LMFDB - Embedded newform 128.4.e.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.e (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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.2
Root			$-1.56339 - 1.24732i$ of defining polynomial
Character	$\chi$	$=$	128.33
Dual form			128.4.e.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.27139 - 3.27139i) q^{3} +(12.6449 - 12.6449i) q^{5} +13.8754i q^{7} -5.59607i q^{9} +O(q^{10})$	\(q+(-3.27139 - 3.27139i) q^{3} +(12.6449 - 12.6449i) q^{5} +13.8754i q^{7} -5.59607i q^{9} +(1.54694 - 1.54694i) q^{11} +(-32.7875 - 32.7875i) q^{13} -82.7326 q^{15} +18.6531 q^{17} +(-86.4042 - 86.4042i) q^{19} +(45.3917 - 45.3917i) q^{21} -134.006i q^{23} -194.786i q^{25} +(-106.634 + 106.634i) q^{27} +(59.7949 + 59.7949i) q^{29} +31.5391 q^{31} -10.1213 q^{33} +(175.453 + 175.453i) q^{35} +(-89.1866 + 89.1866i) q^{37} +214.521i q^{39} +210.504i q^{41} +(119.402 - 119.402i) q^{43} +(-70.7617 - 70.7617i) q^{45} +182.902 q^{47} +150.474 q^{49} +(-61.0213 - 61.0213i) q^{51} +(26.1644 - 26.1644i) q^{53} -39.1219i q^{55} +565.323i q^{57} +(441.584 - 441.584i) q^{59} +(174.485 + 174.485i) q^{61} +77.6476 q^{63} -829.188 q^{65} +(91.7562 + 91.7562i) q^{67} +(-438.385 + 438.385i) q^{69} +348.360i q^{71} +299.436i q^{73} +(-637.222 + 637.222i) q^{75} +(21.4644 + 21.4644i) q^{77} +943.487 q^{79} +546.590 q^{81} +(313.272 + 313.272i) q^{83} +(235.866 - 235.866i) q^{85} -391.224i q^{87} -1412.35i q^{89} +(454.939 - 454.939i) q^{91} +(-103.177 - 103.177i) q^{93} -2185.14 q^{95} +1515.29 q^{97} +(-8.65680 - 8.65680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 10 * q - 2 * q^3 + 2 * q^5	$ 10 q - 2 q^{3} + 2 q^{5} + 18 q^{11} + 2 q^{13} + 124 q^{15} - 4 q^{17} - 26 q^{19} - 52 q^{21} + 184 q^{27} + 202 q^{29} - 368 q^{31} - 4 q^{33} + 476 q^{35} + 10 q^{37} - 838 q^{43} - 194 q^{45} + 944 q^{47} + 94 q^{49} - 1500 q^{51} + 378 q^{53} + 1706 q^{59} - 910 q^{61} - 2628 q^{63} - 492 q^{65} + 1942 q^{67} - 580 q^{69} - 2954 q^{75} + 268 q^{77} + 4416 q^{79} + 482 q^{81} - 2562 q^{83} + 12 q^{85} + 3332 q^{91} + 2192 q^{93} - 6900 q^{95} - 4 q^{97} + 4958 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 + 2 * q^5 + 18 * q^11 + 2 * q^13 + 124 * q^15 - 4 * q^17 - 26 * q^19 - 52 * q^21 + 184 * q^27 + 202 * q^29 - 368 * q^31 - 4 * q^33 + 476 * q^35 + 10 * q^37 - 838 * q^43 - 194 * q^45 + 944 * q^47 + 94 * q^49 - 1500 * q^51 + 378 * q^53 + 1706 * q^59 - 910 * q^61 - 2628 * q^63 - 492 * q^65 + 1942 * q^67 - 580 * q^69 - 2954 * q^75 + 268 * q^77 + 4416 * q^79 + 482 * q^81 - 2562 * q^83 + 12 * q^85 + 3332 * q^91 + 2192 * q^93 - 6900 * q^95 - 4 * q^97 + 4958 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−3.27139	−	3.27139i	−0.629578	−	0.629578i	0.318384	−	0.947962i	$-0.396860\pi$
$3$	−3.27139	−	3.27139i	−0.629578	−	0.629578i	−0.947962	+	0.318384i	$0.896860\pi$
$4$		0			0
$5$	12.6449	−	12.6449i	1.13099	−	1.13099i	0.140981	−	0.990012i	$-0.454974\pi$
$5$	12.6449	−	12.6449i	1.13099	−	1.13099i	0.990012	−	0.140981i	$-0.0450257\pi$
$6$		0			0
$7$			13.8754i			0.749200i	0.927187	+	0.374600i	$0.122220\pi$
$7$			13.8754i			0.749200i	−0.927187	+	0.374600i	$0.877780\pi$
$8$		0			0
$9$		−	5.59607i		−	0.207262i
$10$		0			0
$11$	1.54694	−	1.54694i	0.0424019	−	0.0424019i	−0.685588	−	0.727990i	$-0.740455\pi$
$11$	1.54694	−	1.54694i	0.0424019	−	0.0424019i	0.727990	+	0.685588i	$0.240455\pi$
$12$		0			0
$13$	−32.7875	−	32.7875i	−0.699509	−	0.699509i	0.264796	−	0.964304i	$-0.414695\pi$
$13$	−32.7875	−	32.7875i	−0.699509	−	0.699509i	−0.964304	+	0.264796i	$0.914695\pi$
$14$		0			0
$15$	−82.7326			−1.42410
$16$		0			0
$17$	18.6531			0.266119			0.133060	−	0.991108i	$-0.457520\pi$
$17$	18.6531			0.266119			0.133060	+	0.991108i	$0.457520\pi$
$18$		0			0
$19$	−86.4042	−	86.4042i	−1.04329	−	1.04329i	−0.999020	−	0.0442688i	$-0.985904\pi$
$19$	−86.4042	−	86.4042i	−1.04329	−	1.04329i	−0.0442688	−	0.999020i	$-0.514096\pi$
$20$		0			0
$21$	45.3917	−	45.3917i	0.471680	−	0.471680i
$22$		0			0
$23$		−	134.006i		−	1.21488i	−0.794367	−	0.607438i	$-0.792197\pi$
$23$		−	134.006i		−	1.21488i	0.794367	−	0.607438i	$-0.207803\pi$
$24$		0			0
$25$		−	194.786i		−	1.55829i
$26$		0			0
$27$	−106.634	+	106.634i	−0.760066	+	0.760066i
$28$		0			0
$29$	59.7949	+	59.7949i	0.382884	+	0.382884i	0.872140	−	0.489256i	$-0.162732\pi$
$29$	59.7949	+	59.7949i	0.382884	+	0.382884i	−0.489256	+	0.872140i	$0.662732\pi$
$30$		0			0
$31$	31.5391			0.182729			0.0913645	−	0.995818i	$-0.470877\pi$
$31$	31.5391			0.182729			0.0913645	+	0.995818i	$0.470877\pi$
$32$		0			0
$33$	−10.1213			−0.0533906
$34$		0			0
$35$	175.453	+	175.453i	0.847340	+	0.847340i
$36$		0			0
$37$	−89.1866	+	89.1866i	−0.396275	+	0.396275i	−0.876917	−	0.480642i	$-0.840404\pi$
$37$	−89.1866	+	89.1866i	−0.396275	+	0.396275i	0.480642	+	0.876917i	$0.340404\pi$
$38$		0			0
$39$			214.521i			0.880791i
$40$		0			0
$41$			210.504i			0.801834i	0.916114	+	0.400917i	$0.131308\pi$
$41$			210.504i			0.801834i	−0.916114	+	0.400917i	$0.868692\pi$
$42$		0			0
$43$	119.402	−	119.402i	0.423456	−	0.423456i	−0.462936	−	0.886392i	$-0.653204\pi$
$43$	119.402	−	119.402i	0.423456	−	0.423456i	0.886392	+	0.462936i	$0.153204\pi$
$44$		0			0
$45$	−70.7617	−	70.7617i	−0.234412	−	0.234412i
$46$		0			0
$47$	182.902			0.567638			0.283819	−	0.958878i	$-0.408398\pi$
$47$	182.902			0.567638			0.283819	+	0.958878i	$0.408398\pi$
$48$		0			0
$49$	150.474			0.438699
$50$		0			0
$51$	−61.0213	−	61.0213i	−0.167543	−	0.167543i
$52$		0			0
$53$	26.1644	−	26.1644i	0.0678104	−	0.0678104i	−0.672388	−	0.740199i	$-0.734731\pi$
$53$	26.1644	−	26.1644i	0.0678104	−	0.0678104i	0.740199	+	0.672388i	$0.234731\pi$
$54$		0			0
$55$		−	39.1219i		−	0.0959125i
$56$		0			0
$57$			565.323i			1.31366i
$58$		0			0
$59$	441.584	−	441.584i	0.974395	−	0.974395i	−0.0252856	−	0.999680i	$-0.508050\pi$
$59$	441.584	−	441.584i	0.974395	−	0.974395i	0.999680	+	0.0252856i	$0.00804951\pi$
$60$		0			0
$61$	174.485	+	174.485i	0.366238	+	0.366238i	0.866103	−	0.499865i	$-0.166617\pi$
$61$	174.485	+	174.485i	0.366238	+	0.366238i	−0.499865	+	0.866103i	$0.666617\pi$
$62$		0			0
$63$	77.6476			0.155281
$64$		0			0
$65$	−829.188			−1.58228
$66$		0			0
$67$	91.7562	+	91.7562i	0.167311	+	0.167311i	0.785796	−	0.618486i	$-0.212253\pi$
$67$	91.7562	+	91.7562i	0.167311	+	0.167311i	−0.618486	+	0.785796i	$0.712253\pi$
