LMFDB - Embedded newform 1008.2.q.i.529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.4
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	1008.529
Dual form			1008.2.q.i.625.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61557 - 0.624446i) q^{3} +(1.46043 - 2.52954i) q^{5} +(0.138560 + 2.64212i) q^{7} +(2.22013 - 2.01767i) q^{9} +O(q^{10})$	\(q+(1.61557 - 0.624446i) q^{3} +(1.46043 - 2.52954i) q^{5} +(0.138560 + 2.64212i) q^{7} +(2.22013 - 2.01767i) q^{9} +(-0.676857 - 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(0.779867 - 4.99862i) q^{15} +(1.65514 - 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +(1.87372 + 4.18201i) q^{21} +(1.31415 - 2.27617i) q^{23} +(-1.76573 - 3.05833i) q^{25} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} -3.27458 q^{31} +(-1.82558 - 1.47135i) q^{33} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(-1.97701 - 1.59340i) q^{39} +(-0.904289 - 1.56627i) q^{41} +(2.17129 - 3.76078i) q^{43} +(-1.86144 - 8.56260i) q^{45} -3.97914 q^{47} +(-6.96160 + 0.732185i) q^{49} +(0.883838 - 5.66503i) q^{51} +(-3.22743 + 5.59008i) q^{53} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +12.2140 q^{59} +0.559734 q^{61} +(5.63856 + 5.58629i) q^{63} -4.28200 q^{65} -12.8118 q^{67} +(0.701751 - 4.49793i) q^{69} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-4.76242 - 3.83835i) q^{75} +(3.00371 - 1.95078i) q^{77} -0.767677 q^{79} +(0.857983 - 8.95901i) q^{81} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(0.278597 - 1.78569i) q^{87} +(3.20356 + 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} +(-5.29031 + 2.04480i) q^{93} +6.44514 q^{95} +(-4.14143 + 7.17316i) q^{97} +(-3.86814 - 1.23710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	$ 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.61557	−	0.624446i	0.932750	−	0.360524i
$3$	1.61557	−	0.624446i	0.932750	−	0.360524i
$4$		0			0
$5$	1.46043	−	2.52954i	0.653125	−	1.13125i	−0.329235	−	0.944248i	$-0.606791\pi$
$5$	1.46043	−	2.52954i	0.653125	−	1.13125i	0.982360	−	0.186998i	$-0.0598759\pi$
$6$		0			0
$7$	0.138560	+	2.64212i	0.0523708	+	0.998628i
$7$	0.138560	+	2.64212i	0.0523708	+	0.998628i
$8$		0			0
$9$	2.22013	−	2.01767i	0.740044	−	0.672558i
$10$		0			0
$11$	−0.676857	−	1.17235i	−0.204080	−	0.353477i	0.745759	−	0.666216i	$-0.232087\pi$
$11$	−0.676857	−	1.17235i	−0.204080	−	0.353477i	−0.949839	+	0.312738i	$0.898754\pi$
$12$		0			0
$13$	−0.733001	−	1.26960i	−0.203298	−	0.352123i	0.746291	−	0.665620i	$-0.231833\pi$
$13$	−0.733001	−	1.26960i	−0.203298	−	0.352123i	−0.949589	+	0.313497i	$0.898499\pi$
$14$		0			0
$15$	0.779867	−	4.99862i	0.201361	−	1.29064i
$16$		0			0
$17$	1.65514	−	2.86678i	0.401430	−	0.695297i	−0.592469	−	0.805593i	$-0.701847\pi$
$17$	1.65514	−	2.86678i	0.401430	−	0.695297i	0.993899	+	0.110297i	$0.0351801\pi$
$18$		0			0
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	0.964381	−	0.264516i	$-0.0852123\pi$
$19$	1.10329	+	1.91096i	0.253113	+	0.438404i	−0.711268	+	0.702921i	$0.751879\pi$
$20$		0			0
$21$	1.87372	+	4.18201i	0.408878	+	0.912589i
$22$		0			0
$23$	1.31415	−	2.27617i	0.274019	−	0.474614i	−0.695868	−	0.718169i	$-0.744980\pi$
$23$	1.31415	−	2.27617i	0.274019	−	0.474614i	0.969887	+	0.243555i	$0.0783136\pi$
$24$		0			0
$25$	−1.76573	−	3.05833i	−0.353146	−	0.611666i
$26$		0			0
$27$	2.32685	−	4.64605i	0.447803	−	0.894132i
$28$		0			0
$29$	0.521720	−	0.903646i	0.0968810	−	0.167803i	−0.813511	−	0.581549i	$-0.802447\pi$
$29$	0.521720	−	0.903646i	0.0968810	−	0.167803i	0.910392	+	0.413747i	$0.135780\pi$
$30$		0			0
$31$	−3.27458			−0.588132			−0.294066	−	0.955785i	$-0.595009\pi$
$31$	−3.27458			−0.588132			−0.294066	+	0.955785i	$0.595009\pi$
$32$		0			0
$33$	−1.82558	−	1.47135i	−0.317793	−	0.256130i
$34$		0			0
$35$	6.88572	+	3.50815i	1.16390	+	0.592985i
$36$		0			0
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$		0			0
$39$	−1.97701	−	1.59340i	−0.316575	−	0.255148i
$40$		0			0
$41$	−0.904289	−	1.56627i	−0.141226	−	0.244611i	0.786732	−	0.617294i	$-0.211771\pi$
$41$	−0.904289	−	1.56627i	−0.141226	−	0.244611i	−0.927959	+	0.372683i	$0.878438\pi$
$42$		0			0
$43$	2.17129	−	3.76078i	0.331118	−	0.573514i	−0.651613	−	0.758551i	$-0.725907\pi$
$43$	2.17129	−	3.76078i	0.331118	−	0.573514i	0.982731	+	0.185038i	$0.0592408\pi$
$44$		0			0
$45$	−1.86144	−	8.56260i	−0.277487	−	1.27644i
$46$		0			0
$47$	−3.97914			−0.580417			−0.290209	−	0.956963i	$-0.593725\pi$
$47$	−3.97914			−0.580417			−0.290209	+	0.956963i	$0.593725\pi$
$48$		0			0
$49$	−6.96160	+	0.732185i	−0.994515	+	0.104598i
$50$		0			0
$51$	0.883838	−	5.66503i	0.123762	−	0.793263i
$52$		0			0
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	−0.997934	−	0.0642533i	$-0.979533\pi$
$53$	−3.22743	+	5.59008i	−0.443322	+	0.767856i	0.554612	+	0.832109i	$0.312867\pi$
$54$		0			0
$55$	−3.95402			−0.533160
$56$		0			0
$57$	2.97574	+	2.39834i	0.394146	+	0.317668i
$58$		0			0
$59$	12.2140			1.59013			0.795064	−	0.606526i	$-0.207437\pi$
$59$	12.2140			1.59013			0.795064	+	0.606526i	$0.207437\pi$
$60$		0			0
$61$	0.559734			0.0716666			0.0358333	−	0.999358i	$-0.488591\pi$
$61$	0.559734			0.0716666			0.0358333	+	0.999358i	$0.488591\pi$
$62$		0			0
$63$	5.63856	+	5.58629i	0.710392	+	0.703806i
$64$		0			0
$65$	−4.28200			−0.531117
$66$		0			0
$67$	−12.8118			−1.56521			−0.782603	−	0.622521i	$-0.786109\pi$
$67$	−12.8118			−1.56521			−0.782603	+	0.622521i	$0.786109\pi$
$68$		0			0
$69$	0.701751	−	4.49793i	0.0844809	−	0.541487i
$70$		0			0
$71$	−12.9177			−1.53305			−0.766525	−	0.642214i	$-0.778016\pi$
$71$	−12.9177			−1.53305			−0.766525	+	0.642214i	$0.778016\pi$
$72$		0			0
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	−0.379069	−	0.925368i	$-0.623756\pi$
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	0.990927	−	0.134401i	$-0.0429109\pi$
$74$		0			0
$75$	−4.76242	−	3.83835i	−0.549917	−	0.443214i
$76$		0			0
$77$	3.00371	−	1.95078i	0.342304	−	0.222312i
$78$		0			0
$79$	−0.767677			−0.0863704			−0.0431852	−	0.999067i	$-0.513751\pi$
$79$	−0.767677			−0.0863704			−0.0431852	+	0.999067i	$0.513751\pi$
$80$		0			0
$81$	0.857983	−	8.95901i	0.0953314	−	0.995446i
$82$		0			0
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	−0.806974	−	0.590587i	$-0.798896\pi$
$83$	0.983707	−	1.70383i	0.107976	−	0.187020i	0.914950	+	0.403567i	$0.132230\pi$
$84$		0			0
$85$	−4.83443	−	8.37348i	−0.524368	−	0.908232i
$86$		0			0
$87$	0.278597	−	1.78569i	0.0298687	−	0.191446i
$88$		0			0
$89$	3.20356	+	5.54872i	0.339576	+	0.588163i	0.984353	−	0.176208i	$-0.0563830\pi$
$89$	3.20356	+	5.54872i	0.339576	+	0.588163i	−0.644777	+	0.764371i	$0.723050\pi$
$90$		0			0
$91$	3.25286	−	2.11259i	0.340992	−	0.221460i
$92$		0			0
$93$	−5.29031	+	2.04480i	−0.548580	+	0.212036i
$94$		0			0
$95$	6.44514			0.661258
$96$		0			0
