LMFDB - Embedded newform 74.5.d.b.31.1

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} + 207381 x^{10} + 29788577 x^{8} + 2302194203 x^{6} + 92916575085 x^{4} + \cdots + 6531254919424 $ x^14 + 727x^12 + 207381x^10 + 29788577x^8 + 2302194203x^6 + 92916575085x^4 + 1658451585508x^2 + 6531254919424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$-14.0933i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.b.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} -15.0933i q^{3} +8.00000i q^{4} +(30.6150 - 30.6150i) q^{5} +(30.1866 - 30.1866i) q^{6} -89.3132 q^{7} +(-16.0000 + 16.0000i) q^{8} -146.808 q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} -15.0933i q^{3} +8.00000i q^{4} +(30.6150 - 30.6150i) q^{5} +(30.1866 - 30.1866i) q^{6} -89.3132 q^{7} +(-16.0000 + 16.0000i) q^{8} -146.808 q^{9} +122.460 q^{10} +96.8983i q^{11} +120.746 q^{12} +(78.2564 - 78.2564i) q^{13} +(-178.626 - 178.626i) q^{14} +(-462.081 - 462.081i) q^{15} -64.0000 q^{16} +(79.3162 - 79.3162i) q^{17} +(-293.615 - 293.615i) q^{18} +(438.875 - 438.875i) q^{19} +(244.920 + 244.920i) q^{20} +1348.03i q^{21} +(-193.797 + 193.797i) q^{22} +(52.6127 - 52.6127i) q^{23} +(241.493 + 241.493i) q^{24} -1249.56i q^{25} +313.026 q^{26} +993.252i q^{27} -714.506i q^{28} +(631.285 + 631.285i) q^{29} -1848.32i q^{30} +(225.982 + 225.982i) q^{31} +(-128.000 - 128.000i) q^{32} +1462.51 q^{33} +317.265 q^{34} +(-2734.32 + 2734.32i) q^{35} -1174.46i q^{36} +(498.919 - 1274.85i) q^{37} +1755.50 q^{38} +(-1181.15 - 1181.15i) q^{39} +979.680i q^{40} +39.5488i q^{41} +(-2696.06 + 2696.06i) q^{42} +(-1195.80 + 1195.80i) q^{43} -775.186 q^{44} +(-4494.51 + 4494.51i) q^{45} +210.451 q^{46} -411.809 q^{47} +965.971i q^{48} +5575.85 q^{49} +(2499.11 - 2499.11i) q^{50} +(-1197.14 - 1197.14i) q^{51} +(626.051 + 626.051i) q^{52} +3846.90 q^{53} +(-1986.50 + 1986.50i) q^{54} +(2966.54 + 2966.54i) q^{55} +(1429.01 - 1429.01i) q^{56} +(-6624.07 - 6624.07i) q^{57} +2525.14i q^{58} +(-854.905 + 854.905i) q^{59} +(3696.65 - 3696.65i) q^{60} +(-730.406 - 730.406i) q^{61} +903.929i q^{62} +13111.9 q^{63} -512.000i q^{64} -4791.64i q^{65} +(2925.03 + 2925.03i) q^{66} +634.712i q^{67} +(634.530 + 634.530i) q^{68} +(-794.099 - 794.099i) q^{69} -10937.3 q^{70} +1014.74 q^{71} +(2348.92 - 2348.92i) q^{72} +5160.63i q^{73} +(3547.54 - 1551.86i) q^{74} -18859.9 q^{75} +(3511.00 + 3511.00i) q^{76} -8654.30i q^{77} -4724.59i q^{78} +(-6528.32 + 6528.32i) q^{79} +(-1959.36 + 1959.36i) q^{80} +3100.04 q^{81} +(-79.0976 + 79.0976i) q^{82} +3911.48 q^{83} -10784.2 q^{84} -4856.53i q^{85} -4783.20 q^{86} +(9528.17 - 9528.17i) q^{87} +(-1550.37 - 1550.37i) q^{88} +(1620.63 + 1620.63i) q^{89} -17978.1 q^{90} +(-6989.33 + 6989.33i) q^{91} +(420.902 + 420.902i) q^{92} +(3410.82 - 3410.82i) q^{93} +(-823.618 - 823.618i) q^{94} -26872.3i q^{95} +(-1931.94 + 1931.94i) q^{96} +(6801.01 - 6801.01i) q^{97} +(11151.7 + 11151.7i) q^{98} -14225.4i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$		−	15.0933i		−	1.67703i	−0.544876	−	0.838516i	$-0.683423\pi$
$3$		−	15.0933i		−	1.67703i	0.544876	−	0.838516i	$-0.316577\pi$
$4$			8.00000i			0.500000i
$5$	30.6150	−	30.6150i	1.22460	−	1.22460i	0.258621	−	0.965979i	$-0.416732\pi$
$5$	30.6150	−	30.6150i	1.22460	−	1.22460i	0.965979	−	0.258621i	$-0.0832681\pi$
$6$	30.1866	−	30.1866i	0.838516	−	0.838516i
$7$	−89.3132			−1.82272			−0.911359	−	0.411612i	$-0.864966\pi$
$7$	−89.3132			−1.82272			−0.911359	+	0.411612i	$0.864966\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	−146.808			−1.81244
$10$	122.460			1.22460
$11$			96.8983i			0.800812i	0.916338	+	0.400406i	$0.131131\pi$
$11$			96.8983i			0.800812i	−0.916338	+	0.400406i	$0.868869\pi$
$12$	120.746			0.838516
$13$	78.2564	−	78.2564i	0.463056	−	0.463056i	−0.436600	−	0.899656i	$-0.643817\pi$
$13$	78.2564	−	78.2564i	0.463056	−	0.463056i	0.899656	+	0.436600i	$0.143817\pi$
$14$	−178.626	−	178.626i	−0.911359	−	0.911359i
$15$	−462.081	−	462.081i	−2.05369	−	2.05369i
$16$	−64.0000			−0.250000
$17$	79.3162	−	79.3162i	0.274450	−	0.274450i	−0.556438	−	0.830889i	$-0.687832\pi$
$17$	79.3162	−	79.3162i	0.274450	−	0.274450i	0.830889	+	0.556438i	$0.187832\pi$
$18$	−293.615	−	293.615i	−0.906219	−	0.906219i
$19$	438.875	−	438.875i	1.21572	−	1.21572i	0.246603	−	0.969117i	$-0.420686\pi$
$19$	438.875	−	438.875i	1.21572	−	1.21572i	0.969117	−	0.246603i	$-0.0793145\pi$
$20$	244.920	+	244.920i	0.612300	+	0.612300i
$21$			1348.03i			3.05676i
$22$	−193.797	+	193.797i	−0.400406	+	0.400406i
$23$	52.6127	−	52.6127i	0.0994569	−	0.0994569i	−0.655628	−	0.755084i	$-0.727596\pi$
$23$	52.6127	−	52.6127i	0.0994569	−	0.0994569i	0.755084	+	0.655628i	$0.227596\pi$
$24$	241.493	+	241.493i	0.419258	+	0.419258i
$25$		−	1249.56i		−	1.99929i
$26$	313.026			0.463056
$27$			993.252i			1.36249i
$28$		−	714.506i		−	0.911359i
$29$	631.285	+	631.285i	0.750636	+	0.750636i	0.974598	−	0.223962i	$-0.0718991\pi$
$29$	631.285	+	631.285i	0.750636	+	0.750636i	−0.223962	+	0.974598i	$0.571899\pi$
$30$		−	1848.32i		−	2.05369i
$31$	225.982	+	225.982i	0.235153	+	0.235153i	0.814840	−	0.579686i	$-0.196825\pi$
$31$	225.982	+	225.982i	0.235153	+	0.235153i	−0.579686	+	0.814840i	$0.696825\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	1462.51			1.34299
$34$	317.265			0.274450
$35$	−2734.32	+	2734.32i	−2.23210	+	2.23210i
$36$		−	1174.46i		−	0.906219i
$37$	498.919	−	1274.85i	0.364440	−	0.931227i
$37$	498.919	−	1274.85i	0.364440	−	0.931227i
$38$	1755.50			1.21572
$39$	−1181.15	−	1181.15i	−0.776560	−	0.776560i
$40$			979.680i			0.612300i
$41$			39.5488i			0.0235269i	0.999931	+	0.0117635i	$0.00374452\pi$
$41$			39.5488i			0.0235269i	−0.999931	+	0.0117635i	$0.996255\pi$
$42$	−2696.06	+	2696.06i	−1.52838	+	1.52838i
$43$	−1195.80	+	1195.80i	−0.646728	+	0.646728i	−0.952201	−	0.305473i	$-0.901186\pi$
$43$	−1195.80	+	1195.80i	−0.646728	+	0.646728i	0.305473	+	0.952201i	$0.401186\pi$
$44$	−775.186			−0.400406
$45$	−4494.51	+	4494.51i	−2.21951	+	2.21951i
$46$	210.451			0.0994569
$47$	−411.809			−0.186423			−0.0932116	−	0.995646i	$-0.529713\pi$
$47$	−411.809			−0.186423			−0.0932116	+	0.995646i	$0.529713\pi$
$48$			965.971i			0.419258i
$49$	5575.85			2.32230
$50$	2499.11	−	2499.11i	0.999645	−	0.999645i
$51$	−1197.14	−	1197.14i	−0.460262	−	0.460262i
$52$	626.051	+	626.051i	0.231528	+	0.231528i
$53$	3846.90			1.36949			0.684745	−	0.728782i	$-0.259913\pi$
$53$	3846.90			1.36949			0.684745	+	0.728782i	$0.259913\pi$
$54$	−1986.50	+	1986.50i	−0.681243	+	0.681243i
$55$	2966.54	+	2966.54i	0.980675	+	0.980675i
$56$	1429.01	−	1429.01i	0.455680	−	0.455680i
$57$	−6624.07	−	6624.07i	−2.03880	−	2.03880i
$58$			2525.14i			0.750636i
$59$	−854.905	+	854.905i	−0.245592	+	0.245592i	−0.819159	−	0.573567i	$-0.805559\pi$
$59$	−854.905	+	854.905i	−0.245592	+	0.245592i	0.573567	+	0.819159i	$0.305559\pi$
$60$	3696.65	−	3696.65i	1.02685	−	1.02685i
$61$	−730.406	−	730.406i	−0.196293	−	0.196293i	0.602116	−	0.798409i	$-0.294325\pi$
$61$	−730.406	−	730.406i	−0.196293	−	0.196293i	−0.798409	+	0.602116i	$0.794325\pi$
$62$			903.929i			0.235153i
$63$	13111.9			3.30357
$64$		−	512.000i		−	0.125000i
$65$		−	4791.64i		−	1.13412i
$66$	2925.03	+	2925.03i	0.671494	+	0.671494i
$67$			634.712i			0.141393i	0.997498	+	0.0706963i	$0.0225221\pi$
$67$			634.712i			0.141393i	−0.997498	+	0.0706963i	$0.977478\pi$
$68$	634.530	+	634.530i	0.137225	+	0.137225i
$69$	−794.099	−	794.099i	−0.166793	−	0.166793i
$70$	−10937.3			−2.23210
$71$	1014.74			0.201298			0.100649	−	0.994922i	$-0.467908\pi$
$71$	1014.74			0.201298			0.100649	+	0.994922i	$0.467908\pi$
$72$	2348.92	−	2348.92i	0.453110	−	0.453110i
$73$			5160.63i			0.968405i	0.874956	+	0.484203i	$0.160890\pi$
$73$			5160.63i			0.968405i	−0.874956	+	0.484203i	$0.839110\pi$
$74$	3547.54	−	1551.86i	0.647834	−	0.283393i
