LMFDB - Embedded newform 684.3.g.b.343.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.2
Root			$1.94929 - 0.447510i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.b.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94929 + 0.447510i) q^{2} +(3.59947 - 1.74465i) q^{4} +3.90374 q^{5} +2.64664i q^{7} +(-6.23566 + 5.01164i) q^{8} +O(q^{10})$	\(q+(-1.94929 + 0.447510i) q^{2} +(3.59947 - 1.74465i) q^{4} +3.90374 q^{5} +2.64664i q^{7} +(-6.23566 + 5.01164i) q^{8} +(-7.60953 + 1.74696i) q^{10} -13.2532i q^{11} +1.60050 q^{13} +(-1.18440 - 5.15907i) q^{14} +(9.91236 - 12.5597i) q^{16} -8.10013 q^{17} -4.35890i q^{19} +(14.0514 - 6.81068i) q^{20} +(5.93094 + 25.8343i) q^{22} -38.2047i q^{23} -9.76079 q^{25} +(-3.11984 + 0.716239i) q^{26} +(4.61747 + 9.52650i) q^{28} +51.1656 q^{29} -13.6518i q^{31} +(-13.7015 + 28.9183i) q^{32} +(15.7895 - 3.62489i) q^{34} +10.3318i q^{35} -35.3910 q^{37} +(1.95065 + 8.49676i) q^{38} +(-24.3424 + 19.5641i) q^{40} -8.06155 q^{41} -16.2115i q^{43} +(-23.1223 - 47.7045i) q^{44} +(17.0970 + 74.4721i) q^{46} +1.59429i q^{47} +41.9953 q^{49} +(19.0266 - 4.36805i) q^{50} +(5.76095 - 2.79232i) q^{52} -56.8772 q^{53} -51.7371i q^{55} +(-13.2640 - 16.5036i) q^{56} +(-99.7366 + 22.8971i) q^{58} +106.526i q^{59} -35.9021 q^{61} +(6.10933 + 26.6114i) q^{62} +(13.7670 - 62.5018i) q^{64} +6.24794 q^{65} -47.5191i q^{67} +(-29.1562 + 14.1319i) q^{68} +(-4.62359 - 20.1397i) q^{70} -125.941i q^{71} +34.2172 q^{73} +(68.9874 - 15.8378i) q^{74} +(-7.60477 - 15.6897i) q^{76} +35.0765 q^{77} -71.1726i q^{79} +(38.6953 - 49.0297i) q^{80} +(15.7143 - 3.60763i) q^{82} -149.310i q^{83} -31.6208 q^{85} +(7.25479 + 31.6008i) q^{86} +(66.4202 + 82.6425i) q^{88} +169.809 q^{89} +4.23595i q^{91} +(-66.6541 - 137.517i) q^{92} +(-0.713460 - 3.10773i) q^{94} -17.0160i q^{95} +109.526 q^{97} +(-81.8610 + 18.7933i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.94929	+	0.447510i	−0.974645	+	0.223755i
$2$	−1.94929	+	0.447510i	−0.974645	+	0.223755i
$3$		0			0
$3$		0			0
$4$	3.59947	−	1.74465i	0.899867	−	0.436164i
$5$	3.90374			0.780749			0.390374	−	0.920656i	$-0.372346\pi$
$5$	3.90374			0.780749			0.390374	+	0.920656i	$0.372346\pi$
$6$		0			0
$7$			2.64664i			0.378092i	0.981968	+	0.189046i	$0.0605395\pi$
$7$			2.64664i			0.378092i	−0.981968	+	0.189046i	$0.939461\pi$
$8$	−6.23566	+	5.01164i	−0.779458	+	0.626455i
$9$		0			0
$10$	−7.60953	+	1.74696i	−0.760953	+	0.174696i
$11$		−	13.2532i		−	1.20484i	−0.798181	−	0.602418i	$-0.794204\pi$
$11$		−	13.2532i		−	1.20484i	0.798181	−	0.602418i	$-0.205796\pi$
$12$		0			0
$13$	1.60050			0.123115			0.0615576	−	0.998104i	$-0.480393\pi$
$13$	1.60050			0.123115			0.0615576	+	0.998104i	$0.480393\pi$
$14$	−1.18440	−	5.15907i	−0.0845999	−	0.368505i
$15$		0			0
$16$	9.91236	−	12.5597i	0.619523	−	0.784979i
$17$	−8.10013			−0.476478			−0.238239	−	0.971207i	$-0.576570\pi$
$17$	−8.10013			−0.476478			−0.238239	+	0.971207i	$0.576570\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	14.0514	−	6.81068i	0.702570	−	0.340534i
$21$		0			0
$22$	5.93094	+	25.8343i	0.269588	+	1.17429i
$23$		−	38.2047i		−	1.66108i	−0.556962	−	0.830538i	$-0.688033\pi$
$23$		−	38.2047i		−	1.66108i	0.556962	−	0.830538i	$-0.311967\pi$
$24$		0			0
$25$	−9.76079			−0.390431
$26$	−3.11984	+	0.716239i	−0.119994	+	0.0275477i
$27$		0			0
$28$	4.61747	+	9.52650i	0.164910	+	0.340232i
$29$	51.1656			1.76433			0.882165	−	0.470940i	$-0.156085\pi$
$29$	51.1656			1.76433			0.882165	+	0.470940i	$0.156085\pi$
$30$		0			0
$31$		−	13.6518i		−	0.440381i	−0.975457	−	0.220191i	$-0.929332\pi$
$31$		−	13.6518i		−	0.440381i	0.975457	−	0.220191i	$-0.0706679\pi$
$32$	−13.7015	+	28.9183i	−0.428172	+	0.903697i
$33$		0			0
$34$	15.7895	−	3.62489i	0.464397	−	0.106614i
$35$			10.3318i			0.295195i
$36$		0			0
$37$	−35.3910			−0.956514			−0.478257	−	0.878220i	$-0.658731\pi$
$37$	−35.3910			−0.956514			−0.478257	+	0.878220i	$0.658731\pi$
$38$	1.95065	+	8.49676i	0.0513329	+	0.223599i
$39$		0			0
$40$	−24.3424	+	19.5641i	−0.608561	+	0.489104i
$41$	−8.06155			−0.196623			−0.0983116	−	0.995156i	$-0.531344\pi$
$41$	−8.06155			−0.196623			−0.0983116	+	0.995156i	$0.531344\pi$
$42$		0			0
$43$		−	16.2115i		−	0.377010i	−0.982072	−	0.188505i	$-0.939636\pi$
$43$		−	16.2115i		−	0.377010i	0.982072	−	0.188505i	$-0.0603643\pi$
$44$	−23.1223	−	47.7045i	−0.525506	−	1.08419i
$45$		0			0
$46$	17.0970	+	74.4721i	0.371674	+	1.61896i
$47$			1.59429i			0.0339210i	0.999856	+	0.0169605i	$0.00539895\pi$
$47$			1.59429i			0.0339210i	−0.999856	+	0.0169605i	$0.994601\pi$
$48$		0			0
$49$	41.9953			0.857047
$50$	19.0266	−	4.36805i	0.380532	−	0.0873610i
$51$		0			0
$52$	5.76095	−	2.79232i	0.110787	−	0.0536984i
$53$	−56.8772			−1.07315			−0.536577	−	0.843851i	$-0.680283\pi$
$53$	−56.8772			−1.07315			−0.536577	+	0.843851i	$0.680283\pi$
$54$		0			0
$55$		−	51.7371i		−	0.940675i
$56$	−13.2640	−	16.5036i	−0.236857	−	0.294706i
$57$		0			0
$58$	−99.7366	+	22.8971i	−1.71960	+	0.394778i
$59$			106.526i			1.80553i	0.430135	+	0.902765i	$0.358466\pi$
$59$			106.526i			1.80553i	−0.430135	+	0.902765i	$0.641534\pi$
$60$		0			0
$61$	−35.9021			−0.588558			−0.294279	−	0.955720i	$-0.595080\pi$
$61$	−35.9021			−0.588558			−0.294279	+	0.955720i	$0.595080\pi$
$62$	6.10933	+	26.6114i	0.0985375	+	0.429216i
$63$		0			0
$64$	13.7670	−	62.5018i	0.215109	−	0.976590i
$65$	6.24794			0.0961221
$66$		0			0
$67$		−	47.5191i		−	0.709240i	−0.935011	−	0.354620i	$-0.884610\pi$
$67$		−	47.5191i		−	0.709240i	0.935011	−	0.354620i	$-0.115390\pi$
$68$	−29.1562	+	14.1319i	−0.428767	+	0.207822i
$69$		0			0
$70$	−4.62359	−	20.1397i	−0.0660513	−	0.287710i
$71$		−	125.941i		−	1.77382i	−0.461941	−	0.886911i	$-0.652847\pi$
$71$		−	125.941i		−	1.77382i	0.461941	−	0.886911i	$-0.347153\pi$
$72$		0			0
$73$	34.2172			0.468729			0.234364	−	0.972149i	$-0.424699\pi$
$73$	34.2172			0.468729			0.234364	+	0.972149i	$0.424699\pi$
$74$	68.9874	−	15.8378i	0.932262	−	0.214025i
$75$		0			0
$76$	−7.60477	−	15.6897i	−0.100063	−	0.206444i
$77$	35.0765			0.455539
$78$		0			0
$79$		−	71.1726i		−	0.900919i	−0.892797	−	0.450460i	$-0.851260\pi$
$79$		−	71.1726i		−	0.900919i	0.892797	−	0.450460i	$-0.148740\pi$
$80$	38.6953	−	49.0297i	0.483692	−	0.612871i
$81$		0			0
$82$	15.7143	−	3.60763i	0.191638	−	0.0439954i
$83$		−	149.310i		−	1.79891i	−0.437010	−	0.899457i	$-0.643962\pi$
