LMFDB - Embedded newform 74.5.d.b.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} + 207381 x^{10} + 29788577 x^{8} + 2302194203 x^{6} + 92916575085 x^{4} + \cdots + 6531254919424 $ x^14 + 727x^12 + 207381x^10 + 29788577x^8 + 2302194203x^6 + 92916575085x^4 + 1658451585508x^2 + 6531254919424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.4
Root			$-2.31020i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.b.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} -3.31020i q^{3} +8.00000i q^{4} +(-1.68780 + 1.68780i) q^{5} +(6.62039 - 6.62039i) q^{6} +49.9045 q^{7} +(-16.0000 + 16.0000i) q^{8} +70.0426 q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} -3.31020i q^{3} +8.00000i q^{4} +(-1.68780 + 1.68780i) q^{5} +(6.62039 - 6.62039i) q^{6} +49.9045 q^{7} +(-16.0000 + 16.0000i) q^{8} +70.0426 q^{9} -6.75118 q^{10} +233.955i q^{11} +26.4816 q^{12} +(101.658 - 101.658i) q^{13} +(99.8091 + 99.8091i) q^{14} +(5.58694 + 5.58694i) q^{15} -64.0000 q^{16} +(-61.4208 + 61.4208i) q^{17} +(140.085 + 140.085i) q^{18} +(284.903 - 284.903i) q^{19} +(-13.5024 - 13.5024i) q^{20} -165.194i q^{21} +(-467.910 + 467.910i) q^{22} +(-145.412 + 145.412i) q^{23} +(52.9632 + 52.9632i) q^{24} +619.303i q^{25} +406.634 q^{26} -499.981i q^{27} +399.236i q^{28} +(-26.1154 - 26.1154i) q^{29} +22.3477i q^{30} +(-1138.27 - 1138.27i) q^{31} +(-128.000 - 128.000i) q^{32} +774.437 q^{33} -245.683 q^{34} +(-84.2287 + 84.2287i) q^{35} +560.341i q^{36} +(-991.415 + 944.065i) q^{37} +1139.61 q^{38} +(-336.510 - 336.510i) q^{39} -54.0095i q^{40} -3305.42i q^{41} +(330.388 - 330.388i) q^{42} +(2147.37 - 2147.37i) q^{43} -1871.64 q^{44} +(-118.218 + 118.218i) q^{45} -581.646 q^{46} +1822.81 q^{47} +211.853i q^{48} +89.4638 q^{49} +(-1238.61 + 1238.61i) q^{50} +(203.315 + 203.315i) q^{51} +(813.268 + 813.268i) q^{52} -4210.08 q^{53} +(999.962 - 999.962i) q^{54} +(-394.868 - 394.868i) q^{55} +(-798.473 + 798.473i) q^{56} +(-943.086 - 943.086i) q^{57} -104.462i q^{58} +(-3799.88 + 3799.88i) q^{59} +(-44.6955 + 44.6955i) q^{60} +(-2053.05 - 2053.05i) q^{61} -4553.07i q^{62} +3495.44 q^{63} -512.000i q^{64} +343.158i q^{65} +(1548.87 + 1548.87i) q^{66} +4314.65i q^{67} +(-491.367 - 491.367i) q^{68} +(481.341 + 481.341i) q^{69} -336.915 q^{70} +5164.30 q^{71} +(-1120.68 + 1120.68i) q^{72} +1258.94i q^{73} +(-3870.96 - 94.7002i) q^{74} +2050.01 q^{75} +(2279.23 + 2279.23i) q^{76} +11675.4i q^{77} -1346.04i q^{78} +(614.028 - 614.028i) q^{79} +(108.019 - 108.019i) q^{80} +4018.42 q^{81} +(6610.85 - 6610.85i) q^{82} +1185.87 q^{83} +1321.55 q^{84} -207.332i q^{85} +8589.47 q^{86} +(-86.4471 + 86.4471i) q^{87} +(-3743.28 - 3743.28i) q^{88} +(807.796 + 807.796i) q^{89} -472.870 q^{90} +(5073.22 - 5073.22i) q^{91} +(-1163.29 - 1163.29i) q^{92} +(-3767.89 + 3767.89i) q^{93} +(3645.61 + 3645.61i) q^{94} +961.717i q^{95} +(-423.705 + 423.705i) q^{96} +(-2345.18 + 2345.18i) q^{97} +(178.928 + 178.928i) q^{98} +16386.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$		−	3.31020i		−	0.367800i	−0.982945	−	0.183900i	$-0.941128\pi$
$3$		−	3.31020i		−	0.367800i	0.982945	−	0.183900i	$-0.0588722\pi$
$4$			8.00000i			0.500000i
$5$	−1.68780	+	1.68780i	−0.0675118	+	0.0675118i	−0.740057	−	0.672545i	$-0.765201\pi$
$5$	−1.68780	+	1.68780i	−0.0675118	+	0.0675118i	0.672545	+	0.740057i	$0.265201\pi$
$6$	6.62039	−	6.62039i	0.183900	−	0.183900i
$7$	49.9045			1.01846			0.509230	−	0.860630i	$-0.329930\pi$
$7$	49.9045			1.01846			0.509230	+	0.860630i	$0.329930\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	70.0426			0.864723
$10$	−6.75118			−0.0675118
$11$			233.955i			1.93351i	0.255701	+	0.966756i	$0.417694\pi$
$11$			233.955i			1.93351i	−0.255701	+	0.966756i	$0.582306\pi$
$12$	26.4816			0.183900
$13$	101.658	−	101.658i	0.601529	−	0.601529i	−0.339189	−	0.940718i	$-0.610153\pi$
$13$	101.658	−	101.658i	0.601529	−	0.601529i	0.940718	+	0.339189i	$0.110153\pi$
$14$	99.8091	+	99.8091i	0.509230	+	0.509230i
$15$	5.58694	+	5.58694i	0.0248308	+	0.0248308i
$16$	−64.0000			−0.250000
$17$	−61.4208	+	61.4208i	−0.212529	+	0.212529i	−0.805341	−	0.592812i	$-0.798018\pi$
$17$	−61.4208	+	61.4208i	−0.212529	+	0.212529i	0.592812	+	0.805341i	$0.298018\pi$
$18$	140.085	+	140.085i	0.432362	+	0.432362i
$19$	284.903	−	284.903i	0.789206	−	0.789206i	−0.192158	−	0.981364i	$-0.561549\pi$
$19$	284.903	−	284.903i	0.789206	−	0.789206i	0.981364	+	0.192158i	$0.0615487\pi$
$20$	−13.5024	−	13.5024i	−0.0337559	−	0.0337559i
$21$		−	165.194i		−	0.374589i
$22$	−467.910	+	467.910i	−0.966756	+	0.966756i
$23$	−145.412	+	145.412i	−0.274880	+	0.274880i	−0.831061	−	0.556181i	$-0.812266\pi$
$23$	−145.412	+	145.412i	−0.274880	+	0.274880i	0.556181	+	0.831061i	$0.312266\pi$
$24$	52.9632	+	52.9632i	0.0919499	+	0.0919499i
$25$			619.303i			0.990884i
$26$	406.634			0.601529
$27$		−	499.981i		−	0.685845i
$28$			399.236i			0.509230i
$29$	−26.1154	−	26.1154i	−0.0310528	−	0.0310528i	0.691410	−	0.722463i	$-0.256990\pi$
$29$	−26.1154	−	26.1154i	−0.0310528	−	0.0310528i	−0.722463	+	0.691410i	$0.756990\pi$
$30$			22.3477i			0.0248308i
$31$	−1138.27	−	1138.27i	−1.18446	−	1.18446i	−0.978576	−	0.205886i	$-0.933992\pi$
$31$	−1138.27	−	1138.27i	−1.18446	−	1.18446i	−0.205886	−	0.978576i	$-0.566008\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	774.437			0.711145
$34$	−245.683			−0.212529
$35$	−84.2287	+	84.2287i	−0.0687581	+	0.0687581i
$36$			560.341i			0.432362i
$37$	−991.415	+	944.065i	−0.724189	+	0.689602i
$37$	−991.415	+	944.065i	−0.724189	+	0.689602i
$38$	1139.61			0.789206
$39$	−336.510	−	336.510i	−0.221242	−	0.221242i
$40$		−	54.0095i		−	0.0337559i
$41$		−	3305.42i		−	1.96634i	−0.182684	−	0.983172i	$-0.558478\pi$
$41$		−	3305.42i		−	1.96634i	0.182684	−	0.983172i	$-0.441522\pi$
$42$	330.388	−	330.388i	0.187295	−	0.187295i
$43$	2147.37	−	2147.37i	1.16137	−	1.16137i	0.177190	−	0.984177i	$-0.443299\pi$
$43$	2147.37	−	2147.37i	1.16137	−	1.16137i	0.984177	−	0.177190i	$-0.0567009\pi$
$44$	−1871.64			−0.966756
$45$	−118.218	+	118.218i	−0.0583791	+	0.0583791i
$46$	−581.646			−0.274880
$47$	1822.81			0.825173			0.412586	−	0.910918i	$-0.364625\pi$
$47$	1822.81			0.825173			0.412586	+	0.910918i	$0.364625\pi$
$48$			211.853i			0.0919499i
$49$	89.4638			0.0372611
$50$	−1238.61	+	1238.61i	−0.495442	+	0.495442i
$51$	203.315	+	203.315i	0.0781680	+	0.0781680i
$52$	813.268	+	813.268i	0.300765	+	0.300765i
$53$	−4210.08			−1.49878			−0.749391	−	0.662127i	$-0.769654\pi$
$53$	−4210.08			−1.49878			−0.749391	+	0.662127i	$0.769654\pi$
$54$	999.962	−	999.962i	0.342922	−	0.342922i
$55$	−394.868	−	394.868i	−0.130535	−	0.130535i
$56$	−798.473	+	798.473i	−0.254615	+	0.254615i
$57$	−943.086	−	943.086i	−0.290270	−	0.290270i
$58$		−	104.462i		−	0.0310528i
$59$	−3799.88	+	3799.88i	−1.09161	+	1.09161i	−0.0962496	+	0.995357i	$0.530685\pi$
$59$	−3799.88	+	3799.88i	−1.09161	+	1.09161i	−0.995357	+	0.0962496i	$0.969315\pi$
$60$	−44.6955	+	44.6955i	−0.0124154	+	0.0124154i
$61$	−2053.05	−	2053.05i	−0.551746	−	0.551746i	0.375199	−	0.926944i	$-0.377575\pi$
$61$	−2053.05	−	2053.05i	−0.551746	−	0.551746i	−0.926944	+	0.375199i	$0.877575\pi$
$62$		−	4553.07i		−	1.18446i
$63$	3495.44			0.880686
$64$		−	512.000i		−	0.125000i
$65$			343.158i			0.0812207i
$66$	1548.87	+	1548.87i	0.355572	+	0.355572i
$67$			4314.65i			0.961162i	0.876950	+	0.480581i	$0.159574\pi$
$67$			4314.65i			0.961162i	−0.876950	+	0.480581i	$0.840426\pi$
$68$	−491.367	−	491.367i	−0.106264	−	0.106264i
$69$	481.341	+	481.341i	0.101101	+	0.101101i
$70$	−336.915			−0.0687581
$71$	5164.30			1.02446			0.512230	−	0.858848i	$-0.328819\pi$
$71$	5164.30			1.02446			0.512230	+	0.858848i	$0.328819\pi$
$72$	−1120.68	+	1120.68i	−0.216181	+	0.216181i
$73$			1258.94i			0.236244i	0.992999	+	0.118122i	$0.0376874\pi$
$73$			1258.94i			0.236244i	−0.992999	+	0.118122i	$0.962313\pi$
$74$	−3870.96	−	94.7002i	−0.706895	−	0.0172937i
