LMFDB - Embedded newform 405.4.e.r.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.95327307.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 85x^2 - 68*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.2
Root			$0.500000 + 3.26212i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.r.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.129356 - 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} -4.12208 q^{8} +O(q^{10})$	\(q+(-0.129356 - 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} -4.12208 q^{8} -1.29356 q^{10} +(-24.6423 - 42.6817i) q^{11} +(-36.0900 + 62.5097i) q^{13} +(-1.87792 + 3.25265i) q^{14} +(-31.1991 - 54.0383i) q^{16} -118.017 q^{17} +123.389 q^{19} +(-19.8327 - 34.3512i) q^{20} +(-6.37526 + 11.0423i) q^{22} +(-45.7442 + 79.2312i) q^{23} +(-12.5000 - 21.6506i) q^{25} +18.6739 q^{26} -115.168 q^{28} +(87.2001 + 151.035i) q^{29} +(23.1478 - 40.0932i) q^{31} +(-24.5599 + 42.5390i) q^{32} +(15.2662 + 26.4418i) q^{34} -72.5871 q^{35} +154.977 q^{37} +(-15.9611 - 27.6455i) q^{38} +(-10.3052 + 17.8491i) q^{40} +(-182.101 + 315.409i) q^{41} +(-62.8569 - 108.871i) q^{43} -390.978 q^{44} +23.6692 q^{46} +(-110.762 - 191.845i) q^{47} +(66.1222 - 114.527i) q^{49} +(-3.23390 + 5.60129i) q^{50} +(286.304 + 495.894i) q^{52} +13.6794 q^{53} -246.423 q^{55} +(29.9210 + 51.8247i) q^{56} +(22.5597 - 39.0746i) q^{58} +(119.543 - 207.055i) q^{59} +(27.2729 + 47.2380i) q^{61} -11.9772 q^{62} -486.477 q^{64} +(180.450 + 312.549i) q^{65} +(38.0279 - 65.8662i) q^{67} +(-468.118 + 810.804i) q^{68} +(9.38959 + 16.2633i) q^{70} -728.303 q^{71} -501.815 q^{73} +(-20.0472 - 34.7227i) q^{74} +(489.427 - 847.712i) q^{76} +(-357.742 + 619.628i) q^{77} +(-198.805 - 344.340i) q^{79} -311.991 q^{80} +94.2237 q^{82} +(-684.731 - 1185.99i) q^{83} +(-295.042 + 511.028i) q^{85} +(-16.2619 + 28.1664i) q^{86} +(101.577 + 175.937i) q^{88} -1468.13 q^{89} +1047.87 q^{91} +(362.892 + 628.547i) q^{92} +(-28.6554 + 49.6326i) q^{94} +(308.473 - 534.290i) q^{95} +(-167.512 - 290.139i) q^{97} -34.2133 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8}+O(q^{10}) $ 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8	$ 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98}+O(q^{100}) $ 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8 - 10 * q^10 + 38 * q^11 - 28 * q^13 - 108 * q^14 - 191 * q^16 + 38 * q^17 + 374 * q^19 + 115 * q^20 - 122 * q^22 - 81 * q^23 - 75 * q^25 - 832 * q^26 + 820 * q^28 + 160 * q^29 - 227 * q^31 - 569 * q^32 - 17 * q^34 - 440 * q^35 + 156 * q^37 - 757 * q^38 + 180 * q^40 - 338 * q^41 - 22 * q^43 - 3272 * q^44 - 2850 * q^46 - 472 * q^47 + 197 * q^49 - 25 * q^50 + 1566 * q^52 - 1042 * q^53 + 380 * q^55 - 1254 * q^56 + 2096 * q^58 + 140 * q^59 - 595 * q^61 - 2814 * q^62 - 1836 * q^64 + 140 * q^65 - 878 * q^67 - 3053 * q^68 + 540 * q^70 + 1204 * q^71 + 2588 * q^73 + 2878 * q^74 - 525 * q^76 + 288 * q^77 - 629 * q^79 - 1910 * q^80 - 3364 * q^82 - 1287 * q^83 + 95 * q^85 - 3730 * q^86 + 858 * q^88 - 4308 * q^89 - 880 * q^91 + 1959 * q^92 + 1108 * q^94 + 935 * q^95 - 1392 * q^97 + 5386 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.129356	−	0.224051i	−0.0457343	−	0.0792142i	0.842252	−	0.539084i	$-0.181229\pi$
$2$	−0.129356	−	0.224051i	−0.0457343	−	0.0792142i	−0.887986	+	0.459870i	$0.847896\pi$
$3$		0			0
$3$		0			0
$4$	3.96653	−	6.87024i	0.495817	−	0.858780i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	−7.25871	−	12.5725i	−0.391934	−	0.678849i	0.600771	−	0.799421i	$-0.294860\pi$
$7$	−7.25871	−	12.5725i	−0.391934	−	0.678849i	−0.992705	+	0.120572i	$0.961527\pi$
$8$	−4.12208			−0.182172
$9$		0			0
$10$	−1.29356			−0.0409060
$11$	−24.6423	−	42.6817i	−0.675448	−	1.16991i	−0.976338	−	0.216251i	$-0.930617\pi$
$11$	−24.6423	−	42.6817i	−0.675448	−	1.16991i	0.300890	−	0.953659i	$-0.402716\pi$
$12$		0			0
$13$	−36.0900	+	62.5097i	−0.769967	+	1.33362i	0.167614	+	0.985853i	$0.446394\pi$
$13$	−36.0900	+	62.5097i	−0.769967	+	1.33362i	−0.937580	+	0.347768i	$0.886940\pi$
$14$	−1.87792	+	3.25265i	−0.0358496	+	0.0620934i
$15$		0			0
$16$	−31.1991	−	54.0383i	−0.487485	−	0.844349i
$17$	−118.017			−1.68372			−0.841861	−	0.539694i	$-0.818540\pi$
$17$	−118.017			−1.68372			−0.841861	+	0.539694i	$0.818540\pi$
$18$		0			0
$19$	123.389			1.48986			0.744932	−	0.667141i	$-0.232482\pi$
$19$	123.389			1.48986			0.744932	+	0.667141i	$0.232482\pi$
$20$	−19.8327	−	34.3512i	−0.221736	−	0.384058i
$21$		0			0
$22$	−6.37526	+	11.0423i	−0.0617823	+	0.107010i
$23$	−45.7442	+	79.2312i	−0.414709	+	0.718298i	−0.995398	−	0.0958280i	$-0.969450\pi$
$23$	−45.7442	+	79.2312i	−0.414709	+	0.718298i	0.580688	+	0.814126i	$0.302783\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	18.6739			0.140856
$27$		0			0
$28$	−115.168			−0.777309
$29$	87.2001	+	151.035i	0.558367	+	0.967120i	0.997633	+	0.0687632i	$0.0219053\pi$
$29$	87.2001	+	151.035i	0.558367	+	0.967120i	−0.439266	+	0.898357i	$0.644761\pi$
$30$		0			0
$31$	23.1478	−	40.0932i	0.134112	−	0.232289i	−0.791146	−	0.611627i	$-0.790515\pi$
$31$	23.1478	−	40.0932i	0.134112	−	0.232289i	0.925258	+	0.379339i	$0.123849\pi$
$32$	−24.5599	+	42.5390i	−0.135676	+	0.234997i
$33$		0			0
$34$	15.2662	+	26.4418i	0.0770039	+	0.133375i
$35$	−72.5871			−0.350556
$36$		0			0
$37$	154.977			0.688595			0.344297	−	0.938861i	$-0.388117\pi$
$37$	154.977			0.688595			0.344297	+	0.938861i	$0.388117\pi$
$38$	−15.9611	−	27.6455i	−0.0681379	−	0.118018i
$39$		0			0
$40$	−10.3052	+	17.8491i	−0.0407349	+	0.0705549i
$41$	−182.101	+	315.409i	−0.693645	+	1.20143i	0.276990	+	0.960873i	$0.410663\pi$
$41$	−182.101	+	315.409i	−0.693645	+	1.20143i	−0.970635	+	0.240556i	$0.922670\pi$
$42$		0			0
$43$	−62.8569	−	108.871i	−0.222921	−	0.386110i	0.732773	−	0.680473i	$-0.238226\pi$
$43$	−62.8569	−	108.871i	−0.222921	−	0.386110i	−0.955694	+	0.294363i	$0.904892\pi$
$44$	−390.978			−1.33959
$45$		0			0
$46$	23.6692			0.0758658
$47$	−110.762	−	191.845i	−0.343750	−	0.595392i	0.641376	−	0.767227i	$-0.278364\pi$
$47$	−110.762	−	191.845i	−0.343750	−	0.595392i	−0.985126	+	0.171835i	$0.945031\pi$
$48$		0			0
$49$	66.1222	−	114.527i	0.192776	−	0.333898i
$50$	−3.23390	+	5.60129i	−0.00914686	+	0.0158428i
$51$		0			0
$52$	286.304	+	495.894i	0.763525	+	1.32246i
$53$	13.6794			0.0354530			0.0177265	−	0.999843i	$-0.494357\pi$
$53$	13.6794			0.0354530			0.0177265	+	0.999843i	$0.494357\pi$
$54$		0			0
$55$	−246.423			−0.604139
$56$	29.9210	+	51.8247i	0.0713993	+	0.123667i
$57$		0			0
$58$	22.5597	−	39.0746i	0.0510731	−	0.0884612i
$59$	119.543	−	207.055i	0.263784	−	0.456887i	−0.703461	−	0.710734i	$-0.748363\pi$
$59$	119.543	−	207.055i	0.263784	−	0.456887i	0.967244	+	0.253848i	$0.0816962\pi$
$60$		0			0
$61$	27.2729	+	47.2380i	0.0572448	+	0.0991509i	0.893228	−	0.449605i	$-0.148435\pi$
$61$	27.2729	+	47.2380i	0.0572448	+	0.0991509i	−0.835983	+	0.548756i	$0.815102\pi$
$62$	−11.9772			−0.0245341
$63$		0			0
$64$	−486.477			−0.950150
$65$	180.450	+	312.549i	0.344339	+	0.596413i
$66$		0			0
$67$	38.0279	−	65.8662i	0.0693410	−	0.120102i	−0.829270	−	0.558848i	$-0.811244\pi$
$67$	38.0279	−	65.8662i	0.0693410	−	0.120102i	0.898611	+	0.438745i	$0.144577\pi$
$68$	−468.118	+	810.804i	−0.834818	+	1.44595i
$69$		0			0
