LMFDB - Embedded newform 187.2.d.a.67.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(67,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("187.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.d (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:	$1.49320251780$
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} + 21x^{14} + 172x^{12} + 700x^{10} + 1492x^{8} + 1620x^{6} + 840x^{4} + 196x^{2} + 16 $ x^16 + 21x^14 + 172x^12 + 700x^10 + 1492x^8 + 1620x^6 + 840x^4 + 196*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.15
Root			$-2.24072i$ of defining polynomial
Character	$\chi$	$=$	187.67
Dual form			187.2.d.a.67.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24072 q^{2} -2.96003i q^{3} +3.02082 q^{4} +2.34815i q^{5} -6.63259i q^{6} +2.31788i q^{7} +2.28736 q^{8} -5.76177 q^{9} +O(q^{10})$	\(q+2.24072 q^{2} -2.96003i q^{3} +3.02082 q^{4} +2.34815i q^{5} -6.63259i q^{6} +2.31788i q^{7} +2.28736 q^{8} -5.76177 q^{9} +5.26153i q^{10} -1.00000i q^{11} -8.94170i q^{12} -6.29649 q^{13} +5.19372i q^{14} +6.95058 q^{15} -0.916304 q^{16} +(2.93290 - 2.89795i) q^{17} -12.9105 q^{18} +4.74973 q^{19} +7.09332i q^{20} +6.86100 q^{21} -2.24072i q^{22} +4.50842i q^{23} -6.77065i q^{24} -0.513792 q^{25} -14.1087 q^{26} +8.17492i q^{27} +7.00190i q^{28} -1.38345i q^{29} +15.5743 q^{30} -5.32701i q^{31} -6.62790 q^{32} -2.96003 q^{33} +(6.57180 - 6.49348i) q^{34} -5.44273 q^{35} -17.4052 q^{36} +3.52141i q^{37} +10.6428 q^{38} +18.6378i q^{39} +5.37106i q^{40} -3.26176i q^{41} +15.3736 q^{42} +8.28260 q^{43} -3.02082i q^{44} -13.5295i q^{45} +10.1021i q^{46} -0.844629 q^{47} +2.71229i q^{48} +1.62742 q^{49} -1.15126 q^{50} +(-8.57801 - 8.68147i) q^{51} -19.0205 q^{52} -0.00515784 q^{53} +18.3177i q^{54} +2.34815 q^{55} +5.30183i q^{56} -14.0593i q^{57} -3.09993i q^{58} -9.05394 q^{59} +20.9964 q^{60} -11.3912i q^{61} -11.9363i q^{62} -13.3551i q^{63} -13.0186 q^{64} -14.7851i q^{65} -6.63259 q^{66} -8.76109 q^{67} +(8.85975 - 8.75416i) q^{68} +13.3450 q^{69} -12.1956 q^{70} +12.4932i q^{71} -13.1792 q^{72} -6.49313i q^{73} +7.89048i q^{74} +1.52084i q^{75} +14.3480 q^{76} +2.31788 q^{77} +41.7620i q^{78} +7.60713i q^{79} -2.15162i q^{80} +6.91269 q^{81} -7.30868i q^{82} +7.26107 q^{83} +20.7258 q^{84} +(6.80480 + 6.88688i) q^{85} +18.5590 q^{86} -4.09506 q^{87} -2.28736i q^{88} -11.8361 q^{89} -30.3157i q^{90} -14.5945i q^{91} +13.6191i q^{92} -15.7681 q^{93} -1.89257 q^{94} +11.1531i q^{95} +19.6188i q^{96} +11.3708i q^{97} +3.64658 q^{98} +5.76177i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	$ 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.24072			1.58443			0.792213	−	0.610244i	$-0.208929\pi$
$2$	2.24072			1.58443			0.792213	+	0.610244i	$0.208929\pi$
$3$		−	2.96003i		−	1.70897i	−0.519473	−	0.854487i	$-0.673872\pi$
$3$		−	2.96003i		−	1.70897i	0.519473	−	0.854487i	$-0.326128\pi$
$4$	3.02082			1.51041
$5$			2.34815i			1.05012i	0.851064	+	0.525062i	$0.175958\pi$
$5$			2.34815i			1.05012i	−0.851064	+	0.525062i	$0.824042\pi$
$6$		−	6.63259i		−	2.70774i
$7$			2.31788i			0.876078i	0.898956	+	0.438039i	$0.144327\pi$
$7$			2.31788i			0.876078i	−0.898956	+	0.438039i	$0.855673\pi$
$8$	2.28736			0.808704
$9$	−5.76177			−1.92059
$10$			5.26153i			1.66384i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$		−	8.94170i		−	2.58125i
$13$	−6.29649			−1.74633			−0.873166	−	0.487424i	$-0.837937\pi$
$13$	−6.29649			−1.74633			−0.873166	+	0.487424i	$0.837937\pi$
$14$			5.19372i			1.38808i
$15$	6.95058			1.79463
$16$	−0.916304			−0.229076
$17$	2.93290	−	2.89795i	0.711333	−	0.702855i
$17$	2.93290	−	2.89795i	0.711333	−	0.702855i
$18$	−12.9105			−3.04303
$19$	4.74973			1.08966			0.544831	−	0.838546i	$-0.316594\pi$
$19$	4.74973			1.08966			0.544831	+	0.838546i	$0.316594\pi$
$20$			7.09332i			1.58611i
$21$	6.86100			1.49719
$22$		−	2.24072i		−	0.477723i
$23$			4.50842i			0.940070i	0.882648	+	0.470035i	$0.155759\pi$
$23$			4.50842i			0.940070i	−0.882648	+	0.470035i	$0.844241\pi$
$24$		−	6.77065i		−	1.38205i
$25$	−0.513792			−0.102758
$26$	−14.1087			−2.76693
$27$			8.17492i			1.57326i
$28$			7.00190i			1.32323i
$29$		−	1.38345i		−	0.256901i	−0.991716	−	0.128450i	$-0.959000\pi$
$29$		−	1.38345i		−	0.256901i	0.991716	−	0.128450i	$-0.0410003\pi$
$30$	15.5743			2.84346
$31$		−	5.32701i		−	0.956759i	−0.878153	−	0.478380i	$-0.841224\pi$
$31$		−	5.32701i		−	0.956759i	0.878153	−	0.478380i	$-0.158776\pi$
$32$	−6.62790			−1.17166
$33$	−2.96003			−0.515275
$34$	6.57180	−	6.49348i	1.12705	−	1.11362i
$35$	−5.44273			−0.919989
$36$	−17.4052			−2.90087
$37$			3.52141i			0.578916i	0.957191	+	0.289458i	$0.0934750\pi$
$37$			3.52141i			0.578916i	−0.957191	+	0.289458i	$0.906525\pi$
$38$	10.6428			1.72649
$39$			18.6378i			2.98443i
$40$			5.37106i			0.849238i
$41$		−	3.26176i		−	0.509401i	−0.967020	−	0.254701i	$-0.918023\pi$
$41$		−	3.26176i		−	0.509401i	0.967020	−	0.254701i	$-0.0819769\pi$
$42$	15.3736			2.37219
$43$	8.28260			1.26309			0.631543	−	0.775341i	$-0.282422\pi$
$43$	8.28260			1.26309			0.631543	+	0.775341i	$0.282422\pi$
$44$		−	3.02082i		−	0.455405i
$45$		−	13.5295i		−	2.01686i
$46$			10.1021i			1.48947i
$47$	−0.844629			−0.123202			−0.0616009	−	0.998101i	$-0.519621\pi$
$47$	−0.844629			−0.123202			−0.0616009	+	0.998101i	$0.519621\pi$
$48$			2.71229i			0.391485i
$49$	1.62742			0.232488
$50$	−1.15126			−0.162813
$51$	−8.57801	−	8.68147i	−1.20116	−	1.21565i
$52$	−19.0205			−2.63767
$53$	−0.00515784			−0.000708484			−0.000354242	−	1.00000i	$-0.500113\pi$
$53$	−0.00515784			−0.000708484			−0.000354242		1.00000i	$0.500113\pi$
$54$			18.3177i			2.49272i
$55$	2.34815			0.316624
$56$			5.30183i			0.708487i
$57$		−	14.0593i		−	1.86220i
$58$		−	3.09993i		−	0.407041i
$59$	−9.05394			−1.17872			−0.589361	−	0.807870i	$-0.700620\pi$
$59$	−9.05394			−1.17872			−0.589361	+	0.807870i	$0.700620\pi$
$60$	20.9964			2.71063
$61$		−	11.3912i		−	1.45849i	−0.684252	−	0.729246i	$-0.739871\pi$
$61$		−	11.3912i		−	1.45849i	0.684252	−	0.729246i	$-0.260129\pi$
$62$		−	11.9363i		−	1.51592i
$63$		−	13.3551i		−	1.68259i
$64$	−13.0186			−1.62733
$65$		−	14.7851i		−	1.83386i
$66$	−6.63259			−0.816415
$67$	−8.76109			−1.07034			−0.535169	−	0.844745i	$-0.679752\pi$
$67$	−8.76109			−1.07034			−0.535169	+	0.844745i	$0.679752\pi$
$68$	8.85975	−	8.75416i	1.07440	−	1.06160i
$69$	13.3450			1.60655
$70$	−12.1956			−1.45766
$71$			12.4932i			1.48266i	0.671138	+	0.741332i	$0.265806\pi$
$71$			12.4932i			1.48266i	−0.671138	+	0.741332i	$0.734194\pi$
$72$	−13.1792			−1.55319
$73$		−	6.49313i		−	0.759963i	−0.924994	−	0.379981i	$-0.875930\pi$
