LMFDB - Embedded newform 17.6.b.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,6,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	17.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:	$2.72652493682$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 167x^{4} + 9076x^{2} + 159156 $ x^6 + 167x^4 + 9076x^2 + 159156
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.2
Root			$-6.22955i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.6.b.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.50095 q^{2} +12.4591i q^{3} +40.2661 q^{4} -92.1671i q^{5} -105.914i q^{6} -52.2138i q^{7} -70.2699 q^{8} +87.7709 q^{9} +O(q^{10})$	\(q-8.50095 q^{2} +12.4591i q^{3} +40.2661 q^{4} -92.1671i q^{5} -105.914i q^{6} -52.2138i q^{7} -70.2699 q^{8} +87.7709 q^{9} +783.508i q^{10} -426.209i q^{11} +501.680i q^{12} -682.449 q^{13} +443.867i q^{14} +1148.32 q^{15} -691.155 q^{16} +(-335.976 - 1143.23i) q^{17} -746.136 q^{18} +1924.19 q^{19} -3711.21i q^{20} +650.537 q^{21} +3623.18i q^{22} +187.713i q^{23} -875.500i q^{24} -5369.77 q^{25} +5801.47 q^{26} +4121.11i q^{27} -2102.45i q^{28} -2531.86i q^{29} -9761.80 q^{30} -6165.74i q^{31} +8124.11 q^{32} +5310.18 q^{33} +(2856.11 + 9718.55i) q^{34} -4812.40 q^{35} +3534.19 q^{36} +15440.4i q^{37} -16357.5 q^{38} -8502.70i q^{39} +6476.57i q^{40} +2173.03i q^{41} -5530.18 q^{42} +13046.4 q^{43} -17161.8i q^{44} -8089.59i q^{45} -1595.74i q^{46} -10748.6 q^{47} -8611.17i q^{48} +14080.7 q^{49} +45648.1 q^{50} +(14243.6 - 4185.96i) q^{51} -27479.6 q^{52} -18910.1 q^{53} -35033.3i q^{54} -39282.4 q^{55} +3669.06i q^{56} +23973.7i q^{57} +21523.2i q^{58} +2512.88 q^{59} +46238.3 q^{60} +5101.84i q^{61} +52414.6i q^{62} -4582.85i q^{63} -46945.7 q^{64} +62899.4i q^{65} -45141.6 q^{66} +39943.1 q^{67} +(-13528.4 - 46033.5i) q^{68} -2338.74 q^{69} +40909.9 q^{70} +38560.9i q^{71} -6167.65 q^{72} -21745.2i q^{73} -131258. i q^{74} -66902.5i q^{75} +77479.9 q^{76} -22254.0 q^{77} +72281.0i q^{78} -83096.5i q^{79} +63701.7i q^{80} -30017.0 q^{81} -18472.8i q^{82} +23872.9 q^{83} +26194.6 q^{84} +(-105368. + 30965.9i) q^{85} -110907. q^{86} +31544.7 q^{87} +29949.7i q^{88} +132869. q^{89} +68769.1i q^{90} +35633.3i q^{91} +7558.50i q^{92} +76819.5 q^{93} +91373.5 q^{94} -177347. i q^{95} +101219. i q^{96} -8645.71i q^{97} -119699. q^{98} -37408.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 82 q^{4} - 66 q^{8} + 122 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 + 82 * q^4 - 66 * q^8 + 122 * q^9	$ 6 q - 2 q^{2} + 82 q^{4} - 66 q^{8} + 122 q^{9} - 1212 q^{13} + 1200 q^{15} - 1406 q^{16} - 1802 q^{17} - 1510 q^{18} + 3960 q^{19} + 4312 q^{21} - 226 q^{25} + 7820 q^{26} - 19536 q^{30} - 3394 q^{32} + 13544 q^{33} - 11594 q^{34} - 16656 q^{35} + 8422 q^{36} - 10552 q^{38} + 48880 q^{42} + 24168 q^{43} - 40160 q^{47} - 42574 q^{49} + 139142 q^{50} - 25024 q^{51} - 87580 q^{52} - 10908 q^{53} - 58192 q^{55} + 137928 q^{59} + 122832 q^{60} - 223422 q^{64} - 162592 q^{66} + 217432 q^{67} - 125494 q^{68} - 162920 q^{69} + 94176 q^{70} - 13974 q^{72} + 318104 q^{76} + 164152 q^{77} - 308066 q^{81} - 23976 q^{83} + 418400 q^{84} - 281792 q^{85} - 407512 q^{86} + 237072 q^{87} + 81164 q^{89} + 299704 q^{93} + 442048 q^{94} - 814974 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 82 * q^4 - 66 * q^8 + 122 * q^9 - 1212 * q^13 + 1200 * q^15 - 1406 * q^16 - 1802 * q^17 - 1510 * q^18 + 3960 * q^19 + 4312 * q^21 - 226 * q^25 + 7820 * q^26 - 19536 * q^30 - 3394 * q^32 + 13544 * q^33 - 11594 * q^34 - 16656 * q^35 + 8422 * q^36 - 10552 * q^38 + 48880 * q^42 + 24168 * q^43 - 40160 * q^47 - 42574 * q^49 + 139142 * q^50 - 25024 * q^51 - 87580 * q^52 - 10908 * q^53 - 58192 * q^55 + 137928 * q^59 + 122832 * q^60 - 223422 * q^64 - 162592 * q^66 + 217432 * q^67 - 125494 * q^68 - 162920 * q^69 + 94176 * q^70 - 13974 * q^72 + 318104 * q^76 + 164152 * q^77 - 308066 * q^81 - 23976 * q^83 + 418400 * q^84 - 281792 * q^85 - 407512 * q^86 + 237072 * q^87 + 81164 * q^89 + 299704 * q^93 + 442048 * q^94 - 814974 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−8.50095			−1.50277			−0.751385	−	0.659864i	$-0.770614\pi$
$2$	−8.50095			−1.50277			−0.751385	+	0.659864i	$0.770614\pi$
$3$			12.4591i			0.799252i	0.916678	+	0.399626i	$0.130860\pi$
$3$			12.4591i			0.799252i	−0.916678	+	0.399626i	$0.869140\pi$
$4$	40.2661			1.25832
$5$		−	92.1671i		−	1.64873i	−0.566055	−	0.824367i	$-0.691531\pi$
$5$		−	92.1671i		−	1.64873i	0.566055	−	0.824367i	$-0.308469\pi$
$6$		−	105.914i		−	1.20109i
$7$		−	52.2138i		−	0.402755i	−0.979514	−	0.201377i	$-0.935458\pi$
$7$		−	52.2138i		−	0.402755i	0.979514	−	0.201377i	$-0.0645417\pi$
$8$	−70.2699			−0.388190
$9$	87.7709			0.361197
$10$			783.508i			2.47767i
$11$		−	426.209i		−	1.06204i	−0.847359	−	0.531020i	$-0.821809\pi$
$11$		−	426.209i		−	1.06204i	0.847359	−	0.531020i	$-0.178191\pi$
$12$			501.680i			1.00571i
$13$	−682.449			−1.11998			−0.559992	−	0.828498i	$-0.689196\pi$
$13$	−682.449			−1.11998			−0.559992	+	0.828498i	$0.689196\pi$
$14$			443.867i			0.605247i
$15$	1148.32			1.31775
$16$	−691.155			−0.674956
$17$	−335.976	−	1143.23i	−0.281959	−	0.959427i
$17$	−335.976	−	1143.23i	−0.281959	−	0.959427i
$18$	−746.136			−0.542796
$19$	1924.19			1.22283			0.611413	−	0.791311i	$-0.290601\pi$
$19$	1924.19			1.22283			0.611413	+	0.791311i	$0.290601\pi$
$20$		−	3711.21i		−	2.07463i
$21$	650.537			0.321902
$22$			3623.18i			1.59600i
$23$			187.713i			0.0739905i	0.999315	+	0.0369952i	$0.0117786\pi$
$23$			187.713i			0.0739905i	−0.999315	+	0.0369952i	$0.988221\pi$
$24$		−	875.500i		−	0.310262i
$25$	−5369.77			−1.71833
$26$	5801.47			1.68308
$27$			4121.11i			1.08794i
$28$		−	2102.45i		−	0.506793i
$29$		−	2531.86i		−	0.559043i	−0.960139	−	0.279521i	$-0.909824\pi$
$29$		−	2531.86i		−	0.559043i	0.960139	−	0.279521i	$-0.0901758\pi$
$30$	−9761.80			−1.98028
$31$		−	6165.74i		−	1.15234i	−0.817330	−	0.576170i	$-0.804547\pi$
$31$		−	6165.74i		−	1.15234i	0.817330	−	0.576170i	$-0.195453\pi$
$32$	8124.11			1.40249
$33$	5310.18			0.848837
$34$	2856.11	+	9718.55i	0.423719	+	1.44180i
$35$	−4812.40			−0.664036
$36$	3534.19			0.454500
$37$			15440.4i			1.85419i	0.374827	+	0.927095i	$0.377702\pi$
$37$			15440.4i			1.85419i	−0.374827	+	0.927095i	$0.622298\pi$
$38$	−16357.5			−1.83763
$39$		−	8502.70i		−	0.895149i
$40$			6476.57i			0.640023i
$41$			2173.03i			0.201886i	0.994892	+	0.100943i	$0.0321859\pi$
$41$			2173.03i			0.201886i	−0.994892	+	0.100943i	$0.967814\pi$
$42$	−5530.18			−0.483745
$43$	13046.4			1.07602			0.538010	−	0.842938i	$-0.319176\pi$
$43$	13046.4			1.07602			0.538010	+	0.842938i	$0.319176\pi$
$44$		−	17161.8i		−	1.33638i
$45$		−	8089.59i		−	0.595518i
$46$		−	1595.74i		−	0.111191i
$47$	−10748.6			−0.709754			−0.354877	−	0.934913i	$-0.615477\pi$
$47$	−10748.6			−0.709754			−0.354877	+	0.934913i	$0.615477\pi$
$48$		−	8611.17i		−	0.539460i
$49$	14080.7			0.837789
$50$	45648.1			2.58225
$51$	14243.6	−	4185.96i	0.766823	−	0.225356i
$52$	−27479.6			−1.40929
$53$	−18910.1			−0.924708			−0.462354	−	0.886695i	$-0.652995\pi$
