LMFDB - Embedded newform 342.4.g.g.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,4,Mod(163,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.163");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.1786532220$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$1.56632 - 2.71294i$ of defining polynomial
Character	$\chi$	$=$	342.163
Dual form			342.4.g.g.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.49420 + 11.2483i) q^{5} -25.6033 q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.49420 + 11.2483i) q^{5} -25.6033 q^{7} +8.00000 q^{8} +(-12.9884 - 22.4966i) q^{10} -26.7726 q^{11} +(4.29582 + 7.44059i) q^{13} +(25.6033 - 44.3461i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(4.08468 - 7.07488i) q^{17} +(11.5302 - 82.0125i) q^{19} +51.9536 q^{20} +(26.7726 - 46.3715i) q^{22} +(78.4501 + 135.880i) q^{23} +(-21.8492 - 37.8439i) q^{25} -17.1833 q^{26} +(51.2065 + 88.6923i) q^{28} +(-103.679 - 179.577i) q^{29} +94.5197 q^{31} +(-16.0000 - 27.7128i) q^{32} +(8.16936 + 14.1498i) q^{34} +(166.273 - 287.993i) q^{35} +197.387 q^{37} +(130.520 + 101.983i) q^{38} +(-51.9536 + 89.9862i) q^{40} +(-188.369 + 326.265i) q^{41} +(254.122 - 440.152i) q^{43} +(53.5452 + 92.7431i) q^{44} -313.800 q^{46} +(-183.244 - 317.387i) q^{47} +312.527 q^{49} +87.3968 q^{50} +(17.1833 - 29.7623i) q^{52} +(-101.665 - 176.088i) q^{53} +(173.867 - 301.146i) q^{55} -204.826 q^{56} +414.715 q^{58} +(296.102 - 512.864i) q^{59} +(254.530 + 440.859i) q^{61} +(-94.5197 + 163.713i) q^{62} +64.0000 q^{64} -111.592 q^{65} +(125.360 + 217.129i) q^{67} -32.6774 q^{68} +(332.545 + 575.985i) q^{70} +(-57.7180 + 99.9706i) q^{71} +(416.335 - 721.114i) q^{73} +(-197.387 + 341.885i) q^{74} +(-307.160 + 124.083i) q^{76} +685.466 q^{77} +(-184.715 + 319.935i) q^{79} +(-103.907 - 179.972i) q^{80} +(-376.738 - 652.529i) q^{82} +1288.29 q^{83} +(53.0535 + 91.8913i) q^{85} +(508.244 + 880.304i) q^{86} -214.181 q^{88} +(30.5372 + 52.8919i) q^{89} +(-109.987 - 190.503i) q^{91} +(313.800 - 543.518i) q^{92} +732.975 q^{94} +(847.621 + 662.300i) q^{95} +(-123.755 + 214.350i) q^{97} +(-312.527 + 541.312i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 12 q^{4} + 2 q^{5} - 34 q^{7} + 48 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 - 12 * q^4 + 2 * q^5 - 34 * q^7 + 48 * q^8	$ 6 q - 6 q^{2} - 12 q^{4} + 2 q^{5} - 34 q^{7} + 48 q^{8} + 4 q^{10} + 104 q^{11} - 75 q^{13} + 34 q^{14} - 48 q^{16} - 48 q^{17} + 104 q^{19} - 16 q^{20} - 104 q^{22} - 238 q^{23} - 229 q^{25} + 300 q^{26} + 68 q^{28} - 8 q^{29} + 214 q^{31} - 96 q^{32} - 96 q^{34} - 294 q^{35} + 610 q^{37} + 430 q^{38} + 16 q^{40} + 16 q^{41} + 331 q^{43} - 208 q^{44} + 952 q^{46} - 766 q^{47} + 2284 q^{49} + 916 q^{50} - 300 q^{52} - 118 q^{53} + 1400 q^{55} - 272 q^{56} + 32 q^{58} + 936 q^{59} + 399 q^{61} - 214 q^{62} + 384 q^{64} - 740 q^{65} - 61 q^{67} + 384 q^{68} - 588 q^{70} + 974 q^{71} - 91 q^{73} - 610 q^{74} - 1276 q^{76} + 72 q^{77} + 321 q^{79} + 32 q^{80} + 32 q^{82} + 4296 q^{83} + 1680 q^{85} + 662 q^{86} + 832 q^{88} + 1116 q^{89} - 1367 q^{91} - 952 q^{92} + 3064 q^{94} + 4198 q^{95} - 1382 q^{97} - 2284 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - 12 * q^4 + 2 * q^5 - 34 * q^7 + 48 * q^8 + 4 * q^10 + 104 * q^11 - 75 * q^13 + 34 * q^14 - 48 * q^16 - 48 * q^17 + 104 * q^19 - 16 * q^20 - 104 * q^22 - 238 * q^23 - 229 * q^25 + 300 * q^26 + 68 * q^28 - 8 * q^29 + 214 * q^31 - 96 * q^32 - 96 * q^34 - 294 * q^35 + 610 * q^37 + 430 * q^38 + 16 * q^40 + 16 * q^41 + 331 * q^43 - 208 * q^44 + 952 * q^46 - 766 * q^47 + 2284 * q^49 + 916 * q^50 - 300 * q^52 - 118 * q^53 + 1400 * q^55 - 272 * q^56 + 32 * q^58 + 936 * q^59 + 399 * q^61 - 214 * q^62 + 384 * q^64 - 740 * q^65 - 61 * q^67 + 384 * q^68 - 588 * q^70 + 974 * q^71 - 91 * q^73 - 610 * q^74 - 1276 * q^76 + 72 * q^77 + 321 * q^79 + 32 * q^80 + 32 * q^82 + 4296 * q^83 + 1680 * q^85 + 662 * q^86 + 832 * q^88 + 1116 * q^89 - 1367 * q^91 - 952 * q^92 + 3064 * q^94 + 4198 * q^95 - 1382 * q^97 - 2284 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−6.49420	+	11.2483i	−0.580859	+	1.00608i	0.414519	+	0.910041i	$0.363950\pi$
$5$	−6.49420	+	11.2483i	−0.580859	+	1.00608i	−0.995378	+	0.0960362i	$0.969384\pi$
$6$		0			0
$7$	−25.6033			−1.38245			−0.691223	−	0.722642i	$-0.742928\pi$
$7$	−25.6033			−1.38245			−0.691223	+	0.722642i	$0.742928\pi$
$8$	8.00000			0.353553
$9$		0			0
$10$	−12.9884	−	22.4966i	−0.410729	−	0.711404i
$11$	−26.7726			−0.733841			−0.366920	−	0.930252i	$-0.619588\pi$
$11$	−26.7726			−0.733841			−0.366920	+	0.930252i	$0.619588\pi$
$12$		0			0
$13$	4.29582	+	7.44059i	0.0916498	+	0.158742i	0.908205	−	0.418525i	$-0.137453\pi$
$13$	4.29582	+	7.44059i	0.0916498	+	0.158742i	−0.816556	+	0.577267i	$0.804119\pi$
$14$	25.6033	−	44.3461i	0.488768	−	0.846572i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	4.08468	−	7.07488i	0.0582753	−	0.100936i	−0.835416	−	0.549618i	$-0.814773\pi$
$17$	4.08468	−	7.07488i	0.0582753	−	0.100936i	0.893691	+	0.448682i	$0.148107\pi$
$18$		0			0
$19$	11.5302	−	82.0125i	0.139221	−	0.990261i
$19$	11.5302	−	82.0125i	0.139221	−	0.990261i
$20$	51.9536			0.580859
$21$		0			0
$22$	26.7726	−	46.3715i	0.259452	−	0.449384i
$23$	78.4501	+	135.880i	0.711217	+	1.23186i	0.964401	+	0.264445i	$0.0851888\pi$
$23$	78.4501	+	135.880i	0.711217	+	1.23186i	−0.253184	+	0.967418i	$0.581478\pi$
$24$		0			0
$25$	−21.8492	−	37.8439i	−0.174794	−	0.302752i
$26$	−17.1833			−0.129612
$27$		0			0
$28$	51.2065	+	88.6923i	0.345611	+	0.598617i
$29$	−103.679	−	179.577i	−0.663884	−	1.14988i	−0.979587	−	0.201023i	$-0.935573\pi$
$29$	−103.679	−	179.577i	−0.663884	−	1.14988i	0.315702	−	0.948858i	$-0.397760\pi$
$30$		0			0
$31$	94.5197			0.547621			0.273810	−	0.961784i	$-0.411716\pi$
$31$	94.5197			0.547621			0.273810	+	0.961784i	$0.411716\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$		0			0
$34$	8.16936	+	14.1498i	0.0412069	+	0.0713724i
$35$	166.273	−	287.993i	0.803006	−	1.39085i
$36$		0			0
$37$	197.387			0.877035			0.438517	−	0.898723i	$-0.355504\pi$
$37$	197.387			0.877035			0.438517	+	0.898723i	$0.355504\pi$
$38$	130.520	+	101.983i	0.557187	+	0.435366i
$39$		0			0
$40$	−51.9536	+	89.9862i	−0.205365	+	0.355702i
$41$	−188.369	+	326.265i	−0.717519	+	1.24278i	0.244461	+	0.969659i	$0.421389\pi$
$41$	−188.369	+	326.265i	−0.717519	+	1.24278i	−0.961980	+	0.273120i	$0.911944\pi$
$42$		0			0
$43$	254.122	−	440.152i	0.901238	−	1.56099i	0.0753479	−	0.997157i	$-0.475993\pi$
$43$	254.122	−	440.152i	0.901238	−	1.56099i	0.825890	−	0.563832i	$-0.190673\pi$
$44$	53.5452	+	92.7431i	0.183460	+	0.317762i
$45$		0			0
$46$	−313.800			−1.00581
$47$	−183.244	−	317.387i	−0.568699	−	0.985015i	−0.996695	−	0.0812344i	$-0.974114\pi$
$47$	−183.244	−	317.387i	−0.568699	−	0.985015i	0.427996	−	0.903780i	$-0.359220\pi$
$48$		0			0
$49$	312.527			0.911156
$50$	87.3968			0.247196
$51$		0			0
$52$	17.1833	−	29.7623i	0.0458249	−	0.0793711i
$53$	−101.665	−	176.088i	−0.263485	−	0.456370i	0.703680	−	0.710517i	$-0.251539\pi$
$53$	−101.665	−	176.088i	−0.263485	−	0.456370i	−0.967166	+	0.254147i	$0.918205\pi$
$54$		0			0
$55$	173.867	−	301.146i	0.426258	−	0.738300i
$56$	−204.826			−0.488768
$57$		0			0
$58$	414.715			0.938874
$59$	296.102	−	512.864i	0.653376	−	1.13168i	−0.328922	−	0.944357i	$-0.606685\pi$
