LMFDB - Embedded newform 152.6.b.b.75.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,6,Mod(75,152)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("152.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	152.b (of order $2$, degree $1$, 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:	$24.3783406116$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.6
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.51636 + 1.25289i) q^{2} -8.00180i q^{3} +(28.8605 - 13.8228i) q^{4} +16.6238i q^{5} +(10.0254 + 44.1408i) q^{6} +226.892i q^{7} +(-141.887 + 112.411i) q^{8} +178.971 q^{9} +O(q^{10})$	\(q+(-5.51636 + 1.25289i) q^{2} -8.00180i q^{3} +(28.8605 - 13.8228i) q^{4} +16.6238i q^{5} +(10.0254 + 44.1408i) q^{6} +226.892i q^{7} +(-141.887 + 112.411i) q^{8} +178.971 q^{9} +(-20.8278 - 91.7031i) q^{10} -430.539 q^{11} +(-110.607 - 230.936i) q^{12} +358.880 q^{13} +(-284.271 - 1251.62i) q^{14} +133.020 q^{15} +(641.861 - 797.866i) q^{16} -557.745 q^{17} +(-987.271 + 224.231i) q^{18} +(-1015.54 - 1201.99i) q^{19} +(229.788 + 479.773i) q^{20} +1815.54 q^{21} +(2375.01 - 539.418i) q^{22} +2256.14i q^{23} +(899.486 + 1135.35i) q^{24} +2848.65 q^{25} +(-1979.71 + 449.637i) q^{26} -3376.53i q^{27} +(3136.28 + 6548.23i) q^{28} -3540.10 q^{29} +(-733.789 + 166.660i) q^{30} -956.129 q^{31} +(-2541.10 + 5205.50i) q^{32} +3445.09i q^{33} +(3076.72 - 698.792i) q^{34} -3771.82 q^{35} +(5165.21 - 2473.88i) q^{36} -5844.88 q^{37} +(7108.04 + 5358.26i) q^{38} -2871.69i q^{39} +(-1868.69 - 2358.70i) q^{40} -9078.34i q^{41} +(-10015.2 + 2274.68i) q^{42} -10360.9 q^{43} +(-12425.6 + 5951.25i) q^{44} +2975.19i q^{45} +(-2826.69 - 12445.7i) q^{46} +5313.35i q^{47} +(-6384.36 - 5136.04i) q^{48} -34673.1 q^{49} +(-15714.2 + 3569.04i) q^{50} +4462.96i q^{51} +(10357.5 - 4960.72i) q^{52} -26576.4 q^{53} +(4230.41 + 18626.2i) q^{54} -7157.21i q^{55} +(-25505.1 - 32193.0i) q^{56} +(-9618.09 + 8126.12i) q^{57} +(19528.5 - 4435.35i) q^{58} +34439.4i q^{59} +(3839.04 - 1838.71i) q^{60} -5022.58i q^{61} +(5274.36 - 1197.92i) q^{62} +40607.2i q^{63} +(7495.74 - 31899.1i) q^{64} +5965.96i q^{65} +(-4316.31 - 19004.4i) q^{66} +25652.2i q^{67} +(-16096.8 + 7709.58i) q^{68} +18053.1 q^{69} +(20806.7 - 4725.67i) q^{70} -79295.9 q^{71} +(-25393.7 + 20118.3i) q^{72} +3367.06 q^{73} +(32242.5 - 7322.98i) q^{74} -22794.3i q^{75} +(-45923.8 - 20652.6i) q^{76} -97686.0i q^{77} +(3597.90 + 15841.3i) q^{78} +22696.7 q^{79} +(13263.6 + 10670.2i) q^{80} +16471.7 q^{81} +(11374.1 + 50079.4i) q^{82} -12605.2 q^{83} +(52397.6 - 25095.9i) q^{84} -9271.85i q^{85} +(57154.7 - 12981.1i) q^{86} +28327.2i q^{87} +(61087.9 - 48397.2i) q^{88} +2258.87i q^{89} +(-3727.58 - 16412.2i) q^{90} +81427.1i q^{91} +(31186.1 + 65113.3i) q^{92} +7650.75i q^{93} +(-6657.04 - 29310.4i) q^{94} +(19981.7 - 16882.1i) q^{95} +(41653.3 + 20333.4i) q^{96} +169620. i q^{97} +(191269. - 43441.5i) q^{98} -77054.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−5.51636	+	1.25289i	−0.975165	+	0.221482i
$2$	−5.51636	+	1.25289i	−0.975165	+	0.221482i
$3$		−	8.00180i		−	0.513315i	−0.966502	−	0.256658i	$-0.917379\pi$
$3$		−	8.00180i		−	0.513315i	0.966502	−	0.256658i	$-0.0826213\pi$
$4$	28.8605	−	13.8228i	0.901892	−	0.431962i
$5$			16.6238i			0.297376i	0.988884	+	0.148688i	$0.0475050\pi$
$5$			16.6238i			0.297376i	−0.988884	+	0.148688i	$0.952495\pi$
$6$	10.0254	+	44.1408i	0.113690	+	0.500567i
$7$			226.892i			1.75015i	0.483991	+	0.875073i	$0.339187\pi$
$7$			226.892i			1.75015i	−0.483991	+	0.875073i	$0.660813\pi$
$8$	−141.887	+	112.411i	−0.783821	+	0.620986i
$9$	178.971			0.736507
$10$	−20.8278	−	91.7031i	−0.0658633	−	0.289991i
$11$	−430.539			−1.07283			−0.536415	−	0.843954i	$-0.680222\pi$
$11$	−430.539			−1.07283			−0.536415	+	0.843954i	$0.680222\pi$
$12$	−110.607	−	230.936i	−0.221733	−	0.462955i
$13$	358.880			0.588967			0.294484	−	0.955657i	$-0.404852\pi$
$13$	358.880			0.588967			0.294484	+	0.955657i	$0.404852\pi$
$14$	−284.271	−	1251.62i	−0.387625	−	1.70668i
$15$	133.020			0.152648
$16$	641.861	−	797.866i	0.626818	−	0.779166i
$17$	−557.745			−0.468073			−0.234036	−	0.972228i	$-0.575193\pi$
$17$	−557.745			−0.468073			−0.234036	+	0.972228i	$0.575193\pi$
$18$	−987.271	+	224.231i	−0.718216	+	0.163123i
$19$	−1015.54	−	1201.99i	−0.645375	−	0.763866i
$19$	−1015.54	−	1201.99i	−0.645375	−	0.763866i
$20$	229.788	+	479.773i	0.128455	+	0.268201i
$21$	1815.54			0.898377
$22$	2375.01	−	539.418i	1.04619	−	0.237612i
$23$			2256.14i			0.889295i	0.895706	+	0.444648i	$0.146671\pi$
$23$			2256.14i			0.889295i	−0.895706	+	0.444648i	$0.853329\pi$
$24$	899.486	+	1135.35i	0.318762	+	0.402348i
$25$	2848.65			0.911567
$26$	−1979.71	+	449.637i	−0.574340	+	0.130445i
$27$		−	3376.53i		−	0.891376i
$28$	3136.28	+	6548.23i	0.755997	+	1.57844i
$29$	−3540.10			−0.781665			−0.390832	−	0.920462i	$-0.627813\pi$
$29$	−3540.10			−0.781665			−0.390832	+	0.920462i	$0.627813\pi$
$30$	−733.789	+	166.660i	−0.148857	+	0.0338087i
$31$	−956.129			−0.178695			−0.0893475	−	0.996001i	$-0.528478\pi$
$31$	−956.129			−0.178695			−0.0893475	+	0.996001i	$0.528478\pi$
$32$	−2541.10	+	5205.50i	−0.438680	+	0.898643i
$33$			3445.09i			0.550701i
$34$	3076.72	−	698.792i	0.456448	−	0.103669i
$35$	−3771.82			−0.520452
$36$	5165.21	−	2473.88i	0.664250	−	0.318143i
$37$	−5844.88			−0.701893			−0.350947	−	0.936395i	$-0.614140\pi$
$37$	−5844.88			−0.701893			−0.350947	+	0.936395i	$0.614140\pi$
$38$	7108.04	+	5358.26i	0.798529	+	0.601956i
$39$		−	2871.69i		−	0.302326i
$40$	−1868.69	−	2358.70i	−0.184666	−	0.233090i
$41$		−	9078.34i		−	0.843425i	−0.906730	−	0.421713i	$-0.861429\pi$
$41$		−	9078.34i		−	0.843425i	0.906730	−	0.421713i	$-0.138571\pi$
$42$	−10015.2	+	2274.68i	−0.876066	+	0.198974i
$43$	−10360.9			−0.854531			−0.427266	−	0.904126i	$-0.640523\pi$
$43$	−10360.9			−0.854531			−0.427266	+	0.904126i	$0.640523\pi$
$44$	−12425.6	+	5951.25i	−0.967577	+	0.463422i
$45$			2975.19i			0.219020i
$46$	−2826.69	−	12445.7i	−0.196962	−	0.867209i
$47$			5313.35i			0.350852i	0.984493	+	0.175426i	$0.0561303\pi$
$47$			5313.35i			0.350852i	−0.984493	+	0.175426i	$0.943870\pi$
$48$	−6384.36	−	5136.04i	−0.399958	−	0.321755i
$49$	−34673.1			−2.06301
$50$	−15714.2	+	3569.04i	−0.888928	+	0.201895i
$51$			4462.96i			0.240269i
$52$	10357.5	−	4960.72i	0.531185	−	0.254411i
$53$	−26576.4			−1.29959			−0.649794	−	0.760110i	$-0.725145\pi$
$53$	−26576.4			−1.29959			−0.649794	+	0.760110i	$0.725145\pi$
$54$	4230.41	+	18626.2i	0.197423	+	0.869238i
$55$		−	7157.21i		−	0.319034i
$56$	−25505.1	−	32193.0i	−1.08682	−	1.37180i
$57$	−9618.09	+	8126.12i	−0.392104	+	0.331281i
$58$	19528.5	−	4435.35i	0.762252	−	0.173124i
$59$			34439.4i			1.28803i	0.765013	+	0.644015i	$0.222733\pi$
$59$			34439.4i			1.28803i	−0.765013	+	0.644015i	$0.777267\pi$
$60$	3839.04	−	1838.71i	0.137672	−	0.0659380i
$61$		−	5022.58i		−	0.172823i	−0.996260	−	0.0864117i	$-0.972460\pi$
$61$		−	5022.58i		−	0.172823i	0.996260	−	0.0864117i	$-0.0275400\pi$
$62$	5274.36	−	1197.92i	0.174257	−	0.0395776i
$63$			40607.2i			1.28900i
$64$	7495.74	−	31899.1i	0.228752	−	0.973485i
$65$			5965.96i			0.175145i
$66$	−4316.31	−	19004.4i	−0.121970	−	0.537024i
$67$			25652.2i			0.698132i	0.937098	+	0.349066i	$0.113501\pi$
$67$			25652.2i			0.698132i	−0.937098	+	0.349066i	$0.886499\pi$
$68$	−16096.8	+	7709.58i	−0.422151	+	0.202190i
$69$	18053.1			0.456489
$70$	20806.7	−	4725.67i	0.507526	−	0.115270i
$71$	−79295.9			−1.86683			−0.933415	−	0.358798i	$-0.883187\pi$
$71$	−79295.9			−1.86683			−0.933415	+	0.358798i	$0.883187\pi$
$72$	−25393.7	+	20118.3i	−0.577290	+	0.457361i
$73$	3367.06			0.0739509			0.0369755	−	0.999316i	$-0.488228\pi$
$73$	3367.06			0.0739509			0.0369755	+	0.999316i	$0.488228\pi$
$74$	32242.5	−	7322.98i	0.684461	−	0.155456i
$75$		−	22794.3i		−	0.467922i
$76$	−45923.8	−	20652.6i	−0.912019	−	0.410147i
$77$		−	97686.0i		−	1.87761i
$78$	3597.90	+	15841.3i	0.0669596	+	0.294817i
$79$	22696.7			0.409162			0.204581	−	0.978850i	$-0.434417\pi$
