LMFDB - Embedded newform 74.5.d.a.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + \cdots + 446074380544 $ x^14 + 727x^12 + 198453x^10 + 24875201x^8 + 1392846203x^6 + 29089700589x^4 + 220261242916x^2 + 446074380544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.7
Root			$15.1052i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} +16.1052i q^{3} -8.00000i q^{4} +(-17.1794 - 17.1794i) q^{5} +(-32.2104 - 32.2104i) q^{6} -18.7264 q^{7} +(16.0000 + 16.0000i) q^{8} -178.377 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} +16.1052i q^{3} -8.00000i q^{4} +(-17.1794 - 17.1794i) q^{5} +(-32.2104 - 32.2104i) q^{6} -18.7264 q^{7} +(16.0000 + 16.0000i) q^{8} -178.377 q^{9} +68.7178 q^{10} -90.7271i q^{11} +128.842 q^{12} +(49.3596 + 49.3596i) q^{13} +(37.4528 - 37.4528i) q^{14} +(276.678 - 276.678i) q^{15} -64.0000 q^{16} +(208.621 + 208.621i) q^{17} +(356.755 - 356.755i) q^{18} +(-166.028 - 166.028i) q^{19} +(-137.436 + 137.436i) q^{20} -301.592i q^{21} +(181.454 + 181.454i) q^{22} +(-686.354 - 686.354i) q^{23} +(-257.683 + 257.683i) q^{24} -34.7332i q^{25} -197.438 q^{26} -1568.28i q^{27} +149.811i q^{28} +(0.649856 - 0.649856i) q^{29} +1106.71i q^{30} +(-1085.34 + 1085.34i) q^{31} +(128.000 - 128.000i) q^{32} +1461.18 q^{33} -834.484 q^{34} +(321.709 + 321.709i) q^{35} +1427.02i q^{36} +(203.465 + 1353.80i) q^{37} +664.111 q^{38} +(-794.945 + 794.945i) q^{39} -549.742i q^{40} -630.898i q^{41} +(603.184 + 603.184i) q^{42} +(-2018.85 - 2018.85i) q^{43} -725.817 q^{44} +(3064.43 + 3064.43i) q^{45} +2745.41 q^{46} +2159.18 q^{47} -1030.73i q^{48} -2050.32 q^{49} +(69.4665 + 69.4665i) q^{50} +(-3359.88 + 3359.88i) q^{51} +(394.876 - 394.876i) q^{52} -3422.88 q^{53} +(3136.57 + 3136.57i) q^{54} +(-1558.64 + 1558.64i) q^{55} +(-299.622 - 299.622i) q^{56} +(2673.91 - 2673.91i) q^{57} +2.59942i q^{58} +(-2151.08 - 2151.08i) q^{59} +(-2213.43 - 2213.43i) q^{60} +(-4324.19 + 4324.19i) q^{61} -4341.38i q^{62} +3340.36 q^{63} +512.000i q^{64} -1695.94i q^{65} +(-2922.36 + 2922.36i) q^{66} -3386.60i q^{67} +(1668.97 - 1668.97i) q^{68} +(11053.9 - 11053.9i) q^{69} -1286.84 q^{70} -2134.91 q^{71} +(-2854.04 - 2854.04i) q^{72} +9332.10i q^{73} +(-3114.52 - 2300.66i) q^{74} +559.386 q^{75} +(-1328.22 + 1328.22i) q^{76} +1698.99i q^{77} -3179.78i q^{78} +(1614.17 + 1614.17i) q^{79} +(1099.48 + 1099.48i) q^{80} +10808.9 q^{81} +(1261.80 + 1261.80i) q^{82} +8502.87 q^{83} -2412.74 q^{84} -7167.99i q^{85} +8075.38 q^{86} +(10.4661 + 10.4661i) q^{87} +(1451.63 - 1451.63i) q^{88} +(6123.51 - 6123.51i) q^{89} -12257.7 q^{90} +(-924.326 - 924.326i) q^{91} +(-5490.83 + 5490.83i) q^{92} +(-17479.7 - 17479.7i) q^{93} +(-4318.36 + 4318.36i) q^{94} +5704.53i q^{95} +(2061.47 + 2061.47i) q^{96} +(-4623.75 - 4623.75i) q^{97} +(4100.65 - 4100.65i) q^{98} +16183.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$			16.1052i			1.78947i	0.446601	+	0.894733i	$0.352634\pi$
$3$			16.1052i			1.78947i	−0.446601	+	0.894733i	$0.647366\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−17.1794	−	17.1794i	−0.687178	−	0.687178i	0.274429	−	0.961607i	$-0.411511\pi$
$5$	−17.1794	−	17.1794i	−0.687178	−	0.687178i	−0.961607	+	0.274429i	$0.911511\pi$
$6$	−32.2104	−	32.2104i	−0.894733	−	0.894733i
$7$	−18.7264			−0.382171			−0.191086	−	0.981573i	$-0.561201\pi$
$7$	−18.7264			−0.382171			−0.191086	+	0.981573i	$0.561201\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	−178.377			−2.20219
$10$	68.7178			0.687178
$11$		−	90.7271i		−	0.749811i	−0.927063	−	0.374905i	$-0.877675\pi$
$11$		−	90.7271i		−	0.749811i	0.927063	−	0.374905i	$-0.122325\pi$
$12$	128.842			0.894733
$13$	49.3596	+	49.3596i	0.292068	+	0.292068i	0.837897	−	0.545829i	$-0.183785\pi$
$13$	49.3596	+	49.3596i	0.292068	+	0.292068i	−0.545829	+	0.837897i	$0.683785\pi$
$14$	37.4528	−	37.4528i	0.191086	−	0.191086i
$15$	276.678	−	276.678i	1.22968	−	1.22968i
$16$	−64.0000			−0.250000
$17$	208.621	+	208.621i	0.721872	+	0.721872i	0.968986	−	0.247114i	$-0.0794824\pi$
$17$	208.621	+	208.621i	0.721872	+	0.721872i	−0.247114	+	0.968986i	$0.579482\pi$
$18$	356.755	−	356.755i	1.10110	−	1.10110i
$19$	−166.028	−	166.028i	−0.459911	−	0.459911i	0.438715	−	0.898626i	$-0.355434\pi$
$19$	−166.028	−	166.028i	−0.459911	−	0.459911i	−0.898626	+	0.438715i	$0.855434\pi$
$20$	−137.436	+	137.436i	−0.343589	+	0.343589i
$21$		−	301.592i		−	0.683882i
$22$	181.454	+	181.454i	0.374905	+	0.374905i
$23$	−686.354	−	686.354i	−1.29745	−	1.29745i	−0.930068	−	0.367386i	$-0.880253\pi$
$23$	−686.354	−	686.354i	−1.29745	−	1.29745i	−0.367386	−	0.930068i	$-0.619747\pi$
$24$	−257.683	+	257.683i	−0.447367	+	0.447367i
$25$		−	34.7332i		−	0.0555732i
$26$	−197.438			−0.292068
$27$		−	1568.28i		−	2.15128i
$28$			149.811i			0.191086i
$29$	0.649856	−	0.649856i	0.000772718	−	0.000772718i	−0.706720	−	0.707493i	$-0.749826\pi$
$29$	0.649856	−	0.649856i	0.000772718	−	0.000772718i	0.707493	+	0.706720i	$0.249826\pi$
$30$			1106.71i			1.22968i
$31$	−1085.34	+	1085.34i	−1.12939	+	1.12939i	−0.139114	+	0.990276i	$0.544425\pi$
$31$	−1085.34	+	1085.34i	−1.12939	+	1.12939i	−0.990276	+	0.139114i	$0.955575\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	1461.18			1.34176
$34$	−834.484			−0.721872
$35$	321.709	+	321.709i	0.262620	+	0.262620i
$36$			1427.02i			1.10110i
$37$	203.465	+	1353.80i	0.148623	+	0.988894i
$37$	203.465	+	1353.80i	0.148623	+	0.988894i
$38$	664.111			0.459911
$39$	−794.945	+	794.945i	−0.522647	+	0.522647i
$40$		−	549.742i		−	0.343589i
$41$		−	630.898i		−	0.375311i	−0.982235	−	0.187656i	$-0.939911\pi$
$41$		−	630.898i		−	0.375311i	0.982235	−	0.187656i	$-0.0600889\pi$
$42$	603.184	+	603.184i	0.341941	+	0.341941i
$43$	−2018.85	−	2018.85i	−1.09186	−	1.09186i	−0.995330	−	0.0965281i	$-0.969226\pi$
$43$	−2018.85	−	2018.85i	−1.09186	−	1.09186i	−0.0965281	−	0.995330i	$-0.530774\pi$
$44$	−725.817			−0.374905
$45$	3064.43	+	3064.43i	1.51330	+	1.51330i
$46$	2745.41			1.29745
$47$	2159.18			0.977447			0.488724	−	0.872439i	$-0.337463\pi$
$47$	2159.18			0.977447			0.488724	+	0.872439i	$0.337463\pi$
$48$		−	1030.73i		−	0.447367i
$49$	−2050.32			−0.853945
$50$	69.4665	+	69.4665i	0.0277866	+	0.0277866i
$51$	−3359.88	+	3359.88i	−1.29177	+	1.29177i
$52$	394.876	−	394.876i	0.146034	−	0.146034i
$53$	−3422.88			−1.21854			−0.609270	−	0.792963i	$-0.708537\pi$
$53$	−3422.88			−1.21854			−0.609270	+	0.792963i	$0.708537\pi$
$54$	3136.57	+	3136.57i	1.07564	+	1.07564i
$55$	−1558.64	+	1558.64i	−0.515253	+	0.515253i
$56$	−299.622	−	299.622i	−0.0955428	−	0.0955428i
$57$	2673.91	−	2673.91i	0.822995	−	0.822995i
$58$			2.59942i			0.000772718i
$59$	−2151.08	−	2151.08i	−0.617949	−	0.617949i	0.327056	−	0.945005i	$-0.393943\pi$
$59$	−2151.08	−	2151.08i	−0.617949	−	0.617949i	−0.945005	+	0.327056i	$0.893943\pi$
$60$	−2213.43	−	2213.43i	−0.614841	−	0.614841i
$61$	−4324.19	+	4324.19i	−1.16210	+	1.16210i	−0.178090	+	0.984014i	$0.556992\pi$
$61$	−4324.19	+	4324.19i	−1.16210	+	1.16210i	−0.984014	+	0.178090i	$0.943008\pi$
$62$		−	4341.38i		−	1.12939i
$63$	3340.36			0.841614
$64$			512.000i			0.125000i
$65$		−	1695.94i		−	0.401406i
$66$	−2922.36	+	2922.36i	−0.670880	+	0.670880i
$67$		−	3386.60i		−	0.754423i	−0.926127	−	0.377211i	$-0.876883\pi$
$67$		−	3386.60i		−	0.754423i	0.926127	−	0.377211i	$-0.123117\pi$
$68$	1668.97	−	1668.97i	0.360936	−	0.360936i
$69$	11053.9	−	11053.9i	2.32175	−	2.32175i
$70$	−1286.84			−0.262620
$71$	−2134.91			−0.423509			−0.211754	−	0.977323i	$-0.567918\pi$
$71$	−2134.91			−0.423509			−0.211754	+	0.977323i	$0.567918\pi$
$72$	−2854.04	−	2854.04i	−0.550548	−	0.550548i
$73$			9332.10i			1.75119i	0.483044	+	0.875596i	$0.339531\pi$
$73$			9332.10i			1.75119i	−0.483044	+	0.875596i	$0.660469\pi$
$74$	−3114.52	−	2300.66i	−0.568759	−	0.420135i
$75$	559.386			0.0994463
$76$	−1328.22	+	1328.22i	−0.229955	+	0.229955i
$77$			1698.99i			0.286556i
