LMFDB - Embedded newform 952.2.q.e.681.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(137,952)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("952.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 17 x^{12} - 18 x^{11} + 102 x^{10} - 59 x^{9} + 462 x^{8} - 28 x^{7} + 1148 x^{6} + \cdots + 361 $ x^14 - 3x^13 + 17x^12 - 18x^11 + 102x^10 - 59x^9 + 462x^8 - 28x^7 + 1148x^6 - x^5 + 1982x^4 + 198x^3 + 1563x^2 - 532x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.6
Root			$1.25290 + 2.17009i$ of defining polynomial
Character	$\chi$	$=$	952.681
Dual form			952.2.q.e.137.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25290 + 2.17009i) q^{3} +(-1.89712 + 3.28590i) q^{5} +(-2.54429 - 0.725680i) q^{7} +(-1.63954 + 2.83977i) q^{9} +(2.42361 + 4.19782i) q^{11} -2.44913 q^{13} -9.50763 q^{15} +(-0.500000 - 0.866025i) q^{17} +(3.49743 - 6.05772i) q^{19} +(-1.61295 - 6.43055i) q^{21} +(-2.10665 + 3.64882i) q^{23} +(-4.69811 - 8.13736i) q^{25} -0.699322 q^{27} +3.62181 q^{29} +(-1.59030 - 2.75449i) q^{31} +(-6.07310 + 10.5189i) q^{33} +(7.21132 - 6.98358i) q^{35} +(-2.00524 + 3.47317i) q^{37} +(-3.06852 - 5.31483i) q^{39} +4.63689 q^{41} -11.7265 q^{43} +(-6.22080 - 10.7747i) q^{45} +(-5.66509 + 9.81223i) q^{47} +(5.94678 + 3.69268i) q^{49} +(1.25290 - 2.17009i) q^{51} +(2.39539 + 4.14893i) q^{53} -18.3915 q^{55} +17.5278 q^{57} +(-4.87939 - 8.45135i) q^{59} +(4.77705 - 8.27409i) q^{61} +(6.23222 - 6.03540i) q^{63} +(4.64628 - 8.04759i) q^{65} +(6.54987 + 11.3447i) q^{67} -10.5577 q^{69} -0.382777 q^{71} +(0.295933 + 0.512572i) q^{73} +(11.7726 - 20.3907i) q^{75} +(-3.12008 - 12.4392i) q^{77} +(-4.39081 + 7.60510i) q^{79} +(4.04244 + 7.00171i) q^{81} -5.09035 q^{83} +3.79423 q^{85} +(4.53779 + 7.85968i) q^{87} +(-0.212764 + 0.368518i) q^{89} +(6.23127 + 1.77728i) q^{91} +(3.98500 - 6.90222i) q^{93} +(13.2701 + 22.9844i) q^{95} +1.02209 q^{97} -15.8944 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 4 q^{13} - 12 q^{15} - 7 q^{17} + 3 q^{19} + 18 q^{21} + 18 q^{23} - 15 q^{25} - 36 q^{27} + 10 q^{29} + 10 q^{31} - 21 q^{33} + 19 q^{35} - 11 q^{37}+ \cdots - 40 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 4 * q^9 + 12 * q^11 + 4 * q^13 - 12 * q^15 - 7 * q^17 + 3 * q^19 + 18 * q^21 + 18 * q^23 - 15 * q^25 - 36 * q^27 + 10 * q^29 + 10 * q^31 - 21 * q^33 + 19 * q^35 - 11 * q^37 + 12 * q^39 - 30 * q^43 - 13 * q^45 - 15 * q^47 + 20 * q^49 + 3 * q^51 - 8 * q^53 - 18 * q^55 - 6 * q^57 - 9 * q^59 + 4 * q^61 + 41 * q^63 + 38 * q^65 + 30 * q^67 - 56 * q^69 - 54 * q^71 + 5 * q^73 + 2 * q^75 + 27 * q^77 - 3 * q^79 + 17 * q^81 - 24 * q^83 + 4 * q^85 - 19 * q^87 - 32 * q^89 - 11 * q^91 + 9 * q^93 + 42 * q^95 - 78 * q^97 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.25290	+	2.17009i	0.723365	+	1.25290i	0.959644	+	0.281219i	$0.0907388\pi$
$3$	1.25290	+	2.17009i	0.723365	+	1.25290i	−0.236279	+	0.971685i	$0.575928\pi$
$4$		0			0
$5$	−1.89712	+	3.28590i	−0.848417	+	1.46950i	0.0342041	+	0.999415i	$0.489110\pi$
$5$	−1.89712	+	3.28590i	−0.848417	+	1.46950i	−0.882621	+	0.470086i	$0.844223\pi$
$6$		0			0
$7$	−2.54429	−	0.725680i	−0.961649	−	0.274281i
$7$	−2.54429	−	0.725680i	−0.961649	−	0.274281i
$8$		0			0
$9$	−1.63954	+	2.83977i	−0.546513	+	0.946589i
$10$		0			0
$11$	2.42361	+	4.19782i	0.730746	+	1.26569i	0.956565	+	0.291520i	$0.0941609\pi$
$11$	2.42361	+	4.19782i	0.730746	+	1.26569i	−0.225819	+	0.974169i	$0.572506\pi$
$12$		0			0
$13$	−2.44913			−0.679265			−0.339633	−	0.940558i	$-0.610303\pi$
$13$	−2.44913			−0.679265			−0.339633	+	0.940558i	$0.610303\pi$
$14$		0			0
$15$	−9.50763			−2.45486
$16$		0			0
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$		0			0
$19$	3.49743	−	6.05772i	0.802365	−	1.38974i	−0.115691	−	0.993285i	$-0.536908\pi$
$19$	3.49743	−	6.05772i	0.802365	−	1.38974i	0.918056	−	0.396451i	$-0.129758\pi$
$20$		0			0
$21$	−1.61295	−	6.43055i	−0.351975	−	1.40326i
$22$		0			0
$23$	−2.10665	+	3.64882i	−0.439266	+	0.760831i	−0.997633	−	0.0687630i	$-0.978095\pi$
$23$	−2.10665	+	3.64882i	−0.439266	+	0.760831i	0.558367	+	0.829594i	$0.311428\pi$
$24$		0			0
$25$	−4.69811	−	8.13736i	−0.939621	−	1.62747i
$26$		0			0
$27$	−0.699322			−0.134585
$28$		0			0
$29$	3.62181			0.672554			0.336277	−	0.941763i	$-0.390832\pi$
$29$	3.62181			0.672554			0.336277	+	0.941763i	$0.390832\pi$
$30$		0			0
$31$	−1.59030	−	2.75449i	−0.285627	−	0.494721i	0.687134	−	0.726531i	$-0.258869\pi$
$31$	−1.59030	−	2.75449i	−0.285627	−	0.494721i	−0.972761	+	0.231810i	$0.925535\pi$
$32$		0			0
$33$	−6.07310	+	10.5189i	−1.05719	+	1.83111i
$34$		0			0
$35$	7.21132	−	6.98358i	1.21894	−	1.18044i
$36$		0			0
$37$	−2.00524	+	3.47317i	−0.329659	+	0.570986i	−0.982444	−	0.186557i	$-0.940267\pi$
$37$	−2.00524	+	3.47317i	−0.329659	+	0.570986i	0.652785	+	0.757543i	$0.273600\pi$
$38$		0			0
$39$	−3.06852	−	5.31483i	−0.491357	−	0.851055i
$40$		0			0
$41$	4.63689			0.724161			0.362080	−	0.932147i	$-0.382067\pi$
$41$	4.63689			0.724161			0.362080	+	0.932147i	$0.382067\pi$
$42$		0			0
$43$	−11.7265			−1.78828			−0.894139	−	0.447790i	$-0.852211\pi$
$43$	−11.7265			−1.78828			−0.894139	+	0.447790i	$0.852211\pi$
$44$		0			0
$45$	−6.22080	−	10.7747i	−0.927342	−	1.60620i
$46$		0			0
$47$	−5.66509	+	9.81223i	−0.826339	+	1.43126i	0.0745531	+	0.997217i	$0.476247\pi$
$47$	−5.66509	+	9.81223i	−0.826339	+	1.43126i	−0.900892	+	0.434044i	$0.857086\pi$
$48$		0			0
$49$	5.94678	+	3.69268i	0.849539	+	0.527525i
$50$		0			0
$51$	1.25290	−	2.17009i	0.175442	−	0.303874i
$52$		0			0
$53$	2.39539	+	4.14893i	0.329032	+	0.569900i	0.982320	−	0.187210i	$-0.0599443\pi$
$53$	2.39539	+	4.14893i	0.329032	+	0.569900i	−0.653288	+	0.757109i	$0.726611\pi$
$54$		0			0
$55$	−18.3915			−2.47991
$56$		0			0
$57$	17.5278			2.32161
$58$		0			0
$59$	−4.87939	−	8.45135i	−0.635242	−	1.10027i	−0.986464	−	0.163980i	$-0.947567\pi$
$59$	−4.87939	−	8.45135i	−0.635242	−	1.10027i	0.351221	−	0.936292i	$-0.385766\pi$
$60$		0			0
$61$	4.77705	−	8.27409i	0.611638	−	1.05939i	−0.379326	−	0.925263i	$-0.623844\pi$
$61$	4.77705	−	8.27409i	0.611638	−	1.05939i	0.990964	−	0.134126i	$-0.0428226\pi$
$62$		0			0
$63$	6.23222	−	6.03540i	0.785186	−	0.760388i
$64$		0			0
$65$	4.64628	−	8.04759i	0.576300	−	0.998181i
$66$		0			0
$67$	6.54987	+	11.3447i	0.800194	+	1.38598i	0.919488	+	0.393118i	$0.128603\pi$
$67$	6.54987	+	11.3447i	0.800194	+	1.38598i	−0.119294	+	0.992859i	$0.538063\pi$
$68$		0			0
$69$	−10.5577			−1.27100
