LMFDB - Embedded newform 64.7.f.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,7,Mod(15,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("64.15");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	64.f (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:	$14.7234613517$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			15.2
Character	$\chi$	$=$	64.15
Dual form			64.7.f.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.6946 - 25.6946i) q^{3} +(-141.826 - 141.826i) q^{5} -411.977 q^{7} +591.425i q^{9} +O(q^{10})$	\(q+(-25.6946 - 25.6946i) q^{3} +(-141.826 - 141.826i) q^{5} -411.977 q^{7} +591.425i q^{9} +(44.9619 - 44.9619i) q^{11} +(2355.48 - 2355.48i) q^{13} +7288.34i q^{15} -3212.26 q^{17} +(1628.35 + 1628.35i) q^{19} +(10585.6 + 10585.6i) q^{21} +8469.99 q^{23} +24604.3i q^{25} +(-3534.93 + 3534.93i) q^{27} +(-8578.85 + 8578.85i) q^{29} -17162.0i q^{31} -2310.56 q^{33} +(58429.1 + 58429.1i) q^{35} +(-39117.2 - 39117.2i) q^{37} -121046. q^{39} +68881.9i q^{41} +(36872.5 - 36872.5i) q^{43} +(83879.6 - 83879.6i) q^{45} -62591.7i q^{47} +52075.9 q^{49} +(82537.8 + 82537.8i) q^{51} +(-16287.1 - 16287.1i) q^{53} -12753.5 q^{55} -83679.7i q^{57} +(-56470.6 + 56470.6i) q^{59} +(242781. - 242781. i) q^{61} -243653. i q^{63} -668136. q^{65} +(-337557. - 337557. i) q^{67} +(-217633. - 217633. i) q^{69} -355567. q^{71} +341935. i q^{73} +(632199. - 632199. i) q^{75} +(-18523.3 + 18523.3i) q^{77} +439742. i q^{79} +612806. q^{81} +(686399. + 686399. i) q^{83} +(455583. + 455583. i) q^{85} +440860. q^{87} +599060. i q^{89} +(-970401. + 970401. i) q^{91} +(-440972. + 440972. i) q^{93} -461886. i q^{95} +997682. q^{97} +(26591.6 + 26591.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} - 2 q^{5} + 4 q^{7}+O(q^{10}) $ 22 * q + 2 * q^3 - 2 * q^5 + 4 * q^7	$ 22 q + 2 q^{3} - 2 q^{5} + 4 q^{7} - 1358 q^{11} - 2 q^{13} - 4 q^{17} - 3934 q^{19} - 1460 q^{21} + 13124 q^{23} - 35776 q^{27} - 33202 q^{29} - 4 q^{33} + 112420 q^{35} + 3598 q^{37} - 254396 q^{39} + 267986 q^{43} + 32706 q^{45} + 168066 q^{49} - 301788 q^{51} - 221842 q^{53} + 232708 q^{55} - 39150 q^{59} + 326494 q^{61} + 186412 q^{65} + 122786 q^{67} - 543188 q^{69} + 267012 q^{71} + 275278 q^{75} + 231180 q^{77} - 354298 q^{81} + 288322 q^{83} + 340748 q^{85} - 2029884 q^{87} - 302396 q^{91} - 1173344 q^{93} - 4 q^{97} + 271522 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 - 2 * q^5 + 4 * q^7 - 1358 * q^11 - 2 * q^13 - 4 * q^17 - 3934 * q^19 - 1460 * q^21 + 13124 * q^23 - 35776 * q^27 - 33202 * q^29 - 4 * q^33 + 112420 * q^35 + 3598 * q^37 - 254396 * q^39 + 267986 * q^43 + 32706 * q^45 + 168066 * q^49 - 301788 * q^51 - 221842 * q^53 + 232708 * q^55 - 39150 * q^59 + 326494 * q^61 + 186412 * q^65 + 122786 * q^67 - 543188 * q^69 + 267012 * q^71 + 275278 * q^75 + 231180 * q^77 - 354298 * q^81 + 288322 * q^83 + 340748 * q^85 - 2029884 * q^87 - 302396 * q^91 - 1173344 * q^93 - 4 * q^97 + 271522 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−25.6946	−	25.6946i	−0.951652	−	0.951652i	0.0472320	−	0.998884i	$-0.484960\pi$
$3$	−25.6946	−	25.6946i	−0.951652	−	0.951652i	−0.998884	+	0.0472320i	$0.984960\pi$
$4$		0			0
$5$	−141.826	−	141.826i	−1.13461	−	1.13461i	−0.989401	−	0.145209i	$-0.953615\pi$
$5$	−141.826	−	141.826i	−1.13461	−	1.13461i	−0.145209	−	0.989401i	$-0.546385\pi$
$6$		0			0
$7$	−411.977			−1.20110			−0.600549	−	0.799588i	$-0.705051\pi$
$7$	−411.977			−1.20110			−0.600549	+	0.799588i	$0.705051\pi$
$8$		0			0
$9$			591.425i			0.811283i
$10$		0			0
$11$	44.9619	−	44.9619i	0.0337805	−	0.0337805i	−0.690015	−	0.723795i	$-0.742396\pi$
$11$	44.9619	−	44.9619i	0.0337805	−	0.0337805i	0.723795	+	0.690015i	$0.242396\pi$
$12$		0			0
$13$	2355.48	−	2355.48i	1.07213	−	1.07213i	0.0749450	−	0.997188i	$-0.476122\pi$
$13$	2355.48	−	2355.48i	1.07213	−	1.07213i	0.997188	−	0.0749450i	$-0.0238781\pi$
$14$		0			0
$15$			7288.34i			2.15951i
$16$		0			0
$17$	−3212.26			−0.653829			−0.326915	−	0.945054i	$-0.606009\pi$
$17$	−3212.26			−0.653829			−0.326915	+	0.945054i	$0.606009\pi$
$18$		0			0
$19$	1628.35	+	1628.35i	0.237404	+	0.237404i	0.815774	−	0.578370i	$-0.196311\pi$
$19$	1628.35	+	1628.35i	0.237404	+	0.237404i	−0.578370	+	0.815774i	$0.696311\pi$
$20$		0			0
$21$	10585.6	+	10585.6i	1.14303	+	1.14303i
$22$		0			0
$23$	8469.99			0.696144			0.348072	−	0.937468i	$-0.386836\pi$
$23$	8469.99			0.696144			0.348072	+	0.937468i	$0.386836\pi$
$24$		0			0
$25$			24604.3i			1.57468i
$26$		0			0
$27$	−3534.93	+	3534.93i	−0.179593	+	0.179593i
$28$		0			0
$29$	−8578.85	+	8578.85i	−0.351751	+	0.351751i	−0.860761	−	0.509010i	$-0.830012\pi$
$29$	−8578.85	+	8578.85i	−0.351751	+	0.351751i	0.509010	+	0.860761i	$0.330012\pi$
$30$		0			0
$31$		−	17162.0i		−	0.576082i	−0.957618	−	0.288041i	$-0.906996\pi$
$31$		−	17162.0i		−	0.576082i	0.957618	−	0.288041i	$-0.0930039\pi$
$32$		0			0
$33$	−2310.56			−0.0642946
$34$		0			0
$35$	58429.1	+	58429.1i	1.36278	+	1.36278i
$36$		0			0
$37$	−39117.2	−	39117.2i	−0.772259	−	0.772259i	0.206242	−	0.978501i	$-0.433877\pi$
$37$	−39117.2	−	39117.2i	−0.772259	−	0.772259i	−0.978501	+	0.206242i	$0.933877\pi$
$38$		0			0
$39$	−121046.			−2.04059
$40$		0			0
$41$			68881.9i			0.999433i	0.866189	+	0.499716i	$0.166562\pi$
$41$			68881.9i			0.999433i	−0.866189	+	0.499716i	$0.833438\pi$
$42$		0			0
$43$	36872.5	−	36872.5i	0.463764	−	0.463764i	−0.436123	−	0.899887i	$-0.643649\pi$
$43$	36872.5	−	36872.5i	0.463764	−	0.463764i	0.899887	+	0.436123i	$0.143649\pi$
$44$		0			0
$45$	83879.6	−	83879.6i	0.920489	−	0.920489i
$46$		0			0
$47$		−	62591.7i		−	0.602869i	−0.953487	−	0.301435i	$-0.902534\pi$
$47$		−	62591.7i		−	0.602869i	0.953487	−	0.301435i	$-0.0974655\pi$
$48$		0			0
$49$	52075.9			0.442638
$50$		0			0
$51$	82537.8	+	82537.8i	0.622218	+	0.622218i
$52$		0			0
$53$	−16287.1	−	16287.1i	−0.109400	−	0.109400i	0.650288	−	0.759688i	$-0.274648\pi$
$53$	−16287.1	−	16287.1i	−0.109400	−	0.109400i	−0.759688	+	0.650288i	$0.774648\pi$
$54$		0			0
$55$	−12753.5			−0.0766554
$56$		0			0
$57$		−	83679.7i		−	0.451851i
$58$		0			0
$59$	−56470.6	+	56470.6i	−0.274958	+	0.274958i	−0.831092	−	0.556134i	$-0.812284\pi$
$59$	−56470.6	+	56470.6i	−0.274958	+	0.274958i	0.556134	+	0.831092i	$0.312284\pi$
$60$		0			0
$61$	242781.	−	242781.i	1.06961	−	1.06961i	0.0722192	−	0.997389i	$-0.476992\pi$
$61$	242781.	−	242781.i	1.06961	−	1.06961i	0.997389	−	0.0722192i	$-0.0230081\pi$
$62$		0			0
$63$		−	243653.i		−	0.974431i
$64$		0			0
$65$	−668136.			−2.43290
$66$		0			0
