LMFDB - Embedded newform 144.4.k.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.49627504083$
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:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$-1.56339 + 1.24732i$ of defining polynomial
Character	$\chi$	$=$	144.37
Dual form			144.4.k.a.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81071 + 0.316066i) q^{2} +(7.80020 - 1.77674i) q^{4} +(12.6449 + 12.6449i) q^{5} +13.8754i q^{7} +(-21.3626 + 7.45928i) q^{8} +O(q^{10})$	\(q+(-2.81071 + 0.316066i) q^{2} +(7.80020 - 1.77674i) q^{4} +(12.6449 + 12.6449i) q^{5} +13.8754i q^{7} +(-21.3626 + 7.45928i) q^{8} +(-39.5378 - 31.5445i) q^{10} +(-1.54694 - 1.54694i) q^{11} +(32.7875 - 32.7875i) q^{13} +(-4.38553 - 38.9997i) q^{14} +(57.6864 - 27.7179i) q^{16} -18.6531 q^{17} +(-86.4042 + 86.4042i) q^{19} +(121.099 + 76.1661i) q^{20} +(4.83695 + 3.85908i) q^{22} +134.006i q^{23} +194.786i q^{25} +(-81.7932 + 102.519i) q^{26} +(24.6529 + 108.231i) q^{28} +(59.7949 - 59.7949i) q^{29} -31.5391 q^{31} +(-153.379 + 96.1396i) q^{32} +(52.4284 - 5.89559i) q^{34} +(-175.453 + 175.453i) q^{35} +(89.1866 + 89.1866i) q^{37} +(215.548 - 270.167i) q^{38} +(-364.449 - 175.805i) q^{40} +210.504i q^{41} +(119.402 + 119.402i) q^{43} +(-14.8150 - 9.31796i) q^{44} +(-42.3547 - 376.652i) q^{46} +182.902 q^{47} +150.474 q^{49} +(-61.5653 - 547.489i) q^{50} +(197.494 - 314.004i) q^{52} +(26.1644 + 26.1644i) q^{53} -39.1219i q^{55} +(-103.500 - 296.414i) q^{56} +(-149.167 + 186.965i) q^{58} +(-441.584 - 441.584i) q^{59} +(-174.485 + 174.485i) q^{61} +(88.6475 - 9.96844i) q^{62} +(400.718 - 318.699i) q^{64} +829.188 q^{65} +(91.7562 - 91.7562i) q^{67} +(-145.498 + 33.1416i) q^{68} +(437.692 - 548.601i) q^{70} -348.360i q^{71} -299.436i q^{73} +(-278.867 - 222.489i) q^{74} +(-520.453 + 827.488i) q^{76} +(21.4644 - 21.4644i) q^{77} -943.487 q^{79} +(1079.93 + 378.949i) q^{80} +(-66.5330 - 591.666i) q^{82} +(-313.272 + 313.272i) q^{83} +(-235.866 - 235.866i) q^{85} +(-373.343 - 297.865i) q^{86} +(44.5858 + 21.5076i) q^{88} -1412.35i q^{89} +(454.939 + 454.939i) q^{91} +(238.094 + 1045.27i) q^{92} +(-514.085 + 57.8091i) q^{94} -2185.14 q^{95} +1515.29 q^{97} +(-422.939 + 47.5596i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	−2.81071	+	0.316066i	−0.993737	+	0.111746i
$2$	−2.81071	+	0.316066i	−0.993737	+	0.111746i
$3$		0			0
$3$		0			0
$4$	7.80020	−	1.77674i	0.975026	−	0.222092i
$5$	12.6449	+	12.6449i	1.13099	+	1.13099i	0.990012	+	0.140981i	$0.0450257\pi$
$5$	12.6449	+	12.6449i	1.13099	+	1.13099i	0.140981	+	0.990012i	$0.454974\pi$
$6$		0			0
$7$			13.8754i			0.749200i	0.927187	+	0.374600i	$0.122220\pi$
$7$			13.8754i			0.749200i	−0.927187	+	0.374600i	$0.877780\pi$
$8$	−21.3626	+	7.45928i	−0.944101	+	0.329657i
$9$		0			0
$10$	−39.5378	−	31.5445i	−1.25029	−	0.997526i
$11$	−1.54694	−	1.54694i	−0.0424019	−	0.0424019i	0.685588	−	0.727990i	$-0.259545\pi$
$11$	−1.54694	−	1.54694i	−0.0424019	−	0.0424019i	−0.727990	+	0.685588i	$0.759545\pi$
$12$		0			0
$13$	32.7875	−	32.7875i	0.699509	−	0.699509i	−0.264796	−	0.964304i	$-0.585305\pi$
$13$	32.7875	−	32.7875i	0.699509	−	0.699509i	0.964304	+	0.264796i	$0.0853046\pi$
$14$	−4.38553	−	38.9997i	−0.0837202	−	0.744508i
$15$		0			0
$16$	57.6864	−	27.7179i	0.901350	−	0.433092i
$17$	−18.6531			−0.266119			−0.133060	−	0.991108i	$-0.542480\pi$
$17$	−18.6531			−0.266119			−0.133060	+	0.991108i	$0.542480\pi$
$18$		0			0
$19$	−86.4042	+	86.4042i	−1.04329	+	1.04329i	−0.0442688	+	0.999020i	$0.514096\pi$
$19$	−86.4042	+	86.4042i	−1.04329	+	1.04329i	−0.999020	+	0.0442688i	$0.985904\pi$
$20$	121.099	+	76.1661i	1.35393	+	0.851562i
$21$		0			0
$22$	4.83695	+	3.85908i	0.0468746	+	0.0373981i
$23$			134.006i			1.21488i	0.794367	+	0.607438i	$0.207803\pi$
$23$			134.006i			1.21488i	−0.794367	+	0.607438i	$0.792197\pi$
$24$		0			0
$25$			194.786i			1.55829i
$26$	−81.7932	+	102.519i	−0.616960	+	0.773295i
$27$		0			0
$28$	24.6529	+	108.231i	0.166392	+	0.730489i
$29$	59.7949	−	59.7949i	0.382884	−	0.382884i	−0.489256	−	0.872140i	$-0.662732\pi$
$29$	59.7949	−	59.7949i	0.382884	−	0.382884i	0.872140	+	0.489256i	$0.162732\pi$
$30$		0			0
$31$	−31.5391			−0.182729			−0.0913645	−	0.995818i	$-0.529123\pi$
$31$	−31.5391			−0.182729			−0.0913645	+	0.995818i	$0.529123\pi$
$32$	−153.379	+	96.1396i	−0.847308	+	0.531101i
$33$		0			0
$34$	52.4284	−	5.89559i	0.264453	−	0.0297378i
$35$	−175.453	+	175.453i	−0.847340	+	0.847340i
$36$		0			0
$37$	89.1866	+	89.1866i	0.396275	+	0.396275i	0.876917	−	0.480642i	$-0.159596\pi$
$37$	89.1866	+	89.1866i	0.396275	+	0.396275i	−0.480642	+	0.876917i	$0.659596\pi$
$38$	215.548	−	270.167i	0.920171	−	1.15334i
$39$		0			0
$40$	−364.449	−	175.805i	−1.44061	−	0.694932i
$41$			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	0.886392	−	0.462936i	$-0.153204\pi$
$43$	119.402	+	119.402i	0.423456	+	0.423456i	−0.462936	+	0.886392i	$0.653204\pi$
$44$	−14.8150	−	9.31796i	−0.0507601	−	0.0319258i
$45$		0			0
$46$	−42.3547	−	376.652i	−0.135758	−	1.20727i
$47$	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
$50$	−61.5653	−	547.489i	−0.174133	−	1.54853i
$51$		0			0
$52$	197.494	−	314.004i	0.526683	−	0.837394i
$53$	26.1644	+	26.1644i	0.0678104	+	0.0678104i	0.740199	−	0.672388i	$-0.234731\pi$
$53$	26.1644	+	26.1644i	0.0678104	+	0.0678104i	−0.672388	+	0.740199i	$0.734731\pi$
$54$		0			0
$55$		−	39.1219i		−	0.0959125i
$56$	−103.500	−	296.414i	−0.246979	−	0.707320i
$57$		0			0
$58$	−149.167	+	186.965i	−0.337700	+	0.423272i
$59$	−441.584	−	441.584i	−0.974395	−	0.974395i	0.0252856	−	0.999680i	$-0.491950\pi$
$59$	−441.584	−	441.584i	−0.974395	−	0.974395i	−0.999680	+	0.0252856i	$0.991950\pi$
$60$		0			0
$61$	−174.485	+	174.485i	−0.366238	+	0.366238i	−0.866103	−	0.499865i	$-0.833383\pi$
$61$	−174.485	+	174.485i	−0.366238	+	0.366238i	0.499865	+	0.866103i	$0.333383\pi$
$62$	88.6475	−	9.96844i	0.181585	−	0.0204192i
$63$		0			0
$64$	400.718	−	318.699i	0.782653	−	0.622458i
$65$	829.188			1.58228
$66$		0			0
$67$	91.7562	−	91.7562i	0.167311	−	0.167311i	−0.618486	−	0.785796i	$-0.712253\pi$
$67$	91.7562	−	91.7562i	0.167311	−	0.167311i	0.785796	+	0.618486i	$0.212253\pi$
$68$	−145.498	+	33.1416i	−0.259473	+	0.0591031i
$69$		0			0
$70$	437.692	−	548.601i	0.747346	−	0.936720i
$71$		−	348.360i		−	0.582291i	−0.956679	−	0.291146i	$-0.905964\pi$
$71$		−	348.360i		−	0.582291i	0.956679	−	0.291146i	$-0.0940364\pi$
$72$		0			0
$73$		−	299.436i		−	0.480087i	−0.970762	−	0.240043i	$-0.922838\pi$
$73$		−	299.436i		−	0.480087i	0.970762	−	0.240043i	$-0.0771617\pi$
$74$	−278.867	−	222.489i	−0.438076	−	0.349511i
$75$		0			0
$76$	−520.453	+	827.488i	−0.785526	+	1.24894i