$53$	−18910.1			−0.924708			−0.462354	+	0.886695i	$0.652995\pi$
$54$		−	35033.3i		−	1.63492i
$55$	−39282.4			−1.75102
$56$			3669.06i			0.156345i
$57$			23973.7i			0.977346i
$58$			21523.2i			0.840113i
$59$	2512.88			0.0939815			0.0469907	−	0.998895i	$-0.485037\pi$
$59$	2512.88			0.0939815			0.0469907	+	0.998895i	$0.485037\pi$
$60$	46238.3			1.65815
$61$			5101.84i			0.175551i	0.996140	+	0.0877753i	$0.0279758\pi$
$61$			5101.84i			0.175551i	−0.996140	+	0.0877753i	$0.972024\pi$
$62$			52414.6i			1.73170i
$63$		−	4582.85i		−	0.145474i
$64$	−46945.7			−1.43267
$65$			62899.4i			1.84656i
$66$	−45141.6			−1.27561
$67$	39943.1			1.08706			0.543532	−	0.839388i	$-0.317087\pi$
$67$	39943.1			1.08706			0.543532	+	0.839388i	$0.317087\pi$
$68$	−13528.4	−	46033.5i	−0.354793	−	1.20726i
$69$	−2338.74			−0.0591370
$70$	40909.9			0.997893
$71$			38560.9i			0.907823i	0.891047	+	0.453911i	$0.149972\pi$
$71$			38560.9i			0.907823i	−0.891047	+	0.453911i	$0.850028\pi$
$72$	−6167.65			−0.140213
$73$		−	21745.2i		−	0.477590i	−0.971070	−	0.238795i	$-0.923248\pi$
$73$		−	21745.2i		−	0.477590i	0.971070	−	0.238795i	$-0.0767524\pi$
$74$		−	131258.i		−	2.78642i
$75$		−	66902.5i		−	1.37338i
$76$	77479.9			1.53870
$77$	−22254.0			−0.427741
$78$			72281.0i			1.34520i
$79$		−	83096.5i		−	1.49801i	−0.662564	−	0.749006i	$-0.730532\pi$
$79$		−	83096.5i		−	1.49801i	0.662564	−	0.749006i	$-0.269468\pi$
$80$			63701.7i			1.11282i
$81$	−30017.0			−0.508340
$82$		−	18472.8i		−	0.303387i
$83$	23872.9			0.380374			0.190187	−	0.981748i	$-0.439091\pi$
$83$	23872.9			0.380374			0.190187	+	0.981748i	$0.439091\pi$
$84$	26194.6			0.405055
$85$	−105368.	+	30965.9i	−1.58184	+	0.464875i
$86$	−110907.			−1.61701
$87$	31544.7			0.446816
$88$			29949.7i			0.412273i
$89$	132869.			1.77807			0.889035	−	0.457839i	$-0.151376\pi$
$89$	132869.			1.77807			0.889035	+	0.457839i	$0.151376\pi$
$90$			68769.1i			0.894926i
$91$			35633.3i			0.451079i
$92$			7558.50i			0.0931035i
$93$	76819.5			0.921010
$94$	91373.5			1.06660
$95$		−	177347.i		−	2.01612i
$96$			101219.i			1.12095i
$97$		−	8645.71i		−	0.0932978i	−0.998911	−	0.0466489i	$-0.985146\pi$
$97$		−	8645.71i		−	0.0932978i	0.998911	−	0.0466489i	$-0.0148542\pi$
$98$	−119699.			−1.25900
$99$		−	37408.7i		−	0.383606i
$100$	−216220.			−2.16220
$101$	−34784.3			−0.339297			−0.169648	−	0.985505i	$-0.554263\pi$
$101$	−34784.3			−0.339297			−0.169648	+	0.985505i	$0.554263\pi$
$102$	−121084.	+	35584.6i	−1.15236	+	0.338658i
$103$	54298.8			0.504309			0.252155	−	0.967687i	$-0.418861\pi$
$103$	54298.8			0.504309			0.252155	+	0.967687i	$0.418861\pi$
$104$	47955.7			0.434767
$105$		−	59958.1i		−	0.530731i
$106$	160754.			1.38962
$107$			33711.5i			0.284655i	0.989820	+	0.142327i	$0.0454586\pi$
$107$			33711.5i			0.284655i	−0.989820	+	0.142327i	$0.954541\pi$
$108$			165941.i			1.36897i
$109$			64485.4i			0.519870i	0.965626	+	0.259935i	$0.0837012\pi$
$109$			64485.4i			0.519870i	−0.965626	+	0.259935i	$0.916299\pi$
$110$	333938.			2.63138
$111$	−192373.			−1.48196
$112$			36087.9i			0.271842i
$113$			101591.i			0.748445i	0.927339	+	0.374222i	$0.122090\pi$
$113$			101591.i			0.748445i	−0.927339	+	0.374222i	$0.877910\pi$
$114$		−	203799.i		−	1.46873i
$115$	17301.0			0.121991
$116$		−	101948.i		−	0.703453i
$117$	−59899.2			−0.404535
$118$	−21361.9			−0.141232
$119$	−59692.5	+	17542.6i	−0.386413	+	0.113560i
$120$	−80692.3			−0.511539
$121$	−20603.0			−0.127929
$122$		−	43370.5i		−	0.263812i
$123$	−27073.9			−0.161357
$124$		−	248270.i		−	1.45001i
$125$			206894.i			1.18433i
$126$			38958.6i			0.218614i
$127$	64216.1			0.353293			0.176646	−	0.984274i	$-0.443475\pi$
$127$	64216.1			0.353293			0.176646	+	0.984274i	$0.443475\pi$
$128$	139111.			0.750477
$129$			162547.i			0.860011i
$130$		−	534704.i		−	2.77495i
$131$		−	44738.8i		−	0.227775i	−0.993494	−	0.113887i	$-0.963670\pi$
$131$		−	44738.8i		−	0.227775i	0.993494	−	0.113887i	$-0.0363303\pi$
$132$	213820.			1.06811
$133$		−	100470.i		−	0.492499i
$134$	−339555.			−1.63361
$135$	379830.			1.79372
$136$	23609.0	+	80334.8i	0.109454	+	0.372440i
$137$	−56704.2			−0.258115			−0.129058	−	0.991637i	$-0.541195\pi$
$137$	−56704.2			−0.258115			−0.129058	+	0.991637i	$0.541195\pi$
$138$	19881.5			0.0888693
$139$			179460.i			0.787828i	0.919147	+	0.393914i	$0.128879\pi$
$139$			179460.i			0.787828i	−0.919147	+	0.393914i	$0.871121\pi$
$140$	−193777.			−0.835567
$141$		−	133918.i		−	0.567272i
$142$		−	327804.i		−	1.36425i
$143$			290866.i			1.18947i
$144$	−60663.3			−0.243792
$145$	−233354.			−0.921714
$146$			184854.i			0.717708i
$147$			175433.i			0.669604i
$148$			621725.i			2.33316i
$149$	22888.7			0.0844607			0.0422304	−	0.999108i	$-0.486554\pi$
$149$	22888.7			0.0844607			0.0422304	+	0.999108i	$0.486554\pi$
$150$			568735.i			2.06387i
$151$	369543.			1.31893			0.659466	−	0.751735i	$-0.270783\pi$
$151$	369543.			1.31893			0.659466	+	0.751735i	$0.270783\pi$
$152$	−135213.			−0.474689
$153$	−29488.9	−	100342.i	−0.101843	−	0.346542i
$154$	189180.			0.642797
$155$	−568278.			−1.89990
$156$		−	342371.i		−	1.12638i
$157$	−129581.			−0.419557			−0.209779	−	0.977749i	$-0.567274\pi$
$157$	−129581.			−0.419557			−0.209779	+	0.977749i	$0.567274\pi$
$158$			706399.i			2.25117i
$159$		−	235603.i		−	0.739075i
$160$		−	748776.i		−	2.31234i
$161$	9801.24			0.0298000
$162$	255173.			0.763917
$163$		−	24333.5i		−	0.0717358i	−0.999357	−	0.0358679i	$-0.988580\pi$
$163$		−	24333.5i		−	0.0717358i	0.999357	−	0.0358679i	$-0.0114196\pi$
$164$			87499.3i			0.254036i
$165$		−	489424.i		−	1.39951i
$166$	−202943.			−0.571615
$167$		−	497838.i		−	1.38133i	−0.723175	−	0.690664i	$-0.757318\pi$
$167$		−	497838.i		−	1.38133i	0.723175	−	0.690664i	$-0.242682\pi$
$168$	−45713.2			−0.124959
$169$	94443.9			0.254365
$170$	895730.	−	263240.i	2.37714	−	0.698601i
$171$	168888.			0.441681
$172$	525329.			1.35397
$173$		−	477076.i		−	1.21192i	−0.795496	−	0.605958i	$-0.792790\pi$
$173$		−	477076.i		−	1.21192i	0.795496	−	0.605958i	$-0.207210\pi$
$174$	−268160.			−0.671461
$175$			280376.i			0.692064i
$176$			294576.i			0.716830i
$177$			31308.3i			0.0751148i
$178$	−1.12951e6			−2.67203
$179$	21656.5			0.0505192			0.0252596	−	0.999681i	$-0.491959\pi$
$179$	21656.5			0.0505192			0.0252596	+	0.999681i	$0.491959\pi$
$180$		−	325736.i		−	0.749350i
$181$			609467.i			1.38278i	0.722481	+	0.691391i	$0.243002\pi$
$181$			609467.i			1.38278i	−0.722481	+	0.691391i	$0.756998\pi$
$182$		−	302917.i		−	0.677868i
$183$	−63564.3			−0.140309
$184$		−	13190.6i		−	0.0287224i
$185$	1.42310e6			3.05707
$186$	−653039.			−1.38407
$187$	−487255.	+	143196.i	−1.01895	+	0.299452i
$188$	−432805.			−0.893096
$189$	215179.			0.438172
$190$			1.50762e6i			3.02976i
$191$	−168091.			−0.333396			−0.166698	−	0.986008i	$-0.553310\pi$
$191$	−168091.			−0.333396			−0.166698	+	0.986008i	$0.553310\pi$
$192$		−	584901.i		−	1.14506i
$193$		−	683389.i		−	1.32061i	−0.750998	−	0.660305i	$-0.770427\pi$
$193$		−	683389.i		−	1.32061i	0.750998	−	0.660305i	$-0.229573\pi$
$194$			73496.7i			0.140205i