$73$		−	6.49313i		−	0.759963i	0.924994	−	0.379981i	$-0.124070\pi$
$74$			7.89048i			0.917249i
$75$			1.52084i			0.175611i
$76$	14.3480			1.64583
$77$	2.31788			0.264147
$78$			41.7620i			4.72862i
$79$			7.60713i			0.855869i	0.903810	+	0.427934i	$0.140759\pi$
$79$			7.60713i			0.855869i	−0.903810	+	0.427934i	$0.859241\pi$
$80$		−	2.15162i		−	0.240558i
$81$	6.91269			0.768076
$82$		−	7.30868i		−	0.807109i
$83$	7.26107			0.797006			0.398503	−	0.917167i	$-0.369530\pi$
$83$	7.26107			0.797006			0.398503	+	0.917167i	$0.369530\pi$
$84$	20.7258			2.26137
$85$	6.80480	+	6.88688i	0.738085	+	0.746987i
$86$	18.5590			2.00127
$87$	−4.09506			−0.439037
$88$		−	2.28736i		−	0.243833i
$89$	−11.8361			−1.25463			−0.627314	−	0.778766i	$-0.715846\pi$
$89$	−11.8361			−1.25463			−0.627314	+	0.778766i	$0.715846\pi$
$90$		−	30.3157i		−	3.19556i
$91$		−	14.5945i		−	1.52992i
$92$			13.6191i			1.41989i
$93$	−15.7681			−1.63508
$94$	−1.89257			−0.195204
$95$			11.1531i			1.14428i
$96$			19.6188i			2.00233i
$97$			11.3708i			1.15453i	0.816555	+	0.577267i	$0.195881\pi$
$97$			11.3708i			1.15453i	−0.816555	+	0.577267i	$0.804119\pi$
$98$	3.64658			0.368360
$99$			5.76177i			0.579080i
$100$	−1.55207			−0.155207
$101$	−2.64121			−0.262810			−0.131405	−	0.991329i	$-0.541949\pi$
$101$	−2.64121			−0.262810			−0.131405	+	0.991329i	$0.541949\pi$
$102$	−19.2209	−	19.4527i	−1.90315	−	1.92611i
$103$	7.98156			0.786447			0.393223	−	0.919443i	$-0.371360\pi$
$103$	7.98156			0.786447			0.393223	+	0.919443i	$0.371360\pi$
$104$	−14.4023			−1.41226
$105$			16.1106i			1.57224i
$106$	−0.0115573			−0.00112254
$107$			3.02618i			0.292552i	0.989244	+	0.146276i	$0.0467288\pi$
$107$			3.02618i			0.292552i	−0.989244	+	0.146276i	$0.953271\pi$
$108$			24.6949i			2.37627i
$109$		−	1.85528i		−	0.177703i	−0.996045	−	0.0888516i	$-0.971680\pi$
$109$		−	1.85528i		−	0.177703i	0.996045	−	0.0888516i	$-0.0283197\pi$
$110$	5.26153			0.501668
$111$	10.4235			0.989351
$112$		−	2.12389i		−	0.200688i
$113$			9.95642i			0.936621i	0.883564	+	0.468311i	$0.155137\pi$
$113$			9.95642i			0.936621i	−0.883564	+	0.468311i	$0.844863\pi$
$114$		−	31.5030i		−	2.95052i
$115$	−10.5864			−0.987189
$116$		−	4.17916i		−	0.388025i
$117$	36.2789			3.35399
$118$	−20.2873			−1.86760
$119$	6.71710	+	6.79812i	0.615756	+	0.623183i
$120$	15.8985			1.45133
$121$	−1.00000			−0.0909091
$122$		−	25.5244i		−	2.31087i
$123$	−9.65490			−0.870553
$124$		−	16.0919i		−	1.44510i
$125$			10.5343i			0.942214i
$126$		−	29.9250i		−	2.66593i
$127$	22.0400			1.95573			0.977865	−	0.209236i	$-0.0670975\pi$
$127$	22.0400			1.95573			0.977865	+	0.209236i	$0.0670975\pi$
$128$	−15.9153			−1.40673
$129$		−	24.5167i		−	2.15858i
$130$		−	33.1292i		−	2.90562i
$131$		−	16.0243i		−	1.40005i	−0.714120	−	0.700023i	$-0.753173\pi$
$131$		−	16.0243i		−	1.40005i	0.714120	−	0.700023i	$-0.246827\pi$
$132$	−8.94170			−0.778275
$133$			11.0093i			0.954628i
$134$	−19.6311			−1.69587
$135$	−19.1959			−1.65212
$136$	6.70860	−	6.62865i	0.575258	−	0.568402i
$137$	11.1407			0.951813			0.475907	−	0.879496i	$-0.342120\pi$
$137$	11.1407			0.951813			0.475907	+	0.879496i	$0.342120\pi$
$138$	29.9025			2.54547
$139$		−	1.75498i		−	0.148856i	−0.997226	−	0.0744279i	$-0.976287\pi$
$139$		−	1.75498i		−	0.148856i	0.997226	−	0.0744279i	$-0.0237131\pi$
$140$	−16.4415			−1.38956
$141$			2.50012i			0.210549i
$142$			27.9936i			2.34917i
$143$			6.29649i			0.526539i
$144$	5.27953			0.439961
$145$	3.24855			0.269778
$146$		−	14.5493i		−	1.20411i
$147$		−	4.81720i		−	0.397316i
$148$			10.6375i			0.874399i
$149$	−21.0292			−1.72278			−0.861389	−	0.507945i	$-0.830405\pi$
$149$	−21.0292			−1.72278			−0.861389	+	0.507945i	$0.830405\pi$
$150$			3.40777i			0.278243i
$151$	0.630606			0.0513180			0.0256590	−	0.999671i	$-0.491832\pi$
$151$	0.630606			0.0513180			0.0256590	+	0.999671i	$0.491832\pi$
$152$	10.8643			0.881214
$153$	−16.8987	+	16.6973i	−1.36618	+	1.34990i
$154$	5.19372			0.418522
$155$	12.5086			1.00472
$156$			56.3013i			4.50771i
$157$	5.92518			0.472881			0.236440	−	0.971646i	$-0.424019\pi$
$157$	5.92518			0.472881			0.236440	+	0.971646i	$0.424019\pi$
$158$			17.0454i			1.35606i
$159$			0.0152674i			0.00121078i
$160$		−	15.5633i		−	1.23038i
$161$	−10.4500			−0.823574
$162$	15.4894			1.21696
$163$			8.53205i			0.668281i	0.942523	+	0.334141i	$0.108446\pi$
$163$			8.53205i			0.668281i	−0.942523	+	0.334141i	$0.891554\pi$
$164$		−	9.85318i		−	0.769404i
$165$		−	6.95058i		−	0.541102i
$166$	16.2700			1.26280
$167$			15.0123i			1.16169i	0.814014	+	0.580845i	$0.197278\pi$
$167$			15.0123i			1.16169i	−0.814014	+	0.580845i	$0.802722\pi$
$168$	15.6936			1.21079
$169$	26.6458			2.04967
$170$	15.2476	+	15.4316i	1.16944	+	1.18355i
$171$	−27.3668			−2.09279
$172$	25.0202			1.90777
$173$			10.2403i			0.778552i	0.921121	+	0.389276i	$0.127275\pi$
$173$			10.2403i			0.778552i	−0.921121	+	0.389276i	$0.872725\pi$
$174$	−9.17588			−0.695622
$175$		−	1.19091i		−	0.0900243i
$176$			0.916304i			0.0690690i
$177$			26.7999i			2.01440i
$178$	−26.5215			−1.98787
$179$	−14.2852			−1.06772			−0.533862	−	0.845572i	$-0.679260\pi$
$179$	−14.2852			−1.06772			−0.533862	+	0.845572i	$0.679260\pi$
$180$		−	40.8701i		−	3.04628i
$181$		−	23.8260i		−	1.77097i	−0.464667	−	0.885485i	$-0.653826\pi$
$181$		−	23.8260i		−	1.77097i	0.464667	−	0.885485i	$-0.346174\pi$
$182$		−	32.7022i		−	2.42405i
$183$	−33.7182			−2.49252
$184$			10.3124i			0.760238i
$185$	−8.26878			−0.607933
$186$	−35.3319			−2.59066
$187$	−2.89795	−	2.93290i	−0.211919	−	0.214475i
$188$	−2.55147			−0.186085
$189$	−18.9485			−1.37830
$190$			24.9908i			1.81303i
$191$	6.34339			0.458992			0.229496	−	0.973310i	$-0.426292\pi$
$191$	6.34339			0.458992			0.229496	+	0.973310i	$0.426292\pi$
$192$			38.5355i			2.78106i
$193$		−	12.8933i		−	0.928083i	−0.885814	−	0.464041i	$-0.846399\pi$
$193$		−	12.8933i		−	0.928083i	0.885814	−	0.464041i	$-0.153601\pi$
$194$			25.4789i			1.82928i
$195$	−43.7642			−3.13402
$196$	4.91613			0.351152
$197$		−	3.53908i		−	0.252149i	−0.992021	−	0.126074i	$-0.959762\pi$
$197$		−	3.53908i		−	0.252149i	0.992021	−	0.126074i	$-0.0402378\pi$
$198$			12.9105i			0.917509i
$199$		−	14.6366i		−	1.03756i	−0.854907	−	0.518781i	$-0.826386\pi$
$199$		−	14.6366i		−	1.03756i	0.854907	−	0.518781i	$-0.173614\pi$
$200$	−1.17523			−0.0831011
$201$			25.9331i			1.82918i
$202$	−5.91821			−0.416404
$203$	3.20669			0.225065
$204$	−25.9126	−	26.2251i	−1.81424	−	1.83613i
$205$	7.65909			0.534934
$206$	17.8844			1.24607
$207$		−	25.9765i		−	1.80549i
$208$	5.76950			0.400043
$209$		−	4.74973i		−	0.328545i
