LMFDB - Embedded newform 11.7.d.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,7,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

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("11.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.53059491982$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
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} + 825 x^{18} + 275175 x^{16} + 47589550 x^{14} + 4569013705 x^{12} + 245564683275 x^{10} + \cdots + 17\!\cdots\!25 $ x^20 + 825x^18 + 275175x^16 + 47589550x^14 + 4569013705x^12 + 245564683275x^10 + 7342625961605x^8 + 117784752305650x^6 + 929387807009775x^4 + 2945657032798125*x^2 + 1742746483878125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 5\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.4
Root			$4.59184i$ of defining polynomial
Character	$\chi$	$=$	11.8
Dual form			11.7.d.a.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58098 + 2.17603i) q^{2} +(-12.6315 - 38.8758i) q^{3} +(17.5415 - 53.9871i) q^{4} +(114.702 + 83.3360i) q^{5} +(64.6247 - 88.9483i) q^{6} +(-318.349 - 103.438i) q^{7} +(308.927 - 100.377i) q^{8} +(-761.996 + 553.623i) q^{9} +O(q^{10})$	\(q+(1.58098 + 2.17603i) q^{2} +(-12.6315 - 38.8758i) q^{3} +(17.5415 - 53.9871i) q^{4} +(114.702 + 83.3360i) q^{5} +(64.6247 - 88.9483i) q^{6} +(-318.349 - 103.438i) q^{7} +(308.927 - 100.377i) q^{8} +(-761.996 + 553.623i) q^{9} +381.348i q^{10} +(1277.12 + 374.873i) q^{11} -2320.36 q^{12} +(1890.15 + 2601.56i) q^{13} +(-278.219 - 856.270i) q^{14} +(1790.89 - 5511.79i) q^{15} +(-2232.32 - 1621.87i) q^{16} +(-410.906 + 565.564i) q^{17} +(-2409.40 - 782.862i) q^{18} +(5506.19 - 1789.07i) q^{19} +(6511.12 - 4730.60i) q^{20} +13682.6i q^{21} +(1203.36 + 3371.72i) q^{22} -14163.6 q^{23} +(-7804.43 - 10741.9i) q^{24} +(1383.31 + 4257.39i) q^{25} +(-2672.80 + 8226.04i) q^{26} +(7039.85 + 5114.75i) q^{27} +(-11168.6 + 15372.3i) q^{28} +(17037.1 + 5535.69i) q^{29} +(14825.2 - 4817.00i) q^{30} +(-6119.86 + 4446.34i) q^{31} -28210.6i q^{32} +(-1558.46 - 54384.1i) q^{33} -1880.32 q^{34} +(-27895.2 - 38394.5i) q^{35} +(16521.9 + 50849.3i) q^{36} +(-16161.1 + 49738.7i) q^{37} +(12598.2 + 9153.16i) q^{38} +(77262.4 - 106343. i) q^{39} +(43799.6 + 14231.4i) q^{40} +(-62856.4 + 20423.3i) q^{41} +(-29773.8 + 21631.9i) q^{42} +134226. i q^{43} +(42640.8 - 62372.1i) q^{44} -133539. q^{45} +(-22392.3 - 30820.4i) q^{46} +(-4327.31 - 13318.1i) q^{47} +(-34854.0 + 107270. i) q^{48} +(-4533.49 - 3293.77i) q^{49} +(-7077.23 + 9740.97i) q^{50} +(27177.1 + 8830.37i) q^{51} +(173607. - 56408.3i) q^{52} +(76404.0 - 55510.7i) q^{53} +23405.2i q^{54} +(115248. + 149429. i) q^{55} -108729. q^{56} +(-139103. - 191459. i) q^{57} +(14889.5 + 45825.1i) q^{58} +(63336.0 - 194928. i) q^{59} +(-266151. - 193370. i) q^{60} +(91166.7 - 125480. i) q^{61} +(-19350.8 - 6287.44i) q^{62} +(299846. - 97425.9i) q^{63} +(-81481.2 + 59199.6i) q^{64} +455922. i q^{65} +(115878. - 89371.5i) q^{66} -327447. q^{67} +(23325.2 + 32104.4i) q^{68} +(178907. + 550620. i) q^{69} +(39445.8 - 121402. i) q^{70} +(330998. + 240484. i) q^{71} +(-179831. + 247516. i) q^{72} +(-581986. - 189099. i) q^{73} +(-133783. + 43468.8i) q^{74} +(148036. - 107554. i) q^{75} -328646. i q^{76} +(-367793. - 251443. i) q^{77} +353555. q^{78} +(214164. + 294771. i) q^{79} +(-120891. - 372065. i) q^{80} +(-102264. + 314738. i) q^{81} +(-143816. - 104489. i) q^{82} +(211152. - 290626. i) q^{83} +(738685. + 240013. i) q^{84} +(-94263.6 + 30628.1i) q^{85} +(-292081. + 212209. i) q^{86} -732255. i q^{87} +(432165. - 12384.3i) q^{88} +343832. q^{89} +(-211123. - 290586. i) q^{90} +(-332626. - 1.02372e6i) q^{91} +(-248450. + 764650. i) q^{92} +(250158. + 181750. i) q^{93} +(22139.2 - 30472.0i) q^{94} +(780666. + 253654. i) q^{95} +(-1.09671e6 + 356342. i) q^{96} +(72846.5 - 52926.0i) q^{97} -15072.4i q^{98} +(-1.18070e6 + 421390. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) $ 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.58098	+	2.17603i	0.197622	+	0.272004i	0.896315	−	0.443418i	$-0.146234\pi$
$2$	1.58098	+	2.17603i	0.197622	+	0.272004i	−0.698692	+	0.715422i	$0.746234\pi$
$3$	−12.6315	−	38.8758i	−0.467833	−	1.43984i	−0.855384	−	0.517994i	$-0.826679\pi$
$3$	−12.6315	−	38.8758i	−0.467833	−	1.43984i	0.387551	−	0.921848i	$-0.373321\pi$
$4$	17.5415	−	53.9871i	0.274085	−	0.843548i
$5$	114.702	+	83.3360i	0.917618	+	0.666688i	0.942930	−	0.332991i	$-0.108058\pi$
$5$	114.702	+	83.3360i	0.917618	+	0.666688i	−0.0253123	+	0.999680i	$0.508058\pi$
$6$	64.6247	−	88.9483i	0.299188	−	0.411798i
$7$	−318.349	−	103.438i	−0.928130	−	0.301568i	−0.194333	−	0.980936i	$-0.562254\pi$
$7$	−318.349	−	103.438i	−0.928130	−	0.301568i	−0.733798	+	0.679368i	$0.762254\pi$
$8$	308.927	−	100.377i	0.603374	−	0.196048i
$9$	−761.996	+	553.623i	−1.04526	+	0.759427i
$10$			381.348i			0.381348i
$11$	1277.12	+	374.873i	0.959518	+	0.281647i
$11$	1277.12	+	374.873i	0.959518	+	0.281647i
$12$	−2320.36			−1.34280
$13$	1890.15	+	2601.56i	0.860331	+	1.18414i	0.981491	+	0.191511i	$0.0613387\pi$
$13$	1890.15	+	2601.56i	0.860331	+	1.18414i	−0.121160	+	0.992633i	$0.538661\pi$
$14$	−278.219	−	856.270i	−0.101392	−	0.312052i
$15$	1790.89	−	5511.79i	0.530634	−	1.63312i
$16$	−2232.32	−	1621.87i	−0.544999	−	0.395965i
$17$	−410.906	+	565.564i	−0.0836365	+	0.115116i	−0.848785	−	0.528738i	$-0.822665\pi$
$17$	−410.906	+	565.564i	−0.0836365	+	0.115116i	0.765149	+	0.643854i	$0.222665\pi$
$18$	−2409.40	−	782.862i	−0.413134	−	0.134236i
$19$	5506.19	−	1789.07i	0.802769	−	0.260835i	0.121237	−	0.992624i	$-0.461314\pi$
$19$	5506.19	−	1789.07i	0.802769	−	0.260835i	0.681532	+	0.731788i	$0.261314\pi$
$20$	6511.12	−	4730.60i	0.813889	−	0.591325i
$21$			13682.6i			1.47745i
$22$	1203.36	+	3371.72i	0.113013	+	0.316652i
$23$	−14163.6			−1.16410			−0.582049	−	0.813154i	$-0.697749\pi$
$23$	−14163.6			−1.16410			−0.582049	+	0.813154i	$0.697749\pi$
$24$	−7804.43	−	10741.9i	−0.564557	−	0.777045i
$25$	1383.31	+	4257.39i	0.0885318	+	0.272473i
$26$	−2672.80	+	8226.04i	−0.152071	+	0.468027i
$27$	7039.85	+	5114.75i	0.357661	+	0.259856i
$28$	−11168.6	+	15372.3i	−0.508774	+	0.700268i
$29$	17037.1	+	5535.69i	0.698557	+	0.226975i	0.636702	−	0.771110i	$-0.280298\pi$
$29$	17037.1	+	5535.69i	0.698557	+	0.226975i	0.0618555	+	0.998085i	$0.480298\pi$
$30$	14825.2	−	4817.00i	0.549081	−	0.178407i
$31$	−6119.86	+	4446.34i	−0.205427	+	0.149251i	−0.685742	−	0.727845i	$-0.740522\pi$
$31$	−6119.86	+	4446.34i	−0.205427	+	0.149251i	0.480315	+	0.877096i	$0.340522\pi$
$32$		−	28210.6i		−	0.860918i
$33$	−1558.46	−	54384.1i	−0.0433664	−	1.51332i
$34$	−1880.32			−0.0478404
$35$	−27895.2	−	38394.5i	−0.650617	−	0.895498i
$36$	16521.9	+	50849.3i	0.354123	+	1.08988i
$37$	−16161.1	+	49738.7i	−0.319055	+	0.981950i	0.654998	+	0.755630i	$0.272669\pi$
$37$	−16161.1	+	49738.7i	−0.319055	+	0.981950i	−0.974053	+	0.226320i	$0.927331\pi$
$38$	12598.2	+	9153.16i	0.229593	+	0.166809i
$39$	77262.4	−	106343.i	1.30249	−	1.79272i
$40$	43799.6	+	14231.4i	0.684369	+	0.222365i
$41$	−62856.4	+	20423.3i	−0.912006	+	0.296329i	−0.727183	−	0.686443i	$-0.759171\pi$
$41$	−62856.4	+	20423.3i	−0.912006	+	0.296329i	−0.184823	+	0.982772i	$0.559171\pi$
$42$	−29773.8	+	21631.9i	−0.401871	+	0.291976i
$43$			134226.i			1.68823i	0.536160	+	0.844117i	$0.319874\pi$
$43$			134226.i			1.68823i	−0.536160	+	0.844117i	$0.680126\pi$
$44$	42640.8	−	62372.1i	0.500573	−	0.732204i
$45$	−133539.			−1.46545
$46$	−22392.3	−	30820.4i	−0.230052	−	0.316639i
$47$	−4327.31	−	13318.1i	−0.0416797	−	0.128277i	0.928051	−	0.372452i	$-0.121483\pi$
$47$	−4327.31	−	13318.1i	−0.0416797	−	0.128277i	−0.969731	+	0.244175i	$0.921483\pi$
$48$	−34854.0	+	107270.i	−0.315159	+	0.969959i
$49$	−4533.49	−	3293.77i	−0.0385340	−	0.0279966i
$50$	−7077.23	+	9740.97i	−0.0566178	+	0.0779278i
$51$	27177.1	+	8830.37i	0.204876	+	0.0665684i
$52$	173607.	−	56408.3i	1.23469	−	0.401174i
$53$	76404.0	−	55510.7i	0.513202	−	0.372863i	−0.300835	−	0.953676i	$-0.597265\pi$
$53$	76404.0	−	55510.7i	0.513202	−	0.372863i	0.814037	+	0.580813i	$0.197265\pi$
$54$			23405.2i			0.148639i
$55$	115248.	+	149429.i	0.692699	+	0.898144i
$56$	−108729.			−0.619131
$57$	−139103.	−	191459.i	−0.751124	−	1.03383i
$58$	14889.5	+	45825.1i	0.0763125	+	0.234866i
$59$	63336.0	−	194928.i	0.308386	−	0.949115i	−0.670006	−	0.742356i	$-0.733708\pi$
$59$	63336.0	−	194928.i	0.308386	−	0.949115i	0.978392	−	0.206759i	$-0.0662916\pi$
$60$	−266151.	−	193370.i	−1.23218	−	0.895231i
$61$	91166.7	−	125480.i	0.401649	−	0.552822i	−0.559508	−	0.828825i	$-0.689010\pi$
$61$	91166.7	−	125480.i	0.401649	−	0.552822i	0.961157	+	0.276003i	$0.0890098\pi$
$62$	−19350.8	−	6287.44i	−0.0811938	−	0.0263815i
$63$	299846.	−	97425.9i	1.19916	−	0.389630i
$64$	−81481.2	+	59199.6i	−0.310826	+	0.225828i
$65$			455922.i			1.66016i
$66$	115878.	−	89371.5i	0.403058	−	0.310862i
$67$	−327447.			−1.08872			−0.544360	−	0.838852i	$-0.683227\pi$
$67$	−327447.			−1.08872			−0.544360	+	0.838852i	$0.683227\pi$
$68$	23325.2	+	32104.4i	0.0741822	+	0.102103i
$69$	178907.	+	550620.i	0.544604	+	1.67612i
$70$	39445.8	−	121402.i	0.115002	−	0.353941i
$71$	330998.	+	240484.i	0.924804	+	0.671910i	0.944715	−	0.327892i	$-0.106338\pi$
$71$	330998.	+	240484.i	0.924804	+	0.671910i	−0.0199109	+	0.999802i	$0.506338\pi$
$72$	−179831.	+	247516.i	−0.481799	+	0.663140i
$73$	−581986.	−	189099.i	−1.49604	−	0.486094i	−0.557182	−	0.830391i	$-0.688117\pi$
$73$	−581986.	−	189099.i	−1.49604	−	0.486094i	−0.938861	+	0.344297i	$0.888117\pi$
$74$	−133783.	+	43468.8i	−0.330147	+	0.107271i
$75$	148036.	−	107554.i	0.350900	−	0.254944i
$76$		−	328646.i		−	0.748666i
$77$	−367793.	−	251443.i	−0.805622	−	0.550765i
$78$	353555.			0.745029
