LMFDB - Embedded newform 35.5.g.a.22.11

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			22.11
Character	$\chi$	$=$	35.22
Dual form			35.5.g.a.8.11

$q$-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 $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

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

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	0.954032	+	0.299705i	$0.0968884\pi$
$2$	5.01495	+	5.01495i	1.25374	+	1.25374i	0.299705	+	0.954032i	$0.403112\pi$
$3$	−5.80055	+	5.80055i	−0.644506	+	0.644506i	−0.951660	−	0.307154i	$-0.900623\pi$
$3$	−5.80055	+	5.80055i	−0.644506	+	0.644506i	0.307154	+	0.951660i	$0.400623\pi$
$4$			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	−0.398690	−	0.917086i	$-0.630535\pi$
$13$	87.6088	−	87.6088i	0.518395	−	0.518395i	0.917086	+	0.398690i	$0.130535\pi$
$14$		−	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	0.982798	−	0.184686i	$-0.0591269\pi$
$17$	230.654	+	230.654i	0.798111	+	0.798111i	−0.184686	+	0.982798i	$0.559127\pi$
$18$	−68.7410	+	68.7410i	−0.212163	+	0.212163i
$19$		−	527.538i		−	1.46132i	−0.682739	−	0.730662i	$-0.739211\pi$
$19$		−	527.538i		−	1.46132i	0.682739	−	0.730662i	$-0.260789\pi$
$20$	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	−0.117728	+	0.993046i	$0.537561\pi$
$23$	−587.599	+	587.599i	−1.11077	+	1.11077i	−0.993046	+	0.117728i	$0.962439\pi$
$24$		−	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	$-0.610504\pi$
$29$		−	1581.66i		−	1.88069i	0.340226	−	0.940344i	$-0.389496\pi$
$30$	−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	0.898639	−	0.438690i	$-0.144557\pi$
$37$	629.670	+	629.670i	0.459949	+	0.459949i	−0.438690	+	0.898639i	$0.644557\pi$
$38$	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	−0.971878	−	0.235485i	$-0.924332\pi$
$43$	−1361.59	+	1361.59i	−0.736393	+	0.736393i	0.235485	+	0.971878i	$0.424332\pi$
$44$			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	0.235831	−	0.971794i	$-0.424219\pi$
$47$	−1625.74	−	1625.74i	−0.735963	−	0.735963i	−0.971794	+	0.235831i	$0.924219\pi$
$48$	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	−0.540316	−	0.841462i	$-0.681695\pi$
$53$	845.919	−	845.919i	0.301146	−	0.301146i	0.841462	+	0.540316i	$0.181695\pi$
$54$		−	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	$0.0741485\pi$
$59$			1607.13i			0.461686i	−0.972991	+	0.230843i	$0.925852\pi$
$60$	−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	0.985807	−	0.167881i	$-0.0536924\pi$
$67$	3671.67	+	3671.67i	0.817926	+	0.817926i	−0.167881	+	0.985807i	$0.553692\pi$
$68$	−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	−0.841132	−	0.540830i	$-0.818110\pi$
$73$	−1600.31	+	1600.31i	−0.300302	+	0.300302i	0.540830	+	0.841132i	$0.318110\pi$
$74$			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	$-0.900940\pi$
$79$		−	3822.06i		−	0.612412i	0.951965	−	0.306206i	$-0.0990596\pi$
$80$	−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	−0.939905	−	0.341437i	$-0.889086\pi$
$83$	−4122.84	+	4122.84i	−0.598467	+	0.598467i	0.341437	+	0.939905i	$0.389086\pi$
$84$			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	$-0.977062\pi$
$89$		−	1140.60i		−	0.143997i	0.997405	−	0.0719984i	$-0.0229377\pi$
$90$	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	0.784098	−	0.620637i	$-0.213126\pi$
$97$	1538.00	+	1538.00i	0.163460	+	0.163460i	−0.620637	+	0.784098i	$0.713126\pi$
$98$	−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	−0.991032	−	0.133625i	$-0.957338\pi$
$103$	−9096.24	+	9096.24i	−0.857407	+	0.857407i	0.133625	+	0.991032i	$0.457338\pi$
$104$			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	0.605576	−	0.795787i	$-0.292943\pi$
$107$	−2177.73	−	2177.73i	−0.190211	−	0.190211i	−0.795787	+	0.605576i	$0.792943\pi$
