LMFDB - Embedded newform 152.6.b.b.75.5

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

$q$-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	$0.0826213\pi$
$3$			8.00180i			0.513315i	−0.966502	+	0.256658i	$0.917379\pi$
$4$	28.8605	+	13.8228i	0.901892	+	0.431962i
$5$		−	16.6238i		−	0.297376i	−0.988884	−	0.148688i	$-0.952495\pi$
$5$		−	16.6238i		−	0.297376i	0.988884	−	0.148688i	$-0.0475050\pi$
$6$	10.0254	−	44.1408i	0.113690	−	0.500567i
$7$		−	226.892i		−	1.75015i	−0.483991	−	0.875073i	$-0.660813\pi$
$7$		−	226.892i		−	1.75015i	0.483991	−	0.875073i	$-0.339187\pi$
$8$	−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	$-0.853329\pi$
$23$		−	2256.14i		−	0.889295i	0.895706	−	0.444648i	$-0.146671\pi$
$24$	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	$0.138571\pi$
$41$			9078.34i			0.843425i	−0.906730	+	0.421713i	$0.861429\pi$
$42$	−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	$-0.943870\pi$
$47$		−	5313.35i		−	0.350852i	0.984493	−	0.175426i	$-0.0561303\pi$
$48$	−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	$-0.777267\pi$
$59$		−	34439.4i		−	1.28803i	0.765013	−	0.644015i	$-0.222733\pi$
$60$	3839.04	+	1838.71i	0.137672	+	0.0659380i
$61$			5022.58i			0.172823i	0.996260	+	0.0864117i	$0.0275400\pi$
$61$			5022.58i			0.172823i	−0.996260	+	0.0864117i	$0.972460\pi$
$62$	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	$-0.886499\pi$
$67$		−	25652.2i		−	0.698132i	0.937098	−	0.349066i	$-0.113501\pi$
$68$	−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	$-0.995189\pi$
$89$		−	2258.87i		−	0.0302285i	0.999886	−	0.0151143i	$-0.00481120\pi$
$90$	−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	$-0.632030\pi$
$97$		−	169620.i		−	1.83041i	0.402992	−	0.915204i	$-0.367970\pi$
$98$	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	$0.0916175\pi$
$101$			58203.4i			0.567734i	−0.958864	+	0.283867i	$0.908383\pi$
$102$	−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	$0.119984\pi$
$107$			87182.5i			0.736156i	−0.929795	+	0.368078i	$0.880016\pi$
$108$	−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	$-0.945403\pi$
$113$		−	46335.4i		−	0.341364i	0.985326	−	0.170682i	$-0.0545970\pi$
$114$	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	$0.208680\pi$
$149$			330414.i			1.21925i	−0.792689	+	0.609626i	$0.791320\pi$
$150$	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	$0.159311\pi$
$157$			296408.i			0.959713i	−0.877347	+	0.479857i	$0.840689\pi$
$158$	−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	$0.0313050\pi$
$179$			84183.2i			0.196378i	−0.995168	+	0.0981890i	$0.968695\pi$
$180$	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	$-0.987323\pi$
$191$		−	40148.9i		−	0.0796325i	0.999207	−	0.0398163i	$-0.0126773\pi$
$192$	−255250.	+	59979.4i	−0.499705	+	0.117422i
$193$			832068.i			1.60792i	0.594681	+	0.803962i	$0.297279\pi$
$193$			832068.i			1.60792i	−0.594681	+	0.803962i	$0.702721\pi$
$194$	−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	$-0.874748\pi$
$197$		−	417699.i		−	0.766828i	0.923577	−	0.383414i	$-0.125252\pi$
$198$	425059.	+	96540.3i	0.770524	+	0.175003i
$199$		−	820475.i		−	1.46870i	−0.678772	−	0.734349i	$-0.737488\pi$
$199$		−	820475.i		−	1.46870i	0.678772	−	0.734349i	$-0.262512\pi$
$200$	−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	$-0.981499\pi$
$211$		−	75132.3i		−	0.116177i	0.998311	−	0.0580886i	$-0.0185006\pi$
$212$	−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	$-0.998396\pi$
$227$		−	7823.69i		−	0.0100774i	0.999987	−	0.00503868i	$-0.00160387\pi$
$228$	−165258.	−	367473.i	−0.210535	−	0.468154i
$229$			805865.i			1.01548i	0.861509	+	0.507742i	$0.169520\pi$
$229$			805865.i			1.01548i	−0.861509	+	0.507742i	$0.830480\pi$
$230$	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	$-0.551569\pi$
$239$		−	1.74301e6i		−	1.97381i	0.161302	−	0.986905i	$-0.448431\pi$
$240$	85380.7	+	106132.i	0.0956823	+	0.118938i
$241$			539446.i			0.598281i	0.954209	+	0.299140i	$0.0966999\pi$
$241$			539446.i			0.598281i	−0.954209	+	0.299140i	$0.903300\pi$
$242$	−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	$-0.766024\pi$
$257$		−	1.42019e6i		−	1.34126i	0.741793	−	0.670629i	$-0.233976\pi$
$258$	−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	$0.291154\pi$
$263$			1.77766e6i			1.58474i	−0.610038	+	0.792372i	$0.708846\pi$
$264$	−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	$-0.942732\pi$
