LMFDB - Embedded newform 150.6.g.d.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, 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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	150.31
Dual form			150.6.g.d.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(25.5464 + 49.7230i) q^{5} +(29.1246 + 21.1603i) q^{6} +186.658 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})$	\(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(25.5464 + 49.7230i) q^{5} +(29.1246 + 21.1603i) q^{6} +186.658 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(-157.581 + 158.645i) q^{10} +(150.565 + 463.393i) q^{11} +(-44.4984 + 136.952i) q^{12} +(307.191 - 945.437i) q^{13} +(230.722 + 710.090i) q^{14} +(449.045 + 226.899i) q^{15} +(79.1084 - 243.470i) q^{16} +(-942.241 - 684.578i) q^{17} +324.000 q^{18} +(917.282 + 666.444i) q^{19} +(-798.303 - 403.376i) q^{20} +(1359.09 - 987.434i) q^{21} +(-1576.74 + 1145.57i) q^{22} +(512.783 + 1578.18i) q^{23} -576.000 q^{24} +(-1819.76 + 2540.49i) q^{25} +3976.37 q^{26} +(-225.273 - 693.320i) q^{27} +(-2416.15 + 1755.44i) q^{28} +(-3088.44 + 2243.89i) q^{29} +(-308.124 + 1988.73i) q^{30} +(8360.09 + 6073.96i) q^{31} +1024.00 q^{32} +(3547.67 + 2577.53i) q^{33} +(1439.62 - 4430.68i) q^{34} +(4768.44 + 9281.21i) q^{35} +(400.486 + 1232.57i) q^{36} +(1205.83 - 3711.16i) q^{37} +(-1401.48 + 4313.32i) q^{38} +(-2764.72 - 8508.94i) q^{39} +(547.776 - 3535.53i) q^{40} +(1701.43 - 5236.46i) q^{41} +(5436.35 + 3949.74i) q^{42} +12873.6 q^{43} +(-6306.97 - 4582.28i) q^{44} +(4469.88 - 723.395i) q^{45} +(-5369.93 + 3901.49i) q^{46} +(-13926.4 + 10118.1i) q^{47} +(-711.975 - 2191.23i) q^{48} +18034.3 q^{49} +(-11913.9 - 3782.57i) q^{50} -10482.1 q^{51} +(4915.06 + 15127.0i) q^{52} +(-17765.0 + 12907.1i) q^{53} +(2359.09 - 1713.98i) q^{54} +(-19194.9 + 19324.6i) q^{55} +(-9664.62 - 7021.75i) q^{56} +10204.4 q^{57} +(-12353.8 - 8975.55i) q^{58} +(-5775.98 + 17776.6i) q^{59} +(-7946.45 + 1286.03i) q^{60} +(10813.1 + 33279.3i) q^{61} +(-12773.1 + 39311.5i) q^{62} +(4672.12 - 14379.3i) q^{63} +(1265.73 + 3895.53i) q^{64} +(54857.7 - 8878.03i) q^{65} +(-5420.35 + 16682.1i) q^{66} +(-44877.4 - 32605.3i) q^{67} +18634.8 q^{68} +(12082.4 + 8778.34i) q^{69} +(-29413.7 + 29612.4i) q^{70} +(43218.4 - 31400.0i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(-18849.2 - 58011.9i) q^{73} +15608.6 q^{74} +(189.384 + 28124.4i) q^{75} -18141.2 q^{76} +(28104.3 + 86496.0i) q^{77} +(28952.5 - 21035.2i) q^{78} +(-34865.5 + 25331.3i) q^{79} +(14127.0 - 2286.28i) q^{80} +(-5307.96 - 3856.46i) q^{81} +22023.8 q^{82} +(-83875.9 - 60939.4i) q^{83} +(-8306.00 + 25563.2i) q^{84} +(9968.45 - 64339.6i) q^{85} +(15912.6 + 48974.0i) q^{86} +(-10617.1 + 32676.2i) q^{87} +(9636.19 - 29657.1i) q^{88} +(-20109.1 - 61889.4i) q^{89} +(8277.03 + 16110.3i) q^{90} +(57339.7 - 176474. i) q^{91} +(-21479.7 - 15605.9i) q^{92} +93002.7 q^{93} +(-55705.6 - 40472.5i) q^{94} +(-9704.39 + 62635.3i) q^{95} +(7455.90 - 5417.03i) q^{96} +(14936.3 - 10851.8i) q^{97} +(22291.6 + 68606.4i) q^{98} +39466.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) $ 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9 + 44 * q^10 - 135 * q^11 + 1008 * q^12 + 616 * q^13 - 48 * q^14 + 531 * q^15 - 1792 * q^16 - 3372 * q^17 + 9072 * q^18 + 488 * q^19 - 944 * q^20 - 387 * q^21 - 1920 * q^22 - 620 * q^23 - 16128 * q^24 + 6659 * q^25 - 1616 * q^26 + 5103 * q^27 + 688 * q^28 + 5682 * q^29 + 2844 * q^30 + 3339 * q^31 + 28672 * q^32 + 4320 * q^33 + 14032 * q^34 - 23984 * q^35 - 9072 * q^36 + 4506 * q^37 - 1528 * q^38 - 5544 * q^39 - 5056 * q^40 + 44962 * q^41 - 1548 * q^42 + 38028 * q^43 - 7680 * q^44 + 9396 * q^45 + 7480 * q^46 - 58300 * q^47 + 16128 * q^48 + 114402 * q^49 + 7476 * q^50 + 2448 * q^51 + 9856 * q^52 - 138 * q^53 + 20412 * q^54 + 96850 * q^55 + 2752 * q^56 + 1908 * q^57 + 22728 * q^58 + 40245 * q^59 - 16704 * q^60 + 79380 * q^61 - 54504 * q^62 - 972 * q^63 - 28672 * q^64 + 3532 * q^65 + 4860 * q^66 - 34352 * q^67 - 4352 * q^68 - 16830 * q^69 - 69476 * q^70 + 115860 * q^71 - 36288 * q^72 - 121214 * q^73 - 37856 * q^74 + 21969 * q^75 - 3392 * q^76 + 195005 * q^77 + 14904 * q^78 + 36224 * q^79 + 29696 * q^80 - 45927 * q^81 + 34608 * q^82 + 85051 * q^83 + 1728 * q^84 + 137496 * q^85 - 18568 * q^86 + 127062 * q^87 - 8640 * q^88 - 53826 * q^89 + 3564 * q^90 - 408104 * q^91 + 29920 * q^92 - 185166 * q^93 - 233200 * q^94 - 482004 * q^95 + 64512 * q^96 - 244169 * q^97 - 395952 * q^98 + 99630 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$2$	1.23607	+	3.80423i	0.218508	+	0.672499i
$3$	7.28115	−	5.29007i	0.467086	−	0.339358i
$3$	7.28115	−	5.29007i	0.467086	−	0.339358i
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	25.5464	+	49.7230i	0.456988	+	0.889473i
$5$	25.5464	+	49.7230i	0.456988	+	0.889473i
$6$	29.1246	+	21.1603i	0.330280	+	0.239962i
$7$	186.658			1.43980			0.719899	−	0.694078i	$-0.244188\pi$
$7$	186.658			1.43980			0.719899	+	0.694078i	$0.244188\pi$
$8$	−51.7771	−	37.6183i	−0.286031	−	0.207813i
$9$	25.0304	−	77.0356i	0.103006	−	0.317019i
$10$	−157.581	+	158.645i	−0.498314	+	0.501681i
$11$	150.565	+	463.393i	0.375183	+	1.15470i	0.943355	+	0.331785i	$0.107651\pi$
$11$	150.565	+	463.393i	0.375183	+	1.15470i	−0.568172	+	0.822910i	$0.692349\pi$
$12$	−44.4984	+	136.952i	−0.0892055	+	0.274546i
$13$	307.191	−	945.437i	0.504139	−	1.55158i	−0.298074	−	0.954543i	$-0.596344\pi$
$13$	307.191	−	945.437i	0.504139	−	1.55158i	0.802213	−	0.597038i	$-0.203656\pi$
$14$	230.722	+	710.090i	0.314608	+	0.968263i
$15$	449.045	+	226.899i	0.515302	+	0.260378i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−942.241	−	684.578i	−0.790751	−	0.574514i	0.117435	−	0.993081i	$-0.462533\pi$
$17$	−942.241	−	684.578i	−0.790751	−	0.574514i	−0.908186	+	0.418566i	$0.862533\pi$
$18$	324.000			0.235702
$19$	917.282	+	666.444i	0.582933	+	0.423526i	0.839780	−	0.542926i	$-0.182684\pi$
$19$	917.282	+	666.444i	0.582933	+	0.423526i	−0.256847	+	0.966452i	$0.582684\pi$
$20$	−798.303	−	403.376i	−0.446265	−	0.225494i
$21$	1359.09	−	987.434i	0.672510	−	0.488607i
$22$	−1576.74	+	1145.57i	−0.694550	+	0.504620i
$23$	512.783	+	1578.18i	0.202122	+	0.622068i	0.999819	+	0.0190099i	$0.00605139\pi$
$23$	512.783	+	1578.18i	0.202122	+	0.622068i	−0.797697	+	0.603058i	$0.793949\pi$
$24$	−576.000			−0.204124
$25$	−1819.76	+	2540.49i	−0.582324	+	0.812957i
$26$	3976.37			1.15359
$27$	−225.273	−	693.320i	−0.0594703	−	0.183031i
$28$	−2416.15	+	1755.44i	−0.582411	+	0.423146i
$29$	−3088.44	+	2243.89i	−0.681938	+	0.495457i	−0.874000	−	0.485926i	$-0.838483\pi$
$29$	−3088.44	+	2243.89i	−0.681938	+	0.495457i	0.192062	+	0.981383i	$0.438483\pi$
$30$	−308.124	+	1988.73i	−0.0625062	+	0.403435i
$31$	8360.09	+	6073.96i	1.56245	+	1.13519i	0.933964	+	0.357368i	$0.116326\pi$
$31$	8360.09	+	6073.96i	1.56245	+	1.13519i	0.628488	+	0.777819i	$0.283674\pi$
$32$	1024.00			0.176777
$33$	3547.67	+	2577.53i	0.567098	+	0.412021i
$34$	1439.62	−	4430.68i	0.213574	−	0.657315i
$35$	4768.44	+	9281.21i	0.657971	+	1.28066i
$36$	400.486	+	1232.57i	0.0515028	+	0.158509i
$37$	1205.83	−	3711.16i	0.144804	−	0.445662i	−0.852181	−	0.523247i	$-0.824721\pi$
$37$	1205.83	−	3711.16i	0.144804	−	0.445662i	0.996986	+	0.0775842i	$0.0247207\pi$
$38$	−1401.48	+	4313.32i	−0.157445	+	0.484565i
$39$	−2764.72	−	8508.94i	−0.291065	−	0.895806i
$40$	547.776	−	3535.53i	0.0541319	−	0.349385i
$41$	1701.43	−	5236.46i	0.158072	−	0.486495i	−0.840387	−	0.541986i	$-0.817673\pi$
$41$	1701.43	−	5236.46i	0.158072	−	0.486495i	0.998459	+	0.0554913i	$0.0176725\pi$
$42$	5436.35	+	3949.74i	0.475537	+	0.345498i
$43$	12873.6			1.06176			0.530882	−	0.847446i	$-0.321861\pi$
$43$	12873.6			1.06176			0.530882	+	0.847446i	$0.321861\pi$
$44$	−6306.97	−	4582.28i	−0.491121	−	0.356821i
$45$	4469.88	−	723.395i	0.329052	−	0.0532530i
$46$	−5369.93	+	3901.49i	−0.374175	+	0.271854i
$47$	−13926.4	+	10118.1i	−0.919589	+	0.668121i	−0.943422	−	0.331595i	$-0.892413\pi$
$47$	−13926.4	+	10118.1i	−0.919589	+	0.668121i	0.0238323	+	0.999716i	$0.492413\pi$
$48$	−711.975	−	2191.23i	−0.0446028	−	0.137273i
$49$	18034.3			1.07302
$50$	−11913.9	−	3782.57i	−0.673955	−	0.213975i
$51$	−10482.1			−0.564315
$52$	4915.06	+	15127.0i	0.252070	+	0.775790i
$53$	−17765.0	+	12907.1i	−0.868713	+	0.631157i	−0.930241	−	0.366948i	$-0.880403\pi$
$53$	−17765.0	+	12907.1i	−0.868713	+	0.631157i	0.0615282	+	0.998105i	$0.480403\pi$
$54$	2359.09	−	1713.98i	0.110093	−	0.0799874i
$55$	−19194.9	+	19324.6i	−0.855616	+	0.861397i
$56$	−9664.62	−	7021.75i	−0.411827	−	0.299210i
$57$	10204.4			0.416007
$58$	−12353.8	−	8975.55i	−0.482203	−	0.350341i
$59$	−5775.98	+	17776.6i	−0.216021	+	0.664844i	0.783059	+	0.621948i	$0.213658\pi$
$59$	−5775.98	+	17776.6i	−0.216021	+	0.664844i	−0.999080	+	0.0428960i	$0.986342\pi$
$60$	−7946.45	+	1286.03i	−0.284967	+	0.0461184i
$61$	10813.1	+	33279.3i	0.372071	+	1.14512i	0.945434	+	0.325815i	$0.105639\pi$
$61$	10813.1	+	33279.3i	0.372071	+	1.14512i	−0.573363	+	0.819302i	$0.694361\pi$
$62$	−12773.1	+	39311.5i	−0.422004	+	1.29879i
$63$	4672.12	−	14379.3i	0.148307	−	0.456443i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	54857.7	−	8878.03i	1.61047	−	0.260635i
$66$	−5420.35	+	16682.1i	−0.153168	+	0.471402i
$67$	−44877.4	−	32605.3i	−1.22135	−	0.887364i	−0.225140	−	0.974326i	$-0.572284\pi$
$67$	−44877.4	−	32605.3i	−1.22135	−	0.887364i	−0.996212	+	0.0869627i	$0.972284\pi$
$68$	18634.8			0.488711