$97$	−4.14143	+	7.17316i	−0.420498	+	0.728324i	−0.995988	−	0.0894847i	$-0.971478\pi$
$97$	−4.14143	+	7.17316i	−0.420498	+	0.728324i	0.575490	+	0.817809i	$0.304811\pi$
$98$		0			0
$99$	−3.86814	−	1.23710i	−0.388762	−	0.124333i
$100$		0			0
$101$	8.11331	+	14.0527i	0.807305	+	1.39829i	0.914724	+	0.404079i	$0.132408\pi$
$101$	8.11331	+	14.0527i	0.807305	+	1.39829i	−0.107419	+	0.994214i	$0.534259\pi$
$102$		0			0
$103$	−1.11342	+	1.92849i	−0.109708	+	0.190020i	−0.915652	−	0.401972i	$-0.868325\pi$
$103$	−1.11342	+	1.92849i	−0.109708	+	0.190020i	0.805944	+	0.591992i	$0.201658\pi$
$104$		0			0
$105$	13.3150	+	1.36789i	1.29941	+	0.133493i
$106$		0			0
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	0.884501	+	0.466537i	$0.154499\pi$
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	−0.0382175	+	0.999269i	$0.512168\pi$
$108$		0			0
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$		0			0
$111$	14.6663	+	11.8205i	1.39207	+	1.12196i
$112$		0			0
$113$	−0.844555	−	1.46281i	−0.0794491	−	0.137610i	0.823563	−	0.567224i	$-0.191983\pi$
$113$	−0.844555	−	1.46281i	−0.0794491	−	0.137610i	−0.903012	+	0.429615i	$0.858649\pi$
$114$		0			0
$115$	−3.83845	−	6.64839i	−0.357937	−	0.619966i
$116$		0			0
$117$	−4.18899	−	1.33971i	−0.387272	−	0.123857i
$118$		0			0
$119$	7.80372	+	3.97585i	0.715366	+	0.364466i
$120$		0			0
$121$	4.58373	−	7.93925i	0.416703	−	0.721750i
$122$		0			0
$123$	−2.43900	−	1.96575i	−0.219917	−	0.177245i
$124$		0			0
$125$	4.28942			0.383657
$126$		0			0
$127$	3.96918			0.352208			0.176104	−	0.984372i	$-0.443650\pi$
$127$	3.96918			0.352208			0.176104	+	0.984372i	$0.443650\pi$
$128$		0			0
$129$	1.15946	−	7.43166i	0.102085	−	0.654321i
$130$		0			0
$131$	2.66432	−	4.61473i	0.232782	−	0.403191i	−0.725844	−	0.687860i	$-0.758550\pi$
$131$	2.66432	−	4.61473i	0.232782	−	0.403191i	0.958626	+	0.284669i	$0.0918837\pi$
$132$		0			0
$133$	−4.89611	+	3.17982i	−0.424547	+	0.275725i
$134$		0			0
$135$	−8.35417	−	12.6711i	−0.719013	−	1.09056i
$136$		0			0
$137$	3.74772	+	6.49124i	0.320189	+	0.554584i	0.980527	−	0.196385i	$-0.0629202\pi$
$137$	3.74772	+	6.49124i	0.320189	+	0.554584i	−0.660338	+	0.750969i	$0.729587\pi$
$138$		0			0
$139$	−7.03285	−	12.1812i	−0.596518	−	1.03320i	−0.993331	−	0.115300i	$-0.963217\pi$
$139$	−7.03285	−	12.1812i	−0.596518	−	1.03320i	0.396812	−	0.917900i	$-0.370116\pi$
$140$		0			0
$141$	−6.42858	+	2.48476i	−0.541384	+	0.209255i
$142$		0			0
$143$	−0.992275	+	1.71867i	−0.0829782	+	0.143722i
$144$		0			0
$145$	−1.52388	−	2.63943i	−0.126551	−	0.219193i
$146$		0			0
$147$	−10.7897	+	5.53004i	−0.889923	+	0.456110i
$148$		0			0
$149$	−1.08986	+	1.88769i	−0.0892846	+	0.154645i	−0.907209	−	0.420680i	$-0.861791\pi$
$149$	−1.08986	+	1.88769i	−0.0892846	+	0.154645i	0.817924	+	0.575326i	$0.195125\pi$
$150$		0			0
$151$	7.01387	+	12.1484i	0.570781	+	0.988621i	0.996486	+	0.0837595i	$0.0266927\pi$
$151$	7.01387	+	12.1484i	0.570781	+	0.988621i	−0.425705	+	0.904862i	$0.639974\pi$
$152$		0			0
$153$	−2.10961	−	9.70416i	−0.170552	−	0.784535i
$154$		0			0
$155$	−4.78231	+	8.28320i	−0.384124	+	0.665322i
$156$		0			0
$157$	2.96623			0.236731			0.118365	−	0.992970i	$-0.462235\pi$
$157$	2.96623			0.236731			0.118365	+	0.992970i	$0.462235\pi$
$158$		0			0
$159$	−1.72344	+	11.0465i	−0.136678	+	0.876046i
$160$		0			0
$161$	6.19601	+	3.15675i	0.488314	+	0.248787i
$162$		0			0
$163$	0.194278	+	0.336499i	0.0152170	+	0.0263566i	0.873534	−	0.486764i	$-0.161823\pi$
$163$	0.194278	+	0.336499i	0.0152170	+	0.0263566i	−0.858317	+	0.513120i	$0.828489\pi$
$164$		0			0
$165$	−6.38800	+	2.46907i	−0.497305	+	0.192217i
$166$		0			0
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	0.689606	−	0.724185i	$-0.257784\pi$
$167$	−3.64889	−	6.32006i	−0.282360	−	0.489061i	−0.971965	+	0.235124i	$0.924450\pi$
$168$		0			0
$169$	5.42542	−	9.39710i	0.417340	−	0.722854i
$170$		0			0
$171$	6.30515	+	2.01650i	0.482167	+	0.154206i
$172$		0			0
$173$	−4.05508			−0.308302			−0.154151	−	0.988047i	$-0.549264\pi$
$173$	−4.05508			−0.308302			−0.154151	+	0.988047i	$0.549264\pi$
$174$		0			0
$175$	7.83582	−	5.08903i	0.592332	−	0.384695i
$176$		0			0
$177$	19.7326	−	7.62699i	1.48319	−	0.573280i
$178$		0			0
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	−0.993174	−	0.116639i	$-0.962788\pi$
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	0.597600	+	0.801795i	$0.296121\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$		0			0
$183$	0.904289	−	0.349524i	0.0668470	−	0.0258375i
$184$		0			0
$185$	31.7657			2.33546
$186$		0			0
$187$	−4.48117			−0.327695
$188$		0			0
$189$	12.5978	+	5.50406i	0.916357	+	0.400362i
$190$		0			0
$191$	−8.28714			−0.599637			−0.299818	−	0.953996i	$-0.596926\pi$
$191$	−8.28714			−0.599637			−0.299818	+	0.953996i	$0.596926\pi$
$192$		0			0
$193$	−18.7848			−1.35216			−0.676082	−	0.736827i	$-0.736323\pi$
$193$	−18.7848			−1.35216			−0.676082	+	0.736827i	$0.736323\pi$
$194$		0			0
$195$	−6.91787	+	2.67388i	−0.495399	+	0.191480i
$196$		0			0
$197$	5.99634			0.427222			0.213611	−	0.976919i	$-0.431478\pi$
$197$	5.99634			0.427222			0.213611	+	0.976919i	$0.431478\pi$
$198$		0			0
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	0.489221	+	0.872160i	$0.337281\pi$
$199$	−7.20434	+	12.4783i	−0.510702	+	0.884562i	−0.999923	+	0.0124022i	$0.996052\pi$
$200$		0			0
$201$	−20.6983	+	8.00026i	−1.45995	+	0.564295i
$202$		0			0
$203$	2.45983	+	1.25324i	0.172646	+	0.0879601i
$204$		0			0
$205$	−5.28261			−0.368954
$206$		0			0
$207$	−1.67499	−	7.70492i	−0.116420	−	0.535529i
$208$		0			0
$209$	1.49354	−	2.58690i	0.103311	−	0.178939i
$210$		0			0
$211$	6.92418	+	11.9930i	0.476680	+	0.825634i	0.999643	−	0.0267212i	$-0.00850663\pi$
$211$	6.92418	+	11.9930i	0.476680	+	0.825634i	−0.522963	+	0.852356i	$0.675173\pi$
$212$		0			0
$213$	−20.8695	+	8.06642i	−1.42995	+	0.552702i
$214$		0			0
$215$	−6.34204	−	10.9847i	−0.432523	−	0.749153i
$216$		0			0
$217$	−0.453726	−	8.65184i	−0.0308010	−	0.587325i
$218$		0			0
$219$	2.79158	−	17.8929i	0.188638	−	1.20909i
$220$		0			0
$221$	−4.85287			−0.326439
$222$		0			0
$223$	−2.33756	+	4.04878i	−0.156535	+	0.271126i	−0.933617	−	0.358273i	$-0.883366\pi$
$223$	−2.33756	+	4.04878i	−0.156535	+	0.271126i	0.777082	+	0.629399i	$0.216699\pi$
$224$		0			0
$225$	−10.0909	−	3.22724i	−0.672725	−	0.215149i
$226$		0			0
$227$	9.85631	+	17.0716i	0.654187	+	1.13308i	0.982097	+	0.188376i	$0.0603222\pi$
$227$	9.85631	+	17.0716i	0.654187	+	1.13308i	−0.327910	+	0.944709i	$0.606344\pi$
$228$		0			0
$229$	−14.0364	+	24.3118i	−0.927552	+	1.60657i	−0.140148	+	0.990131i	$0.544758\pi$
$229$	−14.0364	+	24.3118i	−0.927552	+	1.60657i	−0.787404	+	0.616437i	$0.788575\pi$
$230$		0			0
$231$	3.63454	−	5.02728i	0.239135	−	0.330771i
$232$		0			0
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	0.546409	−	0.837518i	$-0.315994\pi$
