LMFDB - Embedded newform 117.4.q.c.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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, 5]))

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

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			82.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.82
Dual form			117.4.q.c.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} -13.8564i q^{5} +(19.5000 - 11.2583i) q^{7} -13.8564i q^{8} +O(q^{10})$	\(q+(3.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} -13.8564i q^{5} +(19.5000 - 11.2583i) q^{7} -13.8564i q^{8} +(24.0000 - 41.5692i) q^{10} +(19.5000 + 11.2583i) q^{11} +(-13.0000 + 45.0333i) q^{13} +78.0000 q^{14} +(40.0000 - 69.2820i) q^{16} +(13.5000 + 23.3827i) q^{17} +(-76.5000 + 44.1673i) q^{19} +(48.0000 - 27.7128i) q^{20} +(39.0000 + 67.5500i) q^{22} +(28.5000 - 49.3634i) q^{23} -67.0000 q^{25} +(-117.000 + 112.583i) q^{26} +(78.0000 + 45.0333i) q^{28} +(-34.5000 + 59.7558i) q^{29} -72.7461i q^{31} +(144.000 - 83.1384i) q^{32} +93.5307i q^{34} +(-156.000 - 270.200i) q^{35} +(-34.5000 - 19.9186i) q^{37} -306.000 q^{38} -192.000 q^{40} +(340.500 + 196.588i) q^{41} +(42.5000 + 73.6122i) q^{43} +90.0666i q^{44} +(171.000 - 98.7269i) q^{46} +342.946i q^{47} +(82.0000 - 142.028i) q^{49} +(-201.000 - 116.047i) q^{50} +(-182.000 + 45.0333i) q^{52} -426.000 q^{53} +(156.000 - 270.200i) q^{55} +(-156.000 - 270.200i) q^{56} +(-207.000 + 119.512i) q^{58} +(16.5000 - 9.52628i) q^{59} +(8.50000 + 14.7224i) q^{61} +(126.000 - 218.238i) q^{62} -64.0000 q^{64} +(624.000 + 180.133i) q^{65} +(142.500 + 82.2724i) q^{67} +(-54.0000 + 93.5307i) q^{68} -1080.80i q^{70} +(-505.500 + 291.851i) q^{71} +1004.59i q^{73} +(-69.0000 - 119.512i) q^{74} +(-306.000 - 176.669i) q^{76} +507.000 q^{77} -1244.00 q^{79} +(-960.000 - 554.256i) q^{80} +(681.000 + 1179.53i) q^{82} +426.084i q^{83} +(324.000 - 187.061i) q^{85} +294.449i q^{86} +(156.000 - 270.200i) q^{88} +(-265.500 - 153.286i) q^{89} +(253.500 + 1024.51i) q^{91} +228.000 q^{92} +(-594.000 + 1028.84i) q^{94} +(612.000 + 1060.02i) q^{95} +(1069.50 - 617.476i) q^{97} +(492.000 - 284.056i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 4 q^{4} + 39 q^{7}+O(q^{10}) $ 2 * q + 6 * q^2 + 4 * q^4 + 39 * q^7	$ 2 q + 6 q^{2} + 4 q^{4} + 39 q^{7} + 48 q^{10} + 39 q^{11} - 26 q^{13} + 156 q^{14} + 80 q^{16} + 27 q^{17} - 153 q^{19} + 96 q^{20} + 78 q^{22} + 57 q^{23} - 134 q^{25} - 234 q^{26} + 156 q^{28} - 69 q^{29} + 288 q^{32} - 312 q^{35} - 69 q^{37} - 612 q^{38} - 384 q^{40} + 681 q^{41} + 85 q^{43} + 342 q^{46} + 164 q^{49} - 402 q^{50} - 364 q^{52} - 852 q^{53} + 312 q^{55} - 312 q^{56} - 414 q^{58} + 33 q^{59} + 17 q^{61} + 252 q^{62} - 128 q^{64} + 1248 q^{65} + 285 q^{67} - 108 q^{68} - 1011 q^{71} - 138 q^{74} - 612 q^{76} + 1014 q^{77} - 2488 q^{79} - 1920 q^{80} + 1362 q^{82} + 648 q^{85} + 312 q^{88} - 531 q^{89} + 507 q^{91} + 456 q^{92} - 1188 q^{94} + 1224 q^{95} + 2139 q^{97} + 984 q^{98}+O(q^{100}) $ 2 * q + 6 * q^2 + 4 * q^4 + 39 * q^7 + 48 * q^10 + 39 * q^11 - 26 * q^13 + 156 * q^14 + 80 * q^16 + 27 * q^17 - 153 * q^19 + 96 * q^20 + 78 * q^22 + 57 * q^23 - 134 * q^25 - 234 * q^26 + 156 * q^28 - 69 * q^29 + 288 * q^32 - 312 * q^35 - 69 * q^37 - 612 * q^38 - 384 * q^40 + 681 * q^41 + 85 * q^43 + 342 * q^46 + 164 * q^49 - 402 * q^50 - 364 * q^52 - 852 * q^53 + 312 * q^55 - 312 * q^56 - 414 * q^58 + 33 * q^59 + 17 * q^61 + 252 * q^62 - 128 * q^64 + 1248 * q^65 + 285 * q^67 - 108 * q^68 - 1011 * q^71 - 138 * q^74 - 612 * q^76 + 1014 * q^77 - 2488 * q^79 - 1920 * q^80 + 1362 * q^82 + 648 * q^85 + 312 * q^88 - 531 * q^89 + 507 * q^91 + 456 * q^92 - 1188 * q^94 + 1224 * q^95 + 2139 * q^97 + 984 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	3.00000	+	1.73205i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	3.00000	+	1.73205i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$		0			0
$3$		0			0
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		−	13.8564i		−	1.23935i	−0.784857	−	0.619677i	$-0.787263\pi$
$5$		−	13.8564i		−	1.23935i	0.784857	−	0.619677i	$-0.212737\pi$
$6$		0			0
$7$	19.5000	−	11.2583i	1.05290	−	0.607893i	0.129441	−	0.991587i	$-0.458682\pi$
$7$	19.5000	−	11.2583i	1.05290	−	0.607893i	0.923460	+	0.383694i	$0.125348\pi$
$8$		−	13.8564i		−	0.612372i
$9$		0			0
$10$	24.0000	−	41.5692i	0.758947	−	1.31453i
$11$	19.5000	+	11.2583i	0.534497	+	0.308592i	0.742846	−	0.669462i	$-0.233475\pi$
$11$	19.5000	+	11.2583i	0.534497	+	0.308592i	−0.208349	+	0.978055i	$0.566809\pi$
$12$		0			0
$13$	−13.0000	+	45.0333i	−0.277350	+	0.960769i
$13$	−13.0000	+	45.0333i	−0.277350	+	0.960769i
$14$	78.0000			1.48903
$15$		0			0
$16$	40.0000	−	69.2820i	0.625000	−	1.08253i
$17$	13.5000	+	23.3827i	0.192602	+	0.333596i	0.946112	−	0.323840i	$-0.104974\pi$
$17$	13.5000	+	23.3827i	0.192602	+	0.333596i	−0.753510	+	0.657437i	$0.771641\pi$
$18$		0			0
$19$	−76.5000	+	44.1673i	−0.923700	+	0.533299i	−0.884814	−	0.465945i	$-0.845714\pi$
$19$	−76.5000	+	44.1673i	−0.923700	+	0.533299i	−0.0388865	+	0.999244i	$0.512381\pi$
$20$	48.0000	−	27.7128i	0.536656	−	0.309839i
$21$		0			0
$22$	39.0000	+	67.5500i	0.377947	+	0.654623i
$23$	28.5000	−	49.3634i	0.258377	−	0.447521i	−0.707431	−	0.706783i	$-0.750146\pi$
$23$	28.5000	−	49.3634i	0.258377	−	0.447521i	0.965807	+	0.259261i	$0.0834791\pi$
$24$		0			0
$25$	−67.0000			−0.536000
$26$	−117.000	+	112.583i	−0.882523	+	0.849208i
$27$		0			0
$28$	78.0000	+	45.0333i	0.526451	+	0.303946i
$29$	−34.5000	+	59.7558i	−0.220913	+	0.382633i	−0.955086	−	0.296330i	$-0.904237\pi$
$29$	−34.5000	+	59.7558i	−0.220913	+	0.382633i	0.734172	+	0.678963i	$0.237570\pi$
$30$		0			0
$31$		−	72.7461i		−	0.421471i	−0.977543	−	0.210735i	$-0.932414\pi$
$31$		−	72.7461i		−	0.421471i	0.977543	−	0.210735i	$-0.0675858\pi$
$32$	144.000	−	83.1384i	0.795495	−	0.459279i
$33$		0			0
$34$			93.5307i			0.471776i
$35$	−156.000	−	270.200i	−0.753395	−	1.30492i
$36$		0			0
$37$	−34.5000	−	19.9186i	−0.153291	−	0.0885026i	0.421393	−	0.906878i	$-0.361541\pi$
$37$	−34.5000	−	19.9186i	−0.153291	−	0.0885026i	−0.574683	+	0.818376i	$0.694875\pi$
$38$	−306.000			−1.30631
$39$		0			0
$40$	−192.000			−0.758947
$41$	340.500	+	196.588i	1.29700	+	0.748826i	0.979886	−	0.199560i	$-0.0639514\pi$
$41$	340.500	+	196.588i	1.29700	+	0.748826i	0.317118	+	0.948386i	$0.397285\pi$
$42$		0			0
$43$	42.5000	+	73.6122i	0.150725	+	0.261064i	0.931494	−	0.363756i	$-0.118506\pi$
$43$	42.5000	+	73.6122i	0.150725	+	0.261064i	−0.780769	+	0.624820i	$0.785172\pi$
$44$			90.0666i			0.308592i
$45$		0			0
$46$	171.000	−	98.7269i	0.548099	−	0.316445i
$47$			342.946i			1.06434i	0.846639	+	0.532168i	$0.178623\pi$
$47$			342.946i			1.06434i	−0.846639	+	0.532168i	$0.821377\pi$
$48$		0			0
$49$	82.0000	−	142.028i	0.239067	−	0.414076i
$50$	−201.000	−	116.047i	−0.568514	−	0.328232i
$51$		0			0
$52$	−182.000	+	45.0333i	−0.485363	+	0.120096i
$53$	−426.000			−1.10407			−0.552034	−	0.833822i	$-0.686148\pi$
$53$	−426.000			−1.10407			−0.552034	+	0.833822i	$0.686148\pi$
$54$		0			0
$55$	156.000	−	270.200i	0.382455	−	0.662432i
$56$	−156.000	−	270.200i	−0.372257	−	0.644768i
$57$		0			0
$58$	−207.000	+	119.512i	−0.468628	+	0.270563i
$59$	16.5000	−	9.52628i	0.0364088	−	0.0210206i	−0.481685	−	0.876344i	$-0.659975\pi$
$59$	16.5000	−	9.52628i	0.0364088	−	0.0210206i	0.518094	+	0.855324i	$0.326642\pi$
$60$		0			0
$61$	8.50000	+	14.7224i	0.0178412	+	0.0309019i	0.874808	−	0.484469i	$-0.160987\pi$