$69$	12082.4	+	8778.34i	0.305512	+	0.221968i
$70$	−29413.7	+	29612.4i	−0.717472	+	0.722319i
$71$	43218.4	−	31400.0i	1.01747	−	0.739237i	0.0517090	−	0.998662i	$-0.483533\pi$
$71$	43218.4	−	31400.0i	1.01747	−	0.739237i	0.965763	+	0.259425i	$0.0835332\pi$
$72$	−4193.94	+	3047.08i	−0.0953436	+	0.0692712i
$73$	−18849.2	−	58011.9i	−0.413986	−	1.27412i	−0.913154	−	0.407614i	$-0.866361\pi$
$73$	−18849.2	−	58011.9i	−0.413986	−	1.27412i	0.499168	−	0.866505i	$-0.333639\pi$
$74$	15608.6			0.331348
$75$	189.384	+	28124.4i	0.00388768	+	0.577337i
$76$	−18141.2			−0.360272
$77$	28104.3	+	86496.0i	0.540189	+	1.66253i
$78$	28952.5	−	21035.2i	0.538828	−	0.391481i
$79$	−34865.5	+	25331.3i	−0.628534	+	0.456657i	−0.855892	−	0.517155i	$-0.826991\pi$
$79$	−34865.5	+	25331.3i	−0.628534	+	0.456657i	0.227358	+	0.973811i	$0.426991\pi$
$80$	14127.0	−	2286.28i	0.246789	−	0.0399397i
$81$	−5307.96	−	3856.46i	−0.0898908	−	0.0653095i
$82$	22023.8			0.361707
$83$	−83875.9	−	60939.4i	−1.33642	−	0.970964i	−0.999568	−	0.0294049i	$-0.990639\pi$
$83$	−83875.9	−	60939.4i	−1.33642	−	0.970964i	−0.336849	−	0.941559i	$-0.609361\pi$
$84$	−8306.00	+	25563.2i	−0.128438	+	0.395292i
$85$	9968.45	−	64339.6i	0.149651	−	0.965897i
$86$	15912.6	+	48974.0i	0.232004	+	0.714035i
$87$	−10617.1	+	32676.2i	−0.150387	+	0.462842i
$88$	9636.19	−	29657.1i	0.132647	−	0.408246i
$89$	−20109.1	−	61889.4i	−0.269102	−	0.828212i	−0.990720	−	0.135920i	$-0.956601\pi$
$89$	−20109.1	−	61889.4i	−0.269102	−	0.828212i	0.721618	−	0.692292i	$-0.243399\pi$
$90$	8277.03	+	16110.3i	0.107713	+	0.209651i
$91$	57339.7	−	176474.i	0.725859	−	2.23396i
$92$	−21479.7	−	15605.9i	−0.264581	−	0.192230i
$93$	93002.7			1.11503
$94$	−55705.6	−	40472.5i	−0.650248	−	0.472433i
$95$	−9704.39	+	62635.3i	−0.110321	+	0.712049i
$96$	7455.90	−	5417.03i	0.0825700	−	0.0599906i
$97$	14936.3	−	10851.8i	0.161181	−	0.117105i	−0.504271	−	0.863545i	$-0.668239\pi$
$97$	14936.3	−	10851.8i	0.161181	−	0.117105i	0.665452	+	0.746441i	$0.268239\pi$
$98$	22291.6	+	68606.4i	0.234464	+	0.721605i
$99$	39466.4			0.404706
$100$	−336.683	−	49998.9i	−0.00336683	−	0.499989i
$101$	14346.3			0.139938			0.0699692	−	0.997549i	$-0.477710\pi$
$101$	14346.3			0.139938			0.0699692	+	0.997549i	$0.477710\pi$
$102$	−12956.5	−	39876.1i	−0.123307	−	0.379501i
$103$	55844.3	−	40573.2i	0.518663	−	0.376831i	−0.297437	−	0.954742i	$-0.596132\pi$
$103$	55844.3	−	40573.2i	0.518663	−	0.376831i	0.816100	+	0.577910i	$0.196132\pi$
$104$	−51471.2	+	37396.0i	−0.466639	+	0.339033i
$105$	83818.0	+	42352.5i	0.741932	+	0.374892i
$106$	−71060.1	−	51628.2i	−0.614273	−	0.446295i
$107$	227597.			1.92180			0.960898	−	0.276904i	$-0.0893083\pi$
$107$	227597.			1.92180			0.960898	+	0.276904i	$0.0893083\pi$
$108$	9436.37	+	6855.93i	0.0778477	+	0.0565597i
$109$	21618.6	−	66535.4i	0.174286	−	0.536397i	−0.825314	−	0.564674i	$-0.809002\pi$
$109$	21618.6	−	66535.4i	0.174286	−	0.536397i	0.999600	+	0.0282769i	$0.00900200\pi$
$110$	−97241.3	−	49135.2i	−0.766247	−	0.387178i
$111$	−10852.5	−	33400.5i	−0.0836029	−	0.257303i
$112$	14766.2	−	45445.7i	0.111231	−	0.342333i
$113$	32755.6	−	100811.i	0.241318	−	0.742700i	−0.754902	−	0.655837i	$-0.772316\pi$
$113$	32755.6	−	100811.i	0.241318	−	0.742700i	0.996220	−	0.0868629i	$-0.0276842\pi$
$114$	12613.3	+	38819.8i	0.0909008	+	0.279764i
$115$	−65372.4	+	65814.0i	−0.460945	+	0.464060i
$116$	18874.9	−	58091.0i	0.130239	−	0.400833i
$117$	−65143.2	−	47329.3i	−0.439951	−	0.319643i
$118$	−74765.8			−0.494309
$119$	−175877.	−	127782.i	−1.13852	−	0.827185i
$120$	−14714.7	−	28640.5i	−0.0932822	−	0.181563i
$121$	−61769.8	+	44878.4i	−0.383542	+	0.278660i
$122$	−113236.	+	82271.0i	−0.688789	+	0.500434i
$123$	−15312.9	−	47128.2i	−0.0912628	−	0.280878i
$124$	−165338.			−0.965648
$125$	−172809.	−	25583.8i	−0.989218	−	0.146450i
$126$	60477.2			0.339364
$127$	−70868.8	−	218112.i	−0.389893	−	1.19997i	−0.932868	−	0.360219i	$-0.882702\pi$
$127$	−70868.8	−	218112.i	−0.389893	−	1.19997i	0.542975	−	0.839749i	$-0.317298\pi$
$128$	−13254.9	+	9630.27i	−0.0715077	+	0.0519534i
$129$	93734.5	−	68102.1i	0.495935	−	0.360318i
$130$	101582.	+	197717.i	0.527178	+	1.02609i
$131$	100538.	+	73045.3i	0.511862	+	0.371890i	0.813530	−	0.581523i	$-0.197543\pi$
$131$	100538.	+	73045.3i	0.511862	+	0.371890i	−0.301667	+	0.953413i	$0.597543\pi$
$132$	−70162.5			−0.350486
$133$	171218.	+	124397.i	0.839306	+	0.609792i
$134$	68566.6	−	211026.i	0.329876	−	1.01525i
$135$	28719.1	−	28913.1i	0.135624	−	0.136540i
$136$	23033.9	+	70890.9i	0.106787	+	0.328657i
$137$	−41762.3	+	128531.i	−0.190101	+	0.585069i	−0.999999	−	0.00150091i	$-0.999522\pi$
$137$	−41762.3	+	128531.i	−0.190101	+	0.585069i	0.809898	+	0.586570i	$0.199522\pi$
$138$	−18460.2	+	56814.6i	−0.0825160	+	0.253958i
$139$	−62514.5	−	192400.i	−0.274437	−	0.844632i	−0.989368	−	0.145436i	$-0.953542\pi$
$139$	−62514.5	−	192400.i	−0.274437	−	0.844632i	0.714930	−	0.699196i	$-0.246458\pi$
$140$	−149010.	−	75293.4i	−0.642532	−	0.324666i
$141$	−47874.7	+	147343.i	−0.202795	+	0.624140i
$142$	172873.	+	125600.i	0.719461	+	0.522719i
$143$	484361.			1.98075
$144$	−16775.8	−	12188.3i	−0.0674181	−	0.0489821i
$145$	−190472.	−	96243.7i	−0.752333	−	0.380148i
$146$	197392.	−	143413.i	0.766384	−	0.556811i
$147$	131310.	−	95402.5i	0.501193	−	0.364138i
$148$	19293.3	+	59378.6i	0.0724022	+	0.222831i
$149$	59858.3			0.220881			0.110441	−	0.993883i	$-0.464774\pi$
$149$	59858.3			0.220881			0.110441	+	0.993883i	$0.464774\pi$
$150$	−106757.	+	35484.1i	−0.387409	+	0.128767i
$151$	−359481.			−1.28302			−0.641510	−	0.767114i	$-0.721692\pi$
$151$	−359481.			−1.28302			−0.641510	+	0.767114i	$0.721692\pi$
$152$	−22423.7	−	69013.1i	−0.0787224	−	0.242283i
$153$	−76321.5	+	55450.8i	−0.263584	+	0.191505i
$154$	−294312.	+	213830.i	−1.00001	+	0.726552i
$155$	−88445.7	+	570857.i	−0.295697	+	1.90853i
$156$	115810.	+	84141.0i	0.381009	+	0.276819i
$157$	−333496.			−1.07979			−0.539897	−	0.841731i	$-0.681537\pi$
$157$	−333496.			−1.07979			−0.539897	+	0.841731i	$0.681537\pi$
$158$	−139462.	−	101325.i	−0.444441	−	0.322905i
$159$	−61070.8	+	187956.i	−0.191576	+	0.589609i
$160$	26159.5	+	50916.4i	0.0807848	+	0.157238i
$161$	95715.1	+	294581.i	0.291015	+	0.895653i
$162$	8109.84	−	24959.5i	0.0242787	−	0.0747221i
$163$	144337.	−	444225.i	0.425510	−	1.30959i	−0.476995	−	0.878906i	$-0.658274\pi$
$163$	144337.	−	444225.i	0.425510	−	1.30959i	0.902505	−	0.430679i	$-0.141726\pi$
$164$	27222.9	+	83783.4i	0.0790359	+	0.243247i
$165$	−37532.6	+	242248.i	−0.107325	+	0.692707i
$166$	128151.	−	394408.i	0.360954	−	1.11090i
$167$	129691.	+	94226.3i	0.359849	+	0.261445i	0.752989	−	0.658033i	$-0.228611\pi$
$167$	129691.	+	94226.3i	0.359849	+	0.261445i	−0.393140	+	0.919479i	$0.628611\pi$
$168$	−107515.			−0.293898
$169$	−499103.	−	362620.i	−1.34423	−	0.976640i
$170$	257084.	−	41605.9i	0.682265	−	0.110416i
$171$	74299.8	−	53982.0i	0.194311	−	0.141175i
$172$	−166639.	+	121070.i	−0.429493	+	0.312045i
$173$	−118552.	−	364867.i	−0.301159	−	0.926871i	−0.981083	−	0.193589i	$-0.937987\pi$
$173$	−118552.	−	364867.i	−0.301159	−	0.926871i	0.679924	−	0.733282i	$-0.262013\pi$
$174$	−137431.			−0.344121
$175$	−339674.	+	474203.i	−0.838430	+	1.17049i
$176$	124733.			0.303530
$177$	51983.8	+	159990.i	0.124720	+	0.383848i
$178$	210585.	−	152999.i	0.498170	−	0.361942i
$179$	48356.9	−	35133.3i	0.112804	−	0.0819571i	−0.529953	−	0.848027i	$-0.677790\pi$
$179$	48356.9	−	35133.3i	0.112804	−	0.0819571i	0.642757	+	0.766070i	$0.277790\pi$
$180$	−51056.1	+	51401.1i	−0.117454	+	0.118247i
$181$	394125.	+	286348.i	0.894205	+	0.649678i	0.936971	−	0.349407i	$-0.113617\pi$
$181$	394125.	+	286348.i	0.894205	+	0.649678i	−0.0427661	+	0.999085i	$0.513617\pi$
$182$	742221.			1.66094
$183$	254782.	+	185110.i	0.562394	+	0.408603i
$184$	32818.1	−	101004.i	0.0714610	−	0.219934i
$185$	215335.	−	34849.3i	0.462578	−	0.0748626i
$186$	114958.	+	353803.i	0.243644	+	0.749859i
$187$	175360.	−	539701.i	0.366712	−	1.12862i
$188$	85110.5	−	261943.i	0.175626	−	0.540521i
$189$	−42049.1	−	129414.i	−0.0856253	−	0.263528i
$190$	−250274.	+	40503.8i	−0.502958	+	0.0813975i
$191$	−143723.	+	442334.i	−0.285064	+	0.877338i	0.701315	+	0.712851i	$0.252597\pi$
$191$	−143723.	+	442334.i	−0.285064	+	0.877338i	−0.986379	+	0.164486i	$0.947403\pi$
$192$	29823.6	+	21668.1i	0.0583858	+	0.0424197i
$193$	−224446.			−0.433730			−0.216865	−	0.976202i	$-0.569583\pi$
$193$	−224446.			−0.433730			−0.216865	+	0.976202i	$0.569583\pi$
$194$	59745.2	+	43407.4i	0.113972	+	0.0828055i
$195$	352462.	−	354843.i	0.663782	−	0.668267i
$196$	−233440.	+	169604.i	−0.434046	+	0.315353i
$197$	660935.	−	480198.i	1.21337	−	0.881565i	0.217838	−	0.975985i	$-0.430100\pi$
$197$	660935.	−	480198.i	1.21337	−	0.881565i	0.995532	+	0.0944197i	$0.0300996\pi$
$198$	48783.2	+	150139.i	0.0884315	+	0.272164i
$199$	−832683.			−1.49055			−0.745276	−	0.666756i	$-0.767682\pi$
$199$	−832683.			−1.49055			−0.745276	+	0.666756i	$0.767682\pi$
$200$	189791.	−	63082.8i	0.335506	−	0.111516i
$201$	−499244.			−0.871610
$202$	17733.0	+	54576.6i	0.0305777	+	0.0941084i
$203$	−576483.	+	418840.i	−0.981854	+	0.713358i
$204$	135683.	−	98579.2i	0.228270	−	0.165848i
$205$	303838.	−	49172.5i	0.504961	−	0.0817217i
$206$	223377.	+	162293.i	0.366750	+	0.266460i
$207$	134411.			0.218027
$208$	−205885.	−	149584.i	−0.329963	−	0.239732i
$209$	−170714.	+	525405.i	−0.270336	+	0.832010i
$210$	−57513.9	+	371213.i	−0.0899963	+	0.580865i
