LMFDB - Embedded newform 105.3.e.a.34.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(34,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.34");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.e (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:	$2.86104277578$
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} - 8 x^{15} + 72 x^{14} - 292 x^{13} + 1148 x^{12} - 2304 x^{11} + 4996 x^{10} - 4490 x^{9} + \cdots + 1849 $ x^16 - 8x^15 + 72x^14 - 292x^13 + 1148x^12 - 2304x^11 + 4996x^10 - 4490x^9 + 9786x^8 - 5744x^7 + 8608x^6 + 4740x^5 + 22841x^4 + 22790x^3 + 18930x^2 + 8170*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.6
Root			$-0.366025 + 0.706606i$ of defining polynomial
Character	$\chi$	$=$	105.34
Dual form			105.3.e.a.34.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93048i q^{2} +1.73205 q^{3} +0.273228 q^{4} +(-4.88618 - 1.06077i) q^{5} -3.34370i q^{6} +(0.433408 - 6.98657i) q^{7} -8.24940i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.93048i q^{2} +1.73205 q^{3} +0.273228 q^{4} +(-4.88618 - 1.06077i) q^{5} -3.34370i q^{6} +(0.433408 - 6.98657i) q^{7} -8.24940i q^{8} +3.00000 q^{9} +(-2.04780 + 9.43270i) q^{10} +4.41485 q^{11} +0.473246 q^{12} +17.0999 q^{13} +(-13.4875 - 0.836687i) q^{14} +(-8.46311 - 1.83731i) q^{15} -14.8324 q^{16} -18.6737 q^{17} -5.79145i q^{18} +18.4030i q^{19} +(-1.33504 - 0.289833i) q^{20} +(0.750684 - 12.1011i) q^{21} -8.52280i q^{22} +33.8925i q^{23} -14.2884i q^{24} +(22.7495 + 10.3662i) q^{25} -33.0111i q^{26} +5.19615 q^{27} +(0.118419 - 1.90893i) q^{28} +23.8461 q^{29} +(-3.54690 + 16.3379i) q^{30} -2.78940i q^{31} -4.36383i q^{32} +7.64674 q^{33} +36.0493i q^{34} +(-9.52886 + 33.6779i) q^{35} +0.819685 q^{36} +61.7879i q^{37} +35.5268 q^{38} +29.6179 q^{39} +(-8.75073 + 40.3081i) q^{40} -53.1240i q^{41} +(-23.3610 - 1.44918i) q^{42} -7.46787i q^{43} +1.20626 q^{44} +(-14.6585 - 3.18231i) q^{45} +65.4289 q^{46} +44.3642 q^{47} -25.6905 q^{48} +(-48.6243 - 6.05606i) q^{49} +(20.0119 - 43.9176i) q^{50} -32.3438 q^{51} +4.67218 q^{52} +30.0947i q^{53} -10.0311i q^{54} +(-21.5717 - 4.68314i) q^{55} +(-57.6350 - 3.57535i) q^{56} +31.8750i q^{57} -46.0345i q^{58} +19.9814i q^{59} +(-2.31236 - 0.502005i) q^{60} -64.6635i q^{61} -5.38489 q^{62} +(1.30022 - 20.9597i) q^{63} -67.7540 q^{64} +(-83.5533 - 18.1391i) q^{65} -14.7619i q^{66} -68.3099i q^{67} -5.10219 q^{68} +58.7035i q^{69} +(65.0147 + 18.3953i) q^{70} +14.6088 q^{71} -24.7482i q^{72} -59.4144 q^{73} +119.281 q^{74} +(39.4033 + 17.9549i) q^{75} +5.02823i q^{76} +(1.91343 - 30.8446i) q^{77} -57.1769i q^{78} -57.2759 q^{79} +(72.4739 + 15.7338i) q^{80} +9.00000 q^{81} -102.555 q^{82} -98.3178 q^{83} +(0.205108 - 3.30636i) q^{84} +(91.2431 + 19.8085i) q^{85} -14.4166 q^{86} +41.3026 q^{87} -36.4199i q^{88} +64.6493i q^{89} +(-6.14341 + 28.2981i) q^{90} +(7.41123 - 119.470i) q^{91} +9.26040i q^{92} -4.83138i q^{93} -85.6444i q^{94} +(19.5214 - 89.9205i) q^{95} -7.55837i q^{96} +182.904 q^{97} +(-11.6911 + 93.8685i) q^{98} +13.2445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) $ 16 * q - 32 * q^4 + 48 * q^9	$ 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.93048i		−	0.965242i	−0.875829	−	0.482621i	$-0.839685\pi$
$2$		−	1.93048i		−	0.965242i	0.875829	−	0.482621i	$-0.160315\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	0.273228			0.0683071
$5$	−4.88618	−	1.06077i	−0.977236	−	0.212154i
$5$	−4.88618	−	1.06077i	−0.977236	−	0.212154i
$6$		−	3.34370i		−	0.557283i
$7$	0.433408	−	6.98657i	0.0619154	−	0.998081i
$7$	0.433408	−	6.98657i	0.0619154	−	0.998081i
$8$		−	8.24940i		−	1.03118i
$9$	3.00000			0.333333
$10$	−2.04780	+	9.43270i	−0.204780	+	0.943270i
$11$	4.41485			0.401350			0.200675	−	0.979658i	$-0.435687\pi$
$11$	4.41485			0.401350			0.200675	+	0.979658i	$0.435687\pi$
$12$	0.473246			0.0394371
$13$	17.0999			1.31538			0.657689	−	0.753290i	$-0.271534\pi$
$13$	17.0999			1.31538			0.657689	+	0.753290i	$0.271534\pi$
$14$	−13.4875	−	0.836687i	−0.963390	−	0.0597633i
$15$	−8.46311	−	1.83731i	−0.564208	−	0.122487i
$16$	−14.8324			−0.927027
$17$	−18.6737			−1.09845			−0.549227	−	0.835673i	$-0.685078\pi$
$17$	−18.6737			−1.09845			−0.549227	+	0.835673i	$0.685078\pi$
$18$		−	5.79145i		−	0.321747i
$19$			18.4030i			0.968580i	0.874908	+	0.484290i	$0.160922\pi$
$19$			18.4030i			0.968580i	−0.874908	+	0.484290i	$0.839078\pi$
$20$	−1.33504	−	0.289833i	−0.0667522	−	0.0144916i
$21$	0.750684	−	12.1011i	0.0357468	−	0.576243i
$22$		−	8.52280i		−	0.387400i
$23$			33.8925i			1.47359i	0.676118	+	0.736793i	$0.263661\pi$
$23$			33.8925i			1.47359i	−0.676118	+	0.736793i	$0.736339\pi$
$24$		−	14.2884i		−	0.595349i
$25$	22.7495	+	10.3662i	0.909981	+	0.414650i
$26$		−	33.0111i		−	1.26966i
$27$	5.19615			0.192450
$28$	0.118419	−	1.90893i	0.00422926	−	0.0681761i
$29$	23.8461			0.822278			0.411139	−	0.911573i	$-0.365131\pi$
$29$	23.8461			0.822278			0.411139	+	0.911573i	$0.365131\pi$
$30$	−3.54690	+	16.3379i	−0.118230	+	0.544597i
$31$		−	2.78940i		−	0.0899806i	−0.998987	−	0.0449903i	$-0.985674\pi$
$31$		−	2.78940i		−	0.0899806i	0.998987	−	0.0449903i	$-0.0143257\pi$
$32$		−	4.36383i		−	0.136370i
$33$	7.64674			0.231719
$34$			36.0493i			1.06027i
$35$	−9.52886	+	33.6779i	−0.272253	+	0.962226i
$36$	0.819685			0.0227690
$37$			61.7879i			1.66994i	0.550294	+	0.834971i	$0.314516\pi$
$37$			61.7879i			1.66994i	−0.550294	+	0.834971i	$0.685484\pi$
$38$	35.5268			0.934914
$39$	29.6179			0.759434
$40$	−8.75073	+	40.3081i	−0.218768	+	1.00770i
$41$		−	53.1240i		−	1.29571i	−0.761764	−	0.647854i	$-0.775667\pi$
$41$		−	53.1240i		−	1.29571i	0.761764	−	0.647854i	$-0.224333\pi$
$42$	−23.3610	−	1.44918i	−0.556214	−	0.0345044i
$43$		−	7.46787i		−	0.173671i	−0.996223	−	0.0868357i	$-0.972324\pi$
$43$		−	7.46787i		−	0.173671i	0.996223	−	0.0868357i	$-0.0276755\pi$
$44$	1.20626			0.0274151
$45$	−14.6585	−	3.18231i	−0.325745	−	0.0707181i
$46$	65.4289			1.42237
$47$	44.3642			0.943919			0.471959	−	0.881620i	$-0.343547\pi$
$47$	44.3642			0.943919			0.471959	+	0.881620i	$0.343547\pi$
$48$	−25.6905			−0.535219
$49$	−48.6243	−	6.05606i	−0.992333	−	0.123593i
$50$	20.0119	−	43.9176i	0.400237	−	0.878352i
$51$	−32.3438			−0.634192
$52$	4.67218			0.0898497
$53$			30.0947i			0.567825i	0.958850	+	0.283912i	$0.0916325\pi$
$53$			30.0947i			0.567825i	−0.958850	+	0.283912i	$0.908368\pi$
$54$		−	10.0311i		−	0.185761i
$55$	−21.5717	−	4.68314i	−0.392214	−	0.0851481i
$56$	−57.6350	−	3.57535i	−1.02920	−	0.0638456i
$57$			31.8750i			0.559210i
$58$		−	46.0345i		−	0.793698i
$59$			19.9814i			0.338668i	0.985559	+	0.169334i	$0.0541617\pi$
$59$			19.9814i			0.338668i	−0.985559	+	0.169334i	$0.945838\pi$
$60$	−2.31236	−	0.502005i	−0.0385394	−	0.00836675i
$61$		−	64.6635i		−	1.06006i	−0.847980	−	0.530029i	$-0.822181\pi$
$61$		−	64.6635i		−	1.06006i	0.847980	−	0.530029i	$-0.177819\pi$
$62$	−5.38489			−0.0868531
$63$	1.30022	−	20.9597i	0.0206385	−	0.332694i
$64$	−67.7540			−1.05866
$65$	−83.5533	−	18.1391i	−1.28544	−	0.279063i
$66$		−	14.7619i		−	0.223665i
$67$		−	68.3099i		−	1.01955i	−0.860307	−	0.509776i	$-0.829728\pi$
$67$		−	68.3099i		−	1.01955i	0.860307	−	0.509776i	$-0.170272\pi$
$68$	−5.10219			−0.0750322
$69$			58.7035i			0.850776i
$70$	65.0147	+	18.3953i	0.928781	+	0.262790i
$71$	14.6088			0.205758			0.102879	−	0.994694i	$-0.467195\pi$
