LMFDB - Embedded newform 74.5.d.b.31.3

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			31.3
Root			$-8.86388i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.b.43.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} -9.86388i q^{3} +8.00000i q^{4} +(0.419185 - 0.419185i) q^{5} +(19.7278 - 19.7278i) q^{6} +41.6300 q^{7} +(-16.0000 + 16.0000i) q^{8} -16.2962 q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} -9.86388i q^{3} +8.00000i q^{4} +(0.419185 - 0.419185i) q^{5} +(19.7278 - 19.7278i) q^{6} +41.6300 q^{7} +(-16.0000 + 16.0000i) q^{8} -16.2962 q^{9} +1.67674 q^{10} -228.773i q^{11} +78.9111 q^{12} +(148.898 - 148.898i) q^{13} +(83.2600 + 83.2600i) q^{14} +(-4.13479 - 4.13479i) q^{15} -64.0000 q^{16} +(246.267 - 246.267i) q^{17} +(-32.5924 - 32.5924i) q^{18} +(-494.875 + 494.875i) q^{19} +(3.35348 + 3.35348i) q^{20} -410.634i q^{21} +(457.545 - 457.545i) q^{22} +(-233.413 + 233.413i) q^{23} +(157.822 + 157.822i) q^{24} +624.649i q^{25} +595.591 q^{26} -638.231i q^{27} +333.040i q^{28} +(914.091 + 914.091i) q^{29} -16.5392i q^{30} +(588.840 + 588.840i) q^{31} +(-128.000 - 128.000i) q^{32} -2256.59 q^{33} +985.068 q^{34} +(17.4507 - 17.4507i) q^{35} -130.370i q^{36} +(-987.154 - 948.519i) q^{37} -1979.50 q^{38} +(-1468.71 - 1468.71i) q^{39} +13.4139i q^{40} +1422.63i q^{41} +(821.267 - 821.267i) q^{42} +(32.8185 - 32.8185i) q^{43} +1830.18 q^{44} +(-6.83113 + 6.83113i) q^{45} -933.651 q^{46} -2789.78 q^{47} +631.289i q^{48} -667.943 q^{49} +(-1249.30 + 1249.30i) q^{50} +(-2429.15 - 2429.15i) q^{51} +(1191.18 + 1191.18i) q^{52} +2543.14 q^{53} +(1276.46 - 1276.46i) q^{54} +(-95.8981 - 95.8981i) q^{55} +(-666.080 + 666.080i) q^{56} +(4881.39 + 4881.39i) q^{57} +3656.36i q^{58} +(-1655.06 + 1655.06i) q^{59} +(33.0783 - 33.0783i) q^{60} +(-76.4126 - 76.4126i) q^{61} +2355.36i q^{62} -678.411 q^{63} -512.000i q^{64} -124.831i q^{65} +(-4513.18 - 4513.18i) q^{66} -2108.11i q^{67} +(1970.14 + 1970.14i) q^{68} +(2302.36 + 2302.36i) q^{69} +69.8027 q^{70} +8193.73 q^{71} +(260.739 - 260.739i) q^{72} +1702.13i q^{73} +(-77.2704 - 3871.35i) q^{74} +6161.46 q^{75} +(-3959.00 - 3959.00i) q^{76} -9523.81i q^{77} -5874.84i q^{78} +(526.264 - 526.264i) q^{79} +(-26.8278 + 26.8278i) q^{80} -7615.43 q^{81} +(-2845.25 + 2845.25i) q^{82} -7301.73 q^{83} +3285.07 q^{84} -206.463i q^{85} +131.274 q^{86} +(9016.48 - 9016.48i) q^{87} +(3660.36 + 3660.36i) q^{88} +(6320.54 + 6320.54i) q^{89} -27.3245 q^{90} +(6198.62 - 6198.62i) q^{91} +(-1867.30 - 1867.30i) q^{92} +(5808.25 - 5808.25i) q^{93} +(-5579.55 - 5579.55i) q^{94} +414.888i q^{95} +(-1262.58 + 1262.58i) q^{96} +(-4623.89 + 4623.89i) q^{97} +(-1335.89 - 1335.89i) q^{98} +3728.13i 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
$3$		−	9.86388i		−	1.09599i	−0.836483	−	0.547994i	$-0.815392\pi$
$3$		−	9.86388i		−	1.09599i	0.836483	−	0.547994i	$-0.184608\pi$
$4$			8.00000i			0.500000i
$5$	0.419185	−	0.419185i	0.0167674	−	0.0167674i	−0.698673	−	0.715441i	$-0.746226\pi$
$5$	0.419185	−	0.419185i	0.0167674	−	0.0167674i	0.715441	+	0.698673i	$0.246226\pi$
$6$	19.7278	−	19.7278i	0.547994	−	0.547994i
$7$	41.6300			0.849592			0.424796	−	0.905289i	$-0.360346\pi$
$7$	41.6300			0.849592			0.424796	+	0.905289i	$0.360346\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	−16.2962			−0.201188
$10$	1.67674			0.0167674
$11$		−	228.773i		−	1.89068i	−0.326081	−	0.945342i	$-0.605728\pi$
$11$		−	228.773i		−	1.89068i	0.326081	−	0.945342i	$-0.394272\pi$
$12$	78.9111			0.547994
$13$	148.898	−	148.898i	0.881052	−	0.881052i	−0.112590	−	0.993642i	$-0.535915\pi$
$13$	148.898	−	148.898i	0.881052	−	0.881052i	0.993642	+	0.112590i	$0.0359145\pi$
$14$	83.2600	+	83.2600i	0.424796	+	0.424796i
$15$	−4.13479	−	4.13479i	−0.0183769	−	0.0183769i
$16$	−64.0000			−0.250000
$17$	246.267	−	246.267i	0.852135	−	0.852135i	−0.138261	−	0.990396i	$-0.544151\pi$
$17$	246.267	−	246.267i	0.852135	−	0.852135i	0.990396	+	0.138261i	$0.0441513\pi$
$18$	−32.5924	−	32.5924i	−0.100594	−	0.100594i
$19$	−494.875	+	494.875i	−1.37084	+	1.37084i	−0.511651	+	0.859193i	$0.670966\pi$
$19$	−494.875	+	494.875i	−1.37084	+	1.37084i	−0.859193	+	0.511651i	$0.829034\pi$
$20$	3.35348	+	3.35348i	0.00838370	+	0.00838370i
$21$		−	410.634i		−	0.931142i
$22$	457.545	−	457.545i	0.945342	−	0.945342i
$23$	−233.413	+	233.413i	−0.441234	+	0.441234i	−0.892427	−	0.451193i	$-0.850999\pi$
$23$	−233.413	+	233.413i	−0.441234	+	0.441234i	0.451193	+	0.892427i	$0.350999\pi$
$24$	157.822	+	157.822i	0.273997	+	0.273997i
$25$			624.649i			0.999438i
$26$	595.591			0.881052
$27$		−	638.231i		−	0.875488i
$28$			333.040i			0.424796i
$29$	914.091	+	914.091i	1.08691	+	1.08691i	0.995845	+	0.0910642i	$0.0290268\pi$
$29$	914.091	+	914.091i	1.08691	+	1.08691i	0.0910642	+	0.995845i	$0.470973\pi$
$30$		−	16.5392i		−	0.0183769i
$31$	588.840	+	588.840i	0.612737	+	0.612737i	0.943658	−	0.330921i	$-0.107359\pi$
$31$	588.840	+	588.840i	0.612737	+	0.612737i	−0.330921	+	0.943658i	$0.607359\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−2256.59			−2.07217
$34$	985.068			0.852135
$35$	17.4507	−	17.4507i	0.0142454	−	0.0142454i
$36$		−	130.370i		−	0.100594i
$37$	−987.154	−	948.519i	−0.721077	−	0.692855i
$37$	−987.154	−	948.519i	−0.721077	−	0.692855i
$38$	−1979.50			−1.37084
$39$	−1468.71	−	1468.71i	−0.965622	−	0.965622i
$40$			13.4139i			0.00838370i
$41$			1422.63i			0.846297i	0.906060	+	0.423149i	$0.139075\pi$
$41$			1422.63i			0.846297i	−0.906060	+	0.423149i	$0.860925\pi$
$42$	821.267	−	821.267i	0.465571	−	0.465571i
$43$	32.8185	−	32.8185i	0.0177493	−	0.0177493i	−0.698176	−	0.715926i	$-0.746005\pi$
$43$	32.8185	−	32.8185i	0.0177493	−	0.0177493i	0.715926	+	0.698176i	$0.246005\pi$
$44$	1830.18			0.945342
$45$	−6.83113	+	6.83113i	−0.00337340	+	0.00337340i
$46$	−933.651			−0.441234
$47$	−2789.78			−1.26291			−0.631457	−	0.775411i	$-0.717543\pi$
$47$	−2789.78			−1.26291			−0.631457	+	0.775411i	$0.717543\pi$
$48$			631.289i			0.273997i
$49$	−667.943			−0.278194
$50$	−1249.30	+	1249.30i	−0.499719	+	0.499719i
$51$	−2429.15	−	2429.15i	−0.933929	−	0.933929i
$52$	1191.18	+	1191.18i	0.440526	+	0.440526i
$53$	2543.14			0.905356			0.452678	−	0.891674i	$-0.350469\pi$
$53$	2543.14			0.905356			0.452678	+	0.891674i	$0.350469\pi$
$54$	1276.46	−	1276.46i	0.437744	−	0.437744i
$55$	−95.8981	−	95.8981i	−0.0317018	−	0.0317018i
$56$	−666.080	+	666.080i	−0.212398	+	0.212398i
$57$	4881.39	+	4881.39i	1.50243	+	1.50243i
$58$			3656.36i			1.08691i
$59$	−1655.06	+	1655.06i	−0.475455	+	0.475455i	−0.903675	−	0.428220i	$-0.859141\pi$
$59$	−1655.06	+	1655.06i	−0.475455	+	0.475455i	0.428220	+	0.903675i	$0.359141\pi$
$60$	33.0783	−	33.0783i	0.00918843	−	0.00918843i
$61$	−76.4126	−	76.4126i	−0.0205355	−	0.0205355i	0.696764	−	0.717300i	$-0.254622\pi$
$61$	−76.4126	−	76.4126i	−0.0205355	−	0.0205355i	−0.717300	+	0.696764i	$0.754622\pi$
$62$			2355.36i			0.612737i
$63$	−678.411			−0.170928
$64$		−	512.000i		−	0.125000i
$65$		−	124.831i		−	0.0295459i
$66$	−4513.18	−	4513.18i	−1.03608	−	1.03608i
$67$		−	2108.11i		−	0.469617i	−0.972042	−	0.234808i	$-0.924554\pi$
$67$		−	2108.11i		−	0.469617i	0.972042	−	0.234808i	$-0.0754463\pi$
$68$	1970.14	+	1970.14i	0.426067	+	0.426067i
$69$	2302.36	+	2302.36i	0.483587	+	0.483587i
$70$	69.8027			0.0142454
$71$	8193.73			1.62542			0.812709	−	0.582669i	$-0.197992\pi$
$71$	8193.73			1.62542			0.812709	+	0.582669i	$0.197992\pi$
$72$	260.739	−	260.739i	0.0502970	−	0.0502970i
$73$			1702.13i			0.319410i	0.987165	+	0.159705i	$0.0510543\pi$
$73$			1702.13i			0.319410i	−0.987165	+	0.159705i	$0.948946\pi$
$74$	−77.2704	−	3871.35i	−0.0141107	−	0.706966i
$75$	6161.46			1.09537
$76$	−3959.00	−	3959.00i	−0.685422	−	0.685422i
$77$		−	9523.81i		−	1.60631i
$78$		−	5874.84i		−	0.965622i
$79$	526.264	−	526.264i	0.0843237	−	0.0843237i	−0.663687	−	0.748011i	$-0.731009\pi$