$68$		0			0
$69$	−438.385	+	438.385i	−0.764860	+	0.764860i
$70$		0			0
$71$			348.360i			0.582291i	0.956679	+	0.291146i	$0.0940364\pi$
$71$			348.360i			0.582291i	−0.956679	+	0.291146i	$0.905964\pi$
$72$		0			0
$73$			299.436i			0.480087i	0.970762	+	0.240043i	$0.0771617\pi$
$73$			299.436i			0.480087i	−0.970762	+	0.240043i	$0.922838\pi$
$74$		0			0
$75$	−637.222	+	637.222i	−0.981067	+	0.981067i
$76$		0			0
$77$	21.4644	+	21.4644i	0.0317675	+	0.0317675i
$78$		0			0
$79$	943.487			1.34368			0.671839	−	0.740697i	$-0.265505\pi$
$79$	943.487			1.34368			0.671839	+	0.740697i	$0.265505\pi$
$80$		0			0
$81$	546.590			0.749781
$82$		0			0
$83$	313.272	+	313.272i	0.414290	+	0.414290i	0.883230	−	0.468940i	$-0.155364\pi$
$83$	313.272	+	313.272i	0.414290	+	0.414290i	−0.468940	+	0.883230i	$0.655364\pi$
$84$		0			0
$85$	235.866	−	235.866i	0.300979	−	0.300979i
$86$		0			0
$87$		−	391.224i		−	0.482111i
$88$		0			0
$89$		−	1412.35i		−	1.68212i	−0.540942	−	0.841060i	$-0.681932\pi$
$89$		−	1412.35i		−	1.68212i	0.540942	−	0.841060i	$-0.318068\pi$
$90$		0			0
$91$	454.939	−	454.939i	0.524072	−	0.524072i
$92$		0			0
$93$	−103.177	−	103.177i	−0.115042	−	0.115042i
$94$		0			0
$95$	−2185.14			−2.35990
$96$		0			0
$97$	1515.29			1.58613			0.793063	−	0.609140i	$-0.208485\pi$
$97$	1515.29			1.58613			0.793063	+	0.609140i	$0.208485\pi$
$98$		0			0
$99$	−8.65680	−	8.65680i	−0.00878830	−	0.00878830i
$100$		0			0
$101$	573.202	−	573.202i	0.564711	−	0.564711i	−0.365931	−	0.930642i	$-0.619249\pi$
$101$	573.202	−	573.202i	0.564711	−	0.564711i	0.930642	+	0.365931i	$0.119249\pi$
$102$		0			0
$103$		−	1021.00i		−	0.976717i	−0.872643	−	0.488359i	$-0.837596\pi$
$103$		−	1021.00i		−	0.976717i	0.872643	−	0.488359i	$-0.162404\pi$
$104$		0			0
$105$		−	1147.95i		−	1.06693i
$106$		0			0
$107$	−1240.79	+	1240.79i	−1.12105	+	1.12105i	−0.129462	+	0.991584i	$0.541325\pi$
$107$	−1240.79	+	1240.79i	−1.12105	+	1.12105i	−0.991584	+	0.129462i	$0.958675\pi$
$108$		0			0
$109$	108.629	+	108.629i	0.0954565	+	0.0954565i	0.753222	−	0.657766i	$-0.228498\pi$
$109$	108.629	+	108.629i	0.0954565	+	0.0954565i	−0.657766	+	0.753222i	$0.728498\pi$
$110$		0			0
$111$	583.528			0.498973
$112$		0			0
$113$	−1722.22			−1.43374			−0.716870	−	0.697207i	$-0.754426\pi$
$113$	−1722.22			−1.43374			−0.716870	+	0.697207i	$0.754426\pi$
$114$		0			0
$115$	−1694.49	−	1694.49i	−1.37402	−	1.37402i
$116$		0			0
$117$	−183.481	+	183.481i	−0.144981	+	0.144981i
$118$		0			0
$119$			258.818i			0.199377i
$120$		0			0
$121$			1326.21i			0.996404i
$122$		0			0
$123$	688.639	−	688.639i	0.504817	−	0.504817i
$124$		0			0
$125$	−882.442	−	882.442i	−0.631424	−	0.631424i
$126$		0			0
$127$	−699.127			−0.488484			−0.244242	−	0.969714i	$-0.578539\pi$
$127$	−699.127			−0.488484			−0.244242	+	0.969714i	$0.578539\pi$
$128$		0			0
$129$	−781.219			−0.533198
$130$		0			0
$131$	197.970	+	197.970i	0.132036	+	0.132036i	0.770036	−	0.638000i	$-0.220238\pi$
$131$	197.970	+	197.970i	0.132036	+	0.132036i	−0.638000	+	0.770036i	$0.720238\pi$
$132$		0			0
$133$	1198.89	−	1198.89i	0.781632	−	0.781632i
$134$		0			0
$135$			2696.76i			1.71926i
$136$		0			0
$137$			271.386i			0.169242i	0.996413	+	0.0846209i	$0.0269679\pi$
$137$			271.386i			0.169242i	−0.996413	+	0.0846209i	$0.973032\pi$
$138$		0			0
$139$	459.937	−	459.937i	0.280657	−	0.280657i	−0.552714	−	0.833371i	$-0.686408\pi$
$139$	459.937	−	459.937i	0.280657	−	0.280657i	0.833371	+	0.552714i	$0.186408\pi$
$140$		0			0
$141$	−598.343	−	598.343i	−0.357373	−	0.357373i
$142$		0			0
$143$	−101.441			−0.0593210
$144$		0			0
$145$	1512.20			0.866079
$146$		0			0
$147$	−492.258	−	492.258i	−0.276196	−	0.276196i
$148$		0			0
$149$	−605.772	+	605.772i	−0.333066	+	0.333066i	−0.853750	−	0.520684i	$-0.825677\pi$
$149$	−605.772	+	605.772i	−0.333066	+	0.333066i	0.520684	+	0.853750i	$0.325677\pi$
$150$		0			0
$151$		−	3534.47i		−	1.90484i	−0.304785	−	0.952421i	$-0.598585\pi$
$151$		−	3534.47i		−	1.90484i	0.304785	−	0.952421i	$-0.401415\pi$
$152$		0			0
$153$		−	104.384i		−	0.0551564i
$154$		0			0
$155$	398.809	−	398.809i	0.206665	−	0.206665i
$156$		0			0
$157$	1233.54	+	1233.54i	0.627051	+	0.627051i	0.947325	−	0.320274i	$-0.103775\pi$
$157$	1233.54	+	1233.54i	0.627051	+	0.627051i	−0.320274	+	0.947325i	$0.603775\pi$
$158$		0			0
$159$	−171.187			−0.0853839
$160$		0			0
$161$	1859.38			0.910186
$162$		0			0
$163$	2569.36	+	2569.36i	1.23465	+	1.23465i	0.962158	+	0.272494i	$0.0878484\pi$
$163$	2569.36	+	2569.36i	1.23465	+	1.23465i	0.272494	+	0.962158i	$0.412152\pi$
$164$		0			0
$165$	−127.983	+	127.983i	−0.0603845	+	0.0603845i
$166$		0			0
$167$			3048.39i			1.41252i	0.707950	+	0.706262i	$0.249620\pi$
$167$			3048.39i			1.41252i	−0.707950	+	0.706262i	$0.750380\pi$
$168$		0			0
$169$		−	46.9618i		−	0.0213754i
$170$		0			0
$171$	−483.524	+	483.524i	−0.216234	+	0.216234i
$172$		0			0
$173$	1522.05	+	1522.05i	0.668898	+	0.668898i	0.957461	−	0.288563i	$-0.0931773\pi$
$173$	1522.05	+	1522.05i	0.668898	+	0.668898i	−0.288563	+	0.957461i	$0.593177\pi$
$174$		0			0
$175$	2702.74			1.16747
$176$		0			0
$177$	−2889.18			−1.22692
$178$		0			0
$179$	302.258	+	302.258i	0.126211	+	0.126211i	0.767391	−	0.641180i	$-0.221555\pi$
$179$	302.258	+	302.258i	0.126211	+	0.126211i	−0.641180	+	0.767391i	$0.721555\pi$
$180$		0			0
$181$	−1696.94	+	1696.94i	−0.696865	+	0.696865i	−0.963733	−	0.266868i	$-0.914011\pi$
$181$	−1696.94	+	1696.94i	−0.696865	+	0.696865i	0.266868	+	0.963733i	$0.414011\pi$
$182$		0			0
$183$		−	1141.62i		−	0.461151i
$184$		0			0
$185$			2255.51i			0.896370i
$186$		0			0
$187$	28.8552	−	28.8552i	0.0112840	−	0.0112840i
$188$		0			0
$189$	−1479.59	−	1479.59i	−0.569442	−	0.569442i
$190$		0			0
$191$	4035.31			1.52872			0.764358	−	0.644792i	$-0.223056\pi$
$191$	4035.31			1.52872			0.764358	+	0.644792i	$0.223056\pi$
$192$		0			0
$193$	−886.172			−0.330508			−0.165254	−	0.986251i	$-0.552844\pi$
$193$	−886.172			−0.330508			−0.165254	+	0.986251i	$0.552844\pi$
$194$		0			0
$195$	2712.59	+	2712.59i	0.996169	+	0.996169i
$196$		0			0
$197$	−3270.12	+	3270.12i	−1.18267	+	1.18267i	−0.203624	+	0.979049i	$0.565272\pi$
$197$	−3270.12	+	3270.12i	−1.18267	+	1.18267i	−0.979049	+	0.203624i	$0.934728\pi$
$198$		0			0
$199$			222.513i			0.0792639i	0.999214	+	0.0396319i	$0.0126185\pi$
$199$			222.513i			0.0792639i	−0.999214	+	0.0396319i	$0.987381\pi$