$233$	−6.90113	−	11.9531i	−0.452108	−	0.783074i	−0.998517	+	0.0544448i	$0.982661\pi$
$234$		0			0
$235$	−5.81127	+	10.0654i	−0.379085	+	0.656595i
$236$		0			0
$237$	−1.24024	+	0.479373i	−0.0805619	+	0.0311386i
$238$		0			0
$239$	−5.53069	−	9.57944i	−0.357751	−	0.619642i	0.629834	−	0.776730i	$-0.283123\pi$
$239$	−5.53069	−	9.57944i	−0.357751	−	0.619642i	−0.987585	+	0.157087i	$0.949790\pi$
$240$		0			0
$241$	11.5849	+	20.0656i	0.746247	+	1.29254i	0.949610	+	0.313435i	$0.101480\pi$
$241$	11.5849	+	20.0656i	0.746247	+	1.29254i	−0.203362	+	0.979104i	$0.565187\pi$
$242$		0			0
$243$	−4.20829	−	15.0097i	−0.269962	−	0.962871i
$244$		0			0
$245$	−8.31486	+	18.6790i	−0.531217	+	1.19336i
$246$		0			0
$247$	1.61743	−	2.80147i	0.102915	−	0.178253i
$248$		0			0
$249$	0.525297	−	3.36693i	0.0332893	−	0.213371i
$250$		0			0
$251$	7.78402			0.491323			0.245662	−	0.969356i	$-0.420995\pi$
$251$	7.78402			0.491323			0.245662	+	0.969356i	$0.420995\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$		0			0
$255$	−13.0392	−	10.5091i	−0.816544	−	0.658106i
$256$		0			0
$257$	−5.18798	+	8.98585i	−0.323618	+	0.560522i	−0.981232	−	0.192833i	$-0.938232\pi$
$257$	−5.18798	+	8.98585i	−0.323618	+	0.560522i	0.657614	+	0.753355i	$0.271566\pi$
$258$		0			0
$259$	−24.1311	+	15.6721i	−1.49944	+	0.973820i
$260$		0			0
$261$	−0.664975	−	3.05888i	−0.0411609	−	0.189340i
$262$		0			0
$263$	−9.56654	−	16.5697i	−0.589898	−	1.02173i	−0.994245	−	0.107128i	$-0.965835\pi$
$263$	−9.56654	−	16.5697i	−0.589898	−	1.02173i	0.404347	−	0.914605i	$-0.367499\pi$
$264$		0			0
$265$	9.42689	+	16.3279i	0.579090	+	1.00301i
$266$		0			0
$267$	8.64045	+	6.96390i	0.528787	+	0.426184i
$268$		0			0
$269$	−4.41840	+	7.65290i	−0.269395	+	0.466605i	−0.968706	−	0.248212i	$-0.920157\pi$
$269$	−4.41840	+	7.65290i	−0.269395	+	0.466605i	0.699311	+	0.714818i	$0.253490\pi$
$270$		0			0
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	0.997744	+	0.0671321i	$0.0213849\pi$
$271$	9.16955	+	15.8821i	0.557010	+	0.964770i	−0.440734	+	0.897638i	$0.645282\pi$
$272$		0			0
$273$	3.93602	−	5.44428i	0.238219	−	0.329503i
$274$		0			0
$275$	−2.39029	+	4.14011i	−0.144140	+	0.249658i
$276$		0			0
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	0.779101	−	0.626899i	$-0.215676\pi$
$277$	−2.55241	−	4.42091i	−0.153360	−	0.265627i	−0.932460	+	0.361272i	$0.882343\pi$
$278$		0			0
$279$	−7.27001	+	6.60704i	−0.435244	+	0.395553i
$280$		0			0
$281$	−0.853180	+	1.47775i	−0.0508964	+	0.0881552i	−0.890351	−	0.455274i	$-0.849541\pi$
$281$	−0.853180	+	1.47775i	−0.0508964	+	0.0881552i	0.839455	+	0.543430i	$0.182875\pi$
$282$		0			0
$283$	12.4883			0.742352			0.371176	−	0.928562i	$-0.378955\pi$
$283$	12.4883			0.742352			0.371176	+	0.928562i	$0.378955\pi$
$284$		0			0
$285$	10.4126	−	4.02465i	0.616788	−	0.238400i
$286$		0			0
$287$	4.01299	−	2.60626i	0.236879	−	0.153843i
$288$		0			0
$289$	3.02104	+	5.23260i	0.177708	+	0.307800i
$290$		0			0
$291$	−2.21151	+	14.1748i	−0.129641	+	0.830944i
$292$		0			0
$293$	−2.60202	−	4.50684i	−0.152012	−	0.263292i	0.779955	−	0.625835i	$-0.215242\pi$
$293$	−2.60202	−	4.50684i	−0.152012	−	0.263292i	−0.931967	+	0.362543i	$0.881909\pi$
$294$		0			0
$295$	17.8377	−	30.8959i	1.03855	−	1.79883i
$296$		0			0
$297$	−7.02175	+	0.416825i	−0.407443	+	0.0241866i
$298$		0			0
$299$	−3.85309			−0.222830
$300$		0			0
$301$	10.2373	+	5.21571i	0.590067	+	0.300628i
$302$		0			0
$303$	21.8828	+	17.6367i	1.25713	+	1.01320i
$304$		0			0
$305$	0.817453	−	1.41587i	0.0468072	−	0.0810725i
$306$		0			0
$307$	−5.00136			−0.285442			−0.142721	−	0.989763i	$-0.545585\pi$
$307$	−5.00136			−0.285442			−0.142721	+	0.989763i	$0.545585\pi$
$308$		0			0
$309$	−0.594560	+	3.81088i	−0.0338234	+	0.216793i
$310$		0			0
$311$	32.3968			1.83706			0.918528	−	0.395355i	$-0.129379\pi$
$311$	32.3968			1.83706			0.918528	+	0.395355i	$0.129379\pi$
$312$		0			0
$313$	1.51907			0.0858629			0.0429315	−	0.999078i	$-0.486330\pi$
$313$	1.51907			0.0858629			0.0429315	+	0.999078i	$0.486330\pi$
$314$		0			0
$315$	22.3655	−	6.10458i	1.26015	−	0.343954i
$316$		0			0
$317$	−21.5089			−1.20806			−0.604029	−	0.796962i	$-0.706439\pi$
$317$	−21.5089			−1.20806			−0.604029	+	0.796962i	$0.706439\pi$
$318$		0			0
$319$	−1.41252			−0.0790860
$320$		0			0
$321$	23.6109	+	19.0295i	1.31783	+	1.06213i
$322$		0			0
$323$	7.30441			0.406428
$324$		0			0
$325$	−2.58856	+	4.48352i	−0.143588	+	0.248701i
$326$		0			0
$327$	−4.16473	+	26.6942i	−0.230310	+	1.47619i
$328$		0			0
$329$	−0.551350	−	10.5134i	−0.0303969	−	0.579621i
$330$		0			0
$331$	−19.4780			−1.07061			−0.535305	−	0.844659i	$-0.679803\pi$
$331$	−19.4780			−1.07061			−0.535305	+	0.844659i	$0.679803\pi$
$332$		0			0
$333$	31.0758	+	9.93858i	1.70294	+	0.544631i
$334$		0			0
$335$	−18.7107	+	32.4079i	−1.02228	+	1.77063i
$336$		0			0
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	0.967316	−	0.253575i	$-0.0816063\pi$
$337$	4.84742	+	8.39598i	0.264056	+	0.457358i	−0.703260	+	0.710933i	$0.748273\pi$
$338$		0			0
$339$	−2.27789	−	1.83590i	−0.123718	−	0.0997122i
$340$		0			0
$341$	2.21642	+	3.83896i	0.120026	+	0.207891i
$342$		0			0
$343$	−2.89912	−	18.2919i	−0.156538	−	0.987672i
$344$		0			0
$345$	−10.3528	−	8.34403i	−0.557379	−	0.449228i
$346$		0			0
$347$	−2.02604			−0.108763			−0.0543817	−	0.998520i	$-0.517319\pi$
$347$	−2.02604			−0.108763			−0.0543817	+	0.998520i	$0.517319\pi$
$348$		0			0
$349$	8.14577	−	14.1089i	0.436033	−	0.755231i	−0.561346	−	0.827581i	$-0.689716\pi$
$349$	8.14577	−	14.1089i	0.436033	−	0.755231i	0.997379	+	0.0723497i	$0.0230498\pi$
$350$		0			0
$351$	−7.60419	+	0.451400i	−0.405882	+	0.0240939i
$352$		0			0
$353$	−8.53072	−	14.7756i	−0.454045	−	0.786428i	0.544588	−	0.838704i	$-0.316686\pi$
$353$	−8.53072	−	14.7756i	−0.454045	−	0.786428i	−0.998633	+	0.0522753i	$0.983353\pi$
$354$		0			0
$355$	−18.8655	+	32.6759i	−1.00127	+	1.73426i
$356$		0			0
$357$	15.0902	+	1.55026i	0.798656	+	0.0820484i
$358$		0			0
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	0.824215	−	0.566277i	$-0.191617\pi$
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	−0.902518	+	0.430652i	$0.858283\pi$
$360$		0			0
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$		0			0
$363$	2.44770	−	15.6887i	0.128471	−	0.823444i
$364$		0			0
$365$	−15.2695	−	26.4475i	−0.799240	−	1.38432i
$366$		0			0
$367$	−5.07874	−	8.79664i	−0.265108	−	0.459181i	0.702484	−	0.711700i	$-0.252074\pi$
$367$	−5.07874	−	8.79664i	−0.265108	−	0.459181i	−0.967592	+	0.252519i	$0.918741\pi$
$368$		0			0
$369$	−5.16787	−	1.65278i	−0.269029	−	0.0860402i
$370$		0			0
$371$	−15.2168	−	7.75270i	−0.790019	−	0.402500i
$372$		0			0
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	−0.320904	−	0.947112i	$-0.603987\pi$
