LMFDB - Embedded newform 208.7.t.c.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,7,Mod(161,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("208.161");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	208.t (of order $4$, degree $2$, not 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:	$47.8512493929$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} + 488 x^{9} + 36205 x^{8} - 155430 x^{7} + 399962 x^{6} + 9502784 x^{5} + \cdots + 56070144 $ x^12 - 6x^11 + 18x^10 + 488x^9 + 36205x^8 - 155430x^7 + 399962x^6 + 9502784x^5 + 275595012x^4 - 541321656x^3 + 523196552x^2 - 242221824*x + 56070144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 5^{2}\cdot 13^{2} $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			177.2
Root			$-6.57888 - 6.57888i$ of defining polynomial
Character	$\chi$	$=$	208.177
Dual form			208.7.t.c.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-26.7789 q^{3} +(-59.0322 - 59.0322i) q^{5} +(226.950 - 226.950i) q^{7} -11.8881 q^{9} +O(q^{10})$	\(q-26.7789 q^{3} +(-59.0322 - 59.0322i) q^{5} +(226.950 - 226.950i) q^{7} -11.8881 q^{9} +(-1078.96 + 1078.96i) q^{11} +(-2073.19 - 727.102i) q^{13} +(1580.82 + 1580.82i) q^{15} +1506.86i q^{17} +(-4280.27 - 4280.27i) q^{19} +(-6077.47 + 6077.47i) q^{21} -19283.9i q^{23} -8655.40i q^{25} +19840.2 q^{27} -34618.4 q^{29} +(-14488.1 - 14488.1i) q^{31} +(28893.4 - 28893.4i) q^{33} -26794.7 q^{35} +(17906.3 - 17906.3i) q^{37} +(55517.9 + 19471.0i) q^{39} +(72322.6 + 72322.6i) q^{41} +122834. i q^{43} +(701.778 + 701.778i) q^{45} +(-78678.8 + 78678.8i) q^{47} +14636.8i q^{49} -40352.0i q^{51} -31278.0 q^{53} +127387. q^{55} +(114621. + 114621. i) q^{57} +(26291.3 - 26291.3i) q^{59} -2955.68 q^{61} +(-2697.99 + 2697.99i) q^{63} +(79462.8 + 165308. i) q^{65} +(229598. + 229598. i) q^{67} +516403. i q^{69} +(58881.7 + 58881.7i) q^{71} +(497137. - 497137. i) q^{73} +231782. i q^{75} +489739. i q^{77} -48045.8 q^{79} -522633. q^{81} +(411022. + 411022. i) q^{83} +(88953.1 - 88953.1i) q^{85} +927044. q^{87} +(-244331. + 244331. i) q^{89} +(-635526. + 305495. i) q^{91} +(387977. + 387977. i) q^{93} +505348. i q^{95} +(417275. + 417275. i) q^{97} +(12826.7 - 12826.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 108 q^{5} - 398 q^{7} + 1940 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 108 * q^5 - 398 * q^7 + 1940 * q^9	$ 12 q + 4 q^{3} + 108 q^{5} - 398 q^{7} + 1940 q^{9} - 1686 q^{11} - 3926 q^{13} + 15268 q^{15} - 1766 q^{19} + 3428 q^{21} + 20464 q^{27} - 90108 q^{29} - 61014 q^{31} - 44452 q^{33} - 158772 q^{35} - 40212 q^{37} - 137852 q^{39} - 190416 q^{41} - 151444 q^{45} - 562446 q^{47} + 509136 q^{53} + 1264036 q^{55} + 939908 q^{57} + 994458 q^{59} + 1013696 q^{61} - 865778 q^{63} - 1130064 q^{65} + 1442386 q^{67} + 655866 q^{71} + 2588228 q^{73} + 75316 q^{79} - 4016140 q^{81} - 894966 q^{83} + 105396 q^{85} - 2109064 q^{87} - 977376 q^{89} - 1088750 q^{91} - 216268 q^{93} + 983388 q^{97} - 2894714 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 + 108 * q^5 - 398 * q^7 + 1940 * q^9 - 1686 * q^11 - 3926 * q^13 + 15268 * q^15 - 1766 * q^19 + 3428 * q^21 + 20464 * q^27 - 90108 * q^29 - 61014 * q^31 - 44452 * q^33 - 158772 * q^35 - 40212 * q^37 - 137852 * q^39 - 190416 * q^41 - 151444 * q^45 - 562446 * q^47 + 509136 * q^53 + 1264036 * q^55 + 939908 * q^57 + 994458 * q^59 + 1013696 * q^61 - 865778 * q^63 - 1130064 * q^65 + 1442386 * q^67 + 655866 * q^71 + 2588228 * q^73 + 75316 * q^79 - 4016140 * q^81 - 894966 * q^83 + 105396 * q^85 - 2109064 * q^87 - 977376 * q^89 - 1088750 * q^91 - 216268 * q^93 + 983388 * q^97 - 2894714 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−26.7789			−0.991813			−0.495906	−	0.868376i	$-0.665164\pi$
$3$	−26.7789			−0.991813			−0.495906	+	0.868376i	$0.665164\pi$
$4$		0			0
$5$	−59.0322	−	59.0322i	−0.472258	−	0.472258i	0.430387	−	0.902645i	$-0.358377\pi$
$5$	−59.0322	−	59.0322i	−0.472258	−	0.472258i	−0.902645	+	0.430387i	$0.858377\pi$
$6$		0			0
$7$	226.950	−	226.950i	0.661660	−	0.661660i	−0.294111	−	0.955771i	$-0.595024\pi$
$7$	226.950	−	226.950i	0.661660	−	0.661660i	0.955771	+	0.294111i	$0.0950235\pi$
$8$		0			0
$9$	−11.8881			−0.0163074
$10$		0			0
$11$	−1078.96	+	1078.96i	−0.810639	+	0.810639i	−0.984730	−	0.174091i	$-0.944301\pi$
$11$	−1078.96	+	1078.96i	−0.810639	+	0.810639i	0.174091	+	0.984730i	$0.444301\pi$
$12$		0			0
$13$	−2073.19	−	727.102i	−0.943648	−	0.330952i
$13$	−2073.19	−	727.102i	−0.943648	−	0.330952i
$14$		0			0
$15$	1580.82	+	1580.82i	0.468391	+	0.468391i
$16$		0			0
$17$			1506.86i			0.306708i	0.988171	+	0.153354i	$0.0490075\pi$
$17$			1506.86i			0.306708i	−0.988171	+	0.153354i	$0.950992\pi$
$18$		0			0
$19$	−4280.27	−	4280.27i	−0.624038	−	0.624038i	0.322524	−	0.946561i	$-0.395469\pi$
$19$	−4280.27	−	4280.27i	−0.624038	−	0.624038i	−0.946561	+	0.322524i	$0.895469\pi$
$20$		0			0
$21$	−6077.47	+	6077.47i	−0.656243	+	0.656243i
$22$		0			0
$23$		−	19283.9i		−	1.58494i	−0.609914	−	0.792468i	$-0.708796\pi$
$23$		−	19283.9i		−	1.58494i	0.609914	−	0.792468i	$-0.291204\pi$
$24$		0			0
$25$		−	8655.40i		−	0.553945i
$26$		0			0
$27$	19840.2			1.00799
$28$		0			0
$29$	−34618.4			−1.41943			−0.709713	−	0.704491i	$-0.751175\pi$
$29$	−34618.4			−1.41943			−0.709713	+	0.704491i	$0.751175\pi$
$30$		0			0
$31$	−14488.1	−	14488.1i	−0.486326	−	0.486326i	0.420819	−	0.907145i	$-0.361743\pi$
$31$	−14488.1	−	14488.1i	−0.486326	−	0.486326i	−0.907145	+	0.420819i	$0.861743\pi$
$32$		0			0
$33$	28893.4	−	28893.4i	0.804002	−	0.804002i
$34$		0			0
$35$	−26794.7			−0.624948
$36$		0			0
$37$	17906.3	−	17906.3i	0.353509	−	0.353509i	−0.507904	−	0.861414i	$-0.669580\pi$
$37$	17906.3	−	17906.3i	0.353509	−	0.353509i	0.861414	+	0.507904i	$0.169580\pi$
$38$		0			0
$39$	55517.9	+	19471.0i	0.935922	+	0.328242i
$40$		0			0
$41$	72322.6	+	72322.6i	1.04936	+	1.04936i	0.998717	+	0.0506380i	$0.0161255\pi$
$41$	72322.6	+	72322.6i	1.04936	+	1.04936i	0.0506380	+	0.998717i	$0.483875\pi$
$42$		0			0
$43$			122834.i			1.54495i	0.635046	+	0.772474i	$0.280981\pi$
$43$			122834.i			1.54495i	−0.635046	+	0.772474i	$0.719019\pi$
$44$		0			0
$45$	701.778	+	701.778i	0.00770127	+	0.00770127i
$46$		0			0
$47$	−78678.8	+	78678.8i	−0.757817	+	0.757817i	−0.975925	−	0.218108i	$-0.930011\pi$
$47$	−78678.8	+	78678.8i	−0.757817	+	0.757817i	0.218108	+	0.975925i	$0.430011\pi$
$48$		0			0
$49$			14636.8i			0.124411i
$50$		0			0
$51$		−	40352.0i		−	0.304197i
$52$		0			0
$53$	−31278.0			−0.210093			−0.105046	−	0.994467i	$-0.533499\pi$
$53$	−31278.0			−0.210093			−0.105046	+	0.994467i	$0.533499\pi$
$54$		0			0
$55$	127387.			0.765661
$56$		0			0
