LMFDB - Embedded newform 35.5.g.a.8.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.g (of order $4$, degree $2$, 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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.11
Character	$\chi$	$=$	35.8
Dual form			35.5.g.a.22.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.01495 - 5.01495i) q^{2} +(-5.80055 - 5.80055i) q^{3} -34.2994i q^{4} +(17.0417 + 18.2915i) q^{5} -58.1789 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-91.7707 - 91.7707i) q^{8} -13.7072i q^{9} +O(q^{10})$	\(q+(5.01495 - 5.01495i) q^{2} +(-5.80055 - 5.80055i) q^{3} -34.2994i q^{4} +(17.0417 + 18.2915i) q^{5} -58.1789 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-91.7707 - 91.7707i) q^{8} -13.7072i q^{9} +(177.194 + 6.26750i) q^{10} +75.9504 q^{11} +(-198.956 + 198.956i) q^{12} +(87.6088 + 87.6088i) q^{13} +131.350i q^{14} +(7.24931 - 204.952i) q^{15} -371.660 q^{16} +(230.654 - 230.654i) q^{17} +(-68.7410 - 68.7410i) q^{18} +527.538i q^{19} +(627.388 - 584.522i) q^{20} +151.926 q^{21} +(380.888 - 380.888i) q^{22} +(-587.599 - 587.599i) q^{23} +1064.64i q^{24} +(-44.1582 + 623.438i) q^{25} +878.707 q^{26} +(-549.354 + 549.354i) q^{27} +(449.178 + 449.178i) q^{28} +1581.66i q^{29} +(-991.470 - 1064.18i) q^{30} -588.270 q^{31} +(-395.524 + 395.524i) q^{32} +(-440.554 - 440.554i) q^{33} -2313.44i q^{34} +(-462.717 - 16.3666i) q^{35} -470.149 q^{36} +(629.670 - 629.670i) q^{37} +(2645.58 + 2645.58i) q^{38} -1016.36i q^{39} +(114.692 - 3242.56i) q^{40} -235.424 q^{41} +(761.900 - 761.900i) q^{42} +(-1361.59 - 1361.59i) q^{43} -2605.06i q^{44} +(250.725 - 233.595i) q^{45} -5893.56 q^{46} +(-1625.74 + 1625.74i) q^{47} +(2155.83 + 2155.83i) q^{48} -343.000i q^{49} +(2905.06 + 3347.96i) q^{50} -2675.84 q^{51} +(3004.93 - 3004.93i) q^{52} +(845.919 + 845.919i) q^{53} +5509.96i q^{54} +(1294.33 + 1389.25i) q^{55} +2403.62 q^{56} +(3060.01 - 3060.01i) q^{57} +(7931.94 + 7931.94i) q^{58} -1607.13i q^{59} +(-7029.75 - 248.647i) q^{60} -2519.75 q^{61} +(-2950.14 + 2950.14i) q^{62} +(179.507 + 179.507i) q^{63} -1979.49i q^{64} +(-109.490 + 3095.50i) q^{65} -4418.72 q^{66} +(3671.67 - 3671.67i) q^{67} +(-7911.31 - 7911.31i) q^{68} +6816.80i q^{69} +(-2402.58 + 2238.42i) q^{70} +6830.43 q^{71} +(-1257.92 + 1257.92i) q^{72} +(-1600.31 - 1600.31i) q^{73} -6315.53i q^{74} +(3872.43 - 3360.14i) q^{75} +18094.3 q^{76} +(-994.632 + 994.632i) q^{77} +(-5096.99 - 5096.99i) q^{78} +3822.06i q^{79} +(-6333.73 - 6798.22i) q^{80} +5262.83 q^{81} +(-1180.64 + 1180.64i) q^{82} +(-4122.84 - 4122.84i) q^{83} -5210.97i q^{84} +(8149.76 + 288.263i) q^{85} -13656.6 q^{86} +(9174.49 - 9174.49i) q^{87} +(-6970.02 - 6970.02i) q^{88} +1140.60i q^{89} +(85.9099 - 2428.84i) q^{90} -2294.61 q^{91} +(-20154.3 + 20154.3i) q^{92} +(3412.29 + 3412.29i) q^{93} +16306.0i q^{94} +(-9649.47 + 8990.17i) q^{95} +4588.52 q^{96} +(1538.00 - 1538.00i) q^{97} +(-1720.13 - 1720.13i) q^{98} -1041.07i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	5.01495	−	5.01495i	1.25374	−	1.25374i	0.299705	−	0.954032i	$-0.403112\pi$
$2$	5.01495	−	5.01495i	1.25374	−	1.25374i	0.954032	−	0.299705i	$-0.0968884\pi$
$3$	−5.80055	−	5.80055i	−0.644506	−	0.644506i	0.307154	−	0.951660i	$-0.400623\pi$
$3$	−5.80055	−	5.80055i	−0.644506	−	0.644506i	−0.951660	+	0.307154i	$0.900623\pi$
$4$		−	34.2994i		−	2.14371i
$5$	17.0417	+	18.2915i	0.681670	+	0.731660i
$5$	17.0417	+	18.2915i	0.681670	+	0.731660i
$6$	−58.1789			−1.61608
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$7$	−13.0958	+	13.0958i	−0.267261	+	0.267261i
$8$	−91.7707	−	91.7707i	−1.43392	−	1.43392i
$9$		−	13.7072i		−	0.169225i
$10$	177.194	+	6.26750i	1.77194	+	0.0626750i
$11$	75.9504			0.627689			0.313845	−	0.949474i	$-0.398383\pi$
$11$	75.9504			0.627689			0.313845	+	0.949474i	$0.398383\pi$
$12$	−198.956	+	198.956i	−1.38164	+	1.38164i
$13$	87.6088	+	87.6088i	0.518395	+	0.518395i	0.917086	−	0.398690i	$-0.130535\pi$
$13$	87.6088	+	87.6088i	0.518395	+	0.518395i	−0.398690	+	0.917086i	$0.630535\pi$
$14$			131.350i			0.670151i
$15$	7.24931	−	204.952i	0.0322192	−	0.910899i
$16$	−371.660			−1.45180
$17$	230.654	−	230.654i	0.798111	−	0.798111i	−0.184686	−	0.982798i	$-0.559127\pi$
$17$	230.654	−	230.654i	0.798111	−	0.798111i	0.982798	+	0.184686i	$0.0591269\pi$
$18$	−68.7410	−	68.7410i	−0.212163	−	0.212163i
$19$			527.538i			1.46132i	0.682739	+	0.730662i	$0.260789\pi$
$19$			527.538i			1.46132i	−0.682739	+	0.730662i	$0.739211\pi$
$20$	627.388	−	584.522i	1.56847	−	1.46130i
$21$	151.926			0.344503
$22$	380.888	−	380.888i	0.786958	−	0.786958i
$23$	−587.599	−	587.599i	−1.11077	−	1.11077i	−0.993046	−	0.117728i	$-0.962439\pi$
$23$	−587.599	−	587.599i	−1.11077	−	1.11077i	−0.117728	−	0.993046i	$-0.537561\pi$
$24$			1064.64i			1.84834i
$25$	−44.1582	+	623.438i	−0.0706531	+	0.997501i
$26$	878.707			1.29986
$27$	−549.354	+	549.354i	−0.753572	+	0.753572i
$28$	449.178	+	449.178i	0.572932	+	0.572932i
$29$			1581.66i			1.88069i	0.340226	+	0.940344i	$0.389496\pi$
$29$			1581.66i			1.88069i	−0.340226	+	0.940344i	$0.610504\pi$
$30$	−991.470	−	1064.18i	−1.10163	−	1.18242i
$31$	−588.270			−0.612144			−0.306072	−	0.952008i	$-0.599015\pi$
$31$	−588.270			−0.612144			−0.306072	+	0.952008i	$0.599015\pi$
$32$	−395.524	+	395.524i	−0.386254	+	0.386254i
$33$	−440.554	−	440.554i	−0.404549	−	0.404549i
$34$		−	2313.44i		−	2.00124i
$35$	−462.717	−	16.3666i	−0.377728	−	0.0133605i
$36$	−470.149			−0.362770
$37$	629.670	−	629.670i	0.459949	−	0.459949i	−0.438690	−	0.898639i	$-0.644557\pi$
$37$	629.670	−	629.670i	0.459949	−	0.459949i	0.898639	+	0.438690i	$0.144557\pi$
$38$	2645.58	+	2645.58i	1.83212	+	1.83212i
$39$		−	1016.36i		−	0.668217i
$40$	114.692	−	3242.56i	0.0716823	−	2.02660i
$41$	−235.424			−0.140050			−0.0700249	−	0.997545i	$-0.522308\pi$
$41$	−235.424			−0.140050			−0.0700249	+	0.997545i	$0.522308\pi$
$42$	761.900	−	761.900i	0.431916	−	0.431916i
$43$	−1361.59	−	1361.59i	−0.736393	−	0.736393i	0.235485	−	0.971878i	$-0.424332\pi$
$43$	−1361.59	−	1361.59i	−0.736393	−	0.736393i	−0.971878	+	0.235485i	$0.924332\pi$
$44$		−	2605.06i		−	1.34559i
$45$	250.725	−	233.595i	0.123815	−	0.115355i
$46$	−5893.56			−2.78524
$47$	−1625.74	+	1625.74i	−0.735963	+	0.735963i	−0.971794	−	0.235831i	$-0.924219\pi$
$47$	−1625.74	+	1625.74i	−0.735963	+	0.735963i	0.235831	+	0.971794i	$0.424219\pi$
$48$	2155.83	+	2155.83i	0.935691	+	0.935691i
$49$		−	343.000i		−	0.142857i
$50$	2905.06	+	3347.96i	1.16202	+	1.33918i
$51$	−2675.84			−1.02877
$52$	3004.93	−	3004.93i	1.11129	−	1.11129i
$53$	845.919	+	845.919i	0.301146	+	0.301146i	0.841462	−	0.540316i	$-0.181695\pi$
$53$	845.919	+	845.919i	0.301146	+	0.301146i	−0.540316	+	0.841462i	$0.681695\pi$
$54$			5509.96i			1.88956i
$55$	1294.33	+	1389.25i	0.427877	+	0.459255i
$56$	2403.62			0.766461
$57$	3060.01	−	3060.01i	0.941832	−	0.941832i
$58$	7931.94	+	7931.94i	2.35789	+	2.35789i
$59$		−	1607.13i		−	0.461686i	−0.972991	−	0.230843i	$-0.925852\pi$
$59$		−	1607.13i		−	0.461686i	0.972991	−	0.230843i	$-0.0741485\pi$
$60$	−7029.75	−	248.647i	−1.95271	−	0.0690687i
$61$	−2519.75			−0.677170			−0.338585	−	0.940936i	$-0.609948\pi$
$61$	−2519.75			−0.677170			−0.338585	+	0.940936i	$0.609948\pi$
$62$	−2950.14	+	2950.14i	−0.767467	+	0.767467i
$63$	179.507	+	179.507i	0.0452272	+	0.0452272i
$64$		−	1979.49i		−	0.483274i
$65$	−109.490	+	3095.50i	−0.0259148	+	0.732663i
$66$	−4418.72			−1.01440
$67$	3671.67	−	3671.67i	0.817926	−	0.817926i	−0.167881	−	0.985807i	$-0.553692\pi$
$67$	3671.67	−	3671.67i	0.817926	−	0.817926i	0.985807	+	0.167881i	$0.0536924\pi$
$68$	−7911.31	−	7911.31i	−1.71092	−	1.71092i
$69$			6816.80i			1.43180i
$70$	−2402.58	+	2238.42i	−0.490323	+	0.456821i
$71$	6830.43			1.35498			0.677488	−	0.735534i	$-0.263069\pi$
$71$	6830.43			1.35498			0.677488	+	0.735534i	$0.263069\pi$
$72$	−1257.92	+	1257.92i	−0.242654	+	0.242654i
$73$	−1600.31	−	1600.31i	−0.300302	−	0.300302i	0.540830	−	0.841132i	$-0.318110\pi$
$73$	−1600.31	−	1600.31i	−0.300302	−	0.300302i	−0.841132	+	0.540830i	$0.818110\pi$
$74$		−	6315.53i		−	1.15331i