$108$	18842.5	−	18842.5i	1.61544	−	1.61544i
$109$			2560.05i			0.215474i	0.994179	+	0.107737i	$0.0343605\pi$
$109$			2560.05i			0.215474i	−0.994179	+	0.107737i	$0.965640\pi$
$110$	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	−0.726075	−	0.687616i	$-0.758657\pi$
$113$	−491.079	+	491.079i	−0.0384587	+	0.0384587i	0.687616	+	0.726075i	$0.258657\pi$
$114$			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	0.869793	−	0.493417i	$-0.164252\pi$
$127$	6070.58	+	6070.58i	0.376377	+	0.376377i	−0.493417	+	0.869793i	$0.664252\pi$
$128$	−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	0.993070	−	0.117528i	$-0.0374970\pi$
$137$	16433.0	+	16433.0i	0.875541	+	0.875541i	−0.117528	+	0.993070i	$0.537497\pi$
$138$	34185.9	−	34185.9i	1.79510	−	1.79510i
$139$			2459.25i			0.127284i	0.997973	+	0.0636419i	$0.0202715\pi$
$139$			2459.25i			0.127284i	−0.997973	+	0.0636419i	$0.979728\pi$
$140$	−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	$-0.642889\pi$
$149$		−	40002.9i		−	1.80185i	0.433973	−	0.900926i	$-0.357111\pi$
$150$	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	0.863584	−	0.504205i	$-0.168214\pi$
$157$	8858.33	+	8858.33i	0.359379	+	0.359379i	−0.504205	+	0.863584i	$0.668214\pi$
$158$	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	−0.619670	−	0.784862i	$-0.712734\pi$
$163$	4388.99	−	4388.99i	0.165192	−	0.165192i	0.784862	+	0.619670i	$0.212734\pi$
$164$		−	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	−0.908649	−	0.417560i	$-0.862885\pi$
$167$	−36986.7	−	36986.7i	−1.32621	−	1.32621i	−0.417560	−	0.908649i	$-0.637115\pi$
$168$	−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	0.201528	−	0.979483i	$-0.435409\pi$
$173$	35346.5	−	35346.5i	1.18101	−	1.18101i	0.979483	−	0.201528i	$-0.0645907\pi$
$174$			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	$0.156042\pi$
$179$			30171.1i			0.941640i	−0.882229	+	0.470820i	$0.843958\pi$
$180$	−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	−0.779938	−	0.625857i	$-0.784749\pi$
$193$	−5739.33	+	5739.33i	−0.154080	+	0.154080i	0.625857	+	0.779938i	$0.284749\pi$
$194$			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	0.125066	−	0.992148i	$-0.460086\pi$
$197$	−33650.6	−	33650.6i	−0.867082	−	0.867082i	−0.992148	+	0.125066i	$0.960086\pi$
$198$	−5220.90	+	5220.90i	−0.133173	+	0.133173i
$199$		−	8221.91i		−	0.207619i	−0.994597	−	0.103809i	$-0.966897\pi$
$199$		−	8221.91i		−	0.207619i	0.994597	−	0.103809i	$-0.0331032\pi$
$200$	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	−0.718604	−	0.695419i	$-0.755219\pi$
$223$	−1152.95	+	1152.95i	−0.0231846	+	0.0231846i	0.695419	+	0.718604i	$0.255219\pi$
$224$			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	0.761000	−	0.648752i	$-0.224709\pi$
$227$	5784.04	+	5784.04i	0.112248	+	0.112248i	−0.648752	+	0.761000i	$0.724709\pi$
$228$	−104957.	+	104957.i	−2.01902	+	2.01902i
$229$			102632.i			1.95710i	0.206001	+	0.978552i	$0.433955\pi$
$229$			102632.i			1.95710i	−0.206001	+	0.978552i	$0.566045\pi$
$230$	−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	−0.535986	−	0.844227i	$-0.680060\pi$
$233$	16734.1	−	16734.1i	0.308241	−	0.308241i	0.844227	+	0.535986i	$0.180060\pi$
$234$			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	$-0.884890\pi$
$239$		−	40418.5i		−	0.707594i	0.935322	−	0.353797i	$-0.115110\pi$
$240$	−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	0.587040	−	0.809558i	$-0.300293\pi$
$257$	−14697.1	−	14697.1i	−0.222518	−	0.222518i	−0.809558	+	0.587040i	$0.800293\pi$
$258$	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	−0.566727	−	0.823906i	$-0.691791\pi$
$263$	17788.8	−	17788.8i	0.257179	−	0.257179i	0.823906	+	0.566727i	$0.191791\pi$
$264$		−	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	$0.00636755\pi$