$211$	96932.1	+	298326.i	0.149886	+	0.461302i	0.997607	−	0.0691406i	$-0.0220257\pi$
$211$	96932.1	+	298326.i	0.149886	+	0.461302i	−0.847721	+	0.530443i	$0.822026\pi$
$212$	108570.	−	334145.i	0.165909	−	0.510617i
$213$	148572.	−	457256.i	0.224381	−	0.690575i
$214$	281325.	+	865831.i	0.419928	+	1.29240i
$215$	328873.	+	640113.i	0.485213	+	0.944411i
$216$	−14417.5	+	44372.5i	−0.0210259	+	0.0647112i
$217$	1.56048e6	+	1.13375e6i	2.24962	+	1.63444i
$218$	279838.			0.398809
$219$	−444131.	−	322680.i	−0.625750	−	0.454634i
$220$	66724.6	−	430662.i	0.0929457	−	0.599902i
$221$	−936674.	+	680533.i	−1.29005	+	0.937279i
$222$	113649.	−	82570.5i	0.154768	−	0.112446i
$223$	294994.	+	907898.i	0.397238	+	1.22257i	0.927205	+	0.374555i	$0.122204\pi$
$223$	294994.	+	907898.i	0.397238	+	1.22257i	−0.529967	+	0.848019i	$0.677796\pi$
$224$	191138.			0.254523
$225$	150159.	+	203776.i	0.197740	+	0.268347i
$226$	423997.			0.552195
$227$	138872.	+	427404.i	0.178875	+	0.550521i	0.999789	−	0.0205308i	$-0.00653562\pi$
$227$	138872.	+	427404.i	0.178875	+	0.550521i	−0.820914	+	0.571052i	$0.806536\pi$
$228$	−132089.	+	95967.9i	−0.168278	+	0.122261i
$229$	407810.	−	296291.i	0.513888	−	0.373362i	−0.300408	−	0.953811i	$-0.597123\pi$
$229$	407810.	−	296291.i	0.513888	−	0.373362i	0.814297	+	0.580449i	$0.197123\pi$
$230$	−331176.	−	167341.i	−0.412800	−	0.208584i
$231$	662201.	+	481117.i	0.816507	+	0.593227i
$232$	244322.			0.298018
$233$	−567687.	−	412449.i	−0.685046	−	0.497715i	0.189982	−	0.981788i	$-0.439157\pi$
$233$	−567687.	−	412449.i	−0.685046	−	0.497715i	−0.875028	+	0.484073i	$0.839157\pi$
$234$	99530.0	−	306322.i	0.118827	−	0.365711i
$235$	−858873.	−	433981.i	−1.01452	−	0.512627i
$236$	−92415.7	−	284426.i	−0.108010	−	0.332422i
$237$	−119857.	+	368882.i	−0.138609	+	0.426596i
$238$	268716.	−	827023.i	0.307504	−	0.946401i
$239$	−5590.88	−	17207.0i	−0.00633119	−	0.0194854i	0.947841	−	0.318743i	$-0.103261\pi$
$239$	−5590.88	−	17207.0i	−0.00633119	−	0.0194854i	−0.954172	+	0.299258i	$0.903261\pi$
$240$	90766.4	−	91379.7i	0.101718	−	0.102405i
$241$	−436344.	+	1.34293e6i	−0.483934	+	1.48940i	0.349585	+	0.936905i	$0.386323\pi$
$241$	−436344.	+	1.34293e6i	−0.483934	+	1.48940i	−0.833519	+	0.552491i	$0.813677\pi$
$242$	−247079.	−	179514.i	−0.271205	−	0.197042i
$243$	−59049.0			−0.0641500
$244$	−452945.	−	329084.i	−0.487047	−	0.353860i
$245$	460710.	+	896719.i	0.490358	+	0.954423i
$246$	160358.	−	116507.i	0.168948	−	0.122748i
$247$	911862.	−	662507.i	0.951014	−	0.690952i
$248$	−204369.	−	628984.i	−0.211002	−	0.649397i
$249$	−933087.			−0.953726
$250$	−116277.	−	689029.i	−0.117664	−	0.697248i
$251$	−818697.			−0.820236			−0.410118	−	0.912032i	$-0.634512\pi$
$251$	−818697.			−0.820236			−0.410118	+	0.912032i	$0.634512\pi$
$252$	74754.0	+	230069.i	0.0741537	+	0.228222i
$253$	−654111.	+	475240.i	−0.642466	+	0.466779i
$254$	742147.	−	539202.i	0.721782	−	0.524405i
$255$	−267779.	−	521200.i	−0.257885	−	0.501943i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−1.56130e6			−1.47453			−0.737263	−	0.675606i	$-0.763882\pi$
$257$	−1.56130e6			−1.47453			−0.737263	+	0.675606i	$0.763882\pi$
$258$	374938.	+	272408.i	0.350679	+	0.254783i
$259$	225078.	−	692719.i	0.208489	−	0.641664i
$260$	−626598.	+	630832.i	−0.574852	+	0.578736i
$261$	95554.2	+	294085.i	0.0868257	+	0.267222i
$262$	−153609.	+	472759.i	−0.138249	+	0.425488i
$263$	448681.	−	1.38090e6i	0.399989	−	1.23104i	−0.525018	−	0.851091i	$-0.675941\pi$
$263$	448681.	−	1.38090e6i	0.399989	−	1.23104i	0.925007	−	0.379950i	$-0.124059\pi$
$264$	−86725.7	−	266914.i	−0.0765840	−	0.235701i
$265$	−1.09561e6	−	553603.i	−0.958388	−	0.484266i
$266$	−261598.	+	805116.i	−0.226689	+	0.697677i
$267$	−473816.	−	344248.i	−0.406754	−	0.295524i
$268$	887544.			0.754837
$269$	−251136.	−	182461.i	−0.211606	−	0.153741i	0.476934	−	0.878939i	$-0.341748\pi$
$269$	−251136.	−	182461.i	−0.211606	−	0.153741i	−0.688540	+	0.725198i	$0.741748\pi$
$270$	145491.	+	73515.3i	0.121458	+	0.0613717i
$271$	1.37755e6	−	1.00085e6i	1.13942	−	0.827837i	0.152382	−	0.988322i	$-0.451306\pi$
$271$	1.37755e6	−	1.00085e6i	1.13942	−	0.827837i	0.987038	+	0.160484i	$0.0513056\pi$
$272$	−241214.	+	175252.i	−0.197688	+	0.143629i
$273$	−516058.	−	1.58826e6i	−0.419075	−	1.28978i
$274$	−540583.			−0.434997
$275$	−1.45124e6	−	460755.i	−1.15720	−	0.367399i
$276$	−238954.			−0.188817
$277$	−457459.	−	1.40791e6i	−0.358222	−	1.10249i	−0.954117	−	0.299433i	$-0.903203\pi$
$277$	−457459.	−	1.40791e6i	−0.358222	−	1.10249i	0.595895	−	0.803062i	$-0.296797\pi$
$278$	654660.	−	475638.i	0.508047	−	0.369118i
$279$	677167.	−	491991.i	0.520817	−	0.378396i
$280$	102247.	−	659935.i	0.0779391	−	0.503044i
$281$	261014.	+	189638.i	0.197196	+	0.143271i	0.682002	−	0.731351i	$-0.261110\pi$
$281$	261014.	+	189638.i	0.197196	+	0.143271i	−0.484806	+	0.874622i	$0.661110\pi$
$282$	−619703.			−0.464046
$283$	−205532.	−	149328.i	−0.152551	−	0.110834i	0.508892	−	0.860831i	$-0.330055\pi$
$283$	−205532.	−	149328.i	−0.152551	−	0.110834i	−0.661442	+	0.749996i	$0.730055\pi$
$284$	−264127.	+	812900.i	−0.194320	+	0.598055i
$285$	260686.	+	507394.i	0.190110	+	0.370027i
$286$	598703.	+	1.84262e6i	0.432809	+	1.33205i
$287$	317586.	−	977428.i	0.227592	−	0.700455i
$288$	25631.1	−	78884.4i	0.0182090	−	0.0560415i
$289$	−19589.2	−	60289.4i	−0.0137966	−	0.0424616i
$290$	130697.	−	843560.i	0.0912579	−	0.589008i
$291$	51346.4	−	158028.i	0.0355449	−	0.109396i
$292$	789566.	+	573653.i	0.541915	+	0.393725i
$293$	−1.06446e6			−0.724367			−0.362184	−	0.932107i	$-0.617969\pi$
$293$	−1.06446e6			−0.724367			−0.362184	+	0.932107i	$0.617969\pi$
$294$	525241.	+	381610.i	0.354397	+	0.257485i
$295$	−1.03146e6	+	166930.i	−0.690079	+	0.111681i
$296$	−202042.	+	146792.i	−0.134033	+	0.0973808i
$297$	287361.	−	208780.i	0.189033	−	0.137340i
$298$	73988.9	+	227714.i	0.0482643	+	0.148542i
$299$	1.64960e6			1.06709
$300$	−266949.	−	362268.i	−0.171248	−	0.232395i
$301$	2.40296e6			1.52873
$302$	−444343.	−	1.36755e6i	−0.280350	−	0.862830i
$303$	104458.	−	75893.0i	0.0653633	−	0.0474892i
$304$	234824.	−	170610.i	0.145733	−	0.105881i
$305$	−1.37851e6	+	1.38783e6i	−0.848518	+	0.854251i
$306$	−305286.	−	221803.i	−0.186382	−	0.135414i
$307$	2.18359e6			1.32229			0.661144	−	0.750259i	$-0.270071\pi$
$307$	2.18359e6			1.32229			0.661144	+	0.750259i	$0.270071\pi$
$308$	−1.17725e6	−	855320.i	−0.707116	−	0.513750i
$309$	191976.	−	590840.i	0.114380	−	0.352025i
$310$	−2.28099e6	+	369150.i	−1.34809	+	0.218172i
$311$	−245790.	−	756465.i	−0.144100	−	0.443494i	0.852794	−	0.522247i	$-0.174906\pi$
$311$	−245790.	−	756465.i	−0.144100	−	0.443494i	−0.996894	+	0.0787532i	$0.974906\pi$
$312$	−176942.	+	544572.i	−0.102907	+	0.316715i
$313$	−487098.	+	1.49913e6i	−0.281032	+	0.864928i	0.706528	+	0.707685i	$0.250260\pi$
$313$	−487098.	+	1.49913e6i	−0.281032	+	0.864928i	−0.987560	+	0.157243i	$0.949740\pi$
$314$	−412223.	−	1.26869e6i	−0.235944	−	0.726160i
$315$	834340.	−	135028.i	0.473769	−	0.0766736i
$316$	213079.	−	655791.i	0.120039	−	0.369443i
$317$	1.06594e6	+	774453.i	0.595780	+	0.432859i	0.844378	−	0.535747i	$-0.179970\pi$
$317$	1.06594e6	+	774453.i	0.595780	+	0.432859i	−0.248599	+	0.968607i	$0.579970\pi$
$318$	−790516.			−0.438372
$319$	−1.50481e6	−	1.09331e6i	−0.827954	−	0.601543i
$320$	−161363.	+	162453.i	−0.0880903	+	0.0886854i
$321$	1.65717e6	−	1.20400e6i	0.897644	−	0.652177i
$322$	−1.00234e6	+	728244.i	−0.538736	+	0.391415i
$323$	−408067.	−	1.25590e6i	−0.217633	−	0.669806i
$324$	104976.			0.0555556
$325$	1.84286e6	+	2.50089e6i	0.967795	+	1.31337i
$326$	1.86834e6			0.973672
$327$	−194568.	−	598818.i	−0.100624	−	0.309689i
$328$	−285082.	+	207124.i	−0.146314	+	0.106303i
$329$	−2.59947e6	+	1.88863e6i	−1.32402	+	0.961960i
$330$	−967957.	+	156652.i	−0.489296	+	0.0791864i
$331$	−2.01087e6	−	1.46098e6i	−1.00882	−	0.732950i	−0.0448580	−	0.998993i	$-0.514284\pi$
$331$	−2.01087e6	−	1.46098e6i	−1.00882	−	0.732950i	−0.963961	+	0.266043i	$0.914284\pi$
$332$	1.65882e6			0.825951
$333$	−255709.	−	185784.i	−0.126368	−	0.0918115i
$334$	−198151.	+	609846.i	−0.0971918	+	0.299126i
$335$	474781.	−	3.06439e6i	0.231143	−	1.49187i
$336$	−132896.	−	409012.i	−0.0642190	−	0.197646i
$337$	1.15209e6	−	3.54577e6i	0.552602	−	1.70073i	−0.149592	−	0.988748i	$-0.547796\pi$
$337$	1.15209e6	−	3.54577e6i	0.552602	−	1.70073i	0.702194	−	0.711986i	$-0.252204\pi$
$338$	762562.	−	2.34692e6i	0.363064	−	1.11740i
$339$	−294800.	−	907303.i	−0.139325	−	0.428798i
$340$	476051.	+	926578.i	0.223335	+	0.434695i
$341$	−1.55589e6	+	4.78853e6i	−0.724590	+	2.23006i
$342$	297199.	+	215928.i	0.137399	+	0.0998259i
$343$	229079.			0.105136
$344$	−666556.	−	484281.i	−0.303697	−	0.220649i
$345$	−127825.	+	825026.i	−0.0578189	+	0.373181i
$346$	1.24150e6	−	902001.i	0.557514	−	0.405057i
$347$	2.90356e6	−	2.10956e6i	1.29452	−	0.940522i	0.294631	−	0.955611i	$-0.404803\pi$
$347$	2.90356e6	−	2.10956e6i	1.29452	−	0.940522i	0.999886	+	0.0150895i	$0.00480333\pi$
$348$	−169874.	−	522819.i	−0.0751933	−	0.231421i
$349$	2.19722e6			0.965629			0.482815	−	0.875723i	$-0.339614\pi$
$349$	2.19722e6			0.965629			0.482815	+	0.875723i	$0.339614\pi$
$350$	−2.22384e6	−	706048.i	−0.970359	−	0.308081i
$351$	−724693.			−0.313969
$352$	154179.	+	474514.i	0.0663237	+	0.204123i
$353$	−1.81427e6	+	1.31814e6i	−0.774934	+	0.563022i	−0.903454	−	0.428685i	$-0.858977\pi$
$353$	−1.81427e6	+	1.31814e6i	−0.774934	+	0.563022i	0.128521	+	0.991707i	$0.458977\pi$
$354$	−544382.	+	395516.i	−0.230885	+	0.167748i
