LMFDB - Embedded newform 153.4.f.b.55.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(55,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("153.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 88 x^{14} + 3086 x^{12} + 54880 x^{10} + 516641 x^{8} + 2403800 x^{6} + 4378064 x^{4} + \cdots + 295936 $ x^16 + 88x^14 + 3086x^12 + 54880x^10 + 516641x^8 + 2403800x^6 + 4378064x^4 + 2140928*x^2 + 295936
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			55.5
Root			$0.496675i$ of defining polynomial
Character	$\chi$	$=$	153.55
Dual form			153.4.f.b.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.49668i q^{2} +5.75996 q^{4} +(-0.574777 + 0.574777i) q^{5} +(2.73692 + 2.73692i) q^{7} +20.5942i q^{8} +(-0.860255 - 0.860255i) q^{10} +(14.2363 + 14.2363i) q^{11} +20.0363 q^{13} +(-4.09628 + 4.09628i) q^{14} +15.2569 q^{16} +(58.0925 - 39.2207i) q^{17} +123.098i q^{19} +(-3.31070 + 3.31070i) q^{20} +(-21.3072 + 21.3072i) q^{22} +(-29.6574 - 29.6574i) q^{23} +124.339i q^{25} +29.9879i q^{26} +(15.7646 + 15.7646i) q^{28} +(17.6364 - 17.6364i) q^{29} +(-54.0799 + 54.0799i) q^{31} +187.588i q^{32} +(58.7006 + 86.9456i) q^{34} -3.14624 q^{35} +(22.3384 - 22.3384i) q^{37} -184.238 q^{38} +(-11.8371 - 11.8371i) q^{40} +(76.6455 + 76.6455i) q^{41} -233.202i q^{43} +(82.0007 + 82.0007i) q^{44} +(44.3874 - 44.3874i) q^{46} -51.1712 q^{47} -328.019i q^{49} -186.095 q^{50} +115.409 q^{52} -1.55884i q^{53} -16.3654 q^{55} +(-56.3647 + 56.3647i) q^{56} +(26.3960 + 26.3960i) q^{58} -588.603i q^{59} +(-513.681 - 513.681i) q^{61} +(-80.9401 - 80.9401i) q^{62} -158.703 q^{64} +(-11.5164 + 11.5164i) q^{65} +266.752 q^{67} +(334.611 - 225.910i) q^{68} -4.70890i q^{70} +(621.733 - 621.733i) q^{71} +(236.509 - 236.509i) q^{73} +(33.4333 + 33.4333i) q^{74} +709.043i q^{76} +77.9274i q^{77} +(-582.906 - 582.906i) q^{79} +(-8.76932 + 8.76932i) q^{80} +(-114.713 + 114.713i) q^{82} +224.694i q^{83} +(-10.8471 + 55.9334i) q^{85} +349.028 q^{86} +(-293.186 + 293.186i) q^{88} -561.132 q^{89} +(54.8379 + 54.8379i) q^{91} +(-170.825 - 170.825i) q^{92} -76.5866i q^{94} +(-70.7542 - 70.7542i) q^{95} +(1257.15 - 1257.15i) q^{97} +490.937 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 48 q^{4} + 32 q^{5} - 8 q^{7} - 20 q^{10} - 96 q^{11} + 120 q^{13} + 288 q^{14} - 200 q^{16} - 16 q^{17} - 384 q^{20} + 4 q^{22} - 208 q^{23} + 904 q^{28} - 320 q^{29} - 624 q^{31} - 788 q^{34} + 1184 q^{35}+ \cdots + 1208 q^{98}+O(q^{100}) $ 16 * q - 48 * q^4 + 32 * q^5 - 8 * q^7 - 20 * q^10 - 96 * q^11 + 120 * q^13 + 288 * q^14 - 200 * q^16 - 16 * q^17 - 384 * q^20 + 4 * q^22 - 208 * q^23 + 904 * q^28 - 320 * q^29 - 624 * q^31 - 788 * q^34 + 1184 * q^35 + 256 * q^37 + 168 * q^38 - 664 * q^40 - 800 * q^41 - 128 * q^44 + 572 * q^46 - 368 * q^47 + 720 * q^50 - 3160 * q^52 + 4296 * q^55 - 576 * q^56 + 1368 * q^58 - 1296 * q^61 - 536 * q^62 + 1752 * q^64 + 4288 * q^65 - 1248 * q^67 + 240 * q^68 - 1488 * q^71 - 1208 * q^73 - 2272 * q^74 - 1256 * q^79 - 384 * q^80 + 3564 * q^82 + 3216 * q^85 - 3224 * q^86 - 1296 * q^88 + 2608 * q^89 - 56 * q^91 + 5072 * q^92 - 160 * q^95 - 4456 * q^97 + 1208 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$			1.49668i			0.529155i	0.964364	+	0.264577i	$0.0852324\pi$
$2$			1.49668i			0.529155i	−0.964364	+	0.264577i	$0.914768\pi$
$3$		0			0
$3$		0			0
$4$	5.75996			0.719995
$5$	−0.574777	+	0.574777i	−0.0514096	+	0.0514096i	−0.732344	−	0.680935i	$-0.761574\pi$
$5$	−0.574777	+	0.574777i	−0.0514096	+	0.0514096i	0.680935	+	0.732344i	$0.261574\pi$
$6$		0			0
$7$	2.73692	+	2.73692i	0.147780	+	0.147780i	0.777126	−	0.629346i	$-0.216677\pi$
$7$	2.73692	+	2.73692i	0.147780	+	0.147780i	−0.629346	+	0.777126i	$0.716677\pi$
$8$			20.5942i			0.910143i
$9$		0			0
$10$	−0.860255	−	0.860255i	−0.0272036	−	0.0272036i
$11$	14.2363	+	14.2363i	0.390219	+	0.390219i	0.874766	−	0.484546i	$-0.161015\pi$
$11$	14.2363	+	14.2363i	0.390219	+	0.390219i	−0.484546	+	0.874766i	$0.661015\pi$
$12$		0			0
$13$	20.0363			0.427468			0.213734	−	0.976892i	$-0.431437\pi$
$13$	20.0363			0.427468			0.213734	+	0.976892i	$0.431437\pi$
$14$	−4.09628	+	4.09628i	−0.0781984	+	0.0781984i
$15$		0			0
$16$	15.2569			0.238389
$17$	58.0925	−	39.2207i	0.828794	−	0.559554i
$17$	58.0925	−	39.2207i	0.828794	−	0.559554i
$18$		0			0
$19$			123.098i			1.48635i	0.669095	+	0.743177i	$0.266682\pi$
$19$			123.098i			1.48635i	−0.669095	+	0.743177i	$0.733318\pi$
$20$	−3.31070	+	3.31070i	−0.0370147	+	0.0370147i
$21$		0			0
$22$	−21.3072	+	21.3072i	−0.206486	+	0.206486i
$23$	−29.6574	−	29.6574i	−0.268869	−	0.268869i	0.559775	−	0.828644i	$-0.310887\pi$
$23$	−29.6574	−	29.6574i	−0.268869	−	0.268869i	−0.828644	+	0.559775i	$0.810887\pi$
$24$		0			0
$25$			124.339i			0.994714i
$26$			29.9879i			0.226196i
$27$		0			0
$28$	15.7646	+	15.7646i	0.106401	+	0.106401i
$29$	17.6364	−	17.6364i	0.112931	−	0.112931i	−0.648383	−	0.761314i	$-0.724555\pi$
$29$	17.6364	−	17.6364i	0.112931	−	0.112931i	0.761314	+	0.648383i	$0.224555\pi$
$30$		0			0
$31$	−54.0799	+	54.0799i	−0.313324	+	0.313324i	−0.846196	−	0.532872i	$-0.821113\pi$
$31$	−54.0799	+	54.0799i	−0.313324	+	0.313324i	0.532872	+	0.846196i	$0.321113\pi$
$32$			187.588i			1.03629i
$33$		0			0
$34$	58.7006	+	86.9456i	0.296090	+	0.438560i
$35$	−3.14624			−0.0151946
$36$		0			0
$37$	22.3384	−	22.3384i	0.0992543	−	0.0992543i	−0.655736	−	0.754990i	$-0.727642\pi$
$37$	22.3384	−	22.3384i	0.0992543	−	0.0992543i	0.754990	+	0.655736i	$0.227642\pi$
$38$	−184.238			−0.786511
$39$		0			0
$40$	−11.8371	−	11.8371i	−0.0467901	−	0.0467901i
$41$	76.6455	+	76.6455i	0.291952	+	0.291952i	0.837851	−	0.545899i	$-0.183812\pi$
$41$	76.6455	+	76.6455i	0.291952	+	0.291952i	−0.545899	+	0.837851i	$0.683812\pi$
$42$		0			0
$43$		−	233.202i		−	0.827047i	−0.910493	−	0.413524i	$-0.864298\pi$
$43$		−	233.202i		−	0.827047i	0.910493	−	0.413524i	$-0.135702\pi$
$44$	82.0007	+	82.0007i	0.280956	+	0.280956i
$45$		0			0
$46$	44.3874	−	44.3874i	0.142273	−	0.142273i
$47$	−51.1712			−0.158810			−0.0794052	−	0.996842i	$-0.525302\pi$
$47$	−51.1712			−0.158810			−0.0794052	+	0.996842i	$0.525302\pi$
$48$		0			0
$49$		−	328.019i		−	0.956322i
$50$	−186.095			−0.526357
$51$		0			0
$52$	115.409			0.307775
$53$		−	1.55884i		−	0.00404007i	−0.999998	−	0.00202003i	$-0.999357\pi$
$53$		−	1.55884i		−	0.00404007i	0.999998	−	0.00202003i	$-0.000642997\pi$
$54$		0			0
$55$	−16.3654			−0.0401221
$56$	−56.3647	+	56.3647i	−0.134501	+	0.134501i
$57$		0			0
$58$	26.3960	+	26.3960i	0.0597580	+	0.0597580i
$59$		−	588.603i		−	1.29881i	−0.760445	−	0.649403i	$-0.775019\pi$
$59$		−	588.603i		−	1.29881i	0.760445	−	0.649403i	$-0.224981\pi$
$60$		0			0
$61$	−513.681	−	513.681i	−1.07820	−	1.07820i	−0.996671	−	0.0815267i	$-0.974020\pi$
$61$	−513.681	−	513.681i	−1.07820	−	1.07820i	−0.0815267	−	0.996671i	$-0.525980\pi$
$62$	−80.9401	−	80.9401i	−0.165797	−	0.165797i
$63$		0			0
$64$	−158.703			−0.309967
