LMFDB - Embedded newform 847.2.b.f.846.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(846,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("847.846");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.b (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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 $ x^16 + 20x^14 + 260x^12 + 2030x^10 + 11605x^8 + 42100x^6 + 106925x^4 + 113575*x^2 + 87025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			846.6
Root			$0.551501 - 0.955228i$ of defining polynomial
Character	$\chi$	$=$	847.846
Dual form			847.2.b.f.846.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.672816i q^{2} +2.65257i q^{3} +1.54732 q^{4} +3.54984i q^{5} +1.78470 q^{6} +(-1.10300 + 2.40487i) q^{7} -2.38669i q^{8} -4.03615 q^{9} +O(q^{10})$	\(q-0.672816i q^{2} +2.65257i q^{3} +1.54732 q^{4} +3.54984i q^{5} +1.78470 q^{6} +(-1.10300 + 2.40487i) q^{7} -2.38669i q^{8} -4.03615 q^{9} +2.38839 q^{10} +4.10438i q^{12} -1.10300 q^{13} +(1.61803 + 0.742118i) q^{14} -9.41620 q^{15} +1.48883 q^{16} +4.17308 q^{17} +2.71559i q^{18} +1.24551 q^{19} +5.49273i q^{20} +(-6.37909 - 2.92579i) q^{21} +2.85410 q^{23} +6.33088 q^{24} -7.60134 q^{25} +0.742118i q^{26} -2.74846i q^{27} +(-1.70670 + 3.72109i) q^{28} -2.04277i q^{29} +6.33538i q^{30} -2.99530i q^{31} -5.77510i q^{32} -2.80772i q^{34} +(-8.53689 - 3.91548i) q^{35} -6.24520 q^{36} +2.76202 q^{37} -0.838003i q^{38} -2.92579i q^{39} +8.47237 q^{40} -5.49660 q^{41} +(-1.96852 + 4.29195i) q^{42} +1.73205i q^{43} -14.3277i q^{45} -1.92029i q^{46} -6.82860i q^{47} +3.94923i q^{48} +(-4.56677 - 5.30515i) q^{49} +5.11431i q^{50} +11.0694i q^{51} -1.70670 q^{52} +1.07985 q^{53} -1.84921 q^{54} +(5.73968 + 2.63253i) q^{56} +3.30382i q^{57} -1.37441 q^{58} -2.28980i q^{59} -14.5699 q^{60} -13.3518 q^{61} -2.01529 q^{62} +(4.45188 - 9.70640i) q^{63} -0.907920 q^{64} -3.91548i q^{65} +0.489806 q^{67} +6.45709 q^{68} +7.57072i q^{69} +(-2.63440 + 5.74376i) q^{70} +10.2062 q^{71} +9.63305i q^{72} +12.5276 q^{73} -1.85833i q^{74} -20.1631i q^{75} +1.92721 q^{76} -1.96852 q^{78} +12.4332i q^{79} +5.28510i q^{80} -4.81795 q^{81} +3.69820i q^{82} +1.61862 q^{83} +(-9.87048 - 4.52714i) q^{84} +14.8138i q^{85} +1.16535 q^{86} +5.41860 q^{87} +2.30985i q^{89} -9.63989 q^{90} +(1.21661 - 2.65257i) q^{91} +4.41620 q^{92} +7.94525 q^{93} -4.59439 q^{94} +4.42137i q^{95} +15.3189 q^{96} +12.6682i q^{97} +(-3.56939 + 3.07260i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{9}+O(q^{10}) $ 16 * q - 32 * q^9	$ 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) $ 16 * q - 32 * q^9 + 8 * q^14 - 20 * q^15 + 16 * q^16 - 8 * q^23 - 40 * q^25 - 60 * q^36 - 36 * q^37 - 20 * q^42 + 48 * q^49 + 20 * q^53 - 4 * q^56 + 28 * q^58 - 140 * q^60 + 12 * q^64 - 4 * q^67 + 100 * q^70 + 44 * q^71 - 20 * q^78 - 56 * q^81 - 24 * q^86 + 80 * q^91 - 60 * q^92 - 20 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	0.672816i		−	0.475753i	−0.971295	−	0.237877i	$-0.923549\pi$
$2$		−	0.672816i		−	0.475753i	0.971295	−	0.237877i	$-0.0764514\pi$
$3$			2.65257i			1.53146i	0.643160	+	0.765732i	$0.277623\pi$
$3$			2.65257i			1.53146i	−0.643160	+	0.765732i	$0.722377\pi$
$4$	1.54732			0.773659
$5$			3.54984i			1.58754i	0.608221	+	0.793768i	$0.291883\pi$
$5$			3.54984i			1.58754i	−0.608221	+	0.793768i	$0.708117\pi$
$6$	1.78470			0.728599
$7$	−1.10300	+	2.40487i	−0.416896	+	0.908954i
$7$	−1.10300	+	2.40487i	−0.416896	+	0.908954i
$8$		−	2.38669i		−	0.843824i
$9$	−4.03615			−1.34538
$10$	2.38839			0.755275
$11$		0			0
$11$		0			0
$12$			4.10438i			1.18483i
$13$	−1.10300			−0.305918			−0.152959	−	0.988233i	$-0.548880\pi$
$13$	−1.10300			−0.305918			−0.152959	+	0.988233i	$0.548880\pi$
$14$	1.61803	+	0.742118i	0.432438	+	0.198339i
$15$	−9.41620			−2.43125
$16$	1.48883			0.372207
$17$	4.17308			1.01212			0.506061	−	0.862498i	$-0.331101\pi$
$17$	4.17308			1.01212			0.506061	+	0.862498i	$0.331101\pi$
$18$			2.71559i			0.640070i
$19$	1.24551			0.285741			0.142870	−	0.989741i	$-0.454367\pi$
$19$	1.24551			0.285741			0.142870	+	0.989741i	$0.454367\pi$
$20$			5.49273i			1.22821i
$21$	−6.37909	−	2.92579i	−1.39203	−	0.638461i
$22$		0			0
$23$	2.85410			0.595121			0.297561	−	0.954703i	$-0.403827\pi$
$23$	2.85410			0.595121			0.297561	+	0.954703i	$0.403827\pi$
$24$	6.33088			1.29229
$25$	−7.60134			−1.52027
$26$			0.742118i			0.145541i
$27$		−	2.74846i		−	0.528941i
$28$	−1.70670	+	3.72109i	−0.322535	+	0.703221i
$29$		−	2.04277i		−	0.379333i	−0.981849	−	0.189666i	$-0.939259\pi$
$29$		−	2.04277i		−	0.379333i	0.981849	−	0.189666i	$-0.0607407\pi$
$30$			6.33538i			1.15668i
$31$		−	2.99530i		−	0.537971i	−0.963144	−	0.268986i	$-0.913312\pi$
$31$		−	2.99530i		−	0.537971i	0.963144	−	0.268986i	$-0.0866884\pi$
$32$		−	5.77510i		−	1.02090i
$33$		0			0
$34$		−	2.80772i		−	0.481520i
$35$	−8.53689	−	3.91548i	−1.44300	−	0.661837i
$36$	−6.24520			−1.04087
$37$	2.76202			0.454074			0.227037	−	0.973886i	$-0.427096\pi$
$37$	2.76202			0.454074			0.227037	+	0.973886i	$0.427096\pi$
$38$		−	0.838003i		−	0.135942i
$39$		−	2.92579i		−	0.468502i
$40$	8.47237			1.33960
$41$	−5.49660			−0.858424			−0.429212	−	0.903204i	$-0.641209\pi$
$41$	−5.49660			−0.858424			−0.429212	+	0.903204i	$0.641209\pi$
$42$	−1.96852	+	4.29195i	−0.303750	+	0.662263i
$43$			1.73205i			0.264135i	0.991241	+	0.132068i	$0.0421616\pi$
$43$			1.73205i			0.264135i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$		−	14.3277i		−	2.13584i
$46$		−	1.92029i		−	0.283131i
$47$		−	6.82860i		−	0.996053i	−0.867162	−	0.498027i	$-0.834058\pi$
$47$		−	6.82860i		−	0.996053i	0.867162	−	0.498027i	$-0.165942\pi$
$48$			3.94923i			0.570022i
$49$	−4.56677	−	5.30515i	−0.652396	−	0.757878i
$50$			5.11431i			0.723272i
$51$			11.0694i			1.55003i
$52$	−1.70670			−0.236676
$53$	1.07985			0.148329			0.0741646	−	0.997246i	$-0.476371\pi$
$53$	1.07985			0.148329			0.0741646	+	0.997246i	$0.476371\pi$
$54$	−1.84921			−0.251645
$55$		0			0
$56$	5.73968	+	2.63253i	0.766997	+	0.351786i
$57$			3.30382i			0.437602i
$58$	−1.37441			−0.180469
$59$		−	2.28980i		−	0.298107i	−0.988829	−	0.149054i	$-0.952377\pi$
$59$		−	2.28980i		−	0.298107i	0.988829	−	0.149054i	$-0.0476227\pi$
$60$	−14.5699			−1.88096
$61$	−13.3518			−1.70952			−0.854761	−	0.519022i	$-0.826296\pi$
$61$	−13.3518			−1.70952			−0.854761	+	0.519022i	$0.826296\pi$
$62$	−2.01529			−0.255941
$63$	4.45188	−	9.70640i	0.560884	−	1.22289i
$64$	−0.907920			−0.113490
$65$		−	3.91548i		−	0.485655i
$66$		0			0
$67$	0.489806			0.0598393			0.0299197	−	0.999552i	$-0.490475\pi$
$67$	0.489806			0.0598393			0.0299197	+	0.999552i	$0.490475\pi$
$68$	6.45709			0.783037
$69$			7.57072i			0.911407i
$70$	−2.63440	+	5.74376i	−0.314871	+	0.686510i
$71$	10.2062			1.21125			0.605625	−	0.795750i	$-0.292923\pi$