$70$	9.38959	+	16.2633i	0.0160324	+	0.0277690i
$71$	−728.303			−1.21738			−0.608688	−	0.793410i	$-0.708304\pi$
$71$	−728.303			−1.21738			−0.608688	+	0.793410i	$0.708304\pi$
$72$		0			0
$73$	−501.815			−0.804562			−0.402281	−	0.915516i	$-0.631782\pi$
$73$	−501.815			−0.804562			−0.402281	+	0.915516i	$0.631782\pi$
$74$	−20.0472	−	34.7227i	−0.0314924	−	0.0545464i
$75$		0			0
$76$	489.427	−	847.712i	0.738699	−	1.27946i
$77$	−357.742	+	619.628i	−0.529461	+	0.917054i
$78$		0			0
$79$	−198.805	−	344.340i	−0.283130	−	0.490396i	0.689024	−	0.724739i	$-0.258040\pi$
$79$	−198.805	−	344.340i	−0.283130	−	0.490396i	−0.972154	+	0.234343i	$0.924706\pi$
$80$	−311.991			−0.436020
$81$		0			0
$82$	94.2237			0.126894
$83$	−684.731	−	1185.99i	−0.905530	−	1.56842i	−0.820205	−	0.572070i	$-0.806141\pi$
$83$	−684.731	−	1185.99i	−0.905530	−	1.56842i	−0.0853248	−	0.996353i	$-0.527193\pi$
$84$		0			0
$85$	−295.042	+	511.028i	−0.376492	+	0.652103i
$86$	−16.2619	+	28.1664i	−0.0203902	+	0.0353169i
$87$		0			0
$88$	101.577	+	175.937i	0.123048	+	0.213125i
$89$	−1468.13			−1.74856			−0.874278	−	0.485425i	$-0.838665\pi$
$89$	−1468.13			−1.74856			−0.874278	+	0.485425i	$0.838665\pi$
$90$		0			0
$91$	1047.87			1.20710
$92$	362.892	+	628.547i	0.411240	+	0.712288i
$93$		0			0
$94$	−28.6554	+	49.6326i	−0.0314423	+	0.0544597i
$95$	308.473	−	534.290i	0.333144	−	0.577022i
$96$		0			0
$97$	−167.512	−	290.139i	−0.175343	−	0.303702i	0.764937	−	0.644105i	$-0.222770\pi$
$97$	−167.512	−	290.139i	−0.175343	−	0.303702i	−0.940280	+	0.340403i	$0.889437\pi$
$98$	−34.2133			−0.0352659
$99$		0			0
$100$	−198.327			−0.198327
$101$	−603.043	−	1044.50i	−0.594109	−	1.02903i	−0.993672	−	0.112321i	$-0.964171\pi$
$101$	−603.043	−	1044.50i	−0.594109	−	1.02903i	0.399563	−	0.916706i	$-0.369162\pi$
$102$		0			0
$103$	−530.555	+	918.948i	−0.507545	+	0.879093i	0.492417	+	0.870359i	$0.336113\pi$
$103$	−530.555	+	918.948i	−0.507545	+	0.879093i	−0.999962	+	0.00873396i	$0.997220\pi$
$104$	148.766	−	257.670i	0.140266	−	0.242948i
$105$		0			0
$106$	−1.76951	−	3.06489i	−0.00162142	−	0.00280838i
$107$	475.578			0.429681			0.214841	−	0.976649i	$-0.431077\pi$
$107$	475.578			0.429681			0.214841	+	0.976649i	$0.431077\pi$
$108$		0			0
$109$	1320.42			1.16030			0.580152	−	0.814508i	$-0.302993\pi$
$109$	1320.42			1.16030			0.580152	+	0.814508i	$0.302993\pi$
$110$	31.8763	+	55.2114i	0.0276299	+	0.0478563i
$111$		0			0
$112$	−452.930	+	784.498i	−0.382124	+	0.661858i
$113$	−34.0875	+	59.0413i	−0.0283777	+	0.0491517i	−0.879865	−	0.475223i	$-0.842367\pi$
$113$	−34.0875	+	59.0413i	−0.0283777	+	0.0491517i	0.851488	+	0.524374i	$0.175701\pi$
$114$		0			0
$115$	228.721	+	396.156i	0.185464	+	0.321233i
$116$	1383.53			1.10739
$117$		0			0
$118$	−61.8547			−0.0482559
$119$	856.650	+	1483.76i	0.659907	+	1.14299i
$120$		0			0
$121$	−548.983	+	950.867i	−0.412459	+	0.714400i
$122$	7.05583	−	12.2211i	0.00523610	−	0.00906920i
$123$		0			0
$124$	−183.633	−	318.062i	−0.132990	−	0.230345i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−593.009			−0.414339			−0.207170	−	0.978305i	$-0.566425\pi$
$127$	−593.009			−0.414339			−0.207170	+	0.978305i	$0.566425\pi$
$128$	259.408	+	449.308i	0.179130	+	0.310262i
$129$		0			0
$130$	46.6846	−	80.8602i	0.0314963	−	0.0545531i
$131$	169.469	−	293.528i	0.113027	−	0.195769i	−0.803962	−	0.594680i	$-0.797279\pi$
$131$	169.469	−	293.528i	0.113027	−	0.195769i	0.916989	+	0.398912i	$0.130612\pi$
$132$		0			0
$133$	−895.646	−	1551.30i	−0.583927	−	1.01139i
$134$	−19.6766			−0.0126850
$135$		0			0
$136$	486.475			0.306727
$137$	−405.721	−	702.729i	−0.253015	−	0.438235i	0.711339	−	0.702849i	$-0.248089\pi$
$137$	−405.721	−	702.729i	−0.253015	−	0.438235i	−0.964354	+	0.264614i	$0.914756\pi$
$138$		0			0
$139$	1553.06	−	2689.98i	0.947691	−	1.64145i	0.197420	−	0.980319i	$-0.436744\pi$
$139$	1553.06	−	2689.98i	0.947691	−	1.64145i	0.750271	−	0.661130i	$-0.229923\pi$
$140$	−287.919	+	498.691i	−0.173812	+	0.301050i
$141$		0			0
$142$	94.2105	+	163.177i	0.0556758	+	0.0964334i
$143$	3557.36			2.08029
$144$		0			0
$145$	872.001			0.499419
$146$	64.9129	+	112.432i	0.0367961	+	0.0637327i
$147$		0			0
$148$	614.720	−	1064.73i	0.341417	−	0.591351i
$149$	1270.51	−	2200.58i	0.698550	−	1.20992i	−0.270419	−	0.962743i	$-0.587162\pi$
$149$	1270.51	−	2200.58i	0.698550	−	1.20992i	0.968969	−	0.247181i	$-0.0795043\pi$
$150$		0			0
$151$	562.685	+	974.599i	0.303249	+	0.525243i	0.976870	−	0.213834i	$-0.0685952\pi$
$151$	562.685	+	974.599i	0.303249	+	0.525243i	−0.673621	+	0.739077i	$0.735262\pi$
$152$	−508.620			−0.271411
$153$		0			0
$154$	185.105			0.0968582
$155$	−115.739	−	200.466i	−0.0599767	−	0.103883i
$156$		0			0
$157$	−1615.03	+	2797.31i	−0.820975	+	1.42197i	0.0839811	+	0.996467i	$0.473236\pi$
$157$	−1615.03	+	2797.31i	−0.820975	+	1.42197i	−0.904957	+	0.425504i	$0.860097\pi$
$158$	−51.4333	+	89.0850i	−0.0258975	+	0.0448559i
$159$		0			0
$160$	122.800	+	212.695i	0.0606760	+	0.105094i
$161$	1328.17			0.650154
$162$		0			0
$163$	−694.054			−0.333512			−0.166756	−	0.985998i	$-0.553329\pi$
$163$	−694.054			−0.333512			−0.166756	+	0.985998i	$0.553329\pi$
$164$	1444.62	+	2502.16i	0.687842	+	1.19138i
$165$		0			0
$166$	−177.148	+	306.830i	−0.0828275	+	0.143462i
$167$	1608.02	−	2785.17i	0.745103	−	1.29056i	−0.205044	−	0.978753i	$-0.565734\pi$
$167$	1608.02	−	2785.17i	0.745103	−	1.29056i	0.950147	−	0.311803i	$-0.100933\pi$
$168$		0			0
$169$	−1506.48	−	2609.29i	−0.685697	−	1.18766i
$170$	152.662			0.0688744
$171$		0			0
$172$	−997.296			−0.442111
$173$	148.773	+	257.683i	0.0653816	+	0.113244i	0.896863	−	0.442308i	$-0.145840\pi$
$173$	148.773	+	257.683i	0.0653816	+	0.113244i	−0.831482	+	0.555552i	$0.812507\pi$
$174$		0			0
$175$	−181.468	+	314.311i	−0.0783867	+	0.135770i
$176$	−1537.63	+	2663.26i	−0.658542	+	1.14063i
$177$		0			0
$178$	189.912	+	328.937i	0.0799690	+	0.138510i
$179$	3450.12			1.44064			0.720320	−	0.693642i	$-0.243995\pi$
$179$	3450.12			1.44064			0.720320	+	0.693642i	$0.243995\pi$
$180$		0			0
$181$	−3089.75			−1.26883			−0.634417	−	0.772991i	$-0.718760\pi$
$181$	−3089.75			−1.26883			−0.634417	+	0.772991i	$0.718760\pi$
$182$	−135.548	−	234.776i	−0.0552060	−	0.0956197i
$183$		0			0
$184$	188.561	−	326.598i	0.0755484	−	0.130854i
$185$	387.442	−	671.069i	0.153974	−	0.266692i
$186$		0			0
$187$	2908.20	+	5037.15i	1.13727	+	1.96980i
$188$	−1757.36			−0.681748
$189$		0			0
$190$	−159.611			−0.0609444
$191$	766.057	+	1326.85i	0.290209	+	0.502657i	0.973859	−	0.227153i	$-0.0729418\pi$
$191$	766.057	+	1326.85i	0.290209	+	0.502657i	−0.683650	+	0.729810i	$0.739608\pi$
$192$		0			0
$193$	2597.21	−	4498.50i	0.968660	−	1.67777i	0.269219	−	0.963079i	$-0.413235\pi$
$193$	2597.21	−	4498.50i	0.968660	−	1.67777i	0.699442	−	0.714690i	$-0.253432\pi$
$194$	−43.3373	+	75.0625i	−0.0160383	+	0.0277792i
$195$		0			0
$196$	−524.552	−	908.550i	−0.191163	−	0.331104i
$197$	2005.61			0.725349			0.362674	−	0.931916i	$-0.381864\pi$
$197$	2005.61			0.725349			0.362674	+	0.931916i	$0.381864\pi$
$198$		0			0
$199$	−2874.68			−1.02402			−0.512011	−	0.858979i	$-0.671099\pi$
$199$	−2874.68			−1.02402			−0.512011	+	0.858979i	$0.671099\pi$
$200$	51.5260	+	89.2457i	0.0182172	+	0.0315531i
$201$		0			0
