LMFDB - Embedded newform 847.2.b.f.846.1

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			846.1
Root			$-1.27939 - 2.21596i$ of defining polynomial
Character	$\chi$	$=$	847.846
Dual form			847.2.b.f.846.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40487i q^{2} -1.72158i q^{3} -3.78339 q^{4} +3.36793i q^{5} -4.14018 q^{6} +(2.55877 + 0.672816i) q^{7} +4.28881i q^{8} +0.0361478 q^{9} +O(q^{10})$	\(q-2.40487i q^{2} -1.72158i q^{3} -3.78339 q^{4} +3.36793i q^{5} -4.14018 q^{6} +(2.55877 + 0.672816i) q^{7} +4.28881i q^{8} +0.0361478 q^{9} +8.09942 q^{10} +6.51342i q^{12} +2.55877 q^{13} +(1.61803 - 6.15351i) q^{14} +5.79817 q^{15} +2.74724 q^{16} +3.95924 q^{17} -0.0869308i q^{18} +0.330604 q^{19} -12.7422i q^{20} +(1.15831 - 4.40514i) q^{21} +2.85410 q^{23} +7.38354 q^{24} -6.34293 q^{25} -6.15351i q^{26} -5.22698i q^{27} +(-9.68083 - 2.54552i) q^{28} +2.49180i q^{29} -13.9438i q^{30} -0.222436i q^{31} +1.97087i q^{32} -9.52144i q^{34} +(-2.26600 + 8.61776i) q^{35} -0.136761 q^{36} -8.38006 q^{37} -0.795060i q^{38} -4.40514i q^{39} -14.4444 q^{40} +9.53117 q^{41} +(-10.5938 - 2.78558i) q^{42} -1.73205i q^{43} +0.121743i q^{45} -6.86374i q^{46} -1.23993i q^{47} -4.72960i q^{48} +(6.09464 + 3.44317i) q^{49} +15.2539i q^{50} -6.81616i q^{51} -9.68083 q^{52} +0.302113 q^{53} -12.5702 q^{54} +(-2.88558 + 10.9741i) q^{56} -0.569163i q^{57} +5.99244 q^{58} -9.03006i q^{59} -21.9367 q^{60} +5.68376 q^{61} -0.534929 q^{62} +(0.0924941 + 0.0243209i) q^{63} +10.2342 q^{64} +8.61776i q^{65} -6.57998 q^{67} -14.9793 q^{68} -4.91358i q^{69} +(20.7246 + 5.44942i) q^{70} +5.35614 q^{71} +0.155031i q^{72} -6.99173 q^{73} +20.1529i q^{74} +10.9199i q^{75} -1.25080 q^{76} -10.5938 q^{78} +2.95520i q^{79} +9.25250i q^{80} -8.89025 q^{81} -22.9212i q^{82} +7.89509 q^{83} +(-4.38233 + 16.6664i) q^{84} +13.3344i q^{85} -4.16535 q^{86} +4.28984 q^{87} -3.66560i q^{89} +0.292776 q^{90} +(6.54732 + 1.72158i) q^{91} -10.7982 q^{92} -0.382942 q^{93} -2.98187 q^{94} +1.11345i q^{95} +3.39302 q^{96} +13.6379i q^{97} +(8.28036 - 14.6568i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.40487i		−	1.70050i	−0.526381	−	0.850249i	$-0.676451\pi$
$2$		−	2.40487i		−	1.70050i	0.526381	−	0.850249i	$-0.323549\pi$
$3$		−	1.72158i		−	0.993957i	−0.867763	−	0.496979i	$-0.834443\pi$
$3$		−	1.72158i		−	0.993957i	0.867763	−	0.496979i	$-0.165557\pi$
$4$	−3.78339			−1.89169
$5$			3.36793i			1.50618i	0.657916	+	0.753091i	$0.271438\pi$
$5$			3.36793i			1.50618i	−0.657916	+	0.753091i	$0.728562\pi$
$6$	−4.14018			−1.69022
$7$	2.55877	+	0.672816i	0.967125	+	0.254301i
$7$	2.55877	+	0.672816i	0.967125	+	0.254301i
$8$			4.28881i			1.51632i
$9$	0.0361478			0.0120493
$10$	8.09942			2.56126
$11$		0			0
$11$		0			0
$12$			6.51342i			1.88026i
$13$	2.55877			0.709676			0.354838	−	0.934928i	$-0.384536\pi$
$13$	2.55877			0.709676			0.354838	+	0.934928i	$0.384536\pi$
$14$	1.61803	−	6.15351i	0.432438	−	1.64459i
$15$	5.79817			1.49708
$16$	2.74724			0.686810
$17$	3.95924			0.960256			0.480128	−	0.877199i	$-0.340590\pi$
$17$	3.95924			0.960256			0.480128	+	0.877199i	$0.340590\pi$
$18$		−	0.0869308i		−	0.0204898i
$19$	0.330604			0.0758459			0.0379229	−	0.999281i	$-0.487926\pi$
$19$	0.330604			0.0758459			0.0379229	+	0.999281i	$0.487926\pi$
$20$		−	12.7422i		−	2.84924i
$21$	1.15831	−	4.40514i	0.252764	−	0.961281i
$22$		0			0
$23$	2.85410			0.595121			0.297561	−	0.954703i	$-0.403827\pi$
$23$	2.85410			0.595121			0.297561	+	0.954703i	$0.403827\pi$
$24$	7.38354			1.50716
$25$	−6.34293			−1.26859
$26$		−	6.15351i		−	1.20680i
$27$		−	5.22698i		−	1.00593i
$28$	−9.68083	−	2.54552i	−1.82950	−	0.481059i
$29$			2.49180i			0.462715i	0.972869	+	0.231358i	$0.0743167\pi$
$29$			2.49180i			0.462715i	−0.972869	+	0.231358i	$0.925683\pi$
$30$		−	13.9438i		−	2.54578i
$31$		−	0.222436i		−	0.0399507i	−0.999800	−	0.0199753i	$-0.993641\pi$
$31$		−	0.222436i		−	0.0399507i	0.999800	−	0.0199753i	$-0.00635877\pi$
$32$			1.97087i			0.348404i
$33$		0			0
$34$		−	9.52144i		−	1.63291i
$35$	−2.26600	+	8.61776i	−0.383023	+	1.45667i
$36$	−0.136761			−0.0227935
$37$	−8.38006			−1.37767			−0.688836	−	0.724917i	$-0.741878\pi$
$37$	−8.38006			−1.37767			−0.688836	+	0.724917i	$0.741878\pi$
$38$		−	0.795060i		−	0.128976i
$39$		−	4.40514i		−	0.705387i
$40$	−14.4444			−2.28386
$41$	9.53117			1.48852			0.744259	−	0.667891i	$-0.232803\pi$
$41$	9.53117			1.48852			0.744259	+	0.667891i	$0.232803\pi$
$42$	−10.5938	−	2.78558i	−1.63466	−	0.429825i
$43$		−	1.73205i		−	0.264135i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$		−	1.73205i		−	0.264135i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$		0			0
$45$			0.121743i			0.0181484i
$46$		−	6.86374i		−	1.01200i
$47$		−	1.23993i		−	0.180863i	−0.995903	−	0.0904313i	$-0.971175\pi$
$47$		−	1.23993i		−	0.180863i	0.995903	−	0.0904313i	$-0.0288246\pi$
$48$		−	4.72960i		−	0.682659i
$49$	6.09464	+	3.44317i	0.870662	+	0.491881i
$50$			15.2539i			2.15723i
$51$		−	6.81616i		−	0.954453i
$52$	−9.68083			−1.34249
$53$	0.302113			0.0414985			0.0207492	−	0.999785i	$-0.493395\pi$
$53$	0.302113			0.0414985			0.0207492	+	0.999785i	$0.493395\pi$
$54$	−12.5702			−1.71059
$55$		0			0
$56$	−2.88558	+	10.9741i	−0.385602	+	1.46647i
$57$		−	0.569163i		−	0.0753875i
$58$	5.99244			0.786846
$59$		−	9.03006i		−	1.17561i	−0.809001	−	0.587807i	$-0.799991\pi$
$59$		−	9.03006i		−	1.17561i	0.809001	−	0.587807i	$-0.200009\pi$
$60$	−21.9367			−2.83202
$61$	5.68376			0.727731			0.363866	−	0.931451i	$-0.381457\pi$
$61$	5.68376			0.727731			0.363866	+	0.931451i	$0.381457\pi$
$62$	−0.534929			−0.0679361
$63$	0.0924941	+	0.0243209i	0.0116532	+	0.00306414i
$64$	10.2342			1.27927
$65$			8.61776i			1.06890i
$66$		0			0
$67$	−6.57998			−0.803872			−0.401936	−	0.915668i	$-0.631663\pi$
$67$	−6.57998			−0.803872			−0.401936	+	0.915668i	$0.631663\pi$
$68$	−14.9793			−1.81651
$69$		−	4.91358i		−	0.591525i
$70$	20.7246	+	5.44942i	2.47706	+	0.651330i
$71$	5.35614			0.635656			0.317828	−	0.948148i	$-0.397046\pi$
$71$	5.35614			0.635656			0.317828	+	0.948148i	$0.397046\pi$
$72$			0.155031i			0.0182706i
$73$	−6.99173			−0.818320			−0.409160	−	0.912463i	$-0.634178\pi$
$73$	−6.99173			−0.818320			−0.409160	+	0.912463i	$0.634178\pi$
$74$			20.1529i			2.34273i
$75$			10.9199i			1.26092i
$76$	−1.25080			−0.143477
$77$		0			0
$78$	−10.5938			−1.19951
$79$			2.95520i			0.332486i	0.986085	+	0.166243i	$0.0531636\pi$
$79$			2.95520i			0.332486i	−0.986085	+	0.166243i	$0.946836\pi$
$80$			9.25250i			1.03446i
$81$	−8.89025			−0.987806
$82$		−	22.9212i		−	2.53122i
$83$	7.89509			0.866599			0.433299	−	0.901250i	$-0.357349\pi$
