LMFDB - Embedded newform 74.5.d.a.31.4

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			31.4
Root			$-3.21245i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.a.43.4

$q$-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 $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

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

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
$3$		−	4.21245i		−	0.468050i	−0.972231	−	0.234025i	$-0.924810\pi$
$3$		−	4.21245i		−	0.468050i	0.972231	−	0.234025i	$-0.0751897\pi$
$4$			8.00000i			0.500000i
$5$	−19.1769	+	19.1769i	−0.767077	+	0.767077i	−0.977591	−	0.210514i	$-0.932486\pi$
$5$	−19.1769	+	19.1769i	−0.767077	+	0.767077i	0.210514	+	0.977591i	$0.432486\pi$
$6$	−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	$-0.691546\pi$
$11$		−	199.490i		−	1.64868i	0.566095	−	0.824340i	$-0.308454\pi$
$12$	33.6996			0.234025
$13$	−144.421	+	144.421i	−0.854561	+	0.854561i	−0.990691	−	0.136130i	$-0.956534\pi$
$13$	−144.421	+	144.421i	−0.854561	+	0.854561i	0.136130	+	0.990691i	$0.456534\pi$
$14$	−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	−0.316373	−	0.948635i	$-0.602465\pi$
$17$	182.724	−	182.724i	0.632262	−	0.632262i	0.948635	+	0.316373i	$0.102465\pi$
$18$	−126.511	−	126.511i	−0.390465	−	0.390465i
$19$	286.750	−	286.750i	0.794321	−	0.794321i	−0.187873	−	0.982193i	$-0.560159\pi$
$19$	286.750	−	286.750i	0.794321	−	0.794321i	0.982193	+	0.187873i	$0.0601592\pi$
$20$	−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	−0.0127919	−	0.999918i	$-0.504072\pi$
$23$	522.190	−	522.190i	0.987126	−	0.987126i	0.999918	+	0.0127919i	$0.00407190\pi$
$24$	−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	0.999231	−	0.0392061i	$-0.0124829\pi$
$29$	807.381	+	807.381i	0.960025	+	0.960025i	−0.0392061	+	0.999231i	$0.512483\pi$
$30$		−	323.127i		−	0.359030i
$31$	−14.9070	−	14.9070i	−0.0155120	−	0.0155120i	0.699308	−	0.714820i	$-0.253491\pi$
$31$	−14.9070	−	14.9070i	−0.0155120	−	0.0155120i	−0.714820	+	0.699308i	$0.753491\pi$
$32$	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	$-0.797214\pi$
$41$		−	1999.86i		−	1.18969i	0.803842	−	0.594843i	$-0.202786\pi$
$42$	−586.777	+	586.777i	−0.332640	+	0.332640i
$43$	−695.357	+	695.357i	−0.376072	+	0.376072i	−0.869683	−	0.493611i	$-0.835677\pi$
$43$	−695.357	+	695.357i	−0.376072	+	0.376072i	0.493611	+	0.869683i	$0.335677\pi$
$44$	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	−0.976804	−	0.214136i	$-0.931306\pi$
$59$	−2654.85	+	2654.85i	−0.762668	+	0.762668i	0.214136	+	0.976804i	$0.431306\pi$
$60$	−646.254	+	646.254i	−0.179515	+	0.179515i
$61$	2147.75	+	2147.75i	0.577198	+	0.577198i	0.934130	−	0.356933i	$-0.116177\pi$
$61$	2147.75	+	2147.75i	0.577198	+	0.577198i	−0.356933	+	0.934130i	$0.616177\pi$
$62$			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	$-0.886276\pi$
$67$		−	3139.82i		−	0.699447i	0.936853	−	0.349723i	$-0.113724\pi$
$68$	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	$-0.921877\pi$
$73$		−	2589.63i		−	0.485951i	0.970032	−	0.242975i	$-0.0781234\pi$
$74$	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	−0.983295	−	0.182018i	$-0.941737\pi$
$79$	−5000.77	+	5000.77i	−0.801277	+	0.801277i	0.182018	+	0.983295i	$0.441737\pi$
