LMFDB - Embedded newform 297.2.e.d.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("297.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	297.100
Dual form			297.2.e.d.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.300767i) q^{2} +(0.939693 + 1.62760i) q^{4} +(0.326352 + 0.565258i) q^{5} +(-0.266044 + 0.460802i) q^{7} +1.34730 q^{8} +0.226682 q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.15270 + 1.99654i) q^{13} +(0.0923963 + 0.160035i) q^{14} +(-1.64543 + 2.84997i) q^{16} +4.41147 q^{17} -4.18479 q^{19} +(-0.613341 + 1.06234i) q^{20} +(0.173648 + 0.300767i) q^{22} +(0.705737 + 1.22237i) q^{23} +(2.28699 - 3.96118i) q^{25} +0.800660 q^{26} -1.00000 q^{28} +(3.17752 - 5.50362i) q^{29} +(1.08125 + 1.87278i) q^{31} +(1.91875 + 3.32337i) q^{32} +(0.766044 - 1.32683i) q^{34} -0.347296 q^{35} -3.16250 q^{37} +(-0.726682 + 1.25865i) q^{38} +(0.439693 + 0.761570i) q^{40} +(-4.65657 - 8.06542i) q^{41} +(6.14930 - 10.6509i) q^{43} -1.87939 q^{44} +0.490200 q^{46} +(-1.93242 + 3.34705i) q^{47} +(3.35844 + 5.81699i) q^{49} +(-0.794263 - 1.37570i) q^{50} +(-2.16637 + 3.75227i) q^{52} -12.6236 q^{53} -0.652704 q^{55} +(-0.358441 + 0.620838i) q^{56} +(-1.10354 - 1.91139i) q^{58} +(-1.61721 - 2.80109i) q^{59} +(4.26604 - 7.38901i) q^{61} +0.751030 q^{62} -5.24897 q^{64} +(-0.752374 + 1.30315i) q^{65} +(-2.48158 - 4.29823i) q^{67} +(4.14543 + 7.18009i) q^{68} +(-0.0603074 + 0.104455i) q^{70} -9.98545 q^{71} -7.49525 q^{73} +(-0.549163 + 0.951178i) q^{74} +(-3.93242 - 6.81115i) q^{76} +(-0.266044 - 0.460802i) q^{77} +(2.43969 - 4.22567i) q^{79} -2.14796 q^{80} -3.23442 q^{82} +(-2.29813 + 3.98048i) q^{83} +(1.43969 + 2.49362i) q^{85} +(-2.13563 - 3.69902i) q^{86} +(-0.673648 + 1.16679i) q^{88} +16.9513 q^{89} -1.22668 q^{91} +(-1.32635 + 2.29731i) q^{92} +(0.671122 + 1.16242i) q^{94} +(-1.36571 - 2.36549i) q^{95} +(-6.32295 + 10.9517i) q^{97} +2.33275 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 6 q^{8} - 12 q^{10} - 3 q^{11} + 9 q^{13} - 3 q^{14} + 6 q^{16} + 6 q^{17} - 18 q^{19} + 3 q^{20} - 6 q^{23} + 6 q^{25} - 24 q^{26} - 6 q^{28} - 6 q^{29} + 9 q^{31} + 9 q^{32}+ \cdots - 24 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 6 * q^8 - 12 * q^10 - 3 * q^11 + 9 * q^13 - 3 * q^14 + 6 * q^16 + 6 * q^17 - 18 * q^19 + 3 * q^20 - 6 * q^23 + 6 * q^25 - 24 * q^26 - 6 * q^28 - 6 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^37 + 9 * q^38 - 3 * q^40 - 6 * q^41 - 3 * q^43 + 12 * q^47 + 12 * q^49 - 15 * q^50 + 6 * q^52 - 6 * q^53 - 6 * q^55 + 6 * q^56 + 3 * q^58 + 21 * q^59 + 21 * q^61 + 30 * q^62 - 6 * q^64 - 21 * q^65 - 3 * q^67 + 9 * q^68 - 6 * q^70 - 24 * q^71 - 12 * q^73 - 15 * q^74 + 3 * q^77 + 9 * q^79 + 18 * q^80 + 42 * q^82 + 3 * q^85 + 6 * q^86 - 3 * q^88 + 24 * q^89 + 6 * q^91 - 9 * q^92 + 18 * q^94 - 18 * q^95 + 3 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.173648	−	0.300767i	0.122788	−	0.212675i	−0.798078	−	0.602554i	$-0.794150\pi$
$2$	0.173648	−	0.300767i	0.122788	−	0.212675i	0.920866	+	0.389879i	$0.127483\pi$
$3$		0			0
$3$		0			0
$4$	0.939693	+	1.62760i	0.469846	+	0.813798i
$5$	0.326352	+	0.565258i	0.145949	+	0.252791i	0.929727	−	0.368251i	$-0.120043\pi$
$5$	0.326352	+	0.565258i	0.145949	+	0.252791i	−0.783778	+	0.621042i	$0.786710\pi$
$6$		0			0
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	1.34730			0.476341
$9$		0			0
$10$	0.226682			0.0716830
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	1.15270	+	1.99654i	0.319702	+	0.553741i	0.980426	−	0.196889i	$-0.0630837\pi$
$13$	1.15270	+	1.99654i	0.319702	+	0.553741i	−0.660723	+	0.750629i	$0.729750\pi$
$14$	0.0923963	+	0.160035i	0.0246939	+	0.0427712i
$15$		0			0
$16$	−1.64543	+	2.84997i	−0.411357	+	0.712492i
$17$	4.41147			1.06994			0.534970	−	0.844871i	$-0.320323\pi$
$17$	4.41147			1.06994			0.534970	+	0.844871i	$0.320323\pi$
$18$		0			0
$19$	−4.18479			−0.960057			−0.480029	−	0.877253i	$-0.659374\pi$
$19$	−4.18479			−0.960057			−0.480029	+	0.877253i	$0.659374\pi$
$20$	−0.613341	+	1.06234i	−0.137147	+	0.237546i
$21$		0			0
$22$	0.173648	+	0.300767i	0.0370219	+	0.0641238i
$23$	0.705737	+	1.22237i	0.147156	+	0.254882i	0.930175	−	0.367115i	$-0.119655\pi$
$23$	0.705737	+	1.22237i	0.147156	+	0.254882i	−0.783019	+	0.621998i	$0.786321\pi$
$24$		0			0
$25$	2.28699	−	3.96118i	0.457398	−	0.792236i
$26$	0.800660			0.157022
$27$		0			0
$28$	−1.00000			−0.188982
$29$	3.17752	−	5.50362i	0.590050	−	1.02200i	−0.404175	−	0.914682i	$-0.632441\pi$
$29$	3.17752	−	5.50362i	0.590050	−	1.02200i	0.994225	−	0.107315i	$-0.0342255\pi$
$30$		0			0
$31$	1.08125	+	1.87278i	0.194199	+	0.336362i	0.946638	−	0.322300i	$-0.104456\pi$
$31$	1.08125	+	1.87278i	0.194199	+	0.336362i	−0.752439	+	0.658662i	$0.771123\pi$
$32$	1.91875	+	3.32337i	0.339190	+	0.587494i
$33$		0			0
$34$	0.766044	−	1.32683i	0.131376	−	0.227549i
$35$	−0.347296			−0.0587038
$36$		0			0
$37$	−3.16250			−0.519912			−0.259956	−	0.965620i	$-0.583708\pi$
$37$	−3.16250			−0.519912			−0.259956	+	0.965620i	$0.583708\pi$
$38$	−0.726682	+	1.25865i	−0.117883	+	0.204180i
$39$		0			0
$40$	0.439693	+	0.761570i	0.0695215	+	0.120415i
$41$	−4.65657	−	8.06542i	−0.727235	−	1.25961i	−0.958048	−	0.286609i	$-0.907472\pi$
$41$	−4.65657	−	8.06542i	−0.727235	−	1.25961i	0.230813	−	0.972998i	$-0.425861\pi$
$42$		0			0
$43$	6.14930	−	10.6509i	0.937759	−	1.62425i	0.168122	−	0.985766i	$-0.446230\pi$
$43$	6.14930	−	10.6509i	0.937759	−	1.62425i	0.769638	−	0.638481i	$-0.220437\pi$
$44$	−1.87939			−0.283328
$45$		0			0
$46$	0.490200			0.0722760
$47$	−1.93242	+	3.34705i	−0.281872	+	0.488217i	−0.971846	−	0.235617i	$-0.924289\pi$
$47$	−1.93242	+	3.34705i	−0.281872	+	0.488217i	0.689974	+	0.723834i	$0.257622\pi$
$48$		0			0
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	−0.794263	−	1.37570i	−0.112326	−	0.194554i
$51$		0			0
$52$	−2.16637	+	3.75227i	−0.300422	+	0.520346i
$53$	−12.6236			−1.73399			−0.866993	−	0.498320i	$-0.833950\pi$
$53$	−12.6236			−1.73399			−0.866993	+	0.498320i	$0.833950\pi$
$54$		0			0
$55$	−0.652704			−0.0880105
$56$	−0.358441	+	0.620838i	−0.0478987	+	0.0829629i
$57$		0			0
$58$	−1.10354	−	1.91139i	−0.144902	−	0.250978i
$59$	−1.61721	−	2.80109i	−0.210543	−	0.364671i	0.741342	−	0.671128i	$-0.234190\pi$
$59$	−1.61721	−	2.80109i	−0.210543	−	0.364671i	−0.951885	+	0.306457i	$0.900857\pi$
$60$		0			0
$61$	4.26604	−	7.38901i	0.546211	−	0.946065i	−0.452319	−	0.891856i	$-0.649403\pi$
$61$	4.26604	−	7.38901i	0.546211	−	0.946065i	0.998530	−	0.0542088i	$-0.0172637\pi$
$62$	0.751030			0.0953809
$63$		0			0
$64$	−5.24897			−0.656121
$65$	−0.752374	+	1.30315i	−0.0933205	+	0.161636i
$66$		0			0
$67$	−2.48158	−	4.29823i	−0.303173	−	0.525112i	0.673680	−	0.739024i	$-0.264713\pi$
$67$	−2.48158	−	4.29823i	−0.303173	−	0.525112i	−0.976853	+	0.213912i	$0.931379\pi$
$68$	4.14543	+	7.18009i	0.502707	+	0.870714i
$69$		0			0
$70$	−0.0603074	+	0.104455i	−0.00720811	+	0.0124848i
$71$	−9.98545			−1.18506			−0.592528	−	0.805550i	$-0.701870\pi$
$71$	−9.98545			−1.18506			−0.592528	+	0.805550i	$0.701870\pi$
$72$		0			0
$73$	−7.49525			−0.877253			−0.438626	−	0.898669i	$-0.644535\pi$
