LMFDB - Embedded newform 105.3.e.a.34.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(34,105)] 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("105.34"); S:= CuspForms(chi, 3); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			34.5
Root			$1.36603 - 2.63709i$ of defining polynomial
Character	$\chi$	$=$	105.34
Dual form			105.3.e.a.34.11

$q$-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} +(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} +(5.29344 - 34.5974i) 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} +(-66.7897 - 10.2189i) 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} - 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}+ \cdots - 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

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	$-0.728466\pi$
$13$	−17.0999			−1.31538			−0.657689	+	0.753290i	$0.728466\pi$
$14$	−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	$-0.314922\pi$
$17$	18.6737			1.09845			0.549227	+	0.835673i	$0.314922\pi$
$18$		−	5.79145i		−	0.321747i
$19$		−	18.4030i		−	0.968580i	−0.874908	−	0.484290i	$-0.839078\pi$
$19$		−	18.4030i		−	0.968580i	0.874908	−	0.484290i	$-0.160922\pi$
$20$	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	$0.0143257\pi$
$31$			2.78940i			0.0899806i	−0.998987	+	0.0449903i	$0.985674\pi$
$32$		−	4.36383i		−	0.136370i
$33$	−7.64674			−0.231719
$34$		−	36.0493i		−	1.06027i
$35$	5.29344	−	34.5974i	0.151241	−	0.988497i
$36$	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	$0.224333\pi$
$41$			53.1240i			1.29571i	−0.761764	+	0.647854i	$0.775667\pi$
$42$	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	$-0.656453\pi$
$47$	−44.3642			−0.943919			−0.471959	+	0.881620i	$0.656453\pi$
$48$	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	$-0.945838\pi$
$59$		−	19.9814i		−	0.338668i	0.985559	−	0.169334i	$-0.0541617\pi$
$60$	−2.31236	−	0.502005i	−0.0385394	−	0.00836675i
$61$			64.6635i			1.06006i	0.847980	+	0.530029i	$0.177819\pi$
$61$			64.6635i			1.06006i	−0.847980	+	0.530029i	$0.822181\pi$
$62$	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
$70$	−66.7897	−	10.2189i	−0.954139	−	0.145984i
$71$	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	$-0.366593\pi$
$73$	59.4144			0.813896			0.406948	+	0.913451i	$0.366593\pi$
$74$	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	$-0.298229\pi$
$83$	98.3178			1.18455			0.592276	+	0.805735i	$0.298229\pi$
$84$	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	$-0.881685\pi$
$89$		−	64.6493i		−	0.726397i	0.931712	−	0.363198i	$-0.118315\pi$
$90$	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	$-0.891824\pi$
$97$	−182.904			−1.88561			−0.942806	+	0.333342i	$0.891824\pi$
$98$	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	$-0.657171\pi$
$101$		−	177.872i		−	1.76111i	0.473947	−	0.880553i	$-0.342829\pi$
$102$			62.4392i			0.612149i
$103$	111.513			1.08265			0.541325	−	0.840814i	$-0.317923\pi$
$103$	111.513			1.08265			0.541325	+	0.840814i	$0.317923\pi$
$104$			141.064i			1.35639i
$105$	−9.16851	+	59.9244i	−0.0873192	+	0.570709i
$106$	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	$0.136789\pi$
$131$			109.157i			0.833260i	−0.909076	+	0.416630i	$0.863211\pi$
$132$	−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	$0.129932\pi$
$139$			110.353i			0.793906i	−0.917839	+	0.396953i	$0.870068\pi$
$140$	1.44632	−	9.45299i	0.0103309	−	0.0675214i
$141$	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	$-0.234188\pi$
