LMFDB - Embedded newform 135.3.i.a.116.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(71,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("135.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.i (of order $6$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.2
Root			$-2.82877i$ of defining polynomial
Character	$\chi$	$=$	135.116
Dual form			135.3.i.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44978 - 1.41438i) q^{2} +(2.00096 + 3.46576i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.97472 + 6.88441i) q^{7} -0.00541780i q^{8} +O(q^{10})$	\(q+(-2.44978 - 1.41438i) q^{2} +(2.00096 + 3.46576i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.97472 + 6.88441i) q^{7} -0.00541780i q^{8} -6.32531 q^{10} +(0.0594938 + 0.0343488i) q^{11} +(4.33957 + 7.51635i) q^{13} +(19.4744 - 11.2435i) q^{14} +(7.99617 - 13.8498i) q^{16} +26.5641i q^{17} +26.6131 q^{19} +(7.74968 + 4.47428i) q^{20} +(-0.0971646 - 0.168294i) q^{22} +(25.6980 - 14.8368i) q^{23} +(2.50000 - 4.33013i) q^{25} -24.5512i q^{26} -31.8130 q^{28} +(0.650245 + 0.375419i) q^{29} +(17.3205 + 30.0000i) q^{31} +(-39.1965 + 22.6301i) q^{32} +(37.5719 - 65.0764i) q^{34} +17.7755i q^{35} -48.4411 q^{37} +(-65.1963 - 37.6411i) q^{38} +(-0.00605729 - 0.0104915i) q^{40} +(-52.4148 + 30.2617i) q^{41} +(-16.6490 + 28.8369i) q^{43} +0.274922i q^{44} -83.9395 q^{46} +(25.1252 + 14.5060i) q^{47} +(-7.09677 - 12.2920i) q^{49} +(-12.2489 + 7.07191i) q^{50} +(-17.3666 + 30.0798i) q^{52} +6.99851i q^{53} +0.153612 q^{55} +(0.0372984 + 0.0215342i) q^{56} +(-1.06197 - 1.83939i) q^{58} +(57.1733 - 33.0090i) q^{59} +(9.50414 - 16.4617i) q^{61} -97.9914i q^{62} +64.0613 q^{64} +(16.8071 + 9.70357i) q^{65} +(-51.2260 - 88.7261i) q^{67} +(-92.0649 + 53.1537i) q^{68} +(25.1413 - 43.5461i) q^{70} +11.3543i q^{71} +53.9568 q^{73} +(118.670 + 68.5142i) q^{74} +(53.2517 + 92.2347i) q^{76} +(-0.472942 + 0.273053i) q^{77} +(-26.7351 + 46.3066i) q^{79} -35.7599i q^{80} +171.207 q^{82} +(-30.5050 - 17.6121i) q^{83} +(29.6996 + 51.4412i) q^{85} +(81.5729 - 47.0961i) q^{86} +(0.000186095 - 0.000322326i) q^{88} +74.9349i q^{89} -68.9943 q^{91} +(102.841 + 59.3755i) q^{92} +(-41.0341 - 71.0732i) q^{94} +(51.5361 - 29.7544i) q^{95} +(-34.4893 + 59.7373i) q^{97} +40.1502i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 16 * q^4 + 2 * q^7	$ 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) $ 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−2.44978	−	1.41438i	−1.22489	−	0.707191i	−0.258935	−	0.965895i	$-0.583371\pi$
$2$	−2.44978	−	1.41438i	−1.22489	−	0.707191i	−0.965957	+	0.258703i	$0.916705\pi$
$3$		0			0
$3$		0			0
$4$	2.00096	+	3.46576i	0.500239	+	0.866440i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		0			0
$7$	−3.97472	+	6.88441i	−0.567817	+	0.983488i	0.428965	+	0.903321i	$0.358879\pi$
$7$	−3.97472	+	6.88441i	−0.567817	+	0.983488i	−0.996781	+	0.0801664i	$0.974455\pi$
$8$		−	0.00541780i		−	0.000677225i
$9$		0			0
$10$	−6.32531			−0.632531
$11$	0.0594938	+	0.0343488i	0.00540853	+	0.00312262i	0.502702	−	0.864460i	$-0.332339\pi$
$11$	0.0594938	+	0.0343488i	0.00540853	+	0.00312262i	−0.497293	+	0.867582i	$0.665673\pi$
$12$		0			0
$13$	4.33957	+	7.51635i	0.333813	+	0.578181i	0.983256	−	0.182229i	$-0.0583313\pi$
$13$	4.33957	+	7.51635i	0.333813	+	0.578181i	−0.649443	+	0.760410i	$0.724998\pi$
$14$	19.4744	−	11.2435i	1.39103	−	0.803110i
$15$		0			0
$16$	7.99617	−	13.8498i	0.499760	−	0.865611i
$17$			26.5641i			1.56260i	0.624158	+	0.781298i	$0.285442\pi$
$17$			26.5641i			1.56260i	−0.624158	+	0.781298i	$0.714558\pi$
$18$		0			0
$19$	26.6131			1.40069			0.700345	−	0.713805i	$-0.253029\pi$
$19$	26.6131			1.40069			0.700345	+	0.713805i	$0.253029\pi$
$20$	7.74968	+	4.47428i	0.387484	+	0.223714i
$21$		0			0
$22$	−0.0971646	−	0.168294i	−0.00441657	−	0.00764973i
$23$	25.6980	−	14.8368i	1.11731	−	0.645077i	0.176594	−	0.984284i	$-0.443492\pi$
$23$	25.6980	−	14.8368i	1.11731	−	0.645077i	0.940712	+	0.339207i	$0.110159\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		−	24.5512i		−	0.944279i
$27$		0			0
$28$	−31.8130			−1.13618
$29$	0.650245	+	0.375419i	0.0224222	+	0.0129455i	0.511169	−	0.859480i	$-0.329213\pi$
$29$	0.650245	+	0.375419i	0.0224222	+	0.0129455i	−0.488747	+	0.872426i	$0.662546\pi$
$30$		0			0
$31$	17.3205	+	30.0000i	0.558727	+	0.967743i	0.997603	+	0.0691954i	$0.0220432\pi$
$31$	17.3205	+	30.0000i	0.558727	+	0.967743i	−0.438877	+	0.898547i	$0.644623\pi$
$32$	−39.1965	+	22.6301i	−1.22489	+	0.707191i
$33$		0			0
$34$	37.5719	−	65.0764i	1.10505	−	1.91401i
$35$			17.7755i			0.507871i
$36$		0			0
$37$	−48.4411			−1.30922			−0.654609	−	0.755967i	$-0.727167\pi$
$37$	−48.4411			−1.30922			−0.654609	+	0.755967i	$0.727167\pi$
$38$	−65.1963	−	37.6411i	−1.71569	−	0.990556i
$39$		0			0
$40$	−0.00605729	−	0.0104915i	−0.000151432	−	0.000262288i
$41$	−52.4148	+	30.2617i	−1.27841	+	0.738091i	−0.976556	−	0.215263i	$-0.930939\pi$
$41$	−52.4148	+	30.2617i	−1.27841	+	0.738091i	−0.301855	+	0.953354i	$0.597606\pi$
$42$		0			0
$43$	−16.6490	+	28.8369i	−0.387186	+	0.670626i	−0.992070	−	0.125688i	$-0.959886\pi$
$43$	−16.6490	+	28.8369i	−0.387186	+	0.670626i	0.604884	+	0.796314i	$0.293220\pi$
$44$			0.274922i			0.00624822i
$45$		0			0
$46$	−83.9395			−1.82477
$47$	25.1252	+	14.5060i	0.534578	+	0.308639i	0.742879	−	0.669426i	$-0.233460\pi$
$47$	25.1252	+	14.5060i	0.534578	+	0.308639i	−0.208301	+	0.978065i	$0.566793\pi$
$48$		0			0
$49$	−7.09677	−	12.2920i	−0.144832	−	0.250856i
$50$	−12.2489	+	7.07191i	−0.244978	+	0.141438i
$51$		0			0
$52$	−17.3666	+	30.0798i	−0.333973	+	0.578458i
$53$			6.99851i			0.132047i	0.997818	+	0.0660237i	$0.0210313\pi$
$53$			6.99851i			0.132047i	−0.997818	+	0.0660237i	$0.978969\pi$
$54$		0			0
$55$	0.153612			0.00279295
$56$	0.0372984	+	0.0215342i	0.000666043	+	0.000384540i
$57$		0			0
$58$	−1.06197	−	1.83939i	−0.0183099	−	0.0317136i
$59$	57.1733	−	33.0090i	0.969039	−	0.559475i	0.0700958	−	0.997540i	$-0.477669\pi$
$59$	57.1733	−	33.0090i	0.969039	−	0.559475i	0.898943	+	0.438065i	$0.144336\pi$
$60$		0			0
$61$	9.50414	−	16.4617i	0.155806	−	0.269863i	−0.777547	−	0.628825i	$-0.783536\pi$
$61$	9.50414	−	16.4617i	0.155806	−	0.269863i	0.933352	+	0.358962i	$0.116869\pi$
$62$		−	97.9914i		−	1.58051i
$63$		0			0
$64$	64.0613			1.00096
$65$	16.8071	+	9.70357i	0.258570	+	0.149286i
$66$		0			0
$67$	−51.2260	−	88.7261i	−0.764568	−	1.32427i	−0.940475	−	0.339864i	$-0.889619\pi$
$67$	−51.2260	−	88.7261i	−0.764568	−	1.32427i	0.175907	−	0.984407i	$-0.443714\pi$
$68$	−92.0649	+	53.1537i	−1.35390	+	0.781672i
$69$		0			0
$70$	25.1413	−	43.5461i	0.359162	−	0.622087i
$71$			11.3543i			0.159919i	0.996798	+	0.0799597i	$0.0254792\pi$
$71$			11.3543i			0.159919i	−0.996798	+	0.0799597i	$0.974521\pi$
$72$		0			0
$73$	53.9568			0.739134			0.369567	−	0.929204i	$-0.379506\pi$
$73$	53.9568			0.739134			0.369567	+	0.929204i	$0.379506\pi$
$74$	118.670	+	68.5142i	1.60365	+	0.925868i
$75$		0			0
$76$	53.2517	+	92.2347i	0.700680	+	1.21361i
$77$	−0.472942	+	0.273053i	−0.00614211	+	0.00354615i
$78$		0			0
$79$	−26.7351	+	46.3066i	−0.338419	+	0.586159i	−0.984136	−	0.177418i	$-0.943225\pi$