$65$	−11.5164	+	11.5164i	−0.0219760	+	0.0219760i
$66$		0			0
$67$	266.752			0.486403			0.243201	−	0.969976i	$-0.421802\pi$
$67$	266.752			0.486403			0.243201	+	0.969976i	$0.421802\pi$
$68$	334.611	−	225.910i	0.596728	−	0.402876i
$69$		0			0
$70$		−	4.70890i		−	0.00804030i
$71$	621.733	−	621.733i	1.03924	−	1.03924i	0.0400429	−	0.999198i	$-0.487251\pi$
$71$	621.733	−	621.733i	1.03924	−	1.03924i	0.999198	−	0.0400429i	$-0.0127495\pi$
$72$		0			0
$73$	236.509	−	236.509i	0.379195	−	0.379195i	−0.491617	−	0.870812i	$-0.663594\pi$
$73$	236.509	−	236.509i	0.379195	−	0.379195i	0.870812	+	0.491617i	$0.163594\pi$
$74$	33.4333	+	33.4333i	0.0525209	+	0.0525209i
$75$		0			0
$76$			709.043i			1.07017i
$77$			77.9274i			0.115333i
$78$		0			0
$79$	−582.906	−	582.906i	−0.830153	−	0.830153i	0.157384	−	0.987537i	$-0.449694\pi$
$79$	−582.906	−	582.906i	−0.830153	−	0.830153i	−0.987537	+	0.157384i	$0.949694\pi$
$80$	−8.76932	+	8.76932i	−0.0122555	+	0.0122555i
$81$		0			0
$82$	−114.713	+	114.713i	−0.154488	+	0.154488i
$83$			224.694i			0.297149i	0.988901	+	0.148574i	$0.0474684\pi$
$83$			224.694i			0.297149i	−0.988901	+	0.148574i	$0.952532\pi$
$84$		0			0
$85$	−10.8471	+	55.9334i	−0.0138415	+	0.0713745i
$86$	349.028			0.437636
$87$		0			0
$88$	−293.186	+	293.186i	−0.355156	+	0.355156i
$89$	−561.132			−0.668313			−0.334157	−	0.942518i	$-0.608451\pi$
$89$	−561.132			−0.668313			−0.334157	+	0.942518i	$0.608451\pi$
$90$		0			0
$91$	54.8379	+	54.8379i	0.0631711	+	0.0631711i
$92$	−170.825	−	170.825i	−0.193584	−	0.193584i
$93$		0			0
$94$		−	76.5866i		−	0.0840352i
$95$	−70.7542	−	70.7542i	−0.0764129	−	0.0764129i
$96$		0			0
$97$	1257.15	−	1257.15i	1.31592	−	1.31592i	0.398938	−	0.916978i	$-0.369379\pi$
$97$	1257.15	−	1257.15i	1.31592	−	1.31592i	0.916978	−	0.398938i	$-0.130621\pi$
$98$	490.937			0.506042
$99$		0			0
$100$			716.190i			0.716190i
$101$	−1943.41			−1.91462			−0.957310	−	0.289064i	$-0.906656\pi$
$101$	−1943.41			−1.91462			−0.957310	+	0.289064i	$0.906656\pi$
$102$		0			0
$103$	−197.134			−0.188585			−0.0942923	−	0.995545i	$-0.530059\pi$
$103$	−197.134			−0.188585			−0.0942923	+	0.995545i	$0.530059\pi$
$104$			412.632i			0.389057i
$105$		0			0
$106$	2.33308			0.00213782
$107$	−1071.43	+	1071.43i	−0.968033	+	0.968033i	−0.999505	−	0.0314720i	$-0.989981\pi$
$107$	−1071.43	+	1071.43i	−0.968033	+	0.968033i	0.0314720	+	0.999505i	$0.489981\pi$
$108$		0			0
$109$	−564.212	−	564.212i	−0.495795	−	0.495795i	0.414331	−	0.910126i	$-0.364016\pi$
$109$	−564.212	−	564.212i	−0.495795	−	0.495795i	−0.910126	+	0.414331i	$0.864016\pi$
$110$		−	24.4937i		−	0.0212308i
$111$		0			0
$112$	41.7569	+	41.7569i	0.0352291	+	0.0352291i
$113$	1134.32	+	1134.32i	0.944317	+	0.944317i	0.998529	−	0.0542129i	$-0.0172650\pi$
$113$	1134.32	+	1134.32i	0.944317	+	0.944317i	−0.0542129	+	0.998529i	$0.517265\pi$
$114$		0			0
$115$	34.0927			0.0276449
$116$	101.585	−	101.585i	0.0813098	−	0.0813098i
$117$		0			0
$118$	880.947			0.687269
$119$	266.339	+	51.6506i	0.205170	+	0.0397883i
$120$		0			0
$121$		−	925.654i		−	0.695458i
$122$	768.813	−	768.813i	0.570533	−	0.570533i
$123$		0			0
$124$	−311.499	+	311.499i	−0.225592	+	0.225592i
$125$	−143.315	−	143.315i	−0.102548	−	0.102548i
$126$		0			0
$127$			2315.35i			1.61775i	0.587980	+	0.808876i	$0.299923\pi$
$127$			2315.35i			1.61775i	−0.587980	+	0.808876i	$0.700077\pi$
$128$			1263.18i			0.872267i
$129$		0			0
$130$	−17.2363	−	17.2363i	−0.0116287	−	0.0116287i
$131$	1255.78	−	1255.78i	0.837541	−	0.837541i	−0.150994	−	0.988535i	$-0.548247\pi$
$131$	1255.78	−	1255.78i	0.837541	−	0.837541i	0.988535	+	0.150994i	$0.0482474\pi$
$132$		0			0
$133$	−336.911	+	336.911i	−0.219653	+	0.219653i
$134$			399.242i			0.257382i
$135$		0			0
$136$	807.719	+	1196.37i	0.509274	+	0.754321i
$137$	−1489.27			−0.928736			−0.464368	−	0.885642i	$-0.653719\pi$
$137$	−1489.27			−0.928736			−0.464368	+	0.885642i	$0.653719\pi$
$138$		0			0
$139$	−1739.62	+	1739.62i	−1.06153	+	1.06153i	−0.0635492	+	0.997979i	$0.520242\pi$
$139$	−1739.62	+	1739.62i	−1.06153	+	1.06153i	−0.997979	+	0.0635492i	$0.979758\pi$
$140$	−18.1222			−0.0109401
$141$		0			0
$142$	930.532	+	930.532i	0.549919	+	0.549919i
$143$	285.244	+	285.244i	0.166806	+	0.166806i
$144$		0			0
$145$			20.2740i			0.0116115i
$146$	353.977	+	353.977i	0.200653	+	0.200653i
$147$		0			0
$148$	128.668	−	128.668i	0.0714627	−	0.0714627i
$149$	1981.35			1.08938			0.544692	−	0.838636i	$-0.316647\pi$
$149$	1981.35			1.08938			0.544692	+	0.838636i	$0.316647\pi$
$150$		0			0
$151$			1293.87i			0.697306i	0.937252	+	0.348653i	$0.113361\pi$
$151$			1293.87i			0.697306i	−0.937252	+	0.348653i	$0.886639\pi$
$152$	−2535.11			−1.35280
$153$		0			0
$154$	−116.632			−0.0610291
$155$		−	62.1678i		−	0.0322157i
$156$		0			0
$157$	3212.58			1.63307			0.816535	−	0.577296i	$-0.195892\pi$
$157$	3212.58			1.63307			0.816535	+	0.577296i	$0.195892\pi$
$158$	872.421	−	872.421i	0.439279	−	0.439279i
$159$		0			0
$160$	−107.821	−	107.821i	−0.0532752	−	0.0532752i
$161$		−	162.340i		−	0.0794669i
$162$		0			0
$163$	442.905	+	442.905i	0.212828	+	0.212828i	0.805468	−	0.592640i	$-0.201914\pi$
$163$	442.905	+	442.905i	0.212828	+	0.212828i	−0.592640	+	0.805468i	$0.701914\pi$
$164$	441.475	+	441.475i	0.210204	+	0.210204i
$165$		0			0
$166$	−336.293			−0.157238
$167$	2645.12	−	2645.12i	1.22566	−	1.22566i	0.260072	−	0.965589i	$-0.416254\pi$
$167$	2645.12	−	2645.12i	1.22566	−	1.22566i	0.965589	−	0.260072i	$-0.0837463\pi$
$168$		0			0
$169$	−1795.55			−0.817271
$170$	−83.7141	−	16.2346i	−0.0377681	−	0.00732431i
$171$		0			0
$172$		−	1343.24i		−	0.595470i
$173$	70.5192	−	70.5192i	0.0309912	−	0.0309912i	−0.691441	−	0.722433i	$-0.743024\pi$
$173$	70.5192	−	70.5192i	0.0309912	−	0.0309912i	0.722433	+	0.691441i	$0.243024\pi$
$174$		0			0
$175$	−340.307	+	340.307i	−0.146999	+	0.146999i
$176$	217.202	+	217.202i	0.0930240	+	0.0930240i
$177$		0			0
$178$		−	839.832i		−	0.353641i
$179$			2170.40i			0.906275i	0.891441	+	0.453138i	$0.149695\pi$
$179$			2170.40i			0.906275i	−0.891441	+	0.453138i	$0.850305\pi$
$180$		0			0
$181$	−1974.50	−	1974.50i	−0.810848	−	0.810848i	0.173913	−	0.984761i	$-0.444359\pi$
$181$	−1974.50	−	1974.50i	−0.810848	−	0.810848i	−0.984761	+	0.173913i	$0.944359\pi$
$182$	−82.0745	+	82.0745i	−0.0334273	+	0.0334273i
$183$		0			0
$184$	610.769	−	610.769i	0.244709	−	0.244709i
$185$			25.6792i			0.0102053i
$186$		0			0
$187$	1385.38	+	268.665i	0.541760	+	0.105063i
$188$	−294.744			−0.114343
$189$		0			0
$190$	105.896	−	105.896i	0.0404342	−	0.0404342i
$191$	−3351.18			−1.26955			−0.634773	−	0.772699i	$-0.718906\pi$
$191$	−3351.18			−1.26955			−0.634773	+	0.772699i	$0.718906\pi$
$192$		0			0
$193$	−1979.89	−	1979.89i	−0.738423	−	0.738423i	0.233850	−	0.972273i	$-0.424868\pi$
$193$	−1979.89	−	1979.89i	−0.738423	−	0.738423i	−0.972273	+	0.233850i	$0.924868\pi$
$194$	1881.54	+	1881.54i	0.696323	+	0.696323i
$195$		0			0
$196$		−	1889.37i		−	0.688548i
