LMFDB - Embedded newform 27.8.c.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,8,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, 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:	$8.43439568807$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{21} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.6
Root			$0.500000 + 11.4952i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.8.c.a.10.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.7051 - 18.5418i) q^{2} +(-165.199 - 286.133i) q^{4} +(-32.6274 - 56.5123i) q^{5} +(-118.194 + 204.717i) q^{7} -4333.37 q^{8} +O(q^{10})$	\(q+(10.7051 - 18.5418i) q^{2} +(-165.199 - 286.133i) q^{4} +(-32.6274 - 56.5123i) q^{5} +(-118.194 + 204.717i) q^{7} -4333.37 q^{8} -1397.12 q^{10} +(2305.59 - 3993.39i) q^{11} +(68.1364 + 118.016i) q^{13} +(2530.55 + 4383.04i) q^{14} +(-25243.8 + 43723.5i) q^{16} -5319.46 q^{17} +38228.5 q^{19} +(-10780.0 + 18671.5i) q^{20} +(-49363.1 - 85499.4i) q^{22} +(-36480.5 - 63186.1i) q^{23} +(36933.4 - 63970.5i) q^{25} +2917.63 q^{26} +78101.7 q^{28} +(35682.4 - 61803.7i) q^{29} +(28810.3 + 49900.8i) q^{31} +(263139. + 455770. i) q^{32} +(-56945.4 + 98632.4i) q^{34} +15425.4 q^{35} +88485.6 q^{37} +(409240. - 708824. i) q^{38} +(141387. + 244889. i) q^{40} +(127791. + 221341. i) q^{41} +(324806. - 562580. i) q^{43} -1.52352e6 q^{44} -1.56211e6 q^{46} +(-522539. + 905063. i) q^{47} +(383832. + 664817. i) q^{49} +(-790752. - 1.36962e6i) q^{50} +(22512.1 - 38992.1i) q^{52} +777845. q^{53} -300901. q^{55} +(512177. - 887116. i) q^{56} +(-763967. - 1.32323e6i) q^{58} +(1.01959e6 + 1.76598e6i) q^{59} +(-927927. + 1.60722e6i) q^{61} +1.23367e6 q^{62} +4.80532e6 q^{64} +(4446.23 - 7701.10i) q^{65} +(1.81717e6 + 3.14743e6i) q^{67} +(878768. + 1.52207e6i) q^{68} +(165131. - 286015. i) q^{70} -1.93117e6 q^{71} -2.06016e6 q^{73} +(947248. - 1.64068e6i) q^{74} +(-6.31529e6 - 1.09384e7i) q^{76} +(545011. + 943987. i) q^{77} +(3.13421e6 - 5.42860e6i) q^{79} +3.29456e6 q^{80} +5.47209e6 q^{82} +(-568792. + 985177. i) q^{83} +(173560. + 300615. i) q^{85} +(-6.95416e6 - 1.20450e7i) q^{86} +(-9.99096e6 + 1.73049e7i) q^{88} +428904. q^{89} -32213.2 q^{91} +(-1.20531e7 + 2.08765e7i) q^{92} +(1.11877e7 + 1.93776e7i) q^{94} +(-1.24730e6 - 2.16038e6i) q^{95} +(5.85362e6 - 1.01388e7i) q^{97} +1.64359e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) $ 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	10.7051	−	18.5418i	0.946207	−	1.63888i	0.192890	−	0.981220i	$-0.438214\pi$
$2$	10.7051	−	18.5418i	0.946207	−	1.63888i	0.753317	−	0.657658i	$-0.228453\pi$
$3$		0			0
$3$		0			0
$4$	−165.199	−	286.133i	−1.29061	−	2.23541i
$5$	−32.6274	−	56.5123i	−0.116731	−	0.202185i	0.801739	−	0.597674i	$-0.203908\pi$
$5$	−32.6274	−	56.5123i	−0.116731	−	0.202185i	−0.918471	+	0.395489i	$0.870575\pi$
$6$		0			0
$7$	−118.194	+	204.717i	−0.130242	+	0.225586i	−0.923770	−	0.382948i	$-0.874909\pi$
$7$	−118.194	+	204.717i	−0.130242	+	0.225586i	0.793528	+	0.608534i	$0.208242\pi$
$8$	−4333.37			−2.99234
$9$		0			0
$10$	−1397.12			−0.441808
$11$	2305.59	−	3993.39i	0.522284	−	0.904623i	−0.477379	−	0.878697i	$-0.658413\pi$
$11$	2305.59	−	3993.39i	0.522284	−	0.904623i	0.999664	−	0.0259259i	$-0.00825339\pi$
$12$		0			0
$13$	68.1364	+	118.016i	0.00860157	+	0.0148984i	0.870294	−	0.492532i	$-0.163929\pi$
$13$	68.1364	+	118.016i	0.00860157	+	0.0148984i	−0.861693	+	0.507431i	$0.830595\pi$
$14$	2530.55	+	4383.04i	0.246472	+	0.426901i
$15$		0			0
$16$	−25243.8	+	43723.5i	−1.54076	+	2.66867i
$17$	−5319.46			−0.262601			−0.131301	−	0.991343i	$-0.541915\pi$
$17$	−5319.46			−0.262601			−0.131301	+	0.991343i	$0.541915\pi$
$18$		0			0
$19$	38228.5			1.27864			0.639321	−	0.768940i	$-0.279215\pi$
$19$	38228.5			1.27864			0.639321	+	0.768940i	$0.279215\pi$
$20$	−10780.0	+	18671.5i	−0.301310	+	0.521885i
$21$		0			0
$22$	−49363.1	−	85499.4i	−0.988378	−	1.71192i
$23$	−36480.5	−	63186.1i	−0.625192	−	1.08286i	−0.988504	−	0.151197i	$-0.951687\pi$
$23$	−36480.5	−	63186.1i	−0.625192	−	1.08286i	0.363311	−	0.931668i	$-0.381646\pi$
$24$		0			0
$25$	36933.4	−	63970.5i	0.472748	−	0.818823i
$26$	2917.63			0.0325554
$27$		0			0
$28$	78101.7			0.672369
$29$	35682.4	−	61803.7i	0.271682	−	0.470567i	−0.697611	−	0.716477i	$-0.745754\pi$
$29$	35682.4	−	61803.7i	0.271682	−	0.470567i	0.969293	+	0.245910i	$0.0790868\pi$
$30$		0			0
$31$	28810.3	+	49900.8i	0.173693	+	0.300844i	0.939708	−	0.341978i	$-0.111097\pi$
$31$	28810.3	+	49900.8i	0.173693	+	0.300844i	−0.766015	+	0.642822i	$0.777763\pi$
$32$	263139.	+	455770.i	1.41958	+	2.45879i
$33$		0			0
$34$	−56945.4	+	98632.4i	−0.248475	+	0.430371i
$35$	15425.4			0.0608133
$36$		0			0
$37$	88485.6			0.287188			0.143594	−	0.989637i	$-0.454134\pi$
$37$	88485.6			0.287188			0.143594	+	0.989637i	$0.454134\pi$
$38$	409240.	−	708824.i	1.20986	−	2.09554i
$39$		0			0
$40$	141387.	+	244889.i	0.349300	+	0.605005i
$41$	127791.	+	221341.i	0.289573	+	0.501555i	0.973708	−	0.227800i	$-0.0731533\pi$
$41$	127791.	+	221341.i	0.289573	+	0.501555i	−0.684135	+	0.729356i	$0.739820\pi$
$42$		0			0
$43$	324806.	−	562580.i	0.622994	−	1.07906i	−0.365931	−	0.930642i	$-0.619249\pi$
$43$	324806.	−	562580.i	0.622994	−	1.07906i	0.988925	−	0.148415i	$-0.0474172\pi$
$44$	−1.52352e6			−2.69627
$45$		0			0
$46$	−1.56211e6			−2.36624
$47$	−522539.	+	905063.i	−0.734135	+	1.27156i	0.220967	+	0.975281i	$0.429079\pi$
$47$	−522539.	+	905063.i	−0.734135	+	1.27156i	−0.955102	+	0.296277i	$0.904255\pi$
$48$		0			0
$49$	383832.	+	664817.i	0.466074	+	0.807264i
$50$	−790752.	−	1.36962e6i	−0.894634	−	1.54955i
$51$		0			0
$52$	22512.1	−	38992.1i	0.0222026	−	0.0384561i
$53$	777845.			0.717675			0.358837	−	0.933400i	$-0.383173\pi$
$53$	777845.			0.717675			0.358837	+	0.933400i	$0.383173\pi$
$54$		0			0
$55$	−300901.			−0.243868
$56$	512177.	−	887116.i	0.389728	−	0.675029i
$57$		0			0
$58$	−763967.	−	1.32323e6i	−0.514134	−	0.890507i
$59$	1.01959e6	+	1.76598e6i	0.646314	+	1.11945i	0.983996	+	0.178189i	$0.0570237\pi$
$59$	1.01959e6	+	1.76598e6i	0.646314	+	1.11945i	−0.337682	+	0.941260i	$0.609643\pi$
$60$		0			0
$61$	−927927.	+	1.60722e6i	−0.523431	+	0.906609i	0.476197	+	0.879339i	$0.342015\pi$
$61$	−927927.	+	1.60722e6i	−0.523431	+	0.906609i	−0.999628	+	0.0272705i	$0.991318\pi$
$62$	1.23367e6			0.657396
$63$		0			0
$64$	4.80532e6			2.29135
$65$	4446.23	−	7701.10i	0.00200815	−	0.00347821i
$66$		0			0
$67$	1.81717e6	+	3.14743e6i	0.738131	+	1.27848i	0.953336	+	0.301911i	$0.0976247\pi$
$67$	1.81717e6	+	3.14743e6i	0.738131	+	1.27848i	−0.215205	+	0.976569i	$0.569042\pi$
$68$	878768.	+	1.52207e6i	0.338917	+	0.587021i
$69$		0			0
$70$	165131.	−	286015.i	0.0575419	−	0.0996656i
$71$	−1.93117e6			−0.640348			−0.320174	−	0.947359i	$-0.603741\pi$
$71$	−1.93117e6			−0.640348			−0.320174	+	0.947359i	$0.603741\pi$
$72$		0			0
$73$	−2.06016e6			−0.619826			−0.309913	−	0.950765i	$-0.600300\pi$
$73$	−2.06016e6			−0.619826			−0.309913	+	0.950765i	$0.600300\pi$
$74$	947248.	−	1.64068e6i	0.271740	−	0.470667i
$75$		0			0
$76$	−6.31529e6	−	1.09384e7i	−1.65024	−	2.85829i
$77$	545011.	+	943987.i	0.136047	+	0.235640i
$78$		0			0
$79$	3.13421e6	−	5.42860e6i	0.715208	−	1.23878i	−0.247671	−	0.968844i	$-0.579665\pi$
$79$	3.13421e6	−	5.42860e6i	0.715208	−	1.23878i	0.962879	−	0.269933i	$-0.0870016\pi$
$80$	3.29456e6			0.719419
$81$		0			0
$82$	5.47209e6			1.09598
$83$	−568792.	+	985177.i	−0.109189	+	0.189122i	−0.915442	−	0.402450i	$-0.868159\pi$