$83$		−	149.310i		−	1.79891i	0.437010	−	0.899457i	$-0.356038\pi$
$84$		0			0
$85$	−31.6208			−0.372010
$86$	7.25479	+	31.6008i	0.0843580	+	0.367452i
$87$		0			0
$88$	66.4202	+	82.6425i	0.754776	+	0.939119i
$89$	169.809			1.90797			0.953983	−	0.299861i	$-0.0969405\pi$
$89$	169.809			1.90797			0.953983	+	0.299861i	$0.0969405\pi$
$90$		0			0
$91$			4.23595i			0.0465488i
$92$	−66.6541	−	137.517i	−0.724501	−	1.49475i
$93$		0			0
$94$	−0.713460	−	3.10773i	−0.00758999	−	0.0330610i
$95$		−	17.0160i		−	0.179116i
$96$		0			0
$97$	109.526			1.12914			0.564569	−	0.825386i	$-0.309042\pi$
$97$	109.526			1.12914			0.564569	+	0.825386i	$0.309042\pi$
$98$	−81.8610	+	18.7933i	−0.835317	+	0.191769i
$99$		0			0
$100$	−35.1336	+	17.0292i	−0.351336	+	0.170292i
$101$	118.435			1.17263			0.586313	−	0.810084i	$-0.300579\pi$
$101$	118.435			1.17263			0.586313	+	0.810084i	$0.300579\pi$
$102$		0			0
$103$		−	34.5985i		−	0.335908i	−0.985795	−	0.167954i	$-0.946284\pi$
$103$		−	34.5985i		−	0.335908i	0.985795	−	0.167954i	$-0.0537160\pi$
$104$	−9.98017	+	8.02112i	−0.0959632	+	0.0771261i
$105$		0			0
$106$	110.870	−	25.4531i	1.04595	−	0.240124i
$107$		−	85.2253i		−	0.796498i	−0.917277	−	0.398249i	$-0.869618\pi$
$107$		−	85.2253i		−	0.796498i	0.917277	−	0.398249i	$-0.130382\pi$
$108$		0			0
$109$	146.541			1.34442			0.672208	−	0.740362i	$-0.265346\pi$
$109$	146.541			1.34442			0.672208	+	0.740362i	$0.265346\pi$
$110$	23.1529	+	100.851i	0.210481	+	0.916824i
$111$		0			0
$112$	33.2409	+	26.2345i	0.296794	+	0.234236i
$113$	−36.0565			−0.319084			−0.159542	−	0.987191i	$-0.551002\pi$
$113$	−36.0565			−0.319084			−0.159542	+	0.987191i	$0.551002\pi$
$114$		0			0
$115$		−	149.141i		−	1.29688i
$116$	184.169	−	89.2662i	1.58766	−	0.769537i
$117$		0			0
$118$	−47.6716	−	207.651i	−0.403996	−	1.75975i
$119$		−	21.4381i		−	0.180152i
$120$		0			0
$121$	−54.6474			−0.451631
$122$	69.9836	−	16.0665i	0.573636	−	0.131693i
$123$		0			0
$124$	−23.8177	−	49.1393i	−0.192078	−	0.396285i
$125$	−135.697			−1.08558
$126$		0			0
$127$			103.364i			0.813890i	0.913453	+	0.406945i	$0.133406\pi$
$127$			103.364i			0.813890i	−0.913453	+	0.406945i	$0.866594\pi$
$128$	1.13432	+	127.995i	0.00886188	+	0.999961i
$129$		0			0
$130$	−12.1790	+	2.79601i	−0.0936850	+	0.0215078i
$131$			85.6520i			0.653832i	0.945053	+	0.326916i	$0.106009\pi$
$131$			85.6520i			0.653832i	−0.945053	+	0.326916i	$0.893991\pi$
$132$		0			0
$133$	11.5364			0.0867402
$134$	21.2653	+	92.6285i	0.158696	+	0.691257i
$135$		0			0
$136$	50.5097	−	40.5949i	0.371395	−	0.298492i
$137$	−89.4114			−0.652638			−0.326319	−	0.945260i	$-0.605808\pi$
$137$	−89.4114			−0.652638			−0.326319	+	0.945260i	$0.605808\pi$
$138$		0			0
$139$		−	175.314i		−	1.26125i	−0.776087	−	0.630625i	$-0.782799\pi$
$139$		−	175.314i		−	1.26125i	0.776087	−	0.630625i	$-0.217201\pi$
$140$	18.0254	+	37.1890i	0.128753	+	0.265636i
$141$		0			0
$142$	56.3600	+	245.496i	0.396901	+	1.72885i
$143$		−	21.2117i		−	0.148334i
$144$		0			0
$145$	199.737			1.37750
$146$	−66.6993	+	15.3125i	−0.456844	+	0.104880i
$147$		0			0
$148$	−127.389	+	61.7451i	−0.860736	+	0.417197i
$149$	−207.665			−1.39372			−0.696862	−	0.717205i	$-0.745421\pi$
$149$	−207.665			−1.39372			−0.696862	+	0.717205i	$0.745421\pi$
$150$		0			0
$151$		−	33.2962i		−	0.220504i	−0.993904	−	0.110252i	$-0.964834\pi$
$151$		−	33.2962i		−	0.220504i	0.993904	−	0.110252i	$-0.0351659\pi$
$152$	21.8452	+	27.1806i	0.143719	+	0.178820i
$153$		0			0
$154$	−68.3742	+	15.6971i	−0.443989	+	0.101929i
$155$		−	53.2932i		−	0.343827i
$156$		0			0
$157$	−232.843			−1.48308			−0.741539	−	0.670910i	$-0.765904\pi$
$157$	−232.843			−1.48308			−0.741539	+	0.670910i	$0.765904\pi$
$158$	31.8505	+	138.736i	0.201585	+	0.878077i
$159$		0			0
$160$	−53.4872	+	112.890i	−0.334295	+	0.705561i
$161$	101.114			0.628039
$162$		0			0
$163$		−	133.148i		−	0.816858i	−0.912790	−	0.408429i	$-0.866077\pi$
$163$		−	133.148i		−	0.816858i	0.912790	−	0.408429i	$-0.133923\pi$
$164$	−29.0173	+	14.0646i	−0.176935	+	0.0857599i
$165$		0			0
$166$	66.8177	+	291.048i	0.402516	+	1.75330i
$167$		−	84.0944i		−	0.503559i	−0.967785	−	0.251780i	$-0.918984\pi$
$167$		−	84.0944i		−	0.503559i	0.967785	−	0.251780i	$-0.0810158\pi$
$168$		0			0
$169$	−166.438			−0.984843
$170$	61.6382	−	14.1506i	0.362578	−	0.0832390i
$171$		0			0
$172$	−28.2834	−	58.3526i	−0.164438	−	0.339259i
$173$	−40.8353			−0.236042			−0.118021	−	0.993011i	$-0.537655\pi$
$173$	−40.8353			−0.236042			−0.118021	+	0.993011i	$0.537655\pi$
$174$		0			0
$175$		−	25.8333i		−	0.147619i
$176$	−166.456	−	131.371i	−0.945771	−	0.746424i
$177$		0			0
$178$	−331.007	+	75.9912i	−1.85959	+	0.426917i
$179$			94.3723i			0.527219i	0.964629	+	0.263610i	$0.0849131\pi$
$179$			94.3723i			0.527219i	−0.964629	+	0.263610i	$0.915087\pi$
$180$		0			0
$181$	101.869			0.562811			0.281405	−	0.959589i	$-0.409199\pi$
$181$	101.869			0.562811			0.281405	+	0.959589i	$0.409199\pi$
$182$	−1.89563	−	8.25709i	−0.0104155	−	0.0453686i
$183$		0			0
$184$	191.468	+	238.232i	1.04059	+	1.29474i
$185$	−138.157			−0.746797
$186$		0			0
$187$			107.353i			0.574078i
$188$	2.78148	+	5.73859i	0.0147951	+	0.0305244i
$189$		0			0
$190$	7.61484	+	33.1692i	0.0400781	+	0.174575i
$191$			96.9894i			0.507798i	0.967231	+	0.253899i	$0.0817131\pi$
$191$			96.9894i			0.507798i	−0.967231	+	0.253899i	$0.918287\pi$
$192$		0			0
$193$	218.158			1.13035			0.565177	−	0.824970i	$-0.308808\pi$
$193$	218.158			1.13035			0.565177	+	0.824970i	$0.308808\pi$
$194$	−213.499	+	49.0142i	−1.10051	+	0.252650i
$195$		0			0
$196$	151.161	−	73.2673i	0.771228	−	0.373813i
$197$	0.646370			0.00328107			0.00164053	−	0.999999i	$-0.499478\pi$
$197$	0.646370			0.00328107			0.00164053	+	0.999999i	$0.499478\pi$
$198$		0			0
$199$			20.5908i			0.103471i	0.998661	+	0.0517356i	$0.0164753\pi$
$199$			20.5908i			0.103471i	−0.998661	+	0.0517356i	$0.983525\pi$
$200$	60.8650	−	48.9175i	0.304325	−	0.244588i
$201$		0			0
$202$	−230.865	+	53.0010i	−1.14290	+	0.262381i
$203$			135.417i			0.667078i
$204$		0			0
$205$	−31.4702			−0.153513
$206$	15.4832	+	67.4426i	0.0751611	+	0.327391i
$207$		0			0
$208$	15.8647	−	20.1017i	0.0762727	−	0.0966429i
$209$	−57.7694			−0.276408
$210$		0			0
$211$			161.772i			0.766690i	0.923605	+	0.383345i	$0.125228\pi$
$211$			161.772i			0.766690i	−0.923605	+	0.383345i	$0.874772\pi$
$212$	−204.728	+	99.2311i	−0.965697	+	0.468071i