$59$	296.102	−	512.864i	0.653376	−	1.13168i	0.982298	−	0.187324i	$-0.0599814\pi$
$60$		0			0
$61$	254.530	+	440.859i	0.534250	+	0.925348i	0.999199	+	0.0400106i	$0.0127392\pi$
$61$	254.530	+	440.859i	0.534250	+	0.925348i	−0.464949	+	0.885337i	$0.653927\pi$
$62$	−94.5197	+	163.713i	−0.193613	+	0.335348i
$63$		0			0
$64$	64.0000			0.125000
$65$	−111.592			−0.212942
$66$		0			0
$67$	125.360	+	217.129i	0.228584	+	0.395919i	0.957389	−	0.288803i	$-0.0932572\pi$
$67$	125.360	+	217.129i	0.228584	+	0.395919i	−0.728805	+	0.684721i	$0.759924\pi$
$68$	−32.6774			−0.0582753
$69$		0			0
$70$	332.545	+	575.985i	0.567811	+	0.983477i
$71$	−57.7180	+	99.9706i	−0.0964771	+	0.167103i	−0.910224	−	0.414116i	$-0.864091\pi$
$71$	−57.7180	+	99.9706i	−0.0964771	+	0.167103i	0.813747	+	0.581219i	$0.197424\pi$
$72$		0			0
$73$	416.335	−	721.114i	0.667512	−	1.15616i	−0.311086	−	0.950382i	$-0.600693\pi$
$73$	416.335	−	721.114i	0.667512	−	1.15616i	0.978598	−	0.205782i	$-0.0659739\pi$
$74$	−197.387	+	341.885i	−0.310079	+	0.537072i
$75$		0			0
$76$	−307.160	+	124.083i	−0.463601	+	0.187281i
$77$	685.466			1.01449
$78$		0			0
$79$	−184.715	+	319.935i	−0.263064	+	0.455640i	−0.967054	−	0.254569i	$-0.918066\pi$
$79$	−184.715	+	319.935i	−0.263064	+	0.455640i	0.703991	+	0.710209i	$0.251400\pi$
$80$	−103.907	−	179.972i	−0.145215	−	0.251519i
$81$		0			0
$82$	−376.738	−	652.529i	−0.507363	−	0.878778i
$83$	1288.29			1.70371			0.851854	−	0.523780i	$-0.175479\pi$
$83$	1288.29			1.70371			0.851854	+	0.523780i	$0.175479\pi$
$84$		0			0
$85$	53.0535	+	91.8913i	0.0676995	+	0.117259i
$86$	508.244	+	880.304i	0.637271	+	1.10379i
$87$		0			0
$88$	−214.181			−0.259452
$89$	30.5372	+	52.8919i	0.0363700	+	0.0629947i	0.883637	−	0.468172i	$-0.155087\pi$
$89$	30.5372	+	52.8919i	0.0363700	+	0.0629947i	−0.847267	+	0.531167i	$0.821754\pi$
$90$		0			0
$91$	−109.987	−	190.503i	−0.126701	−	0.219452i
$92$	313.800	−	543.518i	0.355608	−	0.615932i
$93$		0			0
$94$	732.975			0.804261
$95$	847.621	+	662.300i	0.915411	+	0.715269i
$96$		0			0
$97$	−123.755	+	214.350i	−0.129541	+	0.224371i	−0.923499	−	0.383602i	$-0.874684\pi$
$97$	−123.755	+	214.350i	−0.129541	+	0.224371i	0.793958	+	0.607973i	$0.208017\pi$
$98$	−312.527	+	541.312i	−0.322142	+	0.557967i
$99$		0			0
$100$	−87.3968	+	151.376i	−0.0873968	+	0.151376i
$101$	−423.006	−	732.668i	−0.416739	−	0.721813i	0.578870	−	0.815420i	$-0.303494\pi$
$101$	−423.006	−	732.668i	−0.416739	−	0.721813i	−0.995609	+	0.0936064i	$0.970160\pi$
$102$		0			0
$103$	−1422.55			−1.36085			−0.680427	−	0.732816i	$-0.738206\pi$
$103$	−1422.55			−1.36085			−0.680427	+	0.732816i	$0.738206\pi$
$104$	34.3666	+	59.5247i	0.0324031	+	0.0561238i
$105$		0			0
$106$	406.659			0.372624
$107$	−286.239			−0.258615			−0.129307	−	0.991605i	$-0.541275\pi$
$107$	−286.239			−0.258615			−0.129307	+	0.991605i	$0.541275\pi$
$108$		0			0
$109$	16.1427	−	27.9600i	0.0141852	−	0.0245695i	−0.858846	−	0.512234i	$-0.828818\pi$
$109$	16.1427	−	27.9600i	0.0141852	−	0.0245695i	0.873031	+	0.487665i	$0.162151\pi$
$110$	347.733	+	602.292i	0.301410	+	0.522057i
$111$		0			0
$112$	204.826	−	354.769i	0.172806	−	0.299308i
$113$	297.098			0.247333			0.123666	−	0.992324i	$-0.460535\pi$
$113$	297.098			0.247333			0.123666	+	0.992324i	$0.460535\pi$
$114$		0			0
$115$	−2037.88			−1.65247
$116$	−414.715	+	718.307i	−0.331942	+	0.574941i
$117$		0			0
$118$	592.204	+	1025.73i	0.462007	+	0.800219i
$119$	−104.581	+	181.140i	−0.0805625	+	0.139538i
$120$		0			0
$121$	−614.227			−0.461478
$122$	−1018.12			−0.755543
$123$		0			0
$124$	−189.039	−	327.426i	−0.136905	−	0.237127i
$125$	−1055.98			−0.755596
$126$		0			0
$127$	−1333.60	−	2309.86i	−0.931792	−	1.61391i	−0.780258	−	0.625458i	$-0.784912\pi$
$127$	−1333.60	−	2309.86i	−0.931792	−	1.61391i	−0.151534	−	0.988452i	$-0.548421\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	111.592	−	193.283i	0.0752865	−	0.130400i
$131$	411.138	−	712.112i	0.274208	−	0.474943i	−0.695727	−	0.718307i	$-0.744918\pi$
$131$	411.138	−	712.112i	0.274208	−	0.474943i	0.969935	+	0.243364i	$0.0782509\pi$
$132$		0			0
$133$	−295.210	+	2099.79i	−0.192466	+	1.36898i
$134$	−501.438			−0.323266
$135$		0			0
$136$	32.6774	−	56.5990i	0.0206034	−	0.0356862i
$137$	−1222.61	−	2117.62i	−0.762443	−	1.32059i	−0.941588	−	0.336768i	$-0.890666\pi$
$137$	−1222.61	−	2117.62i	−0.762443	−	1.32059i	0.179144	−	0.983823i	$-0.442667\pi$
$138$		0			0
$139$	−752.171	−	1302.80i	−0.458980	−	0.794977i	0.539927	−	0.841712i	$-0.318452\pi$
$139$	−752.171	−	1302.80i	−0.458980	−	0.794977i	−0.998907	+	0.0467345i	$0.985119\pi$
$140$	−1330.18			−0.803006
$141$		0			0
$142$	−115.436	−	199.941i	−0.0682196	−	0.118160i
$143$	−115.010	−	199.204i	−0.0672564	−	0.116491i
$144$		0			0
$145$	2693.24			1.54249
$146$	832.671	+	1442.23i	0.472002	+	0.817532i
$147$		0			0
$148$	−394.775	−	683.770i	−0.219259	−	0.379767i
$149$	−360.374	+	624.186i	−0.198141	+	0.343190i	−0.947926	−	0.318492i	$-0.896824\pi$
$149$	−360.374	+	624.186i	−0.198141	+	0.343190i	0.749785	+	0.661682i	$0.230157\pi$
$150$		0			0
$151$	1801.25			0.970752			0.485376	−	0.874306i	$-0.338683\pi$
$151$	1801.25			0.970752			0.485376	+	0.874306i	$0.338683\pi$
$152$	92.2414	−	656.100i	0.0492222	−	0.350110i
$153$		0			0
$154$	−685.466	+	1187.26i	−0.358678	+	0.621249i
$155$	−613.830	+	1063.18i	−0.318090	+	0.550948i
$156$		0			0
$157$	−1914.55	+	3316.11i	−0.973236	+	1.68569i	−0.287599	+	0.957751i	$0.592857\pi$
$157$	−1914.55	+	3316.11i	−0.973236	+	1.68569i	−0.685637	+	0.727943i	$0.740476\pi$
$158$	−369.429	−	639.870i	−0.186014	−	0.322186i
$159$		0			0
$160$	415.629			0.205365
$161$	−2008.58	−	3478.96i	−0.983218	−	1.70298i
$162$		0			0
$163$	−956.496			−0.459623			−0.229812	−	0.973235i	$-0.573811\pi$
$163$	−956.496			−0.459623			−0.229812	+	0.973235i	$0.573811\pi$
$164$	1506.95			0.717519
$165$		0			0
$166$	−1288.29	+	2231.38i	−0.602351	+	1.04330i
$167$	−1389.88	−	2407.35i	−0.644027	−	1.11549i	−0.984525	−	0.175242i	$-0.943929\pi$
$167$	−1389.88	−	2407.35i	−0.644027	−	1.11549i	0.340499	−	0.940245i	$-0.389404\pi$
$168$		0			0
$169$	1061.59	−	1838.73i	0.483201	−	0.836928i
$170$	−212.214			−0.0957415
$171$		0			0
$172$	−2032.97			−0.901238
$173$	−154.776	+	268.080i	−0.0680196	+	0.117813i	−0.898029	−	0.439935i	$-0.855001\pi$
$173$	−154.776	+	268.080i	−0.0680196	+	0.117813i	0.830010	+	0.557749i	$0.188335\pi$
$174$		0			0
$175$	559.411	+	968.928i	0.241643	+	0.418538i
$176$	214.181	−	370.972i	0.0917301	−	0.158881i
$177$		0			0
$178$	−122.149			−0.0514350
$179$	−4650.29			−1.94178			−0.970890	−	0.239524i	$-0.923009\pi$
$179$	−4650.29			−1.94178			−0.970890	+	0.239524i	$0.923009\pi$
$180$		0			0
$181$	134.864	+	233.591i	0.0553833	+	0.0959266i	0.892388	−	0.451269i	$-0.149029\pi$
$181$	134.864	+	233.591i	0.0553833	+	0.0959266i	−0.837005	+	0.547196i	$0.815695\pi$
$182$	439.948			0.179182
$183$		0			0
$184$	627.601	+	1087.04i	0.251453	+	0.435529i
$185$	−1281.87	+	2220.27i	−0.509433	+	0.882364i
$186$		0			0
$187$	−109.358	+	189.413i	−0.0427648	+	0.0740708i
$188$	−732.975	+	1269.55i	−0.284349	+	0.492507i
$189$		0			0
$190$	−1994.76	+	805.822i	−0.761658	+	0.307687i
$191$	1949.96			0.738715			0.369357	−	0.929287i	$-0.379578\pi$
$191$	1949.96			0.738715			0.369357	+	0.929287i	$0.379578\pi$
$192$		0			0
$193$	−1465.65	+	2538.58i	−0.546631	+	0.946793i	0.451871	+	0.892083i	$0.350757\pi$
$193$	−1465.65	+	2538.58i	−0.546631	+	0.946793i	−0.998502	+	0.0547095i	$0.982577\pi$