$195$	−783669.			−1.47586
$196$	566976.			1.05420
$197$		−	269740.i		−	0.495199i	−0.968862	−	0.247600i	$-0.920358\pi$
$197$		−	269740.i		−	0.495199i	0.968862	−	0.247600i	$-0.0796418\pi$
$198$			318010.i			0.576471i
$199$			972158.i			1.74022i	0.492857	+	0.870110i	$0.335953\pi$
$199$			972158.i			1.74022i	−0.492857	+	0.870110i	$0.664047\pi$
$200$	377333.			0.667038
$201$			497656.i			0.868838i
$202$	295699.			0.509885
$203$	−132198.			−0.225157
$204$	573536.	−	168552.i	0.964906	−	0.283569i
$205$	200281.			0.332856
$206$	−461591.			−0.757861
$207$			16475.8i			0.0267251i
$208$	471678.			0.755940
$209$		−	820109.i		−	1.29869i
$210$			509701.i			0.797567i
$211$			535453.i			0.827971i	0.910283	+	0.413986i	$0.135864\pi$
$211$			535453.i			0.827971i	−0.910283	+	0.413986i	$0.864136\pi$
$212$	−761438.			−1.16358
$213$	−480434.			−0.725579
$214$		−	286579.i		−	0.427770i
$215$		−	1.20245e6i		−	1.77407i
$216$		−	289590.i		−	0.422327i
$217$	−321937.			−0.464110
$218$		−	548187.i		−	0.781245i
$219$	270925.			0.381715
$220$	−1.58175e6			−2.20334
$221$	229286.	+	780197.i	0.315789	+	1.07454i
$222$	1.63536e6			2.22705
$223$	939911.			1.26568			0.632841	−	0.774282i	$-0.281889\pi$
$223$	939911.			1.26568			0.632841	+	0.774282i	$0.281889\pi$
$224$		−	424191.i		−	0.564861i
$225$	−471309.			−0.620654
$226$		−	863621.i		−	1.12474i
$227$			722316.i			0.930385i	0.885210	+	0.465192i	$0.154015\pi$
$227$			722316.i			0.930385i	−0.885210	+	0.465192i	$0.845985\pi$
$228$			965329.i			1.22981i
$229$	−587808.			−0.740708			−0.370354	−	0.928891i	$-0.620764\pi$
$229$	−587808.			−0.740708			−0.370354	+	0.928891i	$0.620764\pi$
$230$	−147075.			−0.183324
$231$		−	277265.i		−	0.341873i
$232$			177914.i			0.217015i
$233$		−	377987.i		−	0.456129i	−0.973646	−	0.228064i	$-0.926760\pi$
$233$		−	377987.i		−	0.456129i	0.973646	−	0.228064i	$-0.0732396\pi$
$234$	509200.			0.607923
$235$			990669.i			1.17020i
$236$	101184.			0.118258
$237$	1.03531e6			1.19729
$238$	507443.	−	149129.i	0.580690	−	0.170655i
$239$	−435638.			−0.493323			−0.246662	−	0.969102i	$-0.579334\pi$
$239$	−435638.			−0.493323			−0.246662	+	0.969102i	$0.579334\pi$
$240$	−793666.			−0.889426
$241$		−	826581.i		−	0.916733i	−0.888763	−	0.458366i	$-0.848435\pi$
$241$		−	826581.i		−	0.916733i	0.888763	−	0.458366i	$-0.151565\pi$
$242$	175145.			0.192247
$243$			627445.i			0.681647i
$244$			205431.i			0.220898i
$245$		−	1.29778e6i		−	1.38129i
$246$	230154.			0.242483
$247$	−1.31316e6			−1.36955
$248$			433266.i			0.447327i
$249$			297435.i			0.304015i
$250$		−	1.75880e6i		−	1.77978i
$251$	1.48284e6			1.48562			0.742812	−	0.669500i	$-0.233492\pi$
$251$	1.48284e6			1.48562			0.742812	+	0.669500i	$0.233492\pi$
$252$		−	184534.i		−	0.183052i
$253$	80005.2			0.0785809
$254$	−545898.			−0.530918
$255$	−385807.	−	1.31279e6i	−0.371552	−	1.26429i
$256$	319684.			0.304874
$257$	−1.83706e6			−1.73497			−0.867483	−	0.497466i	$-0.834264\pi$
$257$	−1.83706e6			−1.73497			−0.867483	+	0.497466i	$0.834264\pi$
$258$		−	1.38180e6i		−	1.29240i
$259$	806202.			0.746783
$260$			2.53271e6i			2.32355i
$261$		−	222224.i		−	0.201925i
$262$			380322.i			0.342293i
$263$	2.05639e6			1.83323			0.916613	−	0.399777i	$-0.130912\pi$
$263$	2.05639e6			1.83323			0.916613	+	0.399777i	$0.130912\pi$
$264$	−373146.			−0.329510
$265$			1.74289e6i			1.52460i
$266$			854087.i			0.740113i
$267$			1.65543e6i			1.42113i
$268$	1.60836e6			1.36787
$269$		−	521583.i		−	0.439484i	−0.975558	−	0.219742i	$-0.929478\pi$
$269$		−	521583.i		−	0.439484i	0.975558	−	0.219742i	$-0.0705215\pi$
$270$	−3.22892e6			−2.69555
$271$	−1.22269e6			−1.01133			−0.505665	−	0.862730i	$-0.668753\pi$
$271$	−1.22269e6			−1.01133			−0.505665	+	0.862730i	$0.668753\pi$
$272$	232211.	+	790150.i	0.190310	+	0.647571i
$273$	−443959.			−0.360525
$274$	482039.			0.387888
$275$			2.28864e6i			1.82493i
$276$	−94172.0			−0.0744131
$277$			812339.i			0.636119i	0.948071	+	0.318059i	$0.103031\pi$
$277$			812339.i			0.636119i	−0.948071	+	0.318059i	$0.896969\pi$
$278$		−	1.52558e6i		−	1.18392i
$279$		−	541172.i		−	0.416222i
$280$	338167.			0.257772
$281$	−1.24006e6			−0.936863			−0.468431	−	0.883500i	$-0.655181\pi$
$281$	−1.24006e6			−0.936863			−0.468431	+	0.883500i	$0.655181\pi$
$282$			1.13843e6i			0.852480i
$283$		−	1.97855e6i		−	1.46852i	−0.678868	−	0.734260i	$-0.737529\pi$
$283$		−	1.97855e6i		−	1.46852i	0.678868	−	0.734260i	$-0.262471\pi$
$284$			1.55270e6i			1.14233i
$285$	2.20959e6			1.61138
$286$		−	2.47264e6i		−	1.78750i
$287$	113462.			0.0813103
$288$	713060.			0.506577
$289$	−1.19410e6	+	768196.i	−0.840998	+	0.541038i
$290$	1.98373e6			1.38512
$291$	107718.			0.0745684
$292$		−	875593.i		−	0.600959i
$293$	−1.08246e6			−0.736619			−0.368309	−	0.929703i	$-0.620063\pi$
$293$	−1.08246e6			−0.736619			−0.368309	+	0.929703i	$0.620063\pi$
$294$		−	1.49135e6i		−	1.00626i
$295$		−	231605.i		−	0.154951i
$296$		−	1.08500e6i		−	0.719778i
$297$	1.75645e6			1.15543
$298$	−194575.			−0.126925
$299$		−	128105.i		−	0.0828682i
$300$		−	2.69390e6i		−	1.72814i
$301$		−	681204.i		−	0.433372i
$302$	−3.14146e6			−1.98205
$303$		−	433381.i		−	0.271183i
$304$	−1.32992e6			−0.825354
$305$	470222.			0.289436
$306$	250684.	+	853005.i	0.153046	+	0.520773i
$307$	−266625.			−0.161456			−0.0807282	−	0.996736i	$-0.525725\pi$
$307$	−266625.			−0.161456			−0.0807282	+	0.996736i	$0.525725\pi$
$308$	−896083.			−0.538234
$309$			676514.i			0.403070i
$310$	4.83090e6			2.85512
$311$		−	858418.i		−	0.503266i	−0.967823	−	0.251633i	$-0.919032\pi$
$311$		−	858418.i		−	0.503266i	0.967823	−	0.251633i	$-0.0809676\pi$
$312$			597484.i			0.347488i
$313$		−	2.21844e6i		−	1.27993i	−0.768404	−	0.639965i	$-0.778949\pi$
$313$		−	2.21844e6i		−	1.27993i	0.768404	−	0.639965i	$-0.221051\pi$
$314$	1.10156e6			0.630498
$315$	−422388.			−0.239848
$316$		−	3.34597e6i		−	1.88497i
$317$			3.11459e6i			1.74082i	0.492330	+	0.870409i	$0.336145\pi$
$317$			3.11459e6i			1.74082i	−0.492330	+	0.870409i	$0.663855\pi$
$318$			2.00285e6i			1.11066i
$319$	−1.07910e6			−0.593726
$320$			4.32685e6i			2.36209i
$321$	−420015.			−0.227511
$322$	−83319.9			−0.0447826
$323$	−646483.	−	2.19980e6i	−0.344787	−	1.17321i
$324$	−1.20867e6			−0.639652
$325$	3.66460e6			1.92450
$326$			206858.i			0.107802i
$327$	−803430.			−0.415507
$328$		−	152698.i		−	0.0783700i
$329$			561227.i			0.285857i
$330$			4.16057e6i			2.10314i
$331$	−662879.			−0.332556			−0.166278	−	0.986079i	$-0.553175\pi$
$331$	−662879.			−0.332556			−0.166278	+	0.986079i	$0.553175\pi$
$332$	961271.			0.478631
$333$			1.35522e6i			0.669728i
$334$			4.23210e6i			2.07582i
$335$		−	3.68144e6i		−	1.79228i
$336$	−449622.			−0.217270
$337$		−	541004.i		−	0.259493i	−0.991547	−	0.129746i	$-0.958584\pi$
$337$		−	541004.i		−	0.259493i	0.991547	−	0.129746i	$-0.0414164\pi$
$338$	−802863.			−0.382252
$339$	−1.26573e6			−0.598195
$340$	−4.24277e6	+	1.24688e6i	−1.99046	+	0.584960i
$341$	−2.62789e6			−1.22383
$342$	−1.43571e6			−0.663745
$343$		−	1.61277e6i		−	0.740178i
$344$	−916772.			−0.417701
$345$			215555.i			0.0975013i