$213$		0			0
$214$	38.1392	+	166.129i	0.178221	+	0.776303i
$215$		−	63.2854i		−	0.294350i
$216$		0			0
$217$	36.1315			0.166504
$218$	−285.652	+	65.5787i	−1.31033	+	0.300820i
$219$		0			0
$220$	−90.2634	−	186.226i	−0.410288	−	0.846482i
$221$	−12.9642			−0.0586617
$222$		0			0
$223$			171.167i			0.767567i	0.923423	+	0.383784i	$0.125379\pi$
$223$			171.167i			0.767567i	−0.923423	+	0.383784i	$0.874621\pi$
$224$	−76.5364	−	36.2630i	−0.341680	−	0.161888i
$225$		0			0
$226$	70.2845	−	16.1356i	0.310994	−	0.0713966i
$227$			110.173i			0.485343i	0.970109	+	0.242672i	$0.0780237\pi$
$227$			110.173i			0.485343i	−0.970109	+	0.242672i	$0.921976\pi$
$228$		0			0
$229$	184.830			0.807120			0.403560	−	0.914953i	$-0.367773\pi$
$229$	184.830			0.807120			0.403560	+	0.914953i	$0.367773\pi$
$230$	66.7423	+	290.720i	0.290184	+	1.26400i
$231$		0			0
$232$	−319.051	+	256.423i	−1.37522	+	1.10527i
$233$	226.138			0.970550			0.485275	−	0.874362i	$-0.338719\pi$
$233$	226.138			0.970550			0.485275	+	0.874362i	$0.338719\pi$
$234$		0			0
$235$			6.22369i			0.0264838i
$236$	185.851	+	383.438i	0.787506	+	1.62474i
$237$		0			0
$238$	9.59378	+	41.7891i	0.0403100	+	0.175585i
$239$			282.285i			1.18111i	0.806999	+	0.590553i	$0.201090\pi$
$239$			282.285i			1.18111i	−0.806999	+	0.590553i	$0.798910\pi$
$240$		0			0
$241$	−8.68875			−0.0360529			−0.0180265	−	0.999838i	$-0.505738\pi$
$241$	−8.68875			−0.0360529			−0.0180265	+	0.999838i	$0.505738\pi$
$242$	106.524	−	24.4552i	0.440180	−	0.101055i
$243$		0			0
$244$	−129.228	+	62.6367i	−0.529624	+	0.256708i
$245$	163.939			0.669138
$246$		0			0
$247$		−	6.97641i		−	0.0282446i
$248$	68.4180	+	85.1281i	0.275879	+	0.343259i
$249$		0			0
$250$	264.513	−	60.7259i	1.05805	−	0.242903i
$251$		−	273.275i		−	1.08874i	−0.838844	−	0.544372i	$-0.816768\pi$
$251$		−	273.275i		−	1.08874i	0.838844	−	0.544372i	$-0.183232\pi$
$252$		0			0
$253$	−506.335			−2.00132
$254$	−46.2565	−	201.487i	−0.182112	−	0.793255i
$255$		0			0
$256$	−59.4902	−	248.992i	−0.232383	−	0.972624i
$257$	−225.614			−0.877877			−0.438938	−	0.898517i	$-0.644645\pi$
$257$	−225.614			−0.877877			−0.438938	+	0.898517i	$0.644645\pi$
$258$		0			0
$259$		−	93.6673i		−	0.361650i
$260$	22.4893	−	10.9005i	0.0864971	−	0.0419250i
$261$		0			0
$262$	−38.3301	−	166.961i	−0.146298	−	0.637255i
$263$			153.711i			0.584454i	0.956349	+	0.292227i	$0.0943962\pi$
$263$			153.711i			0.584454i	−0.956349	+	0.292227i	$0.905604\pi$
$264$		0			0
$265$	−222.034			−0.837864
$266$	−22.4879	+	5.16267i	−0.0845409	+	0.0194085i
$267$		0			0
$268$	−82.9044	−	171.043i	−0.309345	−	0.638222i
$269$	266.196			0.989575			0.494788	−	0.869014i	$-0.335246\pi$
$269$	266.196			0.989575			0.494788	+	0.869014i	$0.335246\pi$
$270$		0			0
$271$		−	420.472i		−	1.55156i	−0.631005	−	0.775778i	$-0.717357\pi$
$271$		−	420.472i		−	1.55156i	0.631005	−	0.775778i	$-0.282643\pi$
$272$	−80.2914	+	101.735i	−0.295189	+	0.374025i
$273$		0			0
$274$	174.289	−	40.0125i	0.636091	−	0.146031i
$275$			129.362i			0.470406i
$276$		0			0
$277$	−51.6625			−0.186507			−0.0932536	−	0.995642i	$-0.529727\pi$
$277$	−51.6625			−0.186507			−0.0932536	+	0.995642i	$0.529727\pi$
$278$	78.4547	+	341.738i	0.282211	+	1.22927i
$279$		0			0
$280$	−51.7793	−	64.4257i	−0.184926	−	0.230092i
$281$	−412.087			−1.46650			−0.733251	−	0.679958i	$-0.761998\pi$
$281$	−412.087			−1.46650			−0.733251	+	0.679958i	$0.761998\pi$
$282$		0			0
$283$			492.048i			1.73868i	0.494211	+	0.869342i	$0.335457\pi$
$283$			492.048i			1.73868i	−0.494211	+	0.869342i	$0.664543\pi$
$284$	−219.724	−	453.322i	−0.773676	−	1.59620i
$285$		0			0
$286$	9.49246	+	41.3478i	0.0331904	+	0.144573i
$287$		−	21.3360i		−	0.0743416i
$288$		0			0
$289$	−223.388			−0.772969
$290$	−389.346	+	89.3844i	−1.34257	+	0.308222i
$291$		0			0
$292$	123.164	−	59.6972i	0.421794	−	0.204442i
$293$	462.881			1.57980			0.789899	−	0.613237i	$-0.210133\pi$
$293$	462.881			1.57980			0.789899	+	0.613237i	$0.210133\pi$
$294$		0			0
$295$			415.851i			1.40966i
$296$	220.686	−	177.367i	0.745562	−	0.599213i
$297$		0			0
$298$	404.799	−	92.9321i	1.35839	−	0.311853i
$299$		−	61.1466i		−	0.204504i
$300$		0			0
$301$	42.9059			0.142544
$302$	14.9004	+	64.9039i	0.0493390	+	0.214914i
$303$		0			0
$304$	−54.7463	−	43.2070i	−0.180086	−	0.142128i
$305$	−140.152			−0.459516
$306$		0			0
$307$			477.735i			1.55614i	0.628178	+	0.778070i	$0.283801\pi$
$307$			477.735i			1.55614i	−0.628178	+	0.778070i	$0.716199\pi$
$308$	126.257	−	61.1963i	0.409924	−	0.198689i
$309$		0			0
$310$	23.8492	+	103.884i	0.0769330	+	0.335109i
$311$			397.518i			1.27819i	0.769127	+	0.639096i	$0.220691\pi$
$311$			397.518i			1.27819i	−0.769127	+	0.639096i	$0.779309\pi$
$312$		0			0
$313$	−249.717			−0.797818			−0.398909	−	0.916991i	$-0.630611\pi$
$313$	−249.717			−0.797818			−0.398909	+	0.916991i	$0.630611\pi$
$314$	453.879	−	104.200i	1.44548	−	0.331846i
$315$		0			0
$316$	−124.172	−	256.184i	−0.392948	−	0.810708i
$317$	−17.5401			−0.0553317			−0.0276658	−	0.999617i	$-0.508807\pi$
$317$	−17.5401			−0.0553317			−0.0276658	+	0.999617i	$0.508807\pi$
$318$		0			0
$319$		−	678.108i		−	2.12573i
$320$	53.7428	−	243.991i	0.167946	−	0.762471i
$321$		0			0
$322$	−197.101	+	45.2496i	−0.612115	+	0.140527i
$323$			35.3076i			0.109312i
$324$		0			0
$325$	−15.6221			−0.0480681
$326$	59.5850	+	259.544i	0.182776	+	0.796147i
$327$		0			0
$328$	50.2691	−	40.4016i	0.153260	−	0.123176i
$329$	−4.21951			−0.0128252
$330$		0			0
$331$			524.291i			1.58396i	0.610546	+	0.791981i	$0.290950\pi$
$331$			524.291i			1.58396i	−0.610546	+	0.791981i	$0.709050\pi$
$332$	−260.494	−	537.436i	−0.784621	−	1.61878i
$333$		0			0
$334$	37.6331	+	163.924i	0.112674	+	0.490792i
$335$		−	185.502i		−	0.553738i
$336$		0			0
$337$	−10.3787			−0.0307974			−0.0153987	−	0.999881i	$-0.504902\pi$
$337$	−10.3787			−0.0307974			−0.0153987	+	0.999881i	$0.504902\pi$
$338$	324.437	−	74.4829i	0.959872	−	0.220363i
$339$		0			0
$340$	−113.818	+	55.1674i	−0.334759	+	0.162257i
$341$	−180.930			−0.530587
$342$		0			0
$343$			240.832i			0.702134i
$344$	81.2459	+	101.089i	0.236180	+	0.293864i
$345$		0			0
$346$	79.5998	−	18.2742i	0.230057	−	0.0528156i
$347$		−	140.835i		−	0.405864i	−0.979193	−	0.202932i	$-0.934953\pi$
$347$		−	140.835i		−	0.405864i	0.979193	−	0.202932i	$-0.0650470\pi$
$348$		0			0
$349$	588.176			1.68532			0.842659	−	0.538447i	$-0.180989\pi$