$67$	−337557.	−	337557.i	−1.12234	−	1.12234i	−0.991389	−	0.130946i	$-0.958198\pi$
$67$	−337557.	−	337557.i	−1.12234	−	1.12234i	−0.130946	−	0.991389i	$-0.541802\pi$
$68$		0			0
$69$	−217633.	−	217633.i	−0.662487	−	0.662487i
$70$		0			0
$71$	−355567.			−0.993452			−0.496726	−	0.867907i	$-0.665465\pi$
$71$	−355567.			−0.993452			−0.496726	+	0.867907i	$0.665465\pi$
$72$		0			0
$73$			341935.i			0.878971i	0.898250	+	0.439486i	$0.144839\pi$
$73$			341935.i			0.878971i	−0.898250	+	0.439486i	$0.855161\pi$
$74$		0			0
$75$	632199.	−	632199.i	1.49855	−	1.49855i
$76$		0			0
$77$	−18523.3	+	18523.3i	−0.0405737	+	0.0405737i
$78$		0			0
$79$			439742.i			0.891901i	0.895058	+	0.445950i	$0.147134\pi$
$79$			439742.i			0.891901i	−0.895058	+	0.445950i	$0.852866\pi$
$80$		0			0
$81$	612806.			1.15310
$82$		0			0
$83$	686399.	+	686399.i	1.20045	+	1.20045i	0.974031	+	0.226415i	$0.0727005\pi$
$83$	686399.	+	686399.i	1.20045	+	1.20045i	0.226415	+	0.974031i	$0.427299\pi$
$84$		0			0
$85$	455583.	+	455583.i	0.741841	+	0.741841i
$86$		0			0
$87$	440860.			0.669488
$88$		0			0
$89$			599060.i			0.849768i	0.905248	+	0.424884i	$0.139685\pi$
$89$			599060.i			0.849768i	−0.905248	+	0.424884i	$0.860315\pi$
$90$		0			0
$91$	−970401.	+	970401.i	−1.28774	+	1.28774i
$92$		0			0
$93$	−440972.	+	440972.i	−0.548229	+	0.548229i
$94$		0			0
$95$		−	461886.i		−	0.538721i
$96$		0			0
$97$	997682.			1.09314			0.546572	−	0.837412i	$-0.315933\pi$
$97$	997682.			1.09314			0.546572	+	0.837412i	$0.315933\pi$
$98$		0			0
$99$	26591.6	+	26591.6i	0.0274056	+	0.0274056i
$100$		0			0
$101$	−238723.	−	238723.i	−0.231702	−	0.231702i	0.581701	−	0.813403i	$-0.302387\pi$
$101$	−238723.	−	238723.i	−0.231702	−	0.231702i	−0.813403	+	0.581701i	$0.802387\pi$
$102$		0			0
$103$	526787.			0.482085			0.241042	−	0.970515i	$-0.422511\pi$
$103$	526787.			0.482085			0.241042	+	0.970515i	$0.422511\pi$
$104$		0			0
$105$		−	3.00263e6i		−	2.59378i
$106$		0			0
$107$	−1.20835e6	+	1.20835e6i	−0.986375	+	0.986375i	−0.999908	−	0.0135332i	$-0.995692\pi$
$107$	−1.20835e6	+	1.20835e6i	−0.986375	+	0.986375i	0.0135332	+	0.999908i	$0.495692\pi$
$108$		0			0
$109$	−1.65809e6	+	1.65809e6i	−1.28035	+	1.28035i	−0.339879	+	0.940469i	$0.610386\pi$
$109$	−1.65809e6	+	1.65809e6i	−1.28035	+	1.28035i	−0.940469	+	0.339879i	$0.889614\pi$
$110$		0			0
$111$			2.01020e6i			1.46984i
$112$		0			0
$113$	57104.5			0.0395763			0.0197881	−	0.999804i	$-0.493701\pi$
$113$	57104.5			0.0395763			0.0197881	+	0.999804i	$0.493701\pi$
$114$		0			0
$115$	−1.20127e6	−	1.20127e6i	−0.789852	−	0.789852i
$116$		0			0
$117$	1.39309e6	+	1.39309e6i	0.869803	+	0.869803i
$118$		0			0
$119$	1.32338e6			0.785313
$120$		0			0
$121$			1.76752e6i			0.997718i
$122$		0			0
$123$	1.76989e6	−	1.76989e6i	0.951112	−	0.951112i
$124$		0			0
$125$	1.27351e6	−	1.27351e6i	0.652035	−	0.652035i
$126$		0			0
$127$		−	699514.i		−	0.341496i	−0.985315	−	0.170748i	$-0.945382\pi$
$127$		−	699514.i		−	0.341496i	0.985315	−	0.170748i	$-0.0546183\pi$
$128$		0			0
$129$	−1.89485e6			−0.882684
$130$		0			0
$131$	−1.85396e6	−	1.85396e6i	−0.824684	−	0.824684i	0.162092	−	0.986776i	$-0.448176\pi$
$131$	−1.85396e6	−	1.85396e6i	−0.824684	−	0.824684i	−0.986776	+	0.162092i	$0.948176\pi$
$132$		0			0
$133$	−670843.	−	670843.i	−0.285145	−	0.285145i
$134$		0			0
$135$	1.00269e6			0.407536
$136$		0			0
$137$		−	1.00819e6i		−	0.392086i	−0.980595	−	0.196043i	$-0.937191\pi$
$137$		−	1.00819e6i		−	0.392086i	0.980595	−	0.196043i	$-0.0628092\pi$
$138$		0			0
$139$	1.56333e6	−	1.56333e6i	0.582112	−	0.582112i	−0.353371	−	0.935483i	$-0.614965\pi$
$139$	1.56333e6	−	1.56333e6i	0.582112	−	0.582112i	0.935483	+	0.353371i	$0.114965\pi$
$140$		0			0
$141$	−1.60827e6	+	1.60827e6i	−0.573722	+	0.573722i
$142$		0			0
$143$		−	211813.i		−	0.0724344i
$144$		0			0
$145$	2.43341e6			0.798199
$146$		0			0
$147$	−1.33807e6	−	1.33807e6i	−0.421237	−	0.421237i
$148$		0			0
$149$	−1.96711e6	−	1.96711e6i	−0.594661	−	0.594661i	0.344226	−	0.938887i	$-0.388141\pi$
$149$	−1.96711e6	−	1.96711e6i	−0.594661	−	0.594661i	−0.938887	+	0.344226i	$0.888141\pi$
$150$		0			0
$151$	−431913.			−0.125449			−0.0627243	−	0.998031i	$-0.519979\pi$
$151$	−431913.			−0.125449			−0.0627243	+	0.998031i	$0.519979\pi$
$152$		0			0
$153$		−	1.89981e6i		−	0.530440i
$154$		0			0
$155$	−2.43403e6	+	2.43403e6i	−0.653628	+	0.653628i
$156$		0			0
$157$	4.24849e6	−	4.24849e6i	1.09783	−	1.09783i	0.103166	−	0.994664i	$-0.467103\pi$
$157$	4.24849e6	−	4.24849e6i	1.09783	−	1.09783i	0.994664	−	0.103166i	$-0.0328974\pi$
$158$		0			0
$159$			836983.i			0.208221i
$160$		0			0
$161$	−3.48944e6			−0.836138
$162$		0			0
$163$	2.55603e6	+	2.55603e6i	0.590206	+	0.590206i	0.937687	−	0.347481i	$-0.112963\pi$
$163$	2.55603e6	+	2.55603e6i	0.590206	+	0.590206i	−0.347481	+	0.937687i	$0.612963\pi$
$164$		0			0
$165$	327697.	+	327697.i	0.0729493	+	0.0729493i
$166$		0			0
$167$	−646882.			−0.138891			−0.0694457	−	0.997586i	$-0.522123\pi$
$167$	−646882.			−0.138891			−0.0694457	+	0.997586i	$0.522123\pi$
$168$		0			0
$169$		−	6.26972e6i		−	1.29894i
$170$		0			0
$171$	−963048.	+	963048.i	−0.192602	+	0.192602i
$172$		0			0
$173$	−4.10734e6	+	4.10734e6i	−0.793273	+	0.793273i	−0.982025	−	0.188752i	$-0.939556\pi$
$173$	−4.10734e6	+	4.10734e6i	−0.793273	+	0.793273i	0.188752	+	0.982025i	$0.439556\pi$
$174$		0			0
$175$		−	1.01364e7i		−	1.89134i
$176$		0			0
$177$	2.90198e6			0.523329
$178$		0			0
$179$	−1.11716e6	−	1.11716e6i	−0.194786	−	0.194786i	0.602975	−	0.797760i	$-0.293982\pi$
$179$	−1.11716e6	−	1.11716e6i	−0.194786	−	0.194786i	−0.797760	+	0.602975i	$0.793982\pi$
$180$		0			0
$181$	2.49437e6	+	2.49437e6i	0.420654	+	0.420654i	0.885429	−	0.464775i	$-0.153865\pi$
$181$	2.49437e6	+	2.49437e6i	0.420654	+	0.420654i	−0.464775	+	0.885429i	$0.653865\pi$
$182$		0			0
$183$	−1.24763e7			−2.03579
$184$		0			0
$185$			1.10957e7i			1.75243i
$186$		0			0
$187$	−144429.	+	144429.i	−0.0220867	+	0.0220867i
$188$		0			0
$189$	1.45631e6	−	1.45631e6i	0.215709	−	0.215709i
$190$		0			0
$191$			7.12374e6i			1.02237i	0.859471	+	0.511185i	$0.170793\pi$
$191$			7.12374e6i			1.02237i	−0.859471	+	0.511185i	$0.829207\pi$
$192$		0			0
$193$	1.63763e6			0.227795			0.113898	−	0.993492i	$-0.463666\pi$
$193$	1.63763e6			0.227795			0.113898	+	0.993492i	$0.463666\pi$
$194$		0			0
$195$	1.71675e7	+	1.71675e7i	2.31528	+	2.31528i
$196$		0			0
$197$	−8.02811e6	−	8.02811e6i	−1.05006	−	1.05006i	−0.998679	−	0.0513818i	$-0.983637\pi$
$197$	−8.02811e6	−	8.02811e6i	−1.05006	−	1.05006i	−0.0513818	−	0.998679i	$-0.516363\pi$