$75$	3872.43	−	3360.14i	0.688431	−	0.597359i
$76$	18094.3			3.13266
$77$	−994.632	+	994.632i	−0.167757	+	0.167757i
$78$	−5096.99	−	5096.99i	−0.837769	−	0.837769i
$79$			3822.06i			0.612412i	0.951965	+	0.306206i	$0.0990596\pi$
$79$			3822.06i			0.612412i	−0.951965	+	0.306206i	$0.900940\pi$
$80$	−6333.73	−	6798.22i	−0.989646	−	1.06222i
$81$	5262.83			0.802138
$82$	−1180.64	+	1180.64i	−0.175586	+	0.175586i
$83$	−4122.84	−	4122.84i	−0.598467	−	0.598467i	0.341437	−	0.939905i	$-0.389086\pi$
$83$	−4122.84	−	4122.84i	−0.598467	−	0.598467i	−0.939905	+	0.341437i	$0.889086\pi$
$84$		−	5210.97i		−	0.738516i
$85$	8149.76	+	288.263i	1.12799	+	0.0398980i
$86$	−13656.6			−1.84649
$87$	9174.49	−	9174.49i	1.21211	−	1.21211i
$88$	−6970.02	−	6970.02i	−0.900055	−	0.900055i
$89$			1140.60i			0.143997i	0.997405	+	0.0719984i	$0.0229377\pi$
$89$			1140.60i			0.143997i	−0.997405	+	0.0719984i	$0.977062\pi$
$90$	85.9099	−	2428.84i	0.0106062	−	0.299857i
$91$	−2294.61			−0.277094
$92$	−20154.3	+	20154.3i	−2.38118	+	2.38118i
$93$	3412.29	+	3412.29i	0.394530	+	0.394530i
$94$			16306.0i			1.84541i
$95$	−9649.47	+	8990.17i	−1.06919	+	0.996141i
$96$	4588.52			0.497886
$97$	1538.00	−	1538.00i	0.163460	−	0.163460i	−0.620637	−	0.784098i	$-0.713126\pi$
$97$	1538.00	−	1538.00i	0.163460	−	0.163460i	0.784098	+	0.620637i	$0.213126\pi$
$98$	−1720.13	−	1720.13i	−0.179105	−	0.179105i
$99$		−	1041.07i		−	0.106221i
$100$	21383.6	+	1514.60i	2.13836	+	0.151460i
$101$	−3238.10			−0.317430			−0.158715	−	0.987324i	$-0.550735\pi$
$101$	−3238.10			−0.317430			−0.158715	+	0.987324i	$0.550735\pi$
$102$	−13419.2	+	13419.2i	−1.28981	+	1.28981i
$103$	−9096.24	−	9096.24i	−0.857407	−	0.857407i	0.133625	−	0.991032i	$-0.457338\pi$
$103$	−9096.24	−	9096.24i	−0.857407	−	0.857407i	−0.991032	+	0.133625i	$0.957338\pi$
$104$		−	16079.8i		−	1.48667i
$105$	2589.08	+	2778.95i	0.234837	+	0.252059i
$106$	8484.48			0.755116
$107$	−2177.73	+	2177.73i	−0.190211	+	0.190211i	−0.795787	−	0.605576i	$-0.792943\pi$
$107$	−2177.73	+	2177.73i	−0.190211	+	0.190211i	0.605576	+	0.795787i	$0.292943\pi$
$108$	18842.5	+	18842.5i	1.61544	+	1.61544i
$109$		−	2560.05i		−	0.215474i	−0.994179	−	0.107737i	$-0.965640\pi$
$109$		−	2560.05i		−	0.215474i	0.994179	−	0.107737i	$-0.0343605\pi$
$110$	13458.0	+	476.019i	1.11223	+	0.0393404i
$111$	−7304.87			−0.592880
$112$	4867.18	−	4867.18i	0.388009	−	0.388009i
$113$	−491.079	−	491.079i	−0.0384587	−	0.0384587i	0.687616	−	0.726075i	$-0.258657\pi$
$113$	−491.079	−	491.079i	−0.0384587	−	0.0384587i	−0.726075	+	0.687616i	$0.758657\pi$
$114$		−	30691.6i		−	2.36162i
$115$	734.360	−	20761.8i	0.0555282	−	1.56989i
$116$	54250.0			4.03166
$117$	1200.87	−	1200.87i	0.0877253	−	0.0877253i
$118$	−8059.68	−	8059.68i	−0.578834	−	0.578834i
$119$			6041.20i			0.426608i
$120$	−19473.9	+	18143.3i	−1.35235	+	1.25995i
$121$	−8872.53			−0.606006
$122$	−12636.4	+	12636.4i	−0.848993	+	0.848993i
$123$	1365.59	+	1365.59i	0.0902629	+	0.0902629i
$124$			20177.3i			1.31226i
$125$	−12156.2	+	9816.75i	−0.777994	+	0.628272i
$126$	1800.44			0.113406
$127$	6070.58	−	6070.58i	0.376377	−	0.376377i	−0.493417	−	0.869793i	$-0.664252\pi$
$127$	6070.58	−	6070.58i	0.376377	−	0.376377i	0.869793	+	0.493417i	$0.164252\pi$
$128$	−16255.4	−	16255.4i	−0.992153	−	0.992153i
$129$			15796.0i			0.949219i
$130$	14974.7	+	16072.9i	0.886077	+	0.951058i
$131$	2199.94			0.128194			0.0640970	−	0.997944i	$-0.479583\pi$
$131$	2199.94			0.128194			0.0640970	+	0.997944i	$0.479583\pi$
$132$	−15110.8	+	15110.8i	−0.867238	+	0.867238i
$133$	−6908.53	−	6908.53i	−0.390555	−	0.390555i
$134$		−	36826.5i		−	2.05093i
$135$	−19410.5	−	686.562i	−1.06505	−	0.0376715i
$136$	−42334.6			−2.28885
$137$	16433.0	−	16433.0i	0.875541	−	0.875541i	−0.117528	−	0.993070i	$-0.537497\pi$
$137$	16433.0	−	16433.0i	0.875541	−	0.875541i	0.993070	+	0.117528i	$0.0374970\pi$
$138$	34185.9	+	34185.9i	1.79510	+	1.79510i
$139$		−	2459.25i		−	0.127284i	−0.997973	−	0.0636419i	$-0.979728\pi$
$139$		−	2459.25i		−	0.127284i	0.997973	−	0.0636419i	$-0.0202715\pi$
$140$	−561.367	+	15870.9i	−0.0286412	+	0.809741i
$141$	18860.4			0.948665
$142$	34254.3	−	34254.3i	1.69878	−	1.69878i
$143$	6653.92	+	6653.92i	0.325391	+	0.325391i
$144$			5094.42i			0.245680i
$145$	−28930.9	+	26954.2i	−1.37602	+	1.28201i
$146$	−16050.9			−0.753000
$147$	−1989.59	+	1989.59i	−0.0920722	+	0.0920722i
$148$	−21597.3	−	21597.3i	−0.986000	−	0.986000i
$149$			40002.9i			1.80185i	0.433973	+	0.900926i	$0.357111\pi$
$149$			40002.9i			1.80185i	−0.433973	+	0.900926i	$0.642889\pi$
$150$	2569.08	−	36271.0i	0.114181	−	1.61204i
$151$	−11343.6			−0.497503			−0.248751	−	0.968567i	$-0.580020\pi$
$151$	−11343.6			−0.497503			−0.248751	+	0.968567i	$0.580020\pi$
$152$	48412.5	−	48412.5i	2.09542	−	2.09542i
$153$	−3161.63	−	3161.63i	−0.135060	−	0.135060i
$154$			9976.05i			0.420647i
$155$	−10025.1	−	10760.3i	−0.417280	−	0.447881i
$156$	−34860.5			−1.43247
$157$	8858.33	−	8858.33i	0.359379	−	0.359379i	−0.504205	−	0.863584i	$-0.668214\pi$
$157$	8858.33	−	8858.33i	0.359379	−	0.359379i	0.863584	+	0.504205i	$0.168214\pi$
$158$	19167.4	+	19167.4i	0.767804	+	0.767804i
$159$		−	9813.59i		−	0.388181i
$160$	−13975.2	−	494.312i	−0.545905	−	0.0193090i
$161$	15390.2			0.593734
$162$	26392.8	−	26392.8i	1.00567	−	1.00567i
$163$	4388.99	+	4388.99i	0.165192	+	0.165192i	0.784862	−	0.619670i	$-0.212734\pi$
$163$	4388.99	+	4388.99i	0.165192	+	0.165192i	−0.619670	+	0.784862i	$0.712734\pi$
$164$			8074.90i			0.300227i
$165$	550.589	−	15566.2i	0.0202236	−	0.571762i
$166$	−41351.7			−1.50064
$167$	−36986.7	+	36986.7i	−1.32621	+	1.32621i	−0.417560	+	0.908649i	$0.637115\pi$
$167$	−36986.7	+	36986.7i	−1.32621	+	1.32621i	−0.908649	+	0.417560i	$0.862885\pi$
$168$	−13942.3	−	13942.3i	−0.493988	−	0.493988i
$169$		−	13210.4i		−	0.462533i
$170$	42316.3	−	39425.0i	1.46423	−	1.36419i
$171$	7231.08			0.247292
$172$	−46701.8	+	46701.8i	−1.57862	+	1.57862i
$173$	35346.5	+	35346.5i	1.18101	+	1.18101i	0.979483	+	0.201528i	$0.0645907\pi$
$173$	35346.5	+	35346.5i	1.18101	+	1.18101i	0.201528	+	0.979483i	$0.435409\pi$
$174$		−	92019.2i		−	3.03934i
$175$	−7586.13	−	8742.71i	−0.247711	−	0.285476i
$176$	−28227.7			−0.911277
$177$	−9322.24	+	9322.24i	−0.297560	+	0.297560i
$178$	5720.05	+	5720.05i	0.180534	+	0.180534i
$179$		−	30171.1i		−	0.941640i	−0.882229	−	0.470820i	$-0.843958\pi$
$179$		−	30171.1i		−	0.941640i	0.882229	−	0.470820i	$-0.156042\pi$
$180$	−8012.16	−	8599.74i	−0.247289	−	0.265424i
$181$	35744.0			1.09105			0.545526	−	0.838094i	$-0.316330\pi$
$181$	35744.0			1.09105			0.545526	+	0.838094i	$0.316330\pi$
$182$	−11507.4	+	11507.4i	−0.347403	+	0.347403i
$183$	14615.9	+	14615.9i	0.436440	+	0.436440i
$184$			107849.i			3.18552i
$185$	22248.3	+	786.939i	0.650060	+	0.0229931i
$186$	34224.9			0.989274
$187$	17518.3	−	17518.3i	0.500966	−	0.500966i
$188$	55762.0	+	55762.0i	1.57769	+	1.57769i
$189$		−	14388.5i		−	0.402801i
$190$	−3306.34	+	93476.8i	−0.0915885	+	2.58939i
$191$	36695.0			1.00587			0.502933	−	0.864325i	$-0.332254\pi$
$191$	36695.0			1.00587			0.502933	+	0.864325i	$0.332254\pi$
$192$	−11482.1	+	11482.1i	−0.311473	+	0.311473i
$193$	−5739.33	−	5739.33i	−0.154080	−	0.154080i	0.625857	−	0.779938i	$-0.284749\pi$
$193$	−5739.33	−	5739.33i	−0.154080	−	0.154080i	−0.779938	+	0.625857i	$0.784749\pi$
$194$		−	15426.0i		−	0.409873i
$195$	18590.7	−	17320.5i	0.488908	−	0.455503i
$196$	−11764.7			−0.306245
$197$	−33650.6	+	33650.6i	−0.867082	+	0.867082i	−0.992148	−	0.125066i	$-0.960086\pi$
$197$	−33650.6	+	33650.6i	−0.867082	+	0.867082i	0.125066	+	0.992148i	$0.460086\pi$
$198$	−5220.90	−	5220.90i	−0.133173	−	0.133173i
$199$			8221.91i			0.207619i	0.994597	+	0.103809i	$0.0331032\pi$
$199$			8221.91i			0.207619i	−0.994597	+	0.103809i	$0.966897\pi$
$200$	61265.8	−	53160.9i	1.53164	−	1.32902i
$201$	−42595.4			−1.05432
$202$	−16238.9	+	16238.9i	−0.397974	+	0.397974i
$203$	−20713.1	−	20713.1i	−0.502635	−	0.502635i
$204$			91779.9i			2.20540i
$205$	−4012.03	−	4306.25i	−0.0954677	−	0.102469i
$206$	−91234.3			−2.14993
$207$	−8054.35	+	8054.35i	−0.187970	+	0.187970i
$208$	−32560.7	−	32560.7i	−0.752604	−	0.752604i