$157$	232.782			1.48269			0.741345	+	0.671124i	$0.234188\pi$
$158$			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	$-0.616173\pi$
$167$	−119.212			−0.713842			−0.356921	+	0.934135i	$0.616173\pi$
$168$	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	$-0.718773\pi$
$173$	−219.519			−1.26890			−0.634448	+	0.772965i	$0.718773\pi$
$174$			79.7340i			0.458241i
$175$	62.5646	−	163.434i	0.357512	−	0.933908i
$176$	−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	$-0.839121\pi$
$181$		−	175.270i		−	0.968344i	0.874973	−	0.484172i	$-0.160879\pi$
$182$	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	$-0.922575\pi$
$199$		−	95.8567i		−	0.481692i	0.970563	−	0.240846i	$-0.0774248\pi$
$200$	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
$210$	115.683	+	17.6997i	0.550872	+	0.0842842i
$211$	−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	$-0.531129\pi$
$223$	−43.5475			−0.195280			−0.0976402	+	0.995222i	$0.531129\pi$
$224$	−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	$-0.533342\pi$
$227$	−47.4678			−0.209109			−0.104555	+	0.994519i	$0.533342\pi$
$228$			8.70915i			0.0381980i
$229$		−	290.936i		−	1.27046i	−0.772322	−	0.635231i	$-0.780905\pi$
$229$		−	290.936i		−	1.27046i	0.772322	−	0.635231i	$-0.219095\pi$
$230$	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	$-0.767971\pi$
$241$		−	321.050i		−	1.33216i	0.745881	−	0.666079i	$-0.232029\pi$
$242$			195.962i			0.809760i
$243$	−15.5885			−0.0641500
$244$			17.6679i			0.0724095i
$245$	−244.011	−	21.9882i	−0.995965	−	0.0897479i
$246$	−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	$-0.988686\pi$
$251$		−	17.8400i		−	0.0710757i	0.999368	−	0.0355379i	$-0.0113144\pi$
$252$	−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	$-0.447175\pi$
$257$	84.9101			0.330389			0.165195	+	0.986261i	$0.447175\pi$
$258$	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	$0.181659\pi$
$269$			290.639i			1.08044i	−0.841523	+	0.540221i	$0.818341\pi$
$270$	−10.6407	+	49.0137i	−0.0394100	+	0.181532i
$271$			345.145i			1.27360i	0.771031	+	0.636798i	$0.219741\pi$
$271$			345.145i			1.27360i	−0.771031	+	0.636798i	$0.780259\pi$
$272$	−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
$280$	−285.408	−	43.6677i	−1.01931	−	0.155956i
$281$	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	$-0.546848\pi$
$283$	−83.0022			−0.293294			−0.146647	+	0.989189i	$0.546848\pi$
$284$	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	$-0.262335\pi$
$293$	398.001			1.35836			0.679182	+	0.733970i	$0.262335\pi$
$294$	−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	$-0.781974\pi$
$307$	−475.513			−1.54890			−0.774452	+	0.632633i	$0.781974\pi$
$308$	−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	$0.255944\pi$
$311$			447.956i			1.44037i	−0.693781	+	0.720186i	$0.744056\pi$
$312$		−	244.330i		−	0.783109i
$313$	286.382			0.914957			0.457479	−	0.889221i	$-0.348753\pi$
$313$	286.382			0.914957			0.457479	+	0.889221i	$0.348753\pi$
$314$		−	449.383i		−	1.43116i
$315$	15.8803	−	103.792i	0.0504137	−	0.329499i
$316$	−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	$-0.982442\pi$
$349$		−	38.4832i		−	0.110267i	0.998479	−	0.0551335i	$-0.0175585\pi$
$350$	−315.507	−	120.780i	−0.901448	−	0.345086i
$351$	88.8538			0.253145
$352$		−	19.2656i		−	0.0547319i
$353$	70.1203			0.198641			0.0993206	−	0.995055i	$-0.468333\pi$
$353$	70.1203			0.198641			0.0993206	+	0.995055i	$0.468333\pi$
$354$	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	$-0.267950\pi$