$73$	−7.49525			−0.877253			−0.438626	+	0.898669i	$0.644535\pi$
$74$	−0.549163	+	0.951178i	−0.0638389	+	0.110572i
$75$		0			0
$76$	−3.93242	−	6.81115i	−0.451079	−	0.781292i
$77$	−0.266044	−	0.460802i	−0.0303186	−	0.0525133i
$78$		0			0
$79$	2.43969	−	4.22567i	0.274487	−	0.475425i	−0.695519	−	0.718508i	$-0.744825\pi$
$79$	2.43969	−	4.22567i	0.274487	−	0.475425i	0.970006	+	0.243083i	$0.0781587\pi$
$80$	−2.14796			−0.240149
$81$		0			0
$82$	−3.23442			−0.357182
$83$	−2.29813	+	3.98048i	−0.252253	+	0.436915i	−0.964146	−	0.265373i	$-0.914505\pi$
$83$	−2.29813	+	3.98048i	−0.252253	+	0.436915i	0.711893	+	0.702288i	$0.247838\pi$
$84$		0			0
$85$	1.43969	+	2.49362i	0.156157	+	0.270471i
$86$	−2.13563	−	3.69902i	−0.230291	−	0.398875i
$87$		0			0
$88$	−0.673648	+	1.16679i	−0.0718111	+	0.124381i
$89$	16.9513			1.79683			0.898417	−	0.439143i	$-0.144718\pi$
$89$	16.9513			1.79683			0.898417	+	0.439143i	$0.144718\pi$
$90$		0			0
$91$	−1.22668			−0.128591
$92$	−1.32635	+	2.29731i	−0.138282	+	0.239511i
$93$		0			0
$94$	0.671122	+	1.16242i	0.0692209	+	0.119894i
$95$	−1.36571	−	2.36549i	−0.140119	−	0.242694i
$96$		0			0
$97$	−6.32295	+	10.9517i	−0.641998	+	1.11197i	0.342988	+	0.939340i	$0.388561\pi$
$97$	−6.32295	+	10.9517i	−0.641998	+	1.11197i	−0.984986	+	0.172634i	$0.944772\pi$
$98$	2.33275			0.235643
$99$		0			0
$100$	8.59627			0.859627
$101$	8.54576	−	14.8017i	0.850335	−	1.47282i	−0.0305715	−	0.999533i	$-0.509733\pi$
$101$	8.54576	−	14.8017i	0.850335	−	1.47282i	0.880906	−	0.473291i	$-0.156934\pi$
$102$		0			0
$103$	−1.42989	−	2.47665i	−0.140891	−	0.244031i	0.786941	−	0.617028i	$-0.211664\pi$
$103$	−1.42989	−	2.47665i	−0.140891	−	0.244031i	−0.927833	+	0.372997i	$0.878330\pi$
$104$	1.55303	+	2.68993i	0.152287	+	0.263770i
$105$		0			0
$106$	−2.19207	+	3.79677i	−0.212912	+	0.368775i
$107$	−9.92902			−0.959874			−0.479937	−	0.877303i	$-0.659341\pi$
$107$	−9.92902			−0.959874			−0.479937	+	0.877303i	$0.659341\pi$
$108$		0			0
$109$	13.8161			1.32335			0.661673	−	0.749792i	$-0.269847\pi$
$109$	13.8161			1.32335			0.661673	+	0.749792i	$0.269847\pi$
$110$	−0.113341	+	0.196312i	−0.0108066	+	0.0187176i
$111$		0			0
$112$	−0.875515	−	1.51644i	−0.0827284	−	0.143290i
$113$	0.879385	+	1.52314i	0.0827256	+	0.143285i	0.904420	−	0.426644i	$-0.140304\pi$
$113$	0.879385	+	1.52314i	0.0827256	+	0.143285i	−0.821694	+	0.569929i	$0.806971\pi$
$114$		0			0
$115$	−0.460637	+	0.797847i	−0.0429546	+	0.0743996i
$116$	11.9436			1.10893
$117$		0			0
$118$	−1.12330			−0.103408
$119$	−1.17365	+	2.03282i	−0.107588	+	0.186348i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−1.48158	−	2.56617i	−0.134136	−	0.232331i
$123$		0			0
$124$	−2.03209	+	3.51968i	−0.182487	+	0.316077i
$125$	6.24897			0.558925
$126$		0			0
$127$	6.90167			0.612425			0.306212	−	0.951963i	$-0.400938\pi$
$127$	6.90167			0.612425			0.306212	+	0.951963i	$0.400938\pi$
$128$	−4.74897	+	8.22546i	−0.419754	+	0.727035i
$129$		0			0
$130$	0.261297	+	0.452579i	0.0229172	+	0.0396938i
$131$	5.17024	+	8.95513i	0.451726	+	0.782413i	0.998493	−	0.0548718i	$-0.0174750\pi$
$131$	5.17024	+	8.95513i	0.451726	+	0.782413i	−0.546767	+	0.837285i	$0.684142\pi$
$132$		0			0
$133$	1.11334	−	1.92836i	0.0965389	−	0.167210i
$134$	−1.72369			−0.148904
$135$		0			0
$136$	5.94356			0.509656
$137$	7.09240	−	12.2844i	0.605944	−	1.04953i	−0.385957	−	0.922517i	$-0.626129\pi$
$137$	7.09240	−	12.2844i	0.605944	−	1.04953i	0.991901	−	0.127010i	$-0.0405379\pi$
$138$		0			0
$139$	−0.0505072	−	0.0874810i	−0.00428396	−	0.00742004i	0.863875	−	0.503705i	$-0.168030\pi$
$139$	−0.0505072	−	0.0874810i	−0.00428396	−	0.00742004i	−0.868159	+	0.496285i	$0.834697\pi$
$140$	−0.326352	−	0.565258i	−0.0275818	−	0.0477730i
$141$		0			0
$142$	−1.73396	+	3.00330i	−0.145510	+	0.252031i
$143$	−2.30541			−0.192788
$144$		0			0
$145$	4.14796			0.344469
$146$	−1.30154	+	2.25433i	−0.107716	+	0.186570i
$147$		0			0
$148$	−2.97178	−	5.14728i	−0.244279	−	0.423104i
$149$	−1.53074	−	2.65133i	−0.125403	−	0.217205i	0.796487	−	0.604656i	$-0.206689\pi$
$149$	−1.53074	−	2.65133i	−0.125403	−	0.217205i	−0.921891	+	0.387450i	$0.873356\pi$
$150$		0			0
$151$	−9.70099	+	16.8026i	−0.789455	+	1.36738i	0.136846	+	0.990592i	$0.456304\pi$
$151$	−9.70099	+	16.8026i	−0.789455	+	1.36738i	−0.926301	+	0.376784i	$0.877030\pi$
$152$	−5.63816			−0.457315
$153$		0			0
$154$	−0.184793			−0.0148910
$155$	−0.705737	+	1.22237i	−0.0566862	+	0.0981833i
$156$		0			0
$157$	6.36231	+	11.0198i	0.507768	+	0.879479i	0.999960	+	0.00899272i	$0.00286251\pi$
$157$	6.36231	+	11.0198i	0.507768	+	0.879479i	−0.492192	+	0.870487i	$0.663804\pi$
$158$	−0.847296	−	1.46756i	−0.0674073	−	0.116753i
$159$		0			0
$160$	−1.25237	+	2.16918i	−0.0990088	+	0.171488i
$161$	−0.751030			−0.0591894
$162$		0			0
$163$	−12.7888			−1.00170			−0.500848	−	0.865535i	$-0.666978\pi$
$163$	−12.7888			−1.00170			−0.500848	+	0.865535i	$0.666978\pi$
$164$	8.75150	−	15.1580i	0.683377	−	1.18364i
$165$		0			0
$166$	0.798133	+	1.38241i	0.0619472	+	0.107296i
$167$	10.3623	+	17.9480i	0.801860	+	1.38886i	0.918391	+	0.395675i	$0.129489\pi$
$167$	10.3623	+	17.9480i	0.801860	+	1.38886i	−0.116531	+	0.993187i	$0.537177\pi$
$168$		0			0
$169$	3.84255	−	6.65549i	0.295581	−	0.511961i
$170$	1.00000			0.0766965
$171$		0			0
$172$	23.1138			1.76241
$173$	−11.2515	+	19.4882i	−0.855435	+	1.48166i	0.0208050	+	0.999784i	$0.493377\pi$
$173$	−11.2515	+	19.4882i	−0.855435	+	1.48166i	−0.876240	+	0.481874i	$0.839956\pi$
$174$		0			0
$175$	1.21688	+	2.10770i	0.0919876	+	0.159327i
$176$	−1.64543	−	2.84997i	−0.124029	−	0.214824i
$177$		0			0
$178$	2.94356	−	5.09840i	0.220629	−	0.382141i
$179$	10.7219			0.801395			0.400697	−	0.916210i	$-0.368768\pi$
$179$	10.7219			0.801395			0.400697	+	0.916210i	$0.368768\pi$
$180$		0			0
$181$	−4.15745			−0.309021			−0.154510	−	0.987991i	$-0.549380\pi$
$181$	−4.15745			−0.309021			−0.154510	+	0.987991i	$0.549380\pi$
$182$	−0.213011	+	0.368946i	−0.0157894	+	0.0273481i
$183$		0			0
$184$	0.950837	+	1.64690i	0.0700966	+	0.121411i
$185$	−1.03209	−	1.78763i	−0.0758807	−	0.131429i
$186$		0			0
$187$	−2.20574	+	3.82045i	−0.161299	+	0.279379i
$188$	−7.26352			−0.529747
$189$		0			0
$190$	−0.948615			−0.0688198
$191$	1.20187	−	2.08169i	0.0869640	−	0.150626i	−0.819262	−	0.573419i	$-0.805617\pi$
$191$	1.20187	−	2.08169i	0.0869640	−	0.150626i	0.906226	+	0.422793i	$0.138950\pi$
$192$		0			0
$193$	0.226682	+	0.392624i	0.0163169	+	0.0282617i	0.874069	−	0.485803i	$-0.161473\pi$
$193$	0.226682	+	0.392624i	0.0163169	+	0.0282617i	−0.857752	+	0.514064i	$0.828139\pi$
$194$	2.19594	+	3.80347i	0.157659	+	0.273074i
$195$		0			0
$196$	−6.31180	+	10.9324i	−0.450843	+	0.780883i
$197$	19.6236			1.39812			0.699062	−	0.715061i	$-0.253601\pi$
$197$	19.6236			1.39812			0.699062	+	0.715061i	$0.253601\pi$
$198$		0			0
$199$	3.63041			0.257353			0.128677	−	0.991687i	$-0.458927\pi$
$199$	3.63041			0.257353			0.128677	+	0.991687i	$0.458927\pi$
$200$	3.08125	−	5.33688i	0.217877	−	0.377375i
$201$		0			0
$202$	−2.96791	−	5.14057i	−0.208821	−	0.361689i
$203$	1.69072	+	2.92842i	0.118665	+	0.205535i
$204$		0			0
$205$	3.03936	−	5.26433i	0.212278	−	0.367677i
$206$	−0.993193			−0.0691990