$202$	−156.015	+	270.225i	−0.0543424	+	0.0941237i
$203$	1265.92	−	2192.64i	0.437686	−	0.758094i
$204$		0			0
$205$	910.506	+	1577.04i	0.310207	+	0.537295i
$206$	274.522			0.0928488
$207$		0			0
$208$	4503.90			1.50139
$209$	−3040.59	−	5266.45i	−1.00632	−	1.74301i
$210$		0			0
$211$	1374.97	−	2381.52i	0.448610	−	0.777016i	−0.549686	−	0.835372i	$-0.685253\pi$
$211$	1374.97	−	2381.52i	0.448610	−	0.777016i	0.998296	+	0.0583560i	$0.0185858\pi$
$212$	54.2598	−	93.9807i	0.0175782	−	0.0304463i
$213$		0			0
$214$	−61.5190	−	106.554i	−0.0196512	−	0.0340368i
$215$	−628.569			−0.199386
$216$		0			0
$217$	−672.093			−0.210252
$218$	−170.804	−	295.842i	−0.0530657	−	0.0919125i
$219$		0			0
$220$	−977.444	+	1692.98i	−0.299542	+	0.518822i
$221$	4259.23	−	7377.20i	1.29641	−	2.24545i
$222$		0			0
$223$	391.864	+	678.728i	0.117673	+	0.203816i	0.918845	−	0.394618i	$-0.129123\pi$
$223$	391.864	+	678.728i	0.117673	+	0.203816i	−0.801172	+	0.598434i	$0.795790\pi$
$224$	713.093			0.212703
$225$		0			0
$226$	17.6377			0.00519134
$227$	−72.8326	−	126.150i	−0.0212955	−	0.0368848i	0.855181	−	0.518329i	$-0.173446\pi$
$227$	−72.8326	−	126.150i	−0.0212955	−	0.0368848i	−0.876477	+	0.481444i	$0.840112\pi$
$228$		0			0
$229$	1705.91	−	2954.72i	0.492270	−	0.852636i	−0.507691	−	0.861539i	$-0.669501\pi$
$229$	1705.91	−	2954.72i	0.492270	−	0.852636i	0.999960	+	0.00890324i	$0.00283403\pi$
$230$	59.1729	−	102.490i	0.0169641	−	0.0293827i
$231$		0			0
$232$	−359.446	−	622.578i	−0.101719	−	0.176182i
$233$	−134.977			−0.0379511			−0.0189756	−	0.999820i	$-0.506040\pi$
$233$	−134.977			−0.0379511			−0.0189756	+	0.999820i	$0.506040\pi$
$234$		0			0
$235$	−1107.62			−0.307459
$236$	−948.347	−	1642.58i	−0.261577	−	0.453064i
$237$		0			0
$238$	221.626	−	383.867i	0.0603608	−	0.104548i
$239$	−1122.66	+	1944.51i	−0.303845	+	0.526275i	−0.977003	−	0.213223i	$-0.931604\pi$
$239$	−1122.66	+	1944.51i	−0.303845	+	0.526275i	0.673159	+	0.739498i	$0.264937\pi$
$240$		0			0
$241$	−2079.27	−	3601.40i	−0.555757	−	0.962600i	−0.997844	−	0.0656276i	$-0.979095\pi$
$241$	−2079.27	−	3601.40i	−0.555757	−	0.962600i	0.442087	−	0.896972i	$-0.354238\pi$
$242$	284.057			0.0754542
$243$		0			0
$244$	432.715			0.113532
$245$	−330.611	−	572.635i	−0.0862121	−	0.149324i
$246$		0			0
$247$	−4453.11	+	7713.02i	−1.14714	+	1.98691i
$248$	−95.4171	+	165.267i	−0.0244314	+	0.0423165i
$249$		0			0
$250$	16.1695	+	28.0064i	0.00409060	+	0.00708513i
$251$	−3946.14			−0.992343			−0.496171	−	0.868225i	$-0.665261\pi$
$251$	−3946.14			−0.992343			−0.496171	+	0.868225i	$0.665261\pi$
$252$		0			0
$253$	4508.96			1.12046
$254$	76.7094	+	132.865i	0.0189495	+	0.0328215i
$255$		0			0
$256$	−1878.80	+	3254.17i	−0.458690	+	0.794475i
$257$	−2847.92	+	4932.74i	−0.691239	+	1.19726i	0.280193	+	0.959944i	$0.409601\pi$
$257$	−2847.92	+	4932.74i	−0.691239	+	1.19726i	−0.971432	+	0.237317i	$0.923732\pi$
$258$		0			0
$259$	−1124.93	−	1948.44i	−0.269883	−	0.467452i
$260$	2863.04			0.682917
$261$		0			0
$262$	−87.6873			−0.0206769
$263$	1407.03	+	2437.05i	0.329891	+	0.571387i	0.982490	−	0.186316i	$-0.0596548\pi$
$263$	1407.03	+	2437.05i	0.329891	+	0.571387i	−0.652599	+	0.757703i	$0.726321\pi$
$264$		0			0
$265$	34.1985	−	59.2335i	0.00792753	−	0.0137309i
$266$	−231.715	+	401.342i	−0.0534110	+	0.0925106i
$267$		0			0
$268$	−301.678	−	522.521i	−0.0687608	−	0.119097i
$269$	−200.985			−0.0455548			−0.0227774	−	0.999741i	$-0.507251\pi$
$269$	−200.985			−0.0455548			−0.0227774	+	0.999741i	$0.507251\pi$
$270$		0			0
$271$	−2406.05			−0.539326			−0.269663	−	0.962955i	$-0.586912\pi$
$271$	−2406.05			−0.539326			−0.269663	+	0.962955i	$0.586912\pi$
$272$	3682.01	+	6377.43i	0.820790	+	1.42165i
$273$		0			0
$274$	−104.965	+	181.805i	−0.0231429	+	0.0400847i
$275$	−616.057	+	1067.04i	−0.135090	+	0.233982i
$276$		0			0
$277$	4214.67	+	7300.02i	0.914205	+	1.58345i	0.808061	+	0.589098i	$0.200517\pi$
$277$	4214.67	+	7300.02i	0.914205	+	1.58345i	0.106143	+	0.994351i	$0.466150\pi$
$278$	−803.593			−0.173368
$279$		0			0
$280$	299.210			0.0638615
$281$	1987.13	+	3441.81i	0.421859	+	0.730681i	0.996121	−	0.0879906i	$-0.0280445\pi$
$281$	1987.13	+	3441.81i	0.421859	+	0.730681i	−0.574263	+	0.818671i	$0.694711\pi$
$282$		0			0
$283$	1536.20	−	2660.78i	0.322678	−	0.558895i	−0.658362	−	0.752702i	$-0.728750\pi$
$283$	1536.20	−	2660.78i	0.322678	−	0.558895i	0.981040	+	0.193807i	$0.0620836\pi$
$284$	−2888.84	+	5003.62i	−0.603595	+	1.04546i
$285$		0			0
$286$	−460.166	−	797.031i	−0.0951406	−	0.164788i
$287$	5287.28			1.08745
$288$		0			0
$289$	9014.97			1.83492
$290$	−112.799	−	195.373i	−0.0228406	−	0.0395610i
$291$		0			0
$292$	−1990.47	+	3447.59i	−0.398915	+	0.690942i
$293$	1991.11	−	3448.70i	0.397002	−	0.687628i	−0.596352	−	0.802723i	$-0.703384\pi$
$293$	1991.11	−	3448.70i	0.397002	−	0.687628i	0.993355	+	0.115095i	$0.0367172\pi$
$294$		0			0
$295$	−597.717	−	1035.28i	−0.117968	−	0.204326i
$296$	−638.826			−0.125443
$297$		0			0
$298$	−657.391			−0.127791
$299$	−3301.81	−	5718.91i	−0.638625	−	1.10613i
$300$		0			0
$301$	−912.520	+	1580.53i	−0.174740	+	0.302659i
$302$	145.574	−	252.141i	0.0277378	−	0.0480433i
$303$		0			0
$304$	−3849.62	−	6667.74i	−0.726286	−	1.25796i
$305$	272.729			0.0512013
$306$		0			0
$307$	−2996.06			−0.556984			−0.278492	−	0.960439i	$-0.589835\pi$
$307$	−2996.06			−0.556984			−0.278492	+	0.960439i	$0.589835\pi$
$308$	2837.99	+	4915.55i	0.525032	+	0.909381i
$309$		0			0
$310$	−29.9431	+	51.8630i	−0.00548598	+	0.00950200i
$311$	−1539.97	+	2667.30i	−0.280783	+	0.486331i	−0.971578	−	0.236720i	$-0.923928\pi$
$311$	−1539.97	+	2667.30i	−0.280783	+	0.486331i	0.690795	+	0.723051i	$0.257261\pi$
$312$		0			0
$313$	−3976.82	−	6888.06i	−0.718158	−	1.24389i	−0.961729	−	0.274003i	$-0.911652\pi$
$313$	−3976.82	−	6888.06i	−0.718158	−	1.24389i	0.243571	−	0.969883i	$-0.421681\pi$
$314$	835.655			0.150187
$315$		0			0
$316$	−3154.26			−0.561523
$317$	−3416.49	−	5917.53i	−0.605328	−	1.04846i	−0.991999	−	0.126242i	$-0.959708\pi$
$317$	−3416.49	−	5917.53i	−0.605328	−	1.04846i	0.386671	−	0.922218i	$-0.373625\pi$
$318$		0			0
$319$	4297.62	−	7443.69i	0.754296	−	1.30648i
$320$	−1216.19	+	2106.51i	−0.212460	+	0.367992i
$321$		0			0
$322$	−171.808	−	297.580i	−0.0297344	−	0.0515014i
$323$	−14562.0			−2.50852
$324$		0			0
$325$	1804.50			0.307987
$326$	89.7802	+	155.504i	0.0152530	+	0.0264189i
$327$		0			0
$328$	750.636	−	1300.14i	0.126363	−	0.218867i
$329$	−1607.97	+	2785.09i	−0.269454	+	0.466708i
$330$		0			0
$331$	1148.29	+	1988.89i	0.190682	+	0.330270i	0.945476	−	0.325691i	$-0.105597\pi$
$331$	1148.29	+	1988.89i	0.190682	+	0.330270i	−0.754795	+	0.655961i	$0.772264\pi$
$332$	−10864.0			−1.79591
$333$		0			0
$334$	−832.028			−0.136307
$335$	−190.139	−	329.331i	−0.0310102	−	0.0537113i
$336$		0			0
$337$	−3630.74	+	6288.63i	−0.586881	+	1.01651i	0.407757	+	0.913091i	$0.366311\pi$
$337$	−3630.74	+	6288.63i	−0.586881	+	1.01651i	−0.994638	+	0.103418i	$0.967022\pi$
$338$	−389.744	+	675.056i	−0.0627198	+	0.108634i
$339$		0			0
$340$	2340.59	+	4054.02i	0.373342	+	0.646647i
$341$	−2281.66			−0.362342
$342$		0			0
$343$	−6899.32			−1.08609
$344$	259.101	+	448.777i	0.0406099	+	0.0703384i
$345$		0			0
$346$	38.4894	−	66.6657i	0.00598036	−	0.0103583i