$71$	10.2062			1.21125			0.605625	+	0.795750i	$0.292923\pi$
$72$			9.63305i			1.13527i
$73$	12.5276			1.46624			0.733121	−	0.680098i	$-0.238063\pi$
$73$	12.5276			1.46624			0.733121	+	0.680098i	$0.238063\pi$
$74$		−	1.85833i		−	0.216027i
$75$		−	20.1631i		−	2.32824i
$76$	1.92721			0.221066
$77$		0			0
$78$	−1.96852			−0.222891
$79$			12.4332i			1.39885i	0.714708	+	0.699423i	$0.246560\pi$
$79$			12.4332i			1.39885i	−0.714708	+	0.699423i	$0.753440\pi$
$80$			5.28510i			0.590892i
$81$	−4.81795			−0.535328
$82$			3.69820i			0.408398i
$83$	1.61862			0.177666			0.0888332	−	0.996047i	$-0.471686\pi$
$83$	1.61862			0.177666			0.0888332	+	0.996047i	$0.471686\pi$
$84$	−9.87048	−	4.52714i	−1.07696	−	0.493951i
$85$			14.8138i			1.60678i
$86$	1.16535			0.125663
$87$	5.41860			0.580935
$88$		0			0
$89$			2.30985i			0.244844i	0.992478	+	0.122422i	$0.0390661\pi$
$89$			2.30985i			0.244844i	−0.992478	+	0.122422i	$0.960934\pi$
$90$	−9.63989			−1.01613
$91$	1.21661	−	2.65257i	0.127536	−	0.278065i
$92$	4.41620			0.460421
$93$	7.94525			0.823884
$94$	−4.59439			−0.473875
$95$			4.42137i			0.453623i
$96$	15.3189			1.56348
$97$			12.6682i			1.28626i	0.765755	+	0.643132i	$0.222366\pi$
$97$			12.6682i			1.28626i	−0.765755	+	0.643132i	$0.777634\pi$
$98$	−3.56939	+	3.07260i	−0.360563	+	0.310379i
$99$		0			0
$100$	−11.7617			−1.17617
$101$	3.16649			0.315078			0.157539	−	0.987513i	$-0.449644\pi$
$101$	3.16649			0.315078			0.157539	+	0.987513i	$0.449644\pi$
$102$	7.44768			0.737430
$103$			9.73220i			0.958942i	0.877558	+	0.479471i	$0.159171\pi$
$103$			9.73220i			0.958942i	−0.877558	+	0.479471i	$0.840829\pi$
$104$			2.63253i			0.258141i
$105$	10.3861	−	22.6447i	1.01358	−	2.20990i
$106$		−	0.726543i		−	0.0705680i
$107$		−	10.5567i		−	1.02056i	−0.860010	−	0.510278i	$-0.829543\pi$
$107$		−	10.5567i		−	1.02056i	0.860010	−	0.510278i	$-0.170457\pi$
$108$		−	4.25274i		−	0.409220i
$109$			3.04683i			0.291833i	0.989297	+	0.145917i	$0.0466131\pi$
$109$			3.04683i			0.291833i	−0.989297	+	0.145917i	$0.953387\pi$
$110$		0			0
$111$			7.32647i			0.695397i
$112$	−1.64218	+	3.58044i	−0.155172	+	0.338320i
$113$	7.25710			0.682691			0.341345	−	0.939938i	$-0.389117\pi$
$113$	7.25710			0.682691			0.341345	+	0.939938i	$0.389117\pi$
$114$	2.22286			0.208190
$115$			10.1316i			0.944776i
$116$		−	3.16082i		−	0.293474i
$117$	4.45188			0.411576
$118$	−1.54062			−0.141825
$119$	−4.60292	+	10.0357i	−0.421949	+	0.919972i
$120$			22.4736i			2.05155i
$121$		0			0
$122$			8.98330i			0.813310i
$123$		−	14.5801i		−	1.31465i
$124$		−	4.63468i		−	0.416206i
$125$		−	9.23433i		−	0.825944i
$126$	−6.53062	−	2.99530i	−0.581794	−	0.266842i
$127$			6.12976i			0.543928i	0.962307	+	0.271964i	$0.0876732\pi$
$127$			6.12976i			0.543928i	−0.962307	+	0.271964i	$0.912327\pi$
$128$		−	10.9393i		−	0.966909i
$129$	−4.59439			−0.404514
$130$	−2.63440			−0.231052
$131$	18.8287			1.64507			0.822534	−	0.568715i	$-0.192559\pi$
$131$	18.8287			1.64507			0.822534	+	0.568715i	$0.192559\pi$
$132$		0			0
$133$	−1.37381	+	2.99530i	−0.119124	+	0.259725i
$134$		−	0.329550i		−	0.0284687i
$135$	9.75658			0.839713
$136$		−	9.95987i		−	0.854052i
$137$	−2.95939			−0.252837			−0.126419	−	0.991977i	$-0.540348\pi$
$137$	−2.95939			−0.252837			−0.126419	+	0.991977i	$0.540348\pi$
$138$	5.09370			0.433605
$139$	−14.7735			−1.25307			−0.626534	−	0.779394i	$-0.715527\pi$
$139$	−14.7735			−1.25307			−0.626534	+	0.779394i	$0.715527\pi$
$140$	−13.2093	−	6.05849i	−1.11639	−	0.512036i
$141$	18.1134			1.52542
$142$		−	6.86688i		−	0.576256i
$143$		0			0
$144$	−6.00914			−0.500761
$145$	7.25150			0.602204
$146$		−	8.42876i		−	0.697569i
$147$	14.0723	−	12.1137i	1.16066	−	0.999121i
$148$	4.27373			0.351298
$149$		−	7.51223i		−	0.615426i	−0.951479	−	0.307713i	$-0.900436\pi$
$149$		−	7.51223i		−	0.615426i	0.951479	−	0.307713i	$-0.0995637\pi$
$150$	−13.5661			−1.10767
$151$			12.7284i			1.03582i	0.855434	+	0.517912i	$0.173290\pi$
$151$			12.7284i			1.03582i	−0.855434	+	0.517912i	$0.826710\pi$
$152$		−	2.97266i		−	0.241115i
$153$	−16.8432			−1.36169
$154$		0			0
$155$	10.6328			0.854048
$156$		−	4.52714i		−	0.362461i
$157$		−	15.2616i		−	1.21800i	−0.793168	−	0.609002i	$-0.791570\pi$
$157$		−	15.2616i		−	1.21800i	0.793168	−	0.609002i	$-0.208430\pi$
$158$	8.36527			0.665505
$159$			2.86439i			0.227161i
$160$	20.5006			1.62072
$161$	−3.14808	+	6.86374i	−0.248104	+	0.540938i
$162$			3.24160i			0.254684i
$163$	21.0339			1.64750			0.823751	−	0.566951i	$-0.191877\pi$
$163$	21.0339			1.64750			0.823751	+	0.566951i	$0.191877\pi$
$164$	−8.50499			−0.664128
$165$		0			0
$166$		−	1.08903i		−	0.0845253i
$167$	8.34102			0.645447			0.322724	−	0.946493i	$-0.395402\pi$
$167$	8.34102			0.645447			0.322724	+	0.946493i	$0.395402\pi$
$168$	−6.98298	+	15.2249i	−0.538748	+	1.17463i
$169$	−11.7834			−0.906414
$170$	9.96694			0.764430
$171$	−5.02708			−0.384431
$172$			2.68003i			0.204351i
$173$	−16.0588			−1.22093			−0.610466	−	0.792043i	$-0.709018\pi$
$173$	−16.0588			−1.22093			−0.610466	+	0.792043i	$0.709018\pi$
$174$		−	3.64572i		−	0.276381i
$175$	8.38430	−	18.2802i	0.633793	−	1.38185i
$176$		0			0
$177$	6.07388			0.456540
$178$	1.55410			0.116485
$179$	7.36816			0.550722			0.275361	−	0.961341i	$-0.411203\pi$
$179$	7.36816			0.550722			0.275361	+	0.961341i	$0.411203\pi$
$180$		−	22.1695i		−	1.65241i
$181$		−	14.4786i		−	1.07619i	−0.842885	−	0.538094i	$-0.819145\pi$
$181$		−	14.4786i		−	1.07619i	0.842885	−	0.538094i	$-0.180855\pi$
$182$	−1.78470	−	0.818558i	−0.132290	−	0.0606755i
$183$		−	35.4166i		−	2.61807i
$184$		−	6.81187i		−	0.502178i
$185$			9.80473i			0.720858i
$186$		−	5.34569i		−	0.391965i
$187$		0			0
$188$		−	10.5660i		−	0.770606i
$189$	6.60968	+	3.03156i	0.480783	+	0.220513i
$190$	2.97477			0.215813
$191$	1.58944			0.115008			0.0575040	−	0.998345i	$-0.481686\pi$
$191$	1.58944			0.115008			0.0575040	+	0.998345i	$0.481686\pi$
$192$		−	2.40832i		−	0.173806i
$193$		−	11.2031i		−	0.806419i	−0.915108	−	0.403209i	$-0.867895\pi$
$193$		−	11.2031i		−	0.806419i	0.915108	−	0.403209i	$-0.132105\pi$
$194$	8.52340			0.611944
$195$	10.3861			0.743764
$196$	−7.06625	−	8.20875i	−0.504732	−	0.586339i
$197$			15.0339i			1.07112i	0.844496	+	0.535561i	$0.179900\pi$
$197$			15.0339i			1.07112i	−0.844496	+	0.535561i	$0.820100\pi$
$198$		0			0
$199$			21.9453i			1.55566i	0.628476	+	0.777829i	$0.283679\pi$
$199$			21.9453i			1.55566i	−0.628476	+	0.777829i	$0.716321\pi$
$200$			18.1421i			1.28284i
$201$			1.29925i			0.0916418i
$202$		−	2.13047i		−	0.149899i
$203$	4.91259	+	2.25318i	0.344796	+	0.158142i
$204$			17.1279i			1.19919i
$205$		−	19.5120i		−	1.36278i
$206$	6.54798			0.456220
$207$	−11.5196			−0.800666
$208$	−1.64218			−0.113865
$209$		0			0
$210$	−15.2357	−	6.98793i	−1.05137	−	0.482213i
$211$		−	14.3700i		−	0.989271i	−0.869101	−	0.494635i	$-0.835302\pi$