$79$	214164.	+	294771.i	0.434375	+	0.597865i	0.968950	−	0.247255i	$-0.0795286\pi$
$79$	214164.	+	294771.i	0.434375	+	0.597865i	−0.534576	+	0.845121i	$0.679529\pi$
$80$	−120891.	−	372065.i	−0.236116	−	0.726689i
$81$	−102264.	+	314738.i	−0.192429	+	0.592234i
$82$	−143816.	−	104489.i	−0.260835	−	0.189508i
$83$	211152.	−	290626.i	0.369284	−	0.508276i	−0.583422	−	0.812169i	$-0.698287\pi$
$83$	211152.	−	290626.i	0.369284	−	0.508276i	0.952706	+	0.303893i	$0.0982865\pi$
$84$	738685.	+	240013.i	1.24630	+	0.404946i
$85$	−94263.6	+	30628.1i	−0.153493	+	0.0498728i
$86$	−292081.	+	212209.i	−0.459206	+	0.333633i
$87$		−	732255.i		−	1.11200i
$88$	432165.	−	12384.3i	0.634164	−	0.0181729i
$89$	343832.			0.487726			0.243863	−	0.969810i	$-0.421585\pi$
$89$	343832.			0.487726			0.243863	+	0.969810i	$0.421585\pi$
$90$	−211123.	−	290586.i	−0.289606	−	0.398609i
$91$	−332626.	−	1.02372e6i	−0.441400	−	1.35849i
$92$	−248450.	+	764650.i	−0.319062	+	0.981973i
$93$	250158.	+	181750.i	0.311004	+	0.225957i
$94$	22139.2	−	30472.0i	0.0266550	−	0.0366874i
$95$	780666.	+	253654.i	0.910531	+	0.295849i
$96$	−1.09671e6	+	356342.i	−1.23959	+	0.402766i
$97$	72846.5	−	52926.0i	0.0798166	−	0.0579902i	−0.547161	−	0.837027i	$-0.684292\pi$
$97$	72846.5	−	52926.0i	0.0798166	−	0.0579902i	0.626978	+	0.779037i	$0.284292\pi$
$98$		−	15072.4i		−	0.0160141i
$99$	−1.18070e6	+	421390.i	−1.21684	+	0.434289i
$100$	254109.			0.254109
$101$	261390.	+	359772.i	0.253702	+	0.349191i	0.916804	−	0.399338i	$-0.130760\pi$
$101$	261390.	+	359772.i	0.253702	+	0.349191i	−0.663101	+	0.748530i	$0.730760\pi$
$102$	23751.2	+	73098.8i	0.0223813	+	0.0688826i
$103$	390696.	−	1.20244e6i	0.357542	−	1.10040i	−0.596979	−	0.802257i	$-0.703632\pi$
$103$	390696.	−	1.20244e6i	0.357542	−	1.10040i	0.954521	−	0.298144i	$-0.0963676\pi$
$104$	845054.	+	613968.i	0.751250	+	0.545815i
$105$	−1.14026e6	+	1.56943e6i	−0.984995	+	1.35573i
$106$	241586.	+	78496.1i	0.202840	+	0.0659068i
$107$	−1.37431e6	+	446541.i	−1.12185	+	0.364511i	−0.810473	−	0.585776i	$-0.800790\pi$
$107$	−1.37431e6	+	446541.i	−1.12185	+	0.364511i	−0.311376	+	0.950287i	$0.600790\pi$
$108$	399620.	−	290341.i	0.317231	−	0.230482i
$109$		−	195884.i		−	0.151259i	−0.997136	−	0.0756293i	$-0.975903\pi$
$109$		−	195884.i		−	0.151259i	0.997136	−	0.0756293i	$-0.0240966\pi$
$110$	−142957.	+	487027.i	−0.107406	+	0.365910i
$111$	2.13777e6			1.56312
$112$	542892.	+	747227.i	0.386420	+	0.531862i
$113$	−241203.	−	742345.i	−0.167166	−	0.514483i	0.832024	−	0.554740i	$-0.187182\pi$
$113$	−241203.	−	742345.i	−0.167166	−	0.514483i	−0.999189	+	0.0402573i	$0.987182\pi$
$114$	196701.	−	605385.i	0.132768	−	0.408617i
$115$	−1.62459e6	−	1.18034e6i	−1.06820	−	0.776090i
$116$	597712.	−	822680.i	0.382929	−	0.527056i
$117$	−2.88057e6	−	935954.i	−1.79854	−	0.584382i
$118$	524303.	−	170356.i	0.319107	−	0.103684i
$119$	189312.	−	137543.i	0.112341	−	0.0816203i
$120$		−	1.88251e6i		−	1.08941i
$121$	1.49050e6	+	957514.i	0.841349	+	0.540492i
$122$	417181.			0.229745
$123$	1.58794e6	+	2.18561e6i	0.853333	+	1.17451i
$124$	132694.	+	408389.i	0.0695961	+	0.214195i
$125$	488443.	−	1.50327e6i	0.250083	−	0.769675i
$126$	686052.	+	498446.i	0.342962	+	0.249176i
$127$	−986730.	+	1.35812e6i	−0.481712	+	0.663019i	−0.978833	−	0.204662i	$-0.934391\pi$
$127$	−986730.	+	1.35812e6i	−0.481712	+	0.663019i	0.497121	+	0.867681i	$0.334391\pi$
$128$	−1.97475e6	−	641635.i	−0.941634	−	0.305955i
$129$	5.21815e6	−	1.69548e6i	2.43079	−	0.789812i
$130$	−992101.	+	720804.i	−0.451571	+	0.328085i
$131$			241965.i			0.107631i	0.998551	+	0.0538157i	$0.0171383\pi$
$131$			241965.i			0.107631i	−0.998551	+	0.0538157i	$0.982862\pi$
$132$	−2.96338e6	−	869841.i	−1.28844	−	0.378197i
$133$	−1.93795e6			−0.823734
$134$	−517687.	−	712534.i	−0.215156	−	0.296136i
$135$	381243.	+	1.17335e6i	0.154953	+	0.476897i
$136$	−70170.8	+	215963.i	−0.0278958	+	0.0858546i
$137$	−1.19050e6	−	864946.i	−0.462984	−	0.336378i	0.331716	−	0.943379i	$-0.392372\pi$
$137$	−1.19050e6	−	864946.i	−0.462984	−	0.336378i	−0.794701	+	0.607001i	$0.792372\pi$
$138$	−915317.	+	1.25983e6i	−0.348285	+	0.479373i
$139$	792841.	+	257610.i	0.295217	+	0.0959219i	0.452881	−	0.891571i	$-0.350396\pi$
$139$	792841.	+	257610.i	0.295217	+	0.0959219i	−0.157664	+	0.987493i	$0.550396\pi$
$140$	−2.56213e6	+	832486.i	−0.933720	+	0.303384i
$141$	−463091.	+	336455.i	−0.165200	+	0.120024i
$142$			1.10046e6i			0.384335i
$143$	1.43869e6	+	4.03107e6i	0.491992	+	1.37852i
$144$	2.59892e6			0.870374
$145$	1.49287e6	+	2.05476e6i	0.489687	+	0.673996i
$146$	−508623.	−	1.56538e6i	−0.163432	−	0.502992i
$147$	−70783.1	+	217848.i	−0.0222832	+	0.0685806i
$148$	2.40176e6	+	1.74498e6i	0.740874	+	0.538277i
$149$	2.57652e6	−	3.54628e6i	0.778888	−	1.07205i	−0.216515	−	0.976279i	$-0.569469\pi$
$149$	2.57652e6	−	3.54628e6i	0.778888	−	1.07205i	0.995404	−	0.0957688i	$-0.0305309\pi$
$150$	468084.	+	152090.i	0.138691	+	0.0450636i
$151$	−4.28216e6	+	1.39136e6i	−1.24375	+	0.404117i	−0.855676	−	0.517512i	$-0.826858\pi$
$151$	−4.28216e6	+	1.39136e6i	−1.24375	+	0.404117i	−0.388070	+	0.921630i	$0.626858\pi$
$152$	1.52143e6	−	1.10539e6i	0.433233	−	0.314762i
$153$		−	658444.i		−	0.183842i
$154$	−34326.3	−	1.19785e6i	−0.00939863	−	0.327976i
$155$	−1.07250e6			−0.288007
$156$	−4.38583e6	−	6.03658e6i	−1.15526	−	1.59007i
$157$	−511048.	−	1.57284e6i	−0.132057	−	0.406431i	0.863063	−	0.505096i	$-0.168543\pi$
$157$	−511048.	−	1.57284e6i	−0.132057	−	0.406431i	−0.995121	+	0.0986649i	$0.968543\pi$
$158$	−302843.	+	932053.i	−0.0767796	+	0.236303i
$159$	−3.12312e6	−	2.26908e6i	−0.776957	−	0.564492i
$160$	2.35096e6	−	3.23581e6i	0.573964	−	0.789993i
$161$	4.50896e6	+	1.46505e6i	1.08043	+	0.351054i
$162$	−846557.	+	275063.i	−0.199118	+	0.0646974i
$163$	−157349.	+	114320.i	−0.0363329	+	0.0263974i	−0.605803	−	0.795614i	$-0.707148\pi$
$163$	−157349.	+	114320.i	−0.0363329	+	0.0263974i	0.569471	+	0.822012i	$0.307148\pi$
$164$			3.75169e6i			0.850541i
$165$	4.35340e6	−	6.36786e6i	0.969118	−	1.41756i
$166$	966238.			0.211232
$167$	−1.68680e6	−	2.32168e6i	−0.362172	−	0.498486i	0.588581	−	0.808439i	$-0.299687\pi$
$167$	−1.68680e6	−	2.32168e6i	−0.362172	−	0.498486i	−0.950752	+	0.309952i	$0.899687\pi$
$168$	1.37341e6	+	4.22694e6i	0.289650	+	0.891452i
$169$	−1.70391e6	+	5.24411e6i	−0.353010	+	1.08645i
$170$	−215677.	−	156698.i	−0.0438992	−	0.0318946i
$171$	−3.20523e6	+	4.41162e6i	−0.641019	+	0.882286i
$172$	7.24649e6	+	2.35453e6i	1.42411	+	0.462720i
$173$	3.07127e6	−	997917.i	0.593171	−	0.192733i	0.00297858	−	0.999996i	$-0.499052\pi$
$173$	3.07127e6	−	997917.i	0.593171	−	0.192733i	0.590192	+	0.807263i	$0.299052\pi$
$174$	1.59341e6	−	1.15768e6i	0.302468	−	0.219756i
$175$		−	1.49842e6i		−	0.279589i
$176$	−2.24294e6	−	2.90816e6i	−0.411414	−	0.533433i
$177$	−8.37801e6			−1.51085
$178$	543591.	+	748189.i	0.0963857	+	0.132663i
$179$	−294484.	−	906330.i	−0.0513456	−	0.158025i	0.922096	−	0.386961i	$-0.126475\pi$
$179$	−294484.	−	906330.i	−0.0513456	−	0.158025i	−0.973441	+	0.228936i	$0.926475\pi$
$180$	−2.34248e6	+	7.20940e6i	−0.401659	+	1.23618i
$181$	4.54489e6	+	3.30206e6i	0.766457	+	0.556864i	0.900884	−	0.434060i	$-0.142919\pi$
$181$	4.54489e6	+	3.30206e6i	0.766457	+	0.556864i	−0.134427	+	0.990924i	$0.542919\pi$
$182$	1.70177e6	−	2.34228e6i	0.282284	−	0.388530i
$183$	−6.02971e6	−	1.95917e6i	−0.983882	−	0.319683i
$184$	−4.37551e6	+	1.42169e6i	−0.702386	+	0.228219i
$185$	−5.99874e6	+	4.35834e6i	−0.947425	+	0.688344i
$186$			831695.i			0.129248i
$187$	−736790.	+	568254.i	−0.112673	+	0.0868996i
$188$	−794913.			−0.119632
$189$	−1.71207e6	−	2.35646e6i	−0.253592	−	0.349039i
$190$	682259.	+	2.09978e6i	0.0994691	+	0.306134i
$191$	2.61885e6	−	8.05998e6i	0.375846	−	1.15673i	−0.567060	−	0.823676i	$-0.691919\pi$
$191$	2.61885e6	−	8.05998e6i	0.375846	−	1.15673i	0.942906	−	0.333058i	$-0.108081\pi$
$192$	3.33066e6	+	2.41986e6i	0.470572	+	0.341891i
$193$	3.97709e6	−	5.47400e6i	0.553215	−	0.761435i	−0.437229	−	0.899350i	$-0.644040\pi$
$193$	3.97709e6	−	5.47400e6i	0.553215	−	0.761435i	0.990444	+	0.137915i	$0.0440402\pi$
$194$	230337.	+	74841.2i	0.0315471	+	0.0102503i
$195$	1.77243e7	−	5.75898e6i	2.39037	−	0.776680i
$196$	−257345.	+	186972.i	−0.0341781	+	0.0248318i
$197$			8.97795e6i			1.17430i	0.809479	+	0.587149i	$0.199750\pi$
$197$			8.97795e6i			1.17430i	−0.809479	+	0.587149i	$0.800250\pi$
$198$	−2.78362e6	−	1.90303e6i	−0.358603	−	0.245160i
$199$	−9.52498e6			−1.20866			−0.604331	−	0.796734i	$-0.706559\pi$
$199$	−9.52498e6			−1.20866			−0.604331	+	0.796734i	$0.706559\pi$
$200$	854684.	+	1.17637e6i	0.106836	+	0.147047i
$201$	4.13614e6	+	1.27297e7i	0.509340	+	1.56759i
$202$	−369624.	+	1.13758e6i	−0.0448441	+	0.138016i
$203$	−4.85114e6	−	3.52456e6i	−0.579904	−	0.421325i
$204$	953452.	−	1.31231e6i	0.112307	−	0.154578i
$205$	−8.91176e6	−	2.89561e6i	−1.03443	−	0.336107i
$206$	3.23422e6	−	1.05086e6i	0.369972	−	0.120211i
$207$	1.07926e7	−	7.84128e6i	1.21679	−	0.884048i
$208$		−	8.87309e6i		−	0.986018i
$209$	7.70273e6	−	220733.i	0.843735	−	0.0241785i
$210$	−5.21784e6			−0.563421
$211$	−5.28770e6	−	7.27790e6i	−0.562885	−	0.774745i	0.428805	−	0.903397i	$-0.358935\pi$
$211$	−5.28770e6	−	7.27790e6i	−0.562885	−	0.774745i	−0.991690	+	0.128653i	$0.958935\pi$
$212$	−1.65663e6	−	5.09857e6i	−0.173867	−	0.535107i
$213$	5.16800e6	−	1.59055e7i	0.534790	−	1.64591i
$214$	−3.14445e6	−	2.28458e6i	−0.320851	−	0.233112i
$215$	−1.11859e7	+	1.53961e7i	−1.12552	+	1.54915i
$216$	2.68820e6	+	873450.i	0.266748	+	0.0866716i
$217$	2.40817e6	−	782462.i	0.235672	−	0.0765745i
$218$	426250.	−	309689.i	0.0411429	−	0.0298921i
$219$			2.50137e7i			2.38148i
$220$	1.00888e7	−	3.60070e6i	0.947487	−	0.338157i
$221$	−2.24802e6			−0.208269
$222$	3.37977e6	+	4.65185e6i	0.308907	+	0.425174i