$209$			40066.7i			0.917258i
$210$	26920.4	+	952.194i	0.610440	+	0.0215917i
$211$	−30204.5			−0.678432			−0.339216	−	0.940708i	$-0.610162\pi$
$211$	−30204.5			−0.678432			−0.339216	+	0.940708i	$0.610162\pi$
$212$	29014.5	−	29014.5i	0.645571	−	0.645571i
$213$	−39620.3	−	39620.3i	−0.873289	−	0.873289i
$214$			21842.4i			0.476950i
$215$	1701.67	−	48109.4i	0.0368127	−	1.04077i
$216$	100829.			2.16112
$217$	7703.87	−	7703.87i	0.163602	−	0.163602i
$218$	−12838.5	−	12838.5i	−0.270148	−	0.270148i
$219$			18565.4i			0.387093i
$220$	47650.4	−	44394.7i	0.984512	−	0.917246i
$221$	40414.7			0.827474
$222$	−36633.6	+	36633.6i	−0.743315	+	0.743315i
$223$	−1152.95	−	1152.95i	−0.0231846	−	0.0231846i	0.695419	−	0.718604i	$-0.255219\pi$
$223$	−1152.95	−	1152.95i	−0.0231846	−	0.0231846i	−0.718604	+	0.695419i	$0.755219\pi$
$224$		−	10359.4i		−	0.206462i
$225$	8545.60	+	605.285i	0.168802	+	0.0119563i
$226$	−4925.47			−0.0964341
$227$	5784.04	−	5784.04i	0.112248	−	0.112248i	−0.648752	−	0.761000i	$-0.724709\pi$
$227$	5784.04	−	5784.04i	0.112248	−	0.112248i	0.761000	+	0.648752i	$0.224709\pi$
$228$	−104957.	−	104957.i	−2.01902	−	2.01902i
$229$		−	102632.i		−	1.95710i	−0.206001	−	0.978552i	$-0.566045\pi$
$229$		−	102632.i		−	1.95710i	0.206001	−	0.978552i	$-0.433955\pi$
$230$	−100437.	−	107802.i	−1.89861	−	2.03785i
$231$	11538.8			0.216241
$232$	145150.	−	145150.i	2.69675	−	2.69675i
$233$	16734.1	+	16734.1i	0.308241	+	0.308241i	0.844227	−	0.535986i	$-0.180060\pi$
$233$	16734.1	+	16734.1i	0.308241	+	0.308241i	−0.535986	+	0.844227i	$0.680060\pi$
$234$		−	12044.6i		−	0.219969i
$235$	−57442.8	−	2031.79i	−1.04016	−	0.0367912i
$236$	−55123.7			−0.989724
$237$	22170.1	−	22170.1i	0.394703	−	0.394703i
$238$	30296.3	+	30296.3i	0.534855	+	0.534855i
$239$			40418.5i			0.707594i	0.935322	+	0.353797i	$0.115110\pi$
$239$			40418.5i			0.707594i	−0.935322	+	0.353797i	$0.884890\pi$
$240$	−2694.28	+	76172.5i	−0.0467757	+	1.32244i
$241$	27952.5			0.481268			0.240634	−	0.970616i	$-0.422645\pi$
$241$	27952.5			0.481268			0.240634	+	0.970616i	$0.422645\pi$
$242$	−44495.3	+	44495.3i	−0.759772	+	0.759772i
$243$	13970.4	+	13970.4i	0.236589	+	0.236589i
$244$			86425.9i			1.45166i
$245$	6273.99	−	5845.32i	0.104523	−	0.0973814i
$246$	13696.7			0.226332
$247$	−46217.0	+	46217.0i	−0.757543	+	0.757543i
$248$	53986.0	+	53986.0i	0.877763	+	0.877763i
$249$			47829.5i			0.771431i
$250$	−11732.0	+	110193.i	−0.187712	+	1.76309i
$251$	32087.2			0.509312			0.254656	−	0.967032i	$-0.418038\pi$
$251$	32087.2			0.509312			0.254656	+	0.967032i	$0.418038\pi$
$252$	6156.98	−	6156.98i	0.0969543	−	0.0969543i
$253$	−44628.4	−	44628.4i	−0.697221	−	0.697221i
$254$		−	60887.3i		−	0.943755i
$255$	−45601.0	−	48945.2i	−0.701284	−	0.752713i
$256$	−131368.			−2.00452
$257$	−14697.1	+	14697.1i	−0.222518	+	0.222518i	−0.809558	−	0.587040i	$-0.800293\pi$
$257$	−14697.1	+	14697.1i	−0.222518	+	0.222518i	0.587040	+	0.809558i	$0.300293\pi$
$258$	79215.9	+	79215.9i	1.19007	+	1.19007i
$259$			16492.1i			0.245853i
$260$	106174.	+	3755.45i	1.57062	+	0.0555540i
$261$	21680.1			0.318259
$262$	11032.6	−	11032.6i	0.160722	−	0.160722i
$263$	17788.8	+	17788.8i	0.257179	+	0.257179i	0.823906	−	0.566727i	$-0.191791\pi$
$263$	17788.8	+	17788.8i	0.257179	+	0.257179i	−0.566727	+	0.823906i	$0.691791\pi$
$264$			80860.0i			1.16018i
$265$	−1057.20	+	29889.1i	−0.0150544	+	0.425619i
$266$	−69291.9			−0.979308
$267$	6616.10	−	6616.10i	0.0928068	−	0.0928068i
$268$	−125936.	−	125936.i	−1.75340	−	1.75340i
$269$		−	2894.86i		−	0.0400058i	−0.999800	−	0.0200029i	$-0.993632\pi$
$269$		−	2894.86i		−	0.0400058i	0.999800	−	0.0200029i	$-0.00636755\pi$
$270$	−100786.	+	93899.4i	−1.38252	+	1.28806i
$271$	120397.			1.63937			0.819685	−	0.572814i	$-0.194148\pi$
$271$	120397.			1.63937			0.819685	+	0.572814i	$0.194148\pi$
$272$	−85724.9	+	85724.9i	−1.15870	+	1.15870i
$273$	13310.0	+	13310.0i	0.178589	+	0.178589i
$274$		−	164822.i		−	2.19540i
$275$	−3353.83	+	47350.4i	−0.0443482	+	0.626121i
$276$	233812.			3.06937
$277$	53882.9	−	53882.9i	0.702249	−	0.702249i	−0.262644	−	0.964893i	$-0.584594\pi$
$277$	53882.9	−	53882.9i	0.702249	−	0.702249i	0.964893	+	0.262644i	$0.0845944\pi$
$278$	−12333.0	−	12333.0i	−0.159580	−	0.159580i
$279$			8063.54i			0.103590i
$280$	40961.9	+	43965.9i	0.522473	+	0.560789i
$281$	−131983.			−1.67150			−0.835748	−	0.549113i	$-0.814966\pi$
$281$	−131983.			−1.67150			−0.835748	+	0.549113i	$0.814966\pi$
$282$	94584.0	−	94584.0i	1.18938	−	1.18938i
$283$	61319.2	+	61319.2i	0.765639	+	0.765639i	0.977335	−	0.211697i	$-0.0678989\pi$
$283$	61319.2	+	61319.2i	0.765639	+	0.765639i	−0.211697	+	0.977335i	$0.567899\pi$
$284$		−	234280.i		−	2.90468i
$285$	108120.	+	3824.29i	1.33112	+	0.0470827i
$286$	66738.2			0.815910
$287$	3083.06	−	3083.06i	0.0374299	−	0.0374299i
$288$	5421.53	+	5421.53i	0.0653638	+	0.0653638i
$289$		−	22881.7i		−	0.273964i
$290$	−9913.04	+	280261.i	−0.117872	+	3.33247i
$291$	−17842.5			−0.210702
$292$	−54889.7	+	54889.7i	−0.643762	+	0.643762i
$293$	−66889.0	−	66889.0i	−0.779147	−	0.779147i	0.200539	−	0.979686i	$-0.435731\pi$
$293$	−66889.0	−	66889.0i	−0.779147	−	0.779147i	−0.979686	+	0.200539i	$0.935731\pi$
$294$			19955.4i			0.230869i
$295$	29396.8	−	27388.3i	0.337798	−	0.314718i
$296$	−115571.			−1.31906
$297$	−41723.7	+	41723.7i	−0.473009	+	0.473009i
$298$	200613.	+	200613.i	2.25905	+	2.25905i
$299$		−	102958.i		−	1.15164i
$300$	−115251.	−	132822.i	−1.28057	−	1.47580i
$301$	35662.3			0.393619
$302$	−56887.4	+	56887.4i	−0.623737	+	0.623737i
$303$	18782.8	+	18782.8i	0.204585	+	0.204585i
$304$		−	196065.i		−	2.12155i
$305$	−42940.9	−	46090.0i	−0.461606	−	0.495458i
$306$	−31710.8			−0.338660
$307$	13072.6	−	13072.6i	0.138703	−	0.138703i	−0.634346	−	0.773049i	$-0.718731\pi$
$307$	13072.6	−	13072.6i	0.138703	−	0.138703i	0.773049	+	0.634346i	$0.218731\pi$
$308$	34115.3	+	34115.3i	0.359623	+	0.359623i
$309$			105526.i			1.10521i
$310$	−104238.	−	3686.98i	−1.08468	−	0.0383661i
$311$	−34805.2			−0.359851			−0.179926	−	0.983680i	$-0.557586\pi$
$311$	−34805.2			−0.359851			−0.179926	+	0.983680i	$0.557586\pi$
$312$	−93271.9	+	93271.9i	−0.958168	+	0.958168i
$313$	−67248.3	−	67248.3i	−0.686424	−	0.686424i	0.275016	−	0.961440i	$-0.411317\pi$
$313$	−67248.3	−	67248.3i	−0.686424	−	0.686424i	−0.961440	+	0.275016i	$0.911317\pi$
$314$		−	88848.1i		−	0.901133i
$315$	−224.341	+	6342.56i	−0.00226093	+	0.0639210i
$316$	131095.			1.31284
$317$	126470.	−	126470.i	1.25854	−	1.25854i	0.306752	−	0.951790i	$-0.400758\pi$
$317$	126470.	−	126470.i	1.25854	−	1.25854i	0.951790	−	0.306752i	$-0.0992422\pi$
$318$	−49214.7	−	49214.7i	−0.486676	−	0.486676i
$319$			120128.i			1.18049i
$320$	36207.8	−	33734.0i	0.353592	−	0.329433i
$321$	25264.0			0.245184
$322$	77180.9	−	77180.9i	0.744386	−	0.744386i
$323$	121679.	+	121679.i	1.16630	+	1.16630i
$324$		−	180512.i		−	1.71955i
$325$	−58487.3	+	50750.0i	−0.553726	+	0.480473i
$326$	44021.1			0.414215
$327$	−14849.7	+	14849.7i	−0.138874	+	0.138874i
$328$	21605.0	+	21605.0i	0.200820	+	0.200820i
$329$		−	42580.8i		−	0.393389i
$330$	−75302.6	−	80824.9i	−0.691484	−	0.742194i
$331$	−81352.0			−0.742527			−0.371264	−	0.928527i	$-0.621075\pi$
$331$	−81352.0			−0.742527			−0.371264	+	0.928527i	$0.621075\pi$
$332$	−141411.	+	141411.i	−1.28294	+	1.28294i
$333$	−8631.02	−	8631.02i	−0.0778348	−	0.0778348i
$334$			370972.i			3.32544i
$335$	129732.	+	4588.72i	1.15600	+	0.0408886i
$336$	−56464.7			−0.500148
$337$	−111373.	+	111373.i	−0.980661	+	0.980661i	−0.999817	−	0.0191559i	$-0.993902\pi$
$337$	−111373.	+	111373.i	−0.980661	+	0.980661i	0.0191559	+	0.999817i	$0.493902\pi$
$338$	−66249.5	−	66249.5i	−0.579895	−	0.579895i
$339$			5697.05i			0.0495736i
$340$	9887.26	−	279532.i	0.0855299	−	2.41810i
$341$	−44679.4			−0.384236
$342$	36263.5	−	36263.5i	0.310040	−	0.310040i
$343$	4491.86	+	4491.86i	0.0381802	+	0.0381802i
$344$			249908.i			2.11185i
$345$	−124690.	+	116170.i	−1.04759	+	0.976015i
$346$	354522.			2.96135
$347$	9505.40	−	9505.40i	0.0789426	−	0.0789426i	−0.666533	−	0.745476i	$-0.732222\pi$