$355$	2.66538e6	+	1.34679e6i	1.12250	+	0.567192i
$356$	842340.	+	611996.i	0.352259	+	0.255931i
$357$	−1.95656e6			−0.812500
$358$	193428.	+	140533.i	0.0797647	+	0.0579525i
$359$	543875.	−	1.67387e6i	0.222722	−	0.685467i	−0.775793	−	0.630987i	$-0.782650\pi$
$359$	543875.	−	1.67387e6i	0.222722	−	0.685467i	0.998515	−	0.0544798i	$-0.0173500\pi$
$360$	−258650.	−	130694.i	−0.105186	−	0.0531495i
$361$	−367899.	−	1.13228e6i	−0.148580	−	0.457282i
$362$	−602169.	+	1.85328e6i	−0.241516	+	0.743311i
$363$	−212346.	+	653533.i	−0.0845818	+	0.260316i
$364$	917436.	+	2.82358e6i	0.362930	+	1.11698i
$365$	2.40300e6	−	2.41924e6i	0.944108	−	0.950487i
$366$	−389272.	+	1.19806e6i	−0.151897	+	0.467492i
$367$	2.94034e6	+	2.13628e6i	1.13955	+	0.827930i	0.987056	−	0.160375i	$-0.0512702\pi$
$367$	2.94034e6	+	2.13628e6i	1.13955	+	0.827930i	0.152492	+	0.988305i	$0.451270\pi$
$368$	424807.			0.163520
$369$	−360806.	−	262141.i	−0.137946	−	0.100223i
$370$	398743.	+	776107.i	0.151422	+	0.294725i
$371$	−3.31599e6	+	2.40921e6i	−1.25077	+	0.908739i
$372$	−1.20385e6	+	874650.i	−0.451041	+	0.327700i
$373$	870337.	+	2.67862e6i	0.323903	+	0.996872i	0.971933	+	0.235257i	$0.0755932\pi$
$373$	870337.	+	2.67862e6i	0.323903	+	0.996872i	−0.648030	+	0.761615i	$0.724407\pi$
$374$	2.26990e6			0.839128
$375$	−1.39359e6	+	727893.i	−0.511749	+	0.267294i
$376$	1.10169e6			0.401875
$377$	1.17271e6	+	3.60923e6i	0.424950	+	1.30786i
$378$	440344.	−	319929.i	0.158512	−	0.115166i
$379$	−3.01856e6	+	2.19311e6i	−1.07945	+	0.784265i	−0.977587	−	0.210533i	$-0.932480\pi$
$379$	−3.01856e6	+	2.19311e6i	−1.07945	+	0.784265i	−0.101862	+	0.994799i	$0.532480\pi$
$380$	−463441.	−	902034.i	−0.164640	−	0.320453i
$381$	−1.66983e6	−	1.21320e6i	−0.589332	−	0.428175i
$382$	−1.86039e6			−0.652297
$383$	1.25345e6	+	910682.i	0.436625	+	0.317227i	0.784293	−	0.620391i	$-0.213026\pi$
$383$	1.25345e6	+	910682.i	0.436625	+	0.317227i	−0.347667	+	0.937618i	$0.613026\pi$
$384$	−45566.4	+	140239.i	−0.0157695	+	0.0485334i
$385$	−3.58288e6	+	3.60709e6i	−1.23192	+	1.24024i
$386$	−277431.	−	853844.i	−0.0947734	−	0.291683i
$387$	322230.	−	991723.i	0.109368	−	0.336599i
$388$	−91282.5	+	280939.i	−0.0307828	+	0.0947397i
$389$	42373.0	+	130411.i	0.0141976	+	0.0436957i	0.957904	−	0.287088i	$-0.0926871\pi$
$389$	42373.0	+	130411.i	0.0141976	+	0.0436957i	−0.943707	+	0.330783i	$0.892687\pi$
$390$	1.78557e6	+	902234.i	0.594450	+	0.300371i
$391$	597225.	−	1.83807e6i	0.197559	−	0.608023i
$392$	−933762.	−	678418.i	−0.306917	−	0.222988i
$393$	1.11845e6			0.365288
$394$	2.64374e6	+	1.92079e6i	0.857982	+	0.623361i
$395$	−2.15024e6	−	1.08650e6i	−0.693416	−	0.350377i
$396$	−510864.	+	371165.i	−0.163707	+	0.118940i
$397$	−259776.	+	188738.i	−0.0827223	+	0.0601013i	−0.628378	−	0.777908i	$-0.716281\pi$
$397$	−259776.	+	188738.i	−0.0827223	+	0.0601013i	0.545655	+	0.838010i	$0.316281\pi$
$398$	−1.02925e6	−	3.16772e6i	−0.325698	−	1.00239i
$399$	1.90473e6			0.598966
$400$	474576.	+	644033.i	0.148305	+	0.201260i
$401$	4.88172e6			1.51605			0.758023	−	0.652228i	$-0.226166\pi$
$401$	4.88172e6			1.51605			0.758023	+	0.652228i	$0.226166\pi$
$402$	−617099.	−	1.89924e6i	−0.190454	−	0.586157i
$403$	8.31069e6	−	6.03807e6i	2.54903	−	1.85198i
$404$	−185703.	+	134921.i	−0.0566063	+	0.0411269i
$405$	56155.6	−	362447.i	0.0170120	−	0.109801i
$406$	−2.30593e6	−	1.67536e6i	−0.694275	−	0.504421i
$407$	1.90128e6			0.568932
$408$	542731.	+	394317.i	0.161411	+	0.117272i
$409$	−603132.	+	1.85625e6i	−0.178281	+	0.548691i	−0.999768	−	0.0215354i	$-0.993145\pi$
$409$	−603132.	+	1.85625e6i	−0.178281	+	0.548691i	0.821488	+	0.570226i	$0.193145\pi$
$410$	562628.	+	1.09509e6i	0.165296	+	0.321729i
$411$	375861.	+	1.15678e6i	0.109755	+	0.337790i
$412$	−341290.	+	1.05038e6i	−0.0990559	+	0.304863i
$413$	−1.07813e6	+	3.31815e6i	−0.311027	+	0.957241i
$414$	166142.	+	511332.i	0.0476407	+	0.146623i
$415$	887366.	−	5.72735e6i	0.252920	−	1.63243i
$416$	314564.	−	968128.i	0.0891201	−	0.274283i
$417$	−1.47298e6	−	1.07019e6i	−0.414818	−	0.301383i
$418$	−2.20977e6			−0.618596
$419$	−748090.	−	543519.i	−0.208170	−	0.151245i	0.478815	−	0.877916i	$-0.341066\pi$
$419$	−748090.	−	543519.i	−0.208170	−	0.151245i	−0.686985	+	0.726671i	$0.741066\pi$
$420$	−1.48327e6	+	240049.i	−0.410296	+	0.0664013i
$421$	−1.71029e6	+	1.24260e6i	−0.470289	+	0.341685i	−0.797554	−	0.603248i	$-0.793873\pi$
$421$	−1.71029e6	+	1.24260e6i	−0.470289	+	0.341685i	0.327265	+	0.944933i	$0.393873\pi$
$422$	−1.01509e6	+	737503.i	−0.277474	+	0.201596i
$423$	430872.	+	1.32609e6i	0.117084	+	0.360347i
$424$	1.40536e6			0.379642
$425$	3.45382e6	−	1.14798e6i	0.927528	−	0.308293i
$426$	1.92315e6			0.513440
$427$	2.01835e6	+	6.21185e6i	0.535707	+	1.64874i
$428$	−2.94608e6	+	2.14045e6i	−0.777383	+	0.564801i
$429$	3.52671e6	−	2.56230e6i	0.925180	−	0.672183i
$430$	−2.02863e6	+	2.04233e6i	−0.529092	+	0.532666i
$431$	−4.53257e6	−	3.29311e6i	−1.17531	−	0.853911i	−0.183673	−	0.982987i	$-0.558799\pi$
$431$	−4.53257e6	−	3.29311e6i	−1.17531	−	0.853911i	−0.991635	+	0.129077i	$0.958799\pi$
$432$	−186624.			−0.0481125
$433$	917395.	+	666526.i	0.235145	+	0.170843i	0.699118	−	0.715007i	$-0.253576\pi$
$433$	917395.	+	666526.i	0.235145	+	0.170843i	−0.463972	+	0.885850i	$0.653576\pi$
$434$	−2.38420e6	+	7.33781e6i	−0.607601	+	1.87000i
$435$	−1.89599e6	+	306842.i	−0.480410	+	0.0777485i
$436$	345898.	+	1.06457e6i	0.0871430	+	0.268198i
$437$	−581405.	+	1.78938e6i	−0.145638	+	0.448228i
$438$	678572.	−	2.08843e6i	0.169009	−	0.520157i
$439$	244383.	+	752134.i	0.0605215	+	0.186266i	0.976746	−	0.214399i	$-0.0687792\pi$
$439$	244383.	+	752134.i	0.0605215	+	0.186266i	−0.916225	+	0.400665i	$0.868779\pi$
$440$	1.72081e6	−	278492.i	0.423742	−	0.0685775i
$441$	451404.	−	1.38928e6i	0.110527	−	0.340168i
$442$	−3.74670e6	−	2.72213e6i	−0.912206	−	0.662756i
$443$	−2.57929e6			−0.624440			−0.312220	−	0.950010i	$-0.601073\pi$
$443$	−2.57929e6			−0.624440			−0.312220	+	0.950010i	$0.601073\pi$
$444$	454594.	+	330282.i	0.109438	+	0.0795111i
$445$	2.56362e6	−	2.58094e6i	0.613695	−	0.617842i
$446$	−3.08922e6	+	2.24445e6i	−0.735379	+	0.534284i
$447$	435837.	−	316654.i	0.103170	−	0.0749577i
$448$	236259.	+	727132.i	0.0556153	+	0.171166i
$449$	−4.38736e6			−1.02704			−0.513521	−	0.858077i	$-0.671659\pi$
$449$	−4.38736e6			−1.02704			−0.513521	+	0.858077i	$0.671659\pi$
$450$	−589603.	+	823119.i	−0.137255	+	0.191616i
$451$	2.68271e6			0.621059
$452$	524090.	+	1.61298e6i	0.120659	+	0.371350i
$453$	−2.61744e6	+	1.90168e6i	−0.599281	+	0.435403i
$454$	−1.45429e6	+	1.05660e6i	−0.331139	+	0.240586i
$455$	1.02396e7	−	1.65716e6i	2.31876	−	0.375263i
$456$	−528354.	−	383872.i	−0.118991	−	0.0864518i
$457$	−4.18179e6			−0.936637			−0.468318	−	0.883560i	$-0.655140\pi$
$457$	−4.18179e6			−0.936637			−0.468318	+	0.883560i	$0.655140\pi$
$458$	1.63124e6	+	1.18516e6i	0.363374	+	0.264007i
$459$	−262370.	+	807492.i	−0.0581276	+	0.178898i
$460$	227245.	−	1.46671e6i	0.0500726	−	0.323185i
$461$	−775794.	−	2.38765e6i	−0.170018	−	0.523261i	0.829353	−	0.558725i	$-0.188709\pi$
$461$	−775794.	−	2.38765e6i	−0.170018	−	0.523261i	−0.999371	+	0.0354638i	$0.988709\pi$
$462$	−1.01175e6	+	3.11386e6i	−0.220531	+	0.678725i
$463$	−2.22488e6	+	6.84748e6i	−0.482341	+	1.48449i	0.353454	+	0.935452i	$0.385007\pi$
$463$	−2.22488e6	+	6.84748e6i	−0.482341	+	1.48449i	−0.835795	+	0.549042i	$0.814993\pi$
$464$	301998.	+	929455.i	0.0651193	+	0.200417i
$465$	2.37588e6	+	4.62438e6i	0.509557	+	0.991793i
$466$	867349.	−	2.66943e6i	0.185024	−	0.569447i
$467$	−3.70403e6	−	2.69114e6i	−0.785928	−	0.571010i	0.120825	−	0.992674i	$-0.461446\pi$
$467$	−3.70403e6	−	2.69114e6i	−0.785928	−	0.571010i	−0.906752	+	0.421664i	$0.861446\pi$
$468$	1.28834e6			0.271905
$469$	−8.37673e6	−	6.08605e6i	−1.75850	−	1.27763i
$470$	589338.	−	3.80378e6i	0.123061	−	0.794274i
$471$	−2.42823e6	+	1.76421e6i	−0.504357	+	0.366437i
$472$	967789.	−	703140.i	0.199952	−	0.145274i
$473$	1.93832e6	+	5.96552e6i	0.398356	+	1.22601i
$474$	−1.55146e6			−0.317172
$475$	−3.36233e6	+	1.11757e6i	−0.683764	+	0.227270i
$476$	3.47833e6			0.703645
$477$	549637.	+	1.69161e6i	0.110606	+	0.340411i
$478$	58548.4	−	42537.9i	0.0117205	−	0.00851543i
$479$	7.74639e6	−	5.62808e6i	1.54263	−	1.12078i	0.593962	−	0.804493i	$-0.297563\pi$
$479$	7.74639e6	−	5.62808e6i	1.54263	−	1.12078i	0.948663	−	0.316290i	$-0.102437\pi$
$480$	459823.	+	232345.i	0.0910935	+	0.0460288i
$481$	−3.13825e6	−	2.28007e6i	−0.618480	−	0.449352i
$482$	−5.64815e6			−1.10736
$483$	2.25527e6	+	1.63855e6i	0.439876	+	0.319589i
$484$	377504.	−	1.16184e6i	0.0732500	−	0.225440i
$485$	921155.	+	465452.i	0.177819	+	0.0898506i
$486$	−72988.6	−	224636.i	−0.0140173	−	0.0431408i
$487$	−1.27891e6	+	3.93608e6i	−0.244353	+	0.752040i	0.751390	+	0.659859i	$0.229384\pi$
$487$	−1.27891e6	+	3.93608e6i	−0.244353	+	0.752040i	−0.995742	+	0.0921813i	$0.970616\pi$
$488$	692039.	−	2.12988e6i	0.131547	−	0.404860i
$489$	−1.29904e6	−	3.99802e6i	−0.245668	−	0.756090i
$490$	−2.84185e6	+	2.86105e6i	−0.534701	+	0.538314i
$491$	−1.54000e6	+	4.73964e6i	−0.288282	+	0.887242i	0.697113	+	0.716961i	$0.254467\pi$
$491$	−1.54000e6	+	4.73964e6i	−0.288282	+	0.887242i	−0.985396	+	0.170281i	$0.945533\pi$
$492$	641434.	+	466029.i	0.119465	+	0.0867961i
$493$	4.44617e6			0.823890
$494$	3.64745e6	+	2.65003e6i	0.672468	+	0.488577i
$495$	1.00823e6	+	1.96239e6i	0.184946	+	0.359975i
$496$	2.14018e6	−	1.55493e6i	0.390613	−	0.283797i
$497$	8.06706e6	−	5.86106e6i	1.46496	−	1.06435i