$80$	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	0.796021	−	0.605269i	$-0.206935\pi$
$89$	1510.94	+	1510.94i	0.190751	+	0.190751i	−0.605269	+	0.796021i	$0.706935\pi$
$90$	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	−0.237668	−	0.971347i	$-0.576383\pi$
$97$	6903.19	−	6903.19i	0.733679	−	0.733679i	0.971347	+	0.237668i	$0.0763829\pi$
$98$	−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	$-0.936112\pi$
$101$		−	4067.47i		−	0.398733i	0.979925	−	0.199366i	$-0.0638884\pi$
$102$			3078.86i			0.295930i
$103$	−3530.32	−	3530.32i	−0.332766	−	0.332766i	0.520870	−	0.853636i	$-0.325608\pi$
$103$	−3530.32	−	3530.32i	−0.332766	−	0.332766i	−0.853636	+	0.520870i	$0.825608\pi$
$104$			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	−0.993848	−	0.110749i	$-0.964675\pi$
$109$	−10492.1	+	10492.1i	−0.883100	+	0.883100i	0.110749	+	0.993848i	$0.464675\pi$
$110$		−	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	0.841087	−	0.540899i	$-0.181916\pi$
$113$	3833.10	+	3833.10i	0.300188	+	0.300188i	−0.540899	+	0.841087i	$0.681916\pi$
$114$			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	0.811284	−	0.584652i	$-0.198769\pi$
$131$	3889.24	+	3889.24i	0.226633	+	0.226633i	−0.584652	+	0.811284i	$0.698769\pi$
$132$		−	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	$0.107505\pi$
$139$			12804.1i			0.662703i	−0.943507	+	0.331352i	$0.892495\pi$
$140$	−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	$0.0216414\pi$
$151$			3098.02i			0.135872i	−0.997690	+	0.0679361i	$0.978359\pi$
$152$		−	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	0.998621	−	0.0525075i	$-0.0167214\pi$
$163$	25137.3	+	25137.3i	0.946113	+	0.946113i	−0.0525075	+	0.998621i	$0.516721\pi$
$164$	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	−0.921503	−	0.388370i	$-0.873038\pi$
$167$	−14868.5	+	14868.5i	−0.533133	+	0.533133i	0.388370	+	0.921503i	$0.373038\pi$
$168$	−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	$0.0887974\pi$
$173$			16482.6i			0.550722i	−0.961341	+	0.275361i	$0.911203\pi$
$174$	−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	0.171331	−	0.985214i	$-0.445193\pi$
$179$	−26077.6	−	26077.6i	−0.813883	−	0.813883i	−0.985214	+	0.171331i	$0.945193\pi$
$180$	−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	−0.506168	−	0.862435i	$-0.668938\pi$
$191$	12997.0	−	12997.0i	0.356267	−	0.356267i	0.862435	+	0.506168i	$0.168938\pi$
$192$	−2156.77			−0.0585062
$193$	658.999	−	658.999i	0.0176917	−	0.0176917i	−0.698206	−	0.715897i	$-0.746018\pi$
$193$	658.999	−	658.999i	0.0176917	−	0.0176917i	0.715897	+	0.698206i	$0.246018\pi$
$194$	−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	0.704311	−	0.709891i	$-0.251256\pi$
$199$	−220.974	−	220.974i	−0.00558002	−	0.00558002i	−0.709891	+	0.704311i	$0.751256\pi$
$200$	−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	−0.675809	−	0.737077i	$-0.736206\pi$
$227$	3157.08	−	3157.08i	0.0612680	−	0.0612680i	0.737077	+	0.675809i	$0.236206\pi$
$228$	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	$0.209168\pi$
$233$			66323.8i			1.22168i	−0.791754	+	0.610840i	$0.790832\pi$
$234$	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	−0.0625039	+	0.998045i	$0.519909\pi$
$239$	−60579.6	+	60579.6i	−1.06055	+	1.06055i	−0.998045	+	0.0625039i	$0.980091\pi$