$207$		0			0
$208$	−7.58677			−0.526048
$209$	2.09240	−	3.62414i	0.144734	−	0.250687i
$210$		0			0
$211$	−10.8366	−	18.7696i	−0.746024	−	1.29215i	−0.949715	−	0.313116i	$-0.898627\pi$
$211$	−10.8366	−	18.7696i	−0.746024	−	1.29215i	0.203691	−	0.979035i	$-0.434706\pi$
$212$	−11.8623	−	20.5461i	−0.814707	−	1.41111i
$213$		0			0
$214$	−1.72416	+	2.98632i	−0.117861	+	0.204141i
$215$	8.02734			0.547460
$216$		0			0
$217$	−1.15064			−0.0781108
$218$	2.39915	−	4.15545i	0.162491	−	0.281442i
$219$		0			0
$220$	−0.613341	−	1.06234i	−0.0413514	−	0.0716228i
$221$	5.08512	+	8.80769i	0.342062	+	0.592469i
$222$		0			0
$223$	−9.56805	+	16.5723i	−0.640724	+	1.10977i	0.344548	+	0.938769i	$0.388032\pi$
$223$	−9.56805	+	16.5723i	−0.640724	+	1.10977i	−0.985271	+	0.170997i	$0.945301\pi$
$224$	−2.04189			−0.136429
$225$		0			0
$226$	0.610815			0.0406308
$227$	−7.79679	+	13.5044i	−0.517491	+	0.896321i	0.482303	+	0.876005i	$0.339801\pi$
$227$	−7.79679	+	13.5044i	−0.517491	+	0.896321i	−0.999794	+	0.0203161i	$0.993533\pi$
$228$		0			0
$229$	7.70574	+	13.3467i	0.509209	+	0.881977i	0.999943	+	0.0106670i	$0.00339547\pi$
$229$	7.70574	+	13.3467i	0.509209	+	0.881977i	−0.490734	+	0.871310i	$0.663271\pi$
$230$	0.159978	+	0.277089i	0.0105486	+	0.0182707i
$231$		0			0
$232$	4.28106	−	7.41501i	0.281065	−	0.486819i
$233$	−4.29086			−0.281104			−0.140552	−	0.990073i	$-0.544888\pi$
$233$	−4.29086			−0.281104			−0.140552	+	0.990073i	$0.544888\pi$
$234$		0			0
$235$	−2.52259			−0.164556
$236$	3.03936	−	5.26433i	0.197846	−	0.342679i
$237$		0			0
$238$	0.407604	+	0.705990i	0.0264210	+	0.0457626i
$239$	−10.0667	−	17.4360i	−0.651161	−	1.12784i	−0.982842	−	0.184452i	$-0.940949\pi$
$239$	−10.0667	−	17.4360i	−0.651161	−	1.12784i	0.331681	−	0.943392i	$-0.392384\pi$
$240$		0			0
$241$	3.72281	−	6.44810i	0.239807	−	0.415359i	−0.720852	−	0.693090i	$-0.756249\pi$
$241$	3.72281	−	6.44810i	0.239807	−	0.415359i	0.960659	+	0.277731i	$0.0895824\pi$
$242$	−0.347296			−0.0223251
$243$		0			0
$244$	16.0351			1.02654
$245$	−2.19207	+	3.79677i	−0.140046	+	0.242567i
$246$		0			0
$247$	−4.82383	−	8.35511i	−0.306933	−	0.531623i
$248$	1.45677	+	2.52319i	0.0925048	+	0.160223i
$249$		0			0
$250$	1.08512	−	1.87949i	0.0686292	−	0.118869i
$251$	−12.5202			−0.790270			−0.395135	−	0.918623i	$-0.629302\pi$
$251$	−12.5202			−0.790270			−0.395135	+	0.918623i	$0.629302\pi$
$252$		0			0
$253$	−1.41147			−0.0887386
$254$	1.19846	−	2.07580i	0.0751983	−	0.130247i
$255$		0			0
$256$	−3.59967	−	6.23481i	−0.224979	−	0.389676i
$257$	3.24170	+	5.61478i	0.202211	+	0.350241i	0.949241	−	0.314551i	$-0.101854\pi$
$257$	3.24170	+	5.61478i	0.202211	+	0.350241i	−0.747029	+	0.664791i	$0.768521\pi$
$258$		0			0
$259$	0.841367	−	1.45729i	0.0522800	−	0.0905516i
$260$	−2.82800			−0.175385
$261$		0			0
$262$	3.59121			0.221866
$263$	1.04916	−	1.81720i	0.0646942	−	0.112054i	−0.831864	−	0.554979i	$-0.812726\pi$
$263$	1.04916	−	1.81720i	0.0646942	−	0.112054i	0.896558	+	0.442926i	$0.146059\pi$
$264$		0			0
$265$	−4.11974	−	7.13559i	−0.253073	−	0.438336i
$266$	−0.386659	−	0.669713i	−0.0237076	−	0.0410628i
$267$		0			0
$268$	4.66385	−	8.07802i	0.284890	−	0.493444i
$269$	−29.2490			−1.78334			−0.891671	−	0.452685i	$-0.850466\pi$
$269$	−29.2490			−1.78334			−0.891671	+	0.452685i	$0.850466\pi$
$270$		0			0
$271$	−21.7246			−1.31968			−0.659838	−	0.751408i	$-0.729375\pi$
$271$	−21.7246			−1.31968			−0.659838	+	0.751408i	$0.729375\pi$
$272$	−7.25877	+	12.5726i	−0.440128	+	0.762323i
$273$		0			0
$274$	−2.46316	−	4.26632i	−0.148805	−	0.257738i
$275$	2.28699	+	3.96118i	0.137911	+	0.238868i
$276$		0			0
$277$	2.22803	−	3.85905i	0.133869	−	0.231868i	−0.791296	−	0.611434i	$-0.790593\pi$
$277$	2.22803	−	3.85905i	0.133869	−	0.231868i	0.925165	+	0.379565i	$0.123926\pi$
$278$	−0.0350819			−0.00210407
$279$		0			0
$280$	−0.467911			−0.0279630
$281$	−10.2476	+	17.7494i	−0.611322	+	1.05884i	0.379696	+	0.925111i	$0.376029\pi$
$281$	−10.2476	+	17.7494i	−0.611322	+	1.05884i	−0.991018	+	0.133730i	$0.957305\pi$
$282$		0			0
$283$	−3.44356	−	5.96443i	−0.204699	−	0.354548i	0.745338	−	0.666687i	$-0.232288\pi$
$283$	−3.44356	−	5.96443i	−0.204699	−	0.354548i	−0.950037	+	0.312138i	$0.898955\pi$
$284$	−9.38326	−	16.2523i	−0.556794	−	0.964395i
$285$		0			0
$286$	−0.400330	+	0.693392i	−0.0236720	+	0.0410011i
$287$	4.95542			0.292509
$288$		0			0
$289$	2.46110			0.144771
$290$	0.720285	−	1.24757i	0.0422966	−	0.0732598i
$291$		0			0
$292$	−7.04323	−	12.1992i	−0.412174	−	0.713906i
$293$	−6.90420	−	11.9584i	−0.403348	−	0.698619i	0.590780	−	0.806833i	$-0.298820\pi$
$293$	−6.90420	−	11.9584i	−0.403348	−	0.698619i	−0.994128	+	0.108214i	$0.965487\pi$
$294$		0			0
$295$	1.05556	−	1.82828i	0.0614571	−	0.106447i
$296$	−4.26083			−0.247656
$297$		0			0
$298$	−1.06324			−0.0615921
$299$	−1.62701	+	2.81807i	−0.0940925	+	0.162973i
$300$		0			0
$301$	3.27197	+	5.66723i	0.188593	+	0.326653i
$302$	3.36912	+	5.83548i	0.193871	+	0.335794i
$303$		0			0
$304$	6.88578	−	11.9265i	0.394927	−	0.684033i
$305$	5.56893			0.318876
$306$		0			0
$307$	−0.601319			−0.0343191			−0.0171595	−	0.999853i	$-0.505462\pi$
$307$	−0.601319			−0.0343191			−0.0171595	+	0.999853i	$0.505462\pi$
$308$	0.500000	−	0.866025i	0.0284901	−	0.0493464i
$309$		0			0
$310$	0.245100	+	0.424525i	0.0139207	+	0.0241114i
$311$	0.970437	+	1.68085i	0.0550285	+	0.0953121i	0.892227	−	0.451586i	$-0.149142\pi$
$311$	0.970437	+	1.68085i	0.0550285	+	0.0953121i	−0.837199	+	0.546898i	$0.815808\pi$
$312$		0			0
$313$	−1.00980	+	1.74903i	−0.0570773	+	0.0988608i	−0.893152	−	0.449755i	$-0.851511\pi$
$313$	−1.00980	+	1.74903i	−0.0570773	+	0.0988608i	0.836075	+	0.548615i	$0.184845\pi$
$314$	4.41921			0.249391
$315$		0			0
$316$	9.17024			0.515867
$317$	2.92468	−	5.06569i	0.164266	−	0.284518i	−0.772128	−	0.635467i	$-0.780808\pi$
$317$	2.92468	−	5.06569i	0.164266	−	0.284518i	0.936394	+	0.350949i	$0.114141\pi$
$318$		0			0
$319$	3.17752	+	5.50362i	0.177907	+	0.308144i
$320$	−1.71301	−	2.96702i	−0.0957602	−	0.165862i
$321$		0			0
$322$	−0.130415	+	0.225885i	−0.00726774	+	0.0125881i
$323$	−18.4611			−1.02720
$324$		0			0
$325$	10.5449			0.584925
$326$	−2.22075	+	3.84645i	−0.122996	+	0.213035i
$327$		0			0
$328$	−6.27379	−	10.8665i	−0.346412	−	0.600003i
$329$	−1.02822	−	1.78093i	−0.0566875	−	0.0981857i
$330$		0			0
$331$	−5.86097	+	10.1515i	−0.322148	+	0.557976i	−0.980931	−	0.194356i	$-0.937738\pi$
$331$	−5.86097	+	10.1515i	−0.322148	+	0.557976i	0.658783	+	0.752333i	$0.271071\pi$
$332$	−8.63816			−0.474080
$333$		0			0
$334$	7.19759			0.393834
$335$	1.61974	−	2.80547i	0.0884957	−	0.153279i
$336$		0			0
$337$	−6.29813	−	10.9087i	−0.343081	−	0.594234i	0.641922	−	0.766770i	$-0.278137\pi$
$337$	−6.29813	−	10.9087i	−0.343081	−	0.594234i	−0.985003	+	0.172536i	$0.944804\pi$
$338$	−1.33450	−	2.31143i	−0.0725874	−	0.125725i
$339$		0			0
$340$	−2.70574	+	4.68647i	−0.146739	+	0.254160i
$341$	−2.16250			−0.117106
$342$		0			0
$343$	−7.29860			−0.394087
$344$	8.28493	−	14.3499i	0.446693	−	0.773696i
$345$		0			0
$346$	3.90760	+	6.76817i	0.210074	+	0.363859i
$347$	−11.9226	−	20.6506i	−0.640040	−	1.10858i	−0.985423	−	0.170120i	$-0.945585\pi$