$79$	526.264	−	526.264i	0.0843237	−	0.0843237i	0.748011	+	0.663687i	$0.231009\pi$
$80$	−26.8278	+	26.8278i	−0.00419185	+	0.00419185i
$81$	−7615.43			−1.16071
$82$	−2845.25	+	2845.25i	−0.423149	+	0.423149i
$83$	−7301.73			−1.05991			−0.529956	−	0.848025i	$-0.677791\pi$
$83$	−7301.73			−1.05991			−0.529956	+	0.848025i	$0.677791\pi$
$84$	3285.07			0.465571
$85$		−	206.463i		−	0.0285762i
$86$	131.274			0.0177493
$87$	9016.48	−	9016.48i	1.19124	−	1.19124i
$88$	3660.36	+	3660.36i	0.472671	+	0.472671i
$89$	6320.54	+	6320.54i	0.797947	+	0.797947i	0.982772	−	0.184825i	$-0.0591717\pi$
$89$	6320.54	+	6320.54i	0.797947	+	0.797947i	−0.184825	+	0.982772i	$0.559172\pi$
$90$	−27.3245			−0.00337340
$91$	6198.62	−	6198.62i	0.748535	−	0.748535i
$92$	−1867.30	−	1867.30i	−0.220617	−	0.220617i
$93$	5808.25	−	5808.25i	0.671552	−	0.671552i
$94$	−5579.55	−	5579.55i	−0.631457	−	0.631457i
$95$			414.888i			0.0459710i
$96$	−1262.58	+	1262.58i	−0.136998	+	0.136998i
$97$	−4623.89	+	4623.89i	−0.491433	+	0.491433i	−0.908757	−	0.417325i	$-0.862968\pi$
$97$	−4623.89	+	4623.89i	−0.491433	+	0.491433i	0.417325	+	0.908757i	$0.362968\pi$
$98$	−1335.89	−	1335.89i	−0.139097	−	0.139097i
$99$			3728.13i			0.380383i
$100$	−4997.19			−0.499719
$101$			9670.76i			0.948020i	0.880519	+	0.474010i	$0.157194\pi$
$101$			9670.76i			0.948020i	−0.880519	+	0.474010i	$0.842806\pi$
$102$		−	9716.60i		−	0.933929i
$103$	−1299.66	−	1299.66i	−0.122506	−	0.122506i	0.643196	−	0.765702i	$-0.277608\pi$
$103$	−1299.66	−	1299.66i	−0.122506	−	0.122506i	−0.765702	+	0.643196i	$0.777608\pi$
$104$			4764.73i			0.440526i
$105$	−172.131	−	172.131i	−0.0156128	−	0.0156128i
$106$	5086.29	+	5086.29i	0.452678	+	0.452678i
$107$	14756.2			1.28886			0.644432	−	0.764662i	$-0.277094\pi$
$107$	14756.2			1.28886			0.644432	+	0.764662i	$0.277094\pi$
$108$	5105.85			0.437744
$109$	−2851.85	+	2851.85i	−0.240034	+	0.240034i	−0.816864	−	0.576830i	$-0.804290\pi$
$109$	−2851.85	+	2851.85i	−0.240034	+	0.240034i	0.576830	+	0.816864i	$0.304290\pi$
$110$		−	383.592i		−	0.0317018i
$111$	−9356.08	+	9737.17i	−0.759360	+	0.790291i
$112$	−2664.32			−0.212398
$113$	5838.00	+	5838.00i	0.457201	+	0.457201i	0.897736	−	0.440535i	$-0.145211\pi$
$113$	5838.00	+	5838.00i	0.457201	+	0.457201i	−0.440535	+	0.897736i	$0.645211\pi$
$114$			19525.6i			1.50243i
$115$			195.686i			0.0147967i
$116$	−7312.73	+	7312.73i	−0.543455	+	0.543455i
$117$	−2426.47	+	2426.47i	−0.177257	+	0.177257i
$118$	−6620.23			−0.475455
$119$	10252.1	−	10252.1i	0.723967	−	0.723967i
$120$	132.313			0.00918843
$121$	−37696.0			−2.57469
$122$		−	305.650i		−	0.0205355i
$123$	14032.6			0.927531
$124$	−4710.72	+	4710.72i	−0.306368	+	0.306368i
$125$	523.834	+	523.834i	0.0335254	+	0.0335254i
$126$	−1356.82	−	1356.82i	−0.0854638	−	0.0854638i
$127$	−17870.2			−1.10796			−0.553978	−	0.832532i	$-0.686891\pi$
$127$	−17870.2			−1.10796			−0.553978	+	0.832532i	$0.686891\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$	−323.718	−	323.718i	−0.0194530	−	0.0194530i
$130$	249.663	−	249.663i	0.0147729	−	0.0147729i
$131$	−12062.7	−	12062.7i	−0.702916	−	0.702916i	0.262120	−	0.965035i	$-0.415579\pi$
$131$	−12062.7	−	12062.7i	−0.702916	−	0.702916i	−0.965035	+	0.262120i	$0.915579\pi$
$132$		−	18052.7i		−	1.03608i
$133$	−20601.6	+	20601.6i	−1.16466	+	1.16466i
$134$	4216.22	−	4216.22i	0.234808	−	0.234808i
$135$	−267.537	−	267.537i	−0.0146797	−	0.0146797i
$136$			7880.54i			0.426067i
$137$	24774.9			1.31999			0.659996	−	0.751269i	$-0.270558\pi$
$137$	24774.9			1.31999			0.659996	+	0.751269i	$0.270558\pi$
$138$			9209.42i			0.483587i
$139$		−	21116.0i		−	1.09291i	−0.837490	−	0.546453i	$-0.815978\pi$
$139$		−	21116.0i		−	1.09291i	0.837490	−	0.546453i	$-0.184022\pi$
$140$	139.605	+	139.605i	0.00712272	+	0.00712272i
$141$			27518.0i			1.38414i
$142$	16387.5	+	16387.5i	0.812709	+	0.812709i
$143$	−34063.8	−	34063.8i	−1.66579	−	1.66579i
$144$	1042.96			0.0502970
$145$	766.346			0.0364493
$146$	−3404.27	+	3404.27i	−0.159705	+	0.159705i
$147$			6588.51i			0.304897i
$148$	7588.15	−	7897.23i	0.346428	−	0.360538i
$149$	−15001.3			−0.675705			−0.337853	−	0.941199i	$-0.609701\pi$
$149$	−15001.3			−0.675705			−0.337853	+	0.941199i	$0.609701\pi$
$150$	12322.9	+	12322.9i	0.547685	+	0.547685i
$151$			25861.1i			1.13421i	0.823646	+	0.567104i	$0.191936\pi$
$151$			25861.1i			1.13421i	−0.823646	+	0.567104i	$0.808064\pi$
$152$		−	15836.0i		−	0.685422i
$153$	−4013.22	+	4013.22i	−0.171439	+	0.171439i
$154$	19047.6	−	19047.6i	0.803155	−	0.803155i
$155$	493.666			0.0205480
$156$	11749.7	−	11749.7i	0.482811	−	0.482811i
$157$	25722.9			1.04357			0.521785	−	0.853077i	$-0.325266\pi$
$157$	25722.9			1.04357			0.521785	+	0.853077i	$0.325266\pi$
$158$	2105.06			0.0843237
$159$		−	25085.3i		−	0.992258i
$160$	−107.311			−0.00419185
$161$	−9716.97	+	9716.97i	−0.374869	+	0.374869i
$162$	−15230.9	−	15230.9i	−0.580356	−	0.580356i
$163$	34290.4	+	34290.4i	1.29062	+	1.29062i	0.934406	+	0.356210i	$0.115931\pi$
$163$	34290.4	+	34290.4i	1.29062	+	1.29062i	0.356210	+	0.934406i	$0.384069\pi$
$164$	−11381.0			−0.423149
$165$	−945.928	+	945.928i	−0.0347448	+	0.0347448i
$166$	−14603.5	−	14603.5i	−0.529956	−	0.529956i
$167$	17371.0	−	17371.0i	0.622861	−	0.622861i	−0.323401	−	0.946262i	$-0.604826\pi$
$167$	17371.0	−	17371.0i	0.622861	−	0.622861i	0.946262	+	0.323401i	$0.104826\pi$
$168$	6570.14	+	6570.14i	0.232785	+	0.232785i
$169$		−	15780.1i		−	0.552505i
$170$	412.926	−	412.926i	0.0142881	−	0.0142881i
$171$	8064.59	−	8064.59i	0.275797	−	0.275797i
$172$	262.548	+	262.548i	0.00887466	+	0.00887466i
$173$		−	42839.1i		−	1.43136i	−0.698430	−	0.715678i	$-0.746118\pi$
$173$		−	42839.1i		−	1.43136i	0.698430	−	0.715678i	$-0.253882\pi$
$174$	36065.9			1.19124
$175$			26004.1i			0.849114i
$176$			14641.5i			0.472671i
$177$	16325.3	+	16325.3i	0.521092	+	0.521092i
$178$			25282.1i			0.797947i
$179$	−6455.87	−	6455.87i	−0.201488	−	0.201488i	0.599149	−	0.800637i	$-0.295506\pi$
$179$	−6455.87	−	6455.87i	−0.201488	−	0.201488i	−0.800637	+	0.599149i	$0.795506\pi$
$180$	−54.6490	−	54.6490i	−0.00168670	−	0.00168670i
$181$	−3296.50			−0.100623			−0.0503114	−	0.998734i	$-0.516021\pi$
$181$	−3296.50			−0.100623			−0.0503114	+	0.998734i	$0.516021\pi$
$182$	24794.5			0.748535
$183$	−753.725	+	753.725i	−0.0225066	+	0.0225066i
$184$		−	7469.21i		−	0.220617i
$185$	−811.405	+	16.1953i	−0.0237080	+	0.000473201i
$186$	23233.0			0.671552
$187$	−56339.2	−	56339.2i	−1.61112	−	1.61112i
$188$		−	22318.2i		−	0.631457i
$189$		−	26569.5i		−	0.743807i
$190$	−829.776	+	829.776i	−0.0229855	+	0.0229855i
$191$	34213.1	−	34213.1i	0.937833	−	0.937833i	−0.0603445	−	0.998178i	$-0.519220\pi$
$191$	34213.1	−	34213.1i	0.937833	−	0.937833i	0.998178	+	0.0603445i	$0.0192199\pi$
$192$	−5050.31			−0.136998
$193$	−43966.4	+	43966.4i	−1.18034	+	1.18034i	−0.200680	+	0.979657i	$0.564315\pi$
$193$	−43966.4	+	43966.4i	−1.18034	+	1.18034i	−0.979657	+	0.200680i	$0.935685\pi$
$194$	−18495.6			−0.491433
$195$	−1231.32			−0.0323819
$196$		−	5343.55i		−	0.139097i
$197$	−1978.82			−0.0509888			−0.0254944	−	0.999675i	$-0.508116\pi$
$197$	−1978.82			−0.0509888			−0.0254944	+	0.999675i	$0.508116\pi$
$198$	−7456.26	+	7456.26i	−0.190191	+	0.190191i
$199$	1378.48	+	1378.48i	0.0348092	+	0.0348092i	0.724297	−	0.689488i	$-0.242164\pi$
$199$	1378.48	+	1378.48i	0.0348092	+	0.0348092i	−0.689488	+	0.724297i	$0.742164\pi$
$200$	−9994.38	−	9994.38i	−0.249859	−	0.249859i
$201$	−20794.2			−0.514694
$202$	−19341.5	+	19341.5i	−0.474010	+	0.474010i
$203$	38053.6	+	38053.6i	0.923429	+	0.923429i
$204$	19433.2	−	19433.2i	0.466964	−	0.466964i
$205$	596.343	+	596.343i	0.0141902	+	0.0141902i
$206$		−	5198.65i		−	0.122506i
$207$	3803.74	−	3803.74i	0.0887709	−	0.0887709i
$208$	−9529.46	+	9529.46i	−0.220263	+	0.220263i
$209$	113214.	+	113214.i	2.59183	+	2.59183i
$210$		−	688.526i		−	0.0156128i
$211$	−72123.4			−1.61999			−0.809993	−	0.586439i	$-0.800529\pi$