$75$	−18859.9			−3.35288
$76$	3511.00	+	3511.00i	0.607860	+	0.607860i
$77$		−	8654.30i		−	1.45966i
$78$		−	4724.59i		−	0.776560i
$79$	−6528.32	+	6528.32i	−1.04604	+	1.04604i	−0.0471490	+	0.998888i	$0.515014\pi$
$79$	−6528.32	+	6528.32i	−1.04604	+	1.04604i	−0.998888	+	0.0471490i	$0.984986\pi$
$80$	−1959.36	+	1959.36i	−0.306150	+	0.306150i
$81$	3100.04			0.472495
$82$	−79.0976	+	79.0976i	−0.0117635	+	0.0117635i
$83$	3911.48			0.567787			0.283893	−	0.958856i	$-0.408374\pi$
$83$	3911.48			0.567787			0.283893	+	0.958856i	$0.408374\pi$
$84$	−10784.2			−1.52838
$85$		−	4856.53i		−	0.672184i
$86$	−4783.20			−0.646728
$87$	9528.17	−	9528.17i	1.25884	−	1.25884i
$88$	−1550.37	−	1550.37i	−0.200203	−	0.200203i
$89$	1620.63	+	1620.63i	0.204599	+	0.204599i	0.801967	−	0.597368i	$-0.203787\pi$
$89$	1620.63	+	1620.63i	0.204599	+	0.204599i	−0.597368	+	0.801967i	$0.703787\pi$
$90$	−17978.1			−2.21951
$91$	−6989.33	+	6989.33i	−0.844020	+	0.844020i
$92$	420.902	+	420.902i	0.0497285	+	0.0497285i
$93$	3410.82	−	3410.82i	0.394359	−	0.394359i
$94$	−823.618	−	823.618i	−0.0932116	−	0.0932116i
$95$		−	26872.3i		−	2.97754i
$96$	−1931.94	+	1931.94i	−0.209629	+	0.209629i
$97$	6801.01	−	6801.01i	0.722819	−	0.722819i	−0.246359	−	0.969179i	$-0.579234\pi$
$97$	6801.01	−	6801.01i	0.722819	−	0.722819i	0.969179	+	0.246359i	$0.0792343\pi$
$98$	11151.7	+	11151.7i	1.16115	+	1.16115i
$99$		−	14225.4i		−	1.45142i
$100$	9996.45			0.999645
$101$			14647.0i			1.43584i	0.696127	+	0.717919i	$0.254905\pi$
$101$			14647.0i			1.43584i	−0.696127	+	0.717919i	$0.745095\pi$
$102$		−	4788.57i		−	0.460262i
$103$	−8997.68	−	8997.68i	−0.848117	−	0.848117i	0.141781	−	0.989898i	$-0.454717\pi$
$103$	−8997.68	−	8997.68i	−0.848117	−	0.848117i	−0.989898	+	0.141781i	$0.954717\pi$
$104$			2504.21i			0.231528i
$105$	41270.0	+	41270.0i	3.74331	+	3.74331i
$106$	7693.80	+	7693.80i	0.684745	+	0.684745i
$107$	10434.2			0.911360			0.455680	−	0.890144i	$-0.349396\pi$
$107$	10434.2			0.911360			0.455680	+	0.890144i	$0.349396\pi$
$108$	−7946.02			−0.681243
$109$	−1610.88	+	1610.88i	−0.135585	+	0.135585i	−0.771642	−	0.636057i	$-0.780564\pi$
$109$	−1610.88	+	1610.88i	−0.135585	+	0.135585i	0.636057	+	0.771642i	$0.280564\pi$
$110$			11866.2i			0.980675i
$111$	−19241.7	−	7530.33i	−1.56170	−	0.611178i
$112$	5716.04			0.455680
$113$	−2520.71	−	2520.71i	−0.197409	−	0.197409i	0.601480	−	0.798888i	$-0.294578\pi$
$113$	−2520.71	−	2520.71i	−0.197409	−	0.197409i	−0.798888	+	0.601480i	$0.794578\pi$
$114$		−	26496.3i		−	2.03880i
$115$		−	3221.48i		−	0.243590i
$116$	−5050.28	+	5050.28i	−0.375318	+	0.375318i
$117$	−11488.6	+	11488.6i	−0.839260	+	0.839260i
$118$	−3419.62			−0.245592
$119$	−7083.98	+	7083.98i	−0.500246	+	0.500246i
$120$	14786.6			1.02685
$121$	5251.72			0.358700
$122$		−	2921.63i		−	0.196293i
$123$	596.921			0.0394554
$124$	−1807.86	+	1807.86i	−0.117577	+	0.117577i
$125$	−19120.8	−	19120.8i	−1.22373	−	1.22373i
$126$	26223.7	+	26223.7i	1.65178	+	1.65178i
$127$	−16068.4			−0.996245			−0.498123	−	0.867107i	$-0.665977\pi$
$127$	−16068.4			−0.996245			−0.498123	+	0.867107i	$0.665977\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$	18048.6	+	18048.6i	1.08458	+	1.08458i
$130$	9583.28	−	9583.28i	0.567058	−	0.567058i
$131$	−804.942	−	804.942i	−0.0469053	−	0.0469053i	0.683265	−	0.730170i	$-0.260559\pi$
$131$	−804.942	−	804.942i	−0.0469053	−	0.0469053i	−0.730170	+	0.683265i	$0.760559\pi$
$132$			11700.1i			0.671494i
$133$	−39197.3	+	39197.3i	−2.21591	+	2.21591i
$134$	−1269.42	+	1269.42i	−0.0706963	+	0.0706963i
$135$	30408.4	+	30408.4i	1.66850	+	1.66850i
$136$			2538.12i			0.137225i
$137$	−27749.9			−1.47850			−0.739249	−	0.673432i	$-0.764819\pi$
$137$	−27749.9			−1.47850			−0.739249	+	0.673432i	$0.764819\pi$
$138$		−	3176.40i		−	0.166793i
$139$			8373.33i			0.433380i	0.976240	+	0.216690i	$0.0695260\pi$
$139$			8373.33i			0.433380i	−0.976240	+	0.216690i	$0.930474\pi$
$140$	−21874.6	−	21874.6i	−1.11605	−	1.11605i
$141$			6215.56i			0.312638i
$142$	2029.49	+	2029.49i	0.100649	+	0.100649i
$143$	7582.91	+	7582.91i	0.370821	+	0.370821i
$144$	9395.68			0.453110
$145$	38653.6			1.83846
$146$	−10321.3	+	10321.3i	−0.484203	+	0.484203i
$147$		−	84157.9i		−	3.89458i
$148$	10198.8	+	3991.35i	0.465613	+	0.182220i
$149$	15363.0			0.691996			0.345998	−	0.938235i	$-0.387540\pi$
$149$	15363.0			0.691996			0.345998	+	0.938235i	$0.387540\pi$
$150$	−37719.9	−	37719.9i	−1.67644	−	1.67644i
$151$			19541.6i			0.857048i	0.903530	+	0.428524i	$0.140966\pi$
$151$			19541.6i			0.857048i	−0.903530	+	0.428524i	$0.859034\pi$
$152$			14044.0i			0.607860i
$153$	−11644.2	+	11644.2i	−0.497425	+	0.497425i
$154$	17308.6	−	17308.6i	0.729828	−	0.729828i
$155$	13836.9			0.575937
$156$	9449.18	−	9449.18i	0.388280	−	0.388280i
$157$	−21255.3			−0.862320			−0.431160	−	0.902276i	$-0.641895\pi$
$157$	−21255.3			−0.862320			−0.431160	+	0.902276i	$0.641895\pi$
$158$	−26113.3			−1.04604
$159$		−	58062.4i		−	2.29668i
$160$	−7837.44			−0.306150
$161$	−4699.01	+	4699.01i	−0.181282	+	0.181282i
$162$	6200.08	+	6200.08i	0.236248	+	0.236248i
$163$	5203.29	+	5203.29i	0.195841	+	0.195841i	0.798214	−	0.602374i	$-0.205778\pi$
$163$	5203.29	+	5203.29i	0.195841	+	0.195841i	−0.602374	+	0.798214i	$0.705778\pi$
$164$	−316.390			−0.0117635
$165$	44774.9	−	44774.9i	1.64462	−	1.64462i
$166$	7822.97	+	7822.97i	0.283893	+	0.283893i
$167$	18442.8	−	18442.8i	0.661294	−	0.661294i	−0.294391	−	0.955685i	$-0.595117\pi$
$167$	18442.8	−	18442.8i	0.661294	−	0.661294i	0.955685	+	0.294391i	$0.0951169\pi$
$168$	−21568.5	−	21568.5i	−0.764190	−	0.764190i
$169$			16312.9i			0.571159i
$170$	9713.06	−	9713.06i	0.336092	−	0.336092i
$171$	−64430.1	+	64430.1i	−2.20342	+	2.20342i
$172$	−9566.40	−	9566.40i	−0.323364	−	0.323364i
$173$			10710.1i			0.357850i	0.983863	+	0.178925i	$0.0572619\pi$
$173$			10710.1i			0.357850i	−0.983863	+	0.178925i	$0.942738\pi$
$174$	38112.7			1.25884
$175$			111602.i			3.64414i
$176$		−	6201.49i		−	0.200203i
$177$	12903.3	+	12903.3i	0.411866	+	0.411866i
$178$			6482.51i			0.204599i
$179$	−17354.2	−	17354.2i	−0.541625	−	0.541625i	0.382380	−	0.924005i	$-0.375104\pi$
$179$	−17354.2	−	17354.2i	−0.541625	−	0.541625i	−0.924005	+	0.382380i	$0.875104\pi$
$180$	−35956.1	−	35956.1i	−1.10976	−	1.10976i
$181$	36510.0			1.11444			0.557218	−	0.830366i	$-0.311869\pi$
$181$	36510.0			1.11444			0.557218	+	0.830366i	$0.311869\pi$
$182$	−27957.3			−0.844020
$183$	−11024.2	+	11024.2i	−0.329190	+	0.329190i
$184$			1683.61i			0.0497285i
$185$	−23755.1	−	54303.9i	−0.694087	−	1.58667i
$186$	13643.3			0.394359
$187$	7685.60	+	7685.60i	0.219783	+	0.219783i
$188$		−	3294.47i		−	0.0932116i
$189$		−	88710.6i		−	2.48343i
$190$	53744.6	−	53744.6i	1.48877	−	1.48877i
$191$	−14479.4	+	14479.4i	−0.396904	+	0.396904i	−0.877139	−	0.480236i	$-0.840551\pi$
$191$	−14479.4	+	14479.4i	−0.396904	+	0.396904i	0.480236	+	0.877139i	$0.340551\pi$
$192$	−7727.77			−0.209629
$193$	36455.1	−	36455.1i	0.978687	−	0.978687i	−0.0210905	−	0.999778i	$-0.506714\pi$
$193$	36455.1	−	36455.1i	0.978687	−	0.978687i	0.999778	+	0.0210905i	$0.00671382\pi$
$194$	27204.0			0.722819
$195$	−72321.7			−1.90195
$196$			44606.8i			1.16115i
$197$	−41314.8			−1.06457			−0.532284	−	0.846566i	$-0.678666\pi$
$197$	−41314.8			−1.06457			−0.532284	+	0.846566i	$0.678666\pi$
$198$	28450.8	−	28450.8i	0.725711	−	0.725711i
$199$	−43666.5	−	43666.5i	−1.10266	−	1.10266i	−0.994088	−	0.108573i	$-0.965372\pi$
$199$	−43666.5	−	43666.5i	−1.10266	−	1.10266i	−0.108573	−	0.994088i	$-0.534628\pi$
$200$	19992.9	+	19992.9i	0.499823	+	0.499823i
$201$	9579.89			0.237120
$202$	−29294.0	+	29294.0i	−0.717919	+	0.717919i
$203$	−56382.1	−	56382.1i	−1.36820	−	1.36820i
$204$	9577.14	−	9577.14i	0.230131	−	0.230131i
$205$	1210.79	+	1210.79i	0.0288111	+	0.0288111i
$206$		−	35990.7i		−	0.848117i