$79$	−26.7351	+	46.3066i	−0.338419	+	0.586159i	0.645717	+	0.763577i	$0.276559\pi$
$80$		−	35.7599i		−	0.446999i
$81$		0			0
$82$	171.207			2.08789
$83$	−30.5050	−	17.6121i	−0.367530	−	0.212194i	0.304849	−	0.952401i	$-0.401394\pi$
$83$	−30.5050	−	17.6121i	−0.367530	−	0.212194i	−0.672379	+	0.740207i	$0.734727\pi$
$84$		0			0
$85$	29.6996	+	51.4412i	0.349407	+	0.605191i
$86$	81.5729	−	47.0961i	0.948522	−	0.547629i
$87$		0			0
$88$	0.000186095	0	0.000322326i	2.11471e−6	0	3.66279e-6i
$89$			74.9349i			0.841965i	0.907069	+	0.420983i	$0.138315\pi$
$89$			74.9349i			0.841965i	−0.907069	+	0.420983i	$0.861685\pi$
$90$		0			0
$91$	−68.9943			−0.758179
$92$	102.841	+	59.3755i	1.11784	+	0.645386i
$93$		0			0
$94$	−41.0341	−	71.0732i	−0.436533	−	0.756098i
$95$	51.5361	−	29.7544i	0.542485	−	0.313204i
$96$		0			0
$97$	−34.4893	+	59.7373i	−0.355560	+	0.615848i	−0.987214	−	0.159402i	$-0.949043\pi$
$97$	−34.4893	+	59.7373i	−0.355560	+	0.615848i	0.631653	+	0.775251i	$0.282377\pi$
$98$			40.1502i			0.409696i
$99$		0			0
$100$	20.0096			0.200096
$101$	−15.7347	−	9.08446i	−0.155790	−	0.0899451i	0.420079	−	0.907488i	$-0.362003\pi$
$101$	−15.7347	−	9.08446i	−0.155790	−	0.0899451i	−0.575868	+	0.817543i	$0.695336\pi$
$102$		0			0
$103$	23.8052	+	41.2318i	0.231118	+	0.400309i	0.958137	−	0.286309i	$-0.0924282\pi$
$103$	23.8052	+	41.2318i	0.231118	+	0.400309i	−0.727019	+	0.686617i	$0.759095\pi$
$104$	0.0407221	−	0.0235109i	0.000391559	−	0.000226067i
$105$		0			0
$106$	9.89857	−	17.1448i	0.0933827	−	0.161744i
$107$		−	149.680i		−	1.39888i	−0.714693	−	0.699439i	$-0.753433\pi$
$107$		−	149.680i		−	1.39888i	0.714693	−	0.699439i	$-0.246567\pi$
$108$		0			0
$109$	−36.8532			−0.338103			−0.169051	−	0.985607i	$-0.554070\pi$
$109$	−36.8532			−0.338103			−0.169051	+	0.985607i	$0.554070\pi$
$110$	−0.376317	−	0.217267i	−0.00342106	−	0.00197515i
$111$		0			0
$112$	63.5650	+	110.098i	0.567545	+	0.983017i
$113$	53.1170	−	30.6671i	0.470062	−	0.271390i	−0.246204	−	0.969218i	$-0.579183\pi$
$113$	53.1170	−	30.6671i	0.470062	−	0.271390i	0.716266	+	0.697828i	$0.245850\pi$
$114$		0			0
$115$	33.1760	−	57.4626i	0.288487	−	0.499674i
$116$			3.00479i			0.0259034i
$117$		0			0
$118$	−186.750			−1.58262
$119$	−182.879	−	105.585i	−1.53679	−	0.887269i
$120$		0			0
$121$	−60.4976	−	104.785i	−0.499980	−	0.865992i
$122$	−46.5662	+	26.8850i	−0.381690	+	0.220369i
$123$		0			0
$124$	−69.3153	+	120.058i	−0.558994	+	0.968206i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	190.745			1.50193			0.750965	−	0.660342i	$-0.229588\pi$
$127$	190.745			1.50193			0.750965	+	0.660342i	$0.229588\pi$
$128$	−0.150143	−	0.0866848i	−0.00117299	−	0.000677225i
$129$		0			0
$130$	−27.4491	−	47.5433i	−0.211147	−	0.365718i
$131$	24.8473	−	14.3456i	0.189674	−	0.109508i	−0.402156	−	0.915571i	$-0.631739\pi$
$131$	24.8473	−	14.3456i	0.189674	−	0.109508i	0.591830	+	0.806063i	$0.298406\pi$
$132$		0			0
$133$	−105.780	+	183.216i	−0.795335	+	1.37756i
$134$			289.813i			2.16278i
$135$		0			0
$136$	0.143919			0.00105823
$137$	−101.630	−	58.6761i	−0.741825	−	0.428293i	0.0809076	−	0.996722i	$-0.474218\pi$
$137$	−101.630	−	58.6761i	−0.741825	−	0.428293i	−0.822732	+	0.568429i	$0.807551\pi$
$138$		0			0
$139$	−15.7198	−	27.2275i	−0.113092	−	0.195881i	0.803923	−	0.594733i	$-0.202742\pi$
$139$	−15.7198	−	27.2275i	−0.113092	−	0.195881i	−0.917015	+	0.398852i	$0.869409\pi$
$140$	−61.6056	+	35.5680i	−0.440040	+	0.254057i
$141$		0			0
$142$	16.0593	−	27.8155i	0.113094	−	0.195884i
$143$			0.596235i			0.00416948i
$144$		0			0
$145$	1.67893			0.0115788
$146$	−132.182	−	76.3156i	−0.905360	−	0.522710i
$147$		0			0
$148$	−96.9286	−	167.885i	−0.654923	−	1.13436i
$149$	−23.0951	+	13.3340i	−0.155001	+	0.0894896i	−0.575494	−	0.817806i	$-0.695190\pi$
$149$	−23.0951	+	13.3340i	−0.155001	+	0.0894896i	0.420494	+	0.907296i	$0.361857\pi$
$150$		0			0
$151$	50.6215	−	87.6791i	0.335242	−	0.580656i	−0.648289	−	0.761394i	$-0.724515\pi$
$151$	50.6215	−	87.6791i	0.335242	−	0.580656i	0.983531	+	0.180738i	$0.0578486\pi$
$152$		−	0.144185i		−	0.000948583i
$153$		0			0
$154$	1.54481			0.0100312
$155$	67.0821	+	38.7299i	0.432788	+	0.249870i
$156$		0			0
$157$	−139.688	−	241.946i	−0.889731	−	1.54106i	−0.840193	−	0.542288i	$-0.817558\pi$
$157$	−139.688	−	241.946i	−0.889731	−	1.54106i	−0.0495387	−	0.998772i	$-0.515775\pi$
$158$	130.990	−	75.6273i	0.829053	−	0.478654i
$159$		0			0
$160$	−50.6025	+	87.6461i	−0.316266	+	0.547788i
$161$			235.888i			1.46514i
$162$		0			0
$163$	246.776			1.51396			0.756982	−	0.653436i	$-0.226673\pi$
$163$	246.776			1.51396			0.756982	+	0.653436i	$0.226673\pi$
$164$	−209.760	−	121.105i	−1.27902	−	0.738444i
$165$		0			0
$166$	49.8204	+	86.2915i	0.300123	+	0.519828i
$167$	−72.9485	+	42.1168i	−0.436817	+	0.252197i	−0.702247	−	0.711934i	$-0.747820\pi$
$167$	−72.9485	+	42.1168i	−0.436817	+	0.252197i	0.265429	+	0.964130i	$0.414486\pi$
$168$		0			0
$169$	46.8363	−	81.1228i	0.277138	−	0.480017i
$170$		−	168.026i		−	0.988391i
$171$		0			0
$172$	−133.256			−0.774743
$173$	164.087	+	94.7357i	0.948480	+	0.547605i	0.892608	−	0.450833i	$-0.148873\pi$
$173$	164.087	+	94.7357i	0.948480	+	0.547605i	0.0558715	+	0.998438i	$0.482206\pi$
$174$		0			0
$175$	19.8736	+	34.4221i	0.113563	+	0.196698i
$176$	0.951445	−	0.549317i	0.00540594	−	0.00312112i
$177$		0			0
$178$	105.987	−	183.574i	0.595431	−	1.03132i
$179$		−	111.227i		−	0.621378i	−0.950512	−	0.310689i	$-0.899440\pi$
$179$		−	111.227i		−	0.621378i	0.950512	−	0.310689i	$-0.100560\pi$
$180$		0			0
$181$	219.388			1.21209			0.606046	−	0.795430i	$-0.292755\pi$
$181$	219.388			1.21209			0.606046	+	0.795430i	$0.292755\pi$
$182$	169.021	+	97.5843i	0.928686	+	0.536177i
$183$		0			0
$184$	−0.0803827	−	0.139227i	−0.000436863	−	0.000756668i
$185$	−93.8058	+	54.1588i	−0.507058	+	0.292750i
$186$		0			0
$187$	−0.912445	+	1.58040i	−0.00487939	+	0.00845135i
$188$			116.104i			0.617573i
$189$		0			0
$190$	−168.336			−0.885980
$191$	31.7265	+	18.3173i	0.166107	+	0.0959020i	0.580749	−	0.814083i	$-0.302760\pi$
$191$	31.7265	+	18.3173i	0.166107	+	0.0959020i	−0.414642	+	0.909985i	$0.636093\pi$
$192$		0			0
$193$	−76.2245	−	132.025i	−0.394946	−	0.684066i	0.598149	−	0.801385i	$-0.295903\pi$
$193$	−76.2245	−	132.025i	−0.394946	−	0.684066i	−0.993094	+	0.117319i	$0.962570\pi$
$194$	168.983	−	97.5623i	0.871045	−	0.502898i
$195$		0			0
$196$	28.4007	−	49.1914i	0.144901	−	0.250977i
$197$		−	35.7863i		−	0.181657i	−0.995867	−	0.0908283i	$-0.971049\pi$
$197$		−	35.7863i		−	0.181657i	0.995867	−	0.0908283i	$-0.0289514\pi$
$198$		0			0
$199$	−104.576			−0.525509			−0.262754	−	0.964863i	$-0.584631\pi$
$199$	−104.576			−0.525509			−0.262754	+	0.964863i	$0.584631\pi$
$200$	−0.0234598	−	0.0135445i	−0.000117299	−	6.77225e-5i
$201$		0			0
$202$	25.6978	+	44.5099i	0.127217	+	0.220346i
$203$	−5.16908	+	2.98437i	−0.0254635	+	0.0147013i
$204$		0			0
$205$	−67.6673	+	117.203i	−0.330084	+	0.571723i
$206$		−	134.679i		−	0.653779i
$207$		0			0
$208$	138.800			0.667306
$209$	1.58332	+	0.914128i	0.00757567	+	0.00437382i
$210$		0			0
$211$	54.4388	+	94.2907i	0.258004	+	0.446875i	0.965707	−	0.259634i	$-0.0836020\pi$
$211$	54.4388	+	94.2907i	0.258004	+	0.446875i	−0.707703	+	0.706510i	$0.750269\pi$