$211$	−72123.4			−1.61999			−0.809993	+	0.586439i	$0.800529\pi$
$212$			20345.1i			0.452678i
$213$		−	80822.0i		−	1.78144i
$214$	29512.4	+	29512.4i	0.644432	+	0.644432i
$215$		−	27.5140i		−	0.000595220i
$216$	10211.7	+	10211.7i	0.218872	+	0.218872i
$217$	24513.4	+	24513.4i	0.520576	+	0.520576i
$218$	−11407.4			−0.240034
$219$	16789.7			0.350069
$220$	767.185	−	767.185i	0.0158509	−	0.0158509i
$221$		−	73337.2i		−	1.50155i
$222$	−38186.5	+	762.186i	−0.774826	+	0.0154652i
$223$	−13357.1			−0.268597			−0.134299	−	0.990941i	$-0.542878\pi$
$223$	−13357.1			−0.268597			−0.134299	+	0.990941i	$0.542878\pi$
$224$	−5328.64	−	5328.64i	−0.106199	−	0.106199i
$225$		−	10179.4i		−	0.201075i
$226$			23352.0i			0.457201i
$227$	20606.8	−	20606.8i	0.399907	−	0.399907i	−0.478293	−	0.878200i	$-0.658744\pi$
$227$	20606.8	−	20606.8i	0.399907	−	0.399907i	0.878200	+	0.478293i	$0.158744\pi$
$228$	−39051.1	+	39051.1i	−0.751214	+	0.751214i
$229$	−4479.48			−0.0854195			−0.0427098	−	0.999088i	$-0.513599\pi$
$229$	−4479.48			−0.0854195			−0.0427098	+	0.999088i	$0.513599\pi$
$230$	−391.372	+	391.372i	−0.00739834	+	0.00739834i
$231$	−93941.8			−1.76049
$232$	−29250.9			−0.543455
$233$			44934.2i			0.827684i	0.910349	+	0.413842i	$0.135813\pi$
$233$			44934.2i			0.827684i	−0.910349	+	0.413842i	$0.864187\pi$
$234$	−9705.88			−0.177257
$235$	−1169.43	+	1169.43i	−0.0211758	+	0.0211758i
$236$	−13240.5	−	13240.5i	−0.237727	−	0.237727i
$237$	−5191.01	−	5191.01i	−0.0924177	−	0.0924177i
$238$	41008.4			0.723967
$239$	−9788.15	+	9788.15i	−0.171358	+	0.171358i	−0.787576	−	0.616218i	$-0.788664\pi$
$239$	−9788.15	+	9788.15i	−0.171358	+	0.171358i	0.616218	+	0.787576i	$0.288664\pi$
$240$	264.627	+	264.627i	0.00459421	+	0.00459421i
$241$	70247.4	−	70247.4i	1.20947	−	1.20947i	0.238275	−	0.971198i	$-0.423418\pi$
$241$	70247.4	−	70247.4i	1.20947	−	1.20947i	0.971198	−	0.238275i	$-0.0765818\pi$
$242$	−75391.9	−	75391.9i	−1.28734	−	1.28734i
$243$			23421.0i			0.396637i
$244$	611.300	−	611.300i	0.0102677	−	0.0102677i
$245$	−279.992	+	279.992i	−0.00466458	+	0.00466458i
$246$	28065.2	+	28065.2i	0.463765	+	0.463765i
$247$			147372.i			2.41557i
$248$	−18842.9			−0.306368
$249$			72023.4i			1.16165i
$250$			2095.34i			0.0335254i
$251$	6532.43	+	6532.43i	0.103688	+	0.103688i	0.757048	−	0.653360i	$-0.226641\pi$
$251$	6532.43	+	6532.43i	0.103688	+	0.103688i	−0.653360	+	0.757048i	$0.726641\pi$
$252$		−	5427.29i		−	0.0854638i
$253$	53398.5	+	53398.5i	0.834234	+	0.834234i
$254$	−35740.4	−	35740.4i	−0.553978	−	0.553978i
$255$	−2036.53			−0.0313191
$256$	4096.00			0.0625000
$257$	−5608.41	+	5608.41i	−0.0849128	+	0.0849128i	−0.748287	−	0.663375i	$-0.769124\pi$
$257$	−5608.41	+	5608.41i	−0.0849128	+	0.0849128i	0.663375	+	0.748287i	$0.269124\pi$
$258$		−	1294.87i		−	0.0194530i
$259$	−41095.2	−	39486.8i	−0.612621	−	0.588644i
$260$	998.651			0.0147729
$261$	−14896.2	−	14896.2i	−0.218673	−	0.218673i
$262$		−	48251.0i		−	0.702916i
$263$		−	20799.2i		−	0.300701i	−0.988633	−	0.150351i	$-0.951960\pi$
$263$		−	20799.2i		−	0.300701i	0.988633	−	0.150351i	$-0.0480402\pi$
$264$	36105.4	−	36105.4i	0.518041	−	0.518041i
$265$	1066.05	−	1066.05i	0.0151805	−	0.0151805i
$266$	−82406.6			−1.16466
$267$	62345.0	−	62345.0i	0.874539	−	0.874539i
$268$	16864.9			0.234808
$269$	−61895.4			−0.855369			−0.427685	−	0.903928i	$-0.640671\pi$
$269$	−61895.4			−0.855369			−0.427685	+	0.903928i	$0.640671\pi$
$270$		−	1070.15i		−	0.0146797i
$271$	−108567.			−1.47829			−0.739146	−	0.673545i	$-0.764771\pi$
$271$	−108567.			−1.47829			−0.739146	+	0.673545i	$0.764771\pi$
$272$	−15761.1	+	15761.1i	−0.213034	+	0.213034i
$273$	−61142.4	−	61142.4i	−0.820384	−	0.820384i
$274$	49549.9	+	49549.9i	0.659996	+	0.659996i
$275$	142903.			1.88962
$276$	−18418.8	+	18418.8i	−0.241793	+	0.241793i
$277$	7992.91	+	7992.91i	0.104171	+	0.104171i	0.757271	−	0.653101i	$-0.226532\pi$
$277$	7992.91	+	7992.91i	0.104171	+	0.104171i	−0.653101	+	0.757271i	$0.726532\pi$
$278$	42232.1	−	42232.1i	0.546453	−	0.546453i
$279$	−9595.87	−	9595.87i	−0.123275	−	0.123275i
$280$			558.421i			0.00712272i
$281$	8035.34	−	8035.34i	0.101763	−	0.101763i	−0.654392	−	0.756155i	$-0.727075\pi$
$281$	8035.34	−	8035.34i	0.101763	−	0.101763i	0.756155	+	0.654392i	$0.227075\pi$
$282$	−55036.1	+	55036.1i	−0.692069	+	0.692069i
$283$	41589.7	+	41589.7i	0.519294	+	0.519294i	0.917358	−	0.398064i	$-0.130318\pi$
$283$	41589.7	+	41589.7i	0.519294	+	0.519294i	−0.398064	+	0.917358i	$0.630318\pi$
$284$			65549.9i			0.812709i
$285$	4092.41			0.0503836
$286$		−	136255.i		−	1.66579i
$287$			59223.9i			0.719007i
$288$	2085.92	+	2085.92i	0.0251485	+	0.0251485i
$289$		−	37773.8i		−	0.452268i
$290$	1532.69	+	1532.69i	0.0182246	+	0.0182246i
$291$	45609.5	+	45609.5i	0.538604	+	0.538604i
$292$	−13617.1			−0.159705
$293$	44826.2			0.522152			0.261076	−	0.965318i	$-0.415923\pi$
$293$	44826.2			0.522152			0.261076	+	0.965318i	$0.415923\pi$
$294$	−13177.0	+	13177.0i	−0.152448	+	0.152448i
$295$			1387.55i			0.0159443i
$296$	30970.8	−	618.163i	0.353483	−	0.00705537i
$297$	−146010.			−1.65527
$298$	−30002.7	−	30002.7i	−0.337853	−	0.337853i
$299$			69509.3i			0.777500i
$300$			49291.7i			0.547685i
$301$	1366.23	−	1366.23i	0.0150797	−	0.0150797i
$302$	−51722.1	+	51722.1i	−0.567104	+	0.567104i
$303$	95391.2			1.03902
$304$	31672.0	−	31672.0i	0.342711	−	0.342711i
$305$	−64.0620			−0.000688653
$306$	−16052.9			−0.171439
$307$		−	48771.6i		−	0.517476i	−0.965947	−	0.258738i	$-0.916693\pi$
$307$		−	48771.6i		−	0.517476i	0.965947	−	0.258738i	$-0.0833067\pi$
$308$	76190.5			0.803155
$309$	−12819.7	+	12819.7i	−0.134265	+	0.134265i
$310$	987.332	+	987.332i	0.0102740	+	0.0102740i
$311$	−44765.7	−	44765.7i	−0.462833	−	0.462833i	0.436750	−	0.899583i	$-0.356130\pi$
$311$	−44765.7	−	44765.7i	−0.462833	−	0.462833i	−0.899583	+	0.436750i	$0.856130\pi$
$312$	46998.7			0.482811
$313$	50280.3	−	50280.3i	0.513227	−	0.513227i	−0.402287	−	0.915514i	$-0.631785\pi$
$313$	50280.3	−	50280.3i	0.513227	−	0.513227i	0.915514	+	0.402287i	$0.131785\pi$
$314$	51445.9	+	51445.9i	0.521785	+	0.521785i
$315$	−284.380	+	284.380i	−0.00286601	+	0.00286601i
$316$	4210.11	+	4210.11i	0.0421618	+	0.0421618i
$317$		−	33786.6i		−	0.336222i	−0.985768	−	0.168111i	$-0.946233\pi$
$317$		−	33786.6i		−	0.336222i	0.985768	−	0.168111i	$-0.0537668\pi$
$318$	50170.5	−	50170.5i	0.496129	−	0.496129i
$319$	209119.	−	209119.i	2.05500	−	2.05500i
$320$	−214.623	−	214.623i	−0.00209592	−	0.00209592i
$321$		−	145553.i		−	1.41258i
$322$	−38867.9			−0.374869
$323$			243743.i			2.33629i
$324$		−	60923.4i		−	0.580356i
$325$	93008.8	+	93008.8i	0.880557	+	0.880557i
$326$			137161.i			1.29062i
$327$	28130.3	+	28130.3i	0.263074	+	0.263074i
$328$	−22762.0	−	22762.0i	−0.211574	−	0.211574i
$329$	−116138.			−1.07296
$330$	−3783.71			−0.0347448
$331$	17709.4	−	17709.4i	0.161640	−	0.161640i	−0.621653	−	0.783293i	$-0.713539\pi$
$331$	17709.4	−	17709.4i	0.161640	−	0.161640i	0.783293	+	0.621653i	$0.213539\pi$
$332$		−	58413.9i		−	0.529956i
$333$	16086.9	+	15457.3i	0.145072	+	0.139394i
$334$	69483.9			0.622861
$335$	−883.688	−	883.688i	−0.00787425	−	0.00787425i
$336$			26280.5i			0.232785i
$337$			33950.4i			0.298941i	0.988766	+	0.149470i	$0.0477568\pi$
$337$			33950.4i			0.298941i	−0.988766	+	0.149470i	$0.952243\pi$
$338$	31560.2	−	31560.2i	0.276253	−	0.276253i
$339$	57585.3	−	57585.3i	0.501086	−	0.501086i
$340$	1651.70			0.0142881
$341$	134711.	−	134711.i	1.15849	−	1.15849i
$342$	32258.3			0.275797
$343$	−127760.			−1.08594
$344$			1050.19i			0.00887466i
$345$	1930.23			0.0162170
$346$	85678.2	−	85678.2i	0.715678	−	0.715678i
$347$	−13213.5	−	13213.5i	−0.109738	−	0.109738i	0.650106	−	0.759844i	$-0.274725\pi$
$347$	−13213.5	−	13213.5i	−0.109738	−	0.109738i	−0.759844	+	0.650106i	$0.774725\pi$
$348$	72131.9	+	72131.9i	0.595619	+	0.595619i
