LMFDB - Embedded newform 405.4.e.u.271.3

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:	6.0.148347072.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 29x^{4} + 223x^{2} + 243 $ x^6 + 29x^4 + 223x^2 + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.3
Root			$4.00586i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.u.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76174 + 3.05142i) q^{2} +(-2.20744 + 3.82340i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-12.7162 - 22.0252i) q^{7} +12.6321 q^{8} +O(q^{10})$	\(q+(1.76174 + 3.05142i) q^{2} +(-2.20744 + 3.82340i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-12.7162 - 22.0252i) q^{7} +12.6321 q^{8} -17.6174 q^{10} +(35.6781 + 61.7962i) q^{11} +(25.6968 - 44.5081i) q^{13} +(44.8053 - 77.6051i) q^{14} +(39.9139 + 69.1330i) q^{16} -33.3191 q^{17} +113.372 q^{19} +(-11.0372 - 19.1170i) q^{20} +(-125.711 + 217.738i) q^{22} +(-40.9884 + 70.9939i) q^{23} +(-12.5000 - 21.6506i) q^{25} +181.084 q^{26} +112.281 q^{28} +(123.414 + 213.759i) q^{29} +(-111.340 + 192.846i) q^{31} +(-90.1075 + 156.071i) q^{32} +(-58.6995 - 101.671i) q^{34} +127.162 q^{35} +22.3910 q^{37} +(199.731 + 345.945i) q^{38} +(-31.5802 + 54.6985i) q^{40} +(217.113 - 376.050i) q^{41} +(118.425 + 205.118i) q^{43} -315.029 q^{44} -288.843 q^{46} +(53.9919 + 93.5166i) q^{47} +(-151.905 + 263.107i) q^{49} +(44.0435 - 76.2855i) q^{50} +(113.448 + 196.498i) q^{52} -123.961 q^{53} -356.781 q^{55} +(-160.632 - 278.223i) q^{56} +(-434.845 + 753.174i) q^{58} +(-85.5454 + 148.169i) q^{59} +(39.7196 + 68.7963i) q^{61} -784.604 q^{62} +3.63945 q^{64} +(128.484 + 222.540i) q^{65} +(305.753 - 529.580i) q^{67} +(73.5500 - 127.392i) q^{68} +(224.027 + 388.026i) q^{70} +511.102 q^{71} -410.012 q^{73} +(39.4471 + 68.3243i) q^{74} +(-250.262 + 433.466i) q^{76} +(907.381 - 1571.63i) q^{77} +(396.798 + 687.275i) q^{79} -399.139 q^{80} +1529.98 q^{82} +(-135.040 - 233.897i) q^{83} +(83.2977 - 144.276i) q^{85} +(-417.267 + 722.727i) q^{86} +(450.688 + 780.614i) q^{88} +177.400 q^{89} -1307.06 q^{91} +(-180.959 - 313.430i) q^{92} +(-190.239 + 329.504i) q^{94} +(-283.430 + 490.914i) q^{95} +(440.930 + 763.714i) q^{97} -1070.47 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 5 q^{4} - 15 q^{5} + 25 q^{7} + 54 q^{8}+O(q^{10}) $ 6 * q + q^2 - 5 * q^4 - 15 * q^5 + 25 * q^7 + 54 * q^8	$ 6 q + q^{2} - 5 q^{4} - 15 q^{5} + 25 q^{7} + 54 q^{8} - 10 q^{10} + 58 q^{11} + 47 q^{13} + 159 q^{14} + 127 q^{16} - 68 q^{17} - 10 q^{19} - 25 q^{20} - 260 q^{22} - 51 q^{23} - 75 q^{25} - 506 q^{26} + 166 q^{28} + 350 q^{29} - 638 q^{31} + 245 q^{32} + 154 q^{34} - 250 q^{35} - 828 q^{37} + 397 q^{38} - 135 q^{40} + 179 q^{41} + 836 q^{43} - 664 q^{44} + 522 q^{46} + 235 q^{47} - 892 q^{49} + 25 q^{50} + 1335 q^{52} - 1010 q^{53} - 580 q^{55} + 15 q^{56} - 1876 q^{58} + 535 q^{59} + 104 q^{61} - 696 q^{62} - 606 q^{64} + 235 q^{65} + 40 q^{67} + 830 q^{68} + 795 q^{70} - 904 q^{71} - 1420 q^{73} + 1394 q^{74} - 849 q^{76} + 2148 q^{77} + 634 q^{79} - 1270 q^{80} + 1226 q^{82} + 1734 q^{83} + 170 q^{85} + 460 q^{86} + 768 q^{88} + 1704 q^{89} - 2458 q^{91} - 1839 q^{92} - 1751 q^{94} + 25 q^{95} - 76 q^{98}+O(q^{100}) $ 6 * q + q^2 - 5 * q^4 - 15 * q^5 + 25 * q^7 + 54 * q^8 - 10 * q^10 + 58 * q^11 + 47 * q^13 + 159 * q^14 + 127 * q^16 - 68 * q^17 - 10 * q^19 - 25 * q^20 - 260 * q^22 - 51 * q^23 - 75 * q^25 - 506 * q^26 + 166 * q^28 + 350 * q^29 - 638 * q^31 + 245 * q^32 + 154 * q^34 - 250 * q^35 - 828 * q^37 + 397 * q^38 - 135 * q^40 + 179 * q^41 + 836 * q^43 - 664 * q^44 + 522 * q^46 + 235 * q^47 - 892 * q^49 + 25 * q^50 + 1335 * q^52 - 1010 * q^53 - 580 * q^55 + 15 * q^56 - 1876 * q^58 + 535 * q^59 + 104 * q^61 - 696 * q^62 - 606 * q^64 + 235 * q^65 + 40 * q^67 + 830 * q^68 + 795 * q^70 - 904 * q^71 - 1420 * q^73 + 1394 * q^74 - 849 * q^76 + 2148 * q^77 + 634 * q^79 - 1270 * q^80 + 1226 * q^82 + 1734 * q^83 + 170 * q^85 + 460 * q^86 + 768 * q^88 + 1704 * q^89 - 2458 * q^91 - 1839 * q^92 - 1751 * q^94 + 25 * q^95 - 76 * 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 $

$2$	1.76174	+	3.05142i	0.622868	+	1.07884i	0.988949	+	0.148257i	$0.0473662\pi$
$2$	1.76174	+	3.05142i	0.622868	+	1.07884i	−0.366080	+	0.930583i	$0.619300\pi$
$3$		0			0
$3$		0			0
$4$	−2.20744	+	3.82340i	−0.275930	+	0.477925i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−12.7162	−	22.0252i	−0.686612	−	1.18925i	−0.972927	−	0.231111i	$-0.925764\pi$
$7$	−12.7162	−	22.0252i	−0.686612	−	1.18925i	0.286315	−	0.958135i	$-0.407570\pi$
$8$	12.6321			0.558264
$9$		0			0
$10$	−17.6174			−0.557111
$11$	35.6781	+	61.7962i	0.977940	+	1.69384i	0.669870	+	0.742479i	$0.266350\pi$
$11$	35.6781	+	61.7962i	0.977940	+	1.69384i	0.308071	+	0.951363i	$0.400317\pi$
$12$		0			0
$13$	25.6968	−	44.5081i	0.548231	−	0.949563i	−0.450165	−	0.892945i	$-0.648635\pi$
$13$	25.6968	−	44.5081i	0.548231	−	0.949563i	0.998396	−	0.0566179i	$-0.0180317\pi$
$14$	44.8053	−	77.6051i	0.855338	−	1.48149i
$15$		0			0
$16$	39.9139	+	69.1330i	0.623655	+	1.08020i
$17$	−33.3191			−0.475357			−0.237678	−	0.971344i	$-0.576386\pi$
$17$	−33.3191			−0.475357			−0.237678	+	0.971344i	$0.576386\pi$
$18$		0			0
$19$	113.372			1.36891			0.684455	−	0.729055i	$-0.260040\pi$
$19$	113.372			1.36891			0.684455	+	0.729055i	$0.260040\pi$
$20$	−11.0372	−	19.1170i	−0.123400	−	0.213735i
$21$		0			0
$22$	−125.711	+	217.738i	−1.21826	+	2.11008i
$23$	−40.9884	+	70.9939i	−0.371594	+	0.643620i	−0.989811	−	0.142388i	$-0.954522\pi$
$23$	−40.9884	+	70.9939i	−0.371594	+	0.643620i	0.618217	+	0.786008i	$0.287855\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	181.084			1.36590
$27$		0			0
$28$	112.281			0.757828
$29$	123.414	+	213.759i	0.790253	+	1.36876i	0.925810	+	0.377989i	$0.123384\pi$
$29$	123.414	+	213.759i	0.790253	+	1.36876i	−0.135557	+	0.990770i	$0.543282\pi$
$30$		0			0
$31$	−111.340	+	192.846i	−0.645070	+	1.11729i	0.339215	+	0.940709i	$0.389838\pi$
$31$	−111.340	+	192.846i	−0.645070	+	1.11729i	−0.984285	+	0.176585i	$0.943495\pi$
$32$	−90.1075	+	156.071i	−0.497779	+	0.862178i
$33$		0			0
$34$	−58.6995	−	101.671i	−0.296085	−	0.512834i
$35$	127.162			0.614124
$36$		0			0
$37$	22.3910			0.0994880			0.0497440	−	0.998762i	$-0.484159\pi$
$37$	22.3910			0.0994880			0.0497440	+	0.998762i	$0.484159\pi$
$38$	199.731	+	345.945i	0.852651	+	1.47683i
$39$		0			0
$40$	−31.5802	+	54.6985i	−0.124832	+	0.216215i
$41$	217.113	−	376.050i	0.827007	−	1.43242i	−0.0733680	−	0.997305i	$-0.523375\pi$
$41$	217.113	−	376.050i	0.827007	−	1.43242i	0.900375	−	0.435114i	$-0.143292\pi$
$42$		0			0
$43$	118.425	+	205.118i	0.419991	+	0.727446i	0.995938	−	0.0900414i	$-0.0286999\pi$
$43$	118.425	+	205.118i	0.419991	+	0.727446i	−0.575947	+	0.817487i	$0.695367\pi$
$44$	−315.029			−1.07937
$45$		0			0
$46$	−288.843			−0.925817
$47$	53.9919	+	93.5166i	0.167564	+	0.290230i	0.937563	−	0.347816i	$-0.113076\pi$
$47$	53.9919	+	93.5166i	0.167564	+	0.290230i	−0.769999	+	0.638046i	$0.779743\pi$
$48$		0			0
$49$	−151.905	+	263.107i	−0.442872	+	0.767077i
$50$	44.0435	−	76.2855i	0.124574	−	0.215768i
$51$		0			0
$52$	113.448	+	196.498i	0.302547	+	0.524027i
$53$	−123.961			−0.321272			−0.160636	−	0.987014i	$-0.551354\pi$
$53$	−123.961			−0.321272			−0.160636	+	0.987014i	$0.551354\pi$
$54$		0			0
$55$	−356.781			−0.874696
$56$	−160.632	−	278.223i	−0.383311	−	0.663913i