$78$		−	3179.78i		−	0.522647i
$79$	1614.17	+	1614.17i	0.258639	+	0.258639i	0.824500	−	0.565861i	$-0.191456\pi$
$79$	1614.17	+	1614.17i	0.258639	+	0.258639i	−0.565861	+	0.824500i	$0.691456\pi$
$80$	1099.48	+	1099.48i	0.171794	+	0.171794i
$81$	10808.9			1.64745
$82$	1261.80	+	1261.80i	0.187656	+	0.187656i
$83$	8502.87			1.23427			0.617134	−	0.786858i	$-0.288294\pi$
$83$	8502.87			1.23427			0.617134	+	0.786858i	$0.288294\pi$
$84$	−2412.74			−0.341941
$85$		−	7167.99i		−	0.992109i
$86$	8075.38			1.09186
$87$	10.4661	+	10.4661i	0.00138275	+	0.00138275i
$88$	1451.63	−	1451.63i	0.187453	−	0.187453i
$89$	6123.51	−	6123.51i	0.773073	−	0.773073i	−0.205570	−	0.978642i	$-0.565905\pi$
$89$	6123.51	−	6123.51i	0.773073	−	0.773073i	0.978642	+	0.205570i	$0.0659047\pi$
$90$	−12257.7			−1.51330
$91$	−924.326	−	924.326i	−0.111620	−	0.111620i
$92$	−5490.83	+	5490.83i	−0.648727	+	0.648727i
$93$	−17479.7	−	17479.7i	−2.02101	−	2.02101i
$94$	−4318.36	+	4318.36i	−0.488724	+	0.488724i
$95$			5704.53i			0.632081i
$96$	2061.47	+	2061.47i	0.223683	+	0.223683i
$97$	−4623.75	−	4623.75i	−0.491417	−	0.491417i	0.417335	−	0.908753i	$-0.362964\pi$
$97$	−4623.75	−	4623.75i	−0.491417	−	0.491417i	−0.908753	+	0.417335i	$0.862964\pi$
$98$	4100.65	−	4100.65i	0.426973	−	0.426973i
$99$			16183.7i			1.65123i
$100$	−277.866			−0.0277866
$101$			12029.1i			1.17921i	0.807693	+	0.589604i	$0.200716\pi$
$101$			12029.1i			1.17921i	−0.807693	+	0.589604i	$0.799284\pi$
$102$		−	13439.5i		−	1.29177i
$103$	−6308.95	+	6308.95i	−0.594679	+	0.594679i	−0.938892	−	0.344213i	$-0.888146\pi$
$103$	−6308.95	+	6308.95i	−0.594679	+	0.594679i	0.344213	+	0.938892i	$0.388146\pi$
$104$			1579.51i			0.146034i
$105$	−5181.19	+	5181.19i	−0.469949	+	0.469949i
$106$	6845.75	−	6845.75i	0.609270	−	0.609270i
$107$	800.878			0.0699518			0.0349759	−	0.999388i	$-0.488865\pi$
$107$	800.878			0.0699518			0.0349759	+	0.999388i	$0.488865\pi$
$108$	−12546.3			−1.07564
$109$	10116.3	+	10116.3i	0.851468	+	0.851468i	0.990314	−	0.138846i	$-0.0443392\pi$
$109$	10116.3	+	10116.3i	0.851468	+	0.851468i	−0.138846	+	0.990314i	$0.544339\pi$
$110$		−	6234.56i		−	0.515253i
$111$	−21803.1	+	3276.85i	−1.76959	+	0.265956i
$112$	1198.49			0.0955428
$113$	12960.3	−	12960.3i	1.01498	−	1.01498i	0.0150957	−	0.999886i	$-0.495195\pi$
$113$	12960.3	−	12960.3i	1.01498	−	1.01498i	0.999886	−	0.0150957i	$-0.00480529\pi$
$114$			10695.6i			0.822995i
$115$			23582.3i			1.78316i
$116$	−5.19885	−	5.19885i	−0.000386359	−	0.000386359i
$117$	−8804.63	−	8804.63i	−0.643190	−	0.643190i
$118$	8604.32			0.617949
$119$	−3906.72	−	3906.72i	−0.275879	−	0.275879i
$120$	8853.71			0.614841
$121$	6409.60			0.437784
$122$		−	17296.8i		−	1.16210i
$123$	10160.7			0.671607
$124$	8682.75	+	8682.75i	0.564695	+	0.564695i
$125$	−11333.9	+	11333.9i	−0.725367	+	0.725367i
$126$	−6680.73	+	6680.73i	−0.420807	+	0.420807i
$127$	11444.2			0.709544			0.354772	−	0.934953i	$-0.384559\pi$
$127$	11444.2			0.709544			0.354772	+	0.934953i	$0.384559\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	32513.9	−	32513.9i	1.95384	−	1.95384i
$130$	3391.88	+	3391.88i	0.200703	+	0.200703i
$131$	8345.03	−	8345.03i	0.486279	−	0.486279i	−0.420851	−	0.907130i	$-0.638269\pi$
$131$	8345.03	−	8345.03i	0.486279	−	0.486279i	0.907130	+	0.420851i	$0.138269\pi$
$132$		−	11689.4i		−	0.670880i
$133$	3109.10	+	3109.10i	0.175765	+	0.175765i
$134$	6773.21	+	6773.21i	0.377211	+	0.377211i
$135$	−26942.2	+	26942.2i	−1.47831	+	1.47831i
$136$			6675.87i			0.360936i
$137$	1141.42			0.0608141			0.0304070	−	0.999538i	$-0.490320\pi$
$137$	1141.42			0.0608141			0.0304070	+	0.999538i	$0.490320\pi$
$138$			44215.4i			2.32175i
$139$			25300.6i			1.30948i	0.755852	+	0.654742i	$0.227223\pi$
$139$			25300.6i			1.30948i	−0.755852	+	0.654742i	$0.772777\pi$
$140$	2573.67	−	2573.67i	0.131310	−	0.131310i
$141$			34774.0i			1.74911i
$142$	4269.82	−	4269.82i	0.211754	−	0.211754i
$143$	4478.25	−	4478.25i	0.218996	−	0.218996i
$144$	11416.2			0.550548
$145$	−22.3283			−0.00106199
$146$	−18664.2	−	18664.2i	−0.875596	−	0.875596i
$147$		−	33020.9i		−	1.52811i
$148$	10830.4	−	1627.72i	0.494447	−	0.0743117i
$149$	−28257.3			−1.27280			−0.636398	−	0.771361i	$-0.719576\pi$
$149$	−28257.3			−1.27280			−0.636398	+	0.771361i	$0.719576\pi$
$150$	−1118.77	+	1118.77i	−0.0497232	+	0.0497232i
$151$			9514.32i			0.417277i	0.977993	+	0.208638i	$0.0669031\pi$
$151$			9514.32i			0.417277i	−0.977993	+	0.208638i	$0.933097\pi$
$152$		−	5312.89i		−	0.229955i
$153$	−37213.3	−	37213.3i	−1.58970	−	1.58970i
$154$	−3397.98	−	3397.98i	−0.143278	−	0.143278i
$155$	37291.2			1.55218
$156$	6359.56	+	6359.56i	0.261323	+	0.261323i
$157$	−9431.87			−0.382647			−0.191324	−	0.981527i	$-0.561278\pi$
$157$	−9431.87			−0.382647			−0.191324	+	0.981527i	$0.561278\pi$
$158$	−6456.67			−0.258639
$159$		−	55126.1i		−	2.18054i
$160$	−4397.94			−0.171794
$161$	12852.9	+	12852.9i	0.495850	+	0.495850i
$162$	−21617.9	+	21617.9i	−0.823726	+	0.823726i
$163$	−28498.0	+	28498.0i	−1.07261	+	1.07261i	−0.0754561	+	0.997149i	$0.524041\pi$
$163$	−28498.0	+	28498.0i	−1.07261	+	1.07261i	−0.997149	+	0.0754561i	$0.975959\pi$
$164$	−5047.19			−0.187656
$165$	−25102.2	−	25102.2i	−0.922028	−	0.922028i
$166$	−17005.7	+	17005.7i	−0.617134	+	0.617134i
$167$	−33862.6	−	33862.6i	−1.21419	−	1.21419i	−0.969635	−	0.244557i	$-0.921357\pi$
$167$	−33862.6	−	33862.6i	−1.21419	−	1.21419i	−0.244557	−	0.969635i	$-0.578643\pi$
$168$	4825.47	−	4825.47i	0.170971	−	0.170971i
$169$		−	23688.3i		−	0.829392i
$170$	14336.0	+	14336.0i	0.496054	+	0.496054i
$171$	29615.6	+	29615.6i	1.01281	+	1.01281i
$172$	−16150.8	+	16150.8i	−0.545929	+	0.545929i
$173$			21307.1i			0.711923i	0.934501	+	0.355961i	$0.115847\pi$
$173$			21307.1i			0.711923i	−0.934501	+	0.355961i	$0.884153\pi$
$174$	−41.8642			−0.00138275
$175$			650.428i			0.0212385i
$176$			5806.53i			0.187453i
$177$	34643.6	−	34643.6i	1.10580	−	1.10580i
$178$			24494.0i			0.773073i
$179$	−19967.8	+	19967.8i	−0.623194	+	0.623194i	−0.946347	−	0.323153i	$-0.895257\pi$
$179$	−19967.8	+	19967.8i	−0.623194	+	0.623194i	0.323153	+	0.946347i	$0.395257\pi$
$180$	24515.4	−	24515.4i	0.756648	−	0.756648i
$181$	41375.7			1.26296			0.631478	−	0.775394i	$-0.282449\pi$
$181$	41375.7			1.26296			0.631478	+	0.775394i	$0.282449\pi$
$182$	3697.30			0.111620
$183$	−69641.9	−	69641.9i	−2.07955	−	2.07955i
$184$		−	21963.3i		−	0.648727i
$185$	19762.0	−	26752.9i	0.577415	−	0.781677i
$186$	69918.7			2.02101
$187$	18927.6	−	18927.6i	0.541267	−	0.541267i
$188$		−	17273.5i		−	0.488724i
$189$			29368.3i			0.822157i
$190$	−11409.1	−	11409.1i	−0.316041	−	0.316041i
$191$	−38258.9	−	38258.9i	−1.04873	−	1.04873i	−0.998750	−	0.0499838i	$-0.984083\pi$
$191$	−38258.9	−	38258.9i	−1.04873	−	1.04873i	−0.0499838	−	0.998750i	$-0.515917\pi$
$192$	−8245.86			−0.223683
$193$	11383.2	+	11383.2i	0.305599	+	0.305599i	0.843199	−	0.537601i	$-0.180669\pi$
$193$	11383.2	+	11383.2i	0.305599	+	0.305599i	−0.537601	+	0.843199i	$0.680669\pi$
$194$	18495.0			0.491417
$195$	27313.4			0.718302
$196$			16402.6i			0.426973i
$197$	26633.2			0.686264			0.343132	−	0.939287i	$-0.388512\pi$
$197$	26633.2			0.686264			0.343132	+	0.939287i	$0.388512\pi$
$198$	−32367.3	−	32367.3i	−0.825613	−	0.825613i
$199$	15275.4	−	15275.4i	0.385732	−	0.385732i	−0.487430	−	0.873162i	$-0.662066\pi$
$199$	15275.4	−	15275.4i	0.385732	−	0.385732i	0.873162	+	0.487430i	$0.162066\pi$
$200$	555.732	−	555.732i	0.0138933	−	0.0138933i
$201$	54541.9			1.35001
$202$	−24058.2	−	24058.2i	−0.589604	−	0.589604i
$203$	−12.1695	+	12.1695i	−0.000295311	+	0.000295311i
$204$	26879.1	+	26879.1i	0.645883	+	0.645883i
$205$	−10838.5	+	10838.5i	−0.257906	+	0.257906i
$206$		−	25235.8i		−	0.594679i
$207$	122430.	+	122430.i	2.85724	+	2.85724i
$208$	−3159.01	−	3159.01i	−0.0730171	−	0.0730171i
$209$	−15063.2	+	15063.2i	−0.344846	+	0.344846i