$71$	14.6088			0.205758			0.102879	+	0.994694i	$0.467195\pi$
$72$		−	24.7482i		−	0.343725i
$73$	−59.4144			−0.813896			−0.406948	−	0.913451i	$-0.633407\pi$
$73$	−59.4144			−0.813896			−0.406948	+	0.913451i	$0.633407\pi$
$74$	119.281			1.61190
$75$	39.4033	+	17.9549i	0.525378	+	0.239398i
$76$			5.02823i			0.0661609i
$77$	1.91343	−	30.8446i	0.0248497	−	0.400580i
$78$		−	57.1769i		−	0.733038i
$79$	−57.2759			−0.725011			−0.362506	−	0.931982i	$-0.618079\pi$
$79$	−57.2759			−0.725011			−0.362506	+	0.931982i	$0.618079\pi$
$80$	72.4739	+	15.7338i	0.905924	+	0.196673i
$81$	9.00000			0.111111
$82$	−102.555			−1.25067
$83$	−98.3178			−1.18455			−0.592276	−	0.805735i	$-0.701771\pi$
$83$	−98.3178			−1.18455			−0.592276	+	0.805735i	$0.701771\pi$
$84$	0.205108	−	3.30636i	0.00244176	−	0.0393615i
$85$	91.2431	+	19.8085i	1.07345	+	0.233042i
$86$	−14.4166			−0.167635
$87$	41.3026			0.474742
$88$		−	36.4199i		−	0.413862i
$89$			64.6493i			0.726397i	0.931712	+	0.363198i	$0.118315\pi$
$89$			64.6493i			0.726397i	−0.931712	+	0.363198i	$0.881685\pi$
$90$	−6.14341	+	28.2981i	−0.0682601	+	0.314423i
$91$	7.41123	−	119.470i	0.0814421	−	1.31285i
$92$			9.26040i			0.100656i
$93$		−	4.83138i		−	0.0519503i
$94$		−	85.6444i		−	0.911110i
$95$	19.5214	−	89.9205i	0.205488	−	0.946531i
$96$		−	7.55837i		−	0.0787330i
$97$	182.904			1.88561			0.942806	−	0.333342i	$-0.108176\pi$
$97$	182.904			1.88561			0.942806	+	0.333342i	$0.108176\pi$
$98$	−11.6911	+	93.8685i	−0.119297	+	0.957842i
$99$	13.2445			0.133783
$100$	6.21582	+	2.83235i	0.0621582	+	0.0283235i
$101$			177.872i			1.76111i	0.473947	+	0.880553i	$0.342829\pi$
$101$			177.872i			1.76111i	−0.473947	+	0.880553i	$0.657171\pi$
$102$			62.4392i			0.612149i
$103$	−111.513			−1.08265			−0.541325	−	0.840814i	$-0.682077\pi$
$103$	−111.513			−1.08265			−0.541325	+	0.840814i	$0.682077\pi$
$104$		−	141.064i		−	1.35639i
$105$	−16.5045	+	58.3318i	−0.157185	+	0.555541i
$106$	58.0974			0.548088
$107$		−	105.651i		−	0.987391i	−0.869635	−	0.493696i	$-0.835646\pi$
$107$		−	105.651i		−	0.987391i	0.869635	−	0.493696i	$-0.164354\pi$
$108$	1.41974			0.0131457
$109$	32.7650			0.300596			0.150298	−	0.988641i	$-0.451977\pi$
$109$	32.7650			0.300596			0.150298	+	0.988641i	$0.451977\pi$
$110$	−9.04074	+	41.6439i	−0.0821885	+	0.378581i
$111$			107.020i			0.964142i
$112$	−6.42849	+	103.628i	−0.0573972	+	0.925248i
$113$			161.035i			1.42509i	0.701626	+	0.712545i	$0.252458\pi$
$113$			161.035i			1.42509i	−0.701626	+	0.712545i	$0.747542\pi$
$114$	61.5341			0.539773
$115$	35.9522	−	165.605i	0.312628	−	1.44004i
$116$	6.51542			0.0561674
$117$	51.2997			0.438459
$118$	38.5738			0.326897
$119$	−8.09333	+	130.465i	−0.0680111	+	1.09635i
$120$	−15.1567	+	69.8156i	−0.126306	+	0.581797i
$121$	−101.509			−0.838918
$122$	−124.832			−1.02321
$123$		−	92.0135i		−	0.748078i
$124$		−	0.762143i		−	0.00614631i
$125$	−100.162	−	74.7834i	−0.801297	−	0.598267i
$126$	−40.4624	−	2.51006i	−0.321130	−	0.0199211i
$127$			40.4442i			0.318458i	0.987242	+	0.159229i	$0.0509009\pi$
$127$			40.4442i			0.318458i	−0.987242	+	0.159229i	$0.949099\pi$
$128$			113.343i			0.885491i
$129$		−	12.9347i		−	0.100269i
$130$	−35.0172	+	161.298i	−0.269363	+	1.24076i
$131$		−	109.157i		−	0.833260i	−0.909076	−	0.416630i	$-0.863211\pi$
$131$		−	109.157i		−	0.833260i	0.909076	−	0.416630i	$-0.136789\pi$
$132$	2.08931			0.0158281
$133$	128.574	+	7.97601i	0.966722	+	0.0599700i
$134$	−131.871			−0.984114
$135$	−25.3893	−	5.51193i	−0.188069	−	0.0408291i
$136$			154.047i			1.13270i
$137$		−	39.1475i		−	0.285748i	−0.989741	−	0.142874i	$-0.954366\pi$
$137$		−	39.1475i		−	0.285748i	0.989741	−	0.142874i	$-0.0456344\pi$
$138$	113.326			0.821205
$139$		−	110.353i		−	0.793906i	−0.917839	−	0.396953i	$-0.870068\pi$
$139$		−	110.353i		−	0.793906i	0.917839	−	0.396953i	$-0.129932\pi$
$140$	−2.60356	+	9.20176i	−0.0185968	+	0.0657269i
$141$	76.8410			0.544972
$142$		−	28.2021i		−	0.198607i
$143$	75.4935			0.527927
$144$	−44.4973			−0.309009
$145$	−116.516	−	25.2952i	−0.803560	−	0.174450i
$146$			114.699i			0.785607i
$147$	−84.2198	−	10.4894i	−0.572924	−	0.0713565i
$148$			16.8822i			0.114069i
$149$	42.4499			0.284899			0.142449	−	0.989802i	$-0.454502\pi$
$149$	42.4499			0.284899			0.142449	+	0.989802i	$0.454502\pi$
$150$	34.6616	−	76.0676i	0.231077	−	0.507117i
$151$	−45.8041			−0.303338			−0.151669	−	0.988431i	$-0.548465\pi$
$151$	−45.8041			−0.303338			−0.151669	+	0.988431i	$0.548465\pi$
$152$	151.814			0.998776
$153$	−56.0211			−0.366151
$154$	−59.5451	−	3.69384i	−0.386657	−	0.0239860i
$155$	−2.95891	+	13.6295i	−0.0190898	+	0.0879323i
$156$	8.09246			0.0518747
$157$	−232.782			−1.48269			−0.741345	−	0.671124i	$-0.765812\pi$
$157$	−232.782			−1.48269			−0.741345	+	0.671124i	$0.765812\pi$
$158$			110.570i			0.699812i
$159$			52.1256i			0.327834i
$160$	−4.62902	+	21.3224i	−0.0289314	+	0.133265i
$161$	236.792	+	14.6893i	1.47076	+	0.0912377i
$162$		−	17.3744i		−	0.107249i
$163$		−	281.734i		−	1.72843i	−0.503124	−	0.864214i	$-0.667816\pi$
$163$		−	281.734i		−	1.72843i	0.503124	−	0.864214i	$-0.332184\pi$
$164$		−	14.5150i		−	0.0885061i
$165$	−37.3634	−	8.11144i	−0.226445	−	0.0491603i
$166$			189.801i			1.14338i
$167$	119.212			0.713842			0.356921	−	0.934135i	$-0.383827\pi$
$167$	119.212			0.713842			0.356921	+	0.934135i	$0.383827\pi$
$168$	−99.8268	−	6.19269i	−0.594207	−	0.0368613i
$169$	123.407			0.730219
$170$	38.2401	−	176.143i	0.224942	−	1.03614i
$171$			55.2091i			0.322860i
$172$		−	2.04044i		−	0.0118630i
$173$	219.519			1.26890			0.634448	−	0.772965i	$-0.281227\pi$
$173$	219.519			1.26890			0.634448	+	0.772965i	$0.281227\pi$
$174$		−	79.7340i		−	0.458241i
$175$	82.2843	−	154.448i	0.470196	−	0.882562i
$176$	−65.4829			−0.372062
$177$			34.6088i			0.195530i
$178$	124.805			0.701149
$179$	−168.600			−0.941902			−0.470951	−	0.882159i	$-0.656089\pi$
$179$	−168.600			−0.941902			−0.470951	+	0.882159i	$0.656089\pi$
$180$	−4.00513	−	0.869499i	−0.0222507	−	0.00483055i
$181$			175.270i			0.968344i	0.874973	+	0.484172i	$0.160879\pi$
$181$			175.270i			0.968344i	−0.874973	+	0.484172i	$0.839121\pi$
$182$	−230.635	−	14.3073i	−1.26722	−	0.0786114i
$183$		−	112.001i		−	0.612025i
$184$	279.593			1.51953
$185$	65.5428	−	301.907i	0.354285	−	1.63193i
$186$	−9.32690			−0.0501446
$187$	−82.4416			−0.440864
$188$	12.1216			0.0644764
$189$	2.25205	−	36.3033i	0.0119156	−	0.192081i
$190$	−173.590	−	37.6857i	−0.913632	−	0.198346i
$191$	23.0987			0.120936			0.0604679	−	0.998170i	$-0.480741\pi$
$191$	23.0987			0.120936			0.0604679	+	0.998170i	$0.480741\pi$
$192$	−117.353			−0.611216
$193$		−	44.6593i		−	0.231395i	−0.993284	−	0.115698i	$-0.963090\pi$
$193$		−	44.6593i		−	0.231395i	0.993284	−	0.115698i	$-0.0369104\pi$
$194$		−	353.094i		−	1.82007i
$195$	−144.719	−	31.4178i	−0.742146	−	0.161117i
$196$	−13.2855	−	1.65469i	−0.0677834	−	0.00844229i
$197$		−	125.777i		−	0.638461i	−0.947677	−	0.319230i	$-0.896576\pi$
$197$		−	125.777i		−	0.638461i	0.947677	−	0.319230i	$-0.103424\pi$
$198$		−	25.5684i		−	0.129133i
$199$			95.8567i			0.481692i	0.970563	+	0.240846i	$0.0774248\pi$
$199$			95.8567i			0.481692i	−0.970563	+	0.240846i	$0.922575\pi$
$200$	85.5153	−	187.670i	0.427576	−	0.938350i
$201$		−	118.316i		−	0.588638i
$202$	343.379			1.69989
$203$	10.3351	−	166.602i	0.0509116	−	0.820700i
$204$	−8.83725			−0.0433199
