	−5.81949			−0.848859			−0.424430	−	0.905461i	$-0.639525\pi$
$47$	−5.81949			−0.848859			−0.424430	+	0.905461i	$0.639525\pi$
$48$		0			0
$49$	0.620000			0.0885715
$50$	−5.09906	+	1.27986i	−0.721117	+	0.181000i
$51$		0			0
$52$	6.95026	−	3.72361i	0.963828	−	0.516371i
$53$		−	0.551324i		−	0.0757302i	−0.999283	−	0.0378651i	$-0.987944\pi$
$53$		−	0.551324i		−	0.0757302i	0.999283	−	0.0378651i	$-0.0120557\pi$
$54$		0			0
$55$			0.813900i			0.109746i
$56$	−4.80542	−	5.28658i	−0.642151	−	0.706449i
$57$		0			0
$58$	0.0327535	+	0.130492i	0.00430074	+	0.0171345i
$59$	−5.80992			−0.756388			−0.378194	−	0.925726i	$-0.623455\pi$
$59$	−5.80992			−0.756388			−0.378194	+	0.925726i	$0.623455\pi$
$60$		0			0
$61$	−13.7963			−1.76643			−0.883216	−	0.468967i	$-0.844626\pi$
$61$	−13.7963			−1.76643			−0.883216	+	0.468967i	$0.844626\pi$
$62$	2.35778	+	9.39359i	0.299439	+	1.19299i
$63$		0			0
$64$	0.761114	−	7.96371i	0.0951393	−	0.995464i
$65$			11.6402i			1.44379i
$66$		0			0
$67$		−	6.79844i		−	0.830561i	−0.909693	−	0.415281i	$-0.863683\pi$
$67$		−	6.79844i		−	0.830561i	0.909693	−	0.415281i	$-0.136317\pi$
$68$	2.74850	+	5.13018i	0.333304	+	0.622126i
$69$		0			0
$70$	10.2295	−	2.56759i	1.22265	−	0.306885i
$71$	8.34706			0.990614			0.495307	−	0.868718i	$-0.335056\pi$
$71$	8.34706			0.990614			0.495307	+	0.868718i	$0.335056\pi$
$72$		0			0
$73$	−3.65376			−0.427640			−0.213820	−	0.976873i	$-0.568591\pi$
$73$	−3.65376			−0.427640			−0.213820	+	0.976873i	$0.568591\pi$
$74$	−16.3334	+	4.09967i	−1.89872	+	0.476578i
$75$		0			0
$76$	−0.944493	−	1.76293i	−0.108341	−	0.202222i
$77$		−	0.696285i		−	0.0793491i
$78$		0			0
$79$		−	9.13640i		−	1.02793i	−0.857812	−	0.513963i	$-0.828177\pi$
$79$		−	9.13640i		−	1.02793i	0.857812	−	0.513963i	$-0.171823\pi$
$80$	9.83238	+	6.54241i	1.09929	+	0.731463i
$81$		0			0
$82$	1.41485	+	5.63688i	0.156244	+	0.622489i
$83$	−13.3249			−1.46259			−0.731296	−	0.682060i	$-0.761084\pi$
$83$	−13.3249			−1.46259			−0.731296	+	0.682060i	$0.761084\pi$
$84$		0			0
$85$	−8.59193			−0.931926
$86$	−2.97772	−	11.8635i	−0.321096	−	1.27927i
$87$		0			0
$88$	0.576954	−	0.524442i	0.0615035	−	0.0559057i
$89$		−	6.30522i		−	0.668352i	−0.942511	−	0.334176i	$-0.891542\pi$
$89$		−	6.30522i		−	0.668352i	0.942511	−	0.334176i	$-0.108458\pi$
$90$		0			0
$91$		−	9.95808i		−	1.04389i
$92$	8.86549	−	4.74970i	0.924291	−	0.495190i
$93$		0			0
$94$	−7.98239	+	2.00357i	−0.823321	+	0.206653i
$95$	2.95253			0.302923
$96$		0			0
$97$	0.763637			0.0775355			0.0387678	−	0.999248i	$-0.487657\pi$
$97$	0.763637			0.0775355			0.0387678	+	0.999248i	$0.487657\pi$
$98$	0.850433	−	0.213458i	0.0859067	−	0.0215625i
$99$		0			0
$100$	−6.55357	+	3.51108i	−0.655357	+	0.351108i
$101$		−	3.98507i		−	0.396529i	−0.980149	−	0.198265i	$-0.936469\pi$
$101$		−	3.98507i		−	0.396529i	0.980149	−	0.198265i	$-0.0635306\pi$
$102$		0			0
$103$		−	3.42690i		−	0.337663i	−0.985645	−	0.168831i	$-0.946001\pi$
$103$		−	3.42690i		−	0.337663i	0.985645	−	0.168831i	$-0.0539993\pi$
$104$	8.25144	−	7.50043i	0.809120	−	0.735477i
$105$		0			0
$106$	−0.189814	−	0.756232i	−0.0184363	−	0.0734517i
$107$	−17.0524			−1.64851			−0.824257	−	0.566216i	$-0.808407\pi$
$107$	−17.0524			−1.64851			−0.824257	+	0.566216i	$0.808407\pi$
$108$		0			0
$109$	17.0290			1.63108			0.815540	−	0.578701i	$-0.196440\pi$
$109$	17.0290			1.63108			0.815540	+	0.578701i	$0.196440\pi$
$110$	0.280215	+	1.11640i	0.0267175	+	0.106444i
$111$		0			0
$112$	−8.41153	−	5.59698i	−0.794815	−	0.528865i
$113$			5.59646i			0.526470i	0.964732	+	0.263235i	$0.0847895\pi$
$113$			5.59646i			0.526470i	−0.964732	+	0.263235i	$0.915210\pi$
$114$		0			0
$115$			14.8478i			1.38456i
$116$	0.0898536	+	0.167715i	0.00834270	+	0.0155720i
$117$		0			0
$118$	−7.96927	+	2.00028i	−0.733631	+	0.184141i
$119$	7.35034			0.673804
$120$		0			0
$121$	−10.9240			−0.993092
$122$	−18.9239	+	4.74987i	−1.71329	+	0.430033i
$123$		0			0
$124$	6.46818	+	12.0731i	0.580860	+	1.08420i
$125$			3.78684i			0.338705i
$126$		0			0
$127$			12.3155i			1.09282i	0.837518	+	0.546410i	$0.184006\pi$
$127$			12.3155i			1.09282i	−0.837518	+	0.546410i	$0.815994\pi$
$128$	−1.69781	−	11.1856i	−0.150066	−	0.988676i
$129$		0			0
$130$	4.00756	+	15.9664i	0.351486	+	1.40035i
$131$	0.121640			0.0106277			0.00531386	−	0.999986i	$-0.498309\pi$
$131$	0.121640			0.0106277			0.00531386	+	0.999986i	$0.498309\pi$
$132$		0			0
$133$	−2.52587			−0.219020
$134$	−2.34061	−	9.32518i	−0.202198	−	0.805573i
$135$		0			0
$136$	5.53628	+	6.09062i	0.474732	+	0.522266i
$137$			22.0674i			1.88535i	0.333715	+	0.942674i	$0.391698\pi$
$137$			22.0674i			1.88535i	−0.333715	+	0.942674i	$0.608302\pi$
$138$		0			0
$139$			20.8785i			1.77089i	0.464745	+	0.885444i	$0.346146\pi$
$139$			20.8785i			1.77089i	−0.464745	+	0.885444i	$0.653854\pi$
$140$	13.1474	−	7.04374i	1.11116	−	0.595305i
$141$		0			0
$142$	11.4494	−	2.87378i	0.960810	−	0.241162i
$143$	1.08678			0.0908812
$144$		0			0
$145$	−0.280886			−0.0233263
$146$	−5.01174	+	1.25794i	−0.414774	+	0.104108i
$147$		0			0
$148$	−20.9925	+	11.2468i	−1.72558	+	0.924478i
$149$		−	6.25374i		−	0.512326i	−0.966634	−	0.256163i	$-0.917542\pi$
$149$		−	6.25374i		−	0.512326i	0.966634	−	0.256163i	$-0.0824584\pi$
$150$		0			0
$151$			6.92871i			0.563851i	0.959436	+	0.281925i	$0.0909730\pi$
$151$			6.92871i			0.563851i	−0.959436	+	0.281925i	$0.909027\pi$
$152$	−1.90248	−	2.09298i	−0.154312	−	0.169763i
$153$		0			0
$154$	−0.239722	−	0.955070i	−0.0193173	−	0.0769618i
$155$	−20.2198			−1.62410
$156$		0			0
$157$	10.4677			0.835415			0.417708	−	0.908582i	$-0.362834\pi$
$157$	10.4677			0.835415			0.417708	+	0.908582i	$0.362834\pi$
$158$	−3.14554	−	12.5321i	−0.250246	−	0.996999i
$159$		0			0
$160$	15.7392	+	5.58884i	1.24429	+	0.441836i
$161$		−	12.7022i		−	1.00107i
$162$		0			0
$163$		−	7.15864i		−	0.560708i	−0.959897	−	0.280354i	$-0.909548\pi$