$61$	8.50000	+	14.7224i	0.0178412	+	0.0309019i	−0.856967	+	0.515371i	$0.827654\pi$
$62$	126.000	−	218.238i	0.258097	−	0.447037i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	624.000	+	180.133i	1.19073	+	0.343735i
$66$		0			0
$67$	142.500	+	82.2724i	0.259838	+	0.150018i	0.624261	−	0.781216i	$-0.285400\pi$
$67$	142.500	+	82.2724i	0.259838	+	0.150018i	−0.364423	+	0.931234i	$0.618734\pi$
$68$	−54.0000	+	93.5307i	−0.0963009	+	0.166798i
$69$		0			0
$70$		−	1080.80i		−	1.84543i
$71$	−505.500	+	291.851i	−0.844955	+	0.487835i	−0.858945	−	0.512067i	$-0.828880\pi$
$71$	−505.500	+	291.851i	−0.844955	+	0.487835i	0.0139904	+	0.999902i	$0.495547\pi$
$72$		0			0
$73$			1004.59i			1.61066i	0.592826	+	0.805331i	$0.298012\pi$
$73$			1004.59i			1.61066i	−0.592826	+	0.805331i	$0.701988\pi$
$74$	−69.0000	−	119.512i	−0.108393	−	0.187742i
$75$		0			0
$76$	−306.000	−	176.669i	−0.461850	−	0.266649i
$77$	507.000			0.750364
$78$		0			0
$79$	−1244.00			−1.77166			−0.885829	−	0.464012i	$-0.846409\pi$
$79$	−1244.00			−1.77166			−0.885829	+	0.464012i	$0.846409\pi$
$80$	−960.000	−	554.256i	−1.34164	−	0.774597i
$81$		0			0
$82$	681.000	+	1179.53i	0.917120	+	1.58850i
$83$			426.084i			0.563480i	0.959491	+	0.281740i	$0.0909116\pi$
$83$			426.084i			0.563480i	−0.959491	+	0.281740i	$0.909088\pi$
$84$		0			0
$85$	324.000	−	187.061i	0.413444	−	0.238702i
$86$			294.449i			0.369200i
$87$		0			0
$88$	156.000	−	270.200i	0.188973	−	0.327311i
$89$	−265.500	−	153.286i	−0.316213	−	0.182566i	0.333490	−	0.942753i	$-0.391774\pi$
$89$	−265.500	−	153.286i	−0.316213	−	0.182566i	−0.649703	+	0.760188i	$0.725107\pi$
$90$		0			0
$91$	253.500	+	1024.51i	0.292022	+	1.18019i
$92$	228.000			0.258377
$93$		0			0
$94$	−594.000	+	1028.84i	−0.651770	+	1.12890i
$95$	612.000	+	1060.02i	0.660946	+	1.14479i
$96$		0			0
$97$	1069.50	−	617.476i	1.11950	−	0.646342i	0.178225	−	0.983990i	$-0.442965\pi$
$97$	1069.50	−	617.476i	1.11950	−	0.646342i	0.941273	+	0.337647i	$0.109631\pi$
$98$	492.000	−	284.056i	0.507138	−	0.292796i
$99$		0			0
$100$	−134.000	−	232.095i	−0.134000	−	0.232095i
$101$	979.500	−	1696.54i	0.964989	−	1.67141i	0.255345	−	0.966850i	$-0.417811\pi$
$101$	979.500	−	1696.54i	0.964989	−	1.67141i	0.709645	−	0.704560i	$-0.248856\pi$
$102$		0			0
$103$	1856.00			1.77551			0.887753	−	0.460320i	$-0.152265\pi$
$103$	1856.00			1.77551			0.887753	+	0.460320i	$0.152265\pi$
$104$	624.000	+	180.133i	0.588348	+	0.169842i
$105$		0			0
$106$	−1278.00	−	737.854i	−1.17104	−	0.676101i
$107$	−127.500	+	220.836i	−0.115195	+	0.199524i	−0.917858	−	0.396909i	$-0.870083\pi$
$107$	−127.500	+	220.836i	−0.115195	+	0.199524i	0.802663	+	0.596433i	$0.203416\pi$
$108$		0			0
$109$		−	609.682i		−	0.535752i	−0.963453	−	0.267876i	$-0.913678\pi$
$109$		−	609.682i		−	0.535752i	0.963453	−	0.267876i	$-0.0863217\pi$
$110$	936.000	−	540.400i	0.811310	−	0.468410i
$111$		0			0
$112$		−	1801.33i		−	1.51973i
$113$	205.500	+	355.936i	0.171078	+	0.296316i	0.938797	−	0.344471i	$-0.111942\pi$
$113$	205.500	+	355.936i	0.171078	+	0.296316i	−0.767719	+	0.640787i	$0.778608\pi$
$114$		0			0
$115$	−684.000	−	394.908i	−0.554638	−	0.320220i
$116$	−276.000			−0.220913
$117$		0			0
$118$	66.0000			0.0514898
$119$	526.500	+	303.975i	0.405581	+	0.234162i
$120$		0			0
$121$	−412.000	−	713.605i	−0.309542	−	0.536142i
$122$			58.8897i			0.0437018i
$123$		0			0
$124$	252.000	−	145.492i	0.182502	−	0.105368i
$125$		−	803.672i		−	0.575061i
$126$		0			0
$127$	1121.50	−	1942.49i	0.783599	−	1.35723i	−0.146234	−	0.989250i	$-0.546715\pi$
$127$	1121.50	−	1942.49i	0.783599	−	1.35723i	0.929833	−	0.367983i	$-0.119951\pi$
$128$	−1344.00	−	775.959i	−0.928078	−	0.535826i
$129$		0			0
$130$	1560.00	+	1621.20i	1.05247	+	1.09376i
$131$	372.000			0.248105			0.124053	−	0.992276i	$-0.460411\pi$
$131$	372.000			0.248105			0.124053	+	0.992276i	$0.460411\pi$
$132$		0			0
$133$	−994.500	+	1722.52i	−0.648377	+	1.12302i
$134$	285.000	+	493.634i	0.183733	+	0.318235i
$135$		0			0
$136$	324.000	−	187.061i	0.204285	−	0.117944i
$137$	1030.50	−	594.959i	0.642639	−	0.371028i	−0.142991	−	0.989724i	$-0.545672\pi$
$137$	1030.50	−	594.959i	0.642639	−	0.371028i	0.785630	+	0.618696i	$0.212339\pi$
$138$		0			0
$139$	1272.50	+	2204.03i	0.776490	+	1.34492i	0.933953	+	0.357395i	$0.116335\pi$
$139$	1272.50	+	2204.03i	0.776490	+	1.34492i	−0.157464	+	0.987525i	$0.550332\pi$
$140$	624.000	−	1080.80i	0.376697	−	0.652459i
$141$		0			0
$142$	−2022.00			−1.19495
$143$	−760.500	+	731.791i	−0.444729	+	0.427940i
$144$		0			0
$145$	828.000	+	478.046i	0.474218	+	0.273790i
$146$	−1740.00	+	3013.77i	−0.986325	+	1.70836i
$147$		0			0
$148$		−	159.349i		−	0.0885026i
$149$	−1129.50	+	652.117i	−0.621022	+	0.358547i	−0.777267	−	0.629171i	$-0.783394\pi$
$149$	−1129.50	+	652.117i	−0.621022	+	0.358547i	0.156245	+	0.987718i	$0.450061\pi$
$150$		0			0
$151$		−	86.6025i		−	0.0466729i	−0.999728	−	0.0233365i	$-0.992571\pi$
$151$		−	86.6025i		−	0.0466729i	0.999728	−	0.0233365i	$-0.00742890\pi$
$152$	612.000	+	1060.02i	0.326577	+	0.565649i
$153$		0			0
$154$	1521.00	+	878.150i	0.795881	+	0.459502i
$155$	−1008.00			−0.522352
$156$		0			0
$157$	−1534.00			−0.779787			−0.389893	−	0.920860i	$-0.627488\pi$
$157$	−1534.00			−0.779787			−0.389893	+	0.920860i	$0.627488\pi$
$158$	−3732.00	−	2154.67i	−1.87913	−	1.08491i
$159$		0			0
$160$	−1152.00	−	1995.32i	−0.569210	−	0.985901i
$161$		−	1283.45i		−	0.628261i
$162$		0			0
$163$	−1414.50	+	816.662i	−0.679707	+	0.392429i	−0.799745	−	0.600340i	$-0.795032\pi$
$163$	−1414.50	+	816.662i	−0.679707	+	0.392429i	0.120038	+	0.992769i	$0.461698\pi$
$164$			1572.70i			0.748826i
$165$		0			0
$166$	−738.000	+	1278.25i	−0.345060	+	0.597661i
$167$	−1408.50	−	813.198i	−0.652653	−	0.376809i	0.136819	−	0.990596i	$-0.456312\pi$
$167$	−1408.50	−	813.198i	−0.652653	−	0.376809i	−0.789472	+	0.613787i	$0.789645\pi$
$168$		0			0
$169$	−1859.00	−	1170.87i	−0.846154	−	0.532939i
$170$	1296.00			0.584698
$171$		0			0
$172$	−170.000	+	294.449i	−0.0753627	+	0.130532i
$173$	−436.500	−	756.040i	−0.191829	−	0.332258i	0.754027	−	0.656843i	$-0.228109\pi$
$173$	−436.500	−	756.040i	−0.191829	−	0.332258i	−0.945857	+	0.324585i	$0.894775\pi$
$174$		0			0
$175$	−1306.50	+	754.308i	−0.564355	+	0.325830i
$176$	1560.00	−	900.666i	0.668122	−	0.385740i
$177$		0			0
$178$	−531.000	−	919.719i	−0.223596	−	0.387280i
$179$	−643.500	+	1114.57i	−0.268701	+	0.465403i	−0.968527	−	0.248910i	$-0.919928\pi$
$179$	−643.500	+	1114.57i	−0.268701	+	0.465403i	0.699826	+	0.714314i	$0.253261\pi$
$180$		0			0
$181$	2.00000			0.000821319			0.000410660	−	1.00000i	$-0.499869\pi$
$181$	2.00000			0.000821319			0.000410660		1.00000i	$0.499869\pi$
$182$	−1014.00	+	3512.60i	−0.412982	+	1.43061i
$183$		0			0
$184$	−684.000	−	394.908i	−0.274050	−	0.158223i
$185$	−276.000	+	478.046i	−0.109686	+	0.189982i
$186$		0			0
$187$			607.950i			0.237742i
$188$	−1188.00	+	685.892i	−0.460871	+	0.266084i
$189$		0			0
$190$			4240.06i			1.61898i
$191$	−1420.50	−	2460.38i	−0.538135	−	0.932077i	−0.999005	−	0.0446092i	$-0.985796\pi$
$191$	−1420.50	−	2460.38i	−0.538135	−	0.932077i	0.460870	−	0.887468i	$-0.347538\pi$
$192$		0			0
$193$	−3676.50	−	2122.63i	−1.37119	−	0.791659i	−0.380115	−	0.924939i	$-0.624115\pi$
$193$	−3676.50	−	2122.63i	−1.37119	−	0.791659i	−0.991078	+	0.133281i	$0.957449\pi$
$194$	4278.00			1.58321
$195$		0			0
$196$	656.000			0.239067
$197$	−2383.50	−	1376.11i	−0.862017	−	0.497686i	0.00267023	−	0.999996i	$-0.499150\pi$
$197$	−2383.50	−	1376.11i	−0.862017	−	0.497686i	−0.864687	+	0.502311i	$0.832483\pi$