$211$		−	14.3700i		−	0.989271i	0.869101	−	0.494635i	$-0.164698\pi$
$212$	1.67088			0.114756
$213$			27.0726i			1.85499i
$214$	−7.10273			−0.485532
$215$	−6.14850			−0.419324
$216$	−6.55973			−0.446333
$217$	7.20329	+	3.30382i	0.488991	+	0.224278i
$218$	2.04996			0.138840
$219$			33.2303i			2.24550i
$220$		0			0
$221$	−4.60292			−0.309626
$222$	4.92937			0.330837
$223$			17.7224i			1.18678i	0.804916	+	0.593388i	$0.202210\pi$
$223$			17.7224i			1.18678i	−0.804916	+	0.593388i	$0.797790\pi$
$224$	13.8883	+	6.36994i	0.927954	+	0.425610i
$225$	30.6801			2.04534
$226$		−	4.88270i		−	0.324792i
$227$	−4.10131			−0.272214			−0.136107	−	0.990694i	$-0.543459\pi$
$227$	−4.10131			−0.272214			−0.136107	+	0.990694i	$0.543459\pi$
$228$			5.11206i			0.338554i
$229$			9.80126i			0.647686i	0.946111	+	0.323843i	$0.104975\pi$
$229$			9.80126i			0.647686i	−0.946111	+	0.323843i	$0.895025\pi$
$230$	6.81670			0.449480
$231$		0			0
$232$	−4.87547			−0.320090
$233$		−	0.101962i		−	0.00667974i	−0.999994	−	0.00333987i	$-0.998937\pi$
$233$		−	0.101962i		−	0.00667974i	0.999994	−	0.00333987i	$-0.00106312\pi$
$234$		−	2.99530i		−	0.195809i
$235$	24.2404			1.58127
$236$		−	3.54306i		−	0.230633i
$237$	−32.9800			−2.14228
$238$	6.75219	+	3.09692i	0.437680	+	0.200744i
$239$		−	6.13574i		−	0.396888i	−0.980112	−	0.198444i	$-0.936411\pi$
$239$		−	6.13574i		−	0.396888i	0.980112	−	0.198444i	$-0.0635888\pi$
$240$	−14.0191			−0.904931
$241$	4.31560			0.277992			0.138996	−	0.990293i	$-0.455612\pi$
$241$	4.31560			0.277992			0.138996	+	0.990293i	$0.455612\pi$
$242$		0			0
$243$		−	21.0254i		−	1.34878i
$244$	−20.6595			−1.32259
$245$	18.8324	−	16.2113i	1.20316	−	1.03570i
$246$	−9.80975			−0.625447
$247$	−1.37381			−0.0874132
$248$	−7.14886			−0.453953
$249$			4.29350i			0.272090i
$250$	−6.21301			−0.392945
$251$		−	30.6941i		−	1.93739i	−0.248245	−	0.968697i	$-0.579854\pi$
$251$		−	30.6941i		−	1.93739i	0.248245	−	0.968697i	$-0.420146\pi$
$252$	6.88847	−	15.0189i	0.433933	−	0.946101i
$253$		0			0
$254$	4.12420			0.258776
$255$	−39.2946			−2.46072
$256$	−9.17600			−0.573500
$257$			6.73271i			0.419975i	0.977704	+	0.209988i	$0.0673424\pi$
$257$			6.73271i			0.419975i	−0.977704	+	0.209988i	$0.932658\pi$
$258$			3.09118i			0.192449i
$259$	−3.04652	+	6.64230i	−0.189301	+	0.412732i
$260$		−	6.05849i		−	0.375732i
$261$			8.24492i			0.510348i
$262$		−	12.6682i		−	0.782646i
$263$		−	24.4460i		−	1.50741i	−0.657215	−	0.753703i	$-0.728266\pi$
$263$		−	24.4460i		−	1.50741i	0.657215	−	0.753703i	$-0.271734\pi$
$264$		0			0
$265$			3.83330i			0.235478i
$266$	2.01529	+	0.924319i	0.123565	+	0.0566736i
$267$	−6.12705			−0.374969
$268$	0.757886			0.0462952
$269$		−	25.3199i		−	1.54378i	−0.635755	−	0.771891i	$-0.719311\pi$
$269$		−	25.3199i		−	1.54378i	0.635755	−	0.771891i	$-0.280689\pi$
$270$		−	6.56439i		−	0.399496i
$271$	−27.3409			−1.66084			−0.830421	−	0.557136i	$-0.811900\pi$
$271$	−27.3409			−1.66084			−0.830421	+	0.557136i	$0.811900\pi$
$272$	6.21301			0.376719
$273$	7.03615	+	3.22716i	0.425847	+	0.195316i
$274$			1.99112i			0.120288i
$275$		0			0
$276$			11.7143i			0.705118i
$277$		−	22.4190i		−	1.34703i	−0.739175	−	0.673513i	$-0.764784\pi$
$277$		−	22.4190i		−	1.34703i	0.739175	−	0.673513i	$-0.235216\pi$
$278$			9.93983i			0.596151i
$279$			12.0895i			0.723777i
$280$	−9.34505	+	20.3749i	−0.558473	+	1.21764i
$281$			21.5172i			1.28361i	0.766868	+	0.641805i	$0.221814\pi$
$281$			21.5172i			1.28361i	−0.766868	+	0.641805i	$0.778186\pi$
$282$		−	12.1870i		−	0.725723i
$283$	30.9433			1.83939			0.919694	−	0.392637i	$-0.128437\pi$
$283$	30.9433			1.83939			0.919694	+	0.392637i	$0.128437\pi$
$284$	15.7922			0.937094
$285$	−11.7280			−0.694708
$286$		0			0
$287$	6.06276	−	13.2186i	0.357873	−	0.780269i
$288$			23.3091i			1.37350i
$289$	0.414624			0.0243896
$290$		−	4.87893i		−	0.286500i
$291$	−33.6034			−1.96987
$292$	19.3842			1.13437
$293$	24.8510			1.45181			0.725904	−	0.687796i	$-0.241421\pi$
$293$	24.8510			1.45181			0.725904	+	0.687796i	$0.241421\pi$
$294$	−8.15030	−	9.46807i	−0.475335	−	0.552189i
$295$	8.12843			0.473256
$296$		−	6.59210i		−	0.383158i
$297$		0			0
$298$	−5.05435			−0.292791
$299$	−3.14808			−0.182058
$300$		−	31.1988i		−	1.80126i
$301$	−4.16535	−	1.91046i	−0.240087	−	0.110117i
$302$	8.56389			0.492796
$303$			8.39936i			0.482531i
$304$	1.85436			0.106355
$305$		−	47.3967i		−	2.71393i
$306$			11.3324i			0.647828i
$307$	−10.0029			−0.570896			−0.285448	−	0.958394i	$-0.592142\pi$
$307$	−10.0029			−0.570896			−0.285448	+	0.958394i	$0.592142\pi$
$308$		0			0
$309$	−25.8154			−1.46859
$310$		−	7.15393i		−	0.406316i
$311$		−	18.7190i		−	1.06146i	−0.847542	−	0.530728i	$-0.821919\pi$
$311$		−	18.7190i		−	1.06146i	0.847542	−	0.530728i	$-0.178081\pi$
$312$	−6.98298			−0.395333
$313$		−	5.28598i		−	0.298781i	−0.988778	−	0.149391i	$-0.952269\pi$
$313$		−	5.28598i		−	0.298781i	0.988778	−	0.149391i	$-0.0477312\pi$
$314$	−10.2682			−0.579469
$315$	34.4561	+	15.8034i	1.94138	+	0.890423i
$316$			19.2381i			1.08223i
$317$	−28.7541			−1.61499			−0.807497	−	0.589872i	$-0.799178\pi$
$317$	−28.7541			−1.61499			−0.807497	+	0.589872i	$0.799178\pi$
$318$	1.92721			0.108072
$319$		0			0
$320$		−	3.22297i		−	0.180169i
$321$	28.0025			1.56294
$322$	4.61803	+	2.11808i	0.257353	+	0.118036i
$323$	5.19764			0.289204
$324$	−7.45491			−0.414162
$325$	8.38430			0.465077
$326$		−	14.1520i		−	0.783804i
$327$	−8.08193			−0.446932
$328$			13.1187i			0.724359i
$329$	16.4219	+	7.53196i	0.905367	+	0.415250i
$330$		0			0
$331$	12.2266			0.672035			0.336017	−	0.941856i	$-0.390920\pi$
$331$	12.2266			0.672035			0.336017	+	0.941856i	$0.390920\pi$
$332$	2.50452			0.137453
$333$	−11.1479			−0.610903
$334$		−	5.61197i		−	0.307073i
$335$			1.73873i			0.0949971i
$336$	−9.49738	−	4.35601i	−0.518124	−	0.237640i
$337$			36.0841i			1.96563i	0.184603	+	0.982813i	$0.440900\pi$
$337$			36.0841i			1.96563i	−0.184603	+	0.982813i	$0.559100\pi$
$338$			7.92806i			0.431229i
$339$			19.2500i			1.04552i
$340$			22.9216i			1.24310i
$341$		0			0
$342$			3.38230i			0.182894i
$343$	17.7953	−	5.13089i	0.960858	−	0.277042i
$344$	4.13387			0.222884
$345$	−26.8748			−1.44689
$346$			10.8047i			0.580862i
$347$		−	27.5091i		−	1.47677i	−0.674380	−	0.738384i	$-0.735589\pi$
$347$		−	27.5091i		−	1.47677i	0.674380	−	0.738384i	$-0.264411\pi$
$348$	8.38430			0.449445
$349$	−14.1265			−0.756174			−0.378087	−	0.925770i	$-0.623418\pi$
$349$	−14.1265			−0.756174			−0.378087	+	0.925770i	$0.623418\pi$
$350$	−12.2992	−	5.64109i	−0.657421	−	0.301529i
$351$			3.03156i			0.161812i
$352$		0			0
$353$		−	8.23958i		−	0.438549i	−0.975663	−	0.219274i	$-0.929631\pi$
$353$		−	8.23958i		−	0.438549i	0.975663	−	0.219274i	$-0.0703690\pi$
$354$		−	4.08660i		−	0.217200i
$355$			36.2302i			1.92290i
$356$			3.57407i			0.189425i
