LMFDB - Embedded newform 33.6.f.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(2,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("33.2");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.f (of order $10$, degree $4$, 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:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	33.29
Dual form			33.6.f.a.8.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.92830 - 6.48679i) q^{2} +(-5.92302 - 14.4194i) q^{3} +(27.7475 + 85.3981i) q^{4} +(33.7792 + 46.4931i) q^{5} +(-40.6528 + 167.162i) q^{6} +(-11.4606 + 3.72378i) q^{7} +(197.091 - 606.584i) q^{8} +(-172.836 + 170.812i) q^{9} +O(q^{10})$	\(q+(-8.92830 - 6.48679i) q^{2} +(-5.92302 - 14.4194i) q^{3} +(27.7475 + 85.3981i) q^{4} +(33.7792 + 46.4931i) q^{5} +(-40.6528 + 167.162i) q^{6} +(-11.4606 + 3.72378i) q^{7} +(197.091 - 606.584i) q^{8} +(-172.836 + 170.812i) q^{9} -634.222i q^{10} +(234.344 + 325.782i) q^{11} +(1067.04 - 905.916i) q^{12} +(-17.9032 + 24.6416i) q^{13} +(126.479 + 41.0956i) q^{14} +(470.325 - 762.454i) q^{15} +(-3369.87 + 2448.35i) q^{16} +(743.029 - 539.842i) q^{17} +(2651.15 - 403.915i) q^{18} +(1398.06 + 454.258i) q^{19} +(-3033.13 + 4174.75i) q^{20} +(121.576 + 143.199i) q^{21} +(20.9862 - 4428.82i) q^{22} +1182.79i q^{23} +(-9913.93 + 750.885i) q^{24} +(-54.8941 + 168.947i) q^{25} +(319.690 - 103.873i) q^{26} +(3486.71 + 1480.45i) q^{27} +(-636.007 - 875.389i) q^{28} +(335.569 + 1032.78i) q^{29} +(-9145.08 + 3756.51i) q^{30} +(6582.67 + 4782.59i) q^{31} +25559.5 q^{32} +(3309.54 - 5308.70i) q^{33} -10135.8 q^{34} +(-560.260 - 407.053i) q^{35} +(-19382.8 - 10020.2i) q^{36} +(-923.903 - 2843.48i) q^{37} +(-9535.64 - 13124.7i) q^{38} +(461.357 + 112.199i) q^{39} +(34859.6 - 11326.6i) q^{40} +(3447.83 - 10611.3i) q^{41} +(-156.567 - 2067.16i) q^{42} +18700.4i q^{43} +(-21318.7 + 29052.2i) q^{44} +(-13779.8 - 2265.76i) q^{45} +(7672.48 - 10560.3i) q^{46} +(5459.56 + 1773.92i) q^{47} +(55263.4 + 34089.7i) q^{48} +(-13479.7 + 9793.55i) q^{49} +(1586.03 - 1152.32i) q^{50} +(-12185.2 - 7516.50i) q^{51} +(-2601.11 - 845.153i) q^{52} +(-9690.42 + 13337.7i) q^{53} +(-21527.0 - 35835.5i) q^{54} +(-7230.66 + 21900.0i) q^{55} +7685.76i q^{56} +(-1730.65 - 22849.7i) q^{57} +(3703.34 - 11397.7i) q^{58} +(8013.95 - 2603.89i) q^{59} +(78162.4 + 19008.7i) q^{60} +(9774.99 + 13454.1i) q^{61} +(-27748.4 - 85400.8i) q^{62} +(1344.73 - 2601.22i) q^{63} +(-120367. - 87451.6i) q^{64} -1750.42 q^{65} +(-63985.0 + 25929.4i) q^{66} -12306.1 q^{67} +(66718.7 + 48474.0i) q^{68} +(17055.0 - 7005.67i) q^{69} +(2361.70 + 7268.58i) q^{70} +(11143.3 + 15337.4i) q^{71} +(69547.7 + 138505. i) q^{72} +(9033.18 - 2935.06i) q^{73} +(-10196.2 + 31380.6i) q^{74} +(2761.24 - 209.137i) q^{75} +131996. i q^{76} +(-3898.87 - 2861.02i) q^{77} +(-3391.32 - 3994.47i) q^{78} +(46837.8 - 64466.6i) q^{79} +(-227663. - 73972.1i) q^{80} +(695.288 - 59044.9i) q^{81} +(-99616.7 + 72375.7i) q^{82} +(-12279.6 + 8921.66i) q^{83} +(-8855.46 + 14355.8i) q^{84} +(50197.8 + 16310.3i) q^{85} +(121305. - 166962. i) q^{86} +(12904.4 - 10955.9i) q^{87} +(243801. - 77940.6i) q^{88} +87903.7i q^{89} +(108333. + 109616. i) q^{90} +(113.421 - 349.075i) q^{91} +(-101008. + 32819.4i) q^{92} +(29972.6 - 123245. i) q^{93} +(-37237.5 - 51253.1i) q^{94} +(26105.6 + 80344.7i) q^{95} +(-151389. - 368551. i) q^{96} +(24469.8 + 17778.3i) q^{97} +183879. q^{98} +(-96150.6 - 16277.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9}+O(q^{10}) $ 72 * q + 18 * q^3 - 262 * q^4 + 15 * q^6 - 10 * q^7 + 292 * q^9	$ 72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9} + 1854 q^{12} - 10 q^{13} - 762 q^{15} - 10122 q^{16} + 4815 q^{18} + 4460 q^{19} + 4628 q^{22} - 805 q^{24} + 13708 q^{25} + 6108 q^{27} - 28130 q^{28} - 15470 q^{30} + 4340 q^{31} - 508 q^{33} + 18732 q^{34} - 56461 q^{36} + 978 q^{37} + 23360 q^{39} + 69750 q^{40} + 60788 q^{42} - 31356 q^{45} - 52090 q^{46} + 4238 q^{48} - 58448 q^{49} - 178950 q^{51} - 14190 q^{52} + 86600 q^{55} + 266190 q^{57} + 137102 q^{58} + 284090 q^{60} - 77890 q^{61} - 120330 q^{63} - 379114 q^{64} - 323304 q^{66} + 42668 q^{67} - 271816 q^{69} + 87176 q^{70} + 343960 q^{72} + 116440 q^{73} + 326202 q^{75} + 155512 q^{78} - 350590 q^{79} - 208088 q^{81} - 606424 q^{82} - 220680 q^{84} + 665610 q^{85} + 1152974 q^{88} + 293440 q^{90} + 621014 q^{91} + 478456 q^{93} - 521270 q^{94} - 1246430 q^{96} - 1030446 q^{97} - 590000 q^{99}+O(q^{100}) $ 72 * q + 18 * q^3 - 262 * q^4 + 15 * q^6 - 10 * q^7 + 292 * q^9 + 1854 * q^12 - 10 * q^13 - 762 * q^15 - 10122 * q^16 + 4815 * q^18 + 4460 * q^19 + 4628 * q^22 - 805 * q^24 + 13708 * q^25 + 6108 * q^27 - 28130 * q^28 - 15470 * q^30 + 4340 * q^31 - 508 * q^33 + 18732 * q^34 - 56461 * q^36 + 978 * q^37 + 23360 * q^39 + 69750 * q^40 + 60788 * q^42 - 31356 * q^45 - 52090 * q^46 + 4238 * q^48 - 58448 * q^49 - 178950 * q^51 - 14190 * q^52 + 86600 * q^55 + 266190 * q^57 + 137102 * q^58 + 284090 * q^60 - 77890 * q^61 - 120330 * q^63 - 379114 * q^64 - 323304 * q^66 + 42668 * q^67 - 271816 * q^69 + 87176 * q^70 + 343960 * q^72 + 116440 * q^73 + 326202 * q^75 + 155512 * q^78 - 350590 * q^79 - 208088 * q^81 - 606424 * q^82 - 220680 * q^84 + 665610 * q^85 + 1152974 * q^88 + 293440 * q^90 + 621014 * q^91 + 478456 * q^93 - 521270 * q^94 - 1246430 * q^96 - 1030446 * q^97 - 590000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−8.92830	−	6.48679i	−1.57831	−	1.14671i	−0.918595	−	0.395201i	$-0.870675\pi$
$2$	−8.92830	−	6.48679i	−1.57831	−	1.14671i	−0.659720	−	0.751512i	$-0.729325\pi$
$3$	−5.92302	−	14.4194i	−0.379962	−	0.925002i
$3$	−5.92302	−	14.4194i	−0.379962	−	0.925002i
$4$	27.7475	+	85.3981i	0.867110	+	2.66869i
$5$	33.7792	+	46.4931i	0.604261	+	0.831694i	0.996090	−	0.0883444i	$-0.0281576\pi$
$5$	33.7792	+	46.4931i	0.604261	+	0.831694i	−0.391829	+	0.920038i	$0.628158\pi$
$6$	−40.6528	+	167.162i	−0.461012	+	1.89565i
$7$	−11.4606	+	3.72378i	−0.0884021	+	0.0287236i	−0.352884	−	0.935667i	$-0.614799\pi$
$7$	−11.4606	+	3.72378i	−0.0884021	+	0.0287236i	0.264482	+	0.964391i	$0.414799\pi$
$8$	197.091	−	606.584i	1.08879	−	3.35094i
$9$	−172.836	+	170.812i	−0.711258	+	0.702931i
$10$		−	634.222i		−	2.00559i
$11$	234.344	+	325.782i	0.583945	+	0.811793i
$11$	234.344	+	325.782i	0.583945	+	0.811793i
$12$	1067.04	−	905.916i	2.13907	−	1.81608i
$13$	−17.9032	+	24.6416i	−0.0293813	+	0.0404399i	−0.823455	−	0.567382i	$-0.807956\pi$
$13$	−17.9032	+	24.6416i	−0.0293813	+	0.0404399i	0.794074	+	0.607822i	$0.207956\pi$
$14$	126.479	+	41.0956i	0.172464	+	0.0560370i
$15$	470.325	−	762.454i	0.539722	−	0.874954i
$16$	−3369.87	+	2448.35i	−3.29089	+	2.39097i
$17$	743.029	−	539.842i	0.623567	−	0.453048i	−0.230598	−	0.973049i	$-0.574068\pi$
$17$	743.029	−	539.842i	0.623567	−	0.453048i	0.854166	+	0.520001i	$0.174068\pi$
$18$	2651.15	−	403.915i	1.92865	−	0.293839i
$19$	1398.06	+	454.258i	0.888469	+	0.288681i	0.717470	−	0.696590i	$-0.245300\pi$
$19$	1398.06	+	454.258i	0.888469	+	0.288681i	0.171000	+	0.985271i	$0.445300\pi$
$20$	−3033.13	+	4174.75i	−1.69557	+	2.33375i
$21$	121.576	+	143.199i	0.0601589	+	0.0708583i
$22$	20.9862	−	4428.82i	0.00924436	−	1.95088i
$23$			1182.79i			0.466215i	0.972451	+	0.233108i	$0.0748895\pi$
$23$			1182.79i			0.466215i	−0.972451	+	0.233108i	$0.925111\pi$
$24$	−9913.93	+	750.885i	−3.51332	+	0.266100i
$25$	−54.8941	+	168.947i	−0.0175661	+	0.0540629i
$26$	319.690	−	103.873i	0.0927460	−	0.0301350i
$27$	3486.71	+	1480.45i	0.920464	+	0.390827i
$28$	−636.007	−	875.389i	−0.153309	−	0.211011i
$29$	335.569	+	1032.78i	0.0740947	+	0.228040i	0.981244	−	0.192768i	$-0.0617465\pi$
$29$	335.569	+	1032.78i	0.0740947	+	0.228040i	−0.907150	+	0.420808i	$0.861747\pi$
$30$	−9145.08	+	3756.51i	−1.85517	+	0.762047i
$31$	6582.67	+	4782.59i	1.23026	+	0.893838i	0.996910	−	0.0785537i	$-0.0250302\pi$
$31$	6582.67	+	4782.59i	1.23026	+	0.893838i	0.233353	+	0.972392i	$0.425030\pi$
$32$	25559.5			4.41242
$33$	3309.54	−	5308.70i	0.529033	−	0.848601i
$34$	−10135.8			−1.50370
$35$	−560.260	−	407.053i	−0.0773072	−	0.0561669i
$36$	−19382.8	−	10020.2i	−2.49264	−	1.28861i
$37$	−923.903	−	2843.48i	−0.110949	−	0.341465i	0.880132	−	0.474729i	$-0.157454\pi$
$37$	−923.903	−	2843.48i	−0.110949	−	0.341465i	−0.991081	+	0.133264i	$0.957454\pi$
$38$	−9535.64	−	13124.7i	−1.07125	−	1.47445i
$39$	461.357	+	112.199i	0.0485708	+	0.0118122i
$40$	34859.6	−	11326.6i	3.44486	−	1.11930i
$41$	3447.83	−	10611.3i	0.320322	−	0.985848i	−0.653187	−	0.757197i	$-0.726568\pi$
$41$	3447.83	−	10611.3i	0.320322	−	0.985848i	0.973508	−	0.228652i	$-0.0734316\pi$
$42$	−156.567	−	2067.16i	−0.0136955	−	0.180822i
$43$			18700.4i			1.54234i	0.636632	+	0.771168i	$0.280327\pi$
$43$			18700.4i			1.54234i	−0.636632	+	0.771168i	$0.719673\pi$
$44$	−21318.7	+	29052.2i	−1.66008	+	2.26228i
$45$	−13779.8	−	2265.76i	−1.01441	−	0.166794i
$46$	7672.48	−	10560.3i	0.534615	−	0.735835i
$47$	5459.56	+	1773.92i	0.360506	+	0.117136i	0.483669	−	0.875251i	$-0.339304\pi$
$47$	5459.56	+	1773.92i	0.360506	+	0.117136i	−0.123163	+	0.992386i	$0.539304\pi$
$48$	55263.4	+	34089.7i	3.46206	+	2.13560i
$49$	−13479.7	+	9793.55i	−0.802027	+	0.582707i
$50$	1586.03	−	1152.32i	0.0897194	−	0.0651850i
$51$	−12185.2	−	7516.50i	−0.656002	−	0.404660i
$52$	−2601.11	−	845.153i	−0.133399	−	0.0433438i
$53$	−9690.42	+	13337.7i	−0.473863	+	0.652217i	−0.977311	−	0.211809i	$-0.932065\pi$
$53$	−9690.42	+	13337.7i	−0.473863	+	0.652217i	0.503448	+	0.864026i	$0.332065\pi$
$54$	−21527.0	−	35835.5i	−1.00461	−	1.67236i
$55$	−7230.66	+	21900.0i	−0.322308	+	0.976198i
$56$			7685.76i			0.327504i
$57$	−1730.65	−	22849.7i	−0.0705540	−	0.931524i
$58$	3703.34	−	11397.7i	0.144552	−	0.444884i
$59$	8013.95	−	2603.89i	0.299721	−	0.0973852i	−0.155296	−	0.987868i	$-0.549633\pi$
