LMFDB - Embedded newform 115.3.d.b.91.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(91,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.91"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 10 x^{8} + 34 x^{7} + 346 x^{6} - 968 x^{5} + 165 x^{4} + 6972 x^{3} + 19344 x^{2} + \cdots + 225444 $ x^10 - 2x^9 - 10x^8 + 34x^7 + 346x^6 - 968x^5 + 165x^4 + 6972x^3 + 19344x^2 - 89080*x + 225444
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.9
Root			$3.44206 + 2.23607i$ of defining polynomial
Character	$\chi$	$=$	115.91
Dual form			115.3.d.b.91.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.44206 q^{2} -0.0436725 q^{3} +7.84777 q^{4} -2.23607i q^{5} -0.150323 q^{6} -2.33372i q^{7} +13.2442 q^{8} -8.99809 q^{9} -7.69668i q^{10} +16.3982i q^{11} -0.342732 q^{12} +1.02663 q^{13} -8.03281i q^{14} +0.0976548i q^{15} +14.1964 q^{16} +17.1482i q^{17} -30.9720 q^{18} -23.2636i q^{19} -17.5481i q^{20} +0.101920i q^{21} +56.4436i q^{22} +(2.92347 - 22.8134i) q^{23} -0.578410 q^{24} -5.00000 q^{25} +3.53372 q^{26} +0.786022 q^{27} -18.3145i q^{28} -5.00315 q^{29} +0.336133i q^{30} -26.6303 q^{31} -4.11213 q^{32} -0.716151i q^{33} +59.0251i q^{34} -5.21836 q^{35} -70.6150 q^{36} +2.49670i q^{37} -80.0747i q^{38} -0.0448355 q^{39} -29.6150i q^{40} +69.6800 q^{41} +0.350813i q^{42} +26.6617i q^{43} +128.689i q^{44} +20.1203i q^{45} +(10.0628 - 78.5252i) q^{46} +40.1701 q^{47} -0.619993 q^{48} +43.5537 q^{49} -17.2103 q^{50} -0.748905i q^{51} +8.05675 q^{52} -53.7832i q^{53} +2.70554 q^{54} +36.6675 q^{55} -30.9084i q^{56} +1.01598i q^{57} -17.2211 q^{58} +3.94458 q^{59} +0.766372i q^{60} -44.9799i q^{61} -91.6632 q^{62} +20.9991i q^{63} -70.9398 q^{64} -2.29561i q^{65} -2.46503i q^{66} +93.6284i q^{67} +134.575i q^{68} +(-0.127676 + 0.996321i) q^{69} -17.9619 q^{70} -97.9038 q^{71} -119.173 q^{72} +38.8904 q^{73} +8.59379i q^{74} +0.218363 q^{75} -182.567i q^{76} +38.2689 q^{77} -0.154327 q^{78} -103.418i q^{79} -31.7441i q^{80} +80.9485 q^{81} +239.843 q^{82} +59.3507i q^{83} +0.799841i q^{84} +38.3445 q^{85} +91.7712i q^{86} +0.218500 q^{87} +217.182i q^{88} -130.230i q^{89} +69.2554i q^{90} -2.39587i q^{91} +(22.9427 - 179.035i) q^{92} +1.16301 q^{93} +138.268 q^{94} -52.0190 q^{95} +0.179587 q^{96} +142.579i q^{97} +149.915 q^{98} -147.553i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 2 q^{3} + 34 q^{4} + 28 q^{6} - 20 q^{8} - 16 q^{9} - 24 q^{12} - 2 q^{13} - 38 q^{16} - 22 q^{18} + 44 q^{23} + 70 q^{24} - 50 q^{25} - 72 q^{26} + 40 q^{27} - 46 q^{29} + 16 q^{31} + 142 q^{32}+ \cdots + 388 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 2 * q^3 + 34 * q^4 + 28 * q^6 - 20 * q^8 - 16 * q^9 - 24 * q^12 - 2 * q^13 - 38 * q^16 - 22 * q^18 + 44 * q^23 + 70 * q^24 - 50 * q^25 - 72 * q^26 + 40 * q^27 - 46 * q^29 + 16 * q^31 + 142 * q^32 - 60 * q^35 - 110 * q^36 + 72 * q^39 - 84 * q^41 + 86 * q^46 + 112 * q^47 - 236 * q^48 + 50 * q^49 - 10 * q^50 + 52 * q^52 + 30 * q^54 - 10 * q^55 + 246 * q^58 - 262 * q^59 - 136 * q^62 - 224 * q^64 + 124 * q^69 + 130 * q^70 + 236 * q^71 - 406 * q^72 + 168 * q^73 + 10 * q^75 + 300 * q^77 - 254 * q^78 - 258 * q^81 + 140 * q^82 + 540 * q^87 - 182 * q^92 + 100 * q^93 + 262 * q^94 - 90 * q^95 - 332 * q^96 + 388 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	3.44206			1.72103			0.860515	−	0.509426i	$-0.170142\pi$
$2$	3.44206			1.72103			0.860515	+	0.509426i	$0.170142\pi$
$3$	−0.0436725			−0.0145575			−0.00727876	−	0.999974i	$-0.502317\pi$
$3$	−0.0436725			−0.0145575			−0.00727876	+	0.999974i	$0.502317\pi$
$4$	7.84777			1.96194
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−0.150323			−0.0250539
$7$		−	2.33372i		−	0.333389i	−0.986009	−	0.166694i	$-0.946691\pi$
$7$		−	2.33372i		−	0.333389i	0.986009	−	0.166694i	$-0.0533094\pi$
$8$	13.2442			1.65553
$9$	−8.99809			−0.999788
$10$		−	7.69668i		−	0.769668i
$11$			16.3982i			1.49075i	0.666648	+	0.745373i	$0.267729\pi$
$11$			16.3982i			1.49075i	−0.666648	+	0.745373i	$0.732271\pi$
$12$	−0.342732			−0.0285610
$13$	1.02663			0.0789715			0.0394858	−	0.999220i	$-0.487428\pi$
$13$	1.02663			0.0789715			0.0394858	+	0.999220i	$0.487428\pi$
$14$		−	8.03281i		−	0.573772i
$15$			0.0976548i			0.00651032i
$16$	14.1964			0.887275
$17$			17.1482i			1.00872i	0.863494	+	0.504359i	$0.168271\pi$
$17$			17.1482i			1.00872i	−0.863494	+	0.504359i	$0.831729\pi$
$18$	−30.9720			−1.72066
$19$		−	23.2636i		−	1.22440i	−0.790703	−	0.612200i	$-0.790285\pi$
$19$		−	23.2636i		−	1.22440i	0.790703	−	0.612200i	$-0.209715\pi$
$20$		−	17.5481i		−	0.877407i
$21$			0.101920i			0.00485331i
$22$			56.4436i			2.56562i
$23$	2.92347	−	22.8134i	0.127108	−	0.991889i
$23$	2.92347	−	22.8134i	0.127108	−	0.991889i
$24$	−0.578410			−0.0241004
$25$	−5.00000			−0.200000
$26$	3.53372			0.135912
$27$	0.786022			0.0291119
$28$		−	18.3145i		−	0.654090i
$29$	−5.00315			−0.172523			−0.0862613	−	0.996273i	$-0.527492\pi$
$29$	−5.00315			−0.172523			−0.0862613	+	0.996273i	$0.527492\pi$
$30$			0.336133i			0.0112044i
$31$	−26.6303			−0.859043			−0.429521	−	0.903057i	$-0.641318\pi$
$31$	−26.6303			−0.859043			−0.429521	+	0.903057i	$0.641318\pi$
$32$	−4.11213			−0.128504
$33$		−	0.716151i		−	0.0217016i
$34$			59.0251i			1.73603i
$35$	−5.21836			−0.149096
$36$	−70.6150			−1.96153
$37$			2.49670i			0.0674784i	0.999431	+	0.0337392i	$0.0107416\pi$
$37$			2.49670i			0.0674784i	−0.999431	+	0.0337392i	$0.989258\pi$
$38$		−	80.0747i		−	2.10723i
$39$	−0.0448355			−0.00114963
$40$		−	29.6150i		−	0.740376i
$41$	69.6800			1.69951			0.849756	−	0.527176i	$-0.176749\pi$
$41$	69.6800			1.69951			0.849756	+	0.527176i	$0.176749\pi$
$42$			0.350813i			0.00835270i
$43$			26.6617i			0.620040i	0.950730	+	0.310020i	$0.100336\pi$
$43$			26.6617i			0.620040i	−0.950730	+	0.310020i	$0.899664\pi$
$44$			128.689i			2.92476i
$45$			20.1203i			0.447119i
$46$	10.0628	−	78.5252i	0.218756	−	1.70707i
$47$	40.1701			0.854684			0.427342	−	0.904090i	$-0.359450\pi$
$47$	40.1701			0.854684			0.427342	+	0.904090i	$0.359450\pi$
$48$	−0.619993			−0.0129165
$49$	43.5537			0.888852
$50$	−17.2103			−0.344206
$51$		−	0.748905i		−	0.0146844i
$52$	8.05675			0.154938
$53$		−	53.7832i		−	1.01478i	−0.861717	−	0.507389i	$-0.830611\pi$
$53$		−	53.7832i		−	1.01478i	0.861717	−	0.507389i	$-0.169389\pi$
$54$	2.70554			0.0501025
$55$	36.6675			0.666682
$56$		−	30.9084i		−	0.551936i
$57$			1.01598i			0.0178242i
$58$	−17.2211			−0.296916
$59$	3.94458			0.0668572			0.0334286	−	0.999441i	$-0.489357\pi$
$59$	3.94458			0.0668572			0.0334286	+	0.999441i	$0.489357\pi$
$60$			0.766372i			0.0127729i
$61$		−	44.9799i		−	0.737375i	−0.929553	−	0.368688i	$-0.879807\pi$
$61$		−	44.9799i		−	0.737375i	0.929553	−	0.368688i	$-0.120193\pi$