$77$	21.4644	−	21.4644i	0.0317675	−	0.0317675i
$78$		0			0
$79$	−943.487			−1.34368			−0.671839	−	0.740697i	$-0.734495\pi$
$79$	−943.487			−1.34368			−0.671839	+	0.740697i	$0.734495\pi$
$80$	1079.93	+	378.949i	1.50924	+	0.529597i
$81$		0			0
$82$	−66.5330	−	591.666i	−0.0896018	−	0.796812i
$83$	−313.272	+	313.272i	−0.414290	+	0.414290i	−0.883230	−	0.468940i	$-0.844636\pi$
$83$	−313.272	+	313.272i	−0.414290	+	0.414290i	0.468940	+	0.883230i	$0.344636\pi$
$84$		0			0
$85$	−235.866	−	235.866i	−0.300979	−	0.300979i
$86$	−373.343	−	297.865i	−0.468123	−	0.373484i
$87$		0			0
$88$	44.5858	+	21.5076i	0.0540097	+	0.0260536i
$89$		−	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
$92$	238.094	+	1045.27i	0.269815	+	1.18454i
$93$		0			0
$94$	−514.085	+	57.8091i	−0.564083	+	0.0634314i
$95$	−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	$0.208485\pi$
$98$	−422.939	+	47.5596i	−0.435952	+	0.0490229i
$99$		0			0
$100$	346.085	+	1519.37i	0.346085	+	1.51937i
$101$	573.202	+	573.202i	0.564711	+	0.564711i	0.930642	−	0.365931i	$-0.119249\pi$
$101$	573.202	+	573.202i	0.564711	+	0.564711i	−0.365931	+	0.930642i	$0.619249\pi$
$102$		0			0
$103$		−	1021.00i		−	0.976717i	−0.872643	−	0.488359i	$-0.837596\pi$
$103$		−	1021.00i		−	0.976717i	0.872643	−	0.488359i	$-0.162404\pi$
$104$	−455.854	+	944.996i	−0.429809	+	0.891004i
$105$		0			0
$106$	−81.8101	−	65.2708i	−0.0749632	−	0.0598081i
$107$	1240.79	+	1240.79i	1.12105	+	1.12105i	0.991584	+	0.129462i	$0.0413251\pi$
$107$	1240.79	+	1240.79i	1.12105	+	1.12105i	0.129462	+	0.991584i	$0.458675\pi$
$108$		0			0
$109$	−108.629	+	108.629i	−0.0954565	+	0.0954565i	−0.753222	−	0.657766i	$-0.771502\pi$
$109$	−108.629	+	108.629i	−0.0954565	+	0.0954565i	0.657766	+	0.753222i	$0.271502\pi$
$110$	12.3651	+	109.960i	0.0107179	+	0.0953118i
$111$		0			0
$112$	384.596	+	800.421i	0.324472	+	0.675291i
$113$	1722.22			1.43374			0.716870	−	0.697207i	$-0.245574\pi$
$113$	1722.22			1.43374			0.716870	+	0.697207i	$0.245574\pi$
$114$		0			0
$115$	−1694.49	+	1694.49i	−1.37402	+	1.37402i
$116$	360.173	−	572.653i	0.288286	−	0.458357i
$117$		0			0
$118$	1380.73	+	1101.59i	1.07718	+	0.859407i
$119$		−	258.818i		−	0.199377i
$120$		0			0
$121$		−	1326.21i		−	0.996404i
$122$	435.278	−	545.576i	0.323018	−	0.404870i
$123$		0			0
$124$	−246.012	+	56.0368i	−0.178165	+	0.0405827i
$125$	−882.442	+	882.442i	−0.631424	+	0.631424i
$126$		0			0
$127$	699.127			0.488484			0.244242	−	0.969714i	$-0.421461\pi$
$127$	699.127			0.488484			0.244242	+	0.969714i	$0.421461\pi$
$128$	−1025.57	+	1022.42i	−0.708194	+	0.706018i
$129$		0			0
$130$	−2330.61	+	262.078i	−1.57237	+	0.176814i
$131$	−197.970	+	197.970i	−0.132036	+	0.132036i	−0.770036	−	0.638000i	$-0.779762\pi$
$131$	−197.970	+	197.970i	−0.132036	+	0.132036i	0.638000	+	0.770036i	$0.279762\pi$
$132$		0			0
$133$	−1198.89	−	1198.89i	−0.781632	−	0.781632i
$134$	−228.899	+	286.901i	−0.147566	+	0.184959i
$135$		0			0
$136$	398.477	−	139.138i	0.251244	−	0.0877281i
$137$			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	0.833371	−	0.552714i	$-0.186408\pi$
$139$	459.937	+	459.937i	0.280657	+	0.280657i	−0.552714	+	0.833371i	$0.686408\pi$
$140$	−1056.83	+	1680.30i	−0.637991	+	1.01437i
$141$		0			0
$142$	110.105	+	979.139i	0.0650688	+	0.578644i
$143$	−101.441			−0.0593210
$144$		0			0
$145$	1512.20			0.866079
$146$	94.6415	+	841.628i	0.0536478	+	0.477080i
$147$		0			0
$148$	854.135	+	537.213i	0.474389	+	0.298369i
$149$	−605.772	−	605.772i	−0.333066	−	0.333066i	0.520684	−	0.853750i	$-0.325677\pi$
$149$	−605.772	−	605.772i	−0.333066	−	0.333066i	−0.853750	+	0.520684i	$0.825677\pi$
$150$		0			0
$151$		−	3534.47i		−	1.90484i	−0.304785	−	0.952421i	$-0.598585\pi$
$151$		−	3534.47i		−	1.90484i	0.304785	−	0.952421i	$-0.401415\pi$
$152$	1201.30	−	2490.33i	0.641042	−	1.32890i
$153$		0			0
$154$	−53.5461	+	67.1145i	−0.0280186	+	0.0351184i
$155$	−398.809	−	398.809i	−0.206665	−	0.206665i
$156$		0			0
$157$	−1233.54	+	1233.54i	−0.627051	+	0.627051i	−0.947325	−	0.320274i	$-0.896225\pi$
$157$	−1233.54	+	1233.54i	−0.627051	+	0.627051i	0.320274	+	0.947325i	$0.396225\pi$
$158$	2651.87	−	298.204i	1.33526	−	0.150151i
$159$		0			0
$160$	−3155.14	−	723.788i	−1.55897	−	0.357628i
$161$	−1859.38			−0.910186
$162$		0			0
$163$	2569.36	−	2569.36i	1.23465	−	1.23465i	0.272494	−	0.962158i	$-0.412152\pi$
$163$	2569.36	−	2569.36i	1.23465	−	1.23465i	0.962158	−	0.272494i	$-0.0878484\pi$
$164$	374.010	+	1641.97i	0.178081	+	0.781808i
$165$		0			0
$166$	781.503	−	979.532i	0.365400	−	0.457991i
$167$		−	3048.39i		−	1.41252i	−0.707950	−	0.706262i	$-0.750380\pi$
$167$		−	3048.39i		−	1.41252i	0.707950	−	0.706262i	$-0.249620\pi$
$168$		0			0
$169$			46.9618i			0.0213754i
$170$	737.500	+	588.402i	0.332727	+	0.265461i
$171$		0			0
$172$	1143.50	+	719.213i	0.506927	+	0.318834i
$173$	1522.05	−	1522.05i	0.668898	−	0.668898i	−0.288563	−	0.957461i	$-0.593177\pi$
$173$	1522.05	−	1522.05i	0.668898	−	0.668898i	0.957461	+	0.288563i	$0.0931773\pi$
$174$		0			0
$175$	−2702.74			−1.16747
$176$	−132.116	−	46.3596i	−0.0565829	−	0.0198550i
$177$		0			0
$178$	446.395	+	3969.71i	0.187970	+	1.67158i
$179$	−302.258	+	302.258i	−0.126211	+	0.126211i	−0.767391	−	0.641180i	$-0.778445\pi$
$179$	−302.258	+	302.258i	−0.126211	+	0.126211i	0.641180	+	0.767391i	$0.278445\pi$
$180$		0			0
$181$	1696.94	+	1696.94i	0.696865	+	0.696865i	0.963733	−	0.266868i	$-0.0859889\pi$
$181$	1696.94	+	1696.94i	0.696865	+	0.696865i	−0.266868	+	0.963733i	$0.585989\pi$
$182$	−1422.49	−	1134.91i	−0.579353	−	0.462227i
$183$		0			0
$184$	−999.588	−	2862.71i	−0.400492	−	1.14697i
$185$			2255.51i			0.896370i
$186$		0			0
$187$	28.8552	+	28.8552i	0.0112840	+	0.0112840i
$188$	1426.67	−	324.969i	0.553462	−	0.126068i
$189$		0			0
$190$	6141.81	−	690.649i	2.34512	−	0.263710i
$191$	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	$0.552844\pi$
$194$	−4259.04	+	478.931i	−1.57619	+	0.177243i
$195$		0			0
$196$	1173.73	−	267.353i	0.427743	−	0.0974318i
$197$	−3270.12	−	3270.12i	−1.18267	−	1.18267i	−0.979049	−	0.203624i	$-0.934728\pi$
$197$	−3270.12	−	3270.12i	−1.18267	−	1.18267i	−0.203624	−	0.979049i	$-0.565272\pi$
$198$		0			0
$199$			222.513i			0.0792639i	0.999214	+	0.0396319i	$0.0126185\pi$
$199$			222.513i			0.0792639i	−0.999214	+	0.0396319i	$0.987381\pi$
$200$	−1452.97	−	4161.14i	−0.513701	−	1.47118i
$201$		0			0
$202$	−1792.28	−	1429.94i	−0.624278	−	0.498070i
$203$	829.677	+	829.677i	0.286857	+	0.286857i
$204$		0			0
$205$	−2661.80	+	2661.80i	−0.906868	+	0.906868i
$206$	322.702	+	2869.73i	0.109144	+	0.970600i
$207$		0			0
$208$	982.593	−	2800.19i	0.327551	−	0.933453i
$209$	267.325			0.0884748
$210$		0			0