$347$	3712.61	−	6430.43i	0.574361	−	0.994822i	−0.421750	−	0.906712i	$-0.638584\pi$
$347$	3712.61	−	6430.43i	0.574361	−	0.994822i	0.996111	−	0.0881101i	$-0.0280827\pi$
$348$		0			0
$349$	239.080	+	414.098i	0.0366695	+	0.0635134i	0.883778	−	0.467907i	$-0.154992\pi$
$349$	239.080	+	414.098i	0.0366695	+	0.0635134i	−0.847108	+	0.531420i	$0.821658\pi$
$350$	93.8959			0.0143399
$351$		0			0
$352$	2420.85			0.366567
$353$	−2496.54	−	4324.14i	−0.376424	−	0.651985i	0.614115	−	0.789216i	$-0.289513\pi$
$353$	−2496.54	−	4324.14i	−0.376424	−	0.651985i	−0.990539	+	0.137231i	$0.956180\pi$
$354$		0			0
$355$	−1820.76	+	3153.64i	−0.272213	+	0.471488i
$356$	−5823.39	+	10086.4i	−0.866964	+	1.50162i
$357$		0			0
$358$	−446.295	−	773.006i	−0.0658867	−	0.114119i
$359$	6873.09			1.01044			0.505219	−	0.862991i	$-0.331412\pi$
$359$	6873.09			1.01044			0.505219	+	0.862991i	$0.331412\pi$
$360$		0			0
$361$	8365.87			1.21969
$362$	399.678	+	692.262i	0.0580293	+	0.100510i
$363$		0			0
$364$	4156.40	−	7199.10i	0.598502	−	1.03664i
$365$	−1254.54	+	2172.92i	−0.179906	+	0.311605i
$366$		0			0
$367$	4344.36	+	7524.65i	0.617912	+	1.07025i	0.989866	+	0.142004i	$0.0453545\pi$
$367$	4344.36	+	7524.65i	0.617912	+	1.07025i	−0.371954	+	0.928251i	$0.621312\pi$
$368$	5708.70			0.808659
$369$		0			0
$370$	−200.472			−0.0281677
$371$	−99.2948	−	171.984i	−0.0138952	−	0.0240672i
$372$		0			0
$373$	−1747.27	+	3026.36i	−0.242548	+	0.420105i	−0.961439	−	0.275017i	$-0.911316\pi$
$373$	−1747.27	+	3026.36i	−0.242548	+	0.420105i	0.718892	+	0.695122i	$0.244650\pi$
$374$	752.388	−	1303.17i	0.104024	−	0.180175i
$375$		0			0
$376$	456.568	+	790.799i	0.0626216	+	0.108464i
$377$	−12588.2			−1.71970
$378$		0			0
$379$	−5802.83			−0.786468			−0.393234	−	0.919438i	$-0.628644\pi$
$379$	−5802.83			−0.786468			−0.393234	+	0.919438i	$0.628644\pi$
$380$	−2447.14	−	4238.56i	−0.330356	−	0.572194i
$381$		0			0
$382$	198.189	−	343.273i	0.0265450	−	0.0459774i
$383$	−1679.28	+	2908.60i	−0.224040	+	0.388049i	−0.956031	−	0.293266i	$-0.905258\pi$
$383$	−1679.28	+	2908.60i	−0.224040	+	0.388049i	0.731991	+	0.681314i	$0.238591\pi$
$384$		0			0
$385$	1788.71	+	3098.14i	0.236782	+	0.410119i
$386$	−1343.86			−0.177204
$387$		0			0
$388$	−2657.76			−0.347751
$389$	9.56850	+	16.5731i	0.00124715	+	0.00216013i	0.866648	−	0.498920i	$-0.166270\pi$
$389$	9.56850	+	16.5731i	0.00124715	+	0.00216013i	−0.865401	+	0.501080i	$0.832936\pi$
$390$		0			0
$391$	5398.58	−	9350.62i	0.698256	−	1.20941i
$392$	−272.561	+	472.090i	−0.0351184	+	0.0608268i
$393$		0			0
$394$	−259.438	−	449.360i	−0.0331733	−	0.0574579i
$395$	−1988.05			−0.253239
$396$		0			0
$397$	−4348.59			−0.549747			−0.274873	−	0.961480i	$-0.588636\pi$
$397$	−4348.59			−0.549747			−0.274873	+	0.961480i	$0.588636\pi$
$398$	371.857	+	644.076i	0.0468330	+	0.0811171i
$399$		0			0
$400$	−779.976	+	1350.96i	−0.0974970	+	0.168870i
$401$	4250.81	−	7362.61i	0.529364	−	0.916886i	−0.470049	−	0.882640i	$-0.655764\pi$
$401$	4250.81	−	7362.61i	0.529364	−	0.916886i	0.999413	−	0.0342457i	$-0.0109029\pi$
$402$		0			0
$403$	1670.81	+	2893.93i	0.206523	+	0.357709i
$404$	−9567.96			−1.17828
$405$		0			0
$406$	−655.019			−0.0800690
$407$	−3818.98	−	6614.66i	−0.465110	−	0.805594i
$408$		0			0
$409$	1405.33	−	2434.11i	0.169900	−	0.294276i	−0.768484	−	0.639869i	$-0.778989\pi$
$409$	1405.33	−	2434.11i	0.169900	−	0.294276i	0.938385	+	0.345593i	$0.112322\pi$
$410$	235.559	−	408.001i	0.0283742	−	0.0491456i
$411$		0			0
$412$	4208.93	+	7290.07i	0.503298	+	0.871738i
$413$	−3470.93			−0.413543
$414$		0			0
$415$	−6847.31			−0.809930
$416$	−1772.73	−	3070.47i	−0.208931	−	0.361880i
$417$		0			0
$418$	−786.638	+	1362.50i	−0.0920471	+	0.159430i
$419$	−8177.71	+	14164.2i	−0.953478	+	1.65147i	−0.215666	+	0.976467i	$0.569192\pi$
$419$	−8177.71	+	14164.2i	−0.953478	+	1.65147i	−0.737812	+	0.675006i	$0.764141\pi$
$420$		0			0
$421$	2255.45	+	3906.55i	0.261102	+	0.452242i	0.966535	−	0.256535i	$-0.0825808\pi$
$421$	2255.45	+	3906.55i	0.261102	+	0.452242i	−0.705433	+	0.708776i	$0.749248\pi$
$422$	−711.443			−0.0820675
$423$		0			0
$424$	−56.3876			−0.00645854
$425$	1475.21	+	2555.14i	0.168372	+	0.291629i
$426$		0			0
$427$	395.932	−	685.774i	0.0448723	−	0.0777212i
$428$	1886.40	−	3267.33i	0.213043	−	0.369001i
$429$		0			0
$430$	81.3093	+	140.832i	0.00911880	+	0.0157942i
$431$	−5850.47			−0.653845			−0.326923	−	0.945051i	$-0.606012\pi$
$431$	−5850.47			−0.653845			−0.326923	+	0.945051i	$0.606012\pi$
$432$		0			0
$433$	−3836.82			−0.425833			−0.212916	−	0.977070i	$-0.568296\pi$
$433$	−3836.82			−0.425833			−0.212916	+	0.977070i	$0.568296\pi$
$434$	86.9394	+	150.583i	0.00961572	+	0.0166549i
$435$		0			0
$436$	5237.48	−	9071.59i	0.575298	−	0.996446i
$437$	−5644.33	+	9776.27i	−0.617860	+	1.07017i
$438$		0			0
$439$	−8113.67	−	14053.3i	−0.882106	−	1.52785i	−0.848995	−	0.528400i	$-0.822792\pi$
$439$	−8113.67	−	14053.3i	−0.882106	−	1.52785i	−0.0331103	−	0.999452i	$-0.510541\pi$
$440$	1015.77			0.110057
$441$		0			0
$442$	−2203.83			−0.237162
$443$	3352.56	+	5806.81i	0.359560	+	0.622776i	0.987887	−	0.155173i	$-0.0495934\pi$
$443$	3352.56	+	5806.81i	0.359560	+	0.622776i	−0.628327	+	0.777949i	$0.716260\pi$
$444$		0			0
$445$	−3670.33	+	6357.19i	−0.390989	+	0.677213i
$446$	101.380	−	175.595i	0.0107634	−	0.0186428i
$447$		0			0
$448$	3531.20	+	6116.21i	0.372396	+	0.645009i
$449$	−213.100			−0.0223982			−0.0111991	−	0.999937i	$-0.503565\pi$
$449$	−213.100			−0.0223982			−0.0111991	+	0.999937i	$0.503565\pi$
$450$		0			0
$451$	17949.6			1.87408
$452$	270.419	+	468.379i	0.0281403	+	0.0487404i
$453$		0			0
$454$	−18.8427	+	32.6365i	−0.00194787	+	0.00337381i
$455$	2619.67	−	4537.40i	0.269916	−	0.467509i
$456$		0			0
$457$	−8231.03	−	14256.6i	−0.842520	−	1.45929i	−0.887758	−	0.460311i	$-0.847738\pi$
$457$	−8231.03	−	14256.6i	−0.842520	−	1.45929i	0.0452381	−	0.998976i	$-0.485595\pi$
$458$	−882.680			−0.0900545
$459$		0			0
$460$	3628.92			0.367824
$461$	781.029	+	1352.78i	0.0789071	+	0.136671i	0.902779	−	0.430105i	$-0.141524\pi$
$461$	781.029	+	1352.78i	0.0789071	+	0.136671i	−0.823872	+	0.566777i	$0.808190\pi$
$462$		0			0
$463$	2962.14	−	5130.57i	0.297326	−	0.514984i	−0.678197	−	0.734880i	$-0.737238\pi$
$463$	2962.14	−	5130.57i	0.297326	−	0.514984i	0.975523	+	0.219896i	$0.0705717\pi$
$464$	5441.12	−	9424.30i	0.544392	−	0.942914i
$465$		0			0
$466$	17.4601	+	30.2417i	0.00173567	+	0.00300627i
$467$	17905.1			1.77420			0.887098	−	0.461582i	$-0.152718\pi$
$467$	17905.1			1.77420			0.887098	+	0.461582i	$0.152718\pi$
$468$		0			0
$469$	−1104.13			−0.108708
$470$	143.277	+	248.163i	0.0140614	+	0.0243551i
$471$		0			0
$472$	−492.768	+	853.499i	−0.0480540	+	0.0832320i
$473$	−3097.87	+	5365.67i	−0.301142	+	0.521594i
$474$		0			0
$475$	−1542.36	−	2671.45i	−0.148986	−	0.258052i
$476$	13591.7			1.30877
$477$		0			0
$478$	580.893			0.0555846
$479$	4957.72	+	8587.02i	0.472910	+	0.819104i	0.999519	−	0.0310033i	$-0.00987023\pi$
$479$	4957.72	+	8587.02i	0.472910	+	0.819104i	−0.526609	+	0.850107i	$0.676537\pi$
$480$		0			0
$481$	−5593.11	+	9687.55i	−0.530195	+	0.918324i
$482$	−537.933	+	931.727i	−0.0508344	+	0.0880477i
$483$		0			0
$484$	4355.12	+	7543.29i	0.409008	+	0.708423i
$485$	−1675.12			−0.156831