$59$	8013.95	−	2603.89i	0.299721	−	0.0973852i	0.455017	+	0.890483i	$0.349633\pi$
$60$	78162.4	+	19008.7i	2.80298	+	0.681669i
$61$	9774.99	+	13454.1i	0.336350	+	0.462946i	0.943371	−	0.331740i	$-0.107636\pi$
$61$	9774.99	+	13454.1i	0.336350	+	0.462946i	−0.607021	+	0.794686i	$0.707636\pi$
$62$	−27748.4	−	85400.8i	−0.916766	−	2.82152i
$63$	1344.73	−	2601.22i	0.0426860	−	0.0825705i
$64$	−120367.	−	87451.6i	−3.67330	−	2.66881i
$65$	−1750.42			−0.0513876
$66$	−63985.0	+	25929.4i	−1.80808	+	0.732710i
$67$	−12306.1			−0.334913			−0.167457	−	0.985879i	$-0.553555\pi$
$67$	−12306.1			−0.334913			−0.167457	+	0.985879i	$0.553555\pi$
$68$	66718.7	+	48474.0i	1.74975	+	1.27127i
$69$	17055.0	−	7005.67i	0.431250	−	0.177144i
$70$	2361.70	+	7268.58i	0.0576077	+	0.177298i
$71$	11143.3	+	15337.4i	0.262341	+	0.361081i	0.919785	−	0.392422i	$-0.128363\pi$
$71$	11143.3	+	15337.4i	0.262341	+	0.361081i	−0.657444	+	0.753503i	$0.728363\pi$
$72$	69547.7	+	138505.i	1.58107	+	3.14872i
$73$	9033.18	−	2935.06i	0.198396	−	0.0644628i	−0.208133	−	0.978100i	$-0.566739\pi$
$73$	9033.18	−	2935.06i	0.198396	−	0.0644628i	0.406530	+	0.913638i	$0.366739\pi$
$74$	−10196.2	+	31380.6i	−0.216450	+	0.666165i
$75$	2761.24	−	209.137i	0.0566827	−	0.00429317i
$76$			131996.i			2.62137i
$77$	−3898.87	−	2861.02i	−0.0749396	−	0.0549912i
$78$	−3391.32	−	3994.47i	−0.0631149	−	0.0743401i
$79$	46837.8	−	64466.6i	0.844361	−	1.16216i	−0.140716	−	0.990050i	$-0.544940\pi$
$79$	46837.8	−	64466.6i	0.844361	−	1.16216i	0.985077	−	0.172114i	$-0.0550597\pi$
$80$	−227663.	−	73972.1i	−3.97711	−	1.29224i
$81$	695.288	−	59044.9i	0.0117748	−	0.999931i
$82$	−99616.7	+	72375.7i	−1.63605	+	1.18866i
$83$	−12279.6	+	8921.66i	−0.195654	+	0.142151i	−0.681299	−	0.732005i	$-0.738585\pi$
$83$	−12279.6	+	8921.66i	−0.195654	+	0.142151i	0.485645	+	0.874156i	$0.338585\pi$
$84$	−8855.46	+	14355.8i	−0.136934	+	0.221987i
$85$	50197.8	+	16310.3i	0.753594	+	0.244858i
$86$	121305.	−	166962.i	1.76862	−	2.43429i
$87$	12904.4	−	10955.9i	0.182784	−	0.155184i
$88$	243801.	−	77940.6i	3.35606	−	1.07289i
$89$			87903.7i			1.17634i	0.808738	+	0.588169i	$0.200151\pi$
$89$			87903.7i			1.17634i	−0.808738	+	0.588169i	$0.799849\pi$
$90$	108333.	+	109616.i	1.40979	+	1.42649i
$91$	113.421	−	349.075i	0.00143579	−	0.00441892i
$92$	−101008.	+	32819.4i	−1.24418	+	0.404260i
$93$	29972.6	−	123245.i	0.359349	−	1.47762i
$94$	−37237.5	−	51253.1i	−0.434672	−	0.598274i
$95$	26105.6	+	80344.7i	0.296773	+	0.913373i
$96$	−151389.	−	368551.i	−1.67655	−	4.08150i
$97$	24469.8	+	17778.3i	0.264059	+	0.191850i	0.711934	−	0.702246i	$-0.247819\pi$
$97$	24469.8	+	17778.3i	0.264059	+	0.191850i	−0.447876	+	0.894096i	$0.647819\pi$
$98$	183879.			1.93405
$99$	−96150.6	−	16277.9i	−0.985970	−	0.166921i
$100$	−15950.9			−0.159509
$101$	−118548.	−	86130.1i	−1.15635	−	0.840140i	−0.167041	−	0.985950i	$-0.553421\pi$
$101$	−118548.	−	86130.1i	−1.15635	−	0.840140i	−0.989313	+	0.145810i	$0.953421\pi$
$102$	60034.7	+	146152.i	0.571350	+	1.39093i
$103$	−3237.99	−	9965.50i	−0.0300734	−	0.0925563i	0.934893	−	0.354929i	$-0.115495\pi$
$103$	−3237.99	−	9965.50i	−0.0300734	−	0.0925563i	−0.964967	+	0.262373i	$0.915495\pi$
$104$	11418.7	+	15716.4i	0.103522	+	0.142485i
$105$	−2551.01	+	10489.6i	−0.0225807	+	0.0928506i
$106$	173038.	−	56223.4i	1.49581	−	0.486018i
$107$	−35400.3	+	108951.i	−0.298914	+	0.919964i	0.682964	+	0.730452i	$0.260691\pi$
$107$	−35400.3	+	108951.i	−0.298914	+	0.919964i	−0.981878	+	0.189512i	$0.939309\pi$
$108$	−29680.2	+	338837.i	−0.244854	+	2.79532i
$109$		−	101268.i		−	0.816406i	−0.912891	−	0.408203i	$-0.866156\pi$
$109$		−	101268.i		−	0.816406i	0.912891	−	0.408203i	$-0.133844\pi$
$110$	206618.	−	148626.i	1.62812	−	1.17115i
$111$	−35528.9	+	30164.1i	−0.273699	+	0.232371i
$112$	29503.6	−	40608.3i	0.222244	−	0.305893i
$113$	−22076.0	−	7172.93i	−0.162639	−	0.0528446i	0.226566	−	0.973996i	$-0.427250\pi$
$113$	−22076.0	−	7172.93i	−0.162639	−	0.0528446i	−0.389205	+	0.921151i	$0.627250\pi$
$114$	−132770.	+	215236.i	−0.956834	+	1.55114i
$115$	−54991.4	+	39953.6i	−0.387748	+	0.281716i
$116$	−78885.9	+	57314.0i	−0.544320	+	0.395472i
$117$	−1114.78	−	7317.03i	−0.00752881	−	0.0494163i
$118$	−88441.8	−	28736.5i	−0.584726	−	0.189989i
$119$	−6505.31	+	8953.80i	−0.0421115	+	0.0579615i
$120$	−369796.	−	435565.i	−2.34428	−	2.76121i
$121$	−51216.8	+	152690.i	−0.318016	+	0.948085i
$122$		−	183531.i		−	1.11637i
$123$	−173430.	+	13135.7i	−1.03362	+	0.0782869i
$124$	−225771.	+	694852.i	−1.31860	+	4.05825i
$125$	161091.	−	52341.5i	0.922136	−	0.299620i
$126$	−28879.7	+	14501.4i	−0.162057	+	0.0813737i
$127$	−158891.	−	218695.i	−0.874159	−	1.20318i	−0.978005	−	0.208583i	$-0.933115\pi$
$127$	−158891.	−	218695.i	−0.874159	−	1.20318i	0.103845	−	0.994593i	$-0.466885\pi$
$128$	254644.	+	783715.i	1.37376	+	4.22798i
$129$	269647.	−	110763.i	1.42666	−	0.586029i
$130$	15628.3	+	11354.6i	0.0811058	+	0.0589268i
$131$	−94445.5			−0.480842			−0.240421	−	0.970669i	$-0.577286\pi$
$131$	−94445.5			−0.480842			−0.240421	+	0.970669i	$0.577286\pi$
$132$	545185.	+	135325.i	2.72338	+	0.675995i
$133$	−17714.2			−0.0868346
$134$	109872.	+	79826.8i	0.528598	+	0.384049i
$135$	48947.6	+	212117.i	0.231152	+	1.00171i
$136$	−181015.	−	557108.i	−0.839205	−	2.58281i
$137$	−176965.	−	243572.i	−0.805540	−	1.10873i	−0.991996	−	0.126267i	$-0.959700\pi$
$137$	−176965.	−	243572.i	−0.805540	−	1.10873i	0.186457	−	0.982463i	$-0.440300\pi$
$138$	−197716.	−	48083.5i	−0.883782	−	0.214931i
$139$	20390.0	−	6625.13i	0.0895120	−	0.0290842i	−0.263919	−	0.964545i	$-0.585015\pi$
$139$	20390.0	−	6625.13i	0.0895120	−	0.0290842i	0.353431	+	0.935461i	$0.385015\pi$
$140$	19215.7	−	59139.9i	0.0828583	−	0.255012i
$141$	−6758.34	−	89230.3i	−0.0286281	−	0.377976i
$142$		−	209220.i		−	0.870730i
$143$	−12223.3	−	57.9207i	−0.0499860	−	0.000236861i
$144$	164224.	−	998777.i	0.659981	−	4.01386i
$145$	−36681.7	+	50488.0i	−0.144887	+	0.199420i
$146$	−99690.0	−	32391.2i	−0.387052	−	0.125761i
$147$	221057.	+	136361.i	0.843745	+	0.520470i
$148$	217192.	−	157799.i	0.815059	−	0.592175i
$149$	−167641.	+	121798.i	−0.618608	+	0.449445i	−0.852435	−	0.522833i	$-0.824875\pi$
$149$	−167641.	+	121798.i	−0.618608	+	0.449445i	0.233827	+	0.972278i	$0.424875\pi$
$150$	−26009.8	−	16044.3i	−0.0943862	−	0.0582228i
$151$	−413656.	−	134405.i	−1.47638	−	0.479704i	−0.543348	−	0.839507i	$-0.682844\pi$
$151$	−413656.	−	134405.i	−1.47638	−	0.479704i	−0.933028	+	0.359804i	$0.882844\pi$
$152$	551092.	−	758513.i	1.93471	−	2.66289i
$153$	−36210.1	+	220222.i	−0.125055	+	0.760559i
$154$	16251.4	+	50835.1i	0.0552191	+	0.172728i
$155$			467601.i			1.56331i
$156$	3219.89	+	42512.2i	0.0105933	+	0.139863i
$157$	122925.	−	378325.i	0.398008	−	1.22494i	−0.528586	−	0.848880i	$-0.677277\pi$
$157$	122925.	−	378325.i	0.398008	−	1.22494i	0.926594	−	0.376064i	$-0.122723\pi$
$158$	−836363.	+	271751.i	−2.66534	+	0.866020i
$159$	249718.	+	60730.0i	0.783352	+	0.190507i
$160$	863379.	+	1.18834e6i	2.66625	+	3.66978i
$161$	−4404.44	−	13555.5i	−0.0133914	−	0.0412144i
$162$	−389219.	+	522660.i	−1.16522	+	1.56470i
$163$	142381.	+	103446.i	0.419743	+	0.304961i	0.777534	−	0.628840i	$-0.216470\pi$
$163$	142381.	+	103446.i	0.419743	+	0.304961i	−0.357791	+	0.933802i	$0.616470\pi$
$164$	1.00186e6			2.90868
$165$	358612.	−	25452.9i	1.02545	−	0.0727827i
$166$	167509.			0.471811
$167$	143489.	+	104251.i	0.398132	+	0.289260i	0.768780	−	0.639514i	$-0.220864\pi$
$167$	143489.	+	104251.i	0.398132	+	0.289260i	−0.370648	+	0.928773i	$0.620864\pi$
$168$	110824.	−	45522.9i	0.302942	−	0.124439i
$169$	114449.	+	352238.i	0.308245	+	0.948680i
$170$	−342380.	−	471246.i	−0.908628	−	1.25062i
$171$	−319228.	+	160294.i	−0.834854	+	0.419206i
$172$	−1.59697e6	+	518888.i	−4.11601	+	1.33737i
$173$	42340.3	−	130310.i	0.107557	−	0.331026i	−0.882765	−	0.469815i	$-0.844321\pi$
$173$	42340.3	−	130310.i	0.107557	−	0.331026i	0.990322	+	0.138788i	$0.0443208\pi$
$174$	−186282.	+	14109.1i	−0.466443	+	0.0353286i
$175$		−	2140.64i		−	0.00528384i
$176$	−1.58734e6	−	524086.i	−3.86267	−	1.27532i
$177$	−85013.3	−	100133.i	−0.203964	−	0.240240i
$178$	570213.	−	784831.i	1.34892	−	1.85663i
$179$	713545.	+	231845.i	1.66452	+	0.540835i	0.981812	−	0.189856i	$-0.0608023\pi$
$179$	713545.	+	231845.i	1.66452	+	0.540835i	0.682708	+	0.730692i	$0.260802\pi$
$180$	−188865.	−	1.23964e6i	−0.434481	−	2.85177i
$181$	544710.	−	395755.i	1.23586	−	0.897904i	0.238543	−	0.971132i	$-0.423330\pi$
$181$	544710.	−	395755.i	1.23586	−	0.897904i	0.997315	+	0.0732280i	$0.0233301\pi$
$182$	−3277.04	+	2380.91i	−0.00733336	+	0.00532800i
$183$	136102.	−	220638.i	0.300426	−	0.487027i
$184$	717460.	+	233117.i	1.56226	+	0.507609i
$185$	100993.	−	139006.i	0.216952	−	0.298609i
$186$	−1.06707e6	+	905945.i	−2.26157	+	1.92008i
$187$	349995.	+	115557.i	0.731911	+	0.241652i
$188$			515458.i			1.06365i
$189$	−45472.8	−	3983.14i	−0.0925970	−	0.00811095i
$190$	288101.	−	886682.i	0.578975	−	1.78190i
$191$	684411.	−	222378.i	1.35748	−	0.441072i	0.462279	−	0.886735i	$-0.347032\pi$
$191$	684411.	−	222378.i	1.35748	−	0.441072i	0.895201	+	0.445663i	$0.147032\pi$
$192$	−548060.	+	2.25359e6i	−1.07294	+	4.41186i
$193$	−270086.	−	371742.i	−0.521927	−	0.718370i	0.463947	−	0.885863i	$-0.346433\pi$
$193$	−270086.	−	371742.i	−0.521927	−	0.718370i	−0.985873	+	0.167493i	$0.946433\pi$
$194$	−103149.	−	317460.i	−0.196771	−	0.605599i
$195$	10367.8	+	25239.9i	0.0195254	+	0.0475337i
$196$	−1.21038e6	−	879391.i	−2.25051	−	1.63509i
$197$	−35841.7			−0.0657996			−0.0328998	−	0.999459i	$-0.510474\pi$
$197$	−35841.7			−0.0657996			−0.0328998	+	0.999459i	$0.510474\pi$
$198$	752869.	+	769042.i	1.36476	+	1.39408i
$199$	−583205.			−1.04397			−0.521986	−	0.852954i	$-0.674809\pi$
$199$	−583205.			−1.04397			−0.521986	+	0.852954i	$0.674809\pi$