$163$		−	7.15864i		−	0.560708i	0.959897	−	0.280354i	$-0.0904519\pi$
$164$	3.88141	+	7.24480i	0.303087	+	0.565724i
$165$		0			0
$166$	−18.2772	+	4.58757i	−1.41859	+	0.356065i
$167$	23.3702			1.80844			0.904218	−	0.427071i	$-0.140454\pi$
$167$	23.3702			1.80844			0.904218	+	0.427071i	$0.140454\pi$
$168$		0			0
$169$	2.54284			0.195603
$170$	−11.7853	+	2.95809i	−0.903888	+	0.226875i
$171$		0			0
$172$	−8.16888	−	15.2475i	−0.622871	−	1.16261i
$173$			7.41513i			0.563762i	0.959449	+	0.281881i	$0.0909584\pi$
$173$			7.41513i			0.563762i	−0.959449	+	0.281881i	$0.909042\pi$
$174$		0			0
$175$			9.38972i			0.709796i
$176$	0.610830	−	0.917997i	0.0460430	−	0.0691966i
$177$		0			0
$178$	−2.17080	−	8.64865i	−0.162709	−	0.648244i
$179$	−22.6326			−1.69164			−0.845821	−	0.533468i	$-0.820889\pi$
$179$	−22.6326			−1.69164			−0.845821	+	0.533468i	$0.820889\pi$
$180$		0			0
$181$	9.27506			0.689410			0.344705	−	0.938711i	$-0.387979\pi$
$181$	9.27506			0.689410			0.344705	+	0.938711i	$0.387979\pi$
$182$	−3.42844	−	13.6592i	−0.254133	−	1.01248i
$183$		0			0
$184$	10.5252	−	9.56727i	0.775930	−	0.705308i
$185$		−	35.1579i		−	2.58486i
$186$		0			0
$187$			0.802183i			0.0586615i
$188$	−10.2594	+	5.49646i	−0.748241	+	0.400871i
$189$		0			0
$190$	4.04988	−	1.01652i	0.293809	−	0.0737459i
$191$	−15.0302			−1.08754			−0.543772	−	0.839233i	$-0.683004\pi$
$191$	−15.0302			−1.08754			−0.543772	+	0.839233i	$0.683004\pi$
$192$		0			0
$193$	0.536674			0.0386306			0.0193153	−	0.999813i	$-0.493851\pi$
$193$	0.536674			0.0386306			0.0193153	+	0.999813i	$0.493851\pi$
$194$	1.04745	−	0.262910i	0.0752028	−	0.0188758i
$195$		0			0
$196$	1.09302	−	0.585586i	0.0780728	−	0.0418276i
$197$		−	22.2296i		−	1.58380i	−0.610653	−	0.791898i	$-0.709093\pi$
$197$		−	22.2296i		−	1.58380i	0.610653	−	0.791898i	$-0.290907\pi$
$198$		0			0
$199$			3.25410i			0.230677i	0.993326	+	0.115338i	$0.0367953\pi$
$199$			3.25410i			0.230677i	−0.993326	+	0.115338i	$0.963205\pi$
$200$	−7.78049	+	7.07234i	−0.550164	+	0.500090i
$201$		0			0
$202$	−1.37201	−	5.46619i	−0.0965341	−	0.384600i
$203$	0.240296			0.0168655
$204$		0			0
$205$	−12.1335			−0.847438
$206$	−1.17984	−	4.70056i	−0.0822032	−	0.327504i
$207$		0			0
$208$	8.73592	−	13.1289i	0.605727	−	0.910328i
$209$		−	0.275662i		−	0.0190679i
$210$		0			0
$211$			21.0170i			1.44687i	0.690392	+	0.723436i	$0.257438\pi$
$211$			21.0170i			1.44687i	−0.690392	+	0.723436i	$0.742562\pi$
$212$	−0.520722	−	0.971947i	−0.0357633	−	0.0667536i
$213$		0			0
$214$	−23.3901	+	5.87090i	−1.59892	+	0.401327i
$215$	25.5363			1.74156
$216$		0			0
$217$	17.2979			1.17426
$218$	23.3581	−	5.86285i	1.58201	−	0.397082i
$219$		0			0
$220$	0.768723	+	1.43485i	0.0518273	+	0.0967376i
$221$			11.4726i			0.771731i
$222$		0			0
$223$		−	27.5517i		−	1.84500i	−0.385997	−	0.922500i	$-0.626143\pi$
$223$		−	27.5517i		−	1.84500i	0.385997	−	0.922500i	$-0.373857\pi$
$224$	−13.4648	−	4.78121i	−0.899653	−	0.319458i
$225$		0			0
$226$	1.92679	+	7.67647i	0.128168	+	0.510631i
$227$	23.0035			1.52679			0.763397	−	0.645930i	$-0.223530\pi$
$227$	23.0035			1.52679			0.763397	+	0.645930i	$0.223530\pi$
$228$		0			0
$229$	6.61721			0.437277			0.218639	−	0.975806i	$-0.429838\pi$
$229$	6.61721			0.437277			0.218639	+	0.975806i	$0.429838\pi$
$230$	5.11189	+	20.3662i	0.337068	+	1.34291i
$231$		0			0
$232$	0.180991	+	0.199114i	0.0118827	+	0.0130725i
$233$		−	17.2740i		−	1.13166i	−0.824523	−	0.565828i	$-0.808557\pi$
$233$		−	17.2740i		−	1.13166i	0.824523	−	0.565828i	$-0.191443\pi$
$234$		0			0
$235$		−	17.1822i		−	1.12084i
$236$	−10.2425	+	5.48743i	−0.666730	+	0.357201i
$237$		0			0
$238$	10.0822	−	2.53062i	0.653532	−	0.164036i
$239$	9.21011			0.595753			0.297876	−	0.954604i	$-0.403722\pi$
$239$	9.21011			0.595753			0.297876	+	0.954604i	$0.403722\pi$
$240$		0			0
$241$	16.7289			1.07760			0.538802	−	0.842432i	$-0.318877\pi$
$241$	16.7289			1.07760			0.538802	+	0.842432i	$0.318877\pi$
$242$	−14.9841	+	3.76099i	−0.963214	+	0.241766i
$243$		0			0
$244$	−24.3219	+	13.0305i	−1.55705	+	0.834191i
$245$			1.83057i			0.116951i
$246$		0			0
$247$		−	3.94244i		−	0.250852i
$248$	13.0288	+	14.3334i	0.827329	+	0.910169i
$249$		0			0
$250$	1.30376	+	5.19428i	0.0824570	+	0.328515i
$251$	−7.20778			−0.454951			−0.227475	−	0.973784i	$-0.573047\pi$
$251$	−7.20778			−0.454951			−0.227475	+	0.973784i	$0.573047\pi$
$252$		0			0
$253$	1.38626			0.0871532
$254$	4.24005	+	16.8927i	0.266045	+	1.05994i
$255$		0			0
$256$	−6.17988	−	14.7584i	−0.386242	−	0.922397i
$257$			3.09341i			0.192962i	0.995335	+	0.0964809i	$0.0307587\pi$
$257$			3.09341i			0.192962i	−0.995335	+	0.0964809i	$0.969241\pi$
$258$		0			0
$259$			30.0773i			1.86891i
$260$	10.9941	+	20.5208i	0.681823	+	1.27265i
$261$		0			0
$262$	0.166849	−	0.0418790i	0.0103080	−	0.00258729i
$263$	−9.13622			−0.563364			−0.281682	−	0.959508i	$-0.590892\pi$
$263$	−9.13622			−0.563364			−0.281682	+	0.959508i	$0.590892\pi$
$264$		0			0
$265$	1.62780			0.0999949
$266$	−3.46464	+	0.869623i	−0.212431	+	0.0533200i
$267$		0			0
$268$	−6.42108	−	11.9852i	−0.392230	−	0.732112i
$269$		−	19.6554i		−	1.19841i	−0.800596	−	0.599205i	$-0.795484\pi$
$269$		−	19.6554i		−	1.19841i	0.800596	−	0.599205i	$-0.204516\pi$
$270$		0			0
$271$		−	1.32794i		−	0.0806667i	−0.999186	−	0.0403333i	$-0.987158\pi$
$271$		−	1.32794i		−	0.0806667i	0.999186	−	0.0403333i	$-0.0128420\pi$
$272$	9.69084	+	6.44823i	0.587593	+	0.390981i
$273$		0			0
$274$	7.59753	+	30.2691i	0.458983	+	1.82863i
$275$	−1.02475			−0.0617949
$276$		0			0
$277$	23.6080			1.41847			0.709234	−	0.704974i	$-0.249041\pi$
$277$	23.6080			1.41847			0.709234	+	0.704974i	$0.249041\pi$
$278$	7.18818	+	28.6383i	0.431119	+	1.71761i
$279$		0			0
$280$	15.6088	−	14.1881i	0.932803	−	0.847903i
$281$			14.3664i			0.857026i	0.903536	+	0.428513i	$0.140962\pi$
$281$			14.3664i			0.857026i	−0.903536	+	0.428513i	$0.859038\pi$
$282$		0			0