$240$	−5170.03	−	5170.03i	−0.0897575	−	0.0897575i
$241$	−35030.0	+	35030.0i	−0.603124	+	0.603124i	−0.941140	−	0.338016i	$-0.890244\pi$
$241$	−35030.0	+	35030.0i	−0.603124	+	0.603124i	0.338016	+	0.941140i	$0.390244\pi$
$242$	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	0.702119	−	0.712059i	$-0.252237\pi$
$251$	−626.235	−	626.235i	−0.00994008	−	0.00994008i	−0.712059	+	0.702119i	$0.752237\pi$
$252$			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	−0.274627	+	0.961551i	$0.588554\pi$
$257$	−81648.3	+	81648.3i	−1.23618	+	1.23618i	−0.961551	+	0.274627i	$0.911446\pi$
$258$		−	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	$-0.738316\pi$
$263$		−	101344.i		−	1.46516i	0.680682	−	0.732579i	$-0.261684\pi$
$264$	−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	0.498808	−	0.866712i	$-0.333771\pi$
$277$	−28228.9	−	28228.9i	−0.367904	−	0.367904i	−0.866712	+	0.498808i	$0.833771\pi$
$278$	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	−0.570349	−	0.821402i	$-0.693192\pi$
$281$	19823.4	−	19823.4i	0.251053	−	0.251053i	0.821402	+	0.570349i	$0.193192\pi$
$282$	−30620.2	+	30620.2i	−0.385043	+	0.385043i
$283$	2415.84	+	2415.84i	0.0301645	+	0.0301645i	0.722028	−	0.691864i	$-0.243210\pi$
$283$	2415.84	+	2415.84i	0.0301645	+	0.0301645i	−0.691864	+	0.722028i	$0.743210\pi$
$284$		−	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	$-0.859925\pi$
$307$		−	80298.9i		−	0.851987i	0.904726	−	0.425994i	$-0.140075\pi$
$308$	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	0.172735	−	0.984968i	$-0.444739\pi$
$311$	−78560.0	−	78560.0i	−0.812233	−	0.812233i	−0.984968	+	0.172735i	$0.944739\pi$
$312$	19467.7			0.199989
$313$	43754.1	−	43754.1i	0.446611	−	0.446611i	−0.447615	−	0.894226i	$-0.647726\pi$
$313$	43754.1	−	43754.1i	0.446611	−	0.446611i	0.894226	+	0.447615i	$0.147726\pi$
$314$	−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	$-0.920034\pi$
$317$		−	49960.2i		−	0.497171i	0.968610	−	0.248585i	$-0.0799656\pi$
$318$	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	−0.347347	−	0.937737i	$-0.612917\pi$
$331$	64683.8	−	64683.8i	0.590390	−	0.590390i	0.937737	+	0.347347i	$0.112917\pi$
$332$			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	$0.270880\pi$
$337$			170793.i			1.50387i	−0.659235	+	0.751937i	$0.729120\pi$
$338$	−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	0.468305	−	0.883567i	$-0.344865\pi$
$347$	−50001.2	−	50001.2i	−0.415261	−	0.415261i	−0.883567	+	0.468305i	$0.844865\pi$
$348$	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	0.998024	−	0.0628372i	$-0.0200149\pi$
$353$	116533.	+	116533.i	0.935187	+	0.935187i	−0.0628372	+	0.998024i	$0.520015\pi$
$354$		−	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	$-0.885260\pi$
$373$		−	98144.9i		−	0.705424i	0.935732	−	0.352712i	$-0.114740\pi$
$374$			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	−0.871171	−	0.490979i	$-0.836639\pi$
$383$	−55770.1	+	55770.1i	−0.380192	+	0.380192i	0.490979	+	0.871171i	$0.336639\pi$
$384$	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	−0.731641	−	0.681690i	$-0.761245\pi$
$389$	−7558.69	+	7558.69i	−0.0499514	+	0.0499514i	0.681690	+	0.731641i	$0.261245\pi$
