LMFDB - Embedded newform 38.7.d.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9440 x^{18} + 37579488 x^{16} + 83109028728 x^{14} + 112838424559344 x^{12} + \cdots + 83\!\cdots\!96 $ x^20 + 9440x^18 + 37579488x^16 + 83109028728x^14 + 112838424559344x^12 + 97808951849137728x^10 + 54352282696688610576x^8 + 18825433555812367062720x^6 + 3765133606401310416173376x^4 + 360077534420960567854418432*x^2 + 8303121574870947536327197696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$25.0158i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.7.d.a.27.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(18.9396 - 10.9348i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-55.1543 - 95.5300i) q^{5} +(-61.8564 + 107.138i) q^{6} -148.805 q^{7} +181.019i q^{8} +(-125.361 + 217.132i) q^{9} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(18.9396 - 10.9348i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-55.1543 - 95.5300i) q^{5} +(-61.8564 + 107.138i) q^{6} -148.805 q^{7} +181.019i q^{8} +(-125.361 + 217.132i) q^{9} +(540.399 + 312.000i) q^{10} -494.107 q^{11} -699.826i q^{12} +(-1992.01 - 1150.09i) q^{13} +(728.992 - 420.884i) q^{14} +(-2089.20 - 1206.20i) q^{15} +(-512.000 - 886.810i) q^{16} +(-2820.30 - 4884.90i) q^{17} -1418.30i q^{18} +(-6514.87 - 2145.32i) q^{19} -3529.87 q^{20} +(-2818.30 + 1627.15i) q^{21} +(2420.62 - 1397.54i) q^{22} +(3206.71 - 5554.19i) q^{23} +(1979.41 + 3428.43i) q^{24} +(1728.51 - 2993.87i) q^{25} +13011.8 q^{26} +21426.1i q^{27} +(-2380.88 + 4123.80i) q^{28} +(5708.25 + 3295.66i) q^{29} +13646.6 q^{30} +25022.3i q^{31} +(5016.55 + 2896.31i) q^{32} +(-9358.18 + 5402.95i) q^{33} +(27633.2 + 15954.0i) q^{34} +(8207.23 + 14215.3i) q^{35} +(4011.57 + 6948.24i) q^{36} -16573.0i q^{37} +(37984.1 - 7916.96i) q^{38} -50303.8 q^{39} +(17292.8 - 9983.99i) q^{40} +(38905.5 - 22462.1i) q^{41} +(9204.54 - 15942.7i) q^{42} +(-31760.6 - 55011.0i) q^{43} +(-7905.71 + 13693.1i) q^{44} +27656.9 q^{45} +36279.8i q^{46} +(6405.65 - 11094.9i) q^{47} +(-19394.1 - 11197.2i) q^{48} -95506.1 q^{49} +19555.9i q^{50} +(-106831. - 61678.7i) q^{51} +(-63744.4 + 36802.8i) q^{52} +(184401. + 106464. i) q^{53} +(-60602.2 - 104966. i) q^{54} +(27252.1 + 47202.0i) q^{55} -26936.6i q^{56} +(-146847. + 30607.2i) q^{57} -37286.1 q^{58} +(198707. - 114723. i) q^{59} +(-66854.3 + 38598.4i) q^{60} +(8501.44 - 14724.9i) q^{61} +(-70773.7 - 122584. i) q^{62} +(18654.4 - 32310.4i) q^{63} -32768.0 q^{64} +253729. i q^{65} +(30563.7 - 52937.8i) q^{66} +(-170658. - 98529.6i) q^{67} -180499. q^{68} -140259. i q^{69} +(-80414.1 - 46427.1i) q^{70} +(-19743.1 + 11398.7i) q^{71} +(-39305.2 - 22692.8i) q^{72} +(-53692.3 - 92997.8i) q^{73} +(46875.5 + 81190.7i) q^{74} -75603.5i q^{75} +(-163691. + 146220. i) q^{76} +73525.5 q^{77} +(246437. - 142281. i) q^{78} +(604503. - 349010. i) q^{79} +(-56478.0 + 97822.7i) q^{80} +(142901. + 247512. i) q^{81} +(-127065. + 220082. i) q^{82} +875221. q^{83} +104137. i q^{84} +(-311103. + 538846. i) q^{85} +(311189. + 179665. i) q^{86} +144149. q^{87} -89442.9i q^{88} +(-448676. - 259043. i) q^{89} +(-135490. + 78225.5i) q^{90} +(296421. + 171139. i) q^{91} +(-102615. - 177734. i) q^{92} +(273613. + 473912. i) q^{93} +72471.6i q^{94} +(154381. + 740689. i) q^{95} +126682. q^{96} +(-950899. + 549002. i) q^{97} +(467882. - 270132. i) q^{98} +(61941.9 - 107287. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$2$	−4.89898	+	2.82843i	−0.612372	+	0.353553i
$3$	18.9396	−	10.9348i	0.701466	−	0.404992i	−0.106427	−	0.994321i	$-0.533941\pi$
$3$	18.9396	−	10.9348i	0.701466	−	0.404992i	0.807893	+	0.589329i	$0.200608\pi$
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	−55.1543	−	95.5300i	−0.441234	−	0.764240i	0.556547	−	0.830816i	$-0.312126\pi$
$5$	−55.1543	−	95.5300i	−0.441234	−	0.764240i	−0.997781	+	0.0665759i	$0.978793\pi$
$6$	−61.8564	+	107.138i	−0.286372	+	0.496011i
$7$	−148.805			−0.433834			−0.216917	−	0.976190i	$-0.569600\pi$
$7$	−148.805			−0.433834			−0.216917	+	0.976190i	$0.569600\pi$
$8$			181.019i			0.353553i
$9$	−125.361	+	217.132i	−0.171964	+	0.297850i
$10$	540.399	+	312.000i	0.540399	+	0.312000i
$11$	−494.107			−0.371230			−0.185615	−	0.982623i	$-0.559428\pi$
$11$	−494.107			−0.371230			−0.185615	+	0.982623i	$0.559428\pi$
$12$		−	699.826i		−	0.404992i
$13$	−1992.01	−	1150.09i	−0.906696	−	0.523481i	−0.0273297	−	0.999626i	$-0.508700\pi$
$13$	−1992.01	−	1150.09i	−0.906696	−	0.523481i	−0.879367	+	0.476145i	$0.842034\pi$
$14$	728.992	−	420.884i	0.265668	−	0.153383i
$15$	−2089.20	−	1206.20i	−0.619022	−	0.357392i
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$	−2820.30	−	4884.90i	−0.574048	−	0.994281i	−0.996144	−	0.0877296i	$-0.972039\pi$
$17$	−2820.30	−	4884.90i	−0.574048	−	0.994281i	0.422096	−	0.906551i	$-0.361294\pi$
$18$		−	1418.30i		−	0.243193i
$19$	−6514.87	−	2145.32i	−0.949828	−	0.312774i
$19$	−6514.87	−	2145.32i	−0.949828	−	0.312774i
$20$	−3529.87			−0.441234
$21$	−2818.30	+	1627.15i	−0.304320	+	0.175699i
$22$	2420.62	−	1397.54i	0.227331	−	0.131250i
$23$	3206.71	−	5554.19i	0.263558	−	0.456496i	−0.703627	−	0.710570i	$-0.748437\pi$
$23$	3206.71	−	5554.19i	0.263558	−	0.456496i	0.967185	+	0.254074i	$0.0817705\pi$
$24$	1979.41	+	3428.43i	0.143186	+	0.248006i
$25$	1728.51	−	2993.87i	0.110625	−	0.191608i
$26$	13011.8			0.740315
$27$			21426.1i			1.08856i
$28$	−2380.88	+	4123.80i	−0.108458	+	0.187855i
$29$	5708.25	+	3295.66i	0.234050	+	0.135129i	0.612439	−	0.790518i	$-0.290188\pi$
$29$	5708.25	+	3295.66i	0.234050	+	0.135129i	−0.378389	+	0.925647i	$0.623522\pi$
$30$	13646.6			0.505429
$31$			25022.3i			0.839927i	0.907541	+	0.419964i	$0.137957\pi$
$31$			25022.3i			0.839927i	−0.907541	+	0.419964i	$0.862043\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$	−9358.18	+	5402.95i	−0.260405	+	0.150345i
$34$	27633.2	+	15954.0i	0.703063	+	0.405913i
$35$	8207.23	+	14215.3i	0.191422	+	0.331553i
$36$	4011.57	+	6948.24i	0.0859818	+	0.148925i
$37$		−	16573.0i		−	0.327186i	−0.986528	−	0.163593i	$-0.947692\pi$
$37$		−	16573.0i		−	0.327186i	0.986528	−	0.163593i	$-0.0523085\pi$
$38$	37984.1	−	7916.96i	0.692231	−	0.144281i
$39$	−50303.8			−0.848022
$40$	17292.8	−	9983.99i	0.270200	−	0.156000i
$41$	38905.5	−	22462.1i	0.564493	−	0.325910i	−0.190454	−	0.981696i	$-0.560996\pi$
$41$	38905.5	−	22462.1i	0.564493	−	0.325910i	0.754947	+	0.655786i	$0.227663\pi$
$42$	9204.54	−	15942.7i	0.124238	−	0.215186i
$43$	−31760.6	−	55011.0i	−0.399469	−	0.691901i	0.594191	−	0.804324i	$-0.297472\pi$
$43$	−31760.6	−	55011.0i	−0.399469	−	0.691901i	−0.993660	+	0.112423i	$0.964139\pi$
$44$	−7905.71	+	13693.1i	−0.0928074	+	0.160747i
$45$	27656.9			0.303505
$46$			36279.8i			0.372728i
$47$	6405.65	−	11094.9i	0.0616977	−	0.106864i	−0.833527	−	0.552479i	$-0.813682\pi$
$47$	6405.65	−	11094.9i	0.0616977	−	0.106864i	0.895224	+	0.445616i	$0.147015\pi$
$48$	−19394.1	−	11197.2i	−0.175367	−	0.101248i
$49$	−95506.1			−0.811788
$50$			19555.9i			0.156447i
$51$	−106831.	−	61678.7i	−0.805351	−	0.464969i
$52$	−63744.4	+	36802.8i	−0.453348	+	0.261741i
$53$	184401.	+	106464.i	1.23861	+	0.715113i	0.968811	−	0.247803i	$-0.0797085\pi$
$53$	184401.	+	106464.i	1.23861	+	0.715113i	0.269802	+	0.962916i	$0.413042\pi$
$54$	−60602.2	−	104966.i	−0.384864	−	0.666603i
$55$	27252.1	+	47202.0i	0.163799	+	0.283709i
$56$		−	26936.6i		−	0.153383i
$57$	−146847.	+	30607.2i	−0.792943	+	0.165272i
$58$	−37286.1			−0.191101
$59$	198707.	−	114723.i	0.967512	−	0.558593i	0.0690350	−	0.997614i	$-0.478008\pi$
$59$	198707.	−	114723.i	0.967512	−	0.558593i	0.898477	+	0.439021i	$0.144675\pi$
$60$	−66854.3	+	38598.4i	−0.309511	+	0.178696i
$61$	8501.44	−	14724.9i	0.0374544	−	0.0648730i	−0.846691	−	0.532086i	$-0.821408\pi$
$61$	8501.44	−	14724.9i	0.0374544	−	0.0648730i	0.884145	+	0.467213i	$0.154742\pi$
$62$	−70773.7	−	122584.i	−0.296959	−	0.514348i
$63$	18654.4	−	32310.4i	0.0746036	−	0.129217i
$64$	−32768.0			−0.125000
$65$			253729.i			0.923912i
$66$	30563.7	−	52937.8i	0.106310	−	0.184134i
$67$	−170658.	−	98529.6i	−0.567418	−	0.327599i	0.188699	−	0.982035i	$-0.439573\pi$
$67$	−170658.	−	98529.6i	−0.567418	−	0.327599i	−0.756117	+	0.654436i	$0.772906\pi$
$68$	−180499.			−0.574048
$69$		−	140259.i		−	0.426956i
$70$	−80414.1	−	46427.1i	−0.234443	−	0.135356i
$71$	−19743.1	+	11398.7i	−0.0551621	+	0.0318479i	−0.527327	−	0.849662i	$-0.676806\pi$
$71$	−19743.1	+	11398.7i	−0.0551621	+	0.0318479i	0.472165	+	0.881510i	$0.343473\pi$
$72$	−39305.2	−	22692.8i	−0.105306	−	0.0607983i
$73$	−53692.3	−	92997.8i	−0.138020	−	0.239059i	0.788727	−	0.614744i	$-0.210741\pi$
$73$	−53692.3	−	92997.8i	−0.138020	−	0.239059i	−0.926747	+	0.375685i	$0.877407\pi$
$74$	46875.5	+	81190.7i	0.115678	+	0.200360i
$75$		−	75603.5i		−	0.179208i
$76$	−163691.	+	146220.i	−0.372892	+	0.333094i
$77$	73525.5			0.161052
$78$	246437.	−	142281.i	0.519306	−	0.299821i