$283$		−	10.0810i		−	0.599254i	−0.954056	−	0.299627i	$-0.903138\pi$
$283$		−	10.0810i		−	0.599254i	0.954056	−	0.299627i	$-0.0968622\pi$
$284$	14.7153	−	7.88374i	0.873193	−	0.467814i
$285$		0			0
$286$	1.49070	−	0.374164i	0.0881469	−	0.0221248i
$287$	10.3801			0.612717
$288$		0			0
$289$	8.53175			0.501868
$290$	−0.385282	+	0.0967055i	−0.0226246	+	0.00567874i
$291$		0			0
$292$	−6.44133	+	3.45095i	−0.376951	+	0.201952i
$293$			18.1331i			1.05935i	0.848202	+	0.529673i	$0.177685\pi$
$293$			18.1331i			1.05935i	−0.848202	+	0.529673i	$0.822315\pi$
$294$		0			0
$295$		−	17.1540i		−	0.998742i
$296$	−24.9226	+	22.6543i	−1.44860	+	1.31675i
$297$		0			0
$298$	−2.15308	−	8.57804i	−0.124725	−	0.496912i
$299$	19.8259			1.14656
$300$		0			0
$301$	−21.8461			−1.25919
$302$	2.38546	+	9.50388i	0.137268	+	0.546887i
$303$		0			0
$304$	−3.33016	−	2.21587i	−0.190998	−	0.127089i
$305$		−	40.7339i		−	2.33242i
$306$		0			0
$307$		−	1.28850i		−	0.0735388i	−0.999324	−	0.0367694i	$-0.988293\pi$
$307$		−	1.28850i		−	0.0735388i	0.999324	−	0.0367694i	$-0.0117067\pi$
$308$	−0.657636	−	1.22750i	−0.0374723	−	0.0699435i
$309$		0			0
$310$	−27.7348	+	6.96142i	−1.57523	+	0.395382i
$311$	−27.9065			−1.58243			−0.791215	−	0.611538i	$-0.790551\pi$
$311$	−27.9065			−1.58243			−0.791215	+	0.611538i	$0.790551\pi$
$312$		0			0
$313$	−7.56549			−0.427627			−0.213813	−	0.976875i	$-0.568588\pi$
$313$	−7.56549			−0.427627			−0.213813	+	0.976875i	$0.568588\pi$
$314$	14.3582	−	3.60390i	0.810281	−	0.203380i
$315$		0			0
$316$	−8.62927	−	16.1069i	−0.485434	−	0.906082i
$317$			22.0459i			1.23822i	0.785304	+	0.619110i	$0.212506\pi$
$317$			22.0459i			1.23822i	−0.785304	+	0.619110i	$0.787494\pi$
$318$		0			0
$319$			0.0262249i			0.00146831i
$320$	23.5131	+	2.24721i	1.31442	+	0.125623i
$321$		0			0
$322$	−4.37318	−	17.4231i	−0.243708	−	0.970952i
$323$	2.91003			0.161918
$324$		0			0
$325$	−14.6557			−0.812954
$326$	−2.46463	−	9.81926i	−0.136503	−	0.543839i
$327$		0			0
$328$	7.81828	+	8.60112i	0.431692	+	0.474918i
$329$			14.6992i			0.810396i
$330$		0			0
$331$		−	17.5153i		−	0.962728i	−0.876521	−	0.481364i	$-0.840142\pi$
$331$		−	17.5153i		−	0.962728i	0.876521	−	0.481364i	$-0.159858\pi$
$332$	−23.4908	+	12.5852i	−1.28923	+	0.690704i
$333$		0			0
$334$	32.0560	−	8.04604i	1.75403	−	0.440260i
$335$	20.0726			1.09668
$336$		0			0
$337$	−8.24598			−0.449187			−0.224594	−	0.974453i	$-0.572105\pi$
$337$	−8.24598			−0.449187			−0.224594	+	0.974453i	$0.572105\pi$
$338$	3.48793	−	0.875467i	0.189718	−	0.0476191i
$339$		0			0
$340$	−15.1470	+	8.11502i	−0.821462	+	0.440099i
$341$			1.88782i			0.102231i
$342$		0			0
$343$		−	19.2471i		−	1.03925i
$344$	−16.4545	−	18.1021i	−0.887167	−	0.975998i
$345$		0			0
$346$	2.55293	+	10.1711i	0.137247	+	0.546801i
$347$	−22.5261			−1.20926			−0.604631	−	0.796505i	$-0.706680\pi$
$347$	−22.5261			−1.20926			−0.604631	+	0.796505i	$0.706680\pi$
$348$		0			0
$349$	20.1342			1.07776			0.538879	−	0.842383i	$-0.318848\pi$
$349$	20.1342			1.07776			0.538879	+	0.842383i	$0.318848\pi$
$350$	3.23276	+	12.8796i	0.172798	+	0.688441i
$351$		0			0
$352$	0.521800	−	1.46949i	0.0278120	−	0.0783239i
$353$			2.02500i			0.107780i	0.998547	+	0.0538899i	$0.0171620\pi$
$353$			2.02500i			0.107780i	−0.998547	+	0.0538899i	$0.982838\pi$
$354$		0			0
$355$			24.6449i			1.30802i
$356$	−5.95523	−	11.1157i	−0.315627	−	0.589130i
$357$		0			0
$358$	−31.0444	+	7.79211i	−1.64075	+	0.411826i
$359$	27.4427			1.44837			0.724186	−	0.689605i	$-0.242216\pi$
$359$	27.4427			1.44837			0.724186	+	0.689605i	$0.242216\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	12.7223	−	3.19328i	0.668668	−	0.167835i
$363$		0			0
$364$	−9.40533	−	17.5554i	−0.492973	−	0.920154i
$365$		−	10.7878i		−	0.564661i
$366$		0			0
$367$		−	32.3846i		−	1.69046i	−0.534402	−	0.845230i	$-0.679463\pi$
$367$		−	32.3846i		−	1.69046i	0.534402	−	0.845230i	$-0.320537\pi$
$368$	11.1432	−	16.7468i	0.580880	−	0.872987i
$369$		0			0
$370$	−12.1044	−	48.2249i	−0.629278	−	2.50709i
$371$	−1.39257			−0.0722986
$372$		0			0
$373$	25.7809			1.33489			0.667443	−	0.744661i	$-0.267389\pi$
$373$	25.7809			1.33489			0.667443	+	0.744661i	$0.267389\pi$
$374$	0.276181	+	1.10033i	0.0142810	+	0.0568966i
$375$		0			0
$376$	−12.1801	+	11.0715i	−0.628139	+	0.570968i
$377$			0.375061i			0.0193166i
$378$		0			0
$379$			2.14558i			0.110211i	0.998481	+	0.0551056i	$0.0175495\pi$
$379$			2.14558i			0.110211i	−0.998481	+	0.0551056i	$0.982450\pi$
$380$	5.20511	−	2.78864i	0.267017	−	0.143054i
$381$		0			0
$382$	−20.6164	+	5.17469i	−1.05482	+	0.264760i
$383$	1.66493			0.0850738			0.0425369	−	0.999095i	$-0.486456\pi$
$383$	1.66493			0.0850738			0.0425369	+	0.999095i	$0.486456\pi$
$384$		0			0
$385$	2.05580			0.104773
$386$	0.736137	−	0.184770i	0.0374684	−	0.00940454i
$387$		0			0
$388$	1.34624	−	0.721249i	0.0683450	−	0.0366159i
$389$		−	20.3790i		−	1.03326i	−0.856210	−	0.516628i	$-0.827187\pi$
$389$		−	20.3790i		−	1.03326i	0.856210	−	0.516628i	$-0.172813\pi$
$390$		0			0
$391$			14.6340i			0.740075i
$392$	1.29765	−	1.17954i	0.0655411	−	0.0595758i
$393$		0			0
$394$	−7.65337	−	30.4916i	−0.385571	−	1.53615i
$395$	26.9755			1.35728
$396$		0			0
$397$	31.4823			1.58005			0.790026	−	0.613073i	$-0.210067\pi$
$397$	31.4823			1.58005			0.790026	+	0.613073i	$0.210067\pi$
$398$	1.12034	+	4.46354i	0.0561578	+	0.223737i
$399$		0			0
$400$	−8.23732	+	12.3796i	−0.411866	+	0.618980i
$401$			12.2193i			0.610201i	0.952320	+	0.305101i	$0.0986901\pi$
$401$			12.2193i			0.610201i	−0.952320	+	0.305101i	$0.901310\pi$
$402$		0			0
$403$			26.9990i			1.34492i
$404$	−3.76387	−	7.02541i	−0.187260	−	0.349527i
$405$		0			0
$406$	0.329606	−	0.0827308i	0.0163581	−	0.00410586i
$407$	−3.28251			−0.162708
$408$		0			0
$409$	4.15713			0.205557			0.102778	−	0.994704i	$-0.467227\pi$
$409$	4.15713			0.205557			0.102778	+	0.994704i	$0.467227\pi$
$410$	−16.6430	+	4.17739i	−0.821942	+	0.206307i