$198$		0			0
$199$	842.500	+	1459.25i	0.300117	+	0.519818i	0.976162	−	0.217042i	$-0.0696410\pi$
$199$	842.500	+	1459.25i	0.300117	+	0.519818i	−0.676045	+	0.736860i	$0.736308\pi$
$200$			928.379i			0.328232i
$201$		0			0
$202$	5877.00	−	3393.09i	2.04705	−	1.18187i
$203$			1553.65i			0.537167i
$204$		0			0
$205$	2724.00	−	4718.11i	0.928061	−	1.60745i
$206$	5568.00	+	3214.69i	1.88321	+	1.08727i
$207$		0			0
$208$	2600.00	+	2702.00i	0.866719	+	0.900721i
$209$	−1989.00			−0.658287
$210$		0			0
$211$	−840.500	+	1455.79i	−0.274229	+	0.474979i	−0.969940	−	0.243343i	$-0.921756\pi$
$211$	−840.500	+	1455.79i	−0.274229	+	0.474979i	0.695711	+	0.718322i	$0.255089\pi$
$212$	−852.000	−	1475.71i	−0.276017	−	0.478075i
$213$		0			0
$214$	−765.000	+	441.673i	−0.244366	+	0.141085i
$215$	1020.00	−	588.897i	0.323551	−	0.186802i
$216$		0			0
$217$	−819.000	−	1418.55i	−0.256209	−	0.443767i
$218$	1056.00	−	1829.05i	0.328080	−	0.568250i
$219$		0			0
$220$	1248.00			0.382455
$221$	−1228.50	+	303.975i	−0.373927	+	0.0925229i
$222$		0			0
$223$	−3547.50	−	2048.15i	−1.06528	−	0.615042i	−0.138394	−	0.990377i	$-0.544194\pi$
$223$	−3547.50	−	2048.15i	−1.06528	−	0.615042i	−0.926889	+	0.375336i	$0.877527\pi$
$224$	1872.00	−	3242.40i	0.558385	−	0.967151i
$225$		0			0
$226$			1423.75i			0.419054i
$227$	−379.500	+	219.104i	−0.110962	+	0.0640638i	−0.554454	−	0.832215i	$-0.687073\pi$
$227$	−379.500	+	219.104i	−0.110962	+	0.0640638i	0.443492	+	0.896278i	$0.353739\pi$
$228$		0			0
$229$			180.133i			0.0519805i	0.999662	+	0.0259903i	$0.00827389\pi$
$229$			180.133i			0.0519805i	−0.999662	+	0.0259903i	$0.991726\pi$
$230$	−1368.00	−	2369.45i	−0.392188	−	0.679290i
$231$		0			0
$232$	828.000	+	478.046i	0.234314	+	0.135281i
$233$	5778.00			1.62459			0.812295	−	0.583247i	$-0.198218\pi$
$233$	5778.00			1.62459			0.812295	+	0.583247i	$0.198218\pi$
$234$		0			0
$235$	4752.00			1.31909
$236$	66.0000	+	38.1051i	0.0182044	+	0.0105103i
$237$		0			0
$238$	1053.00	+	1823.85i	0.286789	+	0.496734i
$239$			1860.22i			0.503464i	0.967797	+	0.251732i	$0.0810001\pi$
$239$			1860.22i			0.503464i	−0.967797	+	0.251732i	$0.919000\pi$
$240$		0			0
$241$	1783.50	−	1029.70i	0.476703	−	0.275224i	−0.242339	−	0.970192i	$-0.577915\pi$
$241$	1783.50	−	1029.70i	0.476703	−	0.275224i	0.719041	+	0.694967i	$0.244581\pi$
$242$		−	2854.42i		−	0.758219i
$243$		0			0
$244$	−34.0000	+	58.8897i	−0.00892060	+	0.0154509i
$245$	−1968.00	−	1136.23i	−0.513187	−	0.296289i
$246$		0			0
$247$	−994.500	−	4019.22i	−0.256188	−	1.03537i
$248$	−1008.00			−0.258097
$249$		0			0
$250$	1392.00	−	2411.01i	0.352151	−	0.609944i
$251$	2245.50	+	3889.32i	0.564680	+	0.978055i	0.997079	+	0.0763724i	$0.0243338\pi$
$251$	2245.50	+	3889.32i	0.564680	+	0.978055i	−0.432399	+	0.901682i	$0.642333\pi$
$252$		0			0
$253$	1111.50	−	641.725i	0.276203	−	0.159466i
$254$	6729.00	−	3884.99i	1.66226	−	0.959708i
$255$		0			0
$256$	−2432.00	−	4212.35i	−0.593750	−	1.02841i
$257$	2725.50	−	4720.70i	0.661525	−	1.14580i	−0.318690	−	0.947859i	$-0.603243\pi$
$257$	2725.50	−	4720.70i	0.661525	−	1.14580i	0.980215	−	0.197936i	$-0.0634239\pi$
$258$		0			0
$259$	−897.000			−0.215200
$260$	624.000	+	2521.87i	0.148842	+	0.601536i
$261$		0			0
$262$	1116.00	+	644.323i	0.263155	+	0.151933i
$263$	−391.500	+	678.098i	−0.0917906	+	0.158986i	−0.908265	−	0.418396i	$-0.862592\pi$
$263$	−391.500	+	678.098i	−0.0917906	+	0.158986i	0.816474	+	0.577382i	$0.195926\pi$
$264$		0			0
$265$			5902.83i			1.36833i
$266$	−5967.00	+	3445.05i	−1.37541	+	0.794096i
$267$		0			0
$268$			658.179i			0.150018i
$269$	−2542.50	−	4403.74i	−0.576279	−	0.998144i	−0.995901	−	0.0904453i	$-0.971171\pi$
$269$	−2542.50	−	4403.74i	−0.576279	−	0.998144i	0.419623	−	0.907699i	$-0.362162\pi$
$270$		0			0
$271$	−1147.50	−	662.509i	−0.257216	−	0.148504i	0.365848	−	0.930675i	$-0.380779\pi$
$271$	−1147.50	−	662.509i	−0.257216	−	0.148504i	−0.623064	+	0.782171i	$0.714112\pi$
$272$	2160.00			0.481505
$273$		0			0
$274$	4122.00			0.908829
$275$	−1306.50	−	754.308i	−0.286491	−	0.165405i
$276$		0			0
$277$	1710.50	+	2962.67i	0.371025	+	0.642635i	0.989724	−	0.142994i	$-0.0456730\pi$
$277$	1710.50	+	2962.67i	0.371025	+	0.642635i	−0.618698	+	0.785629i	$0.712340\pi$
$278$			8816.14i			1.90200i
$279$		0			0
$280$	−3744.00	+	2161.60i	−0.799096	+	0.461358i
$281$		−	810.600i		−	0.172087i	−0.996291	−	0.0860433i	$-0.972578\pi$
$281$		−	810.600i		−	0.172087i	0.996291	−	0.0860433i	$-0.0274223\pi$
$282$		0			0
$283$	−3588.50	+	6215.46i	−0.753760	+	1.30555i	0.192228	+	0.981350i	$0.438429\pi$
$283$	−3588.50	+	6215.46i	−0.753760	+	1.30555i	−0.945988	+	0.324201i	$0.894905\pi$
$284$	−2022.00	−	1167.40i	−0.422478	−	0.243918i
$285$		0			0
$286$	−3549.00	+	878.150i	−0.733765	+	0.181560i
$287$	8853.00			1.82082
$288$		0			0
$289$	2092.00	−	3623.45i	0.425809	−	0.737523i
$290$	1656.00	+	2868.28i	0.335323	+	0.580796i
$291$		0			0
$292$	−3480.00	+	2009.18i	−0.697437	+	0.402665i
$293$	−8065.50	+	4656.62i	−1.60816	+	0.928473i	−0.618381	+	0.785878i	$0.712211\pi$
$293$	−8065.50	+	4656.62i	−1.60816	+	0.928473i	−0.989781	+	0.142595i	$0.954456\pi$
$294$		0			0
$295$	−132.000	−	228.631i	−0.0260520	−	0.0451234i
$296$	−276.000	+	478.046i	−0.0541965	+	0.0938712i
$297$		0			0
$298$	−4518.00			−0.878257
$299$	1852.50	+	1925.17i	0.358304	+	0.372360i
$300$		0			0
$301$	1657.50	+	956.958i	0.317398	+	0.183250i
$302$	150.000	−	259.808i	0.0285812	−	0.0495041i
$303$		0			0
$304$			7066.77i			1.33325i
$305$	204.000	−	117.779i	0.0382984	−	0.0221116i
$306$		0			0
$307$		−	4777.00i		−	0.888070i	−0.896009	−	0.444035i	$-0.853547\pi$
$307$		−	4777.00i		−	0.888070i	0.896009	−	0.444035i	$-0.146453\pi$
$308$	1014.00	+	1756.30i	0.187591	+	0.324917i
$309$		0			0
$310$	−3024.00	−	1745.91i	−0.554038	−	0.319874i
$311$	−6192.00			−1.12899			−0.564495	−	0.825436i	$-0.690929\pi$
$311$	−6192.00			−1.12899			−0.564495	+	0.825436i	$0.690929\pi$
$312$		0			0
$313$	−770.000			−0.139051			−0.0695255	−	0.997580i	$-0.522149\pi$
$313$	−770.000			−0.139051			−0.0695255	+	0.997580i	$0.522149\pi$
$314$	−4602.00	−	2656.97i	−0.827089	−	0.477520i
$315$		0			0
$316$	−2488.00	−	4309.34i	−0.442914	−	0.767150i
$317$		−	8057.50i		−	1.42762i	−0.700341	−	0.713808i	$-0.746969\pi$
$317$		−	8057.50i		−	1.42762i	0.700341	−	0.713808i	$-0.253031\pi$
$318$		0			0
$319$	−1345.50	+	776.825i	−0.236155	+	0.136344i
$320$			886.810i			0.154919i
$321$		0			0
$322$	2223.00	−	3850.35i	0.384730	−	0.666371i
$323$	−2065.50	−	1192.52i	−0.355813	−	0.205429i
$324$		0			0
$325$	871.000	−	3017.23i	0.148660	−	0.514972i
$326$	−5658.00			−0.961250
$327$		0			0
$328$	2724.00	−	4718.11i	0.458560	−	0.794250i
$329$	3861.00	+	6687.45i	0.647002	+	1.12064i
$330$		0			0
$331$	−4570.50	+	2638.78i	−0.758965	+	0.438189i	−0.828924	−	0.559361i	$-0.811046\pi$
$331$	−4570.50	+	2638.78i	−0.758965	+	0.438189i	0.0699590	+	0.997550i	$0.477713\pi$
$332$	−1476.00	+	852.169i	−0.243994	+	0.140870i
$333$		0			0
$334$	−2817.00	−	4879.19i	−0.461495	−	0.799333i
$335$	1140.00	−	1974.54i	0.185925	−	0.322031i
$336$		0			0
$337$	8278.00			1.33808			0.669038	−	0.743228i	$-0.266706\pi$
$337$	8278.00			1.33808			0.669038	+	0.743228i	$0.266706\pi$
$338$	−3549.00	−	6732.48i	−0.571125	−	1.08343i
$339$		0			0
$340$	1296.00	+	748.246i	0.206722	+	0.119351i
$341$	819.000	−	1418.55i	0.130063	−	0.225275i
$342$		0			0
$343$			4030.48i			0.634477i
$344$	1020.00	−	588.897i	0.159868	−	0.0923000i
$345$		0			0
$346$		−	3024.16i		−	0.469884i