$83$	7.89509			0.866599			0.433299	+	0.901250i	$0.357349\pi$
$84$	−4.38233	+	16.6664i	−0.478152	+	1.81845i
$85$			13.3344i			1.44632i
$86$	−4.16535			−0.449161
$87$	4.28984			0.459919
$88$		0			0
$89$		−	3.66560i		−	0.388553i	−0.980947	−	0.194277i	$-0.937764\pi$
$89$		−	3.66560i		−	0.388553i	0.980947	−	0.194277i	$-0.0622359\pi$
$90$	0.292776			0.0308613
$91$	6.54732	+	1.72158i	0.686345	+	0.180471i
$92$	−10.7982			−1.12579
$93$	−0.382942			−0.0397093
$94$	−2.98187			−0.307557
$95$			1.11345i			0.114238i
$96$	3.39302			0.346299
$97$			13.6379i			1.38472i	0.721552	+	0.692361i	$0.243429\pi$
$97$			13.6379i			1.38472i	−0.721552	+	0.692361i	$0.756571\pi$
$98$	8.28036	−	14.6568i	0.836443	−	1.48056i
$99$		0			0
$100$	23.9978			2.39978
$101$	−10.5657			−1.05133			−0.525663	−	0.850693i	$-0.676183\pi$
$101$	−10.5657			−1.05133			−0.525663	+	0.850693i	$0.676183\pi$
$102$	−16.3920			−1.62305
$103$			17.7099i			1.74501i	0.488604	+	0.872506i	$0.337506\pi$
$103$			17.7099i			1.74501i	−0.488604	+	0.872506i	$0.662494\pi$
$104$			10.9741i			1.07610i
$105$	14.8362	+	3.90110i	1.44786	+	0.380709i
$106$		−	0.726543i		−	0.0705680i
$107$		−	18.1465i		−	1.75429i	−0.480227	−	0.877144i	$-0.659446\pi$
$107$		−	18.1465i		−	1.75429i	0.480227	−	0.877144i	$-0.340554\pi$
$108$			19.7757i			1.90292i
$109$		−	1.48774i		−	0.142500i	−0.997458	−	0.0712499i	$-0.977301\pi$
$109$		−	1.48774i		−	0.142500i	0.997458	−	0.0712499i	$-0.0226988\pi$
$110$		0			0
$111$			14.4270i			1.36935i
$112$	7.02956	+	1.84839i	0.664231	+	0.174656i
$113$	−11.5489			−1.08643			−0.543214	−	0.839594i	$-0.682793\pi$
$113$	−11.5489			−1.08643			−0.543214	+	0.839594i	$0.682793\pi$
$114$	−1.36876			−0.128196
$115$			9.61241i			0.896362i
$116$		−	9.42743i		−	0.875315i
$117$	0.0924941			0.00855108
$118$	−21.7161			−1.99913
$119$	10.1308	+	2.66384i	0.928687	+	0.244194i
$120$			24.8672i			2.27006i
$121$		0			0
$122$		−	13.6687i		−	1.23751i
$123$		−	16.4087i		−	1.47952i
$124$			0.841561i			0.0755745i
$125$		−	4.52290i		−	0.404540i
$126$	0.0584884	−	0.222436i	0.00521056	−	0.0198162i
$127$		−	10.9380i		−	0.970594i	−0.874349	−	0.485297i	$-0.838711\pi$
$127$		−	10.9380i		−	0.970594i	0.874349	−	0.485297i	$-0.161289\pi$
$128$		−	20.6700i		−	1.82699i
$129$	−2.98187			−0.262539
$130$	20.7246			1.81766
$131$	5.67097			0.495475			0.247737	−	0.968827i	$-0.420313\pi$
$131$	5.67097			0.495475			0.247737	+	0.968827i	$0.420313\pi$
$132$		0			0
$133$	0.845942	+	0.222436i	0.0733524	+	0.0192877i
$134$			15.8240i			1.36698i
$135$	17.6041			1.51512
$136$			16.9804i			1.45606i
$137$	−17.6931			−1.51162			−0.755811	−	0.654789i	$-0.772757\pi$
$137$	−17.6931			−1.51162			−0.755811	+	0.654789i	$0.772757\pi$
$138$	−11.8165			−1.00589
$139$	1.78169			0.151121			0.0755605	−	0.997141i	$-0.475925\pi$
$139$	1.78169			0.151121			0.0755605	+	0.997141i	$0.475925\pi$
$140$	8.57314	−	32.6043i	0.724562	−	2.75557i
$141$	−2.13465			−0.179770
$142$		−	12.8808i		−	1.08093i
$143$		0			0
$144$	0.0993067			0.00827556
$145$	−8.39219			−0.696934
$146$			16.8142i			1.39155i
$147$	5.92770	−	10.4924i	0.488909	−	0.865401i
$148$	31.7050			2.60613
$149$		−	14.0316i		−	1.14951i	−0.818326	−	0.574755i	$-0.805097\pi$
$149$		−	14.0316i		−	1.14951i	0.818326	−	0.574755i	$-0.194903\pi$
$150$	26.2609			2.14419
$151$		−	2.04228i		−	0.166198i	−0.996541	−	0.0830992i	$-0.973518\pi$
$151$		−	2.04228i		−	0.166198i	0.996541	−	0.0830992i	$-0.0264818\pi$
$152$			1.41790i			0.115007i
$153$	0.143118			0.0115704
$154$		0			0
$155$	0.749148			0.0601730
$156$			16.6664i			1.33438i
$157$		−	7.62188i		−	0.608293i	−0.952625	−	0.304146i	$-0.901629\pi$
$157$		−	7.62188i		−	0.608293i	0.952625	−	0.304146i	$-0.0983712\pi$
$158$	7.10686			0.565392
$159$		−	0.520114i		−	0.0412477i
$160$	−6.63775			−0.524760
$161$	7.30300	+	1.92029i	0.575557	+	0.151340i
$162$			21.3799i			1.67976i
$163$	−18.7978			−1.47236			−0.736180	−	0.676786i	$-0.763372\pi$
$163$	−18.7978			−1.47236			−0.736180	+	0.676786i	$0.763372\pi$
$164$	−36.0601			−2.81582
$165$		0			0
$166$		−	18.9866i		−	1.47365i
$167$	19.5804			1.51518			0.757589	−	0.652731i	$-0.226377\pi$
$167$	19.5804			1.51518			0.757589	+	0.652731i	$0.226377\pi$
$168$	18.8928	+	4.96777i	1.45761	+	0.383272i
$169$	−6.45268			−0.496360
$170$	32.0675			2.45946
$171$	0.0119506			0.000913888
$172$			6.55302i			0.499663i
$173$	−8.87650			−0.674868			−0.337434	−	0.941349i	$-0.609559\pi$
$173$	−8.87650			−0.674868			−0.337434	+	0.941349i	$0.609559\pi$
$174$		−	10.3165i		−	0.782091i
$175$	−16.2301	−	4.26763i	−1.22688	−	0.322602i
$176$		0			0
$177$	−15.5460			−1.16851
$178$	−8.81529			−0.660734
$179$	8.92364			0.666984			0.333492	−	0.942753i	$-0.391773\pi$
$179$	8.92364			0.666984			0.333492	+	0.942753i	$0.391773\pi$
$180$		−	0.460602i		−	0.0343312i
$181$			12.0749i			0.897517i	0.893653	+	0.448759i	$0.148134\pi$
$181$			12.0749i			0.897517i	−0.893653	+	0.448759i	$0.851866\pi$
$182$	4.14018	−	15.7454i	0.306891	−	1.16713i
$183$		−	9.78507i		−	0.723334i
$184$			12.2407i			0.902396i
$185$		−	28.2234i		−	2.07503i
$186$			0.920926i			0.0675255i
$187$		0			0
$188$			4.69114i			0.342137i
$189$	3.51680	−	13.3747i	0.255810	−	0.972864i
$190$	2.67770			0.194261
$191$	13.0286			0.942716			0.471358	−	0.881942i	$-0.343764\pi$
$191$	13.0286			0.942716			0.471358	+	0.881942i	$0.343764\pi$
$192$		−	17.6190i		−	1.27154i
$193$			13.1052i			0.943336i	0.881776	+	0.471668i	$0.156348\pi$
$193$			13.1052i			0.943336i	−0.881776	+	0.471668i	$0.843652\pi$
$194$	32.7974			2.35472
$195$	14.8362			1.06244
$196$	−23.0584	−	13.0268i	−1.64703	−	0.930488i
$197$		−	5.90687i		−	0.420847i	−0.977610	−	0.210424i	$-0.932516\pi$
$197$		−	5.90687i		−	0.420847i	0.977610	−	0.210424i	$-0.0674843\pi$
$198$		0			0
$199$			7.10548i			0.503694i	0.967767	+	0.251847i	$0.0810380\pi$
$199$			7.10548i			0.503694i	−0.967767	+	0.251847i	$0.918962\pi$
$200$		−	27.2036i		−	1.92359i
$201$			11.3280i			0.799014i
$202$			25.4091i			1.78778i
$203$	−1.67652	+	6.37594i	−0.117669	+	0.447504i
$204$			25.7882i			1.80553i
$205$			32.1003i			2.24198i
$206$	42.5900			2.96739
$207$	0.103170			0.00717078
$208$	7.02956			0.487412
$209$		0			0
$210$	9.38164	−	35.6791i	0.647394	−	2.46209i
$211$		−	0.357401i		−	0.0246045i	−0.999924	−	0.0123023i	$-0.996084\pi$
$211$		−	0.357401i		−	0.0246045i	0.999924	−	0.0123023i	$-0.00391603\pi$
$212$	−1.14301			−0.0785024
$213$		−	9.22104i		−	0.631815i
$214$	−43.6399			−2.98316
$215$	5.83342			0.397836
$216$	22.4175			1.52532
$217$	0.149659	−	0.569163i	0.0101595	−	0.0386373i
$218$	−3.57782			−0.242320
$219$			12.0369i			0.813375i
$220$		0			0
$221$	10.1308			0.681470
$222$	34.6950			2.32857