$57$	114621.	+	114621.i	0.618928	+	0.618928i
$58$		0			0
$59$	26291.3	−	26291.3i	0.128014	−	0.128014i	−0.640197	−	0.768211i	$-0.721147\pi$
$59$	26291.3	−	26291.3i	0.128014	−	0.128014i	0.768211	+	0.640197i	$0.221147\pi$
$60$		0			0
$61$	−2955.68			−0.0130217			−0.00651086	−	0.999979i	$-0.502072\pi$
$61$	−2955.68			−0.0130217			−0.00651086	+	0.999979i	$0.502072\pi$
$62$		0			0
$63$	−2697.99	+	2697.99i	−0.0107899	+	0.0107899i
$64$		0			0
$65$	79462.8	+	165308.i	0.289350	+	0.601939i
$66$		0			0
$67$	229598.	+	229598.i	0.763385	+	0.763385i	0.976933	−	0.213548i	$-0.0685019\pi$
$67$	229598.	+	229598.i	0.763385	+	0.763385i	−0.213548	+	0.976933i	$0.568502\pi$
$68$		0			0
$69$			516403.i			1.57196i
$70$		0			0
$71$	58881.7	+	58881.7i	0.164515	+	0.164515i	0.784563	−	0.620049i	$-0.212887\pi$
$71$	58881.7	+	58881.7i	0.164515	+	0.164515i	−0.620049	+	0.784563i	$0.712887\pi$
$72$		0			0
$73$	497137.	−	497137.i	1.27793	−	1.27793i	0.336107	−	0.941824i	$-0.390890\pi$
$73$	497137.	−	497137.i	1.27793	−	1.27793i	0.941824	−	0.336107i	$-0.109110\pi$
$74$		0			0
$75$			231782.i			0.549410i
$76$		0			0
$77$			489739.i			1.07274i
$78$		0			0
$79$	−48045.8			−0.0974482			−0.0487241	−	0.998812i	$-0.515516\pi$
$79$	−48045.8			−0.0974482			−0.0487241	+	0.998812i	$0.515516\pi$
$80$		0			0
$81$	−522633.			−0.983427
$82$		0			0
$83$	411022.	+	411022.i	0.718837	+	0.718837i	0.968367	−	0.249530i	$-0.0802762\pi$
$83$	411022.	+	411022.i	0.718837	+	0.718837i	−0.249530	+	0.968367i	$0.580276\pi$
$84$		0			0
$85$	88953.1	−	88953.1i	0.144845	−	0.144845i
$86$		0			0
$87$	927044.			1.40781
$88$		0			0
$89$	−244331.	+	244331.i	−0.346584	+	0.346584i	−0.858835	−	0.512252i	$-0.828812\pi$
$89$	−244331.	+	244331.i	−0.346584	+	0.346584i	0.512252	+	0.858835i	$0.328812\pi$
$90$		0			0
$91$	−635526.	+	305495.i	−0.843352	+	0.405396i
$92$		0			0
$93$	387977.	+	387977.i	0.482345	+	0.482345i
$94$		0			0
$95$			505348.i			0.589413i
$96$		0			0
$97$	417275.	+	417275.i	0.457201	+	0.457201i	0.897736	−	0.440535i	$-0.145211\pi$
$97$	417275.	+	417275.i	0.457201	+	0.457201i	−0.440535	+	0.897736i	$0.645211\pi$
$98$		0			0
$99$	12826.7	−	12826.7i	0.0132194	−	0.0132194i
$100$		0			0
$101$			386382.i			0.375019i	0.982263	+	0.187509i	$0.0600415\pi$
$101$			386382.i			0.375019i	−0.982263	+	0.187509i	$0.939958\pi$
$102$		0			0
$103$		−	1.72164e6i		−	1.57554i	−0.615968	−	0.787771i	$-0.711235\pi$
$103$		−	1.72164e6i		−	1.57554i	0.615968	−	0.787771i	$-0.288765\pi$
$104$		0			0
$105$	717533.			0.619832
$106$		0			0
$107$	1.34071e6			1.09442			0.547209	−	0.836996i	$-0.315690\pi$
$107$	1.34071e6			1.09442			0.547209	+	0.836996i	$0.315690\pi$
$108$		0			0
$109$	−830199.	−	830199.i	−0.641066	−	0.641066i	0.309751	−	0.950818i	$-0.399754\pi$
$109$	−830199.	−	830199.i	−0.641066	−	0.641066i	−0.950818	+	0.309751i	$0.899754\pi$
$110$		0			0
$111$	−479512.	+	479512.i	−0.350615	+	0.350615i
$112$		0			0
$113$	1.71627e6			1.18946			0.594731	−	0.803925i	$-0.297258\pi$
$113$	1.71627e6			1.18946			0.594731	+	0.803925i	$0.297258\pi$
$114$		0			0
$115$	−1.13837e6	+	1.13837e6i	−0.748498	+	0.748498i
$116$		0			0
$117$	24646.3	+	8643.83i	0.0153884	+	0.00539695i
$118$		0			0
$119$	341981.	+	341981.i	0.202937	+	0.202937i
$120$		0			0
$121$		−	556751.i		−	0.314271i
$122$		0			0
$123$	−1.93672e6	−	1.93672e6i	−1.04076	−	1.04076i
$124$		0			0
$125$	−1.43333e6	+	1.43333e6i	−0.733863	+	0.733863i
$126$		0			0
$127$			2.98167e6i			1.45562i	0.685778	+	0.727811i	$0.259462\pi$
$127$			2.98167e6i			1.45562i	−0.685778	+	0.727811i	$0.740538\pi$
$128$		0			0
$129$		−	3.28937e6i		−	1.53230i
$130$		0			0
$131$	−673122.			−0.299419			−0.149710	−	0.988730i	$-0.547834\pi$
$131$	−673122.			−0.299419			−0.149710	+	0.988730i	$0.547834\pi$
$132$		0			0
$133$	−1.94281e6			−0.825802
$134$		0			0
$135$	−1.17121e6	−	1.17121e6i	−0.476029	−	0.476029i
$136$		0			0
$137$	−1.01973e6	+	1.01973e6i	−0.396574	+	0.396574i	−0.877023	−	0.480448i	$-0.840474\pi$
$137$	−1.01973e6	+	1.01973e6i	−0.396574	+	0.396574i	0.480448	+	0.877023i	$0.340474\pi$
$138$		0			0
$139$	2.05635e6			0.765689			0.382845	−	0.923813i	$-0.374944\pi$
$139$	2.05635e6			0.765689			0.382845	+	0.923813i	$0.374944\pi$
$140$		0			0
$141$	2.10694e6	−	2.10694e6i	0.751612	−	0.751612i
$142$		0			0
$143$	3.02141e6	−	1.45238e6i	1.03324	−	0.496675i
$144$		0			0
$145$	2.04360e6	+	2.04360e6i	0.670335	+	0.670335i
$146$		0			0
$147$		−	391959.i		−	0.123393i
$148$		0			0
$149$	3.58897e6	+	3.58897e6i	1.08495	+	1.08495i	0.996039	+	0.0889147i	$0.0283399\pi$
$149$	3.58897e6	+	3.58897e6i	1.08495	+	1.08495i	0.0889147	+	0.996039i	$0.471660\pi$
$150$		0			0
$151$	−1.86528e6	+	1.86528e6i	−0.541767	+	0.541767i	−0.924047	−	0.382280i	$-0.875139\pi$
$151$	−1.86528e6	+	1.86528e6i	−0.541767	+	0.541767i	0.382280	+	0.924047i	$0.375139\pi$
$152$		0			0
$153$		−	17913.6i		−	0.00500160i
$154$		0			0
$155$			1.71053e6i			0.459343i
$156$		0			0
$157$	−3.55477e6			−0.918570			−0.459285	−	0.888289i	$-0.651894\pi$
$157$	−3.55477e6			−0.918570			−0.459285	+	0.888289i	$0.651894\pi$
$158$		0			0
$159$	837592.			0.208373
$160$		0			0
$161$	−4.37647e6	−	4.37647e6i	−1.04869	−	1.04869i
$162$		0			0
$163$	367883.	−	367883.i	0.0849467	−	0.0849467i	−0.663357	−	0.748303i	$-0.730869\pi$
$163$	367883.	−	367883.i	0.0849467	−	0.0849467i	0.748303	+	0.663357i	$0.230869\pi$
$164$		0			0
$165$	−3.41129e6			−0.759392
$166$		0			0
$167$	1.91720e6	−	1.91720e6i	0.411641	−	0.411641i	−0.470669	−	0.882310i	$-0.655987\pi$
$167$	1.91720e6	−	1.91720e6i	0.411641	−	0.411641i	0.882310	+	0.470669i	$0.155987\pi$
$168$		0			0
$169$	3.76946e6	+	3.01485e6i	0.780941	+	0.624604i
$170$		0			0
$171$	50884.2	+	50884.2i	0.0101764	+	0.0101764i
$172$		0			0
$173$			5.74042e6i			1.10868i	0.832291	+	0.554339i	$0.187029\pi$
$173$			5.74042e6i			1.10868i	−0.832291	+	0.554339i	$0.812971\pi$
$174$		0			0
$175$	−1.96434e6	−	1.96434e6i	−0.366524	−	0.366524i
$176$		0			0
$177$	−704054.	+	704054.i	−0.126966	+	0.126966i
$178$		0			0
$179$		−	5.25653e6i		−	0.916516i	−0.888819	−	0.458258i	$-0.848473\pi$
$179$		−	5.25653e6i		−	0.916516i	0.888819	−	0.458258i	$-0.151527\pi$
$180$		0			0
$181$		−	2.92299e6i		−	0.492937i	−0.969151	−	0.246469i	$-0.920730\pi$
$181$		−	2.92299e6i		−	0.492937i	0.969151	−	0.246469i	$-0.0792702\pi$
$182$		0			0
$183$	79150.0			0.0129151
$184$		0			0
$185$	−2.11410e6			−0.333895
$186$		0			0
$187$	−1.62584e6	−	1.62584e6i	−0.248630	−	0.248630i
$188$		0			0
$189$	4.50272e6	−	4.50272e6i	0.666945	−	0.666945i
$190$		0			0
$191$	2.82697e6			0.405716			0.202858	−	0.979208i	$-0.434977\pi$
$191$	2.82697e6			0.405716			0.202858	+	0.979208i	$0.434977\pi$
$192$		0			0
$193$	2.02485e6	−	2.02485e6i	0.281657	−	0.281657i	−0.552113	−	0.833770i	$-0.686178\pi$