$198$		0			0
$199$	1.07094e7			1.35896			0.679481	−	0.733693i	$-0.262205\pi$
$199$	1.07094e7			1.35896			0.679481	+	0.733693i	$0.262205\pi$
$200$		0			0
$201$			1.73468e7i			2.13615i
$202$		0			0
$203$	3.53429e6	−	3.53429e6i	0.422487	−	0.422487i
$204$		0			0
$205$	9.76926e6	−	9.76926e6i	1.13397	−	1.13397i
$206$		0			0
$207$			5.00936e6i			0.564770i
$208$		0			0
$209$	146428.			0.0160392
$210$		0			0
$211$	599213.	+	599213.i	0.0637872	+	0.0637872i	0.738281	−	0.674494i	$-0.235638\pi$
$211$	599213.	+	599213.i	0.0637872	+	0.0637872i	−0.674494	+	0.738281i	$0.735638\pi$
$212$		0			0
$213$	9.13616e6	+	9.13616e6i	0.945420	+	0.945420i
$214$		0			0
$215$	−1.04590e7			−1.05238
$216$		0			0
$217$			7.07037e6i			0.691931i
$218$		0			0
$219$	8.78588e6	−	8.78588e6i	0.836475	−	0.836475i
$220$		0			0
$221$	−7.56641e6	+	7.56641e6i	−0.700992	+	0.700992i
$222$		0			0
$223$		−	4.79044e6i		−	0.431977i	−0.976396	−	0.215989i	$-0.930703\pi$
$223$		−	4.79044e6i		−	0.431977i	0.976396	−	0.215989i	$-0.0692975\pi$
$224$		0			0
$225$	−1.45516e7			−1.27751
$226$		0			0
$227$	−1.24849e7	−	1.24849e7i	−1.06735	−	1.06735i	−0.997562	−	0.0697866i	$-0.977768\pi$
$227$	−1.24849e7	−	1.24849e7i	−1.06735	−	1.06735i	−0.0697866	−	0.997562i	$-0.522232\pi$
$228$		0			0
$229$	4.70901e6	+	4.70901e6i	0.392123	+	0.392123i	0.875444	−	0.483320i	$-0.160569\pi$
$229$	4.70901e6	+	4.70901e6i	0.392123	+	0.392123i	−0.483320	+	0.875444i	$0.660569\pi$
$230$		0			0
$231$	951895.			0.0772242
$232$		0			0
$233$		−	7.62544e6i		−	0.602833i	−0.953493	−	0.301417i	$-0.902540\pi$
$233$		−	7.62544e6i		−	0.602833i	0.953493	−	0.301417i	$-0.0974595\pi$
$234$		0			0
$235$	−8.87714e6	+	8.87714e6i	−0.684021	+	0.684021i
$236$		0			0
$237$	1.12990e7	−	1.12990e7i	0.848779	−	0.848779i
$238$		0			0
$239$			1.14653e7i			0.839830i	0.907563	+	0.419915i	$0.137940\pi$
$239$			1.14653e7i			0.839830i	−0.907563	+	0.419915i	$0.862060\pi$
$240$		0			0
$241$	−1.91183e7			−1.36583			−0.682916	−	0.730497i	$-0.739289\pi$
$241$	−1.91183e7			−1.36583			−0.682916	+	0.730497i	$0.739289\pi$
$242$		0			0
$243$	−1.31688e7	−	1.31688e7i	−0.917760	−	0.917760i
$244$		0			0
$245$	−7.38573e6	−	7.38573e6i	−0.502221	−	0.502221i
$246$		0			0
$247$	7.67109e6			0.509057
$248$		0			0
$249$		−	3.52735e7i		−	2.28481i
$250$		0			0
$251$	−1.23788e7	+	1.23788e7i	−0.782810	+	0.782810i	−0.980304	−	0.197494i	$-0.936720\pi$
$251$	−1.23788e7	+	1.23788e7i	−0.782810	+	0.782810i	0.197494	+	0.980304i	$0.436720\pi$
$252$		0			0
$253$	380827.	−	380827.i	0.0235161	−	0.0235161i
$254$		0			0
$255$		−	2.34120e7i		−	1.41195i
$256$		0			0
$257$	2.58515e7			1.52295			0.761475	−	0.648194i	$-0.224475\pi$
$257$	2.58515e7			1.52295			0.761475	+	0.648194i	$0.224475\pi$
$258$		0			0
$259$	1.61154e7	+	1.61154e7i	0.927559	+	0.927559i
$260$		0			0
$261$	−5.07374e6	−	5.07374e6i	−0.285369	−	0.285369i
$262$		0			0
$263$	−4.58883e6			−0.252252			−0.126126	−	0.992014i	$-0.540254\pi$
$263$	−4.58883e6			−0.252252			−0.126126	+	0.992014i	$0.540254\pi$
$264$		0			0
$265$			4.61989e6i			0.248252i
$266$		0			0
$267$	1.53926e7	−	1.53926e7i	0.808684	−	0.808684i
$268$		0			0
$269$	−1.43832e7	+	1.43832e7i	−0.738921	+	0.738921i	−0.972369	−	0.233448i	$-0.924999\pi$
$269$	−1.43832e7	+	1.43832e7i	−0.738921	+	0.738921i	0.233448	+	0.972369i	$0.424999\pi$
$270$		0			0
$271$			1.56022e7i			0.783932i	0.919980	+	0.391966i	$0.128205\pi$
$271$			1.56022e7i			0.783932i	−0.919980	+	0.391966i	$0.871795\pi$
$272$		0			0
$273$	4.98682e7			2.45095
$274$		0			0
$275$	1.10626e6	+	1.10626e6i	0.0531935	+	0.0531935i
$276$		0			0
$277$	−1.49968e7	−	1.49968e7i	−0.705600	−	0.705600i	0.260007	−	0.965607i	$-0.416275\pi$
$277$	−1.49968e7	−	1.49968e7i	−0.705600	−	0.705600i	−0.965607	+	0.260007i	$0.916275\pi$
$278$		0			0
$279$	1.01501e7			0.467365
$280$		0			0
$281$		−	5.16260e6i		−	0.232675i	−0.993210	−	0.116338i	$-0.962885\pi$
$281$		−	5.16260e6i		−	0.232675i	0.993210	−	0.116338i	$-0.0371154\pi$
$282$		0			0
$283$	−7.74606e6	+	7.74606e6i	−0.341760	+	0.341760i	−0.857029	−	0.515269i	$-0.827692\pi$
$283$	−7.74606e6	+	7.74606e6i	−0.341760	+	0.341760i	0.515269	+	0.857029i	$0.327692\pi$
$284$		0			0
$285$	−1.18680e7	+	1.18680e7i	−0.512675	+	0.512675i
$286$		0			0
$287$		−	2.83777e7i		−	1.20042i
$288$		0			0
$289$	−1.38189e7			−0.572508
$290$		0			0
$291$	−2.56350e7	−	2.56350e7i	−1.04029	−	1.04029i
$292$		0			0
$293$	1.94355e7	+	1.94355e7i	0.772668	+	0.772668i	0.978572	−	0.205904i	$-0.0660136\pi$
$293$	1.94355e7	+	1.94355e7i	0.772668	+	0.772668i	−0.205904	+	0.978572i	$0.566014\pi$
$294$		0			0
$295$	1.60180e7			0.623940
$296$		0			0
$297$			317874.i			0.0121335i
$298$		0			0
$299$	1.99509e7	−	1.99509e7i	0.746359	−	0.746359i
$300$		0			0
$301$	−1.51906e7	+	1.51906e7i	−0.557027	+	0.557027i
$302$		0			0
$303$			1.22678e7i			0.441000i
$304$		0			0
$305$	−6.88653e7			−2.42718
$306$		0			0
$307$	−1.20617e7	−	1.20617e7i	−0.416861	−	0.416861i	0.467259	−	0.884120i	$-0.345242\pi$
$307$	−1.20617e7	−	1.20617e7i	−0.416861	−	0.416861i	−0.884120	+	0.467259i	$0.845242\pi$
$308$		0			0
$309$	−1.35356e7	−	1.35356e7i	−0.458777	−	0.458777i
$310$		0			0
$311$	−2.86256e7			−0.951642			−0.475821	−	0.879542i	$-0.657849\pi$
$311$	−2.86256e7			−0.951642			−0.475821	+	0.879542i	$0.657849\pi$
$312$		0			0
$313$		−	4.36158e7i		−	1.42236i	−0.703009	−	0.711181i	$-0.748160\pi$
$313$		−	4.36158e7i		−	1.42236i	0.703009	−	0.711181i	$-0.251840\pi$
$314$		0			0
$315$	−3.45564e7	+	3.45564e7i	−1.10560	+	1.10560i
$316$		0			0
$317$	−1.79251e7	+	1.79251e7i	−0.562708	+	0.562708i	−0.930076	−	0.367368i	$-0.880259\pi$
$317$	−1.79251e7	+	1.79251e7i	−0.562708	+	0.562708i	0.367368	+	0.930076i	$0.380259\pi$
$318$		0			0
$319$			771442.i			0.0237646i
$320$		0			0
$321$	6.20963e7			1.87737
$322$		0			0
$323$	−5.23069e6	−	5.23069e6i	−0.155221	−	0.155221i
$324$		0			0
$325$	5.79549e7	+	5.79549e7i	1.68826	+	1.68826i
$326$		0			0
$327$	8.52078e7			2.43689
$328$		0			0
$329$			2.57863e7i			0.724106i
$330$		0			0
$331$	1.49668e7	−	1.49668e7i	0.412709	−	0.412709i	−0.469972	−	0.882681i	$-0.655736\pi$
$331$	1.49668e7	−	1.49668e7i	0.412709	−	0.412709i	0.882681	+	0.469972i	$0.155736\pi$
$332$		0			0
$333$	2.31349e7	−	2.31349e7i	0.626520	−	0.626520i
$334$		0			0
$335$			9.57489e7i			2.54683i
$336$		0			0
$337$	−1.92483e7			−0.502924			−0.251462	−	0.967867i	$-0.580911\pi$
$337$	−1.92483e7			−0.502924			−0.251462	+	0.967867i	$0.580911\pi$
$338$		0			0
$339$	−1.46728e6	−	1.46728e6i	−0.0376629	−	0.0376629i
$340$		0			0
$341$	−771638.	−	771638.i	−0.0194603	−	0.0194603i