$197$	−1794.75	−	1794.75i	−0.649088	−	0.649088i	0.303685	−	0.952773i	$-0.401783\pi$
$197$	−1794.75	−	1794.75i	−0.649088	−	0.649088i	−0.952773	+	0.303685i	$0.901783\pi$
$198$		0			0
$199$	1926.29	−	1926.29i	0.686186	−	0.686186i	−0.275201	−	0.961387i	$-0.588744\pi$
$199$	1926.29	−	1926.29i	0.686186	−	0.686186i	0.961387	+	0.275201i	$0.0887444\pi$
$200$	−2560.67			−0.905332
$201$		0			0
$202$		−	2908.65i		−	1.01313i
$203$	96.5390			0.0333779
$204$		0			0
$205$	−88.1082			−0.0300183
$206$		−	295.046i		−	0.0997904i
$207$		0			0
$208$	305.692			0.101904
$209$	−1752.47	+	1752.47i	−0.580004	+	0.580004i
$210$		0			0
$211$	295.026	+	295.026i	0.0962581	+	0.0962581i	0.753596	−	0.657338i	$-0.228318\pi$
$211$	295.026	+	295.026i	0.0962581	+	0.0962581i	−0.657338	+	0.753596i	$0.728318\pi$
$212$		−	8.97888i		−	0.00290883i
$213$		0			0
$214$	−1603.59	−	1603.59i	−0.512239	−	0.512239i
$215$	134.039	+	134.039i	0.0425182	+	0.0425182i
$216$		0			0
$217$	−296.025			−0.0926060
$218$	844.442	−	844.442i	0.262352	−	0.262352i
$219$		0			0
$220$	−94.2643			−0.0288877
$221$	1163.96	−	785.839i	0.354283	−	0.239191i
$222$		0			0
$223$			1074.81i			0.322757i	0.986893	+	0.161379i	$0.0515940\pi$
$223$			1074.81i			0.322757i	−0.986893	+	0.161379i	$0.948406\pi$
$224$	−513.414	+	513.414i	−0.153143	+	0.153143i
$225$		0			0
$226$	−1697.71	+	1697.71i	−0.499689	+	0.499689i
$227$	−2386.83	−	2386.83i	−0.697884	−	0.697884i	0.266070	−	0.963954i	$-0.414275\pi$
$227$	−2386.83	−	2386.83i	−0.697884	−	0.697884i	−0.963954	+	0.266070i	$0.914275\pi$
$228$		0			0
$229$			2565.82i			0.740410i	0.928950	+	0.370205i	$0.120713\pi$
$229$			2565.82i			0.740410i	−0.928950	+	0.370205i	$0.879287\pi$
$230$			51.0258i			0.0146284i
$231$		0			0
$232$	363.208	+	363.208i	0.102783	+	0.102783i
$233$	150.071	−	150.071i	0.0421952	−	0.0421952i	−0.685694	−	0.727890i	$-0.740501\pi$
$233$	150.071	−	150.071i	0.0421952	−	0.0421952i	0.727890	+	0.685694i	$0.240501\pi$
$234$		0			0
$235$	29.4120	−	29.4120i	0.00816438	−	0.00816438i
$236$		−	3390.33i		−	0.935134i
$237$		0			0
$238$	−77.3042	+	398.622i	−0.0210542	+	0.108567i
$239$	4285.84			1.15995			0.579975	−	0.814634i	$-0.303062\pi$
$239$	4285.84			1.15995			0.579975	+	0.814634i	$0.303062\pi$
$240$		0			0
$241$	781.219	−	781.219i	0.208808	−	0.208808i	−0.594953	−	0.803761i	$-0.702829\pi$
$241$	781.219	−	781.219i	0.208808	−	0.208808i	0.803761	+	0.594953i	$0.202829\pi$
$242$	1385.40			0.368005
$243$		0			0
$244$	−2958.78	−	2958.78i	−0.776298	−	0.776298i
$245$	188.538	+	188.538i	0.0491642	+	0.0491642i
$246$		0			0
$247$			2466.44i			0.635368i
$248$	−1113.73	−	1113.73i	−0.285170	−	0.285170i
$249$		0			0
$250$	214.495	−	214.495i	0.0542635	−	0.0542635i
$251$	480.822			0.120913			0.0604566	−	0.998171i	$-0.480744\pi$
$251$	480.822			0.120913			0.0604566	+	0.998171i	$0.480744\pi$
$252$		0			0
$253$		−	844.424i		−	0.209836i
$254$	−3465.33			−0.856040
$255$		0			0
$256$	−3160.19			−0.771532
$257$		−	4146.30i		−	1.00638i	−0.864176	−	0.503189i	$-0.832160\pi$
$257$		−	4146.30i		−	1.00638i	0.864176	−	0.503189i	$-0.167840\pi$
$258$		0			0
$259$	122.277			0.0293356
$260$	−66.3342	+	66.3342i	−0.0158226	+	0.0158226i
$261$		0			0
$262$	1879.49	+	1879.49i	0.443188	+	0.443188i
$263$			8011.72i			1.87842i	0.343346	+	0.939209i	$0.388440\pi$
$263$			8011.72i			1.87842i	−0.343346	+	0.939209i	$0.611560\pi$
$264$		0			0
$265$	0.895988	+	0.895988i	0.000207698	+	0.000207698i
$266$	−504.246	−	504.246i	−0.116231	−	0.116231i
$267$		0			0
$268$	1536.48			0.350208
$269$	3943.92	−	3943.92i	0.893922	−	0.893922i	−0.100968	−	0.994890i	$-0.532194\pi$
$269$	3943.92	−	3943.92i	0.893922	−	0.893922i	0.994890	+	0.100968i	$0.0321940\pi$
$270$		0			0
$271$	−3089.50			−0.692524			−0.346262	−	0.938138i	$-0.612549\pi$
$271$	−3089.50			−0.692524			−0.346262	+	0.938138i	$0.612549\pi$
$272$	886.311	−	598.386i	0.197575	−	0.133391i
$273$		0			0
$274$		−	2228.95i		−	0.491445i
$275$	−1770.13	+	1770.13i	−0.388157	+	0.388157i
$276$		0			0
$277$	−414.012	+	414.012i	−0.0898036	+	0.0898036i	−0.750581	−	0.660778i	$-0.770227\pi$
$277$	−414.012	+	414.012i	−0.0898036	+	0.0898036i	0.660778	+	0.750581i	$0.270227\pi$
$278$	−2603.64	−	2603.64i	−0.561712	−	0.561712i
$279$		0			0
$280$		−	64.7943i		−	0.0138293i
$281$			6399.58i			1.35860i	0.733860	+	0.679301i	$0.237717\pi$
$281$			6399.58i			1.35860i	−0.733860	+	0.679301i	$0.762283\pi$
$282$		0			0
$283$	4267.26	+	4267.26i	0.896333	+	0.896333i	0.995110	−	0.0987768i	$-0.0314930\pi$
$283$	4267.26	+	4267.26i	0.896333	+	0.896333i	−0.0987768	+	0.995110i	$0.531493\pi$
$284$	3581.16	−	3581.16i	0.748249	−	0.748249i
$285$		0			0
$286$	−426.917	+	426.917i	−0.0882662	+	0.0882662i
$287$			419.546i			0.0862892i
$288$		0			0
$289$	1836.47	−	4556.86i	0.373799	−	0.927510i
$290$	−30.3436			−0.00614427
$291$		0			0
$292$	1362.28	−	1362.28i	0.273019	−	0.273019i
$293$	7539.51			1.50329			0.751643	−	0.659570i	$-0.229262\pi$
$293$	7539.51			1.50329			0.751643	+	0.659570i	$0.229262\pi$
$294$		0			0
$295$	338.315	+	338.315i	0.0667711	+	0.0667711i
$296$	460.041	+	460.041i	0.0903357	+	0.0903357i
$297$		0			0
$298$			2965.43i			0.576453i
$299$	−594.225	−	594.225i	−0.114933	−	0.114933i
$300$		0			0
$301$	638.257	−	638.257i	0.122221	−	0.122221i
$302$	−1936.50			−0.368983
$303$		0			0
$304$			1878.10i			0.354330i
$305$	590.504			0.110860
$306$		0			0
$307$	5367.77			0.997899			0.498950	−	0.866631i	$-0.333719\pi$
$307$	5367.77			0.997899			0.498950	+	0.866631i	$0.333719\pi$
$308$			448.859i			0.0830394i
$309$		0			0
$310$	93.0450			0.0170471
$311$	−6862.87	+	6862.87i	−1.25131	+	1.25131i	−0.296178	+	0.955133i	$0.595712\pi$
$311$	−6862.87	+	6862.87i	−1.25131	+	1.25131i	−0.955133	+	0.296178i	$0.904288\pi$
$312$		0			0
$313$	2021.32	+	2021.32i	0.365022	+	0.365022i	0.865658	−	0.500636i	$-0.166901\pi$
$313$	2021.32	+	2021.32i	0.365022	+	0.365022i	−0.500636	+	0.865658i	$0.666901\pi$
$314$			4808.19i			0.864146i
$315$		0			0
$316$	−3357.52	−	3357.52i	−0.597707	−	0.597707i
$317$	−4064.38	−	4064.38i	−0.720121	−	0.720121i	0.248509	−	0.968630i	$-0.420059\pi$
$317$	−4064.38	−	4064.38i	−0.720121	−	0.720121i	−0.968630	+	0.248509i	$0.920059\pi$
$318$		0			0
$319$	502.155			0.0881357
$320$	91.2191	−	91.2191i	0.0159353	−	0.0159353i
$321$		0			0
$322$	242.970			0.0420503
$323$	4828.01	+	7151.10i	0.831695	+	1.23188i
$324$		0			0
$325$			2491.30i			0.425208i
$326$	−662.885	+	662.885i	−0.112619	+	0.112619i
$327$		0			0
$328$	−1578.45	+	1578.45i	−0.265718	+	0.265718i
$329$	−140.052	−	140.052i	−0.0234690	−	0.0234690i
$330$		0			0
$331$			5525.96i			0.917626i	0.888533	+	0.458813i	$0.151725\pi$
$331$			5525.96i			0.917626i	−0.888533	+	0.458813i	$0.848275\pi$
$332$			1294.23i			0.213946i
$333$		0			0
$334$	3958.88	+	3958.88i	0.648564	+	0.648564i
$335$	−153.323	+	153.323i	−0.0250058	+	0.0250058i
$336$		0			0
$337$	3165.98	−	3165.98i	0.511757	−	0.511757i	−0.403307	−	0.915065i	$-0.632139\pi$