$357$	−26.6205	−	12.2096i	−1.40890	−	0.646200i
$358$		−	4.95742i		−	0.262008i
$359$			29.9242i			1.57934i	0.613533	+	0.789669i	$0.289748\pi$
$359$			29.9242i			1.57934i	−0.613533	+	0.789669i	$0.710252\pi$
$360$	−34.1957			−1.80227
$361$	−17.4487			−0.918352
$362$	−9.74145			−0.511999
$363$		0			0
$364$	1.88249	−	4.10438i	0.0986692	−	0.215128i
$365$			44.4709i			2.32771i
$366$	−23.8289			−1.24556
$367$		−	4.63468i		−	0.241928i	−0.992657	−	0.120964i	$-0.961401\pi$
$367$		−	4.63468i		−	0.241928i	0.992657	−	0.120964i	$-0.0385986\pi$
$368$	4.24927			0.221509
$369$	22.1851			1.15491
$370$	6.59678			0.342950
$371$	−1.19108	+	2.59690i	−0.0618378	+	0.134824i
$372$	12.2938			0.637405
$373$			15.2702i			0.790662i	0.918539	+	0.395331i	$0.129370\pi$
$373$			15.2702i			0.790662i	−0.918539	+	0.395331i	$0.870630\pi$
$374$		0			0
$375$	24.4947			1.26490
$376$	−16.2978			−0.840493
$377$			2.25318i			0.116045i
$378$	2.03968	−	4.44710i	0.104910	−	0.228734i
$379$	22.7591			1.16906			0.584529	−	0.811373i	$-0.301279\pi$
$379$	22.7591			1.16906			0.584529	+	0.811373i	$0.301279\pi$
$380$			6.84127i			0.350950i
$381$	−16.2596			−0.833007
$382$		−	1.06940i		−	0.0547154i
$383$			28.9146i			1.47746i	0.673999	+	0.738732i	$0.264575\pi$
$383$			28.9146i			1.47746i	−0.673999	+	0.738732i	$0.735425\pi$
$384$	29.0174			1.48079
$385$		0			0
$386$	−7.53765			−0.383656
$387$		−	6.99081i		−	0.355363i
$388$			19.6018i			0.995130i
$389$	−21.9665			−1.11375			−0.556873	−	0.830598i	$-0.687999\pi$
$389$	−21.9665			−1.11375			−0.556873	+	0.830598i	$0.687999\pi$
$390$		−	6.98793i		−	0.353848i
$391$	11.9104			0.602335
$392$	−12.6618	+	10.8995i	−0.639516	+	0.550507i
$393$			49.9444i			2.51936i
$394$	10.1151			0.509590
$395$	−44.1359			−2.22072
$396$		0			0
$397$			3.02008i			0.151573i	0.997124	+	0.0757866i	$0.0241468\pi$
$397$			3.02008i			0.151573i	−0.997124	+	0.0757866i	$0.975853\pi$
$398$	14.7651			0.740109
$399$	−7.94525	−	3.64412i	−0.397760	−	0.182434i
$400$	−11.3171			−0.565855
$401$	7.88407			0.393712			0.196856	−	0.980432i	$-0.436927\pi$
$401$	7.88407			0.393712			0.196856	+	0.980432i	$0.436927\pi$
$402$	0.874155			0.0435989
$403$			3.30382i			0.164575i
$404$	4.89957			0.243763
$405$		−	17.1030i		−	0.849852i
$406$	1.51598	−	3.30527i	0.0752366	−	0.164038i
$407$		0			0
$408$	26.4193			1.30795
$409$	26.5465			1.31264			0.656320	−	0.754483i	$-0.272112\pi$
$409$	26.5465			1.31264			0.656320	+	0.754483i	$0.272112\pi$
$410$	−13.1280			−0.648346
$411$		−	7.84999i		−	0.387211i
$412$			15.0588i			0.741894i
$413$	5.50668	+	2.52566i	0.270966	+	0.124280i
$414$			7.75056i			0.380919i
$415$			5.74583i			0.282052i
$416$			6.36994i			0.312312i
$417$		−	39.1877i		−	1.91903i
$418$		0			0
$419$			7.28466i			0.355879i	0.984041	+	0.177940i	$0.0569431\pi$
$419$			7.28466i			0.355879i	−0.984041	+	0.177940i	$0.943057\pi$
$420$	16.0706	−	35.0386i	0.784165	−	1.70971i
$421$	−23.8041			−1.16014			−0.580070	−	0.814567i	$-0.696975\pi$
$421$	−23.8041			−1.16014			−0.580070	+	0.814567i	$0.696975\pi$
$422$	−9.66836			−0.470648
$423$			27.5612i			1.34007i
$424$		−	2.57728i		−	0.125164i
$425$	−31.7210			−1.53870
$426$	18.2149			0.882515
$427$	14.7271	−	32.1093i	0.712692	−	1.55388i
$428$		−	16.3346i		−	0.789562i
$429$		0			0
$430$			4.13681i			0.199495i
$431$		−	0.640406i		−	0.0308473i	−0.999881	−	0.0154236i	$-0.995090\pi$
$431$		−	0.640406i		−	0.0308473i	0.999881	−	0.0154236i	$-0.00490969\pi$
$432$		−	4.09199i		−	0.196876i
$433$		−	17.2215i		−	0.827611i	−0.910365	−	0.413806i	$-0.864199\pi$
$433$		−	17.2215i		−	0.827611i	0.910365	−	0.413806i	$-0.135801\pi$
$434$	2.22286	−	4.84649i	0.106701	−	0.232639i
$435$			19.2351i			0.922254i
$436$			4.71441i			0.225779i
$437$	3.55483			0.170050
$438$	22.3579			1.06830
$439$	0.0381286			0.00181978			0.000909889	−	1.00000i	$-0.499710\pi$
$439$	0.0381286			0.00181978			0.000909889		1.00000i	$0.499710\pi$
$440$		0			0
$441$	18.4322	+	21.4124i	0.877722	+	1.01964i
$442$			3.09692i			0.147305i
$443$	30.6420			1.45585			0.727923	−	0.685658i	$-0.240486\pi$
$443$	30.6420			1.45585			0.727923	+	0.685658i	$0.240486\pi$
$444$			11.3364i			0.538001i
$445$	−8.19959			−0.388698
$446$	11.9239			0.564613
$447$	19.9267			0.942503
$448$	1.00144	−	2.18343i	0.0473135	−	0.103157i
$449$	−29.5218			−1.39322			−0.696609	−	0.717451i	$-0.745309\pi$
$449$	−29.5218			−1.39322			−0.696609	+	0.717451i	$0.745309\pi$
$450$		−	20.6421i		−	0.973078i
$451$		0			0
$452$	11.2290			0.528170
$453$	−33.7631			−1.58633
$454$			2.75943i			0.129506i
$455$	9.41620	+	4.31878i	0.441438	+	0.202468i
$456$	7.88521			0.369259
$457$			4.24787i			0.198707i	0.995052	+	0.0993534i	$0.0316774\pi$
$457$			4.24787i			0.198707i	−0.995052	+	0.0993534i	$0.968323\pi$
$458$	6.59445			0.308138
$459$		−	11.4695i		−	0.535353i
$460$			15.6768i			0.730935i
$461$	11.8930			0.553913			0.276957	−	0.960882i	$-0.410674\pi$
$461$	11.8930			0.553913			0.276957	+	0.960882i	$0.410674\pi$
$462$		0			0
$463$	29.5007			1.37102			0.685508	−	0.728066i	$-0.259580\pi$
$463$	29.5007			1.37102			0.685508	+	0.728066i	$0.259580\pi$
$464$		−	3.04134i		−	0.141191i
$465$			28.2043i			1.30794i
$466$	−0.0686016			−0.00317791
$467$		−	11.1490i		−	0.515913i	−0.966156	−	0.257957i	$-0.916951\pi$
$467$		−	11.1490i		−	0.515913i	0.966156	−	0.257957i	$-0.0830492\pi$
$468$	6.88847			0.318420
$469$	−0.540257	+	1.17792i	−0.0249468	+	0.0543912i
$470$		−	16.3093i		−	0.752294i
$471$	40.4824			1.86533
$472$	−5.46506			−0.251550
$473$		0			0
$474$			22.1895i			1.01920i
$475$	−9.46758			−0.434402
$476$	−7.12218	+	15.5284i	−0.326445	+	0.711745i
$477$	−4.35844			−0.199559
$478$	−4.12823			−0.188821
$479$	11.3316			0.517753			0.258877	−	0.965910i	$-0.416648\pi$
$479$	11.3316			0.517753			0.258877	+	0.965910i	$0.416648\pi$
$480$			54.3795i			2.48207i
$481$	−3.04652			−0.138909
$482$		−	2.90360i		−	0.132256i
$483$	−18.2066	−	8.35052i	−0.828427	−	0.379962i
$484$		0			0
$485$	−44.9702			−2.04199
$486$	−14.1462			−0.641685
$487$	15.5058			0.702637			0.351318	−	0.936256i	$-0.385733\pi$
$487$	15.5058			0.702637			0.351318	+	0.936256i	$0.385733\pi$
$488$			31.8666i			1.44253i
$489$			55.7940i			2.52309i
$490$	−10.9072	−	12.6708i	−0.492738	−	0.572406i
$491$		−	10.4088i		−	0.469742i	−0.972027	−	0.234871i	$-0.924533\pi$
$491$		−	10.4088i		−	0.469742i	0.972027	−	0.234871i	$-0.0754668\pi$
$492$		−	22.5601i		−	1.01709i
$493$		−	8.52465i		−	0.383931i
$494$			0.924319i			0.0415871i
$495$		0			0
$496$		−	4.45949i		−	0.200237i
$497$	−11.2574	+	24.5445i	−0.504965	+	1.10097i
$498$	2.88874			0.129447
$499$	−23.2190			−1.03942			−0.519712	−	0.854342i	$-0.673961\pi$
$499$	−23.2190			−1.03942			−0.519712	+	0.854342i	$0.673961\pi$
$500$		−	14.2885i		−	0.638999i
$501$			22.1252i			0.988479i
$502$	−20.6515			−0.921721