$79$	604503.	−	349010.i	1.22608	−	0.707875i	0.259869	−	0.965644i	$-0.416321\pi$
$79$	604503.	−	349010.i	1.22608	−	0.707875i	0.966207	+	0.257769i	$0.0829874\pi$
$80$	−56478.0	+	97822.7i	−0.110309	+	0.191060i
$81$	142901.	+	247512.i	0.268894	+	0.465737i
$82$	−127065.	+	220082.i	−0.230453	+	0.399157i
$83$	875221.			1.53068			0.765338	−	0.643628i	$-0.222572\pi$
$83$	875221.			1.53068			0.765338	+	0.643628i	$0.222572\pi$
$84$			104137.i			0.175699i
$85$	−311103.	+	538846.i	−0.506579	+	0.877421i
$86$	311189.	+	179665.i	0.489248	+	0.282467i
$87$	144149.			0.218904
$88$		−	89442.9i		−	0.131250i
$89$	−448676.	−	259043.i	−0.636447	−	0.367453i	0.146797	−	0.989167i	$-0.453103\pi$
$89$	−448676.	−	259043.i	−0.636447	−	0.367453i	−0.783245	+	0.621714i	$0.786437\pi$
$90$	−135490.	+	78225.5i	−0.185858	+	0.107305i
$91$	296421.	+	171139.i	0.393355	+	0.227104i
$92$	−102615.	−	177734.i	−0.131779	−	0.228248i
$93$	273613.	+	473912.i	0.340164	+	0.589181i
$94$			72471.6i			0.0872538i
$95$	154381.	+	740689.i	0.180062	+	0.863903i
$96$	126682.			0.143186
$97$	−950899.	+	549002.i	−1.04188	+	0.601532i	−0.920366	−	0.391058i	$-0.872109\pi$
$97$	−950899.	+	549002.i	−1.04188	+	0.601532i	−0.121517	+	0.992589i	$0.538776\pi$
$98$	467882.	−	270132.i	0.497117	−	0.287011i
$99$	61941.9	−	107287.i	0.0638380	−	0.110571i
$100$	−55312.3	−	95803.8i	−0.0553123	−	0.0958038i
$101$	315256.	−	546039.i	0.305984	−	0.529980i	−0.671496	−	0.741008i	$-0.734348\pi$
$101$	315256.	−	546039.i	0.305984	−	0.529980i	0.977480	+	0.211028i	$0.0676813\pi$
$102$	697814.			0.657566
$103$			55483.4i			0.0507751i	0.999678	+	0.0253876i	$0.00808198\pi$
$103$			55483.4i			0.0507751i	−0.999678	+	0.0253876i	$0.991918\pi$
$104$	208188.	−	360593.i	0.185079	−	0.320566i
$105$	310883.	+	179488.i	0.268552	+	0.155049i
$106$	−1.20450e6			−1.01132
$107$		−	2.37626e6i		−	1.93974i	−0.243632	−	0.969868i	$-0.578339\pi$
$107$		−	2.37626e6i		−	1.93974i	0.243632	−	0.969868i	$-0.421661\pi$
$108$	593777.	+	342818.i	0.471360	+	0.272140i
$109$	−1.78104e6	+	1.02829e6i	−1.37529	+	0.794025i	−0.991588	−	0.129432i	$-0.958685\pi$
$109$	−1.78104e6	+	1.02829e6i	−1.37529	+	0.794025i	−0.383703	+	0.923457i	$0.625351\pi$
$110$	−267015.	−	154161.i	−0.200612	−	0.115824i
$111$	−181222.	−	313885.i	−0.132508	−	0.229510i
$112$	76188.1	+	131962.i	0.0542292	+	0.0939277i
$113$			69343.3i			0.0480584i	0.999711	+	0.0240292i	$0.00764947\pi$
$113$			69343.3i			0.0480584i	−0.999711	+	0.0240292i	$0.992351\pi$
$114$	632832.	−	565291.i	0.427144	−	0.381555i
$115$	−707456.			−0.465164
$116$	182664.	−	105461.i	0.117025	−	0.0675644i
$117$	499443.	−	288354.i	0.311837	−	0.180039i
$118$	−648973.	+	1.12405e6i	−0.394985	+	0.684134i
$119$	419674.	+	726897.i	0.249041	+	0.431352i
$120$	218345.	−	378185.i	0.126357	−	0.218857i
$121$	−1.52742e6			−0.862189
$122$			96182.9i			0.0529686i
$123$	491235.	−	850845.i	0.263982	−	0.457230i
$124$	693438.	+	400356.i	0.363699	+	0.209982i
$125$	−2.10491e6			−1.07771
$126$			211050.i			0.105505i
$127$	−2.78393e6	−	1.60730e6i	−1.35909	−	0.784669i	−0.369585	−	0.929197i	$-0.620500\pi$
$127$	−2.78393e6	−	1.60730e6i	−1.35909	−	0.784669i	−0.989501	+	0.144528i	$0.953834\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$	−1.20306e6	−	694590.i	−0.560428	−	0.323563i
$130$	−717655.	−	1.24301e6i	−0.326652	−	0.565778i
$131$	−813851.	−	1.40963e6i	−0.362019	−	0.627035i	0.626274	−	0.779603i	$-0.284579\pi$
$131$	−813851.	−	1.40963e6i	−0.362019	−	0.627035i	−0.988293	+	0.152568i	$0.951246\pi$
$132$			345789.i			0.150345i
$133$	969444.	+	319234.i	0.412067	+	0.135692i
$134$	1.11474e6			0.463295
$135$	2.04684e6	−	1.18174e6i	0.831920	−	0.480309i
$136$	884262.	−	510529.i	0.351531	−	0.202957i
$137$	−1.23682e6	+	2.14224e6i	−0.481000	+	0.833117i	−0.999762	−	0.0218018i	$-0.993060\pi$
$137$	−1.23682e6	+	2.14224e6i	−0.481000	+	0.833117i	0.518762	+	0.854919i	$0.326393\pi$
$138$	396712.	+	687125.i	0.150952	+	0.261456i
$139$	993264.	−	1.72038e6i	0.369845	−	0.640591i	−0.619696	−	0.784842i	$-0.712744\pi$
$139$	993264.	−	1.72038e6i	0.369845	−	0.640591i	0.989541	+	0.144251i	$0.0460773\pi$
$140$	525263.			0.191422
$141$		−	280177.i		−	0.0999483i
$142$	64480.8	−	111684.i	0.0225198	−	0.0390055i
$143$	984267.	+	568267.i	0.336593	+	0.194332i
$144$	256740.			0.0859818
$145$		−	727079.i		−	0.238494i
$146$	526075.	+	303730.i	0.169040	+	0.0975952i
$147$	−1.80885e6	+	1.04434e6i	−0.569442	+	0.328768i
$148$	−459284.	−	265168.i	−0.141676	−	0.0817966i
$149$	2.44724e6	+	4.23875e6i	0.739807	+	1.28138i	0.952582	+	0.304282i	$0.0984166\pi$
$149$	2.44724e6	+	4.23875e6i	0.739807	+	1.28138i	−0.212775	+	0.977101i	$0.568250\pi$
$150$	213839.	+	370380.i	0.0633597	+	0.109742i
$151$			3.01300e6i			0.875123i	0.899189	+	0.437561i	$0.144158\pi$
$151$			3.01300e6i			0.875123i	−0.899189	+	0.437561i	$0.855842\pi$
$152$	388344.	−	1.17932e6i	0.110582	−	0.335815i
$153$	1.41423e6			0.394862
$154$	−360200.	+	207962.i	−0.0986237	+	0.0569404i
$155$	2.39038e6	−	1.38009e6i	0.641906	−	0.370605i
$156$	−804861.	+	1.39406e6i	−0.212006	+	0.367204i
$157$	3.78651e6	+	6.55843e6i	0.978454	+	1.69473i	0.668030	+	0.744134i	$0.267138\pi$
$157$	3.78651e6	+	6.55843e6i	0.978454	+	1.69473i	0.310424	+	0.950598i	$0.399529\pi$
$158$	−1.97430e6	+	3.41958e6i	−0.500543	+	0.866966i
$159$	4.65663e6			1.15846
$160$		−	638975.i		−	0.156000i
$161$	−477175.	+	826491.i	−0.114340	+	0.198043i
$162$	−1.40014e6	−	808370.i	−0.329326	−	0.190136i
$163$	931199.			0.215020			0.107510	−	0.994204i	$-0.465712\pi$
$163$	931199.			0.215020			0.107510	+	0.994204i	$0.465712\pi$
$164$		−	1.43757e6i		−	0.325910i
$165$	1.03229e6	+	595991.i	0.229799	+	0.132675i
$166$	−4.28769e6	+	2.47550e6i	−0.937344	+	0.541176i
$167$	−1.22284e6	−	706005.i	−0.262554	−	0.151586i	0.362945	−	0.931811i	$-0.381771\pi$
$167$	−1.22284e6	−	706005.i	−0.262554	−	0.151586i	−0.625499	+	0.780225i	$0.715105\pi$
$168$	−294545.	−	510167.i	−0.0621190	−	0.107593i
$169$	232004.	+	401842.i	0.0480656	+	0.0832521i
$170$		−	3.51973e6i		−	0.716412i
$171$	1.28253e6	−	1.14565e6i	0.256495	−	0.229120i
$172$	−2.03268e6			−0.399469
$173$	6.24342e6	−	3.60464e6i	1.20582	−	0.696183i	0.243980	−	0.969780i	$-0.421547\pi$
$173$	6.24342e6	−	3.60464e6i	1.20582	−	0.696183i	0.961844	+	0.273597i	$0.0882134\pi$
$174$	−706184.	+	407715.i	−0.134051	+	0.0773943i
$175$	−257211.	+	445502.i	−0.0479927	+	0.0831258i
$176$	252983.	+	438179.i	0.0464037	+	0.0803736i
$177$	2.50895e6	−	4.34562e6i	0.452451	−	0.783668i
$178$	2.93074e6			0.519657
$179$		−	739943.i		−	0.129015i	−0.997917	−	0.0645074i	$-0.979452\pi$
$179$		−	739943.i		−	0.129015i	0.997917	−	0.0645074i	$-0.0205476\pi$
$180$	442510.	−	766450.i	0.0758762	−	0.131421i
$181$	−9.16046e6	−	5.28879e6i	−1.54483	−	0.891910i	−0.998523	−	0.0543262i	$-0.982699\pi$
$181$	−9.16046e6	−	5.28879e6i	−1.54483	−	0.891910i	−0.546309	−	0.837583i	$-0.683968\pi$
$182$	−1.93622e6			−0.321173
$183$		−	371846.i		−	0.0606749i
$184$	1.00542e6	+	580477.i	0.161396	+	0.0931819i
$185$	−1.58322e6	+	914070.i	−0.250049	+	0.144366i
$186$	−2.68085e6	−	1.54779e6i	−0.416614	−	0.240532i
$187$	1.39353e6	+	2.41366e6i	0.213104	+	0.369107i
$188$	−204981.	−	355037.i	−0.0308489	−	0.0534318i
$189$		−	3.18831e6i		−	0.472253i
$190$	−2.85129e6	−	3.19196e6i	−0.415701	−	0.465369i
$191$	−1.08220e7			−1.55313			−0.776565	−	0.630037i	$-0.783040\pi$
$191$	−1.08220e7			−1.55313			−0.776565	+	0.630037i	$0.783040\pi$
$192$	−620612.	+	358311.i	−0.0876833	+	0.0506240i
$193$	2.79060e6	−	1.61115e6i	0.388173	−	0.224112i	−0.293195	−	0.956053i	$-0.594719\pi$
$193$	2.79060e6	−	1.61115e6i	0.388173	−	0.224112i	0.681368	+	0.731941i	$0.261385\pi$
$194$	3.10562e6	−	5.37910e6i	0.425347	−	0.736723i
$195$	2.77447e6	+	4.80553e6i	0.374177	+	0.648093i
$196$	−1.52810e6	+	2.64674e6i	−0.202947	+	0.351515i
$197$	−4.06910e6			−0.532230			−0.266115	−	0.963941i	$-0.585740\pi$
$197$	−4.06910e6			−0.532230			−0.266115	+	0.963941i	$0.585740\pi$
$198$			700793.i			0.0902805i
$199$	−303295.	+	525322.i	−0.0384863	+	0.0666602i	−0.884627	−	0.466299i	$-0.845587\pi$
$199$	−303295.	+	525322.i	−0.0384863	+	0.0666602i	0.846141	+	0.532960i	$0.178920\pi$
$200$	541948.	+	312894.i	0.0677435	+	0.0391117i
$201$	−4.30960e6			−0.530699
$202$			3.56671e6i			0.432727i
$203$	−849415.	−	490410.i	−0.101539	−	0.0586234i
$204$	−3.41858e6	+	1.97372e6i	−0.402675	+	0.232485i
$205$	−4.29160e6	−	2.47776e6i	−0.498148	−	0.287606i
$206$	−156931.	−	271812.i	−0.0179517	−	0.0310933i
$207$	803996.	+	1.39256e6i	0.0906448	+	0.157001i
$208$			2.35538e6i			0.261741i
$209$	3.21904e6	+	1.06002e6i	0.352604	+	0.116111i
$210$	−2.03068e6			−0.219272
$211$	5.64832e6	−	3.26106e6i	0.601274	−	0.347145i	−0.168269	−	0.985741i	$-0.553818\pi$
$211$	5.64832e6	−	3.26106e6i	0.601274	−	0.347145i	0.769542	+	0.638596i	$0.220484\pi$
$212$	5.90083e6	−	3.40684e6i	0.619306	−	0.357557i
$213$	−249284.	+	431773.i	−0.0257962	+	0.0446804i
$214$	6.72108e6	+	1.16412e7i	0.685800	+	1.18784i