$79$	22696.7			0.409162			0.204581	+	0.978850i	$0.434417\pi$
$80$	13263.6	+	10670.2i	0.231705	+	0.186401i
$81$	16471.7			0.278950
$82$	11374.1	+	50079.4i	0.186803	+	0.822479i
$83$	−12605.2			−0.200841			−0.100421	−	0.994945i	$-0.532019\pi$
$83$	−12605.2			−0.200841			−0.100421	+	0.994945i	$0.532019\pi$
$84$	52397.6	−	25095.9i	0.810239	−	0.388065i
$85$		−	9271.85i		−	0.139194i
$86$	57154.7	−	12981.1i	0.833308	−	0.189263i
$87$			28327.2i			0.401241i
$88$	61087.9	−	48397.2i	0.840908	−	0.666213i
$89$			2258.87i			0.0302285i	0.999886	+	0.0151143i	$0.00481120\pi$
$89$			2258.87i			0.0302285i	−0.999886	+	0.0151143i	$0.995189\pi$
$90$	−3727.58	−	16412.2i	−0.0485088	−	0.213580i
$91$			81427.1i			1.03078i
$92$	31186.1	+	65113.3i	0.384142	+	0.802048i
$93$			7650.75i			0.0917269i
$94$	−6657.04	−	29310.4i	−0.0777073	−	0.342138i
$95$	19981.7	−	16882.1i	0.227155	−	0.191919i
$96$	41653.3	+	20333.4i	0.461288	+	0.225181i
$97$			169620.i			1.83041i	0.402992	+	0.915204i	$0.367970\pi$
$97$			169620.i			1.83041i	−0.402992	+	0.915204i	$0.632030\pi$
$98$	191269.	−	43441.5i	2.01178	−	0.456919i
$99$	−77054.2			−0.790148
$100$	82213.5	−	39376.2i	0.822135	−	0.393762i
$101$		−	58203.4i		−	0.567734i	−0.958864	−	0.283867i	$-0.908383\pi$
$101$		−	58203.4i		−	0.567734i	0.958864	−	0.283867i	$-0.0916175\pi$
$102$	−5591.59	−	24619.3i	−0.0532151	−	0.234302i
$103$	−29365.3			−0.272735			−0.136368	−	0.990658i	$-0.543543\pi$
$103$	−29365.3			−0.272735			−0.136368	+	0.990658i	$0.543543\pi$
$104$	−50920.4	+	40341.9i	−0.461645	+	0.365741i
$105$			30181.3i			0.267156i
$106$	146605.	−	33297.2i	1.26731	−	0.287835i
$107$		−	87182.5i		−	0.736156i	−0.929795	−	0.368078i	$-0.880016\pi$
$107$		−	87182.5i		−	0.736156i	0.929795	−	0.368078i	$-0.119984\pi$
$108$	−46673.0	−	97448.4i	−0.385040	−	0.803925i
$109$	25960.8			0.209292			0.104646	−	0.994510i	$-0.466629\pi$
$109$	25960.8			0.209292			0.104646	+	0.994510i	$0.466629\pi$
$110$	8967.19	+	39481.8i	0.0706602	+	0.311111i
$111$			46769.5i			0.360293i
$112$	181030.	+	145633.i	1.36365	+	1.09702i
$113$			46335.4i			0.341364i	0.985326	+	0.170682i	$0.0545970\pi$
$113$			46335.4i			0.341364i	−0.985326	+	0.170682i	$0.945403\pi$
$114$	42875.7	−	56877.0i	0.308994	−	0.409897i
$115$	−37505.6			−0.264455
$116$	−102169.	+	48934.0i	−0.704977	+	0.337649i
$117$	64229.2			0.433779
$118$	−43148.8	−	189980.i	−0.285275	−	1.25604i
$119$		−	126548.i		−	0.819196i
$120$	−18873.9	+	14952.9i	−0.119649	+	0.0947921i
$121$	24313.2			0.150966
$122$	6292.74	+	27706.4i	0.0382772	+	0.168531i
$123$	−72643.0			−0.432943
$124$	−27594.4	+	13216.4i	−0.161164	+	0.0771894i
$125$			99304.9i			0.568454i
$126$	−50876.3	−	224004.i	−0.285489	−	1.25698i
$127$	24041.4			0.132267			0.0661333	−	0.997811i	$-0.478934\pi$
$127$	24041.4			0.132267			0.0661333	+	0.997811i	$0.478934\pi$
$128$	−1383.16	+	185359.i	−0.00746189	+	0.999972i
$129$			82906.1i			0.438644i
$130$	−7474.69	−	32910.4i	−0.0387913	−	0.170795i
$131$	−309558.			−1.57603			−0.788013	−	0.615659i	$-0.788890\pi$
$131$	−309558.			−1.57603			−0.788013	+	0.615659i	$0.788890\pi$
$132$	47620.7	+	99427.1i	0.237882	+	0.496672i
$133$	272722.	−	230418.i	1.33688	−	1.12950i
$134$	−32139.3	−	141507.i	−0.154623	−	0.680794i
$135$	56130.8			0.265074
$136$	79136.6	−	62696.4i	0.366885	−	0.290667i
$137$	228942.			1.04214			0.521069	−	0.853515i	$-0.325534\pi$
$137$	228942.			1.04214			0.521069	+	0.853515i	$0.325534\pi$
$138$	−99587.7	+	22618.6i	−0.445152	+	0.101104i
$139$	333516.			1.46413			0.732064	−	0.681236i	$-0.238557\pi$
$139$	333516.			1.46413			0.732064	+	0.681236i	$0.238557\pi$
$140$	−108857.	+	52137.0i	−0.469391	+	0.224815i
$141$	42516.4			0.180098
$142$	437425.	−	99348.9i	1.82047	−	0.413468i
$143$	−154512.			−0.631862
$144$	114875.	−	142795.i	0.461656	−	0.573861i
$145$		−	58850.0i		−	0.232448i
$146$	−18573.9	+	4218.55i	−0.0721143	+	0.0163788i
$147$			277447.i			1.05898i
$148$	−168686.	+	80792.4i	−0.633032	+	0.303191i
$149$		−	330414.i		−	1.21925i	−0.792689	−	0.609626i	$-0.791320\pi$
$149$		−	330414.i		−	1.21925i	0.792689	−	0.609626i	$-0.208680\pi$
$150$	28558.7	+	125742.i	0.103636	+	0.456301i
$151$	−539212.			−1.92450			−0.962248	−	0.272175i	$-0.912257\pi$
$151$	−539212.			−1.92450			−0.962248	+	0.272175i	$0.912257\pi$
$152$	279208.	+	56389.6i	0.980209	+	0.197966i
$153$	−99820.3			−0.344739
$154$	122390.	+	538872.i	0.415856	+	1.83098i
$155$		−	15894.5i		−	0.0531396i
$156$	−39694.7	−	82878.4i	−0.130593	−	0.272665i
$157$		−	296408.i		−	0.959713i	−0.877347	−	0.479857i	$-0.840689\pi$
$157$		−	296408.i		−	0.959713i	0.877347	−	0.479857i	$-0.159311\pi$
$158$	−125203.	+	28436.5i	−0.399000	+	0.0906218i
$159$			212659.i			0.667099i
$160$	−86535.3	−	42242.9i	−0.267235	−	0.130453i
$161$	−511900.			−1.55640
$162$	−90864.1	+	20637.3i	−0.272022	+	0.0617823i
$163$	232085.			0.684193			0.342096	−	0.939665i	$-0.388863\pi$
$163$	232085.			0.684193			0.342096	+	0.939665i	$0.388863\pi$
$164$	−125488.	−	262006.i	−0.364328	−	0.760678i
$165$	−57270.6			−0.163765
$166$	69534.6	−	15792.9i	0.195853	−	0.0444826i
$167$	−443971.			−1.23187			−0.615933	−	0.787799i	$-0.711221\pi$
$167$	−443971.			−1.23187			−0.615933	+	0.787799i	$0.711221\pi$
$168$	−257602.	+	204086.i	−0.704167	+	0.557880i
$169$	−242498.			−0.653118
$170$	11616.6	+	51146.9i	0.0308288	+	0.135737i
$171$	−181752.	−	215122.i	−0.475323	−	0.562593i
$172$	−299022.	+	143217.i	−0.770695	+	0.369125i
$173$	−339784.			−0.863153			−0.431576	−	0.902076i	$-0.642042\pi$
$173$	−339784.			−0.863153			−0.431576	+	0.902076i	$0.642042\pi$
$174$	−35490.8	−	156263.i	−0.0888674	−	0.391276i
$175$			646336.i			1.59538i
$176$	−276347.	+	343513.i	−0.672470	+	0.835913i
$177$	275577.			0.661166
$178$	−2830.12	−	12460.8i	−0.00669506	−	0.0294778i
$179$		−	84183.2i		−	0.196378i	−0.995168	−	0.0981890i	$-0.968695\pi$
$179$		−	84183.2i		−	0.196378i	0.995168	−	0.0981890i	$-0.0313050\pi$
$180$	41125.4	+	85865.5i	0.0946081	+	0.197532i
$181$	689207.			1.56370			0.781850	−	0.623466i	$-0.214276\pi$
$181$	689207.			1.56370			0.781850	+	0.623466i	$0.214276\pi$
$182$	−102019.	−	449181.i	−0.228298	−	1.00518i
$183$	−40189.7			−0.0887129
$184$	−253614.	−	320116.i	−0.552240	−	0.697048i
$185$		−	97164.2i		−	0.208726i
$186$	−9585.54	−	42204.3i	−0.0203158	−	0.0894488i
$187$	240131.			0.502163
$188$	73445.3	+	153346.i	0.151555	+	0.316431i
$189$	766108.			1.56004
$190$	−89074.9	+	118163.i	−0.179007	+	0.237463i
$191$			40148.9i			0.0796325i	0.999207	+	0.0398163i	$0.0126773\pi$
$191$			40148.9i			0.0796325i	−0.999207	+	0.0398163i	$0.987323\pi$
$192$	−255250.	−	59979.4i	−0.499705	−	0.117422i
$193$		−	832068.i		−	1.60792i	−0.594681	−	0.803962i	$-0.702721\pi$
$193$		−	832068.i		−	1.60792i	0.594681	−	0.803962i	$-0.297279\pi$
$194$	−212515.	−	935686.i	−0.405401	−	1.78495i
$195$	47738.4			0.0899045
$196$	−1.00068e6	+	479278.i	−1.86061	+	0.891143i
$197$			417699.i			0.766828i	0.923577	+	0.383414i	$0.125252\pi$
$197$			417699.i			0.766828i	−0.923577	+	0.383414i	$0.874748\pi$
$198$	425059.	−	96540.3i	0.770524	−	0.175003i
$199$			820475.i			1.46870i	0.678772	+	0.734349i	$0.262512\pi$
$199$			820475.i			1.46870i	−0.678772	+	0.734349i	$0.737488\pi$
$200$	−404186.	+	320218.i	−0.714506	+	0.566071i
$201$	205264.			0.358362
$202$	72922.4	+	321071.i	0.125743	+	0.553634i
$203$		−	803221.i		−	1.36803i
$204$	61690.5	+	128803.i	0.103787	+	0.216697i
$205$	150917.			0.250815
$206$	161990.	−	36791.4i	0.265962	−	0.0604058i
$207$			403784.i			0.654972i
$208$	230351.	−	286338.i	0.369175	−	0.458903i
$209$	437229.	+	517505.i	0.692378	+	0.819499i
$210$	−37813.8	−	166491.i	−0.0591701	−	0.260521i
$211$			75132.3i			0.116177i	0.998311	+	0.0580886i	$0.0185006\pi$
$211$			75132.3i			0.116177i	−0.998311	+	0.0580886i	$0.981499\pi$
$212$	−767008.	+	367359.i	−1.17209	+	0.561373i
$213$			634510.i			0.958273i
$214$	109230.	+	480930.i	0.163045	+	0.717873i
$215$		−	172238.i		−	0.254117i
$216$	379557.	+	479085.i	0.553532	+	0.698680i
$217$		−	216938.i		−	0.312742i