$347$	9505.40	−	9505.40i	0.0789426	−	0.0789426i	0.745476	+	0.666533i	$0.232222\pi$
$348$	−314680.	−	314680.i	−2.59843	−	2.59843i
$349$		−	187256.i		−	1.53739i	−0.639615	−	0.768696i	$-0.720906\pi$
$349$		−	187256.i		−	1.53739i	0.639615	−	0.768696i	$-0.279094\pi$
$350$	−81888.3	−	5800.16i	−0.668476	−	0.0473482i
$351$	−96256.5			−0.781296
$352$	−30040.2	+	30040.2i	−0.242448	+	0.242448i
$353$	−109193.	−	109193.i	−0.876284	−	0.876284i	0.116864	−	0.993148i	$-0.462716\pi$
$353$	−109193.	−	109193.i	−0.876284	−	0.876284i	−0.993148	+	0.116864i	$0.962716\pi$
$354$			93501.2i			0.746123i
$355$	116402.	+	124939.i	0.923646	+	0.991382i
$356$	39121.9			0.308688
$357$	35042.3	−	35042.3i	0.274952	−	0.274952i
$358$	−151307.	−	151307.i	−1.18057	−	1.18057i
$359$			56473.7i			0.438185i	0.975704	+	0.219092i	$0.0703096\pi$
$359$			56473.7i			0.438185i	−0.975704	+	0.219092i	$0.929690\pi$
$360$	−44446.4	−	1572.10i	−0.342951	−	0.0121304i
$361$	−147976.			−1.13547
$362$	179254.	−	179254.i	1.36789	−	1.36789i
$363$	51465.6	+	51465.6i	0.390574	+	0.390574i
$364$			78704.0i			0.594010i
$365$	2000.01	−	56544.1i	0.0150123	−	0.424426i
$366$	146596.			1.09436
$367$	43447.8	−	43447.8i	0.322579	−	0.322579i	−0.527177	−	0.849756i	$-0.676749\pi$
$367$	43447.8	−	43447.8i	0.322579	−	0.322579i	0.849756	+	0.527177i	$0.176749\pi$
$368$	218387.	+	218387.i	1.61262	+	1.61262i
$369$			3227.00i			0.0236999i
$370$	115521.	−	107628.i	0.843832	−	0.786177i
$371$	−22156.0			−0.160969
$372$	117040.	−	117040.i	0.845760	−	0.845760i
$373$	−31294.2	−	31294.2i	−0.224929	−	0.224929i	0.585641	−	0.810570i	$-0.300843\pi$
$373$	−31294.2	−	31294.2i	−0.224929	−	0.224929i	−0.810570	+	0.585641i	$0.800843\pi$
$374$		−	175707.i		−	1.25616i
$375$	127455.	+	13569.8i	0.906346	+	0.0964965i
$376$	298391.			2.11062
$377$	−138567.	+	138567.i	−0.974939	+	0.974939i
$378$	−72157.4	−	72157.4i	−0.505007	−	0.505007i
$379$			37541.2i			0.261354i	0.991425	+	0.130677i	$0.0417151\pi$
$379$			37541.2i			0.261354i	−0.991425	+	0.130677i	$0.958285\pi$
$380$	308358.	+	330971.i	2.13544	+	2.29204i
$381$	−70425.4			−0.485154
$382$	184024.	−	184024.i	1.26109	−	1.26109i
$383$	−40494.9	−	40494.9i	−0.276060	−	0.276060i	0.555474	−	0.831534i	$-0.312537\pi$
$383$	−40494.9	−	40494.9i	−0.276060	−	0.276060i	−0.831534	+	0.555474i	$0.812537\pi$
$384$			188581.i			1.27890i
$385$	−35143.6	−	1243.05i	−0.237096	−	0.00838626i
$386$	−57564.9			−0.386352
$387$	−18663.6	+	18663.6i	−0.124616	+	0.124616i
$388$	−52752.5	−	52752.5i	−0.350412	−	0.350412i
$389$		−	78442.6i		−	0.518386i	−0.965826	−	0.259193i	$-0.916543\pi$
$389$		−	78442.6i		−	0.518386i	0.965826	−	0.259193i	$-0.0834565\pi$
$390$	6370.02	−	180093.i	0.0418805	−	1.18404i
$391$	−271064.			−1.77304
$392$	−31477.3	+	31477.3i	−0.204845	+	0.204845i
$393$	−12760.8	−	12760.8i	−0.0826218	−	0.0826218i
$394$			337512.i			2.17419i
$395$	−69911.3	+	65134.6i	−0.448077	+	0.417463i
$396$	−35708.0			−0.227707
$397$	−131890.	+	131890.i	−0.836815	+	0.836815i	−0.988438	−	0.151623i	$-0.951550\pi$
$397$	−131890.	+	131890.i	−0.836815	+	0.836815i	0.151623	+	0.988438i	$0.451550\pi$
$398$	41232.5	+	41232.5i	0.260299	+	0.260299i
$399$			80146.6i			0.503430i
$400$	16411.8	−	231707.i	0.102574	−	1.44817i
$401$	260765.			1.62166			0.810832	−	0.585280i	$-0.199015\pi$
$401$	260765.			1.62166			0.810832	+	0.585280i	$0.199015\pi$
$402$	−213614.	+	213614.i	−1.32184	+	1.32184i
$403$	−51537.6	−	51537.6i	−0.317332	−	0.317332i
$404$			111065.i			0.680479i
$405$	89687.8	+	96265.0i	0.546793	+	0.586893i
$406$	−207750.			−1.26034
$407$	47823.7	−	47823.7i	0.288705	−	0.288705i
$408$	245564.	+	245564.i	1.47518	+	1.47518i
$409$		−	253509.i		−	1.51547i	−0.652564	−	0.757734i	$-0.726307\pi$
$409$		−	253509.i		−	1.51547i	0.652564	−	0.757734i	$-0.273693\pi$
$410$	−41715.8	−	1475.52i	−0.248160	−	0.00877762i
$411$	−190641.			−1.12858
$412$	−311996.	+	311996.i	−1.83804	+	1.83804i
$413$	21046.7	+	21046.7i	0.123391	+	0.123391i
$414$			80784.3i			0.471331i
$415$	5152.57	−	145673.i	0.0299177	−	0.845831i
$416$	−69302.8			−0.400465
$417$	−14265.0	+	14265.0i	−0.0820351	+	0.0820351i
$418$	200933.	+	200933.i	1.15000	+	1.15000i
$419$			60645.6i			0.345439i	0.984971	+	0.172719i	$0.0552554\pi$
$419$			60645.6i			0.345439i	−0.984971	+	0.172719i	$0.944745\pi$
$420$	95316.4	−	88803.9i	0.540342	−	0.503424i
$421$	−63976.9			−0.360960			−0.180480	−	0.983579i	$-0.557765\pi$
$421$	−63976.9			−0.360960			−0.180480	+	0.983579i	$0.557765\pi$
$422$	−151474.	+	151474.i	−0.850576	+	0.850576i
$423$	22284.4	+	22284.4i	0.124543	+	0.124543i
$424$		−	155261.i		−	0.863637i
$425$	133613.	+	153984.i	0.739728	+	0.852506i
$426$	−397387.			−2.18975
$427$	32998.1	−	32998.1i	0.180981	−	0.180981i
$428$	74694.8	+	74694.8i	0.407758	+	0.407758i
$429$		−	77192.8i		−	0.419433i
$430$	−232733.	−	249800.i	−1.25869	−	1.35100i
$431$	138787.			0.747129			0.373565	−	0.927604i	$-0.378135\pi$
$431$	138787.			0.747129			0.373565	+	0.927604i	$0.378135\pi$
$432$	204173.	−	204173.i	1.09403	−	1.09403i
$433$	181902.	+	181902.i	0.970201	+	0.970201i	0.999569	−	0.0293680i	$-0.00934947\pi$
$433$	181902.	+	181902.i	0.970201	+	0.970201i	−0.0293680	+	0.999569i	$0.509349\pi$
$434$		−	77269.0i		−	0.410229i
$435$	324164.	+	11465.9i	1.71312	+	0.0605942i
$436$	−87808.3			−0.461915
$437$	309981.	−	309981.i	1.62320	−	1.62320i
$438$	93104.3	+	93104.3i	0.485313	+	0.485313i
$439$		−	291440.i		−	1.51224i	−0.654435	−	0.756118i	$-0.727093\pi$
$439$		−	291440.i		−	1.51224i	0.654435	−	0.756118i	$-0.272907\pi$
$440$	8710.88	−	246274.i	0.0449942	−	1.27207i
$441$	−4701.57			−0.0241750
$442$	202677.	−	202677.i	1.03744	−	1.03744i
$443$	−75828.2	−	75828.2i	−0.386388	−	0.386388i	0.487009	−	0.873397i	$-0.338088\pi$
$443$	−75828.2	−	75828.2i	−0.386388	−	0.386388i	−0.873397	+	0.487009i	$0.838088\pi$
$444$			250553.i			1.27096i
$445$	−20863.3	+	19437.8i	−0.105357	+	0.0981583i
$446$	−11564.0			−0.0581349
$447$	232039.	−	232039.i	1.16130	−	1.16130i
$448$	25923.0	+	25923.0i	0.129160	+	0.129160i
$449$		−	239109.i		−	1.18605i	−0.805184	−	0.593025i	$-0.797933\pi$
$449$		−	239109.i		−	1.18605i	0.805184	−	0.593025i	$-0.202067\pi$
$450$	45891.2	−	39820.3i	0.226623	−	0.196643i
$451$	−17880.5			−0.0879078
$452$	−16843.7	+	16843.7i	−0.0824444	+	0.0824444i
$453$	65798.9	+	65798.9i	0.320643	+	0.320643i
$454$		−	58013.3i		−	0.281459i
$455$	−39104.2	−	41971.9i	−0.188886	−	0.202739i
$456$	−561639.			−2.70102
$457$	34147.5	−	34147.5i	0.163503	−	0.163503i	−0.620614	−	0.784117i	$-0.713116\pi$
$457$	34147.5	−	34147.5i	0.163503	−	0.163503i	0.784117	+	0.620614i	$0.213116\pi$
$458$	−514697.	−	514697.i	−2.45369	−	2.45369i
$459$			253422.i			1.20287i
$460$	−712118.	−	25188.1i	−3.36539	−	0.119037i
$461$	171075.			0.804981			0.402491	−	0.915424i	$-0.368145\pi$
$461$	171075.			0.804981			0.402491	+	0.915424i	$0.368145\pi$
$462$	57866.6	−	57866.6i	0.271109	−	0.271109i
$463$	125583.	+	125583.i	0.585826	+	0.585826i	0.936498	−	0.350672i	$-0.114047\pi$
$463$	125583.	+	125583.i	0.585826	+	0.585826i	−0.350672	+	0.936498i	$0.614047\pi$
$464$		−	587839.i		−	2.73038i
$465$	−4264.55	+	120567.i	−0.0197228	+	0.557601i
$466$	167841.			0.772907
$467$	−126812.	+	126812.i	−0.581469	+	0.581469i	−0.935307	−	0.353838i	$-0.884876\pi$
$467$	−126812.	+	126812.i	−0.581469	+	0.581469i	0.353838	+	0.935307i	$0.384876\pi$
$468$	−41189.2	−	41189.2i	−0.188058	−	0.188058i
$469$			96167.0i			0.437200i
$470$	−298262.	+	277883.i	−1.35021	+	1.25796i
$471$	−102766.			−0.463243
$472$	−147487.	+	147487.i	−0.662020	+	0.662020i
$473$	−103413.	−	103413.i	−0.462226	−	0.462226i
$474$		−	222364.i		−	0.989707i
$475$	−328887.	−	23295.1i	−1.45767	−	0.103247i
$476$	207210.			0.914527
$477$	11595.2	−	11595.2i	0.0509614	−	0.0509614i
$478$	202697.	+	202697.i	0.887137	+	0.887137i
$479$			356277.i			1.55280i	0.630239	+	0.776401i	$0.282957\pi$
$479$			356277.i			1.55280i	−0.630239	+	0.776401i	$0.717043\pi$
$480$	78196.3	+	83930.9i	0.339394	+	0.364283i
$481$	110329.			0.476871
$482$	140181.	−	140181.i	0.603384	−	0.603384i
$483$	−89271.5	−	89271.5i	−0.382665	−	0.382665i
$484$			304323.i			1.29910i
$485$	54342.5	+	1922.13i	0.231023	+	0.00817147i