$503$	−1.15636			−0.0515596			−0.0257798	−	0.999668i	$-0.508207\pi$
$503$	−1.15636			−0.0515596			−0.0257798	+	0.999668i	$0.508207\pi$
$504$	−23.1662	−	10.6253i	−1.03190	−	0.473287i
$505$			11.2405i			0.500197i
$506$		0			0
$507$		−	31.2563i		−	1.38814i
$508$			9.48469i			0.420815i
$509$		−	17.8327i		−	0.790420i	−0.918591	−	0.395210i	$-0.870672\pi$
$509$		−	17.8327i		−	0.790420i	0.918591	−	0.395210i	$-0.129328\pi$
$510$			26.4381i			1.17070i
$511$	−13.8180	+	30.1272i	−0.611270	+	1.33275i
$512$		−	15.7049i		−	0.694065i
$513$		−	3.42325i		−	0.151140i
$514$	4.52988			0.199804
$515$	−34.5477			−1.52235
$516$	−7.10899			−0.312956
$517$		0			0
$518$	4.46905	+	2.04975i	0.196359	+	0.0900607i
$519$		−	42.5973i		−	1.86981i
$520$	−9.34505			−0.409807
$521$		−	35.9158i		−	1.57350i	−0.617273	−	0.786749i	$-0.711763\pi$
$521$		−	35.9158i		−	1.57350i	0.617273	−	0.786749i	$-0.288237\pi$
$522$	5.54732			0.242800
$523$	9.86251			0.431257			0.215629	−	0.976475i	$-0.430820\pi$
$523$	9.86251			0.431257			0.215629	+	0.976475i	$0.430820\pi$
$524$	29.1339			1.27272
$525$	48.4896	+	22.2400i	2.11626	+	0.970632i
$526$	−16.4477			−0.717153
$527$		−	12.4996i		−	0.544492i
$528$		0			0
$529$	−14.8541			−0.645831
$530$	2.57911			0.112029
$531$			9.24199i			0.401068i
$532$	−2.12571	+	4.63468i	−0.0921614	+	0.200939i
$533$	6.06276			0.262607
$534$			4.12238i			0.178393i
$535$	37.4746			1.62017
$536$		−	1.16902i		−	0.0504938i
$537$			19.5446i			0.843411i
$538$	−17.0356			−0.734459
$539$		0			0
$540$	15.0965			0.649651
$541$			20.6287i			0.886897i	0.896300	+	0.443449i	$0.146245\pi$
$541$			20.6287i			0.886897i	−0.896300	+	0.443449i	$0.853755\pi$
$542$			18.3954i			0.790151i
$543$	38.4056			1.64814
$544$		−	24.1000i		−	1.03328i
$545$	−10.8157			−0.463295
$546$	2.17128	−	4.73404i	0.0929224	−	0.202598i
$547$		−	28.8672i		−	1.23427i	−0.786856	−	0.617136i	$-0.788293\pi$
$547$		−	28.8672i		−	1.23427i	0.786856	−	0.617136i	$-0.211707\pi$
$548$	−4.57911			−0.195610
$549$	53.8898			2.29996
$550$		0			0
$551$		−	2.54430i		−	0.108391i
$552$	18.0690			0.769067
$553$	−29.9002	−	13.7139i	−1.27149	−	0.583173i
$554$	−15.0839			−0.640852
$555$	−26.0078			−1.10397
$556$	−22.8592			−0.969448
$557$		−	14.5467i		−	0.616365i	−0.951327	−	0.308183i	$-0.900279\pi$
$557$		−	14.5467i		−	0.616365i	0.951327	−	0.308183i	$-0.0997208\pi$
$558$	8.13399			0.344339
$559$		−	1.91046i		−	0.0808037i
$560$	−12.7100	−	5.82948i	−0.537094	−	0.246340i
$561$		0			0
$562$	14.4771			0.610681
$563$	−6.04411			−0.254729			−0.127365	−	0.991856i	$-0.540652\pi$
$563$	−6.04411			−0.254729			−0.127365	+	0.991856i	$0.540652\pi$
$564$	28.0271			1.18016
$565$			25.7615i			1.08380i
$566$		−	20.8191i		−	0.875094i
$567$	5.31421	−	11.5865i	0.223176	−	0.486589i
$568$		−	24.3590i		−	1.02208i
$569$			13.1065i			0.549455i	0.961522	+	0.274727i	$0.0885876\pi$
$569$			13.1065i			0.549455i	−0.961522	+	0.274727i	$0.911412\pi$
$570$			7.89080i			0.330509i
$571$		−	14.5264i		−	0.607910i	−0.952686	−	0.303955i	$-0.901693\pi$
$571$		−	14.5264i		−	0.607910i	0.952686	−	0.303955i	$-0.0983073\pi$
$572$		0			0
$573$			4.21612i			0.176131i
$574$	−8.89368	−	4.07912i	−0.371215	−	0.170259i
$575$	−21.6950			−0.904744
$576$	3.66450			0.152687
$577$		−	27.4793i		−	1.14398i	−0.820261	−	0.571990i	$-0.806172\pi$
$577$		−	27.4793i		−	1.14398i	0.820261	−	0.571990i	$-0.193828\pi$
$578$		−	0.278966i		−	0.0116034i
$579$	29.7171			1.23500
$580$	11.2204			0.465901
$581$	−1.78534	+	3.89256i	−0.0740683	+	0.161491i
$582$			22.6089i			0.937171i
$583$		0			0
$584$		−	29.8995i		−	1.23725i
$585$			15.8034i			0.653392i
$586$		−	16.7201i		−	0.690702i
$587$		−	14.3085i		−	0.590575i	−0.955408	−	0.295287i	$-0.904585\pi$
$587$		−	14.3085i		−	0.590575i	0.955408	−	0.295287i	$-0.0954154\pi$
$588$	21.7743	−	18.7437i	0.897958	−	0.772979i
$589$		−	3.73069i		−	0.153720i
$590$		−	5.46894i		−	0.225153i
$591$	−39.8786			−1.64039
$592$	4.11218			0.169010
$593$	−31.8607			−1.30836			−0.654181	−	0.756338i	$-0.726987\pi$
$593$	−31.8607			−1.30836			−0.654181	+	0.756338i	$0.726987\pi$
$594$		0			0
$595$	−35.6251	−	16.3396i	−1.46049	−	0.669859i
$596$		−	11.6238i		−	0.476130i
$597$	−58.2114			−2.38243
$598$			2.11808i			0.0866147i
$599$	22.5485			0.921307			0.460653	−	0.887580i	$-0.347615\pi$
$599$	22.5485			0.921307			0.460653	+	0.887580i	$0.347615\pi$
$600$	−48.1232			−1.96462
$601$	−28.9546			−1.18108			−0.590542	−	0.807007i	$-0.701086\pi$
$601$	−28.9546			−1.18108			−0.590542	+	0.807007i	$0.701086\pi$
$602$	−1.28539	+	2.80252i	−0.0523884	+	0.114222i
$603$	−1.97693			−0.0805068
$604$			19.6949i			0.801374i
$605$		0			0
$606$	5.65123			0.229565
$607$	−28.4019			−1.15280			−0.576400	−	0.817168i	$-0.695543\pi$
$607$	−28.4019			−1.15280			−0.576400	+	0.817168i	$0.695543\pi$
$608$		−	7.19297i		−	0.291713i
$609$	−5.97673	+	13.0310i	−0.242189	+	0.528043i
$610$	−31.8893			−1.29116
$611$			7.53196i			0.304710i
$612$	−26.0618			−1.05348
$613$			17.0228i			0.687545i	0.939053	+	0.343773i	$0.111705\pi$
$613$			17.0228i			0.687545i	−0.939053	+	0.343773i	$0.888295\pi$
$614$			6.73012i			0.271606i
$615$	51.7571			2.08705
$616$		0			0
$617$	19.0794			0.768109			0.384055	−	0.923310i	$-0.374527\pi$
$617$	19.0794			0.768109			0.384055	+	0.923310i	$0.374527\pi$
$618$			17.3690i			0.698684i
$619$		−	22.6115i		−	0.908834i	−0.890789	−	0.454417i	$-0.849848\pi$
$619$		−	22.6115i		−	0.908834i	0.890789	−	0.454417i	$-0.150152\pi$
$620$	16.4524			0.660742
$621$		−	7.84438i		−	0.314784i
$622$	−12.5944			−0.504991
$623$	−5.55488	−	2.54777i	−0.222552	−	0.102074i
$624$		−	4.35601i		−	0.174380i
$625$	−5.22633			−0.209053
$626$	−3.55649			−0.142146
$627$		0			0
$628$		−	23.6145i		−	0.942320i
$629$	11.5261			0.459578
$630$	10.6328	−	23.1826i	0.423622	−	0.923619i
$631$	−6.59183			−0.262417			−0.131208	−	0.991355i	$-0.541886\pi$
$631$	−6.59183			−0.262417			−0.131208	+	0.991355i	$0.541886\pi$
$632$	29.6743			1.18038
$633$	38.1174			1.51503
$634$			19.3463i			0.768338i
$635$	−21.7597			−0.863505
$636$			4.43212i			0.175745i
$637$	5.03716	+	5.85159i	0.199580	+	0.231848i
$638$		0			0
$639$	−41.1936			−1.62959
$640$	38.8328			1.53500
$641$	10.3555			0.409017			0.204509	−	0.978865i	$-0.434440\pi$
$641$	10.3555			0.409017			0.204509	+	0.978865i	$0.434440\pi$
$642$		−	18.8405i		−	0.743576i
$643$		−	29.1774i		−	1.15065i	−0.817926	−	0.575323i	$-0.804876\pi$
$643$		−	29.1774i		−	1.15065i	0.817926	−	0.575323i	$-0.195124\pi$
$644$	−4.87108	+	10.6204i	−0.191948	+	0.418502i
$645$		−	16.3093i		−	0.642180i
$646$		−	3.49706i		−	0.137590i
$647$			1.57539i			0.0619349i	0.999520	+	0.0309675i	$0.00985882\pi$
$647$			1.57539i			0.0619349i	−0.999520	+	0.0309675i	$0.990141\pi$
$648$			11.4990i			0.451723i
$649$		0			0
$650$		−	5.64109i		−	0.221262i
$651$	−8.76363	+	19.1073i	−0.343474	+	0.748873i
$652$	32.5461			1.27461