$200$		0			0
$201$		−	600.340i		−	0.210670i
$202$		0			0
$203$	−829.677	+	829.677i	−0.286857	+	0.286857i
$204$		0			0
$205$	2661.80	+	2661.80i	0.906868	+	0.906868i
$206$		0			0
$207$	−749.907			−0.251798
$208$		0			0
$209$	−267.325			−0.0884748
$210$		0			0
$211$	−3527.46	−	3527.46i	−1.15090	−	1.15090i	−0.986372	−	0.164529i	$-0.947390\pi$
$211$	−3527.46	−	3527.46i	−1.15090	−	1.15090i	−0.164529	−	0.986372i	$-0.552610\pi$
$212$		0			0
$213$	1139.62	−	1139.62i	0.366598	−	0.366598i
$214$		0			0
$215$		−	3019.65i		−	0.957852i
$216$		0			0
$217$			437.618i			0.136901i
$218$		0			0
$219$	979.571	−	979.571i	0.302252	−	0.302252i
$220$		0			0
$221$	−611.587	−	611.587i	−0.186153	−	0.186153i
$222$		0			0
$223$	−5841.90			−1.75427			−0.877136	−	0.480242i	$-0.840549\pi$
$223$	−5841.90			−1.75427			−0.877136	+	0.480242i	$0.840549\pi$
$224$		0			0
$225$	−1090.04			−0.322975
$226$		0			0
$227$	−1129.54	−	1129.54i	−0.330265	−	0.330265i	0.522422	−	0.852687i	$-0.325029\pi$
$227$	−1129.54	−	1129.54i	−0.330265	−	0.330265i	−0.852687	+	0.522422i	$0.825029\pi$
$228$		0			0
$229$	2905.40	−	2905.40i	0.838403	−	0.838403i	−0.150246	−	0.988649i	$-0.548006\pi$
$229$	2905.40	−	2905.40i	0.838403	−	0.838403i	0.988649	+	0.150246i	$0.0480065\pi$
$230$		0			0
$231$		−	140.437i		−	0.0400003i
$232$		0			0
$233$			734.054i			0.206393i	0.994661	+	0.103196i	$0.0329070\pi$
$233$			734.054i			0.206393i	−0.994661	+	0.103196i	$0.967093\pi$
$234$		0			0
$235$	2312.78	−	2312.78i	0.641995	−	0.641995i
$236$		0			0
$237$	−3086.51	−	3086.51i	−0.845951	−	0.845951i
$238$		0			0
$239$	511.807			0.138519			0.0692595	−	0.997599i	$-0.477936\pi$
$239$	511.807			0.138519			0.0692595	+	0.997599i	$0.477936\pi$
$240$		0			0
$241$	5920.31			1.58241			0.791204	−	0.611552i	$-0.209455\pi$
$241$	5920.31			1.58241			0.791204	+	0.611552i	$0.209455\pi$
$242$		0			0
$243$	1091.02	+	1091.02i	0.288020	+	0.288020i
$244$		0			0
$245$	1902.73	−	1902.73i	0.496166	−	0.496166i
$246$		0			0
$247$			5665.95i			1.45958i
$248$		0			0
$249$		−	2049.67i		−	0.521656i
$250$		0			0
$251$	−309.332	+	309.332i	−0.0777883	+	0.0777883i	−0.744930	−	0.667142i	$-0.767517\pi$
$251$	−309.332	+	309.332i	−0.0777883	+	0.0777883i	0.667142	+	0.744930i	$0.267517\pi$
$252$		0			0
$253$	−207.300	−	207.300i	−0.0515131	−	0.0515131i
$254$		0			0
$255$	−1543.22			−0.378980
$256$		0			0
$257$	323.723			0.0785730			0.0392865	−	0.999228i	$-0.487491\pi$
$257$	323.723			0.0785730			0.0392865	+	0.999228i	$0.487491\pi$
$258$		0			0
$259$	−1237.50	−	1237.50i	−0.296890	−	0.296890i
$260$		0			0
$261$	334.617	−	334.617i	0.0793573	−	0.0793573i
$262$		0			0
$263$			2689.15i			0.630495i	0.949009	+	0.315248i	$0.102088\pi$
$263$			2689.15i			0.630495i	−0.949009	+	0.315248i	$0.897912\pi$
$264$		0			0
$265$		−	661.691i		−	0.153386i
$266$		0			0
$267$	−4620.34	+	4620.34i	−1.05903	+	1.05903i
$268$		0			0
$269$	−4703.78	−	4703.78i	−1.06615	−	1.06615i	−0.997651	−	0.0684995i	$-0.978179\pi$
$269$	−4703.78	−	4703.78i	−1.06615	−	1.06615i	−0.0684995	−	0.997651i	$-0.521821\pi$
$270$		0			0
$271$	2018.97			0.452561			0.226280	−	0.974062i	$-0.427343\pi$
$271$	2018.97			0.452561			0.226280	+	0.974062i	$0.427343\pi$
$272$		0			0
$273$	−2976.56			−0.659889
$274$		0			0
$275$	−301.324	−	301.324i	−0.0660745	−	0.0660745i
$276$		0			0
$277$	3080.60	−	3080.60i	0.668215	−	0.668215i	−0.289088	−	0.957303i	$-0.593352\pi$
$277$	3080.60	−	3080.60i	0.668215	−	0.668215i	0.957303	+	0.289088i	$0.0933519\pi$
$278$		0			0
$279$		−	176.495i		−	0.0378728i
$280$		0			0
$281$		−	3893.51i		−	0.826575i	−0.910601	−	0.413287i	$-0.864381\pi$
$281$		−	3893.51i		−	0.826575i	0.910601	−	0.413287i	$-0.135619\pi$
$282$		0			0
$283$	2026.38	−	2026.38i	0.425639	−	0.425639i	−0.461501	−	0.887140i	$-0.652689\pi$
$283$	2026.38	−	2026.38i	0.425639	−	0.425639i	0.887140	+	0.461501i	$0.152689\pi$
$284$		0			0
$285$	7148.45	+	7148.45i	1.48575	+	1.48575i
$286$		0			0
$287$	−2920.82			−0.600734
$288$		0			0
$289$	−4565.06			−0.929180
$290$		0			0
$291$	−4957.09	−	4957.09i	−0.998591	−	0.998591i
$292$		0			0
$293$	1001.68	−	1001.68i	0.199724	−	0.199724i	−0.600158	−	0.799882i	$-0.704896\pi$
$293$	1001.68	−	1001.68i	0.199724	−	0.199724i	0.799882	+	0.600158i	$0.204896\pi$
$294$		0			0
$295$		−	11167.6i		−	2.20407i
$296$		0			0
$297$			329.914i			0.0644565i
$298$		0			0
$299$	−4393.72	+	4393.72i	−0.849817	+	0.849817i
$300$		0			0
$301$	1656.75	+	1656.75i	0.317253	+	0.317253i
$302$		0			0
$303$	−3750.33			−0.711059
$304$		0			0
$305$	4412.69			0.828425
$306$		0			0
$307$	2966.54	+	2966.54i	0.551497	+	0.551497i	0.926873	−	0.375376i	$-0.122486\pi$
$307$	2966.54	+	2966.54i	0.551497	+	0.551497i	−0.375376	+	0.926873i	$0.622486\pi$
$308$		0			0
$309$	−3340.08	+	3340.08i	−0.614920	+	0.614920i
$310$		0			0
$311$		−	2911.18i		−	0.530797i	−0.964139	−	0.265399i	$-0.914496\pi$
$311$		−	2911.18i		−	0.530797i	0.964139	−	0.265399i	$-0.0855036\pi$
$312$		0			0
$313$		−	8287.74i		−	1.49665i	−0.663333	−	0.748324i	$-0.730859\pi$
$313$		−	8287.74i		−	1.49665i	0.663333	−	0.748324i	$-0.269141\pi$
$314$		0			0
$315$	981.845	−	981.845i	0.175621	−	0.175621i
$316$		0			0
$317$	−5742.18	−	5742.18i	−1.01739	−	1.01739i	−0.999846	−	0.0175452i	$-0.994415\pi$
$317$	−5742.18	−	5742.18i	−1.01739	−	1.01739i	−0.0175452	−	0.999846i	$-0.505585\pi$
$318$		0			0
$319$	184.999			0.0324700
$320$		0			0
$321$	8118.23			1.41157
$322$		0			0
$323$	−1611.70	−	1611.70i	−0.277639	−	0.277639i
$324$		0			0
$325$	−6386.56	+	6386.56i	−1.09004	+	1.09004i
$326$		0			0
$327$		−	710.734i		−	0.120195i
$328$		0			0
$329$			2537.84i			0.425275i
$330$		0			0
$331$	4499.27	−	4499.27i	0.747136	−	0.747136i	−0.226804	−	0.973940i	$-0.572828\pi$
$331$	4499.27	−	4499.27i	0.747136	−	0.747136i	0.973940	+	0.226804i	$0.0728278\pi$
$332$		0			0
$333$	499.095	+	499.095i	0.0821328	+	0.0821328i
$334$		0			0
$335$	2320.50			0.378454
$336$		0			0
$337$	−5860.06			−0.947234			−0.473617	−	0.880731i	$-0.657052\pi$
$337$	−5860.06			−0.947234			−0.473617	+	0.880731i	$0.657052\pi$
$338$		0			0
$339$	5634.04	+	5634.04i	0.902652	+	0.902652i
$340$		0			0
$341$	48.7893	−	48.7893i	0.00774806	−	0.00774806i
$342$		0			0
$343$			6847.14i			1.07787i
$344$		0			0
$345$			11086.7i			1.73010i
$346$		0			0
$347$	−2029.11	+	2029.11i	−0.313915	+	0.313915i	−0.846424	−	0.532509i	$-0.821249\pi$