$342$		0			0
$343$	2.70146e7			0.669447
$344$		0			0
$345$			6.17321e7i			1.50333i
$346$		0			0
$347$	−5.04931e7	+	5.04931e7i	−1.20849	+	1.20849i	−0.236975	+	0.971516i	$0.576156\pi$
$347$	−5.04931e7	+	5.04931e7i	−1.20849	+	1.20849i	−0.971516	+	0.236975i	$0.923844\pi$
$348$		0			0
$349$	8.31696e6	−	8.31696e6i	0.195654	−	0.195654i	−0.602480	−	0.798134i	$-0.705821\pi$
$349$	8.31696e6	−	8.31696e6i	0.195654	−	0.195654i	0.798134	+	0.602480i	$0.205821\pi$
$350$		0			0
$351$			1.66529e7i			0.385095i
$352$		0			0
$353$	2.48212e7			0.564284			0.282142	−	0.959373i	$-0.408955\pi$
$353$	2.48212e7			0.564284			0.282142	+	0.959373i	$0.408955\pi$
$354$		0			0
$355$	5.04288e7	+	5.04288e7i	1.12718	+	1.12718i
$356$		0			0
$357$	−3.40037e7	−	3.40037e7i	−0.747345	−	0.747345i
$358$		0			0
$359$	−8.53598e7			−1.84489			−0.922444	−	0.386130i	$-0.873812\pi$
$359$	−8.53598e7			−1.84489			−0.922444	+	0.386130i	$0.873812\pi$
$360$		0			0
$361$		−	4.17428e7i		−	0.887279i
$362$		0			0
$363$	4.54157e7	−	4.54157e7i	0.949480	−	0.949480i
$364$		0			0
$365$	4.84953e7	−	4.84953e7i	0.997289	−	0.997289i
$366$		0			0
$367$		−	5.07928e7i		−	1.02755i	−0.857924	−	0.513777i	$-0.828246\pi$
$367$		−	5.07928e7i		−	1.02755i	0.857924	−	0.513777i	$-0.171754\pi$
$368$		0			0
$369$	−4.07385e7			−0.810823
$370$		0			0
$371$	6.70992e6	+	6.70992e6i	0.131400	+	0.131400i
$372$		0			0
$373$	2.15606e7	+	2.15606e7i	0.415466	+	0.415466i	0.883638	−	0.468172i	$-0.155087\pi$
$373$	2.15606e7	+	2.15606e7i	0.415466	+	0.415466i	−0.468172	+	0.883638i	$0.655087\pi$
$374$		0			0
$375$	−6.54445e7			−1.24102
$376$		0			0
$377$			4.04145e7i			0.754247i
$378$		0			0
$379$	9.50195e6	−	9.50195e6i	0.174540	−	0.174540i	−0.614431	−	0.788971i	$-0.710614\pi$
$379$	9.50195e6	−	9.50195e6i	0.174540	−	0.174540i	0.788971	+	0.614431i	$0.210614\pi$
$380$		0			0
$381$	−1.79737e7	+	1.79737e7i	−0.324985	+	0.324985i
$382$		0			0
$383$		−	7.09053e7i		−	1.26207i	−0.775755	−	0.631034i	$-0.782631\pi$
$383$		−	7.09053e7i		−	1.26207i	0.775755	−	0.631034i	$-0.217369\pi$
$384$		0			0
$385$	5.25417e6			0.0920707
$386$		0			0
$387$	2.18073e7	+	2.18073e7i	0.376244	+	0.376244i
$388$		0			0
$389$	−2.91857e7	−	2.91857e7i	−0.495816	−	0.495816i	0.414316	−	0.910133i	$-0.364021\pi$
$389$	−2.91857e7	−	2.91857e7i	−0.495816	−	0.495816i	−0.910133	+	0.414316i	$0.864021\pi$
$390$		0			0
$391$	−2.72078e7			−0.455159
$392$		0			0
$393$			9.52737e7i			1.56962i
$394$		0			0
$395$	6.23669e7	−	6.23669e7i	1.01196	−	1.01196i
$396$		0			0
$397$	−1.98612e7	+	1.98612e7i	−0.317420	+	0.317420i	−0.847775	−	0.530356i	$-0.822058\pi$
$397$	−1.98612e7	+	1.98612e7i	−0.317420	+	0.317420i	0.530356	+	0.847775i	$0.322058\pi$
$398$		0			0
$399$			3.44741e7i			0.542718i
$400$		0			0
$401$	3.50138e7			0.543007			0.271504	−	0.962437i	$-0.412479\pi$
$401$	3.50138e7			0.543007			0.271504	+	0.962437i	$0.412479\pi$
$402$		0			0
$403$	−4.04248e7	−	4.04248e7i	−0.617636	−	0.617636i
$404$		0			0
$405$	−8.69120e7	−	8.69120e7i	−1.30832	−	1.30832i
$406$		0			0
$407$	−3.51757e6			−0.0521746
$408$		0			0
$409$		−	9.66336e7i		−	1.41240i	−0.708011	−	0.706201i	$-0.750408\pi$
$409$		−	9.66336e7i		−	1.41240i	0.708011	−	0.706201i	$-0.249592\pi$
$410$		0			0
$411$	−2.59051e7	+	2.59051e7i	−0.373130	+	0.373130i
$412$		0			0
$413$	2.32646e7	−	2.32646e7i	0.330252	−	0.330252i
$414$		0			0
$415$		−	1.94699e8i		−	2.72407i
$416$		0			0
$417$	−8.03383e7			−1.10794
$418$		0			0
$419$	9.91922e7	+	9.91922e7i	1.34845	+	1.34845i	0.887344	+	0.461109i	$0.152548\pi$
$419$	9.91922e7	+	9.91922e7i	1.34845	+	1.34845i	0.461109	+	0.887344i	$0.347452\pi$
$420$		0			0
$421$	1.70314e7	+	1.70314e7i	0.228246	+	0.228246i	0.811960	−	0.583714i	$-0.198401\pi$
$421$	1.70314e7	+	1.70314e7i	0.228246	+	0.228246i	−0.583714	+	0.811960i	$0.698401\pi$
$422$		0			0
$423$	3.70183e7			0.489097
$424$		0			0
$425$		−	7.90356e7i		−	1.02957i
$426$		0			0
$427$	−1.00020e8	+	1.00020e8i	−1.28470	+	1.28470i
$428$		0			0
$429$	−5.44246e6	+	5.44246e6i	−0.0689324	+	0.0689324i
$430$		0			0
$431$		−	6.19323e7i		−	0.773545i	−0.922175	−	0.386772i	$-0.873590\pi$
$431$		−	6.19323e7i		−	0.773545i	0.922175	−	0.386772i	$-0.126410\pi$
$432$		0			0
$433$	−6.84514e6			−0.0843177			−0.0421588	−	0.999111i	$-0.513424\pi$
$433$	−6.84514e6			−0.0843177			−0.0421588	+	0.999111i	$0.513424\pi$
$434$		0			0
$435$	−6.25255e7	−	6.25255e7i	−0.759608	−	0.759608i
$436$		0			0
$437$	1.37921e7	+	1.37921e7i	0.165267	+	0.165267i
$438$		0			0
$439$	−1.48097e8			−1.75046			−0.875232	−	0.483703i	$-0.839292\pi$
$439$	−1.48097e8			−1.75046			−0.875232	+	0.483703i	$0.839292\pi$
$440$		0			0
$441$			3.07990e7i			0.359104i
$442$		0			0
$443$	1.10015e8	−	1.10015e8i	1.26543	−	1.26543i	0.317013	−	0.948421i	$-0.397320\pi$
$443$	1.10015e8	−	1.10015e8i	1.26543	−	1.26543i	0.948421	−	0.317013i	$-0.102680\pi$
$444$		0			0
$445$	8.49625e7	−	8.49625e7i	0.964155	−	0.964155i
$446$		0			0
$447$			1.01088e8i			1.13182i
$448$		0			0
$449$	−3.03044e7			−0.334785			−0.167393	−	0.985890i	$-0.553535\pi$
$449$	−3.03044e7			−0.334785			−0.167393	+	0.985890i	$0.553535\pi$
$450$		0			0
$451$	3.09706e6	+	3.09706e6i	0.0337614	+	0.0337614i
$452$		0			0
$453$	1.10978e7	+	1.10978e7i	0.119383	+	0.119383i
$454$		0			0
$455$	2.75257e8			2.92216
$456$		0			0
$457$			1.61100e8i			1.68790i	0.536424	+	0.843949i	$0.319775\pi$
$457$			1.61100e8i			1.68790i	−0.536424	+	0.843949i	$0.680225\pi$
$458$		0			0
$459$	1.13551e7	−	1.13551e7i	0.117423	−	0.117423i
$460$		0			0
$461$	1.62650e7	−	1.62650e7i	0.166016	−	0.166016i	−0.619210	−	0.785226i	$-0.712547\pi$
$461$	1.62650e7	−	1.62650e7i	0.166016	−	0.166016i	0.785226	+	0.619210i	$0.212547\pi$
$462$		0			0
$463$			1.68452e8i			1.69720i	0.529038	+	0.848598i	$0.322553\pi$
$463$			1.68452e8i			1.69720i	−0.529038	+	0.848598i	$0.677447\pi$
$464$		0			0
$465$	1.25083e8			1.24405
$466$		0			0
$467$	−7.69239e7	−	7.69239e7i	−0.755284	−	0.755284i	0.220176	−	0.975460i	$-0.429337\pi$
$467$	−7.69239e7	−	7.69239e7i	−0.755284	−	0.755284i	−0.975460	+	0.220176i	$0.929337\pi$
$468$		0			0
$469$	1.39066e8	+	1.39066e8i	1.34804	+	1.34804i
$470$		0			0
$471$	−2.18326e8			−2.08950
$472$		0			0
$473$		−	3.31571e6i		−	0.0313324i
$474$		0			0
$475$	−4.00645e7	+	4.00645e7i	−0.373834	+	0.373834i
$476$		0			0
$477$	9.63262e6	−	9.63262e6i	0.0887543	−	0.0887543i
$478$		0			0
$479$			1.80538e8i			1.64271i	0.570416	+	0.821356i	$0.306782\pi$
$479$			1.80538e8i			1.64271i	−0.570416	+	0.821356i	$0.693218\pi$
$480$		0			0
$481$	−1.84279e8			−1.65593
$482$		0			0
