LMFDB - Embedded newform 85.2.b.a.69.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(69,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("85.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.7
Root			$0.561103 + 0.561103i$ of defining polynomial
Character	$\chi$	$=$	85.69
Dual form			85.2.b.a.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.03032i q^{2} +2.37033i q^{3} -2.12221 q^{4} +(1.70032 - 1.45220i) q^{5} -4.81252 q^{6} -5.03032i q^{7} -0.248119i q^{8} -2.61845 q^{9} +(2.94844 + 3.45220i) q^{10} -1.90812 q^{11} -5.03032i q^{12} +1.04155i q^{13} +10.2132 q^{14} +(3.44220 + 4.03032i) q^{15} -3.74065 q^{16} +1.00000i q^{17} -5.31629i q^{18} -3.31999 q^{19} +(-3.60844 + 3.08188i) q^{20} +11.9235 q^{21} -3.87409i q^{22} +0.125912i q^{23} +0.588123 q^{24} +(0.782203 - 4.93844i) q^{25} -2.11468 q^{26} +0.904410i q^{27} +10.6754i q^{28} +5.56441 q^{29} +(-8.18285 + 6.98877i) q^{30} -4.99629 q^{31} -8.09097i q^{32} -4.52285i q^{33} -2.03032 q^{34} +(-7.30506 - 8.55318i) q^{35} +5.55688 q^{36} +1.56441i q^{37} -6.74065i q^{38} -2.46881 q^{39} +(-0.360320 - 0.421883i) q^{40} +4.72064 q^{41} +24.2085i q^{42} +4.46221i q^{43} +4.04941 q^{44} +(-4.45220 + 3.80252i) q^{45} -0.255643 q^{46} -1.04155i q^{47} -8.86656i q^{48} -18.3041 q^{49} +(10.0266 + 1.58812i) q^{50} -2.37033 q^{51} -2.21039i q^{52} +6.48883i q^{53} -1.83624 q^{54} +(-3.24441 + 2.77097i) q^{55} -1.24812 q^{56} -7.86946i q^{57} +11.2975i q^{58} +2.00000 q^{59} +(-7.30506 - 8.55318i) q^{60} +7.14882 q^{61} -10.1441i q^{62} +13.1716i q^{63} +8.94596 q^{64} +(1.51255 + 1.77097i) q^{65} +9.18285 q^{66} -3.28596i q^{67} -2.12221i q^{68} -0.298453 q^{69} +(17.3657 - 14.8316i) q^{70} -5.65629 q^{71} +0.649686i q^{72} -12.5295i q^{73} -3.17625 q^{74} +(11.7057 + 1.85408i) q^{75} +7.04571 q^{76} +9.59843i q^{77} -5.01249i q^{78} +13.3694 q^{79} +(-6.36032 + 5.43219i) q^{80} -9.99908 q^{81} +9.58442i q^{82} -1.14222i q^{83} -25.3041 q^{84} +(1.45220 + 1.70032i) q^{85} -9.05972 q^{86} +13.1895i q^{87} +0.473440i q^{88} -1.64090 q^{89} +(-7.72034 - 9.03941i) q^{90} +5.23934 q^{91} -0.267212i q^{92} -11.8428i q^{93} +2.11468 q^{94} +(-5.64506 + 4.82131i) q^{95} +19.1782 q^{96} -7.29753i q^{97} -37.1633i q^{98} +4.99629 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{9} + 6 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{16} - 8 q^{19} - 2 q^{20} + 24 q^{21} + 12 q^{24} - 12 q^{25} + 8 q^{29} - 16 q^{30} - 24 q^{31} + 4 q^{34} + 44 q^{39} + 22 q^{40}+ \cdots + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^9 + 6 * q^10 - 4 * q^11 + 12 * q^14 - 8 * q^16 - 8 * q^19 - 2 * q^20 + 24 * q^21 + 12 * q^24 - 12 * q^25 + 8 * q^29 - 16 * q^30 - 24 * q^31 + 4 * q^34 + 44 * q^39 + 22 * q^40 - 12 * q^41 - 32 * q^44 - 22 * q^45 - 8 * q^46 - 16 * q^49 + 44 * q^50 - 8 * q^51 - 20 * q^54 - 8 * q^55 - 8 * q^56 + 16 * q^59 + 12 * q^61 + 48 * q^64 + 20 * q^65 + 24 * q^66 - 8 * q^69 + 40 * q^70 - 20 * q^71 - 40 * q^74 + 4 * q^75 - 24 * q^76 + 24 * q^79 - 26 * q^80 - 8 * q^81 - 72 * q^84 - 2 * q^85 + 40 * q^86 - 48 * q^89 - 74 * q^90 + 36 * q^91 + 4 * q^95 + 16 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.03032i			1.43565i	0.696221	+	0.717827i	$0.254863\pi$
$2$			2.03032i			1.43565i	−0.696221	+	0.717827i	$0.745137\pi$
$3$			2.37033i			1.36851i	0.729244	+	0.684254i	$0.239872\pi$
$3$			2.37033i			1.36851i	−0.729244	+	0.684254i	$0.760128\pi$
$4$	−2.12221			−1.06110
$5$	1.70032	−	1.45220i	0.760408	−	0.649446i
$5$	1.70032	−	1.45220i	0.760408	−	0.649446i
$6$	−4.81252			−1.96470
$7$		−	5.03032i		−	1.90128i	−0.310291	−	0.950641i	$-0.600427\pi$
$7$		−	5.03032i		−	1.90128i	0.310291	−	0.950641i	$-0.399573\pi$
$8$		−	0.248119i		−	0.0877234i
$9$	−2.61845			−0.872815
$10$	2.94844	+	3.45220i	0.932380	+	1.09168i
$11$	−1.90812			−0.575318			−0.287659	−	0.957733i	$-0.592877\pi$
$11$	−1.90812			−0.575318			−0.287659	+	0.957733i	$0.592877\pi$
$12$		−	5.03032i		−	1.45213i
$13$			1.04155i			0.288874i	0.989514	+	0.144437i	$0.0461371\pi$
$13$			1.04155i			0.288874i	−0.989514	+	0.144437i	$0.953863\pi$
$14$	10.2132			2.72959
$15$	3.44220	+	4.03032i	0.888772	+	1.04062i
$16$	−3.74065			−0.935163
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$		−	5.31629i		−	1.25306i
$19$	−3.31999			−0.761658			−0.380829	−	0.924645i	$-0.624361\pi$
$19$	−3.31999			−0.761658			−0.380829	+	0.924645i	$0.624361\pi$
$20$	−3.60844	+	3.08188i	−0.806871	+	0.689129i
$21$	11.9235			2.60192
$22$		−	3.87409i		−	0.825958i
$23$			0.125912i			0.0262545i	0.999914	+	0.0131273i	$0.00417866\pi$
$23$			0.125912i			0.0262545i	−0.999914	+	0.0131273i	$0.995821\pi$
$24$	0.588123			0.120050
$25$	0.782203	−	4.93844i	0.156441	−	0.987687i
$26$	−2.11468			−0.414724
$27$			0.904410i			0.174054i
$28$			10.6754i			2.01746i
$29$	5.56441			1.03328			0.516642	−	0.856201i	$-0.327182\pi$
$29$	5.56441			1.03328			0.516642	+	0.856201i	$0.327182\pi$
$30$	−8.18285	+	6.98877i	−1.49398	+	1.27597i
$31$	−4.99629			−0.897361			−0.448680	−	0.893692i	$-0.648106\pi$
$31$	−4.99629			−0.897361			−0.448680	+	0.893692i	$0.648106\pi$
$32$		−	8.09097i		−	1.43029i
$33$		−	4.52285i		−	0.787328i
$34$	−2.03032			−0.348197
$35$	−7.30506	−	8.55318i	−1.23478	−	1.44575i
$36$	5.55688			0.926147
$37$			1.56441i			0.257187i	0.991697	+	0.128593i	$0.0410462\pi$
$37$			1.56441i			0.257187i	−0.991697	+	0.128593i	$0.958954\pi$
$38$		−	6.74065i		−	1.09348i
$39$	−2.46881			−0.395327
$40$	−0.360320	−	0.421883i	−0.0569716	−	0.0667055i
$41$	4.72064			0.737240			0.368620	−	0.929580i	$-0.379830\pi$
$41$	4.72064			0.737240			0.368620	+	0.929580i	$0.379830\pi$
$42$			24.2085i			3.73546i
$43$			4.46221i			0.680481i	0.940338	+	0.340240i	$0.110508\pi$
$43$			4.46221i			0.680481i	−0.940338	+	0.340240i	$0.889492\pi$
$44$	4.04941			0.610472
$45$	−4.45220	+	3.80252i	−0.663695	+	0.566846i
$46$	−0.255643			−0.0376924
$47$		−	1.04155i		−	0.151926i	−0.997111	−	0.0759629i	$-0.975797\pi$
$47$		−	1.04155i		−	0.151926i	0.997111	−	0.0759629i	$-0.0242031\pi$
$48$		−	8.86656i		−	1.27978i
$49$	−18.3041			−2.61488
$50$	10.0266	+	1.58812i	1.41798	+	0.224595i
$51$	−2.37033			−0.331912
$52$		−	2.21039i		−	0.306525i
$53$			6.48883i			0.891309i	0.895205	+	0.445654i	$0.147029\pi$
$53$			6.48883i			0.891309i	−0.895205	+	0.445654i	$0.852971\pi$
$54$	−1.83624			−0.249881
$55$	−3.24441	+	2.77097i	−0.437477	+	0.373638i
$56$	−1.24812			−0.166787
$57$		−	7.86946i		−	1.04234i
$58$			11.2975i			1.48344i
$59$	2.00000			0.260378			0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000			0.260378			0.130189	+	0.991489i	$0.458442\pi$
$60$	−7.30506	−	8.55318i	−0.943079	−	1.10421i
$61$	7.14882			0.915313			0.457657	−	0.889129i	$-0.348689\pi$
$61$	7.14882			0.915313			0.457657	+	0.889129i	$0.348689\pi$
$62$		−	10.1441i		−	1.28830i
$63$			13.1716i			1.65947i
$64$	8.94596			1.11825
$65$	1.51255	+	1.77097i	0.187608	+	0.219662i
$66$	9.18285			1.13033
$67$		−	3.28596i		−	0.401444i	−0.979648	−	0.200722i	$-0.935671\pi$
$67$		−	3.28596i		−	0.401444i	0.979648	−	0.200722i	$-0.0643289\pi$
$68$		−	2.12221i		−	0.257355i