$207$	−7723.94	+	7723.94i	−0.180260	+	0.180260i
$208$	−5008.41	+	5008.41i	−0.115764	+	0.115764i
$209$	42526.2	+	42526.2i	0.973563	+	0.973563i
$210$			165080.i			3.74331i
$211$	85380.8			1.91776			0.958882	−	0.283805i	$-0.0915968\pi$
$211$	85380.8			1.91776			0.958882	+	0.283805i	$0.0915968\pi$
$212$			30775.2i			0.684745i
$213$		−	15315.8i		−	0.337584i
$214$	20868.3	+	20868.3i	0.455680	+	0.455680i
$215$			73218.9i			1.58397i
$216$	−15892.0	−	15892.0i	−0.340622	−	0.340622i
$217$	−20183.2	−	20183.2i	−0.428618	−	0.428618i
$218$	−6443.53			−0.135585
$219$	77890.9			1.62405
$220$	−23732.3	+	23732.3i	−0.490337	+	0.490337i
$221$		−	12414.0i		−	0.254172i
$222$	−23422.7	−	53544.0i	−0.475260	−	1.08644i
$223$	41120.6			0.826894			0.413447	−	0.910528i	$-0.364325\pi$
$223$	41120.6			0.826894			0.413447	+	0.910528i	$0.364325\pi$
$224$	11432.1	+	11432.1i	0.227840	+	0.227840i
$225$			183444.i			3.62359i
$226$		−	10082.8i		−	0.197409i
$227$	63176.1	−	63176.1i	1.22603	−	1.22603i	0.260576	−	0.965453i	$-0.416087\pi$
$227$	63176.1	−	63176.1i	1.22603	−	1.22603i	0.965453	−	0.260576i	$-0.0839125\pi$
$228$	52992.5	−	52992.5i	1.01940	−	1.01940i
$229$	−76908.4			−1.46657			−0.733285	−	0.679921i	$-0.762014\pi$
$229$	−76908.4			−1.46657			−0.733285	+	0.679921i	$0.762014\pi$
$230$	6442.95	−	6442.95i	0.121795	−	0.121795i
$231$	−130622.			−2.44789
$232$	−20201.1			−0.375318
$233$		−	92105.5i		−	1.69658i	−0.529535	−	0.848288i	$-0.677633\pi$
$233$		−	92105.5i		−	1.69658i	0.529535	−	0.848288i	$-0.322367\pi$
$234$	−45954.5			−0.839260
$235$	−12607.5	+	12607.5i	−0.228294	+	0.228294i
$236$	−6839.24	−	6839.24i	−0.122796	−	0.122796i
$237$	98533.8	+	98533.8i	1.75424	+	1.75424i
$238$	−28335.9			−0.500246
$239$	6682.95	−	6682.95i	0.116996	−	0.116996i	−0.646185	−	0.763181i	$-0.723636\pi$
$239$	6682.95	−	6682.95i	0.116996	−	0.116996i	0.763181	+	0.646185i	$0.223636\pi$
$240$	29573.2	+	29573.2i	0.513424	+	0.513424i
$241$	−31822.1	+	31822.1i	−0.547892	+	0.547892i	−0.925831	−	0.377939i	$-0.876633\pi$
$241$	−31822.1	+	31822.1i	−0.547892	+	0.547892i	0.377939	+	0.925831i	$0.376633\pi$
$242$	10503.4	+	10503.4i	0.179350	+	0.179350i
$243$			33663.6i			0.570096i
$244$	5843.25	−	5843.25i	0.0981465	−	0.0981465i
$245$	170705.	−	170705.i	2.84389	−	2.84389i
$246$	1193.84	+	1193.84i	0.0197277	+	0.0197277i
$247$		−	68689.6i		−	1.12589i
$248$	−7231.43			−0.117577
$249$		−	59037.2i		−	0.952197i
$250$		−	76483.2i		−	1.22373i
$251$	71677.9	+	71677.9i	1.13773	+	1.13773i	0.988857	+	0.148870i	$0.0475636\pi$
$251$	71677.9	+	71677.9i	1.13773	+	1.13773i	0.148870	+	0.988857i	$0.452436\pi$
$252$			104895.i			1.65178i
$253$	5098.08	+	5098.08i	0.0796463	+	0.0796463i
$254$	−32136.9	−	32136.9i	−0.498123	−	0.498123i
$255$	−73301.0			−1.12727
$256$	4096.00			0.0625000
$257$	−47486.4	+	47486.4i	−0.718957	+	0.718957i	−0.968392	−	0.249434i	$-0.919755\pi$
$257$	−47486.4	+	47486.4i	−0.718957	+	0.718957i	0.249434	+	0.968392i	$0.419755\pi$
$258$			72194.3i			1.08458i
$259$	−44560.0	+	113861.i	−0.664272	+	1.69736i
$260$	38333.1			0.567058
$261$	−92677.4	−	92677.4i	−1.36048	−	1.36048i
$262$		−	3219.77i		−	0.0469053i
$263$			51128.2i			0.739179i	0.929195	+	0.369589i	$0.120502\pi$
$263$			51128.2i			0.739179i	−0.929195	+	0.369589i	$0.879498\pi$
$264$	−23400.2	+	23400.2i	−0.335747	+	0.335747i
$265$	117773.	−	117773.i	1.67708	−	1.67708i
$266$	−156789.			−2.21591
$267$	24460.6	−	24460.6i	0.343119	−	0.343119i
$268$	−5077.69			−0.0706963
$269$	−55479.3			−0.766702			−0.383351	−	0.923603i	$-0.625230\pi$
$269$	−55479.3			−0.766702			−0.383351	+	0.923603i	$0.625230\pi$
$270$			121634.i			1.66850i
$271$	88040.9			1.19880			0.599399	−	0.800451i	$-0.295406\pi$
$271$	88040.9			1.19880			0.599399	+	0.800451i	$0.295406\pi$
$272$	−5076.24	+	5076.24i	−0.0686126	+	0.0686126i
$273$	105492.	+	105492.i	1.41545	+	1.41545i
$274$	−55499.9	−	55499.9i	−0.739249	−	0.739249i
$275$	121080.			1.60106
$276$	6352.79	−	6352.79i	0.0833963	−	0.0833963i
$277$	14583.0	+	14583.0i	0.190058	+	0.190058i	0.795721	−	0.605663i	$-0.207092\pi$
$277$	14583.0	+	14583.0i	0.190058	+	0.190058i	−0.605663	+	0.795721i	$0.707092\pi$
$278$	−16746.7	+	16746.7i	−0.216690	+	0.216690i
$279$	−33175.9	−	33175.9i	−0.426201	−	0.426201i
$280$		−	87498.4i		−	1.11605i
$281$	−73723.6	+	73723.6i	−0.933672	+	0.933672i	−0.997933	−	0.0642615i	$-0.979531\pi$
$281$	−73723.6	+	73723.6i	−0.933672	+	0.933672i	0.0642615	+	0.997933i	$0.479531\pi$
$282$	−12431.1	+	12431.1i	−0.156319	+	0.156319i
$283$	50499.0	+	50499.0i	0.630536	+	0.630536i	0.948203	−	0.317666i	$-0.102899\pi$
$283$	50499.0	+	50499.0i	0.630536	+	0.630536i	−0.317666	+	0.948203i	$0.602899\pi$
$284$			8117.95i			0.100649i
$285$	−405592.			−4.99343
$286$			30331.7i			0.370821i
$287$		−	3532.23i		−	0.0428830i
$288$	18791.4	+	18791.4i	0.226555	+	0.226555i
$289$			70938.9i			0.849354i
$290$	77307.1	+	77307.1i	0.919229	+	0.919229i
$291$	−102650.	−	102650.i	−1.21219	−	1.21219i
$292$	−41285.1			−0.484203
$293$	144843.			1.68718			0.843592	−	0.536984i	$-0.180437\pi$
$293$	144843.			1.68718			0.843592	+	0.536984i	$0.180437\pi$
$294$	168316.	−	168316.i	1.94729	−	1.94729i
$295$			52345.9i			0.601504i
$296$	12414.9	+	28380.3i	0.141697	+	0.323917i
$297$	−96244.4			−1.09110
$298$	30726.0	+	30726.0i	0.345998	+	0.345998i
$299$		−	8234.57i		−	0.0921082i
$300$		−	150879.i		−	1.67644i
$301$	106801.	−	106801.i	1.17880	−	1.17880i
$302$	−39083.1	+	39083.1i	−0.428524	+	0.428524i
$303$	221071.			2.40795
$304$	−28088.0	+	28088.0i	−0.303930	+	0.303930i
$305$	−44722.8			−0.480761
$306$	−46576.9			−0.497425
$307$			4925.13i			0.0522565i	0.999659	+	0.0261283i	$0.00831783\pi$
$307$			4925.13i			0.0522565i	−0.999659	+	0.0261283i	$0.991682\pi$
$308$	69234.4			0.729828
$309$	−135805.	+	135805.i	−1.42232	+	1.42232i
$310$	27673.8	+	27673.8i	0.287969	+	0.287969i
$311$	−117456.	−	117456.i	−1.21438	−	1.21438i	−0.969570	−	0.244813i	$-0.921273\pi$
$311$	−117456.	−	117456.i	−1.21438	−	1.21438i	−0.244813	−	0.969570i	$-0.578727\pi$
$312$	37796.7			0.388280
$313$	14075.8	−	14075.8i	0.143676	−	0.143676i	−0.631610	−	0.775286i	$-0.717606\pi$
$313$	14075.8	−	14075.8i	0.143676	−	0.143676i	0.775286	+	0.631610i	$0.217606\pi$
$314$	−42510.6	−	42510.6i	−0.431160	−	0.431160i
$315$	401419.	−	401419.i	4.04555	−	4.04555i
$316$	−52226.5	−	52226.5i	−0.523018	−	0.523018i
$317$			69163.6i			0.688270i	0.938920	+	0.344135i	$0.111828\pi$
$317$			69163.6i			0.688270i	−0.938920	+	0.344135i	$0.888172\pi$
$318$	116125.	−	116125.i	1.14834	−	1.14834i
$319$	−61170.4	+	61170.4i	−0.601118	+	0.601118i
$320$	−15674.9	−	15674.9i	−0.153075	−	0.153075i
$321$		−	157486.i		−	1.52838i
$322$	−18796.0			−0.181282
$323$		−	69619.8i		−	0.667310i
$324$			24800.3i			0.236248i
$325$	−97785.8	−	97785.8i	−0.925783	−	0.925783i
$326$			20813.2i			0.195841i
$327$	24313.5	+	24313.5i	0.227380	+	0.227380i
$328$	−632.781	−	632.781i	−0.00588174	−	0.00588174i
$329$	36780.0			0.339797
$330$	179099.			1.64462
$331$	−40859.1	+	40859.1i	−0.372935	+	0.372935i	−0.868545	−	0.495610i	$-0.834945\pi$
$331$	−40859.1	+	40859.1i	−0.372935	+	0.372935i	0.495610	+	0.868545i	$0.334945\pi$
$332$			31291.9i			0.283893i
$333$	−73245.0	+	187157.i	−0.660526	+	1.68779i
$334$	73771.3			0.661294
$335$	19431.7	+	19431.7i	0.173149	+	0.173149i
$336$		−	86273.9i		−	0.764190i
$337$			64767.3i			0.570290i	0.958484	+	0.285145i	$0.0920418\pi$
$337$			64767.3i			0.570290i	−0.958484	+	0.285145i	$0.907958\pi$
$338$	−32625.7	+	32625.7i	−0.285579	+	0.285579i
$339$	−38045.8	+	38045.8i	−0.331061	+	0.331061i
$340$	38852.2			0.336092
$341$	−21897.3	+	21897.3i	−0.188314	+	0.188314i
$342$	−257721.			−2.20342
$343$	−283556.			−2.41018
$344$		−	38265.6i		−	0.323364i
$345$	−48622.7			−0.408508
$346$	−21420.2	+	21420.2i	−0.178925	+	0.178925i
$347$	22830.0	+	22830.0i	0.189603	+	0.189603i	0.795525	−	0.605921i	$-0.207195\pi$
