LMFDB - Embedded newform 117.4.g.e.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 $ x^8 - 2x^7 + 29x^6 + 2x^5 + 595x^4 - 288x^3 + 2526x^2 + 1872*x + 6084
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$-2.11303 + 3.65987i$ of defining polynomial
Character	$\chi$	$=$	117.100
Dual form			117.4.g.e.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11303 + 3.65987i) q^{2} +(-4.92977 - 8.53861i) q^{4} +5.85953 q^{5} +(12.0627 + 20.8932i) q^{7} +7.85849 q^{8} +O(q^{10})$	\(q+(-2.11303 + 3.65987i) q^{2} +(-4.92977 - 8.53861i) q^{4} +5.85953 q^{5} +(12.0627 + 20.8932i) q^{7} +7.85849 q^{8} +(-12.3814 + 21.4451i) q^{10} +(-16.9446 + 29.3489i) q^{11} +(-40.8020 + 23.0694i) q^{13} -101.955 q^{14} +(22.8329 - 39.5478i) q^{16} +(-24.6978 - 42.7779i) q^{17} +(38.4274 + 66.5582i) q^{19} +(-28.8861 - 50.0322i) q^{20} +(-71.6088 - 124.030i) q^{22} +(3.14582 - 5.44871i) q^{23} -90.6659 q^{25} +(1.78447 - 198.076i) q^{26} +(118.933 - 205.998i) q^{28} +(50.4977 - 87.4645i) q^{29} -307.580 q^{31} +(127.927 + 221.576i) q^{32} +208.749 q^{34} +(70.6819 + 122.425i) q^{35} +(38.0095 - 65.8343i) q^{37} -324.793 q^{38} +46.0471 q^{40} +(-257.209 + 445.499i) q^{41} +(134.092 + 232.254i) q^{43} +334.132 q^{44} +(13.2944 + 23.0266i) q^{46} +460.912 q^{47} +(-119.519 + 207.012i) q^{49} +(191.579 - 331.825i) q^{50} +(398.125 + 234.665i) q^{52} -67.8057 q^{53} +(-99.2874 + 171.971i) q^{55} +(94.7947 + 164.189i) q^{56} +(213.406 + 369.630i) q^{58} +(12.6010 + 21.8256i) q^{59} +(294.416 + 509.944i) q^{61} +(649.925 - 1125.70i) q^{62} -715.927 q^{64} +(-239.080 + 135.176i) q^{65} +(502.230 - 869.888i) q^{67} +(-243.509 + 421.770i) q^{68} -597.411 q^{70} +(447.740 + 775.509i) q^{71} +968.599 q^{73} +(160.630 + 278.219i) q^{74} +(378.876 - 656.233i) q^{76} -817.592 q^{77} -119.053 q^{79} +(133.790 - 231.732i) q^{80} +(-1086.98 - 1882.70i) q^{82} -480.784 q^{83} +(-144.718 - 250.658i) q^{85} -1133.36 q^{86} +(-133.159 + 230.638i) q^{88} +(542.954 - 940.423i) q^{89} +(-974.179 - 574.205i) q^{91} -62.0325 q^{92} +(-973.920 + 1686.88i) q^{94} +(225.167 + 390.000i) q^{95} +(8.32761 + 14.4239i) q^{97} +(-505.092 - 874.845i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8	$ 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8} + 62 q^{10} + 40 q^{11} - 60 q^{13} - 80 q^{14} - 122 q^{16} + 98 q^{17} - 124 q^{19} - 466 q^{20} - 220 q^{22} + 104 q^{23} - 116 q^{25} - 14 q^{26} + 144 q^{28} + 194 q^{29} + 52 q^{31} + 654 q^{32} + 2124 q^{34} + 88 q^{35} - 102 q^{37} - 664 q^{38} - 1996 q^{40} - 1054 q^{41} - 450 q^{43} + 88 q^{44} + 172 q^{46} + 192 q^{47} - 1070 q^{49} + 996 q^{50} + 2280 q^{52} - 524 q^{53} - 204 q^{55} + 2164 q^{56} - 722 q^{58} + 308 q^{59} + 928 q^{61} + 2780 q^{62} + 2052 q^{64} - 2346 q^{65} + 1134 q^{67} + 1786 q^{68} - 4648 q^{70} + 1064 q^{71} + 1904 q^{73} + 1158 q^{74} + 1708 q^{76} - 5016 q^{77} - 1492 q^{79} - 2922 q^{80} - 1734 q^{82} + 808 q^{83} + 1394 q^{85} - 6336 q^{86} - 3060 q^{88} + 1620 q^{89} + 3278 q^{91} - 664 q^{92} + 772 q^{94} + 2204 q^{95} - 2166 q^{97} - 1906 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8 + 62 * q^10 + 40 * q^11 - 60 * q^13 - 80 * q^14 - 122 * q^16 + 98 * q^17 - 124 * q^19 - 466 * q^20 - 220 * q^22 + 104 * q^23 - 116 * q^25 - 14 * q^26 + 144 * q^28 + 194 * q^29 + 52 * q^31 + 654 * q^32 + 2124 * q^34 + 88 * q^35 - 102 * q^37 - 664 * q^38 - 1996 * q^40 - 1054 * q^41 - 450 * q^43 + 88 * q^44 + 172 * q^46 + 192 * q^47 - 1070 * q^49 + 996 * q^50 + 2280 * q^52 - 524 * q^53 - 204 * q^55 + 2164 * q^56 - 722 * q^58 + 308 * q^59 + 928 * q^61 + 2780 * q^62 + 2052 * q^64 - 2346 * q^65 + 1134 * q^67 + 1786 * q^68 - 4648 * q^70 + 1064 * q^71 + 1904 * q^73 + 1158 * q^74 + 1708 * q^76 - 5016 * q^77 - 1492 * q^79 - 2922 * q^80 - 1734 * q^82 + 808 * q^83 + 1394 * q^85 - 6336 * q^86 - 3060 * q^88 + 1620 * q^89 + 3278 * q^91 - 664 * q^92 + 772 * q^94 + 2204 * q^95 - 2166 * q^97 - 1906 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−2.11303	+	3.65987i	−0.747068	+	1.29396i	0.202155	+	0.979354i	$0.435206\pi$
$2$	−2.11303	+	3.65987i	−0.747068	+	1.29396i	−0.949222	+	0.314606i	$0.898128\pi$
$3$		0			0
$3$		0			0
$4$	−4.92977	−	8.53861i	−0.616221	−	1.06733i
$5$	5.85953			0.524093			0.262046	−	0.965055i	$-0.415603\pi$
$5$	5.85953			0.524093			0.262046	+	0.965055i	$0.415603\pi$
$6$		0			0
$7$	12.0627	+	20.8932i	0.651326	+	1.12813i	0.982801	+	0.184666i	$0.0591202\pi$
$7$	12.0627	+	20.8932i	0.651326	+	1.12813i	−0.331476	+	0.943464i	$0.607546\pi$
$8$	7.85849			0.347299
$9$		0			0
$10$	−12.3814	+	21.4451i	−0.391533	+	0.678155i
$11$	−16.9446	+	29.3489i	−0.464453	+	0.804457i	−0.999177	−	0.0405703i	$-0.987083\pi$
$11$	−16.9446	+	29.3489i	−0.464453	+	0.804457i	0.534723	+	0.845027i	$0.320416\pi$
$12$		0			0
$13$	−40.8020	+	23.0694i	−0.870495	+	0.492178i
$13$	−40.8020	+	23.0694i	−0.870495	+	0.492178i
$14$	−101.955			−1.94634
$15$		0			0
$16$	22.8329	−	39.5478i	0.356765	−	0.617934i
$17$	−24.6978	−	42.7779i	−0.352359	−	0.610303i	0.634303	−	0.773084i	$-0.281287\pi$
$17$	−24.6978	−	42.7779i	−0.352359	−	0.610303i	−0.986662	+	0.162781i	$0.947954\pi$
$18$		0			0
$19$	38.4274	+	66.5582i	0.463992	+	0.803658i	0.999155	−	0.0410905i	$-0.0130832\pi$
$19$	38.4274	+	66.5582i	0.463992	+	0.803658i	−0.535163	+	0.844749i	$0.679750\pi$
$20$	−28.8861	−	50.0322i	−0.322957	−	0.559377i
$21$		0			0
$22$	−71.6088	−	124.030i	−0.693957	−	1.20197i
$23$	3.14582	−	5.44871i	0.0285195	−	0.0493972i	−0.851413	−	0.524495i	$-0.824254\pi$
$23$	3.14582	−	5.44871i	0.0285195	−	0.0493972i	0.879933	+	0.475098i	$0.157587\pi$
$24$		0			0
$25$	−90.6659			−0.725327
$26$	1.78447	−	198.076i	0.0134602	−	1.49408i
$27$		0			0
$28$	118.933	−	205.998i	0.802721	−	1.39035i
$29$	50.4977	−	87.4645i	0.323351	−	0.560061i	−0.657826	−	0.753170i	$-0.728524\pi$
$29$	50.4977	−	87.4645i	0.323351	−	0.560061i	0.981177	+	0.193109i	$0.0618572\pi$
$30$		0			0
$31$	−307.580			−1.78203			−0.891016	−	0.453972i	$-0.850007\pi$
$31$	−307.580			−1.78203			−0.891016	+	0.453972i	$0.850007\pi$
$32$	127.927	+	221.576i	0.706704	+	1.22405i
$33$		0			0
$34$	208.749			1.05294
$35$	70.6819	+	122.425i	0.341355	+	0.591244i
$36$		0			0
$37$	38.0095	−	65.8343i	0.168884	−	0.292516i	−0.769144	−	0.639076i	$-0.779317\pi$
$37$	38.0095	−	65.8343i	0.168884	−	0.292516i	0.938028	+	0.346560i	$0.112650\pi$
$38$	−324.793			−1.38653
$39$		0			0
$40$	46.0471			0.182017
$41$	−257.209	+	445.499i	−0.979740	+	1.69696i	−0.316427	+	0.948617i	$0.602483\pi$
$41$	−257.209	+	445.499i	−0.979740	+	1.69696i	−0.663312	+	0.748343i	$0.730850\pi$
$42$		0			0
$43$	134.092	+	232.254i	0.475554	+	0.823684i	0.999608	−	0.0280012i	$-0.00891422\pi$
$43$	134.092	+	232.254i	0.475554	+	0.823684i	−0.524054	+	0.851685i	$0.675581\pi$
$44$	334.132			1.14482
$45$		0			0
$46$	13.2944	+	23.0266i	0.0426120	+	0.0738061i
$47$	460.912			1.43045			0.715223	−	0.698896i	$-0.246325\pi$
$47$	460.912			1.43045			0.715223	+	0.698896i	$0.246325\pi$
$48$		0			0
$49$	−119.519	+	207.012i	−0.348451	+	0.603534i
$50$	191.579	−	331.825i	0.541868	−	0.938544i
$51$		0			0
$52$	398.125	+	234.665i	1.06173	+	0.625811i
$53$	−67.8057			−0.175733			−0.0878663	−	0.996132i	$-0.528005\pi$
$53$	−67.8057			−0.175733			−0.0878663	+	0.996132i	$0.528005\pi$
$54$		0			0
$55$	−99.2874	+	171.971i	−0.243417	+	0.421610i
$56$	94.7947	+	164.189i	0.226205	+	0.391799i
$57$		0			0
$58$	213.406	+	369.630i	0.483130	+	0.836806i