$57$		0			0
$58$	−434.845	+	753.174i	−0.984447	+	1.70511i
$59$	−85.5454	+	148.169i	−0.188764	+	0.326949i	−0.944838	−	0.327537i	$-0.893781\pi$
$59$	−85.5454	+	148.169i	−0.188764	+	0.326949i	0.756074	+	0.654486i	$0.227115\pi$
$60$		0			0
$61$	39.7196	+	68.7963i	0.0833700	+	0.144401i	0.904695	−	0.426059i	$-0.140098\pi$
$61$	39.7196	+	68.7963i	0.0833700	+	0.144401i	−0.821325	+	0.570460i	$0.806765\pi$
$62$	−784.604			−1.60717
$63$		0			0
$64$	3.63945			0.00710830
$65$	128.484	+	222.540i	0.245176	+	0.424658i
$66$		0			0
$67$	305.753	−	529.580i	0.557517	−	0.965648i	−0.440186	−	0.897907i	$-0.645087\pi$
$67$	305.753	−	529.580i	0.557517	−	0.965648i	0.997703	−	0.0677416i	$-0.0215793\pi$
$68$	73.5500	−	127.392i	0.131165	−	0.227185i
$69$		0			0
$70$	224.027	+	388.026i	0.382519	+	0.662542i
$71$	511.102			0.854318			0.427159	−	0.904176i	$-0.359514\pi$
$71$	511.102			0.854318			0.427159	+	0.904176i	$0.359514\pi$
$72$		0			0
$73$	−410.012			−0.657373			−0.328686	−	0.944439i	$-0.606606\pi$
$73$	−410.012			−0.657373			−0.328686	+	0.944439i	$0.606606\pi$
$74$	39.4471	+	68.3243i	0.0619680	+	0.107332i
$75$		0			0
$76$	−250.262	+	433.466i	−0.377724	+	0.654236i
$77$	907.381	−	1571.63i	1.34293	−	2.32602i
$78$		0			0
$79$	396.798	+	687.275i	0.565105	+	0.978791i	0.997040	+	0.0768858i	$0.0244977\pi$
$79$	396.798	+	687.275i	0.565105	+	0.978791i	−0.431935	+	0.901905i	$0.642169\pi$
$80$	−399.139			−0.557814
$81$		0			0
$82$	1529.98			2.06047
$83$	−135.040	−	233.897i	−0.178586	−	0.309319i	0.762811	−	0.646622i	$-0.223819\pi$
$83$	−135.040	−	233.897i	−0.178586	−	0.309319i	−0.941396	+	0.337302i	$0.890486\pi$
$84$		0			0
$85$	83.2977	−	144.276i	0.106293	−	0.184105i
$86$	−417.267	+	722.727i	−0.523198	+	0.906206i
$87$		0			0
$88$	450.688	+	780.614i	0.545949	+	0.945611i
$89$	177.400			0.211284			0.105642	−	0.994404i	$-0.466310\pi$
$89$	177.400			0.211284			0.105642	+	0.994404i	$0.466310\pi$
$90$		0			0
$91$	−1307.06			−1.50569
$92$	−180.959	−	313.430i	−0.205068	−	0.355188i
$93$		0			0
$94$	−190.239	+	329.504i	−0.208741	+	0.361550i
$95$	−283.430	+	490.914i	−0.306097	+	0.530176i
$96$		0			0
$97$	440.930	+	763.714i	0.461543	+	0.799416i	0.999038	−	0.0438508i	$-0.0139626\pi$
$97$	440.930	+	763.714i	0.461543	+	0.799416i	−0.537495	+	0.843267i	$0.680629\pi$
$98$	−1070.47			−1.10340
$99$		0			0
$100$	110.372			0.110372
$101$	−513.017	−	888.572i	−0.505417	−	0.875408i	−0.999980	−	0.00626636i	$-0.998005\pi$
$101$	−513.017	−	888.572i	−0.505417	−	0.875408i	0.494563	−	0.869142i	$-0.335328\pi$
$102$		0			0
$103$	895.139	−	1550.43i	0.856317	−	1.48318i	−0.0191010	−	0.999818i	$-0.506080\pi$
$103$	895.139	−	1550.43i	0.856317	−	1.48318i	0.875418	−	0.483367i	$-0.160586\pi$
$104$	324.603	−	562.229i	0.306057	−	0.530107i
$105$		0			0
$106$	−218.387	−	378.258i	−0.200110	−	0.346601i
$107$	−2007.30			−1.81358			−0.906788	−	0.421587i	$-0.861473\pi$
$107$	−2007.30			−1.81358			−0.906788	+	0.421587i	$0.861473\pi$
$108$		0			0
$109$	−211.654			−0.185989			−0.0929945	−	0.995667i	$-0.529644\pi$
$109$	−211.654			−0.185989			−0.0929945	+	0.995667i	$0.529644\pi$
$110$	−628.554	−	1088.69i	−0.544821	−	0.943657i
$111$		0			0
$112$	1015.11	−	1758.22i	0.856418	−	1.48336i
$113$	−0.972457	+	1.68434i	−0.000809567	+	0.00140221i	−0.866430	−	0.499299i	$-0.833591\pi$
$113$	−0.972457	+	1.68434i	−0.000809567	+	0.00140221i	0.865620	+	0.500701i	$0.166924\pi$
$114$		0			0
$115$	−204.942	−	354.970i	−0.166182	−	0.287836i
$116$	−1089.71			−0.872219
$117$		0			0
$118$	−602.835			−0.470300
$119$	423.693	+	733.858i	0.326386	+	0.565316i
$120$		0			0
$121$	−1880.35	+	3256.86i	−1.41273	+	2.44693i
$122$	−139.951	+	242.402i	−0.103857	+	0.179886i
$123$		0			0
$124$	−491.551	−	851.392i	−0.355989	−	0.616590i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1178.02			−0.823089			−0.411544	−	0.911390i	$-0.635011\pi$
$127$	−1178.02			−0.823089			−0.411544	+	0.911390i	$0.635011\pi$
$128$	727.272	+	1259.67i	0.502206	+	0.869846i
$129$		0			0
$130$	−452.709	+	784.116i	−0.305425	+	0.529012i
$131$	−260.609	+	451.388i	−0.173813	+	0.301053i	−0.939750	−	0.341863i	$-0.888942\pi$
$131$	−260.609	+	451.388i	−0.173813	+	0.301053i	0.765937	+	0.642916i	$0.222275\pi$
$132$		0			0
$133$	−1441.66	−	2497.03i	−0.939910	−	1.62797i
$134$	2154.63			1.38904
$135$		0			0
$136$	−420.889			−0.265374
$137$	224.766	+	389.306i	0.140168	+	0.242778i	0.927560	−	0.373675i	$-0.121902\pi$
$137$	224.766	+	389.306i	0.140168	+	0.242778i	−0.787392	+	0.616453i	$0.788569\pi$
$138$		0			0
$139$	1172.72	−	2031.22i	0.715605	−	1.23946i	−0.247121	−	0.968985i	$-0.579484\pi$
$139$	1172.72	−	2031.22i	0.715605	−	1.23946i	0.962726	−	0.270480i	$-0.0871823\pi$
$140$	−280.704	+	486.193i	−0.169456	+	0.293506i
$141$		0			0
$142$	900.427	+	1559.59i	0.532128	+	0.921673i
$143$	3667.24			2.14455
$144$		0			0
$145$	−1234.14			−0.706824
$146$	−722.333	−	1251.12i	−0.409457	−	0.709200i
$147$		0			0
$148$	−49.4268	+	85.6098i	−0.0274518	+	0.0475478i
$149$	634.691	−	1099.32i	0.348966	−	0.604427i	−0.637100	−	0.770781i	$-0.719866\pi$
$149$	634.691	−	1099.32i	0.348966	−	0.604427i	0.986066	+	0.166354i	$0.0531996\pi$
$150$		0			0
$151$	−1079.16	−	1869.16i	−0.581594	−	1.00735i	−0.995291	−	0.0969350i	$-0.969096\pi$
$151$	−1079.16	−	1869.16i	−0.581594	−	1.00735i	0.413697	−	0.910415i	$-0.364237\pi$
$152$	1432.12			0.764213
$153$		0			0
$154$	6394.27			3.34588
$155$	−556.698	−	964.228i	−0.288484	−	0.499669i
$156$		0			0
$157$	1171.65	−	2029.36i	0.595593	−	1.03160i	−0.397869	−	0.917442i	$-0.630250\pi$
$157$	1171.65	−	2029.36i	0.595593	−	1.03160i	0.993463	−	0.114156i	$-0.0364164\pi$
$158$	−1398.11	+	2421.60i	−0.703972	+	1.21932i
$159$		0			0
$160$	−450.538	−	780.354i	−0.222613	−	0.385578i
$161$	2084.87			1.02056
$162$		0			0
$163$	3399.94			1.63376			0.816882	−	0.576804i	$-0.195700\pi$
$163$	3399.94			1.63376			0.816882	+	0.576804i	$0.195700\pi$
$164$	958.528	+	1660.22i	0.456393	+	0.790496i
$165$		0			0
$166$	475.812	−	824.130i	0.222471	−	0.385331i
$167$	904.608	−	1566.83i	0.419166	−	0.726017i	−0.576690	−	0.816963i	$-0.695656\pi$
$167$	904.608	−	1566.83i	0.419166	−	0.726017i	0.995856	+	0.0909465i	$0.0289892\pi$
$168$		0			0
$169$	−222.146	−	384.769i	−0.101113	−	0.175134i
$170$	586.995			0.264826
$171$		0			0
$172$	−1045.66			−0.463553
$173$	663.704	+	1149.57i	0.291679	+	0.505203i	0.974207	−	0.225657i	$-0.0724527\pi$
$173$	663.704	+	1149.57i	0.291679	+	0.505203i	−0.682528	+	0.730860i	$0.739119\pi$
$174$		0			0
$175$	−317.906	+	550.629i	−0.137322	+	0.237849i
$176$	−2848.10	+	4933.06i	−1.21980	+	2.11275i
$177$		0			0
$178$	312.531	+	541.320i	0.131602	+	0.227942i
$179$	−448.734			−0.187374			−0.0936871	−	0.995602i	$-0.529865\pi$
$179$	−448.734			−0.187374			−0.0936871	+	0.995602i	$0.529865\pi$
$180$		0			0
$181$	−3450.55			−1.41700			−0.708502	−	0.705709i	$-0.750629\pi$
$181$	−3450.55			−1.41700			−0.708502	+	0.705709i	$0.750629\pi$
$182$	−2302.70	−	3988.40i	−0.937845	−	1.62439i
$183$		0			0
$184$	−517.768	+	896.800i	−0.207448	+	0.359310i
$185$	−55.9775	+	96.9559i	−0.0222462	+	0.0385315i
$186$		0			0
$187$	−1188.76	−	2058.99i	−0.464870	−	0.805179i
$188$	−476.736			−0.184944
$189$		0			0
$190$	−1997.31			−0.762634
$191$	796.047	+	1378.79i	0.301570	+	0.522335i	0.976492	−	0.215554i	$-0.0691559\pi$
$191$	796.047	+	1378.79i	0.301570	+	0.522335i	−0.674922	+	0.737890i	$0.735823\pi$