$390$	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	$0.171042\pi$
$397$			161347.i			1.02371i	−0.859070	+	0.511857i	$0.828958\pi$
$398$			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	0.834283	−	0.551337i	$-0.185882\pi$
$401$	45498.0	+	45498.0i	0.282946	+	0.282946i	−0.551337	+	0.834283i	$0.685882\pi$
$402$	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	0.480691	−	0.876890i	$-0.340386\pi$
$409$	−66276.5	−	66276.5i	−0.396199	−	0.396199i	−0.876890	+	0.480691i	$0.840386\pi$
$410$		−	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	−0.992035	−	0.125962i	$-0.959798\pi$
$421$	−198155.	−	198155.i	−1.11800	−	1.11800i	−0.125962	−	0.992035i	$-0.540202\pi$
$422$	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	0.998516	−	0.0544557i	$-0.0173424\pi$
$431$	175370.	+	175370.i	0.944061	+	0.944061i	−0.0544557	+	0.998516i	$0.517342\pi$
$432$			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	0.999519	+	0.0310166i	$0.00987446\pi$
$439$	198606.	+	198606.i	1.03054	+	1.03054i	0.0310166	+	0.999519i	$0.490126\pi$
$440$	122420.			0.632332
$441$	154965.			0.796815
$442$	105557.	−	105557.i	0.540307	−	0.540307i
$443$			167529.i			0.853657i	0.904333	+	0.426828i	$0.140369\pi$
$443$			167529.i			0.853657i	−0.904333	+	0.426828i	$0.859631\pi$
$444$	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	−0.150403	+	0.988625i	$0.548057\pi$
$449$	−229629.	+	229629.i	−1.13903	+	1.13903i	−0.988625	+	0.150403i	$0.951943\pi$
$450$	−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	−0.482656	−	0.875810i	$-0.660328\pi$
$457$	82109.9	−	82109.9i	0.393154	−	0.393154i	0.875810	+	0.482656i	$0.160328\pi$
$458$	−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	−0.744316	−	0.667827i	$-0.767225\pi$
$461$	−16255.6	+	16255.6i	−0.0764893	+	0.0764893i	0.667827	+	0.744316i	$0.267225\pi$
$462$	117056.	+	117056.i	0.548417	+	0.548417i
$463$	−20732.0	+	20732.0i	−0.0967119	+	0.0967119i	−0.753807	−	0.657095i	$-0.771785\pi$
$463$	−20732.0	+	20732.0i	−0.0967119	+	0.0967119i	0.657095	+	0.753807i	$0.271785\pi$
$464$	−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	−0.718602	−	0.695422i	$-0.755218\pi$
$467$	−5055.37	+	5055.37i	−0.0231803	+	0.0231803i	0.695422	+	0.718602i	$0.255218\pi$
$468$	−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	−0.995484	−	0.0949321i	$-0.969737\pi$
$479$	−206623.	+	206623.i	−0.900552	+	0.900552i	0.0949321	+	0.995484i	$0.469737\pi$
$480$			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	−0.000378852	−	1.00000i	$-0.500121\pi$
$487$	237079.	−	237079.i	0.999621	−	0.999621i	1.00000		0.000378852i	$0.000120592\pi$
$488$	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	0.906379	−	0.422466i	$-0.138835\pi$
$499$	120495.	+	120495.i	0.483913	+	0.483913i	−0.422466	+	0.906379i	$0.638835\pi$
$500$	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	−0.599471	−	0.800397i	$-0.704622\pi$
$503$	50836.2	−	50836.2i	0.200926	−	0.200926i	0.800397	+	0.599471i	$0.204622\pi$
$504$	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	$0.279450\pi$
$509$			398680.i			1.53882i	−0.638754	+	0.769411i	$0.720550\pi$
$510$	−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	$0.139919\pi$
$521$			231023.i			0.851099i	−0.904935	+	0.425549i	$0.860081\pi$
$522$		−	204284.i		−	0.749712i