$349$	588.176			1.68532			0.842659	+	0.538447i	$0.180989\pi$
$350$	11.5607	+	50.3566i	0.0330305	+	0.143876i
$351$		0			0
$352$	383.260	+	181.589i	1.08881	+	0.515877i
$353$	67.7579			0.191949			0.0959744	−	0.995384i	$-0.469403\pi$
$353$	67.7579			0.191949			0.0959744	+	0.995384i	$0.469403\pi$
$354$		0			0
$355$		−	491.643i		−	1.38491i
$356$	611.222	−	296.258i	1.71692	−	0.832185i
$357$		0			0
$358$	−42.2325	−	183.959i	−0.117968	−	0.513852i
$359$		−	136.276i		−	0.379598i	−0.981823	−	0.189799i	$-0.939216\pi$
$359$		−	136.276i		−	0.379598i	0.981823	−	0.189799i	$-0.0607836\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−198.572	+	45.5873i	−0.548541	+	0.125932i
$363$		0			0
$364$	7.39026	+	15.2472i	0.0203029	+	0.0418878i
$365$	133.575			0.365959
$366$		0			0
$367$			274.645i			0.748352i	0.927358	+	0.374176i	$0.122074\pi$
$367$			274.645i			0.748352i	−0.927358	+	0.374176i	$0.877926\pi$
$368$	−479.838	−	378.699i	−1.30391	−	1.02907i
$369$		0			0
$370$	269.309	−	61.8268i	0.727862	−	0.167100i
$371$		−	150.534i		−	0.405751i
$372$		0			0
$373$	7.96701			0.0213593			0.0106796	−	0.999943i	$-0.496601\pi$
$373$	7.96701			0.0213593			0.0106796	+	0.999943i	$0.496601\pi$
$374$	−48.0414	−	209.261i	−0.128453	−	0.559523i
$375$		0			0
$376$	−7.98999	−	9.94144i	−0.0212500	−	0.0264400i
$377$	81.8904			0.217216
$378$		0			0
$379$		−	514.957i		−	1.35873i	−0.733803	−	0.679363i	$-0.762256\pi$
$379$		−	514.957i		−	1.35873i	0.733803	−	0.679363i	$-0.237744\pi$
$380$	−29.6871	−	61.2487i	−0.0781239	−	0.161181i
$381$		0			0
$382$	−43.4037	−	189.061i	−0.113622	−	0.494923i
$383$			669.698i			1.74856i	0.485424	+	0.874279i	$0.338665\pi$
$383$			669.698i			1.74856i	−0.485424	+	0.874279i	$0.661335\pi$
$384$		0			0
$385$	136.930			0.355661
$386$	−425.254	+	97.6280i	−1.10169	+	0.252922i
$387$		0			0
$388$	394.237	−	191.086i	1.01607	−	0.492489i
$389$	374.922			0.963809			0.481905	−	0.876224i	$-0.339945\pi$
$389$	374.922			0.963809			0.481905	+	0.876224i	$0.339945\pi$
$390$		0			0
$391$			309.463i			0.791466i
$392$	−261.868	+	210.465i	−0.668032	+	0.536901i
$393$		0			0
$394$	−1.25996	+	0.289257i	−0.00319788	+	0.000734155i
$395$		−	277.840i		−	0.703391i
$396$		0			0
$397$	−32.0134			−0.0806384			−0.0403192	−	0.999187i	$-0.512837\pi$
$397$	−32.0134			−0.0806384			−0.0403192	+	0.999187i	$0.512837\pi$
$398$	−9.21458	−	40.1374i	−0.0231522	−	0.100848i
$399$		0			0
$400$	−96.7524	+	122.592i	−0.241881	+	0.306480i
$401$	−380.066			−0.947796			−0.473898	−	0.880580i	$-0.657153\pi$
$401$	−380.066			−0.947796			−0.473898	+	0.880580i	$0.657153\pi$
$402$		0			0
$403$		−	21.8497i		−	0.0542177i
$404$	426.304	−	206.629i	1.05521	−	0.511457i
$405$		0			0
$406$	−60.6004	−	263.967i	−0.149262	−	0.650165i
$407$			469.044i			1.15244i
$408$		0			0
$409$	116.916			0.285858			0.142929	−	0.989733i	$-0.454348\pi$
$409$	116.916			0.285858			0.142929	+	0.989733i	$0.454348\pi$
$410$	61.3446	−	14.0832i	0.149621	−	0.0343494i
$411$		0			0
$412$	−60.3625	−	124.536i	−0.146511	−	0.302273i
$413$	−281.937			−0.682655
$414$		0			0
$415$		−	582.867i		−	1.40450i
$416$	−21.9292	+	46.2837i	−0.0527145	+	0.111259i
$417$		0			0
$418$	112.609	−	25.8524i	0.269400	−	0.0618478i
$419$			0.146671i			0.000350050i	1.00000		0.000175025i	$5.57122e-5\pi$
$419$			0.146671i			0.000350050i	−1.00000		0.000175025i	$0.999944\pi$
$420$		0			0
$421$	−613.336			−1.45686			−0.728428	−	0.685123i	$-0.759749\pi$
$421$	−613.336			−1.45686			−0.728428	+	0.685123i	$0.759749\pi$
$422$	−72.3944	−	315.340i	−0.171551	−	0.747251i
$423$		0			0
$424$	354.667	−	285.048i	0.836479	−	0.672283i
$425$	79.0636			0.186032
$426$		0			0
$427$		−	95.0199i		−	0.222529i
$428$	−148.689	−	306.766i	−0.347404	−	0.716743i
$429$		0			0
$430$	28.3208	+	123.362i	0.0658624	+	0.286887i
$431$			310.234i			0.719800i	0.932991	+	0.359900i	$0.117189\pi$
$431$			310.234i			0.719800i	−0.932991	+	0.359900i	$0.882811\pi$
$432$		0			0
$433$	−194.780			−0.449838			−0.224919	−	0.974378i	$-0.572212\pi$
$433$	−194.780			−0.449838			−0.224919	+	0.974378i	$0.572212\pi$
$434$	−70.4307	+	16.1692i	−0.162283	+	0.0372562i
$435$		0			0
$436$	527.471	−	255.664i	1.20980	−	0.586385i
$437$	−166.531			−0.381077
$438$		0			0
$439$			340.063i			0.774631i	0.921947	+	0.387315i	$0.126598\pi$
$439$			340.063i			0.774631i	−0.921947	+	0.387315i	$0.873402\pi$
$440$	259.288	+	322.615i	0.589290	+	0.733216i
$441$		0			0
$442$	25.2711	−	5.80163i	0.0571744	−	0.0131259i
$443$		−	643.348i		−	1.45225i	−0.687561	−	0.726127i	$-0.741318\pi$
$443$		−	643.348i		−	1.45225i	0.687561	−	0.726127i	$-0.258682\pi$
$444$		0			0
$445$	662.891			1.48964
$446$	−76.5992	−	333.655i	−0.171747	−	0.748106i
$447$		0			0
$448$	165.420	+	36.4363i	0.369240	+	0.0813309i
$449$	416.379			0.927348			0.463674	−	0.886006i	$-0.346531\pi$
$449$	416.379			0.927348			0.463674	+	0.886006i	$0.346531\pi$
$450$		0			0
$451$			106.841i			0.236899i
$452$	−129.784	+	62.9061i	−0.287133	+	0.139173i
$453$		0			0
$454$	−49.3035	−	214.759i	−0.108598	−	0.473037i
$455$			16.5360i			0.0363430i
$456$		0			0
$457$	814.576			1.78244			0.891221	−	0.453568i	$-0.149849\pi$
$457$	814.576			1.78244			0.891221	+	0.453568i	$0.149849\pi$
$458$	−360.288	+	82.7134i	−0.786655	+	0.180597i
$459$		0			0
$460$	−260.200	−	536.830i	−0.565653	−	1.16702i
$461$	−122.745			−0.266259			−0.133129	−	0.991099i	$-0.542503\pi$
$461$	−122.745			−0.266259			−0.133129	+	0.991099i	$0.542503\pi$
$462$		0			0
$463$			348.734i			0.753206i	0.926375	+	0.376603i	$0.122908\pi$
$463$			348.734i			0.753206i	−0.926375	+	0.376603i	$0.877092\pi$
$464$	507.172	−	642.622i	1.09304	−	1.38496i
$465$		0			0
$466$	−440.809	+	101.199i	−0.945942	+	0.217165i
$467$			41.9400i			0.0898072i	0.998991	+	0.0449036i	$0.0142981\pi$
$467$			41.9400i			0.0898072i	−0.998991	+	0.0449036i	$0.985702\pi$
$468$		0			0
$469$	125.766			0.268158
$470$	−2.78516	−	12.1318i	−0.00592588	−	0.0258123i
$471$		0			0
$472$	−533.871	−	664.262i	−1.13108	−	1.40733i
$473$	−214.854			−0.454236
$474$		0			0
$475$			42.5463i			0.0895711i
$476$	−37.4021	−	77.1659i	−0.0785759	−	0.162113i
$477$		0			0
$478$	−126.325	−	550.255i	−0.264279	−	1.15116i
$479$		−	257.365i		−	0.537297i	−0.963238	−	0.268648i	$-0.913423\pi$
$479$		−	257.365i		−	0.537297i	0.963238	−	0.268648i	$-0.0865770\pi$
$480$		0			0
$481$	−56.6433			−0.117761
$482$	16.9369	−	3.88830i	0.0351388	−	0.00806702i
$483$		0			0