$59$	12.6010	+	21.8256i	0.0278053	+	0.0481603i	0.879593	−	0.475727i	$-0.157815\pi$
$59$	12.6010	+	21.8256i	0.0278053	+	0.0481603i	−0.851788	+	0.523887i	$0.824481\pi$
$60$		0			0
$61$	294.416	+	509.944i	0.617969	+	1.07035i	0.989856	+	0.142076i	$0.0453778\pi$
$61$	294.416	+	509.944i	0.617969	+	1.07035i	−0.371886	+	0.928278i	$0.621289\pi$
$62$	649.925	−	1125.70i	1.33130	−	2.30588i
$63$		0			0
$64$	−715.927			−1.39830
$65$	−239.080	+	135.176i	−0.456220	+	0.257947i
$66$		0			0
$67$	502.230	−	869.888i	0.915778	−	1.58617i	0.110021	−	0.993929i	$-0.464908\pi$
$67$	502.230	−	869.888i	0.915778	−	1.58617i	0.805758	−	0.592245i	$-0.201758\pi$
$68$	−243.509	+	421.770i	−0.434262	+	0.752163i
$69$		0			0
$70$	−597.411			−1.02006
$71$	447.740	+	775.509i	0.748408	+	1.29628i	0.948585	+	0.316522i	$0.102515\pi$
$71$	447.740	+	775.509i	0.748408	+	1.29628i	−0.200177	+	0.979760i	$0.564152\pi$
$72$		0			0
$73$	968.599			1.55296			0.776479	−	0.630143i	$-0.217004\pi$
$73$	968.599			1.55296			0.776479	+	0.630143i	$0.217004\pi$
$74$	160.630	+	278.219i	0.252336	+	0.437059i
$75$		0			0
$76$	378.876	−	656.233i	0.571843	−	0.990462i
$77$	−817.592			−1.21004
$78$		0			0
$79$	−119.053			−0.169551			−0.0847755	−	0.996400i	$-0.527017\pi$
$79$	−119.053			−0.169551			−0.0847755	+	0.996400i	$0.527017\pi$
$80$	133.790	−	231.732i	0.186978	−	0.323855i
$81$		0			0
$82$	−1086.98	−	1882.70i	−1.46386	−	2.53549i
$83$	−480.784			−0.635818			−0.317909	−	0.948121i	$-0.602981\pi$
$83$	−480.784			−0.635818			−0.317909	+	0.948121i	$0.602981\pi$
$84$		0			0
$85$	−144.718	−	250.658i	−0.184669	−	0.319856i
$86$	−1133.36			−1.42109
$87$		0			0
$88$	−133.159	+	230.638i	−0.161304	+	0.279387i
$89$	542.954	−	940.423i	0.646663	−	1.12005i	−0.337252	−	0.941414i	$-0.609497\pi$
$89$	542.954	−	940.423i	0.646663	−	1.12005i	0.983915	−	0.178638i	$-0.0571692\pi$
$90$		0			0
$91$	−974.179	−	574.205i	−1.12222	−	0.661462i
$92$	−62.0325			−0.0702972
$93$		0			0
$94$	−973.920	+	1686.88i	−1.06864	+	1.85094i
$95$	225.167	+	390.000i	0.243175	+	0.421191i
$96$		0			0
$97$	8.32761	+	14.4239i	0.00871692	+	0.0150981i	0.870351	−	0.492432i	$-0.163892\pi$
$97$	8.32761	+	14.4239i	0.00871692	+	0.0150981i	−0.861634	+	0.507530i	$0.830559\pi$
$98$	−505.092	−	874.845i	−0.520632	−	0.901762i
$99$		0			0
$100$	446.962	+	774.160i	0.446962	+	0.774160i
$101$	−479.002	+	829.655i	−0.471906	+	0.817364i	−0.999483	−	0.0321423i	$-0.989767\pi$
$101$	−479.002	+	829.655i	−0.471906	+	0.817364i	0.527578	+	0.849507i	$0.323100\pi$
$102$		0			0
$103$	−2.70560			−0.00258826			−0.00129413	−	0.999999i	$-0.500412\pi$
$103$	−2.70560			−0.00258826			−0.00129413	+	0.999999i	$0.500412\pi$
$104$	−320.642	+	181.291i	−0.302322	+	0.170933i
$105$		0			0
$106$	143.275	−	248.160i	0.131284	−	0.227391i
$107$	675.642	−	1170.25i	0.610437	−	1.05731i	−0.380730	−	0.924686i	$-0.624327\pi$
$107$	675.642	−	1170.25i	0.610437	−	1.05731i	0.991167	−	0.132621i	$-0.0423395\pi$
$108$		0			0
$109$	448.455			0.394075			0.197037	−	0.980396i	$-0.436868\pi$
$109$	448.455			0.394075			0.197037	+	0.980396i	$0.436868\pi$
$110$	−419.594	−	726.758i	−0.363697	−	0.629942i
$111$		0			0
$112$	1101.71			0.929480
$113$	699.423	+	1211.44i	0.582267	+	1.00852i	0.995210	+	0.0977596i	$0.0311676\pi$
$113$	699.423	+	1211.44i	0.582267	+	1.00852i	−0.412943	+	0.910757i	$0.635499\pi$
$114$		0			0
$115$	18.4330	−	31.9269i	0.0149468	−	0.0258887i
$116$	−995.767			−0.797023
$117$		0			0
$118$	−106.505			−0.0830899
$119$	595.846	−	1032.04i	0.459001	−	0.795013i
$120$		0			0
$121$	91.2613	+	158.069i	0.0685659	+	0.118760i
$122$	−2488.44			−1.84666
$123$		0			0
$124$	1516.30	+	2626.30i	1.09813	+	1.90201i
$125$	−1263.70			−0.904231
$126$		0			0
$127$	59.7522	−	103.494i	0.0417492	−	0.0723118i	−0.844396	−	0.535720i	$-0.820040\pi$
$127$	59.7522	−	103.494i	0.0417492	−	0.0723118i	0.886145	+	0.463408i	$0.153374\pi$
$128$	489.356	−	847.590i	0.337917	−	0.585290i
$129$		0			0
$130$	10.4562	−	1160.63i	0.00705437	−	0.783034i
$131$	2251.70			1.50177			0.750886	−	0.660432i	$-0.229627\pi$
$131$	2251.70			1.50177			0.750886	+	0.660432i	$0.229627\pi$
$132$		0			0
$133$	−927.078	+	1605.75i	−0.604420	+	1.04689i
$134$	2122.45	+	3676.19i	1.36830	+	2.36996i
$135$		0			0
$136$	−194.087	−	336.169i	−0.122374	−	0.211958i
$137$	565.310	+	979.146i	0.352538	+	0.610614i	0.986693	−	0.162592i	$-0.0519853\pi$
$137$	565.310	+	979.146i	0.352538	+	0.610614i	−0.634155	+	0.773206i	$0.718652\pi$
$138$		0			0
$139$	297.644	+	515.534i	0.181624	+	0.314583i	0.942434	−	0.334393i	$-0.108531\pi$
$139$	297.644	+	515.534i	0.181624	+	0.314583i	−0.760809	+	0.648975i	$0.775198\pi$
$140$	696.891	−	1207.05i	0.420700	−	0.728674i
$141$		0			0
$142$	−3784.35			−2.23645
$143$	14.3099	−	1588.40i	0.00836821	−	0.928869i
$144$		0			0
$145$	295.893	−	512.501i	0.169466	−	0.293524i
$146$	−2046.68	+	3544.95i	−1.16017	+	2.00947i
$147$		0			0
$148$	−749.511			−0.416280
$149$	−396.587	−	686.910i	−0.218052	−	0.377677i	0.736161	−	0.676807i	$-0.236637\pi$
$149$	−396.587	−	686.910i	−0.218052	−	0.377677i	−0.954212	+	0.299130i	$0.903303\pi$
$150$		0			0
$151$	−134.213			−0.0723317			−0.0361659	−	0.999346i	$-0.511514\pi$
$151$	−134.213			−0.0723317			−0.0361659	+	0.999346i	$0.511514\pi$
$152$	301.981	+	523.047i	0.161144	+	0.279110i
$153$		0			0
$154$	1727.59	−	2992.28i	0.903984	−	1.56575i
$155$	−1802.28			−0.933950
$156$		0			0
$157$	1509.07			0.767114			0.383557	−	0.923517i	$-0.374699\pi$
$157$	1509.07			0.767114			0.383557	+	0.923517i	$0.374699\pi$
$158$	251.563	−	435.719i	0.126666	−	0.219392i
$159$		0			0
$160$	749.593	+	1298.33i	0.370379	+	0.641514i
$161$	151.788			0.0743019
$162$		0			0
$163$	−587.540	−	1017.65i	−0.282329	−	0.489009i	0.689629	−	0.724163i	$-0.257774\pi$
$163$	−587.540	−	1017.65i	−0.282329	−	0.489009i	−0.971958	+	0.235155i	$0.924440\pi$
$164$	5071.93			2.41494
$165$		0			0
$166$	1015.91	−	1759.61i	0.474999	−	0.822723i
$167$	737.007	−	1276.53i	0.341505	−	0.591504i	−0.643208	−	0.765692i	$-0.722397\pi$
$167$	737.007	−	1276.53i	0.341505	−	0.591504i	0.984712	+	0.174188i	$0.0557301\pi$
$168$		0			0
$169$	1132.60	−	1882.56i	0.515522	−	0.856877i
$170$	1223.17			0.551840
$171$		0			0
$172$	1322.08	−	2289.92i	0.586093	−	1.01514i
$173$	−1164.15	−	2016.37i	−0.511612	−	0.886139i	−0.999909	−	0.0134612i	$-0.995715\pi$
$173$	−1164.15	−	2016.37i	−0.511612	−	0.886139i	0.488297	−	0.872678i	$-0.337618\pi$
$174$		0			0
$175$	−1093.68	−	1894.30i	−0.472424	−	0.818263i
$176$	773.790	+	1340.24i	0.331401	+	0.574004i
$177$		0			0
$178$	2294.55	+	3974.28i	0.966202	+	1.67351i
$179$	−1066.93	+	1847.97i	−0.445508	+	0.771642i	−0.998087	−	0.0618183i	$-0.980310\pi$
$179$	−1066.93	+	1847.97i	−0.445508	+	0.771642i	0.552580	+	0.833460i	$0.313643\pi$
$180$		0			0
$181$	−2485.41			−1.02066			−0.510329	−	0.859979i	$-0.670476\pi$
$181$	−2485.41			−1.02066			−0.510329	+	0.859979i	$0.670476\pi$
$182$	4159.98	−	2352.06i	1.69428	−	0.957945i
$183$		0			0
$184$	24.7214	−	42.8186i	0.00990479	−	0.0171556i
$185$	222.718	−	385.758i	0.0885110	−	0.153305i
$186$		0			0
$187$	1673.98			0.654617
$188$	−2272.19	−	3935.55i	−0.881471	−	1.52675i
$189$		0			0
$190$	−1903.13			−0.726673
$191$	−1162.53	−	2013.57i	−0.440408	−	0.762809i	0.557311	−	0.830304i	$-0.311833\pi$
$191$	−1162.53	−	2013.57i	−0.440408	−	0.762809i	−0.997720	+	0.0674941i	$0.978500\pi$
$192$		0			0
$193$	−1675.06	+	2901.29i	−0.624732	+	1.08207i	0.363860	+	0.931453i	$0.381458\pi$
$193$	−1675.06	+	2901.29i	−0.624732	+	1.08207i	−0.988593	+	0.150614i	$0.951875\pi$