$210$		−	20724.7i		−	0.469949i
$211$	−39950.0			−0.897329			−0.448665	−	0.893700i	$-0.648100\pi$
$211$	−39950.0			−0.897329			−0.448665	+	0.893700i	$0.648100\pi$
$212$			27383.0i			0.609270i
$213$		−	34383.1i		−	0.757855i
$214$	−1601.76	+	1601.76i	−0.0349759	+	0.0349759i
$215$			69365.3i			1.50060i
$216$	25092.5	−	25092.5i	0.537820	−	0.537820i
$217$	20324.6	−	20324.6i	0.431620	−	0.431620i
$218$	−40465.2			−0.851468
$219$	−150295.			−3.13370
$220$	12469.1	+	12469.1i	0.257627	+	0.257627i
$221$			20594.9i			0.421672i
$222$	37052.6	−	50160.0i	0.751818	−	1.01777i
$223$	−79047.8			−1.58957			−0.794785	−	0.606891i	$-0.792417\pi$
$223$	−79047.8			−1.58957			−0.794785	+	0.606891i	$0.792417\pi$
$224$	−2396.98	+	2396.98i	−0.0477714	+	0.0477714i
$225$			6195.62i			0.122383i
$226$			51841.2i			1.01498i
$227$	−1601.08	−	1601.08i	−0.0310714	−	0.0310714i	0.691400	−	0.722472i	$-0.256994\pi$
$227$	−1601.08	−	1601.08i	−0.0310714	−	0.0310714i	−0.722472	+	0.691400i	$0.756994\pi$
$228$	−21391.3	−	21391.3i	−0.411498	−	0.411498i
$229$	39765.1			0.758283			0.379142	−	0.925339i	$-0.376219\pi$
$229$	39765.1			0.758283			0.379142	+	0.925339i	$0.376219\pi$
$230$	−47164.7	−	47164.7i	−0.891582	−	0.891582i
$231$	−27362.6			−0.512782
$232$	20.7954			0.000386359
$233$			3585.54i			0.0660454i	0.999455	+	0.0330227i	$0.0105134\pi$
$233$			3585.54i			0.0660454i	−0.999455	+	0.0330227i	$0.989487\pi$
$234$	35218.5			0.643190
$235$	−37093.5	−	37093.5i	−0.671680	−	0.671680i
$236$	−17208.6	+	17208.6i	−0.308974	+	0.308974i
$237$	−25996.5	+	25996.5i	−0.462826	+	0.462826i
$238$	15626.9			0.275879
$239$	30124.4	+	30124.4i	0.527379	+	0.527379i	0.919790	−	0.392411i	$-0.128359\pi$
$239$	30124.4	+	30124.4i	0.527379	+	0.527379i	−0.392411	+	0.919790i	$0.628359\pi$
$240$	−17707.4	+	17707.4i	−0.307420	+	0.307420i
$241$	−63589.9	−	63589.9i	−1.09485	−	1.09485i	−0.995003	−	0.0998453i	$-0.968165\pi$
$241$	−63589.9	−	63589.9i	−1.09485	−	1.09485i	−0.0998453	−	0.995003i	$-0.531835\pi$
$242$	−12819.2	+	12819.2i	−0.218892	+	0.218892i
$243$			47049.1i			0.796781i
$244$	34593.5	+	34593.5i	0.581052	+	0.581052i
$245$	35223.4	+	35223.4i	0.586812	+	0.586812i
$246$	−20321.5	+	20321.5i	−0.335804	+	0.335804i
$247$		−	16390.1i		−	0.268651i
$248$	−34731.0			−0.564695
$249$			136940.i			2.20868i
$250$		−	45335.4i		−	0.725367i
$251$	24224.8	−	24224.8i	0.384515	−	0.384515i	−0.488211	−	0.872726i	$-0.662350\pi$
$251$	24224.8	−	24224.8i	0.384515	−	0.384515i	0.872726	+	0.488211i	$0.162350\pi$
$252$		−	26722.9i		−	0.420807i
$253$	−62270.9	+	62270.9i	−0.972845	+	0.972845i
$254$	−22888.5	+	22888.5i	−0.354772	+	0.354772i
$255$	115442.			1.77535
$256$	4096.00			0.0625000
$257$	64397.4	+	64397.4i	0.974994	+	0.974994i	0.999695	−	0.0247010i	$-0.00786337\pi$
$257$	64397.4	+	64397.4i	0.974994	+	0.974994i	−0.0247010	+	0.999695i	$0.507863\pi$
$258$			130056.i			1.95384i
$259$	−3810.17	−	25351.7i	−0.0567995	−	0.377927i
$260$	−13567.5			−0.200703
$261$	−115.920	+	115.920i	−0.00170167	+	0.00170167i
$262$			33380.1i			0.486279i
$263$		−	55482.7i		−	0.802132i	−0.916049	−	0.401066i	$-0.868640\pi$
$263$		−	55482.7i		−	0.802132i	0.916049	−	0.401066i	$-0.131360\pi$
$264$	23378.8	+	23378.8i	0.335440	+	0.335440i
$265$	58803.1	+	58803.1i	0.837353	+	0.837353i
$266$	−12436.4			−0.175765
$267$	98620.4	+	98620.4i	1.38339	+	1.38339i
$268$	−27092.8			−0.377211
$269$	−83804.2			−1.15814			−0.579070	−	0.815278i	$-0.696584\pi$
$269$	−83804.2			−1.15814			−0.579070	+	0.815278i	$0.696584\pi$
$270$		−	107769.i		−	1.47831i
$271$	28151.9			0.383327			0.191663	−	0.981461i	$-0.438612\pi$
$271$	28151.9			0.383327			0.191663	+	0.981461i	$0.438612\pi$
$272$	−13351.7	−	13351.7i	−0.180468	−	0.180468i
$273$	14886.5	−	14886.5i	0.199740	−	0.199740i
$274$	−2282.84	+	2282.84i	−0.0304070	+	0.0304070i
$275$	−3151.24			−0.0416693
$276$	−88430.9	−	88430.9i	−1.16088	−	1.16088i
$277$	31671.3	−	31671.3i	0.412768	−	0.412768i	−0.469933	−	0.882702i	$-0.655722\pi$
$277$	31671.3	−	31671.3i	0.412768	−	0.412768i	0.882702	+	0.469933i	$0.155722\pi$
$278$	−50601.1	−	50601.1i	−0.654742	−	0.654742i
$279$	193601.	−	193601.i	2.48713	−	2.48713i
$280$			10294.7i			0.131310i
$281$	−5298.31	−	5298.31i	−0.0671004	−	0.0671004i	0.672760	−	0.739861i	$-0.265109\pi$
$281$	−5298.31	−	5298.31i	−0.0671004	−	0.0671004i	−0.739861	+	0.672760i	$0.765109\pi$
$282$	−69548.1	−	69548.1i	−0.874555	−	0.874555i
$283$	67798.9	−	67798.9i	0.846545	−	0.846545i	−0.143155	−	0.989700i	$-0.545725\pi$
$283$	67798.9	−	67798.9i	0.846545	−	0.846545i	0.989700	+	0.143155i	$0.0457249\pi$
$284$			17079.3i			0.211754i
$285$	−91872.6			−1.13109
$286$			17913.0i			0.218996i
$287$			11814.4i			0.143433i
$288$	−22832.3	+	22832.3i	−0.275274	+	0.275274i
$289$			3524.42i			0.0421981i
$290$	44.6567	−	44.6567i	0.000530995	−	0.000530995i
$291$	74466.4	−	74466.4i	0.879375	−	0.879375i
$292$	74656.8			0.875596
$293$	−4879.11			−0.0568337			−0.0284168	−	0.999596i	$-0.509047\pi$
$293$	−4879.11			−0.0568337			−0.0284168	+	0.999596i	$0.509047\pi$
$294$	66041.7	+	66041.7i	0.764053	+	0.764053i
$295$			73908.7i			0.849281i
$296$	−18405.3	+	24916.2i	−0.210068	+	0.284379i
$297$	−142286.			−1.61305
$298$	56514.7	−	56514.7i	0.636398	−	0.636398i
$299$		−	67756.2i		−	0.757891i
$300$		−	4475.08i		−	0.0497232i
$301$	37805.7	+	37805.7i	0.417277	+	0.417277i
$302$	−19028.6	−	19028.6i	−0.208638	−	0.208638i
$303$	−193731.			−2.11015
$304$	10625.8	+	10625.8i	0.114978	+	0.114978i
$305$	148574.			1.59714
$306$	148853.			1.58970
$307$			63026.6i			0.668724i	0.942445	+	0.334362i	$0.108521\pi$
$307$			63026.6i			0.668724i	−0.942445	+	0.334362i	$0.891479\pi$
$308$	13591.9			0.143278
$309$	−101607.	−	101607.i	−1.06416	−	1.06416i
$310$	−74582.4	+	74582.4i	−0.776092	+	0.776092i
$311$	67733.9	−	67733.9i	0.700302	−	0.700302i	−0.264173	−	0.964475i	$-0.585099\pi$
$311$	67733.9	−	67733.9i	0.700302	−	0.700302i	0.964475	+	0.264173i	$0.0850991\pi$
$312$	−25438.3			−0.261323
$313$	−94660.2	−	94660.2i	−0.966227	−	0.966227i	0.0332215	−	0.999448i	$-0.489423\pi$
$313$	−94660.2	−	94660.2i	−0.966227	−	0.966227i	−0.999448	+	0.0332215i	$0.989423\pi$
$314$	18863.7	−	18863.7i	0.191324	−	0.191324i
$315$	−57385.6	−	57385.6i	−0.578338	−	0.578338i
$316$	12913.3	−	12913.3i	0.129320	−	0.129320i
$317$			123083.i			1.22484i	0.790534	+	0.612418i	$0.209803\pi$
$317$			123083.i			1.22484i	−0.790534	+	0.612418i	$0.790197\pi$
$318$	110252.	+	110252.i	1.09027	+	1.09027i
$319$	−58.9595	−	58.9595i	−0.000579392	−	0.000579392i
$320$	8795.88	−	8795.88i	0.0858972	−	0.0858972i
$321$			12898.3i			0.125176i
$322$	−51411.7			−0.495850
$323$		−	69273.8i		−	0.663993i
$324$		−	86471.5i		−	0.823726i
$325$	1714.42	−	1714.42i	0.0162312	−	0.0162312i
$326$		−	113992.i		−	1.07261i
$327$	−162925.	+	162925.i	−1.52367	+	1.52367i
$328$	10094.4	−	10094.4i	0.0938279	−	0.0938279i
$329$	−40433.7			−0.373552
$330$	100409.			0.922028
$331$	−104158.	−	104158.i	−0.950685	−	0.950685i	0.0481548	−	0.998840i	$-0.484666\pi$
$331$	−104158.	−	104158.i	−0.950685	−	0.950685i	−0.998840	+	0.0481548i	$0.984666\pi$
$332$		−	68023.0i		−	0.617134i
$333$	−36293.6	−	241487.i	−0.327297	−	2.17773i
$334$	135450.			1.21419
$335$	−58180.0	+	58180.0i	−0.518423	+	0.518423i
$336$			19301.9i			0.170971i
$337$		−	143471.i		−	1.26329i	−0.775256	−	0.631647i	$-0.782379\pi$
$337$		−	143471.i		−	1.26329i	0.775256	−	0.631647i	$-0.217621\pi$
$338$	47376.5	+	47376.5i	0.414696	+	0.414696i
$339$	208728.	+	208728.i	1.81628	+	1.81628i
$340$	−57343.9			−0.496054
$341$	98470.1	+	98470.1i	0.846829	+	0.846829i
$342$	−118462.			−1.01281
$343$	83357.2			0.708524
$344$		−	64603.1i		−	0.545929i
$345$	−379798.			−3.19091
$346$	−42614.3	−	42614.3i	−0.355961	−	0.355961i
$347$	−56881.4	+	56881.4i	−0.472401	+	0.472401i	−0.902691	−	0.430290i	$-0.858411\pi$
$347$	−56881.4	+	56881.4i	−0.472401	+	0.472401i	0.430290	+	0.902691i	$0.358411\pi$