$205$	−56.3524	+	259.574i	−0.274890	+	1.26621i
$206$			215.274i			1.04502i
$207$			101.677i			0.491196i
$208$	−253.633			−1.21939
$209$			81.2465i			0.388739i
$210$	112.609	+	31.8616i	0.536232	+	0.151722i
$211$	−142.619			−0.675921			−0.337960	−	0.941160i	$-0.609737\pi$
$211$	−142.619			−0.675921			−0.337960	+	0.941160i	$0.609737\pi$
$212$			8.22273i			0.0387865i
$213$	25.3032			0.118795
$214$	−203.957			−0.953072
$215$	−7.92170	+	36.4894i	−0.0368451	+	0.169718i
$216$		−	42.8652i		−	0.198450i
$217$	−19.4883	−	1.20895i	−0.0898079	−	0.00557118i
$218$		−	63.2524i		−	0.290148i
$219$	−102.909			−0.469903
$220$	−5.89402	−	1.27957i	−0.0267910	−	0.00581622i
$221$	−319.319			−1.44488
$222$	206.600			0.930630
$223$	43.5475			0.195280			0.0976402	−	0.995222i	$-0.468871\pi$
$223$	43.5475			0.195280			0.0976402	+	0.995222i	$0.468871\pi$
$224$	−30.4882	−	1.89131i	−0.136108	−	0.00844337i
$225$	68.2486	+	31.0987i	0.303327	+	0.138217i
$226$	310.876			1.37556
$227$	47.4678			0.209109			0.104555	−	0.994519i	$-0.466658\pi$
$227$	47.4678			0.209109			0.104555	+	0.994519i	$0.466658\pi$
$228$			8.70915i			0.0381980i
$229$			290.936i			1.27046i	0.772322	+	0.635231i	$0.219095\pi$
$229$			290.936i			1.27046i	−0.772322	+	0.635231i	$0.780905\pi$
$230$	−319.698	−	69.4051i	−1.38999	−	0.301761i
$231$	3.31416	−	53.4245i	0.0143470	−	0.231275i
$232$		−	196.716i		−	0.847913i
$233$			353.736i			1.51818i	0.650986	+	0.759090i	$0.274356\pi$
$233$			353.736i			1.51818i	−0.650986	+	0.759090i	$0.725644\pi$
$234$		−	99.0334i		−	0.423220i
$235$	−216.771	−	47.0602i	−0.922432	−	0.200256i
$236$			5.45949i			0.0231334i
$237$	−99.2047			−0.418585
$238$	251.861	+	15.6240i	1.05824	+	0.0656472i
$239$	68.4356			0.286342			0.143171	−	0.989698i	$-0.454270\pi$
$239$	68.4356			0.286342			0.143171	+	0.989698i	$0.454270\pi$
$240$	125.529	+	27.2518i	0.523036	+	0.113549i
$241$			321.050i			1.33216i	0.745881	+	0.666079i	$0.232029\pi$
$241$			321.050i			1.33216i	−0.745881	+	0.666079i	$0.767971\pi$
$242$			195.962i			0.809760i
$243$	15.5885			0.0641500
$244$		−	17.6679i		−	0.0724095i
$245$	231.163	+	81.1703i	0.943523	+	0.331307i
$246$	−177.631			−0.722076
$247$			314.690i			1.27405i
$248$	−23.0109			−0.0927857
$249$	−170.291			−0.683902
$250$	−144.368	+	193.361i	−0.577473	+	0.773446i
$251$			17.8400i			0.0710757i	0.999368	+	0.0355379i	$0.0113144\pi$
$251$			17.8400i			0.0710757i	−0.999368	+	0.0355379i	$0.988686\pi$
$252$	0.355258	−	5.72679i	0.00140975	−	0.0227254i
$253$			149.630i			0.591424i
$254$	78.0770			0.307390
$255$	158.038	+	34.3094i	0.619756	+	0.134547i
$256$	−52.2095			−0.203943
$257$	−84.9101			−0.330389			−0.165195	−	0.986261i	$-0.552825\pi$
$257$	−84.9101			−0.330389			−0.165195	+	0.986261i	$0.552825\pi$
$258$	−24.9703			−0.0967841
$259$	431.685	+	26.7793i	1.66674	+	0.103395i
$260$	−22.8291	−	4.95612i	−0.0878044	−	0.0190620i
$261$	71.5382			0.274093
$262$	−210.726			−0.804298
$263$			250.775i			0.953517i	0.879034	+	0.476759i	$0.158188\pi$
$263$			250.775i			0.953517i	−0.879034	+	0.476759i	$0.841812\pi$
$264$		−	63.0811i		−	0.238943i
$265$	31.9236	−	147.048i	0.120466	−	0.554899i
$266$	15.3976	−	248.210i	0.0578856	−	0.933121i
$267$			111.976i			0.419385i
$268$		−	18.6642i		−	0.0696426i
$269$		−	290.639i		−	1.08044i	−0.841523	−	0.540221i	$-0.818341\pi$
$269$		−	290.639i		−	1.08044i	0.841523	−	0.540221i	$-0.181659\pi$
$270$	−10.6407	+	49.0137i	−0.0394100	+	0.181532i
$271$		−	345.145i		−	1.27360i	−0.771031	−	0.636798i	$-0.780259\pi$
$271$		−	345.145i		−	1.27360i	0.771031	−	0.636798i	$-0.219741\pi$
$272$	276.977			1.01830
$273$	12.8366	−	206.928i	0.0470206	−	0.757977i
$274$	−75.5736			−0.275816
$275$	100.436	+	45.7654i	0.365221	+	0.166420i
$276$			16.0395i			0.0581140i
$277$			205.335i			0.741282i	0.928776	+	0.370641i	$0.120862\pi$
$277$			205.335i			0.741282i	−0.928776	+	0.370641i	$0.879138\pi$
$278$	−213.035			−0.766312
$279$		−	8.36819i		−	0.0299935i
$280$	277.823	+	78.6074i	0.992223	+	0.280741i
$281$	113.887			0.405292			0.202646	−	0.979252i	$-0.435046\pi$
$281$	113.887			0.405292			0.202646	+	0.979252i	$0.435046\pi$
$282$		−	148.340i		−	0.526030i
$283$	83.0022			0.293294			0.146647	−	0.989189i	$-0.453152\pi$
$283$	83.0022			0.293294			0.146647	+	0.989189i	$0.453152\pi$
$284$	3.99155			0.0140548
$285$	33.8120	−	155.747i	0.118639	−	0.546480i
$286$		−	145.739i		−	0.509577i
$287$	−371.155	−	23.0244i	−1.29322	−	0.0802243i
$288$		−	13.0915i		−	0.0454565i
$289$	59.7074			0.206600
$290$	−48.8320	+	224.933i	−0.168386	+	0.775630i
$291$	316.800			1.08866
$292$	−16.2337			−0.0555949
$293$	−398.001			−1.35836			−0.679182	−	0.733970i	$-0.737665\pi$
$293$	−398.001			−1.35836			−0.679182	+	0.733970i	$0.737665\pi$
$294$	−20.2496	+	162.585i	−0.0688764	+	0.553010i
$295$	21.1957	−	97.6328i	0.0718499	−	0.330959i
$296$	509.713			1.72200
$297$	22.9402			0.0772398
$298$		−	81.9489i		−	0.274996i
$299$			579.559i			1.93832i
$300$	10.7661	+	4.90578i	0.0358871	+	0.0163526i
$301$	−52.1748	−	3.23663i	−0.173338	−	0.0107529i
$302$			88.4241i			0.292795i
$303$			308.083i			1.01678i
$304$		−	272.962i		−	0.897900i
$305$	−68.5932	+	315.958i	−0.224896	+	1.03593i
$306$			108.148i			0.353425i
$307$	475.513			1.54890			0.774452	−	0.632633i	$-0.218026\pi$
$307$	475.513			1.54890			0.774452	+	0.632633i	$0.218026\pi$
$308$	0.522803	−	8.42764i	0.00169741	−	0.0273625i
$309$	−193.146			−0.625068
$310$	26.3115	+	5.71213i	0.0848760	+	0.0184262i
$311$		−	447.956i		−	1.44037i	−0.693781	−	0.720186i	$-0.744056\pi$
$311$		−	447.956i		−	1.44037i	0.693781	−	0.720186i	$-0.255944\pi$
$312$		−	244.330i		−	0.783109i
$313$	−286.382			−0.914957			−0.457479	−	0.889221i	$-0.651247\pi$
$313$	−286.382			−0.914957			−0.457479	+	0.889221i	$0.651247\pi$
$314$			449.383i			1.43116i
$315$	−28.5866	+	101.034i	−0.0907510	+	0.320742i
$316$	−15.6494			−0.0495234
$317$		−	184.016i		−	0.580493i	−0.956952	−	0.290247i	$-0.906263\pi$
$317$		−	184.016i		−	0.580493i	0.956952	−	0.290247i	$-0.0937374\pi$
$318$	100.628			0.316439
$319$	105.277			0.330021
$320$	331.058	+	71.8715i	1.03456	+	0.224598i
$321$		−	182.993i		−	0.570071i
$322$	28.3574	−	457.124i	0.0880665	−	1.41964i
$323$		−	343.653i		−	1.06394i
$324$	2.45906			0.00758968
$325$	389.015	+	177.262i	1.19697	+	0.545421i
$326$	−543.883			−1.66835
$327$	56.7507			0.173549
$328$	−438.242			−1.33610
$329$	19.2278	−	309.953i	0.0584431	−	0.942108i
$330$	−15.6590	+	72.1294i	−0.0474516	+	0.218574i
$331$	−459.540			−1.38834			−0.694169	−	0.719812i	$-0.744228\pi$
$331$	−459.540			−1.38834			−0.694169	+	0.719812i	$0.744228\pi$
$332$	−26.8632			−0.0809134
$333$			185.364i			0.556647i
$334$		−	230.136i		−	0.689031i
$335$	−72.4612	+	333.775i	−0.216302	+	0.996342i
$336$	−11.1345	+	179.489i	−0.0331383	+	0.534192i
$337$		−	169.732i		−	0.503655i	−0.967772	−	0.251828i	$-0.918968\pi$
$337$		−	169.732i		−	0.503655i	0.967772	−	0.251828i	$-0.0810316\pi$
$338$		−	238.235i		−	0.704839i
$339$			278.921i			0.822777i
$340$	24.9302	+	5.41225i	0.0733242	+	0.0159184i
$341$		−	12.3148i		−	0.0361137i
$342$	106.580			0.311638
$343$	−63.3853	+	337.092i	−0.184797	+	0.982777i
$344$	−61.6055			−0.179086
$345$	62.2710	−	286.836i	0.180496	−	0.831409i
$346$		−	423.778i		−	1.22479i
$347$		−	319.866i		−	0.921805i	−0.887451	−	0.460902i	$-0.847526\pi$
$347$		−	319.866i		−	0.921805i	0.887451	−	0.460902i	$-0.152474\pi$
$348$	11.2850			0.0324283