$347$	−11.9226	−	20.6506i	−0.640040	−	1.10858i	0.345384	−	0.938462i	$-0.387749\pi$
$348$		0			0
$349$	4.24123	−	7.34603i	0.227028	−	0.393224i	−0.729898	−	0.683556i	$-0.760433\pi$
$349$	4.24123	−	7.34603i	0.227028	−	0.393224i	0.956926	+	0.290332i	$0.0937658\pi$
$350$	0.845237			0.0451798
$351$		0			0
$352$	−3.83750			−0.204539
$353$	3.72328	−	6.44891i	0.198170	−	0.343241i	−0.749765	−	0.661704i	$-0.769833\pi$
$353$	3.72328	−	6.44891i	0.198170	−	0.343241i	0.947935	+	0.318463i	$0.103167\pi$
$354$		0			0
$355$	−3.25877	−	5.64436i	−0.172958	−	0.299571i
$356$	15.9290	+	27.5899i	0.844236	+	1.46226i
$357$		0			0
$358$	1.86184	−	3.22481i	0.0984015	−	0.170436i
$359$	22.9290			1.21015			0.605074	−	0.796170i	$-0.293144\pi$
$359$	22.9290			1.21015			0.605074	+	0.796170i	$0.293144\pi$
$360$		0			0
$361$	−1.48751			−0.0782901
$362$	−0.721934	+	1.25043i	−0.0379440	+	0.0657209i
$363$		0			0
$364$	−1.15270	−	1.99654i	−0.0604181	−	0.104647i
$365$	−2.44609	−	4.23675i	−0.128034	−	0.221762i
$366$		0			0
$367$	−7.65317	+	13.2557i	−0.399492	+	0.691941i	−0.993663	−	0.112398i	$-0.964147\pi$
$367$	−7.65317	+	13.2557i	−0.399492	+	0.691941i	0.594171	+	0.804339i	$0.297480\pi$
$368$	−4.64496			−0.242135
$369$		0			0
$370$	−0.716881			−0.0372689
$371$	3.35844	−	5.81699i	0.174362	−	0.302003i
$372$		0			0
$373$	13.6951	+	23.7205i	0.709103	+	1.22820i	0.965190	+	0.261549i	$0.0842334\pi$
$373$	13.6951	+	23.7205i	0.709103	+	1.22820i	−0.256087	+	0.966654i	$0.582433\pi$
$374$	0.766044	+	1.32683i	0.0396112	+	0.0686086i
$375$		0			0
$376$	−2.60354	+	4.50946i	−0.134267	+	0.232558i
$377$	14.6509			0.754562
$378$		0			0
$379$	11.2713			0.578966			0.289483	−	0.957183i	$-0.406517\pi$
$379$	11.2713			0.578966			0.289483	+	0.957183i	$0.406517\pi$
$380$	2.56670	−	4.44566i	0.131669	−	0.228058i
$381$		0			0
$382$	−0.417404	−	0.722965i	−0.0213562	−	0.0369901i
$383$	16.6814	+	28.8930i	0.852379	+	1.47636i	0.879055	+	0.476720i	$0.158174\pi$
$383$	16.6814	+	28.8930i	0.852379	+	1.47636i	−0.0266761	+	0.999644i	$0.508492\pi$
$384$		0			0
$385$	0.173648	−	0.300767i	0.00884993	−	0.0153285i
$386$	0.157451			0.00801406
$387$		0			0
$388$	−23.7665			−1.20656
$389$	6.12449	−	10.6079i	0.310524	−	0.537843i	−0.667952	−	0.744204i	$-0.732829\pi$
$389$	6.12449	−	10.6079i	0.310524	−	0.537843i	0.978476	+	0.206361i	$0.0661622\pi$
$390$		0			0
$391$	3.11334	+	5.39246i	0.157448	+	0.272709i
$392$	4.52481	+	7.83721i	0.228538	+	0.395839i
$393$		0			0
$394$	3.40760	−	5.90214i	0.171673	−	0.297346i
$395$	3.18479			0.160244
$396$		0			0
$397$	−11.4287			−0.573591			−0.286795	−	0.957992i	$-0.592590\pi$
$397$	−11.4287			−0.573591			−0.286795	+	0.957992i	$0.592590\pi$
$398$	0.630415	−	1.09191i	0.0315998	−	0.0547325i
$399$		0			0
$400$	7.52616	+	13.0357i	0.376308	+	0.651784i
$401$	10.8473	+	18.7881i	0.541688	+	0.938231i	0.998807	+	0.0488259i	$0.0155480\pi$
$401$	10.8473	+	18.7881i	0.541688	+	0.938231i	−0.457119	+	0.889405i	$0.651119\pi$
$402$		0			0
$403$	−2.49273	+	4.31753i	−0.124172	+	0.215071i
$404$	32.1215			1.59811
$405$		0			0
$406$	1.17436			0.0582827
$407$	1.58125	−	2.73881i	0.0783797	−	0.135758i
$408$		0			0
$409$	14.2947	+	24.7592i	0.706829	+	1.22426i	0.966027	+	0.258440i	$0.0832083\pi$
$409$	14.2947	+	24.7592i	0.706829	+	1.22426i	−0.259199	+	0.965824i	$0.583458\pi$
$410$	−1.05556	−	1.82828i	−0.0521304	−	0.0902925i
$411$		0			0
$412$	2.68732	−	4.65457i	0.132395	−	0.229314i
$413$	1.72100			0.0846849
$414$		0			0
$415$	−3.00000			−0.147264
$416$	−4.42350	+	7.66172i	−0.216880	+	0.375647i
$417$		0			0
$418$	−0.726682	−	1.25865i	−0.0355432	−	0.0615626i
$419$	−4.30541	−	7.45718i	−0.210333	−	0.364307i	0.741486	−	0.670969i	$-0.234121\pi$
$419$	−4.30541	−	7.45718i	−0.210333	−	0.364307i	−0.951819	+	0.306661i	$0.900788\pi$
$420$		0			0
$421$	17.2160	−	29.8190i	0.839057	−	1.45329i	−0.0516276	−	0.998666i	$-0.516441\pi$
$421$	17.2160	−	29.8190i	0.839057	−	1.45329i	0.890684	−	0.454622i	$-0.150226\pi$
$422$	−7.52704			−0.366410
$423$		0			0
$424$	−17.0077			−0.825969
$425$	10.0890	−	17.4746i	0.489388	−	0.847645i
$426$		0			0
$427$	2.26991	+	3.93161i	0.109849	+	0.190264i
$428$	−9.33022	−	16.1604i	−0.450993	−	0.781143i
$429$		0			0
$430$	1.39393	−	2.41436i	0.0672214	−	0.116431i
$431$	−14.2463			−0.686219			−0.343110	−	0.939295i	$-0.611480\pi$
$431$	−14.2463			−0.686219			−0.343110	+	0.939295i	$0.611480\pi$
$432$		0			0
$433$	−24.6023			−1.18231			−0.591154	−	0.806558i	$-0.701328\pi$
$433$	−24.6023			−1.18231			−0.591154	+	0.806558i	$0.701328\pi$
$434$	−0.199807	+	0.346076i	−0.00959106	+	0.0166122i
$435$		0			0
$436$	12.9829	+	22.4871i	0.621769	+	1.07694i
$437$	−2.95336	−	5.11538i	−0.141279	−	0.244702i
$438$		0			0
$439$	−2.08647	+	3.61387i	−0.0995816	+	0.172480i	−0.911512	−	0.411274i	$-0.865084\pi$
$439$	−2.08647	+	3.61387i	−0.0995816	+	0.172480i	0.811930	+	0.583755i	$0.198417\pi$
$440$	−0.879385			−0.0419230
$441$		0			0
$442$	3.53209			0.168004
$443$	−14.6322	+	25.3438i	−0.695198	+	1.20412i	0.274916	+	0.961468i	$0.411350\pi$
$443$	−14.6322	+	25.3438i	−0.695198	+	1.20412i	−0.970114	+	0.242650i	$0.921983\pi$
$444$		0			0
$445$	5.53209	+	9.58186i	0.262246	+	0.454224i
$446$	3.32295	+	5.75552i	0.157346	+	0.272532i
$447$		0			0
$448$	1.39646	−	2.41874i	0.0659765	−	0.114275i
$449$	15.7956			0.745441			0.372720	−	0.927944i	$-0.378425\pi$
$449$	15.7956			0.745441			0.372720	+	0.927944i	$0.378425\pi$
$450$		0			0
$451$	9.31315			0.438539
$452$	−1.65270	+	2.86257i	−0.0777366	+	0.134644i
$453$		0			0
$454$	2.70780	+	4.69004i	0.127083	+	0.220115i
$455$	−0.400330	−	0.693392i	−0.0187677	−	0.0325067i
$456$		0			0
$457$	−4.74257	+	8.21438i	−0.221848	+	0.384252i	−0.955369	−	0.295414i	$-0.904542\pi$
$457$	−4.74257	+	8.21438i	−0.221848	+	0.384252i	0.733521	+	0.679667i	$0.237876\pi$
$458$	5.35235			0.250099
$459$		0			0
$460$	−1.73143			−0.0807283
$461$	−14.4722	+	25.0667i	−0.674040	+	1.16747i	0.302709	+	0.953083i	$0.402109\pi$
$461$	−14.4722	+	25.0667i	−0.674040	+	1.16747i	−0.976749	+	0.214388i	$0.931224\pi$
$462$		0			0
$463$	11.4402	+	19.8149i	0.531669	+	0.920878i	0.999317	+	0.0369631i	$0.0117684\pi$
$463$	11.4402	+	19.8149i	0.531669	+	0.920878i	−0.467647	+	0.883915i	$0.654898\pi$
$464$	10.4568	+	18.1117i	0.485443	+	0.840812i
$465$		0			0
$466$	−0.745100	+	1.29055i	−0.0345161	+	0.0597836i
$467$	−10.2412			−0.473908			−0.236954	−	0.971521i	$-0.576149\pi$
$467$	−10.2412			−0.473908			−0.236954	+	0.971521i	$0.576149\pi$
$468$		0			0
$469$	2.64084			0.121943
$470$	−0.438044	+	0.758714i	−0.0202055	+	0.0349969i
$471$		0			0
$472$	−2.17886	−	3.77390i	−0.100290	−	0.173708i
$473$	6.14930	+	10.6509i	0.282745	+	0.489729i
$474$		0			0
$475$	−9.57057	+	16.5767i	−0.439128	+	0.760592i
$476$	−4.41147			−0.202200
$477$		0			0
$478$	−6.99226			−0.319818
$479$	9.66550	−	16.7411i	0.441628	−	0.764922i	−0.556183	−	0.831060i	$-0.687735\pi$
$479$	9.66550	−	16.7411i	0.441628	−	0.764922i	0.997810	+	0.0661383i	$0.0210678\pi$
$480$		0			0
$481$	−3.64543	−	6.31407i	−0.166217	−	0.287897i
$482$	−1.29292	−	2.23940i	−0.0588908	−	0.102002i
$483$		0			0
$484$	0.939693	−	1.62760i	0.0427133	−	0.0739816i
$485$	−8.25402			−0.374796