$210$			36.0994i			2.49109i
$211$		−	6.37775i		−	0.439062i	−0.975605	−	0.219531i	$-0.929547\pi$
$211$		−	6.37775i		−	0.439062i	0.975605	−	0.219531i	$-0.0704528\pi$
$212$	−0.0155809			−0.00107010
$213$	36.9801			2.53383
$214$			6.78082i			0.463527i
$215$			19.4488i			1.32639i
$216$			18.6990i			1.27230i
$217$	12.3474			0.838195
$218$		−	4.15715i		−	0.281558i
$219$	−19.2198			−1.29876
$220$	7.09332			0.478231
$221$	−18.4670	+	18.2469i	−1.24222	+	1.22742i
$222$	23.3560			1.56755
$223$	12.6711			0.848518			0.424259	−	0.905541i	$-0.360535\pi$
$223$	12.6711			0.848518			0.424259	+	0.905541i	$0.360535\pi$
$224$		−	15.3627i		−	1.02646i
$225$	2.96035			0.197357
$226$			22.3095i			1.48401i
$227$			17.0571i			1.13212i	0.824364	+	0.566060i	$0.191533\pi$
$227$			17.0571i			1.13212i	−0.824364	+	0.566060i	$0.808467\pi$
$228$		−	42.4706i		−	2.81269i
$229$	4.83939			0.319796			0.159898	−	0.987134i	$-0.448883\pi$
$229$	4.83939			0.319796			0.159898	+	0.987134i	$0.448883\pi$
$230$	−23.7212			−1.56413
$231$		−	6.86100i		−	0.451421i
$232$		−	3.16446i		−	0.207757i
$233$		−	9.66069i		−	0.632893i	−0.948610	−	0.316446i	$-0.897510\pi$
$233$		−	9.66069i		−	0.632893i	0.948610	−	0.316446i	$-0.102490\pi$
$234$	81.2908			5.31415
$235$		−	1.98331i		−	0.129377i
$236$	−27.3503			−1.78035
$237$	22.5173			1.46266
$238$	15.0511	+	15.2327i	0.975620	+	0.987387i
$239$	−11.2802			−0.729657			−0.364829	−	0.931075i	$-0.618872\pi$
$239$	−11.2802			−0.729657			−0.364829	+	0.931075i	$0.618872\pi$
$240$	−6.36885			−0.411107
$241$			6.27529i			0.404227i	0.979362	+	0.202113i	$0.0647809\pi$
$241$			6.27529i			0.404227i	−0.979362	+	0.202113i	$0.935219\pi$
$242$	−2.24072			−0.144039
$243$			4.06301i			0.260642i
$244$		−	34.4107i		−	2.20292i
$245$			3.82141i			0.244141i
$246$	−21.6339			−1.37933
$247$	−29.9066			−1.90291
$248$		−	12.1848i		−	0.773735i
$249$		−	21.4930i		−	1.36206i
$250$			23.6043i			1.49287i
$251$	23.4108			1.47768			0.738839	−	0.673881i	$-0.235374\pi$
$251$	23.4108			1.47768			0.738839	+	0.673881i	$0.235374\pi$
$252$		−	40.3433i		−	2.54139i
$253$	4.50842			0.283442
$254$	49.3853			3.09871
$255$	20.3854	−	20.1424i	1.27658	−	1.26137i
$256$	−9.62441			−0.601526
$257$	−14.0901			−0.878915			−0.439457	−	0.898263i	$-0.644829\pi$
$257$	−14.0901			−0.878915			−0.439457	+	0.898263i	$0.644829\pi$
$258$		−	54.9351i		−	3.42011i
$259$	−8.16221			−0.507175
$260$		−	44.6630i		−	2.76988i
$261$			7.97114i			0.493401i
$262$		−	35.9058i		−	2.21827i
$263$	−0.794363			−0.0489825			−0.0244913	−	0.999700i	$-0.507797\pi$
$263$	−0.794363			−0.0489825			−0.0244913	+	0.999700i	$0.507797\pi$
$264$	−6.77065			−0.416705
$265$		−	0.0121114i		−	0.000743995i
$266$			24.6688i			1.51254i
$267$			35.0353i			2.14413i
$268$	−26.4656			−1.61665
$269$			1.37403i			0.0837761i	0.999122	+	0.0418881i	$0.0133373\pi$
$269$			1.37403i			0.0837761i	−0.999122	+	0.0418881i	$0.986663\pi$
$270$	−43.0126			−2.61766
$271$	−7.50242			−0.455739			−0.227870	−	0.973692i	$-0.573176\pi$
$271$	−7.50242			−0.455739			−0.227870	+	0.973692i	$0.573176\pi$
$272$	−2.68743	+	2.65540i	−0.162949	+	0.161007i
$273$	−43.2002			−2.61460
$274$	24.9631			1.50808
$275$			0.513792i			0.0309828i
$276$	40.3129			2.42655
$277$		−	23.3874i		−	1.40521i	−0.711580	−	0.702605i	$-0.752020\pi$
$277$		−	23.3874i		−	1.40521i	0.711580	−	0.702605i	$-0.247980\pi$
$278$		−	3.93242i		−	0.235851i
$279$			30.6930i			1.83754i
$280$	−12.4495			−0.743999
$281$	−2.50141			−0.149221			−0.0746107	−	0.997213i	$-0.523771\pi$
$281$	−2.50141			−0.149221			−0.0746107	+	0.997213i	$0.523771\pi$
$282$			5.60207i			0.333599i
$283$		−	21.9309i		−	1.30366i	−0.758366	−	0.651829i	$-0.774002\pi$
$283$		−	21.9309i		−	1.30366i	0.758366	−	0.651829i	$-0.225998\pi$
$284$			37.7395i			2.23943i
$285$	33.0134			1.95554
$286$			14.1087i			0.834262i
$287$	7.56038			0.446275
$288$	38.1884			2.25027
$289$	0.203811	−	16.9988i	0.0119889	−	0.999928i
$290$	7.27909			0.427443
$291$	33.6580			1.97307
$292$		−	19.6145i		−	1.14785i
$293$	−12.2357			−0.714818			−0.357409	−	0.933948i	$-0.616340\pi$
$293$	−12.2357			−0.714818			−0.357409	+	0.933948i	$0.616340\pi$
$294$		−	10.7940i		−	0.629518i
$295$		−	21.2600i		−	1.23780i
$296$			8.05472i			0.468171i
$297$	8.17492			0.474357
$298$	−47.1205			−2.72962
$299$		−	28.3872i		−	1.64167i
$300$			4.59417i			0.265245i
$301$			19.1981i			1.10656i
$302$	1.41301			0.0813096
$303$			7.81806i			0.449136i
$304$	−4.35219			−0.249615
$305$	26.7482			1.53160
$306$	−37.8652	+	37.4139i	−2.16461	+	2.13881i
$307$	−5.13879			−0.293286			−0.146643	−	0.989189i	$-0.546847\pi$
$307$	−5.13879			−0.293286			−0.146643	+	0.989189i	$0.546847\pi$
$308$	7.00190			0.398970
$309$		−	23.6257i		−	1.34402i
$310$	28.0282			1.59190
$311$			22.0161i			1.24842i	0.781258	+	0.624208i	$0.214578\pi$
$311$			22.0161i			1.24842i	−0.781258	+	0.624208i	$0.785422\pi$
$312$			42.6313i			2.41352i
$313$			17.8836i			1.01084i	0.862873	+	0.505420i	$0.168663\pi$
$313$			17.8836i			1.01084i	−0.862873	+	0.505420i	$0.831337\pi$
$314$	13.2767			0.749245
$315$	31.3598			1.76692
$316$			22.9797i			1.29271i
$317$		−	18.1880i		−	1.02154i	−0.859717	−	0.510771i	$-0.829360\pi$
$317$		−	18.1880i		−	1.02154i	0.859717	−	0.510771i	$-0.170640\pi$
$318$			0.0342098i			0.00191839i
$319$	−1.38345			−0.0774586
$320$		−	30.5697i		−	1.70890i
$321$	8.95759			0.499964
$322$	−23.4155			−1.30489
$323$	13.9305	−	13.7645i	0.775112	−	0.765875i
$324$	20.8820			1.16011
$325$	3.23508			0.179450
$326$			19.1179i			1.05884i
$327$	−5.49167			−0.303690
$328$		−	7.46082i		−	0.411955i
$329$		−	1.95775i		−	0.107934i
$330$		−	15.5743i		−	0.857336i
$331$	9.00765			0.495105			0.247552	−	0.968874i	$-0.420374\pi$
$331$	9.00765			0.495105			0.247552	+	0.968874i	$0.420374\pi$
$332$	21.9344			1.20380
$333$		−	20.2895i		−	1.11186i
$334$			33.6384i			1.84061i
$335$		−	20.5723i		−	1.12399i
$336$	−6.28676			−0.342971
$337$			24.9696i			1.36018i	0.733129	+	0.680089i	$0.238059\pi$
$337$			24.9696i			1.36018i	−0.733129	+	0.680089i	$0.761941\pi$
$338$	59.7056			3.24756
$339$	29.4713			1.60066
$340$	20.5561	+	20.8040i	1.11481	+	1.12826i
$341$	−5.32701			−0.288474
$342$	−61.3213			−3.31588
$343$			19.9973i			1.07976i
$344$	18.9453			1.02146
$345$			31.3361i			1.68708i
$346$			22.9455i			1.23356i
$347$		−	5.43951i		−	0.292008i	−0.989284	−	0.146004i	$-0.953359\pi$
$347$		−	5.43951i		−	0.292008i	0.989284	−	0.146004i	$-0.0466413\pi$
$348$	−12.3704			−0.663125
$349$	−18.3185			−0.980565			−0.490282	−	0.871564i	$-0.663106\pi$
$349$	−18.3185			−0.980565			−0.490282	+	0.871564i	$0.663106\pi$
$350$		−	2.66849i		−	0.142637i