$349$			38.4832i			0.110267i	0.998479	+	0.0551335i	$0.0175585\pi$
$349$			38.4832i			0.110267i	−0.998479	+	0.0551335i	$0.982442\pi$
$350$	−298.160	−	158.849i	−0.851886	−	0.453853i
$351$	88.8538			0.253145
$352$		−	19.2656i		−	0.0547319i
$353$	−70.1203			−0.198641			−0.0993206	−	0.995055i	$-0.531667\pi$
$353$	−70.1203			−0.198641			−0.0993206	+	0.995055i	$0.531667\pi$
$354$	66.8118			0.188734
$355$	−71.3814	−	15.4966i	−0.201074	−	0.0436525i
$356$			17.6640i			0.0496181i
$357$	−14.0181	+	225.972i	−0.0392662	+	0.632976i
$358$			325.481i			0.909164i
$359$	−477.223			−1.32931			−0.664656	−	0.747150i	$-0.731422\pi$
$359$	−477.223			−1.32931			−0.664656	+	0.747150i	$0.731422\pi$
$360$	−26.2522	+	120.924i	−0.0729227	+	0.335901i
$361$	22.3288			0.0618528
$362$	338.357			0.934687
$363$	−175.819			−0.484350
$364$	2.02496	−	32.6425i	0.00556308	−	0.0896773i
$365$	290.310	+	63.0251i	0.795369	+	0.172672i
$366$	−216.215			−0.590752
$367$	−488.938			−1.33226			−0.666128	−	0.745837i	$-0.732050\pi$
$367$	−488.938			−1.33226			−0.666128	+	0.745837i	$0.732050\pi$
$368$		−	502.708i		−	1.36605i
$369$		−	159.372i		−	0.431903i
$370$	−582.826	−	126.529i	−1.57521	−	0.341971i
$371$	210.259	+	13.0433i	0.566735	+	0.0351571i
$372$		−	1.32007i		−	0.00354858i
$373$		−	557.655i		−	1.49505i	−0.664231	−	0.747527i	$-0.731241\pi$
$373$		−	557.655i		−	1.49505i	0.664231	−	0.747527i	$-0.268759\pi$
$374$			159.152i			0.425541i
$375$	−173.486	−	129.529i	−0.462629	−	0.345410i
$376$		−	365.978i		−	0.973346i
$377$	407.766			1.08161
$378$	−70.0829	−	4.34755i	−0.185405	−	0.0115015i
$379$	148.891			0.392852			0.196426	−	0.980519i	$-0.437066\pi$
$379$	148.891			0.392852			0.196426	+	0.980519i	$0.437066\pi$
$380$	5.33380	−	24.5688i	0.0140363	−	0.0646548i
$381$			70.0515i			0.183862i
$382$		−	44.5918i		−	0.116732i
$383$	407.860			1.06491			0.532454	−	0.846459i	$-0.321270\pi$
$383$	407.860			1.06491			0.532454	+	0.846459i	$0.321270\pi$
$384$			196.316i			0.511238i
$385$	−42.0685	+	148.683i	−0.109269	+	0.386189i
$386$	−86.2141			−0.223353
$387$		−	22.4036i		−	0.0578905i
$388$	49.9747			0.128801
$389$	64.8289			0.166655			0.0833276	−	0.996522i	$-0.473445\pi$
$389$	64.8289			0.166655			0.0833276	+	0.996522i	$0.473445\pi$
$390$	−60.6516	+	279.377i	−0.155517	+	0.716351i
$391$		−	632.899i		−	1.61867i
$392$	−49.9589	+	401.122i	−0.127446	+	1.02327i
$393$		−	189.066i		−	0.481083i
$394$	−242.810			−0.616269
$395$	279.860	+	60.7566i	0.708507	+	0.153814i
$396$	3.61879			0.00913835
$397$	155.102			0.390686			0.195343	−	0.980735i	$-0.437418\pi$
$397$	155.102			0.390686			0.195343	+	0.980735i	$0.437418\pi$
$398$	185.050			0.464949
$399$	222.697	+	13.8149i	0.558137	+	0.0346237i
$400$	−337.431	−	153.757i	−0.843577	−	0.384391i
$401$	−74.3684			−0.185457			−0.0927287	−	0.995691i	$-0.529559\pi$
$401$	−74.3684			−0.185457			−0.0927287	+	0.995691i	$0.529559\pi$
$402$	−228.408			−0.568178
$403$		−	47.6985i		−	0.118358i
$404$			48.5996i			0.120296i
$405$	−43.9756	−	9.54694i	−0.108582	−	0.0235727i
$406$	−321.623	−	19.9517i	−0.792175	−	0.0491421i
$407$			272.784i			0.670231i
$408$			266.817i			0.653964i
$409$			492.571i			1.20433i	0.798371	+	0.602166i	$0.205695\pi$
$409$			492.571i			1.20433i	−0.798371	+	0.602166i	$0.794305\pi$
$410$	501.103	+	108.788i	1.22220	+	0.265335i
$411$		−	67.8054i		−	0.164977i
$412$	−30.4685			−0.0739527
$413$	139.602	+	8.66010i	0.338018	+	0.0209688i
$414$	196.287			0.474123
$415$	480.399	+	104.293i	1.15759	+	0.251308i
$416$		−	74.6210i		−	0.179378i
$417$		−	191.137i		−	0.458362i
$418$	156.845			0.375228
$419$		−	67.0479i		−	0.160019i	−0.996794	−	0.0800095i	$-0.974505\pi$
$419$		−	67.0479i		−	0.160019i	0.996794	−	0.0800095i	$-0.0254951\pi$
$420$	−4.50949	+	15.9379i	−0.0107369	+	0.0379474i
$421$	281.153			0.667822			0.333911	−	0.942605i	$-0.391632\pi$
$421$	281.153			0.667822			0.333911	+	0.942605i	$0.391632\pi$
$422$			275.324i			0.652427i
$423$	133.093			0.314640
$424$	248.263			0.585527
$425$	−424.818	−	193.576i	−0.999572	−	0.455473i
$426$		−	48.8475i		−	0.114666i
$427$	−451.776	−	28.0257i	−1.05802	−	0.0656339i
$428$		−	28.8668i		−	0.0674458i
$429$	130.759			0.304799
$430$	70.4422	+	15.2927i	0.163819	+	0.0355645i
$431$	522.073			1.21131			0.605653	−	0.795729i	$-0.292912\pi$
$431$	522.073			1.21131			0.605653	+	0.795729i	$0.292912\pi$
$432$	−77.0716			−0.178406
$433$	719.737			1.66221			0.831105	−	0.556115i	$-0.187709\pi$
$433$	719.737			1.66221			0.831105	+	0.556115i	$0.187709\pi$
$434$	−2.33385	+	37.6219i	−0.00537754	+	0.0866864i
$435$	−201.812	−	43.8126i	−0.463935	−	0.100719i
$436$	8.95233			0.0205329
$437$	−623.724			−1.42729
$438$			198.664i			0.453571i
$439$		−	279.517i		−	0.636713i	−0.947971	−	0.318356i	$-0.896869\pi$
$439$		−	279.517i		−	0.636713i	0.947971	−	0.318356i	$-0.103131\pi$
$440$	−38.6331	+	177.954i	−0.0878026	+	0.404441i
$441$	−145.873	−	18.1682i	−0.330778	−	0.0411977i
$442$			616.440i			1.39466i
$443$		−	177.382i		−	0.400412i	−0.979754	−	0.200206i	$-0.935839\pi$
$443$		−	177.382i		−	0.400412i	0.979754	−	0.200206i	$-0.0641611\pi$
$444$			29.2408i			0.0658577i
$445$	68.5781	−	315.888i	0.154108	−	0.709861i
$446$		−	84.0678i		−	0.188493i
$447$	73.5254			0.164486
$448$	−29.3651	+	473.368i	−0.0655471	+	1.05663i
$449$	488.199			1.08730			0.543651	−	0.839311i	$-0.317041\pi$
$449$	488.199			1.08730			0.543651	+	0.839311i	$0.317041\pi$
$450$	60.0356	−	131.753i	0.133412	−	0.292784i
$451$		−	234.535i		−	0.520032i
$452$			43.9994i			0.0973439i
$453$	−79.3350			−0.175132
$454$		−	91.6358i		−	0.201841i
$455$	−162.943	+	575.889i	−0.358116	+	1.26569i
$456$	262.949			0.576643
$457$		−	325.536i		−	0.712332i	−0.934423	−	0.356166i	$-0.884084\pi$
$457$		−	325.536i		−	0.712332i	0.934423	−	0.356166i	$-0.115916\pi$
$458$	561.648			1.22630
$459$	−97.0314			−0.211397
$460$	9.82316	−	45.2480i	0.0213547	−	0.0983651i
$461$			342.259i			0.742428i	0.928547	+	0.371214i	$0.121058\pi$
$461$			342.259i			0.742428i	−0.928547	+	0.371214i	$0.878942\pi$
$462$	−103.135	−	6.39793i	−0.223236	−	0.0138483i
$463$			605.535i			1.30785i	0.756559	+	0.653925i	$0.226879\pi$
$463$			605.535i			1.30785i	−0.756559	+	0.653925i	$0.773121\pi$
$464$	−353.695			−0.762274
$465$	−5.12499	+	23.6070i	−0.0110215	+	0.0507677i
$466$	682.881			1.46541
$467$	−229.357			−0.491128			−0.245564	−	0.969380i	$-0.578973\pi$
$467$	−229.357			−0.491128			−0.245564	+	0.969380i	$0.578973\pi$
$468$	14.0166			0.0299499
$469$	−477.252	−	29.6060i	−1.01760	−	0.0631259i
$470$	−90.8491	+	418.474i	−0.193296	+	0.890370i
$471$	−403.191			−0.856032
$472$	164.835			0.349226
$473$		−	32.9695i		−	0.0697030i
$474$			191.513i			0.404036i
$475$	−190.770	+	418.660i	−0.401621	+	0.881390i
$476$	−2.21133	+	35.6468i	−0.00464565	+	0.0748882i
$477$			90.2841i			0.189275i
$478$		−	132.114i		−	0.276389i
$479$		−	114.588i		−	0.239222i	−0.992821	−	0.119611i	$-0.961835\pi$
$479$		−	114.588i		−	0.239222i	0.992821	−	0.119611i	$-0.0381648\pi$
$480$	−8.01770	+	36.9316i	−0.0167035	+	0.0769407i
$481$			1056.57i			2.19661i
$482$	619.782			1.28585
$483$	410.136	+	25.4425i	0.849143	+	0.0526761i
$484$	−27.7352			−0.0573041
$485$	−893.704	−	194.020i	−1.84269	−	0.400041i
$486$		−	30.0933i		−	0.0619203i
$487$			582.868i			1.19685i	0.801177	+	0.598427i	$0.204207\pi$
$487$			582.868i			1.19685i	−0.801177	+	0.598427i	$0.795793\pi$
$488$	−533.436			−1.09311