$75$	2050.01			0.364447
$76$	2279.23	+	2279.23i	0.394603	+	0.394603i
$77$			11675.4i			1.96920i
$78$		−	1346.04i		−	0.221242i
$79$	614.028	−	614.028i	0.0983861	−	0.0983861i	−0.656200	−	0.754587i	$-0.727837\pi$
$79$	614.028	−	614.028i	0.0983861	−	0.0983861i	0.754587	+	0.656200i	$0.227837\pi$
$80$	108.019	−	108.019i	0.0168780	−	0.0168780i
$81$	4018.42			0.612470
$82$	6610.85	−	6610.85i	0.983172	−	0.983172i
$83$	1185.87			0.172140			0.0860699	−	0.996289i	$-0.472569\pi$
$83$	1185.87			0.172140			0.0860699	+	0.996289i	$0.472569\pi$
$84$	1321.55			0.187295
$85$		−	207.332i		−	0.0286964i
$86$	8589.47			1.16137
$87$	−86.4471	+	86.4471i	−0.0114212	+	0.0114212i
$88$	−3743.28	−	3743.28i	−0.483378	−	0.483378i
$89$	807.796	+	807.796i	0.101982	+	0.101982i	0.756257	−	0.654275i	$-0.227026\pi$
$89$	807.796	+	807.796i	0.101982	+	0.101982i	−0.654275	+	0.756257i	$0.727026\pi$
$90$	−472.870			−0.0583791
$91$	5073.22	−	5073.22i	0.612634	−	0.612634i
$92$	−1163.29	−	1163.29i	−0.137440	−	0.137440i
$93$	−3767.89	+	3767.89i	−0.435645	+	0.435645i
$94$	3645.61	+	3645.61i	0.412586	+	0.412586i
$95$			961.717i			0.106561i
$96$	−423.705	+	423.705i	−0.0459750	+	0.0459750i
$97$	−2345.18	+	2345.18i	−0.249248	+	0.249248i	−0.820662	−	0.571414i	$-0.806395\pi$
$97$	−2345.18	+	2345.18i	−0.249248	+	0.249248i	0.571414	+	0.820662i	$0.306395\pi$
$98$	178.928	+	178.928i	0.0186305	+	0.0186305i
$99$			16386.8i			1.67195i
$100$	−4954.42			−0.495442
$101$			5840.97i			0.572588i	0.958142	+	0.286294i	$0.0924234\pi$
$101$			5840.97i			0.572588i	−0.958142	+	0.286294i	$0.907577\pi$
$102$			813.260i			0.0781680i
$103$	−7141.30	−	7141.30i	−0.673136	−	0.673136i	0.285302	−	0.958438i	$-0.407906\pi$
$103$	−7141.30	−	7141.30i	−0.673136	−	0.673136i	−0.958438	+	0.285302i	$0.907906\pi$
$104$			3253.07i			0.300765i
$105$	278.814	+	278.814i	0.0252892	+	0.0252892i
$106$	−8420.16	−	8420.16i	−0.749391	−	0.749391i
$107$	10647.6			0.929998			0.464999	−	0.885311i	$-0.346055\pi$
$107$	10647.6			0.929998			0.464999	+	0.885311i	$0.346055\pi$
$108$	3999.85			0.342922
$109$	6857.13	−	6857.13i	0.577151	−	0.577151i	−0.356967	−	0.934117i	$-0.616189\pi$
$109$	6857.13	−	6857.13i	0.577151	−	0.577151i	0.934117	+	0.356967i	$0.116189\pi$
$110$		−	1579.47i		−	0.130535i
$111$	3125.04	+	3281.78i	0.253635	+	0.266356i
$112$	−3193.89			−0.254615
$113$	−14711.5	−	14711.5i	−1.15212	−	1.15212i	−0.986126	−	0.165996i	$-0.946916\pi$
$113$	−14711.5	−	14711.5i	−1.15212	−	1.15212i	−0.165996	−	0.986126i	$-0.553084\pi$
$114$		−	3772.34i		−	0.290270i
$115$		−	490.850i		−	0.0371153i
$116$	208.923	−	208.923i	0.0155264	−	0.0155264i
$117$	7120.42	−	7120.42i	0.520157	−	0.520157i
$118$	−15199.5			−1.09161
$119$	−3065.18	+	3065.18i	−0.216452	+	0.216452i
$120$	−178.782			−0.0124154
$121$	−40093.9			−2.73847
$122$		−	8212.19i		−	0.551746i
$123$	−10941.6			−0.723220
$124$	9106.15	−	9106.15i	0.592231	−	0.592231i
$125$	−2100.13	−	2100.13i	−0.134408	−	0.134408i
$126$	6990.89	+	6990.89i	0.440343	+	0.440343i
$127$	12752.7			0.790672			0.395336	−	0.918537i	$-0.370628\pi$
$127$	12752.7			0.790672			0.395336	+	0.918537i	$0.370628\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$	−7108.21	−	7108.21i	−0.427150	−	0.427150i
$130$	−686.315	+	686.315i	−0.0406104	+	0.0406104i
$131$	−1.09120	−	1.09120i	−6.35862e−5	−	6.35862e-5i	0.707075	−	0.707139i	$-0.250014\pi$
$131$	−1.09120	−	1.09120i	−6.35862e−5	−	6.35862e-5i	−0.707139	+	0.707075i	$0.750014\pi$
$132$			6195.49i			0.355572i
$133$	14218.0	−	14218.0i	0.803774	−	0.803774i
$134$	−8629.31	+	8629.31i	−0.480581	+	0.480581i
$135$	843.866	+	843.866i	0.0463026	+	0.0463026i
$136$		−	1965.47i		−	0.106264i
$137$	−7915.41			−0.421728			−0.210864	−	0.977515i	$-0.567628\pi$
$137$	−7915.41			−0.421728			−0.210864	+	0.977515i	$0.567628\pi$
$138$			1925.36i			0.101101i
$139$		−	24108.3i		−	1.24778i	−0.781512	−	0.623890i	$-0.785551\pi$
$139$		−	24108.3i		−	1.24778i	0.781512	−	0.623890i	$-0.214449\pi$
$140$	−673.830	−	673.830i	−0.0343791	−	0.0343791i
$141$		−	6033.85i		−	0.303498i
$142$	10328.6	+	10328.6i	0.512230	+	0.512230i
$143$	23783.5	+	23783.5i	1.16306	+	1.16306i
$144$	−4482.73			−0.216181
$145$	88.1550			0.00419286
$146$	−2517.89	+	2517.89i	−0.118122	+	0.118122i
$147$		−	296.143i		−	0.0137046i
$148$	−7552.52	−	7931.32i	−0.344801	−	0.362094i
$149$	840.776			0.0378711			0.0189355	−	0.999821i	$-0.493972\pi$
$149$	840.776			0.0378711			0.0189355	+	0.999821i	$0.493972\pi$
$150$	4100.03	+	4100.03i	0.182223	+	0.182223i
$151$		−	41229.5i		−	1.80823i	−0.427288	−	0.904116i	$-0.640531\pi$
$151$		−	41229.5i		−	1.80823i	0.427288	−	0.904116i	$-0.359469\pi$
$152$			9116.90i			0.394603i
$153$	−4302.07	+	4302.07i	−0.183779	+	0.183779i
$154$	−23350.8	+	23350.8i	−0.984602	+	0.984602i
$155$	3842.33			0.159930
$156$	2692.08	−	2692.08i	0.110621	−	0.110621i
$157$	−19539.1			−0.792692			−0.396346	−	0.918101i	$-0.629722\pi$
$157$	−19539.1			−0.792692			−0.396346	+	0.918101i	$0.629722\pi$
$158$	2456.11			0.0983861
$159$			13936.2i			0.551252i
$160$	432.076			0.0168780
$161$	−7256.70	+	7256.70i	−0.279954	+	0.279954i
$162$	8036.83	+	8036.83i	0.306235	+	0.306235i
$163$	15995.9	+	15995.9i	0.602052	+	0.602052i	0.940857	−	0.338805i	$-0.110023\pi$
$163$	15995.9	+	15995.9i	0.602052	+	0.602052i	−0.338805	+	0.940857i	$0.610023\pi$
$164$	26443.4			0.983172
$165$	−1307.09	+	1307.09i	−0.0480107	+	0.0480107i
$166$	2371.74	+	2371.74i	0.0860699	+	0.0860699i
$167$	26693.9	−	26693.9i	0.957147	−	0.957147i	−0.0419717	−	0.999119i	$-0.513364\pi$
$167$	26693.9	−	26693.9i	0.957147	−	0.957147i	0.999119	+	0.0419717i	$0.0133639\pi$
$168$	2643.10	+	2643.10i	0.0936473	+	0.0936473i
$169$			7892.11i			0.276325i
$170$	414.663	−	414.663i	0.0143482	−	0.0143482i
$171$	19955.4	−	19955.4i	0.682444	−	0.682444i
$172$	17178.9	+	17178.9i	0.580684	+	0.580684i
$173$			16154.6i			0.539763i	0.962894	+	0.269881i	$0.0869845\pi$
$173$			16154.6i			0.539763i	−0.962894	+	0.269881i	$0.913016\pi$
$174$	−345.789			−0.0114212
$175$			30906.0i			1.00918i
$176$		−	14973.1i		−	0.483378i
$177$	12578.4	+	12578.4i	0.401493	+	0.401493i
$178$			3231.18i			0.101982i
$179$	29289.9	+	29289.9i	0.914137	+	0.914137i	0.996595	−	0.0824572i	$-0.0262768\pi$
$179$	29289.9	+	29289.9i	0.914137	+	0.914137i	−0.0824572	+	0.996595i	$0.526277\pi$
$180$	−945.741	−	945.741i	−0.0291895	−	0.0291895i
$181$	−22536.6			−0.687909			−0.343955	−	0.938986i	$-0.611767\pi$
$181$	−22536.6			−0.687909			−0.343955	+	0.938986i	$0.611767\pi$
$182$	20292.9			0.612634
$183$	−6795.99	+	6795.99i	−0.202932	+	0.202932i
$184$		−	4653.17i		−	0.137440i
$185$	79.9173	−	3266.69i	0.00233506	−	0.0954476i
$186$	−15071.6			−0.435645
$187$	−14369.7	−	14369.7i	−0.410927	−	0.410927i
$188$			14582.5i			0.412586i
$189$		−	24951.3i		−	0.698505i
$190$	−1923.43	+	1923.43i	−0.0532807	+	0.0532807i
$191$	10716.5	−	10716.5i	0.293755	−	0.293755i	−0.544807	−	0.838562i	$-0.683397\pi$
$191$	10716.5	−	10716.5i	0.293755	−	0.293755i	0.838562	+	0.544807i	$0.183397\pi$
$192$	−1694.82			−0.0459750
$193$	1260.02	−	1260.02i	0.0338269	−	0.0338269i	−0.689991	−	0.723818i	$-0.742386\pi$
$193$	1260.02	−	1260.02i	0.0338269	−	0.0338269i	0.723818	+	0.689991i	$0.242386\pi$
$194$	−9380.71			−0.249248
$195$	1135.92			0.0298730
$196$			715.711i			0.0186305i
$197$	773.285			0.0199254			0.00996271	−	0.999950i	$-0.496829\pi$
$197$	773.285			0.0199254			0.00996271	+	0.999950i	$0.496829\pi$
$198$	−32773.6	+	32773.6i	−0.835976	+	0.835976i
$199$	−30952.8	−	30952.8i	−0.781616	−	0.781616i	0.198487	−	0.980103i	$-0.436397\pi$
$199$	−30952.8	−	30952.8i	−0.781616	−	0.781616i	−0.980103	+	0.198487i	$0.936397\pi$
$200$	−9908.84	−	9908.84i	−0.247721	−	0.247721i
$201$	14282.4			0.353515
$202$	−11681.9	+	11681.9i	−0.286294	+	0.286294i
$203$	−1303.28	−	1303.28i	−0.0316260	−	0.0316260i
$204$	−1626.52	+	1626.52i	−0.0390840	+	0.0390840i
$205$	5578.88	+	5578.88i	0.132751	+	0.132751i
