LMFDB - Embedded newform 13.5.d.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,5,Mod(5,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("13.5");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34380952009$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.53039932416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 12x^{3} + 529x^{2} - 1334x + 1682 $ x^6 - 2x^5 + 2x^4 - 12x^3 + 529x^2 - 1334*x + 1682
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.1
Root			$3.18200 + 3.18200i$ of defining polynomial
Character	$\chi$	$=$	13.8
Dual form			13.5.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.18200 - 3.18200i) q^{2} -10.6142 q^{3} +4.25023i q^{4} +(-9.43223 - 9.43223i) q^{5} +(33.7744 + 33.7744i) q^{6} +(54.8891 - 54.8891i) q^{7} +(-37.3878 + 37.3878i) q^{8} +31.6617 q^{9} +O(q^{10})$	\(q+(-3.18200 - 3.18200i) q^{2} -10.6142 q^{3} +4.25023i q^{4} +(-9.43223 - 9.43223i) q^{5} +(33.7744 + 33.7744i) q^{6} +(54.8891 - 54.8891i) q^{7} +(-37.3878 + 37.3878i) q^{8} +31.6617 q^{9} +60.0267i q^{10} +(-12.2956 + 12.2956i) q^{11} -45.1129i q^{12} +(-111.098 - 127.351i) q^{13} -349.314 q^{14} +(100.116 + 100.116i) q^{15} +305.939 q^{16} -327.220i q^{17} +(-100.748 - 100.748i) q^{18} +(438.065 + 438.065i) q^{19} +(40.0891 - 40.0891i) q^{20} +(-582.605 + 582.605i) q^{21} +78.2492 q^{22} -229.410i q^{23} +(396.842 - 396.842i) q^{24} -447.066i q^{25} +(-51.7169 + 758.744i) q^{26} +523.687 q^{27} +(233.291 + 233.291i) q^{28} -443.114 q^{29} -637.136i q^{30} +(-424.901 - 424.901i) q^{31} +(-375.294 - 375.294i) q^{32} +(130.508 - 130.508i) q^{33} +(-1041.21 + 1041.21i) q^{34} -1035.45 q^{35} +134.570i q^{36} +(-766.005 + 766.005i) q^{37} -2787.85i q^{38} +(1179.22 + 1351.73i) q^{39} +705.300 q^{40} +(1516.93 + 1516.93i) q^{41} +3707.70 q^{42} +192.875i q^{43} +(-52.2591 - 52.2591i) q^{44} +(-298.641 - 298.641i) q^{45} +(-729.983 + 729.983i) q^{46} +(947.423 - 947.423i) q^{47} -3247.31 q^{48} -3624.63i q^{49} +(-1422.56 + 1422.56i) q^{50} +3473.18i q^{51} +(541.270 - 472.191i) q^{52} -664.279 q^{53} +(-1666.37 - 1666.37i) q^{54} +231.950 q^{55} +4104.36i q^{56} +(-4649.72 - 4649.72i) q^{57} +(1409.99 + 1409.99i) q^{58} +(3925.10 - 3925.10i) q^{59} +(-425.515 + 425.515i) q^{60} +379.956 q^{61} +2704.07i q^{62} +(1737.89 - 1737.89i) q^{63} -2506.66i q^{64} +(-153.302 + 2249.10i) q^{65} -830.554 q^{66} +(-185.119 - 185.119i) q^{67} +1390.76 q^{68} +2435.01i q^{69} +(3294.81 + 3294.81i) q^{70} +(-537.219 - 537.219i) q^{71} +(-1183.76 + 1183.76i) q^{72} +(992.844 - 992.844i) q^{73} +4874.85 q^{74} +4745.26i q^{75} +(-1861.88 + 1861.88i) q^{76} +1349.79i q^{77} +(548.934 - 8053.48i) q^{78} -1497.03 q^{79} +(-2885.69 - 2885.69i) q^{80} -8123.14 q^{81} -9653.72i q^{82} +(6730.18 + 6730.18i) q^{83} +(-2476.21 - 2476.21i) q^{84} +(-3086.41 + 3086.41i) q^{85} +(613.728 - 613.728i) q^{86} +4703.31 q^{87} -919.410i q^{88} +(2523.93 - 2523.93i) q^{89} +1900.55i q^{90} +(-13088.2 - 892.110i) q^{91} +975.046 q^{92} +(4509.99 + 4509.99i) q^{93} -6029.40 q^{94} -8263.86i q^{95} +(3983.45 + 3983.45i) q^{96} +(3477.41 + 3477.41i) q^{97} +(-11533.6 + 11533.6i) q^{98} +(-389.300 + 389.300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24} + 910 q^{26} + 236 q^{27} + 1884 q^{28} + 4184 q^{29} - 3468 q^{31} + 2092 q^{32} + 2324 q^{33} - 5304 q^{34} - 4204 q^{35} - 1758 q^{37} + 1196 q^{39} - 708 q^{40} + 4750 q^{41} + 9532 q^{42} - 3956 q^{44} + 830 q^{45} + 516 q^{46} - 6872 q^{47} - 9436 q^{48} - 322 q^{50} + 3900 q^{52} + 2108 q^{53} - 184 q^{54} + 6408 q^{55} - 5800 q^{57} + 6516 q^{58} + 4372 q^{59} + 1324 q^{60} + 5988 q^{61} - 652 q^{63} - 5018 q^{65} - 4592 q^{66} + 72 q^{67} - 10572 q^{68} + 7368 q^{70} - 14672 q^{71} - 7980 q^{72} + 5874 q^{73} + 1544 q^{74} + 3576 q^{76} + 5720 q^{78} + 2616 q^{79} - 12080 q^{80} - 19450 q^{81} + 19264 q^{83} + 6296 q^{84} + 4164 q^{85} + 29376 q^{86} + 35584 q^{87} - 986 q^{89} - 30888 q^{91} + 5304 q^{92} - 9520 q^{93} - 36156 q^{94} + 20720 q^{96} - 23154 q^{97} - 41426 q^{98} + 17492 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9 - 32 * q^11 - 244 * q^14 + 404 * q^15 + 1044 * q^16 - 802 * q^18 + 732 * q^19 + 428 * q^20 - 2128 * q^21 - 1632 * q^22 - 24 * q^24 + 910 * q^26 + 236 * q^27 + 1884 * q^28 + 4184 * q^29 - 3468 * q^31 + 2092 * q^32 + 2324 * q^33 - 5304 * q^34 - 4204 * q^35 - 1758 * q^37 + 1196 * q^39 - 708 * q^40 + 4750 * q^41 + 9532 * q^42 - 3956 * q^44 + 830 * q^45 + 516 * q^46 - 6872 * q^47 - 9436 * q^48 - 322 * q^50 + 3900 * q^52 + 2108 * q^53 - 184 * q^54 + 6408 * q^55 - 5800 * q^57 + 6516 * q^58 + 4372 * q^59 + 1324 * q^60 + 5988 * q^61 - 652 * q^63 - 5018 * q^65 - 4592 * q^66 + 72 * q^67 - 10572 * q^68 + 7368 * q^70 - 14672 * q^71 - 7980 * q^72 + 5874 * q^73 + 1544 * q^74 + 3576 * q^76 + 5720 * q^78 + 2616 * q^79 - 12080 * q^80 - 19450 * q^81 + 19264 * q^83 + 6296 * q^84 + 4164 * q^85 + 29376 * q^86 + 35584 * q^87 - 986 * q^89 - 30888 * q^91 + 5304 * q^92 - 9520 * q^93 - 36156 * q^94 + 20720 * q^96 - 23154 * q^97 - 41426 * q^98 + 17492 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−3.18200	−	3.18200i	−0.795500	−	0.795500i	0.186883	−	0.982382i	$-0.440162\pi$
$2$	−3.18200	−	3.18200i	−0.795500	−	0.795500i	−0.982382	+	0.186883i	$0.940162\pi$
$3$	−10.6142			−1.17936			−0.589679	−	0.807638i	$-0.700746\pi$
$3$	−10.6142			−1.17936			−0.589679	+	0.807638i	$0.700746\pi$
$4$			4.25023i			0.265639i
$5$	−9.43223	−	9.43223i	−0.377289	−	0.377289i	0.492834	−	0.870123i	$-0.335961\pi$
$5$	−9.43223	−	9.43223i	−0.377289	−	0.377289i	−0.870123	+	0.492834i	$0.835961\pi$
$6$	33.7744	+	33.7744i	0.938179	+	0.938179i
$7$	54.8891	−	54.8891i	1.12019	−	1.12019i	0.128473	−	0.991713i	$-0.458992\pi$
$7$	54.8891	−	54.8891i	1.12019	−	1.12019i	0.991713	−	0.128473i	$-0.0410076\pi$
$8$	−37.3878	+	37.3878i	−0.584184	+	0.584184i
$9$	31.6617			0.390886
$10$			60.0267i			0.600267i
$11$	−12.2956	+	12.2956i	−0.101617	+	0.101617i	−0.756087	−	0.654471i	$-0.772891\pi$
$11$	−12.2956	+	12.2956i	−0.101617	+	0.101617i	0.654471	+	0.756087i	$0.272891\pi$
$12$		−	45.1129i		−	0.313284i
$13$	−111.098	−	127.351i	−0.657384	−	0.753556i
$13$	−111.098	−	127.351i	−0.657384	−	0.753556i
$14$	−349.314			−1.78222
$15$	100.116	+	100.116i	0.444959	+	0.444959i
$16$	305.939			1.19508
$17$		−	327.220i		−	1.13225i	−0.824320	−	0.566124i	$-0.808442\pi$
$17$		−	327.220i		−	1.13225i	0.824320	−	0.566124i	$-0.191558\pi$
$18$	−100.748	−	100.748i	−0.310949	−	0.310949i
$19$	438.065	+	438.065i	1.21348	+	1.21348i	0.969875	+	0.243602i	$0.0783289\pi$
$19$	438.065	+	438.065i	1.21348	+	1.21348i	0.243602	+	0.969875i	$0.421671\pi$
$20$	40.0891	−	40.0891i	0.100223	−	0.100223i
$21$	−582.605	+	582.605i	−1.32110	+	1.32110i
$22$	78.2492			0.161672
$23$		−	229.410i		−	0.433668i	−0.976209	−	0.216834i	$-0.930427\pi$
$23$		−	229.410i		−	0.433668i	0.976209	−	0.216834i	$-0.0695730\pi$
$24$	396.842	−	396.842i	0.688962	−	0.688962i
$25$		−	447.066i		−	0.715306i
$26$	−51.7169	+	758.744i	−0.0765042	+	1.12240i
$27$	523.687			0.718364
$28$	233.291	+	233.291i	0.297565	+	0.297565i
$29$	−443.114			−0.526890			−0.263445	−	0.964674i	$-0.584859\pi$
$29$	−443.114			−0.526890			−0.263445	+	0.964674i	$0.584859\pi$
$30$		−	637.136i		−	0.707929i
$31$	−424.901	−	424.901i	−0.442144	−	0.442144i	0.450588	−	0.892732i	$-0.351214\pi$
$31$	−424.901	−	424.901i	−0.442144	−	0.442144i	−0.892732	+	0.450588i	$0.851214\pi$
$32$	−375.294	−	375.294i	−0.366498	−	0.366498i
$33$	130.508	−	130.508i	0.119842	−	0.119842i
$34$	−1041.21	+	1041.21i	−0.900703	+	0.900703i
$35$	−1035.45			−0.845268
$36$			134.570i			0.103835i
$37$	−766.005	+	766.005i	−0.559536	+	0.559536i	−0.929175	−	0.369639i	$-0.879481\pi$
$37$	−766.005	+	766.005i	−0.559536	+	0.559536i	0.369639	+	0.929175i	$0.379481\pi$
$38$		−	2787.85i		−	1.93064i
$39$	1179.22	+	1351.73i	0.775291	+	0.888712i
$40$	705.300			0.440812
$41$	1516.93	+	1516.93i	0.902396	+	0.902396i	0.995643	−	0.0932471i	$-0.0297247\pi$
$41$	1516.93	+	1516.93i	0.902396	+	0.902396i	−0.0932471	+	0.995643i	$0.529725\pi$
$42$	3707.70			2.10187
$43$			192.875i			0.104313i	0.998639	+	0.0521566i	$0.0166095\pi$
$43$			192.875i			0.104313i	−0.998639	+	0.0521566i	$0.983391\pi$
$44$	−52.2591	−	52.2591i	−0.0269933	−	0.0269933i
$45$	−298.641	−	298.641i	−0.147477	−	0.147477i
$46$	−729.983	+	729.983i	−0.344983	+	0.344983i
$47$	947.423	−	947.423i	0.428892	−	0.428892i	−0.459359	−	0.888251i	$-0.651921\pi$
$47$	947.423	−	947.423i	0.428892	−	0.428892i	0.888251	+	0.459359i	$0.151921\pi$