$62$	−91.6632			−1.47844
$63$			20.9991i			0.333318i
$64$	−70.9398			−1.10843
$65$		−	2.29561i		−	0.0353171i
$66$		−	2.46503i		−	0.0373490i
$67$			93.6284i			1.39744i	0.715396	+	0.698719i	$0.246246\pi$
$67$			93.6284i			1.39744i	−0.715396	+	0.698719i	$0.753754\pi$
$68$			134.575i			1.97905i
$69$	−0.127676	+	0.996321i	−0.00185037	+	0.0144394i
$70$	−17.9619			−0.256599
$71$	−97.9038			−1.37893			−0.689463	−	0.724321i	$-0.742153\pi$
$71$	−97.9038			−1.37893			−0.689463	+	0.724321i	$0.742153\pi$
$72$	−119.173			−1.65518
$73$	38.8904			0.532745			0.266372	−	0.963870i	$-0.414175\pi$
$73$	38.8904			0.532745			0.266372	+	0.963870i	$0.414175\pi$
$74$			8.59379i			0.116132i
$75$	0.218363			0.00291150
$76$		−	182.567i		−	2.40220i
$77$	38.2689			0.496998
$78$	−0.154327			−0.00197855
$79$		−	103.418i		−	1.30908i	−0.756026	−	0.654542i	$-0.772862\pi$
$79$		−	103.418i		−	1.30908i	0.756026	−	0.654542i	$-0.227138\pi$
$80$		−	31.7441i		−	0.396802i
$81$	80.9485			0.999364
$82$	239.843			2.92491
$83$			59.3507i			0.715068i	0.933900	+	0.357534i	$0.116382\pi$
$83$			59.3507i			0.715068i	−0.933900	+	0.357534i	$0.883618\pi$
$84$			0.799841i			0.00952192i
$85$	38.3445			0.451112
$86$			91.7712i			1.06711i
$87$	0.218500			0.00251150
$88$			217.182i			2.46798i
$89$		−	130.230i		−	1.46326i	−0.681701	−	0.731631i	$-0.738760\pi$
$89$		−	130.230i		−	1.46326i	0.681701	−	0.731631i	$-0.261240\pi$
$90$			69.2554i			0.769505i
$91$		−	2.39587i		−	0.0263282i
$92$	22.9427	−	179.035i	0.249378	−	1.94603i
$93$	1.16301			0.0125055
$94$	138.268			1.47094
$95$	−52.0190			−0.547569
$96$	0.179587			0.00187070
$97$			142.579i			1.46989i	0.678126	+	0.734945i	$0.262792\pi$
$97$			142.579i			1.46989i	−0.678126	+	0.734945i	$0.737208\pi$
$98$	149.915			1.52974
$99$		−	147.553i		−	1.49043i
$100$	−39.2388			−0.392388
$101$	96.4847			0.955294			0.477647	−	0.878552i	$-0.341490\pi$
$101$	96.4847			0.955294			0.477647	+	0.878552i	$0.341490\pi$
$102$		−	2.57778i		−	0.0252723i
$103$		−	10.1274i		−	0.0983240i	−0.998791	−	0.0491620i	$-0.984345\pi$
$103$		−	10.1274i		−	0.0983240i	0.998791	−	0.0491620i	$-0.0156551\pi$
$104$	13.5969			0.130740
$105$	0.227899			0.00217047
$106$		−	185.125i		−	1.74646i
$107$			39.0101i			0.364581i	0.983245	+	0.182290i	$0.0583511\pi$
$107$			39.0101i			0.364581i	−0.983245	+	0.182290i	$0.941649\pi$
$108$	6.16852			0.0571159
$109$			43.1074i			0.395481i	0.980254	+	0.197741i	$0.0633603\pi$
$109$			43.1074i			0.395481i	−0.980254	+	0.197741i	$0.936640\pi$
$110$	126.212			1.14738
$111$		−	0.109037i		−	0.000982317i
$112$		−	33.1305i		−	0.295808i
$113$			162.052i			1.43409i	0.697029	+	0.717043i	$0.254505\pi$
$113$			162.052i			1.43409i	−0.697029	+	0.717043i	$0.745495\pi$
$114$			3.49707i			0.0306760i
$115$	−51.0124	−	6.53709i	−0.443586	−	0.0568442i
$116$	−39.2636			−0.338479
$117$	−9.23771			−0.0789548
$118$	13.5775			0.115063
$119$	40.0191			0.336295
$120$			1.29336i			0.0107780i
$121$	−147.901			−1.22232
$122$		−	154.823i		−	1.26904i
$123$	−3.04310			−0.0247407
$124$	−208.989			−1.68539
$125$			11.1803i			0.0894427i
$126$			72.2800i			0.573651i
$127$	−178.661			−1.40678			−0.703389	−	0.710805i	$-0.748331\pi$
$127$	−178.661			−1.40678			−0.703389	+	0.710805i	$0.748331\pi$
$128$	−227.731			−1.77914
$129$		−	1.16439i		−	0.00902624i
$130$		−	7.90164i		−	0.0607818i
$131$	49.5358			0.378136			0.189068	−	0.981964i	$-0.439453\pi$
$131$	49.5358			0.378136			0.189068	+	0.981964i	$0.439453\pi$
$132$		−	5.62019i		−	0.0425772i
$133$	−54.2908			−0.408202
$134$			322.274i			2.40503i
$135$		−	1.75760i		−	0.0130193i
$136$			227.115i			1.66996i
$137$		−	145.643i		−	1.06309i	−0.847031	−	0.531543i	$-0.821612\pi$
$137$		−	145.643i		−	1.06309i	0.847031	−	0.531543i	$-0.178388\pi$
$138$	−0.439467	+	3.42940i	−0.00318454	+	0.0248507i
$139$	−198.891			−1.43087			−0.715435	−	0.698680i	$-0.753771\pi$
$139$	−198.891			−1.43087			−0.715435	+	0.698680i	$0.753771\pi$
$140$	−40.9525			−0.292518
$141$	−1.75433			−0.0124421
$142$	−336.991			−2.37317
$143$			16.8349i			0.117726i
$144$	−127.741			−0.887087
$145$			11.1874i			0.0771544i
$146$	133.863			0.916869
$147$	−1.90210			−0.0129395
$148$			19.5935i			0.132389i
$149$		−	103.183i		−	0.692505i	−0.938141	−	0.346253i	$-0.887454\pi$
$149$		−	103.183i		−	0.692505i	0.938141	−	0.346253i	$-0.112546\pi$
$150$	0.751617			0.00501078
$151$	−199.563			−1.32161			−0.660806	−	0.750557i	$-0.729785\pi$
$151$	−199.563			−1.32161			−0.660806	+	0.750557i	$0.729785\pi$
$152$		−	308.109i		−	2.02703i
$153$		−	154.301i		−	1.00850i
$154$	131.724			0.855349
$155$			59.5472i			0.384176i
$156$	−0.351859			−0.00225551
$157$			224.444i			1.42958i	0.699340	+	0.714789i	$0.253477\pi$
$157$			224.444i			1.42958i	−0.699340	+	0.714789i	$0.746523\pi$
$158$		−	355.969i		−	2.25297i
$159$			2.34885i			0.0147726i
$160$			9.19500i			0.0574688i
$161$	−53.2403	−	6.82258i	−0.330685	−	0.0423763i
$162$	278.630			1.71994
$163$	−43.8177			−0.268820			−0.134410	−	0.990926i	$-0.542914\pi$
$163$	−43.8177			−0.268820			−0.134410	+	0.990926i	$0.542914\pi$
$164$	546.833			3.33434
$165$	−1.60136			−0.00970523
$166$			204.289i			1.23065i
$167$	168.902			1.01139			0.505696	−	0.862712i	$-0.331236\pi$
$167$	168.902			1.01139			0.505696	+	0.862712i	$0.331236\pi$
$168$			1.34985i			0.00803481i
$169$	−167.946			−0.993763
$170$	131.984			0.776377
$171$			209.328i			1.22414i
$172$			209.235i			1.21648i
$173$	56.9816			0.329373			0.164687	−	0.986346i	$-0.447339\pi$
$173$	56.9816			0.329373			0.164687	+	0.986346i	$0.447339\pi$
$174$	0.752091			0.00432236
$175$			11.6686i			0.0666778i
$176$			232.796i			1.32270i
$177$	−0.172270			−0.000973275
$178$		−	448.260i		−	2.51832i
$179$	−243.497			−1.36032			−0.680160	−	0.733064i	$-0.738090\pi$
$179$	−243.497			−1.36032			−0.680160	+	0.733064i	$0.738090\pi$
$180$			157.900i			0.877221i
$181$		−	189.480i		−	1.04685i	−0.852072	−	0.523425i	$-0.824654\pi$
$181$		−	189.480i		−	1.04685i	0.852072	−	0.523425i	$-0.175346\pi$
$182$		−	8.24672i		−	0.0453117i
$183$			1.96439i			0.0107344i
$184$	38.7192	−	302.147i	0.210430	−	1.64210i
$185$	5.58279			0.0301772
$186$	4.00316			0.0215224
$187$	−281.200			−1.50374
$188$	315.246			1.67684
$189$		−	1.83436i		−	0.00970560i
$190$	−179.053			−0.942382
$191$			303.459i			1.58879i	0.607400	+	0.794396i	$0.292213\pi$
$191$			303.459i			1.58879i	−0.607400	+	0.794396i	$0.707787\pi$
$192$	3.09812			0.0161361
$193$	−171.946			−0.890912			−0.445456	−	0.895304i	$-0.646958\pi$
$193$	−171.946			−0.890912			−0.445456	+	0.895304i	$0.646958\pi$
$194$			490.767i			2.52972i
$195$			0.100255i			0.000514130i
$196$	341.800			1.74388
$197$	257.231			1.30574			0.652871	−	0.757470i	$-0.273565\pi$