$347$	22830.0	+	22830.0i	0.189603	+	0.189603i	−0.605921	+	0.795525i	$0.707195\pi$
$348$	76225.3	+	76225.3i	0.629421	+	0.629421i
$349$	−49284.0			−0.404627			−0.202314	−	0.979321i	$-0.564846\pi$
$349$	−49284.0			−0.404627			−0.202314	+	0.979321i	$0.564846\pi$
$350$	−223204.	+	223204.i	−1.82207	+	1.82207i
$351$	77728.4	+	77728.4i	0.630907	+	0.630907i
$352$	12403.0	−	12403.0i	0.100102	−	0.100102i
$353$	−13292.8	−	13292.8i	−0.106676	−	0.106676i	0.651754	−	0.758430i	$-0.274033\pi$
$353$	−13292.8	−	13292.8i	−0.106676	−	0.106676i	−0.758430	+	0.651754i	$0.774033\pi$
$354$			51613.4i			0.411866i
$355$	31066.4	−	31066.4i	0.246510	−	0.246510i
$356$	−12965.0	+	12965.0i	−0.102299	+	0.102299i
$357$	106921.	+	106921.i	0.838929	+	0.838929i
$358$		−	69416.8i		−	0.541625i
$359$	−91430.7			−0.709419			−0.354710	−	0.934976i	$-0.615420\pi$
$359$	−91430.7			−0.709419			−0.354710	+	0.934976i	$0.615420\pi$
$360$		−	143824.i		−	1.10976i
$361$		−	254901.i		−	1.95595i
$362$	73020.1	+	73020.1i	0.557218	+	0.557218i
$363$		−	79265.8i		−	0.601551i
$364$	−55914.7	−	55914.7i	−0.422010	−	0.422010i
$365$	157993.	+	157993.i	1.18591	+	1.18591i
$366$	−44097.0			−0.329190
$367$	−58394.3			−0.433549			−0.216774	−	0.976222i	$-0.569554\pi$
$367$	−58394.3			−0.433549			−0.216774	+	0.976222i	$0.569554\pi$
$368$	−3367.21	+	3367.21i	−0.0248642	+	0.0248642i
$369$		−	5806.06i		−	0.0426411i
$370$	61097.6	−	156118.i	0.446294	−	1.14038i
$371$	−343579.			−2.49620
$372$	27286.5	+	27286.5i	0.197180	+	0.197180i
$373$		−	24663.5i		−	0.177270i	−0.996064	−	0.0886352i	$-0.971749\pi$
$373$		−	24663.5i		−	0.177270i	0.996064	−	0.0886352i	$-0.0282505\pi$
$374$			30742.4i			0.219783i
$375$	−288596.	+	288596.i	−2.05224	+	2.05224i
$376$	6588.94	−	6588.94i	0.0466058	−	0.0466058i
$377$	98804.2			0.695173
$378$	177421.	−	177421.i	1.24171	−	1.24171i
$379$	82581.9			0.574918			0.287459	−	0.957793i	$-0.407189\pi$
$379$	82581.9			0.574918			0.287459	+	0.957793i	$0.407189\pi$
$380$	214978.			1.48877
$381$			242526.i			1.67074i
$382$	−57917.8			−0.396904
$383$	154015.	−	154015.i	1.04994	−	1.04994i	0.0512563	−	0.998686i	$-0.483677\pi$
$383$	154015.	−	154015.i	1.04994	−	1.04994i	0.998686	−	0.0512563i	$-0.0163225\pi$
$384$	−15455.5	−	15455.5i	−0.104815	−	0.104815i
$385$	−264951.	−	264951.i	−1.78749	−	1.78749i
$386$	145820.			0.978687
$387$	175552.	−	175552.i	1.17215	−	1.17215i
$388$	54408.1	+	54408.1i	0.361410	+	0.361410i
$389$	−71853.6	+	71853.6i	−0.474842	+	0.474842i	−0.903477	−	0.428636i	$-0.858994\pi$
$389$	−71853.6	+	71853.6i	−0.474842	+	0.474842i	0.428636	+	0.903477i	$0.358994\pi$
$390$	−144643.	−	144643.i	−0.950975	−	0.950975i
$391$		−	8346.08i		−	0.0545920i
$392$	−89213.6	+	89213.6i	−0.580576	+	0.580576i
$393$	−12149.2	+	12149.2i	−0.0786617	+	0.0786617i
$394$	−82629.7	−	82629.7i	−0.532284	−	0.532284i
$395$			399729.i			2.56195i
$396$	113803.			0.725711
$397$			238989.i			1.51634i	0.652056	+	0.758171i	$0.273907\pi$
$397$			238989.i			1.51634i	−0.652056	+	0.758171i	$0.726093\pi$
$398$		−	174666.i		−	1.10266i
$399$	591617.	+	591617.i	3.71616	+	3.71616i
$400$			79971.6i			0.499823i
$401$	69046.8	+	69046.8i	0.429393	+	0.429393i	0.888421	−	0.459029i	$-0.151802\pi$
$401$	69046.8	+	69046.8i	0.429393	+	0.429393i	−0.459029	+	0.888421i	$0.651802\pi$
$402$	19159.8	+	19159.8i	0.118560	+	0.118560i
$403$	35369.1			0.217778
$404$	−117176.			−0.717919
$405$	94907.7	−	94907.7i	0.578618	−	0.578618i
$406$		−	225528.i		−	1.36820i
$407$	123531.	+	48344.4i	0.745738	+	0.291848i
$408$	38308.6			0.230131
$409$	−170071.	−	170071.i	−1.01668	−	1.01668i	−0.999859	−	0.0168188i	$-0.994646\pi$
$409$	−170071.	−	170071.i	−1.01668	−	1.01668i	−0.0168188	−	0.999859i	$-0.505354\pi$
$410$			4843.14i			0.0288111i
$411$			418838.i			2.47949i
$412$	71981.4	−	71981.4i	0.424059	−	0.424059i
$413$	76354.3	−	76354.3i	0.447645	−	0.447645i
$414$	−30895.8			−0.180260
$415$	119750.	−	119750.i	0.695312	−	0.695312i
$416$	−20033.6			−0.115764
$417$	126381.			0.726792
$418$			170105.i			0.973563i
$419$	174882.			0.996130			0.498065	−	0.867140i	$-0.334044\pi$
$419$	174882.			0.996130			0.498065	+	0.867140i	$0.334044\pi$
$420$	−330160.	+	330160.i	−1.87165	+	1.87165i
$421$	−9202.30	−	9202.30i	−0.0519197	−	0.0519197i	0.680670	−	0.732590i	$-0.261689\pi$
$421$	−9202.30	−	9202.30i	−0.0519197	−	0.0519197i	−0.732590	+	0.680670i	$0.761689\pi$
$422$	170762.	+	170762.i	0.958882	+	0.958882i
$423$	60456.7			0.337881
$424$	−61550.4	+	61550.4i	−0.342373	+	0.342373i
$425$	−99110.1	−	99110.1i	−0.548706	−	0.548706i
$426$	30631.7	−	30631.7i	0.168792	−	0.168792i
$427$	65234.9	+	65234.9i	0.357787	+	0.357787i
$428$			83473.3i			0.455680i
$429$	114451.	−	114451.i	0.621879	−	0.621879i
$430$	−146438.	+	146438.i	−0.791983	+	0.791983i
$431$	−169977.	−	169977.i	−0.915029	−	0.915029i	0.0816330	−	0.996662i	$-0.473986\pi$
$431$	−169977.	−	169977.i	−0.915029	−	0.915029i	−0.996662	+	0.0816330i	$0.973986\pi$
$432$		−	63568.2i		−	0.340622i
$433$	36017.6			0.192105			0.0960527	−	0.995376i	$-0.469378\pi$
$433$	36017.6			0.192105			0.0960527	+	0.995376i	$0.469378\pi$
$434$		−	80732.8i		−	0.428618i
$435$		−	583410.i		−	3.08315i
$436$	−12887.1	−	12887.1i	−0.0677923	−	0.0677923i
$437$		−	46180.8i		−	0.241824i
$438$	155782.	+	155782.i	0.812024	+	0.812024i
$439$	92911.1	+	92911.1i	0.482102	+	0.482102i	0.905802	−	0.423701i	$-0.139269\pi$
$439$	92911.1	+	92911.1i	0.482102	+	0.482102i	−0.423701	+	0.905802i	$0.639269\pi$
$440$	−94929.3			−0.490337
$441$	−818576.			−4.20903
$442$	24828.0	−	24828.0i	0.127086	−	0.127086i
$443$		−	153445.i		−	0.781887i	−0.920415	−	0.390944i	$-0.872149\pi$
$443$		−	153445.i		−	0.781887i	0.920415	−	0.390944i	$-0.127851\pi$
$444$	60242.6	−	153933.i	0.305589	−	0.780849i
$445$	99231.0			0.501103
$446$	82241.2	+	82241.2i	0.413447	+	0.413447i
$447$		−	231878.i		−	1.16050i
$448$			45728.4i			0.227840i
$449$	152957.	−	152957.i	0.758711	−	0.758711i	−0.217377	−	0.976088i	$-0.569750\pi$
$449$	152957.	−	152957.i	0.758711	−	0.758711i	0.976088	+	0.217377i	$0.0697501\pi$
$450$	−366889.	+	366889.i	−1.81180	+	1.81180i
$451$	−3832.21			−0.0188407
$452$	20165.7	−	20165.7i	0.0987043	−	0.0987043i
$453$	294946.			1.43730
$454$	252704.			1.22603
$455$			427957.i			2.06717i
$456$	211970.			1.01940
$457$	−86848.8	+	86848.8i	−0.415845	+	0.415845i	−0.883769	−	0.467924i	$-0.845002\pi$
$457$	−86848.8	+	86848.8i	−0.415845	+	0.415845i	0.467924	+	0.883769i	$0.345002\pi$
$458$	−153817.	−	153817.i	−0.733285	−	0.733285i
$459$	78781.0	+	78781.0i	0.373935	+	0.373935i
$460$	25771.8			0.121795
$461$	115782.	−	115782.i	0.544805	−	0.544805i	−0.380129	−	0.924934i	$-0.624120\pi$
$461$	115782.	−	115782.i	0.544805	−	0.544805i	0.924934	+	0.380129i	$0.124120\pi$
$462$	−261244.	−	261244.i	−1.22394	−	1.22394i
$463$	−269371.	+	269371.i	−1.25658	+	1.25658i	−0.303863	+	0.952716i	$0.598276\pi$
$463$	−269371.	+	269371.i	−1.25658	+	1.25658i	−0.952716	+	0.303863i	$0.901724\pi$
$464$	−40402.2	−	40402.2i	−0.187659	−	0.187659i
$465$		−	208844.i		−	0.965865i
$466$	184211.	−	184211.i	0.848288	−	0.848288i
$467$	192768.	−	192768.i	0.883895	−	0.883895i	−0.110033	−	0.993928i	$-0.535096\pi$
$467$	192768.	−	192768.i	0.883895	−	0.883895i	0.993928	+	0.110033i	$0.0350956\pi$
$468$	−91909.1	−	91909.1i	−0.419630	−	0.419630i
$469$		−	56688.1i		−	0.257719i
$470$	−50430.1			−0.228294
$471$			320813.i			1.44614i
$472$		−	27357.0i		−	0.122796i
$473$	−115871.	−	115871.i	−0.517908	−	0.517908i
$474$			394135.i			1.75424i
$475$	−548399.	−	548399.i	−2.43058	−	2.43058i
$476$	−56671.9	−	56671.9i	−0.250123	−	0.250123i
$477$	−564754.			−2.48212
$478$	26731.8			0.116996
$479$	−56415.1	+	56415.1i	−0.245881	+	0.245881i	−0.819278	−	0.573397i	$-0.805625\pi$
$479$	−56415.1	+	56415.1i	−0.245881	+	0.245881i	0.573397	+	0.819278i	$0.305625\pi$
$480$			118293.i			0.513424i