$200$	91661.2	+	66595.8i	0.162036	+	0.117726i
$201$	72889.1	+	177446.i	0.127254	+	0.309795i
$202$	499723.	+	1.53799e6i	0.861690	+	2.65201i
$203$	−7691.66	−	10586.7i	−0.0131003	−	0.0180310i
$204$	303787.	−	1.24915e6i	0.511086	−	2.10155i
$205$	609818.	−	198142.i	1.01348	−	0.329300i
$206$	−35734.4	+	109979.i	−0.0586702	+	0.180568i
$207$	−202034.	−	204428.i	−0.327718	−	0.331599i
$208$		−	126872.i		−	0.203333i
$209$	179638.	+	561916.i	0.284468	+	0.889827i
$210$	90819.8	−	77106.2i	0.142112	−	0.120654i
$211$	−461639.	+	635391.i	−0.713832	+	0.982506i	0.285874	+	0.958267i	$0.407716\pi$
$211$	−461639.	+	635391.i	−0.713832	+	0.982506i	−0.999706	+	0.0242385i	$0.992284\pi$
$212$	−1.40790e6	−	457455.i	−2.15146	−	0.699050i
$213$	155153.	−	251522.i	0.234321	−	0.379863i
$214$	1.02280e6	−	743111.i	1.52672	−	1.10922i
$215$	−869437.	+	631683.i	−1.28275	+	0.931973i
$216$	1.58522e6	−	1.82320e6i	2.31183	−	2.65889i
$217$	−93250.8	−	30299.0i	−0.134432	−	0.0436797i
$218$	−656904.	+	904150.i	−0.936183	+	1.28854i
$219$	−95825.3	−	112868.i	−0.135011	−	0.159023i
$220$	−2.07085e6	−	9812.85i	−2.88465	−	0.0136691i
$221$			27974.3i			0.0385282i
$222$	512880.	−	38845.7i	0.698447	−	0.0529006i
$223$	−325705.	+	1.00242e6i	−0.438594	+	1.34985i	0.450765	+	0.892643i	$0.351151\pi$
$223$	−325705.	+	1.00242e6i	−0.438594	+	1.34985i	−0.889359	+	0.457210i	$0.848849\pi$
$224$	−292927.	+	95177.8i	−0.390067	+	0.126741i
$225$	−19370.5	−	38576.6i	−0.0255085	−	0.0508004i
$226$	150572.	+	207244.i	0.196098	+	0.269906i
$227$	−335761.	−	1.03337e6i	−0.432480	−	1.33104i	−0.895647	−	0.444765i	$-0.853287\pi$
$227$	−335761.	−	1.03337e6i	−0.432480	−	1.33104i	0.463167	−	0.886271i	$-0.346713\pi$
$228$	1.90330e6	−	781817.i	2.42477	−	0.996020i
$229$	401576.	+	291762.i	0.506034	+	0.367655i	0.811317	−	0.584607i	$-0.198751\pi$
$229$	401576.	+	291762.i	0.506034	+	0.367655i	−0.305283	+	0.952262i	$0.598751\pi$
$230$	750150.			0.935036
$231$	−18160.9	+	73165.0i	−0.0223928	+	0.0902139i
$232$	692604.			0.844821
$233$	−884117.	−	642349.i	−1.06689	−	0.775142i	−0.0915401	−	0.995801i	$-0.529179\pi$
$233$	−884117.	−	642349.i	−1.06689	−	0.775142i	−0.975351	+	0.220660i	$0.929179\pi$
$234$	−37510.9	+	72560.0i	−0.0447835	+	0.0866278i
$235$	101945.	+	313753.i	0.120419	+	0.370611i
$236$	444735.	+	612125.i	0.519782	+	0.715418i
$237$	−1.20699e6	−	293533.i	−1.39583	−	0.339458i
$238$	116163.	−	37743.6i	0.132930	−	0.0431917i
$239$	−104441.	+	321437.i	−0.118271	+	0.364000i	−0.992615	−	0.121306i	$-0.961292\pi$
$239$	−104441.	+	321437.i	−0.118271	+	0.364000i	0.874344	+	0.485306i	$0.161292\pi$
$240$	281822.	+	3.72089e6i	0.315825	+	4.16983i
$241$		−	279007.i		−	0.309437i	−0.987959	−	0.154719i	$-0.950553\pi$
$241$		−	279007.i		−	0.309437i	0.987959	−	0.154719i	$-0.0494471\pi$
$242$	1.44775e6	−	1.03103e6i	1.58911	−	1.13170i
$243$	−855508.	+	339699.i	−0.929412	+	0.369044i
$244$	−877724.	+	1.20808e6i	−0.943808	+	1.29904i
$245$	−910665.	−	295893.i	−0.969267	−	0.314934i
$246$	1.63364e6	+	1.00772e6i	1.72115	+	1.06171i
$247$	−36223.4	+	26317.8i	−0.0377787	+	0.0274478i
$248$	4.19843e6	−	3.05034e6i	4.33469	−	3.14934i
$249$	201377.	+	124221.i	0.205831	+	0.126969i
$250$	−1.77779e6	−	577640.i	−1.79900	−	0.584530i
$251$	422632.	−	581702.i	0.423426	−	0.582796i	−0.543003	−	0.839731i	$-0.682713\pi$
$251$	422632.	−	581702.i	0.423426	−	0.582796i	0.966429	+	0.256935i	$0.0827126\pi$
$252$	259452.	+	42660.5i	0.257369	+	0.0423179i
$253$	−385330.	+	277179.i	−0.378471	+	0.272244i
$254$			2.98327e6i			2.90140i
$255$	−62139.4	−	820427.i	−0.0598435	−	0.790113i
$256$	1.33902e6	−	4.12107e6i	1.27699	−	3.93016i
$257$	744713.	−	241972.i	0.703326	−	0.228524i	0.0645467	−	0.997915i	$-0.479440\pi$
$257$	744713.	−	241972.i	0.703326	−	0.228524i	0.638779	+	0.769390i	$0.279440\pi$
$258$	−3.12598e6	−	760221.i	−2.92373	−	0.711035i
$259$	21177.0	+	29147.6i	0.0196162	+	0.0269994i
$260$	−48569.8	−	149482.i	−0.0445587	−	0.137138i
$261$	−234409.	−	121181.i	−0.212997	−	0.110112i
$262$	843237.	+	612647.i	0.758921	+	0.551388i
$263$	755782.			0.673763			0.336882	−	0.941547i	$-0.390628\pi$
$263$	755782.			0.673763			0.336882	+	0.941547i	$0.390628\pi$
$264$	−2.56790e6	−	3.05382e6i	−2.26761	−	2.69670i
$265$	−947446.			−0.828781
$266$	158158.	+	114908.i	0.137052	+	0.0995743i
$267$	1.26752e6	−	520656.i	1.08812	−	0.446964i
$268$	−341463.	−	1.05091e6i	−0.290407	−	0.893780i
$269$	−1.10226e6	−	1.51713e6i	−0.928758	−	1.27833i	−0.960342	−	0.278824i	$-0.910055\pi$
$269$	−1.10226e6	−	1.51713e6i	−0.928758	−	1.27833i	0.0315845	−	0.999501i	$-0.489945\pi$
$270$	938936.	−	2.21135e6i	0.783839	−	1.84607i
$271$	1.30036e6	−	422511.i	1.07557	−	0.349474i	0.282916	−	0.959145i	$-0.408698\pi$
$271$	1.30036e6	−	422511.i	1.07557	−	0.349474i	0.792655	+	0.609670i	$0.208698\pi$
$272$	−1.18218e6	+	3.63839e6i	−0.968865	+	2.98186i
$273$	−5705.24	+	432.117i	−0.00463305	+	0.000350909i
$274$			3.32262e6i			2.67365i
$275$	−67903.8	+	21708.1i	−0.0541455	+	0.0173097i
$276$	1.07151e6	+	1.26208e6i	0.846684	+	0.997270i
$277$	287471.	−	395670.i	0.225110	−	0.309837i	−0.681491	−	0.731827i	$-0.738668\pi$
$277$	287471.	−	395670.i	0.225110	−	0.309837i	0.906601	+	0.421990i	$0.138668\pi$
$278$	−225024.	−	73114.8i	−0.174629	−	0.0567405i
$279$	−1.95465e6	+	297800.i	−1.50334	+	0.229041i
$280$	−357334.	+	259619.i	−0.272383	+	0.197898i
$281$	−417122.	+	303057.i	−0.315135	+	0.228959i	−0.734097	−	0.679045i	$-0.762394\pi$
$281$	−417122.	+	303057.i	−0.315135	+	0.228959i	0.418962	+	0.908004i	$0.362394\pi$
$282$	−518477.	+	840514.i	−0.388246	+	0.629394i
$283$	1.30973e6	+	425556.i	0.972108	+	0.315857i	0.751667	−	0.659543i	$-0.229250\pi$
$283$	1.30973e6	+	425556.i	0.972108	+	0.315857i	0.220441	+	0.975400i	$0.429250\pi$
$284$	−1.00058e6	+	1.37719e6i	−0.736136	+	1.01320i
$285$	1.00389e6	−	852309.i	0.732109	−	0.621563i
$286$	108757.	+	79807.0i	0.0786220	+	0.0576934i
$287$			134451.i			0.0963519i
$288$	−4.41759e6	+	4.36587e6i	−3.13837	+	3.10163i
$289$	−178098.	+	548128.i	−0.125433	+	0.386044i
$290$	655010.	−	212826.i	0.457354	−	0.148603i
$291$	111417.	−	458139.i	0.0771292	−	0.317150i
$292$	501296.	+	689975.i	0.344063	+	0.473562i
$293$	222246.	+	684004.i	0.151240	+	0.465468i	0.997760	−	0.0668879i	$-0.0213070\pi$
$293$	222246.	+	684004.i	0.151240	+	0.465468i	−0.846521	+	0.532355i	$0.821307\pi$
$294$	−1.08912e6	−	2.65142e6i	−0.734865	−	1.78900i
$295$	391768.	+	284636.i	0.262104	+	0.190430i
$296$	−1.90690e6			−1.26503
$297$	334785.	+	1.48284e6i	0.220229	+	0.975448i
$298$	2.28683e6			1.49174
$299$	−29145.8	−	21175.6i	−0.0188537	−	0.0136980i
$300$	94477.4	+	230001.i	0.0606073	+	0.147546i
$301$	−69636.0	−	214318.i	−0.0443014	−	0.136346i
$302$	2.82139e6	+	3.88331e6i	1.78010	+	2.45010i
$303$	−539779.	+	2.21954e6i	−0.337761	+	1.38885i
$304$	−5.82347e6	+	1.89216e6i	−3.61408	+	1.17429i
$305$	−295332.	+	908939.i	−0.181786	+	0.559481i
$306$	1.75183e6	−	1.73132e6i	1.06952	−	1.05700i
$307$		−	2.51848e6i		−	1.52508i	−0.646940	−	0.762541i	$-0.723952\pi$
$307$		−	2.51848e6i		−	1.52508i	0.646940	−	0.762541i	$-0.276048\pi$
$308$	136141.	−	412342.i	0.0817737	−	0.247674i
$309$	−124517.	+	105716.i	−0.0741880	+	0.0629858i
$310$	3.03323e6	−	4.17488e6i	1.79267	−	2.46740i
$311$	455341.	+	147949.i	0.266954	+	0.0867385i	0.439435	−	0.898274i	$-0.355179\pi$
$311$	455341.	+	147949.i	0.266954	+	0.0867385i	−0.172482	+	0.985013i	$0.555179\pi$
$312$	158988.	−	257738.i	0.0924650	−	0.149897i
$313$	−632978.	+	459885.i	−0.365197	+	0.265331i	−0.755217	−	0.655475i	$-0.772468\pi$
$313$	−632978.	+	459885.i	−0.365197	+	0.265331i	0.390019	+	0.920807i	$0.372468\pi$
$314$	−3.55163e6	+	2.58041e6i	−2.03284	+	1.47695i
$315$	166363.	−	25346.1i	0.0944668	−	0.0143925i
$316$	6.80496e6	+	2.21107e6i	3.83361	+	1.24561i
$317$	833640.	−	1.14741e6i	0.465940	−	0.641312i	−0.509787	−	0.860301i	$-0.670276\pi$
$317$	833640.	−	1.14741e6i	0.465940	−	0.641312i	0.975727	+	0.218989i	$0.0702758\pi$
$318$	−1.83561e6	−	2.16208e6i	−1.01792	−	1.19896i
$319$	−257821.	+	351347.i	−0.141854	+	0.193313i
$320$		−	8.55027e6i		−	4.66772i
$321$	1.78068e6	−	134869.i	0.964545	−	0.0730550i
$322$	−48607.3	+	149598.i	−0.0261253	+	0.0804054i
$323$	1.28403e6	−	417206.i	0.684807	−	0.222507i
$324$	5.06161e6	−	1.57897e6i	2.67871	−	0.835627i
$325$	−3180.34	−	4377.36i	−0.00167019	−	0.00229881i
$326$	−600189.	−	1.84719e6i	−0.312784	−	0.962650i
$327$	−1.46022e6	+	599813.i	−0.755177	+	0.310203i
$328$	−5.75713e6	−	4.18280e6i	−2.95475	−	2.14676i
$329$	−69175.6			−0.0352341
$330$	−3.36690e6	−	2.09899e6i	−1.70194	−	1.06102i
$331$	−1.98391e6			−0.995295			−0.497647	−	0.867379i	$-0.665803\pi$
$331$	−1.98391e6			−0.995295			−0.497647	+	0.867379i	$0.665803\pi$
$332$	−1.10262e6	−	801101.i	−0.549011	−	0.398880i
$333$	645385.	+	333641.i	0.318939	+	0.164880i
$334$	−604858.	−	1.86156e6i	−0.296679	−	0.913085i
$335$	−415689.	−	572147.i	−0.202375	−	0.278545i
$336$	−760295.	−	184900.i	−0.367396	−	0.0893486i
$337$	−147695.	+	47989.0i	−0.0708420	+	0.0230179i	−0.344224	−	0.938888i	$-0.611858\pi$
$337$	−147695.	+	47989.0i	−0.0708420	+	0.0230179i	0.273382	+	0.961906i	$0.411858\pi$
$338$	1.26306e6	−	3.88729e6i	0.601356	−	1.85078i
$339$	27327.7	+	360807.i	0.0129153	+	0.170520i
$340$			4.73937e6i			2.22343i
$341$	−15472.7	+	3.26529e6i	−0.00720579	+	1.52067i
$342$	3.88995e6	+	639607.i	1.79837	+	0.295698i
$343$	237061.	−	326287.i	0.108799	−	0.149749i
$344$	1.13433e7	+	3.68568e6i	5.16827	+	1.67927i
$345$	901820.	+	556294.i	0.407917	+	0.251627i
$346$	−1.22332e6	+	888793.i	−0.549350	+	0.399126i
$347$	2.70621e6	−	1.96617e6i	1.20653	−	0.876594i	0.211617	−	0.977353i	$-0.432127\pi$
$347$	2.70621e6	−	1.96617e6i	1.20653	−	0.876594i	0.994911	+	0.100759i	$0.0321271\pi$
$348$	1.29367e6	+	798012.i	0.572633	+	0.353233i
$349$	2.36896e6	+	769723.i	1.04111	+	0.338276i	0.779172	−	0.626810i	$-0.215640\pi$