$194$	−247.510	−	428.701i	−0.0915990	−	0.158654i
$195$		0			0
$196$	−625.053	−	1082.62i	−0.227789	−	0.394542i
$197$	1236.48			0.447186			0.223593	−	0.974683i	$-0.428221\pi$
$197$	1236.48			0.447186			0.223593	+	0.974683i	$0.428221\pi$
$198$		0			0
$199$	2254.50	+	3904.91i	0.803103	+	1.39102i	0.917564	+	0.397588i	$0.130153\pi$
$199$	2254.50	+	3904.91i	0.803103	+	1.39102i	−0.114461	+	0.993428i	$0.536514\pi$
$200$	−174.794	−	302.752i	−0.0617989	−	0.107039i
$201$		0			0
$202$	1692.02			0.589358
$203$	2654.51	+	4597.75i	0.917784	+	1.58965i
$204$		0			0
$205$	−2446.61	−	4237.65i	−0.833554	−	1.44376i
$206$	1422.55	−	2463.93i	0.481135	−	0.833350i
$207$		0			0
$208$	−137.466			−0.0458249
$209$	−308.693	+	2195.69i	−0.102166	+	0.726694i
$210$		0			0
$211$	0.952349	−	1.64952i	0.000310722	−	0.000538187i	−0.865870	−	0.500269i	$-0.833234\pi$
$211$	0.952349	−	1.64952i	0.000310722	−	0.000538187i	0.866181	+	0.499731i	$0.166568\pi$
$212$	−406.659	+	704.354i	−0.131743	+	0.228185i
$213$		0			0
$214$	286.239	−	495.781i	0.0914342	−	0.158369i
$215$	3300.63	+	5716.87i	1.04698	+	1.81343i
$216$		0			0
$217$	−2420.01			−0.757056
$218$	32.2854	+	55.9200i	0.0100305	+	0.0173733i
$219$		0			0
$220$	−1390.93			−0.426258
$221$	70.1883			0.0213637
$222$		0			0
$223$	2330.11	−	4035.88i	0.699713	−	1.21194i	−0.268853	−	0.963181i	$-0.586645\pi$
$223$	2330.11	−	4035.88i	0.699713	−	1.21194i	0.968566	−	0.248757i	$-0.0800220\pi$
$224$	409.652	+	709.538i	0.122192	+	0.211643i
$225$		0			0
$226$	−297.098	+	514.588i	−0.0874453	+	0.151460i
$227$	4045.15			1.18276			0.591380	−	0.806393i	$-0.298584\pi$
$227$	4045.15			1.18276			0.591380	+	0.806393i	$0.298584\pi$
$228$		0			0
$229$	5062.73			1.46094			0.730468	−	0.682947i	$-0.239302\pi$
$229$	5062.73			1.46094			0.730468	+	0.682947i	$0.239302\pi$
$230$	2037.88	−	3529.72i	0.584235	−	1.01192i
$231$		0			0
$232$	−829.429	−	1436.61i	−0.234719	−	0.406544i
$233$	216.545	−	375.066i	0.0608854	−	0.105457i	−0.833976	−	0.551801i	$-0.813941\pi$
$233$	216.545	−	375.066i	0.0608854	−	0.105457i	0.894861	+	0.446344i	$0.147274\pi$
$234$		0			0
$235$	4760.08			1.32133
$236$	−2368.82			−0.653376
$237$		0			0
$238$	−209.162	−	362.280i	−0.0569663	−	0.0986685i
$239$	4165.22			1.12730			0.563652	−	0.826012i	$-0.309396\pi$
$239$	4165.22			1.12730			0.563652	+	0.826012i	$0.309396\pi$
$240$		0			0
$241$	−2084.71	−	3610.82i	−0.557212	−	0.965119i	−0.997728	−	0.0673743i	$-0.978538\pi$
$241$	−2084.71	−	3610.82i	−0.557212	−	0.965119i	0.440516	−	0.897745i	$-0.354795\pi$
$242$	614.227	−	1063.87i	0.163157	−	0.282596i
$243$		0			0
$244$	1018.12	−	1763.44i	0.267125	−	0.462674i
$245$	−2029.61	+	3515.39i	−0.529253	+	0.916693i
$246$		0			0
$247$	659.753	−	266.520i	0.169956	−	0.0686570i
$248$	756.158			0.193613
$249$		0			0
$250$	1055.98	−	1829.01i	0.267143	−	0.462706i
$251$	−3566.12	−	6176.71i	−0.896780	−	1.55327i	−0.831587	−	0.555395i	$-0.812567\pi$
$251$	−3566.12	−	6176.71i	−0.896780	−	1.55327i	−0.0651931	−	0.997873i	$-0.520766\pi$
$252$		0			0
$253$	−2100.31	−	3637.85i	−0.521920	−	0.903991i
$254$	5334.38			1.31775
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−538.758	−	933.157i	−0.130766	−	0.226493i	0.793206	−	0.608953i	$-0.208410\pi$
$257$	−538.758	−	933.157i	−0.130766	−	0.226493i	−0.923972	+	0.382460i	$0.875077\pi$
$258$		0			0
$259$	−5053.76			−1.21245
$260$	223.183	+	386.565i	0.0532356	+	0.0922067i
$261$		0			0
$262$	822.276	+	1424.22i	0.193895	+	0.335835i
$263$	1244.58	−	2155.68i	0.291803	−	0.505417i	−0.682433	−	0.730948i	$-0.739078\pi$
$263$	1244.58	−	2155.68i	0.291803	−	0.505417i	0.974236	+	0.225530i	$0.0724115\pi$
$264$		0			0
$265$	2640.92			0.612191
$266$	−3341.73	−	2611.11i	−0.770280	−	0.601869i
$267$		0			0
$268$	501.438	−	868.517i	0.114292	−	0.197959i
$269$	−3090.64	+	5353.14i	−0.700519	+	1.21333i	0.267765	+	0.963484i	$0.413715\pi$
$269$	−3090.64	+	5353.14i	−0.700519	+	1.21333i	−0.968284	+	0.249850i	$0.919619\pi$
$270$		0			0
$271$	−3016.36	+	5224.48i	−0.676128	+	1.17109i	0.300010	+	0.953936i	$0.403010\pi$
$271$	−3016.36	+	5224.48i	−0.676128	+	1.17109i	−0.976138	+	0.217152i	$0.930323\pi$
$272$	65.3549	+	113.198i	0.0145688	+	0.0252340i
$273$		0			0
$274$	4890.45			1.07826
$275$	584.961	+	1013.18i	0.128271	+	0.222171i
$276$		0			0
$277$	912.717			0.197978			0.0989889	−	0.995089i	$-0.468439\pi$
$277$	912.717			0.197978			0.0989889	+	0.995089i	$0.468439\pi$
$278$	3008.68			0.649096
$279$		0			0
$280$	1330.18	−	2303.94i	0.283905	−	0.491739i
$281$	−167.443	−	290.020i	−0.0355474	−	0.0615699i	0.847704	−	0.530469i	$-0.177984\pi$
$281$	−167.443	−	290.020i	−0.0355474	−	0.0615699i	−0.883252	+	0.468899i	$0.844651\pi$
$282$		0			0
$283$	1388.47	−	2404.90i	0.291646	−	0.505146i	−0.682553	−	0.730836i	$-0.739130\pi$
$283$	1388.47	−	2404.90i	0.291646	−	0.505146i	0.974199	+	0.225690i	$0.0724637\pi$
$284$	461.744			0.0964771
$285$		0			0
$286$	460.042			0.0951149
$287$	4822.86	−	8353.43i	0.991931	−	1.71808i
$288$		0			0
$289$	2423.13	+	4196.99i	0.493208	+	0.854261i
$290$	−2693.24	+	4664.83i	−0.545353	+	0.944580i
$291$		0			0
$292$	−3330.68			−0.667512
$293$	3067.85			0.611692			0.305846	−	0.952081i	$-0.401061\pi$
$293$	3067.85			0.611692			0.305846	+	0.952081i	$0.401061\pi$
$294$		0			0
$295$	3845.89	+	6661.28i	0.759039	+	1.31469i
$296$	1579.10			0.310079
$297$		0			0
$298$	−720.747	−	1248.37i	−0.140107	−	0.242672i
$299$	−674.016	+	1167.43i	−0.130366	+	0.225800i
$300$		0			0
$301$	−6506.35	+	11269.3i	−1.24591	+	2.15798i
$302$	−1801.25	+	3119.85i	−0.343213	+	0.594462i
$303$		0			0
$304$	1044.16	+	815.867i	0.196995	+	0.153925i
$305$	−6611.88			−1.24129
$306$		0			0
$307$	3743.90	−	6484.63i	0.696013	−	1.20553i	−0.273825	−	0.961779i	$-0.588289\pi$
$307$	3743.90	−	6484.63i	0.696013	−	1.20553i	0.969838	−	0.243750i	$-0.0783776\pi$
$308$	−1370.93	−	2374.52i	−0.253624	−	0.439289i
$309$		0			0
$310$	−1227.66	−	2126.37i	−0.224924	−	0.389579i
$311$	6681.88			1.21831			0.609156	−	0.793051i	$-0.291508\pi$
$311$	6681.88			1.21831			0.609156	+	0.793051i	$0.291508\pi$
$312$		0			0
$313$	−4081.01	−	7068.52i	−0.736972	−	1.27647i	−0.953853	−	0.300275i	$-0.902921\pi$
$313$	−4081.01	−	7068.52i	−0.736972	−	1.27647i	0.216880	−	0.976198i	$-0.430412\pi$
$314$	−3829.11	−	6632.21i	−0.688182	−	1.19197i
$315$		0			0
$316$	1477.72			0.263064
$317$	−1419.77	−	2459.11i	−0.251553	−	0.435702i	0.712401	−	0.701773i	$-0.247608\pi$
$317$	−1419.77	−	2459.11i	−0.251553	−	0.435702i	−0.963954	+	0.266071i	$0.914275\pi$
$318$		0			0
$319$	2775.75	+	4807.74i	0.487185	+	0.843830i
$320$	−415.629	+	719.890i	−0.0726073	+	0.125760i
$321$		0			0
$322$	8034.31			1.39048
$323$	−533.131	−	416.570i	−0.0918397	−	0.0717602i
$324$		0			0
$325$	187.721	−	325.142i	0.0320396	−	0.0554942i
$326$	956.496	−	1656.70i	0.162501	−	0.281461i
$327$		0			0
$328$	−1506.95	+	2610.12i	−0.253681	+	0.439389i
$329$	4691.63	+	8126.15i	0.786195	+	1.36173i
$330$		0			0
$331$	11056.2			1.83597			0.917984	−	0.396617i	$-0.129816\pi$
$331$	11056.2			1.83597			0.917984	+	0.396617i	$0.129816\pi$
$332$	−2576.57	−	4462.75i	−0.425927	−	0.737727i
$333$		0			0
$334$	5559.54			0.910791
$335$	−3256.44			−0.531099
$336$		0			0
$337$	2525.16	−	4373.71i	0.408174	−	0.706977i	−0.586512	−	0.809941i	$-0.699499\pi$
$337$	2525.16	−	4373.71i	0.408174	−	0.706977i	0.994685	+	0.102964i	$0.0328325\pi$