$481$	−60721.6	−	138809.i	−0.262454	−	0.599966i
$482$	−127288.			−0.547892
$483$	70923.6	+	70923.6i	0.304016	+	0.304016i
$484$			42013.8i			0.179350i
$485$		−	416426.i		−	1.77033i
$486$	−67327.2	+	67327.2i	−0.285048	+	0.285048i
$487$	−261846.	+	261846.i	−1.10405	+	1.10405i	−0.110129	+	0.993917i	$0.535127\pi$
$487$	−261846.	+	261846.i	−1.10405	+	1.10405i	−0.993917	+	0.110129i	$0.964873\pi$
$488$	23373.0			0.0981465
$489$	78534.8	−	78534.8i	0.328431	−	0.328431i
$490$	682818.			2.84389
$491$	140879.			0.584365			0.292183	−	0.956363i	$-0.405618\pi$
$491$	140879.			0.584365			0.292183	+	0.956363i	$0.405618\pi$
$492$			4775.37i			0.0197277i
$493$	100142.			0.412025
$494$	137379.	−	137379.i	0.562946	−	0.562946i
$495$	−435511.	−	435511.i	−1.77741	−	1.77741i
$496$	−14462.9	−	14462.9i	−0.0587883	−	0.0587883i
$497$	−90630.0			−0.366910
$498$	118074.	−	118074.i	0.476099	−	0.476099i
$499$	−58185.5	−	58185.5i	−0.233676	−	0.233676i	0.580549	−	0.814225i	$-0.302838\pi$
$499$	−58185.5	−	58185.5i	−0.233676	−	0.233676i	−0.814225	+	0.580549i	$0.802838\pi$
$500$	152966.	−	152966.i	0.611866	−	0.611866i
$501$	−278363.	−	278363.i	−1.10901	−	1.10901i
$502$			286712.i			1.13773i
$503$	−226650.	+	226650.i	−0.895820	+	0.895820i	−0.995063	−	0.0992434i	$-0.968358\pi$
$503$	−226650.	+	226650.i	−0.895820	+	0.895820i	0.0992434	+	0.995063i	$0.468358\pi$
$504$	−209790.	+	209790.i	−0.825891	+	0.825891i
$505$	448417.	+	448417.i	1.75833	+	1.75833i
$506$			20392.3i			0.0796463i
$507$	246215.			0.957852
$508$		−	128548.i		−	0.498123i
$509$		−	14277.9i		−	0.0551096i	−0.999620	−	0.0275548i	$-0.991228\pi$
$509$		−	14277.9i		−	0.0551096i	0.999620	−	0.0275548i	$-0.00877208\pi$
$510$	−146602.	−	146602.i	−0.563637	−	0.563637i
$511$		−	460913.i		−	1.76513i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	435913.	+	435913.i	1.65640	+	1.65640i
$514$	−189946.			−0.718957
$515$	−550928.			−2.07721
$516$	−144389.	+	144389.i	−0.542292	+	0.542292i
$517$		−	39903.6i		−	0.149290i
$518$	−316842.	+	138602.i	−1.18082	+	0.516546i
$519$	161651.			0.600126
$520$	76666.3	+	76666.3i	0.283529	+	0.283529i
$521$		−	93730.5i		−	0.345307i	−0.984983	−	0.172654i	$-0.944766\pi$
$521$		−	93730.5i		−	0.345307i	0.984983	−	0.172654i	$-0.0552341\pi$
$522$		−	370709.i		−	1.36048i
$523$	325894.	−	325894.i	1.19144	−	1.19144i	0.214778	−	0.976663i	$-0.431097\pi$
$523$	325894.	−	325894.i	1.19144	−	1.19144i	0.976663	−	0.214778i	$-0.0689029\pi$
$524$	6439.53	−	6439.53i	0.0234526	−	0.0234526i
$525$	1.68444e6			6.11135
$526$	−102256.	+	102256.i	−0.369589	+	0.369589i
$527$	35848.1			0.129076
$528$	−93600.9			−0.335747
$529$			274305.i			0.980217i
$530$	471091.			1.67708
$531$	125507.	−	125507.i	0.445120	−	0.445120i
$532$	−313579.	−	313579.i	−1.10796	−	1.10796i
$533$	3094.95	+	3094.95i	0.0108943	+	0.0108943i
$534$	97842.4			0.343119
$535$	319442.	−	319442.i	1.11605	−	1.11605i
$536$	−10155.4	−	10155.4i	−0.0353482	−	0.0353482i
$537$	−261932.	+	261932.i	−0.908322	+	0.908322i
$538$	−110959.	−	110959.i	−0.383351	−	0.383351i
$539$			540290.i			1.85973i
$540$	−243267.	+	243267.i	−0.834250	+	0.834250i
$541$	−211642.	+	211642.i	−0.723115	+	0.723115i	−0.969239	−	0.246123i	$-0.920843\pi$
$541$	−211642.	+	211642.i	−0.723115	+	0.723115i	0.246123	+	0.969239i	$0.420843\pi$
$542$	176082.	+	176082.i	0.599399	+	0.599399i
$543$		−	551057.i		−	1.86895i
$544$	−20304.9			−0.0686126
$545$			98634.3i			0.332074i
$546$			421968.i			1.41545i
$547$	−47726.1	−	47726.1i	−0.159507	−	0.159507i	0.622841	−	0.782348i	$-0.285978\pi$
$547$	−47726.1	−	47726.1i	−0.159507	−	0.159507i	−0.782348	+	0.622841i	$0.785978\pi$
$548$		−	222000.i		−	0.739249i
$549$	107229.	+	107229.i	0.355769	+	0.355769i
$550$	242160.	+	242160.i	0.800528	+	0.800528i
$551$	554110.			1.82513
$552$	25411.2			0.0833963
$553$	583065.	−	583065.i	1.90663	−	1.90663i
$554$			58331.8i			0.190058i
$555$	−819625.	+	358543.i	−2.66090	+	1.16401i
$556$	−66986.6			−0.216690
$557$	122218.	+	122218.i	0.393935	+	0.393935i	0.876087	−	0.482152i	$-0.160145\pi$
$557$	122218.	+	122218.i	0.393935	+	0.393935i	−0.482152	+	0.876087i	$0.660145\pi$
$558$		−	132704.i		−	0.426201i
$559$			187158.i			0.598942i
$560$	174997.	−	174997.i	0.558025	−	0.558025i
$561$	116001.	−	116001.i	0.368584	−	0.368584i
$562$	−294895.			−0.933672
$563$	58570.5	−	58570.5i	0.184783	−	0.184783i	−0.608653	−	0.793436i	$-0.708290\pi$
$563$	58570.5	−	58570.5i	0.184783	−	0.184783i	0.793436	+	0.608653i	$0.208290\pi$
$564$	−49724.4			−0.156319
$565$	−154343.			−0.483493
$566$			201996.i			0.630536i
$567$	−276875.			−0.861226
$568$	−16235.9	+	16235.9i	−0.0503245	+	0.0503245i
$569$	−172920.	−	172920.i	−0.534096	−	0.534096i	0.387692	−	0.921789i	$-0.373272\pi$
$569$	−172920.	−	172920.i	−0.534096	−	0.534096i	−0.921789	+	0.387692i	$0.873272\pi$
$570$	−811183.	−	811183.i	−2.49672	−	2.49672i
$571$	−60876.5			−0.186714			−0.0933571	−	0.995633i	$-0.529760\pi$
$571$	−60876.5			−0.186714			−0.0933571	+	0.995633i	$0.529760\pi$
$572$	−60663.3	+	60663.3i	−0.185410	+	0.185410i
$573$	218542.	+	218542.i	0.665620	+	0.665620i
$574$	7064.46	−	7064.46i	0.0214415	−	0.0214415i
$575$	−65742.6	−	65742.6i	−0.198843	−	0.198843i
$576$			75165.5i			0.226555i
$577$	−375038.	+	375038.i	−1.12648	+	1.12648i	−0.135735	+	0.990745i	$0.543340\pi$
$577$	−375038.	+	375038.i	−1.12648	+	1.12648i	−0.990745	+	0.135735i	$0.956660\pi$
$578$	−141878.	+	141878.i	−0.424677	+	0.424677i
$579$	−550228.	−	550228.i	−1.64129	−	1.64129i
$580$			309229.i			0.919229i
$581$	−349347.			−1.03492
$582$		−	410598.i		−	1.21219i
$583$			372758.i			1.09670i
$584$	−82570.1	−	82570.1i	−0.242101	−	0.242101i
$585$			703449.i			2.05552i
$586$	289686.	+	289686.i	0.843592	+	0.843592i
$587$	41480.4	+	41480.4i	0.120383	+	0.120383i	0.764732	−	0.644349i	$-0.222871\pi$
$587$	41480.4	+	41480.4i	0.120383	+	0.120383i	−0.644349	+	0.764732i	$0.722871\pi$
$588$	673263.			1.94729
$589$	198356.			0.571761
$590$	−104692.	+	104692.i	−0.300752	+	0.300752i
$591$			623577.i			1.78532i
$592$	−31930.8	+	81590.4i	−0.0911101	+	0.232807i
$593$	−164920.			−0.468991			−0.234495	−	0.972117i	$-0.575344\pi$
$593$	−164920.			−0.468991			−0.234495	+	0.972117i	$0.575344\pi$
$594$	−192489.	−	192489.i	−0.545548	−	0.545548i
$595$			433752.i			1.22520i
$596$			122904.i			0.345998i
$597$	−659071.	+	659071.i	−1.84920	+	1.84920i
$598$	16469.1	−	16469.1i	0.0460541	−	0.0460541i
$599$	111161.			0.309813			0.154906	−	0.987929i	$-0.450492\pi$
$599$	111161.			0.309813			0.154906	+	0.987929i	$0.450492\pi$
$600$	301759.	−	301759.i	0.838219	−	0.838219i
$601$	534824.			1.48068			0.740341	−	0.672232i	$-0.234664\pi$
$601$	534824.			1.48068			0.740341	+	0.672232i	$0.234664\pi$
$602$	427203.			1.17880
$603$		−	93180.5i		−	0.256266i
$604$	−156332.			−0.428524
$605$	160782.	−	160782.i	0.439264	−	0.439264i
$606$	442142.	+	442142.i	1.20397	+	1.20397i
$607$	503632.	+	503632.i	1.36690	+	1.36690i	0.864828	+	0.502068i	$0.167427\pi$
$607$	503632.	+	503632.i	1.36690	+	1.36690i	0.502068	+	0.864828i	$0.332573\pi$
$608$	−112352.			−0.303930
$609$	−850991.	+	850991.i	−2.29451	+	2.29451i
$610$	−89445.6	−	89445.6i	−0.240380	−	0.240380i
$611$	−32226.7	+	32226.7i	−0.0863244	+	0.0863244i
$612$	−93153.7	−	93153.7i	−0.248712	−	0.248712i
$613$			155535.i			0.413910i	0.978350	+	0.206955i	$0.0663554\pi$
$613$			155535.i			0.413910i	−0.978350	+	0.206955i	$0.933645\pi$
$614$	−9850.25	+	9850.25i	−0.0261283	+	0.0261283i
$615$	18274.8	−	18274.8i	0.0483171	−	0.0483171i
$616$	138469.	+	138469.i	0.364914	+	0.364914i
$617$		−	246479.i		−	0.647454i	−0.946151	−	0.323727i	$-0.895064\pi$
$617$		−	246479.i		−	0.647454i	0.946151	−	0.323727i	$-0.104936\pi$
$618$	−543218.			−1.42232
$619$		−	670760.i		−	1.75060i	−0.483583	−	0.875298i	$-0.660665\pi$
$619$		−	670760.i		−	1.75060i	0.483583	−	0.875298i	$-0.339335\pi$
