LMFDB - Embedded newform 693.2.i.j.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(100,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("693.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15x^{8} + 72x^{6} + 120x^{4} + 72x^{2} + 12 $ x^10 + 15x^8 + 72x^6 + 120x^4 + 72x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.2
Root			$2.42024i$ of defining polynomial
Character	$\chi$	$=$	693.100
Dual form			693.2.i.j.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.534421 + 0.925645i) q^{2} +(0.428788 + 0.742682i) q^{4} +(-1.34592 + 2.33120i) q^{5} +(-0.855706 + 2.50355i) q^{7} -3.05430 q^{8} +O(q^{10})$	\(q+(-0.534421 + 0.925645i) q^{2} +(0.428788 + 0.742682i) q^{4} +(-1.34592 + 2.33120i) q^{5} +(-0.855706 + 2.50355i) q^{7} -3.05430 q^{8} +(-1.43858 - 2.49169i) q^{10} +(0.500000 + 0.866025i) q^{11} -3.28888 q^{13} +(-1.86009 - 2.13003i) q^{14} +(0.774707 - 1.34183i) q^{16} +(-0.534421 - 0.925645i) q^{17} +(3.17886 - 5.50595i) q^{19} -2.30845 q^{20} -1.06884 q^{22} +(-0.774707 + 1.34183i) q^{23} +(-1.12300 - 1.94508i) q^{25} +(1.75765 - 3.04433i) q^{26} +(-2.22626 + 0.437974i) q^{28} +8.57566 q^{29} +(-1.92879 - 3.34076i) q^{31} +(-2.22626 - 3.85599i) q^{32} +1.14242 q^{34} +(-4.68457 - 5.36440i) q^{35} +(-3.91476 + 6.78057i) q^{37} +(3.39770 + 5.88499i) q^{38} +(4.11084 - 7.12018i) q^{40} +6.87715 q^{41} -2.76571 q^{43} +(-0.428788 + 0.742682i) q^{44} +(-0.828039 - 1.43421i) q^{46} +(-4.56647 + 7.90936i) q^{47} +(-5.53553 - 4.28461i) q^{49} +2.40061 q^{50} +(-1.41023 - 2.44259i) q^{52} +(-1.77722 - 3.07824i) q^{53} -2.69184 q^{55} +(2.61358 - 7.64659i) q^{56} +(-4.58301 + 7.93801i) q^{58} +(-0.774707 - 1.34183i) q^{59} +(-6.18471 + 10.7122i) q^{61} +4.12314 q^{62} +7.85787 q^{64} +(4.42656 - 7.66703i) q^{65} +(4.05193 + 7.01815i) q^{67} +(0.458307 - 0.793810i) q^{68} +(7.46906 - 1.46939i) q^{70} -10.4350 q^{71} +(-7.12501 - 12.3409i) q^{73} +(-4.18426 - 7.24736i) q^{74} +5.45223 q^{76} +(-2.59599 + 0.510712i) q^{77} +(-4.69371 + 8.12974i) q^{79} +(2.08538 + 3.61199i) q^{80} +(-3.67530 + 6.36580i) q^{82} -2.46916 q^{83} +2.87715 q^{85} +(1.47806 - 2.56007i) q^{86} +(-1.52715 - 2.64510i) q^{88} +(-5.81498 + 10.0718i) q^{89} +(2.81431 - 8.23388i) q^{91} -1.32874 q^{92} +(-4.88084 - 8.45386i) q^{94} +(8.55698 + 14.8211i) q^{95} +12.6644 q^{97} +(6.92433 - 2.83415i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 10 q^{4} - 4 q^{5} - q^{7} - 12 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 - 10 * q^4 - 4 * q^5 - q^7 - 12 * q^8	$ 10 q + 2 q^{2} - 10 q^{4} - 4 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 5 q^{11} + 10 q^{13} + 10 q^{14} - 16 q^{16} + 2 q^{17} + 3 q^{19} + 16 q^{20} + 4 q^{22} + 16 q^{23} - 7 q^{25} - 10 q^{26} + 4 q^{28} - 5 q^{31} + 4 q^{32} + 40 q^{34} - 26 q^{35} - 15 q^{37} + 6 q^{38} + 6 q^{40} + 44 q^{41} + 6 q^{43} + 10 q^{44} - 16 q^{46} - 2 q^{47} + 31 q^{49} - 68 q^{50} - 40 q^{52} + 6 q^{53} - 8 q^{55} + 12 q^{56} - 12 q^{58} + 16 q^{59} - 12 q^{61} + 8 q^{62} - 8 q^{64} - 28 q^{65} - 7 q^{67} + 10 q^{68} + 32 q^{70} - 