LMFDB - Embedded newform 74.5.d.a.43.4

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			43.4
Root			$3.21245i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} +4.21245i q^{3} -8.00000i q^{4} +(-19.1769 - 19.1769i) q^{5} +(-8.42489 - 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 + 16.0000i) q^{8} +63.2553 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} +4.21245i q^{3} -8.00000i q^{4} +(-19.1769 - 19.1769i) q^{5} +(-8.42489 - 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 + 16.0000i) q^{8} +63.2553 q^{9} +76.7077 q^{10} +199.490i q^{11} +33.6996 q^{12} +(-144.421 - 144.421i) q^{13} +(-139.296 + 139.296i) q^{14} +(80.7817 - 80.7817i) q^{15} -64.0000 q^{16} +(182.724 + 182.724i) q^{17} +(-126.511 + 126.511i) q^{18} +(286.750 + 286.750i) q^{19} +(-153.415 + 153.415i) q^{20} +293.388i q^{21} +(-398.981 - 398.981i) q^{22} +(522.190 + 522.190i) q^{23} +(-67.3991 + 67.3991i) q^{24} +110.508i q^{25} +577.683 q^{26} +607.668i q^{27} -557.184i q^{28} +(807.381 - 807.381i) q^{29} +323.127i q^{30} +(-14.9070 + 14.9070i) q^{31} +(128.000 - 128.000i) q^{32} -840.342 q^{33} -730.895 q^{34} +(-1335.63 - 1335.63i) q^{35} -506.042i q^{36} +(563.418 - 1247.69i) q^{37} -1147.00 q^{38} +(608.365 - 608.365i) q^{39} -613.661i q^{40} +1999.86i q^{41} +(-586.777 - 586.777i) q^{42} +(-695.357 - 695.357i) q^{43} +1595.92 q^{44} +(-1213.04 - 1213.04i) q^{45} -2088.76 q^{46} +3634.49 q^{47} -269.597i q^{48} +2449.84 q^{49} +(-221.017 - 221.017i) q^{50} +(-769.715 + 769.715i) q^{51} +(-1155.37 + 1155.37i) q^{52} -5476.01 q^{53} +(-1215.34 - 1215.34i) q^{54} +(3825.61 - 3825.61i) q^{55} +(1114.37 + 1114.37i) q^{56} +(-1207.92 + 1207.92i) q^{57} +3229.52i q^{58} +(-2654.85 - 2654.85i) q^{59} +(-646.254 - 646.254i) q^{60} +(2147.75 - 2147.75i) q^{61} -59.6280i q^{62} +4405.60 q^{63} +512.000i q^{64} +5539.09i q^{65} +(1680.68 - 1680.68i) q^{66} +3139.82i q^{67} +(1461.79 - 1461.79i) q^{68} +(-2199.70 + 2199.70i) q^{69} +5342.53 q^{70} -8727.42 q^{71} +(1012.08 + 1012.08i) q^{72} +2589.63i q^{73} +(1368.54 + 3622.21i) q^{74} -465.511 q^{75} +(2294.00 - 2294.00i) q^{76} +13894.1i q^{77} +2433.46i q^{78} +(-5000.77 - 5000.77i) q^{79} +(1227.32 + 1227.32i) q^{80} +2563.91 q^{81} +(-3999.72 - 3999.72i) q^{82} +7655.48 q^{83} +2347.11 q^{84} -7008.16i q^{85} +2781.43 q^{86} +(3401.05 + 3401.05i) q^{87} +(-3191.85 + 3191.85i) q^{88} +(1510.94 - 1510.94i) q^{89} +4852.17 q^{90} +(-10058.6 - 10058.6i) q^{91} +(4177.52 - 4177.52i) q^{92} +(-62.7950 - 62.7950i) q^{93} +(-7268.97 + 7268.97i) q^{94} -10998.0i q^{95} +(539.193 + 539.193i) q^{96} +(6903.19 + 6903.19i) q^{97} +(-4899.68 + 4899.68i) q^{98} +12618.8i 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
$3$			4.21245i			0.468050i	0.972231	+	0.234025i	$0.0751897\pi$
$3$			4.21245i			0.468050i	−0.972231	+	0.234025i	$0.924810\pi$
$4$		−	8.00000i		−	0.500000i
$5$	−19.1769	−	19.1769i	−0.767077	−	0.767077i	0.210514	−	0.977591i	$-0.432486\pi$
$5$	−19.1769	−	19.1769i	−0.767077	−	0.767077i	−0.977591	+	0.210514i	$0.932486\pi$
$6$	−8.42489	−	8.42489i	−0.234025	−	0.234025i
$7$	69.6480			1.42139			0.710694	−	0.703502i	$-0.248381\pi$
$7$	69.6480			1.42139			0.710694	+	0.703502i	$0.248381\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	63.2553			0.780930
$10$	76.7077			0.767077
$11$			199.490i			1.64868i	0.566095	+	0.824340i	$0.308454\pi$
$11$			199.490i			1.64868i	−0.566095	+	0.824340i	$0.691546\pi$
$12$	33.6996			0.234025
$13$	−144.421	−	144.421i	−0.854561	−	0.854561i	0.136130	−	0.990691i	$-0.456534\pi$
$13$	−144.421	−	144.421i	−0.854561	−	0.854561i	−0.990691	+	0.136130i	$0.956534\pi$
$14$	−139.296	+	139.296i	−0.710694	+	0.710694i
$15$	80.7817	−	80.7817i	0.359030	−	0.359030i
$16$	−64.0000			−0.250000
$17$	182.724	+	182.724i	0.632262	+	0.632262i	0.948635	−	0.316373i	$-0.102465\pi$
$17$	182.724	+	182.724i	0.632262	+	0.632262i	−0.316373	+	0.948635i	$0.602465\pi$
$18$	−126.511	+	126.511i	−0.390465	+	0.390465i
$19$	286.750	+	286.750i	0.794321	+	0.794321i	0.982193	−	0.187873i	$-0.0601592\pi$
$19$	286.750	+	286.750i	0.794321	+	0.794321i	−0.187873	+	0.982193i	$0.560159\pi$
$20$	−153.415	+	153.415i	−0.383538	+	0.383538i
$21$			293.388i			0.665280i
$22$	−398.981	−	398.981i	−0.824340	−	0.824340i
$23$	522.190	+	522.190i	0.987126	+	0.987126i	0.999918	−	0.0127919i	$-0.00407190\pi$
$23$	522.190	+	522.190i	0.987126	+	0.987126i	−0.0127919	+	0.999918i	$0.504072\pi$
$24$	−67.3991	+	67.3991i	−0.117012	+	0.117012i
$25$			110.508i			0.176813i
$26$	577.683			0.854561
$27$			607.668i			0.833563i
$28$		−	557.184i		−	0.710694i
$29$	807.381	−	807.381i	0.960025	−	0.960025i	−0.0392061	−	0.999231i	$-0.512483\pi$
$29$	807.381	−	807.381i	0.960025	−	0.960025i	0.999231	+	0.0392061i	$0.0124829\pi$
$30$			323.127i			0.359030i
$31$	−14.9070	+	14.9070i	−0.0155120	+	0.0155120i	−0.714820	−	0.699308i	$-0.753491\pi$
$31$	−14.9070	+	14.9070i	−0.0155120	+	0.0155120i	0.699308	+	0.714820i	$0.253491\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−840.342			−0.771664
$34$	−730.895			−0.632262
$35$	−1335.63	−	1335.63i	−1.09031	−	1.09031i
$36$		−	506.042i		−	0.390465i
$37$	563.418	−	1247.69i	0.411554	−	0.911385i
$37$	563.418	−	1247.69i	0.411554	−	0.911385i
$38$	−1147.00			−0.794321
$39$	608.365	−	608.365i	0.399977	−	0.399977i
$40$		−	613.661i		−	0.383538i
$41$			1999.86i			1.18969i	0.803842	+	0.594843i	$0.202786\pi$
$41$			1999.86i			1.18969i	−0.803842	+	0.594843i	$0.797214\pi$
$42$	−586.777	−	586.777i	−0.332640	−	0.332640i
$43$	−695.357	−	695.357i	−0.376072	−	0.376072i	0.493611	−	0.869683i	$-0.335677\pi$
$43$	−695.357	−	695.357i	−0.376072	−	0.376072i	−0.869683	+	0.493611i	$0.835677\pi$
$44$	1595.92			0.824340
$45$	−1213.04	−	1213.04i	−0.599033	−	0.599033i
$46$	−2088.76			−0.987126
$47$	3634.49			1.64531			0.822654	−	0.568542i	$-0.192492\pi$
$47$	3634.49			1.64531			0.822654	+	0.568542i	$0.192492\pi$
$48$		−	269.597i		−	0.117012i
$49$	2449.84			1.02034
$50$	−221.017	−	221.017i	−0.0884067	−	0.0884067i
$51$	−769.715	+	769.715i	−0.295930	+	0.295930i
$52$	−1155.37	+	1155.37i	−0.427281	+	0.427281i
$53$	−5476.01			−1.94945			−0.974726	−	0.223404i	$-0.928283\pi$
$53$	−5476.01			−1.94945			−0.974726	+	0.223404i	$0.928283\pi$
$54$	−1215.34	−	1215.34i	−0.416782	−	0.416782i
$55$	3825.61	−	3825.61i	1.26466	−	1.26466i
$56$	1114.37	+	1114.37i	0.355347	+	0.355347i
$57$	−1207.92	+	1207.92i	−0.371782	+	0.371782i
$58$			3229.52i			0.960025i
$59$	−2654.85	−	2654.85i	−0.762668	−	0.762668i	0.214136	−	0.976804i	$-0.431306\pi$
$59$	−2654.85	−	2654.85i	−0.762668	−	0.762668i	−0.976804	+	0.214136i	$0.931306\pi$
$60$	−646.254	−	646.254i	−0.179515	−	0.179515i
$61$	2147.75	−	2147.75i	0.577198	−	0.577198i	−0.356933	−	0.934130i	$-0.616177\pi$
$61$	2147.75	−	2147.75i	0.577198	−	0.577198i	0.934130	+	0.356933i	$0.116177\pi$
$62$		−	59.6280i		−	0.0155120i
$63$	4405.60			1.11000
$64$			512.000i			0.125000i
$65$			5539.09i			1.31103i
$66$	1680.68	−	1680.68i	0.385832	−	0.385832i
$67$			3139.82i			0.699447i	0.936853	+	0.349723i	$0.113724\pi$
$67$			3139.82i			0.699447i	−0.936853	+	0.349723i	$0.886276\pi$
$68$	1461.79	−	1461.79i	0.316131	−	0.316131i
$69$	−2199.70	+	2199.70i	−0.462024	+	0.462024i
$70$	5342.53			1.09031
$71$	−8727.42			−1.73129			−0.865644	−	0.500660i	$-0.833091\pi$
$71$	−8727.42			−1.73129			−0.865644	+	0.500660i	$0.833091\pi$
$72$	1012.08	+	1012.08i	0.195232	+	0.195232i
$73$			2589.63i			0.485951i	0.970032	+	0.242975i	$0.0781234\pi$
$73$			2589.63i			0.485951i	−0.970032	+	0.242975i	$0.921877\pi$
$74$	1368.54	+	3622.21i	0.249916	+	0.661470i
$75$	−465.511			−0.0827574
$76$	2294.00	−	2294.00i	0.397160	−	0.397160i
$77$			13894.1i			2.34341i
$78$			2433.46i			0.399977i
$79$	−5000.77	−	5000.77i	−0.801277	−	0.801277i	0.182018	−	0.983295i	$-0.441737\pi$