$347$	−2029.11	+	2029.11i	−0.313915	+	0.313915i	0.532509	+	0.846424i	$0.321249\pi$
$348$		0			0
$349$	1943.26	+	1943.26i	0.298053	+	0.298053i	0.840251	−	0.542198i	$-0.182408\pi$
$349$	1943.26	+	1943.26i	0.298053	+	0.298053i	−0.542198	+	0.840251i	$0.682408\pi$
$350$		0			0
$351$	6992.54			1.06335
$352$		0			0
$353$	−7548.63			−1.13817			−0.569084	−	0.822280i	$-0.692702\pi$
$353$	−7548.63			−1.13817			−0.569084	+	0.822280i	$0.692702\pi$
$354$		0			0
$355$	4404.97	+	4404.97i	0.658568	+	0.658568i
$356$		0			0
$357$	846.694	−	846.694i	0.125523	−	0.125523i
$358$		0			0
$359$			5554.15i			0.816537i	0.912862	+	0.408269i	$0.133867\pi$
$359$			5554.15i			0.816537i	−0.912862	+	0.408269i	$0.866133\pi$
$360$		0			0
$361$			8072.37i			1.17690i
$362$		0			0
$363$	4338.56	−	4338.56i	0.627315	−	0.627315i
$364$		0			0
$365$	3786.34	+	3786.34i	0.542975	+	0.542975i
$366$		0			0
$367$	3610.98			0.513601			0.256800	−	0.966464i	$-0.417332\pi$
$367$	3610.98			0.513601			0.256800	+	0.966464i	$0.417332\pi$
$368$		0			0
$369$	1177.99			0.166190
$370$		0			0
$371$	363.040	+	363.040i	0.0508035	+	0.0508035i
$372$		0			0
$373$	−1215.49	+	1215.49i	−0.168728	+	0.168728i	−0.786420	−	0.617692i	$-0.788068\pi$
$373$	−1215.49	+	1215.49i	−0.168728	+	0.168728i	0.617692	+	0.786420i	$0.288068\pi$
$374$		0			0
$375$			5773.62i			0.795062i
$376$		0			0
$377$		−	3921.05i		−	0.535661i
$378$		0			0
$379$	−7347.81	+	7347.81i	−0.995861	+	0.995861i	−0.999991	−	0.00413018i	$-0.998685\pi$
$379$	−7347.81	+	7347.81i	−0.995861	+	0.995861i	0.00413018	+	0.999991i	$0.498685\pi$
$380$		0			0
$381$	2287.12	+	2287.12i	0.307539	+	0.307539i
$382$		0			0
$383$	7668.98			1.02315			0.511575	−	0.859238i	$-0.329062\pi$
$383$	7668.98			1.02315			0.511575	+	0.859238i	$0.329062\pi$
$384$		0			0
$385$	542.831			0.0718577
$386$		0			0
$387$	−668.181	−	668.181i	−0.0877663	−	0.0877663i
$388$		0			0
$389$	200.924	−	200.924i	0.0261884	−	0.0261884i	−0.693891	−	0.720080i	$-0.744105\pi$
$389$	200.924	−	200.924i	0.0261884	−	0.0261884i	0.720080	+	0.693891i	$0.244105\pi$
$390$		0			0
$391$		−	2499.62i		−	0.323302i
$392$		0			0
$393$		−	1295.27i		−	0.166254i
$394$		0			0
$395$	11930.3	−	11930.3i	1.51969	−	1.51969i
$396$		0			0
$397$	−6512.21	−	6512.21i	−0.823271	−	0.823271i	0.163305	−	0.986576i	$-0.447785\pi$
$397$	−6512.21	−	6512.21i	−0.823271	−	0.823271i	−0.986576	+	0.163305i	$0.947785\pi$
$398$		0			0
$399$	−7844.07			−0.984197
$400$		0			0
$401$	5565.10			0.693036			0.346518	−	0.938043i	$-0.387364\pi$
$401$	5565.10			0.693036			0.346518	+	0.938043i	$0.387364\pi$
$402$		0			0
$403$	−1034.09	−	1034.09i	−0.127820	−	0.127820i
$404$		0			0
$405$	6911.57	−	6911.57i	0.847997	−	0.847997i
$406$		0			0
$407$			275.933i			0.0336057i
$408$		0			0
$409$			12077.6i			1.46014i	0.683370	+	0.730072i	$0.260514\pi$
$409$			12077.6i			1.46014i	−0.683370	+	0.730072i	$0.739486\pi$
$410$		0			0
$411$	887.810	−	887.810i	0.106551	−	0.106551i
$412$		0			0
$413$	6127.14	+	6127.14i	0.730017	+	0.730017i
$414$		0			0
$415$	7922.58			0.937119
$416$		0			0
$417$	−3009.26			−0.353391
$418$		0			0
$419$	−1453.03	−	1453.03i	−0.169415	−	0.169415i	0.617307	−	0.786722i	$-0.288224\pi$
$419$	−1453.03	−	1453.03i	−0.169415	−	0.169415i	−0.786722	+	0.617307i	$0.788224\pi$
$420$		0			0
$421$	4822.25	−	4822.25i	0.558247	−	0.558247i	−0.370561	−	0.928808i	$-0.620835\pi$
$421$	4822.25	−	4822.25i	0.558247	−	0.558247i	0.928808	+	0.370561i	$0.120835\pi$
$422$		0			0
$423$		−	1023.53i		−	0.117650i
$424$		0			0
$425$		−	3633.36i		−	0.414692i
$426$		0			0
$427$	−2421.04	+	2421.04i	−0.274385	+	0.274385i
$428$		0			0
$429$	331.852	+	331.852i	0.0373472	+	0.0373472i
$430$		0			0
$431$	−12519.2			−1.39914			−0.699571	−	0.714563i	$-0.746626\pi$
$431$	−12519.2			−1.39914			−0.699571	+	0.714563i	$0.746626\pi$
$432$		0			0
$433$	−2921.40			−0.324235			−0.162117	−	0.986771i	$-0.551832\pi$
$433$	−2921.40			−0.324235			−0.162117	+	0.986771i	$0.551832\pi$
$434$		0			0
$435$	−4946.99	−	4946.99i	−0.545264	−	0.545264i
$436$		0			0
$437$	−11578.7	+	11578.7i	−1.26747	+	1.26747i
$438$		0			0
$439$			1140.50i			0.123993i	0.998076	+	0.0619967i	$0.0197468\pi$
$439$			1140.50i			0.123993i	−0.998076	+	0.0619967i	$0.980253\pi$
$440$		0			0
$441$		−	842.062i		−	0.0909256i
$442$		0			0
$443$	−1843.05	+	1843.05i	−0.197665	+	0.197665i	−0.798999	−	0.601333i	$-0.794637\pi$
$443$	−1843.05	+	1843.05i	−0.197665	+	0.197665i	0.601333	+	0.798999i	$0.294637\pi$
$444$		0			0
$445$	−17859.0	−	17859.0i	−1.90247	−	1.90247i
$446$		0			0
$447$	3963.43			0.419382
$448$		0			0
$449$	1752.13			0.184161			0.0920805	−	0.995752i	$-0.470648\pi$
$449$	1752.13			0.184161			0.0920805	+	0.995752i	$0.470648\pi$
$450$		0			0
$451$	325.637	+	325.637i	0.0339993	+	0.0339993i
$452$		0			0
$453$	−11562.6	+	11562.6i	−1.19925	+	1.19925i
$454$		0			0
$455$		−	11505.3i		−	1.18544i
$456$		0			0
$457$		−	12875.6i		−	1.31794i	−0.752171	−	0.658968i	$-0.770993\pi$
$457$		−	12875.6i		−	1.31794i	0.752171	−	0.658968i	$-0.229007\pi$
$458$		0			0
$459$	−1989.06	+	1989.06i	−0.202268	+	0.202268i
$460$		0			0
$461$	13679.7	+	13679.7i	1.38205	+	1.38205i	0.840968	+	0.541085i	$0.181986\pi$
$461$	13679.7	+	13679.7i	1.38205	+	1.38205i	0.541085	+	0.840968i	$0.318014\pi$
$462$		0			0
$463$	−15002.4			−1.50588			−0.752938	−	0.658091i	$-0.771364\pi$
$463$	−15002.4			−1.50588			−0.752938	+	0.658091i	$0.771364\pi$
$464$		0			0
$465$	−2609.32			−0.260224
$466$		0			0
$467$	9669.42	+	9669.42i	0.958131	+	0.958131i	0.999158	−	0.0410271i	$-0.0130630\pi$
$467$	9669.42	+	9669.42i	0.958131	+	0.958131i	−0.0410271	+	0.999158i	$0.513063\pi$
$468$		0			0
$469$	−1273.15	+	1273.15i	−0.125349	+	0.125349i
$470$		0			0
$471$		−	8070.75i		−	0.789555i
$472$		0			0
$473$		−	369.416i		−	0.0359107i
$474$		0			0
$475$	−16830.4	+	16830.4i	−1.62575	+	1.62575i
$476$		0			0
$477$	−146.418	−	146.418i	−0.0140545	−	0.0140545i
$478$		0			0
$479$	3072.68			0.293099			0.146550	−	0.989203i	$-0.453183\pi$
$479$	3072.68			0.293099			0.146550	+	0.989203i	$0.453183\pi$
$480$		0			0
$481$	5848.41			0.554396
$482$		0			0
$483$	−6082.76	−	6082.76i	−0.573033	−	0.573033i
$484$		0			0
$485$	19160.7	−	19160.7i	1.79390	−	1.79390i
$486$		0			0
$487$			8689.64i			0.808553i	0.914637	+	0.404276i	$0.132477\pi$
$487$			8689.64i			0.808553i	−0.914637	+	0.404276i	$0.867523\pi$
$488$		0			0
$489$		−	16810.8i		−	1.55462i