$83$	−568792.	+	985177.i	−0.109189	+	0.189122i	0.806253	+	0.591571i	$0.201492\pi$
$84$		0			0
$85$	173560.	+	300615.i	0.0306538	+	0.0530939i
$86$	−6.95416e6	−	1.20450e7i	−1.17896	−	2.04202i
$87$		0			0
$88$	−9.99096e6	+	1.73049e7i	−1.56285	+	2.70694i
$89$	428904.			0.0644904			0.0322452	−	0.999480i	$-0.489734\pi$
$89$	428904.			0.0644904			0.0322452	+	0.999480i	$0.489734\pi$
$90$		0			0
$91$	−32213.2			−0.00448114
$92$	−1.20531e7	+	2.08765e7i	−1.61376	+	2.79512i
$93$		0			0
$94$	1.11877e7	+	1.93776e7i	1.38929	+	2.40632i
$95$	−1.24730e6	−	2.16038e6i	−0.149258	−	0.258522i
$96$		0			0
$97$	5.85362e6	−	1.01388e7i	0.651214	−	1.12793i	−0.331615	−	0.943415i	$-0.607594\pi$
$97$	5.85362e6	−	1.01388e7i	0.651214	−	1.12793i	0.982829	−	0.184520i	$-0.0590731\pi$
$98$	1.64359e7			1.76401
$99$		0			0
$100$	−2.44054e7			−2.44054
$101$	9.34885e6	−	1.61927e7i	0.902887	−	1.56385i	0.0791589	−	0.996862i	$-0.474777\pi$
$101$	9.34885e6	−	1.61927e7i	0.902887	−	1.56385i	0.823728	−	0.566985i	$-0.191890\pi$
$102$		0			0
$103$	414577.	+	718068.i	0.0373830	+	0.0647493i	0.884112	−	0.467276i	$-0.154764\pi$
$103$	414577.	+	718068.i	0.0373830	+	0.0647493i	−0.846729	+	0.532025i	$0.821431\pi$
$104$	−295260.	−	511406.i	−0.0257388	−	0.0445809i
$105$		0			0
$106$	8.32692e6	−	1.44226e7i	0.679069	−	1.17618i
$107$	−9.20798e6			−0.726643			−0.363322	−	0.931664i	$-0.618357\pi$
$107$	−9.20798e6			−0.726643			−0.363322	+	0.931664i	$0.618357\pi$
$108$		0			0
$109$	−1.08593e7			−0.803174			−0.401587	−	0.915821i	$-0.631541\pi$
$109$	−1.08593e7			−0.803174			−0.401587	+	0.915821i	$0.631541\pi$
$110$	−3.22118e6	+	5.57925e6i	−0.230749	+	0.399670i
$111$		0			0
$112$	−5.96731e6	−	1.03357e7i	−0.401343	−	0.695146i
$113$	−3.17666e6	−	5.50213e6i	−0.207107	−	0.358720i	0.743695	−	0.668519i	$-0.233072\pi$
$113$	−3.17666e6	−	5.50213e6i	−0.207107	−	0.358720i	−0.950802	+	0.309799i	$0.899738\pi$
$114$		0			0
$115$	−2.38053e6	+	4.12320e6i	−0.145959	+	0.252809i
$116$	−2.35787e7			−1.40255
$117$		0			0
$118$	4.36593e7			2.44619
$119$	628726.	−	1.08899e6i	0.0342017	−	0.0592390i
$120$		0			0
$121$	−887875.	−	1.53784e6i	−0.0455620	−	0.0789157i
$122$	1.98671e7	+	3.44109e7i	0.990548	+	1.71568i
$123$		0			0
$124$	9.51884e6	−	1.64871e7i	0.448340	−	0.776548i
$125$	−9.91820e6			−0.454201
$126$		0			0
$127$	−1.79848e7			−0.779100			−0.389550	−	0.921005i	$-0.627369\pi$
$127$	−1.79848e7			−0.779100			−0.389550	+	0.921005i	$0.627369\pi$
$128$	1.77597e7	−	3.07606e7i	0.748514	−	1.29646i
$129$		0			0
$130$	−95194.7	−	164882.i	−0.00380024	−	0.00658221i
$131$	1.88048e6	+	3.25708e6i	0.0730834	+	0.126584i	0.900251	−	0.435371i	$-0.143383\pi$
$131$	1.88048e6	+	3.25708e6i	0.0730834	+	0.126584i	−0.827168	+	0.561955i	$0.810049\pi$
$132$		0			0
$133$	−4.51836e6	+	7.82603e6i	−0.166533	+	0.288443i
$134$	7.78119e7			2.79370
$135$		0			0
$136$	2.30512e7			0.785792
$137$	652403.	−	1.13000e6i	0.0216767	−	0.0375452i	−0.854984	−	0.518655i	$-0.826433\pi$
$137$	652403.	−	1.13000e6i	0.0216767	−	0.0375452i	0.876660	+	0.481110i	$0.159766\pi$
$138$		0			0
$139$	5.83704e6	+	1.01101e7i	0.184349	+	0.319302i	0.943357	−	0.331779i	$-0.107649\pi$
$139$	5.83704e6	+	1.01101e7i	0.184349	+	0.319302i	−0.759008	+	0.651081i	$0.774316\pi$
$140$	−2.54826e6	−	4.41371e6i	−0.0784865	−	0.135943i
$141$		0			0
$142$	−2.06734e7	+	3.58073e7i	−0.605902	+	1.04945i
$143$	628378.			0.0179699
$144$		0			0
$145$	−4.65689e6			−0.126855
$146$	−2.20542e7	+	3.81990e7i	−0.586484	+	1.01582i
$147$		0			0
$148$	−1.46177e7	−	2.53186e7i	−0.370649	−	0.641984i
$149$	1.59389e7	+	2.76070e7i	0.394736	+	0.683703i	0.993067	−	0.117546i	$-0.0375027\pi$
$149$	1.59389e7	+	2.76070e7i	0.394736	+	0.683703i	−0.598331	+	0.801249i	$0.704169\pi$
$150$		0			0
$151$	−3.55648e7	+	6.16000e7i	−0.840622	+	1.45600i	0.0487485	+	0.998811i	$0.484477\pi$
$151$	−3.55648e7	+	6.16000e7i	−0.840622	+	1.45600i	−0.889370	+	0.457188i	$0.848857\pi$
$152$	−1.65658e8			−3.82613
$153$		0			0
$154$	2.33376e7			0.514913
$155$	1.88001e6	−	3.25627e6i	0.0405507	−	0.0702360i
$156$		0			0
$157$	−3.52217e7	−	6.10057e7i	−0.726375	−	1.25812i	−0.958405	−	0.285411i	$-0.907870\pi$
$157$	−3.52217e7	−	6.10057e7i	−0.726375	−	1.25812i	0.232030	−	0.972709i	$-0.425463\pi$
$158$	−6.71040e7	−	1.16228e8i	−1.35347	−	2.34428i
$159$		0			0
$160$	1.71711e7	−	2.97412e7i	0.331419	−	0.574035i
$161$	1.72471e7			0.325705
$162$		0			0
$163$	3.98423e7			0.720590			0.360295	−	0.932838i	$-0.382676\pi$
$163$	3.98423e7			0.720590			0.360295	+	0.932838i	$0.382676\pi$
$164$	4.22220e7	−	7.31306e7i	0.747455	−	1.29463i
$165$		0			0
$166$	1.21780e7	+	2.10929e7i	0.206631	+	0.357896i
$167$	2.58421e7	+	4.47599e7i	0.429359	+	0.743672i	0.996816	−	0.0797308i	$-0.0254061\pi$
$167$	2.58421e7	+	4.47599e7i	0.429359	+	0.743672i	−0.567457	+	0.823403i	$0.692073\pi$
$168$		0			0
$169$	3.13650e7	−	5.43257e7i	0.499852	−	0.865769i
$170$	7.43193e6			0.116019
$171$		0			0
$172$	−2.14630e8			−3.21618
$173$	9.10891e6	−	1.57771e7i	0.133753	−	0.231668i	−0.791367	−	0.611341i	$-0.790630\pi$
$173$	9.10891e6	−	1.57771e7i	0.133753	−	0.231668i	0.925121	+	0.379673i	$0.123964\pi$
$174$		0			0
$175$	8.73059e6	+	1.51218e7i	0.123143	+	0.213290i
$176$	1.16403e8	+	2.01617e8i	1.60943	+	2.78761i
$177$		0			0
$178$	4.59147e6	−	7.95265e6i	0.0610213	−	0.105692i
$179$	−1.05708e8			−1.37759			−0.688797	−	0.724955i	$-0.741861\pi$
$179$	−1.05708e8			−1.37759			−0.688797	+	0.724955i	$0.741861\pi$
$180$		0			0
$181$	1.29009e8			1.61713			0.808566	−	0.588406i	$-0.200244\pi$
$181$	1.29009e8			1.61713			0.808566	+	0.588406i	$0.200244\pi$
$182$	−344845.	+	597290.i	−0.00424008	+	0.00734404i
$183$		0			0
$184$	1.58084e8	+	2.73809e8i	1.87079	+	3.24030i
$185$	−2.88706e6	−	5.00053e6i	−0.0335239	−	0.0580651i
$186$		0			0
$187$	−1.22645e7	+	2.12427e7i	−0.137152	+	0.237555i
$188$	3.45291e8			3.78994
$189$		0			0
$190$	−5.34097e7			−0.564915
$191$	8.43634e6	−	1.46122e7i	0.0876067	−	0.151739i	−0.818892	−	0.573947i	$-0.805411\pi$
$191$	8.43634e6	−	1.46122e7i	0.0876067	−	0.151739i	0.906499	+	0.422208i	$0.138745\pi$
$192$		0			0
$193$	−3.10280e7	−	5.37420e7i	−0.310672	−	0.538100i	0.667836	−	0.744309i	$-0.267221\pi$
$193$	−3.10280e7	−	5.37420e7i	−0.310672	−	0.538100i	−0.978508	+	0.206208i	$0.933888\pi$
$194$	−1.25327e8	−	2.17073e8i	−1.23237	−	2.13452i
$195$		0			0
$196$	1.26817e8	−	2.19654e8i	1.20304	−	2.08373i
$197$	7.26554e6			0.0677074			0.0338537	−	0.999427i	$-0.489222\pi$
$197$	7.26554e6			0.0677074			0.0338537	+	0.999427i	$0.489222\pi$
$198$		0			0
$199$	6.21194e7			0.558780			0.279390	−	0.960178i	$-0.409868\pi$
$199$	6.21194e7			0.558780			0.279390	+	0.960178i	$0.409868\pi$
$200$	−1.60046e8	+	2.77208e8i	−1.41462	+	2.45020i
$201$		0			0
$202$	−2.00161e8	−	3.46689e8i	−1.70864	−	2.95944i
$203$	8.43485e6	+	1.46096e7i	0.0707687	+	0.122575i
$204$		0			0
$205$	8.33901e6	−	1.44436e7i	0.0676045	−	0.117095i
$206$	1.77524e7			0.141488
$207$		0			0
$208$	−6.88008e6			−0.0530117
$209$	8.81390e7	−	1.52661e8i	0.667815	−	1.15669i
$210$		0			0
$211$	8.98867e7	+	1.55688e8i	0.658729	+	1.14095i	0.980945	+	0.194286i	$0.0622390\pi$
$211$	8.98867e7	+	1.55688e8i	0.658729	+	1.14095i	−0.322216	+	0.946666i	$0.604428\pi$
$212$	−1.28499e8	−	2.22567e8i	−0.926241	−	1.60430i
$213$		0			0
$214$	−9.85725e7	+	1.70733e8i	−0.687555	+	1.19088i
$215$	−4.23903e7			−0.290892
$216$		0			0
$217$	−1.36208e7			−0.0904882
$218$	−1.16250e8	+	2.01351e8i	−0.759969	+	1.31630i
$219$		0			0
$220$	4.97085e7	+	8.60976e7i	0.314740	+	0.545145i