$70$		0			0
$71$	−0.382777			−0.0454273			−0.0227136	−	0.999742i	$-0.507231\pi$
$71$	−0.382777			−0.0454273			−0.0227136	+	0.999742i	$0.507231\pi$
$72$		0			0
$73$	0.295933	+	0.512572i	0.0346364	+	0.0599920i	0.882824	−	0.469704i	$-0.155639\pi$
$73$	0.295933	+	0.512572i	0.0346364	+	0.0599920i	−0.848188	+	0.529696i	$0.822306\pi$
$74$		0			0
$75$	11.7726	−	20.3907i	1.35938	−	2.35451i
$76$		0			0
$77$	−3.12008	−	12.4392i	−0.355566	−	1.41758i
$78$		0			0
$79$	−4.39081	+	7.60510i	−0.494004	+	0.855641i	−0.999976	−	0.00690944i	$-0.997801\pi$
$79$	−4.39081	+	7.60510i	−0.494004	+	0.855641i	0.505972	+	0.862550i	$0.331134\pi$
$80$		0			0
$81$	4.04244	+	7.00171i	0.449160	+	0.777967i
$82$		0			0
$83$	−5.09035			−0.558738			−0.279369	−	0.960184i	$-0.590125\pi$
$83$	−5.09035			−0.558738			−0.279369	+	0.960184i	$0.590125\pi$
$84$		0			0
$85$	3.79423			0.411542
$86$		0			0
$87$	4.53779	+	7.85968i	0.486502	+	0.842646i
$88$		0			0
$89$	−0.212764	+	0.368518i	−0.0225530	+	0.0390629i	−0.877082	−	0.480341i	$-0.840513\pi$
$89$	−0.212764	+	0.368518i	−0.0225530	+	0.0390629i	0.854529	+	0.519404i	$0.173846\pi$
$90$		0			0
$91$	6.23127	+	1.77728i	0.653215	+	0.186310i
$92$		0			0
$93$	3.98500	−	6.90222i	0.413225	−	0.715727i
$94$		0			0
$95$	13.2701	+	22.9844i	1.36148	+	2.35815i
$96$		0			0
$97$	1.02209			0.103778			0.0518889	−	0.998653i	$-0.483476\pi$
$97$	1.02209			0.103778			0.0518889	+	0.998653i	$0.483476\pi$
$98$		0			0
$99$	−15.8944			−1.59745
$100$		0			0
$101$	1.19287	+	2.06611i	0.118695	+	0.205586i	0.919251	−	0.393672i	$-0.128796\pi$
$101$	1.19287	+	2.06611i	0.118695	+	0.205586i	−0.800556	+	0.599258i	$0.795462\pi$
$102$		0			0
$103$	3.08448	−	5.34248i	0.303923	−	0.526410i	−0.673098	−	0.739553i	$-0.735037\pi$
$103$	3.08448	−	5.34248i	0.303923	−	0.526410i	0.977021	+	0.213143i	$0.0683701\pi$
$104$		0			0
$105$	24.1901	+	6.89950i	2.36071	+	0.673322i
$106$		0			0
$107$	−3.37802	+	5.85090i	−0.326565	+	0.565628i	−0.981828	−	0.189773i	$-0.939225\pi$
$107$	−3.37802	+	5.85090i	−0.326565	+	0.565628i	0.655263	+	0.755401i	$0.272558\pi$
$108$		0			0
$109$	5.62300	+	9.73932i	0.538586	+	0.932858i	0.998981	+	0.0451438i	$0.0143746\pi$
$109$	5.62300	+	9.73932i	0.538586	+	0.932858i	−0.460395	+	0.887714i	$0.652292\pi$
$110$		0			0
$111$	−10.0495			−0.953855
$112$		0			0
$113$	−12.2360			−1.15107			−0.575534	−	0.817778i	$-0.695206\pi$
$113$	−12.2360			−1.15107			−0.575534	+	0.817778i	$0.695206\pi$
$114$		0			0
$115$	−7.99311	−	13.8445i	−0.745361	−	1.29100i
$116$		0			0
$117$	4.01544	−	6.95495i	0.371228	−	0.642985i
$118$		0			0
$119$	0.643685	+	2.56626i	0.0590065	+	0.235248i
$120$		0			0
$121$	−6.24777	+	10.8215i	−0.567979	+	0.983769i
$122$		0			0
$123$	5.80958	+	10.0625i	0.523833	+	0.907305i
$124$		0			0
$125$	16.6803			1.49193
$126$		0			0
$127$	0.800731			0.0710534			0.0355267	−	0.999369i	$-0.488689\pi$
$127$	0.800731			0.0710534			0.0355267	+	0.999369i	$0.488689\pi$
$128$		0			0
$129$	−14.6922	−	25.4477i	−1.29358	−	2.24054i
$130$		0			0
$131$	−9.57796	+	16.5895i	−0.836830	+	1.44943i	0.0557011	+	0.998447i	$0.482261\pi$
$131$	−9.57796	+	16.5895i	−0.836830	+	1.44943i	−0.892531	+	0.450985i	$0.851073\pi$
$132$		0			0
$133$	−13.2944	+	12.8746i	−1.15277	+	1.11637i
$134$		0			0
$135$	1.32670	−	2.29791i	0.114184	−	0.197772i
$136$		0			0
$137$	2.26621	+	3.92519i	0.193615	+	0.335352i	0.946446	−	0.322863i	$-0.104645\pi$
$137$	2.26621	+	3.92519i	0.193615	+	0.335352i	−0.752830	+	0.658215i	$0.771312\pi$
$138$		0			0
$139$	−13.9470			−1.18297			−0.591483	−	0.806318i	$-0.701457\pi$
$139$	−13.9470			−1.18297			−0.591483	+	0.806318i	$0.701457\pi$
$140$		0			0
$141$	−28.3913			−2.39098
$142$		0			0
$143$	−5.93573	−	10.2810i	−0.496370	−	0.859739i
$144$		0			0
$145$	−6.87101	+	11.9009i	−0.570606	+	0.988319i
$146$		0			0
$147$	−0.562712	+	17.5316i	−0.0464117	+	1.44599i
$148$		0			0
$149$	9.28211	−	16.0771i	0.760420	−	1.31709i	−0.182215	−	0.983259i	$-0.558327\pi$
$149$	9.28211	−	16.0771i	0.760420	−	1.31709i	0.942634	−	0.333827i	$-0.108340\pi$
$150$		0			0
$151$	10.1905	+	17.6505i	0.829292	+	1.43638i	0.898595	+	0.438780i	$0.144589\pi$
$151$	10.1905	+	17.6505i	0.829292	+	1.43638i	−0.0693029	+	0.997596i	$0.522078\pi$
$152$		0			0
$153$	3.27908			0.265098
$154$		0			0
$155$	12.0680			0.969323
$156$		0			0
$157$	−0.0958880	−	0.166083i	−0.00765269	−	0.0132549i	0.862174	−	0.506613i	$-0.169103\pi$
$157$	−0.0958880	−	0.166083i	−0.00765269	−	0.0132549i	−0.869826	+	0.493358i	$0.835769\pi$
$158$		0			0
$159$	−6.00238	+	10.3964i	−0.476020	+	0.824491i
$160$		0			0
$161$	8.00778	−	7.75488i	0.631102	−	0.611170i
$162$		0			0
$163$	7.22187	−	12.5086i	0.565660	−	0.979753i	−0.431327	−	0.902195i	$-0.641955\pi$
$163$	7.22187	−	12.5086i	0.565660	−	0.979753i	0.996988	−	0.0775572i	$-0.0247120\pi$
$164$		0			0
$165$	−23.0428	−	39.9113i	−1.79388	−	3.10709i
$166$		0			0
$167$	−0.601637			−0.0465561			−0.0232780	−	0.999729i	$-0.507410\pi$
$167$	−0.601637			−0.0465561			−0.0232780	+	0.999729i	$0.507410\pi$
$168$		0			0
$169$	−7.00178			−0.538599
$170$		0			0
$171$	11.4683	+	19.8638i	0.877006	+	1.51902i
$172$		0			0
$173$	2.94987	−	5.10933i	0.224275	−	0.388455i	−0.731827	−	0.681491i	$-0.761332\pi$
$173$	2.94987	−	5.10933i	0.224275	−	0.388455i	0.956102	+	0.293035i	$0.0946654\pi$
$174$		0			0
$175$	6.04820	+	24.1131i	0.457201	+	1.82278i
$176$		0			0
$177$	12.2268	−	21.1775i	0.919024	−	1.59180i
$178$		0			0
$179$	4.46766	+	7.73822i	0.333929	+	0.578381i	0.983278	−	0.182109i	$-0.0582922\pi$
$179$	4.46766	+	7.73822i	0.333929	+	0.578381i	−0.649350	+	0.760490i	$0.724959\pi$
$180$		0			0
$181$	19.7947			1.47133			0.735663	−	0.677347i	$-0.236871\pi$
$181$	19.7947			1.47133			0.735663	+	0.677347i	$0.236871\pi$
$182$		0			0
$183$	23.9407			1.76975
$184$		0			0
$185$	−7.60834	−	13.1780i	−0.559376	−	0.968868i
$186$		0			0
$187$	2.42361	−	4.19782i	0.177232	−	0.306975i
$188$		0			0
$189$	1.77928	+	0.507485i	0.129423	+	0.0369141i
$190$		0			0
$191$	−9.98992	+	17.3031i	−0.722845	+	1.25200i	0.237009	+	0.971507i	$0.423833\pi$
$191$	−9.98992	+	17.3031i	−0.722845	+	1.25200i	−0.959855	+	0.280497i	$0.909501\pi$
$192$		0			0
$193$	10.7977	+	18.7022i	0.777237	+	1.34621i	0.933528	+	0.358503i	$0.116713\pi$
$193$	10.7977	+	18.7022i	0.777237	+	1.34621i	−0.156291	+	0.987711i	$0.549954\pi$
$194$		0			0
$195$	23.2854			1.66750
$196$		0			0
$197$	19.6358			1.39900			0.699498	−	0.714635i	$-0.253407\pi$
$197$	19.6358			1.39900			0.699498	+	0.714635i	$0.253407\pi$