$486$	140121.			0.593242
$487$	55243.2	−	55243.2i	0.232927	−	0.232927i	−0.580986	−	0.813914i	$-0.697333\pi$
$487$	55243.2	−	55243.2i	0.232927	−	0.232927i	0.813914	+	0.580986i	$0.197333\pi$
$488$	231239.	+	231239.i	0.971005	+	0.971005i
$489$		−	50917.1i		−	0.212934i
$490$	2149.75	−	60777.7i	0.00895357	−	0.253135i
$491$	−22553.0			−0.0935495			−0.0467747	−	0.998905i	$-0.514894\pi$
$491$	−22553.0			−0.0935495			−0.0467747	+	0.998905i	$0.514894\pi$
$492$	46838.9	−	46838.9i	0.193498	−	0.193498i
$493$	364816.	+	364816.i	1.50100	+	1.50100i
$494$			463552.i			1.89952i
$495$	19042.7	−	17741.6i	0.0777174	−	0.0724074i
$496$	218636.			0.888708
$497$	−89450.0	+	89450.0i	−0.362132	+	0.362132i
$498$	239862.	+	239862.i	0.967172	+	0.967172i
$499$		−	31665.7i		−	0.127171i	−0.997976	−	0.0635855i	$-0.979746\pi$
$499$		−	31665.7i		−	0.127171i	0.997976	−	0.0635855i	$-0.0202536\pi$
$500$	336709.	+	416949.i	1.34684	+	1.66780i
$501$	429086.			1.70950
$502$	160916.	−	160916.i	0.638543	−	0.638543i
$503$	−84275.0	−	84275.0i	−0.333091	−	0.333091i	0.520668	−	0.853759i	$-0.325683\pi$
$503$	−84275.0	−	84275.0i	−0.333091	−	0.333091i	−0.853759	+	0.520668i	$0.825683\pi$
$504$		−	32946.9i		−	0.129704i
$505$	−55182.9	−	59229.7i	−0.216382	−	0.232251i
$506$	−447618.			−1.74826
$507$	−76627.6	+	76627.6i	−0.298105	+	0.298105i
$508$	−208217.	−	208217.i	−0.806844	−	0.806844i
$509$		−	184416.i		−	0.711807i	−0.934523	−	0.355903i	$-0.884173\pi$
$509$		−	184416.i		−	0.711807i	0.934523	−	0.355903i	$-0.115827\pi$
$510$	−474144.	−	16770.8i	−1.82293	−	0.0644784i
$511$	41914.7			0.160518
$512$	−398719.	+	398719.i	−1.52099	+	1.52099i
$513$	−289805.	−	289805.i	−1.10121	−	1.10121i
$514$			147410.i			0.557957i
$515$	11368.1	−	321400.i	0.0428622	−	1.21180i
$516$	541792.			2.03486
$517$	−123476.	+	123476.i	−0.461956	+	0.461956i
$518$	82706.9	+	82706.9i	0.308235	+	0.308235i
$519$		−	410058.i		−	1.52234i
$520$	294124.	−	274028.i	1.08774	−	1.01342i
$521$	−37375.8			−0.137694			−0.0688470	−	0.997627i	$-0.521932\pi$
$521$	−37375.8			−0.137694			−0.0688470	+	0.997627i	$0.521932\pi$
$522$	108725.	−	108725.i	0.399013	−	0.399013i
$523$	322468.	+	322468.i	1.17892	+	1.17892i	0.980021	+	0.198895i	$0.0637354\pi$
$523$	322468.	+	322468.i	1.17892	+	1.17892i	0.198895	+	0.980021i	$0.436265\pi$
$524$		−	75456.6i		−	0.274811i
$525$	−6708.76	+	94716.3i	−0.0243402	+	0.343642i
$526$	178420.			0.644869
$527$	−135687.	+	135687.i	−0.488559	+	0.488559i
$528$	163736.	+	163736.i	0.587323	+	0.587323i
$529$			410705.i			1.46764i
$530$	144590.	+	155194.i	0.514740	+	0.552488i
$531$	−22029.3			−0.0781288
$532$	−236959.	+	236959.i	−0.837239	+	0.837239i
$533$	−20625.2	−	20625.2i	−0.0726011	−	0.0726011i
$534$		−	66358.9i		−	0.232711i
$535$	−76946.2	−	2721.64i	−0.268831	−	0.00950875i
$536$	−673904.			−2.34568
$537$	−175009.	+	175009.i	−0.606893	+	0.606893i
$538$	−14517.6	−	14517.6i	−0.0501568	−	0.0501568i
$539$		−	26051.0i		−	0.0896699i
$540$	−23548.7	+	665768.i	−0.0807568	+	2.28315i
$541$	372458.			1.27257			0.636287	−	0.771452i	$-0.280469\pi$
$541$	372458.			1.27257			0.636287	+	0.771452i	$0.280469\pi$
$542$	603785.	−	603785.i	2.05534	−	2.05534i
$543$	−207335.	−	207335.i	−0.703189	−	0.703189i
$544$			182459.i			0.616548i
$545$	46827.2	−	43627.7i	0.157654	−	0.146882i
$546$	133498.			0.447806
$547$	413763.	−	413763.i	1.38286	−	1.38286i	0.543348	−	0.839508i	$-0.317157\pi$
$547$	413763.	−	413763.i	1.38286	−	1.38286i	0.839508	−	0.543348i	$-0.182843\pi$
$548$	−563644.	−	563644.i	−1.87691	−	1.87691i
$549$			34538.7i			0.114594i
$550$	220640.	+	254279.i	0.729390	+	0.840592i
$551$	−834385.			−2.74829
$552$	625583.	−	625583.i	2.05308	−	2.05308i
$553$	−50053.0	−	50053.0i	−0.163674	−	0.163674i
$554$		−	540440.i		−	1.76087i
$555$	−124488.	−	133617.i	−0.404148	−	0.433786i
$556$	−84350.9			−0.272860
$557$	−298308.	+	298308.i	−0.961512	+	0.961512i	−0.999286	−	0.0377744i	$-0.987973\pi$
$557$	−298308.	+	298308.i	−0.961512	+	0.961512i	0.0377744	+	0.999286i	$0.487973\pi$
$558$	40438.2	+	40438.2i	0.129875	+	0.129875i
$559$		−	238575.i		−	0.763485i
$560$	171973.	+	6082.83i	0.548385	+	0.0193968i
$561$	−203231.			−0.645751
$562$	−661888.	+	661888.i	−2.09562	+	2.09562i
$563$	83327.3	+	83327.3i	0.262888	+	0.262888i	0.826226	−	0.563338i	$-0.190483\pi$
$563$	83327.3	+	83327.3i	0.262888	+	0.262888i	−0.563338	+	0.826226i	$0.690483\pi$
$564$		−	646901.i		−	2.03367i
$565$	613.732	−	17351.4i	0.00192257	−	0.0543548i
$566$	615026.			1.91982
$567$	−68921.0	+	68921.0i	−0.214380	+	0.214380i
$568$	−626833.	−	626833.i	−1.94292	−	1.94292i
$569$			260413.i			0.804336i	0.915566	+	0.402168i	$0.131743\pi$
$569$			260413.i			0.804336i	−0.915566	+	0.402168i	$0.868257\pi$
$570$	561396.	−	523038.i	1.72790	−	1.60984i
$571$	−94163.6			−0.288809			−0.144405	−	0.989519i	$-0.546127\pi$
$571$	−94163.6			−0.288809			−0.144405	+	0.989519i	$0.546127\pi$
$572$	228226.	−	228226.i	0.697546	−	0.697546i
$573$	−212851.	−	212851.i	−0.648287	−	0.648287i
$574$		−	30922.8i		−	0.0938545i
$575$	392279.	−	340384.i	1.18648	−	1.02952i
$576$	−27133.3			−0.0817819
$577$	−388454.	+	388454.i	−1.16678	+	1.16678i	−0.183816	+	0.982961i	$0.558845\pi$
$577$	−388454.	+	388454.i	−1.16678	+	1.16678i	−0.982961	+	0.183816i	$0.941155\pi$
$578$	−114751.	−	114751.i	−0.343478	−	0.343478i
$579$			66582.6i			0.198611i
$580$	924514.	+	992314.i	2.74826	+	2.94980i
$581$	107984.			0.319894
$582$	−89479.1	+	89479.1i	−0.264165	+	0.264165i
$583$	64247.9	+	64247.9i	0.189026	+	0.189026i
$584$			293723.i			0.861217i
$585$	42430.7	+	1500.81i	0.123985	+	0.00438543i
$586$	−670890.			−1.95369
$587$	−279855.	+	279855.i	−0.812187	+	0.812187i	−0.984961	−	0.172774i	$-0.944727\pi$
$587$	−279855.	+	279855.i	−0.812187	+	0.812187i	0.172774	+	0.984961i	$0.444727\pi$
$588$	68241.8	+	68241.8i	0.197377	+	0.197377i
$589$		−	310335.i		−	0.894540i
$590$	10072.7	−	284775.i	0.0289362	−	0.818083i
$591$	390384.			1.11768
$592$	−234023.	+	234023.i	−0.667753	+	0.667753i
$593$	94876.0	+	94876.0i	0.269803	+	0.269803i	0.829021	−	0.559218i	$-0.188898\pi$
$593$	94876.0	+	94876.0i	0.269803	+	0.269803i	−0.559218	+	0.829021i	$0.688898\pi$
$594$			418484.i			1.18606i
$595$	−110503.	+	102953.i	−0.312132	+	0.290806i
$596$	1.37208e6			3.86265
$597$	47691.6	−	47691.6i	0.133811	−	0.133811i
$598$	−516328.	−	516328.i	−1.44385	−	1.44385i
$599$			335657.i			0.935496i	0.883862	+	0.467748i	$0.154935\pi$
$599$			335657.i			0.935496i	−0.883862	+	0.467748i	$0.845065\pi$
$600$	−663738.	−	47012.6i	−1.84372	−	0.130591i
$601$	−78337.0			−0.216879			−0.108440	−	0.994103i	$-0.534585\pi$
$601$	−78337.0			−0.216879			−0.108440	+	0.994103i	$0.534585\pi$
$602$	178844.	−	178844.i	0.493495	−	0.493495i
$603$	−50328.4	−	50328.4i	−0.138413	−	0.138413i
$604$			389077.i			1.06650i
$605$	−151203.	−	162292.i	−0.413096	−	0.443390i
$606$	188389.			0.512992
$607$	−392159.	+	392159.i	−1.06435	+	1.06435i	−0.0665679	+	0.997782i	$0.521205\pi$
$607$	−392159.	+	392159.i	−1.06435	+	1.06435i	−0.997782	+	0.0665679i	$0.978795\pi$
$608$	−208654.	−	208654.i	−0.564443	−	0.564443i
$609$			240295.i			0.647902i
$610$	−446485.	−	15792.5i	−1.19991	−	0.0424416i
$611$	−284859.			−0.763039
$612$	−108442.	+	108442.i	−0.289531	+	0.289531i
$613$	−309872.	−	309872.i	−0.824634	−	0.824634i	0.162135	−	0.986769i	$-0.448162\pi$
$613$	−309872.	−	309872.i	−0.824634	−	0.824634i	−0.986769	+	0.162135i	$0.948162\pi$
$614$		−	131117.i		−	0.347794i
$615$	−1706.66	+	48250.6i	−0.00451229	+	0.127571i
$616$	182556.			0.481099
$617$	−343853.	+	343853.i	−0.903238	+	0.903238i	−0.995715	−	0.0924768i	$-0.970522\pi$
$617$	−343853.	+	343853.i	−0.903238	+	0.903238i	0.0924768	+	0.995715i	$0.470522\pi$
$618$	529209.	+	529209.i	1.38564	+	1.38564i
$619$		−	166876.i		−	0.435524i	−0.976002	−	0.217762i	$-0.930124\pi$
$619$		−	166876.i		−	0.435524i	0.976002	−	0.217762i	$-0.0698757\pi$
$620$	−369074.	+	343857.i	−0.960129	+	0.894528i
$621$	645600.			1.67410
$622$	−174546.	+	174546.i	−0.451159	+	0.451159i
$623$	−14937.1	−	14937.1i	−0.0384848	−	0.0384848i
$624$			377740.i			0.970115i
$625$	−386725.	−	55059.8i	−0.990016	−	0.140953i