$337$	3165.98	−	3165.98i	0.511757	−	0.511757i	0.915065	+	0.403307i	$0.132139\pi$
$338$		−	2687.35i		−	0.432463i
$339$		0			0
$340$	−62.4788	+	322.174i	−0.00996585	+	0.0513893i
$341$	−1539.80			−0.244530
$342$		0			0
$343$	1836.53	−	1836.53i	0.289105	−	0.289105i
$344$	4802.62			0.752732
$345$		0			0
$346$	105.544	+	105.544i	0.0163991	+	0.0163991i
$347$	6954.35	+	6954.35i	1.07588	+	1.07588i	0.996874	+	0.0790022i	$0.0251734\pi$
$347$	6954.35	+	6954.35i	1.07588	+	1.07588i	0.0790022	+	0.996874i	$0.474827\pi$
$348$		0			0
$349$			9155.23i			1.40421i	0.712075	+	0.702104i	$0.247756\pi$
$349$			9155.23i			1.40421i	−0.712075	+	0.702104i	$0.752244\pi$
$350$	−509.329	−	509.329i	−0.0777851	−	0.0777851i
$351$		0			0
$352$	−2670.57	+	2670.57i	−0.404380	+	0.404380i
$353$	−7025.07			−1.05923			−0.529613	−	0.848239i	$-0.677663\pi$
$353$	−7025.07			−1.05923			−0.529613	+	0.848239i	$0.677663\pi$
$354$		0			0
$355$			714.716i			0.106854i
$356$	−3232.10			−0.481182
$357$		0			0
$358$	−3248.38			−0.479560
$359$		−	8370.77i		−	1.23062i	−0.788285	−	0.615310i	$-0.789031\pi$
$359$		−	8370.77i		−	1.23062i	0.788285	−	0.615310i	$-0.210969\pi$
$360$		0			0
$361$	−8294.23			−1.20925
$362$	2955.19	−	2955.19i	0.429064	−	0.429064i
$363$		0			0
$364$	315.864	+	315.864i	0.0454829	+	0.0454829i
$365$			271.880i			0.0389886i
$366$		0			0
$367$	4661.47	+	4661.47i	0.663015	+	0.663015i	0.956090	−	0.293074i	$-0.0946783\pi$
$367$	4661.47	+	4661.47i	0.663015	+	0.663015i	−0.293074	+	0.956090i	$0.594678\pi$
$368$	−452.479	−	452.479i	−0.0640954	−	0.0640954i
$369$		0			0
$370$	−38.4334			−0.00540016
$371$	4.26643	−	4.26643i	0.000597041	−	0.000597041i
$372$		0			0
$373$	−10437.4			−1.44886			−0.724432	−	0.689347i	$-0.757898\pi$
$373$	−10437.4			−1.44886			−0.724432	+	0.689347i	$0.757898\pi$
$374$	−402.104	+	2073.47i	−0.0555944	+	0.286675i
$375$		0			0
$376$		−	1053.83i		−	0.144540i
$377$	353.369	−	353.369i	0.0482743	−	0.0482743i
$378$		0			0
$379$	−1234.49	+	1234.49i	−0.167313	+	0.167313i	−0.785797	−	0.618484i	$-0.787747\pi$
$379$	−1234.49	+	1234.49i	−0.167313	+	0.167313i	0.618484	+	0.785797i	$0.287747\pi$
$380$	−407.542	−	407.542i	−0.0550169	−	0.0550169i
$381$		0			0
$382$		−	5015.63i		−	0.671786i
$383$			1031.82i			0.137660i	0.997628	+	0.0688298i	$0.0219266\pi$
$383$			1031.82i			0.137660i	−0.997628	+	0.0688298i	$0.978073\pi$
$384$		0			0
$385$	−44.7909	−	44.7909i	−0.00592924	−	0.00592924i
$386$	2963.25	−	2963.25i	0.390740	−	0.390740i
$387$		0			0
$388$	7241.12	−	7241.12i	0.947453	−	0.947453i
$389$		−	7514.99i		−	0.979499i	−0.871863	−	0.489750i	$-0.837088\pi$
$389$		−	7514.99i		−	0.979499i	0.871863	−	0.489750i	$-0.162912\pi$
$390$		0			0
$391$	−2886.05	−	559.688i	−0.373284	−	0.0723903i
$392$	6755.28			0.870390
$393$		0			0
$394$	2686.15	−	2686.15i	0.343468	−	0.343468i
$395$	670.083			0.0853557
$396$		0			0
$397$	−2133.89	−	2133.89i	−0.269766	−	0.269766i	0.559240	−	0.829006i	$-0.311093\pi$
$397$	−2133.89	−	2133.89i	−0.269766	−	0.269766i	−0.829006	+	0.559240i	$0.811093\pi$
$398$	2883.03	+	2883.03i	0.363098	+	0.363098i
$399$		0			0
$400$			1897.03i			0.237129i
$401$	−10503.3	−	10503.3i	−1.30800	−	1.30800i	−0.922856	−	0.385146i	$-0.874151\pi$
$401$	−10503.3	−	10503.3i	−1.30800	−	1.30800i	−0.385146	−	0.922856i	$-0.625849\pi$
$402$		0			0
$403$	−1083.56	+	1083.56i	−0.133936	+	0.133936i
$404$	−11194.0			−1.37852
$405$		0			0
$406$			144.487i			0.0176621i
$407$	636.033			0.0774619
$408$		0			0
$409$	5721.53			0.691714			0.345857	−	0.938287i	$-0.387588\pi$
$409$	5721.53			0.691714			0.345857	+	0.938287i	$0.387588\pi$
$410$		−	131.869i		−	0.0158843i
$411$		0			0
$412$	−1135.49			−0.135780
$413$	1610.96	−	1610.96i	0.191937	−	0.191937i
$414$		0			0
$415$	−129.149	−	129.149i	−0.0152763	−	0.0152763i
$416$			3758.58i			0.442980i
$417$		0			0
$418$	−2622.88	−	2622.88i	−0.306912	−	0.306912i
$419$	−4335.25	−	4335.25i	−0.505467	−	0.505467i	0.407665	−	0.913132i	$-0.366343\pi$
$419$	−4335.25	−	4335.25i	−0.505467	−	0.505467i	−0.913132	+	0.407665i	$0.866343\pi$
$420$		0			0
$421$	−6388.31			−0.739542			−0.369771	−	0.929123i	$-0.620564\pi$
$421$	−6388.31			−0.739542			−0.369771	+	0.929123i	$0.620564\pi$
$422$	−441.559	+	441.559i	−0.0509354	+	0.0509354i
$423$		0			0
$424$	32.1031			0.00367704
$425$	4876.67	+	7223.18i	0.556596	+	0.824413i
$426$		0			0
$427$		−	2811.81i		−	0.318672i
$428$	−6171.42	+	6171.42i	−0.696979	+	0.696979i
$429$		0			0
$430$	−200.613	+	200.613i	−0.0224987	+	0.0224987i
$431$	604.177	+	604.177i	0.0675224	+	0.0675224i	0.740062	−	0.672539i	$-0.234796\pi$
$431$	604.177	+	604.177i	0.0675224	+	0.0675224i	−0.672539	+	0.740062i	$0.734796\pi$
$432$		0			0
$433$		−	10107.4i		−	1.12178i	−0.827889	−	0.560892i	$-0.810458\pi$
$433$		−	10107.4i		−	1.12178i	0.827889	−	0.560892i	$-0.189542\pi$
$434$		−	443.054i		−	0.0490029i
$435$		0			0
$436$	−3249.84	−	3249.84i	−0.356970	−	0.356970i
$437$	3650.77	−	3650.77i	0.399634	−	0.399634i
$438$		0			0
$439$	11609.5	−	11609.5i	1.26217	−	1.26217i	0.312125	−	0.950041i	$-0.398959\pi$
$439$	11609.5	−	11609.5i	1.26217	−	1.26217i	0.950041	−	0.312125i	$-0.101041\pi$
$440$		−	337.033i		−	0.0365168i
$441$		0			0
$442$	1176.15	+	1742.07i	0.126569	+	0.187470i
$443$	−5106.09			−0.547625			−0.273812	−	0.961783i	$-0.588285\pi$
$443$	−5106.09			−0.547625			−0.273812	+	0.961783i	$0.588285\pi$
$444$		0			0
$445$	322.526	−	322.526i	0.0343577	−	0.0343577i
$446$	−1608.65			−0.170788
$447$		0			0
$448$	−434.359	−	434.359i	−0.0458070	−	0.0458070i
$449$	7972.68	+	7972.68i	0.837982	+	0.837982i	0.988593	−	0.150611i	$-0.0481240\pi$
$449$	7972.68	+	7972.68i	0.837982	+	0.837982i	−0.150611	+	0.988593i	$0.548124\pi$
$450$		0			0
$451$			2182.30i			0.227850i
$452$	6533.64	+	6533.64i	0.679904	+	0.679904i
$453$		0			0
$454$	3572.31	−	3572.31i	0.369289	−	0.369289i
$455$	−63.0391			−0.00649521
$456$		0			0
$457$		−	13048.0i		−	1.33557i	−0.744352	−	0.667787i	$-0.767242\pi$
$457$		−	13048.0i		−	1.33557i	0.744352	−	0.667787i	$-0.232758\pi$
$458$	−3840.19			−0.391791
$459$		0			0
$460$	196.373			0.0199042
$461$		−	14147.2i		−	1.42929i	−0.699487	−	0.714645i	$-0.746588\pi$
$461$		−	14147.2i		−	1.42929i	0.699487	−	0.714645i	$-0.253412\pi$
$462$		0			0
$463$	−7778.27			−0.780749			−0.390375	−	0.920656i	$-0.627655\pi$
$463$	−7778.27			−0.780749			−0.390375	+	0.920656i	$0.627655\pi$
$464$	269.077	−	269.077i	0.0269215	−	0.0269215i
$465$		0			0
$466$	224.608	+	224.608i	0.0223278	+	0.0223278i
$467$			3546.16i			0.351384i	0.984445	+	0.175692i	$0.0562163\pi$
$467$			3546.16i			0.351384i	−0.984445	+	0.175692i	$0.943784\pi$
$468$		0			0
$469$	730.081	+	730.081i	0.0718806	+	0.0718806i
$470$	44.0203	+	44.0203i	0.00432022	+	0.00432022i
$471$		0			0
$472$	12121.8			1.18210
$473$	3319.95	−	3319.95i	0.322730	−	0.322730i
$474$		0			0
$475$	−15306.0			−1.47850
$476$	1534.10	+	297.506i	0.147721	+	0.0286474i
$477$		0			0
$478$			6414.51i			0.613793i
$479$	1653.30	−	1653.30i	0.157706	−	0.157706i	−0.623843	−	0.781550i	$-0.714430\pi$