$349$	−86070.9			−0.706652			−0.353326	−	0.935500i	$-0.614949\pi$
$349$	−86070.9			−0.706652			−0.353326	+	0.935500i	$0.614949\pi$
$350$	−52008.2	+	52008.2i	−0.424557	+	0.424557i
$351$	−95031.1	−	95031.1i	−0.771350	−	0.771350i
$352$	−29282.9	+	29282.9i	−0.236335	+	0.236335i
$353$	−118873.	−	118873.i	−0.953968	−	0.953968i	0.0450184	−	0.998986i	$-0.485665\pi$
$353$	−118873.	−	118873.i	−0.953968	−	0.953968i	−0.998986	+	0.0450184i	$0.985665\pi$
$354$			65301.2i			0.521092i
$355$	3434.69	−	3434.69i	0.0272540	−	0.0272540i
$356$	−50564.3	+	50564.3i	−0.398973	+	0.398973i
$357$	−101125.	−	101125.i	−0.793458	−	0.793458i
$358$		−	25823.5i		−	0.201488i
$359$	−214428.			−1.66377			−0.831883	−	0.554951i	$-0.812737\pi$
$359$	−214428.			−1.66377			−0.831883	+	0.554951i	$0.812737\pi$
$360$		−	218.596i		−	0.00168670i
$361$		−	359481.i		−	2.75843i
$362$	−6593.00	−	6593.00i	−0.0503114	−	0.0503114i
$363$			371829.i			2.82182i
$364$	49588.9	+	49588.9i	0.374267	+	0.374267i
$365$	713.509	+	713.509i	0.00535567	+	0.00535567i
$366$	−3014.90			−0.0225066
$367$	−180125.			−1.33734			−0.668669	−	0.743560i	$-0.733136\pi$
$367$	−180125.			−1.33734			−0.668669	+	0.743560i	$0.733136\pi$
$368$	14938.4	−	14938.4i	0.110308	−	0.110308i
$369$		−	23183.4i		−	0.170265i
$370$	−1655.20	−	1590.42i	−0.0120906	−	0.0116174i
$371$	105871.			0.769183
$372$	46466.0	+	46466.0i	0.335776	+	0.335776i
$373$			86574.0i			0.622257i	0.950368	+	0.311129i	$0.100707\pi$
$373$			86574.0i			0.622257i	−0.950368	+	0.311129i	$0.899293\pi$
$374$		−	225357.i		−	1.61112i
$375$	5167.04	−	5167.04i	0.0367434	−	0.0367434i
$376$	44636.4	−	44636.4i	0.315728	−	0.315728i
$377$	272212.			1.91525
$378$	53139.1	−	53139.1i	0.371904	−	0.371904i
$379$	−84573.6			−0.588784			−0.294392	−	0.955685i	$-0.595117\pi$
$379$	−84573.6			−0.588784			−0.294392	+	0.955685i	$0.595117\pi$
$380$	−3319.11			−0.0229855
$381$			176270.i			1.21430i
$382$	136852.			0.937833
$383$	−150603.	+	150603.i	−1.02668	+	1.02668i	−0.0270458	+	0.999634i	$0.508610\pi$
$383$	−150603.	+	150603.i	−1.02668	+	1.02668i	−0.999634	+	0.0270458i	$0.991390\pi$
$384$	−10100.6	−	10100.6i	−0.0684992	−	0.0684992i
$385$	−3992.24	−	3992.24i	−0.0269336	−	0.0269336i
$386$	−175865.			−1.18034
$387$	−534.817	+	534.817i	−0.00357095	+	0.00357095i
$388$	−36991.1	−	36991.1i	−0.245716	−	0.245716i
$389$	−119127.	+	119127.i	−0.787245	+	0.787245i	−0.981042	−	0.193797i	$-0.937920\pi$
$389$	−119127.	+	119127.i	−0.787245	+	0.787245i	0.193797	+	0.981042i	$0.437920\pi$
$390$	−2462.65	−	2462.65i	−0.0161910	−	0.0161910i
$391$			114964.i			0.751981i
$392$	10687.1	−	10687.1i	0.0695484	−	0.0695484i
$393$	−118985.	+	118985.i	−0.770387	+	0.770387i
$394$	−3957.65	−	3957.65i	−0.0254944	−	0.0254944i
$395$		−	441.204i		−	0.00282778i
$396$	−29825.0			−0.190191
$397$		−	140145.i		−	0.889193i	−0.895731	−	0.444596i	$-0.853347\pi$
$397$		−	140145.i		−	0.889193i	0.895731	−	0.444596i	$-0.146653\pi$
$398$			5513.92i			0.0348092i
$399$	203212.	+	203212.i	1.27645	+	1.27645i
$400$		−	39977.5i		−	0.249859i
$401$	−3193.26	−	3193.26i	−0.0198585	−	0.0198585i	0.697108	−	0.716966i	$-0.254470\pi$
$401$	−3193.26	−	3193.26i	−0.0198585	−	0.0198585i	−0.716966	+	0.697108i	$0.754470\pi$
$402$	−41588.3	−	41588.3i	−0.257347	−	0.257347i
$403$	175354.			1.07971
$404$	−77366.0			−0.474010
$405$	−3192.27	+	3192.27i	−0.0194621	+	0.0194621i
$406$			152214.i			0.923429i
$407$	−216995.	+	225834.i	−1.30997	+	1.36333i
$408$	77732.8			0.466964
$409$	−61941.2	−	61941.2i	−0.370282	−	0.370282i	0.497298	−	0.867580i	$-0.334326\pi$
$409$	−61941.2	−	61941.2i	−0.370282	−	0.370282i	−0.867580	+	0.497298i	$0.834326\pi$
$410$			2385.37i			0.0141902i
$411$		−	244377.i		−	1.44669i
$412$	10397.3	−	10397.3i	0.0612528	−	0.0612528i
$413$	−68900.0	+	68900.0i	−0.403942	+	0.403942i
$414$	15215.0			0.0887709
$415$	−3060.78	+	3060.78i	−0.0177720	+	0.0177720i
$416$	−38117.8			−0.220263
$417$	−208286.			−1.19781
$418$			452855.i			2.59183i
$419$	153017.			0.871589			0.435794	−	0.900046i	$-0.356467\pi$
$419$	153017.			0.871589			0.435794	+	0.900046i	$0.356467\pi$
$420$	1377.05	−	1377.05i	0.00780641	−	0.00780641i
$421$	73254.7	+	73254.7i	0.413305	+	0.413305i	0.882888	−	0.469583i	$-0.155596\pi$
$421$	73254.7	+	73254.7i	0.413305	+	0.413305i	−0.469583	+	0.882888i	$0.655596\pi$
$422$	−144247.	−	144247.i	−0.809993	−	0.809993i
$423$	45462.8			0.254083
$424$	−40690.3	+	40690.3i	−0.226339	+	0.226339i
$425$	153830.	+	153830.i	0.851656	+	0.851656i
$426$	161644.	−	161644.i	0.890719	−	0.890719i
$427$	−3181.05	−	3181.05i	−0.0174468	−	0.0174468i
$428$			118050.i			0.644432i
$429$	−336001.	+	336001.i	−1.82569	+	1.82569i
$430$	55.0281	−	55.0281i	0.000297610	−	0.000297610i
$431$	−102609.	−	102609.i	−0.552372	−	0.552372i	0.374753	−	0.927125i	$-0.377728\pi$
$431$	−102609.	−	102609.i	−0.552372	−	0.552372i	−0.927125	+	0.374753i	$0.877728\pi$
$432$			40846.8i			0.218872i
$433$	82659.0			0.440874			0.220437	−	0.975401i	$-0.429252\pi$
$433$	82659.0			0.440874			0.220437	+	0.975401i	$0.429252\pi$
$434$			98053.7i			0.520576i
$435$		−	7559.15i		−	0.0399479i
$436$	−22814.8	−	22814.8i	−0.120017	−	0.120017i
$437$		−	231020.i		−	1.20973i
$438$	33579.3	+	33579.3i	0.175034	+	0.175034i
$439$	−31198.1	−	31198.1i	−0.161882	−	0.161882i	0.621518	−	0.783400i	$-0.286516\pi$
$439$	−31198.1	−	31198.1i	−0.161882	−	0.161882i	−0.783400	+	0.621518i	$0.786516\pi$
$440$	3068.74			0.0158509
$441$	10884.9			0.0559692
$442$	146674.	−	146674.i	0.750775	−	0.750775i
$443$		−	58623.4i		−	0.298719i	−0.988783	−	0.149360i	$-0.952279\pi$
$443$		−	58623.4i		−	0.298719i	0.988783	−	0.149360i	$-0.0477212\pi$
$444$	−77897.4	−	74848.6i	−0.395145	−	0.379680i
$445$	5298.95			0.0267590
$446$	−26714.2	−	26714.2i	−0.134299	−	0.134299i
$447$			147971.i			0.740564i
$448$		−	21314.6i		−	0.106199i
$449$	12777.7	−	12777.7i	0.0633809	−	0.0633809i	−0.674706	−	0.738087i	$-0.735729\pi$
$449$	12777.7	−	12777.7i	0.0633809	−	0.0633809i	0.738087	+	0.674706i	$0.235729\pi$
$450$	20358.8	−	20358.8i	0.100537	−	0.100537i
$451$	325458.			1.60008
$452$	−46704.0	+	46704.0i	−0.228600	+	0.228600i
$453$	255090.			1.24308
$454$	82427.2			0.399907
$455$		−	5196.73i		−	0.0251020i
$456$	−156204.			−0.751214
$457$	171243.	−	171243.i	0.819936	−	0.819936i	−0.166163	−	0.986098i	$-0.553138\pi$
$457$	171243.	−	171243.i	0.819936	−	0.819936i	0.986098	+	0.166163i	$0.0531377\pi$
$458$	−8958.97	−	8958.97i	−0.0427098	−	0.0427098i
$459$	−157175.	−	157175.i	−0.746034	−	0.746034i
$460$	−1565.49			−0.00739834
$461$	243373.	−	243373.i	1.14517	−	1.14517i	0.157684	−	0.987490i	$-0.449597\pi$
$461$	243373.	−	243373.i	1.14517	−	1.14517i	0.987490	−	0.157684i	$-0.0504027\pi$
$462$	−187884.	−	187884.i	−0.880247	−	0.880247i
$463$	199098.	−	199098.i	0.928764	−	0.928764i	−0.0688623	−	0.997626i	$-0.521937\pi$
$463$	199098.	−	199098.i	0.928764	−	0.928764i	0.997626	+	0.0688623i	$0.0219369\pi$
$464$	−58501.8	−	58501.8i	−0.271727	−	0.271727i
$465$		−	4869.46i		−	0.0225204i
$466$	−89868.3	+	89868.3i	−0.413842	+	0.413842i
$467$	−121421.	+	121421.i	−0.556752	+	0.556752i	−0.928381	−	0.371630i	$-0.878799\pi$
$467$	−121421.	+	121421.i	−0.556752	+	0.556752i	0.371630	+	0.928381i	$0.378799\pi$
$468$	−19411.8	−	19411.8i	−0.0886285	−	0.0886285i
$469$		−	87760.6i		−	0.398983i
$470$	−4677.73			−0.0211758
$471$		−	253728.i		−	1.14374i
$472$		−	52961.8i		−	0.237727i
$473$	−7507.98	−	7507.98i	−0.0335584	−	0.0335584i
$474$		−	20764.0i		−	0.0924177i
$475$	−309123.	−	309123.i	−1.37007	−	1.37007i
$476$	82016.8	+	82016.8i	0.361983	+	0.361983i
$477$	−41443.6			−0.182147
$478$	−39152.6			−0.171358
$479$	−113553.	+	113553.i	−0.494913	+	0.494913i	−0.909850	−	0.414937i	$-0.863803\pi$
$479$	−113553.	+	113553.i	−0.494913	+	0.494913i	0.414937	+	0.909850i	$0.363803\pi$
$480$			1058.51i			0.00459421i
$481$	−288217.	+	5752.70i	−1.24575	+	0.0248646i
$482$	280989.			1.20947
$483$	95847.1	+	95847.1i	0.410851	+	0.410851i