$194$	−70.3859			−0.0260485
$195$		0			0
$196$	2356.79			0.858890
$197$	−1929.65	+	3342.25i	−0.697878	+	1.20876i	0.271323	+	0.962488i	$0.412539\pi$
$197$	−1929.65	+	3342.25i	−0.697878	+	1.20876i	−0.969201	+	0.246272i	$0.920794\pi$
$198$		0			0
$199$	2041.80	+	3536.50i	0.727333	+	1.25978i	0.958006	+	0.286747i	$0.0925739\pi$
$199$	2041.80	+	3536.50i	0.727333	+	1.25978i	−0.230673	+	0.973031i	$0.574093\pi$
$200$	−712.497			−0.251906
$201$		0			0
$202$	−2024.29	−	3506.17i	−0.705091	−	1.22125i
$203$	2436.56			0.842428
$204$		0			0
$205$	−1507.13	+	2610.42i	−0.513474	+	0.889364i
$206$	5.71700	−	9.90214i	0.00193360	−	0.00334910i
$207$		0			0
$208$	−19.2827	+	2140.37i	−0.00642794	+	0.713500i
$209$	−2604.55			−0.862011
$210$		0			0
$211$	−1513.65	+	2621.72i	−0.493857	+	0.855386i	−0.999975	−	0.00707871i	$-0.997747\pi$
$211$	−1513.65	+	2621.72i	−0.493857	+	0.855386i	0.506118	+	0.862464i	$0.331080\pi$
$212$	334.266	+	578.966i	0.108290	+	0.187564i
$213$		0			0
$214$	2855.30	+	4945.52i	0.912076	+	1.57976i
$215$	785.716	+	1360.90i	0.249234	+	0.431687i
$216$		0			0
$217$	−3710.25	−	6426.34i	−1.16068	−	2.01036i
$218$	−947.597	+	1641.29i	−0.294401	+	0.509917i
$219$		0			0
$220$	1957.86			0.599994
$221$	1994.58	+	1175.66i	0.607104	+	0.357843i
$222$		0			0
$223$	862.379	−	1493.68i	0.258965	−	0.448540i	−0.707000	−	0.707213i	$-0.749952\pi$
$223$	862.379	−	1493.68i	0.258965	−	0.448540i	0.965965	+	0.258673i	$0.0832853\pi$
$224$	−3086.30	+	5345.63i	−0.920590	+	1.59451i
$225$		0			0
$226$	−5911.60			−1.73997
$227$	−961.637	−	1665.60i	−0.281172	−	0.487005i	0.690502	−	0.723331i	$-0.257390\pi$
$227$	−961.637	−	1665.60i	−0.281172	−	0.487005i	−0.971674	+	0.236326i	$0.924057\pi$
$228$		0			0
$229$	373.993			0.107922			0.0539610	−	0.998543i	$-0.482815\pi$
$229$	373.993			0.107922			0.0539610	+	0.998543i	$0.482815\pi$
$230$	77.8989	+	134.925i	0.0223326	+	0.0386812i
$231$		0			0
$232$	396.835	−	687.339i	0.112300	−	0.194509i
$233$	−3094.49			−0.870073			−0.435036	−	0.900413i	$-0.643265\pi$
$233$	−3094.49			−0.870073			−0.435036	+	0.900413i	$0.643265\pi$
$234$		0			0
$235$	2700.73			0.749686
$236$	124.240	−	215.191i	0.0342685	−	0.0593547i
$237$		0			0
$238$	2518.08	+	4361.44i	0.685810	+	1.18786i
$239$	1221.18			0.330510			0.165255	−	0.986251i	$-0.447155\pi$
$239$	1221.18			0.330510			0.165255	+	0.986251i	$0.447155\pi$
$240$		0			0
$241$	−72.7003	−	125.921i	−0.0194317	−	0.0336567i	0.856146	−	0.516734i	$-0.172852\pi$
$241$	−72.7003	−	125.921i	−0.0194317	−	0.0336567i	−0.875578	+	0.483077i	$0.839519\pi$
$242$	−771.350			−0.204894
$243$		0			0
$244$	2902.81	−	5027.81i	0.761611	−	1.31915i
$245$	−700.323	+	1212.99i	−0.182620	+	0.316308i
$246$		0			0
$247$	−3103.38	−	1829.21i	−0.799446	−	0.471213i
$248$	−2417.11			−0.618899
$249$		0			0
$250$	2670.24	−	4624.98i	0.675522	−	1.17004i
$251$	−492.835	−	853.615i	−0.123934	−	0.214660i	0.797382	−	0.603475i	$-0.206218\pi$
$251$	−492.835	−	853.615i	−0.123934	−	0.214660i	−0.921316	+	0.388815i	$0.872884\pi$
$252$		0			0
$253$	106.609	+	184.652i	0.0264919	+	0.0458854i
$254$	252.516	+	437.371i	0.0623790	+	0.108044i
$255$		0			0
$256$	−795.663	−	1378.13i	−0.194254	−	0.336457i
$257$	1464.66	−	2536.86i	0.355498	−	0.615740i	−0.631705	−	0.775209i	$-0.717645\pi$
$257$	1464.66	−	2536.86i	0.355498	−	0.615740i	0.987203	+	0.159469i	$0.0509781\pi$
$258$		0			0
$259$	1833.99			0.439995
$260$	2332.83	+	1375.03i	0.556445	+	0.327983i
$261$		0			0
$262$	−4757.91	+	8240.94i	−1.12193	+	1.94323i
$263$	1119.00	−	1938.17i	0.262360	−	0.454420i	−0.704509	−	0.709695i	$-0.748833\pi$
$263$	1119.00	−	1938.17i	0.262360	−	0.454420i	0.966869	+	0.255275i	$0.0821660\pi$
$264$		0			0
$265$	−397.310			−0.0921002
$266$	−3917.88	−	6785.97i	−0.903086	−	1.56419i
$267$		0			0
$268$	−9903.50			−2.25729
$269$	962.992	+	1667.95i	0.218270	+	0.378055i	0.954279	−	0.298917i	$-0.0966253\pi$
$269$	962.992	+	1667.95i	0.218270	+	0.378055i	−0.736009	+	0.676972i	$0.763292\pi$
$270$		0			0
$271$	1781.14	−	3085.03i	0.399250	−	0.691521i	−0.594384	−	0.804182i	$-0.702604\pi$
$271$	1781.14	−	3085.03i	0.399250	−	0.691521i	0.993634	+	0.112660i	$0.0359372\pi$
$272$	−2255.69			−0.502837
$273$		0			0
$274$	−4778.06			−1.05348
$275$	1536.30	−	2660.94i	0.336881	−	0.583494i
$276$		0			0
$277$	718.712	+	1244.85i	0.155896	+	0.270020i	0.933385	−	0.358877i	$-0.116840\pi$
$277$	718.712	+	1244.85i	0.155896	+	0.270020i	−0.777489	+	0.628897i	$0.783507\pi$
$278$	−2515.72			−0.542743
$279$		0			0
$280$	555.453	+	962.073i	0.118552	+	0.205339i
$281$	3913.51			0.830820			0.415410	−	0.909634i	$-0.363638\pi$
$281$	3913.51			0.830820			0.415410	+	0.909634i	$0.363638\pi$
$282$		0			0
$283$	1606.16	−	2781.94i	0.337371	−	0.584344i	−0.646566	−	0.762858i	$-0.723796\pi$
$283$	1606.16	−	2781.94i	0.337371	−	0.584344i	0.983937	+	0.178514i	$0.0571289\pi$
$284$	4414.51	−	7646.16i	0.922370	−	1.59759i
$285$		0			0
$286$	5783.08	+	3408.69i	1.19567	+	0.704756i
$287$	−12410.6			−2.55252
$288$		0			0
$289$	1236.54	−	2141.74i	0.251686	−	0.435934i
$290$	1250.46	+	2165.86i	0.253205	+	0.438564i
$291$		0			0
$292$	−4774.97	−	8270.49i	−0.956965	−	1.65751i
$293$	−2450.89	−	4245.06i	−0.488677	−	0.846413i	0.511238	−	0.859439i	$-0.329187\pi$
$293$	−2450.89	−	4245.06i	−0.488677	−	0.846413i	−0.999915	+	0.0130260i	$0.995854\pi$
$294$		0			0
$295$	73.8362	+	127.888i	0.0145726	+	0.0252404i
$296$	298.697	−	517.358i	0.0586534	−	0.101591i
$297$		0			0
$298$	3352.00			0.651598
$299$	−2.65667	+	294.890i	−0.000513844	+	0.0570366i
$300$		0			0
$301$	−3235.03	+	5603.23i	−0.619481	+	1.07297i
$302$	283.595	−	491.202i	0.0540367	−	0.0935943i
$303$		0			0
$304$	3509.64			0.662144
$305$	1725.14	+	2988.03i	0.323873	+	0.560965i
$306$		0			0
$307$	5800.63			1.07837			0.539185	−	0.842188i	$-0.318733\pi$
$307$	5800.63			1.07837			0.539185	+	0.842188i	$0.318733\pi$
$308$	4030.54	+	6981.09i	0.745653	+	1.29151i
$309$		0			0
$310$	3808.26	−	6596.09i	0.697724	−	1.20849i
$311$	4913.51			0.895884			0.447942	−	0.894063i	$-0.352157\pi$
$311$	4913.51			0.895884			0.447942	+	0.894063i	$0.352157\pi$
$312$		0			0
$313$	−8104.97			−1.46364			−0.731822	−	0.681496i	$-0.761330\pi$
$313$	−8104.97			−1.46364			−0.731822	+	0.681496i	$0.761330\pi$
$314$	−3188.71	+	5523.00i	−0.573086	+	0.992615i
$315$		0			0
$316$	586.904	+	1016.55i	0.104481	+	0.180966i
$317$	−5149.92			−0.912455			−0.456227	−	0.889863i	$-0.650800\pi$
$317$	−5149.92			−0.912455			−0.456227	+	0.889863i	$0.650800\pi$
$318$		0			0
$319$	1711.33	+	2964.10i	0.300363	+	0.520244i
$320$	−4195.00			−0.732836
$321$		0			0
$322$	−320.733	+	555.526i	−0.0555085	+	0.0961436i
$323$	1898.15	−	3287.69i	0.326984	−	0.566352i
$324$		0			0
$325$	3699.35	−	2091.61i	0.631393	−	0.356990i
$326$	4965.95			0.843676
$327$		0			0
$328$	−2021.28	+	3500.95i	−0.340263	+	0.589353i
$329$	5559.86	+	9629.96i	0.931687	+	1.61373i
$330$		0			0
$331$	−3030.99	−	5249.83i	−0.503318	−	0.871772i	−0.999993	−	0.00383535i	$-0.998779\pi$
$331$	−3030.99	−	5249.83i	−0.503318	−	0.871772i	0.496675	−	0.867937i	$-0.334554\pi$
$332$	2370.15	+	4105.23i	0.391804	+	0.678625i
$333$		0			0
$334$	3114.63	+	5394.70i	0.510255	+	0.883787i
$335$	2942.83	−	5097.14i	0.479953	−	0.831302i
$336$		0			0
$337$	3743.50			0.605108			0.302554	−	0.953132i	$-0.402161\pi$
$337$	3743.50			0.605108			0.302554	+	0.953132i	$0.402161\pi$
$338$	4496.70	+	8123.07i	0.723634	+	1.30721i
$339$		0			0