$271$		−	432686.i		−	0.357890i	0.983859	−	0.178945i	$-0.0572684\pi$
$272$	−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	$-0.892431\pi$
$277$		−	846779.i		−	0.663087i	0.943440	−	0.331543i	$-0.107569\pi$
$278$	−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	$0.211295\pi$
$281$			1.63102e6i			1.23223i	−0.787655	+	0.616117i	$0.788705\pi$
$282$	−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	$-0.821293\pi$
$307$		−	1.75837e6i		−	1.06479i	0.846497	−	0.532394i	$-0.178707\pi$
$308$	−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	$-0.735476\pi$
$311$		−	2.51973e6i		−	1.47725i	0.674117	−	0.738625i	$-0.264524\pi$
$312$	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	$-0.539926\pi$
$331$		−	3.95526e6i		−	1.98429i	0.125102	−	0.992144i	$-0.460074\pi$
$332$	−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	$0.127745\pi$
$337$			1.62883e6i			0.781272i	−0.920545	+	0.390636i	$0.872255\pi$
$338$	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	$-0.885151\pi$
$349$		−	1.60660e6i		−	0.706065i	0.935611	−	0.353033i	$-0.114849\pi$
$350$	−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	$-0.879240\pi$
$359$		−	1.80872e6i		−	0.740686i	0.928895	−	0.370343i	$-0.120760\pi$
$360$	−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	$0.137230\pi$
$367$			2.15654e6i			0.835781i	−0.908497	+	0.417891i	$0.862770\pi$
$368$	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	$-0.623930\pi$
$379$		−	5.17422e6i		−	1.85032i	0.379576	−	0.925160i	$-0.376070\pi$
$380$	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	$-0.840025\pi$
$389$		−	2.87520e6i		−	0.963372i	0.876344	−	0.481686i	$-0.159975\pi$
$390$	−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	$-0.742185\pi$
$397$		−	4.54879e6i		−	1.44851i	0.689535	−	0.724253i	$-0.257815\pi$
$398$	−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	$0.0554929\pi$
$401$			1.11706e6i			0.346908i	−0.984842	+	0.173454i	$0.944507\pi$
$402$	−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	$-0.887853\pi$
$409$		−	2.33481e6i		−	0.690151i	0.938575	−	0.345075i	$-0.112147\pi$
$410$	−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	$-0.812708\pi$
$433$		−	4.33076e6i		−	1.11005i	0.831832	−	0.555027i	$-0.187292\pi$
$434$	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	$-0.672018\pi$
$449$		−	7.32620e6i		−	1.71500i	0.514488	−	0.857498i	$-0.327982\pi$
$450$	−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	$-0.867164\pi$
$461$		−	3.69887e6i		−	0.810619i	0.914180	−	0.405309i	$-0.132836\pi$
$462$	4.31194e6	+	979338.i	0.939870	+	0.213465i
$463$			5.35356e6i			1.16062i	0.814395	+	0.580310i	$0.197069\pi$
$463$			5.35356e6i			1.16062i	−0.814395	+	0.580310i	$0.802931\pi$
$464$	−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	$0.201696\pi$
$479$			5.94642e6i			1.18418i	−0.805873	+	0.592088i	$0.798304\pi$
$480$	−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	$0.0467251\pi$
$503$			1.65993e6i			0.292529i	−0.989245	+	0.146265i	$0.953275\pi$
$504$	−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	$0.272200\pi$
$521$			9.35142e6i			1.50933i	−0.656112	+	0.754664i	$0.727800\pi$
$522$	3.49504e6	+	793801.i	0.561404	+	0.127507i
$523$			1.06063e7i			1.69555i	0.530354	+	0.847776i	$0.322059\pi$
$523$			1.06063e7i			1.69555i	−0.530354	+	0.847776i	$0.677941\pi$
$524$	−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	$0.307217\pi$
$541$			1.11935e7i			1.64427i	−0.569294	+	0.822134i	$0.692783\pi$
$542$	−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	$-0.871095\pi$
$547$		−	5.51419e6i		−	0.787977i	0.919115	−	0.393988i	$-0.128905\pi$
$548$	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	$-0.675042\pi$
$557$		−	1.24853e7i		−	1.70514i	0.522612	−	0.852571i	$-0.324958\pi$
$558$	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	$0.213854\pi$
$563$			9.36247e6i			1.24486i	−0.782677	+	0.622428i	$0.786146\pi$
$564$	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	$-0.963920\pi$
$569$		−	1.74700e6i		−	0.226210i	0.993583	−	0.113105i	$-0.0360797\pi$
$570$	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	$-0.783369\pi$
$601$		−	1.11436e7i		−	1.25847i	0.777217	−	0.629233i	$-0.216631\pi$
$602$	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	$-0.842302\pi$
$613$		−	8.84591e6i		−	0.950805i	0.879768	−	0.475402i	$-0.157698\pi$