$79$	−5000.77	−	5000.77i	−0.801277	−	0.801277i	−0.983295	+	0.182018i	$0.941737\pi$
$80$	1227.32	+	1227.32i	0.191769	+	0.191769i
$81$	2563.91			0.390780
$82$	−3999.72	−	3999.72i	−0.594843	−	0.594843i
$83$	7655.48			1.11126			0.555630	−	0.831429i	$-0.312477\pi$
$83$	7655.48			1.11126			0.555630	+	0.831429i	$0.312477\pi$
$84$	2347.11			0.332640
$85$		−	7008.16i		−	0.969988i
$86$	2781.43			0.376072
$87$	3401.05	+	3401.05i	0.449339	+	0.449339i
$88$	−3191.85	+	3191.85i	−0.412170	+	0.412170i
$89$	1510.94	−	1510.94i	0.190751	−	0.190751i	−0.605269	−	0.796021i	$-0.706935\pi$
$89$	1510.94	−	1510.94i	0.190751	−	0.190751i	0.796021	+	0.605269i	$0.206935\pi$
$90$	4852.17			0.599033
$91$	−10058.6	−	10058.6i	−1.21466	−	1.21466i
$92$	4177.52	−	4177.52i	0.493563	−	0.493563i
$93$	−62.7950	−	62.7950i	−0.00726037	−	0.00726037i
$94$	−7268.97	+	7268.97i	−0.822654	+	0.822654i
$95$		−	10998.0i		−	1.21861i
$96$	539.193	+	539.193i	0.0585062	+	0.0585062i
$97$	6903.19	+	6903.19i	0.733679	+	0.733679i	0.971347	−	0.237668i	$-0.0763829\pi$
$97$	6903.19	+	6903.19i	0.733679	+	0.733679i	−0.237668	+	0.971347i	$0.576383\pi$
$98$	−4899.68	+	4899.68i	−0.510171	+	0.510171i
$99$			12618.8i			1.28750i
$100$	884.067			0.0884067
$101$			4067.47i			0.398733i	0.979925	+	0.199366i	$0.0638884\pi$
$101$			4067.47i			0.398733i	−0.979925	+	0.199366i	$0.936112\pi$
$102$		−	3078.86i		−	0.295930i
$103$	−3530.32	+	3530.32i	−0.332766	+	0.332766i	−0.853636	−	0.520870i	$-0.825608\pi$
$103$	−3530.32	+	3530.32i	−0.332766	+	0.332766i	0.520870	+	0.853636i	$0.325608\pi$
$104$		−	4621.47i		−	0.427281i
$105$	5626.28	−	5626.28i	0.510321	−	0.510321i
$106$	10952.0	−	10952.0i	0.974726	−	0.974726i
$107$	−3980.95			−0.347711			−0.173856	−	0.984771i	$-0.555623\pi$
$107$	−3980.95			−0.347711			−0.173856	+	0.984771i	$0.555623\pi$
$108$	4861.34			0.416782
$109$	−10492.1	−	10492.1i	−0.883100	−	0.883100i	0.110749	−	0.993848i	$-0.464675\pi$
$109$	−10492.1	−	10492.1i	−0.883100	−	0.883100i	−0.993848	+	0.110749i	$0.964675\pi$
$110$			15302.4i			1.26466i
$111$	5255.81	+	2373.37i	0.426574	+	0.192628i
$112$	−4457.47			−0.355347
$113$	3833.10	−	3833.10i	0.300188	−	0.300188i	−0.540899	−	0.841087i	$-0.681916\pi$
$113$	3833.10	−	3833.10i	0.300188	−	0.300188i	0.841087	+	0.540899i	$0.181916\pi$
$114$		−	4831.67i		−	0.371782i
$115$		−	20028.0i		−	1.51440i
$116$	−6459.05	−	6459.05i	−0.480013	−	0.480013i
$117$	−9135.38	−	9135.38i	−0.667352	−	0.667352i
$118$	10619.4			0.762668
$119$	12726.3	+	12726.3i	0.898690	+	0.898690i
$120$	2585.02			0.179515
$121$	−25155.4			−1.71815
$122$			8591.01i			0.577198i
$123$	−8424.31			−0.556832
$124$	119.256	+	119.256i	0.00775599	+	0.00775599i
$125$	−9866.36	+	9866.36i	−0.631447	+	0.631447i
$126$	−8811.21	+	8811.21i	−0.555002	+	0.555002i
$127$	−11767.5			−0.729584			−0.364792	−	0.931089i	$-0.618860\pi$
$127$	−11767.5			−0.729584			−0.364792	+	0.931089i	$0.618860\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	2929.15	−	2929.15i	0.176020	−	0.176020i
$130$	−11078.2	−	11078.2i	−0.655514	−	0.655514i
$131$	3889.24	−	3889.24i	0.226633	−	0.226633i	−0.584652	−	0.811284i	$-0.698769\pi$
$131$	3889.24	−	3889.24i	0.226633	−	0.226633i	0.811284	+	0.584652i	$0.198769\pi$
$132$			6722.74i			0.385832i
$133$	19971.5	+	19971.5i	1.12904	+	1.12904i
$134$	−6279.63	−	6279.63i	−0.349723	−	0.349723i
$135$	11653.2	−	11653.2i	0.639407	−	0.639407i
$136$			5847.16i			0.316131i
$137$	−4011.56			−0.213733			−0.106867	−	0.994273i	$-0.534082\pi$
$137$	−4011.56			−0.213733			−0.106867	+	0.994273i	$0.534082\pi$
$138$		−	8798.79i		−	0.462024i
$139$		−	12804.1i		−	0.662703i	−0.943507	−	0.331352i	$-0.892495\pi$
$139$		−	12804.1i		−	0.662703i	0.943507	−	0.331352i	$-0.107505\pi$
$140$	−10685.1	+	10685.1i	−0.545156	+	0.545156i
$141$			15310.1i			0.770086i
$142$	17454.8	−	17454.8i	0.865644	−	0.865644i
$143$	28810.6	−	28810.6i	1.40890	−	1.40890i
$144$	−4048.34			−0.195232
$145$	−30966.2			−1.47283
$146$	−5179.26	−	5179.26i	−0.242975	−	0.242975i
$147$			10319.8i			0.477570i
$148$	−9981.49	−	4507.34i	−0.455693	−	0.205777i
$149$	−10327.6			−0.465188			−0.232594	−	0.972574i	$-0.574721\pi$
$149$	−10327.6			−0.465188			−0.232594	+	0.972574i	$0.574721\pi$
$150$	931.021	−	931.021i	0.0413787	−	0.0413787i
$151$		−	3098.02i		−	0.135872i	−0.997690	−	0.0679361i	$-0.978359\pi$
$151$		−	3098.02i		−	0.135872i	0.997690	−	0.0679361i	$-0.0216414\pi$
$152$			9175.99i			0.397160i
$153$	11558.3	+	11558.3i	0.493752	+	0.493752i
$154$	−27788.2	−	27788.2i	−1.17171	−	1.17171i
$155$	571.741			0.0237977
$156$	−4866.92	−	4866.92i	−0.199989	−	0.199989i
$157$	25876.9			1.04982			0.524908	−	0.851159i	$-0.324100\pi$
$157$	25876.9			1.04982			0.524908	+	0.851159i	$0.324100\pi$
$158$	20003.1			0.801277
$159$		−	23067.4i		−	0.912440i
$160$	−4909.29			−0.191769
$161$	36369.5	+	36369.5i	1.40309	+	1.40309i
$162$	−5127.82	+	5127.82i	−0.195390	+	0.195390i
$163$	25137.3	−	25137.3i	0.946113	−	0.946113i	−0.0525075	−	0.998621i	$-0.516721\pi$
$163$	25137.3	−	25137.3i	0.946113	−	0.946113i	0.998621	+	0.0525075i	$0.0167214\pi$
$164$	15998.9			0.594843
$165$	16115.2	+	16115.2i	0.591926	+	0.591926i
$166$	−15311.0	+	15311.0i	−0.555630	+	0.555630i
$167$	−14868.5	−	14868.5i	−0.533133	−	0.533133i	0.388370	−	0.921503i	$-0.373038\pi$
$167$	−14868.5	−	14868.5i	−0.533133	−	0.533133i	−0.921503	+	0.388370i	$0.873038\pi$
$168$	−4694.21	+	4694.21i	−0.166320	+	0.166320i
$169$			13153.8i			0.460550i
$170$	14016.3	+	14016.3i	0.484994	+	0.484994i
$171$	18138.4	+	18138.4i	0.620308	+	0.620308i
$172$	−5562.86	+	5562.86i	−0.188036	+	0.188036i
$173$		−	16482.6i		−	0.550722i	−0.961341	−	0.275361i	$-0.911203\pi$
$173$		−	16482.6i		−	0.550722i	0.961341	−	0.275361i	$-0.0887974\pi$
$174$	−13604.2			−0.449339
$175$			7696.68i			0.251320i
$176$		−	12767.4i		−	0.412170i
$177$	11183.4	−	11183.4i	0.356966	−	0.356966i
$178$			6043.77i			0.190751i
$179$	−26077.6	+	26077.6i	−0.813883	+	0.813883i	−0.985214	−	0.171331i	$-0.945193\pi$
$179$	−26077.6	+	26077.6i	−0.813883	+	0.813883i	0.171331	+	0.985214i	$0.445193\pi$
$180$	−9704.33	+	9704.33i	−0.299516	+	0.299516i
$181$	22685.0			0.692440			0.346220	−	0.938153i	$-0.387465\pi$
$181$	22685.0			0.692440			0.346220	+	0.938153i	$0.387465\pi$
$182$	40234.5			1.21466
$183$	9047.29	+	9047.29i	0.270157	+	0.270157i
$184$			16710.1i			0.493563i
$185$	−34731.4	+	13122.2i	−1.01480	+	0.383409i
$186$	251.180			0.00726037
$187$	−36451.6	+	36451.6i	−1.04240	+	1.04240i
$188$		−	29075.9i		−	0.822654i
$189$			42322.8i			1.18482i
$190$	21995.9	+	21995.9i	0.609305	+	0.609305i
$191$	12997.0	+	12997.0i	0.356267	+	0.356267i	0.862435	−	0.506168i	$-0.168938\pi$
$191$	12997.0	+	12997.0i	0.356267	+	0.356267i	−0.506168	+	0.862435i	$0.668938\pi$
$192$	−2156.77			−0.0585062
$193$	658.999	+	658.999i	0.0176917	+	0.0176917i	0.715897	−	0.698206i	$-0.246018\pi$
$193$	658.999	+	658.999i	0.0176917	+	0.0176917i	−0.698206	+	0.715897i	$0.746018\pi$
$194$	−27612.7			−0.733679
$195$	−23333.1			−0.613626
$196$		−	19598.7i		−	0.510171i
$197$	−18678.2			−0.481286			−0.240643	−	0.970614i	$-0.577358\pi$
$197$	−18678.2			−0.481286			−0.240643	+	0.970614i	$0.577358\pi$
$198$	−25237.6	−	25237.6i	−0.643752	−	0.643752i
$199$	−220.974	+	220.974i	−0.00558002	+	0.00558002i	−0.709891	−	0.704311i	$-0.751256\pi$
$199$	−220.974	+	220.974i	−0.00558002	+	0.00558002i	0.704311	+	0.709891i	$0.251256\pi$
$200$	−1768.13	+	1768.13i	−0.0442033	+	0.0442033i
$201$	−13226.3			−0.327376
$202$	−8134.95	−	8134.95i	−0.199366	−	0.199366i
$203$	56232.5	−	56232.5i	1.36457	−	1.36457i
$204$	6157.72	+	6157.72i	0.147965	+	0.147965i
$205$	38351.2	−	38351.2i	0.912580	−	0.912580i
$206$		−	14121.3i		−	0.332766i
$207$	33031.3	+	33031.3i	0.770876	+	0.770876i
$208$	9242.93	+	9242.93i	0.213640	+	0.213640i
$209$	−57203.8	+	57203.8i	−1.30958	+	1.30958i
$210$			22505.1i			0.510321i
$211$	−11470.3			−0.257639			−0.128819	−	0.991668i	$-0.541119\pi$