$340$	−1426.85	+	2471.37i	−0.227593	+	0.394203i
$341$	5211.82	−	9027.13i	0.827671	−	1.43357i
$342$		0			0
$343$	2508.15			0.394832
$344$	1053.76	+	1825.17i	0.165160	+	0.286065i
$345$		0			0
$346$	9839.55			1.52884
$347$	−1260.20	−	2182.74i	−0.194961	−	0.337682i	0.751927	−	0.659246i	$-0.229125\pi$
$347$	−1260.20	−	2182.74i	−0.194961	−	0.337682i	−0.946888	+	0.321565i	$0.895791\pi$
$348$		0			0
$349$	−5325.37	+	9223.82i	−0.816793	+	1.41473i	0.0912407	+	0.995829i	$0.470917\pi$
$349$	−5325.37	+	9223.82i	−0.816793	+	1.41473i	−0.908033	+	0.418898i	$0.862417\pi$
$350$	9243.88			1.41173
$351$		0			0
$352$	−8670.70			−1.31293
$353$	−4501.41	+	7796.67i	−0.678714	+	1.17557i	0.296655	+	0.954985i	$0.404129\pi$
$353$	−4501.41	+	7796.67i	−0.678714	+	1.17557i	−0.975368	+	0.220582i	$0.929204\pi$
$354$		0			0
$355$	2623.55	+	4544.12i	0.392235	+	0.679371i
$356$	−10706.5			−1.59395
$357$		0			0
$358$	−4508.89	−	7809.63i	−0.665649	−	1.15294i
$359$	11360.9			1.67021			0.835106	−	0.550089i	$-0.185406\pi$
$359$	11360.9			1.67021			0.835106	+	0.550089i	$0.185406\pi$
$360$		0			0
$361$	476.168	−	824.747i	0.0694224	−	0.120243i
$362$	5251.74	−	9096.27i	0.762500	−	1.32069i
$363$		0			0
$364$	−100.440	+	11148.8i	−0.0144629	+	1.60538i
$365$	5675.54			0.813894
$366$		0			0
$367$	6969.42	−	12071.4i	0.991283	−	1.71695i	0.381540	−	0.924352i	$-0.375394\pi$
$367$	6969.42	−	12071.4i	0.991283	−	1.71695i	0.609743	−	0.792599i	$-0.291273\pi$
$368$	−143.656	−	248.820i	−0.0203495	−	0.0352463i
$369$		0			0
$370$	941.217	+	1630.24i	0.132247	+	0.229059i
$371$	−817.922	−	1416.68i	−0.114459	−	0.198249i
$372$		0			0
$373$	−796.535	−	1379.64i	−0.110571	−	0.191515i	0.805430	−	0.592691i	$-0.201935\pi$
$373$	−796.535	−	1379.64i	−0.110571	−	0.191515i	−0.916001	+	0.401177i	$0.868601\pi$
$374$	−3537.16	+	6126.54i	−0.489043	+	0.847048i
$375$		0			0
$376$	3622.07			0.496793
$377$	−42.6458	+	4733.68i	−0.00582592	+	0.646676i
$378$		0			0
$379$	−4568.78	+	7913.36i	−0.619215	+	1.07251i	0.370414	+	0.928867i	$0.379216\pi$
$379$	−4568.78	+	7913.36i	−0.619215	+	1.07251i	−0.989629	+	0.143645i	$0.954118\pi$
$380$	2220.04	−	3845.22i	0.299699	−	0.519094i
$381$		0			0
$382$	9825.86			1.31606
$383$	4775.53	+	8271.47i	0.637124	+	1.10353i	0.986061	+	0.166385i	$0.0532093\pi$
$383$	4775.53	+	8271.47i	0.637124	+	1.10353i	−0.348937	+	0.937146i	$0.613457\pi$
$384$		0			0
$385$	−4790.71			−0.634174
$386$	−7078.88	−	12261.0i	−0.933435	−	1.61676i
$387$		0			0
$388$	82.1064	−	142.212i	0.0107431	−	0.0186076i
$389$	−7366.50			−0.960145			−0.480072	−	0.877229i	$-0.659390\pi$
$389$	−7366.50			−0.960145			−0.480072	+	0.877229i	$0.659390\pi$
$390$		0			0
$391$	−310.779			−0.0401964
$392$	−939.235	+	1626.80i	−0.121017	+	0.209607i
$393$		0			0
$394$	−8154.81	−	14124.5i	−1.04272	−	1.80605i
$395$	−697.596			−0.0888604
$396$		0			0
$397$	5848.24	+	10129.4i	0.739332	+	1.28056i	0.952797	+	0.303609i	$0.0981917\pi$
$397$	5848.24	+	10129.4i	0.739332	+	1.28056i	−0.213465	+	0.976951i	$0.568475\pi$
$398$	−17257.5			−2.17347
$399$		0			0
$400$	−2070.17	+	3585.64i	−0.258771	+	0.448205i
$401$	−7083.82	+	12269.5i	−0.882167	+	1.52796i	−0.0332399	+	0.999447i	$0.510583\pi$
$401$	−7083.82	+	12269.5i	−0.882167	+	1.52796i	−0.848927	+	0.528510i	$0.822751\pi$
$402$		0			0
$403$	12549.9	−	7095.70i	1.55125	−	0.877077i
$404$	9445.47			1.16319
$405$		0			0
$406$	−5148.51	+	8917.48i	−0.629351	+	1.09007i
$407$	1288.11	+	2231.07i	0.156878	+	0.271720i
$408$		0			0
$409$	−1351.85	−	2341.47i	−0.163434	−	0.283076i	0.772664	−	0.634815i	$-0.218924\pi$
$409$	−1351.85	−	2341.47i	−0.163434	−	0.283076i	−0.936098	+	0.351739i	$0.885590\pi$
$410$	−6369.20	−	11031.8i	−0.767200	−	1.32883i
$411$		0			0
$412$	13.3380	+	23.1020i	0.00159494	+	0.00276251i
$413$	−304.006	+	526.553i	−0.0362207	+	0.0627361i
$414$		0			0
$415$	−2817.17			−0.333228
$416$	−10331.3	−	6089.54i	−1.21763	−	0.717703i
$417$		0			0
$418$	5503.48	−	9532.31i	0.643981	−	1.11541i
$419$	3571.26	−	6185.61i	0.416390	−	0.721209i	−0.579183	−	0.815198i	$-0.696628\pi$
$419$	3571.26	−	6185.61i	0.416390	−	0.721209i	0.995573	+	0.0939884i	$0.0299617\pi$
$420$		0			0
$421$	−3406.45			−0.394347			−0.197174	−	0.980369i	$-0.563176\pi$
$421$	−3406.45			−0.394347			−0.197174	+	0.980369i	$0.563176\pi$
$422$	−6396.76	−	11079.5i	−0.737890	−	1.27806i
$423$		0			0
$424$	−532.850			−0.0610318
$425$	2239.25	+	3878.49i	0.255575	+	0.442670i
$426$		0			0
$427$	−7102.92	+	12302.6i	−0.804999	+	1.39430i
$428$	−13323.0			−1.50466
$429$		0			0
$430$	−6640.96			−0.744780
$431$	2586.48	−	4479.92i	0.289064	−	0.500673i	−0.684523	−	0.728992i	$-0.739989\pi$
$431$	2586.48	−	4479.92i	0.289064	−	0.500673i	0.973587	+	0.228318i	$0.0733227\pi$
$432$		0			0
$433$	−5477.49	−	9487.28i	−0.607924	−	1.05296i	−0.991582	−	0.129480i	$-0.958669\pi$
$433$	−5477.49	−	9487.28i	−0.607924	−	1.05296i	0.383658	−	0.923475i	$-0.374664\pi$
$434$	31359.4			3.46844
$435$		0			0
$436$	−2210.78	−	3829.18i	−0.242837	−	0.420606i
$437$	483.542			0.0529313
$438$		0			0
$439$	−5916.22	+	10247.2i	−0.643202	+	1.11406i	0.341511	+	0.939878i	$0.389061\pi$
$439$	−5916.22	+	10247.2i	−0.643202	+	1.11406i	−0.984714	+	0.174181i	$0.944272\pi$
$440$	−780.249	+	1351.43i	−0.0845384	+	0.146425i
$441$		0			0
$442$	−8517.35	+	4815.72i	−0.916582	+	0.518236i
$443$	−13479.8			−1.44570			−0.722852	−	0.691003i	$-0.757169\pi$
$443$	−13479.8			−1.44570			−0.722852	+	0.691003i	$0.757169\pi$
$444$		0			0
$445$	3181.46	−	5510.44i	0.338911	−	0.587011i
$446$	3644.46	+	6312.39i	0.386929	+	0.670180i
$447$		0			0
$448$	−8636.03	−	14958.0i	−0.910746	−	1.57746i
$449$	−3387.17	−	5866.75i	−0.356014	−	0.616635i	0.631277	−	0.775558i	$-0.282531\pi$
$449$	−3387.17	−	5866.75i	−0.356014	−	0.616635i	−0.987291	+	0.158923i	$0.949198\pi$
$450$		0			0
$451$	−8716.61	−	15097.6i	−0.910087	−	1.57632i
$452$	6895.99	−	11944.2i	0.717610	−	1.24294i
$453$		0			0
$454$	8127.86			0.840219
$455$	−5708.23	−	3364.57i	−0.588145	−	0.346667i
$456$		0			0
$457$	2321.18	−	4020.40i	0.237594	−	0.411524i	−0.722430	−	0.691444i	$-0.756975\pi$
$457$	2321.18	−	4020.40i	0.237594	−	0.411524i	0.960023	+	0.279920i	$0.0903080\pi$
$458$	−790.257	+	1368.76i	−0.0806250	+	0.139647i
$459$		0			0
$460$	−363.482			−0.0368422
$461$	1230.18	+	2130.74i	0.124285	+	0.215268i	0.921453	−	0.388489i	$-0.127003\pi$
$461$	1230.18	+	2130.74i	0.124285	+	0.215268i	−0.797168	+	0.603757i	$0.793670\pi$
$462$		0			0
$463$	4290.01			0.430613			0.215306	−	0.976547i	$-0.430925\pi$
$463$	4290.01			0.430613			0.215306	+	0.976547i	$0.430925\pi$
$464$	−2306.02	−	3994.14i	−0.230720	−	0.399620i
$465$		0			0
$466$	6538.75	−	11325.4i	0.650003	−	1.12584i
$467$	8798.99			0.871882			0.435941	−	0.899975i	$-0.356416\pi$
$467$	8798.99			0.871882			0.435941	+	0.899975i	$0.356416\pi$
$468$		0			0
$469$	24233.0			2.38588
$470$	−5706.72	+	9884.32i	−0.560066	+	0.970064i
$471$		0			0
$472$	99.0251	+	171.517i	0.00965678	+	0.0167260i
$473$	−9088.54			−0.883491
$474$		0			0
$475$	−3484.05	−	6034.56i	−0.336546	−	0.582915i
$476$	−11749.5			−1.13138
$477$		0			0
$478$	−2580.39	+	4469.37i	−0.246913	+	0.427666i
$479$	−5486.68	+	9503.21i	−0.523367	+	0.906499i	0.476263	+	0.879303i	$0.341991\pi$
$479$	−5486.68	+	9503.21i	−0.523367	+	0.906499i	−0.999630	+	0.0271958i	$0.991342\pi$
$480$		0			0
$481$	−32.0994	+	3563.03i	−0.00304284	+	0.337755i
$482$	614.470			0.0580671
$483$		0			0
$484$	899.793	−	1558.49i	0.0845035	−	0.146364i
$485$	48.7959	+	84.5170i	0.00456847	+	0.00791283i