$48$	−3247.31			−1.40942
$49$		−	3624.63i		−	1.50963i
$50$	−1422.56	+	1422.56i	−0.569026	+	0.569026i
$51$			3473.18i			1.33533i
$52$	541.270	−	472.191i	0.200174	−	0.174627i
$53$	−664.279			−0.236482			−0.118241	−	0.992985i	$-0.537726\pi$
$53$	−664.279			−0.236482			−0.118241	+	0.992985i	$0.537726\pi$
$54$	−1666.37	−	1666.37i	−0.571458	−	0.571458i
$55$	231.950			0.0766776
$56$			4104.36i			1.30879i
$57$	−4649.72	−	4649.72i	−1.43112	−	1.43112i
$58$	1409.99	+	1409.99i	0.419140	+	0.419140i
$59$	3925.10	−	3925.10i	1.12758	−	1.12758i	0.137009	−	0.990570i	$-0.456251\pi$
$59$	3925.10	−	3925.10i	1.12758	−	1.12758i	0.990570	−	0.137009i	$-0.0437489\pi$
$60$	−425.515	+	425.515i	−0.118199	+	0.118199i
$61$	379.956			0.102111			0.0510556	−	0.998696i	$-0.483741\pi$
$61$	379.956			0.102111			0.0510556	+	0.998696i	$0.483741\pi$
$62$			2704.07i			0.703451i
$63$	1737.89	−	1737.89i	0.437865	−	0.437865i
$64$		−	2506.66i		−	0.611977i
$65$	−153.302	+	2249.10i	−0.0362844	+	0.532332i
$66$	−830.554			−0.190669
$67$	−185.119	−	185.119i	−0.0412384	−	0.0412384i	0.686187	−	0.727425i	$-0.259283\pi$
$67$	−185.119	−	185.119i	−0.0412384	−	0.0412384i	−0.727425	+	0.686187i	$0.759283\pi$
$68$	1390.76			0.300770
$69$			2435.01i			0.511450i
$70$	3294.81	+	3294.81i	0.672410	+	0.672410i
$71$	−537.219	−	537.219i	−0.106570	−	0.106570i	0.651811	−	0.758381i	$-0.274009\pi$
$71$	−537.219	−	537.219i	−0.106570	−	0.106570i	−0.758381	+	0.651811i	$0.774009\pi$
$72$	−1183.76	+	1183.76i	−0.228349	+	0.228349i
$73$	992.844	−	992.844i	0.186310	−	0.186310i	−0.607789	−	0.794099i	$-0.707943\pi$
$73$	992.844	−	992.844i	0.186310	−	0.186310i	0.794099	+	0.607789i	$0.207943\pi$
$74$	4874.85			0.890221
$75$			4745.26i			0.843602i
$76$	−1861.88	+	1861.88i	−0.322347	+	0.322347i
$77$			1349.79i			0.227659i
$78$	548.934	−	8053.48i	0.0902259	−	1.32371i
$79$	−1497.03			−0.239871			−0.119935	−	0.992782i	$-0.538269\pi$
$79$	−1497.03			−0.239871			−0.119935	+	0.992782i	$0.538269\pi$
$80$	−2885.69	−	2885.69i	−0.450889	−	0.450889i
$81$	−8123.14			−1.23809
$82$		−	9653.72i		−	1.43571i
$83$	6730.18	+	6730.18i	0.976946	+	0.976946i	0.999740	−	0.0227945i	$-0.00725633\pi$
$83$	6730.18	+	6730.18i	0.976946	+	0.976946i	−0.0227945	+	0.999740i	$0.507256\pi$
$84$	−2476.21	−	2476.21i	−0.350936	−	0.350936i
$85$	−3086.41	+	3086.41i	−0.427185	+	0.427185i
$86$	613.728	−	613.728i	0.0829810	−	0.0829810i
$87$	4703.31			0.621392
$88$		−	919.410i		−	0.118725i
$89$	2523.93	−	2523.93i	0.318637	−	0.318637i	−0.529606	−	0.848244i	$-0.677660\pi$
$89$	2523.93	−	2523.93i	0.318637	−	0.318637i	0.848244	+	0.529606i	$0.177660\pi$
$90$			1900.55i			0.234636i
$91$	−13088.2	−	892.110i	−1.58052	−	0.107730i
$92$	975.046			0.115199
$93$	4509.99	+	4509.99i	0.521447	+	0.521447i
$94$	−6029.40			−0.682367
$95$		−	8263.86i		−	0.915663i
$96$	3983.45	+	3983.45i	0.432232	+	0.432232i
$97$	3477.41	+	3477.41i	0.369583	+	0.369583i	0.867325	−	0.497742i	$-0.165837\pi$
$97$	3477.41	+	3477.41i	0.369583	+	0.369583i	−0.497742	+	0.867325i	$0.665837\pi$
$98$	−11533.6	+	11533.6i	−1.20091	+	1.20091i
$99$	−389.300	+	389.300i	−0.0397205	+	0.0397205i
$100$	1900.13			0.190013
$101$		−	10905.0i		−	1.06901i	−0.845164	−	0.534507i	$-0.820497\pi$
$101$		−	10905.0i		−	1.06901i	0.845164	−	0.534507i	$-0.179503\pi$
$102$	11051.7	−	11051.7i	1.06225	−	1.06225i
$103$			14124.9i			1.33140i	0.746218	+	0.665702i	$0.231868\pi$
$103$			14124.9i			1.33140i	−0.746218	+	0.665702i	$0.768132\pi$
$104$	8915.07	+	607.661i	0.824248	+	0.0561817i
$105$	10990.5			0.996874
$106$	2113.73	+	2113.73i	0.188122	+	0.188122i
$107$	−17930.4			−1.56611			−0.783055	−	0.621952i	$-0.786340\pi$
$107$	−17930.4			−1.56611			−0.783055	+	0.621952i	$0.786340\pi$
$108$			2225.79i			0.190826i
$109$	2282.57	+	2282.57i	0.192119	+	0.192119i	0.796611	−	0.604492i	$-0.206624\pi$
$109$	2282.57	+	2282.57i	0.192119	+	0.192119i	−0.604492	+	0.796611i	$0.706624\pi$
$110$	−738.064	−	738.064i	−0.0609970	−	0.0609970i
$111$	8130.55	−	8130.55i	0.659893	−	0.659893i
$112$	16792.7	−	16792.7i	1.33871	−	1.33871i
$113$	15915.9			1.24644			0.623222	−	0.782045i	$-0.285823\pi$
$113$	15915.9			1.24644			0.623222	+	0.782045i	$0.285823\pi$
$114$			29590.8i			2.27692i
$115$	−2163.85	+	2163.85i	−0.163618	+	0.163618i
$116$		−	1883.34i		−	0.139963i
$117$	−3517.55	−	4032.15i	−0.256962	−	0.294554i
$118$	−24979.3			−1.79398
$119$	−17960.8	−	17960.8i	−1.26833	−	1.26833i
$120$	−7486.21			−0.519875
$121$			14338.6i			0.979348i
$122$	−1209.02	−	1209.02i	−0.0812294	−	0.0812294i
$123$	−16101.0	−	16101.0i	−1.06425	−	1.06425i
$124$	1805.92	−	1805.92i	0.117451	−	0.117451i
$125$	−10112.0	+	10112.0i	−0.647166	+	0.647166i
$126$	−11059.9			−0.696643
$127$		−	11561.3i		−	0.716805i	−0.933567	−	0.358402i	$-0.883322\pi$
$127$		−	11561.3i		−	0.716805i	0.933567	−	0.358402i	$-0.116678\pi$
$128$	−13980.9	+	13980.9i	−0.853325	+	0.853325i
$129$		−	2047.22i		−	0.123023i
$130$	7644.45	−	6668.84i	0.452334	−	0.394606i
$131$	17110.0			0.997030			0.498515	−	0.866881i	$-0.333879\pi$
$131$	17110.0			0.997030			0.498515	+	0.866881i	$0.333879\pi$
$132$	554.690	+	554.690i	0.0318348	+	0.0318348i
$133$	48090.0			2.71864
$134$			1178.10i			0.0656103i
$135$	−4939.54	−	4939.54i	−0.271031	−	0.271031i
$136$	12234.0	+	12234.0i	0.661441	+	0.661441i
$137$	2077.32	−	2077.32i	0.110678	−	0.110678i	−0.649599	−	0.760277i	$-0.725063\pi$
$137$	2077.32	−	2077.32i	0.110678	−	0.110678i	0.760277	+	0.649599i	$0.225063\pi$
$138$	7748.20	−	7748.20i	0.406858	−	0.406858i
$139$	−4610.11			−0.238606			−0.119303	−	0.992858i	$-0.538066\pi$
$139$	−4610.11			−0.238606			−0.119303	+	0.992858i	$0.538066\pi$
$140$		−	4400.91i		−	0.224536i
$141$	−10056.2	+	10056.2i	−0.505818	+	0.505818i
$142$			3418.86i			0.169553i
$143$	2931.87	+	199.840i	0.143375	+	0.00977260i
$144$	9686.57			0.467138
$145$	4179.55	+	4179.55i	0.198790	+	0.198790i
$146$	−6318.45			−0.296418
$147$			38472.6i			1.78040i
$148$	−3255.69	−	3255.69i	−0.148635	−	0.148635i
$149$	−8173.60	−	8173.60i	−0.368163	−	0.368163i	0.498644	−	0.866807i	$-0.333832\pi$
$149$	−8173.60	−	8173.60i	−0.368163	−	0.368163i	−0.866807	+	0.498644i	$0.833832\pi$
$150$	15099.4	−	15099.4i	0.671085	−	0.671085i
$151$	11911.9	−	11911.9i	0.522430	−	0.522430i	−0.395875	−	0.918305i	$-0.629558\pi$
$151$	11911.9	−	11911.9i	0.522430	−	0.522430i	0.918305	+	0.395875i	$0.129558\pi$
$152$	−32756.6			−1.41779
$153$		−	10360.4i		−	0.442580i
$154$	4295.03	−	4295.03i	0.181103	−	0.181103i
$155$			8015.52i			0.333632i
$156$	−5745.16	+	5011.95i	−0.236077	+	0.205948i
$157$	−20432.2			−0.828924			−0.414462	−	0.910067i	$-0.636030\pi$
$157$	−20432.2			−0.828924			−0.414462	+	0.910067i	$0.636030\pi$
$158$	4763.56	+	4763.56i	0.190817	+	0.190817i
$159$	7050.80			0.278897
$160$			7079.71i			0.276551i
$161$	−12592.1	−	12592.1i	−0.485789	−	0.485789i
$162$	25847.8	+	25847.8i	0.984903	+	0.984903i
$163$	−17004.0	+	17004.0i	−0.639994	+	0.639994i	−0.950554	−	0.310559i	$-0.899484\pi$
$163$	−17004.0	+	17004.0i	−0.639994	+	0.639994i	0.310559	+	0.950554i	$0.399484\pi$
$164$	−6447.29	+	6447.29i	−0.239712	+	0.239712i
$165$	−2461.97			−0.0904304
$166$		−	42830.8i		−	1.55432i
$167$	10106.2	−	10106.2i	0.362374	−	0.362374i	−0.502313	−	0.864686i	$-0.667517\pi$
$167$	10106.2	−	10106.2i	0.362374	−	0.362374i	0.864686	+	0.502313i	$0.167517\pi$
$168$		−	43564.6i		−	1.54353i
$169$	−3875.50	+	28296.8i	−0.135692	+	0.990751i
$170$	19641.9			0.679651
$171$	13869.9	+	13869.9i	0.474331	+	0.474331i
$172$	−819.762			−0.0277097
$173$		−	54054.7i		−	1.80610i	−0.429536	−	0.903050i	$-0.641323\pi$
$173$		−	54054.7i		−	1.80610i	0.429536	−	0.903050i	$-0.358677\pi$
$174$	−14965.9	−	14965.9i	−0.494317	−	0.494317i
$175$	−24539.1	−	24539.1i	−0.801276	−	0.801276i
$176$	−3761.71	+	3761.71i	−0.121439	+	0.121439i
$177$	−41661.9	+	41661.9i	−1.32982	+	1.32982i
$178$	−16062.3			−0.506952
$179$			42924.9i			1.33969i	0.742503	+	0.669843i	$0.233639\pi$
$179$			42924.9i			1.33969i	−0.742503	+	0.669843i	$0.766361\pi$
$180$	1269.29	−	1269.29i	0.0391756	−	0.0391756i
$181$		−	6939.25i		−	0.211814i	−0.994376	−	0.105907i	$-0.966225\pi$
$181$		−	6939.25i		−	0.211814i	0.994376	−	0.105907i	$-0.0337746\pi$
$182$	38808.1	+	44485.5i	1.17160	+	1.34300i
$183$	−4032.94			−0.120426
$184$	8577.14	+	8577.14i	0.253342	+	0.253342i
$185$	14450.3			0.422214
$186$		−	28701.6i		−	0.829621i
$187$	4023.36	+	4023.36i	0.115055	+	0.115055i
$188$	4026.76	+	4026.76i	0.113931	+	0.113931i
$189$	28744.7	−	28744.7i	0.804701	−	0.804701i
$190$	−26295.6	+	26295.6i	−0.728410	+	0.728410i