$211$	−3527.46	+	3527.46i	−1.15090	+	1.15090i	−0.164529	+	0.986372i	$0.552610\pi$
$211$	−3527.46	+	3527.46i	−1.15090	+	1.15090i	−0.986372	+	0.164529i	$0.947390\pi$
$212$	250.575	+	157.600i	0.0811770	+	0.0510567i
$213$		0			0
$214$	−3879.68	−	3095.34i	−1.23930	−	0.988753i
$215$			3019.65i			0.957852i
$216$		0			0
$217$		−	437.618i		−	0.136901i
$218$	270.991	−	339.658i	0.0841918	−	0.105526i
$219$		0			0
$220$	−69.5093	−	305.158i	−0.0213014	−	0.0935172i
$221$	−611.587	+	611.587i	−0.186153	+	0.186153i
$222$		0			0
$223$	5841.90			1.75427			0.877136	−	0.480242i	$-0.159451\pi$
$223$	5841.90			1.75427			0.877136	+	0.480242i	$0.159451\pi$
$224$	−1333.97	−	2128.19i	−0.397901	−	0.634803i
$225$		0			0
$226$	−4840.66	+	544.334i	−1.42476	+	0.160215i
$227$	1129.54	−	1129.54i	0.330265	−	0.330265i	−0.522422	−	0.852687i	$-0.674971\pi$
$227$	1129.54	−	1129.54i	0.330265	−	0.330265i	0.852687	+	0.522422i	$0.174971\pi$
$228$		0			0
$229$	−2905.40	−	2905.40i	−0.838403	−	0.838403i	0.150246	−	0.988649i	$-0.451994\pi$
$229$	−2905.40	−	2905.40i	−0.838403	−	0.838403i	−0.988649	+	0.150246i	$0.951994\pi$
$230$	4227.15	−	5298.29i	1.21187	−	1.51895i
$231$		0			0
$232$	−831.346	+	1723.40i	−0.235261	+	0.487701i
$233$			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
$236$	−4229.02	−	2659.86i	−1.16647	−	0.733654i
$237$		0			0
$238$	81.8036	+	727.463i	0.0222796	+	0.198128i
$239$	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	$0.209455\pi$
$242$	419.171	+	3727.61i	0.111344	+	0.990163i
$243$		0			0
$244$	−1051.00	+	1671.03i	−0.275753	+	0.438430i
$245$	1902.73	+	1902.73i	0.496166	+	0.496166i
$246$		0			0
$247$			5665.95i			1.45958i
$248$	673.757	−	235.259i	0.172515	−	0.0602378i
$249$		0			0
$250$	2201.38	−	2759.20i	0.556910	−	0.698029i
$251$	309.332	+	309.332i	0.0777883	+	0.0777883i	0.744930	−	0.667142i	$-0.232483\pi$
$251$	309.332	+	309.332i	0.0777883	+	0.0777883i	−0.667142	+	0.744930i	$0.732483\pi$
$252$		0			0
$253$	207.300	−	207.300i	0.0515131	−	0.0515131i
$254$	−1965.05	+	220.970i	−0.485425	+	0.0545862i
$255$		0			0
$256$	2559.44	−	3197.89i	0.624863	−	0.780734i
$257$	−323.723			−0.0785730			−0.0392865	−	0.999228i	$-0.512509\pi$
$257$	−323.723			−0.0785730			−0.0392865	+	0.999228i	$0.512509\pi$
$258$		0			0
$259$	−1237.50	+	1237.50i	−0.296890	+	0.296890i
$260$	6467.84	−	1473.25i	1.54276	−	0.351412i
$261$		0			0
$262$	493.865	−	619.009i	0.116455	−	0.145964i
$263$		−	2689.15i		−	0.630495i	−0.949009	−	0.315248i	$-0.897912\pi$
$263$		−	2689.15i		−	0.630495i	0.949009	−	0.315248i	$-0.102088\pi$
$264$		0			0
$265$			661.691i			0.153386i
$266$	3748.67	+	2990.81i	0.864081	+	0.689392i
$267$		0			0
$268$	552.691	−	878.744i	0.125974	−	0.200291i
$269$	−4703.78	+	4703.78i	−1.06615	+	1.06615i	−0.0684995	+	0.997651i	$0.521821\pi$
$269$	−4703.78	+	4703.78i	−1.06615	+	1.06615i	−0.997651	+	0.0684995i	$0.978179\pi$
$270$		0			0
$271$	−2018.97			−0.452561			−0.226280	−	0.974062i	$-0.572657\pi$
$271$	−2018.97			−0.452561			−0.226280	+	0.974062i	$0.572657\pi$
$272$	−1076.03	+	517.023i	−0.239867	+	0.115254i
$273$		0			0
$274$	−85.7760	−	762.789i	−0.0189121	−	0.168182i
$275$	301.324	−	301.324i	0.0660745	−	0.0660745i
$276$		0			0
$277$	−3080.60	−	3080.60i	−0.668215	−	0.668215i	0.289088	−	0.957303i	$-0.406648\pi$
$277$	−3080.60	−	3080.60i	−0.668215	−	0.668215i	−0.957303	+	0.289088i	$0.906648\pi$
$278$	−1438.12	−	1147.38i	−0.310262	−	0.247537i
$279$		0			0
$280$	2439.37	−	5056.87i	0.520643	−	1.07931i
$281$		−	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	0.887140	−	0.461501i	$-0.152689\pi$
$283$	2026.38	+	2026.38i	0.425639	+	0.425639i	−0.461501	+	0.887140i	$0.652689\pi$
$284$	−618.944	−	2717.28i	−0.129323	−	0.567749i
$285$		0			0
$286$	285.121	−	32.0619i	0.0589494	−	0.00662889i
$287$	−2920.82			−0.600734
$288$		0			0
$289$	−4565.06			−0.929180
$290$	−4250.36	+	477.955i	−0.860654	+	0.0967809i
$291$		0			0
$292$	−532.020	−	2335.66i	−0.106624	−	0.468097i
$293$	1001.68	+	1001.68i	0.199724	+	0.199724i	0.799882	−	0.600158i	$-0.204896\pi$
$293$	1001.68	+	1001.68i	0.199724	+	0.199724i	−0.600158	+	0.799882i	$0.704896\pi$
$294$		0			0
$295$		−	11167.6i		−	2.20407i
$296$	−2570.52	−	1239.99i	−0.504759	−	0.243489i
$297$		0			0
$298$	1894.12	+	1511.19i	0.368199	+	0.293761i
$299$	4393.72	+	4393.72i	0.849817	+	0.849817i
$300$		0			0
$301$	−1656.75	+	1656.75i	−0.317253	+	0.317253i
$302$	1117.12	+	9934.38i	0.212859	+	1.89291i
$303$		0			0
$304$	−2589.41	+	7379.29i	−0.488528	+	1.39221i
$305$	−4412.69			−0.828425
$306$		0			0
$307$	2966.54	−	2966.54i	0.551497	−	0.551497i	−0.375376	−	0.926873i	$-0.622486\pi$
$307$	2966.54	−	2966.54i	0.551497	−	0.551497i	0.926873	+	0.375376i	$0.122486\pi$
$308$	129.290	−	205.564i	0.0239188	−	0.0380295i
$309$		0			0
$310$	1246.99	+	994.888i	0.228465	+	0.182277i
$311$			2911.18i			0.530797i	0.964139	+	0.265399i	$0.0855036\pi$
$311$			2911.18i			0.530797i	−0.964139	+	0.265399i	$0.914496\pi$
$312$		0			0
$313$			8287.74i			1.49665i	0.663333	+	0.748324i	$0.269141\pi$
$313$			8287.74i			1.49665i	−0.663333	+	0.748324i	$0.730859\pi$
$314$	3077.24	−	3857.00i	0.553053	−	0.693194i
$315$		0			0
$316$	−7359.39	+	1676.33i	−1.31012	+	0.298421i
$317$	−5742.18	+	5742.18i	−1.01739	+	1.01739i	−0.0175452	+	0.999846i	$0.505585\pi$
$317$	−5742.18	+	5742.18i	−1.01739	+	1.01739i	−0.999846	+	0.0175452i	$0.994415\pi$
$318$		0			0
$319$	−184.999			−0.0324700
$320$	9096.95	+	1037.13i	1.58917	+	0.181179i
$321$		0			0
$322$	5226.19	−	587.687i	0.904485	−	0.101710i
$323$	1611.70	−	1611.70i	0.277639	−	0.277639i
$324$		0			0
$325$	6386.56	+	6386.56i	1.09004	+	1.09004i
$326$	−6409.66	+	8033.83i	−1.08895	+	1.36489i
$327$		0			0
$328$	−1570.21	−	4496.90i	−0.264330	−	0.757012i
$329$			2537.84i			0.425275i
$330$		0			0
$331$	4499.27	+	4499.27i	0.747136	+	0.747136i	0.973940	−	0.226804i	$-0.0728278\pi$
$331$	4499.27	+	4499.27i	0.747136	+	0.747136i	−0.226804	+	0.973940i	$0.572828\pi$
$332$	−1886.98	+	3000.19i	−0.311933	+	0.495954i
$333$		0			0
$334$	963.492	+	8568.15i	0.157844	+	1.40368i
$335$	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	$0.657052\pi$
$338$	−14.8430	−	131.996i	−0.00238862	−	0.0212416i
$339$		0			0
$340$	−2258.87	−	1420.73i	−0.360308	−	0.226617i
$341$	48.7893	+	48.7893i	0.00774806	+	0.00774806i
$342$		0			0
$343$			6847.14i			1.07787i
$344$	−3441.38	−	1660.08i	−0.539380	−	0.260190i
$345$		0			0
$346$	−3796.98	+	4759.12i	−0.589962	+	0.739456i
$347$	2029.11	+	2029.11i	0.313915	+	0.313915i	0.846424	−	0.532509i	$-0.178751\pi$
$347$	2029.11	+	2029.11i	0.313915	+	0.313915i	−0.532509	+	0.846424i	$0.678751\pi$
$348$		0			0
$349$	−1943.26	+	1943.26i	−0.298053	+	0.298053i	−0.840251	−	0.542198i	$-0.817592\pi$