$483$	8.96598e7	+	8.96598e7i	0.795712	+	0.795712i
$484$		0			0
$485$	−1.41497e8	−	1.41497e8i	−1.24029	−	1.24029i
$486$		0			0
$487$	2.76822e7			0.239670			0.119835	−	0.992794i	$-0.461763\pi$
$487$	2.76822e7			0.239670			0.119835	+	0.992794i	$0.461763\pi$
$488$		0			0
$489$		−	1.31353e8i		−	1.12334i
$490$		0			0
$491$	1.13442e8	−	1.13442e8i	0.958361	−	0.958361i	−0.0408060	−	0.999167i	$-0.512993\pi$
$491$	1.13442e8	−	1.13442e8i	0.958361	−	0.958361i	0.999167	+	0.0408060i	$0.0129926\pi$
$492$		0			0
$493$	2.75575e7	−	2.75575e7i	0.229985	−	0.229985i
$494$		0			0
$495$		−	7.54277e6i		−	0.0621892i
$496$		0			0
$497$	1.46486e8			1.19323
$498$		0			0
$499$	−2.96941e7	−	2.96941e7i	−0.238984	−	0.238984i	0.577445	−	0.816429i	$-0.304050\pi$
$499$	−2.96941e7	−	2.96941e7i	−0.238984	−	0.238984i	−0.816429	+	0.577445i	$0.804050\pi$
$500$		0			0
$501$	1.66214e7	+	1.66214e7i	0.132176	+	0.132176i
$502$		0			0
$503$	−1.52573e7			−0.119888			−0.0599438	−	0.998202i	$-0.519092\pi$
$503$	−1.52573e7			−0.119888			−0.0599438	+	0.998202i	$0.519092\pi$
$504$		0			0
$505$			6.77143e7i			0.525783i
$506$		0			0
$507$	−1.61098e8	+	1.61098e8i	−1.23614	+	1.23614i
$508$		0			0
$509$	−1.49274e8	+	1.49274e8i	−1.13196	+	1.13196i	−0.142104	+	0.989852i	$0.545387\pi$
$509$	−1.49274e8	+	1.49274e8i	−1.13196	+	1.13196i	−0.989852	+	0.142104i	$0.954613\pi$
$510$		0			0
$511$		−	1.40869e8i		−	1.05573i
$512$		0			0
$513$	−1.15122e7			−0.0852722
$514$		0			0
$515$	−7.47122e7	−	7.47122e7i	−0.546978	−	0.546978i
$516$		0			0
$517$	−2.81424e6	−	2.81424e6i	−0.0203652	−	0.0203652i
$518$		0			0
$519$	2.11073e8			1.50984
$520$		0			0
$521$		−	1.15110e8i		−	0.813955i	−0.913438	−	0.406977i	$-0.866583\pi$
$521$		−	1.15110e8i		−	0.813955i	0.913438	−	0.406977i	$-0.133417\pi$
$522$		0			0
$523$	−1.70829e8	+	1.70829e8i	−1.19414	+	1.19414i	−0.218250	+	0.975893i	$0.570035\pi$
$523$	−1.70829e8	+	1.70829e8i	−1.19414	+	1.19414i	−0.975893	+	0.218250i	$0.929965\pi$
$524$		0			0
$525$	−2.60451e8	+	2.60451e8i	−1.79990	+	1.79990i
$526$		0			0
$527$			5.51290e7i			0.376659i
$528$		0			0
$529$	−7.62952e7			−0.515383
$530$		0			0
$531$	−3.33981e7	−	3.33981e7i	−0.223069	−	0.223069i
$532$		0			0
$533$	1.62250e8	+	1.62250e8i	1.07152	+	1.07152i
$534$		0			0
$535$	3.42752e8			2.23830
$536$		0			0
$537$			5.74100e7i			0.370736i
$538$		0			0
$539$	2.34143e6	−	2.34143e6i	0.0149525	−	0.0149525i
$540$		0			0
$541$	−6.73179e7	+	6.73179e7i	−0.425147	+	0.425147i	−0.886971	−	0.461825i	$-0.847195\pi$
$541$	−6.73179e7	+	6.73179e7i	−0.425147	+	0.425147i	0.461825	+	0.886971i	$0.347195\pi$
$542$		0			0
$543$		−	1.28184e8i		−	0.800633i
$544$		0			0
$545$	4.70321e8			2.90539
$546$		0			0
$547$	6.44257e7	+	6.44257e7i	0.393638	+	0.393638i	0.875982	−	0.482344i	$-0.160214\pi$
$547$	6.44257e7	+	6.44257e7i	0.393638	+	0.393638i	−0.482344	+	0.875982i	$0.660214\pi$
$548$		0			0
$549$	1.43587e8	+	1.43587e8i	0.867754	+	0.867754i
$550$		0			0
$551$	−2.79388e7			−0.167014
$552$		0			0
$553$		−	1.81163e8i		−	1.07126i
$554$		0			0
$555$	2.85100e8	−	2.85100e8i	1.66770	−	1.66770i
$556$		0			0
$557$	−2.81484e7	+	2.81484e7i	−0.162888	+	0.162888i	−0.783845	−	0.620957i	$-0.786744\pi$
$557$	−2.81484e7	+	2.81484e7i	−0.162888	+	0.162888i	0.620957	+	0.783845i	$0.286744\pi$
$558$		0			0
$559$		−	1.73705e8i		−	0.994434i
$560$		0			0
$561$	7.42211e6			0.0420377
$562$		0			0
$563$	3.25814e7	+	3.25814e7i	0.182576	+	0.182576i	0.792477	−	0.609901i	$-0.208791\pi$
$563$	3.25814e7	+	3.25814e7i	0.182576	+	0.182576i	−0.609901	+	0.792477i	$0.708791\pi$
$564$		0			0
$565$	−8.09892e6	−	8.09892e6i	−0.0449036	−	0.0449036i
$566$		0			0
$567$	−2.52462e8			−1.38499
$568$		0			0
$569$			6.00764e7i			0.326112i	0.986617	+	0.163056i	$0.0521351\pi$
$569$			6.00764e7i			0.326112i	−0.986617	+	0.163056i	$0.947865\pi$
$570$		0			0
$571$	−1.53517e8	+	1.53517e8i	−0.824610	+	0.824610i	−0.986765	−	0.162155i	$-0.948155\pi$
$571$	−1.53517e8	+	1.53517e8i	−0.824610	+	0.824610i	0.162155	+	0.986765i	$0.448155\pi$
$572$		0			0
$573$	1.83042e8	−	1.83042e8i	0.972939	−	0.972939i
$574$		0			0
$575$			2.08399e8i			1.09620i
$576$		0			0
$577$	−3.34357e8			−1.74054			−0.870269	−	0.492577i	$-0.836055\pi$
$577$	−3.34357e8			−1.74054			−0.870269	+	0.492577i	$0.836055\pi$
$578$		0			0
$579$	−4.20783e7	−	4.20783e7i	−0.216782	−	0.216782i
$580$		0			0
$581$	−2.82781e8	−	2.82781e8i	−1.44185	−	1.44185i
$582$		0			0
$583$	−1.46460e6			−0.00739118
$584$		0			0
$585$		−	3.95153e8i		−	1.97377i
$586$		0			0
$587$	−8.00181e7	+	8.00181e7i	−0.395616	+	0.395616i	−0.876684	−	0.481068i	$-0.840249\pi$
$587$	−8.00181e7	+	8.00181e7i	−0.395616	+	0.395616i	0.481068	+	0.876684i	$0.340249\pi$
$588$		0			0
$589$	2.79459e7	−	2.79459e7i	0.136764	−	0.136764i
$590$		0			0
$591$			4.12558e8i			1.99858i
$592$		0			0
$593$	5.20669e7			0.249688			0.124844	−	0.992176i	$-0.460157\pi$
$593$	5.20669e7			0.249688			0.124844	+	0.992176i	$0.460157\pi$
$594$		0			0
$595$	−1.87690e8	−	1.87690e8i	−0.891024	−	0.891024i
$596$		0			0
$597$	−2.75175e8	−	2.75175e8i	−1.29326	−	1.29326i
$598$		0			0
$599$	−4.82128e6			−0.0224327			−0.0112164	−	0.999937i	$-0.503570\pi$
$599$	−4.82128e6			−0.0224327			−0.0112164	+	0.999937i	$0.503570\pi$
$600$		0			0
$601$			4.87391e7i			0.224519i	0.993679	+	0.112260i	$0.0358088\pi$
$601$			4.87391e7i			0.224519i	−0.993679	+	0.112260i	$0.964191\pi$
$602$		0			0
$603$	1.99640e8	−	1.99640e8i	0.910532	−	0.910532i
$604$		0			0
$605$	2.50680e8	−	2.50680e8i	1.13202	−	1.13202i
$606$		0			0
$607$		−	3.50813e8i		−	1.56859i	−0.620387	−	0.784296i	$-0.713024\pi$
$607$		−	3.50813e8i		−	1.56859i	0.620387	−	0.784296i	$-0.286976\pi$
$608$		0			0
$609$	−1.81624e8			−0.804121
$610$		0			0
$611$	−1.47433e8	−	1.47433e8i	−0.646356	−	0.646356i
$612$		0			0
$613$	1.59265e7	+	1.59265e7i	0.0691413	+	0.0691413i	0.740832	−	0.671691i	$-0.234432\pi$
$613$	1.59265e7	+	1.59265e7i	0.0691413	+	0.0691413i	−0.671691	+	0.740832i	$0.734432\pi$
$614$		0			0
$615$	−5.02034e8			−2.15828
$616$		0			0
$617$			3.70913e8i			1.57912i	0.613671	+	0.789562i	$0.289692\pi$
$617$			3.70913e8i			1.57912i	−0.613671	+	0.789562i	$0.710308\pi$
$618$		0			0
$619$	1.41681e7	−	1.41681e7i	0.0597363	−	0.0597363i	−0.676608	−	0.736344i	$-0.736551\pi$
$619$	1.41681e7	−	1.41681e7i	0.0597363	−	0.0597363i	0.736344	+	0.676608i	$0.236551\pi$
$620$		0			0
$621$	−2.99408e7	+	2.99408e7i	−0.125023	+	0.125023i
$622$		0			0
$623$		−	2.46799e8i		−	1.02066i
$624$		0			0
$625$	2.32097e7			0.0950670
$626$		0			0
$627$	−3.76240e6	−	3.76240e6i	−0.0152638	−	0.0152638i
$628$		0			0