$411$		0			0
$412$	−3.23669	−	6.04140i	−0.159460	−	0.297638i
$413$			14.6751i			0.722114i
$414$		0			0
$415$		−	39.3420i		−	1.93122i
$416$	7.46264	−	21.0162i	0.365886	−	1.03040i
$417$		0			0
$418$	−0.0949068	−	0.378116i	−0.00464204	−	0.0184943i
$419$	−23.3825			−1.14231			−0.571155	−	0.820842i	$-0.693505\pi$
$419$	−23.3825			−1.14231			−0.571155	+	0.820842i	$0.693505\pi$
$420$		0			0
$421$	11.6327			0.566942			0.283471	−	0.958981i	$-0.408514\pi$
$421$	11.6327			0.566942			0.283471	+	0.958981i	$0.408514\pi$
$422$	7.23588	+	28.8283i	0.352237	+	1.40334i
$423$		0			0
$424$	−1.04888	−	1.15391i	−0.0509383	−	0.0560388i
$425$		−	10.8178i		−	0.524741i
$426$		0			0
$427$			34.8475i			1.68639i
$428$	−30.0622	+	16.1058i	−1.45311	+	0.778505i
$429$		0			0
$430$	35.0272	−	8.79181i	1.68916	−	0.423979i
$431$	−26.1387			−1.25906			−0.629528	−	0.776978i	$-0.716752\pi$
$431$	−26.1387			−1.25906			−0.629528	+	0.776978i	$0.716752\pi$
$432$		0			0
$433$	18.4623			0.887241			0.443621	−	0.896215i	$-0.353694\pi$
$433$	18.4623			0.887241			0.443621	+	0.896215i	$0.353694\pi$
$434$	23.7269	−	5.95544i	1.13893	−	0.285870i
$435$		0			0
$436$	30.0209	−	16.0837i	1.43774	−	0.770272i
$437$		−	5.02883i		−	0.240562i
$438$		0			0
$439$			22.4909i			1.07343i	0.843762	+	0.536717i	$0.180336\pi$
$439$			22.4909i			1.07343i	−0.843762	+	0.536717i	$0.819664\pi$
$440$	1.54843	+	1.70347i	0.0738185	+	0.0812100i
$441$		0			0
$442$	3.94987	+	15.7366i	0.187876	+	0.748513i
$443$	13.4557			0.639300			0.319650	−	0.947536i	$-0.396435\pi$
$443$	13.4557			0.639300			0.319650	+	0.947536i	$0.396435\pi$
$444$		0			0
$445$	18.6163			0.882499
$446$	−9.48570	−	37.7917i	−0.449161	−	1.78949i
$447$		0			0
$448$	−20.1153	−	1.92247i	−0.950357	−	0.0908283i
$449$			28.5453i			1.34714i	0.739126	+	0.673568i	$0.235239\pi$
$449$			28.5453i			1.34714i	−0.739126	+	0.673568i	$0.764761\pi$
$450$		0			0
$451$			1.13284i			0.0533432i
$452$	5.28581	+	9.86618i	0.248624	+	0.464066i
$453$		0			0
$454$	31.5531	−	7.91979i	1.48086	−	0.371694i
$455$	29.4015			1.37836
$456$		0			0
$457$	7.67310			0.358933			0.179466	−	0.983764i	$-0.442563\pi$
$457$	7.67310			0.358933			0.179466	+	0.983764i	$0.442563\pi$
$458$	9.07659	−	2.27822i	0.424121	−	0.106454i
$459$		0			0
$460$	14.0236	+	26.1756i	0.653854	+	1.22044i
$461$			31.1213i			1.44946i	0.689032	+	0.724731i	$0.258036\pi$
$461$			31.1213i			1.44946i	−0.689032	+	0.724731i	$0.741964\pi$
$462$		0			0
$463$		−	13.7118i		−	0.637241i	−0.947882	−	0.318621i	$-0.896780\pi$
$463$		−	13.7118i		−	0.637241i	0.947882	−	0.318621i	$-0.103220\pi$
$464$	0.316812	+	0.210805i	0.0147076	+	0.00978636i
$465$		0			0
$466$	−5.94720	−	23.6941i	−0.275499	−	1.09761i
$467$	−5.94803			−0.275242			−0.137621	−	0.990485i	$-0.543946\pi$
$467$	−5.94803			−0.275242			−0.137621	+	0.990485i	$0.543946\pi$
$468$		0			0
$469$	−17.1719			−0.792927
$470$	−5.91561	−	23.5682i	−0.272867	−	1.08712i
$471$		0			0
$472$	−12.1600	+	11.0533i	−0.559711	+	0.508769i
$473$		−	2.38419i		−	0.109625i
$474$		0			0
$475$			3.71743i			0.170567i
$476$	12.9581	−	6.94234i	0.593936	−	0.318202i
$477$		0			0
$478$	12.6332	−	3.17092i	0.577829	−	0.145035i
$479$	−0.772094			−0.0352779			−0.0176389	−	0.999844i	$-0.505615\pi$
$479$	−0.772094			−0.0352779			−0.0176389	+	0.999844i	$0.505615\pi$
$480$		0			0
$481$	−46.9455			−2.14053
$482$	22.9465	−	5.75955i	1.04518	−	0.262340i
$483$		0			0
$484$	−19.2583	+	10.3177i	−0.875377	+	0.468984i
$485$			2.25466i			0.102379i
$486$		0			0
$487$			15.1595i			0.686943i	0.939163	+	0.343471i	$0.111603\pi$
$487$			15.1595i			0.686943i	−0.939163	+	0.343471i	$0.888397\pi$
$488$	−28.8753	+	26.2472i	−1.30712	+	1.18815i
$489$		0			0
$490$	0.630241	+	2.51093i	0.0284714	+	0.113432i
$491$	−1.17356			−0.0529622			−0.0264811	−	0.999649i	$-0.508430\pi$
$491$	−1.17356			−0.0529622			−0.0264811	+	0.999649i	$0.508430\pi$
$492$		0			0
$493$	−0.276843			−0.0124684
$494$	−1.35733	−	5.40771i	−0.0610692	−	0.243304i
$495$		0			0
$496$	22.8059	+	15.1749i	1.02402	+	0.681374i
$497$		−	21.0836i		−	0.945726i
$498$		0			0
$499$		−	1.78735i		−	0.0800126i	−0.999199	−	0.0400063i	$-0.987262\pi$
$499$		−	1.78735i		−	0.0800126i	0.999199	−	0.0400063i	$-0.0127378\pi$
$500$	3.57664	+	6.67594i	0.159952	+	0.298557i
$501$		0			0
$502$	−9.88666	+	2.48154i	−0.441263	+	0.110757i
$503$	35.9727			1.60394			0.801971	−	0.597363i	$-0.203785\pi$
$503$	35.9727			1.60394			0.801971	+	0.597363i	$0.203785\pi$
$504$		0			0
$505$	11.7660			0.523582
$506$	1.90148	−	0.477270i	0.0845312	−	0.0212172i
$507$		0			0
$508$	11.6319	+	21.7113i	0.516081	+	0.963285i
$509$		−	17.6134i		−	0.780702i	−0.920666	−	0.390351i	$-0.872354\pi$
$509$		−	17.6134i		−	0.780702i	0.920666	−	0.390351i	$-0.127646\pi$
$510$		0			0
$511$			9.22891i			0.408263i
$512$	−13.5578	−	18.1159i	−0.599177	−	0.800616i
$513$		0			0
$514$	1.06502	+	4.24313i	0.0469761	+	0.187156i
$515$	10.1180			0.445854
$516$		0			0
$517$	−1.60421			−0.0705531
$518$	10.3552	+	41.2560i	0.454983	+	1.81269i
$519$		0			0
$520$	22.1452	+	24.3626i	0.971133	+	1.06837i
$521$		−	17.6811i		−	0.774622i	−0.921949	−	0.387311i	$-0.873404\pi$
$521$		−	17.6811i		−	0.774622i	0.921949	−	0.387311i	$-0.126596\pi$
$522$		0			0
$523$			13.3781i			0.584985i	0.956268	+	0.292493i	$0.0944847\pi$
$523$			13.3781i			0.584985i	−0.956268	+	0.292493i	$0.905515\pi$
$524$	0.214443	−	0.114888i	0.00936797	−	0.00501890i
$525$		0			0
$526$	−12.5318	+	3.14548i	−0.546414	+	0.137150i
$527$	−19.9287			−0.868110
$528$		0			0
$529$	2.28914			0.0995278
$530$	2.23280	−	0.560430i	0.0969865	−	0.0243435i
$531$		0			0
$532$	−4.45293	+	2.38566i	−0.193059	+	0.103432i
$533$			16.2015i			0.701766i
$534$		0			0
$535$		−	50.3476i		−	2.17672i
$536$	−12.9339	−	14.2290i	−0.558660	−	0.614598i
$537$		0			0
$538$	−6.76709	−	26.9606i	−0.291750	−	1.16235i
$539$	0.170910			0.00736164
$540$		0			0