$191$	59008.2			1.61751			0.808753	−	0.588149i	$-0.200143\pi$
$191$	59008.2			1.61751			0.808753	+	0.588149i	$0.200143\pi$
$192$			26606.2i			0.721740i
$193$	−22078.7	+	22078.7i	−0.592734	+	0.592734i	−0.938369	−	0.345635i	$-0.887663\pi$
$193$	−22078.7	+	22078.7i	−0.592734	+	0.592734i	0.345635	+	0.938369i	$0.387663\pi$
$194$		−	22130.2i		−	0.588007i
$195$	1627.18	−	23872.5i	0.0427923	−	0.627810i
$196$	15405.5			0.401018
$197$	24100.3	+	24100.3i	0.620997	+	0.620997i	0.945786	−	0.324789i	$-0.105293\pi$
$197$	24100.3	+	24100.3i	0.620997	+	0.620997i	−0.324789	+	0.945786i	$0.605293\pi$
$198$	2477.51			0.0631952
$199$		−	41899.4i		−	1.05804i	−0.848610	−	0.529020i	$-0.822560\pi$
$199$		−	41899.4i		−	1.05804i	0.848610	−	0.529020i	$-0.177440\pi$
$200$	16714.8	+	16714.8i	0.417870	+	0.417870i
$201$	1964.90	+	1964.90i	0.0486349	+	0.0486349i
$202$	−34699.7	+	34699.7i	−0.850400	+	0.850400i
$203$	−24322.1	+	24322.1i	−0.590214	+	0.590214i
$204$	−14761.8			−0.354715
$205$		−	28616.0i		−	0.680928i
$206$	44945.3	−	44945.3i	1.05913	−	1.05913i
$207$		−	7263.53i		−	0.169515i
$208$	−33989.2	−	38961.6i	−0.785623	−	0.900555i
$209$	−10772.6			−0.246619
$210$	−34971.9	−	34971.9i	−0.793013	−	0.793013i
$211$	16780.3			0.376907			0.188453	−	0.982082i	$-0.439653\pi$
$211$	16780.3			0.376907			0.188453	+	0.982082i	$0.439653\pi$
$212$		−	2823.33i		−	0.0628189i
$213$	5702.16	+	5702.16i	0.125684	+	0.125684i
$214$	57054.5	+	57054.5i	1.24584	+	1.24584i
$215$	1819.24	−	1819.24i	0.0393562	−	0.0393562i
$216$	−19579.5	+	19579.5i	−0.419656	+	0.419656i
$217$	−46644.9			−0.990568
$218$		−	14526.3i		−	0.305662i
$219$	−10538.3	+	10538.3i	−0.219726	+	0.219726i
$220$			985.839i			0.0203686i
$221$	−41671.7	+	36353.4i	−0.853212	+	0.744322i
$222$	−51742.8			−1.04989
$223$	41892.4	+	41892.4i	0.842413	+	0.842413i	0.989172	−	0.146759i	$-0.0468841\pi$
$223$	41892.4	+	41892.4i	0.842413	+	0.842413i	−0.146759	+	0.989172i	$0.546884\pi$
$224$	−41199.1			−0.821092
$225$		−	14154.9i		−	0.279603i
$226$	−50644.2	−	50644.2i	−0.991546	−	0.991546i
$227$	−5605.99	−	5605.99i	−0.108793	−	0.108793i	0.650615	−	0.759408i	$-0.274511\pi$
$227$	−5605.99	−	5605.99i	−0.108793	−	0.108793i	−0.759408	+	0.650615i	$0.774511\pi$
$228$	19762.4	−	19762.4i	0.380163	−	0.380163i
$229$	27198.3	−	27198.3i	0.518646	−	0.518646i	−0.398516	−	0.917162i	$-0.630475\pi$
$229$	27198.3	−	27198.3i	0.518646	−	0.518646i	0.917162	+	0.398516i	$0.130475\pi$
$230$	13770.7			0.260316
$231$		−	14327.0i		−	0.268491i
$232$	16567.0	−	16567.0i	0.307800	−	0.307800i
$233$		−	43413.6i		−	0.799675i	−0.916586	−	0.399838i	$-0.869067\pi$
$233$		−	43413.6i		−	0.799675i	0.916586	−	0.399838i	$-0.130933\pi$
$234$	−1637.45	+	24023.2i	−0.0299044	+	0.438731i
$235$	−17872.6			−0.323633
$236$	16682.6	+	16682.6i	0.299529	+	0.299529i
$237$	15889.9			0.282894
$238$			114303.i			2.01791i
$239$	32702.2	+	32702.2i	0.572507	+	0.572507i	0.932828	−	0.360321i	$-0.117333\pi$
$239$	32702.2	+	32702.2i	0.572507	+	0.572507i	−0.360321	+	0.932828i	$0.617333\pi$
$240$	30629.3	+	30629.3i	0.531759	+	0.531759i
$241$	57128.3	−	57128.3i	0.983597	−	0.983597i	−0.0162706	−	0.999868i	$-0.505179\pi$
$241$	57128.3	−	57128.3i	0.983597	−	0.983597i	0.999868	+	0.0162706i	$0.00517933\pi$
$242$	45625.5	−	45625.5i	0.779071	−	0.779071i
$243$	43802.1			0.741793
$244$			1614.90i			0.0271247i
$245$	−34188.3	+	34188.3i	−0.569568	+	0.569568i
$246$			102467.i			1.69322i
$247$	7119.85	−	104456.i	0.116702	−	1.71214i
$248$	31772.2			0.516587
$249$	−71435.6	−	71435.6i	−1.15217	−	1.15217i
$250$	64352.5			1.02964
$251$			15211.8i			0.241453i	0.992686	+	0.120727i	$0.0385224\pi$
$251$			15211.8i			0.241453i	−0.992686	+	0.120727i	$0.961478\pi$
$252$	7386.41	+	7386.41i	0.116314	+	0.116314i
$253$	2820.74	+	2820.74i	0.0440678	+	0.0440678i
$254$	−36788.2	+	36788.2i	−0.570218	+	0.570218i
$255$	32759.9	−	32759.9i	0.503804	−	0.503804i
$256$	48867.8			0.745663
$257$			61702.7i			0.934196i	0.884205	+	0.467098i	$0.154701\pi$
$257$			61702.7i			0.934196i	−0.884205	+	0.467098i	$0.845299\pi$
$258$	−6514.24	+	6514.24i	−0.0978644	+	0.0978644i
$259$			84090.7i			1.25357i
$260$	−9559.20	−	651.566i	−0.141408	−	0.00963855i
$261$	−14029.8			−0.205954
$262$	−54444.1	−	54444.1i	−0.793137	−	0.793137i
$263$	−89522.0			−1.29425			−0.647126	−	0.762383i	$-0.724029\pi$
$263$	−89522.0			−1.29425			−0.647126	+	0.762383i	$0.724029\pi$
$264$			9758.82i			0.140020i
$265$	6265.63	+	6265.63i	0.0892221	+	0.0892221i
$266$	−153022.	−	153022.i	−2.16268	−	2.16268i
$267$	−26789.5	+	26789.5i	−0.375788	+	0.375788i
$268$	786.799	−	786.799i	0.0109545	−	0.0109545i
$269$	−86647.3			−1.19743			−0.598716	−	0.800962i	$-0.704322\pi$
$269$	−86647.3			−1.19743			−0.598716	+	0.800962i	$0.704322\pi$
$270$			31435.2i			0.431210i
$271$	−22573.5	+	22573.5i	−0.307370	+	0.307370i	−0.843888	−	0.536519i	$-0.819739\pi$
$271$	−22573.5	+	22573.5i	−0.307370	+	0.307370i	0.536519	+	0.843888i	$0.319739\pi$
$272$		−	100109.i		−	1.35312i
$273$	138922.	+	9469.06i	1.86399	+	0.127052i
$274$	−13220.1			−0.176089
$275$	5496.95	+	5496.95i	0.0726869	+	0.0726869i
$276$	−10349.4			−0.135861
$277$			5548.05i			0.0723071i	0.999346	+	0.0361536i	$0.0115105\pi$
$277$			5548.05i			0.0723071i	−0.999346	+	0.0361536i	$0.988489\pi$
$278$	14669.4	+	14669.4i	0.189811	+	0.189811i
$279$	−13453.1	−	13453.1i	−0.172828	−	0.172828i
$280$	38713.3	−	38713.3i	0.493792	−	0.493792i
$281$	14131.8	−	14131.8i	0.178972	−	0.178972i	−0.611936	−	0.790908i	$-0.709609\pi$
$281$	14131.8	−	14131.8i	0.178972	−	0.178972i	0.790908	+	0.611936i	$0.209609\pi$
$282$	63997.4			0.804756
$283$			28614.5i			0.357283i	0.983914	+	0.178642i	$0.0571703\pi$
$283$			28614.5i			0.357283i	−0.983914	+	0.178642i	$0.942830\pi$
$284$	2283.30	−	2283.30i	0.0283091	−	0.0283091i
$285$			87714.5i			1.07989i
$286$	−8693.32	−	9965.10i	−0.106281	−	0.121829i
$287$	166526.			2.02170
$288$	−11882.5	−	11882.5i	−0.143259	−	0.143259i
$289$	−23551.8			−0.281987
$290$		−	26598.7i		−	0.316274i
$291$	−36910.0	−	36910.0i	−0.435871	−	0.435871i
$292$	4219.81	+	4219.81i	0.0494911	+	0.0494911i
$293$	−106780.	+	106780.i	−1.24381	+	1.24381i	−0.285407	+	0.958406i	$0.592129\pi$
$293$	−106780.	+	106780.i	−1.24381	+	1.24381i	−0.958406	+	0.285407i	$0.907871\pi$
$294$	122420.	−	122420.i	1.41631	−	1.41631i
$295$	−74044.9			−0.850846
$296$		−	57278.4i		−	0.653744i
$297$	−6439.05	+	6439.05i	−0.0729977	+	0.0729977i
$298$			52016.7i			0.585748i
$299$	−29215.6	+	25487.0i	−0.326793	+	0.285086i
$300$	−20168.4			−0.224094
$301$	10586.7	+	10586.7i	0.116850	+	0.116850i
$302$	−75807.5			−0.831186
$303$			115748.i			1.26075i
$304$	134021.	+	134021.i	1.45020	+	1.45020i
$305$	−3583.83	−	3583.83i	−0.0385254	−	0.0385254i
$306$	−32966.6	+	32966.6i	−0.352072	+	0.352072i
$307$	77360.6	−	77360.6i	0.820810	−	0.820810i	−0.165414	−	0.986224i	$-0.552896\pi$
$307$	77360.6	−	77360.6i	0.820810	−	0.820810i	0.986224	+	0.165414i	$0.0528960\pi$
$308$	−5736.91			−0.0604751
$309$		−	149924.i		−	1.57020i
$310$	25505.4	−	25505.4i	0.265404	−	0.265404i
$311$			58325.5i			0.603029i	0.953462	+	0.301514i	$0.0974921\pi$
$311$			58325.5i			0.603029i	−0.953462	+	0.301514i	$0.902508\pi$
$312$	−94626.5	−	6449.85i	−0.972084	−	0.0662584i
$313$	−30231.1			−0.308579			−0.154289	−	0.988026i	$-0.549309\pi$
$313$	−30231.1			−0.308579			−0.154289	+	0.988026i	$0.549309\pi$
$314$	65015.1	+	65015.1i	0.659409	+	0.659409i
$315$	−32784.3			−0.330403
$316$		−	6362.74i		−	0.0637191i
$317$	15042.7	+	15042.7i	0.149695	+	0.149695i	0.777982	−	0.628287i	$-0.216244\pi$
$317$	15042.7	+	15042.7i	0.149695	+	0.149695i	−0.628287	+	0.777982i	$0.716244\pi$
$318$	−22435.6	−	22435.6i	−0.221863	−	0.221863i
$319$	5448.36	−	5448.36i	0.0535407	−	0.0535407i
$320$	−23643.4	+	23643.4i	−0.230892	+	0.230892i
$321$	190317.			1.84700
$322$			80136.3i			0.772889i
$323$	143344.	−	143344.i	1.37396	−	1.37396i
$324$		−	34525.2i		−	0.328886i
$325$	−56934.3	+	49668.1i	−0.539023	+	0.470231i
$326$	108213.			1.01823
$327$	−24227.7	−	24227.7i	−0.226577	−	0.226577i
$328$	−113429.			−1.05433
$329$		−	104006.i		−	0.960879i
$330$	7833.97	+	7833.97i	0.0719373	+	0.0719373i
$331$	226.349	+	226.349i	0.00206597	+	0.00206597i	0.708139	−	0.706073i	$-0.249535\pi$
$331$	226.349	+	226.349i	0.00206597	+	0.00206597i	−0.706073	+	0.708139i	$0.749535\pi$
$332$	−28604.8	+	28604.8i	−0.259515	+	0.259515i
$333$	−24253.1	+	24253.1i	−0.218715	+	0.218715i
$334$	−64316.1			−0.576536
$335$			3492.17i			0.0311176i
$336$	−178242.	+	178242.i	−1.57881	+	1.57881i
$337$		−	177613.i		−	1.56392i	−0.623328	−	0.781961i	$-0.714220\pi$