$218$	−143209.	+	32526.0i	−0.204094	+	0.0463542i
$219$		−	26942.5i		−	0.0379602i
$220$	−98932.6	−	206561.i	−0.137811	−	0.287734i
$221$	−200164.			−0.275679
$222$	−58597.0	−	257998.i	−0.0797982	−	0.351345i
$223$	841528.			1.13320			0.566600	−	0.823993i	$-0.308258\pi$
$223$	841528.			1.13320			0.566600	+	0.823993i	$0.308258\pi$
$224$	−1.18109e6	−	576557.i	−1.57276	−	0.767754i
$225$	509826.			0.671376
$226$	−58053.2	−	255603.i	−0.0756057	−	0.332886i
$227$			7823.69i			0.0100774i	0.999987	+	0.00503868i	$0.00160387\pi$
$227$			7823.69i			0.0100774i	−0.999987	+	0.00503868i	$0.998396\pi$
$228$	−165258.	+	367473.i	−0.210535	+	0.468154i
$229$		−	805865.i		−	1.01548i	−0.861509	−	0.507742i	$-0.830480\pi$
$229$		−	805865.i		−	1.01548i	0.861509	−	0.507742i	$-0.169520\pi$
$230$	206895.	−	46990.4i	0.257887	−	0.0585719i
$231$	−781664.			−0.963807
$232$	502294.	−	397945.i	0.612686	−	0.485403i
$233$	1.20290e6			1.45158			0.725790	−	0.687916i	$-0.241474\pi$
$233$	1.20290e6			1.45158			0.725790	+	0.687916i	$0.241474\pi$
$234$	−354312.	+	80472.1i	−0.423005	+	0.0960739i
$235$	−88328.3			−0.104335
$236$	476049.	+	993940.i	0.556380	+	1.16166i
$237$		−	181614.i		−	0.210029i
$238$	158550.	+	698084.i	0.181437	+	0.798851i
$239$			1.74301e6i			1.97381i	0.161302	+	0.986905i	$0.448431\pi$
$239$			1.74301e6i			1.97381i	−0.161302	+	0.986905i	$0.551569\pi$
$240$	85380.7	−	106132.i	0.0956823	−	0.118938i
$241$		−	539446.i		−	0.598281i	−0.954209	−	0.299140i	$-0.903300\pi$
$241$		−	539446.i		−	0.598281i	0.954209	−	0.299140i	$-0.0966999\pi$
$242$	−134121.	+	30461.8i	−0.147217	+	0.0334362i
$243$		−	952300.i		−	1.03457i
$244$	−69426.1	−	144954.i	−0.0746531	−	0.155868i
$245$		−	576399.i		−	0.613491i
$246$	400725.	−	91013.6i	0.422191	−	0.0958889i
$247$	−364456.	−	431371.i	−0.380105	−	0.449892i
$248$	135662.	−	107479.i	0.140065	−	0.110967i
$249$			100864.i			0.103095i
$250$	−124418.	−	547802.i	−0.125902	−	0.554337i
$251$	−791114.			−0.792602			−0.396301	−	0.918121i	$-0.629706\pi$
$251$	−791114.			−0.792602			−0.396301	+	0.918121i	$0.629706\pi$
$252$	561304.	+	1.17195e6i	0.556797	+	1.16253i
$253$		−	971356.i		−	0.954063i
$254$	−132621.	+	30121.2i	−0.128982	+	0.0292946i
$255$	−74191.5			−0.0714502
$256$	−224604.	−	1.02424e6i	−0.214199	−	0.976790i
$257$			1.42019e6i			1.34126i	0.741793	+	0.670629i	$0.233976\pi$
$257$			1.42019e6i			1.34126i	−0.741793	+	0.670629i	$0.766024\pi$
$258$	−103872.	−	457340.i	−0.0971515	−	0.427750i
$259$		−	1.32616e6i		−	1.22842i
$260$	82466.2	+	172181.i	0.0756558	+	0.157962i
$261$	−633576.			−0.575702
$262$	1.70763e6	−	387841.i	1.53688	−	0.349060i
$263$		−	1.77766e6i		−	1.58474i	−0.610038	−	0.792372i	$-0.708846\pi$
$263$		−	1.77766e6i		−	1.58474i	0.610038	−	0.792372i	$-0.291154\pi$
$264$	−387264.	−	488813.i	−0.341978	−	0.431651i
$265$		−	441801.i		−	0.386466i
$266$	−1.21575e6	+	1.61276e6i	−1.05351	+	1.39754i
$267$	18075.0			0.0155168
$268$	354585.	+	740336.i	0.301566	+	0.629640i
$269$	805159.			0.678424			0.339212	−	0.940710i	$-0.389840\pi$
$269$	805159.			0.678424			0.339212	+	0.940710i	$0.389840\pi$
$270$	−309638.	+	70325.7i	−0.258491	+	0.0587090i
$271$			432686.i			0.357890i	0.983859	+	0.178945i	$0.0572684\pi$
$271$			432686.i			0.357890i	−0.983859	+	0.178945i	$0.942732\pi$
$272$	−357995.	+	445006.i	−0.293396	+	0.364706i
$273$	651563.			0.529115
$274$	−1.26293e6	+	286839.i	−1.01626	+	0.230814i
$275$	−1.22646e6			−0.977958
$276$	521024.	−	249545.i	0.411704	−	0.197186i
$277$			846779.i			0.663087i	0.943440	+	0.331543i	$0.107569\pi$
$277$			846779.i			0.663087i	−0.943440	+	0.331543i	$0.892431\pi$
$278$	−1.83979e6	+	417858.i	−1.42777	+	0.324277i
$279$	−171120.			−0.131610
$280$	535171.	−	423992.i	0.407941	−	0.323193i
$281$		−	1.63102e6i		−	1.23223i	−0.787655	−	0.616117i	$-0.788705\pi$
$281$		−	1.63102e6i		−	1.23223i	0.787655	−	0.616117i	$-0.211295\pi$
$282$	−234536.	+	53268.3i	−0.175625	+	0.0398883i
$283$	1.47513e6			1.09487			0.547435	−	0.836848i	$-0.315604\pi$
$283$	1.47513e6			1.09487			0.547435	+	0.836848i	$0.315604\pi$
$284$	−2.28852e6	+	1.09609e6i	−1.68368	+	0.806400i
$285$	−135087.	−	159889.i	−0.0985150	−	0.116602i
$286$	852345.	−	193586.i	0.616170	−	0.139946i
$287$	2.05980e6			1.47612
$288$	−454785.	+	931635.i	−0.323091	+	0.661857i
$289$	−1.10878e6			−0.780908
$290$	73732.5	+	324638.i	0.0514830	+	0.226675i
$291$	1.35726e6			0.939576
$292$	97175.2	−	46542.1i	0.0666957	−	0.0319440i
$293$	877203.			0.596940			0.298470	−	0.954419i	$-0.403524\pi$
$293$	877203.			0.596940			0.298470	+	0.954419i	$0.403524\pi$
$294$	−347610.	−	1.53050e6i	−0.234544	−	1.03268i
$295$	−572515.			−0.383029
$296$	829311.	−	657026.i	0.550159	−	0.435866i
$297$			1.45373e6i			0.956296i
$298$	413972.	+	1.82269e6i	0.270042	+	1.18897i
$299$			809683.i			0.523766i
$300$	−315081.	−	657856.i	−0.202124	−	0.422015i
$301$		−	2.35082e6i		−	1.49555i
$302$	2.97449e6	−	675572.i	1.87670	−	0.426240i
$303$	−465732.			−0.291427
$304$	−1.61086e6	+	38751.1i	−0.999711	+	0.0240491i
$305$	83494.5			0.0513935
$306$	550645.	−	125064.i	0.336177	−	0.0763533i
$307$			1.75837e6i			1.06479i	0.846497	+	0.532394i	$0.178707\pi$
$307$			1.75837e6i			1.06479i	−0.846497	+	0.532394i	$0.821293\pi$
$308$	−1.35029e6	−	2.81927e6i	−0.811057	−	1.69340i
$309$			234975.i			0.139999i
$310$	19914.1	+	87680.0i	0.0117694	+	0.0518199i
$311$			2.51973e6i			1.47725i	0.674117	+	0.738625i	$0.264524\pi$
$311$			2.51973e6i			1.47725i	−0.674117	+	0.738625i	$0.735476\pi$
$312$	322808.	+	407454.i	0.187740	+	0.236969i
$313$	−366648.			−0.211538			−0.105769	−	0.994391i	$-0.533730\pi$
$313$	−366648.			−0.211538			−0.105769	+	0.994391i	$0.533730\pi$
$314$	371367.	+	1.63510e6i	0.212559	+	0.935878i
$315$	−675047.			−0.383316
$316$	655039.	−	313732.i	0.369020	−	0.176742i
$317$	811847.			0.453760			0.226880	−	0.973923i	$-0.427148\pi$
$317$	811847.			0.453760			0.226880	+	0.973923i	$0.427148\pi$
$318$	−266438.	−	1.17310e6i	−0.147750	−	0.650531i
$319$	1.52415e6			0.838594
$320$	530286.	+	124608.i	0.289491	+	0.0680254i
$321$	−697616.			−0.377880
$322$	2.82383e6	−	641354.i	1.51774	−	0.344713i
$323$	566411.	+	670404.i	0.302082	+	0.357545i
$324$	475383.	−	227685.i	0.251583	−	0.120496i
$325$	1.02232e6			0.536883
$326$	−1.28027e6	+	290777.i	−0.667201	+	0.151536i
$327$		−	207733.i		−	0.107433i
$328$	1.02050e6	+	1.28810e6i	0.523756	+	0.661095i
$329$	−1.20556e6			−0.614043
$330$	315925.	−	71753.6i	0.159698	−	0.0362710i
$331$			3.95526e6i			1.98429i	0.125102	+	0.992144i	$0.460074\pi$
$331$			3.95526e6i			1.98429i	−0.125102	+	0.992144i	$0.539926\pi$
$332$	−363791.	+	174238.i	−0.181137	+	0.0867558i
$333$	−1.04606e6			−0.516949
$334$	2.44910e6	−	556246.i	1.20127	−	0.272835i
$335$	−426438.			−0.207608
$336$	1.16533e6	−	1.44856e6i	0.563119	−	0.699985i
$337$		−	1.62883e6i		−	0.781272i	−0.920545	−	0.390636i	$-0.872255\pi$
$337$		−	1.62883e6i		−	0.781272i	0.920545	−	0.390636i	$-0.127745\pi$
$338$	1.33771e6	−	303823.i	0.636897	−	0.144654i
$339$	370767.			0.175227
$340$	−128163.	−	267591.i	−0.0601263	−	0.125538i
$341$	411651.			0.191709
$342$	1.27213e6	+	958975.i	0.588122	+	0.443345i
$343$		−	4.05367e6i		−	1.86043i
$344$	1.47008e6	−	1.16468e6i	0.669800	−	0.530652i
$345$			300112.i			0.135749i
$346$	1.87437e6	−	425712.i	0.841716	−	0.191172i
$347$	1.48791e6			0.663365			0.331683	−	0.943391i	$-0.392384\pi$
$347$	1.48791e6			0.663365			0.331683	+	0.943391i	$0.392384\pi$
$348$	391560.	+	817537.i	0.173321	+	0.361876i
$349$			1.60660e6i			0.706065i	0.935611	+	0.353033i	$0.114849\pi$
$349$			1.60660e6i			0.706065i	−0.935611	+	0.353033i	$0.885151\pi$
$350$	−809787.	−	3.56542e6i	−0.353346	−	1.55575i
$351$		−	1.21177e6i		−	0.524991i
$352$	1.09405e6	−	2.24117e6i	0.470629	−	0.964092i
$353$	455343.			0.194492			0.0972460	−	0.995260i	$-0.468997\pi$
$353$	455343.			0.194492			0.0972460	+	0.995260i	$0.468997\pi$
$354$	−1.52018e6	+	345268.i	−0.644745	+	0.146436i
$355$		−	1.31820e6i		−	0.555151i
$356$	31223.9	+	65192.3i	0.0130576	+	0.0272628i
$357$	−1.01261e6			−0.420506