$223$	−1.17246e6	−	3.60846e6i	−0.105726	−	0.325393i	0.884174	−	0.467158i	$-0.154722\pi$
$223$	−1.17246e6	−	3.60846e6i	−0.105726	−	0.325393i	−0.989900	+	0.141766i	$0.954722\pi$
$224$	−2.91804e6	+	8.98080e6i	−0.259625	+	0.799044i
$225$	−3.41106e6	−	2.47828e6i	−0.299462	−	0.217572i
$226$	1.23403e6	−	1.69850e6i	0.106906	−	0.147143i
$227$	7.68270e6	+	2.49626e6i	0.656804	+	0.213409i	0.618412	−	0.785854i	$-0.287776\pi$
$227$	7.68270e6	+	2.49626e6i	0.656804	+	0.213409i	0.0383924	+	0.999263i	$0.487776\pi$
$228$	−1.27764e7	+	4.15130e6i	−1.07796	+	0.350251i
$229$	−5.27075e6	+	3.82942e6i	−0.438900	+	0.318880i	−0.785198	−	0.619245i	$-0.787439\pi$
$229$	−5.27075e6	+	3.82942e6i	−0.438900	+	0.318880i	0.346298	+	0.938125i	$0.387439\pi$
$230$		−	5.40125e6i		−	0.443926i
$231$	−5.12924e6	+	1.74743e7i	−0.416119	+	1.41764i
$232$	5.81888e6			0.465989
$233$	6.50329e6	+	8.95101e6i	0.514121	+	0.707627i	0.984607	−	0.174780i	$-0.0559215\pi$
$233$	6.50329e6	+	8.95101e6i	0.514121	+	0.707627i	−0.470486	+	0.882407i	$0.655922\pi$
$234$	−2.51746e6	−	7.74793e6i	−0.196478	−	0.604698i
$235$	613525.	−	1.88824e6i	0.0472747	−	0.145497i
$236$	−9.41260e6	−	6.83866e6i	−0.716100	−	0.520277i
$237$	8.75424e6	−	1.20492e7i	0.657617	−	0.905133i
$238$	598597.	+	194496.i	0.0444021	+	0.0144271i
$239$	−7.06277e6	+	2.29483e6i	−0.517346	+	0.168096i	−0.556041	−	0.831155i	$-0.687680\pi$
$239$	−7.06277e6	+	2.29483e6i	−0.517346	+	0.168096i	0.0386944	+	0.999251i	$0.487680\pi$
$240$	−1.29373e7	+	9.39947e6i	−0.935855	+	0.679939i
$241$		−	9.33775e6i		−	0.667100i	−0.942732	−	0.333550i	$-0.891753\pi$
$241$		−	9.33775e6i		−	0.667100i	0.942732	−	0.333550i	$-0.108247\pi$
$242$	272872.	+	4.75719e6i	0.0192537	+	0.335664i
$243$	1.98710e7			1.38484
$244$	−5.17511e6	−	7.12293e6i	−0.356246	−	0.490331i
$245$	−245511.	−	755605.i	−0.0166945	−	0.0513803i
$246$	−2.24546e6	+	6.91081e6i	−0.150834	+	0.464220i
$247$	1.50619e7	+	1.09431e7i	0.999514	+	0.726189i
$248$	−1.44428e6	+	1.98789e6i	−0.0946886	+	0.130328i
$249$	−1.39655e7	−	4.53765e6i	−0.904602	−	0.293923i
$250$	4.04338e6	−	1.31377e6i	0.258777	−	0.0840816i
$251$	1.84348e7	−	1.33937e7i	1.16578	−	0.846991i	0.175285	−	0.984518i	$-0.443915\pi$
$251$	1.84348e7	−	1.33937e7i	1.16578	−	0.846991i	0.990498	+	0.137527i	$0.0439154\pi$
$252$		−	1.78968e7i		−	1.11834i
$253$	−1.80886e7	−	5.30954e6i	−1.11697	−	0.327865i
$254$	−4.51531e6			−0.275541
$255$	2.38138e6	+	3.27769e6i	0.143618	+	0.197673i
$256$	266055.	+	818833.i	0.0158581	+	0.0488063i
$257$	−128669.	+	396004.i	−0.00758012	+	0.0233292i	−0.954775	−	0.297329i	$-0.903904\pi$
$257$	−128669.	+	396004.i	−0.00758012	+	0.0233292i	0.947195	+	0.320658i	$0.103904\pi$
$258$	1.19392e7	+	8.67434e6i	0.695210	+	0.505100i
$259$	1.02897e7	−	1.41626e7i	0.592249	−	0.815161i
$260$	2.46139e7	+	7.99755e6i	1.40043	+	0.455027i
$261$	−1.60469e7	+	5.21395e6i	−0.902547	+	0.293255i
$262$	−526524.	+	382542.i	−0.0292762	+	0.0212704i
$263$		−	1.39390e7i		−	0.766237i	−0.923699	−	0.383118i	$-0.874850\pi$
$263$		−	1.39390e7i		−	0.766237i	0.923699	−	0.383118i	$-0.125150\pi$
$264$	−5.94034e6	−	1.66443e7i	−0.322849	−	0.904595i
$265$	1.33897e7			0.719507
$266$	−3.06385e6	−	4.21703e6i	−0.162788	−	0.224059i
$267$	−4.34311e6	−	1.33667e7i	−0.228175	−	0.702249i
$268$	−5.74390e6	+	1.76779e7i	−0.298402	+	0.918388i
$269$	522234.	+	379425.i	0.0268292	+	0.0194926i	0.601119	−	0.799159i	$-0.294722\pi$
$269$	522234.	+	379425.i	0.0268292	+	0.0194926i	−0.574290	+	0.818652i	$0.694722\pi$
$270$	−1.95050e6	+	2.68463e6i	−0.0990956	+	0.136393i
$271$	−1.83021e7	−	5.94672e6i	−0.919589	−	0.298792i	−0.189291	−	0.981921i	$-0.560619\pi$
$271$	−1.83021e7	−	5.94672e6i	−0.919589	−	0.298792i	−0.730298	+	0.683129i	$0.760619\pi$
$272$	1.83454e6	−	596080.i	0.0911636	−	0.0296209i
$273$	−3.55962e7	+	2.58622e7i	−1.74951	+	1.27109i
$274$		−	3.95802e6i		−	0.192409i
$275$	170671.	+	5.95576e6i	0.00820656	+	0.286377i
$276$	3.28647e7			1.56315
$277$	1.87489e7	+	2.58057e7i	0.882140	+	1.21416i	0.975824	+	0.218559i	$0.0701358\pi$
$277$	1.87489e7	+	2.58057e7i	0.882140	+	1.21416i	−0.0936837	+	0.995602i	$0.529864\pi$
$278$	692899.	+	2.13252e6i	0.0322504	+	0.0992566i
$279$	2.20172e6	−	6.77619e6i	0.101379	−	0.312013i
$280$	−1.24715e7	−	9.06107e6i	−0.568126	−	0.412767i
$281$	−2.20450e7	+	3.03423e7i	−0.993552	+	1.36751i	−0.0643528	+	0.997927i	$0.520498\pi$
$281$	−2.20450e7	+	3.03423e7i	−0.993552	+	1.36751i	−0.929199	+	0.369580i	$0.879502\pi$
$282$	−1.46427e6	−	475771.i	−0.0652943	−	0.0212154i
$283$	−2.15406e7	+	6.99898e6i	−0.950385	+	0.308799i	−0.742872	−	0.669434i	$-0.766537\pi$
$283$	−2.15406e7	+	6.99898e6i	−0.950385	+	0.308799i	−0.207513	+	0.978232i	$0.566537\pi$
$284$	1.87892e7	−	1.36512e7i	0.820264	−	0.595957i
$285$		−	3.35530e7i		−	1.44943i
$286$	−6.49720e6	+	9.50366e6i	−0.277733	+	0.406250i
$287$	2.21228e7			0.935824
$288$	1.56180e7	+	2.14963e7i	0.653805	+	0.899885i
$289$	7.30790e6	+	2.24914e7i	0.302760	+	0.931801i
$290$	−2.11103e6	+	6.49707e6i	−0.0865565	+	0.266393i
$291$	−2.97770e6	−	2.16343e6i	−0.120838	−	0.0877936i
$292$	−2.04178e7	+	2.81027e7i	−0.820087	+	1.12875i
$293$	−1.73452e7	−	5.63581e6i	−0.689569	−	0.224054i	−0.0567888	−	0.998386i	$-0.518086\pi$
$293$	−1.73452e7	−	5.63581e6i	−0.689569	−	0.224054i	−0.632780	+	0.774332i	$0.718086\pi$
$294$	−585950.	+	190387.i	−0.0230579	+	0.00749195i
$295$	2.35093e7	−	1.70805e7i	0.915744	−	0.665327i
$296$			1.69878e7i			0.655033i
$297$	7.07334e6	+	9.17118e6i	0.269995	+	0.350071i
$298$	1.17902e7			0.445527
$299$	−2.67712e7	−	3.68474e7i	−1.00151	−	1.37846i
$300$	−3.20978e6	−	9.87870e6i	−0.118881	−	0.365878i
$301$	1.38841e7	−	4.27308e7i	0.509117	−	1.56690i
$302$	−9.79763e6	−	7.11840e6i	−0.355714	−	0.258441i
$303$	1.06847e7	−	1.47062e7i	0.384090	−	0.528655i
$304$	−1.51932e7	−	4.93657e6i	−0.540790	−	0.175713i
$305$	2.09140e7	−	6.79538e6i	0.737120	−	0.239505i
$306$	1.43280e6	−	1.04099e6i	0.0500057	−	0.0363313i
$307$			3.35084e7i			1.15808i	0.815299	+	0.579040i	$0.196573\pi$
$307$			3.35084e7i			1.15808i	−0.815299	+	0.579040i	$0.803427\pi$
$308$	−2.00263e7	+	1.54454e7i	−0.685407	+	0.528624i
$309$	−5.16808e7			−1.75167
$310$	−1.69560e6	−	2.33380e6i	−0.0569166	−	0.0783390i
$311$	−1.35454e7	−	4.16885e7i	−0.450310	−	1.38591i	−0.876554	−	0.481303i	$-0.840164\pi$
$311$	−1.35454e7	−	4.16885e7i	−0.450310	−	1.38591i	0.426244	−	0.904608i	$-0.359836\pi$
$312$	1.31942e7	−	4.06074e7i	0.434428	−	1.33703i
$313$	2.04323e7	+	1.48450e7i	0.666323	+	0.484112i	0.868792	−	0.495177i	$-0.164897\pi$
$313$	2.04323e7	+	1.48450e7i	0.666323	+	0.484112i	−0.202469	+	0.979289i	$0.564897\pi$
$314$	2.61460e6	−	3.59869e6i	0.0844532	−	0.116240i
$315$	4.25121e7	+	1.38130e7i	1.36013	+	0.441933i
$316$	1.96706e7	−	6.39136e6i	0.623384	−	0.202550i
$317$	1.00699e7	−	7.31623e6i	0.316117	−	0.229673i	−0.418400	−	0.908263i	$-0.637409\pi$
$317$	1.00699e7	−	7.31623e6i	0.316117	−	0.229673i	0.734517	+	0.678590i	$0.237409\pi$
$318$		−	1.03834e7i		−	0.322892i
$319$	1.96832e7	+	1.34565e7i	0.606351	+	0.414534i
$320$	−1.42795e7			−0.435777
$321$	3.47193e7	+	4.77870e7i	1.04968	+	1.44476i
$322$	3.94057e6	+	1.21278e7i	0.118030	+	0.363259i
$323$	−1.25069e6	+	3.84924e6i	−0.0371145	+	0.114227i
$324$	1.51979e7	+	1.10419e7i	0.446836	+	0.324646i
$325$	−8.46121e6	+	1.16459e7i	−0.246481	+	0.339251i
$326$	−497530.	−	161657.i	−0.0143604	−	0.00466597i
$327$	−7.61515e6	+	2.47431e6i	−0.217789	+	0.0707638i
$328$	−1.73680e7	+	1.26186e7i	−0.492186	+	0.357594i
$329$			4.68741e6i			0.131627i
$330$	2.07393e7	−	594314.i	0.577101	−	0.0165377i
$331$	−3.54114e7			−0.976470			−0.488235	−	0.872712i	$-0.662359\pi$
$331$	−3.54114e7			−0.976470			−0.488235	+	0.872712i	$0.662359\pi$
$332$	−1.19861e7	−	1.64975e7i	−0.327540	−	0.450820i
$333$	−1.52218e7	−	4.68479e7i	−0.412224	−	1.26869i
$334$	2.38526e6	−	7.34106e6i	0.0640170	−	0.197024i
$335$	−3.75589e7	−	2.72881e7i	−0.999029	−	0.725837i
$336$	2.21915e7	−	3.05439e7i	0.585017	−	0.805207i
$337$	−2.83401e7	−	9.20826e6i	−0.740477	−	0.240596i	−0.0855987	−	0.996330i	$-0.527280\pi$
$337$	−2.83401e7	−	9.20826e6i	−0.740477	−	0.240596i	−0.654879	+	0.755734i	$0.727280\pi$
$338$	−1.41052e7	+	4.58305e6i	−0.365282	+	0.118687i
$339$	−2.58125e7	+	1.87539e7i	−0.662569	+	0.481384i
$340$			5.62628e6i			0.143148i
$341$	−9.48260e6	+	3.38433e6i	−0.239147	+	0.0853513i
$342$	−1.46672e7			−0.366665
$343$	2.42500e7	+	3.33773e7i	0.600938	+	0.827120i
$344$	1.34732e7	+	4.14662e7i	0.330975	+	1.01864i
$345$	−2.53654e7	+	7.80667e7i	−0.617710	+	1.90112i
$346$	7.02711e6	+	5.10550e6i	0.169648	+	0.123256i
$347$	−1.16591e7	+	1.60474e7i	−0.279047	+	0.384075i	−0.925418	−	0.378948i	$-0.876286\pi$
$347$	−1.16591e7	+	1.60474e7i	−0.279047	+	0.384075i	0.646371	+	0.763023i	$0.276286\pi$
$348$	−3.95323e7	−	1.28448e7i	−0.938025	−	0.304783i
$349$	5.94094e7	−	1.93033e7i	1.39759	−	0.454104i	0.489178	−	0.872184i	$-0.337297\pi$
$349$	5.94094e7	−	1.93033e7i	1.39759	−	0.454104i	0.908410	+	0.418080i	$0.137297\pi$
$350$	3.26061e6	−	2.36897e6i	0.0760492	−	0.0552530i
$351$			2.79822e7i			0.647084i
$352$	1.05754e7	−	3.60282e7i	0.242475	−	0.826066i
$353$	8.28649e7			1.88385			0.941926	−	0.335821i	$-0.109014\pi$
$353$	8.28649e7			1.88385			0.941926	+	0.335821i	$0.109014\pi$
$354$	−1.32455e7	−	1.82308e7i	−0.298578	−	0.410957i
$355$	1.79252e7	+	5.51681e7i	0.400662	+	1.23311i
$356$	6.03132e6	−	1.85625e7i	0.133679	−	0.411421i
$357$	−7.73839e6	−	5.62227e6i	−0.170077	−	0.123568i
$358$	1.50663e6	−	2.07370e6i	0.0328365	−	0.0451956i
$359$	8.05313e7	+	2.61662e7i	1.74053	+	0.565532i	0.994903	−	0.100832i	$-0.0321504\pi$
$359$	8.05313e7	+	2.61662e7i	1.74053	+	0.565532i	0.745626	+	0.666364i	$0.232150\pi$
$360$	−4.12539e7	+	1.34042e7i	−0.884215	+	0.287299i
$361$	−1.09435e7	+	7.95094e6i	−0.232614	+	0.169004i
$362$			1.51103e7i			0.318528i
$363$	1.83968e7	−	7.00392e7i	0.384612	−	1.46427i