$337$		−	177613.i		−	1.56392i	0.623328	−	0.781961i	$-0.285780\pi$
$338$	102372.	−	77708.7i	0.896085	−	0.680199i
$339$	−168934.			−1.47001
$340$	−13117.9	−	13117.9i	−0.113477	−	0.113477i
$341$	10448.8			0.0898584
$342$		−	88268.1i		−	0.754660i
$343$	−67164.0	−	67164.0i	−0.570885	−	0.570885i
$344$	−7211.16	−	7211.16i	−0.0609380	−	0.0609380i
$345$	22967.6	−	22967.6i	0.192964	−	0.192964i
$346$	−172002.	+	172002.i	−1.43675	+	1.43675i
$347$	−99228.7			−0.824097			−0.412048	−	0.911162i	$-0.635187\pi$
$347$	−99228.7			−0.824097			−0.412048	+	0.911162i	$0.635187\pi$
$348$			19990.1i			0.165066i
$349$	57043.4	−	57043.4i	0.468333	−	0.468333i	−0.433041	−	0.901374i	$-0.642560\pi$
$349$	57043.4	−	57043.4i	0.468333	−	0.468333i	0.901374	+	0.433041i	$0.142560\pi$
$350$			156167.i			1.27483i
$351$	−58180.6	−	66692.0i	−0.472241	−	0.541327i
$352$	9228.93			0.0744845
$353$	−57673.9	−	57673.9i	−0.462839	−	0.462839i	0.436746	−	0.899585i	$-0.356131\pi$
$353$	−57673.9	−	57673.9i	−0.462839	−	0.462839i	−0.899585	+	0.436746i	$0.856131\pi$
$354$	265136.			2.11574
$355$			10134.3i			0.0804153i
$356$	10727.3	+	10727.3i	0.0846426	+	0.0846426i
$357$	190640.	+	190640.i	1.49581	+	1.49581i
$358$	136587.	−	136587.i	1.06572	−	1.06572i
$359$	−61424.0	+	61424.0i	−0.476595	+	0.476595i	−0.904041	−	0.427446i	$-0.859413\pi$
$359$	−61424.0	+	61424.0i	−0.476595	+	0.476595i	0.427446	+	0.904041i	$0.359413\pi$
$360$	22331.0			0.172307
$361$			253481.i			1.94505i
$362$	−22080.7	+	22080.7i	−0.168498	+	0.168498i
$363$		−	152193.i		−	1.15500i
$364$	3791.67	−	55628.0i	0.0286172	−	0.419847i
$365$	−18729.5			−0.140585
$366$	12832.8	+	12832.8i	0.0957986	+	0.0957986i
$367$	12040.6			0.0893956			0.0446978	−	0.999001i	$-0.485768\pi$
$367$	12040.6			0.0893956			0.0446978	+	0.999001i	$0.485768\pi$
$368$		−	70185.6i		−	0.518266i
$369$	48028.6	+	48028.6i	0.352734	+	0.352734i
$370$	−45980.7	−	45980.7i	−0.335871	−	0.335871i
$371$	−36461.7	+	36461.7i	−0.264904	+	0.264904i
$372$	−19168.5	+	19168.5i	−0.138517	+	0.138517i
$373$	277584.			1.99515			0.997577	−	0.0695664i	$-0.0221616\pi$
$373$	277584.			1.99515			0.997577	+	0.0695664i	$0.0221616\pi$
$374$		−	25604.7i		−	0.183053i
$375$	107331.	−	107331.i	0.763241	−	0.763241i
$376$			70844.1i			0.501104i
$377$	49229.1	+	56431.0i	0.346369	+	0.397041i
$378$	−182931.			−1.28028
$379$	−27733.2	−	27733.2i	−0.193073	−	0.193073i	0.603950	−	0.797022i	$-0.293593\pi$
$379$	−27733.2	−	27733.2i	−0.193073	−	0.193073i	−0.797022	+	0.603950i	$0.793593\pi$
$380$	35123.3			0.243236
$381$			122715.i			0.845369i
$382$	−187764.	−	187764.i	−1.28673	−	1.28673i
$383$	108554.	+	108554.i	0.740026	+	0.740026i	0.972583	−	0.232557i	$-0.0747093\pi$
$383$	108554.	+	108554.i	0.740026	+	0.740026i	−0.232557	+	0.972583i	$0.574709\pi$
$384$	148396.	−	148396.i	1.00638	−	1.00638i
$385$	12731.5	−	12731.5i	0.0858932	−	0.0858932i
$386$	140509.			0.943039
$387$			6106.76i			0.0407745i
$388$	−14779.8	+	14779.8i	−0.0981758	+	0.0981758i
$389$		−	43160.4i		−	0.285224i	−0.989779	−	0.142612i	$-0.954450\pi$
$389$		−	43160.4i		−	0.285224i	0.989779	−	0.142612i	$-0.0455501\pi$
$390$	−81139.9	+	70784.5i	−0.533464	+	0.465382i
$391$	−75067.6			−0.491020
$392$	135517.	+	135517.i	0.881904	+	0.881904i
$393$	−181610.			−1.17586
$394$		−	153374.i		−	0.988006i
$395$	14120.4	+	14120.4i	0.0905007	+	0.0905007i
$396$	−1654.61	−	1654.61i	−0.0105513	−	0.0105513i
$397$	17786.6	−	17786.6i	0.112853	−	0.112853i	−0.648425	−	0.761278i	$-0.724572\pi$
$397$	17786.6	−	17786.6i	0.112853	−	0.112853i	0.761278	+	0.648425i	$0.224572\pi$
$398$	−133324.	+	133324.i	−0.841670	+	0.841670i
$399$	−510438.			−3.20625
$400$		−	136775.i		−	0.854844i
$401$	−65586.8	+	65586.8i	−0.407875	+	0.407875i	−0.880997	−	0.473122i	$-0.843127\pi$
$401$	−65586.8	+	65586.8i	−0.407875	+	0.407875i	0.473122	+	0.880997i	$0.343127\pi$
$402$		−	12504.6i		−	0.0773780i
$403$	−6905.89	+	101317.i	−0.0425216	+	0.623839i
$404$	46348.8			0.283972
$405$	76619.2	+	76619.2i	0.467119	+	0.467119i
$406$	154786.			0.939031
$407$		−	18837.0i		−	0.113716i
$408$	−129855.	−	129855.i	−0.780076	−	0.780076i
$409$	119608.	+	119608.i	0.715010	+	0.715010i	0.967579	−	0.252569i	$-0.0812753\pi$
$409$	119608.	+	119608.i	0.715010	+	0.715010i	−0.252569	+	0.967579i	$0.581275\pi$
$410$	−91056.1	+	91056.1i	−0.541678	+	0.541678i
$411$	−22049.1	+	22049.1i	−0.130529	+	0.130529i
$412$	−60033.9			−0.353673
$413$		−	430891.i		−	2.52620i
$414$	−23112.5	+	23112.5i	−0.134849	+	0.134849i
$415$		−	126961.i		−	0.737182i
$416$	−6099.63	+	89488.4i	−0.0352466	+	0.517107i
$417$	48932.8			0.281402
$418$	34278.2	+	34278.2i	0.196185	+	0.196185i
$419$	191751.			1.09222			0.546108	−	0.837715i	$-0.316109\pi$
$419$	191751.			1.09222			0.546108	+	0.837715i	$0.316109\pi$
$420$			46712.3i			0.264809i
$421$	−91033.0	−	91033.0i	−0.513611	−	0.513611i	0.402020	−	0.915631i	$-0.368308\pi$
$421$	−91033.0	−	91033.0i	−0.513611	−	0.513611i	−0.915631	+	0.402020i	$0.868308\pi$
$422$	−53394.8	−	53394.8i	−0.299829	−	0.299829i
$423$	29997.1	−	29997.1i	0.167648	−	0.167648i
$424$	24835.9	−	24835.9i	0.138149	−	0.138149i
$425$	−146289.			−0.809904
$426$		−	36288.5i		−	0.199963i
$427$	20855.4	−	20855.4i	0.114384	−	0.114384i
$428$		−	76208.3i		−	0.416020i
$429$	−31119.5	−	2121.14i	−0.169090	−	0.0115254i
$430$	−11577.6			−0.0626157
$431$	79266.9	+	79266.9i	0.426714	+	0.426714i	0.887508	−	0.460793i	$-0.152435\pi$
$431$	79266.9	+	79266.9i	0.426714	+	0.426714i	−0.460793	+	0.887508i	$0.652435\pi$
$432$	160216.			0.858499
$433$			286146.i			1.52620i	0.646281	+	0.763100i	$0.276324\pi$
$433$			286146.i			1.52620i	−0.646281	+	0.763100i	$0.723676\pi$
$434$	148424.	+	148424.i	0.787996	+	0.787996i
$435$	−44362.7	−	44362.7i	−0.234444	−	0.234444i
$436$	−9701.44	+	9701.44i	−0.0510344	+	0.0510344i
$437$	100497.	−	100497.i	0.526246	−	0.526246i
$438$	67065.5			0.349583
$439$			340895.i			1.76885i	0.466682	+	0.884425i	$0.345449\pi$
$439$			340895.i			1.76885i	−0.466682	+	0.884425i	$0.654551\pi$
$440$	−8672.08	+	8672.08i	−0.0447938	+	0.0447938i
$441$		−	114762.i		−	0.590094i
$442$	248276.	+	16922.8i	1.27084	+	0.0866218i
$443$	330900.			1.68612			0.843060	−	0.537819i	$-0.180752\pi$
$443$	330900.			1.68612			0.843060	+	0.537819i	$0.180752\pi$
$444$	34556.7	+	34556.7i	0.175294	+	0.175294i
$445$	−47612.5			−0.240437
$446$		−	266603.i		−	1.34028i
$447$	86756.4	+	86756.4i	0.434197	+	0.434197i
$448$	−137588.	−	137588.i	−0.685528	−	0.685528i
$449$	−193937.	+	193937.i	−0.961986	+	0.961986i	−0.999303	−	0.0373176i	$-0.988119\pi$
$449$	−193937.	+	193937.i	−0.961986	+	0.961986i	0.0373176	+	0.999303i	$0.488119\pi$
$450$	−45040.9	+	45040.9i	−0.222424	+	0.222424i
$451$	−37303.1			−0.183397
$452$			67646.0i			0.331105i
$453$	−126436.	+	126436.i	−0.616132	+	0.616132i
$454$			35676.5i			0.173089i
$455$	115037.	+	131866.i	0.555666	+	0.636956i
$456$	347685.			1.67208
$457$	−267925.	−	267925.i	−1.28286	−	1.28286i	−0.939031	−	0.343833i	$-0.888275\pi$
$457$	−267925.	−	267925.i	−1.28286	−	1.28286i	−0.343833	−	0.939031i	$-0.611725\pi$
$458$	−173090.			−0.825165
$459$		−	171361.i		−	0.813366i
$460$	−9196.85	−	9196.85i	−0.0434634	−	0.0434634i
$461$	−209234.	−	209234.i	−0.984532	−	0.984532i	0.0153503	−	0.999882i	$-0.495114\pi$
$461$	−209234.	−	209234.i	−0.984532	−	0.984532i	−0.999882	+	0.0153503i	$0.995114\pi$
$462$	−45588.4	+	45588.4i	−0.213585	+	0.213585i
$463$	−190788.	+	190788.i	−0.890000	+	0.890000i	−0.994522	−	0.104523i	$-0.966668\pi$
$463$	−190788.	+	190788.i	−0.890000	+	0.890000i	0.104523	+	0.994522i	$0.466668\pi$
$464$	−135566.			−0.629673
$465$		−	85078.5i		−	0.393472i
$466$	−138142.	+	138142.i	−0.636141	+	0.636141i
$467$		−	60121.0i		−	0.275672i	−0.990455	−	0.137836i	$-0.955985\pi$
$467$		−	60121.0i		−	0.275672i	0.990455	−	0.137836i	$-0.0440147\pi$
$468$	17137.6	−	14950.4i	0.0782451	−	0.0682592i
$469$	−20322.1			−0.0923894
$470$	56870.7	+	56870.7i	0.257450	+	0.257450i
$471$	216872.			0.977599
$472$			293501.i			1.31743i
$473$	−2371.51	−	2371.51i	−0.0105999	−	0.0105999i
$474$	−50561.5	−	50561.5i	−0.225042	−	0.225042i
$475$	195844.	−	195844.i	0.868007	−	0.868007i
$476$	76337.5	−	76337.5i	0.336918	−	0.336918i
$477$	−21032.2			−0.0924375
$478$		−	208117.i		−	0.910859i
$479$	148108.	−	148108.i	0.645518	−	0.645518i	−0.306389	−	0.951906i	$-0.599121\pi$
$479$	148108.	−	148108.i	0.645518	−	0.645518i	0.951906	+	0.306389i	$0.0991208\pi$
$480$		−	75145.7i		−	0.326153i
$481$	182653.	+	12449.8i	0.789472	+	0.0538113i
$482$	−363564.			−1.56490
$483$	133656.	+	133656.i	0.572919	+	0.572919i