$269$			2894.86i			0.0400058i	−0.999800	+	0.0200029i	$0.993632\pi$
$270$	−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	0.964893	−	0.262644i	$-0.0845944\pi$
$277$	53882.9	+	53882.9i	0.702249	+	0.702249i	−0.262644	+	0.964893i	$0.584594\pi$
$278$	−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	−0.211697	−	0.977335i	$-0.567899\pi$
$283$	61319.2	−	61319.2i	0.765639	−	0.765639i	0.977335	+	0.211697i	$0.0678989\pi$
$284$			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	−0.979686	−	0.200539i	$-0.935731\pi$
$293$	−66889.0	+	66889.0i	−0.779147	+	0.779147i	0.200539	+	0.979686i	$0.435731\pi$
$294$		−	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	0.773049	−	0.634346i	$-0.218731\pi$
$307$	13072.6	+	13072.6i	0.138703	+	0.138703i	−0.634346	+	0.773049i	$0.718731\pi$
$308$	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	−0.961440	−	0.275016i	$-0.911317\pi$
$313$	−67248.3	+	67248.3i	−0.686424	+	0.686424i	0.275016	+	0.961440i	$0.411317\pi$
$314$			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	0.951790	+	0.306752i	$0.0992422\pi$
$317$	126470.	+	126470.i	1.25854	+	1.25854i	0.306752	+	0.951790i	$0.400758\pi$
$318$	−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	0.0191559	−	0.999817i	$-0.493902\pi$
$337$	−111373.	−	111373.i	−0.980661	−	0.980661i	−0.999817	+	0.0191559i	$0.993902\pi$
$338$	−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	0.745476	−	0.666533i	$-0.232222\pi$
$347$	9505.40	+	9505.40i	0.0789426	+	0.0789426i	−0.666533	+	0.745476i	$0.732222\pi$
$348$	−314680.	+	314680.i	−2.59843	+	2.59843i
$349$			187256.i			1.53739i	0.639615	+	0.768696i	$0.279094\pi$
$349$			187256.i			1.53739i	−0.639615	+	0.768696i	$0.720906\pi$
$350$	−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	−0.993148	−	0.116864i	$-0.962716\pi$
$353$	−109193.	+	109193.i	−0.876284	+	0.876284i	0.116864	+	0.993148i	$0.462716\pi$
$354$		−	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	$-0.929690\pi$
$359$		−	56473.7i		−	0.438185i	0.975704	−	0.219092i	$-0.0703096\pi$
$360$	−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	0.849756	−	0.527177i	$-0.176749\pi$
$367$	43447.8	+	43447.8i	0.322579	+	0.322579i	−0.527177	+	0.849756i	$0.676749\pi$
$368$	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	−0.810570	−	0.585641i	$-0.800843\pi$
$373$	−31294.2	+	31294.2i	−0.224929	+	0.224929i	0.585641	+	0.810570i	$0.300843\pi$
$374$			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	$-0.958285\pi$
$379$		−	37541.2i		−	0.261354i	0.991425	−	0.130677i	$-0.0417151\pi$
$380$	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	−0.831534	−	0.555474i	$-0.812537\pi$
$383$	−40494.9	+	40494.9i	−0.276060	+	0.276060i	0.555474	+	0.831534i	$0.312537\pi$
$384$		−	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	$0.0834565\pi$
$389$			78442.6i			0.518386i	−0.965826	+	0.259193i	$0.916543\pi$
$390$	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	0.151623	−	0.988438i	$-0.451550\pi$
$397$	−131890.	−	131890.i	−0.836815	−	0.836815i	−0.988438	+	0.151623i	$0.951550\pi$
$398$	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	$0.273693\pi$
$409$			253509.i			1.51547i	−0.652564	+	0.757734i	$0.726307\pi$
$410$	−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	$-0.944745\pi$
$419$		−	60645.6i		−	0.345439i	0.984971	−	0.172719i	$-0.0552554\pi$
$420$	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	−0.0293680	−	0.999569i	$-0.509349\pi$
$433$	181902.	−	181902.i	0.970201	−	0.970201i	0.999569	+	0.0293680i	$0.00934947\pi$
$434$			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	$0.272907\pi$
$439$			291440.i			1.51224i	−0.654435	+	0.756118i	$0.727093\pi$
$440$	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	−0.873397	−	0.487009i	$-0.838088\pi$