$349$	−1943.26	+	1943.26i	−0.298053	+	0.298053i	0.542198	+	0.840251i	$0.317592\pi$
$350$	7596.61	−	854.242i	1.16016	−	0.130460i
$351$		0			0
$352$	385.991	+	88.5463i	0.0584472	+	0.0134078i
$353$	7548.63			1.13817			0.569084	−	0.822280i	$-0.307298\pi$
$353$	7548.63			1.13817			0.569084	+	0.822280i	$0.307298\pi$
$354$		0			0
$355$	4404.97	−	4404.97i	0.658568	−	0.658568i
$356$	−2509.38	−	11016.6i	−0.373586	−	1.64011i
$357$		0			0
$358$	754.026	−	945.092i	0.111317	−	0.139524i
$359$		−	5554.15i		−	0.816537i	−0.912862	−	0.408269i	$-0.866133\pi$
$359$		−	5554.15i		−	0.816537i	0.912862	−	0.408269i	$-0.133867\pi$
$360$		0			0
$361$		−	8072.37i		−	1.17690i
$362$	−5305.95	−	4233.26i	−0.770372	−	0.614628i
$363$		0			0
$364$	4356.92	+	2740.31i	0.627376	+	0.394591i
$365$	3786.34	−	3786.34i	0.542975	−	0.542975i
$366$		0			0
$367$	−3610.98			−0.513601			−0.256800	−	0.966464i	$-0.582668\pi$
$367$	−3610.98			−0.513601			−0.256800	+	0.966464i	$0.582668\pi$
$368$	3714.36	+	7730.32i	0.526153	+	1.09503i
$369$		0			0
$370$	−712.889	−	6339.59i	−0.100166	−	0.890756i
$371$	−363.040	+	363.040i	−0.0508035	+	0.0508035i
$372$		0			0
$373$	1215.49	+	1215.49i	0.168728	+	0.168728i	0.786420	−	0.617692i	$-0.211932\pi$
$373$	1215.49	+	1215.49i	0.168728	+	0.168728i	−0.617692	+	0.786420i	$0.711932\pi$
$374$	−90.2238	−	71.9836i	−0.0124742	−	0.00995236i
$375$		0			0
$376$	−3907.26	+	1364.32i	−0.535908	+	0.187126i
$377$		−	3921.05i		−	0.535661i
$378$		0			0
$379$	−7347.81	−	7347.81i	−0.995861	−	0.995861i	0.00413018	−	0.999991i	$-0.498685\pi$
$379$	−7347.81	−	7347.81i	−0.995861	−	0.995861i	−0.999991	+	0.00413018i	$0.998685\pi$
$380$	−17044.6	+	3882.43i	−2.30097	+	0.524117i
$381$		0			0
$382$	−11342.1	+	1275.42i	−1.51914	+	0.170828i
$383$	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
$386$	2490.77	−	280.088i	0.328438	−	0.0369330i
$387$		0			0
$388$	11819.6	−	2692.27i	1.54651	−	0.352267i
$389$	200.924	+	200.924i	0.0261884	+	0.0261884i	0.720080	−	0.693891i	$-0.244105\pi$
$389$	200.924	+	200.924i	0.0261884	+	0.0261884i	−0.693891	+	0.720080i	$0.744105\pi$
$390$		0			0
$391$		−	2499.62i		−	0.323302i
$392$	−3214.51	+	1122.43i	−0.414176	+	0.144620i
$393$		0			0
$394$	10224.9	+	8157.80i	1.30742	+	1.04311i
$395$	−11930.3	−	11930.3i	−1.51969	−	1.51969i
$396$		0			0
$397$	6512.21	−	6512.21i	0.823271	−	0.823271i	−0.163305	−	0.986576i	$-0.552215\pi$
$397$	6512.21	−	6512.21i	0.823271	−	0.823271i	0.986576	+	0.163305i	$0.0522153\pi$
$398$	−70.3286	−	625.419i	−0.00885743	−	0.0787674i
$399$		0			0
$400$	5399.06	+	11236.5i	0.674883	+	1.40457i
$401$	−5565.10			−0.693036			−0.346518	−	0.938043i	$-0.612636\pi$
$401$	−5565.10			−0.693036			−0.346518	+	0.938043i	$0.612636\pi$
$402$		0			0
$403$	−1034.09	+	1034.09i	−0.127820	+	0.127820i
$404$	5489.53	+	3452.67i	0.676025	+	0.425189i
$405$		0			0
$406$	−2594.22	−	2069.75i	−0.317115	−	0.253005i
$407$		−	275.933i		−	0.0336057i
$408$		0			0
$409$		−	12077.6i		−	1.46014i	−0.683370	−	0.730072i	$-0.739486\pi$
$409$		−	12077.6i		−	1.46014i	0.683370	−	0.730072i	$-0.260514\pi$
$410$	6640.24	−	8322.85i	0.799850	−	1.00253i
$411$		0			0
$412$	−1814.05	−	7963.99i	−0.216921	−	0.952324i
$413$	6127.14	−	6127.14i	0.730017	−	0.730017i
$414$		0			0
$415$	−7922.58			−0.937119
$416$	−1876.74	+	8181.09i	−0.221189	+	0.964209i
$417$		0			0
$418$	−751.373	+	84.4922i	−0.0879207	+	0.00988672i
$419$	1453.03	−	1453.03i	0.169415	−	0.169415i	−0.617307	−	0.786722i	$-0.711776\pi$
$419$	1453.03	−	1453.03i	0.169415	−	0.169415i	0.786722	+	0.617307i	$0.211776\pi$
$420$		0			0
$421$	−4822.25	−	4822.25i	−0.558247	−	0.558247i	0.370561	−	0.928808i	$-0.379165\pi$
$421$	−4822.25	−	4822.25i	−0.558247	−	0.558247i	−0.928808	+	0.370561i	$0.879165\pi$
$422$	8799.76	−	11029.6i	1.01508	−	1.27230i
$423$		0			0
$424$	−754.105	−	363.770i	−0.0863740	−	0.0416657i
$425$		−	3633.36i		−	0.414692i
$426$		0			0
$427$	−2421.04	−	2421.04i	−0.274385	−	0.274385i
$428$	11883.0	+	7473.87i	1.34203	+	0.844073i
$429$		0			0
$430$	−954.407	−	8487.36i	−0.107036	−	0.951853i
$431$	−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	$0.551832\pi$
$434$	138.316	+	1230.02i	0.0152981	+	0.136043i
$435$		0			0
$436$	−654.322	+	1040.33i	−0.0718724	+	0.114273i
$437$	−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	$0.980253\pi$
$440$	291.821	+	835.743i	0.0316182	+	0.0905511i
$441$		0			0
$442$	1525.69	−	1912.30i	0.164185	−	0.205789i
$443$	1843.05	+	1843.05i	0.197665	+	0.197665i	0.798999	−	0.601333i	$-0.205363\pi$
$443$	1843.05	+	1843.05i	0.197665	+	0.197665i	−0.601333	+	0.798999i	$0.705363\pi$
$444$		0			0
$445$	17859.0	−	17859.0i	1.90247	−	1.90247i
$446$	−16419.9	+	1846.42i	−1.74328	+	0.196033i
$447$		0			0
$448$	4422.07	+	5560.12i	0.466346	+	0.586364i
$449$	−1752.13			−0.184161			−0.0920805	−	0.995752i	$-0.529352\pi$
$449$	−1752.13			−0.184161			−0.0920805	+	0.995752i	$0.529352\pi$
$450$		0			0
$451$	325.637	−	325.637i	0.0339993	−	0.0339993i
$452$	13433.7	−	3059.93i	1.39793	−	0.318423i
$453$		0			0
$454$	−2817.80	+	3531.82i	−0.291291	+	0.365102i
$455$			11505.3i			1.18544i
$456$		0			0
$457$			12875.6i			1.31794i	0.752171	+	0.658968i	$0.229007\pi$
$457$			12875.6i			1.31794i	−0.752171	+	0.658968i	$0.770993\pi$
$458$	9084.54	+	7247.95i	0.926840	+	0.739464i
$459$		0			0
$460$	−10206.7	+	16228.0i	−1.03454	+	1.64486i
$461$	13679.7	−	13679.7i	1.38205	−	1.38205i	0.541085	−	0.840968i	$-0.318014\pi$
$461$	13679.7	−	13679.7i	1.38205	−	1.38205i	0.840968	−	0.541085i	$-0.181986\pi$
$462$		0			0
$463$	15002.4			1.50588			0.752938	−	0.658091i	$-0.228636\pi$
$463$	15002.4			1.50588			0.752938	+	0.658091i	$0.228636\pi$
$464$	1791.97	−	5106.74i	0.179289	−	0.510936i
$465$		0			0
$466$	−232.009	−	2063.22i	−0.0230636	−	0.205100i
$467$	−9669.42	+	9669.42i	−0.958131	+	0.958131i	−0.999158	−	0.0410271i	$-0.986937\pi$
$467$	−9669.42	+	9669.42i	−0.958131	+	0.958131i	0.0410271	+	0.999158i	$0.486937\pi$
$468$		0			0
$469$	1273.15	+	1273.15i	0.125349	+	0.125349i
$470$	−7231.54	−	5769.56i	−0.709715	−	0.566234i
$471$		0			0
$472$	12727.3	+	6139.46i	1.24114	+	0.598711i
$473$		−	369.416i		−	0.0359107i
$474$		0			0
$475$	−16830.4	−	16830.4i	−1.62575	−	1.62575i
$476$	−459.853	−	2018.84i	−0.0442801	−	0.194397i
$477$		0			0
$478$	−1438.54	+	161.765i	−0.137651	+	0.0154789i
$479$	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
$482$	−16640.3	+	1871.21i	−1.57250	+	0.176828i
$483$		0			0
$484$	−2356.34	−	10344.7i	−0.221294	−	0.971520i
$485$	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	$0.867523\pi$
$488$	2425.91	−	5028.98i	0.225033	−	0.466498i
$489$		0			0
$490$	−5949.40	−	4746.63i	−0.548503	−	0.437614i
$491$	−11194.3	−	11194.3i	−1.02891	−	1.02891i	−0.999570	−	0.0293379i	$-0.990660\pi$