$484$	−60942.5			−0.260153
$485$		−	65599.4i		−	0.278880i
$486$	−139378.	−	139378.i	−0.590096	−	0.590096i
$487$	3165.79	+	3165.79i	0.0133482	+	0.0133482i	0.713749	−	0.700401i	$-0.246996\pi$
$487$	3165.79	+	3165.79i	0.0133482	+	0.0133482i	−0.700401	+	0.713749i	$0.746996\pi$
$488$	−14205.7	+	14205.7i	−0.0596517	+	0.0596517i
$489$	180484.	−	180484.i	0.754783	−	0.754783i
$490$	217574.			0.906183
$491$			65145.7i			0.270223i	0.990830	+	0.135112i	$0.0431393\pi$
$491$			65145.7i			0.270223i	−0.990830	+	0.135112i	$0.956861\pi$
$492$	68432.9	−	68432.9i	0.282706	−	0.282706i
$493$			144996.i			0.596570i
$494$	−355035.	+	309724.i	−1.45485	+	1.26917i
$495$	7343.94			0.0299722
$496$	−129994.	−	129994.i	−0.528396	−	0.528396i
$497$	−58974.9			−0.238756
$498$			454616.i			1.83310i
$499$	−153058.	−	153058.i	−0.614689	−	0.614689i	0.329476	−	0.944164i	$-0.393128\pi$
$499$	−153058.	−	153058.i	−0.614689	−	0.614689i	−0.944164	+	0.329476i	$0.893128\pi$
$500$	−42978.2	−	42978.2i	−0.171913	−	0.171913i
$501$	−107270.	+	107270.i	−0.427368	+	0.427368i
$502$	48403.9	−	48403.9i	0.192076	−	0.192076i
$503$	19798.3			0.0782513			0.0391257	−	0.999234i	$-0.487543\pi$
$503$	19798.3			0.0782513			0.0391257	+	0.999234i	$0.487543\pi$
$504$			129951.i			0.511587i
$505$	−102858.	+	102858.i	−0.403327	+	0.403327i
$506$		−	17951.2i		−	0.0701119i
$507$	41135.4	−	300349.i	0.160029	−	1.16845i
$508$	49138.3			0.190411
$509$	−202867.	−	202867.i	−0.783025	−	0.783025i	0.197315	−	0.980340i	$-0.436778\pi$
$509$	−202867.	−	202867.i	−0.783025	−	0.783025i	−0.980340	+	0.197315i	$0.936778\pi$
$510$	−208484.			−0.801552
$511$		−	108993.i		−	0.417403i
$512$	68197.0	+	68197.0i	0.260151	+	0.260151i
$513$	229409.	+	229409.i	0.871718	+	0.871718i
$514$	196338.	−	196338.i	0.743153	−	0.743153i
$515$	133229.	−	133229.i	0.502324	−	0.502324i
$516$	8701.14			0.0326796
$517$			23298.3i			0.0871651i
$518$	267576.	−	267576.i	0.997214	−	0.997214i
$519$			573749.i			2.13004i
$520$	−78357.3	−	89820.5i	−0.289783	−	0.332176i
$521$	−331272.			−1.22042			−0.610211	−	0.792239i	$-0.708915\pi$
$521$	−331272.			−1.22042			−0.610211	+	0.792239i	$0.708915\pi$
$522$	44642.7	+	44642.7i	0.163836	+	0.163836i
$523$	−140330.			−0.513035			−0.256517	−	0.966540i	$-0.582575\pi$
$523$	−140330.			−0.513035			−0.256517	+	0.966540i	$0.582575\pi$
$524$			72721.5i			0.264850i
$525$	260463.	+	260463.i	0.944991	+	0.944991i
$526$	284859.	+	284859.i	1.02958	+	1.02958i
$527$	−139036.	+	139036.i	−0.500617	+	0.500617i
$528$	39927.6	−	39927.6i	0.143221	−	0.143221i
$529$	227212.			0.811932
$530$		−	39874.4i		−	0.141952i
$531$	124276.	−	124276.i	0.440754	−	0.440754i
$532$			204394.i			0.722177i
$533$	24654.6	−	361710.i	0.0867846	−	1.27323i
$534$	170488.			0.597878
$535$	169124.	+	169124.i	0.590876	+	0.590876i
$536$	13842.4			0.0481816
$537$		−	455614.i		−	1.57997i
$538$	275712.	+	275712.i	0.952556	+	0.952556i
$539$	44567.0	+	44567.0i	0.153404	+	0.153404i
$540$	20994.2	−	20994.2i	0.0719964	−	0.0719964i
$541$	219246.	−	219246.i	0.749094	−	0.749094i	−0.225215	−	0.974309i	$-0.572309\pi$
$541$	219246.	−	219246.i	0.749094	−	0.749094i	0.974309	+	0.225215i	$0.0723085\pi$
$542$	143658.			0.489025
$543$			73654.8i			0.249805i
$544$	−122804.	+	122804.i	−0.414967	+	0.414967i
$545$		−	43059.4i		−	0.144969i
$546$	−411918.	−	472179.i	−1.38174	−	1.58388i
$547$	−58487.2			−0.195473			−0.0977363	−	0.995212i	$-0.531160\pi$
$547$	−58487.2			−0.195473			−0.0977363	+	0.995212i	$0.531160\pi$
$548$	8829.08	+	8829.08i	0.0294005	+	0.0294005i
$549$	12030.1			0.0399138
$550$		−	34982.6i		−	0.115645i
$551$	−194113.	−	194113.i	−0.639368	−	0.639368i
$552$	−91039.6	−	91039.6i	−0.298781	−	0.298781i
$553$	−82170.9	+	82170.9i	−0.268700	+	0.268700i
$554$	17653.9	−	17653.9i	0.0575203	−	0.0575203i
$555$	−153378.			−0.497941
$556$		−	19594.0i		−	0.0633832i
$557$	−425684.	+	425684.i	−1.37207	+	1.37207i	−0.514706	+	0.857367i	$0.672099\pi$
$557$	−425684.	+	425684.i	−1.37207	+	1.37207i	−0.857367	+	0.514706i	$0.827901\pi$
$558$			85615.5i			0.274969i
$559$	24562.8	−	21428.0i	0.0786057	−	0.0685738i
$560$	−316786.			−1.01016
$561$	−42704.9	−	42704.9i	−0.135691	−	0.135691i
$562$	−89934.7			−0.284744
$563$			206889.i			0.652711i	0.945247	+	0.326355i	$0.105821\pi$
$563$			206889.i			0.652711i	−0.945247	+	0.326355i	$0.894179\pi$
$564$	−42741.0	−	42741.0i	−0.134365	−	0.134365i
$565$	−150122.	−	150122.i	−0.470270	−	0.470270i
$566$	91051.1	−	91051.1i	0.284219	−	0.284219i
$567$	−445872.	+	445872.i	−1.38690	+	1.38690i
$568$	40170.8			0.124513
$569$			323276.i			0.998503i	0.866457	+	0.499252i	$0.166392\pi$
$569$			323276.i			0.998503i	−0.866457	+	0.499252i	$0.833608\pi$
$570$	279107.	−	279107.i	0.859056	−	0.859056i
$571$		−	506321.i		−	1.55294i	−0.630157	−	0.776468i	$-0.717009\pi$
$571$		−	506321.i		−	1.55294i	0.630157	−	0.776468i	$-0.282991\pi$
$572$	−849.365	+	12461.1i	−0.00259598	+	0.0380860i
$573$	−626327.			−1.90762
$574$	−529884.	−	529884.i	−1.60826	−	1.60826i
$575$	−102562.			−0.310205
$576$		−	79365.2i		−	0.239213i
$577$	280725.	+	280725.i	0.843197	+	0.843197i	0.989273	−	0.146076i	$-0.0466645\pi$
$577$	280725.	+	280725.i	0.843197	+	0.843197i	−0.146076	+	0.989273i	$0.546665\pi$
$578$	74941.8	+	74941.8i	0.224320	+	0.224320i
$579$	234349.	−	234349.i	0.699045	−	0.699045i
$580$	−17764.0	+	17764.0i	−0.0528063	+	0.0528063i
$581$	738827.			2.18872
$582$			234895.i			0.693471i
$583$	8167.71	−	8167.71i	0.0240305	−	0.0240305i
$584$			74240.4i			0.217678i
$585$	−4853.79	+	71210.5i	−0.0141830	+	0.208081i
$586$	679549.			1.97891
$587$	275790.	+	275790.i	0.800390	+	0.800390i	0.983156	−	0.182766i	$-0.0585051\pi$
$587$	275790.	+	275790.i	0.800390	+	0.800390i	−0.182766	+	0.983156i	$0.558505\pi$
$588$	−163517.			−0.472944
$589$		−	372268.i		−	1.07306i
$590$	235611.	+	235611.i	0.676848	+	0.676848i
$591$	−255806.	−	255806.i	−0.732378	−	0.732378i
$592$	−234351.	+	234351.i	−0.668688	+	0.668688i
$593$	111455.	−	111455.i	0.316949	−	0.316949i	−0.530645	−	0.847594i	$-0.678050\pi$
$593$	111455.	−	111455.i	0.316949	−	0.316949i	0.847594	+	0.530645i	$0.178050\pi$
$594$	40978.1			0.116139
$595$			338821.i			0.957053i
$596$	34739.6	−	34739.6i	0.0977986	−	0.0977986i
$597$			444730.i			1.24781i
$598$	174064.	+	11864.4i	0.486750	+	0.0331774i
$599$	420853.			1.17294			0.586471	−	0.809970i	$-0.300517\pi$
$599$	420853.			1.17294			0.586471	+	0.809970i	$0.300517\pi$
$600$	−177415.	−	177415.i	−0.492819	−	0.492819i
$601$	−452645.			−1.25317			−0.626583	−	0.779354i	$-0.715547\pi$
$601$	−452645.			−1.25317			−0.626583	+	0.779354i	$0.715547\pi$
$602$		−	67374.0i		−	0.185908i
$603$	−5861.20	−	5861.20i	−0.0161195	−	0.0161195i
$604$	50628.4	+	50628.4i	0.138778	+	0.138778i
$605$	135245.	−	135245.i	0.369497	−	0.369497i
$606$	368310.	−	368310.i	1.00293	−	1.00293i
$607$	162861.			0.442018			0.221009	−	0.975272i	$-0.429065\pi$
$607$	162861.			0.442018			0.221009	+	0.975272i	$0.429065\pi$
$608$		−	328806.i		−	0.889474i
$609$	258161.	−	258161.i	0.696074	−	0.696074i
$610$			22807.5i			0.0612940i
$611$	−225912.	−	15398.4i	−0.605141	−	0.0412471i
$612$	44033.8			0.117567
$613$	273075.	+	273075.i	0.726709	+	0.726709i	0.969963	−	0.243254i	$-0.0782147\pi$
$613$	273075.	+	273075.i	0.726709	+	0.726709i	−0.243254	+	0.969963i	$0.578215\pi$
$614$	−492322.			−1.30591
$615$			303737.i			0.803058i
$616$	−50465.6	−	50465.6i	−0.132995	−	0.132995i
$617$	46986.8	+	46986.8i	0.123426	+	0.123426i	0.766122	−	0.642696i	$-0.222184\pi$
$617$	46986.8	+	46986.8i	0.123426	+	0.123426i	−0.642696	+	0.766122i	$0.722184\pi$
$618$	−477059.	+	477059.i	−1.24909	+	1.24909i
$619$	−1416.97	+	1416.97i	−0.00369812	+	0.00369812i	−0.708953	−	0.705255i	$-0.750832\pi$
$619$	−1416.97	+	1416.97i	−0.00369812	+	0.00369812i	0.705255	+	0.708953i	$0.250832\pi$
$620$	−34067.8			−0.0886258
$621$		−	120139.i		−	0.311531i
$622$	185592.	−	185592.i	0.479709	−	0.479709i
$623$		−	277072.i		−	0.713866i
$624$	360769.	+	413547.i	0.926531	+	1.06208i
$625$	−88659.6			−0.226969
$626$	96195.5	+	96195.5i	0.245474	+	0.245474i
$627$	114342.			0.290852
$628$		−	86841.3i		−	0.220195i
$629$	250652.	+	250652.i	0.633534	+	0.633534i
$630$	104319.	+	104319.i	0.262836	+	0.262836i
$631$	−178788.	+	178788.i	−0.449034	+	0.449034i	−0.895033	−	0.445999i	$-0.852848\pi$
$631$	−178788.	+	178788.i	−0.449034	+	0.449034i	0.445999	+	0.895033i	$0.352848\pi$
$632$	55970.8	−	55970.8i	0.140129	−	0.140129i
$633$	−178109.			−0.444508
$634$		−	95731.5i		−	0.238164i
$635$	−109049.	+	109049.i	−0.270442	+	0.270442i
$636$			29967.5i			0.0740860i