$206$		−	28565.2i		−	0.673136i
$207$	−10185.0	+	10185.0i	−0.237695	+	0.237695i
$208$	−6506.14	+	6506.14i	−0.150382	+	0.150382i
$209$	66654.5	+	66654.5i	1.52594	+	1.52594i
$210$			1115.25i			0.0252892i
$211$	−11959.2			−0.268618			−0.134309	−	0.990939i	$-0.542882\pi$
$211$	−11959.2			−0.268618			−0.134309	+	0.990939i	$0.542882\pi$
$212$		−	33680.6i		−	0.749391i
$213$		−	17094.9i		−	0.376796i
$214$	21295.1	+	21295.1i	0.464999	+	0.464999i
$215$			7248.64i			0.156812i
$216$	7999.69	+	7999.69i	0.171461	+	0.171461i
$217$	−56804.8	−	56804.8i	−1.20633	−	1.20633i
$218$	27428.5			0.577151
$219$	4167.35			0.0868905
$220$	3158.95	−	3158.95i	0.0652675	−	0.0652675i
$221$			12487.9i			0.255685i
$222$	−313.476	+	12813.6i	−0.00636061	+	0.259996i
$223$	−60137.1			−1.20930			−0.604648	−	0.796492i	$-0.706686\pi$
$223$	−60137.1			−1.20930			−0.604648	+	0.796492i	$0.706686\pi$
$224$	−6387.78	−	6387.78i	−0.127308	−	0.127308i
$225$			43377.6i			0.856841i
$226$		−	58845.8i		−	1.15212i
$227$	−32314.8	+	32314.8i	−0.627119	+	0.627119i	−0.947342	−	0.320223i	$-0.896242\pi$
$227$	−32314.8	+	32314.8i	−0.627119	+	0.627119i	0.320223	+	0.947342i	$0.396242\pi$
$228$	7544.69	−	7544.69i	0.145135	−	0.145135i
$229$	−1068.51			−0.0203754			−0.0101877	−	0.999948i	$-0.503243\pi$
$229$	−1068.51			−0.0203754			−0.0101877	+	0.999948i	$0.503243\pi$
$230$	981.700	−	981.700i	0.0185577	−	0.0185577i
$231$	38647.9			0.724273
$232$	835.693			0.0155264
$233$		−	12306.5i		−	0.226685i	−0.993556	−	0.113343i	$-0.963844\pi$
$233$		−	12306.5i		−	0.226685i	0.993556	−	0.113343i	$-0.0361558\pi$
$234$	28481.7			0.520157
$235$	−3076.53	+	3076.53i	−0.0557089	+	0.0557089i
$236$	−30399.1	−	30399.1i	−0.545803	−	0.545803i
$237$	−2032.55	−	2032.55i	−0.0361864	−	0.0361864i
$238$	−12260.7			−0.216452
$239$	−18839.1	+	18839.1i	−0.329811	+	0.329811i	−0.852515	−	0.522703i	$-0.824923\pi$
$239$	−18839.1	+	18839.1i	−0.329811	+	0.329811i	0.522703	+	0.852515i	$0.324923\pi$
$240$	−357.564	−	357.564i	−0.00620771	−	0.00620771i
$241$	39992.8	−	39992.8i	0.688569	−	0.688569i	−0.273346	−	0.961916i	$-0.588131\pi$
$241$	39992.8	−	39992.8i	0.688569	−	0.688569i	0.961916	+	0.273346i	$0.0881305\pi$
$242$	−80187.8	−	80187.8i	−1.36923	−	1.36923i
$243$		−	53800.2i		−	0.911111i
$244$	16424.4	−	16424.4i	0.275873	−	0.275873i
$245$	−150.997	+	150.997i	−0.00251556	+	0.00251556i
$246$	−21883.2	−	21883.2i	−0.361610	−	0.361610i
$247$		−	57925.7i		−	0.949461i
$248$	36424.6			0.592231
$249$		−	3925.47i		−	0.0633130i
$250$		−	8400.52i		−	0.134408i
$251$	79655.9	+	79655.9i	1.26436	+	1.26436i	0.948958	+	0.315401i	$0.102139\pi$
$251$	79655.9	+	79655.9i	1.26436	+	1.26436i	0.315401	+	0.948958i	$0.397861\pi$
$252$			27963.6i			0.440343i
$253$	−34019.8	−	34019.8i	−0.531484	−	0.531484i
$254$	25505.5	+	25505.5i	0.395336	+	0.395336i
$255$	−686.308			−0.0105545
$256$	4096.00			0.0625000
$257$	−25962.9	+	25962.9i	−0.393085	+	0.393085i	−0.875785	−	0.482701i	$-0.839656\pi$
$257$	−25962.9	+	25962.9i	−0.393085	+	0.393085i	0.482701	+	0.875785i	$0.339656\pi$
$258$		−	28432.8i		−	0.427150i
$259$	−49476.1	+	47113.1i	−0.737558	+	0.702332i
$260$	−2745.26			−0.0406104
$261$	−1829.19	−	1829.19i	−0.0268521	−	0.0268521i
$262$		−	4.36481i		−	6.35862e-5i
$263$			19098.4i			0.276111i	0.990424	+	0.138056i	$0.0440853\pi$
$263$			19098.4i			0.276111i	−0.990424	+	0.138056i	$0.955915\pi$
$264$	−12391.0	+	12391.0i	−0.177786	+	0.177786i
$265$	7105.76	−	7105.76i	0.101186	−	0.101186i
$266$	56871.9			0.803774
$267$	2673.96	−	2673.96i	0.0375088	−	0.0375088i
$268$	−34517.2			−0.480581
$269$	−31186.0			−0.430978			−0.215489	−	0.976506i	$-0.569134\pi$
$269$	−31186.0			−0.430978			−0.215489	+	0.976506i	$0.569134\pi$
$270$			3375.46i			0.0463026i
$271$	95947.3			1.30645			0.653227	−	0.757162i	$-0.273415\pi$
$271$	95947.3			1.30645			0.653227	+	0.757162i	$0.273415\pi$
$272$	3930.93	−	3930.93i	0.0531322	−	0.0531322i
$273$	−16793.4	−	16793.4i	−0.225327	−	0.225327i
$274$	−15830.8	−	15830.8i	−0.210864	−	0.210864i
$275$	−144889.			−1.91589
$276$	−3850.73	+	3850.73i	−0.0505504	+	0.0505504i
$277$	85868.6	+	85868.6i	1.11912	+	1.11912i	0.991871	+	0.127244i	$0.0406131\pi$
$277$	85868.6	+	85868.6i	1.11912	+	1.11912i	0.127244	+	0.991871i	$0.459387\pi$
$278$	48216.7	−	48216.7i	0.623890	−	0.623890i
$279$	−79727.3	−	79727.3i	−1.02423	−	1.02423i
$280$		−	2695.32i		−	0.0343791i
$281$	−37325.8	+	37325.8i	−0.472711	+	0.472711i	−0.902791	−	0.430080i	$-0.858485\pi$
$281$	−37325.8	+	37325.8i	−0.472711	+	0.472711i	0.430080	+	0.902791i	$0.358485\pi$
$282$	12067.7	−	12067.7i	0.151749	−	0.151749i
$283$	47733.9	+	47733.9i	0.596011	+	0.596011i	0.939249	−	0.343238i	$-0.111524\pi$
$283$	47733.9	+	47733.9i	0.596011	+	0.596011i	−0.343238	+	0.939249i	$0.611524\pi$
$284$			41314.4i			0.512230i
$285$	3183.47			0.0391933
$286$			95134.0i			1.16306i
$287$		−	164956.i		−	2.00264i
$288$	−8965.45	−	8965.45i	−0.108090	−	0.108090i
$289$			75976.0i			0.909663i
$290$	176.310	+	176.310i	0.00209643	+	0.00209643i
$291$	7763.00	+	7763.00i	0.0916735	+	0.0916735i
$292$	−10071.6			−0.118122
$293$	−135942.			−1.58350			−0.791752	−	0.610843i	$-0.790831\pi$
$293$	−135942.			−1.58350			−0.791752	+	0.610843i	$0.790831\pi$
$294$	592.286	−	592.286i	0.00685231	−	0.00685231i
$295$		−	12826.9i		−	0.147393i
$296$	757.602	−	30967.7i	0.00864684	−	0.353448i
$297$	116973.			1.32609
$298$	1681.55	+	1681.55i	0.0189355	+	0.0189355i
$299$			29564.6i			0.330697i
$300$			16400.1i			0.182223i
$301$	107163.	−	107163.i	1.18281	−	1.18281i
$302$	82459.0	−	82459.0i	0.904116	−	0.904116i
$303$	19334.8			0.210598
$304$	−18233.8	+	18233.8i	−0.197301	+	0.197301i
$305$	6930.25			0.0744988
$306$	−17208.3			−0.183779
$307$			157225.i			1.66818i	0.551625	+	0.834092i	$0.314008\pi$
$307$			157225.i			1.66818i	−0.551625	+	0.834092i	$0.685992\pi$
$308$	−93403.3			−0.984602
$309$	−23639.1	+	23639.1i	−0.247579	+	0.247579i
$310$	7684.66	+	7684.66i	0.0799652	+	0.0799652i
$311$	50107.7	+	50107.7i	0.518064	+	0.518064i	0.916985	−	0.398921i	$-0.130615\pi$
$311$	50107.7	+	50107.7i	0.518064	+	0.518064i	−0.398921	+	0.916985i	$0.630615\pi$
$312$	10768.3			0.110621
$313$	−27869.5	+	27869.5i	−0.284473	+	0.284473i	−0.834890	−	0.550417i	$-0.814469\pi$
$313$	−27869.5	+	27869.5i	−0.284473	+	0.284473i	0.550417	+	0.834890i	$0.314469\pi$
$314$	−39078.2	−	39078.2i	−0.396346	−	0.396346i
$315$	−5899.60	+	5899.60i	−0.0594568	+	0.0594568i
$316$	4912.22	+	4912.22i	0.0491931	+	0.0491931i
$317$			135535.i			1.34876i	0.738386	+	0.674378i	$0.235588\pi$
$317$			135535.i			1.34876i	−0.738386	+	0.674378i	$0.764412\pi$
$318$	−27872.4	+	27872.4i	−0.275626	+	0.275626i
$319$	6109.83	−	6109.83i	0.0600410	−	0.0600410i
$320$	864.152	+	864.152i	0.00843898	+	0.00843898i
$321$		−	35245.5i		−	0.342053i
$322$	−29026.8			−0.279954
$323$			34998.0i			0.335458i
$324$			32147.3i			0.306235i
$325$	62957.4	+	62957.4i	0.596046	+	0.596046i
$326$			63983.6i			0.602052i
$327$	−22698.4	−	22698.4i	−0.212276	−	0.212276i
$328$	52886.8	+	52886.8i	0.491586	+	0.491586i
$329$	90966.4			0.840406
$330$	−5228.37			−0.0480107
$331$	51775.2	−	51775.2i	0.472569	−	0.472569i	−0.430176	−	0.902745i	$-0.641548\pi$
$331$	51775.2	−	51775.2i	0.472569	−	0.472569i	0.902745	+	0.430176i	$0.141548\pi$
$332$			9486.97i			0.0860699i
$333$	−69441.3	+	66124.7i	−0.626223	+	0.596315i
$334$	106776.			0.957147
$335$	−7282.26	−	7282.26i	−0.0648898	−	0.0648898i
$336$			10572.4i			0.0936473i
$337$		−	117901.i		−	1.03815i	−0.854730	−	0.519073i	$-0.826277\pi$
$337$		−	117901.i		−	1.03815i	0.854730	−	0.519073i	$-0.173723\pi$
$338$	−15784.2	+	15784.2i	−0.138162	+	0.138162i
$339$	−48697.8	+	48697.8i	−0.423750	+	0.423750i
$340$	1658.65			0.0143482
$341$	266303.	−	266303.i	2.29017	−	2.29017i
$342$	79821.4			0.682444
$343$	−115356.			−0.980511
$344$			68715.8i			0.580684i
$345$	−1624.81			−0.0136510
$346$	−32309.1	+	32309.1i	−0.269881	+	0.269881i