$346$			4.05560e6i			1.82123i
$347$			2.28483e6i			1.01866i	0.860571	+	0.509331i	$0.170107\pi$
$347$			2.28483e6i			1.01866i	−0.860571	+	0.509331i	$0.829893\pi$
$348$	1.27018e6			0.562236
$349$	3.20796e6			1.40982			0.704912	−	0.709295i	$-0.250987\pi$
$349$	3.20796e6			1.40982			0.704912	+	0.709295i	$0.250987\pi$
$350$		−	2.38347e6i		−	1.04001i
$351$		−	2.81245e6i		−	1.21847i
$352$		−	3.46257e6i		−	1.48950i
$353$	1.52041e6			0.649416			0.324708	−	0.945814i	$-0.394734\pi$
$353$	1.52041e6			0.649416			0.324708	+	0.945814i	$0.394734\pi$
$354$		−	266150.i		−	0.112880i
$355$	3.55404e6			1.49676
$356$	5.35012e6			2.23738
$357$	−218565.	−	743715.i	−0.0907632	−	0.308842i
$358$	−184101.			−0.0759187
$359$	2.32904e6			0.953765			0.476883	−	0.878967i	$-0.341767\pi$
$359$	2.32904e6			0.953765			0.476883	+	0.878967i	$0.341767\pi$
$360$			568455.i			0.231174i
$361$	1.22643e6			0.495305
$362$		−	5.18105e6i		−	2.07800i
$363$		−	256695.i		−	0.102247i
$364$			1.43481e6i			0.567600i
$365$	−2.00419e6			−0.787419
$366$	540357.			0.210852
$367$		−	2.24848e6i		−	0.871413i	−0.900089	−	0.435707i	$-0.856499\pi$
$367$		−	2.24848e6i		−	0.871413i	0.900089	−	0.435707i	$-0.143501\pi$
$368$		−	129739.i		−	0.0499403i
$369$			190728.i			0.0729205i
$370$	−1.20977e7			−4.59407
$371$			987371.i			0.372431i
$372$	3.09322e6			1.15892
$373$	−3.85968e6			−1.43641			−0.718207	−	0.695830i	$-0.755037\pi$
$373$	−3.85968e6			−1.43641			−0.718207	+	0.695830i	$0.755037\pi$
$374$	4.14213e6	−	1.21730e6i	1.53125	−	0.450007i
$375$	−2.57771e6			−0.946578
$376$	755305.			0.275520
$377$			1.72787e6i			0.626119i
$378$	−1.82922e6			−0.658472
$379$			3.79587e6i			1.35742i	0.734408	+	0.678709i	$0.237460\pi$
$379$			3.79587e6i			1.35742i	−0.734408	+	0.678709i	$0.762540\pi$
$380$		−	7.14109e6i		−	2.53691i
$381$			800075.i			0.282370i
$382$	1.42893e6			0.501017
$383$	4.39219e6			1.52997			0.764987	−	0.644046i	$-0.222746\pi$
$383$	4.39219e6			1.52997			0.764987	+	0.644046i	$0.222746\pi$
$384$			1.73320e6i			0.599820i
$385$			2.05109e6i			0.705232i
$386$			5.80945e6i			1.98457i
$387$	1.14510e6			0.388655
$388$		−	348129.i		−	0.117398i
$389$	−3.77518e6			−1.26492			−0.632461	−	0.774592i	$-0.717955\pi$
$389$	−3.77518e6			−1.26492			−0.632461	+	0.774592i	$0.717955\pi$
$390$	6.66193e6			2.21788
$391$	214600.	−	63067.2i	0.0709884	−	0.0208623i
$392$	−989451.			−0.325221
$393$	557405.			0.182049
$394$			2.29305e6i			0.744171i
$395$	−7.65876e6			−2.46982
$396$		−	1.50630e6i		−	0.482697i
$397$		−	892552.i		−	0.284222i	−0.989851	−	0.142111i	$-0.954611\pi$
$397$		−	892552.i		−	0.284222i	0.989851	−	0.142111i	$-0.0453890\pi$
$398$		−	8.26427e6i		−	2.61515i
$399$	1.25176e6			0.393631
$400$	3.71134e6			1.15980
$401$			25330.1i			0.00786639i	0.999992	+	0.00393319i	$0.00125198\pi$
$401$			25330.1i			0.00786639i	−0.999992	+	0.00393319i	$0.998748\pi$
$402$		−	4.23054e6i		−	1.30566i
$403$			4.20780e6i			1.29060i
$404$	−1.40063e6			−0.426942
$405$			2.76657e6i			0.838117i
$406$	1.12381e6			0.338359
$407$	6.58083e6			1.96922
$408$	−1.00090e6	+	294147.i	−0.297673	+	0.0874810i
$409$	−4.23404e6			−1.25154			−0.625772	−	0.780006i	$-0.715216\pi$
$409$	−4.23404e6			−1.25154			−0.625772	+	0.780006i	$0.715216\pi$
$410$	−1.70258e6			−0.500206
$411$		−	706483.i		−	0.206299i
$412$	2.18640e6			0.634581
$413$		−	131207.i		−	0.0378515i
$414$		−	140060.i		−	0.0401617i
$415$		−	2.20030e6i		−	0.627136i
$416$	−5.54429e6			−1.57077
$417$	−2.23591e6			−0.629673
$418$			6.97170e6i			1.95163i
$419$			246703.i			0.0686499i	0.999411	+	0.0343249i	$0.0109281\pi$
$419$			246703.i			0.0686499i	−0.999411	+	0.0343249i	$0.989072\pi$
$420$		−	2.41428e6i		−	0.667828i
$421$	1.35295e6			0.372029			0.186014	−	0.982547i	$-0.440443\pi$
$421$	1.35295e6			0.372029			0.186014	+	0.982547i	$0.440443\pi$
$422$		−	4.55186e6i		−	1.24425i
$423$	−943416.			−0.256361
$424$	1.32881e6			0.358963
$425$	1.80411e6	+	6.13889e6i	0.484497	+	1.64861i
$426$	4.08414e6			1.09038
$427$	266387.			0.0707038
$428$			1.35743e6i			0.358186i
$429$	−3.62393e6			−0.950684
$430$			1.02220e7i			2.66602i
$431$			4.17269e6i			1.08199i	0.841026	+	0.540995i	$0.181952\pi$
$431$			4.17269e6i			1.08199i	−0.841026	+	0.540995i	$0.818048\pi$
$432$		−	2.84832e6i		−	0.734311i
$433$	501987.			0.128669			0.0643343	−	0.997928i	$-0.479508\pi$
$433$	501987.			0.128669			0.0643343	+	0.997928i	$0.479508\pi$
$434$	2.73677e6			0.697451
$435$		−	2.90739e6i		−	0.736681i
$436$			2.59658e6i			0.654162i
$437$			361197.i			0.0904776i
$438$	−2.30312e6			−0.573629
$439$		−	1.51628e6i		−	0.375508i	−0.982216	−	0.187754i	$-0.939879\pi$
$439$		−	1.51628e6i		−	0.375508i	0.982216	−	0.187754i	$-0.0601208\pi$
$440$	2.76037e6			0.679730
$441$	1.23588e6			0.302607
$442$	−1.94915e6	−	6.63242e6i	−0.474559	−	1.61479i
$443$	−3.64921e6			−0.883466			−0.441733	−	0.897147i	$-0.645636\pi$
$443$	−3.64921e6			−0.883466			−0.441733	+	0.897147i	$0.645636\pi$
$444$	−7.74613e6			−1.86478
$445$		−	1.22462e7i		−	2.93157i
$446$	−7.99014e6			−1.90203
$447$			285172.i			0.0675054i
$448$			2.45121e6i			0.577014i
$449$			5.94186e6i			1.39093i	0.718558	+	0.695467i	$0.244803\pi$
$449$			5.94186e6i			1.39093i	−0.718558	+	0.695467i	$0.755197\pi$
$450$	4.00658e6			0.932701
$451$	926163.			0.214411
$452$			4.09068e6i			0.941780i
$453$			4.60417e6i			1.05416i
$454$		−	6.14037e6i		−	1.39815i
$455$	3.28422e6			0.743710
$456$		−	1.68463e6i		−	0.379396i
$457$	5.20530e6			1.16588			0.582942	−	0.812513i	$-0.301901\pi$
$457$	5.20530e6			1.16588			0.582942	+	0.812513i	$0.301901\pi$
$458$	4.99693e6			1.11311
$459$	4.71138e6	−	1.38459e6i	1.04380	−	0.306754i
$460$	696644.			0.153503
$461$	7.05940e6			1.54709			0.773545	−	0.633742i	$-0.218482\pi$
$461$	7.05940e6			1.54709			0.773545	+	0.633742i	$0.218482\pi$
$462$			2.35701e6i			0.513756i
$463$	1.43048e6			0.310119			0.155059	−	0.987905i	$-0.450443\pi$
$463$	1.43048e6			0.310119			0.155059	+	0.987905i	$0.450443\pi$
$464$			1.74991e6i			0.377329i
$465$		−	7.08023e6i		−	1.51850i
$466$			3.21325e6i			0.685456i
$467$	−734225.			−0.155789			−0.0778945	−	0.996962i	$-0.524820\pi$
$467$	−734225.			−0.155789			−0.0778945	+	0.996962i	$0.524820\pi$
$468$	−2.41191e6			−0.509033
$469$		−	2.08559e6i		−	0.437820i
$470$		−	8.42163e6i		−	1.75854i
$471$		−	1.61446e6i		−	0.335332i
$472$	−176580.			−0.0364827
$473$		−	5.56051e6i		−	1.14278i
$474$	−8.80110e6			−1.79925
$475$	−1.03325e7			−2.10122
$476$	−2.40359e6	+	706372.i	−0.486230	+	0.142895i
$477$	−1.65976e6			−0.334002
$478$	3.70334e6			0.741351
$479$			1.72368e6i			0.343256i	0.985162	+	0.171628i	$0.0549027\pi$
$479$			1.72368e6i			0.343256i	−0.985162	+	0.171628i	$0.945097\pi$
$480$	9.32907e6			1.84814
$481$		−	1.05373e7i		−	2.07666i
$482$			7.02672e6i			1.37764i
$483$			122115.i			0.0238177i
$484$	−829605.			−0.160975
$485$	−796850.			−0.153823
$486$		−	5.33388e6i		−	1.02436i
$487$		−	3.22348e6i		−	0.615890i	−0.951404	−	0.307945i	$-0.900359\pi$
$487$		−	3.22348e6i		−	0.615890i	0.951404	−	0.307945i	$-0.0996412\pi$
$488$		−	358506.i		−	0.0681470i
$489$	303174.			0.0573349