$221$	−362449.	−	627780.i	−0.00225878	−	0.00391232i
$222$		0			0
$223$	−3.72429e7	+	6.45066e7i	−0.224893	+	0.389527i	−0.956287	−	0.292428i	$-0.905537\pi$
$223$	−3.72429e7	+	6.45066e7i	−0.224893	+	0.389527i	0.731394	+	0.681955i	$0.238870\pi$
$224$	−1.24405e8			−0.739556
$225$		0			0
$226$	−1.36026e8			−0.783866
$227$	−1.06638e8	+	1.84702e8i	−0.605090	+	1.04805i	0.386948	+	0.922102i	$0.373529\pi$
$227$	−1.06638e8	+	1.84702e8i	−0.605090	+	1.04805i	−0.992037	+	0.125944i	$0.959804\pi$
$228$		0			0
$229$	−7.52916e7	−	1.30409e8i	−0.414307	−	0.717601i	0.581048	−	0.813869i	$-0.302643\pi$
$229$	−7.52916e7	−	1.30409e8i	−0.414307	−	0.717601i	−0.995355	+	0.0962682i	$0.969309\pi$
$230$	5.09677e7	+	8.82786e7i	0.276215	+	0.478418i
$231$		0			0
$232$	−1.54625e8	+	2.67818e8i	−0.812964	+	1.40810i
$233$	1.27302e8			0.659309			0.329654	−	0.944102i	$-0.393068\pi$
$233$	1.27302e8			0.659309			0.329654	+	0.944102i	$0.393068\pi$
$234$		0			0
$235$	6.81963e7			0.342786
$236$	3.36870e8	−	5.83476e8i	1.66828	−	2.88955i
$237$		0			0
$238$	−1.34612e7	−	2.33154e7i	−0.0647237	−	0.112105i
$239$	1.55897e8	+	2.70021e8i	0.738659	+	1.27940i	0.953099	+	0.302658i	$0.0978740\pi$
$239$	1.55897e8	+	2.70021e8i	0.738659	+	1.27940i	−0.214440	+	0.976737i	$0.568793\pi$
$240$		0			0
$241$	−2.32957e7	+	4.03494e7i	−0.107205	+	0.185685i	−0.914637	−	0.404276i	$-0.867524\pi$
$241$	−2.32957e7	+	4.03494e7i	−0.107205	+	0.185685i	0.807432	+	0.589961i	$0.200857\pi$
$242$	−3.80192e7			−0.172444
$243$		0			0
$244$	6.13169e8			2.70219
$245$	2.50469e7	−	4.33825e7i	0.108811	−	0.188466i
$246$		0			0
$247$	2.60475e6	+	4.51156e6i	0.0109983	+	0.0190497i
$248$	−1.24846e8	−	2.16239e8i	−0.519747	−	0.900229i
$249$		0			0
$250$	−1.06175e8	+	1.83901e8i	−0.429768	+	0.744380i
$251$	−2.93904e8			−1.17313			−0.586567	−	0.809901i	$-0.699521\pi$
$251$	−2.93904e8			−1.17313			−0.586567	+	0.809901i	$0.699521\pi$
$252$		0			0
$253$	−3.36436e8			−1.30611
$254$	−1.92529e8	+	3.33471e8i	−0.737190	+	1.27685i
$255$		0			0
$256$	−7.26979e7	−	1.25916e8i	−0.270821	−	0.469075i
$257$	1.43637e7	+	2.48786e7i	0.0527837	+	0.0914240i	0.891210	−	0.453591i	$-0.149857\pi$
$257$	1.43637e7	+	2.48786e7i	0.0527837	+	0.0914240i	−0.838426	+	0.545015i	$0.816524\pi$
$258$		0			0
$259$	−1.04584e7	+	1.81145e7i	−0.0374040	+	0.0647856i
$260$	−2.93805e6			−0.0103670
$261$		0			0
$262$	8.05229e7			0.276608
$263$	−1.05540e8	+	1.82800e8i	−0.357743	+	0.619630i	−0.987583	−	0.157095i	$-0.949787\pi$
$263$	−1.05540e8	+	1.82800e8i	−0.357743	+	0.619630i	0.629840	+	0.776725i	$0.283120\pi$
$264$		0			0
$265$	−2.53791e7	−	4.39578e7i	−0.0837751	−	0.145103i
$266$	9.67391e7	+	1.67557e8i	0.315149	+	0.545854i
$267$		0			0
$268$	6.00388e8	−	1.03990e9i	1.90529	−	3.30005i
$269$	3.22090e8			1.00889			0.504446	−	0.863444i	$-0.331697\pi$
$269$	3.22090e8			1.00889			0.504446	+	0.863444i	$0.331697\pi$
$270$		0			0
$271$	−3.74530e8			−1.14313			−0.571563	−	0.820558i	$-0.693663\pi$
$271$	−3.74530e8			−1.14313			−0.571563	+	0.820558i	$0.693663\pi$
$272$	1.34283e8	−	2.32586e8i	0.404605	−	0.700796i
$273$		0			0
$274$	−1.39681e7	−	2.41934e7i	−0.0410214	−	0.0710511i
$275$	−1.70306e8	−	2.94979e8i	−0.493817	−	0.855317i
$276$		0			0
$277$	8.96175e7	−	1.55222e8i	0.253346	−	0.438808i	−0.711099	−	0.703092i	$-0.751802\pi$
$277$	8.96175e7	−	1.55222e8i	0.253346	−	0.438808i	0.964445	+	0.264284i	$0.0851357\pi$
$278$	2.49945e8			0.697730
$279$		0			0
$280$	−6.68440e7			−0.181974
$281$	1.99247e8	−	3.45106e8i	0.535697	−	0.927854i	−0.463432	−	0.886132i	$-0.653382\pi$
$281$	1.99247e8	−	3.45106e8i	0.535697	−	0.927854i	0.999129	−	0.0417220i	$-0.0132844\pi$
$282$		0			0
$283$	1.71350e8	+	2.96786e8i	0.449397	+	0.778379i	0.998347	−	0.0574763i	$-0.0183054\pi$
$283$	1.71350e8	+	2.96786e8i	0.449397	+	0.778379i	−0.548949	+	0.835856i	$0.684972\pi$
$284$	3.19027e8	+	5.52570e8i	0.826443	+	1.43144i
$285$		0			0
$286$	6.72685e6	−	1.16512e7i	0.0170032	−	0.0294504i
$287$	−6.04165e7			−0.150858
$288$		0			0
$289$	−3.82042e8			−0.931041
$290$	−4.98525e7	+	8.63471e7i	−0.120031	+	0.207900i
$291$		0			0
$292$	3.40335e8	+	5.89477e8i	0.799957	+	1.38557i
$293$	−3.04388e8	−	5.27216e8i	−0.706954	−	1.22448i	−0.965982	−	0.258610i	$-0.916735\pi$
$293$	−3.04388e8	−	5.27216e8i	−0.706954	−	1.22448i	0.259028	−	0.965870i	$-0.416598\pi$
$294$		0			0
$295$	6.65332e7	−	1.15239e8i	0.150890	−	0.261350i
$296$	−3.83441e8			−0.859365
$297$		0			0
$298$	6.82511e8			1.49401
$299$	4.97130e6	−	8.61055e6i	0.0107553	−	0.0186287i
$300$		0			0
$301$	7.67799e7	+	1.32987e8i	0.162280	+	0.281077i
$302$	7.61449e8	+	1.31887e9i	1.59080	+	2.75535i
$303$		0			0
$304$	−9.65031e8	+	1.67148e9i	−1.97008	+	3.41228i
$305$	1.21103e8			0.244403
$306$		0			0
$307$	5.84300e8			1.15253			0.576265	−	0.817263i	$-0.304510\pi$
$307$	5.84300e8			1.15253			0.576265	+	0.817263i	$0.304510\pi$
$308$	1.80070e8	−	3.11891e8i	0.351168	−	0.608240i
$309$		0			0
$310$	−4.02514e7	−	6.97175e7i	−0.0767388	−	0.132915i
$311$	−1.46239e8	−	2.53294e8i	−0.275678	−	0.477489i	0.694628	−	0.719369i	$-0.255569\pi$
$311$	−1.46239e8	−	2.53294e8i	−0.275678	−	0.477489i	−0.970306	+	0.241881i	$0.922236\pi$
$312$		0			0
$313$	4.13742e8	−	7.16621e8i	0.762648	−	1.32094i	−0.178834	−	0.983879i	$-0.557232\pi$
$313$	4.13742e8	−	7.16621e8i	0.762648	−	1.32094i	0.941481	−	0.337065i	$-0.109434\pi$
$314$	−1.50821e9			−2.74921
$315$		0			0
$316$	−2.07107e9			−3.69223
$317$	1.21830e7	−	2.11016e7i	0.0214807	−	0.0372057i	−0.855085	−	0.518487i	$-0.826495\pi$
$317$	1.21830e7	−	2.11016e7i	0.0214807	−	0.0372057i	0.876566	+	0.481282i	$0.159829\pi$
$318$		0			0
$319$	−1.64538e8	−	2.84987e8i	−0.283790	−	0.491539i
$320$	−1.56785e8	−	2.71560e8i	−0.267473	−	0.463277i
$321$		0			0
$322$	1.84632e8	−	3.19791e8i	0.308184	−	0.533791i
$323$	−2.03355e8			−0.335773
$324$		0			0
$325$	1.00660e7			0.0162655
$326$	4.26516e8	−	7.38748e8i	0.681827	−	1.18096i
$327$		0			0
$328$	−5.53768e8	−	9.59154e8i	−0.866501	−	1.50082i
$329$	−1.23521e8	−	2.13945e8i	−0.191230	−	0.331221i
$330$		0			0
$331$	8.03016e6	−	1.39086e7i	0.0121710	−	0.0210808i	−0.859876	−	0.510503i	$-0.829459\pi$
$331$	8.03016e6	−	1.39086e7i	0.0121710	−	0.0210808i	0.872047	+	0.489423i	$0.162792\pi$
$332$	3.75855e8			0.563686
$333$		0			0
$334$	1.10657e9			1.62505
$335$	1.18579e8	−	2.05385e8i	0.172326	−	0.298478i
$336$		0			0
$337$	1.21283e8	+	2.10068e8i	0.172621	+	0.298989i	0.939335	−	0.343000i	$-0.111443\pi$
$337$	1.21283e8	+	2.10068e8i	0.172621	+	0.298989i	−0.766714	+	0.641988i	$0.778110\pi$
$338$	−6.71531e8	−	1.16313e9i	−0.945927	−	1.63839i
$339$		0			0
$340$	5.73439e7	−	9.93225e7i	0.0791245	−	0.137048i
$341$	2.65698e8			0.362868
$342$		0			0
$343$	−3.76141e8			−0.503293
$344$	−1.40750e9	+	2.43787e9i	−1.86421	+	3.22891i
$345$		0			0
$346$	−1.95024e8	−	3.37791e8i	−0.253117	−	0.438411i
$347$	2.06422e8	+	3.57534e8i	0.265218	+	0.459372i	0.967621	−	0.252408i	$-0.0812226\pi$
$347$	2.06422e8	+	3.57534e8i	0.265218	+	0.459372i	−0.702402	+	0.711780i	$0.747889\pi$
$348$		0			0
$349$	−2.60275e8	+	4.50809e8i	−0.327750	+	0.567680i	−0.982065	−	0.188542i	$-0.939624\pi$
$349$	−2.60275e8	+	4.50809e8i	−0.327750	+	0.567680i	0.654315	+	0.756222i	$0.272957\pi$
$350$	3.73847e8			0.466075
$351$		0			0
$352$	2.42676e9			2.96570
$353$	−7.22672e8	+	1.25170e9i	−0.874439	+	1.51457i	−0.0170799	+	0.999854i	$0.505437\pi$
$353$	−7.22672e8	+	1.25170e9i	−0.874439	+	1.51457i	−0.857359	+	0.514719i	$0.827896\pi$
$354$		0			0
$355$	6.30090e7	+	1.09135e8i	0.0747487	+	0.129469i