$193$	2.02485e6	−	2.02485e6i	0.281657	−	0.281657i	0.833770	+	0.552113i	$0.186178\pi$
$194$		0			0
$195$	−2.12793e6	−	4.42676e6i	−0.286981	−	0.597011i
$196$		0			0
$197$	−8.90467e6	−	8.90467e6i	−1.16471	−	1.16471i	−0.983431	−	0.181283i	$-0.941975\pi$
$197$	−8.90467e6	−	8.90467e6i	−1.16471	−	1.16471i	−0.181283	−	0.983431i	$-0.558025\pi$
$198$		0			0
$199$		−	7.50433e6i		−	0.952253i	−0.879377	−	0.476127i	$-0.842040\pi$
$199$		−	7.50433e6i		−	0.952253i	0.879377	−	0.476127i	$-0.157960\pi$
$200$		0			0
$201$	−6.14839e6	−	6.14839e6i	−0.757135	−	0.757135i
$202$		0			0
$203$	−7.85663e6	+	7.85663e6i	−0.939178	+	0.939178i
$204$		0			0
$205$		−	8.53872e6i		−	0.991132i
$206$		0			0
$207$			229248.i			0.0258461i
$208$		0			0
$209$	9.23649e6			1.01174
$210$		0			0
$211$	−1.20767e7			−1.28559			−0.642795	−	0.766039i	$-0.722225\pi$
$211$	−1.20767e7			−1.28559			−0.642795	+	0.766039i	$0.722225\pi$
$212$		0			0
$213$	−1.57679e6	−	1.57679e6i	−0.163168	−	0.163168i
$214$		0			0
$215$	7.25117e6	−	7.25117e6i	0.729613	−	0.729613i
$216$		0			0
$217$	−6.57615e6			−0.643566
$218$		0			0
$219$	−1.33128e7	+	1.33128e7i	−1.26747	+	1.26747i
$220$		0			0
$221$	1.09564e6	−	3.12401e6i	0.101506	−	0.289424i
$222$		0			0
$223$	−1.39585e6	−	1.39585e6i	−0.125871	−	0.125871i	0.641365	−	0.767236i	$-0.278368\pi$
$223$	−1.39585e6	−	1.39585e6i	−0.125871	−	0.125871i	−0.767236	+	0.641365i	$0.778368\pi$
$224$		0			0
$225$			102896.i			0.00903339i
$226$		0			0
$227$	−3.97620e6	−	3.97620e6i	−0.339931	−	0.339931i	0.516410	−	0.856341i	$-0.327268\pi$
$227$	−3.97620e6	−	3.97620e6i	−0.339931	−	0.339931i	−0.856341	+	0.516410i	$0.827268\pi$
$228$		0			0
$229$	−1.50029e6	+	1.50029e6i	−0.124931	+	0.124931i	−0.766808	−	0.641877i	$-0.778156\pi$
$229$	−1.50029e6	+	1.50029e6i	−0.124931	+	0.124931i	0.641877	+	0.766808i	$0.278156\pi$
$230$		0			0
$231$		−	1.31147e7i		−	1.06395i
$232$		0			0
$233$		−	1.00047e7i		−	0.790925i	−0.918482	−	0.395462i	$-0.870584\pi$
$233$		−	1.00047e7i		−	0.790925i	0.918482	−	0.395462i	$-0.129416\pi$
$234$		0			0
$235$	9.28916e6			0.715769
$236$		0			0
$237$	1.28662e6			0.0966504
$238$		0			0
$239$	−1.28236e7	−	1.28236e7i	−0.939328	−	0.939328i	0.0589339	−	0.998262i	$-0.481230\pi$
$239$	−1.28236e7	−	1.28236e7i	−0.939328	−	0.939328i	−0.998262	+	0.0589339i	$0.981230\pi$
$240$		0			0
$241$	−1.66353e7	+	1.66353e7i	−1.18844	+	1.18844i	−0.210946	+	0.977498i	$0.567655\pi$
$241$	−1.66353e7	+	1.66353e7i	−1.18844	+	1.18844i	−0.977498	+	0.210946i	$0.932345\pi$
$242$		0			0
$243$	−467938.			−0.0326114
$244$		0			0
$245$	864045.	−	864045.i	0.0587541	−	0.0587541i
$246$		0			0
$247$	5.76164e6	+	1.19860e7i	0.382345	+	0.795398i
$248$		0			0
$249$	−1.10067e7	−	1.10067e7i	−0.712952	−	0.712952i
$250$		0			0
$251$			1.39680e7i			0.883310i	0.897185	+	0.441655i	$0.145608\pi$
$251$			1.39680e7i			0.883310i	−0.897185	+	0.441655i	$0.854392\pi$
$252$		0			0
$253$	2.08066e7	+	2.08066e7i	1.28481	+	1.28481i
$254$		0			0
$255$	−2.38207e6	+	2.38207e6i	−0.143659	+	0.143659i
$256$		0			0
$257$			2.30963e7i			1.36064i	0.732916	+	0.680319i	$0.238159\pi$
$257$			2.30963e7i			1.36064i	−0.732916	+	0.680319i	$0.761841\pi$
$258$		0			0
$259$		−	8.12766e6i		−	0.467806i
$260$		0			0
$261$	411546.			0.0231471
$262$		0			0
$263$	3.02571e7			1.66326			0.831630	−	0.555329i	$-0.187408\pi$
$263$	3.02571e7			1.66326			0.831630	+	0.555329i	$0.187408\pi$
$264$		0			0
$265$	1.84641e6	+	1.84641e6i	0.0992180	+	0.0992180i
$266$		0			0
$267$	6.54292e6	−	6.54292e6i	0.343746	−	0.343746i
$268$		0			0
$269$	5.40474e6			0.277663			0.138832	−	0.990316i	$-0.455665\pi$
$269$	5.40474e6			0.277663			0.138832	+	0.990316i	$0.455665\pi$
$270$		0			0
$271$	7.80124e6	−	7.80124e6i	0.391973	−	0.391973i	−0.483417	−	0.875390i	$-0.660605\pi$
$271$	7.80124e6	−	7.80124e6i	0.391973	−	0.391973i	0.875390	+	0.483417i	$0.160605\pi$
$272$		0			0
$273$	1.70187e7	−	8.18083e6i	0.836447	−	0.402077i
$274$		0			0
$275$	9.33883e6	+	9.33883e6i	0.449050	+	0.449050i
$276$		0			0
$277$		−	2.88491e7i		−	1.35735i	−0.734438	−	0.678676i	$-0.762554\pi$
$277$		−	2.88491e7i		−	1.35735i	0.734438	−	0.678676i	$-0.237446\pi$
$278$		0			0
$279$	172236.	+	172236.i	0.00793069	+	0.00793069i
$280$		0			0
$281$	−1.77577e7	+	1.77577e7i	−0.800328	+	0.800328i	−0.983147	−	0.182819i	$-0.941478\pi$
$281$	−1.77577e7	+	1.77577e7i	−0.800328	+	0.800328i	0.182819	+	0.983147i	$0.441478\pi$
$282$		0			0
$283$			2.27638e7i			1.00435i	0.864766	+	0.502175i	$0.167467\pi$
$283$			2.27638e7i			1.00435i	−0.864766	+	0.502175i	$0.832533\pi$
$284$		0			0
$285$		−	1.35327e7i		−	0.584587i
$286$		0			0
$287$	3.28272e7			1.38863
$288$		0			0
$289$	2.18670e7			0.905930
$290$		0			0
$291$	−1.11742e7	−	1.11742e7i	−0.453458	−	0.453458i
$292$		0			0
$293$	1.38173e7	−	1.38173e7i	0.549314	−	0.549314i	−0.376928	−	0.926242i	$-0.623020\pi$
$293$	1.38173e7	−	1.38173e7i	0.549314	−	0.549314i	0.926242	+	0.376928i	$0.123020\pi$
$294$		0			0
$295$	−3.10407e6			−0.120911
$296$		0			0
$297$	−2.14068e7	+	2.14068e7i	−0.817113	+	0.817113i
$298$		0			0
$299$	−1.40214e7	+	3.99793e7i	−0.524538	+	1.49562i
$300$		0			0
$301$	2.78772e7	+	2.78772e7i	1.02223	+	1.02223i
$302$		0			0
$303$		−	1.03469e7i		−	0.371949i
$304$		0			0
$305$	174480.	+	174480.i	0.00614960	+	0.00614960i
$306$		0			0
$307$	−3.53325e7	+	3.53325e7i	−1.22112	+	1.22112i	−0.253890	+	0.967233i	$0.581710\pi$
$307$	−3.53325e7	+	3.53325e7i	−1.22112	+	1.22112i	−0.967233	+	0.253890i	$0.918290\pi$
$308$		0			0
$309$			4.61036e7i			1.56264i
$310$		0			0
$311$			2.33450e7i			0.776091i	0.921640	+	0.388045i	$0.126850\pi$
$311$			2.33450e7i			0.776091i	−0.921640	+	0.388045i	$0.873150\pi$
$312$		0			0
$313$	4.68746e6			0.152864			0.0764320	−	0.997075i	$-0.475647\pi$
$313$	4.68746e6			0.152864			0.0764320	+	0.997075i	$0.475647\pi$
$314$		0			0
$315$	318537.			0.0101913
$316$		0			0
$317$	1.08194e7	+	1.08194e7i	0.339646	+	0.339646i	0.856234	−	0.516588i	$-0.172798\pi$
$317$	1.08194e7	+	1.08194e7i	0.339646	+	0.339646i	−0.516588	+	0.856234i	$0.672798\pi$
$318$		0			0
$319$	3.73519e7	−	3.73519e7i	1.15064	−	1.15064i
$320$		0			0
$321$	−3.59028e7			−1.08546
$322$		0			0
$323$	6.44976e6	−	6.44976e6i	0.191397	−	0.191397i
$324$		0			0
$325$	−6.29335e6	+	1.79443e7i	−0.183329	+	0.522729i
$326$		0			0
$327$	2.22319e7	+	2.22319e7i	0.635818	+	0.635818i
$328$		0			0
$329$			3.57122e7i			1.00283i
$330$		0			0
$331$	2.31847e7	+	2.31847e7i	0.639319	+	0.639319i	0.950388	−	0.311068i	$-0.100687\pi$
$331$	2.31847e7	+	2.31847e7i	0.639319	+	0.639319i	−0.311068	+	0.950388i	$0.600687\pi$
$332$		0			0
$333$	−212871.	+	212871.i	−0.00576480	+	0.00576480i
$334$		0			0
$335$		−	2.71073e7i		−	0.721029i