$620$			110695.i			0.287969i
$621$	52257.7	+	52257.7i	0.135509	+	0.135509i
$622$		−	469826.i		−	1.21438i
$623$	−144743.	−	144743.i	−0.372926	−	0.372926i
$624$	75593.4	+	75593.4i	0.194140	+	0.194140i
$625$	−389794.			−0.997872
$626$	56303.1			0.143676
$627$	641861.	−	641861.i	1.63270	−	1.63270i
$628$		−	170043.i		−	0.431160i
$629$	−61543.9	−	140689.i	−0.155555	−	0.355596i
$630$	1.60568e6			4.04555
$631$	−405278.	−	405278.i	−1.01787	−	1.01787i	−0.999837	−	0.0180371i	$-0.994258\pi$
$631$	−405278.	−	405278.i	−1.01787	−	1.01787i	−0.0180371	−	0.999837i	$-0.505742\pi$
$632$		−	208906.i		−	0.523018i
$633$		−	1.28868e6i		−	3.21615i
$634$	−138327.	+	138327.i	−0.344135	+	0.344135i
$635$	−491935.	+	491935.i	−1.22000	+	1.22000i
$636$	464499.			1.14834
$637$	436346.	−	436346.i	1.07536	−	1.07536i
$638$	−244682.			−0.601118
$639$	−148972.			−0.364841
$640$		−	62699.5i		−	0.153075i
$641$	−569763.			−1.38669			−0.693343	−	0.720608i	$-0.743863\pi$
$641$	−569763.			−1.38669			−0.693343	+	0.720608i	$0.743863\pi$
$642$	314972.	−	314972.i	0.764190	−	0.764190i
$643$	414725.	+	414725.i	1.00309	+	1.00309i	0.999995	+	0.00309100i	$0.000983898\pi$
$643$	414725.	+	414725.i	1.00309	+	1.00309i	0.00309100	+	0.999995i	$0.499016\pi$
$644$	−37592.1	−	37592.1i	−0.0906410	−	0.0906410i
$645$	1.10511e6			2.65636
$646$	139240.	−	139240.i	0.333655	−	0.333655i
$647$	−131144.	−	131144.i	−0.313285	−	0.313285i	0.532896	−	0.846181i	$-0.321104\pi$
$647$	−131144.	−	131144.i	−0.313285	−	0.313285i	−0.846181	+	0.532896i	$0.821104\pi$
$648$	−49600.6	+	49600.6i	−0.118124	+	0.118124i
$649$	−82838.9	−	82838.9i	−0.196673	−	0.196673i
$650$		−	391143.i		−	0.925783i
$651$	−304631.	+	304631.i	−0.718806	+	0.718806i
$652$	−41626.3	+	41626.3i	−0.0979203	+	0.0979203i
$653$	−279898.	−	279898.i	−0.656406	−	0.656406i	0.298122	−	0.954528i	$-0.403640\pi$
$653$	−279898.	−	279898.i	−0.656406	−	0.656406i	−0.954528	+	0.298122i	$0.903640\pi$
$654$			97254.0i			0.227380i
$655$	−49286.6			−0.114880
$656$		−	2531.12i		−	0.00588174i
$657$		−	757620.i		−	1.75518i
$658$	73560.0	+	73560.0i	0.169899	+	0.169899i
$659$		−	313308.i		−	0.721441i	−0.932674	−	0.360721i	$-0.882531\pi$
$659$		−	313308.i		−	0.721441i	0.932674	−	0.360721i	$-0.117469\pi$
$660$	358199.	+	358199.i	0.822312	+	0.822312i
$661$	68883.3	+	68883.3i	0.157656	+	0.157656i	0.781527	−	0.623871i	$-0.214441\pi$
$661$	68883.3	+	68883.3i	0.157656	+	0.157656i	−0.623871	+	0.781527i	$0.714441\pi$
$662$	−163437.			−0.372935
$663$	−187368.			−0.426254
$664$	−62583.7	+	62583.7i	−0.141947	+	0.141947i
$665$			2.40005e6i			5.42722i
$666$	−520805.	+	227825.i	−1.17416	+	0.513633i
$667$	66427.2			0.149312
$668$	147543.	+	147543.i	0.330647	+	0.330647i
$669$		−	620646.i		−	1.38673i
$670$			77726.8i			0.173149i
$671$	70775.1	−	70775.1i	0.157194	−	0.157194i
$672$	172548.	−	172548.i	0.382095	−	0.382095i
$673$	491936.			1.08612			0.543061	−	0.839693i	$-0.317265\pi$
$673$	491936.			1.08612			0.543061	+	0.839693i	$0.317265\pi$
$674$	−129535.	+	129535.i	−0.285145	+	0.285145i
$675$	1.24113e6			2.72401
$676$	−130503.			−0.285579
$677$		−	784746.i		−	1.71219i	−0.516819	−	0.856095i	$-0.672884\pi$
$677$		−	784746.i		−	1.71219i	0.516819	−	0.856095i	$-0.327116\pi$
$678$	−152183.			−0.331061
$679$	−607420.	+	607420.i	−1.31750	+	1.31750i
$680$	77704.5	+	77704.5i	0.168046	+	0.168046i
$681$	−953535.	−	953535.i	−2.05609	−	2.05609i
$682$	−87589.1			−0.188314
$683$	528227.	−	528227.i	1.13235	−	1.13235i	0.142559	−	0.989786i	$-0.454467\pi$
$683$	528227.	−	528227.i	1.13235	−	1.13235i	0.989786	−	0.142559i	$-0.0455332\pi$
$684$	−515441.	−	515441.i	−1.10171	−	1.10171i
$685$	−849564.	+	849564.i	−1.81057	+	1.81057i
$686$	−567112.	−	567112.i	−1.20509	−	1.20509i
$687$			1.16080e6i			2.45949i
$688$	76531.2	−	76531.2i	0.161682	−	0.161682i
$689$	301045.	−	301045.i	0.634151	−	0.634151i
$690$	−97245.4	−	97245.4i	−0.204254	−	0.204254i
$691$			355095.i			0.743685i	0.928296	+	0.371842i	$0.121274\pi$
$691$			355095.i			0.743685i	−0.928296	+	0.371842i	$0.878726\pi$
$692$	−85680.7			−0.178925
$693$			1.27052e6i			2.64554i
$694$			91319.8i			0.189603i
$695$	256350.	+	256350.i	0.530717	+	0.530717i
$696$			304901.i			0.629421i
$697$	3136.86	+	3136.86i	0.00645698	+	0.00645698i
$698$	−98568.0	−	98568.0i	−0.202314	−	0.202314i
$699$	−1.39017e6			−2.84521
$700$	−892815.			−1.82207
$701$	−493537.	+	493537.i	−1.00435	+	1.00435i	−0.00435714	+	0.999991i	$0.501387\pi$
$701$	−493537.	+	493537.i	−1.00435	+	1.00435i	−0.999991	+	0.00435714i	$0.998613\pi$
$702$			310914.i			0.630907i
$703$	−340536.	−	778462.i	−0.689054	−	1.57517i
$704$	49611.9			0.100102
$705$	190289.	+	190289.i	0.382856	+	0.382856i
$706$		−	53171.3i		−	0.106676i
$707$		−	1.30817e6i		−	2.61713i
$708$	−103227.	+	103227.i	−0.205933	+	0.205933i
$709$	216688.	−	216688.i	0.431064	−	0.431064i	−0.457926	−	0.888990i	$-0.651408\pi$
$709$	216688.	−	216688.i	0.431064	−	0.431064i	0.888990	+	0.457926i	$0.151408\pi$
$710$	124266.			0.246510
$711$	958406.	−	958406.i	1.89588	−	1.89588i
$712$	−51860.1			−0.102299
$713$	23779.1			0.0467752
$714$			427683.i			0.838929i
$715$	464302.			0.908214
$716$	138834.	−	138834.i	0.270812	−	0.270812i
$717$	−100868.	−	100868.i	−0.196207	−	0.196207i
$718$	−182861.	−	182861.i	−0.354710	−	0.354710i
$719$	535416.			1.03570			0.517849	−	0.855472i	$-0.326733\pi$
$719$	535416.			1.03570			0.517849	+	0.855472i	$0.326733\pi$
$720$	287649.	−	287649.i	0.554878	−	0.554878i
$721$	803611.	+	803611.i	1.54588	+	1.54588i
$722$	509803.	−	509803.i	0.977975	−	0.977975i
$723$	480300.	+	480300.i	0.918833	+	0.918833i
$724$			292080.i			0.557218i
$725$	788826.	−	788826.i	1.50074	−	1.50074i
$726$	158532.	−	158532.i	0.300776	−	0.300776i
$727$	−127653.	−	127653.i	−0.241525	−	0.241525i	0.575956	−	0.817481i	$-0.304630\pi$
$727$	−127653.	−	127653.i	−0.241525	−	0.241525i	−0.817481	+	0.575956i	$0.804630\pi$
$728$		−	223659.i		−	0.422010i
$729$	759198.			1.42857
$730$			631971.i			1.18591i
$731$			189693.i			0.354990i
$732$	−88193.9	−	88193.9i	−0.164595	−	0.164595i
$733$			807186.i			1.50233i	0.660114	+	0.751166i	$0.270508\pi$
$733$			807186.i			1.50233i	−0.660114	+	0.751166i	$0.729492\pi$
$734$	−116789.	−	116789.i	−0.216774	−	0.216774i
$735$	−2.57649e6	−	2.57649e6i	−4.76930	−	4.76930i
$736$	−13468.9			−0.0248642
$737$	−61502.5			−0.113229
$738$	11612.1	−	11612.1i	0.0213206	−	0.0213206i
$739$		−	680780.i		−	1.24657i	−0.781993	−	0.623287i	$-0.785797\pi$
$739$		−	680780.i		−	1.24657i	0.781993	−	0.623287i	$-0.214203\pi$
$740$	434431.	−	190041.i	0.793337	−	0.347043i
$741$	−1.03675e6			−1.88816
$742$	−687158.	−	687158.i	−1.24810	−	1.24810i
$743$			572958.i			1.03788i	0.854812	+	0.518938i	$0.173672\pi$
$743$			572958.i			1.03788i	−0.854812	+	0.518938i	$0.826328\pi$
$744$			109146.i			0.197180i
$745$	470338.	−	470338.i	0.847418	−	0.847418i
$746$	49326.9	−	49326.9i	0.0886352	−	0.0886352i
$747$	−574235.			−1.02908
$748$	−61484.8	+	61484.8i	−0.109892	+	0.109892i
$749$	−931908.			−1.66115
$750$	−1.15438e6			−2.05224
$751$			742295.i			1.31612i	0.752964	+	0.658061i	$0.228623\pi$
$751$			742295.i			1.31612i	−0.752964	+	0.658061i	$0.771377\pi$
$752$	26355.8			0.0466058
$753$	1.08186e6	−	1.08186e6i	1.90800	−	1.90800i
$754$	197608.	+	197608.i	0.347586	+	0.347586i
$755$	598265.	+	598265.i	1.04954	+	1.04954i
$756$	709684.			1.24171
$757$	9211.52	−	9211.52i	0.0160746	−	0.0160746i	−0.699024	−	0.715098i	$-0.746382\pi$
$757$	9211.52	−	9211.52i	0.0160746	−	0.0160746i	0.715098	+	0.699024i	$0.246382\pi$
$758$	165164.	+	165164.i	0.287459	+	0.287459i
$759$	76946.9	−	76946.9i	0.133570	−	0.133570i
$760$	429957.	+	429957.i	0.744385	+	0.744385i
$761$		−	288650.i		−	0.498428i	−0.968448	−	0.249214i	$-0.919828\pi$
$761$		−	288650.i		−	0.498428i	0.968448	−	0.249214i	$-0.0801722\pi$
$762$	−485051.	+	485051.i	−0.835368	+	0.835368i