$192$		0			0
$193$	−221.650	+	383.908i	−0.0826668	+	0.143183i	−0.904395	−	0.426697i	$-0.859677\pi$
$193$	−221.650	+	383.908i	−0.0826668	+	0.143183i	0.821728	+	0.569880i	$0.193010\pi$
$194$	−1553.61	+	2690.93i	−0.574961	+	0.995862i
$195$		0			0
$196$	−670.644	−	1161.59i	−0.244404	−	0.423320i
$197$	−208.992			−0.0755839			−0.0377919	−	0.999286i	$-0.512032\pi$
$197$	−208.992			−0.0755839			−0.0377919	+	0.999286i	$0.512032\pi$
$198$		0			0
$199$	−479.916			−0.170957			−0.0854783	−	0.996340i	$-0.527242\pi$
$199$	−479.916			−0.170957			−0.0854783	+	0.996340i	$0.527242\pi$
$200$	−157.901	−	273.492i	−0.0558264	−	0.0966941i
$201$		0			0
$202$	1807.60	−	3130.86i	0.629617	−	1.09053i
$203$	3138.71	−	5436.41i	1.08519	−	1.87961i
$204$		0			0
$205$	1085.56	+	1880.25i	0.369849	+	0.640597i
$206$	6308.00			2.13349
$207$		0			0
$208$	4102.63			1.36763
$209$	4044.89	+	7005.95i	1.33871	+	2.31872i
$210$		0			0
$211$	1316.07	−	2279.50i	0.429393	−	0.743731i	−0.567426	−	0.823424i	$-0.692061\pi$
$211$	1316.07	−	2279.50i	0.429393	−	0.743731i	0.996819	+	0.0796934i	$0.0253941\pi$
$212$	273.638	−	473.954i	0.0886486	−	0.153544i
$213$		0			0
$214$	−3536.33	−	6125.10i	−1.12962	−	1.95656i
$215$	−1184.25			−0.375651
$216$		0			0
$217$	5663.28			1.77165
$218$	−372.879	−	645.846i	−0.115847	−	0.200652i
$219$		0			0
$220$	787.573	−	1364.12i	0.241355	−	0.418040i
$221$	−856.192	+	1482.97i	−0.260605	+	0.451381i
$222$		0			0
$223$	−1676.61	−	2903.97i	−0.503471	−	0.872038i	−0.999992	−	0.00401278i	$-0.998723\pi$
$223$	−1676.61	−	2903.97i	−0.503471	−	0.872038i	0.496521	−	0.868025i	$-0.334611\pi$
$224$	4583.31			1.36712
$225$		0			0
$226$	−6.85286			−0.00201701
$227$	−345.382	−	598.219i	−0.100986	−	0.174913i	0.811105	−	0.584900i	$-0.198866\pi$
$227$	−345.382	−	598.219i	−0.100986	−	0.174913i	−0.912091	+	0.409988i	$0.865533\pi$
$228$		0			0
$229$	334.066	−	578.619i	0.0964003	−	0.166970i	−0.813792	−	0.581156i	$-0.802600\pi$
$229$	334.066	−	578.619i	0.0964003	−	0.166970i	0.910192	+	0.414186i	$0.135934\pi$
$230$	722.108	−	1250.73i	0.207019	−	0.358567i
$231$		0			0
$232$	1558.97	+	2700.21i	0.441170	+	0.764128i
$233$	−940.537			−0.264449			−0.132225	−	0.991220i	$-0.542212\pi$
$233$	−940.537			−0.264449			−0.132225	+	0.991220i	$0.542212\pi$
$234$		0			0
$235$	−539.919			−0.149874
$236$	−377.673	−	654.149i	−0.104171	−	0.180430i
$237$		0			0
$238$	−1492.87	+	2585.73i	−0.406591	+	0.704236i
$239$	−553.702	+	959.039i	−0.149858	+	0.259561i	−0.931175	−	0.364573i	$-0.881215\pi$
$239$	−553.702	+	959.039i	−0.149858	+	0.259561i	0.781317	+	0.624134i	$0.214548\pi$
$240$		0			0
$241$	−614.431	−	1064.23i	−0.164228	−	0.284451i	0.772153	−	0.635437i	$-0.219180\pi$
$241$	−614.431	−	1064.23i	−0.164228	−	0.284451i	−0.936381	+	0.350985i	$0.885847\pi$
$242$	−13250.7			−3.51979
$243$		0			0
$244$	−350.715			−0.0920172
$245$	−759.526	−	1315.54i	−0.198058	−	0.343047i
$246$		0			0
$247$	2913.29	−	5045.96i	0.750478	−	1.29987i
$248$	−1406.45	+	2436.04i	−0.360119	+	0.623745i
$249$		0			0
$250$	220.217	+	381.427i	0.0557111	+	0.0964944i
$251$	738.480			0.185707			0.0928534	−	0.995680i	$-0.470401\pi$
$251$	738.480			0.185707			0.0928534	+	0.995680i	$0.470401\pi$
$252$		0			0
$253$	−5849.54			−1.45359
$254$	−2075.36	−	3594.63i	−0.512676	−	0.887981i
$255$		0			0
$256$	−2547.97	+	4413.21i	−0.622062	+	1.07744i
$257$	−3156.28	+	5466.84i	−0.766084	+	1.32690i	0.173588	+	0.984818i	$0.444464\pi$
$257$	−3156.28	+	5466.84i	−0.766084	+	1.32690i	−0.939672	+	0.342078i	$0.888869\pi$
$258$		0			0
$259$	−284.729	−	493.165i	−0.0683097	−	0.118316i
$260$	−1134.48			−0.270606
$261$		0			0
$262$	−1836.50			−0.433051
$263$	−2996.81	−	5190.62i	−0.702628	−	1.21699i	−0.967541	−	0.252715i	$-0.918677\pi$
$263$	−2996.81	−	5190.62i	−0.702628	−	1.21699i	0.264913	−	0.964272i	$-0.414657\pi$
$264$		0			0
$265$	309.903	−	536.768i	0.0718385	−	0.124428i
$266$	5079.66	−	8798.24i	1.17088	−	2.02802i
$267$		0			0
$268$	1349.86	+	2338.03i	0.307672	+	0.532903i
$269$	−1749.70			−0.396584			−0.198292	−	0.980143i	$-0.563539\pi$
$269$	−1749.70			−0.396584			−0.198292	+	0.980143i	$0.563539\pi$
$270$		0			0
$271$	−1931.68			−0.432994			−0.216497	−	0.976283i	$-0.569463\pi$
$271$	−1931.68			−0.432994			−0.216497	+	0.976283i	$0.569463\pi$
$272$	−1329.90	−	2303.45i	−0.296459	−	0.513482i
$273$		0			0
$274$	−791.957	+	1371.71i	−0.174613	+	0.302438i
$275$	891.952	−	1544.91i	0.195588	−	0.338768i
$276$		0			0
$277$	1895.77	+	3283.58i	0.411213	+	0.712242i	0.995023	−	0.0996484i	$-0.0317718\pi$
$277$	1895.77	+	3283.58i	0.411213	+	0.712242i	−0.583809	+	0.811891i	$0.698438\pi$
$278$	8264.13			1.78291
$279$		0			0
$280$	1606.32			0.342843
$281$	−2244.68	−	3887.90i	−0.476536	−	0.825384i	0.523103	−	0.852269i	$-0.324774\pi$
$281$	−2244.68	−	3887.90i	−0.476536	−	0.825384i	−0.999639	+	0.0268857i	$0.991441\pi$
$282$		0			0
$283$	−1566.93	+	2714.00i	−0.329132	+	0.570073i	−0.982340	−	0.187105i	$-0.940089\pi$
$283$	−1566.93	+	2714.00i	−0.329132	+	0.570073i	0.653208	+	0.757179i	$0.273423\pi$
$284$	−1128.23	+	1954.15i	−0.235732	+	0.408300i
$285$		0			0
$286$	6460.72	+	11190.3i	1.33577	+	2.31362i
$287$	−11043.4			−2.27133
$288$		0			0
$289$	−3802.84			−0.774036
$290$	−2174.22	−	3765.87i	−0.440258	−	0.762550i
$291$		0			0
$292$	905.077	−	1567.64i	0.181389	−	0.314175i
$293$	−1398.75	+	2422.71i	−0.278894	+	0.483058i	−0.971110	−	0.238632i	$-0.923301\pi$
$293$	−1398.75	+	2422.71i	−0.278894	+	0.483058i	0.692216	+	0.721690i	$0.256634\pi$
$294$		0			0
$295$	−427.727	−	740.845i	−0.0844178	−	0.146216i
$296$	282.845			0.0555406
$297$		0			0
$298$	4472.64			0.869439
$299$	2106.54	+	3648.63i	0.407438	+	0.705704i
$300$		0			0
$301$	3011.83	−	5216.65i	0.576742	−	0.998946i
$302$	3802.39	−	6585.93i	0.724513	−	1.25489i
$303$		0			0
$304$	4525.12	+	7837.73i	0.853728	+	1.47870i
$305$	−397.196			−0.0745684
$306$		0			0
$307$	−6839.91			−1.27158			−0.635789	−	0.771863i	$-0.719325\pi$
$307$	−6839.91			−1.27158			−0.635789	+	0.771863i	$0.719325\pi$
$308$	4005.98	+	6938.57i	0.741111	+	1.28364i
$309$		0			0
$310$	1961.51	−	3397.44i	0.359375	−	0.622456i
$311$	−1209.70	+	2095.27i	−0.220566	+	0.382032i	−0.954980	−	0.296670i	$-0.904124\pi$
$311$	−1209.70	+	2095.27i	−0.220566	+	0.382032i	0.734414	+	0.678702i	$0.237457\pi$
$312$		0			0
$313$	−1951.59	−	3380.25i	−0.352429	−	0.610425i	0.634245	−	0.773132i	$-0.281311\pi$
$313$	−1951.59	−	3380.25i	−0.352429	−	0.610425i	−0.986674	+	0.162707i	$0.947978\pi$
$314$	8256.59			1.48391
$315$		0			0
$316$	−3503.64			−0.623718
$317$	−4947.36	−	8569.09i	−0.876567	−	1.51826i	−0.855084	−	0.518489i	$-0.826495\pi$
$317$	−4947.36	−	8569.09i	−0.876567	−	1.51826i	−0.0214825	−	0.999769i	$-0.506839\pi$
$318$		0			0
$319$	−8806.32	+	15253.0i	−1.54564	+	2.67713i
$320$	−9.09863	+	15.7593i	−0.00158946	+	0.00275303i
$321$		0			0
$322$	3673.00	+	6361.81i	0.635677	+	1.10102i
$323$	−3777.44			−0.650720
$324$		0			0
$325$	−1284.84			−0.219292
$326$	5989.80	+	10374.6i	1.01762	+	1.76257i
$327$		0			0
$328$	2742.58	−	4750.29i	0.461688	−	0.799668i
$329$	1373.15	−	2378.36i	0.230103	−	0.398551i
$330$		0			0
$331$	−2081.52	−	3605.30i	−0.345651	−	0.598686i	0.639820	−	0.768524i	$-0.279009\pi$
$331$	−2081.52	−	3605.30i	−0.345651	−	0.598686i	−0.985472	+	0.169839i	$0.945675\pi$
$332$	1192.38			0.197109
$333$		0			0
$334$	6374.73			1.04434
$335$	1528.76	+	2647.90i	0.249329	+	0.431851i
$336$		0			0