$198$		0			0
$199$	−10.1784	−	17.6295i	−0.721529	−	1.24973i	−0.960387	−	0.278670i	$-0.910106\pi$
$199$	−10.1784	−	17.6295i	−0.721529	−	1.24973i	0.238858	−	0.971055i	$-0.423227\pi$
$200$		0			0
$201$	−16.4127	+	28.4277i	−1.15766	+	2.00513i
$202$		0			0
$203$	−9.21493	−	2.62828i	−0.646761	−	0.184469i
$204$		0			0
$205$	−8.79673	+	15.2364i	−0.614390	+	1.06415i
$206$		0			0
$207$	−6.90786	−	11.9648i	−0.480130	−	0.831609i
$208$		0			0
$209$	33.9056			2.34530
$210$		0			0
$211$	−8.61581			−0.593137			−0.296569	−	0.955012i	$-0.595842\pi$
$211$	−8.61581			−0.593137			−0.296569	+	0.955012i	$0.595842\pi$
$212$		0			0
$213$	−0.479583	−	0.830663i	−0.0328605	−	0.0569161i
$214$		0			0
$215$	22.2466	−	38.5322i	1.51720	−	2.62787i
$216$		0			0
$217$	2.04731	+	8.16226i	0.138981	+	0.554090i
$218$		0			0
$219$	−0.741553	+	1.28441i	−0.0501095	+	0.0867922i
$220$		0			0
$221$	1.22456	+	2.12101i	0.0823730	+	0.142674i
$222$		0			0
$223$	−11.1008			−0.743366			−0.371683	−	0.928360i	$-0.621219\pi$
$223$	−11.1008			−0.743366			−0.371683	+	0.928360i	$0.621219\pi$
$224$		0			0
$225$	30.8109			2.05406
$226$		0			0
$227$	11.9154	+	20.6381i	0.790854	+	1.36980i	0.925439	+	0.378897i	$0.123697\pi$
$227$	11.9154	+	20.6381i	0.790854	+	1.36980i	−0.134584	+	0.990902i	$0.542970\pi$
$228$		0			0
$229$	−3.26882	+	5.66176i	−0.216010	+	0.374140i	−0.953584	−	0.301126i	$-0.902638\pi$
$229$	−3.26882	+	5.66176i	−0.216010	+	0.374140i	0.737575	+	0.675266i	$0.235971\pi$
$230$		0			0
$231$	23.0851	−	22.3560i	1.51889	−	1.47092i
$232$		0			0
$233$	10.3810	−	17.9803i	0.680079	−	1.17793i	−0.294877	−	0.955535i	$-0.595279\pi$
$233$	10.3810	−	17.9803i	0.680079	−	1.17793i	0.974956	−	0.222397i	$-0.0713880\pi$
$234$		0			0
$235$	−21.4947	−	37.2299i	−1.40216	−	2.42861i
$236$		0			0
$237$	−22.0050			−1.42938
$238$		0			0
$239$	−12.1185			−0.783884			−0.391942	−	0.919990i	$-0.628197\pi$
$239$	−12.1185			−0.783884			−0.391942	+	0.919990i	$0.628197\pi$
$240$		0			0
$241$	9.29257	+	16.0952i	0.598587	+	1.03678i	0.993030	+	0.117862i	$0.0376042\pi$
$241$	9.29257	+	16.0952i	0.598587	+	1.03678i	−0.394443	+	0.918920i	$0.629063\pi$
$242$		0			0
$243$	−11.1786	+	19.3618i	−0.717105	+	1.24206i
$244$		0			0
$245$	−23.4155	+	12.5351i	−1.49596	+	0.800838i
$246$		0			0
$247$	−8.56564	+	14.8361i	−0.545018	+	0.944000i
$248$		0			0
$249$	−6.37772	−	11.0465i	−0.404172	−	0.700046i
$250$		0			0
$251$	21.3552			1.34793			0.673966	−	0.738763i	$-0.264590\pi$
$251$	21.3552			1.34793			0.673966	+	0.738763i	$0.264590\pi$
$252$		0			0
$253$	−20.4228			−1.28397
$254$		0			0
$255$	4.75381	+	8.23385i	0.297695	+	0.515624i
$256$		0			0
$257$	1.37406	−	2.37994i	0.0857113	−	0.148456i	−0.819983	−	0.572388i	$-0.806017\pi$
$257$	1.37406	−	2.37994i	0.0857113	−	0.148456i	0.905694	+	0.423932i	$0.139350\pi$
$258$		0			0
$259$	7.62231	−	7.38158i	0.473627	−	0.458669i
$260$		0			0
$261$	−5.93811	+	10.2851i	−0.367560	+	0.636632i
$262$		0			0
$263$	−2.11910	−	3.67040i	−0.130670	−	0.226326i	0.793265	−	0.608876i	$-0.208379\pi$
$263$	−2.11910	−	3.67040i	−0.130670	−	0.226326i	−0.923935	+	0.382550i	$0.875046\pi$
$264$		0			0
$265$	−18.1773			−1.11662
$266$		0			0
$267$	−1.06629			−0.0652561
$268$		0			0
$269$	1.39595	+	2.41785i	0.0851123	+	0.147419i	0.905439	−	0.424476i	$-0.139542\pi$
$269$	1.39595	+	2.41785i	0.0851123	+	0.147419i	−0.820327	+	0.571895i	$0.806208\pi$
$270$		0			0
$271$	14.1315	−	24.4765i	0.858428	−	1.48684i	−0.0150004	−	0.999887i	$-0.504775\pi$
$271$	14.1315	−	24.4765i	0.858428	−	1.48684i	0.873428	−	0.486953i	$-0.161892\pi$
$272$		0			0
$273$	3.95032	+	15.7492i	0.239084	+	0.953186i
$274$		0			0
$275$	22.7728	−	39.4436i	1.37325	−	2.37854i
$276$		0			0
$277$	1.50831	+	2.61247i	0.0906256	+	0.156968i	0.907775	−	0.419458i	$-0.137780\pi$
$277$	1.50831	+	2.61247i	0.0906256	+	0.156968i	−0.817149	+	0.576427i	$0.804447\pi$
$278$		0			0
$279$	10.4295			0.624396
$280$		0			0
$281$	−7.02716			−0.419205			−0.209602	−	0.977787i	$-0.567217\pi$
$281$	−7.02716			−0.419205			−0.209602	+	0.977787i	$0.567217\pi$
$282$		0			0
$283$	4.25950	+	7.37767i	0.253201	+	0.438557i	0.964405	−	0.264428i	$-0.0851833\pi$
$283$	4.25950	+	7.37767i	0.253201	+	0.438557i	−0.711204	+	0.702985i	$0.751850\pi$
$284$		0			0
$285$	−33.2522	+	57.5945i	−1.96969	+	3.41161i
$286$		0			0
$287$	−11.7976	−	3.36490i	−0.696389	−	0.198624i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	1.28058	+	2.21804i	0.0750692	+	0.130024i
$292$		0			0
$293$	6.99134			0.408438			0.204219	−	0.978925i	$-0.434534\pi$
$293$	6.99134			0.408438			0.204219	+	0.978925i	$0.434534\pi$
$294$		0			0
$295$	37.0271			2.15580
$296$		0			0
$297$	−1.69488	−	2.93563i	−0.0983472	−	0.170342i
$298$		0			0
$299$	5.15944	−	8.93641i	0.298378	−	0.516806i
$300$		0			0
$301$	29.8356	+	8.50970i	1.71970	+	0.490491i
$302$		0			0
$303$	−2.98911	+	5.17728i	−0.171720	+	0.297427i
$304$		0			0
$305$	18.1252	+	31.3938i	1.03785	+	1.79761i
$306$		0			0
$307$	29.8285			1.70240			0.851201	−	0.524840i	$-0.175875\pi$
$307$	29.8285			1.70240			0.851201	+	0.524840i	$0.175875\pi$
$308$		0			0
$309$	15.4582			0.879389
$310$		0			0
$311$	−4.38236	−	7.59047i	−0.248501	−	0.430416i	0.714609	−	0.699524i	$-0.246605\pi$
$311$	−4.38236	−	7.59047i	−0.248501	−	0.430416i	−0.963110	+	0.269108i	$0.913271\pi$
$312$		0			0
$313$	−3.91210	+	6.77596i	−0.221125	+	0.383000i	−0.955150	−	0.296123i	$-0.904306\pi$
$313$	−3.91210	+	6.77596i	−0.221125	+	0.383000i	0.734025	+	0.679123i	$0.237640\pi$
$314$		0			0
$315$	8.00847	+	31.9283i	0.451226	+	1.79896i
$316$		0			0
$317$	7.98415	−	13.8290i	0.448435	−	0.776711i	−0.549850	−	0.835264i	$-0.685315\pi$
$317$	7.98415	−	13.8290i	0.448435	−	0.776711i	0.998284	+	0.0585522i	$0.0186484\pi$
$318$		0			0
$319$	8.77787	+	15.2037i	0.491466	+	0.851244i
$320$		0			0
$321$	−16.9293			−0.944903
$322$		0			0
$323$	−6.99485			−0.389204
$324$		0			0
$325$	11.5063	+	19.9294i	0.638252	+	1.10549i
$326$		0			0
$327$	−14.0902	+	24.4049i	−0.779188	+	1.34959i
$328$		0			0
$329$	21.5342	−	20.8541i	1.18722	−	1.14972i
$330$		0			0
$331$	8.67544	−	15.0263i	0.476845	−	0.825920i	−0.522803	−	0.852454i	$-0.675114\pi$
$331$	8.67544	−	15.0263i	0.476845	−	0.825920i	0.999648	+	0.0265335i	$0.00844686\pi$
$332$		0			0
$333$	−6.57533	−	11.3888i	−0.360326	−	0.624103i
$334$		0			0
$335$	−49.7035			−2.71559
$336$		0			0
$337$	28.3325			1.54337			0.771685	−	0.636005i	$-0.219414\pi$
$337$	28.3325			1.54337			0.771685	+	0.636005i	$0.219414\pi$