$356$	−7.08544e7	−	1.22723e8i	−0.0832323	−	0.144163i
$357$		0			0
$358$	−1.13161e9	+	1.96001e9i	−1.30349	+	2.25771i
$359$	1.00008e9			1.14079			0.570395	−	0.821371i	$-0.306790\pi$
$359$	1.00008e9			1.14079			0.570395	+	0.821371i	$0.306790\pi$
$360$		0			0
$361$	5.67544e8			0.634927
$362$	1.38106e9	−	2.39206e9i	1.53014	−	2.65028i
$363$		0			0
$364$	5.32157e6	+	9.21723e6i	0.00578342	+	0.0100172i
$365$	6.72175e7	+	1.16424e8i	0.0723532	+	0.125319i
$366$		0			0
$367$	−3.98743e8	+	6.90644e8i	−0.421078	+	0.729328i	−0.996045	−	0.0888481i	$-0.971681\pi$
$367$	−3.98743e8	+	6.90644e8i	−0.421078	+	0.729328i	0.574967	+	0.818176i	$0.305015\pi$
$368$	3.68362e9			3.85308
$369$		0			0
$370$	−1.23625e8			−0.126882
$371$	−9.19363e7	+	1.59238e8i	−0.0934713	+	0.161897i
$372$		0			0
$373$	−1.30751e8	−	2.26468e8i	−0.130456	−	0.225957i	0.793396	−	0.608705i	$-0.208311\pi$
$373$	−1.30751e8	−	2.26468e8i	−0.130456	−	0.225957i	−0.923853	+	0.382749i	$0.874978\pi$
$374$	2.62585e8	+	4.54811e8i	0.259549	+	0.449552i
$375$		0			0
$376$	2.26435e9	−	3.92198e9i	2.19678	−	3.80494i
$377$	9.72507e6			0.00934756
$378$		0			0
$379$	−3.42925e8			−0.323565			−0.161782	−	0.986826i	$-0.551724\pi$
$379$	−3.42925e8			−0.323565			−0.161782	+	0.986826i	$0.551724\pi$
$380$	−4.12103e8	+	7.13784e8i	−0.385268	+	0.667305i
$381$		0			0
$382$	−1.80624e8	−	3.12850e8i	−0.165788	−	0.287153i
$383$	5.05976e8	+	8.76376e8i	0.460187	+	0.797067i	0.998970	−	0.0453777i	$-0.0144491\pi$
$383$	5.05976e8	+	8.76376e8i	0.460187	+	0.797067i	−0.538783	+	0.842444i	$0.681116\pi$
$384$		0			0
$385$	3.55646e7	−	6.15997e7i	0.0317618	−	0.0550131i
$386$	−1.32863e9			−1.17584
$387$		0			0
$388$	−3.86804e9			−3.36186
$389$	−6.08222e8	+	1.05347e9i	−0.523888	+	0.907400i	0.475725	+	0.879594i	$0.342186\pi$
$389$	−6.08222e8	+	1.05347e9i	−0.523888	+	0.907400i	−0.999613	+	0.0278066i	$0.991148\pi$
$390$		0			0
$391$	1.94057e8	+	3.36116e8i	0.164176	+	0.284361i
$392$	−1.66329e9	−	2.88090e9i	−1.39465	−	2.41561i
$393$		0			0
$394$	7.77784e7	−	1.34716e8i	0.0640652	−	0.110964i
$395$	−4.09044e8			−0.333949
$396$		0			0
$397$	1.05353e9			0.845043			0.422522	−	0.906353i	$-0.361145\pi$
$397$	1.05353e9			0.845043			0.422522	+	0.906353i	$0.361145\pi$
$398$	6.64994e8	−	1.15180e9i	0.528722	−	0.915773i
$399$		0			0
$400$	1.86468e9	+	3.22972e9i	1.45678	+	2.52322i
$401$	8.32350e8	+	1.44167e9i	0.644616	+	1.11651i	0.984390	+	0.176000i	$0.0563159\pi$
$401$	8.32350e8	+	1.44167e9i	0.644616	+	1.11651i	−0.339774	+	0.940507i	$0.610351\pi$
$402$		0			0
$403$	−3.92606e6	+	6.80013e6i	−0.00298806	+	0.00517547i
$404$	−6.17767e9			−4.66112
$405$		0			0
$406$	3.61184e8			0.267847
$407$	2.04011e8	−	3.53358e8i	0.149994	−	0.259797i
$408$		0			0
$409$	9.26033e6	+	1.60394e7i	0.00669260	+	0.0115919i	0.869352	−	0.494193i	$-0.164536\pi$
$409$	9.26033e6	+	1.60394e7i	0.00669260	+	0.0115919i	−0.862660	+	0.505785i	$0.831203\pi$
$410$	−1.78540e8	−	3.09240e8i	−0.127936	−	0.221591i
$411$		0			0
$412$	1.36975e8	−	2.37248e8i	0.0964942	−	0.167133i
$413$	−4.82036e8			−0.336709
$414$		0			0
$415$	7.42329e7			0.0509833
$416$	−3.58587e7	+	6.21091e7i	−0.0244213	+	0.0422988i
$417$		0			0
$418$	−1.88708e9	−	3.26851e9i	−1.26378	−	2.18894i
$419$	−7.91691e8	−	1.37125e9i	−0.525783	−	0.910683i	−0.999549	−	0.0300324i	$-0.990439\pi$
$419$	−7.91691e8	−	1.37125e9i	−0.525783	−	0.910683i	0.473766	−	0.880651i	$-0.342894\pi$
$420$		0			0
$421$	−7.10933e8	+	1.23137e9i	−0.464345	+	0.804270i	−0.999172	−	0.0406923i	$-0.987044\pi$
$421$	−7.10933e8	+	1.23137e9i	−0.464345	+	0.804270i	0.534826	+	0.844962i	$0.320377\pi$
$422$	3.84899e9			2.49318
$423$		0			0
$424$	−3.37069e9			−2.14753
$425$	−1.96466e8	+	3.40289e8i	−0.124144	+	0.215024i
$426$		0			0
$427$	−2.19350e8	−	3.79926e8i	−0.136345	−	0.236157i
$428$	1.52115e9	+	2.63470e9i	0.937817	+	1.62435i
$429$		0			0
$430$	−4.53792e8	+	7.85991e8i	−0.275244	+	0.476736i
$431$	1.76729e9			1.06326			0.531628	−	0.846978i	$-0.321580\pi$
$431$	1.76729e9			1.06326			0.531628	+	0.846978i	$0.321580\pi$
$432$		0			0
$433$	1.43174e9			0.847535			0.423767	−	0.905771i	$-0.360707\pi$
$433$	1.43174e9			0.847535			0.423767	+	0.905771i	$0.360707\pi$
$434$	−1.45812e8	+	2.52553e8i	−0.0856206	+	0.148299i
$435$		0			0
$436$	1.79394e9	+	3.10720e9i	1.03659	+	1.79542i
$437$	−1.39459e9	−	2.41551e9i	−0.799398	−	1.38460i
$438$		0			0
$439$	3.70176e8	−	6.41164e8i	0.208825	−	0.361696i	−0.742520	−	0.669824i	$-0.766369\pi$
$439$	3.70176e8	−	6.41164e8i	0.208825	−	0.361696i	0.951345	+	0.308129i	$0.0997027\pi$
$440$	1.30392e9			0.729736
$441$		0			0
$442$	−1.55202e7			−0.00854910
$443$	1.16814e9	−	2.02328e9i	0.638386	−	1.10572i	−0.347401	−	0.937717i	$-0.612936\pi$
$443$	1.16814e9	−	2.02328e9i	0.638386	−	1.10572i	0.985787	−	0.168000i	$-0.0537309\pi$
$444$		0			0
$445$	−1.39940e7	−	2.42384e7i	−0.00752806	−	0.0130390i
$446$	7.97379e8	+	1.38110e9i	0.425591	+	0.737146i
$447$		0			0
$448$	−5.67958e8	+	9.83732e8i	−0.298430	+	0.516897i
$449$	5.43412e8			0.283313			0.141657	−	0.989916i	$-0.454757\pi$
$449$	5.43412e8			0.283313			0.141657	+	0.989916i	$0.454757\pi$
$450$		0			0
$451$	1.17854e9			0.604958
$452$	−1.04956e9	+	1.81789e9i	−0.534592	+	0.925940i
$453$		0			0
$454$	2.28313e9	+	3.95450e9i	1.14508	+	1.98334i
$455$	1.05103e6	+	1.82044e6i	0.000523090	+	0.000906018i
$456$		0			0
$457$	−8.93333e8	+	1.54730e9i	−0.437831	+	0.758345i	−0.997522	−	0.0703559i	$-0.977586\pi$
$457$	−8.93333e8	+	1.54730e9i	−0.437831	+	0.758345i	0.559691	+	0.828701i	$0.310920\pi$
$458$	−3.22402e9			−1.56808
$459$		0			0
$460$	1.57304e9			0.753508
$461$	−1.17001e9	+	2.02652e9i	−0.556209	+	0.963382i	0.441599	+	0.897212i	$0.354411\pi$
$461$	−1.17001e9	+	2.02652e9i	−0.556209	+	0.963382i	−0.997808	+	0.0661700i	$0.978922\pi$
$462$		0			0
$463$	−1.84161e9	−	3.18976e9i	−0.862312	−	1.49357i	−0.869692	−	0.493595i	$-0.835683\pi$
$463$	−1.84161e9	−	3.18976e9i	−0.862312	−	1.49357i	0.00738049	−	0.999973i	$-0.497651\pi$
$464$	1.80152e9	+	3.12032e9i	0.837192	+	1.45006i
$465$		0			0
$466$	1.36278e9	−	2.36040e9i	0.623843	−	1.08053i
$467$	−8.38332e8			−0.380897			−0.190448	−	0.981697i	$-0.560994\pi$
$467$	−8.38332e8			−0.380897			−0.190448	+	0.981697i	$0.560994\pi$
$468$		0			0
$469$	−8.59111e8			−0.384542
$470$	7.30049e8	−	1.26448e9i	0.324347	−	0.561785i
$471$		0			0
$472$	−4.41826e9	−	7.65266e9i	−1.93399	−	3.34977i
$473$	−1.49773e9	−	2.59415e9i	−0.650760	−	1.12715i
$474$		0			0
$475$	1.41191e9	−	2.44550e9i	0.604475	−	1.04698i
$476$	−4.15459e8			−0.176565
$477$		0			0
$478$	6.67556e9			2.79570
$479$	1.38683e9	−	2.40207e9i	0.576567	−	0.998644i	−0.419302	−	0.907847i	$-0.637725\pi$
$479$	1.38683e9	−	2.40207e9i	0.576567	−	0.998644i	0.995869	−	0.0907972i	$-0.0289415\pi$
$480$		0			0
$481$	6.02909e6	+	1.04427e7i	0.00247027	+	0.00427863i
$482$	4.98767e8	+	8.63890e8i	0.202877	+	0.351394i
$483$		0			0
$484$	−2.93352e8	+	5.08100e8i	−0.117606	+	0.203700i
$485$	−7.63954e8			−0.304068
$486$		0			0
$487$	6.08195e8			0.238612			0.119306	−	0.992858i	$-0.461933\pi$
$487$	6.08195e8			0.238612			0.119306	+	0.992858i	$0.461933\pi$
$488$	4.02105e9	−	6.96467e9i	1.56628	−	2.71288i
$489$		0			0
$490$	−5.36259e8	−	9.28828e8i	−0.205915	−	0.356656i
$491$	1.37347e9	+	2.37892e9i	0.523641	+	0.906973i	0.999621	+	0.0275169i	$0.00876000\pi$
$491$	1.37347e9	+	2.37892e9i	0.523641	+	0.906973i	−0.475980	+	0.879456i	$0.657907\pi$
$492$		0			0
$493$	−1.89811e8	+	3.28762e8i	−0.0713439	+	0.123571i
$494$	1.11537e8			0.0416268
$495$		0			0
$496$	−2.90912e9			−1.07047