$498$	−1.15336e6	−	3.54967e6i	−0.208397	−	0.641379i
$499$	169660.			0.0305020			0.0152510	−	0.999884i	$-0.495145\pi$
$499$	169660.			0.0305020			0.0152510	+	0.999884i	$0.495145\pi$
$500$	2.47750e6	−	1.29403e6i	0.443188	−	0.231483i
$501$	1.44277e6			0.256804
$502$	−1.01197e6	−	3.11451e6i	−0.179228	−	0.551608i
$503$	−7.18526e6	+	5.22040e6i	−1.26626	+	0.919992i	−0.999047	−	0.0436460i	$-0.986103\pi$
$503$	−7.18526e6	+	5.22040e6i	−1.26626	+	0.919992i	−0.267213	+	0.963638i	$0.586103\pi$
$504$	−782834.	+	568762.i	−0.137276	+	0.0997365i
$505$	366497.	+	713343.i	0.0639502	+	0.124471i
$506$	−2.61645e6	−	1.90096e6i	−0.454292	−	0.330063i
$507$	−5.55233e6			−0.959302
$508$	2.96859e6	+	2.15681e6i	0.510377	+	0.370810i
$509$	492221.	−	1.51490e6i	0.0842104	−	0.259173i	−0.900082	−	0.435721i	$-0.856493\pi$
$509$	492221.	−	1.51490e6i	0.0842104	−	0.259173i	0.984292	+	0.176549i	$0.0564933\pi$
$510$	1.65177e6	−	1.66293e6i	0.281206	−	0.283106i
$511$	−3.51836e6	−	1.08284e7i	−0.596057	−	1.83448i
$512$	81007.0	−	249314.i	0.0136568	−	0.0420312i
$513$	255420.	−	786102.i	0.0428511	−	0.131882i
$514$	−1.92987e6	−	5.93952e6i	−0.322196	−	0.991617i
$515$	3.44405e6	+	1.74025e6i	0.572204	+	0.289130i
$516$	−572854.	+	1.76306e6i	−0.0947152	+	0.291504i
$517$	−6.78549e6	−	4.92995e6i	−1.11649	−	0.811178i
$518$	2.91347e6			0.477075
$519$	−2.79337e6	−	2.02950e6i	−0.455208	−	0.330728i
$520$	−3.17435e6	−	1.60397e6i	−0.514809	−	0.260129i
$521$	4.14855e6	−	3.01410e6i	0.669579	−	0.486478i	−0.200305	−	0.979734i	$-0.564193\pi$
$521$	4.14855e6	−	3.01410e6i	0.669579	−	0.486478i	0.869884	+	0.493256i	$0.164193\pi$
$522$	−1.00066e6	+	727019.i	−0.160734	+	0.116780i
$523$	2.71904e6	+	8.36835e6i	0.434672	+	1.33778i	0.893422	+	0.449218i	$0.148297\pi$
$523$	2.71904e6	+	8.36835e6i	0.434672	+	1.33778i	−0.458750	+	0.888565i	$0.651703\pi$
$524$	−1.98835e6			−0.316348
$525$	35350.1	+	5.24964e6i	0.00559748	+	0.831249i
$526$	5.80785e6			0.915274
$527$	−3.71912e6	−	1.14463e7i	−0.583329	−	1.79530i
$528$	908203.	−	659848.i	0.141775	−	0.103005i
$529$	2.97939e6	−	2.16466e6i	0.462902	−	0.336318i
$530$	751782.	−	4.85224e6i	0.116252	−	0.750331i
$531$	1.22486e6	+	889912.i	0.188517	+	0.136965i
$532$	−3.38620e6			−0.518720
$533$	−4.42808e6	−	3.21719e6i	−0.675146	−	0.490522i
$534$	723927.	−	2.22802e6i	0.109861	−	0.338116i
$535$	5.81428e6	+	1.13168e7i	0.878237	+	1.70938i
$536$	1.09707e6	+	3.37642e6i	0.164938	+	0.507627i
$537$	166236.	−	511622.i	0.0248765	−	0.0765621i
$538$	383701.	−	1.18091e6i	0.0571528	−	0.175898i
$539$	2.71534e6	+	8.35695e6i	0.402580	+	1.23901i
$540$	−99832.3	+	644350.i	−0.0147328	+	0.0950905i
$541$	−551105.	+	1.69613e6i	−0.0809545	+	0.249152i	−0.983340	−	0.181778i	$-0.941815\pi$
$541$	−551105.	+	1.69613e6i	−0.0809545	+	0.249152i	0.902385	+	0.430931i	$0.141815\pi$
$542$	5.51020e6	+	4.00339e6i	0.805692	+	0.585369i
$543$	4.38448e6			0.638144
$544$	−964855.	−	701008.i	−0.139786	−	0.101561i
$545$	3.86062e6	−	624793.i	0.556757	−	0.0901042i
$546$	5.40423e6	−	3.92640e6i	0.775804	−	0.563655i
$547$	−3.94383e6	+	2.86536e6i	−0.563573	+	0.409460i	−0.832765	−	0.553627i	$-0.813243\pi$
$547$	−3.94383e6	+	2.86536e6i	−0.563573	+	0.409460i	0.269192	+	0.963087i	$0.413243\pi$
$548$	−668197.	−	2.05650e6i	−0.0950503	−	0.292535i
$549$	2.83435e6			0.401349
$550$	−41011.3	−	6.09036e6i	−0.00578092	−	0.858492i
$551$	−4.32840e6			−0.607363
$552$	−295363.	−	909034.i	−0.0412580	−	0.126979i
$553$	−6.50794e6	+	4.72829e6i	−0.904963	+	0.657494i
$554$	4.79057e6	−	3.48055e6i	0.663152	−	0.481808i
$555$	1.38353e6	−	1.39288e6i	0.190659	−	0.191947i
$556$	2.61864e6	+	1.90255e6i	0.359243	+	0.261006i
$557$	−6.98847e6			−0.954431			−0.477215	−	0.878786i	$-0.658354\pi$
$557$	−6.98847e6			−0.954431			−0.477215	+	0.878786i	$0.658354\pi$
$558$	2.70867e6	+	1.96796e6i	0.368273	+	0.267566i
$559$	3.95465e6	−	1.21712e7i	0.535277	−	1.64741i
$560$	2.63692e6	−	426754.i	0.355327	−	0.0575052i
$561$	−1.57824e6	−	4.85731e6i	−0.211721	−	0.651612i
$562$	−398794.	+	1.22736e6i	−0.0532609	+	0.163920i
$563$	2.17508e6	−	6.69420e6i	0.289204	−	0.890078i	−0.695903	−	0.718136i	$-0.744996\pi$
$563$	2.17508e6	−	6.69420e6i	0.289204	−	0.890078i	0.985107	−	0.171942i	$-0.0550042\pi$
$564$	−765995.	−	2.35749e6i	−0.101398	−	0.312070i
$565$	5.84944e6	−	946659.i	0.770891	−	0.124759i
$566$	314025.	−	966470.i	0.0412025	−	0.126808i
$567$	−990774.	−	719840.i	−0.129425	−	0.0940325i
$568$	−3.41893e6			−0.444652
$569$	1.14531e7	+	8.32113e6i	1.48300	+	1.07746i	0.976575	+	0.215177i	$0.0690328\pi$
$569$	1.14531e7	+	8.32113e6i	1.48300	+	1.07746i	0.506424	+	0.862285i	$0.330967\pi$
$570$	−1.60802e6	+	1.61888e6i	−0.207302	+	0.208703i
$571$	2.73438e6	−	1.98665e6i	0.350969	−	0.254994i	−0.398306	−	0.917252i	$-0.630402\pi$
$571$	2.73438e6	−	1.98665e6i	0.350969	−	0.254994i	0.749276	+	0.662258i	$0.230402\pi$
$572$	−6.26970e6	+	4.55521e6i	−0.801229	+	0.582127i
$573$	1.29351e6	+	3.98101e6i	0.164582	+	0.506531i
$574$	4.11092e6			0.520785
$575$	−4.94250e6	−	1.56920e6i	−0.623415	−	0.197929i
$576$	331776.			0.0416667
$577$	−632326.	−	1.94610e6i	−0.0790682	−	0.243347i	0.903707	−	0.428151i	$-0.140835\pi$
$577$	−632326.	−	1.94610e6i	−0.0790682	−	0.243347i	−0.982775	+	0.184804i	$0.940835\pi$
$578$	205141.	−	149044.i	0.0255407	−	0.0185564i
$579$	−1.63423e6	+	1.18734e6i	−0.202589	+	0.147190i
$580$	3.37065e6	−	545497.i	0.416048	−	0.0673322i
$581$	−1.56561e7	−	1.13748e7i	−1.92417	−	1.39799i
$582$	664642.			0.0813355
$583$	−8.65583e6	−	6.28883e6i	−1.05472	−	0.766300i
$584$	−1.20635e6	+	3.71276e6i	−0.146366	+	0.450469i
$585$	689184.	−	4.44821e6i	0.0832617	−	0.537398i
$586$	−1.31574e6	−	4.04943e6i	−0.158280	−	0.487136i
$587$	−164824.	+	507276.i	−0.0197435	+	0.0607643i	−0.960443	−	0.278477i	$-0.910170\pi$
$587$	−164824.	+	507276.i	−0.0197435	+	0.0607643i	0.940699	+	0.339241i	$0.110170\pi$
$588$	−802497.	+	2.46983e6i	−0.0957194	+	0.294594i
$589$	3.62060e6	+	1.11431e7i	0.430024	+	1.32348i
$590$	−1.91000e6	−	3.71759e6i	−0.225893	−	0.439674i
$591$	2.27209e6	−	6.99278e6i	0.267582	−	0.823534i
$592$	−808168.	−	587168.i	−0.0947758	−	0.0688586i
$593$	3.70808e6			0.433025			0.216512	−	0.976280i	$-0.430532\pi$
$593$	3.70808e6			0.433025			0.216512	+	0.976280i	$0.430532\pi$
$594$	1.14944e6	+	835120.i	0.133666	+	0.0971142i
$595$	1.86069e6	−	1.20095e7i	0.215468	−	1.39070i
$596$	−774821.	+	562941.i	−0.0893482	+	0.0649153i
$597$	−6.06290e6	+	4.40495e6i	−0.696216	+	0.505831i
$598$	2.03901e6	+	6.27544e6i	0.233167	+	0.717614i
$599$	−8.60593e6			−0.980010			−0.490005	−	0.871720i	$-0.663005\pi$
$599$	−8.60593e6			−0.980010			−0.490005	+	0.871720i	$0.663005\pi$
$600$	1.04818e6	−	1.46332e6i	0.118866	−	0.165944i
$601$	−1.50484e7			−1.69944			−0.849718	−	0.527238i	$-0.823228\pi$
$601$	−1.50484e7			−1.69944			−0.849718	+	0.527238i	$0.823228\pi$
$602$	2.97022e6	+	9.14140e6i	0.334039	+	1.02807i
$603$	−3.63507e6	+	2.64103e6i	−0.407117	+	0.295788i
$604$	4.65322e6	−	3.38076e6i	0.518993	−	0.377070i
$605$	−3.80949e6	−	1.92490e6i	−0.423134	−	0.213806i
$606$	417831.	+	303572.i	0.0462188	+	0.0335799i
$607$	−6.83460e6			−0.752907			−0.376454	−	0.926435i	$-0.622857\pi$
$607$	−6.83460e6			−0.752907			−0.376454	+	0.926435i	$0.622857\pi$
$608$	939296.	+	682439.i	0.103049	+	0.0748695i
$609$	−1.98177e6	+	6.09927e6i	−0.216526	+	0.666400i
$610$	−6.98354e6	−	3.52873e6i	−0.759891	−	0.383967i
$611$	5.28798e6	+	1.62747e7i	0.573042	+	1.76364i
$612$	466436.	−	1.43554e6i	0.0503400	−	0.154931i
$613$	275091.	−	846642.i	0.0295682	−	0.0910015i	−0.935183	−	0.354164i	$-0.884765\pi$
$613$	275091.	−	846642.i	0.0295682	−	0.0910015i	0.964752	+	0.263162i	$0.0847655\pi$
$614$	2.69907e6	+	8.30688e6i	0.288930	+	0.889236i
$615$	1.95217e6	−	1.96536e6i	0.208127	−	0.209534i
$616$	1.79867e6	−	5.53575e6i	0.190985	−	0.587793i
$617$	1.50750e7	+	1.09526e7i	1.59421	+	1.15826i	0.897607	+	0.440798i	$0.145304\pi$
$617$	1.50750e7	+	1.09526e7i	1.59421	+	1.15826i	0.696599	+	0.717461i	$0.254696\pi$
$618$	2.48498e6			0.261729
$619$	−5.06819e6	−	3.68226e6i	−0.531651	−	0.386267i	0.289324	−	0.957231i	$-0.406569\pi$
$619$	−5.06819e6	−	3.68226e6i	−0.531651	−	0.386267i	−0.820975	+	0.570964i	$0.806569\pi$
$620$	−4.22379e6	−	8.22112e6i	−0.441289	−	0.858918i
$621$	978670.	−	711046.i	0.101837	−	0.0739892i
$622$	2.57395e6	−	1.87008e6i	0.266762	−	0.193814i
$623$	−3.75353e6	−	1.15522e7i	−0.387453	−	1.19246i
$624$	−2.29039e6			−0.235476
$625$	−3.14255e6	−	9.24618e6i	−0.321797	−	0.946809i
$626$	−6.30513e6			−0.643070
$627$	1.53643e6	+	4.72864e6i	0.156079	+	0.480361i
$628$	4.31686e6	−	3.13638e6i	0.436786	−	0.317343i
$629$	−3.67676e6	+	2.67133e6i	−0.370544	+	0.269216i
$630$	1.54498e6	+	3.00711e6i	0.155085	+	0.301855i
$631$	−9.78772e6	−	7.11120e6i	−0.978607	−	0.711000i	−0.0212102	−	0.999775i	$-0.506752\pi$
$631$	−9.78772e6	−	7.11120e6i	−0.978607	−	0.711000i	−0.957397	+	0.288775i	$0.906752\pi$
$632$	2.75816e6			0.274679
$633$	2.28394e6	+	1.65938e6i	0.226556	+	0.164603i
$634$	−1.62862e6	+	5.01236e6i	−0.160915	+	0.495244i
$635$	9.03474e6	−	9.09578e6i	0.889162	−	0.895170i
$636$	−977132.	−	3.00730e6i	−0.0957879	−	0.294805i
$637$	5.53997e6	−	1.70503e7i	0.540952	−	1.66488i
$638$	2.29915e6	−	7.07606e6i	0.223623	−	0.688240i
$639$	−1.33714e6	−	4.11531e6i	−0.129547	−	0.398703i
$640$	−817462.	−	413057.i	−0.0788893	−	0.0398621i
$641$	1.20024e6	−	3.69396e6i	0.115378	−	0.355097i	−0.876648	−	0.481133i	$-0.840225\pi$
$641$	1.20024e6	−	3.69396e6i	0.115378	−	0.355097i	0.992026	+	0.126036i	$0.0402254\pi$