$486$		0			0
$487$	2604.79	+	4511.62i	0.242370	+	0.419797i	0.961389	−	0.275193i	$-0.0887419\pi$
$487$	2604.79	+	4511.62i	0.242370	+	0.419797i	−0.719019	+	0.694991i	$0.755409\pi$
$488$	2313.67	+	4007.39i	0.214620	+	0.371733i
$489$		0			0
$490$	−2959.60	−	5126.18i	−0.272860	−	0.472607i
$491$	−4389.61	+	7603.03i	−0.403463	+	0.698819i	−0.994141	−	0.108089i	$-0.965527\pi$
$491$	−4389.61	+	7603.03i	−0.403463	+	0.698819i	0.590678	+	0.806907i	$0.298860\pi$
$492$		0			0
$493$	−4988.73			−0.455742
$494$	13252.2	−	7492.79i	1.20697	−	0.682422i
$495$		0			0
$496$	−7022.95	+	12164.1i	−0.635766	+	1.10118i
$497$	−10801.9	+	18709.5i	−0.974915	+	1.68860i
$498$		0			0
$499$	−15590.1			−1.39861			−0.699305	−	0.714823i	$-0.746507\pi$
$499$	−15590.1			−1.39861			−0.699305	+	0.714823i	$0.746507\pi$
$500$	6229.75	+	10790.2i	0.557206	+	0.965109i
$501$		0			0
$502$	4165.49			0.370349
$503$	−32.1955	−	55.7642i	−0.00285393	−	0.00494314i	0.864595	−	0.502470i	$-0.167575\pi$
$503$	−32.1955	−	55.7642i	−0.00285393	−	0.00494314i	−0.867449	+	0.497526i	$0.834242\pi$
$504$		0			0
$505$	−2806.73	+	4861.39i	−0.247322	+	0.428375i
$506$	−901.072			−0.0791651
$507$		0			0
$508$	−1178.26			−0.102907
$509$	1607.08	−	2783.54i	0.139946	−	0.242393i	−0.787530	−	0.616276i	$-0.788641\pi$
$509$	1607.08	−	2783.54i	0.139946	−	0.242393i	0.927476	+	0.373883i	$0.121974\pi$
$510$		0			0
$511$	11683.9	+	20237.2i	1.01148	+	1.75194i
$512$	14554.7			1.25632
$513$		0			0
$514$	6189.73	+	10720.9i	0.531162	+	0.919999i
$515$	−15.8535			−0.00135649
$516$		0			0
$517$	−7809.97	+	13527.3i	−0.664376	+	1.15073i
$518$	−3875.27	+	6712.17i	−0.328706	+	0.569335i
$519$		0			0
$520$	−1878.81	+	1062.28i	−0.158445	+	0.0895848i
$521$	3053.01			0.256727			0.128363	−	0.991727i	$-0.459028\pi$
$521$	3053.01			0.256727			0.128363	+	0.991727i	$0.459028\pi$
$522$		0			0
$523$	−2548.01	+	4413.28i	−0.213034	+	0.368985i	−0.952663	−	0.304030i	$-0.901668\pi$
$523$	−2548.01	+	4413.28i	−0.213034	+	0.368985i	0.739629	+	0.673015i	$0.235001\pi$
$524$	−11100.4	−	19226.4i	−0.925423	−	1.60288i
$525$		0			0
$526$	4728.96	+	8190.80i	0.392001	+	0.678966i
$527$	7596.55	+	13157.6i	0.627915	+	1.08758i
$528$		0			0
$529$	6063.71	+	10502.6i	0.498373	+	0.863208i
$530$	839.526	−	1454.10i	0.0688051	−	0.119174i
$531$		0			0
$532$	18281.1			1.48983
$533$	217.216	−	24110.9i	0.0176523	−	1.95940i
$534$		0			0
$535$	3958.95	−	6857.09i	0.319925	−	0.554127i
$536$	3946.77	−	6836.00i	0.318049	−	0.550877i
$537$		0			0
$538$	−8139.31			−0.652250
$539$	−4050.39	−	7015.48i	−0.323678	−	0.560627i
$540$		0			0
$541$	7861.99			0.624793			0.312397	−	0.949952i	$-0.398868\pi$
$541$	7861.99			0.624793			0.312397	+	0.949952i	$0.398868\pi$
$542$	7527.21	+	13037.5i	0.596534	+	1.03323i
$543$		0			0
$544$	6319.04	−	10944.9i	0.498027	−	0.862608i
$545$	2627.73			0.206532
$546$		0			0
$547$	−6317.48			−0.493814			−0.246907	−	0.969039i	$-0.579414\pi$
$547$	−6317.48			−0.493814			−0.246907	+	0.969039i	$0.579414\pi$
$548$	5573.70	−	9653.93i	0.434483	−	0.752546i
$549$		0			0
$550$	6492.47	+	11245.3i	0.503345	+	0.871820i
$551$	7761.98			0.600130
$552$		0			0
$553$	−1436.11	−	2487.41i	−0.110433	−	0.191275i
$554$	−6074.63			−0.465860
$555$		0			0
$556$	2934.63	−	5082.92i	0.223842	−	0.387705i
$557$	−485.617	+	841.113i	−0.0369412	+	0.0639840i	−0.883905	−	0.467667i	$-0.845095\pi$
$557$	−485.617	+	841.113i	−0.0369412	+	0.0639840i	0.846964	+	0.531651i	$0.178428\pi$
$558$		0			0
$559$	−10829.2	−	6383.00i	−0.819367	−	0.482955i
$560$	6455.50			0.487134
$561$		0			0
$562$	−8269.35	+	14322.9i	−0.620679	+	1.07505i
$563$	4664.24	+	8078.71i	0.349155	+	0.604755i	0.986100	−	0.166155i	$-0.0531352\pi$
$563$	4664.24	+	8078.71i	0.349155	+	0.604755i	−0.636944	+	0.770910i	$0.719802\pi$
$564$		0			0
$565$	4098.29	+	7098.45i	0.305162	+	0.528556i
$566$	6787.70	+	11756.6i	0.504079	+	0.873090i
$567$		0			0
$568$	3518.56	+	6094.33i	0.259922	+	0.450198i
$569$	8726.08	−	15114.0i	0.642911	−	1.11355i	−0.341869	−	0.939748i	$-0.611060\pi$
$569$	8726.08	−	15114.0i	0.642911	−	1.11355i	0.984780	−	0.173807i	$-0.0556067\pi$
$570$		0			0
$571$	−20181.4			−1.47910			−0.739548	−	0.673103i	$-0.764961\pi$
$571$	−20181.4			−1.47910			−0.739548	+	0.673103i	$0.764961\pi$
$572$	−13633.2	+	7708.23i	−0.996563	+	0.563457i
$573$		0			0
$574$	26223.9	−	45421.1i	1.90691	−	3.30286i
$575$	−285.218	+	494.012i	−0.0206859	+	0.0358291i
$576$		0			0
$577$	6382.72			0.460513			0.230257	−	0.973130i	$-0.426043\pi$
$577$	6382.72			0.460513			0.230257	+	0.973130i	$0.426043\pi$
$578$	5225.67	+	9051.12i	0.376054	+	0.651344i
$579$		0			0
$580$	−5834.73			−0.417714
$581$	−5799.57	−	10045.1i	−0.414125	−	0.717285i
$582$		0			0
$583$	1148.94	−	1990.02i	0.0816197	−	0.141369i
$584$	7611.72			0.539341
$585$		0			0
$586$	20715.2			1.46030
$587$	−387.763	+	671.626i	−0.0272653	+	0.0472248i	−0.879336	−	0.476202i	$-0.842013\pi$
$587$	−387.763	+	671.626i	−0.0272653	+	0.0472248i	0.852071	+	0.523427i	$0.175347\pi$
$588$		0			0
$589$	−11819.5	−	20472.0i	−0.826849	−	1.43214i
$590$	−624.072			−0.0435468
$591$		0			0
$592$	−1735.74	−	3006.38i	−0.120504	−	0.208719i
$593$	17843.3			1.23564			0.617821	−	0.786319i	$-0.288016\pi$
$593$	17843.3			1.23564			0.617821	+	0.786319i	$0.288016\pi$
$594$		0			0
$595$	3491.38	−	6047.24i	0.240559	−	0.416660i
$596$	−3910.17	+	6772.61i	−0.268736	+	0.465464i
$597$		0			0
$598$	−1073.65	−	632.835i	−0.0734192	−	0.0432751i
$599$	24373.3			1.66255			0.831274	−	0.555863i	$-0.187612\pi$
$599$	24373.3			1.66255			0.831274	+	0.555863i	$0.187612\pi$
$600$		0			0
$601$	1763.50	−	3054.46i	0.119691	−	0.207311i	−0.799954	−	0.600061i	$-0.795143\pi$
$601$	1763.50	−	3054.46i	0.119691	−	0.207311i	0.919645	+	0.392750i	$0.128476\pi$
$602$	−13671.4	−	23679.6i	−0.925589	−	1.60317i
$603$		0			0
$604$	661.638	+	1145.99i	0.0445723	+	0.0772015i
$605$	534.748	+	926.211i	0.0359349	+	0.0622411i
$606$		0			0
$607$	−3995.77	−	6920.88i	−0.267189	−	0.462784i	0.700946	−	0.713214i	$-0.252761\pi$
$607$	−3995.77	−	6920.88i	−0.267189	−	0.462784i	−0.968135	+	0.250430i	$0.919428\pi$
$608$	−9831.82	+	17029.2i	−0.655811	+	1.13590i
$609$		0			0
$610$	−14581.1			−0.967821
$611$	−18806.1	+	10633.0i	−1.24520	+	0.704034i
$612$		0			0
$613$	8166.09	−	14144.1i	0.538051	−	0.931932i	−0.460958	−	0.887422i	$-0.652494\pi$
$613$	8166.09	−	14144.1i	0.538051	−	0.931932i	0.999009	−	0.0445098i	$-0.0141726\pi$
$614$	−12256.9	+	21229.5i	−0.805615	+	1.39537i
$615$		0			0
$616$	−6425.04			−0.420247
$617$	−9676.82	−	16760.8i	−0.631401	−	1.09362i	−0.987266	−	0.159081i	$-0.949147\pi$
$617$	−9676.82	−	16760.8i	−0.631401	−	1.09362i	0.355865	−	0.934537i	$-0.384186\pi$
$618$		0			0
$619$	−9982.52			−0.648193			−0.324096	−	0.946024i	$-0.605060\pi$
$619$	−9982.52			−0.648193			−0.324096	+	0.946024i	$0.605060\pi$
$620$	8884.79	+	15388.9i	0.575519	+	0.996829i
$621$		0			0
$622$	−10382.4	+	17982.8i	−0.669286	+	1.15924i
$623$	26198.0			1.68475
$624$		0			0
$625$	3928.53			0.251426
$626$	17126.0	−	29663.2i	1.09344	−	1.89389i
$627$		0			0
$628$	−7439.36	−	12885.4i	−0.472712	−	0.818761i
$629$	−3755.00			−0.238031
$630$		0			0
$631$	287.887	+	498.636i	0.0181626	+	0.0314586i	0.874964	−	0.484188i	$-0.160885\pi$
$631$	287.887	+	498.636i	0.0181626	+	0.0314586i	−0.856801	+	0.515647i	$0.827552\pi$
$632$	−935.578			−0.0588850
$633$		0			0
$634$	10881.9	−	18848.0i	0.681666	−	1.18068i
$635$	350.120	−	606.426i	0.0218805	−	0.0378981i
$636$		0			0