$626$	−674493.			−1.72119
$627$	232409.	−	232409.i	0.591178	−	0.591178i
$628$	−303836.	−	303836.i	−0.770405	−	0.770405i
$629$		−	290472.i		−	0.734181i
$630$	30682.6	+	32932.7i	0.0773055	+	0.0829747i
$631$	586336.			1.47261			0.736305	−	0.676650i	$-0.236569\pi$
$631$	586336.			1.47261			0.736305	+	0.676650i	$0.236569\pi$
$632$	350753.	−	350753.i	0.878148	−	0.878148i
$633$	175203.	+	175203.i	0.437253	+	0.437253i
$634$		−	1.26848e6i		−	3.15576i
$635$	214493.	+	7586.78i	0.531944	+	0.0188153i
$636$	−336601.			−0.832148
$637$	30049.8	−	30049.8i	0.0740564	−	0.0740564i
$638$	602434.	+	602434.i	1.48002	+	1.48002i
$639$		−	93626.2i		−	0.229295i
$640$	20315.4	−	574357.i	0.0495982	−	1.40224i
$641$	285959.			0.695966			0.347983	−	0.937501i	$-0.386867\pi$
$641$	285959.			0.695966			0.347983	+	0.937501i	$0.386867\pi$
$642$	126698.	−	126698.i	0.307397	−	0.307397i
$643$	−10719.7	−	10719.7i	−0.0259276	−	0.0259276i	0.694024	−	0.719952i	$-0.255836\pi$
$643$	−10719.7	−	10719.7i	−0.0259276	−	0.0259276i	−0.719952	+	0.694024i	$0.755836\pi$
$644$		−	527874.i		−	1.27280i
$645$	−288932.	+	269191.i	−0.694506	+	0.647054i
$646$	1.22043e6			2.92447
$647$	437318.	−	437318.i	1.04469	−	1.04469i	0.0457394	−	0.998953i	$-0.485436\pi$
$647$	437318.	−	437318.i	1.04469	−	1.04469i	0.998953	−	0.0457394i	$-0.0145644\pi$
$648$	−482973.	−	482973.i	−1.15020	−	1.15020i
$649$		−	122062.i		−	0.289796i
$650$	−38802.1	+	547819.i	−0.0918393	+	1.29661i
$651$	−89373.4			−0.210885
$652$	150540.	−	150540.i	0.354125	−	0.354125i
$653$	417145.	+	417145.i	0.978274	+	0.978274i	0.999769	−	0.0214948i	$-0.00684253\pi$
$653$	417145.	+	417145.i	0.978274	+	0.978274i	−0.0214948	+	0.999769i	$0.506843\pi$
$654$			148941.i			0.348224i
$655$	37490.8	+	40240.2i	0.0873859	+	0.0937944i
$656$	87497.6			0.203324
$657$	−21935.8	+	21935.8i	−0.0508186	+	0.0508186i
$658$	−213541.	−	213541.i	−0.493206	−	0.493206i
$659$			756930.i			1.74295i	0.490440	+	0.871475i	$0.336836\pi$
$659$			756930.i			1.74295i	−0.490440	+	0.871475i	$0.663164\pi$
$660$	−533912.	−	18884.9i	−1.22569	−	0.0433537i
$661$	−260817.			−0.596943			−0.298472	−	0.954418i	$-0.596477\pi$
$661$	−260817.			−0.596943			−0.298472	+	0.954418i	$0.596477\pi$
$662$	−407976.	+	407976.i	−0.930934	+	0.930934i
$663$	−234427.	−	234427.i	−0.533312	−	0.533312i
$664$			756712.i			1.71630i
$665$	8634.03	−	244101.i	0.0195241	−	0.551984i
$666$	−86568.3			−0.195169
$667$	929381.	−	929381.i	2.08902	−	2.08902i
$668$	1.26862e6	+	1.26862e6i	2.84301	+	2.84301i
$669$			13375.5i			0.0298852i
$670$	673612.	−	627587.i	1.50058	−	1.39806i
$671$	−191376.			−0.425052
$672$	−60090.3	+	60090.3i	−0.133066	+	0.133066i
$673$	−41288.5	−	41288.5i	−0.0911588	−	0.0911588i	0.660057	−	0.751216i	$-0.270532\pi$
$673$	−41288.5	−	41288.5i	−0.0911588	−	0.0911588i	−0.751216	+	0.660057i	$0.770532\pi$
$674$			1.11706e6i			2.45898i
$675$	−318230.	−	366747.i	−0.698447	−	0.804931i
$676$	−453109.			−0.991539
$677$	−14140.5	+	14140.5i	−0.0308523	+	0.0308523i	−0.722365	−	0.691512i	$-0.756945\pi$
$677$	−14140.5	+	14140.5i	−0.0308523	+	0.0308523i	0.691512	+	0.722365i	$0.256945\pi$
$678$	28570.4	+	28570.4i	0.0621523	+	0.0621523i
$679$			40282.7i			0.0873733i
$680$	−721455.	−	774363.i	−1.56024	−	1.67466i
$681$	−67101.2			−0.144689
$682$	−224065.	+	224065.i	−0.481731	+	0.481731i
$683$	337178.	+	337178.i	0.722800	+	0.722800i	0.969175	−	0.246375i	$-0.0792394\pi$
$683$	337178.	+	337178.i	0.722800	+	0.722800i	−0.246375	+	0.969175i	$0.579239\pi$
$684$		−	248022.i		−	0.530124i
$685$	580632.	+	20537.4i	1.23743	+	0.0437688i
$686$	45052.9			0.0957358
$687$	−595325.	+	595325.i	−1.26136	+	1.26136i
$688$	506049.	+	506049.i	1.06909	+	1.06909i
$689$			148220.i			0.312225i
$690$	−42724.3	+	1.20790e6i	−0.0897380	+	2.53707i
$691$	−565385.			−1.18410			−0.592049	−	0.805902i	$-0.701681\pi$
$691$	−565385.			−1.18410			−0.592049	+	0.805902i	$0.701681\pi$
$692$	1.21236e6	−	1.21236e6i	2.53175	−	2.53175i
$693$	13633.6	+	13633.6i	0.0283887	+	0.0283887i
$694$		−	95338.2i		−	0.197947i
$695$	44983.4	−	41909.9i	0.0931285	−	0.0867655i
$696$	−1.68390e6			−3.47614
$697$	−54301.5	+	54301.5i	−0.111775	+	0.111775i
$698$	−939078.	−	939078.i	−1.92748	−	1.92748i
$699$		−	194134.i		−	0.397326i
$700$	−299870.	+	260200.i	−0.611979	+	0.531021i
$701$	564548.			1.14885			0.574427	−	0.818556i	$-0.305225\pi$
$701$	564548.			1.14885			0.574427	+	0.818556i	$0.305225\pi$
$702$	−482721.	+	482721.i	−0.979540	+	0.979540i
$703$	332175.	+	332175.i	0.672135	+	0.672135i
$704$		−	150343.i		−	0.303346i
$705$	321414.	+	344985.i	0.646676	+	0.694100i
$706$	−1.09519e6			−2.19726
$707$	42405.5	−	42405.5i	0.0848367	−	0.0848367i
$708$	319748.	+	319748.i	0.637883	+	0.637883i
$709$			103288.i			0.205475i	0.994709	+	0.102737i	$0.0327602\pi$
$709$			103288.i			0.205475i	−0.994709	+	0.102737i	$0.967240\pi$
$710$	1.21031e6	+	42809.7i	2.40094	+	0.0849231i
$711$	52389.8			0.103635
$712$	104674.	−	104674.i	0.206480	−	0.206480i
$713$	345667.	+	345667.i	0.679953	+	0.679953i
$714$		−	351471.i		−	0.689434i
$715$	−8315.83	+	235105.i	−0.0162665	+	0.459885i
$716$	−1.03485e6			−2.01861
$717$	234450.	−	234450.i	0.456049	−	0.456049i
$718$	283213.	+	283213.i	0.549369	+	0.549369i
$719$			17971.7i			0.0347641i	0.999849	+	0.0173820i	$0.00553316\pi$
$719$			17971.7i			0.0347641i	−0.999849	+	0.0173820i	$0.994467\pi$
$720$	−93184.6	+	86817.8i	−0.179754	+	0.167473i
$721$	238245.			0.458304
$722$	−742090.	+	742090.i	−1.42358	+	1.42358i
$723$	−162140.	−	162140.i	−0.310180	−	0.310180i
$724$		−	1.22600e6i		−	2.33890i
$725$	−986066.	−	69843.1i	−1.87599	−	0.132876i
$726$	516195.			0.979355
$727$	21242.5	−	21242.5i	0.0401918	−	0.0401918i	−0.686725	−	0.726917i	$-0.740952\pi$
$727$	21242.5	−	21242.5i	0.0401918	−	0.0401918i	0.726917	+	0.686725i	$0.240952\pi$
$728$	210578.	+	210578.i	0.397330	+	0.397330i
$729$		−	588361.i		−	1.10710i
$730$	−273536.	−	293596.i	−0.513297	−	0.550940i
$731$	−628113.			−1.17545
$732$	501318.	−	501318.i	0.935602	−	0.935602i
$733$	529740.	+	529740.i	0.985950	+	0.985950i	0.999903	−	0.0139530i	$-0.00444153\pi$
$733$	529740.	+	529740.i	0.985950	+	0.985950i	−0.0139530	+	0.999903i	$0.504442\pi$
$734$		−	435777.i		−	0.808858i
$735$	−70298.6	−	2486.51i	−0.130128	−	0.00460274i
$736$	464820.			0.858082
$737$	278865.	−	278865.i	0.513404	−	0.513404i
$738$	16183.3	+	16183.3i	0.0297134	+	0.0297134i
$739$		−	596812.i		−	1.09282i	−0.837518	−	0.546410i	$-0.815994\pi$
$739$		−	596812.i		−	1.09282i	0.837518	−	0.546410i	$-0.184006\pi$
$740$	26991.5	−	763104.i	0.0492906	−	1.39354i
$741$	536168.			0.976482
$742$	−111111.	+	111111.i	−0.201813	+	0.201813i
$743$	−431072.	−	431072.i	−0.780859	−	0.780859i	0.199117	−	0.979976i	$-0.436193\pi$
$743$	−431072.	−	431072.i	−0.780859	−	0.780859i	−0.979976	+	0.199117i	$0.936193\pi$
$744$		−	626297.i		−	1.13145i
$745$	−731713.	+	681719.i	−1.31834	+	1.22827i
$746$	−313877.			−0.564004
$747$	−56512.6	+	56512.6i	−0.101275	+	0.101275i
$748$	−600867.	−	600867.i	−1.07393	−	1.07393i
$749$		−	57038.2i		−	0.101672i
$750$	707232.	−	571128.i	1.25730	−	1.01534i
$751$	−173893.			−0.308320			−0.154160	−	0.988046i	$-0.549267\pi$
$751$	−173893.			−0.308320			−0.154160	+	0.988046i	$0.549267\pi$
$752$	604223.	−	604223.i	1.06847	−	1.06847i
$753$	−186123.	−	186123.i	−0.328254	−	0.328254i
$754$			1.38981e6i			2.44464i
$755$	−193314.	−	207491.i	−0.339132	−	0.364003i
$756$	−493516.			−0.863491
$757$	38121.2	−	38121.2i	0.0665234	−	0.0665234i	−0.673062	−	0.739586i	$-0.735021\pi$
$757$	38121.2	−	38121.2i	0.0665234	−	0.0665234i	0.739586	+	0.673062i	$0.235021\pi$
$758$	188267.	+	188267.i	0.327669	+	0.327669i
$759$			517739.i			0.898726i
$760$	1.71057e6	+	60504.2i	2.96152	+	0.104751i
$761$	189381.			0.327014			0.163507	−	0.986542i	$-0.447719\pi$
$761$	189381.			0.327014			0.163507	+	0.986542i	$0.447719\pi$
$762$	−353180.	+	353180.i	−0.608255	+	0.608255i
$763$	33525.9	+	33525.9i	0.0575879	+	0.0575879i
$764$		−	1.25862e6i		−	2.15629i
$765$	3951.28	−	111710.i	0.00675173	−	0.190885i
$766$	−406160.			−0.692213
$767$	140799.	−	140799.i	0.239336	−	0.239336i
$768$	762010.	+	762010.i	1.29193	+	1.29193i