$523$	110607.	−	110607.i	0.404370	−	0.404370i	−0.475400	−	0.879770i	$-0.657697\pi$
$523$	110607.	−	110607.i	0.404370	−	0.404370i	0.879770	+	0.475400i	$0.157697\pi$
$524$	−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	−0.810845	−	0.585261i	$-0.800992\pi$
$541$	−66024.0	+	66024.0i	−0.225583	+	0.225583i	0.585261	+	0.810845i	$0.300992\pi$
$542$	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	0.0846714	−	0.996409i	$-0.473016\pi$
$547$	−272800.	−	272800.i	−0.911737	−	0.911737i	−0.996409	+	0.0846714i	$0.973016\pi$
$548$		−	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	0.950694	+	0.310131i	$0.100373\pi$
$557$	391170.	+	391170.i	1.26082	+	1.26082i	0.310131	+	0.950694i	$0.399627\pi$
$558$			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	−0.954745	−	0.297426i	$-0.903872\pi$
$563$	−208350.	+	208350.i	−0.657319	+	0.657319i	0.297426	+	0.954745i	$0.403872\pi$
$564$	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	0.216906	−	0.976193i	$-0.430404\pi$
$569$	−245827.	−	245827.i	−0.759287	−	0.759287i	−0.976193	+	0.216906i	$0.930404\pi$
$570$	−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	−0.956807	−	0.290725i	$-0.906104\pi$
$577$	−221758.	+	221758.i	−0.666082	+	0.666082i	0.290725	+	0.956807i	$0.406104\pi$
$578$	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	0.655206	−	0.755450i	$-0.272582\pi$
$587$	−34541.0	−	34541.0i	−0.100244	−	0.100244i	−0.755450	+	0.655206i	$0.772582\pi$
$588$	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	0.744122	−	0.668044i	$-0.232868\pi$
$607$	28031.0	+	28031.0i	0.0760785	+	0.0760785i	−0.668044	+	0.744122i	$0.732868\pi$
$608$	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	$-0.977630\pi$
$613$		−	52773.8i		−	0.140442i	0.997531	−	0.0702211i	$-0.0223705\pi$
$614$	−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	$-0.764041\pi$
$617$		−	514111.i		−	1.35048i	0.737600	−	0.675238i	$-0.235959\pi$
$618$	59485.1			0.155751
$619$			625597.i			1.63273i	0.577539	+	0.816363i	$0.304013\pi$
$619$			625597.i			1.63273i	−0.577539	+	0.816363i	$0.695987\pi$
$620$			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	0.926253	−	0.376904i	$-0.123011\pi$
$631$	218729.	+	218729.i	0.549349	+	0.549349i	−0.376904	+	0.926253i	$0.623011\pi$
$632$			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	0.627841	−	0.778342i	$-0.283939\pi$
$643$	−62224.6	−	62224.6i	−0.150501	−	0.150501i	−0.778342	+	0.627841i	$0.783939\pi$
$644$	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	0.953126	−	0.302575i	$-0.0978463\pi$
$647$	272326.	+	272326.i	0.650551	+	0.650551i	−0.302575	+	0.953126i	$0.597846\pi$
$648$	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	0.00528820	−	0.999986i	$-0.498317\pi$
$653$	−424148.	−	424148.i	−0.994698	−	0.994698i	−0.999986	+	0.00528820i	$0.998317\pi$
$654$		−	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	$0.0992169\pi$
$659$			266367.i			0.613352i	−0.951814	+	0.306676i	$0.900783\pi$
$660$	128921.	+	128921.i	0.295963	+	0.295963i
$661$	−569447.	−	569447.i	−1.30332	−	1.30332i	−0.926142	−	0.377175i	$-0.876895\pi$
$661$	−569447.	−	569447.i	−1.30332	−	1.30332i	−0.377175	−	0.926142i	$-0.623105\pi$
$662$	−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	$-0.653275\pi$