$642$	6.62867e6	+	4.81601e6i	0.634730	+	0.461158i
$643$	−4.67755e6			−0.446161			−0.223080	−	0.974800i	$-0.571611\pi$
$643$	−4.67755e6			−0.446161			−0.223080	+	0.974800i	$0.571611\pi$
$644$	−4.00937e6	−	2.91298e6i	−0.380944	−	0.276772i
$645$	5.78082e6	+	2.92100e6i	0.547130	+	0.276460i
$646$	4.27334e6	−	3.10476e6i	0.402889	−	0.292716i
$647$	685444.	−	498004.i	0.0643741	−	0.0467706i	−0.555133	−	0.831762i	$-0.687333\pi$
$647$	685444.	−	498004.i	0.0643741	−	0.0467706i	0.619507	+	0.784991i	$0.287333\pi$
$648$	129757.	+	399352.i	0.0121393	+	0.0373610i
$649$	−9.10723e6			−0.848739
$650$	−7.23605e6	+	1.01019e7i	−0.671766	+	0.937822i
$651$	1.73597e7			1.60543
$652$	2.30940e6	+	7.10760e6i	0.212755	+	0.654793i
$653$	−9.80057e6	+	7.12053e6i	−0.899432	+	0.653476i	−0.938320	−	0.345768i	$-0.887618\pi$
$653$	−9.80057e6	+	7.12053e6i	−0.899432	+	0.653476i	0.0388880	+	0.999244i	$0.487618\pi$
$654$	2.03754e6	−	1.48036e6i	0.186278	−	0.135339i
$655$	−1.06365e6	+	6.86512e6i	−0.0968710	+	0.625237i
$656$	−1.14033e6	−	828496.i	−0.103459	−	0.0751676i
$657$	−4.94078e6			−0.446563
$658$	−1.03979e7	−	7.55452e6i	−0.936226	−	0.680208i
$659$	−1.90798e6	+	5.87215e6i	−0.171143	+	0.526725i	−0.999436	−	0.0335702i	$-0.989312\pi$
$659$	−1.90798e6	+	5.87215e6i	−0.171143	+	0.526725i	0.828293	+	0.560295i	$0.189312\pi$
$660$	−1.79240e6	−	3.48870e6i	−0.160168	−	0.311748i
$661$	2.00518e6	+	6.17132e6i	0.178505	+	0.549382i	0.999776	−	0.0211560i	$-0.00673468\pi$
$661$	2.00518e6	+	6.17132e6i	0.178505	+	0.549382i	−0.821271	+	0.570538i	$0.806735\pi$
$662$	3.07233e6	−	9.45566e6i	0.272473	−	0.838585i
$663$	−3.22000e6	+	9.91014e6i	−0.284493	+	0.875580i
$664$	2.05042e6	+	6.31053e6i	0.180477	+	0.555451i
$665$	−1.81140e6	+	1.16914e7i	−0.158841	+	1.02521i
$666$	390689.	−	1.20242e6i	0.0341307	−	0.105044i
$667$	−5.12497e6	−	3.72351e6i	−0.446043	−	0.324069i
$668$	−2.56492e6			−0.222399
$669$	6.95074e6	+	5.05001e6i	0.600435	+	0.436241i
$670$	1.22445e7	−	1.98162e6i	1.05379	−	0.170543i
$671$	−1.37933e7	+	1.00214e7i	−1.18267	+	0.859257i
$672$	1.39170e6	−	1.01113e6i	0.118884	−	0.0863744i
$673$	6.44678e6	+	1.98411e7i	0.548662	+	1.68861i	0.712120	+	0.702058i	$0.247735\pi$
$673$	6.44678e6	+	1.98411e7i	0.548662	+	1.68861i	−0.163458	+	0.986550i	$0.552265\pi$
$674$	1.49130e7			1.26449
$675$	2.17132e6	+	689374.i	0.183427	+	0.0582365i
$676$	9.87081e6			0.830780
$677$	122537.	+	377129.i	0.0102753	+	0.0316241i	0.956063	−	0.293162i	$-0.0947076\pi$
$677$	122537.	+	377129.i	0.0102753	+	0.0316241i	−0.945787	+	0.324786i	$0.894708\pi$
$678$	3.08719e6	−	2.24298e6i	0.257922	−	0.187392i
$679$	2.78798e6	−	2.02559e6i	0.232068	−	0.168607i
$680$	−2.93648e6	+	2.95632e6i	−0.243531	+	0.245177i
$681$	3.27214e6	+	2.37735e6i	0.270374	+	0.196438i
$682$	−2.01398e7			−1.65804
$683$	−6.23274e6	−	4.52835e6i	−0.511243	−	0.371440i	0.302052	−	0.953292i	$-0.402328\pi$
$683$	−6.23274e6	−	4.52835e6i	−0.511243	−	0.371440i	−0.813295	+	0.581852i	$0.802328\pi$
$684$	−454080.	+	1.39751e6i	−0.0371101	+	0.114213i
$685$	−7.45784e6	+	1.20696e6i	−0.607277	+	0.0982803i
$686$	283157.	+	871469.i	0.0229730	+	0.0707036i
$687$	1.40192e6	−	4.31468e6i	0.113327	−	0.348784i
$688$	1.01841e6	−	3.13434e6i	0.0820258	−	0.252449i
$689$	6.74555e6	+	2.07607e7i	0.541339	+	1.66607i
$690$	−3.29659e6	+	533512.i	−0.263598	+	0.0426600i
$691$	−3.64517e6	+	1.12187e7i	−0.290417	+	0.893813i	0.694305	+	0.719681i	$0.255712\pi$
$691$	−3.64517e6	+	1.12187e7i	−0.290417	+	0.893813i	−0.984722	+	0.174132i	$0.944288\pi$
$692$	4.96599e6	+	3.60800e6i	0.394222	+	0.286419i
$693$	7.36673e6			0.582696
$694$	1.16143e7	+	8.43825e6i	0.915362	+	0.665049i
$695$	7.96968e6	−	8.02353e6i	0.625863	−	0.630091i
$696$	1.77894e6	−	1.29248e6i	0.139200	−	0.101135i
$697$	−5.18792e6	+	3.76925e6i	−0.404494	+	0.293882i
$698$	2.71592e6	+	8.35873e6i	0.210998	+	0.649384i
$699$	−6.31530e6			−0.488879
$700$	−62844.6	−	9.33270e6i	−0.00484756	−	0.719883i
$701$	−1.14421e7			−0.879449			−0.439725	−	0.898133i	$-0.644924\pi$
$701$	−1.14421e7			−0.879449			−0.439725	+	0.898133i	$0.644924\pi$
$702$	−895770.	−	2.75690e6i	−0.0686047	−	0.211143i
$703$	3.57937e6	−	2.60056e6i	0.273161	−	0.198463i
$704$	−1.61458e6	+	1.17306e6i	−0.122780	+	0.0892051i
$705$	−8.54937e6	+	1.38361e6i	−0.647831	+	0.104843i
$706$	−7.25707e6	−	5.27257e6i	−0.547961	−	0.398117i
$707$	2.67786e6			0.201483
$708$	−2.17753e6	−	1.58207e6i	−0.163260	−	0.118615i
$709$	4.61543e6	−	1.42048e7i	0.344823	−	1.06126i	−0.616855	−	0.787077i	$-0.711593\pi$
$709$	4.61543e6	−	1.42048e7i	0.344823	−	1.06126i	0.961678	−	0.274181i	$-0.0884066\pi$
$710$	−1.82892e6	+	1.18044e7i	−0.136160	+	0.878818i
$711$	1.07871e6	+	3.31994e6i	0.0800262	+	0.246295i
$712$	−1.28698e6	+	3.96092e6i	−0.0951420	+	0.292817i
$713$	−5.29891e6	+	1.63084e7i	−0.390358	+	1.20140i
$714$	−2.41844e6	−	7.44321e6i	−0.177538	−	0.546405i
$715$	1.23737e7	+	2.40839e7i	0.905178	+	1.76182i
$716$	−295531.	+	909551.i	−0.0215437	+	0.0663047i
$717$	−131734.	−	95710.3i	−0.00956974	−	0.00695282i
$718$	7.04006e6			0.509642
$719$	1.80640e7	+	1.31243e7i	1.30315	+	0.946790i	0.999981	−	0.00614811i	$-0.00195702\pi$
$719$	1.80640e7	+	1.31243e7i	1.30315	+	0.946790i	0.303164	+	0.952938i	$0.401957\pi$
$720$	177480.	−	1.14551e6i	0.0127590	−	0.0823508i
$721$	1.04238e7	−	7.57333e6i	0.746771	−	0.542561i
$722$	3.85269e6	−	2.79914e6i	0.275056	−	0.199840i
$723$	3.92709e6	+	1.20864e7i	0.279399	+	0.859903i
$724$	−7.79464e6			−0.552649
$725$	−80331.0	−	1.19295e7i	−0.00567595	−	0.842903i
$726$	−2.74866e6			−0.193544
$727$	7.05657e6	+	2.17179e7i	0.495174	+	1.52399i	0.816686	+	0.577082i	$0.195809\pi$
$727$	7.05657e6	+	2.17179e7i	0.495174	+	1.52399i	−0.321513	+	0.946905i	$0.604191\pi$
$728$	−9.60751e6	+	6.98027e6i	−0.671866	+	0.488139i
$729$	−429945.	+	312373.i	−0.0299636	+	0.0217698i
$730$	1.21736e7	+	6.15122e6i	0.845496	+	0.427222i
$731$	−1.21300e7	−	8.81297e6i	−0.839591	−	0.609998i
$732$	−5.03884e6			−0.347578
$733$	−1.07969e7	−	7.84444e6i	−0.742234	−	0.539264i	0.151176	−	0.988507i	$-0.451694\pi$
$733$	−1.07969e7	−	7.84444e6i	−0.742234	−	0.539264i	−0.893410	+	0.449242i	$0.851694\pi$
$734$	−4.49244e6	+	1.38263e7i	−0.307781	+	0.947254i
$735$	8.09821e6	+	4.09196e6i	0.552930	+	0.279391i
$736$	525090.	+	1.61606e6i	0.0357305	+	0.109967i
$737$	8.35209e6	−	2.57051e7i	0.566404	−	1.74321i
$738$	551263.	−	1.69661e6i	0.0372579	−	0.114668i
$739$	−4.50682e6	−	1.38706e7i	−0.303570	−	0.934293i	−0.980207	−	0.197976i	$-0.936563\pi$
$739$	−4.50682e6	−	1.38706e7i	−0.303570	−	0.934293i	0.676636	−	0.736317i	$-0.263437\pi$
$740$	−2.45961e6	+	2.47623e6i	−0.165115	+	0.166231i
$741$	3.13470e6	−	9.64762e6i	0.209725	−	0.645468i
$742$	−1.32640e7	−	9.63683e6i	−0.884430	−	0.642576i
$743$	−1.32763e6			−0.0882276			−0.0441138	−	0.999027i	$-0.514046\pi$
$743$	−1.32763e6			−0.0882276			−0.0441138	+	0.999027i	$0.514046\pi$
$744$	−4.81541e6	−	3.49860e6i	−0.318934	−	0.231719i
$745$	1.52916e6	+	2.97633e6i	0.100940	+	0.196468i
$746$	−9.11429e6	+	6.62192e6i	−0.599619	+	0.435649i
$747$	−6.79395e6	+	4.93609e6i	−0.445472	+	0.323655i
$748$	2.80575e6	+	8.63522e6i	0.183356	+	0.564312i
$749$	4.24828e7			2.76700
$750$	−4.49164e6	−	4.40181e6i	−0.291576	−	0.285745i
$751$	1.98859e7			1.28661			0.643303	−	0.765612i	$-0.277564\pi$
$751$	1.98859e7			1.28661			0.643303	+	0.765612i	$0.277564\pi$
$752$	1.36177e6	+	4.19109e6i	0.0878130	+	0.270261i
$753$	−5.96106e6	+	4.33096e6i	−0.383121	+	0.278354i
$754$	−1.22808e7	+	8.92252e6i	−0.786680	+	0.571556i
$755$	−9.18345e6	−	1.78745e7i	−0.586325	−	1.14121i
$756$	1.76138e6	+	1.27971e6i	0.112085	+	0.0814345i
$757$	−6.61009e6			−0.419245			−0.209622	−	0.977782i	$-0.567223\pi$
$757$	−6.61009e6			−0.419245			−0.209622	+	0.977782i	$0.567223\pi$
$758$	−1.20742e7	−	8.77245e6i	−0.763285	−	0.554559i
$759$	−2.24864e6	+	6.92059e6i	−0.141682	+	0.436052i
$760$	2.85870e6	−	2.87801e6i	0.179529	−	0.180742i
$761$	4.53632e6	+	1.39613e7i	0.283950	+	0.873908i	0.986711	+	0.162483i	$0.0519501\pi$
$761$	4.53632e6	+	1.39613e7i	0.283950	+	0.873908i	−0.702761	+	0.711426i	$0.748050\pi$
$762$	2.55128e6	−	7.85202e6i	0.159173	−	0.489885i
$763$	4.03530e6	−	1.24194e7i	0.250937	−	0.772304i
$764$	−2.29957e6	−	7.07734e6i	−0.142532	−	0.438669i
$765$	−4.70692e6	−	2.37837e6i	−0.290793	−	0.146935i
$766$	−1.91510e6	+	5.89406e6i	−0.117928	+	0.362946i
$767$	1.50324e7	+	1.09217e7i	0.922654	+	0.670348i
$768$	−589824.			−0.0360844
$769$	3.44648e6	+	2.50401e6i	0.210165	+	0.152693i	0.687888	−	0.725817i	$-0.258538\pi$
$769$	3.44648e6	+	2.50401e6i	0.210165	+	0.152693i	−0.477724	+	0.878510i	$0.658538\pi$
$770$	−1.81509e7	−	9.17149e6i	−1.10324	−	0.557459i
$771$	−1.13680e7	+	8.25936e6i	−0.688731	+	0.500392i
$772$	2.90529e6	−	2.11082e6i	0.175447	−	0.127470i
$773$	−7.50553e6	−	2.30996e7i	−0.451786	−	1.39045i	−0.874867	−	0.484362i	$-0.839052\pi$
$773$	−7.50553e6	−	2.30996e7i	−0.451786	−	1.39045i	0.423081	−	0.906092i	$-0.360948\pi$
$774$	4.17104e6			0.250260
$775$	−3.06442e7	+	1.01855e7i	−1.83271	+	0.609158i
$776$	−1.18159e6			−0.0704386
$777$	−2.02570e6	−	6.23447e6i	−0.120371	−	0.370465i
$778$	−443736.	+	322393.i	−0.0262830	+	0.0190957i
$779$	5.05050e6	−	3.66940e6i	0.298188	−	0.216646i
$780$	−1.22522e6	+	7.90793e6i	−0.0721067	+	0.465400i
$781$	2.10577e7	+	1.52993e7i	1.23533	+	0.897521i
$782$	7.73064e6			0.452063
$783$	2.25148e6	+	1.63579e6i	0.131239	+	0.0953507i
$784$	1.42666e6	−	4.39081e6i	0.0828954	−	0.255126i
$785$	−8.51961e6	−	1.65824e7i	−0.493453	−	0.960448i
$786$	1.38248e6	+	4.25483e6i	0.0798183	+	0.245655i