$769$			444810.i			0.752179i	0.926583	+	0.376090i	$0.122732\pi$
$769$			444810.i			0.752179i	−0.926583	+	0.376090i	$0.877268\pi$
$770$	−182477.	+	170009.i	−0.307770	+	0.286742i
$771$	170502.			0.286828
$772$	−196856.	+	196856.i	−0.330304	+	0.330304i
$773$	−810826.	−	810826.i	−1.35696	−	1.35696i	−0.877635	−	0.479329i	$-0.840880\pi$
$773$	−810826.	−	810826.i	−1.35696	−	1.35696i	−0.479329	−	0.877635i	$-0.659120\pi$
$774$			187194.i			0.312471i
$775$	25976.9	−	366750.i	0.0432498	−	0.610614i
$776$	−282286.			−0.468777
$777$	95663.1	−	95663.1i	0.158454	−	0.158454i
$778$	−393386.	−	393386.i	−0.649919	−	0.649919i
$779$		−	124195.i		−	0.204658i
$780$	−594084.	−	637651.i	−0.976469	−	1.04808i
$781$	518774.			0.850504
$782$	−1.35937e6	+	1.35937e6i	−2.22293	+	2.22293i
$783$	−868890.	−	868890.i	−1.41723	−	1.41723i
$784$			127479.i			0.207399i
$785$	312993.	+	11070.8i	0.507921	+	0.0179655i
$786$	−127990.			−0.207172
$787$	659695.	−	659695.i	1.06511	−	1.06511i	0.0673806	−	0.997727i	$-0.478536\pi$
$787$	659695.	−	659695.i	1.06511	−	1.06511i	0.997727	−	0.0673806i	$-0.0214642\pi$
$788$	1.15420e6	+	1.15420e6i	1.85878	+	1.85878i
$789$		−	206370.i		−	0.331506i
$790$	−23954.8	+	677248.i	−0.0383829	+	1.08516i
$791$	12862.1			0.0205570
$792$	−95539.6	+	95539.6i	−0.152312	+	0.152312i
$793$	−220752.	−	220752.i	−0.351041	−	0.351041i
$794$			1.32284e6i			2.09829i
$795$	179505.	−	167241.i	0.284016	−	0.264611i
$796$	282007.			0.445075
$797$	373331.	−	373331.i	0.587729	−	0.587729i	−0.349287	−	0.937016i	$-0.613576\pi$
$797$	373331.	−	373331.i	0.587729	−	0.587729i	0.937016	+	0.349287i	$0.113576\pi$
$798$	401931.	+	401931.i	0.631169	+	0.631169i
$799$			749969.i			1.17476i
$800$	−229119.	−	264051.i	−0.357999	−	0.412579i
$801$	15634.4			0.0243678
$802$	1.30772e6	−	1.30772e6i	2.03314	−	2.03314i
$803$	−121544.	−	121544.i	−0.188496	−	0.188496i
$804$			1.46100e6i			2.26015i
$805$	262275.	+	281509.i	0.404730	+	0.434411i
$806$	−516917.			−0.795703
$807$	−16791.8	+	16791.8i	−0.0257840	+	0.0257840i
$808$	297163.	+	297163.i	0.455168	+	0.455168i
$809$			824584.i			1.25990i	0.776634	+	0.629952i	$0.216926\pi$
$809$			824584.i			1.25990i	−0.776634	+	0.629952i	$0.783074\pi$
$810$	932544.	+	32984.8i	1.42134	+	0.0502740i
$811$	469009.			0.713081			0.356541	−	0.934280i	$-0.383956\pi$
$811$	469009.			0.713081			0.356541	+	0.934280i	$0.383956\pi$
$812$	−710447.	+	710447.i	−1.07751	+	1.07751i
$813$	−698369.	−	698369.i	−1.05658	−	1.05658i
$814$		−	479667.i		−	0.723921i
$815$	−5485.20	+	155077.i	−0.00825804	+	0.233471i
$816$	994504.			1.49357
$817$	718291.	−	718291.i	1.07611	−	1.07611i
$818$	−1.27133e6	−	1.27133e6i	−1.90000	−	1.90000i
$819$			31452.8i			0.0468912i
$820$	−147702.	+	137610.i	−0.219664	+	0.204655i
$821$	88089.6			0.130689			0.0653444	−	0.997863i	$-0.479185\pi$
$821$	88089.6			0.130689			0.0653444	+	0.997863i	$0.479185\pi$
$822$	−956057.	+	956057.i	−1.41495	+	1.41495i
$823$	619299.	+	619299.i	0.914326	+	0.914326i	0.996609	−	0.0822833i	$-0.0262212\pi$
$823$	619299.	+	619299.i	0.914326	+	0.914326i	−0.0822833	+	0.996609i	$0.526221\pi$
$824$			1.66954e6i			2.45890i
$825$	294112.	−	255204.i	0.432121	−	0.374956i
$826$	211096.			0.309400
$827$	−44733.2	+	44733.2i	−0.0654062	+	0.0654062i	−0.739053	−	0.673647i	$-0.764727\pi$
$827$	−44733.2	+	44733.2i	−0.0654062	+	0.0654062i	0.673647	+	0.739053i	$0.264727\pi$
$828$	276259.	+	276259.i	0.402955	+	0.402955i
$829$			264797.i			0.385305i	0.981267	+	0.192653i	$0.0617090\pi$
$829$			264797.i			0.385305i	−0.981267	+	0.192653i	$0.938291\pi$
$830$	−704704.	−	756384.i	−1.02294	−	1.09796i
$831$	−625101.			−0.905207
$832$	173421.	−	173421.i	0.250527	−	0.250527i
$833$	−79114.4	−	79114.4i	−0.114016	−	0.114016i
$834$			143077.i			0.205701i
$835$	−1.30686e6	−	46224.6i	−1.87437	−	0.0662979i
$836$	1.37427e6			1.96634
$837$	323169.	−	323169.i	0.461294	−	0.461294i
$838$	304135.	+	304135.i	0.433090	+	0.433090i
$839$			1.35708e6i			1.92789i	0.266110	+	0.963943i	$0.414261\pi$
$839$			1.35708e6i			1.92789i	−0.266110	+	0.963943i	$0.585739\pi$
$840$	17424.6	−	492628.i	0.0246947	−	0.698169i
$841$	−1.79436e6			−2.53699
$842$	−320841.	+	320841.i	−0.452549	+	0.452549i
$843$	765574.	+	765574.i	1.07729	+	1.07729i
$844$			1.03600e6i			1.45436i
$845$	241638.	−	225128.i	0.338417	−	0.315295i
$846$	223510.			0.312289
$847$	116193.	−	116193.i	0.161962	−	0.161962i
$848$	−314394.	−	314394.i	−0.437203	−	0.437203i
$849$		−	711371.i		−	0.986917i
$850$	1.44229e6	+	102157.i	1.99624	+	0.141394i
$851$	−739988.			−1.02180
$852$	−1.35895e6	+	1.35895e6i	−1.87208	+	1.87208i
$853$	−239249.	−	239249.i	−0.328816	−	0.328816i	0.523320	−	0.852136i	$-0.324693\pi$
$853$	−239249.	−	239249.i	−0.328816	−	0.328816i	−0.852136	+	0.523320i	$0.824693\pi$
$854$		−	330968.i		−	0.453806i
$855$	123230.	+	132267.i	0.168572	+	0.180934i
$856$	399703.			0.545494
$857$	−397948.	+	397948.i	−0.541832	+	0.541832i	−0.924066	−	0.382234i	$-0.875155\pi$
$857$	−397948.	+	397948.i	−0.541832	+	0.541832i	0.382234	+	0.924066i	$0.375155\pi$
$858$	−387118.	−	387118.i	−0.525859	−	0.525859i
$859$		−	352827.i		−	0.478163i	−0.971000	−	0.239081i	$-0.923154\pi$
$859$		−	352827.i		−	0.478163i	0.971000	−	0.239081i	$-0.0768462\pi$
$860$	−1.65013e6	−	58366.2i	−2.23111	−	0.0789159i
$861$	−35766.9			−0.0482475
$862$	696012.	−	696012.i	0.936704	−	0.936704i
$863$	697837.	+	697837.i	0.936984	+	0.936984i	0.998129	−	0.0611447i	$-0.0194751\pi$
$863$	697837.	+	697837.i	0.936984	+	0.936984i	−0.0611447	+	0.998129i	$0.519475\pi$
$864$		−	434566.i		−	0.582141i
$865$	−44174.7	+	1.24891e6i	−0.0590393	+	1.66916i
$866$	1.82446e6			2.43275
$867$	−132727.	+	132727.i	−0.176571	+	0.176571i
$868$	−264238.	−	264238.i	−0.350717	−	0.350717i
$869$			290287.i			0.384404i
$870$	1.68317e6	−	1.56817e6i	2.22377	−	2.07183i
$871$	643341.			0.848018
$872$	−234938.	+	234938.i	−0.308972	+	0.308972i
$873$	−21081.7	−	21081.7i	−0.0276616	−	0.0276616i
$874$		−	3.10908e6i		−	4.07014i
$875$	30636.3	−	287753.i	0.0400148	−	0.375840i
$876$	636781.			0.829816
$877$	−259189.	+	259189.i	−0.336990	+	0.336990i	−0.855233	−	0.518243i	$-0.826586\pi$
$877$	−259189.	+	259189.i	−0.336990	+	0.336990i	0.518243	+	0.855233i	$0.326586\pi$
$878$	−1.46156e6	−	1.46156e6i	−1.89595	−	1.89595i
$879$			775986.i			1.00433i
$880$	−481050.	−	516328.i	−0.621190	−	0.666745i
$881$	978078.			1.26015			0.630074	−	0.776535i	$-0.283024\pi$
$881$	978078.			1.26015			0.630074	+	0.776535i	$0.283024\pi$
$882$	−23578.1	+	23578.1i	−0.0303091	+	0.0303091i
$883$	461432.	+	461432.i	0.591816	+	0.591816i	0.938122	−	0.346306i	$-0.112564\pi$
$883$	461432.	+	461432.i	0.591816	+	0.591816i	−0.346306	+	0.938122i	$0.612564\pi$
$884$		−	1.38620e6i		−	1.77387i
$885$	−329385.	−	11650.6i	−0.420550	−	0.0148752i
$886$	−760550.			−0.968858
$887$	474502.	−	474502.i	0.603102	−	0.603102i	−0.338033	−	0.941134i	$-0.609761\pi$
$887$	474502.	−	474502.i	0.603102	−	0.603102i	0.941134	+	0.338033i	$0.109761\pi$
$888$	670373.	+	670373.i	0.850140	+	0.850140i
$889$			158998.i			0.201182i
$890$	−7148.70	+	202108.i	−0.00902500	+	0.255154i
$891$	399714.			0.503494
$892$	−39545.5	+	39545.5i	−0.0497012	+	0.0497012i
$893$	−857641.	−	857641.i	−1.07548	−	1.07548i
$894$		−	2.32733e6i		−	2.91194i
$895$	551875.	−	514168.i	0.688961	−	0.641888i
$896$	425756.			0.530328
$897$	−597211.	+	597211.i	−0.742238	+	0.742238i
$898$	−1.19912e6	−	1.19912e6i	−1.48700	−	1.48700i
$899$		−	930442.i		−	1.15125i
$900$	20760.9	−	293109.i	0.0256308	−	0.361863i
$901$	390230.			0.480696
$902$	−89669.9	+	89669.9i	−0.110213	+	0.110213i
$903$	−206861.	−	206861.i	−0.253690	−	0.253690i
$904$			90133.3i			0.110293i
$905$	609139.	+	653811.i	0.743737	+	0.798279i
$906$	659956.			0.804005
$907$	−425264.	+	425264.i	−0.516945	+	0.516945i	−0.916646	−	0.399701i	$-0.869114\pi$
$907$	−425264.	+	425264.i	−0.516945	+	0.516945i	0.399701	+	0.916646i	$0.369114\pi$
$908$	−198389.	−	198389.i	−0.240628	−	0.240628i
$909$			44385.3i			0.0537170i
$910$	−406593.	−	14381.5i	−0.490995	−	0.0173669i
$911$	482049.			0.580837			0.290419	−	0.956900i	$-0.406205\pi$
$911$	482049.			0.580837			0.290419	+	0.956900i	$0.406205\pi$