48 q^{71} - 17 q^{73} - 36 q^{74} + 60 q^{76} - 2 q^{77} - 7 q^{79} + 16 q^{80} - 8 q^{82} + 24 q^{83} + 4 q^{85} - 18 q^{86} - 6 q^{88} - 6 q^{89} + 11 q^{91} - 136 q^{92} - 82 q^{94} - 18 q^{95} - 28 q^{97} + 38 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 10 * q^4 - 4 * q^5 - q^7 - 12 * q^8 - 2 * q^10 + 5 * q^11 + 10 * q^13 + 10 * q^14 - 16 * q^16 + 2 * q^17 + 3 * q^19 + 16 * q^20 + 4 * q^22 + 16 * q^23 - 7 * q^25 - 10 * q^26 + 4 * q^28 - 5 * q^31 + 4 * q^32 + 40 * q^34 - 26 * q^35 - 15 * q^37 + 6 * q^38 + 6 * q^40 + 44 * q^41 + 6 * q^43 + 10 * q^44 - 16 * q^46 - 2 * q^47 + 31 * q^49 - 68 * q^50 - 40 * q^52 + 6 * q^53 - 8 * q^55 + 12 * q^56 - 12 * q^58 + 16 * q^59 - 12 * q^61 + 8 * q^62 - 8 * q^64 - 28 * q^65 - 7 * q^67 + 10 * q^68 + 32 * q^70 - 48 * q^71 - 17 * q^73 - 36 * q^74 + 60 * q^76 - 2 * q^77 - 7 * q^79 + 16 * q^80 - 8 * q^82 + 24 * q^83 + 4 * q^85 - 18 * q^86 - 6 * q^88 - 6 * q^89 + 11 * q^91 - 136 * q^92 - 82 * q^94 - 18 * q^95 - 28 * q^97 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.534421	+	0.925645i	−0.377893	+	0.654530i	−0.990755	−	0.135660i	$-0.956685\pi$
$2$	−0.534421	+	0.925645i	−0.377893	+	0.654530i	0.612863	+	0.790190i	$0.290018\pi$
$3$		0			0
$3$		0			0
$4$	0.428788	+	0.742682i	0.214394	+	0.371341i
$5$	−1.34592	+	2.33120i	−0.601913	+	1.04254i	0.390618	+	0.920553i	$0.372261\pi$
$5$	−1.34592	+	2.33120i	−0.601913	+	1.04254i	−0.992531	+	0.121991i	$0.961072\pi$
$6$		0			0
$7$	−0.855706	+	2.50355i	−0.323427	+	0.946253i
$7$	−0.855706	+	2.50355i	−0.323427	+	0.946253i
$8$	−3.05430			−1.07986
$9$		0			0
$10$	−1.43858	−	2.49169i	−0.454917	−	0.787940i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−3.28888			−0.912171			−0.456085	−	0.889936i	$-0.650749\pi$
$13$	−3.28888			−0.912171			−0.456085	+	0.889936i	$0.650749\pi$
$14$	−1.86009	−	2.13003i	−0.497130	−	0.569275i
$15$		0			0
$16$	0.774707	−	1.34183i	0.193677	−	0.335458i
$17$	−0.534421	−	0.925645i	−0.129616	−	0.224502i	0.793912	−	0.608033i	$-0.208041\pi$
$17$	−0.534421	−	0.925645i	−0.129616	−	0.224502i	−0.923528	+	0.383531i	$0.874708\pi$
$18$		0			0
$19$	3.17886	−	5.50595i	0.729281	−	1.26315i	−0.227907	−	0.973683i	$-0.573188\pi$
$19$	3.17886	−	5.50595i	0.729281	−	1.26315i	0.957188	−	0.289468i	$-0.0934785\pi$
$20$	−2.30845			−0.516186
$21$		0			0
$22$	−1.06884			−0.227878
$23$	−0.774707	+	1.34183i	−0.161537	+	0.279791i	−0.935420	−	0.353538i	$-0.884979\pi$
$23$	−0.774707	+	1.34183i	−0.161537	+	0.279791i	0.773883	+	0.633329i	$0.218312\pi$
$24$		0			0
$25$	−1.12300	−	1.94508i	−0.224599	−	0.389017i
$26$	1.75765	−	3.04433i	0.344703	−	0.597043i
$27$		0			0
$28$	−2.22626	+	0.437974i	−0.420723	+	0.0827693i
$29$	8.57566			1.59246			0.796230	−	0.604994i	$-0.206825\pi$
$29$	8.57566			1.59246			0.796230	+	0.604994i	$0.206825\pi$
$30$		0			0
$31$	−1.92879	−	3.34076i	−0.346421	−	0.600018i	0.639190	−	0.769049i	$-0.279270\pi$
$31$	−1.92879	−	3.34076i	−0.346421	−	0.600018i	−0.985611	+	0.169031i	$0.945936\pi$
$32$	−2.22626	−	3.85599i	−0.393551	−	0.681650i
$33$		0			0
$34$	1.14242			0.195924