$197$	257.231			1.30574			0.652871	+	0.757470i	$0.273565\pi$
$198$		−	507.885i		−	2.56507i
$199$		−	179.782i		−	0.903425i	−0.892163	−	0.451713i	$-0.850813\pi$
$199$		−	179.782i		−	0.903425i	0.892163	−	0.451713i	$-0.149187\pi$
$200$	−66.2212			−0.331106
$201$		−	4.08899i		−	0.0203432i
$202$	332.106			1.64409
$203$			11.6760i			0.0575171i
$204$		−	5.87724i		−	0.0288100i
$205$		−	155.809i		−	0.760045i
$206$		−	34.8590i		−	0.169219i
$207$	−26.3057	+	205.277i	−0.127081	+	0.991679i
$208$	14.5745			0.0700695
$209$	381.481			1.82527
$210$	0.784442			0.00373544
$211$	338.952			1.60641			0.803204	−	0.595704i	$-0.203127\pi$
$211$	338.952			1.60641			0.803204	+	0.595704i	$0.203127\pi$
$212$		−	422.078i		−	1.99094i
$213$	4.27571			0.0200737
$214$			134.275i			0.627454i
$215$	59.6174			0.277290
$216$	10.4103			0.0481957
$217$			62.1478i			0.286395i
$218$			148.378i			0.680634i
$219$	−1.69844			−0.00775544
$220$	287.758			1.30799
$221$			17.6049i			0.0796600i
$222$		−	0.375313i		−	0.00169060i
$223$	−302.953			−1.35853			−0.679266	−	0.733892i	$-0.737702\pi$
$223$	−302.953			−1.35853			−0.679266	+	0.733892i	$0.737702\pi$
$224$			9.59657i			0.0428418i
$225$	44.9905			0.199958
$226$			557.791i			2.46810i
$227$		−	391.761i		−	1.72582i	−0.505358	−	0.862910i	$-0.668640\pi$
$227$		−	391.761i		−	1.72582i	0.505358	−	0.862910i	$-0.331360\pi$
$228$			7.97318i			0.0349701i
$229$		−	130.299i		−	0.568993i	−0.958677	−	0.284497i	$-0.908174\pi$
$229$		−	130.299i		−	0.568993i	0.958677	−	0.284497i	$-0.0918265\pi$
$230$	−175.588	−	22.5010i	−0.763425	−	0.0978306i
$231$	−1.67130			−0.00723506
$232$	−66.2630			−0.285616
$233$	251.192			1.07808			0.539039	−	0.842281i	$-0.318788\pi$
$233$	251.192			1.07808			0.539039	+	0.842281i	$0.318788\pi$
$234$	−31.7967			−0.135884
$235$		−	89.8231i		−	0.382226i
$236$	30.9561			0.131170
$237$			4.51651i			0.0190570i
$238$	137.748			0.578774
$239$	−10.6827			−0.0446976			−0.0223488	−	0.999750i	$-0.507114\pi$
$239$	−10.6827			−0.0446976			−0.0223488	+	0.999750i	$0.507114\pi$
$240$			1.38635i			0.00577644i
$241$			414.415i			1.71957i	0.510659	+	0.859783i	$0.329401\pi$
$241$			414.415i			1.71957i	−0.510659	+	0.859783i	$0.670599\pi$
$242$	−509.084			−2.10365
$243$	−10.6094			−0.0436602
$244$		−	352.992i		−	1.44669i
$245$		−	97.3891i		−	0.397507i
$246$	−10.4745			−0.0425794
$247$		−	23.8831i		−	0.0966928i
$248$	−352.699			−1.42217
$249$		−	2.59200i		−	0.0104096i
$250$			38.4834i			0.153934i
$251$		−	248.441i		−	0.989807i	−0.868948	−	0.494903i	$-0.835203\pi$
$251$		−	248.441i		−	0.989807i	0.868948	−	0.494903i	$-0.164797\pi$
$252$			164.796i			0.653951i
$253$	374.100	+	47.9397i	1.47865	+	0.189485i
$254$	−614.961			−2.42111
$255$	−1.67460			−0.00656707
$256$	−500.103			−1.95353
$257$	−390.471			−1.51934			−0.759671	−	0.650308i	$-0.774640\pi$
$257$	−390.471			−1.51934			−0.759671	+	0.650308i	$0.774640\pi$
$258$		−	4.00788i		−	0.0155344i
$259$	5.82660			0.0224965
$260$		−	18.0155i		−	0.0692902i
$261$	45.0188			0.172486
$262$	170.505			0.650783
$263$			302.380i			1.14973i	0.818247	+	0.574867i	$0.194946\pi$
$263$			302.380i			1.14973i	−0.818247	+	0.574867i	$0.805054\pi$
$264$		−	9.48489i		−	0.0359276i
$265$	−120.263			−0.453822
$266$	−186.872			−0.702527
$267$			5.68749i			0.0213014i
$268$			734.774i			2.74169i
$269$	295.154			1.09723			0.548614	−	0.836076i	$-0.315156\pi$
$269$	295.154			1.09723			0.548614	+	0.836076i	$0.315156\pi$
$270$		−	6.04976i		−	0.0224065i
$271$	−118.669			−0.437892			−0.218946	−	0.975737i	$-0.570262\pi$
$271$	−118.669			−0.437892			−0.218946	+	0.975737i	$0.570262\pi$
$272$			243.443i			0.895010i
$273$			0.104634i			0.000383274i
$274$		−	501.311i		−	1.82960i
$275$		−	81.9910i		−	0.298149i
$276$	−1.00197	+	7.81890i	−0.00363032	+	0.0283293i
$277$	359.091			1.29636			0.648178	−	0.761489i	$-0.275531\pi$
$277$	359.091			1.29636			0.648178	+	0.761489i	$0.275531\pi$
$278$	−684.594			−2.46257
$279$	239.622			0.858861
$280$	−69.1133			−0.246833
$281$		−	199.129i		−	0.708645i	−0.935123	−	0.354322i	$-0.884712\pi$
$281$		−	199.129i		−	0.708645i	0.935123	−	0.354322i	$-0.115288\pi$
$282$	−6.03851			−0.0214132
$283$		−	120.934i		−	0.427330i	−0.976907	−	0.213665i	$-0.931460\pi$
$283$		−	120.934i		−	0.427330i	0.976907	−	0.213665i	$-0.0685401\pi$
$284$	−768.326			−2.70537
$285$	2.27180			0.00797124
$286$			57.9467i			0.202611i
$287$		−	162.614i		−	0.566599i
$288$	37.0013			0.128477
$289$	−5.06080			−0.0175114
$290$			38.5077i			0.132785i
$291$		−	6.22680i		−	0.0213979i
$292$	305.203			1.04521
$293$			431.892i			1.47404i	0.675874	+	0.737018i	$0.263766\pi$
$293$			431.892i			1.47404i	−0.675874	+	0.737018i	$0.736234\pi$
$294$	−6.54715			−0.0222692
$295$		−	8.82034i		−	0.0298995i
$296$			33.0669i			0.111713i
$297$			12.8894i			0.0433985i
$298$		−	355.163i		−	1.19182i
$299$	3.00133	−	23.4210i	0.0100379	−	0.0783310i
$300$	1.71366			0.00571220
$301$	62.2211			0.206715
$302$	−686.909			−2.27453
$303$	−4.21373			−0.0139067
$304$		−	330.260i		−	1.08638i
$305$	−100.578			−0.329764
$306$		−	531.113i		−	1.73566i
$307$	265.975			0.866368			0.433184	−	0.901306i	$-0.357390\pi$
$307$	265.975			0.866368			0.433184	+	0.901306i	$0.357390\pi$
$308$	300.325			0.975082
$309$			0.442288i			0.00143135i
$310$			204.965i			0.661178i
$311$	110.534			0.355414			0.177707	−	0.984083i	$-0.443132\pi$
$311$	110.534			0.355414			0.177707	+	0.984083i	$0.443132\pi$
$312$	−0.593813			−0.00190325
$313$			462.215i			1.47673i	0.674404	+	0.738363i	$0.264401\pi$
$313$			462.215i			1.47673i	−0.674404	+	0.738363i	$0.735599\pi$
$314$			772.549i			2.46035i
$315$	46.9553			0.149064
$316$		−	811.597i		−	2.56835i
$317$	552.548			1.74305			0.871527	−	0.490348i	$-0.163130\pi$
$317$	552.548			1.74305			0.871527	+	0.490348i	$0.163130\pi$
$318$			8.08488i			0.0254241i
$319$		−	82.0427i		−	0.257187i
$320$			158.626i			0.495707i
$321$		−	1.70367i		−	0.00530739i
$322$	−183.256	−	23.4837i	−0.569118	−	0.0729308i
$323$	398.929			1.23507
$324$	635.265			1.96070
$325$	−5.13315			−0.0157943
$326$	−150.823			−0.462648
$327$		−	1.88261i		−	0.00575722i
$328$	922.859			2.81360
$329$		−	93.7459i		−	0.284942i
$330$	−5.51199			−0.0167030
$331$	33.4106			0.100938			0.0504692	−	0.998726i	$-0.483928\pi$
$331$	33.4106			0.100938			0.0504692	+	0.998726i	$0.483928\pi$
$332$			465.770i			1.40292i
$333$		−	22.4655i		−	0.0674641i
$334$	581.372			1.74063
$335$	209.359			0.624953
$336$			1.44689i			0.00430623i
$337$		−	232.884i		−	0.691049i	−0.938410	−	0.345525i	$-0.887701\pi$
$337$		−	232.884i		−	0.691049i	0.938410	−	0.345525i	$-0.112299\pi$
$338$	−578.080			−1.71030
$339$		−	7.07721i		−	0.0208767i
$340$	300.919			0.885056
$341$		−	436.690i		−	1.28061i
$342$			720.520i			2.10678i