$348$	83.7285	−	83.7285i	0.000691377	−	0.000691377i
$349$	−94152.4			−0.773002			−0.386501	−	0.922289i	$-0.626316\pi$
$349$	−94152.4			−0.773002			−0.386501	+	0.922289i	$0.626316\pi$
$350$	−1300.86	−	1300.86i	−0.0106192	−	0.0106192i
$351$	77409.7	−	77409.7i	0.628321	−	0.628321i
$352$	−11613.1	−	11613.1i	−0.0937263	−	0.0937263i
$353$	−65406.7	+	65406.7i	−0.524896	+	0.524896i	−0.919046	−	0.394150i	$-0.871039\pi$
$353$	−65406.7	+	65406.7i	−0.524896	+	0.524896i	0.394150	+	0.919046i	$0.371039\pi$
$354$			138574.i			1.10580i
$355$	36676.5	+	36676.5i	0.291026	+	0.291026i
$356$	−48988.1	−	48988.1i	−0.386536	−	0.386536i
$357$	62918.4	−	62918.4i	0.493675	−	0.493675i
$358$		−	79871.0i		−	0.623194i
$359$	98394.7			0.763454			0.381727	−	0.924275i	$-0.375330\pi$
$359$	98394.7			0.763454			0.381727	+	0.924275i	$0.375330\pi$
$360$			98061.6i			0.756648i
$361$		−	75190.5i		−	0.576964i
$362$	−82751.3	+	82751.3i	−0.631478	+	0.631478i
$363$			103228.i			0.783400i
$364$	−7394.61	+	7394.61i	−0.0558100	+	0.0558100i
$365$	160320.	−	160320.i	1.20338	−	1.20338i
$366$	278568.			2.07955
$367$	192551.			1.42960			0.714800	−	0.699329i	$-0.246518\pi$
$367$	192551.			1.42960			0.714800	+	0.699329i	$0.246518\pi$
$368$	43926.6	+	43926.6i	0.324364	+	0.324364i
$369$			112538.i			0.826507i
$370$	13981.7	+	93029.8i	0.102131	+	0.679546i
$371$	64098.1			0.465690
$372$	−139837.	+	139837.i	−1.01050	+	1.01050i
$373$		−	58181.1i		−	0.418181i	−0.977896	−	0.209091i	$-0.932950\pi$
$373$		−	58181.1i		−	0.418181i	0.977896	−	0.209091i	$-0.0670503\pi$
$374$			75710.3i			0.541267i
$375$	−182534.	−	182534.i	−1.29802	−	1.29802i
$376$	34546.9	+	34546.9i	0.244362	+	0.244362i
$377$	64.1532			0.000451373
$378$	−58736.5	−	58736.5i	−0.411078	−	0.411078i
$379$	−148456.			−1.03352			−0.516759	−	0.856131i	$-0.672862\pi$
$379$	−148456.			−1.03352			−0.516759	+	0.856131i	$0.672862\pi$
$380$	45636.3			0.316041
$381$			184312.i			1.26970i
$382$	153035.			1.04873
$383$	−1840.77	−	1840.77i	−0.0125488	−	0.0125488i	0.700805	−	0.713353i	$-0.252825\pi$
$383$	−1840.77	−	1840.77i	−0.0125488	−	0.0125488i	−0.713353	+	0.700805i	$0.752825\pi$
$384$	16491.7	−	16491.7i	0.111842	−	0.111842i
$385$	29187.7	−	29187.7i	0.196915	−	0.196915i
$386$	−45533.0			−0.305599
$387$	360117.	+	360117.i	2.40448	+	2.40448i
$388$	−36990.0	+	36990.0i	−0.245709	+	0.245709i
$389$	17200.6	+	17200.6i	0.113669	+	0.113669i	0.761654	−	0.647984i	$-0.224388\pi$
$389$	17200.6	+	17200.6i	0.113669	+	0.113669i	−0.647984	+	0.761654i	$0.724388\pi$
$390$	−54626.9	+	54626.9i	−0.359151	+	0.359151i
$391$		−	286376.i		−	1.87319i
$392$	−32805.2	−	32805.2i	−0.213486	−	0.213486i
$393$	134398.	+	134398.i	0.870179	+	0.870179i
$394$	−53266.5	+	53266.5i	−0.343132	+	0.343132i
$395$		−	55461.0i		−	0.355462i
$396$	129469.			0.825613
$397$			39243.2i			0.248991i	0.992220	+	0.124496i	$0.0397312\pi$
$397$			39243.2i			0.248991i	−0.992220	+	0.124496i	$0.960269\pi$
$398$			61101.5i			0.385732i
$399$	−50072.7	+	50072.7i	−0.314525	+	0.314525i
$400$			2222.93i			0.0138933i
$401$	−120450.	+	120450.i	−0.749064	+	0.749064i	−0.974304	−	0.225239i	$-0.927684\pi$
$401$	−120450.	+	120450.i	−0.749064	+	0.749064i	0.225239	+	0.974304i	$0.427684\pi$
$402$	−109084.	+	109084.i	−0.675007	+	0.675007i
$403$	−107144.			−0.659718
$404$	96232.7			0.589604
$405$	−185692.	−	185692.i	−1.13209	−	1.13209i
$406$		−	48.6778i		−	0.000295311i
$407$	122826.	−	18459.8i	0.741483	−	0.111439i
$408$	−107516.			−0.645883
$409$	94473.8	−	94473.8i	0.564761	−	0.564761i	−0.365895	−	0.930656i	$-0.619237\pi$
$409$	94473.8	−	94473.8i	0.564761	−	0.564761i	0.930656	+	0.365895i	$0.119237\pi$
$410$		−	43353.9i		−	0.257906i
$411$			18382.8i			0.108825i
$412$	50471.6	+	50471.6i	0.297339	+	0.297339i
$413$	40281.9	+	40281.9i	0.236162	+	0.236162i
$414$	−489720.			−2.85724
$415$	−146075.	−	146075.i	−0.848162	−	0.848162i
$416$	12636.0			0.0730171
$417$	−407470.			−2.34328
$418$		−	60252.9i		−	0.344846i
$419$	299736.			1.70730			0.853651	−	0.520846i	$-0.174383\pi$
$419$	299736.			1.70730			0.853651	+	0.520846i	$0.174383\pi$
$420$	41449.5	+	41449.5i	0.234974	+	0.234974i
$421$	−4982.01	+	4982.01i	−0.0281087	+	0.0281087i	−0.721021	−	0.692913i	$-0.756327\pi$
$421$	−4982.01	+	4982.01i	−0.0281087	+	0.0281087i	0.692913	+	0.721021i	$0.256327\pi$
$422$	79900.0	−	79900.0i	0.448665	−	0.448665i
$423$	−385149.			−2.15253
$424$	−54766.0	−	54766.0i	−0.304635	−	0.304635i
$425$	7246.08	−	7246.08i	0.0401167	−	0.0401167i
$426$	68766.2	+	68766.2i	0.378928	+	0.378928i
$427$	80976.4	−	80976.4i	0.444123	−	0.444123i
$428$		−	6407.03i		−	0.0349759i
$429$	72123.1	+	72123.1i	0.391886	+	0.391886i
$430$	−138731.	−	138731.i	−0.750301	−	0.750301i
$431$	−100084.	+	100084.i	−0.538780	+	0.538780i	−0.923170	−	0.384391i	$-0.874412\pi$
$431$	−100084.	+	100084.i	−0.538780	+	0.538780i	0.384391	+	0.923170i	$0.374412\pi$
$432$			100370.i			0.537820i
$433$	195739.			1.04400			0.522001	−	0.852945i	$-0.325186\pi$
$433$	195739.			1.04400			0.522001	+	0.852945i	$0.325186\pi$
$434$			81298.3i			0.431620i
$435$		−	359.602i		−	0.00190039i
$436$	80930.4	−	80930.4i	0.425734	−	0.425734i
$437$			227908.i			1.19343i
$438$	300591.	−	300591.i	1.56685	−	1.56685i
$439$	−108866.	+	108866.i	−0.564890	+	0.564890i	−0.930692	−	0.365803i	$-0.880794\pi$
$439$	−108866.	+	108866.i	−0.564890	+	0.564890i	0.365803	+	0.930692i	$0.380794\pi$
$440$	−49876.5			−0.257627
$441$	365731.			1.88055
$442$	−41189.8	−	41189.8i	−0.210836	−	0.210836i
$443$			170934.i			0.871004i	0.900188	+	0.435502i	$0.143429\pi$
$443$			170934.i			0.871004i	−0.900188	+	0.435502i	$0.856571\pi$
$444$	26214.8	+	174425.i	0.132978	+	0.884796i
$445$	−210397.			−1.06248
$446$	158096.	−	158096.i	0.794785	−	0.794785i
$447$		−	455090.i		−	2.27763i
$448$		−	9587.91i		−	0.0477714i
$449$	−72459.7	−	72459.7i	−0.359421	−	0.359421i	0.504178	−	0.863600i	$-0.331795\pi$
$449$	−72459.7	−	72459.7i	−0.359421	−	0.359421i	−0.863600	+	0.504178i	$0.831795\pi$
$450$	−12391.2	−	12391.2i	−0.0611914	−	0.0611914i
$451$	−57239.6			−0.281412
$452$	−103682.	−	103682.i	−0.507491	−	0.507491i
$453$	−153230.			−0.746702
$454$	6404.31			0.0310714
$455$			31758.8i			0.153406i
$456$	85565.2			0.411498
$457$	238333.	+	238333.i	1.14117	+	1.14117i	0.988236	+	0.152939i	$0.0488739\pi$
$457$	238333.	+	238333.i	1.14117	+	1.14117i	0.152939	+	0.988236i	$0.451126\pi$
$458$	−79530.3	+	79530.3i	−0.379142	+	0.379142i
$459$	327177.	−	327177.i	1.55295	−	1.55295i
$460$	188659.			0.891582
$461$	−35237.3	−	35237.3i	−0.165806	−	0.165806i	0.619327	−	0.785133i	$-0.287406\pi$
$461$	−35237.3	−	35237.3i	−0.165806	−	0.165806i	−0.785133	+	0.619327i	$0.787406\pi$
$462$	54725.1	−	54725.1i	0.256391	−	0.256391i
$463$	186902.	+	186902.i	0.871870	+	0.871870i	0.992676	−	0.120806i	$-0.0385478\pi$
$463$	186902.	+	186902.i	0.871870	+	0.871870i	−0.120806	+	0.992676i	$0.538548\pi$
$464$	−41.5908	+	41.5908i	−0.000193180	+	0.000193180i
$465$			600583.i			2.77758i
$466$	−7171.08	−	7171.08i	−0.0330227	−	0.0330227i
$467$	206870.	+	206870.i	0.948556	+	0.948556i	0.998740	−	0.0501835i	$-0.0159806\pi$
$467$	206870.	+	206870.i	0.948556	+	0.948556i	−0.0501835	+	0.998740i	$0.515981\pi$
$468$	−70437.0	+	70437.0i	−0.321595	+	0.321595i
$469$			63418.8i			0.288319i
$470$	148374.			0.671680
$471$		−	151902.i		−	0.684734i
$472$		−	68834.5i		−	0.308974i
$473$	−183164.	+	183164.i	−0.818687	+	0.818687i
$474$		−	103986.i		−	0.462826i
$475$	−5766.68	+	5766.68i	−0.0255587	+	0.0255587i
$476$	−31253.7	+	31253.7i	−0.137939	+	0.137939i
$477$	610564.			2.68346
$478$	−120498.			−0.527379
$479$	−224838.	−	224838.i	−0.979940	−	0.979940i	0.0198625	−	0.999803i	$-0.493677\pi$
$479$	−224838.	−	224838.i	−0.979940	−	0.979940i	−0.999803	+	0.0198625i	$0.993677\pi$
$480$		−	70829.7i		−	0.307420i
$481$	−56779.8	+	76865.7i	−0.245416	+	0.332233i
$482$	254360.			1.09485