$486$		0			0
$487$	27.2104			1.23302			0.616510	−	0.787347i	$-0.288546\pi$
$487$	27.2104			1.23302			0.616510	+	0.787347i	$0.288546\pi$
$488$	5.74763	−	9.95518i	0.260183	−	0.450650i
$489$		0			0
$490$	0.761297	+	1.31860i	0.0343919	+	0.0595685i
$491$	−18.0189	−	31.2096i	−0.813181	−	1.40847i	−0.910627	−	0.413230i	$-0.864401\pi$
$491$	−18.0189	−	31.2096i	−0.813181	−	1.40847i	0.0974459	−	0.995241i	$-0.468933\pi$
$492$		0			0
$493$	14.0175	−	24.2791i	0.631318	−	1.09348i
$494$	−3.35059			−0.150750
$495$		0			0
$496$	−7.11650			−0.319540
$497$	2.65657	−	4.60132i	0.119164	−	0.206397i
$498$		0			0
$499$	3.94609	+	6.83483i	0.176651	+	0.305969i	0.940731	−	0.339152i	$-0.110140\pi$
$499$	3.94609	+	6.83483i	0.176651	+	0.305969i	−0.764080	+	0.645121i	$0.776807\pi$
$500$	5.87211	+	10.1708i	0.262609	+	0.454852i
$501$		0			0
$502$	−2.17412	+	3.76568i	−0.0970355	+	0.168070i
$503$	37.2550			1.66112			0.830558	−	0.556932i	$-0.188022\pi$
$503$	37.2550			1.66112			0.830558	+	0.556932i	$0.188022\pi$
$504$		0			0
$505$	11.1557			0.496422
$506$	−0.245100	+	0.424525i	−0.0108960	+	0.0188725i
$507$		0			0
$508$	6.48545	+	11.2331i	0.287745	+	0.498390i
$509$	2.04458	+	3.54131i	0.0906243	+	0.156966i	0.907774	−	0.419460i	$-0.137780\pi$
$509$	2.04458	+	3.54131i	0.0906243	+	0.156966i	−0.817150	+	0.576426i	$0.804447\pi$
$510$		0			0
$511$	1.99407	−	3.45383i	0.0882125	−	0.152788i
$512$	−21.4962			−0.950006
$513$		0			0
$514$	2.25166			0.0993164
$515$	0.933296	−	1.61652i	0.0411259	−	0.0712322i
$516$		0			0
$517$	−1.93242	−	3.34705i	−0.0849877	−	0.147203i
$518$	−0.292204	−	0.506111i	−0.0128387	−	0.0222373i
$519$		0			0
$520$	−1.01367	+	1.75573i	−0.0444524	+	0.0769938i
$521$	−7.29322			−0.319522			−0.159761	−	0.987156i	$-0.551072\pi$
$521$	−7.29322			−0.319522			−0.159761	+	0.987156i	$0.551072\pi$
$522$		0			0
$523$	−14.3105			−0.625753			−0.312876	−	0.949794i	$-0.601293\pi$
$523$	−14.3105			−0.625753			−0.312876	+	0.949794i	$0.601293\pi$
$524$	−9.71688	+	16.8301i	−0.424484	+	0.735228i
$525$		0			0
$526$	−0.364370	−	0.631108i	−0.0158873	−	0.0275176i
$527$	4.76991	+	8.26173i	0.207781	+	0.359887i
$528$		0			0
$529$	10.5039	−	18.1932i	0.456690	−	0.791010i
$530$	−2.86154			−0.124297
$531$		0			0
$532$	4.18479			0.181434
$533$	10.7353	−	18.5941i	0.464997	−	0.805399i
$534$		0			0
$535$	−3.24035	−	5.61245i	−0.140093	−	0.242648i
$536$	−3.34343	−	5.79098i	−0.144414	−	0.250132i
$537$		0			0
$538$	−5.07903	+	8.79714i	−0.218973	+	0.379272i
$539$	−6.71688			−0.289317
$540$		0			0
$541$	−36.1411			−1.55383			−0.776915	−	0.629606i	$-0.783216\pi$
$541$	−36.1411			−1.55383			−0.776915	+	0.629606i	$0.783216\pi$
$542$	−3.77244	+	6.53406i	−0.162040	+	0.280662i
$543$		0			0
$544$	8.46451	+	14.6610i	0.362913	+	0.628583i
$545$	4.50892	+	7.80968i	0.193141	+	0.334530i
$546$		0			0
$547$	9.39352	−	16.2701i	0.401638	−	0.695657i	−0.592286	−	0.805728i	$-0.701774\pi$
$547$	9.39352	−	16.2701i	0.401638	−	0.695657i	0.993924	+	0.110071i	$0.0351077\pi$
$548$	26.6587			1.13880
$549$		0			0
$550$	1.58853			0.0677350
$551$	−13.2973	+	23.0315i	−0.566482	+	0.981176i
$552$		0			0
$553$	1.29813	+	2.24843i	0.0552022	+	0.0956131i
$554$	−0.773785	−	1.34024i	−0.0328750	−	0.0569411i
$555$		0			0
$556$	0.0949225	−	0.164411i	0.00402561	−	0.00697256i
$557$	3.99319			0.169197			0.0845985	−	0.996415i	$-0.473039\pi$
$557$	3.99319			0.169197			0.0845985	+	0.996415i	$0.473039\pi$
$558$		0			0
$559$	28.3533			1.19922
$560$	0.571452	−	0.989783i	0.0241482	−	0.0418260i
$561$		0			0
$562$	3.55896	+	6.16431i	0.150126	+	0.260026i
$563$	−11.3452	−	19.6505i	−0.478145	−	0.828171i	0.521541	−	0.853226i	$-0.325357\pi$
$563$	−11.3452	−	19.6505i	−0.478145	−	0.828171i	−0.999686	+	0.0250550i	$0.992024\pi$
$564$		0			0
$565$	−0.573978	+	0.994159i	−0.0241474	+	0.0418246i
$566$	−2.39187			−0.100538
$567$		0			0
$568$	−13.4534			−0.564491
$569$	12.6604	−	21.9285i	0.530753	−	0.919292i	−0.468603	−	0.883409i	$-0.655242\pi$
$569$	12.6604	−	21.9285i	0.530753	−	0.919292i	0.999356	−	0.0358828i	$-0.0114243\pi$
$570$		0			0
$571$	−16.6570	−	28.8508i	−0.697075	−	1.20737i	−0.969476	−	0.245186i	$-0.921151\pi$
$571$	−16.6570	−	28.8508i	−0.697075	−	1.20737i	0.272401	−	0.962184i	$-0.412182\pi$
$572$	−2.16637	−	3.75227i	−0.0905807	−	0.156890i
$573$		0			0
$574$	0.860500	−	1.49043i	0.0359166	−	0.0622093i
$575$	6.45605			0.269236
$576$		0			0
$577$	−1.18479			−0.0493236			−0.0246618	−	0.999696i	$-0.507851\pi$
$577$	−1.18479			−0.0493236			−0.0246618	+	0.999696i	$0.507851\pi$
$578$	0.427366	−	0.740220i	0.0177761	−	0.0307891i
$579$		0			0
$580$	3.89780	+	6.75119i	0.161847	+	0.280328i
$581$	−1.22281	−	2.11797i	−0.0507308	−	0.0878682i
$582$		0			0
$583$	6.31180	−	10.9324i	0.261408	−	0.452772i
$584$	−10.0983			−0.417872
$585$		0			0
$586$	−4.79561			−0.198105
$587$	15.9021	−	27.5433i	0.656352	−	1.13683i	−0.325202	−	0.945645i	$-0.605432\pi$
$587$	15.9021	−	27.5433i	0.656352	−	1.13683i	0.981553	−	0.191190i	$-0.0612345\pi$
$588$		0			0
$589$	−4.52481	−	7.83721i	−0.186442	−	0.322927i
$590$	−0.366592	−	0.634956i	−0.0150924	−	0.0261407i
$591$		0			0
$592$	5.20368	−	9.01303i	0.213870	−	0.370433i
$593$	−26.3381			−1.08158			−0.540789	−	0.841159i	$-0.681874\pi$
$593$	−26.3381			−1.08158			−0.540789	+	0.841159i	$0.681874\pi$
$594$		0			0
$595$	−1.53209			−0.0628095
$596$	2.87686	−	4.98287i	0.117841	−	0.204106i
$597$		0			0
$598$	0.565055	+	0.978704i	0.0231068	+	0.0400222i
$599$	7.63223	+	13.2194i	0.311844	+	0.540130i	0.978762	−	0.205002i	$-0.0657199\pi$
$599$	7.63223	+	13.2194i	0.311844	+	0.540130i	−0.666917	+	0.745132i	$0.732387\pi$
$600$		0			0
$601$	−4.25356	+	7.36737i	−0.173506	+	0.300521i	−0.939643	−	0.342156i	$-0.888843\pi$
$601$	−4.25356	+	7.36737i	−0.173506	+	0.300521i	0.766137	+	0.642677i	$0.222176\pi$
$602$	2.27269			0.0926279
$603$		0			0
$604$	−36.4638			−1.48369
$605$	0.326352	−	0.565258i	0.0132681	−	0.0229810i
$606$		0			0
$607$	−6.26011	−	10.8428i	−0.254090	−	0.440097i	0.710558	−	0.703639i	$-0.248443\pi$
$607$	−6.26011	−	10.8428i	−0.254090	−	0.440097i	−0.964648	+	0.263542i	$0.915109\pi$
$608$	−8.02956	−	13.9076i	−0.325642	−	0.564028i
$609$		0			0
$610$	0.967034	−	1.67495i	0.0391541	−	0.0678168i
$611$	−8.91002			−0.360461
$612$		0			0
$613$	−8.52259			−0.344224			−0.172112	−	0.985077i	$-0.555059\pi$
$613$	−8.52259			−0.344224			−0.172112	+	0.985077i	$0.555059\pi$
$614$	−0.104418	+	0.180857i	−0.00421397	+	0.00729880i
$615$		0			0
$616$	−0.358441	−	0.620838i	−0.0144420	−	0.0250143i
$617$	−10.2442	−	17.7435i	−0.412417	−	0.714327i	0.582737	−	0.812661i	$-0.301982\pi$
$617$	−10.2442	−	17.7435i	−0.412417	−	0.714327i	−0.995153	+	0.0983341i	$0.968649\pi$
$618$		0			0
$619$	13.4008	−	23.2109i	0.538623	−	0.932923i	−0.460355	−	0.887735i	$-0.652278\pi$
$619$	13.4008	−	23.2109i	0.538623	−	0.932923i	0.998978	−	0.0451883i	$-0.0143888\pi$
$620$	−2.65270			−0.106535
$621$		0			0
$622$	0.674059			0.0270273
$623$	−4.50980	+	7.81120i	−0.180681	+	0.312949i
$624$		0			0
$625$	−9.39558	−	16.2736i	−0.375823	−	0.650945i
$626$	0.350700	+	0.607430i	0.0140168	+	0.0242778i
$627$		0			0
$628$	−11.9572	+	20.7105i	−0.477146	+	0.826440i
$629$	−13.9513			−0.556275