$484$		−	301568.i		−	1.28734i
$485$			3876.53i			0.0164801i
$486$	−46842.0	+	46842.0i	−0.198318	+	0.198318i
$487$	−72313.4	+	72313.4i	−0.304902	+	0.304902i	−0.842928	−	0.538026i	$-0.819170\pi$
$487$	−72313.4	+	72313.4i	−0.304902	+	0.304902i	0.538026	+	0.842928i	$0.319170\pi$
$488$	2445.20			0.0102677
$489$	338236.	−	338236.i	1.41450	−	1.41450i
$490$	−1119.97			−0.00466458
$491$	336707.			1.39665			0.698327	−	0.715779i	$-0.253928\pi$
$491$	336707.			1.39665			0.698327	+	0.715779i	$0.253928\pi$
$492$			112261.i			0.463765i
$493$	450221.			1.85239
$494$	−294743.	+	294743.i	−1.20779	+	1.20779i
$495$	1562.78	+	1562.78i	0.00637803	+	0.00637803i
$496$	−37685.8	−	37685.8i	−0.153184	−	0.153184i
$497$	341105.			1.38094
$498$	−144047.	+	144047.i	−0.580825	+	0.580825i
$499$	−33523.0	−	33523.0i	−0.134630	−	0.134630i	0.636580	−	0.771210i	$-0.280348\pi$
$499$	−33523.0	−	33523.0i	−0.134630	−	0.134630i	−0.771210	+	0.636580i	$0.780348\pi$
$500$	−4190.67	+	4190.67i	−0.0167627	+	0.0167627i
$501$	−171345.	−	171345.i	−0.682648	−	0.682648i
$502$			26129.7i			0.103688i
$503$	156227.	−	156227.i	0.617474	−	0.617474i	−0.327409	−	0.944883i	$-0.606175\pi$
$503$	156227.	−	156227.i	0.617474	−	0.617474i	0.944883	+	0.327409i	$0.106175\pi$
$504$	10854.6	−	10854.6i	0.0427319	−	0.0427319i
$505$	4053.83	+	4053.83i	0.0158958	+	0.0158958i
$506$			213594.i			0.834234i
$507$	−155653.			−0.605539
$508$		−	142962.i		−	0.553978i
$509$		−	37175.1i		−	0.143488i	−0.997423	−	0.0717441i	$-0.977143\pi$
$509$		−	37175.1i		−	0.143488i	0.997423	−	0.0717441i	$-0.0228565\pi$
$510$	−4073.05	−	4073.05i	−0.0156596	−	0.0156596i
$511$			70859.9i			0.271368i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	315844.	+	315844.i	1.20016	+	1.20016i
$514$	−22433.6			−0.0849128
$515$	−1089.60			−0.00410820
$516$	2589.74	−	2589.74i	0.00972651	−	0.00972651i
$517$			638225.i			2.38777i
$518$	−3216.77	−	161164.i	−0.0119884	−	0.600633i
$519$	−422560.			−1.56875
$520$	1997.30	+	1997.30i	0.00738647	+	0.00738647i
$521$		−	194228.i		−	0.715543i	−0.933809	−	0.357772i	$-0.883537\pi$
$521$		−	194228.i		−	0.715543i	0.933809	−	0.357772i	$-0.116463\pi$
$522$		−	59584.9i		−	0.218673i
$523$	108191.	−	108191.i	0.395538	−	0.395538i	−0.481118	−	0.876656i	$-0.659769\pi$
$523$	108191.	−	108191.i	0.395538	−	0.395538i	0.876656	+	0.481118i	$0.159769\pi$
$524$	96501.9	−	96501.9i	0.351458	−	0.351458i
$525$	256502.			0.930618
$526$	41598.4	−	41598.4i	0.150351	−	0.150351i
$527$	290024.			1.04427
$528$	144422.			0.518041
$529$			170878.i			0.610625i
$530$	4264.19			0.0151805
$531$	26971.2	−	26971.2i	0.0956557	−	0.0956557i
$532$	−164813.	−	164813.i	−0.582329	−	0.582329i
$533$	211826.	+	211826.i	0.745632	+	0.745632i
$534$	249380.			0.874539
$535$	6185.58	−	6185.58i	0.0216109	−	0.0216109i
$536$	33729.8	+	33729.8i	0.117404	+	0.117404i
$537$	−63680.0	+	63680.0i	−0.220828	+	0.220828i
$538$	−123791.	−	123791.i	−0.427685	−	0.427685i
$539$			152807.i			0.525976i
$540$	2140.29	−	2140.29i	0.00733983	−	0.00733983i
$541$	−133505.	+	133505.i	−0.456145	+	0.456145i	−0.897388	−	0.441243i	$-0.854538\pi$
$541$	−133505.	+	133505.i	−0.456145	+	0.456145i	0.441243	+	0.897388i	$0.354538\pi$
$542$	−217134.	−	217134.i	−0.739146	−	0.739146i
$543$			32516.3i			0.110281i
$544$	−63044.3			−0.213034
$545$			2390.90i			0.00804950i
$546$		−	244570.i		−	0.820384i
$547$	413647.	+	413647.i	1.38247	+	1.38247i	0.840216	+	0.542251i	$0.182428\pi$
$547$	413647.	+	413647.i	1.38247	+	1.38247i	0.542251	+	0.840216i	$0.317572\pi$
$548$			198199.i			0.659996i
$549$	1245.24	+	1245.24i	0.00413149	+	0.00413149i
$550$	285805.	+	285805.i	0.944810	+	0.944810i
$551$	−904721.			−2.97997
$552$	−73675.4			−0.241793
$553$	21908.4	−	21908.4i	0.0716407	−	0.0716407i
$554$			31971.6i			0.104171i
$555$	159.749	+	8003.60i	0.000518622	+	0.0259836i
$556$	168928.			0.546453
$557$	30623.4	+	30623.4i	0.0987059	+	0.0987059i	0.754735	−	0.656029i	$-0.227765\pi$
$557$	30623.4	+	30623.4i	0.0987059	+	0.0987059i	−0.656029	+	0.754735i	$0.727765\pi$
$558$		−	38383.5i		−	0.123275i
$559$		−	9773.20i		−	0.0312761i
$560$	−1116.84	+	1116.84i	−0.00356136	+	0.00356136i
$561$	−555723.	+	555723.i	−1.76576	+	1.76576i
$562$	32141.4			0.101763
$563$	182487.	−	182487.i	0.575724	−	0.575724i	−0.357999	−	0.933722i	$-0.616541\pi$
$563$	182487.	−	182487.i	0.575724	−	0.575724i	0.933722	+	0.357999i	$0.116541\pi$
$564$	−220144.			−0.692069
$565$	4894.40			0.0153321
$566$			166359.i			0.519294i
$567$	−317030.			−0.986131
$568$	−131100.	+	131100.i	−0.406355	+	0.406355i
$569$	−365764.	−	365764.i	−1.12974	−	1.12974i	−0.990220	−	0.139516i	$-0.955445\pi$
$569$	−365764.	−	365764.i	−1.12974	−	1.12974i	−0.139516	−	0.990220i	$-0.544555\pi$
$570$	8184.82	+	8184.82i	0.0251918	+	0.0251918i
$571$	217566.			0.667297			0.333649	−	0.942697i	$-0.391720\pi$
$571$	217566.			0.667297			0.333649	+	0.942697i	$0.391720\pi$
$572$	272510.	−	272510.i	0.832895	−	0.832895i
$573$	−337474.	−	337474.i	−1.02785	−	1.02785i
$574$	−118448.	+	118448.i	−0.359504	+	0.359504i
$575$	−145801.	−	145801.i	−0.440986	−	0.440986i
$576$			8343.66i			0.0251485i
$577$	−60861.3	+	60861.3i	−0.182806	+	0.182806i	−0.792577	−	0.609772i	$-0.791261\pi$
$577$	−60861.3	+	60861.3i	−0.182806	+	0.182806i	0.609772	+	0.792577i	$0.291261\pi$
$578$	75547.7	−	75547.7i	0.226134	−	0.226134i
$579$	433679.	+	433679.i	1.29363	+	1.29363i
$580$			6130.77i			0.0182246i
$581$	−303971.			−0.900492
$582$			182438.i			0.538604i
$583$		−	581802.i		−	1.71174i
$584$	−27234.2	−	27234.2i	−0.0798524	−	0.0798524i
$585$			2034.28i			0.00594428i
$586$	89652.5	+	89652.5i	0.261076	+	0.261076i
$587$	−200973.	−	200973.i	−0.583259	−	0.583259i	0.352538	−	0.935797i	$-0.385319\pi$
$587$	−200973.	−	200973.i	−0.583259	−	0.583259i	−0.935797	+	0.352538i	$0.885319\pi$
$588$	−52708.1			−0.152448
$589$	−582804.			−1.67993
$590$	−2775.10	+	2775.10i	−0.00797214	+	0.00797214i
$591$			19518.9i			0.0558831i
$592$	63177.9	+	60705.2i	0.180269	+	0.173214i
$593$	−102455.			−0.291356			−0.145678	−	0.989332i	$-0.546536\pi$
$593$	−102455.			−0.291356			−0.145678	+	0.989332i	$0.546536\pi$
$594$	−292020.	−	292020.i	−0.827635	−	0.827635i
$595$		−	8595.05i		−	0.0242781i
$596$		−	120011.i		−	0.337853i
$597$	13597.2	−	13597.2i	0.0381505	−	0.0381505i
$598$	−139019.	+	139019.i	−0.388750	+	0.388750i
$599$	648356.			1.80701			0.903503	−	0.428581i	$-0.140986\pi$
$599$	648356.			1.80701			0.903503	+	0.428581i	$0.140986\pi$
$600$	−98583.4	+	98583.4i	−0.273843	+	0.273843i
$601$	−72834.4			−0.201645			−0.100823	−	0.994904i	$-0.532147\pi$
$601$	−72834.4			−0.201645			−0.100823	+	0.994904i	$0.532147\pi$
$602$	5464.94			0.0150797
$603$			34354.2i			0.0944812i
$604$	−206888.			−0.567104
$605$	−15801.6	+	15801.6i	−0.0431708	+	0.0431708i
$606$	190782.	+	190782.i	0.519509	+	0.519509i
$607$	−401043.	−	401043.i	−1.08846	−	1.08846i	−0.995687	−	0.0927752i	$-0.970426\pi$
$607$	−401043.	−	401043.i	−1.08846	−	1.08846i	−0.0927752	−	0.995687i	$-0.529574\pi$
$608$	126688.			0.342711
$609$	375356.	−	375356.i	1.01207	−	1.01207i
$610$	−128.124	−	128.124i	−0.000344327	−	0.000344327i
$611$	−415392.	+	415392.i	−1.11269	+	1.11269i
$612$	−32105.8	−	32105.8i	−0.0857196	−	0.0857196i
$613$			412517.i			1.09779i	0.835890	+	0.548897i	$0.184952\pi$
$613$			412517.i			1.09779i	−0.835890	+	0.548897i	$0.815048\pi$
$614$	97543.2	−	97543.2i	0.258738	−	0.258738i
$615$	5882.26	−	5882.26i	0.0155523	−	0.0155523i
$616$	152381.	+	152381.i	0.401577	+	0.401577i
$617$		−	18944.7i		−	0.0497642i	−0.999690	−	0.0248821i	$-0.992079\pi$
$617$		−	18944.7i		−	0.0497642i	0.999690	−	0.0248821i	$-0.00792104\pi$
$618$	−51278.9			−0.134265
$619$			692500.i			1.80733i	0.428236	+	0.903667i	$0.359135\pi$
$619$			692500.i			1.80733i	−0.428236	+	0.903667i	$0.640865\pi$
$620$			3949.33i			0.0102740i
$621$	148971.	+	148971.i	0.386295	+	0.386295i
$622$		−	179063.i		−	0.462833i