$483$	−206999.	+	206999.i	−0.887307	+	0.887307i
$484$		−	51276.8i		−	0.218892i
$485$			158867.i			0.675382i
$486$	−94098.3	−	94098.3i	−0.398391	−	0.398391i
$487$	−198378.	−	198378.i	−0.836440	−	0.836440i	0.151949	−	0.988388i	$-0.451445\pi$
$487$	−198378.	−	198378.i	−0.836440	−	0.836440i	−0.988388	+	0.151949i	$0.951445\pi$
$488$	−138374.			−0.581052
$489$	−458967.	−	458967.i	−1.91939	−	1.91939i
$490$	−140894.			−0.586812
$491$	−303671.			−1.25962			−0.629812	−	0.776748i	$-0.716868\pi$
$491$	−303671.			−1.25962			−0.629812	+	0.776748i	$0.716868\pi$
$492$		−	81286.0i		−	0.335804i
$493$	271.147			0.00111561
$494$	32780.2	+	32780.2i	0.134325	+	0.134325i
$495$	278026.	−	278026.i	1.13469	−	1.13469i
$496$	69462.0	−	69462.0i	0.282348	−	0.282348i
$497$	39979.1			0.161853
$498$	−273881.	−	273881.i	−1.10434	−	1.10434i
$499$	−131685.	+	131685.i	−0.528855	+	0.528855i	−0.920231	−	0.391376i	$-0.871999\pi$
$499$	−131685.	+	131685.i	−0.528855	+	0.528855i	0.391376	+	0.920231i	$0.371999\pi$
$500$	90670.8	+	90670.8i	0.362683	+	0.362683i
$501$	545364.	−	545364.i	2.17276	−	2.17276i
$502$			96899.2i			0.384515i
$503$	−215652.	−	215652.i	−0.852349	−	0.852349i	0.138073	−	0.990422i	$-0.455909\pi$
$503$	−215652.	−	215652.i	−0.852349	−	0.852349i	−0.990422	+	0.138073i	$0.955909\pi$
$504$	53445.8	+	53445.8i	0.210403	+	0.210403i
$505$	206653.	−	206653.i	0.810325	−	0.810325i
$506$		−	249083.i		−	0.972845i
$507$	381504.			1.48417
$508$		−	91553.9i		−	0.354772i
$509$		−	14522.4i		−	0.0560534i	−0.999607	−	0.0280267i	$-0.991078\pi$
$509$		−	14522.4i		−	0.0560534i	0.999607	−	0.0280267i	$-0.00892234\pi$
$510$	−230884.	+	230884.i	−0.887673	+	0.887673i
$511$		−	174756.i		−	0.669255i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−260379.	+	260379.i	−0.989397	+	0.989397i
$514$	−257589.			−0.974994
$515$	216768.			0.817300
$516$	−260111.	−	260111.i	−0.976922	−	0.976922i
$517$		−	195896.i		−	0.732900i
$518$	58323.7	+	43083.1i	0.217363	+	0.160564i
$519$	−343156.			−1.27396
$520$	27135.0	−	27135.0i	0.100351	−	0.100351i
$521$			438916.i			1.61699i	0.588506	+	0.808493i	$0.299716\pi$
$521$			438916.i			1.61699i	−0.588506	+	0.808493i	$0.700284\pi$
$522$		−	463.679i		−	0.00170167i
$523$	−200303.	−	200303.i	−0.732290	−	0.732290i	0.238783	−	0.971073i	$-0.423252\pi$
$523$	−200303.	−	200303.i	−0.732290	−	0.732290i	−0.971073	+	0.238783i	$0.923252\pi$
$524$	−66760.2	−	66760.2i	−0.243139	−	0.243139i
$525$	−10475.3			−0.0380055
$526$	110965.	+	110965.i	0.401066	+	0.401066i
$527$	−452851.			−1.63055
$528$	−93515.4			−0.335440
$529$			662321.i			2.36678i
$530$	−235213.			−0.837353
$531$	383704.	+	383704.i	1.36084	+	1.36084i
$532$	24872.8	−	24872.8i	0.0878823	−	0.0878823i
$533$	31140.9	−	31140.9i	0.109617	−	0.109617i
$534$	−394481.			−1.38339
$535$	−13758.6	−	13758.6i	−0.0480693	−	0.0480693i
$536$	54185.7	−	54185.7i	0.188606	−	0.188606i
$537$	−321585.	−	321585.i	−1.11518	−	1.11518i
$538$	167608.	−	167608.i	0.579070	−	0.579070i
$539$			186020.i			0.640297i
$540$	215538.	+	215538.i	0.739156	+	0.739156i
$541$	243047.	+	243047.i	0.830418	+	0.830418i	0.987574	−	0.157156i	$-0.0502326\pi$
$541$	243047.	+	243047.i	0.830418	+	0.830418i	−0.157156	+	0.987574i	$0.550233\pi$
$542$	−56303.8	+	56303.8i	−0.191663	+	0.191663i
$543$			666363.i			2.26002i
$544$	53407.0			0.180468
$545$		−	347585.i		−	1.17022i
$546$			59545.8i			0.199740i
$547$	229291.	−	229291.i	0.766325	−	0.766325i	−0.211132	−	0.977458i	$-0.567715\pi$
$547$	229291.	−	229291.i	0.766325	−	0.766325i	0.977458	+	0.211132i	$0.0677150\pi$
$548$		−	9131.36i		−	0.0304070i
$549$	771338.	−	771338.i	2.55917	−	2.55917i
$550$	6302.49	−	6302.49i	0.0208347	−	0.0208347i
$551$	−215.788			−0.000710763
$552$	353724.			1.16088
$553$	−30227.5	−	30227.5i	−0.0988444	−	0.0988444i
$554$			126685.i			0.412768i
$555$	430861.	+	318272.i	1.39878	+	1.03327i
$556$	202404.			0.654742
$557$	130650.	−	130650.i	0.421113	−	0.421113i	−0.464474	−	0.885587i	$-0.653757\pi$
$557$	130650.	−	130650.i	0.421113	−	0.421113i	0.885587	+	0.464474i	$0.153757\pi$
$558$			774404.i			2.48713i
$559$		−	199299.i		−	0.637795i
$560$	−20589.4	−	20589.4i	−0.0656549	−	0.0656549i
$561$	304832.	+	304832.i	0.968579	+	0.968579i
$562$	21193.2			0.0671004
$563$	−414380.	−	414380.i	−1.30732	−	1.30732i	−0.923343	−	0.383976i	$-0.874555\pi$
$563$	−414380.	−	414380.i	−1.30732	−	1.30732i	−0.383976	−	0.923343i	$-0.625445\pi$
$564$	278192.			0.874555
$565$	−445302.			−1.39495
$566$			271196.i			0.846545i
$567$	−202412.			−0.629609
$568$	−34158.5	−	34158.5i	−0.105877	−	0.105877i
$569$	33073.8	−	33073.8i	0.102155	−	0.102155i	−0.654182	−	0.756337i	$-0.726987\pi$
$569$	33073.8	−	33073.8i	0.102155	−	0.102155i	0.756337	+	0.654182i	$0.226987\pi$
$570$	183745.	−	183745.i	0.565544	−	0.565544i
$571$	−106772.			−0.327481			−0.163741	−	0.986503i	$-0.552356\pi$
$571$	−106772.			−0.327481			−0.163741	+	0.986503i	$0.552356\pi$
$572$	−35826.0	−	35826.0i	−0.109498	−	0.109498i
$573$	616167.	−	616167.i	1.87667	−	1.87667i
$574$	−23628.9	−	23628.9i	−0.0717166	−	0.0717166i
$575$	−23839.3	+	23839.3i	−0.0721037	+	0.0721037i
$576$		−	91329.2i		−	0.275274i
$577$	−314660.	−	314660.i	−0.945126	−	0.945126i	0.0534445	−	0.998571i	$-0.482980\pi$
$577$	−314660.	−	314660.i	−0.945126	−	0.945126i	−0.998571	+	0.0534445i	$0.982980\pi$
$578$	−7048.85	−	7048.85i	−0.0210990	−	0.0210990i
$579$	−183329.	+	183329.i	−0.546858	+	0.546858i
$580$			178.627i			0.000530995i
$581$	−159228.			−0.471702
$582$			297865.i			0.879375i
$583$			310548.i			0.913674i
$584$	−149314.	+	149314.i	−0.437798	+	0.437798i
$585$			302517.i			0.883972i
$586$	9758.23	−	9758.23i	0.0284168	−	0.0284168i
$587$	122380.	−	122380.i	0.355168	−	0.355168i	−0.506860	−	0.862028i	$-0.669194\pi$
$587$	122380.	−	122380.i	0.355168	−	0.355168i	0.862028	+	0.506860i	$0.169194\pi$
$588$	−264167.			−0.764053
$589$	360395.			1.03884
$590$	−147817.	−	147817.i	−0.424641	−	0.424641i
$591$			428934.i			1.22805i
$592$	−13021.8	−	86642.9i	−0.0371558	−	0.247223i
$593$	−228088.			−0.648624			−0.324312	−	0.945950i	$-0.605133\pi$
$593$	−228088.			−0.648624			−0.324312	+	0.945950i	$0.605133\pi$
$594$	284571.	−	284571.i	0.806526	−	0.806526i
$595$			134230.i			0.379155i
$596$			226059.i			0.636398i
$597$	246013.	+	246013.i	0.690255	+	0.690255i
$598$	135512.	+	135512.i	0.378945	+	0.378945i
$599$	−143065.			−0.398732			−0.199366	−	0.979925i	$-0.563888\pi$
$599$	−143065.			−0.398732			−0.199366	+	0.979925i	$0.563888\pi$
$600$	8950.17	+	8950.17i	0.0248616	+	0.0248616i
$601$	25941.8			0.0718209			0.0359104	−	0.999355i	$-0.488567\pi$
$601$	25941.8			0.0718209			0.0359104	+	0.999355i	$0.488567\pi$
$602$	−151223.			−0.417277
$603$			604094.i			1.66138i
$604$	76114.6			0.208638
$605$	−110113.	−	110113.i	−0.300836	−	0.300836i
$606$	387462.	−	387462.i	1.05508	−	1.05508i
$607$	90425.1	−	90425.1i	0.245421	−	0.245421i	−0.573667	−	0.819088i	$-0.694480\pi$
$607$	90425.1	−	90425.1i	0.245421	−	0.245421i	0.819088	+	0.573667i	$0.194480\pi$
$608$	−42503.1			−0.114978
$609$	−195.991	−	195.991i	−0.000528448	−	0.000528448i
$610$	−297149.	+	297149.i	−0.798572	+	0.798572i
$611$	106576.	+	106576.i	0.285481	+	0.285481i
$612$	−297706.	+	297706.i	−0.794850	+	0.794850i
$613$			440270.i			1.17165i	0.810437	+	0.585826i	$0.199230\pi$
$613$			440270.i			1.17165i	−0.810437	+	0.585826i	$0.800770\pi$
$614$	−126053.	−	126053.i	−0.334362	−	0.334362i
$615$	−174556.	−	174556.i	−0.461514	−	0.461514i
$616$	−27183.8	+	27183.8i	−0.0716390	+	0.0716390i
$617$		−	160802.i		−	0.422398i	−0.977443	−	0.211199i	$-0.932263\pi$
$617$		−	160802.i		−	0.422398i	0.977443	−	0.211199i	$-0.0677368\pi$
$618$	406427.			1.06416
$619$		−	28646.9i		−	0.0747646i	−0.999301	−	0.0373823i	$-0.988098\pi$
$619$		−	28646.9i		−	0.0747646i	0.999301	−	0.0373823i	$-0.0119019\pi$
$620$		−	298330.i		−	0.776092i
$621$	−1.07640e6	+	1.07640e6i	−2.79119	+	2.79119i