$215$	−3.50346e6	+	6.06818e6i	−0.352519	+	0.610581i
$216$	−3.87854e6			−0.384864
$217$		−	3.72344e6i		−	0.364389i
$218$	5.81686e6	−	1.00751e7i	0.561460	−	0.972478i
$219$	−2.03382e6	−	1.17423e6i	−0.193633	−	0.111794i
$220$	1.74413e6			0.163799
$221$			1.29744e7i			1.20201i
$222$	1.77560e6	+	1.02514e6i	0.162288	+	0.0936971i
$223$	8.60924e6	−	4.97055e6i	0.776337	−	0.448219i	−0.0587934	−	0.998270i	$-0.518725\pi$
$223$	8.60924e6	−	4.97055e6i	0.776337	−	0.448219i	0.835131	+	0.550052i	$0.185392\pi$
$224$	−746488.	−	430985.i	−0.0664169	−	0.0383458i
$225$	433377.	+	750631.i	0.0380468	+	0.0658990i
$226$	−196133.	−	339712.i	−0.0169912	−	0.0294296i
$227$		−	1.75602e7i		−	1.50124i	−0.660733	−	0.750621i	$-0.729754\pi$
$227$		−	1.75602e7i		−	1.50124i	0.660733	−	0.750621i	$-0.270246\pi$
$228$	−1.50135e6	+	4.55927e6i	−0.126671	+	0.384672i
$229$	−2.24752e7			−1.87153			−0.935767	−	0.352618i	$-0.885291\pi$
$229$	−2.24752e7			−1.87153			−0.935767	+	0.352618i	$0.885291\pi$
$230$	3.46581e6	−	2.00099e6i	0.284853	−	0.164460i
$231$	1.39254e6	−	803985.i	0.112972	−	0.0652247i
$232$	−596578.	+	1.03330e6i	−0.0477753	+	0.0827492i
$233$	7.05277e6	+	1.22157e7i	0.557560	+	0.965723i	0.997699	+	0.0677930i	$0.0215957\pi$
$233$	7.05277e6	+	1.22157e7i	0.557560	+	0.965723i	−0.440139	+	0.897930i	$0.645071\pi$
$234$	−1.63117e6	+	2.82528e6i	−0.127307	+	0.220502i
$235$	−1.41319e6			−0.108893
$236$		−	7.34229e6i		−	0.558593i
$237$	7.63269e6	−	1.32202e7i	0.573367	−	0.993100i
$238$	−4.11195e6	−	2.37404e6i	−0.305012	−	0.176099i
$239$	−6.28191e6			−0.460148			−0.230074	−	0.973173i	$-0.573897\pi$
$239$	−6.28191e6			−0.460148			−0.230074	+	0.973173i	$0.573897\pi$
$240$			2.47030e6i			0.178696i
$241$	−764677.	−	441486.i	−0.0546295	−	0.0315403i	0.472437	−	0.881365i	$-0.343375\pi$
$241$	−764677.	−	441486.i	−0.0546295	−	0.0315403i	−0.527066	+	0.849824i	$0.676708\pi$
$242$	7.48280e6	−	4.32019e6i	0.527980	−	0.304830i
$243$	−8.11402e6	−	4.68463e6i	−0.565480	−	0.326480i
$244$	−272046.	−	471198.i	−0.0187272	−	0.0324365i
$245$	5.26757e6	+	9.12370e6i	0.358189	+	0.620401i
$246$			5.55769e6i			0.373327i
$247$	1.05104e7	+	1.17662e7i	0.697474	+	0.780808i
$248$	−4.52952e6			−0.296959
$249$	1.65763e7	−	9.57034e6i	1.07372	−	0.619911i
$250$	1.03119e7	−	5.95359e6i	0.659962	−	0.381029i
$251$	−1.15055e7	+	1.99281e7i	−0.727585	+	1.26021i	0.230316	+	0.973116i	$0.426024\pi$
$251$	−1.15055e7	+	1.99281e7i	−0.727585	+	1.26021i	−0.957901	+	0.287099i	$0.907309\pi$
$252$	−596941.	−	1.03393e6i	−0.0373018	−	0.0646086i
$253$	−1.58446e6	+	2.74436e6i	−0.0978407	+	0.169465i
$254$	1.81845e7			1.10969
$255$			1.36074e7i			0.820642i
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	−3.47794e6	−	2.00799e6i	−0.204891	−	0.118294i	0.394044	−	0.919092i	$-0.371076\pi$
$257$	−3.47794e6	−	2.00799e6i	−0.204891	−	0.118294i	−0.598935	+	0.800798i	$0.704409\pi$
$258$	7.85839e6			0.457588
$259$			2.46614e6i			0.141944i
$260$	7.03155e6	+	4.05967e6i	0.400066	+	0.230978i
$261$	−1.43119e6	+	826297.i	−0.0804962	+	0.0464745i
$262$	7.97408e6	+	4.60384e6i	0.443381	+	0.255986i
$263$	6.63127e6	+	1.14857e7i	0.364527	+	0.631379i	0.988700	−	0.149907i	$-0.0478975\pi$
$263$	6.63127e6	+	1.14857e7i	0.364527	+	0.631379i	−0.624173	+	0.781286i	$0.714564\pi$
$264$	−978038.	−	1.69401e6i	−0.0531550	−	0.0920671i
$265$		−	2.34878e7i		−	1.26213i
$266$	−5.65222e6	+	1.17808e6i	−0.300313	+	0.0625937i
$267$	−1.13303e7			−0.595262
$268$	−5.46107e6	+	3.15295e6i	−0.283709	+	0.163799i
$269$	4.70629e6	−	2.71718e6i	0.241781	−	0.139592i	−0.374214	−	0.927342i	$-0.622087\pi$
$269$	4.70629e6	−	2.71718e6i	0.241781	−	0.139592i	0.615995	+	0.787750i	$0.288754\pi$
$270$	−6.68494e6	+	1.15786e7i	−0.339630	+	0.588256i
$271$	1.42466e6	+	2.46759e6i	0.0715821	+	0.123984i	0.899595	−	0.436725i	$-0.143862\pi$
$271$	1.42466e6	+	2.46759e6i	0.0715821	+	0.123984i	−0.828013	+	0.560709i	$0.810529\pi$
$272$	−2.88799e6	+	5.00214e6i	−0.143512	+	0.248570i
$273$	7.48546e6			0.367901
$274$		−	1.39930e7i		−	0.680237i
$275$	−854069.	+	1.47929e6i	−0.0410672	+	0.0711304i
$276$	−3.88696e6	−	2.24414e6i	−0.184877	−	0.106739i
$277$	2.95782e7			1.39166			0.695828	−	0.718209i	$-0.255038\pi$
$277$	2.95782e7			1.39166			0.695828	+	0.718209i	$0.255038\pi$
$278$			1.12375e7i			0.523040i
$279$	−5.43315e6	−	3.13683e6i	−0.250172	−	0.144437i
$280$	−2.57325e6	+	1.48567e6i	−0.117222	+	0.0676780i
$281$	−3.20759e7	−	1.85190e7i	−1.44564	−	0.834641i	−0.447423	−	0.894323i	$-0.647658\pi$
$281$	−3.20759e7	−	1.85190e7i	−1.44564	−	0.834641i	−0.998217	+	0.0596817i	$0.980991\pi$
$282$	792461.	+	1.37258e6i	0.0353371	+	0.0612056i
$283$	−9.93380e6	−	1.72058e7i	−0.438284	−	0.759131i	0.559273	−	0.828984i	$-0.311080\pi$
$283$	−9.93380e6	−	1.72058e7i	−0.438284	−	0.759131i	−0.997557	+	0.0698528i	$0.977747\pi$
$284$			729517.i			0.0318479i
$285$	1.10232e7	+	1.23402e7i	0.476181	+	0.533075i
$286$	−6.42920e6			−0.274827
$287$	−5.78932e6	+	3.34247e6i	−0.244896	+	0.141391i
$288$	−1.25777e6	+	726171.i	−0.0526529	+	0.0303991i
$289$	−3.83939e6	+	6.65001e6i	−0.159063	+	0.275505i
$290$	2.05649e6	+	3.56194e6i	0.0843203	+	0.146047i
$291$	−1.20064e7	+	2.07957e7i	−0.487231	+	0.843908i
$292$	−3.43631e6			−0.138020
$293$		−	1.40507e7i		−	0.558592i	−0.960205	−	0.279296i	$-0.909899\pi$
$293$		−	1.40507e7i		−	0.558592i	0.960205	−	0.279296i	$-0.0901011\pi$
$294$	5.90767e6	−	1.02324e7i	0.232474	−	0.402656i
$295$	−2.19190e7	−	1.26550e7i	−0.853799	−	0.492941i
$296$	3.00003e6			0.115678
$297$		−	1.05868e7i		−	0.404105i
$298$	−2.39780e7	−	1.38437e7i	−0.906075	−	0.523123i
$299$	−1.27756e7	+	7.37601e6i	−0.477935	+	0.275936i
$300$	−2.09519e6	−	1.20966e6i	−0.0775995	−	0.0448021i
$301$	4.72613e6	+	8.18590e6i	0.173303	+	0.300170i
$302$	−8.52206e6	−	1.47606e7i	−0.309403	−	0.535901i
$303$		−	1.37890e7i		−	0.495684i
$304$	1.43312e6	+	6.87585e6i	0.0510109	+	0.244740i
$305$	−1.87556e6			−0.0661047
$306$	−6.92827e6	+	4.00004e6i	−0.241802	+	0.139605i
$307$	4.83308e7	−	2.79038e7i	1.67036	−	0.964380i	0.702918	−	0.711271i	$-0.251880\pi$
$307$	4.83308e7	−	2.79038e7i	1.67036	−	0.964380i	0.967438	−	0.253109i	$-0.0814531\pi$
$308$	1.17641e6	−	2.03760e6i	0.0402630	−	0.0697375i
$309$	606698.	+	1.05083e6i	0.0205635	+	0.0356170i
$310$	−7.80694e6	+	1.35220e7i	−0.262057	+	0.453896i
$311$	−9.15168e6			−0.304242			−0.152121	−	0.988362i	$-0.548610\pi$
$311$	−9.15168e6			−0.304242			−0.152121	+	0.988362i	$0.548610\pi$
$312$		−	9.10597e6i		−	0.299821i
$313$	2.45222e7	−	4.24736e7i	0.799697	−	1.38512i	−0.120116	−	0.992760i	$-0.538327\pi$
$313$	2.45222e7	−	4.24736e7i	0.799697	−	1.38512i	0.919813	−	0.392357i	$-0.128340\pi$
$314$	−3.71001e7	−	2.14198e7i	−1.19836	−	0.691872i
$315$	−4.11548e6			−0.131671
$316$		−	2.23366e7i		−	0.707875i
$317$	3.41900e7	+	1.97396e7i	1.07330	+	0.619670i	0.929081	−	0.369876i	$-0.120600\pi$
$317$	3.41900e7	+	1.97396e7i	1.07330	+	0.619670i	0.144219	+	0.989546i	$0.453933\pi$
$318$	−2.28128e7	+	1.31710e7i	−0.709409	+	0.409577i
$319$	−2.82048e6	−	1.62841e6i	−0.0868863	−	0.0501639i
$320$	1.80730e6	+	3.13033e6i	0.0551543	+	0.0955300i
$321$	−2.59839e7	−	4.50054e7i	−0.785577	−	1.36066i
$322$		−	5.39862e6i		−	0.161702i
$323$	7.89421e6	+	3.78749e7i	0.234262	+	1.12394i
$324$	9.14567e6			0.268894
$325$	−6.88643e6	+	3.97588e6i	−0.200606	+	0.115820i
$326$	−4.56193e6	+	2.63383e6i	−0.131673	+	0.0760212i
$327$	−2.24881e7	+	3.89506e7i	−0.643147	+	1.11396i
$328$	4.06607e6	+	7.04264e6i	0.115227	+	0.199579i
$329$	−953191.	+	1.65098e6i	−0.0267666	+	0.0463610i
$330$	−6.74287e6			−0.187630
$331$			6.39030e7i			1.76213i	0.472999	+	0.881063i	$0.343171\pi$
$331$			6.39030e7i			1.76213i	−0.472999	+	0.881063i	$0.656829\pi$
$332$	1.40035e7	−	2.42548e7i	0.382669	−	0.662802i
$333$	3.59853e6	+	2.07761e6i	0.0974524	+	0.0562641i
$334$	7.98754e6			0.214375
$335$			2.17373e7i			0.578191i
$336$	2.88594e6	+	1.66620e6i	0.0760799	+	0.0439247i
$337$	3.67660e7	−	2.12269e7i	0.960632	−	0.554621i	0.0642644	−	0.997933i	$-0.479530\pi$
$337$	3.67660e7	−	2.12269e7i	0.960632	−	0.554621i	0.896367	+	0.443312i	$0.146197\pi$
$338$	−2.27316e6	−	1.31241e6i	−0.0588682	−	0.0339875i
$339$	758254.	+	1.31333e6i	0.0194632	+	0.0337113i
$340$	9.95530e6	+	1.72431e7i	0.253290	+	0.438711i
$341$		−	1.23637e7i		−	0.311806i
$342$	−3.04271e6	+	9.24005e6i	−0.0760645	+	0.230992i
$343$	3.17185e7			0.786015
$344$	9.95805e6	−	5.74928e6i	0.244624	−	0.141234i
$345$	−1.33989e7	+	7.73587e6i	−0.326297	+	0.188387i
$346$	−2.03909e7	+	3.53181e7i	−0.492276	+	0.852647i
$347$	2.37138e7	+	4.10735e7i	0.567561	+	0.983044i	0.996806	+	0.0798562i	$0.0254461\pi$
$347$	2.37138e7	+	4.10735e7i	0.567561	+	0.983044i	−0.429246	+	0.903188i	$0.641221\pi$
$348$	2.30639e6	−	3.99478e6i	0.0547261	−	0.0947883i
$349$	6.81894e7			1.60413			0.802067	−	0.597235i	$-0.203734\pi$
$349$	6.81894e7			1.60413			0.802067	+	0.597235i	$0.203734\pi$
$350$		−	2.91001e6i		−	0.0678719i
$351$	2.46419e7	−	4.26810e7i	0.569840	−	0.986992i