$211$	−11470.3			−0.257639			−0.128819	+	0.991668i	$0.541119\pi$
$212$			43808.1i			0.974726i
$213$		−	36763.8i		−	0.810329i
$214$	7961.89	−	7961.89i	0.173856	−	0.173856i
$215$			26669.6i			0.576952i
$216$	−9722.68	+	9722.68i	−0.208391	+	0.208391i
$217$	−1038.24	+	1038.24i	−0.0220485	+	0.0220485i
$218$	41968.4			0.883100
$219$	−10908.7			−0.227449
$220$	−30604.9	−	30604.9i	−0.632332	−	0.632332i
$221$		−	52778.3i		−	1.08061i
$222$	−15258.4	+	5764.89i	−0.309601	+	0.116973i
$223$	62440.7			1.25562			0.627809	−	0.778367i	$-0.283952\pi$
$223$	62440.7			1.25562			0.627809	+	0.778367i	$0.283952\pi$
$224$	8914.94	−	8914.94i	0.177673	−	0.177673i
$225$			6990.24i			0.138079i
$226$			15332.4i			0.300188i
$227$	3157.08	+	3157.08i	0.0612680	+	0.0612680i	0.737077	−	0.675809i	$-0.236206\pi$
$227$	3157.08	+	3157.08i	0.0612680	+	0.0612680i	−0.675809	+	0.737077i	$0.736206\pi$
$228$	9663.35	+	9663.35i	0.185891	+	0.185891i
$229$	23594.7			0.449929			0.224965	−	0.974367i	$-0.427773\pi$
$229$	23594.7			0.449929			0.224965	+	0.974367i	$0.427773\pi$
$230$	40056.0	+	40056.0i	0.757202	+	0.757202i
$231$	−58528.1			−1.09683
$232$	25836.2			0.480013
$233$		−	66323.8i		−	1.22168i	−0.791754	−	0.610840i	$-0.790832\pi$
$233$		−	66323.8i		−	1.22168i	0.791754	−	0.610840i	$-0.209168\pi$
$234$	36541.5			0.667352
$235$	−69698.2	−	69698.2i	−1.26208	−	1.26208i
$236$	−21238.8	+	21238.8i	−0.381334	+	0.381334i
$237$	21065.5	−	21065.5i	0.375038	−	0.375038i
$238$	−50905.4			−0.898690
$239$	−60579.6	−	60579.6i	−1.06055	−	1.06055i	−0.998045	−	0.0625039i	$-0.980091\pi$
$239$	−60579.6	−	60579.6i	−1.06055	−	1.06055i	−0.0625039	−	0.998045i	$-0.519909\pi$
$240$	−5170.03	+	5170.03i	−0.0897575	+	0.0897575i
$241$	−35030.0	−	35030.0i	−0.603124	−	0.603124i	0.338016	−	0.941140i	$-0.390244\pi$
$241$	−35030.0	−	35030.0i	−0.603124	−	0.603124i	−0.941140	+	0.338016i	$0.890244\pi$
$242$	50310.8	−	50310.8i	0.859074	−	0.859074i
$243$			60021.4i			1.01647i
$244$	−17182.0	−	17182.0i	−0.288599	−	0.288599i
$245$	−46980.4	−	46980.4i	−0.782680	−	0.782680i
$246$	16848.6	−	16848.6i	0.278416	−	0.278416i
$247$		−	82825.3i		−	1.35759i
$248$	−477.024			−0.00775599
$249$			32248.3i			0.520125i
$250$		−	39465.5i		−	0.631447i
$251$	−626.235	+	626.235i	−0.00994008	+	0.00994008i	−0.712059	−	0.702119i	$-0.752237\pi$
$251$	−626.235	+	626.235i	−0.00994008	+	0.00994008i	0.702119	+	0.712059i	$0.252237\pi$
$252$		−	35244.8i		−	0.555002i
$253$	−104172.	+	104172.i	−1.62746	+	1.62746i
$254$	23534.9	−	23534.9i	0.364792	−	0.364792i
$255$	29521.5			0.454002
$256$	4096.00			0.0625000
$257$	−81648.3	−	81648.3i	−1.23618	−	1.23618i	−0.961551	−	0.274627i	$-0.911446\pi$
$257$	−81648.3	−	81648.3i	−1.23618	−	1.23618i	−0.274627	−	0.961551i	$-0.588554\pi$
$258$			11716.6i			0.176020i
$259$	39240.9	−	86898.8i	0.584978	−	1.29543i
$260$	44312.7			0.655514
$261$	51071.1	−	51071.1i	0.749712	−	0.749712i
$262$			15557.0i			0.226633i
$263$			101344.i			1.46516i	0.680682	+	0.732579i	$0.261684\pi$
$263$			101344.i			1.46516i	−0.680682	+	0.732579i	$0.738316\pi$
$264$	−13445.5	−	13445.5i	−0.192916	−	0.192916i
$265$	105013.	+	105013.i	1.49538	+	1.49538i
$266$	−79886.2			−1.12904
$267$	6364.76	+	6364.76i	0.0892811	+	0.0892811i
$268$	25118.5			0.349723
$269$	−57952.5			−0.800880			−0.400440	−	0.916323i	$-0.631143\pi$
$269$	−57952.5			−0.800880			−0.400440	+	0.916323i	$0.631143\pi$
$270$			46612.8i			0.639407i
$271$	−20499.4			−0.279127			−0.139563	−	0.990213i	$-0.544570\pi$
$271$	−20499.4			−0.279127			−0.139563	+	0.990213i	$0.544570\pi$
$272$	−11694.3	−	11694.3i	−0.158066	−	0.158066i
$273$	42371.4	−	42371.4i	0.568522	−	0.568522i
$274$	8023.12	−	8023.12i	0.106867	−	0.106867i
$275$	−22045.3			−0.291509
$276$	17597.6	+	17597.6i	0.231012	+	0.231012i
$277$	−28228.9	+	28228.9i	−0.367904	+	0.367904i	−0.866712	−	0.498808i	$-0.833771\pi$
$277$	−28228.9	+	28228.9i	−0.367904	+	0.367904i	0.498808	+	0.866712i	$0.333771\pi$
$278$	25608.2	+	25608.2i	0.331352	+	0.331352i
$279$	−942.947	+	942.947i	−0.0121138	+	0.0121138i
$280$		−	42740.3i		−	0.545156i
$281$	19823.4	+	19823.4i	0.251053	+	0.251053i	0.821402	−	0.570349i	$-0.193192\pi$
$281$	19823.4	+	19823.4i	0.251053	+	0.251053i	−0.570349	+	0.821402i	$0.693192\pi$
$282$	−30620.2	−	30620.2i	−0.385043	−	0.385043i
$283$	2415.84	−	2415.84i	0.0301645	−	0.0301645i	−0.691864	−	0.722028i	$-0.743210\pi$
$283$	2415.84	−	2415.84i	0.0301645	−	0.0301645i	0.722028	+	0.691864i	$0.243210\pi$
$284$			69819.4i			0.865644i
$285$	46328.3			0.570370
$286$			115242.i			1.40890i
$287$			139286.i			1.69100i
$288$	8096.68	−	8096.68i	0.0976162	−	0.0976162i
$289$		−	16745.0i		−	0.200488i
$290$	61932.3	−	61932.3i	0.736413	−	0.736413i
$291$	−29079.3	+	29079.3i	−0.343398	+	0.343398i
$292$	20717.0			0.242975
$293$	155148.			1.80722			0.903610	−	0.428357i	$-0.140907\pi$
$293$	155148.			1.80722			0.903610	+	0.428357i	$0.140907\pi$
$294$	−20639.6	−	20639.6i	−0.238785	−	0.238785i
$295$			101824.i			1.17005i
$296$	28977.7	−	10948.3i	0.330735	−	0.124958i
$297$	−121224.			−1.37428
$298$	20655.3	−	20655.3i	0.232594	−	0.232594i
$299$		−	150830.i		−	1.68712i
$300$			3724.08i			0.0413787i
$301$	−48430.2	−	48430.2i	−0.534544	−	0.534544i
$302$	6196.05	+	6196.05i	0.0679361	+	0.0679361i
$303$	−17134.0			−0.186627
$304$	−18352.0	−	18352.0i	−0.198580	−	0.198580i
$305$	−82374.5			−0.885510
$306$	−46233.0			−0.493752
$307$			80298.9i			0.851987i	0.904726	+	0.425994i	$0.140075\pi$
$307$			80298.9i			0.851987i	−0.904726	+	0.425994i	$0.859925\pi$
$308$	111153.			1.17171
$309$	−14871.3	−	14871.3i	−0.155751	−	0.155751i
$310$	−1143.48	+	1143.48i	−0.0118989	+	0.0118989i
$311$	−78560.0	+	78560.0i	−0.812233	+	0.812233i	−0.984968	−	0.172735i	$-0.944739\pi$
$311$	−78560.0	+	78560.0i	−0.812233	+	0.812233i	0.172735	+	0.984968i	$0.444739\pi$
$312$	19467.7			0.199989
$313$	43754.1	+	43754.1i	0.446611	+	0.446611i	0.894226	−	0.447615i	$-0.147726\pi$
$313$	43754.1	+	43754.1i	0.446611	+	0.446611i	−0.447615	+	0.894226i	$0.647726\pi$
$314$	−51753.9	+	51753.9i	−0.524908	+	0.524908i
$315$	−84485.9	−	84485.9i	−0.851458	−	0.851458i
$316$	−40006.2	+	40006.2i	−0.400639	+	0.400639i
$317$			49960.2i			0.497171i	0.968610	+	0.248585i	$0.0799656\pi$
$317$			49960.2i			0.497171i	−0.968610	+	0.248585i	$0.920034\pi$
$318$	46134.8	+	46134.8i	0.456220	+	0.456220i
$319$	161065.	+	161065.i	1.58277	+	1.58277i
$320$	9818.58	−	9818.58i	0.0958846	−	0.0958846i
$321$		−	16769.5i		−	0.162746i
$322$	−145478.			−1.40309
$323$			104792.i			1.00444i
$324$		−	20511.3i		−	0.195390i
$325$	15959.7	−	15959.7i	0.151098	−	0.151098i
$326$			100549.i			0.946113i
$327$	44197.5	−	44197.5i	0.413335	−	0.413335i
$328$	−31997.8	+	31997.8i	−0.297421	+	0.297421i
$329$	253135.			2.33862
$330$	−64460.7			−0.591926
$331$	64683.8	+	64683.8i	0.590390	+	0.590390i	0.937737	−	0.347347i	$-0.112917\pi$
$331$	64683.8	+	64683.8i	0.590390	+	0.590390i	−0.347347	+	0.937737i	$0.612917\pi$
$332$		−	61243.8i		−	0.555630i
$333$	35639.1	−	78922.8i	0.321395	−	0.711728i
$334$	59474.2			0.533133
$335$	60212.0	−	60212.0i	0.536529	−	0.536529i
$336$		−	18776.9i		−	0.166320i
$337$		−	170793.i		−	1.50387i	−0.659235	−	0.751937i	$-0.729120\pi$
$337$		−	170793.i		−	1.50387i	0.659235	−	0.751937i	$-0.270880\pi$
$338$	−26307.5	−	26307.5i	−0.230275	−	0.230275i
$339$	16146.7	+	16146.7i	0.140503	+	0.140503i
$340$	−56065.3			−0.484994
$341$	−2973.80	−	2973.80i	−0.0255743	−	0.0255743i
$342$	−72553.8			−0.620308
$343$	3401.58			0.0289130
$344$		−	22251.4i		−	0.188036i
$345$	84366.8			0.708816
$346$	32965.1	+	32965.1i	0.275361	+	0.275361i
$347$	−50001.2	+	50001.2i	−0.415261	+	0.415261i	−0.883567	−	0.468305i	$-0.844865\pi$
$347$	−50001.2	+	50001.2i	−0.415261	+	0.415261i	0.468305	+	0.883567i	$0.344865\pi$
$348$	27208.4	−	27208.4i	0.224670	−	0.224670i