$338$	2123.18	+	3677.46i	0.341674	+	0.591797i
$339$		0			0
$340$	212.214	−	367.565i	0.0338497	−	0.0586295i
$341$	−2530.54			−0.401866
$342$		0			0
$343$	780.217			0.122822
$344$	2032.97	−	3521.22i	0.318636	−	0.551893i
$345$		0			0
$346$	−309.552	−	536.160i	−0.0480972	−	0.0833067i
$347$	−3007.43	+	5209.01i	−0.465265	+	0.805863i	−0.999213	−	0.0396541i	$-0.987374\pi$
$347$	−3007.43	+	5209.01i	−0.465265	+	0.805863i	0.533948	+	0.845517i	$0.320708\pi$
$348$		0			0
$349$	−2514.51			−0.385669			−0.192834	−	0.981231i	$-0.561768\pi$
$349$	−2514.51			−0.385669			−0.192834	+	0.981231i	$0.561768\pi$
$350$	−2237.64			−0.341735
$351$		0			0
$352$	428.362	+	741.945i	0.0648630	+	0.112346i
$353$	−4578.03			−0.690266			−0.345133	−	0.938554i	$-0.612166\pi$
$353$	−4578.03			−0.690266			−0.345133	+	0.938554i	$0.612166\pi$
$354$		0			0
$355$	−749.665	−	1298.46i	−0.112079	−	0.194127i
$356$	122.149	−	211.568i	0.0181850	−	0.0314974i
$357$		0			0
$358$	4650.29	−	8054.53i	0.686523	−	1.18909i
$359$	3986.22	−	6904.33i	0.586029	−	1.01503i	−0.408717	−	0.912661i	$-0.634024\pi$
$359$	3986.22	−	6904.33i	0.586029	−	1.01503i	0.994746	−	0.102371i	$-0.0326430\pi$
$360$		0			0
$361$	−6593.11	−	1891.24i	−0.961235	−	0.275731i
$362$	−539.456			−0.0783238
$363$		0			0
$364$	−439.948	+	762.013i	−0.0633504	+	0.109726i
$365$	5407.53	+	9366.11i	0.775460	+	1.34314i
$366$		0			0
$367$	−2732.75	−	4733.26i	−0.388688	−	0.673227i	0.603585	−	0.797298i	$-0.293738\pi$
$367$	−2732.75	−	4733.26i	−0.388688	−	0.673227i	−0.992273	+	0.124071i	$0.960405\pi$
$368$	−2510.40			−0.355608
$369$		0			0
$370$	−2563.75	−	4440.54i	−0.360224	−	0.623926i
$371$	2602.95	+	4508.44i	0.364254	+	0.630907i
$372$		0			0
$373$	9245.54			1.28342			0.641710	−	0.766947i	$-0.278225\pi$
$373$	9245.54			1.28342			0.641710	+	0.766947i	$0.278225\pi$
$374$	−218.715	−	378.826i	−0.0302393	−	0.0523760i
$375$		0			0
$376$	−1465.95	−	2539.10i	−0.201065	−	0.348255i
$377$	890.771	−	1542.86i	0.121690	−	0.210773i
$378$		0			0
$379$	6098.42			0.826530			0.413265	−	0.910611i	$-0.364388\pi$
$379$	6098.42			0.826530			0.413265	+	0.910611i	$0.364388\pi$
$380$	599.034	−	4260.84i	0.0808679	−	0.575202i
$381$		0			0
$382$	−1949.96	+	3377.44i	−0.261175	+	0.452368i
$383$	2264.90	−	3922.93i	0.302170	−	0.523374i	−0.674457	−	0.738314i	$-0.735622\pi$
$383$	2264.90	−	3922.93i	0.302170	−	0.523374i	0.976627	+	0.214940i	$0.0689555\pi$
$384$		0			0
$385$	−4451.55	+	7710.32i	−0.589278	+	1.02066i
$386$	−2931.30	−	5077.16i	−0.386526	−	0.669484i
$387$		0			0
$388$	990.042			0.129541
$389$	−2779.46	−	4814.17i	−0.362273	−	0.627475i	0.626061	−	0.779774i	$-0.284666\pi$
$389$	−2779.46	−	4814.17i	−0.362273	−	0.627475i	−0.988335	+	0.152298i	$0.951333\pi$
$390$		0			0
$391$	1281.77			0.165786
$392$	2500.21			0.322142
$393$		0			0
$394$	−1236.48	+	2141.65i	−0.158104	+	0.273844i
$395$	−2399.15	−	4155.45i	−0.305606	−	0.529324i
$396$		0			0
$397$	−4695.83	+	8133.41i	−0.593645	+	1.02822i	0.400092	+	0.916475i	$0.368978\pi$
$397$	−4695.83	+	8133.41i	−0.593645	+	1.02822i	−0.993737	+	0.111748i	$0.964355\pi$
$398$	−9018.01			−1.13576
$399$		0			0
$400$	699.175			0.0873968
$401$	4766.06	−	8255.07i	0.593531	−	1.02803i	−0.400222	−	0.916418i	$-0.631067\pi$
$401$	4766.06	−	8255.07i	0.593531	−	1.02803i	0.993752	−	0.111607i	$-0.0355998\pi$
$402$		0			0
$403$	406.040	+	703.282i	0.0501893	+	0.0869304i
$404$	−1692.02	+	2930.67i	−0.208370	+	0.360907i
$405$		0			0
$406$	−10618.0			−1.29794
$407$	−5284.58			−0.643604
$408$		0			0
$409$	−3289.74	−	5698.00i	−0.397720	−	0.688871i	0.595725	−	0.803189i	$-0.296865\pi$
$409$	−3289.74	−	5698.00i	−0.397720	−	0.688871i	−0.993444	+	0.114318i	$0.963532\pi$
$410$	9786.44			1.17882
$411$		0			0
$412$	2845.10	+	4927.86i	0.340214	+	0.589267i
$413$	−7581.18	+	13131.0i	−0.903258	+	1.56449i
$414$		0			0
$415$	−8366.38	+	14491.0i	−0.989613	+	1.71406i
$416$	137.466	−	238.099i	0.0162015	−	0.0280619i
$417$		0			0
$418$	−3494.35	−	2730.36i	−0.408886	−	0.319489i
$419$	−4136.42			−0.482285			−0.241143	−	0.970490i	$-0.577522\pi$
$419$	−4136.42			−0.482285			−0.241143	+	0.970490i	$0.577522\pi$
$420$		0			0
$421$	−3896.23	+	6748.47i	−0.451047	+	0.781235i	−0.998451	−	0.0556325i	$-0.982282\pi$
$421$	−3896.23	+	6748.47i	−0.451047	+	0.781235i	0.547405	+	0.836868i	$0.315616\pi$
$422$	1.90470	+	3.29903i	0.000219714	+	0.000380555i
$423$		0			0
$424$	−813.317	−	1408.71i	−0.0931561	−	0.161351i
$425$	−356.988			−0.0407446
$426$		0			0
$427$	−6516.80	−	11287.4i	−0.738571	−	1.27924i
$428$	572.479	+	991.562i	0.0646537	+	0.111984i
$429$		0			0
$430$	−13202.5			−1.48066
$431$	−3675.30	−	6365.80i	−0.410749	−	0.711438i	0.584223	−	0.811593i	$-0.301399\pi$
$431$	−3675.30	−	6365.80i	−0.410749	−	0.711438i	−0.994972	+	0.100155i	$0.968066\pi$
$432$		0			0
$433$	−5346.31	−	9260.08i	−0.593365	−	1.02774i	−0.993775	−	0.111403i	$-0.964466\pi$
$433$	−5346.31	−	9260.08i	−0.593365	−	1.02774i	0.400410	−	0.916336i	$-0.368868\pi$
$434$	2420.01	−	4191.58i	0.267660	−	0.463600i
$435$		0			0
$436$	−129.142			−0.0141852
$437$	12048.4	−	4867.18i	1.31888	−	0.532789i
$438$		0			0
$439$	4809.83	−	8330.87i	0.522917	−	0.905719i	−0.476727	−	0.879051i	$-0.658177\pi$
$439$	4809.83	−	8330.87i	0.522917	−	0.905719i	0.999644	−	0.0266676i	$-0.00848958\pi$
$440$	1390.93	−	2409.17i	0.150705	−	0.261029i
$441$		0			0
$442$	−70.1883	+	121.570i	−0.00755321	+	0.0130825i
$443$	6302.23	+	10915.8i	0.675909	+	1.17071i	0.976202	+	0.216862i	$0.0695822\pi$
$443$	6302.23	+	10915.8i	0.675909	+	1.17071i	−0.300293	+	0.953847i	$0.597084\pi$
$444$		0			0
$445$	−793.258			−0.0845034
$446$	4660.23	+	8071.75i	0.494772	+	0.856970i
$447$		0			0
$448$	−1638.61			−0.172806
$449$	−14957.9			−1.57218			−0.786088	−	0.618114i	$-0.787897\pi$
$449$	−14957.9			−1.57218			−0.786088	+	0.618114i	$0.787897\pi$
$450$		0			0
$451$	5043.13	−	8734.96i	0.526545	−	0.912002i
$452$	−594.195	−	1029.18i	−0.0618332	−	0.107098i
$453$		0			0
$454$	−4045.15	+	7006.41i	−0.418168	+	0.724289i
$455$	2857.11			0.294381
$456$		0			0
$457$	−2003.50			−0.205076			−0.102538	−	0.994729i	$-0.532696\pi$
$457$	−2003.50			−0.205076			−0.102538	+	0.994729i	$0.532696\pi$
$458$	−5062.73	+	8768.90i	−0.516519	+	0.894637i
$459$		0			0
$460$	4075.76	+	7059.43i	0.413116	+	0.715538i
$461$	−567.329	+	982.642i	−0.0573170	+	0.0992759i	−0.893260	−	0.449540i	$-0.851588\pi$
$461$	−567.329	+	982.642i	−0.0573170	+	0.0992759i	0.835943	+	0.548816i	$0.184921\pi$
$462$		0			0
$463$	−2934.33			−0.294536			−0.147268	−	0.989097i	$-0.547048\pi$
$463$	−2934.33			−0.294536			−0.147268	+	0.989097i	$0.547048\pi$
$464$	3317.72			0.331942
$465$		0			0
$466$	433.089	+	750.132i	0.0430525	+	0.0745691i
$467$	930.578			0.0922098			0.0461049	−	0.998937i	$-0.485319\pi$
$467$	930.578			0.0922098			0.0461049	+	0.998937i	$0.485319\pi$
$468$		0			0
$469$	−3209.61	−	5559.21i	−0.316005	−	0.547336i
$470$	−4760.08	+	8244.70i	−0.467162	+	0.809149i
$471$		0			0
$472$	2368.82	−	4102.91i	0.231003	−	0.400110i
$473$	−6803.51	+	11784.0i	−0.661365	+	1.14552i
$474$		0			0
$475$	−3355.60	+	1355.56i	−0.324138	+	0.130942i
$476$	836.649			0.0805625
$477$		0			0
$478$	−4165.22	+	7214.38i	−0.398562	+	0.690330i
$479$	7799.60	+	13509.3i	0.743994	+	1.28863i	0.950663	+	0.310224i	$0.100404\pi$
$479$	7799.60	+	13509.3i	0.743994	+	1.28863i	−0.206670	+	0.978411i	$0.566263\pi$
$480$		0			0
$481$	847.942	+	1468.68i	0.0803801	+	0.139222i
$482$	8338.84			0.788016