$352$	−2.47871e6	−	1.43109e6i	−0.0568327	−	0.0328124i
$353$	−3.90652e7			−0.888108			−0.444054	−	0.896000i	$-0.646460\pi$
$353$	−3.90652e7			−0.888108			−0.444054	+	0.896000i	$0.646460\pi$
$354$			2.83855e7i			0.639862i
$355$	2.17784e6	+	1.25737e6i	0.0486788	+	0.0281047i
$356$	−1.43576e7	+	8.28938e6i	−0.318224	+	0.183726i
$357$	1.58969e7	+	9.17809e6i	0.349388	+	0.201719i
$358$	2.09288e6	+	3.62497e6i	0.0456136	+	0.0790051i
$359$	−3.08646e7	−	5.34590e7i	−0.667079	−	1.15541i	−0.978717	−	0.205213i	$-0.934211\pi$
$359$	−3.08646e7	−	5.34590e7i	−0.667079	−	1.15541i	0.311639	−	0.950201i	$-0.399122\pi$
$360$			5.00643e6i			0.107305i
$361$	3.78411e7	+	2.79529e7i	0.804345	+	0.594163i
$362$	5.98359e7			1.26135
$363$	−2.89287e7	+	1.67020e7i	−0.604796	+	0.349179i
$364$	9.48548e6	−	5.47644e6i	0.196678	−	0.113552i
$365$	−5.92272e6	+	1.02585e7i	−0.121799	+	0.210962i
$366$	1.05174e6	+	1.82166e6i	0.0214518	+	0.0371557i
$367$	2.57087e7	−	4.45288e7i	0.520095	−	0.900831i	−0.479632	−	0.877470i	$-0.659230\pi$
$367$	2.57087e7	−	4.45288e7i	0.520095	−	0.900831i	0.999727	−	0.0233612i	$-0.00743679\pi$
$368$	−6.56735e6			−0.131779
$369$			1.12635e7i			0.224179i
$370$	5.17076e6	−	8.95603e6i	0.102082	−	0.176811i
$371$	−2.74398e7	−	1.58424e7i	−0.537352	−	0.310240i
$372$	1.75112e7			0.340164
$373$			6.60232e7i			1.27224i	0.771589	+	0.636121i	$0.219462\pi$
$373$			6.60232e7i			1.27224i	−0.771589	+	0.636121i	$0.780538\pi$
$374$	−1.36537e7	−	7.88299e6i	−0.260998	−	0.150687i
$375$	−3.98661e7	+	2.30167e7i	−0.755980	+	0.436465i
$376$	2.00839e6	+	1.15955e6i	0.0377820	+	0.0218134i
$377$	−7.58060e6	−	1.31300e7i	−0.141475	−	0.245042i
$378$	9.01790e6	+	1.56195e7i	0.166967	+	0.289195i
$379$		−	1.57637e7i		−	0.289562i	−0.989464	−	0.144781i	$-0.953752\pi$
$379$		−	1.57637e7i		−	0.289562i	0.989464	−	0.144781i	$-0.0462478\pi$
$380$	2.29967e7	+	7.57270e6i	0.419096	+	0.138007i
$381$	−7.03019e7			−1.27114
$382$	5.30168e7	−	3.06093e7i	0.951094	−	0.549114i
$383$	5.30808e7	−	3.06462e7i	0.944803	−	0.545482i	0.0533403	−	0.998576i	$-0.483013\pi$
$383$	5.30808e7	−	3.06462e7i	0.944803	−	0.545482i	0.891463	+	0.453094i	$0.149680\pi$
$384$	2.02691e6	−	3.51071e6i	0.0357965	−	0.0620014i
$385$	−4.05525e6	−	7.02389e6i	−0.0710616	−	0.123082i
$386$	−9.11406e6	+	1.57860e7i	−0.158471	+	0.274480i
$387$	1.59262e7			0.274777
$388$			3.51361e7i			0.601532i
$389$	−1.65539e7	+	2.86722e7i	−0.281223	+	0.487093i	−0.971686	−	0.236274i	$-0.924074\pi$
$389$	−1.65539e7	+	2.86722e7i	−0.281223	+	0.487093i	0.690463	+	0.723368i	$0.257407\pi$
$390$	−2.71842e7	−	1.56948e7i	−0.458271	−	0.264583i
$391$	−3.61756e7			−0.605181
$392$		−	1.72885e7i		−	0.287011i
$393$	−3.08280e7	−	1.77986e7i	−0.507888	−	0.293229i
$394$	1.99344e7	−	1.15091e7i	0.325923	−	0.188172i
$395$	−6.66818e7	−	3.84988e7i	−1.08197	−	0.624677i
$396$	−1.98214e6	−	3.43317e6i	−0.0319190	−	0.0552853i
$397$	1.32223e7	+	2.29017e7i	0.211317	+	0.366012i	0.952127	−	0.305703i	$-0.0988914\pi$
$397$	1.32223e7	+	2.29017e7i	0.211317	+	0.366012i	−0.740810	+	0.671715i	$0.765558\pi$
$398$		−	3.43139e6i		−	0.0544278i
$399$	2.18516e7	−	4.55450e6i	0.344005	−	0.0717005i
$400$	−3.53999e6			−0.0553123
$401$	−6.97389e7	+	4.02638e7i	−1.08154	+	0.624427i	−0.931311	−	0.364225i	$-0.881334\pi$
$401$	−6.97389e7	+	4.02638e7i	−1.08154	+	0.624427i	−0.150228	+	0.988651i	$0.548001\pi$
$402$	2.11126e7	−	1.21894e7i	0.324986	−	0.187631i
$403$	2.87778e7	−	4.98447e7i	0.439686	−	0.761559i
$404$	−1.00882e7	−	1.74732e7i	−0.152992	−	0.264990i
$405$	1.57632e7	−	2.73027e7i	0.237290	−	0.410998i
$406$	5.54836e6			0.0829061
$407$			8.18882e6i			0.121461i
$408$	1.11650e7	−	1.93384e7i	0.164392	−	0.284734i
$409$	−4.51148e7	−	2.60470e7i	−0.659400	−	0.380705i	0.132648	−	0.991163i	$-0.457652\pi$
$409$	−4.51148e7	−	2.60470e7i	−0.659400	−	0.380705i	−0.792048	+	0.610458i	$0.790985\pi$
$410$	2.80326e7			0.406736
$411$			5.40975e7i			0.779204i
$412$	1.53760e6	+	887734.i	0.0219863	+	0.0126938i
$413$	−2.95685e7	+	1.70714e7i	−0.419739	+	0.242336i
$414$	−7.87752e6	−	4.54809e6i	−0.111017	−	0.0640956i
$415$	−4.82722e7	−	8.36099e7i	−0.675387	−	1.16980i
$416$	−6.66203e6	−	1.15390e7i	−0.0925393	−	0.160283i
$417$		−	4.34445e7i		−	0.599137i
$418$	−1.87682e7	+	3.91182e6i	−0.256977	+	0.0535612i
$419$	4.68678e7			0.637136			0.318568	−	0.947900i	$-0.396798\pi$
$419$	4.68678e7			0.637136			0.318568	+	0.947900i	$0.396798\pi$
$420$	9.94825e6	−	5.74363e6i	0.134276	−	0.0775244i
$421$	−2.26219e6	+	1.30608e6i	−0.0303168	+	0.0175034i	−0.515082	−	0.857141i	$-0.672238\pi$
$421$	−2.26219e6	+	1.30608e6i	−0.0303168	+	0.0175034i	0.484765	+	0.874644i	$0.338905\pi$
$422$	−1.84473e7	+	3.19517e7i	−0.245469	+	0.425165i
$423$	1.60604e6	+	2.78175e6i	0.0212195	+	0.0367533i
$424$	−1.92720e7	+	3.33801e7i	−0.252831	+	0.437916i
$425$	−1.94997e7			−0.254016
$426$		−	2.82033e6i		−	0.0364814i
$427$	−1.26506e6	+	2.19114e6i	−0.0162490	+	0.0281441i
$428$	−6.58528e7	−	3.80202e7i	−0.839930	−	0.484934i
$429$	2.48555e7			0.314811
$430$		−	3.96372e7i		−	0.498537i
$431$	−1.14701e7	−	6.62225e6i	−0.143263	−	0.0827130i	0.426655	−	0.904414i	$-0.359692\pi$
$431$	−1.14701e7	−	6.62225e6i	−0.143263	−	0.0827130i	−0.569918	+	0.821701i	$0.693025\pi$
$432$	1.90009e7	−	1.09702e7i	0.235680	−	0.136070i
$433$	−6.94296e7	−	4.00852e7i	−0.855226	−	0.493765i	0.00718459	−	0.999974i	$-0.497713\pi$
$433$	−6.94296e7	−	4.00852e7i	−0.855226	−	0.493765i	−0.862411	+	0.506209i	$0.831046\pi$
$434$	1.05315e7	+	1.82410e7i	0.128831	+	0.223142i
$435$	−7.95044e6	−	1.37706e7i	−0.0965881	−	0.167295i
$436$			6.58102e7i			0.794025i
$437$	−3.28068e7	+	2.93054e7i	−0.393115	+	0.351159i
$438$	1.32849e7			0.158101
$439$	3.36563e7	−	1.94315e7i	0.397807	−	0.229674i	−0.287730	−	0.957712i	$-0.592901\pi$
$439$	3.36563e7	−	1.94315e7i	0.397807	−	0.229674i	0.685537	+	0.728037i	$0.259567\pi$
$440$	−8.54448e6	+	4.93316e6i	−0.100306	+	0.0579118i
$441$	1.19728e7	−	2.07375e7i	0.139598	−	0.241791i
$442$	−3.66971e7	−	6.35612e7i	−0.424976	−	0.736080i
$443$	8.66767e6	−	1.50128e7i	0.0996991	−	0.172684i	−0.811861	−	0.583851i	$-0.801545\pi$
$443$	8.66767e6	−	1.50128e7i	0.0996991	−	0.172684i	0.911560	+	0.411167i	$0.134879\pi$
$444$	−1.15982e7			−0.132508
$445$			5.71493e7i			0.648531i
$446$	−2.81177e7	+	4.87012e7i	−0.316938	+	0.548953i
$447$	9.26996e7	+	5.35201e7i	1.03790	+	0.599231i
$448$	4.87604e6			0.0542292
$449$			3.90109e6i			0.0430970i	0.999768	+	0.0215485i	$0.00685963\pi$
$449$			3.90109e6i			0.0430970i	−0.999768	+	0.0215485i	$0.993140\pi$
$450$	−4.24621e6	−	2.45155e6i	−0.0465977	−	0.0269032i
$451$	−1.92234e7	+	1.10987e7i	−0.209557	+	0.120988i
$452$	1.92170e6	+	1.10949e6i	0.0208099	+	0.0120146i
$453$	3.29465e7	+	5.70651e7i	0.354417	+	0.613869i
$454$	4.96676e7	+	8.60268e7i	0.530769	+	0.919319i
$455$		−	3.77562e7i		−	0.400824i
$456$	−5.54049e6	−	2.65822e7i	−0.0584324	−	0.280348i
$457$	−1.46953e8			−1.53968			−0.769840	−	0.638237i	$-0.779664\pi$
$457$	−1.46953e8			−1.53968			−0.769840	+	0.638237i	$0.779664\pi$
$458$	1.10106e8	−	6.35696e7i	1.14608	−	0.661687i
$459$	1.04664e8	−	6.04280e7i	1.08233	−	0.624885i
$460$	−1.13193e7	+	1.96056e7i	−0.116291	+	0.201422i
$461$	8.72487e7	+	1.51119e8i	0.890546	+	1.54247i	0.839222	+	0.543788i	$0.183011\pi$
$461$	8.72487e7	+	1.51119e8i	0.890546	+	1.54247i	0.0513233	+	0.998682i	$0.483656\pi$
$462$	−4.54803e6	+	7.87741e6i	−0.0461208	+	0.0798836i
$463$	−5.14201e7			−0.518072			−0.259036	−	0.965868i	$-0.583405\pi$
$463$	−5.14201e7			−0.518072			−0.259036	+	0.965868i	$0.583405\pi$
$464$		−	6.74951e6i		−	0.0675644i
$465$	3.01819e7	−	5.22765e7i	0.300184	−	0.519933i
$466$	−6.91027e7	−	3.98965e7i	−0.682869	−	0.394255i
$467$	4.07560e7			0.400166			0.200083	−	0.979779i	$-0.435879\pi$
$467$	4.07560e7			0.400166			0.200083	+	0.979779i	$0.435879\pi$
$468$		−	1.84546e7i		−	0.180039i
$469$	2.53948e7	+	1.46617e7i	0.246165	+	0.142123i
$470$	6.92321e6	−	3.99712e6i	0.0666828	−	0.0384994i
$471$	1.43430e8	+	8.28093e7i	1.37270	+	0.792532i
$472$	2.07671e7	+	3.59697e7i	0.197493	+	0.342067i
$473$	1.56931e7	+	2.71813e7i	0.148295	+	0.256854i
$474$			8.63540e7i			0.810863i
$475$	−1.76838e7	+	1.57965e7i	−0.165004	+	0.147394i
$476$	2.68592e7			0.249041
$477$	−4.62335e7	+	2.66929e7i	−0.425992	+	0.245947i
$478$	3.07749e7	−	1.77679e7i	0.281782	−	0.162687i
$479$	6.36352e7	−	1.10219e8i	0.579017	−	1.00289i	−0.416576	−	0.909101i	$-0.636770\pi$
$479$	6.36352e7	−	1.10219e8i	0.579017	−	1.00289i	0.995592	−	0.0937853i	$-0.0298967\pi$
$480$	−6.98705e6	−	1.21019e7i	−0.0631786	−	0.109429i
$481$	−1.90604e7	+	3.30136e7i	−0.171276	+	0.296659i
$482$	4.99485e6			0.0446048
$483$			2.08712e7i			0.185228i
$484$	−2.44387e7	+	4.23291e7i	−0.215547	+	0.373339i
$485$	1.04892e8	+	6.05596e7i	0.919429	+	0.530833i
$486$	5.30005e7			0.461712
$487$			1.70187e7i			0.147347i	0.997282	+	0.0736733i	$0.0234722\pi$
$487$			1.70187e7i			0.147347i	−0.997282	+	0.0736733i	$0.976528\pi$
$488$	2.66550e6	+	1.53893e6i	0.0229361	+	0.0132421i