$349$	−24999.4			−0.205248			−0.102624	−	0.994720i	$-0.532724\pi$
$349$	−24999.4			−0.205248			−0.102624	+	0.994720i	$0.532724\pi$
$350$	−15393.4	−	15393.4i	−0.125660	−	0.125660i
$351$	87759.9	−	87759.9i	0.712331	−	0.712331i
$352$	25534.8	+	25534.8i	0.206085	+	0.206085i
$353$	116533.	−	116533.i	0.935187	−	0.935187i	−0.0628372	−	0.998024i	$-0.520015\pi$
$353$	116533.	−	116533.i	0.935187	−	0.935187i	0.998024	+	0.0628372i	$0.0200149\pi$
$354$			44733.6i			0.356966i
$355$	167365.	+	167365.i	1.32803	+	1.32803i
$356$	−12087.5	−	12087.5i	−0.0953757	−	0.0953757i
$357$	−53609.1	+	53609.1i	−0.420631	+	0.420631i
$358$		−	104310.i		−	0.813883i
$359$	−60037.0			−0.465833			−0.232917	−	0.972497i	$-0.574827\pi$
$359$	−60037.0			−0.465833			−0.232917	+	0.972497i	$0.574827\pi$
$360$		−	38817.3i		−	0.299516i
$361$			34129.9i			0.261891i
$362$	−45370.1	+	45370.1i	−0.346220	+	0.346220i
$363$		−	105966.i		−	0.804178i
$364$	−80468.9	+	80468.9i	−0.607331	+	0.607331i
$365$	49661.1	−	49661.1i	0.372761	−	0.372761i
$366$	−36189.2			−0.270157
$367$	21.3647			0.000158622			7.93112e−5	−	1.00000i	$-0.499975\pi$
$367$	21.3647			0.000158622			7.93112e−5		1.00000i	$0.499975\pi$
$368$	−33420.1	−	33420.1i	−0.246782	−	0.246782i
$369$			126502.i			0.929061i
$370$	43218.4	−	95707.1i	0.315694	−	0.699102i
$371$	−381393.			−2.77093
$372$	−502.360	+	502.360i	−0.00363019	+	0.00363019i
$373$			98144.9i			0.705424i	0.935732	+	0.352712i	$0.114740\pi$
$373$			98144.9i			0.705424i	−0.935732	+	0.352712i	$0.885260\pi$
$374$		−	145807.i		−	1.04240i
$375$	−41561.5	−	41561.5i	−0.295549	−	0.295549i
$376$	58151.8	+	58151.8i	0.411327	+	0.411327i
$377$	−233205.			−1.64080
$378$	−84645.6	−	84645.6i	−0.592408	−	0.592408i
$379$	−74487.3			−0.518565			−0.259283	−	0.965801i	$-0.583486\pi$
$379$	−74487.3			−0.518565			−0.259283	+	0.965801i	$0.583486\pi$
$380$	−87983.6			−0.609305
$381$		−	49569.8i		−	0.341482i
$382$	−51987.9			−0.356267
$383$	−55770.1	−	55770.1i	−0.380192	−	0.380192i	0.490979	−	0.871171i	$-0.336639\pi$
$383$	−55770.1	−	55770.1i	−0.380192	−	0.380192i	−0.871171	+	0.490979i	$0.836639\pi$
$384$	4313.55	−	4313.55i	0.0292531	−	0.0292531i
$385$	266446.	−	266446.i	1.79758	−	1.79758i
$386$	−2636.00			−0.0176917
$387$	−43985.0	−	43985.0i	−0.293686	−	0.293686i
$388$	55225.5	−	55225.5i	0.366839	−	0.366839i
$389$	−7558.69	−	7558.69i	−0.0499514	−	0.0499514i	0.681690	−	0.731641i	$-0.261245\pi$
$389$	−7558.69	−	7558.69i	−0.0499514	−	0.0499514i	−0.731641	+	0.681690i	$0.761245\pi$
$390$	46666.3	−	46666.3i	0.306813	−	0.306813i
$391$			190833.i			1.24825i
$392$	39197.4	+	39197.4i	0.255085	+	0.255085i
$393$	16383.2	+	16383.2i	0.106075	+	0.106075i
$394$	37356.5	−	37356.5i	0.240643	−	0.240643i
$395$			191799.i			1.22928i
$396$	100951.			0.643752
$397$		−	161347.i		−	1.02371i	−0.859070	−	0.511857i	$-0.828958\pi$
$397$		−	161347.i		−	1.02371i	0.859070	−	0.511857i	$-0.171042\pi$
$398$		−	883.898i		−	0.00558002i
$399$	−84129.0	+	84129.0i	−0.528445	+	0.528445i
$400$		−	7072.53i		−	0.0442033i
$401$	45498.0	−	45498.0i	0.282946	−	0.282946i	−0.551337	−	0.834283i	$-0.685882\pi$
$401$	45498.0	−	45498.0i	0.282946	−	0.282946i	0.834283	+	0.551337i	$0.185882\pi$
$402$	26452.6	−	26452.6i	0.163688	−	0.163688i
$403$	4305.77			0.0265119
$404$	32539.8			0.199366
$405$	−49167.9	−	49167.9i	−0.299759	−	0.299759i
$406$			224930.i			1.36457i
$407$	248901.	+	112396.i	1.50258	+	0.678521i
$408$	−24630.9			−0.147965
$409$	−66276.5	+	66276.5i	−0.396199	+	0.396199i	−0.876890	−	0.480691i	$-0.840386\pi$
$409$	−66276.5	+	66276.5i	−0.396199	+	0.396199i	0.480691	+	0.876890i	$0.340386\pi$
$410$			153405.i			0.912580i
$411$		−	16898.5i		−	0.100038i
$412$	28242.6	+	28242.6i	0.166383	+	0.166383i
$413$	−184905.	−	184905.i	−1.08405	−	1.08405i
$414$	−132125.			−0.770876
$415$	−146808.	−	146808.i	−0.852422	−	0.852422i
$416$	−36971.7			−0.213640
$417$	53936.5			0.310178
$418$		−	228815.i		−	1.30958i
$419$	−214467.			−1.22161			−0.610804	−	0.791782i	$-0.709154\pi$
$419$	−214467.			−1.22161			−0.610804	+	0.791782i	$0.709154\pi$
$420$	−45010.3	−	45010.3i	−0.255160	−	0.255160i
$421$	−198155.	+	198155.i	−1.11800	+	1.11800i	−0.125962	+	0.992035i	$0.540202\pi$
$421$	−198155.	+	198155.i	−1.11800	+	1.11800i	−0.992035	+	0.125962i	$0.959798\pi$
$422$	22940.7	−	22940.7i	0.128819	−	0.128819i
$423$	229900.			1.28487
$424$	−87616.2	−	87616.2i	−0.487363	−	0.487363i
$425$	−20192.5	+	20192.5i	−0.111792	+	0.111792i
$426$	73527.6	+	73527.6i	0.405164	+	0.405164i
$427$	149587.	−	149587.i	0.820421	−	0.820421i
$428$			31847.6i			0.173856i
$429$	121363.	+	121363.i	0.659434	+	0.659434i
$430$	−53339.2	−	53339.2i	−0.288476	−	0.288476i
$431$	175370.	−	175370.i	0.944061	−	0.944061i	−0.0544557	−	0.998516i	$-0.517342\pi$
$431$	175370.	−	175370.i	0.944061	−	0.944061i	0.998516	+	0.0544557i	$0.0173424\pi$
$432$		−	38890.7i		−	0.208391i
$433$	249227.			1.32929			0.664645	−	0.747159i	$-0.268583\pi$
$433$	249227.			1.32929			0.664645	+	0.747159i	$0.268583\pi$
$434$		−	4152.97i		−	0.0220485i
$435$		−	130443.i		−	0.689356i
$436$	−83936.9	+	83936.9i	−0.441550	+	0.441550i
$437$			299476.i			1.56819i
$438$	21817.4	−	21817.4i	0.113725	−	0.113725i
$439$	198606.	−	198606.i	1.03054	−	1.03054i	0.0310166	−	0.999519i	$-0.490126\pi$
$439$	198606.	−	198606.i	1.03054	−	1.03054i	0.999519	−	0.0310166i	$-0.00987446\pi$
$440$	122420.			0.632332
$441$	154965.			0.796815
$442$	105557.	+	105557.i	0.540307	+	0.540307i
$443$		−	167529.i		−	0.853657i	−0.904333	−	0.426828i	$-0.859631\pi$
$443$		−	167529.i		−	0.853657i	0.904333	−	0.426828i	$-0.140369\pi$
$444$	18986.9	−	42046.5i	0.0963139	−	0.213287i
$445$	−57950.4			−0.292642
$446$	−124881.	+	124881.i	−0.627809	+	0.627809i
$447$		−	43504.6i		−	0.217731i
$448$			35659.8i			0.177673i
$449$	−229629.	−	229629.i	−1.13903	−	1.13903i	−0.988625	−	0.150403i	$-0.951943\pi$
$449$	−229629.	−	229629.i	−1.13903	−	1.13903i	−0.150403	−	0.988625i	$-0.548057\pi$
$450$	−13980.5	−	13980.5i	−0.0690394	−	0.0690394i
$451$	−398953.			−1.96141
$452$	−30664.8	−	30664.8i	−0.150094	−	0.150094i
$453$	13050.3			0.0635950
$454$	−12628.3			−0.0612680
$455$			385787.i			1.86348i
$456$	−38653.4			−0.185891
$457$	82109.9	+	82109.9i	0.393154	+	0.393154i	0.875810	−	0.482656i	$-0.160328\pi$
$457$	82109.9	+	82109.9i	0.393154	+	0.393154i	−0.482656	+	0.875810i	$0.660328\pi$
$458$	−47189.5	+	47189.5i	−0.224965	+	0.224965i
$459$	−111035.	+	111035.i	−0.527031	+	0.527031i
$460$	−160224.			−0.757202
$461$	−16255.6	−	16255.6i	−0.0764893	−	0.0764893i	0.667827	−	0.744316i	$-0.267225\pi$
$461$	−16255.6	−	16255.6i	−0.0764893	−	0.0764893i	−0.744316	+	0.667827i	$0.767225\pi$
$462$	117056.	−	117056.i	0.548417	−	0.548417i
$463$	−20732.0	−	20732.0i	−0.0967119	−	0.0967119i	0.657095	−	0.753807i	$-0.271785\pi$
$463$	−20732.0	−	20732.0i	−0.0967119	−	0.0967119i	−0.753807	+	0.657095i	$0.771785\pi$
$464$	−51672.4	+	51672.4i	−0.240006	+	0.240006i
$465$			2408.43i			0.0111385i
$466$	132648.	+	132648.i	0.610840	+	0.610840i
$467$	−5055.37	−	5055.37i	−0.0231803	−	0.0231803i	0.695422	−	0.718602i	$-0.255218\pi$
$467$	−5055.37	−	5055.37i	−0.0231803	−	0.0231803i	−0.718602	+	0.695422i	$0.755218\pi$
$468$	−73083.1	+	73083.1i	−0.333676	+	0.333676i
$469$			218682.i			0.994184i
$470$	278793.			1.26208
$471$			109005.i			0.491366i
$472$		−	84955.1i		−	0.381334i
$473$	138717.	−	138717.i	0.620022	−	0.620022i
$474$			84261.9i			0.375038i
$475$	−31688.2	+	31688.2i	−0.140447	+	0.140447i
$476$	101811.	−	101811.i	0.449345	−	0.449345i
$477$	−346387.			−1.52238
$478$	242318.			1.06055
$479$	−206623.	−	206623.i	−0.900552	−	0.900552i	0.0949321	−	0.995484i	$-0.469737\pi$
$479$	−206623.	−	206623.i	−0.900552	−	0.900552i	−0.995484	+	0.0949321i	$0.969737\pi$
$480$		−	20680.1i		−	0.0897575i
$481$	−261561.	+	98822.7i	−1.13053	+	0.427136i
$482$	140120.			0.603124
$483$	−153204.	+	153204.i	−0.656715	+	0.656715i