$486$		0			0
$487$	11910.8			1.10828			0.554138	−	0.832425i	$-0.313048\pi$
$487$	11910.8			1.10828			0.554138	+	0.832425i	$0.313048\pi$
$488$	−112.421	−	194.719i	−0.0104284	−	0.0180625i
$489$		0			0
$490$	−85.5331	+	148.148i	−0.00788570	+	0.0136584i
$491$	5531.88	−	9581.50i	0.508453	−	0.880666i	−0.491499	−	0.870878i	$-0.663551\pi$
$491$	5531.88	−	9581.50i	0.508453	−	0.880666i	0.999952	−	0.00978823i	$-0.00311574\pi$
$492$		0			0
$493$	−10291.1	−	17824.7i	−0.940135	−	1.62836i
$494$	2304.15			0.209856
$495$		0			0
$496$	−2888.76			−0.261510
$497$	5286.54	+	9156.56i	0.477130	+	0.826414i
$498$		0			0
$499$	−4673.62	+	8094.95i	−0.419279	+	0.726212i	−0.995867	−	0.0908227i	$-0.971050\pi$
$499$	−4673.62	+	8094.95i	−0.419279	+	0.726212i	0.576588	+	0.817035i	$0.304384\pi$
$500$	−495.817	+	858.780i	−0.0443472	+	0.0768116i
$501$		0			0
$502$	510.457	+	884.138i	0.0453841	+	0.0786076i
$503$	19474.2			1.72627			0.863135	−	0.504973i	$-0.168498\pi$
$503$	19474.2			1.72627			0.863135	+	0.504973i	$0.168498\pi$
$504$		0			0
$505$	−6030.43			−0.531387
$506$	−583.262	−	1010.24i	−0.0512434	−	0.0887562i
$507$		0			0
$508$	−2352.19	+	4074.12i	−0.205436	+	0.355826i
$509$	11082.0	−	19194.7i	0.965035	−	1.67149i	0.255514	−	0.966805i	$-0.417755\pi$
$509$	11082.0	−	19194.7i	0.965035	−	1.67149i	0.709521	−	0.704684i	$-0.248911\pi$
$510$		0			0
$511$	3642.53	+	6309.05i	0.315335	+	0.546176i
$512$	5122.66			0.442172
$513$		0			0
$514$	1473.58			0.126453
$515$	2652.77	+	4594.74i	0.226981	+	0.393142i
$516$		0			0
$517$	−5458.83	+	9454.98i	−0.464370	+	0.804312i
$518$	−291.034	+	504.085i	−0.0246859	+	0.0427572i
$519$		0			0
$520$	−743.830	−	1288.35i	−0.0627290	−	0.108650i
$521$	254.564			0.0214062			0.0107031	−	0.999943i	$-0.496593\pi$
$521$	254.564			0.0214062			0.0107031	+	0.999943i	$0.496593\pi$
$522$		0			0
$523$	4049.92			0.338606			0.169303	−	0.985564i	$-0.445848\pi$
$523$	4049.92			0.338606			0.169303	+	0.985564i	$0.445848\pi$
$524$	−1344.41	−	2328.58i	−0.112081	−	0.194131i
$525$		0			0
$526$	364.016	−	630.495i	0.0301747	−	0.0522640i
$527$	−2731.83	+	4731.67i	−0.225807	+	0.391110i
$528$		0			0
$529$	1898.44	+	3288.20i	0.156032	+	0.270256i
$530$	−17.6951			−0.00145024
$531$		0			0
$532$	−14210.4			−1.15808
$533$	−13144.1	−	22766.2i	−1.06817	−	1.85012i
$534$		0			0
$535$	1188.95	−	2059.31i	0.0960796	−	0.166415i
$536$	−156.754	+	271.506i	−0.0126320	+	0.0218792i
$537$		0			0
$538$	25.9986	+	45.0309i	0.00208342	+	0.00360859i
$539$	−6517.60			−0.520841
$540$		0			0
$541$	−4085.88			−0.324705			−0.162353	−	0.986733i	$-0.551908\pi$
$541$	−4085.88			−0.324705			−0.162353	+	0.986733i	$0.551908\pi$
$542$	311.238	+	539.079i	0.0246657	+	0.0427222i
$543$		0			0
$544$	2898.48	−	5020.32i	0.228440	−	0.395670i
$545$	3301.05	−	5717.58i	0.259452	−	0.449384i
$546$		0			0
$547$	7696.10	+	13330.0i	0.601575	+	1.04196i	0.992583	+	0.121571i	$0.0387932\pi$
$547$	7696.10	+	13330.0i	0.601575	+	1.04196i	−0.391008	+	0.920387i	$0.627873\pi$
$548$	−6437.22			−0.501796
$549$		0			0
$550$	318.763			0.0247129
$551$	10759.5	+	18636.1i	0.831891	+	1.44088i
$552$		0			0
$553$	−2886.13	+	4998.93i	−0.221937	+	0.384405i
$554$	1090.39	−	1888.60i	0.0836211	−	0.144836i
$555$		0			0
$556$	−12320.6	−	21339.8i	−0.939762	−	1.62772i
$557$	10897.6			0.828987			0.414493	−	0.910052i	$-0.363959\pi$
$557$	10897.6			0.828987			0.414493	+	0.910052i	$0.363959\pi$
$558$		0			0
$559$	9074.02			0.686566
$560$	2264.65	+	3922.49i	0.170891	+	0.295992i
$561$		0			0
$562$	514.095	−	890.439i	0.0385868	−	0.0668343i
$563$	−775.845	+	1343.80i	−0.0580781	+	0.100594i	−0.893603	−	0.448859i	$-0.851831\pi$
$563$	−775.845	+	1343.80i	−0.0580781	+	0.100594i	0.835525	+	0.549453i	$0.185164\pi$
$564$		0			0
$565$	170.438	+	295.207i	0.0126909	+	0.0219813i
$566$	−794.870			−0.0590298
$567$		0			0
$568$	3002.12			0.221772
$569$	−623.475	−	1079.89i	−0.0459357	−	0.0795630i	0.842143	−	0.539254i	$-0.181294\pi$
$569$	−623.475	−	1079.89i	−0.0459357	−	0.0795630i	−0.888079	+	0.459691i	$0.847960\pi$
$570$		0			0
$571$	−2098.29	+	3634.34i	−0.153784	+	0.266362i	−0.932616	−	0.360871i	$-0.882479\pi$
$571$	−2098.29	+	3634.34i	−0.153784	+	0.266362i	0.778832	+	0.627233i	$0.215813\pi$
$572$	14110.4	−	24439.9i	1.03144	−	1.78651i
$573$		0			0
$574$	−683.943	−	1184.62i	−0.0497338	−	0.0861415i
$575$	2287.21			0.165884
$576$		0			0
$577$	20585.1			1.48521			0.742607	−	0.669728i	$-0.233589\pi$
$577$	20585.1			1.48521			0.742607	+	0.669728i	$0.233589\pi$
$578$	−1166.14	−	2019.82i	−0.0839189	−	0.145352i
$579$		0			0
$580$	3458.82	−	5990.85i	0.247620	−	0.428891i
$581$	−9940.53	+	17217.5i	−0.709815	+	1.22944i
$582$		0			0
$583$	−337.091	−	583.859i	−0.0239466	−	0.0414768i
$584$	2068.52			0.146569
$585$		0			0
$586$	−1030.25			−0.0726265
$587$	−2427.89	−	4205.23i	−0.170715	−	0.295687i	0.767955	−	0.640504i	$-0.221274\pi$
$587$	−2427.89	−	4205.23i	−0.170715	−	0.295687i	−0.938670	+	0.344817i	$0.887941\pi$
$588$		0			0
$589$	2856.19	−	4947.06i	0.199808	−	0.346078i
$590$	−154.637	+	267.839i	−0.0107903	+	0.0186894i
$591$		0			0
$592$	−4835.13	−	8374.68i	−0.335680	−	0.581414i
$593$	23965.6			1.65961			0.829804	−	0.558055i	$-0.188452\pi$
$593$	23965.6			1.65961			0.829804	+	0.558055i	$0.188452\pi$
$594$		0			0
$595$	8566.50			0.590239
$596$	−10079.0	−	17457.4i	−0.692706	−	1.19980i
$597$		0			0
$598$	−854.220	+	1479.55i	−0.0584141	+	0.101176i
$599$	7114.56	−	12322.8i	0.485297	−	0.840560i	−0.514560	−	0.857454i	$-0.672045\pi$
$599$	7114.56	−	12322.8i	0.485297	−	0.840560i	0.999857	+	0.0168947i	$0.00537802\pi$
$600$		0			0
$601$	4438.98	+	7688.55i	0.301281	+	0.521834i	0.976426	−	0.215851i	$-0.0692524\pi$
$601$	4438.98	+	7688.55i	0.301281	+	0.521834i	−0.675145	+	0.737685i	$0.735919\pi$
$602$	472.161			0.0319665
$603$		0			0
$604$	8927.64			0.601424
$605$	2744.92	+	4754.33i	0.184457	+	0.319490i
$606$		0			0
$607$	5438.36	−	9419.51i	0.363651	−	0.629862i	−0.624908	−	0.780699i	$-0.714863\pi$
$607$	5438.36	−	9419.51i	0.363651	−	0.629862i	0.988559	+	0.150837i	$0.0481968\pi$
$608$	−3030.42	+	5248.85i	−0.202138	+	0.350113i
$609$		0			0
$610$	−35.2791	−	61.1053i	−0.00234166	−	0.00405587i
$611$	15989.5			1.05870
$612$		0			0
$613$	−19544.8			−1.28778			−0.643890	−	0.765118i	$-0.722680\pi$
$613$	−19544.8			−1.28778			−0.643890	+	0.765118i	$0.722680\pi$
$614$	387.559	+	671.272i	0.0254733	+	0.0441210i
$615$		0			0
$616$	1474.64	−	2554.16i	0.0964530	−	0.167062i
$617$	2520.88	−	4366.29i	0.164484	−	0.284895i	−0.771988	−	0.635637i	$-0.780737\pi$
$617$	2520.88	−	4366.29i	0.164484	−	0.284895i	0.936472	+	0.350742i	$0.114071\pi$
$618$		0			0
$619$	2604.03	+	4510.31i	0.169087	+	0.292867i	0.938099	−	0.346367i	$-0.112585\pi$
$619$	2604.03	+	4510.31i	0.169087	+	0.292867i	−0.769012	+	0.639234i	$0.779252\pi$
$620$	−1836.33			−0.118950
$621$		0			0
$622$	796.818			0.0513657
$623$	10656.7	+	18458.0i	0.685318	+	1.18701i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−1028.85	+	1782.03i	−0.0656889	+	0.113777i
$627$		0			0
$628$	12812.1	+	22191.2i	0.814107	+	1.41007i
$629$	−18289.9			−1.15940
$630$		0			0
$631$	−20284.6			−1.27974			−0.639872	−	0.768482i	$-0.721013\pi$
$631$	−20284.6			−1.27974			−0.639872	+	0.768482i	$0.721013\pi$