$338$		0			0
$339$	−15.3306	−	26.5533i	−0.832642	−	1.44218i
$340$		0			0
$341$	7.70856	−	13.3516i	0.417442	−	0.723030i
$342$		0			0
$343$	−12.4506	−	13.7107i	−0.672269	−	0.740307i
$344$		0			0
$345$	20.0292	−	34.6916i	1.07834	−	1.86773i
$346$		0			0
$347$	−5.68798	−	9.85188i	−0.305347	−	0.528876i	0.671992	−	0.740559i	$-0.265439\pi$
$347$	−5.68798	−	9.85188i	−0.305347	−	0.528876i	−0.977339	+	0.211682i	$0.932106\pi$
$348$		0			0
$349$	−22.5889			−1.20915			−0.604577	−	0.796547i	$-0.706658\pi$
$349$	−22.5889			−1.20915			−0.604577	+	0.796547i	$0.706658\pi$
$350$		0			0
$351$	1.71273			0.0914187
$352$		0			0
$353$	−5.35720	−	9.27894i	−0.285135	−	0.493868i	0.687507	−	0.726178i	$-0.258705\pi$
$353$	−5.35720	−	9.27894i	−0.285135	−	0.493868i	−0.972642	+	0.232310i	$0.925372\pi$
$354$		0			0
$355$	0.726173	−	1.25777i	0.0385413	−	0.0667554i
$356$		0			0
$357$	−4.76254	+	4.61213i	−0.252060	+	0.244100i
$358$		0			0
$359$	17.1649	−	29.7304i	0.905928	−	1.56911i	0.0862609	−	0.996273i	$-0.472508\pi$
$359$	17.1649	−	29.7304i	0.905928	−	1.56911i	0.819667	−	0.572840i	$-0.194159\pi$
$360$		0			0
$361$	−14.9640	−	25.9184i	−0.787578	−	1.36412i
$362$		0			0
$363$	−31.3114			−1.64342
$364$		0			0
$365$	−2.24568			−0.117544
$366$		0			0
$367$	9.55179	+	16.5442i	0.498599	+	0.863599i	0.999999	−	0.00161682i	$-0.000514651\pi$
$367$	9.55179	+	16.5442i	0.498599	+	0.863599i	−0.501400	+	0.865216i	$0.667181\pi$
$368$		0			0
$369$	−7.60237	+	13.1677i	−0.395764	+	0.685483i
$370$		0			0
$371$	−3.08375	−	12.2944i	−0.160100	−	0.638291i
$372$		0			0
$373$	7.94904	−	13.7681i	0.411585	−	0.712887i	−0.583478	−	0.812129i	$-0.698309\pi$
$373$	7.94904	−	13.7681i	0.411585	−	0.712887i	0.995063	+	0.0992421i	$0.0316418\pi$
$374$		0			0
$375$	20.8988	+	36.1978i	1.07921	+	1.86924i
$376$		0			0
$377$	−8.87028			−0.456843
$378$		0			0
$379$	−15.4844			−0.795382			−0.397691	−	0.917519i	$-0.630188\pi$
$379$	−15.4844			−0.795382			−0.397691	+	0.917519i	$0.630188\pi$
$380$		0			0
$381$	1.00324	+	1.73766i	0.0513975	+	0.0890231i
$382$		0			0
$383$	5.33007	−	9.23195i	0.272354	−	0.471730i	−0.697110	−	0.716964i	$-0.745531\pi$
$383$	5.33007	−	9.23195i	0.272354	−	0.471730i	0.969464	+	0.245233i	$0.0788646\pi$
$384$		0			0
$385$	46.7932	+	13.3463i	2.38480	+	0.680193i
$386$		0			0
$387$	19.2261	−	33.3006i	0.977317	−	1.69276i
$388$		0			0
$389$	4.51583	+	7.82165i	0.228962	+	0.396573i	0.957501	−	0.288431i	$-0.0931336\pi$
$389$	4.51583	+	7.82165i	0.228962	+	0.396573i	−0.728539	+	0.685004i	$0.759800\pi$
$390$		0			0
$391$	4.21329			0.213075
$392$		0			0
$393$	−48.0011			−2.42133
$394$		0			0
$395$	−16.6597	−	28.8555i	−0.838243	−	1.45188i
$396$		0			0
$397$	3.78845	−	6.56178i	0.190137	−	0.329326i	−0.755159	−	0.655542i	$-0.772440\pi$
$397$	3.78845	−	6.56178i	0.190137	−	0.329326i	0.945295	+	0.326216i	$0.105774\pi$
$398$		0			0
$399$	−44.5956	−	12.7196i	−2.23257	−	0.636774i
$400$		0			0
$401$	−3.01951	+	5.22994i	−0.150787	+	0.261171i	−0.931517	−	0.363698i	$-0.881514\pi$
$401$	−3.01951	+	5.22994i	−0.150787	+	0.261171i	0.780730	+	0.624869i	$0.214847\pi$
$402$		0			0
$403$	3.89486	+	6.74609i	0.194017	+	0.336047i
$404$		0			0
$405$	−30.6759			−1.52430
$406$		0			0
$407$	−19.4396			−0.963587
$408$		0			0
$409$	5.68422	+	9.84536i	0.281067	+	0.486822i	0.971648	−	0.236433i	$-0.0759785\pi$
$409$	5.68422	+	9.84536i	0.281067	+	0.486822i	−0.690581	+	0.723255i	$0.742645\pi$
$410$		0			0
$411$	−5.67869	+	9.83578i	−0.280109	+	0.485163i
$412$		0			0
$413$	6.28158	+	25.0435i	0.309096	+	1.23231i
$414$		0			0
$415$	9.65699	−	16.7264i	0.474043	−	0.821067i
$416$		0			0
$417$	−17.4742	−	30.2662i	−0.855716	−	1.48214i
$418$		0			0
$419$	−7.81481			−0.381778			−0.190889	−	0.981612i	$-0.561137\pi$
$419$	−7.81481			−0.381778			−0.190889	+	0.981612i	$0.561137\pi$
$420$		0			0
$421$	−10.9355			−0.532964			−0.266482	−	0.963840i	$-0.585861\pi$
$421$	−10.9355			−0.532964			−0.266482	+	0.963840i	$0.585861\pi$
$422$		0			0
$423$	−18.5763	−	32.1751i	−0.903210	−	1.56441i
$424$		0			0
$425$	−4.69811	+	8.13736i	−0.227892	+	0.394720i
$426$		0			0
$427$	−18.1585	+	17.5850i	−0.878752	+	0.851000i
$428$		0			0
$429$	14.8738	−	25.7622i	0.718114	−	1.24381i
$430$		0			0
$431$	9.48300	+	16.4250i	0.456780	+	0.791166i	0.998789	−	0.0492067i	$-0.0156693\pi$
$431$	9.48300	+	16.4250i	0.456780	+	0.791166i	−0.542009	+	0.840373i	$0.682336\pi$
$432$		0			0
$433$	−2.06964			−0.0994607			−0.0497304	−	0.998763i	$-0.515836\pi$
$433$	−2.06964			−0.0994607			−0.0497304	+	0.998763i	$0.515836\pi$
$434$		0			0
$435$	−34.4349			−1.65103
$436$		0			0
$437$	14.7357	+	25.5229i	0.704903	+	1.22093i
$438$		0			0
$439$	16.9081	−	29.2858i	0.806981	−	1.39773i	−0.107964	−	0.994155i	$-0.534433\pi$
$439$	16.9081	−	29.2858i	0.806981	−	1.39773i	0.914945	−	0.403578i	$-0.132234\pi$
$440$		0			0
$441$	−20.2363	+	10.8332i	−0.963634	+	0.515865i
$442$		0			0
$443$	−4.48752	+	7.77261i	−0.213208	+	0.369288i	−0.952717	−	0.303859i	$-0.901725\pi$
$443$	−4.48752	+	7.77261i	−0.213208	+	0.369288i	0.739508	+	0.673147i	$0.235058\pi$
$444$		0			0
$445$	−0.807277	−	1.39824i	−0.0382686	−	0.0662832i
$446$		0			0
$447$	46.5184			2.20024
$448$		0			0
$449$	−17.8245			−0.841190			−0.420595	−	0.907249i	$-0.638179\pi$
$449$	−17.8245			−0.841190			−0.420595	+	0.907249i	$0.638179\pi$
$450$		0			0
$451$	11.2380	+	19.4648i	0.529178	+	0.916562i
$452$		0			0
$453$	−25.5355	+	44.2287i	−1.19976	+	2.07805i
$454$		0			0
$455$	−17.6614	+	17.1037i	−0.827981	+	0.801832i
$456$		0			0
$457$	−8.90163	+	15.4181i	−0.416401	+	0.721227i	−0.995574	−	0.0939771i	$-0.970042\pi$
$457$	−8.90163	+	15.4181i	−0.416401	+	0.721227i	0.579174	+	0.815204i	$0.303375\pi$
$458$		0			0
$459$	0.349661	+	0.605631i	0.0163208	+	0.0282684i
$460$		0			0
$461$	−1.49574			−0.0696634			−0.0348317	−	0.999393i	$-0.511090\pi$
$461$	−1.49574			−0.0696634			−0.0348317	+	0.999393i	$0.511090\pi$
$462$		0			0
$463$	−18.5747			−0.863238			−0.431619	−	0.902056i	$-0.642057\pi$
$463$	−18.5747			−0.863238			−0.431619	+	0.902056i	$0.642057\pi$
$464$		0			0
$465$	15.1200	+	26.1887i	0.701174	+	1.21447i
$466$		0			0
$467$	−3.76900	+	6.52810i	−0.174408	+	0.302084i	−0.939956	−	0.341295i	$-0.889135\pi$
$467$	−3.76900	+	6.52810i	−0.174408	+	0.302084i	0.765548	+	0.643379i	$0.222468\pi$
$468$		0			0
$469$	−8.43211	−	33.6173i	−0.389359	−	1.55230i
$470$		0			0
$471$	0.240277	−	0.416172i	0.0110714	−	0.0191762i
$472$		0			0
$473$	−28.4205	−	49.2258i	−1.30678	−	2.26340i