$484$			201243.i			0.859074i
$485$		−	264764.i		−	1.12558i
$486$	−120043.	−	120043.i	−0.508234	−	0.508234i
$487$	237079.	+	237079.i	0.999621	+	0.999621i	1.00000		0.000378852i	$-0.000120592\pi$
$487$	237079.	+	237079.i	0.999621	+	0.999621i	−0.000378852		1.00000i	$0.500121\pi$
$488$	68728.1			0.288599
$489$	105889.	+	105889.i	0.442828	+	0.442828i
$490$	187921.			0.782680
$491$	194287.			0.805901			0.402950	−	0.915222i	$-0.367985\pi$
$491$	194287.			0.805901			0.402950	+	0.915222i	$0.367985\pi$
$492$			67394.5i			0.278416i
$493$	295056.			1.21398
$494$	165651.	+	165651.i	0.678796	+	0.678796i
$495$	241990.	−	241990.i	0.987614	−	0.987614i
$496$	954.049	−	954.049i	0.00387799	−	0.00387799i
$497$	−607847.			−2.46083
$498$	−64496.6	−	64496.6i	−0.260063	−	0.260063i
$499$	120495.	−	120495.i	0.483913	−	0.483913i	−0.422466	−	0.906379i	$-0.638835\pi$
$499$	120495.	−	120495.i	0.483913	−	0.483913i	0.906379	+	0.422466i	$0.138835\pi$
$500$	78930.9	+	78930.9i	0.315724	+	0.315724i
$501$	62632.9	−	62632.9i	0.249533	−	0.249533i
$502$		−	2504.94i		−	0.00994008i
$503$	50836.2	+	50836.2i	0.200926	+	0.200926i	0.800397	−	0.599471i	$-0.204622\pi$
$503$	50836.2	+	50836.2i	0.200926	+	0.200926i	−0.599471	+	0.800397i	$0.704622\pi$
$504$	70489.6	+	70489.6i	0.277501	+	0.277501i
$505$	78001.6	−	78001.6i	0.305859	−	0.305859i
$506$		−	416687.i		−	1.62746i
$507$	−55409.5			−0.215560
$508$			94139.7i			0.364792i
$509$		−	398680.i		−	1.53882i	−0.638754	−	0.769411i	$-0.720550\pi$
$509$		−	398680.i		−	1.53882i	0.638754	−	0.769411i	$-0.279450\pi$
$510$	−59043.0	+	59043.0i	−0.227001	+	0.227001i
$511$			180363.i			0.690724i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−174249.	+	174249.i	−0.662117	+	0.662117i
$514$	326593.			1.23618
$515$	135401.			0.510515
$516$	−23433.2	−	23433.2i	−0.0880102	−	0.0880102i
$517$			725045.i			2.71259i
$518$	95315.9	+	252279.i	0.355227	+	0.940205i
$519$	69431.9			0.257765
$520$	−88625.5	+	88625.5i	−0.327757	+	0.327757i
$521$		−	231023.i		−	0.851099i	−0.904935	−	0.425549i	$-0.860081\pi$
$521$		−	231023.i		−	0.851099i	0.904935	−	0.425549i	$-0.139919\pi$
$522$			204284.i			0.749712i
$523$	110607.	+	110607.i	0.404370	+	0.404370i	0.879770	−	0.475400i	$-0.157697\pi$
$523$	110607.	+	110607.i	0.404370	+	0.404370i	−0.475400	+	0.879770i	$0.657697\pi$
$524$	−31113.9	−	31113.9i	−0.113316	−	0.113316i
$525$	−32421.9			−0.117630
$526$	−202687.	−	202687.i	−0.732579	−	0.732579i
$527$	−5447.73			−0.0196153
$528$	53781.9			0.192916
$529$			265523.i			0.948837i
$530$	−420052.			−1.49538
$531$	−167933.	−	167933.i	−0.595590	−	0.595590i
$532$	159772.	−	159772.i	0.564519	−	0.564519i
$533$	288822.	−	288822.i	1.01666	−	1.01666i
$534$	−25459.0			−0.0892811
$535$	76342.3	+	76342.3i	0.266721	+	0.266721i
$536$	−50237.1	+	50237.1i	−0.174862	+	0.174862i
$537$	−109851.	−	109851.i	−0.380937	−	0.380937i
$538$	115905.	−	115905.i	0.400440	−	0.400440i
$539$			488719.i			1.68222i
$540$	−93225.6	−	93225.6i	−0.319704	−	0.319704i
$541$	−66024.0	−	66024.0i	−0.225583	−	0.225583i	0.585261	−	0.810845i	$-0.300992\pi$
$541$	−66024.0	−	66024.0i	−0.225583	−	0.225583i	−0.810845	+	0.585261i	$0.800992\pi$
$542$	40998.7	−	40998.7i	0.139563	−	0.139563i
$543$			95559.5i			0.324097i
$544$	46777.3			0.158066
$545$			402413.i			1.35481i
$546$			169486.i			0.568522i
$547$	−272800.	+	272800.i	−0.911737	+	0.911737i	−0.996409	−	0.0846714i	$-0.973016\pi$
$547$	−272800.	+	272800.i	−0.911737	+	0.911737i	0.0846714	+	0.996409i	$0.473016\pi$
$548$			32092.5i			0.106867i
$549$	135857.	−	135857.i	0.450751	−	0.450751i
$550$	44090.7	−	44090.7i	0.145754	−	0.145754i
$551$	463033.			1.52514
$552$	−70390.3			−0.231012
$553$	−348294.	−	348294.i	−1.13893	−	1.13893i
$554$		−	112916.i		−	0.367904i
$555$	−55276.4	−	146304.i	−0.179454	−	0.474975i
$556$	−102433.			−0.331352
$557$	391170.	−	391170.i	1.26082	−	1.26082i	0.310131	−	0.950694i	$-0.399627\pi$
$557$	391170.	−	391170.i	1.26082	−	1.26082i	0.950694	−	0.310131i	$-0.100373\pi$
$558$		−	3771.79i		−	0.0121138i
$559$			200848.i			0.642753i
$560$	85480.5	+	85480.5i	0.272578	+	0.272578i
$561$	−153551.	−	153551.i	−0.487894	−	0.487894i
$562$	−79293.5			−0.251053
$563$	−208350.	−	208350.i	−0.657319	−	0.657319i	0.297426	−	0.954745i	$-0.403872\pi$
$563$	−208350.	−	208350.i	−0.657319	−	0.657319i	−0.954745	+	0.297426i	$0.903872\pi$
$564$	122481.			0.385043
$565$	−147014.			−0.460534
$566$			9663.38i			0.0301645i
$567$	178571.			0.555450
$568$	−139639.	−	139639.i	−0.432822	−	0.432822i
$569$	−245827.	+	245827.i	−0.759287	+	0.759287i	−0.976193	−	0.216906i	$-0.930404\pi$
$569$	−245827.	+	245827.i	−0.759287	+	0.759287i	0.216906	+	0.976193i	$0.430404\pi$
$570$	−92656.6	+	92656.6i	−0.285185	+	0.285185i
$571$	−579445.			−1.77722			−0.888608	−	0.458668i	$-0.848327\pi$
$571$	−579445.			−1.77722			−0.888608	+	0.458668i	$0.848327\pi$
$572$	−230484.	−	230484.i	−0.704449	−	0.704449i
$573$	−54749.1	+	54749.1i	−0.166751	+	0.166751i
$574$	−278573.	−	278573.i	−0.845502	−	0.845502i
$575$	−57706.3	+	57706.3i	−0.174537	+	0.174537i
$576$			32386.7i			0.0976162i
$577$	−221758.	−	221758.i	−0.666082	−	0.666082i	0.290725	−	0.956807i	$-0.406104\pi$
$577$	−221758.	−	221758.i	−0.666082	−	0.666082i	−0.956807	+	0.290725i	$0.906104\pi$
$578$	33490.0	+	33490.0i	0.100244	+	0.100244i
$579$	−2776.00	+	2776.00i	−0.00828060	+	0.00828060i
$580$			247729.i			0.736413i
$581$	533188.			1.57953
$582$		−	116317.i		−	0.343398i
$583$		−	1.09241e6i		−	3.21402i
$584$	−41434.1	+	41434.1i	−0.121488	+	0.121488i
$585$			350377.i			1.02382i
$586$	−310296.	+	310296.i	−0.903610	+	0.903610i
$587$	−34541.0	+	34541.0i	−0.100244	+	0.100244i	−0.755450	−	0.655206i	$-0.772582\pi$
$587$	−34541.0	+	34541.0i	−0.100244	+	0.100244i	0.655206	+	0.755450i	$0.272582\pi$
$588$	82558.6			0.238785
$589$	−8549.16			−0.0246430
$590$	−203647.	−	203647.i	−0.585025	−	0.585025i
$591$		−	78681.1i		−	0.225266i
$592$	−36058.7	+	79851.9i	−0.102889	+	0.227846i
$593$	−162820.			−0.463019			−0.231509	−	0.972833i	$-0.574366\pi$
$593$	−162820.			−0.463019			−0.231509	+	0.972833i	$0.574366\pi$
$594$	242448.	−	242448.i	0.687140	−	0.687140i
$595$		−	488104.i		−	1.37873i
$596$			82621.1i			0.232594i
$597$	−930.843	−	930.843i	−0.00261173	−	0.00261173i
$598$	301660.	+	301660.i	0.843560	+	0.843560i
$599$	236840.			0.660086			0.330043	−	0.943966i	$-0.392937\pi$
$599$	236840.			0.660086			0.330043	+	0.943966i	$0.392937\pi$
$600$	−7448.17	−	7448.17i	−0.0206894	−	0.0206894i
$601$	232467.			0.643595			0.321797	−	0.946809i	$-0.395713\pi$
$601$	232467.			0.643595			0.321797	+	0.946809i	$0.395713\pi$
$602$	193721.			0.534544
$603$			198610.i			0.546219i
$604$	−24784.2			−0.0679361
$605$	482403.	+	482403.i	1.31795	+	1.31795i
$606$	34268.0	−	34268.0i	0.0933134	−	0.0933134i
$607$	28031.0	−	28031.0i	0.0760785	−	0.0760785i	−0.668044	−	0.744122i	$-0.732868\pi$
$607$	28031.0	−	28031.0i	0.0760785	−	0.0760785i	0.744122	+	0.668044i	$0.232868\pi$
$608$	73407.9			0.198580
$609$	236876.	+	236876.i	0.638685	+	0.638685i
$610$	164749.	−	164749.i	0.442755	−	0.442755i
$611$	−524895.	−	524895.i	−1.40602	−	1.40602i
$612$	92466.0	−	92466.0i	0.246876	−	0.246876i
$613$			52773.8i			0.140442i	0.997531	+	0.0702211i	$0.0223705\pi$
$613$			52773.8i			0.140442i	−0.997531	+	0.0702211i	$0.977630\pi$
$614$	−160598.	−	160598.i	−0.425994	−	0.425994i
$615$	161552.	+	161552.i	0.427133	+	0.427133i
$616$	−222306.	+	222306.i	−0.585853	+	0.585853i
$617$			514111.i			1.35048i	0.737600	+	0.675238i	$0.235959\pi$
$617$			514111.i			1.35048i	−0.737600	+	0.675238i	$0.764041\pi$
$618$	59485.1			0.155751
$619$		−	625597.i		−	1.63273i	−0.577539	−	0.816363i	$-0.695987\pi$
$619$		−	625597.i		−	1.63273i	0.577539	−	0.816363i	$-0.304013\pi$
$620$		−	4573.93i		−	0.0118989i
$621$	−317318.	+	317318.i	−0.822832	+	0.822832i
$622$		−	314240.i		−	0.812233i