$490$		0			0
$491$	11194.3	−	11194.3i	1.02891	−	1.02891i	0.0293379	−	0.999570i	$-0.490660\pi$
$491$	11194.3	−	11194.3i	1.02891	−	1.02891i	0.999570	−	0.0293379i	$-0.00933987\pi$
$492$		0			0
$493$	1115.36	+	1115.36i	0.101893	+	0.101893i
$494$		0			0
$495$	−218.929			−0.0198790
$496$		0			0
$497$	−4833.62			−0.436253
$498$		0			0
$499$	−1632.72	−	1632.72i	−0.146474	−	0.146474i	0.630067	−	0.776541i	$-0.283027\pi$
$499$	−1632.72	−	1632.72i	−0.146474	−	0.146474i	−0.776541	+	0.630067i	$0.783027\pi$
$500$		0			0
$501$	9972.47	−	9972.47i	0.889295	−	0.889295i
$502$		0			0
$503$		−	6901.81i		−	0.611802i	−0.952063	−	0.305901i	$-0.901042\pi$
$503$		−	6901.81i		−	0.611802i	0.952063	−	0.305901i	$-0.0989577\pi$
$504$		0			0
$505$		−	14496.2i		−	1.27737i
$506$		0			0
$507$	−153.630	+	153.630i	−0.0134575	+	0.0134575i
$508$		0			0
$509$	−92.9712	−	92.9712i	−0.00809603	−	0.00809603i	0.703047	−	0.711143i	$-0.251822\pi$
$509$	−92.9712	−	92.9712i	−0.00809603	−	0.00809603i	−0.711143	+	0.703047i	$0.751822\pi$
$510$		0			0
$511$	−4154.79			−0.359681
$512$		0			0
$513$	18427.3			1.58594
$514$		0			0
$515$	−12910.4	−	12910.4i	−1.10466	−	1.10466i
$516$		0			0
$517$	282.939	−	282.939i	0.0240689	−	0.0240689i
$518$		0			0
$519$		−	9958.43i		−	0.842248i
$520$		0			0
$521$			11931.3i			1.00330i	0.865071	+	0.501649i	$0.167273\pi$
$521$			11931.3i			1.00330i	−0.865071	+	0.501649i	$0.832727\pi$
$522$		0			0
$523$	−9702.46	+	9702.46i	−0.811203	+	0.811203i	−0.984814	−	0.173611i	$-0.944456\pi$
$523$	−9702.46	+	9702.46i	−0.811203	+	0.811203i	0.173611	+	0.984814i	$0.444456\pi$
$524$		0			0
$525$	−8841.69	−	8841.69i	−0.735015	−	0.735015i
$526$		0			0
$527$	588.301			0.0486277
$528$		0			0
$529$	−5790.59			−0.475926
$530$		0			0
$531$	−2471.13	−	2471.13i	−0.201955	−	0.201955i
$532$		0			0
$533$	6901.89	−	6901.89i	0.560889	−	0.560889i
$534$		0			0
$535$			31379.4i			2.53579i
$536$		0			0
$537$		−	1977.60i		−	0.158920i
$538$		0			0
$539$	232.774	−	232.774i	0.0186017	−	0.0186017i
$540$		0			0
$541$	8556.67	+	8556.67i	0.680000	+	0.680000i	0.960000	−	0.280000i	$-0.0903345\pi$
$541$	8556.67	+	8556.67i	0.680000	+	0.680000i	−0.280000	+	0.960000i	$0.590334\pi$
$542$		0			0
$543$	11102.7			0.877462
$544$		0			0
$545$	2747.20			0.215921
$546$		0			0
$547$	−45.1953	−	45.1953i	−0.00353274	−	0.00353274i	0.705338	−	0.708871i	$-0.250795\pi$
$547$	−45.1953	−	45.1953i	−0.00353274	−	0.00353274i	−0.708871	+	0.705338i	$0.750795\pi$
$548$		0			0
$549$	976.430	−	976.430i	0.0759071	−	0.0759071i
$550$		0			0
$551$		−	10333.1i		−	0.798917i
$552$		0			0
$553$			13091.2i			1.00668i
$554$		0			0
$555$	7378.64	−	7378.64i	0.564335	−	0.564335i
$556$		0			0
$557$	−4279.60	−	4279.60i	−0.325552	−	0.325552i	0.525340	−	0.850892i	$-0.323938\pi$
$557$	−4279.60	−	4279.60i	−0.325552	−	0.325552i	−0.850892	+	0.525340i	$0.823938\pi$
$558$		0			0
$559$	−7829.77			−0.592422
$560$		0			0
$561$	−188.793			−0.0142083
$562$		0			0
$563$	14593.9	+	14593.9i	1.09247	+	1.09247i	0.995265	+	0.0972023i	$0.0309894\pi$
$563$	14593.9	+	14593.9i	1.09247	+	1.09247i	0.0972023	+	0.995265i	$0.469011\pi$
$564$		0			0
$565$	−21777.3	+	21777.3i	−1.62155	+	1.62155i
$566$		0			0
$567$			7584.14i			0.561736i
$568$		0			0
$569$			21728.1i			1.60086i	0.599425	+	0.800431i	$0.295396\pi$
$569$			21728.1i			1.60086i	−0.599425	+	0.800431i	$0.704604\pi$
$570$		0			0
$571$	16078.0	−	16078.0i	1.17836	−	1.17836i	0.198202	−	0.980161i	$-0.436490\pi$
$571$	16078.0	−	16078.0i	1.17836	−	1.17836i	0.980161	−	0.198202i	$-0.0635102\pi$
$572$		0			0
$573$	−13201.0	−	13201.0i	−0.962446	−	0.962446i
$574$		0			0
$575$	−26102.5			−1.89313
$576$		0			0
$577$	−26648.2			−1.92267			−0.961335	−	0.275383i	$-0.911195\pi$
$577$	−26648.2			−1.92267			−0.961335	+	0.275383i	$0.911195\pi$
$578$		0			0
$579$	2899.01	+	2899.01i	0.208081	+	0.208081i
$580$		0			0
$581$	−4346.77	+	4346.77i	−0.310386	+	0.310386i
$582$		0			0
$583$		−	80.9495i		−	0.00575058i
$584$		0			0
$585$			4640.20i			0.327946i
$586$		0			0
$587$	1342.62	−	1342.62i	0.0944050	−	0.0944050i	−0.658327	−	0.752732i	$-0.728736\pi$
$587$	1342.62	−	1342.62i	0.0944050	−	0.0944050i	0.752732	+	0.658327i	$0.228736\pi$
$588$		0			0
$589$	−2725.11	−	2725.11i	−0.190639	−	0.190639i
$590$		0			0
$591$	21395.7			1.48917
$592$		0			0
$593$	4474.79			0.309878			0.154939	−	0.987924i	$-0.450482\pi$
$593$	4474.79			0.309878			0.154939	+	0.987924i	$0.450482\pi$
$594$		0			0
$595$	3272.73	+	3272.73i	0.225494	+	0.225494i
$596$		0			0
$597$	727.925	−	727.925i	0.0499028	−	0.0499028i
$598$		0			0
$599$			12603.8i			0.859725i	0.902894	+	0.429863i	$0.141438\pi$
$599$			12603.8i			0.859725i	−0.902894	+	0.429863i	$0.858562\pi$
$600$		0			0
$601$		−	7220.64i		−	0.490077i	−0.969513	−	0.245038i	$-0.921199\pi$
$601$		−	7220.64i		−	0.490077i	0.969513	−	0.245038i	$-0.0788006\pi$
$602$		0			0
$603$	513.474	−	513.474i	0.0346771	−	0.0346771i
$604$		0			0
$605$	16769.8	+	16769.8i	1.12693	+	1.12693i
$606$		0			0
$607$	13695.6			0.915796			0.457898	−	0.889005i	$-0.348603\pi$
$607$	13695.6			0.915796			0.457898	+	0.889005i	$0.348603\pi$
$608$		0			0
$609$	5428.39			0.361198
$610$		0			0
$611$	−5996.90	−	5996.90i	−0.397068	−	0.397068i
$612$		0			0
$613$	2358.34	−	2358.34i	0.155387	−	0.155387i	−0.625132	−	0.780519i	$-0.714955\pi$
$613$	2358.34	−	2358.34i	0.155387	−	0.155387i	0.780519	+	0.625132i	$0.214955\pi$
$614$		0			0
$615$		−	17415.5i		−	1.14189i
$616$		0			0
$617$		−	4186.39i		−	0.273157i	−0.990629	−	0.136579i	$-0.956389\pi$
$617$		−	4186.39i		−	0.273157i	0.990629	−	0.136579i	$-0.0436106\pi$
$618$		0			0
$619$	−4800.50	+	4800.50i	−0.311710	+	0.311710i	−0.845572	−	0.533862i	$-0.820740\pi$
$619$	−4800.50	+	4800.50i	−0.311710	+	0.311710i	0.533862	+	0.845572i	$0.320740\pi$
$620$		0			0
$621$	14289.6	+	14289.6i	0.923387	+	0.923387i
$622$		0			0
$623$	19596.9			1.26024
$624$		0			0
$625$	2031.54			0.130018
$626$		0			0
$627$	874.522	+	874.522i	0.0557018	+	0.0557018i
$628$		0			0
$629$	−1663.60	+	1663.60i	−0.105457	+	0.105457i
$630$		0			0
$631$		−	16106.3i		−	1.01614i	−0.861316	−	0.508069i	$-0.830360\pi$
$631$		−	16106.3i		−	1.01614i	0.861316	−	0.508069i	$-0.169640\pi$
$632$		0			0
$633$			23079.3i			1.44917i
$634$		0			0
$635$	−8840.39	+	8840.39i	−0.552473	+	0.552473i
$636$		0			0
$637$	−4933.66	−	4933.66i	−0.306874	−	0.306874i
$638$		0			0
$639$	1949.45			0.120687