$637$	100.935	−	11203.7i	0.00627814	−	0.696873i
$638$	−14464.3			−0.897566
$639$		0			0
$640$	2867.40	−	4966.48i	0.177100	−	0.306746i
$641$	−12260.9	−	21236.5i	−0.755500	−	1.30856i	−0.945125	−	0.326708i	$-0.894061\pi$
$641$	−12260.9	−	21236.5i	−0.755500	−	1.30856i	0.189625	−	0.981857i	$-0.439273\pi$
$642$		0			0
$643$	11333.5	+	19630.2i	0.695099	+	1.20395i	0.970147	+	0.242517i	$0.0779730\pi$
$643$	11333.5	+	19630.2i	0.695099	+	1.20395i	−0.275048	+	0.961431i	$0.588694\pi$
$644$	−748.281	−	1296.06i	−0.0457864	−	0.0793043i
$645$		0			0
$646$	8021.67	+	13893.9i	0.488558	+	0.846207i
$647$	−1198.73	+	2076.25i	−0.0728389	+	0.126161i	−0.900144	−	0.435592i	$-0.856539\pi$
$647$	−1198.73	+	2076.25i	−0.0728389	+	0.126161i	0.827306	+	0.561752i	$0.189873\pi$
$648$		0			0
$649$	−854.078			−0.0516572
$650$	−161.791	+	17958.8i	−0.00976302	+	1.08369i
$651$		0			0
$652$	−5792.87	+	10033.5i	−0.347954	+	0.602674i
$653$	10001.0	−	17322.3i	0.599342	−	1.03809i	−0.393576	−	0.919292i	$-0.628762\pi$
$653$	10001.0	−	17322.3i	0.599342	−	1.03809i	0.992918	−	0.118799i	$-0.0379045\pi$
$654$		0			0
$655$	13193.9			0.787068
$656$	11745.7	+	20344.1i	0.699073	+	1.21083i
$657$		0			0
$658$	−46992.5			−2.78413
$659$	−1758.98	−	3046.64i	−0.103976	−	0.180091i	0.809343	−	0.587336i	$-0.199823\pi$
$659$	−1758.98	−	3046.64i	−0.103976	−	0.180091i	−0.913319	+	0.407244i	$0.866490\pi$
$660$		0			0
$661$	−6791.71	+	11763.6i	−0.399647	+	0.692209i	−0.993682	−	0.112230i	$-0.964201\pi$
$661$	−6791.71	+	11763.6i	−0.399647	+	0.692209i	0.594035	+	0.804439i	$0.297534\pi$
$662$	25618.2			1.50405
$663$		0			0
$664$	−3778.24			−0.220819
$665$	−5432.25	+	9408.93i	−0.316772	+	0.548665i
$666$		0			0
$667$	−317.713	−	550.295i	−0.0184436	−	0.0319453i
$668$	−14533.1			−0.841770
$669$		0			0
$670$	12436.6	+	21540.8i	0.717114	+	1.24208i
$671$	−19955.1			−1.14807
$672$		0			0
$673$	5447.92	−	9436.07i	0.312038	−	0.540466i	−0.666765	−	0.745268i	$-0.732322\pi$
$673$	5447.92	−	9436.07i	0.312038	−	0.540466i	0.978804	+	0.204801i	$0.0656549\pi$
$674$	−7910.11	+	13700.7i	−0.452057	+	0.782985i
$675$		0			0
$676$	−21657.9	−	390.264i	−1.23224	−	0.0222044i
$677$	−1449.03			−0.0822609			−0.0411305	−	0.999154i	$-0.513096\pi$
$677$	−1449.03			−0.0822609			−0.0411305	+	0.999154i	$0.513096\pi$
$678$		0			0
$679$	−200.907	+	347.982i	−0.0113551	+	0.0196676i
$680$	−1137.26	−	1969.80i	−0.0641353	−	0.111086i
$681$		0			0
$682$	22025.4	+	38149.2i	1.23665	+	2.14195i
$683$	−7683.21	−	13307.7i	−0.430439	−	0.745543i	0.566472	−	0.824081i	$-0.308308\pi$
$683$	−7683.21	−	13307.7i	−0.430439	−	0.745543i	−0.996911	+	0.0785385i	$0.974975\pi$
$684$		0			0
$685$	3312.45	+	5737.34i	0.184763	+	0.320018i
$686$	−5299.79	+	9179.51i	−0.294966	+	0.510897i
$687$		0			0
$688$	12246.9			0.678644
$689$	2766.61	−	1564.24i	0.152974	−	0.0864918i
$690$		0			0
$691$	1009.85	−	1749.12i	0.0555957	−	0.0962946i	−0.836888	−	0.547374i	$-0.815628\pi$
$691$	1009.85	−	1749.12i	0.0555957	−	0.0962946i	0.892484	+	0.451079i	$0.148961\pi$
$692$	−11478.0	+	19880.5i	−0.630532	+	1.09211i
$693$		0			0
$694$	10651.4			0.582595
$695$	1744.05	+	3020.79i	0.0951880	+	0.164870i
$696$		0			0
$697$	25410.0			1.38088
$698$	−22505.3	−	38980.3i	−1.22040	−	2.11379i
$699$		0			0
$700$	−10783.1	+	18677.0i	−0.582235	+	1.00846i
$701$	−28031.6			−1.51033			−0.755164	−	0.655536i	$-0.772443\pi$
$701$	−28031.6			−1.51033			−0.755164	+	0.655536i	$0.772443\pi$
$702$		0			0
$703$	5842.42			0.313444
$704$	12131.1	−	21011.7i	0.649443	−	1.12487i
$705$		0			0
$706$	−19023.2	−	32949.2i	−1.01409	−	1.75646i
$707$	−23112.3			−1.22946
$708$		0			0
$709$	−9802.22	−	16977.9i	−0.519224	−	0.899323i	−0.999750	−	0.0223423i	$-0.992888\pi$
$709$	−9802.22	−	16977.9i	−0.519224	−	0.899323i	0.480526	−	0.876980i	$-0.340446\pi$
$710$	−22174.5			−1.17211
$711$		0			0
$712$	4266.79	−	7390.31i	0.224586	−	0.388994i
$713$	−967.590	+	1675.91i	−0.0508226	+	0.0880274i
$714$		0			0
$715$	83.8493	−	9307.26i	0.00438571	−	0.486813i
$716$	21038.8			1.09812
$717$		0			0
$718$	−24005.9	+	41579.5i	−1.24776	+	2.16119i
$719$	−7363.71	−	12754.3i	−0.381947	−	0.661552i	0.609393	−	0.792868i	$-0.291413\pi$
$719$	−7363.71	−	12754.3i	−0.381947	−	0.661552i	−0.991341	+	0.131316i	$0.958080\pi$
$720$		0			0
$721$	−32.6369	−	56.5287i	−0.00168580	−	0.00291989i
$722$	2012.31	+	3485.43i	0.103726	+	0.179659i
$723$		0			0
$724$	12252.5	+	21221.9i	0.628950	+	1.08937i
$725$	−4578.42	+	7930.05i	−0.234535	+	0.406227i
$726$		0			0
$727$	−16890.5			−0.861668			−0.430834	−	0.902431i	$-0.641781\pi$
$727$	−16890.5			−0.861668			−0.430834	+	0.902431i	$0.641781\pi$
$728$	−7655.57	−	4512.38i	−0.389745	−	0.229725i
$729$		0			0
$730$	−11992.6	+	20771.7i	−0.608034	+	1.05315i
$731$	6623.56	−	11472.3i	0.335131	−	0.580465i
$732$		0			0
$733$	12553.6			0.632578			0.316289	−	0.948663i	$-0.397563\pi$
$733$	12553.6			0.632578			0.316289	+	0.948663i	$0.397563\pi$
$734$	29453.1	+	51014.3i	1.48111	+	2.56536i
$735$		0			0
$736$	1609.74			0.0806194
$737$	17020.2	+	29479.8i	0.850673	+	1.47341i
$738$		0			0
$739$	18937.4	−	32800.5i	0.942656	−	1.63273i	0.182278	−	0.983247i	$-0.441653\pi$
$739$	18937.4	−	32800.5i	0.942656	−	1.63273i	0.760378	−	0.649481i	$-0.225014\pi$
$740$	−4391.78			−0.218169
$741$		0			0
$742$	6913.16			0.342035
$743$	17941.3	−	31075.3i	0.885872	−	1.53438i	0.0411616	−	0.999153i	$-0.486894\pi$
$743$	17941.3	−	31075.3i	0.885872	−	1.53438i	0.844711	−	0.535223i	$-0.179773\pi$
$744$		0			0
$745$	−2323.82	−	4024.97i	−0.114279	−	0.197938i
$746$	6732.40			0.330416
$747$		0			0
$748$	−8252.32	−	14293.4i	−0.403389	−	0.698690i
$749$	32600.3			1.59037
$750$		0			0
$751$	90.8447	−	157.348i	0.00441407	−	0.00764540i	−0.863810	−	0.503818i	$-0.831928\pi$
$751$	90.8447	−	157.348i	0.00441407	−	0.00764540i	0.868224	+	0.496172i	$0.165262\pi$
$752$	10524.0	−	18228.1i	0.510333	−	0.883922i
$753$		0			0
$754$	−17234.5	−	10158.5i	−0.832420	−	0.490649i
$755$	−786.425			−0.0379085
$756$		0			0
$757$	245.526	−	425.264i	0.0117884	−	0.0204181i	−0.860071	−	0.510174i	$-0.829581\pi$
$757$	245.526	−	425.264i	0.0117884	−	0.0204181i	0.871859	+	0.489756i	$0.162914\pi$
$758$	−19307.9	−	33442.3i	−0.925191	−	1.60248i
$759$		0			0
$760$	1769.47	+	3064.81i	0.0844545	+	0.146279i
$761$	−4056.50	−	7026.07i	−0.193230	−	0.334684i	0.753089	−	0.657919i	$-0.228563\pi$
$761$	−4056.50	−	7026.07i	−0.193230	−	0.334684i	−0.946319	+	0.323235i	$0.895230\pi$
$762$		0			0
$763$	5409.58	+	9369.67i	0.256671	+	0.444567i
$764$	−11462.0	+	19852.8i	−0.542777	+	0.940118i
$765$		0			0
$766$	−40363.3			−1.90390
$767$	−1017.65	−	599.830i	−0.0479078	−	0.0282381i
$768$		0			0
$769$	−9932.33	+	17203.3i	−0.465759	+	0.806719i	−0.999235	−	0.0390962i	$-0.987552\pi$
$769$	−9932.33	+	17203.3i	−0.465759	+	0.806719i	0.533476	+	0.845815i	$0.320885\pi$
$770$	10122.9	−	17533.4i	0.473771	−	0.820596i
$771$		0			0
$772$	33030.6			1.53989
$773$	4523.71	+	7835.29i	0.210487	+	0.364574i	0.951867	−	0.306511i	$-0.0991617\pi$
$773$	4523.71	+	7835.29i	0.210487	+	0.364574i	−0.741380	+	0.671085i	$0.765828\pi$
$774$		0			0
$775$	27887.0			1.29256
$776$	65.4424	+	113.350i	0.00302738	+	0.00524358i
$777$		0			0
$778$	15565.6	−	26960.4i	0.717293	−	1.24239i
$779$	−39535.5			−1.81837
$780$		0			0
$781$	−30347.1			−1.39040
$782$	656.685	−	1137.41i	0.0300294	−	0.0520125i
$783$		0			0
$784$	5457.92	+	9453.39i	0.248630	+	0.430639i
$785$	8842.45			0.402039
$786$		0			0
$787$	7509.20	+	13006.3i	0.340120	+	0.589105i	0.984455	−	0.175639i	$-0.0561991\pi$