$637$	−461600.	+	402689.i	−1.13759	+	0.992410i
$638$	−34673.3			−0.0851832
$639$	−17009.3	−	17009.3i	−0.0416566	−	0.0416566i
$640$	263742.			0.643901
$641$			144162.i			0.350861i	0.984492	+	0.175431i	$0.0561318\pi$
$641$			144162.i			0.350861i	−0.984492	+	0.175431i	$0.943868\pi$
$642$	−605589.	−	605589.i	−1.46929	−	1.46929i
$643$	−524066.	−	524066.i	−1.26755	−	1.26755i	−0.947351	−	0.320197i	$-0.896251\pi$
$643$	−524066.	−	524066.i	−1.26755	−	1.26755i	−0.320197	−	0.947351i	$-0.603749\pi$
$644$	53519.4	−	53519.4i	0.129045	−	0.129045i
$645$	−19309.8	+	19309.8i	−0.0464151	+	0.0464151i
$646$	−912238.			−2.18597
$647$		−	437650.i		−	1.04549i	−0.852490	−	0.522743i	$-0.824909\pi$
$647$		−	437650.i		−	1.04549i	0.852490	−	0.522743i	$-0.175091\pi$
$648$	303706.	−	303706.i	0.723274	−	0.723274i
$649$			96523.0i			0.229161i
$650$	339209.	+	23120.9i	0.802861	+	0.0547239i
$651$	495099.			1.16823
$652$	−72270.9	−	72270.9i	−0.170008	−	0.170008i
$653$	730912.			1.71411			0.857055	−	0.515224i	$-0.172291\pi$
$653$	730912.			1.71411			0.857055	+	0.515224i	$0.172291\pi$
$654$			154185.i			0.360485i
$655$	−161386.	−	161386.i	−0.376169	−	0.376169i
$656$	464088.	+	464088.i	1.07843	+	1.07843i
$657$	31435.2	−	31435.2i	0.0728258	−	0.0728258i
$658$	−330948.	+	330948.i	−0.764379	+	0.764379i
$659$	−486709.			−1.12072			−0.560362	−	0.828248i	$-0.689338\pi$
$659$	−486709.			−1.12072			−0.560362	+	0.828248i	$0.689338\pi$
$660$		−	10463.9i		−	0.0240219i
$661$	−309199.	+	309199.i	−0.707677	+	0.707677i	−0.966046	−	0.258369i	$-0.916815\pi$
$661$	−309199.	+	309199.i	−0.707677	+	0.707677i	0.258369	+	0.966046i	$0.416815\pi$
$662$		−	1440.49i		−	0.00328695i
$663$	442313.	−	385864.i	1.00624	−	0.877823i
$664$	−503253.			−1.14143
$665$	−453596.	−	453596.i	−1.02571	−	1.02571i
$666$	154346.			0.347975
$667$			101655.i			0.228495i
$668$	42953.8	+	42953.8i	0.0962606	+	0.0962606i
$669$	−444655.	−	444655.i	−0.993507	−	0.993507i
$670$	11112.1	−	11112.1i	0.0247540	−	0.0247540i
$671$	−4671.79	+	4671.79i	−0.0103762	+	0.0103762i
$672$	437297.			0.968361
$673$		−	881739.i		−	1.94675i	−0.229223	−	0.973374i	$-0.573618\pi$
$673$		−	881739.i		−	1.94675i	0.229223	−	0.973374i	$-0.426382\pi$
$674$	−565164.	+	565164.i	−1.24410	+	1.24410i
$675$		−	234123.i		−	0.513850i
$676$	−120268.	−	16471.7i	−0.263182	−	0.0360451i
$677$	758538.			1.65501			0.827504	−	0.561459i	$-0.189760\pi$
$677$	758538.			1.65501			0.827504	+	0.561459i	$0.189760\pi$
$678$	537549.	+	537549.i	1.16939	+	1.16939i
$679$	381744.			0.828004
$680$		−	230788.i		−	0.499109i
$681$	59503.2	+	59503.2i	0.128306	+	0.128306i
$682$	−33248.1	−	33248.1i	−0.0714823	−	0.0714823i
$683$	28598.4	−	28598.4i	0.0613056	−	0.0613056i	−0.675789	−	0.737095i	$-0.736197\pi$
$683$	28598.4	−	28598.4i	0.0613056	−	0.0613056i	0.737095	+	0.675789i	$0.236197\pi$
$684$	−58950.3	+	58950.3i	−0.126001	+	0.126001i
$685$	−39187.5			−0.0835154
$686$			427432.i			0.908277i
$687$	−288689.	+	288689.i	−0.611669	+	0.611669i
$688$			59008.0i			0.124662i
$689$	73800.0	+	84596.5i	0.155460	+	0.178202i
$690$	−146166.			−0.307006
$691$	450386.	+	450386.i	0.943255	+	0.943255i	0.998474	−	0.0552191i	$-0.0175857\pi$
$691$	450386.	+	450386.i	0.943255	+	0.943255i	−0.0552191	+	0.998474i	$0.517586\pi$
$692$	229745.			0.479771
$693$			42736.7i			0.0889886i
$694$	315745.	+	315745.i	0.655569	+	0.655569i
$695$	43483.6	+	43483.6i	0.0900235	+	0.0900235i
$696$	−175846.	+	175846.i	−0.363007	+	0.363007i
$697$	496369.	−	496369.i	1.02174	−	1.02174i
$698$	−363024.			−0.745117
$699$			460801.i			0.943103i
$700$	104297.	−	104297.i	0.212850	−	0.212850i
$701$			186839.i			0.380217i	0.981763	+	0.190109i	$0.0608840\pi$
$701$			186839.i			0.380217i	−0.981763	+	0.190109i	$0.939116\pi$
$702$	−27083.5	+	397344.i	−0.0549579	+	0.806293i
$703$	−671120.			−1.35797
$704$	30820.9	+	30820.9i	0.0621870	+	0.0621870i
$705$	189704.			0.381679
$706$			367036.i			0.736376i
$707$	−598566.	−	598566.i	−1.19749	−	1.19749i
$708$	−177073.	−	177073.i	−0.353252	−	0.353252i
$709$	514880.	−	514880.i	1.02427	−	1.02427i	0.0245696	−	0.999698i	$-0.492178\pi$
$709$	514880.	−	514880.i	1.02427	−	1.02427i	0.999698	−	0.0245696i	$-0.00782152\pi$
$710$	32247.4	−	32247.4i	0.0639703	−	0.0639703i
$711$	−47398.7			−0.0937621
$712$			188728.i			0.372285i
$713$	−97476.6	+	97476.6i	−0.191744	+	0.191744i
$714$		−	1.21323e6i		−	2.37984i
$715$	−25769.1	−	29539.0i	−0.0504067	−	0.0577808i
$716$	−182441.			−0.355873
$717$	−347108.	−	347108.i	−0.675191	−	0.675191i
$718$	390902.			0.758262
$719$			418590.i			0.809714i	0.914380	+	0.404857i	$0.132679\pi$
$719$			418590.i			0.809714i	−0.914380	+	0.404857i	$0.867321\pi$
$720$	−91365.9	−	91365.9i	−0.176246	−	0.176246i
$721$	775301.	+	775301.i	1.49142	+	1.49142i
$722$	806577.	−	806577.i	1.54729	−	1.54729i
$723$	−606373.	+	606373.i	−1.16001	+	1.16001i
$724$	29493.4			0.0562662
$725$			198101.i			0.376887i
$726$	−484279.	+	484279.i	−0.918804	+	0.918804i
$727$			37672.0i			0.0712770i	0.999365	+	0.0356385i	$0.0113465\pi$
$727$			37672.0i			0.0712770i	−0.999365	+	0.0356385i	$0.988654\pi$
$728$	522694.	−	455986.i	0.986245	−	0.860377i
$729$	193049.			0.363255
$730$	59597.1	+	59597.1i	0.111835	+	0.111835i
$731$	63112.5			0.118108
$732$		−	17140.9i		−	0.0319898i
$733$	−75085.2	−	75085.2i	−0.139748	−	0.139748i	0.633772	−	0.773520i	$-0.281506\pi$
$733$	−75085.2	−	75085.2i	−0.139748	−	0.139748i	−0.773520	+	0.633772i	$0.781506\pi$
$734$	−38313.2	−	38313.2i	−0.0711142	−	0.0711142i
$735$	362883.	−	362883.i	0.671725	−	0.671725i
$736$	−86096.3	+	86096.3i	−0.158938	+	0.158938i
$737$	4552.31			0.00838101
$738$		−	305654.i		−	0.561199i
$739$	585813.	−	585813.i	1.07268	−	1.07268i	0.0755377	−	0.997143i	$-0.475933\pi$
$739$	585813.	−	585813.i	1.07268	−	1.07268i	0.997143	−	0.0755377i	$-0.0240673\pi$
$740$			61416.9i			0.112156i
$741$	−75571.7	+	1.10872e6i	−0.137633	+	2.01923i
$742$	232042.			0.421462
$743$	−516242.	−	516242.i	−0.935138	−	0.935138i	0.0628830	−	0.998021i	$-0.479971\pi$
$743$	−516242.	−	516242.i	−0.935138	−	0.935138i	−0.998021	+	0.0628830i	$0.979971\pi$
$744$	−337237.			−0.609241
$745$			154190.i			0.277808i
$746$	−883271.	−	883271.i	−1.58714	−	1.58714i
$747$	213089.	+	213089.i	0.381874	+	0.381874i
$748$	−17100.2	+	17100.2i	−0.0305632	+	0.0305632i
$749$	−984184.	+	984184.i	−1.75433	+	1.75433i
$750$	−683052.			−1.21432
$751$		−	87646.4i		−	0.155401i	−0.996977	−	0.0777006i	$-0.975242\pi$
$751$		−	87646.4i		−	0.155401i	0.996977	−	0.0777006i	$-0.0247578\pi$
$752$	289854.	−	289854.i	0.512559	−	0.512559i
$753$		−	161461.i		−	0.284760i
$754$	22916.5	−	336210.i	0.0403093	−	0.591382i
$755$	−224712.			−0.394214
$756$	122172.	+	122172.i	0.213760	+	0.213760i
$757$	−22005.4			−0.0384005			−0.0192003	−	0.999816i	$-0.506112\pi$
$757$	−22005.4			−0.0384005			−0.0192003	+	0.999816i	$0.506112\pi$
$758$			176494.i			0.307179i
$759$	−29939.9	−	29939.9i	−0.0519718	−	0.0519718i
$760$	308967.	+	308967.i	0.534915	+	0.534915i
$761$	−320291.	+	320291.i	−0.553064	+	0.553064i	−0.927324	−	0.374260i	$-0.877897\pi$
$761$	−320291.	+	320291.i	−0.553064	+	0.553064i	0.374260	+	0.927324i	$0.377897\pi$
$762$	390478.	−	390478.i	0.672491	−	0.672491i
$763$	250576.			0.430419
$764$			250798.i			0.429673i
$765$	−97721.2	+	97721.2i	−0.166980	+	0.166980i
$766$		−	690835.i		−	1.17738i
$767$	−935936.	−	63794.5i	−1.59095	−	0.108441i
$768$	−518693.			−0.879404
$769$	620676.	+	620676.i	1.04957	+	1.04957i	0.998705	+	0.0508666i	$0.0161983\pi$
$769$	620676.	+	620676.i	1.04957	+	1.04957i	0.0508666	+	0.998705i	$0.483802\pi$
$770$	−81023.4			−0.136656
$771$		−	654927.i		−	1.10175i
$772$	−93839.6	−	93839.6i	−0.157453	−	0.157453i
$773$	−145577.	−	145577.i	−0.243632	−	0.243632i	0.574719	−	0.818351i	$-0.305111\pi$
$773$	−145577.	−	145577.i	−0.243632	−	0.243632i	−0.818351	+	0.574719i	$0.805111\pi$
$774$	19431.7	−	19431.7i	0.0324361	−	0.0324361i
$775$	−189959.	+	189959.i	−0.316269	+	0.316269i
$776$	−260025.			−0.431809
$777$		−	892557.i		−	1.47841i
$778$	−137336.	+	137336.i	−0.226895	+	0.226895i
$779$			1.32903e6i			2.19007i
$780$	101463.	+	6915.87i	0.166771	+	0.0113673i
$781$	13210.9			0.0216585
$782$	238865.	+	238865.i	0.390606	+	0.390606i
$783$	−232053.			−0.378498
$784$		−	1.10892e6i		−	1.80413i
$785$	192721.	+	192721.i	0.312744	+	0.312744i
$786$	577882.	+	577882.i	0.935393	+	0.935393i
$787$	−576271.	+	576271.i	−0.930416	+	0.930416i	−0.997732	−	0.0673158i	$-0.978557\pi$
$787$	−576271.	+	576271.i	−0.930416	+	0.930416i	0.0673158	+	0.997732i	$0.478557\pi$
$788$	−102432.	+	102432.i	−0.164961	+	0.164961i