$640$		0			0
$641$	−6682.21			−0.411749			−0.205875	−	0.978578i	$-0.566004\pi$
$641$	−6682.21			−0.411749			−0.205875	+	0.978578i	$0.566004\pi$
$642$		0			0
$643$	−4983.47	−	4983.47i	−0.305644	−	0.305644i	0.537573	−	0.843217i	$-0.319341\pi$
$643$	−4983.47	−	4983.47i	−0.305644	−	0.305644i	−0.843217	+	0.537573i	$0.819341\pi$
$644$		0			0
$645$	−9878.43	+	9878.43i	−0.603043	+	0.603043i
$646$		0			0
$647$			5078.45i			0.308585i	0.988025	+	0.154292i	$0.0493098\pi$
$647$			5078.45i			0.308585i	−0.988025	+	0.154292i	$0.950690\pi$
$648$		0			0
$649$		−	1366.21i		−	0.0826324i
$650$		0			0
$651$	1431.62	−	1431.62i	0.0861896	−	0.0861896i
$652$		0			0
$653$	−6189.91	−	6189.91i	−0.370949	−	0.370949i	0.496874	−	0.867823i	$-0.334481\pi$
$653$	−6189.91	−	6189.91i	−0.370949	−	0.370949i	−0.867823	+	0.496874i	$0.834481\pi$
$654$		0			0
$655$	5006.62			0.298664
$656$		0			0
$657$	1675.67			0.0995037
$658$		0			0
$659$	5751.19	+	5751.19i	0.339962	+	0.339962i	0.856353	−	0.516391i	$-0.172725\pi$
$659$	5751.19	+	5751.19i	0.339962	+	0.339962i	−0.516391	+	0.856353i	$0.672725\pi$
$660$		0			0
$661$	6305.38	−	6305.38i	0.371030	−	0.371030i	−0.496822	−	0.867852i	$-0.665500\pi$
$661$	6305.38	−	6305.38i	0.371030	−	0.371030i	0.867852	+	0.496822i	$0.165500\pi$
$662$		0			0
$663$			4001.47i			0.234396i
$664$		0			0
$665$		−	30319.7i		−	1.76804i
$666$		0			0
$667$	8012.87	−	8012.87i	0.465157	−	0.465157i
$668$		0			0
$669$	19111.1	+	19111.1i	1.10445	+	1.10445i
$670$		0			0
$671$	539.837			0.0310584
$672$		0			0
$673$	14664.4			0.839925			0.419963	−	0.907541i	$-0.362043\pi$
$673$	14664.4			0.839925			0.419963	+	0.907541i	$0.362043\pi$
$674$		0			0
$675$	20770.9	+	20770.9i	1.18440	+	1.18440i
$676$		0			0
$677$	−5795.16	+	5795.16i	−0.328990	+	0.328990i	−0.852202	−	0.523212i	$-0.824733\pi$
$677$	−5795.16	+	5795.16i	−0.328990	+	0.328990i	0.523212	+	0.852202i	$0.324733\pi$
$678$		0			0
$679$			21025.2i			1.18833i
$680$		0			0
$681$			7390.32i			0.415855i
$682$		0			0
$683$	−13134.1	+	13134.1i	−0.735816	+	0.735816i	−0.971765	−	0.235950i	$-0.924180\pi$
$683$	−13134.1	+	13134.1i	−0.735816	+	0.735816i	0.235950	+	0.971765i	$0.424180\pi$
$684$		0			0
$685$	3431.65	+	3431.65i	0.191411	+	0.191411i
$686$		0			0
$687$	−19009.4			−1.05568
$688$		0			0
$689$	−1715.73			−0.0948679
$690$		0			0
$691$	14324.0	+	14324.0i	0.788583	+	0.788583i	0.981262	−	0.192679i	$-0.0617175\pi$
$691$	14324.0	+	14324.0i	0.788583	+	0.788583i	−0.192679	+	0.981262i	$0.561718\pi$
$692$		0			0
$693$	120.116	−	120.116i	0.00658419	−	0.00658419i
$694$		0			0
$695$		−	11631.7i		−	0.634843i
$696$		0			0
$697$			3926.54i			0.213383i
$698$		0			0
$699$	2401.37	−	2401.37i	0.129940	−	0.129940i
$700$		0			0
$701$	−15987.2	−	15987.2i	−0.861382	−	0.861382i	0.130117	−	0.991499i	$-0.458465\pi$
$701$	−15987.2	−	15987.2i	−0.861382	−	0.861382i	−0.991499	+	0.130117i	$0.958465\pi$
$702$		0			0
$703$	15412.2			0.826859
$704$		0			0
$705$	−15132.0			−0.808373
$706$		0			0
$707$	7953.40	+	7953.40i	0.423081	+	0.423081i
$708$		0			0
$709$	−19580.4	+	19580.4i	−1.03718	+	1.03718i	−0.0378960	+	0.999282i	$0.512066\pi$
$709$	−19580.4	+	19580.4i	−1.03718	+	1.03718i	−0.999282	+	0.0378960i	$0.987934\pi$
$710$		0			0
$711$		−	5279.82i		−	0.278493i
$712$		0			0
$713$		−	4226.43i		−	0.221993i
$714$		0			0
$715$	−1282.71	+	1282.71i	−0.0670916	+	0.0670916i
$716$		0			0
$717$	−1674.32	−	1674.32i	−0.0872085	−	0.0872085i
$718$		0			0
$719$	2111.24			0.109507			0.0547537	−	0.998500i	$-0.482563\pi$
$719$	2111.24			0.109507			0.0547537	+	0.998500i	$0.482563\pi$
$720$		0			0
$721$	14166.7			0.731757
$722$		0			0
$723$	−19367.6	−	19367.6i	−0.996250	−	0.996250i
$724$		0			0
$725$	11647.2	−	11647.2i	0.596645	−	0.596645i
$726$		0			0
$727$		−	14763.6i		−	0.753164i	−0.926383	−	0.376582i	$-0.877099\pi$
$727$		−	14763.6i		−	0.753164i	0.926383	−	0.376582i	$-0.122901\pi$
$728$		0			0
$729$		−	21896.2i		−	1.11244i
$730$		0			0
$731$	2227.21	−	2227.21i	0.112690	−	0.112690i
$732$		0			0
$733$	−3419.77	−	3419.77i	−0.172322	−	0.172322i	0.615677	−	0.787999i	$-0.288883\pi$
$733$	−3419.77	−	3419.77i	−0.172322	−	0.172322i	−0.787999	+	0.615677i	$0.788883\pi$
$734$		0			0
$735$	−12449.1			−0.624751
$736$		0			0
$737$	283.883			0.0141886
$738$		0			0
$739$	−11324.8	−	11324.8i	−0.563723	−	0.563723i	0.366640	−	0.930363i	$-0.380508\pi$
$739$	−11324.8	−	11324.8i	−0.563723	−	0.563723i	−0.930363	+	0.366640i	$0.880508\pi$
$740$		0			0
$741$	18535.5	−	18535.5i	0.918919	−	0.918919i
$742$		0			0
$743$			20313.3i			1.00299i	0.865160	+	0.501495i	$0.167217\pi$
$743$			20313.3i			1.00299i	−0.865160	+	0.501495i	$0.832783\pi$
$744$		0			0
$745$			15319.9i			0.753391i
$746$		0			0
$747$	1753.09	−	1753.09i	0.0858665	−	0.0858665i
$748$		0			0
$749$	−17216.5	−	17216.5i	−0.839888	−	0.839888i
$750$		0			0
$751$	−28755.3			−1.39720			−0.698598	−	0.715514i	$-0.746192\pi$
$751$	−28755.3			−1.39720			−0.698598	+	0.715514i	$0.746192\pi$
$752$		0			0
$753$	2023.89			0.0979477
$754$		0			0
$755$	−44693.0	−	44693.0i	−2.15436	−	2.15436i
$756$		0			0
$757$	23006.0	−	23006.0i	1.10458	−	1.10458i	0.110730	−	0.993850i	$-0.464681\pi$
$757$	23006.0	−	23006.0i	1.10458	−	1.10458i	0.993850	−	0.110730i	$-0.0353190\pi$
$758$		0			0
$759$			1356.31i			0.0648631i
$760$		0			0
$761$			9298.53i			0.442932i	0.975168	+	0.221466i	$0.0710843\pi$
$761$			9298.53i			0.442932i	−0.975168	+	0.221466i	$0.928916\pi$
$762$		0			0
$763$	−1507.27	+	1507.27i	−0.0715160	+	0.0715160i
$764$		0			0
$765$	−1319.92	−	1319.92i	−0.0623815	−	0.0623815i
$766$		0			0
$767$	−28956.8			−1.36319
$768$		0			0
$769$	−20402.0			−0.956717			−0.478358	−	0.878165i	$-0.658768\pi$
$769$	−20402.0			−0.956717			−0.478358	+	0.878165i	$0.658768\pi$
$770$		0			0
$771$	−1059.02	−	1059.02i	−0.0494679	−	0.0494679i
$772$		0			0
$773$	−7337.03	+	7337.03i	−0.341390	+	0.341390i	−0.856890	−	0.515500i	$-0.827606\pi$
$773$	−7337.03	+	7337.03i	−0.341390	+	0.341390i	0.515500	+	0.856890i	$0.327606\pi$
$774$		0			0
$775$		−	6143.40i		−	0.284745i
$776$		0			0
$777$			8096.67i			0.373831i
$778$		0			0
$779$	18188.4	−	18188.4i	0.836544	−	0.836544i
$780$		0			0
$781$	538.893	+	538.893i	0.0246903	+	0.0246903i
$782$		0			0
$783$	−12752.4			−0.582034
$784$		0			0
$785$	31195.9			1.41838
$786$		0			0
$787$	−11928.6	−	11928.6i	−0.540292	−	0.540292i	0.383323	−	0.923615i	$-0.374780\pi$