$490$			1.10323e7i			2.07576i
$491$	−3.53364e6			−0.661482			−0.330741	−	0.943722i	$-0.607299\pi$
$491$	−3.53364e6			−0.661482			−0.330741	+	0.943722i	$0.607299\pi$
$492$	−1.09016e6			−0.203039
$493$	−2.89450e6	+	850645.i	−0.536361	+	0.157627i
$494$	1.11631e7			2.05811
$495$	−3.44785e6			−0.632464
$496$			4.26148e6i			0.777779i
$497$	2.01341e6			0.365630
$498$		−	2.52848e6i		−	0.456864i
$499$			4.37349e6i			0.786279i	0.919479	+	0.393139i	$0.128611\pi$
$499$			4.37349e6i			0.786279i	−0.919479	+	0.393139i	$0.871389\pi$
$500$			8.33082e6i			1.49026i
$501$	6.20262e6			1.10403
$502$	−1.26055e7			−2.23255
$503$			6.22586e6i			1.09718i	0.836090	+	0.548592i	$0.184836\pi$
$503$			6.22586e6i			1.09718i	−0.836090	+	0.548592i	$0.815164\pi$
$504$			322037.i			0.0564715i
$505$			3.20596e6i			0.559410i
$506$	−680120.			−0.118089
$507$			1.17669e6i			0.203302i
$508$	2.58573e6			0.444554
$509$	−5.11234e6			−0.874631			−0.437316	−	0.899308i	$-0.644071\pi$
$509$	−5.11234e6			−0.874631			−0.437316	+	0.899308i	$0.644071\pi$
$510$	3.27973e6	+	1.11600e7i	0.558358	+	1.89993i
$511$	−1.13540e6			−0.192352
$512$	−7.16918e6			−1.20863
$513$			7.92981e6i			1.33036i
$514$	1.56168e7			2.60725
$515$		−	5.00456e6i		−	0.831472i
$516$			6.54513e6i			1.08217i
$517$			4.58116e6i			0.753787i
$518$	−6.85349e6			−1.12224
$519$	5.94394e6			0.968626
$520$		−	4.41993e6i		−	0.716815i
$521$		−	7.91571e6i		−	1.27760i	−0.769372	−	0.638801i	$-0.779431\pi$
$521$		−	7.91571e6i		−	1.27760i	0.769372	−	0.638801i	$-0.220569\pi$
$522$			1.88911e6i			0.303446i
$523$	7.72670e6			1.23521			0.617604	−	0.786489i	$-0.288104\pi$
$523$	7.72670e6			1.23521			0.617604	+	0.786489i	$0.288104\pi$
$524$		−	1.80146e6i		−	0.286613i
$525$	−3.49324e6			−0.553133
$526$	−1.74813e7			−2.75492
$527$	−7.04886e6	+	2.07154e6i	−1.10559	+	0.324912i
$528$	−3.67016e6			−0.572928
$529$	6.40111e6			0.994525
$530$		−	1.48162e7i		−	2.29112i
$531$	220558.			0.0339458
$532$		−	4.04552e6i		−	0.619720i
$533$		−	1.48298e6i		−	0.226109i
$534$		−	1.40727e7i		−	2.13562i
$535$	3.10709e6			0.469320
$536$	−2.80680e6			−0.421988
$537$			269821.i			0.0403776i
$538$			4.43395e6i			0.660443i
$539$		−	6.00133e6i		−	0.889765i
$540$	1.52943e7			2.25707
$541$		−	2.33668e6i		−	0.343246i	−0.985163	−	0.171623i	$-0.945099\pi$
$541$		−	2.33668e6i		−	0.343246i	0.985163	−	0.171623i	$-0.0549011\pi$
$542$	1.03940e7			1.51980
$543$	−7.59341e6			−1.10519
$544$	−2.72950e6	−	9.28774e6i	−0.395445	−	1.34559i
$545$	5.94343e6			0.857129
$546$	3.77407e6			0.541787
$547$			1.26927e7i			1.81378i	0.421364	+	0.906891i	$0.361551\pi$
$547$			1.26927e7i			1.81378i	−0.421364	+	0.906891i	$0.638449\pi$
$548$	−2.28326e6			−0.324791
$549$			447793.i			0.0634084i
$550$		−	1.94556e7i		−	2.74245i
$551$		−	4.87180e6i		−	0.683613i
$552$	164343.			0.0229564
$553$	−4.33879e6			−0.603331
$554$		−	6.90566e6i		−	0.955940i
$555$			1.77305e7i			2.44337i
$556$			7.22617e6i			0.991337i
$557$	−398976.			−0.0544890			−0.0272445	−	0.999629i	$-0.508673\pi$
$557$	−398976.			−0.0544890			−0.0272445	+	0.999629i	$0.508673\pi$
$558$			4.60048e6i			0.625485i
$559$	−8.90353e6			−1.20513
$560$	3.32611e6			0.448195
$561$	−1.78409e6	−	6.07076e6i	−0.239337	−	0.814397i
$562$	1.05417e7			1.40789
$563$	4.81547e6			0.640277			0.320138	−	0.947371i	$-0.396271\pi$
$563$	4.81547e6			0.640277			0.320138	+	0.947371i	$0.396271\pi$
$564$		−	5.39236e6i		−	0.713808i
$565$	9.36336e6			1.23399
$566$			1.68195e7i			2.20685i
$567$			1.56730e6i			0.204736i
$568$		−	2.70967e6i		−	0.352408i
$569$	−7.56736e6			−0.979860			−0.489930	−	0.871762i	$-0.662978\pi$
$569$	−7.56736e6			−0.979860			−0.489930	+	0.871762i	$0.662978\pi$
$570$	−1.87836e7			−2.42154
$571$		−	4.23691e6i		−	0.543825i	−0.962322	−	0.271912i	$-0.912344\pi$
$571$		−	4.23691e6i		−	0.543825i	0.962322	−	0.271912i	$-0.0876561\pi$
$572$			1.17120e7i			1.49673i
$573$		−	2.09426e6i		−	0.266467i
$574$	−964535.			−0.122191
$575$		−	1.00798e6i		−	0.127140i
$576$	−4.12046e6			−0.517476
$577$	3.56144e6			0.445334			0.222667	−	0.974895i	$-0.428524\pi$
$577$	3.56144e6			0.445334			0.222667	+	0.974895i	$0.428524\pi$
$578$	1.01510e7	−	6.53039e6i	1.26383	−	0.813055i
$579$	8.51441e6			1.05550
$580$	−9.39628e6			−1.15981
$581$		−	1.24650e6i		−	0.153197i
$582$	−915703.			−0.112059
$583$			8.05967e6i			0.982077i
$584$			1.52803e6i			0.185396i
$585$			5.52073e6i			0.666971i
$586$	9.20194e6			1.10697
$587$	−9.70530e6			−1.16256			−0.581278	−	0.813705i	$-0.697447\pi$
$587$	−9.70530e6			−1.16256			−0.581278	+	0.813705i	$0.697447\pi$
$588$			7.06401e6i			0.842574i
$589$		−	1.18641e7i		−	1.40911i
$590$			1.96886e6i			0.232855i
$591$	3.36072e6			0.395789
$592$		−	1.06717e7i		−	1.25150i
$593$	2.04380e6			0.238672			0.119336	−	0.992854i	$-0.461923\pi$
$593$	2.04380e6			0.238672			0.119336	+	0.992854i	$0.461923\pi$
$594$	−1.49315e7			−1.73635
$595$	1.61685e6	+	5.50168e6i	0.187231	+	0.637093i
$596$	921638.			0.106278
$597$	−1.21122e7			−1.39087
$598$			1.08901e6i			0.124532i
$599$	−5.77410e6			−0.657532			−0.328766	−	0.944411i	$-0.606633\pi$
$599$	−5.77410e6			−0.657532			−0.328766	+	0.944411i	$0.606633\pi$
$600$			4.70123e6i			0.533131i
$601$		−	365716.i		−	0.0413007i	−0.999787	−	0.0206503i	$-0.993426\pi$
$601$		−	365716.i		−	0.0413007i	0.999787	−	0.0206503i	$-0.00657368\pi$
$602$			5.79088e6i			0.651259i
$603$	3.50584e6			0.392644
$604$	1.48801e7			1.65963
$605$			1.89892e6i			0.210921i
$606$			3.68415e6i			0.407526i
$607$		−	275964.i		−	0.0304005i	−0.999884	−	0.0152002i	$-0.995161\pi$
$607$		−	275964.i		−	0.0304005i	0.999884	−	0.0152002i	$-0.00483858\pi$
$608$	1.56324e7			1.71501
$609$		−	1.64707e6i		−	0.179957i
$610$	−3.99733e6			−0.434956
$611$	7.33539e6			0.794914
$612$	−1.18740e6	−	4.04040e6i	−0.128150	−	0.436059i
$613$	−8.74854e6			−0.940339			−0.470170	−	0.882576i	$-0.655807\pi$
$613$	−8.74854e6			−0.940339			−0.470170	+	0.882576i	$0.655807\pi$
$614$	2.26657e6			0.242632
$615$			2.49533e6i			0.266035i
$616$	1.56379e6			0.166045
$617$			4.86898e6i			0.514902i	0.966291	+	0.257451i	$0.0828827\pi$
$617$			4.86898e6i			0.514902i	−0.966291	+	0.257451i	$0.917117\pi$
$618$		−	5.75101e6i		−	0.605721i
$619$		−	1.32188e7i		−	1.38665i	−0.720625	−	0.693325i	$-0.756145\pi$
$619$		−	1.32188e7i		−	1.38665i	0.720625	−	0.693325i	$-0.243855\pi$
$620$	−2.28824e7			−2.39068
$621$	−773587.			−0.0804971
$622$			7.29737e6i			0.756293i
$623$		−	6.93761e6i		−	0.716126i
$624$			5.87669e6i			0.604186i
$625$	2.28828e6			0.234320
$626$			1.88588e7i			1.92344i
$627$	1.02178e7			1.03798
$628$	−5.21771e6			−0.527936
$629$	1.76519e7	−	5.18760e6i	1.77896	−	0.522805i
$630$	3.59070e6			0.360436
$631$	−8.33370e6			−0.833229			−0.416615	−	0.909083i	$-0.636784\pi$
$631$	−8.33370e6			−0.833229			−0.416615	+	0.909083i	$0.636784\pi$
$632$			5.83918e6i			0.581513i
$633$	−6.67126e6			−0.661757
$634$		−	2.64770e7i		−	2.61605i
$635$		−	5.91861e6i		−	0.582486i
$636$		−	9.48683e6i		−	0.929990i
$637$	−9.60937e6			−0.938310
$638$	9.17340e6			0.892233
$639$			3.38452e6i			0.327903i
$640$		−	1.28215e7i		−	1.23734i