$541$	−36.1273			−1.55323			−0.776617	−	0.629974i	$-0.783066\pi$
$541$	−36.1273			−1.55323			−0.776617	+	0.629974i	$0.783066\pi$
$542$	−0.457193	−	1.82149i	−0.0196381	−	0.0782397i
$543$		0			0
$544$	15.5126	+	5.50838i	0.665099	+	0.236170i
$545$			50.2785i			2.15370i
$546$		0			0
$547$			25.8430i			1.10497i	0.833524	+	0.552483i	$0.186319\pi$
$547$			25.8430i			1.10497i	−0.833524	+	0.552483i	$0.813681\pi$
$548$	20.8425	+	38.9034i	0.890349	+	1.66187i
$549$		0			0
$550$	−1.40562	+	0.352809i	−0.0599358	+	0.0150438i
$551$	0.0951342			0.00405285
$552$		0			0
$553$	−23.0773			−0.981348
$554$	32.3823	−	8.12793i	1.37579	−	0.345322i
$555$		0			0
$556$	19.7196	+	36.8073i	0.836296	+	1.56098i
$557$		−	39.2104i		−	1.66140i	−0.556723	−	0.830698i	$-0.687942\pi$
$557$		−	39.2104i		−	1.66140i	0.556723	−	0.830698i	$-0.312058\pi$
$558$		0			0
$559$		−	34.0980i		−	1.44219i
$560$	16.5252	−	24.8353i	0.698319	−	1.04948i
$561$		0			0
$562$	4.94616	+	19.7059i	0.208641	+	0.831242i
$563$	−14.1863			−0.597881			−0.298941	−	0.954272i	$-0.596633\pi$
$563$	−14.1863			−0.597881			−0.298941	+	0.954272i	$0.596633\pi$
$564$		0			0
$565$	−16.5237			−0.695157
$566$	−3.47076	−	13.8278i	−0.145887	−	0.581225i
$567$		0			0
$568$	17.4702	−	15.8801i	0.733034	−	0.666316i
$569$		−	31.6156i		−	1.32539i	−0.748888	−	0.662697i	$-0.769412\pi$
$569$		−	31.6156i		−	1.32539i	0.748888	−	0.662697i	$-0.230588\pi$
$570$		0			0
$571$		−	17.4106i		−	0.728613i	−0.931279	−	0.364306i	$-0.881306\pi$
$571$		−	17.4106i		−	0.728613i	0.931279	−	0.364306i	$-0.118694\pi$
$572$	1.91592	−	1.02646i	0.0801087	−	0.0429183i
$573$		0			0
$574$	14.2380	−	3.57373i	0.594283	−	0.149164i
$575$	−18.6943			−0.779606
$576$		0			0
$577$	13.0631			0.543824			0.271912	−	0.962322i	$-0.412344\pi$
$577$	13.0631			0.543824			0.271912	+	0.962322i	$0.412344\pi$
$578$	11.7027	−	2.93737i	0.486769	−	0.122178i
$579$		0			0
$580$	−0.495184	+	0.265295i	−0.0205614	+	0.0110158i
$581$			33.6568i			1.39632i
$582$		0			0
$583$		−	0.151979i		−	0.00629433i
$584$	−7.64724	+	6.95122i	−0.316445	+	0.287643i
$585$		0			0
$586$	6.24298	+	24.8725i	0.257895	+	1.02747i
$587$	−16.0572			−0.662750			−0.331375	−	0.943499i	$-0.607512\pi$
$587$	−16.0572			−0.662750			−0.331375	+	0.943499i	$0.607512\pi$
$588$		0			0
$589$	6.84831			0.282180
$590$	−5.90589	−	23.5295i	−0.243141	−	0.968694i
$591$		0			0
$592$	−26.3859	+	39.6546i	−1.08446	+	1.62979i
$593$			16.1931i			0.664970i	0.943109	+	0.332485i	$0.107887\pi$
$593$			16.1931i			0.664970i	−0.943109	+	0.332485i	$0.892113\pi$
$594$		0			0
$595$			21.7021i			0.889698i
$596$	−5.90661	−	11.0249i	−0.241944	−	0.451598i
$597$		0			0
$598$	27.1945	−	6.82579i	1.11206	−	0.279127i
$599$	2.45358			0.100251			0.0501253	−	0.998743i	$-0.484038\pi$
$599$	2.45358			0.100251			0.0501253	+	0.998743i	$0.484038\pi$
$600$		0			0
$601$	−24.9671			−1.01843			−0.509215	−	0.860639i	$-0.670064\pi$
$601$	−24.9671			−1.01843			−0.509215	+	0.860639i	$0.670064\pi$
$602$	−29.9655	+	7.52133i	−1.22130	+	0.306546i
$603$		0			0
$604$	6.54412	+	12.2149i	0.266276	+	0.497015i
$605$		−	32.2535i		−	1.31129i
$606$		0			0
$607$			44.8579i			1.82073i	0.413810	+	0.910363i	$0.364198\pi$
$607$			44.8579i			1.82073i	−0.413810	+	0.910363i	$0.635802\pi$
$608$	−5.33075	−	1.89290i	−0.216191	−	0.0767672i
$609$		0			0
$610$	−14.0241	−	55.8733i	−0.567821	−	2.26224i
$611$	−22.9430			−0.928174
$612$		0			0
$613$	0.906174			0.0366000			0.0183000	−	0.999833i	$-0.494175\pi$
$613$	0.906174			0.0366000			0.0183000	+	0.999833i	$0.494175\pi$
$614$	−0.443615	−	1.76740i	−0.0179029	−	0.0713263i
$615$		0			0
$616$	−1.32467	−	1.45731i	−0.0533725	−	0.0587167i
$617$		−	31.3497i		−	1.26209i	−0.775746	−	0.631046i	$-0.782626\pi$
$617$		−	31.3497i		−	1.26209i	0.775746	−	0.631046i	$-0.217374\pi$
$618$		0			0
$619$			11.5713i			0.465091i	0.972586	+	0.232545i	$0.0747054\pi$
$619$			11.5713i			0.465091i	−0.972586	+	0.232545i	$0.925295\pi$
$620$	−35.6462	+	19.0975i	−1.43159	+	0.766973i
$621$		0			0
$622$	−38.2783	+	9.60783i	−1.53482	+	0.385239i
$623$	−15.9261			−0.638067
$624$		0			0
$625$	−29.7679			−1.19072
$626$	−10.3773	+	2.60470i	−0.414761	+	0.104105i
$627$		0			0
$628$	18.4539	−	9.88669i	0.736390	−	0.394522i
$629$		−	34.6518i		−	1.38166i
$630$		0			0
$631$			22.0269i			0.876875i	0.898762	+	0.438438i	$0.144468\pi$
$631$			22.0269i			0.876875i	−0.898762	+	0.438438i	$0.855532\pi$
$632$	−17.3819	−	19.1223i	−0.691413	−	0.760644i
$633$		0			0
$634$	7.59011	+	30.2396i	0.301442	+	1.20097i
$635$	−36.3618			−1.44297
$636$		0			0
$637$	2.44431			0.0968473
$638$	0.00902888	+	0.0359718i	0.000357457	+	0.00142414i
$639$		0			0
$640$	33.0258	−	5.01282i	1.30546	−	0.198149i
$641$			2.38922i			0.0943686i	0.998886	+	0.0471843i	$0.0150248\pi$
$641$			2.38922i			0.0943686i	−0.998886	+	0.0471843i	$0.984975\pi$
$642$		0			0
$643$		−	42.7246i		−	1.68489i	−0.538779	−	0.842447i	$-0.681114\pi$
$643$		−	42.7246i		−	1.68489i	0.538779	−	0.842447i	$-0.318886\pi$
$644$	−11.9971	−	22.3930i	−0.472752	−	0.882410i
$645$		0			0
$646$	3.99158	−	1.00188i	0.157047	−	0.0394186i
$647$	38.9756			1.53229			0.766144	−	0.642669i	$-0.222173\pi$
$647$	38.9756			1.53229			0.766144	+	0.642669i	$0.222173\pi$
$648$		0			0
$649$	−1.60157			−0.0628673
$650$	−20.1028	+	5.04578i	−0.788495	+	0.197912i
$651$		0			0
$652$	−6.76129	−	12.6202i	−0.264792	−	0.494245i
$653$			26.9237i			1.05361i	0.849987	+	0.526804i	$0.176610\pi$
$653$			26.9237i			1.05361i	−0.849987	+	0.526804i	$0.823390\pi$
$654$		0			0
$655$			0.359145i			0.0140329i
$656$	13.6853	+	9.10613i	0.534322	+	0.355535i
$657$		0			0
$658$	5.06076	+	20.1624i	0.197289	+	0.786014i
$659$	−6.08999			−0.237232			−0.118616	−	0.992940i	$-0.537846\pi$
$659$	−6.08999			−0.237232			−0.118616	+	0.992940i	$0.537846\pi$
$660$		0			0
$661$	−46.9680			−1.82684			−0.913421	−	0.407016i	$-0.866569\pi$
$661$	−46.9680			−1.82684			−0.913421	+	0.407016i	$0.866569\pi$