$623$	105234.	−	105234.i	0.271132	−	0.271132i
$624$	−38935.4	+	38935.4i	−0.0999943	+	0.0999943i
$625$	447481.			1.14555
$626$	−175016.			−0.446611
$627$	−240968.	−	240968.i	−0.612949	−	0.612949i
$628$		−	207015.i		−	0.524908i
$629$	330932.	−	125032.i	0.836445	−	0.316025i
$630$	337944.			0.851458
$631$	218729.	−	218729.i	0.549349	−	0.549349i	−0.376904	−	0.926253i	$-0.623011\pi$
$631$	218729.	−	218729.i	0.549349	−	0.549349i	0.926253	+	0.376904i	$0.123011\pi$
$632$		−	160025.i		−	0.400639i
$633$		−	48318.2i		−	0.120588i
$634$	−99920.3	−	99920.3i	−0.248585	−	0.248585i
$635$	225664.	+	225664.i	0.559647	+	0.559647i
$636$	−184539.			−0.456220
$637$	−353808.	−	353808.i	−0.871944	−	0.871944i
$638$	−644259.			−1.58277
$639$	−552056.			−1.35201
$640$			39274.3i			0.0958846i
$641$	38109.6			0.0927511			0.0463755	−	0.998924i	$-0.485233\pi$
$641$	38109.6			0.0927511			0.0463755	+	0.998924i	$0.485233\pi$
$642$	33539.1	+	33539.1i	0.0813731	+	0.0813731i
$643$	−62224.6	+	62224.6i	−0.150501	+	0.150501i	−0.778342	−	0.627841i	$-0.783939\pi$
$643$	−62224.6	+	62224.6i	−0.150501	+	0.150501i	0.627841	+	0.778342i	$0.283939\pi$
$644$	290956.	−	290956.i	0.701544	−	0.701544i
$645$	−112344.			−0.270042
$646$	−209584.	−	209584.i	−0.502219	−	0.502219i
$647$	272326.	−	272326.i	0.650551	−	0.650551i	−0.302575	−	0.953126i	$-0.597846\pi$
$647$	272326.	−	272326.i	0.650551	−	0.650551i	0.953126	+	0.302575i	$0.0978463\pi$
$648$	41022.6	+	41022.6i	0.0976951	+	0.0976951i
$649$	529616.	−	529616.i	1.25740	−	1.25740i
$650$			63838.8i			0.151098i
$651$	−4373.54	−	4373.54i	−0.0103198	−	0.0103198i
$652$	−201098.	−	201098.i	−0.473056	−	0.473056i
$653$	−424148.	+	424148.i	−0.994698	+	0.994698i	−0.999986	−	0.00528820i	$-0.998317\pi$
$653$	−424148.	+	424148.i	−0.994698	+	0.994698i	0.00528820	+	0.999986i	$0.498317\pi$
$654$			176790.i			0.413335i
$655$	−149167.			−0.347689
$656$		−	127991.i		−	0.297421i
$657$			163808.i			0.379493i
$658$	−506269.	+	506269.i	−1.16931	+	1.16931i
$659$		−	266367.i		−	0.613352i	−0.951814	−	0.306676i	$-0.900783\pi$
$659$		−	266367.i		−	0.613352i	0.951814	−	0.306676i	$-0.0992169\pi$
$660$	128921.	−	128921.i	0.295963	−	0.295963i
$661$	−569447.	+	569447.i	−1.30332	+	1.30332i	−0.377175	+	0.926142i	$0.623105\pi$
$661$	−569447.	+	569447.i	−1.30332	+	1.30332i	−0.926142	+	0.377175i	$0.876895\pi$
$662$	−258735.			−0.590390
$663$	222326.			0.505781
$664$	122488.	+	122488.i	0.277815	+	0.277815i
$665$		−	765985.i		−	1.73212i
$666$	86567.3	+	229124.i	0.195167	+	0.516561i
$667$	843212.			1.89533
$668$	−118948.	+	118948.i	−0.266566	+	0.266566i
$669$			263028.i			0.587692i
$670$			240848.i			0.536529i
$671$	428456.	+	428456.i	0.951614	+	0.951614i
$672$	37553.7	+	37553.7i	0.0831600	+	0.0831600i
$673$	32355.9			0.0714369			0.0357185	−	0.999362i	$-0.488628\pi$
$673$	32355.9			0.0714369			0.0357185	+	0.999362i	$0.488628\pi$
$674$	341587.	+	341587.i	0.751937	+	0.751937i
$675$	−67152.4			−0.147385
$676$	105230.			0.230275
$677$			812423.i			1.77258i	0.463134	+	0.886288i	$0.346725\pi$
$677$			812423.i			1.77258i	−0.463134	+	0.886288i	$0.653275\pi$
$678$	−64586.9			−0.140503
$679$	480793.	+	480793.i	1.04284	+	1.04284i
$680$	112131.	−	112131.i	0.242497	−	0.242497i
$681$	−13299.0	+	13299.0i	−0.0286765	+	0.0286765i
$682$	11895.2			0.0255743
$683$	33054.4	+	33054.4i	0.0708579	+	0.0708579i	0.741648	−	0.670790i	$-0.234045\pi$
$683$	33054.4	+	33054.4i	0.0708579	+	0.0708579i	−0.670790	+	0.741648i	$0.734045\pi$
$684$	145108.	−	145108.i	0.310154	−	0.310154i
$685$	76929.3	+	76929.3i	0.163950	+	0.163950i
$686$	−6803.16	+	6803.16i	−0.0144565	+	0.0144565i
$687$			99391.6i			0.210589i
$688$	44502.8	+	44502.8i	0.0940180	+	0.0940180i
$689$	790850.	+	790850.i	1.66593	+	1.66593i
$690$	−168734.	+	168734.i	−0.354408	+	0.354408i
$691$		−	523499.i		−	1.09638i	−0.836355	−	0.548188i	$-0.815318\pi$
$691$		−	523499.i		−	1.09638i	0.836355	−	0.548188i	$-0.184682\pi$
$692$	−131860.			−0.275361
$693$			878875.i			1.83004i
$694$		−	200005.i		−	0.415261i
$695$	−245543.	+	245543.i	−0.508344	+	0.508344i
$696$			108834.i			0.224670i
$697$	−365423.	+	365423.i	−0.752194	+	0.752194i
$698$	49998.7	−	49998.7i	0.102624	−	0.102624i
$699$	279386.			0.571807
$700$	61573.5			0.125660
$701$	107321.	+	107321.i	0.218398	+	0.218398i	0.807823	−	0.589425i	$-0.200646\pi$
$701$	107321.	+	107321.i	0.218398	+	0.218398i	−0.589425	+	0.807823i	$0.700646\pi$
$702$			351040.i			0.712331i
$703$	519334.	−	196214.i	1.05084	−	0.397026i
$704$	−102139.			−0.206085
$705$	293600.	−	293600.i	0.590715	−	0.590715i
$706$			466131.i			0.935187i
$707$			283291.i			0.566754i
$708$	−89467.2	−	89467.2i	−0.178483	−	0.178483i
$709$	−539094.	−	539094.i	−1.07244	−	1.07244i	−0.997163	−	0.0752745i	$-0.976017\pi$
$709$	−539094.	−	539094.i	−1.07244	−	1.07244i	−0.0752745	−	0.997163i	$-0.523983\pi$
$710$	−669460.			−1.32803
$711$	−316325.	−	316325.i	−0.625741	−	0.625741i
$712$	48350.1			0.0953757
$713$	−15568.6			−0.0306246
$714$		−	214436.i		−	0.420631i
$715$	−1.10500e6			−2.16147
$716$	208621.	+	208621.i	0.406941	+	0.406941i
$717$	255188.	−	255188.i	0.496389	−	0.496389i
$718$	120074.	−	120074.i	0.232917	−	0.232917i
$719$	−14756.3			−0.0285444			−0.0142722	−	0.999898i	$-0.504543\pi$
$719$	−14756.3			−0.0285444			−0.0142722	+	0.999898i	$0.504543\pi$
$720$	77634.7	+	77634.7i	0.149758	+	0.149758i
$721$	−245880.	+	245880.i	−0.472990	+	0.472990i
$722$	−68259.7	−	68259.7i	−0.130945	−	0.130945i
$723$	147562.	−	147562.i	0.282292	−	0.282292i
$724$		−	181480.i		−	0.346220i
$725$	89222.4	+	89222.4i	0.169745	+	0.169745i
$726$	211932.	+	211932.i	0.402089	+	0.402089i
$727$	−543736.	+	543736.i	−1.02877	+	1.02877i	−0.0291996	+	0.999574i	$0.509296\pi$
$727$	−543736.	+	543736.i	−1.02877	+	1.02877i	−0.999574	+	0.0291996i	$0.990704\pi$
$728$		−	321876.i		−	0.607331i
$729$	−45160.3			−0.0849771
$730$			198645.i			0.372761i
$731$		−	254117.i		−	0.475552i
$732$	72378.3	−	72378.3i	0.135079	−	0.135079i
$733$			199595.i			0.371486i	0.982598	+	0.185743i	$0.0594692\pi$
$733$			199595.i			0.371486i	−0.982598	+	0.185743i	$0.940531\pi$
$734$	−42.7294	+	42.7294i	−7.93112e−5	+	7.93112e-5i
$735$	197902.	−	197902.i	0.366333	−	0.366333i
$736$	133681.			0.246782
$737$	−626363.			−1.15316
$738$	−253004.	−	253004.i	−0.464530	−	0.464530i
$739$			743712.i			1.36181i	0.732373	+	0.680904i	$0.238413\pi$
$739$			743712.i			1.36181i	−0.732373	+	0.680904i	$0.761587\pi$
$740$	104977.	+	277851.i	0.191704	+	0.507398i
$741$	348897.			0.635420
$742$	762786.	−	762786.i	1.38546	−	1.38546i
$743$		−	323198.i		−	0.585451i	−0.956196	−	0.292726i	$-0.905438\pi$
$743$		−	323198.i		−	0.585451i	0.956196	−	0.292726i	$-0.0945623\pi$
$744$		−	2009.44i		−	0.00363019i
$745$	198052.	+	198052.i	0.356835	+	0.356835i
$746$	−196290.	−	196290.i	−0.352712	−	0.352712i
$747$	484249.			0.867816
$748$	291613.	+	291613.i	0.521199	+	0.521199i
$749$	−277265.			−0.494232
$750$	166246.			0.295549
$751$		−	117607.i		−	0.208522i	−0.994550	−	0.104261i	$-0.966752\pi$
$751$		−	117607.i		−	0.208522i	0.994550	−	0.104261i	$-0.0332477\pi$
$752$	−232607.			−0.411327
$753$	−2637.98	−	2637.98i	−0.00465245	−	0.00465245i
$754$	466411.	−	466411.i	0.820400	−	0.820400i
$755$	−59410.5	+	59410.5i	−0.104224	+	0.104224i
$756$	338583.			0.592408
$757$	65440.6	+	65440.6i	0.114197	+	0.114197i	0.761896	−	0.647699i	$-0.224269\pi$
$757$	65440.6	+	65440.6i	0.114197	+	0.114197i	−0.647699	+	0.761896i	$0.724269\pi$
$758$	148975.	−	148975.i	0.259283	−	0.259283i
$759$	−438818.	−	438818.i	−0.761730	−	0.761730i
$760$	175967.	−	175967.i	0.304652	−	0.304652i
$761$		−	333975.i		−	0.576693i	−0.957526	−	0.288347i	$-0.906894\pi$
$761$		−	333975.i		−	0.576693i	0.957526	−	0.288347i	$-0.0931055\pi$
$762$	99139.6	+	99139.6i	0.170741	+	0.170741i
$763$	−730754.	−	730754.i	−1.25523	−	1.25523i
$764$	103976.	−	103976.i	0.178134	−	0.178134i