$336$		0			0
$337$		−	4.41611e7i		−	1.15385i	−0.816796	−	0.576926i	$-0.804252\pi$
$337$		−	4.41611e7i		−	1.15385i	0.816796	−	0.576926i	$-0.195748\pi$
$338$		0			0
$339$	−4.59600e7			−1.17972
$340$		0			0
$341$	3.12643e7			0.788470
$342$		0			0
$343$	3.00222e7	+	3.00222e7i	0.743978	+	0.743978i
$344$		0			0
$345$	3.04844e7	−	3.04844e7i	0.742370	−	0.742370i
$346$		0			0
$347$	−3.10492e7			−0.743125			−0.371563	−	0.928408i	$-0.621178\pi$
$347$	−3.10492e7			−0.743125			−0.371563	+	0.928408i	$0.621178\pi$
$348$		0			0
$349$	2.34300e7	−	2.34300e7i	0.551182	−	0.551182i	−0.375600	−	0.926782i	$-0.622563\pi$
$349$	2.34300e7	−	2.34300e7i	0.551182	−	0.551182i	0.926782	+	0.375600i	$0.122563\pi$
$350$		0			0
$351$	−4.11326e7	−	1.44258e7i	−0.951184	−	0.333595i
$352$		0			0
$353$	2.38002e7	+	2.38002e7i	0.541073	+	0.541073i	0.923843	−	0.382771i	$-0.125030\pi$
$353$	2.38002e7	+	2.38002e7i	0.541073	+	0.541073i	−0.382771	+	0.923843i	$0.625030\pi$
$354$		0			0
$355$		−	6.95183e6i		−	0.155387i
$356$		0			0
$357$	−9.15788e6	−	9.15788e6i	−0.201275	−	0.201275i
$358$		0			0
$359$	−8.33411e6	+	8.33411e6i	−0.180126	+	0.180126i	−0.791411	−	0.611285i	$-0.790653\pi$
$359$	−8.33411e6	+	8.33411e6i	−0.180126	+	0.180126i	0.611285	+	0.791411i	$0.290653\pi$
$360$		0			0
$361$		−	1.04044e7i		−	0.221154i
$362$		0			0
$363$			1.49092e7i			0.311698i
$364$		0			0
$365$	−5.86941e7			−1.20702
$366$		0			0
$367$	6.65880e6			0.134709			0.0673547	−	0.997729i	$-0.478544\pi$
$367$	6.65880e6			0.134709			0.0673547	+	0.997729i	$0.478544\pi$
$368$		0			0
$369$	−859775.	−	859775.i	−0.0171122	−	0.0171122i
$370$		0			0
$371$	−7.09853e6	+	7.09853e6i	−0.139010	+	0.139010i
$372$		0			0
$373$	−8.65202e7			−1.66721			−0.833606	−	0.552359i	$-0.813728\pi$
$373$	−8.65202e7			−1.66721			−0.833606	+	0.552359i	$0.813728\pi$
$374$		0			0
$375$	3.83829e7	−	3.83829e7i	0.727854	−	0.727854i
$376$		0			0
$377$	7.17706e7	+	2.51711e7i	1.33944	+	0.469762i
$378$		0			0
$379$	−2.61552e7	−	2.61552e7i	−0.480441	−	0.480441i	0.424831	−	0.905272i	$-0.360333\pi$
$379$	−2.61552e7	−	2.61552e7i	−0.480441	−	0.480441i	−0.905272	+	0.424831i	$0.860333\pi$
$380$		0			0
$381$		−	7.98460e7i		−	1.44370i
$382$		0			0
$383$	−1.10676e7	−	1.10676e7i	−0.196996	−	0.196996i	0.601715	−	0.798711i	$-0.294484\pi$
$383$	−1.10676e7	−	1.10676e7i	−0.196996	−	0.196996i	−0.798711	+	0.601715i	$0.794484\pi$
$384$		0			0
$385$	2.89104e7	−	2.89104e7i	0.506607	−	0.506607i
$386$		0			0
$387$		−	1.46026e6i		−	0.0251940i
$388$		0			0
$389$			8.76405e6i			0.148887i	0.997225	+	0.0744434i	$0.0237180\pi$
$389$			8.76405e6i			0.148887i	−0.997225	+	0.0744434i	$0.976282\pi$
$390$		0			0
$391$	2.90581e7			0.486113
$392$		0			0
$393$	1.80255e7			0.296968
$394$		0			0
$395$	2.83625e6	+	2.83625e6i	0.0460207	+	0.0460207i
$396$		0			0
$397$	−5.90667e7	+	5.90667e7i	−0.943998	+	0.943998i	−0.998513	−	0.0545150i	$-0.982639\pi$
$397$	−5.90667e7	+	5.90667e7i	−0.943998	+	0.943998i	0.0545150	+	0.998513i	$0.482639\pi$
$398$		0			0
$399$	5.20265e7			0.819041
$400$		0			0
$401$	8.06645e6	−	8.06645e6i	0.125098	−	0.125098i	−0.641786	−	0.766884i	$-0.721806\pi$
$401$	8.06645e6	−	8.06645e6i	0.125098	−	0.125098i	0.766884	+	0.641786i	$0.221806\pi$
$402$		0			0
$403$	1.95024e7	+	4.05711e7i	0.297970	+	0.619871i
$404$		0			0
$405$	3.08522e7	+	3.08522e7i	0.464431	+	0.464431i
$406$		0			0
$407$			3.86404e7i			0.573137i
$408$		0			0
$409$	2.51714e7	+	2.51714e7i	0.367907	+	0.367907i	0.866713	−	0.498807i	$-0.166228\pi$
$409$	2.51714e7	+	2.51714e7i	0.367907	+	0.367907i	−0.498807	+	0.866713i	$0.666228\pi$
$410$		0			0
$411$	2.73074e7	−	2.73074e7i	0.393328	−	0.393328i
$412$		0			0
$413$		−	1.19336e7i		−	0.169403i
$414$		0			0
$415$		−	4.85270e7i		−	0.678952i
$416$		0			0
$417$	−5.50669e7			−0.759421
$418$		0			0
$419$	9.44795e6			0.128439			0.0642193	−	0.997936i	$-0.479544\pi$
$419$	9.44795e6			0.128439			0.0642193	+	0.997936i	$0.479544\pi$
$420$		0			0
$421$	−2.21073e7	−	2.21073e7i	−0.296272	−	0.296272i	0.543280	−	0.839552i	$-0.317182\pi$
$421$	−2.21073e7	−	2.21073e7i	−0.296272	−	0.296272i	−0.839552	+	0.543280i	$0.817182\pi$
$422$		0			0
$423$	935338.	−	935338.i	0.0123580	−	0.0123580i
$424$		0			0
$425$	1.30424e7			0.169900
$426$		0			0
$427$	−670790.	+	670790.i	−0.00861595	+	0.00861595i
$428$		0			0
$429$	−8.09101e7	+	3.88932e7i	−1.02478	+	0.492609i
$430$		0			0
$431$	2.99941e7	+	2.99941e7i	0.374631	+	0.374631i	0.869161	−	0.494530i	$-0.164660\pi$
$431$	2.99941e7	+	2.99941e7i	0.374631	+	0.374631i	−0.494530	+	0.869161i	$0.664660\pi$
$432$		0			0
$433$			4.58030e7i			0.564196i	0.959386	+	0.282098i	$0.0910304\pi$
$433$			4.58030e7i			0.564196i	−0.959386	+	0.282098i	$0.908970\pi$
$434$		0			0
$435$	−5.47254e7	−	5.47254e7i	−0.664847	−	0.664847i
$436$		0			0
$437$	−8.25404e7	+	8.25404e7i	−0.989059	+	0.989059i
$438$		0			0
$439$		−	3.19412e7i		−	0.377536i	−0.982022	−	0.188768i	$-0.939551\pi$
$439$		−	3.19412e7i		−	0.377536i	0.982022	−	0.188768i	$-0.0604494\pi$
$440$		0			0
$441$		−	174004.i		−	0.00202882i
$442$		0			0
$443$	−3.61373e7			−0.415666			−0.207833	−	0.978164i	$-0.566641\pi$
$443$	−3.61373e7			−0.415666			−0.207833	+	0.978164i	$0.566641\pi$
$444$		0			0
$445$	2.88468e7			0.327354
$446$		0			0
$447$	−9.61089e7	−	9.61089e7i	−1.07607	−	1.07607i
$448$		0			0
$449$	8.98341e7	−	8.98341e7i	0.992436	−	0.992436i	−0.00753584	−	0.999972i	$-0.502399\pi$
$449$	8.98341e7	−	8.98341e7i	0.992436	−	0.992436i	0.999972	+	0.00753584i	$0.00239876\pi$
$450$		0			0
$451$	−1.56066e8			−1.70130
$452$		0			0
$453$	4.99502e7	−	4.99502e7i	0.537331	−	0.537331i
$454$		0			0
$455$	5.55505e7	+	1.94824e7i	0.589731	+	0.206828i
$456$		0			0
$457$	−7.00089e7	−	7.00089e7i	−0.733507	−	0.733507i	0.237806	−	0.971313i	$-0.423572\pi$
$457$	−7.00089e7	−	7.00089e7i	−0.733507	−	0.733507i	−0.971313	+	0.237806i	$0.923572\pi$
$458$		0			0
$459$			2.98964e7i			0.309158i
$460$		0			0
$461$	3.59349e7	+	3.59349e7i	0.366787	+	0.366787i	0.866304	−	0.499517i	$-0.166489\pi$
$461$	3.59349e7	+	3.59349e7i	0.366787	+	0.366787i	−0.499517	+	0.866304i	$0.666489\pi$
$462$		0			0
$463$	1.69301e7	−	1.69301e7i	0.170576	−	0.170576i	−0.616657	−	0.787232i	$-0.711513\pi$
$463$	1.69301e7	−	1.69301e7i	0.170576	−	0.170576i	0.787232	+	0.616657i	$0.211513\pi$
$464$		0			0
$465$		−	4.58063e7i		−	0.455582i
$466$		0			0
$467$		−	1.42553e7i		−	0.139967i	−0.997548	−	0.0699835i	$-0.977705\pi$
$467$		−	1.42553e7i		−	0.139967i	0.997548	−	0.0699835i	$-0.0222947\pi$
$468$		0			0
$469$	1.04214e8			1.01020
$470$		0			0
$471$	9.51930e7			0.911050
$472$		0			0
$473$	−1.32533e8	−	1.32533e8i	−1.25240	−	1.25240i
$474$		0			0
$475$	−3.70475e7	+	3.70475e7i	−0.345683	+	0.345683i
$476$		0			0