$443$	−75828.2	+	75828.2i	−0.386388	+	0.386388i	0.487009	+	0.873397i	$0.338088\pi$
$444$		−	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	$0.202067\pi$
$449$			239109.i			1.18605i	−0.805184	+	0.593025i	$0.797933\pi$
$450$	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	0.784117	−	0.620614i	$-0.213116\pi$
$457$	34147.5	+	34147.5i	0.163503	+	0.163503i	−0.620614	+	0.784117i	$0.713116\pi$
$458$	−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	−0.350672	−	0.936498i	$-0.614047\pi$
$463$	125583.	−	125583.i	0.585826	−	0.585826i	0.936498	+	0.350672i	$0.114047\pi$
$464$			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	0.353838	−	0.935307i	$-0.384876\pi$
$467$	−126812.	−	126812.i	−0.581469	−	0.581469i	−0.935307	+	0.353838i	$0.884876\pi$
$468$	−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	$-0.717043\pi$
$479$		−	356277.i		−	1.55280i	0.630239	−	0.776401i	$-0.282957\pi$
$480$	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	0.813914	−	0.580986i	$-0.197333\pi$
$487$	55243.2	+	55243.2i	0.232927	+	0.232927i	−0.580986	+	0.813914i	$0.697333\pi$
$488$	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	$0.0202536\pi$
$499$			31665.7i			0.127171i	−0.997976	+	0.0635855i	$0.979746\pi$
$500$	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	−0.853759	−	0.520668i	$-0.825683\pi$
$503$	−84275.0	+	84275.0i	−0.333091	+	0.333091i	0.520668	+	0.853759i	$0.325683\pi$
$504$			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	$0.115827\pi$
$509$			184416.i			0.711807i	−0.934523	+	0.355903i	$0.884173\pi$
$510$	−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	0.198895	−	0.980021i	$-0.436265\pi$
$523$	322468.	−	322468.i	1.17892	−	1.17892i	0.980021	−	0.198895i	$-0.0637354\pi$
$524$			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	0.839508	+	0.543348i	$0.182843\pi$
$547$	413763.	+	413763.i	1.38286	+	1.38286i	0.543348	+	0.839508i	$0.317157\pi$
$548$	−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	0.0377744	−	0.999286i	$-0.487973\pi$
$557$	−298308.	−	298308.i	−0.961512	−	0.961512i	−0.999286	+	0.0377744i	$0.987973\pi$
$558$	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	−0.563338	−	0.826226i	$-0.690483\pi$
$563$	83327.3	−	83327.3i	0.262888	−	0.262888i	0.826226	+	0.563338i	$0.190483\pi$
$564$			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	$-0.868257\pi$
$569$		−	260413.i		−	0.804336i	0.915566	−	0.402168i	$-0.131743\pi$
$570$	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	−0.982961	−	0.183816i	$-0.941155\pi$
$577$	−388454.	−	388454.i	−1.16678	−	1.16678i	−0.183816	−	0.982961i	$-0.558845\pi$
$578$	−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	0.172774	−	0.984961i	$-0.444727\pi$
$587$	−279855.	−	279855.i	−0.812187	−	0.812187i	−0.984961	+	0.172774i	$0.944727\pi$
$588$	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	−0.559218	−	0.829021i	$-0.688898\pi$
$593$	94876.0	−	94876.0i	0.269803	−	0.269803i	0.829021	+	0.559218i	$0.188898\pi$
$594$		−	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	$-0.845065\pi$
$599$		−	335657.i		−	0.935496i	0.883862	−	0.467748i	$-0.154935\pi$
$600$	−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	−0.997782	−	0.0665679i	$-0.978795\pi$
$607$	−392159.	−	392159.i	−1.06435	−	1.06435i	−0.0665679	−	0.997782i	$-0.521205\pi$
$608$	−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	−0.986769	−	0.162135i	$-0.948162\pi$
$613$	−309872.	+	309872.i	−0.824634	+	0.824634i	0.162135	+	0.986769i	$0.448162\pi$
$614$			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	0.0924768	−	0.995715i	$-0.470522\pi$
$617$	−343853.	−	343853.i	−0.903238	−	0.903238i	−0.995715	+	0.0924768i	$0.970522\pi$
$618$	529209.	−	529209.i	1.38564	−	1.38564i
$619$			166876.i			0.435524i	0.976002	+	0.217762i	$0.0698757\pi$