$347$	−48103.1	−	48103.1i	−0.399498	−	0.399498i	0.478558	−	0.878056i	$-0.341160\pi$
$347$	−48103.1	−	48103.1i	−0.399498	−	0.399498i	−0.878056	+	0.478558i	$0.841160\pi$
$348$	−691.577	−	691.577i	−0.00571061	−	0.00571061i
$349$	223109.			1.83175			0.915877	−	0.401460i	$-0.131497\pi$
$349$	223109.			1.83175			0.915877	+	0.401460i	$0.131497\pi$
$350$	−61812.0	+	61812.0i	−0.504588	+	0.504588i
$351$	−50827.3	−	50827.3i	−0.412556	−	0.412556i
$352$	29946.2	−	29946.2i	0.241689	−	0.241689i
$353$	−2943.08	−	2943.08i	−0.0236185	−	0.0236185i	0.695199	−	0.718817i	$-0.255316\pi$
$353$	−2943.08	−	2943.08i	−0.0236185	−	0.0236185i	−0.718817	+	0.695199i	$0.755316\pi$
$354$			50313.5i			0.401493i
$355$	−8716.29	+	8716.29i	−0.0691632	+	0.0691632i
$356$	−6462.37	+	6462.37i	−0.0509908	+	0.0509908i
$357$	10146.3	+	10146.3i	0.0796110	+	0.0796110i
$358$			117160.i			0.914137i
$359$	−159558.			−1.23802			−0.619012	−	0.785382i	$-0.712467\pi$
$359$	−159558.			−1.23802			−0.619012	+	0.785382i	$0.712467\pi$
$360$		−	3782.96i		−	0.0291895i
$361$		−	32018.7i		−	0.245691i
$362$	−45073.2	−	45073.2i	−0.343955	−	0.343955i
$363$			132719.i			1.00721i
$364$	40585.8	+	40585.8i	0.306317	+	0.306317i
$365$	−2124.84	−	2124.84i	−0.0159493	−	0.0159493i
$366$	−27184.0			−0.202932
$367$	123620.			0.917816			0.458908	−	0.888484i	$-0.348241\pi$
$367$	123620.			0.917816			0.458908	+	0.888484i	$0.348241\pi$
$368$	9306.34	−	9306.34i	0.0687200	−	0.0687200i
$369$		−	231520.i		−	1.70034i
$370$	6693.22	−	6373.55i	0.0488913	−	0.0465563i
$371$	−210102.			−1.52645
$372$	−30143.1	−	30143.1i	−0.217822	−	0.217822i
$373$		−	751.823i		−	0.00540378i	−0.999996	−	0.00270189i	$-0.999140\pi$
$373$		−	751.823i		−	0.00540378i	0.999996	−	0.00270189i	$-0.000860040\pi$
$374$		−	57478.8i		−	0.410927i
$375$	−6951.84	+	6951.84i	−0.0494353	+	0.0494353i
$376$	−29164.9	+	29164.9i	−0.206293	+	0.206293i
$377$	−5309.71			−0.0373584
$378$	49902.6	−	49902.6i	0.349253	−	0.349253i
$379$	−74594.0			−0.519309			−0.259654	−	0.965702i	$-0.583609\pi$
$379$	−74594.0			−0.519309			−0.259654	+	0.965702i	$0.583609\pi$
$380$	−7693.74			−0.0532807
$381$		−	42214.1i		−	0.290809i
$382$	42865.9			0.293755
$383$	64275.1	−	64275.1i	0.438173	−	0.438173i	−0.453224	−	0.891397i	$-0.649726\pi$
$383$	64275.1	−	64275.1i	0.438173	−	0.438173i	0.891397	+	0.453224i	$0.149726\pi$
$384$	−3389.64	−	3389.64i	−0.0229875	−	0.0229875i
$385$	−19705.7	−	19705.7i	−0.132945	−	0.132945i
$386$	5040.07			0.0338269
$387$	150407.	−	150407.i	1.00426	−	1.00426i
$388$	−18761.4	−	18761.4i	−0.124624	−	0.124624i
$389$	−15727.8	+	15727.8i	−0.103937	+	0.103937i	−0.757163	−	0.653226i	$-0.773415\pi$
$389$	−15727.8	+	15727.8i	−0.103937	+	0.103937i	0.653226	+	0.757163i	$0.273415\pi$
$390$	2271.84	+	2271.84i	0.0149365	+	0.0149365i
$391$		−	17862.6i		−	0.116840i
$392$	−1431.42	+	1431.42i	−0.00931527	+	0.00931527i
$393$	−3.61209	+	3.61209i	−2.33870e−5	+	2.33870e-5i
$394$	1546.57	+	1546.57i	0.00996271	+	0.00996271i
$395$			2072.71i			0.0132845i
$396$	−131094.			−0.835976
$397$			108246.i			0.686800i	0.939189	+	0.343400i	$0.111579\pi$
$397$			108246.i			0.686800i	−0.939189	+	0.343400i	$0.888421\pi$
$398$		−	123811.i		−	0.781616i
$399$	−47064.3	−	47064.3i	−0.295628	−	0.295628i
$400$		−	39635.4i		−	0.247721i
$401$	106855.	+	106855.i	0.664517	+	0.664517i	0.956441	−	0.291925i	$-0.0942957\pi$
$401$	106855.	+	106855.i	0.664517	+	0.664517i	−0.291925	+	0.956441i	$0.594296\pi$
$402$	28564.7	+	28564.7i	0.176757	+	0.176757i
$403$	−231429.			−1.42498
$404$	−46727.8			−0.286294
$405$	−6782.27	+	6782.27i	−0.0413490	+	0.0413490i
$406$		−	5213.11i		−	0.0316260i
$407$	−220869.	−	231946.i	−1.33335	−	1.40023i
$408$	−6506.08			−0.0390840
$409$	−58853.3	−	58853.3i	−0.351823	−	0.351823i	0.508964	−	0.860788i	$-0.330028\pi$
$409$	−58853.3	−	58853.3i	−0.351823	−	0.351823i	−0.860788	+	0.508964i	$0.830028\pi$
$410$			22315.5i			0.132751i
$411$			26201.6i			0.155111i
$412$	57130.4	−	57130.4i	0.336568	−	0.336568i
$413$	−189631.	+	189631.i	−1.11176	+	1.11176i
$414$	−40740.0			−0.237695
$415$	−2001.51	+	2001.51i	−0.0116215	+	0.0116215i
$416$	−26024.6			−0.150382
$417$	−79803.4			−0.458933
$418$			266618.i			1.52594i
$419$	−18234.9			−0.103866			−0.0519332	−	0.998651i	$-0.516538\pi$
$419$	−18234.9			−0.103866			−0.0519332	+	0.998651i	$0.516538\pi$
$420$	−2230.51	+	2230.51i	−0.0126446	+	0.0126446i
$421$	−18324.8	−	18324.8i	−0.103389	−	0.103389i	0.653520	−	0.756909i	$-0.273291\pi$
$421$	−18324.8	−	18324.8i	−0.103389	−	0.103389i	−0.756909	+	0.653520i	$0.773291\pi$
$422$	−23918.3	−	23918.3i	−0.134309	−	0.134309i
$423$	127674.			0.713546
$424$	67361.3	−	67361.3i	0.374696	−	0.374696i
$425$	−38038.1	−	38038.1i	−0.210591	−	0.210591i
$426$	34189.7	−	34189.7i	0.188398	−	0.188398i
$427$	−102456.	−	102456.i	−0.561931	−	0.561931i
$428$			85180.4i			0.464999i
$429$	78728.1	−	78728.1i	0.427775	−	0.427775i
$430$	−14497.3	+	14497.3i	−0.0784060	+	0.0784060i
$431$	−160911.	−	160911.i	−0.866227	−	0.866227i	0.125826	−	0.992052i	$-0.459842\pi$
$431$	−160911.	−	160911.i	−0.866227	−	0.866227i	−0.992052	+	0.125826i	$0.959842\pi$
$432$			31998.8i			0.171461i
$433$	−217603.			−1.16062			−0.580309	−	0.814397i	$-0.697068\pi$
$433$	−217603.			−1.16062			−0.580309	+	0.814397i	$0.697068\pi$
$434$		−	227219.i		−	1.20633i
$435$		−	291.810i		−	0.00154213i
$436$	54857.0	+	54857.0i	0.288575	+	0.288575i
$437$			82856.4i			0.433874i
$438$	8334.71	+	8334.71i	0.0434452	+	0.0434452i
$439$	137885.	+	137885.i	0.715463	+	0.715463i	0.967673	−	0.252210i	$-0.0811574\pi$
$439$	137885.	+	137885.i	0.715463	+	0.715463i	−0.252210	+	0.967673i	$0.581157\pi$
$440$	12635.8			0.0652675
$441$	6266.28			0.0322205
$442$	−24975.8	+	24975.8i	−0.127842	+	0.127842i
$443$			236571.i			1.20546i	0.797944	+	0.602731i	$0.205921\pi$
$443$			236571.i			1.20546i	−0.797944	+	0.602731i	$0.794079\pi$
$444$	−26254.2	+	25000.3i	−0.133178	+	0.126818i
$445$	−2726.79			−0.0137699
$446$	−120274.	−	120274.i	−0.604648	−	0.604648i
$447$		−	2783.13i		−	0.0139290i
$448$		−	25551.1i		−	0.127308i
$449$	225890.	−	225890.i	1.12048	−	1.12048i	0.128813	−	0.991669i	$-0.458883\pi$
$449$	225890.	−	225890.i	1.12048	−	1.12048i	0.991669	−	0.128813i	$-0.0411167\pi$
$450$	−86755.1	+	86755.1i	−0.428420	+	0.428420i
$451$	773320.			3.80195
$452$	117692.	−	117692.i	0.576061	−	0.576061i
$453$	−136478.			−0.665067
$454$	−129259.			−0.627119
$455$			17125.1i			0.0827201i
$456$	30178.7			0.145135
$457$	−38112.1	+	38112.1i	−0.182486	+	0.182486i	−0.792438	−	0.609952i	$-0.791189\pi$
$457$	−38112.1	+	38112.1i	−0.182486	+	0.182486i	0.609952	+	0.792438i	$0.291189\pi$
$458$	−2137.01	−	2137.01i	−0.0101877	−	0.0101877i
$459$	30709.2	+	30709.2i	0.145762	+	0.145762i
$460$	3926.80			0.0185577
$461$	78661.0	−	78661.0i	0.370133	−	0.370133i	−0.497393	−	0.867525i	$-0.665709\pi$
$461$	78661.0	−	78661.0i	0.370133	−	0.370133i	0.867525	+	0.497393i	$0.165709\pi$
$462$	77295.8	+	77295.8i	0.362136	+	0.362136i
$463$	−51106.7	+	51106.7i	−0.238405	+	0.238405i	−0.816190	−	0.577784i	$-0.803918\pi$
$463$	−51106.7	+	51106.7i	−0.238405	+	0.238405i	0.577784	+	0.816190i	$0.303918\pi$
$464$	1671.39	+	1671.39i	0.00776320	+	0.00776320i
$465$		−	12718.9i		−	0.0588224i
$466$	24613.0	−	24613.0i	0.113343	−	0.113343i
$467$	−209535.	+	209535.i	−0.960779	+	0.960779i	−0.999259	−	0.0384802i	$-0.987748\pi$
$467$	−209535.	+	209535.i	−0.960779	+	0.960779i	0.0384802	+	0.999259i	$0.487748\pi$
$468$	56963.4	+	56963.4i	0.260078	+	0.260078i
$469$			215321.i			0.978905i
$470$	−12306.1			−0.0557089
$471$			64678.2i			0.291552i
$472$		−	121596.i		−	0.545803i
$473$	502387.	+	502387.i	2.24552	+	2.24552i
$474$		−	8130.21i		−	0.0361864i
$475$	176441.	+	176441.i	0.782011	+	0.782011i
$476$	−24521.4	−	24521.4i	−0.108226	−	0.108226i
$477$	−294885.			−1.29603
$478$	−75356.6			−0.329811
$479$	137528.	−	137528.i	0.599403	−	0.599403i	−0.340751	−	0.940154i	$-0.610681\pi$