$497$	2.28252e8	−	3.95344e8i	0.0834002	−	0.144453i
$498$		0			0
$499$	−1.14164e9	−	1.97737e9i	−0.411316	−	0.712421i	0.583718	−	0.811957i	$-0.301597\pi$
$499$	−1.14164e9	−	1.97737e9i	−0.411316	−	0.712421i	−0.995034	+	0.0995360i	$0.968264\pi$
$500$	1.63847e9	+	2.83792e9i	0.586198	+	1.01532i
$501$		0			0
$502$	−3.14627e9	+	5.44951e9i	−1.11003	+	1.92262i
$503$	−5.24355e9			−1.83712			−0.918559	−	0.395283i	$-0.870647\pi$
$503$	−5.24355e9			−1.83712			−0.918559	+	0.395283i	$0.870647\pi$
$504$		0			0
$505$	−1.22012e9			−0.421581
$506$	−3.60158e9	+	6.23813e9i	−1.23585	+	2.14056i
$507$		0			0
$508$	2.97107e9	+	5.14604e9i	1.00552	+	1.74161i
$509$	7.15597e8	+	1.23945e9i	0.240523	+	0.416598i	0.960863	−	0.277023i	$-0.0893478\pi$
$509$	7.15597e8	+	1.23945e9i	0.240523	+	0.416598i	−0.720341	+	0.693621i	$0.756014\pi$
$510$		0			0
$511$	2.43497e8	−	4.21750e8i	0.0807274	−	0.139824i
$512$	1.43352e9			0.472018
$513$		0			0
$514$	6.15059e8			0.199777
$515$	2.70531e7	−	4.68574e7i	0.00872755	−	0.0151166i
$516$		0			0
$517$	2.40952e9	+	4.17340e9i	0.766854	+	1.32823i
$518$	2.23917e8	+	3.87836e8i	0.0707838	+	0.122601i
$519$		0			0
$520$	−1.92672e7	+	3.33717e7i	−0.00600905	+	0.0104080i
$521$	5.00475e9			1.55042			0.775211	−	0.631702i	$-0.217643\pi$
$521$	5.00475e9			1.55042			0.775211	+	0.631702i	$0.217643\pi$
$522$		0			0
$523$	−4.38432e9			−1.34013			−0.670064	−	0.742304i	$-0.733733\pi$
$523$	−4.38432e9			−1.34013			−0.670064	+	0.742304i	$0.733733\pi$
$524$	6.21305e8	−	1.07613e9i	0.188645	−	0.326743i
$525$		0			0
$526$	2.25963e9	+	3.91380e9i	0.676998	+	1.17260i
$527$	−1.53255e8	−	2.65446e8i	−0.0456119	−	0.0790021i
$528$		0			0
$529$	−9.59243e8	+	1.66146e9i	−0.281731	+	0.487972i
$530$	−1.08674e9			−0.317074
$531$		0			0
$532$	2.98571e9			0.859719
$533$	−1.74145e7	+	3.01628e7i	−0.00498157	+	0.00862833i
$534$		0			0
$535$	3.00433e8	+	5.20365e8i	0.0848221	+	0.146916i
$536$	−7.87447e9	−	1.36390e10i	−2.20874	−	3.82565i
$537$		0			0
$538$	3.44801e9	−	5.97213e9i	0.954620	−	1.65345i
$539$	3.53983e9			0.973693
$540$		0			0
$541$	−5.37230e9			−1.45871			−0.729357	−	0.684133i	$-0.760181\pi$
$541$	−5.37230e9			−1.45871			−0.729357	+	0.684133i	$0.760181\pi$
$542$	−4.00938e9	+	6.94446e9i	−1.08163	+	1.87344i
$543$		0			0
$544$	−1.39976e9	−	2.42445e9i	−0.372784	−	0.645680i
$545$	3.54311e8	+	6.13685e8i	0.0937556	+	0.162389i
$546$		0			0
$547$	−1.22120e8	+	2.11518e8i	−0.0319029	+	0.0552575i	−0.881536	−	0.472117i	$-0.843490\pi$
$547$	−1.22120e8	+	2.11518e8i	−0.0319029	+	0.0552575i	0.849633	+	0.527374i	$0.176823\pi$
$548$	−4.31105e8			−0.111905
$549$		0			0
$550$	−7.29259e9			−1.86901
$551$	1.36408e9	−	2.36266e9i	0.347384	−	0.601687i
$552$		0			0
$553$	7.40886e8	+	1.28325e9i	0.186300	+	0.322682i
$554$	−1.91873e9	−	3.32334e9i	−0.479435	−	0.830405i
$555$		0			0
$556$	1.92854e9	−	3.34034e9i	0.475847	−	0.824192i
$557$	−5.52077e9			−1.35365			−0.676825	−	0.736144i	$-0.736645\pi$
$557$	−5.52077e9			−1.35365			−0.676825	+	0.736144i	$0.736645\pi$
$558$		0			0
$559$	8.85243e7			0.0214349
$560$	−3.89396e8	+	6.74453e8i	−0.0936986	+	0.162291i
$561$		0			0
$562$	−4.26592e9	−	7.38878e9i	−1.01376	−	1.75588i
$563$	2.31199e9	+	4.00448e9i	0.546017	+	0.945728i	0.998542	+	0.0539770i	$0.0171898\pi$
$563$	2.31199e9	+	4.00448e9i	0.546017	+	0.945728i	−0.452526	+	0.891751i	$0.649477\pi$
$564$		0			0
$565$	−2.07292e8	+	3.59040e8i	−0.0483519	+	0.0837479i
$566$	7.33726e9			1.70089
$567$		0			0
$568$	8.36847e9			1.91614
$569$	−2.27221e9	+	3.93559e9i	−0.517078	+	0.895605i	0.482726	+	0.875772i	$0.339647\pi$
$569$	−2.27221e9	+	3.93559e9i	−0.517078	+	0.895605i	−0.999803	+	0.0198332i	$0.993686\pi$
$570$		0			0
$571$	1.39633e9	+	2.41851e9i	0.313878	+	0.543653i	0.979198	−	0.202905i	$-0.0650383\pi$
$571$	1.39633e9	+	2.41851e9i	0.313878	+	0.543653i	−0.665320	+	0.746558i	$0.731705\pi$
$572$	−1.03807e8	−	1.79799e8i	−0.0231922	−	0.0401700i
$573$		0			0
$574$	−6.46766e8	+	1.12023e9i	−0.142743	+	0.247238i
$575$	−5.38940e9			−1.18223
$576$		0			0
$577$	4.63375e9			1.00419			0.502096	−	0.864812i	$-0.332562\pi$
$577$	4.63375e9			1.00419			0.502096	+	0.864812i	$0.332562\pi$
$578$	−4.08980e9	+	7.08374e9i	−0.880957	+	1.52586i
$579$		0			0
$580$	7.69312e8	+	1.33249e9i	0.163721	+	0.283573i
$581$	−1.34455e8	−	2.32883e8i	−0.0284421	−	0.0492631i
$582$		0			0
$583$	1.79339e9	−	3.10624e9i	0.374830	−	0.649225i
$584$	8.92742e9			1.85473
$585$		0			0
$586$	−1.30340e10			−2.67570
$587$	2.49329e9	−	4.31850e9i	0.508791	−	0.881251i	−0.491158	−	0.871071i	$-0.663426\pi$
$587$	2.49329e9	−	4.31850e9i	0.508791	−	0.881251i	0.999948	−	0.0101804i	$-0.00324059\pi$
$588$		0			0
$589$	1.10137e9	+	1.90763e9i	0.222091	+	0.384673i
$590$	−1.42449e9	−	2.46729e9i	−0.285547	−	0.494581i
$591$		0			0
$592$	−2.23371e9	+	3.86890e9i	−0.442488	+	0.766411i
$593$	1.08733e9			0.214126			0.107063	−	0.994252i	$-0.465855\pi$
$593$	1.08733e9			0.214126			0.107063	+	0.994252i	$0.465855\pi$
$594$		0			0
$595$	−8.20549e7			−0.0159696
$596$	5.26618e9	−	9.12128e9i	1.01890	−	1.76479i
$597$		0			0
$598$	−1.06437e8	−	1.84354e8i	−0.0203534	−	0.0352531i
$599$	7.88181e8	+	1.36517e9i	0.149841	+	0.259533i	0.931169	−	0.364589i	$-0.118790\pi$
$599$	7.88181e8	+	1.36517e9i	0.149841	+	0.259533i	−0.781327	+	0.624122i	$0.785457\pi$
$600$		0			0
$601$	2.98739e9	−	5.17431e9i	0.561347	−	0.972282i	−0.436032	−	0.899931i	$-0.643617\pi$
$601$	2.98739e9	−	5.17431e9i	0.561347	−	0.972282i	0.997379	−	0.0723505i	$-0.0230500\pi$
$602$	3.28775e9			0.614201
$603$		0			0
$604$	2.35010e10			4.33967
$605$	−5.79381e7	+	1.00352e8i	−0.0106370	+	0.0184239i
$606$		0			0
$607$	2.07004e9	+	3.58541e9i	0.375680	+	0.650696i	0.990429	−	0.138027i	$-0.0440759\pi$
$607$	2.07004e9	+	3.58541e9i	0.375680	+	0.650696i	−0.614749	+	0.788723i	$0.710743\pi$
$608$	1.00594e10	+	1.74234e10i	1.81514	+	3.14391i
$609$		0			0
$610$	1.29643e9	−	2.24547e9i	0.231256	−	0.400547i
$611$	−1.42416e8			−0.0252588
$612$		0			0
$613$	−3.24640e9			−0.569234			−0.284617	−	0.958641i	$-0.591866\pi$
$613$	−3.24640e9			−0.569234			−0.284617	+	0.958641i	$0.591866\pi$
$614$	6.25500e9	−	1.08340e10i	1.09053	−	1.88886i
$615$		0			0
$616$	−2.36174e9	−	4.09065e9i	−0.407098	−	0.705114i
$617$	2.56649e9	+	4.44529e9i	0.439887	+	0.761907i	0.997680	−	0.0680728i	$-0.0216850\pi$
$617$	2.56649e9	+	4.44529e9i	0.439887	+	0.761907i	−0.557793	+	0.829980i	$0.688352\pi$
$618$		0			0
$619$	−4.08023e7	+	7.06717e7i	−0.00691461	+	0.0119765i	−0.869462	−	0.494000i	$-0.835534\pi$
$619$	−4.08023e7	+	7.06717e7i	−0.00691461	+	0.0119765i	0.862547	+	0.505976i	$0.168868\pi$
$620$	−1.24230e9			−0.209342
$621$		0			0
$622$	−6.26203e9			−1.04339
$623$	−5.06937e7	+	8.78041e7i	−0.00839936	+	0.0145481i
$624$		0			0
$625$	−2.56182e9	−	4.43720e9i	−0.419728	−	0.726990i
$626$	−8.85830e9	−	1.53430e10i	−1.44325	−	2.49977i
$627$		0			0
$628$	−1.16371e10	+	2.01561e10i	−1.87494	+	3.24749i
$629$	−4.70696e8			−0.0754160
$630$		0			0
$631$	5.87381e9			0.930716			0.465358	−	0.885123i	$-0.345926\pi$
$631$	5.87381e9			0.930716			0.465358	+	0.885123i	$0.345926\pi$
$632$	−1.35817e10	+	2.35242e10i	−2.14015	+	3.70684i
$633$		0			0
$634$	−2.60842e8	−	4.51791e8i	−0.0406504	−	0.0704085i
$635$	5.86798e8	+	1.01636e9i	0.0909454	+	0.157522i
$636$		0			0
$637$	−5.23059e7	+	9.05964e7i	−0.00801793	+	0.0138875i
$638$	−7.04557e9			−1.07410
$639$		0			0
$640$	−2.31781e9			−0.349500
$641$	8.24069e8	−	1.42733e9i	0.123583	−	0.214053i	−0.797595	−	0.603193i	$-0.793895\pi$