$69$	−0.298453			−0.0359296
$70$	17.3657	−	14.8316i	2.07560	−	1.77272i
$71$	−5.65629			−0.671278			−0.335639	−	0.941991i	$-0.608952\pi$
$71$	−5.65629			−0.671278			−0.335639	+	0.941991i	$0.608952\pi$
$72$			0.649686i			0.0765663i
$73$		−	12.5295i		−	1.46646i	−0.679980	−	0.733231i	$-0.738011\pi$
$73$		−	12.5295i		−	1.46646i	0.679980	−	0.733231i	$-0.261989\pi$
$74$	−3.17625			−0.369231
$75$	11.7057	+	1.85408i	1.35166	+	0.214090i
$76$	7.04571			0.808198
$77$			9.59843i			1.09384i
$78$		−	5.01249i		−	0.567553i
$79$	13.3694			1.50418			0.752088	−	0.659063i	$-0.229047\pi$
$79$	13.3694			1.50418			0.752088	+	0.659063i	$0.229047\pi$
$80$	−6.36032	+	5.43219i	−0.711105	+	0.607338i
$81$	−9.99908			−1.11101
$82$			9.58442i			1.05842i
$83$		−	1.14222i		−	0.125375i	−0.998033	−	0.0626874i	$-0.980033\pi$
$83$		−	1.14222i		−	0.125375i	0.998033	−	0.0626874i	$-0.0199671\pi$
$84$	−25.3041			−2.76091
$85$	1.45220	+	1.70032i	0.157514	+	0.184426i
$86$	−9.05972			−0.976935
$87$			13.1895i			1.41406i
$88$			0.473440i			0.0504689i
$89$	−1.64090			−0.173935			−0.0869677	−	0.996211i	$-0.527718\pi$
$89$	−1.64090			−0.173935			−0.0869677	+	0.996211i	$0.527718\pi$
$90$	−7.72034	−	9.03941i	−0.813795	−	0.952837i
$91$	5.23934			0.549232
$92$		−	0.267212i		−	0.0278588i
$93$		−	11.8428i		−	1.22805i
$94$	2.11468			0.218113
$95$	−5.64506	+	4.82131i	−0.579171	+	0.494656i
$96$	19.1782			1.95737
$97$		−	7.29753i		−	0.740952i	−0.928842	−	0.370476i	$-0.879195\pi$
$97$		−	7.29753i		−	0.740952i	0.928842	−	0.370476i	$-0.120805\pi$
$98$		−	37.1633i		−	3.75406i
$99$	4.99629			0.502146
$100$	−1.66000	+	10.4804i	−0.166000	+	1.04804i
$101$	−4.93103			−0.490655			−0.245328	−	0.969440i	$-0.578896\pi$
$101$	−4.93103			−0.490655			−0.245328	+	0.969440i	$0.578896\pi$
$102$		−	4.81252i		−	0.476511i
$103$			3.47715i			0.342613i	0.985218	+	0.171307i	$0.0547989\pi$
$103$			3.47715i			0.342613i	−0.985218	+	0.171307i	$0.945201\pi$
$104$	0.258429			0.0253410
$105$	20.2738	−	17.3154i	1.97852	−	1.68981i
$106$	−13.1744			−1.27961
$107$			15.8116i			1.52857i	0.644881	+	0.764283i	$0.276907\pi$
$107$			15.8116i			1.52857i	−0.644881	+	0.764283i	$0.723093\pi$
$108$		−	1.91934i		−	0.184689i
$109$	−3.40065			−0.325723			−0.162861	−	0.986649i	$-0.552072\pi$
$109$	−3.40065			−0.325723			−0.162861	+	0.986649i	$0.552072\pi$
$110$	−5.62597	−	6.58720i	−0.536415	−	0.628065i
$111$	−3.70815			−0.351962
$112$			18.8167i			1.77801i
$113$			16.9426i			1.59383i	0.604095	+	0.796913i	$0.293535\pi$
$113$			16.9426i			1.59383i	−0.604095	+	0.796913i	$0.706465\pi$
$114$	15.9775			1.49643
$115$	0.182850	+	0.214092i	0.0170509	+	0.0199642i
$116$	−11.8088			−1.09642
$117$		−	2.72724i		−	0.252134i
$118$			4.06064i			0.373813i
$119$	5.03032			0.461129
$120$	1.00000	−	0.854075i	0.0912871	−	0.0779661i
$121$	−7.35910			−0.669009
$122$			14.5144i			1.31407i
$123$			11.1895i			1.00892i
$124$	10.6032			0.952193
$125$	−5.84162	−	9.53286i	−0.522491	−	0.852645i
$126$	−26.7426			−2.38242
$127$		−	0.340924i		−	0.0302521i	−0.999886	−	0.0151260i	$-0.995185\pi$
$127$		−	0.340924i		−	0.0302521i	0.999886	−	0.0151260i	$-0.00481495\pi$
$128$			1.98125i			0.175119i
$129$	−10.5769			−0.931244
$130$	−3.59565	+	3.07095i	−0.315359	+	0.269340i
$131$	−14.5457			−1.27086			−0.635430	−	0.772159i	$-0.719177\pi$
$131$	−14.5457			−1.27086			−0.635430	+	0.772159i	$0.719177\pi$
$132$			9.59843i			0.835436i
$133$			16.7006i			1.44813i
$134$	6.67157			0.576335
$135$	1.31339	+	1.53779i	0.113038	+	0.132352i
$136$	0.248119			0.0212760
$137$			15.5686i			1.33011i	0.746793	+	0.665056i	$0.231592\pi$
$137$			15.5686i			1.33011i	−0.746793	+	0.665056i	$0.768408\pi$
$138$		−	0.605956i		−	0.0515824i
$139$	18.9314			1.60574			0.802869	−	0.596156i	$-0.203306\pi$
$139$	18.9314			1.60574			0.802869	+	0.596156i	$0.203306\pi$
$140$	15.5028	+	18.1516i	1.31023	+	1.53409i
$141$	2.46881			0.207912
$142$		−	11.4841i		−	0.963723i
$143$		−	1.98740i		−	0.166195i
$144$	9.79469			0.816224
$145$	9.46129	−	8.08066i	0.785717	−	0.671062i
$146$	25.4388			2.10533
$147$		−	43.3868i		−	3.57848i
$148$		−	3.31999i		−	0.272902i
$149$	12.8087			1.04933			0.524665	−	0.851309i	$-0.324191\pi$
$149$	12.8087			1.04933			0.524665	+	0.851309i	$0.324191\pi$
$150$	−3.76437	+	23.7663i	−0.307360	+	1.94051i
$151$	−6.55688			−0.533591			−0.266796	−	0.963753i	$-0.585965\pi$
$151$	−6.55688			−0.533591			−0.266796	+	0.963753i	$0.585965\pi$
$152$			0.823754i			0.0668152i
$153$		−	2.61845i		−	0.211689i
$154$	−19.4879			−1.57038
$155$	−8.49532	+	7.25564i	−0.682360	+	0.582787i
$156$	5.23934			0.419483
$157$		−	11.1138i		−	0.886975i	−0.896281	−	0.443487i	$-0.853741\pi$
$157$		−	11.1138i		−	0.886975i	0.896281	−	0.443487i	$-0.146259\pi$
$158$			27.1442i			2.15948i
$159$	−15.3806			−1.21976
$160$	−11.7497	−	13.7573i	−0.928898	−	1.08761i
$161$	0.633380			0.0499173
$162$		−	20.3014i		−	1.59502i
$163$		−	16.6936i		−	1.30754i	−0.756693	−	0.653770i	$-0.773186\pi$
$163$		−	16.6936i		−	1.30754i	0.756693	−	0.653770i	$-0.226814\pi$
$164$	−10.0182			−0.782288
$165$	−6.56811	−	7.69032i	−0.511327	−	0.598690i
$166$	2.31907			0.179995
$167$		−	17.1516i		−	1.32723i	−0.748074	−	0.663616i	$-0.769021\pi$
$167$		−	17.1516i		−	1.32723i	0.748074	−	0.663616i	$-0.230979\pi$
$168$		−	2.95845i		−	0.228249i
$169$	11.9152			0.916552
$170$	−3.45220	+	2.94844i	−0.264772	+	0.226135i
$171$	8.69322			0.664787
$172$		−	9.46973i		−	0.722060i
$173$		−	14.3051i		−	1.08759i	−0.839217	−	0.543797i	$-0.816986\pi$
$173$		−	14.3051i		−	1.08759i	0.839217	−	0.543797i	$-0.183014\pi$
$174$	−26.7788			−2.03010
$175$	−24.8419	−	3.93473i	−1.87787	−	0.297438i
$176$	7.13759			0.538016
$177$			4.74065i			0.356329i
$178$		−	3.33156i		−	0.249711i
$179$	−8.74065			−0.653307			−0.326653	−	0.945144i	$-0.605921\pi$
$179$	−8.74065			−0.653307			−0.326653	+	0.945144i	$0.605921\pi$
$180$	9.44850	−	8.06973i	0.704250	−	0.601482i
$181$	−9.70815			−0.721601			−0.360801	−	0.932643i	$-0.617497\pi$
$181$	−9.70815			−0.721601			−0.360801	+	0.932643i	$0.617497\pi$
$182$			10.6375i			0.788507i
$183$			16.9450i			1.25261i
$184$	0.0312413			0.00230314
$185$	2.27184	+	2.66000i	0.167029	+	0.195567i
$186$	24.0448			1.76305
$187$		−	1.90812i		−	0.139535i
$188$			2.21039i			0.161209i
$189$	4.54947			0.330925
$190$	−9.78881	−	11.4613i	−0.710155	−	0.831489i
$191$	16.1819			1.17088			0.585442	−	0.810714i	$-0.300921\pi$
$191$	16.1819			1.17088			0.585442	+	0.810714i	$0.300921\pi$
$192$			21.2048i			1.53033i
$193$			9.21688i			0.663445i	0.943377	+	0.331723i	$0.107630\pi$
$193$			9.21688i			0.663445i	−0.943377	+	0.331723i	$0.892370\pi$
$194$	14.8163			1.06375
$195$	−4.19779	+	3.58522i	−0.300610	+	0.256743i
$196$	38.8452			2.77465
$197$			0.151156i			0.0107694i	0.999986	+	0.00538472i	$0.00171402\pi$
$197$			0.151156i			0.0107694i	−0.999986	+	0.00538472i	$0.998286\pi$
$198$			10.1441i			0.720909i
$199$	−15.3395			−1.08739			−0.543695	−	0.839283i	$-0.682975\pi$
$199$	−15.3395			−1.08739			−0.543695	+	0.839283i	$0.682975\pi$
$200$	−1.22532	−	0.194079i	−0.0866433	−	0.0137235i
$201$	7.78881			0.549380