$479$	137528.	−	137528.i	0.599403	−	0.599403i	0.940154	+	0.340751i	$0.110681\pi$
$480$		−	1430.26i		−	0.00620771i
$481$	−4813.54	+	196758.i	−0.0208053	+	0.850437i
$482$	159971.			0.688569
$483$	24021.1	+	24021.1i	0.102967	+	0.102967i
$484$		−	320751.i		−	1.36923i
$485$		−	7916.36i		−	0.0336544i
$486$	107600.	−	107600.i	0.455555	−	0.455555i
$487$	175903.	−	175903.i	0.741678	−	0.741678i	−0.231223	−	0.972901i	$-0.574273\pi$
$487$	175903.	−	175903.i	0.741678	−	0.741678i	0.972901	+	0.231223i	$0.0742727\pi$
$488$	65697.5			0.275873
$489$	52949.6	−	52949.6i	0.221434	−	0.221434i
$490$	−603.987			−0.00251556
$491$	−64006.3			−0.265497			−0.132749	−	0.991150i	$-0.542380\pi$
$491$	−64006.3			−0.265497			−0.132749	+	0.991150i	$0.542380\pi$
$492$		−	87532.8i		−	0.361610i
$493$	3208.06			0.0131992
$494$	115851.	−	115851.i	0.474730	−	0.474730i
$495$	−27657.6	−	27657.6i	−0.112877	−	0.112877i
$496$	72849.2	+	72849.2i	0.296116	+	0.296116i
$497$	257722.			1.04337
$498$	7850.94	−	7850.94i	0.0316565	−	0.0316565i
$499$	−94970.4	−	94970.4i	−0.381406	−	0.381406i	0.490203	−	0.871608i	$-0.336923\pi$
$499$	−94970.4	−	94970.4i	−0.381406	−	0.381406i	−0.871608	+	0.490203i	$0.836923\pi$
$500$	16801.0	−	16801.0i	0.0672041	−	0.0672041i
$501$	−88362.0	−	88362.0i	−0.352038	−	0.352038i
$502$			318624.i			1.26436i
$503$	−167458.	+	167458.i	−0.661865	+	0.661865i	−0.955820	−	0.293954i	$-0.905029\pi$
$503$	−167458.	+	167458.i	−0.661865	+	0.661865i	0.293954	+	0.955820i	$0.405029\pi$
$504$	−55927.1	+	55927.1i	−0.220172	+	0.220172i
$505$	−9858.37	−	9858.37i	−0.0386565	−	0.0386565i
$506$		−	136079.i		−	0.531484i
$507$	26124.4			0.101632
$508$			102022.i			0.395336i
$509$		−	114447.i		−	0.441744i	−0.975303	−	0.220872i	$-0.929110\pi$
$509$		−	114447.i		−	0.441744i	0.975303	−	0.220872i	$-0.0708902\pi$
$510$	−1372.62	−	1372.62i	−0.00527727	−	0.00527727i
$511$			62827.0i			0.240605i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	−142446.	−	142446.i	−0.541272	−	0.541272i
$514$	−103851.			−0.393085
$515$	24106.1			0.0908893
$516$	56865.7	−	56865.7i	0.213575	−	0.213575i
$517$			426455.i			1.59548i
$518$	−193178.	−	4725.97i	−0.719945	−	0.0176129i
$519$	53474.8			0.198525
$520$	−5490.52	−	5490.52i	−0.0203052	−	0.0203052i
$521$			389079.i			1.43338i	0.697390	+	0.716692i	$0.254345\pi$
$521$			389079.i			1.43338i	−0.697390	+	0.716692i	$0.745655\pi$
$522$		−	7316.76i		−	0.0268521i
$523$	−274760.	+	274760.i	−1.00450	+	1.00450i	−0.00451156	+	0.999990i	$0.501436\pi$
$523$	−274760.	+	274760.i	−1.00450	+	1.00450i	−0.999990	+	0.00451156i	$0.998564\pi$
$524$	8.72962	−	8.72962i	3.17931e−5	−	3.17931e-5i
$525$	102305.			0.371175
$526$	−38196.7	+	38196.7i	−0.138056	+	0.138056i
$527$	139827.			0.503465
$528$	−49564.0			−0.177786
$529$			237552.i			0.848882i
$530$	28423.0			0.101186
$531$	−266154.	+	266154.i	−0.943938	+	0.943938i
$532$	113744.	+	113744.i	0.401887	+	0.401887i
$533$	−336024.	−	336024.i	−1.18281	−	1.18281i
$534$	10695.9			0.0375088
$535$	−17970.9	+	17970.9i	−0.0627859	+	0.0627859i
$536$	−69034.5	−	69034.5i	−0.240290	−	0.240290i
$537$	96955.3	−	96955.3i	0.336219	−	0.336219i
$538$	−62371.9	−	62371.9i	−0.215489	−	0.215489i
$539$			20930.5i			0.0720447i
$540$	−6750.92	+	6750.92i	−0.0231513	+	0.0231513i
$541$	397792.	−	397792.i	1.35913	−	1.35913i	0.484142	−	0.874989i	$-0.339132\pi$
$541$	397792.	−	397792.i	1.35913	−	1.35913i	0.874989	−	0.484142i	$-0.160868\pi$
$542$	191895.	+	191895.i	0.653227	+	0.653227i
$543$			74600.6i			0.253013i
$544$	15723.7			0.0531322
$545$			23146.9i			0.0779290i
$546$		−	67173.4i		−	0.225327i
$547$	−47674.0	−	47674.0i	−0.159333	−	0.159333i	0.622938	−	0.782271i	$-0.285939\pi$
$547$	−47674.0	−	47674.0i	−0.159333	−	0.159333i	−0.782271	+	0.622938i	$0.785939\pi$
$548$		−	63323.3i		−	0.210864i
$549$	−143801.	−	143801.i	−0.477108	−	0.477108i
$550$	−289778.	−	289778.i	−0.957943	−	0.957943i
$551$	−14880.7			−0.0490141
$552$	−15402.9			−0.0505504
$553$	30642.8	−	30642.8i	0.100202	−	0.100202i
$554$			343474.i			1.11912i
$555$	−10813.4	−	264.542i	−0.0351056	−	0.000858833i
$556$	192867.			0.623890
$557$	−180274.	−	180274.i	−0.581062	−	0.581062i	0.354133	−	0.935195i	$-0.384776\pi$
$557$	−180274.	−	180274.i	−0.581062	−	0.581062i	−0.935195	+	0.354133i	$0.884776\pi$
$558$		−	318909.i		−	1.02423i
$559$		−	436596.i		−	1.39719i
$560$	5390.64	−	5390.64i	0.0171895	−	0.0171895i
$561$	−47566.5	+	47566.5i	−0.151139	+	0.151139i
$562$	−149303.			−0.472711
$563$	28701.4	−	28701.4i	0.0905497	−	0.0905497i	−0.660381	−	0.750931i	$-0.729605\pi$
$563$	28701.4	−	28701.4i	0.0905497	−	0.0905497i	0.750931	+	0.660381i	$0.229605\pi$
$564$	48270.8			0.151749
$565$	49659.9			0.155564
$566$			190936.i			0.596011i
$567$	200537.			0.623776
$568$	−82628.9	+	82628.9i	−0.256115	+	0.256115i
$569$	−314810.	−	314810.i	−0.972353	−	0.972353i	0.0272750	−	0.999628i	$-0.491317\pi$
$569$	−314810.	−	314810.i	−0.972353	−	0.972353i	−0.999628	+	0.0272750i	$0.991317\pi$
$570$	6366.95	+	6366.95i	0.0195966	+	0.0195966i
$571$	−82405.3			−0.252745			−0.126373	−	0.991983i	$-0.540333\pi$
$571$	−82405.3			−0.252745			−0.126373	+	0.991983i	$0.540333\pi$
$572$	−190268.	+	190268.i	−0.581532	+	0.581532i
$573$	−35473.6	−	35473.6i	−0.108043	−	0.108043i
$574$	329911.	−	329911.i	1.00132	−	1.00132i
$575$	−90053.8	−	90053.8i	−0.272374	−	0.272374i
$576$		−	35861.8i		−	0.108090i
$577$	−259634.	+	259634.i	−0.779848	+	0.779848i	−0.979805	−	0.199957i	$-0.935920\pi$
$577$	−259634.	+	259634.i	−0.779848	+	0.779848i	0.199957	+	0.979805i	$0.435920\pi$
$578$	−151952.	+	151952.i	−0.454832	+	0.454832i
$579$	−4170.90	−	4170.90i	−0.0124415	−	0.0124415i
$580$			705.240i			0.00209643i
$581$	59180.4			0.175318
$582$			31052.0i			0.0916735i
$583$		−	984969.i		−	2.89791i
$584$	−20143.1	−	20143.1i	−0.0590610	−	0.0590610i
$585$			24035.6i			0.0702335i
$586$	−271884.	−	271884.i	−0.791752	−	0.791752i
$587$	271121.	+	271121.i	0.786842	+	0.786842i	0.980975	−	0.194133i	$-0.0621894\pi$
$587$	271121.	+	271121.i	0.786842	+	0.786842i	−0.194133	+	0.980975i	$0.562189\pi$
$588$	2369.14			0.00685231
$589$	−648593.			−1.86957
$590$	25653.7	−	25653.7i	0.0736964	−	0.0736964i
$591$		−	2559.73i		−	0.00732856i
$592$	63450.5	−	60420.1i	0.181047	−	0.172400i
$593$	−130700.			−0.371676			−0.185838	−	0.982580i	$-0.559500\pi$
$593$	−130700.			−0.371676			−0.185838	+	0.982580i	$0.559500\pi$
$594$	233946.	+	233946.i	0.663044	+	0.663044i
$595$		−	10346.8i		−	0.0292262i
$596$			6726.21i			0.0189355i
$597$	−102460.	+	102460.i	−0.287478	+	0.287478i
$598$	−59129.3	+	59129.3i	−0.165348	+	0.165348i
$599$	526857.			1.46838			0.734191	−	0.678943i	$-0.237562\pi$
$599$	526857.			1.46838			0.734191	+	0.678943i	$0.237562\pi$
$600$	−32800.2	+	32800.2i	−0.0911117	+	0.0911117i
$601$	448332.			1.24123			0.620613	−	0.784117i	$-0.286884\pi$
$601$	448332.			1.24123			0.620613	+	0.784117i	$0.286884\pi$
$602$	428654.			1.18281
$603$			302210.i			0.831139i
$604$	329836.			0.904116
$605$	67670.3	−	67670.3i	0.184879	−	0.184879i
$606$	38669.5	+	38669.5i	0.105299	+	0.105299i
$607$	−306657.	−	306657.i	−0.832293	−	0.832293i	0.155537	−	0.987830i	$-0.450289\pi$
$607$	−306657.	−	306657.i	−0.832293	−	0.832293i	−0.987830	+	0.155537i	$0.950289\pi$
$608$	−72935.2			−0.197301
$609$	−4314.11	+	4314.11i	−0.0116320	+	0.0116320i
$610$	13860.5	+	13860.5i	0.0372494	+	0.0372494i
$611$	185304.	−	185304.i	0.496366	−	0.496366i
$612$	−34416.6	−	34416.6i	−0.0918893	−	0.0918893i
$613$			144353.i			0.384153i	0.981380	+	0.192076i	$0.0615221\pi$
$613$			144353.i			0.384153i	−0.981380	+	0.192076i	$0.938478\pi$
$614$	−314449.	+	314449.i	−0.834092	+	0.834092i
$615$	18467.2	−	18467.2i	0.0488259	−	0.0488259i
$616$	−186807.	−	186807.i	−0.492301	−	0.492301i
$617$		−	416386.i		−	1.09377i	−0.837207	−	0.546885i	$-0.815813\pi$
$617$		−	416386.i		−	1.09377i	0.837207	−	0.546885i	$-0.184187\pi$