$223$		−	7.99684i		−	0.535508i	−0.963487	−	0.267754i	$-0.913719\pi$
$223$		−	7.99684i		−	0.535508i	0.963487	−	0.267754i	$-0.0862814\pi$
$224$	−1.32603	+	5.04301i	−0.0885994	+	0.336950i
$225$	−0.229283			−0.0152856
$226$			27.7736i			1.84747i
$227$	−27.4257			−1.82031			−0.910155	−	0.414268i	$-0.864038\pi$
$227$	−27.4257			−1.82031			−0.910155	+	0.414268i	$0.864038\pi$
$228$			2.15336i			0.142610i
$229$		−	0.177967i		−	0.0117604i	−0.999983	−	0.00588018i	$-0.998128\pi$
$229$		−	0.177967i		−	0.0117604i	0.999983	−	0.00588018i	$-0.00187173\pi$
$230$	23.1166			1.52426
$231$		0			0
$232$	−10.6868			−0.701625
$233$			8.71447i			0.570904i	0.958393	+	0.285452i	$0.0921437\pi$
$233$			8.71447i			0.570904i	−0.958393	+	0.285452i	$0.907856\pi$
$234$		−	0.222436i		−	0.0145411i
$235$	4.17600			0.272412
$236$			34.1642i			2.22390i
$237$	5.08763			0.330477
$238$	6.40618	−	24.3632i	0.415251	−	1.57923i
$239$		−	4.65639i		−	0.301197i	−0.988595	−	0.150599i	$-0.951880\pi$
$239$		−	4.65639i		−	0.301197i	0.988595	−	0.150599i	$-0.0481201\pi$
$240$	15.9290			1.02821
$241$	6.84861			0.441158			0.220579	−	0.975369i	$-0.429205\pi$
$241$	6.84861			0.441158			0.220579	+	0.975369i	$0.429205\pi$
$242$		0			0
$243$		−	0.375639i		−	0.0240972i
$244$	−21.5039			−1.37664
$245$	−11.5963	+	20.5263i	−0.740863	+	1.31138i
$246$	−39.4608			−2.51593
$247$	0.845942			0.0538260
$248$	0.953985			0.0605781
$249$		−	13.5921i		−	0.861362i
$250$	−10.8770			−0.687920
$251$			9.40501i			0.593639i	0.954934	+	0.296820i	$0.0959260\pi$
$251$			9.40501i			0.593639i	−0.954934	+	0.296820i	$0.904074\pi$
$252$	−0.349941	−	0.0920152i	−0.0220442	−	0.00579641i
$253$		0			0
$254$	−26.3045			−1.65049
$255$	22.9563			1.43758
$256$	−29.2404			−1.82753
$257$		−	5.70864i		−	0.356095i	−0.984022	−	0.178047i	$-0.943022\pi$
$257$		−	5.70864i		−	0.356095i	0.984022	−	0.178047i	$-0.0569781\pi$
$258$			7.17100i			0.446447i
$259$	−21.4427	−	5.63824i	−1.33238	−	0.350343i
$260$		−	32.6043i		−	2.02203i
$261$			0.0900731i			0.00557539i
$262$		−	13.6379i		−	0.842554i
$263$			3.07375i			0.189535i	0.995499	+	0.0947677i	$0.0302108\pi$
$263$			3.07375i			0.189535i	−0.995499	+	0.0947677i	$0.969789\pi$
$264$		0			0
$265$			1.01750i			0.0625043i
$266$	0.534929	−	2.03438i	0.0327986	−	0.124736i
$267$	−6.31065			−0.386205
$268$	24.8946			1.52068
$269$		−	11.9261i		−	0.727145i	−0.931566	−	0.363572i	$-0.881557\pi$
$269$		−	11.9261i		−	0.727145i	0.931566	−	0.363572i	$-0.118443\pi$
$270$		−	42.3355i		−	2.57646i
$271$	−1.55416			−0.0944087			−0.0472044	−	0.998885i	$-0.515031\pi$
$271$	−1.55416			−0.0944087			−0.0472044	+	0.998885i	$0.515031\pi$
$272$	10.8770			0.659513
$273$	2.96385	−	11.2718i	0.179380	−	0.682198i
$274$			42.5495i			2.57051i
$275$		0			0
$276$			18.5900i			1.11898i
$277$			12.6309i			0.758918i	0.925209	+	0.379459i	$0.123890\pi$
$277$			12.6309i			0.758918i	−0.925209	+	0.379459i	$0.876110\pi$
$278$		−	4.28473i		−	0.256981i
$279$		−	0.00804058i		−	0.000481377i
$280$	−36.9599	−	9.71842i	−2.20878	−	0.580787i
$281$			18.1496i			1.08272i	0.840792	+	0.541358i	$0.182090\pi$
$281$			18.1496i			1.08272i	−0.840792	+	0.541358i	$0.817910\pi$
$282$			5.13354i			0.305698i
$283$	−19.2128			−1.14208			−0.571042	−	0.820921i	$-0.693461\pi$
$283$	−19.2128			−1.14208			−0.571042	+	0.820921i	$0.693461\pi$
$284$	−20.2643			−1.20247
$285$	1.91690			0.113547
$286$		0			0
$287$	24.3881	+	6.41272i	1.43958	+	0.378531i
$288$			0.0712427i			0.00419802i
$289$	−1.32445			−0.0779091
$290$			20.1821i			1.18513i
$291$	23.4788			1.37635
$292$	26.4524			1.54801
$293$	22.2004			1.29696			0.648481	−	0.761231i	$-0.275405\pi$
$293$	22.2004			1.29696			0.648481	+	0.761231i	$0.275405\pi$
$294$	−25.2329	−	14.2553i	−1.47161	−	0.831388i
$295$	30.4126			1.77069
$296$		−	35.9404i		−	2.08900i
$297$		0			0
$298$	−33.7440			−1.95474
$299$	7.30300			0.422343
$300$		−	41.3142i		−	2.38527i
$301$	1.16535	−	4.43192i	0.0671698	−	0.255452i
$302$	−4.91141			−0.282620
$303$			18.1897i			1.04497i
$304$	0.908249			0.0520917
$305$			19.1425i			1.09610i
$306$		−	0.344179i		−	0.0196754i
$307$	8.33503			0.475705			0.237853	−	0.971301i	$-0.423556\pi$
$307$	8.33503			0.475705			0.237853	+	0.971301i	$0.423556\pi$
$308$		0			0
$309$	30.4891			1.73447
$310$		−	1.80160i		−	0.102324i
$311$			24.0042i			1.36115i	0.732677	+	0.680577i	$0.238271\pi$
$311$			24.0042i			1.36115i	−0.732677	+	0.680577i	$0.761729\pi$
$312$	18.8928			1.06959
$313$			33.1290i			1.87256i	0.351256	+	0.936280i	$0.385755\pi$
$313$			33.1290i			1.87256i	−0.351256	+	0.936280i	$0.614245\pi$
$314$	−18.3296			−1.03440
$315$	−0.0819109	+	0.311513i	−0.00461516	+	0.0175518i
$316$		−	11.1807i		−	0.628961i
$317$	14.3722			0.807221			0.403611	−	0.914931i	$-0.367755\pi$
$317$	14.3722			0.807221			0.403611	+	0.914931i	$0.367755\pi$
$318$	−1.25080			−0.0701416
$319$		0			0
$320$			34.4679i			1.92681i
$321$	−31.2407			−1.74369
$322$	4.61803	−	17.5627i	0.257353	−	0.978733i
$323$	1.30894			0.0728314
$324$	33.6352			1.86862
$325$	−16.2301			−0.900285
$326$			45.2063i			2.50375i
$327$	−2.56127			−0.141639
$328$			40.8773i			2.25707i
$329$	0.834246	−	3.17270i	0.0459935	−	0.174917i
$330$		0			0
$331$	−6.28233			−0.345308			−0.172654	−	0.984983i	$-0.555234\pi$
$331$	−6.28233			−0.345308			−0.172654	+	0.984983i	$0.555234\pi$
$332$	−29.8702			−1.63934
$333$	−0.302921			−0.0166000
$334$		−	47.0883i		−	2.57656i
$335$		−	22.1609i		−	1.21078i
$336$	3.18215	−	12.1020i	0.173601	−	0.660217i
$337$		−	23.4303i		−	1.27633i	−0.769899	−	0.638166i	$-0.779693\pi$
$337$		−	23.4303i		−	1.27633i	0.769899	−	0.638166i	$-0.220307\pi$
$338$			15.5178i			0.844059i
$339$			19.8824i			1.07986i
$340$		−	50.4492i		−	2.73599i
$341$		0			0
$342$		−	0.0287397i		−	0.00155406i
$343$	13.2782	+	12.9109i	0.716954	+	0.697121i
$344$	7.42843			0.400514
$345$	16.5486			0.890945
$346$			21.3468i			1.14761i
$347$			17.9331i			0.962697i	0.876529	+	0.481349i	$0.159853\pi$
$347$			17.9331i			0.962697i	−0.876529	+	0.481349i	$0.840147\pi$
$348$	−16.2301			−0.870026
$349$	−21.7893			−1.16635			−0.583176	−	0.812346i	$-0.698190\pi$
$349$	−21.7893			−1.16635			−0.583176	+	0.812346i	$0.698190\pi$
$350$	−10.2631	+	39.0313i	−0.548585	+	2.08631i
$351$		−	13.3747i		−	0.713887i
$352$		0			0
$353$			16.3753i			0.871570i	0.900051	+	0.435785i	$0.143529\pi$
$353$			16.3753i			0.871570i	−0.900051	+	0.435785i	$0.856471\pi$
$354$			37.3861i			1.98705i
$355$			18.0391i			0.957415i
$356$			13.8684i			0.735024i
$357$	4.58602	−	17.4410i	0.242718	−	0.923075i
$358$		−	21.4602i		−	1.13420i
$359$			18.2087i			0.961019i	0.876990	+	0.480509i	$0.159548\pi$
$359$			18.2087i			0.961019i	−0.876990	+	0.480509i	$0.840452\pi$