$373$	12.7423	−	22.0703i	0.659771	−	1.14276i	0.980675	−	0.195645i	$-0.0626799\pi$
$374$		0			0
$375$	6.92985	−	2.67851i	0.357856	−	0.138318i
$376$		0			0
$377$	−1.52969			−0.0787829
$378$		0			0
$379$	−9.85497			−0.506216			−0.253108	−	0.967438i	$-0.581453\pi$
$379$	−9.85497			−0.506216			−0.253108	+	0.967438i	$0.581453\pi$
$380$		0			0
$381$	6.41250	−	2.47854i	0.328522	−	0.126980i
$382$		0			0
$383$	−13.6563	+	23.6535i	−0.697806	+	1.20864i	0.271419	+	0.962461i	$0.412507\pi$
$383$	−13.6563	+	23.6535i	−0.697806	+	1.20864i	−0.969225	+	0.246175i	$0.920826\pi$
$384$		0			0
$385$	−0.547870	−	10.4470i	−0.0279220	−	0.532428i
$386$		0			0
$387$	−2.76748	−	12.7304i	−0.140679	−	0.647122i
$388$		0			0
$389$	−2.09223	−	3.62385i	−0.106080	−	0.183736i	0.808099	−	0.589047i	$-0.200497\pi$
$389$	−2.09223	−	3.62385i	−0.106080	−	0.183736i	−0.914179	+	0.405311i	$0.867163\pi$
$390$		0			0
$391$	−4.35019	−	7.53475i	−0.219999	−	0.381049i
$392$		0			0
$393$	1.42274	−	9.11914i	0.0717676	−	0.460000i
$394$		0			0
$395$	−1.12114	+	1.94187i	−0.0564107	+	0.0977062i
$396$		0			0
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	0.937745	+	0.347323i	$0.112909\pi$
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	−0.168082	+	0.985773i	$0.553757\pi$
$398$		0			0
$399$	−5.92439	+	8.19458i	−0.296591	+	0.410242i
$400$		0			0
$401$	3.42402	−	5.93057i	0.170987	−	0.296158i	−0.767778	−	0.640716i	$-0.778638\pi$
$401$	3.42402	−	5.93057i	0.170987	−	0.296158i	0.938765	+	0.344557i	$0.111971\pi$
$402$		0			0
$403$	2.40027	+	4.15739i	0.119566	+	0.207095i
$404$		0			0
$405$	−21.4092	−	15.2543i	−1.06383	−	0.757994i
$406$		0			0
$407$	7.36113	−	12.7499i	0.364878	−	0.631987i
$408$		0			0
$409$	−18.2698			−0.903384			−0.451692	−	0.892174i	$-0.649179\pi$
$409$	−18.2698			−0.903384			−0.451692	+	0.892174i	$0.649179\pi$
$410$		0			0
$411$	10.1081	+	8.14680i	0.498597	+	0.401852i
$412$		0			0
$413$	1.69237	+	32.2709i	0.0832763	+	1.58795i
$414$		0			0
$415$	−2.87328	−	4.97666i	−0.141044	−	0.244295i
$416$		0			0
$417$	−18.9686	−	15.2880i	−0.928896	−	0.748658i
$418$		0			0
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	−0.998366	−	0.0571410i	$-0.981802\pi$
$419$	−11.2310	−	19.4526i	−0.548669	−	0.950322i	0.449698	−	0.893181i	$-0.351532\pi$
$420$		0			0
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	−0.492232	−	0.870464i	$-0.663819\pi$
$421$	10.4177	−	18.0440i	0.507728	−	0.879411i	0.999960	−	0.00894684i	$-0.00284791\pi$
$422$		0			0
$423$	−8.83422	+	8.02861i	−0.429535	+	0.390364i
$424$		0			0
$425$	−11.6901			−0.567053
$426$		0			0
$427$	0.0775568	+	1.47888i	0.00375324	+	0.0715682i
$428$		0			0
$429$	−0.529872	+	3.39626i	−0.0255825	+	0.163973i
$430$		0			0
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	−0.512370	−	0.858765i	$-0.671232\pi$
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	0.999897	+	0.0143427i	$0.00456557\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$		0			0
$435$	−4.11011	−	3.31260i	−0.197065	−	0.158827i
$436$		0			0
$437$	5.79956			0.277431
$438$		0			0
$439$	35.4781			1.69328			0.846639	−	0.532168i	$-0.178623\pi$
$439$	35.4781			1.69328			0.846639	+	0.532168i	$0.178623\pi$
$440$		0			0
$441$	−13.9784	+	15.6718i	−0.665637	+	0.746276i
$442$		0			0
$443$	19.2063			0.912517			0.456258	−	0.889847i	$-0.349189\pi$
$443$	19.2063			0.912517			0.456258	+	0.889847i	$0.349189\pi$
$444$		0			0
$445$	18.7143			0.887144
$446$		0			0
$447$	−0.581980	+	3.73025i	−0.0275267	+	0.176435i
$448$		0			0
$449$	−29.6082			−1.39730			−0.698648	−	0.715465i	$-0.746215\pi$
$449$	−29.6082			−1.39730			−0.698648	+	0.715465i	$0.746215\pi$
$450$		0			0
$451$	−1.22415	+	2.12029i	−0.0576429	+	0.0998405i
$452$		0			0
$453$	18.9174	+	15.2468i	0.888818	+	0.716356i
$454$		0			0
$455$	−0.593314	−	11.3136i	−0.0278150	−	0.530388i
$456$		0			0
$457$	−9.56196			−0.447290			−0.223645	−	0.974671i	$-0.571796\pi$
$457$	−9.56196			−0.447290			−0.223645	+	0.974671i	$0.571796\pi$
$458$		0			0
$459$	−9.46795	−	14.3604i	−0.441926	−	0.670287i
$460$		0			0
$461$	10.9187	−	18.9118i	0.508536	−	0.880809i	−0.491416	−	0.870925i	$-0.663520\pi$
$461$	10.9187	−	18.9118i	0.508536	−	0.880809i	0.999951	−	0.00988416i	$-0.00314628\pi$
$462$		0			0
$463$	−13.0744	−	22.6456i	−0.607621	−	1.05243i	−0.991631	−	0.129102i	$-0.958791\pi$
$463$	−13.0744	−	22.6456i	−0.607621	−	1.05243i	0.384010	−	0.923329i	$-0.374543\pi$
$464$		0			0
$465$	−2.55374	+	16.3684i	−0.118427	+	0.759065i
$466$		0			0
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	0.913758	+	0.406258i	$0.133167\pi$
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	−0.105049	+	0.994467i	$0.533500\pi$
$468$		0			0
$469$	−1.77520	−	33.8502i	−0.0819711	−	1.56306i
$470$		0			0
$471$	4.79215	−	1.85225i	0.220811	−	0.0853473i
$472$		0			0
$473$	−5.87861			−0.270299
$474$		0			0
$475$	3.89623	−	6.74848i	0.178771	−	0.309641i
$476$		0			0
$477$	4.11362	+	18.9226i	0.188350	+	0.866407i
$478$		0			0
$479$	−14.9054	−	25.8170i	−0.681047	−	1.17961i	−0.974662	−	0.223684i	$-0.928192\pi$
$479$	−14.9054	−	25.8170i	−0.681047	−	1.17961i	0.293615	−	0.955924i	$-0.405142\pi$
$480$		0			0
$481$	7.97172	−	13.8074i	0.363479	−	0.629565i
$482$		0			0
$483$	11.9813	+	1.23088i	0.545168	+	0.0560069i
$484$		0			0
$485$	12.0965	+	20.9518i	0.549276	+	0.951374i
$486$		0			0
$487$	11.2253	−	19.4428i	0.508667	−	0.881037i	−0.491283	−	0.871000i	$-0.663472\pi$
$487$	11.2253	−	19.4428i	0.508667	−	0.881037i	0.999950	−	0.0100365i	$-0.00319477\pi$
$488$		0			0
$489$	0.523994	+	0.422321i	0.0236958	+	0.0190980i
$490$		0			0
$491$	−17.5222	−	30.3494i	−0.790767	−	1.36965i	−0.925493	−	0.378765i	$-0.876349\pi$
$491$	−17.5222	−	30.3494i	−0.790767	−	1.36965i	0.134726	−	0.990883i	$-0.456984\pi$
$492$		0			0
$493$	−1.72704	−	2.99132i	−0.0777819	−	0.134722i
$494$		0			0
$495$	−8.77845	+	7.97792i	−0.394562	+	0.358581i
$496$		0			0
$497$	−1.78988	−	34.1302i	−0.0802871	−	1.53095i
$498$		0			0
$499$	−4.46760	+	7.73811i	−0.199997	+	0.346405i	−0.948527	−	0.316696i	$-0.897427\pi$
$499$	−4.46760	+	7.73811i	−0.199997	+	0.346405i	0.748530	+	0.663101i	$0.230760\pi$
$500$		0			0
$501$	−9.84158	−	7.93197i	−0.439689	−	0.354374i
$502$		0			0
$503$	12.6403			0.563603			0.281802	−	0.959473i	$-0.409068\pi$
$503$	12.6403			0.563603			0.281802	+	0.959473i	$0.409068\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$		0			0
$507$	2.89716	−	18.5696i	0.128667	−	0.824703i
$508$		0			0
$509$	14.0555	−	24.3449i	0.623000	−	1.07907i	−0.365924	−	0.930645i	$-0.619247\pi$
$509$	14.0555	−	24.3449i	0.623000	−	1.07907i	0.988924	−	0.148423i	$-0.0474196\pi$
$510$		0			0
$511$	24.6479	+	12.5576i	1.09036	+	0.555517i
$512$		0			0
$513$	11.4456	−	0.679434i	0.505336	−	0.0299978i
$514$		0			0
$515$	3.25214	+	5.63287i	0.143306	+	0.248214i
$516$		0			0
$517$	2.69331	+	4.66495i	0.118452	+	0.205164i
$518$		0			0