$641$	8.24069e8	−	1.42733e9i	0.123583	−	0.214053i	0.921178	+	0.389141i	$0.127228\pi$
$642$		0			0
$643$	−2.07980e9	−	3.60232e9i	−0.308520	−	0.534373i	0.669519	−	0.742795i	$-0.266500\pi$
$643$	−2.07980e9	−	3.60232e9i	−0.308520	−	0.534373i	−0.978039	+	0.208422i	$0.933167\pi$
$644$	−2.84919e9	−	4.93494e9i	−0.420360	−	0.728084i
$645$		0			0
$646$	−2.17694e9	+	3.77056e9i	−0.317711	+	0.550291i
$647$	3.14826e9			0.456988			0.228494	−	0.973545i	$-0.426620\pi$
$647$	3.14826e9			0.456988			0.228494	+	0.973545i	$0.426620\pi$
$648$		0			0
$649$	9.40301e9			1.35024
$650$	1.07758e8	−	1.86642e8i	0.0153905	−	0.0266571i
$651$		0			0
$652$	−6.58190e9	−	1.14002e10i	−0.930004	−	1.61081i
$653$	−6.14384e9	−	1.06414e10i	−0.863463	−	1.49556i	−0.868565	−	0.495575i	$-0.834958\pi$
$653$	−6.14384e9	−	1.06414e10i	−0.863463	−	1.49556i	0.00510246	−	0.999987i	$-0.498376\pi$
$654$		0			0
$655$	1.22710e8	−	2.12540e8i	0.0170623	−	0.0295527i
$656$	−1.29038e10			−1.78465
$657$		0			0
$658$	−5.28924e9			−0.723774
$659$	2.76278e9	−	4.78528e9i	0.376052	−	0.651341i	−0.614432	−	0.788970i	$-0.710615\pi$
$659$	2.76278e9	−	4.78528e9i	0.376052	−	0.651341i	0.990484	+	0.137629i	$0.0439480\pi$
$660$		0			0
$661$	1.98631e9	+	3.44039e9i	0.267511	+	0.463342i	0.968218	−	0.250106i	$-0.0804656\pi$
$661$	1.98631e9	+	3.44039e9i	0.267511	+	0.463342i	−0.700708	+	0.713449i	$0.747132\pi$
$662$	−1.71927e8	−	2.97787e8i	−0.0230326	−	0.0398936i
$663$		0			0
$664$	2.46479e9	−	4.26914e9i	0.326732	−	0.565916i
$665$	5.89690e8			0.0777585
$666$		0			0
$667$	−5.20684e9			−0.679413
$668$	8.53818e9	−	1.47886e10i	1.10828	−	1.91959i
$669$		0			0
$670$	−2.53880e9	−	4.39733e9i	−0.326112	−	0.564843i
$671$	4.27883e9	+	7.41116e9i	0.546760	+	0.947016i
$672$		0			0
$673$	6.56024e9	−	1.13627e10i	0.829597	−	1.43690i	−0.0687581	−	0.997633i	$-0.521904\pi$
$673$	6.56024e9	−	1.13627e10i	0.829597	−	1.43690i	0.898355	−	0.439270i	$-0.144763\pi$
$674$	5.19338e9			0.653341
$675$		0			0
$676$	−2.07258e10			−2.58047
$677$	−5.73199e9	+	9.92810e9i	−0.709978	+	1.22972i	0.254886	+	0.966971i	$0.417962\pi$
$677$	−5.73199e9	+	9.92810e9i	−0.709978	+	1.22972i	−0.964865	+	0.262748i	$0.915371\pi$
$678$		0			0
$679$	1.38372e9	+	2.39667e9i	0.169631	+	0.293809i
$680$	−7.52101e8	−	1.30268e9i	−0.0917266	−	0.158875i
$681$		0			0
$682$	2.84433e9	−	4.92652e9i	0.343348	−	0.594696i
$683$	−7.63032e9			−0.916368			−0.458184	−	0.888857i	$-0.651500\pi$
$683$	−7.63032e9			−0.916368			−0.458184	+	0.888857i	$0.651500\pi$
$684$		0			0
$685$	−8.51449e7			−0.0101214
$686$	−4.02663e9	+	6.97433e9i	−0.476220	+	0.824837i
$687$		0			0
$688$	1.63986e10	+	2.84033e10i	1.91977	+	3.32513i
$689$	5.29996e7	+	9.17980e7i	0.00617313	+	0.0106922i
$690$		0			0
$691$	−4.78482e9	+	8.28755e9i	−0.551686	+	0.955549i	0.446467	+	0.894800i	$0.352682\pi$
$691$	−4.78482e9	+	8.28755e9i	−0.551686	+	0.955549i	−0.998153	+	0.0607485i	$0.980651\pi$
$692$	−6.01912e9			−0.690497
$693$		0			0
$694$	8.83910e9			1.00381
$695$	3.80895e8	−	6.59730e8i	0.0430387	−	0.0745451i
$696$		0			0
$697$	−6.79782e8	−	1.17742e9i	−0.0760422	−	0.131709i
$698$	5.57254e9	+	9.65192e9i	0.620239	+	1.07429i
$699$		0			0
$700$	2.88456e9	−	4.99621e9i	0.317861	−	0.550551i
$701$	1.24509e10			1.36517			0.682586	−	0.730805i	$-0.260855\pi$
$701$	1.24509e10			1.36517			0.682586	+	0.730805i	$0.260855\pi$
$702$		0			0
$703$	3.38267e9			0.367211
$704$	1.10791e10	−	1.91895e10i	1.19674	−	2.07281i
$705$		0			0
$706$	1.54726e10	+	2.67993e10i	1.65480	+	2.86620i
$707$	2.20995e9	+	3.82774e9i	0.235188	+	0.407357i
$708$		0			0
$709$	−7.92899e9	+	1.37334e10i	−0.835518	+	1.44716i	0.0580897	+	0.998311i	$0.481499\pi$
$709$	−7.92899e9	+	1.37334e10i	−0.835518	+	1.44716i	−0.893608	+	0.448849i	$0.851834\pi$
$710$	2.69807e9			0.282911
$711$		0			0
$712$	−1.85860e9			−0.192977
$713$	2.10203e9	−	3.64082e9i	0.217183	−	0.376171i
$714$		0			0
$715$	−2.05023e7	−	3.55111e7i	−0.00209765	−	0.00363323i
$716$	1.74628e10	+	3.02464e10i	1.77794	+	3.07949i
$717$		0			0
$718$	1.07060e10	−	1.85433e10i	1.07942	−	1.86962i
$719$	−1.79885e10			−1.80486			−0.902432	−	0.430833i	$-0.858220\pi$
$719$	−1.79885e10			−1.80486			−0.902432	+	0.430833i	$0.858220\pi$
$720$		0			0
$721$	−1.96001e8			−0.0194754
$722$	6.07562e9	−	1.05233e10i	0.600773	−	1.04057i
$723$		0			0
$724$	−2.13121e10	−	3.69137e10i	−2.08709	−	3.61495i
$725$	−2.63574e9	−	4.56524e9i	−0.256874	−	0.444919i
$726$		0			0
$727$	−8.60459e9	+	1.49036e10i	−0.830538	+	1.43853i	0.0670741	+	0.997748i	$0.478634\pi$
$727$	−8.60459e9	+	1.49036e10i	−0.830538	+	1.43853i	−0.897612	+	0.440786i	$0.854700\pi$
$728$	1.39592e8			0.0134091
$729$		0			0
$730$	2.87828e9			0.273844
$731$	−1.72779e9	+	2.99262e9i	−0.163599	+	0.283362i
$732$		0			0
$733$	−1.01647e10	−	1.76058e10i	−0.953304	−	1.65117i	−0.738202	−	0.674580i	$-0.764325\pi$
$733$	−1.01647e10	−	1.76058e10i	−0.953304	−	1.65117i	−0.215102	−	0.976592i	$-0.569009\pi$
$734$	8.53718e9	+	1.47868e10i	0.796853	+	1.38019i
$735$		0			0
$736$	1.91989e10	−	3.32535e10i	1.77502	−	3.07443i
$737$	1.67586e10			1.54206
$738$		0			0
$739$	−8.40068e9			−0.765700			−0.382850	−	0.923810i	$-0.625057\pi$
$739$	−8.40068e9			−0.765700			−0.382850	+	0.923810i	$0.625057\pi$
$740$	−9.53876e8	+	1.65216e9i	−0.0865328	+	0.149879i
$741$		0			0
$742$	1.96838e9	+	3.40933e9i	0.176886	+	0.306376i
$743$	−5.00275e9	−	8.66502e9i	−0.447454	−	0.775013i	0.550766	−	0.834660i	$-0.314336\pi$
$743$	−5.00275e9	−	8.66502e9i	−0.447454	−	0.775013i	−0.998220	+	0.0596473i	$0.981002\pi$
$744$		0			0
$745$	1.04009e9	−	1.80149e9i	0.0921562	−	0.159619i
$746$	−5.59882e9			−0.493754
$747$		0			0
$748$	8.10431e9			0.708044
$749$	1.08832e9	−	1.88503e9i	0.0946395	−	0.163920i
$750$		0			0
$751$	6.51619e9	+	1.12864e10i	0.561376	+	0.972332i	0.997377	+	0.0723858i	$0.0230613\pi$
$751$	6.51619e9	+	1.12864e10i	0.561376	+	0.972332i	−0.436000	+	0.899946i	$0.643605\pi$
$752$	−2.63817e10	−	4.56944e10i	−2.26225	−	3.91833i
$753$		0			0
$754$	1.04108e8	−	1.80320e8i	0.00884472	−	0.0153195i
$755$	4.64154e9			0.392508
$756$		0			0
$757$	−8.11633e9			−0.680024			−0.340012	−	0.940421i	$-0.610431\pi$
$757$	−8.11633e9			−0.680024			−0.340012	+	0.940421i	$0.610431\pi$
$758$	−3.67104e9	+	6.35843e9i	−0.306159	+	0.530283i
$759$		0			0
$760$	5.40500e9	+	9.36173e9i	0.446630	+	0.773586i
$761$	1.10813e9	+	1.91934e9i	0.0911476	+	0.157872i	0.907994	−	0.418983i	$-0.137613\pi$
$761$	1.10813e9	+	1.91934e9i	0.0911476	+	0.157872i	−0.816847	+	0.576855i	$0.804280\pi$
$762$		0			0
$763$	1.28350e9	−	2.22309e9i	0.104607	−	0.181185i
$764$	−5.57469e9			−0.452266
$765$		0			0
$766$	2.16661e10			1.74173
$767$	−1.38942e8	+	2.40655e8i	−0.0111186	+	0.0192580i
$768$		0			0
$769$	−6.59962e9	−	1.14309e10i	−0.523332	−	0.906437i	−0.999631	−	0.0271540i	$-0.991356\pi$
$769$	−6.59962e9	−	1.14309e10i	−0.523332	−	0.906437i	0.476300	−	0.879283i	$-0.341978\pi$
$770$	−7.61446e8	−	1.31886e9i	−0.0601065	−	0.104108i
$771$		0			0
$772$	−1.02516e10	+	1.77562e10i	−0.801917	+	1.38896i
$773$	−1.25254e10			−0.975355			−0.487677	−	0.873024i	$-0.662156\pi$
$773$	−1.25254e10			−0.975355			−0.487677	+	0.873024i	$0.662156\pi$
$774$		0			0
$775$	4.25624e9			0.328451
$776$	−2.53659e10	+	4.39350e10i	−1.94865	+	3.37517i
$777$		0			0
$778$	1.30222e10	+	2.25550e10i	0.991413	+	1.71718i
$779$	4.88527e9	+	8.46154e9i	0.370261	+	0.641310i
$780$		0			0
$781$	−4.45248e9	+	7.71192e9i	−0.334444	+	0.579274i
$782$	8.30959e9			0.621378
$783$		0			0
$784$	−3.87575e10			−2.87243
$785$	−2.29838e9	+	3.98092e9i	−0.169582	+	0.293724i