$358$	105472.	+	464385.i	0.0434941	+	0.191501i
$359$			1.80872e6i			0.740686i	0.928895	+	0.370343i	$0.120760\pi$
$359$			1.80872e6i			0.740686i	−0.928895	+	0.370343i	$0.879240\pi$
$360$	−334442.	−	422140.i	−0.136008	−	0.171672i
$361$	−413466.	+	2.44133e6i	−0.166983	+	0.985960i
$362$	−3.80192e6	+	863500.i	−1.52487	+	0.346331i
$363$		−	194550.i		−	0.0774932i
$364$	1.12555e6	+	2.35003e6i	0.445257	+	0.929651i
$365$			55973.4i			0.0219912i
$366$	221701.	−	50353.2i	0.0865097	−	0.0196483i
$367$		−	2.15654e6i		−	0.835781i	−0.908497	−	0.417891i	$-0.862770\pi$
$367$		−	2.15654e6i		−	0.835781i	0.908497	−	0.417891i	$-0.137230\pi$
$368$	1.80009e6	+	1.44813e6i	0.692908	+	0.557426i
$369$		−	1.62476e6i		−	0.621189i
$370$	121736.	+	535993.i	0.0462290	+	0.203542i
$371$		−	6.02997e6i		−	2.27447i
$372$	105755.	+	220805.i	0.0396225	+	0.0827277i
$373$	−4.33043e6			−1.61161			−0.805804	−	0.592183i	$-0.798266\pi$
$373$	−4.33043e6			−1.61161			−0.805804	+	0.592183i	$0.798266\pi$
$374$	−1.32465e6	+	300858.i	−0.489691	+	0.111220i
$375$	794617.			0.291796
$376$	−597277.	−	753895.i	−0.217874	−	0.275005i
$377$	−1.27047e6			−0.460375
$378$	−4.22613e6	+	959848.i	−1.52129	+	0.345520i
$379$			5.17422e6i			1.85032i	0.379576	+	0.925160i	$0.376070\pi$
$379$			5.17422e6i			1.85032i	−0.379576	+	0.925160i	$0.623930\pi$
$380$	343324.	−	763430.i	0.121968	−	0.271213i
$381$		−	192374.i		−	0.0678945i
$382$	−50302.1	−	221476.i	−0.0176371	−	0.0776548i
$383$	−3.87178e6			−1.34870			−0.674348	−	0.738414i	$-0.735575\pi$
$383$	−3.87178e6			−1.34870			−0.674348	+	0.738414i	$0.735575\pi$
$384$	1.48320e6	+	11067.8i	0.513301	+	0.00383030i
$385$	1.62392e6			0.558357
$386$	1.04249e6	+	4.58999e6i	0.356126	+	1.56799i
$387$	−1.85431e6			−0.629368
$388$	2.34462e6	+	4.89532e6i	0.790666	+	1.65083i
$389$			2.87520e6i			0.963372i	0.876344	+	0.481686i	$0.159975\pi$
$389$			2.87520e6i			0.963372i	−0.876344	+	0.481686i	$0.840025\pi$
$390$	−263342.	+	59810.9i	−0.0876717	+	0.0199122i
$391$		−	1.25835e6i		−	0.416255i
$392$	4.91965e6	−	3.89762e6i	1.61703	−	1.28110i
$393$			2.47702e6i			0.808998i
$394$	−523330.	−	2.30418e6i	−0.169838	−	0.747783i
$395$			377306.i			0.121675i
$396$	−2.22383e6	+	1.06510e6i	−0.712628	+	0.341314i
$397$			4.54879e6i			1.44851i	0.689535	+	0.724253i	$0.257815\pi$
$397$			4.54879e6i			1.44851i	−0.689535	+	0.724253i	$0.742185\pi$
$398$	−1.02796e6	−	4.52604e6i	−0.325289	−	1.43222i
$399$	−1.84375e6	−	2.18227e6i	−0.579790	−	0.686240i
$400$	1.82844e6	−	2.27284e6i	0.571387	−	0.710262i
$401$		−	1.11706e6i		−	0.346908i	−0.984842	−	0.173454i	$-0.944507\pi$
$401$		−	1.11706e6i		−	0.346908i	0.984842	−	0.173454i	$-0.0554929\pi$
$402$	−1.13231e6	+	257172.i	−0.349462	+	0.0793705i
$403$	−343136.			−0.105245
$404$	−804533.	−	1.67978e6i	−0.245240	−	0.512035i
$405$			273823.i			0.0829531i
$406$	1.00635e6	+	4.43086e6i	0.302993	+	1.33405i
$407$	2.51645e6			0.753013
$408$	−501684.	−	633235.i	−0.149204	−	0.188328i
$409$			2.33481e6i			0.690151i	0.938575	+	0.345075i	$0.112147\pi$
$409$			2.33481e6i			0.690151i	−0.938575	+	0.345075i	$0.887853\pi$
$410$	−832511.	+	189082.i	−0.244585	+	0.0555508i
$411$		−	1.83195e6i		−	0.534945i
$412$	−847498.	+	405910.i	−0.245978	+	0.117811i
$413$	−7.81404e6			−2.25424
$414$	−505896.	−	2.22742e6i	−0.145064	−	0.638706i
$415$		−	209546.i		−	0.0597254i
$416$	−911952.	+	1.86815e6i	−0.258368	+	0.529271i
$417$		−	2.66872e6i		−	0.751560i
$418$	−3.06029e6	−	2.30694e6i	−0.856686	−	0.645798i
$419$	−6.05354e6			−1.68451			−0.842256	−	0.539078i	$-0.818773\pi$
$419$	−6.05354e6			−1.68451			−0.842256	+	0.539078i	$0.818773\pi$
$420$	417190.	+	871049.i	0.115401	+	0.240946i
$421$	3.22542e6			0.886913			0.443457	−	0.896296i	$-0.353752\pi$
$421$	3.22542e6			0.886913			0.443457	+	0.896296i	$0.353752\pi$
$422$	−94132.4	−	414457.i	−0.0257311	−	0.113292i
$423$			950938.i			0.258405i
$424$	3.77083e6	−	2.98746e6i	1.01864	−	0.807026i
$425$	−1.58882e6			−0.426680
$426$	−794970.	−	3.50019e6i	−0.212240	−	0.934474i
$427$	1.13958e6			0.302466
$428$	−1.20510e6	−	2.51613e6i	−0.317991	−	0.663933i
$429$			1.23637e6i			0.324345i
$430$	215796.	+	950130.i	0.0562822	+	0.247806i
$431$	2.65820e6			0.689277			0.344638	−	0.938735i	$-0.388002\pi$
$431$	2.65820e6			0.689277			0.344638	+	0.938735i	$0.388002\pi$
$432$	−2.69402e6	−	2.16726e6i	−0.694530	−	0.558730i
$433$			4.33076e6i			1.11005i	0.831832	+	0.555027i	$0.187292\pi$
$433$			4.33076e6i			1.11005i	−0.831832	+	0.555027i	$0.812708\pi$
$434$	271799.	+	1.19671e6i	0.0692667	+	0.304975i
$435$	−470906.			−0.119319
$436$	749243.	−	358850.i	0.188758	−	0.0904060i
$437$	2.71186e6	−	2.29119e6i	0.679302	−	0.573929i
$438$	33756.0	+	148625.i	0.00840747	+	0.0370174i
$439$	3.96046e6			0.980808			0.490404	−	0.871495i	$-0.336849\pi$
$439$	3.96046e6			0.980808			0.490404	+	0.871495i	$0.336849\pi$
$440$	804546.	+	1.01551e6i	0.198116	+	0.250066i
$441$	−6.20548e6			−1.51942
$442$	1.10417e6	−	250783.i	0.268833	−	0.0610579i
$443$	−6.50427e6			−1.57467			−0.787334	−	0.616527i	$-0.788539\pi$
$443$	−6.50427e6			−1.57467			−0.787334	+	0.616527i	$0.788539\pi$
$444$	646485.	+	1.34979e6i	0.155633	+	0.324945i
$445$	−37551.1			−0.00898923
$446$	−4.64218e6	+	1.05434e6i	−1.10506	+	0.250983i
$447$	−2.64391e6			−0.625860
$448$	7.23767e6	+	1.70073e6i	1.70374	+	0.400349i
$449$			7.32620e6i			1.71500i	0.514488	+	0.857498i	$0.327982\pi$
$449$			7.32620e6i			1.71500i	−0.514488	+	0.857498i	$0.672018\pi$
$450$	−2.81239e6	+	638756.i	−0.654702	+	0.148697i
$451$			3.90858e6i			0.904853i
$452$	640485.	+	1.33727e6i	0.147456	+	0.307873i
$453$			4.31466e6i			0.987873i
$454$	−9802.22	−	43158.3i	−0.00223195	−	0.00982709i
$455$	−1.35363e6			−0.306529
$456$	451218.	−	2.23416e6i	0.101619	−	0.503156i
$457$	−1.49910e6			−0.335769			−0.167884	−	0.985807i	$-0.553694\pi$
$457$	−1.49910e6			−0.335769			−0.167884	+	0.985807i	$0.553694\pi$
$458$	1.00966e6	+	4.44544e6i	0.224911	+	0.990265i
$459$			1.88324e6i			0.417229i
$460$	−1.08243e6	+	518432.i	−0.238510	+	0.114235i
$461$			3.69887e6i			0.810619i	0.914180	+	0.405309i	$0.132836\pi$
$461$			3.69887e6i			0.810619i	−0.914180	+	0.405309i	$0.867164\pi$
$462$	4.31194e6	−	979338.i	0.939870	−	0.213465i
$463$		−	5.35356e6i		−	1.16062i	−0.814395	−	0.580310i	$-0.802931\pi$
$463$		−	5.35356e6i		−	1.16062i	0.814395	−	0.580310i	$-0.197069\pi$
$464$	−2.27225e6	+	2.82453e6i	−0.489961	+	0.609047i
$465$	−127185.			−0.0272774
$466$	−6.63565e6	+	1.50710e6i	−1.41553	+	0.321498i
$467$	4.66607e6			0.990055			0.495028	−	0.868877i	$-0.335158\pi$
$467$	4.66607e6			0.990055			0.495028	+	0.868877i	$0.335158\pi$
$468$	1.85369e6	−	887827.i	0.391221	−	0.187376i
$469$	−5.82028e6			−1.22183
$470$	487251.	−	110665.i	0.101744	−	0.0231083i
$471$	−2.37180e6			−0.492636
$472$	−3.87135e6	−	4.88650e6i	−0.799849	−	1.00959i
$473$	4.46079e6			0.916767
$474$	227543.	+	1.00185e6i	0.0465176	+	0.204813i
$475$	−2.89291e6	−	3.42405e6i	−0.588303	−	0.696315i
$476$	−1.74924e6	−	3.65224e6i	−0.353861	−	0.738826i
$477$	−4.75640e6			−0.957156
$478$	−2.18380e6	−	9.61508e6i	−0.437163	−	1.92479i
$479$		−	5.94642e6i		−	1.18418i	−0.805873	−	0.592088i	$-0.798304\pi$
$479$		−	5.94642e6i		−	1.18418i	0.805873	−	0.592088i	$-0.201696\pi$
$480$	−338019.	+	692438.i	−0.0669635	+	0.137176i
$481$	−2.09761e6			−0.413392
$482$	675865.	+	2.97578e6i	0.132508	+	0.583422i
$483$			4.09612e6i			0.798922i
$484$	701693.	−	336077.i	0.136155	−	0.0652116i
$485$	−2.81973e6			−0.544319
$486$	1.19313e6	+	5.25323e6i	0.229137	+	1.00887i
$487$	8.95415e6			1.71081			0.855405	−	0.517959i	$-0.173308\pi$
$487$	8.95415e6			1.71081			0.855405	+	0.517959i	$0.173308\pi$
$488$	564591.	+	712638.i	0.107321	+	0.135463i
$489$		−	1.85710e6i		−	0.351207i
$490$	722164.	+	3.17963e6i	0.135877	+	0.598254i
$491$	6.59121e6			1.23385			0.616924	−	0.787023i	$-0.288379\pi$
$491$	6.59121e6			1.23385			0.616924	+	0.787023i	$0.288379\pi$
$492$	−2.09652e6	+	1.00413e6i	−0.390468	+	0.187015i
$493$	1.97447e6			0.365876
$494$	2.55093e6	+	1.92297e6i	0.470307	+	0.354533i
$495$		−	1.28094e6i		−	0.234971i