$662$	−6.03029	−	24.0251i	−0.234374	−	0.933763i
$663$		0			0
$664$	−27.8886	+	25.3503i	−1.08229	+	0.983783i
$665$		−	7.45769i		−	0.289197i
$666$		0			0
$667$			0.478414i			0.0185243i
$668$	41.2000	−	22.0729i	1.59408	−	0.854028i
$669$		0			0
$670$	27.5329	−	6.91073i	1.06369	−	0.266985i
$671$	−3.80311			−0.146817
$672$		0			0
$673$	36.4495			1.40502			0.702512	−	0.711672i	$-0.252062\pi$
$673$	36.4495			1.40502			0.702512	+	0.711672i	$0.252062\pi$
$674$	−11.3107	+	2.83898i	−0.435673	+	0.109354i
$675$		0			0
$676$	4.48286	−	2.40169i	0.172418	−	0.0923729i
$677$		−	2.06690i		−	0.0794376i	−0.999211	−	0.0397188i	$-0.987354\pi$
$677$		−	2.06690i		−	0.0794376i	0.999211	−	0.0397188i	$-0.0126462\pi$
$678$		0			0
$679$		−	1.92884i		−	0.0740222i
$680$	−17.9827	+	16.3460i	−0.689606	+	0.626841i
$681$		0			0
$682$	0.649951	+	2.58945i	0.0248879	+	0.0991553i
$683$	−4.08310			−0.156235			−0.0781176	−	0.996944i	$-0.524891\pi$
$683$	−4.08310			−0.156235			−0.0781176	+	0.996944i	$0.524891\pi$
$684$		0			0
$685$	−65.1547			−2.48943
$686$	−6.62652	−	26.4006i	−0.253002	−	1.00798i
$687$		0			0
$688$	−28.8024	−	19.1649i	−1.09808	−	0.730656i
$689$		−	2.17356i		−	0.0828061i
$690$		0			0
$691$		−	26.1465i		−	0.994660i	−0.867561	−	0.497330i	$-0.834314\pi$
$691$		−	26.1465i		−	0.994660i	0.867561	−	0.497330i	$-0.165686\pi$
$692$	7.00354	+	13.0724i	0.266235	+	0.496938i
$693$		0			0
$694$	−30.8982	+	7.75543i	−1.17288	+	0.294392i
$695$	−61.6443			−2.33830
$696$		0			0
$697$	−11.9588			−0.452972
$698$	27.6174	−	6.93193i	1.04533	−	0.262378i
$699$		0			0
$700$	8.86852	+	16.5534i	0.335199	+	0.625661i
$701$		−	6.65445i		−	0.251335i	−0.992072	−	0.125668i	$-0.959893\pi$
$701$		−	6.65445i		−	0.251335i	0.992072	−	0.125668i	$-0.0401073\pi$
$702$		0			0
$703$			11.9077i			0.449108i
$704$	0.209810	−	2.19529i	0.00790752	−	0.0827382i
$705$		0			0
$706$	0.697181	+	2.77762i	0.0262387	+	0.104537i
$707$	−10.0658			−0.378562
$708$		0			0
$709$	−14.8268			−0.556831			−0.278416	−	0.960461i	$-0.589809\pi$
$709$	−14.8268			−0.556831			−0.278416	+	0.960461i	$0.589809\pi$
$710$	8.48493	+	33.8046i	0.318434	+	1.26866i
$711$		0			0
$712$	−11.9956	−	13.1967i	−0.449553	−	0.494567i
$713$			34.4390i			1.28975i
$714$		0			0
$715$			3.20875i			0.120001i
$716$	−39.8998	+	21.3763i	−1.49112	+	0.798872i
$717$		0			0
$718$	37.6422	−	9.44817i	1.40480	−	0.352603i
$719$	−25.5110			−0.951399			−0.475700	−	0.879608i	$-0.657805\pi$
$719$	−25.5110			−0.951399			−0.475700	+	0.879608i	$0.657805\pi$
$720$		0			0
$721$	−8.65590			−0.322362
$722$	−1.37167	+	0.344287i	−0.0510481	+	0.0128130i
$723$		0			0
$724$	16.3513	−	8.76023i	0.607692	−	0.325571i
$725$		−	0.353654i		−	0.0131344i
$726$		0			0
$727$		−	38.8167i		−	1.43963i	−0.694166	−	0.719815i	$-0.744227\pi$
$727$		−	38.8167i		−	1.43963i	0.694166	−	0.719815i	$-0.255773\pi$
$728$	−18.9451	−	20.8420i	−0.702151	−	0.772457i
$729$		0			0
$730$	−3.71411	−	14.7973i	−0.137465	−	0.547673i
$731$	25.1687			0.930897
$732$		0			0
$733$	−18.7833			−0.693775			−0.346888	−	0.937907i	$-0.612761\pi$
$733$	−18.7833			−0.693775			−0.346888	+	0.937907i	$0.612761\pi$
$734$	−11.1496	−	44.4208i	−0.411539	−	1.63960i
$735$		0			0
$736$	9.51906	−	26.8075i	0.350877	−	0.988136i
$737$		−	1.87407i		−	0.0690323i
$738$		0			0
$739$			37.3401i			1.37358i	0.726858	+	0.686788i	$0.240980\pi$
$739$			37.3401i			1.37358i	−0.726858	+	0.686788i	$0.759020\pi$
$740$	−33.2064	−	61.9810i	−1.22069	−	2.27847i
$741$		0			0
$742$	−1.91014	+	0.479444i	−0.0701235	+	0.0176009i
$743$	42.8214			1.57096			0.785482	−	0.618885i	$-0.212415\pi$
$743$	42.8214			1.57096			0.785482	+	0.618885i	$0.212415\pi$
$744$		0			0
$745$	18.4643			0.676481
$746$	35.3628	−	8.87603i	1.29472	−	0.324975i
$747$		0			0
$748$	0.757656	+	1.41420i	0.0277027	+	0.0517081i
$749$			43.0720i			1.57382i
$750$		0			0
$751$		−	20.4533i		−	0.746352i	−0.927760	−	0.373176i	$-0.878269\pi$
$751$		−	20.4533i		−	0.746352i	0.927760	−	0.373176i	$-0.121731\pi$
$752$	−12.8952	+	19.3798i	−0.470240	+	0.706708i
$753$		0			0
$754$	0.129129	+	0.514458i	0.00470259	+	0.0187355i
$755$	−20.4572			−0.744514
$756$		0			0
$757$	−14.0962			−0.512336			−0.256168	−	0.966632i	$-0.582460\pi$
$757$	−14.0962			−0.512336			−0.256168	+	0.966632i	$0.582460\pi$
$758$	0.738696	+	2.94302i	0.0268306	+	0.106895i
$759$		0			0
$760$	6.17958	−	5.61714i	0.224157	−	0.203755i
$761$			44.8554i			1.62601i	0.582259	+	0.813003i	$0.302169\pi$
$761$			44.8554i			1.62601i	−0.582259	+	0.813003i	$0.697831\pi$
$762$		0			0
$763$		−	43.0129i		−	1.55717i
$764$	−26.4972	+	14.1959i	−0.958634	+	0.513589i
$765$		0			0
$766$	2.28372	−	0.573212i	0.0825142	−	0.0207110i
$767$	−22.9053			−0.827062
$768$		0			0
$769$	9.69718			0.349689			0.174845	−	0.984596i	$-0.444058\pi$
$769$	9.69718			0.349689			0.174845	+	0.984596i	$0.444058\pi$
$770$	2.81987	−	0.707786i	0.101621	−	0.0255068i
$771$		0			0
$772$	0.946120	−	0.506885i	0.0340516	−	0.0182432i
$773$			8.60844i			0.309624i	0.987944	+	0.154812i	$0.0494772\pi$
$773$			8.60844i			0.309624i	−0.987944	+	0.154812i	$0.950523\pi$
$774$		0			0
$775$		−	25.4581i		−	0.914481i
$776$	1.59827	−	1.45281i	0.0573747	−	0.0521527i
$777$		0			0
$778$	−7.01622	−	27.9532i	−0.251544	−	1.00217i
$779$	4.10951			0.147239
$780$		0			0
$781$	2.30097			0.0823350
$782$	5.03830	+	20.0730i	0.180169	+	0.717809i
$783$		0			0
$784$	1.37384	−	2.06470i	0.0490656	−	0.0737392i
$785$			30.9062i			1.10309i
$786$		0			0
$787$			37.0833i			1.32188i	0.750441	+	0.660938i	$0.229841\pi$
$787$			37.0833i			1.32188i	−0.750441	+	0.660938i	$0.770159\pi$
$788$	−20.9957	−	39.1894i	−0.747942	−	1.39606i
$789$		0			0
$790$	37.0014	−	9.28731i	1.31645	−	0.330428i
$791$	14.1359			0.502615
$792$		0			0
$793$	−54.3910			−1.93148
$794$	43.1832	−	10.8390i	1.53251	−	0.384660i
$795$		0			0
$796$	3.07347	+	5.73676i	0.108936	+	0.203334i
$797$			17.3756i			0.615476i	0.951471	+	0.307738i	$0.0995720\pi$