$349$	2.36896e6	+	769723.i	1.04111	+	0.338276i	0.261933	+	0.965086i	$0.415640\pi$
$350$	−13885.9	+	19112.3i	−0.00605904	+	0.00833956i
$351$	−98904.0	+	59413.4i	−0.0428495	+	0.0257405i
$352$	5.98971e6	+	8.32682e6i	2.57661	+	3.58197i
$353$		−	957821.i		−	0.409117i	−0.978854	−	0.204559i	$-0.934424\pi$
$353$		−	957821.i		−	0.409117i	0.978854	−	0.204559i	$-0.0655759\pi$
$354$	109481.	+	1.44548e6i	0.0464335	+	0.613062i
$355$	−336671.	+	1.03617e6i	−0.141787	+	0.436375i
$356$	−7.50681e6	+	2.43911e6i	−3.13928	+	1.02001i
$357$	167639.	+	40768.9i	0.0696153	+	0.0169301i
$358$	−4.86681e6	−	6.69859e6i	−2.00695	−	2.76233i
$359$	−1.00203e6	−	3.08393e6i	−0.410340	−	1.26290i	−0.916353	−	0.400372i	$-0.868881\pi$
$359$	−1.00203e6	−	3.08393e6i	−0.410340	−	1.26290i	0.506012	−	0.862526i	$-0.331119\pi$
$360$	−4.09026e6	+	7.91208e6i	−1.66339	+	3.21762i
$361$	−254979.	−	185253.i	−0.102976	−	0.0748164i
$362$	−7.43051e6			−2.98021
$363$	2.50505e6	−	165873.i	0.997815	−	0.0660709i
$364$	32957.5			0.0130377
$365$	441593.	+	320836.i	0.173496	+	0.126052i
$366$	−2.64639e6	+	1.08706e6i	−1.03265	+	0.424179i
$367$	−977844.	−	3.00949e6i	−0.378969	−	1.16635i	−0.940761	−	0.339069i	$-0.889888\pi$
$367$	−977844.	−	3.00949e6i	−0.378969	−	1.16635i	0.561792	−	0.827279i	$-0.310112\pi$
$368$	−2.89588e6	−	3.98583e6i	−1.11471	−	1.53426i
$369$	1.21664e6	+	2.42295e6i	0.465153	+	0.926356i
$370$	−1.80340e6	+	585960.i	−0.684837	+	0.222517i
$371$	61391.4	−	188943.i	0.0231565	−	0.0712684i
$372$	1.13566e7	−	860151.i	4.25491	−	0.322268i
$373$			3.12105e6i			1.16153i	0.814073	+	0.580763i	$0.197246\pi$
$373$			3.12105e6i			1.16153i	−0.814073	+	0.580763i	$0.802754\pi$
$374$	−2.37527e6	−	3.30207e6i	−0.878079	−	1.22069i
$375$	−1.70887e6	−	2.01280e6i	−0.627526	−	0.739133i
$376$	2.15206e6	−	2.96206e6i	0.785028	−	1.08050i
$377$	−31457.0	−	10221.0i	−0.0113989	−	0.00370374i
$378$	380156.	+	330535.i	0.136846	+	0.118984i
$379$	2.06750e6	−	1.50213e6i	0.739347	−	0.537167i	−0.153159	−	0.988201i	$-0.548945\pi$
$379$	2.06750e6	−	1.50213e6i	0.739347	−	0.537167i	0.892507	+	0.451034i	$0.148945\pi$
$380$	−6.13692e6	+	4.45873e6i	−2.18017	+	1.58399i
$381$	−2.21232e6	+	3.58644e6i	−0.780794	+	1.26576i
$382$	−7.55314e6	−	2.45416e6i	−2.64831	−	0.860489i
$383$	−2.48242e6	+	3.41676e6i	−0.864726	+	1.19019i	0.115696	+	0.993285i	$0.463090\pi$
$383$	−2.48242e6	+	3.41676e6i	−0.864726	+	1.19019i	−0.980422	+	0.196909i	$0.936910\pi$
$384$	9.79240e6	−	8.31377e6i	3.38892	−	2.87720i
$385$	1316.91	−	277913.i	0.000452797	−	0.0955558i
$386$			5.07102e6i			1.73231i
$387$	−3.19425e6	−	3.23209e6i	−1.08416	−	1.09700i
$388$	−839259.	+	2.58297e6i	−0.283020	+	0.871045i
$389$	−741083.	+	240792.i	−0.248309	+	0.0806806i	−0.430527	−	0.902578i	$-0.641672\pi$
$389$	−741083.	+	240792.i	−0.248309	+	0.0806806i	0.182218	+	0.983258i	$0.441672\pi$
$390$	71159.4	−	292603.i	0.0236903	−	0.0974130i
$391$	638518.	+	878844.i	0.211218	+	0.290717i
$392$	3.28389e6	+	1.01068e7i	1.07938	+	3.32199i
$393$	559403.	+	1.36184e6i	0.182702	+	0.444780i
$394$	320005.	+	232497.i	0.103852	+	0.0754532i
$395$	4.57939e6			1.47678
$396$	−1.27784e6	−	8.66274e6i	−0.409485	−	2.77599i
$397$	−2.25030e6			−0.716580			−0.358290	−	0.933610i	$-0.616640\pi$
$397$	−2.25030e6			−0.716580			−0.358290	+	0.933610i	$0.616640\pi$
$398$	5.20703e6	+	3.78313e6i	1.64771	+	1.19714i
$399$	104922.	+	255427.i	0.0329938	+	0.0803222i
$400$	−228655.	−	703727.i	−0.0714546	−	0.219915i
$401$	39531.4	+	54410.3i	0.0122767	+	0.0168974i	0.815111	−	0.579304i	$-0.196676\pi$
$401$	39531.4	+	54410.3i	0.0122767	+	0.0168974i	−0.802835	+	0.596202i	$0.796676\pi$
$402$	500276.	−	2.05710e6i	0.154399	−	0.634879i
$403$	−235701.	+	76584.0i	−0.0722936	+	0.0234896i
$404$	4.06594e6	−	1.25137e7i	1.23939	−	3.81444i
$405$	2.76867e6	−	1.96216e6i	0.838751	−	0.594426i
$406$			144415.i			0.0434808i
$407$	709844.	−	967343.i	0.212411	−	0.289464i
$408$	−6.96098e6	+	5.90989e6i	−2.07024	+	1.75764i
$409$	−3.76389e6	+	5.18055e6i	−1.11257	+	1.53133i	−0.295004	+	0.955496i	$0.595321\pi$
$409$	−3.76389e6	+	5.18055e6i	−1.11257	+	1.53133i	−0.817570	+	0.575830i	$0.804679\pi$
$410$	−6.72994e6	−	2.18669e6i	−1.97721	−	0.642433i
$411$	−2.46398e6	+	3.99441e6i	−0.719503	+	1.16640i
$412$	761188.	−	553036.i	0.220927	−	0.160513i
$413$	−82148.5	+	59684.4i	−0.0236987	+	0.0172181i
$414$	477746.	+	3.13574e6i	0.136992	+	0.899166i
$415$	−829591.	−	269550.i	−0.236452	−	0.0768280i
$416$	−457596.	+	629826.i	−0.129643	+	0.178438i
$417$	−216301.	−	254770.i	−0.0609141	−	0.0717479i
$418$	2.04117e6	−	6.18223e6i	0.571396	−	1.73063i
$419$		−	5.03505e6i		−	1.40110i	−0.713604	−	0.700549i	$-0.752938\pi$
$419$		−	5.03505e6i		−	1.40110i	0.713604	−	0.700549i	$-0.247062\pi$
$420$	−966574.	+	73208.7i	−0.267369	+	0.0202507i
$421$	1.68370e6	−	5.18188e6i	0.462976	−	1.42489i	−0.398535	−	0.917153i	$-0.630481\pi$
$421$	1.68370e6	−	5.18188e6i	0.462976	−	1.42489i	0.861511	−	0.507740i	$-0.169519\pi$
$422$	8.24329e6	−	2.67841e6i	2.25330	−	0.732143i
$423$	−1.24661e6	+	625964.i	−0.338751	+	0.170098i
$424$	6.18056e6	+	8.50681e6i	1.66960	+	2.29801i
$425$	50416.6	+	155166.i	0.0135395	+	0.0416701i
$426$	−3.01682e6	+	1.23922e6i	−0.805427	+	0.330844i
$427$	−162128.	−	117793.i	−0.0430316	−	0.0312643i
$428$	−1.02865e7			−2.71429
$429$	71563.7	+	176595.i	0.0187737	+	0.0463271i
$430$	1.18602e7			3.09329
$431$	−2.59556e6	−	1.88578e6i	−0.673034	−	0.488988i	0.198005	−	0.980201i	$-0.436554\pi$
$431$	−2.59556e6	−	1.88578e6i	−0.673034	−	0.488988i	−0.871039	+	0.491213i	$0.836554\pi$
$432$	−1.53744e7	+	3.54777e6i	−3.96360	+	0.914632i
$433$	−1.08868e6	−	3.35060e6i	−0.279048	−	0.858822i	−0.988120	−	0.153685i	$-0.950886\pi$
$433$	−1.08868e6	−	3.35060e6i	−0.279048	−	0.858822i	0.709072	−	0.705136i	$-0.249114\pi$
$434$	636027.	+	875416.i	0.162088	+	0.223095i
$435$	945271.	+	229885.i	0.239515	+	0.0582488i
$436$	8.64809e6	−	2.80994e6i	2.17873	−	0.707913i
$437$	−537290.	+	1.65361e6i	−0.134588	+	0.414218i
$438$	123405.	+	1.62932e6i	0.0307361	+	0.405808i
$439$		−	2.04566e6i		−	0.506608i	−0.967387	−	0.253304i	$-0.918483\pi$
$439$		−	2.04566e6i		−	0.506608i	0.967387	−	0.253304i	$-0.0815174\pi$
$440$	1.18591e7	+	8.70231e6i	2.92025	+	2.14290i
$441$	656907.	−	3.99517e6i	0.160845	−	0.978225i
$442$	181463.	−	249763.i	0.0441808	−	0.0608096i
$443$	775795.	+	252071.i	0.187818	+	0.0610258i	0.401416	−	0.915896i	$-0.368518\pi$
$443$	775795.	+	252071.i	0.187818	+	0.0610258i	−0.213598	+	0.976922i	$0.568518\pi$
$444$	−3.56179e6	−	2.19712e6i	−0.857455	−	0.528927i
$445$	−4.08692e6	+	2.96932e6i	−0.978353	+	0.710815i
$446$	9.41046e6	−	6.83710e6i	2.24013	−	1.62755i
$447$	2.74920e6	+	1.69586e6i	0.650785	+	0.401441i
$448$	1.70513e6	+	554030.i	0.401386	+	0.130418i
$449$	−3.41773e6	+	4.70410e6i	−0.800058	+	1.10119i	0.192724	+	0.981253i	$0.438268\pi$
$449$	−3.41773e6	+	4.70410e6i	−0.800058	+	1.10119i	−0.992782	+	0.119932i	$0.961732\pi$
$450$	−77292.3	+	470075.i	−0.0179931	+	0.109430i
$451$	4.26496e6	−	1.36346e6i	0.987355	−	0.315647i
$452$		−	2.08428e6i		−	0.479855i
$453$	512061.	+	6.76074e6i	0.117240	+	1.54792i
$454$	−3.70545e6	+	1.14042e7i	−0.843727	+	2.59672i
$455$	20060.9	−	6518.17i	0.00454278	−	0.00147604i
$456$	−1.42014e7	−	3.45370e6i	−3.19830	−	0.777808i
$457$	−2.37119e6	−	3.26367e6i	−0.531100	−	0.730997i	0.456197	−	0.889879i	$-0.349211\pi$
$457$	−2.37119e6	−	3.26367e6i	−0.531100	−	0.730997i	−0.987298	+	0.158882i	$0.949211\pi$
$458$	−1.69279e6	−	5.20988e6i	−0.377086	−	1.16055i
$459$	3.38994e6	−	782255.i	0.751035	−	0.173307i
$460$	−4.93783e6	−	3.58755e6i	−1.08803	−	0.790502i
$461$	321773.			0.0705176			0.0352588	−	0.999378i	$-0.488774\pi$
$461$	321773.			0.0705176			0.0352588	+	0.999378i	$0.488774\pi$
$462$	636752.	−	535433.i	0.138792	−	0.116708i
$463$	2.64070e6			0.572488			0.286244	−	0.958157i	$-0.407593\pi$
$463$	2.64070e6			0.572488			0.286244	+	0.958157i	$0.407593\pi$
$464$	−3.65942e6	−	2.65873e6i	−0.789074	−	0.573296i
$465$	6.74250e6	−	2.76961e6i	1.44607	−	0.594000i
$466$	3.72688e6	+	1.14702e7i	0.795025	+	2.44683i
$467$	4.40651e6	+	6.06504e6i	0.934980	+	1.28689i	0.957885	+	0.287152i	$0.0927084\pi$
$467$	4.40651e6	+	6.06504e6i	0.934980	+	1.28689i	−0.0229052	+	0.999738i	$0.507292\pi$
$468$	593928.	−	298230.i	0.125348	−	0.0629414i
$469$	141035.	−	45825.1i	0.0296070	−	0.00961991i
$470$	1.12506e6	−	3.46257e6i	0.234926	−	0.723027i
$471$	−6.18329e6	+	468325.i	−1.28430	+	0.0972736i
$472$		−	5.37434e6i		−	1.11038i
$473$	−6.09224e6	+	4.38232e6i	−1.25206	+	0.900639i
$474$	8.87227e6	+	1.04502e7i	1.81380	+	2.13639i
$475$	−153491.	+	211262.i	−0.0312139	+	0.0429622i
$476$	−945143.	−	307096.i	−0.191197	−	0.0621236i
$477$	−603397.	−	3.96048e6i	−0.121425	−	0.796987i
$478$	3.01758e6	−	2.19240e6i	0.604072	−	0.438884i
$479$	−144717.	+	105143.i	−0.0288190	+	0.0209383i	−0.602102	−	0.798420i	$-0.705670\pi$
$479$	−144717.	+	105143.i	−0.0288190	+	0.0209383i	0.573282	+	0.819358i	$0.305670\pi$
$480$	1.20213e7	−	1.94879e7i	2.38148	−	3.86067i
$481$	86608.7	+	28140.9i	0.0170686	+	0.00554594i
$482$	−1.80986e6	+	2.49106e6i	−0.354836	+	0.488389i
$483$	−169373.	+	143798.i	−0.0330352	+	0.0280470i
$484$	−1.44606e7	−	137048.i	−2.80590	−	0.0265924i
$485$			1.73821e6i			0.335543i
$486$	9.84178e6	+	2.51656e6i	1.89009	+	0.483301i
$487$	2.83415e6	−	8.72262e6i	0.541503	−	1.66657i	−0.187661	−	0.982234i	$-0.560091\pi$
$487$	2.83415e6	−	8.72262e6i	0.541503	−	1.66657i	0.729163	−	0.684340i	$-0.239909\pi$
$488$	1.00876e7	−	3.27767e6i	1.91752	−	0.623039i
$489$	648297.	−	2.66576e6i	0.122603	−	0.504137i
$490$	6.21129e6	+	8.54911e6i	1.16867	+	1.60854i
$491$	−860286.	−	2.64769e6i	−0.161042	−	0.495636i	0.837681	−	0.546160i	$-0.183911\pi$
$491$	−860286.	−	2.64769e6i	−0.161042	−	0.495636i	−0.998723	+	0.0505236i	$0.983911\pi$