$202$		−	10.0116i		−	0.704412i
$203$		−	27.9908i		−	1.96457i
$204$	5.03032			0.352193
$205$	8.02662	−	6.85534i	0.560603	−	0.478797i
$206$	−7.05972			−0.491874
$207$		−	0.329695i		−	0.0229154i
$208$		−	3.89608i		−	0.270144i
$209$	6.33493			0.438196
$210$	35.1558	+	41.1624i	2.42598	+	2.84047i
$211$	25.4226			1.75017			0.875083	−	0.483972i	$-0.160806\pi$
$211$	25.4226			1.75017			0.875083	+	0.483972i	$0.160806\pi$
$212$		−	13.7706i		−	0.945771i
$213$		−	13.4073i		−	0.918650i
$214$	−32.1026			−2.19449
$215$	6.48004	+	7.58720i	0.441935	+	0.517443i
$216$	0.224401			0.0152686
$217$			25.1330i			1.70614i
$218$		−	6.90441i		−	0.467626i
$219$	29.6989			2.00687
$220$	6.88532	−	5.88058i	0.464208	−	0.396469i
$221$	−1.04155			−0.0700623
$222$		−	7.52874i		−	0.505296i
$223$			12.0116i			0.804354i	0.915562	+	0.402177i	$0.131746\pi$
$223$			12.0116i			0.804354i	−0.915562	+	0.402177i	$0.868254\pi$
$224$	−40.7002			−2.71939
$225$	−2.04815	+	12.9310i	−0.136544	+	0.862068i
$226$	−34.3989			−2.28818
$227$		−	6.92965i		−	0.459937i	−0.973198	−	0.229969i	$-0.926138\pi$
$227$		−	6.92965i		−	0.459937i	0.973198	−	0.229969i	$-0.0738624\pi$
$228$			16.7006i			1.10603i
$229$	15.0822			0.996659			0.498329	−	0.866988i	$-0.333947\pi$
$229$	15.0822			0.996659			0.498329	+	0.866988i	$0.333947\pi$
$230$	−0.434675	+	0.371245i	−0.0286616	+	0.0244792i
$231$	−22.7514			−1.49693
$232$		−	1.38064i		−	0.0906432i
$233$			9.12881i			0.598048i	0.954246	+	0.299024i	$0.0966611\pi$
$233$			9.12881i			0.598048i	−0.954246	+	0.299024i	$0.903339\pi$
$234$	5.53718			0.361977
$235$	−1.51255	−	1.77097i	−0.0986676	−	0.115526i
$236$	−4.24441			−0.276288
$237$			31.6899i			2.05848i
$238$			10.2132i			0.662022i
$239$	1.08573			0.0702303			0.0351151	−	0.999383i	$-0.488820\pi$
$239$	1.08573			0.0702303			0.0351151	+	0.999383i	$0.488820\pi$
$240$	−12.8761	−	15.0760i	−0.831147	−	0.973154i
$241$	−1.17869			−0.0759262			−0.0379631	−	0.999279i	$-0.512087\pi$
$241$	−1.17869			−0.0759262			−0.0379631	+	0.999279i	$0.512087\pi$
$242$		−	14.9413i		−	0.960465i
$243$		−	20.9879i		−	1.34637i
$244$	−15.1713			−0.971242
$245$	−31.1230	+	26.5814i	−1.98837	+	1.69822i
$246$	−22.7182			−1.44846
$247$		−	3.45794i		−	0.220023i
$248$			1.23968i			0.0787195i
$249$	2.70743			0.171577
$250$	19.3548	−	11.8604i	1.22410	−	0.750116i
$251$	24.3432			1.53653			0.768266	−	0.640131i	$-0.221120\pi$
$251$	24.3432			1.53653			0.768266	+	0.640131i	$0.221120\pi$
$252$		−	27.9529i		−	1.76087i
$253$		−	0.240255i		−	0.0151047i
$254$	0.692184			0.0434315
$255$	−4.03032	+	3.44220i	−0.252389	+	0.215559i
$256$	13.8694			0.866834
$257$			4.60596i			0.287312i	0.989628	+	0.143656i	$0.0458858\pi$
$257$			4.60596i			0.287312i	−0.989628	+	0.143656i	$0.954114\pi$
$258$		−	21.4745i		−	1.33694i
$259$	7.86946			0.488985
$260$	−3.20993	−	3.75837i	−0.199072	−	0.233084i
$261$	−14.5701			−0.901866
$262$		−	29.5324i		−	1.82452i
$263$			11.6058i			0.715647i	0.933789	+	0.357823i	$0.116481\pi$
$263$			11.6058i			0.715647i	−0.933789	+	0.357823i	$0.883519\pi$
$264$	−1.12221			−0.0690671
$265$	9.42311	+	11.0331i	0.578857	+	0.677758i
$266$	−33.9076			−2.07901
$267$		−	3.88948i		−	0.238032i
$268$			6.97350i			0.425974i
$269$	−27.6284			−1.68453			−0.842267	−	0.539061i	$-0.818779\pi$
$269$	−27.6284			−1.68453			−0.842267	+	0.539061i	$0.818779\pi$
$270$	−3.12221	+	2.66660i	−0.190011	+	0.162284i
$271$	−1.44128			−0.0875515			−0.0437757	−	0.999041i	$-0.513939\pi$
$271$	−1.44128			−0.0875515			−0.0437757	+	0.999041i	$0.513939\pi$
$272$		−	3.74065i		−	0.226810i
$273$			12.4189i			0.751628i
$274$	−31.6092			−1.90958
$275$	−1.49253	+	9.42311i	−0.0900031	+	0.568235i
$276$	0.633380			0.0381250
$277$		−	2.34753i		−	0.141049i	−0.997510	−	0.0705246i	$-0.977533\pi$
$277$		−	2.34753i		−	0.141049i	0.997510	−	0.0705246i	$-0.0224673\pi$
$278$			38.4368i			2.30528i
$279$	13.0825			0.783230
$280$	−2.12221	+	1.81252i	−0.126826	+	0.108319i
$281$	−13.4588			−0.802887			−0.401444	−	0.915884i	$-0.631491\pi$
$281$	−13.4588			−0.802887			−0.401444	+	0.915884i	$0.631491\pi$
$282$			5.01249i			0.298489i
$283$		−	22.1973i		−	1.31949i	−0.751488	−	0.659747i	$-0.770664\pi$
$283$		−	22.1973i		−	1.31949i	0.751488	−	0.659747i	$-0.229336\pi$
$284$	12.0038			0.712296
$285$	−11.4281	−	13.3806i	−0.676941	−	0.792600i
$286$	4.03506			0.238598
$287$		−	23.7463i		−	1.40170i
$288$			21.1857i			1.24838i
$289$	−1.00000			−0.0588235
$290$	16.4063	+	19.2095i	0.963413	+	1.12802i
$291$	17.2975			1.01400
$292$			26.5901i			1.55607i
$293$		−	5.63430i		−	0.329159i	−0.986364	−	0.164580i	$-0.947373\pi$
$293$		−	5.63430i		−	0.329159i	0.986364	−	0.164580i	$-0.0526268\pi$
$294$	88.0891			5.13746
$295$	3.40065	−	2.90441i	0.197993	−	0.169101i
$296$	0.388159			0.0225613
$297$		−	1.72572i		−	0.100136i
$298$			26.0058i			1.50648i
$299$	−0.131144			−0.00758426
$300$	−24.8419	−	3.93473i	−1.43425	−	0.227172i
$301$	22.4464			1.29379
$302$		−	13.3126i		−	0.766053i
$303$		−	11.6881i		−	0.671466i
$304$	12.4189			0.712275
$305$	12.1553	−	10.3816i	0.696011	−	0.594446i
$306$	5.31629			0.303912
$307$			29.3623i			1.67580i	0.545826	+	0.837899i	$0.316216\pi$
$307$			29.3623i			1.67580i	−0.545826	+	0.837899i	$0.683784\pi$
$308$		−	20.3699i		−	1.16068i
$309$	−8.24197			−0.468869
$310$	−14.7313	−	17.2482i	−0.836681	−	0.979634i
$311$	12.4351			0.705131			0.352566	−	0.935787i	$-0.385309\pi$
$311$	12.4351			0.705131			0.352566	+	0.935787i	$0.385309\pi$
$312$			0.612560i			0.0346794i
$313$		−	15.3708i		−	0.868808i	−0.900718	−	0.434404i	$-0.856959\pi$
$313$		−	15.3708i		−	0.868808i	0.900718	−	0.434404i	$-0.143041\pi$
$314$	22.5645			1.27339
$315$	19.1279	+	22.3960i	1.07773	+	1.26187i
$316$	−28.3726			−1.59609
$317$			23.4837i			1.31898i	0.751714	+	0.659489i	$0.229227\pi$
$317$			23.4837i			1.31898i	−0.751714	+	0.659489i	$0.770773\pi$
$318$		−	31.2276i		−	1.75116i
$319$	−10.6175			−0.594467
$320$	15.2110	−	12.9914i	0.850322	−	0.726239i
$321$	−37.4787			−2.09185
$322$			1.28596i			0.0716640i
$323$		−	3.31999i		−	0.184729i
$324$	21.2201			1.17890
$325$	5.14363	+	0.814704i	0.285317	+	0.0451916i
$326$	33.8933			1.87718
$327$		−	8.06064i		−	0.445755i
$328$		−	1.17128i		−	0.0646732i
$329$	−5.23934			−0.288854
$330$	15.6138	−	13.3354i	0.859513	−	0.734088i
$331$	−35.6839			−1.96136			−0.980681	−	0.195614i	$-0.937330\pi$
$331$	−35.6839			−1.96136			−0.980681	+	0.195614i	$0.937330\pi$
$332$			2.42403i			0.133036i
$333$		−	4.09631i		−	0.224476i
$334$	34.8233			1.90545
$335$	−4.77189	−	5.58720i	−0.260716	−	0.305262i
$336$	−44.6017			−2.43322
$337$		−	27.9833i		−	1.52435i	−0.647371	−	0.762175i	$-0.724132\pi$
$337$		−	27.9833i		−	1.52435i	0.647371	−	0.762175i	$-0.275868\pi$
$338$			24.1916i			1.31585i
$339$	−40.1595			−2.18116
$340$	−3.08188	−	3.60844i	−0.167138	−	0.195695i
$341$	9.53350			0.516268
$342$			17.6500i			0.954404i
$343$			56.8635i			3.07034i
$344$	1.10716			0.0596941
$345$	−0.507467	+	0.433415i	−0.0273211	+	0.0233343i
$346$	29.0439			1.56141
$347$			13.9904i			0.751045i	0.926813	+	0.375522i	$0.122537\pi$