$367$	488.938			1.33226			0.666128	+	0.745837i	$0.267950\pi$
$368$		−	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	$-0.678730\pi$
$383$	−407.860			−1.06491			−0.532454	+	0.846459i	$0.678730\pi$
$384$		−	196.316i		−	0.511238i
$385$	23.3697	−	152.742i	0.0607006	−	0.396733i
$386$	−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	$-0.562582\pi$
$397$	−155.102			−0.390686			−0.195343	+	0.980735i	$0.562582\pi$
$398$	−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	$-0.794305\pi$
$409$		−	492.571i		−	1.20433i	0.798371	−	0.602166i	$-0.205695\pi$
$410$	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	$0.0254951\pi$
$419$			67.0479i			0.160019i	−0.996794	+	0.0800095i	$0.974505\pi$
$420$	−2.50510	+	16.3731i	−0.00596452	+	0.0389835i
$421$	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	$-0.812291\pi$
$433$	−719.737			−1.66221			−0.831105	+	0.556115i	$0.812291\pi$
$434$	−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	$0.103131\pi$
$439$			279.517i			0.636713i	−0.947971	+	0.318356i	$0.896869\pi$
$440$	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
$455$	−90.5174	+	591.612i	−0.198939	+	1.30025i
$456$	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	$-0.878942\pi$
$461$		−	342.259i		−	0.742428i	0.928547	−	0.371214i	$-0.121058\pi$
$462$	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	$-0.421027\pi$
$467$	229.357			0.491128			0.245564	+	0.969380i	$0.421027\pi$
$468$	−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	$0.0381648\pi$
$479$			114.588i			0.239222i	−0.992821	+	0.119611i	$0.961835\pi$
$480$	−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
$490$	−42.4480	+	471.060i	−0.0866285	+	0.961347i
$491$	−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	$-0.435879\pi$
$503$	201.284			0.400167			0.200084	+	0.979779i	$0.435879\pi$
$504$	−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	$0.0668061\pi$
$509$			212.090i			0.416680i	−0.978056	+	0.208340i	$0.933194\pi$
$510$	−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	$0.280272\pi$
$521$			803.441i			1.54211i	−0.636766	+	0.771057i	$0.719728\pi$
$522$		−	138.103i		−	0.264566i
$523$	−931.800			−1.78164			−0.890822	−	0.454352i	$-0.849871\pi$
$523$	−931.800			−1.78164			−0.890822	+	0.454352i	$0.849871\pi$
$524$			29.8248i			0.0569176i
$525$	−108.365	+	283.076i	−0.206410	+	0.539192i
$526$	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
$560$	−78.5146	+	513.163i	−0.140205	+	0.916363i
$561$	−142.793			−0.254533
$562$		−	219.857i		−	0.391205i
$563$	408.888			0.726266			0.363133	−	0.931737i	$-0.381707\pi$
$563$	408.888			0.726266			0.363133	+	0.931737i	$0.381707\pi$
$564$	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	$-0.692704\pi$
$577$	−656.728			−1.13818			−0.569088	+	0.822276i	$0.692704\pi$
$578$		−	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	$-0.362632\pi$
$587$	491.065			0.836567			0.418283	+	0.908317i	$0.362632\pi$
$588$	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	$-0.360613\pi$
$593$	502.906			0.848071			0.424036	+	0.905645i	$0.360613\pi$
$594$			44.2858i			0.0745551i
$595$	98.8482	−	646.062i	0.166131	−	1.08582i
$596$	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	$-0.611195\pi$
$601$		−	1129.40i		−	1.87921i	0.342267	−	0.939603i	$-0.388805\pi$
$602$	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	$-0.658987\pi$
$607$	−581.462			−0.957927			−0.478963	+	0.877835i	$0.658987\pi$
$608$	−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	$0.0347076\pi$