$492$	−5.93401e6	−	1.44461e7i	−1.10519	−	2.69053i
$493$	806874.	+	586228.i	0.149516	+	0.108630i
$494$	494131.			0.0911014
$495$	−2.49108e6	−	5.02019e6i	−0.456956	−	0.920889i
$496$	−3.38922e7			−6.18579
$497$	−184822.	−	134281.i	−0.0335631	−	0.0243850i
$498$	−992159.	−	2.41537e6i	−0.179270	−	0.436426i
$499$	2.80302e6	+	8.62680e6i	0.503935	+	1.55095i	0.802554	+	0.596579i	$0.203474\pi$
$499$	2.80302e6	+	8.62680e6i	0.503935	+	1.55095i	−0.298620	+	0.954372i	$0.596526\pi$
$500$	8.93972e6	+	1.23045e7i	1.59919	+	2.20109i
$501$	653340.	−	2.68649e6i	0.116291	−	0.478180i
$502$	−7.54676e6	+	2.45209e6i	−1.33660	+	0.434287i
$503$	−1.65824e6	+	5.10355e6i	−0.292232	+	0.899398i	0.691905	+	0.721989i	$0.256772\pi$
$503$	−1.65824e6	+	5.10355e6i	−0.292232	+	0.899398i	−0.984137	+	0.177410i	$0.943228\pi$
$504$	−1.31282e6	−	1.32837e6i	−0.230213	−	0.232940i
$505$		−	8.42107e6i		−	1.46940i
$506$	5.23834e6	+	24822.2i	0.909531	+	0.00430986i
$507$	4.40116e6	−	3.73660e6i	0.760410	−	0.645590i
$508$	1.42673e7	−	1.96372e7i	2.45291	−	3.37615i
$509$	−1.02504e7	−	3.33055e6i	−1.75366	−	0.569799i	−0.757149	−	0.653242i	$-0.773409\pi$
$509$	−1.02504e7	−	3.33055e6i	−1.75366	−	0.569799i	−0.996513	+	0.0834424i	$0.973409\pi$
$510$	−4.76713e6	+	7.72810e6i	−0.811581	+	1.31567i
$511$	−92596.3	+	67275.1i	−0.0156870	+	0.0113973i
$512$	−1.73543e7	+	1.26086e7i	−2.92572	+	2.12566i
$513$	4.20213e6	+	3.65363e6i	0.704980	+	0.612959i
$514$	−8.21864e6	−	2.67040e6i	−1.37212	−	0.445829i
$515$	353950.	−	487171.i	0.0588063	−	0.0809400i
$516$	1.69410e7	+	1.99540e7i	2.80100	+	3.29917i
$517$	701504.	+	2.19433e6i	0.115426	+	0.361057i
$518$		−	397609.i		−	0.0651076i
$519$	−2.12977e6	+	161309.i	−0.347067	+	0.0262870i
$520$	−344992.	+	1.06178e6i	−0.0559501	+	0.172197i
$521$	3.69343e6	−	1.20007e6i	0.596122	−	0.193692i	0.00461192	−	0.999989i	$-0.498532\pi$
$521$	3.69343e6	−	1.20007e6i	0.596122	−	0.193692i	0.591510	+	0.806298i	$0.298532\pi$
$522$	1.30680e6	+	2.60250e6i	0.209910	+	0.418037i
$523$	5.31322e6	+	7.31301e6i	0.849382	+	1.16907i	0.983999	+	0.178177i	$0.0570199\pi$
$523$	5.31322e6	+	7.31301e6i	0.849382	+	1.16907i	−0.134616	+	0.990898i	$0.542980\pi$
$524$	−2.62063e6	−	8.06546e6i	−0.416943	−	1.28322i
$525$	−30866.7	+	12679.1i	−0.00488756	+	0.00200766i
$526$	−6.74785e6	−	4.90260e6i	−1.06341	−	0.772613i
$527$	7.47296e6			1.17210
$528$	1.84486e6	+	2.59925e7i	0.287990	+	4.05755i
$529$	5.03736e6			0.782643
$530$	8.45908e6	+	6.14588e6i	1.30808	+	0.950374i
$531$	−940320.	+	1.81893e6i	−0.144724	+	0.279949i
$532$	−491525.	−	1.51276e6i	−0.0752951	−	0.231735i
$533$	199753.	+	274937.i	0.0304562	+	0.0419193i
$534$	−1.46941e7	−	3.57353e6i	−2.22993	−	0.542306i
$535$	−6.26125e6	+	2.03440e6i	−0.945750	+	0.307293i
$536$	−2.42542e6	+	7.46467e6i	−0.364649	+	1.12227i
$537$	−883291.	−	1.16621e7i	−0.132181	−	1.74518i
$538$			2.06955e7i			3.08262i
$539$	−6.34944e6	−	2.09637e6i	−0.941377	−	0.310811i
$540$	−1.67562e7	+	1.00657e7i	−2.47281	+	1.48546i
$541$	−5.45663e6	+	7.51040e6i	−0.801551	+	1.10324i	0.191022	+	0.981586i	$0.438820\pi$
$541$	−5.45663e6	+	7.51040e6i	−0.801551	+	1.10324i	−0.992573	+	0.121654i	$0.961180\pi$
$542$	−1.43507e7	−	4.66283e6i	−2.09834	−	0.681791i
$543$	−8.93286e6	−	5.51030e6i	−1.30014	−	0.802002i
$544$	1.89914e7	−	1.37981e7i	2.75144	−	1.99904i
$545$	4.70826e6	−	3.42075e6i	0.678999	−	0.493322i
$546$	53741.1	+	33150.6i	0.00771481	+	0.00475894i
$547$	1.59375e6	+	517840.i	0.227746	+	0.0739992i	0.420667	−	0.907215i	$-0.361796\pi$
$547$	1.59375e6	+	517840.i	0.227746	+	0.0739992i	−0.192921	+	0.981214i	$0.561796\pi$
$548$	1.58902e7	−	2.18710e7i	2.26037	−	3.11113i
$549$	−3.98760e6	−	655662.i	−0.564651	−	0.0928430i
$550$	747081.	+	246661.i	0.105308	+	0.0347692i
$551$			1.59632e6i			0.223996i
$552$	−888137.	−	1.17261e7i	−0.124060	−	1.63796i
$553$	−296730.	+	913241.i	−0.0412618	+	0.126991i
$554$	−5.13325e6	+	1.66789e6i	−0.710588	+	0.230884i
$555$	−2.60256e6	−	632927.i	−0.358648	−	0.0872211i
$556$	1.13155e6	+	1.55744e6i	0.155233	+	0.213660i
$557$	258596.	+	795875.i	0.0353169	+	0.108694i	0.967161	−	0.254165i	$-0.0818006\pi$
$557$	258596.	+	795875.i	0.0353169	+	0.108694i	−0.931844	+	0.362859i	$0.881801\pi$
$558$	1.93834e7	+	1.00205e7i	2.63539	+	1.36240i
$559$	−460807.	−	334796.i	−0.0623720	−	0.0453159i
$560$	2.88461e6			0.388702
$561$	−406776.	−	5.73115e6i	−0.0545693	−	0.768837i
$562$	5.69005e6			0.759933
$563$	1.90465e6	+	1.38381e6i	0.253248	+	0.183995i	0.707165	−	0.707049i	$-0.249974\pi$
$563$	1.90465e6	+	1.38381e6i	0.253248	+	0.183995i	−0.453917	+	0.891044i	$0.649974\pi$
$564$	7.43257e6	−	3.05307e6i	0.983878	−	0.404146i
$565$	−412218.	−	1.26868e6i	−0.0543258	−	0.167198i
$566$	−8.93313e6	−	1.22954e7i	−1.17209	−	1.61325i
$567$	211902.	+	679280.i	0.0276807	+	0.0887342i
$568$	1.14996e7	−	3.73646e6i	1.49559	−	0.485948i
$569$	−704265.	+	2.16751e6i	−0.0911918	+	0.280659i	−0.986243	−	0.165305i	$-0.947139\pi$
$569$	−704265.	+	2.16751e6i	−0.0911918	+	0.280659i	0.895051	+	0.445964i	$0.147139\pi$
$570$	−1.44918e7	+	1.09762e6i	−1.86825	+	0.141502i
$571$			2.80576e6i			0.360130i	0.983655	+	0.180065i	$0.0576308\pi$
$571$			2.80576e6i			0.360130i	−0.983655	+	0.180065i	$0.942369\pi$
$572$	−334220.	−	1.04545e6i	−0.0427112	−	0.133602i
$573$	−7.26033e6	−	8.55161e6i	−0.923783	−	1.08808i
$574$	872157.	−	1.20042e6i	0.110488	−	0.152074i
$575$	−199828.	−	64927.9i	−0.0252050	−	0.00818959i
$576$	3.57415e7	−	5.44538e6i	4.48866	−	0.683868i
$577$	−3.48974e6	+	2.53544e6i	−0.436368	+	0.317040i	−0.784190	−	0.620520i	$-0.786921\pi$
$577$	−3.48974e6	+	2.53544e6i	−0.436368	+	0.317040i	0.347822	+	0.937561i	$0.386921\pi$
$578$	5.14570e6	−	3.73857e6i	0.640655	−	0.465463i
$579$	−3.76055e6	+	6.09631e6i	−0.466182	+	0.755737i
$580$	−5.32940e6	−	1.73163e6i	−0.657822	−	0.213739i
$581$	107510.	−	147974.i	0.0132132	−	0.0181864i
$582$	−3.96662e6	+	3.36767e6i	−0.485414	+	0.412118i
$583$	−6.61608e6	−	31350.7i	−0.806175	−	0.00382010i
$584$		−	6.05786e6i		−	0.735000i
$585$	302535.	−	298993.i	0.0365498	−	0.0361220i
$586$	2.45271e6	−	7.54865e6i	0.295054	−	0.908083i
$587$	4.98581e6	−	1.61999e6i	0.597228	−	0.194051i	0.00522438	−	0.999986i	$-0.498337\pi$
$587$	4.98581e6	−	1.61999e6i	0.597228	−	0.194051i	0.592004	+	0.805935i	$0.298337\pi$
$588$	−5.51116e6	+	2.26615e7i	−0.657354	+	2.70300i
$589$	7.03045e6	+	9.67659e6i	0.835017	+	1.14930i
$590$	−1.65145e6	−	5.08263e6i	−0.195314	−	0.601116i
$591$	212291.	+	516814.i	0.0250013	+	0.0608647i
$592$	1.00753e7	+	7.32011e6i	1.18155	+	0.858447i
$593$	−7.70266e6			−0.899506			−0.449753	−	0.893153i	$-0.648488\pi$
$593$	−7.70266e6			−0.899506			−0.449753	+	0.893153i	$0.648488\pi$
$594$	6.62983e6	−	1.54109e7i	0.770967	−	1.79210i
$595$	−636034.			−0.0736526
$596$	−1.50530e7	−	1.09366e7i	−1.73583	−	1.26115i
$597$	3.45434e6	+	8.40944e6i	0.396670	+	0.965676i
$598$	122860.	+	378125.i	0.0140494	+	0.0432396i
$599$	9.86850e6	+	1.35828e7i	1.12379	+	1.54676i	0.799363	+	0.600849i	$0.205171\pi$
$599$	9.86850e6	+	1.35828e7i	1.12379	+	1.54676i	0.324424	+	0.945912i	$0.394829\pi$
$600$	417357.	−	1.71614e6i	0.0473292	−	0.194615i
$601$	4.33349e6	−	1.40804e6i	0.489386	−	0.159011i	−0.0539209	−	0.998545i	$-0.517172\pi$
$601$	4.33349e6	−	1.40804e6i	0.489386	−	0.159011i	0.543307	+	0.839534i	$0.317172\pi$
$602$	−768502.	+	2.36520e6i	−0.0864278	+	0.265997i
$603$	2.12693e6	−	2.10203e6i	0.238210	−	0.235421i
$604$		−	3.90548e7i		−	4.35595i
$605$	−8.82910e6	+	2.77652e6i	−0.980681	+	0.308399i
$606$	1.92170e7	−	1.63152e7i	2.12570	−	1.80473i
$607$	−4.69528e6	+	6.46250e6i	−0.517237	+	0.711916i	−0.985119	−	0.171875i	$-0.945017\pi$
$607$	−4.69528e6	+	6.46250e6i	−0.517237	+	0.711916i	0.467882	+	0.883791i	$0.345017\pi$
$608$	3.57337e7	+	1.16106e7i	3.92030	+	1.27378i
$609$	−107095.	+	173614.i	−0.0117011	+	0.0189689i
$610$	8.53290e6	−	6.19952e6i	0.928479	−	0.674580i
$611$	−141456.	+	102774.i	−0.0153291	+	0.0111373i
$612$	−1.98113e7	+	3.01835e6i	−2.13813	+	0.325755i
$613$	3.36721e6	+	1.09407e6i	0.361925	+	0.117597i	0.484334	−	0.874883i	$-0.339062\pi$
$613$	3.36721e6	+	1.09407e6i	0.361925	+	0.117597i	−0.122409	+	0.992480i	$0.539062\pi$
$614$	−1.63369e7	+	2.24858e7i	−1.74883	+	2.40706i
$615$	−6.46905e6	−	7.61959e6i	−0.689688	−	0.812351i
$616$	−2.50388e6	+	1.80111e6i	−0.265865	+	0.191244i
$617$		−	2.48344e6i		−	0.262628i	−0.991341	−	0.131314i	$-0.958080\pi$
$617$		−	2.48344e6i		−	0.262628i	0.991341	−	0.131314i	$-0.0419196\pi$
$618$	1.79748e6	−	136142.i	0.189319	−	0.0143391i
$619$	−595167.	+	1.83173e6i	−0.0624327	+	0.192148i	−0.977408	−	0.211362i	$-0.932210\pi$
$619$	−595167.	+	1.83173e6i	−0.0624327	+	0.192148i	0.914975	+	0.403510i	$0.132210\pi$
$620$	−3.99322e7	+	1.29748e7i	−4.17200	+	1.35556i
$621$	−1.75106e6	+	4.12404e6i	−0.182210	+	0.429135i
$622$	−3.10570e6	−	4.27463e6i	−0.321873	−	0.443020i
$623$	−327334.	−	1.00743e6i	−0.0337887	−	0.103991i
$624$	−1.82941e6	+	751467.i	−0.188084	+	0.0772589i
$625$	8.32413e6	+	6.04784e6i	0.852391	+	0.619299i
$626$	8.63459e6			0.880655
$627$	7.03847e6	−	5.91851e6i	0.715005	−	0.601234i
$628$	3.57191e7			3.61411
$629$	−2.22152e6	−	1.61403e6i	−0.223884	−	0.162661i
$630$	−1.64975e6	−	852861.i	−0.165602	−	0.0856105i
$631$	−3.35035e6	−	1.03113e7i	−0.334978	−	1.03096i	−0.966733	−	0.255788i	$-0.917665\pi$
$631$	−3.35035e6	−	1.03113e7i	−0.334978	−	1.03096i	0.631755	−	0.775168i	$-0.282335\pi$
$632$	−2.98732e7	−	4.11169e7i	−2.97501	−	4.09475i
$633$	1.18962e7	+	2.89310e6i	1.18005	+	0.286981i
$634$	−1.48860e7	+	4.83674e6i	−1.47080	+	0.477892i
$635$	4.80059e6	−	1.47747e7i	0.472454	−	1.45407i
$636$	1.74283e6	+	2.30105e7i	0.170849	+	2.25571i
$637$		−	507496.i		−	0.0495546i
$638$	4.58102e6	−	1.46450e6i	0.445564	−	0.142442i
$639$	−4.54576e6	−	747439.i	−0.440407	−	0.0724141i
$640$	−2.78356e7	+	3.83125e7i	−2.68628	+	3.69735i
$641$	−4.45804e6	−	1.44851e6i	−0.428548	−	0.139244i	0.0867982	−	0.996226i	$-0.472336\pi$