$360$	−0.522133			−0.0275188
$361$	−18.8907			−0.994247
$362$	29.0384			1.52623
$363$		0			0
$364$	−24.7710	−	6.51342i	−1.29835	−	0.341396i
$365$		−	23.5476i		−	1.23254i
$366$	−23.5318			−1.23003
$367$			0.841561i			0.0439292i	0.999759	+	0.0219646i	$0.00699210\pi$
$367$			0.841561i			0.0439292i	−0.999759	+	0.0219646i	$0.993008\pi$
$368$	7.84090			0.408735
$369$	0.344531			0.0179356
$370$	−67.8736			−3.52858
$371$	0.773039	+	0.203267i	0.0401342	+	0.0105531i
$372$	1.44882			0.0751178
$373$			25.9152i			1.34184i	0.741530	+	0.670920i	$0.234101\pi$
$373$			25.9152i			1.34184i	−0.741530	+	0.670920i	$0.765899\pi$
$374$		0			0
$375$	−7.78655			−0.402095
$376$	5.31783			0.274246
$377$			6.37594i			0.328378i
$378$	−32.1643	−	8.45744i	−1.65435	−	0.435004i
$379$	8.80317			0.452188			0.226094	−	0.974105i	$-0.427404\pi$
$379$	8.80317			0.452188			0.226094	+	0.974105i	$0.427404\pi$
$380$		−	4.21262i		−	0.216103i
$381$	−18.8308			−0.964729
$382$		−	31.3320i		−	1.60309i
$383$		−	13.0944i		−	0.669092i	−0.942379	−	0.334546i	$-0.891417\pi$
$383$		−	13.0944i		−	0.669092i	0.942379	−	0.334546i	$-0.108583\pi$
$384$	−35.5852			−1.81595
$385$		0			0
$386$	31.5164			1.60414
$387$		−	0.0626099i		−	0.00318264i
$388$		−	51.5975i		−	2.61947i
$389$	−10.0467			−0.509386			−0.254693	−	0.967022i	$-0.581974\pi$
$389$	−10.0467			−0.509386			−0.254693	+	0.967022i	$0.581974\pi$
$390$		−	35.6791i		−	1.80668i
$391$	11.3001			0.571469
$392$	−14.7671	+	26.1387i	−0.745850	+	1.32020i
$393$		−	9.76305i		−	0.492481i
$394$	−14.2052			−0.715649
$395$	−9.95290			−0.500785
$396$		0			0
$397$		−	15.4703i		−	0.776431i	−0.921569	−	0.388215i	$-0.873092\pi$
$397$		−	15.4703i		−	0.776431i	0.921569	−	0.388215i	$-0.126908\pi$
$398$	17.0877			0.856531
$399$	0.382942	−	1.45636i	0.0191711	−	0.0729092i
$400$	−17.4255			−0.871277
$401$	−32.2447			−1.61023			−0.805113	−	0.593122i	$-0.797895\pi$
$401$	−32.2447			−1.61023			−0.805113	+	0.593122i	$0.797895\pi$
$402$	27.2423			1.35872
$403$		−	0.569163i		−	0.0283520i
$404$	39.9741			1.98879
$405$		−	29.9417i		−	1.48782i
$406$	15.3333	+	4.03181i	0.760979	+	0.200096i
$407$		0			0
$408$	29.2332			1.44726
$409$	−5.03296			−0.248864			−0.124432	−	0.992228i	$-0.539711\pi$
$409$	−5.03296			−0.248864			−0.124432	+	0.992228i	$0.539711\pi$
$410$	77.1969			3.81248
$411$			30.4601i			1.50249i
$412$		−	67.0035i		−	3.30103i
$413$	6.07557	−	23.1059i	0.298959	−	1.13697i
$414$		−	0.248109i		−	0.0121939i
$415$			26.5901i			1.30526i
$416$			5.04301i			0.247254i
$417$		−	3.06733i		−	0.150208i
$418$		0			0
$419$		−	16.8991i		−	0.825577i	−0.910827	−	0.412789i	$-0.864555\pi$
$419$		−	16.8991i		−	0.825577i	0.910827	−	0.412789i	$-0.135445\pi$
$420$	−56.1311	−	14.7594i	−2.73892	−	0.720184i
$421$	24.9500			1.21599			0.607994	−	0.793942i	$-0.291974\pi$
$421$	24.9500			1.21599			0.607994	+	0.793942i	$0.291974\pi$
$422$	−0.859502			−0.0418399
$423$		−	0.0448209i		−	0.00217926i
$424$			1.29571i			0.0629250i
$425$	−25.1132			−1.21817
$426$	−22.1754			−1.07440
$427$	14.5435	+	3.82413i	0.703807	+	0.185063i
$428$			68.6552i			3.31857i
$429$		0			0
$430$		−	14.0286i		−	0.676519i
$431$		−	20.0053i		−	0.963622i	−0.876275	−	0.481811i	$-0.839979\pi$
$431$		−	20.0053i		−	0.963622i	0.876275	−	0.481811i	$-0.160021\pi$
$432$		−	14.3598i		−	0.690885i
$433$		−	38.5306i		−	1.85166i	−0.377936	−	0.925832i	$-0.623366\pi$
$433$		−	38.5306i		−	1.85166i	0.377936	−	0.925832i	$-0.376634\pi$
$434$	−1.36876	−	0.359909i	−0.0657027	−	0.0172762i
$435$			14.4479i			0.692722i
$436$			5.62870i			0.269566i
$437$	0.943579			0.0451375
$438$	28.9470			1.38314
$439$	−24.1486			−1.15255			−0.576275	−	0.817256i	$-0.695494\pi$
$439$	−24.1486			−1.15255			−0.576275	+	0.817256i	$0.695494\pi$
$440$		0			0
$441$	0.220308	+	0.124463i	0.0104909	+	0.00592681i
$442$		−	24.3632i		−	1.15884i
$443$	20.4613			0.972145			0.486073	−	0.873918i	$-0.338429\pi$
$443$	20.4613			0.972145			0.486073	+	0.873918i	$0.338429\pi$
$444$		−	54.5828i		−	2.59039i
$445$	12.3455			0.585232
$446$	−19.2313			−0.910630
$447$	−24.1565			−1.14256
$448$	26.1869	+	6.88571i	1.23721	+	0.325319i
$449$	0.723387			0.0341387			0.0170694	−	0.999854i	$-0.494566\pi$
$449$	0.723387			0.0341387			0.0170694	+	0.999854i	$0.494566\pi$
$450$			0.551396i			0.0259931i
$451$		0			0
$452$	43.6939			2.05519
$453$	−3.51596			−0.165194
$454$			65.9553i			3.09543i
$455$	−5.79817	+	22.0509i	−0.271822	+	1.03376i
$456$	2.44103			0.114312
$457$		−	19.8078i		−	0.926570i	−0.886209	−	0.463285i	$-0.846671\pi$
$457$		−	19.8078i		−	0.926570i	0.886209	−	0.463285i	$-0.153329\pi$
$458$	−0.427986			−0.0199985
$459$		−	20.6949i		−	0.965953i
$460$		−	36.3674i		−	1.69564i
$461$	−35.2596			−1.64220			−0.821102	−	0.570781i	$-0.806640\pi$
$461$	−35.2596			−1.64220			−0.821102	+	0.570781i	$0.806640\pi$
$462$		0			0
$463$	18.0616			0.839393			0.419696	−	0.907665i	$-0.362137\pi$
$463$	18.0616			0.839393			0.419696	+	0.907665i	$0.362137\pi$
$464$			6.84556i			0.317797i
$465$		−	1.28972i		−	0.0598094i
$466$	20.9571			0.970821
$467$		−	32.1510i		−	1.48777i	−0.668308	−	0.743884i	$-0.732981\pi$
$467$		−	32.1510i		−	1.48777i	0.668308	−	0.743884i	$-0.267019\pi$
$468$	−0.349941			−0.0161760
$469$	−16.8367	−	4.42712i	−0.777445	−	0.204425i
$470$		−	10.0427i		−	0.463236i
$471$	−13.1217			−0.604617
$472$	38.7282			1.78261
$473$		0			0
$474$		−	12.2351i		−	0.561975i
$475$	−2.09700			−0.0962170
$476$	−38.3287	−	10.0783i	−1.75679	−	0.461939i
$477$	0.0109207			0.000500027
$478$	−11.1980			−0.512185
$479$	−33.4874			−1.53008			−0.765039	−	0.643984i	$-0.777280\pi$
$479$	−33.4874			−1.53008			−0.765039	+	0.643984i	$0.777280\pi$
$480$			11.4274i			0.521589i
$481$	−21.4427			−0.977701
$482$		−	16.4700i		−	0.750188i
$483$	3.30593	−	12.5727i	0.150425	−	0.572079i
$484$		0			0
$485$	−45.9315			−2.08564
$486$	−0.903362			−0.0409773
$487$	−39.5403			−1.79174			−0.895871	−	0.444315i	$-0.853447\pi$
$487$	−39.5403			−1.79174			−0.895871	+	0.444315i	$0.853447\pi$
$488$			24.3766i			1.10347i
$489$			32.3621i			1.46346i
$490$	49.3630	+	27.8877i	2.22999	+	1.25984i
$491$			19.8538i			0.895991i	0.894036	+	0.447996i	$0.147862\pi$
$491$			19.8538i			0.895991i	−0.894036	+	0.447996i	$0.852138\pi$
$492$			62.0805i			2.79880i
$493$			9.86561i			0.444325i
$494$		−	2.03438i		−	0.0915310i
$495$		0			0
$496$		−	0.611085i		−	0.0274385i
$497$	13.7051	+	3.60370i	0.614759	+	0.161648i
$498$	−32.6871			−1.46474
$499$	−42.3220			−1.89459			−0.947297	−	0.320355i	$-0.896198\pi$
$499$	−42.3220			−1.89459			−0.947297	+	0.320355i	$0.896198\pi$
$500$			17.1119i			0.765266i
$501$		−	33.7093i		−	1.50602i