$653$	14.5691			0.570134			0.285067	−	0.958508i	$-0.407984\pi$
$653$	14.5691			0.570134			0.285067	+	0.958508i	$0.407984\pi$
$654$			5.43766i			0.212629i
$655$			66.8387i			2.61160i
$656$	−8.18350			−0.319512
$657$	−50.5632			−1.97266
$658$	5.06763	−	11.0489i	0.197557	−	0.430731i
$659$			28.4616i			1.10871i	0.832281	+	0.554353i	$0.187034\pi$
$659$			28.4616i			1.10871i	−0.832281	+	0.554353i	$0.812966\pi$
$660$		0			0
$661$		−	32.7887i		−	1.27533i	−0.770313	−	0.637666i	$-0.779900\pi$
$661$		−	32.7887i		−	1.27533i	0.770313	−	0.637666i	$-0.220100\pi$
$662$		−	8.22626i		−	0.319723i
$663$		−	12.2096i		−	0.474181i
$664$		−	3.86314i		−	0.149919i
$665$	−10.6328	−	4.87679i	−0.412323	−	0.189114i
$666$			7.50051i			0.290639i
$667$		−	5.83027i		−	0.225749i
$668$	12.9062			0.499356
$669$	−47.0099			−1.81751
$670$	1.16985			0.0451951
$671$		0			0
$672$	−16.8967	+	36.8398i	−0.651806	+	1.42113i
$673$		−	10.2694i		−	0.395858i	−0.980216	−	0.197929i	$-0.936579\pi$
$673$		−	10.2694i		−	0.395858i	0.980216	−	0.197929i	$-0.0634215\pi$
$674$	24.2780			0.935153
$675$			20.8920i			0.804132i
$676$	−18.2326			−0.701256
$677$	−35.0099			−1.34554			−0.672769	−	0.739852i	$-0.734895\pi$
$677$	−35.0099			−1.34554			−0.672769	+	0.739852i	$0.734895\pi$
$678$	12.9517			0.497408
$679$	−30.4654	−	13.9731i	−1.16916	−	0.536238i
$680$	35.3559			1.35584
$681$		−	10.8790i		−	0.416885i
$682$		0			0
$683$	−18.0603			−0.691059			−0.345529	−	0.938408i	$-0.612301\pi$
$683$	−18.0603			−0.691059			−0.345529	+	0.938408i	$0.612301\pi$
$684$	−7.77850			−0.297418
$685$		−	10.5053i		−	0.401388i
$686$	−3.45215	−	11.9730i	−0.131804	−	0.457131i
$687$	−25.9986			−0.991907
$688$			2.57873i			0.0983131i
$689$	−1.19108			−0.0453765
$690$			18.0818i			0.688363i
$691$		−	23.6161i		−	0.898398i	−0.893432	−	0.449199i	$-0.851709\pi$
$691$		−	23.6161i		−	0.898398i	0.893432	−	0.449199i	$-0.148291\pi$
$692$	−24.8481			−0.944585
$693$		0			0
$694$	−18.5086			−0.702577
$695$		−	52.4434i		−	1.98929i
$696$		−	12.9325i		−	0.490206i
$697$	−22.9378			−0.868830
$698$			9.50453i			0.359752i
$699$	0.270461			0.0102298
$700$	12.9732	−	28.2853i	0.490340	−	1.06908i
$701$		−	36.7279i		−	1.38719i	−0.720363	−	0.693597i	$-0.756025\pi$
$701$		−	36.7279i		−	1.38719i	0.720363	−	0.693597i	$-0.243975\pi$
$702$	2.03968			0.0769828
$703$	3.44014			0.129747
$704$		0			0
$705$			64.2995i			2.42166i
$706$	−5.54373			−0.208641
$707$	−3.49265	+	7.61500i	−0.131355	+	0.286391i
$708$	9.39822			0.353207
$709$	−25.4613			−0.956219			−0.478109	−	0.878300i	$-0.658678\pi$
$709$	−25.4613			−0.956219			−0.478109	+	0.878300i	$0.658678\pi$
$710$	24.3763			0.914826
$711$		−	50.1823i		−	1.88198i
$712$	5.51290			0.206605
$713$		−	8.54889i		−	0.320158i
$714$	−8.21481	+	17.9107i	−0.307431	+	0.670290i
$715$		0			0
$716$	11.4009			0.426071
$717$	16.2755			0.607820
$718$	20.1335			0.751375
$719$		−	30.5473i		−	1.13922i	−0.821914	−	0.569612i	$-0.807094\pi$
$719$		−	30.5473i		−	1.13922i	0.821914	−	0.569612i	$-0.192906\pi$
$720$		−	21.3315i		−	0.794976i
$721$	−23.4047	−	10.7346i	−0.871635	−	0.399779i
$722$			11.7398i			0.436909i
$723$			11.4474i			0.425735i
$724$		−	22.4030i		−	0.832602i
$725$			15.5278i			0.576688i
$726$		0			0
$727$		−	2.80772i		−	0.104133i	−0.998644	−	0.0520663i	$-0.983419\pi$
$727$		−	2.80772i		−	0.104133i	0.998644	−	0.0520663i	$-0.0165807\pi$
$728$	−6.33088	−	2.90368i	−0.234638	−	0.107618i
$729$	41.3174			1.53028
$730$	29.9207			1.10742
$731$			7.22799i			0.267337i
$732$		−	54.8008i		−	2.02549i
$733$	−6.75560			−0.249524			−0.124762	−	0.992187i	$-0.539817\pi$
$733$	−6.75560			−0.249524			−0.124762	+	0.992187i	$0.539817\pi$
$734$	−3.11829			−0.115098
$735$	43.0017	+	49.9544i	1.58614	+	1.84259i
$736$		−	16.4827i		−	0.607561i
$737$		0			0
$738$		−	14.9265i		−	0.549452i
$739$			12.6084i			0.463809i	0.972739	+	0.231905i	$0.0744957\pi$
$739$			12.6084i			0.463809i	−0.972739	+	0.231905i	$0.925504\pi$
$740$			15.1710i			0.557698i
$741$		−	3.64412i		−	0.133870i
$742$	1.74724	+	0.801378i	0.0641431	+	0.0294195i
$743$			7.01399i			0.257318i	0.991689	+	0.128659i	$0.0410673\pi$
$743$			7.01399i			0.257318i	−0.991689	+	0.128659i	$0.958933\pi$
$744$		−	18.9629i		−	0.695213i
$745$	26.6672			0.977010
$746$	10.2741			0.376160
$747$	−6.53298			−0.239029
$748$		0			0
$749$	25.3875	+	11.6441i	0.927639	+	0.425465i
$750$		−	16.4805i		−	0.601782i
$751$	8.92542			0.325693			0.162847	−	0.986651i	$-0.447932\pi$
$751$	8.92542			0.325693			0.162847	+	0.986651i	$0.447932\pi$
$752$		−	10.1666i		−	0.370738i
$753$	81.4184			2.96705
$754$	1.51598			0.0552086
$755$	−45.1838			−1.64441
$756$	10.2273	+	4.69078i	0.371962	+	0.170602i
$757$	28.3234			1.02943			0.514716	−	0.857361i	$-0.327897\pi$
$757$	28.3234			1.02943			0.514716	+	0.857361i	$0.327897\pi$
$758$		−	15.3127i		−	0.556183i
$759$		0			0
$760$	10.5525			0.382778
$761$	7.02091			0.254508			0.127254	−	0.991870i	$-0.459384\pi$
$761$	7.02091			0.254508			0.127254	+	0.991870i	$0.459384\pi$
$762$			10.9398i			0.396305i
$763$	−7.32721	−	3.36066i	−0.265263	−	0.121664i
$764$	2.45937			0.0889770
$765$		−	59.7905i		−	2.16173i
$766$	19.4542			0.702908
$767$			2.52566i			0.0911963i
$768$		−	24.3400i		−	0.878295i
$769$	−27.4453			−0.989703			−0.494851	−	0.868978i	$-0.664778\pi$
$769$	−27.4453			−0.989703			−0.494851	+	0.868978i	$0.664778\pi$
$770$		0			0
$771$	−17.8590			−0.643177
$772$		−	17.3348i		−	0.623893i
$773$			28.6264i			1.02962i	0.857305	+	0.514809i	$0.172137\pi$
$773$			28.6264i			1.02962i	−0.857305	+	0.514809i	$0.827863\pi$
$774$	−4.70353			−0.169065
$775$			22.7683i			0.817861i
$776$	30.2352			1.08538
$777$	−17.6192	−	8.08111i	−0.632085	−	0.289908i
$778$			14.7794i			0.529868i
$779$	−6.84609			−0.245287
$780$	16.0706			0.575419
$781$		0			0
$782$		−	8.01352i		−	0.286563i
$783$	−5.61447			−0.200645
$784$	−6.79915	−	7.89846i	−0.242827	−	0.282088i
$785$	54.1760			1.93363
$786$	33.6034			1.19860
$787$	−7.62353			−0.271749			−0.135875	−	0.990726i	$-0.543384\pi$
$787$	−7.62353			−0.271749			−0.135875	+	0.990726i	$0.543384\pi$
$788$			23.2623i			0.828684i
$789$	64.8449			2.30854
$790$			29.6954i			1.05651i
$791$	−8.00460	+	17.4524i	−0.284611	+	0.620535i
$792$		0			0
$793$	14.7271			0.522973
$794$	2.03196			0.0721114
$795$	−10.1681			−0.360626
$796$			33.9563i			1.20355i
$797$			34.7434i			1.23067i	0.788264	+	0.615337i	$0.210980\pi$
$797$			34.7434i			1.23067i	−0.788264	+	0.615337i	$0.789020\pi$
$798$	−2.45182	+	5.34569i	−0.0867936	+	0.189235i
$799$		−	28.4963i		−	1.00813i
$800$			43.8985i			1.55205i
$801$		−	9.32290i		−	0.329408i
$802$		−	5.30453i		−	0.187309i
$803$		0			0
$804$			2.01035i			0.0708995i
$805$	−24.3651	−	11.1752i	−0.858758	−	0.393873i
$806$	2.22286			0.0782971
$807$	67.1629			2.36425
$808$		−	7.55745i		−	0.265870i
$809$		−	22.4247i		−	0.788412i	−0.919022	−	0.394206i	$-0.871020\pi$