$622$			270936.i			0.700302i
$623$	−114671.	+	114671.i	−0.295446	+	0.295446i
$624$	50876.5	−	50876.5i	0.130662	−	0.130662i
$625$	367710.			0.941338
$626$	378641.			0.966227
$627$	−242596.	−	242596.i	−0.617090	−	0.617090i
$628$			75455.0i			0.191324i
$629$	−239983.	+	324877.i	−0.606568	+	0.821142i
$630$	229542.			0.578338
$631$	−121496.	+	121496.i	−0.305143	+	0.305143i	−0.843022	−	0.537879i	$-0.819226\pi$
$631$	−121496.	+	121496.i	−0.305143	+	0.305143i	0.537879	+	0.843022i	$0.319226\pi$
$632$			51653.3i			0.129320i
$633$		−	643403.i		−	1.60574i
$634$	−246165.	−	246165.i	−0.612418	−	0.612418i
$635$	−196606.	−	196606.i	−0.487583	−	0.487583i
$636$	−441009.			−1.09027
$637$	−101203.	−	101203.i	−0.249410	−	0.249410i
$638$	235.838			0.000579392
$639$	380819.			0.932647
$640$			35183.5i			0.0858972i
$641$	−567299.			−1.38069			−0.690345	−	0.723480i	$-0.742541\pi$
$641$	−567299.			−1.38069			−0.690345	+	0.723480i	$0.742541\pi$
$642$	−25796.6	−	25796.6i	−0.0625882	−	0.0625882i
$643$	−210883.	+	210883.i	−0.510058	+	0.510058i	−0.914544	−	0.404486i	$-0.867450\pi$
$643$	−210883.	+	210883.i	−0.510058	+	0.510058i	0.404486	+	0.914544i	$0.367450\pi$
$644$	102823.	−	102823.i	0.247925	−	0.247925i
$645$	−1.11714e6			−2.68528
$646$	138548.	+	138548.i	0.331997	+	0.331997i
$647$	373004.	−	373004.i	0.891055	−	0.891055i	−0.103567	−	0.994622i	$-0.533026\pi$
$647$	373004.	−	373004.i	0.891055	−	0.891055i	0.994622	+	0.103567i	$0.0330257\pi$
$648$	172943.	+	172943.i	0.411863	+	0.411863i
$649$	−195161.	+	195161.i	−0.463344	+	0.463344i
$650$			6857.67i			0.0162312i
$651$	327331.	+	327331.i	0.772370	+	0.772370i
$652$	227984.	+	227984.i	0.536303	+	0.536303i
$653$	406883.	−	406883.i	0.954209	−	0.954209i	−0.0447872	−	0.998997i	$-0.514261\pi$
$653$	406883.	−	406883.i	0.954209	−	0.954209i	0.998997	+	0.0447872i	$0.0142610\pi$
$654$		−	651700.i		−	1.52367i
$655$	−286726.			−0.668320
$656$			40377.5i			0.0938279i
$657$		−	1.66464e6i		−	3.85646i
$658$	80867.3	−	80867.3i	0.186776	−	0.186776i
$659$			515331.i			1.18663i	0.804971	+	0.593315i	$0.202181\pi$
$659$			515331.i			1.18663i	−0.804971	+	0.593315i	$0.797819\pi$
$660$	−200818.	+	200818.i	−0.461014	+	0.461014i
$661$	−108672.	+	108672.i	−0.248723	+	0.248723i	−0.820447	−	0.571723i	$-0.806275\pi$
$661$	−108672.	+	108672.i	−0.248723	+	0.248723i	0.571723	+	0.820447i	$0.306275\pi$
$662$	416632.			0.950685
$663$	−331685.			−0.754568
$664$	136046.	+	136046.i	0.308567	+	0.308567i
$665$		−	106825.i		−	0.241563i
$666$	555560.	+	410386.i	1.25251	+	0.925218i
$667$	−892.062			−0.00200513
$668$	−270901.	+	270901.i	−0.607096	+	0.607096i
$669$		−	1.27308e6i		−	2.84448i
$670$		−	232720.i		−	0.518423i
$671$	392321.	+	392321.i	0.871358	+	0.871358i
$672$	−38603.8	−	38603.8i	−0.0854853	−	0.0854853i
$673$	538303.			1.18849			0.594247	−	0.804283i	$-0.297450\pi$
$673$	538303.			1.18849			0.594247	+	0.804283i	$0.297450\pi$
$674$	286942.	+	286942.i	0.631647	+	0.631647i
$675$	−54471.5			−0.119553
$676$	−189506.			−0.414696
$677$		−	79620.7i		−	0.173720i	−0.996221	−	0.0868598i	$-0.972317\pi$
$677$		−	79620.7i		−	0.173720i	0.996221	−	0.0868598i	$-0.0276832\pi$
$678$	−834913.			−1.81628
$679$	86586.1	+	86586.1i	0.187806	+	0.187806i
$680$	114688.	−	114688.i	0.248027	−	0.248027i
$681$	25785.7	−	25785.7i	0.0556012	−	0.0556012i
$682$	−393880.			−0.846829
$683$	76616.8	+	76616.8i	0.164241	+	0.164241i	0.784443	−	0.620201i	$-0.212949\pi$
$683$	76616.8	+	76616.8i	0.164241	+	0.164241i	−0.620201	+	0.784443i	$0.712949\pi$
$684$	236925.	−	236925.i	0.506406	−	0.506406i
$685$	−19609.0	−	19609.0i	−0.0417901	−	0.0417901i
$686$	−166714.	+	166714.i	−0.354262	+	0.354262i
$687$			640425.i			1.35692i
$688$	129206.	+	129206.i	0.272965	+	0.272965i
$689$	−168952.	−	168952.i	−0.355897	−	0.355897i
$690$	759597.	−	759597.i	1.59546	−	1.59546i
$691$			109656.i			0.229655i	0.993385	+	0.114827i	$0.0366315\pi$
$691$			109656.i			0.229655i	−0.993385	+	0.114827i	$0.963369\pi$
$692$	170457.			0.355961
$693$		−	303061.i		−	0.631051i
$694$		−	227525.i		−	0.472401i
$695$	434650.	−	434650.i	0.899849	−	0.899849i
$696$			334.914i			0.000691377i
$697$	131619.	−	131619.i	0.270927	−	0.270927i
$698$	188305.	−	188305.i	0.386501	−	0.386501i
$699$	−57745.9			−0.118186
$700$	5203.42			0.0106192
$701$	41649.9	+	41649.9i	0.0847574	+	0.0847574i	0.748214	−	0.663457i	$-0.230911\pi$
$701$	41649.9	+	41649.9i	0.0847574	+	0.0847574i	−0.663457	+	0.748214i	$0.730911\pi$
$702$			309639.i			0.628321i
$703$	190987.	−	258549.i	0.386450	−	0.523157i
$704$	46452.3			0.0937263
$705$	597399.	−	597399.i	1.20195	−	1.20195i
$706$		−	261627.i		−	0.524896i
$707$		−	225261.i		−	0.450659i
$708$	−277148.	−	277148.i	−0.552899	−	0.552899i
$709$	279963.	+	279963.i	0.556939	+	0.556939i	0.928435	−	0.371496i	$-0.121155\pi$
$709$	279963.	+	279963.i	0.556939	+	0.556939i	−0.371496	+	0.928435i	$0.621155\pi$
$710$	−146706.			−0.291026
$711$	−287931.	−	287931.i	−0.569573	−	0.569573i
$712$	195952.			0.386536
$713$	1.48986e6			2.93067
$714$			251674.i			0.493675i
$715$	−153868.			−0.300978
$716$	159742.	+	159742.i	0.311597	+	0.311597i
$717$	−485160.	+	485160.i	−0.943728	+	0.943728i
$718$	−196789.	+	196789.i	−0.381727	+	0.381727i
$719$	612341.			1.18450			0.592250	−	0.805754i	$-0.298240\pi$
$719$	612341.			1.18450			0.592250	+	0.805754i	$0.298240\pi$
$720$	−196123.	−	196123.i	−0.378324	−	0.378324i
$721$	118144.	−	118144.i	0.227269	−	0.227269i
$722$	150381.	+	150381.i	0.288482	+	0.288482i
$723$	1.02413e6	−	1.02413e6i	1.95919	−	1.95919i
$724$		−	331005.i		−	0.631478i
$725$	−22.5716	−	22.5716i	−4.29424e−5	−	4.29424e-5i
$726$	−206456.	−	206456.i	−0.391700	−	0.391700i
$727$	−238127.	+	238127.i	−0.450547	+	0.450547i	−0.895536	−	0.444989i	$-0.853208\pi$
$727$	−238127.	+	238127.i	−0.450547	+	0.450547i	0.444989	+	0.895536i	$0.353208\pi$
$728$		−	29578.4i		−	0.0558100i
$729$	117788.			0.221639
$730$			641281.i			1.20338i
$731$		−	842347.i		−	1.57636i
$732$	−557135.	+	557135.i	−1.03977	+	1.03977i
$733$		−	291296.i		−	0.542159i	−0.962557	−	0.271079i	$-0.912619\pi$
$733$		−	291296.i		−	0.542159i	0.962557	−	0.271079i	$-0.0873806\pi$
$734$	−385103.	+	385103.i	−0.714800	+	0.714800i
$735$	−567280.	+	567280.i	−1.05008	+	1.05008i
$736$	−175707.			−0.324364
$737$	−307257.			−0.565674
$738$	−225076.	−	225076.i	−0.413254	−	0.413254i
$739$			1.03614e6i			1.89727i	0.316370	+	0.948636i	$0.397536\pi$
$739$			1.03614e6i			1.89727i	−0.316370	+	0.948636i	$0.602464\pi$
$740$	−214023.	−	158096.i	−0.390838	−	0.288708i
$741$	263966.			0.480742
$742$	−128196.	+	128196.i	−0.232845	+	0.232845i
$743$		−	107255.i		−	0.194284i	−0.995271	−	0.0971422i	$-0.969030\pi$
$743$		−	107255.i		−	0.194284i	0.995271	−	0.0971422i	$-0.0309702\pi$
$744$		−	559350.i		−	1.01050i
$745$	485445.	+	485445.i	0.874637	+	0.874637i
$746$	116362.	+	116362.i	0.209091	+	0.209091i
$747$	−1.51672e6			−2.71809
$748$	−151421.	−	151421.i	−0.270634	−	0.270634i
$749$	−14997.6			−0.0267336
$750$	730136.			1.29802
$751$			349562.i			0.619790i	0.950771	+	0.309895i	$0.100294\pi$
$751$			349562.i			0.619790i	−0.950771	+	0.309895i	$0.899706\pi$
$752$	−138188.			−0.244362
$753$	390145.	+	390145.i	0.688076	+	0.688076i
$754$	−128.306	+	128.306i	−0.000225687	+	0.000225687i
$755$	163451.	−	163451.i	0.286743	−	0.286743i
$756$	234946.			0.411078
$757$	−247044.	−	247044.i	−0.431104	−	0.431104i	0.457900	−	0.889004i	$-0.348602\pi$
$757$	−247044.	−	247044.i	−0.431104	−	0.431104i	−0.889004	+	0.457900i	$0.848602\pi$
$758$	296911.	−	296911.i	0.516759	−	0.516759i
$759$	−1.00288e6	−	1.00288e6i	−1.74087	−	1.74087i
$760$	−91272.5	+	91272.5i	−0.158020	+	0.158020i
$761$		−	657307.i		−	1.13501i	−0.823371	−	0.567504i	$-0.807909\pi$
$761$		−	657307.i		−	1.13501i	0.823371	−	0.567504i	$-0.192091\pi$
$762$	−368623.	−	368623.i	−0.634852	−	0.634852i
$763$	−189442.	−	189442.i	−0.325407	−	0.325407i