$347$			13.9904i			0.751045i	−0.926813	+	0.375522i	$0.877463\pi$
$348$		−	27.9908i		−	1.50046i
$349$	17.8396			0.954932			0.477466	−	0.878650i	$-0.341555\pi$
$349$	17.8396			0.954932			0.477466	+	0.878650i	$0.341555\pi$
$350$	7.98877	−	50.4371i	0.427018	−	2.69598i
$351$	−0.941988			−0.0502796
$352$			15.4385i			0.822874i
$353$		−	14.0831i		−	0.749568i	−0.927112	−	0.374784i	$-0.877717\pi$
$353$		−	14.0831i		−	0.749568i	0.927112	−	0.374784i	$-0.122283\pi$
$354$	−9.62505			−0.511566
$355$	−9.61753	+	8.21409i	−0.510445	+	0.435959i
$356$	3.48234			0.184563
$357$			11.9235i			0.631059i
$358$		−	17.7463i		−	0.937923i
$359$	−14.1007			−0.744205			−0.372102	−	0.928192i	$-0.621363\pi$
$359$	−14.1007			−0.744205			−0.372102	+	0.928192i	$0.621363\pi$
$360$	0.943478	+	1.10468i	0.0497256	+	0.0582216i
$361$	−7.97765			−0.419877
$362$		−	19.7107i		−	1.03597i
$363$		−	17.4435i		−	0.915544i
$364$	−11.1190			−0.582792
$365$	−18.1953	−	21.3041i	−0.952388	−	1.11511i
$366$	−34.4039			−1.79832
$367$		−	18.0080i		−	0.940009i	−0.882664	−	0.470004i	$-0.844252\pi$
$367$		−	18.0080i		−	0.940009i	0.882664	−	0.470004i	$-0.155748\pi$
$368$		−	0.470994i		−	0.0245523i
$369$	−12.3607			−0.643474
$370$	−5.40065	+	4.61256i	−0.280766	+	0.239796i
$371$	32.6409			1.69463
$372$			25.1330i			1.30308i
$373$			10.9036i			0.564567i	0.959331	+	0.282284i	$0.0910919\pi$
$373$			10.9036i			0.564567i	−0.959331	+	0.282284i	$0.908908\pi$
$374$	3.87409			0.200324
$375$	22.5960	−	13.8466i	1.16685	−	0.715033i
$376$	−0.258429			−0.0133274
$377$			5.79561i			0.298489i
$378$			9.23689i			0.475094i
$379$	22.8199			1.17218			0.586091	−	0.810245i	$-0.300666\pi$
$379$	22.8199			1.17218			0.586091	+	0.810245i	$0.300666\pi$
$380$	11.9800	−	10.2318i	0.614560	−	0.524881i
$381$	0.808100			0.0414002
$382$			32.8545i			1.68098i
$383$			0.315946i			0.0161441i	0.999967	+	0.00807204i	$0.00256944\pi$
$383$			0.315946i			0.0161441i	−0.999967	+	0.00807204i	$0.997431\pi$
$384$	−4.69620			−0.239652
$385$	13.9389	+	16.3204i	0.710392	+	0.831767i
$386$	−18.7132			−0.952478
$387$		−	11.6841i		−	0.593934i
$388$			15.4869i			0.786227i
$389$	−9.05972			−0.459346			−0.229673	−	0.973268i	$-0.573766\pi$
$389$	−9.05972			−0.459346			−0.229673	+	0.973268i	$0.573766\pi$
$390$	−7.27916	−	8.52285i	−0.368595	−	0.431572i
$391$	−0.125912			−0.00636766
$392$			4.54161i			0.229386i
$393$		−	34.4779i		−	1.73918i
$394$	−0.306896			−0.0154612
$395$	22.7323	−	19.4151i	1.14379	−	0.976880i
$396$	−10.6032			−0.532829
$397$			9.25690i			0.464591i	0.972645	+	0.232295i	$0.0746236\pi$
$397$			9.25690i			0.464591i	−0.972645	+	0.232295i	$0.925376\pi$
$398$		−	31.1442i		−	1.56112i
$399$	−39.5859			−1.98178
$400$	−2.92595	+	18.4730i	−0.146297	+	0.923649i
$401$	−13.0783			−0.653100			−0.326550	−	0.945180i	$-0.605886\pi$
$401$	−13.0783			−0.653100			−0.326550	+	0.945180i	$0.605886\pi$
$402$			15.8138i			0.788720i
$403$		−	5.20389i		−	0.259224i
$404$	10.4647			0.520636
$405$	−17.0017	+	14.5207i	−0.844820	+	0.721540i
$406$	56.8302			2.82044
$407$		−	2.98507i		−	0.147964i
$408$			0.588123i			0.0291164i
$409$	−5.12881			−0.253603			−0.126802	−	0.991928i	$-0.540471\pi$
$409$	−5.12881			−0.253603			−0.126802	+	0.991928i	$0.540471\pi$
$410$	13.9185	+	16.2966i	0.687388	+	0.804832i
$411$	−36.9026			−1.82027
$412$		−	7.37922i		−	0.363548i
$413$		−	10.0606i		−	0.495052i
$414$	0.669386			0.0328985
$415$	−1.65874	−	1.94214i	−0.0814241	−	0.0953360i
$416$	8.42715			0.413175
$417$			44.8735i			2.19747i
$418$			12.8619i			0.629098i
$419$	−31.5464			−1.54114			−0.770572	−	0.637353i	$-0.780030\pi$
$419$	−31.5464			−1.54114			−0.770572	+	0.637353i	$0.780030\pi$
$420$	−43.0252	+	36.7468i	−2.09942	+	1.79306i
$421$	5.26595			0.256647			0.128323	−	0.991732i	$-0.459040\pi$
$421$	5.26595			0.256647			0.128323	+	0.991732i	$0.459040\pi$
$422$			51.6161i			2.51263i
$423$			2.72724i			0.132603i
$424$	1.61000			0.0781886
$425$	4.93844	+	0.782203i	0.239549	+	0.0379424i
$426$	27.2210			1.31886
$427$		−	35.9609i		−	1.74027i
$428$		−	33.5555i		−	1.62197i
$429$	4.71078			0.227439
$430$	−15.4045	+	13.1566i	−0.742869	+	0.634466i
$431$	35.6270			1.71609			0.858047	−	0.513572i	$-0.171678\pi$
$431$	35.6270			1.71609			0.858047	+	0.513572i	$0.171678\pi$
$432$		−	3.38308i		−	0.162769i
$433$			20.2868i			0.974919i	0.873145	+	0.487460i	$0.162076\pi$
$433$			20.2868i			0.974919i	−0.873145	+	0.487460i	$0.837924\pi$
$434$	−51.0280			−2.44942
$435$	19.1538	+	22.4263i	0.918354	+	1.07526i
$436$	7.21688			0.345626
$437$		−	0.418028i		−	0.0199970i
$438$			60.2983i			2.88117i
$439$	8.73187			0.416749			0.208375	−	0.978049i	$-0.433183\pi$
$439$	8.73187			0.416749			0.208375	+	0.978049i	$0.433183\pi$
$440$	0.687532	+	0.805001i	0.0327768	+	0.0383769i
$441$	47.9284			2.28230
$442$		−	2.11468i		−	0.100585i
$443$		−	4.44159i		−	0.211026i	−0.994418	−	0.105513i	$-0.966351\pi$
$443$		−	4.44159i		−	0.211026i	0.994418	−	0.105513i	$-0.0336485\pi$
$444$	7.86946			0.373468
$445$	−2.79007	+	2.38293i	−0.132262	+	0.112962i
$446$	−24.3874			−1.15477
$447$			30.3608i			1.43602i
$448$		−	45.0011i		−	2.12610i
$449$	7.37262			0.347935			0.173968	−	0.984751i	$-0.444341\pi$
$449$	7.37262			0.347935			0.173968	+	0.984751i	$0.444341\pi$
$450$	−26.2541	−	4.15841i	−1.23763	−	0.196029i
$451$	−9.00752			−0.424148
$452$		−	35.9557i		−	1.69121i
$453$		−	15.5419i		−	0.730224i
$454$	14.0694			0.660311
$455$	8.90857	−	7.60859i	0.417640	−	0.356696i
$456$	−1.95256			−0.0914372
$457$			13.9940i			0.654612i	0.944918	+	0.327306i	$0.106141\pi$
$457$			13.9940i			0.654612i	−0.944918	+	0.327306i	$0.893859\pi$
$458$			30.6217i			1.43086i
$459$	−0.904410			−0.0422142
$460$	−0.388047	−	0.454347i	−0.0180928	−	0.0211840i
$461$	30.9983			1.44373			0.721867	−	0.692032i	$-0.243284\pi$
$461$	30.9983			1.44373			0.721867	+	0.692032i	$0.243284\pi$
$462$		−	46.1927i		−	2.14908i
$463$			14.3185i			0.665436i	0.943026	+	0.332718i	$0.107966\pi$
$463$			14.3185i			0.665436i	−0.943026	+	0.332718i	$0.892034\pi$
$464$	−20.8145			−0.966289
$465$	−17.1982	−	20.1367i	−0.797549	−	0.933816i
$466$	−18.5344			−0.858591
$467$		−	16.4305i		−	0.760313i	−0.924922	−	0.380157i	$-0.875870\pi$
$467$		−	16.4305i		−	0.760313i	0.924922	−	0.380157i	$-0.124130\pi$
$468$			5.78777i			0.267540i
$469$	−16.5295			−0.763259
$470$	3.59565	−	3.07095i	0.165855	−	0.141653i
$471$	26.3432			1.21383
$472$		−	0.496238i		−	0.0228412i
$473$		−	8.51441i		−	0.391493i
$474$	−64.3406			−2.95526
$475$	−2.59691	+	16.3956i	−0.119154	+	0.752280i
$476$	−10.6754			−0.489305
$477$		−	16.9906i		−	0.777948i
$478$			2.20439i			0.100826i
$479$	10.9889			0.502095			0.251047	−	0.967975i	$-0.419225\pi$
$479$	10.9889			0.502095			0.251047	+	0.967975i	$0.419225\pi$
$480$	32.6092	−	27.8507i	1.48840	−	1.27121i
$481$	−1.62941			−0.0742946
$482$		−	2.39312i		−	0.109004i
$483$			1.50132i			0.0683122i
$484$	15.6175			0.709888
$485$	−10.5975	−	12.4082i	−0.481208	−	0.563426i
$486$	42.6121			1.93292
$487$		−	8.78775i		−	0.398211i	−0.979978	−	0.199105i	$-0.936196\pi$
$487$		−	8.78775i		−	0.398211i	0.979978	−	0.199105i	$-0.0638036\pi$