$786$		0			0
$787$	−3.66640e9	−	6.35038e9i	−0.268119	−	0.464396i	0.700257	−	0.713891i	$-0.253069\pi$
$787$	−3.66640e9	−	6.35038e9i	−0.268119	−	0.464396i	−0.968376	+	0.249495i	$0.919735\pi$
$788$	−1.20026e9	−	2.07891e9i	−0.0873841	−	0.151354i
$789$		0			0
$790$	−4.37886e9	+	7.58441e9i	−0.315985	+	0.547302i
$791$	1.50184e9			0.107896
$792$		0			0
$793$	−2.52903e8			−0.0180093
$794$	1.12781e10	−	1.95343e10i	0.799586	−	1.38492i
$795$		0			0
$796$	−1.02620e10	−	1.77744e10i	−0.721170	−	1.24910i
$797$	−9.72182e9	−	1.68387e10i	−0.680211	−	1.17816i	−0.974916	−	0.222571i	$-0.928555\pi$
$797$	−9.72182e9	−	1.68387e10i	−0.680211	−	1.17816i	0.294706	−	0.955588i	$-0.404778\pi$
$798$		0			0
$799$	2.77962e9	−	4.81445e9i	0.192785	−	0.333913i
$800$	3.88745e10			2.68441
$801$		0			0
$802$	3.56416e10			2.43976
$803$	−4.74987e9	+	8.22701e9i	−0.323726	+	0.560709i
$804$		0			0
$805$	−5.62727e8	−	9.74671e8i	−0.0380200	−	0.0658526i
$806$	8.40577e7	+	1.45592e8i	0.00565464	+	0.00979412i
$807$		0			0
$808$	−4.05121e10	+	7.01689e10i	−2.70175	+	4.67956i
$809$	2.66596e10			1.77025			0.885123	−	0.465356i	$-0.154074\pi$
$809$	2.66596e10			1.77025			0.885123	+	0.465356i	$0.154074\pi$
$810$		0			0
$811$	2.23929e10			1.47413			0.737066	−	0.675820i	$-0.236210\pi$
$811$	2.23929e10			1.47413			0.737066	+	0.675820i	$0.236210\pi$
$812$	2.78685e9	−	4.82697e9i	0.182670	−	0.316394i
$813$		0			0
$814$	−4.36793e9	−	7.56547e9i	−0.283851	−	0.491644i
$815$	−1.29995e9	−	2.25158e9i	−0.0841154	−	0.145692i
$816$		0			0
$817$	1.24168e10	−	2.15066e10i	0.796587	−	1.37973i
$818$	3.96531e8			0.0253303
$819$		0			0
$820$	−5.51037e9			−0.349006
$821$	9.93766e9	−	1.72125e10i	0.626734	−	1.08553i	−0.361469	−	0.932384i	$-0.617725\pi$
$821$	9.93766e9	−	1.72125e10i	0.626734	−	1.08553i	0.988203	−	0.153151i	$-0.0489420\pi$
$822$		0			0
$823$	−8.48625e9	−	1.46986e10i	−0.530660	−	0.919130i	−0.999360	−	0.0357725i	$-0.988611\pi$
$823$	−8.48625e9	−	1.46986e10i	−0.530660	−	0.919130i	0.468700	−	0.883357i	$-0.344723\pi$
$824$	−1.79652e9	−	3.11166e9i	−0.111863	−	0.193752i
$825$		0			0
$826$	−5.16025e9	+	8.93781e9i	−0.318596	+	0.551825i
$827$	−1.89569e10			−1.16546			−0.582730	−	0.812666i	$-0.698015\pi$
$827$	−1.89569e10			−1.16546			−0.582730	+	0.812666i	$0.698015\pi$
$828$		0			0
$829$	−3.77995e9			−0.230433			−0.115217	−	0.993340i	$-0.536756\pi$
$829$	−3.77995e9			−0.230433			−0.115217	+	0.993340i	$0.536756\pi$
$830$	7.94671e8	−	1.37641e9i	0.0482407	−	0.0835554i
$831$		0			0
$832$	3.27417e8	+	5.67103e8i	0.0197092	+	0.0341374i
$833$	−2.04178e9	−	3.53647e9i	−0.122392	−	0.211988i
$834$		0			0
$835$	1.68632e9	−	2.92080e9i	0.100239	−	0.173620i
$836$	−5.82418e10			−3.44757
$837$		0			0
$838$	−3.39006e10			−1.99000
$839$	−6.28559e9	+	1.08870e10i	−0.367434	+	0.636414i	−0.989164	−	0.146818i	$-0.953097\pi$
$839$	−6.28559e9	+	1.08870e10i	−0.367434	+	0.636414i	0.621730	+	0.783232i	$0.286430\pi$
$840$		0			0
$841$	6.07848e9	+	1.05282e10i	0.352378	+	0.610337i
$842$	1.52212e10	+	2.63639e10i	0.878733	+	1.52201i
$843$		0			0
$844$	2.96983e10	−	5.14390e10i	1.70033	−	2.94506i
$845$	−4.09343e9			−0.233394
$846$		0			0
$847$	4.19765e8			0.0237363
$848$	−1.96357e10	+	3.40101e10i	−1.10576	+	1.91524i
$849$		0			0
$850$	4.20638e9	+	7.28566e9i	0.234932	+	0.406914i
$851$	−3.22800e9	−	5.59106e9i	−0.179548	−	0.310986i
$852$		0			0
$853$	−3.38980e9	+	5.87130e9i	−0.187004	+	0.323901i	−0.944250	−	0.329229i	$-0.893211\pi$
$853$	−3.38980e9	+	5.87130e9i	−0.187004	+	0.323901i	0.757246	+	0.653130i	$0.226545\pi$
$854$	−9.39267e9			−0.516044
$855$		0			0
$856$	3.99016e10			2.17436
$857$	1.10047e10	−	1.90608e10i	0.597237	−	1.03445i	−0.395989	−	0.918255i	$-0.629598\pi$
$857$	1.10047e10	−	1.90608e10i	0.597237	−	1.03445i	0.993227	−	0.116191i	$-0.0370683\pi$
$858$		0			0
$859$	1.05339e10	+	1.82452e10i	0.567039	+	0.982140i	0.996857	+	0.0792243i	$0.0252443\pi$
$859$	1.05339e10	+	1.82452e10i	0.567039	+	0.982140i	−0.429818	+	0.902915i	$0.641422\pi$
$860$	7.00281e9	+	1.21292e10i	0.375429	+	0.650262i
$861$		0			0
$862$	1.89191e10	−	3.27688e10i	1.00606	−	1.74255i
$863$	−1.10986e10			−0.587800			−0.293900	−	0.955836i	$-0.594953\pi$
$863$	−1.10986e10			−0.587800			−0.293900	+	0.955836i	$0.594953\pi$
$864$		0			0
$865$	−1.18880e9			−0.0624529
$866$	1.53270e10	−	2.65471e10i	0.801943	−	1.38901i
$867$		0			0
$868$	2.25013e9	+	3.89734e9i	0.116785	+	0.202278i
$869$	−1.44524e10	−	2.50322e10i	−0.747084	−	1.29399i
$870$		0			0
$871$	−2.47631e8	+	4.28909e8i	−0.0126982	+	0.0219939i
$872$	4.70574e10			2.40337
$873$		0			0
$874$	−5.97171e10			−3.02558
$875$	1.17227e9	−	2.03043e9i	0.0591560	−	0.102461i
$876$		0			0
$877$	3.74513e9	+	6.48675e9i	0.187486	+	0.324735i	0.944411	−	0.328766i	$-0.106633\pi$
$877$	3.74513e9	+	6.48675e9i	0.187486	+	0.324735i	−0.756926	+	0.653501i	$0.773300\pi$
$878$	−7.92555e9	−	1.37275e10i	−0.395184	−	0.684478i
$879$		0			0
$880$	7.59589e9	−	1.31565e10i	0.375741	−	0.650803i
$881$	3.40216e10			1.67625			0.838124	−	0.545479i	$-0.183652\pi$
$881$	3.40216e10			1.67625			0.838124	+	0.545479i	$0.183652\pi$
$882$		0			0
$883$	−1.52483e8			−0.00745350			−0.00372675	−	0.999993i	$-0.501186\pi$
$883$	−1.52483e8			−0.00745350			−0.00372675	+	0.999993i	$0.501186\pi$
$884$	−1.19752e8	+	2.07417e8i	−0.00583043	+	0.0100986i
$885$		0			0
$886$	−2.50102e10	−	4.33190e10i	−1.20809	−	2.09247i
$887$	1.61805e10	+	2.80255e10i	0.778502	+	1.34840i	0.932805	+	0.360381i	$0.117353\pi$
$887$	1.61805e10	+	2.80255e10i	0.778502	+	1.34840i	−0.154303	+	0.988024i	$0.549313\pi$
$888$		0			0
$889$	2.12569e9	−	3.68180e9i	0.101471	−	0.175754i
$890$	−5.99231e8			−0.0284924
$891$		0			0
$892$	2.46099e10			1.16100
$893$	−1.99758e10	+	3.45992e10i	−0.938696	+	1.62587i
$894$		0			0
$895$	3.44897e9	+	5.97379e9i	0.160808	+	0.278528i
$896$	4.19816e9	+	7.27142e9i	0.194976	+	0.337708i
$897$		0			0
$898$	5.81728e9	−	1.00758e10i	0.268073	−	0.464316i
$899$	4.11207e9			0.188756
$900$		0			0
$901$	−4.13772e9			−0.188462
$902$	1.26164e10	−	2.18522e10i	0.572416	−	0.991453i
$903$		0			0
$904$	1.37656e10	+	2.38428e10i	0.619736	+	1.07341i
$905$	−4.20923e9	−	7.29060e9i	−0.188770	−	0.326959i
$906$		0			0
$907$	−5.07730e9	+	8.79415e9i	−0.225948	+	0.391353i	−0.956603	−	0.291393i	$-0.905881\pi$
$907$	−5.07730e9	+	8.79415e9i	−0.225948	+	0.391353i	0.730656	+	0.682746i	$0.239214\pi$
$908$	7.04656e10			3.12375
$909$		0			0
$910$	4.50056e7			0.00197980
$911$	2.06340e9	−	3.57392e9i	0.0904210	−	0.156614i	−0.817267	−	0.576259i	$-0.804512\pi$
$911$	2.06340e9	−	3.57392e9i	0.0904210	−	0.156614i	0.907688	+	0.419645i	$0.137845\pi$
$912$		0			0
$913$	2.62280e9	+	4.54282e9i	0.114056	+	0.197550i
$914$	1.91264e10	+	3.31280e10i	0.828557	+	1.43510i
$915$		0			0
$916$	−2.48761e10	+	4.30867e10i	−1.06942	+	1.85229i
$917$	−8.89042e8			−0.0380741
$918$		0			0
$919$	−8.67341e9			−0.368625			−0.184313	−	0.982868i	$-0.559006\pi$
$919$	−8.67341e9			−0.368625			−0.184313	+	0.982868i	$0.559006\pi$
$920$	1.03157e10	−	1.78673e10i	0.436759	−	0.756489i
$921$		0			0
$922$	2.50503e10	+	4.33883e10i	1.05258	+	1.82312i
$923$	−1.31583e8	−	2.27908e8i	−0.00550800	−	0.00954013i
$924$		0			0
$925$	3.26808e9	−	5.66047e9i	0.135768	−	0.235156i
$926$	−7.88585e10			−3.26370
$927$		0			0
$928$	3.75577e10			1.54270
$929$	−1.95971e10	+	3.39432e10i	−0.801930	+	1.38898i	0.116414	+	0.993201i	$0.462860\pi$
$929$	−1.95971e10	+	3.39432e10i	−0.801930	+	1.38898i	−0.918344	+	0.395783i	$0.870473\pi$
$930$		0			0