$797$			17.3756i			0.615476i	−0.951471	+	0.307738i	$0.900428\pi$
$798$		0			0
$799$		−	16.9349i		−	0.599112i
$800$	−7.03671	+	19.8167i	−0.248785	+	0.700625i
$801$		0			0
$802$	4.20694	+	16.7608i	0.148552	+	0.591843i
$803$	−1.00720			−0.0355434
$804$		0			0
$805$	37.5035			1.32182
$806$	9.29542	+	37.0337i	0.327417	+	1.30446i
$807$		0			0
$808$	−7.58153	−	8.34067i	−0.266717	−	0.293424i
$809$			50.9075i			1.78981i	0.446253	+	0.894907i	$0.352758\pi$
$809$			50.9075i			1.78981i	−0.446253	+	0.894907i	$0.647242\pi$
$810$		0			0
$811$			35.0490i			1.23074i	0.788240	+	0.615368i	$0.210993\pi$
$811$			35.0490i			1.23074i	−0.788240	+	0.615368i	$0.789007\pi$
$812$	0.423626	−	0.226958i	0.0148664	−	0.00796467i
$813$		0			0
$814$	−4.50250	+	1.13012i	−0.157813	+	0.0396108i
$815$	21.1361			0.740365
$816$		0			0
$817$	−8.64895			−0.302589
$818$	5.70219	−	1.43124i	0.199372	−	0.0500423i
$819$		0			0
$820$	−21.3905	+	11.4600i	−0.746988	+	0.400199i
$821$			17.8629i			0.623421i	0.950177	+	0.311710i	$0.100902\pi$
$821$			17.8629i			0.623421i	−0.950177	+	0.311710i	$0.899098\pi$
$822$		0			0
$823$			39.7173i			1.38446i	0.721678	+	0.692229i	$0.243371\pi$
$823$			39.7173i			1.38446i	−0.721678	+	0.692229i	$0.756629\pi$
$824$	−6.51963	−	7.17243i	−0.227122	−	0.249864i
$825$		0			0
$826$	5.05244	+	20.1293i	0.175797	+	0.700388i
$827$	−27.0227			−0.939673			−0.469836	−	0.882754i	$-0.655687\pi$
$827$	−27.0227			−0.939673			−0.469836	+	0.882754i	$0.655687\pi$
$828$		0			0
$829$	1.47937			0.0513806			0.0256903	−	0.999670i	$-0.491822\pi$
$829$	1.47937			0.0513806			0.0256903	+	0.999670i	$0.491822\pi$
$830$	−13.5449	−	53.9641i	−0.470152	−	1.87312i
$831$		0			0
$832$	3.00065	−	31.3965i	0.104029	−	1.08848i
$833$			1.80422i			0.0625124i
$834$		0			0
$835$			69.0010i			2.38788i
$836$	−0.260361	−	0.485974i	−0.00900477	−	0.0168077i
$837$		0			0
$838$	−32.0730	+	8.05029i	−1.10794	+	0.278093i
$839$	46.0701			1.59052			0.795258	−	0.606271i	$-0.207335\pi$
$839$	46.0701			1.59052			0.795258	+	0.606271i	$0.207335\pi$
$840$		0			0
$841$	28.9909			0.999688
$842$	15.9561	−	4.00498i	0.549885	−	0.138021i
$843$		0			0
$844$	19.8504	+	37.0516i	0.683280	+	1.27537i
$845$			7.50781i			0.258276i
$846$		0			0
$847$			27.5926i			0.948093i
$848$	−1.83599	−	1.22166i	−0.0630483	−	0.0419520i
$849$		0			0
$850$	−3.72443	−	14.8384i	−0.127747	−	0.508953i
$851$	−59.8819			−2.05273
$852$		0			0
$853$	−20.4781			−0.701157			−0.350578	−	0.936533i	$-0.614015\pi$
$853$	−20.4781			−0.701157			−0.350578	+	0.936533i	$0.614015\pi$
$854$	11.9975	+	47.7992i	0.410548	+	1.63565i
$855$		0			0
$856$	−35.6902	+	32.4418i	−1.21987	+	1.10884i
$857$		−	14.3664i		−	0.490748i	−0.969428	−	0.245374i	$-0.921089\pi$
$857$		−	14.3664i		−	0.490748i	0.969428	−	0.245374i	$-0.0789108\pi$
$858$		0			0
$859$		−	35.3946i		−	1.20765i	−0.797117	−	0.603824i	$-0.793643\pi$
$859$		−	35.3946i		−	1.20765i	0.797117	−	0.603824i	$-0.206357\pi$
$860$	45.0188	−	24.1188i	1.53513	−	0.822446i
$861$		0			0
$862$	−35.8535	+	8.99921i	−1.22118	+	0.306514i
$863$	22.8375			0.777398			0.388699	−	0.921365i	$-0.372925\pi$
$863$	22.8375			0.777398			0.388699	+	0.921365i	$0.372925\pi$
$864$		0			0
$865$	−21.8934			−0.744398
$866$	25.3241	−	6.35632i	0.860548	−	0.215997i
$867$		0			0
$868$	30.4951	−	16.3378i	1.03507	−	0.554539i
$869$		−	2.51856i		−	0.0854362i
$870$		0			0
$871$		−	26.8024i		−	0.908166i
$872$	35.6413	−	32.3973i	1.20697	−	1.09711i
$873$		0			0
$874$	−1.73136	−	6.89787i	−0.0585641	−	0.233324i
$875$	9.56505			0.323358
$876$		0			0
$877$	4.10895			0.138750			0.0693748	−	0.997591i	$-0.477900\pi$
$877$	4.10895			0.138750			0.0693748	+	0.997591i	$0.477900\pi$
$878$	7.74333	+	30.8500i	0.261325	+	1.04114i
$879$		0			0
$880$	2.71041	+	1.80349i	0.0913680	+	0.0607957i
$881$		−	41.3020i		−	1.39150i	−0.718284	−	0.695750i	$-0.755072\pi$
$881$		−	41.3020i		−	1.39150i	0.718284	−	0.695750i	$-0.244928\pi$
$882$		0			0
$883$		−	22.6656i		−	0.762759i	−0.924419	−	0.381380i	$-0.875449\pi$
$883$		−	22.6656i		−	0.762759i	0.924419	−	0.381380i	$-0.124551\pi$
$884$	10.8358	+	20.2254i	0.364447	+	0.680255i
$885$		0			0
$886$	18.4567	−	4.63263i	0.620066	−	0.155636i
$887$	27.0039			0.906703			0.453351	−	0.891332i	$-0.350228\pi$
$887$	27.0039			0.906703			0.453351	+	0.891332i	$0.350228\pi$
$888$		0			0
$889$	31.1072			1.04330
$890$	25.5354	−	6.40936i	0.855948	−	0.214842i
$891$		0			0
$892$	−26.0224	−	48.5718i	−0.871295	−	1.62631i
$893$			5.81949i			0.194742i
$894$		0			0
$895$		−	66.8234i		−	2.23366i
$896$	−28.2533	+	4.28843i	−0.943877	+	0.143267i
$897$		0			0
$898$	9.82777	+	39.1546i	0.327957	+	1.30661i
$899$	−0.651508			−0.0217290
$900$		0			0
$901$	1.60437			0.0534492
$902$	0.390021	+	1.55387i	0.0129863	+	0.0517383i
$903$		0			0
$904$	10.6472	+	11.7133i	0.354119	+	0.389577i
$905$			27.3849i			0.910304i
$906$		0			0
$907$			24.2152i			0.804054i	0.915628	+	0.402027i	$0.131694\pi$
$907$			24.2152i			0.804054i	−0.915628	+	0.402027i	$0.868306\pi$
$908$	40.5536	−	21.7266i	1.34582	−	0.721023i
$909$		0			0
$910$	40.3290	−	10.1226i	1.33689	−	0.335559i
$911$	27.7852			0.920563			0.460282	−	0.887773i	$-0.347748\pi$
$911$	27.7852			0.920563			0.460282	+	0.887773i	$0.347748\pi$
$912$		0			0
$913$	−3.67316			−0.121564
$914$	10.5249	−	2.64175i	0.348134	−	0.0873813i
$915$		0			0
$916$	11.6657	−	6.24990i	0.385445	−	0.206503i
$917$		−	0.307246i		−	0.0101461i
$918$		0			0
$919$		−	20.4590i		−	0.674880i	−0.941347	−	0.337440i	$-0.890439\pi$
$919$		−	20.4590i		−	0.674880i	0.941347	−	0.337440i	$-0.109561\pi$
$920$	28.2476	+	31.0761i	0.931297	+	1.02455i
$921$		0			0
$922$	10.7146	+	42.6880i	0.352868	+	1.40585i
$923$	32.9078			1.08317
$924$		0			0
$925$	44.2661			1.45546
$926$	−4.72079	−	18.8080i	−0.155135	−	0.618069i
$927$		0			0
$928$	0.507137	+	0.180079i	0.0166476	+	0.00591139i
$929$			18.3021i			0.600473i	0.953865	+	0.300236i	$0.0970656\pi$