$474$		0			0
$475$	−65.7251			−3.01568
$476$		0			0
$477$	−15.7093			−0.719281
$478$		0			0
$479$	17.3354	+	30.0257i	0.792073	+	1.37191i	0.924681	+	0.380742i	$0.124332\pi$
$479$	17.3354	+	30.0257i	0.792073	+	1.37191i	−0.132608	+	0.991169i	$0.542335\pi$
$480$		0			0
$481$	4.91108	−	8.50623i	0.223926	−	0.387851i
$482$		0			0
$483$	26.8618	+	7.66152i	1.22225	+	0.348611i
$484$		0			0
$485$	−1.93903	+	3.35850i	−0.0880468	+	0.152501i
$486$		0			0
$487$	−6.84046	−	11.8480i	−0.309971	−	0.536886i	0.668385	−	0.743816i	$-0.266986\pi$
$487$	−6.84046	−	11.8480i	−0.309971	−	0.536886i	−0.978356	+	0.206930i	$0.933653\pi$
$488$		0			0
$489$	36.1933			1.63672
$490$		0			0
$491$	37.3533			1.68573			0.842865	−	0.538124i	$-0.180867\pi$
$491$	37.3533			1.68573			0.842865	+	0.538124i	$0.180867\pi$
$492$		0			0
$493$	−1.81091	−	3.13658i	−0.0815592	−	0.141265i
$494$		0			0
$495$	30.1536	−	52.2275i	1.35530	−	2.34745i
$496$		0			0
$497$	0.973894	+	0.277774i	0.0436851	+	0.0124599i
$498$		0			0
$499$	−4.34280	+	7.52195i	−0.194410	+	0.336729i	−0.946707	−	0.322096i	$-0.895613\pi$
$499$	−4.34280	+	7.52195i	−0.194410	+	0.336729i	0.752297	+	0.658825i	$0.228946\pi$
$500$		0			0
$501$	−0.753794	−	1.30561i	−0.0336770	−	0.0583304i
$502$		0			0
$503$	−15.1280			−0.674523			−0.337261	−	0.941411i	$-0.609501\pi$
$503$	−15.1280			−0.674523			−0.337261	+	0.941411i	$0.609501\pi$
$504$		0			0
$505$	−9.05206			−0.402811
$506$		0			0
$507$	−8.77257	−	15.1945i	−0.389603	−	0.674813i
$508$		0			0
$509$	−3.06228	+	5.30403i	−0.135733	+	0.235097i	−0.925877	−	0.377824i	$-0.876672\pi$
$509$	−3.06228	+	5.30403i	−0.135733	+	0.235097i	0.790144	+	0.612921i	$0.210006\pi$
$510$		0			0
$511$	−0.380976	−	1.51888i	−0.0168534	−	0.0671914i
$512$		0			0
$513$	−2.44583	+	4.23630i	−0.107986	+	0.187037i
$514$		0			0
$515$	11.7032	+	20.2706i	0.515706	+	0.893230i
$516$		0			0
$517$	−54.9199			−2.41537
$518$		0			0
$519$	14.7836			0.648930
$520$		0			0
$521$	−5.98786	−	10.3713i	−0.262333	−	0.454374i	0.704528	−	0.709676i	$-0.251159\pi$
$521$	−5.98786	−	10.3713i	−0.262333	−	0.454374i	−0.966861	+	0.255302i	$0.917825\pi$
$522$		0			0
$523$	−18.1217	+	31.3876i	−0.792405	+	1.37249i	0.132069	+	0.991241i	$0.457838\pi$
$523$	−18.1217	+	31.3876i	−0.792405	+	1.37249i	−0.924474	+	0.381245i	$0.875495\pi$
$524$		0			0
$525$	−44.7499	+	43.3366i	−1.95304	+	1.89136i
$526$		0			0
$527$	−1.59030	+	2.75449i	−0.0692748	+	0.119987i
$528$		0			0
$529$	2.62409	+	4.54505i	0.114091	+	0.197611i
$530$		0			0
$531$	31.9998			1.38867
$532$		0			0
$533$	−11.3563			−0.491897
$534$		0			0
$535$	−12.8170	−	22.1997i	−0.554127	−	0.959776i
$536$		0			0
$537$	−11.1951	+	19.3905i	−0.483104	+	0.836761i
$538$		0			0
$539$	−1.08851	+	33.9131i	−0.0468853	+	1.46074i
$540$		0			0
$541$	−6.09082	+	10.5496i	−0.261865	+	0.453563i	−0.966737	−	0.255771i	$-0.917671\pi$
$541$	−6.09082	+	10.5496i	−0.261865	+	0.453563i	0.704873	+	0.709334i	$0.251004\pi$
$542$		0			0
$543$	24.8008	+	42.9563i	1.06431	+	1.84343i
$544$		0			0
$545$	−42.6700			−1.82778
$546$		0			0
$547$	−32.7211			−1.39905			−0.699526	−	0.714607i	$-0.746605\pi$
$547$	−32.7211			−1.39905			−0.699526	+	0.714607i	$0.746605\pi$
$548$		0			0
$549$	15.6643	+	27.1314i	0.668537	+	1.15794i
$550$		0			0
$551$	12.6670	−	21.9399i	0.539634	−	0.934673i
$552$		0			0
$553$	16.6903	−	16.1632i	0.709745	−	0.687330i
$554$		0			0
$555$	19.0650	−	33.0216i	0.809266	−	1.40169i
$556$		0			0
$557$	−12.8868	−	22.3207i	−0.546033	−	0.945757i	−0.998541	−	0.0539964i	$-0.982804\pi$
$557$	−12.8868	−	22.3207i	−0.546033	−	0.945757i	0.452508	−	0.891760i	$-0.350529\pi$
$558$		0			0
$559$	28.7197			1.21471
$560$		0			0
$561$	12.1462			0.512813
$562$		0			0
$563$	−18.7259	−	32.4342i	−0.789202	−	1.36694i	−0.926456	−	0.376402i	$-0.877161\pi$
$563$	−18.7259	−	32.4342i	−0.789202	−	1.36694i	0.137254	−	0.990536i	$-0.456172\pi$
$564$		0			0
$565$	23.2132	−	40.2064i	0.976585	−	1.69149i
$566$		0			0
$567$	−5.20411	−	20.7479i	−0.218552	−	0.871328i
$568$		0			0
$569$	−21.3286	+	36.9423i	−0.894143	+	1.54870i	−0.0592815	+	0.998241i	$0.518881\pi$
$569$	−21.3286	+	36.9423i	−0.894143	+	1.54870i	−0.834862	+	0.550460i	$0.814452\pi$
$570$		0			0
$571$	−6.22898	−	10.7889i	−0.260675	−	0.451502i	0.705747	−	0.708464i	$-0.250612\pi$
$571$	−6.22898	−	10.7889i	−0.260675	−	0.451502i	−0.966421	+	0.256963i	$0.917278\pi$
$572$		0			0
$573$	−50.0657			−2.09152
$574$		0			0
$575$	39.5890			1.65098
$576$		0			0
$577$	19.8446	+	34.3718i	0.826141	+	1.43092i	0.901044	+	0.433727i	$0.142802\pi$
$577$	19.8446	+	34.3718i	0.826141	+	1.43092i	−0.0749035	+	0.997191i	$0.523865\pi$
$578$		0			0
$579$	−27.0570	+	46.8642i	−1.12445	+	1.94761i
$580$		0			0
$581$	12.9513	+	3.69397i	0.537311	+	0.153252i
$582$		0			0
$583$	−11.6110	+	20.1108i	−0.480877	+	0.832904i
$584$		0			0
$585$	15.2355	+	26.3887i	0.629911	+	1.09104i
$586$		0			0
$587$	9.17691			0.378772			0.189386	−	0.981903i	$-0.439350\pi$
$587$	9.17691			0.378772			0.189386	+	0.981903i	$0.439350\pi$
$588$		0			0
$589$	−22.2479			−0.916708
$590$		0			0
$591$	24.6018	+	42.6116i	1.01198	+	1.75281i
$592$		0			0
$593$	12.4274	−	21.5249i	0.510332	−	0.883921i	−0.489596	−	0.871949i	$-0.662856\pi$
$593$	12.4274	−	21.5249i	0.510332	−	0.883921i	0.999928	−	0.0119716i	$-0.00381078\pi$
$594$		0			0
$595$	−9.65362	−	2.75340i	−0.395760	−	0.112878i
$596$		0			0
$597$	25.5052	−	44.1763i	1.04386	−	1.80801i
$598$		0			0
$599$	2.22606	+	3.85564i	0.0909542	+	0.157537i	0.907913	−	0.419159i	$-0.137675\pi$
$599$	2.22606	+	3.85564i	0.0909542	+	0.157537i	−0.816959	+	0.576696i	$0.804342\pi$
$600$		0			0
$601$	−36.3507			−1.48277			−0.741387	−	0.671077i	$-0.765832\pi$
$601$	−36.3507			−1.48277			−0.741387	+	0.671077i	$0.765832\pi$
$602$		0			0
$603$	−42.9551			−1.74927
$604$		0			0
$605$	−23.7055	−	41.0591i	−0.963766	−	1.66929i
$606$		0			0
$607$	−7.73025	+	13.3892i	−0.313761	+	0.543451i	−0.979173	−	0.203026i	$-0.934923\pi$
$607$	−7.73025	+	13.3892i	−0.313761	+	0.543451i	0.665412	+	0.746476i	$0.268256\pi$
$608$		0			0
$609$	−5.84181	−	23.2903i	−0.236722	−	0.943769i
$610$		0			0
$611$	13.8745	−	24.0314i	0.561303	−	0.972206i
$612$		0			0
$613$	−4.47856	−	7.75709i	−0.180887	−	0.313306i	0.761296	−	0.648405i	$-0.224564\pi$
$613$	−4.47856	−	7.75709i	−0.180887	−	0.313306i	−0.942183	+	0.335099i	$0.891230\pi$
$614$		0			0
$615$	−44.0858			−1.77771
$616$		0			0
$617$	37.4791			1.50885			0.754427	−	0.656384i	$-0.227915\pi$