$347$	3433.50	+	5947.00i	0.531181	+	0.920033i	0.999338	+	0.0363875i	$0.0115851\pi$
$347$	3433.50	+	5947.00i	0.531181	+	0.920033i	−0.468156	+	0.883646i	$0.655082\pi$
$348$		0			0
$349$	10525.5	+	6076.90i	1.61438	+	0.932060i	0.988340	+	0.152266i	$0.0486571\pi$
$349$	10525.5	+	6076.90i	1.61438	+	0.932060i	0.626036	+	0.779794i	$0.284676\pi$
$350$	−5226.00			−0.798118
$351$		0			0
$352$	3744.00			0.566920
$353$	−5029.50	−	2903.78i	−0.758338	−	0.437827i	0.0703608	−	0.997522i	$-0.477585\pi$
$353$	−5029.50	−	2903.78i	−0.758338	−	0.437827i	−0.828699	+	0.559695i	$0.810918\pi$
$354$		0			0
$355$	4044.00	+	7004.41i	0.604601	+	1.04720i
$356$		−	1226.29i		−	0.182566i
$357$		0			0
$358$	−3861.00	+	2229.15i	−0.570001	+	0.329090i
$359$		−	1340.61i		−	0.197088i	−0.995133	−	0.0985439i	$-0.968581\pi$
$359$		−	1340.61i		−	0.197088i	0.995133	−	0.0985439i	$-0.0314185\pi$
$360$		0			0
$361$	472.000	−	817.528i	0.0688147	−	0.119191i
$362$	6.00000	+	3.46410i	0.000871141	+	0.000502953i
$363$		0			0
$364$	−3042.00	+	2927.17i	−0.438033	+	0.421498i
$365$	13920.0			1.99618
$366$		0			0
$367$	−1832.50	+	3173.98i	−0.260642	+	0.451446i	−0.966413	−	0.256995i	$-0.917268\pi$
$367$	−1832.50	+	3173.98i	−0.260642	+	0.451446i	0.705770	+	0.708441i	$0.250601\pi$
$368$	−2280.00	−	3949.08i	−0.322971	−	0.559402i
$369$		0			0
$370$	−1656.00	+	956.092i	−0.232679	+	0.134337i
$371$	−8307.00	+	4796.05i	−1.16247	+	0.671155i
$372$		0			0
$373$	−2685.50	−	4651.42i	−0.372788	−	0.645688i	0.617205	−	0.786802i	$-0.288265\pi$
$373$	−2685.50	−	4651.42i	−0.372788	−	0.645688i	−0.989993	+	0.141114i	$0.954931\pi$
$374$	−1053.00	+	1823.85i	−0.145586	+	0.252163i
$375$		0			0
$376$	4752.00			0.651770
$377$	−2242.50	−	2330.47i	−0.306352	−	0.318370i
$378$		0			0
$379$	−9967.50	−	5754.74i	−1.35091	−	0.779950i	−0.362536	−	0.931970i	$-0.618089\pi$
$379$	−9967.50	−	5754.74i	−1.35091	−	0.779950i	−0.988377	+	0.152020i	$0.951422\pi$
$380$	−2448.00	+	4240.06i	−0.330473	+	0.572396i
$381$		0			0
$382$		−	9841.51i		−	1.31816i
$383$	−2095.50	+	1209.84i	−0.279569	+	0.161409i	−0.633228	−	0.773965i	$-0.718271\pi$
$383$	−2095.50	+	1209.84i	−0.279569	+	0.161409i	0.353659	+	0.935374i	$0.384937\pi$
$384$		0			0
$385$		−	7025.20i		−	0.929967i
$386$	−7353.00	−	12735.8i	−0.969580	−	1.67936i
$387$		0			0
$388$	4278.00	+	2469.90i	0.559749	+	0.323171i
$389$	9858.00			1.28489			0.642443	−	0.766334i	$-0.277921\pi$
$389$	9858.00			1.28489			0.642443	+	0.766334i	$0.277921\pi$
$390$		0			0
$391$	1539.00			0.199055
$392$	−1968.00	−	1136.23i	−0.253569	−	0.146398i
$393$		0			0
$394$	−4767.00	−	8256.69i	−0.609538	−	1.05575i
$395$			17237.4i			2.19571i
$396$		0			0
$397$	−7552.50	+	4360.44i	−0.954784	+	0.551245i	−0.894564	−	0.446941i	$-0.852514\pi$
$397$	−7552.50	+	4360.44i	−0.954784	+	0.551245i	−0.0602200	+	0.998185i	$0.519180\pi$
$398$			5837.01i			0.735133i
$399$		0			0
$400$	−2680.00	+	4641.90i	−0.335000	+	0.580237i
$401$	6568.50	+	3792.33i	0.817993	+	0.472269i	0.849724	−	0.527228i	$-0.176769\pi$
$401$	6568.50	+	3792.33i	0.817993	+	0.472269i	−0.0317308	+	0.999496i	$0.510102\pi$
$402$		0			0
$403$	3276.00	+	945.700i	0.404936	+	0.116895i
$404$	7836.00			0.964989
$405$		0			0
$406$	−2691.00	+	4660.95i	−0.328946	+	0.569751i
$407$	−448.500	−	776.825i	−0.0546224	−	0.0946088i
$408$		0			0
$409$	3727.50	−	2152.07i	0.450643	−	0.260179i	−0.257459	−	0.966289i	$-0.582885\pi$
$409$	3727.50	−	2152.07i	0.450643	−	0.260179i	0.708102	+	0.706110i	$0.249552\pi$
$410$	16344.0	−	9436.21i	1.96871	−	1.13664i
$411$		0			0
$412$	3712.00	+	6429.37i	0.443876	+	0.768817i
$413$	214.500	−	371.525i	0.0255565	−	0.0442652i
$414$		0			0
$415$	5904.00			0.698352
$416$	1872.00	+	7565.60i	0.220631	+	0.891668i
$417$		0			0
$418$	−5967.00	−	3445.05i	−0.698219	−	0.403117i
$419$	2698.50	−	4673.94i	0.314631	−	0.544957i	−0.664728	−	0.747085i	$-0.731453\pi$
$419$	2698.50	−	4673.94i	0.314631	−	0.544957i	0.979359	+	0.202129i	$0.0647859\pi$
$420$		0			0
$421$			7260.76i			0.840541i	0.907399	+	0.420270i	$0.138065\pi$
$421$			7260.76i			0.840541i	−0.907399	+	0.420270i	$0.861935\pi$
$422$	−5043.00	+	2911.58i	−0.581728	+	0.335861i
$423$		0			0
$424$			5902.83i			0.676101i
$425$	−904.500	−	1566.64i	−0.103235	−	0.178808i
$426$		0			0
$427$	331.500	+	191.392i	0.0375700	+	0.0216911i
$428$	−1020.00			−0.115195
$429$		0			0
$430$	4080.00			0.457570
$431$	421.500	+	243.353i	0.0471066	+	0.0271970i	0.523368	−	0.852107i	$-0.324675\pi$
$431$	421.500	+	243.353i	0.0471066	+	0.0271970i	−0.476262	+	0.879304i	$0.658009\pi$
$432$		0			0
$433$	−6069.50	−	10512.7i	−0.673629	−	1.16676i	−0.976867	−	0.213846i	$-0.931401\pi$
$433$	−6069.50	−	10512.7i	−0.673629	−	1.16676i	0.303238	−	0.952915i	$-0.401932\pi$
$434$		−	5674.20i		−	0.627581i
$435$		0			0
$436$	2112.00	−	1219.36i	0.231987	−	0.133938i
$437$			5035.07i			0.551167i
$438$		0			0
$439$	−230.500	+	399.238i	−0.0250596	+	0.0434045i	−0.878283	−	0.478141i	$-0.841311\pi$
$439$	−230.500	+	399.238i	−0.0250596	+	0.0434045i	0.853224	+	0.521545i	$0.174644\pi$
$440$	−3744.00	−	2161.60i	−0.405655	−	0.234205i
$441$		0			0
$442$	−4212.00	−	1215.90i	−0.453268	−	0.130847i
$443$	−12156.0			−1.30372			−0.651861	−	0.758338i	$-0.726012\pi$
$443$	−12156.0			−1.30372			−0.651861	+	0.758338i	$0.726012\pi$
$444$		0			0
$445$	−2124.00	+	3678.88i	−0.226263	+	0.391900i
$446$	−7095.00	−	12288.9i	−0.753269	−	1.30470i
$447$		0			0
$448$	−1248.00	+	720.533i	−0.131613	+	0.0759866i
$449$	256.500	−	148.090i	0.0269599	−	0.0155653i	−0.486459	−	0.873703i	$-0.661712\pi$
$449$	256.500	−	148.090i	0.0269599	−	0.0155653i	0.513419	+	0.858138i	$0.328379\pi$
$450$		0			0
$451$	4426.50	+	7666.92i	0.462164	+	0.800491i
$452$	−822.000	+	1423.75i	−0.0855390	+	0.148158i
$453$		0			0
$454$	−1518.00			−0.156924
$455$	14196.0	−	3512.60i	1.46268	−	0.361919i
$456$		0			0
$457$	529.500	+	305.707i	0.0541990	+	0.0312918i	0.526855	−	0.849955i	$-0.323371\pi$
$457$	529.500	+	305.707i	0.0541990	+	0.0312918i	−0.472656	+	0.881247i	$0.656705\pi$
$458$	−312.000	+	540.400i	−0.0318314	+	0.0551337i
$459$		0			0
$460$		−	3159.26i		−	0.320220i
$461$	11368.5	−	6563.61i	1.14855	−	0.663119i	0.200020	−	0.979792i	$-0.435899\pi$
$461$	11368.5	−	6563.61i	1.14855	−	0.663119i	0.948535	+	0.316673i	$0.102566\pi$
$462$		0			0
$463$		−	834.848i		−	0.0837985i	−0.999122	−	0.0418992i	$-0.986659\pi$
$463$		−	834.848i		−	0.0837985i	0.999122	−	0.0418992i	$-0.0133408\pi$
$464$	2760.00	+	4780.46i	0.276142	+	0.478292i
$465$		0			0
$466$	17334.0	+	10007.8i	1.72314	+	0.994854i
$467$	−14496.0			−1.43639			−0.718196	−	0.695841i	$-0.755032\pi$
$467$	−14496.0			−1.43639			−0.718196	+	0.695841i	$0.755032\pi$
$468$		0			0
$469$	3705.00			0.364778
$470$	14256.0	+	8230.71i	1.39911	+	0.807775i
$471$		0			0
$472$	−132.000	−	228.631i	−0.0128724	−	0.0222957i
$473$			1913.92i			0.186051i
$474$		0			0
$475$	5125.50	−	2959.21i	0.495103	−	0.285848i
$476$			2431.80i			0.234162i
$477$		0			0
$478$	−3222.00	+	5580.67i	−0.308307	+	0.534004i
$479$	7705.50	+	4448.77i	0.735017	+	0.424362i	0.820255	−	0.571998i	$-0.193832\pi$
$479$	7705.50	+	4448.77i	0.735017	+	0.424362i	−0.0852376	+	0.996361i	$0.527165\pi$
$480$		0			0
$481$	1345.50	−	1294.71i	0.127546	−	0.122731i
$482$	7134.00			0.674159
$483$		0			0
$484$	1648.00	−	2854.42i	0.154771	−	0.268071i
$485$	−8556.00	−	14819.4i	−0.801047	−	1.38745i
$486$		0			0
$487$	4117.50	−	2377.24i	0.383125	−	0.221197i	−0.296052	−	0.955172i	$-0.595670\pi$
$487$	4117.50	−	2377.24i	0.383125	−	0.221197i	0.679177	+	0.733975i	$0.262337\pi$