$619$			166876.i			0.435524i	−0.976002	+	0.217762i	$0.930124\pi$
$620$	−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	−0.719952	−	0.694024i	$-0.755836\pi$
$643$	−10719.7	+	10719.7i	−0.0259276	+	0.0259276i	0.694024	+	0.719952i	$0.255836\pi$
$644$			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	0.998953	+	0.0457394i	$0.0145644\pi$
$647$	437318.	+	437318.i	1.04469	+	1.04469i	0.0457394	+	0.998953i	$0.485436\pi$
$648$	−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	−0.0214948	−	0.999769i	$-0.506843\pi$
$653$	417145.	−	417145.i	0.978274	−	0.978274i	0.999769	+	0.0214948i	$0.00684253\pi$
$654$		−	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	$-0.663164\pi$
$659$		−	756930.i		−	1.74295i	0.490440	−	0.871475i	$-0.336836\pi$
$660$	−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	−0.751216	−	0.660057i	$-0.770532\pi$
$673$	−41288.5	+	41288.5i	−0.0911588	+	0.0911588i	0.660057	+	0.751216i	$0.270532\pi$
$674$		−	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	0.691512	−	0.722365i	$-0.256945\pi$
$677$	−14140.5	−	14140.5i	−0.0308523	−	0.0308523i	−0.722365	+	0.691512i	$0.756945\pi$
$678$	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	−0.246375	−	0.969175i	$-0.579239\pi$
$683$	337178.	−	337178.i	0.722800	−	0.722800i	0.969175	+	0.246375i	$0.0792394\pi$
$684$			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	$-0.967240\pi$
$709$		−	103288.i		−	0.205475i	0.994709	−	0.102737i	$-0.0327602\pi$
$710$	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	$-0.994467\pi$
$719$		−	17971.7i		−	0.0347641i	0.999849	−	0.0173820i	$-0.00553316\pi$
$720$	−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	0.726917	−	0.686725i	$-0.240952\pi$
$727$	21242.5	+	21242.5i	0.0401918	+	0.0401918i	−0.686725	+	0.726917i	$0.740952\pi$
$728$	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	−0.0139530	−	0.999903i	$-0.504442\pi$
$733$	529740.	−	529740.i	0.985950	−	0.985950i	0.999903	+	0.0139530i	$0.00444153\pi$
$734$			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	$0.184006\pi$
$739$			596812.i			1.09282i	−0.837518	+	0.546410i	$0.815994\pi$
$740$	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	−0.979976	−	0.199117i	$-0.936193\pi$
$743$	−431072.	+	431072.i	−0.780859	+	0.780859i	0.199117	+	0.979976i	$0.436193\pi$
$744$			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	0.739586	−	0.673062i	$-0.235021\pi$
$757$	38121.2	+	38121.2i	0.0665234	+	0.0665234i	−0.673062	+	0.739586i	$0.735021\pi$
$758$	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	$-0.877268\pi$
$769$		−	444810.i		−	0.752179i	0.926583	−	0.376090i	$-0.122732\pi$
$770$	−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	−0.479329	+	0.877635i	$0.659120\pi$
$773$	−810826.	+	810826.i	−1.35696	+	1.35696i	−0.877635	+	0.479329i	$0.840880\pi$
$774$		−	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	0.997727	+	0.0673806i	$0.0214642\pi$
$787$	659695.	+	659695.i	1.06511	+	1.06511i	0.0673806	+	0.997727i	$0.478536\pi$
$788$	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	0.937016	−	0.349287i	$-0.113576\pi$
$797$	373331.	+	373331.i	0.587729	+	0.587729i	−0.349287	+	0.937016i	$0.613576\pi$
$798$	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	$-0.783074\pi$
$809$		−	824584.i		−	1.25990i	0.776634	−	0.629952i	$-0.216926\pi$
$810$	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	−0.0822833	−	0.996609i	$-0.526221\pi$
$823$	619299.	−	619299.i	0.914326	−	0.914326i	0.996609	+	0.0822833i	$0.0262212\pi$
$824$		−	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	0.673647	−	0.739053i	$-0.264727\pi$
$827$	−44733.2	−	44733.2i	−0.0654062	−	0.0654062i	−0.739053	+	0.673647i	$0.764727\pi$
$828$	276259.	−	276259.i	0.402955	−	0.402955i
$829$		−	264797.i		−	0.385305i	−0.981267	−	0.192653i	$-0.938291\pi$