$364$	−6.11023e7			−1.26693
$365$	−5.09963e7	−	7.01904e7i	−1.04872	−	1.44344i
$366$	−5.26963e6	−	1.62182e7i	−0.107482	−	0.330796i
$367$	−9.52716e6	+	2.93216e7i	−0.192737	+	0.593184i	0.807259	+	0.590198i	$0.200950\pi$
$367$	−9.52716e6	+	2.93216e7i	−0.192737	+	0.593184i	−0.999996	+	0.00298553i	$0.999050\pi$
$368$	3.16176e7	+	2.29715e7i	0.634432	+	0.460942i
$369$	3.65895e7	−	5.03612e7i	0.728245	−	1.00234i
$370$	−1.89678e7	−	6.16300e6i	−0.374465	−	0.121671i
$371$	−3.00650e7	+	9.76872e6i	−0.588762	+	0.191300i
$372$	1.42003e7	−	1.03171e7i	0.275848	−	0.200415i
$373$		−	8.92126e7i		−	1.71909i	−0.511056	−	0.859547i	$-0.670746\pi$
$373$		−	8.92126e7i		−	1.71909i	0.511056	−	0.859547i	$-0.329254\pi$
$374$	−2.40139e6	−	704880.i	−0.0459037	−	0.0134741i
$375$	−6.46106e7			−1.22521
$376$	−2.67365e6	−	3.67996e6i	−0.0502969	−	0.0692277i
$377$	1.78012e7	+	5.47864e7i	0.332219	+	1.02247i
$378$	2.42099e6	−	7.45103e6i	0.0448246	−	0.137956i
$379$	727085.	+	528259.i	0.0133557	+	0.00970351i	0.594443	−	0.804138i	$-0.297373\pi$
$379$	727085.	+	528259.i	0.0133557	+	0.00970351i	−0.581087	+	0.813841i	$0.697373\pi$
$380$	2.73881e7	−	3.76964e7i	0.499127	−	0.686989i
$381$	6.52617e7	+	2.12048e7i	1.18000	+	0.383407i
$382$	2.16791e7	−	7.04397e6i	0.388912	−	0.126365i
$383$	4.51095e7	−	3.27740e7i	0.802919	−	0.583355i	−0.108850	−	0.994058i	$-0.534717\pi$
$383$	4.51095e7	−	3.27740e7i	0.802919	−	0.583355i	0.911769	+	0.410703i	$0.134717\pi$
$384$			8.48747e7i			1.49894i
$385$	−2.12324e7	−	5.94914e7i	−0.372064	−	1.04249i
$386$	1.81993e7			0.316441
$387$	−7.43107e7	−	1.02280e8i	−1.28209	−	1.76465i
$388$	−1.57949e6	−	4.86117e6i	−0.0270409	−	0.0832234i
$389$	−2.67795e7	+	8.24190e7i	−0.454940	+	1.40016i	0.416265	+	0.909243i	$0.363339\pi$
$389$	−2.67795e7	+	8.24190e7i	−0.454940	+	1.40016i	−0.871205	+	0.490919i	$0.836661\pi$
$390$	4.05535e7	+	2.94639e7i	0.683651	+	0.496702i
$391$	5.81990e6	−	8.01040e6i	0.0973610	−	0.134006i
$392$	−1.73113e6	−	562480.i	−0.0287391	−	0.00933789i
$393$	9.40658e6	−	3.05638e6i	0.154972	−	0.0503535i
$394$	−1.95363e7	+	1.41940e7i	−0.319414	+	0.232068i
$395$			5.16584e7i			0.838204i
$396$	2.03845e6	+	7.11342e7i	0.0328258	+	1.14549i
$397$	6.14799e7			0.982566			0.491283	−	0.871000i	$-0.336528\pi$
$397$	6.14799e7			0.982566			0.491283	+	0.871000i	$0.336528\pi$
$398$	−1.50588e7	−	2.07266e7i	−0.238859	−	0.328761i
$399$	2.44792e7	+	7.53392e7i	0.385370	+	1.18605i
$400$	3.81696e6	−	1.17474e7i	0.0596400	−	0.183553i
$401$	−6.00737e7	−	4.36461e7i	−0.931647	−	0.676881i	0.0147483	−	0.999891i	$-0.495305\pi$
$401$	−6.00737e7	−	4.36461e7i	−0.931647	−	0.676881i	−0.946396	+	0.323010i	$0.895305\pi$
$402$	−2.11612e7	+	2.91258e7i	−0.325733	+	0.448332i
$403$	−2.31349e7	−	7.51698e6i	−0.353470	−	0.114849i
$404$	2.40082e7	−	7.80074e6i	0.364096	−	0.118302i
$405$	−3.79589e7	+	2.75788e7i	−0.571411	+	0.415155i
$406$		−	1.61285e7i		−	0.240999i
$407$	−3.92853e7	+	5.74639e7i	−0.582703	+	0.852338i
$408$	9.28210e6			0.136668
$409$	−1.62956e7	−	2.24289e7i	−0.238177	−	0.327822i	0.673150	−	0.739506i	$-0.264941\pi$
$409$	−1.62956e7	−	2.24289e7i	−0.238177	−	0.327822i	−0.911327	+	0.411684i	$0.864941\pi$
$410$	−7.78837e6	−	2.39702e7i	−0.113004	−	0.347792i
$411$	−1.85877e7	+	5.72070e7i	−0.267732	+	0.823994i
$412$	−5.80628e7	−	4.21851e7i	−0.830245	−	0.603208i
$413$	−4.03259e7	+	5.55038e7i	−0.572445	+	0.787903i
$414$	3.41257e7	+	1.10881e7i	0.480929	+	0.156263i
$415$	4.84392e7	−	1.57388e7i	0.677724	−	0.220206i
$416$	7.33916e7	−	5.33221e7i	1.01945	−	0.740674i
$417$		−	3.40763e7i		−	0.469942i
$418$	1.26582e7	+	1.64124e7i	0.173318	+	0.224721i
$419$	−1.25518e8			−1.70633			−0.853166	−	0.521640i	$-0.825320\pi$
$419$	−1.25518e8			−1.70633			−0.853166	+	0.521640i	$0.825320\pi$
$420$	6.47270e7	+	8.90891e7i	0.873651	+	1.20248i
$421$	−1.94154e7	−	5.97544e7i	−0.260196	−	0.800800i	−0.992761	−	0.120103i	$-0.961677\pi$
$421$	−1.94154e7	−	5.97544e7i	−0.260196	−	0.800800i	0.732566	−	0.680696i	$-0.238323\pi$
$422$	7.47719e6	−	2.30124e7i	0.0994949	−	0.306214i
$423$	1.06706e7	+	7.75264e6i	0.140983	+	0.102430i
$424$	1.80313e7	−	2.48179e7i	0.236553	−	0.325588i
$425$	−2.97624e6	−	967038.i	−0.0387704	−	0.0125973i
$426$	4.27813e7	−	1.39005e7i	0.553382	−	0.179805i
$427$	−4.20022e7	+	3.05164e7i	−0.539496	+	0.391967i
$428$			8.20282e7i			1.04624i
$429$	1.38538e8	−	1.06848e8i	1.75468	−	1.35331i
$430$	−5.11870e7			−0.643804
$431$	2.45691e7	+	3.38164e7i	0.306872	+	0.422373i	0.934402	−	0.356219i	$-0.115934\pi$
$431$	2.45691e7	+	3.38164e7i	0.306872	+	0.422373i	−0.627531	+	0.778592i	$0.715934\pi$
$432$	−7.41969e6	−	2.28355e7i	−0.0920311	−	0.283243i
$433$	1.55355e7	−	4.78132e7i	0.191364	−	0.588958i	−0.808636	−	0.588310i	$-0.799794\pi$
$433$	1.55355e7	−	4.78132e7i	0.191364	−	0.588958i	1.00000		0.000648514i	$-0.000206429\pi$
$434$	5.50993e6	+	4.00320e6i	0.0674026	+	0.0489709i
$435$	6.10232e7	−	8.39912e7i	0.741357	−	1.02039i
$436$	−1.05752e7	−	3.43610e6i	−0.127594	−	0.0414578i
$437$	−7.79874e7	+	2.53396e7i	−0.934501	+	0.303638i
$438$	−5.44307e7	+	3.95462e7i	−0.647771	+	0.470633i
$439$			2.94588e7i			0.348194i	0.984728	+	0.174097i	$0.0557007\pi$
$439$			2.94588e7i			0.348194i	−0.984728	+	0.174097i	$0.944299\pi$
$440$	5.06024e7	+	3.45944e7i	0.594036	+	0.406114i
$441$	5.27800e6			0.0615395
$442$	−3.55408e6	−	4.89177e6i	−0.0411585	−	0.0566499i
$443$	−1.00270e7	−	3.08600e7i	−0.115335	−	0.354965i	0.876682	−	0.481071i	$-0.159752\pi$
$443$	−1.00270e7	−	3.08600e7i	−0.115335	−	0.354965i	−0.992017	+	0.126106i	$0.959752\pi$
$444$	3.74996e7	−	1.15412e8i	0.428428	−	1.31857i
$445$	3.94383e7	+	2.86536e7i	0.447546	+	0.325161i
$446$	5.99849e6	−	8.25621e6i	0.0676141	−	0.0930629i
$447$	−1.70410e8	−	5.53695e7i	−1.90797	−	0.619937i
$448$	3.20629e7	−	1.04179e7i	0.356590	−	0.115863i
$449$	1.13987e8	−	8.28164e7i	1.25926	−	0.914908i	0.260542	−	0.965463i	$-0.416099\pi$
$449$	1.13987e8	−	8.28164e7i	1.25926	−	0.914908i	0.998721	+	0.0505542i	$0.0160988\pi$
$450$		−	1.13407e7i		−	0.124452i
$451$	−8.79311e7	+	2.51979e6i	−0.958546	+	0.0274685i
$452$	−4.43081e7			−0.479809
$453$	1.08180e8	+	1.48897e8i	1.16373	+	1.60174i
$454$	6.71424e6	+	2.06643e7i	0.0717513	+	0.220828i
$455$	4.71596e7	−	1.45142e8i	0.500652	−	1.54085i
$456$	−6.21907e7	−	4.51842e7i	−0.655889	−	0.476532i
$457$	−2.11933e6	+	2.91700e6i	−0.0222049	+	0.0305625i	−0.819975	−	0.572399i	$-0.806013\pi$
$457$	−2.11933e6	+	2.91700e6i	−0.0222049	+	0.0305625i	0.797770	+	0.602962i	$0.206013\pi$
$458$	−1.66659e7	−	5.41507e6i	−0.173473	−	0.0563648i
$459$	−5.78543e6	+	1.87980e6i	−0.0598271	+	0.0194390i
$460$	−9.22207e7	+	6.70022e7i	−0.947447	+	0.688360i
$461$		−	1.41254e7i		−	0.144178i	−0.997398	−	0.0720890i	$-0.977033\pi$
$461$		−	1.41254e7i		−	0.144178i	0.997398	−	0.0720890i	$-0.0229666\pi$
$462$	−4.61339e7	+	1.64652e7i	−0.467837	+	0.166971i
$463$	1.58186e8			1.59377			0.796886	−	0.604130i	$-0.206479\pi$
$463$	1.58186e8			1.59377			0.796886	+	0.604130i	$0.206479\pi$
$464$	−2.90540e7	−	3.99895e7i	−0.290839	−	0.400306i
$465$	1.35473e7	+	4.16943e7i	0.134739	+	0.414685i
$466$	−9.19611e6	+	2.83027e7i	−0.0908754	+	0.279686i
$467$	1.14804e8	+	8.34101e7i	1.12721	+	0.818970i	0.985287	−	0.170907i	$-0.0546699\pi$
$467$	1.14804e8	+	8.34101e7i	1.12721	+	0.818970i	0.141928	+	0.989877i	$0.454670\pi$
$468$	−1.01059e8	+	1.39096e8i	−0.985909	+	1.35699i
$469$	1.04242e8	+	3.38704e7i	1.01047	+	0.328323i
$470$	5.07883e6	−	1.65021e6i	0.0489182	−	0.0158945i
$471$	−5.46902e7	+	3.97347e7i	−0.523416	+	0.380284i
$472$		−	6.65761e7i		−	0.633129i
$473$	−5.03178e7	+	1.71423e8i	−0.475487	+	1.61989i
$474$	4.00596e7			0.376159
$475$	1.52335e7	+	2.09672e7i	0.142141	+	0.195641i
$476$	−4.10475e6	−	1.26331e7i	−0.0380597	−	0.117136i
$477$	−2.74875e7	+	8.45979e7i	−0.253268	+	0.779479i
$478$	−1.61597e7	−	1.17407e7i	−0.147962	−	0.107501i
$479$	−2.59812e7	+	3.57601e7i	−0.236403	+	0.325381i	−0.910691	−	0.413087i	$-0.864450\pi$
$479$	−2.59812e7	+	3.57601e7i	−0.236403	+	0.325381i	0.674289	+	0.738468i	$0.264450\pi$
$480$	−1.55491e8	−	5.05220e7i	−1.40599	−	0.456832i
$481$	−1.59945e8	+	5.19694e7i	−1.43726	+	0.466995i
$482$	2.03192e7	−	1.47628e7i	0.181454	−	0.131834i
$483$		−	1.93795e8i		−	1.71989i
$484$	7.78390e7	−	6.36717e7i	0.686532	−	0.561578i
$485$	1.27663e7			0.111902
$486$	3.14156e7	+	4.32399e7i	0.273676	+	0.376682i
$487$	−2.35805e7	−	7.25732e7i	−0.204157	−	0.628332i	−0.999747	−	0.0224960i	$-0.992839\pi$
$487$	−2.35805e7	−	7.25732e7i	−0.204157	−	0.628332i	0.795589	−	0.605836i	$-0.207161\pi$
$488$	1.55686e7	−	4.79153e7i	0.133965	−	0.412301i
$489$	6.43184e6	+	4.67301e6i	0.0550059	+	0.0399641i
$490$	1.25607e6	−	1.72884e6i	0.0106764	−	0.0146949i
$491$	2.01639e8	+	6.55165e7i	1.70345	+	0.553485i	0.989222	−	0.146425i	$-0.0467767\pi$
$491$	2.01639e8	+	6.55165e7i	1.70345	+	0.553485i	0.714231	+	0.699910i	$0.246777\pi$
$492$	1.45850e8	−	4.73894e7i	1.22464	−	0.397911i
$493$	−1.01314e7	+	7.36092e6i	−0.0845533	+	0.0614316i
$494$			5.00760e7i			0.415383i
$495$	−1.70546e8	−	5.00603e7i	−1.40613	−	0.412741i
$496$	2.08729e7			0.171056
$497$	−8.04976e7	−	1.10795e8i	−0.655713	−	0.902511i
$498$	−1.22050e7	−	3.75632e7i	−0.0988214	−	0.304141i
$499$	−4.97835e7	+	1.53218e8i	−0.400668	+	1.23313i	0.523792	+	0.851846i	$0.324517\pi$
$499$	−4.97835e7	+	1.53218e8i	−0.400668	+	1.23313i	−0.924459	+	0.381281i	$0.875483\pi$
$500$	−7.25893e7	−	5.27392e7i	−0.580714	−	0.421913i
$501$	−6.89503e7	+	9.49020e7i	−0.548306	+	0.754679i
$502$	5.82901e7	+	1.89396e7i	0.460769	+	0.149713i
$503$	−1.40890e8	+	4.57778e7i	−1.10707	+	0.359709i	−0.804819	−	0.593520i	$-0.797738\pi$
$503$	−1.40890e8	+	4.57778e7i	−1.10707	+	0.359709i	−0.302251	+	0.953229i	$0.597738\pi$
$504$	8.28513e7	−	6.01950e7i	0.647154	−	0.470185i
$505$			6.30499e7i			0.489565i
$506$	−1.70439e7	−	4.77555e7i	−0.131558	−	0.368614i