$491$	−11194.3	−	11194.3i	−1.02891	−	1.02891i	−0.0293379	−	0.999570i	$-0.509340\pi$
$492$		0			0
$493$	−1115.36	+	1115.36i	−0.101893	+	0.101893i
$494$	−1790.81	−	15925.4i	−0.163102	−	1.45044i
$495$		0			0
$496$	−1819.38	+	874.198i	−0.164703	+	0.0791384i
$497$	4833.62			0.436253
$498$		0			0
$499$	−1632.72	+	1632.72i	−0.146474	+	0.146474i	−0.776541	−	0.630067i	$-0.783027\pi$
$499$	−1632.72	+	1632.72i	−0.146474	+	0.146474i	0.630067	+	0.776541i	$0.283027\pi$
$500$	−5315.36	+	8451.10i	−0.475420	+	0.755889i
$501$		0			0
$502$	−967.213	−	771.674i	−0.0859936	−	0.0686086i
$503$			6901.81i			0.611802i	0.952063	+	0.305901i	$0.0989577\pi$
$503$			6901.81i			0.611802i	−0.952063	+	0.305901i	$0.901042\pi$
$504$		0			0
$505$			14496.2i			1.27737i
$506$	−517.139	+	648.180i	−0.0454341	+	0.0569468i
$507$		0			0
$508$	5453.34	−	1242.17i	0.476285	−	0.108489i
$509$	−92.9712	+	92.9712i	−0.00809603	+	0.00809603i	−0.711143	−	0.703047i	$-0.751822\pi$
$509$	−92.9712	+	92.9712i	−0.00809603	+	0.00809603i	0.703047	+	0.711143i	$0.251822\pi$
$510$		0			0
$511$	4154.79			0.359681
$512$	−6183.11	+	9797.29i	−0.533706	+	0.845670i
$513$		0			0
$514$	909.891	−	102.318i	0.0780809	−	0.00878023i
$515$	12910.4	−	12910.4i	1.10466	−	1.10466i
$516$		0			0
$517$	−282.939	−	282.939i	−0.0240689	−	0.0240689i
$518$	3087.12	−	3869.38i	0.261854	−	0.328206i
$519$		0			0
$520$	−17713.6	+	6185.15i	−1.49383	+	0.521609i
$521$			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	0.173611	−	0.984814i	$-0.444456\pi$
$523$	−9702.46	−	9702.46i	−0.811203	−	0.811203i	−0.984814	+	0.173611i	$0.944456\pi$
$524$	−1192.47	+	1895.95i	−0.0994144	+	0.158063i
$525$		0			0
$526$	849.949	+	7558.43i	0.0704554	+	0.626546i
$527$	588.301			0.0486277
$528$		0			0
$529$	−5790.59			−0.475926
$530$	−209.138	−	1859.82i	−0.0171403	−	0.152425i
$531$		0			0
$532$	−11481.7	−	7221.48i	−0.935706	−	0.588517i
$533$	6901.89	+	6901.89i	0.560889	+	0.560889i
$534$		0			0
$535$			31379.4i			2.53579i
$536$	−1275.71	+	2644.58i	−0.102803	+	0.213113i
$537$		0			0
$538$	11734.3	−	14707.7i	0.940335	−	1.17861i
$539$	−232.774	−	232.774i	−0.0186017	−	0.0186017i
$540$		0			0
$541$	−8556.67	+	8556.67i	−0.680000	+	0.680000i	−0.960000	−	0.280000i	$-0.909666\pi$
$541$	−8556.67	+	8556.67i	−0.680000	+	0.680000i	0.280000	+	0.960000i	$0.409666\pi$
$542$	5674.75	−	638.128i	0.449726	−	0.0505719i
$543$		0			0
$544$	2860.99	−	1793.30i	0.225485	−	0.141336i
$545$	−2747.20			−0.215921
$546$		0			0
$547$	−45.1953	+	45.1953i	−0.00353274	+	0.00353274i	−0.708871	−	0.705338i	$-0.750795\pi$
$547$	−45.1953	+	45.1953i	−0.00353274	+	0.00353274i	0.705338	+	0.708871i	$0.250795\pi$
$548$	482.183	+	2116.87i	0.0375873	+	0.165015i
$549$		0			0
$550$	−751.696	+	942.172i	−0.0582771	+	0.0730443i
$551$			10333.1i			0.798917i
$552$		0			0
$553$		−	13091.2i		−	1.00668i
$554$	9632.37	+	7685.02i	0.738700	+	0.589360i
$555$		0			0
$556$	4404.79	+	2770.41i	0.335980	+	0.211316i
$557$	−4279.60	+	4279.60i	−0.325552	+	0.325552i	−0.850892	−	0.525340i	$-0.823938\pi$
$557$	−4279.60	+	4279.60i	−0.325552	+	0.325552i	0.525340	+	0.850892i	$0.323938\pi$
$558$		0			0
$559$	7829.77			0.592422
$560$	−5258.06	+	14984.4i	−0.396774	+	1.13073i
$561$		0			0
$562$	1230.61	+	10943.5i	0.0923665	+	0.821398i
$563$	−14593.9	+	14593.9i	−1.09247	+	1.09247i	−0.0972023	+	0.995265i	$0.530989\pi$
$563$	−14593.9	+	14593.9i	−1.09247	+	1.09247i	−0.995265	+	0.0972023i	$0.969011\pi$
$564$		0			0
$565$	21777.3	+	21777.3i	1.62155	+	1.62155i
$566$	−6336.05	−	5055.11i	−0.470537	−	0.375410i
$567$		0			0
$568$	2598.51	+	7441.86i	0.191956	+	0.549742i
$569$			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	0.980161	+	0.198202i	$0.0635102\pi$
$571$	16078.0	+	16078.0i	1.17836	+	1.17836i	0.198202	+	0.980161i	$0.436490\pi$
$572$	−791.259	+	180.234i	−0.0578395	+	0.0131747i
$573$		0			0
$574$	8209.59	−	923.171i	0.596971	−	0.0671297i
$575$	−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	$0.911195\pi$
$578$	12831.1	−	1442.86i	0.923361	−	0.103832i
$579$		0			0
$580$	11795.5	−	2686.79i	0.844449	−	0.192349i
$581$	−4346.77	−	4346.77i	−0.310386	−	0.310386i
$582$		0			0
$583$		−	80.9495i		−	0.00575058i
$584$	2233.58	+	6396.72i	0.158264	+	0.453250i
$585$		0			0
$586$	−3132.05	−	2498.85i	−0.220791	−	0.176154i
$587$	−1342.62	−	1342.62i	−0.0944050	−	0.0944050i	0.658327	−	0.752732i	$-0.271264\pi$
$587$	−1342.62	−	1342.62i	−0.0944050	−	0.0944050i	−0.752732	+	0.658327i	$0.771264\pi$
$588$		0			0
$589$	2725.11	−	2725.11i	0.190639	−	0.190639i
$590$	3529.68	+	31388.8i	0.246296	+	2.19026i
$591$		0			0
$592$	7616.92	+	2672.79i	0.528806	+	0.185559i
$593$	−4474.79			−0.309878			−0.154939	−	0.987924i	$-0.549518\pi$
$593$	−4474.79			−0.309878			−0.154939	+	0.987924i	$0.549518\pi$
$594$		0			0
$595$	3272.73	−	3272.73i	0.225494	−	0.225494i
$596$	−5801.45	−	3648.85i	−0.398719	−	0.250776i
$597$		0			0
$598$	−13738.2	−	10960.8i	−0.939458	−	0.749531i
$599$		−	12603.8i		−	0.859725i	−0.902894	−	0.429863i	$-0.858562\pi$
$599$		−	12603.8i		−	0.859725i	0.902894	−	0.429863i	$-0.141438\pi$
$600$		0			0
$601$			7220.64i			0.490077i	0.969513	+	0.245038i	$0.0788006\pi$
$601$			7220.64i			0.490077i	−0.969513	+	0.245038i	$0.921199\pi$
$602$	4133.00	−	5180.28i	0.279814	−	0.350718i
$603$		0			0
$604$	−6279.83	−	27569.6i	−0.423051	−	1.85727i
$605$	16769.8	−	16769.8i	1.12693	−	1.12693i
$606$		0			0
$607$	−13695.6			−0.915796			−0.457898	−	0.889005i	$-0.651397\pi$
$607$	−13695.6			−0.915796			−0.457898	+	0.889005i	$0.651397\pi$
$608$	4945.74	−	21559.5i	0.329895	−	1.43808i
$609$		0			0
$610$	12402.8	−	1394.70i	0.823236	−	0.0925733i
$611$	5996.90	−	5996.90i	0.397068	−	0.397068i
$612$		0			0
$613$	−2358.34	−	2358.34i	−0.155387	−	0.155387i	0.625132	−	0.780519i	$-0.285045\pi$
$613$	−2358.34	−	2358.34i	−0.155387	−	0.155387i	−0.780519	+	0.625132i	$0.785045\pi$
$614$	−7400.47	+	9275.72i	−0.486415	+	0.609670i
$615$		0			0
$616$	−298.426	+	618.644i	−0.0195194	+	0.0404641i
$617$		−	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	0.533862	−	0.845572i	$-0.320740\pi$
$619$	−4800.50	−	4800.50i	−0.311710	−	0.311710i	−0.845572	+	0.533862i	$0.820740\pi$
$620$	−3819.37	−	2402.21i	−0.247403	−	0.155605i
$621$		0			0
$622$	−920.125	−	8182.50i	−0.0593145	−	0.527473i
$623$	19596.9			1.26024
$624$		0			0
$625$	2031.54			0.130018
$626$	−2619.47	−	23294.5i	−0.167245	−	1.48727i
$627$		0			0
$628$	−7430.17	+	11813.5i	−0.472127	+	0.750654i
$629$	−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	$-0.169640\pi$
$632$	20155.3	−	7037.73i	1.26857	−	0.442952i
$633$		0			0
$634$	14324.7	−	17954.5i	0.897330	−	1.12471i
$635$	8840.39	+	8840.39i	0.552473	+	0.552473i
$636$		0			0
