LMFDB - Embedded newform 17.8.b.a.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,8,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, 8, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 8 $
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:	$5.31054543323$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16832x^{8} + 93191572x^{6} + 192821327856x^{4} + 116860780245888x^{2} + 9421474370420736 $ x^10 + 16832x^8 + 93191572x^6 + 192821327856x^4 + 116860780245888x^2 + 9421474370420736
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.3
Root			$-9.73524i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.8.b.a.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.2698 q^{2} -9.73524i q^{3} -0.992706 q^{4} -181.480i q^{5} +109.714i q^{6} +1340.88i q^{7} +1453.72 q^{8} +2092.23 q^{9} +O(q^{10})$	\(q-11.2698 q^{2} -9.73524i q^{3} -0.992706 q^{4} -181.480i q^{5} +109.714i q^{6} +1340.88i q^{7} +1453.72 q^{8} +2092.23 q^{9} +2045.24i q^{10} +5783.08i q^{11} +9.66423i q^{12} +834.906 q^{13} -15111.4i q^{14} -1766.75 q^{15} -16255.9 q^{16} +(12887.2 - 15628.8i) q^{17} -23578.9 q^{18} -9260.11 q^{19} +180.157i q^{20} +13053.8 q^{21} -65173.9i q^{22} +107751. i q^{23} -14152.3i q^{24} +45189.9 q^{25} -9409.18 q^{26} -41659.3i q^{27} -1331.10i q^{28} +101843. i q^{29} +19910.9 q^{30} -20966.7i q^{31} -2875.12 q^{32} +56299.7 q^{33} +(-145236. + 176132. i) q^{34} +243344. q^{35} -2076.96 q^{36} -30107.7i q^{37} +104359. q^{38} -8128.01i q^{39} -263821. i q^{40} +395730. i q^{41} -147113. q^{42} -564125. q^{43} -5740.90i q^{44} -379698. i q^{45} -1.21433e6i q^{46} +502222. q^{47} +158256. i q^{48} -974426. q^{49} -509279. q^{50} +(-152150. - 125460. i) q^{51} -828.816 q^{52} +253229. q^{53} +469490. i q^{54} +1.04952e6 q^{55} +1.94926e6i q^{56} +90149.4i q^{57} -1.14775e6i q^{58} +2.58041e6 q^{59} +1753.87 q^{60} +1.00567e6i q^{61} +236290. i q^{62} +2.80543e6i q^{63} +2.11316e6 q^{64} -151519. i q^{65} -634483. q^{66} -3.93496e6 q^{67} +(-12793.2 + 15514.8i) q^{68} +1.04898e6 q^{69} -2.74243e6 q^{70} -3.95445e6i q^{71} +3.04150e6 q^{72} -5.07004e6i q^{73} +339306. i q^{74} -439935. i q^{75} +9192.56 q^{76} -7.75444e6 q^{77} +91600.6i q^{78} +811675. i q^{79} +2.95013e6i q^{80} +4.17013e6 q^{81} -4.45977e6i q^{82} -3.58083e6 q^{83} -12958.6 q^{84} +(-2.83631e6 - 2.33878e6i) q^{85} +6.35754e6 q^{86} +991466. q^{87} +8.40696e6i q^{88} +5.31432e6 q^{89} +4.27910e6i q^{90} +1.11951e6i q^{91} -106965. i q^{92} -204116. q^{93} -5.65992e6 q^{94} +1.68053e6i q^{95} +27990.0i q^{96} -1.41602e7i q^{97} +1.09815e7 q^{98} +1.20995e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 18 q^{2} + 690 q^{4} - 3330 q^{8} - 11794 q^{9}+O(q^{10}) $ 10 * q - 18 * q^2 + 690 * q^4 - 3330 * q^8 - 11794 * q^9	$ 10 q - 18 q^{2} + 690 q^{4} - 3330 q^{8} - 11794 q^{9} - 316 q^{13} + 13824 q^{15} + 92226 q^{16} - 29454 q^{17} + 94106 q^{18} - 90184 q^{19} - 137648 q^{21} + 78370 q^{25} - 180420 q^{26} + 781392 q^{30} - 1019778 q^{32} + 418160 q^{33} + 1123478 q^{34} - 460704 q^{35} - 1026218 q^{36} - 1583880 q^{38} + 1939504 q^{42} - 112936 q^{43} + 3214512 q^{47} - 230842 q^{49} - 359514 q^{50} - 102928 q^{51} + 4611732 q^{52} - 4396356 q^{53} + 2187488 q^{55} - 6096552 q^{59} - 12859152 q^{60} + 4541698 q^{64} + 4831808 q^{66} - 10368488 q^{67} - 712902 q^{68} + 7389760 q^{69} + 11368032 q^{70} + 15426330 q^{72} - 14210712 q^{76} + 7163520 q^{77} + 20826346 q^{81} + 7060104 q^{83} - 85725280 q^{84} + 8300608 q^{85} + 30033048 q^{86} + 855264 q^{87} + 24760956 q^{89} - 39868160 q^{93} - 54883072 q^{94} + 81770994 q^{98}+O(q^{100}) $ 10 * q - 18 * q^2 + 690 * q^4 - 3330 * q^8 - 11794 * q^9 - 316 * q^13 + 13824 * q^15 + 92226 * q^16 - 29454 * q^17 + 94106 * q^18 - 90184 * q^19 - 137648 * q^21 + 78370 * q^25 - 180420 * q^26 + 781392 * q^30 - 1019778 * q^32 + 418160 * q^33 + 1123478 * q^34 - 460704 * q^35 - 1026218 * q^36 - 1583880 * q^38 + 1939504 * q^42 - 112936 * q^43 + 3214512 * q^47 - 230842 * q^49 - 359514 * q^50 - 102928 * q^51 + 4611732 * q^52 - 4396356 * q^53 + 2187488 * q^55 - 6096552 * q^59 - 12859152 * q^60 + 4541698 * q^64 + 4831808 * q^66 - 10368488 * q^67 - 712902 * q^68 + 7389760 * q^69 + 11368032 * q^70 + 15426330 * q^72 - 14210712 * q^76 + 7163520 * q^77 + 20826346 * q^81 + 7060104 * q^83 - 85725280 * q^84 + 8300608 * q^85 + 30033048 * q^86 + 855264 * q^87 + 24760956 * q^89 - 39868160 * q^93 - 54883072 * q^94 + 81770994 * 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 $

$2$	−11.2698			−0.996115			−0.498057	−	0.867144i	$-0.665953\pi$
$2$	−11.2698			−0.996115			−0.498057	+	0.867144i	$0.665953\pi$
$3$		−	9.73524i		−	0.208172i	−0.994568	−	0.104086i	$-0.966808\pi$
$3$		−	9.73524i		−	0.208172i	0.994568	−	0.104086i	$-0.0331917\pi$
$4$	−0.992706			−0.00775551
$5$		−	181.480i		−	0.649284i	−0.945837	−	0.324642i	$-0.894756\pi$
$5$		−	181.480i		−	0.649284i	0.945837	−	0.324642i	$-0.105244\pi$
$6$			109.714i			0.207363i
$7$			1340.88i			1.47757i	0.673941	+	0.738785i	$0.264600\pi$
$7$			1340.88i			1.47757i	−0.673941	+	0.738785i	$0.735400\pi$
$8$	1453.72			1.00384
$9$	2092.23			0.956664
$10$			2045.24i			0.646761i
$11$			5783.08i			1.31004i	0.755611	+	0.655021i	$0.227340\pi$
$11$			5783.08i			1.31004i	−0.755611	+	0.655021i	$0.772660\pi$
$12$			9.66423i			0.00161448i
$13$	834.906			0.105399			0.0526994	−	0.998610i	$-0.483217\pi$
$13$	834.906			0.105399			0.0526994	+	0.998610i	$0.483217\pi$
$14$		−	15111.4i		−	1.47183i
$15$	−1766.75			−0.135163
$16$	−16255.9			−0.992184
$17$	12887.2	−	15628.8i	0.636192	−	0.771531i
$17$	12887.2	−	15628.8i	0.636192	−	0.771531i
$18$	−23578.9			−0.952948
$19$	−9260.11			−0.309727			−0.154863	−	0.987936i	$-0.549494\pi$
$19$	−9260.11			−0.309727			−0.154863	+	0.987936i	$0.549494\pi$
$20$			180.157i			0.00503553i
$21$	13053.8			0.307589
$22$		−	65173.9i		−	1.30495i
$23$			107751.i			1.84661i	0.384071	+	0.923303i	$0.374522\pi$
$23$			107751.i			1.84661i	−0.384071	+	0.923303i	$0.625478\pi$
$24$		−	14152.3i		−	0.208971i
$25$	45189.9			0.578431
$26$	−9409.18			−0.104989
$27$		−	41659.3i		−	0.407323i
$28$		−	1331.10i		−	0.0114593i
$29$			101843.i			0.775422i	0.921781	+	0.387711i	$0.126734\pi$
$29$			101843.i			0.775422i	−0.921781	+	0.387711i	$0.873266\pi$
$30$	19910.9			0.134637
$31$		−	20966.7i		−	0.126405i	−0.998001	−	0.0632025i	$-0.979869\pi$
$31$		−	20966.7i		−	0.126405i	0.998001	−	0.0632025i	$-0.0201314\pi$
$32$	−2875.12			−0.0155107
$33$	56299.7			0.272714
$34$	−145236.	+	176132.i	−0.633720	+	0.768533i
$35$	243344.			0.959362
$36$	−2076.96			−0.00741943
$37$		−	30107.7i		−	0.0977173i	−0.998806	−	0.0488586i	$-0.984442\pi$
$37$		−	30107.7i		−	0.0977173i	0.998806	−	0.0488586i	$-0.0155584\pi$
$38$	104359.			0.308523
$39$		−	8128.01i		−	0.0219411i
$40$		−	263821.i		−	0.651777i
$41$			395730.i			0.896716i	0.893854	+	0.448358i	$0.147991\pi$
$41$			395730.i			0.896716i	−0.893854	+	0.448358i	$0.852009\pi$
$42$	−147113.			−0.306393
$43$	−564125.			−1.08202			−0.541010	−	0.841016i	$-0.681958\pi$
$43$	−564125.			−1.08202			−0.541010	+	0.841016i	$0.681958\pi$
$44$		−	5740.90i		−	0.0101600i
$45$		−	379698.i		−	0.621146i
$46$		−	1.21433e6i		−	1.83943i
$47$	502222.			0.705591			0.352796	−	0.935700i	$-0.385231\pi$
$47$	502222.			0.705591			0.352796	+	0.935700i	$0.385231\pi$