$483$		0			0
$484$	1228.45	+	2127.74i	0.115369	+	0.199826i
$485$	−1607.38	−	2784.07i	−0.150490	−	0.260656i
$486$		0			0
$487$	13580.1			1.26360			0.631799	−	0.775132i	$-0.282317\pi$
$487$	13580.1			1.26360			0.631799	+	0.775132i	$0.282317\pi$
$488$	2036.24	+	3526.87i	0.188886	+	0.327160i
$489$		0			0
$490$	−4059.22	−	7030.77i	−0.374238	−	0.648200i
$491$	398.489	−	690.202i	0.0366264	−	0.0634387i	−0.847131	−	0.531384i	$-0.821672\pi$
$491$	398.489	−	690.202i	0.0366264	−	0.0634387i	0.883758	+	0.467945i	$0.155006\pi$
$492$		0			0
$493$	−1693.98			−0.154752
$494$	−198.126	+	1409.25i	−0.0180448	+	0.128350i
$495$		0			0
$496$	−756.158	+	1309.70i	−0.0684526	+	0.118563i
$497$	1477.77	−	2559.57i	0.133374	−	0.231011i
$498$		0			0
$499$	−4450.66	+	7708.78i	−0.399277	+	0.691567i	−0.993637	−	0.112632i	$-0.964072\pi$
$499$	−4450.66	+	7708.78i	−0.399277	+	0.691567i	0.594360	+	0.804199i	$0.297405\pi$
$500$	2111.95	+	3658.01i	0.188899	+	0.327183i
$501$		0			0
$502$	14264.5			1.26824
$503$	−10112.6	−	17515.5i	−0.896416	−	1.55264i	−0.832042	−	0.554712i	$-0.812828\pi$
$503$	−10112.6	−	17515.5i	−0.896416	−	1.55264i	−0.0643734	−	0.997926i	$-0.520505\pi$
$504$		0			0
$505$	10988.3			0.968266
$506$	8401.26			0.738106
$507$		0			0
$508$	−5334.38	+	9239.43i	−0.465896	+	0.806955i
$509$	10533.2	+	18244.0i	0.917240	+	1.58871i	0.803588	+	0.595185i	$0.202921\pi$
$509$	10533.2	+	18244.0i	0.917240	+	1.58871i	0.113651	+	0.993521i	$0.463745\pi$
$510$		0			0
$511$	−10659.5	+	18462.9i	−0.922799	+	1.59833i
$512$	512.000			0.0441942
$513$		0			0
$514$	2155.03			0.184931
$515$	9238.32	−	16001.2i	0.790464	−	1.36912i
$516$		0			0
$517$	4905.91	+	8497.29i	0.417334	+	0.722844i
$518$	5053.76	−	8753.37i	0.428667	−	0.742473i
$519$		0			0
$520$	−892.734			−0.0752865
$521$	1660.93			0.139668			0.0698338	−	0.997559i	$-0.477753\pi$
$521$	1660.93			0.139668			0.0698338	+	0.997559i	$0.477753\pi$
$522$		0			0
$523$	−11157.9	−	19326.0i	−0.932889	−	1.61581i	−0.778356	−	0.627823i	$-0.783946\pi$
$523$	−11157.9	−	19326.0i	−0.932889	−	1.61581i	−0.154532	−	0.987988i	$-0.549387\pi$
$524$	−3289.10			−0.274208
$525$		0			0
$526$	2489.16	+	4311.36i	0.206336	+	0.357384i
$527$	386.083	−	668.715i	0.0319128	−	0.0552745i
$528$		0			0
$529$	−6225.34	+	10782.6i	−0.511658	+	0.886217i
$530$	−2640.92	+	4574.21i	−0.216442	+	0.374889i
$531$		0			0
$532$	7864.30	−	3176.94i	0.640903	−	0.258905i
$533$	−3236.80			−0.263042
$534$		0			0
$535$	1858.89	−	3219.70i	0.150219	−	0.260186i
$536$	1002.88	+	1737.03i	0.0808166	+	0.139978i
$537$		0			0
$538$	−6181.28	−	10706.3i	−0.495342	−	0.857957i
$539$	−8367.16			−0.668644
$540$		0			0
$541$	5689.92	+	9855.22i	0.452178	+	0.783196i	0.998521	−	0.0543657i	$-0.0173137\pi$
$541$	5689.92	+	9855.22i	0.452178	+	0.783196i	−0.546343	+	0.837562i	$0.683980\pi$
$542$	−6032.71	−	10449.0i	−0.478095	−	0.828084i
$543$		0			0
$544$	−261.420			−0.0206034
$545$	209.668	+	363.155i	0.0164792	+	0.0285429i
$546$		0			0
$547$	8265.48	+	14316.2i	0.646081	+	1.11905i	0.984051	+	0.177888i	$0.0569266\pi$
$547$	8265.48	+	14316.2i	0.646081	+	1.11905i	−0.337969	+	0.941157i	$0.609740\pi$
$548$	−4890.45	+	8470.50i	−0.381222	+	0.660295i
$549$		0			0
$550$	−2339.84			−0.181402
$551$	−15923.0	+	6432.40i	−1.23111	+	0.497331i
$552$		0			0
$553$	4729.30	−	8191.38i	0.363671	−	0.629897i
$554$	−912.717	+	1580.87i	−0.0699957	+	0.121236i
$555$		0			0
$556$	−3008.68	+	5211.19i	−0.229490	+	0.397489i
$557$	−3662.66	−	6343.91i	−0.278621	−	0.482586i	0.692421	−	0.721493i	$-0.256544\pi$
$557$	−3662.66	−	6343.91i	−0.278621	−	0.482586i	−0.971042	+	0.238908i	$0.923211\pi$
$558$		0			0
$559$	4366.65			0.330393
$560$	2660.36	+	4607.88i	0.200751	+	0.347712i
$561$		0			0
$562$	669.773			0.0502716
$563$	−10864.0			−0.813258			−0.406629	−	0.913593i	$-0.633296\pi$
$563$	−10864.0			−0.813258			−0.406629	+	0.913593i	$0.633296\pi$
$564$		0			0
$565$	−1929.41	+	3341.84i	−0.143665	+	0.248836i
$566$	2776.94	+	4809.80i	0.206225	+	0.357192i
$567$		0			0
$568$	−461.744	+	799.765i	−0.0341098	+	0.0590799i
$569$	19930.0			1.46838			0.734192	−	0.678941i	$-0.237561\pi$
$569$	19930.0			1.46838			0.734192	+	0.678941i	$0.237561\pi$
$570$		0			0
$571$	1218.32			0.0892906			0.0446453	−	0.999003i	$-0.485784\pi$
$571$	1218.32			0.0892906			0.0446453	+	0.999003i	$0.485784\pi$
$572$	−460.042	+	796.816i	−0.0336282	+	0.0582457i
$573$		0			0
$574$	9645.72	+	16706.9i	0.701401	+	1.21486i
$575$	3428.15	−	5937.72i	0.248632	−	0.430644i
$576$		0			0
$577$	−9186.43			−0.662801			−0.331400	−	0.943490i	$-0.607521\pi$
$577$	−9186.43			−0.662801			−0.331400	+	0.943490i	$0.607521\pi$
$578$	−9692.52			−0.697501
$579$		0			0
$580$	−5386.48	−	9329.65i	−0.385623	−	0.667919i
$581$	−32984.3			−2.35528
$582$		0			0
$583$	2721.83	+	4714.35i	0.193356	+	0.334903i
$584$	3330.68	−	5768.91i	0.236001	−	0.408766i
$585$		0			0
$586$	−3067.85	+	5313.67i	−0.216266	+	0.374583i
$587$	272.446	−	471.890i	0.0191568	−	0.0331805i	−0.856288	−	0.516499i	$-0.827235\pi$
$587$	272.446	−	471.890i	0.0191568	−	0.0331805i	0.875445	+	0.483318i	$0.160568\pi$
$588$		0			0
$589$	1089.83	−	7751.80i	0.0762404	−	0.542287i
$590$	−15383.6			−1.07344
$591$		0			0
$592$	−1579.10	+	2735.08i	−0.109629	+	0.189884i
$593$	6061.77	+	10499.3i	0.419776	+	0.727073i	0.995917	−	0.0902776i	$-0.0287754\pi$
$593$	6061.77	+	10499.3i	0.419776	+	0.727073i	−0.576141	+	0.817350i	$0.695442\pi$
$594$		0			0
$595$	−1358.34	−	2352.72i	−0.0935908	−	0.162104i
$596$	2882.99			0.198141
$597$		0			0
$598$	−1348.03	−	2334.86i	−0.0921825	−	0.159665i
$599$	−12652.6	−	21915.0i	−0.863058	−	1.49486i	−0.868962	−	0.494879i	$-0.835213\pi$
$599$	−12652.6	−	21915.0i	−0.863058	−	1.49486i	0.00590371	−	0.999983i	$-0.498121\pi$
$600$		0			0
$601$	−15329.1			−1.04041			−0.520206	−	0.854041i	$-0.674145\pi$
$601$	−15329.1			−1.04041			−0.520206	+	0.854041i	$0.674145\pi$
$602$	−13012.7	−	22538.6i	−0.880993	−	1.52592i
$603$		0			0
$604$	−3602.50	−	6239.71i	−0.242688	−	0.420348i
$605$	3988.91	−	6909.00i	0.268053	−	0.464282i
$606$		0			0
$607$	−1137.90			−0.0760891			−0.0380446	−	0.999276i	$-0.512113\pi$
$607$	−1137.90			−0.0760891			−0.0380446	+	0.999276i	$0.512113\pi$
$608$	−2457.28	+	992.667i	−0.163908	+	0.0662137i
$609$		0			0
$610$	6611.88	−	11452.1i	0.438864	−	0.760135i
$611$	1574.37	−	2726.88i	0.104242	−	0.180553i
$612$		0			0
$613$	6426.89	−	11131.7i	0.423458	−	0.733451i	−0.572817	−	0.819683i	$-0.694149\pi$
$613$	6426.89	−	11131.7i	0.423458	−	0.733451i	0.996275	+	0.0862324i	$0.0274827\pi$
$614$	7487.81	+	12969.3i	0.492155	+	0.852438i
$615$		0			0
$616$	5483.73			0.358678
$617$	−9015.61	−	15615.5i	−0.588257	−	1.01889i	−0.994461	−	0.105109i	$-0.966481\pi$
$617$	−9015.61	−	15615.5i	−0.588257	−	1.01889i	0.406203	−	0.913783i	$-0.366852\pi$
$618$		0			0
$619$	−28147.3			−1.82768			−0.913841	−	0.406071i	$-0.866898\pi$
$619$	−28147.3			−1.82768			−0.913841	+	0.406071i	$0.866898\pi$
$620$	4910.64			0.318090
$621$		0			0
$622$	−6681.88	+	11573.4i	−0.430738	+	0.746060i
$623$	−781.851	−	1354.21i	−0.0502796	−	0.0870868i
$624$		0			0
$625$	9588.88	−	16608.4i	0.613688	−	1.06294i
$626$	16324.0			1.04224
$627$		0			0
$628$	15316.4			0.973236
$629$	806.264	−	1396.49i	0.0511095	−	0.0885242i
$630$		0			0
$631$	−512.279	−	887.293i	−0.0323193	−	0.0559787i	0.849413	−	0.527728i	$-0.176956\pi$
$631$	−512.279	−	887.293i	−0.0323193	−	0.0559787i	−0.881733	+	0.471749i	$0.843623\pi$