$623$	263124.	+	263124.i	0.677929	+	0.677929i
$624$	93997.5	+	93997.5i	0.241405	+	0.241405i
$625$	−389966.			−0.998313
$626$	201121.			0.513227
$627$	1.11673e6	−	1.11673e6i	2.84062	−	2.84062i
$628$			205784.i			0.521785i
$629$	−476692.	+	9514.57i	−1.20486	+	0.0240485i
$630$	−1137.52			−0.00286601
$631$	−161432.	−	161432.i	−0.405445	−	0.405445i	0.474702	−	0.880147i	$-0.342556\pi$
$631$	−161432.	−	161432.i	−0.405445	−	0.405445i	−0.880147	+	0.474702i	$0.842556\pi$
$632$			16840.4i			0.0421618i
$633$			711417.i			1.77548i
$634$	67573.3	−	67573.3i	0.168111	−	0.168111i
$635$	−7490.92	+	7490.92i	−0.0185775	+	0.0185775i
$636$	200682.			0.496129
$637$	−99455.3	+	99455.3i	−0.245103	+	0.245103i
$638$	836476.			2.05500
$639$	−133527.			−0.327014
$640$		−	858.491i		−	0.00209592i
$641$	352728.			0.858467			0.429233	−	0.903194i	$-0.358784\pi$
$641$	352728.			0.858467			0.429233	+	0.903194i	$0.358784\pi$
$642$	291107.	−	291107.i	0.706289	−	0.706289i
$643$	−121050.	−	121050.i	−0.292781	−	0.292781i	0.545397	−	0.838178i	$-0.316379\pi$
$643$	−121050.	−	121050.i	−0.292781	−	0.292781i	−0.838178	+	0.545397i	$0.816379\pi$
$644$	−77735.8	−	77735.8i	−0.187434	−	0.187434i
$645$	−271.395			−0.000652353
$646$	−487485.	+	487485.i	−1.16814	+	1.16814i
$647$	−312890.	−	312890.i	−0.747452	−	0.747452i	0.226548	−	0.974000i	$-0.427256\pi$
$647$	−312890.	−	312890.i	−0.747452	−	0.747452i	−0.974000	+	0.226548i	$0.927256\pi$
$648$	121847.	−	121847.i	0.290178	−	0.290178i
$649$	378632.	+	378632.i	0.898934	+	0.898934i
$650$			372035.i			0.880557i
$651$	241798.	−	241798.i	0.570545	−	0.570545i
$652$	−274323.	+	274323.i	−0.645308	+	0.645308i
$653$	−24052.3	−	24052.3i	−0.0564066	−	0.0564066i	0.678341	−	0.734747i	$-0.262699\pi$
$653$	−24052.3	−	24052.3i	−0.0564066	−	0.0564066i	−0.734747	+	0.678341i	$0.762699\pi$
$654$			112521.i			0.263074i
$655$	−10113.0			−0.0235721
$656$		−	91048.0i		−	0.211574i
$657$		−	27738.4i		−	0.0642614i
$658$	−232277.	−	232277.i	−0.536481	−	0.536481i
$659$		−	410288.i		−	0.944752i	−0.881397	−	0.472376i	$-0.843396\pi$
$659$		−	410288.i		−	0.944752i	0.881397	−	0.472376i	$-0.156604\pi$
$660$	−7567.42	−	7567.42i	−0.0173724	−	0.0173724i
$661$	−434781.	−	434781.i	−0.995102	−	0.995102i	0.00488646	−	0.999988i	$-0.498445\pi$
$661$	−434781.	−	434781.i	−0.995102	−	0.995102i	−0.999988	+	0.00488646i	$0.998445\pi$
$662$	70837.7			0.161640
$663$	−723390.			−1.64568
$664$	116828.	−	116828.i	0.264978	−	0.264978i
$665$			17271.8i			0.0390566i
$666$	1259.22	+	63088.3i	0.00283891	+	0.142233i
$667$	−426721.			−0.959162
$668$	138968.	+	138968.i	0.311430	+	0.311430i
$669$			131753.i			0.294379i
$670$		−	3534.75i		−	0.00787425i
$671$	−17481.1	+	17481.1i	−0.0388261	+	0.0388261i
$672$	−52561.1	+	52561.1i	−0.116393	+	0.116393i
$673$	11069.6			0.0244401			0.0122200	−	0.999925i	$-0.496110\pi$
$673$	11069.6			0.0244401			0.0122200	+	0.999925i	$0.496110\pi$
$674$	−67900.8	+	67900.8i	−0.149470	+	0.149470i
$675$	398670.			0.874996
$676$	126241.			0.276253
$677$			49954.5i			0.108993i	0.998514	+	0.0544963i	$0.0173553\pi$
$677$			49954.5i			0.108993i	−0.998514	+	0.0544963i	$0.982645\pi$
$678$	230341.			0.501086
$679$	−192493.	+	192493.i	−0.417517	+	0.417517i
$680$	3303.40	+	3303.40i	0.00714404	+	0.00714404i
$681$	−203263.	−	203263.i	−0.438293	−	0.438293i
$682$	538842.			1.15849
$683$	540.685	−	540.685i	0.00115905	−	0.00115905i	−0.706527	−	0.707686i	$-0.749739\pi$
$683$	540.685	−	540.685i	0.00115905	−	0.00115905i	0.707686	+	0.706527i	$0.249739\pi$
$684$	64516.7	+	64516.7i	0.137899	+	0.137899i
$685$	10385.3	−	10385.3i	0.0221328	−	0.0221328i
$686$	−255520.	−	255520.i	−0.542971	−	0.542971i
$687$			44185.1i			0.0936187i
$688$	−2100.38	+	2100.38i	−0.00443733	+	0.00443733i
$689$	378668.	−	378668.i	0.797665	−	0.797665i
$690$	3860.45	+	3860.45i	0.00810849	+	0.00810849i
$691$		−	406883.i		−	0.852144i	−0.904689	−	0.426072i	$-0.859897\pi$
$691$		−	406883.i		−	0.852144i	0.904689	−	0.426072i	$-0.140103\pi$
$692$	342713.			0.715678
$693$			155202.i			0.323170i
$694$		−	52853.9i		−	0.109738i
$695$	−8851.52	−	8851.52i	−0.0183252	−	0.0183252i
$696$			288527.i			0.595619i
$697$	350346.	+	350346.i	0.721159	+	0.721159i
$698$	−172142.	−	172142.i	−0.353326	−	0.353326i
$699$	443225.			0.907132
$700$	−208033.			−0.424557
$701$	309980.	−	309980.i	0.630809	−	0.630809i	−0.317462	−	0.948271i	$-0.602831\pi$
$701$	309980.	−	309980.i	0.630809	−	0.630809i	0.948271	+	0.317462i	$0.102831\pi$
$702$		−	380125.i		−	0.771350i
$703$	957916.	−	19119.6i	1.93828	−	0.0386873i
$704$	−117132.			−0.236335
$705$	11535.1	+	11535.1i	0.0232084	+	0.0232084i
$706$		−	475492.i		−	0.953968i
$707$			402594.i			0.805430i
$708$	−130602.	+	130602.i	−0.260546	+	0.260546i
$709$	199022.	−	199022.i	0.395921	−	0.395921i	−0.480871	−	0.876792i	$-0.659679\pi$
$709$	199022.	−	199022.i	0.395921	−	0.395921i	0.876792	+	0.480871i	$0.159679\pi$
$710$	13738.8			0.0272540
$711$	−8576.11	+	8576.11i	−0.0169649	+	0.0169649i
$712$	−202257.			−0.398973
$713$	−274886.			−0.540720
$714$		−	404502.i		−	0.793458i
$715$	−28558.0			−0.0558620
$716$	51647.0	−	51647.0i	0.100744	−	0.100744i
$717$	96549.2	+	96549.2i	0.187806	+	0.187806i
$718$	−428856.	−	428856.i	−0.831883	−	0.831883i
$719$	491351.			0.950460			0.475230	−	0.879862i	$-0.342365\pi$
$719$	491351.			0.950460			0.475230	+	0.879862i	$0.342365\pi$
$720$	437.192	−	437.192i	0.000843349	−	0.000843349i
$721$	−54104.9	−	54104.9i	−0.104080	−	0.104080i
$722$	718962.	−	718962.i	1.37921	−	1.37921i
$723$	−692912.	−	692912.i	−1.32557	−	1.32557i
$724$		−	26372.0i		−	0.0503114i
$725$	−570985.	+	570985.i	−1.08630	+	1.08630i
$726$	−743657.	+	743657.i	−1.41091	+	1.41091i
$727$	−104442.	−	104442.i	−0.197610	−	0.197610i	0.601365	−	0.798975i	$-0.294624\pi$
$727$	−104442.	−	104442.i	−0.197610	−	0.197610i	−0.798975	+	0.601365i	$0.794624\pi$
$728$			198356.i			0.374267i
$729$	−385827.			−0.726002
$730$			2854.04i			0.00535567i
$731$		−	16164.2i		−	0.0302496i
$732$	−6029.80	−	6029.80i	−0.0112533	−	0.0112533i
$733$			945135.i			1.75908i	0.475824	+	0.879541i	$0.342150\pi$
$733$			945135.i			1.75908i	−0.475824	+	0.879541i	$0.657850\pi$
$734$	−360249.	−	360249.i	−0.668669	−	0.668669i
$735$	2761.81	+	2761.81i	0.00511233	+	0.00511233i
$736$	59753.6			0.110308
$737$	−482278.			−0.887897
$738$	46366.8	−	46366.8i	0.0851324	−	0.0851324i
$739$			331637.i			0.607259i	0.952790	+	0.303629i	$0.0981985\pi$
$739$			331637.i			0.607259i	−0.952790	+	0.303629i	$0.901802\pi$
$740$	−129.562	−	6491.24i	−0.000236600	−	0.0118540i
$741$	1.45366e6			2.64743
$742$	211742.	+	211742.i	0.384591	+	0.384591i
$743$		−	281251.i		−	0.509468i	−0.967011	−	0.254734i	$-0.918012\pi$
$743$		−	281251.i		−	0.509468i	0.967011	−	0.254734i	$-0.0819879\pi$
$744$			185864.i			0.335776i
$745$	−6288.33	+	6288.33i	−0.0113298	+	0.0113298i
$746$	−173148.	+	173148.i	−0.311129	+	0.311129i
$747$	118991.			0.213241
$748$	450713.	−	450713.i	0.805559	−	0.805559i
$749$	614301.			1.09501
$750$	20668.1			0.0367434
$751$			114550.i			0.203102i	0.994830	+	0.101551i	$0.0323806\pi$
$751$			114550.i			0.203102i	−0.994830	+	0.101551i	$0.967619\pi$
$752$	178546.			0.315728
$753$	64435.2	−	64435.2i	0.113640	−	0.113640i
$754$	544424.	+	544424.i	0.957624	+	0.957624i
$755$	10840.6	+	10840.6i	0.0190177	+	0.0190177i
$756$	212556.			0.371904
$757$	−188444.	+	188444.i	−0.328844	+	0.328844i	−0.852147	−	0.523303i	$-0.824700\pi$
$757$	−188444.	+	188444.i	−0.328844	+	0.328844i	0.523303	+	0.852147i	$0.324700\pi$
$758$	−169147.	−	169147.i	−0.294392	−	0.294392i
$759$	526716.	−	526716.i	0.914309	−	0.914309i
$760$	−6638.21	−	6638.21i	−0.0114927	−	0.0114927i
$761$			41512.5i			0.0716820i	0.999358	+	0.0358410i	$0.0114110\pi$
$761$			41512.5i			0.0716820i	−0.999358	+	0.0358410i	$0.988589\pi$
$762$	−352539.	+	352539.i	−0.607152	+	0.607152i
$763$	−118722.	+	118722.i	−0.203931	+	0.203931i
$764$	273705.	+	273705.i	0.468917	+	0.468917i