$48$			158256.i			0.206545i
$49$	−974426.			−1.18321
$50$	−509279.			−0.576183
$51$	−152150.	−	125460.i	−0.160611	−	0.132437i
$52$	−828.816			−0.000817422
$53$	253229.			0.233640			0.116820	−	0.993153i	$-0.462730\pi$
$53$	253229.			0.233640			0.116820	+	0.993153i	$0.462730\pi$
$54$			469490.i			0.405740i
$55$	1.04952e6			0.850588
$56$			1.94926e6i			1.48324i
$57$			90149.4i			0.0644764i
$58$		−	1.14775e6i		−	0.772409i
$59$	2.58041e6			1.63571			0.817855	−	0.575424i	$-0.195163\pi$
$59$	2.58041e6			1.63571			0.817855	+	0.575424i	$0.195163\pi$
$60$	1753.87			0.00104826
$61$			1.00567e6i			0.567285i	0.958930	+	0.283642i	$0.0915428\pi$
$61$			1.00567e6i			0.567285i	−0.958930	+	0.283642i	$0.908457\pi$
$62$			236290.i			0.125914i
$63$			2.80543e6i			1.41354i
$64$	2.11316e6			1.00763
$65$		−	151519.i		−	0.0684337i
$66$	−634483.			−0.271654
$67$	−3.93496e6			−1.59837			−0.799187	−	0.601083i	$-0.794736\pi$
$67$	−3.93496e6			−1.59837			−0.799187	+	0.601083i	$0.794736\pi$
$68$	−12793.2	+	15514.8i	−0.00493400	+	0.00598362i
$69$	1.04898e6			0.384412
$70$	−2.74243e6			−0.955634
$71$		−	3.95445e6i		−	1.31124i	−0.755092	−	0.655619i	$-0.772408\pi$
$71$		−	3.95445e6i		−	1.31124i	0.755092	−	0.655619i	$-0.227592\pi$
$72$	3.04150e6			0.960338
$73$		−	5.07004e6i		−	1.52539i	−0.646758	−	0.762696i	$-0.723875\pi$
$73$		−	5.07004e6i		−	1.52539i	0.646758	−	0.762696i	$-0.276125\pi$
$74$			339306.i			0.0973376i
$75$		−	439935.i		−	0.120413i
$76$	9192.56			0.00240209
$77$	−7.75444e6			−1.93568
$78$			91600.6i			0.0218558i
$79$			811675.i			0.185220i	0.995702	+	0.0926099i	$0.0295209\pi$
$79$			811675.i			0.185220i	−0.995702	+	0.0926099i	$0.970479\pi$
$80$			2.95013e6i			0.644209i
$81$	4.17013e6			0.871871
$82$		−	4.45977e6i		−	0.893232i
$83$	−3.58083e6			−0.687401			−0.343700	−	0.939079i	$-0.611680\pi$
$83$	−3.58083e6			−0.687401			−0.343700	+	0.939079i	$0.611680\pi$
$84$	−12958.6			−0.00238551
$85$	−2.83631e6	−	2.33878e6i	−0.500942	−	0.413069i
$86$	6.35754e6			1.07782
$87$	991466.			0.161421
$88$			8.40696e6i			1.31507i
$89$	5.31432e6			0.799065			0.399533	−	0.916719i	$-0.369172\pi$
$89$	5.31432e6			0.799065			0.399533	+	0.916719i	$0.369172\pi$
$90$			4.27910e6i			0.618733i
$91$			1.11951e6i			0.155734i
$92$		−	106965.i		−	0.0143214i
$93$	−204116.			−0.0263140
$94$	−5.65992e6			−0.702850
$95$			1.68053e6i			0.201100i
$96$			27990.0i			0.00322889i
$97$		−	1.41602e7i		−	1.57532i	−0.616109	−	0.787661i	$-0.711292\pi$
$97$		−	1.41602e7i		−	1.57532i	0.616109	−	0.787661i	$-0.288708\pi$
$98$	1.09815e7			1.17861
$99$			1.20995e7i			1.25327i
$100$	−44860.3			−0.00448603
$101$	−1.23888e7			−1.19648			−0.598238	−	0.801318i	$-0.704132\pi$
$101$	−1.23888e7			−1.19648			−0.598238	+	0.801318i	$0.704132\pi$
$102$	1.71469e6	+	1.41391e6i	0.159987	+	0.131923i
$103$	1.21917e7			1.09935			0.549674	−	0.835379i	$-0.314752\pi$
$103$	1.21917e7			1.09935			0.549674	+	0.835379i	$0.314752\pi$
$104$	1.21372e6			0.105804
$105$		−	2.36901e6i		−	0.199712i
$106$	−2.85382e6			−0.232732
$107$		−	1.24578e6i		−	0.0983099i	−0.998791	−	0.0491550i	$-0.984347\pi$
$107$		−	1.24578e6i		−	0.0983099i	0.998791	−	0.0491550i	$-0.0156528\pi$
$108$			41355.4i			0.00315900i
$109$			1.87674e7i			1.38807i	0.719940	+	0.694037i	$0.244169\pi$
$109$			1.87674e7i			1.38807i	−0.719940	+	0.694037i	$0.755831\pi$
$110$	−1.18278e7			−0.847283
$111$	−293106.			−0.0203420
$112$		−	2.17973e7i		−	1.46602i
$113$		−	1.49197e6i		−	0.0972716i	−0.998817	−	0.0486358i	$-0.984513\pi$
$113$		−	1.49197e6i		−	0.0972716i	0.998817	−	0.0486358i	$-0.0154874\pi$
$114$		−	1.01596e6i		−	0.0642259i
$115$	1.95547e7			1.19897
$116$		−	101100.i		−	0.00601380i
$117$	1.74681e6			0.100831
$118$	−2.90806e7			−1.62936
$119$	2.09563e7	+	1.72803e7i	1.13999	+	0.940018i
$120$	−2.56836e6			−0.135682
$121$	−1.39569e7			−0.716208
$122$		−	1.13337e7i		−	0.565081i
$123$	3.85252e6			0.186671
$124$			20813.8i			0.000980337i
$125$		−	2.23792e7i		−	1.02485i
$126$		−	3.16165e7i		−	1.40805i
$127$	−2.30800e7			−0.999823			−0.499912	−	0.866076i	$-0.666634\pi$
$127$	−2.30800e7			−0.999823			−0.499912	+	0.866076i	$0.666634\pi$
$128$	−2.34468e7			−0.988209
$129$			5.49189e6i			0.225246i
$130$			1.70758e6i			0.0681678i
$131$			2.80146e7i			1.08877i	0.838837	+	0.544383i	$0.183236\pi$
$131$			2.80146e7i			1.08877i	−0.838837	+	0.544383i	$0.816764\pi$
$132$	−55889.0			−0.00211504
$133$		−	1.24167e7i		−	0.457642i
$134$	4.43460e7			1.59216
$135$	−7.56034e6			−0.264468
$136$	1.87344e7	−	2.27198e7i	0.638635	−	0.774493i
$137$	9.25192e6			0.307404			0.153702	−	0.988117i	$-0.450880\pi$
$137$	9.25192e6			0.307404			0.153702	+	0.988117i	$0.450880\pi$
$138$	−1.18218e7			−0.382918
$139$			2.55874e7i			0.808119i	0.914733	+	0.404059i	$0.132401\pi$
$139$			2.55874e7i			0.808119i	−0.914733	+	0.404059i	$0.867599\pi$
$140$	−241569.			−0.00744034
$141$		−	4.88925e6i		−	0.146884i
$142$			4.45656e7i			1.30614i
$143$			4.82833e6i			0.138077i
$144$	−3.40111e7			−0.949187
$145$	1.84825e7			0.503469
$146$			5.71381e7i			1.51946i
$147$			9.48627e6i			0.246311i
$148$			29888.1i			0.000757848i
$149$	2.91086e7			0.720890			0.360445	−	0.932780i	$-0.382625\pi$
$149$	2.91086e7			0.720890			0.360445	+	0.932780i	$0.382625\pi$
$150$			4.95795e6i			0.119945i
$151$	6.19449e7			1.46415			0.732076	−	0.681223i	$-0.238552\pi$
$151$	6.19449e7			1.46415			0.732076	+	0.681223i	$0.238552\pi$
$152$	−1.34616e7			−0.310916
$153$	2.69630e7	−	3.26989e7i	0.608623	−	0.738096i
$154$	8.73906e7			1.92816
$155$	−3.80505e6			−0.0820727
$156$			8068.72i			0.000170164i
$157$	−6.50819e7			−1.34218			−0.671091	−	0.741375i	$-0.734174\pi$
$157$	−6.50819e7			−1.34218			−0.671091	+	0.741375i	$0.734174\pi$
$158$		−	9.14737e6i		−	0.184500i
$159$		−	2.46524e6i		−	0.0486373i
$160$			521777.i			0.0100708i
$161$	−1.44482e8			−2.72849
$162$	−4.69964e7			−0.868484
$163$		−	2.63730e7i		−	0.476983i	−0.971145	−	0.238492i	$-0.923347\pi$
$163$		−	2.63730e7i		−	0.476983i	0.971145	−	0.238492i	$-0.0766529\pi$
$164$		−	392843.i		−	0.00695449i
$165$		−	1.02173e7i		−	0.177069i
$166$	4.03550e7			0.684730
$167$		−	7.74984e7i		−	1.28761i	−0.765189	−	0.643806i	$-0.777355\pi$
$167$		−	7.74984e7i		−	1.28761i	0.765189	−	0.643806i	$-0.222645\pi$
$168$	1.89765e7			0.308770
$169$	−6.20514e7			−0.988891
$170$	3.19645e7	+	2.63574e7i	0.498996	+	0.411464i
$171$	−1.93742e7			−0.296304
$172$	560010.			0.00839163
$173$		−	8.07573e7i		−	1.18582i	−0.805267	−	0.592912i	$-0.797978\pi$
$173$		−	8.07573e7i		−	1.18582i	0.805267	−	0.592912i	$-0.202022\pi$
$174$	−1.11736e7			−0.160794
$175$			6.05944e7i			0.854672i
$176$		−	9.40095e7i		−	1.29980i
$177$		−	2.51209e7i		−	0.340509i
$178$	−5.98910e7			−0.795961
$179$	4.00077e7			0.521385			0.260692	−	0.965422i	$-0.416049\pi$
$179$	4.00077e7			0.521385			0.260692	+	0.965422i	$0.416049\pi$
$180$			376928.i			0.00481731i
$181$		−	6.80903e6i		−	0.0853513i	−0.999089	−	0.0426756i	$-0.986412\pi$
$181$		−	6.80903e6i		−	0.0853513i	0.999089	−	0.0426756i	$-0.0135882\pi$
$182$		−	1.26166e7i		−	0.155129i
$183$	9.79044e6			0.118093
$184$			1.56640e8i			1.85370i
$185$	−5.46395e6			−0.0634462
$186$	2.30034e6			0.0262118
$187$	9.03824e7	+	7.45279e7i	1.01074	+	0.833438i
$188$	−498559.			−0.00547222
$189$	5.58602e7			0.601848
$190$		−	1.89391e7i		−	0.200319i