$912$	−1.13728e6	+	1.13728e6i	−1.36735	+	1.36735i
$913$	−313131.	−	313131.i	−0.375651	−	0.375651i
$914$		−	342495.i		−	0.409980i
$915$	−18266.4	+	516428.i	−0.0218178	+	0.616833i
$916$	−3.52023e6			−4.19547
$917$	−28809.9	+	28809.9i	−0.0342613	+	0.0342613i
$918$	1.27090e6	+	1.27090e6i	1.50808	+	1.50808i
$919$			1231.53i			0.00145819i	1.00000		0.000729096i	$0.000232078\pi$
$919$			1231.53i			0.00145819i	−1.00000		0.000729096i	$0.999768\pi$
$920$	−1.97272e6	+	1.83793e6i	−2.33071	+	2.17147i
$921$	−151657.			−0.178789
$922$	857934.	−	857934.i	1.00923	−	1.00923i
$923$	598406.	+	598406.i	0.702413	+	0.702413i
$924$		−	395775.i		−	0.463558i
$925$	364755.	+	420366.i	0.426303	+	0.491297i
$926$	1.25958e6			1.46894
$927$	−124684.	+	124684.i	−0.145095	+	0.145095i
$928$	−625584.	−	625584.i	−0.726423	−	0.726423i
$929$		−	1.43314e6i		−	1.66057i	−0.557342	−	0.830283i	$-0.688179\pi$
$929$		−	1.43314e6i		−	1.66057i	0.557342	−	0.830283i	$-0.311821\pi$
$930$	583252.	+	626025.i	0.674358	+	0.723812i
$931$	180946.			0.208761
$932$	573970.	−	573970.i	0.660781	−	0.660781i
$933$	201889.	+	201889.i	0.231926	+	0.231926i
$934$			1.27191e6i			1.45802i
$935$	618978.	+	21893.7i	0.708030	+	0.0250436i
$936$	−220410.			−0.251582
$937$	−36611.0	+	36611.0i	−0.0416996	+	0.0416996i	−0.727649	−	0.685950i	$-0.759387\pi$
$937$	−36611.0	+	36611.0i	−0.0416996	+	0.0416996i	0.685950	+	0.727649i	$0.259387\pi$
$938$	482272.	+	482272.i	0.548134	+	0.548134i
$939$			780154.i			0.884808i
$940$	−69689.3	+	1.97025e6i	−0.0788698	+	2.22980i
$941$	−1.64250e6			−1.85492			−0.927462	−	0.373918i	$-0.878014\pi$
$941$	−1.64250e6			−1.85492			−0.927462	+	0.373918i	$0.878014\pi$
$942$	−515368.	+	515368.i	−0.580785	+	0.580785i
$943$	138335.	+	138335.i	0.155564	+	0.155564i
$944$			597306.i			0.670275i
$945$	263187.	−	245204.i	0.294714	−	0.274577i
$946$	−1.03723e6			−1.15902
$947$	−215799.	+	215799.i	−0.240630	+	0.240630i	−0.817111	−	0.576481i	$-0.804426\pi$
$947$	−215799.	+	215799.i	−0.240630	+	0.240630i	0.576481	+	0.817111i	$0.304426\pi$
$948$	−760421.	−	760421.i	−0.846130	−	0.846130i
$949$		−	280402.i		−	0.311350i
$950$	−1.76618e6	+	1.53253e6i	−1.95698	+	1.69809i
$951$	−1.46719e6			−1.62227
$952$	554405.	−	554405.i	0.611721	−	0.611721i
$953$	−675833.	−	675833.i	−0.744139	−	0.744139i	0.229233	−	0.973372i	$-0.426378\pi$
$953$	−675833.	−	675833.i	−0.744139	−	0.744139i	−0.973372	+	0.229233i	$0.926378\pi$
$954$		−	116299.i		−	0.127784i
$955$	625347.	+	671207.i	0.685669	+	0.735952i
$956$	1.38633e6			1.51688
$957$	696806.	−	696806.i	0.760831	−	0.760831i
$958$	1.78671e6	+	1.78671e6i	1.94681	+	1.94681i
$959$			430408.i			0.467997i
$960$	−405701.	−	14349.9i	−0.440214	−	0.0155707i
$961$	−577459.			−0.625280
$962$	553296.	−	553296.i	0.597871	−	0.597871i
$963$	29850.6	+	29850.6i	0.0321884	+	0.0321884i
$964$		−	958756.i		−	1.03170i
$965$	7172.81	−	202789.i	0.00770255	−	0.217766i
$966$	−895384.			−0.959522
$967$	167436.	−	167436.i	0.179059	−	0.179059i	−0.611886	−	0.790946i	$-0.709589\pi$
$967$	167436.	−	167436.i	0.179059	−	0.179059i	0.790946	+	0.611886i	$0.209589\pi$
$968$	814239.	+	814239.i	0.868962	+	0.868962i
$969$		−	1.41161e6i		−	1.50337i
$970$	282164.	−	262885.i	0.299888	−	0.279398i
$971$	−406368.			−0.431004			−0.215502	−	0.976503i	$-0.569139\pi$
$971$	−406368.			−0.431004			−0.215502	+	0.976503i	$0.569139\pi$
$972$	479176.	−	479176.i	0.507180	−	0.507180i
$973$	32205.8	+	32205.8i	0.0340180	+	0.0340180i
$974$		−	554083.i		−	0.584060i
$975$	633637.	+	44880.5i	0.666547	+	0.0472116i
$976$	936489.			0.983113
$977$	816231.	−	816231.i	0.855114	−	0.855114i	−0.135644	−	0.990758i	$-0.543310\pi$
$977$	816231.	−	816231.i	0.855114	−	0.855114i	0.990758	+	0.135644i	$0.0433102\pi$
$978$	−255347.	−	255347.i	−0.266964	−	0.266964i
$979$			86629.0i			0.0903853i
$980$	−200491.	−	215194.i	−0.208758	−	0.224067i
$981$	−35091.1			−0.0364636
$982$	−113102.	+	113102.i	−0.117286	+	0.117286i
$983$	−519170.	−	519170.i	−0.537283	−	0.537283i	0.385447	−	0.922730i	$-0.374047\pi$
$983$	−519170.	−	519170.i	−0.537283	−	0.537283i	−0.922730	+	0.385447i	$0.874047\pi$
$984$		−	250642.i		−	0.258859i
$985$	−1.18898e6	−	42055.3i	−1.22547	−	0.0433459i
$986$	3.65907e6			3.76371
$987$	−246992.	+	246992.i	−0.253541	+	0.253541i
$988$	1.58522e6	+	1.58522e6i	1.62396	+	1.62396i
$989$			1.60014e6i			1.63593i
$990$	6524.89	−	184472.i	0.00665738	−	0.188217i
$991$	382417.			0.389395			0.194697	−	0.980863i	$-0.437627\pi$
$991$	382417.			0.389395			0.194697	+	0.980863i	$0.437627\pi$
$992$	232675.	−	232675.i	0.236443	−	0.236443i
$993$	471887.	+	471887.i	0.478563	+	0.478563i
$994$			897174.i			0.908038i
$995$	−150391.	+	140116.i	−0.151906	+	0.141527i
$996$	1.64052e6			1.65373
$997$	−429735.	+	429735.i	−0.432325	+	0.432325i	−0.889419	−	0.457093i	$-0.848890\pi$
$997$	−429735.	+	429735.i	−0.432325	+	0.432325i	0.457093	+	0.889419i	$0.348890\pi$
$998$	−158802.	−	158802.i	−0.159439	−	0.159439i
$999$			691824.i			0.693210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.8.11	✓	24
5.2	odd	4	inner	35.5.g.a.22.11	yes	24
5.3	odd	4		175.5.g.c.57.2		24
5.4	even	2		175.5.g.c.43.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.11	✓	24	1.1	even	1	trivial
35.5.g.a.22.11	yes	24	5.2	odd	4	inner
175.5.g.c.43.2		24	5.4	even	2
175.5.g.c.57.2		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.01495 - 5.01495i) q^{2} +(-5.80055 - 5.80055i) q^{3} -34.2994i q^{4} +(17.0417 + 18.2915i) q^{5} -58.1789 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-91.7707 - 91.7707i) q^{8} -13.7072i q^{9} +O(q^{10})\)	\(q+(5.01495 - 5.01495i) q^{2} +(-5.80055 - 5.80055i) q^{3} -34.2994i q^{4} +(17.0417 + 18.2915i) q^{5} -58.1789 q^{6} +(-13.0958 + 13.0958i) q^{7} +(-91.7707 - 91.7707i) q^{8} -13.7072i q^{9} +(177.194 + 6.26750i) q^{10} +75.9504 q^{11} +(-198.956 + 198.956i) q^{12} +(87.6088 + 87.6088i) q^{13} +131.350i q^{14} +(7.24931 - 204.952i) q^{15} -371.660 q^{16} +(230.654 - 230.654i) q^{17} +(-68.7410 - 68.7410i) q^{18} +527.538i q^{19} +(627.388 - 584.522i) q^{20} +151.926 q^{21} +(380.888 - 380.888i) q^{22} +(-587.599 - 587.599i) q^{23} +1064.64i q^{24} +(-44.1582 + 623.438i) q^{25} +878.707 q^{26} +(-549.354 + 549.354i) q^{27} +(449.178 + 449.178i) q^{28} +1581.66i q^{29} +(-991.470 - 1064.18i) q^{30} -588.270 q^{31} +(-395.524 + 395.524i) q^{32} +(-440.554 - 440.554i) q^{33} -2313.44i q^{34} +(-462.717 - 16.3666i) q^{35} -470.149 q^{36} +(629.670 - 629.670i) q^{37} +(2645.58 + 2645.58i) q^{38} -1016.36i q^{39} +(114.692 - 3242.56i) q^{40} -235.424 q^{41} +(761.900 - 761.900i) q^{42} +(-1361.59 - 1361.59i) q^{43} -2605.06i q^{44} +(250.725 - 233.595i) q^{45} -5893.56 q^{46} +(-1625.74 + 1625.74i) q^{47} +(2155.83 + 2155.83i) q^{48} -343.000i q^{49} +(2905.06 + 3347.96i) q^{50} -2675.84 q^{51} +(3004.93 - 3004.93i) q^{52} +(845.919 + 845.919i) q^{53} +5509.96i q^{54} +(1294.33 + 1389.25i) q^{55} +2403.62 q^{56} +(3060.01 - 3060.01i) q^{57} +(7931.94 + 7931.94i) q^{58} -1607.13i q^{59} +(-7029.75 - 248.647i) q^{60} -2519.75 q^{61} +(-2950.14 + 2950.14i) q^{62} +(179.507 + 179.507i) q^{63} -1979.49i q^{64} +(-109.490 + 3095.50i) q^{65} -4418.72 q^{66} +(3671.67 - 3671.67i) q^{67} +(-7911.31 - 7911.31i) q^{68} +6816.80i q^{69} +(-2402.58 + 2238.42i) q^{70} +6830.43 q^{71} +(-1257.92 + 1257.92i) q^{72} +(-1600.31 - 1600.31i) q^{73} -6315.53i q^{74} +(3872.43 - 3360.14i) q^{75} +18094.3 q^{76} +(-994.632 + 994.632i) q^{77} +(-5096.99 - 5096.99i) q^{78} +3822.06i q^{79} +(-6333.73 - 6798.22i) q^{80} +5262.83 q^{81} +(-1180.64 + 1180.64i) q^{82} +(-4122.84 - 4122.84i) q^{83} -5210.97i q^{84} +(8149.76 + 288.263i) q^{85} -13656.6 q^{86} +(9174.49 - 9174.49i) q^{87} +(-6970.02 - 6970.02i) q^{88} +1140.60i q^{89} +(85.9099 - 2428.84i) q^{90} -2294.61 q^{91} +(-20154.3 + 20154.3i) q^{92} +(3412.29 + 3412.29i) q^{93} +16306.0i q^{94} +(-9649.47 + 8990.17i) q^{95} +4588.52 q^{96} +(1538.00 - 1538.00i) q^{97} +(-1720.13 - 1720.13i) q^{98} -1041.07i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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