$502$	22.6178			1.00948
$503$	22.7626			1.01493			0.507467	−	0.861671i	$-0.330582\pi$
$503$	22.7626			1.01493			0.507467	+	0.861671i	$0.330582\pi$
$504$	−0.104307	+	0.396689i	−0.00464622	+	0.0176699i
$505$		−	35.5845i		−	1.58349i
$506$		0			0
$507$			11.1088i			0.493361i
$508$			41.3828i			1.83607i
$509$		−	31.6346i		−	1.40218i	−0.713074	−	0.701089i	$-0.752698\pi$
$509$		−	31.6346i		−	1.40218i	0.713074	−	0.701089i	$-0.247302\pi$
$510$		−	55.2069i		−	2.44460i
$511$	−17.8902	−	4.70415i	−0.791418	−	0.208099i
$512$			28.9792i			1.28071i
$513$		−	1.72806i		−	0.0762959i
$514$	−13.7285			−0.605539
$515$	−59.6458			−2.62831
$516$	11.2816			0.496643
$517$		0			0
$518$	−13.5592	+	51.5667i	−0.595758	+	2.26571i
$519$			15.2816i			0.670790i
$520$	−36.9599			−1.62080
$521$			27.6431i			1.21107i	0.795820	+	0.605533i	$0.207040\pi$
$521$			27.6431i			1.21107i	−0.795820	+	0.605533i	$0.792960\pi$
$522$	0.216614			0.00948093
$523$	−39.7393			−1.73768			−0.868840	−	0.495093i	$-0.835134\pi$
$523$	−39.7393			−1.73768			−0.868840	+	0.495093i	$0.835134\pi$
$524$	−21.4555			−0.937286
$525$	−7.34708	+	27.9415i	−0.320653	+	1.21947i
$526$	7.39195			0.322304
$527$		−	0.880677i		−	0.0383629i
$528$		0			0
$529$	−14.8541			−0.645831
$530$	2.44694			0.106288
$531$		−	0.326417i		−	0.0141653i
$532$	−3.20052	−	0.841561i	−0.138760	−	0.0364863i
$533$	24.3881			1.05637
$534$			15.1763i			0.656741i
$535$	61.1161			2.64228
$536$		−	28.2202i		−	1.21893i
$537$		−	15.3628i		−	0.662953i
$538$	−28.6806			−1.23651
$539$		0			0
$540$	−66.6031			−2.86614
$541$			5.89488i			0.253441i	0.991938	+	0.126720i	$0.0404451\pi$
$541$			5.89488i			0.253441i	−0.991938	+	0.126720i	$0.959555\pi$
$542$			3.73756i			0.160542i
$543$	20.7879			0.892094
$544$			7.80314i			0.334557i
$545$	5.01060			0.214631
$546$	−27.1071	−	7.12767i	−1.16008	−	0.305036i
$547$			5.87034i			0.250997i	0.992094	+	0.125499i	$0.0400531\pi$
$547$			5.87034i			0.250997i	−0.992094	+	0.125499i	$0.959947\pi$
$548$	66.9398			2.85953
$549$	0.205456			0.00876864
$550$		0			0
$551$			0.823799i			0.0350950i
$552$	21.0734			0.896943
$553$	−1.98831	+	7.56169i	−0.0845514	+	0.321556i
$554$	30.3757			1.29054
$555$	−48.5890			−2.06249
$556$	−6.74082			−0.285875
$557$		−	13.5359i		−	0.573536i	−0.958000	−	0.286768i	$-0.907419\pi$
$557$		−	13.5359i		−	0.573536i	0.958000	−	0.286768i	$-0.0925808\pi$
$558$	−0.0193365			−0.000818581
$559$		−	4.43192i		−	0.187450i
$560$	−6.22523	+	23.6750i	−0.263064	+	1.00045i
$561$		0			0
$562$	43.6475			1.84116
$563$	32.8714			1.38536			0.692682	−	0.721243i	$-0.256429\pi$
$563$	32.8714			1.38536			0.692682	+	0.721243i	$0.256429\pi$
$564$	8.07619			0.340069
$565$		−	38.8958i		−	1.63636i
$566$			46.2043i			1.94211i
$567$	−22.7481	−	5.98151i	−0.955332	−	0.251200i
$568$			22.9714i			0.963860i
$569$		−	25.7198i		−	1.07823i	−0.842232	−	0.539115i	$-0.818759\pi$
$569$		−	25.7198i		−	1.07823i	0.842232	−	0.539115i	$-0.181241\pi$
$570$		−	4.60989i		−	0.193087i
$571$			16.0855i			0.673156i	0.941656	+	0.336578i	$0.109270\pi$
$571$			16.0855i			0.673156i	−0.941656	+	0.336578i	$0.890730\pi$
$572$		0			0
$573$		−	22.4298i		−	0.937019i
$574$	15.4218	−	58.6501i	0.643691	−	2.44801i
$575$	−18.1034			−0.754963
$576$	0.369943			0.0154143
$577$			5.97961i			0.248934i	0.992224	+	0.124467i	$0.0397221\pi$
$577$			5.97961i			0.248934i	−0.992224	+	0.124467i	$0.960278\pi$
$578$			3.18514i			0.132484i
$579$	22.5618			0.937635
$580$	31.7509			1.31838
$581$	20.2017	+	5.31195i	0.838110	+	0.220377i
$582$		−	56.4635i		−	2.34049i
$583$		0			0
$584$		−	29.9862i		−	1.24084i
$585$			0.311513i			0.0128795i
$586$		−	53.3890i		−	2.20548i
$587$			29.8075i			1.23029i	0.788415	+	0.615144i	$0.210902\pi$
$587$			29.8075i			1.23029i	−0.788415	+	0.615144i	$0.789098\pi$
$588$	−22.4268	+	39.6969i	−0.924865	+	1.63707i
$589$		−	0.0735383i		−	0.00303009i
$590$		−	73.1382i		−	3.01105i
$591$	−10.1692			−0.418304
$592$	−23.0220			−0.946199
$593$	27.7811			1.14083			0.570416	−	0.821356i	$-0.306782\pi$
$593$	27.7811			1.14083			0.570416	+	0.821356i	$0.306782\pi$
$594$		0			0
$595$	−8.97161	+	34.1197i	−0.367800	+	1.39877i
$596$			53.0868i			2.17452i
$597$	12.2327			0.500651
$598$		−	17.5627i		−	0.718194i
$599$	24.1040			0.984862			0.492431	−	0.870352i	$-0.336108\pi$
$599$	24.1040			0.984862			0.492431	+	0.870352i	$0.336108\pi$
$600$	−46.8333			−1.91196
$601$	17.8194			0.726870			0.363435	−	0.931620i	$-0.381604\pi$
$601$	17.8194			0.726870			0.363435	+	0.931620i	$0.381604\pi$
$602$	−10.6582	−	2.80252i	−0.434395	−	0.114222i
$603$	−0.237852			−0.00968608
$604$			7.72673i			0.314396i
$605$		0			0
$606$	43.7439			1.77697
$607$	−17.1827			−0.697426			−0.348713	−	0.937230i	$-0.613381\pi$
$607$	−17.1827			−0.697426			−0.348713	+	0.937230i	$0.613381\pi$
$608$			0.651578i			0.0264250i
$609$	10.9767	+	2.88627i	0.444799	+	0.116958i
$610$	46.0352			1.86391
$611$		−	3.17270i		−	0.128354i
$612$	−0.541470			−0.0218876
$613$		−	43.3094i		−	1.74925i	−0.484801	−	0.874625i	$-0.661108\pi$
$613$		−	43.3094i		−	1.74925i	0.484801	−	0.874625i	$-0.338892\pi$
$614$		−	20.0446i		−	0.808936i
$615$	55.2633			2.22843
$616$		0			0
$617$	−43.5171			−1.75193			−0.875967	−	0.482371i	$-0.839776\pi$
$617$	−43.5171			−1.75193			−0.875967	+	0.482371i	$0.839776\pi$
$618$		−	73.3223i		−	2.94946i
$619$			18.6923i			0.751305i	0.926761	+	0.375653i	$0.122581\pi$
$619$			18.6923i			0.751305i	−0.926761	+	0.375653i	$0.877419\pi$
$620$	−2.83432			−0.113829
$621$		−	14.9183i		−	0.598653i
$622$	57.7269			2.31464
$623$	2.46628	−	9.37945i	0.0988094	−	0.375780i
$624$		−	12.1020i		−	0.484467i
$625$	−16.4819			−0.659275
$626$	79.6707			3.18428
$627$		0			0
$628$			28.8365i			1.15070i
$629$	−33.1786			−1.32292
$630$	0.749148	+	0.196985i	0.0298468	+	0.00784806i
$631$	−14.6230			−0.582130			−0.291065	−	0.956703i	$-0.594010\pi$
$631$	−14.6230			−0.582130			−0.291065	+	0.956703i	$0.594010\pi$
$632$	−12.6743			−0.504156
$633$	−0.615296			−0.0244558
$634$		−	34.5632i		−	1.37268i
$635$	36.8385			1.46189
$636$			1.96779i			0.0780280i
$637$	15.5948	+	8.81029i	0.617888	+	0.349076i
$638$		0			0
$639$	0.193613			0.00765920
$640$	69.6152			2.75178
$641$	48.1511			1.90185			0.950927	−	0.309416i	$-0.100134\pi$
$641$	48.1511			1.90185			0.950927	+	0.309416i	$0.100134\pi$
$642$			75.1298i			2.96514i
$643$		−	23.4440i		−	0.924542i	−0.886739	−	0.462271i	$-0.847035\pi$
$643$		−	23.4440i		−	0.924542i	0.886739	−	0.462271i	$-0.152965\pi$
$644$	−27.6301	−	7.26519i	−1.08878	−	0.286288i
$645$		−	10.0427i		−	0.395432i
$646$		−	3.14783i		−	0.123850i
$647$		−	2.36141i		−	0.0928366i	−0.998922	−	0.0464183i	$-0.985219\pi$