$484$	−196.702	+	95.3408i	−0.406408	+	0.196985i
$485$	427.563			0.881573
$486$		0			0
$487$			312.131i			0.640927i	0.947261	+	0.320463i	$0.103839\pi$
$487$			312.131i			0.640927i	−0.947261	+	0.320463i	$0.896161\pi$
$488$	223.873	−	179.928i	0.458756	−	0.368705i
$489$		0			0
$490$	−319.565	+	73.3643i	−0.652172	+	0.149723i
$491$		−	855.711i		−	1.74279i	−0.490581	−	0.871396i	$-0.663215\pi$
$491$		−	855.711i		−	1.74279i	0.490581	−	0.871396i	$-0.336785\pi$
$492$		0			0
$493$	−414.448			−0.840665
$494$	3.12201	+	13.5991i	0.00631987	+	0.0275285i
$495$		0			0
$496$	−171.462	−	135.322i	−0.345690	−	0.272826i
$497$	333.321			0.670667
$498$		0			0
$499$			437.337i			0.876427i	0.898871	+	0.438214i	$0.144389\pi$
$499$			437.337i			0.876427i	−0.898871	+	0.438214i	$0.855611\pi$
$500$	−488.438	+	236.745i	−0.976876	+	0.473489i
$501$		0			0
$502$	122.293	+	532.692i	0.243612	+	1.06114i
$503$		−	454.628i		−	0.903834i	−0.892060	−	0.451917i	$-0.850740\pi$
$503$		−	454.628i		−	0.903834i	0.892060	−	0.451917i	$-0.149260\pi$
$504$		0			0
$505$	462.341			0.915527
$506$	986.994	−	226.590i	1.95058	−	0.447806i
$507$		0			0
$508$	180.335	+	372.056i	0.354989	+	0.732393i
$509$	−330.296			−0.648912			−0.324456	−	0.945901i	$-0.605181\pi$
$509$	−330.296			−0.648912			−0.324456	+	0.945901i	$0.605181\pi$
$510$		0			0
$511$			90.5606i			0.177222i
$512$	227.390	+	458.735i	0.444121	+	0.895967i
$513$		0			0
$514$	439.788	−	100.965i	0.855619	−	0.196429i
$515$		−	135.064i		−	0.262260i
$516$		0			0
$517$	21.1294			0.0408693
$518$	41.9171	+	182.585i	0.0809210	+	0.352480i
$519$		0			0
$520$	−38.9600	+	31.3124i	−0.0749231	+	0.0602161i
$521$	156.351			0.300098			0.150049	−	0.988679i	$-0.452057\pi$
$521$	156.351			0.300098			0.150049	+	0.988679i	$0.452057\pi$
$522$		0			0
$523$			383.630i			0.733518i	0.930316	+	0.366759i	$0.119533\pi$
$523$			383.630i			0.733518i	−0.930316	+	0.366759i	$0.880467\pi$
$524$	149.433	+	308.302i	0.285178	+	0.588362i
$525$		0			0
$526$	−68.7874	−	299.628i	−0.130774	−	0.569635i
$527$			110.581i			0.209832i
$528$		0			0
$529$	−930.602			−1.75917
$530$	432.809	−	99.3624i	0.816620	−	0.187476i
$531$		0			0
$532$	41.5251	−	20.1271i	0.0780546	−	0.0378329i
$533$	−12.9025			−0.0242073
$534$		0			0
$535$		−	332.698i		−	0.621865i
$536$	238.148	+	296.313i	0.444307	+	0.552823i
$537$		0			0
$538$	−518.893	+	119.125i	−0.964485	+	0.221422i
$539$		−	556.572i		−	1.03260i
$540$		0			0
$541$	−167.893			−0.310337			−0.155169	−	0.987888i	$-0.549592\pi$
$541$	−167.893			−0.310337			−0.155169	+	0.987888i	$0.549592\pi$
$542$	188.165	+	819.622i	0.347169	+	1.51222i
$543$		0			0
$544$	110.984	−	234.242i	0.204015	−	0.430592i
$545$	572.060			1.04965
$546$		0			0
$547$		−	93.9282i		−	0.171715i	−0.996307	−	0.0858576i	$-0.972637\pi$
$547$		−	93.9282i		−	0.171715i	0.996307	−	0.0858576i	$-0.0273630\pi$
$548$	−321.834	+	155.992i	−0.587288	+	0.284657i
$549$		0			0
$550$	−57.8906	−	252.164i	−0.105256	−	0.458479i
$551$		−	223.026i		−	0.404765i
$552$		0			0
$553$	188.368			0.340630
$554$	100.705	−	23.1195i	0.181778	−	0.0417319i
$555$		0			0
$556$	−305.862	−	631.037i	−0.550112	−	1.13496i
$557$	−658.999			−1.18312			−0.591561	−	0.806260i	$-0.701488\pi$
$557$	−658.999			−1.18312			−0.591561	+	0.806260i	$0.701488\pi$
$558$		0			0
$559$		−	25.9464i		−	0.0464158i
$560$	129.764	+	102.413i	0.231721	+	0.182880i
$561$		0			0
$562$	803.277	−	184.413i	1.42932	−	0.328137i
$563$			709.470i			1.26016i	0.776531	+	0.630079i	$0.216978\pi$
$563$			709.470i			1.26016i	−0.776531	+	0.630079i	$0.783022\pi$
$564$		0			0
$565$	−140.755			−0.249124
$566$	−220.196	−	959.144i	−0.389039	−	1.69460i
$567$		0			0
$568$	631.172	+	785.328i	1.11122	+	1.38262i
$569$	−613.773			−1.07869			−0.539344	−	0.842086i	$-0.681328\pi$
$569$	−613.773			−1.07869			−0.539344	+	0.842086i	$0.681328\pi$
$570$		0			0
$571$		−	436.257i		−	0.764022i	−0.924158	−	0.382011i	$-0.875232\pi$
$571$		−	436.257i		−	0.764022i	0.924158	−	0.382011i	$-0.124768\pi$
$572$	−37.0071	−	76.3510i	−0.0646978	−	0.133481i
$573$		0			0
$574$	9.54809	+	41.5901i	0.0166343	+	0.0724567i
$575$			372.908i			0.648536i
$576$		0			0
$577$	356.629			0.618074			0.309037	−	0.951050i	$-0.399993\pi$
$577$	356.629			0.618074			0.309037	+	0.951050i	$0.399993\pi$
$578$	435.448	−	99.9683i	0.753370	−	0.172956i
$579$		0			0
$580$	718.948	−	348.473i	1.23957	−	0.600815i
$581$	395.170			0.680154
$582$		0			0
$583$			753.805i			1.29298i
$584$	−213.367	+	171.484i	−0.365354	+	0.293637i
$585$		0			0
$586$	−902.290	+	207.144i	−1.53974	+	0.353488i
$587$		−	411.394i		−	0.700842i	−0.936592	−	0.350421i	$-0.886039\pi$
$587$		−	411.394i		−	0.700842i	0.936592	−	0.350421i	$-0.113961\pi$
$588$		0			0
$589$	−59.5069			−0.101030
$590$	−186.098	−	810.615i	−0.315420	−	1.37392i
$591$		0			0
$592$	−350.809	+	444.499i	−0.592582	+	0.750843i
$593$	−110.332			−0.186057			−0.0930285	−	0.995663i	$-0.529655\pi$
$593$	−110.332			−0.186057			−0.0930285	+	0.995663i	$0.529655\pi$
$594$		0			0
$595$		−	83.6890i		−	0.140654i
$596$	−747.483	+	362.303i	−1.25417	+	0.607892i
$597$		0			0
$598$	27.3637	+	119.193i	0.0457587	+	0.199319i
$599$			679.317i			1.13408i	0.823689	+	0.567042i	$0.191912\pi$
$599$			679.317i			1.13408i	−0.823689	+	0.567042i	$0.808088\pi$
$600$		0			0
$601$	−873.422			−1.45328			−0.726641	−	0.687018i	$-0.758920\pi$
$601$	−873.422			−1.45328			−0.726641	+	0.687018i	$0.758920\pi$
$602$	−83.6361	+	19.2008i	−0.138930	+	0.0318950i
$603$		0			0
$604$	−58.0903	−	119.849i	−0.0961760	−	0.198425i
$605$	−213.329			−0.352610
$606$		0			0
$607$		−	14.0258i		−	0.0231067i	−0.999933	−	0.0115534i	$-0.996322\pi$
$607$		−	14.0258i		−	0.0231067i	0.999933	−	0.0115534i	$-0.00367763\pi$
$608$	126.052	+	59.7235i	0.207322	+	0.0982294i
$609$		0			0
$610$	273.198	−	62.7196i	0.447865	−	0.102819i
$611$			2.55165i			0.00417619i
$612$		0			0
$613$	22.8620			0.0372953			0.0186477	−	0.999826i	$-0.494064\pi$
$613$	22.8620			0.0372953			0.0186477	+	0.999826i	$0.494064\pi$
$614$	−213.791	−	931.244i	−0.348194	−	1.51668i
$615$		0			0
$616$	−218.725	+	175.791i	−0.355073	+	0.285374i
$617$	−935.677			−1.51649			−0.758247	−	0.651968i	$-0.773944\pi$
$617$	−935.677			−1.51649			−0.758247	+	0.651968i	$0.773944\pi$
$618$		0			0
$619$			256.561i			0.414476i	0.978291	+	0.207238i	$0.0664475\pi$
$619$			256.561i			0.414476i	−0.978291	+	0.207238i	$0.933553\pi$
$620$	−92.9782	−	191.827i	−0.149965	−	0.309399i