$789$	950207.			1.52639
$790$		−	89862.0i		−	0.143986i
$791$	873607.	−	873607.i	1.39625	−	1.39625i
$792$		−	29110.1i		−	0.0464081i
$793$	−42212.3	−	48387.7i	−0.0671263	−	0.0769465i
$794$	−113194.			−0.179549
$795$	−66504.7	−	66504.7i	−0.105225	−	0.105225i
$796$	178082.			0.281057
$797$		−	110238.i		−	0.173546i	−0.996228	−	0.0867728i	$-0.972345\pi$
$797$		−	110238.i		−	0.173546i	0.996228	−	0.0867728i	$-0.0276554\pi$
$798$	1.62421e6	+	1.62421e6i	2.55057	+	2.55057i
$799$	−310016.	−	310016.i	−0.485613	−	0.485613i
$800$	−167781.	+	167781.i	−0.262158	+	0.262158i
$801$	79911.9	−	79911.9i	0.124551	−	0.124551i
$802$	417394.			0.648929
$803$			24415.2i			0.0378643i
$804$	−8351.26	+	8351.26i	−0.0129193	+	0.0129193i
$805$			237544.i			0.366565i
$806$	344365.	−	300416.i	0.530090	−	0.462438i
$807$	919694.			1.41220
$808$	407714.	+	407714.i	0.624500	+	0.624500i
$809$	629068.			0.961171			0.480585	−	0.876948i	$-0.340424\pi$
$809$	629068.			0.961171			0.480585	+	0.876948i	$0.340424\pi$
$810$		−	487605.i		−	0.743186i
$811$	−148443.	−	148443.i	−0.225692	−	0.225692i	0.585198	−	0.810890i	$-0.301017\pi$
$811$	−148443.	−	148443.i	−0.225692	−	0.225692i	−0.810890	+	0.585198i	$0.801017\pi$
$812$	−103375.	−	103375.i	−0.156784	−	0.156784i
$813$	239601.	−	239601.i	0.362499	−	0.362499i
$814$	−59939.2	+	59939.2i	−0.0904612	+	0.0904612i
$815$	320771.			0.482926
$816$			1.06258e6i			1.59582i
$817$	−84491.8	+	84491.8i	−0.126582	+	0.126582i
$818$		−	761183.i		−	1.13758i
$819$	−414397.	−	28245.8i	−0.617801	−	0.0421100i
$820$	121625.			0.180881
$821$	−758940.	−	758940.i	−1.12596	−	1.12596i	−0.990828	−	0.135127i	$-0.956856\pi$
$821$	−758940.	−	758940.i	−1.12596	−	1.12596i	−0.135127	−	0.990828i	$-0.543144\pi$
$822$	140321.			0.207672
$823$		−	166698.i		−	0.246110i	−0.992400	−	0.123055i	$-0.960731\pi$
$823$		−	166698.i		−	0.246110i	0.992400	−	0.123055i	$-0.0392692\pi$
$824$	−528097.	−	528097.i	−0.777784	−	0.777784i
$825$	−58345.8	−	58345.8i	−0.0857239	−	0.0857239i
$826$	−1.37109e6	+	1.37109e6i	−2.00959	+	2.00959i
$827$	−138220.	+	138220.i	−0.202096	+	0.202096i	−0.800898	−	0.598801i	$-0.795644\pi$
$827$	−138220.	+	138220.i	−0.202096	+	0.202096i	0.598801	+	0.800898i	$0.295644\pi$
$828$	30871.7			0.0450297
$829$		−	543425.i		−	0.790735i	−0.918523	−	0.395367i	$-0.870617\pi$
$829$		−	543425.i		−	0.790735i	0.918523	−	0.395367i	$-0.129383\pi$
$830$	−403990.	+	403990.i	−0.586428	+	0.586428i
$831$		−	58888.3i		−	0.0852760i
$832$	−319225.	+	278485.i	−0.461159	+	0.402304i
$833$	−1.18605e6			−1.70928
$834$	−155704.	−	155704.i	−0.223855	−	0.223855i
$835$	−190649.			−0.273439
$836$		−	45785.8i		−	0.0655116i
$837$	−222515.	−	222515.i	−0.317621	−	0.317621i
$838$	−610150.	−	610150.i	−0.868858	−	0.868858i
$839$	606122.	−	606122.i	0.861066	−	0.861066i	−0.130396	−	0.991462i	$-0.541625\pi$
$839$	606122.	−	606122.i	0.861066	−	0.861066i	0.991462	+	0.130396i	$0.0416249\pi$
$840$	−410911.	+	410911.i	−0.582357	+	0.582357i
$841$	−510931.			−0.722387
$842$			579334.i			0.817155i
$843$	−149998.	+	149998.i	−0.211072	+	0.211072i
$844$			71319.9i			0.100121i
$845$	303457.	−	230348.i	0.424995	−	0.322604i
$846$	−190901.			−0.266728
$847$	787035.	+	787035.i	1.09705	+	1.09705i
$848$	−203229.			−0.282614
$849$		−	303720.i		−	0.421365i
$850$	465491.	+	465491.i	0.644278	+	0.644278i
$851$	175729.	+	175729.i	0.242653	+	0.242653i
$852$	−24235.5	+	24235.5i	−0.0333866	+	0.0333866i
$853$	62074.2	−	62074.2i	0.0853126	−	0.0853126i	−0.663163	−	0.748475i	$-0.730786\pi$
$853$	62074.2	−	62074.2i	0.0853126	−	0.0853126i	0.748475	+	0.663163i	$0.230786\pi$
$854$	−132724.			−0.181984
$855$		−	261648.i		−	0.357920i
$856$	670377.	−	670377.i	0.914896	−	0.914896i
$857$		−	1.08636e6i		−	1.47915i	−0.673075	−	0.739575i	$-0.735027\pi$
$857$		−	1.08636e6i		−	1.47915i	0.673075	−	0.739575i	$-0.264973\pi$
$858$	92272.9	+	105772.i	0.125343	+	0.143680i
$859$	605719.			0.820890			0.410445	−	0.911885i	$-0.365373\pi$
$859$	605719.			0.820890			0.410445	+	0.911885i	$0.365373\pi$
$860$	7732.18	+	7732.18i	0.0104545	+	0.0104545i
$861$	−1.76754e6			−2.38431
$862$		−	504454.i		−	0.678902i
$863$	973176.	+	973176.i	1.30668	+	1.30668i	0.923796	+	0.382886i	$0.125070\pi$
$863$	973176.	+	973176.i	1.30668	+	1.30668i	0.382886	+	0.923796i	$0.374930\pi$
$864$	−196537.	−	196537.i	−0.263279	−	0.263279i
$865$	−509857.	+	509857.i	−0.681421	+	0.681421i
$866$	910515.	−	910515.i	1.21409	−	1.21409i
$867$	249984.			0.332563
$868$		−	198251.i		−	0.263134i
$869$	18406.9	−	18406.9i	0.0243749	−	0.0243749i
$870$			282324.i			0.373001i
$871$	−3008.74	+	44141.5i	−0.00396595	+	0.0581849i
$872$	−170680.			−0.224466
$873$	110101.	+	110101.i	0.144465	+	0.144465i
$874$	−639560.			−0.837257
$875$			1.11007e6i			1.44989i
$876$	−44790.0	−	44790.0i	−0.0583678	−	0.0583678i
$877$	−344616.	−	344616.i	−0.448060	−	0.448060i	0.446649	−	0.894709i	$-0.352617\pi$
$877$	−344616.	−	344616.i	−0.448060	−	0.448060i	−0.894709	+	0.446649i	$0.852617\pi$
$878$	1.08473e6	−	1.08473e6i	1.40712	−	1.40712i
$879$	1.13339e6	−	1.13339e6i	1.46690	−	1.46690i
$880$	70962.5			0.0916355
$881$			1.26661e6i			1.63189i	0.578131	+	0.815944i	$0.303782\pi$
$881$			1.26661e6i			1.63189i	−0.578131	+	0.815944i	$0.696218\pi$
$882$	−365173.	+	365173.i	−0.469420	+	0.469420i
$883$			1.09189e6i			1.40042i	0.713939	+	0.700208i	$0.246909\pi$
$883$			1.09189e6i			1.40042i	−0.713939	+	0.700208i	$0.753091\pi$
$884$	−154510.	−	177114.i	−0.197721	−	0.226647i
$885$	785929.			1.00345
$886$	−1.05292e6	−	1.05292e6i	−1.34131	−	1.34131i
$887$	−944100.			−1.19997			−0.599985	−	0.800011i	$-0.704827\pi$
$887$	−944100.			−1.19997			−0.599985	+	0.800011i	$0.704827\pi$
$888$			607966.i			0.770998i
$889$	−634592.	−	634592.i	−0.802954	−	0.802954i
$890$	151503.	+	151503.i	0.191267	+	0.191267i
$891$	99878.8	−	99878.8i	0.125811	−	0.125811i
$892$	−178052.	+	178052.i	−0.223778	+	0.223778i
$893$	830066.			1.04090
$894$		−	552117.i		−	0.690806i
$895$	404877.	−	404877.i	0.505449	−	0.505449i
$896$			1.53480e6i			1.91177i
$897$	310101.	−	270525.i	0.385406	−	0.336219i
$898$	1.23422e6			1.53052
$899$	188280.	+	188280.i	0.232961	+	0.232961i
$900$	60161.5			0.0742735
$901$			217365.i			0.267757i
$902$	118698.	+	118698.i	0.145892	+	0.145892i
$903$	−112370.	−	112370.i	−0.137808	−	0.137808i
$904$	−595058.	+	595058.i	−0.728153	+	0.728153i
$905$	−65452.6	+	65452.6i	−0.0799152	+	0.0799152i
$906$	804638.			0.980266
$907$			187956.i			0.228477i	0.993453	+	0.114238i	$0.0364428\pi$
$907$			187956.i			0.228477i	−0.993453	+	0.114238i	$0.963557\pi$
$908$	23826.7	−	23826.7i	0.0288996	−	0.0288996i
$909$		−	345272.i		−	0.417862i
$910$	53550.4	−	785644.i	0.0646666	−	0.948730i
$911$	−73322.2			−0.0883484			−0.0441742	−	0.999024i	$-0.514066\pi$
$911$	−73322.2			−0.0883484			−0.0441742	+	0.999024i	$0.514066\pi$
$912$	−1.42253e6	−	1.42253e6i	−1.71030	−	1.71030i
$913$	−165503.			−0.198548
$914$			1.70507e6i			2.04104i
$915$	38039.6	+	38039.6i	0.0454353	+	0.0454353i
$916$	115599.	+	115599.i	0.137773	+	0.137773i
$917$	939155.	−	939155.i	1.11686	−	1.11686i
$918$	−545270.	+	545270.i	−0.647033	+	0.647033i
$919$	−1.15961e6			−1.37304			−0.686519	−	0.727112i	$-0.740862\pi$
$919$	−1.15961e6			−1.37304			−0.686519	+	0.727112i	$0.740862\pi$
$920$		−	161803.i		−	0.191166i
$921$	−821122.	+	821122.i	−0.968030	+	0.968030i
$922$			1.33156e6i			1.56639i
$923$	−8731.39	+	128099.i	−0.0102490	+	0.150364i
$924$	60892.9			0.0713218
$925$	342455.	+	342455.i	0.400239	+	0.400239i
$926$	1.21418e6			1.41599
$927$			447218.i			0.520427i
$928$	166298.	+	166298.i	0.193104	+	0.193104i
$929$	687885.	+	687885.i	0.797048	+	0.797048i	0.982629	−	0.185581i	$-0.0594168\pi$
$929$	687885.	+	687885.i	0.797048	+	0.797048i	−0.185581	+	0.982629i	$0.559417\pi$
$930$	−270720.	+	270720.i	−0.313007	+	0.313007i
$931$	1.58782e6	−	1.58782e6i	1.83191	−	1.83191i
$932$	184517.			0.212425
$933$		−	619080.i		−	0.711187i
$934$	−191305.	+	191305.i	−0.219297	+	0.219297i
$935$		−	75898.6i		−	0.0868181i
$936$	282267.	+	19239.6i	0.322187	+	0.0219606i
$937$	−881043.			−1.00350			−0.501751	−	0.865012i	$-0.667311\pi$
$937$	−881043.			−1.00350			−0.501751	+	0.865012i	$0.667311\pi$
$938$	64664.8	+	64664.8i	0.0734958	+	0.0734958i
$939$	320880.			0.363925
$940$		−	75962.7i		−	0.0859696i
$941$	−864102.	−	864102.i	−0.975856	−	0.975856i	0.0238591	−	0.999715i	$-0.492405\pi$
$941$	−864102.	−	864102.i	−0.975856	−	0.975856i	−0.999715	+	0.0238591i	$0.992405\pi$
$942$	−690085.	−	690085.i	−0.777680	−	0.777680i
$943$	347999.	−	347999.i	0.391340	−	0.391340i