$212$	−24.2552	+	14.0037i	−0.114411	+	0.0660553i
$213$		0			0
$214$	−211.705	+	366.683i	−0.989274	+	1.71347i
$215$			74.4566i			0.346310i
$216$		0			0
$217$	−275.377			−1.26902
$218$	90.2823	+	52.1245i	0.414139	+	0.239103i
$219$		0			0
$220$	0.307372	+	0.532384i	0.00139714	+	0.00241993i
$221$	−199.665	+	115.277i	−0.903464	+	0.521615i
$222$		0			0
$223$	134.485	−	232.934i	0.603070	−	1.04455i	−0.389283	−	0.921118i	$-0.627277\pi$
$223$	134.485	−	232.934i	0.603070	−	1.04455i	0.992353	−	0.123430i	$-0.0393895\pi$
$224$		−	359.793i		−	1.60622i
$225$		0			0
$226$	−173.500			−0.767700
$227$	71.7385	+	41.4183i	0.316029	+	0.182459i	0.649621	−	0.760258i	$-0.274928\pi$
$227$	71.7385	+	41.4183i	0.316029	+	0.182459i	−0.333592	+	0.942717i	$0.608261\pi$
$228$		0			0
$229$	94.5387	+	163.746i	0.412833	+	0.715047i	0.995198	−	0.0978799i	$-0.0312061\pi$
$229$	94.5387	+	163.746i	0.412833	+	0.715047i	−0.582366	+	0.812927i	$0.697873\pi$
$230$	−162.548	+	93.8472i	−0.706731	+	0.408031i
$231$		0			0
$232$	0.00203395	−	0.00352290i	8.76701e−6	−	1.51849e-5i
$233$		−	273.780i		−	1.17502i	−0.809216	−	0.587512i	$-0.800108\pi$
$233$		−	273.780i		−	1.17502i	0.809216	−	0.587512i	$-0.199892\pi$
$234$		0			0
$235$	64.8729			0.276055
$236$	228.803	+	132.099i	0.969503	+	0.559743i
$237$		0			0
$238$	298.675	+	517.320i	1.25494	+	2.17362i
$239$	44.2330	−	25.5379i	0.185075	−	0.106853i	−0.404600	−	0.914494i	$-0.632589\pi$
$239$	44.2330	−	25.5379i	0.185075	−	0.106853i	0.589675	+	0.807641i	$0.299256\pi$
$240$		0			0
$241$	−95.5289	+	165.461i	−0.396385	+	0.686560i	−0.993277	−	0.115762i	$-0.963069\pi$
$241$	−95.5289	+	165.461i	−0.396385	+	0.686560i	0.596892	+	0.802322i	$0.296402\pi$
$242$			342.267i			1.41433i
$243$		0			0
$244$	76.0695			0.311760
$245$	−27.4857	−	15.8689i	−0.112186	−	0.0647709i
$246$		0			0
$247$	115.489	+	200.034i	0.467569	+	0.809852i
$248$	0.162534	−	0.0938392i	0.000655380	−	0.000378384i
$249$		0			0
$250$	−15.8133	+	27.3894i	−0.0632531	+	0.109558i
$251$		−	169.083i		−	0.673637i	−0.941570	−	0.336818i	$-0.890649\pi$
$251$		−	169.083i		−	0.673637i	0.941570	−	0.336818i	$-0.109351\pi$
$252$		0			0
$253$	2.03850			0.00805731
$254$	−467.284	−	269.787i	−1.83970	−	1.06215i
$255$		0			0
$256$	−127.877	−	221.490i	−0.499521	−	0.865195i
$257$	−247.257	+	142.754i	−0.962090	+	0.555463i	−0.896816	−	0.442404i	$-0.854126\pi$
$257$	−247.257	+	142.754i	−0.962090	+	0.555463i	−0.0652745	+	0.997867i	$0.520792\pi$
$258$		0			0
$259$	192.540	−	333.489i	0.743396	−	1.28760i
$260$			77.6657i			0.298714i
$261$		0			0
$262$	−81.1606			−0.309773
$263$	−62.0090	−	35.8009i	−0.235776	−	0.136125i	0.377458	−	0.926027i	$-0.376798\pi$
$263$	−62.0090	−	35.8009i	−0.235776	−	0.136125i	−0.613234	+	0.789902i	$0.710132\pi$
$264$		0			0
$265$	7.82457	+	13.5526i	0.0295267	+	0.0511417i
$266$	518.274	−	299.226i	1.94840	−	1.12491i
$267$		0			0
$268$	205.002	−	355.074i	0.764934	−	1.32490i
$269$		−	39.6463i		−	0.147384i	−0.997281	−	0.0736920i	$-0.976522\pi$
$269$		−	39.6463i		−	0.147384i	0.997281	−	0.0736920i	$-0.0234782\pi$
$270$		0			0
$271$	397.832			1.46801			0.734007	−	0.679142i	$-0.237648\pi$
$271$	397.832			1.46801			0.734007	+	0.679142i	$0.237648\pi$
$272$	367.907	+	212.411i	1.35260	+	0.780924i
$273$		0			0
$274$	165.981	+	287.487i	0.605770	+	1.04922i
$275$	0.297469	−	0.171744i	0.00108171	−	0.000624523i
$276$		0			0
$277$	−68.4595	+	118.575i	−0.247146	+	0.428070i	−0.962733	−	0.270454i	$-0.912826\pi$
$277$	−68.4595	+	118.575i	−0.247146	+	0.428070i	0.715587	+	0.698524i	$0.246159\pi$
$278$			88.9352i			0.319911i
$279$		0			0
$280$	0.0963041			0.000343943
$281$	381.758	+	220.408i	1.35857	+	0.784370i	0.989431	−	0.145005i	$-0.0463198\pi$
$281$	381.758	+	220.408i	1.35857	+	0.784370i	0.369137	+	0.929375i	$0.379653\pi$
$282$		0			0
$283$	−84.1670	−	145.782i	−0.297410	−	0.515129i	0.678133	−	0.734939i	$-0.262789\pi$
$283$	−84.1670	−	145.782i	−0.297410	−	0.515129i	−0.975543	+	0.219810i	$0.929456\pi$
$284$	−39.3512	+	22.7194i	−0.138561	+	0.0799979i
$285$		0			0
$286$	0.843305	−	1.46065i	0.00294862	−	0.00510716i
$287$		−	481.127i		−	1.67640i
$288$		0			0
$289$	−416.653			−1.44171
$290$	−4.11300	−	2.37464i	−0.0141828	−	0.00818842i
$291$		0			0
$292$	107.965	+	187.001i	0.369744	+	0.640416i
$293$	388.737	−	224.438i	1.32675	−	0.765999i	0.341953	−	0.939717i	$-0.388912\pi$
$293$	388.737	−	224.438i	1.32675	−	0.765999i	0.984795	+	0.173718i	$0.0555782\pi$
$294$		0			0
$295$	73.8104	−	127.843i	0.250205	−	0.433367i
$296$			0.262444i			0.000886636i
$297$		0			0
$298$	75.4373			0.253145
$299$	223.037	+	128.770i	0.745943	+	0.430670i
$300$		0			0
$301$	−132.350	−	229.237i	−0.439702	−	0.761585i
$302$	−248.024	+	143.196i	−0.821270	+	0.474161i
$303$		0			0
$304$	212.803	−	368.585i	0.700010	−	1.21245i
$305$		−	42.5038i		−	0.139357i
$306$		0			0
$307$	−492.512			−1.60427			−0.802137	−	0.597140i	$-0.796304\pi$
$307$	−492.512			−1.60427			−0.802137	+	0.597140i	$0.796304\pi$
$308$	−1.89267	−	1.09274i	−0.00614505	−	0.00354785i
$309$		0			0
$310$	−109.558	−	189.760i	−0.353412	−	0.612128i
$311$	−71.5497	+	41.3092i	−0.230063	+	0.132827i	−0.610601	−	0.791938i	$-0.709072\pi$
$311$	−71.5497	+	41.3092i	−0.230063	+	0.132827i	0.380538	+	0.924765i	$0.375739\pi$
$312$		0			0
$313$	−96.1876	+	166.602i	−0.307308	+	0.532274i	−0.977773	−	0.209668i	$-0.932762\pi$
$313$	−96.1876	+	166.602i	−0.307308	+	0.532274i	0.670464	+	0.741942i	$0.266095\pi$
$314$			790.288i			2.51684i
$315$		0			0
$316$	−213.983			−0.677162
$317$	31.6063	+	18.2479i	0.0997043	+	0.0575643i	0.549023	−	0.835807i	$-0.315000\pi$
$317$	31.6063	+	18.2479i	0.0997043	+	0.0575643i	−0.449319	+	0.893372i	$0.648333\pi$
$318$		0			0
$319$	0.0257904	+	0.0446702i	8.08476e−5	+	0.000140032i
$320$	124.054	−	71.6227i	0.387669	−	0.223821i
$321$		0			0
$322$	333.636	−	577.874i	1.03614	−	1.79464i
$323$			706.954i			2.18871i
$324$		0			0
$325$	43.3957			0.133525
$326$	−604.548	−	349.036i	−1.85444	−	1.07066i
$327$		0			0
$328$	0.163952	+	0.283973i	0.000499854	+	0.000865772i
$329$	−199.731	+	115.315i	−0.607085	+	0.350501i
$330$		0			0
$331$	−142.388	+	246.624i	−0.430176	+	0.745087i	−0.996888	−	0.0788292i	$-0.974882\pi$
$331$	−142.388	+	246.624i	−0.430176	+	0.745087i	0.566712	+	0.823916i	$0.308215\pi$
$332$		−	140.964i		−	0.424590i
$333$		0			0
$334$	238.277			0.713405
$335$	−198.398	−	114.545i	−0.592232	−	0.341925i
$336$		0			0
$337$	122.391	+	211.988i	0.363178	+	0.629043i	0.988482	−	0.151338i	$-0.0483583\pi$
$337$	122.391	+	211.988i	0.363178	+	0.629043i	−0.625304	+	0.780381i	$0.715025\pi$
$338$	−229.477	+	132.489i	−0.678927	+	0.391979i
$339$		0			0
$340$	−118.855	+	205.863i	−0.349574	+	0.605481i
$341$			2.37975i			0.00697875i
$342$		0			0
$343$	−276.692			−0.806681
$344$	0.156233	+	0.0902010i	0.000454165	+	0.000262212i
$345$		0			0
$346$	−267.985	−	464.164i	−0.774523	−	1.34151i
$347$	219.275	−	126.599i	0.631918	−	0.364838i	−0.149577	−	0.988750i	$-0.547791\pi$
$347$	219.275	−	126.599i	0.631918	−	0.364838i	0.781494	+	0.623912i	$0.214458\pi$
$348$		0			0
$349$	−259.518	+	449.498i	−0.743603	+	1.28796i	0.207241	+	0.978290i	$0.433551\pi$
$349$	−259.518	+	449.498i	−0.743603	+	1.28796i	−0.950845	+	0.309669i	$0.899782\pi$