$677$		−	812423.i		−	1.77258i	0.463134	−	0.886288i	$-0.346725\pi$
$678$	−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	−0.670790	−	0.741648i	$-0.734045\pi$
$683$	33054.4	−	33054.4i	0.0708579	−	0.0708579i	0.741648	+	0.670790i	$0.234045\pi$
$684$	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	$0.184682\pi$
$691$			523499.i			1.09638i	−0.836355	+	0.548188i	$0.815318\pi$
$692$	−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	−0.589425	−	0.807823i	$-0.700646\pi$
$701$	107321.	−	107321.i	0.218398	−	0.218398i	0.807823	+	0.589425i	$0.200646\pi$
$702$		−	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	−0.0752745	+	0.997163i	$0.523983\pi$
$709$	−539094.	+	539094.i	−1.07244	+	1.07244i	−0.997163	+	0.0752745i	$0.976017\pi$
$710$	−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	−0.999574	−	0.0291996i	$-0.990704\pi$
$727$	−543736.	−	543736.i	−1.02877	−	1.02877i	−0.0291996	−	0.999574i	$-0.509296\pi$
$728$			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	$-0.940531\pi$
$733$		−	199595.i		−	0.371486i	0.982598	−	0.185743i	$-0.0594692\pi$
$734$	−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	$-0.761587\pi$
$739$		−	743712.i		−	1.36181i	0.732373	−	0.680904i	$-0.238413\pi$
$740$	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	$0.0945623\pi$
$743$			323198.i			0.585451i	−0.956196	+	0.292726i	$0.905438\pi$
$744$			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	$0.0332477\pi$
$751$			117607.i			0.208522i	−0.994550	+	0.104261i	$0.966752\pi$
$752$	−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	−0.647699	−	0.761896i	$-0.724269\pi$
$757$	65440.6	−	65440.6i	0.114197	−	0.114197i	0.761896	+	0.647699i	$0.224269\pi$
$758$	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	$0.0931055\pi$
$761$			333975.i			0.576693i	−0.957526	+	0.288347i	$0.906894\pi$
$762$	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	0.667728	−	0.744405i	$-0.267267\pi$
$769$	−45343.9	−	45343.9i	−0.0766772	−	0.0766772i	−0.744405	+	0.667728i	$0.767267\pi$
$770$		−	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	0.900188	−	0.435501i	$-0.143429\pi$
$797$	295173.	+	295173.i	0.464687	+	0.464687i	−0.435501	+	0.900188i	$0.643429\pi$
$798$			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	0.738868	−	0.673851i	$-0.235361\pi$
$809$	42552.5	+	42552.5i	0.0650172	+	0.0650172i	−0.673851	+	0.738868i	$0.735361\pi$
$810$	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	−0.476896	−	0.878960i	$-0.658238\pi$
$827$	274983.	−	274983.i	0.402064	−	0.402064i	0.878960	+	0.476896i	$0.158238\pi$
$828$	264250.	+	264250.i	0.385438	+	0.385438i
$829$	−547862.	−	547862.i	−0.797190	−	0.797190i	0.185461	−	0.982652i	$-0.440622\pi$
$829$	−547862.	−	547862.i	−0.797190	−	0.797190i	−0.982652	+	0.185461i	$0.940622\pi$
$830$	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	$-0.958519\pi$
$839$		−	182945.i		−	0.259895i	0.991521	−	0.129947i	$-0.0414809\pi$
$840$	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	−0.985011	−	0.172491i	$-0.944818\pi$
$853$	−842209.	−	842209.i	−1.15750	−	1.15750i	−0.172491	−	0.985011i	$-0.555182\pi$
$854$		−	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	−0.736956	−	0.675941i	$-0.763737\pi$
$857$	−44811.9	+	44811.9i	−0.0610144	+	0.0610144i	0.675941	+	0.736956i	$0.263737\pi$