$765$			3364.56i			0.00574918i
$766$	−602411.			−1.02668
$767$			492869.i			0.837800i
$768$		−	40402.5i		−	0.0684992i
$769$	434322.	+	434322.i	0.734444	+	0.734444i	0.971497	−	0.237053i	$-0.0761814\pi$
$769$	434322.	+	434322.i	0.734444	+	0.734444i	−0.237053	+	0.971497i	$0.576181\pi$
$770$		−	15968.9i		−	0.0269336i
$771$	55320.7	+	55320.7i	0.0930633	+	0.0930633i
$772$	−351731.	−	351731.i	−0.590168	−	0.590168i
$773$	−334031.			−0.559020			−0.279510	−	0.960143i	$-0.590172\pi$
$773$	−334031.			−0.559020			−0.279510	+	0.960143i	$0.590172\pi$
$774$	−2139.27			−0.00357095
$775$	−367818.	+	367818.i	−0.612392	+	0.612392i
$776$		−	147965.i		−	0.245716i
$777$	−389494.	+	405359.i	−0.645146	+	0.671425i
$778$	−476507.			−0.787245
$779$	−704022.	−	704022.i	−1.16014	−	1.16014i
$780$		−	9850.58i		−	0.0161910i
$781$		−	1.87450e6i		−	3.07315i
$782$	−229927.	+	229927.i	−0.375991	+	0.375991i
$783$	583401.	−	583401.i	0.951576	−	0.951576i
$784$	42748.4			0.0695484
$785$	10782.7	−	10782.7i	0.0174979	−	0.0174979i
$786$	−475942.			−0.770387
$787$	998022.			1.61135			0.805676	−	0.592356i	$-0.201802\pi$
$787$	998022.			1.61135			0.805676	+	0.592356i	$0.201802\pi$
$788$		−	15830.6i		−	0.0254944i
$789$	−205161.			−0.329565
$790$	882.408	−	882.408i	0.00141389	−	0.00141389i
$791$	243036.	+	243036.i	0.388434	+	0.388434i
$792$	−59650.1	−	59650.1i	−0.0950957	−	0.0950957i
$793$	−22755.3			−0.0361857
$794$	280290.	−	280290.i	0.444596	−	0.444596i
$795$	−10515.4	−	10515.4i	−0.0166376	−	0.0166376i
$796$	−11027.8	+	11027.8i	−0.0174046	+	0.0174046i
$797$	−319375.	−	319375.i	−0.502788	−	0.502788i	0.409516	−	0.912303i	$-0.365698\pi$
$797$	−319375.	−	319375.i	−0.502788	−	0.502788i	−0.912303	+	0.409516i	$0.865698\pi$
$798$			812849.i			1.27645i
$799$	−687030.	+	687030.i	−1.07617	+	1.07617i
$800$	79955.0	−	79955.0i	0.124930	−	0.124930i
$801$	−103001.	−	103001.i	−0.160537	−	0.160537i
$802$		−	12773.1i		−	0.0198585i
$803$	389402.			0.603903
$804$		−	166353.i		−	0.257347i
$805$			8146.41i			0.0125711i
$806$	350708.	+	350708.i	0.539853	+	0.539853i
$807$			610529.i			0.937474i
$808$	−154732.	−	154732.i	−0.237005	−	0.237005i
$809$	−2424.91	−	2424.91i	−0.00370508	−	0.00370508i	0.705252	−	0.708957i	$-0.250834\pi$
$809$	−2424.91	−	2424.91i	−0.00370508	−	0.00370508i	−0.708957	+	0.705252i	$0.750834\pi$
$810$	−12769.1			−0.0194621
$811$	503796.			0.765972			0.382986	−	0.923754i	$-0.374896\pi$
$811$	503796.			0.765972			0.382986	+	0.923754i	$0.374896\pi$
$812$	−304429.	+	304429.i	−0.461715	+	0.461715i
$813$			1.07089e6i			1.62019i
$814$	−885658.	+	17677.4i	−1.33665	+	0.0266789i
$815$	28748.0			0.0432805
$816$	155466.	+	155466.i	0.233482	+	0.233482i
$817$			32482.1i			0.0486631i
$818$		−	247765.i		−	0.370282i
$819$	−101014.	+	101014.i	−0.150596	+	0.150596i
$820$	−4770.75	+	4770.75i	−0.00709510	+	0.00709510i
$821$	135542.			0.201088			0.100544	−	0.994933i	$-0.467942\pi$
$821$	135542.			0.201088			0.100544	+	0.994933i	$0.467942\pi$
$822$	488754.	−	488754.i	0.723347	−	0.723347i
$823$	−639911.			−0.944757			−0.472378	−	0.881396i	$-0.656604\pi$
$823$	−639911.			−0.944757			−0.472378	+	0.881396i	$0.656604\pi$
$824$	41589.2			0.0612528
$825$		−	1.40957e6i		−	2.07100i
$826$	−275600.			−0.403942
$827$	−637094.	+	637094.i	−0.931521	+	0.931521i	−0.997801	−	0.0662799i	$-0.978887\pi$
$827$	−637094.	+	637094.i	−0.931521	+	0.931521i	0.0662799	+	0.997801i	$0.478887\pi$
$828$	30429.9	+	30429.9i	0.0443854	+	0.0443854i
$829$	−161166.	−	161166.i	−0.234512	−	0.234512i	0.580061	−	0.814573i	$-0.303029\pi$
$829$	−161166.	−	161166.i	−0.234512	−	0.234512i	−0.814573	+	0.580061i	$0.803029\pi$
$830$	−12243.1			−0.0177720
$831$	78841.2	−	78841.2i	0.114170	−	0.114170i
$832$	−76235.7	−	76235.7i	−0.110132	−	0.110132i
$833$	−164492.	+	164492.i	−0.237059	+	0.237059i
$834$	−416572.	−	416572.i	−0.598905	−	0.598905i
$835$		−	14563.3i		−	0.0208875i
$836$	−905711.	+	905711.i	−1.29592	+	1.29592i
$837$	375816.	−	375816.i	0.536444	−	0.536444i
$838$	306034.	+	306034.i	0.435794	+	0.435794i
$839$		−	10918.3i		−	0.0155107i	−0.999970	−	0.00775536i	$-0.997531\pi$
$839$		−	10918.3i		−	0.0155107i	0.999970	−	0.00775536i	$-0.00246863\pi$
$840$	5508.20			0.00780641
$841$			963842.i			1.36274i
$842$			293019.i			0.413305i
$843$	−79259.7	−	79259.7i	−0.111531	−	0.111531i
$844$		−	576987.i		−	0.809993i
$845$	−6614.78	−	6614.78i	−0.00926408	−	0.00926408i
$846$	90925.6	+	90925.6i	0.127041	+	0.127041i
$847$	−1.56928e6			−2.18743
$848$	−162761.			−0.226339
$849$	410236.	−	410236.i	0.569140	−	0.569140i
$850$			615321.i			0.851656i
$851$	451811.	−	9017.95i	0.623875	−	0.0124523i
$852$	646576.			0.890719
$853$	306706.	+	306706.i	0.421525	+	0.421525i	0.885729	−	0.464203i	$-0.153659\pi$
$853$	306706.	+	306706.i	0.421525	+	0.421525i	−0.464203	+	0.885729i	$0.653659\pi$
$854$		−	12724.2i		−	0.0174468i
$855$		−	6761.11i		−	0.00924880i
$856$	−236099.	+	236099.i	−0.322216	+	0.322216i
$857$	−191457.	+	191457.i	−0.260681	+	0.260681i	−0.825330	−	0.564650i	$-0.809011\pi$
$857$	−191457.	+	191457.i	−0.260681	+	0.260681i	0.564650	+	0.825330i	$0.309011\pi$
$858$	−1.34400e6			−1.82569
$859$	−295893.	+	295893.i	−0.401004	+	0.401004i	−0.878587	−	0.477583i	$-0.841513\pi$
$859$	−295893.	+	295893.i	−0.401004	+	0.401004i	0.477583	+	0.878587i	$0.341513\pi$
$860$	220.112			0.000297610
$861$	584178.			0.788023
$862$		−	410437.i		−	0.552372i
$863$	−156578.			−0.210237			−0.105118	−	0.994460i	$-0.533522\pi$
$863$	−156578.			−0.210237			−0.105118	+	0.994460i	$0.533522\pi$
$864$	−81693.5	+	81693.5i	−0.109436	+	0.109436i
$865$	−17957.5	−	17957.5i	−0.0240001	−	0.0240001i
$866$	165318.	+	165318.i	0.220437	+	0.220437i
$867$	−372597.			−0.495679
$868$	−196107.	+	196107.i	−0.260288	+	0.260288i
$869$	−120395.	−	120395.i	−0.159429	−	0.159429i
$870$	15118.3	−	15118.3i	0.0199740	−	0.0199740i
$871$	−313893.	−	313893.i	−0.413757	−	0.413757i
$872$		−	91259.1i		−	0.120017i
$873$	75351.9	−	75351.9i	0.0988703	−	0.0988703i
$874$	462040.	−	462040.i	0.604863	−	0.604863i
$875$	21807.2	+	21807.2i	0.0284829	+	0.0284829i
$876$			134317.i			0.175034i
$877$	1.20541e6			1.56723			0.783617	−	0.621244i	$-0.213372\pi$
$877$	1.20541e6			1.56723			0.783617	+	0.621244i	$0.213372\pi$
$878$		−	124792.i		−	0.161882i
$879$		−	442161.i		−	0.572272i
$880$	6137.48	+	6137.48i	0.00792546	+	0.00792546i
$881$			628321.i			0.809524i	0.914422	+	0.404762i	$0.132646\pi$
$881$			628321.i			0.809524i	−0.914422	+	0.404762i	$0.867354\pi$
$882$	21769.9	+	21769.9i	0.0279846	+	0.0279846i
$883$	−760524.	−	760524.i	−0.975419	−	0.975419i	0.0242858	−	0.999705i	$-0.492269\pi$
$883$	−760524.	−	760524.i	−0.975419	−	0.975419i	−0.999705	+	0.0242858i	$0.992269\pi$
$884$	586698.			0.750775
$885$	13686.6			0.0174747
$886$	117247.	−	117247.i	0.149360	−	0.149360i
$887$			799761.i			1.01651i	0.861206	+	0.508257i	$0.169710\pi$
$887$			799761.i			1.01651i	−0.861206	+	0.508257i	$0.830290\pi$
$888$	−6097.49	−	305492.i	−0.00773259	−	0.387413i
$889$	−743937.			−0.941310
$890$	10597.9	+	10597.9i	0.0133795	+	0.0133795i
$891$			1.74220e6i			2.19454i
$892$		−	106857.i		−	0.134299i
$893$	1.38059e6	−	1.38059e6i	1.73126	−	1.73126i
$894$	−295943.	+	295943.i	−0.370282	+	0.370282i
$895$	−5412.41			−0.00675685
$896$	42629.1	−	42629.1i	0.0530995	−	0.0530995i
$897$	685631.			0.852130
$898$	51110.6			0.0633809
$899$			1.07651e6i			1.33198i
$900$	81435.3			0.100537
$901$	626292.	−	626292.i	0.771485	−	0.771485i
$902$	650916.	+	650916.i	0.800040	+	0.800040i
$903$	−13476.4	−	13476.4i	−0.0165271	−	0.0165271i
$904$	−186816.			−0.228600
$905$	−1381.84	+	1381.84i	−0.00168718	+	0.00168718i
$906$	510181.	+	510181.i	0.621538	+	0.621538i
$907$	133248.	−	133248.i	0.161974	−	0.161974i	−0.621467	−	0.783441i	$-0.713463\pi$
$907$	133248.	−	133248.i	0.161974	−	0.161974i	0.783441	+	0.621467i	$0.213463\pi$
$908$	164854.	+	164854.i	0.199953	+	0.199953i