$641$	−4.45804e6	−	1.44851e6i	−0.428548	−	0.139244i	−0.515346	+	0.856982i	$0.672336\pi$
$642$	−1.67733e7	−	1.03467e7i	−1.60613	−	0.990752i
$643$	−1.25747e7	+	9.13607e6i	−1.19942	+	0.871429i	−0.994228	−	0.107292i	$-0.965782\pi$
$643$	−1.25747e7	+	9.13607e6i	−1.19942	+	0.871429i	−0.205192	+	0.978722i	$0.565782\pi$
$644$	1.03540e6	−	752261.i	0.0983768	−	0.0714749i
$645$	1.42582e7	+	8.79525e6i	1.34947	+	0.832432i
$646$	−1.41705e7	−	4.60428e6i	−1.33599	−	0.434090i
$647$	−5.26869e6	+	7.25173e6i	−0.494814	+	0.681053i	−0.981267	−	0.192654i	$-0.938290\pi$
$647$	−5.26869e6	+	7.25173e6i	−0.494814	+	0.681053i	0.486453	+	0.873707i	$0.338290\pi$
$648$	−3.56787e7	−	1.20590e7i	−3.33788	−	1.12817i
$649$	2.72632e6	+	2.00060e6i	0.254077	+	0.186444i
$650$			59712.5i			0.00554347i
$651$	115434.	+	1.52408e6i	0.0106754	+	0.140947i
$652$	−4.88336e6	+	1.50294e7i	−0.449884	+	1.38460i
$653$	1.03576e7	−	3.36539e6i	0.950553	−	0.308853i	0.207613	−	0.978211i	$-0.433431\pi$
$653$	1.03576e7	−	3.36539e6i	0.950553	−	0.308853i	0.742940	+	0.669358i	$0.233431\pi$
$654$	1.69281e7	+	4.11682e6i	1.54762	+	0.376373i
$655$	−3.19029e6	−	4.39106e6i	−0.290554	−	0.399914i
$656$	1.43615e7	+	4.42003e7i	1.30299	+	4.01019i
$657$	−1.05991e6	+	2.05026e6i	−0.0957979	+	0.185309i
$658$	617620.	+	448727.i	0.0556105	+	0.0404034i
$659$	2.17424e7			1.95026			0.975131	−	0.221627i	$-0.0711368\pi$
$659$	2.17424e7			1.95026			0.975131	+	0.221627i	$0.0711368\pi$
$660$	1.21242e7	+	2.99185e7i	1.08341	+	2.67350i
$661$	5.30552e6			0.472307			0.236153	−	0.971716i	$-0.424113\pi$
$661$	5.30552e6			0.472307			0.236153	+	0.971716i	$0.424113\pi$
$662$	1.77129e7	+	1.28692e7i	1.57089	+	1.14132i
$663$	403371.	−	165692.i	0.0356387	−	0.0146393i
$664$	2.99154e6	+	9.20700e6i	0.263314	+	0.810398i
$665$	−598372.	−	823588.i	−0.0524707	−	0.0722197i
$666$	−3.59793e6	−	7.16532e6i	−0.314317	−	0.625965i
$667$	−1.22155e6	+	396907.i	−0.106316	+	0.0345441i
$668$	−4.92135e6	+	1.51464e7i	−0.426720	+	1.31331i
$669$	1.63834e7	−	1.24088e6i	1.41527	−	0.107193i
$670$			7.80478e6i			0.671698i
$671$	−2.09240e6	+	6.33741e6i	−0.179407	+	0.543382i
$672$	3.10742e6	+	3.66008e6i	0.265446	+	0.312657i
$673$	1.26010e7	−	1.73437e7i	1.07242	−	1.47606i	0.204824	−	0.978799i	$-0.434338\pi$
$673$	1.26010e7	−	1.73437e7i	1.07242	−	1.47606i	0.867599	−	0.497264i	$-0.165662\pi$
$674$	1.62996e6	+	529605.i	0.138206	+	0.0449058i
$675$	−441517.	+	507800.i	−0.0372982	+	0.0428976i
$676$	−2.69048e7	+	1.95475e7i	−2.26445	+	1.64522i
$677$	6.75797e6	−	4.90995e6i	0.566688	−	0.411723i	−0.267212	−	0.963638i	$-0.586103\pi$
$677$	6.75797e6	−	4.90995e6i	0.566688	−	0.411723i	0.833901	+	0.551914i	$0.186103\pi$
$678$	2.09649e6	−	3.39866e6i	0.175153	−	0.283945i
$679$	−346641.	−	112630.i	−0.0288540	−	0.00937522i
$680$	1.97871e7	−	2.72346e7i	1.64101	−	2.25865i
$681$	−1.29118e7	+	1.09621e7i	−1.06689	+	0.905788i
$682$	2.13194e7	−	2.90531e7i	1.75515	−	2.39184i
$683$			2.02486e6i			0.166090i	0.996546	+	0.0830450i	$0.0264645\pi$
$683$			2.02486e6i			0.166090i	−0.996546	+	0.0830450i	$0.973535\pi$
$684$	−2.25466e7	−	2.28137e7i	−1.84264	−	1.86447i
$685$	5.34666e6	−	1.64553e7i	0.435368	−	1.33992i
$686$	−4.23310e6	+	1.37542e6i	−0.343438	+	0.111590i
$687$	1.82848e6	−	7.51859e6i	0.147808	−	0.607777i
$688$	−4.57850e7	−	6.30177e7i	−3.68767	−	5.07565i
$689$	−155174.	−	477575.i	−0.0124529	−	0.0383260i
$690$	−4.44315e6	−	1.08167e7i	−0.355278	−	0.864910i
$691$	3.50313e6	+	2.54517e6i	0.279101	+	0.202779i	0.718525	−	0.695501i	$-0.244817\pi$
$691$	3.50313e6	+	2.54517e6i	0.279101	+	0.202779i	−0.439424	+	0.898280i	$0.644817\pi$
$692$	1.23031e7			0.976670
$693$	1.16256e6	−	171489.i	0.0919565	−	0.0135645i
$694$	−3.69160e7			−2.90948
$695$	996782.	+	724204.i	0.0782777	+	0.0568721i
$696$	−4.10231e6	−	9.98690e6i	−0.321000	−	0.781462i
$697$	−3.16660e6	−	9.74581e6i	−0.246895	−	0.759864i
$698$	−1.61578e7	−	2.22393e7i	−1.25529	−	1.72775i
$699$	−4.02561e6	+	1.65530e7i	−0.311629	+	1.28140i
$700$	182807.	−	59397.6i	0.0141009	−	0.00458167i
$701$	2.82250e6	−	8.68677e6i	0.216940	−	0.667672i	−0.782070	−	0.623190i	$-0.785836\pi$
$701$	2.82250e6	−	8.68677e6i	0.216940	−	0.667672i	0.999010	−	0.0444819i	$-0.0141637\pi$
$702$	1.26845e6	+	111108.i	0.0971469	+	0.00850950i
$703$		−	4.39505e6i		−	0.335410i
$704$	282925.	−	5.97071e7i	0.0215149	−	4.54040i
$705$	3.92030e6	−	3.32834e6i	0.297062	−	0.252206i
$706$	−6.21318e6	+	8.55171e6i	−0.469140	+	0.645716i
$707$	1.67936e6	+	545658.i	0.126356	+	0.0410555i
$708$	6.19227e6	−	1.00384e7i	0.464266	−	0.752631i
$709$	1.20486e7	−	8.75384e6i	0.900164	−	0.654008i	−0.0383438	−	0.999265i	$-0.512208\pi$
$709$	1.20486e7	−	8.75384e6i	0.900164	−	0.654008i	0.938508	+	0.345257i	$0.112208\pi$
$710$	9.72730e6	−	7.06730e6i	0.724180	−	0.526148i
$711$	2.91647e6	+	1.91426e7i	0.216363	+	1.42013i
$712$	5.33210e7	+	1.73251e7i	3.94184	+	1.28078i
$713$	−5.65678e6	+	7.78589e6i	−0.416721	+	0.573568i
$714$	−1.23227e6	−	1.45144e6i	−0.0904610	−	0.106550i
$715$	−410200.	−	570255.i	−0.0300076	−	0.0417161i
$716$			6.73685e7i			4.91105i
$717$	5.25352e6	−	397904.i	0.381639	−	0.0289055i
$718$	−1.10584e7	+	3.40342e7i	−0.800535	+	2.46379i
$719$	−1.08555e7	+	3.52716e6i	−0.783118	+	0.254450i	−0.673171	−	0.739487i	$-0.735068\pi$
$719$	−1.08555e7	+	3.52716e6i	−0.783118	+	0.254450i	−0.109947	+	0.993937i	$0.535068\pi$
$720$	5.19836e7	−	2.61026e7i	3.73710	−	1.87652i
$721$	74218.6	+	102153.i	0.00531710	+	0.00731836i
$722$	1.07483e6	+	3.30798e6i	0.0767355	+	0.236168i
$723$	−4.02310e6	+	1.65257e6i	−0.286230	+	0.117574i
$724$	4.89110e7	+	3.55360e7i	3.46785	+	2.51954i
$725$	−192905.			−0.0136301
$726$	−2.34418e7	−	1.47688e7i	−1.65063	−	1.03993i
$727$	−1.76770e7			−1.24043			−0.620216	−	0.784431i	$-0.712955\pi$
$727$	−1.76770e7			−1.24043			−0.620216	+	0.784431i	$0.712955\pi$
$728$	−189389.	−	137599.i	−0.0132442	−	0.00962250i
$729$	9.96543e6	+	1.03238e7i	0.694508	+	0.719485i
$730$	−1.86148e6	−	5.72904e6i	−0.129286	−	0.397901i
$731$	1.00952e7	+	1.38949e7i	0.698752	+	0.961750i
$732$	2.26186e7	+	5.50071e6i	1.56023	+	0.379438i
$733$	−1.23440e7	+	4.01082e6i	−0.848589	+	0.275723i	−0.700855	−	0.713304i	$-0.747198\pi$
$733$	−1.23440e7	+	4.01082e6i	−0.848589	+	0.275723i	−0.147734	+	0.989027i	$0.547198\pi$
$734$	−1.07915e7	+	3.32127e7i	−0.739333	+	2.27543i
$735$	1.12730e6	+	1.48838e7i	0.0769702	+	1.01624i
$736$			3.02314e7i			2.05714i
$737$	−2.88385e6	−	4.00910e6i	−0.195571	−	0.271880i
$738$	4.85464e6	−	2.95249e7i	0.328107	−	1.99548i
$739$	2.08179e6	−	2.86533e6i	0.140225	−	0.193003i	−0.733129	−	0.680090i	$-0.761941\pi$
$739$	2.08179e6	−	2.86533e6i	0.140225	−	0.193003i	0.873353	+	0.487087i	$0.161941\pi$
$740$	1.46731e7	+	4.76759e6i	0.985016	+	0.320051i
$741$	594038.	+	366437.i	0.0397438	+	0.0245162i
$742$	−1.77376e6	+	1.28871e6i	−0.118273	+	0.0859301i
$743$	−1.14764e7	+	8.33808e6i	−0.762663	+	0.554107i	−0.899726	−	0.436455i	$-0.856234\pi$
$743$	−1.14764e7	+	8.33808e6i	−0.762663	+	0.554107i	0.137063	+	0.990562i	$0.456234\pi$
$744$	−6.88513e7	−	4.24715e7i	−4.56016	−	2.81297i
$745$	−1.13256e7	−	3.67990e6i	−0.747600	−	0.242910i
$746$	2.02456e7	−	2.78657e7i	1.33194	−	1.83325i
$747$	598424.	−	3.63949e6i	0.0392381	−	0.238638i
$748$	−156824.	+	3.30953e7i	−0.0102485	+	2.16278i
$749$		−	1.38047e6i		−	0.0899127i
$750$	2.20071e6	+	2.90560e7i	0.142860	+	1.88618i
$751$	939946.	−	2.89286e6i	0.0608140	−	0.187166i	−0.916034	−	0.401100i	$-0.868628\pi$
$751$	939946.	−	2.89286e6i	0.0608140	−	0.187166i	0.976848	+	0.213934i	$0.0686278\pi$
$752$	−2.27412e7	+	7.38905e6i	−1.46645	+	0.476479i
$753$	−1.08910e7	−	2.64864e6i	−0.699973	−	0.170230i
$754$	214556.	+	295311.i	0.0137440	+	0.0189170i
$755$	−7.72407e6	−	2.37722e7i	−0.493150	−	1.51776i
$756$	−921603.	−	3.99381e6i	−0.0586461	−	0.254146i
$757$	−1.65483e7	−	1.20230e7i	−1.04957	−	0.762560i	−0.0774424	−	0.996997i	$-0.524675\pi$
$757$	−1.65483e7	−	1.20230e7i	−1.04957	−	0.762560i	−0.972131	+	0.234437i	$0.924675\pi$
$758$	−2.82033e7			−1.78290
$759$	6.27906e6	+	3.91448e6i	0.395631	+	0.246644i
$760$	5.38810e7			3.38378
$761$	−2.22848e7	−	1.61909e7i	−1.39491	−	1.01346i	−0.995306	−	0.0967781i	$-0.969146\pi$
$761$	−2.22848e7	−	1.61909e7i	−1.39491	−	1.01346i	−0.399608	−	0.916686i	$-0.630854\pi$
$762$	4.30168e7	−	1.76700e7i	2.68380	−	1.10242i
$763$	377100.	+	1.16059e6i	0.0234501	+	0.0721720i
$764$	3.79814e7	+	5.22769e7i	2.35417	+	3.24023i
$765$	−1.14620e7	+	5.75542e6i	−0.708118	+	0.355568i
$766$	4.43276e7	−	1.44029e7i	2.72962	−	0.886907i
$767$	−79311.1	+	244095.i	−0.00486795	+	0.0149820i
$768$	−6.73543e7	+	5.10144e6i	−4.12062	+	0.312097i
$769$			1.43542e7i			0.875312i	0.899142	+	0.437656i	$0.144191\pi$
$769$			1.43542e7i			0.875312i	−0.899142	+	0.437656i	$0.855809\pi$
$770$	−1.81452e6	+	2.47275e6i	−0.110290	+	0.150298i
$771$	−7.90004e6	−	9.30508e6i	−0.478623	−	0.563747i
$772$	2.42518e7	−	3.33798e7i	1.46454	−	2.01577i
$773$	−2.43431e7	−	7.90956e6i	−1.46530	−	0.476106i	−0.535618	−	0.844460i	$-0.679921\pi$
$773$	−2.43431e7	−	7.90956e6i	−1.46530	−	0.476106i	−0.929686	+	0.368354i	$0.879921\pi$
$774$	7.55336e6	+	4.95775e7i	0.453198	+	2.97462i
$775$	−1.16935e6	+	849584.i	−0.0699344	+	0.0508103i
$776$	1.56068e7	−	1.13390e7i	0.930380	−	0.675960i
$777$	294858.	−	478001.i	0.0175211	−	0.0284038i
$778$	8.17858e6	+	2.65738e6i	0.484427	+	0.157400i
$779$	9.64056e6	−	1.32691e7i	0.569192	−	0.783425i
$780$	−1.86776e6	+	1.58573e6i	−0.109922	+	0.0933240i
$781$	−2.38529e6	+	7.22449e6i	−0.139931	+	0.423818i
$782$		−	1.19885e7i		−	0.701049i
$783$	−358942.	+	4.09779e6i	−0.0209228	+	0.238861i
$784$	2.14466e7	−	6.60059e7i	1.24615	−	3.83524i
$785$	2.17418e7	−	7.06435e6i	1.25928	−	0.409164i
$786$	3.83947e6	−	1.57877e7i	0.221674	−	0.911510i
$787$	−6.56599e6	−	9.03731e6i	−0.377888	−	0.520119i	0.577135	−	0.816649i	$-0.304171\pi$