$343$		−	215.995i		−	0.629722i
$344$			353.115i			1.02650i
$345$	2.22784	+	0.285491i	0.00645751	+	0.000827511i
$346$	196.134			0.566861
$347$	−409.753			−1.18084			−0.590422	−	0.807095i	$-0.701039\pi$
$347$	−409.753			−1.18084			−0.590422	+	0.807095i	$0.701039\pi$
$348$	1.71474			0.00492742
$349$	−21.3405			−0.0611476			−0.0305738	−	0.999533i	$-0.509733\pi$
$349$	−21.3405			−0.0611476			−0.0305738	+	0.999533i	$0.509733\pi$
$350$			40.1641i			0.114754i
$351$	0.806954			0.00229901
$352$		−	67.4316i		−	0.191567i
$353$	−146.395			−0.414716			−0.207358	−	0.978265i	$-0.566486\pi$
$353$	−146.395			−0.414716			−0.207358	+	0.978265i	$0.566486\pi$
$354$	−0.592962			−0.00167503
$355$			218.919i			0.616675i
$356$		−	1022.02i		−	2.87083i
$357$	−1.74774			−0.00489562
$358$	−838.132			−2.34115
$359$			598.255i			1.66645i	0.552936	+	0.833224i	$0.313508\pi$
$359$			598.255i			1.66645i	−0.552936	+	0.833224i	$0.686492\pi$
$360$			266.479i			0.740219i
$361$	−180.196			−0.499157
$362$		−	652.200i		−	1.80166i
$363$	6.45922			0.0177940
$364$		−	18.8022i		−	0.0516545i
$365$		−	86.9615i		−	0.238251i
$366$			6.76153i			0.0184741i
$367$		−	619.595i		−	1.68827i	−0.536131	−	0.844135i	$-0.680115\pi$
$367$		−	619.595i		−	1.68827i	0.536131	−	0.844135i	$-0.319885\pi$
$368$	41.5028	−	323.869i	0.112779	−	0.880079i
$369$	−626.987			−1.69915
$370$	19.2163			0.0519359
$371$	−125.515			−0.338316
$372$	9.12707			0.0245351
$373$		−	68.4568i		−	0.183530i	−0.995781	−	0.0917651i	$-0.970749\pi$
$373$		−	68.4568i		−	0.183530i	0.995781	−	0.0917651i	$-0.0292509\pi$
$374$	−967.906			−2.58798
$375$		−	0.488274i		−	0.00130206i
$376$	532.023			1.41496
$377$	−5.13639			−0.0136244
$378$		−	6.31397i		−	0.0167036i
$379$			516.055i			1.36162i	0.732459	+	0.680811i	$0.238372\pi$
$379$			516.055i			1.36162i	−0.732459	+	0.680811i	$0.761628\pi$
$380$	−408.233			−1.07430
$381$	7.80257			0.0204792
$382$			1044.53i			2.73436i
$383$			209.197i			0.546207i	0.961985	+	0.273103i	$0.0880501\pi$
$383$			209.197i			0.546207i	−0.961985	+	0.273103i	$0.911950\pi$
$384$	9.94557			0.0258999
$385$		−	85.5718i		−	0.222264i
$386$	−591.848			−1.53329
$387$		−	239.905i		−	0.619909i
$388$			1118.93i			2.88384i
$389$			620.747i			1.59575i	0.602823	+	0.797875i	$0.294042\pi$
$389$			620.747i			1.59575i	−0.602823	+	0.797875i	$0.705958\pi$
$390$			0.345085i			0.000884832i
$391$	391.210	+	50.1323i	1.00054	+	0.128216i
$392$	576.837			1.47152
$393$	−2.16335			−0.00550472
$394$	885.404			2.24722
$395$	−231.249			−0.585440
$396$		−	1157.96i		−	2.92414i
$397$	−465.455			−1.17243			−0.586216	−	0.810155i	$-0.699383\pi$
$397$	−465.455			−1.17243			−0.586216	+	0.810155i	$0.699383\pi$
$398$		−	618.819i		−	1.55482i
$399$	2.37102			0.00594240
$400$	−70.9820			−0.177455
$401$			59.9490i			0.149499i	0.997202	+	0.0747494i	$0.0238157\pi$
$401$			59.9490i			0.149499i	−0.997202	+	0.0747494i	$0.976184\pi$
$402$		−	14.0745i		−	0.0350113i
$403$	−27.3395			−0.0678399
$404$	757.190			1.87423
$405$		−	181.006i		−	0.446929i
$406$			40.1894i			0.0989886i
$407$	−40.9414			−0.100593
$408$		−	9.91869i		−	0.0243105i
$409$	−252.327			−0.616936			−0.308468	−	0.951235i	$-0.599816\pi$
$409$	−252.327			−0.616936			−0.308468	+	0.951235i	$0.599816\pi$
$410$		−	536.305i		−	1.30806i
$411$			6.36059i			0.0154759i
$412$		−	79.4773i		−	0.192906i
$413$		−	9.20555i		−	0.0222895i
$414$	−90.5457	+	706.577i	−0.218709	+	1.70671i
$415$	132.712			0.319788
$416$	−4.22164			−0.0101482
$417$	8.68607			0.0208299
$418$	1313.08			3.14134
$419$		−	390.700i		−	0.932458i	−0.884664	−	0.466229i	$-0.845612\pi$
$419$		−	390.700i		−	0.932458i	0.884664	−	0.466229i	$-0.154388\pi$
$420$	1.78850			0.00425833
$421$		−	378.872i		−	0.899934i	−0.893045	−	0.449967i	$-0.851436\pi$
$421$		−	378.872i		−	0.899934i	0.893045	−	0.449967i	$-0.148564\pi$
$422$	1166.69			2.76467
$423$	−361.455			−0.854503
$424$		−	712.318i		−	1.68000i
$425$		−	85.7410i		−	0.201744i
$426$	14.7172			0.0345475
$427$	−104.971			−0.245833
$428$			306.143i			0.715286i
$429$		−	0.735222i		−	0.00171380i
$430$	205.207			0.477225
$431$			327.359i			0.759534i	0.925082	+	0.379767i	$0.123996\pi$
$431$			327.359i			0.759534i	−0.925082	+	0.379767i	$0.876004\pi$
$432$	11.1587			0.0258303
$433$		−	133.102i		−	0.307396i	−0.988118	−	0.153698i	$-0.950882\pi$
$433$		−	133.102i		−	0.307396i	0.988118	−	0.153698i	$-0.0491182\pi$
$434$			213.916i			0.492895i
$435$		−	0.488582i		−	0.00112318i
$436$			338.297i			0.775911i
$437$	−530.723	−	68.0106i	−1.21447	−	0.155631i
$438$	−5.84613			−0.0133473
$439$	247.458			0.563686			0.281843	−	0.959461i	$-0.409054\pi$
$439$	247.458			0.563686			0.281843	+	0.959461i	$0.409054\pi$
$440$	485.634			1.10371
$441$	−391.901			−0.888663
$442$			60.5969i			0.137097i
$443$	626.572			1.41438			0.707192	−	0.707021i	$-0.249961\pi$
$443$	626.572			1.41438			0.707192	+	0.707021i	$0.249961\pi$
$444$		−	0.855699i		−	0.00192725i
$445$	−291.204			−0.654390
$446$	−1042.78			−2.33807
$447$			4.50628i			0.0100812i
$448$			165.554i			0.369540i
$449$	203.993			0.454327			0.227164	−	0.973857i	$-0.427055\pi$
$449$	203.993			0.454327			0.227164	+	0.973857i	$0.427055\pi$
$450$	154.860			0.344133
$451$			1142.63i			2.53354i
$452$			1271.74i			2.81359i
$453$	8.71544			0.0192394
$454$		−	1348.46i		−	2.97019i
$455$	−5.35733			−0.0117743
$456$			13.4559i			0.0295086i
$457$		−	341.855i		−	0.748041i	−0.927421	−	0.374020i	$-0.877979\pi$
$457$		−	341.855i		−	0.748041i	0.927421	−	0.374020i	$-0.122021\pi$
$458$		−	448.498i		−	0.979254i
$459$			13.4789i			0.0293657i
$460$	−400.334	−	51.3015i	−0.870291	−	0.111525i
$461$	368.514			0.799380			0.399690	−	0.916650i	$-0.369118\pi$
$461$	368.514			0.799380			0.399690	+	0.916650i	$0.369118\pi$
$462$	−5.75271			−0.0124517
$463$	−419.855			−0.906814			−0.453407	−	0.891304i	$-0.649792\pi$
$463$	−419.855			−0.906814			−0.453407	+	0.891304i	$0.649792\pi$
$464$	−71.0268			−0.153075
$465$		−	2.60058i		−	0.00559264i
$466$	864.618			1.85540
$467$		−	135.385i		−	0.289904i	−0.989439	−	0.144952i	$-0.953697\pi$
$467$		−	135.385i		−	0.289904i	0.989439	−	0.144952i	$-0.0463028\pi$
$468$	−72.4954			−0.154905
$469$	218.503			0.465891
$470$		−	309.177i		−	0.657822i
$471$		−	9.80203i		−	0.0208111i
$472$	52.2429			0.110684
$473$	−437.205			−0.924323
$474$			15.5461i			0.0327976i
$475$			116.318i			0.244880i
$476$	314.061			0.659792
$477$			483.946i			1.01456i
$478$	−36.7706			−0.0769259
$479$		−	834.130i		−	1.74140i	−0.491816	−	0.870699i	$-0.663667\pi$
$479$		−	834.130i		−	1.74140i	0.491816	−	0.870699i	$-0.336333\pi$
$480$		−	0.401569i		−	0.000836602i
$481$			2.56319i			0.00532887i
$482$			1426.44i			2.95942i
$483$	2.32514	+	0.297959i	0.00481395	+	0.000616893i
$484$	−1160.69			−2.39813