$489$		−	487.977i		−	0.997908i
$490$	156.698	−	446.257i	0.319792	−	0.910728i
$491$	−874.580			−1.78122			−0.890611	−	0.454765i	$-0.849723\pi$
$491$	−874.580			−1.78122			−0.890611	+	0.454765i	$0.849723\pi$
$492$		−	25.1407i		−	0.0510990i
$493$	−445.294			−0.903234
$494$	607.504			1.22977
$495$	−64.7152	−	14.0494i	−0.130738	−	0.0283827i
$496$			41.3735i			0.0834144i
$497$	6.33158	−	102.066i	0.0127396	−	0.205363i
$498$			328.745i			0.660131i
$499$	−701.389			−1.40559			−0.702794	−	0.711393i	$-0.748065\pi$
$499$	−701.389			−1.40559			−0.702794	+	0.711393i	$0.748065\pi$
$500$	−27.3671	−	20.4329i	−0.0547343	−	0.0408659i
$501$	206.481			0.412137
$502$	34.4399			0.0686053
$503$	−201.284			−0.400167			−0.200084	−	0.979779i	$-0.564121\pi$
$503$	−201.284			−0.400167			−0.200084	+	0.979779i	$0.564121\pi$
$504$	−172.905	−	10.7261i	−0.343066	−	0.0212819i
$505$	188.681	−	869.114i	0.373626	−	1.72102i
$506$	288.859			0.570867
$507$	213.747			0.421592
$508$			11.0505i			0.0217530i
$509$		−	212.090i		−	0.416680i	−0.978056	−	0.208340i	$-0.933194\pi$
$509$		−	212.090i		−	0.416680i	0.978056	−	0.208340i	$-0.0668061\pi$
$510$	66.2337	−	305.089i	0.129870	−	0.598215i
$511$	−25.7507	+	415.103i	−0.0503927	+	0.812335i
$512$			554.161i			1.08235i
$513$			95.6249i			0.186403i
$514$			163.918i			0.318906i
$515$	544.872	+	118.290i	1.05800	+	0.229689i
$516$		−	3.53414i		−	0.00684910i
$517$	195.861			0.378842
$518$	51.6971	−	833.362i	0.0998013	−	1.60881i
$519$	380.218			0.732598
$520$	−149.637	+	689.265i	−0.287763	+	1.32551i
$521$		−	803.441i		−	1.54211i	−0.636766	−	0.771057i	$-0.719728\pi$
$521$		−	803.441i		−	1.54211i	0.636766	−	0.771057i	$-0.280272\pi$
$522$		−	138.103i		−	0.264566i
$523$	931.800			1.78164			0.890822	−	0.454352i	$-0.150129\pi$
$523$	931.800			1.78164			0.890822	+	0.454352i	$0.150129\pi$
$524$		−	29.8248i		−	0.0569176i
$525$	142.521	−	267.512i	0.271468	−	0.509547i
$526$	484.117			0.920375
$527$			52.0884i			0.0988395i
$528$	−113.420			−0.214810
$529$	−619.701			−1.17146
$530$	−283.874	−	61.6280i	−0.535612	−	0.116279i
$531$			59.9443i			0.112889i
$532$	35.1301	+	2.17927i	0.0660340	+	0.00409638i
$533$		−	908.417i		−	1.70435i
$534$	216.168			0.404809
$535$	−112.071	+	516.229i	−0.209479	+	0.964914i
$536$	−563.516			−1.05134
$537$	−292.025			−0.543807
$538$	−561.074			−1.04289
$539$	−214.669	−	26.7366i	−0.398273	−	0.0496041i
$540$	−6.93709	−	1.50602i	−0.0128465	−	0.00278892i
$541$	−223.137			−0.412452			−0.206226	−	0.978504i	$-0.566118\pi$
$541$	−223.137			−0.412452			−0.206226	+	0.978504i	$0.566118\pi$
$542$	−666.296			−1.22933
$543$			303.577i			0.559074i
$544$			81.4888i			0.149796i
$545$	−160.096	−	34.7562i	−0.293754	−	0.0637728i
$546$	−399.471	−	24.7809i	−0.731631	−	0.0453863i
$547$		−	793.104i		−	1.44992i	−0.688793	−	0.724958i	$-0.741859\pi$
$547$		−	793.104i		−	1.44992i	0.688793	−	0.724958i	$-0.258141\pi$
$548$		−	10.6962i		−	0.0195186i
$549$		−	193.991i		−	0.353353i
$550$	88.3494	−	193.890i	0.160635	−	0.352527i
$551$			438.840i			0.796442i
$552$	484.269			0.877299
$553$	−24.8238	+	400.162i	−0.0448893	+	0.723620i
$554$	396.396			0.715517
$555$	113.523	−	522.918i	0.204547	−	0.942194i
$556$		−	30.1516i		−	0.0542294i
$557$		−	516.090i		−	0.926553i	−0.886214	−	0.463277i	$-0.846674\pi$
$557$		−	516.090i		−	0.926553i	0.886214	−	0.463277i	$-0.153326\pi$
$558$	−16.1547			−0.0289510
$559$		−	127.700i		−	0.228444i
$560$	141.336	−	499.525i	0.252386	−	0.892009i
$561$	−142.793			−0.254533
$562$		−	219.857i		−	0.391205i
$563$	−408.888			−0.726266			−0.363133	−	0.931737i	$-0.618293\pi$
$563$	−408.888			−0.726266			−0.363133	+	0.931737i	$0.618293\pi$
$564$	20.9952			0.0372255
$565$	170.822	−	786.847i	0.302339	−	1.39265i
$566$		−	160.234i		−	0.283100i
$567$	3.90067	−	62.8791i	0.00687948	−	0.110898i
$568$		−	120.514i		−	0.212173i
$569$	16.5028			0.0290031			0.0145016	−	0.999895i	$-0.495384\pi$
$569$	16.5028			0.0290031			0.0145016	+	0.999895i	$0.495384\pi$
$570$	−300.667	−	65.2736i	−0.527486	−	0.114515i
$571$	817.072			1.43095			0.715475	−	0.698639i	$-0.246210\pi$
$571$	817.072			1.43095			0.715475	+	0.698639i	$0.246210\pi$
$572$	20.6270			0.0360612
$573$	40.0082			0.0698223
$574$	−44.4482	+	716.509i	−0.0774358	+	1.24827i
$575$	−351.338	+	771.038i	−0.611022	+	1.34094i
$576$	−203.262			−0.352886
$577$	656.728			1.13818			0.569088	−	0.822276i	$-0.307296\pi$
$577$	656.728			1.13818			0.569088	+	0.822276i	$0.307296\pi$
$578$		−	115.264i		−	0.199419i
$579$		−	77.3522i		−	0.133596i
$580$	−31.8355	−	6.91137i	−0.0548889	−	0.0119162i
$581$	−42.6117	+	686.904i	−0.0733420	+	1.18228i
$582$		−	611.577i		−	1.05082i
$583$			132.864i			0.227896i
$584$			490.134i			0.839270i
$585$	−250.660	−	54.4173i	−0.428478	−	0.0930210i
$586$			768.334i			1.31115i
$587$	−491.065			−0.836567			−0.418283	−	0.908317i	$-0.637368\pi$
$587$	−491.065			−0.836567			−0.418283	+	0.908317i	$0.637368\pi$
$588$	−23.0112	−	2.86601i	−0.0391348	−	0.00487416i
$589$	51.3333			0.0871534
$590$	−188.479	−	40.9180i	−0.319455	−	0.0693525i
$591$		−	217.852i		−	0.368615i
$592$		−	916.464i		−	1.54808i
$593$	−502.906			−0.848071			−0.424036	−	0.905645i	$-0.639387\pi$
$593$	−502.906			−0.848071			−0.424036	+	0.905645i	$0.639387\pi$
$594$		−	44.2858i		−	0.0745551i
$595$	177.939	−	628.891i	0.299057	−	1.05696i
$596$	11.5985			0.0194606
$597$			166.029i			0.278105i
$598$	1118.83			1.87095
$599$	1069.00			1.78464			0.892318	−	0.451407i	$-0.149078\pi$
$599$	1069.00			1.78464			0.892318	+	0.451407i	$0.149078\pi$
$600$	148.117	−	325.054i	0.246861	−	0.541757i
$601$			1129.40i			1.87921i	0.342267	+	0.939603i	$0.388805\pi$
$601$			1129.40i			1.87921i	−0.342267	+	0.939603i	$0.611195\pi$
$602$	−6.24827	+	100.723i	−0.0103792	+	0.167313i
$603$		−	204.930i		−	0.339850i
$604$	−12.5150			−0.0207202
$605$	495.992	+	107.678i	0.819821	+	0.177980i
$606$	594.749			0.981435
$607$	581.462			0.957927			0.478963	−	0.877835i	$-0.341013\pi$
$607$	581.462			0.957927			0.478963	+	0.877835i	$0.341013\pi$
$608$	80.3076			0.132085
$609$	17.9009	−	288.563i	0.0293938	−	0.473832i
$610$	609.952	+	132.418i	0.999921	+	0.217079i
$611$	758.624			1.24161
$612$	−15.3066			−0.0250107
$613$		−	532.436i		−	0.868574i	−0.900775	−	0.434287i	$-0.857000\pi$
$613$		−	532.436i		−	0.868574i	0.900775	−	0.434287i	$-0.143000\pi$
$614$		−	917.971i		−	1.49507i
$615$	−97.6053	+	449.595i	−0.158708	+	0.731048i
$616$	−254.450	−	15.7846i	−0.413068	−	0.0256244i
$617$		−	767.792i		−	1.24439i	−0.782860	−	0.622197i	$-0.786240\pi$
$617$		−	767.792i		−	1.24439i	0.782860	−	0.622197i	$-0.213760\pi$
$618$			372.865i			0.603342i
$619$		−	134.721i		−	0.217642i	−0.994061	−	0.108821i	$-0.965292\pi$
$619$		−	134.721i		−	0.217642i	0.994061	−	0.108821i	$-0.0347076\pi$
$620$	−0.808459	+	3.72397i	−0.00130397	+	0.00600640i
$621$			176.111i			0.283592i
$622$	−864.772			−1.39031
$623$	451.677	+	28.0195i	0.725003	+	0.0449751i
$624$	−439.306			−0.704016
$625$	410.082	+	471.654i	0.656132	+	0.754647i
$626$			552.855i			0.883156i
$627$			140.723i			0.224439i
$628$	−63.6028			−0.101278
$629$		−	1153.81i		−	1.83435i
$630$	195.044	+	55.1859i	0.309594	+	0.0875967i
$631$	−523.600			−0.829793			−0.414897	−	0.909869i	$-0.636182\pi$
$631$	−523.600			−0.829793			−0.414897	+	0.909869i	$0.636182\pi$
$632$			472.492i			0.747614i
$633$	−247.024			−0.390243
$634$	−355.241			−0.560317
$635$	42.9021	−	197.618i	0.0675623	−	0.311209i