$787$	−6.56599e6	−	9.03731e6i	−0.377888	−	0.520119i	−0.955024	+	0.296530i	$0.904171\pi$
$788$	−994518.	−	3.06081e6i	−0.0570554	−	0.175599i
$789$	−4.47652e6	−	1.08979e7i	−0.256005	−	0.623232i
$790$	−4.08862e7	−	2.97056e7i	−2.33082	−	1.69344i
$791$	279715.			0.0158955
$792$	−2.88243e7	+	5.51152e7i	−1.63285	+	3.12218i
$793$	−506534.			−0.0286039
$794$	2.00914e7	+	1.45972e7i	1.13099	+	0.821712i
$795$	5.61175e6	+	1.36616e7i	0.314905	+	0.766624i
$796$	−1.61825e7	−	4.98046e7i	−0.905238	−	2.78604i
$797$	−1.49060e7	−	2.05163e7i	−0.831218	−	1.14407i	−0.987695	−	0.156392i	$-0.950014\pi$
$797$	−1.49060e7	−	2.05163e7i	−0.831218	−	1.14407i	0.156477	−	0.987682i	$-0.449986\pi$
$798$	720132.	−	2.96114e6i	0.0400318	−	0.164608i
$799$	5.01425e6	−	1.62923e6i	0.277868	−	0.0902848i
$800$	−1.40306e6	+	4.31818e6i	−0.0775090	+	0.238548i
$801$	−1.50150e7	−	1.51929e7i	−0.826885	−	0.836680i
$802$		−	742223.i		−	0.0407473i
$803$	3.07306e6	+	2.25503e6i	0.168183	+	0.123414i
$804$	−1.31310e7	+	1.11483e7i	−0.716404	+	0.608229i
$805$	481457.	−	662668.i	0.0261859	−	0.0360418i
$806$	2.60120e6	+	845180.i	0.141038	+	0.0458260i
$807$	−1.53473e7	+	2.48798e7i	−0.829561	+	1.34482i
$808$	−7.56100e7	+	5.49338e7i	−4.07428	+	2.96014i
$809$	8.70475e6	−	6.32437e6i	0.467611	−	0.339739i	−0.328898	−	0.944365i	$-0.606677\pi$
$809$	8.70475e6	−	6.32437e6i	0.467611	−	0.339739i	0.796510	+	0.604626i	$0.206677\pi$
$810$	−3.74476e7	−	440968.i	−2.00545	−	0.0236153i
$811$	3.16273e7	+	1.02763e7i	1.68853	+	0.548637i	0.986536	−	0.163543i	$-0.0522923\pi$
$811$	3.16273e7	+	1.02763e7i	1.68853	+	0.548637i	0.701996	+	0.712181i	$0.252292\pi$
$812$	690656.	−	950607.i	0.0367597	−	0.0505954i
$813$	−1.37944e7	−	1.62478e7i	−0.731941	−	0.862119i
$814$	−1.26126e7	+	4.03212e6i	−0.667183	+	0.213291i
$815$			1.01141e7i			0.533374i
$816$	5.94654e7	−	4.50393e6i	3.12636	−	0.236792i
$817$	−8.49479e6	+	2.61443e7i	−0.445243	+	1.37032i
$818$	6.72102e7	−	2.18379e7i	3.51198	−	1.14111i
$819$	40023.1	+	79706.4i	0.00208498	+	0.00415225i
$820$	3.38419e7	+	4.65794e7i	1.75760	+	2.41913i
$821$	−2.55389e6	−	7.86005e6i	−0.132234	−	0.406975i	0.862915	−	0.505348i	$-0.168636\pi$
$821$	−2.55389e6	−	7.86005e6i	−0.132234	−	0.406975i	−0.995150	+	0.0983735i	$0.968636\pi$
$822$	4.79100e7	−	1.96799e7i	2.47313	−	1.01588i
$823$	−1.83274e7	−	1.33156e7i	−0.943193	−	0.685270i	0.00599424	−	0.999982i	$-0.498092\pi$
$823$	−1.83274e7	−	1.33156e7i	−0.943193	−	0.685270i	−0.949187	+	0.314712i	$0.898092\pi$
$824$	−6.68310e6			−0.342894
$825$	715213.	+	850552.i	0.0365848	+	0.0435077i
$826$	1.12061e6			0.0571482
$827$	1.57465e7	+	1.14405e7i	0.800606	+	0.581674i	0.911092	−	0.412203i	$-0.135241\pi$
$827$	1.57465e7	+	1.14405e7i	0.800606	+	0.581674i	−0.110486	+	0.993878i	$0.535241\pi$
$828$	1.18518e7	−	2.29257e7i	0.600769	−	1.16211i
$829$	−1.86965e6	−	5.75418e6i	−0.0944872	−	0.290802i	0.892633	−	0.450785i	$-0.148856\pi$
$829$	−1.86965e6	−	5.75418e6i	−0.0944872	−	0.290802i	−0.987120	+	0.159983i	$0.948856\pi$
$830$	5.65832e6	+	7.78800e6i	0.285097	+	0.392402i
$831$	−7.40800e6	−	1.80158e6i	−0.372133	−	0.0905007i
$832$	4.30989e6	−	1.40037e6i	0.215853	−	0.0701349i
$833$	−4.72881e6	+	1.45538e7i	−0.236124	+	0.726714i
$834$	278555.	+	3.67776e6i	0.0138674	+	0.183092i
$835$			1.01927e7i			0.505912i
$836$	−4.30020e7	+	3.09325e7i	−2.12801	+	1.53073i
$837$	1.58715e7	+	2.64209e7i	0.783076	+	1.30357i
$838$	−3.26613e7	+	4.49544e7i	−1.60666	+	2.21137i
$839$	−2.68295e7	−	8.71742e6i	−1.31585	−	0.427546i	−0.434784	−	0.900535i	$-0.643175\pi$
$839$	−2.68295e7	−	8.71742e6i	−1.31585	−	0.427546i	−0.881069	+	0.472988i	$0.843175\pi$
$840$	5.86003e6	+	3.61480e6i	0.286551	+	0.176761i
$841$	1.56398e7	−	1.13630e7i	0.762505	−	0.553992i
$842$	−4.86463e7	+	3.53436e7i	−2.36466	+	1.71803i
$843$	6.84050e6	+	4.21961e6i	0.331527	+	0.204505i
$844$	−6.70705e7	−	2.17925e7i	−3.24097	−	1.05306i
$845$	−1.25106e7	+	1.72194e7i	−0.602751	+	0.829615i
$846$	1.51906e7	+	2.49772e6i	0.729709	+	0.119983i
$847$	18392.1	−	1.94064e6i	0.000880892	−	0.0929473i
$848$		−	6.86719e7i		−	3.27936i
$849$	−1.62130e6	−	2.14060e7i	−0.0771958	−	1.01922i
$850$	556396.	−	1.71241e6i	0.0264142	−	0.0812945i
$851$	3.36323e6	−	1.09278e6i	0.159196	−	0.0517260i
$852$	2.57846e7	+	6.27068e6i	1.21692	+	0.295948i
$853$	−1.04187e7	−	1.43401e7i	−0.490277	−	0.674809i	0.490162	−	0.871632i	$-0.336938\pi$
$853$	−1.04187e7	−	1.43401e7i	−0.490277	−	0.674809i	−0.980439	+	0.196823i	$0.936938\pi$
$854$	683427.	+	2.10337e6i	0.0320662	+	0.0986897i
$855$	−1.82358e7	−	9.42727e6i	−0.853121	−	0.441032i
$856$	5.91108e7	+	4.29465e7i	2.75729	+	2.00329i
$857$	2.52692e7			1.17528			0.587638	−	0.809124i	$-0.300058\pi$
$857$	2.52692e7			1.17528			0.587638	+	0.809124i	$0.300058\pi$
$858$	506593.	−	2.04091e6i	0.0234931	−	0.0946468i
$859$	1.52627e7			0.705745			0.352873	−	0.935671i	$-0.385205\pi$
$859$	1.52627e7			0.705745			0.352873	+	0.935671i	$0.385205\pi$
$860$	−7.80692e7	−	5.67206e7i	−3.59943	−	2.61514i
$861$	1.93870e6	−	796358.i	0.0891257	−	0.0366101i
$862$	1.09412e7	+	3.36736e7i	0.501531	+	1.54355i
$863$	−1.07723e6	−	1.48269e6i	−0.0492361	−	0.0677676i	0.783689	−	0.621153i	$-0.213336\pi$
$863$	−1.07723e6	−	1.48269e6i	−0.0492361	−	0.0677676i	−0.832925	+	0.553386i	$0.813336\pi$
$864$	8.91185e7	+	3.78396e7i	4.06147	+	1.72450i
$865$	7.48873e6	−	2.43324e6i	0.340305	−	0.110572i
$866$	−1.20146e7	+	3.69772e7i	−0.544396	+	1.67548i
$867$	8.95853e6	−	678522.i	0.404752	−	0.0306561i
$868$		−	8.80416e6i		−	0.396633i
$869$	3.19782e7	+	151531.i	1.43650	+	0.00680692i
$870$	−6.94845e6	−	8.18425e6i	−0.311236	−	0.366590i
$871$	220318.	−	303241.i	0.00984020	−	0.0135439i
$872$	−6.14276e7	−	1.99590e7i	−2.73572	−	0.888891i
$873$	−7.26600e6	+	1.10701e6i	−0.322671	+	0.0491604i
$874$	1.55237e7	−	1.12786e7i	0.687411	−	0.499433i
$875$	−1.65129e6	+	1.19973e6i	−0.0729126	+	0.0529741i
$876$	6.97981e6	−	1.13151e7i	0.307315	−	0.498194i
$877$	6.31095e6	+	2.05055e6i	0.277074	+	0.0900268i	0.444258	−	0.895899i	$-0.353467\pi$
$877$	6.31095e6	+	2.05055e6i	0.277074	+	0.0900268i	−0.167184	+	0.985926i	$0.553467\pi$
$878$	−1.32698e7	+	1.82643e7i	−0.580934	+	0.799587i
$879$	8.54652e6	−	7.25602e6i	0.373093	−	0.316757i
$880$	−2.92526e7	−	9.15034e7i	−1.27338	−	3.98318i
$881$			3.87751e7i			1.68311i	0.540171	+	0.841555i	$0.318360\pi$
$881$			3.87751e7i			1.68311i	−0.540171	+	0.841555i	$0.681640\pi$
$882$	−3.17809e7	+	3.14088e7i	−1.37561	+	1.35950i
$883$	4.82541e6	−	1.48511e7i	0.208273	−	0.640997i	−0.791290	−	0.611440i	$-0.790590\pi$
$883$	4.82541e6	−	1.48511e7i	0.208273	−	0.640997i	0.999563	−	0.0295569i	$-0.00940961\pi$
$884$	−2.38895e6	+	776218.i	−0.102820	+	0.0334082i
$885$	1.78382e6	−	7.33495e6i	0.0765583	−	0.314803i
$886$	−5.29139e6	−	7.28298e6i	−0.226457	−	0.311691i
$887$	−1.06897e7	−	3.28995e7i	−0.456202	−	1.40404i	−0.869719	−	0.493548i	$-0.835700\pi$
$887$	−1.06897e7	−	3.28995e7i	−0.456202	−	1.40404i	0.413517	−	0.910496i	$-0.364300\pi$
$888$	1.12946e7	+	2.74963e7i	0.480662	+	1.17015i
$889$	2.63536e6	+	1.91470e6i	0.111837	+	0.0812544i
$890$	5.57505e7			2.35925
$891$	1.93987e7	−	1.36103e7i	0.818613	−	0.574346i
$892$	−9.46420e7			−3.98265
$893$	6.82699e6	+	4.96010e6i	0.286484	+	0.208143i
$894$	−1.35450e7	−	3.29746e7i	−0.566805	−	1.37986i
$895$	1.33238e7	+	4.10064e7i	0.555995	+	1.71118i
$896$	−5.83676e6	−	8.03362e6i	−0.242886	−	0.334304i
$897$	−132708.	+	545687.i	−0.00550701	+	0.0226445i
$898$	6.10289e7	−	1.98295e7i	2.52549	−	0.820580i
$899$	−2.73040e6	+	8.40332e6i	−0.112675	+	0.346778i
$900$	2.75688e6	−	2.72461e6i	0.113452	−	0.112124i
$901$			1.51416e7i			0.621384i
$902$	−4.69233e7	−	1.54925e7i	−1.92031	−	0.634023i
$903$	−2.67787e6	+	2.27351e6i	−0.109287	+	0.0927851i
$904$	−8.70198e6	+	1.19772e7i	−0.354158	+	0.487457i
$905$	3.67997e7	+	1.19570e7i	1.49356	+	0.485288i
$906$	3.92836e7	−	6.36835e7i	1.58998	−	2.57755i
$907$	2.84816e7	−	2.06931e7i	1.14960	−	0.835231i	0.161169	−	0.986927i	$-0.448473\pi$
$907$	2.84816e7	−	2.06931e7i	1.14960	−	0.835231i	0.988427	+	0.151696i	$0.0484735\pi$
$908$	7.89310e7	−	5.73467e7i	3.17712	−	2.30831i
$909$	3.52014e7	−	5.36310e6i	1.41303	−	0.215281i
$910$	−221391.	−	71934.4i	−0.00886252	−	0.00287961i
$911$	1.33017e7	−	1.83082e7i	0.531020	−	0.730887i	−0.456265	−	0.889844i	$-0.650813\pi$
$911$	1.33017e7	−	1.83082e7i	0.531020	−	0.730887i	0.987286	+	0.158957i	$0.0508131\pi$
$912$	6.17762e7	+	7.27633e7i	2.45943	+	2.89685i
$913$	−5.78417e6	−	1.90974e6i	−0.229649	−	0.0758223i
$914$			4.45204e7i			1.76276i
$915$	1.48556e7	−	1.12517e6i	0.586593	−	0.0444287i
$916$	−1.37732e7	+	4.23895e7i	−0.542370	+	1.66924i
$917$	1.08240e6	−	351694.i	0.0425075	−	0.0138115i
$918$	−3.53407e7	−	1.50056e7i	−1.38410	−	0.587688i
$919$	−2.10214e7	−	2.89334e7i	−0.821055	−	1.13008i	−0.989523	−	0.144378i	$-0.953882\pi$
$919$	−2.10214e7	−	2.89334e7i	−0.821055	−	1.13008i	0.168468	−	0.985707i	$-0.446118\pi$
$920$	1.33969e7	+	4.12314e7i	0.521837	+	1.60605i
$921$	−3.63149e7	+	1.49170e7i	−1.41070	+	0.579473i
$922$	−2.87289e6	−	2.08727e6i	−0.111299	−	0.0808634i
$923$	−577437.			−0.0223100
$924$	−6.75207e6	+	479237.i	−0.260170	+	0.0184659i
$925$	531113.			0.0204095
$926$	−2.35770e7	−	1.71297e7i	−0.903567	−	0.656480i
$927$	2.26187e6	+	1.16930e6i	0.0864506	+	0.0446919i
$928$	8.57698e6	+	2.63972e7i	0.326937	+	1.00621i
$929$	−1.36003e7	−	1.87192e7i	−0.517022	−	0.711619i	0.468062	−	0.883696i	$-0.344952\pi$
$929$	−1.36003e7	−	1.87192e7i	−0.517022	−	0.711619i	−0.985084	+	0.172076i	$0.944952\pi$
$930$	−7.81649e7	−	1.90093e7i	−2.96350	−	0.720706i
$931$	−2.32942e7	+	7.56875e6i	−0.880793	+	0.286187i
$932$	3.03233e7	−	9.33255e7i	1.14350	−	3.51933i
$933$	−563662.	−	7.44203e6i	−0.0211990	−	0.279890i
$934$		−	8.27345e7i		−	3.10327i
$935$	6.44997e6	+	2.01758e7i	0.241284	+	0.754746i
$936$	−4.65811e6	−	765912.i	−0.173788	−	0.0285752i