$809$		−	22.4247i		−	0.788412i	0.919022	−	0.394206i	$-0.128980\pi$
$810$	−11.5071			−0.404320
$811$	19.5492			0.686464			0.343232	−	0.939251i	$-0.388478\pi$
$811$	19.5492			0.686464			0.343232	+	0.939251i	$0.388478\pi$
$812$	7.60134	+	3.48639i	0.266755	+	0.122348i
$813$		−	72.5238i		−	2.54352i
$814$		0			0
$815$			74.6669i			2.61547i
$816$			16.4805i			0.576932i
$817$			2.15729i			0.0754742i
$818$		−	17.8609i		−	0.624493i
$819$	−4.91043	+	10.7062i	−0.171584	+	0.374104i
$820$		−	30.1913i		−	1.05433i
$821$			18.3901i			0.641818i	0.947110	+	0.320909i	$0.103988\pi$
$821$			18.3901i			0.641818i	−0.947110	+	0.320909i	$0.896012\pi$
$822$	−5.28160			−0.184217
$823$	22.2604			0.775950			0.387975	−	0.921670i	$-0.373175\pi$
$823$	22.2604			0.775950			0.387975	+	0.921670i	$0.373175\pi$
$824$	23.2278			0.809178
$825$		0			0
$826$	1.69931	−	3.70498i	0.0591264	−	0.128913i
$827$			46.5155i			1.61750i	0.588151	+	0.808751i	$0.299856\pi$
$827$			46.5155i			1.61750i	−0.588151	+	0.808751i	$0.700144\pi$
$828$	−17.8245			−0.619442
$829$		−	20.7816i		−	0.721776i	−0.932609	−	0.360888i	$-0.882474\pi$
$829$		−	20.7816i		−	0.721776i	0.932609	−	0.360888i	$-0.117526\pi$
$830$	3.86589			0.134187
$831$	59.4680			2.06292
$832$	1.00144			0.0347186
$833$	−19.0575	−	22.1388i	−0.660304	−	0.767065i
$834$	−26.3661			−0.912984
$835$			29.6092i			1.02467i
$836$		0			0
$837$	−8.23245			−0.284555
$838$	4.90124			0.169311
$839$		−	7.54175i		−	0.260370i	−0.991490	−	0.130185i	$-0.958443\pi$
$839$		−	7.54175i		−	0.260370i	0.991490	−	0.130185i	$-0.0415571\pi$
$840$	−54.0460	−	24.7884i	−1.86476	−	0.855282i
$841$	24.8271			0.856107
$842$			16.0158i			0.551940i
$843$	−57.0760			−1.96580
$844$		−	22.2349i		−	0.765358i
$845$		−	41.8291i		−	1.43896i
$846$	18.5436			0.637544
$847$		0			0
$848$	1.60772			0.0552092
$849$			82.0793i			2.81696i
$850$			21.3424i			0.732039i
$851$	7.88309			0.270229
$852$			41.8900i			1.43513i
$853$	1.58216			0.0541720			0.0270860	−	0.999633i	$-0.491377\pi$
$853$	1.58216			0.0541720			0.0270860	+	0.999633i	$0.491377\pi$
$854$	−21.6037	−	9.90860i	−0.739262	−	0.339065i
$855$		−	17.8453i		−	0.610297i
$856$	−25.1956			−0.861169
$857$	52.3232			1.78733			0.893664	−	0.448737i	$-0.148126\pi$
$857$	52.3232			1.78733			0.893664	+	0.448737i	$0.148126\pi$
$858$		0			0
$859$		−	7.18932i		−	0.245296i	−0.992450	−	0.122648i	$-0.960861\pi$
$859$		−	7.18932i		−	0.245296i	0.992450	−	0.122648i	$-0.0391387\pi$
$860$	−9.51368			−0.324414
$861$	35.0633	+	16.0819i	1.19495	+	0.548070i
$862$	−0.430876			−0.0146757
$863$	−43.8560			−1.49288			−0.746438	−	0.665455i	$-0.768238\pi$
$863$	−43.8560			−1.49288			−0.746438	+	0.665455i	$0.768238\pi$
$864$	−15.8726			−0.539997
$865$		−	57.0063i		−	1.93827i
$866$	−11.5869			−0.393738
$867$			1.09982i			0.0373519i
$868$	11.1458	+	5.11206i	0.378313	+	0.173515i
$869$		0			0
$870$	12.9417			0.438765
$871$	−0.540257			−0.0183059
$872$	7.27184			0.246256
$873$		−	51.1309i		−	1.73052i
$874$		−	2.39175i		−	0.0809020i
$875$	22.2073	+	10.1855i	0.750745	+	0.344332i
$876$			51.4179i			1.73725i
$877$			14.3775i			0.485494i	0.970090	+	0.242747i	$0.0780484\pi$
$877$			14.3775i			0.485494i	−0.970090	+	0.242747i	$0.921952\pi$
$878$		−	0.0256535i		−	0.000865765i
$879$			65.9190i			2.22339i
$880$		0			0
$881$		−	2.45261i		−	0.0826304i	−0.999146	−	0.0413152i	$-0.986845\pi$
$881$		−	2.45261i		−	0.0826304i	0.999146	−	0.0413152i	$-0.0131548\pi$
$882$	14.4066	−	12.4015i	0.485095	−	0.417579i
$883$	4.78704			0.161097			0.0805484	−	0.996751i	$-0.474333\pi$
$883$	4.78704			0.161097			0.0805484	+	0.996751i	$0.474333\pi$
$884$	−7.12218			−0.239545
$885$			21.5613i			0.724774i
$886$		−	20.6165i		−	0.692624i
$887$	35.8413			1.20343			0.601717	−	0.798709i	$-0.294483\pi$
$887$	35.8413			1.20343			0.601717	+	0.798709i	$0.294483\pi$
$888$	17.4860			0.586793
$889$	−14.7413	−	6.76114i	−0.494406	−	0.226761i
$890$			5.51682i			0.184924i
$891$		0			0
$892$			27.4221i			0.918161i
$893$		−	8.50512i		−	0.284613i
$894$		−	13.4070i		−	0.448399i
$895$			26.1558i			0.874291i
$896$	26.3076	+	12.0661i	0.878876	+	0.403100i
$897$		−	8.35052i		−	0.278816i
$898$			19.8627i			0.662828i
$899$	−6.11870			−0.204070
$900$	47.4719			1.58240
$901$	4.50631			0.150127
$902$		0			0
$903$	5.06763	−	11.0489i	0.168640	−	0.367685i
$904$		−	17.3205i		−	0.576071i
$905$	51.3967			1.70849
$906$			22.7163i			0.754700i
$907$	7.18813			0.238678			0.119339	−	0.992854i	$-0.461922\pi$
$907$	7.18813			0.238678			0.119339	+	0.992854i	$0.461922\pi$
$908$	−6.34603			−0.210601
$909$	−12.7804			−0.423900
$910$	2.90575	−	6.33538i	0.0963245	−	0.210016i
$911$	20.0130			0.663060			0.331530	−	0.943445i	$-0.392435\pi$
$911$	20.0130			0.663060			0.331530	+	0.943445i	$0.392435\pi$
$912$			4.91883i			0.162879i
$913$		0			0
$914$	2.85803			0.0945354
$915$	125.723			4.15628
$916$			15.1657i			0.501088i
$917$	−20.7681	+	45.2805i	−0.685822	+	1.49529i
$918$	−7.71690			−0.254696
$919$			3.54390i			0.116903i	0.998290	+	0.0584513i	$0.0186162\pi$
$919$			3.54390i			0.116903i	−0.998290	+	0.0584513i	$0.981384\pi$
$920$	24.1810			0.797224
$921$		−	26.5335i		−	0.874307i
$922$		−	8.00182i		−	0.263526i
$923$	−11.2574			−0.370543
$924$		0			0
$925$	−20.9951			−0.690314
$926$		−	19.8486i		−	0.652265i
$927$		−	39.2806i		−	1.29014i
$928$	−11.7972			−0.387262
$929$			27.2210i			0.893092i	0.894761	+	0.446546i	$0.147346\pi$
$929$			27.2210i			0.893092i	−0.894761	+	0.446546i	$0.852654\pi$
$930$	18.9763			0.622259
$931$	−5.68798	−	6.60764i	−0.186416	−	0.216557i
$932$		−	0.157767i		−	0.00516784i
$933$	49.6535			1.62558
$934$	−7.50122			−0.245447
$935$		0			0
$936$		−	10.6253i		−	0.347298i
$937$	−47.9616			−1.56684			−0.783418	−	0.621495i	$-0.786526\pi$
$937$	−47.9616			−1.56684			−0.783418	+	0.621495i	$0.786526\pi$
$938$	0.792523	+	0.363494i	0.0258768	+	0.0118685i
$939$	14.0214			0.457573
$940$	37.5076			1.22336
$941$	−10.4613			−0.341028			−0.170514	−	0.985355i	$-0.554543\pi$
$941$	−10.4613			−0.341028			−0.170514	+	0.985355i	$0.554543\pi$
$942$		−	27.2372i		−	0.887437i
$943$	−15.6879			−0.510867
$944$		−	3.40913i		−	0.110958i
$945$	−10.7615	+	23.4633i	−0.350073	+	0.763260i
$946$		0			0
$947$	−31.5419			−1.02497			−0.512487	−	0.858695i	$-0.671276\pi$
$947$	−31.5419			−1.02497			−0.512487	+	0.858695i	$0.671276\pi$
$948$	−51.0306			−1.65740
$949$	−13.8180			−0.448550
$950$			6.36994i			0.206668i
$951$		−	76.2725i		−	2.47330i
$952$	23.9522	+	10.9858i	0.776294	+	0.356051i
$953$			3.69767i			0.119779i	0.998205	+	0.0598897i	$0.0190749\pi$
$953$			3.69767i			0.119779i	−0.998205	+	0.0598897i	$0.980925\pi$
$954$			2.93243i			0.0949410i
$955$			5.64226i			0.182579i
$956$		−	9.49395i		−	0.307056i
$957$		0			0
$958$		−	7.62407i		−	0.246323i
$959$	3.26421	−	7.11693i	0.105407	−	0.229818i
$960$	8.54916			0.275923