$637$	4933.66	−	4933.66i	0.306874	−	0.306874i
$638$	519.978	−	58.4717i	0.0322667	−	0.00362840i
$639$		0			0
$640$	−25896.7	−	39.8373i	−1.59946	−	0.00246048i
$641$	6682.21			0.411749			0.205875	−	0.978578i	$-0.433996\pi$
$641$	6682.21			0.411749			0.205875	+	0.978578i	$0.433996\pi$
$642$		0			0
$643$	−4983.47	+	4983.47i	−0.305644	+	0.305644i	−0.843217	−	0.537573i	$-0.819341\pi$
$643$	−4983.47	+	4983.47i	−0.305644	+	0.305644i	0.537573	+	0.843217i	$0.319341\pi$
$644$	−14503.6	+	3303.64i	−0.887455	+	0.202145i
$645$		0			0
$646$	−4020.63	+	5039.43i	−0.244875	+	0.306926i
$647$		−	5078.45i		−	0.308585i	−0.988025	−	0.154292i	$-0.950690\pi$
$647$		−	5078.45i		−	0.308585i	0.988025	−	0.154292i	$-0.0493098\pi$
$648$		0			0
$649$			1366.21i			0.0826324i
$650$	−19969.3	−	15932.2i	−1.20502	−	0.961404i
$651$		0			0
$652$	15476.5	−	24606.7i	0.929610	−	1.47802i
$653$	−6189.91	+	6189.91i	−0.370949	+	0.370949i	−0.867823	−	0.496874i	$-0.834481\pi$
$653$	−6189.91	+	6189.91i	−0.370949	+	0.370949i	0.496874	+	0.867823i	$0.334481\pi$
$654$		0			0
$655$	−5006.62			−0.298664
$656$	5834.72	+	12143.2i	0.347267	+	0.722733i
$657$		0			0
$658$	−802.123	−	7133.12i	−0.0475228	−	0.422611i
$659$	−5751.19	+	5751.19i	−0.339962	+	0.339962i	−0.856353	−	0.516391i	$-0.827275\pi$
$659$	−5751.19	+	5751.19i	−0.339962	+	0.339962i	0.516391	+	0.856353i	$0.327275\pi$
$660$		0			0
$661$	−6305.38	−	6305.38i	−0.371030	−	0.371030i	0.496822	−	0.867852i	$-0.334500\pi$
$661$	−6305.38	−	6305.38i	−0.371030	−	0.371030i	−0.867852	+	0.496822i	$0.834500\pi$
$662$	−14068.2	−	11224.1i	−0.825946	−	0.658967i
$663$		0			0
$664$	4355.51	−	9029.08i	0.254558	−	0.527705i
$665$		−	30319.7i		−	1.76804i
$666$		0			0
$667$	8012.87	+	8012.87i	0.465157	+	0.465157i
$668$	−5416.20	−	23778.1i	−0.313711	−	1.37725i
$669$		0			0
$670$	−6522.24	+	733.429i	−0.376084	+	0.0422908i
$671$	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	$0.362043\pi$
$674$	16471.0	−	1852.16i	0.941302	−	0.105850i
$675$		0			0
$676$	83.4389	+	366.312i	0.00474732	+	0.0208416i
$677$	−5795.16	−	5795.16i	−0.328990	−	0.328990i	0.523212	−	0.852202i	$-0.324733\pi$
$677$	−5795.16	−	5795.16i	−0.328990	−	0.328990i	−0.852202	+	0.523212i	$0.824733\pi$
$678$		0			0
$679$			21025.2i			1.18833i
$680$	6798.09	+	3279.31i	0.383375	+	0.184935i
$681$		0			0
$682$	−152.553	−	121.712i	−0.00856534	−	0.00683371i
$683$	13134.1	+	13134.1i	0.735816	+	0.735816i	0.971765	−	0.235950i	$-0.0758200\pi$
$683$	13134.1	+	13134.1i	0.735816	+	0.735816i	−0.235950	+	0.971765i	$0.575820\pi$
$684$		0			0
$685$	−3431.65	+	3431.65i	−0.191411	+	0.191411i
$686$	−2164.15	−	19245.3i	−0.120448	−	1.07112i
$687$		0			0
$688$	10197.4	+	3578.30i	0.565077	+	0.198287i
$689$	1715.73			0.0948679
$690$		0			0
$691$	14324.0	−	14324.0i	0.788583	−	0.788583i	−0.192679	−	0.981262i	$-0.561718\pi$
$691$	14324.0	−	14324.0i	0.788583	−	0.788583i	0.981262	+	0.192679i	$0.0617175\pi$
$692$	9168.02	−	14576.6i	0.503636	−	0.800750i
$693$		0			0
$694$	−6344.58	−	5061.92i	−0.347027	−	0.276870i
$695$			11631.7i			0.634843i
$696$		0			0
$697$		−	3926.54i		−	0.213383i
$698$	4847.76	−	6076.15i	0.262880	−	0.329493i
$699$		0			0
$700$	−21081.9	+	4802.06i	−1.13832	+	0.259287i
$701$	−15987.2	+	15987.2i	−0.861382	+	0.861382i	−0.991499	−	0.130117i	$-0.958465\pi$
$701$	−15987.2	+	15987.2i	−0.861382	+	0.861382i	0.130117	+	0.991499i	$0.458465\pi$
$702$		0			0
$703$	−15412.2			−0.826859
$704$	−1112.90	−	126.880i	−0.0595794	−	0.00679255i
$705$		0			0
$706$	−21217.0	+	2385.86i	−1.13104	+	0.127186i
$707$	−7953.40	+	7953.40i	−0.423081	+	0.423081i
$708$		0			0
$709$	19580.4	+	19580.4i	1.03718	+	1.03718i	0.999282	+	0.0378960i	$0.0120656\pi$
$709$	19580.4	+	19580.4i	1.03718	+	1.03718i	0.0378960	+	0.999282i	$0.487934\pi$
$710$	−10988.8	+	13773.4i	−0.580851	+	0.728035i
$711$		0			0
$712$	10535.1	+	30171.4i	0.554522	+	1.58809i
$713$		−	4226.43i		−	0.221993i
$714$		0			0
$715$	−1282.71	−	1282.71i	−0.0670916	−	0.0670916i
$716$	−1820.64	+	2894.70i	−0.0950285	+	0.151090i
$717$		0			0
$718$	1755.48	+	15611.1i	0.0912448	+	0.811423i
$719$	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
$722$	2551.40	+	22689.1i	0.131514	+	1.16953i
$723$		0			0
$724$	16251.5	+	10221.5i	0.834229	+	0.524692i
$725$	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	$-0.122901\pi$
$728$	−13112.2	−	6325.14i	−0.667541	−	0.322013i
$729$		0			0
$730$	−9445.57	+	11839.0i	−0.478899	+	0.600250i
$731$	−2227.21	−	2227.21i	−0.112690	−	0.112690i
$732$		0			0
$733$	3419.77	−	3419.77i	0.172322	−	0.172322i	−0.615677	−	0.787999i	$-0.711117\pi$
$733$	3419.77	−	3419.77i	0.172322	−	0.172322i	0.787999	+	0.615677i	$0.211117\pi$
$734$	10149.4	−	1141.31i	0.510384	−	0.0573929i
$735$		0			0
$736$	−12883.3	−	20553.7i	−0.645223	−	1.02938i
$737$	−283.883			−0.0141886
$738$		0			0
$739$	−11324.8	+	11324.8i	−0.563723	+	0.563723i	−0.930363	−	0.366640i	$-0.880508\pi$
$739$	−11324.8	+	11324.8i	−0.563723	+	0.563723i	0.366640	+	0.930363i	$0.380508\pi$
$740$	4007.45	+	17593.4i	0.199077	+	0.873984i
$741$		0			0
$742$	905.657	−	1135.15i	0.0448083	−	0.0561625i
$743$		−	20313.3i		−	1.00299i	−0.865160	−	0.501495i	$-0.832783\pi$
$743$		−	20313.3i		−	1.00299i	0.865160	−	0.501495i	$-0.167217\pi$
$744$		0			0
$745$		−	15319.9i		−	0.753391i
$746$	−3800.57	−	3032.22i	−0.186526	−	0.148817i
$747$		0			0
$748$	276.345	+	173.808i	0.0135082	+	0.00849608i
$749$	−17216.5	+	17216.5i	−0.839888	+	0.839888i
$750$		0			0
$751$	28755.3			1.39720			0.698598	−	0.715514i	$-0.253808\pi$
$751$	28755.3			1.39720			0.698598	+	0.715514i	$0.253808\pi$
$752$	10551.0	−	5069.65i	0.511641	−	0.245839i
$753$		0			0
$754$	1239.31	+	11020.9i	0.0598581	+	0.532306i
$755$	44693.0	−	44693.0i	2.15436	−	2.15436i
$756$		0			0
$757$	−23006.0	−	23006.0i	−1.10458	−	1.10458i	−0.993850	−	0.110730i	$-0.964681\pi$
$757$	−23006.0	−	23006.0i	−1.10458	−	1.10458i	−0.110730	−	0.993850i	$-0.535319\pi$
$758$	22975.0	+	18330.2i	1.10091	+	0.878340i
$759$		0			0
$760$	46680.3	−	16299.6i	2.22799	−	0.777958i
$761$			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
$764$	31476.2	−	7169.69i	1.49054	−	0.339516i
$765$		0			0
$766$	−21555.3	+	2423.90i	−1.01674	+	0.114333i
$767$	−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	$0.658768\pi$
$770$	−1525.74	+	171.570i	−0.0714076	+	0.00802981i
$771$		0			0
$772$	−6912.32	+	1574.50i	−0.322254	+	0.0734033i
$773$	−7337.03	−	7337.03i	−0.341390	−	0.341390i	0.515500	−	0.856890i	$-0.327606\pi$
$773$	−7337.03	−	7337.03i	−0.341390	−	0.341390i	−0.856890	+	0.515500i	$0.827606\pi$
$774$		0			0
$775$		−	6143.40i		−	0.284745i
$776$	−32370.4	+	11303.0i	−1.49746	+	0.522877i
$777$		0			0
$778$	−628.246	−	501.235i	−0.0289508	−	0.0230979i