$519$	−6.55127	+	2.53218i	−0.287569	+	0.111150i
$520$		0			0
$521$	4.23768	−	7.33988i	0.185656	−	0.321566i	−0.758141	−	0.652090i	$-0.773892\pi$
$521$	4.23768	−	7.33988i	0.185656	−	0.321566i	0.943797	+	0.330524i	$0.107226\pi$
$522$		0			0
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	−0.956339	−	0.292259i	$-0.905593\pi$
$523$	−16.7236	−	28.9662i	−0.731273	−	1.26660i	0.225066	−	0.974344i	$-0.427740\pi$
$524$		0			0
$525$	9.48149	−	13.1147i	0.413806	−	0.572374i
$526$		0			0
$527$	−5.41988	+	9.38751i	−0.236094	+	0.408926i
$528$		0			0
$529$	8.04603	+	13.9361i	0.349827	+	0.605919i
$530$		0			0
$531$	27.1167	−	24.6439i	1.17677	−	1.06945i
$532$		0			0
$533$	−1.32569	+	2.29616i	−0.0574220	+	0.0994579i
$534$		0			0
$535$	51.1387			2.21092
$536$		0			0
$537$	−2.82614	+	18.1144i	−0.121957	+	0.781693i
$538$		0			0
$539$	5.57039	+	7.66586i	0.239934	+	0.330192i
$540$		0			0
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$		0			0
$543$	−31.7155	+	12.2586i	−1.36104	+	0.526067i
$544$		0			0
$545$	22.7803	+	39.4567i	0.975802	+	1.69014i
$546$		0			0
$547$	2.88599	−	4.99869i	0.123396	−	0.213728i	−0.797709	−	0.603043i	$-0.793955\pi$
$547$	2.88599	−	4.99869i	0.123396	−	0.213728i	0.921105	+	0.389315i	$0.127288\pi$
$548$		0			0
$549$	1.24268	−	1.12936i	0.0530364	−	0.0481999i
$550$		0			0
$551$	2.30244			0.0980874
$552$		0			0
$553$	−0.106369	−	2.02829i	−0.00452329	−	0.0862518i
$554$		0			0
$555$	51.3198	−	19.8360i	2.17840	−	0.841992i
$556$		0			0
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	−0.258661	−	0.965968i	$-0.583281\pi$
$557$	16.6911	−	28.9098i	0.707223	−	1.22495i	0.965883	−	0.258977i	$-0.0833855\pi$
$558$		0			0
$559$	−6.36623			−0.269263
$560$		0			0
$561$	−7.23964	+	2.79825i	−0.305658	+	0.118142i
$562$		0			0
$563$	−2.19131			−0.0923528			−0.0461764	−	0.998933i	$-0.514704\pi$
$563$	−2.19131			−0.0923528			−0.0461764	+	0.998933i	$0.514704\pi$
$564$		0			0
$565$	−4.93367			−0.207561
$566$		0			0
$567$	23.7897	+	1.02553i	0.999072	+	0.0430683i
$568$		0			0
$569$	18.9860			0.795936			0.397968	−	0.917399i	$-0.369716\pi$
$569$	18.9860			0.795936			0.397968	+	0.917399i	$0.369716\pi$
$570$		0			0
$571$	21.7380			0.909709			0.454854	−	0.890566i	$-0.349691\pi$
$571$	21.7380			0.909709			0.454854	+	0.890566i	$0.349691\pi$
$572$		0			0
$573$	−13.3885	+	5.17488i	−0.559311	+	0.216184i
$574$		0			0
$575$	−9.28172			−0.387074
$576$		0			0
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	0.341443	+	0.939903i	$0.389084\pi$
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	−0.984701	+	0.174253i	$0.944249\pi$
$578$		0			0
$579$	−30.3482	+	11.7301i	−1.26123	+	0.487488i
$580$		0			0
$581$	4.63803	+	2.36299i	0.192418	+	0.0980333i
$582$		0			0
$583$	8.73804			0.361893
$584$		0			0
$585$	−9.50661	+	8.63968i	−0.393050	+	0.357207i
$586$		0			0
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	−0.611886	−	0.790946i	$-0.709589\pi$
$587$	9.18332	−	15.9060i	0.379036	−	0.656510i	0.990922	+	0.134436i	$0.0429222\pi$
$588$		0			0
$589$	−3.61282	−	6.25759i	−0.148864	−	0.257840i
$590$		0			0
$591$	9.68751	−	3.74440i	0.398491	−	0.154024i
$592$		0			0
$593$	13.8775	+	24.0365i	0.569880	+	0.987061i	0.996577	+	0.0826662i	$0.0263435\pi$
$593$	13.8775	+	24.0365i	0.569880	+	0.987061i	−0.426698	+	0.904394i	$0.640323\pi$
$594$		0			0
$595$	21.4539	−	13.9334i	0.879524	−	0.571213i
$596$		0			0
$597$	−3.84710	+	24.6583i	−0.157451	+	1.00920i
$598$		0			0
$599$	−0.402823			−0.0164589			−0.00822945	−	0.999966i	$-0.502620\pi$
$599$	−0.402823			−0.0164589			−0.00822945	+	0.999966i	$0.502620\pi$
$600$		0			0
$601$	12.3733	−	21.4312i	0.504717	−	0.874196i	−0.495268	−	0.868740i	$-0.664930\pi$
$601$	12.3733	−	21.4312i	0.504717	−	0.874196i	0.999985	−	0.00545577i	$-0.00173663\pi$
$602$		0			0
$603$	−28.4438	+	25.8500i	−1.15832	+	1.05269i
$604$		0			0
$605$	−13.3885	−	23.1895i	−0.544318	−	0.942787i
$606$		0			0
$607$	12.0348	−	20.8449i	0.488479	−	0.846070i	−0.511434	−	0.859323i	$-0.670885\pi$
$607$	12.0348	−	20.8449i	0.488479	−	0.846070i	0.999912	+	0.0132531i	$0.00421872\pi$
$608$		0			0
$609$	4.75661	+	0.488662i	0.192748	+	0.0198016i
$610$		0			0
$611$	2.91672	+	5.05190i	0.117998	+	0.204378i
$612$		0			0
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$		0			0
$615$	−8.53443	+	3.29871i	−0.344142	+	0.133017i
$616$		0			0
$617$	−20.9315	−	36.2544i	−0.842669	−	1.45955i	−0.887630	−	0.460558i	$-0.847650\pi$
$617$	−20.9315	−	36.2544i	−0.842669	−	1.45955i	0.0449604	−	0.998989i	$-0.485684\pi$
$618$		0			0
$619$	7.41095	+	12.8361i	0.297871	+	0.515928i	0.975649	−	0.219339i	$-0.0703900\pi$
$619$	7.41095	+	12.8361i	0.297871	+	0.515928i	−0.677777	+	0.735267i	$0.737057\pi$
$620$		0			0
$621$	−7.51737	−	11.4019i	−0.301662	−	0.457543i
$622$		0			0
$623$	−14.2165	+	9.23301i	−0.569572	+	0.369913i
$624$		0			0
$625$	15.0930	−	26.1419i	0.603722	−	1.04568i
$626$		0			0
$627$	0.797548	−	5.11195i	0.0318510	−	0.204152i
$628$		0			0
$629$	36.0007			1.43544
$630$		0			0
$631$	21.0294			0.837169			0.418585	−	0.908178i	$-0.362526\pi$
$631$	21.0294			0.837169			0.418585	+	0.908178i	$0.362526\pi$
$632$		0			0
$633$	18.6755	+	15.0518i	0.742285	+	0.598255i
$634$		0			0
$635$	5.79673	−	10.0402i	0.230036	−	0.398434i
$636$		0			0
$637$	6.03244	+	8.30173i	0.239014	+	0.328926i
$638$		0			0
$639$	−28.6790	+	26.0637i	−1.13453	+	1.03107i
$640$		0			0
$641$	−5.96592	−	10.3333i	−0.235640	−	0.408140i	0.723819	−	0.689990i	$-0.242385\pi$
$641$	−5.96592	−	10.3333i	−0.235640	−	0.408140i	−0.959458	+	0.281850i	$0.909052\pi$
$642$		0			0
$643$	19.9678	+	34.5852i	0.787452	+	1.36391i	0.927524	+	0.373765i	$0.121933\pi$
$643$	19.9678	+	34.5852i	0.787452	+	1.36391i	−0.140072	+	0.990141i	$0.544733\pi$
$644$		0			0
$645$	−17.1054	−	13.7863i	−0.673524	−	0.542837i
$646$		0			0
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	−0.875582	−	0.483070i	$-0.839522\pi$
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	0.856142	+	0.516741i	$0.172855\pi$
$648$		0			0
$649$	−8.26714	−	14.3191i	−0.324514	−	0.562074i
$650$		0			0
$651$	−6.13564	−	13.6943i	−0.240475	−	0.536723i
$652$		0			0
$653$	−11.3573	+	19.6715i	−0.444447	+	0.769804i	−0.998014	−	0.0630004i	$-0.979933\pi$
$653$	−11.3573	+	19.6715i	−0.444447	+	0.769804i	0.553567	+	0.832805i	$0.313266\pi$
$654$		0			0
$655$	−7.78211	−	13.4790i	−0.304072	−	0.526668i
$656$		0			0
$657$	−6.66315	−	30.6504i	−0.259954	−	1.19579i
$658$		0			0
$659$	19.1943	−	33.2454i	0.747702	−	1.29506i	−0.201220	−	0.979546i	$-0.564491\pi$
$659$	19.1943	−	33.2454i	0.747702	−	1.29506i	0.948922	−	0.315512i	$-0.102176\pi$
$660$		0			0
$661$	33.9258			1.31956			0.659780	−	0.751459i	$-0.270649\pi$
$661$	33.9258			1.31956			0.659780	+	0.751459i	$0.270649\pi$
$662$		0			0
$663$	−7.84015	+	3.03036i	−0.304486	+	0.117689i
$664$		0			0
$665$	0.893040	+	17.0288i	0.0346306	+	0.660350i