$787$	7509.20	+	13006.3i	0.340120	+	0.589105i	−0.644335	+	0.764743i	$0.722866\pi$
$788$	38050.9			1.72019
$789$		0			0
$790$	1474.04	−	2553.11i	0.0663848	−	0.114982i
$791$	−16873.9	+	29226.4i	−0.758491	+	1.31375i
$792$		0			0
$793$	−23776.9	−	14014.7i	−1.06474	−	0.627587i
$794$	−49429.9			−2.20932
$795$		0			0
$796$	20131.2	−	34868.2i	0.896396	−	1.55260i
$797$	15970.5	+	27661.8i	0.709794	+	1.22940i	0.964933	+	0.262495i	$0.0845453\pi$
$797$	15970.5	+	27661.8i	0.709794	+	1.22940i	−0.255139	+	0.966904i	$0.582121\pi$
$798$		0			0
$799$	−11383.5	−	19716.9i	−0.504030	−	0.873006i
$800$	−11598.6	−	20089.4i	−0.512592	−	0.887835i
$801$		0			0
$802$	−29936.6	−	51851.7i	−1.31808	−	2.28298i
$803$	−16412.5	+	28427.3i	−0.721277	+	1.24929i
$804$		0			0
$805$	889.409			0.0389411
$806$	−548.868	+	60924.3i	−0.0239864	+	2.66249i
$807$		0			0
$808$	−3764.23	+	6519.84i	−0.163892	+	0.283870i
$809$	13630.0	−	23607.9i	0.592344	−	1.02597i	−0.401572	−	0.915827i	$-0.631536\pi$
$809$	13630.0	−	23607.9i	0.592344	−	1.02597i	0.993916	−	0.110142i	$-0.0351306\pi$
$810$		0			0
$811$	−20707.8			−0.896607			−0.448303	−	0.893881i	$-0.647972\pi$
$811$	−20707.8			−0.896607			−0.448303	+	0.893881i	$0.647972\pi$
$812$	−12011.7	−	20804.8i	−0.519121	−	0.899145i
$813$		0			0
$814$	−10887.2			−0.468793
$815$	−3442.71	−	5962.95i	−0.147967	−	0.256286i
$816$		0			0
$817$	−10305.6	+	17849.8i	−0.441307	+	0.764366i
$818$	11426.0			0.488385
$819$		0			0
$820$	29719.1			1.26565
$821$	7829.28	−	13560.7i	0.332818	−	0.576458i	−0.650245	−	0.759724i	$-0.725334\pi$
$821$	7829.28	−	13560.7i	0.332818	−	0.576458i	0.983063	+	0.183267i	$0.0586672\pi$
$822$		0			0
$823$	2053.29	+	3556.40i	0.0869662	+	0.150630i	0.906227	−	0.422791i	$-0.138949\pi$
$823$	2053.29	+	3556.40i	0.0869662	+	0.150630i	−0.819261	+	0.573421i	$0.805616\pi$
$824$	−21.2619			−0.000898900
$825$		0			0
$826$	−1284.74	−	2225.24i	−0.0541186	−	0.0937362i
$827$	−16747.3			−0.704184			−0.352092	−	0.935965i	$-0.614530\pi$
$827$	−16747.3			−0.704184			−0.352092	+	0.935965i	$0.614530\pi$
$828$		0			0
$829$	14578.5	−	25250.8i	0.610776	−	1.05790i	−0.380334	−	0.924849i	$-0.624191\pi$
$829$	14578.5	−	25250.8i	0.610776	−	1.05790i	0.991110	−	0.133046i	$-0.0424758\pi$
$830$	5952.76	−	10310.5i	0.248944	−	0.431183i
$831$		0			0
$832$	29211.2	−	16516.0i	1.21721	−	0.688210i
$833$	11807.4			0.491119
$834$		0			0
$835$	4318.52	−	7479.89i	0.178980	−	0.310003i
$836$	12839.8	+	22239.2i	0.531189	+	0.920047i
$837$		0			0
$838$	15092.3	+	26140.7i	0.622144	+	1.07758i
$839$	22909.7	+	39680.8i	0.942707	+	1.63282i	0.760278	+	0.649598i	$0.225063\pi$
$839$	22909.7	+	39680.8i	0.942707	+	1.63282i	0.182429	+	0.983219i	$0.441604\pi$
$840$		0			0
$841$	7094.47	+	12288.0i	0.290888	+	0.503833i
$842$	7197.92	−	12467.2i	0.294604	−	0.510270i
$843$		0			0
$844$	29847.7			1.21730
$845$	6636.51	−	11030.9i	0.270181	−	0.449083i
$846$		0			0
$847$	−2201.72	+	3813.49i	−0.0893175	+	0.154703i
$848$	−1548.20	+	2681.57i	−0.0626952	+	0.108591i
$849$		0			0
$850$	−18926.4			−0.763729
$851$	−239.142	−	414.205i	−0.00963298	−	0.0166848i
$852$		0			0
$853$	17351.1			0.696471			0.348235	−	0.937407i	$-0.386781\pi$
$853$	17351.1			0.696471			0.348235	+	0.937407i	$0.386781\pi$
$854$	−30017.3	−	51991.5i	−1.20278	−	2.08327i
$855$		0			0
$856$	5309.52	−	9196.36i	0.212004	−	0.367202i
$857$	21768.1			0.867659			0.433829	−	0.900995i	$-0.357162\pi$
$857$	21768.1			0.867659			0.433829	+	0.900995i	$0.357162\pi$
$858$		0			0
$859$	−29878.4			−1.18677			−0.593387	−	0.804918i	$-0.702209\pi$
$859$	−29878.4			−1.18677			−0.593387	+	0.804918i	$0.702209\pi$
$860$	7746.80	−	13417.8i	0.307167	−	0.532029i
$861$		0			0
$862$	10930.6	+	18932.4i	0.431901	+	0.748074i
$863$	15067.7			0.594335			0.297168	−	0.954825i	$-0.403958\pi$
$863$	15067.7			0.594335			0.297168	+	0.954825i	$0.403958\pi$
$864$		0			0
$865$	−6821.40	−	11815.0i	−0.268132	−	0.464419i
$866$	46296.3			1.81664
$867$		0			0
$868$	−36581.4	+	63360.8i	−1.43047	+	2.47765i
$869$	2017.31	−	3494.08i	0.0787486	−	0.136397i
$870$		0			0
$871$	−424.138	+	47079.3i	−0.0164999	+	1.83148i
$872$	3524.17			0.136862
$873$		0			0
$874$	−1021.74	+	1769.70i	−0.0395432	+	0.0684909i
$875$	−15243.7	−	26402.8i	−0.588949	−	1.02009i
$876$		0			0
$877$	10559.8	+	18290.1i	0.406588	+	0.704232i	0.994505	−	0.104690i	$-0.0333850\pi$
$877$	10559.8	+	18290.1i	0.406588	+	0.704232i	−0.587917	+	0.808922i	$0.700052\pi$
$878$	−25002.3	−	43305.2i	−0.961032	−	1.66456i
$879$		0			0
$880$	4534.05	+	7853.20i	0.173685	+	0.300831i
$881$	15826.2	−	27411.9i	0.605221	−	1.04827i	−0.386795	−	0.922166i	$-0.626418\pi$
$881$	15826.2	−	27411.9i	0.605221	−	1.04827i	0.992016	−	0.126108i	$-0.0402487\pi$
$882$		0			0
$883$	11701.6			0.445969			0.222984	−	0.974822i	$-0.428420\pi$
$883$	11701.6			0.445969			0.222984	+	0.974822i	$0.428420\pi$
$884$	205.646	−	22826.7i	0.00782423	−	0.868488i
$885$		0			0
$886$	28483.3	−	49334.5i	1.08004	−	1.87068i
$887$	11254.0	−	19492.4i	0.426010	−	0.737871i	−0.570504	−	0.821295i	$-0.693252\pi$
$887$	11254.0	−	19492.4i	0.426010	−	0.737871i	0.996514	+	0.0834239i	$0.0265855\pi$
$888$		0			0
$889$	2883.10			0.108769
$890$	13445.0	+	23287.4i	0.506379	+	0.877075i
$891$		0			0
$892$	−17005.3			−0.638318
$893$	17711.7	+	30677.5i	0.663716	+	1.14959i
$894$		0			0
$895$	−6251.69	+	10828.2i	−0.233487	+	0.404412i
$896$	23611.9			0.880377
$897$		0			0
$898$	28628.7			1.06387
$899$	−15532.1	+	26902.3i	−0.576222	+	0.998046i
$900$		0			0
$901$	1674.65	+	2900.58i	0.0619210	+	0.107250i
$902$	73673.8			2.71959
$903$		0			0
$904$	5496.41	+	9520.06i	0.202221	+	0.350257i
$905$	−14563.3			−0.534919
$906$		0			0
$907$	−9359.32	+	16210.8i	−0.342636	+	0.593464i	−0.984921	−	0.173002i	$-0.944653\pi$
$907$	−9359.32	+	16210.8i	−0.342636	+	0.593464i	0.642285	+	0.766466i	$0.277987\pi$
$908$	−9481.29	+	16422.1i	−0.346528	+	0.600205i
$909$		0			0
$910$	24375.6	−	13781.9i	0.887958	−	0.502052i
$911$	−18616.7			−0.677057			−0.338529	−	0.940956i	$-0.609929\pi$
$911$	−18616.7			−0.677057			−0.338529	+	0.940956i	$0.609929\pi$
$912$		0			0
$913$	8146.69	−	14110.5i	0.295308	−	0.511488i
$914$	9809.44	+	16990.4i	0.354997	+	0.614873i
$915$		0			0
$916$	−1843.70	−	3193.38i	−0.0665038	−	0.115188i
$917$	27161.7	+	47045.4i	0.978143	+	1.69419i
$918$		0			0
$919$	27382.2	+	47427.3i	0.982867	+	1.70238i	0.651056	+	0.759030i	$0.274326\pi$
$919$	27382.2	+	47427.3i	0.982867	+	1.70238i	0.331812	+	0.943346i	$0.392340\pi$
$920$	144.856	−	250.897i	0.00519103	−	0.00899113i
$921$		0			0
$922$	−10397.6			−0.371397
$923$	−36159.2	−	21313.2i	−1.28949	−	0.760056i
$924$		0			0
$925$	−3446.16	+	5968.93i	−0.122496	+	0.212170i
$926$	−9064.90	+	15700.9i	−0.321697	+	0.557195i
$927$		0			0
$928$	25840.1			0.914055
$929$	−15916.0	−	27567.4i	−0.562097	−	0.973581i	−0.997313	−	0.0732550i	$-0.976661\pi$
$929$	−15916.0	−	27567.4i	−0.562097	−	0.973581i	0.435216	−	0.900326i	$-0.356672\pi$
$930$		0			0
$931$	−18371.2			−0.646713
$932$	15255.1	+	26422.7i	0.536157	+	0.928651i
$933$		0			0
$934$	−18592.5	+	32203.2i	−0.651355	+	1.12818i
$935$	9808.73			0.343080
$936$		0			0
$937$	−27408.7			−0.955607			−0.477803	−	0.878467i	$-0.658567\pi$
$937$	−27408.7			−0.955607			−0.477803	+	0.878467i	$0.658567\pi$
$938$	−51205.1	+	88689.8i	−1.78241	+	3.08723i
$939$		0			0
$940$	−13314.0	−	23060.5i	−0.461972	−	0.800159i
$941$	−54837.8			−1.89975			−0.949874	−	0.312634i	$-0.898789\pi$