$489$	1.76365e7	−	1.01825e7i	0.150830	−	0.0870815i
$490$	−5.16114e7	−	2.97979e7i	−0.438690	−	0.253278i
$491$	−4.85718e7	−	8.41288e7i	−0.410336	−	0.710723i	0.584590	−	0.811329i	$-0.301255\pi$
$491$	−4.85718e7	−	8.41288e7i	−0.410336	−	0.710723i	−0.994926	+	0.100606i	$0.967922\pi$
$492$	−1.57195e7	−	2.72270e7i	−0.131991	−	0.228615i
$493$		−	3.71790e7i		−	0.310282i
$494$	−8.47699e7	−	2.79144e7i	−0.703171	−	0.231551i
$495$	−1.36655e7			−0.112670
$496$	2.21900e7	−	1.28114e7i	0.181850	−	0.104991i
$497$	2.93787e6	−	1.69618e6i	0.0239312	−	0.0138167i
$498$	−5.41380e7	+	9.37698e7i	−0.438343	+	0.759233i
$499$	−2.07776e6	−	3.59878e6i	−0.0167222	−	0.0289637i	0.857543	−	0.514412i	$-0.171990\pi$
$499$	−2.07776e6	−	3.59878e6i	−0.0167222	−	0.0289637i	−0.874265	+	0.485448i	$0.838656\pi$
$500$	−3.36786e7	+	5.83330e7i	−0.269429	+	0.466664i
$501$	−3.08800e7			−0.245564
$502$		−	1.30170e8i		−	1.02896i
$503$	−2.57762e7	+	4.46456e7i	−0.202542	+	0.350812i	−0.949347	−	0.314231i	$-0.898253\pi$
$503$	−2.57762e7	+	4.46456e7i	−0.202542	+	0.350812i	0.746805	+	0.665043i	$0.231587\pi$
$504$	5.84880e6	+	3.37681e6i	0.0456852	+	0.0263763i
$505$	−6.95508e7			−0.540042
$506$		−	1.79261e7i		−	0.138368i
$507$	8.78811e6	+	5.07382e6i	0.0674328	+	0.0389324i
$508$	−8.90857e7	+	5.14337e7i	−0.679543	+	0.392334i
$509$	1.52096e8	+	8.78128e7i	1.15336	+	0.665893i	0.949704	−	0.313149i	$-0.101384\pi$
$509$	1.52096e8	+	8.78128e7i	1.15336	+	0.665893i	0.203657	+	0.979042i	$0.434717\pi$
$510$	−3.84875e7	−	6.66622e7i	−0.290141	−	0.502538i
$511$	7.98968e6	+	1.38385e7i	0.0598779	+	0.103712i
$512$		−	5.93164e6i		−	0.0441942i
$513$	4.59658e7	−	1.39588e8i	0.340473	−	1.03394i
$514$	2.27178e7			0.167293
$515$	5.30033e6	−	3.06014e6i	0.0388044	−	0.0224037i
$516$	−3.84981e7	+	2.22269e7i	−0.280214	+	0.161782i
$517$	−3.16507e6	+	5.48207e6i	−0.0229040	+	0.0396710i
$518$	−6.97530e6	−	1.20816e7i	−0.0501849	−	0.0869229i
$519$	7.88318e7	−	1.36541e8i	0.563897	−	0.976698i
$520$	−4.59299e7			−0.326652
$521$		−	2.66620e8i		−	1.88530i	−0.333788	−	0.942648i	$-0.608327\pi$
$521$		−	2.66620e8i		−	1.88530i	0.333788	−	0.942648i	$-0.391673\pi$
$522$	4.67424e6	−	8.09602e6i	0.0328624	−	0.0569194i
$523$	2.13842e8	+	1.23462e8i	1.49482	+	0.863033i	0.999982	−	0.00595466i	$-0.00189544\pi$
$523$	2.13842e8	+	1.23462e8i	1.49482	+	0.863033i	0.494834	+	0.868987i	$0.335229\pi$
$524$	−5.20865e7			−0.362019
$525$			1.12502e7i			0.0777466i
$526$	−6.49729e7	−	3.75121e7i	−0.446452	−	0.257759i
$527$	1.22231e8	−	7.05703e7i	0.835124	−	0.482159i
$528$	9.58277e6	+	5.53262e6i	0.0651013	+	0.0375862i
$529$	5.34519e7	+	9.25814e7i	0.361074	+	0.625399i
$530$	6.64334e7	+	1.15066e8i	0.446230	+	0.772893i
$531$			5.75275e7i			0.384231i
$532$	2.43580e7	−	2.17583e7i	0.161773	−	0.144507i
$533$	−1.03334e8			−0.682432
$534$	5.55069e7	−	3.20469e7i	0.364522	−	0.210457i
$535$	−2.27004e8	+	1.31061e8i	−1.48242	+	0.855878i
$536$	1.78358e7	−	3.08925e7i	0.115824	−	0.200613i
$537$	−8.09111e6	−	1.40142e7i	−0.0522499	−	0.0904995i
$538$	−1.53707e7	+	2.66228e7i	−0.0987066	+	0.170965i
$539$	4.71902e7			0.301360
$540$		−	7.56314e7i		−	0.480309i
$541$	−1.23049e8	+	2.13127e8i	−0.777116	+	1.34600i	0.156481	+	0.987681i	$0.449985\pi$
$541$	−1.23049e8	+	2.13127e8i	−0.777116	+	1.34600i	−0.933597	+	0.358324i	$0.883348\pi$
$542$	−1.39588e7	−	8.05911e6i	−0.0876698	−	0.0506162i
$543$	−2.31327e8			−1.44486
$544$		−	3.26738e7i		−	0.202957i
$545$	1.96464e8	+	1.13429e8i	1.21365	+	0.700702i
$546$	−3.66711e7	+	2.11721e7i	−0.225292	+	0.130072i
$547$	−1.63248e8	−	9.42511e7i	−0.997436	−	0.575870i	−0.0899474	−	0.995947i	$-0.528670\pi$
$547$	−1.63248e8	−	9.42511e7i	−0.997436	−	0.575870i	−0.907489	+	0.420077i	$0.862003\pi$
$548$	3.95783e7	+	6.85516e7i	0.240500	+	0.416558i
$549$	2.13151e6	+	3.69188e6i	0.0128816	+	0.0223116i
$550$		−	9.66269e6i		−	0.0580778i
$551$	−3.01182e7	−	3.37168e7i	−0.180042	−	0.201554i
$552$	2.53895e7			0.150952
$553$	−8.99530e7	+	5.19344e7i	−0.531913	+	0.307100i
$554$	−1.44903e8	+	8.36596e7i	−0.852211	+	0.492025i
$555$	−1.99903e7	+	3.46242e7i	−0.116934	+	0.202536i
$556$	−3.17844e7	−	5.50523e7i	−0.184923	−	0.320296i
$557$	1.30307e7	−	2.25699e7i	0.0754056	−	0.130606i	−0.825857	−	0.563880i	$-0.809308\pi$
$557$	1.30307e7	−	2.25699e7i	0.0754056	−	0.130606i	0.901263	+	0.433273i	$0.142642\pi$
$558$	3.54892e7			0.204265
$559$			1.46110e8i			0.836459i
$560$	8.40420e6	−	1.45565e7i	0.0478556	−	0.0828883i
$561$	5.27857e7	+	3.04758e7i	0.298970	+	0.172610i
$562$	2.09519e8			1.18036
$563$		−	2.60621e8i		−	1.46044i	−0.683212	−	0.730220i	$-0.739418\pi$
$563$		−	2.60621e8i		−	1.46044i	0.683212	−	0.730220i	$-0.260582\pi$
$564$	−7.76450e6	−	4.48283e6i	−0.0432789	−	0.0249871i
$565$	6.62437e6	−	3.82458e6i	0.0367282	−	0.0212050i
$566$	9.73309e7	+	5.61940e7i	0.536787	+	0.309914i
$567$	−2.12644e7	−	3.68310e7i	−0.116655	−	0.202052i
$568$	−2.06338e6	−	3.57389e6i	−0.0112599	−	0.0195027i
$569$		−	2.37683e8i		−	1.29021i	−0.764093	−	0.645106i	$-0.776813\pi$
$569$		−	2.37683e8i		−	1.29021i	0.764093	−	0.645106i	$-0.223187\pi$
$570$	−8.89057e7	−	2.92763e7i	−0.480070	−	0.158085i
$571$	−2.02413e8			−1.08725			−0.543625	−	0.839328i	$-0.682949\pi$
$571$	−2.02413e8			−1.08725			−0.543625	+	0.839328i	$0.682949\pi$
$572$	3.14965e7	−	1.81845e7i	0.168296	−	0.0971659i
$573$	−2.04964e8	+	1.18336e8i	−1.08947	+	0.629005i
$574$	1.89078e7	−	3.27494e7i	0.0999785	−	0.173168i
$575$	−1.10857e7	−	1.92010e7i	−0.0583121	−	0.101000i
$576$	4.10784e6	−	7.11499e6i	0.0214954	−	0.0372312i
$577$	−8.73319e6			−0.0454617			−0.0227308	−	0.999742i	$-0.507236\pi$
$577$	−8.73319e6			−0.0454617			−0.0227308	+	0.999742i	$0.507236\pi$
$578$		−	4.34377e7i		−	0.224949i
$579$	3.52352e7	−	6.10291e7i	0.181527	−	0.314414i
$580$	−2.01494e7	−	1.16333e7i	−0.103271	−	0.0596235i
$581$	−1.30237e8			−0.664059
$582$		−	1.35837e8i		−	0.689048i
$583$	−9.11137e7	−	5.26045e7i	−0.459810	−	0.265471i
$584$	1.68344e7	−	9.71935e6i	0.0845199	−	0.0487976i
$585$	−5.50928e7	−	3.18079e7i	−0.275187	−	0.158879i
$586$	3.97414e7	+	6.88341e7i	0.197492	+	0.342067i
$587$	−1.26717e8	−	2.19480e8i	−0.626500	−	1.08513i	−0.988249	−	0.152854i	$-0.951154\pi$
$587$	−1.26717e8	−	2.19480e8i	−0.626500	−	1.08513i	0.361749	−	0.932275i	$-0.382180\pi$
$588$			6.68376e7i			0.328768i
$589$	5.36807e7	−	1.63017e8i	0.262708	−	0.797786i
$590$	1.43175e8			0.697124
$591$	−7.70670e7	+	4.44947e7i	−0.373341	+	0.215549i
$592$	−1.46971e7	+	8.48536e6i	−0.0708379	+	0.0408983i
$593$	1.25034e8	−	2.16566e8i	0.599606	−	1.03855i	−0.393273	−	0.919422i	$-0.628657\pi$
$593$	1.25034e8	−	2.16566e8i	0.599606	−	1.03855i	0.992879	−	0.119126i	$-0.0380092\pi$
$594$	2.99439e7	+	5.18644e7i	0.142873	+	0.247463i
$595$	4.62937e7	−	8.01830e7i	0.219771	−	0.380655i
$596$	1.56624e8			0.739807
$597$			1.32658e7i			0.0623464i
$598$	4.17250e7	−	7.22699e7i	0.195116	−	0.337951i
$599$	2.84445e8	+	1.64224e8i	1.32348	+	0.764112i	0.984282	−	0.176603i	$-0.0565108\pi$
$599$	2.84445e8	+	1.64224e8i	1.32348	+	0.764112i	0.339199	+	0.940715i	$0.389844\pi$
$600$	1.36857e7			0.0633597
$601$		−	2.05797e8i		−	0.948014i	−0.880521	−	0.474007i	$-0.842807\pi$
$601$		−	2.05797e8i		−	0.948014i	0.880521	−	0.474007i	$-0.157193\pi$
$602$	−4.63064e7	−	2.67350e7i	−0.212252	−	0.122544i
$603$	4.27879e7	−	2.47036e7i	0.195150	−	0.112670i
$604$	8.34988e7	+	4.82081e7i	0.378939	+	0.218781i
$605$	8.42437e7	+	1.45914e8i	0.380427	+	0.658919i
$606$	3.90012e7	+	6.75520e7i	0.175251	+	0.303543i
$607$			2.72271e8i			1.21741i	0.793398	+	0.608704i	$0.208310\pi$
$607$			2.72271e8i			1.21741i	−0.793398	+	0.608704i	$0.791690\pi$
$608$	−2.64687e7	−	2.96312e7i	−0.117766	−	0.131837i
$609$	−2.14501e7			−0.0949680
$610$	9.18835e6	−	5.30490e6i	0.0404807	−	0.0233715i
$611$	−2.55202e7	+	1.47341e7i	−0.111882	+	0.0645953i
$612$	2.26276e7	−	3.91922e7i	0.0987154	−	0.170980i
$613$	−8.84445e7	−	1.53190e8i	−0.383963	−	0.665044i	0.607662	−	0.794196i	$-0.292108\pi$
$613$	−8.84445e7	−	1.53190e8i	−0.383963	−	0.665044i	−0.991625	+	0.129152i	$0.958774\pi$
$614$	−1.57848e8	+	2.73400e8i	−0.681920	+	1.18112i
$615$	−1.08375e8			−0.465912
$616$			1.33095e7i			0.0569404i
$617$	−2.19916e8	+	3.80905e8i	−0.936270	+	1.62167i	−0.163916	+	0.986474i	$0.552413\pi$
$617$	−2.19916e8	+	3.80905e8i	−0.936270	+	1.62167i	−0.772354	+	0.635192i	$0.780921\pi$
$618$	−5.94440e6	−	3.43200e6i	−0.0251850	−	0.0145406i
$619$	−1.05041e8			−0.442880			−0.221440	−	0.975174i	$-0.571076\pi$
$619$	−1.05041e8			−0.442880			−0.221440	+	0.975174i	$0.571076\pi$
$620$		−	8.83255e7i		−	0.370605i
$621$	1.19005e8	+	6.87074e7i	0.496923	+	0.286899i
$622$	4.48339e7	−	2.58849e7i	0.186310	−	0.107566i
$623$	6.67651e7	+	3.85469e7i	0.276112	+	0.159413i
$624$	2.57556e7	+	4.46100e7i	0.106003	+	0.183602i
$625$	8.90868e7	+	1.54303e8i	0.364900	+	0.632025i
$626$			2.77437e8i			1.13094i
$627$	7.25583e7	−	1.51232e7i	0.294364	−	0.0613538i
$628$	2.42337e8			0.978454
$629$	−8.09573e7	+	4.67407e7i	−0.325315	+	0.187821i