$496$	−613702.	+	762863.i	−0.112009	+	0.139233i
$497$		−	1.79916e7i		−	3.26723i
$498$	−126371.	−	556402.i	−0.0228336	−	0.100534i
$499$	1.03324e6			0.185759			0.0928797	−	0.995677i	$-0.470393\pi$
$499$	1.03324e6			0.185759			0.0928797	+	0.995677i	$0.470393\pi$
$500$	1.37267e6	+	2.86599e6i	0.245551	+	0.512684i
$501$			3.55256e6i			0.632335i
$502$	4.36408e6	−	991178.i	0.772917	−	0.175547i
$503$		−	1.65993e6i		−	0.292529i	−0.989245	−	0.146265i	$-0.953275\pi$
$503$		−	1.65993e6i		−	0.292529i	0.989245	−	0.146265i	$-0.0467251\pi$
$504$	−4.56467e6	−	5.76162e6i	−0.800449	−	1.01034i
$505$	967564.			0.168831
$506$	1.21700e6	+	5.35835e6i	0.211307	+	0.930369i
$507$			1.94042e6i			0.335255i
$508$	693847.	−	332319.i	0.119290	−	0.0571341i
$509$	−1.07901e6			−0.184600			−0.0923001	−	0.995731i	$-0.529422\pi$
$509$	−1.07901e6			−0.184600			−0.0923001	+	0.995731i	$0.529422\pi$
$510$	409267.	−	92953.7i	0.0696757	−	0.0158249i
$511$			763959.i			0.129425i
$512$	2.52225e6	+	5.36867e6i	0.425220	+	0.905090i
$513$	−4.05856e6	+	3.42899e6i	−0.680892	+	0.575272i
$514$	−1.77933e6	−	7.83426e6i	−0.297064	−	1.30795i
$515$		−	488163.i		−	0.0811049i
$516$	1.14599e6	+	2.39271e6i	0.189477	+	0.395609i
$517$		−	2.28761e6i		−	0.376405i
$518$	1.66153e6	+	7.31556e6i	0.272071	+	1.19791i
$519$			2.71888e6i			0.443070i
$520$	−670637.	−	846491.i	−0.108762	−	0.137282i
$521$		−	9.35142e6i		−	1.50933i	−0.656112	−	0.754664i	$-0.727800\pi$
$521$		−	9.35142e6i		−	1.50933i	0.656112	−	0.754664i	$-0.272200\pi$
$522$	3.49504e6	−	793801.i	0.561404	−	0.127507i
$523$		−	1.06063e7i		−	1.69555i	−0.530354	−	0.847776i	$-0.677941\pi$
$523$		−	1.06063e7i		−	1.69555i	0.530354	−	0.847776i	$-0.322059\pi$
$524$	−8.93400e6	+	4.27895e6i	−1.42140	+	0.680783i
$525$	5.17185e6			0.818931
$526$	2.22721e6	+	9.80621e6i	0.350992	+	1.54539i
$527$	533276.			0.0836422
$528$	2.74872e6	+	2.21127e6i	0.429087	+	0.345189i
$529$	1.34619e6			0.209154
$530$	553527.	+	2.43713e6i	0.0855952	+	0.376868i
$531$			6.16367e6i			0.948643i
$532$	4.68590e6	−	1.04198e7i	0.717818	−	1.59617i
$533$		−	3.25803e6i		−	0.496750i
$534$	−99708.5	+	22646.0i	−0.0151314	+	0.00343668i
$535$	1.44931e6			0.218915
$536$	−2.88358e6	−	3.63971e6i	−0.433530	−	0.547211i
$537$	−673617.			−0.100804
$538$	−4.44155e6	+	1.00878e6i	−0.661575	+	0.150258i
$539$	1.49281e7			2.21326
$540$	1.61997e6	−	775884.i	0.239068	−	0.114502i
$541$		−	1.11935e7i		−	1.64427i	−0.569294	−	0.822134i	$-0.692783\pi$
$541$		−	1.11935e7i		−	1.64427i	0.569294	−	0.822134i	$-0.307217\pi$
$542$	−542107.	−	2.38685e6i	−0.0792660	−	0.349002i
$543$		−	5.51490e6i		−	0.802671i
$544$	1.41729e6	−	2.90334e6i	0.205334	−	0.420630i
$545$			431568.i			0.0622383i
$546$	−3.59426e6	+	816336.i	−0.515974	+	0.117189i
$547$			5.51419e6i			0.787977i	0.919115	+	0.393988i	$0.128905\pi$
$547$			5.51419e6i			0.787977i	−0.919115	+	0.393988i	$0.871095\pi$
$548$	6.60740e6	−	3.16462e6i	0.939895	−	0.450164i
$549$		−	898898.i		−	0.127286i
$550$	6.76558e6	−	1.53661e6i	0.953670	−	0.216600i
$551$	3.59511e6	+	4.25517e6i	0.504467	+	0.597087i
$552$	−2.56150e6	+	2.02936e6i	−0.357806	+	0.283473i
$553$			5.14971e6i			0.716093i
$554$	−1.06092e6	−	4.67114e6i	−0.146862	−	0.646619i
$555$	−777488.			−0.107142
$556$	9.62544e6	−	4.61011e6i	1.32049	−	0.632448i
$557$			1.24853e7i			1.70514i	0.522612	+	0.852571i	$0.324958\pi$
$557$			1.24853e7i			1.70514i	−0.522612	+	0.852571i	$0.675042\pi$
$558$	943958.	−	214394.i	0.128342	−	0.0291492i
$559$	−3.71833e6			−0.503291
$560$	−2.42098e6	+	3.00940e6i	−0.326228	+	0.405518i
$561$		−	1.92148e6i		−	0.257768i
$562$	2.04348e6	+	8.99729e6i	0.272917	+	1.20163i
$563$		−	9.36247e6i		−	1.24486i	−0.782677	−	0.622428i	$-0.786146\pi$
$563$		−	9.36247e6i		−	1.24486i	0.782677	−	0.622428i	$-0.213854\pi$
$564$	1.22705e6	−	587694.i	0.162429	−	0.0777954i
$565$	−770272.			−0.101513
$566$	−8.13733e6	+	1.84817e6i	−1.06768	+	0.242494i
$567$			3.73731e6i			0.488204i
$568$	1.12510e7	−	8.91369e6i	1.46326	−	1.15928i
$569$			1.74700e6i			0.226210i	0.993583	+	0.113105i	$0.0360797\pi$
$569$			1.74700e6i			0.226210i	−0.993583	+	0.113105i	$0.963920\pi$
$570$	945514.	+	712759.i	0.121894	+	0.0918873i
$571$	6.11866e6			0.785356			0.392678	−	0.919676i	$-0.371549\pi$
$571$	6.11866e6			0.785356			0.392678	+	0.919676i	$0.371549\pi$
$572$	−4.45930e6	+	2.13579e6i	−0.569871	+	0.272940i
$573$	321263.			0.0408766
$574$	−1.13626e7	+	2.58070e6i	−1.43946	+	0.326933i
$575$			6.42694e6i			0.810652i
$576$	1.34152e6	−	5.70903e6i	0.168477	−	0.716979i
$577$	9.67666e6			1.21000			0.605001	−	0.796225i	$-0.293173\pi$
$577$	9.67666e6			1.21000			0.605001	+	0.796225i	$0.293173\pi$
$578$	6.11642e6	−	1.38918e6i	0.761514	−	0.172957i
$579$	−6.65804e6			−0.825372
$580$	−813471.	−	1.69844e6i	−0.100409	−	0.209643i
$581$		−	2.86001e6i		−	0.351502i
$582$	−7.48717e6	+	1.70050e6i	−0.916242	+	0.208099i
$583$	1.14422e7			1.39424
$584$	−477741.	+	378493.i	−0.0579643	+	0.0459225i
$585$			1.06774e6i			0.128995i
$586$	−4.83897e6	+	1.09904e6i	−0.582115	+	0.132211i
$587$	7.87414e6			0.943209			0.471604	−	0.881810i	$-0.343675\pi$
$587$	7.87414e6			0.943209			0.471604	+	0.881810i	$0.343675\pi$
$588$	3.83508e6	+	8.00726e6i	0.457437	+	0.955082i
$589$	970985.	+	1.14926e6i	0.115325	+	0.136499i
$590$	3.15820e6	−	717298.i	0.373517	−	0.0848339i
$591$	3.34234e6			0.393624
$592$	−3.75160e6	+	4.66343e6i	−0.439959	+	0.546891i
$593$	1.44981e7			1.69307			0.846534	−	0.532335i	$-0.178685\pi$
$593$	1.44981e7			1.69307			0.846534	+	0.532335i	$0.178685\pi$
$594$	−1.82136e6	−	8.01930e6i	−0.211802	−	0.932546i
$595$	2.10371e6			0.243609
$596$	−4.56725e6	−	9.53594e6i	−0.526670	−	1.09963i
$597$	6.56527e6			0.753905
$598$	−1.01444e6	−	4.46650e6i	−0.116004	−	0.510758i
$599$	8.78031e6			0.999869			0.499934	−	0.866063i	$-0.333357\pi$
$599$	8.78031e6			0.999869			0.499934	+	0.866063i	$0.333357\pi$
$600$	2.56232e6	+	3.23421e6i	0.290573	+	0.366767i
$601$			1.11436e7i			1.25847i	0.777217	+	0.629233i	$0.216631\pi$
$601$			1.11436e7i			1.25847i	−0.777217	+	0.629233i	$0.783369\pi$
$602$	2.94531e6	+	1.29680e7i	0.331238	+	1.45841i
$603$			4.59101e6i			0.514179i
$604$	−1.55619e7	+	7.45340e6i	−1.73569	+	0.831309i
$605$			404179.i			0.0448937i
$606$	2.56915e6	−	583510.i	0.284189	−	0.0645457i
$607$	1.07344e7			1.18252			0.591258	−	0.806482i	$-0.298632\pi$
$607$	1.07344e7			1.18252			0.591258	+	0.806482i	$0.298632\pi$
$608$	8.83755e6	−	2.23200e6i	0.969556	−	0.244869i
$609$	−6.42721e6			−0.702230
$610$	−460586.	+	104609.i	−0.0501172	+	0.0113827i
$611$			1.90686e6i			0.206640i
$612$	−2.88087e6	+	1.37979e6i	−0.310917	+	0.148914i
$613$			8.84591e6i			0.950805i	0.879768	+	0.475402i	$0.157698\pi$
$613$			8.84591e6i			0.950805i	−0.879768	+	0.475402i	$0.842302\pi$
$614$	−2.20304e6	−	9.69978e6i	−0.235831	−	1.03834i
$615$		−	1.20760e6i		−	0.128747i
$616$	1.09809e7	+	1.38604e7i	1.16597	+	1.47171i
$617$	1.76166e6			0.186299			0.0931493	−	0.995652i	$-0.470307\pi$
$617$	1.76166e6			0.186299			0.0931493	+	0.995652i	$0.470307\pi$
$618$	−294398.	−	1.29621e6i	−0.0310072	−	0.136522i
$619$	−7.38236e6			−0.774406			−0.387203	−	0.921995i	$-0.626559\pi$
$619$	−7.38236e6			−0.774406			−0.387203	+	0.921995i	$0.626559\pi$
$620$	−219707.	−	458725.i	−0.0229543	−	0.0479262i
$621$	7.61791e6			0.792696
$622$	−3.15695e6	−	1.38998e7i	−0.327183	−	1.44056i
$623$	−512520.			−0.0529043
$624$	−2.29122e6	−	1.84322e6i	−0.235562	−	0.189503i
$625$	7.25120e6			0.742523
$626$	2.02257e6	−	459370.i	0.206285	−	0.0468518i
$627$	4.14097e6	−	3.49862e6i	0.420662	−	0.355408i
$628$	−4.09719e6	−	8.55451e6i	−0.414560	−	0.865557i
$629$	3.25995e6			0.328537
$630$	3.72380e6	−	845758.i	0.373797	−	0.0848975i
$631$		−	7.76892e6i		−	0.776761i	−0.921499	−	0.388380i	$-0.873035\pi$
$631$		−	7.76892e6i		−	0.776761i	0.921499	−	0.388380i	$-0.126965\pi$
$632$	−3.22036e6	+	2.55135e6i	−0.320710	+	0.254084i
$633$	601193.			0.0596355
$634$	−4.47844e6	+	1.01715e6i	−0.442490	+	0.100499i
$635$			399660.i			0.0393329i
$636$	2.93953e6	+	6.13744e6i	0.288161	+	0.601651i