$618$	−94556.5			−0.247579
$619$			15208.2i			0.0396915i	0.999803	+	0.0198458i	$0.00631752\pi$
$619$			15208.2i			0.0396915i	−0.999803	+	0.0198458i	$0.993682\pi$
$620$			30738.6i			0.0799652i
$621$	72703.0	+	72703.0i	0.188525	+	0.188525i
$622$			200431.i			0.518064i
$623$	40312.7	+	40312.7i	0.103864	+	0.103864i
$624$	21536.6	+	21536.6i	0.0553106	+	0.0553106i
$625$	−379975.			−0.972736
$626$	−111478.			−0.284473
$627$	220640.	−	220640.i	0.561240	−	0.561240i
$628$		−	156313.i		−	0.396346i
$629$	2908.28	−	118879.i	0.00735081	−	0.300471i
$630$	−23598.4			−0.0594568
$631$	225256.	+	225256.i	0.565740	+	0.565740i	0.930932	−	0.365192i	$-0.118997\pi$
$631$	225256.	+	225256.i	0.565740	+	0.565740i	−0.365192	+	0.930932i	$0.618997\pi$
$632$			19648.9i			0.0491931i
$633$			39587.2i			0.0987978i
$634$	−271070.	+	271070.i	−0.674378	+	0.674378i
$635$	−21524.0	+	21524.0i	−0.0533797	+	0.0533797i
$636$	−111490.			−0.275626
$637$	9094.76	−	9094.76i	0.0224136	−	0.0224136i
$638$	24439.3			0.0600410
$639$	361721.			0.885875
$640$			3456.61i			0.00843898i
$641$	152653.			0.371527			0.185764	−	0.982594i	$-0.440524\pi$
$641$	152653.			0.371527			0.185764	+	0.982594i	$0.440524\pi$
$642$	70491.0	−	70491.0i	0.171027	−	0.171027i
$643$	396371.	+	396371.i	0.958693	+	0.958693i	0.999180	−	0.0404870i	$-0.0128909\pi$
$643$	396371.	+	396371.i	0.958693	+	0.958693i	−0.0404870	+	0.999180i	$0.512891\pi$
$644$	−58053.6	−	58053.6i	−0.139977	−	0.139977i
$645$	23994.4			0.0576754
$646$	−69995.9	+	69995.9i	−0.167729	+	0.167729i
$647$	−461658.	−	461658.i	−1.10284	−	1.10284i	−0.994067	−	0.108771i	$-0.965308\pi$
$647$	−461658.	−	461658.i	−1.10284	−	1.10284i	−0.108771	−	0.994067i	$-0.534692\pi$
$648$	−64294.6	+	64294.6i	−0.153117	+	0.153117i
$649$	−889001.	−	889001.i	−2.11063	−	2.11063i
$650$			251829.i			0.596046i
$651$	−188035.	+	188035.i	−0.443687	+	0.443687i
$652$	−127967.	+	127967.i	−0.301026	+	0.301026i
$653$	468463.	+	468463.i	1.09862	+	1.09862i	0.994572	+	0.104051i	$0.0331806\pi$
$653$	468463.	+	468463.i	1.09862	+	1.09862i	0.104051	+	0.994572i	$0.466819\pi$
$654$		−	90793.8i		−	0.212276i
$655$	3.68345			8.58564e−6
$656$			211547.i			0.491586i
$657$			88179.7i			0.204286i
$658$	181933.	+	181933.i	0.420203	+	0.420203i
$659$			710739.i			1.63659i	0.574800	+	0.818294i	$0.305080\pi$
$659$			710739.i			1.63659i	−0.574800	+	0.818294i	$0.694920\pi$
$660$	−10456.7	−	10456.7i	−0.0240054	−	0.0240054i
$661$	−531467.	−	531467.i	−1.21639	−	1.21639i	−0.968887	−	0.247505i	$-0.920389\pi$
$661$	−531467.	−	531467.i	−1.21639	−	1.21639i	−0.247505	−	0.968887i	$-0.579611\pi$
$662$	207101.			0.472569
$663$	41337.4			0.0940407
$664$	−18973.9	+	18973.9i	−0.0430350	+	0.0430350i
$665$			47994.0i			0.108529i
$666$	−271132.	−	6633.05i	−0.611269	−	0.0149543i
$667$	7594.97			0.0170716
$668$	213551.	+	213551.i	0.478574	+	0.478574i
$669$			199066.i			0.444779i
$670$		−	29129.0i		−	0.0648898i
$671$	480320.	−	480320.i	1.06681	−	1.06681i
$672$	−21144.8	+	21144.8i	−0.0468237	+	0.0468237i
$673$	−2536.16			−0.00559947			−0.00279974	−	0.999996i	$-0.500891\pi$
$673$	−2536.16			−0.00559947			−0.00279974	+	0.999996i	$0.500891\pi$
$674$	235803.	−	235803.i	0.519073	−	0.519073i
$675$	309639.			0.679593
$676$	−63136.9			−0.138162
$677$		−	655716.i		−	1.43067i	−0.698784	−	0.715333i	$-0.746275\pi$
$677$		−	655716.i		−	1.43067i	0.698784	−	0.715333i	$-0.253725\pi$
$678$	−194791.			−0.423750
$679$	−117035.	+	117035.i	−0.253850	+	0.253850i
$680$	3317.31	+	3317.31i	0.00717410	+	0.00717410i
$681$	106968.	+	106968.i	0.230654	+	0.230654i
$682$	1.06521e6			2.29017
$683$	327395.	−	327395.i	0.701829	−	0.701829i	−0.262974	−	0.964803i	$-0.584703\pi$
$683$	327395.	−	327395.i	0.701829	−	0.701829i	0.964803	+	0.262974i	$0.0847034\pi$
$684$	159643.	+	159643.i	0.341222	+	0.341222i
$685$	13359.6	−	13359.6i	0.0284716	−	0.0284716i
$686$	−230712.	−	230712.i	−0.490256	−	0.490256i
$687$			3536.96i			0.00749406i
$688$	−137432.	+	137432.i	−0.290342	+	0.290342i
$689$	−427990.	+	427990.i	−0.901562	+	0.901562i
$690$	−3249.62	−	3249.62i	−0.00682550	−	0.00682550i
$691$			128175.i			0.268441i	0.990952	+	0.134220i	$0.0428530\pi$
$691$			128175.i			0.268441i	−0.990952	+	0.134220i	$0.957147\pi$
$692$	−129236.			−0.269881
$693$			817776.i			1.70282i
$694$		−	192413.i		−	0.399498i
$695$	40690.0	+	40690.0i	0.0842399	+	0.0842399i
$696$		−	2766.31i		−	0.00571061i
$697$	203022.	+	203022.i	0.417905	+	0.417905i
$698$	446219.	+	446219.i	0.915877	+	0.915877i
$699$	−40737.0			−0.0833748
$700$	−247248.			−0.504588
$701$	502670.	−	502670.i	1.02293	−	1.02293i	0.0232012	−	0.999731i	$-0.492614\pi$
$701$	502670.	−	502670.i	1.02293	−	1.02293i	0.999731	−	0.0232012i	$-0.00738584\pi$
$702$		−	203309.i		−	0.412556i
$703$	−13490.2	+	551424.i	−0.0272965	+	1.11577i
$704$	119785.			0.241689
$705$	10183.9	+	10183.9i	0.0204897	+	0.0204897i
$706$		−	11772.3i		−	0.0236185i
$707$			291491.i			0.583158i
$708$	−100627.	+	100627.i	−0.200746	+	0.200746i
$709$	−219493.	+	219493.i	−0.436645	+	0.436645i	−0.890881	−	0.454236i	$-0.849912\pi$
$709$	−219493.	+	219493.i	−0.436645	+	0.436645i	0.454236	+	0.890881i	$0.349912\pi$
$710$	−34865.2			−0.0691632
$711$	43008.1	−	43008.1i	0.0850768	−	0.0850768i
$712$	−25849.5			−0.0509908
$713$	331035.			0.651170
$714$			40585.4i			0.0796110i
$715$	−80283.4			−0.157041
$716$	−234319.	+	234319.i	−0.457069	+	0.457069i
$717$	62361.3	+	62361.3i	0.121304	+	0.121304i
$718$	−319115.	−	319115.i	−0.619012	−	0.619012i
$719$	102462.			0.198200			0.0991002	−	0.995077i	$-0.468404\pi$
$719$	102462.			0.198200			0.0991002	+	0.995077i	$0.468404\pi$
$720$	7565.93	−	7565.93i	0.0145948	−	0.0145948i
$721$	−356383.	−	356383.i	−0.685562	−	0.685562i
$722$	64037.3	−	64037.3i	0.122845	−	0.122845i
$723$	−132384.	−	132384.i	−0.253256	−	0.253256i
$724$		−	180293.i		−	0.343955i
$725$	16173.3	−	16173.3i	0.0307697	−	0.0307697i
$726$	−265437.	+	265437.i	−0.503604	+	0.503604i
$727$	118931.	+	118931.i	0.225022	+	0.225022i	0.810610	−	0.585587i	$-0.199136\pi$
$727$	118931.	+	118931.i	0.225022	+	0.225022i	−0.585587	+	0.810610i	$0.699136\pi$
$728$			162343.i			0.306317i
$729$	147402.			0.277364
$730$		−	8499.36i		−	0.0159493i
$731$			263786.i			0.493648i
$732$	−54367.9	−	54367.9i	−0.101466	−	0.101466i
$733$		−	234215.i		−	0.435921i	−0.975958	−	0.217960i	$-0.930060\pi$
$733$		−	234215.i		−	0.435921i	0.975958	−	0.217960i	$-0.0699403\pi$
$734$	247240.	+	247240.i	0.458908	+	0.458908i
$735$	499.829	+	499.829i	0.000925224	+	0.000925224i
$736$	37225.4			0.0687200
$737$	−1.00943e6			−1.85842
$738$	463041.	−	463041.i	0.850172	−	0.850172i
$739$			912388.i			1.67067i	0.549742	+	0.835335i	$0.314726\pi$
$739$			912388.i			1.67067i	−0.549742	+	0.835335i	$0.685274\pi$
$740$	26133.6	+	639.339i	0.0477238	+	0.00116753i
$741$	−191745.			−0.349211
$742$	−420204.	−	420204.i	−0.763225	−	0.763225i
$743$		−	5846.91i		−	0.0105913i	−0.999986	−	0.00529564i	$-0.998314\pi$
$743$		−	5846.91i		−	0.0105913i	0.999986	−	0.00529564i	$-0.00168566\pi$
$744$		−	120573.i		−	0.217822i
$745$	−1419.06	+	1419.06i	−0.00255675	+	0.00255675i
$746$	1503.65	−	1503.65i	0.00270189	−	0.00270189i
$747$	83061.5			0.148853
$748$	114958.	−	114958.i	0.205463	−	0.205463i
$749$	531361.			0.947166
$750$	−27807.4			−0.0494353
$751$		−	300650.i		−	0.533067i	−0.963826	−	0.266533i	$-0.914122\pi$
$751$		−	300650.i		−	0.533067i	0.963826	−	0.266533i	$-0.0858783\pi$
$752$	−116660.			−0.206293
$753$	263677.	−	263677.i	0.465031	−	0.465031i
$754$	−10619.4	−	10619.4i	−0.0186792	−	0.0186792i
$755$	69586.9	+	69586.9i	0.122077	+	0.122077i
$756$	199611.			0.349253
$757$	413243.	−	413243.i	0.721129	−	0.721129i	−0.247706	−	0.968835i	$-0.579677\pi$
$757$	413243.	−	413243.i	0.721129	−	0.721129i	0.968835	+	0.247706i	$0.0796767\pi$
$758$	−149188.	−	149188.i	−0.259654	−	0.259654i
$759$	−112612.	+	112612.i	−0.195480	+	0.195480i
$760$	−15387.5	−	15387.5i	−0.0266404	−	0.0266404i