$632$	−1477.72	+	2559.48i	−0.0930070	+	0.161093i
$633$		0			0
$634$	5679.08			0.355749
$635$	34642.5			2.16496
$636$		0			0
$637$	1342.56	+	2325.38i	0.0835073	+	0.144639i
$638$	−11103.0			−0.688984
$639$		0			0
$640$	−831.257	−	1439.78i	−0.0513411	−	0.0889255i
$641$	8738.48	−	15135.5i	0.538454	−	0.932630i	−0.460533	−	0.887642i	$-0.652342\pi$
$641$	8738.48	−	15135.5i	0.538454	−	0.932630i	0.998988	−	0.0449875i	$-0.0143248\pi$
$642$		0			0
$643$	6716.23	−	11632.9i	0.411917	−	0.713460i	−0.583183	−	0.812341i	$-0.698193\pi$
$643$	6716.23	−	11632.9i	0.411917	−	0.713460i	0.995099	+	0.0988805i	$0.0315262\pi$
$644$	−8034.31	+	13915.8i	−0.491609	+	0.851492i
$645$		0			0
$646$	1254.65	−	506.841i	0.0764142	−	0.0308690i
$647$	2658.09			0.161515			0.0807575	−	0.996734i	$-0.474266\pi$
$647$	2658.09			0.161515			0.0807575	+	0.996734i	$0.474266\pi$
$648$		0			0
$649$	−7927.43	+	13730.7i	−0.479474	+	0.830474i
$650$	375.442	+	650.284i	0.0226554	+	0.0392404i
$651$		0			0
$652$	1912.99	+	3313.40i	0.114906	+	0.199023i
$653$	9989.77			0.598668			0.299334	−	0.954148i	$-0.403236\pi$
$653$	9989.77			0.598668			0.299334	+	0.954148i	$0.403236\pi$
$654$		0			0
$655$	5340.02	+	9249.19i	0.318553	+	0.551749i
$656$	−3013.90	−	5220.23i	−0.179380	−	0.310695i
$657$		0			0
$658$	−18766.5			−1.11185
$659$	10032.3	+	17376.5i	0.593025	+	1.02715i	0.993822	+	0.110983i	$0.0353998\pi$
$659$	10032.3	+	17376.5i	0.593025	+	1.02715i	−0.400797	+	0.916167i	$0.631267\pi$
$660$		0			0
$661$	−11859.5	−	20541.3i	−0.697855	−	1.20872i	−0.969209	−	0.246241i	$-0.920805\pi$
$661$	−11859.5	−	20541.3i	−0.697855	−	1.20872i	0.271354	−	0.962480i	$-0.412529\pi$
$662$	−11056.2	+	19150.0i	−0.649113	+	1.12430i
$663$		0			0
$664$	10306.3			0.602351
$665$	−21701.8	−	16957.0i	−1.26551	−	0.988821i
$666$		0			0
$667$	16267.2	−	28175.6i	0.944331	−	1.63563i
$668$	−5559.54	+	9629.40i	−0.322013	+	0.557743i
$669$		0			0
$670$	3256.44	−	5640.32i	0.187772	−	0.325231i
$671$	−6814.44	−	11803.0i	−0.392054	−	0.679058i
$672$		0			0
$673$	−10144.0			−0.581014			−0.290507	−	0.956873i	$-0.593824\pi$
$673$	−10144.0			−0.581014			−0.290507	+	0.956873i	$0.593824\pi$
$674$	5050.33	+	8747.43i	0.288622	+	0.499908i
$675$		0			0
$676$	−8492.73			−0.483201
$677$	16883.4			0.958469			0.479234	−	0.877687i	$-0.340914\pi$
$677$	16883.4			0.958469			0.479234	+	0.877687i	$0.340914\pi$
$678$		0			0
$679$	3168.54	−	5488.07i	0.179083	−	0.310181i
$680$	424.428	+	735.130i	0.0239354	+	0.0414573i
$681$		0			0
$682$	2530.54	−	4383.02i	0.142081	−	0.246092i
$683$	16610.2			0.930560			0.465280	−	0.885164i	$-0.345954\pi$
$683$	16610.2			0.930560			0.465280	+	0.885164i	$0.345954\pi$
$684$		0			0
$685$	31759.5			1.77149
$686$	−780.217	+	1351.38i	−0.0434240	+	0.0752125i
$687$		0			0
$688$	4065.95	+	7042.43i	0.225309	+	0.390247i
$689$	873.467	−	1512.89i	0.0482967	−	0.0836524i
$690$		0			0
$691$	24812.1			1.36598			0.682992	−	0.730426i	$-0.260678\pi$
$691$	24812.1			1.36598			0.682992	+	0.730426i	$0.260678\pi$
$692$	1238.21			0.0680196
$693$		0			0
$694$	−6014.85	−	10418.0i	−0.328992	−	0.569831i
$695$	19539.0			1.06641
$696$		0			0
$697$	1538.85	+	2665.37i	0.0836273	+	0.144847i
$698$	2514.51	−	4355.25i	0.136355	−	0.236173i
$699$		0			0
$700$	2237.64	−	3875.71i	0.120821	−	0.209269i
$701$	6533.58	−	11316.5i	0.352025	−	0.609726i	−0.634579	−	0.772858i	$-0.718826\pi$
$701$	6533.58	−	11316.5i	0.352025	−	0.609726i	0.986604	+	0.163132i	$0.0521597\pi$
$702$		0			0
$703$	2275.91	−	16188.2i	0.122102	−	0.868494i
$704$	−1713.45			−0.0917301
$705$		0			0
$706$	4578.03	−	7929.37i	0.244046	−	0.422700i
$707$	10830.3	+	18758.7i	0.576119	+	0.997868i
$708$		0			0
$709$	−5222.61	−	9045.83i	−0.276642	−	0.479158i	0.693906	−	0.720066i	$-0.255888\pi$
$709$	−5222.61	−	9045.83i	−0.276642	−	0.479158i	−0.970548	+	0.240907i	$0.922555\pi$
$710$	2998.66			0.158504
$711$		0			0
$712$	244.297	+	423.135i	0.0128587	+	0.0222720i
$713$	7415.08	+	12843.3i	0.389477	+	0.674594i
$714$		0			0
$715$	2987.60			0.156266
$716$	9300.57	+	16109.1i	0.485445	+	0.840816i
$717$		0			0
$718$	7972.44	+	13808.7i	0.414385	+	0.717736i
$719$	324.001	−	561.185i	0.0168055	−	0.0291080i	−0.857500	−	0.514483i	$-0.827984\pi$
$719$	324.001	−	561.185i	0.0168055	−	0.0291080i	0.874306	+	0.485375i	$0.161317\pi$
$720$		0			0
$721$	36421.9			1.88131
$722$	9868.83	−	9528.36i	0.508698	−	0.491148i
$723$		0			0
$724$	539.456	−	934.366i	0.0276916	−	0.0479633i
$725$	−4530.59	+	7847.22i	−0.232086	+	0.401984i
$726$		0			0
$727$	−8436.61	+	14612.6i	−0.430394	+	0.745465i	−0.996907	−	0.0785881i	$-0.974959\pi$
$727$	−8436.61	+	14612.6i	−0.430394	+	0.745465i	0.566513	+	0.824053i	$0.308292\pi$
$728$	−879.897	−	1524.03i	−0.0447955	−	0.0775881i
$729$		0			0
$730$	−21630.1			−1.09667
$731$	−2076.01	−	3595.76i	−0.105040	−	0.181934i
$732$		0			0
$733$	−23662.1			−1.19233			−0.596166	−	0.802861i	$-0.703310\pi$
$733$	−23662.1			−1.19233			−0.596166	+	0.802861i	$0.703310\pi$
$734$	10931.0			0.549688
$735$		0			0
$736$	2510.40	−	4348.15i	0.125727	−	0.217765i
$737$	−3356.20	−	5813.12i	−0.167744	−	0.290541i
$738$		0			0
$739$	−8638.65	+	14962.6i	−0.430011	+	0.744800i	−0.996874	−	0.0790119i	$-0.974823\pi$
$739$	−8638.65	+	14962.6i	−0.430011	+	0.744800i	0.566863	+	0.823812i	$0.308157\pi$
$740$	10255.0			0.509433
$741$		0			0
$742$	−10411.8			−0.515133
$743$	12899.3	−	22342.2i	0.636915	−	1.10317i	−0.349190	−	0.937052i	$-0.613543\pi$
$743$	12899.3	−	22342.2i	0.636915	−	1.10317i	0.986106	−	0.166118i	$-0.0531233\pi$
$744$		0			0
$745$	−4680.68	−	8107.17i	−0.230184	−	0.398690i
$746$	−9245.54	+	16013.7i	−0.453758	+	0.785932i
$747$		0			0
$748$	874.861			0.0427648
$749$	7328.66			0.357521
$750$		0			0
$751$	−7578.27	−	13125.9i	−0.368222	−	0.637780i	0.621065	−	0.783759i	$-0.286700\pi$
$751$	−7578.27	−	13125.9i	−0.368222	−	0.637780i	−0.989288	+	0.145979i	$0.953367\pi$
$752$	5863.80			0.284349
$753$		0			0
$754$	1781.54	+	3085.72i	0.0860476	+	0.149039i
$755$	−11697.7	+	20261.0i	−0.563870	+	0.976651i
$756$		0			0
$757$	−3727.46	+	6456.14i	−0.178965	+	0.309977i	−0.941526	−	0.336939i	$-0.890608\pi$
$757$	−3727.46	+	6456.14i	−0.178965	+	0.309977i	0.762561	+	0.646916i	$0.223942\pi$
$758$	−6098.42	+	10562.8i	−0.292222	+	0.506144i
$759$		0			0
$760$	6780.97	+	5298.40i	0.323647	+	0.252886i
$761$	−23295.2			−1.10966			−0.554830	−	0.831964i	$-0.687217\pi$
$761$	−23295.2			−1.10966			−0.554830	+	0.831964i	$0.687217\pi$
$762$		0			0
$763$	−413.306	+	715.867i	−0.0196103	+	0.0339661i
$764$	−3899.93	−	6754.88i	−0.184679	−	0.319873i
$765$		0			0
$766$	4529.81	+	7845.86i	0.213667	+	0.370082i
$767$	5088.01			0.239527
$768$		0			0
$769$	18986.9	+	32886.3i	0.890358	+	1.54215i	0.839446	+	0.543443i	$0.182880\pi$
$769$	18986.9	+	32886.3i	0.890358	+	1.54215i	0.0509122	+	0.998703i	$0.483787\pi$
$770$	−8903.10	−	15420.6i	−0.416683	−	0.721716i
$771$		0			0
$772$	11725.2			0.546631
$773$	4169.69	+	7222.11i	0.194014	+	0.336043i	0.946577	−	0.322478i	$-0.104516\pi$
$773$	4169.69	+	7222.11i	0.194014	+	0.336043i	−0.752563	+	0.658521i	$0.771182\pi$
$774$		0			0
$775$	−2065.18	−	3577.00i	−0.0957206	−	0.165793i
$776$	−990.042	+	1714.80i	−0.0457995	+	0.0793271i
$777$		0			0
$778$	11117.8			0.512332
$779$	24585.9	+	19210.5i	1.13078	+	0.883553i
$780$		0			0
$781$	1545.26	−	2676.47i	0.0707988	−	0.122627i
$782$	−1281.77	+	2220.10i	−0.0586140	+	0.101522i