$647$		−	2.36141i		−	0.0928366i	0.998922	−	0.0464183i	$-0.0147807\pi$
$648$		−	38.1286i		−	1.49783i
$649$		0			0
$650$			39.0313i			1.53093i
$651$	−0.979863	−	0.257650i	−0.0384038	−	0.0100981i
$652$	71.1195			2.78525
$653$	−33.1101			−1.29570			−0.647850	−	0.761768i	$-0.724332\pi$
$653$	−33.1101			−1.29570			−0.647850	+	0.761768i	$0.724332\pi$
$654$			6.15952i			0.240856i
$655$			19.0994i			0.746275i
$656$	26.1844			1.02233
$657$	−0.252736			−0.00986017
$658$	−7.62993	−	2.00625i	−0.297446	−	0.0782118i
$659$		−	4.56667i		−	0.177892i	−0.996036	−	0.0889462i	$-0.971650\pi$
$659$		−	4.56667i		−	0.177892i	0.996036	−	0.0889462i	$-0.0283499\pi$
$660$		0			0
$661$		−	13.7734i		−	0.535722i	−0.963458	−	0.267861i	$-0.913683\pi$
$661$		−	13.7734i		−	0.535722i	0.963458	−	0.267861i	$-0.0863167\pi$
$662$			15.1082i			0.587196i
$663$		−	17.4410i		−	0.677352i
$664$			33.8605i			1.31404i
$665$	−0.749148	+	2.84907i	−0.0290507	+	0.110482i
$666$			0.728485i			0.0282282i
$667$			7.11185i			0.275372i
$668$	−74.0803			−2.86625
$669$	−13.7672			−0.532272
$670$	−53.2940			−2.05893
$671$		0			0
$672$	8.68197	+	2.28288i	0.334914	+	0.0880640i
$673$			29.9766i			1.15551i	0.816209	+	0.577757i	$0.196072\pi$
$673$			29.9766i			1.15551i	−0.816209	+	0.577757i	$0.803928\pi$
$674$	−56.3469			−2.17040
$675$			33.1544i			1.27611i
$676$	24.4130			0.938961
$677$	13.7766			0.529479			0.264740	−	0.964320i	$-0.414714\pi$
$677$	13.7766			0.529479			0.264740	+	0.964320i	$0.414714\pi$
$678$	47.8145			1.83631
$679$	−9.17582	+	34.8963i	−0.352135	+	1.33920i
$680$	−57.1887			−2.19309
$681$			47.2157i			1.80931i
$682$		0			0
$683$	14.5882			0.558201			0.279101	−	0.960262i	$-0.409964\pi$
$683$	14.5882			0.558201			0.279101	+	0.960262i	$0.409964\pi$
$684$	−0.0452139			−0.00172880
$685$		−	59.5890i		−	2.27678i
$686$	31.0489	−	31.9322i	1.18545	−	1.21918i
$687$	−0.306385			−0.0116893
$688$		−	4.75836i		−	0.181411i
$689$	0.773039			0.0294505
$690$		−	39.7971i		−	1.51505i
$691$			19.9764i			0.759938i	0.924999	+	0.379969i	$0.124065\pi$
$691$			19.9764i			0.759938i	−0.924999	+	0.379969i	$0.875935\pi$
$692$	33.5832			1.27664
$693$		0			0
$694$	43.1266			1.63706
$695$			6.00060i			0.227616i
$696$			18.3983i			0.697386i
$697$	37.7361			1.42936
$698$			52.4003i			1.98338i
$699$	15.0027			0.567454
$700$	61.4048	+	16.1461i	2.32088	+	0.610265i
$701$			41.4302i			1.56480i	0.622778	+	0.782399i	$0.286004\pi$
$701$			41.4302i			1.56480i	−0.622778	+	0.782399i	$0.713996\pi$
$702$	−32.1643			−1.21396
$703$	−2.77048			−0.104491
$704$		0			0
$705$		−	7.18934i		−	0.270766i
$706$	39.3805			1.48210
$707$	−27.0352	−	7.10877i	−1.01676	−	0.267353i
$708$	58.8166			2.21046
$709$	15.1482			0.568903			0.284451	−	0.958690i	$-0.408189\pi$
$709$	15.1482			0.568903			0.284451	+	0.958690i	$0.408189\pi$
$710$	43.3816			1.62808
$711$			0.106824i			0.00400622i
$712$	15.7211			0.589172
$713$		−	0.634855i		−	0.0237755i
$714$	−41.9433	−	11.0288i	−1.56969	−	0.412742i
$715$		0			0
$716$	−33.7616			−1.26173
$717$	−8.01638			−0.299377
$718$	43.7895			1.63421
$719$		−	25.7442i		−	0.960098i	−0.877242	−	0.480049i	$-0.840619\pi$
$719$		−	25.7442i		−	0.960098i	0.877242	−	0.480049i	$-0.159381\pi$
$720$			0.334458i			0.0124645i
$721$	−11.9155	+	45.3157i	−0.443758	+	1.68764i
$722$			45.4296i			1.69072i
$723$		−	11.7905i		−	0.438492i
$724$		−	45.6839i		−	1.69783i
$725$		−	15.8053i		−	0.586994i
$726$		0			0
$727$		−	9.52144i		−	0.353130i	−0.984289	−	0.176565i	$-0.943501\pi$
$727$		−	9.52144i		−	0.353130i	0.984289	−	0.176565i	$-0.0564987\pi$
$728$	−7.38354	+	28.0802i	−0.273652	+	1.04072i
$729$	−27.3174			−1.01176
$730$	−56.6289			−2.09593
$731$		−	6.85760i		−	0.253637i
$732$			37.0207i			1.36833i
$733$	39.7320			1.46753			0.733767	−	0.679402i	$-0.237761\pi$
$733$	39.7320			1.46753			0.733767	+	0.679402i	$0.237761\pi$
$734$	2.02384			0.0747014
$735$	35.3377	+	19.9641i	1.30345	+	0.736386i
$736$			5.62506i			0.207343i
$737$		0			0
$738$		−	0.828552i		−	0.0304994i
$739$		−	28.5519i		−	1.05030i	−0.851010	−	0.525149i	$-0.824010\pi$
$739$		−	28.5519i		−	1.05030i	0.851010	−	0.525149i	$-0.175990\pi$
$740$			106.780i			3.92531i
$741$		−	1.45636i		−	0.0535007i
$742$	0.488830	−	1.85906i	0.0179455	−	0.0682481i
$743$			0.145438i			0.00533560i	0.999996	+	0.00266780i	$0.000849188\pi$
$743$			0.145438i			0.00533560i	−0.999996	+	0.00266780i	$0.999151\pi$
$744$		−	1.64237i		−	0.0602121i
$745$	47.2572			1.73137
$746$	62.3227			2.28180
$747$	0.285391			0.0104419
$748$		0			0
$749$	12.2093	−	46.4328i	0.446117	−	1.69662i
$750$			18.7256i			0.683763i
$751$	9.10902			0.332393			0.166196	−	0.986093i	$-0.446851\pi$
$751$	9.10902			0.332393			0.166196	+	0.986093i	$0.446851\pi$
$752$		−	3.40639i		−	0.124218i
$753$	16.1915			0.590052
$754$	15.3333			0.558406
$755$	6.87825			0.250325
$756$	−13.3054	+	50.6015i	−0.483913	+	1.84036i
$757$	−19.4693			−0.707624			−0.353812	−	0.935316i	$-0.615115\pi$
$757$	−19.4693			−0.707624			−0.353812	+	0.935316i	$0.615115\pi$
$758$		−	21.1705i		−	0.768946i
$759$		0			0
$760$	−4.77538			−0.173221
$761$	−13.0673			−0.473689			−0.236845	−	0.971548i	$-0.576113\pi$
$761$	−13.0673			−0.473689			−0.236845	+	0.971548i	$0.576113\pi$
$762$			45.2855i			1.64052i
$763$	1.00098	−	3.80679i	0.0362378	−	0.137815i
$764$	−49.2922			−1.78333
$765$			0.482010i			0.0174271i
$766$	−31.4903			−1.13779
$767$		−	23.1059i		−	0.834305i
$768$			50.3398i			1.81648i
$769$	−28.5921			−1.03106			−0.515529	−	0.856872i	$-0.672405\pi$
$769$	−28.5921			−1.03106			−0.515529	+	0.856872i	$0.672405\pi$
$770$		0			0
$771$	−9.82790			−0.353943
$772$		−	49.5822i		−	1.78450i
$773$		−	7.74692i		−	0.278637i	−0.990248	−	0.139319i	$-0.955509\pi$
$773$		−	7.74692i		−	0.278637i	0.990248	−	0.139319i	$-0.0444912\pi$
$774$	−0.150568			−0.00541207
$775$			1.41090i			0.0506809i
$776$	−58.4904			−2.09968
$777$	−9.70670	+	36.9153i	−0.348226	+	1.32433i
$778$			24.1609i			0.866210i
$779$	3.15105			0.112898
$780$	−56.1311			−2.00981
$781$		0			0
$782$		−	27.1751i		−	0.971781i
$783$	13.0246			0.465461
$784$	16.7434	+	9.45920i	0.597979	+	0.337829i
$785$	25.6700			0.916200
$786$	−23.4788			−0.837462
$787$	22.1352			0.789033			0.394517	−	0.918889i	$-0.370912\pi$
$787$	22.1352			0.789033			0.394517	+	0.918889i	$0.370912\pi$
$788$			22.3480i			0.796113i
$789$	5.29171			0.188390
$790$			23.9354i			0.851583i
$791$	−29.5510	−	7.77029i	−1.05071	−	0.276280i
$792$		0			0
$793$	14.5435			0.516453
$794$	−37.2039			−1.32032
$795$	1.75170			0.0621266
$796$		−	26.8828i		−	0.952835i
$797$			16.0101i			0.567106i	0.958956	+	0.283553i	$0.0915133\pi$
$797$			16.0101i			0.567106i	−0.958956	+	0.283553i	$0.908487\pi$