$630$		0			0
$631$	18.9736			0.755327			0.377663	−	0.925943i	$-0.376728\pi$
$631$	18.9736			0.755327			0.377663	+	0.925943i	$0.376728\pi$
$632$	3.28699	−	5.69323i	0.130749	−	0.226465i
$633$		0			0
$634$	−1.01573	−	1.75930i	−0.0403398	−	0.0698706i
$635$	2.25237	+	3.90123i	0.0893827	+	0.154815i
$636$		0			0
$637$	−7.74257	+	13.4105i	−0.306772	+	0.531345i
$638$	2.20708			0.0873792
$639$		0			0
$640$	−6.19934			−0.245050
$641$	−14.8157	+	25.6615i	−0.585184	+	1.01357i	0.409669	+	0.912234i	$0.365644\pi$
$641$	−14.8157	+	25.6615i	−0.585184	+	1.01357i	−0.994852	+	0.101334i	$0.967689\pi$
$642$		0			0
$643$	−21.7886	−	37.7390i	−0.859260	−	1.48828i	−0.872636	−	0.488371i	$-0.837591\pi$
$643$	−21.7886	−	37.7390i	−0.859260	−	1.48828i	0.0133759	−	0.999911i	$-0.495742\pi$
$644$	−0.705737	−	1.22237i	−0.0278099	−	0.0481682i
$645$		0			0
$646$	−3.20574	+	5.55250i	−0.126128	+	0.218460i
$647$	21.0583			0.827887			0.413944	−	0.910302i	$-0.364151\pi$
$647$	21.0583			0.827887			0.413944	+	0.910302i	$0.364151\pi$
$648$		0			0
$649$	3.23442			0.126962
$650$	1.83110	−	3.17156i	0.0718216	−	0.124399i
$651$		0			0
$652$	−12.0175	−	20.8150i	−0.470643	−	0.815178i
$653$	0.669778	+	1.16009i	0.0262104	+	0.0453978i	0.878833	−	0.477129i	$-0.158323\pi$
$653$	0.669778	+	1.16009i	0.0262104	+	0.0453978i	−0.852623	+	0.522527i	$0.824989\pi$
$654$		0			0
$655$	−3.37464	+	5.84504i	−0.131858	+	0.228385i
$656$	30.6483			1.19661
$657$		0			0
$658$	−0.714193			−0.0278421
$659$	−9.47296	+	16.4077i	−0.369014	+	0.639151i	−0.989412	−	0.145136i	$-0.953638\pi$
$659$	−9.47296	+	16.4077i	−0.369014	+	0.639151i	0.620397	+	0.784288i	$0.286971\pi$
$660$		0			0
$661$	−13.8059	−	23.9125i	−0.536986	−	0.930087i	−0.999064	−	0.0432483i	$-0.986229\pi$
$661$	−13.8059	−	23.9125i	−0.536986	−	0.930087i	0.462078	−	0.886839i	$-0.347104\pi$
$662$	2.03549	+	3.52558i	0.0791117	+	0.137025i
$663$		0			0
$664$	−3.09627	+	5.36289i	−0.120158	+	0.208121i
$665$	1.45336			0.0563590
$666$		0			0
$667$	8.96997			0.347319
$668$	−19.4748	+	33.7313i	−0.753502	+	1.30510i
$669$		0			0
$670$	−0.562529	−	0.974329i	−0.0217324	−	0.0376416i
$671$	4.26604	+	7.38901i	0.164689	+	0.285249i
$672$		0			0
$673$	−10.3712	+	17.9635i	−0.399782	+	0.692442i	−0.993699	−	0.112084i	$-0.964247\pi$
$673$	−10.3712	+	17.9635i	−0.399782	+	0.692442i	0.593917	+	0.804526i	$0.297581\pi$
$674$	−4.37464			−0.168505
$675$		0			0
$676$	14.4433			0.555510
$677$	−13.8032	+	23.9078i	−0.530500	+	0.918852i	0.468867	+	0.883269i	$0.344662\pi$
$677$	−13.8032	+	23.9078i	−0.530500	+	0.918852i	−0.999367	+	0.0355834i	$0.988671\pi$
$678$		0			0
$679$	−3.36437	−	5.82726i	−0.129113	−	0.223630i
$680$	1.93969	+	3.35965i	0.0743838	+	0.128837i
$681$		0			0
$682$	−0.375515	+	0.650411i	−0.0143792	+	0.0249055i
$683$	−31.4843			−1.20471			−0.602357	−	0.798227i	$-0.705772\pi$
$683$	−31.4843			−1.20471			−0.602357	+	0.798227i	$0.705772\pi$
$684$		0			0
$685$	9.25847			0.353748
$686$	−1.26739	+	2.19518i	−0.0483891	+	0.0838124i
$687$		0			0
$688$	20.2365	+	35.0506i	0.771509	+	1.33629i
$689$	−14.5513	−	25.2036i	−0.554360	−	0.960179i
$690$		0			0
$691$	11.9440	−	20.6877i	0.454372	−	0.786996i	−0.544280	−	0.838904i	$-0.683197\pi$
$691$	11.9440	−	20.6877i	0.454372	−	0.786996i	0.998652	+	0.0519080i	$0.0165303\pi$
$692$	−42.2918			−1.60769
$693$		0			0
$694$	−8.28136			−0.314356
$695$	0.0329662	−	0.0570992i	0.00125048	−	0.00216590i
$696$		0			0
$697$	−20.5424	−	35.5804i	−0.778097	−	1.34770i
$698$	−1.47296	−	2.55125i	−0.0557525	−	0.0965662i
$699$		0			0
$700$	−2.28699	+	3.96118i	−0.0864401	+	0.149719i
$701$	−7.03684			−0.265778			−0.132889	−	0.991131i	$-0.542425\pi$
$701$	−7.03684			−0.265778			−0.132889	+	0.991131i	$0.542425\pi$
$702$		0			0
$703$	13.2344			0.499146
$704$	2.62449	−	4.54574i	0.0989140	−	0.171324i
$705$		0			0
$706$	−1.29308	−	2.23968i	−0.0486657	−	0.0842915i
$707$	4.54710	+	7.87581i	0.171011	+	0.296200i
$708$		0			0
$709$	6.45037	−	11.1724i	0.242249	−	0.419587i	−0.719106	−	0.694901i	$-0.755448\pi$
$709$	6.45037	−	11.1724i	0.242249	−	0.419587i	0.961354	+	0.275314i	$0.0887817\pi$
$710$	−2.26352			−0.0849483
$711$		0			0
$712$	22.8384			0.855906
$713$	−1.52616	+	2.64339i	−0.0571551	+	0.0989956i
$714$		0			0
$715$	−0.752374	−	1.30315i	−0.0281372	−	0.0487350i
$716$	10.0753	+	17.4510i	0.376532	+	0.652173i
$717$		0			0
$718$	3.98158	−	6.89630i	0.148591	−	0.257368i
$719$	−17.2671			−0.643956			−0.321978	−	0.946747i	$-0.604348\pi$
$719$	−17.2671			−0.643956			−0.321978	+	0.946747i	$0.604348\pi$
$720$		0			0
$721$	1.52166			0.0566696
$722$	−0.258304	+	0.447395i	−0.00961307	+	0.0166503i
$723$		0			0
$724$	−3.90673	−	6.76665i	−0.145192	−	0.251481i
$725$	−14.5339	−	25.1735i	−0.539775	−	0.934919i
$726$		0			0
$727$	−20.3033	+	35.1664i	−0.753009	+	1.30425i	0.193348	+	0.981130i	$0.438065\pi$
$727$	−20.3033	+	35.1664i	−0.753009	+	1.30425i	−0.946358	+	0.323121i	$0.895268\pi$
$728$	−1.65270			−0.0612533
$729$		0			0
$730$	−1.69904			−0.0628841
$731$	27.1275	−	46.9862i	1.00335	−	1.73785i
$732$		0			0
$733$	7.87464	+	13.6393i	0.290856	+	0.503778i	0.974012	−	0.226494i	$-0.0727265\pi$
$733$	7.87464	+	13.6393i	0.290856	+	0.503778i	−0.683156	+	0.730272i	$0.739393\pi$
$734$	2.65792	+	4.60365i	0.0981056	+	0.169924i
$735$		0			0
$736$	−2.70826	+	4.69085i	−0.0998279	+	0.172907i
$737$	4.96316			0.182820
$738$		0			0
$739$	2.27538			0.0837011			0.0418506	−	0.999124i	$-0.486675\pi$
$739$	2.27538			0.0837011			0.0418506	+	0.999124i	$0.486675\pi$
$740$	1.93969	−	3.35965i	0.0713045	−	0.123503i
$741$		0			0
$742$	−1.16637	−	2.02022i	−0.0428189	−	0.0741646i
$743$	−17.5868	−	30.4612i	−0.645196	−	1.11751i	−0.984256	−	0.176748i	$-0.943442\pi$
$743$	−17.5868	−	30.4612i	−0.645196	−	1.11751i	0.339060	−	0.940765i	$-0.389891\pi$
$744$		0			0
$745$	0.999123	−	1.73053i	0.0366050	−	0.0634018i
$746$	9.51249			0.348277
$747$		0			0
$748$	−8.29086			−0.303144
$749$	2.64156	−	4.57531i	0.0965205	−	0.167178i
$750$		0			0
$751$	16.7533	+	29.0176i	0.611337	+	1.05887i	0.991015	+	0.133748i	$0.0427013\pi$
$751$	16.7533	+	29.0176i	0.611337	+	1.05887i	−0.379678	+	0.925118i	$0.623965\pi$
$752$	−6.35932	−	11.0147i	−0.231900	−	0.401663i
$753$		0			0
$754$	2.54411	−	4.40653i	0.0926510	−	0.160476i
$755$	−12.6637			−0.460881
$756$		0			0
$757$	45.4570			1.65216			0.826081	−	0.563551i	$-0.190565\pi$
$757$	45.4570			1.65216			0.826081	+	0.563551i	$0.190565\pi$
$758$	1.95723	−	3.39003i	0.0710899	−	0.123131i
$759$		0			0
$760$	−1.84002	−	3.18701i	−0.0667446	−	0.115605i
$761$	−14.6370	−	25.3520i	−0.530590	−	0.919009i	−0.999363	−	0.0356900i	$-0.988637\pi$
$761$	−14.6370	−	25.3520i	−0.530590	−	0.919009i	0.468773	−	0.883319i	$-0.344696\pi$
$762$		0			0
$763$	−3.67571	+	6.36651i	−0.133070	+	0.230483i
$764$	4.51754			0.163439
$765$		0			0
$766$	11.5868			0.418647
$767$	3.72833	−	6.45766i	0.134622	−	0.233173i
$768$		0			0
$769$	22.1830	+	38.4221i	0.799941	+	1.38554i	0.919654	+	0.392730i	$0.128469\pi$
$769$	22.1830	+	38.4221i	0.799941	+	1.38554i	−0.119713	+	0.992809i	$0.538198\pi$
$770$	−0.0603074	−	0.104455i	−0.00217333	−	0.00376431i
$771$		0			0
$772$	−0.426022	+	0.737892i	−0.0153329	+	0.0265573i