$337$	−4852.47	+	8404.72i	−0.784364	+	1.35856i	0.145014	+	0.989430i	$0.453677\pi$
$337$	−4852.47	+	8404.72i	−0.784364	+	1.35856i	−0.929378	+	0.369129i	$0.879656\pi$
$338$	782.727	−	1355.72i	0.125961	−	0.218170i
$339$		0			0
$340$	367.750	+	636.961i	0.0586589	+	0.101600i
$341$	−15889.5			−2.52336
$342$		0			0
$343$	−996.691			−0.156899
$344$	1495.95	+	2591.06i	0.234466	+	0.406107i
$345$		0			0
$346$	−2338.55	+	4050.48i	−0.363355	+	0.629350i
$347$	2716.19	−	4704.58i	0.420210	−	0.727825i	−0.575750	−	0.817626i	$-0.695290\pi$
$347$	2716.19	−	4704.58i	0.420210	−	0.727825i	0.995960	+	0.0898011i	$0.0286231\pi$
$348$		0			0
$349$	−5285.97	−	9155.57i	−0.810749	−	1.40426i	−0.912341	−	0.409432i	$-0.865727\pi$
$349$	−5285.97	−	9155.57i	−0.810749	−	1.40426i	0.101592	−	0.994826i	$-0.467607\pi$
$350$	−2240.27			−0.342135
$351$		0			0
$352$	−12859.5			−1.94719
$353$	4821.49	+	8351.07i	0.726975	+	1.25916i	0.958156	+	0.286247i	$0.0924077\pi$
$353$	4821.49	+	8351.07i	0.726975	+	1.25916i	−0.231181	+	0.972911i	$0.574259\pi$
$354$		0			0
$355$	−1277.75	+	2213.13i	−0.191031	+	0.330876i
$356$	−391.599	+	678.270i	−0.0582998	+	0.100978i
$357$		0			0
$358$	−790.552	−	1369.28i	−0.116709	−	0.202147i
$359$	−3002.18			−0.441362			−0.220681	−	0.975346i	$-0.570828\pi$
$359$	−3002.18			−0.441362			−0.220681	+	0.975346i	$0.570828\pi$
$360$		0			0
$361$	5994.17			0.873913
$362$	−6078.97	−	10529.1i	−0.882607	−	1.52872i
$363$		0			0
$364$	2885.27	−	4997.43i	0.415465	−	0.719606i
$365$	1025.03	−	1775.40i	0.146993	−	0.254599i
$366$		0			0
$367$	574.638	+	995.302i	0.0817326	+	0.141565i	0.903994	−	0.427545i	$-0.140621\pi$
$367$	574.638	+	995.302i	0.0817326	+	0.141565i	−0.822262	+	0.569110i	$0.807288\pi$
$368$	−6544.03			−0.926986
$369$		0			0
$370$	−394.471			−0.0554258
$371$	1576.32	+	2730.27i	0.220589	+	0.382071i
$372$		0			0
$373$	256.607	−	444.456i	0.0356209	−	0.0616972i	−0.847665	−	0.530531i	$-0.821992\pi$
$373$	256.607	−	444.456i	0.0356209	−	0.0616972i	0.883286	+	0.468834i	$0.155326\pi$
$374$	4188.57	−	7254.81i	0.579106	−	1.00304i
$375$		0			0
$376$	682.029	+	1181.31i	0.0935451	+	0.162025i
$377$	12685.3			1.73296
$378$		0			0
$379$	12560.0			1.70228			0.851138	−	0.524942i	$-0.175913\pi$
$379$	12560.0			1.70228			0.851138	+	0.524942i	$0.175913\pi$
$380$	−1251.31	−	2167.33i	−0.168923	−	0.292583i
$381$		0			0
$382$	−2804.85	+	4858.15i	−0.375677	+	0.650692i
$383$	136.995	−	237.282i	0.0182771	−	0.0316568i	−0.856742	−	0.515745i	$-0.827515\pi$
$383$	136.995	−	237.282i	0.0182771	−	0.0316568i	0.875019	+	0.484088i	$0.160849\pi$
$384$		0			0
$385$	4536.91	+	7858.15i	0.600577	+	1.04023i
$386$	−1561.95			−0.205962
$387$		0			0
$388$	−3893.31			−0.509415
$389$	3423.21	+	5929.18i	0.446179	+	0.772805i	0.998134	−	0.0610691i	$-0.0194510\pi$
$389$	3423.21	+	5929.18i	0.446179	+	0.772805i	−0.551954	+	0.833874i	$0.686118\pi$
$390$		0			0
$391$	1365.69	−	2365.45i	0.176640	−	0.305949i
$392$	−1918.88	+	3323.59i	−0.247239	+	0.428231i
$393$		0			0
$394$	−368.188	−	637.721i	−0.0470788	−	0.0815429i
$395$	−3967.98			−0.505445
$396$		0			0
$397$	−12117.5			−1.53189			−0.765943	−	0.642909i	$-0.777727\pi$
$397$	−12117.5			−1.53189			−0.765943	+	0.642909i	$0.777727\pi$
$398$	−845.486	−	1464.43i	−0.106483	−	0.184435i
$399$		0			0
$400$	997.848	−	1728.32i	0.124731	−	0.216041i
$401$	1508.40	−	2612.63i	0.187845	−	0.325358i	−0.756686	−	0.653778i	$-0.773183\pi$
$401$	1508.40	−	2612.63i	0.187845	−	0.325358i	0.944532	+	0.328421i	$0.106516\pi$
$402$		0			0
$403$	5722.13	+	9911.02i	0.707294	+	1.22507i
$404$	4529.82			0.557839
$405$		0			0
$406$	22118.4			2.70373
$407$	798.868	+	1383.68i	0.0972933	+	0.168517i
$408$		0			0
$409$	−3267.56	+	5659.59i	−0.395038	+	0.684226i	−0.993106	−	0.117219i	$-0.962602\pi$
$409$	−3267.56	+	5659.59i	−0.395038	+	0.684226i	0.598068	+	0.801445i	$0.295935\pi$
$410$	−3824.96	+	6625.02i	−0.460735	+	0.798016i
$411$		0			0
$412$	3951.93	+	6844.95i	0.472568	+	0.818511i
$413$	4351.26			0.518430
$414$		0			0
$415$	1350.40			0.159732
$416$	4630.94	+	8021.03i	0.545795	+	0.945344i
$417$		0			0
$418$	−14252.1	+	24685.3i	−1.66768	+	2.88851i
$419$	−3574.22	+	6190.74i	−0.416736	+	0.721807i	−0.995609	−	0.0936102i	$-0.970159\pi$
$419$	−3574.22	+	6190.74i	−0.416736	+	0.721807i	0.578873	+	0.815418i	$0.303493\pi$
$420$		0			0
$421$	−7400.77	−	12818.5i	−0.856749	−	1.48393i	−0.875013	−	0.484100i	$-0.839147\pi$
$421$	−7400.77	−	12818.5i	−0.856749	−	1.48393i	0.0182632	−	0.999833i	$-0.494186\pi$
$422$	9274.28			1.06982
$423$		0			0
$424$	−1565.89			−0.179354
$425$	416.489	+	721.379i	0.0475357	+	0.0823342i
$426$		0			0
$427$	1010.17	−	1749.66i	0.114486	−	0.198295i
$428$	4430.99	−	7674.70i	0.500420	−	0.866754i
$429$		0			0
$430$	−2086.33	−	3613.64i	−0.233981	−	0.405268i
$431$	2284.19			0.255280			0.127640	−	0.991821i	$-0.459260\pi$
$431$	2284.19			0.255280			0.127640	+	0.991821i	$0.459260\pi$
$432$		0			0
$433$	5529.26			0.613670			0.306835	−	0.951763i	$-0.400730\pi$
$433$	5529.26			0.613670			0.306835	+	0.951763i	$0.400730\pi$
$434$	9977.21	+	17281.0i	1.10351	+	1.91133i
$435$		0			0
$436$	467.214	−	809.239i	0.0513200	−	0.0888888i
$437$	−4646.93	+	8048.71i	−0.508679	+	0.881057i
$438$		0			0
$439$	5930.81	+	10272.5i	0.644788	+	1.11681i	0.984350	+	0.176223i	$0.0563878\pi$
$439$	5930.81	+	10272.5i	0.644788	+	1.11681i	−0.339562	+	0.940584i	$0.610279\pi$
$440$	−4506.88			−0.488311
$441$		0			0
$442$	−6033.55			−0.649291
$443$	7646.81	+	13244.7i	0.820115	+	1.42048i	0.905596	+	0.424141i	$0.139424\pi$
$443$	7646.81	+	13244.7i	0.820115	+	1.42048i	−0.0854817	+	0.996340i	$0.527243\pi$
$444$		0			0
$445$	−443.499	+	768.162i	−0.0472446	+	0.0818301i
$446$	5907.49	−	10232.1i	0.627193	−	1.08633i
$447$		0			0
$448$	−46.2801	−	80.1595i	−0.00488065	−	0.00845353i
$449$	12998.8			1.36626			0.683129	−	0.730297i	$-0.260619\pi$
$449$	12998.8			1.36626			0.683129	+	0.730297i	$0.260619\pi$
$450$		0			0
$451$	30984.6			3.23506
$452$	−4.29329	−	7.43619i	−0.000446768	−	0.000773825i
$453$		0			0
$454$	1216.95	−	2107.81i	0.125802	−	0.217895i
$455$	3267.66	−	5659.75i	0.336682	−	0.583150i
$456$		0			0
$457$	−7155.97	−	12394.5i	−0.732477	−	1.26869i	−0.955821	−	0.293948i	$-0.905031\pi$
$457$	−7155.97	−	12394.5i	−0.732477	−	1.26869i	0.223344	−	0.974740i	$-0.428303\pi$
$458$	2354.14			0.240179
$459$		0			0
$460$	1809.59			0.183419
$461$	−2145.17	−	3715.54i	−0.216725	−	0.375379i	0.737080	−	0.675806i	$-0.236204\pi$
$461$	−2145.17	−	3715.54i	−0.216725	−	0.375379i	−0.953805	+	0.300427i	$0.902871\pi$
$462$		0			0
$463$	7255.14	−	12566.3i	0.728240	−	1.26135i	−0.229386	−	0.973335i	$-0.573672\pi$
$463$	7255.14	−	12566.3i	0.728240	−	1.26135i	0.957626	−	0.288013i	$-0.0929947\pi$
$464$	−9851.85	+	17063.9i	−0.985691	+	1.70727i
$465$		0			0
$466$	−1656.98	−	2869.97i	−0.164717	−	0.285298i
$467$	−7393.05			−0.732569			−0.366285	−	0.930503i	$-0.619370\pi$
$467$	−7393.05			−0.732569			−0.366285	+	0.930503i	$0.619370\pi$
$468$		0			0
$469$	−15552.1			−1.53119
$470$	−951.195	−	1647.52i	−0.0933518	−	0.161690i
$471$		0			0
$472$	−1080.62	+	1871.68i	−0.105380	+	0.182524i
$473$	−8450.34	+	14636.4i	−0.821452	+	1.42280i
$474$		0			0
$475$	−1417.15	−	2454.57i	−0.136891	−	0.237102i
$476$	−3741.11			−0.360239
$477$		0			0
$478$	−3901.91			−0.373366
$479$	−6754.93	−	11699.9i	−0.644344	−	1.11604i	−0.984453	−	0.175650i	$-0.943797\pi$