$632$	819.490	+	1419.40i	0.0515784	+	0.0893364i
$633$		0			0
$634$	−883.888	+	1530.94i	−0.0553686	+	0.0959012i
$635$	−1482.52	+	2567.81i	−0.0926491	+	0.160473i
$636$		0			0
$637$	4772.70	+	8266.56i	0.296862	+	0.514180i
$638$	−2223.69			−0.137989
$639$		0			0
$640$	2594.08			0.160219
$641$	−10426.2	−	18058.7i	−0.642449	−	1.11275i	−0.984885	−	0.173212i	$-0.944585\pi$
$641$	−10426.2	−	18058.7i	−0.642449	−	1.11275i	0.342436	−	0.939541i	$-0.388748\pi$
$642$		0			0
$643$	1093.61	−	1894.19i	0.0670729	−	0.116174i	−0.830539	−	0.556961i	$-0.811967\pi$
$643$	1093.61	−	1894.19i	0.0670729	−	0.116174i	0.897612	+	0.440787i	$0.145301\pi$
$644$	5268.25	−	9124.88i	0.322357	−	0.558339i
$645$		0			0
$646$	1883.68	+	3262.63i	0.114725	+	0.198710i
$647$	−17044.1			−1.03566			−0.517831	−	0.855483i	$-0.673260\pi$
$647$	−17044.1			−1.03566			−0.517831	+	0.855483i	$0.673260\pi$
$648$		0			0
$649$	−11783.3			−0.712688
$650$	−233.423	−	404.301i	−0.0140856	−	0.0243969i
$651$		0			0
$652$	−2752.99	+	4768.32i	−0.165361	+	0.286414i
$653$	4237.13	−	7338.93i	0.253923	−	0.439808i	−0.710679	−	0.703516i	$-0.751612\pi$
$653$	4237.13	−	7338.93i	0.253923	−	0.439808i	0.964602	+	0.263708i	$0.0849456\pi$
$654$		0			0
$655$	−847.343	−	1467.64i	−0.0505472	−	0.0875504i
$656$	22725.6			1.35257
$657$		0			0
$658$	832.005			0.0492932
$659$	12780.1	+	22135.7i	0.755450	+	1.30848i	0.945151	+	0.326635i	$0.105915\pi$
$659$	12780.1	+	22135.7i	0.755450	+	1.30848i	−0.189701	+	0.981842i	$0.560752\pi$
$660$		0			0
$661$	−604.797	+	1047.54i	−0.0355883	+	0.0616407i	−0.883271	−	0.468863i	$-0.844664\pi$
$661$	−604.797	+	1047.54i	−0.0355883	+	0.0616407i	0.847683	+	0.530504i	$0.177997\pi$
$662$	297.076	−	514.551i	0.0174414	−	0.0302093i
$663$		0			0
$664$	2822.52	+	4888.74i	0.164962	+	0.285723i
$665$	−8956.46			−0.522281
$666$		0			0
$667$	−15955.6			−0.926241
$668$	−12756.5	−	22094.9i	−0.738869	−	1.27976i
$669$		0			0
$670$	−49.1914	+	85.2020i	−0.00283646	+	0.00491290i
$671$	1344.13	−	2328.10i	0.0773318	−	0.133943i
$672$		0			0
$673$	4349.11	+	7532.87i	0.249102	+	0.431457i	0.963277	−	0.268510i	$-0.0865312\pi$
$673$	4349.11	+	7532.87i	0.249102	+	0.431457i	−0.714175	+	0.699967i	$0.753198\pi$
$674$	1878.64			0.107362
$675$		0			0
$676$	−23902.0			−1.35992
$677$	−4212.24	−	7295.82i	−0.239128	−	0.414182i	0.721336	−	0.692585i	$-0.243528\pi$
$677$	−4212.24	−	7295.82i	−0.239128	−	0.414182i	−0.960464	+	0.278403i	$0.910195\pi$
$678$		0			0
$679$	−2431.84	+	4212.07i	−0.137445	+	0.238062i
$680$	1216.19	−	2106.50i	0.0685863	−	0.118795i
$681$		0			0
$682$	295.147	+	511.209i	0.0165715	+	0.0287026i
$683$	17828.6			0.998817			0.499408	−	0.866367i	$-0.333551\pi$
$683$	17828.6			0.998817			0.499408	+	0.866367i	$0.333551\pi$
$684$		0			0
$685$	−4057.21			−0.226304
$686$	892.470	+	1545.80i	0.0496715	+	0.0860336i
$687$		0			0
$688$	−3922.15	+	6793.37i	−0.217341	+	0.376446i
$689$	−493.689	+	855.095i	−0.0272976	+	0.0472809i
$690$		0			0
$691$	−7262.54	−	12579.1i	−0.399826	−	0.692519i	0.593878	−	0.804555i	$-0.297596\pi$
$691$	−7262.54	−	12579.1i	−0.399826	−	0.692519i	−0.993704	+	0.112036i	$0.964263\pi$
$692$	2360.45			0.129669
$693$		0			0
$694$	−1921.00			−0.105072
$695$	−7765.31	−	13449.9i	−0.423820	−	0.734078i
$696$		0			0
$697$	21491.0	−	37223.5i	1.16791	−	2.02287i
$698$	61.8529	−	107.132i	0.00335411	−	0.00580949i
$699$		0			0
$700$	1439.60	+	2493.45i	0.0777309	+	0.134634i
$701$	−18815.5			−1.01377			−0.506883	−	0.862015i	$-0.669202\pi$
$701$	−18815.5			−1.01377			−0.506883	+	0.862015i	$0.669202\pi$
$702$		0			0
$703$	19122.4			1.02591
$704$	11987.9	+	20763.6i	0.641777	+	1.11159i
$705$		0			0
$706$	−645.886	+	1118.71i	−0.0344310	+	0.0596362i
$707$	−8754.63	+	15163.5i	−0.465703	+	0.806621i
$708$		0			0
$709$	6467.21	+	11201.5i	0.342569	+	0.593346i	0.984909	−	0.173073i	$-0.0553697\pi$
$709$	6467.21	+	11201.5i	0.342569	+	0.593346i	−0.642340	+	0.766420i	$0.722036\pi$
$710$	942.105			0.0497980
$711$		0			0
$712$	6051.75			0.318538
$713$	2117.75	+	3668.06i	0.111235	+	0.192665i
$714$		0			0
$715$	8893.40	−	15403.8i	0.465167	−	0.805692i
$716$	13685.0	−	23703.2i	0.714293	−	1.23719i
$717$		0			0
$718$	−889.076	−	1539.92i	−0.0462117	−	0.0800411i
$719$	8471.10			0.439386			0.219693	−	0.975569i	$-0.429494\pi$
$719$	8471.10			0.439386			0.219693	+	0.975569i	$0.429494\pi$
$720$		0			0
$721$	15404.6			0.795695
$722$	−1082.18	−	1874.39i	−0.0557818	−	0.0966169i
$723$		0			0
$724$	−12255.6	+	21227.3i	−0.629109	+	1.08965i
$725$	2180.00	−	3775.87i	0.111673	−	0.193424i
$726$		0			0
$727$	−12184.7	−	21104.6i	−0.621605	−	1.07665i	−0.989187	−	0.146660i	$-0.953148\pi$
$727$	−12184.7	−	21104.6i	−0.621605	−	1.07665i	0.367582	−	0.929991i	$-0.380186\pi$
$728$	−4319.40			−0.219900
$729$		0			0
$730$	649.129			0.0329114
$731$	7418.17	+	12848.7i	0.375337	+	0.650102i
$732$		0			0
$733$	17705.9	−	30667.5i	0.892199	−	1.54533i	0.0549659	−	0.998488i	$-0.482495\pi$
$733$	17705.9	−	30667.5i	0.892199	−	1.54533i	0.837233	−	0.546846i	$-0.184172\pi$
$734$	1123.94	−	1946.72i	0.0565196	−	0.0978947i
$735$		0			0
$736$	−2246.94	−	3891.82i	−0.112532	−	0.194911i
$737$	−3748.37			−0.187345
$738$		0			0
$739$	−24447.0			−1.21691			−0.608456	−	0.793588i	$-0.708211\pi$
$739$	−24447.0			−1.21691			−0.608456	+	0.793588i	$0.708211\pi$
$740$	−3073.60	−	5323.63i	−0.152686	−	0.264460i
$741$		0			0
$742$	−25.6888	+	44.4943i	−0.00127098	+	0.00220140i
$743$	−12063.0	+	20893.7i	−0.595623	+	1.03165i	0.397836	+	0.917457i	$0.369761\pi$
$743$	−12063.0	+	20893.7i	−0.595623	+	1.03165i	−0.993459	+	0.114192i	$0.963572\pi$
$744$		0			0
$745$	−6352.53	−	11002.9i	−0.312401	−	0.541094i
$746$	904.081			0.0443710
$747$		0			0
$748$	46141.9			2.25550
$749$	−3452.08	−	5979.19i	−0.168406	−	0.291689i
$750$		0			0
$751$	−5941.19	+	10290.4i	−0.288678	+	0.500005i	−0.973494	−	0.228711i	$-0.926549\pi$
$751$	−5941.19	+	10290.4i	−0.288678	+	0.500005i	0.684816	+	0.728716i	$0.259882\pi$
$752$	−6911.31	+	11970.7i	−0.335146	+	0.580490i
$753$		0			0
$754$	1628.36	+	2820.41i	0.0786491	+	0.136224i
$755$	5626.85			0.271234
$756$		0			0
$757$	−14601.3			−0.701049			−0.350525	−	0.936554i	$-0.613997\pi$
$757$	−14601.3			−0.701049			−0.350525	+	0.936554i	$0.613997\pi$
$758$	750.632	+	1300.13i	0.0359686	+	0.0622994i
$759$		0			0
$760$	−1271.55	+	2202.39i	−0.0606894	+	0.105117i
$761$	−10148.2	+	17577.1i	−0.483404	+	0.837281i	−0.999818	−	0.0190580i	$-0.993933\pi$
$761$	−10148.2	+	17577.1i	−0.483404	+	0.837281i	0.516414	+	0.856339i	$0.327267\pi$
$762$		0			0
$763$	−9584.54	−	16600.9i	−0.454762	−	0.787671i
$764$	12154.4			0.575562
$765$		0			0
$766$	868.902			0.0409853
$767$	8628.65	+	14945.3i	0.406209	+	0.703575i
$768$		0			0
$769$	−18161.0	+	31455.8i	−0.851629	+	1.47506i	0.0281090	+	0.999605i	$0.491051\pi$
$769$	−18161.0	+	31455.8i	−0.851629	+	1.47506i	−0.879738	+	0.475459i	$0.842282\pi$
$770$	462.762	−	801.527i	0.0216582	−	0.0375130i
$771$		0			0
$772$	−20603.9	−	35686.9i	−0.960556	−	1.66373i
$773$	−28930.9			−1.34615			−0.673073	−	0.739576i	$-0.735026\pi$
$773$	−28930.9			−1.34615			−0.673073	+	0.739576i	$0.735026\pi$
$774$		0			0
$775$	−1157.39			−0.0536448
$776$	690.497	+	1195.98i	0.0319425	+	0.0553261i
$777$		0			0
$778$	2.47549	−	4.28767i	0.000114075	−	0.000197584i