$479$	1653.30	−	1653.30i	0.157706	−	0.157706i	0.781550	+	0.623843i	$0.214430\pi$
$480$		0			0
$481$	447.579	−	447.579i	0.0424280	−	0.0424280i
$482$	1169.23	+	1169.23i	0.110492	+	0.110492i
$483$		0			0
$484$		−	5331.73i		−	0.500726i
$485$			1445.16i			0.135302i
$486$		0			0
$487$	−2352.91	−	2352.91i	−0.218934	−	0.218934i	0.589115	−	0.808049i	$-0.299476\pi$
$487$	−2352.91	−	2352.91i	−0.218934	−	0.218934i	−0.808049	+	0.589115i	$0.799476\pi$
$488$	10578.8	−	10578.8i	0.981315	−	0.981315i
$489$		0			0
$490$	−282.179	+	282.179i	−0.0260154	+	0.0260154i
$491$			5511.23i			0.506554i	0.967394	+	0.253277i	$0.0815085\pi$
$491$			5511.23i			0.506554i	−0.967394	+	0.253277i	$0.918492\pi$
$492$		0			0
$493$	332.831	−	1716.26i	0.0304056	−	0.156788i
$494$	−3691.46			−0.336208
$495$		0			0
$496$	−825.092	+	825.092i	−0.0746930	+	0.0746930i
$497$	3403.27			0.307158
$498$		0			0
$499$	10717.0	+	10717.0i	0.961438	+	0.961438i	0.999284	−	0.0378459i	$-0.0120496\pi$
$499$	10717.0	+	10717.0i	0.961438	+	0.961438i	−0.0378459	+	0.999284i	$0.512050\pi$
$500$	−825.486	−	825.486i	−0.0738338	−	0.0738338i
$501$		0			0
$502$			719.634i			0.0639817i
$503$	−7580.21	−	7580.21i	−0.671938	−	0.671938i	0.286225	−	0.958163i	$-0.407600\pi$
$503$	−7580.21	−	7580.21i	−0.671938	−	0.671938i	−0.958163	+	0.286225i	$0.907600\pi$
$504$		0			0
$505$	1117.03	−	1117.03i	0.0984299	−	0.0984299i
$506$	1263.83			0.111036
$507$		0			0
$508$			13336.4i			1.16477i
$509$	−12724.1			−1.10803			−0.554013	−	0.832508i	$-0.686904\pi$
$509$	−12724.1			−1.10803			−0.554013	+	0.832508i	$0.686904\pi$
$510$		0			0
$511$	1294.61			0.112075
$512$			5375.64i			0.464008i
$513$		0			0
$514$	6205.67			0.532530
$515$	113.308	−	113.308i	0.00969506	−	0.00969506i
$516$		0			0
$517$	−728.490	−	728.490i	−0.0619709	−	0.0619709i
$518$			183.009i			0.0155231i
$519$		0			0
$520$	−237.172	−	237.172i	−0.0200013	−	0.0200013i
$521$	−9567.51	−	9567.51i	−0.804530	−	0.804530i	0.179270	−	0.983800i	$-0.442626\pi$
$521$	−9567.51	−	9567.51i	−0.804530	−	0.804530i	−0.983800	+	0.179270i	$0.942626\pi$
$522$		0			0
$523$	−7104.82			−0.594019			−0.297010	−	0.954875i	$-0.595989\pi$
$523$	−7104.82			−0.594019			−0.297010	+	0.954875i	$0.595989\pi$
$524$	7233.24	−	7233.24i	0.603026	−	0.603026i
$525$		0			0
$526$	−11990.9			−0.993973
$527$	−1020.59	+	5262.69i	−0.0843594	+	0.435003i
$528$		0			0
$529$		−	10407.9i		−	0.855419i
$530$	−1.34100	+	1.34100i	−0.000109905	+	0.000109905i
$531$		0			0
$532$	−1940.59	+	1940.59i	−0.158149	+	0.158149i
$533$	1535.69	+	1535.69i	0.124800	+	0.124800i
$534$		0			0
$535$		−	1231.67i		−	0.0995324i
$536$			5493.55i			0.442696i
$537$		0			0
$538$	5902.76	+	5902.76i	0.473023	+	0.473023i
$539$	4669.78	−	4669.78i	0.373175	−	0.373175i
$540$		0			0
$541$	−11677.6	+	11677.6i	−0.928023	+	0.928023i	−0.997578	−	0.0695555i	$-0.977842\pi$
$541$	−11677.6	+	11677.6i	−0.928023	+	0.928023i	0.0695555	+	0.997578i	$0.477842\pi$
$542$		−	4623.98i		−	0.366452i
$543$		0			0
$544$	7357.34	+	10897.5i	0.579859	+	0.858869i
$545$	648.592			0.0509773
$546$		0			0
$547$	548.342	−	548.342i	0.0428618	−	0.0428618i	−0.685351	−	0.728213i	$-0.740351\pi$
$547$	548.342	−	548.342i	0.0428618	−	0.0428618i	0.728213	+	0.685351i	$0.240351\pi$
$548$	−8578.14			−0.668686
$549$		0			0
$550$	−2649.32	−	2649.32i	−0.205395	−	0.205395i
$551$	2171.01	+	2171.01i	0.167855	+	0.167855i
$552$		0			0
$553$		−	3190.74i		−	0.245360i
$554$	−619.642	−	619.642i	−0.0475200	−	0.0475200i
$555$		0			0
$556$	−10020.1	+	10020.1i	−0.764295	+	0.764295i
$557$	14283.2			1.08653			0.543267	−	0.839560i	$-0.317187\pi$
$557$	14283.2			1.08653			0.543267	+	0.839560i	$0.317187\pi$
$558$		0			0
$559$		−	4672.52i		−	0.353536i
$560$	−48.0019			−0.00362223
$561$		0			0
$562$	−9578.10			−0.718910
$563$			7158.60i			0.535877i	0.963436	+	0.267939i	$0.0863424\pi$
$563$			7158.60i			0.535877i	−0.963436	+	0.267939i	$0.913658\pi$
$564$		0			0
$565$	−1303.96			−0.0970939
$566$	−6386.70	+	6386.70i	−0.474299	+	0.474299i
$567$		0			0
$568$	12804.1	+	12804.1i	0.945858	+	0.945858i
$569$			4328.74i			0.318929i	0.987204	+	0.159464i	$0.0509767\pi$
$569$			4328.74i			0.318929i	−0.987204	+	0.159464i	$0.949023\pi$
$570$		0			0
$571$	9148.34	+	9148.34i	0.670483	+	0.670483i	0.957827	−	0.287344i	$-0.0927723\pi$
$571$	9148.34	+	9148.34i	0.670483	+	0.670483i	−0.287344	+	0.957827i	$0.592772\pi$
$572$	1642.99	+	1642.99i	0.120100	+	0.120100i
$573$		0			0
$574$	−627.923			−0.0456603
$575$	3687.57	−	3687.57i	0.267448	−	0.267448i
$576$		0			0
$577$	14654.1			1.05729			0.528645	−	0.848843i	$-0.322700\pi$
$577$	14654.1			1.05729			0.528645	+	0.848843i	$0.322700\pi$
$578$	6820.13	+	2748.61i	0.490796	+	0.197797i
$579$		0			0
$580$			116.778i			0.00836022i
$581$	−614.969	+	614.969i	−0.0439126	+	0.0439126i
$582$		0			0
$583$	22.1922	−	22.1922i	0.00157651	−	0.00157651i
$584$	4870.71	+	4870.71i	0.345122	+	0.345122i
$585$		0			0
$586$			11284.2i			0.795471i
$587$			12094.6i			0.850419i	0.905095	+	0.425209i	$0.139799\pi$
$587$			12094.6i			0.850419i	−0.905095	+	0.425209i	$0.860201\pi$
$588$		0			0
$589$	−6657.16	−	6657.16i	−0.465710	−	0.465710i
$590$	−506.348	+	506.348i	−0.0353322	+	0.0353322i
$591$		0			0
$592$	340.815	−	340.815i	0.0236611	−	0.0236611i
$593$			8913.39i			0.617249i	0.951184	+	0.308625i	$0.0998687\pi$
$593$			8913.39i			0.617249i	−0.951184	+	0.308625i	$0.900131\pi$
$594$		0			0
$595$	−182.773	+	123.398i	−0.0125932	+	0.00850221i
$596$	11412.5			0.784352
$597$		0			0
$598$	889.361	−	889.361i	0.0608172	−	0.0608172i
$599$	−17664.7			−1.20494			−0.602470	−	0.798142i	$-0.705817\pi$
$599$	−17664.7			−1.20494			−0.602470	+	0.798142i	$0.705817\pi$
$600$		0			0
$601$	−2346.22	−	2346.22i	−0.159242	−	0.159242i	0.622989	−	0.782231i	$-0.285918\pi$
$601$	−2346.22	−	2346.22i	−0.159242	−	0.159242i	−0.782231	+	0.622989i	$0.785918\pi$
$602$	955.263	+	955.263i	0.0646738	+	0.0646738i
$603$		0			0
$604$			7452.62i			0.502057i
$605$	532.045	+	532.045i	0.0357532	+	0.0357532i
$606$		0			0
$607$	10813.0	−	10813.0i	0.723042	−	0.723042i	−0.246182	−	0.969224i	$-0.579176\pi$
$607$	10813.0	−	10813.0i	0.723042	−	0.723042i	0.969224	+	0.246182i	$0.0791761\pi$
$608$	−23091.8			−1.54029
$609$		0			0
$610$			883.792i			0.0586618i
$611$	−1025.28			−0.0678863
$612$		0			0
$613$	13570.8			0.894160			0.447080	−	0.894494i	$-0.352464\pi$
$613$	13570.8			0.894160			0.447080	+	0.894494i	$0.352464\pi$
$614$			8033.81i			0.528043i
$615$		0			0
$616$	−1604.85			−0.104970
$617$	−12451.6	+	12451.6i	−0.812450	+	0.812450i	−0.985001	−	0.172551i	$-0.944799\pi$
$617$	−12451.6	+	12451.6i	−0.812450	+	0.812450i	0.172551	+	0.985001i	$0.444799\pi$
$618$		0			0
$619$	14955.7	+	14955.7i	0.971116	+	0.971116i	0.999594	−	0.0284784i	$-0.00906618\pi$
$619$	14955.7	+	14955.7i	0.971116	+	0.971116i	−0.0284784	+	0.999594i	$0.509066\pi$
$620$		−	358.084i		−	0.0231952i
$621$		0			0
$622$	−10271.5	−	10271.5i	−0.662137	−	0.662137i