$629$	1.25655e8	+	1.25655e8i	0.504925	+	0.504925i
$630$		0			0
$631$	1.53432e8			0.610699			0.305350	−	0.952240i	$-0.401227\pi$
$631$	1.53432e8			0.610699			0.305350	+	0.952240i	$0.401227\pi$
$632$		0			0
$633$		−	3.07931e7i		−	0.121406i
$634$		0			0
$635$	−9.92094e7	+	9.92094e7i	−0.387464	+	0.387464i
$636$		0			0
$637$	1.22664e8	−	1.22664e8i	0.474567	−	0.474567i
$638$		0			0
$639$		−	2.10291e8i		−	0.805970i
$640$		0			0
$641$	−9.63888e7			−0.365976			−0.182988	−	0.983115i	$-0.558577\pi$
$641$	−9.63888e7			−0.365976			−0.182988	+	0.983115i	$0.558577\pi$
$642$		0			0
$643$	2.96341e8	+	2.96341e8i	1.11470	+	1.11470i	0.992506	+	0.122198i	$0.0389941\pi$
$643$	2.96341e8	+	2.96341e8i	1.11470	+	1.11470i	0.122198	+	0.992506i	$0.461006\pi$
$644$		0			0
$645$	2.68739e8	+	2.68739e8i	1.00150	+	1.00150i
$646$		0			0
$647$	2.51144e8			0.927279			0.463640	−	0.886024i	$-0.346543\pi$
$647$	2.51144e8			0.927279			0.463640	+	0.886024i	$0.346543\pi$
$648$		0			0
$649$			5.07805e6i			0.0185765i
$650$		0			0
$651$	1.81670e8	−	1.81670e8i	0.658477	−	0.658477i
$652$		0			0
$653$	1.19499e8	−	1.19499e8i	0.429165	−	0.429165i	−0.459179	−	0.888344i	$-0.651856\pi$
$653$	1.19499e8	−	1.19499e8i	0.429165	−	0.429165i	0.888344	+	0.459179i	$0.151856\pi$
$654$		0			0
$655$			5.25881e8i			1.87139i
$656$		0			0
$657$	−2.02229e8			−0.713094
$658$		0			0
$659$	1.46053e8	+	1.46053e8i	0.510333	+	0.510333i	0.914629	−	0.404295i	$-0.132483\pi$
$659$	1.46053e8	+	1.46053e8i	0.510333	+	0.510333i	−0.404295	+	0.914629i	$0.632483\pi$
$660$		0			0
$661$	−1.39338e8	−	1.39338e8i	−0.482464	−	0.482464i	0.423454	−	0.905918i	$-0.360818\pi$
$661$	−1.39338e8	−	1.39338e8i	−0.482464	−	0.482464i	−0.905918	+	0.423454i	$0.860818\pi$
$662$		0			0
$663$	3.88832e8			1.33420
$664$		0			0
$665$			1.90286e8i			0.647057i
$666$		0			0
$667$	−7.26627e7	+	7.26627e7i	−0.244869	+	0.244869i
$668$		0			0
$669$	−1.23089e8	+	1.23089e8i	−0.411092	+	0.411092i
$670$		0			0
$671$		−	2.18318e7i		−	0.0722638i
$672$		0			0
$673$	1.12659e8			0.369590			0.184795	−	0.982777i	$-0.440838\pi$
$673$	1.12659e8			0.369590			0.184795	+	0.982777i	$0.440838\pi$
$674$		0			0
$675$	−8.69747e7	−	8.69747e7i	−0.282801	−	0.282801i
$676$		0			0
$677$	2.59382e8	+	2.59382e8i	0.835938	+	0.835938i	0.988321	−	0.152384i	$-0.0486949\pi$
$677$	2.59382e8	+	2.59382e8i	0.835938	+	0.835938i	−0.152384	+	0.988321i	$0.548695\pi$
$678$		0			0
$679$	−4.11022e8			−1.31297
$680$		0			0
$681$			6.41587e8i			2.03149i
$682$		0			0
$683$	1.80845e8	−	1.80845e8i	0.567604	−	0.567604i	−0.363853	−	0.931456i	$-0.618539\pi$
$683$	1.80845e8	−	1.80845e8i	0.567604	−	0.567604i	0.931456	+	0.363853i	$0.118539\pi$
$684$		0			0
$685$	−1.42988e8	+	1.42988e8i	−0.444865	+	0.444865i
$686$		0			0
$687$		−	2.41992e8i		−	0.746330i
$688$		0			0
$689$	−7.67279e7			−0.234583
$690$		0			0
$691$	3.89481e8	+	3.89481e8i	1.18046	+	1.18046i	0.979625	+	0.200838i	$0.0643664\pi$
$691$	3.89481e8	+	3.89481e8i	1.18046	+	1.18046i	0.200838	+	0.979625i	$0.435634\pi$
$692$		0			0
$693$	−1.09551e7	−	1.09551e7i	−0.0329168	−	0.0329168i
$694$		0			0
$695$	−4.43442e8			−1.32094
$696$		0			0
$697$		−	2.21267e8i		−	0.653458i
$698$		0			0
$699$	−1.95933e8	+	1.95933e8i	−0.573687	+	0.573687i
$700$		0			0
$701$	−1.36109e8	+	1.36109e8i	−0.395122	+	0.395122i	−0.876509	−	0.481386i	$-0.840133\pi$
$701$	−1.36109e8	+	1.36109e8i	−0.395122	+	0.395122i	0.481386	+	0.876509i	$0.340133\pi$
$702$		0			0
$703$		−	1.27393e8i		−	0.366674i
$704$		0			0
$705$	4.56189e8			1.30190
$706$		0			0
$707$	9.83483e7	+	9.83483e7i	0.278297	+	0.278297i
$708$		0			0
$709$	−3.01255e8	−	3.01255e8i	−0.845270	−	0.845270i	0.144268	−	0.989539i	$-0.453917\pi$
$709$	−3.01255e8	−	3.01255e8i	−0.845270	−	0.845270i	−0.989539	+	0.144268i	$0.953917\pi$
$710$		0			0
$711$	−2.60074e8			−0.723584
$712$		0			0
$713$		−	1.45362e8i		−	0.401036i
$714$		0			0
$715$	−3.00407e7	+	3.00407e7i	−0.0821848	+	0.0821848i
$716$		0			0
$717$	2.94596e8	−	2.94596e8i	0.799226	−	0.799226i
$718$		0			0
$719$		−	3.57293e8i		−	0.961253i	−0.876925	−	0.480626i	$-0.840409\pi$
$719$		−	3.57293e8i		−	0.961253i	0.876925	−	0.480626i	$-0.159591\pi$
$720$		0			0
$721$	−2.17024e8			−0.579031
$722$		0			0
$723$	4.91236e8	+	4.91236e8i	1.29980	+	1.29980i
$724$		0			0
$725$	−2.11077e8	−	2.11077e8i	−0.553894	−	0.553894i
$726$		0			0
$727$	−7.94049e7			−0.206654			−0.103327	−	0.994647i	$-0.532949\pi$
$727$	−7.94049e7			−0.206654			−0.103327	+	0.994647i	$0.532949\pi$
$728$		0			0
$729$			2.30001e8i			0.593672i
$730$		0			0
$731$	−1.18444e8	+	1.18444e8i	−0.303223	+	0.303223i
$732$		0			0
$733$	−2.46020e8	+	2.46020e8i	−0.624680	+	0.624680i	−0.946725	−	0.322044i	$-0.895630\pi$
$733$	−2.46020e8	+	2.46020e8i	−0.624680	+	0.624680i	0.322044	+	0.946725i	$0.395630\pi$
$734$		0			0
$735$			3.79547e8i			0.955879i
$736$		0			0
$737$	−3.03544e7			−0.0758262
$738$		0			0
$739$	−2.05535e8	−	2.05535e8i	−0.509276	−	0.509276i	0.405028	−	0.914304i	$-0.367262\pi$
$739$	−2.05535e8	−	2.05535e8i	−0.509276	−	0.509276i	−0.914304	+	0.405028i	$0.867262\pi$
$740$		0			0
$741$	−1.97106e8	−	1.97106e8i	−0.484445	−	0.484445i
$742$		0			0
$743$	1.49313e8			0.364024			0.182012	−	0.983296i	$-0.441739\pi$
$743$	1.49313e8			0.364024			0.182012	+	0.983296i	$0.441739\pi$
$744$		0			0
$745$			5.57975e8i			1.34942i
$746$		0			0
$747$	−4.05954e8	+	4.05954e8i	−0.973901	+	0.973901i
$748$		0			0
$749$	4.97813e8	−	4.97813e8i	1.18473	−	1.18473i
$750$		0			0
$751$			2.61119e8i			0.616478i	0.951309	+	0.308239i	$0.0997397\pi$
$751$			2.61119e8i			0.616478i	−0.951309	+	0.308239i	$0.900260\pi$
$752$		0			0
$753$	6.36135e8			1.48992
$754$		0			0
$755$	6.12566e7	+	6.12566e7i	0.142335	+	0.142335i
$756$		0			0
$757$	4.05024e8	+	4.05024e8i	0.933670	+	0.933670i	0.997933	−	0.0642632i	$-0.0204697\pi$
$757$	4.05024e8	+	4.05024e8i	0.933670	+	0.933670i	−0.0642632	+	0.997933i	$0.520470\pi$
$758$		0			0
$759$	−1.95704e7			−0.0447583
$760$		0			0
$761$		−	1.35070e8i		−	0.306481i	−0.988189	−	0.153240i	$-0.951029\pi$
$761$		−	1.35070e8i		−	0.306481i	0.988189	−	0.153240i	$-0.0489709\pi$
$762$		0			0
$763$	6.83094e8	−	6.83094e8i	1.53782	−	1.53782i
$764$		0			0
$765$	−2.69443e8	+	2.69443e8i	−0.601843	+	0.601843i
$766$		0			0
$767$			2.66030e8i			0.589583i
$768$		0			0
$769$	3.00152e8			0.660028			0.330014	−	0.943976i	$-0.392946\pi$
$769$	3.00152e8			0.660028			0.330014	+	0.943976i	$0.392946\pi$
$770$		0			0
$771$	−6.64243e8	−	6.64243e8i	−1.44932	−	1.44932i
$772$		0			0
$773$	3.89585e7	+	3.89585e7i	0.0843458	+	0.0843458i	0.748021	−	0.663675i	$-0.231004\pi$