$779$	−22469.3	+	38918.0i	−1.03344	+	1.78996i
$780$		0			0
$781$	17947.0	+	31085.2i	0.822274	+	1.42422i
$782$	−2793.36			−0.127737
$783$		0			0
$784$	−8251.80			−0.375902
$785$	8075.13	+	13986.5i	0.367151	+	0.635925i
$786$		0			0
$787$	−10564.1	+	18297.6i	−0.478489	+	0.828767i	−0.999696	−	0.0246632i	$-0.992149\pi$
$787$	−10564.1	+	18297.6i	−0.478489	+	0.828767i	0.521207	+	0.853430i	$0.325482\pi$
$788$	7955.32	−	13779.0i	0.359640	−	0.622915i
$789$		0			0
$790$	257.166	+	445.425i	0.0115817	+	0.0200601i
$791$	989.726			0.0444887
$792$		0			0
$793$	−3937.11			−0.176306
$794$	562.517	+	974.308i	0.0251423	+	0.0435477i
$795$		0			0
$796$	−11402.5	+	19749.7i	−0.507728	+	0.879410i
$797$	−1382.94	+	2395.32i	−0.0614632	+	0.106457i	−0.895120	−	0.445826i	$-0.852910\pi$
$797$	−1382.94	+	2395.32i	−0.0614632	+	0.106457i	0.833656	+	0.552283i	$0.186243\pi$
$798$		0			0
$799$	13071.7	+	22640.9i	0.578779	+	1.00247i
$800$	1228.00			0.0542702
$801$		0			0
$802$	−2199.47			−0.0968405
$803$	12365.9	+	21418.3i	0.543440	+	0.941265i
$804$		0			0
$805$	3320.44	−	5751.17i	0.145379	−	0.251804i
$806$	432.259	−	748.694i	0.0188904	−	0.0327191i
$807$		0			0
$808$	2485.79	+	4305.52i	0.108230	+	0.187460i
$809$	−16756.6			−0.728220			−0.364110	−	0.931356i	$-0.618627\pi$
$809$	−16756.6			−0.728220			−0.364110	+	0.931356i	$0.618627\pi$
$810$		0			0
$811$	17829.6			0.771987			0.385993	−	0.922502i	$-0.373859\pi$
$811$	17829.6			0.771987			0.385993	+	0.922502i	$0.373859\pi$
$812$	−10042.6	−	17394.4i	−0.434024	−	0.751751i
$813$		0			0
$814$	−988.017	+	1711.29i	−0.0425429	+	0.0736865i
$815$	−1735.13	+	3005.34i	−0.0745756	+	0.129169i
$816$		0			0
$817$	−7755.86	−	13433.5i	−0.332121	−	0.575251i
$818$	−727.154			−0.0310811
$819$		0			0
$820$	14446.2			0.615224
$821$	−3378.74	−	5852.15i	−0.143628	−	0.248771i	0.785232	−	0.619202i	$-0.212544\pi$
$821$	−3378.74	−	5852.15i	−0.143628	−	0.248771i	−0.928860	+	0.370430i	$0.879210\pi$
$822$		0			0
$823$	−3560.64	+	6167.21i	−0.150809	+	0.261210i	−0.931525	−	0.363677i	$-0.881521\pi$
$823$	−3560.64	+	6167.21i	−0.150809	+	0.261210i	0.780716	+	0.624886i	$0.214855\pi$
$824$	2186.99	−	3787.98i	0.0924604	−	0.160146i
$825$		0			0
$826$	448.986	+	777.666i	0.0189131	+	0.0327584i
$827$	1171.74			0.0492688			0.0246344	−	0.999697i	$-0.492158\pi$
$827$	1171.74			0.0492688			0.0246344	+	0.999697i	$0.492158\pi$
$828$		0			0
$829$	23617.8			0.989483			0.494742	−	0.869040i	$-0.335263\pi$
$829$	23617.8			0.989483			0.494742	+	0.869040i	$0.335263\pi$
$830$	885.741	+	1534.15i	0.0370416	+	0.0641579i
$831$		0			0
$832$	17557.0	−	30409.5i	0.731584	−	1.26714i
$833$	−7803.53	+	13516.1i	−0.324581	+	0.562191i
$834$		0			0
$835$	−8040.09	−	13925.8i	−0.333220	−	0.577154i
$836$	−48242.4			−1.99581
$837$		0			0
$838$	4231.35			0.174427
$839$	−17527.2	−	30358.0i	−0.721222	−	1.24919i	−0.960510	−	0.278244i	$-0.910247\pi$
$839$	−17527.2	−	30358.0i	−0.721222	−	1.24919i	0.239288	−	0.970949i	$-0.423086\pi$
$840$		0			0
$841$	−3013.21	+	5219.03i	−0.123548	+	0.213991i
$842$	583.512	−	1010.67i	0.0238826	−	0.0413659i
$843$		0			0
$844$	−10907.7	−	18892.7i	−0.444857	−	0.770515i
$845$	−15064.8			−0.613306
$846$		0			0
$847$	15939.6			0.646627
$848$	−426.784	−	739.212i	−0.0172828	−	0.0299347i
$849$		0			0
$850$	381.655	−	661.046i	0.0154008	−	0.0266749i
$851$	−7089.28	+	12279.0i	−0.285567	+	0.494616i
$852$		0			0
$853$	16386.2	+	28381.7i	0.657740	+	1.13924i	0.981199	+	0.192996i	$0.0618206\pi$
$853$	16386.2	+	28381.7i	0.657740	+	1.13924i	−0.323460	+	0.946242i	$0.604846\pi$
$854$	−204.865			−0.00820882
$855$		0			0
$856$	−1960.37			−0.0782758
$857$	−1751.96	−	3034.49i	−0.0698319	−	0.120952i	0.828995	−	0.559256i	$-0.188913\pi$
$857$	−1751.96	−	3034.49i	−0.0698319	−	0.120952i	−0.898827	+	0.438303i	$0.855580\pi$
$858$		0			0
$859$	−15522.0	+	26885.0i	−0.616537	+	1.06787i	0.373576	+	0.927600i	$0.378132\pi$
$859$	−15522.0	+	26885.0i	−0.616537	+	1.06787i	−0.990113	+	0.140274i	$0.955202\pi$
$860$	−2493.24	+	4318.42i	−0.0988591	+	0.171229i
$861$		0			0
$862$	756.795	+	1310.81i	0.0299032	+	0.0517938i
$863$	−26333.6			−1.03871			−0.519354	−	0.854559i	$-0.673827\pi$
$863$	−26333.6			−1.03871			−0.519354	+	0.854559i	$0.673827\pi$
$864$		0			0
$865$	1487.73			0.0584790
$866$	496.316	+	859.644i	0.0194752	+	0.0337320i
$867$		0			0
$868$	−2665.88	+	4617.44i	−0.104246	+	0.180560i
$869$	−9798.01	+	16970.6i	−0.382479	+	0.662474i
$870$		0			0
$871$	2744.85	+	4754.22i	0.106780	+	0.184949i
$872$	−5442.87			−0.211375
$873$		0			0
$874$	2920.52			0.113030
$875$	907.339	+	1571.56i	0.0350556	+	0.0607181i
$876$		0			0
$877$	20488.7	−	35487.4i	0.788886	−	1.36639i	−0.137764	−	0.990465i	$-0.543992\pi$
$877$	20488.7	−	35487.4i	0.788886	−	1.36639i	0.926650	−	0.375925i	$-0.122675\pi$
$878$	−2099.11	+	3635.76i	−0.0806850	+	0.139751i
$879$		0			0
$880$	7688.16	+	13316.3i	0.294509	+	0.510104i
$881$	−37022.4			−1.41579			−0.707897	−	0.706315i	$-0.750356\pi$
$881$	−37022.4			−1.41579			−0.707897	+	0.706315i	$0.750356\pi$
$882$		0			0
$883$	−36037.9			−1.37347			−0.686734	−	0.726909i	$-0.740956\pi$
$883$	−36037.9			−1.37347			−0.686734	+	0.726909i	$0.740956\pi$
$884$	−33788.7	−	58523.8i	−1.28556	−	2.22666i
$885$		0			0
$886$	867.350	−	1502.29i	0.0328885	−	0.0569645i
$887$	732.525	−	1268.77i	0.0277292	−	0.0480284i	−0.851828	−	0.523822i	$-0.824506\pi$
$887$	732.525	−	1268.77i	0.0277292	−	0.0480284i	0.879557	+	0.475794i	$0.157839\pi$
$888$		0			0
$889$	4304.48	+	7455.59i	0.162393	+	0.281274i
$890$	1899.12			0.0715265
$891$		0			0
$892$	6217.36			0.233377
$893$	−13666.8	−	23671.5i	−0.512140	−	0.887053i
$894$		0			0
$895$	8625.31	−	14939.5i	0.322137	−	0.557957i
$896$	3765.94	−	6522.79i	0.140414	−	0.243205i
$897$		0			0
$898$	27.5658	+	47.7453i	0.00102437	+	0.00177426i
$899$	8073.96			0.299535
$900$		0			0
$901$	−1614.40			−0.0596930
$902$	−2321.89	−	4021.62i	−0.0857099	−	0.148454i
$903$		0			0
$904$	140.512	−	243.373i	0.00516963	−	0.00895406i
$905$	−7724.37	+	13379.0i	−0.283720	+	0.491418i
$906$		0			0
$907$	−16830.4	−	29151.1i	−0.616146	−	1.06720i	−0.990182	−	0.139782i	$-0.955360\pi$
$907$	−16830.4	−	29151.1i	−0.616146	−	1.06720i	0.374037	−	0.927414i	$-0.377973\pi$
$908$	−1155.57			−0.0422346
$909$		0			0
$910$	−1355.48			−0.0493778
$911$	12996.4	+	22510.4i	0.472655	+	0.818663i	0.999510	−	0.0312922i	$-0.00996224\pi$
$911$	12996.4	+	22510.4i	0.472655	+	0.818663i	−0.526855	+	0.849955i	$0.676629\pi$
$912$		0			0
$913$	−33746.6	+	58450.9i	−1.22328	+	2.11878i
$914$	−2129.47	+	3688.35i	−0.0770641	+	0.133479i
$915$		0			0
$916$	−13533.1	−	23440.0i	−0.488151	−	0.845503i
$917$	−4920.50			−0.177196
$918$		0			0
$919$	1149.54			0.0412620			0.0206310	−	0.999787i	$-0.493432\pi$
$919$	1149.54			0.0412620			0.0206310	+	0.999787i	$0.493432\pi$
$920$	−942.806	−	1632.99i	−0.0337863	−	0.0585196i
$921$		0			0
$922$	202.062	−	349.982i	0.00721752	−	0.0125011i
$923$	26284.5	−	45526.0i	0.937338	−	1.62352i
$924$		0			0
$925$	−1937.21	−	3355.34i	−0.0688595	−	0.119268i
$926$	−1532.68			−0.0543921
$927$		0			0
$928$	−8566.50			−0.303027
$929$	961.599	+	1665.54i	0.0339602	+	0.0588208i	0.882506	−	0.470301i	$-0.155855\pi$
$929$	961.599	+	1665.54i	0.0339602	+	0.0588208i	−0.848546	+	0.529122i	$0.822521\pi$
$930$		0			0