$479$	−6754.93	−	11699.9i	−0.644344	−	1.11604i	0.340109	−	0.940386i	$-0.389536\pi$
$480$		0			0
$481$	575.376	−	996.580i	0.0545424	−	0.0944702i
$482$	2164.93	−	3749.77i	0.204585	−	0.354352i
$483$		0			0
$484$	−8301.53	−	14378.7i	−0.779632	−	1.35036i
$485$	−4409.30			−0.412817
$486$		0			0
$487$	−11140.0			−1.03655			−0.518277	−	0.855213i	$-0.673427\pi$
$487$	−11140.0			−1.03655			−0.518277	+	0.855213i	$0.673427\pi$
$488$	501.740	+	869.040i	0.0465425	+	0.0806139i
$489$		0			0
$490$	2676.17	−	4635.26i	0.246729	−	0.427347i
$491$	−1006.37	+	1743.09i	−0.0924988	+	0.160213i	−0.908562	−	0.417750i	$-0.862819\pi$
$491$	−1006.37	+	1743.09i	−0.0924988	+	0.160213i	0.816063	+	0.577963i	$0.196152\pi$
$492$		0			0
$493$	−4112.03	−	7122.24i	−0.375652	−	0.650648i
$494$	20529.8			1.86980
$495$		0			0
$496$	−17776.0			−1.60920
$497$	−6499.29	−	11257.1i	−0.586585	−	1.01600i
$498$		0			0
$499$	−3676.49	+	6367.87i	−0.329824	+	0.571272i	−0.982477	−	0.186385i	$-0.940323\pi$
$499$	−3676.49	+	6367.87i	−0.329824	+	0.571272i	0.652653	+	0.757657i	$0.273656\pi$
$500$	−275.930	+	477.925i	−0.0246800	+	0.0427469i
$501$		0			0
$502$	1301.01	+	2253.41i	0.115671	+	0.200348i
$503$	16898.3			1.49793			0.748965	−	0.662609i	$-0.230551\pi$
$503$	16898.3			1.49793			0.748965	+	0.662609i	$0.230551\pi$
$504$		0			0
$505$	5130.17			0.452059
$506$	−10305.4	−	17849.4i	−0.905394	−	1.56819i
$507$		0			0
$508$	2600.41	−	4504.04i	0.227115	−	0.393375i
$509$	9679.31	−	16765.1i	0.842884	−	1.45992i	−0.0445620	−	0.999007i	$-0.514189\pi$
$509$	9679.31	−	16765.1i	0.842884	−	1.45992i	0.887446	−	0.460911i	$-0.152477\pi$
$510$		0			0
$511$	5213.80	+	9030.57i	0.451360	+	0.781779i
$512$	−6319.06			−0.545440
$513$		0			0
$514$	−22242.2			−1.90868
$515$	4475.69	+	7752.13i	0.382957	+	0.663300i
$516$		0			0
$517$	−3852.65	+	6672.99i	−0.327736	+	0.567655i
$518$	1003.24	−	1737.66i	0.0850959	−	0.147390i
$519$		0			0
$520$	1623.02	+	2811.15i	0.136873	+	0.237071i
$521$	−146.772			−0.0123420			−0.00617100	−	0.999981i	$-0.501964\pi$
$521$	−146.772			−0.0123420			−0.00617100	+	0.999981i	$0.501964\pi$
$522$		0			0
$523$	−2872.03			−0.240125			−0.120062	−	0.992766i	$-0.538309\pi$
$523$	−2872.03			−0.240125			−0.120062	+	0.992766i	$0.538309\pi$
$524$	−1150.56	−	1992.83i	−0.0959205	−	0.166139i
$525$		0			0
$526$	10559.2	−	18289.0i	0.875289	−	1.51605i
$527$	3709.73	−	6425.44i	0.306638	−	0.531113i
$528$		0			0
$529$	2723.41	+	4717.08i	0.223836	+	0.387695i
$530$	2183.87			0.178984
$531$		0			0
$532$	12729.5			1.03740
$533$	−11158.2	−	19326.5i	−0.906781	−	1.57059i
$534$		0			0
$535$	5018.24	−	8691.84i	0.405528	−	0.702395i
$536$	3862.29	−	6689.69i	0.311242	−	0.539087i
$537$		0			0
$538$	−3082.51	−	5339.07i	−0.247020	−	0.427851i
$539$	−21678.7			−1.73241
$540$		0			0
$541$	−3810.28			−0.302804			−0.151402	−	0.988472i	$-0.548379\pi$
$541$	−3810.28			−0.302804			−0.151402	+	0.988472i	$0.548379\pi$
$542$	−3403.12	−	5894.38i	−0.269698	−	0.467131i
$543$		0			0
$544$	3002.30	−	5200.14i	0.236622	−	0.409842i
$545$	529.135	−	916.490i	0.0415884	−	0.0720332i
$546$		0			0
$547$	−2972.79	−	5149.03i	−0.232372	−	0.402480i	0.726134	−	0.687554i	$-0.241315\pi$
$547$	−2972.79	−	5149.03i	−0.232372	−	0.402480i	−0.958506	+	0.285073i	$0.907982\pi$
$548$	−1984.63			−0.154707
$549$		0			0
$550$	6285.54			0.487303
$551$	13991.6	+	24234.2i	1.08178	+	1.87371i
$552$		0			0
$553$	10091.6	−	17479.1i	0.776016	−	1.34410i
$554$	−6679.72	+	11569.6i	−0.512264	+	0.887267i
$555$		0			0
$556$	5177.44	+	8967.59i	0.394914	+	0.684012i
$557$	−10872.2			−0.827059			−0.413530	−	0.910491i	$-0.635704\pi$
$557$	−10872.2			−0.827059			−0.413530	+	0.910491i	$0.635704\pi$
$558$		0			0
$559$	12172.5			0.921007
$560$	5075.55	+	8791.11i	0.383002	+	0.663379i
$561$		0			0
$562$	7909.08	−	13698.9i	0.593638	−	1.02821i
$563$	−6787.54	+	11756.4i	−0.508100	+	0.880056i	0.491856	+	0.870677i	$0.336319\pi$
$563$	−6787.54	+	11756.4i	−0.508100	+	0.880056i	−0.999956	+	0.00937903i	$0.997015\pi$
$564$		0			0
$565$	−4.86228	−	8.42172i	−0.000362049	−	0.000627088i
$566$	−11042.1			−0.820024
$567$		0			0
$568$	6456.27			0.476935
$569$	−10321.3	−	17877.0i	−0.760442	−	1.31712i	−0.942623	−	0.333859i	$-0.891649\pi$
$569$	−10321.3	−	17877.0i	−0.760442	−	1.31712i	0.182181	−	0.983265i	$-0.441684\pi$
$570$		0			0
$571$	1365.39	−	2364.92i	0.100069	−	0.173325i	−0.811644	−	0.584153i	$-0.801427\pi$
$571$	1365.39	−	2364.92i	0.100069	−	0.173325i	0.911713	+	0.410828i	$0.134760\pi$
$572$	−8095.23	+	14021.3i	−0.591745	+	1.02493i
$573$		0			0
$574$	−19455.6	−	33698.1i	−1.41474	−	2.45040i
$575$	2049.42			0.148638
$576$		0			0
$577$	21953.4			1.58394			0.791970	−	0.610560i	$-0.209055\pi$
$577$	21953.4			1.58394			0.791970	+	0.610560i	$0.209055\pi$
$578$	−6699.61	−	11604.1i	−0.482123	−	0.835061i
$579$		0			0
$580$	2724.28	−	4718.60i	0.195034	−	0.337809i
$581$	−3434.41	+	5948.57i	−0.245238	+	0.424765i
$582$		0			0
$583$	−4422.70	−	7660.34i	−0.314185	−	0.544184i
$584$	−5179.29			−0.366988
$585$		0			0
$586$	−9856.92			−0.694856
$587$	−5527.67	−	9574.21i	−0.388674	−	0.673203i	0.603598	−	0.797289i	$-0.293733\pi$
$587$	−5527.67	−	9574.21i	−0.388674	−	0.673203i	−0.992271	+	0.124086i	$0.960400\pi$
$588$		0			0
$589$	−12622.8	+	21863.3i	−0.883042	+	1.52947i
$590$	1507.09	−	2610.35i	0.105162	−	0.182147i
$591$		0			0
$592$	893.713	+	1547.96i	0.0620462	+	0.107467i
$593$	16538.0			1.14525			0.572625	−	0.819817i	$-0.305925\pi$
$593$	16538.0			1.14525			0.572625	+	0.819817i	$0.305925\pi$
$594$		0			0
$595$	−4236.93			−0.291928
$596$	2802.09	+	4853.36i	0.192581	+	0.333559i
$597$		0			0
$598$	−7422.33	+	12855.8i	−0.507561	+	0.879122i
$599$	3201.79	−	5545.67i	0.218400	−	0.378280i	−0.735919	−	0.677070i	$-0.763250\pi$
$599$	3201.79	−	5545.67i	0.218400	−	0.378280i	0.954319	+	0.298790i	$0.0965829\pi$
$600$		0			0
$601$	7105.18	+	12306.5i	0.482240	+	0.835264i	0.999792	−	0.0203874i	$-0.00648995\pi$
$601$	7105.18	+	12306.5i	0.482240	+	0.835264i	−0.517552	+	0.855652i	$0.673157\pi$
$602$	21224.3			1.43694
$603$		0			0
$604$	9528.72			0.641917
$605$	−9401.75	−	16284.3i	−0.631794	−	1.09430i
$606$		0			0
$607$	4457.86	−	7721.24i	0.298087	−	0.516302i	−0.677611	−	0.735420i	$-0.736985\pi$
$607$	4457.86	−	7721.24i	0.298087	−	0.516302i	0.975698	+	0.219118i	$0.0703180\pi$
$608$	−10215.7	+	17694.0i	−0.681414	+	1.18024i
$609$		0			0
$610$	−699.755	−	1212.01i	−0.0464463	−	0.0804474i
$611$	5549.66			0.367455
$612$		0			0
$613$	−15372.5			−1.01287			−0.506436	−	0.862277i	$-0.669037\pi$
$613$	−15372.5			−1.01287			−0.506436	+	0.862277i	$0.669037\pi$
$614$	−12050.1	−	20871.4i	−0.792026	−	1.37183i
$615$		0			0
$616$	11462.1	−	19852.9i	0.749710	−	1.29854i
$617$	−8663.73	+	15006.0i	−0.565298	+	0.979124i	0.431724	+	0.902006i	$0.357905\pi$
$617$	−8663.73	+	15006.0i	−0.565298	+	0.979124i	−0.997022	+	0.0771187i	$0.975428\pi$
$618$		0			0
$619$	14393.7	+	24930.6i	0.934621	+	1.61881i	0.775308	+	0.631583i	$0.217595\pi$
$619$	14393.7	+	24930.6i	0.934621	+	1.61881i	0.159313	+	0.987228i	$0.449072\pi$
$620$	4915.51			0.318406
$621$		0			0
$622$	−8524.73			−0.549535
$623$	−2255.85	−	3907.25i	−0.145070	−	0.251269i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	6876.38	−	11910.2i	0.439034	−	0.760429i
$627$		0			0
$628$	5172.72	+	8959.41i	0.328685	+	0.569298i
$629$	−746.047			−0.0472923
$630$		0			0
$631$	18091.0			1.14135			0.570675	−	0.821176i	$-0.306682\pi$