$350$		−	112.435i		−	0.321244i
$351$		0			0
$352$	−3.10927			−0.00883315
$353$	−595.687	−	343.920i	−1.68750	−	0.974277i	−0.956425	−	0.291977i	$-0.905687\pi$
$353$	−595.687	−	343.920i	−1.68750	−	0.974277i	−0.731072	−	0.682300i	$-0.760980\pi$
$354$		0			0
$355$	12.6945	+	21.9875i	0.0357590	+	0.0619365i
$356$	−259.706	+	149.942i	−0.729513	+	0.421184i
$357$		0			0
$358$	−157.317	+	272.481i	−0.439433	+	0.761121i
$359$		−	340.488i		−	0.948435i	−0.880408	−	0.474218i	$-0.842731\pi$
$359$		−	340.488i		−	0.948435i	0.880408	−	0.474218i	$-0.157269\pi$
$360$		0			0
$361$	347.258			0.961933
$362$	−537.454	−	310.299i	−1.48468	−	0.857180i
$363$		0			0
$364$	−138.055	−	239.118i	−0.379271	−	0.656916i
$365$	104.487	−	60.3256i	0.286266	−	0.165275i
$366$		0			0
$367$	133.356	−	230.980i	0.363368	−	0.629373i	−0.625144	−	0.780509i	$-0.714960\pi$
$367$	133.356	−	230.980i	0.363368	−	0.629373i	0.988513	+	0.151136i	$0.0482933\pi$
$368$		−	474.549i		−	1.28954i
$369$		0			0
$370$	306.405			0.828122
$371$	−48.1806	−	27.8171i	−0.129867	−	0.0749787i
$372$		0			0
$373$	−140.463	−	243.288i	−0.376576	−	0.652248i	0.613986	−	0.789317i	$-0.289565\pi$
$373$	−140.463	−	243.288i	−0.376576	−	0.652248i	−0.990562	+	0.137069i	$0.956232\pi$
$374$	4.47059	−	2.58109i	0.0119534	−	0.00690132i
$375$		0			0
$376$	0.0785908	−	0.136123i	0.000209018	−	0.000362030i
$377$			6.51663i			0.0172855i
$378$		0			0
$379$	−532.151			−1.40409			−0.702046	−	0.712131i	$-0.747730\pi$
$379$	−532.151			−1.40409			−0.702046	+	0.712131i	$0.747730\pi$
$380$	206.243	+	119.074i	0.542745	+	0.313354i
$381$		0			0
$382$	−51.8153	−	89.7467i	−0.135642	−	0.234939i
$383$	−316.930	+	182.979i	−0.827493	+	0.477753i	−0.852993	−	0.521922i	$-0.825215\pi$
$383$	−316.930	+	182.979i	−0.827493	+	0.477753i	0.0255008	+	0.999675i	$0.491882\pi$
$384$		0			0
$385$	−0.610566	+	1.05753i	−0.00158589	+	0.00274683i
$386$			431.242i			1.11721i
$387$		0			0
$388$	−276.047			−0.711461
$389$	82.2932	+	47.5120i	0.211551	+	0.122139i	0.602032	−	0.798472i	$-0.294358\pi$
$389$	82.2932	+	47.5120i	0.211551	+	0.122139i	−0.390481	+	0.920611i	$0.627691\pi$
$390$		0			0
$391$	394.126	+	682.646i	1.00799	+	1.74590i
$392$	−0.0665955	+	0.0384489i	−0.000169886	+	9.80839e-5i
$393$		0			0
$394$	−50.6156	+	87.6687i	−0.128466	+	0.222509i
$395$			119.563i			0.302691i
$396$		0			0
$397$	691.691			1.74229			0.871147	−	0.491023i	$-0.163377\pi$
$397$	691.691			1.74229			0.871147	+	0.491023i	$0.163377\pi$
$398$	256.189	+	147.911i	0.643691	+	0.371635i
$399$		0			0
$400$	−39.9808	−	69.2488i	−0.0999521	−	0.173122i
$401$	−57.8355	+	33.3913i	−0.144228	+	0.0832701i	−0.570378	−	0.821383i	$-0.693203\pi$
$401$	−57.8355	+	33.3913i	−0.144228	+	0.0832701i	0.426149	+	0.904653i	$0.359870\pi$
$402$		0			0
$403$	−150.327	+	260.374i	−0.373020	+	0.646090i
$404$		−	72.7105i		−	0.179976i
$405$		0			0
$406$	16.8842			0.0415866
$407$	−2.88195	−	1.66389i	−0.00708095	−	0.00408819i
$408$		0			0
$409$	−55.5485	−	96.2128i	−0.135815	−	0.235239i	0.790093	−	0.612987i	$-0.210032\pi$
$409$	−55.5485	−	96.2128i	−0.135815	−	0.235239i	−0.925909	+	0.377748i	$0.876699\pi$
$410$	331.540	−	191.415i	0.808635	−	0.466865i
$411$		0			0
$412$	−95.2663	+	165.006i	−0.231229	+	0.400500i
$413$			524.806i			1.27072i
$414$		0			0
$415$	−78.7635			−0.189792
$416$	−340.192	−	196.410i	−0.817769	−	0.472139i
$417$		0			0
$418$	−2.58585	−	4.47883i	−0.00618625	−	0.0107149i
$419$	333.765	−	192.699i	0.796576	−	0.459903i	−0.0456967	−	0.998955i	$-0.514551\pi$
$419$	333.765	−	192.699i	0.796576	−	0.459903i	0.842272	+	0.539052i	$0.181217\pi$
$420$		0			0
$421$	32.4176	−	56.1490i	0.0770015	−	0.133371i	−0.824953	−	0.565201i	$-0.808799\pi$
$421$	32.4176	−	56.1490i	0.0770015	−	0.133371i	0.901955	+	0.431830i	$0.142132\pi$
$422$		−	307.989i		−	0.729832i
$423$		0			0
$424$	0.0379165			8.94258e−5
$425$	115.026	+	66.4103i	0.270650	+	0.156260i
$426$		0			0
$427$	75.5525	+	130.861i	0.176938	+	0.306466i
$428$	518.755	−	299.503i	1.21204	−	0.699774i
$429$		0			0
$430$	105.310	−	182.402i	0.244907	−	0.424192i
$431$			205.696i			0.477253i	0.971111	+	0.238626i	$0.0766972\pi$
$431$			205.696i			0.477253i	−0.971111	+	0.238626i	$0.923303\pi$
$432$		0			0
$433$	−346.035			−0.799156			−0.399578	−	0.916699i	$-0.630843\pi$
$433$	−346.035			−0.799156			−0.399578	+	0.916699i	$0.630843\pi$
$434$	674.613	+	389.488i	1.55441	+	0.897438i
$435$		0			0
$436$	−73.7416	−	127.724i	−0.169132	−	0.292946i
$437$	683.905	−	394.853i	1.56500	−	0.903553i
$438$		0			0
$439$	276.226	−	478.437i	0.629216	−	1.08983i	−0.358494	−	0.933532i	$-0.616710\pi$
$439$	276.226	−	478.437i	0.629216	−	1.08983i	0.987709	−	0.156301i	$-0.0499571\pi$
$440$		0	0.000832242i		0	1.89146e-6i
$441$		0			0
$442$	652.183			1.47553
$443$	−37.5855	−	21.7000i	−0.0848430	−	0.0489841i	0.456978	−	0.889478i	$-0.348932\pi$
$443$	−37.5855	−	21.7000i	−0.0848430	−	0.0489841i	−0.541821	+	0.840494i	$0.682265\pi$
$444$		0			0
$445$	83.7798	+	145.111i	0.188269	+	0.326092i
$446$	−658.917	+	380.426i	−1.47739	+	0.852972i
$447$		0			0
$448$	−254.626	+	441.024i	−0.568361	+	0.984429i
$449$			651.887i			1.45186i	0.687766	+	0.725932i	$0.258591\pi$
$449$			651.887i			1.45186i	−0.687766	+	0.725932i	$0.741409\pi$
$450$		0			0
$451$	−4.15781			−0.00921909
$452$	212.570	+	122.727i	0.470287	+	0.271520i
$453$		0			0
$454$	−117.163	−	202.931i	−0.258067	−	0.446986i
$455$	−133.607	+	77.1379i	−0.293641	+	0.169534i
$456$		0			0
$457$	230.589	−	399.393i	0.504572	−	0.873945i	−0.495414	−	0.868657i	$-0.664984\pi$
$457$	230.589	−	399.393i	0.504572	−	0.873945i	0.999986	−	0.00528755i	$-0.00168309\pi$
$458$		−	534.856i		−	1.16781i
$459$		0			0
$460$	265.535			0.577251
$461$	632.194	+	364.998i	1.37135	+	0.791752i	0.991099	−	0.133129i	$-0.0425026\pi$
$461$	632.194	+	364.998i	1.37135	+	0.791752i	0.380256	+	0.924881i	$0.375836\pi$
$462$		0			0
$463$	4.69689	+	8.13525i	0.0101445	+	0.0175707i	0.871053	−	0.491189i	$-0.163438\pi$
$463$	4.69689	+	8.13525i	0.0101445	+	0.0175707i	−0.860909	+	0.508760i	$0.830104\pi$
$464$	10.3989	−	6.00383i	0.0224115	−	0.0129393i
$465$		0			0
$466$	−387.230	+	670.703i	−0.830966	+	1.43928i
$467$		−	56.2899i		−	0.120535i	−0.998182	−	0.0602676i	$-0.980805\pi$
$467$		−	56.2899i		−	0.120535i	0.998182	−	0.0602676i	$-0.0191954\pi$
$468$		0			0
$469$	814.436			1.73654
$470$	−158.925	−	91.7551i	−0.338137	−	0.195224i
$471$		0			0
$472$	−0.178836	−	0.309754i	−0.000378891	−	0.000656258i
$473$	−1.98102	+	1.14375i	−0.00418821	+	0.00241807i
$474$		0			0
$475$	66.5328	−	115.238i	0.140069	−	0.242607i
$476$		−	845.084i		−	1.77539i
$477$		0			0
$478$	−144.482			−0.302263
$479$	649.023	+	374.714i	1.35495	+	0.782283i	0.988939	−	0.148325i	$-0.0473882\pi$
$479$	649.023	+	374.714i	1.35495	+	0.782283i	0.366016	+	0.930609i	$0.380722\pi$
$480$		0			0
$481$	−210.213	−	364.100i	−0.437034	−	0.756965i
$482$	468.050	−	270.229i	0.971058	−	0.560641i
$483$		0			0
$484$	242.106	−	419.341i	0.500220	−	0.866406i
$485$			154.241i			0.318023i
$486$		0			0
$487$	−440.830			−0.905196			−0.452598	−	0.891715i	$-0.649503\pi$
$487$	−440.830			−0.905196			−0.452598	+	0.891715i	$0.649503\pi$
$488$	−0.0891860	−	0.0514916i	−0.000182758	−	0.000105515i
$489$		0			0