$929$			18.3021i			0.600473i	−0.953865	+	0.300236i	$0.902934\pi$
$930$		0			0
$931$		−	0.620000i		−	0.0203197i
$932$	−16.3151	−	30.4529i	−0.534420	−	0.997517i
$933$		0			0
$934$	−8.15871	+	2.04783i	−0.266961	+	0.0670070i
$935$	−2.36847			−0.0774572
$936$		0			0
$937$	7.13707			0.233158			0.116579	−	0.993181i	$-0.462807\pi$
$937$	7.13707			0.233158			0.116579	+	0.993181i	$0.462807\pi$
$938$	−23.5542	+	5.91207i	−0.769071	+	0.193036i
$939$		0			0
$940$	−16.2285	−	30.2911i	−0.529314	−	0.987986i
$941$		−	25.4987i		−	0.831235i	−0.909539	−	0.415618i	$-0.863565\pi$
$941$		−	25.4987i		−	0.831235i	0.909539	−	0.415618i	$-0.136435\pi$
$942$		0			0
$943$			20.6661i			0.672979i
$944$	−12.8740	+	19.3479i	−0.419013	+	0.629722i
$945$		0			0
$946$	−0.820844	−	3.27031i	−0.0266880	−	0.106327i
$947$	−43.8870			−1.42614			−0.713069	−	0.701094i	$-0.752695\pi$
$947$	−43.8870			−1.42614			−0.713069	+	0.701094i	$0.752695\pi$
$948$		0			0
$949$	−14.4047			−0.467597
$950$	1.27986	+	5.09906i	0.0415242	+	0.165435i
$951$		0			0
$952$	15.3841	−	13.9839i	0.498601	−	0.453220i
$953$			9.67270i			0.313329i	0.987652	+	0.156665i	$0.0500742\pi$
$953$			9.67270i			0.313329i	−0.987652	+	0.156665i	$0.949926\pi$
$954$		0			0
$955$		−	44.3770i		−	1.43601i
$956$	16.2368	−	8.69889i	0.525136	−	0.281342i
$957$		0			0
$958$	−1.05905	+	0.265822i	−0.0342165	+	0.00858831i
$959$	55.7394			1.79992
$960$		0			0
$961$	−15.8993			−0.512881
$962$	−64.3935	+	16.1627i	−2.07613	+	0.521107i
$963$		0			0
$964$	29.4920	−	15.8004i	0.949872	−	0.508895i
$965$			1.58455i			0.0510083i
$966$		0			0
$967$		−	12.0766i		−	0.388356i	−0.980966	−	0.194178i	$-0.937796\pi$
$967$		−	12.0766i		−	0.388356i	0.980966	−	0.194178i	$-0.0622040\pi$
$968$	−22.8637	+	20.7827i	−0.734868	+	0.667983i
$969$		0			0
$970$	0.776249	+	3.09264i	0.0249239	+	0.0992986i
$971$	−4.87568			−0.156468			−0.0782341	−	0.996935i	$-0.524928\pi$
$971$	−4.87568			−0.156468			−0.0782341	+	0.996935i	$0.524928\pi$
$972$		0			0
$973$	52.7362			1.69065
$974$	5.21922	+	20.7938i	0.167235	+	0.666276i
$975$		0			0
$976$	−30.5707	+	45.9437i	−0.978544	+	1.47062i
$977$		−	53.8709i		−	1.72348i	−0.507347	−	0.861742i	$-0.669374\pi$
$977$		−	53.8709i		−	1.72348i	0.507347	−	0.861742i	$-0.330626\pi$
$978$		0			0
$979$		−	1.73811i		−	0.0555502i
$980$	1.72896	+	3.22717i	0.0552296	+	0.103088i
$981$		0			0
$982$	−1.60974	+	0.404043i	−0.0513688	+	0.0128935i
$983$	47.9060			1.52796			0.763982	−	0.645237i	$-0.223242\pi$
$983$	47.9060			1.52796			0.763982	+	0.645237i	$0.223242\pi$
$984$		0			0
$985$	65.6336			2.09126
$986$	−0.379736	+	0.0953134i	−0.0120933	+	0.00303540i
$987$		0			0
$988$	−3.72361	−	6.95026i	−0.118464	−	0.221117i
$989$		−	43.4941i		−	1.38303i
$990$		0			0
$991$			20.5876i			0.653987i	0.945027	+	0.326993i	$0.106036\pi$
$991$			20.5876i			0.653987i	−0.945027	+	0.326993i	$0.893964\pi$
$992$	36.5066	+	12.9631i	1.15909	+	0.411580i
$993$		0			0
$994$	−7.25879	−	28.9196i	−0.230235	−	0.917273i
$995$	−9.60782			−0.304588
$996$		0			0
$997$	−0.774038			−0.0245140			−0.0122570	−	0.999925i	$-0.503902\pi$
$997$	−0.774038			−0.0245140			−0.0122570	+	0.999925i	$0.503902\pi$
$998$	−0.615360	−	2.45164i	−0.0194789	−	0.0776054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.c.b.647.29	yes	32
3.2	odd	2	inner	684.2.c.b.647.4	yes	32
4.3	odd	2	inner	684.2.c.b.647.3	✓	32
12.11	even	2	inner	684.2.c.b.647.30	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.c.b.647.3	✓	32	4.3	odd	2	inner
684.2.c.b.647.4	yes	32	3.2	odd	2	inner
684.2.c.b.647.29	yes	32	1.1	even	1	trivial
684.2.c.b.647.30	yes	32	12.11	even	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37167 - 0.344287i) q^{2} +(1.76293 - 0.944493i) q^{4} +2.95253i q^{5} -2.52587i q^{7} +(2.09298 - 1.90248i) q^{8} +O(q^{10})\)	\(q+(1.37167 - 0.344287i) q^{2} +(1.76293 - 0.944493i) q^{4} +2.95253i q^{5} -2.52587i q^{7} +(2.09298 - 1.90248i) q^{8} +(1.01652 + 4.04988i) q^{10} +0.275662 q^{11} +3.94244 q^{13} +(-0.869623 - 3.46464i) q^{14} +(2.21587 - 3.33016i) q^{16} +2.91003i q^{17} -1.00000i q^{19} +(2.78864 + 5.20511i) q^{20} +(0.378116 - 0.0949068i) q^{22} +5.02883 q^{23} -3.71743 q^{25} +(5.40771 - 1.35733i) q^{26} +(-2.38566 - 4.45293i) q^{28} +0.0951342i q^{29} +6.84831i q^{31} +(1.89290 - 5.33075i) q^{32} +(1.00188 + 3.99158i) q^{34} +7.45769 q^{35} -11.9077 q^{37} +(-0.344287 - 1.37167i) q^{38} +(5.61714 + 6.17958i) q^{40} +4.10951i q^{41} -8.64895i q^{43} +(0.485974 - 0.260361i) q^{44} +(6.89787 - 1.73136i) q^{46} -5.81949 q^{47} +0.620000 q^{49} +(-5.09906 + 1.27986i) q^{50} +(6.95026 - 3.72361i) q^{52} -0.551324i q^{53} +0.813900i q^{55} +(-4.80542 - 5.28658i) q^{56} +(0.0327535 + 0.130492i) q^{58} -5.80992 q^{59} -13.7963 q^{61} +(2.35778 + 9.39359i) q^{62} +(0.761114 - 7.96371i) q^{64} +11.6402i q^{65} -6.79844i q^{67} +(2.74850 + 5.13018i) q^{68} +(10.2295 - 2.56759i) q^{70} +8.34706 q^{71} -3.65376 q^{73} +(-16.3334 + 4.09967i) q^{74} +(-0.944493 - 1.76293i) q^{76} -0.696285i q^{77} -9.13640i q^{79} +(9.83238 + 6.54241i) q^{80} +(1.41485 + 5.63688i) q^{82} -13.3249 q^{83} -8.59193 q^{85} +(-2.97772 - 11.8635i) q^{86} +(0.576954 - 0.524442i) q^{88} -6.30522i q^{89} -9.95808i q^{91} +(8.86549 - 4.74970i) q^{92} +(-7.98239 + 2.00357i) q^{94} +2.95253 q^{95} +0.763637 q^{97} +(0.850433 - 0.213458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 24 q^{16} - 64 q^{25} + 48 q^{34} + 32 q^{37} + 8 q^{40} + 32 q^{46} + 16 q^{49} - 32 q^{58} + 56 q^{64} - 72 q^{70} - 48 q^{73} - 112 q^{82} - 16 q^{85} - 40 q^{88} + 88 q^{94} - 128 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 24 * q^16 - 64 * q^25 + 48 * q^34 + 32 * q^37 + 8 * q^40 + 32 * q^46 + 16 * q^49 - 32 * q^58 + 56 * q^64 - 72 * q^70 - 48 * q^73 - 112 * q^82 - 16 * q^85 - 40 * q^88 + 88 * q^94 - 128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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