$765$		−	443303.i		−	0.757492i
$766$	223080.			0.380192
$767$			766831.i			1.30349i
$768$			17254.2i			0.0292531i
$769$	−45343.9	+	45343.9i	−0.0766772	+	0.0766772i	−0.744405	−	0.667728i	$-0.767267\pi$
$769$	−45343.9	+	45343.9i	−0.0766772	+	0.0766772i	0.667728	+	0.744405i	$0.267267\pi$
$770$			1.06578e6i			1.79758i
$771$	343939.	−	343939.i	0.578593	−	0.578593i
$772$	5271.99	−	5271.99i	0.00884586	−	0.00884586i
$773$	−16725.0			−0.0279903			−0.0139951	−	0.999902i	$-0.504455\pi$
$773$	−16725.0			−0.0279903			−0.0139951	+	0.999902i	$0.504455\pi$
$774$	175940.			0.293686
$775$	−1647.35	−	1647.35i	−0.00274272	−	0.00274272i
$776$			220902.i			0.366839i
$777$	366057.	+	165300.i	0.606326	+	0.273799i
$778$	30234.8			0.0499514
$779$	−573460.	+	573460.i	−0.944992	+	0.944992i
$780$			186665.i			0.306813i
$781$		−	1.74104e6i		−	2.85434i
$782$	−381666.	−	381666.i	−0.624123	−	0.624123i
$783$	490619.	+	490619.i	0.800242	+	0.800242i
$784$	−156790.			−0.255085
$785$	−496240.	−	496240.i	−0.805290	−	0.805290i
$786$	−65532.9			−0.106075
$787$	1.14597e6			1.85022			0.925110	−	0.379699i	$-0.123972\pi$
$787$	1.14597e6			1.85022			0.925110	+	0.379699i	$0.123972\pi$
$788$			149426.i			0.240643i
$789$	−426904.			−0.685767
$790$	−383597.	−	383597.i	−0.614641	−	0.614641i
$791$	266967.	−	266967.i	0.426683	−	0.426683i
$792$	−201901.	+	201901.i	−0.321876	+	0.321876i
$793$	−620360.			−0.986501
$794$	322693.	+	322693.i	0.511857	+	0.511857i
$795$	−442362.	+	442362.i	−0.699912	+	0.699912i
$796$	1767.80	+	1767.80i	0.00279001	+	0.00279001i
$797$	295173.	−	295173.i	0.464687	−	0.464687i	−0.435501	−	0.900188i	$-0.643429\pi$
$797$	295173.	−	295173.i	0.464687	−	0.464687i	0.900188	+	0.435501i	$0.143429\pi$
$798$		−	336516.i		−	0.528445i
$799$	664107.	+	664107.i	1.04027	+	1.04027i
$800$	14145.1	+	14145.1i	0.0221017	+	0.0221017i
$801$	95575.0	−	95575.0i	0.148963	−	0.148963i
$802$			181992.i			0.282946i
$803$	−516606.			−0.801177
$804$			105810.i			0.163688i
$805$		−	1.39491e6i		−	2.15255i
$806$	−8611.53	+	8611.53i	−0.0132559	+	0.0132559i
$807$		−	244122.i		−	0.374852i
$808$	−65079.6	+	65079.6i	−0.0996832	+	0.0996832i
$809$	42552.5	−	42552.5i	0.0650172	−	0.0650172i	−0.673851	−	0.738868i	$-0.735361\pi$
$809$	42552.5	−	42552.5i	0.0650172	−	0.0650172i	0.738868	+	0.673851i	$0.235361\pi$
$810$	196672.			0.299759
$811$	961733.			1.46222			0.731110	−	0.682260i	$-0.239003\pi$
$811$	961733.			1.46222			0.731110	+	0.682260i	$0.239003\pi$
$812$	−449860.	−	449860.i	−0.682284	−	0.682284i
$813$		−	86352.5i		−	0.130645i
$814$	−722595.	+	273010.i	−1.09055	+	0.412031i
$815$	−964111.			−1.45148
$816$	49261.7	−	49261.7i	0.0739826	−	0.0739826i
$817$		−	398787.i		−	0.597443i
$818$		−	265106.i		−	0.396199i
$819$	−636261.	−	636261.i	−0.948566	−	0.948566i
$820$	−306810.	−	306810.i	−0.456290	−	0.456290i
$821$	−677574.			−1.00524			−0.502620	−	0.864507i	$-0.667631\pi$
$821$	−677574.			−1.00524			−0.502620	+	0.864507i	$0.667631\pi$
$822$	33796.9	+	33796.9i	0.0500189	+	0.0500189i
$823$	−795294.			−1.17416			−0.587081	−	0.809528i	$-0.699723\pi$
$823$	−795294.			−1.17416			−0.587081	+	0.809528i	$0.699723\pi$
$824$	−112970.			−0.166383
$825$		−	92864.9i		−	0.136441i
$826$	739619.			1.08405
$827$	274983.	+	274983.i	0.402064	+	0.402064i	0.878960	−	0.476896i	$-0.158238\pi$
$827$	274983.	+	274983.i	0.402064	+	0.402064i	−0.476896	+	0.878960i	$0.658238\pi$
$828$	264250.	−	264250.i	0.385438	−	0.385438i
$829$	−547862.	+	547862.i	−0.797190	+	0.797190i	−0.982652	−	0.185461i	$-0.940622\pi$
$829$	−547862.	+	547862.i	−0.797190	+	0.797190i	0.185461	+	0.982652i	$0.440622\pi$
$830$	587234.			0.852422
$831$	−118913.	−	118913.i	−0.172197	−	0.172197i
$832$	73943.5	−	73943.5i	0.106820	−	0.106820i
$833$	447644.	+	447644.i	0.645124	+	0.645124i
$834$	−107873.	+	107873.i	−0.155089	+	0.155089i
$835$			570266.i			0.817908i
$836$	457630.	+	457630.i	0.654790	+	0.654790i
$837$	−9058.51	−	9058.51i	−0.0129302	−	0.0129302i
$838$	428934.	−	428934.i	0.610804	−	0.610804i
$839$			182945.i			0.259895i	0.991521	+	0.129947i	$0.0414809\pi$
$839$			182945.i			0.259895i	−0.991521	+	0.129947i	$0.958519\pi$
$840$	180041.			0.255160
$841$		−	596447.i		−	0.843296i
$842$		−	792619.i		−	1.11800i
$843$	−83504.9	+	83504.9i	−0.117505	+	0.117505i
$844$			91762.8i			0.128819i
$845$	252249.	−	252249.i	0.353277	−	0.353277i
$846$	−459801.	+	459801.i	−0.642435	+	0.642435i
$847$	−1.75202e6			−2.44215
$848$	350465.			0.487363
$849$	10176.6	+	10176.6i	0.0141185	+	0.0141185i
$850$		−	80770.1i		−	0.111792i
$851$	945740.	−	357318.i	1.30591	−	0.493397i
$852$	−294110.			−0.405164
$853$	−842209.	+	842209.i	−1.15750	+	1.15750i	−0.172491	+	0.985011i	$0.555182\pi$
$853$	−842209.	+	842209.i	−1.15750	+	1.15750i	−0.985011	+	0.172491i	$0.944818\pi$
$854$			598346.i			0.820421i
$855$		−	695679.i		−	0.951648i
$856$	−63695.2	−	63695.2i	−0.0869278	−	0.0869278i
$857$	−44811.9	−	44811.9i	−0.0610144	−	0.0610144i	0.675941	−	0.736956i	$-0.263737\pi$
$857$	−44811.9	−	44811.9i	−0.0610144	−	0.0610144i	−0.736956	+	0.675941i	$0.763737\pi$
$858$	−485452.			−0.659434
$859$	−578695.	−	578695.i	−0.784266	−	0.784266i	0.196282	−	0.980548i	$-0.437113\pi$
$859$	−578695.	−	578695.i	−0.784266	−	0.784266i	−0.980548	+	0.196282i	$0.937113\pi$
$860$	213357.			0.288476
$861$	−586736.			−0.791474
$862$			701479.i			0.944061i
$863$	340724.			0.457489			0.228745	−	0.973486i	$-0.426538\pi$
$863$	340724.			0.457489			0.228745	+	0.973486i	$0.426538\pi$
$864$	77781.5	+	77781.5i	0.104195	+	0.104195i
$865$	−316085.	+	316085.i	−0.422446	+	0.422446i
$866$	−498455.	+	498455.i	−0.664645	+	0.664645i
$867$	70537.3			0.0938385
$868$	8305.94	+	8305.94i	0.0110243	+	0.0110243i
$869$	997605.	−	997605.i	1.32105	−	1.32105i
$870$	260887.	+	260887.i	0.344678	+	0.344678i
$871$	453455.	−	453455.i	0.597720	−	0.597720i
$872$		−	335748.i		−	0.441550i
$873$	436663.	+	436663.i	0.572952	+	0.572952i
$874$	−598951.	−	598951.i	−0.784095	−	0.784095i
$875$	−687172.	+	687172.i	−0.897531	+	0.897531i
$876$			87269.5i			0.113725i
$877$	1.09589e6			1.42485			0.712424	−	0.701749i	$-0.247597\pi$
$877$	1.09589e6			1.42485			0.712424	+	0.701749i	$0.247597\pi$
$878$			794423.i			1.03054i
$879$			653553.i			0.845868i
$880$	−244839.	+	244839.i	−0.316166	+	0.316166i
$881$			1.28790e6i			1.65932i	0.558272	+	0.829658i	$0.311465\pi$
$881$			1.28790e6i			1.65932i	−0.558272	+	0.829658i	$0.688535\pi$
$882$	−309931.	+	309931.i	−0.398407	+	0.398407i
$883$	738003.	−	738003.i	0.946535	−	0.946535i	−0.0521061	−	0.998642i	$-0.516593\pi$
$883$	738003.	−	738003.i	0.946535	−	0.946535i	0.998642	+	0.0521061i	$0.0165934\pi$
$884$	−422226.			−0.540307
$885$	−428926.			−0.547641
$886$	335059.	+	335059.i	0.426828	+	0.426828i
$887$		−	999295.i		−	1.27013i	−0.772461	−	0.635063i	$-0.780974\pi$
$887$		−	999295.i		−	1.27013i	0.772461	−	0.635063i	$-0.219026\pi$
$888$	46119.2	+	122067.i	0.0584865	+	0.154800i
$889$	−819580.			−1.03702
$890$	115901.	−	115901.i	0.146321	−	0.146321i
$891$			511475.i			0.644272i
$892$		−	499525.i		−	0.627809i
$893$	1.04219e6	+	1.04219e6i	1.30690	+	1.30690i
$894$	87009.2	+	87009.2i	0.108865	+	0.108865i
$895$	1.00018e6			1.24862
$896$	−71319.5	−	71319.5i	−0.0888367	−	0.0888367i
$897$	635364.			0.789656
$898$	918516.			1.13903
$899$			24071.3i			0.0297838i
$900$	55921.9			0.0690394
$901$	−1.00060e6	−	1.00060e6i	−1.23257	−	1.23257i
$902$	797906.	−	797906.i	0.980706	−	0.980706i
$903$	204010.	−	204010.i	0.250193	−	0.250193i
$904$	122659.			0.150094
$905$	−435029.	−	435029.i	−0.531155	−	0.531155i
$906$	−26100.5	+	26100.5i	−0.0317975	+	0.0317975i
$907$	−624169.	−	624169.i	−0.758731	−	0.758731i	0.217361	−	0.976091i	$-0.430255\pi$
$907$	−624169.	−	624169.i	−0.758731	−	0.758731i	−0.976091	+	0.217361i	$0.930255\pi$
$908$	25256.6	−	25256.6i	0.0306340	−	0.0306340i
$909$			257289.i			0.311382i