$488$	204.000	−	117.779i	0.0189235	−	0.0109255i
$489$		0			0
$490$	−3936.00	−	6817.35i	−0.362878	−	0.628524i
$491$	−817.500	+	1415.95i	−0.0751390	+	0.130145i	−0.901147	−	0.433514i	$-0.857273\pi$
$491$	−817.500	+	1415.95i	−0.0751390	+	0.130145i	0.826008	+	0.563659i	$0.190607\pi$
$492$		0			0
$493$	−1863.00			−0.170193
$494$	3978.00	−	13780.2i	0.362305	−	1.25506i
$495$		0			0
$496$	−5040.00	−	2909.85i	−0.456255	−	0.263419i
$497$	−6571.50	+	11382.2i	−0.593103	+	1.02728i
$498$		0			0
$499$		−	14434.9i		−	1.29498i	−0.762074	−	0.647490i	$-0.775819\pi$
$499$		−	14434.9i		−	1.29498i	0.762074	−	0.647490i	$-0.224181\pi$
$500$	2784.00	−	1607.34i	0.249009	−	0.143765i
$501$		0			0
$502$			15557.3i			1.38318i
$503$	6343.50	+	10987.3i	0.562312	+	0.973952i	0.997294	+	0.0735133i	$0.0234211\pi$
$503$	6343.50	+	10987.3i	0.562312	+	0.973952i	−0.434983	+	0.900439i	$0.643246\pi$
$504$		0			0
$505$	−23508.0	−	13572.4i	−2.07147	−	1.19596i
$506$	4446.00			0.390610
$507$		0			0
$508$	8972.00			0.783599
$509$	4978.50	+	2874.34i	0.433533	+	0.250300i	0.700850	−	0.713308i	$-0.252804\pi$
$509$	4978.50	+	2874.34i	0.433533	+	0.250300i	−0.267318	+	0.963608i	$0.586137\pi$
$510$		0			0
$511$	11310.0	+	19589.5i	0.979109	+	1.69587i
$512$		−	4434.05i		−	0.382733i
$513$		0			0
$514$	16353.0	−	9441.41i	1.40331	−	0.810200i
$515$		−	25717.5i		−	2.20048i
$516$		0			0
$517$	−3861.00	+	6687.45i	−0.328446	+	0.568885i
$518$	−2691.00	−	1553.65i	−0.228254	−	0.131783i
$519$		0			0
$520$	2496.00	−	8646.40i	0.210494	−	0.729172i
$521$	−6054.00			−0.509080			−0.254540	−	0.967062i	$-0.581924\pi$
$521$	−6054.00			−0.509080			−0.254540	+	0.967062i	$0.581924\pi$
$522$		0			0
$523$	7401.50	−	12819.8i	0.618824	−	1.07183i	−0.370877	−	0.928682i	$-0.620943\pi$
$523$	7401.50	−	12819.8i	0.618824	−	1.07183i	0.989701	−	0.143153i	$-0.0457240\pi$
$524$	744.000	+	1288.65i	0.0620263	+	0.107433i
$525$		0			0
$526$	−2349.00	+	1356.20i	−0.194717	+	0.112420i
$527$	1701.00	−	982.073i	0.140601	−	0.0811760i
$528$		0			0
$529$	4459.00	+	7723.21i	0.366483	+	0.634767i
$530$	−10224.0	+	17708.5i	−0.837929	+	1.45133i
$531$		0			0
$532$	−7956.00			−0.648377
$533$	−13279.5	+	12778.2i	−1.07917	+	1.03843i
$534$		0			0
$535$	3060.00	+	1766.69i	0.247281	+	0.142768i
$536$	1140.00	−	1974.54i	0.0918666	−	0.159118i
$537$		0			0
$538$		−	17615.0i		−	1.41159i
$539$	3198.00	−	1846.37i	0.255561	−	0.147548i
$540$		0			0
$541$		−	21470.5i		−	1.70626i	−0.521695	−	0.853132i	$-0.674700\pi$
$541$		−	21470.5i		−	1.70626i	0.521695	−	0.853132i	$-0.325300\pi$
$542$	−2295.00	−	3975.06i	−0.181880	−	0.315025i
$543$		0			0
$544$	3888.00	+	2244.74i	0.306428	+	0.176916i
$545$	−8448.00			−0.663986
$546$		0			0
$547$	−13516.0			−1.05649			−0.528247	−	0.849091i	$-0.677151\pi$
$547$	−13516.0			−1.05649			−0.528247	+	0.849091i	$0.677151\pi$
$548$	4122.00	+	2379.84i	0.321320	+	0.185514i
$549$		0			0
$550$	−2613.00	−	4525.85i	−0.202579	−	0.350878i
$551$		−	6095.09i		−	0.471251i
$552$		0			0
$553$	−24258.0	+	14005.4i	−1.86538	+	1.07698i
$554$			11850.7i			0.908822i
$555$		0			0
$556$	−5090.00	+	8816.14i	−0.388245	+	0.672460i
$557$	−2503.50	−	1445.40i	−0.190443	−	0.109952i	0.401747	−	0.915751i	$-0.368403\pi$
$557$	−2503.50	−	1445.40i	−0.190443	−	0.109952i	−0.592190	+	0.805798i	$0.701736\pi$
$558$		0			0
$559$	−3867.50	+	956.958i	−0.292626	+	0.0724061i
$560$	−24960.0			−1.88349
$561$		0			0
$562$	1404.00	−	2431.80i	0.105381	−	0.182525i
$563$	5791.50	+	10031.2i	0.433539	+	0.750912i	0.997175	−	0.0751113i	$-0.0239312\pi$
$563$	5791.50	+	10031.2i	0.433539	+	0.750912i	−0.563636	+	0.826023i	$0.690598\pi$
$564$		0			0
$565$	4932.00	−	2847.49i	0.367240	−	0.212026i
$566$	−21531.0	+	12430.9i	−1.59897	+	0.923164i
$567$		0			0
$568$	4044.00	+	7004.41i	0.298737	+	0.517427i
$569$	6439.50	−	11153.5i	0.474443	−	0.821759i	−0.525129	−	0.851023i	$-0.675983\pi$
$569$	6439.50	−	11153.5i	0.474443	−	0.821759i	0.999572	+	0.0292638i	$0.00931628\pi$
$570$		0			0
$571$	−11636.0			−0.852805			−0.426402	−	0.904534i	$-0.640219\pi$
$571$	−11636.0			−0.852805			−0.426402	+	0.904534i	$0.640219\pi$
$572$	−4056.00	−	1170.87i	−0.296486	−	0.0855881i
$573$		0			0
$574$	26559.0	+	15333.8i	1.93127	+	1.11502i
$575$	−1909.50	+	3307.35i	−0.138490	+	0.239871i
$576$		0			0
$577$			12311.4i			0.888269i	0.895960	+	0.444134i	$0.146489\pi$
$577$			12311.4i			0.888269i	−0.895960	+	0.444134i	$0.853511\pi$
$578$	12552.0	−	7246.90i	0.903277	−	0.521507i
$579$		0			0
$580$			3824.37i			0.273790i
$581$	4797.00	+	8308.65i	0.342535	+	0.593289i
$582$		0			0
$583$	−8307.00	−	4796.05i	−0.590121	−	0.340707i
$584$	13920.0			0.986325
$585$		0			0
$586$	−32262.0			−2.27428
$587$	13549.5	+	7822.81i	0.952722	+	0.550054i	0.893925	−	0.448216i	$-0.147940\pi$
$587$	13549.5	+	7822.81i	0.952722	+	0.550054i	0.0587964	+	0.998270i	$0.481274\pi$
$588$		0			0
$589$	3213.00	+	5565.08i	0.224770	+	0.389313i
$590$		−	914.523i		−	0.0638141i
$591$		0			0
$592$	−2760.00	+	1593.49i	−0.191614	+	0.110628i
$593$		−	25821.4i		−	1.78813i	−0.447942	−	0.894063i	$-0.647843\pi$
$593$		−	25821.4i		−	1.78813i	0.447942	−	0.894063i	$-0.352157\pi$
$594$		0			0
$595$	4212.00	−	7295.40i	0.290210	−	0.502659i
$596$	−4518.00	−	2608.47i	−0.310511	−	0.179274i
$597$		0			0
$598$	2223.00	+	8984.15i	0.152015	+	0.614363i
$599$	−1668.00			−0.113777			−0.0568887	−	0.998381i	$-0.518118\pi$
$599$	−1668.00			−0.113777			−0.0568887	+	0.998381i	$0.518118\pi$
$600$		0			0
$601$	−6849.50	+	11863.7i	−0.464887	+	0.805207i	−0.999196	−	0.0400813i	$-0.987238\pi$
$601$	−6849.50	+	11863.7i	−0.464887	+	0.805207i	0.534310	+	0.845289i	$0.320572\pi$
$602$	3315.00	+	5741.75i	0.224434	+	0.388731i
$603$		0			0
$604$	300.000	−	173.205i	0.0202100	−	0.0116682i
$605$	−9888.00	+	5708.84i	−0.664470	+	0.383632i
$606$		0			0
$607$	11586.5	+	20068.4i	0.774764	+	1.34193i	0.934927	+	0.354839i	$0.115464\pi$
$607$	11586.5	+	20068.4i	0.774764	+	1.34193i	−0.160164	+	0.987090i	$0.551202\pi$
$608$	−7344.00	+	12720.2i	−0.489866	+	0.848473i
$609$		0			0
$610$	816.000			0.0541621
$611$	−15444.0	−	4458.30i	−1.02258	−	0.295194i
$612$		0			0
$613$	14389.5	+	8307.78i	0.948102	+	0.547387i	0.892491	−	0.451066i	$-0.148956\pi$
$613$	14389.5	+	8307.78i	0.948102	+	0.547387i	0.0556111	+	0.998453i	$0.482289\pi$
$614$	8274.00	−	14331.0i	0.543830	−	0.941941i
$615$		0			0
$616$		−	7025.20i		−	0.459502i
$617$	−24589.5	+	14196.8i	−1.60443	+	0.926321i	−0.613849	+	0.789423i	$0.710380\pi$
$617$	−24589.5	+	14196.8i	−1.60443	+	0.926321i	−0.990585	+	0.136897i	$0.956287\pi$
$618$		0			0
$619$		−	6245.78i		−	0.405556i	−0.979225	−	0.202778i	$-0.935003\pi$
$619$		−	6245.78i		−	0.405556i	0.979225	−	0.202778i	$-0.0649969\pi$
$620$	−2016.00	−	3491.81i	−0.130588	−	0.226185i
$621$		0			0
$622$	−18576.0	−	10724.9i	−1.19748	−	0.691363i
$623$	−6903.00			−0.443921
$624$		0			0
$625$	−19511.0			−1.24870
$626$	−2310.00	−	1333.68i	−0.147486	−	0.0851510i
$627$		0			0
$628$	−3068.00	−	5313.93i	−0.194947	−	0.337658i
$629$		−	1075.60i		−	0.0681830i
$630$		0			0
$631$	19381.5	−	11189.9i	1.22277	−	0.705964i	0.257259	−	0.966342i	$-0.417181\pi$
$631$	19381.5	−	11189.9i	1.22277	−	0.705964i	0.965507	+	0.260378i	$0.0838472\pi$
$632$			17237.4i			1.08491i
$633$		0			0
$634$	13956.0	−	24172.5i	0.874233	−	1.51422i
$635$	−26916.0	−	15540.0i	−1.68209	−	0.971157i
$636$		0			0
$637$	5330.00	+	5539.10i	0.331526	+	0.344532i
$638$	−5382.00			−0.333974
$639$		0			0
$640$	−10752.0	+	18623.0i	−0.664078	+	1.15022i
$641$	9913.50	+	17170.7i	0.610858	+	1.05804i	0.991096	+	0.133148i	$0.0425085\pi$