$191$	1.06003e7			0.110078			0.0550391	−	0.998484i	$-0.482472\pi$
$191$	1.06003e7			0.110078			0.0550391	+	0.998484i	$0.482472\pi$
$192$		−	2.05721e7i		−	0.209761i
$193$			1.05434e8i			1.05568i	0.849345	+	0.527839i	$0.176997\pi$
$193$			1.05434e8i			1.05568i	−0.849345	+	0.527839i	$0.823003\pi$
$194$			1.59582e8i			1.56920i
$195$	−1.47507e6			−0.0142460
$196$	967318.			0.00917642
$197$		−	7.34973e7i		−	0.684920i	−0.939532	−	0.342460i	$-0.888740\pi$
$197$		−	7.34973e7i		−	0.684920i	0.939532	−	0.342460i	$-0.111260\pi$
$198$		−	1.36358e8i		−	1.24840i
$199$		−	4.61952e7i		−	0.415538i	−0.978178	−	0.207769i	$-0.933380\pi$
$199$		−	4.61952e7i		−	0.415538i	0.978178	−	0.207769i	$-0.0666203\pi$
$200$	6.56933e7			0.580652
$201$			3.83078e7i			0.332737i
$202$	1.39619e8			1.19183
$203$	−1.36560e8			−1.14574
$204$	151040.	+	124545.i	0.00124562	+	0.00102712i
$205$	7.18171e7			0.582223
$206$	−1.37398e8			−1.09508
$207$			2.25440e8i			1.76658i
$208$	−1.35722e7			−0.104575
$209$		−	5.35520e7i		−	0.405755i
$210$			2.66982e7i			0.198936i
$211$		−	1.62815e8i		−	1.19318i	−0.802546	−	0.596590i	$-0.796522\pi$
$211$		−	1.62815e8i		−	1.19318i	0.802546	−	0.596590i	$-0.203478\pi$
$212$	−251382.			−0.00181200
$213$	−3.84975e7			−0.272963
$214$			1.40396e7i			0.0979280i
$215$			1.02377e8i			0.702538i
$216$		−	6.05607e7i		−	0.408887i
$217$	2.81139e7			0.186772
$218$		−	2.11504e8i		−	1.38268i
$219$	−4.93580e7			−0.317544
$220$	−1.04186e6			−0.00659675
$221$	1.07596e7	−	1.30485e7i	0.0670539	−	0.0813184i
$222$	3.30323e6			0.0202630
$223$	−7.65887e7			−0.462485			−0.231243	−	0.972896i	$-0.574279\pi$
$223$	−7.65887e7			−0.462485			−0.231243	+	0.972896i	$0.574279\pi$
$224$		−	3.85520e6i		−	0.0229181i
$225$	9.45475e7			0.553364
$226$			1.68141e7i			0.0968937i
$227$		−	6.64444e7i		−	0.377023i	−0.982071	−	0.188512i	$-0.939634\pi$
$227$		−	6.64444e7i		−	0.377023i	0.982071	−	0.188512i	$-0.0603663\pi$
$228$		−	89491.8i		−	0.000500048i
$229$	1.54121e8			0.848084			0.424042	−	0.905643i	$-0.360611\pi$
$229$	1.54121e8			0.848084			0.424042	+	0.905643i	$0.360611\pi$
$230$	−2.20377e8			−1.19431
$231$			7.54913e7i			0.402954i
$232$			1.48051e8i			0.778400i
$233$			1.03207e8i			0.534522i	0.963624	+	0.267261i	$0.0861185\pi$
$233$			1.03207e8i			0.534522i	−0.963624	+	0.267261i	$0.913881\pi$
$234$	−1.96861e7			−0.100440
$235$		−	9.11434e7i		−	0.458129i
$236$	−2.56159e6			−0.0126858
$237$	7.90185e6			0.0385575
$238$	−2.36173e8	−	1.94744e8i	−1.13556	−	0.936366i
$239$	1.00214e7			0.0474826			0.0237413	−	0.999718i	$-0.492442\pi$
$239$	1.00214e7			0.0474826			0.0237413	+	0.999718i	$0.492442\pi$
$240$	2.87203e7			0.134106
$241$		−	2.58640e8i		−	1.19024i	−0.803636	−	0.595121i	$-0.797104\pi$
$241$		−	2.58640e8i		−	1.19024i	0.803636	−	0.595121i	$-0.202896\pi$
$242$	1.57290e8			0.713425
$243$		−	1.31706e8i		−	0.588822i
$244$		−	998335.i		−	0.00439959i
$245$			1.76839e8i			0.768240i
$246$	−4.34170e7			−0.185946
$247$	−7.73132e6			−0.0326448
$248$		−	3.04797e7i		−	0.126890i
$249$			3.48602e7i			0.143098i
$250$			2.52208e8i			1.02087i
$251$	5.22128e7			0.208410			0.104205	−	0.994556i	$-0.466770\pi$
$251$	5.22128e7			0.208410			0.104205	+	0.994556i	$0.466770\pi$
$252$		−	2.78497e6i		−	0.0109627i
$253$	−6.23134e8			−2.41913
$254$	2.60106e8			0.995938
$255$	−2.27686e7	+	2.76122e7i	−0.0859894	+	0.104282i
$256$	−6.24519e6			−0.0232651
$257$	3.93545e8			1.44620			0.723099	−	0.690744i	$-0.242717\pi$
$257$	3.93545e8			1.44620			0.723099	+	0.690744i	$0.242717\pi$
$258$		−	6.18922e7i		−	0.224371i
$259$	4.03709e7			0.144384
$260$			150414.i			0.000530739i
$261$			2.13078e8i			0.741819i
$262$		−	3.15717e8i		−	1.08454i
$263$	4.50386e8			1.52665			0.763326	−	0.646013i	$-0.223565\pi$
$263$	4.50386e8			1.52665			0.763326	+	0.646013i	$0.223565\pi$
$264$	8.18437e7			0.273761
$265$		−	4.59560e7i		−	0.151699i
$266$			1.39933e8i			0.455864i
$267$		−	5.17361e7i		−	0.166343i
$268$	3.90626e6			0.0123962
$269$			5.16491e8i			1.61782i	0.587935	+	0.808909i	$0.299941\pi$
$269$			5.16491e8i			1.61782i	−0.587935	+	0.808909i	$0.700059\pi$
$270$	8.52031e7			0.263440
$271$	−1.28639e8			−0.392627			−0.196313	−	0.980541i	$-0.562897\pi$
$271$	−1.28639e8			−0.392627			−0.196313	+	0.980541i	$0.562897\pi$
$272$	−2.09494e8	+	2.54060e8i	−0.631220	+	0.765501i
$273$	1.08987e7			0.0324195
$274$	−1.04267e8			−0.306210
$275$			2.61337e8i			0.757768i
$276$	−1.04133e6			−0.00298131
$277$			5.17053e8i			1.46169i	0.682543	+	0.730845i	$0.260874\pi$
$277$			5.17053e8i			1.46169i	−0.682543	+	0.730845i	$0.739126\pi$
$278$		−	2.88364e8i		−	0.804979i
$279$		−	4.38671e7i		−	0.120927i
$280$	3.53753e8			0.963046
$281$	2.97615e8			0.800170			0.400085	−	0.916478i	$-0.368981\pi$
$281$	2.97615e8			0.800170			0.400085	+	0.916478i	$0.368981\pi$
$282$			5.51006e7i			0.146314i
$283$		−	6.36824e8i		−	1.67019i	−0.550103	−	0.835097i	$-0.685412\pi$
$283$		−	6.36824e8i		−	1.67019i	0.550103	−	0.835097i	$-0.314588\pi$
$284$			3.92560e6i			0.0101693i
$285$	1.63603e7			0.0418635
$286$		−	5.44141e7i		−	0.137540i
$287$	−5.30627e8			−1.32496
$288$	−6.01540e6			−0.0148385
$289$	−7.81772e7	−	4.02823e8i	−0.190519	−	0.981684i
$290$	−2.08293e8			−0.501513
$291$	−1.37853e8			−0.327938
$292$			5.03306e6i			0.0118302i
$293$	1.47396e8			0.342333			0.171167	−	0.985242i	$-0.445246\pi$
$293$	1.47396e8			0.342333			0.171167	+	0.985242i	$0.445246\pi$
$294$		−	1.06908e8i		−	0.245354i
$295$		−	4.68293e8i		−	1.06204i
$296$		−	4.37680e7i		−	0.0980925i
$297$	2.40919e8			0.533609
$298$	−3.28046e8			−0.718089
$299$			8.99620e7i			0.194630i
$300$			436726.i			0.000933865i
$301$		−	7.56425e8i		−	1.59876i
$302$	−6.98103e8			−1.45846
$303$			1.20608e8i			0.249073i
$304$	1.50532e8			0.307306
$305$	1.82509e8			0.368329
$306$	−3.03866e8	+	3.68508e8i	−0.606258	+	0.735228i
$307$	−9.32079e8			−1.83852			−0.919260	−	0.393651i	$-0.871212\pi$
$307$	−9.32079e8			−1.83852			−0.919260	+	0.393651i	$0.871212\pi$
$308$	7.69788e6			0.0150122
$309$		−	1.18689e8i		−	0.228853i
$310$	4.28819e7			0.0817539
$311$		−	6.73465e8i		−	1.26956i	−0.772692	−	0.634781i	$-0.781090\pi$
$311$		−	6.73465e8i		−	1.26956i	0.772692	−	0.634781i	$-0.218910\pi$
$312$		−	1.18158e7i		−	0.0220253i
$313$			9.22735e8i			1.70087i	0.526079	+	0.850436i	$0.323662\pi$
$313$			9.22735e8i			1.70087i	−0.526079	+	0.850436i	$0.676338\pi$
$314$	7.33457e8			1.33697
$315$	5.09130e8			0.917787
$316$		−	805754.i		−	0.00143647i
$317$			1.25264e8i			0.220861i	0.993884	+	0.110430i	$0.0352229\pi$
$317$			1.25264e8i			0.220861i	−0.993884	+	0.110430i	$0.964777\pi$
$318$			2.77827e7i			0.0484483i
$319$	−5.88966e8			−1.01583
$320$		−	3.83497e8i		−	0.654241i
$321$	−1.21279e7			−0.0204654
$322$	1.62827e9			2.71789
$323$	−1.19337e8	+	1.44724e8i	−0.197046	+	0.238963i
$324$	−4.13972e6			−0.00676181
$325$	3.77293e7			0.0609659
$326$			2.97217e8i			0.475130i
$327$	1.82706e8			0.288958
$328$			5.75278e8i			0.900160i
$329$			6.73421e8i			1.04256i
$330$			1.15146e8i			0.176381i
$331$	−1.08117e8			−0.163868			−0.0819341	−	0.996638i	$-0.526110\pi$
$331$	−1.08117e8			−0.163868			−0.0819341	+	0.996638i	$0.526110\pi$
$332$	3.55471e6			0.00533115
$333$		−	6.29921e7i		−	0.0934827i
$334$			8.73387e8i			1.28261i
$335$			7.14117e8i			1.03780i
$336$	−2.12202e8			−0.305185
$337$		−	7.83029e8i		−	1.11448i	−0.830351	−	0.557241i	$-0.811860\pi$