$666$		0			0
$667$	−1.37124	−	2.37505i	−0.0530944	−	0.0919623i
$668$		0			0
$669$	−1.24825	+	8.00077i	−0.0482602	+	0.309328i
$670$		0			0
$671$	−0.378860	−	0.656205i	−0.0146257	−	0.0253325i
$672$		0			0
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	0.368626	+	0.929578i	$0.379828\pi$
$673$	−16.1030	+	27.8912i	−0.620725	+	1.07513i	−0.989351	+	0.145549i	$0.953505\pi$
$674$		0			0
$675$	−18.3177	+	1.08738i	−0.705050	+	0.0418532i
$676$		0			0
$677$	−37.9684			−1.45924			−0.729622	−	0.683850i	$-0.760304\pi$
$677$	−37.9684			−1.45924			−0.729622	+	0.683850i	$0.760304\pi$
$678$		0			0
$679$	−19.5262	−	9.94823i	−0.749346	−	0.381778i
$680$		0			0
$681$	26.5839	+	21.4257i	1.01870	+	0.821034i
$682$		0			0
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	−0.973942	−	0.226796i	$-0.927175\pi$
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	0.683382	+	0.730061i	$0.260508\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$		0			0
$687$	−7.49540	+	48.0424i	−0.285967	+	1.83293i
$688$		0			0
$689$	9.46285			0.360506
$690$		0			0
$691$	−2.69148			−0.102389			−0.0511943	−	0.998689i	$-0.516303\pi$
$691$	−2.69148			−0.102389			−0.0511943	+	0.998689i	$0.516303\pi$
$692$		0			0
$693$	2.73259	−	10.3915i	0.103803	−	0.394740i
$694$		0			0
$695$	−41.0840			−1.55841
$696$		0			0
$697$	−5.98689			−0.226770
$698$		0			0
$699$	−18.6133	−	15.0017i	−0.704021	−	0.567416i
$700$		0			0
$701$	−11.8515			−0.447625			−0.223813	−	0.974632i	$-0.571850\pi$
$701$	−11.8515			−0.447625			−0.223813	+	0.974632i	$0.571850\pi$
$702$		0			0
$703$	−11.9988	+	20.7826i	−0.452544	+	0.783829i
$704$		0			0
$705$	−3.10320	+	19.8902i	−0.116873	+	0.749109i
$706$		0			0
$707$	−36.0047	+	23.3835i	−1.35410	+	0.879427i
$708$		0			0
$709$	−41.0333			−1.54104			−0.770520	−	0.637416i	$-0.780003\pi$
$709$	−41.0333			−1.54104			−0.770520	+	0.637416i	$0.780003\pi$
$710$		0			0
$711$	−1.70434	+	1.54892i	−0.0639179	+	0.0580891i
$712$		0			0
$713$	−4.30328	+	7.45351i	−0.161159	+	0.279136i
$714$		0			0
$715$	2.89830	+	5.02001i	0.108390	+	0.187738i
$716$		0			0
$717$	−14.9171	−	12.0226i	−0.557088	−	0.448993i
$718$		0			0
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	0.602516	−	0.798107i	$-0.294165\pi$
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	−0.992439	+	0.122741i	$0.960832\pi$
$720$		0			0
$721$	−5.24958	−	2.67457i	−0.195505	−	0.0996060i
$722$		0			0
$723$	31.2461	+	25.1832i	1.16205	+	0.936574i
$724$		0			0
$725$	−3.68487			−0.136853
$726$		0			0
$727$	−1.32165	+	2.28917i	−0.0490173	+	0.0849005i	−0.889493	−	0.456949i	$-0.848942\pi$
$727$	−1.32165	+	2.28917i	−0.0490173	+	0.0849005i	0.840476	+	0.541849i	$0.182276\pi$
$728$		0			0
$729$	−16.1715	−	21.6213i	−0.598945	−	0.800790i
$730$		0			0
$731$	−7.18756	−	12.4492i	−0.265841	−	0.460451i
$732$		0			0
$733$	−7.07446	+	12.2533i	−0.261301	+	0.452587i	−0.966588	−	0.256335i	$-0.917485\pi$
$733$	−7.07446	+	12.2533i	−0.261301	+	0.452587i	0.705287	+	0.708922i	$0.250818\pi$
$734$		0			0
$735$	−1.76921	+	35.3694i	−0.0652583	+	1.30462i
$736$		0			0
$737$	8.67174	+	15.0199i	0.319428	+	0.553265i
$738$		0			0
$739$	7.85905	−	13.6123i	0.289100	−	0.500736i	−0.684495	−	0.729017i	$-0.739977\pi$
$739$	7.85905	−	13.6123i	0.289100	−	0.500736i	0.973595	+	0.228282i	$0.0733107\pi$
$740$		0			0
$741$	0.863704	−	5.53598i	0.0317289	−	0.203369i
$742$		0			0
$743$	−10.5496	−	18.2724i	−0.387026	−	0.670348i	0.605022	−	0.796208i	$-0.293164\pi$
$743$	−10.5496	−	18.2724i	−0.387026	−	0.670348i	−0.992048	+	0.125861i	$0.959831\pi$
$744$		0			0
$745$	3.18333	+	5.51368i	0.116628	+	0.202006i
$746$		0			0
$747$	−1.25381	−	5.76753i	−0.0458747	−	0.211023i
$748$		0			0
$749$	−38.8480	+	25.2301i	−1.41947	+	0.921888i
$750$		0			0
$751$	6.51848	−	11.2903i	0.237863	−	0.411990i	−0.722238	−	0.691644i	$-0.756887\pi$
$751$	6.51848	−	11.2903i	0.237863	−	0.411990i	0.960101	+	0.279654i	$0.0902199\pi$
$752$		0			0
$753$	12.5756	−	4.86071i	0.458282	−	0.177134i
$754$		0			0
$755$	40.9732			1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$		0			0
$759$	−5.74814	+	2.22176i	−0.208644	+	0.0806447i
$760$		0			0
$761$	3.02038	−	5.23146i	0.109489	−	0.189640i	−0.806074	−	0.591814i	$-0.798412\pi$
$761$	3.02038	−	5.23146i	0.109489	−	0.189640i	0.915563	+	0.402174i	$0.131745\pi$
$762$		0			0
$763$	−36.7719	−	18.7346i	−1.33123	−	0.678238i
$764$		0			0
$765$	−27.6280	−	8.83594i	−0.998894	−	0.319464i
$766$		0			0
$767$	−8.95288	−	15.5068i	−0.323270	−	0.559920i
$768$		0			0
$769$	0.108129	+	0.187285i	0.00389924	+	0.00675368i	0.867968	−	0.496619i	$-0.165425\pi$
$769$	0.108129	+	0.187285i	0.00389924	+	0.00675368i	−0.864069	+	0.503373i	$0.832092\pi$
$770$		0			0
$771$	−2.77037	+	17.7569i	−0.0997724	+	0.639499i
$772$		0			0
$773$	18.8132	−	32.5854i	0.676663	−	1.17202i	−0.299316	−	0.954154i	$-0.596759\pi$
$773$	18.8132	−	32.5854i	0.676663	−	1.17202i	0.975980	−	0.217861i	$-0.0699081\pi$
$774$		0			0
$775$	5.78202	+	10.0148i	0.207696	+	0.359741i
$776$		0			0
$777$	−29.1991	+	40.3881i	−1.04751	+	1.44891i
$778$		0			0
$779$	1.99539	−	3.45612i	0.0714923	−	0.123828i
$780$		0			0
$781$	8.74345	+	15.1441i	0.312865	+	0.541898i
$782$		0			0
$783$	−2.98442	−	4.52659i	−0.106654	−	0.161767i
$784$		0			0
$785$	4.33198	−	7.50321i	0.154615	−	0.267801i
$786$		0			0
$787$	−30.8135			−1.09838			−0.549191	−	0.835697i	$-0.685064\pi$
$787$	−30.8135			−1.09838			−0.549191	+	0.835697i	$0.685064\pi$
$788$		0			0
$789$	−25.8023	−	20.7958i	−0.918587	−	0.740349i
$790$		0			0
$791$	3.74791	−	2.43410i	0.133260	−	0.0865468i
$792$		0			0
$793$	−0.410286	−	0.710636i	−0.0145697	−	0.0252354i
$794$		0			0
$795$	25.4257	+	20.4922i	0.901756	+	0.726784i
$796$		0			0
$797$	−17.9792	−	31.1408i	−0.636855	−	1.10306i	−0.986119	−	0.166040i	$-0.946902\pi$
$797$	−17.9792	−	31.1408i	−0.636855	−	1.10306i	0.349264	−	0.937024i	$-0.386431\pi$
$798$		0			0
$799$	−6.58602	+	11.4073i	−0.232997	+	0.403562i
$800$		0			0
$801$	18.3078	+	5.85517i	0.646876	+	0.206882i
$802$		0			0
$803$	−14.1537			−0.499472
$804$		0			0
$805$	17.0340	−	11.0628i	0.600369	−	0.389914i
$806$		0			0
$807$	−2.35941	+	15.1229i	−0.0830553	+	0.532350i
$808$		0			0
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	0.288511	+	0.957477i	$0.406840\pi$
$809$	−19.4818	+	33.7435i	−0.684943	+	1.18636i	−0.973455	+	0.228880i	$0.926494\pi$
$810$		0			0
$811$	28.2811			0.993082			0.496541	−	0.868013i	$-0.334603\pi$
$811$	28.2811			0.993082			0.496541	+	0.868013i	$0.334603\pi$
$812$		0			0
$813$	24.7316	+	19.9328i	0.867374	+	0.699073i
$814$		0			0
$815$	1.13492			0.0397544
$816$		0			0
$817$	9.58227			0.335241
$818$		0			0
$819$	2.95926	−	11.2535i	0.103405	−	0.393227i
$820$		0			0
$821$	41.5834			1.45127			0.725635	−	0.688080i	$-0.241546\pi$
$821$	41.5834			1.45127			0.725635	+	0.688080i	$0.241546\pi$