$621$		0			0
$622$	−177.893	−	774.877i	−0.286002	−	1.24578i
$623$			449.423i			0.721386i
$624$		0			0
$625$	−285.707			−0.457132
$626$	486.771	−	111.751i	0.777589	−	0.178516i
$627$		0			0
$628$	−838.112	+	406.231i	−1.33457	+	0.646865i
$629$	286.672			0.455758
$630$		0			0
$631$			530.971i			0.841476i	0.907182	+	0.420738i	$0.138229\pi$
$631$			530.971i			0.841476i	−0.907182	+	0.420738i	$0.861771\pi$
$632$	356.691	+	443.808i	0.564385	+	0.702228i
$633$		0			0
$634$	34.1908	−	7.84939i	0.0539288	−	0.0123807i
$635$			403.507i			0.635444i
$636$		0			0
$637$	67.2134			0.105516
$638$	303.460	+	1321.83i	0.475643	+	2.07183i
$639$		0			0
$640$	4.42810	+	499.660i	0.00691890	+	0.780718i
$641$	394.362			0.615230			0.307615	−	0.951511i	$-0.400469\pi$
$641$	394.362			0.615230			0.307615	+	0.951511i	$0.400469\pi$
$642$		0			0
$643$		−	4.02353i		−	0.00625743i	−0.999995	−	0.00312871i	$-0.999004\pi$
$643$		−	4.02353i		−	0.00625743i	0.999995	−	0.00312871i	$-0.000995902\pi$
$644$	363.958	−	176.409i	0.565151	−	0.273928i
$645$		0			0
$646$	−15.8005	−	68.8249i	−0.0244590	−	0.106540i
$647$			627.845i			0.970394i	0.874405	+	0.485197i	$0.161252\pi$
$647$			627.845i			0.970394i	−0.874405	+	0.485197i	$0.838748\pi$
$648$		0			0
$649$	1411.81			2.17537
$650$	30.4521	−	6.99106i	0.0468493	−	0.0107555i
$651$		0			0
$652$	−232.297	−	479.262i	−0.356284	−	0.735064i
$653$	548.722			0.840309			0.420155	−	0.907453i	$-0.361976\pi$
$653$	548.722			0.840309			0.420155	+	0.907453i	$0.361976\pi$
$654$		0			0
$655$			334.364i			0.510479i
$656$	−79.9090	+	101.250i	−0.121813	+	0.154345i
$657$		0			0
$658$	8.22504	−	1.88827i	0.0125001	−	0.00286971i
$659$		−	499.633i		−	0.758168i	−0.925362	−	0.379084i	$-0.876239\pi$
$659$		−	499.633i		−	0.758168i	0.925362	−	0.379084i	$-0.123761\pi$
$660$		0			0
$661$	−655.267			−0.991326			−0.495663	−	0.868515i	$-0.665075\pi$
$661$	−655.267			−0.991326			−0.495663	+	0.868515i	$0.665075\pi$
$662$	−234.626	−	1022.00i	−0.354419	−	1.54380i
$663$		0			0
$664$	748.287	+	931.046i	1.12694	+	1.40218i
$665$	45.0353			0.0677223
$666$		0			0
$667$		−	1954.77i		−	2.93069i
$668$	−146.716	−	302.695i	−0.219634	−	0.453136i
$669$		0			0
$670$	83.0141	+	361.598i	0.123902	+	0.539698i
$671$			475.817i			0.709117i
$672$		0			0
$673$	686.513			1.02008			0.510039	−	0.860151i	$-0.329631\pi$
$673$	686.513			1.02008			0.510039	+	0.860151i	$0.329631\pi$
$674$	20.2311	−	4.64458i	0.0300165	−	0.00689107i
$675$		0			0
$676$	−599.090	+	290.377i	−0.886228	+	0.429553i
$677$	639.146			0.944085			0.472043	−	0.881576i	$-0.343517\pi$
$677$	639.146			0.944085			0.472043	+	0.881576i	$0.343517\pi$
$678$		0			0
$679$			289.877i			0.426918i
$680$	197.177	−	158.472i	0.289966	−	0.233047i
$681$		0			0
$682$	352.686	−	80.9681i	0.517135	−	0.118722i
$683$			839.655i			1.22936i	0.788775	+	0.614682i	$0.210716\pi$
$683$			839.655i			1.22936i	−0.788775	+	0.614682i	$0.789284\pi$
$684$		0			0
$685$	−349.039			−0.509546
$686$	−107.775	−	469.451i	−0.157106	−	0.684331i
$687$		0			0
$688$	−203.610	−	160.694i	−0.295945	−	0.233567i
$689$	−91.0319			−0.132122
$690$		0			0
$691$			1091.05i			1.57895i	0.613783	+	0.789475i	$0.289647\pi$
$691$			1091.05i			1.57895i	−0.613783	+	0.789475i	$0.710353\pi$
$692$	−146.985	+	71.2434i	−0.212406	+	0.102953i
$693$		0			0
$694$	63.0249	+	274.528i	0.0908140	+	0.395573i
$695$		−	684.380i		−	0.984720i
$696$		0			0
$697$	65.2996			0.0936867
$698$	−1146.53	+	263.215i	−1.64259	+	0.377098i
$699$		0			0
$700$	−45.0702	−	92.9862i	−0.0643860	−	0.132837i
$701$	−431.165			−0.615071			−0.307536	−	0.951537i	$-0.599504\pi$
$701$	−431.165			−0.615071			−0.307536	+	0.951537i	$0.599504\pi$
$702$		0			0
$703$			154.266i			0.219439i
$704$	−828.349	−	182.457i	−1.17663	−	0.259171i
$705$		0			0
$706$	−132.080	+	30.3223i	−0.187082	+	0.0429495i
$707$			313.456i			0.443360i
$708$		0			0
$709$	−197.989			−0.279251			−0.139626	−	0.990204i	$-0.544590\pi$
$709$	−197.989			−0.279251			−0.139626	+	0.990204i	$0.544590\pi$
$710$	220.015	+	958.355i	0.309880	+	1.34980i
$711$		0			0
$712$	−1058.87	+	851.021i	−1.48718	+	1.19525i
$713$	−521.564			−0.731506
$714$		0			0
$715$		−	82.8052i		−	0.115811i
$716$	164.647	+	339.690i	0.229954	+	0.474427i
$717$		0			0
$718$	60.9847	+	265.641i	0.0849369	+	0.369973i
$719$			555.460i			0.772545i	0.922385	+	0.386273i	$0.126238\pi$
$719$			555.460i			0.772545i	−0.922385	+	0.386273i	$0.873762\pi$
$720$		0			0
$721$	91.5699			0.127004
$722$	37.0365	−	8.50269i	0.0512971	−	0.0117766i
$723$		0			0
$724$	366.674	−	177.726i	0.506455	−	0.245478i
$725$	−499.416			−0.688850
$726$		0			0
$727$			8.18995i			0.0112654i	0.999984	+	0.00563271i	$0.00179296\pi$
$727$			8.18995i			0.0112654i	−0.999984	+	0.00563271i	$0.998207\pi$
$728$	−21.2290	−	26.4139i	−0.0291607	−	0.0362829i
$729$		0			0
$730$	−260.377	+	59.7762i	−0.356681	+	0.0818852i
$731$			131.315i			0.179637i
$732$		0			0
$733$	−491.152			−0.670058			−0.335029	−	0.942208i	$-0.608746\pi$
$733$	−491.152			−0.670058			−0.335029	+	0.942208i	$0.608746\pi$
$734$	−122.907	−	535.364i	−0.167448	−	0.729378i
$735$		0			0
$736$	1104.82	+	523.462i	1.50111	+	0.711226i
$737$	−629.780			−0.854518
$738$		0			0
$739$		−	1037.82i		−	1.40436i	−0.712000	−	0.702180i	$-0.752210\pi$
$739$		−	1037.82i		−	1.40436i	0.712000	−	0.702180i	$-0.247790\pi$
$740$	−497.294	+	241.037i	−0.672018	+	0.325726i
$741$		0			0
$742$	67.3653	+	293.434i	0.0907888	+	0.395463i
$743$			148.421i			0.199759i	0.995000	+	0.0998795i	$0.0318457\pi$
$743$			148.421i			0.199759i	−0.995000	+	0.0998795i	$0.968154\pi$
$744$		0			0
$745$	−810.670			−1.08815
$746$	−15.5300	+	3.56532i	−0.0208177	+	0.00477925i
$747$		0			0
$748$	187.293	+	386.413i	0.250392	+	0.516594i
$749$	225.561			0.301149
$750$		0			0
$751$			443.027i			0.589916i	0.955510	+	0.294958i	$0.0953056\pi$
$751$			443.027i			0.589916i	−0.955510	+	0.294958i	$0.904694\pi$
$752$	20.0237	+	15.8032i	0.0266273	+	0.0210148i
$753$		0			0
$754$	−159.628	+	36.6468i	−0.211709	+	0.0486032i
$755$		−	129.980i		−	0.172159i
$756$		0			0
$757$	878.626			1.16067			0.580334	−	0.814379i	$-0.302922\pi$
$757$	878.626			1.16067			0.580334	+	0.814379i	$0.302922\pi$
$758$	230.448	+	1003.80i	0.304022	+	1.32428i
$759$		0			0
$760$	85.2781	+	106.106i	0.112208	+	0.139613i
$761$	750.924			0.986760			0.493380	−	0.869814i	$-0.335761\pi$
$761$	750.924			0.986760			0.493380	+	0.869814i	$0.335761\pi$