$636$			14.2422i			0.0223934i
$637$	−831.472	−	103.558i	−1.30529	−	0.162572i
$638$		−	203.235i		−	0.318550i
$639$	43.8265			0.0685861
$640$	120.231	−	553.814i	0.187861	−	0.865334i
$641$	−849.495			−1.32526			−0.662632	−	0.748945i	$-0.730561\pi$
$641$	−849.495			−1.32526			−0.662632	+	0.748945i	$0.730561\pi$
$642$	−353.265			−0.550256
$643$	−1132.67			−1.76153			−0.880766	−	0.473552i	$-0.842972\pi$
$643$	−1132.67			−1.76153			−0.880766	+	0.473552i	$0.842972\pi$
$644$	64.6984	+	4.01352i	0.100463	+	0.00623218i
$645$	−13.7208	+	63.2014i	−0.0212725	+	0.0979867i
$646$	−663.416			−1.02696
$647$	786.565			1.21571			0.607856	−	0.794048i	$-0.292030\pi$
$647$	786.565			1.21571			0.607856	+	0.794048i	$0.292030\pi$
$648$		−	74.2446i		−	0.114575i
$649$			88.2149i			0.135924i
$650$	342.201	−	750.988i	0.526463	−	1.15537i
$651$	−33.7548	−	2.09396i	−0.0518506	−	0.00321652i
$652$		−	76.9777i		−	0.118064i
$653$			540.284i			0.827388i	0.910416	+	0.413694i	$0.135762\pi$
$653$			540.284i			0.827388i	−0.910416	+	0.413694i	$0.864238\pi$
$654$		−	109.556i		−	0.167517i
$655$	−115.791	+	533.361i	−0.176780	+	0.814292i
$656$			787.959i			1.20116i
$657$	−178.243			−0.271299
$658$	−598.360	−	37.1189i	−0.909362	−	0.0564117i
$659$	−742.966			−1.12741			−0.563707	−	0.825975i	$-0.690625\pi$
$659$	−742.966			−1.12741			−0.563707	+	0.825975i	$0.690625\pi$
$660$	−10.2087	−	2.21628i	−0.0154678	−	0.00335800i
$661$		−	54.1922i		−	0.0819852i	−0.999159	−	0.0409926i	$-0.986948\pi$
$661$		−	54.1922i		−	0.0819852i	0.999159	−	0.0409926i	$-0.0130520\pi$
$662$			887.135i			1.34008i
$663$	−553.076			−0.834203
$664$			811.063i			1.22148i
$665$	−619.775	−	175.360i	−0.931993	−	0.263699i
$666$	357.842			0.537300
$667$			808.202i			1.21170i
$668$	32.5720			0.0487605
$669$	75.4265			0.112745
$670$	644.347	+	139.885i	0.961712	+	0.208784i
$671$		−	285.480i		−	0.425454i
$672$	−52.8071	−	3.27585i	−0.0785819	−	0.00487478i
$673$			571.161i			0.848680i	0.905503	+	0.424340i	$0.139494\pi$
$673$			571.161i			0.848680i	−0.905503	+	0.424340i	$0.860506\pi$
$674$	−327.665			−0.486149
$675$	118.210	+	53.8646i	0.175126	+	0.0797993i
$676$	33.7183			0.0498792
$677$	602.915			0.890568			0.445284	−	0.895389i	$-0.353103\pi$
$677$	602.915			0.890568			0.445284	+	0.895389i	$0.353103\pi$
$678$	538.453			0.794179
$679$	79.2721	−	1277.87i	0.116748	−	1.88199i
$680$	163.409	−	752.701i	0.240307	−	1.10691i
$681$	82.2166			0.120729
$682$	−23.7735			−0.0348585
$683$		−	209.345i		−	0.306508i	−0.988187	−	0.153254i	$-0.951025\pi$
$683$		−	209.345i		−	0.306508i	0.988187	−	0.153254i	$-0.0489752\pi$
$684$			15.0847i			0.0220536i
$685$	−41.5265	+	191.282i	−0.0606227	+	0.279243i
$686$	650.752	+	122.364i	0.948618	+	0.178374i
$687$			503.916i			0.733502i
$688$			110.767i			0.160998i
$689$			514.617i			0.746904i
$690$	−553.733	−	120.213i	−0.802511	−	0.174222i
$691$		−	1172.79i		−	1.69723i	−0.529012	−	0.848614i	$-0.677437\pi$
$691$		−	1172.79i		−	1.69723i	0.529012	−	0.848614i	$-0.322563\pi$
$692$	59.9789			0.0866747
$693$	5.74029	−	92.5339i	0.00828324	−	0.133527i
$694$	−617.497			−0.889765
$695$	−117.059	+	539.204i	−0.168430	+	0.775834i
$696$		−	340.722i		−	0.489543i
$697$			992.023i			1.42328i
$698$	74.2912			0.106434
$699$			612.688i			0.876521i
$700$	22.4824	−	42.1997i	0.0321177	−	0.0602853i
$701$	971.815			1.38633			0.693163	−	0.720781i	$-0.256217\pi$
$701$	971.815			1.38633			0.693163	+	0.720781i	$0.256217\pi$
$702$		−	171.531i		−	0.244346i
$703$	−1137.08			−1.61747
$704$	−299.124			−0.424892
$705$	−375.459	−	81.5107i	−0.532566	−	0.115618i
$706$			135.366i			0.191737i
$707$	1242.71	+	77.0910i	1.75773	+	0.109040i
$708$			9.45612i			0.0133561i
$709$	1208.71			1.70481			0.852404	−	0.522884i	$-0.175144\pi$
$709$	1208.71			1.70481			0.852404	+	0.522884i	$0.175144\pi$
$710$	−29.9160	+	137.801i	−0.0421352	+	0.194086i
$711$	−171.828			−0.241670
$712$	533.318			0.749043
$713$	94.5396			0.132594
$714$	436.236	+	27.0616i	0.610975	+	0.0379014i
$715$	−368.875	−	80.0814i	−0.515909	−	0.112002i
$716$	−46.0664			−0.0643386
$717$	118.534			0.165319
$718$			921.271i			1.28311i
$719$			90.6345i			0.126056i	0.998012	+	0.0630282i	$0.0200758\pi$
$719$			90.6345i			0.126056i	−0.998012	+	0.0630282i	$0.979924\pi$
$720$	217.422	+	47.2014i	0.301975	+	0.0655576i
$721$	−48.3305	+	779.093i	−0.0670326	+	1.08057i
$722$		−	43.1055i		−	0.0597029i
$723$			556.075i			0.769121i
$724$			47.8888i			0.0661448i
$725$	542.487	+	247.194i	0.748257	+	0.340957i
$726$			339.416i			0.467515i
$727$	640.742			0.881351			0.440676	−	0.897666i	$-0.354739\pi$
$727$	640.742			0.881351			0.440676	+	0.897666i	$0.354739\pi$
$728$	−985.554	−	61.1382i	−1.35378	−	0.0839811i
$729$	27.0000			0.0370370
$730$	121.669	−	560.438i	0.166670	−	0.767724i
$731$			139.453i			0.190770i
$732$		−	30.6017i		−	0.0418056i
$733$	416.075			0.567632			0.283816	−	0.958879i	$-0.408399\pi$
$733$	416.075			0.567632			0.283816	+	0.958879i	$0.408399\pi$
$734$			943.887i			1.28595i
$735$	400.386	+	140.591i	0.544743	+	0.191280i
$736$	147.901			0.200952
$737$		−	301.578i		−	0.409197i
$738$	−307.665			−0.416891
$739$	422.001			0.571043			0.285522	−	0.958372i	$-0.407833\pi$
$739$	422.001			0.571043			0.285522	+	0.958372i	$0.407833\pi$
$740$	17.9082	−	82.4895i	0.0242002	−	0.111472i
$741$			545.059i			0.735572i
$742$	25.1798	−	405.901i	0.0339351	−	0.547037i
$743$			502.909i			0.676862i	0.940991	+	0.338431i	$0.109896\pi$
$743$			502.909i			0.676862i	−0.940991	+	0.338431i	$0.890104\pi$
$744$	−39.8560			−0.0535699
$745$	−207.418	−	45.0296i	−0.278413	−	0.0604424i
$746$	−1076.54			−1.44309
$747$	−294.954			−0.394851
$748$	−22.5254			−0.0301142
$749$	−738.137	−	45.7899i	−0.985497	−	0.0611347i
$750$	−250.053	+	334.912i	−0.333404	+	0.446549i
$751$	544.242			0.724689			0.362345	−	0.932044i	$-0.381976\pi$
$751$	544.242			0.724689			0.362345	+	0.932044i	$0.381976\pi$
$752$	−658.029			−0.875038
$753$			30.8998i			0.0410356i
$754$		−	787.185i		−	1.04401i
$755$	223.807	+	48.5876i	0.296433	+	0.0643545i
$756$	0.615325	−	9.91909i	0.000813921	−	0.0131205i
$757$			145.240i			0.191863i	0.995388	+	0.0959316i	$0.0305830\pi$
$757$			145.240i			0.191863i	−0.995388	+	0.0959316i	$0.969417\pi$
$758$		−	287.432i		−	0.379197i
$759$			259.167i			0.341459i
$760$	−741.790	−	161.040i	−0.976040	−	0.211894i
$761$			875.755i			1.15079i	0.817874	+	0.575397i	$0.195153\pi$
$761$			875.755i			1.15079i	−0.817874	+	0.575397i	$0.804847\pi$
$762$	135.233			0.177471
$763$	14.2006	−	228.915i	0.0186115	−	0.300020i
$764$	6.31124			0.00826078
$765$	273.729	+	59.4256i	0.357816	+	0.0776805i
$766$		−	787.367i		−	1.02789i
$767$			341.681i			0.445477i
$768$	−90.4296			−0.117747
$769$		−	790.946i		−	1.02854i	−0.857629	−	0.514269i	$-0.828063\pi$
$769$		−	790.946i		−	1.02854i	0.857629	−	0.514269i	$-0.171937\pi$
$770$	287.030	+	81.2125i	0.372766	+	0.105471i
$771$	−147.069			−0.190750
$772$		−	12.2022i		−	0.0158060i
$773$	243.540			0.315059			0.157529	−	0.987514i	$-0.449647\pi$
$773$	243.540			0.315059			0.157529	+	0.987514i	$0.449647\pi$
$774$	−43.2498			−0.0558783
$775$	28.9156	−	63.4575i	0.0373104	−	0.0818806i
$776$		−	1508.85i		−	1.94440i
$777$	747.701	+	46.3831i	0.962292	+	0.0596952i
$778$		−	125.151i		−	0.160863i
$779$	977.643			1.25500
$780$	−39.5412	−	8.58425i	−0.0506939	−	0.0110054i
$781$	64.4958			0.0825810
$782$	−1221.80			−1.56241