$909$		−	157597.i		−	0.190730i
$910$	10393.5	−	10393.5i	0.0125510	−	0.0125510i
$911$	−59075.8	+	59075.8i	−0.0711825	+	0.0711825i	−0.741802	−	0.670619i	$-0.766028\pi$
$911$	−59075.8	+	59075.8i	−0.0711825	+	0.0711825i	0.670619	+	0.741802i	$0.266028\pi$
$912$	−312409.	−	312409.i	−0.375607	−	0.375607i
$913$			1.67044e6i			2.00396i
$914$	684971.			0.819936
$915$			631.900i			0.000754755i
$916$		−	35835.9i		−	0.0427098i
$917$	−502172.	−	502172.i	−0.597192	−	0.597192i
$918$		−	628701.i		−	0.746034i
$919$	412460.	+	412460.i	0.488372	+	0.488372i	0.907792	−	0.419420i	$-0.137767\pi$
$919$	412460.	+	412460.i	0.488372	+	0.488372i	−0.419420	+	0.907792i	$0.637767\pi$
$920$	−3130.98	−	3130.98i	−0.00369917	−	0.00369917i
$921$	−481078.			−0.567147
$922$	973494.			1.14517
$923$	1.22003e6	−	1.22003e6i	1.43208	−	1.43208i
$924$		−	751534.i		−	0.880247i
$925$	592491.	−	616624.i	0.692466	−	0.720671i
$926$	796393.			0.928764
$927$	21179.6	+	21179.6i	0.0246466	+	0.0246466i
$928$		−	234007.i		−	0.271727i
$929$			363273.i			0.420922i	0.977602	+	0.210461i	$0.0674964\pi$
$929$			363273.i			0.420922i	−0.977602	+	0.210461i	$0.932504\pi$
$930$	9738.93	−	9738.93i	0.0112602	−	0.0112602i
$931$	330548.	−	330548.i	0.381360	−	0.381360i
$932$	−359473.			−0.413842
$933$	−441564.	+	441564.i	−0.507259	+	0.507259i
$934$	−485686.			−0.556752
$935$	−47233.1			−0.0540285
$936$		−	77647.1i		−	0.0886285i
$937$	−350225.			−0.398903			−0.199452	−	0.979908i	$-0.563916\pi$
$937$	−350225.			−0.398903			−0.199452	+	0.979908i	$0.563916\pi$
$938$	175521.	−	175521.i	0.199491	−	0.199491i
$939$	−495959.	−	495959.i	−0.562490	−	0.562490i
$940$	−9355.46	−	9355.46i	−0.0105879	−	0.0105879i
$941$	−1.53166e6			−1.72975			−0.864876	−	0.501985i	$-0.832603\pi$
$941$	−1.53166e6			−1.72975			−0.864876	+	0.501985i	$0.832603\pi$
$942$	507456.	−	507456.i	0.571869	−	0.571869i
$943$	−332059.	−	332059.i	−0.373415	−	0.373415i
$944$	105924.	−	105924.i	0.118864	−	0.118864i
$945$	−11137.6	−	11137.6i	−0.0124717	−	0.0124717i
$946$		−	30031.9i		−	0.0335584i
$947$	−977973.	+	977973.i	−1.09050	+	1.09050i	−0.0950286	+	0.995475i	$0.530294\pi$
$947$	−977973.	+	977973.i	−1.09050	+	1.09050i	−0.995475	+	0.0950286i	$0.969706\pi$
$948$	41528.1	−	41528.1i	0.0462088	−	0.0462088i
$949$	253444.	+	253444.i	0.281417	+	0.281417i
$950$		−	1.23649e6i		−	1.37007i
$951$	−333268.			−0.368495
$952$			328067.i			0.361983i
$953$			462445.i			0.509184i	0.967049	+	0.254592i	$0.0819411\pi$
$953$			462445.i			0.509184i	−0.967049	+	0.254592i	$0.918059\pi$
$954$	−82887.2	−	82887.2i	−0.0910733	−	0.0910733i
$955$		−	28683.2i		−	0.0314500i
$956$	−78305.2	−	78305.2i	−0.0856791	−	0.0856791i
$957$	−2.06273e6	−	2.06273e6i	−2.25226	−	2.25226i
$958$	−454213.			−0.494913
$959$	1.03138e6			1.12145
$960$	−2117.01	+	2117.01i	−0.00229711	+	0.00229711i
$961$		−	230055.i		−	0.249107i
$962$	−587940.	−	564929.i	−0.635306	−	0.610442i
$963$	−240470.			−0.259304
$964$	561979.	+	561979.i	0.604736	+	0.604736i
$965$			36860.1i			0.0395823i
$966$			383388.i			0.410851i
$967$	1.16299e6	−	1.16299e6i	1.24372	−	1.24372i	0.285278	−	0.958445i	$-0.407914\pi$
$967$	1.16299e6	−	1.16299e6i	1.24372	−	1.24372i	0.958445	−	0.285278i	$-0.0920859\pi$
$968$	603136.	−	603136.i	0.643671	−	0.643671i
$969$	2.40425e6			2.56054
$970$	−7753.06	+	7753.06i	−0.00824005	+	0.00824005i
$971$	−891615.			−0.945669			−0.472834	−	0.881151i	$-0.656769\pi$
$971$	−891615.			−0.945669			−0.472834	+	0.881151i	$0.656769\pi$
$972$	−187368.			−0.198318
$973$		−	879060.i		−	0.928524i
$974$	−289254.			−0.304902
$975$	917428.	−	917428.i	0.965079	−	0.965079i
$976$	4890.40	+	4890.40i	0.00513387	+	0.00513387i
$977$	743587.	+	743587.i	0.779010	+	0.779010i	0.979662	−	0.200653i	$-0.0643063\pi$
$977$	743587.	+	743587.i	0.779010	+	0.779010i	−0.200653	+	0.979662i	$0.564306\pi$
$978$	1.35294e6			1.41450
$979$	1.44597e6	−	1.44597e6i	1.50867	−	1.50867i
$980$	−2239.93	−	2239.93i	−0.00233229	−	0.00233229i
$981$	46474.3	−	46474.3i	0.0482920	−	0.0482920i
$982$	673413.	+	673413.i	0.698327	+	0.698327i
$983$		−	1.06116e6i		−	1.09818i	−0.835762	−	0.549092i	$-0.814974\pi$
$983$		−	1.06116e6i		−	1.09818i	0.835762	−	0.549092i	$-0.185026\pi$
$984$	−224522.	+	224522.i	−0.231883	+	0.231883i
$985$	−829.493	+	829.493i	−0.000854949	+	0.000854949i
$986$	900441.	+	900441.i	0.926193	+	0.926193i
$987$			1.14558e6i			1.17595i
$988$	−1.17897e6			−1.20779
$989$			15320.5i			0.0156632i
$990$			6251.10i			0.00637803i
$991$	478651.	+	478651.i	0.487384	+	0.487384i	0.907480	−	0.420096i	$-0.138004\pi$
$991$	478651.	+	478651.i	0.487384	+	0.487384i	−0.420096	+	0.907480i	$0.638004\pi$
$992$		−	150743.i		−	0.153184i
$993$	−174684.	−	174684.i	−0.177155	−	0.177155i
$994$	682210.	+	682210.i	0.690471	+	0.690471i
$995$	1155.68			0.00116732
$996$	−576187.			−0.580825
$997$	−277587.	+	277587.i	−0.279260	+	0.279260i	−0.832814	−	0.553554i	$-0.813271\pi$
$997$	−277587.	+	277587.i	−0.279260	+	0.279260i	0.553554	+	0.832814i	$0.313271\pi$
$998$		−	134092.i		−	0.134630i
$999$	−605374.	+	630032.i	−0.606586	+	0.631294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.b.31.3	✓	14
37.6	odd	4	inner	74.5.d.b.43.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.b.31.3	✓	14	1.1	even	1	trivial
74.5.d.b.43.5	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} -9.86388i q^{3} +8.00000i q^{4} +(0.419185 - 0.419185i) q^{5} +(19.7278 - 19.7278i) q^{6} +41.6300 q^{7} +(-16.0000 + 16.0000i) q^{8} -16.2962 q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} -9.86388i q^{3} +8.00000i q^{4} +(0.419185 - 0.419185i) q^{5} +(19.7278 - 19.7278i) q^{6} +41.6300 q^{7} +(-16.0000 + 16.0000i) q^{8} -16.2962 q^{9} +1.67674 q^{10} -228.773i q^{11} +78.9111 q^{12} +(148.898 - 148.898i) q^{13} +(83.2600 + 83.2600i) q^{14} +(-4.13479 - 4.13479i) q^{15} -64.0000 q^{16} +(246.267 - 246.267i) q^{17} +(-32.5924 - 32.5924i) q^{18} +(-494.875 + 494.875i) q^{19} +(3.35348 + 3.35348i) q^{20} -410.634i q^{21} +(457.545 - 457.545i) q^{22} +(-233.413 + 233.413i) q^{23} +(157.822 + 157.822i) q^{24} +624.649i q^{25} +595.591 q^{26} -638.231i q^{27} +333.040i q^{28} +(914.091 + 914.091i) q^{29} -16.5392i q^{30} +(588.840 + 588.840i) q^{31} +(-128.000 - 128.000i) q^{32} -2256.59 q^{33} +985.068 q^{34} +(17.4507 - 17.4507i) q^{35} -130.370i q^{36} +(-987.154 - 948.519i) q^{37} -1979.50 q^{38} +(-1468.71 - 1468.71i) q^{39} +13.4139i q^{40} +1422.63i q^{41} +(821.267 - 821.267i) q^{42} +(32.8185 - 32.8185i) q^{43} +1830.18 q^{44} +(-6.83113 + 6.83113i) q^{45} -933.651 q^{46} -2789.78 q^{47} +631.289i q^{48} -667.943 q^{49} +(-1249.30 + 1249.30i) q^{50} +(-2429.15 - 2429.15i) q^{51} +(1191.18 + 1191.18i) q^{52} +2543.14 q^{53} +(1276.46 - 1276.46i) q^{54} +(-95.8981 - 95.8981i) q^{55} +(-666.080 + 666.080i) q^{56} +(4881.39 + 4881.39i) q^{57} +3656.36i q^{58} +(-1655.06 + 1655.06i) q^{59} +(33.0783 - 33.0783i) q^{60} +(-76.4126 - 76.4126i) q^{61} +2355.36i q^{62} -678.411 q^{63} -512.000i q^{64} -124.831i q^{65} +(-4513.18 - 4513.18i) q^{66} -2108.11i q^{67} +(1970.14 + 1970.14i) q^{68} +(2302.36 + 2302.36i) q^{69} +69.8027 q^{70} +8193.73 q^{71} +(260.739 - 260.739i) q^{72} +1702.13i q^{73} +(-77.2704 - 3871.35i) q^{74} +6161.46 q^{75} +(-3959.00 - 3959.00i) q^{76} -9523.81i q^{77} -5874.84i q^{78} +(526.264 - 526.264i) q^{79} +(-26.8278 + 26.8278i) q^{80} -7615.43 q^{81} +(-2845.25 + 2845.25i) q^{82} -7301.73 q^{83} +3285.07 q^{84} -206.463i q^{85} +131.274 q^{86} +(9016.48 - 9016.48i) q^{87} +(3660.36 + 3660.36i) q^{88} +(6320.54 + 6320.54i) q^{89} -27.3245 q^{90} +(6198.62 - 6198.62i) q^{91} +(-1867.30 - 1867.30i) q^{92} +(5808.25 - 5808.25i) q^{93} +(-5579.55 - 5579.55i) q^{94} +414.888i q^{95} +(-1262.58 + 1262.58i) q^{96} +(-4623.89 + 4623.89i) q^{97} +(-1335.89 - 1335.89i) q^{98} +3728.13i 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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