$351$		−	51.4733i		−	2.74744i
$352$			6.62790i			0.353268i
$353$	−18.3563			−0.977006			−0.488503	−	0.872562i	$-0.662457\pi$
$353$	−18.3563			−0.977006			−0.488503	+	0.872562i	$0.662457\pi$
$354$			60.0510i			3.19168i
$355$	−29.3357			−1.55698
$356$	−35.7548			−1.89500
$357$	20.1226	−	19.8828i	1.06500	−	1.05231i
$358$	−32.0090			−1.69173
$359$	5.62726			0.296996			0.148498	−	0.988913i	$-0.452556\pi$
$359$	5.62726			0.296996			0.148498	+	0.988913i	$0.452556\pi$
$360$		−	30.9468i		−	1.63104i
$361$	3.55989			0.187363
$362$		−	53.3873i		−	2.80597i
$363$			2.96003i			0.155361i
$364$		−	44.0874i		−	2.31081i
$365$	15.2468			0.798055
$366$	−75.5531			−3.94922
$367$			15.8833i			0.829100i	0.910026	+	0.414550i	$0.136061\pi$
$367$			15.8833i			0.829100i	−0.910026	+	0.414550i	$0.863939\pi$
$368$		−	4.13108i		−	0.215348i
$369$			18.7935i			0.978351i
$370$	−18.5280			−0.963225
$371$		−	0.0119553i		−	0.000620687i
$372$	−47.6325			−2.46963
$373$	7.79989			0.403863			0.201932	−	0.979400i	$-0.435278\pi$
$373$	7.79989			0.403863			0.201932	+	0.979400i	$0.435278\pi$
$374$	−6.49348	−	6.57180i	−0.335770	−	0.339820i
$375$	31.1818			1.61022
$376$	−1.93197			−0.0996337
$377$			8.71090i			0.448634i
$378$	−42.4583			−2.18382
$379$			12.3406i			0.633893i	0.948443	+	0.316947i	$0.102658\pi$
$379$			12.3406i			0.633893i	−0.948443	+	0.316947i	$0.897342\pi$
$380$			33.6913i			1.72833i
$381$		−	65.2389i		−	3.34229i
$382$	14.2138			0.727239
$383$	7.07483			0.361507			0.180754	−	0.983528i	$-0.442146\pi$
$383$	7.07483			0.361507			0.180754	+	0.983528i	$0.442146\pi$
$384$			47.1097i			2.40406i
$385$			5.44273i			0.277387i
$386$		−	28.8903i		−	1.47048i
$387$	−47.7225			−2.42587
$388$			34.3492i			1.74382i
$389$	0.408540			0.0207138			0.0103569	−	0.999946i	$-0.496703\pi$
$389$	0.408540			0.0207138			0.0103569	+	0.999946i	$0.496703\pi$
$390$	−98.0633			−4.96563
$391$	13.0652	+	13.2227i	0.660733	+	0.668703i
$392$	3.72249			0.188014
$393$	−47.4323			−2.39264
$394$		−	7.93007i		−	0.399511i
$395$	−17.8627			−0.898767
$396$			17.4052i			0.874647i
$397$		−	8.62291i		−	0.432771i	−0.976308	−	0.216386i	$-0.930573\pi$
$397$		−	8.62291i		−	0.432771i	0.976308	−	0.216386i	$-0.0694268\pi$
$398$		−	32.7965i		−	1.64394i
$399$	32.5879			1.63143
$400$	0.470790			0.0235395
$401$			1.11453i			0.0556570i	0.999613	+	0.0278285i	$0.00885924\pi$
$401$			1.11453i			0.0556570i	−0.999613	+	0.0278285i	$0.991141\pi$
$402$			58.1087i			2.89820i
$403$			33.5415i			1.67082i
$404$	−7.97862			−0.396951
$405$			16.2320i			0.806575i
$406$	7.18528			0.356599
$407$	3.52141			0.174550
$408$	−19.6210	−	19.8576i	−0.971383	−	0.983100i
$409$	9.34797			0.462227			0.231114	−	0.972927i	$-0.425763\pi$
$409$	9.34797			0.462227			0.231114	+	0.972927i	$0.425763\pi$
$410$	17.1619			0.847564
$411$		−	32.9768i		−	1.62662i
$412$	24.1108			1.18786
$413$		−	20.9860i		−	1.03265i
$414$		−	58.2059i		−	2.86067i
$415$			17.0501i			0.836954i
$416$	41.7325			2.04610
$417$	−5.19480			−0.254391
$418$		−	10.6428i		−	0.520556i
$419$		−	3.40364i		−	0.166279i	−0.996538	−	0.0831393i	$-0.973505\pi$
$419$		−	3.40364i		−	0.166279i	0.996538	−	0.0831393i	$-0.0264947\pi$
$420$			48.6673i			2.37472i
$421$	10.7701			0.524902			0.262451	−	0.964945i	$-0.415469\pi$
$421$	10.7701			0.524902			0.262451	+	0.964945i	$0.415469\pi$
$422$		−	14.2907i		−	0.695662i
$423$	4.86656			0.236620
$424$	−0.0117978			−0.000572954
$425$	−1.50690	+	1.48894i	−0.0730954	+	0.0722243i
$426$	82.8619			4.01467
$427$	26.4034			1.27775
$428$			9.14154i			0.441873i
$429$	18.6378			0.899841
$430$			43.5792i			2.10158i
$431$		−	3.61091i		−	0.173932i	−0.996211	−	0.0869658i	$-0.972283\pi$
$431$		−	3.61091i		−	0.173932i	0.996211	−	0.0869658i	$-0.0277171\pi$
$432$		−	7.49071i		−	0.360397i
$433$	−39.6227			−1.90415			−0.952074	−	0.305869i	$-0.901053\pi$
$433$	−39.6227			−1.90415			−0.952074	+	0.305869i	$0.901053\pi$
$434$	27.6670			1.32806
$435$		−	9.61581i		−	0.461043i
$436$		−	5.60445i		−	0.268404i
$437$			21.4137i			1.02436i
$438$	−43.0662			−2.05778
$439$			15.1511i			0.723123i	0.932348	+	0.361561i	$0.117756\pi$
$439$			15.1511i			0.723123i	−0.932348	+	0.361561i	$0.882244\pi$
$440$	5.37106			0.256055
$441$	−9.37680			−0.446514
$442$	−41.3793	+	40.8861i	−1.96821	+	1.94475i
$443$	24.5559			1.16669			0.583344	−	0.812225i	$-0.301744\pi$
$443$	24.5559			1.16669			0.583344	+	0.812225i	$0.301744\pi$
$444$	31.4874			1.49432
$445$		−	27.7930i		−	1.31751i
$446$	28.3923			1.34441
$447$			62.2470i			2.94418i
$448$		−	30.1757i		−	1.42567i
$449$			16.8411i			0.794779i	0.917650	+	0.397389i	$0.130084\pi$
$449$			16.8411i			0.794779i	−0.917650	+	0.397389i	$0.869916\pi$
$450$	6.63331			0.312697
$451$	−3.26176			−0.153590
$452$			30.0765i			1.41468i
$453$		−	1.86661i		−	0.0877011i
$454$			38.2202i			1.79376i
$455$	34.2701			1.60661
$456$		−	32.1587i		−	1.50597i
$457$	−9.97080			−0.466414			−0.233207	−	0.972427i	$-0.574922\pi$
$457$	−9.97080			−0.466414			−0.233207	+	0.972427i	$0.574922\pi$
$458$	10.8437			0.506693
$459$	23.6905	+	23.9762i	1.10578	+	1.11911i
$460$	−31.9796			−1.49106
$461$	−15.1829			−0.707139			−0.353570	−	0.935408i	$-0.615032\pi$
$461$	−15.1829			−0.707139			−0.353570	+	0.935408i	$0.615032\pi$
$462$		−	15.3736i		−	0.715243i
$463$	−32.7423			−1.52166			−0.760832	−	0.648949i	$-0.775209\pi$
$463$	−32.7423			−1.52166			−0.760832	+	0.648949i	$0.775209\pi$
$464$			1.26766i			0.0588499i
$465$		−	37.0258i		−	1.71703i
$466$		−	21.6469i		−	1.00277i
$467$	−6.89228			−0.318937			−0.159468	−	0.987203i	$-0.550978\pi$
$467$	−6.89228			−0.318937			−0.159468	+	0.987203i	$0.550978\pi$
$468$	109.592			5.06589
$469$		−	20.3072i		−	0.937699i
$470$		−	4.44404i		−	0.204988i
$471$		−	17.5387i		−	0.808141i
$472$	−20.7096			−0.953237
$473$		−	8.28260i		−	0.380834i
$474$	50.4549			2.31747
$475$	−2.44037			−0.111972
$476$	20.2911	+	20.5359i	0.930042	+	0.941260i
$477$	0.0297183			0.00136071
$478$	−25.2758			−1.15609
$479$		−	22.1304i		−	1.01116i	−0.862779	−	0.505582i	$-0.831278\pi$
$479$		−	22.1304i		−	1.01116i	0.862779	−	0.505582i	$-0.168722\pi$
$480$	−46.0677			−2.10270
$481$		−	22.1725i		−	1.01098i
$482$			14.0611i			0.640468i
$483$			30.9323i			1.40747i
$484$	−3.02082			−0.137310
$485$	−26.7004			−1.21240
$486$			9.10405i			0.412968i
$487$		−	5.82873i		−	0.264125i	−0.991241	−	0.132062i	$-0.957840\pi$
$487$		−	5.82873i		−	0.264125i	0.991241	−	0.132062i	$-0.0421599\pi$
$488$		−	26.0557i		−	1.17949i
$489$	25.2551			1.14208
$490$			8.56271i			0.386824i
$491$	8.65543			0.390614			0.195307	−	0.980742i	$-0.437430\pi$
$491$	8.65543			0.390614			0.195307	+	0.980742i	$0.437430\pi$