$477$	371835.			0.00342606
$478$		0			0
$479$	−6.01971e7	+	6.01971e7i	−0.547733	+	0.547733i	−0.925785	−	0.378051i	$-0.876594\pi$
$479$	−6.01971e7	+	6.01971e7i	−0.547733	+	0.547733i	0.378051	+	0.925785i	$0.376594\pi$
$480$		0			0
$481$	−5.01430e7	+	2.41036e7i	−0.450583	+	0.216594i
$482$		0			0
$483$	1.17197e8	+	1.17197e8i	1.04010	+	1.04010i
$484$		0			0
$485$		−	4.92653e7i		−	0.431833i
$486$		0			0
$487$	−477050.	−	477050.i	−0.00413026	−	0.00413026i	0.705039	−	0.709169i	$-0.250930\pi$
$487$	−477050.	−	477050.i	−0.00413026	−	0.00413026i	−0.709169	+	0.705039i	$0.750930\pi$
$488$		0			0
$489$	−9.85151e6	+	9.85151e6i	−0.0842512	+	0.0842512i
$490$		0			0
$491$			4.45000e7i			0.375937i	0.982175	+	0.187969i	$0.0601904\pi$
$491$			4.45000e7i			0.375937i	−0.982175	+	0.187969i	$0.939810\pi$
$492$		0			0
$493$		−	5.21650e7i		−	0.435350i
$494$		0			0
$495$	−1.51438e6			−0.0124859
$496$		0			0
$497$	2.67263e7			0.217706
$498$		0			0
$499$	−9.09143e7	−	9.09143e7i	−0.731695	−	0.731695i	0.239260	−	0.970956i	$-0.423095\pi$
$499$	−9.09143e7	−	9.09143e7i	−0.731695	−	0.731695i	−0.970956	+	0.239260i	$0.923095\pi$
$500$		0			0
$501$	−5.13407e7	+	5.13407e7i	−0.408271	+	0.408271i
$502$		0			0
$503$	−1.02124e8			−0.802462			−0.401231	−	0.915977i	$-0.631417\pi$
$503$	−1.02124e8			−0.802462			−0.401231	+	0.915977i	$0.631417\pi$
$504$		0			0
$505$	2.28090e7	−	2.28090e7i	0.177106	−	0.177106i
$506$		0			0
$507$	−1.00942e8	−	8.07344e7i	−0.774548	−	0.619490i
$508$		0			0
$509$	6.78573e7	+	6.78573e7i	0.514569	+	0.514569i	0.915923	−	0.401354i	$-0.131460\pi$
$509$	6.78573e7	+	6.78573e7i	0.514569	+	0.514569i	−0.401354	+	0.915923i	$0.631460\pi$
$510$		0			0
$511$		−	2.25650e8i		−	1.69111i
$512$		0			0
$513$	−8.49215e7	−	8.49215e7i	−0.629022	−	0.629022i
$514$		0			0
$515$	−1.01632e8	+	1.01632e8i	−0.744062	+	0.744062i
$516$		0			0
$517$		−	1.69783e8i		−	1.22863i
$518$		0			0
$519$		−	1.53722e8i		−	1.09960i
$520$		0			0
$521$	2.12858e8			1.50514			0.752570	−	0.658512i	$-0.228814\pi$
$521$	2.12858e8			1.50514			0.752570	+	0.658512i	$0.228814\pi$
$522$		0			0
$523$	2.19853e8			1.53684			0.768419	−	0.639947i	$-0.221044\pi$
$523$	2.19853e8			1.53684			0.768419	+	0.639947i	$0.221044\pi$
$524$		0			0
$525$	5.26029e7	+	5.26029e7i	0.363523	+	0.363523i
$526$		0			0
$527$	2.18316e7	−	2.18316e7i	0.149160	−	0.149160i
$528$		0			0
$529$	−2.23833e8			−1.51202
$530$		0			0
$531$	−312553.	+	312553.i	−0.00208757	+	0.00208757i
$532$		0			0
$533$	−9.73529e7	−	2.02525e8i	−0.642935	−	1.33751i
$534$		0			0
$535$	−7.91450e7	−	7.91450e7i	−0.516847	−	0.516847i
$536$		0			0
$537$			1.40764e8i			0.909013i
$538$		0			0
$539$	−1.57926e7	−	1.57926e7i	−0.100852	−	0.100852i
$540$		0			0
$541$	2.90497e7	−	2.90497e7i	0.183464	−	0.183464i	−0.609400	−	0.792863i	$-0.708589\pi$
$541$	2.90497e7	−	2.90497e7i	0.183464	−	0.183464i	0.792863	+	0.609400i	$0.208589\pi$
$542$		0			0
$543$			7.82746e7i			0.488901i
$544$		0			0
$545$			9.80170e7i			0.605497i
$546$		0			0
$547$	−7.53180e7			−0.460189			−0.230095	−	0.973168i	$-0.573904\pi$
$547$	−7.53180e7			−0.460189			−0.230095	+	0.973168i	$0.573904\pi$
$548$		0			0
$549$	35137.3			0.000212350
$550$		0			0
$551$	1.48176e8	+	1.48176e8i	0.885775	+	0.885775i
$552$		0			0
$553$	−1.09040e7	+	1.09040e7i	−0.0644776	+	0.0644776i
$554$		0			0
$555$	5.66133e7			0.331161
$556$		0			0
$557$	−8.76993e7	+	8.76993e7i	−0.507493	+	0.507493i	−0.913756	−	0.406263i	$-0.866832\pi$
$557$	−8.76993e7	+	8.76993e7i	−0.507493	+	0.507493i	0.406263	+	0.913756i	$0.366832\pi$
$558$		0			0
$559$	8.93129e7	−	2.54659e8i	0.511304	−	1.45789i
$560$		0			0
$561$	4.35383e7	+	4.35383e7i	0.246594	+	0.246594i
$562$		0			0
$563$		−	1.67475e8i		−	0.938479i	−0.883071	−	0.469240i	$-0.844528\pi$
$563$		−	1.67475e8i		−	0.938479i	0.883071	−	0.469240i	$-0.155472\pi$
$564$		0			0
$565$	−1.01315e8	−	1.01315e8i	−0.561733	−	0.561733i
$566$		0			0
$567$	−1.18611e8	+	1.18611e8i	−0.650694	+	0.650694i
$568$		0			0
$569$			1.19766e8i			0.650123i	0.945693	+	0.325061i	$0.105385\pi$
$569$			1.19766e8i			0.650123i	−0.945693	+	0.325061i	$0.894615\pi$
$570$		0			0
$571$			2.90574e7i			0.156081i	0.996950	+	0.0780403i	$0.0248663\pi$
$571$			2.90574e7i			0.156081i	−0.996950	+	0.0780403i	$0.975134\pi$
$572$		0			0
$573$	−7.57034e7			−0.402394
$574$		0			0
$575$	−1.66910e8			−0.877968
$576$		0			0
$577$	−6.36575e7	−	6.36575e7i	−0.331377	−	0.331377i	0.521732	−	0.853109i	$-0.325286\pi$
$577$	−6.36575e7	−	6.36575e7i	−0.331377	−	0.331377i	−0.853109	+	0.521732i	$0.825286\pi$
$578$		0			0
$579$	−5.42233e7	+	5.42233e7i	−0.279351	+	0.279351i
$580$		0			0
$581$	1.86562e8			0.951252
$582$		0			0
$583$	3.37477e7	−	3.37477e7i	0.170310	−	0.170310i
$584$		0			0
$585$	−944658.	−	1.96519e6i	−0.00471854	−	0.00981604i
$586$		0			0
$587$	1.47686e8	+	1.47686e8i	0.730172	+	0.730172i	0.970654	−	0.240482i	$-0.0773054\pi$
$587$	1.47686e8	+	1.47686e8i	0.730172	+	0.730172i	−0.240482	+	0.970654i	$0.577305\pi$
$588$		0			0
$589$			1.24026e8i			0.606972i
$590$		0			0
$591$	2.38458e8	+	2.38458e8i	1.15518	+	1.15518i
$592$		0			0
$593$	−4.33390e7	+	4.33390e7i	−0.207833	+	0.207833i	−0.803346	−	0.595513i	$-0.796949\pi$
$593$	−4.33390e7	+	4.33390e7i	−0.207833	+	0.207833i	0.595513	+	0.803346i	$0.296949\pi$
$594$		0			0
$595$		−	4.03757e7i		−	0.191677i
$596$		0			0
$597$			2.00958e8i			0.944457i
$598$		0			0
$599$	2.22396e8			1.03477			0.517387	−	0.855751i	$-0.326905\pi$
$599$	2.22396e8			1.03477			0.517387	+	0.855751i	$0.326905\pi$
$600$		0			0
$601$	−2.60139e8			−1.19835			−0.599173	−	0.800620i	$-0.704504\pi$
$601$	−2.60139e8			−1.19835			−0.599173	+	0.800620i	$0.704504\pi$
$602$		0			0
$603$	−2.72947e6	−	2.72947e6i	−0.0124488	−	0.0124488i
$604$		0			0
$605$	−3.28662e7	+	3.28662e7i	−0.148417	+	0.148417i
$606$		0			0
$607$	−4.04305e8			−1.80777			−0.903884	−	0.427778i	$-0.859296\pi$
$607$	−4.04305e8			−1.80777			−0.903884	+	0.427778i	$0.859296\pi$
$608$		0			0
$609$	2.10392e8	−	2.10392e8i	0.931489	−	0.931489i
$610$		0			0
$611$	2.20324e8	−	1.05909e8i	0.965913	−	0.464311i
$612$		0			0
$613$	1.29644e8	+	1.29644e8i	0.562820	+	0.562820i	0.930107	−	0.367288i	$-0.119714\pi$
$613$	1.29644e8	+	1.29644e8i	0.562820	+	0.562820i	−0.367288	+	0.930107i	$0.619714\pi$
$614$		0			0
$615$			2.28658e8i			0.983017i
$616$		0			0
$617$	1.27030e8	+	1.27030e8i	0.540818	+	0.540818i	0.923769	−	0.382951i	$-0.125092\pi$
$617$	1.27030e8	+	1.27030e8i	0.540818	+	0.540818i	−0.382951	+	0.923769i	$0.625092\pi$
$618$		0			0
$619$	1.21031e8	−	1.21031e8i	0.510300	−	0.510300i	−0.404318	−	0.914618i	$-0.632491\pi$
$619$	1.21031e8	−	1.21031e8i	0.510300	−	0.510300i	0.914618	+	0.404318i	$0.132491\pi$
$620$		0			0