$773$	3.89585e7	+	3.89585e7i	0.0843458	+	0.0843458i	−0.663675	+	0.748021i	$0.731004\pi$
$774$		0			0
$775$	4.22261e8			0.907143
$776$		0			0
$777$		−	8.28157e8i		−	1.76543i
$778$		0			0
$779$	−1.12164e8	+	1.12164e8i	−0.237269	+	0.237269i
$780$		0			0
$781$	−1.59870e7	+	1.59870e7i	−0.0335593	+	0.0335593i
$782$		0			0
$783$		−	6.06513e7i		−	0.126344i
$784$		0			0
$785$	−1.20509e9			−2.49122
$786$		0			0
$787$	−4.96033e8	−	4.96033e8i	−1.01762	−	1.01762i	−0.999842	−	0.0177796i	$-0.994340\pi$
$787$	−4.96033e8	−	4.96033e8i	−1.01762	−	1.01762i	−0.0177796	−	0.999842i	$-0.505660\pi$
$788$		0			0
$789$	1.17908e8	+	1.17908e8i	0.240056	+	0.240056i
$790$		0			0
$791$	−2.35257e7			−0.0475350
$792$		0			0
$793$		−	1.14373e9i		−	2.29352i
$794$		0			0
$795$	1.18706e8	−	1.18706e8i	0.236250	−	0.236250i
$796$		0			0
$797$	−3.36288e8	+	3.36288e8i	−0.664257	+	0.664257i	−0.956381	−	0.292123i	$-0.905638\pi$
$797$	−3.36288e8	+	3.36288e8i	−0.664257	+	0.664257i	0.292123	+	0.956381i	$0.405638\pi$
$798$		0			0
$799$			2.01061e8i			0.394174i
$800$		0			0
$801$	−3.54299e8			−0.689402
$802$		0			0
$803$	1.53740e7	+	1.53740e7i	0.0296921	+	0.0296921i
$804$		0			0
$805$	4.94894e8	+	4.94894e8i	0.948690	+	0.948690i
$806$		0			0
$807$	7.39140e8			1.40639
$808$		0			0
$809$			2.41708e8i			0.456506i	0.973602	+	0.228253i	$0.0733013\pi$
$809$			2.41708e8i			0.456506i	−0.973602	+	0.228253i	$0.926699\pi$
$810$		0			0
$811$	−4.40043e8	+	4.40043e8i	−0.824959	+	0.824959i	−0.986814	−	0.161855i	$-0.948252\pi$
$811$	−4.40043e8	+	4.40043e8i	−0.824959	+	0.824959i	0.161855	+	0.986814i	$0.448252\pi$
$812$		0			0
$813$	4.00893e8	−	4.00893e8i	0.746030	−	0.746030i
$814$		0			0
$815$		−	7.25025e8i		−	1.33931i
$816$		0			0
$817$	1.20083e8			0.220199
$818$		0			0
$819$	−5.73920e8	−	5.73920e8i	−1.04472	−	1.04472i
$820$		0			0
$821$	−2.57117e8	−	2.57117e8i	−0.464624	−	0.464624i	0.435544	−	0.900168i	$-0.356556\pi$
$821$	−2.57117e8	−	2.57117e8i	−0.464624	−	0.464624i	−0.900168	+	0.435544i	$0.856556\pi$
$822$		0			0
$823$	9.19926e8			1.65026			0.825132	−	0.564940i	$-0.191101\pi$
$823$	9.19926e8			1.65026			0.825132	+	0.564940i	$0.191101\pi$
$824$		0			0
$825$		−	5.68497e7i		−	0.101243i
$826$		0			0
$827$	4.44970e8	−	4.44970e8i	0.786709	−	0.786709i	−0.194245	−	0.980953i	$-0.562226\pi$
$827$	4.44970e8	−	4.44970e8i	0.786709	−	0.786709i	0.980953	+	0.194245i	$0.0622256\pi$
$828$		0			0
$829$	3.19132e8	−	3.19132e8i	0.560153	−	0.560153i	−0.369198	−	0.929351i	$-0.620368\pi$
$829$	3.19132e8	−	3.19132e8i	0.560153	−	0.560153i	0.929351	+	0.369198i	$0.120368\pi$
$830$		0			0
$831$			7.70672e8i			1.34297i
$832$		0			0
$833$	−1.67281e8			−0.289410
$834$		0			0
$835$	9.17448e7	+	9.17448e7i	0.157588	+	0.157588i
$836$		0			0
$837$	6.06667e7	+	6.06667e7i	0.103460	+	0.103460i
$838$		0			0
$839$	−3.41595e8			−0.578397			−0.289198	−	0.957269i	$-0.593389\pi$
$839$	−3.41595e8			−0.578397			−0.289198	+	0.957269i	$0.593389\pi$
$840$		0			0
$841$			4.47630e8i			0.752543i
$842$		0			0
$843$	−1.32651e8	+	1.32651e8i	−0.221426	+	0.221426i
$844$		0			0
$845$	−8.89211e8	+	8.89211e8i	−1.47379	+	1.47379i
$846$		0			0
$847$		−	7.28176e8i		−	1.19836i
$848$		0			0
$849$	3.98064e8			0.650473
$850$		0			0
$851$	−3.31323e8	−	3.31323e8i	−0.537604	−	0.537604i
$852$		0			0
$853$	−7.26055e8	−	7.26055e8i	−1.16983	−	1.16983i	−0.982249	−	0.187580i	$-0.939936\pi$
$853$	−7.26055e8	−	7.26055e8i	−1.16983	−	1.16983i	−0.187580	−	0.982249i	$-0.560064\pi$
$854$		0			0
$855$	2.73171e8			0.437055
$856$		0			0
$857$		−	1.03657e9i		−	1.64686i	−0.567414	−	0.823432i	$-0.692056\pi$
$857$		−	1.03657e9i		−	1.64686i	0.567414	−	0.823432i	$-0.307944\pi$
$858$		0			0
$859$	3.46895e8	−	3.46895e8i	0.547291	−	0.547291i	−0.378366	−	0.925656i	$-0.623514\pi$
$859$	3.46895e8	−	3.46895e8i	0.547291	−	0.547291i	0.925656	+	0.378366i	$0.123514\pi$
$860$		0			0
$861$	−7.29155e8	+	7.29155e8i	−1.14238	+	1.14238i
$862$		0			0
$863$			2.30709e8i			0.358948i	0.983763	+	0.179474i	$0.0574396\pi$
$863$			2.30709e8i			0.358948i	−0.983763	+	0.179474i	$0.942560\pi$
$864$		0			0
$865$	1.16506e9			1.80011
$866$		0			0
$867$	3.55072e8	+	3.55072e8i	0.544828	+	0.544828i
$868$		0			0
$869$	1.97716e7	+	1.97716e7i	0.0301289	+	0.0301289i
$870$		0			0
$871$	−1.59021e9			−2.40659
$872$		0			0
$873$			5.90054e8i			0.886848i
$874$		0			0
$875$	−5.24655e8	+	5.24655e8i	−0.783159	+	0.783159i
$876$		0			0
$877$	1.79911e7	−	1.79911e7i	0.0266722	−	0.0266722i	−0.693645	−	0.720317i	$-0.743996\pi$
$877$	1.79911e7	−	1.79911e7i	0.0266722	−	0.0266722i	0.720317	+	0.693645i	$0.243996\pi$
$878$		0			0
$879$		−	9.98775e8i		−	1.47062i
$880$		0			0
$881$	6.42117e8			0.939045			0.469523	−	0.882920i	$-0.344426\pi$
$881$	6.42117e8			0.939045			0.469523	+	0.882920i	$0.344426\pi$
$882$		0			0
$883$	−4.47721e8	−	4.47721e8i	−0.650317	−	0.650317i	0.302752	−	0.953069i	$-0.402095\pi$
$883$	−4.47721e8	−	4.47721e8i	−0.650317	−	0.650317i	−0.953069	+	0.302752i	$0.902095\pi$
$884$		0			0
$885$	−4.11577e8	−	4.11577e8i	−0.593774	−	0.593774i
$886$		0			0
$887$	−5.17347e8			−0.741329			−0.370664	−	0.928767i	$-0.620870\pi$
$887$	−5.17347e8			−0.741329			−0.370664	+	0.928767i	$0.620870\pi$
$888$		0			0
$889$			2.88183e8i			0.410170i
$890$		0			0
$891$	2.75529e7	−	2.75529e7i	0.0389524	−	0.0389524i
$892$		0			0
$893$	1.01921e8	−	1.01921e8i	0.143123	−	0.143123i
$894$		0			0
$895$			3.16885e8i			0.442011i
$896$		0			0
$897$	−1.02526e9			−1.42055
$898$		0			0
$899$	1.47231e8	+	1.47231e8i	0.202637	+	0.202637i
$900$		0			0
$901$	5.23186e7	+	5.23186e7i	0.0715289	+	0.0715289i
$902$		0			0
$903$	7.80634e8			1.06019
$904$		0			0
$905$		−	7.07535e8i		−	0.954557i
$906$		0			0
$907$	2.47278e8	−	2.47278e8i	0.331409	−	0.331409i	−0.521713	−	0.853121i	$-0.674707\pi$
$907$	2.47278e8	−	2.47278e8i	0.331409	−	0.331409i	0.853121	+	0.521713i	$0.174707\pi$
$908$		0			0
$909$	1.41187e8	−	1.41187e8i	0.187976	−	0.187976i
$910$		0			0
$911$			1.40425e9i			1.85733i	0.370919	+	0.928665i	$0.379043\pi$
$911$			1.40425e9i			1.85733i	−0.370919	+	0.928665i	$0.620957\pi$
$912$		0			0
$913$	6.17236e7			0.0811034
$914$		0			0
$915$	1.76947e9	+	1.76947e9i	2.30983	+	2.30983i
$916$		0			0
$917$	7.63790e8	+	7.63790e8i	0.990526	+	0.990526i
$918$		0			0
$919$	8.17828e8			1.05370			0.526848	−	0.849959i	$-0.323374\pi$
$919$	8.17828e8			1.05370			0.526848	+	0.849959i	$0.323374\pi$
$920$		0			0
$921$			6.19839e8i			0.793414i
$922$		0			0
$923$	−8.37530e8	+	8.37530e8i	−1.06511	+	1.06511i
$924$		0			0
$925$	9.62454e8	−	9.62454e8i	1.21606	−	1.21606i
$926$		0			0