$798$	−3.50235	−	0.920926i	−0.123982	−	0.0326004i
$799$		−	4.90918i		−	0.173674i
$800$		−	12.5011i		−	0.441980i
$801$		−	0.132504i		−	0.00468179i
$802$			77.5443i			2.73819i
$803$		0			0
$804$		−	42.8581i		−	1.51149i
$805$	−6.46738	+	24.5960i	−0.227945	+	0.866894i
$806$	−1.36876			−0.0482126
$807$	−20.5317			−0.722751
$808$		−	45.3142i		−	1.59415i
$809$			14.9223i			0.524639i	0.964981	+	0.262320i	$0.0844875\pi$
$809$			14.9223i			0.524639i	−0.964981	+	0.262320i	$0.915513\pi$
$810$	−72.0058			−2.53003
$811$	−6.89031			−0.241951			−0.120976	−	0.992655i	$-0.538602\pi$
$811$	−6.89031			−0.241951			−0.120976	+	0.992655i	$0.538602\pi$
$812$	6.34293	−	24.1227i	0.222593	−	0.846539i
$813$			2.67562i			0.0938382i
$814$		0			0
$815$		−	63.3097i		−	2.21764i
$816$		−	18.7256i		−	0.655527i
$817$		−	0.572624i		−	0.0200336i
$818$			12.1036i			0.423192i
$819$	0.236671	+	0.0622316i	0.00826997	+	0.00217455i
$820$		−	121.448i		−	4.24114i
$821$		−	16.2509i		−	0.567162i	−0.958948	−	0.283581i	$-0.908478\pi$
$821$		−	16.2509i		−	0.567162i	0.958948	−	0.283581i	$-0.0915224\pi$
$822$	73.2526			2.55498
$823$	8.89861			0.310186			0.155093	−	0.987900i	$-0.450432\pi$
$823$	8.89861			0.310186			0.155093	+	0.987900i	$0.450432\pi$
$824$	−75.9545			−2.64600
$825$		0			0
$826$	−55.5666	−	14.6109i	−1.93341	−	0.508380i
$827$		−	0.562239i		−	0.0195510i	−0.999952	−	0.00977549i	$-0.996888\pi$
$827$		−	0.562239i		−	0.0195510i	0.999952	−	0.00977549i	$-0.00311168\pi$
$828$	−0.390331			−0.0135649
$829$			6.47699i			0.224955i	0.993654	+	0.112478i	$0.0358786\pi$
$829$			6.47699i			0.224955i	−0.993654	+	0.112478i	$0.964121\pi$
$830$	63.9456			2.21959
$831$	21.7452			0.754332
$832$	26.1869			0.907867
$833$	24.1301	+	13.6323i	0.836058	+	0.472332i
$834$	−7.37652			−0.255428
$835$			65.9454i			2.28214i
$836$		0			0
$837$	−1.16267			−0.0401877
$838$	−40.6402			−1.40389
$839$			12.4170i			0.428683i	0.976759	+	0.214341i	$0.0687605\pi$
$839$			12.4170i			0.428683i	−0.976759	+	0.214341i	$0.931240\pi$
$840$	−16.7311	+	63.6296i	−0.577277	+	2.19543i
$841$	22.7909			0.785895
$842$		−	60.0014i		−	2.06779i
$843$	31.2461			1.07617
$844$			1.35219i			0.0465442i
$845$		−	21.7322i		−	0.747609i
$846$	−0.107788			−0.00370584
$847$		0			0
$848$	0.829977			0.0285015
$849$			33.0765i			1.13518i
$850$			60.3938i			2.07149i
$851$	−23.9175			−0.819883
$852$			34.8867i			1.19520i
$853$	−48.5706			−1.66303			−0.831513	−	0.555505i	$-0.812525\pi$
$853$	−48.5706			−1.66303			−0.831513	+	0.555505i	$0.812525\pi$
$854$	9.19652	−	34.9751i	0.314698	−	1.19682i
$855$			0.0402489i			0.00137648i
$856$	77.8268			2.66007
$857$	−10.2702			−0.350825			−0.175412	−	0.984495i	$-0.556126\pi$
$857$	−10.2702			−0.350825			−0.175412	+	0.984495i	$0.556126\pi$
$858$		0			0
$859$			50.0409i			1.70737i	0.520787	+	0.853687i	$0.325639\pi$
$859$			50.0409i			1.70737i	−0.520787	+	0.853687i	$0.674361\pi$
$860$	−22.0701			−0.752584
$861$	11.0400	−	41.9862i	0.376244	−	1.43088i
$862$	−48.1101			−1.63864
$863$	−23.6080			−0.803626			−0.401813	−	0.915722i	$-0.631620\pi$
$863$	−23.6080			−0.803626			−0.401813	+	0.915722i	$0.631620\pi$
$864$	10.3017			0.350471
$865$		−	29.8954i		−	1.01647i
$866$	−92.6610			−3.14875
$867$			2.28016i			0.0774383i
$868$	−0.566216	+	2.15336i	−0.0192186	+	0.0730900i
$869$		0			0
$870$	34.7452			1.17797
$871$	−16.8367			−0.570489
$872$	6.38063			0.216075
$873$			0.492981i			0.0166849i
$874$		−	2.26918i		−	0.0767562i
$875$	3.04308	−	11.5731i	0.102875	−	0.391241i
$876$		−	45.5401i		−	1.53866i
$877$		−	40.3865i		−	1.36376i	−0.731466	−	0.681878i	$-0.761163\pi$
$877$		−	40.3865i		−	1.36376i	0.731466	−	0.681878i	$-0.238837\pi$
$878$			58.0742i			1.95991i
$879$		−	38.2199i		−	1.28912i
$880$		0			0
$881$		−	15.4238i		−	0.519640i	−0.965657	−	0.259820i	$-0.916337\pi$
$881$		−	15.4238i		−	0.519640i	0.965657	−	0.259820i	$-0.0836632\pi$
$882$	0.299317	−	0.529811i	0.0100785	−	0.0178397i
$883$	−21.2723			−0.715871			−0.357936	−	0.933746i	$-0.616519\pi$
$883$	−21.2723			−0.715871			−0.357936	+	0.933746i	$0.616519\pi$
$884$	−38.3287			−1.28913
$885$		−	52.3578i		−	1.75999i
$886$		−	49.2067i		−	1.65313i
$887$	−52.6456			−1.76766			−0.883832	−	0.467804i	$-0.845045\pi$
$887$	−52.6456			−1.76766			−0.883832	+	0.467804i	$0.845045\pi$
$888$	−61.8745			−2.07637
$889$	7.35930	−	27.9880i	0.246823	−	0.938686i
$890$		−	29.6893i		−	0.995186i
$891$		0			0
$892$			30.2551i			1.01302i
$893$		−	0.409927i		−	0.0137177i
$894$			58.0932i			1.94293i
$895$			30.0542i			1.00460i
$896$	13.9071	−	52.8900i	0.464605	−	1.76693i
$897$		−	12.5727i		−	0.419791i
$898$		−	1.73965i		−	0.0580529i
$899$	0.554266			0.0184858
$900$	0.867467			0.0289156
$901$	1.19614			0.0398491
$902$		0			0
$903$	−7.62993	−	2.00625i	−0.253908	−	0.0667639i
$904$		−	49.5310i		−	1.64738i
$905$	−40.6672			−1.35182
$906$			8.45541i			0.280912i
$907$	−48.8193			−1.62102			−0.810510	−	0.585725i	$-0.800810\pi$
$907$	−48.8193			−1.62102			−0.810510	+	0.585725i	$0.800810\pi$
$908$	103.762			3.44347
$909$	−0.381927			−0.0126677
$910$	53.0295	+	13.9438i	1.75791	+	0.462233i
$911$	8.39025			0.277981			0.138991	−	0.990294i	$-0.455614\pi$
$911$	8.39025			0.277981			0.138991	+	0.990294i	$0.455614\pi$
$912$		−	1.56363i		−	0.0517769i
$913$		0			0
$914$	−47.6351			−1.57563
$915$	32.9554			1.08947
$916$			0.673316i			0.0222470i
$917$	14.5107	+	3.81552i	0.479186	+	0.126000i
$918$	−49.7684			−1.64260
$919$		−	11.9849i		−	0.395345i	−0.980268	−	0.197673i	$-0.936662\pi$
$919$		−	11.9849i		−	0.395345i	0.980268	−	0.197673i	$-0.0633383\pi$
$920$	−41.2258			−1.35917
$921$		−	14.3495i		−	0.472831i
$922$			84.7947i			2.79257i
$923$	13.7051			0.451110
$924$		0			0
$925$	53.1541			1.74770
$926$		−	43.4357i		−	1.42739i
$927$			0.640176i			0.0210261i
$928$	−4.91101			−0.161212
$929$		−	35.5102i		−	1.16505i	−0.812813	−	0.582525i	$-0.802065\pi$
$929$		−	35.5102i		−	1.16505i	0.812813	−	0.582525i	$-0.197935\pi$
$930$	−3.10161			−0.101706
$931$	2.01491	+	1.13833i	0.0660361	+	0.0373071i
$932$		−	32.9702i		−	1.07998i
$933$	41.3253			1.35293
$934$	−77.3188			−2.52995
$935$		0			0
$936$			0.396689i			0.0129662i
$937$	−34.0379			−1.11197			−0.555985	−	0.831192i	$-0.687659\pi$
$937$	−34.0379			−1.11197			−0.555985	+	0.831192i	$0.687659\pi$
$938$	−10.6466	+	40.4899i	−0.347625	+	1.32204i
$939$	57.0343			1.86124
$940$	−15.7994			−0.515320
$941$	54.7684			1.78540			0.892700	−	0.450651i	$-0.148808\pi$
$941$	54.7684			1.78540			0.892700	+	0.450651i	$0.148808\pi$
$942$			31.5560i			1.02815i
$943$	27.2029			0.885849
$944$		−	24.8077i		−	0.807423i
$945$	45.0449	+	11.8443i	1.46531	+	0.385296i
$946$		0			0