$621$		−	3.82597e8i		−	1.59759i
$622$		0			0
$623$			1.10902e8i			0.458642i
$624$		0			0
$625$	3.39841e7			0.139199
$626$		0			0
$627$	−2.47344e8			−1.00346
$628$		0			0
$629$	2.69823e7	+	2.69823e7i	0.108424	+	0.108424i
$630$		0			0
$631$	−2.73690e8	+	2.73690e8i	−1.08936	+	1.08936i	−0.0937662	+	0.995594i	$0.529891\pi$
$631$	−2.73690e8	+	2.73690e8i	−1.08936	+	1.08936i	−0.995594	+	0.0937662i	$0.970109\pi$
$632$		0			0
$633$	3.23402e8			1.27506
$634$		0			0
$635$	1.76015e8	−	1.76015e8i	0.687428	−	0.687428i
$636$		0			0
$637$	1.06425e7	−	3.03450e7i	0.0411741	−	0.117400i
$638$		0			0
$639$	−699989.	−	699989.i	−0.00268280	−	0.00268280i
$640$		0			0
$641$			5.16969e7i			0.196286i	0.995172	+	0.0981432i	$0.0312903\pi$
$641$			5.16969e7i			0.196286i	−0.995172	+	0.0981432i	$0.968710\pi$
$642$		0			0
$643$	−3.00222e7	−	3.00222e7i	−0.112930	−	0.112930i	0.648384	−	0.761314i	$-0.275445\pi$
$643$	−3.00222e7	−	3.00222e7i	−0.112930	−	0.112930i	−0.761314	+	0.648384i	$0.775445\pi$
$644$		0			0
$645$	−1.94179e8	+	1.94179e8i	−0.723640	+	0.723640i
$646$		0			0
$647$			1.57925e8i			0.583094i	0.956557	+	0.291547i	$0.0941699\pi$
$647$			1.57925e8i			0.583094i	−0.956557	+	0.291547i	$0.905830\pi$
$648$		0			0
$649$			5.67346e7i			0.207546i
$650$		0			0
$651$	1.76102e8			0.638297
$652$		0			0
$653$	2.73657e8			0.982804			0.491402	−	0.870933i	$-0.336485\pi$
$653$	2.73657e8			0.982804			0.491402	+	0.870933i	$0.336485\pi$
$654$		0			0
$655$	3.97359e7	+	3.97359e7i	0.141403	+	0.141403i
$656$		0			0
$657$	−5.90999e6	+	5.90999e6i	−0.0208397	+	0.0208397i
$658$		0			0
$659$	4.27581e8			1.49404			0.747019	−	0.664803i	$-0.231484\pi$
$659$	4.27581e8			1.49404			0.747019	+	0.664803i	$0.231484\pi$
$660$		0			0
$661$	1.22478e8	−	1.22478e8i	0.424086	−	0.424086i	−0.462522	−	0.886608i	$-0.653055\pi$
$661$	1.22478e8	−	1.22478e8i	0.424086	−	0.424086i	0.886608	+	0.462522i	$0.153055\pi$
$662$		0			0
$663$	−2.93400e7	+	8.36576e7i	−0.100675	+	0.287055i
$664$		0			0
$665$	1.14688e8	+	1.14688e8i	0.389991	+	0.389991i
$666$		0			0
$667$			6.67578e8i			2.24970i
$668$		0			0
$669$	3.73795e7	+	3.73795e7i	0.124840	+	0.124840i
$670$		0			0
$671$	3.18906e6	−	3.18906e6i	0.0105559	−	0.0105559i
$672$		0			0
$673$			5.75888e8i			1.88926i	0.328132	+	0.944632i	$0.393581\pi$
$673$			5.75888e8i			1.88926i	−0.328132	+	0.944632i	$0.606419\pi$
$674$		0			0
$675$		−	1.71725e8i		−	0.558370i
$676$		0			0
$677$	6.47353e7			0.208629			0.104315	−	0.994544i	$-0.466735\pi$
$677$	6.47353e7			0.208629			0.104315	+	0.994544i	$0.466735\pi$
$678$		0			0
$679$	1.89401e8			0.605024
$680$		0			0
$681$	1.06478e8	+	1.06478e8i	0.337148	+	0.337148i
$682$		0			0
$683$	4.03051e7	−	4.03051e7i	0.126502	−	0.126502i	−0.641021	−	0.767523i	$-0.721489\pi$
$683$	4.03051e7	−	4.03051e7i	0.126502	−	0.126502i	0.767523	+	0.641021i	$0.221489\pi$
$684$		0			0
$685$	1.20394e8			0.374571
$686$		0			0
$687$	4.01762e7	−	4.01762e7i	0.123908	−	0.123908i
$688$		0			0
$689$	6.48454e7	+	2.27423e7i	0.198254	+	0.0695307i
$690$		0			0
$691$	−5.72778e7	−	5.72778e7i	−0.173601	−	0.173601i	0.614958	−	0.788559i	$-0.289173\pi$
$691$	−5.72778e7	−	5.72778e7i	−0.173601	−	0.173601i	−0.788559	+	0.614958i	$0.789173\pi$
$692$		0			0
$693$		−	5.82205e6i		−	0.0174935i
$694$		0			0
$695$	−1.21391e8	−	1.21391e8i	−0.361603	−	0.361603i
$696$		0			0
$697$	−1.08980e8	+	1.08980e8i	−0.321846	+	0.321846i
$698$		0			0
$699$			2.67915e8i			0.784449i
$700$		0			0
$701$			3.34829e8i			0.972005i	0.873958	+	0.486002i	$0.161545\pi$
$701$			3.34829e8i			0.972005i	−0.873958	+	0.486002i	$0.838455\pi$
$702$		0			0
$703$	−1.53288e8			−0.441206
$704$		0			0
$705$	−2.48754e8			−0.709909
$706$		0			0
$707$	8.76893e7	+	8.76893e7i	0.248135	+	0.248135i
$708$		0			0
$709$	3.70614e8	−	3.70614e8i	1.03988	−	1.03988i	0.0407092	−	0.999171i	$-0.487038\pi$
$709$	3.70614e8	−	3.70614e8i	1.03988	−	1.03988i	0.999171	−	0.0407092i	$-0.0129617\pi$
$710$		0			0
$711$	571171.			0.00158912
$712$		0			0
$713$	−2.79388e8	+	2.79388e8i	−0.770796	+	0.770796i
$714$		0			0
$715$	−2.64098e8	−	9.26232e7i	−0.722514	−	0.253397i
$716$		0			0
$717$	3.43403e8	+	3.43403e8i	0.931638	+	0.931638i
$718$		0			0
$719$			4.72918e8i			1.27233i	0.771554	+	0.636164i	$0.219480\pi$
$719$			4.72918e8i			1.27233i	−0.771554	+	0.636164i	$0.780520\pi$
$720$		0			0
$721$	−3.90725e8	−	3.90725e8i	−1.04247	−	1.04247i
$722$		0			0
$723$	4.45475e8	−	4.45475e8i	1.17871	−	1.17871i
$724$		0			0
$725$			2.99636e8i			0.786285i
$726$		0			0
$727$			4.64054e8i			1.20772i	0.797091	+	0.603859i	$0.206371\pi$
$727$			4.64054e8i			1.20772i	−0.797091	+	0.603859i	$0.793629\pi$
$728$		0			0
$729$	3.93531e8			1.01577
$730$		0			0
$731$	−1.85094e8			−0.473848
$732$		0			0
$733$	−2.99117e8	−	2.99117e8i	−0.759503	−	0.759503i	0.216729	−	0.976232i	$-0.430461\pi$
$733$	−2.99117e8	−	2.99117e8i	−0.759503	−	0.759503i	−0.976232	+	0.216729i	$0.930461\pi$
$734$		0			0
$735$	−2.31382e7	+	2.31382e7i	−0.0582731	+	0.0582731i
$736$		0			0
$737$	−4.95454e8			−1.23766
$738$		0			0
$739$	4.58741e8	−	4.58741e8i	1.13667	−	1.13667i	0.147626	−	0.989043i	$-0.452837\pi$
$739$	4.58741e8	−	4.58741e8i	1.13667	−	1.13667i	0.989043	−	0.147626i	$-0.0471633\pi$
$740$		0			0
$741$	−1.54291e8	−	3.20973e8i	−0.379215	−	0.788886i
$742$		0			0
$743$	1.06908e7	+	1.06908e7i	0.0260643	+	0.0260643i	0.720019	−	0.693955i	$-0.244133\pi$
$743$	1.06908e7	+	1.06908e7i	0.0260643	+	0.0260643i	−0.693955	+	0.720019i	$0.744133\pi$
$744$		0			0
$745$		−	4.23730e8i		−	1.02476i
$746$		0			0
$747$	−4.88625e6	−	4.88625e6i	−0.0117223	−	0.0117223i
$748$		0			0
$749$	3.04273e8	−	3.04273e8i	0.724133	−	0.724133i
$750$		0			0
$751$			1.10624e8i			0.261174i	0.991437	+	0.130587i	$0.0416862\pi$
$751$			1.10624e8i			0.261174i	−0.991437	+	0.130587i	$0.958314\pi$
$752$		0			0
$753$		−	3.74048e8i		−	0.876078i
$754$		0			0
$755$	2.20223e8			0.511707
$756$		0			0
$757$	3.71077e8			0.855413			0.427707	−	0.903918i	$-0.359322\pi$
$757$	3.71077e8			0.855413			0.427707	+	0.903918i	$0.359322\pi$
$758$		0			0
$759$	−5.57178e8	−	5.57178e8i	−1.27429	−	1.27429i
$760$		0			0
$761$	−1.01154e8	+	1.01154e8i	−0.229525	+	0.229525i	−0.812494	−	0.582969i	$-0.801891\pi$
$761$	−1.01154e8	+	1.01154e8i	−0.229525	+	0.229525i	0.582969	+	0.812494i	$0.301891\pi$
$762$		0			0
$763$	−3.76827e8			−0.848336
$764$		0			0
$765$	−1.05748e6	+	1.05748e6i	−0.00236204	+	0.00236204i
$766$		0			0
$767$	−7.36235e7	+	3.53906e7i	−0.163166	+	0.0784335i
$768$		0			0
$769$	−3.84131e8	−	3.84131e8i	−0.844697	−	0.844697i	0.144769	−	0.989466i	$-0.453756\pi$
$769$	−3.84131e8	−	3.84131e8i	−0.844697	−	0.844697i	−0.989466	+	0.144769i	$0.953756\pi$
$770$		0			0
$771$		−	6.18494e8i		−	1.34950i
$772$		0			0