$492$	−29.1657			−1.31489
$493$	−4.00918	−	4.05753i	−0.180564	−	0.182742i
$494$	−67.0122			−3.01502
$495$	−13.5295			−0.608105
$496$			4.88116i			0.219171i
$497$	−28.9577			−1.29893
$498$		−	48.1597i		−	2.15809i
$499$		−	24.6867i		−	1.10513i	−0.833470	−	0.552565i	$-0.813649\pi$
$499$		−	24.6867i		−	1.10513i	0.833470	−	0.552565i	$-0.186351\pi$
$500$			31.8221i			1.42313i
$501$	44.4369			1.98530
$502$	52.4571			2.34127
$503$		−	35.5049i		−	1.58308i	−0.611114	−	0.791542i	$-0.709278\pi$
$503$		−	35.5049i		−	1.58308i	0.611114	−	0.791542i	$-0.290722\pi$
$504$		−	30.5479i		−	1.36071i
$505$		−	6.20195i		−	0.275983i
$506$	10.1021			0.449093
$507$		−	78.8722i		−	3.50284i
$508$	66.5787			2.95395
$509$	−32.3749			−1.43499			−0.717497	−	0.696561i	$-0.754712\pi$
$509$	−32.3749			−1.43499			−0.717497	+	0.696561i	$0.754712\pi$
$510$	45.6778	−	45.1335i	2.02265	−	1.99854i
$511$	15.0503			0.665786
$512$	10.2650			0.453653
$513$			38.8286i			1.71433i
$514$	−31.5719			−1.39258
$515$			18.7419i			0.825866i
$516$		−	74.0606i		−	3.26033i
$517$			0.844629i			0.0371467i
$518$	−18.2892			−0.803582
$519$	30.3114			1.33052
$520$		−	33.8188i		−	1.48305i
$521$			31.6223i			1.38540i	0.721227	+	0.692699i	$0.243579\pi$
$521$			31.6223i			1.38540i	−0.721227	+	0.692699i	$0.756421\pi$
$522$			17.8611i			0.781758i
$523$	38.9703			1.70405			0.852026	−	0.523499i	$-0.175374\pi$
$523$	38.9703			1.70405			0.852026	+	0.523499i	$0.175374\pi$
$524$		−	48.4063i		−	2.11464i
$525$	−3.52513			−0.153849
$526$	−1.77994			−0.0776093
$527$	−15.4374	−	15.6236i	−0.672463	−	0.680574i
$528$	2.71229			0.118037
$529$	2.67417			0.116268
$530$		−	0.0271382i		−	0.00117881i
$531$	52.1667			2.26384
$532$			33.2571i			1.44188i
$533$			20.5376i			0.889584i
$534$			78.5043i			3.39721i
$535$	−7.10592			−0.307216
$536$	−20.0398			−0.865586
$537$			42.2845i			1.82471i
$538$			3.07881i			0.132737i
$539$		−	1.62742i		−	0.0700978i
$540$	−57.9873			−2.49538
$541$		−	12.8857i		−	0.553999i	−0.960870	−	0.276999i	$-0.910660\pi$
$541$		−	12.8857i		−	0.553999i	0.960870	−	0.276999i	$-0.0893400\pi$
$542$	−16.8108			−0.722085
$543$	−70.5256			−3.02654
$544$	−19.4390	+	19.2073i	−0.833439	+	0.823506i
$545$	4.35646			0.186610
$546$	−96.7995			−4.14263
$547$		−	34.0853i		−	1.45738i	−0.684843	−	0.728691i	$-0.740129\pi$
$547$		−	34.0853i		−	1.45738i	0.684843	−	0.728691i	$-0.259871\pi$
$548$	33.6540			1.43763
$549$			65.6334i			2.80117i
$550$			1.15126i			0.0490900i
$551$		−	6.57103i		−	0.279935i
$552$	30.5249			1.29923
$553$	−17.6324			−0.749807
$554$		−	52.4045i		−	2.22645i
$555$			24.4758i			1.03894i
$556$		−	5.30148i		−	0.224833i
$557$	4.69060			0.198747			0.0993736	−	0.995050i	$-0.468316\pi$
$557$	4.69060			0.198747			0.0993736	+	0.995050i	$0.468316\pi$
$558$			68.7744i			2.91145i
$559$	−52.1513			−2.20577
$560$	4.98720			0.210747
$561$	−8.68147	+	8.57801i	−0.366532	+	0.362164i
$562$	−5.60494			−0.236430
$563$	8.45355			0.356275			0.178137	−	0.984006i	$-0.442993\pi$
$563$	8.45355			0.356275			0.178137	+	0.984006i	$0.442993\pi$
$564$			7.55242i			0.318014i
$565$	−23.3791			−0.983568
$566$		−	49.1410i		−	2.06555i
$567$			16.0228i			0.672894i
$568$			28.5763i			1.19904i
$569$	−8.83612			−0.370429			−0.185215	−	0.982698i	$-0.559298\pi$
$569$	−8.83612			−0.370429			−0.185215	+	0.982698i	$0.559298\pi$
$570$	73.9736			3.09841
$571$			40.2729i			1.68537i	0.538409	+	0.842684i	$0.319026\pi$
$571$			40.2729i			1.68537i	−0.538409	+	0.842684i	$0.680974\pi$
$572$			19.0205i			0.795288i
$573$		−	18.7766i		−	0.784405i
$574$	16.9407			0.707090
$575$		−	2.31639i		−	0.0966001i
$576$	75.0104			3.12543
$577$	22.3195			0.929171			0.464586	−	0.885528i	$-0.346203\pi$
$577$	22.3195			0.929171			0.464586	+	0.885528i	$0.346203\pi$
$578$	0.456682	−	38.0895i	0.0189955	−	1.58431i
$579$	−38.1647			−1.58607
$580$	9.81328			0.407474
$581$			16.8303i			0.698239i
$582$	75.4182			3.12618
$583$			0.00515784i			0.000213616i
$584$		−	14.8521i		−	0.614585i
$585$			85.1882i			3.52210i
$586$	−27.4168			−1.13258
$587$	2.36266			0.0975174			0.0487587	−	0.998811i	$-0.484473\pi$
$587$	2.36266			0.0975174			0.0487587	+	0.998811i	$0.484473\pi$
$588$		−	14.5519i		−	0.600109i
$589$		−	25.3018i		−	1.04254i
$590$		−	47.6376i		−	1.96121i
$591$	−10.4758			−0.430916
$592$		−	3.22668i		−	0.132616i
$593$	−5.59160			−0.229620			−0.114810	−	0.993387i	$-0.536626\pi$
$593$	−5.59160			−0.229620			−0.114810	+	0.993387i	$0.536626\pi$
$594$	18.3177			0.751584
$595$	−15.9630	+	15.7727i	−0.654419	+	0.646619i
$596$	−63.5253			−2.60210
$597$	−43.3248			−1.77317
$598$		−	63.6077i		−	2.60111i
$599$	−37.0317			−1.51307			−0.756536	−	0.653952i	$-0.773110\pi$
$599$	−37.0317			−1.51307			−0.756536	+	0.653952i	$0.773110\pi$
$600$			3.47871i			0.142018i
$601$		−	14.0028i		−	0.571188i	−0.958351	−	0.285594i	$-0.907809\pi$
$601$		−	14.0028i		−	0.571188i	0.958351	−	0.285594i	$-0.0921908\pi$
$602$			43.0175i			1.75326i
$603$	50.4794			2.05568
$604$	1.90495			0.0775111
$605$		−	2.34815i		−	0.0954657i
$606$			17.5181i			0.711623i
$607$			6.08158i			0.246844i	0.992354	+	0.123422i	$0.0393869\pi$
$607$			6.08158i			0.246844i	−0.992354	+	0.123422i	$0.960613\pi$
$608$	−31.4807			−1.27671
$609$		−	9.49188i		−	0.384630i
$610$	59.9351			2.42670
$611$	5.31819			0.215151
$612$	−51.0479	+	50.4395i	−2.06349	+	2.03889i
$613$	−19.1572			−0.773753			−0.386876	−	0.922132i	$-0.626446\pi$
$613$	−19.1572			−0.773753			−0.386876	+	0.922132i	$0.626446\pi$
$614$	−11.5146			−0.464691
$615$		−	22.6711i		−	0.914188i
$616$	5.30183			0.213617
$617$		−	30.6157i		−	1.23254i	−0.787534	−	0.616271i	$-0.788643\pi$
$617$		−	30.6157i		−	1.23254i	0.787534	−	0.616271i	$-0.211357\pi$
$618$		−	52.9384i		−	2.12950i
$619$		−	21.0864i		−	0.847534i	−0.905771	−	0.423767i	$-0.860707\pi$
$619$		−	21.0864i		−	0.847534i	0.905771	−	0.423767i	$-0.139293\pi$
$620$	37.7862			1.51753
$621$	−36.8560			−1.47898
$622$			49.3318i			1.97802i
$623$		−	27.4348i		−	1.09915i
$624$		−	17.0779i		−	0.683662i
$625$	−27.3050			−1.09220
$626$			40.0721i			1.60160i
$627$	−14.0593			−0.561475
$628$	17.8989			0.714243
$629$	10.2048	+	10.3279i	0.406894	+	0.411802i
$630$	70.2684			2.79956
$631$	5.06618			0.201682			0.100841	−	0.994903i	$-0.467847\pi$
$631$	5.06618			0.201682			0.100841	+	0.994903i	$0.467847\pi$
$632$			17.4002i			0.692144i
$633$	−18.8783			−0.750346
$634$		−	40.7543i		−	1.61856i
$635$			51.7531i			2.05376i
$636$			0.0461199i			0.00182877i
$637$	−10.2470			−0.406001
$638$	−3.09993			−0.122727
$639$		−	71.9827i		−	2.84759i
$640$		−	37.3715i		−	1.47724i