$762$		0			0
$763$			387.842i			0.508312i
$764$	169.213	+	349.111i	0.221483	+	0.456951i
$765$		0			0
$766$	−299.696	−	1305.44i	−0.391249	−	1.70422i
$767$			170.495i			0.222288i
$768$		0			0
$769$	−315.536			−0.410319			−0.205160	−	0.978729i	$-0.565771\pi$
$769$	−315.536			−0.410319			−0.205160	+	0.978729i	$0.565771\pi$
$770$	−266.916	+	61.2773i	−0.346644	+	0.0795810i
$771$		0			0
$772$	785.254	−	380.611i	1.01717	−	0.493019i
$773$	110.053			0.142371			0.0711853	−	0.997463i	$-0.477322\pi$
$773$	110.053			0.142371			0.0711853	+	0.997463i	$0.477322\pi$
$774$		0			0
$775$			133.252i			0.171939i
$776$	−682.970	+	548.907i	−0.880116	+	0.707354i
$777$		0			0
$778$	−730.832	+	167.781i	−0.939372	+	0.215657i
$779$			35.1395i			0.0451085i
$780$		0			0
$781$	−1669.13			−2.13716
$782$	−138.488	−	603.234i	−0.177094	−	0.771399i
$783$		0			0
$784$	416.273	−	527.447i	0.530960	−	0.672764i
$785$	−908.961			−1.15791
$786$		0			0
$787$		−	660.023i		−	0.838657i	−0.907834	−	0.419329i	$-0.862265\pi$
$787$		−	660.023i		−	0.838657i	0.907834	−	0.419329i	$-0.137735\pi$
$788$	2.32659	−	1.12769i	0.00295253	−	0.00143108i
$789$		0			0
$790$	124.336	+	541.590i	0.157387	+	0.685557i
$791$		−	95.4285i		−	0.120643i
$792$		0			0
$793$	−57.4612			−0.0724605
$794$	62.4035	−	14.3263i	0.0785939	−	0.0180432i
$795$		0			0
$796$	35.9238	+	74.1159i	0.0451304	+	0.0931104i
$797$	−764.458			−0.959170			−0.479585	−	0.877495i	$-0.659213\pi$
$797$	−764.458			−0.959170			−0.479585	+	0.877495i	$0.659213\pi$
$798$		0			0
$799$		−	12.9139i		−	0.0161626i
$800$	133.737	−	282.265i	0.167172	−	0.352832i
$801$		0			0
$802$	740.859	−	170.083i	0.923765	−	0.212074i
$803$		−	453.487i		−	0.564742i
$804$		0			0
$805$	394.724			0.490340
$806$	9.77797	+	42.5915i	0.0121315	+	0.0528430i
$807$		0			0
$808$	−738.523	+	593.555i	−0.914013	+	0.734597i
$809$	1281.35			1.58387			0.791933	−	0.610608i	$-0.209075\pi$
$809$	1281.35			1.58387			0.791933	+	0.610608i	$0.209075\pi$
$810$		0			0
$811$		−	1115.57i		−	1.37555i	−0.725925	−	0.687774i	$-0.758588\pi$
$811$		−	1115.57i		−	1.37555i	0.725925	−	0.687774i	$-0.241412\pi$
$812$	236.256	+	487.429i	0.290955	+	0.600282i
$813$		0			0
$814$	−209.902	−	914.304i	−0.257865	−	1.12322i
$815$		−	519.775i		−	0.637761i
$816$		0			0
$817$	−70.6641			−0.0864921
$818$	−227.903	+	52.3211i	−0.278610	+	0.0639622i
$819$		0			0
$820$	−113.276	+	54.9047i	−0.138142	+	0.0669569i
$821$	766.597			0.933736			0.466868	−	0.884327i	$-0.345382\pi$
$821$	766.597			0.933736			0.466868	+	0.884327i	$0.345382\pi$
$822$		0			0
$823$			169.190i			0.205577i	0.994703	+	0.102789i	$0.0327766\pi$
$823$			169.190i			0.205577i	−0.994703	+	0.102789i	$0.967223\pi$
$824$	173.395	+	215.745i	0.210431	+	0.261826i
$825$		0			0
$826$	549.577	−	126.170i	0.665347	−	0.152748i
$827$		−	1514.19i		−	1.83095i	−0.402380	−	0.915473i	$-0.631817\pi$
$827$		−	1514.19i		−	1.83095i	0.402380	−	0.915473i	$-0.368183\pi$
$828$		0			0
$829$	485.979			0.586224			0.293112	−	0.956078i	$-0.405309\pi$
$829$	485.979			0.586224			0.293112	+	0.956078i	$0.405309\pi$
$830$	260.839	+	1136.18i	0.314264	+	1.36889i
$831$		0			0
$832$	22.0340	−	100.034i	0.0264832	−	0.120233i
$833$	−340.167			−0.408364
$834$		0			0
$835$		−	328.283i		−	0.393153i
$836$	−207.939	+	100.788i	−0.248731	+	0.120559i
$837$		0			0
$838$	−0.0656367	−	0.285904i	−7.83254e−5	−	0.000341175i
$839$		−	1289.35i		−	1.53677i	−0.639989	−	0.768384i	$-0.721061\pi$
$839$		−	1289.35i		−	1.53677i	0.639989	−	0.768384i	$-0.278939\pi$
$840$		0			0
$841$	1776.92			2.11286
$842$	1195.57	−	274.474i	1.41992	−	0.325979i
$843$		0			0
$844$	282.235	+	582.292i	0.334402	+	0.689919i
$845$	−649.733			−0.768915
$846$		0			0
$847$		−	144.632i		−	0.170758i
$848$	−563.787	+	714.358i	−0.664844	+	0.842404i
$849$		0			0
$850$	−154.118	+	35.3818i	−0.181315	+	0.0416256i
$851$			1352.10i			1.58884i
$852$		0			0
$853$	785.466			0.920828			0.460414	−	0.887704i	$-0.347701\pi$
$853$	785.466			0.920828			0.460414	+	0.887704i	$0.347701\pi$
$854$	42.5223	+	185.221i	0.0497920	+	0.216887i
$855$		0			0
$856$	427.118	+	531.436i	0.498970	+	0.620837i
$857$	80.7663			0.0942431			0.0471215	−	0.998889i	$-0.484995\pi$
$857$	80.7663			0.0942431			0.0471215	+	0.998889i	$0.484995\pi$
$858$		0			0
$859$			81.9821i			0.0954390i	0.998861	+	0.0477195i	$0.0151954\pi$
$859$			81.9821i			0.0954390i	−0.998861	+	0.0477195i	$0.984805\pi$
$860$	−110.411	−	227.794i	−0.128385	−	0.264876i
$861$		0			0
$862$	−138.833	−	604.736i	−0.161059	−	0.701549i
$863$			1154.64i			1.33794i	0.743289	+	0.668971i	$0.233265\pi$
$863$			1154.64i			1.33794i	−0.743289	+	0.668971i	$0.766735\pi$
$864$		0			0
$865$	−159.410			−0.184289
$866$	379.682	−	87.1658i	0.438432	−	0.100653i
$867$		0			0
$868$	130.054	−	63.0369i	0.149832	−	0.0726232i
$869$	−943.265			−1.08546
$870$		0			0
$871$		−	76.0542i		−	0.0873183i
$872$	−913.783	+	734.412i	−1.04792	+	0.842216i
$873$		0			0
$874$	324.617	−	74.5241i	0.371415	−	0.0852679i
$875$		−	359.142i		−	0.410448i
$876$		0			0
$877$	1055.61			1.20367			0.601833	−	0.798622i	$-0.294437\pi$
$877$	1055.61			1.20367			0.601833	+	0.798622i	$0.294437\pi$
$878$	−152.182	−	662.881i	−0.173327	−	0.754990i
$879$		0			0
$880$	−649.800	−	512.837i	−0.738410	−	0.582769i
$881$	1253.11			1.42237			0.711185	−	0.703005i	$-0.248159\pi$
$881$	1253.11			1.42237			0.711185	+	0.703005i	$0.248159\pi$
$882$		0			0
$883$		−	327.627i		−	0.371038i	−0.982641	−	0.185519i	$-0.940603\pi$
$883$		−	327.627i		−	0.371038i	0.982641	−	0.185519i	$-0.0593966\pi$
$884$	−46.6644	+	22.6181i	−0.0527878	+	0.0255861i
$885$		0			0
$886$	287.905	+	1254.07i	0.324949	+	1.41543i
$887$			879.152i			0.991152i	0.868565	+	0.495576i	$0.165043\pi$
$887$			879.152i			0.991152i	−0.868565	+	0.495576i	$0.834957\pi$
$888$		0			0
$889$	−273.568			−0.307725
$890$	−1292.17	+	296.650i	−1.45187	+	0.333315i
$891$		0			0
$892$	298.628	+	616.112i	0.334785	+	0.690709i
$893$	6.94934			0.00778201
$894$		0			0
$895$			368.405i			0.411626i
$896$	−338.757	+	3.00214i	−0.378077	+	0.00335060i
$897$		0			0
$898$	−811.645	+	186.334i	−0.903836	+	0.207499i
$899$		−	698.503i		−	0.776978i
$900$		0			0
$901$	460.713			0.511335
$902$	−47.8126	−	208.265i	−0.0530073	−	0.230892i
$903$		0			0
$904$	224.836	−	180.702i	0.248712	−	0.199892i
$905$	397.670			0.439414
$906$		0			0
$907$		−	957.974i		−	1.05620i	−0.849182	−	0.528100i	$-0.822904\pi$