$641$	9913.50	+	17170.7i	0.610858	+	1.05804i	−0.380239	+	0.924888i	$0.624158\pi$
$642$		0			0
$643$	−7318.50	+	4225.34i	−0.448855	+	0.259146i	−0.707346	−	0.706867i	$-0.750108\pi$
$643$	−7318.50	+	4225.34i	−0.448855	+	0.259146i	0.258492	+	0.966013i	$0.416775\pi$
$644$	4446.00	−	2566.90i	0.272045	−	0.157065i
$645$		0			0
$646$	−4131.00	−	7155.10i	−0.251598	−	0.435780i
$647$	1474.50	−	2553.91i	0.0895959	−	0.155185i	−0.817744	−	0.575581i	$-0.804776\pi$
$647$	1474.50	−	2553.91i	0.0895959	−	0.155185i	0.907340	+	0.420397i	$0.138109\pi$
$648$		0			0
$649$	429.000			0.0259472
$650$	7839.00	−	7543.08i	0.473032	−	0.455175i
$651$		0			0
$652$	−5658.00	−	3266.65i	−0.339853	−	0.196214i
$653$	6019.50	−	10426.1i	0.360737	−	0.624815i	−0.627345	−	0.778741i	$-0.715859\pi$
$653$	6019.50	−	10426.1i	0.360737	−	0.624815i	0.988082	+	0.153926i	$0.0491919\pi$
$654$		0			0
$655$		−	5154.58i		−	0.307490i
$656$	27240.0	−	15727.0i	1.62126	−	0.936032i
$657$		0			0
$658$			26749.8i			1.58483i
$659$	1681.50	+	2912.44i	0.0993960	+	0.172159i	0.911435	−	0.411445i	$-0.134976\pi$
$659$	1681.50	+	2912.44i	0.0993960	+	0.172159i	−0.812039	+	0.583603i	$0.801642\pi$
$660$		0			0
$661$	8797.50	+	5079.24i	0.517675	+	0.298880i	0.735983	−	0.677000i	$-0.236720\pi$
$661$	8797.50	+	5079.24i	0.517675	+	0.298880i	−0.218308	+	0.975880i	$0.570054\pi$
$662$	−18282.0			−1.07334
$663$		0			0
$664$	5904.00			0.345060
$665$	23868.0	+	13780.2i	1.39182	+	0.803569i
$666$		0			0
$667$	1966.50	+	3406.08i	0.114158	+	0.197727i
$668$		−	6505.58i		−	0.376809i
$669$		0			0
$670$	6840.00	−	3949.08i	0.394406	−	0.227711i
$671$			382.783i			0.0220226i
$672$		0			0
$673$	9084.50	−	15734.8i	0.520329	−	0.901237i	−0.479391	−	0.877601i	$-0.659142\pi$
$673$	9084.50	−	15734.8i	0.520329	−	0.901237i	0.999721	−	0.0236358i	$-0.00752419\pi$
$674$	24834.0	+	14337.9i	1.41924	+	0.819400i
$675$		0			0
$676$	338.000	−	8781.50i	0.0192308	−	0.499630i
$677$	−9042.00			−0.513312			−0.256656	−	0.966503i	$-0.582621\pi$
$677$	−9042.00			−0.513312			−0.256656	+	0.966503i	$0.582621\pi$
$678$		0			0
$679$	13903.5	−	24081.6i	0.785813	−	1.36107i
$680$	−2592.00	−	4489.48i	−0.146175	−	0.253182i
$681$		0			0
$682$	4914.00	−	2837.10i	0.275904	−	0.159293i
$683$	10792.5	−	6231.05i	0.604632	−	0.349084i	−0.166230	−	0.986087i	$-0.553159\pi$
$683$	10792.5	−	6231.05i	0.604632	−	0.349084i	0.770862	+	0.637003i	$0.219826\pi$
$684$		0			0
$685$	−8244.00	−	14279.0i	−0.459835	−	0.796458i
$686$	−6981.00	+	12091.4i	−0.388536	+	0.672964i
$687$		0			0
$688$	6800.00			0.376813
$689$	5538.00	−	19184.2i	0.306213	−	1.06075i
$690$		0			0
$691$	−3739.50	−	2159.00i	−0.205872	−	0.118860i	0.393520	−	0.919316i	$-0.371257\pi$
$691$	−3739.50	−	2159.00i	−0.205872	−	0.118860i	−0.599391	+	0.800456i	$0.704591\pi$
$692$	1746.00	−	3024.16i	0.0959147	−	0.166129i
$693$		0			0
$694$			23788.0i			1.30112i
$695$	30540.0	−	17632.3i	1.66683	−	0.962346i
$696$		0			0
$697$			10615.7i			0.576901i
$698$	21051.0	+	36461.4i	1.14154	+	1.97720i
$699$		0			0
$700$	−5226.00	−	3017.23i	−0.282177	−	0.162915i
$701$	18270.0			0.984377			0.492189	−	0.870489i	$-0.336197\pi$
$701$	18270.0			0.984377			0.492189	+	0.870489i	$0.336197\pi$
$702$		0			0
$703$	3519.00			0.188793
$704$	−1248.00	−	720.533i	−0.0668122	−	0.0385740i
$705$		0			0
$706$	−10059.0	−	17422.7i	−0.536226	−	0.928770i
$707$		−	44110.1i		−	2.34644i
$708$		0			0
$709$	1411.50	−	814.930i	0.0747673	−	0.0431669i	−0.462150	−	0.886802i	$-0.652922\pi$
$709$	1411.50	−	814.930i	0.0747673	−	0.0431669i	0.536918	+	0.843635i	$0.319589\pi$
$710$			28017.7i			1.48096i
$711$		0			0
$712$	−2124.00	+	3678.88i	−0.111798	+	0.193640i
$713$	−3591.00	−	2073.26i	−0.188617	−	0.108898i
$714$		0			0
$715$	10140.0	+	10537.8i	0.530370	+	0.551177i
$716$	−5148.00			−0.268701
$717$		0			0
$718$	2322.00	−	4021.82i	0.120691	−	0.209043i
$719$	4915.50	+	8513.90i	0.254961	+	0.441606i	0.964885	−	0.262673i	$-0.0846039\pi$
$719$	4915.50	+	8513.90i	0.254961	+	0.441606i	−0.709924	+	0.704279i	$0.751271\pi$
$720$		0			0
$721$	36192.0	−	20895.5i	1.86943	−	1.07932i
$722$	2832.00	−	1635.06i	0.145978	−	0.0842804i
$723$		0			0
$724$	4.00000	+	6.92820i	0.000205330	+	0.000355642i
$725$	2311.50	−	4003.64i	0.118410	−	0.205091i
$726$		0			0
$727$	−15464.0			−0.788897			−0.394448	−	0.918918i	$-0.629064\pi$
$727$	−15464.0			−0.788897			−0.394448	+	0.918918i	$0.629064\pi$
$728$	14196.0	−	3512.60i	0.722718	−	0.178826i
$729$		0			0
$730$	41760.0	+	24110.1i	2.11727	+	1.22241i
$731$	−1147.50	+	1987.53i	−0.0580599	+	0.100563i
$732$		0			0
$733$		−	12616.3i		−	0.635733i	−0.948136	−	0.317866i	$-0.897034\pi$
$733$		−	12616.3i		−	0.635733i	0.948136	−	0.317866i	$-0.102966\pi$
$734$	−10995.0	+	6347.97i	−0.552906	+	0.319220i
$735$		0			0
$736$		−	9477.78i		−	0.474668i
$737$	1852.50	+	3208.62i	0.0925885	+	0.160368i
$738$		0			0
$739$	−14101.5	−	8141.50i	−0.701938	−	0.405264i	0.106131	−	0.994352i	$-0.466154\pi$
$739$	−14101.5	−	8141.50i	−0.701938	−	0.405264i	−0.808069	+	0.589088i	$0.799487\pi$
$740$	−2208.00			−0.109686
$741$		0			0
$742$	−33228.0			−1.64399
$743$	−9358.50	−	5403.13i	−0.462086	−	0.266786i	0.250835	−	0.968030i	$-0.419295\pi$
$743$	−9358.50	−	5403.13i	−0.462086	−	0.266786i	−0.712921	+	0.701244i	$0.752628\pi$
$744$		0			0
$745$	9036.00	+	15650.8i	0.444367	+	0.769666i
$746$		−	18605.7i		−	0.913140i
$747$		0			0
$748$	−2106.00	+	1215.90i	−0.102945	+	0.0594354i
$749$			5741.75i			0.280105i
$750$		0			0
$751$	6807.50	−	11790.9i	0.330771	−	0.572913i	−0.651892	−	0.758312i	$-0.726024\pi$
$751$	6807.50	−	11790.9i	0.330771	−	0.572913i	0.982663	+	0.185399i	$0.0593578\pi$
$752$	23760.0	+	13717.8i	1.15218	+	0.665210i
$753$		0			0
$754$	−2691.00	−	10875.5i	−0.129974	−	0.525284i
$755$	−1200.00			−0.0578443
$756$		0			0
$757$	−2775.50	+	4807.31i	−0.133259	+	0.230812i	−0.924931	−	0.380135i	$-0.875878\pi$
$757$	−2775.50	+	4807.31i	−0.133259	+	0.230812i	0.791672	+	0.610947i	$0.209211\pi$
$758$	−19935.0	−	34528.4i	−0.955240	−	1.65452i
$759$		0			0
$760$	14688.0	−	8480.12i	0.701039	−	0.404745i
$761$	−8731.50	+	5041.13i	−0.415922	+	0.240133i	−0.693331	−	0.720619i	$-0.743858\pi$
$761$	−8731.50	+	5041.13i	−0.415922	+	0.240133i	0.277409	+	0.960752i	$0.410524\pi$
$762$		0			0
$763$	−6864.00	−	11888.8i	−0.325680	−	0.564093i
$764$	5682.00	−	9841.51i	0.269067	−	0.466039i
$765$		0			0
$766$	−8382.00			−0.395371
$767$	214.500	+	866.891i	0.0100980	+	0.0408105i
$768$		0			0
$769$	25771.5	+	14879.2i	1.20851	+	0.697733i	0.962434	−	0.271517i	$-0.0875253\pi$
$769$	25771.5	+	14879.2i	1.20851	+	0.697733i	0.246076	+	0.969250i	$0.420859\pi$
$770$	12168.0	−	21075.6i	0.569486	−	0.986379i
$771$		0			0
$772$		−	16981.0i		−	0.791659i
$773$	−24019.5	+	13867.7i	−1.11762	+	0.645259i	−0.940793	−	0.338983i	$-0.889917\pi$
$773$	−24019.5	+	13867.7i	−1.11762	+	0.645259i	−0.176829	+	0.984242i	$0.556584\pi$
$774$		0			0
$775$			4873.99i			0.225908i
$776$	−8556.00	−	14819.4i	−0.395802	−	0.685550i
$777$		0			0
$778$	29574.0	+	17074.6i	1.36283	+	0.786828i
$779$	−34731.0			−1.59739
$780$		0			0
$781$	−13143.0			−0.602168
$782$	4617.00	+	2665.63i	0.211130	+	0.121896i
$783$		0			0
$784$	−6560.00	−	11362.3i	−0.298834	−	0.517595i
$785$			21255.7i			0.966432i
$786$		0			0
$787$	−27322.5	+	15774.7i	−1.23754	+	0.714493i	−0.968590	−	0.248662i	$-0.920009\pi$
$787$	−27322.5	+	15774.7i	−1.23754	+	0.714493i	−0.268947	+	0.963155i	$0.586676\pi$
$788$		−	11008.9i		−	0.497686i
$789$		0			0
$790$	−29856.0	+	51712.1i	−1.34459	+	2.32890i