$614$	−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	$0.126965\pi$
$631$			7.76892e6i			0.776761i	−0.921499	+	0.388380i	$0.873035\pi$
$632$	−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	$0.239757\pi$
$641$			1.42307e7i			1.36798i	−0.729491	+	0.683990i	$0.760243\pi$
$642$	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	$-0.929823\pi$
$647$		−	4.65708e6i		−	0.437374i	0.975795	−	0.218687i	$-0.0701774\pi$
$648$	−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	$-0.937660\pi$
$653$		−	4.24081e6i		−	0.389194i	0.980883	−	0.194597i	$-0.0623399\pi$
$654$	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	$0.240561\pi$
$659$			1.52919e7i			1.37166i	−0.727761	+	0.685831i	$0.759439\pi$
$660$	−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	$-0.797932\pi$
$673$		−	1.39362e7i		−	1.18606i	0.805182	−	0.593028i	$-0.202068\pi$
$674$	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	$-0.729454\pi$
$683$		−	1.83174e7i		−	1.50249i	0.660024	−	0.751245i	$-0.270546\pi$
$684$	−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	$0.0955739\pi$
$701$			7.69607e6i			0.591526i	−0.955261	+	0.295763i	$0.904426\pi$
$702$	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	$0.0116957\pi$
$709$			983382.i			0.0734694i	−0.999325	+	0.0367347i	$0.988304\pi$
$710$	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	$-0.923459\pi$
$719$		−	6.60244e6i		−	0.476302i	0.971228	−	0.238151i	$-0.0765413\pi$
$720$	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	$-0.802337\pi$
$727$		−	1.65829e7i		−	1.16366i	0.813311	−	0.581829i	$-0.197663\pi$
$728$	−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	$0.147358\pi$
$733$			1.29924e7i			0.893162i	−0.894743	+	0.446581i	$0.852642\pi$
$734$	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	$-0.846077\pi$
$757$		−	1.46610e7i		−	0.929876i	0.885343	−	0.464938i	$-0.153923\pi$
$758$	−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	$-0.865600\pi$
$787$		−	1.42408e7i		−	0.819591i	0.912177	−	0.409796i	$-0.134400\pi$
$788$	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	$-0.868811\pi$
$811$		−	1.50060e7i		−	0.801146i	0.916265	−	0.400573i	$-0.131189\pi$
$812$	−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	$-0.994118\pi$
$821$		−	713772.i		−	0.0369574i	0.999829	−	0.0184787i	$-0.00588229\pi$
$822$	2.29523e6	−	1.01057e7i	0.118480	−	0.521659i
$823$			1.40864e7i			0.724935i	0.931996	+	0.362468i	$0.118066\pi$
$823$			1.40864e7i			0.724935i	−0.931996	+	0.362468i	$0.881934\pi$
$824$	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	$0.0569569\pi$
$827$			7.00116e6i			0.355964i	−0.984034	+	0.177982i	$0.943043\pi$
$828$	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	$0.171896\pi$
$853$			2.18525e7i			1.02832i	−0.857694	+	0.514160i	$0.828104\pi$
$854$	−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	$-0.733927\pi$
$857$		−	3.19025e7i		−	1.48379i	0.670515	−	0.741896i	$-0.266073\pi$
$858$	−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	$0.0514688\pi$
$907$			7.97715e6i			0.321980i	−0.986956	+	0.160990i	$0.948531\pi$
$908$	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	$0.256838\pi$
$919$			3.69774e7i			1.44427i	−0.691754	+	0.722133i	$0.743162\pi$
$920$	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	$-0.923931\pi$
$953$		−	1.32732e7i		−	0.473417i	0.971581	−	0.236709i	$-0.0760687\pi$
$954$	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	$-0.954203\pi$
$967$		−	8.33848e6i		−	0.286761i	0.989668	−	0.143381i	$-0.0457973\pi$
$968$	−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	$-0.898229\pi$
$971$		−	1.84683e7i		−	0.628608i	0.949322	−	0.314304i	$-0.101771\pi$
$972$	−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	$-0.916199\pi$
$977$		−	1.55288e7i		−	0.520477i	0.965544	−	0.260239i	$-0.0838013\pi$
$978$	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	$-0.937447\pi$
$997$		−	1.22565e7i		−	0.390506i	0.980753	−	0.195253i	$-0.0625528\pi$
$998$	−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.75.5	✓	96
4.3	odd	2		608.6.b.b.303.37		96
8.3	odd	2	inner	152.6.b.b.75.91	yes	96
8.5	even	2		608.6.b.b.303.38		96
19.18	odd	2	inner	152.6.b.b.75.92	yes	96
76.75	even	2		608.6.b.b.303.59		96
152.37	odd	2		608.6.b.b.303.60		96
152.75	even	2	inner	152.6.b.b.75.6	yes	96

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

Modular forms

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