$623$	−1535.77	−	1535.77i	−0.0987633	−	0.0987633i
$624$		0			0
$625$	−15377.7			−0.984170
$626$	−3025.26	+	3025.26i	−0.193153	+	0.193153i
$627$		0			0
$628$	18504.4			1.17580
$629$	421.566	−	2173.82i	0.0267232	−	0.137800i
$630$		0			0
$631$			5652.30i			0.356600i	0.983976	+	0.178300i	$0.0570598\pi$
$631$			5652.30i			0.356600i	−0.983976	+	0.178300i	$0.942940\pi$
$632$	12004.5	−	12004.5i	0.755558	−	0.755558i
$633$		0			0
$634$	6083.05	−	6083.05i	0.381055	−	0.381055i
$635$	−1330.81	−	1330.81i	−0.0831680	−	0.0831680i
$636$		0			0
$637$		−	6572.29i		−	0.408797i
$638$			751.563i			0.0466374i
$639$		0			0
$640$	−726.046	−	726.046i	−0.0448429	−	0.0448429i
$641$	−15125.0	+	15125.0i	−0.931982	+	0.931982i	−0.997830	−	0.0658478i	$-0.979025\pi$
$641$	−15125.0	+	15125.0i	−0.931982	+	0.931982i	0.0658478	+	0.997830i	$0.479025\pi$
$642$		0			0
$643$	−4112.50	+	4112.50i	−0.252226	+	0.252226i	−0.821883	−	0.569657i	$-0.807076\pi$
$643$	−4112.50	+	4112.50i	−0.252226	+	0.252226i	0.569657	+	0.821883i	$0.307076\pi$
$644$		−	935.071i		−	0.0572158i
$645$		0			0
$646$	−10702.9	+	7225.96i	−0.651855	+	0.440095i
$647$	24007.9			1.45881			0.729404	−	0.684084i	$-0.239798\pi$
$647$	24007.9			1.45881			0.729404	+	0.684084i	$0.239798\pi$
$648$		0			0
$649$	8379.54	−	8379.54i	0.506819	−	0.506819i
$650$	−3728.67			−0.225001
$651$		0			0
$652$	2551.12	+	2551.12i	0.153235	+	0.153235i
$653$	−756.860	−	756.860i	−0.0453572	−	0.0453572i	0.684064	−	0.729422i	$-0.260211\pi$
$653$	−756.860	−	756.860i	−0.0453572	−	0.0453572i	−0.729422	+	0.684064i	$0.760211\pi$
$654$		0			0
$655$			1443.59i			0.0861153i
$656$	1169.37	+	1169.37i	0.0695981	+	0.0695981i
$657$		0			0
$658$	209.612	−	209.612i	0.0124187	−	0.0124187i
$659$	12742.8			0.753245			0.376623	−	0.926367i	$-0.377085\pi$
$659$	12742.8			0.753245			0.376623	+	0.926367i	$0.377085\pi$
$660$		0			0
$661$			1443.34i			0.0849312i	0.999098	+	0.0424656i	$0.0135213\pi$
$661$			1443.34i			0.0849312i	−0.999098	+	0.0424656i	$0.986479\pi$
$662$	−8270.57			−0.485566
$663$		0			0
$664$	−4627.38			−0.270448
$665$		−	387.297i		−	0.0225846i
$666$		0			0
$667$	−1046.10			−0.0607273
$668$	15235.8	−	15235.8i	0.882471	−	0.882471i
$669$		0			0
$670$	−229.475	−	229.475i	−0.0132319	−	0.0132319i
$671$		−	14625.9i		−	0.841467i
$672$		0			0
$673$	−3389.13	−	3389.13i	−0.194118	−	0.194118i	0.603355	−	0.797473i	$-0.293830\pi$
$673$	−3389.13	−	3389.13i	−0.194118	−	0.194118i	−0.797473	+	0.603355i	$0.793830\pi$
$674$	4738.45	+	4738.45i	0.270799	+	0.270799i
$675$		0			0
$676$	−10342.3			−0.588432
$677$	15674.7	−	15674.7i	0.889846	−	0.889846i	−0.104662	−	0.994508i	$-0.533376\pi$
$677$	15674.7	−	15674.7i	0.889846	−	0.889846i	0.994508	+	0.104662i	$0.0333759\pi$
$678$		0			0
$679$	6881.42			0.388932
$680$	−1151.90	−	223.387i	−0.0649610	−	0.0125978i
$681$		0			0
$682$		−	2304.58i		−	0.129394i
$683$	21436.1	−	21436.1i	1.20092	−	1.20092i	0.227034	−	0.973887i	$-0.427097\pi$
$683$	21436.1	−	21436.1i	1.20092	−	1.20092i	0.973887	−	0.227034i	$-0.0729029\pi$
$684$		0			0
$685$	855.998	−	855.998i	0.0477460	−	0.0477460i
$686$	2748.68	+	2748.68i	0.152981	+	0.152981i
$687$		0			0
$688$		−	3557.94i		−	0.197159i
$689$		−	31.2335i		−	0.00172700i
$690$		0			0
$691$	−18537.6	−	18537.6i	−1.02056	−	1.02056i	−0.999784	−	0.0207713i	$-0.993388\pi$
$691$	−18537.6	−	18537.6i	−1.02056	−	1.02056i	−0.0207713	−	0.999784i	$-0.506612\pi$
$692$	406.188	−	406.188i	0.0223135	−	0.0223135i
$693$		0			0
$694$	−10408.4	+	10408.4i	−0.569305	+	0.569305i
$695$		−	1999.78i		−	0.109146i
$696$		0			0
$697$	7458.62	+	1446.44i	0.405330	+	0.0786051i
$698$	−13702.4			−0.743043
$699$		0			0
$700$	−1960.16	+	1960.16i	−0.105838	+	0.105838i
$701$	−10843.2			−0.584228			−0.292114	−	0.956384i	$-0.594359\pi$
$701$	−10843.2			−0.584228			−0.292114	+	0.956384i	$0.594359\pi$
$702$		0			0
$703$	2749.82	+	2749.82i	0.147527	+	0.147527i
$704$	−2259.35	−	2259.35i	−0.120955	−	0.120955i
$705$		0			0
$706$		−	10514.3i		−	0.560494i
$707$	−5318.96	−	5318.96i	−0.282942	−	0.282942i
$708$		0			0
$709$	3788.77	−	3788.77i	0.200691	−	0.200691i	−0.599605	−	0.800296i	$-0.704676\pi$
$709$	3788.77	−	3788.77i	0.200691	−	0.200691i	0.800296	+	0.599605i	$0.204676\pi$
$710$	−1069.70			−0.0565423
$711$		0			0
$712$		−	11556.1i		−	0.608261i
$713$	3207.74			0.168486
$714$		0			0
$715$	−327.903			−0.0171509
$716$			12501.4i			0.652514i
$717$		0			0
$718$	12528.3			0.651188
$719$	5780.09	−	5780.09i	0.299806	−	0.299806i	−0.541132	−	0.840938i	$-0.682004\pi$
$719$	5780.09	−	5780.09i	0.299806	−	0.299806i	0.840938	+	0.541132i	$0.182004\pi$
$720$		0			0
$721$	−539.541	−	539.541i	−0.0278690	−	0.0278690i
$722$		−	12413.8i		−	0.639879i
$723$		0			0
$724$	−11373.1	−	11373.1i	−0.583807	−	0.583807i
$725$	2192.90	+	2192.90i	0.112334	+	0.112334i
$726$		0			0
$727$	−22324.8			−1.13890			−0.569451	−	0.822026i	$-0.692844\pi$
$727$	−22324.8			−1.13890			−0.569451	+	0.822026i	$0.692844\pi$
$728$	−1129.34	+	1129.34i	−0.0574948	+	0.0574948i
$729$		0			0
$730$	−406.915			−0.0206310
$731$	−9146.36	−	13547.3i	−0.462778	−	0.685452i
$732$		0			0
$733$		−	7293.42i		−	0.367515i	−0.982972	−	0.183758i	$-0.941174\pi$
$733$		−	7293.42i		−	0.367515i	0.982972	−	0.183758i	$-0.0588261\pi$
$734$	−6976.70	+	6976.70i	−0.350838	+	0.350838i
$735$		0			0
$736$	5563.37	−	5563.37i	0.278626	−	0.278626i
$737$	3797.57	+	3797.57i	0.189804	+	0.189804i
$738$		0			0
$739$			12956.5i			0.644945i	0.946579	+	0.322472i	$0.104514\pi$
$739$			12956.5i			0.644945i	−0.946579	+	0.322472i	$0.895486\pi$
$740$			147.911i			0.00734774i
$741$		0			0
$742$	6.38547	+	6.38547i	0.000315927	+	0.000315927i
$743$	−10116.8	+	10116.8i	−0.499528	+	0.499528i	−0.911291	−	0.411763i	$-0.864913\pi$
$743$	−10116.8	+	10116.8i	−0.499528	+	0.499528i	0.411763	+	0.911291i	$0.364913\pi$
$744$		0			0
$745$	−1138.83	+	1138.83i	−0.0560048	+	0.0560048i
$746$		−	15621.3i		−	0.766673i
$747$		0			0
$748$	7979.75	+	1547.50i	0.390065	+	0.0756447i
$749$	−5864.87			−0.286112
$750$		0			0
$751$	−16468.4	+	16468.4i	−0.800189	+	0.800189i	−0.983125	−	0.182936i	$-0.941440\pi$
$751$	−16468.4	+	16468.4i	−0.800189	+	0.800189i	0.182936	+	0.983125i	$0.441440\pi$
$752$	−780.713			−0.0378586
$753$		0			0
$754$	528.878	+	528.878i	0.0255446	+	0.0255446i
$755$	−743.684	−	743.684i	−0.0358483	−	0.0358483i
$756$		0			0
$757$			615.306i			0.0295425i	0.999891	+	0.0147712i	$0.00470201\pi$
$757$			615.306i			0.0295425i	−0.999891	+	0.0147712i	$0.995298\pi$
$758$	−1847.63	−	1847.63i	−0.0885343	−	0.0885343i
$759$		0			0
$760$	1457.13	−	1457.13i	0.0695467	−	0.0695467i
$761$	2678.42			0.127586			0.0637928	−	0.997963i	$-0.479680\pi$
$761$	2678.42			0.127586			0.0637928	+	0.997963i	$0.479680\pi$
$762$		0			0
$763$		−	3088.41i		−	0.146537i
$764$	−19302.7			−0.914067
$765$		0			0
$766$	−1544.30			−0.0728432
$767$		−	11793.4i		−	0.555197i
$768$		0			0
$769$	8111.73			0.380385			0.190193	−	0.981747i	$-0.439089\pi$
$769$	8111.73			0.380385			0.190193	+	0.981747i	$0.439089\pi$