$931$	1.46733e10	+	2.54149e10i	0.595942	+	1.03220i
$932$	−2.10301e10	−	3.64252e10i	−0.850914	−	1.47383i
$933$		0			0
$934$	−8.97444e9	+	1.55442e10i	−0.360407	+	0.624243i
$935$	1.60063e9			0.0640400
$936$		0			0
$937$	−8.74627e9			−0.347324			−0.173662	−	0.984805i	$-0.555560\pi$
$937$	−8.74627e9			−0.347324			−0.173662	+	0.984805i	$0.555560\pi$
$938$	−9.19688e9	+	1.59295e10i	−0.363857	+	0.630218i
$939$		0			0
$940$	−1.12659e10	−	1.95132e10i	−0.442405	−	0.766268i
$941$	2.00195e10	+	3.46747e10i	0.783229	+	1.35659i	0.930051	+	0.367429i	$0.119762\pi$
$941$	2.00195e10	+	3.46747e10i	0.783229	+	1.35659i	−0.146823	+	0.989163i	$0.546905\pi$
$942$		0			0
$943$	9.32380e9	−	1.61493e10i	0.362078	−	0.627137i
$944$	−1.02953e11			−3.98325
$945$		0			0
$946$	−6.41336e10			−2.46301
$947$	−9.20351e9	+	1.59409e10i	−0.352151	+	0.609943i	−0.986626	−	0.163000i	$-0.947883\pi$
$947$	−9.20351e9	+	1.59409e10i	−0.352151	+	0.609943i	0.634475	+	0.772943i	$0.281216\pi$
$948$		0			0
$949$	−1.40372e8	−	2.43131e8i	−0.00533148	−	0.00923439i
$950$	−3.02292e10	−	5.23586e10i	−1.14392	−	1.98132i
$951$		0			0
$952$	−2.72451e9	+	4.71898e9i	−0.102343	+	0.177263i
$953$	1.36320e10			0.510194			0.255097	−	0.966915i	$-0.417893\pi$
$953$	1.36320e10			0.510194			0.255097	+	0.966915i	$0.417893\pi$
$954$		0			0
$955$	−1.10102e9			−0.0409058
$956$	5.15078e10	−	8.92142e10i	1.90665	−	3.30241i
$957$		0			0
$958$	−2.96924e10	−	5.14288e10i	−1.09110	−	1.88985i
$959$	1.54220e8	+	2.67116e8i	0.00564644	+	0.00977992i
$960$		0			0
$961$	1.20962e10	−	2.09513e10i	0.439662	−	0.761517i
$962$	2.58168e8			0.00934954
$963$		0			0
$964$	1.53937e10			0.553444
$965$	−2.02472e9	+	3.50693e9i	−0.0725304	+	0.125626i
$966$		0			0
$967$	2.82952e9	+	4.90087e9i	0.100628	+	0.174293i	0.911944	−	0.410315i	$-0.134581\pi$
$967$	2.82952e9	+	4.90087e9i	0.100628	+	0.174293i	−0.811315	+	0.584609i	$0.801248\pi$
$968$	3.84749e9	+	6.66405e9i	0.136337	+	0.236143i
$969$		0			0
$970$	−8.17821e9	+	1.41651e10i	−0.287711	+	0.498331i
$971$	9.65547e9			0.338459			0.169230	−	0.985577i	$-0.445872\pi$
$971$	9.65547e9			0.338459			0.169230	+	0.985577i	$0.445872\pi$
$972$		0			0
$973$	−2.75961e9			−0.0960400
$974$	6.51079e9	−	1.12770e10i	0.225776	−	0.391055i
$975$		0			0
$976$	−4.68488e10	−	8.11445e10i	−1.61296	−	2.79373i
$977$	2.13798e10	+	3.70308e10i	0.733453	+	1.27038i	0.955399	+	0.295318i	$0.0954257\pi$
$977$	2.13798e10	+	3.70308e10i	0.733453	+	1.27038i	−0.221946	+	0.975059i	$0.571241\pi$
$978$		0			0
$979$	9.88876e8	−	1.71278e9i	0.0336824	−	0.0583395i
$980$	−1.65509e10			−0.561732
$981$		0			0
$982$	5.88125e10			1.98189
$983$	1.84845e10	−	3.20161e10i	0.620684	−	1.07506i	−0.368675	−	0.929558i	$-0.620188\pi$
$983$	1.84845e10	−	3.20161e10i	0.620684	−	1.07506i	0.989359	−	0.145497i	$-0.0464782\pi$
$984$		0			0
$985$	−2.37056e8	−	4.10592e8i	−0.00790357	−	0.0136894i
$986$	4.06389e9	+	7.03887e9i	0.135012	+	0.233848i
$987$		0			0
$988$	8.60603e8	−	1.49061e9i	0.0283892	−	0.0491716i
$989$	−4.73963e10			−1.55796
$990$		0			0
$991$	−5.13146e10			−1.67488			−0.837440	−	0.546530i	$-0.815948\pi$
$991$	−5.13146e10			−1.67488			−0.837440	+	0.546530i	$0.815948\pi$
$992$	−1.51622e10	+	2.62617e10i	−0.493142	+	0.854146i
$993$		0			0
$994$	−4.88692e9	−	8.46440e9i	−0.157828	−	0.273365i
$995$	−2.02679e9	−	3.51051e9i	−0.0652272	−	0.112977i
$996$		0			0
$997$	−2.28440e10	+	3.95670e10i	−0.730028	+	1.26445i	0.226843	+	0.973931i	$0.427160\pi$
$997$	−2.28440e10	+	3.95670e10i	−0.730028	+	1.26445i	−0.956871	+	0.290514i	$0.906174\pi$
$998$	−4.88854e10			−1.55676
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.8.c.a.19.6		12
3.2	odd	2		9.8.c.a.7.1	yes	12
4.3	odd	2		432.8.i.c.289.4		12
9.2	odd	6		81.8.a.e.1.6		6
9.4	even	3	inner	27.8.c.a.10.6		12
9.5	odd	6		9.8.c.a.4.1	✓	12
9.7	even	3		81.8.a.c.1.1		6
12.11	even	2		144.8.i.c.97.3		12
36.23	even	6		144.8.i.c.49.3		12
36.31	odd	6		432.8.i.c.145.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.1	✓	12	9.5	odd	6
9.8.c.a.7.1	yes	12	3.2	odd	2
27.8.c.a.10.6		12	9.4	even	3	inner
27.8.c.a.19.6		12	1.1	even	1	trivial
81.8.a.c.1.1		6	9.7	even	3
81.8.a.e.1.6		6	9.2	odd	6
144.8.i.c.49.3		12	36.23	even	6
144.8.i.c.97.3		12	12.11	even	2
432.8.i.c.145.4		12	36.31	odd	6
432.8.i.c.289.4		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(10.7051 - 18.5418i) q^{2} +(-165.199 - 286.133i) q^{4} +(-32.6274 - 56.5123i) q^{5} +(-118.194 + 204.717i) q^{7} -4333.37 q^{8} +O(q^{10})\)	\(q+(10.7051 - 18.5418i) q^{2} +(-165.199 - 286.133i) q^{4} +(-32.6274 - 56.5123i) q^{5} +(-118.194 + 204.717i) q^{7} -4333.37 q^{8} -1397.12 q^{10} +(2305.59 - 3993.39i) q^{11} +(68.1364 + 118.016i) q^{13} +(2530.55 + 4383.04i) q^{14} +(-25243.8 + 43723.5i) q^{16} -5319.46 q^{17} +38228.5 q^{19} +(-10780.0 + 18671.5i) q^{20} +(-49363.1 - 85499.4i) q^{22} +(-36480.5 - 63186.1i) q^{23} +(36933.4 - 63970.5i) q^{25} +2917.63 q^{26} +78101.7 q^{28} +(35682.4 - 61803.7i) q^{29} +(28810.3 + 49900.8i) q^{31} +(263139. + 455770. i) q^{32} +(-56945.4 + 98632.4i) q^{34} +15425.4 q^{35} +88485.6 q^{37} +(409240. - 708824. i) q^{38} +(141387. + 244889. i) q^{40} +(127791. + 221341. i) q^{41} +(324806. - 562580. i) q^{43} -1.52352e6 q^{44} -1.56211e6 q^{46} +(-522539. + 905063. i) q^{47} +(383832. + 664817. i) q^{49} +(-790752. - 1.36962e6i) q^{50} +(22512.1 - 38992.1i) q^{52} +777845. q^{53} -300901. q^{55} +(512177. - 887116. i) q^{56} +(-763967. - 1.32323e6i) q^{58} +(1.01959e6 + 1.76598e6i) q^{59} +(-927927. + 1.60722e6i) q^{61} +1.23367e6 q^{62} +4.80532e6 q^{64} +(4446.23 - 7701.10i) q^{65} +(1.81717e6 + 3.14743e6i) q^{67} +(878768. + 1.52207e6i) q^{68} +(165131. - 286015. i) q^{70} -1.93117e6 q^{71} -2.06016e6 q^{73} +(947248. - 1.64068e6i) q^{74} +(-6.31529e6 - 1.09384e7i) q^{76} +(545011. + 943987. i) q^{77} +(3.13421e6 - 5.42860e6i) q^{79} +3.29456e6 q^{80} +5.47209e6 q^{82} +(-568792. + 985177. i) q^{83} +(173560. + 300615. i) q^{85} +(-6.95416e6 - 1.20450e7i) q^{86} +(-9.99096e6 + 1.73049e7i) q^{88} +428904. q^{89} -32213.2 q^{91} +(-1.20531e7 + 2.08765e7i) q^{92} +(1.11877e7 + 1.93776e7i) q^{94} +(-1.24730e6 - 2.16038e6i) q^{95} +(5.85362e6 - 1.01388e7i) q^{97} +1.64359e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8}+O(q^{10}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8	\( 12 q + 9 q^{2} - 321 q^{4} + 180 q^{5} - 84 q^{7} - 5922 q^{8} + 252 q^{10} + 8460 q^{11} - 1848 q^{13} + 16272 q^{14} - 12417 q^{16} - 30564 q^{17} + 24432 q^{19} + 40788 q^{20} - 35001 q^{22} + 51588 q^{23} + 4746 q^{25} - 536472 q^{26} + 75516 q^{28} + 414648 q^{29} + 8196 q^{31} + 1048977 q^{32} - 106623 q^{34} - 2210616 q^{35} + 139344 q^{37} + 1952685 q^{38} + 305496 q^{40} + 1731582 q^{41} + 408372 q^{43} - 5169114 q^{44} - 1684008 q^{46} + 1631484 q^{47} - 179010 q^{49} + 1654461 q^{50} + 681594 q^{52} - 2835648 q^{53} - 16056 q^{55} + 1784466 q^{56} - 948384 q^{58} + 2055636 q^{59} - 2723196 q^{61} + 1026828 q^{62} + 7178178 q^{64} + 1387620 q^{65} + 3806556 q^{67} - 2142639 q^{68} + 953442 q^{70} - 2408400 q^{71} - 10670052 q^{73} - 9846504 q^{74} - 6727827 q^{76} - 3478824 q^{77} + 6020916 q^{79} + 38072448 q^{80} + 9403002 q^{82} - 9605052 q^{83} - 1698624 q^{85} - 34278561 q^{86} - 16459029 q^{88} + 24630264 q^{89} + 13570104 q^{91} - 39143394 q^{92} + 12602808 q^{94} - 10422072 q^{95} + 9977226 q^{97} + 95833314 q^{98}+O(q^{100}) \) 12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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