$858$	−485452.			−0.659434
$859$	−578695.	+	578695.i	−0.784266	+	0.784266i	−0.980548	−	0.196282i	$-0.937113\pi$
$859$	−578695.	+	578695.i	−0.784266	+	0.784266i	0.196282	+	0.980548i	$0.437113\pi$
$860$	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	$-0.688535\pi$
$881$		−	1.28790e6i		−	1.65932i	0.558272	−	0.829658i	$-0.311465\pi$
$882$	−309931.	−	309931.i	−0.398407	−	0.398407i
$883$	738003.	+	738003.i	0.946535	+	0.946535i	0.998642	−	0.0521061i	$-0.0165934\pi$
$883$	738003.	+	738003.i	0.946535	+	0.946535i	−0.0521061	+	0.998642i	$0.516593\pi$
$884$	−422226.			−0.540307
$885$	−428926.			−0.547641
$886$	335059.	−	335059.i	0.426828	−	0.426828i
$887$			999295.i			1.27013i	0.772461	+	0.635063i	$0.219026\pi$
$887$			999295.i			1.27013i	−0.772461	+	0.635063i	$0.780974\pi$
$888$	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	−0.976091	−	0.217361i	$-0.930255\pi$
$907$	−624169.	+	624169.i	−0.758731	+	0.758731i	0.217361	+	0.976091i	$0.430255\pi$
$908$	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	−0.134512	−	0.990912i	$-0.542947\pi$
$911$	710744.	−	710744.i	0.856400	−	0.856400i	0.990912	+	0.134512i	$0.0429467\pi$
$912$	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	0.0423662	−	0.999102i	$-0.486510\pi$
$919$	−808022.	−	808022.i	−0.956736	−	0.956736i	−0.999102	+	0.0423662i	$0.986510\pi$
$920$	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	$-0.912668\pi$
$929$		−	467654.i		−	0.541867i	0.962598	−	0.270934i	$-0.0873324\pi$
$930$	−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	−0.821084	−	0.570807i	$-0.806630\pi$
$947$	−224450.	+	224450.i	−0.250277	+	0.250277i	0.570807	+	0.821084i	$0.306630\pi$
$948$	−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	$0.0934617\pi$
$953$			525704.i			0.578836i	−0.957203	+	0.289418i	$0.906538\pi$
$954$	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	−0.712147	−	0.702030i	$-0.752277\pi$
$967$	−9460.48	+	9460.48i	−0.0101172	+	0.0101172i	0.702030	+	0.712147i	$0.252277\pi$
$968$	−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	0.939050	−	0.343779i	$-0.111707\pi$
$977$	568203.	+	568203.i	0.595271	+	0.595271i	−0.343779	+	0.939050i	$0.611707\pi$
$978$	−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	$-0.685341\pi$
$983$		−	1.61413e6i		−	1.67044i	0.549917	−	0.835220i	$-0.314659\pi$
$984$	−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	0.999254	+	0.0386261i	$0.0122981\pi$
$991$	1.01928e6	+	1.01928e6i	1.03788	+	1.03788i	0.0386261	+	0.999254i	$0.487702\pi$
$992$		−	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	0.231488	−	0.972838i	$-0.425641\pi$
$997$	1.19711e6	−	1.19711e6i	1.20433	−	1.20433i	0.972838	−	0.231488i	$-0.0743593\pi$
$998$		−	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.31.4	✓	14
37.6	odd	4	inner	74.5.d.a.43.4	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.4	✓	14	1.1	even	1	trivial
74.5.d.a.43.4	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} -4.21245i q^{3} +8.00000i q^{4} +(-19.1769 + 19.1769i) q^{5} +(-8.42489 + 8.42489i) q^{6} +69.6480 q^{7} +(16.0000 - 16.0000i) q^{8} +63.2553 q^{9} +O(q^{10})\)	\(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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