$490$	44.8893	+	77.7505i	0.0916108	+	0.158675i
$491$	327.433	−	189.043i	0.666869	−	0.385017i	−0.128020	−	0.991772i	$-0.540862\pi$
$491$	327.433	−	189.043i	0.666869	−	0.385017i	0.794889	+	0.606755i	$0.207529\pi$
$492$		0			0
$493$	−9.97268	+	17.2732i	−0.0202286	+	0.0350369i
$494$		−	653.385i		−	1.32264i
$495$		0			0
$496$	553.991			1.11692
$497$	−78.1675	−	45.1300i	−0.157279	−	0.0908049i
$498$		0			0
$499$	286.566	+	496.347i	0.574281	+	0.994684i	0.996119	+	0.0880128i	$0.0280516\pi$
$499$	286.566	+	496.347i	0.574281	+	0.994684i	−0.421838	+	0.906671i	$0.638615\pi$
$500$	38.7484	−	22.3714i	0.0774968	−	0.0447428i
$501$		0			0
$502$	−239.148	+	414.216i	−0.476390	+	0.825132i
$503$		−	300.050i		−	0.596522i	−0.954484	−	0.298261i	$-0.903593\pi$
$503$		−	300.050i		−	0.596522i	0.954484	−	0.298261i	$-0.0964065\pi$
$504$		0			0
$505$	−40.6269			−0.0804494
$506$	−4.99388	−	2.88322i	−0.00986933	−	0.00569806i
$507$		0			0
$508$	381.673	+	661.077i	0.751325	+	1.30133i
$509$	−643.429	+	371.484i	−1.26410	+	0.729831i	−0.973866	−	0.227124i	$-0.927068\pi$
$509$	−643.429	+	371.484i	−1.26410	+	0.729831i	−0.290238	+	0.956954i	$0.593735\pi$
$510$		0			0
$511$	−214.463	+	371.461i	−0.419693	+	0.726930i
$512$			724.164i			1.41438i
$513$		0			0
$514$	807.635			1.57127
$515$	92.1971	+	53.2300i	0.179023	+	0.103359i
$516$		0			0
$517$	0.996528	+	1.72604i	0.00192752	+	0.00333856i
$518$	−943.361	+	544.650i	−1.82116	+	1.05145i
$519$		0			0
$520$	0.0525720	−	0.0910574i	0.000101100	−	0.000175110i
$521$		−	682.606i		−	1.31018i	−0.755549	−	0.655092i	$-0.772630\pi$
$521$		−	682.606i		−	1.31018i	0.755549	−	0.655092i	$-0.227370\pi$
$522$		0			0
$523$	430.700			0.823518			0.411759	−	0.911293i	$-0.364915\pi$
$523$	430.700			0.823518			0.411759	+	0.911293i	$0.364915\pi$
$524$	99.4367	+	57.4098i	0.189765	+	0.109561i
$525$		0			0
$526$	101.272	+	175.409i	0.192533	+	0.333477i
$527$	−796.925	+	460.105i	−1.51219	+	0.873064i
$528$		0			0
$529$	175.759	−	304.424i	0.332249	−	0.575471i
$530$		−	44.2678i		−	0.0835241i
$531$		0			0
$532$	−846.642			−1.59143
$533$	−454.916	−	262.646i	−0.853500	−	0.492769i
$534$		0			0
$535$	−167.347	−	289.854i	−0.312798	−	0.541783i
$536$	−0.480701	+	0.277533i	−0.000896830	+	0.000517785i
$537$		0			0
$538$	−56.0751	+	97.1249i	−0.104229	+	0.180529i
$539$		−	0.975061i		−	0.00180902i
$540$		0			0
$541$	−297.028			−0.549034			−0.274517	−	0.961582i	$-0.588518\pi$
$541$	−297.028			−0.549034			−0.274517	+	0.961582i	$0.588518\pi$
$542$	−974.601	−	562.686i	−1.79816	−	1.03817i
$543$		0			0
$544$	−601.150	−	1041.22i	−1.10505	−	1.91401i
$545$	−71.3659	+	41.2031i	−0.130947	+	0.0756020i
$546$		0			0
$547$	−425.338	+	736.708i	−0.777584	+	1.34681i	0.155747	+	0.987797i	$0.450222\pi$
$547$	−425.338	+	736.708i	−0.777584	+	1.34681i	−0.933331	+	0.359018i	$0.883112\pi$
$548$		−	469.634i		−	0.856996i
$549$		0			0
$550$	−0.971646			−0.00176663
$551$	17.3050	+	9.99107i	0.0314066	+	0.0181326i
$552$		0			0
$553$	−212.529	−	368.111i	−0.384320	−	0.665662i
$554$	335.422	−	193.656i	0.605454	−	0.349559i
$555$		0			0
$556$	62.9092	−	108.962i	0.113146	−	0.195975i
$557$			571.248i			1.02558i	0.858514	+	0.512790i	$0.171388\pi$
$557$			571.248i			1.02558i	−0.858514	+	0.512790i	$0.828612\pi$
$558$		0			0
$559$	−288.998			−0.516991
$560$	246.186	+	142.136i	0.439618	+	0.253814i
$561$		0			0
$562$	−623.482	−	1079.90i	−1.10940	−	1.92154i
$563$	−451.760	+	260.824i	−0.802415	+	0.463275i	−0.844315	−	0.535847i	$-0.819992\pi$
$563$	−451.760	+	260.824i	−0.802415	+	0.463275i	0.0418998	+	0.999122i	$0.486659\pi$
$564$		0			0
$565$	68.5737	−	118.773i	0.121369	−	0.210218i
$566$			476.177i			0.841303i
$567$		0			0
$568$	0.0615152			0.000108301
$569$	−912.977	−	527.108i	−1.60453	−	0.926376i	−0.990565	−	0.137042i	$-0.956240\pi$
$569$	−912.977	−	527.108i	−1.60453	−	0.926376i	−0.613964	−	0.789334i	$-0.710426\pi$
$570$		0			0
$571$	−182.461	−	316.032i	−0.319546	−	0.553470i	0.660847	−	0.750521i	$-0.270197\pi$
$571$	−182.461	−	316.032i	−0.319546	−	0.553470i	−0.980393	+	0.197050i	$0.936864\pi$
$572$	−2.06641	+	1.19304i	−0.00361260	+	0.00208574i
$573$		0			0
$574$	−680.498	+	1178.66i	−1.18554	+	2.05341i
$575$		−	148.368i		−	0.258031i
$576$		0			0
$577$	77.3098			0.133986			0.0669929	−	0.997753i	$-0.478660\pi$
$577$	77.3098			0.133986			0.0669929	+	0.997753i	$0.478660\pi$
$578$	1020.71	+	589.307i	1.76593	+	1.01956i
$579$		0			0
$580$	3.35946	+	5.81875i	0.00579217	+	0.0100323i
$581$	242.497	−	140.006i	0.417379	−	0.240974i
$582$		0			0
$583$	−0.240390	+	0.416368i	−0.000412333	+	0.000714182i
$584$		−	0.292327i		−	0.000500561i
$585$		0			0
$586$	−1269.76			−2.16683
$587$	113.472	+	65.5132i	0.193309	+	0.111607i	0.593531	−	0.804811i	$-0.297734\pi$
$587$	113.472	+	65.5132i	0.193309	+	0.111607i	−0.400222	+	0.916418i	$0.631067\pi$
$588$		0			0
$589$	460.953	+	798.394i	0.782603	+	1.35551i
$590$	−361.639	+	208.792i	−0.612947	+	0.353885i
$591$		0			0
$592$	−387.343	+	670.898i	−0.654296	+	1.13327i
$593$		−	525.116i		−	0.885525i	−0.896639	−	0.442762i	$-0.853998\pi$
$593$		−	525.116i		−	0.885525i	0.896639	−	0.442762i	$-0.146002\pi$
$594$		0			0
$595$	−472.190			−0.793597
$596$	−92.4246	−	53.3614i	−0.155075	−	0.0895325i
$597$		0			0
$598$	−364.261	−	630.919i	−0.609132	−	1.05505i
$599$	851.013	−	491.333i	1.42072	−	0.820255i	0.424363	−	0.905492i	$-0.360498\pi$
$599$	851.013	−	491.333i	1.42072	−	0.820255i	0.996361	+	0.0852374i	$0.0271649\pi$
$600$		0			0
$601$	415.553	−	719.759i	0.691436	−	1.19760i	−0.279932	−	0.960020i	$-0.590312\pi$
$601$	415.553	−	719.759i	0.691436	−	1.19760i	0.971367	−	0.237582i	$-0.0763549\pi$
$602$			748.775i			1.24381i
$603$		0			0
$604$	405.166			0.670805
$605$	−234.306	−	135.277i	−0.387283	−	0.223598i
$606$		0			0
$607$	83.8988	+	145.317i	0.138219	+	0.239402i	0.926822	−	0.375500i	$-0.122529\pi$
$607$	83.8988	+	145.317i	0.138219	+	0.239402i	−0.788604	+	0.614902i	$0.789196\pi$
$608$	−1043.14	+	602.258i	−1.71569	+	0.990556i
$609$		0			0
$610$	−60.1166	+	104.125i	−0.0985519	+	0.170697i
$611$			251.799i			0.412110i
$612$		0			0
$613$	833.750			1.36011			0.680057	−	0.733159i	$-0.261955\pi$
$613$	833.750			1.36011			0.680057	+	0.733159i	$0.261955\pi$
$614$	1206.55	+	696.601i	1.96506	+	1.13453i
$615$		0			0
$616$	0.00147935	+	0.00256231i	2.40154e−6	+	4.15959e-6i
$617$	40.4387	−	23.3473i	0.0655408	−	0.0378400i	−0.466872	−	0.884325i	$-0.654619\pi$
$617$	40.4387	−	23.3473i	0.0655408	−	0.0378400i	0.532412	+	0.846485i	$0.321286\pi$
$618$		0			0
$619$	499.429	−	865.037i	0.806833	−	1.39748i	−0.108214	−	0.994128i	$-0.534513\pi$
$619$	499.429	−	865.037i	0.806833	−	1.39748i	0.915047	−	0.403347i	$-0.132153\pi$
$620$			309.987i			0.499979i
$621$		0			0
$622$	233.708			0.375737
$623$	−515.883	−	297.845i	−0.828063	−	0.478082i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	471.277	−	272.092i	0.752839	−	0.434652i
$627$		0			0
$628$	559.019	−	968.249i	0.890157	−	1.54180i
$629$		−	1286.80i		−	2.04578i
$630$		0			0
$631$	−676.922			−1.07278			−0.536388	−	0.843971i	$-0.680212\pi$
$631$	−676.922			−1.07278			−0.536388	+	0.843971i	$0.680212\pi$
$632$	0.250880	+	0.144846i	0.000396962	+	0.000229186i
$633$		0			0
$634$	−51.6190	−	89.4067i	−0.0814180	−	0.141020i