$822$		0			0
$823$	−8.45998			−0.294896			−0.147448	−	0.989070i	$-0.547106\pi$
$823$	−8.45998			−0.294896			−0.147448	+	0.989070i	$0.547106\pi$
$824$		0			0
$825$	−1.27641	+	8.18125i	−0.0444389	+	0.284834i
$826$		0			0
$827$	−44.2823			−1.53985			−0.769923	−	0.638137i	$-0.779706\pi$
$827$	−44.2823			−1.53985			−0.769923	+	0.638137i	$0.779706\pi$
$828$		0			0
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	−0.973533	−	0.228547i	$-0.926603\pi$
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	0.684694	+	0.728831i	$0.259936\pi$
$830$		0			0
$831$	−6.88422	−	5.54844i	−0.238811	−	0.192473i
$832$		0			0
$833$	−9.42339	+	21.1693i	−0.326501	+	0.733471i
$834$		0			0
$835$	−21.3158			−0.737665
$836$		0			0
$837$	−7.61946	+	15.2139i	−0.263367	+	0.525868i
$838$		0			0
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	0.488945	+	0.872314i	$0.337382\pi$
$839$	−14.8006	+	25.6354i	−0.510974	+	0.885033i	−0.999919	+	0.0127182i	$0.995952\pi$
$840$		0			0
$841$	13.9556	+	24.1718i	0.481228	+	0.833512i
$842$		0			0
$843$	−0.455595	+	2.92017i	−0.0156915	+	0.100576i
$844$		0			0
$845$	−15.8469	−	27.4477i	−0.545151	−	0.944228i
$846$		0			0
$847$	21.6116	+	11.0107i	0.742583	+	0.378332i
$848$		0			0
$849$	20.1757	−	7.79827i	0.692429	−	0.267636i
$850$		0			0
$851$	28.5839			0.979844
$852$		0			0
$853$	−15.0619	+	26.0880i	−0.515710	+	0.893236i	0.484124	+	0.875000i	$0.339139\pi$
$853$	−15.0619	+	26.0880i	−0.515710	+	0.893236i	−0.999834	+	0.0182366i	$0.994195\pi$
$854$		0			0
$855$	14.3091	−	13.0042i	0.489360	−	0.444734i
$856$		0			0
$857$	−18.5447	−	32.1204i	−0.633475	−	1.09721i	−0.986836	−	0.161724i	$-0.948295\pi$
$857$	−18.5447	−	32.1204i	−0.633475	−	1.09721i	0.353361	−	0.935487i	$-0.385039\pi$
$858$		0			0
$859$	−1.89166	+	3.27646i	−0.0645427	+	0.111791i	−0.896491	−	0.443062i	$-0.853892\pi$
$859$	−1.89166	+	3.27646i	−0.0645427	+	0.111791i	0.831948	+	0.554853i	$0.187226\pi$
$860$		0			0
$861$	4.85579	−	6.71650i	0.165485	−	0.228898i
$862$		0			0
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	0.862368	−	0.506282i	$-0.168981\pi$
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	−0.869637	+	0.493691i	$0.835647\pi$
$864$		0			0
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$		0			0
$867$	8.14818	+	6.56715i	0.276727	+	0.223032i
$868$		0			0
$869$	0.519608	+	0.899987i	0.0176265	+	0.0305300i
$870$		0			0
$871$	9.39105	+	16.2658i	0.318203	+	0.551145i
$872$		0			0
$873$	5.27858	+	24.2814i	0.178653	+	0.821801i
$874$		0			0
$875$	0.594342	+	11.3332i	0.0200924	+	0.383130i
$876$		0			0
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	−0.945291	−	0.326228i	$-0.894222\pi$
$877$	−5.63038	+	9.75210i	−0.190124	+	0.329305i	0.755167	+	0.655532i	$0.227556\pi$
$878$		0			0
$879$	−7.01803	−	5.65629i	−0.236712	−	0.190782i
$880$		0			0
$881$	−35.4810			−1.19538			−0.597692	−	0.801726i	$-0.703916\pi$
$881$	−35.4810			−1.19538			−0.597692	+	0.801726i	$0.703916\pi$
$882$		0			0
$883$	5.30092			0.178390			0.0891952	−	0.996014i	$-0.471571\pi$
$883$	5.30092			0.178390			0.0891952	+	0.996014i	$0.471571\pi$
$884$		0			0
$885$	9.52530	−	61.0531i	0.320189	−	2.05228i
$886$		0			0
$887$	28.7832	−	49.8540i	0.966446	−	1.67393i	0.260767	−	0.965402i	$-0.416025\pi$
$887$	28.7832	−	49.8540i	0.966446	−	1.67393i	0.705679	−	0.708532i	$-0.250642\pi$
$888$		0			0
$889$	0.549971	+	10.4871i	0.0184454	+	0.351725i
$890$		0			0
$891$	−11.0838	+	5.05812i	−0.371323	+	0.169453i
$892$		0			0
$893$	−4.39016	−	7.60398i	−0.146911	−	0.254458i
$894$		0			0
$895$	15.4585	+	26.7749i	0.516720	+	0.894985i
$896$		0			0
$897$	−6.22494	+	2.40605i	−0.207845	+	0.0803356i
$898$		0			0
$899$	−1.70842	+	2.95906i	−0.0569788	+	0.0986903i
$900$		0			0
$901$	10.6837	+	18.5047i	0.355925	+	0.616480i
$902$		0			0
$903$	19.7960	+	2.03370i	0.658769	+	0.0676774i
$904$		0			0
$905$	−28.6700	+	49.6579i	−0.953023	+	1.65068i
$906$		0			0
$907$	10.4486	+	18.0975i	0.346939	+	0.600917i	0.985704	−	0.168485i	$-0.0538876\pi$
$907$	10.4486	+	18.0975i	0.346939	+	0.600917i	−0.638765	+	0.769402i	$0.720554\pi$
$908$		0			0
$909$	46.3664	+	14.8288i	1.53787	+	0.491840i
$910$		0			0
$911$	−11.3819	+	19.7141i	−0.377101	+	0.653157i	−0.990639	−	0.136508i	$-0.956412\pi$
$911$	−11.3819	+	19.7141i	−0.377101	+	0.653157i	0.613539	+	0.789665i	$0.289746\pi$
$912$		0			0
$913$	−2.66332			−0.0881430
$914$		0			0
$915$	0.436518	−	2.79789i	0.0144308	−	0.0924955i
$916$		0			0
$917$	12.5618	+	6.40002i	0.414828	+	0.211347i
$918$		0			0
$919$	−18.6515	−	32.3054i	−0.615257	−	1.06566i	−0.990339	−	0.138664i	$-0.955719\pi$
$919$	−18.6515	−	32.3054i	−0.615257	−	1.06566i	0.375083	−	0.926991i	$-0.377614\pi$
$920$		0			0
$921$	−8.08004	+	3.12308i	−0.266246	+	0.102909i
$922$		0			0
$923$	9.46870	+	16.4003i	0.311666	+	0.539822i
$924$		0			0
$925$	19.2031	−	33.2607i	0.631394	−	1.09361i
$926$		0			0
$927$	1.41914	+	6.52802i	0.0466106	+	0.214408i
$928$		0			0
$929$	5.66725			0.185937			0.0929683	−	0.995669i	$-0.470364\pi$
$929$	5.66725			0.185937			0.0929683	+	0.995669i	$0.470364\pi$
$930$		0			0
$931$	−9.07987	−	12.4955i	−0.297581	−	0.409524i
$932$		0			0
$933$	52.3394	−	20.2301i	1.71351	−	0.662304i
$934$		0			0
$935$	−6.54444	+	11.3353i	−0.214026	+	0.370704i
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$		0			0
$939$	2.45416	−	0.948578i	0.0800886	−	0.0309557i
$940$		0			0
$941$	20.4552			0.666819			0.333410	−	0.942782i	$-0.391801\pi$
$941$	20.4552			0.666819			0.333410	+	0.942782i	$0.391801\pi$
$942$		0			0
$943$	−4.75348			−0.154795
$944$		0			0
$945$	32.3211	−	23.8284i	1.05140	−	0.775139i
$946$		0			0
$947$	4.76687			0.154902			0.0774512	−	0.996996i	$-0.475322\pi$
$947$	4.76687			0.154902			0.0774512	+	0.996996i	$0.475322\pi$
$948$		0			0
$949$	−15.3277			−0.497558
$950$		0			0
$951$	−34.7491	+	13.4311i	−1.12682	+	0.435534i
$952$		0			0
$953$	−48.9412			−1.58536			−0.792680	−	0.609638i	$-0.791315\pi$
$953$	−48.9412			−1.58536			−0.792680	+	0.609638i	$0.791315\pi$
$954$		0			0
$955$	−12.1028	+	20.9627i	−0.391638	+	0.678337i
$956$		0			0
$957$	−2.28203	+	0.882044i	−0.0737675	+	0.0285124i
$958$		0			0
$959$	−16.6313	+	10.8013i	−0.537054	+	0.348794i
$960$		0			0
$961$	−20.2771			−0.654101
$962$		0			0
$963$	50.0279	+	15.9998i	1.61213	+	0.515587i
$964$		0			0
$965$	−27.4340	+	47.5171i	−0.883132	+	1.52963i
$966$		0			0
$967$	2.95856	+	5.12438i	0.0951409	+	0.164789i	0.909667	−	0.415337i	$-0.136336\pi$
$967$	2.95856	+	5.12438i	0.0951409	+	0.164789i	−0.814526	+	0.580126i	$0.803003\pi$
$968$		0			0
$969$	11.8008	−	4.56121i	0.379096	−	0.146527i
$970$		0			0
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	−0.999200	+	0.0399914i	$0.987267\pi$
$972$		0			0
$973$	31.2099	−	20.2695i	1.00054	−	0.649809i
$974$		0			0
$975$	−1.38229	+	8.85987i	−0.0442686	+	0.283743i
$976$		0			0