$631$	18091.0			1.14135			0.570675	+	0.821176i	$0.306682\pi$
$632$	5012.38	+	8681.70i	0.315478	+	0.546423i
$633$		0			0
$634$	17431.9	−	30193.0i	1.09197	−	1.89135i
$635$	2945.05	−	5100.97i	0.184048	−	0.318781i
$636$		0			0
$637$	7806.94	+	13522.0i	0.485592	+	0.841070i
$638$	−62057.7			−3.85092
$639$		0			0
$640$	−7272.72			−0.449187
$641$	−9788.76	−	16954.6i	−0.603171	−	1.04472i	−0.992338	−	0.123556i	$-0.960570\pi$
$641$	−9788.76	−	16954.6i	−0.603171	−	1.04472i	0.389167	−	0.921167i	$-0.372763\pi$
$642$		0			0
$643$	14985.9	−	25956.3i	0.919106	−	1.59194i	0.118329	−	0.992974i	$-0.462246\pi$
$643$	14985.9	−	25956.3i	0.919106	−	1.59194i	0.800777	−	0.598963i	$-0.204420\pi$
$644$	−4602.23	+	7971.30i	−0.281605	+	0.487753i
$645$		0			0
$646$	−6654.87	−	11526.6i	−0.405313	−	0.702023i
$647$	−3635.64			−0.220915			−0.110457	−	0.993881i	$-0.535232\pi$
$647$	−3635.64			−0.220915			−0.110457	+	0.993881i	$0.535232\pi$
$648$		0			0
$649$	−12208.4			−0.738399
$650$	−2263.55	−	3920.58i	−0.136590	−	0.236581i
$651$		0			0
$652$	−7505.17	+	12999.3i	−0.450805	+	0.780818i
$653$	9703.64	−	16807.2i	0.581520	−	1.00722i	−0.413779	−	0.910377i	$-0.635791\pi$
$653$	9703.64	−	16807.2i	0.581520	−	1.00722i	0.995299	−	0.0968453i	$-0.0308752\pi$
$654$		0			0
$655$	−1303.04	−	2256.94i	−0.0777315	−	0.134635i
$656$	34663.3			2.06307
$657$		0			0
$658$	9676.49			0.573296
$659$	2813.93	+	4873.87i	0.166335	+	0.288101i	0.937129	−	0.348984i	$-0.113473\pi$
$659$	2813.93	+	4873.87i	0.166335	+	0.288101i	−0.770793	+	0.637085i	$0.780140\pi$
$660$		0			0
$661$	8331.49	−	14430.6i	0.490253	−	0.849144i	−0.509684	−	0.860362i	$-0.670238\pi$
$661$	8331.49	−	14430.6i	0.490253	−	0.849144i	0.999937	+	0.0112181i	$0.00357089\pi$
$662$	7334.18	−	12703.2i	0.430591	−	0.745805i
$663$		0			0
$664$	−1705.84	−	2954.60i	−0.0996979	−	0.172682i
$665$	14416.6			0.840681
$666$		0			0
$667$	−20234.1			−1.17461
$668$	3993.74	+	6917.36i	0.231321	+	0.400660i
$669$		0			0
$670$	−5386.57	+	9329.81i	−0.310599	+	0.537973i
$671$	−2834.24	+	4909.04i	−0.163062	+	0.282431i
$672$		0			0
$673$	6319.38	+	10945.5i	0.361953	+	0.626921i	0.988282	−	0.152638i	$-0.0487768\pi$
$673$	6319.38	+	10945.5i	0.361953	+	0.626921i	−0.626329	+	0.779559i	$0.715443\pi$
$674$	−34195.1			−1.95422
$675$		0			0
$676$	1961.50			0.111601
$677$	12658.0	+	21924.3i	0.718591	+	1.24464i	0.961558	+	0.274602i	$0.0885461\pi$
$677$	12658.0	+	21924.3i	0.718591	+	1.24464i	−0.242967	+	0.970035i	$0.578121\pi$
$678$		0			0
$679$	11213.9	−	19423.1i	0.633802	−	1.09778i
$680$	1052.22	−	1822.50i	0.0593395	−	0.102779i
$681$		0			0
$682$	−27993.2	−	48485.6i	−1.57172	−	2.72230i
$683$	24818.4			1.39041			0.695204	−	0.718812i	$-0.255314\pi$
$683$	24818.4			1.39041			0.695204	+	0.718812i	$0.255314\pi$
$684$		0			0
$685$	−2247.66			−0.125370
$686$	−1755.91	−	3041.32i	−0.0977273	−	0.169269i
$687$		0			0
$688$	−9453.60	+	16374.1i	−0.523859	+	0.907351i
$689$	−3185.40	+	5517.28i	−0.176131	+	0.305068i
$690$		0			0
$691$	−9978.98	−	17284.1i	−0.549375	−	0.951546i	−0.998317	−	0.0579852i	$-0.981532\pi$
$691$	−9978.98	−	17284.1i	−0.549375	−	0.951546i	0.448942	−	0.893561i	$-0.351801\pi$
$692$	−5860.35			−0.321932
$693$		0			0
$694$	19140.9			1.04694
$695$	5863.62	+	10156.1i	0.320028	+	0.554305i
$696$		0			0
$697$	−7233.99	+	12529.6i	−0.393124	+	0.680910i
$698$	18625.0	−	32259.4i	1.00998	−	1.74934i
$699$		0			0
$700$	−1403.52	−	2430.96i	−0.0757828	−	0.131260i
$701$	−5624.21			−0.303029			−0.151515	−	0.988455i	$-0.548415\pi$
$701$	−5624.21			−0.303029			−0.151515	+	0.988455i	$0.548415\pi$
$702$		0			0
$703$	2538.51			0.136190
$704$	129.849	+	224.904i	0.00695149	+	0.0120403i
$705$		0			0
$706$	−16988.4	+	29424.8i	−0.905620	+	1.56858i
$707$	−13047.3	+	22598.6i	−0.694051	+	1.20213i
$708$		0			0
$709$	3857.72	+	6681.76i	0.204344	+	0.353933i	0.949923	−	0.312483i	$-0.101161\pi$
$709$	3857.72	+	6681.76i	0.204344	+	0.353933i	−0.745580	+	0.666416i	$0.767827\pi$
$710$	−9004.27			−0.475950
$711$		0			0
$712$	2240.92			0.117952
$713$	−9127.25	−	15808.9i	−0.479408	−	0.830360i
$714$		0			0
$715$	−9168.11	+	15879.6i	−0.479535	+	0.830579i
$716$	990.555	−	1715.69i	0.0517022	−	0.0895508i
$717$		0			0
$718$	−5289.05	−	9160.91i	−0.274910	−	0.476159i
$719$	21647.8			1.12285			0.561424	−	0.827528i	$-0.310254\pi$
$719$	21647.8			1.12285			0.561424	+	0.827528i	$0.310254\pi$
$720$		0			0
$721$	−45531.2			−2.35183
$722$	10560.2	+	18290.7i	0.544333	+	0.942812i
$723$		0			0
$724$	7616.90	−	13192.9i	0.390994	−	0.677222i
$725$	3085.34	−	5343.97i	0.158051	−	0.273752i
$726$		0			0
$727$	1535.65	+	2659.82i	0.0783412	+	0.135691i	0.902534	−	0.430618i	$-0.141704\pi$
$727$	1535.65	+	2659.82i	0.0783412	+	0.135691i	−0.824193	+	0.566309i	$0.808371\pi$
$728$	−16510.9			−0.840570
$729$		0			0
$730$	7223.33			0.366229
$731$	−3945.80	−	6834.33i	−0.199645	−	0.345796i
$732$		0			0
$733$	−7326.01	+	12689.0i	−0.369157	+	0.639399i	−0.989434	−	0.144984i	$-0.953687\pi$
$733$	−7326.01	+	12689.0i	−0.369157	+	0.639399i	0.620277	+	0.784383i	$0.287020\pi$
$734$	−2024.72	+	3506.92i	−0.101817	+	0.176353i
$735$		0			0
$736$	−7386.72	−	12794.2i	−0.369943	−	0.640760i
$737$	43634.7			2.18087
$738$		0			0
$739$	17610.9			0.876629			0.438314	−	0.898822i	$-0.355576\pi$
$739$	17610.9			0.876629			0.438314	+	0.898822i	$0.355576\pi$
$740$	−247.134	−	428.049i	−0.0122768	−	0.0212640i
$741$		0			0
$742$	−5554.13	+	9620.04i	−0.274796	+	0.475960i
$743$	8394.09	−	14539.0i	0.414468	−	0.717879i	−0.580905	−	0.813972i	$-0.697301\pi$
$743$	8394.09	−	14539.0i	0.414468	−	0.717879i	0.995372	+	0.0960925i	$0.0306345\pi$
$744$		0			0
$745$	3173.46	+	5496.59i	0.156062	+	0.270308i
$746$	1808.30			0.0887485
$747$		0			0
$748$	10496.5			0.513087
$749$	25525.2	+	44211.0i	1.24522	+	2.15679i
$750$		0			0
$751$	−11757.1	+	20363.9i	−0.571269	+	0.989467i	0.425167	+	0.905115i	$0.360215\pi$
$751$	−11757.1	+	20363.9i	−0.571269	+	0.989467i	−0.996436	+	0.0843523i	$0.973118\pi$
$752$	−4310.05	+	7465.23i	−0.209005	+	0.362007i
$753$		0			0
$754$	22348.2	+	38708.2i	1.07941	+	1.86959i
$755$	10791.6			0.520193
$756$		0			0
$757$	24817.4			1.19155			0.595775	−	0.803151i	$-0.296845\pi$
$757$	24817.4			1.19155			0.595775	+	0.803151i	$0.296845\pi$
$758$	22127.4	+	38325.8i	1.06029	+	1.83648i
$759$		0			0
$760$	−3580.30	+	6201.26i	−0.170883	+	0.295978i
$761$	−16258.9	+	28161.2i	−0.774485	+	1.34145i	0.160599	+	0.987020i	$0.448658\pi$
$761$	−16258.9	+	28161.2i	−0.774485	+	1.34145i	−0.935084	+	0.354427i	$0.884676\pi$
$762$		0			0
$763$	2691.44	+	4661.72i	0.127702	+	0.221187i
$764$	−7028.91			−0.332850
$765$		0			0
$766$	965.398			0.0455369
$767$	4396.48	+	7614.93i	0.206972	+	0.358486i
$768$		0			0
$769$	−9028.92	+	15638.5i	−0.423395	+	0.733342i	−0.996269	−	0.0863014i	$-0.972495\pi$
$769$	−9028.92	+	15638.5i	−0.423395	+	0.733342i	0.572874	+	0.819644i	$0.305829\pi$
$770$	−15985.7	+	27688.0i	−0.748161	+	1.29585i
$771$		0			0
$772$	−978.557	−	1694.91i	−0.0456205	−	0.0790171i
$773$	38147.2			1.77498			0.887491	−	0.460825i	$-0.152447\pi$
$773$	38147.2			1.77498			0.887491	+	0.460825i	$0.152447\pi$
$774$		0			0
$775$	5566.98			0.258028
$776$	5569.86	+	9647.28i	0.257663	+	0.446285i
$777$		0			0
$778$	−12061.6	+	20891.3i	−0.555822	+	0.962712i
$779$	24614.5	−	42633.5i	1.13210	−	1.96085i
$780$		0			0
$781$	18235.1	+	31584.1i	0.835472	+	1.44708i
$782$	9623.98			0.440093
$783$		0			0