$770$	67.0374	−	67.0374i	0.00313748	−	0.00313748i
$771$		0			0
$772$	−11404.1	−	11404.1i	−0.531661	−	0.531661i
$773$		−	14345.3i		−	0.667481i	−0.942665	−	0.333740i	$-0.891689\pi$
$773$		−	14345.3i		−	0.667481i	0.942665	−	0.333740i	$-0.108311\pi$
$774$		0			0
$775$	−6724.26	−	6724.26i	−0.311668	−	0.311668i
$776$	25889.9	+	25889.9i	1.19767	+	1.19767i
$777$		0			0
$778$	11247.5			0.518307
$779$	−9434.94	+	9434.94i	−0.433943	+	0.433943i
$780$		0			0
$781$	17702.4			0.811064
$782$	837.670	−	4319.48i	0.0383057	−	0.197525i
$783$		0			0
$784$		−	5004.54i		−	0.227977i
$785$	−1846.52	+	1846.52i	−0.0839555	+	0.0839555i
$786$		0			0
$787$	−3820.33	+	3820.33i	−0.173037	+	0.173037i	−0.788312	−	0.615275i	$-0.789045\pi$
$787$	−3820.33	+	3820.33i	−0.173037	+	0.173037i	0.615275	+	0.788312i	$0.289045\pi$
$788$	−10337.7	−	10337.7i	−0.467340	−	0.467340i
$789$		0			0
$790$			1002.90i			0.0451664i
$791$			6209.09i			0.279102i
$792$		0			0
$793$	−10292.3	−	10292.3i	−0.460895	−	0.460895i
$794$	3193.74	−	3193.74i	0.142748	−	0.142748i
$795$		0			0
$796$	11095.4	−	11095.4i	0.494051	−	0.494051i
$797$			24962.7i			1.10944i	0.832038	+	0.554719i	$0.187174\pi$
$797$			24962.7i			1.10944i	−0.832038	+	0.554719i	$0.812826\pi$
$798$		0			0
$799$	−2972.66	+	2006.97i	−0.131621	+	0.0888629i
$800$	−23324.6			−1.03081
$801$		0			0
$802$	15720.0	−	15720.0i	0.692135	−	0.692135i
$803$	6734.03			0.295939
$804$		0			0
$805$	93.3092	+	93.3092i	0.00408536	+	0.00408536i
$806$	−1621.74	−	1621.74i	−0.0708728	−	0.0708728i
$807$		0			0
$808$		−	40023.0i		−	1.74258i
$809$	22875.2	+	22875.2i	0.994126	+	0.994126i	0.999983	−	0.00585676i	$-0.00186427\pi$
$809$	22875.2	+	22875.2i	0.994126	+	0.994126i	−0.00585676	+	0.999983i	$0.501864\pi$
$810$		0			0
$811$	−12837.7	+	12837.7i	−0.555848	+	0.555848i	−0.928123	−	0.372275i	$-0.878578\pi$
$811$	−12837.7	+	12837.7i	−0.555848	+	0.555848i	0.372275	+	0.928123i	$0.378578\pi$
$812$	556.061			0.0240319
$813$		0			0
$814$			951.935i			0.0409893i
$815$	−509.143			−0.0218828
$816$		0			0
$817$	28706.9			1.22928
$818$			8563.26i			0.366024i
$819$		0			0
$820$	−507.500			−0.0216130
$821$	−22482.6	+	22482.6i	−0.955721	+	0.955721i	−0.999060	−	0.0433397i	$-0.986200\pi$
$821$	−22482.6	+	22482.6i	−0.955721	+	0.955721i	0.0433397	+	0.999060i	$0.486200\pi$
$822$		0			0
$823$	−23777.0	−	23777.0i	−1.00707	−	1.00707i	−0.999975	−	0.00709128i	$-0.997743\pi$
$823$	−23777.0	−	23777.0i	−1.00707	−	1.00707i	−0.00709128	−	0.999975i	$-0.502257\pi$
$824$		−	4059.82i		−	0.171639i
$825$		0			0
$826$	2411.08	+	2411.08i	0.101565	+	0.101565i
$827$	3394.68	+	3394.68i	0.142738	+	0.142738i	0.774865	−	0.632127i	$-0.217818\pi$
$827$	3394.68	+	3394.68i	0.142738	+	0.142738i	−0.632127	+	0.774865i	$0.717818\pi$
$828$		0			0
$829$	4599.00			0.192678			0.0963389	−	0.995349i	$-0.469287\pi$
$829$	4599.00			0.192678			0.0963389	+	0.995349i	$0.469287\pi$
$830$	193.294	−	193.294i	0.00808352	−	0.00808352i
$831$		0			0
$832$	−3179.83			−0.132501
$833$	−12865.1	−	19055.4i	−0.535114	−	0.792594i
$834$		0			0
$835$			3040.71i			0.126022i
$836$	−10094.2	+	10094.2i	−0.417600	+	0.417600i
$837$		0			0
$838$	6488.45	−	6488.45i	0.267470	−	0.267470i
$839$	−21296.4	−	21296.4i	−0.876321	−	0.876321i	0.116831	−	0.993152i	$-0.462726\pi$
$839$	−21296.4	−	21296.4i	−0.876321	−	0.876321i	−0.993152	+	0.116831i	$0.962726\pi$
$840$		0			0
$841$			23766.9i			0.974493i
$842$		−	9561.23i		−	0.391332i
$843$		0			0
$844$	1699.34	+	1699.34i	0.0693054	+	0.0693054i
$845$	1032.04	−	1032.04i	0.0420156	−	0.0420156i
$846$		0			0
$847$	2533.44	−	2533.44i	0.102775	−	0.102775i
$848$		−	23.7831i		−	0.000963108i
$849$		0			0
$850$	−10810.7	+	7298.79i	−0.436242	+	0.294525i
$851$	−1325.00			−0.0533728
$852$		0			0
$853$	−30470.1	+	30470.1i	−1.22307	+	1.22307i	−0.256531	+	0.966536i	$0.582579\pi$
$853$	−30470.1	+	30470.1i	−1.22307	+	1.22307i	−0.966536	+	0.256531i	$0.917421\pi$
$854$	4208.36			0.168627
$855$		0			0
$856$	−22065.3	−	22065.3i	−0.881049	−	0.881049i
$857$	8446.07	+	8446.07i	0.336654	+	0.336654i	0.855106	−	0.518453i	$-0.173492\pi$
$857$	8446.07	+	8446.07i	0.336654	+	0.336654i	−0.518453	+	0.855106i	$0.673492\pi$
$858$		0			0
$859$			11237.0i			0.446335i	0.974780	+	0.223168i	$0.0716397\pi$
$859$			11237.0i			0.446335i	−0.974780	+	0.223168i	$0.928360\pi$
$860$	772.062	+	772.062i	0.0306129	+	0.0306129i
$861$		0			0
$862$	−904.256	+	904.256i	−0.0357298	+	0.0357298i
$863$	22755.7			0.897583			0.448791	−	0.893637i	$-0.351855\pi$
$863$	22755.7			0.897583			0.448791	+	0.893637i	$0.351855\pi$
$864$		0			0
$865$			81.0656i			0.00318649i
$866$	15127.5			0.593597
$867$		0			0
$868$	−1705.09			−0.0666759
$869$		−	16596.9i		−	0.647884i
$870$		0			0
$871$	5344.74			0.207921
$872$	11619.5	−	11619.5i	0.451245	−	0.451245i
$873$		0			0
$874$	5464.02	+	5464.02i	0.211468	+	0.211468i
$875$		−	784.481i		−	0.0303089i
$876$		0			0
$877$	25825.6	+	25825.6i	0.994378	+	0.994378i	0.999984	−	0.00560613i	$-0.00178450\pi$
$877$	25825.6	+	25825.6i	0.994378	+	0.994378i	−0.00560613	+	0.999984i	$0.501784\pi$
$878$	17375.6	+	17375.6i	0.667881	+	0.667881i
$879$		0			0
$880$	−249.686			−0.00956466
$881$	−13415.9	+	13415.9i	−0.513045	+	0.513045i	−0.915458	−	0.402413i	$-0.868171\pi$
$881$	−13415.9	+	13415.9i	−0.513045	+	0.513045i	0.402413	+	0.915458i	$0.368171\pi$
$882$		0			0
$883$	28154.1			1.07300			0.536501	−	0.843899i	$-0.319746\pi$
$883$	28154.1			1.07300			0.536501	+	0.843899i	$0.319746\pi$
$884$	6704.37	−	4526.40i	0.255082	−	0.172217i
$885$		0			0
$886$		−	7642.16i		−	0.289778i
$887$	10563.8	−	10563.8i	0.399884	−	0.399884i	−0.478308	−	0.878192i	$-0.658750\pi$
$887$	10563.8	−	10563.8i	0.399884	−	0.399884i	0.878192	+	0.478308i	$0.158750\pi$
$888$		0			0
$889$	−6336.94	+	6336.94i	−0.239071	+	0.239071i
$890$	482.716	+	482.716i	0.0181805	+	0.0181805i
$891$		0			0
$892$			6190.89i			0.232384i
$893$		−	6299.09i		−	0.236048i
$894$		0			0
$895$	−1247.50	−	1247.50i	−0.0465913	−	0.0465913i
$896$	−3457.22	+	3457.22i	−0.128904	+	0.128904i
$897$		0			0
$898$	−11932.5	+	11932.5i	−0.443422	+	0.443422i
$899$			1907.55i			0.0707680i
$900$		0			0
$901$	−61.1389	−	90.5571i	−0.00226064	−	0.00334838i
$902$	−3266.19			−0.120568
$903$		0			0
$904$	−23360.4	+	23360.4i	−0.859463	+	0.859463i
$905$	2269.80			0.0833708
$906$		0			0
$907$	36144.8	+	36144.8i	1.32323	+	1.32323i	0.911148	+	0.412080i	$0.135198\pi$
$907$	36144.8	+	36144.8i	1.32323	+	1.32323i	0.412080	+	0.911148i	$0.364802\pi$
$908$	−13748.1	−	13748.1i	−0.502474	−	0.502474i
$909$		0			0
$910$		−	94.3491i		−	0.00343697i
$911$	7029.06	+	7029.06i	0.255634	+	0.255634i	0.823276	−	0.567641i	$-0.192144\pi$
$911$	7029.06	+	7029.06i	0.255634	+	0.255634i	−0.567641	+	0.823276i	$0.692144\pi$
$912$		0			0
$913$	−3198.81	+	3198.81i	−0.115953	+	0.115953i
$914$	19528.5			0.706725
$915$		0			0
$916$			14779.0i			0.533092i
$917$	6873.93			0.247543
$918$		0			0