$485$	318.817			0.657355
$486$	−36.5183			−0.0751405
$487$	204.555			0.420032			0.210016	−	0.977698i	$-0.432648\pi$
$487$	204.555			0.420032			0.210016	+	0.977698i	$0.432648\pi$
$488$		−	595.725i		−	1.22075i
$489$	1.91363			0.00391335
$490$		−	335.219i		−	0.684121i
$491$	−275.996			−0.562109			−0.281054	−	0.959692i	$-0.590684\pi$
$491$	−275.996			−0.562109			−0.281054	+	0.959692i	$0.590684\pi$
$492$	−23.8816			−0.0485398
$493$		−	85.7951i		−	0.174027i
$494$		−	82.2071i		−	0.166411i
$495$	−329.938			−0.666541
$496$	−378.055			−0.762208
$497$			228.480i			0.459719i
$498$		−	8.92180i		−	0.0179153i
$499$	246.943			0.494875			0.247437	−	0.968904i	$-0.420412\pi$
$499$	246.943			0.494875			0.247437	+	0.968904i	$0.420412\pi$
$500$			87.7407i			0.175481i
$501$	−7.37639			−0.0147233
$502$		−	855.150i		−	1.70349i
$503$		−	365.693i		−	0.727025i	−0.931589	−	0.363512i	$-0.881577\pi$
$503$		−	365.693i		−	0.727025i	0.931589	−	0.363512i	$-0.118423\pi$
$504$			278.117i			0.551819i
$505$		−	215.746i		−	0.427221i
$506$	1287.67	+	165.011i	2.54481	+	0.326109i
$507$	7.33463			0.0144667
$508$	−1402.09			−2.76002
$509$	186.361			0.366132			0.183066	−	0.983101i	$-0.441398\pi$
$509$	186.361			0.366132			0.183066	+	0.983101i	$0.441398\pi$
$510$	−5.76408			−0.0113021
$511$		−	90.7593i		−	0.177611i
$512$	−810.460			−1.58293
$513$		−	18.2857i		−	0.0356447i
$514$	−1344.02			−2.61483
$515$	−22.6455			−0.0439718
$516$		−	9.13783i		−	0.0177090i
$517$			658.718i			1.27412i
$518$	20.0555			0.0387172
$519$	−2.48853			−0.00479486
$520$		−	30.4037i		−	0.0584686i
$521$		−	197.384i		−	0.378857i	−0.981895	−	0.189428i	$-0.939337\pi$
$521$		−	197.384i		−	0.378857i	0.981895	−	0.189428i	$-0.0606635\pi$
$522$	154.957			0.296853
$523$			225.053i			0.430313i	0.976580	+	0.215156i	$0.0690261\pi$
$523$			225.053i			0.430313i	−0.976580	+	0.215156i	$0.930974\pi$
$524$	388.746			0.741881
$525$		−	0.509598i		−	0.000970663i
$526$			1040.81i			1.97873i
$527$		−	456.662i		−	0.866532i
$528$		−	10.1668i		−	0.0192553i
$529$	−511.907	−	133.389i	−0.967687	−	0.252153i
$530$	−413.952			−0.781042
$531$	−35.4937			−0.0668430
$532$	−426.062			−0.800868
$533$	71.5356			0.134213
$534$			19.5767i			0.0366604i
$535$	87.2293			0.163045
$536$			1240.04i			2.31350i
$537$	10.6341			0.0198029
$538$	1015.94			1.88836
$539$			714.203i			1.32505i
$540$		−	13.7932i		−	0.0255430i
$541$	−568.646			−1.05110			−0.525550	−	0.850762i	$-0.676141\pi$
$541$	−568.646			−1.05110			−0.525550	+	0.850762i	$0.676141\pi$
$542$	−408.465			−0.753626
$543$			8.27506i			0.0152395i
$544$		−	70.5156i		−	0.129624i
$545$	96.3911			0.176864
$546$			0.360155i			0.000659625i
$547$	145.784			0.266515			0.133257	−	0.991081i	$-0.457456\pi$
$547$	145.784			0.266515			0.133257	+	0.991081i	$0.457456\pi$
$548$		−	1142.97i		−	2.08571i
$549$			404.733i			0.737219i
$550$		−	282.218i		−	0.513124i
$551$			116.391i			0.211237i
$552$	−1.69097	+	13.1955i	−0.00306334	+	0.0239049i
$553$	−241.348			−0.436434
$554$	1236.01			2.23107
$555$	−0.243815			−0.000439306
$556$	−1560.85			−2.80728
$557$		−	507.563i		−	0.911245i	−0.890173	−	0.455622i	$-0.849417\pi$
$557$		−	507.563i		−	0.911245i	0.890173	−	0.455622i	$-0.150583\pi$
$558$	824.794			1.47812
$559$			27.3717i			0.0489655i
$560$	−74.0820			−0.132289
$561$	12.2807			0.0218907
$562$		−	685.415i		−	1.21960i
$563$			173.558i			0.308274i	0.988049	+	0.154137i	$0.0492597\pi$
$563$			173.558i			0.308274i	−0.988049	+	0.154137i	$0.950740\pi$
$564$	−13.7676			−0.0244106
$565$	362.358			0.641342
$566$		−	416.263i		−	0.735447i
$567$		−	188.911i		−	0.333177i
$568$	−1296.66			−2.28286
$569$			456.073i			0.801534i	0.916180	+	0.400767i	$0.131256\pi$
$569$			456.073i			0.801534i	−0.916180	+	0.400767i	$0.868744\pi$
$570$	7.81968			0.0137187
$571$		−	193.134i		−	0.338238i	−0.985596	−	0.169119i	$-0.945908\pi$
$571$		−	193.134i		−	0.338238i	0.985596	−	0.169119i	$-0.0540922\pi$
$572$			132.116i			0.230973i
$573$		−	13.2528i		−	0.0231289i
$574$		−	559.726i		−	0.975133i
$575$	−14.6174	+	114.067i	−0.0254215	+	0.198378i
$576$	638.323			1.10820
$577$	−256.538			−0.444606			−0.222303	−	0.974978i	$-0.571357\pi$
$577$	−256.538			−0.444606			−0.222303	+	0.974978i	$0.571357\pi$
$578$	−17.4196			−0.0301377
$579$	7.50932			0.0129695
$580$			87.7961i			0.151373i
$581$	138.508			0.238396
$582$		−	21.4330i		−	0.0368265i
$583$	881.948			1.51278
$584$	515.074			0.881975
$585$			20.6561i			0.0353097i
$586$			1486.60i			2.53686i
$587$	1026.07			1.74799			0.873993	−	0.485938i	$-0.161522\pi$
$587$	1026.07			1.74799			0.873993	+	0.485938i	$0.161522\pi$
$588$	−14.9273			−0.0253865
$589$			619.518i			1.05181i
$590$		−	30.3601i		−	0.0514578i
$591$	−11.2339			−0.0190083
$592$			35.4442i			0.0598719i
$593$	−974.347			−1.64308			−0.821540	−	0.570151i	$-0.806885\pi$
$593$	−974.347			−1.64308			−0.821540	+	0.570151i	$0.806885\pi$
$594$			44.3659i			0.0746901i
$595$		−	89.4855i		−	0.150396i
$596$		−	809.759i		−	1.35866i
$597$			7.85152i			0.0131516i
$598$	10.3307	−	80.6163i	0.0172755	−	0.134810i
$599$	−593.457			−0.990746			−0.495373	−	0.868680i	$-0.664969\pi$
$599$	−593.457			−0.990746			−0.495373	+	0.868680i	$0.664969\pi$
$600$	2.89205			0.00482008
$601$	−167.443			−0.278608			−0.139304	−	0.990250i	$-0.544486\pi$
$601$	−167.443			−0.278608			−0.139304	+	0.990250i	$0.544486\pi$
$602$	214.169			0.355762
$603$		−	842.477i		−	1.39714i
$604$	−1566.13			−2.59292
$605$			330.717i			0.546640i
$606$	−14.5039			−0.0239339
$607$	238.549			0.392996			0.196498	−	0.980504i	$-0.437043\pi$
$607$	238.549			0.392996			0.196498	+	0.980504i	$0.437043\pi$
$608$			95.6630i			0.157340i
$609$		−	0.509919i		−	0.000837306i
$610$	−346.196			−0.567534
$611$	41.2399			0.0674957
$612$		−	1210.92i		−	1.97863i
$613$		−	686.568i		−	1.12001i	−0.828488	−	0.560007i	$-0.810799\pi$
$613$		−	686.568i		−	1.12001i	0.828488	−	0.560007i	$-0.189201\pi$
$614$	915.501			1.49104
$615$			6.80458i			0.0110644i
$616$	506.842			0.822796
$617$			387.430i			0.627925i	0.949435	+	0.313962i	$0.101657\pi$
$617$			387.430i			0.627925i	−0.949435	+	0.313962i	$0.898343\pi$
$618$			1.52238i			0.00246340i
$619$		−	310.811i		−	0.502118i	−0.967972	−	0.251059i	$-0.919221\pi$
$619$		−	310.811i		−	0.502118i	0.967972	−	0.251059i	$-0.0807789\pi$
$620$			467.313i			0.753731i
$621$	2.29792	−	17.9319i	0.00370035	−	0.0288758i
$622$	380.464			0.611678
$623$	−303.921			−0.487835
$624$	−0.636503			−0.00102004
$625$	25.0000			0.0400000
$626$			1590.97i			2.54149i
$627$	−16.6603			−0.0265714
$628$			1761.38i			2.80475i
$629$	−42.8139			−0.0680666
$630$	161.623			0.256544
$631$		−	252.000i		−	0.399366i	−0.979861	−	0.199683i	$-0.936009\pi$
$631$		−	252.000i		−	0.399366i	0.979861	−	0.199683i	$-0.0639913\pi$