$941$	−54837.8			−1.89975			−0.949874	+	0.312634i	$0.898789\pi$
$942$		0			0
$943$	1618.27	+	2802.92i	0.0558833	+	0.0967928i
$944$	1150.87			0.0396799
$945$		0			0
$946$	19204.3	−	33262.9i	0.660028	−	1.14320i
$947$	−19853.9	+	34388.0i	−0.681273	+	1.18000i	0.293320	+	0.956014i	$0.405240\pi$
$947$	−19853.9	+	34388.0i	−0.681273	+	1.18000i	−0.974593	+	0.223984i	$0.928094\pi$
$948$		0			0
$949$	−39520.8	+	22345.0i	−1.35184	+	0.764332i
$950$	29447.6			1.00569
$951$		0			0
$952$	4682.45	−	8110.24i	0.159411	−	0.276107i
$953$	−8553.32	−	14814.8i	−0.290734	−	0.503566i	0.683250	−	0.730185i	$-0.260566\pi$
$953$	−8553.32	−	14814.8i	−0.290734	−	0.503566i	−0.973983	+	0.226619i	$0.927233\pi$
$954$		0			0
$955$	−6811.90	−	11798.6i	−0.230815	−	0.399783i
$956$	−6020.15	−	10427.2i	−0.203667	−	0.352761i
$957$		0			0
$958$	−23187.0	−	40161.1i	−0.781982	−	1.35443i
$959$	−13638.4	+	23622.3i	−0.459234	+	0.795417i
$960$		0			0
$961$	64814.4			2.17564
$962$	−12972.4	−	7646.25i	−0.434768	−	0.256263i
$963$		0			0
$964$	−716.791	+	1241.52i	−0.0239484	+	0.0414799i
$965$	−9815.06	+	17000.2i	−0.327417	+	0.567104i
$966$		0			0
$967$	−23417.5			−0.778756			−0.389378	−	0.921078i	$-0.627310\pi$
$967$	−23417.5			−0.778756			−0.389378	+	0.921078i	$0.627310\pi$
$968$	717.175	+	1242.18i	0.0238129	+	0.0412452i
$969$		0			0
$970$	−412.428			−0.0136518
$971$	8215.31	+	14229.3i	0.271516	+	0.470279i	0.969250	−	0.246077i	$-0.0791417\pi$
$971$	8215.31	+	14229.3i	0.271516	+	0.470279i	−0.697734	+	0.716357i	$0.745808\pi$
$972$		0			0
$973$	−7180.78	+	12437.5i	−0.236593	+	0.409792i
$974$	−22015.9			−0.724267
$975$		0			0
$976$	26889.5			0.881879
$977$	−5277.32	+	9140.58i	−0.172811	+	0.299318i	−0.939402	−	0.342819i	$-0.888618\pi$
$977$	−5277.32	+	9140.58i	−0.172811	+	0.299318i	0.766591	+	0.642136i	$0.221952\pi$
$978$		0			0
$979$	18400.3	+	31870.2i	0.600689	+	1.04042i
$980$	13809.7			0.450138
$981$		0			0
$982$	−18550.7	−	32130.8i	−0.602829	−	1.04413i
$983$	−1534.33			−0.0497839			−0.0248919	−	0.999690i	$-0.507924\pi$
$983$	−1534.33			−0.0497839			−0.0248919	+	0.999690i	$0.507924\pi$
$984$		0			0
$985$	−11306.9	+	19584.1i	−0.365753	+	0.633502i
$986$	10541.3	−	18258.1i	0.340471	−	0.589712i
$987$		0			0
$988$	−319.965	+	35516.1i	−0.0103031	+	1.14364i
$989$	1687.31			0.0542502
$990$		0			0
$991$	9009.08	−	15604.2i	0.288782	−	0.500185i	−0.684737	−	0.728790i	$-0.740083\pi$
$991$	9009.08	−	15604.2i	0.288782	−	0.500185i	0.973519	+	0.228605i	$0.0734165\pi$
$992$	−39347.8	−	68152.5i	−1.25937	−	2.18129i
$993$		0			0
$994$	−45649.6	−	79067.3i	−1.45666	−	2.52300i
$995$	11964.0	+	20722.2i	0.381190	+	0.660240i
$996$		0			0
$997$	−24143.8	−	41818.4i	−0.766944	−	1.32839i	−0.939213	−	0.343336i	$-0.888443\pi$
$997$	−24143.8	−	41818.4i	−0.766944	−	1.32839i	0.172269	−	0.985050i	$-0.444890\pi$
$998$	32942.2	−	57057.6i	1.04486	−	1.80975i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.g.e.100.1		8
3.2	odd	2		39.4.e.c.22.4	yes	8
12.11	even	2		624.4.q.i.529.2		8
13.3	even	3	inner	117.4.g.e.55.1		8
13.4	even	6		1521.4.a.bb.1.1		4
13.9	even	3		1521.4.a.v.1.4		4
39.17	odd	6		507.4.a.i.1.4		4
39.20	even	12		507.4.b.h.337.2		8
39.29	odd	6		39.4.e.c.16.4	✓	8
39.32	even	12		507.4.b.h.337.7		8
39.35	odd	6		507.4.a.m.1.1		4
156.107	even	6		624.4.q.i.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.c.16.4	✓	8	39.29	odd	6
39.4.e.c.22.4	yes	8	3.2	odd	2
117.4.g.e.55.1		8	13.3	even	3	inner
117.4.g.e.100.1		8	1.1	even	1	trivial
507.4.a.i.1.4		4	39.17	odd	6
507.4.a.m.1.1		4	39.35	odd	6
507.4.b.h.337.2		8	39.20	even	12
507.4.b.h.337.7		8	39.32	even	12
624.4.q.i.289.2		8	156.107	even	6
624.4.q.i.529.2		8	12.11	even	2
1521.4.a.v.1.4		4	13.9	even	3
1521.4.a.bb.1.1		4	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11303 + 3.65987i) q^{2} +(-4.92977 - 8.53861i) q^{4} +5.85953 q^{5} +(12.0627 + 20.8932i) q^{7} +7.85849 q^{8} +O(q^{10})\)	\(q+(-2.11303 + 3.65987i) q^{2} +(-4.92977 - 8.53861i) q^{4} +5.85953 q^{5} +(12.0627 + 20.8932i) q^{7} +7.85849 q^{8} +(-12.3814 + 21.4451i) q^{10} +(-16.9446 + 29.3489i) q^{11} +(-40.8020 + 23.0694i) q^{13} -101.955 q^{14} +(22.8329 - 39.5478i) q^{16} +(-24.6978 - 42.7779i) q^{17} +(38.4274 + 66.5582i) q^{19} +(-28.8861 - 50.0322i) q^{20} +(-71.6088 - 124.030i) q^{22} +(3.14582 - 5.44871i) q^{23} -90.6659 q^{25} +(1.78447 - 198.076i) q^{26} +(118.933 - 205.998i) q^{28} +(50.4977 - 87.4645i) q^{29} -307.580 q^{31} +(127.927 + 221.576i) q^{32} +208.749 q^{34} +(70.6819 + 122.425i) q^{35} +(38.0095 - 65.8343i) q^{37} -324.793 q^{38} +46.0471 q^{40} +(-257.209 + 445.499i) q^{41} +(134.092 + 232.254i) q^{43} +334.132 q^{44} +(13.2944 + 23.0266i) q^{46} +460.912 q^{47} +(-119.519 + 207.012i) q^{49} +(191.579 - 331.825i) q^{50} +(398.125 + 234.665i) q^{52} -67.8057 q^{53} +(-99.2874 + 171.971i) q^{55} +(94.7947 + 164.189i) q^{56} +(213.406 + 369.630i) q^{58} +(12.6010 + 21.8256i) q^{59} +(294.416 + 509.944i) q^{61} +(649.925 - 1125.70i) q^{62} -715.927 q^{64} +(-239.080 + 135.176i) q^{65} +(502.230 - 869.888i) q^{67} +(-243.509 + 421.770i) q^{68} -597.411 q^{70} +(447.740 + 775.509i) q^{71} +968.599 q^{73} +(160.630 + 278.219i) q^{74} +(378.876 - 656.233i) q^{76} -817.592 q^{77} -119.053 q^{79} +(133.790 - 231.732i) q^{80} +(-1086.98 - 1882.70i) q^{82} -480.784 q^{83} +(-144.718 - 250.658i) q^{85} -1133.36 q^{86} +(-133.159 + 230.638i) q^{88} +(542.954 - 940.423i) q^{89} +(-974.179 - 574.205i) q^{91} -62.0325 q^{92} +(-973.920 + 1686.88i) q^{94} +(225.167 + 390.000i) q^{95} +(8.32761 + 14.4239i) q^{97} +(-505.092 - 874.845i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8	\( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8} + 62 q^{10} + 40 q^{11} - 60 q^{13} - 80 q^{14} - 122 q^{16} + 98 q^{17} - 124 q^{19} - 466 q^{20} - 220 q^{22} + 104 q^{23} - 116 q^{25} - 14 q^{26} + 144 q^{28} + 194 q^{29} + 52 q^{31} + 654 q^{32} + 2124 q^{34} + 88 q^{35} - 102 q^{37} - 664 q^{38} - 1996 q^{40} - 1054 q^{41} - 450 q^{43} + 88 q^{44} + 172 q^{46} + 192 q^{47} - 1070 q^{49} + 996 q^{50} + 2280 q^{52} - 524 q^{53} - 204 q^{55} + 2164 q^{56} - 722 q^{58} + 308 q^{59} + 928 q^{61} + 2780 q^{62} + 2052 q^{64} - 2346 q^{65} + 1134 q^{67} + 1786 q^{68} - 4648 q^{70} + 1064 q^{71} + 1904 q^{73} + 1158 q^{74} + 1708 q^{76} - 5016 q^{77} - 1492 q^{79} - 2922 q^{80} - 1734 q^{82} + 808 q^{83} + 1394 q^{85} - 6336 q^{86} - 3060 q^{88} + 1620 q^{89} + 3278 q^{91} - 664 q^{92} + 772 q^{94} + 2204 q^{95} - 2166 q^{97} - 1906 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 22 * q^4 + 12 * q^5 + 14 * q^7 - 108 * q^8 + 62 * q^10 + 40 * q^11 - 60 * q^13 - 80 * q^14 - 122 * q^16 + 98 * q^17 - 124 * q^19 - 466 * q^20 - 220 * q^22 + 104 * q^23 - 116 * q^25 - 14 * q^26 + 144 * q^28 + 194 * q^29 + 52 * q^31 + 654 * q^32 + 2124 * q^34 + 88 * q^35 - 102 * q^37 - 664 * q^38 - 1996 * q^40 - 1054 * q^41 - 450 * q^43 + 88 * q^44 + 172 * q^46 + 192 * q^47 - 1070 * q^49 + 996 * q^50 + 2280 * q^52 - 524 * q^53 - 204 * q^55 + 2164 * q^56 - 722 * q^58 + 308 * q^59 + 928 * q^61 + 2780 * q^62 + 2052 * q^64 - 2346 * q^65 + 1134 * q^67 + 1786 * q^68 - 4648 * q^70 + 1064 * q^71 + 1904 * q^73 + 1158 * q^74 + 1708 * q^76 - 5016 * q^77 - 1492 * q^79 - 2922 * q^80 - 1734 * q^82 + 808 * q^83 + 1394 * q^85 - 6336 * q^86 - 3060 * q^88 + 1620 * q^89 + 3278 * q^91 - 664 * q^92 + 772 * q^94 + 2204 * q^95 - 2166 * q^97 - 1906 * q^98

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