$977$	22.8455			0.730893			0.365447	−	0.930832i	$-0.380916\pi$
$977$	22.8455			0.730893			0.365447	+	0.930832i	$0.380916\pi$
$978$		0			0
$979$	4.33670	−	7.51139i	0.138602	−	0.240065i
$980$		0			0
$981$	9.94067	+	45.7270i	0.317381	+	1.45995i
$982$		0			0
$983$	−15.6351	−	27.0809i	−0.498684	−	0.863745i	0.501315	−	0.865265i	$-0.332850\pi$
$983$	−15.6351	−	27.0809i	−0.498684	−	0.863745i	−0.999999	+	0.00151933i	$0.999516\pi$
$984$		0			0
$985$	8.75726	−	15.1680i	0.279029	−	0.483293i
$986$		0			0
$987$	−7.45578	−	16.6408i	−0.237320	−	0.529682i
$988$		0			0
$989$	−5.70679	−	9.88444i	−0.181465	−	0.314307i
$990$		0			0
$991$	−3.50732	+	6.07485i	−0.111414	+	0.192974i	−0.916340	−	0.400400i	$-0.868871\pi$
$991$	−3.50732	+	6.07485i	−0.111414	+	0.192974i	0.804927	+	0.593374i	$0.202204\pi$
$992$		0			0
$993$	−31.4681	+	12.1630i	−0.998611	+	0.385981i
$994$		0			0
$995$	21.0429	+	36.4474i	0.667105	+	1.15546i
$996$		0			0
$997$	10.6439	+	18.4358i	0.337095	+	0.583866i	0.983885	−	0.178802i	$-0.0572222\pi$
$997$	10.6439	+	18.4358i	0.337095	+	0.583866i	−0.646790	+	0.762668i	$0.723889\pi$
$998$		0			0
$999$	56.4112	−	3.34868i	1.78477	−	0.105948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.i.529.4		10
3.2	odd	2		3024.2.q.i.2881.2		10
4.3	odd	2		63.2.h.b.25.1	yes	10
7.2	even	3		1008.2.t.i.961.3		10
9.4	even	3		1008.2.t.i.193.3		10
9.5	odd	6		3024.2.t.i.1873.4		10
12.11	even	2		189.2.h.b.46.5		10
21.2	odd	6		3024.2.t.i.289.4		10
28.3	even	6		441.2.f.f.295.5		10
28.11	odd	6		441.2.f.e.295.5		10
28.19	even	6		441.2.g.f.79.5		10
28.23	odd	6		63.2.g.b.16.5	yes	10
28.27	even	2		441.2.h.f.214.1		10
36.7	odd	6		567.2.e.f.487.5		10
36.11	even	6		567.2.e.e.487.1		10
36.23	even	6		189.2.g.b.172.1		10
36.31	odd	6		63.2.g.b.4.5	✓	10
63.23	odd	6		3024.2.q.i.2305.2		10
63.58	even	3	inner	1008.2.q.i.625.4		10
84.11	even	6		1323.2.f.e.883.1		10
84.23	even	6		189.2.g.b.100.1		10
84.47	odd	6		1323.2.g.f.667.1		10
84.59	odd	6		1323.2.f.f.883.1		10
84.83	odd	2		1323.2.h.f.802.5		10
252.11	even	6		3969.2.a.bc.1.5		5
252.23	even	6		189.2.h.b.37.5		10
252.31	even	6		441.2.f.f.148.5		10
252.59	odd	6		1323.2.f.f.442.1		10
252.67	odd	6		441.2.f.e.148.5		10
252.79	odd	6		567.2.e.f.163.5		10
252.95	even	6		1323.2.f.e.442.1		10
252.103	even	6		441.2.h.f.373.1		10
252.115	even	6		3969.2.a.ba.1.1		5
252.131	odd	6		1323.2.h.f.226.5		10
252.139	even	6		441.2.g.f.67.5		10
252.151	odd	6		3969.2.a.z.1.1		5
252.167	odd	6		1323.2.g.f.361.1		10
252.191	even	6		567.2.e.e.163.1		10
252.227	odd	6		3969.2.a.bb.1.5		5
252.247	odd	6		63.2.h.b.58.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	36.31	odd	6
63.2.g.b.16.5	yes	10	28.23	odd	6
63.2.h.b.25.1	yes	10	4.3	odd	2
63.2.h.b.58.1	yes	10	252.247	odd	6
189.2.g.b.100.1		10	84.23	even	6
189.2.g.b.172.1		10	36.23	even	6
189.2.h.b.37.5		10	252.23	even	6
189.2.h.b.46.5		10	12.11	even	2
441.2.f.e.148.5		10	252.67	odd	6
441.2.f.e.295.5		10	28.11	odd	6
441.2.f.f.148.5		10	252.31	even	6
441.2.f.f.295.5		10	28.3	even	6
441.2.g.f.67.5		10	252.139	even	6
441.2.g.f.79.5		10	28.19	even	6
441.2.h.f.214.1		10	28.27	even	2
441.2.h.f.373.1		10	252.103	even	6
567.2.e.e.163.1		10	252.191	even	6
567.2.e.e.487.1		10	36.11	even	6
567.2.e.f.163.5		10	252.79	odd	6
567.2.e.f.487.5		10	36.7	odd	6
1008.2.q.i.529.4		10	1.1	even	1	trivial
1008.2.q.i.625.4		10	63.58	even	3	inner
1008.2.t.i.193.3		10	9.4	even	3
1008.2.t.i.961.3		10	7.2	even	3
1323.2.f.e.442.1		10	252.95	even	6
1323.2.f.e.883.1		10	84.11	even	6
1323.2.f.f.442.1		10	252.59	odd	6
1323.2.f.f.883.1		10	84.59	odd	6
1323.2.g.f.361.1		10	252.167	odd	6
1323.2.g.f.667.1		10	84.47	odd	6
1323.2.h.f.226.5		10	252.131	odd	6
1323.2.h.f.802.5		10	84.83	odd	2
3024.2.q.i.2305.2		10	63.23	odd	6
3024.2.q.i.2881.2		10	3.2	odd	2
3024.2.t.i.289.4		10	21.2	odd	6
3024.2.t.i.1873.4		10	9.5	odd	6
3969.2.a.z.1.1		5	252.151	odd	6
3969.2.a.ba.1.1		5	252.115	even	6
3969.2.a.bb.1.5		5	252.227	odd	6
3969.2.a.bc.1.5		5	252.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.61557 - 0.624446i) q^{3} +(1.46043 - 2.52954i) q^{5} +(0.138560 + 2.64212i) q^{7} +(2.22013 - 2.01767i) q^{9} +O(q^{10})\)	\(q+(1.61557 - 0.624446i) q^{3} +(1.46043 - 2.52954i) q^{5} +(0.138560 + 2.64212i) q^{7} +(2.22013 - 2.01767i) q^{9} +(-0.676857 - 1.17235i) q^{11} +(-0.733001 - 1.26960i) q^{13} +(0.779867 - 4.99862i) q^{15} +(1.65514 - 2.86678i) q^{17} +(1.10329 + 1.91096i) q^{19} +(1.87372 + 4.18201i) q^{21} +(1.31415 - 2.27617i) q^{23} +(-1.76573 - 3.05833i) q^{25} +(2.32685 - 4.64605i) q^{27} +(0.521720 - 0.903646i) q^{29} -3.27458 q^{31} +(-1.82558 - 1.47135i) q^{33} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +(-1.97701 - 1.59340i) q^{39} +(-0.904289 - 1.56627i) q^{41} +(2.17129 - 3.76078i) q^{43} +(-1.86144 - 8.56260i) q^{45} -3.97914 q^{47} +(-6.96160 + 0.732185i) q^{49} +(0.883838 - 5.66503i) q^{51} +(-3.22743 + 5.59008i) q^{53} -3.95402 q^{55} +(2.97574 + 2.39834i) q^{57} +12.2140 q^{59} +0.559734 q^{61} +(5.63856 + 5.58629i) q^{63} -4.28200 q^{65} -12.8118 q^{67} +(0.701751 - 4.49793i) q^{69} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} +(-4.76242 - 3.83835i) q^{75} +(3.00371 - 1.95078i) q^{77} -0.767677 q^{79} +(0.857983 - 8.95901i) q^{81} +(0.983707 - 1.70383i) q^{83} +(-4.83443 - 8.37348i) q^{85} +(0.278597 - 1.78569i) q^{87} +(3.20356 + 5.54872i) q^{89} +(3.25286 - 2.11259i) q^{91} +(-5.29031 + 2.04480i) q^{93} +6.44514 q^{95} +(-4.14143 + 7.17316i) q^{97} +(-3.86814 - 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9}+O(q^{10}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9	\( 10 q + q^{3} + 4 q^{5} + 4 q^{7} + 11 q^{9} - 4 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} + 13 q^{21} - 3 q^{23} - q^{25} + 7 q^{27} + 7 q^{29} - 6 q^{31} + 14 q^{33} - 5 q^{35} - 2 q^{39} + 5 q^{41} + 7 q^{43} - 16 q^{45} + 54 q^{47} - 8 q^{49} + 9 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} + 60 q^{59} + 28 q^{61} + 59 q^{63} + 22 q^{65} - 4 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} + 14 q^{75} + 11 q^{77} - 8 q^{79} + 23 q^{81} - 9 q^{83} - 6 q^{85} - 2 q^{87} + 28 q^{89} + 4 q^{91} - 6 q^{93} - 28 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q + q^3 + 4 * q^5 + 4 * q^7 + 11 * q^9 - 4 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 + 13 * q^21 - 3 * q^23 - q^25 + 7 * q^27 + 7 * q^29 - 6 * q^31 + 14 * q^33 - 5 * q^35 - 2 * q^39 + 5 * q^41 + 7 * q^43 - 16 * q^45 + 54 * q^47 - 8 * q^49 + 9 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 + 60 * q^59 + 28 * q^61 + 59 * q^63 + 22 * q^65 - 4 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 + 14 * q^75 + 11 * q^77 - 8 * q^79 + 23 * q^81 - 9 * q^83 - 6 * q^85 - 2 * q^87 + 28 * q^89 + 4 * q^91 - 6 * q^93 - 28 * q^95 - 12 * q^97 - 35 * q^99

Introduction

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