$617$	37.4791			1.50885			0.754427	+	0.656384i	$0.227915\pi$
$618$		0			0
$619$	13.2390	+	22.9306i	0.532120	+	0.921659i	0.999297	+	0.0374948i	$0.0119378\pi$
$619$	13.2390	+	22.9306i	0.532120	+	0.921659i	−0.467177	+	0.884164i	$0.654729\pi$
$620$		0			0
$621$	1.47322	−	2.55170i	0.0591185	−	0.102396i
$622$		0			0
$623$	0.808759	−	0.783217i	0.0324023	−	0.0313789i
$624$		0			0
$625$	−8.15389	+	14.1229i	−0.326155	+	0.564918i
$626$		0			0
$627$	42.4805	+	73.5783i	1.69651	+	2.93844i
$628$		0			0
$629$	4.01047			0.159908
$630$		0			0
$631$	12.7300			0.506774			0.253387	−	0.967365i	$-0.418455\pi$
$631$	12.7300			0.506774			0.253387	+	0.967365i	$0.418455\pi$
$632$		0			0
$633$	−10.7948	−	18.6971i	−0.429054	−	0.743144i
$634$		0			0
$635$	−1.51908	+	2.63113i	−0.0602829	+	0.104413i
$636$		0			0
$637$	−14.5644	−	9.04383i	−0.577063	−	0.358329i
$638$		0			0
$639$	0.627579	−	1.08700i	0.0248266	−	0.0430010i
$640$		0			0
$641$	4.92340	+	8.52758i	0.194463	+	0.336819i	0.946724	−	0.322045i	$-0.104370\pi$
$641$	4.92340	+	8.52758i	0.194463	+	0.336819i	−0.752262	+	0.658865i	$0.771037\pi$
$642$		0			0
$643$	19.3523			0.763182			0.381591	−	0.924331i	$-0.375376\pi$
$643$	19.3523			0.763182			0.381591	+	0.924331i	$0.375376\pi$
$644$		0			0
$645$	111.491			4.38997
$646$		0			0
$647$	−13.6119	−	23.5765i	−0.535140	−	0.926889i	−0.999157	−	0.0410629i	$-0.986926\pi$
$647$	−13.6119	−	23.5765i	−0.535140	−	0.926889i	0.464017	−	0.885826i	$-0.346408\pi$
$648$		0			0
$649$	23.6515	−	40.9656i	0.928402	−	1.60804i
$650$		0			0
$651$	−15.1478	+	14.6694i	−0.593688	+	0.574939i
$652$		0			0
$653$	−14.1783	+	24.5575i	−0.554838	+	0.961008i	0.443078	+	0.896483i	$0.353886\pi$
$653$	−14.1783	+	24.5575i	−0.554838	+	0.961008i	−0.997916	+	0.0645246i	$0.979447\pi$
$654$		0			0
$655$	−36.3410	−	62.9445i	−1.41996	−	2.45945i
$656$		0			0
$657$	−1.94078			−0.0757170
$658$		0			0
$659$	28.5156			1.11081			0.555405	−	0.831580i	$-0.312563\pi$
$659$	28.5156			1.11081			0.555405	+	0.831580i	$0.312563\pi$
$660$		0			0
$661$	3.97422	+	6.88355i	0.154579	+	0.267739i	0.932906	−	0.360121i	$-0.117264\pi$
$661$	3.97422	+	6.88355i	0.154579	+	0.267739i	−0.778326	+	0.627860i	$0.783931\pi$
$662$		0			0
$663$	−3.06852	+	5.31483i	−0.119171	+	0.206411i
$664$		0			0
$665$	−17.0835	−	68.1087i	−0.662469	−	2.64114i
$666$		0			0
$667$	−7.62988	+	13.2153i	−0.295430	+	0.511700i
$668$		0			0
$669$	−13.9083	−	24.0898i	−0.537725	−	0.931367i
$670$		0			0
$671$	46.3108			1.78781
$672$		0			0
$673$	43.0255			1.65851			0.829255	−	0.558870i	$-0.188765\pi$
$673$	43.0255			1.65851			0.829255	+	0.558870i	$0.188765\pi$
$674$		0			0
$675$	3.28549	+	5.69064i	0.126459	+	0.219033i
$676$		0			0
$677$	4.28728	−	7.42579i	0.164774	−	0.285396i	−0.771801	−	0.635864i	$-0.780644\pi$
$677$	4.28728	−	7.42579i	0.164774	−	0.285396i	0.936575	+	0.350468i	$0.113977\pi$
$678$		0			0
$679$	−2.60049	−	0.741712i	−0.0997978	−	0.0284643i
$680$		0			0
$681$	−29.8578	+	51.7152i	−1.14415	+	1.98173i
$682$		0			0
$683$	16.0291	+	27.7632i	0.613337	+	1.06233i	0.990674	+	0.136255i	$0.0435066\pi$
$683$	16.0291	+	27.7632i	0.613337	+	1.06233i	−0.377337	+	0.926076i	$0.623160\pi$
$684$		0			0
$685$	−17.1971			−0.657066
$686$		0			0
$687$	−16.3821			−0.625015
$688$		0			0
$689$	−5.86661	−	10.1613i	−0.223500	−	0.387113i
$690$		0			0
$691$	15.2241	−	26.3689i	0.579151	−	1.00312i	−0.416426	−	0.909170i	$-0.636718\pi$
$691$	15.2241	−	26.3689i	0.579151	−	1.00312i	0.995577	−	0.0939491i	$-0.0299491\pi$
$692$		0			0
$693$	40.4400	+	11.5343i	1.53619	+	0.438151i
$694$		0			0
$695$	26.4590	−	45.8284i	1.00365	−	1.73837i
$696$		0			0
$697$	−2.31845	−	4.01567i	−0.0878174	−	0.152104i
$698$		0			0
$699$	52.0254			1.96778
$700$		0			0
$701$	−5.57614			−0.210608			−0.105304	−	0.994440i	$-0.533582\pi$
$701$	−5.57614			−0.210608			−0.105304	+	0.994440i	$0.533582\pi$
$702$		0			0
$703$	14.0263	+	24.2943i	0.529013	+	0.916278i
$704$		0			0
$705$	53.8616	−	93.2910i	2.02855	−	3.51354i
$706$		0			0
$707$	−1.53567	−	6.12242i	−0.0577547	−	0.230257i
$708$		0			0
$709$	17.5955	−	30.4763i	0.660814	−	1.14456i	−0.319588	−	0.947556i	$-0.603545\pi$
$709$	17.5955	−	30.4763i	0.660814	−	1.14456i	0.980402	−	0.197007i	$-0.0631220\pi$
$710$		0			0
$711$	−14.3978	−	24.9377i	−0.539960	−	0.935238i
$712$		0			0
$713$	13.4008			0.501865
$714$		0			0
$715$	45.0431			1.68452
$716$		0			0
$717$	−15.1834	−	26.2984i	−0.567034	−	0.982132i
$718$		0			0
$719$	3.13525	−	5.43041i	0.116925	−	0.202520i	−0.801623	−	0.597830i	$-0.796030\pi$
$719$	3.13525	−	5.43041i	0.116925	−	0.202520i	0.918548	+	0.395310i	$0.129363\pi$
$720$		0			0
$721$	−11.7247	+	11.3544i	−0.436652	+	0.422861i
$722$		0			0
$723$	−23.2854	+	40.3315i	−0.865993	+	1.49994i
$724$		0			0
$725$	−17.0157	−	29.4720i	−0.631946	−	1.09456i
$726$		0			0
$727$	−11.3407			−0.420603			−0.210301	−	0.977637i	$-0.567444\pi$
$727$	−11.3407			−0.420603			−0.210301	+	0.977637i	$0.567444\pi$
$728$		0			0
$729$	−31.7681			−1.17659
$730$		0			0
$731$	5.86326	+	10.1555i	0.216860	+	0.375613i
$732$		0			0
$733$	17.0272	−	29.4920i	0.628915	−	1.08931i	−0.358855	−	0.933393i	$-0.616833\pi$
$733$	17.0272	−	29.4920i	0.628915	−	1.08931i	0.987770	−	0.155919i	$-0.0498338\pi$
$734$		0			0
$735$	−56.5397	−	35.1086i	−2.08550	−	1.29500i
$736$		0			0
$737$	−31.7487	+	54.9903i	−1.16948	+	2.02559i
$738$		0			0
$739$	7.17361	+	12.4251i	0.263886	+	0.457063i	0.967271	−	0.253745i	$-0.0816625\pi$
$739$	7.17361	+	12.4251i	0.263886	+	0.457063i	−0.703385	+	0.710809i	$0.748329\pi$
$740$		0			0
$741$	−42.9277			−1.57699
$742$		0			0
$743$	26.5838			0.975264			0.487632	−	0.873049i	$-0.337861\pi$
$743$	26.5838			0.975264			0.487632	+	0.873049i	$0.337861\pi$
$744$		0			0
$745$	35.2185	+	61.0002i	1.29031	+	2.23487i
$746$		0			0
$747$	8.34583	−	14.4554i	0.305358	−	0.528896i
$748$		0			0
$749$	12.8405	−	12.4350i	0.469182	−	0.454365i
$750$		0			0
$751$	−2.51641	+	4.35856i	−0.0918252	+	0.159046i	−0.908279	−	0.418365i	$-0.862603\pi$
$751$	−2.51641	+	4.35856i	−0.0918252	+	0.159046i	0.816454	+	0.577411i	$0.195937\pi$
$752$		0			0
$753$	26.7561	+	46.3429i	0.975046	+	1.68883i
$754$		0			0
$755$	−77.3303			−2.81434
$756$		0			0
$757$	−21.2568			−0.772592			−0.386296	−	0.922375i	$-0.626246\pi$
$757$	−21.2568			−0.772592			−0.386296	+	0.922375i	$0.626246\pi$
$758$		0			0
$759$	−25.5878	−	44.3193i	−0.928777	−	1.60869i
$760$		0			0
$761$	15.3007	−	26.5016i	0.554651	−	0.960684i	−0.443280	−	0.896383i	$-0.646185\pi$