$947$	−17.4024			−0.565501			−0.282750	−	0.959194i	$-0.591247\pi$
$947$	−17.4024			−0.565501			−0.282750	+	0.959194i	$0.591247\pi$
$948$	−19.2485			−0.625161
$949$	−17.8902			−0.580742
$950$			5.04301i			0.163617i
$951$		−	24.7429i		−	0.802343i
$952$	−11.4247	+	43.4490i	−0.370276	+	1.40819i
$953$			5.02084i			0.162641i	0.996688	+	0.0813205i	$0.0259137\pi$
$953$			5.02084i			0.162641i	−0.996688	+	0.0813205i	$0.974086\pi$
$954$		−	0.0262629i		−	0.000850294i
$955$			43.8793i			1.41990i
$956$			17.6169i			0.569772i
$957$		0			0
$958$			80.5327i			2.60189i
$959$	−45.2726	−	11.9042i	−1.46193	−	0.384407i
$960$	59.3394			1.91517
$961$	30.9505			0.998404
$962$			51.5667i			1.66258i
$963$		−	0.655957i		−	0.0211379i
$964$	−25.9109			−0.834535
$965$	−44.1375			−1.42084
$966$	−30.2357	−	7.95033i	−0.972819	−	0.255798i
$967$		−	47.8640i		−	1.53920i	−0.638525	−	0.769601i	$-0.720455\pi$
$967$		−	47.8640i		−	1.53920i	0.638525	−	0.769601i	$-0.279545\pi$
$968$		0			0
$969$		−	2.25345i		−	0.0723913i
$970$			110.459i			3.54663i
$971$		−	48.2135i		−	1.54725i	−0.633647	−	0.773623i	$-0.718443\pi$
$971$		−	48.2135i		−	1.54725i	0.633647	−	0.773623i	$-0.281557\pi$
$972$			1.42119i			0.0455846i
$973$	4.55894	+	1.19875i	0.146153	+	0.0384302i
$974$			95.0891i			3.04685i
$975$			27.9415i			0.894845i
$976$	15.6146			0.499813
$977$	−47.3991			−1.51643			−0.758215	−	0.652004i	$-0.773928\pi$
$977$	−47.3991			−1.51643			−0.758215	+	0.652004i	$0.773928\pi$
$978$	77.8265			2.48862
$979$		0			0
$980$	43.8734	−	77.6589i	1.40149	−	2.48072i
$981$		−	0.0537786i		−	0.00171702i
$982$	47.7458			1.52363
$983$		−	24.2686i		−	0.774048i	−0.922070	−	0.387024i	$-0.873503\pi$
$983$		−	24.2686i		−	0.774048i	0.922070	−	0.387024i	$-0.126497\pi$
$984$	70.3738			2.24343
$985$	19.8939			0.633873
$986$	23.7255			0.755574
$987$	−5.46208	−	1.43623i	−0.173860	−	0.0457156i
$988$	−3.20052			−0.101822
$989$		−	4.94345i		−	0.157193i
$990$		0			0
$991$	26.5976			0.844902			0.422451	−	0.906386i	$-0.361170\pi$
$991$	26.5976			0.844902			0.422451	+	0.906386i	$0.361170\pi$
$992$	0.438393			0.0139190
$993$			10.8156i			0.343221i
$994$	8.66641	−	32.9590i	0.274882	−	1.04540i
$995$	−23.9308			−0.758656
$996$			51.4240i			1.62943i
$997$	7.24781			0.229540			0.114770	−	0.993392i	$-0.463387\pi$
$997$	7.24781			0.229540			0.114770	+	0.993392i	$0.463387\pi$
$998$			101.779i			3.22175i
$999$			43.8024i			1.38585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.b.f.846.1		16
7.6	odd	2	inner	847.2.b.f.846.2		16
11.2	odd	10		847.2.l.i.524.3		16
11.3	even	5		847.2.l.e.475.2		16
11.4	even	5		847.2.l.j.699.3		16
11.5	even	5		847.2.l.i.118.4		16
11.6	odd	10		77.2.l.b.41.2	yes	16
11.7	odd	10		847.2.l.e.699.1		16
11.8	odd	10		847.2.l.j.475.4		16
11.9	even	5		77.2.l.b.62.1	yes	16
11.10	odd	2	inner	847.2.b.f.846.15		16
33.17	even	10		693.2.bu.d.118.3		16
33.20	odd	10		693.2.bu.d.370.4		16
77.6	even	10		77.2.l.b.41.1	✓	16
77.9	even	15		539.2.s.c.227.2		16
77.13	even	10		847.2.l.i.524.4		16
77.17	even	30		539.2.s.c.19.2		16
77.20	odd	10		77.2.l.b.62.2	yes	16
77.27	odd	10		847.2.l.i.118.3		16
77.31	odd	30		539.2.s.b.117.1		16
77.39	odd	30		539.2.s.c.19.1		16
77.41	even	10		847.2.l.j.475.3		16
77.48	odd	10		847.2.l.j.699.4		16
77.53	even	15		539.2.s.b.117.2		16
77.61	even	30		539.2.s.b.129.2		16
77.62	even	10		847.2.l.e.699.2		16
77.69	odd	10		847.2.l.e.475.1		16
77.72	odd	30		539.2.s.b.129.1		16
77.75	odd	30		539.2.s.c.227.1		16
77.76	even	2	inner	847.2.b.f.846.16		16
231.20	even	10		693.2.bu.d.370.3		16
231.83	odd	10		693.2.bu.d.118.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.l.b.41.1	✓	16	77.6	even	10
77.2.l.b.41.2	yes	16	11.6	odd	10
77.2.l.b.62.1	yes	16	11.9	even	5
77.2.l.b.62.2	yes	16	77.20	odd	10
539.2.s.b.117.1		16	77.31	odd	30
539.2.s.b.117.2		16	77.53	even	15
539.2.s.b.129.1		16	77.72	odd	30
539.2.s.b.129.2		16	77.61	even	30
539.2.s.c.19.1		16	77.39	odd	30
539.2.s.c.19.2		16	77.17	even	30
539.2.s.c.227.1		16	77.75	odd	30
539.2.s.c.227.2		16	77.9	even	15
693.2.bu.d.118.3		16	33.17	even	10
693.2.bu.d.118.4		16	231.83	odd	10
693.2.bu.d.370.3		16	231.20	even	10
693.2.bu.d.370.4		16	33.20	odd	10
847.2.b.f.846.1		16	1.1	even	1	trivial
847.2.b.f.846.2		16	7.6	odd	2	inner
847.2.b.f.846.15		16	11.10	odd	2	inner
847.2.b.f.846.16		16	77.76	even	2	inner
847.2.l.e.475.1		16	77.69	odd	10
847.2.l.e.475.2		16	11.3	even	5
847.2.l.e.699.1		16	11.7	odd	10
847.2.l.e.699.2		16	77.62	even	10
847.2.l.i.118.3		16	77.27	odd	10
847.2.l.i.118.4		16	11.5	even	5
847.2.l.i.524.3		16	11.2	odd	10
847.2.l.i.524.4		16	77.13	even	10
847.2.l.j.475.3		16	77.41	even	10
847.2.l.j.475.4		16	11.8	odd	10
847.2.l.j.699.3		16	11.4	even	5
847.2.l.j.699.4		16	77.48	odd	10

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)

\(f(q)\)	\(=\)	\(q-2.40487i q^{2} -1.72158i q^{3} -3.78339 q^{4} +3.36793i q^{5} -4.14018 q^{6} +(2.55877 + 0.672816i) q^{7} +4.28881i q^{8} +0.0361478 q^{9} +O(q^{10})\)	\(q-2.40487i q^{2} -1.72158i q^{3} -3.78339 q^{4} +3.36793i q^{5} -4.14018 q^{6} +(2.55877 + 0.672816i) q^{7} +4.28881i q^{8} +0.0361478 q^{9} +8.09942 q^{10} +6.51342i q^{12} +2.55877 q^{13} +(1.61803 - 6.15351i) q^{14} +5.79817 q^{15} +2.74724 q^{16} +3.95924 q^{17} -0.0869308i q^{18} +0.330604 q^{19} -12.7422i q^{20} +(1.15831 - 4.40514i) q^{21} +2.85410 q^{23} +7.38354 q^{24} -6.34293 q^{25} -6.15351i q^{26} -5.22698i q^{27} +(-9.68083 - 2.54552i) q^{28} +2.49180i q^{29} -13.9438i q^{30} -0.222436i q^{31} +1.97087i q^{32} -9.52144i q^{34} +(-2.26600 + 8.61776i) q^{35} -0.136761 q^{36} -8.38006 q^{37} -0.795060i q^{38} -4.40514i q^{39} -14.4444 q^{40} +9.53117 q^{41} +(-10.5938 - 2.78558i) q^{42} -1.73205i q^{43} +0.121743i q^{45} -6.86374i q^{46} -1.23993i q^{47} -4.72960i q^{48} +(6.09464 + 3.44317i) q^{49} +15.2539i q^{50} -6.81616i q^{51} -9.68083 q^{52} +0.302113 q^{53} -12.5702 q^{54} +(-2.88558 + 10.9741i) q^{56} -0.569163i q^{57} +5.99244 q^{58} -9.03006i q^{59} -21.9367 q^{60} +5.68376 q^{61} -0.534929 q^{62} +(0.0924941 + 0.0243209i) q^{63} +10.2342 q^{64} +8.61776i q^{65} -6.57998 q^{67} -14.9793 q^{68} -4.91358i q^{69} +(20.7246 + 5.44942i) q^{70} +5.35614 q^{71} +0.155031i q^{72} -6.99173 q^{73} +20.1529i q^{74} +10.9199i q^{75} -1.25080 q^{76} -10.5938 q^{78} +2.95520i q^{79} +9.25250i q^{80} -8.89025 q^{81} -22.9212i q^{82} +7.89509 q^{83} +(-4.38233 + 16.6664i) q^{84} +13.3344i q^{85} -4.16535 q^{86} +4.28984 q^{87} -3.66560i q^{89} +0.292776 q^{90} +(6.54732 + 1.72158i) q^{91} -10.7982 q^{92} -0.382942 q^{93} -2.98187 q^{94} +1.11345i q^{95} +3.39302 q^{96} +13.6379i q^{97} +(8.28036 - 14.6568i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more