$641$			1.18813e7i			1.14214i	0.820901	+	0.571070i	$0.193472\pi$
$641$			1.18813e7i			1.14214i	−0.820901	+	0.571070i	$0.806528\pi$
$642$	3.57052e6			0.341896
$643$			1.89814e7i			1.81051i	0.424870	+	0.905254i	$0.360320\pi$
$643$			1.89814e7i			1.81051i	−0.424870	+	0.905254i	$0.639680\pi$
$644$	394658.			0.0374978
$645$	1.49815e7			1.41793
$646$	5.49572e6	+	1.87004e7i	0.518135	+	1.76307i
$647$	5.13716e6			0.482461			0.241231	−	0.970468i	$-0.422449\pi$
$647$	5.13716e6			0.482461			0.241231	+	0.970468i	$0.422449\pi$
$648$	2.10929e6			0.197332
$649$		−	1.07101e6i		−	0.0998121i
$650$	−3.11525e7			−2.89208
$651$		−	4.01104e6i		−	0.370941i
$652$		−	979816.i		−	0.0902663i
$653$			3.66473e6i			0.336325i	0.985759	+	0.168162i	$0.0537833\pi$
$653$			3.66473e6i			0.336325i	−0.985759	+	0.168162i	$0.946217\pi$
$654$	6.82992e6			0.624412
$655$	−4.12344e6			−0.375540
$656$		−	1.50190e6i		−	0.136264i
$657$		−	1.90859e6i		−	0.172504i
$658$		−	4.77096e6i		−	0.429577i
$659$	−1.74894e7			−1.56878			−0.784390	−	0.620268i	$-0.787024\pi$
$659$	−1.74894e7			−1.56878			−0.784390	+	0.620268i	$0.787024\pi$
$660$		−	1.97072e7i		−	1.76102i
$661$	1.01514e7			0.903696			0.451848	−	0.892095i	$-0.350765\pi$
$661$	1.01514e7			0.903696			0.451848	+	0.892095i	$0.350765\pi$
$662$	5.63510e6			0.499755
$663$	−9.72055e6	+	2.85670e6i	−0.858830	+	0.252395i
$664$	−1.67755e6			−0.147657
$665$	−9.25999e6			−0.812001
$666$		−	1.15206e7i		−	1.00645i
$667$	475265.			0.0413639
$668$		−	2.00460e7i		−	1.73815i
$669$			1.17104e7i			1.01160i
$670$			3.12958e7i			2.69339i
$671$	2.17445e6			0.186442
$672$	5.28504e6			0.451466
$673$		−	1.29476e7i		−	1.10193i	−0.834530	−	0.550963i	$-0.814261\pi$
$673$		−	1.29476e7i		−	1.10193i	0.834530	−	0.550963i	$-0.185739\pi$
$674$			4.59905e6i			0.389958i
$675$		−	2.21294e7i		−	1.86943i
$676$	3.80289e6			0.320072
$677$			3.01652e6i			0.252950i	0.991970	+	0.126475i	$0.0403664\pi$
$677$			3.01652e6i			0.252950i	−0.991970	+	0.126475i	$0.959634\pi$
$678$	1.07599e7			0.898950
$679$	−451426.			−0.0375761
$680$	7.40422e6	−	2.17597e6i	0.614055	−	0.180460i
$681$	−8.99940e6			−0.743611
$682$	2.23396e7			1.83914
$683$		−	1.18964e7i		−	0.975810i	−0.872897	−	0.487905i	$-0.837761\pi$
$683$		−	1.18964e7i		−	0.975810i	0.872897	−	0.487905i	$-0.162239\pi$
$684$	6.80047e6			0.555775
$685$			5.22626e6i			0.425563i
$686$			1.37100e7i			1.11232i
$687$		−	7.32356e6i		−	0.592012i
$688$	−9.01711e6			−0.726267
$689$	1.29052e7			1.03566
$690$		−	1.83242e6i		−	0.146522i
$691$		−	5.11208e6i		−	0.407289i	−0.979045	−	0.203644i	$-0.934721\pi$
$691$		−	5.11208e6i		−	0.407289i	0.979045	−	0.203644i	$-0.0652786\pi$
$692$		−	1.92100e7i		−	1.52497i
$693$	−1.95325e6			−0.154499
$694$		−	1.94232e7i		−	1.53081i
$695$	1.65403e7			1.29892
$696$	−2.21665e6			−0.173450
$697$	2.48427e6	−	730084.i	0.193694	−	0.0569234i
$698$	−2.72707e7			−2.11864
$699$	4.70938e6			0.364562
$700$			1.12897e7i			0.870836i
$701$	3.63687e6			0.279533			0.139767	−	0.990184i	$-0.455365\pi$
$701$	3.63687e6			0.279533			0.139767	+	0.990184i	$0.455365\pi$
$702$			2.39085e7i			1.83109i
$703$			2.97103e7i			2.26735i
$704$			2.00087e7i			1.52155i
$705$	−1.23428e7			−0.935282
$706$	−1.29249e7			−0.975922
$707$			1.81622e6i			0.136653i
$708$			1.26066e6i			0.0945182i
$709$			1.16176e7i			0.867966i	0.900921	+	0.433983i	$0.142892\pi$
$709$			1.16176e7i			0.867966i	−0.900921	+	0.433983i	$0.857108\pi$
$710$	−3.02127e7			−2.24928
$711$		−	7.29345e6i		−	0.541077i
$712$	−9.33670e6			−0.690229
$713$	1.15739e6			0.0852622
$714$	1.85801e6	+	6.32228e6i	0.136396	+	0.464118i
$715$	2.68083e7			1.96112
$716$	872025.			0.0635692
$717$		−	5.42766e6i		−	0.394289i
$718$	−1.97991e7			−1.43329
$719$			5.78331e6i			0.417210i	0.978000	+	0.208605i	$0.0668923\pi$
$719$			5.78331e6i			0.417210i	−0.978000	+	0.208605i	$0.933108\pi$
$720$			5.59116e6i			0.401949i
$721$		−	2.83515e6i		−	0.203113i
$722$	−1.04258e7			−0.744330
$723$	1.02985e7			0.732700
$724$			2.45409e7i			1.73998i
$725$			1.35955e7i			0.960619i
$726$			2.18215e6i			0.153654i
$727$	−1.80894e7			−1.26937			−0.634684	−	0.772772i	$-0.718870\pi$
$727$	−1.80894e7			−1.26937			−0.634684	+	0.772772i	$0.718870\pi$
$728$		−	2.50395e6i		−	0.175104i
$729$	−1.51115e7			−1.05315
$730$	1.70375e7			1.18331
$731$	−4.38328e6	−	1.49151e7i	−0.303393	−	1.03236i
$732$	−2.55949e6			−0.176553
$733$	−5.16718e6			−0.355217			−0.177608	−	0.984101i	$-0.556836\pi$
$733$	−5.16718e6			−0.355217			−0.177608	+	0.984101i	$0.556836\pi$
$734$			1.91142e7i			1.30953i
$735$	1.61691e7			1.10400
$736$			1.52501e6i			0.103771i
$737$		−	1.70241e7i		−	1.15451i
$738$		−	1.62137e6i		−	0.109583i
$739$	−9.97913e6			−0.672174			−0.336087	−	0.941831i	$-0.609104\pi$
$739$	−9.97913e6			−0.672174			−0.336087	+	0.941831i	$0.609104\pi$
$740$	5.73026e7			3.84676
$741$		−	1.63609e7i		−	1.09461i
$742$		−	8.39359e6i		−	0.559677i
$743$		−	1.59724e6i		−	0.106145i	−0.998591	−	0.0530725i	$-0.983099\pi$
$743$		−	1.59724e6i		−	0.106145i	0.998591	−	0.0530725i	$-0.0169014\pi$
$744$	−5.39810e6			−0.357527
$745$		−	2.10958e6i		−	0.139253i
$746$	3.28110e7			2.15860
$747$	2.09535e6			0.137390
$748$	−1.96199e7	+	5.76594e6i	−1.28216	+	0.376805i
$749$	1.76021e6			0.114646
$750$	2.19130e7			1.42249
$751$		−	1.64962e7i		−	1.06730i	−0.845707	−	0.533648i	$-0.820821\pi$
$751$		−	1.64962e7i		−	1.06730i	0.845707	−	0.533648i	$-0.179179\pi$
$752$	7.42896e6			0.479053
$753$			1.84748e7i			1.18739i
$754$		−	1.46885e7i		−	0.940913i
$755$		−	3.40597e7i		−	2.17457i
$756$	8.66442e6			0.551360
$757$	−2.15408e7			−1.36623			−0.683114	−	0.730312i	$-0.739375\pi$
$757$	−2.15408e7			−1.36623			−0.683114	+	0.730312i	$0.739375\pi$
$758$		−	3.22685e7i		−	2.03989i
$759$			996792.i			0.0628059i
$760$			1.24622e7i			0.782637i
$761$	−1.75451e7			−1.09823			−0.549116	−	0.835746i	$-0.685036\pi$
$761$	−1.75451e7			−1.09823			−0.549116	+	0.835746i	$0.685036\pi$
$762$		−	6.80140e6i		−	0.424337i
$763$	3.36703e6			0.209380
$764$	−6.76836e6			−0.419517
$765$	−9.24826e6	+	2.71790e6i	−0.571356	+	0.167912i
$766$	−3.73377e7			−2.29920
$767$	−1.71491e6			−0.105258
$768$			3.98297e6i			0.243671i
$769$	8.55838e6			0.521886			0.260943	−	0.965354i	$-0.415967\pi$
$769$	8.55838e6			0.521886			0.260943	+	0.965354i	$0.415967\pi$
$770$		−	1.74362e7i		−	1.05980i
$771$		−	2.28881e7i		−	1.38667i
$772$		−	2.75174e7i		−	1.66174i
$773$	1.26354e7			0.760573			0.380287	−	0.924869i	$-0.375825\pi$
$773$	1.26354e7			0.760573			0.380287	+	0.924869i	$0.375825\pi$
$774$	−9.73441e6			−0.584060
$775$			3.31086e7i			1.98010i
$776$			607533.i			0.0362173i
$777$			1.00446e7i			0.596868i
$778$	3.20926e7			1.90089
$779$			4.18132e6i			0.246871i
$780$	−3.15553e7			−1.85710
$781$	1.64350e7			0.964144
$782$	−1.82430e6	+	536131.i	−0.106679	+	0.0313512i
$783$	1.04341e7			0.608205
$784$	−9.73196e6			−0.565471
$785$			1.19431e7i			0.691739i
$786$	−4.73847e6			−0.273578
$787$		−	2.82263e7i		−	1.62449i	−0.583317	−	0.812244i	$-0.698246\pi$
$787$		−	2.82263e7i		−	1.62449i	0.583317	−	0.812244i	$-0.301754\pi$
$788$		−	1.08614e7i		−	0.623118i