$488$		−	1.77376i		−	0.0802943i
$489$	39.5692			1.78938
$490$	−53.9687	−	63.1896i	−2.43806	−	2.85462i
$491$	15.7845			0.712346			0.356173	−	0.934420i	$-0.384081\pi$
$491$	15.7845			0.712346			0.356173	+	0.934420i	$0.384081\pi$
$492$		−	23.7463i		−	1.07057i
$493$			5.56441i			0.250608i
$494$	7.02073			0.315878
$495$	8.49532	−	7.25564i	0.381836	−	0.326117i
$496$	18.6894			0.839179
$497$			28.4530i			1.27629i
$498$			5.49696i			0.246325i
$499$	8.26885			0.370165			0.185082	−	0.982723i	$-0.440745\pi$
$499$	8.26885			0.370165			0.185082	+	0.982723i	$0.440745\pi$
$500$	12.3971	+	20.2307i	0.554417	+	0.904744i
$501$	40.6549			1.81633
$502$			49.4246i			2.20593i
$503$			3.15345i			0.140605i	0.997526	+	0.0703026i	$0.0223965\pi$
$503$			3.15345i			0.140605i	−0.997526	+	0.0703026i	$0.977603\pi$
$504$	3.26813			0.145574
$505$	−8.38434	+	7.16086i	−0.373098	+	0.318654i
$506$	0.487795			0.0216852
$507$			28.2428i			1.25431i
$508$			0.723510i			0.0321006i
$509$	−22.8444			−1.01256			−0.506280	−	0.862369i	$-0.668980\pi$
$509$	−22.8444			−1.01256			−0.506280	+	0.862369i	$0.668980\pi$
$510$	−6.98877	−	8.18285i	−0.309468	−	0.362343i
$511$	−63.0272			−2.78816
$512$			32.1217i			1.41959i
$513$		−	3.00263i		−	0.132569i
$514$	−9.35157			−0.412480
$515$	5.04953	+	5.91227i	0.222509	+	0.260526i
$516$	22.4464			0.988146
$517$			1.98740i			0.0874057i
$518$			15.9775i			0.702013i
$519$	33.9076			1.48838
$520$	0.439412	−	0.375291i	0.0192695	−	0.0164576i
$521$	−35.6931			−1.56374			−0.781872	−	0.623439i	$-0.785735\pi$
$521$	−35.6931			−1.56374			−0.781872	+	0.623439i	$0.785735\pi$
$522$		−	29.5820i		−	1.29477i
$523$			16.0974i			0.703891i	0.936021	+	0.351945i	$0.114480\pi$
$523$			16.0974i			0.703891i	−0.936021	+	0.351945i	$0.885520\pi$
$524$	30.8689			1.34851
$525$	9.32660	−	58.8835i	0.407046	−	2.56989i
$526$	−23.5636			−1.02742
$527$		−	4.99629i		−	0.217642i
$528$			16.9184i			0.736280i
$529$	22.9841			0.999311
$530$	−22.4008	+	19.1319i	−0.973027	+	0.831038i
$531$	−5.23689			−0.227262
$532$		−	35.4422i		−	1.53661i
$533$			4.91679i			0.212970i
$534$	7.89689			0.341732
$535$	22.9617	+	26.8849i	0.992720	+	1.16233i
$536$	−0.815311			−0.0352161
$537$		−	20.7182i		−	0.894056i
$538$		−	56.0945i		−	2.41841i
$539$	34.9264			1.50439
$540$	−2.78728	−	3.26351i	−0.119945	−	0.140439i
$541$	−43.3563			−1.86403			−0.932017	−	0.362414i	$-0.881953\pi$
$541$	−43.3563			−1.86403			−0.932017	+	0.362414i	$0.881953\pi$
$542$		−	2.92626i		−	0.125694i
$543$		−	23.0115i		−	0.987517i
$544$	8.09097			0.346897
$545$	−5.78220	+	4.93844i	−0.247682	+	0.211539i
$546$	−25.2144			−1.07908
$547$		−	23.3908i		−	1.00012i	−0.865991	−	0.500060i	$-0.833311\pi$
$547$		−	23.3908i		−	1.00012i	0.865991	−	0.500060i	$-0.166689\pi$
$548$		−	33.0397i		−	1.41139i
$549$	−18.7188			−0.798899
$550$	−19.1319	−	3.03032i	−0.815789	−	0.129213i
$551$	−18.4738			−0.787010
$552$			0.0740520i			0.00315186i
$553$		−	67.2524i		−	2.85986i
$554$	4.76624			0.202498
$555$	−6.30506	+	5.38499i	−0.267635	+	0.228580i
$556$	−40.1763			−1.70385
$557$		−	14.6974i		−	0.622748i	−0.950287	−	0.311374i	$-0.899211\pi$
$557$		−	14.6974i		−	0.622748i	0.950287	−	0.311374i	$-0.100789\pi$
$558$			26.5617i			1.12445i
$559$	−4.64762			−0.196573
$560$	27.3257	+	31.9945i	1.15472	+	1.35201i
$561$	4.52285			0.190955
$562$		−	27.3258i		−	1.15267i
$563$		−	3.13206i		−	0.132001i	−0.997820	−	0.0660004i	$-0.978976\pi$
$563$		−	3.13206i		−	0.132001i	0.997820	−	0.0660004i	$-0.0210239\pi$
$564$	−5.23934			−0.220616
$565$	24.6041	+	28.8079i	1.03510	+	1.21196i
$566$	45.0677			1.89434
$567$			50.2986i			2.11234i
$568$			1.40343i			0.0588868i
$569$	−1.47115			−0.0616737			−0.0308369	−	0.999524i	$-0.509817\pi$
$569$	−1.47115			−0.0616737			−0.0308369	+	0.999524i	$0.509817\pi$
$570$	27.1670	−	23.2027i	1.13790	−	0.971853i
$571$	8.35447			0.349624			0.174812	−	0.984602i	$-0.444068\pi$
$571$	8.35447			0.349624			0.174812	+	0.984602i	$0.444068\pi$
$572$			4.21767i			0.176350i
$573$			38.3565i			1.60236i
$574$	48.2127			2.01236
$575$	0.621810	+	0.0984890i	0.0259313	+	0.00410727i
$576$	−23.4245			−0.976021
$577$		−	13.3390i		−	0.555309i	−0.960681	−	0.277654i	$-0.910443\pi$
$577$		−	13.3390i		−	0.555309i	0.960681	−	0.277654i	$-0.0895570\pi$
$578$		−	2.03032i		−	0.0844503i
$579$	−21.8470			−0.907931
$580$	−20.0788	+	17.1488i	−0.833728	+	0.712066i
$581$	−5.74573			−0.238373
$582$			35.1196i			1.45575i
$583$		−	12.3814i		−	0.512786i
$584$	−3.10880			−0.128643
$585$	−3.96052	−	4.63720i	−0.163747	−	0.191725i
$586$	11.4394			0.472559
$587$		−	30.8029i		−	1.27137i	−0.771947	−	0.635687i	$-0.780717\pi$
$587$		−	30.8029i		−	1.27137i	0.771947	−	0.635687i	$-0.219283\pi$
$588$			92.0757i			3.79714i
$589$	16.5877			0.683482
$590$	5.89689	+	6.90441i	0.242771	+	0.284250i
$591$	−0.358290			−0.0147381
$592$		−	5.85190i		−	0.240511i
$593$			33.2200i			1.36418i	0.731267	+	0.682091i	$0.238929\pi$
$593$			33.2200i			1.36418i	−0.731267	+	0.682091i	$0.761071\pi$
$594$	3.50376			0.143761
$595$	8.55318	−	7.30506i	0.350646	−	0.299478i
$596$	−27.1827			−1.11345
$597$		−	36.3597i		−	1.48810i
$598$		−	0.266265i		−	0.0108884i
$599$	−19.0233			−0.777269			−0.388634	−	0.921392i	$-0.627053\pi$
$599$	−19.0233			−0.777269			−0.388634	+	0.921392i	$0.627053\pi$
$600$	0.460032	−	2.90441i	0.0187807	−	0.118572i
$601$	−15.0239			−0.612836			−0.306418	−	0.951897i	$-0.599131\pi$
$601$	−15.0239			−0.612836			−0.306418	+	0.951897i	$0.599131\pi$
$602$			45.5733i			1.85743i
$603$			8.60412i			0.350387i
$604$	13.9151			0.566196
$605$	−12.5128	+	10.6869i	−0.508720	+	0.434485i
$606$	23.7307			0.963993
$607$		−	30.9629i		−	1.25674i	−0.777913	−	0.628372i	$-0.783722\pi$
$607$		−	30.9629i		−	1.25674i	0.777913	−	0.628372i	$-0.216278\pi$
$608$			26.8619i			1.08940i
$609$	66.3472			2.68852
$610$	21.0779	+	24.6792i	0.853419	+	0.999232i
$611$	1.08483			0.0438874
$612$			5.55688i			0.224624i
$613$		−	36.0215i		−	1.45490i	−0.686163	−	0.727448i	$-0.740706\pi$
$613$		−	36.0215i		−	1.45490i	0.686163	−	0.727448i	$-0.259294\pi$
$614$	−59.6150			−2.40587
$615$	16.2494	+	19.0257i	0.655238	+	0.767190i
$616$	2.38155			0.0959556
$617$		−	43.3363i		−	1.74465i	−0.488922	−	0.872327i	$-0.662610\pi$
$617$		−	43.3363i		−	1.74465i	0.488922	−	0.872327i	$-0.337390\pi$
$618$		−	16.7338i		−	0.673134i
$619$	−23.4651			−0.943142			−0.471571	−	0.881828i	$-0.656313\pi$
$619$	−23.4651			−0.943142			−0.471571	+	0.881828i	$0.656313\pi$
$620$	18.0288	−	15.3980i	0.724055	−	0.618398i
$621$	−0.113876			−0.00456970
$622$			25.2473i			1.01232i
$623$			8.25427i			0.330700i
$624$	9.23498			0.369695
$625$	−23.7763	−	7.72572i	−0.951053	−	0.309029i
$626$	31.2076			1.24731
$627$			15.0158i			0.599675i
$628$			23.5857i			0.941172i
$629$	−1.56441			−0.0623769
$630$	−45.4711	+	38.8358i	−1.81161	+	1.54725i
$631$	0.0249777			0.000994348			0.000497174	−	1.00000i	$-0.499842\pi$
$631$	0.0249777			0.000994348			0.000497174		1.00000i	$0.499842\pi$
$632$		−	3.31721i		−	0.131951i
$633$			60.2599i			2.39512i
$634$	−47.6796			−1.89360