$637$	−1.24435e7			−1.21505
$638$	−8.40778e6	+	1.90959e6i	−0.817767	+	0.185733i
$639$	−1.41917e7			−1.37493
$640$	−3.08137e6	−	22993.5i	−0.297368	−	0.00221899i
$641$		−	1.42307e7i		−	1.36798i	−0.729491	−	0.683990i	$-0.760243\pi$
$641$		−	1.42307e7i		−	1.36798i	0.729491	−	0.683990i	$-0.239757\pi$
$642$	3.84830e6	−	874035.i	0.368495	−	0.0836934i
$643$	−1.61884e7			−1.54410			−0.772052	−	0.635560i	$-0.780769\pi$
$643$	−1.61884e7			−1.54410			−0.772052	+	0.635560i	$0.780769\pi$
$644$	−1.47737e7	+	7.07588e6i	−1.40370	+	0.672304i
$645$	−1.37822e6			−0.130442
$646$	−3.96447e6	−	2.98854e6i	−0.373769	−	0.281759i
$647$			4.65708e6i			0.437374i	0.975795	+	0.218687i	$0.0701774\pi$
$647$			4.65708e6i			0.437374i	−0.975795	+	0.218687i	$0.929823\pi$
$648$	−2.33712e6	+	1.85160e6i	−0.218647	+	0.173224i
$649$		−	1.48275e7i		−	1.38184i
$650$	−5.63951e6	+	1.28086e6i	−0.523550	+	0.118910i
$651$	−1.73589e6			−0.160535
$652$	6.69810e6	−	3.20806e6i	0.617068	−	0.295545i
$653$			4.24081e6i			0.389194i	0.980883	+	0.194597i	$0.0623399\pi$
$653$			4.24081e6i			0.389194i	−0.980883	+	0.194597i	$0.937660\pi$
$654$	260266.	+	1.14593e6i	0.0237943	+	0.104764i
$655$		−	5.14603e6i		−	0.468672i
$656$	−7.24329e6	−	5.82703e6i	−0.657168	−	0.528674i
$657$	602607.			0.0544654
$658$	6.65030e6	−	1.51043e6i	0.598792	−	0.135999i
$659$		−	1.52919e7i		−	1.37166i	−0.727761	−	0.685831i	$-0.759439\pi$
$659$		−	1.52919e7i		−	1.37166i	0.727761	−	0.685831i	$-0.240561\pi$
$660$	−1.65286e6	+	791638.i	−0.147698	+	0.0707403i
$661$	−1.01725e7			−0.905573			−0.452786	−	0.891619i	$-0.649570\pi$
$661$	−1.01725e7			−0.905573			−0.452786	+	0.891619i	$0.649570\pi$
$662$	−4.95550e6	−	2.18186e7i	−0.439483	−	1.93501i
$663$			1.60167e6i			0.141510i
$664$	1.78850e6	−	1.41695e6i	0.157424	−	0.124720i
$665$	3.83042e6	+	4.53369e6i	0.335886	+	0.397555i
$666$	5.77047e6	−	1.31060e6i	0.504111	−	0.114495i
$667$		−	7.98695e6i		−	0.695131i
$668$	−1.28132e7	+	6.13691e6i	−1.11101	+	0.532119i
$669$		−	6.73374e6i		−	0.581689i
$670$	2.35239e6	−	534279.i	0.202452	−	0.0459813i
$671$			2.16242e6i			0.185410i
$672$	−4.61349e6	+	9.45082e6i	−0.394100	+	0.807321i
$673$			1.39362e7i			1.18606i	0.805182	+	0.593028i	$0.202068\pi$
$673$			1.39362e7i			1.18606i	−0.805182	+	0.593028i	$0.797932\pi$
$674$	2.04075e6	+	8.98524e6i	0.173037	+	0.761868i
$675$		−	9.61854e6i		−	0.812549i
$676$	−6.99862e6	+	3.35200e6i	−0.589042	+	0.282122i
$677$	8.34747e6			0.699976			0.349988	−	0.936754i	$-0.386186\pi$
$677$	8.34747e6			0.699976			0.349988	+	0.936754i	$0.386186\pi$
$678$	−2.04528e6	+	464530.i	−0.170875	+	0.0388096i
$679$	−3.84855e7			−3.20348
$680$	1.04225e6	+	1.31555e6i	0.0864373	+	0.109103i
$681$	62603.6			0.00517287
$682$	−2.27082e6	+	515753.i	−0.186948	+	0.0424601i
$683$			1.83174e7i			1.50249i	0.660024	+	0.751245i	$0.270546\pi$
$683$			1.83174e7i			1.50249i	−0.660024	+	0.751245i	$0.729454\pi$
$684$	−8.21904e6	−	3.69621e6i	−0.671709	−	0.302076i
$685$			3.80590e6i			0.309907i
$686$	5.07880e6	+	2.23615e7i	0.412050	+	1.81422i
$687$	−6.44836e6			−0.521264
$688$	−6.65029e6	+	8.26664e6i	−0.535635	+	0.665821i
$689$	−9.53772e6			−0.765415
$690$	−376007.	−	1.65553e6i	−0.0300659	−	0.132377i
$691$	625406.			0.0498273			0.0249136	−	0.999690i	$-0.492069\pi$
$691$	625406.			0.0498273			0.0249136	+	0.999690i	$0.492069\pi$
$692$	−9.80635e6	+	4.69676e6i	−0.778470	+	0.372849i
$693$		−	1.74830e7i		−	1.38287i
$694$	−8.20785e6	+	1.86419e6i	−0.646890	+	0.146923i
$695$			5.54431e6i			0.435397i
$696$	−3.18427e6	−	4.01925e6i	−0.249165	−	0.314501i
$697$			5.06340e6i			0.394784i
$698$	−2.01289e6	−	8.86260e6i	−0.156380	−	0.688530i
$699$		−	9.62539e6i		−	0.745119i
$700$	8.93416e6	+	1.86536e7i	0.689142	+	1.43886i
$701$		−	7.69607e6i		−	0.591526i	−0.955261	−	0.295763i	$-0.904426\pi$
$701$		−	7.69607e6i		−	0.591526i	0.955261	−	0.295763i	$-0.0955739\pi$
$702$	1.51821e6	+	6.68456e6i	0.116276	+	0.511953i
$703$	5.93569e6	+	7.02549e6i	0.452984	+	0.536152i
$704$	−3.22721e6	+	1.37338e7i	−0.245412	+	1.04438i
$705$			706785.i			0.0535568i
$706$	−2.51184e6	+	570494.i	−0.189662	+	0.0430764i
$707$	1.32059e7			0.993618
$708$	7.95331e6	−	3.80924e6i	0.596300	−	0.285598i
$709$		−	983382.i		−	0.0734694i	−0.999325	−	0.0367347i	$-0.988304\pi$
$709$		−	983382.i		−	0.0734694i	0.999325	−	0.0367347i	$-0.0116957\pi$
$710$	1.65156e6	+	7.27168e6i	0.122956	+	0.541363i
$711$	4.06206e6			0.301351
$712$	−253921.	−	320504.i	−0.0187715	−	0.0236938i
$713$		−	2.15716e6i		−	0.158913i
$714$	5.58593e6	−	1.26869e6i	0.410062	−	0.0931343i
$715$		−	2.56858e6i		−	0.187901i
$716$	−1.16365e6	−	2.42957e6i	−0.0848278	−	0.177112i
$717$	1.39472e7			1.01319
$718$	−2.26612e6	−	9.97753e6i	−0.164048	−	0.722291i
$719$			6.60244e6i			0.476302i	0.971228	+	0.238151i	$0.0765413\pi$
$719$			6.60244e6i			0.476302i	−0.971228	+	0.238151i	$0.923459\pi$
$720$	2.37380e6	+	1.90966e6i	0.170653	+	0.137285i
$721$		−	6.66275e6i		−	0.477326i
$722$	−777893.	−	1.39853e7i	−0.0555363	−	0.998457i
$723$	−4.31653e6			−0.307107
$724$	1.98909e7	−	9.52676e6i	1.41029	−	0.675459i
$725$	−1.00845e7			−0.712540
$726$	243749.	+	1.07321e6i	0.0171633	+	0.0755687i
$727$			1.65829e7i			1.16366i	0.813311	+	0.581829i	$0.197663\pi$
$727$			1.65829e7i			1.16366i	−0.813311	+	0.581829i	$0.802337\pi$
$728$	−9.15326e6	−	1.15534e7i	−0.640099	−	0.807946i
$729$	−3.61748e6			−0.252108
$730$	−70128.5	−	308770.i	−0.00487065	−	0.0214451i
$731$	5.77876e6			0.399983
$732$	−1.15990e6	+	555533.i	−0.0800094	+	0.0383206i
$733$		−	1.29924e7i		−	0.893162i	−0.894743	−	0.446581i	$-0.852642\pi$
$733$		−	1.29924e7i		−	0.893162i	0.894743	−	0.446581i	$-0.147358\pi$
$734$	2.70191e6	+	1.18963e7i	0.185110	+	0.815024i
$735$	−4.61223e6			−0.314914
$736$	−1.17443e7	−	5.73308e6i	−0.799159	−	0.390116i
$737$		−	1.10443e7i		−	0.748978i
$738$	2.03565e6	+	8.96278e6i	0.137582	+	0.605761i
$739$	−1.86179e7			−1.25406			−0.627031	−	0.778995i	$-0.715730\pi$
$739$	−1.86179e7			−1.25406			−0.627031	+	0.778995i	$0.715730\pi$
$740$	−1.34308e6	−	2.80421e6i	−0.0901618	−	0.188248i
$741$	−3.45174e6	+	2.91630e6i	−0.230936	+	0.195114i
$742$	7.55488e6	+	3.32635e7i	0.503753	+	2.21798i
$743$	1.06123e7			0.705238			0.352619	−	0.935767i	$-0.385291\pi$
$743$	1.06123e7			0.705238			0.352619	+	0.935767i	$0.385291\pi$
$744$	−860025.	−	1.08554e6i	−0.0569611	−	0.0718975i
$745$	5.49275e6			0.362576
$746$	2.38882e7	−	5.42555e6i	1.57158	−	0.356941i
$747$	−2.25596e6			−0.147921
$748$	6.93031e6	−	3.31928e6i	0.452896	−	0.216915i
$749$	1.97810e7			1.28838
$750$	−4.38340e6	+	995567.i	−0.284550	+	0.0646275i
$751$	−1.91418e7			−1.23846			−0.619231	−	0.785209i	$-0.712555\pi$
$751$	−1.91418e7			−1.23846			−0.619231	+	0.785209i	$0.712555\pi$
$752$	4.23934e6	+	3.41044e6i	0.273372	+	0.219920i
$753$			6.33034e6i			0.406855i
$754$	7.00838e6	−	1.59176e6i	0.448941	−	0.101965i
$755$		−	8.96376e6i		−	0.572299i
$756$	2.21103e7	−	1.05897e7i	1.40699	−	0.673877i
$757$			1.46610e7i			0.929876i	0.885343	+	0.464938i	$0.153923\pi$
$757$			1.46610e7i			0.929876i	−0.885343	+	0.464938i	$0.846077\pi$
$758$	−6.48272e6	−	2.85429e7i	−0.409812	−	1.80437i
$759$	−7.77259e6			−0.489735
$760$	−937410.	+	4.64150e6i	−0.0588702	+	0.291491i
$761$	−1.98360e7			−1.24163			−0.620814	−	0.783958i	$-0.713198\pi$
$761$	−1.98360e7			−1.24163			−0.620814	+	0.783958i	$0.713198\pi$
$762$	241023.	+	1.06121e6i	0.0150374	+	0.0662083i
$763$			5.89030e6i			0.366291i
$764$	554970.	+	1.15872e6i	0.0343982	+	0.0718199i
$765$		−	1.65940e6i		−	0.102517i
$766$	2.13582e7	−	4.85091e6i	1.31520	−	0.298711i
$767$			1.23596e7i			0.758607i
$768$	−8.19575e6	+	1.79723e6i	−0.501401	+	0.109952i
$769$	−2.05644e7			−1.25401			−0.627005	−	0.779015i	$-0.715719\pi$
$769$	−2.05644e7			−1.25401			−0.627005	+	0.779015i	$0.715719\pi$
$770$	−8.95811e6	+	2.03459e6i	−0.544490	+	0.123666i
$771$	1.13640e7			0.688488
$772$	−1.15015e7	−	2.40139e7i	−0.694562	−	1.45017i
$773$	2.73890e7			1.64864			0.824322	−	0.566121i	$-0.191556\pi$
$773$	2.73890e7			1.64864			0.824322	+	0.566121i	$0.191556\pi$