$635$	369.377	−	213.260i	0.581695	−	0.335842i
$636$		0			0
$637$	61.5938	−	106.684i	0.0966936	−	0.167478i
$638$		−	0.145910i		−	0.000228699i
$639$		0			0
$640$	−0.387666			−0.000605729
$641$	−620.711	−	358.367i	−0.968347	−	0.559076i	−0.0696153	−	0.997574i	$-0.522177\pi$
$641$	−620.711	−	358.367i	−0.968347	−	0.559076i	−0.898732	+	0.438498i	$0.855511\pi$
$642$		0			0
$643$	176.092	+	305.000i	0.273860	+	0.474339i	0.969847	−	0.243715i	$-0.0783662\pi$
$643$	176.092	+	305.000i	0.273860	+	0.474339i	−0.695987	+	0.718054i	$0.745033\pi$
$644$	−817.531	+	472.002i	−1.26946	+	0.732922i
$645$		0			0
$646$	999.904	−	1731.88i	1.54784	−	2.68094i
$647$			719.658i			1.11230i	0.831082	+	0.556150i	$0.187722\pi$
$647$			719.658i			1.11230i	−0.831082	+	0.556150i	$0.812278\pi$
$648$		0			0
$649$	4.53528			0.00698810
$650$	−106.310	−	61.3781i	−0.163554	−	0.0944279i
$651$		0			0
$652$	493.788	+	855.266i	0.757344	+	1.31176i
$653$	925.220	−	534.176i	1.41688	−	0.818034i	0.420853	−	0.907129i	$-0.361731\pi$
$653$	925.220	−	534.176i	1.41688	−	0.818034i	0.996023	+	0.0890951i	$0.0283975\pi$
$654$		0			0
$655$	32.0777	−	55.5602i	0.0489736	−	0.0848248i
$656$			967.911i			1.47547i
$657$		0			0
$658$	652.396			0.991484
$659$	−896.771	−	517.751i	−1.36081	−	0.785662i	−0.371075	−	0.928603i	$-0.621011\pi$
$659$	−896.771	−	517.751i	−1.36081	−	0.785662i	−0.989731	+	0.142941i	$0.954344\pi$
$660$		0			0
$661$	559.316	+	968.764i	0.846166	+	1.46560i	0.884604	+	0.466342i	$0.154428\pi$
$661$	559.316	+	968.764i	0.846166	+	1.46560i	−0.0384381	+	0.999261i	$0.512238\pi$
$662$	697.641	−	402.783i	1.05384	−	0.608434i
$663$		0			0
$664$	−0.0954187	+	0.165270i	−0.000143703	+	0.000248901i
$665$			473.061i			0.711370i
$666$		0			0
$667$	22.2800			0.0334033
$668$	−291.934	−	168.548i	−0.437026	−	0.252317i
$669$		0			0
$670$	324.021	+	561.220i	0.483613	+	0.837642i
$671$	1.13087	−	0.652911i	0.00168536	−	0.000973042i
$672$		0			0
$673$	199.783	−	346.035i	0.296855	−	0.514168i	−0.678560	−	0.734545i	$-0.737396\pi$
$673$	199.783	−	346.035i	0.296855	−	0.514168i	0.975415	+	0.220377i	$0.0707289\pi$
$674$		−	692.431i		−	1.02735i
$675$		0			0
$676$	374.870			0.554541
$677$	−43.7403	−	25.2535i	−0.0646091	−	0.0373021i	0.467347	−	0.884074i	$-0.345210\pi$
$677$	−43.7403	−	25.2535i	−0.0646091	−	0.0373021i	−0.531957	+	0.846772i	$0.678543\pi$
$678$		0			0
$679$	−274.171	−	474.878i	−0.403786	−	0.699378i
$680$	0.278698	−	0.160907i	0.000409851	−	0.000236627i
$681$		0			0
$682$	3.36588	−	5.82988i	0.00493531	−	0.00854821i
$683$			857.907i			1.25609i	0.778179	+	0.628043i	$0.216144\pi$
$683$			857.907i			1.25609i	−0.778179	+	0.628043i	$0.783856\pi$
$684$		0			0
$685$	−262.408			−0.383077
$686$	677.835	+	391.348i	0.988097	+	0.570478i
$687$		0			0
$688$	266.256	+	461.170i	0.387001	+	0.670305i
$689$	−52.6033	+	30.3705i	−0.0763473	+	0.0440791i
$690$		0			0
$691$	106.360	−	184.220i	0.153921	−	0.266599i	−0.778744	−	0.627341i	$-0.784143\pi$
$691$	106.360	−	184.220i	0.153921	−	0.266599i	0.932666	+	0.360742i	$0.117476\pi$
$692$			758.248i			1.09573i
$693$		0			0
$694$	−716.236			−1.03204
$695$	−60.8824	−	35.1505i	−0.0876006	−	0.0505763i
$696$		0			0
$697$	−803.877	−	1392.36i	−1.15334	−	1.99764i
$698$	1271.52	−	734.114i	1.82167	−	1.05174i
$699$		0			0
$700$	−79.5324	+	137.754i	−0.113618	+	0.196792i
$701$		−	991.279i		−	1.41409i	−0.707167	−	0.707046i	$-0.750027\pi$
$701$		−	991.279i		−	1.41409i	0.707167	−	0.707046i	$-0.249973\pi$
$702$		0			0
$703$	−1289.17			−1.83381
$704$	3.81125	+	2.20043i	0.00541371	+	0.00312560i
$705$		0			0
$706$	972.869	+	1685.06i	1.37800	+	2.38677i
$707$	125.082	−	72.2163i	0.176920	−	0.102145i
$708$		0			0
$709$	−403.573	+	699.009i	−0.569215	+	0.985909i	0.427429	+	0.904049i	$0.359419\pi$
$709$	−403.573	+	699.009i	−0.569215	+	0.985909i	−0.996644	+	0.0818599i	$0.973914\pi$
$710$		−	71.8193i		−	0.101154i
$711$		0			0
$712$	0.405983			0.000570200
$713$	890.207	+	513.961i	1.24854	+	0.720843i
$714$		0			0
$715$	0.666611	+	1.15460i	0.000932324	+	0.00161483i
$716$	385.485	−	222.560i	0.538387	−	0.310838i
$717$		0			0
$718$	−481.581	+	834.122i	−0.670725	+	1.16173i
$719$			61.3194i			0.0852843i	0.999090	+	0.0426422i	$0.0135775\pi$
$719$			61.3194i			0.0852843i	−0.999090	+	0.0426422i	$0.986422\pi$
$720$		0			0
$721$	−378.476			−0.524931
$722$	−850.706	−	491.155i	−1.17826	−	0.680270i
$723$		0			0
$724$	438.987	+	760.348i	0.606336	+	1.05020i
$725$	3.25122	−	1.87710i	0.00448445	−	0.00258910i
$726$		0			0
$727$	227.024	−	393.217i	0.312275	−	0.540876i	−0.666579	−	0.745434i	$-0.732242\pi$
$727$	227.024	−	393.217i	0.312275	−	0.540876i	0.978855	+	0.204558i	$0.0655756\pi$
$728$			0.373797i			0.000513458i
$729$		0			0
$730$	−341.294			−0.467526
$731$	−766.028	−	442.266i	−1.04792	−	0.605015i
$732$		0			0
$733$	−146.499	−	253.744i	−0.199863	−	0.346172i	0.748621	−	0.662998i	$-0.230716\pi$
$733$	−146.499	−	253.744i	−0.199863	−	0.346172i	−0.948484	+	0.316826i	$0.897383\pi$
$734$	−653.388	+	377.234i	−0.890174	+	0.513942i
$735$		0			0
$736$	−671.516	+	1163.10i	−0.912386	+	1.58030i
$737$		−	7.03821i		−	0.00954981i
$738$		0			0
$739$	−228.122			−0.308690			−0.154345	−	0.988017i	$-0.549327\pi$
$739$	−228.122			−0.308690			−0.154345	+	0.988017i	$0.549327\pi$
$740$	−375.403	−	216.739i	−0.507301	−	0.292890i
$741$		0			0
$742$	78.6881	+	136.292i	0.106049	+	0.183682i
$743$	177.764	−	102.632i	0.239252	−	0.138132i	−0.375581	−	0.926790i	$-0.622557\pi$
$743$	177.764	−	102.632i	0.239252	−	0.138132i	0.614833	+	0.788657i	$0.289223\pi$
$744$		0			0
$745$	−29.8156	+	51.6422i	−0.0400210	+	0.0693184i
$746$			794.672i			1.06524i
$747$		0			0
$748$	−7.30306			−0.00976345
$749$	1030.46	+	594.935i	1.37578	+	0.794306i
$750$		0			0
$751$	−96.3048	−	166.805i	−0.128235	−	0.222110i	0.794758	−	0.606927i	$-0.207598\pi$
$751$	−96.3048	−	166.805i	−0.128235	−	0.222110i	−0.922993	+	0.384817i	$0.874265\pi$
$752$	401.810	−	231.985i	0.534322	−	0.308491i
$753$		0			0
$754$	9.21701	−	15.9643i	0.0122241	−	0.0211728i
$755$		−	226.386i		−	0.299850i
$756$		0			0
$757$	750.204			0.991023			0.495512	−	0.868601i	$-0.334981\pi$
$757$	750.204			0.991023			0.495512	+	0.868601i	$0.334981\pi$
$758$	1303.65	+	752.665i	1.71986	+	0.992962i
$759$		0			0
$760$	−0.161203	−	0.279212i	−0.000212110	−	0.000367385i
$761$	−897.102	+	517.942i	−1.17885	+	0.680607i	−0.955747	−	0.294188i	$-0.904951\pi$
$761$	−897.102	+	517.942i	−1.17885	+	0.680607i	−0.223099	+	0.974796i	$0.571617\pi$
$762$		0			0
$763$	146.481	−	253.713i	0.191980	−	0.332520i
$764$			146.608i			0.191896i
$765$		0			0
$766$	1035.21			1.35145
$767$	496.215	+	286.490i	0.646956	+	0.373520i
$768$		0			0
$769$	92.5951	+	160.379i	0.120410	+	0.208556i	0.919929	−	0.392084i	$-0.128246\pi$
$769$	92.5951	+	160.379i	0.120410	+	0.208556i	−0.799520	+	0.600640i	$0.794912\pi$
$770$	2.99151	−	1.72715i	0.00388507	−	0.00224305i
$771$		0			0
$772$	305.044	−	528.352i	0.395135	−	0.684393i
$773$		−	1178.69i		−	1.52482i	−0.647093	−	0.762411i	$-0.724015\pi$
$773$		−	1178.69i		−	1.52482i	0.647093	−	0.762411i	$-0.275985\pi$
$774$		0			0
$775$	173.205			0.223491
$776$	0.323645	+	0.186857i	0.000417068	+	0.000240794i
$777$		0			0
$778$	−134.400	−	232.788i	−0.172751	−	0.299214i