$937$	−2.03696e7	+	2.80363e7i	−0.757937	+	1.04321i	0.239445	+	0.970910i	$0.423034\pi$
$937$	−2.03696e7	+	2.80363e7i	−0.757937	+	1.04321i	−0.997383	+	0.0723016i	$0.976966\pi$
$938$	−1.55646e6	−	505725.i	−0.0577605	−	0.0187675i
$939$	1.03804e7	+	6.40322e6i	0.384193	+	0.236992i
$940$	−2.39652e7	+	1.74117e7i	−0.884630	+	0.642721i
$941$	4.36389e6	−	3.17055e6i	0.160657	−	0.116724i	−0.504552	−	0.863381i	$-0.668342\pi$
$941$	4.36389e6	−	3.17055e6i	0.160657	−	0.116724i	0.665209	+	0.746657i	$0.268342\pi$
$942$	5.82442e7	+	3.59284e7i	2.13858	+	1.31920i
$943$	1.25509e7	+	4.07805e6i	0.459618	+	0.149339i
$944$	−2.06307e7	+	2.83957e7i	−0.753502	+	1.03711i
$945$	−1.35084e6	−	2.24872e6i	−0.0492069	−	0.0819134i
$946$	8.28205e7	+	392449.i	3.00891	+	0.0142579i
$947$			5.31448e6i			0.192569i	0.995354	+	0.0962843i	$0.0306958\pi$
$947$			5.31448e6i			0.192569i	−0.995354	+	0.0962843i	$0.969304\pi$
$948$	−8.42379e6	−	1.11219e8i	−0.304430	−	4.01938i
$949$	−89398.0	+	275139.i	−0.00322227	+	0.00991714i
$950$	2.74082e6	−	890546.i	0.0985307	−	0.0320146i
$951$	−2.14825e7	−	5.22443e6i	−0.770255	−	0.187322i
$952$	4.14909e6	+	5.71074e6i	0.148375	+	0.204221i
$953$	3.85665e6	+	1.18696e7i	0.137556	+	0.423352i	0.995979	−	0.0895897i	$-0.0285556\pi$
$953$	3.85665e6	+	1.18696e7i	0.137556	+	0.423352i	−0.858423	+	0.512942i	$0.828556\pi$
$954$	−2.03034e7	+	3.92744e7i	−0.722269	+	1.39714i
$955$	3.34579e7	+	2.43086e7i	1.18711	+	0.862485i
$956$	−3.03481e7			−1.07396
$957$	6.59328e6	+	1.63658e6i	0.232714	+	0.0577640i
$958$	1.97411e6			0.0694957
$959$	2.93514e6	+	2.13250e6i	0.103058	+	0.0748761i
$960$	−1.23289e8	+	5.06434e7i	−4.31765	+	1.77356i
$961$	1.16115e7	+	3.57365e7i	0.405583	+	1.24826i
$962$	−590724.	−	813062.i	−0.0205801	−	0.0283261i
$963$	−1.24917e7	−	2.48774e7i	−0.434067	−	0.864448i
$964$	2.38267e7	−	7.74176e6i	0.825792	−	0.268316i
$965$	8.16013e6	−	2.51143e7i	0.282084	−	0.868166i
$966$	2.44500e6	−	185186.i	0.0843018	−	0.00638505i
$967$			3.76609e6i			0.129516i	0.997901	+	0.0647582i	$0.0206276\pi$
$967$			3.76609e6i			0.129516i	−0.997901	+	0.0647582i	$0.979372\pi$
$968$	8.25250e7	+	6.11612e7i	2.83072	+	2.09791i
$969$	−1.36212e7	−	1.60437e7i	−0.466020	−	0.548904i
$970$	1.12754e7	−	1.55193e7i	0.384771	−	0.529592i
$971$	2.89706e6	+	941311.i	0.0986073	+	0.0320394i	0.357905	−	0.933758i	$-0.383491\pi$
$971$	2.89706e6	+	941311.i	0.0986073	+	0.0320394i	−0.259298	+	0.965797i	$0.583491\pi$
$972$	−5.27478e7	−	6.36329e7i	−1.79077	−	2.16031i
$973$	−209012.	+	151856.i	−0.00707765	+	0.00514221i
$974$	−8.18859e7	+	5.94936e7i	−2.76574	+	2.00943i
$975$	−44281.5	+	71785.6i	−0.00149180	+	0.00241839i
$976$	−6.58808e7	−	2.14060e7i	−2.21378	−	0.719301i
$977$	−1.39379e7	+	1.91838e7i	−0.467154	+	0.642982i	−0.975973	−	0.217892i	$-0.930082\pi$
$977$	−1.39379e7	+	1.91838e7i	−0.467154	+	0.642982i	0.508819	+	0.860873i	$0.330082\pi$
$978$	−2.30804e7	+	1.95953e7i	−0.771607	+	0.655096i
$979$	−2.86375e7	+	2.05997e7i	−0.954944	+	0.686917i
$980$		−	8.59793e7i		−	2.85975i
$981$	1.72978e7	+	1.75027e7i	0.573877	+	0.580675i
$982$	−9.49410e6	+	2.92198e7i	−0.314178	+	0.966939i
$983$	611169.	−	198581.i	0.0201733	−	0.00655471i	−0.298913	−	0.954280i	$-0.596624\pi$
$983$	611169.	−	198581.i	0.0201733	−	0.00655471i	0.319086	+	0.947726i	$0.396624\pi$
$984$	−2.62137e7	+	1.07789e8i	−0.863058	+	3.54884i
$985$	−1.21070e6	−	1.66639e6i	−0.0397601	−	0.0547251i
$986$	−3.40127e6	−	1.04680e7i	−0.111416	−	0.342904i
$987$	409729.	+	997467.i	0.0133876	+	0.0325916i
$988$	−3.25260e6	−	2.36315e6i	−0.106008	−	0.0770193i
$989$	−2.21185e7			−0.719061
$990$	−1.03238e7	+	6.09808e7i	−0.334774	+	1.97745i
$991$	1.66360e7			0.538102			0.269051	−	0.963126i	$-0.413290\pi$
$991$	1.66360e7			0.538102			0.269051	+	0.963126i	$0.413290\pi$
$992$	1.68250e8	+	1.22241e8i	5.42844	+	3.94399i
$993$	1.17507e7	+	2.86067e7i	0.378174	+	0.920650i
$994$	779091.	+	2.39780e6i	0.0250105	+	0.0769744i
$995$	−1.97002e7	−	2.71150e7i	−0.630831	−	0.868264i
$996$	−5.02051e6	+	2.06440e7i	−0.160361	+	0.659396i
$997$	−773129.	+	251205.i	−0.0246328	+	0.00800369i	−0.321307	−	0.946975i	$-0.604122\pi$
$997$	−773129.	+	251205.i	−0.0246328	+	0.00800369i	0.296675	+	0.954979i	$0.404122\pi$
$998$	3.09340e7	−	9.52051e7i	0.983128	−	3.02576i
$999$	988254.	−	1.12822e7i	0.0313296	−	0.357668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.f.a.29.1	yes	72
3.2	odd	2	inner	33.6.f.a.29.18	yes	72
11.8	odd	10	inner	33.6.f.a.8.18	yes	72
33.8	even	10	inner	33.6.f.a.8.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.f.a.8.1	✓	72	33.8	even	10	inner
33.6.f.a.8.18	yes	72	11.8	odd	10	inner
33.6.f.a.29.1	yes	72	1.1	even	1	trivial
33.6.f.a.29.18	yes	72	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.92830 - 6.48679i) q^{2} +(-5.92302 - 14.4194i) q^{3} +(27.7475 + 85.3981i) q^{4} +(33.7792 + 46.4931i) q^{5} +(-40.6528 + 167.162i) q^{6} +(-11.4606 + 3.72378i) q^{7} +(197.091 - 606.584i) q^{8} +(-172.836 + 170.812i) q^{9} +O(q^{10})\)	\(q+(-8.92830 - 6.48679i) q^{2} +(-5.92302 - 14.4194i) q^{3} +(27.7475 + 85.3981i) q^{4} +(33.7792 + 46.4931i) q^{5} +(-40.6528 + 167.162i) q^{6} +(-11.4606 + 3.72378i) q^{7} +(197.091 - 606.584i) q^{8} +(-172.836 + 170.812i) q^{9} -634.222i q^{10} +(234.344 + 325.782i) q^{11} +(1067.04 - 905.916i) q^{12} +(-17.9032 + 24.6416i) q^{13} +(126.479 + 41.0956i) q^{14} +(470.325 - 762.454i) q^{15} +(-3369.87 + 2448.35i) q^{16} +(743.029 - 539.842i) q^{17} +(2651.15 - 403.915i) q^{18} +(1398.06 + 454.258i) q^{19} +(-3033.13 + 4174.75i) q^{20} +(121.576 + 143.199i) q^{21} +(20.9862 - 4428.82i) q^{22} +1182.79i q^{23} +(-9913.93 + 750.885i) q^{24} +(-54.8941 + 168.947i) q^{25} +(319.690 - 103.873i) q^{26} +(3486.71 + 1480.45i) q^{27} +(-636.007 - 875.389i) q^{28} +(335.569 + 1032.78i) q^{29} +(-9145.08 + 3756.51i) q^{30} +(6582.67 + 4782.59i) q^{31} +25559.5 q^{32} +(3309.54 - 5308.70i) q^{33} -10135.8 q^{34} +(-560.260 - 407.053i) q^{35} +(-19382.8 - 10020.2i) q^{36} +(-923.903 - 2843.48i) q^{37} +(-9535.64 - 13124.7i) q^{38} +(461.357 + 112.199i) q^{39} +(34859.6 - 11326.6i) q^{40} +(3447.83 - 10611.3i) q^{41} +(-156.567 - 2067.16i) q^{42} +18700.4i q^{43} +(-21318.7 + 29052.2i) q^{44} +(-13779.8 - 2265.76i) q^{45} +(7672.48 - 10560.3i) q^{46} +(5459.56 + 1773.92i) q^{47} +(55263.4 + 34089.7i) q^{48} +(-13479.7 + 9793.55i) q^{49} +(1586.03 - 1152.32i) q^{50} +(-12185.2 - 7516.50i) q^{51} +(-2601.11 - 845.153i) q^{52} +(-9690.42 + 13337.7i) q^{53} +(-21527.0 - 35835.5i) q^{54} +(-7230.66 + 21900.0i) q^{55} +7685.76i q^{56} +(-1730.65 - 22849.7i) q^{57} +(3703.34 - 11397.7i) q^{58} +(8013.95 - 2603.89i) q^{59} +(78162.4 + 19008.7i) q^{60} +(9774.99 + 13454.1i) q^{61} +(-27748.4 - 85400.8i) q^{62} +(1344.73 - 2601.22i) q^{63} +(-120367. - 87451.6i) q^{64} -1750.42 q^{65} +(-63985.0 + 25929.4i) q^{66} -12306.1 q^{67} +(66718.7 + 48474.0i) q^{68} +(17055.0 - 7005.67i) q^{69} +(2361.70 + 7268.58i) q^{70} +(11143.3 + 15337.4i) q^{71} +(69547.7 + 138505. i) q^{72} +(9033.18 - 2935.06i) q^{73} +(-10196.2 + 31380.6i) q^{74} +(2761.24 - 209.137i) q^{75} +131996. i q^{76} +(-3898.87 - 2861.02i) q^{77} +(-3391.32 - 3994.47i) q^{78} +(46837.8 - 64466.6i) q^{79} +(-227663. - 73972.1i) q^{80} +(695.288 - 59044.9i) q^{81} +(-99616.7 + 72375.7i) q^{82} +(-12279.6 + 8921.66i) q^{83} +(-8855.46 + 14355.8i) q^{84} +(50197.8 + 16310.3i) q^{85} +(121305. - 166962. i) q^{86} +(12904.4 - 10955.9i) q^{87} +(243801. - 77940.6i) q^{88} +87903.7i q^{89} +(108333. + 109616. i) q^{90} +(113.421 - 349.075i) q^{91} +(-101008. + 32819.4i) q^{92} +(29972.6 - 123245. i) q^{93} +(-37237.5 - 51253.1i) q^{94} +(26105.6 + 80344.7i) q^{95} +(-151389. - 368551. i) q^{96} +(24469.8 + 17778.3i) q^{97} +183879. q^{98} +(-96150.6 - 16277.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9}+O(q^{10}) \) 72 * q + 18 * q^3 - 262 * q^4 + 15 * q^6 - 10 * q^7 + 292 * q^9	\( 72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9} + 1854 q^{12} - 10 q^{13} - 762 q^{15} - 10122 q^{16} + 4815 q^{18} + 4460 q^{19} + 4628 q^{22} - 805 q^{24} + 13708 q^{25} + 6108 q^{27} - 28130 q^{28} - 15470 q^{30} + 4340 q^{31} - 508 q^{33} + 18732 q^{34} - 56461 q^{36} + 978 q^{37} + 23360 q^{39} + 69750 q^{40} + 60788 q^{42} - 31356 q^{45} - 52090 q^{46} + 4238 q^{48} - 58448 q^{49} - 178950 q^{51} - 14190 q^{52} + 86600 q^{55} + 266190 q^{57} + 137102 q^{58} + 284090 q^{60} - 77890 q^{61} - 120330 q^{63} - 379114 q^{64} - 323304 q^{66} + 42668 q^{67} - 271816 q^{69} + 87176 q^{70} + 343960 q^{72} + 116440 q^{73} + 326202 q^{75} + 155512 q^{78} - 350590 q^{79} - 208088 q^{81} - 606424 q^{82} - 220680 q^{84} + 665610 q^{85} + 1152974 q^{88} + 293440 q^{90} + 621014 q^{91} + 478456 q^{93} - 521270 q^{94} - 1246430 q^{96} - 1030446 q^{97} - 590000 q^{99}+O(q^{100}) \) 72 * q + 18 * q^3 - 262 * q^4 + 15 * q^6 - 10 * q^7 + 292 * q^9 + 1854 * q^12 - 10 * q^13 - 762 * q^15 - 10122 * q^16 + 4815 * q^18 + 4460 * q^19 + 4628 * q^22 - 805 * q^24 + 13708 * q^25 + 6108 * q^27 - 28130 * q^28 - 15470 * q^30 + 4340 * q^31 - 508 * q^33 + 18732 * q^34 - 56461 * q^36 + 978 * q^37 + 23360 * q^39 + 69750 * q^40 + 60788 * q^42 - 31356 * q^45 - 52090 * q^46 + 4238 * q^48 - 58448 * q^49 - 178950 * q^51 - 14190 * q^52 + 86600 * q^55 + 266190 * q^57 + 137102 * q^58 + 284090 * q^60 - 77890 * q^61 - 120330 * q^63 - 379114 * q^64 - 323304 * q^66 + 42668 * q^67 - 271816 * q^69 + 87176 * q^70 + 343960 * q^72 + 116440 * q^73 + 326202 * q^75 + 155512 * q^78 - 350590 * q^79 - 208088 * q^81 - 606424 * q^82 - 220680 * q^84 + 665610 * q^85 + 1152974 * q^88 + 293440 * q^90 + 621014 * q^91 + 478456 * q^93 - 521270 * q^94 - 1246430 * q^96 - 1030446 * q^97 - 590000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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