$931$	8158.76	−	14131.4i	0.287210	−	0.497462i
$932$	−535.389	+	927.322i	−0.0188168	+	0.0325917i
$933$		0			0
$934$	−2316.14	−	4011.66i	−0.0811416	−	0.140541i
$935$	29082.0			1.01720
$936$		0			0
$937$	3511.90			0.122443			0.0612213	−	0.998124i	$-0.480500\pi$
$937$	3511.90			0.122443			0.0612213	+	0.998124i	$0.480500\pi$
$938$	142.827	+	247.383i	0.00497170	+	0.00861123i
$939$		0			0
$940$	−4393.40	+	7609.59i	−0.152443	+	0.264040i
$941$	−3424.08	+	5930.68i	−0.118620	+	0.205456i	−0.919221	−	0.393742i	$-0.871180\pi$
$941$	−3424.08	+	5930.68i	−0.118620	+	0.205456i	0.800601	+	0.599198i	$0.204514\pi$
$942$		0			0
$943$	−16660.1	−	28856.2i	−0.575322	−	0.996487i
$944$	−14918.6			−0.514363
$945$		0			0
$946$	1602.92			0.0550902
$947$	24178.6	+	41878.6i	0.829673	+	1.43704i	0.898295	+	0.439393i	$0.144806\pi$
$947$	24178.6	+	41878.6i	0.829673	+	1.43704i	−0.0686220	+	0.997643i	$0.521860\pi$
$948$		0			0
$949$	18110.5	−	31368.3i	0.619486	−	1.07298i
$950$	−399.029	+	691.138i	−0.0136276	+	0.0236037i
$951$		0			0
$952$	−3531.18	−	6116.19i	−0.120217	−	0.208221i
$953$	−38701.1			−1.31548			−0.657740	−	0.753245i	$-0.728488\pi$
$953$	−38701.1			−1.31548			−0.657740	+	0.753245i	$0.728488\pi$
$954$		0			0
$955$	7660.57			0.259571
$956$	8906.15	+	15425.9i	0.301303	+	0.521872i
$957$		0			0
$958$	1282.62	−	2221.57i	0.0432564	−	0.0749223i
$959$	−5890.02	+	10201.8i	−0.198330	+	0.343518i
$960$		0			0
$961$	13823.9	+	23943.6i	0.464028	+	0.803720i
$962$	2894.01			0.0969924
$963$		0			0
$964$	−32990.0			−1.10222
$965$	−12986.1	−	22492.5i	−0.433198	−	0.750321i
$966$		0			0
$967$	12156.4	−	21055.4i	0.404263	−	0.700204i	−0.589972	−	0.807423i	$-0.700861\pi$
$967$	12156.4	−	21055.4i	0.404263	−	0.700204i	0.994235	+	0.107219i	$0.0341947\pi$
$968$	2262.95	−	3919.55i	0.0751385	−	0.130144i
$969$		0			0
$970$	216.687	+	375.312i	0.00717257	+	0.0124233i
$971$	37464.3			1.23820			0.619098	−	0.785314i	$-0.287499\pi$
$971$	37464.3			1.23820			0.619098	+	0.785314i	$0.287499\pi$
$972$		0			0
$973$	−45092.9			−1.48573
$974$	−1540.74	−	2668.64i	−0.0506863	−	0.0877912i
$975$		0			0
$976$	1701.78	−	2947.56i	0.0558120	−	0.0966692i
$977$	1593.05	−	2759.24i	0.0521659	−	0.0903540i	−0.838763	−	0.544496i	$-0.816721\pi$
$977$	1593.05	−	2759.24i	0.0521659	−	0.0903540i	0.890929	+	0.454142i	$0.150054\pi$
$978$		0			0
$979$	36178.1	+	62662.3i	1.18106	+	2.04565i
$980$	−5245.52			−0.170982
$981$		0			0
$982$	−2862.33			−0.0930150
$983$	15172.8	+	26280.1i	0.492307	+	0.852700i	0.999961	−	0.00886069i	$-0.00282048\pi$
$983$	15172.8	+	26280.1i	0.492307	+	0.852700i	−0.507654	+	0.861561i	$0.669487\pi$
$984$		0			0
$985$	5014.02	−	8684.54i	0.162193	−	0.280926i
$986$	−2662.43	+	4611.46i	−0.0859929	+	0.148944i
$987$		0			0
$988$	35326.8	+	61187.9i	1.13755	+	1.97029i
$989$	11501.3			0.369789
$990$		0			0
$991$	3443.75			0.110388			0.0551940	−	0.998476i	$-0.482422\pi$
$991$	3443.75			0.110388			0.0551940	+	0.998476i	$0.482422\pi$
$992$	1137.02	+	1969.37i	0.0363914	+	0.0630318i
$993$		0			0
$994$	1367.69	−	2368.92i	0.0436425	−	0.0755910i
$995$	−7186.69	+	12447.7i	−0.228978	+	0.396602i
$996$		0			0
$997$	2283.95	+	3955.91i	0.0725510	+	0.125662i	0.900019	−	0.435851i	$-0.143553\pi$
$997$	2283.95	+	3955.91i	0.0725510	+	0.125662i	−0.827468	+	0.561513i	$0.810219\pi$
$998$	2418.25			0.0767017
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.r.271.2		6
3.2	odd	2		405.4.e.t.271.2		6
9.2	odd	6		405.4.e.t.136.2		6
9.4	even	3		135.4.a.g.1.2	yes	3
9.5	odd	6		135.4.a.f.1.2	✓	3
9.7	even	3	inner	405.4.e.r.136.2		6
36.23	even	6		2160.4.a.bm.1.2		3
36.31	odd	6		2160.4.a.be.1.2		3
45.4	even	6		675.4.a.q.1.2		3
45.13	odd	12		675.4.b.k.649.3		6
45.14	odd	6		675.4.a.r.1.2		3
45.22	odd	12		675.4.b.k.649.4		6
45.23	even	12		675.4.b.l.649.4		6
45.32	even	12		675.4.b.l.649.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.f.1.2	✓	3	9.5	odd	6
135.4.a.g.1.2	yes	3	9.4	even	3
405.4.e.r.136.2		6	9.7	even	3	inner
405.4.e.r.271.2		6	1.1	even	1	trivial
405.4.e.t.136.2		6	9.2	odd	6
405.4.e.t.271.2		6	3.2	odd	2
675.4.a.q.1.2		3	45.4	even	6
675.4.a.r.1.2		3	45.14	odd	6
675.4.b.k.649.3		6	45.13	odd	12
675.4.b.k.649.4		6	45.22	odd	12
675.4.b.l.649.3		6	45.32	even	12
675.4.b.l.649.4		6	45.23	even	12
2160.4.a.be.1.2		3	36.31	odd	6
2160.4.a.bm.1.2		3	36.23	even	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.129356 - 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} -4.12208 q^{8} +O(q^{10})\)	\(q+(-0.129356 - 0.224051i) q^{2} +(3.96653 - 6.87024i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.25871 - 12.5725i) q^{7} -4.12208 q^{8} -1.29356 q^{10} +(-24.6423 - 42.6817i) q^{11} +(-36.0900 + 62.5097i) q^{13} +(-1.87792 + 3.25265i) q^{14} +(-31.1991 - 54.0383i) q^{16} -118.017 q^{17} +123.389 q^{19} +(-19.8327 - 34.3512i) q^{20} +(-6.37526 + 11.0423i) q^{22} +(-45.7442 + 79.2312i) q^{23} +(-12.5000 - 21.6506i) q^{25} +18.6739 q^{26} -115.168 q^{28} +(87.2001 + 151.035i) q^{29} +(23.1478 - 40.0932i) q^{31} +(-24.5599 + 42.5390i) q^{32} +(15.2662 + 26.4418i) q^{34} -72.5871 q^{35} +154.977 q^{37} +(-15.9611 - 27.6455i) q^{38} +(-10.3052 + 17.8491i) q^{40} +(-182.101 + 315.409i) q^{41} +(-62.8569 - 108.871i) q^{43} -390.978 q^{44} +23.6692 q^{46} +(-110.762 - 191.845i) q^{47} +(66.1222 - 114.527i) q^{49} +(-3.23390 + 5.60129i) q^{50} +(286.304 + 495.894i) q^{52} +13.6794 q^{53} -246.423 q^{55} +(29.9210 + 51.8247i) q^{56} +(22.5597 - 39.0746i) q^{58} +(119.543 - 207.055i) q^{59} +(27.2729 + 47.2380i) q^{61} -11.9772 q^{62} -486.477 q^{64} +(180.450 + 312.549i) q^{65} +(38.0279 - 65.8662i) q^{67} +(-468.118 + 810.804i) q^{68} +(9.38959 + 16.2633i) q^{70} -728.303 q^{71} -501.815 q^{73} +(-20.0472 - 34.7227i) q^{74} +(489.427 - 847.712i) q^{76} +(-357.742 + 619.628i) q^{77} +(-198.805 - 344.340i) q^{79} -311.991 q^{80} +94.2237 q^{82} +(-684.731 - 1185.99i) q^{83} +(-295.042 + 511.028i) q^{85} +(-16.2619 + 28.1664i) q^{86} +(101.577 + 175.937i) q^{88} -1468.13 q^{89} +1047.87 q^{91} +(362.892 + 628.547i) q^{92} +(-28.6554 + 49.6326i) q^{94} +(308.473 - 534.290i) q^{95} +(-167.512 - 290.139i) q^{97} -34.2133 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8}+O(q^{10}) \) 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8	\( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98}+O(q^{100}) \) 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8 - 10 * q^10 + 38 * q^11 - 28 * q^13 - 108 * q^14 - 191 * q^16 + 38 * q^17 + 374 * q^19 + 115 * q^20 - 122 * q^22 - 81 * q^23 - 75 * q^25 - 832 * q^26 + 820 * q^28 + 160 * q^29 - 227 * q^31 - 569 * q^32 - 17 * q^34 - 440 * q^35 + 156 * q^37 - 757 * q^38 + 180 * q^40 - 338 * q^41 - 22 * q^43 - 3272 * q^44 - 2850 * q^46 - 472 * q^47 + 197 * q^49 - 25 * q^50 + 1566 * q^52 - 1042 * q^53 + 380 * q^55 - 1254 * q^56 + 2096 * q^58 + 140 * q^59 - 595 * q^61 - 2814 * q^62 - 1836 * q^64 + 140 * q^65 - 878 * q^67 - 3053 * q^68 + 540 * q^70 + 1204 * q^71 + 2588 * q^73 + 2878 * q^74 - 525 * q^76 + 288 * q^77 - 629 * q^79 - 1910 * q^80 - 3364 * q^82 - 1287 * q^83 + 95 * q^85 - 3730 * q^86 + 858 * q^88 - 4308 * q^89 - 880 * q^91 + 1959 * q^92 + 1108 * q^94 + 935 * q^95 - 1392 * q^97 + 5386 * q^98

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