$337$		−	7.83029e8i		−	1.11448i	0.830351	−	0.557241i	$-0.188140\pi$
$338$	6.99304e8			0.985049
$339$	−1.45247e7			−0.0202492
$340$	2.81562e6	+	2.32172e6i	0.00388506	+	0.00320356i
$341$	1.21252e8			0.165596
$342$	2.18343e8			0.295153
$343$		−	2.02316e8i		−	0.270708i
$344$	−8.20077e8			−1.08618
$345$		−	1.90370e8i		−	0.249592i
$346$			9.10114e8i			1.18122i
$347$		−	1.37878e9i		−	1.77151i	−0.464156	−	0.885753i	$-0.653642\pi$
$347$		−	1.37878e9i		−	1.77151i	0.464156	−	0.885753i	$-0.346358\pi$
$348$	−984234.			−0.00125190
$349$	1.28126e9			1.61342			0.806711	−	0.590946i	$-0.201246\pi$
$349$	1.28126e9			1.61342			0.806711	+	0.590946i	$0.201246\pi$
$350$		−	6.82884e8i		−	0.851351i
$351$		−	3.47816e7i		−	0.0429313i
$352$		−	1.66270e7i		−	0.0203196i
$353$	−9.04425e8			−1.09436			−0.547181	−	0.837014i	$-0.684299\pi$
$353$	−9.04425e8			−1.09436			−0.547181	+	0.837014i	$0.684299\pi$
$354$			2.83106e8i			0.339186i
$355$	−7.17654e8			−0.851365
$356$	−5.27555e6			−0.00619716
$357$	1.68228e8	−	2.04015e8i	0.195685	−	0.237314i
$358$	−4.50877e8			−0.519359
$359$	4.17207e8			0.475906			0.237953	−	0.971277i	$-0.423524\pi$
$359$	4.17207e8			0.475906			0.237953	+	0.971277i	$0.423524\pi$
$360$		−	5.51972e8i		−	0.623532i
$361$	−8.08122e8			−0.904069
$362$			7.67360e7i			0.0850197i
$363$			1.35873e8i			0.149094i
$364$		−	1.11135e6i		−	0.00120780i
$365$	−9.20112e8			−0.990412
$366$	−1.10336e8			−0.117634
$367$			5.32275e8i			0.562089i	0.959695	+	0.281044i	$0.0906808\pi$
$367$			5.32275e8i			0.562089i	−0.959695	+	0.281044i	$0.909319\pi$
$368$		−	1.75160e9i		−	1.83217i
$369$			8.27955e8i			0.857856i
$370$	6.15774e7			0.0631997
$371$			3.39550e8i			0.345219i
$372$	202627.			0.000204079
$373$	1.26420e9			1.26135			0.630676	−	0.776047i	$-0.282778\pi$
$373$	1.26420e9			1.26135			0.630676	+	0.776047i	$0.282778\pi$
$374$	−1.01859e9	−	8.39911e8i	−1.00681	−	0.830200i
$375$	−2.17867e8			−0.213345
$376$	7.30088e8			0.708301
$377$			8.50293e7i			0.0817286i
$378$	−6.29531e8			−0.599509
$379$		−	1.13321e9i		−	1.06923i	−0.845095	−	0.534617i	$-0.820456\pi$
$379$		−	1.13321e9i		−	1.06923i	0.845095	−	0.534617i	$-0.179544\pi$
$380$		−	1.66827e6i		−	0.00155964i
$381$			2.24689e8i			0.208135i
$382$	−1.19463e8			−0.109650
$383$	1.84833e9			1.68106			0.840529	−	0.541766i	$-0.182244\pi$
$383$	1.84833e9			1.68106			0.840529	+	0.541766i	$0.182244\pi$
$384$			2.28260e8i			0.205717i
$385$			1.40728e9i			1.25680i
$386$		−	1.18822e9i		−	1.05158i
$387$	−1.18028e9			−1.03513
$388$			1.40569e7i			0.0122174i
$389$	−1.95204e8			−0.168138			−0.0840690	−	0.996460i	$-0.526792\pi$
$389$	−1.95204e8			−0.168138			−0.0840690	+	0.996460i	$0.526792\pi$
$390$	1.66237e7			0.0141906
$391$	1.68402e9	+	1.38861e9i	1.42471	+	1.17480i
$392$	−1.41654e9			−1.18776
$393$	2.72729e8			0.226651
$394$			8.28297e8i			0.682259i
$395$	1.47303e8			0.120260
$396$		−	1.20113e7i		−	0.00971975i
$397$		−	1.46433e9i		−	1.17455i	−0.809386	−	0.587276i	$-0.800200\pi$
$397$		−	1.46433e9i		−	1.17455i	0.809386	−	0.587276i	$-0.199800\pi$
$398$			5.20608e8i			0.413924i
$399$	−1.20880e8			−0.0952683
$400$	−7.34605e8			−0.573910
$401$			3.82480e8i			0.296212i	0.988971	+	0.148106i	$0.0473177\pi$
$401$			3.82480e8i			0.296212i	−0.988971	+	0.148106i	$0.952682\pi$
$402$		−	4.31719e8i		−	0.331444i
$403$		−	1.75052e7i		−	0.0133229i
$404$	1.22984e7			0.00927929
$405$		−	7.56797e8i		−	0.566092i
$406$	1.53899e9			1.14129
$407$	1.74115e8			0.128014
$408$	−2.21182e8	−	1.82384e8i	−0.161228	−	0.132946i
$409$	9.94154e7			0.0718492			0.0359246	−	0.999355i	$-0.488562\pi$
$409$	9.94154e7			0.0718492			0.0359246	+	0.999355i	$0.488562\pi$
$410$	−8.09361e8			−0.579961
$411$		−	9.00697e7i		−	0.0639930i
$412$	−1.21028e7			−0.00852601
$413$			3.46003e9i			2.41688i
$414$		−	2.54065e9i		−	1.75972i
$415$			6.49849e8i			0.446318i
$416$	−2.40045e6			−0.00163481
$417$	2.49100e8			0.168228
$418$			6.03517e8i			0.404178i
$419$		−	4.80667e6i		−	0.00319224i	−0.999999	−	0.00159612i	$-0.999492\pi$
$419$		−	4.80667e6i		−	0.00319224i	0.999999	−	0.00159612i	$-0.000508061\pi$
$420$			2.35173e6i			0.00154887i
$421$	1.43850e8			0.0939558			0.0469779	−	0.998896i	$-0.485041\pi$
$421$	1.43850e8			0.0939558			0.0469779	+	0.998896i	$0.485041\pi$
$422$			1.83489e9i			1.18854i
$423$	1.05076e9			0.675014
$424$	3.68122e8			0.234537
$425$	5.82373e8	−	7.06262e8i	0.367993	−	0.446277i
$426$	4.33857e8			0.271902
$427$	−1.34849e9			−0.838203
$428$			1.23669e6i			0.000762444i
$429$	4.70049e7			0.0287437
$430$		−	1.15377e9i		−	0.699808i
$431$			3.48593e8i			0.209724i	0.994487	+	0.104862i	$0.0334400\pi$
$431$			3.48593e8i			0.209724i	−0.994487	+	0.104862i	$0.966560\pi$
$432$			6.77211e8i			0.404139i
$433$	4.06627e8			0.240707			0.120353	−	0.992731i	$-0.461597\pi$
$433$	4.06627e8			0.240707			0.120353	+	0.992731i	$0.461597\pi$
$434$	−3.16837e8			−0.186047
$435$		−	1.79931e8i		−	0.104808i
$436$		−	1.86306e7i		−	0.0107652i
$437$		−	9.97787e8i		−	0.571943i
$438$	5.56253e8			0.316310
$439$			1.42570e9i			0.804270i	0.915580	+	0.402135i	$0.131732\pi$
$439$			1.42570e9i			0.804270i	−0.915580	+	0.402135i	$0.868268\pi$
$440$	1.52570e9			0.853855
$441$	−2.03872e9			−1.13194
$442$	−1.21258e8	+	1.47054e8i	−0.0667934	+	0.0810025i
$443$	2.27492e9			1.24323			0.621616	−	0.783322i	$-0.286476\pi$
$443$	2.27492e9			1.24323			0.621616	+	0.783322i	$0.286476\pi$
$444$	290968.			0.000157763
$445$		−	9.64443e8i		−	0.518820i
$446$	8.63136e8			0.460688
$447$		−	2.83379e8i		−	0.150069i
$448$			2.83351e9i			1.48885i
$449$		−	2.35939e9i		−	1.23009i	−0.788491	−	0.615047i	$-0.789137\pi$
$449$		−	2.35939e9i		−	1.23009i	0.788491	−	0.615047i	$-0.210863\pi$
$450$	−1.06553e9			−0.551214
$451$	−2.28854e9			−1.17474
$452$			1.48109e6i			0.000754391i
$453$		−	6.03048e8i		−	0.304795i
$454$			7.48812e8i			0.375558i
$455$	2.03169e8			0.101116
$456$			1.31052e8i			0.0647240i
$457$	−2.50521e9			−1.22783			−0.613913	−	0.789374i	$-0.710405\pi$
$457$	−2.50521e9			−1.22783			−0.613913	+	0.789374i	$0.710405\pi$
$458$	−1.73691e9			−0.844789
$459$	−6.51083e8	−	5.36873e8i	−0.314262	−	0.259136i
$460$	−1.94121e7			−0.00929864
$461$	−4.50046e8			−0.213946			−0.106973	−	0.994262i	$-0.534116\pi$
$461$	−4.50046e8			−0.213946			−0.106973	+	0.994262i	$0.534116\pi$
$462$		−	8.50768e8i		−	0.401388i
$463$	−2.73938e8			−0.128268			−0.0641340	−	0.997941i	$-0.520429\pi$
$463$	−2.73938e8			−0.128268			−0.0641340	+	0.997941i	$0.520429\pi$
$464$		−	1.65555e9i		−	0.769362i
$465$			3.70430e7i			0.0170852i
$466$		−	1.16312e9i		−	0.532445i
$467$	−7.85850e8			−0.357051			−0.178526	−	0.983935i	$-0.557133\pi$
$467$	−7.85850e8			−0.357051			−0.178526	+	0.983935i	$0.557133\pi$
$468$	−1.73407e6			−0.000781999
$469$		−	5.27632e9i		−	2.36171i
$470$			1.02716e9i			0.456349i
$471$			6.33588e8i			0.279405i
$472$	3.75118e9			1.64199
$473$		−	3.26238e9i		−	1.41749i
$474$	−8.90518e7			−0.0384077
$475$	−4.18463e8			−0.179155
$476$	−2.08035e7	−	1.71542e7i	−0.00884121	−	0.00729033i
$477$	5.29811e8			0.223515
$478$	−1.12938e8			−0.0472981
$479$			2.05967e9i			0.856295i	0.903709	+	0.428147i	$0.140834\pi$
$479$			2.05967e9i			0.856295i	−0.903709	+	0.428147i	$0.859166\pi$
$480$	5.07963e6			0.00209646
$481$		−	2.51371e7i		−	0.0102993i
$482$			2.91481e9i			1.18562i
$483$			1.40656e9i			0.567995i