$773$	−5.38813e8	−	5.38813e8i	−1.16654	−	1.16654i	−0.983015	−	0.183525i	$-0.941249\pi$
$773$	−5.38813e8	−	5.38813e8i	−1.16654	−	1.16654i	−0.183525	−	0.983015i	$-0.558751\pi$
$774$		0			0
$775$	−1.25401e8	+	1.25401e8i	−0.269398	+	0.269398i
$776$		0			0
$777$			2.17650e8i			0.463976i
$778$		0			0
$779$		−	6.19121e8i		−	1.30967i
$780$		0			0
$781$	−1.27062e8			−0.266724
$782$		0			0
$783$	−6.86836e8			−1.43076
$784$		0			0
$785$	2.09846e8	+	2.09846e8i	0.433802	+	0.433802i
$786$		0			0
$787$	4.57567e8	−	4.57567e8i	0.938708	−	0.938708i	−0.0595191	−	0.998227i	$-0.518957\pi$
$787$	4.57567e8	−	4.57567e8i	0.938708	−	0.938708i	0.998227	+	0.0595191i	$0.0189567\pi$
$788$		0			0
$789$	−8.10254e8			−1.64964
$790$		0			0
$791$	3.89507e8	−	3.89507e8i	0.787020	−	0.787020i
$792$		0			0
$793$	6.12770e6	+	2.14908e6i	0.0122879	+	0.00430956i
$794$		0			0
$795$	−4.94449e7	−	4.94449e7i	−0.0984057	−	0.0984057i
$796$		0			0
$797$			8.44943e8i			1.66899i	0.551019	+	0.834493i	$0.314239\pi$
$797$			8.44943e8i			1.66899i	−0.551019	+	0.834493i	$0.685761\pi$
$798$		0			0
$799$	−1.18558e8	−	1.18558e8i	−0.232429	−	0.232429i
$800$		0			0
$801$	2.90462e6	−	2.90462e6i	0.00565186	−	0.00565186i
$802$		0			0
$803$			1.07278e9i			2.07188i
$804$		0			0
$805$			5.16706e8i			0.990503i
$806$		0			0
$807$	−1.44733e8			−0.275390
$808$		0			0
$809$	2.45542e8			0.463745			0.231873	−	0.972746i	$-0.425515\pi$
$809$	2.45542e8			0.463745			0.231873	+	0.972746i	$0.425515\pi$
$810$		0			0
$811$	1.09257e8	+	1.09257e8i	0.204827	+	0.204827i	0.802064	−	0.597238i	$-0.203735\pi$
$811$	1.09257e8	+	1.09257e8i	0.204827	+	0.204827i	−0.597238	+	0.802064i	$0.703735\pi$
$812$		0			0
$813$	−2.08909e8	+	2.08909e8i	−0.388764	+	0.388764i
$814$		0			0
$815$	−4.34339e7			−0.0802335
$816$		0			0
$817$	5.25764e8	−	5.25764e8i	0.964106	−	0.964106i
$818$		0			0
$819$	7.55517e6	−	3.63174e6i	0.0137528	−	0.00661094i
$820$		0			0
$821$	1.25745e7	+	1.25745e7i	0.0227228	+	0.0227228i	0.718377	−	0.695654i	$-0.244885\pi$
$821$	1.25745e7	+	1.25745e7i	0.0227228	+	0.0227228i	−0.695654	+	0.718377i	$0.744885\pi$
$822$		0			0
$823$		−	4.10647e8i		−	0.736664i	−0.929694	−	0.368332i	$-0.879929\pi$
$823$		−	4.10647e8i		−	0.736664i	0.929694	−	0.368332i	$-0.120071\pi$
$824$		0			0
$825$	−2.50084e8	−	2.50084e8i	−0.445373	−	0.445373i
$826$		0			0
$827$	2.06338e8	−	2.06338e8i	0.364807	−	0.364807i	−0.500772	−	0.865579i	$-0.666951\pi$
$827$	2.06338e8	−	2.06338e8i	0.364807	−	0.364807i	0.865579	+	0.500772i	$0.166951\pi$
$828$		0			0
$829$			7.12094e8i			1.24990i	0.780667	+	0.624948i	$0.214880\pi$
$829$			7.12094e8i			1.24990i	−0.780667	+	0.624948i	$0.785120\pi$
$830$		0			0
$831$			7.72548e8i			1.34624i
$832$		0			0
$833$	−2.20556e7			−0.0381579
$834$		0			0
$835$	−2.26353e8			−0.388801
$836$		0			0
$837$	−2.87448e8	−	2.87448e8i	−0.490210	−	0.490210i
$838$		0			0
$839$	−5.24119e8	+	5.24119e8i	−0.887450	+	0.887450i	−0.994278	−	0.106828i	$-0.965931\pi$
$839$	−5.24119e8	+	5.24119e8i	−0.887450	+	0.887450i	0.106828	+	0.994278i	$0.465931\pi$
$840$		0			0
$841$	6.03610e8			1.01477
$842$		0			0
$843$	4.75533e8	−	4.75533e8i	0.793775	−	0.793775i
$844$		0			0
$845$	−4.45463e7	−	4.00492e8i	−0.0738315	−	0.663780i
$846$		0			0
$847$	−1.26354e8	−	1.26354e8i	−0.207941	−	0.207941i
$848$		0			0
$849$		−	6.09590e8i		−	0.996127i
$850$		0			0
$851$	−3.45304e8	−	3.45304e8i	−0.560290	−	0.560290i
$852$		0			0
$853$	6.79176e8	−	6.79176e8i	1.09430	−	1.09430i	0.0992327	−	0.995064i	$-0.468361\pi$
$853$	6.79176e8	−	6.79176e8i	1.09430	−	1.09430i	0.995064	−	0.0992327i	$-0.0316388\pi$
$854$		0			0
$855$		−	6.00761e6i		−	0.00961177i
$856$		0			0
$857$			5.61022e7i			0.0891329i	0.999006	+	0.0445664i	$0.0141906\pi$
$857$			5.61022e7i			0.0891329i	−0.999006	+	0.0445664i	$0.985809\pi$
$858$		0			0
$859$	1.73672e8			0.273999			0.137000	−	0.990571i	$-0.456254\pi$
$859$	1.73672e8			0.273999			0.137000	+	0.990571i	$0.456254\pi$
$860$		0			0
$861$	−8.79077e8			−1.37726
$862$		0			0
$863$	2.66613e8	+	2.66613e8i	0.414809	+	0.414809i	0.883410	−	0.468601i	$-0.155242\pi$
$863$	2.66613e8	+	2.66613e8i	0.414809	+	0.414809i	−0.468601	+	0.883410i	$0.655242\pi$
$864$		0			0
$865$	3.38870e8	−	3.38870e8i	0.523582	−	0.523582i
$866$		0			0
$867$	−5.85574e8			−0.898513
$868$		0			0
$869$	5.18395e7	−	5.18395e7i	0.0789953	−	0.0789953i
$870$		0			0
$871$	−3.09060e8	−	6.42942e8i	−0.467722	−	0.973010i
$872$		0			0
$873$	−4.96059e6	−	4.96059e6i	−0.00745574	−	0.00745574i
$874$		0			0
$875$			6.50585e8i			0.971136i
$876$		0			0
$877$	−6.40494e8	−	6.40494e8i	−0.949547	−	0.949547i	0.0492402	−	0.998787i	$-0.484320\pi$
$877$	−6.40494e8	−	6.40494e8i	−0.949547	−	0.949547i	−0.998787	+	0.0492402i	$0.984320\pi$
$878$		0			0
$879$	−3.70013e8	+	3.70013e8i	−0.544817	+	0.544817i
$880$		0			0
$881$			1.00220e9i			1.46564i	0.680424	+	0.732819i	$0.261796\pi$
$881$			1.00220e9i			1.46564i	−0.680424	+	0.732819i	$0.738204\pi$
$882$		0			0
$883$			8.07443e8i			1.17282i	0.810016	+	0.586408i	$0.199458\pi$
$883$			8.07443e8i			1.17282i	−0.810016	+	0.586408i	$0.800542\pi$
$884$		0			0
$885$	8.31237e7			0.119921
$886$		0			0
$887$	1.06089e8			0.152019			0.0760097	−	0.997107i	$-0.475782\pi$
$887$	1.06089e8			0.152019			0.0760097	+	0.997107i	$0.475782\pi$
$888$		0			0
$889$	6.76688e8	+	6.76688e8i	0.963127	+	0.963127i
$890$		0			0
$891$	5.63901e8	−	5.63901e8i	0.797204	−	0.797204i
$892$		0			0
$893$	6.73533e8			0.945812
$894$		0			0
$895$	−3.10305e8	+	3.10305e8i	−0.432832	+	0.432832i
$896$		0			0
$897$	3.75477e8	−	1.07060e9i	0.520243	−	1.48338i
$898$		0			0
$899$	5.01556e8	+	5.01556e8i	0.690304	+	0.690304i
$900$		0			0
$901$		−	4.71315e7i		−	0.0644372i
$902$		0			0
$903$	−7.46521e8	−	7.46521e8i	−1.01386	−	1.01386i
$904$		0			0
$905$	−1.72550e8	+	1.72550e8i	−0.232793	+	0.232793i
$906$		0			0
$907$		−	8.30405e8i		−	1.11293i	−0.830871	−	0.556465i	$-0.812157\pi$
$907$		−	8.30405e8i		−	1.11293i	0.830871	−	0.556465i	$-0.187843\pi$
$908$		0			0
$909$		−	4.59334e6i		−	0.00611557i
$910$		0			0
$911$	8.82985e8			1.16788			0.583940	−	0.811797i	$-0.301510\pi$
$911$	8.82985e8			1.16788			0.583940	+	0.811797i	$0.301510\pi$
$912$		0			0
$913$	−8.86952e8			−1.16543
$914$		0			0
$915$	−4.67240e6	−	4.67240e6i	−0.00609925	−	0.00609925i
$916$		0			0
$917$	−1.52765e8	+	1.52765e8i	−0.198114	+	0.198114i
$918$		0			0
$919$	−3.41065e8			−0.439431			−0.219715	−	0.975564i	$-0.570513\pi$
$919$	−3.41065e8			−0.439431			−0.219715	+	0.975564i	$0.570513\pi$
$920$		0			0
$921$	9.46168e8	−	9.46168e8i	1.21113	−	1.21113i
$922$		0			0
$923$	−7.92601e7	−	1.64886e8i	−0.100798	−	0.209691i
$924$		0			0
$925$	−1.54986e8	−	1.54986e8i	−0.195825	−	0.195825i
$926$		0			0
$927$			2.04669e7i			0.0256929i