$779$	−1394.92	+	805.359i	−1.79066	+	1.03384i
$780$		0			0
$781$	−0.390005	+	0.675509i	−0.000499367	+	0.000864928i
$782$		−	2229.78i		−	2.85138i
$783$		0			0
$784$	−226.988			−0.289525
$785$	−541.009	−	312.351i	−0.689183	−	0.397900i
$786$		0			0
$787$	57.1483	+	98.9837i	0.0726153	+	0.125773i	0.900047	−	0.435793i	$-0.143532\pi$
$787$	57.1483	+	98.9837i	0.0726153	+	0.125773i	−0.827431	+	0.561567i	$0.810199\pi$
$788$	124.027	−	71.6069i	0.157394	−	0.0908717i
$789$		0			0
$790$	169.108	−	292.903i	0.214061	−	0.370764i
$791$			487.572i			0.616400i
$792$		0			0
$793$	164.975			0.208040
$794$	−1694.49	−	978.315i	−2.13412	−	1.23214i
$795$		0			0
$796$	−209.253	−	362.436i	−0.262880	−	0.455322i
$797$	942.410	−	544.101i	1.18245	−	0.682686i	0.225868	−	0.974158i	$-0.427478\pi$
$797$	942.410	−	544.101i	1.18245	−	0.682686i	0.956579	+	0.291472i	$0.0941449\pi$
$798$		0			0
$799$	−385.340	+	667.428i	−0.482278	+	0.835330i
$800$			226.301i			0.282877i
$801$		0			0
$802$	188.912			0.235552
$803$	3.21010	+	1.85335i	0.00399763	+	0.00230803i
$804$		0			0
$805$	263.731	+	456.795i	0.327616	+	0.567447i
$806$	736.538	−	425.240i	0.913819	−	0.527594i
$807$		0			0
$808$	−0.0492178	+	0.0852478i	−6.09131e−5	+	0.000105505i
$809$			1058.49i			1.30840i	0.756322	+	0.654199i	$0.226994\pi$
$809$			1058.49i			1.30840i	−0.756322	+	0.654199i	$0.773006\pi$
$810$		0			0
$811$	−325.951			−0.401913			−0.200956	−	0.979600i	$-0.564405\pi$
$811$	−325.951			−0.401913			−0.200956	+	0.979600i	$0.564405\pi$
$812$	−20.6862	−	11.9432i	−0.0254756	−	0.0147084i
$813$		0			0
$814$	4.70676	+	8.15235i	0.00578226	+	0.0100152i
$815$	477.880	−	275.904i	0.586355	−	0.338532i
$816$		0			0
$817$	−443.082	+	767.440i	−0.542328	+	0.939339i
$818$			314.267i			0.384190i
$819$		0			0
$820$	−541.597			−0.660485
$821$	494.193	+	285.323i	0.601941	+	0.347531i	0.769805	−	0.638280i	$-0.220354\pi$
$821$	494.193	+	285.323i	0.601941	+	0.347531i	−0.167864	+	0.985810i	$0.553687\pi$
$822$		0			0
$823$	580.756	+	1005.90i	0.705658	+	1.22223i	0.966454	+	0.256841i	$0.0826817\pi$
$823$	580.756	+	1005.90i	0.705658	+	1.22223i	−0.260796	+	0.965394i	$0.583985\pi$
$824$	0.223386	−	0.128972i	0.000271099	−	0.000156519i
$825$		0			0
$826$	742.277	−	1285.66i	0.898640	−	1.55649i
$827$		−	422.843i		−	0.511297i	−0.966770	−	0.255649i	$-0.917711\pi$
$827$		−	422.843i		−	0.511297i	0.966770	−	0.255649i	$-0.0822890\pi$
$828$		0			0
$829$	455.988			0.550046			0.275023	−	0.961438i	$-0.411315\pi$
$829$	455.988			0.550046			0.275023	+	0.961438i	$0.411315\pi$
$830$	192.954	+	111.402i	0.232474	+	0.134219i
$831$		0			0
$832$	277.998	+	481.507i	0.334133	+	0.578735i
$833$	326.525	−	188.520i	0.391987	−	0.226314i
$834$		0			0
$835$	−94.1761	+	163.118i	−0.112786	+	0.195351i
$836$			7.31652i			0.00875182i
$837$		0			0
$838$	−1090.20			−1.30096
$839$	900.311	+	519.795i	1.07308	+	0.619541i	0.929020	−	0.370029i	$-0.120652\pi$
$839$	900.311	+	519.795i	1.07308	+	0.619541i	0.144056	+	0.989570i	$0.453985\pi$
$840$		0			0
$841$	−420.218	−	727.839i	−0.499665	−	0.865445i
$842$	−158.832	+	91.7019i	−0.188637	+	0.108910i
$843$		0			0
$844$	−217.859	+	377.343i	−0.258127	+	0.447089i
$845$		−	209.458i		−	0.247880i
$846$		0			0
$847$	961.844			1.13559
$848$	96.9277	+	55.9612i	0.114302	+	0.0659920i
$849$		0			0
$850$	−187.859	−	325.382i	−0.221011	−	0.382802i
$851$	−1244.84	+	718.709i	−1.46280	+	0.844547i
$852$		0			0
$853$	366.610	−	634.988i	0.429789	−	0.744417i	−0.567065	−	0.823673i	$-0.691921\pi$
$853$	366.610	−	634.988i	0.429789	−	0.744417i	0.996854	+	0.0792562i	$0.0252545\pi$
$854$		−	427.441i		−	0.500516i
$855$		0			0
$856$	−0.810936			−0.000947355
$857$	−163.543	−	94.4217i	−0.190832	−	0.110177i	0.401540	−	0.915842i	$-0.368475\pi$
$857$	−163.543	−	94.4217i	−0.190832	−	0.110177i	−0.592372	+	0.805665i	$0.701808\pi$
$858$		0			0
$859$	−626.637	−	1085.37i	−0.729496	−	1.26352i	−0.957096	−	0.289770i	$-0.906421\pi$
$859$	−626.637	−	1085.37i	−0.729496	−	1.26352i	0.227600	−	0.973755i	$-0.426912\pi$
$860$	−258.049	+	148.984i	−0.300057	+	0.173238i
$861$		0			0
$862$	290.933	−	503.911i	0.337509	−	0.584583i
$863$			1407.42i			1.63085i	0.578865	+	0.815423i	$0.303496\pi$
$863$			1407.42i			1.63085i	−0.578865	+	0.815423i	$0.696504\pi$
$864$		0			0
$865$	423.671			0.489793
$866$	847.710	+	489.426i	0.978880	+	0.565156i
$867$		0			0
$868$	−551.017	−	954.390i	−0.634813	−	1.09953i
$869$	−3.18115	+	1.83664i	−0.00366070	+	0.00211350i
$870$		0			0
$871$	444.598	−	770.066i	0.510445	−	0.884117i
$872$			0.199663i			0.000228972i
$873$		0			0
$874$	−2233.89			−2.55594
$875$	76.9701	+	44.4387i	0.0879658	+	0.0507871i
$876$		0			0
$877$	387.079	+	670.440i	0.441367	+	0.764470i	0.997791	−	0.0664286i	$-0.0211605\pi$
$877$	387.079	+	670.440i	0.441367	+	0.764470i	−0.556424	+	0.830898i	$0.687827\pi$
$878$	−1353.39	+	781.378i	−1.54144	+	0.889952i
$879$		0			0
$880$	1.22831	−	2.12750i	0.00139581	−	0.00241761i
$881$		−	1442.00i		−	1.63678i	−0.574662	−	0.818391i	$-0.694866\pi$
$881$		−	1442.00i		−	1.63678i	0.574662	−	0.818391i	$-0.305134\pi$
$882$		0			0
$883$	1399.40			1.58483			0.792415	−	0.609983i	$-0.208824\pi$
$883$	1399.40			1.58483			0.792415	+	0.609983i	$0.208824\pi$
$884$	−799.044	−	461.328i	−0.903896	−	0.521865i
$885$		0			0
$886$	61.3841	+	106.320i	0.0692823	+	0.120000i
$887$	−1215.08	+	701.524i	−1.36987	+	0.790895i	−0.990911	−	0.134518i	$-0.957051\pi$
$887$	−1215.08	+	701.524i	−1.36987	+	0.790895i	−0.378959	+	0.925413i	$0.623718\pi$
$888$		0			0
$889$	−758.158	+	1313.17i	−0.852822	+	1.47713i
$890$		−	473.987i		−	0.532569i
$891$		0			0
$892$	1076.39			1.20672
$893$	668.659	+	386.050i	0.748778	+	0.432307i
$894$		0			0
$895$	−124.355	−	215.389i	−0.138944	−	0.240659i
$896$	1.19355	−	0.689096i	0.00133209	−	0.000769080i
$897$		0			0
$898$	922.018	−	1596.98i	1.02675	−	1.77838i
$899$			26.0098i			0.0289319i
$900$		0			0
$901$	−185.909			−0.206337
$902$	10.1857	+	5.88074i	0.0112924	+	0.00651966i
$903$		0			0
$904$	−0.166148	−	0.287777i	−0.000183792	−	0.000318338i
$905$	424.844	−	245.284i	0.469441	−	0.271032i
$906$		0			0
$907$	456.415	−	790.534i	0.503214	−	0.871592i	−0.496780	−	0.867877i	$-0.665484\pi$
$907$	456.415	−	790.534i	0.503214	−	0.871592i	0.999993	−	0.00371472i	$-0.00118244\pi$
$908$			331.505i			0.365093i
$909$		0			0
$910$	436.410			0.479572
$911$	757.008	+	437.059i	0.830963	+	0.479757i	0.854182	−	0.519973i	$-0.174058\pi$
$911$	757.008	+	437.059i	0.830963	+	0.479757i	−0.0232190	+	0.999730i	$0.507391\pi$
$912$		0			0
$913$	−1.20991	−	2.09562i	−0.00132520	−	0.00229531i
$914$	−1129.79	+	652.284i	−1.23609	+	0.713658i
$915$		0			0
$916$	−378.336	+	655.297i	−0.413030	+	0.715390i
$917$			228.079i			0.248723i
$918$		0			0
$919$	−234.165			−0.254804			−0.127402	−	0.991851i	$-0.540664\pi$
$919$	−234.165			−0.254804			−0.127402	+	0.991851i	$0.540664\pi$
$920$	−0.311321	−	0.179741i	−0.000338392	−	0.000195371i
$921$		0			0
$922$	−1032.49	−	1788.33i	−1.11984	−	1.93962i
$923$	−85.3427	+	49.2726i	−0.0924623	+	0.0533831i
$924$		0			0
$925$	−121.103	+	209.756i	−0.130922	+	0.226763i
$926$		−	26.5728i		−	0.0286963i
$927$		0			0
$928$	−33.9831			−0.0366197
$929$	−200.544	−	115.784i	−0.215870	−	0.124633i	0.388166	−	0.921589i	$-0.373109\pi$