$484$	1.38551e7			0.00555456
$485$	−2.56980e9			−1.02283
$486$			1.48429e9i			0.586534i
$487$			1.41049e8i			0.0553373i	0.999617	+	0.0276686i	$0.00880832\pi$
$487$			1.41049e8i			0.0553373i	−0.999617	+	0.0276686i	$0.991192\pi$
$488$			1.46196e9i			0.569463i
$489$	−2.56748e8			−0.0992945
$490$		−	1.99293e9i		−	0.765255i
$491$	−2.96070e9			−1.12878			−0.564390	−	0.825508i	$-0.690889\pi$
$491$	−2.96070e9			−1.12878			−0.564390	+	0.825508i	$0.690889\pi$
$492$	−3.82442e6			−0.00144773
$493$	1.59168e9	+	1.31247e9i	0.598262	+	0.493318i
$494$	8.71300e7			0.0325180
$495$	2.19582e9			0.813728
$496$			3.40834e8i			0.125417i
$497$	5.30245e9			1.93744
$498$		−	3.92866e8i		−	0.142542i
$499$		−	2.78980e9i		−	1.00513i	−0.864541	−	0.502563i	$-0.832390\pi$
$499$		−	2.78980e9i		−	1.00513i	0.864541	−	0.502563i	$-0.167610\pi$
$500$			2.22160e7i			0.00794823i
$501$	−7.54465e8			−0.268045
$502$	−5.88425e8			−0.207600
$503$			4.97120e9i			1.74170i	0.491548	+	0.870851i	$0.336431\pi$
$503$			4.97120e9i			1.74170i	−0.491548	+	0.870851i	$0.663569\pi$
$504$			4.07830e9i			1.41897i
$505$			2.24832e9i			0.776852i
$506$	7.02256e9			2.40973
$507$			6.04086e8i			0.205859i
$508$	2.29117e7			0.00775414
$509$	−4.95725e9			−1.66620			−0.833102	−	0.553119i	$-0.813437\pi$
$509$	−4.95725e9			−1.66620			−0.833102	+	0.553119i	$0.813437\pi$
$510$	2.56596e8	−	3.11182e8i	0.0856553	−	0.103877i
$511$	6.79833e9			2.25387
$512$	3.07157e9			1.01138
$513$			3.85769e8i			0.126159i
$514$	−4.43515e9			−1.44058
$515$		−	2.21256e9i		−	0.713789i
$516$		−	5.45183e6i		−	0.00174690i
$517$			2.90439e9i			0.924354i
$518$	−4.54970e8			−0.143823
$519$	−7.86191e8			−0.246855
$520$		−	2.20265e8i		−	0.0686965i
$521$		−	1.64511e9i		−	0.509639i	−0.966989	−	0.254820i	$-0.917984\pi$
$521$		−	1.64511e9i		−	0.509639i	0.966989	−	0.254820i	$-0.0820161\pi$
$522$		−	2.40134e9i		−	0.738937i
$523$	2.45495e9			0.750389			0.375194	−	0.926946i	$-0.377576\pi$
$523$	2.45495e9			0.750389			0.375194	+	0.926946i	$0.377576\pi$
$524$		−	2.78102e7i		−	0.00844394i
$525$	5.89901e8			0.177919
$526$	−5.07574e9			−1.52072
$527$	−3.27684e8	−	2.70203e8i	−0.0975254	−	0.0804179i
$528$	−9.15205e8			−0.270582
$529$	−8.20548e9			−2.40996
$530$			5.17913e8i			0.151109i
$531$	5.39880e9			1.56483
$532$			1.23262e7i			0.00354925i
$533$			3.30397e8i			0.0945128i
$534$			5.83053e8i			0.165697i
$535$	−2.26084e8			−0.0638310
$536$	−5.72031e9			−1.60451
$537$		−	3.89485e8i		−	0.108538i
$538$		−	5.82072e9i		−	1.61153i
$539$		−	5.63518e9i		−	1.55006i
$540$	7.50519e6			0.00205108
$541$			1.68819e9i			0.458384i	0.973381	+	0.229192i	$0.0736084\pi$
$541$			1.68819e9i			0.458384i	−0.973381	+	0.229192i	$0.926392\pi$
$542$	1.44973e9			0.391101
$543$	−6.62875e7			−0.0177677
$544$	−3.70523e7	+	4.49345e7i	−0.00986777	+	0.0119670i
$545$	3.40592e9			0.901253
$546$	−1.22826e8			−0.0322935
$547$		−	9.53791e8i		−	0.249171i	−0.992209	−	0.124586i	$-0.960240\pi$
$547$		−	9.53791e8i		−	0.249171i	0.992209	−	0.124586i	$-0.0397601\pi$
$548$	−9.18444e6			−0.00238408
$549$			2.10409e9i			0.542701i
$550$		−	2.94520e9i		−	0.754824i
$551$		−	9.43077e8i		−	0.240169i
$552$	1.52492e9			0.385888
$553$	−1.08836e9			−0.273675
$554$		−	5.82705e9i		−	1.45601i
$555$			5.31929e7i			0.0132077i
$556$		−	2.54008e7i		−	0.00626738i
$557$	−2.97677e9			−0.729880			−0.364940	−	0.931031i	$-0.618911\pi$
$557$	−2.97677e9			−0.729880			−0.364940	+	0.931031i	$0.618911\pi$
$558$			4.94371e8i			0.120457i
$559$	−4.70991e8			−0.114044
$560$	−3.95579e9			−0.951864
$561$	7.25547e8	−	8.79894e8i	0.173498	−	0.210407i
$562$	−3.35404e9			−0.797061
$563$	−2.79052e9			−0.659030			−0.329515	−	0.944150i	$-0.606885\pi$
$563$	−2.79052e9			−0.659030			−0.329515	+	0.944150i	$0.606885\pi$
$564$			4.85359e6i			0.00113916i
$565$	−2.70763e8			−0.0631568
$566$			7.17685e9i			1.66370i
$567$			5.59166e9i			1.28825i
$568$		−	5.74864e9i		−	1.31627i
$569$	1.84290e8			0.0419381			0.0209690	−	0.999780i	$-0.493325\pi$
$569$	1.84290e8			0.0419381			0.0209690	+	0.999780i	$0.493325\pi$
$570$	−1.84377e8			−0.0417008
$571$			4.32214e9i			0.971566i	0.874080	+	0.485783i	$0.161465\pi$
$571$			4.32214e9i			0.971566i	−0.874080	+	0.485783i	$0.838535\pi$
$572$		−	4.79311e6i		−	0.00107086i
$573$		−	1.03196e8i		−	0.0229152i
$574$	5.98004e9			1.31981
$575$			4.86926e9i			1.06813i
$576$	4.42121e9			0.963968
$577$	5.07158e9			1.09908			0.549538	−	0.835469i	$-0.314804\pi$
$577$	5.07158e9			1.09908			0.549538	+	0.835469i	$0.314804\pi$
$578$	8.81038e8	+	4.53971e9i	0.189779	+	0.977869i
$579$	1.02643e9			0.219762
$580$	−1.83477e7			−0.00390466
$581$		−	4.80147e9i		−	1.01568i
$582$	1.55357e9			0.326664
$583$			1.46444e9i			0.306078i
$584$		−	7.37040e9i		−	1.53125i
$585$		−	3.17012e8i		−	0.0654681i
$586$	−1.66112e9			−0.341003
$587$	−1.06866e9			−0.218075			−0.109038	−	0.994038i	$-0.534777\pi$
$587$	−1.06866e9			−0.218075			−0.109038	+	0.994038i	$0.534777\pi$
$588$		−	9.41707e6i		−	0.00191027i
$589$			1.94154e8i			0.0391510i
$590$			5.27755e9i			1.05791i
$591$	−7.15514e8			−0.142581
$592$			4.89429e8i			0.0969536i
$593$	2.06599e9			0.406853			0.203426	−	0.979090i	$-0.434792\pi$
$593$	2.06599e9			0.406853			0.203426	+	0.979090i	$0.434792\pi$
$594$	−2.71510e9			−0.531536
$595$	3.13603e9	−	3.80316e9i	0.610338	−	0.740177i
$596$	−2.88963e7			−0.00559087
$597$	−4.49721e8			−0.0865034
$598$		−	1.01385e9i		−	0.193874i
$599$	3.49423e9			0.664289			0.332145	−	0.943228i	$-0.392228\pi$
$599$	3.49423e9			0.664289			0.332145	+	0.943228i	$0.392228\pi$
$600$		−	6.39540e8i		−	0.120875i
$601$			1.88346e8i			0.0353912i	0.999843	+	0.0176956i	$0.00563298\pi$
$601$			1.88346e8i			0.0353912i	−0.999843	+	0.0176956i	$0.994367\pi$
$602$			8.52473e9i			1.59255i
$603$	−8.23282e9			−1.52911
$604$	−6.14930e7			−0.0113552
$605$			2.53290e9i			0.465022i
$606$		−	1.35922e9i		−	0.248105i
$607$			1.55905e9i			0.282943i	0.989942	+	0.141472i	$0.0451834\pi$
$607$			1.55905e9i			0.282943i	−0.989942	+	0.141472i	$0.954817\pi$
$608$	2.66239e7			0.00480407
$609$			1.32944e9i			0.238511i
$610$	−2.05683e9			−0.366898
$611$	4.19308e8			0.0743685
$612$	−2.67663e7	+	3.24604e7i	−0.00472018	+	0.00572431i
$613$	6.51258e9			1.14193			0.570967	−	0.820973i	$-0.306568\pi$
$613$	6.51258e9			1.14193			0.570967	+	0.820973i	$0.306568\pi$
$614$	1.05043e10			1.83138
$615$		−	6.99157e8i		−	0.121203i
$616$	−1.12728e10			−1.94311
$617$		−	9.31298e9i		−	1.59621i	−0.602516	−	0.798106i	$-0.705835\pi$
$617$		−	9.31298e9i		−	1.59621i	0.602516	−	0.798106i	$-0.294165\pi$
$618$			1.33760e9i			0.227964i
$619$		−	3.90386e9i		−	0.661572i	−0.943706	−	0.330786i	$-0.892686\pi$
$619$		−	3.90386e9i		−	0.661572i	0.943706	−	0.330786i	$-0.107314\pi$
$620$	3.77729e6			0.000636516
$621$	4.48883e9			0.752165
$622$			7.58978e9i			1.26463i
$623$			7.12588e9i			1.18067i
$624$			1.32128e8i			0.0217696i
$625$	−5.30926e8			−0.0869869
$626$		−	1.03990e10i		−	1.69426i
$627$	−5.21341e8			−0.0844667
$628$	6.46072e7			0.0104093
$629$	−4.70546e8	−	3.88005e8i	−0.0753919	−	0.0621670i
$630$	−5.73777e9			−0.914221
$631$	−5.56074e9			−0.881109			−0.440554	−	0.897726i	$-0.645218\pi$
$631$	−5.56074e9			−0.881109			−0.440554	+	0.897726i	$0.645218\pi$
$632$			1.17994e9i			0.185931i
$633$	−1.58504e9			−0.248387
$634$		−	1.41169e9i		−	0.220003i
$635$			4.18857e9i			0.649169i