$928$		0			0
$929$	4.85048e8	+	4.85048e8i	0.604976	+	0.604976i	0.941629	−	0.336653i	$-0.109295\pi$
$929$	4.85048e8	+	4.85048e8i	0.604976	+	0.604976i	−0.336653	+	0.941629i	$0.609295\pi$
$930$		0			0
$931$	6.26497e7	−	6.26497e7i	0.0776372	−	0.0776372i
$932$		0			0
$933$		−	6.25154e8i		−	0.769737i
$934$		0			0
$935$			1.91954e8i			0.234834i
$936$		0			0
$937$	−1.08617e9			−1.32032			−0.660162	−	0.751123i	$-0.729512\pi$
$937$	−1.08617e9			−1.32032			−0.660162	+	0.751123i	$0.729512\pi$
$938$		0			0
$939$	−1.25525e8			−0.151612
$940$		0			0
$941$	6.01251e8	+	6.01251e8i	0.721584	+	0.721584i	0.968928	−	0.247344i	$-0.0795578\pi$
$941$	6.01251e8	+	6.01251e8i	0.721584	+	0.721584i	−0.247344	+	0.968928i	$0.579558\pi$
$942$		0			0
$943$	1.39466e9	−	1.39466e9i	1.66316	−	1.66316i
$944$		0			0
$945$	−5.31611e8			−0.629940
$946$		0			0
$947$	−4.43941e8	+	4.43941e8i	−0.522727	+	0.522727i	−0.918394	−	0.395667i	$-0.870513\pi$
$947$	−4.43941e8	+	4.43941e8i	−0.522727	+	0.522727i	0.395667	+	0.918394i	$0.370513\pi$
$948$		0			0
$949$	−1.39213e9	+	6.69192e8i	−1.62885	+	0.782982i
$950$		0			0
$951$	−2.89733e8	−	2.89733e8i	−0.336865	−	0.336865i
$952$		0			0
$953$			4.31464e8i			0.498501i	0.968439	+	0.249250i	$0.0801842\pi$
$953$			4.31464e8i			0.498501i	−0.968439	+	0.249250i	$0.919816\pi$
$954$		0			0
$955$	−1.66883e8	−	1.66883e8i	−0.191602	−	0.191602i
$956$		0			0
$957$	−1.00024e9	+	1.00024e9i	−1.14122	+	1.14122i
$958$		0			0
$959$			4.62856e8i			0.524795i
$960$		0			0
$961$		−	4.67691e8i		−	0.526974i
$962$		0			0
$963$	−1.59384e7			−0.0178471
$964$		0			0
$965$	−2.39062e8			−0.266029
$966$		0			0
$967$	1.87564e8	+	1.87564e8i	0.207429	+	0.207429i	0.803174	−	0.595745i	$-0.203143\pi$
$967$	1.87564e8	+	1.87564e8i	0.207429	+	0.207429i	−0.595745	+	0.803174i	$0.703143\pi$
$968$		0			0
$969$	−1.72718e8	+	1.72718e8i	−0.189830	+	0.189830i
$970$		0			0
$971$	2.27350e7			0.0248334			0.0124167	−	0.999923i	$-0.496048\pi$
$971$	2.27350e7			0.0248334			0.0124167	+	0.999923i	$0.496048\pi$
$972$		0			0
$973$	4.66688e8	−	4.66688e8i	0.506626	−	0.506626i
$974$		0			0
$975$	1.68529e8	−	4.80530e8i	0.181828	−	0.518450i
$976$		0			0
$977$	−2.59001e8	−	2.59001e8i	−0.277727	−	0.277727i	0.554474	−	0.832201i	$-0.312919\pi$
$977$	−2.59001e8	−	2.59001e8i	−0.277727	−	0.277727i	−0.832201	+	0.554474i	$0.812919\pi$
$978$		0			0
$979$		−	5.27247e8i		−	0.561909i
$980$		0			0
$981$	9.86946e6	+	9.86946e6i	0.0104541	+	0.0104541i
$982$		0			0
$983$	−4.20575e8	+	4.20575e8i	−0.442775	+	0.442775i	−0.892944	−	0.450169i	$-0.851364\pi$
$983$	−4.20575e8	+	4.20575e8i	−0.442775	+	0.442775i	0.450169	+	0.892944i	$0.351364\pi$
$984$		0			0
$985$			1.05132e9i			1.10009i
$986$		0			0
$987$		−	9.56336e8i		−	0.994624i
$988$		0			0
$989$	2.36872e9			2.44864
$990$		0			0
$991$	−1.02287e9			−1.05099			−0.525497	−	0.850795i	$-0.676121\pi$
$991$	−1.02287e9			−1.05099			−0.525497	+	0.850795i	$0.676121\pi$
$992$		0			0
$993$	−6.20862e8	−	6.20862e8i	−0.634085	−	0.634085i
$994$		0			0
$995$	−4.42997e8	+	4.42997e8i	−0.449709	+	0.449709i
$996$		0			0
$997$	−1.93138e9			−1.94887			−0.974434	−	0.224675i	$-0.927868\pi$
$997$	−1.93138e9			−1.94887			−0.974434	+	0.224675i	$0.927868\pi$
$998$		0			0
$999$	3.55265e8	−	3.55265e8i	0.356333	−	0.356333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.7.t.c.177.2		12
4.3	odd	2		13.7.d.a.8.5	yes	12
12.11	even	2		117.7.j.b.73.2		12
13.5	odd	4	inner	208.7.t.c.161.2		12
52.31	even	4		13.7.d.a.5.5	✓	12
156.83	odd	4		117.7.j.b.109.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.d.a.5.5	✓	12	52.31	even	4
13.7.d.a.8.5	yes	12	4.3	odd	2
117.7.j.b.73.2		12	12.11	even	2
117.7.j.b.109.2		12	156.83	odd	4
208.7.t.c.161.2		12	13.5	odd	4	inner
208.7.t.c.177.2		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	208.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-26.7789 q^{3} +(-59.0322 - 59.0322i) q^{5} +(226.950 - 226.950i) q^{7} -11.8881 q^{9} +O(q^{10})\)	\(q-26.7789 q^{3} +(-59.0322 - 59.0322i) q^{5} +(226.950 - 226.950i) q^{7} -11.8881 q^{9} +(-1078.96 + 1078.96i) q^{11} +(-2073.19 - 727.102i) q^{13} +(1580.82 + 1580.82i) q^{15} +1506.86i q^{17} +(-4280.27 - 4280.27i) q^{19} +(-6077.47 + 6077.47i) q^{21} -19283.9i q^{23} -8655.40i q^{25} +19840.2 q^{27} -34618.4 q^{29} +(-14488.1 - 14488.1i) q^{31} +(28893.4 - 28893.4i) q^{33} -26794.7 q^{35} +(17906.3 - 17906.3i) q^{37} +(55517.9 + 19471.0i) q^{39} +(72322.6 + 72322.6i) q^{41} +122834. i q^{43} +(701.778 + 701.778i) q^{45} +(-78678.8 + 78678.8i) q^{47} +14636.8i q^{49} -40352.0i q^{51} -31278.0 q^{53} +127387. q^{55} +(114621. + 114621. i) q^{57} +(26291.3 - 26291.3i) q^{59} -2955.68 q^{61} +(-2697.99 + 2697.99i) q^{63} +(79462.8 + 165308. i) q^{65} +(229598. + 229598. i) q^{67} +516403. i q^{69} +(58881.7 + 58881.7i) q^{71} +(497137. - 497137. i) q^{73} +231782. i q^{75} +489739. i q^{77} -48045.8 q^{79} -522633. q^{81} +(411022. + 411022. i) q^{83} +(88953.1 - 88953.1i) q^{85} +927044. q^{87} +(-244331. + 244331. i) q^{89} +(-635526. + 305495. i) q^{91} +(387977. + 387977. i) q^{93} +505348. i q^{95} +(417275. + 417275. i) q^{97} +(12826.7 - 12826.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 108 q^{5} - 398 q^{7} + 1940 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 108 * q^5 - 398 * q^7 + 1940 * q^9	\( 12 q + 4 q^{3} + 108 q^{5} - 398 q^{7} + 1940 q^{9} - 1686 q^{11} - 3926 q^{13} + 15268 q^{15} - 1766 q^{19} + 3428 q^{21} + 20464 q^{27} - 90108 q^{29} - 61014 q^{31} - 44452 q^{33} - 158772 q^{35} - 40212 q^{37} - 137852 q^{39} - 190416 q^{41} - 151444 q^{45} - 562446 q^{47} + 509136 q^{53} + 1264036 q^{55} + 939908 q^{57} + 994458 q^{59} + 1013696 q^{61} - 865778 q^{63} - 1130064 q^{65} + 1442386 q^{67} + 655866 q^{71} + 2588228 q^{73} + 75316 q^{79} - 4016140 q^{81} - 894966 q^{83} + 105396 q^{85} - 2109064 q^{87} - 977376 q^{89} - 1088750 q^{91} - 216268 q^{93} + 983388 q^{97} - 2894714 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 + 108 * q^5 - 398 * q^7 + 1940 * q^9 - 1686 * q^11 - 3926 * q^13 + 15268 * q^15 - 1766 * q^19 + 3428 * q^21 + 20464 * q^27 - 90108 * q^29 - 61014 * q^31 - 44452 * q^33 - 158772 * q^35 - 40212 * q^37 - 137852 * q^39 - 190416 * q^41 - 151444 * q^45 - 562446 * q^47 + 509136 * q^53 + 1264036 * q^55 + 939908 * q^57 + 994458 * q^59 + 1013696 * q^61 - 865778 * q^63 - 1130064 * q^65 + 1442386 * q^67 + 655866 * q^71 + 2588228 * q^73 + 75316 * q^79 - 4016140 * q^81 - 894966 * q^83 + 105396 * q^85 - 2109064 * q^87 - 977376 * q^89 - 1088750 * q^91 - 216268 * q^93 + 983388 * q^97 - 2894714 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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