$773$	21.6372			0.778237			0.389118	−	0.921188i	$-0.372780\pi$
$773$	21.6372			0.778237			0.389118	+	0.921188i	$0.372780\pi$
$774$		0			0
$775$	9.89124			0.355304
$776$	−8.51889	+	14.7551i	−0.305810	+	0.529679i
$777$		0			0
$778$	−2.12701	−	3.68409i	−0.0762571	−	0.132081i
$779$	19.4868	+	33.7521i	0.698187	+	1.20930i
$780$		0			0
$781$	4.99273	−	8.64766i	0.178654	−	0.309437i
$782$	2.16250			0.0773310
$783$		0			0
$784$	−22.1043			−0.789440
$785$	−4.15270	+	7.19269i	−0.148216	+	0.256718i
$786$		0			0
$787$	−9.39171	−	16.2669i	−0.334778	−	0.579853i	0.648664	−	0.761075i	$-0.275328\pi$
$787$	−9.39171	−	16.2669i	−0.334778	−	0.579853i	−0.983442	+	0.181222i	$0.941995\pi$
$788$	18.4402	+	31.9393i	0.656903	+	1.13779i
$789$		0			0
$790$	0.553033	−	0.957882i	0.0196760	−	0.0340799i
$791$	−0.935822			−0.0332740
$792$		0			0
$793$	19.6699			0.698500
$794$	−1.98457	+	3.43738i	−0.0704299	+	0.121988i
$795$		0			0
$796$	3.41147	+	5.90885i	0.120916	+	0.209434i
$797$	13.8601	+	24.0064i	0.490950	+	0.850350i	0.999946	−	0.0104192i	$-0.00331660\pi$
$797$	13.8601	+	24.0064i	0.490950	+	0.850350i	−0.508996	+	0.860769i	$0.669983\pi$
$798$		0			0
$799$	−8.52481	+	14.7654i	−0.301586	+	0.522363i
$800$	17.5526			0.620579
$801$		0			0
$802$	7.53445			0.266051
$803$	3.74763	−	6.49108i	0.132251	−	0.229065i
$804$		0			0
$805$	−0.245100	−	0.424525i	−0.00863864	−	0.0149626i
$806$	0.865715	+	1.49946i	0.0304935	+	0.0528163i
$807$		0			0
$808$	11.5137	−	19.9423i	0.405050	−	0.701566i
$809$	5.05737			0.177808			0.0889038	−	0.996040i	$-0.471664\pi$
$809$	5.05737			0.177808			0.0889038	+	0.996040i	$0.471664\pi$
$810$		0			0
$811$	25.6709			0.901426			0.450713	−	0.892669i	$-0.351170\pi$
$811$	25.6709			0.901426			0.450713	+	0.892669i	$0.351170\pi$
$812$	−3.17752	+	5.50362i	−0.111509	+	0.193139i
$813$		0			0
$814$	−0.549163	−	0.951178i	−0.0192482	−	0.0333388i
$815$	−4.17365	−	7.22897i	−0.146197	−	0.253220i
$816$		0			0
$817$	−25.7335	+	44.5718i	−0.900303	+	1.55937i
$818$	9.92902			0.347160
$819$		0			0
$820$	11.4243			0.398953
$821$	1.93242	−	3.34705i	0.0674419	−	0.116813i	−0.830333	−	0.557268i	$-0.811850\pi$
$821$	1.93242	−	3.34705i	0.0674419	−	0.116813i	0.897775	+	0.440455i	$0.145183\pi$
$822$		0			0
$823$	−13.9179	−	24.1065i	−0.485146	−	0.840298i	0.514708	−	0.857366i	$-0.327900\pi$
$823$	−13.9179	−	24.1065i	−0.485146	−	0.840298i	−0.999854	+	0.0170673i	$0.994567\pi$
$824$	−1.92649	−	3.33678i	−0.0671124	−	0.116242i
$825$		0			0
$826$	0.298849	−	0.517621i	0.0103983	−	0.0180103i
$827$	1.24392			0.0432553			0.0216276	−	0.999766i	$-0.493115\pi$
$827$	1.24392			0.0432553			0.0216276	+	0.999766i	$0.493115\pi$
$828$		0			0
$829$	−31.5794			−1.09680			−0.548398	−	0.836217i	$-0.684762\pi$
$829$	−31.5794			−1.09680			−0.548398	+	0.836217i	$0.684762\pi$
$830$	−0.520945	+	0.902302i	−0.0180822	+	0.0313194i
$831$		0			0
$832$	−6.05051	−	10.4798i	−0.209764	−	0.363321i
$833$	14.8157	+	25.6615i	0.513333	+	0.889118i
$834$		0			0
$835$	−6.76352	+	11.7148i	−0.234061	+	0.405406i
$836$	7.86484			0.272011
$837$		0			0
$838$	−2.99050			−0.103305
$839$	4.93360	−	8.54525i	0.170327	−	0.295015i	−0.768207	−	0.640201i	$-0.778851\pi$
$839$	4.93360	−	8.54525i	0.170327	−	0.295015i	0.938534	+	0.345186i	$0.112184\pi$
$840$		0			0
$841$	−5.69325	−	9.86100i	−0.196319	−	0.340034i
$842$	−5.97906	−	10.3560i	−0.206052	−	0.356892i
$843$		0			0
$844$	20.3662	−	35.2753i	0.701033	−	1.21422i
$845$	5.01609			0.172559
$846$		0			0
$847$	0.532089			0.0182828
$848$	20.7713	−	35.9769i	0.713288	−	1.23545i
$849$		0			0
$850$	−3.50387	−	6.06888i	−0.120182	−	0.208161i
$851$	−2.23190	−	3.86576i	−0.0765084	−	0.132516i
$852$		0			0
$853$	−28.7683	+	49.8282i	−0.985009	+	1.70608i	−0.343110	+	0.939295i	$0.611480\pi$
$853$	−28.7683	+	49.8282i	−0.985009	+	1.70608i	−0.641898	+	0.766790i	$0.721853\pi$
$854$	1.57667			0.0539524
$855$		0			0
$856$	−13.3773			−0.457228
$857$	−7.70187	+	13.3400i	−0.263091	+	0.455687i	−0.967062	−	0.254542i	$-0.918075\pi$
$857$	−7.70187	+	13.3400i	−0.263091	+	0.455687i	0.703971	+	0.710229i	$0.251409\pi$
$858$		0			0
$859$	21.2866	+	36.8694i	0.726289	+	1.25797i	0.958441	+	0.285290i	$0.0920898\pi$
$859$	21.2866	+	36.8694i	0.726289	+	1.25797i	−0.232153	+	0.972679i	$0.574577\pi$
$860$	7.54323	+	13.0653i	0.257222	+	0.445522i
$861$		0			0
$862$	−2.47384	+	4.28482i	−0.0842594	+	0.145941i
$863$	38.3536			1.30557			0.652786	−	0.757542i	$-0.273600\pi$
$863$	38.3536			1.30557			0.652786	+	0.757542i	$0.273600\pi$
$864$		0			0
$865$	−14.6878			−0.499400
$866$	−4.27214	+	7.39956i	−0.145173	+	0.251447i
$867$		0			0
$868$	−1.08125	−	1.87278i	−0.0367001	−	0.0635664i
$869$	2.43969	+	4.22567i	0.0827609	+	0.143346i
$870$		0			0
$871$	5.72106	−	9.90916i	0.193851	−	0.335759i
$872$	18.6144			0.630364
$873$		0			0
$874$	−2.05138			−0.0693891
$875$	−1.66250	+	2.87954i	−0.0562029	+	0.0973463i
$876$		0			0
$877$	6.23514	+	10.7996i	0.210546	+	0.364676i	0.951885	−	0.306454i	$-0.0991426\pi$
$877$	6.23514	+	10.7996i	0.210546	+	0.364676i	−0.741340	+	0.671130i	$0.765809\pi$
$878$	0.724622	+	1.25508i	0.0244548	+	0.0423570i
$879$		0			0
$880$	1.07398	−	1.86018i	0.0362038	−	0.0627068i
$881$	22.9172			0.772099			0.386049	−	0.922478i	$-0.373839\pi$
$881$	22.9172			0.772099			0.386049	+	0.922478i	$0.373839\pi$
$882$		0			0
$883$	44.2300			1.48846			0.744229	−	0.667925i	$-0.232817\pi$
$883$	44.2300			1.48846			0.744229	+	0.667925i	$0.232817\pi$
$884$	−9.55690	+	16.5530i	−0.321433	+	0.556739i
$885$		0			0
$886$	5.08172	+	8.80180i	0.170724	+	0.295702i
$887$	12.3871	+	21.4551i	0.415919	+	0.720393i	0.995524	−	0.0945044i	$-0.0301267\pi$
$887$	12.3871	+	21.4551i	0.415919	+	0.720393i	−0.579605	+	0.814897i	$0.696793\pi$
$888$		0			0
$889$	−1.83615	+	3.18031i	−0.0615826	+	0.106664i
$890$	3.84255			0.128803
$891$		0			0
$892$	−35.9641			−1.20417
$893$	8.08677	−	14.0067i	0.270613	−	0.468716i
$894$		0			0
$895$	3.49912	+	6.06066i	0.116963	+	0.202585i
$896$	−2.52687	−	4.37667i	−0.0844169	−	0.146214i
$897$		0			0
$898$	2.74288	−	4.75080i	0.0915310	−	0.158536i
$899$	13.7428			0.458348
$900$		0			0
$901$	−55.6887			−1.85526
$902$	1.61721	−	2.80109i	0.0538472	−	0.0932662i
$903$		0			0
$904$	1.18479	+	2.05212i	0.0394056	+	0.0682525i
$905$	−1.35679	−	2.35003i	−0.0451013	−	0.0781177i
$906$		0			0
$907$	−15.2490	+	26.4120i	−0.506334	+	0.876996i	0.493639	+	0.869667i	$0.335666\pi$
$907$	−15.2490	+	26.4120i	−0.506334	+	0.876996i	−0.999973	+	0.00732909i	$0.997667\pi$
$908$	−29.3063			−0.972565
$909$		0			0
$910$	−0.278066			−0.00921780
$911$	26.9413	−	46.6638i	0.892606	−	1.54604i	0.0558672	−	0.998438i	$-0.482208\pi$
$911$	26.9413	−	46.6638i	0.892606	−	1.54604i	0.836739	−	0.547602i	$-0.184459\pi$
$912$		0			0
$913$	−2.29813	−	3.98048i	−0.0760571	−	0.131735i
$914$	1.64708	+	2.85282i	0.0544805	+	0.0943630i
$915$		0			0
$916$	−14.4820	+	25.0836i	−0.478500	+	0.828787i
$917$	−5.50206			−0.181694
$918$		0			0
$919$	5.19841			0.171480			0.0857398	−	0.996318i	$-0.472675\pi$
$919$	5.19841			0.171480			0.0857398	+	0.996318i	$0.472675\pi$
$920$	−0.620615	+	1.07494i	−0.0204611	+	0.0354396i
$921$		0			0
$922$	5.02616	+	8.70556i	0.165528	+	0.286702i
$923$	−11.5103	−	19.9364i	−0.378865	−	0.656214i