$761$			790269.i			1.36460i	0.731072	+	0.682300i	$0.239020\pi$
$761$			790269.i			1.36460i	−0.731072	+	0.682300i	$0.760980\pi$
$762$	84428.2	−	84428.2i	0.145404	−	0.145404i
$763$	342202.	−	342202.i	0.587805	−	0.587805i
$764$	85731.7	+	85731.7i	0.146877	+	0.146877i
$765$		−	14522.0i		−	0.0248145i
$766$	257100.			0.438173
$767$			772581.i			1.31327i
$768$		−	13558.6i		−	0.0229875i
$769$	411113.	+	411113.i	0.695197	+	0.695197i	0.963371	−	0.268173i	$-0.0864200\pi$
$769$	411113.	+	411113.i	0.695197	+	0.695197i	−0.268173	+	0.963371i	$0.586420\pi$
$770$		−	78822.9i		−	0.132945i
$771$	85942.2	+	85942.2i	0.144576	+	0.144576i
$772$	10080.1	+	10080.1i	0.0169134	+	0.0169134i
$773$	−877996.			−1.46938			−0.734689	−	0.678404i	$-0.762672\pi$
$773$	−877996.			−1.46938			−0.734689	+	0.678404i	$0.762672\pi$
$774$	601629.			1.00426
$775$	704933.	−	704933.i	1.17367	−	1.17367i
$776$		−	75045.7i		−	0.124624i
$777$	155954.	+	163776.i	0.258317	+	0.271273i
$778$	−62911.2			−0.103937
$779$	−941726.	−	941726.i	−1.55185	−	1.55185i
$780$			9087.35i			0.0149365i
$781$			1.20821e6i			1.98081i
$782$	35725.2	−	35725.2i	0.0584199	−	0.0584199i
$783$	−13057.2	+	13057.2i	−0.0212974	+	0.0212974i
$784$	−5725.69			−0.00931527
$785$	32978.0	−	32978.0i	0.0535161	−	0.0535161i
$786$	−14.4484			−2.33870e−5
$787$	−377958.			−0.610230			−0.305115	−	0.952316i	$-0.598695\pi$
$787$	−377958.			−0.610230			−0.305115	+	0.952316i	$0.598695\pi$
$788$			6186.28i			0.00996271i
$789$	63219.3			0.101554
$790$	−4145.41	+	4145.41i	−0.00664223	+	0.00664223i
$791$	−734168.	−	734168.i	−1.17339	−	1.17339i
$792$	−262189.	−	262189.i	−0.417988	−	0.417988i
$793$	−417419.			−0.663783
$794$	−216492.	+	216492.i	−0.343400	+	0.343400i
$795$	−23521.5	−	23521.5i	−0.0372160	−	0.0372160i
$796$	247622.	−	247622.i	0.390808	−	0.390808i
$797$	661267.	+	661267.i	1.04102	+	1.04102i	0.999122	+	0.0419016i	$0.0133416\pi$
$797$	661267.	+	661267.i	1.04102	+	1.04102i	0.0419016	+	0.999122i	$0.486658\pi$
$798$		−	188257.i		−	0.295628i
$799$	−111958.	+	111958.i	−0.175373	+	0.175373i
$800$	79270.7	−	79270.7i	0.123861	−	0.123861i
$801$	56580.1	+	56580.1i	0.0881858	+	0.0881858i
$802$			427420.i			0.664517i
$803$	−294536.			−0.456780
$804$			114259.i			0.176757i
$805$		−	24495.7i		−	0.0378005i
$806$	−462858.	−	462858.i	−0.712489	−	0.712489i
$807$			103232.i			0.158513i
$808$	−93455.5	−	93455.5i	−0.143147	−	0.143147i
$809$	−521171.	−	521171.i	−0.796311	−	0.796311i	0.186201	−	0.982512i	$-0.440383\pi$
$809$	−521171.	−	521171.i	−0.796311	−	0.796311i	−0.982512	+	0.186201i	$0.940383\pi$
$810$	−27129.1			−0.0413490
$811$	183338.			0.278747			0.139374	−	0.990240i	$-0.455491\pi$
$811$	183338.			0.278747			0.139374	+	0.990240i	$0.455491\pi$
$812$	10426.2	−	10426.2i	0.0158130	−	0.0158130i
$813$		−	317605.i		−	0.480513i
$814$	22155.6	−	905630.i	0.0334375	−	1.36679i
$815$	−53995.7			−0.0812912
$816$	−13012.2	−	13012.2i	−0.0195420	−	0.0195420i
$817$		−	1.22358e6i		−	1.83311i
$818$		−	235413.i		−	0.351823i
$819$	355342.	−	355342.i	0.529759	−	0.529759i
$820$	−44631.0	+	44631.0i	−0.0663757	+	0.0663757i
$821$	666952.			0.989483			0.494742	−	0.869040i	$-0.335263\pi$
$821$	666952.			0.989483			0.494742	+	0.869040i	$0.335263\pi$
$822$	−52403.2	+	52403.2i	−0.0775557	+	0.0775557i
$823$	235887.			0.348260			0.174130	−	0.984723i	$-0.444289\pi$
$823$	235887.			0.348260			0.174130	+	0.984723i	$0.444289\pi$
$824$	228522.			0.336568
$825$			479611.i			0.704662i
$826$	−758526.			−1.11176
$827$	272725.	−	272725.i	0.398762	−	0.398762i	−0.479034	−	0.877796i	$-0.659013\pi$
$827$	272725.	−	272725.i	0.398762	−	0.398762i	0.877796	+	0.479034i	$0.159013\pi$
$828$	−81480.0	−	81480.0i	−0.118848	−	0.118848i
$829$	583830.	+	583830.i	0.849527	+	0.849527i	0.990074	−	0.140547i	$-0.0448861\pi$
$829$	583830.	+	583830.i	0.849527	+	0.849527i	−0.140547	+	0.990074i	$0.544886\pi$
$830$	−8006.04			−0.0116215
$831$	284242.	−	284242.i	0.411610	−	0.411610i
$832$	−52049.1	−	52049.1i	−0.0751912	−	0.0751912i
$833$	−5494.94	+	5494.94i	−0.00791905	+	0.00791905i
$834$	−159607.	−	159607.i	−0.229466	−	0.229466i
$835$			90107.6i			0.129238i
$836$	−533236.	+	533236.i	−0.762969	+	0.762969i
$837$	−569112.	+	569112.i	−0.812357	+	0.812357i
$838$	−36469.8	−	36469.8i	−0.0519332	−	0.0519332i
$839$			319416.i			0.453767i	0.973922	+	0.226883i	$0.0728536\pi$
$839$			319416.i			0.453767i	−0.973922	+	0.226883i	$0.927146\pi$
$840$	−8922.03			−0.0126446
$841$		−	705917.i		−	0.998071i
$842$		−	73299.0i		−	0.103389i
$843$	123556.	+	123556.i	0.173863	+	0.173863i
$844$		−	95673.3i		−	0.134309i
$845$	−13320.3	−	13320.3i	−0.0186552	−	0.0186552i
$846$	255348.	+	255348.i	0.356773	+	0.356773i
$847$	−2.00087e6			−2.78902
$848$	269445.			0.374696
$849$	158009.	−	158009.i	0.219213	−	0.219213i
$850$		−	152152.i		−	0.210591i
$851$	6885.25	−	281441.i	0.00950738	−	0.388623i
$852$	136759.			0.188398
$853$	−164868.	−	164868.i	−0.226589	−	0.226589i	0.584677	−	0.811266i	$-0.301221\pi$
$853$	−164868.	−	164868.i	−0.226589	−	0.226589i	−0.811266	+	0.584677i	$0.801221\pi$
$854$		−	409825.i		−	0.561931i
$855$			67361.2i			0.0921462i
$856$	−170361.	+	170361.i	−0.232500	+	0.232500i
$857$	−212599.	+	212599.i	−0.289468	+	0.289468i	−0.836870	−	0.547402i	$-0.815617\pi$
$857$	−212599.	+	212599.i	−0.289468	+	0.289468i	0.547402	+	0.836870i	$0.315617\pi$
$858$	314912.			0.427775
$859$	226582.	−	226582.i	0.307071	−	0.307071i	−0.536701	−	0.843772i	$-0.680330\pi$
$859$	226582.	−	226582.i	0.307071	−	0.307071i	0.843772	+	0.536701i	$0.180330\pi$
$860$	−57989.1			−0.0784060
$861$	−546036.			−0.736571
$862$		−	643644.i		−	0.866227i
$863$	−533130.			−0.715832			−0.357916	−	0.933754i	$-0.616513\pi$
$863$	−533130.			−0.715832			−0.357916	+	0.933754i	$0.616513\pi$
$864$	−63997.5	+	63997.5i	−0.0857306	+	0.0857306i
$865$	−27265.6	−	27265.6i	−0.0364404	−	0.0364404i
$866$	−435206.	−	435206.i	−0.580309	−	0.580309i
$867$	251495.			0.334574
$868$	454438.	−	454438.i	0.603164	−	0.603164i
$869$	143655.	+	143655.i	0.190231	+	0.190231i
$870$	583.621	−	583.621i	0.000771067	−	0.000771067i
$871$	438621.	+	438621.i	0.578167	+	0.578167i
$872$			219428.i			0.288575i
$873$	−164262.	+	164262.i	−0.215531	+	0.215531i
$874$	−165713.	+	165713.i	−0.216937	+	0.216937i
$875$	−104806.	−	104806.i	−0.136889	−	0.136889i
$876$			33338.8i			0.0434452i
$877$	−904744.			−1.17632			−0.588161	−	0.808744i	$-0.700148\pi$
$877$	−904744.			−1.17632			−0.588161	+	0.808744i	$0.700148\pi$
$878$			551539.i			0.715463i
$879$			449996.i			0.582412i
$880$	25271.6	+	25271.6i	0.0326337	+	0.0326337i
$881$			151474.i			0.195158i	0.995228	+	0.0975791i	$0.0311099\pi$
$881$			151474.i			0.195158i	−0.995228	+	0.0975791i	$0.968890\pi$
$882$	12532.6	+	12532.6i	0.0161103	+	0.0161103i
$883$	−598959.	−	598959.i	−0.768203	−	0.768203i	0.209587	−	0.977790i	$-0.432788\pi$
$883$	−598959.	−	598959.i	−0.768203	−	0.768203i	−0.977790	+	0.209587i	$0.932788\pi$
$884$	−99903.1			−0.127842
$885$	−42459.4			−0.0542110
$886$	−473142.	+	473142.i	−0.602731	+	0.602731i
$887$			615345.i			0.782117i	0.920366	+	0.391058i	$0.127891\pi$
$887$			615345.i			0.782117i	−0.920366	+	0.391058i	$0.872109\pi$
$888$	−102509.	−	2507.81i	−0.129998	−	0.00318031i
$889$	636420.			0.805268
$890$	−5453.58	−	5453.58i	−0.00688496	−	0.00688496i
$891$			940128.i			1.18422i
$892$		−	481097.i		−	0.604648i
$893$	519324.	−	519324.i	0.651231	−	0.651231i
$894$	5566.27	−	5566.27i	0.00696449	−	0.00696449i
$895$	−98870.7			−0.123430
$896$	51102.3	−	51102.3i	0.0636538	−	0.0636538i
$897$	97864.8			0.121630
$898$	903561.			1.12048
$899$			59452.7i			0.0735617i
$900$	−347021.			−0.428420
$901$	258587.	−	258587.i	0.318534	−	0.318534i
$902$	1.54664e6	+	1.54664e6i	1.90097	+	1.90097i
$903$	−354732.	−	354732.i	−0.435036	−	0.435036i
$904$	470766.			0.576061
$905$	38037.2	−	38037.2i	0.0464420	−	0.0464420i
$906$	−272955.	−	272955.i	−0.332533	−	0.332533i