$787$	−11928.6	−	11928.6i	−0.540292	−	0.540292i	−0.923615	+	0.383323i	$0.874780\pi$
$788$		0			0
$789$	8797.25	−	8797.25i	0.396946	−	0.396946i
$790$		0			0
$791$		−	23896.4i		−	1.07416i
$792$		0			0
$793$		−	11441.8i		−	0.512373i
$794$		0			0
$795$	−2164.65	+	2164.65i	−0.0965686	+	0.0965686i
$796$		0			0
$797$	6576.18	+	6576.18i	0.292271	+	0.292271i	0.837977	−	0.545706i	$-0.183738\pi$
$797$	6576.18	+	6576.18i	0.292271	+	0.292271i	−0.545706	+	0.837977i	$0.683738\pi$
$798$		0			0
$799$	3411.68			0.151060
$800$		0			0
$801$	−7903.61			−0.348639
$802$		0			0
$803$	463.211	+	463.211i	0.0203566	+	0.0203566i
$804$		0			0
$805$	23511.7	−	23511.7i	1.02941	−	1.02941i
$806$		0			0
$807$			30775.8i			1.34245i
$808$		0			0
$809$		−	29320.9i		−	1.27425i	−0.770760	−	0.637126i	$-0.780123\pi$
$809$		−	29320.9i		−	1.27425i	0.770760	−	0.637126i	$-0.219877\pi$
$810$		0			0
$811$	−14487.9	+	14487.9i	−0.627297	+	0.627297i	−0.947387	−	0.320090i	$-0.896287\pi$
$811$	−14487.9	+	14487.9i	−0.627297	+	0.627297i	0.320090	+	0.947387i	$0.396287\pi$
$812$		0			0
$813$	−6604.84	−	6604.84i	−0.284922	−	0.284922i
$814$		0			0
$815$	64978.7			2.79276
$816$		0			0
$817$	−20633.6			−0.883574
$818$		0			0
$819$	−2545.87	−	2545.87i	−0.108620	−	0.108620i
$820$		0			0
$821$	−20259.2	+	20259.2i	−0.861208	+	0.861208i	−0.991479	−	0.130270i	$-0.958415\pi$
$821$	−20259.2	+	20259.2i	−0.861208	+	0.861208i	0.130270	+	0.991479i	$0.458415\pi$
$822$		0			0
$823$		−	24605.9i		−	1.04217i	−0.853504	−	0.521086i	$-0.825527\pi$
$823$		−	24605.9i		−	1.04217i	0.853504	−	0.521086i	$-0.174473\pi$
$824$		0			0
$825$			1971.49i			0.0831982i
$826$		0			0
$827$	−24095.8	+	24095.8i	−1.01317	+	1.01317i	−0.0132601	+	0.999912i	$0.504221\pi$
$827$	−24095.8	+	24095.8i	−1.01317	+	1.01317i	−0.999912	+	0.0132601i	$0.995779\pi$
$828$		0			0
$829$	914.616	+	914.616i	0.0383184	+	0.0383184i	0.726006	−	0.687688i	$-0.241374\pi$
$829$	914.616	+	914.616i	0.0383184	+	0.0383184i	−0.687688	+	0.726006i	$0.741374\pi$
$830$		0			0
$831$	−20155.7			−0.841388
$832$		0			0
$833$	2806.80			0.116746
$834$		0			0
$835$	38546.6	+	38546.6i	1.59756	+	1.59756i
$836$		0			0
$837$	−3363.16	+	3363.16i	−0.138886	+	0.138886i
$838$		0			0
$839$			28847.5i			1.18704i	0.804819	+	0.593521i	$0.202263\pi$
$839$			28847.5i			1.18704i	−0.804819	+	0.593521i	$0.797737\pi$
$840$		0			0
$841$		−	17238.1i		−	0.706800i
$842$		0			0
$843$	−12737.2	+	12737.2i	−0.520394	+	0.520394i
$844$		0			0
$845$	−593.827	−	593.827i	−0.0241755	−	0.0241755i
$846$		0			0
$847$	−18401.7			−0.746506
$848$		0			0
$849$	−13258.2			−0.535947
$850$		0			0
$851$	11951.5	+	11951.5i	0.481426	+	0.481426i
$852$		0			0
$853$	−41.5562	+	41.5562i	−0.00166806	+	0.00166806i	−0.707940	−	0.706272i	$-0.750375\pi$
$853$	−41.5562	+	41.5562i	−0.00166806	+	0.00166806i	0.706272	+	0.707940i	$0.250375\pi$
$854$		0			0
$855$			12228.2i			0.489118i
$856$		0			0
$857$			20953.6i			0.835194i	0.908632	+	0.417597i	$0.137128\pi$
$857$			20953.6i			0.835194i	−0.908632	+	0.417597i	$0.862872\pi$
$858$		0			0
$859$	29316.3	−	29316.3i	1.16444	−	1.16444i	0.180953	−	0.983492i	$-0.442082\pi$
$859$	29316.3	−	29316.3i	1.16444	−	1.16444i	0.983492	−	0.180953i	$-0.0579181\pi$
$860$		0			0
$861$	9555.13	+	9555.13i	0.378209	+	0.378209i
$862$		0			0
$863$	3389.59			0.133700			0.0668499	−	0.997763i	$-0.478705\pi$
$863$	3389.59			0.133700			0.0668499	+	0.997763i	$0.478705\pi$
$864$		0			0
$865$	38492.3			1.51304
$866$		0			0
$867$	14934.1	+	14934.1i	0.584992	+	0.584992i
$868$		0			0
$869$	1459.52	−	1459.52i	0.0569745	−	0.0569745i
$870$		0			0
$871$		−	6016.91i		−	0.234070i
$872$		0			0
$873$		−	8479.66i		−	0.328743i
$874$		0			0
$875$	12244.2	−	12244.2i	0.473063	−	0.473063i
$876$		0			0
$877$	13912.5	+	13912.5i	0.535681	+	0.535681i	0.922257	−	0.386576i	$-0.126342\pi$
$877$	13912.5	+	13912.5i	0.535681	+	0.535681i	−0.386576	+	0.922257i	$0.626342\pi$
$878$		0			0
$879$	−6553.79			−0.251484
$880$		0			0
$881$	−1497.48			−0.0572660			−0.0286330	−	0.999590i	$-0.509115\pi$
$881$	−1497.48			−0.0572660			−0.0286330	+	0.999590i	$0.509115\pi$
$882$		0			0
$883$	−4143.81	−	4143.81i	−0.157928	−	0.157928i	0.623720	−	0.781648i	$-0.285621\pi$
$883$	−4143.81	−	4143.81i	−0.157928	−	0.157928i	−0.781648	+	0.623720i	$0.785621\pi$
$884$		0			0
$885$	−36533.4	+	36533.4i	−1.38763	+	1.38763i
$886$		0			0
$887$		−	18058.0i		−	0.683573i	−0.939778	−	0.341787i	$-0.888968\pi$
$887$		−	18058.0i		−	0.683573i	0.939778	−	0.341787i	$-0.111032\pi$
$888$		0			0
$889$		−	9700.66i		−	0.365973i
$890$		0			0
$891$	845.544	−	845.544i	0.0317921	−	0.0317921i
$892$		0			0
$893$	−15803.5	−	15803.5i	−0.592211	−	0.592211i
$894$		0			0
$895$	7644.03			0.285488
$896$		0			0
$897$	28747.1			1.07005
$898$		0			0
$899$	1885.88	+	1885.88i	0.0699640	+	0.0699640i
$900$		0			0
$901$	488.045	−	488.045i	0.0180457	−	0.0180457i
$902$		0			0
$903$		−	10839.7i		−	0.399472i
$904$		0			0
$905$			42915.2i			1.57630i
$906$		0			0
$907$	−21423.5	+	21423.5i	−0.784295	+	0.784295i	−0.980552	−	0.196257i	$-0.937121\pi$
$907$	−21423.5	+	21423.5i	−0.784295	+	0.784295i	0.196257	+	0.980552i	$0.437121\pi$
$908$		0			0
$909$	−3207.68	−	3207.68i	−0.117043	−	0.117043i
$910$		0			0
$911$	31977.7			1.16297			0.581487	−	0.813556i	$-0.302471\pi$
$911$	31977.7			1.16297			0.581487	+	0.813556i	$0.302471\pi$
$912$		0			0
$913$	969.228			0.0351334
$914$		0			0
$915$	−14435.6	−	14435.6i	−0.521559	−	0.521559i
$916$		0			0
$917$	−2746.91	+	2746.91i	−0.0989215	+	0.0989215i
$918$		0			0
$919$		−	40696.7i		−	1.46078i	−0.683029	−	0.730391i	$-0.739338\pi$
$919$		−	40696.7i		−	1.46078i	0.683029	−	0.730391i	$-0.260662\pi$
$920$		0			0
$921$		−	19409.4i		−	0.694421i
$922$		0			0
$923$	11421.8	−	11421.8i	0.407318	−	0.407318i
$924$		0			0
$925$	17372.4	+	17372.4i	0.617513	+	0.617513i
$926$		0			0
$927$	−5713.57			−0.202436
$928$		0			0
$929$	−11467.5			−0.404989			−0.202495	−	0.979283i	$-0.564905\pi$
$929$	−11467.5			−0.404989			−0.202495	+	0.979283i	$0.564905\pi$
$930$		0			0
$931$	−13001.6	−	13001.6i	−0.457690	−	0.457690i
$932$		0			0
$933$	−9523.60	+	9523.60i	−0.334179	+	0.334179i
$934$		0			0
$935$		−	729.742i		−	0.0255242i
$936$		0			0
$937$			14100.2i			0.491603i	0.969320	+	0.245802i	$0.0790512\pi$
$937$			14100.2i			0.491603i	−0.969320	+	0.245802i	$0.920949\pi$
$938$		0			0
$939$	−27112.4	+	27112.4i	−0.942257	+	0.942257i
$940$		0			0