$929$	−200.544	−	115.784i	−0.215870	−	0.124633i	−0.604037	+	0.796957i	$0.706442\pi$
$930$		0			0
$931$	−188.867	−	327.127i	−0.202865	−	0.351372i
$932$	948.857	−	547.823i	1.01809	−	0.587793i
$933$		0			0
$934$	−79.6155	+	137.898i	−0.0852414	+	0.147643i
$935$			4.08058i			0.00436426i
$936$		0			0
$937$	−140.899			−0.150372			−0.0751861	−	0.997170i	$-0.523955\pi$
$937$	−140.899			−0.150372			−0.0751861	+	0.997170i	$0.523955\pi$
$938$	−1995.19	−	1151.92i	−2.12707	−	1.22806i
$939$		0			0
$940$	129.808	+	224.834i	0.138094	+	0.239185i
$941$	442.126	−	255.262i	0.469847	−	0.271266i	−0.246329	−	0.969186i	$-0.579224\pi$
$941$	442.126	−	255.262i	0.469847	−	0.271266i	0.716176	+	0.697920i	$0.245891\pi$
$942$		0			0
$943$	−897.972	+	1555.33i	−0.952251	+	1.64935i
$944$		−	1055.78i		−	1.11841i
$945$		0			0
$946$	6.47077			0.00684014
$947$	724.176	+	418.103i	0.764706	+	0.441503i	0.830983	−	0.556298i	$-0.187779\pi$
$947$	724.176	+	418.103i	0.764706	+	0.441503i	−0.0662770	+	0.997801i	$0.521112\pi$
$948$		0			0
$949$	234.149	+	405.559i	0.246733	+	0.427354i
$950$	−325.982	+	188.206i	−0.343139	+	0.198111i
$951$		0			0
$952$	−0.572039	+	0.990800i	−0.000600881	+	0.00104076i
$953$			914.987i			0.960112i	0.877238	+	0.480056i	$0.159384\pi$
$953$			914.987i			0.960112i	−0.877238	+	0.480056i	$0.840616\pi$
$954$		0			0
$955$	81.9174			0.0857773
$956$	177.017	+	102.201i	0.185164	+	0.106904i
$957$		0			0
$958$	−1059.98	−	1835.93i	−1.10645	−	1.91642i
$959$	807.901	−	466.442i	0.842441	−	0.486384i
$960$		0			0
$961$	−119.501	+	206.982i	−0.124351	+	0.215382i
$962$			1189.29i			1.23627i
$963$		0			0
$964$	−764.597			−0.793150
$965$	−295.216	−	170.443i	−0.305924	−	0.176625i
$966$		0			0
$967$	636.666	+	1102.74i	0.658393	+	1.14037i	0.981032	+	0.193848i	$0.0620968\pi$
$967$	636.666	+	1102.74i	0.658393	+	1.14037i	−0.322639	+	0.946522i	$0.604570\pi$
$968$	−0.567704	+	0.327764i	−0.000586472	+	0.000338600i
$969$		0			0
$970$	218.156	−	377.857i	0.224903	−	0.389543i
$971$		−	1246.37i		−	1.28360i	−0.766872	−	0.641800i	$-0.778188\pi$
$971$		−	1246.37i		−	1.28360i	0.766872	−	0.641800i	$-0.221812\pi$
$972$		0			0
$973$	249.927			0.256862
$974$	1079.94	+	623.503i	1.10877	+	0.640147i
$975$		0			0
$976$	−151.993	−	263.260i	−0.155731	−	0.269734i
$977$	−1011.30	+	583.875i	−1.03511	+	0.597620i	−0.918444	−	0.395551i	$-0.870554\pi$
$977$	−1011.30	+	583.875i	−1.03511	+	0.597620i	−0.116665	+	0.993171i	$0.537220\pi$
$978$		0			0
$979$	−2.57392	+	4.45816i	−0.00262913	+	0.00455379i
$980$		−	127.012i		−	0.129604i
$981$		0			0
$982$	−1069.52			−1.08912
$983$	82.9062	+	47.8659i	0.0843400	+	0.0486937i	0.541577	−	0.840651i	$-0.317828\pi$
$983$	82.9062	+	47.8659i	0.0843400	+	0.0486937i	−0.457237	+	0.889345i	$0.651161\pi$
$984$		0			0
$985$	−40.0103	−	69.2999i	−0.0406196	−	0.0703553i
$986$	48.8618	−	28.2104i	0.0495556	−	0.0286109i
$987$		0			0
$988$	−462.179	+	800.517i	−0.467792	+	0.810240i
$989$			988.069i			0.999059i
$990$		0			0
$991$	−1725.68			−1.74135			−0.870674	−	0.491860i	$-0.836317\pi$
$991$	−1725.68			−1.74135			−0.870674	+	0.491860i	$0.836317\pi$
$992$	−1357.81	−	783.931i	−1.36876	−	0.790253i
$993$		0			0
$994$	127.662	+	221.118i	0.128433	+	0.222452i
$995$	−202.511	+	116.920i	−0.203529	+	0.117507i
$996$		0			0
$997$	−366.854	+	635.410i	−0.367958	+	0.637322i	−0.989246	−	0.146260i	$-0.953276\pi$
$997$	−366.854	+	635.410i	−0.367958	+	0.637322i	0.621288	+	0.783582i	$0.286610\pi$
$998$		−	1621.26i		−	1.62451i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.i.a.116.2		16
3.2	odd	2		45.3.i.a.11.7	✓	16
4.3	odd	2		2160.3.bs.c.1601.8		16
5.2	odd	4		675.3.i.c.224.13		32
5.3	odd	4		675.3.i.c.224.4		32
5.4	even	2		675.3.j.b.251.7		16
9.2	odd	6		405.3.c.a.161.4		16
9.4	even	3		45.3.i.a.41.7	yes	16
9.5	odd	6	inner	135.3.i.a.71.2		16
9.7	even	3		405.3.c.a.161.13		16
12.11	even	2		720.3.bs.c.641.5		16
15.2	even	4		225.3.i.b.74.4		32
15.8	even	4		225.3.i.b.74.13		32
15.14	odd	2		225.3.j.b.101.2		16
36.23	even	6		2160.3.bs.c.881.8		16
36.31	odd	6		720.3.bs.c.401.5		16
45.4	even	6		225.3.j.b.176.2		16
45.13	odd	12		225.3.i.b.149.4		32
45.14	odd	6		675.3.j.b.476.7		16
45.22	odd	12		225.3.i.b.149.13		32
45.23	even	12		675.3.i.c.449.13		32
45.32	even	12		675.3.i.c.449.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.7	✓	16	3.2	odd	2
45.3.i.a.41.7	yes	16	9.4	even	3
135.3.i.a.71.2		16	9.5	odd	6	inner
135.3.i.a.116.2		16	1.1	even	1	trivial
225.3.i.b.74.4		32	15.2	even	4
225.3.i.b.74.13		32	15.8	even	4
225.3.i.b.149.4		32	45.13	odd	12
225.3.i.b.149.13		32	45.22	odd	12
225.3.j.b.101.2		16	15.14	odd	2
225.3.j.b.176.2		16	45.4	even	6
405.3.c.a.161.4		16	9.2	odd	6
405.3.c.a.161.13		16	9.7	even	3
675.3.i.c.224.4		32	5.3	odd	4
675.3.i.c.224.13		32	5.2	odd	4
675.3.i.c.449.4		32	45.32	even	12
675.3.i.c.449.13		32	45.23	even	12
675.3.j.b.251.7		16	5.4	even	2
675.3.j.b.476.7		16	45.14	odd	6
720.3.bs.c.401.5		16	36.31	odd	6
720.3.bs.c.641.5		16	12.11	even	2
2160.3.bs.c.881.8		16	36.23	even	6
2160.3.bs.c.1601.8		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.44978 - 1.41438i) q^{2} +(2.00096 + 3.46576i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.97472 + 6.88441i) q^{7} -0.00541780i q^{8} +O(q^{10})\)	\(q+(-2.44978 - 1.41438i) q^{2} +(2.00096 + 3.46576i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.97472 + 6.88441i) q^{7} -0.00541780i q^{8} -6.32531 q^{10} +(0.0594938 + 0.0343488i) q^{11} +(4.33957 + 7.51635i) q^{13} +(19.4744 - 11.2435i) q^{14} +(7.99617 - 13.8498i) q^{16} +26.5641i q^{17} +26.6131 q^{19} +(7.74968 + 4.47428i) q^{20} +(-0.0971646 - 0.168294i) q^{22} +(25.6980 - 14.8368i) q^{23} +(2.50000 - 4.33013i) q^{25} -24.5512i q^{26} -31.8130 q^{28} +(0.650245 + 0.375419i) q^{29} +(17.3205 + 30.0000i) q^{31} +(-39.1965 + 22.6301i) q^{32} +(37.5719 - 65.0764i) q^{34} +17.7755i q^{35} -48.4411 q^{37} +(-65.1963 - 37.6411i) q^{38} +(-0.00605729 - 0.0104915i) q^{40} +(-52.4148 + 30.2617i) q^{41} +(-16.6490 + 28.8369i) q^{43} +0.274922i q^{44} -83.9395 q^{46} +(25.1252 + 14.5060i) q^{47} +(-7.09677 - 12.2920i) q^{49} +(-12.2489 + 7.07191i) q^{50} +(-17.3666 + 30.0798i) q^{52} +6.99851i q^{53} +0.153612 q^{55} +(0.0372984 + 0.0215342i) q^{56} +(-1.06197 - 1.83939i) q^{58} +(57.1733 - 33.0090i) q^{59} +(9.50414 - 16.4617i) q^{61} -97.9914i q^{62} +64.0613 q^{64} +(16.8071 + 9.70357i) q^{65} +(-51.2260 - 88.7261i) q^{67} +(-92.0649 + 53.1537i) q^{68} +(25.1413 - 43.5461i) q^{70} +11.3543i q^{71} +53.9568 q^{73} +(118.670 + 68.5142i) q^{74} +(53.2517 + 92.2347i) q^{76} +(-0.472942 + 0.273053i) q^{77} +(-26.7351 + 46.3066i) q^{79} -35.7599i q^{80} +171.207 q^{82} +(-30.5050 - 17.6121i) q^{83} +(29.6996 + 51.4412i) q^{85} +(81.5729 - 47.0961i) q^{86} +(0.000186095 - 0.000322326i) q^{88} +74.9349i q^{89} -68.9943 q^{91} +(102.841 + 59.3755i) q^{92} +(-41.0341 - 71.0732i) q^{94} +(51.5361 - 29.7544i) q^{95} +(-34.4893 + 59.7373i) q^{97} +40.1502i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 16 * q^4 + 2 * q^7	\( 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) \) 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Introduction

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