$779$	−18188.4	−	18188.4i	−0.836544	−	0.836544i
$780$		0			0
$781$	−538.893	+	538.893i	−0.0246903	+	0.0246903i
$782$	790.044	+	7025.71i	0.0361278	+	0.321277i
$783$		0			0
$784$	8680.29	−	4170.81i	0.395422	−	0.189997i
$785$	−31195.9			−1.41838
$786$		0			0
$787$	−11928.6	+	11928.6i	−0.540292	+	0.540292i	−0.923615	−	0.383323i	$-0.874780\pi$
$787$	−11928.6	+	11928.6i	−0.540292	+	0.540292i	0.383323	+	0.923615i	$0.374780\pi$
$788$	−31317.8	−	19697.5i	−1.41580	−	0.890474i
$789$		0			0
$790$	37303.3	+	29761.8i	1.67999	+	1.34035i
$791$			23896.4i			1.07416i
$792$		0			0
$793$			11441.8i			0.512373i
$794$	−16245.7	+	20362.2i	−0.726117	+	0.910112i
$795$		0			0
$796$	395.347	+	1735.65i	0.0176039	+	0.0772843i
$797$	6576.18	−	6576.18i	0.292271	−	0.292271i	−0.545706	−	0.837977i	$-0.683738\pi$
$797$	6576.18	−	6576.18i	0.292271	−	0.292271i	0.837977	+	0.545706i	$0.183738\pi$
$798$		0			0
$799$	−3411.68			−0.151060
$800$	−18726.7	−	29876.2i	−0.827611	−	1.32035i
$801$		0			0
$802$	15641.9	−	1758.94i	0.688696	−	0.0774441i
$803$	−463.211	+	463.211i	−0.0203566	+	0.0203566i
$804$		0			0
$805$	−23511.7	−	23511.7i	−1.02941	−	1.02941i
$806$	2579.69	−	3233.37i	0.112736	−	0.141303i
$807$		0			0
$808$	−16520.8	−	7969.40i	−0.719304	−	0.346983i
$809$		−	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	0.320090	−	0.947387i	$-0.396287\pi$
$811$	−14487.9	−	14487.9i	−0.627297	−	0.627297i	−0.947387	+	0.320090i	$0.896287\pi$
$812$	7945.77	+	4997.53i	0.343401	+	0.215984i
$813$		0			0
$814$	87.2131	+	775.569i	0.00375530	+	0.0333952i
$815$	64978.7			2.79276
$816$		0			0
$817$	−20633.6			−0.883574
$818$	3817.32	+	33946.7i	0.163165	+	1.45100i
$819$		0			0
$820$	−16033.2	+	25491.9i	−0.682811	+	1.08563i
$821$	−20259.2	−	20259.2i	−0.861208	−	0.861208i	0.130270	−	0.991479i	$-0.458415\pi$
$821$	−20259.2	−	20259.2i	−0.861208	−	0.861208i	−0.991479	+	0.130270i	$0.958415\pi$
$822$		0			0
$823$		−	24605.9i		−	1.04217i	−0.853504	−	0.521086i	$-0.825527\pi$
$823$		−	24605.9i		−	1.04217i	0.853504	−	0.521086i	$-0.174473\pi$
$824$	7615.90	+	21811.1i	0.321981	+	0.922119i
$825$		0			0
$826$	−15285.0	+	19158.2i	−0.643868	+	0.807021i
$827$	24095.8	+	24095.8i	1.01317	+	1.01317i	0.999912	+	0.0132601i	$0.00422096\pi$
$827$	24095.8	+	24095.8i	1.01317	+	1.01317i	0.0132601	+	0.999912i	$0.495779\pi$
$828$		0			0
$829$	−914.616	+	914.616i	−0.0383184	+	0.0383184i	−0.726006	−	0.687688i	$-0.758626\pi$
$829$	−914.616	+	914.616i	−0.0383184	+	0.0383184i	0.687688	+	0.726006i	$0.258626\pi$
$830$	22268.1	−	2504.06i	0.931249	−	0.104719i
$831$		0			0
$832$	2689.22	−	23587.9i	0.112057	−	0.982887i
$833$	−2806.80			−0.116746
$834$		0			0
$835$	38546.6	−	38546.6i	1.59756	−	1.59756i
$836$	2085.19	−	474.966i	0.0862652	−	0.0196496i
$837$		0			0
$838$	−3624.79	+	4543.30i	−0.149423	+	0.187286i
$839$		−	28847.5i		−	1.18704i	−0.804819	−	0.593521i	$-0.797737\pi$
$839$		−	28847.5i		−	1.18704i	0.804819	−	0.593521i	$-0.202263\pi$
$840$		0			0
$841$			17238.1i			0.706800i
$842$	15078.1	+	12029.8i	0.617132	+	0.492369i
$843$		0			0
$844$	−21247.5	+	33782.3i	−0.866552	+	1.37776i
$845$	−593.827	+	593.827i	−0.0241755	+	0.0241755i
$846$		0			0
$847$	18401.7			0.746506
$848$	2234.55	+	784.107i	0.0904890	+	0.0317528i
$849$		0			0
$850$	1148.38	+	10212.3i	0.0463402	+	0.412094i
$851$	−11951.5	+	11951.5i	−0.481426	+	0.481426i
$852$		0			0
$853$	41.5562	+	41.5562i	0.00166806	+	0.00166806i	0.707940	−	0.706272i	$-0.249625\pi$
$853$	41.5562	+	41.5562i	0.00166806	+	0.00166806i	−0.706272	+	0.707940i	$0.749625\pi$
$854$	7570.07	+	6039.65i	0.303328	+	0.242005i
$855$		0			0
$856$	−35761.9	−	17251.1i	−1.42794	−	0.688821i
$857$			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	0.983492	+	0.180953i	$0.0579181\pi$
$859$	29316.3	+	29316.3i	1.16444	+	1.16444i	0.180953	+	0.983492i	$0.442082\pi$
$860$	5365.12	+	23553.9i	0.212732	+	0.933930i
$861$		0			0
$862$	35188.0	−	3956.90i	1.39038	−	0.156349i
$863$	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
$866$	8211.22	−	923.355i	0.322204	−	0.0362320i
$867$		0			0
$868$	−777.532	−	3413.51i	−0.0304046	−	0.133482i
$869$	1459.52	+	1459.52i	0.0569745	+	0.0569745i
$870$		0			0
$871$		−	6016.91i		−	0.234070i
$872$	1510.30	−	3130.89i	0.0586527	−	0.121588i
$873$		0			0
$874$	36203.9	+	28884.7i	1.40116	+	1.11789i
$875$	−12244.2	−	12244.2i	−0.473063	−	0.473063i
$876$		0			0
$877$	−13912.5	+	13912.5i	−0.535681	+	0.535681i	−0.922257	−	0.386576i	$-0.873658\pi$
$877$	−13912.5	+	13912.5i	−0.535681	+	0.535681i	0.386576	+	0.922257i	$0.373658\pi$
$878$	−360.473	−	3205.62i	−0.0138558	−	0.123217i
$879$		0			0
$880$	−1084.37	−	2256.80i	−0.0415389	−	0.0864508i
$881$	1497.48			0.0572660			0.0286330	−	0.999590i	$-0.490885\pi$
$881$	1497.48			0.0572660			0.0286330	+	0.999590i	$0.490885\pi$
$882$		0			0
$883$	−4143.81	+	4143.81i	−0.157928	+	0.157928i	−0.781648	−	0.623720i	$-0.785621\pi$
$883$	−4143.81	+	4143.81i	−0.157928	+	0.157928i	0.623720	+	0.781648i	$0.285621\pi$
$884$	−3683.87	+	5857.13i	−0.140161	+	0.222847i
$885$		0			0
$886$	−5762.80	−	4597.75i	−0.218516	−	0.174339i
$887$			18058.0i			0.683573i	0.939778	+	0.341787i	$0.111032\pi$
$887$			18058.0i			0.683573i	−0.939778	+	0.341787i	$0.888968\pi$
$888$		0			0
$889$			9700.66i			0.365973i
$890$	−44551.9	+	55841.1i	−1.67796	+	2.10314i
$891$		0			0
$892$	45568.0	−	10379.5i	1.71046	−	0.389610i
$893$	−15803.5	+	15803.5i	−0.592211	+	0.592211i
$894$		0			0
$895$	−7644.03			−0.285488
$896$	−14186.5	−	14230.2i	−0.528949	−	0.530579i
$897$		0			0
$898$	4924.74	−	553.789i	0.183008	−	0.0205793i
$899$	−1885.88	+	1885.88i	−0.0699640	+	0.0699640i
$900$		0			0
$901$	−488.045	−	488.045i	−0.0180457	−	0.0180457i
$902$	−812.350	+	1018.20i	−0.0299870	+	0.0375856i
$903$		0			0
$904$	−36791.0	+	12846.5i	−1.35360	+	0.472642i
$905$			42915.2i			1.57630i
$906$		0			0
$907$	−21423.5	−	21423.5i	−0.784295	−	0.784295i	0.196257	−	0.980552i	$-0.437121\pi$
$907$	−21423.5	−	21423.5i	−0.784295	−	0.784295i	−0.980552	+	0.196257i	$0.937121\pi$
$908$	6803.74	−	10817.5i	0.248667	−	0.395366i
$909$		0			0
$910$	−3636.43	−	32338.1i	−0.132469	−	1.17802i
$911$	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
$914$	−4069.54	−	36189.7i	−0.147274	−	1.30968i
$915$		0			0
$916$	−27824.9	−	17500.6i	−1.00367	−	0.631261i
$917$	−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	$-0.260662\pi$
$920$	23559.0	−	48838.3i	0.844257	−	1.75017i
$921$		0			0
$922$	−34126.0	+	42773.3i	−1.21896	+	1.52784i
$923$	−11421.8	−	11421.8i	−0.407318	−	0.407318i
$924$		0			0
$925$	−17372.4	+	17372.4i	−0.617513	+	0.617513i
$926$	−42167.4	+	4741.75i	−1.49645	+	0.168276i
$927$		0			0
$928$	−3422.64	+	14920.0i	−0.121071	+	0.527771i