$783$		0			0
$784$	−2500.21	+	4330.50i	−0.113895	+	0.197271i
$785$	−24867.0	−	43070.9i	−1.13063	−	1.95830i
$786$		0			0
$787$	−42901.7			−1.94318			−0.971588	−	0.236680i	$-0.923941\pi$
$787$	−42901.7			−1.94318			−0.971588	+	0.236680i	$0.923941\pi$
$788$	−2472.96	−	4283.29i	−0.111796	−	0.193637i
$789$		0			0
$790$	9596.59			0.432192
$791$	−7606.67			−0.341924
$792$		0			0
$793$	−2186.83	+	3787.71i	−0.0979278	+	0.169616i
$794$	−9391.66	−	16266.8i	−0.419770	−	0.727063i
$795$		0			0
$796$	9018.01	−	15619.7i	0.401552	−	0.695508i
$797$	−5540.21			−0.246229			−0.123114	−	0.992392i	$-0.539288\pi$
$797$	−5540.21			−0.246229			−0.123114	+	0.992392i	$0.539288\pi$
$798$		0			0
$799$	−2993.97			−0.132564
$800$	−699.175	+	1211.01i	−0.0308995	+	0.0535194i
$801$		0			0
$802$	9532.13	+	16510.1i	0.419690	+	0.726924i
$803$	−11146.4	+	19306.1i	−0.489847	+	0.848440i
$804$		0			0
$805$	52176.4			2.28444
$806$	−1624.16			−0.0709784
$807$		0			0
$808$	−3384.05	−	5861.34i	−0.147340	−	0.255200i
$809$	−20817.8			−0.904715			−0.452357	−	0.891837i	$-0.649417\pi$
$809$	−20817.8			−0.904715			−0.452357	+	0.891837i	$0.649417\pi$
$810$		0			0
$811$	10334.0	+	17899.0i	0.447441	+	0.774991i	0.998219	−	0.0596612i	$-0.0190020\pi$
$811$	10334.0	+	17899.0i	0.447441	+	0.774991i	−0.550777	+	0.834652i	$0.685669\pi$
$812$	10618.0	−	18391.0i	0.458892	−	0.794824i
$813$		0			0
$814$	5284.58	−	9153.15i	0.227548	−	0.394125i
$815$	6211.68	−	10758.9i	0.266976	−	0.462416i
$816$		0			0
$817$	−33167.9	−	25916.2i	−1.42032	−	1.10978i
$818$	13159.0			0.562461
$819$		0			0
$820$	−9786.44	+	16950.6i	−0.416777	+	0.721879i
$821$	−3750.50	−	6496.07i	−0.159432	−	0.276144i	0.775232	−	0.631676i	$-0.217633\pi$
$821$	−3750.50	−	6496.07i	−0.159432	−	0.276144i	−0.934664	+	0.355532i	$0.884300\pi$
$822$		0			0
$823$	181.148	+	313.757i	0.00767244	+	0.0132891i	0.869836	−	0.493341i	$-0.164224\pi$
$823$	181.148	+	313.757i	0.00767244	+	0.0132891i	−0.862164	+	0.506630i	$0.830891\pi$
$824$	−11380.4			−0.481135
$825$		0			0
$826$	−15162.4	−	26262.0i	−0.638700	−	1.10626i
$827$	−4389.51	−	7602.85i	−0.184568	−	0.319682i	0.758863	−	0.651251i	$-0.225755\pi$
$827$	−4389.51	−	7602.85i	−0.184568	−	0.319682i	−0.943431	+	0.331569i	$0.892422\pi$
$828$		0			0
$829$	11789.0			0.493909			0.246954	−	0.969027i	$-0.420570\pi$
$829$	11789.0			0.493909			0.246954	+	0.969027i	$0.420570\pi$
$830$	−16732.8	−	28982.0i	−0.699762	−	1.21202i
$831$		0			0
$832$	274.933	+	476.198i	0.0114562	+	0.0198428i
$833$	1276.57	−	2211.09i	0.0530979	−	0.0919683i
$834$		0			0
$835$	36104.7			1.49635
$836$	8223.48	−	3322.04i	0.340209	−	0.137434i
$837$		0			0
$838$	4136.42	−	7164.49i	0.170514	−	0.295338i
$839$	−5380.60	+	9319.48i	−0.221405	+	0.383485i	−0.955235	−	0.295848i	$-0.904398\pi$
$839$	−5380.60	+	9319.48i	−0.221405	+	0.383485i	0.733830	+	0.679334i	$0.237731\pi$
$840$		0			0
$841$	−9304.03	+	16115.1i	−0.381485	+	0.660751i
$842$	−7792.46	−	13496.9i	−0.318938	−	0.552417i
$843$		0			0
$844$	−7.61879			−0.000310722
$845$	13788.4	+	23882.2i	0.561343	+	0.972274i
$846$		0			0
$847$	15726.2			0.637968
$848$	3253.27			0.131743
$849$		0			0
$850$	356.988	−	618.322i	0.0144054	−	0.0249509i
$851$	15485.1	+	26820.9i	0.623762	+	1.08039i
$852$		0			0
$853$	−2445.13	+	4235.09i	−0.0981472	+	0.169996i	−0.910918	−	0.412588i	$-0.864625\pi$
$853$	−2445.13	+	4235.09i	−0.0981472	+	0.169996i	0.812771	+	0.582584i	$0.197958\pi$
$854$	26067.2			1.04450
$855$		0			0
$856$	−2289.91			−0.0914342
$857$	−15162.2	+	26261.7i	−0.604353	+	1.04677i	0.387801	+	0.921743i	$0.373235\pi$
$857$	−15162.2	+	26261.7i	−0.604353	+	1.04677i	−0.992153	+	0.125026i	$0.960098\pi$
$858$		0			0
$859$	7535.78	+	13052.4i	0.299322	+	0.518441i	0.975981	−	0.217856i	$-0.0699062\pi$
$859$	7535.78	+	13052.4i	0.299322	+	0.518441i	−0.676659	+	0.736296i	$0.736573\pi$
$860$	13202.5	−	22867.5i	0.523492	−	0.906714i
$861$		0			0
$862$	14701.2			0.580887
$863$	−283.180			−0.0111698			−0.00558490	−	0.999984i	$-0.501778\pi$
$863$	−283.180			−0.0111698			−0.00558490	+	0.999984i	$0.501778\pi$
$864$		0			0
$865$	−2010.29	−	3481.93i	−0.0790196	−	0.136866i
$866$	21385.2			0.839145
$867$		0			0
$868$	4840.02	+	8383.17i	0.189264	+	0.327815i
$869$	4945.30	−	8565.50i	0.193047	−	0.334367i
$870$		0			0
$871$	−1077.05	+	1865.50i	−0.0418993	+	0.0725717i
$872$	129.142	−	223.680i	0.00501524	−	0.00868665i
$873$		0			0
$874$	−3618.17	+	25735.6i	−0.140030	+	0.996017i
$875$	27036.4			1.04457
$876$		0			0
$877$	1100.91	−	1906.84i	0.0423891	−	0.0734200i	−0.844052	−	0.536261i	$-0.819836\pi$
$877$	1100.91	−	1906.84i	0.0423891	−	0.0734200i	0.886442	+	0.462841i	$0.153170\pi$
$878$	9619.66	+	16661.7i	0.369758	+	0.640440i
$879$		0			0
$880$	2781.87	+	4818.33i	0.106564	+	0.184575i
$881$	−21218.9			−0.811443			−0.405722	−	0.913997i	$-0.632980\pi$
$881$	−21218.9			−0.811443			−0.405722	+	0.913997i	$0.632980\pi$
$882$		0			0
$883$	4365.12	+	7560.60i	0.166362	+	0.288148i	0.937138	−	0.348958i	$-0.113465\pi$
$883$	4365.12	+	7560.60i	0.166362	+	0.288148i	−0.770776	+	0.637106i	$0.780131\pi$
$884$	−140.377	−	243.139i	−0.00534092	−	0.00925075i
$885$		0			0
$886$	−25208.9			−0.955880
$887$	−5773.98	−	10000.8i	−0.218570	−	0.378574i	0.735801	−	0.677197i	$-0.236806\pi$
$887$	−5773.98	−	10000.8i	−0.218570	−	0.378574i	−0.954371	+	0.298624i	$0.903472\pi$
$888$		0			0
$889$	34144.4	+	59139.8i	1.28815	+	2.23114i
$890$	793.258	−	1373.96i	0.0298765	−	0.0517476i
$891$		0			0
$892$	−18640.9			−0.699713
$893$	−28142.6	+	11368.7i	−1.05460	+	0.426025i
$894$		0			0
$895$	30199.9	−	52307.7i	1.12790	−	1.95358i
$896$	1638.61	−	2838.15i	0.0610960	−	0.105821i
$897$		0			0
$898$	14957.9	−	25907.9i	0.555848	−	0.962758i
$899$	−9799.68	−	16973.5i	−0.363557	−	0.629699i
$900$		0			0
$901$	−1661.07			−0.0614188
$902$	10086.3	+	17469.9i	0.372323	+	0.644883i
$903$		0			0
$904$	2376.78			0.0874453
$905$	−3503.34			−0.128679
$906$		0			0
$907$	3641.48	−	6307.22i	0.133311	−	0.230902i	−0.791640	−	0.610988i	$-0.790772\pi$
$907$	3641.48	−	6307.22i	0.133311	−	0.230902i	0.924951	+	0.380086i	$0.124106\pi$
$908$	−8090.31	−	14012.8i	−0.295690	−	0.512150i
$909$		0			0
$910$	−2857.11	+	4948.66i	−0.104079	+	0.180271i
$911$	−32720.6			−1.18999			−0.594995	−	0.803729i	$-0.702846\pi$
$911$	−32720.6			−1.18999			−0.594995	+	0.803729i	$0.702846\pi$
$912$		0			0
$913$	−34490.8			−1.25025
$914$	2003.50	−	3470.16i	0.0725053	−	0.125583i
$915$		0			0
$916$	−10125.5	−	17537.8i	−0.365234	−	0.632604i
$917$	−10526.5	+	18232.4i	−0.379078	+	0.656583i
$918$		0			0
$919$	1970.84			0.0707421			0.0353710	−	0.999374i	$-0.488739\pi$
$919$	1970.84			0.0707421			0.0353710	+	0.999374i	$0.488739\pi$
$920$	−16303.1			−0.584235
$921$		0			0
$922$	−1134.66	−	1965.28i	−0.0405292	−	0.0701987i
$923$	−991.786			−0.0353684
$924$		0			0
$925$	−4312.76	−	7469.92i	−0.153300	−	0.265524i
$926$	2934.33	−	5082.42i	0.104134	−	0.180366i
$927$		0			0
$928$	−3317.72	+	5746.45i	−0.117359	+	0.203272i
$929$	5378.74	−	9316.25i	0.189958	−	0.329017i	−0.755278	−	0.655404i	$-0.772498\pi$
$929$	5378.74	−	9316.25i	0.189958	−	0.329017i	0.945236	+	0.326388i	$0.105832\pi$
$930$		0			0
$931$	3603.49	−	25631.1i	0.126852	−	0.902283i
$932$	−1732.36			−0.0608854
$933$		0			0
$934$	−930.578	+	1611.81i	−0.0326011	+	0.0564668i
$935$	−1420.38	−	2460.17i	−0.0496806	−	0.0860494i
$936$		0			0
$937$	−16289.2	−	28213.7i	−0.567923	−	0.983671i	−0.996771	−	0.0802948i	$-0.974414\pi$