$927$			3.11555e8i			0.391107i
$928$		0			0
$929$	9.02460e8			1.12559			0.562796	−	0.826596i	$-0.309726\pi$
$929$	9.02460e8			1.12559			0.562796	+	0.826596i	$0.309726\pi$
$930$		0			0
$931$	8.47979e7	+	8.47979e7i	0.105084	+	0.105084i
$932$		0			0
$933$	7.35524e8	+	7.35524e8i	0.905632	+	0.905632i
$934$		0			0
$935$	4.09677e7			0.0501195
$936$		0			0
$937$		−	8.55187e8i		−	1.03954i	−0.854305	−	0.519771i	$-0.826017\pi$
$937$		−	8.55187e8i		−	1.03954i	0.854305	−	0.519771i	$-0.173983\pi$
$938$		0			0
$939$	−1.12069e9	+	1.12069e9i	−1.35359	+	1.35359i
$940$		0			0
$941$	−6.02375e8	+	6.02375e8i	−0.722933	+	0.722933i	−0.969202	−	0.246269i	$-0.920795\pi$
$941$	−6.02375e8	+	6.02375e8i	−0.722933	+	0.722933i	0.246269	+	0.969202i	$0.420795\pi$
$942$		0			0
$943$			5.83429e8i			0.695750i
$944$		0			0
$945$	−4.13086e8			−0.489491
$946$		0			0
$947$	4.57925e8	+	4.57925e8i	0.539193	+	0.539193i	0.923292	−	0.384099i	$-0.125488\pi$
$947$	4.57925e8	+	4.57925e8i	0.539193	+	0.539193i	−0.384099	+	0.923292i	$0.625488\pi$
$948$		0			0
$949$	8.05419e8	+	8.05419e8i	0.942374	+	0.942374i
$950$		0			0
$951$	9.21155e8			1.07100
$952$		0			0
$953$			1.03047e9i			1.19057i	0.803513	+	0.595287i	$0.202962\pi$
$953$			1.03047e9i			1.19057i	−0.803513	+	0.595287i	$0.797038\pi$
$954$		0			0
$955$	1.01033e9	−	1.01033e9i	1.15999	−	1.15999i
$956$		0			0
$957$	1.98219e7	−	1.98219e7i	0.0226157	−	0.0226157i
$958$		0			0
$959$			4.15352e8i			0.470934i
$960$		0			0
$961$	5.92968e8			0.668130
$962$		0			0
$963$	−7.14650e8	−	7.14650e8i	−0.800229	−	0.800229i
$964$		0			0
$965$	−2.32259e8	−	2.32259e8i	−0.258459	−	0.258459i
$966$		0			0
$967$	−1.42057e9			−1.57103			−0.785513	−	0.618845i	$-0.787601\pi$
$967$	−1.42057e9			−1.57103			−0.785513	+	0.618845i	$0.787601\pi$
$968$		0			0
$969$			2.68801e8i			0.295434i
$970$		0			0
$971$	5.17352e8	−	5.17352e8i	0.565104	−	0.565104i	−0.365649	−	0.930753i	$-0.619153\pi$
$971$	5.17352e8	−	5.17352e8i	0.565104	−	0.565104i	0.930753	+	0.365649i	$0.119153\pi$
$972$		0			0
$973$	−6.44056e8	+	6.44056e8i	−0.699174	+	0.699174i
$974$		0			0
$975$		−	2.97826e9i		−	3.21328i
$976$		0			0
$977$	−1.73570e9			−1.86119			−0.930594	−	0.366054i	$-0.880709\pi$
$977$	−1.73570e9			−1.86119			−0.930594	+	0.366054i	$0.880709\pi$
$978$		0			0
$979$	2.69349e7	+	2.69349e7i	0.0287056	+	0.0287056i
$980$		0			0
$981$	−9.80635e8	−	9.80635e8i	−1.03872	−	1.03872i
$982$		0			0
$983$	−5.18747e8			−0.546129			−0.273064	−	0.961996i	$-0.588037\pi$
$983$	−5.18747e8			−0.546129			−0.273064	+	0.961996i	$0.588037\pi$
$984$		0			0
$985$			2.27719e9i			2.38282i
$986$		0			0
$987$	6.62569e8	−	6.62569e8i	0.689096	−	0.689096i
$988$		0			0
$989$	3.12310e8	−	3.12310e8i	0.322847	−	0.322847i
$990$		0			0
$991$			6.01846e8i			0.618392i	0.950998	+	0.309196i	$0.100060\pi$
$991$			6.01846e8i			0.618392i	−0.950998	+	0.309196i	$0.899940\pi$
$992$		0			0
$993$	−7.69130e8			−0.785510
$994$		0			0
$995$	−1.51888e9	−	1.51888e9i	−1.54189	−	1.54189i
$996$		0			0
$997$	−7.87235e8	−	7.87235e8i	−0.794363	−	0.794363i	0.187837	−	0.982200i	$-0.439852\pi$
$997$	−7.87235e8	−	7.87235e8i	−0.794363	−	0.794363i	−0.982200	+	0.187837i	$0.939852\pi$
$998$		0			0
$999$	2.76554e8			0.277385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.7.f.a.15.2		22
4.3	odd	2		16.7.f.a.11.9	yes	22
8.3	odd	2		128.7.f.b.31.2		22
8.5	even	2		128.7.f.a.31.10		22
16.3	odd	4	inner	64.7.f.a.47.2		22
16.5	even	4		128.7.f.b.95.2		22
16.11	odd	4		128.7.f.a.95.10		22
16.13	even	4		16.7.f.a.3.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.9	✓	22	16.13	even	4
16.7.f.a.11.9	yes	22	4.3	odd	2
64.7.f.a.15.2		22	1.1	even	1	trivial
64.7.f.a.47.2		22	16.3	odd	4	inner
128.7.f.a.31.10		22	8.5	even	2
128.7.f.a.95.10		22	16.11	odd	4
128.7.f.b.31.2		22	8.3	odd	2
128.7.f.b.95.2		22	16.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	64.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-25.6946 - 25.6946i) q^{3} +(-141.826 - 141.826i) q^{5} -411.977 q^{7} +591.425i q^{9} +O(q^{10})\)	\(q+(-25.6946 - 25.6946i) q^{3} +(-141.826 - 141.826i) q^{5} -411.977 q^{7} +591.425i q^{9} +(44.9619 - 44.9619i) q^{11} +(2355.48 - 2355.48i) q^{13} +7288.34i q^{15} -3212.26 q^{17} +(1628.35 + 1628.35i) q^{19} +(10585.6 + 10585.6i) q^{21} +8469.99 q^{23} +24604.3i q^{25} +(-3534.93 + 3534.93i) q^{27} +(-8578.85 + 8578.85i) q^{29} -17162.0i q^{31} -2310.56 q^{33} +(58429.1 + 58429.1i) q^{35} +(-39117.2 - 39117.2i) q^{37} -121046. q^{39} +68881.9i q^{41} +(36872.5 - 36872.5i) q^{43} +(83879.6 - 83879.6i) q^{45} -62591.7i q^{47} +52075.9 q^{49} +(82537.8 + 82537.8i) q^{51} +(-16287.1 - 16287.1i) q^{53} -12753.5 q^{55} -83679.7i q^{57} +(-56470.6 + 56470.6i) q^{59} +(242781. - 242781. i) q^{61} -243653. i q^{63} -668136. q^{65} +(-337557. - 337557. i) q^{67} +(-217633. - 217633. i) q^{69} -355567. q^{71} +341935. i q^{73} +(632199. - 632199. i) q^{75} +(-18523.3 + 18523.3i) q^{77} +439742. i q^{79} +612806. q^{81} +(686399. + 686399. i) q^{83} +(455583. + 455583. i) q^{85} +440860. q^{87} +599060. i q^{89} +(-970401. + 970401. i) q^{91} +(-440972. + 440972. i) q^{93} -461886. i q^{95} +997682. q^{97} +(26591.6 + 26591.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} - 2 q^{5} + 4 q^{7}+O(q^{10}) \) 22 * q + 2 * q^3 - 2 * q^5 + 4 * q^7	\( 22 q + 2 q^{3} - 2 q^{5} + 4 q^{7} - 1358 q^{11} - 2 q^{13} - 4 q^{17} - 3934 q^{19} - 1460 q^{21} + 13124 q^{23} - 35776 q^{27} - 33202 q^{29} - 4 q^{33} + 112420 q^{35} + 3598 q^{37} - 254396 q^{39} + 267986 q^{43} + 32706 q^{45} + 168066 q^{49} - 301788 q^{51} - 221842 q^{53} + 232708 q^{55} - 39150 q^{59} + 326494 q^{61} + 186412 q^{65} + 122786 q^{67} - 543188 q^{69} + 267012 q^{71} + 275278 q^{75} + 231180 q^{77} - 354298 q^{81} + 288322 q^{83} + 340748 q^{85} - 2029884 q^{87} - 302396 q^{91} - 1173344 q^{93} - 4 q^{97} + 271522 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 - 2 * q^5 + 4 * q^7 - 1358 * q^11 - 2 * q^13 - 4 * q^17 - 3934 * q^19 - 1460 * q^21 + 13124 * q^23 - 35776 * q^27 - 33202 * q^29 - 4 * q^33 + 112420 * q^35 + 3598 * q^37 - 254396 * q^39 + 267986 * q^43 + 32706 * q^45 + 168066 * q^49 - 301788 * q^51 - 221842 * q^53 + 232708 * q^55 - 39150 * q^59 + 326494 * q^61 + 186412 * q^65 + 122786 * q^67 - 543188 * q^69 + 267012 * q^71 + 275278 * q^75 + 231180 * q^77 - 354298 * q^81 + 288322 * q^83 + 340748 * q^85 - 2029884 * q^87 - 302396 * q^91 - 1173344 * q^93 - 4 * q^97 + 271522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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