$635$	−0.495091	−	0.579680i	−0.0196471	−	0.0230039i
$636$	32.6409			1.29430
$637$		−	19.0647i		−	0.755371i
$638$		−	21.5570i		−	0.853450i
$639$	14.8107			0.585902
$640$	2.87718	+	3.36876i	0.113730	+	0.133162i
$641$	−8.98010			−0.354693			−0.177346	−	0.984149i	$-0.556751\pi$
$641$	−8.98010			−0.354693			−0.177346	+	0.984149i	$0.556751\pi$
$642$		−	76.0937i		−	3.00318i
$643$			1.78174i			0.0702648i	0.999383	+	0.0351324i	$0.0111853\pi$
$643$			1.78174i			0.0702648i	−0.999383	+	0.0351324i	$0.988815\pi$
$644$	−1.34416			−0.0529674
$645$	−17.9841	+	15.3598i	−0.708125	+	0.604792i
$646$	6.74065			0.265207
$647$			10.9052i			0.428728i	0.976754	+	0.214364i	$0.0687679\pi$
$647$			10.9052i			0.428728i	−0.976754	+	0.214364i	$0.931232\pi$
$648$			2.48096i			0.0974614i
$649$	−3.81623			−0.149800
$650$	−1.65411	+	10.4432i	−0.0648796	+	0.409617i
$651$	−59.5733			−2.33486
$652$			35.4272i			1.38744i
$653$		−	6.26014i		−	0.244978i	−0.992470	−	0.122489i	$-0.960912\pi$
$653$		−	6.26014i		−	0.244978i	0.992470	−	0.122489i	$-0.0390877\pi$
$654$	16.3657			0.639950
$655$	−24.7323	+	21.1233i	−0.966372	+	0.825354i
$656$	−17.6583			−0.689440
$657$			32.8077i			1.27995i
$658$		−	10.6375i		−	0.414694i
$659$	−23.0608			−0.898320			−0.449160	−	0.893451i	$-0.648277\pi$
$659$	−23.0608			−0.898320			−0.449160	+	0.893451i	$0.648277\pi$
$660$	13.9389	+	16.3204i	0.542571	+	0.635272i
$661$	14.9050			0.579738			0.289869	−	0.957066i	$-0.406388\pi$
$661$	14.9050			0.579738			0.289869	+	0.957066i	$0.406388\pi$
$662$		−	72.4497i		−	2.81584i
$663$		−	2.46881i		−	0.0958808i
$664$	−0.283406			−0.0109983
$665$	24.2527	+	28.3965i	0.940481	+	1.10117i
$666$	8.31683			0.322271
$667$			0.700627i			0.0271284i
$668$			36.3993i			1.40833i
$669$	−28.4713			−1.10077
$670$	11.3438	−	9.68848i	0.438250	−	0.374299i
$671$	−13.6408			−0.526596
$672$		−	96.4726i		−	3.72151i
$673$		−	40.8225i		−	1.57359i	−0.617213	−	0.786796i	$-0.711738\pi$
$673$		−	40.8225i		−	1.57359i	0.617213	−	0.786796i	$-0.288262\pi$
$674$	56.8152			2.18844
$675$	4.46637	+	0.707432i	0.171911	+	0.0272291i
$676$	−25.2865			−0.972556
$677$			19.5678i			0.752050i	0.926610	+	0.376025i	$0.122709\pi$
$677$			19.5678i			0.752050i	−0.926610	+	0.376025i	$0.877291\pi$
$678$		−	81.5367i		−	3.13140i
$679$	−36.7089			−1.40876
$680$	0.421883	−	0.360320i	0.0161785	−	0.0138176i
$681$	16.4255			0.629428
$682$			19.3561i			0.741183i
$683$			6.38789i			0.244426i	0.992504	+	0.122213i	$0.0389991\pi$
$683$			6.38789i			0.244426i	−0.992504	+	0.122213i	$0.961001\pi$
$684$	−18.4488			−0.705408
$685$	22.6087	+	26.4716i	0.863836	+	1.01143i
$686$	−115.451			−4.40794
$687$			35.7497i			1.36394i
$688$		−	16.6916i		−	0.636360i
$689$	−6.75844			−0.257476
$690$	−0.879973	−	1.03032i	−0.0335000	−	0.0392237i
$691$	20.5657			0.782355			0.391177	−	0.920315i	$-0.372068\pi$
$691$	20.5657			0.782355			0.391177	+	0.920315i	$0.372068\pi$
$692$			30.3583i			1.15405i
$693$		−	25.1330i		−	0.954723i
$694$	−28.4050			−1.07824
$695$	32.1895	−	27.4922i	1.22102	−	1.04284i
$696$	3.27256			0.124046
$697$			4.72064i			0.178807i
$698$			36.2201i			1.37095i
$699$	−21.6383			−0.818434
$700$	52.7197	+	8.35031i	1.99262	+	0.315612i
$701$	14.1756			0.535403			0.267702	−	0.963502i	$-0.413736\pi$
$701$	14.1756			0.535403			0.267702	+	0.963502i	$0.413736\pi$
$702$		−	1.91254i		−	0.0721842i
$703$		−	5.19381i		−	0.195888i
$704$	−17.0699			−0.643347
$705$	4.19779	−	3.58522i	0.158098	−	0.135027i
$706$	28.5932			1.07612
$707$			24.8046i			0.932875i
$708$		−	10.0606i		−	0.378102i
$709$	8.69879			0.326690			0.163345	−	0.986569i	$-0.447772\pi$
$709$	8.69879			0.326690			0.163345	+	0.986569i	$0.447772\pi$
$710$	−16.6772	−	19.5267i	−0.625886	−	0.732823i
$711$	−35.0071			−1.31287
$712$			0.407139i			0.0152582i
$713$		−	0.629095i		−	0.0235598i
$714$	−24.2085			−0.905982
$715$	−2.88611	−	3.37922i	−0.107934	−	0.126376i
$716$	18.5495			0.693226
$717$			2.57354i			0.0961107i
$718$		−	28.6289i		−	1.06842i
$719$	−7.42944			−0.277071			−0.138536	−	0.990357i	$-0.544240\pi$
$719$	−7.42944			−0.277071			−0.138536	+	0.990357i	$0.544240\pi$
$720$	16.6541	−	14.2239i	0.620663	−	0.530093i
$721$	17.4912			0.651405
$722$		−	16.1972i		−	0.602798i
$723$		−	2.79388i		−	0.103906i
$724$	20.6027			0.765693
$725$	4.35249	−	27.4795i	0.161648	−	1.02056i
$726$	35.4158			1.31440
$727$		−	6.25530i		−	0.231996i	−0.993249	−	0.115998i	$-0.962993\pi$
$727$		−	6.25530i		−	0.231996i	0.993249	−	0.115998i	$-0.0370067\pi$
$728$		−	1.29998i		−	0.0481804i
$729$	19.7508			0.731511
$730$	43.2543	−	36.9424i	1.60091	−	1.36730i
$731$	−4.46221			−0.165041
$732$		−	35.9609i		−	1.32915i
$733$			37.1550i			1.37235i	0.727436	+	0.686176i	$0.240712\pi$
$733$			37.1550i			1.37235i	−0.727436	+	0.686176i	$0.759288\pi$
$734$	36.5620			1.34953
$735$	−63.0065	−	73.7716i	−2.32403	−	2.72111i
$736$	1.01875			0.0375517
$737$			6.27000i			0.230958i
$738$		−	25.0963i		−	0.923807i
$739$	23.0688			0.848601			0.424301	−	0.905521i	$-0.360520\pi$
$739$	23.0688			0.848601			0.424301	+	0.905521i	$0.360520\pi$
$740$	−4.82131	−	5.64506i	−0.177235	−	0.207517i
$741$	8.19645			0.301104
$742$			66.2715i			2.43290i
$743$		−	48.0717i		−	1.76358i	−0.471641	−	0.881791i	$-0.656338\pi$
$743$		−	48.0717i		−	1.76358i	0.471641	−	0.881791i	$-0.343662\pi$
$744$	−2.93844			−0.107728
$745$	21.7790	−	18.6009i	0.797919	−	0.681483i
$746$	−22.1378			−0.810523
$747$			2.99084i			0.109429i
$748$			4.04941i			0.148061i
$749$	79.5375			2.90624
$750$	28.1130	+	45.8771i	1.02654	+	1.67520i
$751$	37.7366			1.37703			0.688514	−	0.725223i	$-0.258263\pi$
$751$	37.7366			1.37703			0.688514	+	0.725223i	$0.258263\pi$
$752$			3.89608i			0.142075i
$753$			57.7014i			2.10276i
$754$	−11.7670			−0.428527
$755$	−11.1488	+	9.52194i	−0.405747	+	0.346539i
$756$	−9.65492			−0.351146
$757$			6.03403i			0.219310i	0.993970	+	0.109655i	$0.0349747\pi$
$757$			6.03403i			0.219310i	−0.993970	+	0.109655i	$0.965025\pi$
$758$			46.3318i			1.68285i
$759$	0.569483			0.0206709
$760$	1.19626	+	1.40065i	0.0433929	+	0.0508068i
$761$	0.199624			0.00723636			0.00361818	−	0.999993i	$-0.498848\pi$
$761$	0.199624			0.00723636			0.00361818	+	0.999993i	$0.498848\pi$
$762$			1.64070i			0.0594364i
$763$			17.1064i			0.619292i
$764$	−34.3414			−1.24243
$765$	−3.80252	−	4.45220i	−0.137480	−	0.160970i
$766$	−0.641472			−0.0231773
$767$			2.08310i			0.0752164i
$768$			32.8749i			1.18627i
$769$	−43.4861			−1.56815			−0.784074	−	0.620668i	$-0.786862\pi$
$769$	−43.4861			−1.56815			−0.784074	+	0.620668i	$0.786862\pi$
$770$	−33.1358	+	28.3004i	−1.19413	+	1.01988i
$771$	−10.9176			−0.393188
$772$		−	19.5601i		−	0.703984i
$773$			39.3075i			1.41379i	0.707317	+	0.706896i	$0.249905\pi$
$773$			39.3075i			1.41379i	−0.707317	+	0.706896i	$0.750095\pi$
$774$	23.7224			0.852684
$775$	−3.90812	+	24.6739i	−0.140384	+	0.886312i
$776$	−1.81066			−0.0649988
$777$			18.6532i			0.669180i
$778$		−	18.3942i		−	0.659462i
$779$	−15.6725			−0.561525
$780$	8.90857	−	7.60859i	0.318978	−	0.272431i
$781$	10.7929			0.386199
$782$		−	0.255643i		−	0.00914176i
$783$			5.03250i			0.179847i