$924$		0			0
$925$	−7.23261	+	12.5273i	−0.237807	+	0.411893i
$926$	7.94625			0.261130
$927$		0			0
$928$	24.3874			0.800557
$929$	−11.9368	+	20.6751i	−0.391632	+	0.678327i	−0.992665	−	0.120897i	$-0.961423\pi$
$929$	−11.9368	+	20.6751i	−0.391632	+	0.678327i	0.601033	+	0.799224i	$0.294756\pi$
$930$		0			0
$931$	−14.0544	−	24.3429i	−0.460614	−	0.797806i
$932$	−4.03209	−	6.98378i	−0.132075	−	0.228761i
$933$		0			0
$934$	−1.77837	+	3.08023i	−0.0581901	+	0.100788i
$935$	−2.87939			−0.0941660
$936$		0			0
$937$	18.7219			0.611619			0.305809	−	0.952093i	$-0.401073\pi$
$937$	18.7219			0.611619			0.305809	+	0.952093i	$0.401073\pi$
$938$	0.458578	−	0.794280i	0.0149731	−	0.0259342i
$939$		0			0
$940$	−2.37046	−	4.10576i	−0.0773160	−	0.133915i
$941$	16.7814	+	29.0662i	0.547057	+	0.947530i	0.998474	+	0.0552174i	$0.0175852\pi$
$941$	16.7814	+	29.0662i	0.547057	+	0.947530i	−0.451418	+	0.892313i	$0.649081\pi$
$942$		0			0
$943$	6.57263	−	11.3841i	0.214034	−	0.370718i
$944$	10.6440			0.346434
$945$		0			0
$946$	4.27126			0.138871
$947$	−21.8380	+	37.8245i	−0.709638	+	1.22913i	0.255353	+	0.966848i	$0.417808\pi$
$947$	−21.8380	+	37.8245i	−0.709638	+	1.22913i	−0.964991	+	0.262282i	$0.915525\pi$
$948$		0			0
$949$	−8.63980	−	14.9646i	−0.280460	−	0.485771i
$950$	3.32383	+	5.75703i	0.107839	+	0.186783i
$951$		0			0
$952$	−1.58125	+	2.73881i	−0.0512487	+	0.0887653i
$953$	−39.4397			−1.27758			−0.638789	−	0.769382i	$-0.720564\pi$
$953$	−39.4397			−1.27758			−0.638789	+	0.769382i	$0.720564\pi$
$954$		0			0
$955$	1.56893			0.0507692
$956$	18.9192	−	32.7690i	0.611891	−	1.05983i
$957$		0			0
$958$	−3.35679	−	5.81413i	−0.108453	−	0.187846i
$959$	3.77379	+	6.53639i	0.121862	+	0.211071i
$960$		0			0
$961$	13.1618	−	22.7969i	0.424574	−	0.735383i
$962$	−2.53209			−0.0816378
$963$		0			0
$964$	13.9932			0.450690
$965$	−0.147956	+	0.256267i	−0.00476287	+	0.00824953i
$966$		0			0
$967$	−3.29426	−	5.70583i	−0.105936	−	0.183487i	0.808184	−	0.588930i	$-0.200451\pi$
$967$	−3.29426	−	5.70583i	−0.105936	−	0.183487i	−0.914120	+	0.405443i	$0.867117\pi$
$968$	−0.673648	−	1.16679i	−0.0216519	−	0.0375021i
$969$		0			0
$970$	−1.43330	+	2.48254i	−0.0460204	+	0.0797096i
$971$	−17.0327			−0.546606			−0.273303	−	0.961928i	$-0.588116\pi$
$971$	−17.0327			−0.546606			−0.273303	+	0.961928i	$0.588116\pi$
$972$		0			0
$973$	0.0537486			0.00172310
$974$	4.72503	−	8.18400i	0.151400	−	0.262232i
$975$		0			0
$976$	14.0390	+	24.3162i	0.449376	+	0.778342i
$977$	3.77450	+	6.53763i	0.120757	+	0.209157i	0.920066	−	0.391762i	$-0.128134\pi$
$977$	3.77450	+	6.53763i	0.120757	+	0.209157i	−0.799309	+	0.600920i	$0.794801\pi$
$978$		0			0
$979$	−8.47565	+	14.6803i	−0.270883	+	0.469183i
$980$	−8.23947			−0.263200
$981$		0			0
$982$	−12.5158			−0.399395
$983$	−1.92350	+	3.33159i	−0.0613500	+	0.106261i	−0.895069	−	0.445928i	$-0.852874\pi$
$983$	−1.92350	+	3.33159i	−0.0613500	+	0.106261i	0.833719	+	0.552189i	$0.186207\pi$
$984$		0			0
$985$	6.40420	+	11.0924i	0.204055	+	0.353433i
$986$	−4.86824	−	8.43204i	−0.155036	−	0.268531i
$987$		0			0
$988$	9.06583	−	15.7025i	0.288422	−	0.499562i
$989$	17.3592			0.551989
$990$		0			0
$991$	40.1121			1.27420			0.637101	−	0.770781i	$-0.280134\pi$
$991$	40.1121			1.27420			0.637101	+	0.770781i	$0.280134\pi$
$992$	−4.14930	+	7.18680i	−0.131740	+	0.228181i
$993$		0			0
$994$	−0.922618	−	1.59802i	−0.0292637	−	0.0506862i
$995$	1.18479	+	2.05212i	0.0375604	+	0.0650566i
$996$		0			0
$997$	8.28240	−	14.3455i	0.262306	−	0.454328i	−0.704548	−	0.709656i	$-0.748850\pi$
$997$	8.28240	−	14.3455i	0.262306	−	0.454328i	0.966854	+	0.255328i	$0.0821836\pi$
$998$	2.74092			0.0867625
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.d.100.2		6
3.2	odd	2		99.2.e.d.34.2	✓	6
9.2	odd	6		891.2.a.l.1.2		3
9.4	even	3	inner	297.2.e.d.199.2		6
9.5	odd	6		99.2.e.d.67.2	yes	6
9.7	even	3		891.2.a.k.1.2		3
33.32	even	2		1089.2.e.h.727.2		6
99.32	even	6		1089.2.e.h.364.2		6
99.43	odd	6		9801.2.a.bd.1.2		3
99.65	even	6		9801.2.a.be.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.d.34.2	✓	6	3.2	odd	2
99.2.e.d.67.2	yes	6	9.5	odd	6
297.2.e.d.100.2		6	1.1	even	1	trivial
297.2.e.d.199.2		6	9.4	even	3	inner
891.2.a.k.1.2		3	9.7	even	3
891.2.a.l.1.2		3	9.2	odd	6
1089.2.e.h.364.2		6	99.32	even	6
1089.2.e.h.727.2		6	33.32	even	2
9801.2.a.bd.1.2		3	99.43	odd	6
9801.2.a.be.1.2		3	99.65	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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.300767i) q^{2} +(0.939693 + 1.62760i) q^{4} +(0.326352 + 0.565258i) q^{5} +(-0.266044 + 0.460802i) q^{7} +1.34730 q^{8} +0.226682 q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.15270 + 1.99654i) q^{13} +(0.0923963 + 0.160035i) q^{14} +(-1.64543 + 2.84997i) q^{16} +4.41147 q^{17} -4.18479 q^{19} +(-0.613341 + 1.06234i) q^{20} +(0.173648 + 0.300767i) q^{22} +(0.705737 + 1.22237i) q^{23} +(2.28699 - 3.96118i) q^{25} +0.800660 q^{26} -1.00000 q^{28} +(3.17752 - 5.50362i) q^{29} +(1.08125 + 1.87278i) q^{31} +(1.91875 + 3.32337i) q^{32} +(0.766044 - 1.32683i) q^{34} -0.347296 q^{35} -3.16250 q^{37} +(-0.726682 + 1.25865i) q^{38} +(0.439693 + 0.761570i) q^{40} +(-4.65657 - 8.06542i) q^{41} +(6.14930 - 10.6509i) q^{43} -1.87939 q^{44} +0.490200 q^{46} +(-1.93242 + 3.34705i) q^{47} +(3.35844 + 5.81699i) q^{49} +(-0.794263 - 1.37570i) q^{50} +(-2.16637 + 3.75227i) q^{52} -12.6236 q^{53} -0.652704 q^{55} +(-0.358441 + 0.620838i) q^{56} +(-1.10354 - 1.91139i) q^{58} +(-1.61721 - 2.80109i) q^{59} +(4.26604 - 7.38901i) q^{61} +0.751030 q^{62} -5.24897 q^{64} +(-0.752374 + 1.30315i) q^{65} +(-2.48158 - 4.29823i) q^{67} +(4.14543 + 7.18009i) q^{68} +(-0.0603074 + 0.104455i) q^{70} -9.98545 q^{71} -7.49525 q^{73} +(-0.549163 + 0.951178i) q^{74} +(-3.93242 - 6.81115i) q^{76} +(-0.266044 - 0.460802i) q^{77} +(2.43969 - 4.22567i) q^{79} -2.14796 q^{80} -3.23442 q^{82} +(-2.29813 + 3.98048i) q^{83} +(1.43969 + 2.49362i) q^{85} +(-2.13563 - 3.69902i) q^{86} +(-0.673648 + 1.16679i) q^{88} +16.9513 q^{89} -1.22668 q^{91} +(-1.32635 + 2.29731i) q^{92} +(0.671122 + 1.16242i) q^{94} +(-1.36571 - 2.36549i) q^{95} +(-6.32295 + 10.9517i) q^{97} +2.33275 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 6 q^{8} - 12 q^{10} - 3 q^{11} + 9 q^{13} - 3 q^{14} + 6 q^{16} + 6 q^{17} - 18 q^{19} + 3 q^{20} - 6 q^{23} + 6 q^{25} - 24 q^{26} - 6 q^{28} - 6 q^{29} + 9 q^{31} + 9 q^{32}+ \cdots - 24 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 6 * q^8 - 12 * q^10 - 3 * q^11 + 9 * q^13 - 3 * q^14 + 6 * q^16 + 6 * q^17 - 18 * q^19 + 3 * q^20 - 6 * q^23 + 6 * q^25 - 24 * q^26 - 6 * q^28 - 6 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^37 + 9 * q^38 - 3 * q^40 - 6 * q^41 - 3 * q^43 + 12 * q^47 + 12 * q^49 - 15 * q^50 + 6 * q^52 - 6 * q^53 - 6 * q^55 + 6 * q^56 + 3 * q^58 + 21 * q^59 + 21 * q^61 + 30 * q^62 - 6 * q^64 - 21 * q^65 - 3 * q^67 + 9 * q^68 - 6 * q^70 - 24 * q^71 - 12 * q^73 - 15 * q^74 + 3 * q^77 + 9 * q^79 + 18 * q^80 + 42 * q^82 + 3 * q^85 + 6 * q^86 - 3 * q^88 + 24 * q^89 + 6 * q^91 - 9 * q^92 + 18 * q^94 - 18 * q^95 + 3 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more