$941$	21058.7	+	21058.7i	0.729538	+	0.729538i	0.970528	−	0.240989i	$-0.0774719\pi$
$941$	21058.7	+	21058.7i	0.729538	+	0.729538i	−0.240989	+	0.970528i	$0.577472\pi$
$942$		0			0
$943$	28208.8			0.974129
$944$		0			0
$945$	−37418.5			−1.28807
$946$		0			0
$947$	24998.9	+	24998.9i	0.857820	+	0.857820i	0.991081	−	0.133261i	$-0.0425448\pi$
$947$	24998.9	+	24998.9i	0.857820	+	0.857820i	−0.133261	+	0.991081i	$0.542545\pi$
$948$		0			0
$949$	9817.75	−	9817.75i	0.335825	−	0.335825i
$950$		0			0
$951$			37569.8i			1.28106i
$952$		0			0
$953$		−	6456.01i		−	0.219445i	−0.993962	−	0.109722i	$-0.965004\pi$
$953$		−	6456.01i		−	0.219445i	0.993962	−	0.109722i	$-0.0349961\pi$
$954$		0			0
$955$	51026.0	−	51026.0i	1.72897	−	1.72897i
$956$		0			0
$957$	−605.202	−	605.202i	−0.0204424	−	0.0204424i
$958$		0			0
$959$	−3765.59			−0.126796
$960$		0			0
$961$	−28796.3			−0.966610
$962$		0			0
$963$	6943.57	+	6943.57i	0.232350	+	0.232350i
$964$		0			0
$965$	−11205.5	+	11205.5i	−0.373802	+	0.373802i
$966$		0			0
$967$			15099.9i			0.502153i	0.967967	+	0.251076i	$0.0807845\pi$
$967$			15099.9i			0.502153i	−0.967967	+	0.251076i	$0.919215\pi$
$968$		0			0
$969$			10545.0i			0.349591i
$970$		0			0
$971$	−6223.12	+	6223.12i	−0.205674	+	0.205674i	−0.802426	−	0.596752i	$-0.796458\pi$
$971$	−6223.12	+	6223.12i	−0.205674	+	0.205674i	0.596752	+	0.802426i	$0.296458\pi$
$972$		0			0
$973$	6381.80	+	6381.80i	0.210268	+	0.210268i
$974$		0			0
$975$	41785.8			1.37253
$976$		0			0
$977$	−34900.0			−1.14284			−0.571418	−	0.820659i	$-0.693607\pi$
$977$	−34900.0			−1.14284			−0.571418	+	0.820659i	$0.693607\pi$
$978$		0			0
$979$	−2184.82	−	2184.82i	−0.0713251	−	0.0713251i
$980$		0			0
$981$	607.895	−	607.895i	0.0197845	−	0.0197845i
$982$		0			0
$983$			21221.5i			0.688567i	0.938866	+	0.344283i	$0.111878\pi$
$983$			21221.5i			0.688567i	−0.938866	+	0.344283i	$0.888122\pi$
$984$		0			0
$985$			82700.7i			2.67519i
$986$		0			0
$987$	8302.24	−	8302.24i	0.267744	−	0.267744i
$988$		0			0
$989$	−16000.6	−	16000.6i	−0.514447	−	0.514447i
$990$		0			0
$991$	−23985.3			−0.768838			−0.384419	−	0.923159i	$-0.625598\pi$
$991$	−23985.3			−0.768838			−0.384419	+	0.923159i	$0.625598\pi$
$992$		0			0
$993$	−29437.7			−0.940761
$994$		0			0
$995$	2813.65	+	2813.65i	0.0896469	+	0.0896469i
$996$		0			0
$997$	−10763.8	+	10763.8i	−0.341919	+	0.341919i	−0.857088	−	0.515169i	$-0.827729\pi$
$997$	−10763.8	+	10763.8i	−0.341919	+	0.341919i	0.515169	+	0.857088i	$0.327729\pi$
$998$		0			0
$999$		−	19020.7i		−	0.602391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.e.a.33.2		10
4.3	odd	2		128.4.e.b.33.4		10
8.3	odd	2		16.4.e.a.13.5	yes	10
8.5	even	2		64.4.e.a.17.4		10
16.3	odd	4		16.4.e.a.5.5	✓	10
16.5	even	4	inner	128.4.e.a.97.2		10
16.11	odd	4		128.4.e.b.97.4		10
16.13	even	4		64.4.e.a.49.4		10
24.5	odd	2		576.4.k.a.145.5		10
24.11	even	2		144.4.k.a.109.1		10
32.3	odd	8		1024.4.b.j.513.8		10
32.5	even	8		1024.4.a.m.1.8		10
32.11	odd	8		1024.4.a.n.1.8		10
32.13	even	8		1024.4.b.k.513.8		10
32.19	odd	8		1024.4.b.j.513.3		10
32.21	even	8		1024.4.a.m.1.3		10
32.27	odd	8		1024.4.a.n.1.3		10
32.29	even	8		1024.4.b.k.513.3		10
48.29	odd	4		576.4.k.a.433.5		10
48.35	even	4		144.4.k.a.37.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.5	✓	10	16.3	odd	4
16.4.e.a.13.5	yes	10	8.3	odd	2
64.4.e.a.17.4		10	8.5	even	2
64.4.e.a.49.4		10	16.13	even	4
128.4.e.a.33.2		10	1.1	even	1	trivial
128.4.e.a.97.2		10	16.5	even	4	inner
128.4.e.b.33.4		10	4.3	odd	2
128.4.e.b.97.4		10	16.11	odd	4
144.4.k.a.37.1		10	48.35	even	4
144.4.k.a.109.1		10	24.11	even	2
576.4.k.a.145.5		10	24.5	odd	2
576.4.k.a.433.5		10	48.29	odd	4
1024.4.a.m.1.3		10	32.21	even	8
1024.4.a.m.1.8		10	32.5	even	8
1024.4.a.n.1.3		10	32.27	odd	8
1024.4.a.n.1.8		10	32.11	odd	8
1024.4.b.j.513.3		10	32.19	odd	8
1024.4.b.j.513.8		10	32.3	odd	8
1024.4.b.k.513.3		10	32.29	even	8
1024.4.b.k.513.8		10	32.13	even	8

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.27139 - 3.27139i) q^{3} +(12.6449 - 12.6449i) q^{5} +13.8754i q^{7} -5.59607i q^{9} +O(q^{10})\)	\(q+(-3.27139 - 3.27139i) q^{3} +(12.6449 - 12.6449i) q^{5} +13.8754i q^{7} -5.59607i q^{9} +(1.54694 - 1.54694i) q^{11} +(-32.7875 - 32.7875i) q^{13} -82.7326 q^{15} +18.6531 q^{17} +(-86.4042 - 86.4042i) q^{19} +(45.3917 - 45.3917i) q^{21} -134.006i q^{23} -194.786i q^{25} +(-106.634 + 106.634i) q^{27} +(59.7949 + 59.7949i) q^{29} +31.5391 q^{31} -10.1213 q^{33} +(175.453 + 175.453i) q^{35} +(-89.1866 + 89.1866i) q^{37} +214.521i q^{39} +210.504i q^{41} +(119.402 - 119.402i) q^{43} +(-70.7617 - 70.7617i) q^{45} +182.902 q^{47} +150.474 q^{49} +(-61.0213 - 61.0213i) q^{51} +(26.1644 - 26.1644i) q^{53} -39.1219i q^{55} +565.323i q^{57} +(441.584 - 441.584i) q^{59} +(174.485 + 174.485i) q^{61} +77.6476 q^{63} -829.188 q^{65} +(91.7562 + 91.7562i) q^{67} +(-438.385 + 438.385i) q^{69} +348.360i q^{71} +299.436i q^{73} +(-637.222 + 637.222i) q^{75} +(21.4644 + 21.4644i) q^{77} +943.487 q^{79} +546.590 q^{81} +(313.272 + 313.272i) q^{83} +(235.866 - 235.866i) q^{85} -391.224i q^{87} -1412.35i q^{89} +(454.939 - 454.939i) q^{91} +(-103.177 - 103.177i) q^{93} -2185.14 q^{95} +1515.29 q^{97} +(-8.65680 - 8.65680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 10 * q - 2 * q^3 + 2 * q^5	\( 10 q - 2 q^{3} + 2 q^{5} + 18 q^{11} + 2 q^{13} + 124 q^{15} - 4 q^{17} - 26 q^{19} - 52 q^{21} + 184 q^{27} + 202 q^{29} - 368 q^{31} - 4 q^{33} + 476 q^{35} + 10 q^{37} - 838 q^{43} - 194 q^{45} + 944 q^{47} + 94 q^{49} - 1500 q^{51} + 378 q^{53} + 1706 q^{59} - 910 q^{61} - 2628 q^{63} - 492 q^{65} + 1942 q^{67} - 580 q^{69} - 2954 q^{75} + 268 q^{77} + 4416 q^{79} + 482 q^{81} - 2562 q^{83} + 12 q^{85} + 3332 q^{91} + 2192 q^{93} - 6900 q^{95} - 4 q^{97} + 4958 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 + 2 * q^5 + 18 * q^11 + 2 * q^13 + 124 * q^15 - 4 * q^17 - 26 * q^19 - 52 * q^21 + 184 * q^27 + 202 * q^29 - 368 * q^31 - 4 * q^33 + 476 * q^35 + 10 * q^37 - 838 * q^43 - 194 * q^45 + 944 * q^47 + 94 * q^49 - 1500 * q^51 + 378 * q^53 + 1706 * q^59 - 910 * q^61 - 2628 * q^63 - 492 * q^65 + 1942 * q^67 - 580 * q^69 - 2954 * q^75 + 268 * q^77 + 4416 * q^79 + 482 * q^81 - 2562 * q^83 + 12 * q^85 + 3332 * q^91 + 2192 * q^93 - 6900 * q^95 - 4 * q^97 + 4958 * q^99

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