$787$	−3.74028e6	+	1.15114e7i	−0.215262	+	0.662508i	0.783873	+	0.620921i	$0.213241\pi$
$787$	−3.74028e6	+	1.15114e7i	−0.215262	+	0.662508i	−0.999135	+	0.0415866i	$0.986759\pi$
$788$	−4.03928e6	+	1.24316e7i	−0.231733	+	0.713201i
$789$	−4.03813e6	−	1.24281e7i	−0.230934	−	0.710742i
$790$	1.47544e6	−	9.52298e6i	0.0841113	−	0.542882i
$791$	6.11410e6	−	1.88173e7i	0.347449	−	1.06934i
$792$	−2.04346e6	−	1.48466e6i	−0.115758	−	0.0841034i
$793$	3.47852e7			1.96432
$794$	−1.03910e6	−	754953.i	−0.0584935	−	0.0424980i
$795$	−1.09059e7	+	1.76499e6i	−0.611989	+	0.0990429i
$796$	1.07785e7	−	7.83102e6i	0.602941	−	0.438062i
$797$	1.14010e7	−	8.28329e6i	0.635764	−	0.461910i	−0.222628	−	0.974903i	$-0.571464\pi$
$797$	1.14010e7	−	8.28329e6i	0.635764	−	0.461910i	0.858392	+	0.512994i	$0.171464\pi$
$798$	2.35438e6	+	7.24604e6i	0.130879	+	0.402804i
$799$	2.00487e7			1.11101
$800$	−1.86344e6	+	2.60146e6i	−0.102941	+	0.143712i
$801$	−5.27102e6			−0.290278
$802$	6.03414e6	+	1.85712e7i	0.331268	+	1.01954i
$803$	2.40443e7	−	1.74692e7i	1.31590	−	0.956057i
$804$	6.46235e6	−	4.69517e6i	0.352574	−	0.256160i
$805$	−1.22023e7	+	1.22847e7i	−0.663669	+	0.668153i
$806$	3.32428e7	+	2.41523e7i	1.80244	+	1.30955i
$807$	−2.79379e6			−0.151011
$808$	−742810.	−	539683.i	−0.0400267	−	0.0290811i
$809$	−2.18908e6	+	6.73730e6i	−0.117595	+	0.361922i	−0.992480	−	0.122411i	$-0.960937\pi$
$809$	−2.18908e6	+	6.73730e6i	−0.117595	+	0.361922i	0.874884	+	0.484332i	$0.160937\pi$
$810$	1.44824e6	−	234380.i	0.0775583	−	0.0125519i
$811$	3.70599e6	+	1.14059e7i	0.197857	+	0.608942i	0.999931	+	0.0117177i	$0.00372994\pi$
$811$	3.70599e6	+	1.14059e7i	0.197857	+	0.608942i	−0.802074	+	0.597225i	$0.796270\pi$
$812$	3.52315e6	−	1.08432e7i	0.187517	−	0.577119i
$813$	4.73559e6	−	1.45747e7i	0.251274	−	0.773343i
$814$	2.35011e6	+	7.23291e6i	0.124316	+	0.382606i
$815$	2.57755e7	−	4.17145e6i	1.35929	−	0.219985i
$816$	−829219.	+	2.55207e6i	−0.0435957	+	0.134174i
$817$	1.18087e7	+	8.57952e6i	0.618937	+	0.449684i
$818$	−7.80710e6			−0.407950
$819$	−1.21595e7	−	8.83440e6i	−0.633441	−	0.460222i
$820$	−3.47052e6	+	3.49397e6i	−0.180244	+	0.181461i
$821$	1.31456e7	−	9.55087e6i	0.680650	−	0.494521i	−0.192923	−	0.981214i	$-0.561797\pi$
$821$	1.31456e7	−	9.55087e6i	0.680650	−	0.494521i	0.873573	+	0.486693i	$0.161797\pi$
$822$	−3.93607e6	+	2.85972e6i	−0.203181	+	0.147620i
$823$	3.27167e6	+	1.00692e7i	0.168372	+	0.518196i	0.999269	−	0.0382303i	$-0.0121721\pi$
$823$	3.27167e6	+	1.00692e7i	0.168372	+	0.518196i	−0.830897	+	0.556427i	$0.812172\pi$
$824$	−4.41775e6			−0.226664
$825$	−1.30041e7	+	4.32232e6i	−0.665190	+	0.221096i
$826$	−1.39557e7			−0.711705
$827$	3.51615e6	+	1.08216e7i	0.178774	+	0.550209i	0.999786	−	0.0207020i	$-0.00659014\pi$
$827$	3.51615e6	+	1.08216e7i	0.178774	+	0.550209i	−0.821012	+	0.570911i	$0.806590\pi$
$828$	−1.73986e6	+	1.26408e6i	−0.0881938	+	0.0640766i
$829$	244334.	−	177519.i	0.0123480	−	0.00897137i	−0.581594	−	0.813479i	$-0.697571\pi$
$829$	244334.	−	177519.i	0.0123480	−	0.00897137i	0.593942	+	0.804508i	$0.297571\pi$
$830$	2.28850e7	−	3.70365e6i	1.15307	−	0.186610i
$831$	−1.07788e7	−	7.83125e6i	−0.541461	−	0.393394i
$832$	4.07180e6			0.203929
$833$	−1.69926e7	−	1.23459e7i	−0.848492	−	0.616466i
$834$	2.25052e6	−	6.92639e6i	0.112039	−	0.344819i
$835$	−1.37207e6	+	8.85580e6i	−0.0681022	+	0.439553i
$836$	−2.73143e6	−	8.40648e6i	−0.135168	−	0.416005i
$837$	2.32789e6	−	7.16452e6i	0.114855	−	0.353487i
$838$	1.14298e6	−	3.51773e6i	0.0562249	−	0.173042i
$839$	−7.38266e6	−	2.27215e7i	−0.362083	−	1.11438i	−0.951788	−	0.306757i	$-0.900756\pi$
$839$	−7.38266e6	−	2.27215e7i	−0.362083	−	1.11438i	0.589705	−	0.807619i	$-0.299244\pi$
$840$	−2.74662e6	−	5.34598e6i	−0.134308	−	0.261414i
$841$	−1.83483e6	+	5.64702e6i	−0.0894552	+	0.275315i
$842$	−6.84116e6	−	4.97039e6i	−0.332544	−	0.241608i
$843$	2.90368e6			0.140728
$844$	−4.06034e6	−	2.95001e6i	−0.196203	−	0.142550i
$845$	5.28027e6	−	3.40806e7i	0.254398	−	1.64197i
$846$	−4.51215e6	+	3.27827e6i	−0.216749	+	0.157478i
$847$	−1.15298e7	+	8.37692e6i	−0.552223	+	0.401214i
$848$	1.73712e6	+	5.34632e6i	0.0829547	+	0.255308i
$849$	−2.28647e6			−0.108867
$850$	8.63634e6	+	1.17201e7i	0.409999	+	0.556397i
$851$	6.47523e6			0.306501
$852$	2.37714e6	+	7.31610e6i	0.112191	+	0.345287i
$853$	−702167.	+	510154.i	−0.0330421	+	0.0240065i	−0.604184	−	0.796845i	$-0.706501\pi$
$853$	−702167.	+	510154.i	−0.0330421	+	0.0240065i	0.571142	+	0.820852i	$0.306501\pi$
$854$	−2.11365e7	+	1.53565e7i	−0.991717	+	0.720525i
$855$	4.58224e6	+	2.31537e6i	0.214369	+	0.108319i
$856$	−1.17843e7	−	8.56180e6i	−0.549692	−	0.399375i
$857$	−1.31106e6			−0.0609778			−0.0304889	−	0.999535i	$-0.509706\pi$
$857$	−1.31106e6			−0.0609778			−0.0304889	+	0.999535i	$0.509706\pi$
$858$	1.41068e7	+	1.02492e7i	0.654201	+	0.475305i
$859$	1.73495e6	−	5.33963e6i	0.0802240	−	0.246904i	−0.902898	−	0.429855i	$-0.858565\pi$
$859$	1.73495e6	−	5.33963e6i	0.0802240	−	0.246904i	0.983122	+	0.182951i	$0.0585648\pi$
$860$	−1.02770e7	−	5.19289e6i	−0.473828	−	0.239421i
$861$	−2.85827e6	−	8.79685e6i	−0.131400	−	0.404408i
$862$	6.92515e6	−	2.13134e7i	0.317440	−	0.976979i
$863$	−1.19306e7	+	3.67187e7i	−0.545301	+	1.67827i	0.174971	+	0.984574i	$0.444017\pi$
$863$	−1.19306e7	+	3.67187e7i	−0.545301	+	1.67827i	−0.720272	+	0.693692i	$0.755983\pi$
$864$	−230680.	−	709960.i	−0.0105130	−	0.0323556i
$865$	1.51137e7	−	1.52158e7i	0.686801	−	0.691441i
$866$	−1.40165e6	+	4.31385e6i	−0.0635106	+	0.195465i
$867$	−461567.	−	335348.i	−0.0208539	−	0.0151512i
$868$	−3.08617e7			−1.39034
$869$	−1.69879e7	−	1.23424e7i	−0.763115	−	0.554435i
$870$	−3.51087e6	−	6.83349e6i	−0.157259	−	0.306087i
$871$	−4.46122e7	+	3.24127e7i	−1.99255	+	1.44767i
$872$	−3.62229e6	+	2.63175e6i	−0.161322	+	0.117207i
$873$	−462118.	−	1.42225e6i	−0.0205219	−	0.0631598i
$874$	−7.52586e6			−0.333256
$875$	−3.22563e7	−	4.77543e6i	−1.42428	−	0.210859i
$876$	8.78362e6			0.386735
$877$	−1.37231e7	−	4.22353e7i	−0.602494	−	1.85429i	−0.513176	−	0.858283i	$-0.671531\pi$
$877$	−1.37231e7	−	4.22353e7i	−0.602494	−	1.85429i	−0.0893181	−	0.996003i	$-0.528469\pi$
$878$	−2.55921e6	+	1.85938e6i	−0.112039	+	0.0814013i
$879$	−7.75047e6	+	5.63104e6i	−0.338342	+	0.245820i
$880$	3.18649e6	+	6.20213e6i	0.138709	+	0.269981i
$881$	−1.84845e7	−	1.34298e7i	−0.802358	−	0.582947i	0.109247	−	0.994015i	$-0.465156\pi$
$881$	−1.84845e7	−	1.34298e7i	−0.802358	−	0.582947i	−0.911605	+	0.411067i	$0.865156\pi$
$882$	5.84310e6			0.252914
$883$	−7.84526e6	−	5.69991e6i	−0.338614	−	0.246018i	0.405463	−	0.914112i	$-0.367110\pi$
$883$	−7.84526e6	−	5.69991e6i	−0.338614	−	0.246018i	−0.744077	+	0.668094i	$0.767110\pi$
$884$	5.72444e6	−	1.76180e7i	0.246378	−	0.758274i
$885$	−6.62718e6	+	6.67195e6i	−0.284427	+	0.286349i
$886$	−3.18818e6	−	9.81221e6i	−0.136445	−	0.419935i
$887$	−1.10561e6	+	3.40271e6i	−0.0471837	+	0.145217i	−0.971873	−	0.235507i	$-0.924325\pi$
$887$	−1.10561e6	+	3.40271e6i	−0.0471837	+	0.145217i	0.924689	+	0.380723i	$0.124325\pi$
$888$	−694558.	+	2.13763e6i	−0.0295581	+	0.0909704i
$889$	−1.32282e7	−	4.07123e7i	−0.561368	−	1.72771i
$890$	1.29873e7	+	6.56236e6i	0.549595	+	0.277706i
$891$	987860.	−	3.04032e6i	0.0416870	−	0.128299i
$892$	−1.23569e7	−	8.97779e6i	−0.519992	−	0.377796i
$893$	−1.95176e7			−0.819025
$894$	1.74335e6	+	1.26662e6i	0.0729525	+	0.0530031i
$895$	2.98228e6	+	1.50692e6i	0.124449	+	0.0628830i
$896$	−2.47414e6	+	1.79757e6i	−0.102957	+	0.0748024i
$897$	1.20110e7	−	8.72648e6i	0.498422	−	0.362124i
$898$	−5.42308e6	−	1.66905e7i	−0.224417	−	0.690684i
$899$	−3.94489e7			−1.62793
$900$	−3.86012e6	−	1.22555e6i	−0.158853	−	0.0504343i
$901$	2.55748e7			1.04954
$902$	3.31602e6	+	1.02057e7i	0.135706	+	0.417661i
$903$	1.74963e7	−	1.27118e7i	0.714047	−	0.518786i
$904$	−5.48834e6	+	3.98751e6i	−0.223367	+	0.162286i
$905$	−4.16965e6	+	2.69122e7i	−0.169230	+	1.09227i
$906$	−1.04697e7	−	7.60672e6i	−0.423756	−	0.307877i
$907$	3.25457e7			1.31364			0.656819	−	0.754048i	$-0.271902\pi$
$907$	3.25457e7			1.31364			0.656819	+	0.754048i	$0.271902\pi$
$908$	−5.81714e6	−	4.22640e6i	−0.234150	−	0.170120i
$909$	359094.	−	1.10518e6i	0.0144144	−	0.0443631i
$910$	1.89611e7	+	3.69055e7i	0.759031	+	1.47736i
$911$	2.48257e6	+	7.64056e6i	0.0991072	+	0.305020i	0.988302	−	0.152508i	$-0.0487349\pi$
$911$	2.48257e6	+	7.64056e6i	0.0991072	+	0.305020i	−0.889195	+	0.457528i	$0.848735\pi$
$912$	807253.	−	2.48447e6i	0.0321383	−	0.0989115i
$913$	1.56101e7	−	4.80428e7i	0.619766	−	1.90744i
$914$	−5.16897e6	−	1.59085e7i	−0.204663	−	0.629887i
$915$	−2.69547e6	+	1.73974e7i	−0.106434	+	0.686960i
$916$	−2.49231e6	+	7.67054e6i	−0.0981439	+	0.302056i
$917$	1.87663e7	+	1.36345e7i	0.736979	+	0.535447i
$918$	−3.39619e6			−0.133010
$919$	2.68461e7	+	1.95048e7i	1.04856	+	0.761822i	0.971938	−	0.235239i	$-0.0755871\pi$
$919$	2.68461e7	+	1.95048e7i	1.04856	+	0.761822i	0.0766201	+	0.997060i	$0.475587\pi$
$920$	5.86060e6	−	948465.i	0.228282	−	0.0369447i
$921$	1.58991e7	−	1.15514e7i	0.617622	−	0.448729i
$922$	8.12422e6	−	5.90259e6i	0.314742	−	0.228673i
$923$	−1.64104e7	−	5.05061e7i	−0.634038	−	1.95137i
$924$	−1.30964e7			−0.504629
$925$	7.23385e6	+	9.81684e6i	0.277981	+	0.377240i
$926$	−2.87995e7			−1.10372
$927$	−1.72778e6	−	5.31756e6i	−0.0660373	−	0.203242i
$928$	−3.16257e6	+	2.29774e6i	−0.120551	+	0.0875852i
$929$	−3.16517e7	+	2.29963e7i	−1.20326	+	0.874217i	−0.994601	−	0.103772i	$-0.966909\pi$
$929$	−3.16517e7	+	2.29963e7i	−1.20326	+	0.874217i	−0.208656	+	0.977989i	$0.566909\pi$