$763$	143873.	−	143873.i	0.247133	−	0.247133i
$764$	−115836.	−	115836.i	−0.198452	−	0.198452i
$765$			712975.i			1.21829i
$766$	616060.			1.04994
$767$			133804.i			0.227445i
$768$		−	61822.1i		−	0.104815i
$769$	385232.	+	385232.i	0.651432	+	0.651432i	0.953338	−	0.301906i	$-0.0976227\pi$
$769$	385232.	+	385232.i	0.651432	+	0.651432i	−0.301906	+	0.953338i	$0.597623\pi$
$770$		−	1.05981e6i		−	1.78749i
$771$	716726.	+	716726.i	1.20571	+	1.20571i
$772$	291641.	+	291641.i	0.489344	+	0.489344i
$773$	−267159.			−0.447106			−0.223553	−	0.974692i	$-0.571766\pi$
$773$	−267159.			−0.447106			−0.223553	+	0.974692i	$0.571766\pi$
$774$	702210.			1.17215
$775$	282377.	−	282377.i	0.470139	−	0.470139i
$776$			217632.i			0.361410i
$777$	1.71854e6	+	672558.i	2.84654	+	1.11401i
$778$	−287414.			−0.474842
$779$	17357.0	+	17357.0i	0.0286022	+	0.0286022i
$780$		−	578573.i		−	0.950975i
$781$			98326.9i			0.161202i
$782$	16692.2	−	16692.2i	0.0272960	−	0.0272960i
$783$	−627025.	+	627025.i	−1.02273	+	1.02273i
$784$	−356854.			−0.580576
$785$	−650732.	+	650732.i	−1.05600	+	1.05600i
$786$	−48596.9			−0.0786617
$787$	735763.			1.18792			0.593962	−	0.804493i	$-0.297563\pi$
$787$	735763.			1.18792			0.593962	+	0.804493i	$0.297563\pi$
$788$		−	330519.i		−	0.532284i
$789$	771694.			1.23963
$790$	−799458.	+	799458.i	−1.28098	+	1.28098i
$791$	225133.	+	225133.i	0.359820	+	0.359820i
$792$	227606.	+	227606.i	0.362856	+	0.362856i
$793$	−114318.			−0.181789
$794$	−477978.	+	477978.i	−0.758171	+	0.758171i
$795$	−1.77758e6	−	1.77758e6i	−2.81251	−	2.81251i
$796$	349332.	−	349332.i	0.551331	−	0.551331i
$797$	−792427.	−	792427.i	−1.24751	−	1.24751i	−0.956818	−	0.290687i	$-0.906116\pi$
$797$	−792427.	−	792427.i	−1.24751	−	1.24751i	−0.290687	−	0.956818i	$-0.593884\pi$
$798$			2.36647e6i			3.71616i
$799$	−32663.1	+	32663.1i	−0.0511640	+	0.0511640i
$800$	−159943.	+	159943.i	−0.249911	+	0.249911i
$801$	−237920.	−	237920.i	−0.370823	−	0.370823i
$802$			276187.i			0.429393i
$803$	−500056.			−0.775511
$804$			76639.1i			0.118560i
$805$			287720.i			0.443996i
$806$	70738.2	+	70738.2i	0.108889	+	0.108889i
$807$			837365.i			1.28578i
$808$	−234352.	−	234352.i	−0.358959	−	0.358959i
$809$	345820.	+	345820.i	0.528389	+	0.528389i	0.920092	−	0.391703i	$-0.128114\pi$
$809$	345820.	+	345820.i	0.528389	+	0.528389i	−0.391703	+	0.920092i	$0.628114\pi$
$810$	379631.			0.578618
$811$	−1.12531e6			−1.71092			−0.855461	−	0.517867i	$-0.826726\pi$
$811$	−1.12531e6			−1.71092			−0.855461	+	0.517867i	$0.826726\pi$
$812$	451057.	−	451057.i	0.684099	−	0.684099i
$813$		−	1.32883e6i		−	2.01042i
$814$	150373.	+	343750.i	0.226945	+	0.518793i
$815$	318597.			0.479653
$816$	76617.1	+	76617.1i	0.115066	+	0.115066i
$817$			1.04961e6i			1.57248i
$818$		−	680283.i		−	1.01668i
$819$	1.02609e6	−	1.02609e6i	1.52974	−	1.52974i
$820$	−9686.29	+	9686.29i	−0.0144055	+	0.0144055i
$821$	43852.9			0.0650596			0.0325298	−	0.999471i	$-0.489644\pi$
$821$	43852.9			0.0650596			0.0325298	+	0.999471i	$0.489644\pi$
$822$	−837676.	+	837676.i	−1.23975	+	1.23975i
$823$	−1.11924e6			−1.65244			−0.826219	−	0.563348i	$-0.809513\pi$
$823$	−1.11924e6			−1.65244			−0.826219	+	0.563348i	$0.809513\pi$
$824$	287926.			0.424059
$825$		−	1.82749e6i		−	2.68502i
$826$	305417.			0.447645
$827$	−519239.	+	519239.i	−0.759200	+	0.759200i	−0.976177	−	0.216976i	$-0.930381\pi$
$827$	−519239.	+	519239.i	−0.759200	+	0.759200i	0.216976	+	0.976177i	$0.430381\pi$
$828$	−61791.6	−	61791.6i	−0.0901298	−	0.0901298i
$829$	13987.0	+	13987.0i	0.0203523	+	0.0203523i	0.717210	−	0.696857i	$-0.245419\pi$
$829$	13987.0	+	13987.0i	0.0203523	+	0.0203523i	−0.696857	+	0.717210i	$0.745419\pi$
$830$	479000.			0.695312
$831$	220105.	−	220105.i	0.318733	−	0.318733i
$832$	−40067.3	−	40067.3i	−0.0578820	−	0.0578820i
$833$	442255.	−	442255.i	0.637357	−	0.637357i
$834$	252762.	+	252762.i	0.363396	+	0.363396i
$835$		−	1.12925e6i		−	1.61964i
$836$	−340210.	+	340210.i	−0.486782	+	0.486782i
$837$	−224457.	+	224457.i	−0.320393	+	0.320393i
$838$	349763.	+	349763.i	0.498065	+	0.498065i
$839$			563267.i			0.800185i	0.916475	+	0.400092i	$0.131022\pi$
$839$			563267.i			0.800185i	−0.916475	+	0.400092i	$0.868978\pi$
$840$	−1.32064e6			−1.87165
$841$			89760.2i			0.126909i
$842$		−	36809.2i		−	0.0519197i
$843$	1.11273e6	+	1.11273e6i	1.56580	+	1.56580i
$844$			683046.i			0.958882i
$845$	499418.	+	499418.i	0.699441	+	0.699441i
$846$	120913.	+	120913.i	0.168940	+	0.168940i
$847$	−469048.			−0.653809
$848$	−246202.			−0.342373
$849$	762197.	−	762197.i	1.05743	−	1.05743i
$850$		−	396440.i		−	0.548706i
$851$	−40823.8	−	93322.8i	−0.0563709	−	0.128863i
$852$	122527.			0.168792
$853$	−563706.	−	563706.i	−0.774737	−	0.774737i	0.204194	−	0.978931i	$-0.434543\pi$
$853$	−563706.	−	563706.i	−0.774737	−	0.774737i	−0.978931	+	0.204194i	$0.934543\pi$
$854$			260940.i			0.357787i
$855$			3.94506e6i			5.39661i
$856$	−166947.	+	166947.i	−0.227840	+	0.227840i
$857$	−683245.	+	683245.i	−0.930283	+	0.930283i	−0.997723	−	0.0674407i	$-0.978517\pi$
$857$	−683245.	+	683245.i	−0.930283	+	0.930283i	0.0674407	+	0.997723i	$0.478517\pi$
$858$	457805.			0.621879
$859$	99152.8	−	99152.8i	0.134375	−	0.134375i	−0.636720	−	0.771095i	$-0.719709\pi$
$859$	99152.8	−	99152.8i	0.134375	−	0.134375i	0.771095	+	0.636720i	$0.219709\pi$
$860$	−585751.			−0.791983
$861$	−53313.0			−0.0719162
$862$		−	679907.i		−	0.915029i
$863$	281574.			0.378069			0.189035	−	0.981970i	$-0.439464\pi$
$863$	281574.			0.378069			0.189035	+	0.981970i	$0.439464\pi$
$864$	127136.	−	127136.i	0.170311	−	0.170311i
$865$	327890.	+	327890.i	0.438223	+	0.438223i
$866$	72035.3	+	72035.3i	0.0960527	+	0.0960527i
$867$	1.07070e6			1.42439
$868$	161466.	−	161466.i	0.214309	−	0.214309i
$869$	−632583.	−	632583.i	−0.837679	−	0.837679i
$870$	1.16682e6	−	1.16682e6i	1.54158	−	1.54158i
$871$	49670.3	+	49670.3i	0.0654727	+	0.0654727i
$872$		−	51548.2i		−	0.0677923i
$873$	−998439.	+	998439.i	−1.31007	+	1.31007i
$874$	92361.6	−	92361.6i	0.120912	−	0.120912i
$875$	1.70774e6	+	1.70774e6i	2.23052	+	2.23052i
$876$			623127.i			0.812024i
$877$	−558989.			−0.726782			−0.363391	−	0.931637i	$-0.618381\pi$
$877$	−558989.			−0.726782			−0.363391	+	0.931637i	$0.618381\pi$
$878$			371645.i			0.482102i
$879$		−	2.18616e6i		−	2.82946i
$880$	−189859.	−	189859.i	−0.245169	−	0.245169i
$881$		−	674837.i		−	0.869455i	−0.900562	−	0.434728i	$-0.856845\pi$
$881$		−	674837.i		−	0.869455i	0.900562	−	0.434728i	$-0.143155\pi$
$882$	−1.63715e6	−	1.63715e6i	−2.10452	−	2.10452i
$883$	−321620.	−	321620.i	−0.412498	−	0.412498i	0.470110	−	0.882608i	$-0.344214\pi$
$883$	−321620.	−	321620.i	−0.412498	−	0.412498i	−0.882608	+	0.470110i	$0.844214\pi$
$884$	99312.0			0.127086
$885$	790071.			1.00874
$886$	306889.	−	306889.i	0.390944	−	0.390944i
$887$			1.26866e6i			1.61250i	0.591576	+	0.806249i	$0.298506\pi$
$887$			1.26866e6i			1.61250i	−0.591576	+	0.806249i	$0.701494\pi$
$888$	428352.	−	187382.i	0.543219	−	0.237630i
$889$	1.43512e6			1.81587
$890$	198462.	+	198462.i	0.250552	+	0.250552i
$891$			300389.i			0.378380i
$892$			328965.i			0.413447i
$893$	−180733.	+	180733.i	−0.226638	+	0.226638i
$894$	463757.	−	463757.i	0.580250	−	0.580250i
$895$	−1.06260e6			−1.32655
$896$	−91456.7	+	91456.7i	−0.113920	+	0.113920i
$897$	−124287.			−0.154469
$898$	611827.			0.758711
$899$			285318.i			0.353029i
$900$	−1.46755e6			−1.81180
$901$	305121.	−	305121.i	0.375857	−	0.375857i
$902$	−7664.42	−	7664.42i	−0.00942033	−	0.00942033i
$903$	−1.61198e6	−	1.61198e6i	−1.97689	−	1.97689i
$904$	80662.8			0.0987043
$905$	1.11775e6	−	1.11775e6i	1.36474	−	1.36474i
$906$	589893.	+	589893.i	0.718649	+	0.718649i
$907$	498377.	−	498377.i	0.605820	−	0.605820i	−0.336031	−	0.941851i	$-0.609085\pi$
$907$	498377.	−	498377.i	0.605820	−	0.605820i	0.941851	+	0.336031i	$0.109085\pi$