$630$	2.01616e7	−	1.16403e7i	0.0806314	−	0.0465526i
$631$	7.57046e7	−	1.31124e8i	0.301325	−	0.521909i	−0.675112	−	0.737716i	$-0.735905\pi$
$631$	7.57046e7	−	1.31124e8i	0.301325	−	0.521909i	0.976436	+	0.215806i	$0.0692379\pi$
$632$	6.31775e7	+	1.09427e8i	0.250272	+	0.433483i
$633$	7.13179e7	−	1.23526e8i	0.281182	−	0.487021i
$634$	−2.23328e8			−0.876346
$635$			3.54598e8i			1.38489i
$636$	7.45062e7	−	1.29048e8i	0.289615	−	0.501628i
$637$	1.90249e8	+	1.09840e8i	0.736046	+	0.424956i
$638$	1.84233e7			0.0709424
$639$		−	5.71583e6i		−	0.0219067i
$640$	−1.77078e7	−	1.02236e7i	−0.0675499	−	0.0390000i
$641$	1.65739e8	−	9.56892e7i	0.629288	−	0.363320i	−0.151188	−	0.988505i	$-0.548310\pi$
$641$	1.65739e8	−	9.56892e7i	0.629288	−	0.363320i	0.780476	+	0.625185i	$0.214977\pi$
$642$	2.54589e8	+	1.46987e8i	0.962131	+	0.555487i
$643$	1.84232e8	+	3.19100e8i	0.693000	+	1.20031i	0.970850	+	0.239687i	$0.0770447\pi$
$643$	1.84232e8	+	3.19100e8i	0.693000	+	1.20031i	−0.277851	+	0.960624i	$0.589622\pi$
$644$	1.52696e7	+	2.64477e7i	0.0571702	+	0.0990217i
$645$			1.53238e8i			0.571069i
$646$	−1.45800e8	−	1.63220e8i	−0.540829	−	0.605447i
$647$	3.03515e8			1.12064			0.560322	−	0.828275i	$-0.310677\pi$
$647$	3.03515e8			1.12064			0.560322	+	0.828275i	$0.310677\pi$
$648$	−4.48044e7	+	2.58679e7i	−0.164663	+	0.0950682i
$649$	−9.81823e7	+	5.66856e7i	−0.359169	+	0.207366i
$650$	2.24910e7	−	3.89555e7i	0.0818971	−	0.141850i
$651$	−4.07150e7	−	7.05204e7i	−0.147574	−	0.255606i
$652$	1.48992e7	−	2.58061e7i	0.0537551	−	0.0931066i
$653$	1.73938e8			0.624677			0.312338	−	0.949971i	$-0.398888\pi$
$653$	1.73938e8			0.624677			0.312338	+	0.949971i	$0.398888\pi$
$654$		−	2.54424e8i		−	0.909547i
$655$	−8.97748e7	+	1.55494e8i	−0.319470	+	0.553339i
$656$	−3.98392e7	−	2.30012e7i	−0.141123	−	0.0814776i
$657$	2.69238e7			0.0949380
$658$		−	1.07841e7i		−	0.0378536i
$659$	−1.55447e8	−	8.97476e7i	−0.543159	−	0.313593i	0.203199	−	0.979137i	$-0.434866\pi$
$659$	−1.55447e8	−	8.97476e7i	−0.543159	−	0.313593i	−0.746358	+	0.665544i	$0.768199\pi$
$660$	3.30332e7	−	1.90717e7i	0.114900	−	0.0663373i
$661$	−1.15507e8	−	6.66880e7i	−0.399948	−	0.230910i	0.286513	−	0.958076i	$-0.407504\pi$
$661$	−1.15507e8	−	6.66880e7i	−0.399948	−	0.230910i	−0.686462	+	0.727166i	$0.740837\pi$
$662$	−1.80745e8	−	3.13059e8i	−0.623006	−	1.07908i
$663$	1.41872e8	+	2.45729e8i	0.486806	+	0.843172i
$664$			1.58432e8i			0.541176i
$665$	−2.29726e7	−	1.10218e8i	−0.0781169	−	0.374790i
$666$	−2.35055e7			−0.0795695
$667$	3.66094e7	−	2.11365e7i	0.123372	−	0.0712287i
$668$	−3.91308e7	+	2.25922e7i	−0.131277	+	0.0757929i
$669$	1.08704e8	−	1.88280e8i	0.363050	−	0.628820i
$670$	−6.14824e7	−	1.06491e8i	−0.204422	−	0.354068i
$671$	−4.20062e6	+	7.27569e6i	−0.0139042	+	0.0240828i
$672$	−1.88509e7			−0.0621190
$673$		−	1.56725e8i		−	0.514153i	−0.966391	−	0.257076i	$-0.917241\pi$
$673$		−	1.56725e8i		−	0.514153i	0.966391	−	0.257076i	$-0.0827592\pi$
$674$	−1.20077e8	+	2.07980e8i	−0.392176	+	0.679269i
$675$	6.41469e7	+	3.70352e7i	0.208576	+	0.120421i
$676$	1.48482e7			0.0480656
$677$			2.21243e8i			0.713024i	0.934291	+	0.356512i	$0.116034\pi$
$677$			2.21243e8i			0.713024i	−0.934291	+	0.356512i	$0.883966\pi$
$678$	−7.42934e6	−	4.28933e6i	−0.0238375	−	0.0137626i
$679$	1.41498e8	−	8.16942e7i	0.452004	−	0.260965i
$680$	−9.75416e7	−	5.63157e7i	−0.310215	−	0.179103i
$681$	−1.92016e8	−	3.32582e8i	−0.607991	−	1.05307i
$682$	3.49698e7	+	6.05694e7i	0.110240	+	0.190941i
$683$		−	3.56731e8i		−	1.11964i	−0.828614	−	0.559820i	$-0.810870\pi$
$683$		−	3.56731e8i		−	1.11964i	0.828614	−	0.559820i	$-0.189130\pi$
$684$	−1.12286e7	−	5.38729e7i	−0.0350880	−	0.168346i
$685$	2.72864e8			0.848935
$686$	−1.55388e8	+	8.97135e7i	−0.481334	+	0.277898i
$687$	−4.25672e8	+	2.45762e8i	−1.31282	+	0.757956i
$688$	−3.25228e7	+	5.63312e7i	−0.0998673	+	0.172975i
$689$	−2.44886e8	−	4.24155e8i	−0.748697	−	1.29678i
$690$	4.37607e7	−	7.57957e7i	0.133210	−	0.230727i
$691$	−6.55122e7			−0.198558			−0.0992792	−	0.995060i	$-0.531654\pi$
$691$	−6.55122e7			−0.198558			−0.0992792	+	0.995060i	$0.531654\pi$
$692$		−	2.30697e8i		−	0.696183i
$693$	−9.21726e6	+	1.59648e7i	−0.0276951	+	0.0479692i
$694$	−2.32347e8	−	1.34145e8i	−0.695117	−	0.401326i
$695$	−2.19131e8			−0.652754
$696$			2.60938e7i			0.0773943i
$697$	−2.19450e8	−	1.26700e8i	−0.648093	−	0.374177i
$698$	−3.34058e8	+	1.92869e8i	−0.982327	+	0.567147i
$699$	2.67153e8	+	1.54241e8i	0.782219	+	0.451614i
$700$	8.23075e6	+	1.42561e7i	0.0239964	+	0.0415629i
$701$	−8.15715e7	−	1.41286e8i	−0.236802	−	0.410152i	0.722993	−	0.690855i	$-0.242766\pi$
$701$	−8.15715e7	−	1.41286e8i	−0.236802	−	0.410152i	−0.959795	+	0.280703i	$0.909432\pi$
$702$			2.78791e8i			0.805876i
$703$	−3.55543e7	+	1.07971e8i	−0.102335	+	0.310771i
$704$	1.61909e7			0.0464037
$705$	−2.67653e7	+	1.54530e7i	−0.0763845	+	0.0441006i
$706$	1.91380e8	−	1.10493e8i	0.543853	−	0.313994i
$707$	−4.69116e7	+	8.12532e7i	−0.132746	+	0.229923i
$708$	−8.02863e7	−	1.39060e8i	−0.226226	−	0.391834i
$709$	2.98499e8	−	5.17015e8i	0.837536	−	1.45066i	−0.0544121	−	0.998519i	$-0.517328\pi$
$709$	2.98499e8	−	5.17015e8i	0.837536	−	1.45066i	0.891948	−	0.452137i	$-0.149338\pi$
$710$	−1.42256e7			−0.0397461
$711$			1.75010e8i			0.486915i
$712$	4.68918e7	−	8.12190e7i	0.129914	−	0.225018i
$713$	1.38979e8	+	8.02393e7i	0.383424	+	0.221370i
$714$	−1.03838e8			−0.285274
$715$		−	1.25369e8i		−	0.342983i
$716$	−2.05059e7	−	1.18391e7i	−0.0558650	−	0.0322537i
$717$	−1.18977e8	+	6.86912e7i	−0.322778	+	0.186356i
$718$	3.02410e8	+	1.74596e8i	0.817001	+	0.471696i
$719$	−2.74448e8	−	4.75358e8i	−0.738369	−	1.27889i	−0.953229	−	0.302248i	$-0.902263\pi$
$719$	−2.74448e8	−	4.75358e8i	−0.738369	−	1.27889i	0.214860	−	0.976645i	$-0.431070\pi$
$720$	−1.41603e7	−	2.45264e7i	−0.0379381	−	0.0657107i
$721$		−	8.25620e6i		−	0.0220280i
$722$	−2.64446e8	−	2.99099e7i	−0.702627	−	0.0794701i
$723$	−1.93102e7			−0.0510943
$724$	−2.93135e8	+	1.69241e8i	−0.772416	+	0.445955i
$725$	1.97335e7	−	1.13932e7i	0.0517834	−	0.0298972i
$726$	9.44807e7	−	1.63645e8i	0.246907	−	0.427655i
$727$	−1.40261e8	−	2.42939e8i	−0.365033	−	0.632256i	0.623748	−	0.781625i	$-0.285609\pi$
$727$	−1.40261e8	−	2.42939e8i	−0.365033	−	0.632256i	−0.988782	+	0.149369i	$0.952276\pi$
$728$	−3.09794e7	+	5.36580e7i	−0.0802933	+	0.139072i
$729$	−4.13251e8			−1.06667
$730$		−	6.70080e7i		−	0.172249i
$731$	−1.79149e8	+	3.10295e8i	−0.458629	+	0.794369i
$732$	−1.03049e7	−	5.94953e6i	−0.0262730	−	0.0151687i
$733$	5.29236e8			1.34381			0.671905	−	0.740638i	$-0.265477\pi$
$733$	5.29236e8			1.34381			0.671905	+	0.740638i	$0.265477\pi$
$734$			2.90861e8i			0.735525i
$735$	1.99531e8	+	1.15199e8i	0.502515	+	0.290127i
$736$	3.21733e7	−	1.85753e7i	0.0806979	−	0.0465910i
$737$	8.43234e7	+	4.86842e7i	0.210642	+	0.121614i
$738$	−3.18580e7	−	5.51797e7i	−0.0792592	−	0.137281i
$739$	−1.66952e7	−	2.89169e7i	−0.0413674	−	0.0716504i	0.844600	−	0.535397i	$-0.179838\pi$
$739$	−1.66952e7	−	2.89169e7i	−0.0413674	−	0.0716504i	−0.885968	+	0.463747i	$0.846505\pi$
$740$			5.85005e7i			0.144366i
$741$	3.27723e8	+	1.07918e8i	0.805475	+	0.265239i
$742$	1.79236e8			0.438746
$743$	−1.42101e8	+	8.20421e7i	−0.346442	+	0.200019i	−0.663117	−	0.748516i	$-0.730767\pi$
$743$	−1.42101e8	+	8.20421e7i	−0.346442	+	0.200019i	0.316675	+	0.948534i	$0.397434\pi$
$744$	−8.57872e7	+	4.95292e7i	−0.208307	+	0.120266i
$745$	2.69952e8	−	4.67571e8i	0.652856	−	1.13078i
$746$	−1.86742e8	−	3.23446e8i	−0.449806	−	0.779086i
$747$	−1.09719e8	+	1.90039e8i	−0.263221	+	0.455911i
$748$	8.91858e7			0.213104
$749$			3.53599e8i			0.841522i
$750$	1.30202e8	−	2.25517e8i	0.308627	−	0.534558i
$751$	3.17934e8	+	1.83560e8i	0.750616	+	0.433368i	0.825916	−	0.563793i	$-0.190658\pi$
$751$	3.17934e8	+	1.83560e8i	0.750616	+	0.433368i	−0.0753005	+	0.997161i	$0.523992\pi$
$752$	−1.31188e7			−0.0308489
$753$			5.03240e8i			1.17866i
$754$	7.42744e7	+	4.28823e7i	0.173271	+	0.100038i
$755$	2.87832e8	−	1.66180e8i	0.668804	−	0.386134i
$756$	−8.83570e7	−	5.10129e7i	−0.204492	−	0.118063i
$757$	−1.61703e6	−	2.80077e6i	−0.00372761	−	0.00645640i	0.864156	−	0.503225i	$-0.167853\pi$
$757$	−1.61703e6	−	2.80077e6i	−0.00372761	−	0.00645640i	−0.867883	+	0.496768i	$0.834520\pi$
$758$	4.45866e7	+	7.72263e7i	0.102376	+	0.177320i
$759$			6.93028e7i			0.158499i
$760$	−1.34079e8	+	2.79459e7i	−0.305436	+	0.0636615i
$761$	3.41749e8			0.775449			0.387724	−	0.921775i	$-0.373261\pi$
$761$	3.41749e8			0.775449			0.387724	+	0.921775i	$0.373261\pi$
$762$	3.44408e8	−	1.98844e8i	0.778409	−	0.449415i
$763$	2.65028e8	−	1.53014e8i	0.596647	−	0.344475i
$764$	−1.73152e8	+	2.99908e8i	−0.388282	+	0.672525i
$765$	−7.80007e7	−	1.35101e8i	−0.174226	−	0.301769i
$766$	−1.73361e8	+	3.00270e8i	−0.385714	+	0.668077i
$767$	−5.27768e8			−1.16965
$768$			2.29319e7i			0.0506240i
$769$	−3.33301e8	+	5.77294e8i	−0.732922	+	1.26946i	0.222708	+	0.974885i	$0.428510\pi$