$791$	8014.50	+	4627.17i	0.360256	+	0.207994i
$792$		0			0
$793$	−773.500	+	191.392i	−0.0346378	+	0.00857064i
$794$	−30210.0			−1.35027
$795$		0			0
$796$	−3370.00	+	5837.01i	−0.150058	+	0.259909i
$797$	727.500	+	1260.07i	0.0323330	+	0.0560023i	0.881739	−	0.471737i	$-0.156373\pi$
$797$	727.500	+	1260.07i	0.0323330	+	0.0560023i	−0.849406	+	0.527740i	$0.823040\pi$
$798$		0			0
$799$	−8019.00	+	4629.77i	−0.355059	+	0.204993i
$800$	−9648.00	+	5570.28i	−0.426385	+	0.246174i
$801$		0			0
$802$	13137.0	+	22754.0i	0.578408	+	1.00183i
$803$	−11310.0	+	19589.5i	−0.497038	+	0.860894i
$804$		0			0
$805$	−17784.0			−0.778638
$806$	8190.00	+	8511.30i	0.357916	+	0.371957i
$807$		0			0
$808$	−23508.0	−	13572.4i	−1.02353	−	0.590933i
$809$	829.500	−	1436.74i	0.0360490	−	0.0624388i	−0.847438	−	0.530894i	$-0.821856\pi$
$809$	829.500	−	1436.74i	0.0360490	−	0.0624388i	0.883487	+	0.468456i	$0.155189\pi$
$810$		0			0
$811$			4402.87i			0.190636i	0.995447	+	0.0953180i	$0.0303868\pi$
$811$			4402.87i			0.190636i	−0.995447	+	0.0953180i	$0.969613\pi$
$812$	−5382.00	+	3107.30i	−0.232600	+	0.134292i
$813$		0			0
$814$		−	3107.30i		−	0.133797i
$815$	11316.0	+	19599.9i	0.486359	+	0.842398i
$816$		0			0
$817$	−6502.50	−	3754.22i	−0.278450	−	0.160763i
$818$	14910.0			0.637306
$819$		0			0
$820$	21792.0			0.928061
$821$	24856.5	+	14350.9i	1.05664	+	0.610049i	0.924500	−	0.381183i	$-0.124483\pi$
$821$	24856.5	+	14350.9i	1.05664	+	0.610049i	0.132136	+	0.991232i	$0.457816\pi$
$822$		0			0
$823$	−7889.50	−	13665.0i	−0.334156	−	0.578776i	0.649166	−	0.760647i	$-0.275118\pi$
$823$	−7889.50	−	13665.0i	−0.334156	−	0.578776i	−0.983322	+	0.181871i	$0.941785\pi$
$824$		−	25717.5i		−	1.08727i
$825$		0			0
$826$	1287.00	−	743.050i	0.0542136	−	0.0313003i
$827$			7354.29i			0.309231i	0.987975	+	0.154615i	$0.0494138\pi$
$827$			7354.29i			0.309231i	−0.987975	+	0.154615i	$0.950586\pi$
$828$		0			0
$829$	−8685.50	+	15043.7i	−0.363884	+	0.630266i	−0.988596	−	0.150589i	$-0.951883\pi$
$829$	−8685.50	+	15043.7i	−0.363884	+	0.630266i	0.624712	+	0.780855i	$0.285216\pi$
$830$	17712.0	+	10226.0i	0.740714	+	0.427651i
$831$		0			0
$832$	832.000	−	2882.13i	0.0346688	−	0.120096i
$833$	4428.00			0.184179
$834$		0			0
$835$	−11268.0	+	19516.7i	−0.467000	+	0.808868i
$836$	−3978.00	−	6890.10i	−0.164572	−	0.285047i
$837$		0			0
$838$	16191.0	−	9347.88i	0.667433	−	0.385343i
$839$	−25525.5	+	14737.2i	−1.05034	+	0.606416i	−0.922745	−	0.385410i	$-0.874060\pi$
$839$	−25525.5	+	14737.2i	−1.05034	+	0.606416i	−0.127598	+	0.991826i	$0.540727\pi$
$840$		0			0
$841$	9814.00	+	16998.3i	0.402395	+	0.696968i
$842$	−12576.0	+	21782.3i	−0.514724	+	0.891528i
$843$		0			0
$844$	−6724.00			−0.274229
$845$	−16224.0	+	25759.1i	−0.660500	+	1.04868i
$846$		0			0
$847$	−16068.0	−	9276.86i	−0.651834	−	0.376336i
$848$	−17040.0	+	29514.1i	−0.690042	+	1.19519i
$849$		0			0
$850$		−	6266.56i		−	0.252872i
$851$	−1966.50	+	1135.36i	−0.0792136	+	0.0457340i
$852$		0			0
$853$			2909.85i			0.116801i	0.998293	+	0.0584005i	$0.0186000\pi$
$853$			2909.85i			0.116801i	−0.998293	+	0.0584005i	$0.981400\pi$
$854$	663.000	+	1148.35i	0.0265660	+	0.0460137i
$855$		0			0
$856$	3060.00	+	1766.69i	0.122183	+	0.0705424i
$857$	5346.00			0.213087			0.106544	−	0.994308i	$-0.466022\pi$
$857$	5346.00			0.213087			0.106544	+	0.994308i	$0.466022\pi$
$858$		0			0
$859$	24244.0			0.962974			0.481487	−	0.876453i	$-0.340097\pi$
$859$	24244.0			0.962974			0.481487	+	0.876453i	$0.340097\pi$
$860$	4080.00	+	2355.59i	0.161775	+	0.0934011i
$861$		0			0
$862$	843.000	+	1460.12i	0.0333094	+	0.0576936i
$863$		−	32780.8i		−	1.29301i	−0.762908	−	0.646507i	$-0.776229\pi$
$863$		−	32780.8i		−	1.29301i	0.762908	−	0.646507i	$-0.223771\pi$
$864$		0			0
$865$	−10476.0	+	6048.32i	−0.411786	+	0.237745i
$866$		−	42050.7i		−	1.65005i
$867$		0			0
$868$	3276.00	−	5674.20i	0.128104	−	0.221883i
$869$	−24258.0	−	14005.4i	−0.946946	−	0.546720i
$870$		0			0
$871$	−5557.50	+	5347.71i	−0.216198	+	0.208037i
$872$	−8448.00			−0.328080
$873$		0			0
$874$	−8721.00	+	15105.2i	−0.337520	+	0.584601i
$875$	−9048.00	−	15671.6i	−0.349575	−	0.605482i
$876$		0			0
$877$	−3934.50	+	2271.58i	−0.151492	+	0.0874640i	−0.573830	−	0.818974i	$-0.694543\pi$
$877$	−3934.50	+	2271.58i	−0.151492	+	0.0874640i	0.422338	+	0.906439i	$0.361210\pi$
$878$	−1383.00	+	798.475i	−0.0531594	+	0.0306916i
$879$		0			0
$880$	−12480.0	−	21616.0i	−0.478069	−	0.828040i
$881$	−10258.5	+	17768.2i	−0.392302	+	0.679486i	−0.992753	−	0.120175i	$-0.961654\pi$
$881$	−10258.5	+	17768.2i	−0.392302	+	0.679486i	0.600451	+	0.799661i	$0.294988\pi$
$882$		0			0
$883$	−23852.0			−0.909042			−0.454521	−	0.890736i	$-0.650189\pi$
$883$	−23852.0			−0.909042			−0.454521	+	0.890736i	$0.650189\pi$
$884$	−3510.00	−	3647.70i	−0.133545	−	0.138784i
$885$		0			0
$886$	−36468.0	−	21054.8i	−1.38281	−	0.798364i
$887$	19378.5	−	33564.5i	0.733558	−	1.27056i	−0.221794	−	0.975093i	$-0.571191\pi$
$887$	19378.5	−	33564.5i	0.733558	−	1.27056i	0.955353	−	0.295467i	$-0.0954753\pi$
$888$		0			0
$889$		−	50504.9i		−	1.90538i
$890$	−12744.0	+	7357.75i	−0.479977	+	0.277115i
$891$		0			0
$892$		−	16385.2i		−	0.615042i
$893$	−15147.0	−	26235.4i	−0.567609	−	0.983128i
$894$		0			0
$895$	15444.0	+	8916.60i	0.576800	+	0.333016i
$896$	−34944.0			−1.30290
$897$		0			0
$898$	1026.00			0.0381270
$899$	4347.00	+	2509.74i	0.161269	+	0.0931085i
$900$		0			0
$901$	−5751.00	−	9961.02i	−0.212645	−	0.368313i
$902$			30667.7i			1.13206i
$903$		0			0
$904$	4932.00	−	2847.49i	0.181456	−	0.104763i
$905$		−	27.7128i		−	0.00101791i
$906$		0			0
$907$	19535.5	−	33836.5i	0.715177	−	1.23872i	−0.247714	−	0.968833i	$-0.579679\pi$
$907$	19535.5	−	33836.5i	0.715177	−	1.23872i	0.962891	−	0.269890i	$-0.0869873\pi$
$908$	−1518.00	−	876.418i	−0.0554808	−	0.0320319i
$909$		0			0
$910$	48672.0	+	14050.4i	1.77303	+	0.511831i
$911$	53040.0			1.92897			0.964486	−	0.264134i	$-0.0850860\pi$
$911$	53040.0			1.92897			0.964486	+	0.264134i	$0.0850860\pi$
$912$		0			0
$913$	−4797.00	+	8308.65i	−0.173886	+	0.301179i
$914$	1059.00	+	1834.24i	0.0383245	+	0.0663800i
$915$		0			0
$916$	−624.000	+	360.267i	−0.0225082	+	0.0129951i
$917$	7254.00	−	4188.10i	0.261230	−	0.150821i
$918$		0			0
$919$	−183.500	−	317.831i	−0.00658662	−	0.0114084i	0.862713	−	0.505693i	$-0.168763\pi$
$919$	−183.500	−	317.831i	−0.00658662	−	0.0114084i	−0.869300	+	0.494285i	$0.835430\pi$
$920$	−5472.00	+	9477.78i	−0.196094	+	0.339645i
$921$		0			0
$922$	45474.0			1.62430
$923$	−6571.50	−	26558.4i	−0.234348	−	0.947108i
$924$		0			0
$925$	2311.50	+	1334.55i	0.0821639	+	0.0474374i
$926$	1446.00	−	2504.55i	0.0513159	−	0.0888817i
$927$		0			0
$928$			11473.1i			0.405844i
$929$	25924.5	−	14967.5i	0.915560	−	0.528599i	0.0333441	−	0.999444i	$-0.489384\pi$
$929$	25924.5	−	14967.5i	0.915560	−	0.528599i	0.882216	+	0.470845i	$0.156051\pi$
$930$		0			0
$931$			14486.9i			0.509976i
$932$	11556.0	+	20015.6i	0.406147	+	0.703468i
$933$		0			0
$934$	−43488.0	−	25107.8i	−1.52352	−	0.879607i
$935$	8424.00			0.294646
$936$		0			0
$937$	42166.0			1.47012			0.735060	−	0.678002i	$-0.237154\pi$
$937$	42166.0			1.47012			0.735060	+	0.678002i	$0.237154\pi$
$938$	11115.0	+	6417.25i	0.386906	+	0.223380i
$939$		0			0
$940$	9504.00	+	16461.4i	0.329773	+	0.571183i
$941$			35022.1i			1.21327i	0.794981	+	0.606635i	$0.207481\pi$
$941$			35022.1i			1.21327i	−0.794981	+	0.606635i	$0.792519\pi$
$942$		0			0
$943$	19408.5	−	11205.5i	0.670231	−	0.386958i
$944$		−	1524.20i		−	0.0525515i