$636$			2.44726e6i			0.000377207i
$637$	−8.13553e8			−0.124709
$638$	6.63750e9			1.01189
$639$		−	8.27359e9i		−	1.25441i
$640$			4.25513e9i			0.641628i
$641$			4.88359e9i			0.732379i	0.930540	+	0.366189i	$0.119338\pi$
$641$			4.88359e9i			0.732379i	−0.930540	+	0.366189i	$0.880662\pi$
$642$	1.36679e8			0.0203859
$643$		−	7.57678e9i		−	1.12395i	−0.827155	−	0.561974i	$-0.810042\pi$
$643$		−	7.57678e9i		−	1.12395i	0.827155	−	0.561974i	$-0.189958\pi$
$644$	1.43428e8			0.0211608
$645$	9.96669e8			0.146249
$646$	1.34490e9	−	1.63100e9i	0.196280	−	0.238035i
$647$	−2.00383e8			−0.0290868			−0.0145434	−	0.999894i	$-0.504629\pi$
$647$	−2.00383e8			−0.0290868			−0.0145434	+	0.999894i	$0.504629\pi$
$648$	6.06219e9			0.875219
$649$			1.49227e10i			2.14285i
$650$	−4.25200e8			−0.0607290
$651$		−	2.73696e8i		−	0.0388808i
$652$			2.61806e7i			0.00369925i
$653$		−	3.52835e8i		−	0.0495879i	−0.999693	−	0.0247940i	$-0.992107\pi$
$653$		−	3.52835e8i		−	0.0495879i	0.999693	−	0.0247940i	$-0.00789297\pi$
$654$	−2.05905e9			−0.287835
$655$	5.08409e9			0.706918
$656$		−	6.43296e9i		−	0.889708i
$657$		−	1.06077e10i		−	1.45929i
$658$		−	7.58929e9i		−	1.03851i
$659$	−1.26579e10			−1.72290			−0.861452	−	0.507839i	$-0.830444\pi$
$659$	−1.26579e10			−1.72290			−0.861452	+	0.507839i	$0.830444\pi$
$660$			1.01428e7i			0.00137326i
$661$	2.37300e9			0.319589			0.159794	−	0.987150i	$-0.448917\pi$
$661$	2.37300e9			0.319589			0.159794	+	0.987150i	$0.448917\pi$
$662$	1.21845e9			0.163232
$663$	−1.27031e8	−	1.04747e8i	−0.0169282	−	0.0139587i
$664$	−5.20550e9			−0.690040
$665$	−2.25339e9			−0.297140
$666$			7.09905e8i			0.0931194i
$667$	−1.09737e10			−1.43190
$668$			7.69331e7i			0.00998609i
$669$			7.45610e8i			0.0962764i
$670$		−	8.04792e9i		−	1.03377i
$671$	−5.81587e9			−0.743166
$672$	−3.75313e7			−0.00477091
$673$			5.89136e9i			0.745011i	0.928030	+	0.372506i	$0.121501\pi$
$673$			5.89136e9i			0.745011i	−0.928030	+	0.372506i	$0.878499\pi$
$674$			8.82454e9i			1.11015i
$675$		−	1.88258e9i		−	0.235608i
$676$	6.15988e7			0.00766936
$677$			3.71173e9i			0.459744i	0.973221	+	0.229872i	$0.0738307\pi$
$677$			3.71173e9i			0.459744i	−0.973221	+	0.229872i	$0.926169\pi$
$678$	1.63690e8			0.0201705
$679$	1.89872e10			2.32765
$680$	−4.12319e9	−	3.39992e9i	−0.502866	−	0.414655i
$681$	−6.46853e8			−0.0784857
$682$	−1.36648e9			−0.164952
$683$		−	1.14125e10i		−	1.37060i	−0.728263	−	0.685298i	$-0.759672\pi$
$683$		−	1.14125e10i		−	1.37060i	0.728263	−	0.685298i	$-0.240328\pi$
$684$	1.92329e7			0.00229799
$685$		−	1.67904e9i		−	0.199593i
$686$			2.28005e9i			0.269656i
$687$		−	1.50041e9i		−	0.176547i
$688$	9.17038e9			1.07356
$689$	2.11422e8			0.0246254
$690$			2.14542e9i			0.248622i
$691$		−	5.70644e9i		−	0.657948i	−0.944339	−	0.328974i	$-0.893297\pi$
$691$		−	5.70644e9i		−	0.657948i	0.944339	−	0.328974i	$-0.106703\pi$
$692$			8.01682e7i			0.00919668i
$693$	−1.62240e10			−1.85179
$694$			1.55385e10i			1.76462i
$695$	4.64362e9			0.524698
$696$	1.44131e9			0.162041
$697$	6.18476e9	+	5.09986e9i	0.691844	+	0.570484i
$698$	−1.44395e10			−1.60715
$699$	1.00475e9			0.111272
$700$		−	6.01524e7i		−	0.00662842i
$701$	1.20522e10			1.32146			0.660730	−	0.750624i	$-0.270247\pi$
$701$	1.20522e10			1.32146			0.660730	+	0.750624i	$0.270247\pi$
$702$			3.91980e8i			0.0427645i
$703$			2.78800e8i			0.0302656i
$704$			1.22206e10i			1.32004i
$705$	−8.87303e8			−0.0953696
$706$	1.01926e10			1.09011
$707$		−	1.66119e10i		−	1.76788i
$708$			2.49377e7i			0.00264082i
$709$			3.97961e9i			0.419352i	0.977771	+	0.209676i	$0.0672410\pi$
$709$			3.97961e9i			0.419352i	−0.977771	+	0.209676i	$0.932759\pi$
$710$	8.08778e9			0.848057
$711$			1.69821e9i			0.177193i
$712$	7.72550e9			0.802134
$713$	2.25919e9			0.233421
$714$	−1.89588e9	+	2.29920e9i	−0.194925	+	0.236392i
$715$	8.76246e8			0.0896510
$716$	−3.97159e7			−0.00404361
$717$		−	9.75605e7i		−	0.00988455i
$718$	−4.70182e9			−0.474057
$719$			1.26059e10i			1.26480i	0.774642	+	0.632400i	$0.217930\pi$
$719$			1.26059e10i			1.26480i	−0.774642	+	0.632400i	$0.782070\pi$
$720$			6.17234e9i			0.616292i
$721$			1.63477e10i			1.62436i
$722$	9.10734e9			0.900557
$723$	−2.51792e9			−0.247775
$724$			6.75936e6i			0.000661943i
$725$			4.60228e9i			0.448528i
$726$		−	1.53126e9i		−	0.148515i
$727$	−1.31885e10			−1.27299			−0.636494	−	0.771282i	$-0.719616\pi$
$727$	−1.31885e10			−1.27299			−0.636494	+	0.771282i	$0.719616\pi$
$728$			1.62745e9i			0.156332i
$729$	7.83789e9			0.749295
$730$	1.03694e10			0.986563
$731$	−7.27000e9	+	8.81657e9i	−0.688373	+	0.834812i
$732$	−9.71903e6			−0.000915870
$733$	−5.16161e9			−0.484085			−0.242042	−	0.970266i	$-0.577817\pi$
$733$	−5.16161e9			−0.484085			−0.242042	+	0.970266i	$0.577817\pi$
$734$		−	5.99861e9i		−	0.559905i
$735$	1.72157e9			0.159926
$736$		−	3.09797e8i		−	0.0286421i
$737$		−	2.27562e10i		−	2.09394i
$738$		−	9.33085e9i		−	0.854523i
$739$	1.10100e10			1.00353			0.501766	−	0.865004i	$-0.332684\pi$
$739$	1.10100e10			1.00353			0.501766	+	0.865004i	$0.332684\pi$
$740$	5.42410e6			0.000492058
$741$			7.52662e7i			0.00679573i
$742$		−	3.82665e9i		−	0.343878i
$743$		−	1.21999e10i		−	1.09118i	−0.838053	−	0.545588i	$-0.816306\pi$
$743$		−	1.21999e10i		−	1.09118i	0.838053	−	0.545588i	$-0.183694\pi$
$744$	−2.96727e8			−0.0264150
$745$		−	5.28263e9i		−	0.468062i
$746$	−1.42473e10			−1.25645
$747$	−7.49190e9			−0.657612
$748$	−8.97231e7	−	7.39843e7i	−0.00783878	−	0.00646374i
$749$	1.67044e9			0.145260
$750$	2.45531e9			0.212516
$751$			3.48173e9i			0.299954i	0.988689	+	0.149977i	$0.0479200\pi$
$751$			3.48173e9i			0.299954i	−0.988689	+	0.149977i	$0.952080\pi$
$752$	−8.16409e9			−0.700077
$753$		−	5.08304e8i		−	0.0433851i
$754$		−	9.58259e8i		−	0.0814110i
$755$		−	1.12418e10i		−	0.950649i
$756$	−5.54528e7			−0.00466764
$757$	4.98292e9			0.417492			0.208746	−	0.977970i	$-0.433062\pi$
$757$	4.98292e9			0.417492			0.208746	+	0.977970i	$0.433062\pi$
$758$			1.27710e10i			1.06508i
$759$			6.06635e9i			0.503595i
$760$			2.44301e9i			0.201873i
$761$	−1.21391e10			−0.998481			−0.499241	−	0.866463i	$-0.666388\pi$
$761$	−1.21391e10			−0.998481			−0.499241	+	0.866463i	$0.666388\pi$
$762$		−	2.53219e9i		−	0.207326i
$763$	−2.51650e10			−2.05097
$764$	−1.05230e7			−0.000853713
$765$	−5.93420e9	−	4.89325e9i	−0.479234	−	0.395169i
$766$	−2.08302e10			−1.67453
$767$	2.15440e9			0.172402
$768$			6.07984e7i			0.00484315i
$769$	−3.52402e9			−0.279445			−0.139723	−	0.990191i	$-0.544621\pi$
$769$	−3.52402e9			−0.279445			−0.139723	+	0.990191i	$0.544621\pi$
$770$		−	1.58597e10i		−	1.25192i
$771$		−	3.83125e9i		−	0.301058i
$772$		−	1.04665e8i		−	0.00818732i
$773$	1.50830e10			1.17452			0.587258	−	0.809400i	$-0.300207\pi$
$773$	1.50830e10			1.17452			0.587258	+	0.809400i	$0.300207\pi$
$774$	1.33014e10			1.03111
$775$		−	9.47484e8i		−	0.0731166i
$776$		−	2.05850e10i		−	1.58137i
$777$		−	3.93020e8i		−	0.0300567i
$778$	2.19990e9			0.167485
$779$		−	3.66450e9i		−	0.277737i
$780$	1.46431e6			0.000110485
$781$	2.28689e10			1.71778
$782$	−1.89784e10	−	1.56493e10i	−1.41918	−	1.17023i
$783$	4.24271e9			0.315847
$784$	1.58402e10			1.17396
$785$			1.18111e10i			0.871457i
$786$	−3.07358e9			−0.225770
$787$			1.44317e10i			1.05538i	0.849438	+	0.527688i	$0.176941\pi$
$787$			1.44317e10i			1.05538i	−0.849438	+	0.527688i	$0.823059\pi$