$937$	−16289.2	−	28213.7i	−0.567923	−	0.983671i	0.428848	−	0.903377i	$-0.358920\pi$
$938$	12838.5			0.446898
$939$		0			0
$940$	−9520.16	−	16489.4i	−0.330334	−	0.572154i
$941$	22922.7	+	39703.3i	0.794112	+	1.37544i	0.923402	+	0.383835i	$0.125397\pi$
$941$	22922.7	+	39703.3i	0.794112	+	1.37544i	−0.129290	+	0.991607i	$0.541270\pi$
$942$		0			0
$943$	−59110.3			−2.04125
$944$	4737.63	+	8205.82i	0.163344	+	0.282920i
$945$		0			0
$946$	−13607.0	−	23568.0i	−0.467655	−	0.810003i
$947$	−14122.0	+	24460.0i	−0.484586	+	0.839328i	−0.999843	−	0.0177080i	$-0.994363\pi$
$947$	−14122.0	+	24460.0i	−0.484586	+	0.839328i	0.515257	+	0.857036i	$0.327696\pi$
$948$		0			0
$949$	7154.01			0.244709
$950$	1007.70	−	7167.64i	0.0344149	−	0.244788i
$951$		0			0
$952$	−836.649	+	1449.12i	−0.0284831	+	0.0493342i
$953$	−22346.7	+	38705.7i	−0.759582	+	1.31563i	0.183483	+	0.983023i	$0.441263\pi$
$953$	−22346.7	+	38705.7i	−0.759582	+	1.31563i	−0.943064	+	0.332611i	$0.892070\pi$
$954$		0			0
$955$	−12663.5	+	21933.7i	−0.429089	+	0.743204i
$956$	−8330.45	−	14428.8i	−0.281826	−	0.488137i
$957$		0			0
$958$	−31198.4			−1.05217
$959$	31302.8	+	54218.1i	1.05404	+	1.82564i
$960$		0			0
$961$	−20857.0			−0.700112
$962$	−3391.77			−0.113675
$963$		0			0
$964$	−8338.84	+	14443.3i	−0.278606	+	0.482560i
$965$	−19036.4	−	32972.1i	−0.635031	−	1.09991i
$966$		0			0
$967$	−22790.5	+	39474.3i	−0.757905	+	1.31273i	0.186013	+	0.982547i	$0.440443\pi$
$967$	−22790.5	+	39474.3i	−0.757905	+	1.31273i	−0.943917	+	0.330182i	$0.892890\pi$
$968$	−4913.82			−0.163157
$969$		0			0
$970$	6429.53			0.212824
$971$	−2367.98	+	4101.46i	−0.0782616	+	0.135553i	−0.902500	−	0.430690i	$-0.858270\pi$
$971$	−2367.98	+	4101.46i	−0.0782616	+	0.135553i	0.824238	+	0.566243i	$0.191604\pi$
$972$		0			0
$973$	19258.0	+	33355.9i	0.634516	+	1.09901i
$974$	−13580.1	+	23521.4i	−0.446749	+	0.773792i
$975$		0			0
$976$	−8144.96			−0.267125
$977$	57565.1			1.88503			0.942514	−	0.334167i	$-0.108455\pi$
$977$	57565.1			1.88503			0.942514	+	0.334167i	$0.108455\pi$
$978$		0			0
$979$	−817.560	−	1416.06i	−0.0266898	−	0.0462281i
$980$	16236.9			0.529253
$981$		0			0
$982$	796.977	+	1380.40i	0.0258987	+	0.0448579i
$983$	17314.2	−	29989.0i	0.561786	−	0.973043i	−0.435554	−	0.900162i	$-0.643448\pi$
$983$	17314.2	−	29989.0i	0.561786	−	0.973043i	0.997341	−	0.0728802i	$-0.0232191\pi$
$984$		0			0
$985$	−8029.95	+	13908.3i	−0.259752	+	0.449903i
$986$	1693.98	−	2934.05i	0.0547132	−	0.0947661i
$987$		0			0
$988$	−2242.76	−	1752.41i	−0.0722183	−	0.0564288i
$989$	79743.5			2.56390
$990$		0			0
$991$	−15787.8	+	27345.2i	−0.506069	+	0.876537i	0.493906	+	0.869515i	$0.335569\pi$
$991$	−15787.8	+	27345.2i	−0.506069	+	0.876537i	−0.999975	+	0.00702215i	$0.997765\pi$
$992$	−1512.32	−	2619.41i	−0.0484033	−	0.0838369i
$993$		0			0
$994$	2955.54	+	5119.14i	0.0943099	+	0.163350i
$995$	−58564.8			−1.86596
$996$		0			0
$997$	−19361.7	−	33535.4i	−0.615035	−	1.06527i	−0.990378	−	0.138386i	$-0.955808\pi$
$997$	−19361.7	−	33535.4i	−0.615035	−	1.06527i	0.375343	−	0.926886i	$-0.377525\pi$
$998$	−8901.33	−	15417.6i	−0.282331	−	0.489012i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.4.g.g.163.1		6
3.2	odd	2		114.4.e.e.49.3	yes	6
19.7	even	3	inner	342.4.g.g.235.1		6
57.8	even	6		2166.4.a.w.1.1		3
57.11	odd	6		2166.4.a.s.1.1		3
57.26	odd	6		114.4.e.e.7.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.e.7.3	✓	6	57.26	odd	6
114.4.e.e.49.3	yes	6	3.2	odd	2
342.4.g.g.163.1		6	1.1	even	1	trivial
342.4.g.g.235.1		6	19.7	even	3	inner
2166.4.a.s.1.1		3	57.11	odd	6
2166.4.a.w.1.1		3	57.8	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.49420 + 11.2483i) q^{5} -25.6033 q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-6.49420 + 11.2483i) q^{5} -25.6033 q^{7} +8.00000 q^{8} +(-12.9884 - 22.4966i) q^{10} -26.7726 q^{11} +(4.29582 + 7.44059i) q^{13} +(25.6033 - 44.3461i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(4.08468 - 7.07488i) q^{17} +(11.5302 - 82.0125i) q^{19} +51.9536 q^{20} +(26.7726 - 46.3715i) q^{22} +(78.4501 + 135.880i) q^{23} +(-21.8492 - 37.8439i) q^{25} -17.1833 q^{26} +(51.2065 + 88.6923i) q^{28} +(-103.679 - 179.577i) q^{29} +94.5197 q^{31} +(-16.0000 - 27.7128i) q^{32} +(8.16936 + 14.1498i) q^{34} +(166.273 - 287.993i) q^{35} +197.387 q^{37} +(130.520 + 101.983i) q^{38} +(-51.9536 + 89.9862i) q^{40} +(-188.369 + 326.265i) q^{41} +(254.122 - 440.152i) q^{43} +(53.5452 + 92.7431i) q^{44} -313.800 q^{46} +(-183.244 - 317.387i) q^{47} +312.527 q^{49} +87.3968 q^{50} +(17.1833 - 29.7623i) q^{52} +(-101.665 - 176.088i) q^{53} +(173.867 - 301.146i) q^{55} -204.826 q^{56} +414.715 q^{58} +(296.102 - 512.864i) q^{59} +(254.530 + 440.859i) q^{61} +(-94.5197 + 163.713i) q^{62} +64.0000 q^{64} -111.592 q^{65} +(125.360 + 217.129i) q^{67} -32.6774 q^{68} +(332.545 + 575.985i) q^{70} +(-57.7180 + 99.9706i) q^{71} +(416.335 - 721.114i) q^{73} +(-197.387 + 341.885i) q^{74} +(-307.160 + 124.083i) q^{76} +685.466 q^{77} +(-184.715 + 319.935i) q^{79} +(-103.907 - 179.972i) q^{80} +(-376.738 - 652.529i) q^{82} +1288.29 q^{83} +(53.0535 + 91.8913i) q^{85} +(508.244 + 880.304i) q^{86} -214.181 q^{88} +(30.5372 + 52.8919i) q^{89} +(-109.987 - 190.503i) q^{91} +(313.800 - 543.518i) q^{92} +732.975 q^{94} +(847.621 + 662.300i) q^{95} +(-123.755 + 214.350i) q^{97} +(-312.527 + 541.312i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 12 q^{4} + 2 q^{5} - 34 q^{7} + 48 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 - 12 * q^4 + 2 * q^5 - 34 * q^7 + 48 * q^8	\( 6 q - 6 q^{2} - 12 q^{4} + 2 q^{5} - 34 q^{7} + 48 q^{8} + 4 q^{10} + 104 q^{11} - 75 q^{13} + 34 q^{14} - 48 q^{16} - 48 q^{17} + 104 q^{19} - 16 q^{20} - 104 q^{22} - 238 q^{23} - 229 q^{25} + 300 q^{26} + 68 q^{28} - 8 q^{29} + 214 q^{31} - 96 q^{32} - 96 q^{34} - 294 q^{35} + 610 q^{37} + 430 q^{38} + 16 q^{40} + 16 q^{41} + 331 q^{43} - 208 q^{44} + 952 q^{46} - 766 q^{47} + 2284 q^{49} + 916 q^{50} - 300 q^{52} - 118 q^{53} + 1400 q^{55} - 272 q^{56} + 32 q^{58} + 936 q^{59} + 399 q^{61} - 214 q^{62} + 384 q^{64} - 740 q^{65} - 61 q^{67} + 384 q^{68} - 588 q^{70} + 974 q^{71} - 91 q^{73} - 610 q^{74} - 1276 q^{76} + 72 q^{77} + 321 q^{79} + 32 q^{80} + 32 q^{82} + 4296 q^{83} + 1680 q^{85} + 662 q^{86} + 832 q^{88} + 1116 q^{89} - 1367 q^{91} - 952 q^{92} + 3064 q^{94} + 4198 q^{95} - 1382 q^{97} - 2284 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - 12 * q^4 + 2 * q^5 - 34 * q^7 + 48 * q^8 + 4 * q^10 + 104 * q^11 - 75 * q^13 + 34 * q^14 - 48 * q^16 - 48 * q^17 + 104 * q^19 - 16 * q^20 - 104 * q^22 - 238 * q^23 - 229 * q^25 + 300 * q^26 + 68 * q^28 - 8 * q^29 + 214 * q^31 - 96 * q^32 - 96 * q^34 - 294 * q^35 + 610 * q^37 + 430 * q^38 + 16 * q^40 + 16 * q^41 + 331 * q^43 - 208 * q^44 + 952 * q^46 - 766 * q^47 + 2284 * q^49 + 916 * q^50 - 300 * q^52 - 118 * q^53 + 1400 * q^55 - 272 * q^56 + 32 * q^58 + 936 * q^59 + 399 * q^61 - 214 * q^62 + 384 * q^64 - 740 * q^65 - 61 * q^67 + 384 * q^68 - 588 * q^70 + 974 * q^71 - 91 * q^73 - 610 * q^74 - 1276 * q^76 + 72 * q^77 + 321 * q^79 + 32 * q^80 + 32 * q^82 + 4296 * q^83 + 1680 * q^85 + 662 * q^86 + 832 * q^88 + 1116 * q^89 - 1367 * q^91 - 952 * q^92 + 3064 * q^94 + 4198 * q^95 - 1382 * q^97 - 2284 * q^98

Introduction

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