$764$	−306071.	+	306071.i	−0.524367	+	0.524367i
$765$			1.27861e6i			2.18481i
$766$	7363.08			0.0125488
$767$		−	212353.i		−	0.360966i
$768$			65966.9i			0.111842i
$769$	128881.	−	128881.i	0.217940	−	0.217940i	−0.589690	−	0.807630i	$-0.700750\pi$
$769$	128881.	−	128881.i	0.217940	−	0.217940i	0.807630	+	0.589690i	$0.200750\pi$
$770$			116751.i			0.196915i
$771$	−1.03713e6	+	1.03713e6i	−1.74472	+	1.74472i
$772$	91065.9	−	91065.9i	0.152799	−	0.152799i
$773$	−385897.			−0.645821			−0.322910	−	0.946430i	$-0.604661\pi$
$773$	−385897.			−0.645821			−0.322910	+	0.946430i	$0.604661\pi$
$774$	−1.44047e6			−2.40448
$775$	37697.5	+	37697.5i	0.0627638	+	0.0627638i
$776$		−	147960.i		−	0.245709i
$777$	408294.	−	61363.5i	0.676287	−	0.101641i
$778$	−68802.3			−0.113669
$779$	−104747.	+	104747.i	−0.172610	+	0.172610i
$780$		−	218508.i		−	0.359151i
$781$			193694.i			0.317551i
$782$	572751.	+	572751.i	0.936596	+	0.936596i
$783$	−1019.16	−	1019.16i	−0.00166233	−	0.00166233i
$784$	131221.			0.213486
$785$	162034.	+	162034.i	0.262947	+	0.262947i
$786$	−537593.			−0.870179
$787$	899504.			1.45229			0.726145	−	0.687541i	$-0.241310\pi$
$787$	899504.			1.45229			0.726145	+	0.687541i	$0.241310\pi$
$788$		−	213066.i		−	0.343132i
$789$	893559.			1.43539
$790$	110922.	+	110922.i	0.177731	+	0.177731i
$791$	−242700.	+	242700.i	−0.387897	+	0.387897i
$792$	−258939.	+	258939.i	−0.412806	+	0.412806i
$793$	−426880.			−0.678828
$794$	−78486.5	−	78486.5i	−0.124496	−	0.124496i
$795$	−947036.	+	947036.i	−1.49842	+	1.49842i
$796$	−122203.	−	122203.i	−0.192866	−	0.192866i
$797$	−335054.	+	335054.i	−0.527470	+	0.527470i	−0.919817	−	0.392347i	$-0.871663\pi$
$797$	−335054.	+	335054.i	−0.527470	+	0.527470i	0.392347	+	0.919817i	$0.371663\pi$
$798$		−	200291.i		−	0.314525i
$799$	450451.	+	450451.i	0.705592	+	0.705592i
$800$	−4445.85	−	4445.85i	−0.00694665	−	0.00694665i
$801$	−1.09230e6	+	1.09230e6i	−1.70245	+	1.70245i
$802$		−	481801.i		−	0.749064i
$803$	846674.			1.31306
$804$		−	436335.i		−	0.675007i
$805$		−	441612.i		−	0.681474i
$806$	214288.	−	214288.i	0.329859	−	0.329859i
$807$		−	1.34968e6i		−	2.07245i
$808$	−192465.	+	192465.i	−0.294802	+	0.294802i
$809$	−222333.	+	222333.i	−0.339709	+	0.339709i	−0.856258	−	0.516549i	$-0.827216\pi$
$809$	−222333.	+	222333.i	−0.339709	+	0.339709i	0.516549	+	0.856258i	$0.327216\pi$
$810$	742766.			1.13209
$811$	595816.			0.905879			0.452940	−	0.891541i	$-0.350375\pi$
$811$	595816.			0.905879			0.452940	+	0.891541i	$0.350375\pi$
$812$	97.3556	+	97.3556i	0.000147655	+	0.000147655i
$813$			453392.i			0.685950i
$814$	−208732.	+	282571.i	−0.315022	+	0.426461i
$815$	979161.			1.47414
$816$	215032.	−	215032.i	0.322941	−	0.322941i
$817$			670369.i			1.00432i
$818$			377895.i			0.564761i
$819$	164879.	+	164879.i	0.245809	+	0.245809i
$820$	86707.9	+	86707.9i	0.128953	+	0.128953i
$821$	−331895.			−0.492397			−0.246198	−	0.969219i	$-0.579181\pi$
$821$	−331895.			−0.492397			−0.246198	+	0.969219i	$0.579181\pi$
$822$	−36765.6	−	36765.6i	−0.0544124	−	0.0544124i
$823$	91339.3			0.134852			0.0674261	−	0.997724i	$-0.478521\pi$
$823$	91339.3			0.134852			0.0674261	+	0.997724i	$0.478521\pi$
$824$	−201886.			−0.297339
$825$		−	50751.4i		−	0.0745659i
$826$	−161128.			−0.236162
$827$	−395246.	−	395246.i	−0.577906	−	0.577906i	0.356420	−	0.934326i	$-0.383997\pi$
$827$	−395246.	−	395246.i	−0.577906	−	0.577906i	−0.934326	+	0.356420i	$0.883997\pi$
$828$	979440.	−	979440.i	1.42862	−	1.42862i
$829$	−388657.	+	388657.i	−0.565532	+	0.565532i	−0.930874	−	0.365341i	$-0.880952\pi$
$829$	−388657.	+	388657.i	−0.565532	+	0.565532i	0.365341	+	0.930874i	$0.380952\pi$
$830$	584299.			0.848162
$831$	510073.	+	510073.i	0.738635	+	0.738635i
$832$	−25272.1	+	25272.1i	−0.0365085	+	0.0365085i
$833$	−427740.	−	427740.i	−0.616439	−	0.616439i
$834$	814941.	−	814941.i	1.17164	−	1.17164i
$835$			1.16348e6i			1.66873i
$836$	120506.	+	120506.i	0.172423	+	0.172423i
$837$	1.70213e6	+	1.70213e6i	2.42963	+	2.42963i
$838$	−599471.	+	599471.i	−0.853651	+	0.853651i
$839$		−	8143.99i		−	0.0115695i	−0.999983	−	0.00578473i	$-0.998159\pi$
$839$		−	8143.99i		−	0.0115695i	0.999983	−	0.00578473i	$-0.00184135\pi$
$840$	−165798.			−0.234974
$841$			707280.i			0.999999i
$842$		−	19928.0i		−	0.0281087i
$843$	85330.4	−	85330.4i	0.120074	−	0.120074i
$844$			319600.i			0.448665i
$845$	−406951.	+	406951.i	−0.569940	+	0.569940i
$846$	770298.	−	770298.i	1.07626	−	1.07626i
$847$	−120029.			−0.167308
$848$	219064.			0.304635
$849$	1.09192e6	+	1.09192e6i	1.51486	+	1.51486i
$850$			28984.3i			0.0401167i
$851$	789533.	−	1.06883e6i	1.09021	−	1.47588i
$852$	−275065.			−0.378928
$853$	−285421.	+	285421.i	−0.392273	+	0.392273i	−0.875497	−	0.483224i	$-0.839466\pi$
$853$	−285421.	+	285421.i	−0.392273	+	0.392273i	0.483224	+	0.875497i	$0.339466\pi$
$854$			323906.i			0.444123i
$855$		−	1.01756e6i		−	1.39196i
$856$	12814.1	+	12814.1i	0.0174880	+	0.0174880i
$857$	−774922.	−	774922.i	−1.05511	−	1.05511i	−0.998390	−	0.0567159i	$-0.981937\pi$
$857$	−774922.	−	774922.i	−1.05511	−	1.05511i	−0.0567159	−	0.998390i	$-0.518063\pi$
$858$	−288492.			−0.391886
$859$	−966818.	−	966818.i	−1.31026	−	1.31026i	−0.921220	−	0.389042i	$-0.872806\pi$
$859$	−966818.	−	966818.i	−1.31026	−	1.31026i	−0.389042	−	0.921220i	$-0.627194\pi$
$860$	554923.			0.750301
$861$	−190274.			−0.256669
$862$		−	400337.i		−	0.538780i
$863$	−861441.			−1.15666			−0.578328	−	0.815804i	$-0.696295\pi$
$863$	−861441.			−1.15666			−0.578328	+	0.815804i	$0.696295\pi$
$864$	−200740.	−	200740.i	−0.268910	−	0.268910i
$865$	366045.	−	366045.i	0.489218	−	0.489218i
$866$	−391478.	+	391478.i	−0.522001	+	0.522001i
$867$	−56761.5			−0.0755120
$868$	−162597.	−	162597.i	−0.215810	−	0.215810i
$869$	146449.	−	146449.i	0.193930	−	0.193930i
$870$	719.204	+	719.204i	0.000950197	+	0.000950197i
$871$	167161.	−	167161.i	0.220343	−	0.220343i
$872$			323721.i			0.425734i
$873$	824772.	+	824772.i	1.08219	+	1.08219i
$874$	−455815.	−	455815.i	−0.596714	−	0.596714i
$875$	212242.	−	212242.i	0.277214	−	0.277214i
$876$			1.20236e6i			1.56685i
$877$	686259.			0.892254			0.446127	−	0.894970i	$-0.352803\pi$
$877$	686259.			0.892254			0.446127	+	0.894970i	$0.352803\pi$
$878$		−	435464.i		−	0.564890i
$879$		−	78579.1i		−	0.101702i
$880$	99753.0	−	99753.0i	0.128813	−	0.128813i
$881$			697855.i			0.899112i	0.893252	+	0.449556i	$0.148418\pi$
$881$			697855.i			0.899112i	−0.893252	+	0.449556i	$0.851582\pi$
$882$	−731463.	+	731463.i	−0.940275	+	0.940275i
$883$	31922.4	−	31922.4i	0.0409424	−	0.0409424i	−0.686339	−	0.727282i	$-0.740783\pi$
$883$	31922.4	−	31922.4i	0.0409424	−	0.0409424i	0.727282	+	0.686339i	$0.240783\pi$
$884$	164759.			0.210836
$885$	−1.19031e6			−1.51976
$886$	−341867.	−	341867.i	−0.435502	−	0.435502i
$887$		−	1.16507e6i		−	1.48082i	−0.672154	−	0.740411i	$-0.734631\pi$
$887$		−	1.16507e6i		−	1.48082i	0.672154	−	0.740411i	$-0.265369\pi$
$888$	−401280.	−	296421.i	−0.508887	−	0.375909i
$889$	−214309.			−0.271167
$890$	420794.	−	420794.i	0.531239	−	0.531239i
$891$		−	980663.i		−	1.23528i
$892$			632382.i			0.794785i
$893$	−358484.	−	358484.i	−0.449539	−	0.449539i
$894$	910180.	+	910180.i	1.13881	+	1.13881i
$895$	686070.			0.856490
$896$	19175.8	+	19175.8i	0.0238857	+	0.0238857i
$897$	1.09123e6			1.35622
$898$	289839.			0.359421
$899$			1410.63i			0.00174540i
$900$	49565.0			0.0611914
$901$	−714084.	−	714084.i	−0.879629	−	0.879629i
$902$	114479.	−	114479.i	0.140706	−	0.140706i
$903$	−608868.	+	608868.i	−0.746703	+	0.746703i
$904$	414730.			0.507491
$905$	−710811.	−	710811.i	−0.867875	−	0.867875i
$906$	306460.	−	306460.i	0.373351	−	0.373351i
$907$	117022.	+	117022.i	0.142251	+	0.142251i	0.774646	−	0.632395i	$-0.217928\pi$
$907$	117022.	+	117022.i	0.142251	+	0.142251i	−0.632395	+	0.774646i	$0.717928\pi$
$908$	−12808.6	+	12808.6i	−0.0155357	+	0.0155357i