$908$	505409.	+	505409.i	0.613015	+	0.613015i
$909$		−	2.15029e6i		−	2.60237i
$910$	−855914.	+	855914.i	−1.03359	+	1.03359i
$911$	53147.0	−	53147.0i	0.0640386	−	0.0640386i	−0.674362	−	0.738401i	$-0.735581\pi$
$911$	53147.0	−	53147.0i	0.0640386	−	0.0640386i	0.738401	+	0.674362i	$0.235581\pi$
$912$	423940.	+	423940.i	0.509700	+	0.509700i
$913$			379016.i			0.454691i
$914$	−347395.			−0.415845
$915$			675014.i			0.806252i
$916$		−	615267.i		−	0.733285i
$917$	71891.9	+	71891.9i	0.0854952	+	0.0854952i
$918$			315124.i			0.373935i
$919$	415051.	+	415051.i	0.491440	+	0.491440i	0.908760	−	0.417320i	$-0.137030\pi$
$919$	415051.	+	415051.i	0.491440	+	0.491440i	−0.417320	+	0.908760i	$0.637030\pi$
$920$	51543.6	+	51543.6i	0.0608975	+	0.0608975i
$921$	74336.4			0.0876359
$922$	463130.			0.544805
$923$	79410.2	−	79410.2i	0.0932123	−	0.0932123i
$924$		−	1.04497e6i		−	1.22394i
$925$	−1.59300e6	−	623427.i	−1.86179	−	0.728622i
$926$	−1.07749e6			−1.25658
$927$	1.32093e6	+	1.32093e6i	1.53716	+	1.53716i
$928$		−	161609.i		−	0.187659i
$929$			980220.i			1.13577i	0.823106	+	0.567887i	$0.192239\pi$
$929$			980220.i			1.13577i	−0.823106	+	0.567887i	$0.807761\pi$
$930$	417688.	−	417688.i	0.482933	−	0.482933i
$931$	2.44710e6	−	2.44710e6i	2.82327	−	2.82327i
$932$	736844.			0.848288
$933$	−1.77280e6	+	1.77280e6i	−2.03656	+	2.03656i
$934$	771071.			0.883895
$935$	470589.			0.538293
$936$		−	367636.i		−	0.419630i
$937$	−693605.			−0.790011			−0.395006	−	0.918679i	$-0.629257\pi$
$937$	−693605.			−0.790011			−0.395006	+	0.918679i	$0.629257\pi$
$938$	113376.	−	113376.i	0.128860	−	0.128860i
$939$	−212450.	−	212450.i	−0.240949	−	0.240949i
$940$	−100860.	−	100860.i	−0.114147	−	0.114147i
$941$	−1.51182e6			−1.70734			−0.853669	−	0.520816i	$-0.825628\pi$
$941$	−1.51182e6			−1.70734			−0.853669	+	0.520816i	$0.825628\pi$
$942$	−641626.	+	641626.i	−0.723069	+	0.723069i
$943$	2080.77	+	2080.77i	0.00233992	+	0.00233992i
$944$	54713.9	−	54713.9i	0.0613980	−	0.0613980i
$945$	−2.71587e6	−	2.71587e6i	−3.04121	−	3.04121i
$946$		−	463484.i		−	0.517908i
$947$	−394073.	+	394073.i	−0.439417	+	0.439417i	−0.891816	−	0.452399i	$-0.850568\pi$
$947$	−394073.	+	394073.i	−0.439417	+	0.439417i	0.452399	+	0.891816i	$0.350568\pi$
$948$	−788270.	+	788270.i	−0.877119	+	0.877119i
$949$	403853.	+	403853.i	0.448426	+	0.448426i
$950$		−	2.19360e6i		−	2.43058i
$951$	1.04391e6			1.15425
$952$		−	226687.i		−	0.250123i
$953$			1.29125e6i			1.42176i	0.703314	+	0.710879i	$0.251703\pi$
$953$			1.29125e6i			1.42176i	−0.703314	+	0.710879i	$0.748297\pi$
$954$	−1.12951e6	−	1.12951e6i	−1.24106	−	1.24106i
$955$			886576.i			0.972096i
$956$	53463.6	+	53463.6i	0.0584982	+	0.0584982i
$957$	923263.	+	923263.i	1.00810	+	1.00810i
$958$	−225660.			−0.245881
$959$	2.47844e6			2.69489
$960$	−236586.	+	236586.i	−0.256712	+	0.256712i
$961$		−	821385.i		−	0.889406i
$962$	156174.	−	399061.i	0.168756	−	0.431210i
$963$	−1.53181e6			−1.65178
$964$	−254577.	−	254577.i	−0.273946	−	0.273946i
$965$		−	2.23215e6i		−	2.39700i
$966$			283694.i			0.304016i
$967$	73179.4	−	73179.4i	0.0782593	−	0.0782593i	−0.666894	−	0.745153i	$-0.732376\pi$
$967$	73179.4	−	73179.4i	0.0782593	−	0.0782593i	0.745153	+	0.666894i	$0.232376\pi$
$968$	−84027.6	+	84027.6i	−0.0896749	+	0.0896749i
$969$	−1.05079e6			−1.11910
$970$	832851.	−	832851.i	0.885165	−	0.885165i
$971$	−272925.			−0.289471			−0.144735	−	0.989470i	$-0.546233\pi$
$971$	−272925.			−0.289471			−0.144735	+	0.989470i	$0.546233\pi$
$972$	−269309.			−0.285048
$973$		−	747849.i		−	0.789929i
$974$	−1.04738e6			−1.10405
$975$	−1.47591e6	+	1.47591e6i	−1.55257	+	1.55257i
$976$	46746.0	+	46746.0i	0.0490733	+	0.0490733i
$977$	652196.	+	652196.i	0.683264	+	0.683264i	0.960734	−	0.277470i	$-0.0894959\pi$
$977$	652196.	+	652196.i	0.683264	+	0.683264i	−0.277470	+	0.960734i	$0.589496\pi$
$978$	314139.			0.328431
$979$	−157036.	+	157036.i	−0.163845	+	0.163845i
$980$	1.36564e6	+	1.36564e6i	1.42195	+	1.42195i
$981$	236490.	−	236490.i	0.245739	−	0.245739i
$982$	281759.	+	281759.i	0.292183	+	0.292183i
$983$			805131.i			0.833219i	0.909085	+	0.416610i	$0.136782\pi$
$983$			805131.i			0.833219i	−0.909085	+	0.416610i	$0.863218\pi$
$984$	−9550.74	+	9550.74i	−0.00986386	+	0.00986386i
$985$	−1.26485e6	+	1.26485e6i	−1.30367	+	1.30367i
$986$	200284.	+	200284.i	0.206012	+	0.206012i
$987$		−	555131.i		−	0.569851i
$988$	549516.			0.562946
$989$			125829.i			0.128643i
$990$		−	1.74204e6i		−	1.77741i
$991$	−671913.	−	671913.i	−0.684173	−	0.684173i	0.276765	−	0.960938i	$-0.410738\pi$
$991$	−671913.	−	671913.i	−0.684173	−	0.684173i	−0.960938	+	0.276765i	$0.910738\pi$
$992$		−	57851.4i		−	0.0587883i
$993$	616699.	+	616699.i	0.625424	+	0.625424i
$994$	−181260.	−	181260.i	−0.183455	−	0.183455i
$995$	−2.67370e6			−2.70064
$996$	472297.			0.476099
$997$	526360.	−	526360.i	0.529532	−	0.529532i	−0.390901	−	0.920433i	$-0.627836\pi$
$997$	526360.	−	526360.i	0.529532	−	0.529532i	0.920433	+	0.390901i	$0.127836\pi$
$998$		−	232742.i		−	0.233676i
$999$	1.26625e6	+	495552.i	1.26878	+	0.496545i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.b.31.1	✓	14	1.1	even	1	trivial
74.5.d.b.43.7	yes	14	37.6	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} -15.0933i q^{3} +8.00000i q^{4} +(30.6150 - 30.6150i) q^{5} +(30.1866 - 30.1866i) q^{6} -89.3132 q^{7} +(-16.0000 + 16.0000i) q^{8} -146.808 q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} -15.0933i q^{3} +8.00000i q^{4} +(30.6150 - 30.6150i) q^{5} +(30.1866 - 30.1866i) q^{6} -89.3132 q^{7} +(-16.0000 + 16.0000i) q^{8} -146.808 q^{9} +122.460 q^{10} +96.8983i q^{11} +120.746 q^{12} +(78.2564 - 78.2564i) q^{13} +(-178.626 - 178.626i) q^{14} +(-462.081 - 462.081i) q^{15} -64.0000 q^{16} +(79.3162 - 79.3162i) q^{17} +(-293.615 - 293.615i) q^{18} +(438.875 - 438.875i) q^{19} +(244.920 + 244.920i) q^{20} +1348.03i q^{21} +(-193.797 + 193.797i) q^{22} +(52.6127 - 52.6127i) q^{23} +(241.493 + 241.493i) q^{24} -1249.56i q^{25} +313.026 q^{26} +993.252i q^{27} -714.506i q^{28} +(631.285 + 631.285i) q^{29} -1848.32i q^{30} +(225.982 + 225.982i) q^{31} +(-128.000 - 128.000i) q^{32} +1462.51 q^{33} +317.265 q^{34} +(-2734.32 + 2734.32i) q^{35} -1174.46i q^{36} +(498.919 - 1274.85i) q^{37} +1755.50 q^{38} +(-1181.15 - 1181.15i) q^{39} +979.680i q^{40} +39.5488i q^{41} +(-2696.06 + 2696.06i) q^{42} +(-1195.80 + 1195.80i) q^{43} -775.186 q^{44} +(-4494.51 + 4494.51i) q^{45} +210.451 q^{46} -411.809 q^{47} +965.971i q^{48} +5575.85 q^{49} +(2499.11 - 2499.11i) q^{50} +(-1197.14 - 1197.14i) q^{51} +(626.051 + 626.051i) q^{52} +3846.90 q^{53} +(-1986.50 + 1986.50i) q^{54} +(2966.54 + 2966.54i) q^{55} +(1429.01 - 1429.01i) q^{56} +(-6624.07 - 6624.07i) q^{57} +2525.14i q^{58} +(-854.905 + 854.905i) q^{59} +(3696.65 - 3696.65i) q^{60} +(-730.406 - 730.406i) q^{61} +903.929i q^{62} +13111.9 q^{63} -512.000i q^{64} -4791.64i q^{65} +(2925.03 + 2925.03i) q^{66} +634.712i q^{67} +(634.530 + 634.530i) q^{68} +(-794.099 - 794.099i) q^{69} -10937.3 q^{70} +1014.74 q^{71} +(2348.92 - 2348.92i) q^{72} +5160.63i q^{73} +(3547.54 - 1551.86i) q^{74} -18859.9 q^{75} +(3511.00 + 3511.00i) q^{76} -8654.30i q^{77} -4724.59i q^{78} +(-6528.32 + 6528.32i) q^{79} +(-1959.36 + 1959.36i) q^{80} +3100.04 q^{81} +(-79.0976 + 79.0976i) q^{82} +3911.48 q^{83} -10784.2 q^{84} -4856.53i q^{85} -4783.20 q^{86} +(9528.17 - 9528.17i) q^{87} +(-1550.37 - 1550.37i) q^{88} +(1620.63 + 1620.63i) q^{89} -17978.1 q^{90} +(-6989.33 + 6989.33i) q^{91} +(420.902 + 420.902i) q^{92} +(3410.82 - 3410.82i) q^{93} +(-823.618 - 823.618i) q^{94} -26872.3i q^{95} +(-1931.94 + 1931.94i) q^{96} +(6801.01 - 6801.01i) q^{97} +(11151.7 + 11151.7i) q^{98} -14225.4i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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