$632$		−	1369.69i		−	2.16723i
$633$	−14.8029			−0.0233853
$634$	1901.90			2.99985
$635$			399.497i			0.629130i
$636$			18.4332i			0.0289831i
$637$	44.7136			0.0701940
$638$		−	282.396i		−	0.442627i
$639$	880.947			1.37863
$640$			509.221i			0.795658i
$641$		−	1062.69i		−	1.65787i	−0.559348	−	0.828933i	$-0.688948\pi$
$641$		−	1062.69i		−	1.65787i	0.559348	−	0.828933i	$-0.311052\pi$
$642$		−	5.86414i		−	0.00913417i
$643$		−	456.325i		−	0.709681i	−0.934927	−	0.354841i	$-0.884535\pi$
$643$		−	456.325i		−	0.709681i	0.934927	−	0.354841i	$-0.115465\pi$
$644$	−417.817	−	53.5420i	−0.648785	−	0.0831398i
$645$	−2.60365			−0.00403666
$646$	1373.14			2.12560
$647$	52.0609			0.0804651			0.0402325	−	0.999190i	$-0.487190\pi$
$647$	52.0609			0.0804651			0.0402325	+	0.999190i	$0.487190\pi$
$648$	1072.10			1.65448
$649$			64.6840i			0.0996671i
$650$	−17.6686			−0.0271825
$651$		−	2.71415i		−	0.00416921i
$652$	−343.871			−0.527410
$653$	617.978			0.946368			0.473184	−	0.880964i	$-0.343105\pi$
$653$	617.978			0.946368			0.473184	+	0.880964i	$0.343105\pi$
$654$		−	6.48006i		−	0.00990834i
$655$		−	110.765i		−	0.169108i
$656$	989.206			1.50794
$657$	−349.939			−0.532632
$658$		−	322.679i		−	0.490394i
$659$		−	558.354i		−	0.847275i	−0.905832	−	0.423637i	$-0.860753\pi$
$659$		−	558.354i		−	0.847275i	0.905832	−	0.423637i	$-0.139247\pi$
$660$	−12.5671			−0.0190411
$661$		−	371.214i		−	0.561595i	−0.959767	−	0.280798i	$-0.909401\pi$
$661$		−	371.214i		−	0.561595i	0.959767	−	0.280798i	$-0.0905990\pi$
$662$	115.001			0.173718
$663$		−	0.768849i		−	0.00115965i
$664$			786.055i			1.18382i
$665$			121.398i			0.182553i
$666$		−	77.3277i		−	0.116108i
$667$	−14.6266	+	114.139i	−0.0219289	+	0.171123i
$668$	1325.51			1.98429
$669$	13.2307			0.0197769
$670$	720.627			1.07556
$671$	737.590			1.09924
$672$		−	0.419107i		−	0.000623671i
$673$	630.324			0.936589			0.468294	−	0.883573i	$-0.344869\pi$
$673$	630.324			0.936589			0.468294	+	0.883573i	$0.344869\pi$
$674$		−	801.599i		−	1.18932i
$675$	−3.93011			−0.00582239
$676$	−1318.00			−1.94971
$677$			966.907i			1.42822i	0.700032	+	0.714112i	$0.253169\pi$
$677$			966.907i			1.42822i	−0.700032	+	0.714112i	$0.746831\pi$
$678$		−	24.3602i		−	0.0359294i
$679$	332.741			0.490045
$680$	507.845			0.746830
$681$			17.1092i			0.0251236i
$682$		−	1503.11i		−	2.20398i
$683$	−265.192			−0.388275			−0.194137	−	0.980974i	$-0.562191\pi$
$683$	−265.192			−0.388275			−0.194137	+	0.980974i	$0.562191\pi$
$684$			1642.76i			2.40169i
$685$	−325.667			−0.475426
$686$		−	743.467i		−	1.08377i
$687$			5.69051i			0.00828313i
$688$			378.501i			0.550146i
$689$		−	55.2155i		−	0.0801385i
$690$	7.66836	+	0.982677i	0.0111136	+	0.00142417i
$691$	702.913			1.01724			0.508620	−	0.860991i	$-0.330156\pi$
$691$	702.913			1.01724			0.508620	+	0.860991i	$0.330156\pi$
$692$	447.178			0.646212
$693$	−344.347			−0.496893
$694$	−1410.39			−2.03227
$695$			444.733i			0.639904i
$696$	2.89387			0.00415786
$697$			1194.89i			1.71433i
$698$	−73.4553			−0.105237
$699$	−10.9702			−0.0156941
$700$			91.5726i			0.130818i
$701$		−	905.753i		−	1.29209i	−0.763301	−	0.646044i	$-0.776422\pi$
$701$		−	905.753i		−	1.29209i	0.763301	−	0.646044i	$-0.223578\pi$
$702$	2.77758			0.00395667
$703$	58.0822			0.0826206
$704$		−	1163.29i		−	1.65239i
$705$			3.92280i			0.00556426i
$706$	−503.899			−0.713738
$707$		−	225.169i		−	0.318485i
$708$	−1.35193			−0.00190951
$709$			917.543i			1.29414i	0.762432	+	0.647068i	$0.224005\pi$
$709$			917.543i			1.29414i	−0.762432	+	0.647068i	$0.775995\pi$
$710$			753.534i			1.06132i
$711$			930.561i			1.30881i
$712$		−	1724.80i		−	2.42247i
$713$	−77.8531	+	607.530i	−0.109191	+	0.852075i
$714$	−6.01582			−0.00842551
$715$	37.6440			0.0526489
$716$	−1910.91			−2.66887
$717$	0.466542			0.000650686
$718$			2059.23i			2.86801i
$719$	−1126.87			−1.56728			−0.783639	−	0.621216i	$-0.786639\pi$
$719$	−1126.87			−1.56728			−0.783639	+	0.621216i	$0.786639\pi$
$720$			285.637i			0.396717i
$721$	−23.6345			−0.0327801
$722$	−620.244			−0.859063
$723$		−	18.0986i		−	0.0250326i
$724$		−	1486.99i		−	2.05386i
$725$	25.0158			0.0345045
$726$	22.2330			0.0306240
$727$			176.237i			0.242417i	0.992627	+	0.121209i	$0.0386770\pi$
$727$			176.237i			0.242417i	−0.992627	+	0.121209i	$0.961323\pi$
$728$		−	31.7315i		−	0.0435872i
$729$	−728.073			−0.998729
$730$		−	299.327i		−	0.410036i
$731$	−457.201			−0.625446
$732$			15.4161i			0.0210602i
$733$		−	1089.28i		−	1.48605i	−0.669262	−	0.743027i	$-0.733389\pi$
$733$		−	1089.28i		−	1.48605i	0.669262	−	0.743027i	$-0.266611\pi$
$734$		−	2132.68i		−	2.90556i
$735$			4.25323i			0.00578671i
$736$	−12.0217	+	93.8119i	−0.0163338	+	0.127462i
$737$	−1535.34			−2.08323
$738$	−2158.13			−2.92429
$739$	667.801			0.903655			0.451827	−	0.892105i	$-0.350772\pi$
$739$	667.801			0.903655			0.451827	+	0.892105i	$0.350772\pi$
$740$	43.8124			0.0592060
$741$			1.04304i			0.00140761i
$742$	−432.030			−0.582251
$743$			111.460i			0.150014i	0.997183	+	0.0750068i	$0.0238978\pi$
$743$			111.460i			0.150014i	−0.997183	+	0.0750068i	$0.976102\pi$
$744$	15.4032			0.0207033
$745$	−230.725			−0.309698
$746$		−	235.632i		−	0.315861i
$747$		−	534.043i		−	0.714917i
$748$	−2206.79			−2.95025
$749$	91.0388			0.121547
$750$		−	1.68067i		−	0.00224089i
$751$			452.088i			0.601981i	0.953627	+	0.300991i	$0.0973173\pi$
$751$			452.088i			0.601981i	−0.953627	+	0.300991i	$0.902683\pi$
$752$	570.271			0.758340
$753$			10.8501i			0.0144091i
$754$	−17.6797			−0.0234479
$755$			446.237i			0.591042i
$756$		−	14.3956i		−	0.0190418i
$757$			216.404i			0.285871i	0.989732	+	0.142935i	$0.0456541\pi$
$757$			216.404i			0.285871i	−0.989732	+	0.142935i	$0.954346\pi$
$758$			1776.29i			2.34339i
$759$	−16.3379	−	2.09365i	−0.0215255	−	0.00275843i
$760$	−688.953			−0.906517
$761$	−653.530			−0.858778			−0.429389	−	0.903120i	$-0.641271\pi$
$761$	−653.530			−0.858778			−0.429389	+	0.903120i	$0.641271\pi$
$762$	26.8569			0.0352453
$763$	100.601			0.131849
$764$			2381.48i			3.11712i
$765$	−345.028			−0.451017
$766$			720.069i			0.940038i
$767$	4.04962			0.00527982
$768$	21.8407			0.0284385
$769$		−	713.959i		−	0.928426i	−0.885724	−	0.464213i	$-0.846337\pi$
$769$		−	713.959i		−	0.928426i	0.885724	−	0.464213i	$-0.153663\pi$
$770$		−	294.543i		−	0.382524i
$771$	17.0529			0.0221178
$772$	−1349.39			−1.74792
$773$		−	31.4153i		−	0.0406407i	−0.999794	−	0.0203204i	$-0.993531\pi$
$773$		−	31.4153i		−	0.0406407i	0.999794	−	0.0203204i	$-0.00646862\pi$
$774$		−	825.766i		−	1.06688i
$775$	133.152			0.171809
$776$			1888.36i			2.43345i
$777$	−0.254463			−0.000327494
$778$			2136.65i			2.74633i
$779$		−	1621.01i		−	2.08088i
$780$			0.786780i			0.00100869i