$909$		−	2.14572e6i		−	2.59684i
$910$	−63517.6	−	63517.6i	−0.0767029	−	0.0767029i
$911$	−773469.	−	773469.i	−0.931979	−	0.931979i	0.0658502	−	0.997830i	$-0.479024\pi$
$911$	−773469.	−	773469.i	−0.931979	−	0.931979i	−0.997830	+	0.0658502i	$0.979024\pi$
$912$	−171130.	+	171130.i	−0.205749	+	0.205749i
$913$		−	771441.i		−	0.925467i
$914$	−953333.			−1.14117
$915$			2.39282e6i			2.85804i
$916$		−	318121.i		−	0.379142i
$917$	−156272.	+	156272.i	−0.185842	+	0.185842i
$918$			1.30871e6i			1.55295i
$919$	139945.	−	139945.i	0.165702	−	0.165702i	−0.619385	−	0.785087i	$-0.712618\pi$
$919$	139945.	−	139945.i	0.165702	−	0.165702i	0.785087	+	0.619385i	$0.212618\pi$
$920$	−377318.	+	377318.i	−0.445791	+	0.445791i
$921$	−1.01506e6			−1.19666
$922$	140949.			0.165806
$923$	−105378.	−	105378.i	−0.123694	−	0.123694i
$924$			218901.i			0.256391i
$925$	47021.7	−	7067.01i	0.0549560	−	0.00825947i
$926$	−747608.			−0.871870
$927$	1.12537e6	−	1.12537e6i	1.30960	−	1.30960i
$928$		−	166.363i		−	0.000193180i
$929$			306950.i			0.355661i	0.984061	+	0.177830i	$0.0569079\pi$
$929$			306950.i			0.355661i	−0.984061	+	0.177830i	$0.943092\pi$
$930$	−1.20117e6	−	1.20117e6i	−1.38879	−	1.38879i
$931$	340411.	+	340411.i	0.392739	+	0.392739i
$932$	28684.3			0.0330227
$933$	1.09087e6	+	1.09087e6i	1.25317	+	1.25317i
$934$	−827479.			−0.948556
$935$	−650330.			−0.743894
$936$		−	281748.i		−	0.321595i
$937$	675441.			0.769322			0.384661	−	0.923058i	$-0.374318\pi$
$937$	675441.			0.769322			0.384661	+	0.923058i	$0.374318\pi$
$938$	−126838.	−	126838.i	−0.144159	−	0.144159i
$939$	1.52452e6	−	1.52452e6i	1.72903	−	1.72903i
$940$	−296748.	+	296748.i	−0.335840	+	0.335840i
$941$	−491879.			−0.555494			−0.277747	−	0.960654i	$-0.589588\pi$
$941$	−491879.			−0.555494			−0.277747	+	0.960654i	$0.589588\pi$
$942$	303804.	+	303804.i	0.342367	+	0.342367i
$943$	−433019.	+	433019.i	−0.486950	+	0.486950i
$944$	137669.	+	137669.i	0.154487	+	0.154487i
$945$	504531.	−	504531.i	0.564968	−	0.564968i
$946$		−	732656.i		−	0.818687i
$947$	608349.	+	608349.i	0.678348	+	0.678348i	0.959626	−	0.281278i	$-0.0907583\pi$
$947$	608349.	+	608349.i	0.678348	+	0.678348i	−0.281278	+	0.959626i	$0.590758\pi$
$948$	207972.	+	207972.i	0.231413	+	0.231413i
$949$	−460628.	+	460628.i	−0.511468	+	0.511468i
$950$		−	23066.7i		−	0.0255587i
$951$	−1.98227e6			−2.19180
$952$		−	125015.i		−	0.137939i
$953$		−	801066.i		−	0.882028i	−0.897500	−	0.441014i	$-0.854619\pi$
$953$		−	801066.i		−	0.882028i	0.897500	−	0.441014i	$-0.145381\pi$
$954$	−1.22113e6	+	1.22113e6i	−1.34173	+	1.34173i
$955$			1.31453e6i			1.44133i
$956$	240996.	−	240996.i	0.263690	−	0.263690i
$957$	949.555	−	949.555i	0.00103680	−	0.00103680i
$958$	899354.			0.979940
$959$	−21374.7			−0.0232414
$960$	141659.	+	141659.i	0.153710	+	0.153710i
$961$		−	1.43242e6i		−	1.55104i
$962$	−40171.8	−	267291.i	−0.0434082	−	0.288825i
$963$	−142859.			−0.154047
$964$	−508719.	+	508719.i	−0.547424	+	0.547424i
$965$		−	391116.i		−	0.420001i
$966$		−	827995.i		−	0.887307i
$967$	−425109.	−	425109.i	−0.454619	−	0.454619i	0.442265	−	0.896884i	$-0.354175\pi$
$967$	−425109.	−	425109.i	−0.454619	−	0.454619i	−0.896884	+	0.442265i	$0.854175\pi$
$968$	102554.	+	102554.i	0.109446	+	0.109446i
$969$	1.11567e6			1.18819
$970$	−317734.	−	317734.i	−0.337691	−	0.337691i
$971$	44378.3			0.0470687			0.0235344	−	0.999723i	$-0.492508\pi$
$971$	44378.3			0.0470687			0.0235344	+	0.999723i	$0.492508\pi$
$972$	376393.			0.398391
$973$		−	473788.i		−	0.500447i
$974$	793510.			0.836440
$975$	27611.0	+	27611.0i	0.0290451	+	0.0290451i
$976$	276748.	−	276748.i	0.290526	−	0.290526i
$977$	381699.	−	381699.i	0.399882	−	0.399882i	−0.478309	−	0.878191i	$-0.658750\pi$
$977$	381699.	−	381699.i	0.399882	−	0.399882i	0.878191	+	0.478309i	$0.158750\pi$
$978$	1.83587e6			1.91939
$979$	−555568.	−	555568.i	−0.579658	−	0.579658i
$980$	281787.	−	281787.i	0.293406	−	0.293406i
$981$	−1.80452e6	−	1.80452e6i	−1.87510	−	1.87510i
$982$	607343.	−	607343.i	0.629812	−	0.629812i
$983$			1.43590e6i			1.48599i	0.669294	+	0.742997i	$0.266597\pi$
$983$			1.43590e6i			1.48599i	−0.669294	+	0.742997i	$0.733403\pi$
$984$	162572.	+	162572.i	0.167902	+	0.167902i
$985$	−457544.	−	457544.i	−0.471586	−	0.471586i
$986$	−542.294	+	542.294i	−0.000557804	+	0.000557804i
$987$		−	651192.i		−	0.668459i
$988$	−131121.			−0.134325
$989$			2.77128e6i			2.83327i
$990$			1.11211e6i			1.13469i
$991$	678137.	−	678137.i	0.690510	−	0.690510i	−0.271834	−	0.962344i	$-0.587630\pi$
$991$	678137.	−	678137.i	0.690510	−	0.690510i	0.962344	+	0.271834i	$0.0876301\pi$
$992$			277848.i			0.282348i
$993$	1.67749e6	−	1.67749e6i	1.70122	−	1.70122i
$994$	−79958.2	+	79958.2i	−0.0809264	+	0.0809264i
$995$	−524845.			−0.530133
$996$	1.09552e6			1.10434
$997$	−51948.2	−	51948.2i	−0.0522613	−	0.0522613i	0.680493	−	0.732754i	$-0.261766\pi$
$997$	−51948.2	−	51948.2i	−0.0522613	−	0.0522613i	−0.732754	+	0.680493i	$0.761766\pi$
$998$		−	526742.i		−	0.528855i
$999$	2.12313e6	−	319091.i	2.12739	−	0.319730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.43.7	yes	14
37.31	odd	4	inner	74.5.d.a.31.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.1	✓	14	37.31	odd	4	inner
74.5.d.a.43.7	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +16.1052i q^{3} -8.00000i q^{4} +(-17.1794 - 17.1794i) q^{5} +(-32.2104 - 32.2104i) q^{6} -18.7264 q^{7} +(16.0000 + 16.0000i) q^{8} -178.377 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} +16.1052i q^{3} -8.00000i q^{4} +(-17.1794 - 17.1794i) q^{5} +(-32.2104 - 32.2104i) q^{6} -18.7264 q^{7} +(16.0000 + 16.0000i) q^{8} -178.377 q^{9} +68.7178 q^{10} -90.7271i q^{11} +128.842 q^{12} +(49.3596 + 49.3596i) q^{13} +(37.4528 - 37.4528i) q^{14} +(276.678 - 276.678i) q^{15} -64.0000 q^{16} +(208.621 + 208.621i) q^{17} +(356.755 - 356.755i) q^{18} +(-166.028 - 166.028i) q^{19} +(-137.436 + 137.436i) q^{20} -301.592i q^{21} +(181.454 + 181.454i) q^{22} +(-686.354 - 686.354i) q^{23} +(-257.683 + 257.683i) q^{24} -34.7332i q^{25} -197.438 q^{26} -1568.28i q^{27} +149.811i q^{28} +(0.649856 - 0.649856i) q^{29} +1106.71i q^{30} +(-1085.34 + 1085.34i) q^{31} +(128.000 - 128.000i) q^{32} +1461.18 q^{33} -834.484 q^{34} +(321.709 + 321.709i) q^{35} +1427.02i q^{36} +(203.465 + 1353.80i) q^{37} +664.111 q^{38} +(-794.945 + 794.945i) q^{39} -549.742i q^{40} -630.898i q^{41} +(603.184 + 603.184i) q^{42} +(-2018.85 - 2018.85i) q^{43} -725.817 q^{44} +(3064.43 + 3064.43i) q^{45} +2745.41 q^{46} +2159.18 q^{47} -1030.73i q^{48} -2050.32 q^{49} +(69.4665 + 69.4665i) q^{50} +(-3359.88 + 3359.88i) q^{51} +(394.876 - 394.876i) q^{52} -3422.88 q^{53} +(3136.57 + 3136.57i) q^{54} +(-1558.64 + 1558.64i) q^{55} +(-299.622 - 299.622i) q^{56} +(2673.91 - 2673.91i) q^{57} +2.59942i q^{58} +(-2151.08 - 2151.08i) q^{59} +(-2213.43 - 2213.43i) q^{60} +(-4324.19 + 4324.19i) q^{61} -4341.38i q^{62} +3340.36 q^{63} +512.000i q^{64} -1695.94i q^{65} +(-2922.36 + 2922.36i) q^{66} -3386.60i q^{67} +(1668.97 - 1668.97i) q^{68} +(11053.9 - 11053.9i) q^{69} -1286.84 q^{70} -2134.91 q^{71} +(-2854.04 - 2854.04i) q^{72} +9332.10i q^{73} +(-3114.52 - 2300.66i) q^{74} +559.386 q^{75} +(-1328.22 + 1328.22i) q^{76} +1698.99i q^{77} -3179.78i q^{78} +(1614.17 + 1614.17i) q^{79} +(1099.48 + 1099.48i) q^{80} +10808.9 q^{81} +(1261.80 + 1261.80i) q^{82} +8502.87 q^{83} -2412.74 q^{84} -7167.99i q^{85} +8075.38 q^{86} +(10.4661 + 10.4661i) q^{87} +(1451.63 - 1451.63i) q^{88} +(6123.51 - 6123.51i) q^{89} -12257.7 q^{90} +(-924.326 - 924.326i) q^{91} +(-5490.83 + 5490.83i) q^{92} +(-17479.7 - 17479.7i) q^{93} +(-4318.36 + 4318.36i) q^{94} +5704.53i q^{95} +(2061.47 + 2061.47i) q^{96} +(-4623.75 - 4623.75i) q^{97} +(4100.65 - 4100.65i) q^{98} +16183.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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