$641$		−	42.7871i		−	1.68999i	−0.534774	−	0.844995i	$-0.679603\pi$
$641$		−	42.7871i		−	1.68999i	0.534774	−	0.844995i	$-0.320397\pi$
$642$	20.0714			0.792156
$643$			40.3684i			1.59197i	0.605315	+	0.795986i	$0.293047\pi$
$643$			40.3684i			1.59197i	−0.605315	+	0.795986i	$0.706953\pi$
$644$	−31.5675			−1.24393
$645$	57.5689			2.26677
$646$	31.2143	−	30.8422i	1.22811	−	1.21347i
$647$	−26.0275			−1.02325			−0.511623	−	0.859210i	$-0.670956\pi$
$647$	−26.0275			−1.02325			−0.511623	+	0.859210i	$0.670956\pi$
$648$	15.8118			0.621146
$649$			9.05394i			0.355398i
$650$	7.24891			0.284326
$651$		−	36.5486i		−	1.43245i
$652$			25.7737i			1.00938i
$653$		−	29.1795i		−	1.14188i	−0.820991	−	0.570941i	$-0.806578\pi$
$653$		−	29.1795i		−	1.14188i	0.820991	−	0.570941i	$-0.193422\pi$
$654$	−12.3053			−0.481175
$655$	37.6273			1.47022
$656$			2.98876i			0.116692i
$657$			37.4119i			1.45958i
$658$		−	4.38677i		−	0.171014i
$659$	32.8299			1.27887			0.639436	−	0.768844i	$-0.279168\pi$
$659$	32.8299			1.27887			0.639436	+	0.768844i	$0.279168\pi$
$660$		−	20.9964i		−	0.817285i
$661$	−4.78015			−0.185926			−0.0929630	−	0.995670i	$-0.529634\pi$
$661$	−4.78015			−0.185926			−0.0929630	+	0.995670i	$0.529634\pi$
$662$	20.1836			0.784457
$663$	54.0113	+	54.6628i	2.09763	+	2.12293i
$664$	16.6087			0.644542
$665$	−25.8515			−1.00248
$666$		−	45.4631i		−	1.76166i
$667$	6.23719			0.241505
$668$			45.3495i			1.75462i
$669$		−	37.5068i		−	1.45010i
$670$		−	46.0968i		−	1.78087i
$671$	−11.3912			−0.439752
$672$	−45.4740			−1.75420
$673$			28.5831i			1.10180i	0.834573	+	0.550898i	$0.185715\pi$
$673$			28.5831i			1.10180i	−0.834573	+	0.550898i	$0.814285\pi$
$674$			55.9497i			2.15510i
$675$		−	4.20021i		−	0.161666i
$676$	80.4919			3.09584
$677$			23.0160i			0.884576i	0.896873	+	0.442288i	$0.145833\pi$
$677$			23.0160i			0.884576i	−0.896873	+	0.442288i	$0.854167\pi$
$678$	66.0369			2.53613
$679$	−26.3563			−1.01146
$680$	15.5650	+	15.7528i	0.596892	+	0.604091i
$681$	50.4895			1.93476
$682$	−11.9363			−0.457066
$683$			51.2946i			1.96273i	0.192142	+	0.981367i	$0.438456\pi$
$683$			51.2946i			1.96273i	−0.192142	+	0.981367i	$0.561544\pi$
$684$	−82.6701			−3.16097
$685$			26.1600i			0.999521i
$686$			44.8084i			1.71079i
$687$		−	14.3247i		−	0.546523i
$688$	−7.58938			−0.289343
$689$	0.0324763			0.00123725
$690$			70.2154i			2.67305i
$691$		−	19.9704i		−	0.759711i	−0.925046	−	0.379856i	$-0.875974\pi$
$691$		−	19.9704i		−	0.759711i	0.925046	−	0.379856i	$-0.124026\pi$
$692$			30.9339i			1.17593i
$693$	−13.3551			−0.507319
$694$		−	12.1884i		−	0.462666i
$695$	4.12096			0.156317
$696$	−9.36688			−0.355051
$697$	−9.45241	−	9.56642i	−0.358035	−	0.362354i
$698$	−41.0465			−1.55363
$699$	−28.5959			−1.08160
$700$		−	3.59752i		−	0.135973i
$701$	23.1138			0.872996			0.436498	−	0.899705i	$-0.356219\pi$
$701$	23.1138			0.872996			0.436498	+	0.899705i	$0.356219\pi$
$702$		−	115.337i		−	4.35312i
$703$			16.7257i			0.630822i
$704$			13.0186i			0.490658i
$705$	−5.87066			−0.221102
$706$	−41.1312			−1.54799
$707$		−	6.12202i		−	0.230242i
$708$			80.9576i			3.04257i
$709$		−	17.3766i		−	0.652594i	−0.945267	−	0.326297i	$-0.894199\pi$
$709$		−	17.3766i		−	0.652594i	0.945267	−	0.326297i	$-0.105801\pi$
$710$	−65.7331			−2.46692
$711$		−	43.8305i		−	1.64377i
$712$	−27.0735			−1.01462
$713$	24.0164			0.899421
$714$	45.0891	−	44.5518i	1.68742	−	1.66731i
$715$	−14.7851			−0.552930
$716$	−43.1528			−1.61270
$717$			33.3898i			1.24697i
$718$	12.6091			0.470568
$719$			16.7373i			0.624197i	0.950050	+	0.312099i	$0.101032\pi$
$719$			16.7373i			0.624197i	−0.950050	+	0.312099i	$0.898968\pi$
$720$			12.3971i			0.462013i
$721$			18.5003i			0.688988i
$722$	7.97672			0.296863
$723$	18.5750			0.690813
$724$		−	71.9739i		−	2.67489i
$725$			0.710808i			0.0263987i
$726$			6.63259i			0.246158i
$727$	21.7155			0.805382			0.402691	−	0.915336i	$-0.368075\pi$
$727$	21.7155			0.805382			0.402691	+	0.915336i	$0.368075\pi$
$728$		−	33.3829i		−	1.23725i
$729$	32.7647			1.21351
$730$	34.1638			1.26446
$731$	24.2920	−	24.0025i	0.898474	−	0.887766i
$732$	−101.857			−3.76473
$733$	21.9399			0.810368			0.405184	−	0.914235i	$-0.367207\pi$
$733$	21.9399			0.810368			0.405184	+	0.914235i	$0.367207\pi$
$734$			35.5899i			1.31365i
$735$	11.3115			0.417231
$736$		−	29.8813i		−	1.10144i
$737$			8.76109i			0.322719i
$738$			42.1110i			1.55013i
$739$	7.71145			0.283670			0.141835	−	0.989890i	$-0.454700\pi$
$739$	7.71145			0.283670			0.141835	+	0.989890i	$0.454700\pi$
$740$	−24.9785			−0.918226
$741$			88.5244i			3.25202i
$742$		−	0.0267884i		−	0.000983433i
$743$		−	21.3390i		−	0.782851i	−0.920210	−	0.391426i	$-0.871982\pi$
$743$		−	21.3390i		−	0.782851i	0.920210	−	0.391426i	$-0.128018\pi$
$744$	−36.0673			−1.32229
$745$		−	49.3796i		−	1.80913i
$746$	17.4774			0.639892
$747$	−41.8366			−1.53072
$748$	−8.75416	−	8.85975i	−0.320084	−	0.323945i
$749$	−7.01434			−0.256298
$750$	69.8695			2.55127
$751$			14.4537i			0.527424i	0.964601	+	0.263712i	$0.0849468\pi$
$751$			14.4537i			0.527424i	−0.964601	+	0.263712i	$0.915053\pi$
$752$	0.773937			0.0282226
$753$		−	69.2968i		−	2.52531i
$754$			19.5187i			0.710828i
$755$			1.48076i			0.0538902i
$756$	−57.2400			−2.08180
$757$	−46.7662			−1.69975			−0.849873	−	0.526988i	$-0.823321\pi$
$757$	−46.7662			−1.69975			−0.849873	+	0.526988i	$0.823321\pi$
$758$			27.6518i			1.00436i
$759$		−	13.3450i		−	0.484395i
$760$			25.5110i			0.925383i
$761$	30.1696			1.09365			0.546823	−	0.837248i	$-0.315837\pi$
$761$	30.1696			1.09365			0.546823	+	0.837248i	$0.315837\pi$
$762$		−	146.182i		−	5.29562i
$763$	4.30032			0.155682
$764$	19.1622			0.693265
$765$	−39.2077	−	39.6806i	−1.41756	−	1.43466i
$766$	15.8527			0.572781
$767$	57.0080			2.05844
$768$			28.4885i			1.02799i
$769$	19.0649			0.687498			0.343749	−	0.939062i	$-0.388303\pi$
$769$	19.0649			0.687498			0.343749	+	0.939062i	$0.388303\pi$
$770$			12.1956i			0.439500i
$771$			41.7070i			1.50204i
$772$		−	38.9484i		−	1.40178i
$773$	−27.0938			−0.974497			−0.487248	−	0.873263i	$-0.661999\pi$
$773$	−27.0938			−0.974497			−0.487248	+	0.873263i	$0.661999\pi$
$774$	−106.933			−3.84361
$775$			2.73698i			0.0983150i
$776$			26.0092i			0.933677i
$777$			24.1604i			0.866749i
$778$	0.915423			0.0328195
$779$		−	15.4925i		−	0.555075i
$780$	−132.204			−4.73365
$781$	12.4932			0.447040
$782$	29.2753	+	29.6284i	1.04688	+	1.05951i
$783$	11.3096			0.404173
$784$	−1.49121			−0.0532575
$785$			13.9132i			0.496583i
$786$	−106.282			−3.79097
$787$		−	5.54906i		−	0.197803i	−0.995097	−	0.0989013i	$-0.968467\pi$
$787$		−	5.54906i		−	0.197803i	0.995097	−	0.0989013i	$-0.0315328\pi$