$788$			7.29612e7i			0.00531191i
$789$		−	4.38462e9i		−	0.317806i
$790$	−1.66007e9			−0.119793
$791$	2.00056e9			0.143726
$792$			1.75892e10i			1.25808i
$793$			8.39640e8i			0.0597911i
$794$			1.65027e10i			1.16999i
$795$	−4.47393e8			−0.0315794
$796$			4.58582e7i			0.00322271i
$797$	−2.21165e10			−1.54744			−0.773718	−	0.633530i	$-0.781605\pi$
$797$	−2.21165e10			−1.54744			−0.773718	+	0.633530i	$0.781605\pi$
$798$	1.36229e9			0.0948982
$799$	6.47225e9	−	7.84910e9i	0.448892	−	0.544385i
$800$	−1.29926e8			−0.00897186
$801$	1.11187e10			0.764437
$802$		−	4.31045e9i		−	0.295061i
$803$	2.93205e10			1.99833
$804$		−	3.80283e7i		−	0.00258054i
$805$			2.62206e10i			1.77156i
$806$			1.97280e8i			0.0132712i
$807$	5.02816e9			0.336784
$808$	−1.80098e10			−1.20107
$809$			2.52729e10i			1.67817i	0.544000	+	0.839085i	$0.316909\pi$
$809$			2.52729e10i			1.67817i	−0.544000	+	0.839085i	$0.683091\pi$
$810$			8.52891e9i			0.563892i
$811$			3.18823e9i			0.209882i	0.994478	+	0.104941i	$0.0334655\pi$
$811$			3.18823e9i			0.209882i	−0.994478	+	0.104941i	$0.966535\pi$
$812$	1.35564e8			0.00888580
$813$			1.25233e9i			0.0817339i
$814$	−1.96224e9			−0.127516
$815$	−4.78618e9			−0.309697
$816$	2.47334e9	+	2.03948e9i	0.159356	+	0.131402i
$817$	5.22385e9			0.335130
$818$	−1.12039e9			−0.0715701
$819$			2.34227e9i			0.148985i
$820$	−7.12933e7			−0.00451544
$821$		−	1.12444e10i		−	0.709147i	−0.935028	−	0.354574i	$-0.884626\pi$
$821$		−	1.12444e10i		−	0.709147i	0.935028	−	0.354574i	$-0.115374\pi$
$822$			1.01506e9i			0.0637443i
$823$			4.92004e8i			0.0307659i	0.999882	+	0.0153829i	$0.00489674\pi$
$823$			4.92004e8i			0.0307659i	−0.999882	+	0.0153829i	$0.995103\pi$
$824$	1.77233e10			1.10357
$825$	2.54418e9			0.157746
$826$		−	3.89937e10i		−	2.40749i
$827$			1.50602e10i			0.925896i	0.886385	+	0.462948i	$0.153208\pi$
$827$			1.50602e10i			0.925896i	−0.886385	+	0.462948i	$0.846792\pi$
$828$		−	2.23795e8i		−	0.0137008i
$829$	2.03521e10			1.24070			0.620351	−	0.784324i	$-0.286990\pi$
$829$	2.03521e10			1.24070			0.620351	+	0.784324i	$0.286990\pi$
$830$		−	7.32364e9i		−	0.444584i
$831$	5.03363e9			0.304283
$832$	1.76429e9			0.106203
$833$	−1.25576e10	+	1.52291e10i	−0.752750	+	0.912884i
$834$	−2.80729e9			−0.167574
$835$	−1.40644e10			−0.836025
$836$			5.31613e7i			0.00314684i
$837$	−8.73458e8			−0.0514877
$838$			5.41700e7i			0.00317984i
$839$			9.34797e9i			0.546450i	0.961950	+	0.273225i	$0.0880904\pi$
$839$			9.34797e9i			0.546450i	−0.961950	+	0.273225i	$0.911910\pi$
$840$		−	3.44387e9i		−	0.200479i
$841$	6.87788e9			0.398721
$842$	−1.62116e9			−0.0935908
$843$		−	2.89735e9i		−	0.166573i
$844$			1.61628e8i			0.00925373i
$845$			1.12611e10i			0.642071i
$846$	−1.18418e10			−0.672391
$847$		−	1.87145e10i		−	1.05825i
$848$	−4.11647e9			−0.231814
$849$	−6.19963e9			−0.347687
$850$	−6.56320e9	+	7.95940e9i	−0.366563	+	0.444543i
$851$	3.24414e9			0.180445
$852$	3.82167e7			0.00211697
$853$		−	3.01288e10i		−	1.66211i	−0.556189	−	0.831056i	$-0.687737\pi$
$853$		−	3.01288e10i		−	1.66211i	0.556189	−	0.831056i	$-0.312263\pi$
$854$	1.51971e10			0.834946
$855$			3.51604e9i			0.192386i
$856$		−	1.81101e9i		−	0.0986875i
$857$		−	9.63658e9i		−	0.522986i	−0.965205	−	0.261493i	$-0.915785\pi$
$857$		−	9.63658e9i		−	0.522986i	0.965205	−	0.261493i	$-0.0842149\pi$
$858$	−5.29734e8			−0.0286320
$859$	−1.94466e10			−1.04681			−0.523404	−	0.852085i	$-0.675338\pi$
$859$	−1.94466e10			−1.04681			−0.523404	+	0.852085i	$0.675338\pi$
$860$		−	1.01631e8i		−	0.00544854i
$861$			5.16578e9i			0.275820i
$862$		−	3.92855e9i		−	0.208909i
$863$	4.07602e9			0.215873			0.107936	−	0.994158i	$-0.465576\pi$
$863$	4.07602e9			0.215873			0.107936	+	0.994158i	$0.465576\pi$
$864$			1.19775e8i			0.00631785i
$865$	−1.46559e10			−0.769936
$866$	−4.58258e9			−0.239771
$867$	−3.92158e9	+	7.61074e8i	−0.204359	+	0.0396607i
$868$	−2.79089e7			−0.00144852
$869$	−4.69398e9			−0.242645
$870$			2.02778e9i			0.104401i
$871$	−3.28532e9			−0.168467
$872$			2.72825e10i			1.39340i
$873$		−	2.96264e10i		−	1.50705i
$874$			1.12448e10i			0.569721i
$875$	3.00079e10			1.51429
$876$	4.89980e7			0.00246271
$877$		−	1.49339e10i		−	0.747612i	−0.927507	−	0.373806i	$-0.878053\pi$
$877$		−	1.49339e10i		−	0.747612i	0.927507	−	0.373806i	$-0.121947\pi$
$878$		−	1.60673e10i		−	0.801145i
$879$		−	1.43494e9i		−	0.0712642i
$880$	−1.70609e10			−0.843940
$881$			1.55484e10i			0.766073i	0.923733	+	0.383036i	$0.125122\pi$
$881$			1.55484e10i			0.766073i	−0.923733	+	0.383036i	$0.874878\pi$
$882$	2.29758e10			1.12754
$883$	3.92273e9			0.191746			0.0958730	−	0.995394i	$-0.469436\pi$
$883$	3.92273e9			0.191746			0.0958730	+	0.995394i	$0.469436\pi$
$884$	−1.06811e7	+	1.29534e7i	−0.000520038	+	0.000630666i
$885$	−4.55895e9			−0.221087
$886$	−2.56377e10			−1.23840
$887$			8.20990e9i			0.395007i	0.980302	+	0.197504i	$0.0632834\pi$
$887$			8.20990e9i			0.395007i	−0.980302	+	0.197504i	$0.936717\pi$
$888$	−4.26092e8			−0.0204201
$889$		−	3.09476e10i		−	1.47731i
$890$			1.08690e10i			0.516804i
$891$			2.41162e10i			1.14219i
$892$	7.60301e7			0.00358681
$893$	−4.65063e9			−0.218540
$894$			3.19361e9i			0.149486i
$895$		−	7.26061e9i		−	0.338526i
$896$		−	3.14394e10i		−	1.46015i
$897$	8.75802e8			0.0405165
$898$			2.65898e10i			1.22531i
$899$	2.13531e9			0.0980173
$900$	−9.38578e7			−0.00429162
$901$	3.26342e9	−	3.95765e9i	0.148640	−	0.180260i
$902$	2.57912e10			1.17017
$903$	−7.36398e9			−0.332817
$904$		−	2.16890e9i		−	0.0976451i
$905$	−1.23570e9			−0.0554172
$906$			6.79620e9i			0.303611i
$907$		−	2.87835e9i		−	0.128091i	−0.997947	−	0.0640455i	$-0.979600\pi$
$907$		−	2.87835e9i		−	0.128091i	0.997947	−	0.0640455i	$-0.0204003\pi$
$908$			6.59598e7i			0.00292401i
$909$	−2.59201e10			−1.14463
$910$	−2.28967e9			−0.100723
$911$			8.67655e9i			0.380218i	0.981763	+	0.190109i	$0.0608842\pi$
$911$			8.67655e9i			0.380218i	−0.981763	+	0.190109i	$0.939116\pi$
$912$		−	1.46546e9i		−	0.0639725i
$913$		−	2.07082e10i		−	0.900523i
$914$	2.82330e10			1.22305
$915$		−	1.77677e9i		−	0.0766757i
$916$	−1.52997e8			−0.00657733
$917$	−3.75643e10			−1.60873
$918$	7.33754e9	+	6.05042e9i	0.313041	+	0.258129i
$919$	−3.38295e10			−1.43778			−0.718889	−	0.695125i	$-0.755349\pi$
$919$	−3.38295e10			−1.43778			−0.718889	+	0.695125i	$0.755349\pi$
$920$	2.84270e10			1.20358
$921$			9.07401e9i			0.382728i
$922$	5.07191e9			0.213115
$923$		−	3.30159e9i		−	0.138203i
$924$		−	7.49407e7i		−	0.00312511i
$925$		−	1.36056e9i		−	0.0565227i
$926$	3.08721e9			0.127770
$927$	2.55079e10			1.05171
$928$		−	2.92811e8i		−	0.0120273i
$929$		−	2.87996e10i		−	1.17850i	−0.807950	−	0.589252i	$-0.799423\pi$
$929$		−	2.87996e10i		−	1.17850i	0.807950	−	0.589252i	$-0.200577\pi$
$930$		−	4.17466e8i		−	0.0170189i
$931$	9.02329e9			0.366472
$932$		−	1.02455e8i		−	0.00414549i
$933$	−6.55634e9			−0.264287
$934$	8.85633e9			0.355664
$935$	1.35253e10	−	1.64026e10i	0.541138	−	0.656255i
$936$	2.53937e9			0.101218
$937$	2.44266e9			0.0970005			0.0485002	−	0.998823i	$-0.484556\pi$
$937$	2.44266e9			0.0970005			0.0485002	+	0.998823i	$0.484556\pi$
$938$			5.94628e10i			2.35253i
$939$	8.98304e9			0.354074
$940$			9.04786e7i			0.00355303i
$941$			1.68559e10i			0.659459i	0.944075	+	0.329730i	$0.106958\pi$