$784$	68.4694			2.44534
$785$	−16.1395	−	18.8970i	−0.576042	−	0.674463i
$786$	70.0013			2.49686
$787$			24.0203i			0.856230i	0.903724	+	0.428115i	$0.140822\pi$
$787$			24.0203i			0.856230i	−0.903724	+	0.428115i	$0.859178\pi$
$788$		−	0.320785i		−	0.0114275i
$789$	−27.5096			−0.979369
$790$	39.4189	+	46.1539i	1.40246	+	1.64208i
$791$	85.2267			3.03031
$792$		−	1.23968i		−	0.0440500i
$793$			7.44586i			0.264410i
$794$	−18.7945			−0.666992
$795$	−26.1521	+	22.3358i	−0.927518	+	0.792170i
$796$	32.5537			1.15383
$797$		−	27.4915i		−	0.973797i	−0.873458	−	0.486899i	$-0.838128\pi$
$797$		−	27.4915i		−	0.973797i	0.873458	−	0.486899i	$-0.161872\pi$
$798$		−	80.3722i		−	2.84514i
$799$	1.04155			0.0368474
$800$	−39.9567	−	6.32878i	−1.41268	−	0.223756i
$801$	4.29661			0.151813
$802$		−	26.5532i		−	0.937626i
$803$			23.9076i			0.843683i
$804$	−16.5295			−0.582949
$805$	1.07695	−	0.919797i	0.0379575	−	0.0324186i
$806$	10.5656			0.372157
$807$		−	65.4883i		−	2.30530i
$808$			1.22348i			0.0430419i
$809$	41.3790			1.45481			0.727404	−	0.686209i	$-0.240726\pi$
$809$	41.3790			1.45481			0.727404	+	0.686209i	$0.240726\pi$
$810$	−29.4817	−	34.5189i	−1.03588	−	1.21287i
$811$	−41.3679			−1.45262			−0.726311	−	0.687366i	$-0.758767\pi$
$811$	−41.3679			−1.45262			−0.726311	+	0.687366i	$0.758767\pi$
$812$			59.4022i			2.08461i
$813$		−	3.41630i		−	0.119815i
$814$	6.06064			0.212425
$815$	−24.2425	−	28.3845i	−0.849176	−	0.994264i
$816$	8.86656			0.310392
$817$		−	14.8145i		−	0.518294i
$818$		−	10.4131i		−	0.364087i
$819$	−13.7189			−0.479378
$820$	−17.0341	+	14.5484i	−0.594858	+	0.508054i
$821$	−31.6564			−1.10482			−0.552409	−	0.833574i	$-0.686291\pi$
$821$	−31.6564			−1.10482			−0.552409	+	0.833574i	$0.686291\pi$
$822$		−	74.9241i		−	2.61328i
$823$			47.2174i			1.64590i	0.568116	+	0.822948i	$0.307672\pi$
$823$			47.2174i			1.64590i	−0.568116	+	0.822948i	$0.692328\pi$
$824$	0.862746			0.0300552
$825$	−22.3358	−	3.53779i	−0.777634	−	0.123170i
$826$	20.4263			0.710723
$827$			40.9254i			1.42311i	0.702628	+	0.711557i	$0.252010\pi$
$827$			40.9254i			1.42311i	−0.702628	+	0.711557i	$0.747990\pi$
$828$			0.699680i			0.0243156i
$829$	−33.9963			−1.18074			−0.590371	−	0.807132i	$-0.701018\pi$
$829$	−33.9963			−1.18074			−0.590371	+	0.807132i	$0.701018\pi$
$830$	3.94317	−	3.36777i	0.136870	−	0.116897i
$831$	5.56441			0.193027
$832$			9.31767i			0.323032i
$833$		−	18.3041i		−	0.634201i
$834$	−91.1077			−3.15480
$835$	−24.9076	−	29.1633i	−0.861965	−	1.00924i
$836$	−13.4440			−0.464971
$837$		−	4.51870i		−	0.156189i
$838$		−	64.0494i		−	2.21255i
$839$	22.9314			0.791679			0.395839	−	0.918320i	$-0.370454\pi$
$839$	22.9314			0.791679			0.395839	+	0.918320i	$0.370454\pi$
$840$	−4.29627	−	5.03032i	−0.148236	−	0.173563i
$841$	1.96261			0.0676761
$842$			10.6916i			0.368456i
$843$		−	31.9019i		−	1.09876i
$844$	−53.9521			−1.85711
$845$	20.2597	−	17.3033i	0.696953	−	0.595251i
$846$	−5.53718			−0.190372
$847$			37.0186i			1.27198i
$848$		−	24.2724i		−	0.833519i
$849$	52.6149			1.80574
$850$	−1.58812	+	10.0266i	−0.0544722	+	0.343910i
$851$	−0.196978			−0.00675232
$852$			28.4530i			0.974782i
$853$		−	4.50549i		−	0.154265i	−0.997021	−	0.0771325i	$-0.975424\pi$
$853$		−	4.50549i		−	0.154265i	0.997021	−	0.0771325i	$-0.0245764\pi$
$854$	73.0122			2.49842
$855$	14.7813	−	12.6243i	0.505509	−	0.431743i
$856$	3.92316			0.134091
$857$		−	56.4346i		−	1.92777i	−0.266321	−	0.963884i	$-0.585808\pi$
$857$		−	56.4346i		−	1.92777i	0.266321	−	0.963884i	$-0.414192\pi$
$858$			9.56441i			0.326523i
$859$	3.02509			0.103215			0.0516074	−	0.998667i	$-0.483566\pi$
$859$	3.02509			0.103215			0.0516074	+	0.998667i	$0.483566\pi$
$860$	−13.7520	−	16.1016i	−0.468939	−	0.549061i
$861$	56.2866			1.91824
$862$			72.3343i			2.46372i
$863$			37.0247i			1.26033i	0.776460	+	0.630167i	$0.217014\pi$
$863$			37.0247i			1.26033i	−0.776460	+	0.630167i	$0.782986\pi$
$864$	7.31755			0.248948
$865$	−20.7739	−	24.3232i	−0.706333	−	0.827015i
$866$	−41.1886			−1.39965
$867$		−	2.37033i		−	0.0805005i
$868$		−	53.3374i		−	1.81039i
$869$	−25.5104			−0.865380
$870$	−45.5327	+	38.8884i	−1.54370	+	1.31844i
$871$	3.42250			0.115967
$872$			0.843766i			0.0285735i
$873$			19.1082i			0.646714i
$874$	0.848731			0.0287088
$875$	−47.9534	+	29.3852i	−1.62112	+	0.993403i
$876$	−63.0272			−2.12949
$877$		−	31.0032i		−	1.04690i	−0.852055	−	0.523452i	$-0.824644\pi$
$877$		−	31.0032i		−	1.04690i	0.852055	−	0.523452i	$-0.175356\pi$
$878$			17.7285i			0.598308i
$879$	13.3551			0.450457
$880$	12.1362	−	10.3652i	0.409112	−	0.349412i
$881$	−53.0789			−1.78827			−0.894137	−	0.447793i	$-0.852210\pi$
$881$	−53.0789			−1.78827			−0.894137	+	0.447793i	$0.852210\pi$
$882$			97.3100i			3.27660i
$883$			56.9680i			1.91713i	0.284882	+	0.958563i	$0.408046\pi$
$883$			56.9680i			1.91713i	−0.284882	+	0.958563i	$0.591954\pi$
$884$	2.21039			0.0743433
$885$	6.88440	+	8.06064i	0.231416	+	0.270956i
$886$	9.01786			0.302961
$887$		−	45.0418i		−	1.51235i	−0.654367	−	0.756177i	$-0.727065\pi$
$887$		−	45.0418i		−	1.51235i	0.654367	−	0.756177i	$-0.272935\pi$
$888$			0.920063i			0.0308753i
$889$	−1.71495			−0.0575177
$890$	−4.83811	−	5.66473i	−0.162174	−	0.189882i
$891$	19.0794			0.639184
$892$		−	25.4910i		−	0.853503i
$893$			3.45794i			0.115716i
$894$	−61.6422			−2.06162
$895$	−14.8619	+	12.6932i	−0.496780	+	0.424287i
$896$	9.96631			0.332951
$897$		−	0.310854i		−	0.0103791i
$898$			14.9688i			0.499515i
$899$	−27.8014			−0.927229
$900$	4.34661	−	27.4423i	0.144887	−	0.914744i
$901$	−6.48883			−0.216174
$902$		−	18.2882i		−	0.608930i
$903$			53.2052i			1.77056i
$904$	4.20378			0.139816
$905$	−16.5070	+	14.0982i	−0.548711	+	0.468641i
$906$	31.5552			1.04835
$907$		−	2.07329i		−	0.0688423i	−0.999407	−	0.0344212i	$-0.989041\pi$
$907$		−	2.07329i		−	0.0688423i	0.999407	−	0.0344212i	$-0.0109588\pi$
$908$			14.7062i			0.488041i
$909$	12.9116			0.428251
$910$	15.4479	+	18.0873i	0.512092	+	0.599587i
$911$	37.7535			1.25083			0.625415	−	0.780293i	$-0.284930\pi$
$911$	37.7535			1.25083			0.625415	+	0.780293i	$0.284930\pi$
$912$			29.4369i			0.974754i
$913$			2.17949i			0.0721304i
$914$	−28.4123			−0.939796
$915$	24.6077	+	28.8121i	0.813504	+	0.952497i
$916$	−32.0075			−1.05756
$917$			73.1693i			2.41626i
$918$		−	1.83624i		−	0.0606050i
$919$	−19.6202			−0.647209			−0.323605	−	0.946192i	$-0.604895\pi$
$919$	−19.6202			−0.647209			−0.323605	+	0.946192i	$0.604895\pi$
$920$	0.0531203	−	0.0453687i	0.00175132	−	0.00149576i
$921$	−69.5983			−2.29334
$922$			62.9365i			2.07270i
$923$		−	5.89131i		−	0.193915i
$924$	48.2832			1.58840
$925$	7.72572	+	1.22368i	0.254020	+	0.0402344i
$926$	−29.0711			−0.955335
$927$		−	9.10471i		−	0.299038i
$928$		−	45.0214i		−	1.47790i
$929$	32.3131			1.06016			0.530079	−	0.847948i	$-0.322162\pi$
$929$	32.3131			1.06016			0.530079	+	0.847948i	$0.322162\pi$
$930$	40.8839	−	34.9180i	1.34064	−	1.14500i
$931$	60.7696			1.99164
$932$		−	19.3732i		−	0.634591i
$933$			29.4753i			0.964978i
$934$	33.3592			1.09155
$935$	−2.77097	−	3.24441i	−0.0906205	−	0.106104i