$507$	2.25392e8			1.72947
$508$	5.60121e7	+	7.70941e7i	0.427259	+	0.588071i
$509$	−8.04394e7	−	2.47567e8i	−0.609980	−	1.87733i	−0.458027	−	0.888938i	$-0.651444\pi$
$509$	−8.04394e7	−	2.47567e8i	−0.609980	−	1.87733i	−0.151953	−	0.988388i	$-0.548556\pi$
$510$	−3.36744e6	+	1.03639e7i	−0.0253857	+	0.0781292i
$511$	1.65715e8	+	1.20399e8i	1.24193	+	0.902317i
$512$	−7.94708e7	+	1.09382e8i	−0.592103	+	0.814960i
$513$	4.79134e7	+	1.55680e7i	0.354899	+	0.115314i
$514$	−1.06514e6	+	346085.i	−0.00784364	+	0.00254855i
$515$	1.45020e8	−	1.05363e8i	1.06171	−	0.771378i
$516$		−	3.11454e8i		−	2.26697i
$517$	−533898.	−	1.86310e7i	−0.00386355	−	0.134823i
$518$	4.70861e7			0.338769
$519$	−7.75895e7	−	1.06793e8i	−0.555010	−	0.763906i
$520$	4.57639e7	+	1.40847e8i	0.325472	+	1.00170i
$521$	−5.64334e6	+	1.73684e7i	−0.0399046	+	0.122814i	−0.969024	−	0.246965i	$-0.920567\pi$
$521$	−5.64334e6	+	1.73684e7i	−0.0399046	+	0.122814i	0.929120	+	0.369779i	$0.120567\pi$
$522$	−3.67155e7	−	2.66754e7i	−0.258130	−	0.187542i
$523$	1.09219e8	−	1.50327e8i	0.763472	−	1.05083i	−0.233445	−	0.972370i	$-0.575000\pi$
$523$	1.09219e8	−	1.50327e8i	0.763472	−	1.05083i	0.996917	−	0.0784597i	$-0.0250002\pi$
$524$	1.30630e7	+	4.24443e6i	0.0907923	+	0.0295002i
$525$	−5.82523e7	+	1.89273e7i	−0.402564	+	0.130801i
$526$	3.03316e7	−	2.20372e7i	0.208419	−	0.151426i
$527$		−	5.28820e6i		−	0.0361307i
$528$	−8.47252e7	+	1.23930e8i	−0.575587	+	0.841929i
$529$	5.25710e7			0.355123
$530$	2.11689e7	+	2.91365e7i	0.142191	+	0.195709i
$531$	5.96549e7	+	1.83599e8i	0.398440	+	1.22627i
$532$	−3.39944e7	+	1.04624e8i	−0.225774	+	0.694859i
$533$	−1.71940e8	−	1.24922e8i	−1.13552	−	0.825005i
$534$	2.22200e7	−	3.05833e7i	0.145922	−	0.200845i
$535$	−1.94850e8	−	6.33105e7i	−1.27244	−	0.413442i
$536$	−1.01157e8	+	3.28680e7i	−0.656905	+	0.213441i
$537$	−3.15145e7	+	2.28966e7i	−0.203511	+	0.147859i
$538$			1.73626e6i			0.0111498i
$539$	−4.55505e6	−	5.90601e6i	−0.0290889	−	0.0377162i
$540$	7.00331e7			0.444756
$541$	4.20977e7	+	5.79425e7i	0.265868	+	0.365936i	0.920989	−	0.389588i	$-0.127382\pi$
$541$	4.20977e7	+	5.79425e7i	0.265868	+	0.365936i	−0.655121	+	0.755524i	$0.727382\pi$
$542$	−1.59950e7	−	4.92276e7i	−0.100459	−	0.309180i
$543$	7.09612e7	−	2.18396e8i	0.443222	−	1.36410i
$544$	1.59549e7	+	1.15919e7i	0.0991052	+	0.0720042i
$545$	1.63242e7	−	2.24684e7i	0.100842	−	0.138798i
$546$	−1.12554e8	−	3.65709e7i	−0.691484	−	0.224677i
$547$	−1.94691e8	+	6.32590e7i	−1.18955	+	0.386509i	−0.835908	−	0.548870i	$-0.815058\pi$
$547$	−1.94691e8	+	6.32590e7i	−1.18955	+	0.386509i	−0.353646	+	0.935379i	$0.615058\pi$
$548$	−6.75790e7	+	4.90990e7i	−0.410648	+	0.298353i
$549$			1.46087e8i			0.882868i
$550$	−1.26901e7	+	9.78731e6i	−0.0762740	+	0.0588268i
$551$	1.03713e8			0.619983
$552$	1.10539e8	+	1.52143e8i	0.657199	+	0.904557i
$553$	−3.76883e7	−	1.15993e8i	−0.222859	−	0.685891i
$554$	−2.65123e7	+	8.15966e7i	−0.155926	+	0.479891i
$555$	2.45207e8	+	1.78153e8i	1.43434	+	1.04211i
$556$	2.78152e7	−	3.82844e7i	0.161830	−	0.222739i
$557$	1.15689e8	+	3.75898e7i	0.669465	+	0.217522i	0.623977	−	0.781443i	$-0.285516\pi$
$557$	1.15689e8	+	3.75898e7i	0.669465	+	0.217522i	0.0454878	+	0.998965i	$0.485516\pi$
$558$	1.82261e7	−	5.92201e6i	0.104904	−	0.0340852i
$559$	−3.49198e8	+	2.53707e8i	−1.99911	+	1.45244i
$560$			1.30951e8i			0.745667i
$561$	3.13981e7	+	2.14654e7i	0.177834	+	0.121577i
$562$	−1.00878e8			−0.568315
$563$	1.05284e8	+	1.44911e8i	0.589979	+	0.812037i	0.994745	−	0.102383i	$-0.0326469\pi$
$563$	1.05284e8	+	1.44911e8i	0.589979	+	0.812037i	−0.404766	+	0.914420i	$0.632647\pi$
$564$	1.00409e7	+	3.09028e7i	0.0559677	+	0.172251i
$565$	3.41976e7	−	1.05250e8i	0.189605	−	0.583546i
$566$	−4.92853e7	−	3.58079e7i	−0.271812	−	0.197483i
$567$	6.51115e7	−	8.96183e7i	0.357198	−	0.491640i
$568$	1.26393e8	+	4.10676e7i	0.689729	+	0.224107i
$569$	2.23029e8	−	7.24664e7i	1.21067	−	0.393369i	0.366991	−	0.930224i	$-0.380388\pi$
$569$	2.23029e8	−	7.24664e7i	1.21067	−	0.393369i	0.843674	+	0.536855i	$0.180388\pi$
$570$	7.30124e7	−	5.30466e7i	0.394250	−	0.286440i
$571$		−	8.33547e7i		−	0.447736i	−0.974619	−	0.223868i	$-0.928132\pi$
$571$		−	8.33547e7i		−	0.447736i	0.974619	−	0.223868i	$-0.0718684\pi$
$572$	2.42862e8	−	6.95958e6i	1.29769	−	0.0371873i
$573$	−3.46418e8			−1.84135
$574$	3.49757e7	+	4.81399e7i	0.184940	+	0.254548i
$575$	−1.95926e7	−	6.02999e7i	−0.103060	−	0.317185i
$576$	2.93142e7	−	9.02197e7i	0.153395	−	0.472100i
$577$	−2.02005e8	−	1.46765e8i	−1.05156	−	0.764003i	−0.0790519	−	0.996871i	$-0.525189\pi$
$577$	−2.02005e8	−	1.46765e8i	−1.05156	−	0.764003i	−0.972509	+	0.232867i	$0.925189\pi$
$578$	−3.73884e7	+	5.14607e7i	−0.193621	+	0.266497i
$579$	−2.63042e8	−	8.54676e7i	−1.35516	−	0.440318i
$580$	1.37118e8	−	4.45523e7i	0.702764	−	0.228342i
$581$	−9.72817e7	+	7.06793e7i	−0.496024	+	0.360382i
$582$		−	9.89990e6i		−	0.0502183i
$583$	1.18386e8	−	4.22520e7i	0.597442	−	0.213227i
$584$	−1.98772e8			−0.997970
$585$	−2.52409e8	−	3.47411e8i	−1.26077	−	1.73531i
$586$	−1.51588e7	−	4.66539e7i	−0.0753305	−	0.231843i
$587$	4.45315e6	−	1.37054e7i	0.0220168	−	0.0677606i	−0.939444	−	0.342701i	$-0.888658\pi$
$587$	4.45315e6	−	1.37054e7i	0.0220168	−	0.0677606i	0.961461	+	0.274941i	$0.0886582\pi$
$588$	1.05193e7	+	7.64275e6i	0.0517436	+	0.0375939i
$589$	−2.57423e7	+	3.54313e7i	−0.125980	+	0.173397i
$590$	7.43355e7	+	2.41531e7i	0.361943	+	0.117602i
$591$	3.49025e8	−	1.13405e8i	1.69081	−	0.549376i
$592$	1.16747e8	−	8.48213e7i	0.562703	−	0.408827i
$593$		−	1.00527e8i		−	0.482078i	−0.970515	−	0.241039i	$-0.922512\pi$
$593$		−	1.00527e8i		−	0.482078i	0.970515	−	0.241039i	$-0.0774882\pi$
$594$	−8.77398e6	+	2.98913e7i	−0.0418637	+	0.142621i
$595$	3.31768e7			0.157501
$596$	−1.46257e8	−	2.01306e8i	−0.690842	−	0.950863i
$597$	1.20315e8	+	3.70291e8i	0.565452	+	1.74028i
$598$	3.78564e7	−	1.16510e8i	0.177026	−	0.544829i
$599$	−8.05471e7	−	5.85209e7i	−0.374774	−	0.272289i	0.384414	−	0.923161i	$-0.374404\pi$
$599$	−8.05471e7	−	5.85209e7i	−0.374774	−	0.272289i	−0.759188	+	0.650872i	$0.774404\pi$
$600$	3.49364e7	−	4.80858e7i	0.161743	−	0.222620i
$601$	−9.28410e7	−	3.01659e7i	−0.427677	−	0.138961i	0.0872659	−	0.996185i	$-0.472187\pi$
$601$	−9.28410e7	−	3.01659e7i	−0.427677	−	0.138961i	−0.514943	+	0.857224i	$0.672187\pi$
$602$	1.14934e8	−	3.73443e7i	0.526816	−	0.171173i
$603$	2.49513e8	−	1.81282e8i	1.13800	−	0.826804i
$604$			2.55588e8i			1.15992i
$605$	9.11684e7	+	2.34041e8i	0.411698	+	1.05688i
$606$	4.88934e7			0.219701
$607$	1.82003e8	+	2.50505e8i	0.813789	+	1.12008i	0.990728	+	0.135863i	$0.0433806\pi$
$607$	1.82003e8	+	2.50505e8i	0.813789	+	1.12008i	−0.176939	+	0.984222i	$0.556619\pi$
$608$	−5.04707e7	−	1.55333e8i	−0.224558	−	0.691118i
$609$	−7.57428e7	+	2.33112e8i	−0.335343	+	1.03208i
$610$	4.78516e7	+	3.47662e7i	0.210818	+	0.153168i
$611$	2.64686e7	−	3.64309e7i	0.116040	−	0.159715i
$612$	−3.55475e7	−	1.15501e7i	−0.155080	−	0.0503884i
$613$	8.22364e7	−	2.67202e7i	0.357012	−	0.116000i	−0.125019	−	0.992154i	$-0.539899\pi$
$613$	8.22364e7	−	2.67202e7i	0.357012	−	0.116000i	0.482031	+	0.876154i	$0.339899\pi$
$614$	−7.29154e7	+	5.29761e7i	−0.315002	+	0.228863i
$615$			3.83027e8i			1.64666i
$616$	−1.38860e8	−	4.07597e7i	−0.594068	−	0.174377i
$617$	1.28154e7			0.0545605			0.0272802	−	0.999628i	$-0.491315\pi$
$617$	1.28154e7			0.0545605			0.0272802	+	0.999628i	$0.491315\pi$
$618$	−8.17062e7	−	1.12459e8i	−0.346170	−	0.476462i
$619$	−2.67870e7	−	8.24419e7i	−0.112941	−	0.347597i	0.878571	−	0.477612i	$-0.158497\pi$
$619$	−2.67870e7	−	8.24419e7i	−0.112941	−	0.347597i	−0.991512	+	0.130015i	$0.958497\pi$
$620$	−1.88133e7	+	5.79013e7i	−0.0789385	+	0.242948i
$621$	−9.97094e7	−	7.24431e7i	−0.416353	−	0.302498i
$622$	6.93005e7	−	9.53839e7i	0.287982	−	0.396373i
$623$	−1.09458e8	−	3.55652e7i	−0.452674	−	0.147083i
$624$	−3.44948e8	+	1.12080e8i	−1.41971	+	0.461292i
$625$	2.37889e8	−	1.72836e8i	0.974393	−	0.707938i
$626$			6.79309e7i			0.276914i
$627$	−1.05878e8	−	2.96661e8i	−0.429540	−	1.20353i
$628$	−9.38778e7			−0.379039
$629$	−2.14897e7	−	2.95781e7i	−0.0863533	−	0.118855i
$630$	3.71532e7	+	1.14346e8i	0.148585	+	0.457297i
$631$	5.75752e7	−	1.77198e8i	0.229164	−	0.705296i	−0.768678	−	0.639636i	$-0.779085\pi$
$631$	5.75752e7	−	1.77198e8i	0.229164	−	0.705296i	0.997842	−	0.0656592i	$-0.0209150\pi$
$632$	9.57491e7	+	6.95658e7i	0.379301	+	0.275578i
$633$	−2.16142e8	+	2.97494e8i	−0.852174	+	1.17292i
$634$	3.18407e7	+	1.03457e7i	0.124944	+	0.0405967i
$635$	−2.26360e8	+	7.35489e7i	−0.884054	+	0.287247i
$636$	−1.77285e8	+	1.28805e8i	−0.689129	+	0.500682i
$637$		−	1.80199e7i		−	0.0697161i
$638$	1.83704e6	+	6.41058e7i	0.00707388	+	0.246851i
$639$	−3.85356e8			−1.47693
$640$	−1.73037e8	−	2.38165e8i	−0.660083	−	0.908526i
$641$	1.45542e8	+	4.47932e8i	0.552604	+	1.70074i	0.702187	+	0.711992i	$0.252207\pi$
$641$	1.45542e8	+	4.47932e8i	0.552604	+	1.70074i	−0.149583	+	0.988749i	$0.547793\pi$
$642$	−4.90955e7	+	1.51100e8i	−0.185540	+	0.571032i
$643$	1.04210e8	+	7.57132e7i	0.391992	+	0.284799i	0.766271	−	0.642517i	$-0.222110\pi$
$643$	1.04210e8	+	7.57132e7i	0.391992	+	0.284799i	−0.374279	+	0.927316i	$0.622110\pi$
$644$	1.58187e8	−	2.17726e8i	0.592263	−	0.815180i
$645$	7.39828e8	+	2.40385e8i	2.75709	+	0.895834i
$646$	−1.03534e7	+	3.36402e6i	−0.0384048	+	0.0124785i
$647$	1.97403e8	−	1.43421e8i	0.728853	−	0.529543i	−0.160347	−	0.987061i	$-0.551261\pi$
$647$	1.97403e8	−	1.43421e8i	0.728853	−	0.529543i	0.889201	+	0.457518i	$0.151261\pi$
$648$			1.07496e8i			0.395064i
$649$	1.53961e8	−	2.25204e8i	0.563218	−	0.823837i
$650$	−3.87188e7			−0.140988
$651$	−6.08376e7	−	8.37358e7i	−0.220510	−	0.303507i
$652$	3.41170e6	+	1.05001e7i	0.0123092	+	0.0378837i
$653$	−1.48870e8	+	4.58176e8i	−0.534649	+	1.64548i	0.209758	+	0.977753i	$0.432732\pi$