$774$	1.02290e7	−	2.32324e6i	0.613738	−	0.139393i
$775$	−2.72368e6			−0.162893
$776$	−1.90671e7	−	2.40668e7i	−1.13666	−	1.43471i
$777$	−1.06116e7			−0.630565
$778$	−3.60231e6	−	1.58607e7i	−0.213369	−	0.939447i
$779$	−1.09121e7	+	9.21939e6i	−0.644264	+	0.544325i
$780$	1.37776e6	−	659877.i	0.0810841	−	0.0388353i
$781$	3.41400e7			2.00279
$782$	1.57657e6	+	6.94151e6i	0.0921927	+	0.405917i
$783$			1.19532e7i			0.696757i
$784$	−2.22553e7	+	2.76644e7i	−1.29313	+	1.60743i
$785$	4.92744e6			0.285396
$786$	−3.10343e6	−	1.36641e7i	−0.179178	−	0.788906i
$787$			1.42408e7i			0.819591i	0.912177	+	0.409796i	$0.134400\pi$
$787$			1.42408e7i			0.819591i	−0.912177	+	0.409796i	$0.865600\pi$
$788$	5.77376e6	+	1.20550e7i	0.331240	+	0.691596i
$789$	−1.42245e7			−0.813474
$790$	−472723.	−	2.08136e6i	−0.0269488	−	0.118653i
$791$	−1.05131e7			−0.597436
$792$	1.09330e7	−	8.66170e6i	0.619335	−	0.490671i
$793$		−	1.80251e6i		−	0.101787i
$794$	−5.69913e6	−	2.50928e7i	−0.320817	−	1.41253i
$795$	−3.53520e6			−0.198379
$796$	1.13412e7	+	2.36793e7i	0.634422	+	1.32461i
$797$	−208544.			−0.0116293			−0.00581464	−	0.999983i	$-0.501851\pi$
$797$	−208544.			−0.0116293			−0.00581464	+	0.999983i	$0.501851\pi$
$798$	1.29050e7	+	9.72817e6i	0.717380	+	0.540784i
$799$		−	2.96350e6i		−	0.164224i
$800$	−7.23871e6	+	1.48286e7i	−0.399886	+	0.819174i
$801$			404273.i			0.0222635i
$802$	1.39955e6	+	6.16210e6i	0.0768338	+	0.338293i
$803$	−1.44965e6			−0.0793368
$804$	5.92402e6	−	2.83731e6i	0.323204	−	0.154799i
$805$		−	8.50973e6i		−	0.462835i
$806$	1.89286e6	−	429911.i	0.102632	−	0.0233099i
$807$		−	6.44272e6i		−	0.348245i
$808$	6.54268e6	+	8.25830e6i	0.352555	+	0.445002i
$809$	5.59084e6			0.300335			0.150167	−	0.988661i	$-0.452019\pi$
$809$	5.59084e6			0.300335			0.150167	+	0.988661i	$0.452019\pi$
$810$	−343070.	−	1.51051e6i	−0.0183726	−	0.0808930i
$811$			1.50060e7i			0.801146i	0.916265	+	0.400573i	$0.131189\pi$
$811$			1.50060e7i			0.801146i	−0.916265	+	0.400573i	$0.868811\pi$
$812$	−1.11027e7	−	2.31814e7i	−0.590936	−	1.23381i
$813$	3.46226e6			0.183710
$814$	−1.38817e7	+	3.15283e6i	−0.734311	+	0.166778i
$815$			3.85814e6i			0.203463i
$816$	3.56084e6	+	2.86460e6i	0.187209	+	0.150605i
$817$	1.05219e7	+	1.24538e7i	0.551493	+	0.652747i
$818$	−2.92526e6	−	1.28797e7i	−0.152856	−	0.673011i
$819$			1.45731e7i			0.759176i
$820$	4.35554e6	−	2.08609e6i	0.226208	−	0.108342i
$821$			713772.i			0.0369574i	0.999829	+	0.0184787i	$0.00588229\pi$
$821$			713772.i			0.0369574i	−0.999829	+	0.0184787i	$0.994118\pi$
$822$	2.29523e6	+	1.01057e7i	0.118480	+	0.521659i
$823$		−	1.40864e7i		−	0.724935i	−0.931996	−	0.362468i	$-0.881934\pi$
$823$		−	1.40864e7i		−	0.724935i	0.931996	−	0.362468i	$-0.118066\pi$
$824$	4.16655e6	−	3.30097e6i	0.213776	−	0.169365i
$825$			9.81385e6i			0.502001i
$826$	4.31051e7	−	9.79012e6i	2.19826	−	0.499273i
$827$		−	7.00116e6i		−	0.355964i	−0.984034	−	0.177982i	$-0.943043\pi$
$827$		−	7.00116e6i		−	0.355964i	0.984034	−	0.177982i	$-0.0569569\pi$
$828$	5.58141e6	+	1.16534e7i	0.282923	+	0.590714i
$829$	−3.30995e7			−1.67276			−0.836382	−	0.548147i	$-0.815334\pi$
$829$	−3.30995e7			−1.67276			−0.836382	+	0.548147i	$0.815334\pi$
$830$	262538.	+	1.15593e6i	0.0132281	+	0.0582421i
$831$	6.77575e6			0.340373
$832$	2.69007e6	−	1.14480e7i	0.134727	−	0.573350i
$833$	1.93387e7			0.965640
$834$	3.34361e6	+	1.47217e7i	0.166457	+	0.732894i
$835$		−	7.38049e6i		−	0.366327i
$836$	1.97720e7	+	8.89174e6i	0.978443	+	0.440019i
$837$			3.22840e6i			0.159284i
$838$	3.33935e7	−	7.58441e6i	1.64268	−	0.373088i
$839$	−1.53849e7			−0.754551			−0.377276	−	0.926101i	$-0.623139\pi$
$839$	−1.53849e7			−0.754551			−0.377276	+	0.926101i	$0.623139\pi$
$840$	−3.39270e6	−	4.28233e6i	−0.165900	−	0.209402i
$841$	−7.97884e6			−0.389000
$842$	−1.77926e7	+	4.04109e6i	−0.864887	+	0.196435i
$843$	−1.30511e7			−0.632525
$844$	1.03854e6	+	2.16836e6i	0.0501841	+	0.104779i
$845$		−	4.03125e6i		−	0.194222i
$846$	−1.19142e6	−	5.24572e6i	−0.0572320	−	0.251987i
$847$			5.51648e6i			0.264213i
$848$	−1.70583e7	+	2.12044e7i	−0.814605	+	1.01259i
$849$		−	1.18036e7i		−	0.562014i
$850$	8.76450e6	−	1.99061e6i	0.416083	−	0.0945017i
$851$		−	1.31868e7i		−	0.624190i
$852$	8.77069e6	+	1.83123e7i	0.413937	+	0.864258i
$853$		−	2.18525e7i		−	1.02832i	−0.857694	−	0.514160i	$-0.828104\pi$
$853$		−	2.18525e7i		−	1.02832i	0.857694	−	0.514160i	$-0.171896\pi$
$854$	−6.28636e6	+	1.42777e6i	−0.294954	+	0.0669907i
$855$	3.57615e6	−	3.02141e6i	0.167302	−	0.141350i
$856$	9.80023e6	+	1.23700e7i	0.457143	+	0.577015i
$857$			3.19025e7i			1.48379i	0.670515	+	0.741896i	$0.266073\pi$
$857$			3.19025e7i			1.48379i	−0.670515	+	0.741896i	$0.733927\pi$
$858$	−1.54904e6	−	6.82029e6i	−0.0718363	−	0.316289i
$859$	2.13208e7			0.985871			0.492935	−	0.870066i	$-0.335924\pi$
$859$	2.13208e7			0.985871			0.492935	+	0.870066i	$0.335924\pi$
$860$	−2.38081e6	−	4.97089e6i	−0.109769	−	0.229186i
$861$		−	1.64821e7i		−	0.757714i
$862$	−1.46636e7	+	3.33042e6i	−0.672158	+	0.152662i
$863$	2.15232e6			0.0983740			0.0491870	−	0.998790i	$-0.484337\pi$
$863$	2.15232e6			0.0983740			0.0491870	+	0.998790i	$0.484337\pi$
$864$	1.75765e7	+	8.58011e6i	0.801029	+	0.391029i
$865$		−	5.64851e6i		−	0.256681i
$866$	−5.42596e6	−	2.38900e7i	−0.245856	−	1.08249i
$867$			8.87221e6i			0.400852i
$868$	−2.99869e6	−	6.26095e6i	−0.135093	−	0.282060i
$869$	−9.77183e6			−0.438961
$870$	2.59769e6	−	589993.i	0.116356	−	0.0264270i
$871$			9.20606e6i			0.411177i
$872$	−3.68350e6	+	2.91827e6i	−0.164047	+	0.129967i
$873$			3.03571e7i			1.34811i
$874$	−1.20890e7	+	1.60367e7i	−0.535317	+	0.710128i
$875$	−2.25315e7			−0.994878
$876$	−372421.	−	777576.i	−0.0163973	−	0.0342360i
$877$	−1.35344e7			−0.594208			−0.297104	−	0.954845i	$-0.596021\pi$
$877$	−1.35344e7			−0.594208			−0.297104	+	0.954845i	$0.596021\pi$
$878$	−2.18473e7	+	4.96201e6i	−0.956449	+	0.217231i
$879$		−	7.01920e6i		−	0.306419i
$880$	−5.71050e6	−	4.59394e6i	−0.248581	−	0.199976i
$881$	5.65521e6			0.245476			0.122738	−	0.992439i	$-0.460832\pi$
$881$	5.65521e6			0.245476			0.122738	+	0.992439i	$0.460832\pi$
$882$	3.42317e7	−	7.77478e6i	1.48169	−	0.336524i
$883$	−2.35203e7			−1.01517			−0.507587	−	0.861600i	$-0.669463\pi$
$883$	−2.35203e7			−1.01517			−0.507587	+	0.861600i	$0.669463\pi$
$884$	−5.77683e6	+	2.76682e6i	−0.248633	+	0.119083i
$885$			4.58115e6i			0.196615i
$886$	3.58799e7	−	8.14912e6i	1.53556	−	0.348760i
$887$	−3.20321e7			−1.36702			−0.683512	−	0.729939i	$-0.739548\pi$
$887$	−3.20321e7			−1.36702			−0.683512	+	0.729939i	$0.739548\pi$
$888$	−5.25738e6	−	6.63598e6i	−0.223737	−	0.282405i
$889$			5.45480e6i			0.231486i
$890$	207146.	−	47047.4i	0.00876598	−	0.00199095i
$891$	−7.09173e6			−0.299266
$892$	2.42870e7	−	1.16323e7i	1.02202	−	0.489499i
$893$	6.38660e6	−	5.39591e6i	0.268004	−	0.226431i
$894$	1.45848e7	−	3.31252e6i	0.610317	−	0.138617i
$895$	1.39945e6			0.0583981
$896$	−4.20564e7	−	313829.i	−1.75010	−	0.0130594i
$897$	6.47892e6			0.268857
$898$	−9.17891e6	−	4.04140e7i	−0.379840	−	1.67240i
$899$	3.38479e6			0.139680
$900$	1.47139e7	−	7.04722e6i	0.605509	−	0.290009i
$901$	1.48228e7			0.608302
$902$	−4.89702e6	−	2.15612e7i	−0.200408	−	0.882380i
$903$	−1.88107e7			−0.767691
$904$	−5.20859e6	−	6.57439e6i	−0.211982	−	0.267568i
$905$			1.14573e7i			0.465007i
$906$	−5.40579e6	−	2.38012e7i	−0.218796	−	0.963339i
$907$		−	7.97715e6i		−	0.321980i	−0.986956	−	0.160990i	$-0.948531\pi$
$907$		−	7.97715e6i		−	0.321980i	0.986956	−	0.160990i	$-0.0514688\pi$
$908$	108145.	+	225796.i	0.00435304	+	0.00908870i
$909$		−	1.04167e7i		−	0.418140i
$910$	7.46711e6	−	1.69595e6i	0.298916	−	0.0678905i
$911$	2.41136e7			0.962645			0.481323	−	0.876544i	$-0.340157\pi$
$911$	2.41136e7			0.962645			0.481323	+	0.876544i	$0.340157\pi$
$912$	310078.	+	1.28898e7i	0.0123448	+	0.513167i
$913$	5.42702e6			0.215469
$914$	8.26959e6	−	1.87821e6i	0.327430	−	0.0743666i
$915$		−	668106.i		−	0.0263811i
$916$	−1.11393e7	−	2.32577e7i	−0.438651	−	0.915857i
$917$		−	7.02362e7i		−	2.75827i