$761$	15.3007	−	26.5016i	0.554651	−	0.960684i	0.997931	−	0.0643002i	$-0.0204815\pi$
$762$		0			0
$763$	−7.23888	−	28.8601i	−0.262065	−	1.04481i
$764$		0			0
$765$	−6.22080	+	10.7747i	−0.224913	+	0.389562i
$766$		0			0
$767$	11.9502	+	20.6984i	0.431498	+	0.747377i
$768$		0			0
$769$	2.38477			0.0859971			0.0429986	−	0.999075i	$-0.486309\pi$
$769$	2.38477			0.0859971			0.0429986	+	0.999075i	$0.486309\pi$
$770$		0			0
$771$	6.88625			0.248002
$772$		0			0
$773$	7.77011	+	13.4582i	0.279471	+	0.484059i	0.971253	−	0.238048i	$-0.0765074\pi$
$773$	7.77011	+	13.4582i	0.279471	+	0.484059i	−0.691782	+	0.722106i	$0.743174\pi$
$774$		0			0
$775$	−14.9428	+	25.8818i	−0.536763	+	0.929700i
$776$		0			0
$777$	25.5687	+	7.29271i	0.917274	+	0.261625i
$778$		0			0
$779$	16.2172	−	28.0890i	0.581041	−	1.00639i
$780$		0			0
$781$	−0.927703	−	1.60683i	−0.0331958	−	0.0574968i
$782$		0			0
$783$	−2.53282			−0.0905155
$784$		0			0
$785$	0.727643			0.0259707
$786$		0			0
$787$	−12.5593	−	21.7533i	−0.447690	−	0.775422i	0.550545	−	0.834805i	$-0.314420\pi$
$787$	−12.5593	−	21.7533i	−0.447690	−	0.775422i	−0.998235	+	0.0593835i	$0.981087\pi$
$788$		0			0
$789$	5.31007	−	9.19731i	0.189044	−	0.327433i
$790$		0			0
$791$	31.1319	+	8.87944i	1.10692	+	0.315716i
$792$		0			0
$793$	−11.6996	+	20.2643i	−0.415465	+	0.719606i
$794$		0			0
$795$	−22.7745	−	39.4465i	−0.807727	−	1.39902i
$796$		0			0
$797$	21.0066			0.744093			0.372046	−	0.928214i	$-0.378656\pi$
$797$	21.0066			0.744093			0.372046	+	0.928214i	$0.378656\pi$
$798$		0			0
$799$	11.3302			0.400833
$800$		0			0
$801$	−0.697671	−	1.20840i	−0.0246510	−	0.0426968i
$802$		0			0
$803$	−1.43445	+	2.48455i	−0.0506208	+	0.0876778i
$804$		0			0
$805$	10.2901	+	41.0247i	0.362678	+	1.44593i
$806$		0			0
$807$	−3.49797	+	6.05867i	−0.123134	+	0.213275i
$808$		0			0
$809$	3.70147	+	6.41113i	0.130137	+	0.225403i	0.923729	−	0.383046i	$-0.125125\pi$
$809$	3.70147	+	6.41113i	0.130137	+	0.225403i	−0.793592	+	0.608450i	$0.791792\pi$
$810$		0			0
$811$	36.8579			1.29426			0.647128	−	0.762381i	$-0.275970\pi$
$811$	36.8579			1.29426			0.647128	+	0.762381i	$0.275970\pi$
$812$		0			0
$813$	70.8217			2.48383
$814$		0			0
$815$	27.4015	+	47.4607i	0.959831	+	1.66248i
$816$		0			0
$817$	−41.0126	+	71.0360i	−1.43485	+	2.48523i
$818$		0			0
$819$	−15.2635	+	14.7814i	−0.533350	+	0.516505i
$820$		0			0
$821$	16.7761	−	29.0570i	0.585489	−	1.01410i	−0.409326	−	0.912388i	$-0.634236\pi$
$821$	16.7761	−	29.0570i	0.585489	−	1.01410i	0.994814	−	0.101708i	$-0.0324307\pi$
$822$		0			0
$823$	19.3302	+	33.4809i	0.673809	+	1.16707i	0.976815	+	0.214083i	$0.0686764\pi$
$823$	19.3302	+	33.4809i	0.673809	+	1.16707i	−0.303006	+	0.952989i	$0.597990\pi$
$824$		0			0
$825$	114.128			3.97344
$826$		0			0
$827$	6.04811			0.210314			0.105157	−	0.994456i	$-0.466466\pi$
$827$	6.04811			0.210314			0.105157	+	0.994456i	$0.466466\pi$
$828$		0			0
$829$	−23.9268	−	41.4425i	−0.831014	−	1.43936i	−0.897235	−	0.441553i	$-0.854428\pi$
$829$	−23.9268	−	41.4425i	−0.831014	−	1.43936i	0.0662215	−	0.997805i	$-0.478906\pi$
$830$		0			0
$831$	−3.77954	+	6.54636i	−0.131111	+	0.227091i
$832$		0			0
$833$	0.224563	−	6.99640i	0.00778064	−	0.242411i
$834$		0			0
$835$	1.14138	−	1.97692i	0.0394990	−	0.0684142i
$836$		0			0
$837$	1.11214	+	1.92628i	0.0384410	+	0.0665818i
$838$		0			0
$839$	−18.7792			−0.648329			−0.324165	−	0.946001i	$-0.605083\pi$
$839$	−18.7792			−0.648329			−0.324165	+	0.946001i	$0.605083\pi$
$840$		0			0
$841$	−15.8825			−0.547671
$842$		0			0
$843$	−8.80436	−	15.2496i	−0.303238	−	0.525224i
$844$		0			0
$845$	13.2832	−	23.0072i	0.456956	−	0.791471i
$846$		0			0
$847$	23.7490	−	22.9990i	0.816026	−	0.790254i
$848$		0			0
$849$	−10.6735	+	18.4870i	−0.366313	+	0.634473i
$850$		0			0
$851$	−8.44865	−	14.6335i	−0.289616	−	0.501629i
$852$		0			0
$853$	5.42303			0.185681			0.0928404	−	0.995681i	$-0.470405\pi$
$853$	5.42303			0.185681			0.0928404	+	0.995681i	$0.470405\pi$
$854$		0			0
$855$	−87.0272			−2.97627
$856$		0			0
$857$	−9.80300	−	16.9793i	−0.334864	−	0.580001i	0.648595	−	0.761134i	$-0.275357\pi$
$857$	−9.80300	−	16.9793i	−0.334864	−	0.580001i	−0.983459	+	0.181132i	$0.942024\pi$
$858$		0			0
$859$	−10.3706	+	17.9624i	−0.353839	+	0.612868i	−0.986919	−	0.161219i	$-0.948457\pi$
$859$	−10.3706	+	17.9624i	−0.353839	+	0.612868i	0.633079	+	0.774087i	$0.281791\pi$
$860$		0			0
$861$	−7.47908	−	29.8178i	−0.254887	−	1.01619i
$862$		0			0
$863$	12.8605	−	22.2750i	0.437776	−	0.758249i	−0.559742	−	0.828667i	$-0.689100\pi$
$863$	12.8605	−	22.2750i	0.437776	−	0.758249i	0.997518	+	0.0704174i	$0.0224331\pi$
$864$		0			0
$865$	11.1925	+	19.3860i	0.380557	+	0.659144i
$866$		0			0
$867$	−2.50581			−0.0851017
$868$		0			0
$869$	−42.5664			−1.44397
$870$		0			0
$871$	−16.0415	−	27.7846i	−0.543544	−	0.941446i
$872$		0			0
$873$	−1.67576	+	2.90250i	−0.0567159	+	0.0982349i
$874$		0			0
$875$	−42.4394	−	12.1045i	−1.43471	−	0.409208i
$876$		0			0
$877$	28.6500	−	49.6233i	0.967443	−	1.67566i	0.264539	−	0.964375i	$-0.414780\pi$
$877$	28.6500	−	49.6233i	0.967443	−	1.67566i	0.702904	−	0.711285i	$-0.251886\pi$
$878$		0			0
$879$	8.75948	+	15.1719i	0.295450	+	0.511734i
$880$		0			0
$881$	36.9570			1.24511			0.622557	−	0.782575i	$-0.286094\pi$
$881$	36.9570			1.24511			0.622557	+	0.782575i	$0.286094\pi$
$882$		0			0
$883$	−53.0813			−1.78633			−0.893165	−	0.449730i	$-0.851520\pi$
$883$	−53.0813			−1.78633			−0.893165	+	0.449730i	$0.851520\pi$
$884$		0			0
$885$	46.3914	+	80.3523i	1.55943	+	2.70101i
$886$		0			0
$887$	−14.7980	+	25.6310i	−0.496870	+	0.860604i	−0.999993	−	0.00361058i	$-0.998851\pi$
$887$	−14.7980	+	25.6310i	−0.496870	+	0.860604i	0.503124	+	0.864214i	$0.332184\pi$
$888$		0			0
$889$	−2.03729	−	0.581075i	−0.0683285	−	0.0194886i
$890$		0			0
$891$	−19.5946	+	33.9388i	−0.656443	+	1.13699i
$892$		0			0
$893$	39.6265	+	68.6351i	1.32605	+	2.29679i
$894$		0			0
$895$	−33.9027			−1.13324
$896$		0			0
$897$	25.8571			0.863345
$898$		0			0
$899$	−5.75979	−	9.97625i	−0.192100	−	0.332726i
$900$		0			0
$901$	2.39539	−	4.14893i	0.0798019	−	0.138221i
$902$		0			0
$903$	18.9143	+	75.4079i	0.629429	+	2.50942i
$904$		0			0
$905$	−37.5528	+	65.0434i	−1.24830	+	2.16212i
$906$		0			0
$907$	−23.9859	−	41.5448i	−0.796439	−	1.37947i	−0.921921	−	0.387377i	$-0.873381\pi$
$907$	−23.9859	−	41.5448i	−0.796439	−	1.37947i	0.125482	−	0.992096i	$-0.459952\pi$
$908$		0			0
$909$	−7.82304			−0.259474
$910$		0			0