$789$			2.56207e7i			1.46521i
$790$	6.51067e7			3.71158
$791$	5.30446e6			0.301440
$792$			2.62871e6i			0.148912i
$793$		−	3.48175e6i		−	0.196614i
$794$			7.58754e6i			0.427120i
$795$	−2.17149e7			−1.21854
$796$			3.91451e7i			2.18975i
$797$	8.07435e6			0.450258			0.225129	−	0.974329i	$-0.427720\pi$
$797$	8.07435e6			0.450258			0.225129	+	0.974329i	$0.427720\pi$
$798$	−1.06412e7			−0.591536
$799$	3.61128e6	+	1.22882e7i	0.200122	+	0.680957i
$800$	−4.36246e7			−2.40994
$801$	1.16620e7			0.642234
$802$		−	215330.i		−	0.0118214i
$803$	−9.26798e6			−0.507220
$804$			2.00387e7i			1.09327i
$805$		−	903352.i		−	0.0491323i
$806$		−	3.57703e7i		−	1.93948i
$807$	6.49846e6			0.351258
$808$	2.44429e6			0.131712
$809$			3.17376e7i			1.70491i	0.522798	+	0.852456i	$0.324888\pi$
$809$			3.17376e7i			1.70491i	−0.522798	+	0.852456i	$0.675112\pi$
$810$		−	2.35185e7i		−	1.25950i
$811$			1.43905e7i			0.768286i	0.923274	+	0.384143i	$0.125503\pi$
$811$			1.43905e7i			0.768286i	−0.923274	+	0.384143i	$0.874497\pi$
$812$	−5.32311e6			−0.283319
$813$		−	1.52336e7i		−	0.808308i
$814$	−5.59433e7			−2.95929
$815$	−2.24275e6			−0.118273
$816$	−9.84456e6	+	2.89314e6i	−0.517572	+	0.152105i
$817$	2.51039e7			1.31579
$818$	3.59933e7			1.88078
$819$			3.12757e6i			0.162928i
$820$	8.06456e6			0.418838
$821$			2.24839e7i			1.16416i	0.813131	+	0.582081i	$0.197761\pi$
$821$			2.24839e7i			1.16416i	−0.813131	+	0.582081i	$0.802239\pi$
$822$			6.00577e6i			0.310020i
$823$			3.28688e7i			1.69155i	0.533543	+	0.845773i	$0.320860\pi$
$823$			3.28688e7i			1.69155i	−0.533543	+	0.845773i	$0.679140\pi$
$824$	−3.81557e6			−0.195768
$825$	−2.85144e7			−1.45858
$826$			1.11539e6i			0.0568820i
$827$			2.64779e7i			1.34623i	0.739537	+	0.673116i	$0.235045\pi$
$827$			2.64779e7i			1.34623i	−0.739537	+	0.673116i	$0.764955\pi$
$828$			663416.i			0.0336287i
$829$	−1.20532e6			−0.0609140			−0.0304570	−	0.999536i	$-0.509696\pi$
$829$	−1.20532e6			−0.0609140			−0.0304570	+	0.999536i	$0.509696\pi$
$830$			1.87046e7i			0.942441i
$831$	−1.01210e7			−0.508419
$832$	3.20380e7			1.60457
$833$	−4.73078e6	−	1.60975e7i	−0.236222	−	0.803797i
$834$	1.90074e7			0.946253
$835$	−4.58843e7			−2.27745
$836$		−	3.30226e7i		−	1.63416i
$837$	2.54097e7			1.25368
$838$		−	2.09721e6i		−	0.103165i
$839$		−	1.82466e7i		−	0.894904i	−0.894308	−	0.447452i	$-0.852331\pi$
$839$		−	1.82466e7i		−	0.894904i	0.894308	−	0.447452i	$-0.147669\pi$
$840$			4.21325e6i			0.206025i
$841$	1.41008e7			0.687471
$842$	−1.15014e7			−0.559073
$843$		−	1.54500e7i		−	0.748789i
$844$			2.15606e7i			1.04185i
$845$		−	8.70462e6i		−	0.419380i
$846$	8.01993e6			0.385252
$847$			1.07576e6i			0.0515239i
$848$	1.30698e7			0.624138
$849$	2.46509e7			1.17372
$850$	−1.53367e7	−	5.21864e7i	−0.728088	−	2.47748i
$851$	−2.89837e6			−0.137192
$852$	−1.93452e7			−0.913008
$853$			7.11178e6i			0.334662i	0.985901	+	0.167331i	$0.0535148\pi$
$853$			7.11178e6i			0.334662i	−0.985901	+	0.167331i	$0.946485\pi$
$854$	−2.26454e6			−0.106252
$855$		−	1.55659e7i		−	0.728215i
$856$		−	2.36890e6i		−	0.110500i
$857$			3.32856e7i			1.54812i	0.633113	+	0.774059i	$0.281777\pi$
$857$			3.32856e7i			1.54812i	−0.633113	+	0.774059i	$0.718223\pi$
$858$	3.08068e7			1.42866
$859$	1.87077e7			0.865044			0.432522	−	0.901623i	$-0.357624\pi$
$859$	1.87077e7			0.865044			0.432522	+	0.901623i	$0.357624\pi$
$860$		−	4.84181e7i		−	2.23234i
$861$			1.41363e6i			0.0649874i
$862$		−	3.54718e7i		−	1.62598i
$863$	1.74479e7			0.797471			0.398736	−	0.917066i	$-0.369449\pi$
$863$	1.74479e7			0.797471			0.398736	+	0.917066i	$0.369449\pi$
$864$			3.34803e7i			1.52583i
$865$	−4.39707e7			−1.99813
$866$	−4.26737e6			−0.193359
$867$	−9.57103e6	−	1.48774e7i	−0.432425	−	0.672169i
$868$	−1.29631e7			−0.583998
$869$	−3.54165e7			−1.59095
$870$			2.47155e7i			1.10706i
$871$	−2.72592e7			−1.21750
$872$		−	4.53138e6i		−	0.201809i
$873$		−	758841.i		−	0.0336989i
$874$		−	3.07052e6i		−	0.135967i
$875$	1.08027e7			0.476995
$876$	1.09091e7			0.480318
$877$		−	1.68743e7i		−	0.740845i	−0.928863	−	0.370422i	$-0.879213\pi$
$877$		−	1.68743e7i		−	0.740845i	0.928863	−	0.370422i	$-0.120787\pi$
$878$			1.28898e7i			0.564302i
$879$		−	1.34865e7i		−	0.588744i
$880$	2.71503e7			1.18186
$881$		−	1.24244e7i		−	0.539305i	−0.962958	−	0.269652i	$-0.913091\pi$
$881$		−	1.24244e7i		−	0.539305i	0.962958	−	0.269652i	$-0.0869088\pi$
$882$	−1.05061e7			−0.454748
$883$	1.23060e7			0.531148			0.265574	−	0.964091i	$-0.414439\pi$
$883$	1.23060e7			0.531148			0.265574	+	0.964091i	$0.414439\pi$
$884$	9.23248e6	+	3.14155e7i	0.397363	+	1.35211i
$885$	2.88559e6			0.123844
$886$	3.10218e7			1.32765
$887$		−	6.21137e6i		−	0.265081i	−0.991178	−	0.132540i	$-0.957687\pi$
$887$		−	6.21137e6i		−	0.265081i	0.991178	−	0.132540i	$-0.0423134\pi$
$888$	1.35181e7			0.575284
$889$		−	3.35297e6i		−	0.142290i
$890$			1.04104e8i			4.40547i
$891$			1.27935e7i			0.539877i
$892$	3.78466e7			1.59263
$893$	−2.06824e7			−0.867907
$894$		−	2.42423e6i		−	0.101445i
$895$		−	1.99602e6i		−	0.0832928i
$896$		−	7.26354e6i		−	0.302258i
$897$	1.59607e6			0.0662325
$898$		−	5.05115e7i		−	2.09025i
$899$	−1.56108e7			−0.644208
$900$	−1.89778e7			−0.780980
$901$	6.35335e6	+	2.16186e7i	0.260730	+	0.887190i
$902$	−7.87326e6			−0.322210
$903$	8.48719e6			0.346373
$904$		−	7.13880e6i		−	0.290539i
$905$	5.61728e7			2.27984
$906$		−	3.91398e7i		−	1.58416i
$907$		−	3.64815e7i		−	1.47250i	−0.676712	−	0.736248i	$-0.736596\pi$
$907$		−	3.64815e7i		−	1.47250i	0.676712	−	0.736248i	$-0.263404\pi$
$908$			2.90849e7i			1.17072i
$909$	−3.05305e6			−0.122553
$910$	−2.79190e7			−1.11762
$911$			3.38686e7i			1.35207i	0.736867	+	0.676037i	$0.236304\pi$
$911$			3.38686e7i			1.35207i	−0.736867	+	0.676037i	$0.763696\pi$
$912$		−	1.65696e7i		−	0.659666i
$913$		−	1.01749e7i		−	0.403972i
$914$	−4.42500e7			−1.75206
$915$			5.85854e6i			0.231333i
$916$	−2.36688e7			−0.932045
$917$	−2.33598e6			−0.0917374
$918$	−4.00512e7	+	1.17703e7i	−1.56859	+	0.460980i
$919$	3.90947e7			1.52696			0.763482	−	0.645829i	$-0.223488\pi$
$919$	3.90947e7			1.52696			0.763482	+	0.645829i	$0.223488\pi$
$920$	−1.21574e6			−0.0473556
$921$		−	3.32191e6i		−	0.129044i
$922$	−6.00116e7			−2.32492
$923$		−	2.63158e7i		−	1.01675i
$924$		−	1.11644e7i		−	0.430184i
$925$		−	8.29114e7i		−	3.18610i
$926$	−1.21604e7			−0.466037
$927$	4.76585e6			0.182155
$928$		−	2.05691e7i		−	0.784054i
$929$		−	4.50805e7i		−	1.71376i	−0.515517	−	0.856880i	$-0.672400\pi$
$929$		−	4.50805e7i		−	1.71376i	0.515517	−	0.856880i	$-0.327600\pi$
$930$			6.01887e7i			2.28196i
$931$	2.70940e7			1.02447
$932$		−	1.52201e7i		−	0.573954i
$933$	1.06951e7			0.402236
$934$	6.24161e6			0.234115
$935$	1.31979e7	+	4.49089e7i	0.493716	+	1.67998i
$936$	4.20911e6			0.157036
$937$	2.58502e7			0.961868			0.480934	−	0.876757i	$-0.340298\pi$
$937$	2.58502e7			0.961868			0.480934	+	0.876757i	$0.340298\pi$
$938$			1.77295e7i			0.657943i
$939$	2.76397e7			1.02299
$940$			3.98904e7i			1.47248i
$941$		−	8.12617e6i		−	0.299166i	−0.988749	−	0.149583i	$-0.952207\pi$