$784$	−24252.5			−1.10480
$785$	5858.27	+	10146.8i	0.266357	+	0.461345i
$786$		0			0
$787$	2400.88	−	4158.44i	0.108745	−	0.188351i	−0.806517	−	0.591211i	$-0.798650\pi$
$787$	2400.88	−	4158.44i	0.108745	−	0.188351i	0.915262	+	0.402859i	$0.131984\pi$
$788$	461.337	−	799.059i	0.0208559	−	0.0361235i
$789$		0			0
$790$	−6990.55	−	12108.0i	−0.314826	−	0.545295i
$791$	49.4640			0.00222343
$792$		0			0
$793$	4082.66			0.182824
$794$	−21347.8	−	36975.5i	−0.954163	−	1.65266i
$795$		0			0
$796$	1059.39	−	1834.91i	0.0471721	−	0.0817044i
$797$	7735.49	−	13398.3i	0.343796	−	0.595472i	−0.641338	−	0.767258i	$-0.721621\pi$
$797$	7735.49	−	13398.3i	0.343796	−	0.595472i	0.985134	+	0.171786i	$0.0549539\pi$
$798$		0			0
$799$	−1798.96	−	3115.89i	−0.0796528	−	0.137963i
$800$	4505.38			0.199111
$801$		0			0
$802$	10629.6			0.468012
$803$	−14628.4	−	25337.2i	−0.642871	−	1.11349i
$804$		0			0
$805$	−5212.18	+	9027.75i	−0.228205	+	0.395263i
$806$	−20161.8	+	34921.2i	−0.881102	+	1.52611i
$807$		0			0
$808$	−6480.47	−	11224.5i	−0.282156	−	0.488709i
$809$	−17007.6			−0.739129			−0.369564	−	0.929205i	$-0.620493\pi$
$809$	−17007.6			−0.739129			−0.369564	+	0.929205i	$0.620493\pi$
$810$		0			0
$811$	−7552.52			−0.327010			−0.163505	−	0.986543i	$-0.552280\pi$
$811$	−7552.52			−0.327010			−0.163505	+	0.986543i	$0.552280\pi$
$812$	13857.1	+	24001.1i	0.598876	+	1.03728i
$813$		0			0
$814$	−2814.79	+	4875.36i	−0.121202	+	0.209928i
$815$	−8499.84	+	14722.2i	−0.365321	+	0.632754i
$816$		0			0
$817$	13426.0	+	23254.6i	0.574930	+	0.995807i
$818$	−23026.4			−0.984227
$819$		0			0
$820$	−9585.28			−0.408210
$821$	−1872.60	−	3243.44i	−0.0796031	−	0.137877i	0.823476	−	0.567352i	$-0.192032\pi$
$821$	−1872.60	−	3243.44i	−0.0796031	−	0.137877i	−0.903079	+	0.429475i	$0.858699\pi$
$822$		0			0
$823$	15010.5	−	25999.0i	0.635764	−	1.10118i	−0.350589	−	0.936529i	$-0.614019\pi$
$823$	15010.5	−	25999.0i	0.635764	−	1.10118i	0.986353	−	0.164646i	$-0.0526481\pi$
$824$	11307.5	−	19585.1i	0.478051	−	0.828008i
$825$		0			0
$826$	7665.79	+	13277.5i	0.322914	+	0.559303i
$827$	−7918.68			−0.332962			−0.166481	−	0.986045i	$-0.553240\pi$
$827$	−7918.68			−0.332962			−0.166481	+	0.986045i	$0.553240\pi$
$828$		0			0
$829$	−6976.17			−0.292271			−0.146135	−	0.989265i	$-0.546683\pi$
$829$	−6976.17			−0.292271			−0.146135	+	0.989265i	$0.546683\pi$
$830$	2379.06	+	4120.65i	0.0994920	+	0.172325i
$831$		0			0
$832$	93.5221	−	161.985i	0.00389699	−	0.00674978i
$833$	5061.34	−	8766.50i	0.210522	−	0.364635i
$834$		0			0
$835$	4523.04	+	7834.14i	0.187457	+	0.324684i
$836$	−35715.4			−1.47756
$837$		0			0
$838$	−25187.4			−1.03829
$839$	−4328.96	−	7497.97i	−0.178131	−	0.308532i	0.763109	−	0.646270i	$-0.223672\pi$
$839$	−4328.96	−	7497.97i	−0.178131	−	0.308532i	−0.941240	+	0.337737i	$0.890339\pi$
$840$		0			0
$841$	−18267.3	+	31640.0i	−0.748999	+	1.29731i
$842$	26076.4	−	45165.7i	1.06728	−	1.84859i
$843$		0			0
$844$	5810.30	+	10063.7i	0.236965	+	0.410436i
$845$	2221.46			0.0904386
$846$		0			0
$847$	95643.8			3.88000
$848$	−4947.79	−	8569.82i	−0.200363	−	0.347039i
$849$		0			0
$850$	−1467.49	+	2541.76i	−0.0592169	+	0.102567i
$851$	−917.770	+	1589.62i	−0.0369692	+	0.0640325i
$852$		0			0
$853$	−9492.39	−	16441.3i	−0.381024	−	0.659952i	0.610185	−	0.792259i	$-0.291095\pi$
$853$	−9492.39	−	16441.3i	−0.381024	−	0.659952i	−0.991209	+	0.132306i	$0.957762\pi$
$854$	7118.60			0.285238
$855$		0			0
$856$	−25356.3			−1.01245
$857$	18217.2	+	31553.1i	0.726124	+	1.25768i	0.958510	+	0.285059i	$0.0920133\pi$
$857$	18217.2	+	31553.1i	0.726124	+	1.25768i	−0.232386	+	0.972624i	$0.574653\pi$
$858$		0			0
$859$	8742.51	−	15142.5i	0.347253	−	0.601461i	−0.638507	−	0.769616i	$-0.720448\pi$
$859$	8742.51	−	15142.5i	0.347253	−	0.601461i	0.985761	+	0.168155i	$0.0537810\pi$
$860$	2614.16	−	4527.86i	0.103654	−	0.179533i
$861$		0			0
$862$	4024.14	+	6970.02i	0.159006	+	0.275406i
$863$	−10423.6			−0.411152			−0.205576	−	0.978641i	$-0.565907\pi$
$863$	−10423.6			−0.411152			−0.205576	+	0.978641i	$0.565907\pi$
$864$		0			0
$865$	−6637.04			−0.260886
$866$	9741.11	+	16872.1i	0.382236	+	0.662052i
$867$		0			0
$868$	−12501.4	+	21653.0i	−0.488852	+	0.846717i
$869$	−28314.0	+	49041.3i	−1.10528	+	1.91440i
$870$		0			0
$871$	−15713.7	−	27217.0i	−0.611296	−	1.05880i
$872$	−2673.63			−0.103831
$873$		0			0
$874$	−32746.7			−1.26736
$875$	−1589.53	−	2753.15i	−0.0614124	−	0.106369i
$876$		0			0
$877$	−3936.62	+	6818.42i	−0.151574	+	0.262533i	−0.931806	−	0.362956i	$-0.881767\pi$
$877$	−3936.62	+	6818.42i	−0.151574	+	0.262533i	0.780232	+	0.625490i	$0.215101\pi$
$878$	−20897.1	+	36194.8i	−0.803237	+	1.39125i
$879$		0			0
$880$	−14240.5	−	24665.3i	−0.545509	−	0.944849i
$881$	−35135.0			−1.34362			−0.671809	−	0.740725i	$-0.734482\pi$
$881$	−35135.0			−1.34362			−0.671809	+	0.740725i	$0.734482\pi$
$882$		0			0
$883$	33069.4			1.26033			0.630167	−	0.776460i	$-0.282987\pi$
$883$	33069.4			1.26033			0.630167	+	0.776460i	$0.282987\pi$
$884$	−3779.99	−	6547.13i	−0.143818	−	0.249100i
$885$		0			0
$886$	−26943.3	+	46667.2i	−1.02165	+	1.76954i
$887$	25739.6	−	44582.2i	0.974351	−	1.68763i	0.292293	−	0.956329i	$-0.405582\pi$
$887$	25739.6	−	44582.2i	0.974351	−	1.68763i	0.682059	−	0.731297i	$-0.261085\pi$
$888$		0			0
$889$	14980.0	+	25946.1i	0.565143	+	0.978856i
$890$	−3125.31			−0.117709
$891$		0			0
$892$	14804.1			0.555692
$893$	6121.15	+	10602.2i	0.229380	+	0.397298i
$894$		0			0
$895$	1121.84	−	1943.08i	0.0418981	−	0.0725697i
$896$	18496.3	−	32036.6i	0.689641	−	1.19449i
$897$		0			0
$898$	22900.4	+	39664.7i	0.850999	+	1.47397i
$899$	−54963.3			−2.03907
$900$		0			0
$901$	4130.28			0.152719
$902$	54586.8	+	94547.2i	2.01501	+	3.49011i
$903$		0			0
$904$	−12.2841	+	21.2768i	−0.000451952	+	0.000782804i
$905$	8626.39	−	14941.3i	0.316852	−	0.548803i
$906$		0			0
$907$	5404.90	+	9361.55i	0.197868	+	0.342718i	0.947837	−	0.318755i	$-0.103265\pi$
$907$	5404.90	+	9361.55i	0.197868	+	0.342718i	−0.749969	+	0.661473i	$0.769931\pi$
$908$	3049.64			0.111460
$909$		0			0
$910$	23027.0			0.838834
$911$	−15769.9	−	27314.2i	−0.573523	−	0.993371i	−0.996200	−	0.0870907i	$-0.972243\pi$
$911$	−15769.9	−	27314.2i	−0.573523	−	0.993371i	0.422677	−	0.906280i	$-0.361090\pi$
$912$		0			0
$913$	9635.96	−	16690.0i	0.349292	−	0.604992i
$914$	25213.9	−	43671.7i	0.912474	−	1.58045i
$915$		0			0
$916$	1474.86	+	2554.53i	0.0531996	+	0.0921443i
$917$	13255.9			0.477368
$918$		0			0
$919$	3592.53			0.128952			0.0644759	−	0.997919i	$-0.479462\pi$
$919$	3592.53			0.128952			0.0644759	+	0.997919i	$0.479462\pi$
$920$	−2588.84	−	4484.00i	−0.0927734	−	0.160688i
$921$		0			0
$922$	7558.45	−	13091.6i	0.269983	−	0.467624i
$923$	13133.7	−	22748.1i	0.468363	−	0.811229i
$924$		0			0
$925$	−279.887	−	484.779i	−0.00994880	−	0.0172318i
$926$	51126.7			1.81439
$927$		0			0
$928$	−44482.0			−1.57348
$929$	−15807.4	−	27379.1i	−0.558259	−	0.966933i	−0.997642	−	0.0686331i	$-0.978136\pi$
$929$	−15807.4	−	27379.1i	−0.558259	−	0.966933i	0.439383	−	0.898300i	$-0.355197\pi$
$930$		0			0
$931$	−17221.8	+	29829.0i	−0.606252	+	1.05006i
$932$	2076.18	−	3596.05i	0.0729695	−	0.126387i
$933$		0			0
$934$	−13024.6	−	22559.3i	−0.456294	−	0.790325i
$935$	11887.6			0.415793
$936$		0			0
$937$	−20891.5			−0.728382			−0.364191	−	0.931324i	$-0.618654\pi$
$937$	−20891.5			−0.728382			−0.364191	+	0.931324i	$0.618654\pi$