$788$		−	10.6909i		−	0.380848i
$789$			2.35134i			0.0837099i
$790$	−40.0252			−1.42403
$791$	−23.0778			−0.820553
$792$			13.1792i			0.468304i
$793$			71.7245i			2.54701i
$794$		−	19.3215i		−	0.685694i
$795$	−0.0358500			−0.00127147
$796$		−	44.2145i		−	1.56714i
$797$	−11.1573			−0.395212			−0.197606	−	0.980281i	$-0.563317\pi$
$797$	−11.1573			−0.395212			−0.197606	+	0.980281i	$0.563317\pi$
$798$	73.0202			2.58489
$799$	−2.47721	+	2.44769i	−0.0876374	+	0.0865930i
$800$	3.40536			0.120398
$801$	68.1971			2.40963
$802$			2.49735i			0.0881845i
$803$	−6.49313			−0.229137
$804$			78.3391i			2.76281i
$805$		−	24.5381i		−	0.864854i
$806$			75.1569i			2.64729i
$807$	4.06717			0.143171
$808$	−6.04140			−0.212536
$809$		−	41.0144i		−	1.44199i	−0.692941	−	0.720994i	$-0.743685\pi$
$809$		−	41.0144i		−	1.44199i	0.692941	−	0.720994i	$-0.256315\pi$
$810$			36.3713i			1.27796i
$811$			3.49654i			0.122780i	0.998114	+	0.0613900i	$0.0195534\pi$
$811$			3.49654i			0.122780i	−0.998114	+	0.0613900i	$0.980447\pi$
$812$	9.68680			0.339940
$813$			22.2074i			0.778846i
$814$	7.89048			0.276561
$815$	−20.0345			−0.701778
$816$	7.86006	+	7.95487i	0.275157	+	0.278476i
$817$	39.3401			1.37634
$818$	20.9462			0.732365
$819$			84.0903i			2.93835i
$820$	23.1367			0.807969
$821$			11.2187i			0.391535i	0.980650	+	0.195768i	$0.0627198\pi$
$821$			11.2187i			0.391535i	−0.980650	+	0.195768i	$0.937280\pi$
$822$		−	73.8916i		−	2.57727i
$823$			44.9646i			1.56737i	0.621161	+	0.783683i	$0.286661\pi$
$823$			44.9646i			1.56737i	−0.621161	+	0.783683i	$0.713339\pi$
$824$	18.2567			0.636002
$825$	1.52084			0.0529488
$826$		−	47.0236i		−	1.63616i
$827$		−	0.586580i		−	0.0203974i	−0.999948	−	0.0101987i	$-0.996754\pi$
$827$		−	0.586580i		−	0.0203974i	0.999948	−	0.0101987i	$-0.00324640\pi$
$828$		−	78.4701i		−	2.72703i
$829$	−20.9260			−0.726790			−0.363395	−	0.931635i	$-0.618383\pi$
$829$	−20.9260			−0.726790			−0.363395	+	0.931635i	$0.618383\pi$
$830$			38.2044i			1.32609i
$831$	−69.2273			−2.40147
$832$	81.9717			2.84186
$833$	4.77305	−	4.71617i	0.165376	−	0.163406i
$834$	−11.6401			−0.403063
$835$	−35.2512			−1.21992
$836$		−	14.3480i		−	0.496238i
$837$	43.5479			1.50524
$838$		−	7.62659i		−	0.263456i
$839$		−	19.9281i		−	0.687994i	−0.938971	−	0.343997i	$-0.888219\pi$
$839$		−	19.9281i		−	0.687994i	0.938971	−	0.343997i	$-0.111781\pi$
$840$			36.8508i			1.27147i
$841$	27.0861			0.934002
$842$	24.1327			0.831668
$843$			7.40423i			0.255015i
$844$		−	19.2660i		−	0.663163i
$845$			62.5681i			2.15241i
$846$	10.9046			0.374907
$847$		−	2.31788i		−	0.0796434i
$848$	0.00472615			0.000162297
$849$	−64.9162			−2.22792
$850$	−3.37654	+	3.33630i	−0.115814	+	0.114434i
$851$	−15.8760			−0.544221
$852$	111.710			3.82712
$853$		−	24.3840i		−	0.834891i	−0.908702	−	0.417446i	$-0.862925\pi$
$853$		−	24.3840i		−	0.834891i	0.908702	−	0.417446i	$-0.137075\pi$
$854$	59.1627			2.02450
$855$		−	64.2613i		−	2.19769i
$856$			6.92197i			0.236588i
$857$		−	4.15612i		−	0.141970i	−0.997477	−	0.0709852i	$-0.977386\pi$
$857$		−	4.15612i		−	0.141970i	0.997477	−	0.0709852i	$-0.0226143\pi$
$858$	41.7620			1.42573
$859$	25.6342			0.874628			0.437314	−	0.899309i	$-0.355930\pi$
$859$	25.6342			0.874628			0.437314	+	0.899309i	$0.355930\pi$
$860$			58.7511i			2.00340i
$861$		−	22.3789i		−	0.762672i
$862$		−	8.09104i		−	0.275582i
$863$	40.0702			1.36401			0.682003	−	0.731350i	$-0.261109\pi$
$863$	40.0702			1.36401			0.682003	+	0.731350i	$0.261109\pi$
$864$		−	54.1825i		−	1.84333i
$865$	−24.0456			−0.817575
$866$	−88.7834			−3.01698
$867$	−50.3169	−	0.603286i	−1.70885	−	0.0204887i
$868$	37.2992			1.26602
$869$	7.60713			0.258054
$870$		−	21.5463i		−	0.730488i
$871$	55.1641			1.86916
$872$		−	4.24369i		−	0.143709i
$873$		−	65.5162i		−	2.21739i
$874$			47.9822i			1.62302i
$875$	−24.4172			−0.825453
$876$	−58.0596			−1.96165
$877$		−	54.2838i		−	1.83304i	−0.399994	−	0.916518i	$-0.630988\pi$
$877$		−	54.2838i		−	1.83304i	0.399994	−	0.916518i	$-0.369012\pi$
$878$			33.9493i			1.14574i
$879$			36.2181i			1.22161i
$880$	−2.15162			−0.0725310
$881$			17.8098i			0.600028i	0.953935	+	0.300014i	$0.0969914\pi$
$881$			17.8098i			0.600028i	−0.953935	+	0.300014i	$0.903009\pi$
$882$	−21.0108			−0.707469
$883$	3.28862			0.110671			0.0553355	−	0.998468i	$-0.482377\pi$
$883$	3.28862			0.110671			0.0553355	+	0.998468i	$0.482377\pi$
$884$	−55.7853	+	55.1205i	−1.87626	+	1.85390i
$885$	−62.9301			−2.11537
$886$	55.0229			1.84853
$887$		−	26.3021i		−	0.883140i	−0.897227	−	0.441570i	$-0.854422\pi$
$887$		−	26.3021i		−	0.883140i	0.897227	−	0.441570i	$-0.145578\pi$
$888$	23.8422			0.800092
$889$			51.0861i			1.71337i
$890$		−	62.2763i		−	2.08751i
$891$		−	6.91269i		−	0.231584i
$892$	38.2770			1.28161
$893$	−4.01175			−0.134248
$894$			139.478i			4.66484i
$895$		−	33.5437i		−	1.12124i
$896$		−	36.8898i		−	1.23240i
$897$	−84.0269			−2.80558
$898$			37.7361i			1.25927i
$899$	−7.36967			−0.245792
$900$	8.94267			0.298089
$901$	−0.0151274	+	0.0149471i	−0.000503968	+	0.000497962i
$902$	−7.30868			−0.243353
$903$	56.8269			1.89108
$904$			22.7739i			0.757449i
$905$	55.9469			1.85974
$906$		−	4.18255i		−	0.138956i
$907$		−	2.45533i		−	0.0815278i	−0.999169	−	0.0407639i	$-0.987021\pi$
$907$		−	2.45533i		−	0.0815278i	0.999169	−	0.0407639i	$-0.0129792\pi$
$908$			51.5264i			1.70996i
$909$	15.2181			0.504751
$910$	76.7896			2.54555
$911$		−	26.5673i		−	0.880215i	−0.897945	−	0.440108i	$-0.854940\pi$
$911$		−	26.5673i		−	0.880215i	0.897945	−	0.440108i	$-0.145060\pi$
$912$			12.8826i			0.426586i
$913$		−	7.26107i		−	0.240306i
$914$	−22.3417			−0.738999
$915$		−	79.1754i		−	2.61746i
$916$	14.6189			0.483022
$917$	37.1424			1.22655
$918$	53.0837	+	53.7240i	1.75202	+	1.77315i
$919$	29.8932			0.986087			0.493043	−	0.870005i	$-0.335884\pi$
$919$	29.8932			0.986087			0.493043	+	0.870005i	$0.335884\pi$
$920$	−24.2150			−0.798344
$921$			15.2110i			0.501219i
$922$	−34.0206			−1.12041
$923$		−	78.6630i		−	2.58922i
$924$		−	20.7258i		−	0.681829i
$925$		−	1.80927i		−	0.0594884i
$926$	−73.3663			−2.41097
$927$	−45.9879			−1.51044
$928$			9.16939i			0.301000i
$929$		−	15.1066i		−	0.495631i	−0.968807	−	0.247815i	$-0.920287\pi$
$929$		−	15.1066i		−	0.495631i	0.968807	−	0.247815i	$-0.0797126\pi$
$930$		−	82.9644i		−	2.72051i
$931$	7.72979			0.253333
$932$		−	29.1832i		−	0.955926i
$933$	65.1682			2.13351
$934$	−15.4436			−0.505332
$935$	6.88688	−	6.80480i	0.225225	−	0.222541i
$936$	82.9829			2.71238
$937$	−42.5190			−1.38903			−0.694517	−	0.719476i	$-0.744382\pi$
$937$	−42.5190			−1.38903			−0.694517	+	0.719476i	$0.744382\pi$