$944$	1.20084e6	−	1.20084e6i	1.34754	−	1.34754i
$945$	−542254.			−0.607210
$946$			15092.3i			0.0168645i
$947$	−433523.	+	433523.i	−0.483407	+	0.483407i	−0.906218	−	0.422811i	$-0.861043\pi$
$947$	−433523.	+	433523.i	−0.483407	+	0.483407i	0.422811	+	0.906218i	$0.361043\pi$
$948$			67535.5i			0.0751477i
$949$	−236742.	−	16136.6i	−0.262872	−	0.0179176i
$950$	−1.24635e6			−1.38100
$951$	−159666.	−	159666.i	−0.176544	−	0.176544i
$952$	1.34303e6			1.48187
$953$			566100.i			0.623314i	0.950195	+	0.311657i	$0.100884\pi$
$953$			566100.i			0.623314i	−0.950195	+	0.311657i	$0.899116\pi$
$954$	66924.5	+	66924.5i	0.0735340	+	0.0735340i
$955$	−556579.	−	556579.i	−0.610267	−	0.610267i
$956$	−138992.	+	138992.i	−0.152080	+	0.152080i
$957$	−57830.1	+	57830.1i	−0.0631437	+	0.0631437i
$958$	−942560.			−1.02702
$959$		−	228045.i		−	0.247960i
$960$	250956.	−	250956.i	0.272305	−	0.272305i
$961$		−	562440.i		−	0.609017i
$962$	−541586.	−	620817.i	−0.585217	−	0.670831i
$963$	−567708.			−0.612170
$964$	242808.	+	242808.i	0.261282	+	0.261282i
$965$	416503.			0.447264
$966$		−	850584.i		−	0.911513i
$967$	974852.	+	974852.i	1.04252	+	1.04252i	0.999055	+	0.0434690i	$0.0138410\pi$
$967$	974852.	+	974852.i	1.04252	+	1.04252i	0.0434690	+	0.999055i	$0.486159\pi$
$968$	−536089.	−	536089.i	−0.572119	−	0.572119i
$969$	−1.52148e6	+	1.52148e6i	−1.62039	+	1.62039i
$970$	−208737.	+	208737.i	−0.221849	+	0.221849i
$971$	−381768.			−0.404912			−0.202456	−	0.979291i	$-0.564892\pi$
$971$	−381768.			−0.404912			−0.202456	+	0.979291i	$0.564892\pi$
$972$			186169.i			0.197049i
$973$	−253045.	+	253045.i	−0.267283	+	0.267283i
$974$		−	20147.1i		−	0.0212371i
$975$	604313.	−	527189.i	0.635701	−	0.554571i
$976$	116243.			0.122031
$977$	214163.	+	214163.i	0.224365	+	0.224365i	0.810334	−	0.585969i	$-0.199286\pi$
$977$	214163.	+	214163.i	0.224365	+	0.224365i	−0.585969	+	0.810334i	$0.699286\pi$
$978$	−1.14860e6			−1.20086
$979$			62066.4i			0.0647577i
$980$	−145308.	−	145308.i	−0.151300	−	0.151300i
$981$	72270.1	+	72270.1i	0.0750967	+	0.0750967i
$982$	207293.	−	207293.i	0.214962	−	0.214962i
$983$	−135747.	+	135747.i	−0.140483	+	0.140483i	−0.773851	−	0.633368i	$-0.781672\pi$
$983$	−135747.	+	135747.i	−0.140483	+	0.140483i	0.633368	+	0.773851i	$0.281672\pi$
$984$	1.20396e6			1.24343
$985$		−	454639.i		−	0.468591i
$986$	461376.	−	461376.i	0.474571	−	0.474571i
$987$			1.10395e6i			1.13322i
$988$	443962.	+	30261.0i	0.454812	+	0.0310005i
$989$	44247.5			0.0452372
$990$	−23368.4	−	23368.4i	−0.0238429	−	0.0238429i
$991$	261503.			0.266275			0.133137	−	0.991098i	$-0.457495\pi$
$991$	261503.			0.266275			0.133137	+	0.991098i	$0.457495\pi$
$992$			318925.i			0.324090i
$993$	−2402.52	−	2402.52i	−0.00243652	−	0.00243652i
$994$	187658.	+	187658.i	0.189930	+	0.189930i
$995$	−395205.	+	395205.i	−0.399186	+	0.399186i
$996$	303618.	−	303618.i	0.306061	−	0.306061i
$997$	379173.			0.381459			0.190729	−	0.981643i	$-0.438915\pi$
$997$	379173.			0.381459			0.190729	+	0.981643i	$0.438915\pi$
$998$			974061.i			0.977969i
$999$	−401147.	+	401147.i	−0.401950	+	0.401950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.5.d.a.8.1	yes	6
3.2	odd	2		117.5.j.a.73.3		6
4.3	odd	2		208.5.t.c.177.3		6
13.5	odd	4	inner	13.5.d.a.5.1	✓	6
13.8	odd	4		169.5.d.a.70.3		6
13.12	even	2		169.5.d.a.99.3		6
39.5	even	4		117.5.j.a.109.3		6
52.31	even	4		208.5.t.c.161.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.5.d.a.5.1	✓	6	13.5	odd	4	inner
13.5.d.a.8.1	yes	6	1.1	even	1	trivial
117.5.j.a.73.3		6	3.2	odd	2
117.5.j.a.109.3		6	39.5	even	4
169.5.d.a.70.3		6	13.8	odd	4
169.5.d.a.99.3		6	13.12	even	2
208.5.t.c.161.3		6	52.31	even	4
208.5.t.c.177.3		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.18200 - 3.18200i) q^{2} -10.6142 q^{3} +4.25023i q^{4} +(-9.43223 - 9.43223i) q^{5} +(33.7744 + 33.7744i) q^{6} +(54.8891 - 54.8891i) q^{7} +(-37.3878 + 37.3878i) q^{8} +31.6617 q^{9} +O(q^{10})\)	\(q+(-3.18200 - 3.18200i) q^{2} -10.6142 q^{3} +4.25023i q^{4} +(-9.43223 - 9.43223i) q^{5} +(33.7744 + 33.7744i) q^{6} +(54.8891 - 54.8891i) q^{7} +(-37.3878 + 37.3878i) q^{8} +31.6617 q^{9} +60.0267i q^{10} +(-12.2956 + 12.2956i) q^{11} -45.1129i q^{12} +(-111.098 - 127.351i) q^{13} -349.314 q^{14} +(100.116 + 100.116i) q^{15} +305.939 q^{16} -327.220i q^{17} +(-100.748 - 100.748i) q^{18} +(438.065 + 438.065i) q^{19} +(40.0891 - 40.0891i) q^{20} +(-582.605 + 582.605i) q^{21} +78.2492 q^{22} -229.410i q^{23} +(396.842 - 396.842i) q^{24} -447.066i q^{25} +(-51.7169 + 758.744i) q^{26} +523.687 q^{27} +(233.291 + 233.291i) q^{28} -443.114 q^{29} -637.136i q^{30} +(-424.901 - 424.901i) q^{31} +(-375.294 - 375.294i) q^{32} +(130.508 - 130.508i) q^{33} +(-1041.21 + 1041.21i) q^{34} -1035.45 q^{35} +134.570i q^{36} +(-766.005 + 766.005i) q^{37} -2787.85i q^{38} +(1179.22 + 1351.73i) q^{39} +705.300 q^{40} +(1516.93 + 1516.93i) q^{41} +3707.70 q^{42} +192.875i q^{43} +(-52.2591 - 52.2591i) q^{44} +(-298.641 - 298.641i) q^{45} +(-729.983 + 729.983i) q^{46} +(947.423 - 947.423i) q^{47} -3247.31 q^{48} -3624.63i q^{49} +(-1422.56 + 1422.56i) q^{50} +3473.18i q^{51} +(541.270 - 472.191i) q^{52} -664.279 q^{53} +(-1666.37 - 1666.37i) q^{54} +231.950 q^{55} +4104.36i q^{56} +(-4649.72 - 4649.72i) q^{57} +(1409.99 + 1409.99i) q^{58} +(3925.10 - 3925.10i) q^{59} +(-425.515 + 425.515i) q^{60} +379.956 q^{61} +2704.07i q^{62} +(1737.89 - 1737.89i) q^{63} -2506.66i q^{64} +(-153.302 + 2249.10i) q^{65} -830.554 q^{66} +(-185.119 - 185.119i) q^{67} +1390.76 q^{68} +2435.01i q^{69} +(3294.81 + 3294.81i) q^{70} +(-537.219 - 537.219i) q^{71} +(-1183.76 + 1183.76i) q^{72} +(992.844 - 992.844i) q^{73} +4874.85 q^{74} +4745.26i q^{75} +(-1861.88 + 1861.88i) q^{76} +1349.79i q^{77} +(548.934 - 8053.48i) q^{78} -1497.03 q^{79} +(-2885.69 - 2885.69i) q^{80} -8123.14 q^{81} -9653.72i q^{82} +(6730.18 + 6730.18i) q^{83} +(-2476.21 - 2476.21i) q^{84} +(-3086.41 + 3086.41i) q^{85} +(613.728 - 613.728i) q^{86} +4703.31 q^{87} -919.410i q^{88} +(2523.93 - 2523.93i) q^{89} +1900.55i q^{90} +(-13088.2 - 892.110i) q^{91} +975.046 q^{92} +(4509.99 + 4509.99i) q^{93} -6029.40 q^{94} -8263.86i q^{95} +(3983.45 + 3983.45i) q^{96} +(3477.41 + 3477.41i) q^{97} +(-11533.6 + 11533.6i) q^{98} +(-389.300 + 389.300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} - 14 q^{5} + 32 q^{6} + 48 q^{7} - 96 q^{8} - 58 q^{9} - 32 q^{11} - 244 q^{14} + 404 q^{15} + 1044 q^{16} - 802 q^{18} + 732 q^{19} + 428 q^{20} - 2128 q^{21} - 1632 q^{22} - 24 q^{24} + 910 q^{26} + 236 q^{27} + 1884 q^{28} + 4184 q^{29} - 3468 q^{31} + 2092 q^{32} + 2324 q^{33} - 5304 q^{34} - 4204 q^{35} - 1758 q^{37} + 1196 q^{39} - 708 q^{40} + 4750 q^{41} + 9532 q^{42} - 3956 q^{44} + 830 q^{45} + 516 q^{46} - 6872 q^{47} - 9436 q^{48} - 322 q^{50} + 3900 q^{52} + 2108 q^{53} - 184 q^{54} + 6408 q^{55} - 5800 q^{57} + 6516 q^{58} + 4372 q^{59} + 1324 q^{60} + 5988 q^{61} - 652 q^{63} - 5018 q^{65} - 4592 q^{66} + 72 q^{67} - 10572 q^{68} + 7368 q^{70} - 14672 q^{71} - 7980 q^{72} + 5874 q^{73} + 1544 q^{74} + 3576 q^{76} + 5720 q^{78} + 2616 q^{79} - 12080 q^{80} - 19450 q^{81} + 19264 q^{83} + 6296 q^{84} + 4164 q^{85} + 29376 q^{86} + 35584 q^{87} - 986 q^{89} - 30888 q^{91} + 5304 q^{92} - 9520 q^{93} - 36156 q^{94} + 20720 q^{96} - 23154 q^{97} - 41426 q^{98} + 17492 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 - 14 * q^5 + 32 * q^6 + 48 * q^7 - 96 * q^8 - 58 * q^9 - 32 * q^11 - 244 * q^14 + 404 * q^15 + 1044 * q^16 - 802 * q^18 + 732 * q^19 + 428 * q^20 - 2128 * q^21 - 1632 * q^22 - 24 * q^24 + 910 * q^26 + 236 * q^27 + 1884 * q^28 + 4184 * q^29 - 3468 * q^31 + 2092 * q^32 + 2324 * q^33 - 5304 * q^34 - 4204 * q^35 - 1758 * q^37 + 1196 * q^39 - 708 * q^40 + 4750 * q^41 + 9532 * q^42 - 3956 * q^44 + 830 * q^45 + 516 * q^46 - 6872 * q^47 - 9436 * q^48 - 322 * q^50 + 3900 * q^52 + 2108 * q^53 - 184 * q^54 + 6408 * q^55 - 5800 * q^57 + 6516 * q^58 + 4372 * q^59 + 1324 * q^60 + 5988 * q^61 - 652 * q^63 - 5018 * q^65 - 4592 * q^66 + 72 * q^67 - 10572 * q^68 + 7368 * q^70 - 14672 * q^71 - 7980 * q^72 + 5874 * q^73 + 1544 * q^74 + 3576 * q^76 + 5720 * q^78 + 2616 * q^79 - 12080 * q^80 - 19450 * q^81 + 19264 * q^83 + 6296 * q^84 + 4164 * q^85 + 29376 * q^86 + 35584 * q^87 - 986 * q^89 - 30888 * q^91 + 5304 * q^92 - 9520 * q^93 - 36156 * q^94 + 20720 * q^96 - 23154 * q^97 - 41426 * q^98 + 17492 * q^99

Introduction

L-functions

Modular forms

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