$769$	−3.33301e8	+	5.77294e8i	−0.732922	+	1.26946i	−0.955629	+	0.294572i	$0.904823\pi$
$770$	3.97331e7	+	2.29399e7i	0.0870323	+	0.0502481i
$771$	−8.78276e7			−0.191632
$772$		−	1.03114e8i		−	0.224112i
$773$	4.25211e7	+	2.45496e7i	0.0920590	+	0.0531503i	0.545323	−	0.838226i	$-0.316407\pi$
$773$	4.25211e7	+	2.45496e7i	0.0920590	+	0.0531503i	−0.453264	+	0.891376i	$0.649740\pi$
$774$	−7.80222e7	+	4.50461e7i	−0.168266	+	0.0971482i
$775$	7.49134e7	+	4.32513e7i	0.160936	+	0.0929167i
$776$	−9.93799e7	−	1.72131e8i	−0.212674	−	0.368361i
$777$	2.69667e7	+	4.67077e7i	0.0574863	+	0.0995692i
$778$		−	1.87286e8i		−	0.397710i
$779$	−3.01652e8	+	6.28729e7i	−0.638108	+	0.133000i
$780$	1.77566e8			0.374177
$781$	9.75521e6	−	5.63217e6i	0.0204778	−	0.0118229i
$782$	1.77223e8	−	1.02320e8i	0.370596	−	0.213964i
$783$	−7.06131e7	+	1.22305e8i	−0.147096	+	0.254777i
$784$	4.88991e7	+	8.46958e7i	0.101474	+	0.175757i
$785$	4.17685e8	−	7.23451e8i	0.863455	−	1.49555i
$786$	2.01368e8			0.414689
$787$			8.47445e8i			1.73855i	0.494329	+	0.869275i	$0.335414\pi$
$787$			8.47445e8i			1.73855i	−0.494329	+	0.869275i	$0.664586\pi$
$788$	−6.51056e7	+	1.12766e8i	−0.133058	+	0.230462i
$789$	2.51187e8	+	1.45023e8i	0.511406	+	0.295260i
$790$	4.35564e8			0.883427
$791$		−	1.03186e7i		−	0.0208493i
$792$	1.94209e7	+	1.12127e7i	0.0390926	+	0.0225701i
$793$	−3.38700e7	+	1.95548e7i	−0.0679196	+	0.0392134i
$794$	−1.29551e8	−	7.47965e7i	−0.258810	−	0.149424i
$795$	−2.56833e8	−	4.44848e8i	−0.511152	−	0.885341i
$796$	9.70543e6	+	1.68103e7i	0.0192431	+	0.0333301i
$797$			4.54660e7i			0.0898074i	0.998991	+	0.0449037i	$0.0142981\pi$
$797$			4.54660e7i			0.0898074i	−0.998991	+	0.0449037i	$0.985702\pi$
$798$	−9.41686e7	+	8.41181e7i	−0.185309	+	0.165532i
$799$	−7.22633e7			−0.141670
$800$	1.73423e7	−	1.00126e7i	0.0338718	−	0.0195559i
$801$	1.12493e8	−	6.49480e7i	0.218891	−	0.126377i
$802$	2.27766e8	−	3.94503e8i	0.441536	−	0.764764i
$803$	2.65297e7	+	4.59509e7i	0.0512373	+	0.0887456i
$804$	−6.89536e7	+	1.19431e8i	−0.132675	+	0.229800i
$805$	1.05273e8			0.201804
$806$			3.25584e8i			0.621811i
$807$	5.94235e7	−	1.02924e8i	0.113067	−	0.195838i
$808$	9.88436e7	+	5.70674e7i	0.187376	+	0.108182i
$809$	2.23432e8			0.421987			0.210994	−	0.977487i	$-0.432330\pi$
$809$	2.23432e8			0.421987			0.210994	+	0.977487i	$0.432330\pi$
$810$			1.78340e8i			0.335579i
$811$	4.10424e8	+	2.36958e8i	0.769431	+	0.444231i	0.832672	−	0.553767i	$-0.186810\pi$
$811$	4.10424e8	+	2.36958e8i	0.769431	+	0.444231i	−0.0632404	+	0.997998i	$0.520143\pi$
$812$	−2.71813e7	+	1.56931e7i	−0.0507694	+	0.0293117i
$813$	5.39650e7	+	3.11567e7i	0.100425	+	0.0579803i
$814$	−2.31615e7	−	4.01169e7i	−0.0429431	−	0.0743796i
$815$	−5.13596e7	−	8.89575e7i	−0.0948744	−	0.164327i
$816$			1.26318e8i			0.232485i
$817$	8.89001e7	+	4.26526e8i	0.163018	+	0.782130i
$818$	2.94689e8			0.538398
$819$	−7.43196e7	+	4.29084e7i	−0.135286	+	0.0781072i
$820$	−1.37331e8	+	7.92883e7i	−0.249074	+	0.143803i
$821$	−8.30608e7	+	1.43865e8i	−0.150095	+	0.259972i	−0.931262	−	0.364350i	$-0.881291\pi$
$821$	−8.30608e7	+	1.43865e8i	−0.150095	+	0.259972i	0.781167	+	0.624322i	$0.214625\pi$
$822$	−1.53011e8	−	2.65022e8i	−0.275490	−	0.477163i
$823$	2.38473e8	−	4.13047e8i	0.427799	−	0.740969i	−0.568879	−	0.822422i	$-0.692623\pi$
$823$	2.38473e8	−	4.13047e8i	0.427799	−	0.740969i	0.996677	+	0.0814525i	$0.0259559\pi$
$824$	−1.00436e7			−0.0179517
$825$			3.73562e7i			0.0665274i
$826$	9.65704e7	−	1.67265e8i	0.171358	−	0.296800i
$827$	−4.96249e8	−	2.86509e8i	−0.877370	−	0.506550i	−0.00757962	−	0.999971i	$-0.502413\pi$
$827$	−4.96249e8	−	2.86509e8i	−0.877370	−	0.506550i	−0.869790	+	0.493421i	$0.835746\pi$
$828$	5.14558e7			0.0906448
$829$		−	5.14633e8i		−	0.903304i	−0.892194	−	0.451652i	$-0.850835\pi$
$829$		−	5.14633e8i		−	0.903304i	0.892194	−	0.451652i	$-0.149165\pi$
$830$	4.72969e8	+	2.73069e8i	0.827177	+	0.477571i
$831$	5.60198e8	−	3.23430e8i	0.976199	−	0.563609i
$832$	6.52743e7	+	3.76861e7i	0.113337	+	0.0654352i
$833$	2.69356e8	+	4.66538e8i	0.466006	+	0.807146i
$834$	1.22880e8	+	2.12834e8i	0.211827	+	0.366895i
$835$			1.55757e8i			0.267539i
$836$	8.08807e7	−	7.22484e7i	0.138429	−	0.123654i
$837$	−5.36130e8			−0.914310
$838$	−2.29604e8	+	1.32562e8i	−0.390165	+	0.225262i
$839$	−2.78940e8	+	1.61046e8i	−0.472308	+	0.272687i	−0.717206	−	0.696862i	$-0.754579\pi$
$839$	−2.78940e8	+	1.61046e8i	−0.472308	+	0.272687i	0.244897	+	0.969549i	$0.421246\pi$
$840$	−3.24909e7	+	5.62758e7i	−0.0548180	+	0.0949476i
$841$	−2.75689e8	−	4.77507e8i	−0.463480	−	0.802772i
$842$	7.38829e6	−	1.27969e7i	0.0123768	−	0.0214372i
$843$	−8.10006e8			−1.35209
$844$		−	2.08708e8i		−	0.347145i
$845$	2.55920e7	−	4.43266e7i	0.0424164	−	0.0734674i
$846$	−1.57359e7	−	9.08514e6i	−0.0259885	−	0.0150045i
$847$	2.27288e8			0.374046
$848$		−	2.18038e8i		−	0.357557i
$849$	−3.76284e8	−	2.17248e8i	−0.614883	−	0.355003i
$850$	9.55285e7	−	5.51534e7i	0.155552	−	0.0898081i
$851$	−9.20495e7	−	5.31448e7i	−0.149359	−	0.0862327i
$852$	7.97710e6	+	1.38167e7i	0.0128981	+	0.0223402i
$853$	−2.50779e8	−	4.34362e8i	−0.404058	−	0.699849i	0.590153	−	0.807291i	$-0.299067\pi$
$853$	−2.50779e8	−	4.34362e8i	−0.404058	−	0.699849i	−0.994211	+	0.107442i	$0.965734\pi$
$854$		−	1.43125e7i		−	0.0229795i
$855$	−1.80181e8	−	5.93328e7i	−0.288277	−	0.0949284i
$856$	4.30149e8			0.685800
$857$	−9.26651e8	+	5.35002e8i	−1.47222	+	0.849989i	−0.999512	−	0.0312281i	$-0.990058\pi$
$857$	−9.26651e8	+	5.35002e8i	−1.47222	+	0.849989i	−0.472712	+	0.881217i	$0.656725\pi$
$858$	−1.21766e8	+	7.03019e7i	−0.192782	+	0.111303i
$859$	5.19183e7	−	8.99251e7i	0.0819107	−	0.141873i	−0.822160	−	0.569257i	$-0.807231\pi$
$859$	5.19183e7	−	8.99251e7i	0.0819107	−	0.141873i	0.904071	+	0.427383i	$0.140564\pi$
$860$	1.12111e8	+	1.94182e8i	0.176259	+	0.305290i
$861$	−7.30982e7	+	1.26610e8i	−0.114524	+	0.198362i
$862$	7.49222e7			0.116974
$863$		−	1.03962e8i		−	0.161750i	−0.996724	−	0.0808749i	$-0.974229\pi$
$863$		−	1.03962e8i		−	0.161750i	0.996724	−	0.0808749i	$-0.0257714\pi$
$864$	−6.20566e7	+	1.07485e8i	−0.0962159	+	0.166651i
$865$	−6.88703e8	−	3.97623e8i	−1.06410	−	0.614360i
$866$	4.53512e8			0.698289
$867$			1.67931e8i			0.257676i
$868$	−1.03187e8	−	5.95750e7i	−0.157785	−	0.0910972i
$869$	−2.98689e8	+	1.72448e8i	−0.455156	+	0.262784i
$870$	7.78981e7	+	4.49745e7i	0.118296	+	0.0682981i
$871$	2.26636e8	+	3.92544e8i	0.342984	+	0.594066i
$872$	−1.86139e8	−	3.22403e8i	−0.280730	−	0.486239i
$873$		−	2.75295e8i		−	0.413766i
$874$	7.78317e7	−	2.36358e8i	0.116580	−	0.354027i
$875$	3.13221e8			0.467549
$876$	−6.50823e7	+	3.75753e7i	−0.0968167	+	0.0558971i
$877$	−4.20947e8	+	2.43034e8i	−0.624064	+	0.360304i	−0.778450	−	0.627707i	$-0.783994\pi$
$877$	−4.20947e8	+	2.43034e8i	−0.624064	+	0.360304i	0.154386	+	0.988011i	$0.450660\pi$
$878$	−1.09921e8	+	1.90389e8i	−0.162404	+	0.281292i
$879$	−1.53641e8	−	2.66114e8i	−0.226225	−	0.391834i
$880$	2.79062e7	−	4.83349e7i	0.0409498	−	0.0709272i
$881$	9.18803e8			1.34368			0.671838	−	0.740698i	$-0.265505\pi$
$881$	9.18803e8			1.34368			0.671838	+	0.740698i	$0.265505\pi$
$882$			1.35457e8i			0.197421i
$883$	2.70064e8	−	4.67765e8i	0.392270	−	0.679432i	−0.600478	−	0.799641i	$-0.705023\pi$
$883$	2.70064e8	−	4.67765e8i	0.392270	−	0.679432i	0.992749	+	0.120209i	$0.0383565\pi$
$884$	3.59556e8	+	2.07590e8i	0.520487	+	0.300504i
$885$	−5.53517e8			−0.798548
$886$			9.80635e7i			0.140996i
$887$	−4.11622e8	−	2.37650e8i	−0.589831	−	0.340539i	0.175200	−	0.984533i	$-0.443943\pi$
$887$	−4.11622e8	−	2.37650e8i	−0.589831	−	0.340539i	−0.765031	+	0.643994i	$0.777276\pi$
$888$	5.68193e7	−	3.28046e7i	0.0811441	−	0.0468486i
$889$	4.14262e8	+	2.39174e8i	0.589617	+	0.340416i
$890$	−1.61643e8	−	2.79973e8i	−0.229290	−	0.397143i
$891$	−7.06084e7	−	1.22297e8i	−0.0998213	−	0.172895i
$892$		−	3.18115e8i		−	0.448219i
$893$	−6.55340e7	+	5.85397e7i	−0.0920264	+	0.0822046i
$894$	−6.05511e8			−0.847441
$895$	−7.06868e7	+	4.08110e7i	−0.0985983	+	0.0569257i
$896$	−2.38876e7	+	1.37915e7i	−0.0332085	+	0.0191729i
$897$	−1.61310e8	+	2.79397e8i	−0.223503	+	0.387119i
$898$	−1.10339e7	−	1.91114e7i	−0.0152371	−	0.0263914i
$899$	−8.24649e7	+	1.42833e8i	−0.113498	+	0.196585i
$900$	2.77361e7			0.0380468
$901$		−	1.20104e9i		−	1.64204i
$902$	6.27835e7	−	1.08744e8i	0.0855512	−	0.148179i
$903$	1.79022e8	+	1.03358e8i	0.243132	+	0.140373i
$904$	−1.25525e7			−0.0169912
$905$			1.16680e9i			1.57416i
$906$	−3.22809e8	−	1.86374e8i	−0.434071	−	0.250611i
$907$	1.55992e8	−	9.00622e7i	0.209065	−	0.120704i	−0.391812	−	0.920045i	$-0.628152\pi$
$907$	1.55992e8	−	9.00622e7i	0.209065	−	0.120704i	0.600877	+	0.799342i	$0.294818\pi$
$908$	−4.86641e8	−	2.80963e8i	−0.650057	−	0.375311i
$909$	7.90418e7	+	1.36904e8i	0.105236	+	0.182274i
$910$	1.06791e8	+	1.84967e8i	0.141713	+	0.245454i
$911$		−	3.16985e8i		−	0.419260i	−0.977781	−	0.209630i	$-0.932774\pi$