$930$	−1.46554e7	+	1.47544e7i	−0.555637	+	0.559391i
$931$	1.65425e7	+	1.20188e7i	0.625499	+	0.454452i
$932$	1.12272e7			0.423381
$933$	−5.79138e6	−	4.20769e6i	−0.217810	−	0.158248i
$934$	5.65926e6	−	1.74174e7i	0.212272	−	0.653305i
$935$	3.13154e7	−	5.06801e6i	1.17146	−	0.189587i
$936$	1.59248e6	+	4.90115e6i	0.0594134	+	0.182856i
$937$	1.06006e7	−	3.26253e7i	0.394440	−	1.21396i	−0.534956	−	0.844880i	$-0.679672\pi$
$937$	1.06006e7	−	3.26253e7i	0.394440	−	1.21396i	0.929397	−	0.369082i	$-0.120328\pi$
$938$	1.27985e7	−	3.93898e7i	0.474955	−	1.46176i
$939$	4.38389e6	+	1.34922e7i	0.162254	+	0.499366i
$940$	1.51989e7	−	2.45975e6i	0.561038	−	0.0907970i
$941$	−7.55669e6	+	2.32571e7i	−0.278200	+	0.856212i	0.710155	+	0.704046i	$0.248625\pi$
$941$	−7.55669e6	+	2.32571e7i	−0.278200	+	0.856212i	−0.988355	+	0.152166i	$0.951375\pi$
$942$	−9.71293e6	−	7.05686e6i	−0.356634	−	0.259110i
$943$	9.13656e6			0.334583
$944$	3.87116e6	+	2.81256e6i	0.141387	+	0.102724i
$945$	5.36065e6	−	5.39687e6i	0.195271	−	0.196590i
$946$	−2.02983e7	+	1.47476e7i	−0.737449	+	0.535788i
$947$	2.79577e7	−	2.03124e7i	1.01304	−	0.736016i	0.0481944	−	0.998838i	$-0.484653\pi$
$947$	2.79577e7	−	2.03124e7i	1.01304	−	0.736016i	0.964844	+	0.262822i	$0.0846533\pi$
$948$	−1.91771e6	−	5.90212e6i	−0.0693047	−	0.213298i
$949$	−6.06370e7			−2.18561
$950$	−8.40757e6	−	1.14097e7i	−0.302247	−	0.410170i
$951$	1.18582e7			0.425175
$952$	4.29946e6	+	1.32324e7i	0.153752	+	0.473200i
$953$	−1.42579e7	+	1.03589e7i	−0.508537	+	0.369474i	−0.812268	−	0.583284i	$-0.801767\pi$
$953$	−1.42579e7	+	1.03589e7i	−0.508537	+	0.369474i	0.303731	+	0.952758i	$0.401767\pi$
$954$	−5.75587e6	+	4.18189e6i	−0.204758	+	0.148765i
$955$	−2.56658e7	+	4.15369e6i	−0.910639	+	0.147376i
$956$	234194.	+	170152.i	0.00828763	+	0.00602132i
$957$	−1.67405e7			−0.590864
$958$	3.09855e7	+	2.25123e7i	1.09080	+	0.792513i
$959$	−7.79528e6	+	2.39914e7i	−0.273707	+	0.842382i
$960$	−315519.	+	2.03646e6i	−0.0110496	+	0.0713179i
$961$	2.41512e7	+	7.43297e7i	0.843587	+	2.59629i
$962$	4.79482e6	−	1.47570e7i	0.167046	−	0.514113i
$963$	5.69684e6	−	1.75331e7i	0.197956	−	0.609245i
$964$	−6.98150e6	−	2.14869e7i	−0.241967	−	0.744698i
$965$	−5.73379e6	−	1.11602e7i	−0.198209	−	0.385791i
$966$	−3.44574e6	+	1.06049e7i	−0.118807	+	0.365649i
$967$	1.03043e7	+	7.48654e6i	0.354367	+	0.257463i	0.750699	−	0.660644i	$-0.229717\pi$
$967$	1.03043e7	+	7.48654e6i	0.354367	+	0.257463i	−0.396331	+	0.918107i	$0.629717\pi$
$968$	4.88651e6			0.167614
$969$	−9.61500e6	−	6.98571e6i	−0.328958	−	0.239002i
$970$	−632075.	+	4.07961e6i	−0.0215695	+	0.139216i
$971$	−1.03892e7	+	7.54820e6i	−0.353618	+	0.256918i	−0.750385	−	0.661001i	$-0.770132\pi$
$971$	−1.03892e7	+	7.54820e6i	−0.353618	+	0.256918i	0.396767	+	0.917919i	$0.370132\pi$
$972$	764346.	−	555330.i	0.0259492	−	0.0188532i
$973$	−1.16688e7	−	3.59130e7i	−0.395135	−	1.21610i
$974$	−1.65545e7			−0.559139
$975$	2.66480e7	+	8.46051e6i	0.897745	+	0.285026i
$976$	8.95794e6			0.301012
$977$	1.49714e7	+	4.60771e7i	0.501793	+	1.54436i	0.806095	+	0.591786i	$0.201577\pi$
$977$	1.49714e7	+	4.60771e7i	0.501793	+	1.54436i	−0.304302	+	0.952576i	$0.598423\pi$
$978$	1.36037e7	−	9.88366e6i	0.454789	−	0.330423i
$979$	2.56514e7	−	1.86368e7i	0.855369	−	0.621462i
$980$	−1.43968e7	−	7.27459e6i	−0.478852	−	0.241960i
$981$	−4.58447e6	−	3.33081e6i	−0.152095	−	0.110504i
$982$	−1.99342e7			−0.659661
$983$	1.53240e7	+	1.11335e7i	0.505809	+	0.367492i	0.811232	−	0.584725i	$-0.198798\pi$
$983$	1.53240e7	+	1.11335e7i	0.505809	+	0.367492i	−0.305422	+	0.952217i	$0.598798\pi$
$984$	−980023.	+	3.01620e6i	−0.0322663	+	0.0993054i
$985$	4.07614e7	+	2.05964e7i	1.33862	+	0.676396i
$986$	5.49577e6	+	1.69143e7i	0.180027	+	0.554065i
$987$	−8.93620e6	+	2.75028e7i	−0.291985	+	0.898636i
$988$	−5.57280e6	+	1.71513e7i	−0.181627	+	0.558992i
$989$	6.60135e6	+	2.03169e7i	0.214606	+	0.660490i
$990$	−6.21915e6	+	6.26117e6i	−0.201671	+	0.203033i
$991$	6.48422e6	−	1.99564e7i	0.209736	−	0.645502i	−0.789749	−	0.613430i	$-0.789789\pi$
$991$	6.48422e6	−	1.99564e7i	0.209736	−	0.645502i	0.999486	−	0.0320720i	$-0.0102106\pi$
$992$	8.56073e6	+	6.21973e6i	0.276205	+	0.200675i
$993$	−2.23701e7			−0.719938
$994$	3.22682e7	+	2.34443e7i	1.03588	+	0.752611i
$995$	−2.12721e7	−	4.14036e7i	−0.681164	−	1.32581i
$996$	1.20781e7	−	8.77527e6i	0.385790	−	0.280293i
$997$	−2.09726e7	+	1.52375e7i	−0.668213	+	0.485485i	−0.869426	−	0.494063i	$-0.835511\pi$
$997$	−2.09726e7	+	1.52375e7i	−0.668213	+	0.485485i	0.201214	+	0.979547i	$0.435511\pi$
$998$	209712.	+	645426.i	0.00666494	+	0.0205126i
$999$	−2.84467e6			−0.0901816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.d.31.4	✓	28
25.21	even	5	inner	150.6.g.d.121.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.d.31.4	✓	28	1.1	even	1	trivial
150.6.g.d.121.4	yes	28	25.21	even	5	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(25.5464 + 49.7230i) q^{5} +(29.1246 + 21.1603i) q^{6} +186.658 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\)	\(q+(1.23607 + 3.80423i) q^{2} +(7.28115 - 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(25.5464 + 49.7230i) q^{5} +(29.1246 + 21.1603i) q^{6} +186.658 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(-157.581 + 158.645i) q^{10} +(150.565 + 463.393i) q^{11} +(-44.4984 + 136.952i) q^{12} +(307.191 - 945.437i) q^{13} +(230.722 + 710.090i) q^{14} +(449.045 + 226.899i) q^{15} +(79.1084 - 243.470i) q^{16} +(-942.241 - 684.578i) q^{17} +324.000 q^{18} +(917.282 + 666.444i) q^{19} +(-798.303 - 403.376i) q^{20} +(1359.09 - 987.434i) q^{21} +(-1576.74 + 1145.57i) q^{22} +(512.783 + 1578.18i) q^{23} -576.000 q^{24} +(-1819.76 + 2540.49i) q^{25} +3976.37 q^{26} +(-225.273 - 693.320i) q^{27} +(-2416.15 + 1755.44i) q^{28} +(-3088.44 + 2243.89i) q^{29} +(-308.124 + 1988.73i) q^{30} +(8360.09 + 6073.96i) q^{31} +1024.00 q^{32} +(3547.67 + 2577.53i) q^{33} +(1439.62 - 4430.68i) q^{34} +(4768.44 + 9281.21i) q^{35} +(400.486 + 1232.57i) q^{36} +(1205.83 - 3711.16i) q^{37} +(-1401.48 + 4313.32i) q^{38} +(-2764.72 - 8508.94i) q^{39} +(547.776 - 3535.53i) q^{40} +(1701.43 - 5236.46i) q^{41} +(5436.35 + 3949.74i) q^{42} +12873.6 q^{43} +(-6306.97 - 4582.28i) q^{44} +(4469.88 - 723.395i) q^{45} +(-5369.93 + 3901.49i) q^{46} +(-13926.4 + 10118.1i) q^{47} +(-711.975 - 2191.23i) q^{48} +18034.3 q^{49} +(-11913.9 - 3782.57i) q^{50} -10482.1 q^{51} +(4915.06 + 15127.0i) q^{52} +(-17765.0 + 12907.1i) q^{53} +(2359.09 - 1713.98i) q^{54} +(-19194.9 + 19324.6i) q^{55} +(-9664.62 - 7021.75i) q^{56} +10204.4 q^{57} +(-12353.8 - 8975.55i) q^{58} +(-5775.98 + 17776.6i) q^{59} +(-7946.45 + 1286.03i) q^{60} +(10813.1 + 33279.3i) q^{61} +(-12773.1 + 39311.5i) q^{62} +(4672.12 - 14379.3i) q^{63} +(1265.73 + 3895.53i) q^{64} +(54857.7 - 8878.03i) q^{65} +(-5420.35 + 16682.1i) q^{66} +(-44877.4 - 32605.3i) q^{67} +18634.8 q^{68} +(12082.4 + 8778.34i) q^{69} +(-29413.7 + 29612.4i) q^{70} +(43218.4 - 31400.0i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(-18849.2 - 58011.9i) q^{73} +15608.6 q^{74} +(189.384 + 28124.4i) q^{75} -18141.2 q^{76} +(28104.3 + 86496.0i) q^{77} +(28952.5 - 21035.2i) q^{78} +(-34865.5 + 25331.3i) q^{79} +(14127.0 - 2286.28i) q^{80} +(-5307.96 - 3856.46i) q^{81} +22023.8 q^{82} +(-83875.9 - 60939.4i) q^{83} +(-8306.00 + 25563.2i) q^{84} +(9968.45 - 64339.6i) q^{85} +(15912.6 + 48974.0i) q^{86} +(-10617.1 + 32676.2i) q^{87} +(9636.19 - 29657.1i) q^{88} +(-20109.1 - 61889.4i) q^{89} +(8277.03 + 16110.3i) q^{90} +(57339.7 - 176474. i) q^{91} +(-21479.7 - 15605.9i) q^{92} +93002.7 q^{93} +(-55705.6 - 40472.5i) q^{94} +(-9704.39 + 62635.3i) q^{95} +(7455.90 - 5417.03i) q^{96} +(14936.3 - 10851.8i) q^{97} +(22291.6 + 68606.4i) q^{98} +39466.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9	\( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) 28 * q - 28 * q^2 + 63 * q^3 - 112 * q^4 + 11 * q^5 + 252 * q^6 - 62 * q^7 - 448 * q^8 - 567 * q^9 + 44 * q^10 - 135 * q^11 + 1008 * q^12 + 616 * q^13 - 48 * q^14 + 531 * q^15 - 1792 * q^16 - 3372 * q^17 + 9072 * q^18 + 488 * q^19 - 944 * q^20 - 387 * q^21 - 1920 * q^22 - 620 * q^23 - 16128 * q^24 + 6659 * q^25 - 1616 * q^26 + 5103 * q^27 + 688 * q^28 + 5682 * q^29 + 2844 * q^30 + 3339 * q^31 + 28672 * q^32 + 4320 * q^33 + 14032 * q^34 - 23984 * q^35 - 9072 * q^36 + 4506 * q^37 - 1528 * q^38 - 5544 * q^39 - 5056 * q^40 + 44962 * q^41 - 1548 * q^42 + 38028 * q^43 - 7680 * q^44 + 9396 * q^45 + 7480 * q^46 - 58300 * q^47 + 16128 * q^48 + 114402 * q^49 + 7476 * q^50 + 2448 * q^51 + 9856 * q^52 - 138 * q^53 + 20412 * q^54 + 96850 * q^55 + 2752 * q^56 + 1908 * q^57 + 22728 * q^58 + 40245 * q^59 - 16704 * q^60 + 79380 * q^61 - 54504 * q^62 - 972 * q^63 - 28672 * q^64 + 3532 * q^65 + 4860 * q^66 - 34352 * q^67 - 4352 * q^68 - 16830 * q^69 - 69476 * q^70 + 115860 * q^71 - 36288 * q^72 - 121214 * q^73 - 37856 * q^74 + 21969 * q^75 - 3392 * q^76 + 195005 * q^77 + 14904 * q^78 + 36224 * q^79 + 29696 * q^80 - 45927 * q^81 + 34608 * q^82 + 85051 * q^83 + 1728 * q^84 + 137496 * q^85 - 18568 * q^86 + 127062 * q^87 - 8640 * q^88 - 53826 * q^89 + 3564 * q^90 - 408104 * q^91 + 29920 * q^92 - 185166 * q^93 - 233200 * q^94 - 482004 * q^95 + 64512 * q^96 - 244169 * q^97 - 395952 * q^98 + 99630 * q^99

Introduction

L-functions

Modular forms

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Database

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