$907$	−541631.	+	541631.i	−0.658399	+	0.658399i	−0.955001	−	0.296602i	$-0.904147\pi$
$907$	−541631.	+	541631.i	−0.658399	+	0.658399i	0.296602	+	0.955001i	$0.404147\pi$
$908$	−258518.	−	258518.i	−0.313559	−	0.313559i
$909$			409117.i			0.495130i
$910$	−34250.2	+	34250.2i	−0.0413600	+	0.0413600i
$911$	419589.	−	419589.i	0.505578	−	0.505578i	−0.407588	−	0.913166i	$-0.633630\pi$
$911$	419589.	−	419589.i	0.505578	−	0.505578i	0.913166	+	0.407588i	$0.133630\pi$
$912$	60357.5	+	60357.5i	0.0725674	+	0.0725674i
$913$			277440.i			0.332834i
$914$	−152448.			−0.182486
$915$		−	22940.5i		−	0.0274006i
$916$		−	8548.04i		−	0.0101877i
$917$	−54.4560	−	54.4560i	−6.47600e−5	−	6.47600e-5i
$918$			122837.i			0.145762i
$919$	649601.	+	649601.i	0.769159	+	0.769159i	0.977958	−	0.208800i	$-0.0669557\pi$
$919$	649601.	+	649601.i	0.769159	+	0.769159i	−0.208800	+	0.977958i	$0.566956\pi$
$920$	7853.60	+	7853.60i	0.00927883	+	0.00927883i
$921$	520445.			0.613558
$922$	314644.			0.370133
$923$	524995.	−	524995.i	0.616243	−	0.616243i
$924$			309183.i			0.362136i
$925$	−584662.	−	613986.i	−0.683315	−	0.717587i
$926$	−204427.			−0.238405
$927$	−500195.	−	500195.i	−0.582077	−	0.582077i
$928$			6685.54i			0.00776320i
$929$		−	930670.i		−	1.07836i	−0.842190	−	0.539181i	$-0.818734\pi$
$929$		−	930670.i		−	1.07836i	0.842190	−	0.539181i	$-0.181266\pi$
$930$	25437.7	−	25437.7i	0.0294112	−	0.0294112i
$931$	25488.5	−	25488.5i	0.0294066	−	0.0294066i
$932$	98452.1			0.113343
$933$	165866.	−	165866.i	0.190544	−	0.190544i
$934$	−838142.			−0.960779
$935$	48506.2			0.0554849
$936$			227854.i			0.260078i
$937$	1.46523e6			1.66888			0.834441	−	0.551098i	$-0.185791\pi$
$937$	1.46523e6			1.66888			0.834441	+	0.551098i	$0.185791\pi$
$938$	−430642.	+	430642.i	−0.489452	+	0.489452i
$939$	92253.5	+	92253.5i	0.104629	+	0.104629i
$940$	−24612.2	−	24612.2i	−0.0278545	−	0.0278545i
$941$	820104.			0.926168			0.463084	−	0.886314i	$-0.346743\pi$
$941$	820104.			0.926168			0.463084	+	0.886314i	$0.346743\pi$
$942$	−129356.	+	129356.i	−0.145776	+	0.145776i
$943$	480647.	+	480647.i	0.540509	+	0.540509i
$944$	243193.	−	243193.i	0.272902	−	0.272902i
$945$	42112.7	+	42112.7i	0.0471574	+	0.0471574i
$946$			2.00955e6i			2.24552i
$947$	−380735.	+	380735.i	−0.424544	+	0.424544i	−0.886765	−	0.462221i	$-0.847053\pi$
$947$	−380735.	+	380735.i	−0.424544	+	0.424544i	0.462221	+	0.886765i	$0.347053\pi$
$948$	16260.4	−	16260.4i	0.0180932	−	0.0180932i
$949$	127982.	+	127982.i	0.142108	+	0.142108i
$950$			705765.i			0.782011i
$951$	448648.			0.496072
$952$		−	98085.7i		−	0.108226i
$953$		−	302788.i		−	0.333390i	−0.986009	−	0.166695i	$-0.946690\pi$
$953$		−	302788.i		−	0.333390i	0.986009	−	0.166695i	$-0.0533095\pi$
$954$	−589770.	−	589770.i	−0.648016	−	0.648016i
$955$			36174.4i			0.0396638i
$956$	−150713.	−	150713.i	−0.164906	−	0.164906i
$957$	−20224.7	−	20224.7i	−0.0220830	−	0.0220830i
$958$	550110.			0.599403
$959$	−395015.			−0.429513
$960$	2860.51	−	2860.51i	0.00310385	−	0.00310385i
$961$			1.66779e6i			1.80590i
$962$	−403143.	+	383889.i	−0.435621	+	0.414816i
$963$	745782.			0.804191
$964$	319942.	+	319942.i	0.344285	+	0.344285i
$965$			4253.30i			0.00456743i
$966$			96084.4i			0.102967i
$967$	566458.	−	566458.i	0.605779	−	0.605779i	−0.336061	−	0.941840i	$-0.609095\pi$
$967$	566458.	−	566458.i	0.605779	−	0.605779i	0.941840	+	0.336061i	$0.109095\pi$
$968$	641502.	−	641502.i	0.684617	−	0.684617i
$969$	115850.			0.123381
$970$	15832.7	−	15832.7i	0.0168272	−	0.0168272i
$971$	−990599.			−1.05065			−0.525327	−	0.850901i	$-0.676057\pi$
$971$	−990599.			−1.05065			−0.525327	+	0.850901i	$0.676057\pi$
$972$	430402.			0.455555
$973$		−	1.20312e6i		−	1.27081i
$974$	703612.			0.741678
$975$	208401.	−	208401.i	0.219226	−	0.219226i
$976$	131395.	+	131395.i	0.137936	+	0.137936i
$977$	483970.	+	483970.i	0.507025	+	0.507025i	0.913612	−	0.406587i	$-0.133281\pi$
$977$	483970.	+	483970.i	0.507025	+	0.507025i	−0.406587	+	0.913612i	$0.633281\pi$
$978$	211798.			0.221434
$979$	−188988.	+	188988.i	−0.197182	+	0.197182i
$980$	−1207.97	−	1207.97i	−0.00125778	−	0.00125778i
$981$	480291.	−	480291.i	0.499076	−	0.499076i
$982$	−128013.	−	128013.i	−0.132749	−	0.132749i
$983$		−	1.08591e6i		−	1.12379i	−0.827208	−	0.561897i	$-0.810072\pi$
$983$		−	1.08591e6i		−	1.12379i	0.827208	−	0.561897i	$-0.189928\pi$
$984$	175066.	−	175066.i	0.180805	−	0.180805i
$985$	−1305.15	+	1305.15i	−0.00134520	+	0.00134520i
$986$	6416.12	+	6416.12i	0.00659961	+	0.00659961i
$987$		−	301117.i		−	0.309101i
$988$	463405.			0.474730
$989$			624504.i			0.638473i
$990$		−	110630.i		−	0.112877i
$991$	632355.	+	632355.i	0.643893	+	0.643893i	0.951510	−	0.307617i	$-0.0995315\pi$
$991$	632355.	+	632355.i	0.643893	+	0.643893i	−0.307617	+	0.951510i	$0.599532\pi$
$992$			291397.i			0.296116i
$993$	−171386.	−	171386.i	−0.173811	−	0.173811i
$994$	515445.	+	515445.i	0.521686	+	0.521686i
$995$	104484.			0.105537
$996$	31403.7			0.0316565
$997$	−410113.	+	410113.i	−0.412585	+	0.412585i	−0.882638	−	0.470053i	$-0.844235\pi$
$997$	−410113.	+	410113.i	−0.412585	+	0.412585i	0.470053	+	0.882638i	$0.344235\pi$
$998$		−	379881.i		−	0.381406i
$999$	472014.	+	495688.i	0.472960	+	0.496681i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} -3.31020i q^{3} +8.00000i q^{4} +(-1.68780 + 1.68780i) q^{5} +(6.62039 - 6.62039i) q^{6} +49.9045 q^{7} +(-16.0000 + 16.0000i) q^{8} +70.0426 q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} -3.31020i q^{3} +8.00000i q^{4} +(-1.68780 + 1.68780i) q^{5} +(6.62039 - 6.62039i) q^{6} +49.9045 q^{7} +(-16.0000 + 16.0000i) q^{8} +70.0426 q^{9} -6.75118 q^{10} +233.955i q^{11} +26.4816 q^{12} +(101.658 - 101.658i) q^{13} +(99.8091 + 99.8091i) q^{14} +(5.58694 + 5.58694i) q^{15} -64.0000 q^{16} +(-61.4208 + 61.4208i) q^{17} +(140.085 + 140.085i) q^{18} +(284.903 - 284.903i) q^{19} +(-13.5024 - 13.5024i) q^{20} -165.194i q^{21} +(-467.910 + 467.910i) q^{22} +(-145.412 + 145.412i) q^{23} +(52.9632 + 52.9632i) q^{24} +619.303i q^{25} +406.634 q^{26} -499.981i q^{27} +399.236i q^{28} +(-26.1154 - 26.1154i) q^{29} +22.3477i q^{30} +(-1138.27 - 1138.27i) q^{31} +(-128.000 - 128.000i) q^{32} +774.437 q^{33} -245.683 q^{34} +(-84.2287 + 84.2287i) q^{35} +560.341i q^{36} +(-991.415 + 944.065i) q^{37} +1139.61 q^{38} +(-336.510 - 336.510i) q^{39} -54.0095i q^{40} -3305.42i q^{41} +(330.388 - 330.388i) q^{42} +(2147.37 - 2147.37i) q^{43} -1871.64 q^{44} +(-118.218 + 118.218i) q^{45} -581.646 q^{46} +1822.81 q^{47} +211.853i q^{48} +89.4638 q^{49} +(-1238.61 + 1238.61i) q^{50} +(203.315 + 203.315i) q^{51} +(813.268 + 813.268i) q^{52} -4210.08 q^{53} +(999.962 - 999.962i) q^{54} +(-394.868 - 394.868i) q^{55} +(-798.473 + 798.473i) q^{56} +(-943.086 - 943.086i) q^{57} -104.462i q^{58} +(-3799.88 + 3799.88i) q^{59} +(-44.6955 + 44.6955i) q^{60} +(-2053.05 - 2053.05i) q^{61} -4553.07i q^{62} +3495.44 q^{63} -512.000i q^{64} +343.158i q^{65} +(1548.87 + 1548.87i) q^{66} +4314.65i q^{67} +(-491.367 - 491.367i) q^{68} +(481.341 + 481.341i) q^{69} -336.915 q^{70} +5164.30 q^{71} +(-1120.68 + 1120.68i) q^{72} +1258.94i q^{73} +(-3870.96 - 94.7002i) q^{74} +2050.01 q^{75} +(2279.23 + 2279.23i) q^{76} +11675.4i q^{77} -1346.04i q^{78} +(614.028 - 614.028i) q^{79} +(108.019 - 108.019i) q^{80} +4018.42 q^{81} +(6610.85 - 6610.85i) q^{82} +1185.87 q^{83} +1321.55 q^{84} -207.332i q^{85} +8589.47 q^{86} +(-86.4471 + 86.4471i) q^{87} +(-3743.28 - 3743.28i) q^{88} +(807.796 + 807.796i) q^{89} -472.870 q^{90} +(5073.22 - 5073.22i) q^{91} +(-1163.29 - 1163.29i) q^{92} +(-3767.89 + 3767.89i) q^{93} +(3645.61 + 3645.61i) q^{94} +961.717i q^{95} +(-423.705 + 423.705i) q^{96} +(-2345.18 + 2345.18i) q^{97} +(178.928 + 178.928i) q^{98} +16386.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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