$911$		−	3.16985e8i		−	0.419260i	0.977781	−	0.209630i	$-0.0672259\pi$
$912$	1.02329e8	+	1.14555e8i	0.134900	+	0.151018i
$913$	−4.32453e8			−0.568233
$914$	7.19921e8	−	4.15646e8i	0.942858	−	0.544359i
$915$	−3.55224e7	+	2.05089e7i	−0.0463702	+	0.0267719i
$916$	−3.59604e8	+	6.22852e8i	−0.467884	+	0.810398i
$917$	1.21105e8	+	2.09760e8i	0.157056	+	0.272029i
$918$	−3.41832e8	+	5.92071e8i	−0.441860	+	0.765325i
$919$	5.50031e8			0.708664			0.354332	−	0.935120i	$-0.384708\pi$
$919$	5.50031e8			0.708664			0.354332	+	0.935120i	$0.384708\pi$
$920$		−	1.28063e8i		−	0.164460i
$921$	6.10244e8	−	1.05697e9i	0.781132	−	1.35296i
$922$	−8.54859e8	−	4.93553e8i	−1.09069	−	0.629711i
$923$	5.24381e7			0.0666870
$924$		−	5.14550e7i		−	0.0652247i
$925$	−4.96173e7	−	2.86466e7i	−0.0626914	−	0.0361949i
$926$	2.51906e8	−	1.45438e8i	0.317253	−	0.183166i
$927$	−1.20472e7	−	6.95547e6i	−0.0151234	−	0.00873147i
$928$	1.90905e7	+	3.30657e7i	0.0238876	+	0.0413746i
$929$	2.16187e8	+	3.74447e8i	0.269639	+	0.467028i	0.968769	−	0.247967i	$-0.0797624\pi$
$929$	2.16187e8	+	3.74447e8i	0.269639	+	0.467028i	−0.699130	+	0.714995i	$0.746429\pi$
$930$			3.41469e8i			0.424524i
$931$	6.22210e8	+	2.04891e8i	0.771059	+	0.253906i
$932$	4.51377e8			0.557560
$933$	−1.73329e8	+	1.00072e8i	−0.213416	+	0.123216i
$934$	−1.99663e8	+	1.15275e8i	−0.245051	+	0.141480i
$935$	1.53718e8	−	2.66248e8i	0.188057	−	0.325725i
$936$	5.21976e7	+	9.04088e7i	0.0636536	+	0.110251i
$937$	−5.84238e8	+	1.01193e9i	−0.710184	+	1.23007i	0.254604	+	0.967045i	$0.418055\pi$
$937$	−5.84238e8	+	1.01193e9i	−0.710184	+	1.23007i	−0.964788	+	0.263029i	$0.915278\pi$
$938$	−1.65878e8			−0.200993
$939$		−	1.07258e9i		−	1.29548i
$940$	−2.26111e7	+	3.91636e7i	−0.0272232	+	0.0471519i
$941$	6.45843e7	+	3.72878e7i	0.0775101	+	0.0447505i	0.538254	−	0.842783i	$-0.319084\pi$
$941$	6.45843e7	+	3.72878e7i	0.0775101	+	0.0447505i	−0.460744	+	0.887533i	$0.652417\pi$
$942$	−9.36881e8			−1.12081
$943$		−	2.88118e8i		−	0.343586i
$944$	−2.03476e8	−	1.17477e8i	−0.241878	−	0.139648i
$945$	−3.04579e8	+	1.75849e8i	−0.360915	+	0.208374i
$946$	−1.53761e8	−	8.87737e7i	−0.181623	−	0.104860i
$947$	4.81516e8	+	8.34011e8i	0.566971	+	0.982023i	0.996863	+	0.0791426i	$0.0252183\pi$
$947$	4.81516e8	+	8.34011e8i	0.566971	+	0.982023i	−0.429892	+	0.902880i	$0.641448\pi$
$948$	−2.44246e8	−	4.23047e8i	−0.286683	−	0.496550i
$949$			2.47004e8i			0.289005i
$950$	4.19535e7	−	1.27404e8i	0.0489325	−	0.148598i
$951$	8.63392e8			1.00384
$952$	−1.31582e8	+	7.59692e7i	−0.152506	+	0.0880494i
$953$	4.04231e8	−	2.33383e8i	0.467036	−	0.269644i	−0.247962	−	0.968770i	$-0.579761\pi$
$953$	4.04231e8	−	2.33383e8i	0.467036	−	0.269644i	0.714998	+	0.699126i	$0.246427\pi$
$954$	1.50998e8	−	2.61536e8i	0.173911	−	0.301222i
$955$	5.96880e8	+	1.03383e9i	0.685294	+	1.18696i
$956$	−1.00511e8	+	1.74089e8i	−0.115037	+	0.199250i
$957$	−7.12251e7			−0.0812638
$958$			7.19950e8i			0.818853i
$959$	1.84045e8	−	3.18775e8i	0.208674	−	0.361434i
$960$	6.84588e7	+	3.95247e7i	0.0773777	+	0.0446740i
$961$	2.61389e8			0.294522
$962$		−	2.15644e8i		−	0.242221i
$963$	5.15963e8	+	2.97891e8i	0.577750	+	0.333564i
$964$	−2.44697e7	+	1.41276e7i	−0.0273147	+	0.0157702i
$965$	−3.07827e8	−	1.77724e8i	−0.342551	−	0.197772i
$966$	−5.90326e7	−	1.02248e8i	−0.0654879	−	0.113428i
$967$	−4.87240e8	−	8.43924e8i	−0.538844	−	0.933306i	−0.998967	−	0.0454501i	$-0.985528\pi$
$967$	−4.87240e8	−	8.43924e8i	−0.538844	−	0.933306i	0.460122	−	0.887855i	$-0.347806\pi$
$968$		−	2.76492e8i		−	0.304830i
$969$	5.63667e8	+	6.31014e8i	0.619514	+	0.693534i
$970$	−6.85154e8			−0.750711
$971$	1.06752e9	−	6.16330e8i	1.16605	−	0.673218i	0.213302	−	0.976986i	$-0.431578\pi$
$971$	1.06752e9	−	6.16330e8i	1.16605	−	0.673218i	0.952746	+	0.303768i	$0.0982447\pi$
$972$	−2.59649e8	+	1.49908e8i	−0.282740	+	0.163240i
$973$	−1.47803e8	+	2.56002e8i	−0.160451	+	0.277910i
$974$	−4.81362e7	−	8.33743e7i	−0.0520949	−	0.0902309i
$975$	−8.69507e7	+	1.50603e8i	−0.0938122	+	0.162488i
$976$	−1.74110e7			−0.0187272
$977$			8.07129e8i			0.865485i	0.901518	+	0.432742i	$0.142454\pi$
$977$			8.07129e8i			0.865485i	−0.901518	+	0.432742i	$0.857546\pi$
$978$	−5.76006e7	+	9.97672e7i	−0.0615759	+	0.106653i
$979$	2.21694e8	+	1.27995e8i	0.236268	+	0.136409i
$980$	3.37124e8			0.358189
$981$		−	5.15629e8i		−	0.546173i
$982$	4.75904e8	+	2.74764e8i	0.502557	+	0.290151i
$983$	9.77049e8	−	5.64099e8i	1.02862	−	0.593875i	0.112032	−	0.993705i	$-0.464264\pi$
$983$	9.77049e8	−	5.64099e8i	1.02862	−	0.593875i	0.916589	+	0.399830i	$0.130931\pi$
$984$	1.54019e8	+	8.89231e7i	0.161655	+	0.0933317i
$985$	2.24428e8	+	3.88721e8i	0.234838	+	0.406752i
$986$	1.05158e8	+	1.82139e8i	0.109701	+	0.190008i
$987$			4.16917e7i			0.0433609i
$988$	4.94240e8	−	1.03014e8i	0.512468	−	0.106813i
$989$	−4.07388e8			−0.421134
$990$	6.69468e7	−	3.86517e7i	0.0689960	−	0.0398349i
$991$	−1.92121e7	+	1.10921e7i	−0.0197403	+	0.0113971i	−0.509838	−	0.860271i	$-0.670295\pi$
$991$	−1.92121e7	+	1.10921e7i	−0.0197403	+	0.0113971i	0.490097	+	0.871668i	$0.336961\pi$
$992$	−7.24723e7	+	1.25526e8i	−0.0742398	+	0.128587i
$993$	6.98764e8	+	1.21030e9i	0.713646	+	1.23607i
$994$	−9.59505e6	+	1.66191e7i	−0.00976986	+	0.0169219i
$995$	6.69120e7			0.0679258
$996$		−	6.12502e8i		−	0.619911i
$997$	−9.06596e7	+	1.57027e8i	−0.0914804	+	0.158449i	−0.908134	−	0.418679i	$-0.862493\pi$
$997$	−9.06596e7	+	1.57027e8i	−0.0914804	+	0.158449i	0.816654	+	0.577128i	$0.195827\pi$
$998$	2.03578e7	+	1.17536e7i	0.0204804	+	0.0118244i
$999$	3.55094e8			0.356162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.31.4	yes	20
3.2	odd	2		342.7.m.a.145.9		20
19.8	odd	6	inner	38.7.d.a.27.4	✓	20
57.8	even	6		342.7.m.a.217.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.4	✓	20	19.8	odd	6	inner
38.7.d.a.31.4	yes	20	1.1	even	1	trivial
342.7.m.a.145.9		20	3.2	odd	2
342.7.m.a.217.9		20	57.8	even	6

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(18.9396 - 10.9348i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-55.1543 - 95.5300i) q^{5} +(-61.8564 + 107.138i) q^{6} -148.805 q^{7} +181.019i q^{8} +(-125.361 + 217.132i) q^{9} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(18.9396 - 10.9348i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-55.1543 - 95.5300i) q^{5} +(-61.8564 + 107.138i) q^{6} -148.805 q^{7} +181.019i q^{8} +(-125.361 + 217.132i) q^{9} +(540.399 + 312.000i) q^{10} -494.107 q^{11} -699.826i q^{12} +(-1992.01 - 1150.09i) q^{13} +(728.992 - 420.884i) q^{14} +(-2089.20 - 1206.20i) q^{15} +(-512.000 - 886.810i) q^{16} +(-2820.30 - 4884.90i) q^{17} -1418.30i q^{18} +(-6514.87 - 2145.32i) q^{19} -3529.87 q^{20} +(-2818.30 + 1627.15i) q^{21} +(2420.62 - 1397.54i) q^{22} +(3206.71 - 5554.19i) q^{23} +(1979.41 + 3428.43i) q^{24} +(1728.51 - 2993.87i) q^{25} +13011.8 q^{26} +21426.1i q^{27} +(-2380.88 + 4123.80i) q^{28} +(5708.25 + 3295.66i) q^{29} +13646.6 q^{30} +25022.3i q^{31} +(5016.55 + 2896.31i) q^{32} +(-9358.18 + 5402.95i) q^{33} +(27633.2 + 15954.0i) q^{34} +(8207.23 + 14215.3i) q^{35} +(4011.57 + 6948.24i) q^{36} -16573.0i q^{37} +(37984.1 - 7916.96i) q^{38} -50303.8 q^{39} +(17292.8 - 9983.99i) q^{40} +(38905.5 - 22462.1i) q^{41} +(9204.54 - 15942.7i) q^{42} +(-31760.6 - 55011.0i) q^{43} +(-7905.71 + 13693.1i) q^{44} +27656.9 q^{45} +36279.8i q^{46} +(6405.65 - 11094.9i) q^{47} +(-19394.1 - 11197.2i) q^{48} -95506.1 q^{49} +19555.9i q^{50} +(-106831. - 61678.7i) q^{51} +(-63744.4 + 36802.8i) q^{52} +(184401. + 106464. i) q^{53} +(-60602.2 - 104966. i) q^{54} +(27252.1 + 47202.0i) q^{55} -26936.6i q^{56} +(-146847. + 30607.2i) q^{57} -37286.1 q^{58} +(198707. - 114723. i) q^{59} +(-66854.3 + 38598.4i) q^{60} +(8501.44 - 14724.9i) q^{61} +(-70773.7 - 122584. i) q^{62} +(18654.4 - 32310.4i) q^{63} -32768.0 q^{64} +253729. i q^{65} +(30563.7 - 52937.8i) q^{66} +(-170658. - 98529.6i) q^{67} -180499. q^{68} -140259. i q^{69} +(-80414.1 - 46427.1i) q^{70} +(-19743.1 + 11398.7i) q^{71} +(-39305.2 - 22692.8i) q^{72} +(-53692.3 - 92997.8i) q^{73} +(46875.5 + 81190.7i) q^{74} -75603.5i q^{75} +(-163691. + 146220. i) q^{76} +73525.5 q^{77} +(246437. - 142281. i) q^{78} +(604503. - 349010. i) q^{79} +(-56478.0 + 97822.7i) q^{80} +(142901. + 247512. i) q^{81} +(-127065. + 220082. i) q^{82} +875221. q^{83} +104137. i q^{84} +(-311103. + 538846. i) q^{85} +(311189. + 179665. i) q^{86} +144149. q^{87} -89442.9i q^{88} +(-448676. - 259043. i) q^{89} +(-135490. + 78225.5i) q^{90} +(296421. + 171139. i) q^{91} +(-102615. - 177734. i) q^{92} +(273613. + 473912. i) q^{93} +72471.6i q^{94} +(154381. + 740689. i) q^{95} +126682. q^{96} +(-950899. + 549002. i) q^{97} +(467882. - 270132. i) q^{98} +(61941.9 - 107287. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Introduction

L-functions

Modular forms

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Database

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