$653$	−1.48870e8	+	4.58176e8i	−0.534649	+	1.64548i	−0.744407	+	0.667727i	$0.767268\pi$
$654$	−1.74236e7	−	1.26590e7i	−0.0622880	−	0.0452548i
$655$	−2.01644e7	+	2.77539e7i	−0.0717566	+	0.0987645i
$656$	1.73439e8	+	5.63538e7i	0.614378	+	0.199624i
$657$	5.48160e8	−	1.78108e8i	1.93291	−	0.628040i
$658$	−1.01999e7	+	7.41070e6i	−0.0358031	+	0.0260125i
$659$		−	9.26853e7i		−	0.323858i	−0.986802	−	0.161929i	$-0.948228\pi$
$659$		−	9.26853e7i		−	0.323858i	0.986802	−	0.161929i	$-0.0517716\pi$
$660$	−2.67417e8	−	3.46729e8i	−0.930159	−	1.20603i
$661$	−2.27789e8			−0.788730			−0.394365	−	0.918954i	$-0.629035\pi$
$661$	−2.27789e8			−0.788730			−0.394365	+	0.918954i	$0.629035\pi$
$662$	−5.59847e7	−	7.70563e7i	−0.192972	−	0.265604i
$663$	2.83959e7	+	8.73936e7i	0.0974350	+	0.299874i
$664$	3.60586e7	−	1.10977e8i	0.123170	−	0.379078i
$665$	−2.22287e8	−	1.61501e8i	−0.755873	−	0.549174i
$666$	7.78771e7	−	1.07189e8i	0.263625	−	0.362849i
$667$	−2.41306e8	−	7.84052e7i	−0.813189	−	0.264221i
$668$	−1.54930e8	+	5.03398e7i	−0.519763	+	0.168881i
$669$	−1.25472e8	+	9.11606e7i	−0.419052	+	0.304459i
$670$		−	1.24871e8i		−	0.415181i
$671$	1.63470e8	−	1.26077e8i	0.541090	−	0.417320i
$672$	3.85994e8			1.27196
$673$	−2.66764e8	−	3.67169e8i	−0.875149	−	1.20454i	−0.977741	−	0.209815i	$-0.932714\pi$
$673$	−2.66764e8	−	3.67169e8i	−0.875149	−	1.20454i	0.102592	−	0.994724i	$-0.467286\pi$
$674$	−2.47677e7	−	7.62270e7i	−0.0808920	−	0.248960i
$675$	−1.20372e7	+	3.70467e7i	−0.0391394	+	0.120459i
$676$	2.53225e8	+	1.83979e8i	0.819722	+	0.595563i
$677$	−1.06431e8	+	1.46489e8i	−0.343006	+	0.472107i	−0.945316	−	0.326155i	$-0.894247\pi$
$677$	−1.06431e8	+	1.46489e8i	−0.343006	+	0.472107i	0.602311	+	0.798262i	$0.294247\pi$
$678$	−8.16180e7	−	2.65193e7i	−0.261877	−	0.0850889i
$679$	−2.86651e7	+	9.31387e6i	−0.0915682	+	0.0297523i
$680$	−2.60463e7	+	1.89237e7i	−0.0828359	+	0.0601838i
$681$		−	3.30202e8i		−	1.04553i
$682$	−2.23562e7	−	1.52839e7i	−0.0704766	−	0.0481815i
$683$	1.06800e8			0.335204			0.167602	−	0.985855i	$-0.446398\pi$
$683$	1.06800e8			0.335204			0.167602	+	0.985855i	$0.446398\pi$
$684$	1.81946e8	+	2.50427e8i	0.568557	+	0.782552i
$685$	−6.44714e7	−	1.98422e8i	−0.200583	−	0.617332i
$686$	−3.42912e7	+	1.05538e8i	−0.106221	+	0.326915i
$687$	2.15449e8	+	1.56533e8i	0.664469	+	0.482765i
$688$	2.17698e8	−	2.99636e8i	0.668481	−	0.920086i
$689$	2.88829e8	+	9.38464e7i	0.883047	+	0.286919i
$690$	−2.09978e8	+	6.82259e7i	−0.639184	+	0.207684i
$691$	−4.93262e8	+	3.58376e8i	−1.49501	+	1.08619i	−0.522692	+	0.852522i	$0.675072\pi$
$691$	−4.93262e8	+	3.58376e8i	−1.49501	+	1.08619i	−0.972317	+	0.233665i	$0.924928\pi$
$692$		−	1.83314e8i		−	0.553194i
$693$	4.19461e8	−	1.20203e7i	1.26035	−	0.0361172i
$694$	−5.33525e7			−0.159616
$695$	6.94725e7	+	9.56207e7i	0.206947	+	0.284838i
$696$	−7.35012e7	−	2.26213e8i	−0.218005	−	0.670951i
$697$	1.42774e7	−	4.39413e7i	0.0421649	−	0.129770i
$698$	1.35930e8	+	9.87587e7i	0.399713	+	0.290408i
$699$	2.65831e8	−	3.65885e8i	0.778349	−	1.07130i
$700$	−8.08954e7	−	2.62845e7i	−0.235847	−	0.0766312i
$701$	−9.42331e7	+	3.06182e7i	−0.273558	+	0.0888843i	−0.442583	−	0.896727i	$-0.645938\pi$
$701$	−9.42331e7	+	3.06182e7i	−0.273558	+	0.0888843i	0.169026	+	0.985612i	$0.445938\pi$
$702$	−6.08902e7	+	4.42393e7i	−0.176009	+	0.127878i
$703$			3.02784e8i			0.871500i
$704$	−1.26253e8	+	4.50598e7i	−0.361847	+	0.129143i
$705$	−8.11564e7			−0.231609
$706$	1.31008e8	+	1.80317e8i	0.372291	+	0.512415i
$707$	−4.59991e7	−	1.41571e8i	−0.130164	−	0.400604i
$708$	−1.46963e8	+	4.52305e8i	−0.414102	+	1.27447i
$709$	−2.25681e8	−	1.63967e8i	−0.633224	−	0.460064i	0.224292	−	0.974522i	$-0.427993\pi$
$709$	−2.25681e8	−	1.63967e8i	−0.633224	−	0.460064i	−0.857516	+	0.514458i	$0.827993\pi$
$710$	−9.17081e7	+	1.26225e8i	−0.256231	+	0.352672i
$711$	−3.26384e8	−	1.06049e8i	−0.908071	−	0.295050i
$712$	1.06219e8	−	3.45127e7i	0.294281	−	0.0956178i
$713$	8.66791e7	−	6.29761e7i	0.239137	−	0.173743i
$714$		−	2.57277e7i		−	0.0706815i
$715$	−1.70913e8	+	5.82267e8i	−0.467581	+	1.59296i
$716$	−5.40958e7			−0.147375
$717$	1.78427e8	+	2.45583e8i	0.484064	+	0.666256i
$718$	7.03798e7	+	2.16607e8i	0.190141	+	0.585193i
$719$	1.31928e8	−	4.06034e8i	0.354937	−	1.09238i	−0.601109	−	0.799167i	$-0.705274\pi$
$719$	1.31928e8	−	4.06034e8i	0.354937	−	1.09238i	0.956046	−	0.293217i	$-0.0947259\pi$
$720$	2.98102e8	+	2.16584e8i	0.798670	+	0.580268i
$721$	−2.48755e8	+	3.42382e8i	−0.663691	+	0.913493i
$722$	−3.46030e7	−	1.12432e7i	−0.0919395	−	0.0298730i
$723$	−3.63012e8	+	1.17950e8i	−0.960519	+	0.312092i
$724$	2.57993e8	−	1.87443e8i	0.679816	−	0.493915i
$725$			8.01912e7i			0.210433i
$726$	1.81492e8	−	7.06985e7i	0.474295	−	0.184757i
$727$	−2.95847e8			−0.769952			−0.384976	−	0.922927i	$-0.625790\pi$
$727$	−2.95847e8			−0.769952			−0.384976	+	0.922927i	$0.625790\pi$
$728$	−2.05514e8	−	2.82866e8i	−0.532658	−	0.733140i
$729$	−1.76449e8	−	5.43055e8i	−0.455447	−	1.40172i
$730$	7.21124e7	−	2.21939e8i	0.185371	−	0.570513i
$731$	−7.59135e7	−	5.51544e7i	−0.194342	−	0.141198i
$732$	−2.11540e8	+	2.91160e8i	−0.539336	+	0.742332i
$733$	6.02375e7	+	1.95723e7i	0.152952	+	0.0496971i	0.384492	−	0.923128i	$-0.374377\pi$
$733$	6.02375e7	+	1.95723e7i	0.152952	+	0.0496971i	−0.231540	+	0.972825i	$0.574377\pi$
$734$	−7.88669e7	+	2.56254e7i	−0.199437	+	0.0648011i
$735$	−2.62736e7	+	1.90889e7i	−0.0661693	+	0.0480748i
$736$			3.99562e8i			1.00219i
$737$	−4.18188e8	−	1.22751e8i	−1.04465	−	0.306635i
$738$	1.67435e8			0.416559
$739$	2.68116e8	+	3.69029e8i	0.664337	+	0.914382i	0.999615	−	0.0277372i	$-0.00883016\pi$
$739$	2.68116e8	+	3.69029e8i	0.664337	+	0.914382i	−0.335278	+	0.942119i	$0.608830\pi$
$740$	1.30067e8	+	4.00306e8i	0.320976	+	0.987864i
$741$	2.35167e8	−	7.23770e8i	0.577992	−	1.77888i
$742$	−6.87892e7	−	4.99783e7i	−0.168387	−	0.122340i
$743$	8.99593e7	−	1.23818e8i	0.219321	−	0.301869i	−0.685152	−	0.728400i	$-0.740264\pi$
$743$	8.99593e7	−	1.23818e8i	0.219321	−	0.301869i	0.904473	+	0.426531i	$0.140264\pi$
$744$	9.55241e7	+	3.10377e7i	0.231950	+	0.0753651i
$745$	5.91066e8	−	1.92049e8i	1.42944	−	0.464454i
$746$	1.94129e8	−	1.41043e8i	0.467600	−	0.339732i
$747$			3.38354e8i			0.811727i
$748$	1.77540e7	+	4.97452e7i	0.0424221	+	0.118863i
$749$	4.83700e8			1.15115
$750$	−1.02148e8	−	1.40595e8i	−0.242129	−	0.333261i
$751$	4.20581e7	+	1.29441e8i	0.0992955	+	0.305600i	0.988349	−	0.152203i	$-0.0486366\pi$
$751$	4.20581e7	+	1.29441e8i	0.0992955	+	0.305600i	−0.889054	+	0.457803i	$0.848637\pi$
$752$	−1.19403e7	+	3.67486e7i	−0.0280778	+	0.0864146i
$753$	−7.53549e8	−	5.47485e8i	−1.76493	−	1.28229i
$754$	−9.10736e7	+	1.25352e8i	−0.212461	+	0.292427i
$755$	−6.07123e8	−	1.97266e8i	−1.41070	−	0.458365i
$756$	−1.57251e8	+	5.10938e7i	−0.363938	+	0.118250i
$757$	4.76653e8	−	3.46308e8i	1.09879	−	0.798317i	0.117927	−	0.993022i	$-0.462375\pi$
$757$	4.76653e8	−	3.46308e8i	1.09879	−	0.798317i	0.980862	+	0.194705i	$0.0623750\pi$
$758$			2.41733e6i			0.00555044i
$759$	2.20733e7	+	7.70274e8i	0.0504827	+	1.76165i
$760$	2.66630e8			0.607391
$761$	4.21466e8	+	5.80098e8i	0.956331	+	1.31628i	0.948657	+	0.316306i	$0.102443\pi$
$761$	4.21466e8	+	5.80098e8i	0.956331	+	1.31628i	0.00767351	+	0.999971i	$0.497557\pi$
$762$	5.70351e7	+	1.75536e8i	0.128907	+	0.396736i
$763$	−2.02618e7	+	6.23595e7i	−0.0456147	+	0.140388i
$764$	−3.89196e8	−	2.82768e8i	−0.872748	−	0.634088i
$765$	5.48721e7	−	7.55250e7i	0.122565	−	0.168697i
$766$	1.42634e8	+	4.63447e7i	0.317350	+	0.103113i
$767$	6.26833e8	−	2.03670e8i	1.38920	−	0.451379i
$768$	2.84721e7	−	2.06862e7i	0.0628544	−	0.0456664i
$769$		−	8.70288e8i		−	1.91375i	−0.290508	−	0.956873i	$-0.593824\pi$
$769$		−	8.70288e8i		−	1.91375i	0.290508	−	0.956873i	$-0.406176\pi$
$770$	9.58871e7	−	1.40257e8i	0.210033	−	0.307222i
$771$	1.70202e7			0.0371366
$772$	−2.25761e8	−	3.10734e8i	−0.490679	−	0.675361i
$773$	−1.01964e8	−	3.13814e8i	−0.220755	−	0.679413i	−0.998695	−	0.0510746i	$-0.983735\pi$
$773$	−1.01964e8	−	3.13814e8i	−0.220755	−	0.679413i	0.777940	−	0.628338i	$-0.216265\pi$
$774$	1.05081e8	−	3.23405e8i	0.226621	−	0.697467i
$775$	−2.73955e7	−	1.99040e7i	−0.0588537	−	0.0427597i
$776$	1.71917e7	−	2.36624e7i	0.0367904	−	0.0506376i
$777$	−6.80556e8	−	2.21126e8i	−1.45078	−	0.471386i
$778$	−2.21684e8	+	7.20295e7i	−0.470756	+	0.152958i
$779$	−3.09561e8	+	2.24909e8i	−0.654837	+	0.475767i
$780$		−	1.05791e9i		−	2.22927i
$781$	3.32572e8	+	4.31208e8i	0.698125	+	0.905178i
$782$	2.66320e7			0.0556909
$783$	9.16250e7	+	1.26111e8i	0.190866	+	0.262705i
$784$	4.77810e6	+	1.47055e7i	0.00991532	+	0.0305162i
$785$	7.24562e7	−	2.22997e8i	0.149784	−	0.460989i
$786$	2.15224e7	+	1.56369e7i	0.0443224	+	0.0322021i
$787$	−3.28483e8	+	4.52117e8i	−0.673889	+	0.927528i	−0.999841	−	0.0178583i	$-0.994315\pi$
$787$	−3.28483e8	+	4.52117e8i	−0.673889	+	0.927528i	0.325952	+	0.945386i	$0.394315\pi$
$788$	4.84694e8	+	1.57486e8i	0.990578	+	0.321858i
$789$	−5.41887e8	+	1.76070e8i	−1.10326	+	0.358471i
$790$	−1.12410e8	+	8.16709e7i	−0.227995	+	0.165648i
$791$			2.61274e8i			0.527919i
$792$	−3.22452e8	+	2.48693e8i	−0.649067	+	0.500597i
$793$	4.98763e8			1.00017
$794$	9.71985e7	+	1.33782e8i	0.194177	+	0.267262i
$795$	−1.69133e8	−	5.20537e8i	−0.336609	−	1.03598i
$796$	−1.67082e8	+	5.14226e8i	−0.331277	+	1.01956i
$797$	6.90169e8	+	5.01437e8i	1.36327	+	0.990470i	0.998230	+	0.0594768i	$0.0189432\pi$
$797$	6.90169e8	+	5.01437e8i	1.36327	+	0.990470i	0.365036	+	0.930993i	$0.381057\pi$
$798$	−1.25239e8	+	1.72377e8i	−0.246452	+	0.339212i
$799$	9.31035e6	+	3.02512e6i	0.0182526	+	0.00593064i
$800$	1.20103e8	−	3.90240e7i	0.234577	−	0.0762187i
$801$	−2.61999e8	+	1.90353e8i	−0.509802	+	0.370393i
$802$		−	1.99726e8i		−	0.387179i
$803$	−6.72377e8	−	4.59672e8i	−1.29857	−	0.887772i
$804$	7.59796e8			1.46194