$929$	11467.5			0.404989			0.202495	−	0.979283i	$-0.435095\pi$
$929$	11467.5			0.404989			0.202495	+	0.979283i	$0.435095\pi$
$930$		0			0
$931$	−13001.6	+	13001.6i	−0.457690	+	0.457690i
$932$	1304.22	+	5725.77i	0.0458382	+	0.201238i
$933$		0			0
$934$	24121.8	−	30234.1i	0.845063	−	1.05920i
$935$			729.742i			0.0255242i
$936$		0			0
$937$		−	14100.2i		−	0.491603i	−0.969320	−	0.245802i	$-0.920949\pi$
$937$		−	14100.2i		−	0.491603i	0.969320	−	0.245802i	$-0.0790512\pi$
$938$	−3980.87	−	3176.07i	−0.138571	−	0.110557i
$939$		0			0
$940$	22149.3	+	13930.9i	0.768544	+	0.483379i
$941$	21058.7	−	21058.7i	0.729538	−	0.729538i	−0.240989	−	0.970528i	$-0.577472\pi$
$941$	21058.7	−	21058.7i	0.729538	−	0.729538i	0.970528	+	0.240989i	$0.0774719\pi$
$942$		0			0
$943$	−28208.8			−0.974129
$944$	−37713.1	−	13233.6i	−1.30027	−	0.456268i
$945$		0			0
$946$	116.760	+	1038.32i	0.00401288	+	0.0356858i
$947$	−24998.9	+	24998.9i	−0.857820	+	0.857820i	−0.991081	−	0.133261i	$-0.957455\pi$
$947$	−24998.9	+	24998.9i	−0.857820	+	0.857820i	0.133261	+	0.991081i	$0.457455\pi$
$948$		0			0
$949$	−9817.75	−	9817.75i	−0.335825	−	0.335825i
$950$	52624.8	+	41985.8i	1.79724	+	1.43389i
$951$		0			0
$952$	1930.60	+	5529.02i	0.0657259	+	0.188232i
$953$		−	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
$956$	3992.20	−	909.347i	0.135059	−	0.0307640i
$957$		0			0
$958$	−8636.43	+	971.169i	−0.291263	+	0.0327527i
$959$	−3765.59			−0.126796
$960$		0			0
$961$	−28796.3			−0.966610
$962$	−16438.2	+	1848.48i	−0.550924	+	0.0619516i
$963$		0			0
$964$	46179.6	−	10518.8i	1.54289	−	0.351441i
$965$	−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	$0.919215\pi$
$968$	9892.60	+	28331.3i	0.328471	+	0.940706i
$969$		0			0
$970$	−59911.1	−	47799.1i	−1.98312	−	1.58220i
$971$	6223.12	+	6223.12i	0.205674	+	0.205674i	0.802426	−	0.596752i	$-0.203542\pi$
$971$	6223.12	+	6223.12i	0.205674	+	0.205674i	−0.596752	+	0.802426i	$0.703542\pi$
$972$		0			0
$973$	−6381.80	+	6381.80i	−0.210268	+	0.210268i
$974$	−2746.50	−	24424.1i	−0.0903526	−	0.803489i
$975$		0			0
$976$	−5229.06	+	14901.8i	−0.171494	+	0.488723i
$977$	34900.0			1.14284			0.571418	−	0.820659i	$-0.306393\pi$
$977$	34900.0			1.14284			0.571418	+	0.820659i	$0.306393\pi$
$978$		0			0
$979$	−2184.82	+	2184.82i	−0.0713251	+	0.0713251i
$980$	18222.3	+	11461.0i	0.593969	+	0.373580i
$981$		0			0
$982$	35002.2	+	27925.9i	1.13744	+	0.907487i
$983$		−	21221.5i		−	0.688567i	−0.938866	−	0.344283i	$-0.888122\pi$
$983$		−	21221.5i		−	0.688567i	0.938866	−	0.344283i	$-0.111878\pi$
$984$		0			0
$985$		−	82700.7i		−	2.67519i
$986$	2782.42	−	3487.48i	0.0898686	−	0.112641i
$987$		0			0
$988$	10066.9	+	44195.6i	0.324161	+	1.42313i
$989$	−16000.6	+	16000.6i	−0.514447	+	0.514447i
$990$		0			0
$991$	23985.3			0.768838			0.384419	−	0.923159i	$-0.374402\pi$
$991$	23985.3			0.768838			0.384419	+	0.923159i	$0.374402\pi$
$992$	4837.45	−	3032.16i	0.154828	−	0.0970476i
$993$		0			0
$994$	−13585.9	+	1527.74i	−0.433520	+	0.0487495i
$995$	−2813.65	+	2813.65i	−0.0896469	+	0.0896469i
$996$		0			0
$997$	10763.8	+	10763.8i	0.341919	+	0.341919i	0.857088	−	0.515169i	$-0.172271\pi$
$997$	10763.8	+	10763.8i	0.341919	+	0.341919i	−0.515169	+	0.857088i	$0.672271\pi$
$998$	4073.06	−	5105.15i	0.129189	−	0.161925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.a.37.1		10
3.2	odd	2		16.4.e.a.5.5	✓	10
4.3	odd	2		576.4.k.a.433.5		10
12.11	even	2		64.4.e.a.49.4		10
16.3	odd	4		576.4.k.a.145.5		10
16.13	even	4	inner	144.4.k.a.109.1		10
24.5	odd	2		128.4.e.b.97.4		10
24.11	even	2		128.4.e.a.97.2		10
48.5	odd	4		128.4.e.b.33.4		10
48.11	even	4		128.4.e.a.33.2		10
48.29	odd	4		16.4.e.a.13.5	yes	10
48.35	even	4		64.4.e.a.17.4		10
96.5	odd	8		1024.4.b.j.513.3		10
96.11	even	8		1024.4.b.k.513.3		10
96.29	odd	8		1024.4.a.n.1.3		10
96.35	even	8		1024.4.a.m.1.8		10
96.53	odd	8		1024.4.b.j.513.8		10
96.59	even	8		1024.4.b.k.513.8		10
96.77	odd	8		1024.4.a.n.1.8		10
96.83	even	8		1024.4.a.m.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.5	✓	10	3.2	odd	2
16.4.e.a.13.5	yes	10	48.29	odd	4
64.4.e.a.17.4		10	48.35	even	4
64.4.e.a.49.4		10	12.11	even	2
128.4.e.a.33.2		10	48.11	even	4
128.4.e.a.97.2		10	24.11	even	2
128.4.e.b.33.4		10	48.5	odd	4
128.4.e.b.97.4		10	24.5	odd	2
144.4.k.a.37.1		10	1.1	even	1	trivial
144.4.k.a.109.1		10	16.13	even	4	inner
576.4.k.a.145.5		10	16.3	odd	4
576.4.k.a.433.5		10	4.3	odd	2
1024.4.a.m.1.3		10	96.83	even	8
1024.4.a.m.1.8		10	96.35	even	8
1024.4.a.n.1.3		10	96.29	odd	8
1024.4.a.n.1.8		10	96.77	odd	8
1024.4.b.j.513.3		10	96.5	odd	8
1024.4.b.j.513.8		10	96.53	odd	8
1024.4.b.k.513.3		10	96.11	even	8
1024.4.b.k.513.8		10	96.59	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81071 + 0.316066i) q^{2} +(7.80020 - 1.77674i) q^{4} +(12.6449 + 12.6449i) q^{5} +13.8754i q^{7} +(-21.3626 + 7.45928i) q^{8} +O(q^{10})\)	\(q+(-2.81071 + 0.316066i) q^{2} +(7.80020 - 1.77674i) q^{4} +(12.6449 + 12.6449i) q^{5} +13.8754i q^{7} +(-21.3626 + 7.45928i) q^{8} +(-39.5378 - 31.5445i) q^{10} +(-1.54694 - 1.54694i) q^{11} +(32.7875 - 32.7875i) q^{13} +(-4.38553 - 38.9997i) q^{14} +(57.6864 - 27.7179i) q^{16} -18.6531 q^{17} +(-86.4042 + 86.4042i) q^{19} +(121.099 + 76.1661i) q^{20} +(4.83695 + 3.85908i) q^{22} +134.006i q^{23} +194.786i q^{25} +(-81.7932 + 102.519i) q^{26} +(24.6529 + 108.231i) q^{28} +(59.7949 - 59.7949i) q^{29} -31.5391 q^{31} +(-153.379 + 96.1396i) q^{32} +(52.4284 - 5.89559i) q^{34} +(-175.453 + 175.453i) q^{35} +(89.1866 + 89.1866i) q^{37} +(215.548 - 270.167i) q^{38} +(-364.449 - 175.805i) q^{40} +210.504i q^{41} +(119.402 + 119.402i) q^{43} +(-14.8150 - 9.31796i) q^{44} +(-42.3547 - 376.652i) q^{46} +182.902 q^{47} +150.474 q^{49} +(-61.5653 - 547.489i) q^{50} +(197.494 - 314.004i) q^{52} +(26.1644 + 26.1644i) q^{53} -39.1219i q^{55} +(-103.500 - 296.414i) q^{56} +(-149.167 + 186.965i) q^{58} +(-441.584 - 441.584i) q^{59} +(-174.485 + 174.485i) q^{61} +(88.6475 - 9.96844i) q^{62} +(400.718 - 318.699i) q^{64} +829.188 q^{65} +(91.7562 - 91.7562i) q^{67} +(-145.498 + 33.1416i) q^{68} +(437.692 - 548.601i) q^{70} -348.360i q^{71} -299.436i q^{73} +(-278.867 - 222.489i) q^{74} +(-520.453 + 827.488i) q^{76} +(21.4644 - 21.4644i) q^{77} -943.487 q^{79} +(1079.93 + 378.949i) q^{80} +(-66.5330 - 591.666i) q^{82} +(-313.272 + 313.272i) q^{83} +(-235.866 - 235.866i) q^{85} +(-373.343 - 297.865i) q^{86} +(44.5858 + 21.5076i) q^{88} -1412.35i q^{89} +(454.939 + 454.939i) q^{91} +(238.094 + 1045.27i) q^{92} +(-514.085 + 57.8091i) q^{94} -2185.14 q^{95} +1515.29 q^{97} +(-422.939 + 47.5596i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

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