$918$	−2.35949e6	−	1.03886e7i	−0.0924084	−	0.406867i
$919$		−	3.69774e7i		−	1.44427i	−0.691754	−	0.722133i	$-0.743162\pi$
$919$		−	3.69774e7i		−	1.44427i	0.691754	−	0.722133i	$-0.256838\pi$
$920$	5.32156e6	−	4.21603e6i	0.207286	−	0.164223i
$921$	1.40701e7			0.546572
$922$	−4.63427e6	−	2.04043e7i	−0.179537	−	0.790487i
$923$	−2.84577e7			−1.09950
$924$	−2.25592e7	+	1.08048e7i	−0.869249	+	0.416328i
$925$	−1.66500e7			−0.639823
$926$	6.70742e6	+	2.95322e7i	0.257056	+	1.13180i
$927$	−5.25554e6			−0.200871
$928$	8.99576e6	−	1.84280e7i	0.342901	−	0.702438i
$929$	2.35418e7			0.894953			0.447476	−	0.894296i	$-0.352323\pi$
$929$	2.35418e7			0.894953			0.447476	+	0.894296i	$0.352323\pi$
$930$	701597.	−	159348.i	0.0265999	−	0.00604144i
$931$	3.52118e7	+	4.16767e7i	1.33142	+	1.57587i
$932$	3.47164e7	−	1.66275e7i	1.30917	−	0.627027i
$933$	2.01624e7			0.758295
$934$	−2.57398e7	+	5.84607e6i	−0.965467	+	0.219279i
$935$			3.99190e6i			0.149331i
$936$	−9.11328e6	+	7.22004e6i	−0.340005	+	0.269371i
$937$	−3.23504e7			−1.20374			−0.601868	−	0.798596i	$-0.705577\pi$
$937$	−3.23504e7			−1.20374			−0.601868	+	0.798596i	$0.705577\pi$
$938$	3.21068e7	−	7.29217e6i	1.19149	−	0.270613i
$939$			2.93384e6i			0.108586i
$940$	−2.54920e6	+	1.22094e6i	−0.0940989	+	0.0450687i
$941$	9.28108e6			0.341684			0.170842	−	0.985298i	$-0.445351\pi$
$941$	9.28108e6			0.341684			0.170842	+	0.985298i	$0.445351\pi$
$942$	1.30837e7	−	2.97160e6i	0.480401	−	0.109110i
$943$	2.04820e7			0.750054
$944$	2.74780e7	+	2.21053e7i	1.00359	+	0.807360i
$945$			1.27356e7i			0.463918i
$946$	−2.46074e7	+	5.58888e6i	−0.893999	+	0.203047i
$947$	2.43417e7			0.882016			0.441008	−	0.897503i	$-0.354621\pi$
$947$	2.43417e7			0.882016			0.441008	+	0.897503i	$0.354621\pi$
$948$	−2.51042e6	−	5.24149e6i	−0.0907246	−	0.189424i
$949$	1.20837e6			0.0435547
$950$	2.02483e7	+	1.52638e7i	0.727913	+	0.548724i
$951$		−	6.49623e6i		−	0.232922i
$952$	1.42253e7	+	1.79555e7i	0.508709	+	0.642103i
$953$			1.32732e7i			0.473417i	0.971581	+	0.236709i	$0.0760687\pi$
$953$			1.32732e7i			0.473417i	−0.971581	+	0.236709i	$0.923931\pi$
$954$	2.62381e7	−	5.95924e6i	0.933385	−	0.211992i
$955$	−667429.			−0.0236808
$956$	2.40933e7	+	5.03042e7i	0.852611	+	1.78016i
$957$		−	1.21960e7i		−	0.430463i
$958$	7.45020e6	+	3.28026e7i	0.262273	+	1.15477i
$959$			5.19452e7i			1.82389i
$960$	997087.	−	4.24324e6i	0.0349185	−	0.148600i
$961$	−2.77150e7			−0.968068
$962$	1.15712e7	−	2.62807e6i	0.403125	−	0.0915587i
$963$		−	1.56032e7i		−	0.542184i
$964$	−7.45664e6	−	1.55687e7i	−0.258435	−	0.539585i
$965$	1.38322e7			0.478158
$966$	−5.13198e6	−	2.25957e7i	−0.176947	−	0.779081i
$967$			8.33848e6i			0.286761i	0.989668	+	0.143381i	$0.0457973\pi$
$967$			8.33848e6i			0.286761i	−0.989668	+	0.143381i	$0.954203\pi$
$968$	−3.44973e6	+	2.73306e6i	−0.118330	+	0.0937479i
$969$	5.36444e6	−	4.53230e6i	0.183533	−	0.155063i
$970$	1.55547e7	−	3.53281e6i	0.530801	−	0.120557i
$971$			1.84683e7i			0.628608i	0.949322	+	0.314304i	$0.101771\pi$
$971$			1.84683e7i			0.628608i	−0.949322	+	0.314304i	$0.898229\pi$
$972$	−1.31634e7	−	2.74839e7i	−0.446893	−	0.933066i
$973$			7.56721e7i			2.56244i
$974$	−4.93944e7	+	1.12186e7i	−1.66832	+	0.378913i
$975$		−	8.18042e6i		−	0.275590i
$976$	−4.00735e6	−	3.22380e6i	−0.134658	−	0.108329i
$977$			1.55288e7i			0.520477i	0.965544	+	0.260239i	$0.0838013\pi$
$977$			1.55288e7i			0.520477i	−0.965544	+	0.260239i	$0.916199\pi$
$978$	2.32674e6	+	1.02444e7i	0.0777858	+	0.342484i
$979$		−	972534.i		−	0.0324301i
$980$	−7.96744e6	−	1.66352e7i	−0.265005	−	0.553302i
$981$	4.64624e6			0.154145
$982$	−3.63595e7	+	8.25806e6i	−1.20320	+	0.273275i
$983$	−3.02143e7			−0.997307			−0.498654	−	0.866801i	$-0.666172\pi$
$983$	−3.02143e7			−0.997307			−0.498654	+	0.866801i	$0.666172\pi$
$984$	1.03071e7	−	8.16584e6i	0.339350	−	0.268852i
$985$	−6.94375e6			−0.228036
$986$	−1.08919e7	+	2.47379e6i	−0.356789	+	0.0810348i
$987$			9.64663e6i			0.315197i
$988$	−1.64811e7	−	7.41179e6i	−0.537149	−	0.241563i
$989$		−	2.33757e7i		−	0.759930i
$990$	1.60487e6	+	7.06611e6i	0.0520417	+	0.229135i
$991$	3.57254e7			1.15556			0.577780	−	0.816192i	$-0.303919\pi$
$991$	3.57254e7			1.15556			0.577780	+	0.816192i	$0.303919\pi$
$992$	2.42962e6	−	4.97713e6i	0.0783898	−	0.160583i
$993$	3.16492e7			1.01857
$994$	2.25415e7	+	9.92483e7i	0.723630	+	3.18608i
$995$	−1.36394e7			−0.436756
$996$	1.39422e6	+	2.91098e6i	0.0445331	+	0.0929804i
$997$			1.22565e7i			0.390506i	0.980753	+	0.195253i	$0.0625528\pi$
$997$			1.22565e7i			0.390506i	−0.980753	+	0.195253i	$0.937447\pi$
$998$	−5.69974e6	+	1.29454e6i	−0.181146	+	0.0411423i
$999$			1.97354e7i			0.625651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.6	yes	96
4.3	odd	2		608.6.b.b.303.60		96
8.3	odd	2	inner	152.6.b.b.75.92	yes	96
8.5	even	2		608.6.b.b.303.59		96
19.18	odd	2	inner	152.6.b.b.75.91	yes	96
76.75	even	2		608.6.b.b.303.38		96
152.37	odd	2		608.6.b.b.303.37		96
152.75	even	2	inner	152.6.b.b.75.5	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.5	✓	96	152.75	even	2	inner
152.6.b.b.75.6	yes	96	1.1	even	1	trivial
152.6.b.b.75.91	yes	96	19.18	odd	2	inner
152.6.b.b.75.92	yes	96	8.3	odd	2	inner
608.6.b.b.303.37		96	152.37	odd	2
608.6.b.b.303.38		96	76.75	even	2
608.6.b.b.303.59		96	8.5	even	2
608.6.b.b.303.60		96	4.3	odd	2

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.51636 + 1.25289i) q^{2} -8.00180i q^{3} +(28.8605 - 13.8228i) q^{4} +16.6238i q^{5} +(10.0254 + 44.1408i) q^{6} +226.892i q^{7} +(-141.887 + 112.411i) q^{8} +178.971 q^{9} +O(q^{10})\)	\(q+(-5.51636 + 1.25289i) q^{2} -8.00180i q^{3} +(28.8605 - 13.8228i) q^{4} +16.6238i q^{5} +(10.0254 + 44.1408i) q^{6} +226.892i q^{7} +(-141.887 + 112.411i) q^{8} +178.971 q^{9} +(-20.8278 - 91.7031i) q^{10} -430.539 q^{11} +(-110.607 - 230.936i) q^{12} +358.880 q^{13} +(-284.271 - 1251.62i) q^{14} +133.020 q^{15} +(641.861 - 797.866i) q^{16} -557.745 q^{17} +(-987.271 + 224.231i) q^{18} +(-1015.54 - 1201.99i) q^{19} +(229.788 + 479.773i) q^{20} +1815.54 q^{21} +(2375.01 - 539.418i) q^{22} +2256.14i q^{23} +(899.486 + 1135.35i) q^{24} +2848.65 q^{25} +(-1979.71 + 449.637i) q^{26} -3376.53i q^{27} +(3136.28 + 6548.23i) q^{28} -3540.10 q^{29} +(-733.789 + 166.660i) q^{30} -956.129 q^{31} +(-2541.10 + 5205.50i) q^{32} +3445.09i q^{33} +(3076.72 - 698.792i) q^{34} -3771.82 q^{35} +(5165.21 - 2473.88i) q^{36} -5844.88 q^{37} +(7108.04 + 5358.26i) q^{38} -2871.69i q^{39} +(-1868.69 - 2358.70i) q^{40} -9078.34i q^{41} +(-10015.2 + 2274.68i) q^{42} -10360.9 q^{43} +(-12425.6 + 5951.25i) q^{44} +2975.19i q^{45} +(-2826.69 - 12445.7i) q^{46} +5313.35i q^{47} +(-6384.36 - 5136.04i) q^{48} -34673.1 q^{49} +(-15714.2 + 3569.04i) q^{50} +4462.96i q^{51} +(10357.5 - 4960.72i) q^{52} -26576.4 q^{53} +(4230.41 + 18626.2i) q^{54} -7157.21i q^{55} +(-25505.1 - 32193.0i) q^{56} +(-9618.09 + 8126.12i) q^{57} +(19528.5 - 4435.35i) q^{58} +34439.4i q^{59} +(3839.04 - 1838.71i) q^{60} -5022.58i q^{61} +(5274.36 - 1197.92i) q^{62} +40607.2i q^{63} +(7495.74 - 31899.1i) q^{64} +5965.96i q^{65} +(-4316.31 - 19004.4i) q^{66} +25652.2i q^{67} +(-16096.8 + 7709.58i) q^{68} +18053.1 q^{69} +(20806.7 - 4725.67i) q^{70} -79295.9 q^{71} +(-25393.7 + 20118.3i) q^{72} +3367.06 q^{73} +(32242.5 - 7322.98i) q^{74} -22794.3i q^{75} +(-45923.8 - 20652.6i) q^{76} -97686.0i q^{77} +(3597.90 + 15841.3i) q^{78} +22696.7 q^{79} +(13263.6 + 10670.2i) q^{80} +16471.7 q^{81} +(11374.1 + 50079.4i) q^{82} -12605.2 q^{83} +(52397.6 - 25095.9i) q^{84} -9271.85i q^{85} +(57154.7 - 12981.1i) q^{86} +28327.2i q^{87} +(61087.9 - 48397.2i) q^{88} +2258.87i q^{89} +(-3727.58 - 16412.2i) q^{90} +81427.1i q^{91} +(31186.1 + 65113.3i) q^{92} +7650.75i q^{93} +(-6657.04 - 29310.4i) q^{94} +(19981.7 - 16882.1i) q^{95} +(41653.3 + 20333.4i) q^{96} +169620. i q^{97} +(191269. - 43441.5i) q^{98} -77054.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Introduction

L-functions

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