$829$		−	264797.i		−	0.385305i	0.981267	−	0.192653i	$-0.0617090\pi$
$830$	−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	$-0.585739\pi$
$839$		−	1.35708e6i		−	1.92789i	0.266110	−	0.963943i	$-0.414261\pi$
$840$	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	−0.852136	−	0.523320i	$-0.824693\pi$
$853$	−239249.	+	239249.i	−0.328816	+	0.328816i	0.523320	+	0.852136i	$0.324693\pi$
$854$			330968.i			0.453806i
$855$	123230.	−	132267.i	0.168572	−	0.180934i
$856$	399703.			0.545494
$857$	−397948.	−	397948.i	−0.541832	−	0.541832i	0.382234	−	0.924066i	$-0.375155\pi$
$857$	−397948.	−	397948.i	−0.541832	−	0.541832i	−0.924066	+	0.382234i	$0.875155\pi$
$858$	−387118.	+	387118.i	−0.525859	+	0.525859i
$859$			352827.i			0.478163i	0.971000	+	0.239081i	$0.0768462\pi$
$859$			352827.i			0.478163i	−0.971000	+	0.239081i	$0.923154\pi$
$860$	−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	−0.0611447	−	0.998129i	$-0.519475\pi$
$863$	697837.	−	697837.i	0.936984	−	0.936984i	0.998129	+	0.0611447i	$0.0194751\pi$
$864$			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	0.518243	−	0.855233i	$-0.326586\pi$
$877$	−259189.	−	259189.i	−0.336990	−	0.336990i	−0.855233	+	0.518243i	$0.826586\pi$
$878$	−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	−0.346306	−	0.938122i	$-0.612564\pi$
$883$	461432.	−	461432.i	0.591816	−	0.591816i	0.938122	+	0.346306i	$0.112564\pi$
$884$			1.38620e6i			1.77387i
$885$	−329385.	+	11650.6i	−0.420550	+	0.0148752i
$886$	−760550.			−0.968858
$887$	474502.	+	474502.i	0.603102	+	0.603102i	0.941134	−	0.338033i	$-0.109761\pi$
$887$	474502.	+	474502.i	0.603102	+	0.603102i	−0.338033	+	0.941134i	$0.609761\pi$
$888$	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	0.399701	−	0.916646i	$-0.369114\pi$
$907$	−425264.	−	425264.i	−0.516945	−	0.516945i	−0.916646	+	0.399701i	$0.869114\pi$
$908$	−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	$-0.999768\pi$
$919$		−	1231.53i		−	0.00145819i	1.00000		0.000729096i	$-0.000232078\pi$
$920$	−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	$0.311821\pi$
$929$			1.43314e6i			1.66057i	−0.557342	+	0.830283i	$0.688179\pi$
$930$	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	0.685950	−	0.727649i	$-0.259387\pi$
$937$	−36611.0	−	36611.0i	−0.0416996	−	0.0416996i	−0.727649	+	0.685950i	$0.759387\pi$
$938$	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	0.576481	−	0.817111i	$-0.304426\pi$
$947$	−215799.	−	215799.i	−0.240630	−	0.240630i	−0.817111	+	0.576481i	$0.804426\pi$
$948$	−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	−0.973372	−	0.229233i	$-0.926378\pi$
$953$	−675833.	+	675833.i	−0.744139	+	0.744139i	0.229233	+	0.973372i	$0.426378\pi$
$954$			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	0.790946	−	0.611886i	$-0.209589\pi$
$967$	167436.	+	167436.i	0.179059	+	0.179059i	−0.611886	+	0.790946i	$0.709589\pi$
$968$	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	0.990758	−	0.135644i	$-0.0433102\pi$
$977$	816231.	+	816231.i	0.855114	+	0.855114i	−0.135644	+	0.990758i	$0.543310\pi$
$978$	−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	−0.922730	−	0.385447i	$-0.874047\pi$
$983$	−519170.	+	519170.i	−0.537283	+	0.537283i	0.385447	+	0.922730i	$0.374047\pi$
$984$			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	0.457093	−	0.889419i	$-0.348890\pi$
$997$	−429735.	−	429735.i	−0.432325	−	0.432325i	−0.889419	+	0.457093i	$0.848890\pi$
$998$	−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.22.11	yes	24
5.2	odd	4		175.5.g.c.43.2		24
5.3	odd	4	inner	35.5.g.a.8.11	✓	24
5.4	even	2		175.5.g.c.57.2		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
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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