$941$		−	8.12617e6i		−	0.299166i	0.988749	−	0.149583i	$-0.0477931\pi$
$942$			1.37244e7i			0.503926i
$943$	−407906.			−0.0149376
$944$	−1.73679e6			−0.0634334
$945$		−	1.98324e7i		−	0.722430i
$946$			4.72696e7i			1.71733i
$947$			2.98990e7i			1.08338i	0.840578	+	0.541691i	$0.182216\pi$
$947$			2.98990e7i			1.08338i	−0.840578	+	0.541691i	$0.817784\pi$
$948$	4.16878e7			1.50657
$949$			1.48400e7i			0.534893i
$950$	8.78359e7			3.15764
$951$	−3.88050e7			−1.39135
$952$	4.19459e6	−	1.23272e6i	0.150002	−	0.0440830i
$953$	−5.53260e7			−1.97332			−0.986659	−	0.162799i	$-0.947948\pi$
$953$	−5.53260e7			−1.97332			−0.986659	+	0.162799i	$0.947948\pi$
$954$	1.41095e7			0.501928
$955$			1.54924e7i			0.549681i
$956$	−1.75415e7			−0.620757
$957$		−	1.34446e7i		−	0.474536i
$958$		−	1.46529e7i		−	0.515835i
$959$			2.96074e6i			0.103957i
$960$	−5.39086e7			−1.88790
$961$	−9.38715e6			−0.327888
$962$			8.95769e7i			3.12075i
$963$			2.95889e6i			0.102816i
$964$		−	3.32832e7i		−	1.15354i
$965$	−6.29859e7			−2.17734
$966$		−	1.03809e6i		−	0.0357925i
$967$	−489793.			−0.0168440			−0.00842202	−	0.999965i	$-0.502681\pi$
$967$	−489793.			−0.0168440			−0.00842202	+	0.999965i	$0.502681\pi$
$968$	1.44777e6			0.0496607
$969$	2.74075e7	−	8.05459e6i	0.937692	−	0.275571i
$970$	6.77398e6			0.231161
$971$	−2.62829e6			−0.0894593			−0.0447296	−	0.998999i	$-0.514243\pi$
$971$	−2.62829e6			−0.0894593			−0.0447296	+	0.998999i	$0.514243\pi$
$972$			2.52648e7i			0.857728i
$973$	9.37031e6			0.317301
$974$			2.74027e7i			0.925540i
$975$			4.56576e7i			1.53816i
$976$		−	3.52616e6i		−	0.118489i
$977$	−2.96424e7			−0.993520			−0.496760	−	0.867888i	$-0.665477\pi$
$977$	−2.96424e7			−0.993520			−0.496760	+	0.867888i	$0.665477\pi$
$978$	−2.57726e6			−0.0861612
$979$		−	5.66300e7i		−	1.88838i
$980$		−	5.22565e7i		−	1.73810i
$981$			5.65994e6i			0.187776i
$982$	3.00393e7			0.994055
$983$		−	2.21240e7i		−	0.730263i	−0.930956	−	0.365131i	$-0.881024\pi$
$983$		−	2.21240e7i		−	0.730263i	0.930956	−	0.365131i	$-0.118976\pi$
$984$	1.90248e6			0.0626373
$985$	−2.48612e7			−0.816452
$986$	2.46060e7	−	7.23129e6i	0.806026	−	0.236877i
$987$	−6.99238e6			−0.228472
$988$	−5.28761e7			−1.72332
$989$			2.44899e6i			0.0796153i
$990$	2.93100e7			0.950448
$991$			5.22482e7i			1.69000i	0.534764	+	0.845001i	$0.320401\pi$
$991$			5.22482e7i			1.69000i	−0.534764	+	0.845001i	$0.679599\pi$
$992$		−	5.00911e7i		−	1.61615i
$993$		−	8.25888e6i		−	0.265796i
$994$	−1.71159e7			−0.549457
$995$	8.96010e7			2.86916
$996$			1.19766e7i			0.382546i
$997$			2.19323e7i			0.698790i	0.936975	+	0.349395i	$0.113613\pi$
$997$			2.19323e7i			0.698790i	−0.936975	+	0.349395i	$0.886387\pi$
$998$		−	3.71788e7i		−	1.18160i
$999$	−6.36315e7			−2.01724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.6.b.a.16.2	yes	6
3.2	odd	2		153.6.d.b.118.6		6
4.3	odd	2		272.6.b.c.33.3		6
17.4	even	4		289.6.a.f.1.6		6
17.13	even	4		289.6.a.f.1.5		6
17.16	even	2	inner	17.6.b.a.16.1	✓	6
51.50	odd	2		153.6.d.b.118.5		6
68.67	odd	2		272.6.b.c.33.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.6.b.a.16.1	✓	6	17.16	even	2	inner
17.6.b.a.16.2	yes	6	1.1	even	1	trivial
153.6.d.b.118.5		6	51.50	odd	2
153.6.d.b.118.6		6	3.2	odd	2
272.6.b.c.33.3		6	4.3	odd	2
272.6.b.c.33.4		6	68.67	odd	2
289.6.a.f.1.5		6	17.13	even	4
289.6.a.f.1.6		6	17.4	even	4

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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.50095 q^{2} +12.4591i q^{3} +40.2661 q^{4} -92.1671i q^{5} -105.914i q^{6} -52.2138i q^{7} -70.2699 q^{8} +87.7709 q^{9} +O(q^{10})\)	\(q-8.50095 q^{2} +12.4591i q^{3} +40.2661 q^{4} -92.1671i q^{5} -105.914i q^{6} -52.2138i q^{7} -70.2699 q^{8} +87.7709 q^{9} +783.508i q^{10} -426.209i q^{11} +501.680i q^{12} -682.449 q^{13} +443.867i q^{14} +1148.32 q^{15} -691.155 q^{16} +(-335.976 - 1143.23i) q^{17} -746.136 q^{18} +1924.19 q^{19} -3711.21i q^{20} +650.537 q^{21} +3623.18i q^{22} +187.713i q^{23} -875.500i q^{24} -5369.77 q^{25} +5801.47 q^{26} +4121.11i q^{27} -2102.45i q^{28} -2531.86i q^{29} -9761.80 q^{30} -6165.74i q^{31} +8124.11 q^{32} +5310.18 q^{33} +(2856.11 + 9718.55i) q^{34} -4812.40 q^{35} +3534.19 q^{36} +15440.4i q^{37} -16357.5 q^{38} -8502.70i q^{39} +6476.57i q^{40} +2173.03i q^{41} -5530.18 q^{42} +13046.4 q^{43} -17161.8i q^{44} -8089.59i q^{45} -1595.74i q^{46} -10748.6 q^{47} -8611.17i q^{48} +14080.7 q^{49} +45648.1 q^{50} +(14243.6 - 4185.96i) q^{51} -27479.6 q^{52} -18910.1 q^{53} -35033.3i q^{54} -39282.4 q^{55} +3669.06i q^{56} +23973.7i q^{57} +21523.2i q^{58} +2512.88 q^{59} +46238.3 q^{60} +5101.84i q^{61} +52414.6i q^{62} -4582.85i q^{63} -46945.7 q^{64} +62899.4i q^{65} -45141.6 q^{66} +39943.1 q^{67} +(-13528.4 - 46033.5i) q^{68} -2338.74 q^{69} +40909.9 q^{70} +38560.9i q^{71} -6167.65 q^{72} -21745.2i q^{73} -131258. i q^{74} -66902.5i q^{75} +77479.9 q^{76} -22254.0 q^{77} +72281.0i q^{78} -83096.5i q^{79} +63701.7i q^{80} -30017.0 q^{81} -18472.8i q^{82} +23872.9 q^{83} +26194.6 q^{84} +(-105368. + 30965.9i) q^{85} -110907. q^{86} +31544.7 q^{87} +29949.7i q^{88} +132869. q^{89} +68769.1i q^{90} +35633.3i q^{91} +7558.50i q^{92} +76819.5 q^{93} +91373.5 q^{94} -177347. i q^{95} +101219. i q^{96} -8645.71i q^{97} -119699. q^{98} -37408.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 82 q^{4} - 66 q^{8} + 122 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 + 82 * q^4 - 66 * q^8 + 122 * q^9	\( 6 q - 2 q^{2} + 82 q^{4} - 66 q^{8} + 122 q^{9} - 1212 q^{13} + 1200 q^{15} - 1406 q^{16} - 1802 q^{17} - 1510 q^{18} + 3960 q^{19} + 4312 q^{21} - 226 q^{25} + 7820 q^{26} - 19536 q^{30} - 3394 q^{32} + 13544 q^{33} - 11594 q^{34} - 16656 q^{35} + 8422 q^{36} - 10552 q^{38} + 48880 q^{42} + 24168 q^{43} - 40160 q^{47} - 42574 q^{49} + 139142 q^{50} - 25024 q^{51} - 87580 q^{52} - 10908 q^{53} - 58192 q^{55} + 137928 q^{59} + 122832 q^{60} - 223422 q^{64} - 162592 q^{66} + 217432 q^{67} - 125494 q^{68} - 162920 q^{69} + 94176 q^{70} - 13974 q^{72} + 318104 q^{76} + 164152 q^{77} - 308066 q^{81} - 23976 q^{83} + 418400 q^{84} - 281792 q^{85} - 407512 q^{86} + 237072 q^{87} + 81164 q^{89} + 299704 q^{93} + 442048 q^{94} - 814974 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 82 * q^4 - 66 * q^8 + 122 * q^9 - 1212 * q^13 + 1200 * q^15 - 1406 * q^16 - 1802 * q^17 - 1510 * q^18 + 3960 * q^19 + 4312 * q^21 - 226 * q^25 + 7820 * q^26 - 19536 * q^30 - 3394 * q^32 + 13544 * q^33 - 11594 * q^34 - 16656 * q^35 + 8422 * q^36 - 10552 * q^38 + 48880 * q^42 + 24168 * q^43 - 40160 * q^47 - 42574 * q^49 + 139142 * q^50 - 25024 * q^51 - 87580 * q^52 - 10908 * q^53 - 58192 * q^55 + 137928 * q^59 + 122832 * q^60 - 223422 * q^64 - 162592 * q^66 + 217432 * q^67 - 125494 * q^68 - 162920 * q^69 + 94176 * q^70 - 13974 * q^72 + 318104 * q^76 + 164152 * q^77 - 308066 * q^81 - 23976 * q^83 + 418400 * q^84 - 281792 * q^85 - 407512 * q^86 + 237072 * q^87 + 81164 * q^89 + 299704 * q^93 + 442048 * q^94 - 814974 * q^98

Introduction

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