$805$	3.95096e8	+	5.43803e8i	0.757382	+	1.04245i
$806$	−2.02186e7	−	6.22264e7i	−0.0386141	−	0.118842i
$807$	8.15384e6	−	2.50949e7i	0.0155146	−	0.0477491i
$808$	1.16863e8	+	8.49061e7i	0.221536	+	0.160955i
$809$	−1.76476e8	+	2.42899e8i	−0.333304	+	0.458754i	−0.942471	−	0.334288i	$-0.891504\pi$
$809$	−1.76476e8	+	2.42899e8i	−0.333304	+	0.458754i	0.609167	+	0.793042i	$0.291504\pi$
$810$	−1.20025e8	−	3.89983e7i	−0.225847	−	0.0733823i
$811$	−1.43631e8	+	4.66686e7i	−0.269269	+	0.0874908i	−0.440539	−	0.897733i	$-0.645213\pi$
$811$	−1.43631e8	+	4.66686e7i	−0.269269	+	0.0874908i	0.171270	+	0.985224i	$0.445213\pi$
$812$	−2.75377e8	+	2.00073e8i	−0.514351	+	0.373698i
$813$			7.86625e8i			1.46385i
$814$	−1.87152e8	+	5.36313e6i	−0.346994	+	0.00994362i
$815$	−2.75752e7			−0.0509385
$816$	−4.63461e7	−	6.37899e7i	−0.0852988	−	0.117404i
$817$	2.40140e8	+	7.39076e8i	0.440351	+	1.35526i
$818$	2.30431e7	−	7.09193e7i	0.0420998	−	0.129570i
$819$	8.20213e8	+	5.95919e8i	1.49305	+	1.08477i
$820$	−3.12651e8	+	4.30327e8i	−0.567045	+	0.780471i
$821$	−6.68215e8	−	2.17116e8i	−1.20750	−	0.392340i	−0.364984	−	0.931014i	$-0.618926\pi$
$821$	−6.68215e8	−	2.17116e8i	−1.20750	−	0.392340i	−0.842515	+	0.538674i	$0.818926\pi$
$822$	−1.53871e8	+	4.99957e7i	−0.277039	+	0.0900155i
$823$	4.02760e8	−	2.92622e8i	0.722515	−	0.524938i	−0.164672	−	0.986348i	$-0.552656\pi$
$823$	4.02760e8	−	2.92622e8i	0.722515	−	0.524938i	0.887187	+	0.461410i	$0.152656\pi$
$824$		−	4.10683e8i		−	0.734048i
$825$	2.29379e8	−	8.18651e7i	0.408499	−	0.145793i
$826$	−1.84532e8			−0.327441
$827$	−6.07256e8	−	8.35816e8i	−1.07363	−	1.47773i	−0.866345	−	0.499446i	$-0.833537\pi$
$827$	−6.07256e8	−	8.35816e8i	−1.07363	−	1.47773i	−0.207286	−	0.978280i	$-0.566463\pi$
$828$	−2.34010e8	−	7.20208e8i	−0.412233	−	1.26872i
$829$	−1.75581e8	+	5.40383e8i	−0.308187	+	0.948502i	0.670282	+	0.742107i	$0.266173\pi$
$829$	−1.75581e8	+	5.40383e8i	−0.308187	+	0.948502i	−0.978469	+	0.206395i	$0.933827\pi$
$830$	1.10830e8	+	8.05224e7i	0.193830	+	0.140826i
$831$	7.66389e8	−	1.05484e9i	1.33551	−	1.83817i
$832$	−3.08023e8	−	1.00083e8i	−0.534827	−	0.173776i
$833$	3.72567e6	−	1.21054e6i	0.00644569	−	0.00209433i
$834$	7.41511e7	−	5.38739e7i	0.127826	−	0.0928711i
$835$		−	4.06873e8i		−	0.698875i
$836$	1.23201e8	−	4.19720e8i	0.210860	−	0.718358i
$837$	−6.58248e7			−0.112257
$838$	−1.98441e8	−	2.73131e8i	−0.337209	−	0.464129i
$839$	1.18653e8	+	3.65176e8i	0.200906	+	0.618324i	0.999857	+	0.0169281i	$0.00538864\pi$
$839$	1.18653e8	+	3.65176e8i	0.200906	+	0.618324i	−0.798951	+	0.601396i	$0.794611\pi$
$840$	−1.94722e8	+	5.99294e8i	−0.328532	+	1.01112i
$841$	−2.21603e8	−	1.61004e8i	−0.372552	−	0.270675i
$842$	9.93322e7	−	1.36719e8i	0.166400	−	0.229030i
$843$	1.45804e9	+	4.73746e8i	2.43381	+	0.790793i
$844$	−4.85667e8	+	1.57803e8i	−0.807813	+	0.262474i
$845$	−6.32466e8	+	4.59513e8i	−1.04825	+	0.761602i
$846$			3.54763e7i			0.0585905i
$847$	−3.75456e8	−	4.58998e8i	−0.617887	−	0.755371i
$848$	−2.60589e8			−0.427335
$849$	5.44181e8	+	7.49001e8i	0.889243	+	1.22394i
$850$	−2.60106e6	−	8.00525e6i	−0.00423540	−	0.0130352i
$851$	2.28899e8	−	7.04478e8i	0.371411	−	1.14309i
$852$	−7.68035e8	−	5.58010e8i	−1.24183	−	0.902243i
$853$	4.34323e8	−	5.97794e8i	0.699787	−	0.963174i	−0.300170	−	0.953886i	$-0.597043\pi$
$853$	4.34323e8	−	5.97794e8i	0.699787	−	0.963174i	0.999957	−	0.00928814i	$-0.00295655\pi$
$854$	−1.32809e8	−	4.31523e7i	−0.213233	−	0.0692836i
$855$	−7.35293e8	+	2.38911e8i	−1.17642	+	0.382242i
$856$	−3.79741e8	+	2.75898e8i	−0.605432	+	0.439872i
$857$		−	6.02254e8i		−	0.956835i	−0.878132	−	0.478418i	$-0.841211\pi$
$857$		−	6.02254e8i		−	0.956835i	0.878132	−	0.478418i	$-0.158789\pi$
$858$	4.51531e8	+	1.32538e8i	0.714868	+	0.209835i
$859$	6.89322e8			1.08753			0.543767	−	0.839236i	$-0.316998\pi$
$859$	6.89322e8			1.08753			0.543767	+	0.839236i	$0.316998\pi$
$860$	6.34971e8	+	8.73963e8i	0.998295	+	1.37403i
$861$	−2.79444e8	−	8.60040e8i	−0.437809	−	1.34744i
$862$	−3.47424e7	+	1.06926e8i	−0.0542423	+	0.166941i
$863$	5.72360e8	+	4.15844e8i	0.890506	+	0.646991i	0.936010	−	0.351973i	$-0.114489\pi$
$863$	5.72360e8	+	4.15844e8i	0.890506	+	0.646991i	−0.0455035	+	0.998964i	$0.514489\pi$
$864$	1.44290e8	−	1.98598e8i	0.223715	−	0.307917i
$865$	4.35444e8	+	1.41484e8i	0.672797	+	0.218605i
$866$	1.28604e8	−	4.17861e7i	0.198017	−	0.0643396i
$867$	7.82061e8	−	5.68200e8i	1.20001	−	0.871855i
$868$		−	1.43736e8i		−	0.219789i
$869$	1.63011e8	+	4.56742e8i	0.248403	+	0.696003i
$870$	2.79244e8			0.424059
$871$	−6.18922e8	−	8.51874e8i	−0.936660	−	1.28920i
$872$	−1.96622e7	−	6.05140e7i	−0.0296540	−	0.0912655i
$873$	−2.62077e7	+	8.06589e7i	−0.0393900	+	0.121230i
$874$	−1.78436e8	−	1.29642e8i	−0.267269	−	0.194182i
$875$	−3.10990e8	+	4.28041e8i	−0.464219	+	0.638942i
$876$	1.35042e9	+	4.38778e8i	2.00889	+	0.652728i
$877$	−4.95398e8	+	1.60964e8i	−0.734438	+	0.238633i	−0.652272	−	0.757985i	$-0.726184\pi$
$877$	−4.95398e8	+	1.60964e8i	−0.734438	+	0.238633i	−0.0821663	+	0.996619i	$0.526184\pi$
$878$	−6.41033e7	+	4.65738e7i	−0.0947102	+	0.0688110i
$879$			7.45498e8i			1.09769i
$880$	−1.49154e7	−	5.20490e8i	−0.0218870	−	0.763773i
$881$	−4.57403e8			−0.668915			−0.334458	−	0.942411i	$-0.608553\pi$
$881$	−4.57403e8			−0.668915			−0.334458	+	0.942411i	$0.608553\pi$
$882$	8.34441e6	+	1.14851e7i	0.0121616	+	0.0167390i
$883$	9.23869e7	+	2.84338e8i	0.134193	+	0.413002i	0.995464	−	0.0951437i	$-0.0303311\pi$
$883$	9.23869e7	+	2.84338e8i	0.134193	+	0.413002i	−0.861271	+	0.508146i	$0.830331\pi$
$884$	−3.94336e7	+	1.21364e8i	−0.0570834	+	0.175685i
$885$	−9.60976e8	−	6.98190e8i	−1.38638	−	1.00727i
$886$	5.12999e7	−	7.06082e7i	0.0737590	−	0.101521i
$887$	−8.28437e8	−	2.69175e8i	−1.18710	−	0.385713i	−0.352102	−	0.935962i	$-0.614533\pi$
$887$	−8.28437e8	−	2.69175e8i	−1.18710	−	0.385713i	−0.835001	+	0.550248i	$0.814533\pi$
$888$	6.60415e8	−	2.14582e8i	0.943144	−	0.306446i
$889$	4.54605e8	−	3.30290e8i	0.647037	−	0.470100i
$890$			1.31120e8i			0.185994i
$891$	−2.48590e8	+	3.63621e8i	−0.351440	+	0.514062i
$892$	−2.15377e8			−0.303462
$893$	−4.76540e7	−	6.55902e7i	−0.0669184	−	0.0921052i
$894$	−1.48928e8	−	4.58355e8i	−0.208432	−	0.641489i
$895$	4.17519e7	−	1.28499e8i	0.0582381	−	0.179238i
$896$	5.62290e8	+	4.08527e8i	0.781693	+	0.567933i
$897$	−1.09431e9	+	1.50619e9i	−1.51622	+	2.08690i
$898$	3.60422e8	+	1.17108e8i	0.497717	+	0.161718i
$899$	−1.28878e8	+	4.18751e7i	−0.177379	+	0.0576338i
$900$	−1.93630e8	+	1.40681e8i	−0.265611	+	0.192978i
$901$			6.60210e7i			0.0902626i
$902$	−1.44500e8	−	1.87357e8i	−0.196902	−	0.255300i
$903$	−1.83657e9			−2.49427
$904$	−1.49028e8	−	2.05120e8i	−0.201727	−	0.277653i
$905$	2.46129e8	+	7.57506e8i	0.332060	+	1.02198i
$906$	−1.52974e8	+	4.70806e8i	−0.205700	+	0.633079i
$907$	−2.38497e7	−	1.73278e7i	−0.0319640	−	0.0232232i	0.571689	−	0.820471i	$-0.306289\pi$
$907$	−2.38497e7	−	1.73278e7i	−0.0319640	−	0.0232232i	−0.603653	+	0.797248i	$0.706289\pi$
$908$	2.69532e8	−	3.70978e8i	0.360041	−	0.495554i
$909$	−3.98356e8	−	1.29434e8i	−0.530371	−	0.172328i
$910$	3.90393e8	−	1.26846e8i	0.518057	−	0.168327i
$911$	1.09812e9	−	7.97828e8i	1.45242	−	1.05525i	0.467165	−	0.884170i	$-0.345275\pi$
$911$	1.09812e9	−	7.97828e8i	1.45242	−	1.05525i	0.985258	−	0.171077i	$-0.0547246\pi$
$912$			6.53004e8i			0.860857i
$913$	3.78614e8	−	2.92008e8i	0.497490	−	0.383692i
$914$	−9.69810e6			−0.0127013
$915$	−5.28351e8	−	7.27213e8i	−0.689699	−	0.949289i
$916$	1.14283e8	+	3.51726e8i	0.148694	+	0.457634i
$917$	2.50283e7	−	7.70293e7i	0.0324582	−	0.0998960i
$918$	−1.32371e7	−	9.61735e6i	−0.0171106	−	0.0124316i
$919$	4.71793e6	−	6.49368e6i	0.00607862	−	0.00836651i	−0.805967	−	0.591961i	$-0.798354\pi$
$919$	4.71793e6	−	6.49368e6i	0.00607862	−	0.00836651i	0.812045	+	0.583594i	$0.198354\pi$
$920$	−6.20359e8	−	2.01567e8i	−0.796672	−	0.258855i
$921$	1.30267e9	−	4.23262e8i	1.66745	−	0.541789i
$922$	3.07374e7	−	2.23320e7i	0.0392170	−	0.0284928i
$923$			1.31566e9i			1.67317i
$924$	8.53414e8	+	5.83438e8i	1.08179	+	0.739570i
$925$	−2.34113e8			−0.295801
$926$	2.50089e8	+	3.44218e8i	0.314965	+	0.433512i
$927$	3.67988e8	+	1.13255e9i	0.461950	+	1.42173i
$928$	1.56165e8	−	4.80627e8i	0.195407	−	0.601401i
$929$	7.79013e8	+	5.65986e8i	0.971623	+	0.705925i	0.955821	−	0.293950i	$-0.0949698\pi$
$929$	7.79013e8	+	5.65986e8i	0.971623	+	0.705925i	0.0158021	+	0.999875i	$0.494970\pi$
$930$	−6.93101e7	+	9.53972e7i	−0.0861684	+	0.118601i
$931$	−3.08550e7	−	1.00254e7i	−0.0382364	−	0.0124238i
$932$	5.97316e8	−	1.94080e8i	0.737831	−	0.239736i
$933$	−1.44957e9	+	1.05318e9i	−1.78482	+	1.29675i
$934$			3.81687e8i			0.468454i
$935$	−1.31867e8	+	3.77885e6i	−0.161325	+	0.00462301i
$936$	−9.83834e8			−1.19976
$937$	−4.40151e8	−	6.05815e8i	−0.535035	−	0.736413i	0.452852	−	0.891586i	$-0.350407\pi$
$937$	−4.40151e8	−	6.05815e8i	−0.535035	−	0.736413i	−0.987887	+	0.155173i	$0.950407\pi$
$938$	9.11019e7	+	2.80383e8i	0.110387	+	0.339737i
$939$	3.19018e8	−	9.81836e8i	0.385317	−	1.18588i
$940$	−9.11783e7	−	6.62449e7i	−0.109776	−	0.0797570i
$941$	6.32736e8	−	8.70887e8i	0.759371	−	1.04518i	−0.237895	−	0.971291i	$-0.576457\pi$
$941$	6.32736e8	−	8.70887e8i	0.759371	−	1.04518i	0.997266	−	0.0738937i	$-0.0235425\pi$
$942$	−1.72928e8	−	5.61877e7i	−0.206877	−	0.0672185i
$943$	8.90271e8	−	2.89267e8i	1.06166	−	0.344956i
$944$	−4.57535e8	+	3.32419e8i	−0.543887	+	0.395157i
$945$		−	4.12968e8i		−	0.489352i
$946$	−4.52573e8	+	1.61523e8i	−0.534583	+	0.190792i
$947$	3.65054e8			0.429840			0.214920	−	0.976632i	$-0.431051\pi$
$947$	3.65054e8			0.429840			0.214920	+	0.976632i	$0.431051\pi$
$948$	−4.96938e8	−	6.83976e8i	−0.583280	−	0.802816i
$949$	−6.08086e8	−	1.87150e9i	−0.711487	−	2.18973i
$950$	−2.15413e7	+	6.62973e7i	−0.0251247	+	0.0773259i