$938$	−27398.7	−	47456.0i	−0.953732	−	1.65191i
$939$		0			0
$940$	1191.84	−	2064.33i	0.0413548	−	0.0716286i
$941$	−18884.6	+	32709.1i	−0.654219	+	1.13314i	0.327870	+	0.944723i	$0.393669\pi$
$941$	−18884.6	+	32709.1i	−0.654219	+	1.13314i	−0.982089	+	0.188417i	$0.939664\pi$
$942$		0			0
$943$	17798.2	+	30827.4i	0.614622	+	1.06456i
$944$	−13657.8			−0.470894
$945$		0			0
$946$	−59549.1			−2.04663
$947$	5215.42	+	9033.37i	0.178963	+	0.309974i	0.941526	−	0.336941i	$-0.109392\pi$
$947$	5215.42	+	9033.37i	0.178963	+	0.309974i	−0.762562	+	0.646915i	$0.776059\pi$
$948$		0			0
$949$	−10536.0	+	18248.8i	−0.360392	+	0.624217i
$950$	4993.29	−	8648.63i	0.170530	−	0.295367i
$951$		0			0
$952$	5352.12	+	9270.15i	0.182209	+	0.315596i
$953$	−33865.3			−1.15111			−0.575553	−	0.817764i	$-0.695213\pi$
$953$	−33865.3			−1.15111			−0.575553	+	0.817764i	$0.695213\pi$
$954$		0			0
$955$	−7960.47			−0.269733
$956$	−2444.53	−	4234.05i	−0.0827005	−	0.143242i
$957$		0			0
$958$	23800.8	−	41224.2i	0.802683	−	1.39029i
$959$	5716.35	−	9901.01i	0.192482	−	0.333389i
$960$		0			0
$961$	−9897.47	−	17142.9i	−0.332230	−	0.575440i
$962$	4054.65			0.135891
$963$		0			0
$964$	5425.28			0.181262
$965$	−1108.25	−	1919.54i	−0.0369697	−	0.0640334i
$966$		0			0
$967$	23290.9	−	40341.0i	0.774544	−	1.34155i	−0.160506	−	0.987035i	$-0.551313\pi$
$967$	23290.9	−	40341.0i	0.774544	−	1.34155i	0.935050	−	0.354515i	$-0.115354\pi$
$968$	−23752.7	+	41140.9i	−0.788678	+	1.36603i
$969$		0			0
$970$	−7768.04	−	13454.6i	−0.257131	−	0.445363i
$971$	13829.5			0.457065			0.228532	−	0.973536i	$-0.426607\pi$
$971$	13829.5			0.457065			0.228532	+	0.973536i	$0.426607\pi$
$972$		0			0
$973$	−59650.5			−1.96537
$974$	−19625.8	−	33992.9i	−0.645637	−	1.11828i
$975$		0			0
$976$	−3170.73	+	5491.86i	−0.103988	+	0.180113i
$977$	−7971.80	+	13807.6i	−0.261045	+	0.452142i	−0.966520	−	0.256592i	$-0.917400\pi$
$977$	−7971.80	+	13807.6i	−0.261045	+	0.452142i	0.705475	+	0.708735i	$0.250734\pi$
$978$		0			0
$979$	6329.27	+	10962.6i	0.206624	+	0.357882i
$980$	6706.44			0.218601
$981$		0			0
$982$	−7091.85			−0.230458
$983$	14555.8	+	25211.4i	0.472286	+	0.818024i	0.999497	−	0.0317108i	$-0.0100956\pi$
$983$	14555.8	+	25211.4i	0.472286	+	0.818024i	−0.527211	+	0.849734i	$0.676762\pi$
$984$		0			0
$985$	522.479	−	904.960i	0.0169011	−	0.0292735i
$986$	14488.6	−	25095.1i	0.467964	−	0.810537i
$987$		0			0
$988$	12861.8	+	22277.3i	0.414159	+	0.717345i
$989$	−19416.1			−0.624265
$990$		0			0
$991$	8745.85			0.280344			0.140172	−	0.990127i	$-0.455234\pi$
$991$	8745.85			0.280344			0.140172	+	0.990127i	$0.455234\pi$
$992$	−20065.1	−	34753.7i	−0.642204	−	1.11233i
$993$		0			0
$994$	22900.1	−	39664.1i	0.730731	−	1.26566i
$995$	1199.79	−	2078.10i	0.0382270	−	0.0662112i
$996$		0			0
$997$	−22513.4	−	38994.4i	−0.715153	−	1.23868i	−0.962900	−	0.269857i	$-0.913024\pi$
$997$	−22513.4	−	38994.4i	−0.715153	−	1.23868i	0.247747	−	0.968825i	$-0.420310\pi$
$998$	−25908.0			−0.821748
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.u.271.3		6
3.2	odd	2		405.4.e.s.271.1		6
9.2	odd	6		405.4.e.s.136.1		6
9.4	even	3		405.4.a.g.1.1	✓	3
9.5	odd	6		405.4.a.i.1.3	yes	3
9.7	even	3	inner	405.4.e.u.136.3		6
45.4	even	6		2025.4.a.r.1.3		3
45.14	odd	6		2025.4.a.p.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.g.1.1	✓	3	9.4	even	3
405.4.a.i.1.3	yes	3	9.5	odd	6
405.4.e.s.136.1		6	9.2	odd	6
405.4.e.s.271.1		6	3.2	odd	2
405.4.e.u.136.3		6	9.7	even	3	inner
405.4.e.u.271.3		6	1.1	even	1	trivial
2025.4.a.p.1.1		3	45.14	odd	6
2025.4.a.r.1.3		3	45.4	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)

\(f(q)\)	\(=\)	\(q+(1.76174 + 3.05142i) q^{2} +(-2.20744 + 3.82340i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-12.7162 - 22.0252i) q^{7} +12.6321 q^{8} +O(q^{10})\)	\(q+(1.76174 + 3.05142i) q^{2} +(-2.20744 + 3.82340i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-12.7162 - 22.0252i) q^{7} +12.6321 q^{8} -17.6174 q^{10} +(35.6781 + 61.7962i) q^{11} +(25.6968 - 44.5081i) q^{13} +(44.8053 - 77.6051i) q^{14} +(39.9139 + 69.1330i) q^{16} -33.3191 q^{17} +113.372 q^{19} +(-11.0372 - 19.1170i) q^{20} +(-125.711 + 217.738i) q^{22} +(-40.9884 + 70.9939i) q^{23} +(-12.5000 - 21.6506i) q^{25} +181.084 q^{26} +112.281 q^{28} +(123.414 + 213.759i) q^{29} +(-111.340 + 192.846i) q^{31} +(-90.1075 + 156.071i) q^{32} +(-58.6995 - 101.671i) q^{34} +127.162 q^{35} +22.3910 q^{37} +(199.731 + 345.945i) q^{38} +(-31.5802 + 54.6985i) q^{40} +(217.113 - 376.050i) q^{41} +(118.425 + 205.118i) q^{43} -315.029 q^{44} -288.843 q^{46} +(53.9919 + 93.5166i) q^{47} +(-151.905 + 263.107i) q^{49} +(44.0435 - 76.2855i) q^{50} +(113.448 + 196.498i) q^{52} -123.961 q^{53} -356.781 q^{55} +(-160.632 - 278.223i) q^{56} +(-434.845 + 753.174i) q^{58} +(-85.5454 + 148.169i) q^{59} +(39.7196 + 68.7963i) q^{61} -784.604 q^{62} +3.63945 q^{64} +(128.484 + 222.540i) q^{65} +(305.753 - 529.580i) q^{67} +(73.5500 - 127.392i) q^{68} +(224.027 + 388.026i) q^{70} +511.102 q^{71} -410.012 q^{73} +(39.4471 + 68.3243i) q^{74} +(-250.262 + 433.466i) q^{76} +(907.381 - 1571.63i) q^{77} +(396.798 + 687.275i) q^{79} -399.139 q^{80} +1529.98 q^{82} +(-135.040 - 233.897i) q^{83} +(83.2977 - 144.276i) q^{85} +(-417.267 + 722.727i) q^{86} +(450.688 + 780.614i) q^{88} +177.400 q^{89} -1307.06 q^{91} +(-180.959 - 313.430i) q^{92} +(-190.239 + 329.504i) q^{94} +(-283.430 + 490.914i) q^{95} +(440.930 + 763.714i) q^{97} -1070.47 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 5 q^{4} - 15 q^{5} + 25 q^{7} + 54 q^{8}+O(q^{10}) \) 6 * q + q^2 - 5 * q^4 - 15 * q^5 + 25 * q^7 + 54 * q^8	\( 6 q + q^{2} - 5 q^{4} - 15 q^{5} + 25 q^{7} + 54 q^{8} - 10 q^{10} + 58 q^{11} + 47 q^{13} + 159 q^{14} + 127 q^{16} - 68 q^{17} - 10 q^{19} - 25 q^{20} - 260 q^{22} - 51 q^{23} - 75 q^{25} - 506 q^{26} + 166 q^{28} + 350 q^{29} - 638 q^{31} + 245 q^{32} + 154 q^{34} - 250 q^{35} - 828 q^{37} + 397 q^{38} - 135 q^{40} + 179 q^{41} + 836 q^{43} - 664 q^{44} + 522 q^{46} + 235 q^{47} - 892 q^{49} + 25 q^{50} + 1335 q^{52} - 1010 q^{53} - 580 q^{55} + 15 q^{56} - 1876 q^{58} + 535 q^{59} + 104 q^{61} - 696 q^{62} - 606 q^{64} + 235 q^{65} + 40 q^{67} + 830 q^{68} + 795 q^{70} - 904 q^{71} - 1420 q^{73} + 1394 q^{74} - 849 q^{76} + 2148 q^{77} + 634 q^{79} - 1270 q^{80} + 1226 q^{82} + 1734 q^{83} + 170 q^{85} + 460 q^{86} + 768 q^{88} + 1704 q^{89} - 2458 q^{91} - 1839 q^{92} - 1751 q^{94} + 25 q^{95} - 76 q^{98}+O(q^{100}) \) 6 * q + q^2 - 5 * q^4 - 15 * q^5 + 25 * q^7 + 54 * q^8 - 10 * q^10 + 58 * q^11 + 47 * q^13 + 159 * q^14 + 127 * q^16 - 68 * q^17 - 10 * q^19 - 25 * q^20 - 260 * q^22 - 51 * q^23 - 75 * q^25 - 506 * q^26 + 166 * q^28 + 350 * q^29 - 638 * q^31 + 245 * q^32 + 154 * q^34 - 250 * q^35 - 828 * q^37 + 397 * q^38 - 135 * q^40 + 179 * q^41 + 836 * q^43 - 664 * q^44 + 522 * q^46 + 235 * q^47 - 892 * q^49 + 25 * q^50 + 1335 * q^52 - 1010 * q^53 - 580 * q^55 + 15 * q^56 - 1876 * q^58 + 535 * q^59 + 104 * q^61 - 696 * q^62 - 606 * q^64 + 235 * q^65 + 40 * q^67 + 830 * q^68 + 795 * q^70 - 904 * q^71 - 1420 * q^73 + 1394 * q^74 - 849 * q^76 + 2148 * q^77 + 634 * q^79 - 1270 * q^80 + 1226 * q^82 + 1734 * q^83 + 170 * q^85 + 460 * q^86 + 768 * q^88 + 1704 * q^89 - 2458 * q^91 - 1839 * q^92 - 1751 * q^94 + 25 * q^95 - 76 * q^98

Introduction

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