$936$	−0.676681			−0.0221180
$937$		−	31.9433i		−	1.04354i	−0.853085	−	0.521771i	$-0.825271\pi$
$937$		−	31.9433i		−	1.04354i	0.853085	−	0.521771i	$-0.174729\pi$
$938$		−	33.5601i		−	1.09578i
$939$	36.4338			1.18897
$940$	3.20993	+	3.75837i	0.104696	+	0.122585i
$941$	50.1401			1.63452			0.817260	−	0.576269i	$-0.195492\pi$
$941$	50.1401			1.63452			0.817260	+	0.576269i	$0.195492\pi$
$942$			53.4853i			1.74264i
$943$			0.594387i			0.0193559i
$944$	−7.48130			−0.243496
$945$	7.73557	−	6.60676i	0.251638	−	0.214918i
$946$	17.2870			0.562049
$947$			14.0277i			0.455839i	0.973680	+	0.227919i	$0.0731923\pi$
$947$			14.0277i			0.455839i	−0.973680	+	0.227919i	$0.926808\pi$
$948$		−	67.2524i		−	2.18426i
$949$	13.0501			0.423623
$950$	−33.2883	−	5.27256i	−1.08001	−	0.171064i
$951$	−55.6641			−1.80503
$952$		−	1.24812i		−	0.0404518i
$953$		−	15.8829i		−	0.514497i	−0.966345	−	0.257248i	$-0.917184\pi$
$953$		−	15.8829i		−	0.514497i	0.966345	−	0.257248i	$-0.0828158\pi$
$954$	34.4965			1.11686
$955$	27.5145	−	23.4995i	0.890349	−	0.760425i
$956$	−2.30415			−0.0745216
$957$		−	25.1670i		−	0.813533i
$958$			22.3110i			0.720835i
$959$	78.3149			2.52892
$960$	30.7938	+	36.0551i	0.993865	+	1.16367i
$961$	−6.03704			−0.194743
$962$		−	3.30822i		−	0.106661i
$963$		−	41.4018i		−	1.33415i
$964$	2.50143			0.0805656
$965$	13.3848	+	15.6717i	0.430872	+	0.504489i
$966$	−3.04815			−0.0980728
$967$			10.6518i			0.342538i	0.985224	+	0.171269i	$0.0547867\pi$
$967$			10.6518i			0.342538i	−0.985224	+	0.171269i	$0.945213\pi$
$968$			1.82593i			0.0586877i
$969$	7.86946			0.252804
$970$	25.1926	−	21.5164i	0.808885	−	0.690849i
$971$	−17.3640			−0.557236			−0.278618	−	0.960402i	$-0.589876\pi$
$971$	−17.3640			−0.557236			−0.278618	+	0.960402i	$0.589876\pi$
$972$			44.5406i			1.42864i
$973$		−	95.2309i		−	3.05296i
$974$	17.8420			0.571693
$975$	−1.93111	+	12.1921i	−0.0618451	+	0.390459i
$976$	−26.7413			−0.855967
$977$			15.3732i			0.491833i	0.969291	+	0.245917i	$0.0790889\pi$
$977$			15.3732i			0.491833i	−0.969291	+	0.245917i	$0.920911\pi$
$978$			80.3382i			2.56893i
$979$	3.13103			0.100068
$980$	66.0494	−	56.4111i	2.10987	−	1.80199i
$981$	8.90441			0.284296
$982$			32.0477i			1.02268i
$983$		−	40.3343i		−	1.28647i	−0.765671	−	0.643233i	$-0.777593\pi$
$983$		−	40.3343i		−	1.28647i	0.765671	−	0.643233i	$-0.222407\pi$
$984$	2.77632			0.0885058
$985$	0.219510	+	0.257015i	0.00699417	+	0.00818917i
$986$	−11.2975			−0.359787
$987$		−	12.4189i		−	0.395299i
$988$			7.33846i			0.233468i
$989$	−0.561847			−0.0178657
$990$	14.7313	+	17.2482i	0.468191	+	0.548185i
$991$	26.3296			0.836386			0.418193	−	0.908358i	$-0.362664\pi$
$991$	26.3296			0.836386			0.418193	+	0.908358i	$0.362664\pi$
$992$			40.4248i			1.28349i
$993$		−	84.5824i		−	2.68414i
$994$	−57.7687			−1.83231
$995$	−26.0822	+	22.2761i	−0.826861	+	0.706201i
$996$	−5.74573			−0.182060
$997$			46.9367i			1.48650i	0.669014	+	0.743250i	$0.266717\pi$
$997$			46.9367i			1.48650i	−0.669014	+	0.743250i	$0.733283\pi$
$998$			16.7884i			0.531428i
$999$	−1.41486			−0.0447643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.b.a.69.7	yes	8
3.2	odd	2		765.2.b.c.154.2		8
4.3	odd	2		1360.2.e.d.1089.2		8
5.2	odd	4		425.2.a.h.1.1		4
5.3	odd	4		425.2.a.g.1.4		4
5.4	even	2	inner	85.2.b.a.69.2	✓	8
15.2	even	4		3825.2.a.bh.1.4		4
15.8	even	4		3825.2.a.bj.1.1		4
15.14	odd	2		765.2.b.c.154.7		8
17.16	even	2		1445.2.b.e.579.7		8
20.3	even	4		6800.2.a.bw.1.3		4
20.7	even	4		6800.2.a.bt.1.2		4
20.19	odd	2		1360.2.e.d.1089.7		8
85.33	odd	4		7225.2.a.v.1.4		4
85.67	odd	4		7225.2.a.w.1.1		4
85.84	even	2		1445.2.b.e.579.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.b.a.69.2	✓	8	5.4	even	2	inner
85.2.b.a.69.7	yes	8	1.1	even	1	trivial
425.2.a.g.1.4		4	5.3	odd	4
425.2.a.h.1.1		4	5.2	odd	4
765.2.b.c.154.2		8	3.2	odd	2
765.2.b.c.154.7		8	15.14	odd	2
1360.2.e.d.1089.2		8	4.3	odd	2
1360.2.e.d.1089.7		8	20.19	odd	2
1445.2.b.e.579.2		8	85.84	even	2
1445.2.b.e.579.7		8	17.16	even	2
3825.2.a.bh.1.4		4	15.2	even	4
3825.2.a.bj.1.1		4	15.8	even	4
6800.2.a.bt.1.2		4	20.7	even	4
6800.2.a.bw.1.3		4	20.3	even	4
7225.2.a.v.1.4		4	85.33	odd	4
7225.2.a.w.1.1		4	85.67	odd	4

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.03032i q^{2} +2.37033i q^{3} -2.12221 q^{4} +(1.70032 - 1.45220i) q^{5} -4.81252 q^{6} -5.03032i q^{7} -0.248119i q^{8} -2.61845 q^{9} +(2.94844 + 3.45220i) q^{10} -1.90812 q^{11} -5.03032i q^{12} +1.04155i q^{13} +10.2132 q^{14} +(3.44220 + 4.03032i) q^{15} -3.74065 q^{16} +1.00000i q^{17} -5.31629i q^{18} -3.31999 q^{19} +(-3.60844 + 3.08188i) q^{20} +11.9235 q^{21} -3.87409i q^{22} +0.125912i q^{23} +0.588123 q^{24} +(0.782203 - 4.93844i) q^{25} -2.11468 q^{26} +0.904410i q^{27} +10.6754i q^{28} +5.56441 q^{29} +(-8.18285 + 6.98877i) q^{30} -4.99629 q^{31} -8.09097i q^{32} -4.52285i q^{33} -2.03032 q^{34} +(-7.30506 - 8.55318i) q^{35} +5.55688 q^{36} +1.56441i q^{37} -6.74065i q^{38} -2.46881 q^{39} +(-0.360320 - 0.421883i) q^{40} +4.72064 q^{41} +24.2085i q^{42} +4.46221i q^{43} +4.04941 q^{44} +(-4.45220 + 3.80252i) q^{45} -0.255643 q^{46} -1.04155i q^{47} -8.86656i q^{48} -18.3041 q^{49} +(10.0266 + 1.58812i) q^{50} -2.37033 q^{51} -2.21039i q^{52} +6.48883i q^{53} -1.83624 q^{54} +(-3.24441 + 2.77097i) q^{55} -1.24812 q^{56} -7.86946i q^{57} +11.2975i q^{58} +2.00000 q^{59} +(-7.30506 - 8.55318i) q^{60} +7.14882 q^{61} -10.1441i q^{62} +13.1716i q^{63} +8.94596 q^{64} +(1.51255 + 1.77097i) q^{65} +9.18285 q^{66} -3.28596i q^{67} -2.12221i q^{68} -0.298453 q^{69} +(17.3657 - 14.8316i) q^{70} -5.65629 q^{71} +0.649686i q^{72} -12.5295i q^{73} -3.17625 q^{74} +(11.7057 + 1.85408i) q^{75} +7.04571 q^{76} +9.59843i q^{77} -5.01249i q^{78} +13.3694 q^{79} +(-6.36032 + 5.43219i) q^{80} -9.99908 q^{81} +9.58442i q^{82} -1.14222i q^{83} -25.3041 q^{84} +(1.45220 + 1.70032i) q^{85} -9.05972 q^{86} +13.1895i q^{87} +0.473440i q^{88} -1.64090 q^{89} +(-7.72034 - 9.03941i) q^{90} +5.23934 q^{91} -0.267212i q^{92} -11.8428i q^{93} +2.11468 q^{94} +(-5.64506 + 4.82131i) q^{95} +19.1782 q^{96} -7.29753i q^{97} -37.1633i q^{98} +4.99629 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{9} + 6 q^{10} - 4 q^{11} + 12 q^{14} - 8 q^{16} - 8 q^{19} - 2 q^{20} + 24 q^{21} + 12 q^{24} - 12 q^{25} + 8 q^{29} - 16 q^{30} - 24 q^{31} + 4 q^{34} + 44 q^{39} + 22 q^{40}+ \cdots + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^9 + 6 * q^10 - 4 * q^11 + 12 * q^14 - 8 * q^16 - 8 * q^19 - 2 * q^20 + 24 * q^21 + 12 * q^24 - 12 * q^25 + 8 * q^29 - 16 * q^30 - 24 * q^31 + 4 * q^34 + 44 * q^39 + 22 * q^40 - 12 * q^41 - 32 * q^44 - 22 * q^45 - 8 * q^46 - 16 * q^49 + 44 * q^50 - 8 * q^51 - 20 * q^54 - 8 * q^55 - 8 * q^56 + 16 * q^59 + 12 * q^61 + 48 * q^64 + 20 * q^65 + 24 * q^66 - 8 * q^69 + 40 * q^70 - 20 * q^71 - 40 * q^74 + 4 * q^75 - 24 * q^76 + 24 * q^79 - 26 * q^80 - 8 * q^81 - 72 * q^84 - 2 * q^85 + 40 * q^86 - 48 * q^89 - 74 * q^90 + 36 * q^91 + 4 * q^95 + 16 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more