$951$	−4.11622e8	−	2.99061e8i	−0.478583	−	0.347711i
$952$	4.46775e7	−	6.14934e7i	0.0517820	−	0.0712717i
$953$	−1.04928e9	−	3.40931e8i	−1.21230	−	0.393901i	−0.368030	−	0.929814i	$-0.619968\pi$
$953$	−1.04928e9	−	3.40931e8i	−1.21230	−	0.393901i	−0.844273	+	0.535913i	$0.819968\pi$
$954$	−2.27545e8	+	7.39338e7i	−0.262073	+	0.0851526i
$955$	9.72074e8	−	7.06253e8i	1.11606	−	0.810868i
$956$			4.21553e8i			0.482479i
$957$	2.74502e8	−	9.35176e8i	0.313192	−	1.06698i
$958$	−1.18891e8			−0.135223
$959$	2.89525e8	+	3.98497e8i	0.328269	+	0.451824i
$960$	1.80372e8	+	5.55127e8i	0.203871	+	0.627450i
$961$	−2.56571e8	+	7.89644e8i	−0.289093	+	0.889736i
$962$	−3.65957e8	−	2.65883e8i	−0.411060	−	0.298652i
$963$	8.00006e8	−	1.10111e9i	0.895807	−	1.23297i
$964$	−5.04118e8	−	1.63798e8i	−0.562731	−	0.182842i
$965$	9.12362e8	−	2.96444e8i	1.01528	−	0.329884i
$966$	4.21704e8	−	3.06386e8i	0.467817	−	0.339889i
$967$			5.05504e8i			0.559043i	0.960139	+	0.279522i	$0.0901759\pi$
$967$			5.05504e8i			0.559043i	−0.960139	+	0.279522i	$0.909824\pi$
$968$	5.56569e8	+	1.46191e8i	0.613610	+	0.161174i
$969$	1.65440e8			0.181832
$970$	2.01832e7	+	2.77799e7i	0.0221144	+	0.0304379i
$971$	4.61419e8	+	1.42010e9i	0.504009	+	1.55118i	0.802431	+	0.596745i	$0.203540\pi$
$971$	4.61419e8	+	1.42010e9i	0.504009	+	1.55118i	−0.298422	+	0.954434i	$0.596460\pi$
$972$	3.48566e8	−	1.07278e9i	0.379565	−	1.16818i
$973$	−2.25753e8	−	1.64020e8i	−0.245073	−	0.178056i
$974$	1.20641e8	−	1.66048e8i	0.130563	−	0.179704i
$975$	5.59619e8	+	1.81831e8i	0.603780	+	0.196180i
$976$	−4.07026e8	+	1.32251e8i	−0.437797	+	0.142249i
$977$	−1.27146e9	+	9.23770e8i	−1.36339	+	0.990559i	−0.365166	+	0.930942i	$0.618988\pi$
$977$	−1.27146e9	+	9.23770e8i	−1.36339	+	0.990559i	−0.998221	+	0.0596166i	$0.981012\pi$
$978$			2.13838e7i			0.0228596i
$979$	4.39114e8	+	1.28893e8i	0.467982	+	0.137367i
$980$	−4.50996e7			−0.0479175
$981$	1.08446e8	+	1.49263e8i	0.114870	+	0.158105i
$982$	1.76221e8	+	5.42353e8i	0.186090	+	0.572727i
$983$	−1.53639e8	+	4.72851e8i	−0.161748	+	0.497810i	−0.998782	−	0.0493413i	$-0.984288\pi$
$983$	−1.53639e8	+	4.72851e8i	−0.161748	+	0.497810i	0.837034	+	0.547151i	$0.184288\pi$
$984$	7.09942e8	+	5.15803e8i	0.745140	+	0.541376i
$985$	−7.48187e8	+	1.02979e9i	−0.782891	+	1.07756i
$986$	−3.20352e7	−	1.04089e7i	−0.0334192	−	0.0108586i
$987$	1.82227e8	−	5.92090e7i	0.189522	−	0.0615795i
$988$	8.54994e8	−	6.21190e8i	0.886528	−	0.644100i
$989$		−	1.90112e9i		−	1.96527i
$990$	−1.60696e8	−	4.50257e8i	−0.165615	−	0.464039i
$991$	−5.86143e8			−0.602258			−0.301129	−	0.953583i	$-0.597364\pi$
$991$	−5.86143e8			−0.602258			−0.301129	+	0.953583i	$0.597364\pi$
$992$	1.25434e8	+	1.72645e8i	0.128493	+	0.176855i
$993$	4.47299e8	+	1.37664e9i	0.456825	+	1.40596i
$994$	1.13829e8	−	3.50330e8i	0.115903	−	0.356713i
$995$	−1.09254e9	−	7.93774e8i	−1.10909	−	0.805800i
$996$	−4.89950e8	+	6.74358e8i	−0.495876	+	0.682515i
$997$	1.55898e9	+	5.06544e8i	1.57310	+	0.511130i	0.960267	−	0.279083i	$-0.0900306\pi$
$997$	1.55898e9	+	5.06544e8i	1.57310	+	0.511130i	0.612831	+	0.790214i	$0.290031\pi$
$998$	−4.12114e8	+	1.33904e8i	−0.414596	+	0.134711i
$999$	−3.68173e8	+	2.67493e8i	−0.369279	+	0.268297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.7.d.a.8.4	yes	20
3.2	odd	2		99.7.k.a.19.2		20
11.2	odd	10		121.7.b.c.120.12		20
11.7	odd	10	inner	11.7.d.a.7.4	✓	20
11.9	even	5		121.7.b.c.120.9		20
33.29	even	10		99.7.k.a.73.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.7.d.a.7.4	✓	20	11.7	odd	10	inner
11.7.d.a.8.4	yes	20	1.1	even	1	trivial
99.7.k.a.19.2		20	3.2	odd	2
99.7.k.a.73.2		20	33.29	even	10
121.7.b.c.120.9		20	11.9	even	5
121.7.b.c.120.12		20	11.2	odd	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58098 + 2.17603i) q^{2} +(-12.6315 - 38.8758i) q^{3} +(17.5415 - 53.9871i) q^{4} +(114.702 + 83.3360i) q^{5} +(64.6247 - 88.9483i) q^{6} +(-318.349 - 103.438i) q^{7} +(308.927 - 100.377i) q^{8} +(-761.996 + 553.623i) q^{9} +O(q^{10})\)	\(q+(1.58098 + 2.17603i) q^{2} +(-12.6315 - 38.8758i) q^{3} +(17.5415 - 53.9871i) q^{4} +(114.702 + 83.3360i) q^{5} +(64.6247 - 88.9483i) q^{6} +(-318.349 - 103.438i) q^{7} +(308.927 - 100.377i) q^{8} +(-761.996 + 553.623i) q^{9} +381.348i q^{10} +(1277.12 + 374.873i) q^{11} -2320.36 q^{12} +(1890.15 + 2601.56i) q^{13} +(-278.219 - 856.270i) q^{14} +(1790.89 - 5511.79i) q^{15} +(-2232.32 - 1621.87i) q^{16} +(-410.906 + 565.564i) q^{17} +(-2409.40 - 782.862i) q^{18} +(5506.19 - 1789.07i) q^{19} +(6511.12 - 4730.60i) q^{20} +13682.6i q^{21} +(1203.36 + 3371.72i) q^{22} -14163.6 q^{23} +(-7804.43 - 10741.9i) q^{24} +(1383.31 + 4257.39i) q^{25} +(-2672.80 + 8226.04i) q^{26} +(7039.85 + 5114.75i) q^{27} +(-11168.6 + 15372.3i) q^{28} +(17037.1 + 5535.69i) q^{29} +(14825.2 - 4817.00i) q^{30} +(-6119.86 + 4446.34i) q^{31} -28210.6i q^{32} +(-1558.46 - 54384.1i) q^{33} -1880.32 q^{34} +(-27895.2 - 38394.5i) q^{35} +(16521.9 + 50849.3i) q^{36} +(-16161.1 + 49738.7i) q^{37} +(12598.2 + 9153.16i) q^{38} +(77262.4 - 106343. i) q^{39} +(43799.6 + 14231.4i) q^{40} +(-62856.4 + 20423.3i) q^{41} +(-29773.8 + 21631.9i) q^{42} +134226. i q^{43} +(42640.8 - 62372.1i) q^{44} -133539. q^{45} +(-22392.3 - 30820.4i) q^{46} +(-4327.31 - 13318.1i) q^{47} +(-34854.0 + 107270. i) q^{48} +(-4533.49 - 3293.77i) q^{49} +(-7077.23 + 9740.97i) q^{50} +(27177.1 + 8830.37i) q^{51} +(173607. - 56408.3i) q^{52} +(76404.0 - 55510.7i) q^{53} +23405.2i q^{54} +(115248. + 149429. i) q^{55} -108729. q^{56} +(-139103. - 191459. i) q^{57} +(14889.5 + 45825.1i) q^{58} +(63336.0 - 194928. i) q^{59} +(-266151. - 193370. i) q^{60} +(91166.7 - 125480. i) q^{61} +(-19350.8 - 6287.44i) q^{62} +(299846. - 97425.9i) q^{63} +(-81481.2 + 59199.6i) q^{64} +455922. i q^{65} +(115878. - 89371.5i) q^{66} -327447. q^{67} +(23325.2 + 32104.4i) q^{68} +(178907. + 550620. i) q^{69} +(39445.8 - 121402. i) q^{70} +(330998. + 240484. i) q^{71} +(-179831. + 247516. i) q^{72} +(-581986. - 189099. i) q^{73} +(-133783. + 43468.8i) q^{74} +(148036. - 107554. i) q^{75} -328646. i q^{76} +(-367793. - 251443. i) q^{77} +353555. q^{78} +(214164. + 294771. i) q^{79} +(-120891. - 372065. i) q^{80} +(-102264. + 314738. i) q^{81} +(-143816. - 104489. i) q^{82} +(211152. - 290626. i) q^{83} +(738685. + 240013. i) q^{84} +(-94263.6 + 30628.1i) q^{85} +(-292081. + 212209. i) q^{86} -732255. i q^{87} +(432165. - 12384.3i) q^{88} +343832. q^{89} +(-211123. - 290586. i) q^{90} +(-332626. - 1.02372e6i) q^{91} +(-248450. + 764650. i) q^{92} +(250158. + 181750. i) q^{93} +(22139.2 - 30472.0i) q^{94} +(780666. + 253654. i) q^{95} +(-1.09671e6 + 356342. i) q^{96} +(72846.5 - 52926.0i) q^{97} -15072.4i q^{98} +(-1.18070e6 + 421390. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9}+O(q^{10}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9	\( 20 q - 5 q^{2} - 39 q^{3} + 215 q^{4} + 181 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} - 704 q^{9} - 3498 q^{11} - 3006 q^{12} - 1805 q^{13} + 7170 q^{14} - 525 q^{15} - 2185 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 5144 q^{20} - 2915 q^{22} + 7816 q^{23} - 123775 q^{24} - 30416 q^{25} - 131310 q^{26} - 18687 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 71211 q^{31} + 5951 q^{33} - 228190 q^{34} - 377445 q^{35} - 119626 q^{36} - 205731 q^{37} + 127220 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} - 20170 q^{42} - 537812 q^{44} - 805524 q^{45} - 714610 q^{46} + 25329 q^{47} - 935824 q^{48} + 304010 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} - 110919 q^{53} - 5511 q^{55} - 862620 q^{56} - 1435995 q^{57} - 667940 q^{58} - 581009 q^{59} + 664640 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 124615 q^{64} + 272910 q^{66} - 960956 q^{67} - 1822680 q^{68} - 624034 q^{69} - 1987140 q^{70} - 288895 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 550845 q^{75} + 623095 q^{77} + 1703080 q^{78} + 1662955 q^{79} + 1190956 q^{80} + 1465924 q^{81} - 282095 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} + 735635 q^{86} - 1860485 q^{88} + 1111620 q^{89} + 4118080 q^{90} + 650935 q^{91} + 4407784 q^{92} - 1556453 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1189281 q^{97} + 252208 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 39 * q^3 + 215 * q^4 + 181 * q^5 - 405 * q^6 - 365 * q^7 + 1595 * q^8 - 704 * q^9 - 3498 * q^11 - 3006 * q^12 - 1805 * q^13 + 7170 * q^14 - 525 * q^15 - 2185 * q^16 + 3635 * q^17 + 11970 * q^18 + 23845 * q^19 + 5144 * q^20 - 2915 * q^22 + 7816 * q^23 - 123775 * q^24 - 30416 * q^25 - 131310 * q^26 - 18687 * q^27 + 226540 * q^28 + 134595 * q^29 + 220420 * q^30 - 71211 * q^31 + 5951 * q^33 - 228190 * q^34 - 377445 * q^35 - 119626 * q^36 - 205731 * q^37 + 127220 * q^38 + 443075 * q^39 + 704340 * q^40 + 490975 * q^41 - 20170 * q^42 - 537812 * q^44 - 805524 * q^45 - 714610 * q^46 + 25329 * q^47 - 935824 * q^48 + 304010 * q^49 + 417855 * q^50 + 1169565 * q^51 + 1468510 * q^52 - 110919 * q^53 - 5511 * q^55 - 862620 * q^56 - 1435995 * q^57 - 667940 * q^58 - 581009 * q^59 + 664640 * q^60 + 892675 * q^61 + 2337360 * q^62 + 900840 * q^63 + 124615 * q^64 + 272910 * q^66 - 960956 * q^67 - 1822680 * q^68 - 624034 * q^69 - 1987140 * q^70 - 288895 * q^71 + 954565 * q^72 - 806585 * q^73 - 404170 * q^74 - 550845 * q^75 + 623095 * q^77 + 1703080 * q^78 + 1662955 * q^79 + 1190956 * q^80 + 1465924 * q^81 - 282095 * q^82 + 14645 * q^83 - 2604390 * q^84 - 33365 * q^85 + 735635 * q^86 - 1860485 * q^88 + 1111620 * q^89 + 4118080 * q^90 + 650935 * q^91 + 4407784 * q^92 - 1556453 * q^93 - 5913080 * q^94 - 4329525 * q^95 - 6429020 * q^96 - 1189281 * q^97 + 252208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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