$945$		0			0
$946$	−3315.00	+	5741.75i	−0.113932	+	0.197337i
$947$	2251.50	+	1299.90i	0.0772586	+	0.0446053i	0.538132	−	0.842861i	$-0.319130\pi$
$947$	2251.50	+	1299.90i	0.0772586	+	0.0446053i	−0.460873	+	0.887466i	$0.652464\pi$
$948$		0			0
$949$	−45240.0	−	13059.7i	−1.54747	−	0.446717i
$950$	20502.0			0.700182
$951$		0			0
$952$	4212.00	−	7295.40i	0.143395	−	0.248367i
$953$	5311.50	+	9199.79i	0.180542	+	0.312708i	0.942065	−	0.335430i	$-0.108882\pi$
$953$	5311.50	+	9199.79i	0.180542	+	0.312708i	−0.761523	+	0.648137i	$0.775548\pi$
$954$		0			0
$955$	−34092.0	+	19683.0i	−1.15517	+	0.666940i
$956$	−6444.00	+	3720.45i	−0.218006	+	0.125866i
$957$		0			0
$958$	15411.0	+	26692.6i	0.519736	+	0.900209i
$959$	13396.5	−	23203.4i	0.451090	−	0.781311i
$960$		0			0
$961$	24499.0			0.822362
$962$	6279.00	−	1553.65i	0.210440	−	0.0520703i
$963$		0			0
$964$	7134.00	+	4118.82i	0.238351	+	0.137612i
$965$	−29412.0	+	50943.1i	−0.981146	+	1.69939i
$966$		0			0
$967$			20199.2i			0.671729i	0.941910	+	0.335864i	$0.109028\pi$
$967$			20199.2i			0.671729i	−0.941910	+	0.335864i	$0.890972\pi$
$968$	−9888.00	+	5708.84i	−0.328319	+	0.189555i
$969$		0			0
$970$		−	59277.7i		−	1.96216i
$971$	−1162.50	−	2013.51i	−0.0384206	−	0.0665464i	0.846176	−	0.532904i	$-0.178899\pi$
$971$	−1162.50	−	2013.51i	−0.0384206	−	0.0665464i	−0.884596	+	0.466358i	$0.845566\pi$
$972$		0			0
$973$	49627.5	+	28652.5i	1.63513	+	0.944045i
$974$	16470.0			0.541820
$975$		0			0
$976$	1360.00			0.0446030
$977$	−28525.5	−	16469.2i	−0.934096	−	0.539300i	−0.0459912	−	0.998942i	$-0.514645\pi$
$977$	−28525.5	−	16469.2i	−0.934096	−	0.539300i	−0.888105	+	0.459641i	$0.847978\pi$
$978$		0			0
$979$	−3451.50	−	5978.17i	−0.112677	−	0.195162i
$980$		−	9089.80i		−	0.296289i
$981$		0			0
$982$	−4905.00	+	2831.90i	−0.159394	+	0.0920261i
$983$		−	42702.0i		−	1.38554i	−0.721161	−	0.692768i	$-0.756391\pi$
$983$		−	42702.0i		−	1.38554i	0.721161	−	0.692768i	$-0.243609\pi$
$984$		0			0
$985$	−19068.0	+	33026.7i	−0.616809	+	1.06834i
$986$	−5589.00	−	3226.81i	−0.180517	−	0.104222i
$987$		0			0
$988$	11934.0	−	11483.5i	0.384283	−	0.369776i
$989$	4845.00			0.155776
$990$		0			0
$991$	2421.50	−	4194.16i	0.0776201	−	0.134442i	−0.824603	−	0.565712i	$-0.808601\pi$
$991$	2421.50	−	4194.16i	0.0776201	−	0.134442i	0.902223	+	0.431271i	$0.141935\pi$
$992$	−6048.00	−	10475.4i	−0.193573	−	0.335278i
$993$		0			0
$994$	−39429.0	+	22764.3i	−1.25816	+	0.726400i
$995$	20220.0	−	11674.0i	0.644238	−	0.371951i
$996$		0			0
$997$	−5471.50	−	9476.92i	−0.173806	−	0.301040i	0.765942	−	0.642910i	$-0.222273\pi$
$997$	−5471.50	−	9476.92i	−0.173806	−	0.301040i	−0.939747	+	0.341870i	$0.888940\pi$
$998$	25002.0	−	43304.7i	0.793011	−	1.37353i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.c.82.1		2
3.2	odd	2		13.4.e.a.4.1	✓	2
12.11	even	2		208.4.w.a.17.1		2
13.6	odd	12		1521.4.a.q.1.1		2
13.7	odd	12		1521.4.a.q.1.2		2
13.10	even	6	inner	117.4.q.c.10.1		2
39.2	even	12		169.4.c.i.146.1		4
39.5	even	4		169.4.c.i.22.1		4
39.8	even	4		169.4.c.i.22.2		4
39.11	even	12		169.4.c.i.146.2		4
39.17	odd	6		169.4.b.b.168.1		2
39.20	even	12		169.4.a.h.1.1		2
39.23	odd	6		13.4.e.a.10.1	yes	2
39.29	odd	6		169.4.e.b.23.1		2
39.32	even	12		169.4.a.h.1.2		2
39.35	odd	6		169.4.b.b.168.2		2
39.38	odd	2		169.4.e.b.147.1		2
156.23	even	6		208.4.w.a.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.a.4.1	✓	2	3.2	odd	2
13.4.e.a.10.1	yes	2	39.23	odd	6
117.4.q.c.10.1		2	13.10	even	6	inner
117.4.q.c.82.1		2	1.1	even	1	trivial
169.4.a.h.1.1		2	39.20	even	12
169.4.a.h.1.2		2	39.32	even	12
169.4.b.b.168.1		2	39.17	odd	6
169.4.b.b.168.2		2	39.35	odd	6
169.4.c.i.22.1		4	39.5	even	4
169.4.c.i.22.2		4	39.8	even	4
169.4.c.i.146.1		4	39.2	even	12
169.4.c.i.146.2		4	39.11	even	12
169.4.e.b.23.1		2	39.29	odd	6
169.4.e.b.147.1		2	39.38	odd	2
208.4.w.a.17.1		2	12.11	even	2
208.4.w.a.49.1		2	156.23	even	6
1521.4.a.q.1.1		2	13.6	odd	12
1521.4.a.q.1.2		2	13.7	odd	12

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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} -13.8564i q^{5} +(19.5000 - 11.2583i) q^{7} -13.8564i q^{8} +O(q^{10})\)	\(q+(3.00000 + 1.73205i) q^{2} +(2.00000 + 3.46410i) q^{4} -13.8564i q^{5} +(19.5000 - 11.2583i) q^{7} -13.8564i q^{8} +(24.0000 - 41.5692i) q^{10} +(19.5000 + 11.2583i) q^{11} +(-13.0000 + 45.0333i) q^{13} +78.0000 q^{14} +(40.0000 - 69.2820i) q^{16} +(13.5000 + 23.3827i) q^{17} +(-76.5000 + 44.1673i) q^{19} +(48.0000 - 27.7128i) q^{20} +(39.0000 + 67.5500i) q^{22} +(28.5000 - 49.3634i) q^{23} -67.0000 q^{25} +(-117.000 + 112.583i) q^{26} +(78.0000 + 45.0333i) q^{28} +(-34.5000 + 59.7558i) q^{29} -72.7461i q^{31} +(144.000 - 83.1384i) q^{32} +93.5307i q^{34} +(-156.000 - 270.200i) q^{35} +(-34.5000 - 19.9186i) q^{37} -306.000 q^{38} -192.000 q^{40} +(340.500 + 196.588i) q^{41} +(42.5000 + 73.6122i) q^{43} +90.0666i q^{44} +(171.000 - 98.7269i) q^{46} +342.946i q^{47} +(82.0000 - 142.028i) q^{49} +(-201.000 - 116.047i) q^{50} +(-182.000 + 45.0333i) q^{52} -426.000 q^{53} +(156.000 - 270.200i) q^{55} +(-156.000 - 270.200i) q^{56} +(-207.000 + 119.512i) q^{58} +(16.5000 - 9.52628i) q^{59} +(8.50000 + 14.7224i) q^{61} +(126.000 - 218.238i) q^{62} -64.0000 q^{64} +(624.000 + 180.133i) q^{65} +(142.500 + 82.2724i) q^{67} +(-54.0000 + 93.5307i) q^{68} -1080.80i q^{70} +(-505.500 + 291.851i) q^{71} +1004.59i q^{73} +(-69.0000 - 119.512i) q^{74} +(-306.000 - 176.669i) q^{76} +507.000 q^{77} -1244.00 q^{79} +(-960.000 - 554.256i) q^{80} +(681.000 + 1179.53i) q^{82} +426.084i q^{83} +(324.000 - 187.061i) q^{85} +294.449i q^{86} +(156.000 - 270.200i) q^{88} +(-265.500 - 153.286i) q^{89} +(253.500 + 1024.51i) q^{91} +228.000 q^{92} +(-594.000 + 1028.84i) q^{94} +(612.000 + 1060.02i) q^{95} +(1069.50 - 617.476i) q^{97} +(492.000 - 284.056i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 4 q^{4} + 39 q^{7}+O(q^{10}) \) 2 * q + 6 * q^2 + 4 * q^4 + 39 * q^7	\( 2 q + 6 q^{2} + 4 q^{4} + 39 q^{7} + 48 q^{10} + 39 q^{11} - 26 q^{13} + 156 q^{14} + 80 q^{16} + 27 q^{17} - 153 q^{19} + 96 q^{20} + 78 q^{22} + 57 q^{23} - 134 q^{25} - 234 q^{26} + 156 q^{28} - 69 q^{29} + 288 q^{32} - 312 q^{35} - 69 q^{37} - 612 q^{38} - 384 q^{40} + 681 q^{41} + 85 q^{43} + 342 q^{46} + 164 q^{49} - 402 q^{50} - 364 q^{52} - 852 q^{53} + 312 q^{55} - 312 q^{56} - 414 q^{58} + 33 q^{59} + 17 q^{61} + 252 q^{62} - 128 q^{64} + 1248 q^{65} + 285 q^{67} - 108 q^{68} - 1011 q^{71} - 138 q^{74} - 612 q^{76} + 1014 q^{77} - 2488 q^{79} - 1920 q^{80} + 1362 q^{82} + 648 q^{85} + 312 q^{88} - 531 q^{89} + 507 q^{91} + 456 q^{92} - 1188 q^{94} + 1224 q^{95} + 2139 q^{97} + 984 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 + 4 * q^4 + 39 * q^7 + 48 * q^10 + 39 * q^11 - 26 * q^13 + 156 * q^14 + 80 * q^16 + 27 * q^17 - 153 * q^19 + 96 * q^20 + 78 * q^22 + 57 * q^23 - 134 * q^25 - 234 * q^26 + 156 * q^28 - 69 * q^29 + 288 * q^32 - 312 * q^35 - 69 * q^37 - 612 * q^38 - 384 * q^40 + 681 * q^41 + 85 * q^43 + 342 * q^46 + 164 * q^49 - 402 * q^50 - 364 * q^52 - 852 * q^53 + 312 * q^55 - 312 * q^56 - 414 * q^58 + 33 * q^59 + 17 * q^61 + 252 * q^62 - 128 * q^64 + 1248 * q^65 + 285 * q^67 - 108 * q^68 - 1011 * q^71 - 138 * q^74 - 612 * q^76 + 1014 * q^77 - 2488 * q^79 - 1920 * q^80 + 1362 * q^82 + 648 * q^85 + 312 * q^88 - 531 * q^89 + 507 * q^91 + 456 * q^92 - 1188 * q^94 + 1224 * q^95 + 2139 * q^97 + 984 * q^98

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