$941$			1.68559e10i			0.659459i	−0.944075	+	0.329730i	$0.893042\pi$
$942$		−	7.14038e9i		−	0.278319i
$943$	−4.26403e10			−1.65588
$944$	−4.19470e10			−1.62293
$945$		−	1.01375e10i		−	0.390770i
$946$			3.67662e10i			1.41198i
$947$			3.11941e9i			0.119357i	0.998218	+	0.0596784i	$0.0190075\pi$
$947$			3.11941e9i			0.119357i	−0.998218	+	0.0596784i	$0.980992\pi$
$948$	−7.84421e6			−0.000299034
$949$		−	4.23300e9i		−	0.160774i
$950$	4.71598e9			0.178459
$951$	1.21948e9			0.0459771
$952$	3.04646e10	+	2.51206e10i	1.14437	+	0.943628i
$953$	3.09228e10			1.15732			0.578661	−	0.815568i	$-0.303576\pi$
$953$	3.09228e10			1.15732			0.578661	+	0.815568i	$0.303576\pi$
$954$	−5.97084e9			−0.222647
$955$		−	1.92374e9i		−	0.0714720i
$956$	−9.94828e6			−0.000368252
$957$			5.73373e9i			0.211468i
$958$		−	2.32120e10i		−	0.852968i
$959$			1.24058e10i			0.454211i
$960$	−3.73344e9			−0.136195
$961$	2.70730e10			0.984022
$962$			2.83289e8i			0.0102593i
$963$		−	2.60645e9i		−	0.0940496i
$964$			2.56753e8i			0.00923095i
$965$	1.91342e10			0.685434
$966$		−	1.58516e10i		−	0.565788i
$967$	2.19940e10			0.782187			0.391094	−	0.920351i	$-0.372097\pi$
$967$	2.19940e10			0.782187			0.391094	+	0.920351i	$0.372097\pi$
$968$	−2.02893e10			−0.718958
$969$	1.40892e9	+	1.16178e9i	0.0497455	+	0.0410194i
$970$	2.89610e10			1.01886
$971$	2.37732e10			0.833336			0.416668	−	0.909059i	$-0.363198\pi$
$971$	2.37732e10			0.833336			0.416668	+	0.909059i	$0.363198\pi$
$972$			1.30745e8i			0.00456662i
$973$	−3.43098e10			−1.19405
$974$		−	1.58958e9i		−	0.0551223i
$975$		−	3.67304e8i		−	0.0126914i
$976$		−	1.63481e10i		−	0.562851i
$977$	−3.19823e10			−1.09718			−0.548591	−	0.836091i	$-0.684836\pi$
$977$	−3.19823e10			−1.09718			−0.548591	+	0.836091i	$0.684836\pi$
$978$	2.89348e9			0.0989087
$979$			3.07331e10i			1.04681i
$980$		−	1.75549e8i		−	0.00595810i
$981$			3.92657e10i			1.32792i
$982$	3.33664e10			1.12439
$983$			3.41146e10i			1.14552i	0.819722	+	0.572761i	$0.194128\pi$
$983$			3.41146e10i			1.14552i	−0.819722	+	0.572761i	$0.805872\pi$
$984$	5.60047e9			0.187388
$985$	−1.33383e10			−0.444707
$986$	−1.79378e10	−	1.47913e10i	−0.595937	−	0.491401i
$987$	6.55592e9			0.217032
$988$	7.67492e6			0.000253177
$989$		−	6.07851e10i		−	1.99807i
$990$	−2.47464e10			−0.810566
$991$			5.48617e9i			0.179065i	0.995984	+	0.0895326i	$0.0285373\pi$
$991$			5.48617e9i			0.179065i	−0.995984	+	0.0895326i	$0.971463\pi$
$992$			6.02818e7i			0.00196063i
$993$			1.05254e9i			0.0341128i
$994$	−5.97573e10			−1.92992
$995$	−8.38351e9			−0.269802
$996$		−	3.46059e7i		−	0.00110980i
$997$			3.21399e10i			1.02710i	0.858061	+	0.513548i	$0.171669\pi$
$997$			3.21399e10i			1.02710i	−0.858061	+	0.513548i	$0.828331\pi$
$998$			3.14403e10i			1.00122i
$999$	−1.25426e9			−0.0398025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.8.b.a.16.3	✓	10
3.2	odd	2		153.8.d.b.118.8		10
4.3	odd	2		272.8.b.c.33.6		10
17.4	even	4		289.8.a.f.1.7		10
17.13	even	4		289.8.a.f.1.8		10
17.16	even	2	inner	17.8.b.a.16.4	yes	10
51.50	odd	2		153.8.d.b.118.7		10
68.67	odd	2		272.8.b.c.33.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.8.b.a.16.3	✓	10	1.1	even	1	trivial
17.8.b.a.16.4	yes	10	17.16	even	2	inner
153.8.d.b.118.7		10	51.50	odd	2
153.8.d.b.118.8		10	3.2	odd	2
272.8.b.c.33.5		10	68.67	odd	2
272.8.b.c.33.6		10	4.3	odd	2
289.8.a.f.1.7		10	17.4	even	4
289.8.a.f.1.8		10	17.13	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-11.2698 q^{2} -9.73524i q^{3} -0.992706 q^{4} -181.480i q^{5} +109.714i q^{6} +1340.88i q^{7} +1453.72 q^{8} +2092.23 q^{9} +O(q^{10})\)	\(q-11.2698 q^{2} -9.73524i q^{3} -0.992706 q^{4} -181.480i q^{5} +109.714i q^{6} +1340.88i q^{7} +1453.72 q^{8} +2092.23 q^{9} +2045.24i q^{10} +5783.08i q^{11} +9.66423i q^{12} +834.906 q^{13} -15111.4i q^{14} -1766.75 q^{15} -16255.9 q^{16} +(12887.2 - 15628.8i) q^{17} -23578.9 q^{18} -9260.11 q^{19} +180.157i q^{20} +13053.8 q^{21} -65173.9i q^{22} +107751. i q^{23} -14152.3i q^{24} +45189.9 q^{25} -9409.18 q^{26} -41659.3i q^{27} -1331.10i q^{28} +101843. i q^{29} +19910.9 q^{30} -20966.7i q^{31} -2875.12 q^{32} +56299.7 q^{33} +(-145236. + 176132. i) q^{34} +243344. q^{35} -2076.96 q^{36} -30107.7i q^{37} +104359. q^{38} -8128.01i q^{39} -263821. i q^{40} +395730. i q^{41} -147113. q^{42} -564125. q^{43} -5740.90i q^{44} -379698. i q^{45} -1.21433e6i q^{46} +502222. q^{47} +158256. i q^{48} -974426. q^{49} -509279. q^{50} +(-152150. - 125460. i) q^{51} -828.816 q^{52} +253229. q^{53} +469490. i q^{54} +1.04952e6 q^{55} +1.94926e6i q^{56} +90149.4i q^{57} -1.14775e6i q^{58} +2.58041e6 q^{59} +1753.87 q^{60} +1.00567e6i q^{61} +236290. i q^{62} +2.80543e6i q^{63} +2.11316e6 q^{64} -151519. i q^{65} -634483. q^{66} -3.93496e6 q^{67} +(-12793.2 + 15514.8i) q^{68} +1.04898e6 q^{69} -2.74243e6 q^{70} -3.95445e6i q^{71} +3.04150e6 q^{72} -5.07004e6i q^{73} +339306. i q^{74} -439935. i q^{75} +9192.56 q^{76} -7.75444e6 q^{77} +91600.6i q^{78} +811675. i q^{79} +2.95013e6i q^{80} +4.17013e6 q^{81} -4.45977e6i q^{82} -3.58083e6 q^{83} -12958.6 q^{84} +(-2.83631e6 - 2.33878e6i) q^{85} +6.35754e6 q^{86} +991466. q^{87} +8.40696e6i q^{88} +5.31432e6 q^{89} +4.27910e6i q^{90} +1.11951e6i q^{91} -106965. i q^{92} -204116. q^{93} -5.65992e6 q^{94} +1.68053e6i q^{95} +27990.0i q^{96} -1.41602e7i q^{97} +1.09815e7 q^{98} +1.20995e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 18 q^{2} + 690 q^{4} - 3330 q^{8} - 11794 q^{9}+O(q^{10}) \) 10 * q - 18 * q^2 + 690 * q^4 - 3330 * q^8 - 11794 * q^9	\( 10 q - 18 q^{2} + 690 q^{4} - 3330 q^{8} - 11794 q^{9} - 316 q^{13} + 13824 q^{15} + 92226 q^{16} - 29454 q^{17} + 94106 q^{18} - 90184 q^{19} - 137648 q^{21} + 78370 q^{25} - 180420 q^{26} + 781392 q^{30} - 1019778 q^{32} + 418160 q^{33} + 1123478 q^{34} - 460704 q^{35} - 1026218 q^{36} - 1583880 q^{38} + 1939504 q^{42} - 112936 q^{43} + 3214512 q^{47} - 230842 q^{49} - 359514 q^{50} - 102928 q^{51} + 4611732 q^{52} - 4396356 q^{53} + 2187488 q^{55} - 6096552 q^{59} - 12859152 q^{60} + 4541698 q^{64} + 4831808 q^{66} - 10368488 q^{67} - 712902 q^{68} + 7389760 q^{69} + 11368032 q^{70} + 15426330 q^{72} - 14210712 q^{76} + 7163520 q^{77} + 20826346 q^{81} + 7060104 q^{83} - 85725280 q^{84} + 8300608 q^{85} + 30033048 q^{86} + 855264 q^{87} + 24760956 q^{89} - 39868160 q^{93} - 54883072 q^{94} + 81770994 q^{98}+O(q^{100}) \) 10 * q - 18 * q^2 + 690 * q^4 - 3330 * q^8 - 11794 * q^9 - 316 * q^13 + 13824 * q^15 + 92226 * q^16 - 29454 * q^17 + 94106 * q^18 - 90184 * q^19 - 137648 * q^21 + 78370 * q^25 - 180420 * q^26 + 781392 * q^30 - 1019778 * q^32 + 418160 * q^33 + 1123478 * q^34 - 460704 * q^35 - 1026218 * q^36 - 1583880 * q^38 + 1939504 * q^42 - 112936 * q^43 + 3214512 * q^47 - 230842 * q^49 - 359514 * q^50 - 102928 * q^51 + 4611732 * q^52 - 4396356 * q^53 + 2187488 * q^55 - 6096552 * q^59 - 12859152 * q^60 + 4541698 * q^64 + 4831808 * q^66 - 10368488 * q^67 - 712902 * q^68 + 7389760 * q^69 + 11368032 * q^70 + 15426330 * q^72 - 14210712 * q^76 + 7163520 * q^77 + 20826346 * q^81 + 7060104 * q^83 - 85725280 * q^84 + 8300608 * q^85 + 30033048 * q^86 + 855264 * q^87 + 24760956 * q^89 - 39868160 * q^93 - 54883072 * q^94 + 81770994 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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