$907$		−	957.974i		−	1.05620i	0.849182	−	0.528100i	$-0.177096\pi$
$908$	192.214	+	396.564i	0.211689	+	0.436744i
$909$		0			0
$910$	−7.40005	−	32.2336i	−0.00813192	−	0.0354215i
$911$		−	940.851i		−	1.03277i	−0.856357	−	0.516383i	$-0.827278\pi$
$911$		−	940.851i		−	1.03277i	0.856357	−	0.516383i	$-0.172722\pi$
$912$		0			0
$913$	−1978.83			−2.16740
$914$	−1587.85	+	364.531i	−1.73725	+	0.398831i
$915$		0			0
$916$	665.291	−	322.465i	0.726301	−	0.352036i
$917$	−226.690			−0.247209
$918$		0			0
$919$		−	1560.81i		−	1.69838i	−0.528087	−	0.849190i	$-0.677091\pi$
$919$		−	1560.81i		−	1.69838i	0.528087	−	0.849190i	$-0.322909\pi$
$920$	747.443	+	929.996i	0.812438	+	1.01087i
$921$		0			0
$922$	239.266	−	54.9298i	0.259508	−	0.0595767i
$923$		−	201.569i		−	0.218385i
$924$		0			0
$925$	345.444			0.373453
$926$	−156.062	−	679.784i	−0.168534	−	0.734108i
$927$		0			0
$928$	−701.045	+	1479.62i	−0.755437	+	1.59442i
$929$	851.219			0.916274			0.458137	−	0.888881i	$-0.348517\pi$
$929$	851.219			0.916274			0.458137	+	0.888881i	$0.348517\pi$
$930$		0			0
$931$		−	183.053i		−	0.196620i
$932$	813.978	−	394.533i	0.873366	−	0.423319i
$933$		0			0
$934$	−18.7686	−	81.7532i	−0.0200948	−	0.0875302i
$935$			419.077i			0.448211i
$936$		0			0
$937$	−1552.45			−1.65683			−0.828415	−	0.560115i	$-0.810757\pi$
$937$	−1552.45			−1.65683			−0.828415	+	0.560115i	$0.810757\pi$
$938$	−245.154	+	56.2815i	−0.261359	+	0.0600016i
$939$		0			0
$940$	10.8582	+	22.4020i	0.0115513	+	0.0238319i
$941$	1257.79			1.33665			0.668325	−	0.743869i	$-0.267012\pi$
$941$	1257.79			1.33665			0.668325	+	0.743869i	$0.267012\pi$
$942$		0			0
$943$			307.990i			0.326606i
$944$	1337.93	+	1055.93i	1.41730	+	1.11857i
$945$		0			0
$946$	418.812	−	96.1492i	0.442719	−	0.101638i
$947$		−	1009.67i		−	1.06618i	−0.846058	−	0.533091i	$-0.821030\pi$
$947$		−	1009.67i		−	1.06618i	0.846058	−	0.533091i	$-0.178970\pi$
$948$		0			0
$949$	54.7646			0.0577077
$950$	−19.0399	−	82.9351i	−0.0200420	−	0.0873001i
$951$		0			0
$952$	107.440	+	133.681i	0.112857	+	0.140421i
$953$	−703.529			−0.738225			−0.369113	−	0.929385i	$-0.620338\pi$
$953$	−703.529			−0.738225			−0.369113	+	0.929385i	$0.620338\pi$
$954$		0			0
$955$			378.622i			0.396463i
$956$	492.489	+	1016.07i	0.515156	+	1.06284i
$957$		0			0
$958$	115.174	+	501.680i	0.120223	+	0.523674i
$959$		−	236.640i		−	0.246757i
$960$		0			0
$961$	774.628			0.806064
$962$	110.414	−	25.3484i	0.114776	−	0.0263497i
$963$		0			0
$964$	−31.2749	+	15.1589i	−0.0324428	+	0.0157250i
$965$	851.634			0.882522
$966$		0			0
$967$			1185.74i			1.22620i	0.790004	+	0.613102i	$0.210079\pi$
$967$			1185.74i			1.22620i	−0.790004	+	0.613102i	$0.789921\pi$
$968$	340.763	−	273.873i	0.352027	−	0.282926i
$969$		0			0
$970$	−833.445	+	191.339i	−0.859221	+	0.197256i
$971$		−	1118.65i		−	1.15206i	−0.817430	−	0.576028i	$-0.804602\pi$
$971$		−	1118.65i		−	1.15206i	0.817430	−	0.576028i	$-0.195398\pi$
$972$		0			0
$973$	463.993			0.476868
$974$	−139.682	−	608.435i	−0.143411	−	0.624677i
$975$		0			0
$976$	−355.874	+	450.918i	−0.364625	+	0.462006i
$977$	1310.18			1.34102			0.670511	−	0.741900i	$-0.266075\pi$
$977$	1310.18			1.34102			0.670511	+	0.741900i	$0.266075\pi$
$978$		0			0
$979$		−	2250.51i		−	2.29879i
$980$	590.093	−	286.017i	0.602136	−	0.291854i
$981$		0			0
$982$	382.939	+	1668.03i	0.389958	+	1.69860i
$983$		−	72.0290i		−	0.0732747i	−0.999329	−	0.0366373i	$-0.988335\pi$
$983$		−	72.0290i		−	0.0732747i	0.999329	−	0.0366373i	$-0.0116646\pi$
$984$		0			0
$985$	2.52326			0.00256169
$986$	807.879	−	185.469i	0.819350	−	0.188103i
$987$		0			0
$988$	−12.1714	−	25.1114i	−0.0123193	−	0.0254164i
$989$	−619.354			−0.626243
$990$		0			0
$991$			289.057i			0.291683i	0.989308	+	0.145841i	$0.0465889\pi$
$991$			289.057i			0.291683i	−0.989308	+	0.145841i	$0.953411\pi$
$992$	394.788	+	187.050i	0.397971	+	0.188559i
$993$		0			0
$994$	−649.741	+	149.165i	−0.653662	+	0.150065i
$995$			80.3812i			0.0807851i
$996$		0			0
$997$	419.170			0.420432			0.210216	−	0.977655i	$-0.432583\pi$
$997$	419.170			0.420432			0.210216	+	0.977655i	$0.432583\pi$
$998$	−195.713	−	852.498i	−0.196105	−	0.854206i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.b.343.2		14
3.2	odd	2		76.3.b.b.39.13	✓	14
4.3	odd	2	inner	684.3.g.b.343.1		14
12.11	even	2		76.3.b.b.39.14	yes	14
24.5	odd	2		1216.3.d.d.191.11		14
24.11	even	2		1216.3.d.d.191.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.13	✓	14	3.2	odd	2
76.3.b.b.39.14	yes	14	12.11	even	2
684.3.g.b.343.1		14	4.3	odd	2	inner
684.3.g.b.343.2		14	1.1	even	1	trivial
1216.3.d.d.191.4		14	24.11	even	2
1216.3.d.d.191.11		14	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94929 + 0.447510i) q^{2} +(3.59947 - 1.74465i) q^{4} +3.90374 q^{5} +2.64664i q^{7} +(-6.23566 + 5.01164i) q^{8} +O(q^{10})\)	\(q+(-1.94929 + 0.447510i) q^{2} +(3.59947 - 1.74465i) q^{4} +3.90374 q^{5} +2.64664i q^{7} +(-6.23566 + 5.01164i) q^{8} +(-7.60953 + 1.74696i) q^{10} -13.2532i q^{11} +1.60050 q^{13} +(-1.18440 - 5.15907i) q^{14} +(9.91236 - 12.5597i) q^{16} -8.10013 q^{17} -4.35890i q^{19} +(14.0514 - 6.81068i) q^{20} +(5.93094 + 25.8343i) q^{22} -38.2047i q^{23} -9.76079 q^{25} +(-3.11984 + 0.716239i) q^{26} +(4.61747 + 9.52650i) q^{28} +51.1656 q^{29} -13.6518i q^{31} +(-13.7015 + 28.9183i) q^{32} +(15.7895 - 3.62489i) q^{34} +10.3318i q^{35} -35.3910 q^{37} +(1.95065 + 8.49676i) q^{38} +(-24.3424 + 19.5641i) q^{40} -8.06155 q^{41} -16.2115i q^{43} +(-23.1223 - 47.7045i) q^{44} +(17.0970 + 74.4721i) q^{46} +1.59429i q^{47} +41.9953 q^{49} +(19.0266 - 4.36805i) q^{50} +(5.76095 - 2.79232i) q^{52} -56.8772 q^{53} -51.7371i q^{55} +(-13.2640 - 16.5036i) q^{56} +(-99.7366 + 22.8971i) q^{58} +106.526i q^{59} -35.9021 q^{61} +(6.10933 + 26.6114i) q^{62} +(13.7670 - 62.5018i) q^{64} +6.24794 q^{65} -47.5191i q^{67} +(-29.1562 + 14.1319i) q^{68} +(-4.62359 - 20.1397i) q^{70} -125.941i q^{71} +34.2172 q^{73} +(68.9874 - 15.8378i) q^{74} +(-7.60477 - 15.6897i) q^{76} +35.0765 q^{77} -71.1726i q^{79} +(38.6953 - 49.0297i) q^{80} +(15.7143 - 3.60763i) q^{82} -149.310i q^{83} -31.6208 q^{85} +(7.25479 + 31.6008i) q^{86} +(66.4202 + 82.6425i) q^{88} +169.809 q^{89} +4.23595i q^{91} +(-66.6541 - 137.517i) q^{92} +(-0.713460 - 3.10773i) q^{94} -17.0160i q^{95} +109.526 q^{97} +(-81.8610 + 18.7933i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more