$781$		−	1605.45i		−	2.05563i
$782$	1346.57	+	172.558i	1.72195	+	0.220663i
$783$	−3.93259			−0.00502247
$784$	618.307			0.788656
$785$	501.872			0.639327
$786$	−7.44639			−0.00947378
$787$			311.831i			0.396227i	0.980179	+	0.198113i	$0.0634815\pi$
$787$			311.831i			0.396227i	−0.980179	+	0.198113i	$0.936519\pi$
$788$	2018.69			2.56179
$789$		−	13.2057i		−	0.0167373i
$790$	−795.972			−1.00756
$791$	378.184			0.478108
$792$		−	1954.22i		−	2.46745i
$793$		−	46.1777i		−	0.0582317i
$794$	−1602.13			−2.01779
$795$	5.25219			0.00660652
$796$		−	1410.88i		−	1.77247i
$797$		−	94.6765i		−	0.118791i	−0.998235	−	0.0593955i	$-0.981083\pi$
$797$		−	94.6765i		−	0.118791i	0.998235	−	0.0593955i	$-0.0189173\pi$
$798$	8.16118			0.0102270
$799$			688.845i			0.862135i
$800$	20.5607			0.0257008
$801$			1171.82i			1.46295i
$802$			206.348i			0.257292i
$803$			637.732i			0.794187i
$804$		−	32.0894i		−	0.0399122i
$805$	−15.2557	+	119.049i	−0.0189512	+	0.147887i
$806$	−94.1042			−0.116755
$807$	−12.8901			−0.0159729
$808$	1277.87			1.58152
$809$	−645.736			−0.798190			−0.399095	−	0.916910i	$-0.630676\pi$
$809$	−645.736			−0.798190			−0.399095	+	0.916910i	$0.630676\pi$
$810$		−	623.035i		−	0.769178i
$811$	−906.212			−1.11740			−0.558700	−	0.829370i	$-0.688700\pi$
$811$	−906.212			−1.11740			−0.558700	+	0.829370i	$0.688700\pi$
$812$			91.6303i			0.112845i
$813$	5.18257			0.00637462
$814$	−140.923			−0.173124
$815$			97.9794i			0.120220i
$816$		−	10.6318i		−	0.0130291i
$817$	620.248			0.759178
$818$	−868.524			−1.06177
$819$			21.5583i			0.0263227i
$820$		−	1222.75i		−	1.49116i
$821$	654.650			0.797381			0.398690	−	0.917086i	$-0.369465\pi$
$821$	654.650			0.797381			0.398690	+	0.917086i	$0.369465\pi$
$822$			21.8935i			0.0266345i
$823$	995.028			1.20903			0.604513	−	0.796595i	$-0.293368\pi$
$823$	995.028			1.20903			0.604513	+	0.796595i	$0.293368\pi$
$824$		−	134.129i		−	0.162778i
$825$			3.58076i			0.00434031i
$826$		−	31.6860i		−	0.0383608i
$827$		−	326.367i		−	0.394640i	−0.980339	−	0.197320i	$-0.936776\pi$
$827$		−	326.367i		−	0.394640i	0.980339	−	0.197320i	$-0.0632238\pi$
$828$	−206.441	+	1610.97i	−0.249325	+	1.94562i
$829$	693.960			0.837104			0.418552	−	0.908193i	$-0.362538\pi$
$829$	693.960			0.837104			0.418552	+	0.908193i	$0.362538\pi$
$830$	456.803			0.550365
$831$	−15.6824			−0.0188717
$832$	−72.8289			−0.0875348
$833$			746.868i			0.896601i
$834$	29.8980			0.0358489
$835$		−	377.677i		−	0.452308i
$836$	2993.78			3.58107
$837$	−20.9320			−0.0250084
$838$		−	1344.81i		−	1.60479i
$839$		−	343.739i		−	0.409700i	−0.978793	−	0.204850i	$-0.934329\pi$
$839$		−	343.739i		−	0.409700i	0.978793	−	0.204850i	$-0.0656707\pi$
$840$	3.01835			0.00359328
$841$	−815.968			−0.970236
$842$		−	1304.10i		−	1.54881i
$843$			8.69648i			0.0103161i
$844$	2660.02			3.15168
$845$			375.539i			0.444425i
$846$	−1244.15			−1.47062
$847$			345.160i			0.407509i
$848$		−	763.528i		−	0.900387i
$849$			5.28151i			0.00622086i
$850$		−	295.126i		−	0.347207i
$851$	56.9583	+	7.29904i	0.0669310	+	0.00857701i
$852$	33.5548			0.0393835
$853$	−24.5062			−0.0287295			−0.0143647	−	0.999897i	$-0.504573\pi$
$853$	−24.5062			−0.0287295			−0.0143647	+	0.999897i	$0.504573\pi$
$854$	−361.315			−0.423086
$855$	468.072			0.547453
$856$			516.660i			0.603575i
$857$	1674.09			1.95343			0.976715	−	0.214542i	$-0.0688260\pi$
$857$	1674.09			1.95343			0.976715	+	0.214542i	$0.0688260\pi$
$858$		−	2.53068i		−	0.00294951i
$859$	−137.574			−0.160156			−0.0800778	−	0.996789i	$-0.525517\pi$
$859$	−137.574			−0.160156			−0.0800778	+	0.996789i	$0.525517\pi$
$860$	467.864			0.544028
$861$			7.10176i			0.00824827i
$862$			1126.79i			1.30718i
$863$	−312.225			−0.361791			−0.180895	−	0.983502i	$-0.557900\pi$
$863$	−312.225			−0.361791			−0.180895	+	0.983502i	$0.557900\pi$
$864$	−3.23223			−0.00374100
$865$		−	127.415i		−	0.147300i
$866$		−	458.146i		−	0.529037i
$867$	0.221018			0.000254923
$868$			487.722i			0.561891i
$869$	1695.86			1.95151
$870$		−	1.68173i		−	0.00193302i
$871$			96.1217i			0.110358i
$872$			570.925i			0.654731i
$873$		−	1282.94i		−	1.46958i
$874$	−1826.78	−	234.096i	−2.09014	−	0.267845i
$875$	26.0918			0.0298192
$876$	−13.3290			−0.0152157
$877$	984.015			1.12202			0.561012	−	0.827808i	$-0.310412\pi$
$877$	984.015			1.12202			0.561012	+	0.827808i	$0.310412\pi$
$878$	851.765			0.970120
$879$		−	18.8618i		−	0.0214583i
$880$	520.547			0.591530
$881$		−	1250.48i		−	1.41939i	−0.704509	−	0.709695i	$-0.748833\pi$
$881$		−	1250.48i		−	1.41939i	0.704509	−	0.709695i	$-0.251167\pi$
$882$	−1348.94			−1.52942
$883$	−788.969			−0.893510			−0.446755	−	0.894656i	$-0.647420\pi$
$883$	−788.969			−0.893510			−0.446755	+	0.894656i	$0.647420\pi$
$884$			138.159i			0.156288i
$885$			0.385207i			0.000435262i
$886$	2156.70			2.43420
$887$	−298.078			−0.336051			−0.168026	−	0.985783i	$-0.553739\pi$
$887$	−298.078			−0.336051			−0.168026	+	0.985783i	$0.553739\pi$
$888$		−	1.44412i		−	0.00162626i
$889$			416.945i			0.469004i
$890$	−1002.34			−1.12622
$891$			1327.41i			1.48980i
$892$	−2377.50			−2.66536
$893$		−	934.502i		−	1.04648i
$894$			15.5109i			0.0173500i
$895$			544.476i			0.608354i
$896$			531.460i			0.593147i
$897$	−0.131076	+	1.02285i	−0.000146127	+	0.00114030i
$898$	702.156			0.781911
$899$	133.236			0.148204
$900$	353.075			0.392305
$901$	922.285			1.02362
$902$			3932.99i			4.36030i
$903$	−2.71735			−0.00300925
$904$			2146.25i			2.37417i
$905$	−423.689			−0.468165
$906$	29.9990			0.0331115
$907$		−	371.856i		−	0.409984i	−0.978764	−	0.204992i	$-0.934283\pi$
$907$		−	371.856i		−	0.409984i	0.978764	−	0.204992i	$-0.0657169\pi$
$908$		−	3074.45i		−	3.38596i
$909$	−868.178			−0.955092
$910$	−18.4402			−0.0202640
$911$		−	564.051i		−	0.619156i	−0.950874	−	0.309578i	$-0.899812\pi$
$911$		−	564.051i		−	0.619156i	0.950874	−	0.309578i	$-0.100188\pi$
$912$			14.4233i			0.0158150i
$913$	−973.245			−1.06599
$914$		−	1176.68i		−	1.28740i
$915$	4.39250			0.00480055
$916$		−	1022.56i		−	1.11633i
$917$		−	115.603i		−	0.126066i
$918$			46.3951i			0.0505393i
$919$		−	31.1434i		−	0.0338883i	−0.999856	−	0.0169442i	$-0.994606\pi$
$919$		−	31.1434i		−	0.0338883i	0.999856	−	0.0169442i	$-0.00539376\pi$
$920$	−675.621	−	86.5788i	−0.734371	−	0.0941074i
$921$	−11.6158			−0.0126122
$922$	1268.45			1.37576
$923$	−100.511			−0.108896
$924$	−13.1160			−0.0141948
$925$		−	12.4835i		−	0.0134957i
$926$	−1445.16			−1.56065
$927$			91.1270i			0.0983032i
$928$	20.5736			0.0221698
$929$	−348.046			−0.374646			−0.187323	−	0.982298i	$-0.559981\pi$
$929$	−348.046			−0.374646			−0.187323	+	0.982298i	$0.559981\pi$
$930$		−	8.95135i		−	0.00962510i
$931$		−	1013.22i		−	1.08831i
$932$	1971.30			2.11513