$910$	−771573.	−	771573.i	−0.931739	−	0.931739i
$911$	710744.	+	710744.i	0.856400	+	0.856400i	0.990912	−	0.134512i	$-0.0429467\pi$
$911$	710744.	+	710744.i	0.856400	+	0.856400i	−0.134512	+	0.990912i	$0.542947\pi$
$912$	77306.8	−	77306.8i	0.0929454	−	0.0929454i
$913$			1.52719e6i			1.83211i
$914$	−328440.			−0.393154
$915$		−	346998.i		−	0.414463i
$916$		−	188758.i		−	0.224965i
$917$	270878.	−	270878.i	0.322133	−	0.322133i
$918$		−	444142.i		−	0.527031i
$919$	−808022.	+	808022.i	−0.956736	+	0.956736i	−0.999102	−	0.0423662i	$-0.986510\pi$
$919$	−808022.	+	808022.i	−0.956736	+	0.956736i	0.0423662	+	0.999102i	$0.486510\pi$
$920$	320448.	−	320448.i	0.378601	−	0.378601i
$921$	−338255.			−0.398772
$922$	65022.4			0.0764893
$923$	1.26042e6	+	1.26042e6i	1.47949	+	1.47949i
$924$			468225.i			0.548417i
$925$	137880.	+	62262.3i	0.161145	+	0.0727683i
$926$	82928.2			0.0967119
$927$	−223311.	+	223311.i	−0.259867	+	0.259867i
$928$		−	206690.i		−	0.240006i
$929$			467654.i			0.541867i	0.962598	+	0.270934i	$0.0873324\pi$
$929$			467654.i			0.541867i	−0.962598	+	0.270934i	$0.912668\pi$
$930$	−4816.86	−	4816.86i	−0.00556926	−	0.00556926i
$931$	702491.	+	702491.i	0.810478	+	0.810478i
$932$	−530591.			−0.610840
$933$	−330930.	−	330930.i	−0.380165	−	0.380165i
$934$	20221.5			0.0231803
$935$	1.39806e6			1.59920
$936$		−	292332.i		−	0.333676i
$937$	642478.			0.731778			0.365889	−	0.930659i	$-0.380765\pi$
$937$	642478.			0.731778			0.365889	+	0.930659i	$0.380765\pi$
$938$	−437364.	−	437364.i	−0.497092	−	0.497092i
$939$	−184312.	+	184312.i	−0.209036	+	0.209036i
$940$	−557586.	+	557586.i	−0.631039	+	0.631039i
$941$	576416.			0.650964			0.325482	−	0.945548i	$-0.394473\pi$
$941$	576416.			0.650964			0.325482	+	0.945548i	$0.394473\pi$
$942$	−218010.	−	218010.i	−0.245683	−	0.245683i
$943$	−1.04431e6	+	1.04431e6i	−1.17437	+	1.17437i
$944$	169910.	+	169910.i	0.190667	+	0.190667i
$945$	811621.	−	811621.i	0.908845	−	0.908845i
$946$			554868.i			0.620022i
$947$	−224450.	−	224450.i	−0.250277	−	0.250277i	0.570807	−	0.821084i	$-0.306630\pi$
$947$	−224450.	−	224450.i	−0.250277	−	0.250277i	−0.821084	+	0.570807i	$0.806630\pi$
$948$	−168524.	−	168524.i	−0.187519	−	0.187519i
$949$	373997.	−	373997.i	0.415275	−	0.415275i
$950$		−	126753.i		−	0.140447i
$951$	−210455.			−0.232700
$952$			407243.i			0.449345i
$953$		−	525704.i		−	0.578836i	−0.957203	−	0.289418i	$-0.906538\pi$
$953$		−	525704.i		−	0.578836i	0.957203	−	0.289418i	$-0.0934617\pi$
$954$	692773.	−	692773.i	0.761192	−	0.761192i
$955$		−	498484.i		−	0.546568i
$956$	−484637.	+	484637.i	−0.530274	+	0.530274i
$957$	−678477.	+	678477.i	−0.740817	+	0.740817i
$958$	826494.			0.900552
$959$	−279397.			−0.303798
$960$	41360.3	+	41360.3i	0.0448787	+	0.0448787i
$961$			923077.i			0.999519i
$962$	325477.	−	720768.i	0.351698	−	0.778835i
$963$	−251816.			−0.271538
$964$	−280240.	+	280240.i	−0.301562	+	0.301562i
$965$		−	25275.1i		−	0.0271418i
$966$		−	612818.i		−	0.656715i
$967$	−9460.48	−	9460.48i	−0.0101172	−	0.0101172i	0.702030	−	0.712147i	$-0.252277\pi$
$967$	−9460.48	−	9460.48i	−0.0101172	−	0.0101172i	−0.712147	+	0.702030i	$0.752277\pi$
$968$	−402486.	−	402486.i	−0.429537	−	0.429537i
$969$	−441431.			−0.470127
$970$	529527.	+	529527.i	0.562788	+	0.562788i
$971$	455315.			0.482918			0.241459	−	0.970411i	$-0.422374\pi$
$971$	455315.			0.482918			0.241459	+	0.970411i	$0.422374\pi$
$972$	480171.			0.508234
$973$		−	891779.i		−	0.941958i
$974$	−948317.			−0.999621
$975$	67229.4	+	67229.4i	0.0707213	+	0.0707213i
$976$	−137456.	+	137456.i	−0.144299	+	0.144299i
$977$	568203.	−	568203.i	0.595271	−	0.595271i	−0.343779	−	0.939050i	$-0.611707\pi$
$977$	568203.	−	568203.i	0.595271	−	0.595271i	0.939050	+	0.343779i	$0.111707\pi$
$978$	−423558.			−0.442828
$979$	301418.	+	301418.i	0.314488	+	0.314488i
$980$	−375843.	+	375843.i	−0.391340	+	0.391340i
$981$	−663681.	−	663681.i	−0.689639	−	0.689639i
$982$	−388575.	+	388575.i	−0.402950	+	0.402950i
$983$			1.61413e6i			1.67044i	0.549917	+	0.835220i	$0.314659\pi$
$983$			1.61413e6i			1.67044i	−0.549917	+	0.835220i	$0.685341\pi$
$984$	−134789.	−	134789.i	−0.139208	−	0.139208i
$985$	358191.	+	358191.i	0.369184	+	0.369184i
$986$	−590111.	+	590111.i	−0.606988	+	0.606988i
$987$			1.06632e6i			1.09459i
$988$	−662602.			−0.678796
$989$		−	726217.i		−	0.742461i
$990$			967960.i			0.987614i
$991$	1.01928e6	−	1.01928e6i	1.03788	−	1.03788i	0.0386261	−	0.999254i	$-0.487702\pi$
$991$	1.01928e6	−	1.01928e6i	1.03788	−	1.03788i	0.999254	−	0.0386261i	$-0.0122981\pi$
$992$			3816.19i			0.00387799i
$993$	−272477.	+	272477.i	−0.276332	+	0.276332i
$994$	1.21569e6	−	1.21569e6i	1.23042	−	1.23042i
$995$	8475.22			0.00856061
$996$	257986.			0.260063
$997$	1.19711e6	+	1.19711e6i	1.20433	+	1.20433i	0.972838	+	0.231488i	$0.0743593\pi$
$997$	1.19711e6	+	1.19711e6i	1.20433	+	1.20433i	0.231488	+	0.972838i	$0.425641\pi$
$998$			481979.i			0.483913i
$999$	758179.	+	342371.i	0.759698	+	0.343056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.43.4	yes	14
37.31	odd	4	inner	74.5.d.a.31.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.4	✓	14	37.31	odd	4	inner
74.5.d.a.43.4	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +4.21245i q^{3} -8.00000i q^{4} +(-19.1769 - 19.1769i) q^{5} +(-8.42489 - 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 + 16.0000i) q^{8} +63.2553 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} +4.21245i q^{3} -8.00000i q^{4} +(-19.1769 - 19.1769i) q^{5} +(-8.42489 - 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 + 16.0000i) q^{8} +63.2553 q^{9} +76.7077 q^{10} +199.490i q^{11} +33.6996 q^{12} +(-144.421 - 144.421i) q^{13} +(-139.296 + 139.296i) q^{14} +(80.7817 - 80.7817i) q^{15} -64.0000 q^{16} +(182.724 + 182.724i) q^{17} +(-126.511 + 126.511i) q^{18} +(286.750 + 286.750i) q^{19} +(-153.415 + 153.415i) q^{20} +293.388i q^{21} +(-398.981 - 398.981i) q^{22} +(522.190 + 522.190i) q^{23} +(-67.3991 + 67.3991i) q^{24} +110.508i q^{25} +577.683 q^{26} +607.668i q^{27} -557.184i q^{28} +(807.381 - 807.381i) q^{29} +323.127i q^{30} +(-14.9070 + 14.9070i) q^{31} +(128.000 - 128.000i) q^{32} -840.342 q^{33} -730.895 q^{34} +(-1335.63 - 1335.63i) q^{35} -506.042i q^{36} +(563.418 - 1247.69i) q^{37} -1147.00 q^{38} +(608.365 - 608.365i) q^{39} -613.661i q^{40} +1999.86i q^{41} +(-586.777 - 586.777i) q^{42} +(-695.357 - 695.357i) q^{43} +1595.92 q^{44} +(-1213.04 - 1213.04i) q^{45} -2088.76 q^{46} +3634.49 q^{47} -269.597i q^{48} +2449.84 q^{49} +(-221.017 - 221.017i) q^{50} +(-769.715 + 769.715i) q^{51} +(-1155.37 + 1155.37i) q^{52} -5476.01 q^{53} +(-1215.34 - 1215.34i) q^{54} +(3825.61 - 3825.61i) q^{55} +(1114.37 + 1114.37i) q^{56} +(-1207.92 + 1207.92i) q^{57} +3229.52i q^{58} +(-2654.85 - 2654.85i) q^{59} +(-646.254 - 646.254i) q^{60} +(2147.75 - 2147.75i) q^{61} -59.6280i q^{62} +4405.60 q^{63} +512.000i q^{64} +5539.09i q^{65} +(1680.68 - 1680.68i) q^{66} +3139.82i q^{67} +(1461.79 - 1461.79i) q^{68} +(-2199.70 + 2199.70i) q^{69} +5342.53 q^{70} -8727.42 q^{71} +(1012.08 + 1012.08i) q^{72} +2589.63i q^{73} +(1368.54 + 3622.21i) q^{74} -465.511 q^{75} +(2294.00 - 2294.00i) q^{76} +13894.1i q^{77} +2433.46i q^{78} +(-5000.77 - 5000.77i) q^{79} +(1227.32 + 1227.32i) q^{80} +2563.91 q^{81} +(-3999.72 - 3999.72i) q^{82} +7655.48 q^{83} +2347.11 q^{84} -7008.16i q^{85} +2781.43 q^{86} +(3401.05 + 3401.05i) q^{87} +(-3191.85 + 3191.85i) q^{88} +(1510.94 - 1510.94i) q^{89} +4852.17 q^{90} +(-10058.6 - 10058.6i) q^{91} +(4177.52 - 4177.52i) q^{92} +(-62.7950 - 62.7950i) q^{93} +(-7268.97 + 7268.97i) q^{94} -10998.0i q^{95} +(539.193 + 539.193i) q^{96} +(6903.19 + 6903.19i) q^{97} +(-4899.68 + 4899.68i) q^{98} +12618.8i 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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