$938$		−	45.5027i		−	1.48572i
$939$	52.9360			1.72750
$940$		−	5.99122i		−	0.195412i
$941$			13.3442i			0.435009i	0.976059	+	0.217505i	$0.0697917\pi$
$941$			13.3442i			0.435009i	−0.976059	+	0.217505i	$0.930208\pi$
$942$		−	39.2993i		−	1.28044i
$943$	14.7054			0.478873
$944$	8.29616			0.270017
$945$		−	44.4939i		−	1.44739i
$946$		−	18.5590i		−	0.603404i
$947$			33.9113i			1.10197i	0.834515	+	0.550985i	$0.185748\pi$
$947$			33.9113i			1.10197i	−0.834515	+	0.550985i	$0.814252\pi$
$948$	68.0207			2.20921
$949$			40.8839i			1.32715i
$950$	−5.46818			−0.177411
$951$	−53.8371			−1.74579
$952$	15.3644	+	15.5497i	0.497964	+	0.503970i
$953$	26.6886			0.864528			0.432264	−	0.901747i	$-0.357715\pi$
$953$	26.6886			0.864528			0.432264	+	0.901747i	$0.357715\pi$
$954$	0.0665903			0.00215594
$955$			14.8952i			0.481998i
$956$	−34.0755			−1.10208
$957$			4.09506i			0.132375i
$958$		−	49.5880i		−	1.60211i
$959$			25.8228i			0.833862i
$960$	−90.4871			−2.92046
$961$	2.62296			0.0846115
$962$		−	49.6823i		−	1.60182i
$963$		−	17.4362i		−	0.561873i
$964$			18.9565i			0.610547i
$965$	30.2754			0.974601
$966$			69.3105i			2.23003i
$967$	−2.38544			−0.0767107			−0.0383553	−	0.999264i	$-0.512212\pi$
$967$	−2.38544			−0.0767107			−0.0383553	+	0.999264i	$0.512212\pi$
$968$	−2.28736			−0.0735185
$969$	−40.7432	−	41.2346i	−1.30886	−	1.32465i
$970$	−59.8281			−1.92096
$971$	−39.9802			−1.28303			−0.641513	−	0.767112i	$-0.721693\pi$
$971$	−39.9802			−1.28303			−0.641513	+	0.767112i	$0.721693\pi$
$972$			12.2736i			0.393676i
$973$	4.06785			0.130409
$974$		−	13.0605i		−	0.418486i
$975$		−	9.57594i		−	0.306676i
$976$			10.4378i			0.334106i
$977$	−53.9773			−1.72689			−0.863443	−	0.504446i	$-0.831697\pi$
$977$	−53.9773			−1.72689			−0.863443	+	0.504446i	$0.831697\pi$
$978$	56.5895			1.80953
$979$			11.8361i			0.378285i
$980$			11.5438i			0.368753i
$981$			10.6897i			0.341295i
$982$	19.3944			0.618899
$983$		−	9.73216i		−	0.310408i	−0.987882	−	0.155204i	$-0.950397\pi$
$983$		−	9.73216i		−	0.310408i	0.987882	−	0.155204i	$-0.0496034\pi$
$984$	−22.0842			−0.704020
$985$	8.31027			0.264787
$986$	−8.98343	−	9.09179i	−0.286091	−	0.289541i
$987$	−5.79500			−0.184457
$988$	−90.3423			−2.87417
$989$			37.3414i			1.18739i
$990$	−30.3157			−0.963498
$991$		−	3.03904i		−	0.0965383i	−0.998834	−	0.0482691i	$-0.984629\pi$
$991$		−	3.03904i		−	0.0965383i	0.998834	−	0.0482691i	$-0.0153705\pi$
$992$			35.3069i			1.12099i
$993$		−	26.6629i		−	0.846121i
$994$	−64.8860			−2.05806
$995$	34.3689			1.08957
$996$		−	64.9263i		−	2.05727i
$997$			44.8003i			1.41884i	0.704787	+	0.709419i	$0.251043\pi$
$997$			44.8003i			1.41884i	−0.704787	+	0.709419i	$0.748957\pi$
$998$		−	55.3160i		−	1.75100i
$999$	−28.7872			−0.910787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.d.a.67.15	✓	16
3.2	odd	2		1683.2.g.b.1189.1		16
4.3	odd	2		2992.2.b.g.1937.16		16
17.4	even	4		3179.2.a.bc.1.1		8
17.13	even	4		3179.2.a.bb.1.1		8
17.16	even	2	inner	187.2.d.a.67.16	yes	16
51.50	odd	2		1683.2.g.b.1189.2		16
68.67	odd	2		2992.2.b.g.1937.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.d.a.67.15	✓	16	1.1	even	1	trivial
187.2.d.a.67.16	yes	16	17.16	even	2	inner
1683.2.g.b.1189.1		16	3.2	odd	2
1683.2.g.b.1189.2		16	51.50	odd	2
2992.2.b.g.1937.1		16	68.67	odd	2
2992.2.b.g.1937.16		16	4.3	odd	2
3179.2.a.bb.1.1		8	17.13	even	4
3179.2.a.bc.1.1		8	17.4	even	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.24072 q^{2} -2.96003i q^{3} +3.02082 q^{4} +2.34815i q^{5} -6.63259i q^{6} +2.31788i q^{7} +2.28736 q^{8} -5.76177 q^{9} +O(q^{10})\)	\(q+2.24072 q^{2} -2.96003i q^{3} +3.02082 q^{4} +2.34815i q^{5} -6.63259i q^{6} +2.31788i q^{7} +2.28736 q^{8} -5.76177 q^{9} +5.26153i q^{10} -1.00000i q^{11} -8.94170i q^{12} -6.29649 q^{13} +5.19372i q^{14} +6.95058 q^{15} -0.916304 q^{16} +(2.93290 - 2.89795i) q^{17} -12.9105 q^{18} +4.74973 q^{19} +7.09332i q^{20} +6.86100 q^{21} -2.24072i q^{22} +4.50842i q^{23} -6.77065i q^{24} -0.513792 q^{25} -14.1087 q^{26} +8.17492i q^{27} +7.00190i q^{28} -1.38345i q^{29} +15.5743 q^{30} -5.32701i q^{31} -6.62790 q^{32} -2.96003 q^{33} +(6.57180 - 6.49348i) q^{34} -5.44273 q^{35} -17.4052 q^{36} +3.52141i q^{37} +10.6428 q^{38} +18.6378i q^{39} +5.37106i q^{40} -3.26176i q^{41} +15.3736 q^{42} +8.28260 q^{43} -3.02082i q^{44} -13.5295i q^{45} +10.1021i q^{46} -0.844629 q^{47} +2.71229i q^{48} +1.62742 q^{49} -1.15126 q^{50} +(-8.57801 - 8.68147i) q^{51} -19.0205 q^{52} -0.00515784 q^{53} +18.3177i q^{54} +2.34815 q^{55} +5.30183i q^{56} -14.0593i q^{57} -3.09993i q^{58} -9.05394 q^{59} +20.9964 q^{60} -11.3912i q^{61} -11.9363i q^{62} -13.3551i q^{63} -13.0186 q^{64} -14.7851i q^{65} -6.63259 q^{66} -8.76109 q^{67} +(8.85975 - 8.75416i) q^{68} +13.3450 q^{69} -12.1956 q^{70} +12.4932i q^{71} -13.1792 q^{72} -6.49313i q^{73} +7.89048i q^{74} +1.52084i q^{75} +14.3480 q^{76} +2.31788 q^{77} +41.7620i q^{78} +7.60713i q^{79} -2.15162i q^{80} +6.91269 q^{81} -7.30868i q^{82} +7.26107 q^{83} +20.7258 q^{84} +(6.80480 + 6.88688i) q^{85} +18.5590 q^{86} -4.09506 q^{87} -2.28736i q^{88} -11.8361 q^{89} -30.3157i q^{90} -14.5945i q^{91} +13.6191i q^{92} -15.7681 q^{93} -1.89257 q^{94} +11.1531i q^{95} +19.6188i q^{96} +11.3708i q^{97} +3.64658 q^{98} +5.76177i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9	\( 16 q - 2 q^{2} + 10 q^{4} - 6 q^{8} - 20 q^{9} - 16 q^{13} + 4 q^{15} + 6 q^{16} + 4 q^{17} - 10 q^{18} + 20 q^{19} + 12 q^{21} + 4 q^{25} - 12 q^{26} + 28 q^{30} - 34 q^{32} + 4 q^{33} - 6 q^{34} + 12 q^{35} - 18 q^{36} + 8 q^{43} + 14 q^{47} - 42 q^{49} - 34 q^{50} - 18 q^{51} - 44 q^{52} + 26 q^{53} + 8 q^{55} - 30 q^{59} + 72 q^{60} - 10 q^{64} - 8 q^{66} + 10 q^{67} + 22 q^{68} + 4 q^{69} - 8 q^{70} - 46 q^{72} + 36 q^{76} - 10 q^{77} - 8 q^{81} - 8 q^{83} + 92 q^{84} - 2 q^{85} + 56 q^{86} + 8 q^{87} + 10 q^{89} - 20 q^{93} + 8 q^{94} + 38 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 10 * q^4 - 6 * q^8 - 20 * q^9 - 16 * q^13 + 4 * q^15 + 6 * q^16 + 4 * q^17 - 10 * q^18 + 20 * q^19 + 12 * q^21 + 4 * q^25 - 12 * q^26 + 28 * q^30 - 34 * q^32 + 4 * q^33 - 6 * q^34 + 12 * q^35 - 18 * q^36 + 8 * q^43 + 14 * q^47 - 42 * q^49 - 34 * q^50 - 18 * q^51 - 44 * q^52 + 26 * q^53 + 8 * q^55 - 30 * q^59 + 72 * q^60 - 10 * q^64 - 8 * q^66 + 10 * q^67 + 22 * q^68 + 4 * q^69 - 8 * q^70 - 46 * q^72 + 36 * q^76 - 10 * q^77 - 8 * q^81 - 8 * q^83 + 92 * q^84 - 2 * q^85 + 56 * q^86 + 8 * q^87 + 10 * q^89 - 20 * q^93 + 8 * q^94 + 38 * q^98

Introduction

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