$919$	−20224.2			−0.725937			−0.362968	−	0.931801i	$-0.618237\pi$
$919$	−20224.2			−0.725937			−0.362968	+	0.931801i	$0.618237\pi$
$920$			702.113i			0.0251608i
$921$		0			0
$922$	21173.8			0.756315
$923$	12457.2	−	12457.2i	0.444242	−	0.444242i
$924$		0			0
$925$	2777.54	+	2777.54i	0.0987297	+	0.0987297i
$926$		−	11641.5i		−	0.413137i
$927$		0			0
$928$	3308.38	+	3308.38i	0.117029	+	0.117029i
$929$	840.813	+	840.813i	0.0296945	+	0.0296945i	0.721798	−	0.692104i	$-0.243316\pi$
$929$	840.813	+	840.813i	0.0296945	+	0.0296945i	−0.692104	+	0.721798i	$0.743316\pi$
$930$		0			0
$931$	40378.6			1.42143
$932$	864.404	−	864.404i	0.0303804	−	0.0303804i
$933$		0			0
$934$	−5307.44			−0.185937
$935$	−950.709	+	641.863i	−0.0332529	+	0.0224505i
$936$		0			0
$937$			37390.7i			1.30363i	0.758378	+	0.651815i	$0.225992\pi$
$937$			37390.7i			1.30363i	−0.758378	+	0.651815i	$0.774008\pi$
$938$	−1092.69	+	1092.69i	−0.0380359	+	0.0380359i
$939$		0			0
$940$	169.412	−	169.412i	0.00587832	−	0.00587832i
$941$	26248.6	+	26248.6i	0.909331	+	0.909331i	0.996218	−	0.0868875i	$-0.0276921\pi$
$941$	26248.6	+	26248.6i	0.909331	+	0.909331i	−0.0868875	+	0.996218i	$0.527692\pi$
$942$		0			0
$943$		−	4546.21i		−	0.156993i
$944$		−	8980.25i		−	0.309621i
$945$		0			0
$946$	4968.88	+	4968.88i	0.170774	+	0.170774i
$947$	−36161.1	+	36161.1i	−1.24084	+	1.24084i	−0.281192	+	0.959651i	$0.590730\pi$
$947$	−36161.1	+	36161.1i	−1.24084	+	1.24084i	−0.959651	+	0.281192i	$0.909270\pi$
$948$		0			0
$949$	4738.77	−	4738.77i	0.162094	−	0.162094i
$950$		−	22908.1i		−	0.782353i
$951$		0			0
$952$	−1063.70	+	5485.03i	−0.0362131	+	0.186734i
$953$	1138.42			0.0386958			0.0193479	−	0.999813i	$-0.493841\pi$
$953$	1138.42			0.0386958			0.0193479	+	0.999813i	$0.493841\pi$
$954$		0			0
$955$	1926.18	−	1926.18i	0.0652669	−	0.0652669i
$956$	24686.3			0.835159
$957$		0			0
$958$	2474.46	+	2474.46i	0.0834510	+	0.0834510i
$959$	−4076.02	−	4076.02i	−0.137249	−	0.137249i
$960$		0			0
$961$			23941.7i			0.803656i
$962$	669.881	+	669.881i	0.0224510	+	0.0224510i
$963$		0			0
$964$	4499.80	−	4499.80i	0.150341	−	0.150341i
$965$	2275.99			0.0759241
$966$		0			0
$967$		−	4270.42i		−	0.142014i	−0.997476	−	0.0710070i	$-0.977379\pi$
$967$		−	4270.42i		−	0.142014i	0.997476	−	0.0710070i	$-0.0226213\pi$
$968$	19063.1			0.632966
$969$		0			0
$970$	−2162.93			−0.0715954
$971$			8703.18i			0.287640i	0.989604	+	0.143820i	$0.0459386\pi$
$971$			8703.18i			0.287640i	−0.989604	+	0.143820i	$0.954061\pi$
$972$		0			0
$973$	−9522.39			−0.313745
$974$	3521.55	−	3521.55i	0.115850	−	0.115850i
$975$		0			0
$976$	−7837.17	−	7837.17i	−0.257031	−	0.257031i
$977$			10690.5i			0.350072i	0.984562	+	0.175036i	$0.0560041\pi$
$977$			10690.5i			0.350072i	−0.984562	+	0.175036i	$0.943996\pi$
$978$		0			0
$979$	−7988.46	−	7988.46i	−0.260789	−	0.260789i
$980$	1085.97	+	1085.97i	0.0353980	+	0.0353980i
$981$		0			0
$982$	−8248.51			−0.268045
$983$	−31067.0	+	31067.0i	−1.00802	+	1.00802i	−0.00805257	+	0.999968i	$0.502563\pi$
$983$	−31067.0	+	31067.0i	−1.00802	+	1.00802i	−0.999968	+	0.00805257i	$0.997437\pi$
$984$		0			0
$985$	2063.16			0.0667387
$986$	2568.68	+	498.139i	0.0829648	+	0.0160892i
$987$		0			0
$988$			14206.6i			0.457462i
$989$	−6916.17	+	6916.17i	−0.222367	+	0.222367i
$990$		0			0
$991$	11977.7	−	11977.7i	0.383939	−	0.383939i	−0.488580	−	0.872519i	$-0.662485\pi$
$991$	11977.7	−	11977.7i	0.383939	−	0.383939i	0.872519	+	0.488580i	$0.162485\pi$
$992$	−10144.8	−	10144.8i	−0.324694	−	0.324694i
$993$		0			0
$994$			5093.59i			0.162534i
$995$			2214.37i			0.0705531i
$996$		0			0
$997$	7884.24	+	7884.24i	0.250448	+	0.250448i	0.821154	−	0.570706i	$-0.193331\pi$
$997$	7884.24	+	7884.24i	0.250448	+	0.250448i	−0.570706	+	0.821154i	$0.693331\pi$
$998$	−16039.8	+	16039.8i	−0.508749	+	0.508749i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.f.b.55.5		16
3.2	odd	2		51.4.e.a.4.4	✓	16
17.13	even	4	inner	153.4.f.b.64.4		16
51.8	odd	8		867.4.a.p.1.4		8
51.26	odd	8		867.4.a.q.1.4		8
51.47	odd	4		51.4.e.a.13.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.e.a.4.4	✓	16	3.2	odd	2
51.4.e.a.13.5	yes	16	51.47	odd	4
153.4.f.b.55.5		16	1.1	even	1	trivial
153.4.f.b.64.4		16	17.13	even	4	inner
867.4.a.p.1.4		8	51.8	odd	8
867.4.a.q.1.4		8	51.26	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.49668i q^{2} +5.75996 q^{4} +(-0.574777 + 0.574777i) q^{5} +(2.73692 + 2.73692i) q^{7} +20.5942i q^{8} +(-0.860255 - 0.860255i) q^{10} +(14.2363 + 14.2363i) q^{11} +20.0363 q^{13} +(-4.09628 + 4.09628i) q^{14} +15.2569 q^{16} +(58.0925 - 39.2207i) q^{17} +123.098i q^{19} +(-3.31070 + 3.31070i) q^{20} +(-21.3072 + 21.3072i) q^{22} +(-29.6574 - 29.6574i) q^{23} +124.339i q^{25} +29.9879i q^{26} +(15.7646 + 15.7646i) q^{28} +(17.6364 - 17.6364i) q^{29} +(-54.0799 + 54.0799i) q^{31} +187.588i q^{32} +(58.7006 + 86.9456i) q^{34} -3.14624 q^{35} +(22.3384 - 22.3384i) q^{37} -184.238 q^{38} +(-11.8371 - 11.8371i) q^{40} +(76.6455 + 76.6455i) q^{41} -233.202i q^{43} +(82.0007 + 82.0007i) q^{44} +(44.3874 - 44.3874i) q^{46} -51.1712 q^{47} -328.019i q^{49} -186.095 q^{50} +115.409 q^{52} -1.55884i q^{53} -16.3654 q^{55} +(-56.3647 + 56.3647i) q^{56} +(26.3960 + 26.3960i) q^{58} -588.603i q^{59} +(-513.681 - 513.681i) q^{61} +(-80.9401 - 80.9401i) q^{62} -158.703 q^{64} +(-11.5164 + 11.5164i) q^{65} +266.752 q^{67} +(334.611 - 225.910i) q^{68} -4.70890i q^{70} +(621.733 - 621.733i) q^{71} +(236.509 - 236.509i) q^{73} +(33.4333 + 33.4333i) q^{74} +709.043i q^{76} +77.9274i q^{77} +(-582.906 - 582.906i) q^{79} +(-8.76932 + 8.76932i) q^{80} +(-114.713 + 114.713i) q^{82} +224.694i q^{83} +(-10.8471 + 55.9334i) q^{85} +349.028 q^{86} +(-293.186 + 293.186i) q^{88} -561.132 q^{89} +(54.8379 + 54.8379i) q^{91} +(-170.825 - 170.825i) q^{92} -76.5866i q^{94} +(-70.7542 - 70.7542i) q^{95} +(1257.15 - 1257.15i) q^{97} +490.937 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 48 q^{4} + 32 q^{5} - 8 q^{7} - 20 q^{10} - 96 q^{11} + 120 q^{13} + 288 q^{14} - 200 q^{16} - 16 q^{17} - 384 q^{20} + 4 q^{22} - 208 q^{23} + 904 q^{28} - 320 q^{29} - 624 q^{31} - 788 q^{34} + 1184 q^{35}+ \cdots + 1208 q^{98}+O(q^{100}) \) 16 * q - 48 * q^4 + 32 * q^5 - 8 * q^7 - 20 * q^10 - 96 * q^11 + 120 * q^13 + 288 * q^14 - 200 * q^16 - 16 * q^17 - 384 * q^20 + 4 * q^22 - 208 * q^23 + 904 * q^28 - 320 * q^29 - 624 * q^31 - 788 * q^34 + 1184 * q^35 + 256 * q^37 + 168 * q^38 - 664 * q^40 - 800 * q^41 - 128 * q^44 + 572 * q^46 - 368 * q^47 + 720 * q^50 - 3160 * q^52 + 4296 * q^55 - 576 * q^56 + 1368 * q^58 - 1296 * q^61 - 536 * q^62 + 1752 * q^64 + 4288 * q^65 - 1248 * q^67 + 240 * q^68 - 1488 * q^71 - 1208 * q^73 - 2272 * q^74 - 1256 * q^79 - 384 * q^80 + 3564 * q^82 + 3216 * q^85 - 3224 * q^86 - 1296 * q^88 + 2608 * q^89 - 56 * q^91 + 5072 * q^92 - 160 * q^95 - 4456 * q^97 + 1208 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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