$911$	−18.1999			−0.602990			−0.301495	−	0.953468i	$-0.597486\pi$
$911$	−18.1999			−0.602990			−0.301495	+	0.953468i	$0.597486\pi$
$912$		0			0
$913$	−12.3370	−	21.3683i	−0.408296	−	0.707189i
$914$		0			0
$915$	−45.4184	+	78.6670i	−1.50149	+	2.60065i
$916$		0			0
$917$	36.4078	−	35.2579i	1.20229	−	1.16432i
$918$		0			0
$919$	−15.1309	+	26.2074i	−0.499121	+	0.864503i	−0.999999	−	0.00101469i	$-0.999677\pi$
$919$	−15.1309	+	26.2074i	−0.499121	+	0.864503i	0.500878	+	0.865518i	$0.333010\pi$
$920$		0			0
$921$	37.3723	+	64.7306i	1.23146	+	2.13295i
$922$		0			0
$923$	0.937469			0.0308572
$924$		0			0
$925$	37.6833			1.23902
$926$		0			0
$927$	10.1143	+	17.5184i	0.332196	+	0.575380i
$928$		0			0
$929$	−2.10196	+	3.64071i	−0.0689631	+	0.119448i	−0.898445	−	0.439086i	$-0.855302\pi$
$929$	−2.10196	+	3.64071i	−0.0689631	+	0.119448i	0.829482	+	0.558533i	$0.188636\pi$
$930$		0			0
$931$	43.1676	−	23.1090i	1.41476	−	0.757368i
$932$		0			0
$933$	10.9814	−	19.0203i	0.359513	−	0.622695i
$934$		0			0
$935$	9.19574	+	15.9275i	0.300733	+	0.520885i
$936$		0			0
$937$	−11.6210			−0.379643			−0.189822	−	0.981819i	$-0.560791\pi$
$937$	−11.6210			−0.379643			−0.189822	+	0.981819i	$0.560791\pi$
$938$		0			0
$939$	−19.6060			−0.639816
$940$		0			0
$941$	24.0611	+	41.6750i	0.784368	+	1.35857i	0.929376	+	0.369135i	$0.120346\pi$
$941$	24.0611	+	41.6750i	0.784368	+	1.35857i	−0.145007	+	0.989431i	$0.546321\pi$
$942$		0			0
$943$	−9.76829	+	16.9192i	−0.318099	+	0.550964i
$944$		0			0
$945$	−5.04304	+	4.88377i	−0.164050	+	0.158869i
$946$		0			0
$947$	−3.74681	+	6.48967i	−0.121755	+	0.210886i	−0.920460	−	0.390837i	$-0.872186\pi$
$947$	−3.74681	+	6.48967i	−0.121755	+	0.210886i	0.798705	+	0.601723i	$0.205519\pi$
$948$		0			0
$949$	−0.724778	−	1.25535i	−0.0235273	−	0.0407505i
$950$		0			0
$951$	40.0135			1.29753
$952$		0			0
$953$	38.4095			1.24421			0.622103	−	0.782935i	$-0.286278\pi$
$953$	38.4095			1.24421			0.622103	+	0.782935i	$0.286278\pi$
$954$		0			0
$955$	−37.9041	−	65.6518i	−1.22655	−	2.12444i
$956$		0			0
$957$	−21.9957	+	38.0976i	−0.711019	+	1.23152i
$958$		0			0
$959$	−2.91745	−	11.6313i	−0.0942094	−	0.375596i
$960$		0			0
$961$	10.4419	−	18.0858i	0.336834	−	0.583414i
$962$		0			0
$963$	−11.0768	−	19.1856i	−0.356945	−	0.618246i
$964$		0			0
$965$	−81.9382			−2.63768
$966$		0			0
$967$	−3.36687			−0.108271			−0.0541357	−	0.998534i	$-0.517240\pi$
$967$	−3.36687			−0.108271			−0.0541357	+	0.998534i	$0.517240\pi$
$968$		0			0
$969$	−8.76388	−	15.1795i	−0.281536	−	0.487636i
$970$		0			0
$971$	8.47530	−	14.6796i	0.271985	−	0.471092i	−0.697385	−	0.716697i	$-0.745653\pi$
$971$	8.47530	−	14.6796i	0.271985	−	0.471092i	0.969370	+	0.245605i	$0.0789865\pi$
$972$		0			0
$973$	35.4850	+	10.1210i	1.13760	+	0.324465i
$974$		0			0
$975$	−28.8325	+	49.9393i	−0.923378	+	1.59934i
$976$		0			0
$977$	2.21229	+	3.83180i	0.0707775	+	0.122590i	0.899242	−	0.437451i	$-0.144119\pi$
$977$	2.21229	+	3.83180i	0.0707775	+	0.122590i	−0.828465	+	0.560041i	$0.810785\pi$
$978$		0			0
$979$	−2.06263			−0.0659219
$980$		0			0
$981$	−36.8766			−1.17738
$982$		0			0
$983$	22.3910	+	38.7824i	0.714162	+	1.23697i	0.963282	+	0.268493i	$0.0865255\pi$
$983$	22.3910	+	38.7824i	0.714162	+	1.23697i	−0.249119	+	0.968473i	$0.580141\pi$
$984$		0			0
$985$	−37.2515	+	64.5215i	−1.18693	+	2.05583i
$986$		0			0
$987$	72.2355	+	20.6030i	2.29928	+	0.655801i
$988$		0			0
$989$	24.7036	−	42.7879i	0.785529	−	1.36058i
$990$		0			0
$991$	−14.6544	−	25.3822i	−0.465513	−	0.806292i	0.533711	−	0.845667i	$-0.320797\pi$
$991$	−14.6544	−	25.3822i	−0.465513	−	0.806292i	−0.999225	+	0.0393743i	$0.987464\pi$
$992$		0			0
$993$	43.4780			1.37973
$994$		0			0
$995$	77.2386			2.44863
$996$		0			0
$997$	11.0921	+	19.2121i	0.351290	+	0.608452i	0.986476	−	0.163907i	$-0.0524097\pi$
$997$	11.0921	+	19.2121i	0.351290	+	0.608452i	−0.635186	+	0.772360i	$0.719076\pi$
$998$		0			0
$999$	1.40231	−	2.42887i	0.0443670	−	0.0768460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.q.e.681.6	yes	14
7.2	even	3		6664.2.a.v.1.2		7
7.4	even	3	inner	952.2.q.e.137.6	✓	14
7.5	odd	6		6664.2.a.y.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.q.e.137.6	✓	14	7.4	even	3	inner
952.2.q.e.681.6	yes	14	1.1	even	1	trivial
6664.2.a.v.1.2		7	7.2	even	3
6664.2.a.y.1.6		7	7.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25290 + 2.17009i) q^{3} +(-1.89712 + 3.28590i) q^{5} +(-2.54429 - 0.725680i) q^{7} +(-1.63954 + 2.83977i) q^{9} +(2.42361 + 4.19782i) q^{11} -2.44913 q^{13} -9.50763 q^{15} +(-0.500000 - 0.866025i) q^{17} +(3.49743 - 6.05772i) q^{19} +(-1.61295 - 6.43055i) q^{21} +(-2.10665 + 3.64882i) q^{23} +(-4.69811 - 8.13736i) q^{25} -0.699322 q^{27} +3.62181 q^{29} +(-1.59030 - 2.75449i) q^{31} +(-6.07310 + 10.5189i) q^{33} +(7.21132 - 6.98358i) q^{35} +(-2.00524 + 3.47317i) q^{37} +(-3.06852 - 5.31483i) q^{39} +4.63689 q^{41} -11.7265 q^{43} +(-6.22080 - 10.7747i) q^{45} +(-5.66509 + 9.81223i) q^{47} +(5.94678 + 3.69268i) q^{49} +(1.25290 - 2.17009i) q^{51} +(2.39539 + 4.14893i) q^{53} -18.3915 q^{55} +17.5278 q^{57} +(-4.87939 - 8.45135i) q^{59} +(4.77705 - 8.27409i) q^{61} +(6.23222 - 6.03540i) q^{63} +(4.64628 - 8.04759i) q^{65} +(6.54987 + 11.3447i) q^{67} -10.5577 q^{69} -0.382777 q^{71} +(0.295933 + 0.512572i) q^{73} +(11.7726 - 20.3907i) q^{75} +(-3.12008 - 12.4392i) q^{77} +(-4.39081 + 7.60510i) q^{79} +(4.04244 + 7.00171i) q^{81} -5.09035 q^{83} +3.79423 q^{85} +(4.53779 + 7.85968i) q^{87} +(-0.212764 + 0.368518i) q^{89} +(6.23127 + 1.77728i) q^{91} +(3.98500 - 6.90222i) q^{93} +(13.2701 + 22.9844i) q^{95} +1.02209 q^{97} -15.8944 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 4 q^{13} - 12 q^{15} - 7 q^{17} + 3 q^{19} + 18 q^{21} + 18 q^{23} - 15 q^{25} - 36 q^{27} + 10 q^{29} + 10 q^{31} - 21 q^{33} + 19 q^{35} - 11 q^{37}+ \cdots - 40 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 4 * q^9 + 12 * q^11 + 4 * q^13 - 12 * q^15 - 7 * q^17 + 3 * q^19 + 18 * q^21 + 18 * q^23 - 15 * q^25 - 36 * q^27 + 10 * q^29 + 10 * q^31 - 21 * q^33 + 19 * q^35 - 11 * q^37 + 12 * q^39 - 30 * q^43 - 13 * q^45 - 15 * q^47 + 20 * q^49 + 3 * q^51 - 8 * q^53 - 18 * q^55 - 6 * q^57 - 9 * q^59 + 4 * q^61 + 41 * q^63 + 38 * q^65 + 30 * q^67 - 56 * q^69 - 54 * q^71 + 5 * q^73 + 2 * q^75 + 27 * q^77 - 3 * q^79 + 17 * q^81 - 24 * q^83 + 4 * q^85 - 19 * q^87 - 32 * q^89 - 11 * q^91 + 9 * q^93 + 42 * q^95 - 78 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more