$619$			134.721i			0.217642i	−0.994061	+	0.108821i	$0.965292\pi$
$620$	−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
$630$	−200.369	−	30.6567i	−0.318046	−	0.0486615i
$631$	−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	$-0.157028\pi$
$643$	1132.67			1.76153			0.880766	+	0.473552i	$0.157028\pi$
$644$	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	$-0.707970\pi$
$647$	−786.565			−1.21571			−0.607856	+	0.794048i	$0.707970\pi$
$648$		−	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	$0.0130520\pi$
$661$			54.1922i			0.0819852i	−0.999159	+	0.0409926i	$0.986948\pi$
$662$			887.135i			1.34008i
$663$	553.076			0.834203
$664$		−	811.063i		−	1.22148i
$665$	−636.696	−	97.4153i	−0.957438	−	0.146489i
$666$	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	$-0.646897\pi$
$677$	−602.915			−0.890568			−0.445284	+	0.895389i	$0.646897\pi$
$678$	−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	$0.322563\pi$
$691$			1172.79i			1.69723i	−0.529012	+	0.848614i	$0.677437\pi$
$692$	−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
$700$	17.0944	−	44.6548i	0.0244206	−	0.0637926i
$701$	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	$-0.979924\pi$
$719$		−	90.6345i		−	0.126056i	0.998012	−	0.0630282i	$-0.0200758\pi$
$720$	−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	$-0.645261\pi$
$727$	−640.742			−0.881351			−0.440676	+	0.897666i	$0.645261\pi$
$728$	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	$-0.591601\pi$
$733$	−416.075			−0.567632			−0.283816	+	0.958879i	$0.591601\pi$
$734$		−	943.887i		−	1.28595i
$735$	422.640	+	38.0848i	0.575020	+	0.0518160i
$736$	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	$-0.804847\pi$
$761$		−	875.755i		−	1.15079i	0.817874	−	0.575397i	$-0.195153\pi$
$762$	−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	$0.171937\pi$
$769$			790.946i			1.02854i	−0.857629	+	0.514269i	$0.828063\pi$
$770$	−294.867	−	45.1149i	−0.382944	−	0.0585908i
$771$	−147.069			−0.190750
$772$		−	12.2022i		−	0.0158060i
$773$	−243.540			−0.315059			−0.157529	−	0.987514i	$-0.550353\pi$
$773$	−243.540			−0.315059			−0.157529	+	0.987514i	$0.550353\pi$
$774$	−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	$-0.415770\pi$
$787$	411.660			0.523075			0.261538	+	0.965193i	$0.415770\pi$
$788$		−	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	$-0.467930\pi$
$797$	160.324			0.201159			0.100579	+	0.994929i	$0.467930\pi$
$798$	−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
$805$	1172.59	+	179.408i	1.45664	+	0.222867i
$806$	−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	$0.132362\pi$
$811$			655.202i			0.807895i	−0.914782	+	0.403947i	$0.867638\pi$
$812$	−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	$0.218358\pi$
$829$			1050.24i			1.26688i	−0.773791	+	0.633441i	$0.781642\pi$
$830$	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	$0.0431077\pi$
$839$			226.552i			0.270026i	−0.990844	+	0.135013i	$0.956892\pi$
$840$	494.341	+	75.6348i	0.588501	+	0.0900414i
$841$	−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	$-0.572988\pi$
$853$	−387.766			−0.454591			−0.227295	+	0.973826i	$0.572988\pi$
$854$	−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	$-0.593530\pi$
$857$	−496.415			−0.579248			−0.289624	+	0.957141i	$0.593530\pi$
$858$		−	252.428i		−	0.294205i
$859$		−	654.574i		−	0.762018i	−0.924571	−	0.381009i	$-0.875577\pi$
$859$		−	654.574i		−	0.762018i	0.924571	−	0.381009i	$-0.124423\pi$