$933$	−4.82729			−0.00517395
$934$		−	466.004i		−	0.498933i
$935$			628.782i			0.672494i
$936$	−122.347			−0.130712
$937$			1626.37i			1.73572i	0.496808	+	0.867860i	$0.334505\pi$
$937$			1626.37i			1.73572i	−0.496808	+	0.867860i	$0.665495\pi$
$938$	752.099			0.801811
$939$		−	20.1861i		−	0.0214975i
$940$		−	704.911i		−	0.749906i
$941$			604.582i			0.642489i	0.946996	+	0.321244i	$0.104101\pi$
$941$			604.582i			0.642489i	−0.946996	+	0.321244i	$0.895899\pi$
$942$		−	33.7392i		−	0.0358165i
$943$	203.708	−	1589.64i	0.216021	−	1.68573i
$944$	55.9988			0.0593208
$945$	−4.10175			−0.00434048
$946$	−1504.88			−1.59079
$947$	−370.557			−0.391296			−0.195648	−	0.980674i	$-0.562681\pi$
$947$	−370.557			−0.391296			−0.195648	+	0.980674i	$0.562681\pi$
$948$			35.4445i			0.0373887i
$949$	39.9260			0.0420717
$950$			400.374i			0.421446i
$951$	−24.1312			−0.0253745
$952$	530.024			0.556747
$953$		−	477.703i		−	0.501263i	−0.968083	−	0.250631i	$-0.919362\pi$
$953$		−	477.703i		−	0.501263i	0.968083	−	0.250631i	$-0.0806382\pi$
$954$			1665.77i			1.74609i
$955$	678.556			0.710530
$956$	−83.8356			−0.0876941
$957$			3.58301i			0.00374401i
$958$		−	2871.12i		−	2.99700i
$959$	−339.890			−0.354421
$960$		−	6.92761i		−	0.00721626i
$961$	−251.825			−0.262045
$962$			8.82264i			0.00917114i
$963$		−	351.017i		−	0.364503i
$964$			3252.24i			3.37369i
$965$			384.483i			0.398428i
$966$	8.00326	+	1.02559i	0.00828495	+	0.00106169i
$967$	−668.967			−0.691796			−0.345898	−	0.938272i	$-0.612426\pi$
$967$	−668.967			−0.691796			−0.345898	+	0.938272i	$0.612426\pi$
$968$	−1958.84			−2.02359
$969$	−17.4222			−0.0179796
$970$	1097.39			1.13133
$971$			1839.11i			1.89404i	0.321178	+	0.947019i	$0.395921\pi$
$971$			1839.11i			1.89404i	−0.321178	+	0.947019i	$0.604079\pi$
$972$	−83.2603			−0.0856588
$973$			464.156i			0.477036i
$974$	704.092			0.722887
$975$	0.224178			0.000229926
$976$		−	638.553i		−	0.654255i
$977$			1078.15i			1.10353i	0.834000	+	0.551764i	$0.186045\pi$
$977$			1078.15i			1.10353i	−0.834000	+	0.551764i	$0.813955\pi$
$978$	6.58683			0.00673500
$979$	2135.54			2.18135
$980$		−	764.287i		−	0.779885i
$981$		−	387.885i		−	0.395397i
$982$	−949.993			−0.967406
$983$		−	1248.18i		−	1.26977i	−0.772608	−	0.634884i	$-0.781048\pi$
$983$		−	1248.18i		−	1.26977i	0.772608	−	0.634884i	$-0.218952\pi$
$984$	−40.3036			−0.0409590
$985$		−	575.186i		−	0.583945i
$986$		−	295.312i		−	0.299505i
$987$			4.09412i			0.00414805i
$988$		−	187.429i		−	0.189706i
$989$	608.246	+	77.9449i	0.615011	+	0.0788118i
$990$	−1135.66			−1.14714
$991$	800.574			0.807845			0.403922	−	0.914793i	$-0.367647\pi$
$991$	800.574			0.807845			0.403922	+	0.914793i	$0.367647\pi$
$992$	109.507			0.110391
$993$	−1.45912			−0.00146941
$994$			786.442i			0.791190i
$995$	−402.004			−0.404024
$996$		−	20.3414i		−	0.0204231i
$997$	372.888			0.374010			0.187005	−	0.982359i	$-0.440122\pi$
$997$	372.888			0.374010			0.187005	+	0.982359i	$0.440122\pi$
$998$	849.991			0.851694
$999$			1.96246i			0.00196443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.d.b.91.9	✓	10
3.2	odd	2		1035.3.g.b.91.2		10
4.3	odd	2		1840.3.k.b.321.5		10
5.2	odd	4		575.3.c.d.574.20		20
5.3	odd	4		575.3.c.d.574.1		20
5.4	even	2		575.3.d.g.551.2		10
23.22	odd	2	inner	115.3.d.b.91.10	yes	10
69.68	even	2		1035.3.g.b.91.1		10
92.91	even	2		1840.3.k.b.321.6		10
115.22	even	4		575.3.c.d.574.19		20
115.68	even	4		575.3.c.d.574.2		20
115.114	odd	2		575.3.d.g.551.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.d.b.91.9	✓	10	1.1	even	1	trivial
115.3.d.b.91.10	yes	10	23.22	odd	2	inner
575.3.c.d.574.1		20	5.3	odd	4
575.3.c.d.574.2		20	115.68	even	4
575.3.c.d.574.19		20	115.22	even	4
575.3.c.d.574.20		20	5.2	odd	4
575.3.d.g.551.1		10	115.114	odd	2
575.3.d.g.551.2		10	5.4	even	2
1035.3.g.b.91.1		10	69.68	even	2
1035.3.g.b.91.2		10	3.2	odd	2
1840.3.k.b.321.5		10	4.3	odd	2
1840.3.k.b.321.6		10	92.91	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.44206 q^{2} -0.0436725 q^{3} +7.84777 q^{4} -2.23607i q^{5} -0.150323 q^{6} -2.33372i q^{7} +13.2442 q^{8} -8.99809 q^{9} -7.69668i q^{10} +16.3982i q^{11} -0.342732 q^{12} +1.02663 q^{13} -8.03281i q^{14} +0.0976548i q^{15} +14.1964 q^{16} +17.1482i q^{17} -30.9720 q^{18} -23.2636i q^{19} -17.5481i q^{20} +0.101920i q^{21} +56.4436i q^{22} +(2.92347 - 22.8134i) q^{23} -0.578410 q^{24} -5.00000 q^{25} +3.53372 q^{26} +0.786022 q^{27} -18.3145i q^{28} -5.00315 q^{29} +0.336133i q^{30} -26.6303 q^{31} -4.11213 q^{32} -0.716151i q^{33} +59.0251i q^{34} -5.21836 q^{35} -70.6150 q^{36} +2.49670i q^{37} -80.0747i q^{38} -0.0448355 q^{39} -29.6150i q^{40} +69.6800 q^{41} +0.350813i q^{42} +26.6617i q^{43} +128.689i q^{44} +20.1203i q^{45} +(10.0628 - 78.5252i) q^{46} +40.1701 q^{47} -0.619993 q^{48} +43.5537 q^{49} -17.2103 q^{50} -0.748905i q^{51} +8.05675 q^{52} -53.7832i q^{53} +2.70554 q^{54} +36.6675 q^{55} -30.9084i q^{56} +1.01598i q^{57} -17.2211 q^{58} +3.94458 q^{59} +0.766372i q^{60} -44.9799i q^{61} -91.6632 q^{62} +20.9991i q^{63} -70.9398 q^{64} -2.29561i q^{65} -2.46503i q^{66} +93.6284i q^{67} +134.575i q^{68} +(-0.127676 + 0.996321i) q^{69} -17.9619 q^{70} -97.9038 q^{71} -119.173 q^{72} +38.8904 q^{73} +8.59379i q^{74} +0.218363 q^{75} -182.567i q^{76} +38.2689 q^{77} -0.154327 q^{78} -103.418i q^{79} -31.7441i q^{80} +80.9485 q^{81} +239.843 q^{82} +59.3507i q^{83} +0.799841i q^{84} +38.3445 q^{85} +91.7712i q^{86} +0.218500 q^{87} +217.182i q^{88} -130.230i q^{89} +69.2554i q^{90} -2.39587i q^{91} +(22.9427 - 179.035i) q^{92} +1.16301 q^{93} +138.268 q^{94} -52.0190 q^{95} +0.179587 q^{96} +142.579i q^{97} +149.915 q^{98} -147.553i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 2 q^{3} + 34 q^{4} + 28 q^{6} - 20 q^{8} - 16 q^{9} - 24 q^{12} - 2 q^{13} - 38 q^{16} - 22 q^{18} + 44 q^{23} + 70 q^{24} - 50 q^{25} - 72 q^{26} + 40 q^{27} - 46 q^{29} + 16 q^{31} + 142 q^{32}+ \cdots + 388 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 2 * q^3 + 34 * q^4 + 28 * q^6 - 20 * q^8 - 16 * q^9 - 24 * q^12 - 2 * q^13 - 38 * q^16 - 22 * q^18 + 44 * q^23 + 70 * q^24 - 50 * q^25 - 72 * q^26 + 40 * q^27 - 46 * q^29 + 16 * q^31 + 142 * q^32 - 60 * q^35 - 110 * q^36 + 72 * q^39 - 84 * q^41 + 86 * q^46 + 112 * q^47 - 236 * q^48 + 50 * q^49 - 10 * q^50 + 52 * q^52 + 30 * q^54 - 10 * q^55 + 246 * q^58 - 262 * q^59 - 136 * q^62 - 224 * q^64 + 124 * q^69 + 130 * q^70 + 236 * q^71 - 406 * q^72 + 168 * q^73 + 10 * q^75 + 300 * q^77 - 254 * q^78 - 258 * q^81 + 140 * q^82 + 540 * q^87 - 182 * q^92 + 100 * q^93 + 262 * q^94 - 90 * q^95 - 332 * q^96 + 388 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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