$783$	123.908			0.158247
$784$	721.217	+	89.8262i	0.919919	+	0.114574i
$785$	1137.42	+	246.929i	1.44894	+	0.314559i
$786$	−364.988			−0.464362
$787$	−411.660			−0.523075			−0.261538	−	0.965193i	$-0.584230\pi$
$787$	−411.660			−0.523075			−0.261538	+	0.965193i	$0.584230\pi$
$788$		−	34.3658i		−	0.0436114i
$789$			434.355i			0.550513i
$790$	117.290	−	540.266i	0.148468	−	0.683881i
$791$	1125.08	+	69.7939i	1.42236	+	0.0882350i
$792$		−	109.260i		−	0.137954i
$793$		−	1105.74i		−	1.39438i
$794$		−	299.423i		−	0.377107i
$795$	55.2933	−	254.695i	0.0695513	−	0.320371i
$796$			26.1908i			0.0329030i
$797$	−160.324			−0.201159			−0.100579	−	0.994929i	$-0.532070\pi$
$797$	−160.324			−0.201159			−0.100579	+	0.994929i	$0.532070\pi$
$798$	26.6694	−	429.913i	0.0334202	−	0.538738i
$799$	−828.444			−1.03685
$800$	45.2365	−	99.2750i	0.0565456	−	0.124094i
$801$			193.948i			0.242132i
$802$			143.567i			0.179011i
$803$	−262.306			−0.326657
$804$		−	32.3274i		−	0.0402082i
$805$	−1141.43	−	322.957i	−1.41792	−	0.401189i
$806$	−92.0812			−0.114245
$807$		−	503.402i		−	0.623794i
$808$	1467.34			1.81601
$809$	−798.455			−0.986965			−0.493483	−	0.869756i	$-0.664276\pi$
$809$	−798.455			−0.986965			−0.493483	+	0.869756i	$0.664276\pi$
$810$	−18.4302	+	84.8943i	−0.0227534	+	0.104808i
$811$		−	655.202i		−	0.807895i	−0.914782	−	0.403947i	$-0.867638\pi$
$811$		−	655.202i		−	0.807895i	0.914782	−	0.403947i	$-0.132362\pi$
$812$	2.82383	−	45.5205i	0.00347763	−	0.0560597i
$813$		−	597.808i		−	0.735311i
$814$	526.605			0.646935
$815$	−298.855	+	1376.60i	−0.366693	+	1.68908i
$816$	479.737			0.587913
$817$	137.431			0.168215
$818$	950.902			1.16247
$819$	22.2337	−	358.409i	0.0271474	−	0.437618i
$820$	−15.3971	+	70.9229i	−0.0187769	+	0.0864914i
$821$	518.401			0.631426			0.315713	−	0.948855i	$-0.397756\pi$
$821$	518.401			0.631426			0.315713	+	0.948855i	$0.397756\pi$
$822$	−130.897			−0.159243
$823$		−	475.494i		−	0.577757i	−0.957366	−	0.288879i	$-0.906718\pi$
$823$		−	475.494i		−	0.577757i	0.957366	−	0.288879i	$-0.0932824\pi$
$824$			919.915i			1.11640i
$825$	173.960	+	79.2679i	0.210860	+	0.0960824i
$826$	16.7182	−	269.499i	0.0202399	−	0.326270i
$827$			200.944i			0.242979i	0.992593	+	0.121490i	$0.0387671\pi$
$827$			200.944i			0.242979i	−0.992593	+	0.121490i	$0.961233\pi$
$828$			27.7812i			0.0335522i
$829$		−	1050.24i		−	1.26688i	−0.773791	−	0.633441i	$-0.781642\pi$
$829$		−	1050.24i		−	1.26688i	0.773791	−	0.633441i	$-0.218358\pi$
$830$	201.336	−	927.403i	0.242573	−	1.11735i
$831$			355.651i			0.427979i
$832$	−1158.59			−1.39253
$833$	907.996	+	113.089i	1.09003	+	0.135761i
$834$	−368.987			−0.442430
$835$	−582.490	−	126.456i	−0.697592	−	0.151445i
$836$			22.1989i			0.0265537i
$837$		−	14.4941i		−	0.0173168i
$838$	−129.435			−0.154457
$839$		−	226.552i		−	0.270026i	−0.990844	−	0.135013i	$-0.956892\pi$
$839$		−	226.552i		−	0.270026i	0.990844	−	0.135013i	$-0.0431077\pi$
$840$	481.203	+	136.152i	0.572860	+	0.162086i
$841$	−272.365			−0.323859
$842$		−	542.762i		−	0.644610i
$843$	197.258			0.233995
$844$	−38.9676			−0.0461702
$845$	−602.989	−	130.907i	−0.713597	−	0.154919i
$846$		−	256.933i		−	0.303703i
$847$	−43.9948	+	709.201i	−0.0519419	+	0.837309i
$848$		−	446.378i		−	0.526389i
$849$	143.764			0.169333
$850$	−373.696	+	820.105i	−0.439642	+	0.964829i
$851$	−2094.14			−2.46080
$852$	6.91357			0.00811451
$853$	387.766			0.454591			0.227295	−	0.973826i	$-0.427012\pi$
$853$	387.766			0.454591			0.227295	+	0.973826i	$0.427012\pi$
$854$	−54.1031	+	872.147i	−0.0633526	+	1.02125i
$855$	58.5642	−	269.761i	0.0684961	−	0.315510i
$856$	−871.556			−1.01817
$857$	496.415			0.579248			0.289624	−	0.957141i	$-0.406470\pi$
$857$	496.415			0.579248			0.289624	+	0.957141i	$0.406470\pi$
$858$		−	252.428i		−	0.294205i
$859$			654.574i			0.762018i	0.924571	+	0.381009i	$0.124423\pi$
$859$			654.574i			0.762018i	−0.924571	+	0.381009i	$0.875577\pi$
$860$	−2.16443	+	9.96993i	−0.00251678	+	0.0115929i
$861$	−642.859	−	39.8794i	−0.746642	−	0.0463175i
$862$		−	1007.85i		−	1.16920i
$863$			46.8424i			0.0542785i	0.999632	+	0.0271393i	$0.00863976\pi$
$863$			46.8424i			0.0542785i	−0.999632	+	0.0271393i	$0.991360\pi$
$864$		−	22.6751i		−	0.0262443i
$865$	−1072.61	−	232.860i	−1.24001	−	0.269202i
$866$		−	1389.44i		−	1.60444i
$867$	103.416			0.119281
$868$	−5.32476	−	0.330318i	−0.00613452	−	0.000380551i
$869$	−252.864			−0.290983
$870$	−84.5795	+	389.595i	−0.0972179	+	0.447810i
$871$		−	1168.09i		−	1.34110i
$872$		−	270.292i		−	0.309968i
$873$	548.713			0.628537
$874$			1204.09i			1.37768i
$875$	−565.890	+	667.378i	−0.646732	+	0.762718i
$876$	−28.1176			−0.0320977
$877$			249.527i			0.284523i	0.989829	+	0.142262i	$0.0454375\pi$
$877$			249.527i			0.284523i	−0.989829	+	0.142262i	$0.954563\pi$
$878$	−539.603			−0.614582
$879$	−689.358			−0.784252
$880$	319.961	+	69.4624i	0.363593	+	0.0789346i
$881$		−	17.6465i		−	0.0200301i	−0.999950	−	0.0100151i	$-0.996812\pi$
$881$		−	17.6465i		−	0.0200301i	0.999950	−	0.0100151i	$-0.00318795\pi$
$882$	−35.0734	+	281.606i	−0.0397658	+	0.319281i
$883$			667.850i			0.756342i	0.925736	+	0.378171i	$0.123447\pi$
$883$			667.850i			0.756342i	−0.925736	+	0.378171i	$0.876553\pi$
$884$	−87.2470			−0.0986957
$885$	36.7120	−	169.105i	0.0414825	−	0.191079i
$886$	−342.434			−0.386494
$887$	−914.069			−1.03052			−0.515259	−	0.857035i	$-0.672304\pi$
$887$	−914.069			−1.03052			−0.515259	+	0.857035i	$0.672304\pi$
$888$	882.849			0.994199
$889$	282.566	+	17.5288i	0.317847	+	0.0197175i
$890$	−609.818	−	132.389i	−0.685188	−	0.148752i
$891$	39.7336			0.0445944
$892$	11.8984			0.0133390
$893$			816.435i			0.914261i
$894$		−	141.940i		−	0.158769i
$895$	823.812	+	178.846i	0.920461	+	0.199828i
$896$	791.878	+	49.1236i	0.883792	+	0.0548255i
$897$			1003.83i			1.11909i
$898$		−	942.460i		−	1.04951i
$899$		−	66.5161i		−	0.0739890i
$900$	18.6475	+	8.49705i	0.0207194	+	0.00944117i
$901$		−	561.980i		−	0.623729i
$902$	−452.765			−0.501957
$903$	−90.3694	−	5.60601i	−0.100077	−	0.00620821i
$904$	1328.44			1.46952
$905$	185.922	−	856.402i	0.205438	−	0.946301i
$906$			153.155i			0.169045i
$907$		−	1793.14i		−	1.97700i	−0.151213	−	0.988501i	$-0.548318\pi$
$907$		−	1793.14i		−	1.97700i	0.151213	−	0.988501i	$-0.451682\pi$
$908$	12.9695			0.0142836
$909$			533.615i			0.587035i
$910$	1111.75	+	314.558i	1.22170	+	0.345669i
$911$	−1179.54			−1.29477			−0.647385	−	0.762163i	$-0.724137\pi$
$911$	−1179.54			−1.29477			−0.647385	+	0.762163i	$0.724137\pi$
$912$		−	472.783i		−	0.518403i
$913$	−434.058			−0.475420
$914$	−628.442			−0.687573
$915$	−118.807	+	547.255i	−0.129844	+	0.598093i
$916$			79.4920i			0.0867817i
$917$	−762.634	−	47.3095i	−0.831661	−	0.0515916i
$918$			187.318i			0.204050i
$919$	279.371			0.303995			0.151998	−	0.988381i	$-0.451429\pi$
$919$	279.371			0.303995			0.151998	+	0.988381i	$0.451429\pi$
$920$	−1366.14	−	296.584i	−1.48494	−	0.322374i
$921$	823.613			0.894260
$922$	660.727			0.716623
$923$	249.810			0.270650
$924$	0.905522	−	14.5971i	0.000980002	−	0.0157977i
$925$	−640.508	+	1405.64i	−0.692441	+	1.51962i
$926$	1168.98			1.26239
$927$	−334.539			−0.360883
$928$		−	104.060i		−	0.112134i
$929$		−	140.394i		−	0.151123i	−0.997141	−	0.0755617i	$-0.975925\pi$
$929$		−	140.394i		−	0.151123i	0.997141	−	0.0755617i	$-0.0240750\pi$
$930$	45.5729	+	9.89371i	0.0490032	+	0.0106384i