$860$	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
$875$	479.068	−	732.201i	0.547506	−	0.836801i
$876$	−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	$0.00318795\pi$
$881$			17.6465i			0.0200301i	−0.999950	+	0.0100151i	$0.996812\pi$
$882$	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	$-0.327696\pi$
$887$	914.069			1.03052			0.515259	+	0.857035i	$0.327696\pi$
$888$	−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
$910$	1142.10	+	174.743i	1.25505	+	0.192025i
$911$	−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	$0.0240750\pi$
$929$			140.394i			0.151123i	−0.997141	+	0.0755617i	$0.975925\pi$
$930$	−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	$-0.321814\pi$
$937$	995.104			1.06201			0.531005	+	0.847369i	$0.321814\pi$
$938$	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	$-0.861335\pi$
$941$		−	794.165i		−	0.843959i	0.906605	−	0.421979i	$-0.138665\pi$
$942$			778.354i			0.826278i
$943$	−1800.51			−1.90934
$944$			296.373i			0.313955i
$945$	−27.5055	+	179.773i	−0.0291064	+	0.190236i
$946$	−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	$0.309496\pi$
$971$			1604.46i			1.65238i	−0.563392	+	0.826190i	$0.690504\pi$
$972$	−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
$980$	−66.6708	−	6.00781i	−0.0680315	−	0.00613042i
$981$	98.2950			0.100199
$982$			1688.36i			1.71931i
$983$	931.691			0.947804			0.473902	−	0.880578i	$-0.342845\pi$
$983$	931.691			0.947804			0.473902	+	0.880578i	$0.342845\pi$
$984$	−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	$-0.766117\pi$
$997$	−1479.52			−1.48398			−0.741988	+	0.670413i	$0.766117\pi$
$998$			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.34.5	✓	16
3.2	odd	2		315.3.e.e.244.11		16
4.3	odd	2		1680.3.bd.c.769.16		16
5.2	odd	4		525.3.h.e.76.12		16
5.3	odd	4		525.3.h.e.76.5		16
5.4	even	2	inner	105.3.e.a.34.12	yes	16
7.6	odd	2	inner	105.3.e.a.34.6	yes	16
15.14	odd	2		315.3.e.e.244.6		16
20.19	odd	2		1680.3.bd.c.769.2		16
21.20	even	2		315.3.e.e.244.12		16
28.27	even	2		1680.3.bd.c.769.1		16
35.13	even	4		525.3.h.e.76.6		16
35.27	even	4		525.3.h.e.76.11		16
35.34	odd	2	inner	105.3.e.a.34.11	yes	16
105.104	even	2		315.3.e.e.244.5		16
140.139	even	2		1680.3.bd.c.769.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.e.a.34.5	✓	16	1.1	even	1	trivial
105.3.e.a.34.6	yes	16	7.6	odd	2	inner
105.3.e.a.34.11	yes	16	35.34	odd	2	inner
105.3.e.a.34.12	yes	16	5.4	even	2	inner
315.3.e.e.244.5		16	105.104	even	2
315.3.e.e.244.6		16	15.14	odd	2
315.3.e.e.244.11		16	3.2	odd	2
315.3.e.e.244.12		16	21.20	even	2
525.3.h.e.76.5		16	5.3	odd	4
525.3.h.e.76.6		16	35.13	even	4
525.3.h.e.76.11		16	35.27	even	4
525.3.h.e.76.12		16	5.2	odd	4
1680.3.bd.c.769.1		16	28.27	even	2
1680.3.bd.c.769.2		16	20.19	odd	2
1680.3.bd.c.769.15		16	140.139	even	2
1680.3.bd.c.769.16		16	4.3	odd	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
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} +(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} +(5.29344 - 34.5974i) 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} +(-66.7897 - 10.2189i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4} + 48 q^{9} - 56 q^{11} - 84 q^{14} + 24 q^{15} + 112 q^{16} - 12 q^{21} + 16 q^{25} - 32 q^{29} - 72 q^{30} - 4 q^{35} - 96 q^{36} + 72 q^{39} + 568 q^{44} - 96 q^{46} - 152 q^{49} - 96 q^{50}+ \cdots - 168 q^{99}+O(q^{100}) \) 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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