$961$	22.0282			0.710587
$962$			2.04975i			0.0660865i
$963$			42.6084i			1.37304i
$964$	6.67760			0.215071
$965$	39.7693			1.28022
$966$	−5.61836	+	12.2497i	−0.180768	+	0.394127i
$967$		−	22.8572i		−	0.735038i	−0.930016	−	0.367519i	$-0.880207\pi$
$967$		−	22.8572i		−	0.735038i	0.930016	−	0.367519i	$-0.119793\pi$
$968$		0			0
$969$			13.7871i			0.442906i
$970$			30.2567i			0.971483i
$971$		−	1.02730i		−	0.0329675i	−0.999864	−	0.0164837i	$-0.994753\pi$
$971$		−	1.02730i		−	0.0329675i	0.999864	−	0.0164837i	$-0.00524718\pi$
$972$		−	32.5329i		−	1.04349i
$973$	16.2952	−	35.5282i	0.522399	−	1.13898i
$974$		−	10.4326i		−	0.334282i
$975$			22.2400i			0.712249i
$976$	−19.8785			−0.636297
$977$	20.2745			0.648638			0.324319	−	0.945948i	$-0.394865\pi$
$977$	20.2745			0.648638			0.324319	+	0.945948i	$0.394865\pi$
$978$	37.5391			1.20037
$979$		0			0
$980$	29.1397	−	25.0840i	0.930834	−	0.801280i
$981$		−	12.2974i		−	0.392627i
$982$	−7.00320			−0.223481
$983$		−	19.6549i		−	0.626894i	−0.949606	−	0.313447i	$-0.898516\pi$
$983$		−	19.6549i		−	0.626894i	0.949606	−	0.313447i	$-0.101484\pi$
$984$	−34.7983			−1.10933
$985$	−53.3680			−1.70044
$986$	−5.73552			−0.182656
$987$	−19.9791	+	43.5602i	−0.635941	+	1.38654i
$988$	−2.12571			−0.0676280
$989$			4.94345i			0.157193i
$990$		0			0
$991$	12.4581			0.395744			0.197872	−	0.980228i	$-0.436597\pi$
$991$	12.4581			0.395744			0.197872	+	0.980228i	$0.436597\pi$
$992$	−17.2981			−0.549216
$993$			32.4320i			1.02920i
$994$	16.5139	+	7.57418i	0.523790	+	0.240238i
$995$	−77.9021			−2.46966
$996$			6.64341i			0.210505i
$997$	20.0672			0.635533			0.317767	−	0.948169i	$-0.397067\pi$
$997$	20.0672			0.635533			0.317767	+	0.948169i	$0.397067\pi$
$998$			15.6221i			0.494509i
$999$		−	7.59130i		−	0.240178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.b.f.846.6		16
7.6	odd	2	inner	847.2.b.f.846.5		16
11.2	odd	10		847.2.l.i.524.2		16
11.3	even	5		847.2.l.e.475.3		16
11.4	even	5		847.2.l.j.699.2		16
11.5	even	5		847.2.l.i.118.1		16
11.6	odd	10		77.2.l.b.41.3	✓	16
11.7	odd	10		847.2.l.e.699.4		16
11.8	odd	10		847.2.l.j.475.1		16
11.9	even	5		77.2.l.b.62.4	yes	16
11.10	odd	2	inner	847.2.b.f.846.12		16
33.17	even	10		693.2.bu.d.118.1		16
33.20	odd	10		693.2.bu.d.370.2		16
77.6	even	10		77.2.l.b.41.4	yes	16
77.9	even	15		539.2.s.b.227.1		16
77.13	even	10		847.2.l.i.524.1		16
77.17	even	30		539.2.s.b.19.1		16
77.20	odd	10		77.2.l.b.62.3	yes	16
77.27	odd	10		847.2.l.i.118.2		16
77.31	odd	30		539.2.s.c.117.2		16
77.39	odd	30		539.2.s.b.19.2		16
77.41	even	10		847.2.l.j.475.2		16
77.48	odd	10		847.2.l.j.699.1		16
77.53	even	15		539.2.s.c.117.1		16
77.61	even	30		539.2.s.c.129.1		16
77.62	even	10		847.2.l.e.699.3		16
77.69	odd	10		847.2.l.e.475.4		16
77.72	odd	30		539.2.s.c.129.2		16
77.75	odd	30		539.2.s.b.227.2		16
77.76	even	2	inner	847.2.b.f.846.11		16
231.20	even	10		693.2.bu.d.370.1		16
231.83	odd	10		693.2.bu.d.118.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.l.b.41.3	✓	16	11.6	odd	10
77.2.l.b.41.4	yes	16	77.6	even	10
77.2.l.b.62.3	yes	16	77.20	odd	10
77.2.l.b.62.4	yes	16	11.9	even	5
539.2.s.b.19.1		16	77.17	even	30
539.2.s.b.19.2		16	77.39	odd	30
539.2.s.b.227.1		16	77.9	even	15
539.2.s.b.227.2		16	77.75	odd	30
539.2.s.c.117.1		16	77.53	even	15
539.2.s.c.117.2		16	77.31	odd	30
539.2.s.c.129.1		16	77.61	even	30
539.2.s.c.129.2		16	77.72	odd	30
693.2.bu.d.118.1		16	33.17	even	10
693.2.bu.d.118.2		16	231.83	odd	10
693.2.bu.d.370.1		16	231.20	even	10
693.2.bu.d.370.2		16	33.20	odd	10
847.2.b.f.846.5		16	7.6	odd	2	inner
847.2.b.f.846.6		16	1.1	even	1	trivial
847.2.b.f.846.11		16	77.76	even	2	inner
847.2.b.f.846.12		16	11.10	odd	2	inner
847.2.l.e.475.3		16	11.3	even	5
847.2.l.e.475.4		16	77.69	odd	10
847.2.l.e.699.3		16	77.62	even	10
847.2.l.e.699.4		16	11.7	odd	10
847.2.l.i.118.1		16	11.5	even	5
847.2.l.i.118.2		16	77.27	odd	10
847.2.l.i.524.1		16	77.13	even	10
847.2.l.i.524.2		16	11.2	odd	10
847.2.l.j.475.1		16	11.8	odd	10
847.2.l.j.475.2		16	77.41	even	10
847.2.l.j.699.1		16	77.48	odd	10
847.2.l.j.699.2		16	11.4	even	5

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.672816i q^{2} +2.65257i q^{3} +1.54732 q^{4} +3.54984i q^{5} +1.78470 q^{6} +(-1.10300 + 2.40487i) q^{7} -2.38669i q^{8} -4.03615 q^{9} +O(q^{10})\)	\(q-0.672816i q^{2} +2.65257i q^{3} +1.54732 q^{4} +3.54984i q^{5} +1.78470 q^{6} +(-1.10300 + 2.40487i) q^{7} -2.38669i q^{8} -4.03615 q^{9} +2.38839 q^{10} +4.10438i q^{12} -1.10300 q^{13} +(1.61803 + 0.742118i) q^{14} -9.41620 q^{15} +1.48883 q^{16} +4.17308 q^{17} +2.71559i q^{18} +1.24551 q^{19} +5.49273i q^{20} +(-6.37909 - 2.92579i) q^{21} +2.85410 q^{23} +6.33088 q^{24} -7.60134 q^{25} +0.742118i q^{26} -2.74846i q^{27} +(-1.70670 + 3.72109i) q^{28} -2.04277i q^{29} +6.33538i q^{30} -2.99530i q^{31} -5.77510i q^{32} -2.80772i q^{34} +(-8.53689 - 3.91548i) q^{35} -6.24520 q^{36} +2.76202 q^{37} -0.838003i q^{38} -2.92579i q^{39} +8.47237 q^{40} -5.49660 q^{41} +(-1.96852 + 4.29195i) q^{42} +1.73205i q^{43} -14.3277i q^{45} -1.92029i q^{46} -6.82860i q^{47} +3.94923i q^{48} +(-4.56677 - 5.30515i) q^{49} +5.11431i q^{50} +11.0694i q^{51} -1.70670 q^{52} +1.07985 q^{53} -1.84921 q^{54} +(5.73968 + 2.63253i) q^{56} +3.30382i q^{57} -1.37441 q^{58} -2.28980i q^{59} -14.5699 q^{60} -13.3518 q^{61} -2.01529 q^{62} +(4.45188 - 9.70640i) q^{63} -0.907920 q^{64} -3.91548i q^{65} +0.489806 q^{67} +6.45709 q^{68} +7.57072i q^{69} +(-2.63440 + 5.74376i) q^{70} +10.2062 q^{71} +9.63305i q^{72} +12.5276 q^{73} -1.85833i q^{74} -20.1631i q^{75} +1.92721 q^{76} -1.96852 q^{78} +12.4332i q^{79} +5.28510i q^{80} -4.81795 q^{81} +3.69820i q^{82} +1.61862 q^{83} +(-9.87048 - 4.52714i) q^{84} +14.8138i q^{85} +1.16535 q^{86} +5.41860 q^{87} +2.30985i q^{89} -9.63989 q^{90} +(1.21661 - 2.65257i) q^{91} +4.41620 q^{92} +7.94525 q^{93} -4.59439 q^{94} +4.42137i q^{95} +15.3189 q^{96} +12.6682i q^{97} +(-3.56939 + 3.07260i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{9}+O(q^{10}) \) 16 * q - 32 * q^9	\( 16 q - 32 q^{9} + 8 q^{14} - 20 q^{15} + 16 q^{16} - 8 q^{23} - 40 q^{25} - 60 q^{36} - 36 q^{37} - 20 q^{42} + 48 q^{49} + 20 q^{53} - 4 q^{56} + 28 q^{58} - 140 q^{60} + 12 q^{64} - 4 q^{67} + 100 q^{70} + 44 q^{71} - 20 q^{78} - 56 q^{81} - 24 q^{86} + 80 q^{91} - 60 q^{92} - 20 q^{93}+O(q^{100}) \) 16 * q - 32 * q^9 + 8 * q^14 - 20 * q^15 + 16 * q^16 - 8 * q^23 - 40 * q^25 - 60 * q^36 - 36 * q^37 - 20 * q^42 + 48 * q^49 + 20 * q^53 - 4 * q^56 + 28 * q^58 - 140 * q^60 + 12 * q^64 - 4 * q^67 + 100 * q^70 + 44 * q^71 - 20 * q^78 - 56 * q^81 - 24 * q^86 + 80 * q^91 - 60 * q^92 - 20 * q^93

Introduction

L-functions

Modular forms

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Database

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