$931$	111.450	−	894.834i	0.119710	−	0.961154i
$932$			96.6507i			0.103702i
$933$		−	775.882i		−	0.831599i
$934$			442.770i			0.474058i
$935$	402.825	+	87.4517i	0.430828	+	0.0935312i
$936$		−	423.192i		−	0.452128i
$937$	−995.104			−1.06201			−0.531005	−	0.847369i	$-0.678186\pi$
$937$	−995.104			−1.06201			−0.531005	+	0.847369i	$0.678186\pi$
$938$	−57.1540	+	921.328i	−0.0609318	+	0.982226i
$939$	−496.028			−0.528251
$940$	−59.2281	−	12.8582i	−0.0630086	−	0.0136789i
$941$			794.165i			0.843959i	0.906605	+	0.421979i	$0.138665\pi$
$941$			794.165i			0.843959i	−0.906605	+	0.421979i	$0.861335\pi$
$942$			778.354i			0.826278i
$943$	1800.51			1.90934
$944$		−	296.373i		−	0.313955i
$945$	−49.5134	+	174.995i	−0.0523951	+	0.185180i
$946$	−63.6472			−0.0672803
$947$		−	1716.44i		−	1.81250i	−0.422741	−	0.906251i	$-0.638932\pi$
$947$		−	1716.44i		−	1.81250i	0.422741	−	0.906251i	$-0.361068\pi$
$948$	−27.1056			−0.0285924
$949$	−1015.98			−1.07058
$950$	808.217	+	368.279i	0.850755	+	0.387662i
$951$		−	318.726i		−	0.335148i
$952$	1076.26	+	66.7651i	1.13052	+	0.0701314i
$953$			828.732i			0.869603i	0.900526	+	0.434802i	$0.143181\pi$
$953$			828.732i			0.869603i	−0.900526	+	0.434802i	$0.856819\pi$
$954$	174.292			0.182696
$955$	−112.865	−	24.5025i	−0.118183	−	0.0256570i
$956$	18.6986			0.0195592
$957$	182.345			0.190538
$958$	−221.210			−0.230908
$959$	−273.507	−	16.9668i	−0.285200	−	0.0176922i
$960$	573.410	+	124.485i	0.597302	+	0.129672i
$961$	953.219			0.991903
$962$	2039.69			2.12026
$963$		−	316.953i		−	0.329130i
$964$			87.7200i			0.0909958i
$965$	−47.3733	+	218.213i	−0.0490915	+	0.226128i
$966$	49.1165	−	791.762i	0.0508452	−	0.819629i
$967$			557.371i			0.576392i	0.957571	+	0.288196i	$0.0930555\pi$
$967$			557.371i			0.576392i	−0.957571	+	0.288196i	$0.906944\pi$
$968$			837.390i			0.865072i
$969$		−	595.224i		−	0.614266i
$970$	−374.552	+	1725.28i	−0.386136	+	1.77864i
$971$		−	1604.46i		−	1.65238i	−0.563392	−	0.826190i	$-0.690504\pi$
$971$		−	1604.46i		−	1.65238i	0.563392	−	0.826190i	$-0.309496\pi$
$972$	4.25921			0.00438190
$973$	−770.988	−	47.8278i	−0.792383	−	0.0491550i
$974$	1125.22			1.15525
$975$	673.794	+	307.026i	0.691071	+	0.314899i
$976$			959.118i			0.982702i
$977$		−	430.292i		−	0.440422i	−0.975452	−	0.220211i	$-0.929325\pi$
$977$		−	430.292i		−	0.440422i	0.975452	−	0.220211i	$-0.0706746\pi$
$978$	−942.033			−0.963224
$979$			285.417i			0.291539i
$980$	63.1603	+	22.1780i	0.0644493	+	0.0226306i
$981$	98.2950			0.100199
$982$			1688.36i			1.71931i
$983$	−931.691			−0.947804			−0.473902	−	0.880578i	$-0.657155\pi$
$983$	−931.691			−0.947804			−0.473902	+	0.880578i	$0.657155\pi$
$984$	−759.057			−0.771399
$985$	−133.420	+	614.568i	−0.135452	+	0.623927i
$986$			859.634i			0.871840i
$987$	33.3035	−	536.855i	0.0337421	−	0.543926i
$988$			85.9823i			0.0870266i
$989$	253.105			0.255920
$990$	−27.1222	+	124.932i	−0.0273962	+	0.126194i
$991$	364.551			0.367861			0.183931	−	0.982939i	$-0.441118\pi$
$991$	364.551			0.367861			0.183931	+	0.982939i	$0.441118\pi$
$992$	−12.1724			−0.0122706
$993$	−795.946			−0.801557
$994$	−197.036	−	12.2230i	−0.198226	−	0.0122968i
$995$	101.682	−	468.373i	0.102193	−	0.470727i
$996$	−46.5285			−0.0467153
$997$	1479.52			1.48398			0.741988	−	0.670413i	$-0.233883\pi$
$997$	1479.52			1.48398			0.741988	+	0.670413i	$0.233883\pi$
$998$			1354.02i			1.35673i
$999$			321.059i			0.321381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.e.a.34.6	yes	16
3.2	odd	2		315.3.e.e.244.12		16
4.3	odd	2		1680.3.bd.c.769.1		16
5.2	odd	4		525.3.h.e.76.11		16
5.3	odd	4		525.3.h.e.76.6		16
5.4	even	2	inner	105.3.e.a.34.11	yes	16
7.6	odd	2	inner	105.3.e.a.34.5	✓	16
15.14	odd	2		315.3.e.e.244.5		16
20.19	odd	2		1680.3.bd.c.769.15		16
21.20	even	2		315.3.e.e.244.11		16
28.27	even	2		1680.3.bd.c.769.16		16
35.13	even	4		525.3.h.e.76.5		16
35.27	even	4		525.3.h.e.76.12		16
35.34	odd	2	inner	105.3.e.a.34.12	yes	16
105.104	even	2		315.3.e.e.244.6		16
140.139	even	2		1680.3.bd.c.769.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.5	✓	16	7.6	odd	2	inner
105.3.e.a.34.6	yes	16	1.1	even	1	trivial
105.3.e.a.34.11	yes	16	5.4	even	2	inner
105.3.e.a.34.12	yes	16	35.34	odd	2	inner
315.3.e.e.244.5		16	15.14	odd	2
315.3.e.e.244.6		16	105.104	even	2
315.3.e.e.244.11		16	21.20	even	2
315.3.e.e.244.12		16	3.2	odd	2
525.3.h.e.76.5		16	35.13	even	4
525.3.h.e.76.6		16	5.3	odd	4
525.3.h.e.76.11		16	5.2	odd	4
525.3.h.e.76.12		16	35.27	even	4
1680.3.bd.c.769.1		16	4.3	odd	2
1680.3.bd.c.769.2		16	140.139	even	2
1680.3.bd.c.769.15		16	20.19	odd	2
1680.3.bd.c.769.16		16	28.27	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.93048i q^{2} +1.73205 q^{3} +0.273228 q^{4} +(-4.88618 - 1.06077i) q^{5} -3.34370i q^{6} +(0.433408 - 6.98657i) q^{7} -8.24940i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.93048i q^{2} +1.73205 q^{3} +0.273228 q^{4} +(-4.88618 - 1.06077i) q^{5} -3.34370i q^{6} +(0.433408 - 6.98657i) q^{7} -8.24940i q^{8} +3.00000 q^{9} +(-2.04780 + 9.43270i) q^{10} +4.41485 q^{11} +0.473246 q^{12} +17.0999 q^{13} +(-13.4875 - 0.836687i) q^{14} +(-8.46311 - 1.83731i) q^{15} -14.8324 q^{16} -18.6737 q^{17} -5.79145i q^{18} +18.4030i q^{19} +(-1.33504 - 0.289833i) q^{20} +(0.750684 - 12.1011i) q^{21} -8.52280i q^{22} +33.8925i q^{23} -14.2884i q^{24} +(22.7495 + 10.3662i) q^{25} -33.0111i q^{26} +5.19615 q^{27} +(0.118419 - 1.90893i) q^{28} +23.8461 q^{29} +(-3.54690 + 16.3379i) q^{30} -2.78940i q^{31} -4.36383i q^{32} +7.64674 q^{33} +36.0493i q^{34} +(-9.52886 + 33.6779i) q^{35} +0.819685 q^{36} +61.7879i q^{37} +35.5268 q^{38} +29.6179 q^{39} +(-8.75073 + 40.3081i) q^{40} -53.1240i q^{41} +(-23.3610 - 1.44918i) q^{42} -7.46787i q^{43} +1.20626 q^{44} +(-14.6585 - 3.18231i) q^{45} +65.4289 q^{46} +44.3642 q^{47} -25.6905 q^{48} +(-48.6243 - 6.05606i) q^{49} +(20.0119 - 43.9176i) q^{50} -32.3438 q^{51} +4.67218 q^{52} +30.0947i q^{53} -10.0311i q^{54} +(-21.5717 - 4.68314i) q^{55} +(-57.6350 - 3.57535i) q^{56} +31.8750i q^{57} -46.0345i q^{58} +19.9814i q^{59} +(-2.31236 - 0.502005i) q^{60} -64.6635i q^{61} -5.38489 q^{62} +(1.30022 - 20.9597i) q^{63} -67.7540 q^{64} +(-83.5533 - 18.1391i) q^{65} -14.7619i q^{66} -68.3099i q^{67} -5.10219 q^{68} +58.7035i q^{69} +(65.0147 + 18.3953i) q^{70} +14.6088 q^{71} -24.7482i q^{72} -59.4144 q^{73} +119.281 q^{74} +(39.4033 + 17.9549i) q^{75} +5.02823i q^{76} +(1.91343 - 30.8446i) q^{77} -57.1769i q^{78} -57.2759 q^{79} +(72.4739 + 15.7338i) q^{80} +9.00000 q^{81} -102.555 q^{82} -98.3178 q^{83} +(0.205108 - 3.30636i) q^{84} +(91.2431 + 19.8085i) q^{85} -14.4166 q^{86} +41.3026 q^{87} -36.4199i q^{88} +64.6493i q^{89} +(-6.14341 + 28.2981i) q^{90} +(7.41123 - 119.470i) q^{91} +9.26040i q^{92} -4.83138i q^{93} -85.6444i q^{94} +(19.5214 - 89.9205i) q^{95} -7.55837i q^{96} +182.904 q^{97} +(-11.6911 + 93.8685i) q^{98} +13.2445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9}+O(q^{10}) \) 16 * q - 32 * q^4 + 48 * q^9	\( 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50} + 24 q^{51} + 444 q^{56} - 288 q^{60} - 992 q^{64} - 296 q^{65} + 504 q^{70} - 56 q^{71} - 48 q^{74} + 464 q^{79} + 144 q^{81} + 228 q^{84} + 608 q^{85} - 456 q^{86} - 88 q^{91} - 24 q^{95} - 168 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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