$35$	−4.68457	−	5.36440i	−0.791836	−	0.906749i
$36$		0			0
$37$	−3.91476	+	6.78057i	−0.643583	+	1.11472i	0.341044	+	0.940047i	$0.389219\pi$
$37$	−3.91476	+	6.78057i	−0.643583	+	1.11472i	−0.984627	+	0.174671i	$0.944114\pi$
$38$	3.39770	+	5.88499i	0.551180	+	0.954672i
$39$		0			0
$40$	4.11084	−	7.12018i	0.649981	−	1.12580i
$41$	6.87715			1.07403			0.537015	−	0.843573i	$-0.319552\pi$
$41$	6.87715			1.07403			0.537015	+	0.843573i	$0.319552\pi$
$42$		0			0
$43$	−2.76571			−0.421767			−0.210884	−	0.977511i	$-0.567634\pi$
$43$	−2.76571			−0.421767			−0.210884	+	0.977511i	$0.567634\pi$
$44$	−0.428788	+	0.742682i	−0.0646422	+	0.111964i
$45$		0			0
$46$	−0.828039	−	1.43421i	−0.122088	−	0.211462i
$47$	−4.56647	+	7.90936i	−0.666089	+	1.15370i	0.312900	+	0.949786i	$0.398699\pi$
$47$	−4.56647	+	7.90936i	−0.666089	+	1.15370i	−0.978989	+	0.203913i	$0.934634\pi$
$48$		0			0
$49$	−5.53553	−	4.28461i	−0.790790	−	0.612087i
$50$	2.40061			0.339498
$51$		0			0
$52$	−1.41023	−	2.44259i	−0.195564	−	0.338727i
$53$	−1.77722	−	3.07824i	−0.244120	−	0.422829i	0.717764	−	0.696287i	$-0.245166\pi$
$53$	−1.77722	−	3.07824i	−0.244120	−	0.422829i	−0.961884	+	0.273458i	$0.911832\pi$
$54$		0			0
$55$	−2.69184			−0.362967
$56$	2.61358	−	7.64659i	0.349255	−	1.02182i
$57$		0			0
$58$	−4.58301	+	7.93801i	−0.601779	+	1.04231i
$59$	−0.774707	−	1.34183i	−0.100858	−	0.174692i	0.811180	−	0.584796i	$-0.198826\pi$
$59$	−0.774707	−	1.34183i	−0.100858	−	0.174692i	−0.912038	+	0.410105i	$0.865492\pi$
$60$		0			0
$61$	−6.18471	+	10.7122i	−0.791871	+	1.37156i	0.132936	+	0.991125i	$0.457560\pi$
$61$	−6.18471	+	10.7122i	−0.791871	+	1.37156i	−0.924807	+	0.380436i	$0.875774\pi$
$62$	4.12314			0.523639
$63$		0			0
$64$	7.85787			0.982233
$65$	4.42656	−	7.66703i	0.549048	−	0.950978i
$66$		0			0
$67$	4.05193	+	7.01815i	0.495022	+	0.857403i	0.999984	−	0.00573872i	$-0.00182670\pi$
$67$	4.05193	+	7.01815i	0.495022	+	0.857403i	−0.504962	+	0.863142i	$0.668493\pi$
$68$	0.458307	−	0.793810i	0.0555778	−	0.0962636i
$69$		0			0
$70$	7.46906	−	1.46939i	0.892723	−	0.175626i
$71$	−10.4350			−1.23841			−0.619206	−	0.785229i	$-0.712545\pi$
$71$	−10.4350			−1.23841			−0.619206	+	0.785229i	$0.712545\pi$
$72$		0			0
$73$	−7.12501	−	12.3409i	−0.833919	−	1.44439i	−0.894907	−	0.446252i	$-0.852758\pi$
$73$	−7.12501	−	12.3409i	−0.833919	−	1.44439i	0.0609879	−	0.998139i	$-0.480575\pi$
$74$	−4.18426	−	7.24736i	−0.486411	−	0.842488i
$75$		0			0
$76$	5.45223			0.625413
$77$	−2.59599	+	0.510712i	−0.295841	+	0.0582010i
$78$		0			0
$79$	−4.69371	+	8.12974i	−0.528083	+	0.914667i	0.471381	+	0.881930i	$0.343756\pi$
$79$	−4.69371	+	8.12974i	−0.528083	+	0.914667i	−0.999464	+	0.0327372i	$0.989578\pi$
$80$	2.08538	+	3.61199i	0.233153	+	0.403833i
$81$		0			0
$82$	−3.67530	+	6.36580i	−0.405869	+	0.702985i
$83$	−2.46916			−0.271026			−0.135513	−	0.990776i	$-0.543268\pi$
$83$	−2.46916			−0.271026			−0.135513	+	0.990776i	$0.543268\pi$
$84$		0			0
$85$	2.87715			0.312071
$86$	1.47806	−	2.56007i	0.159383	−	0.276059i
$87$		0			0
$88$	−1.52715	−	2.64510i	−0.162795	−	0.281969i
$89$	−5.81498	+	10.0718i	−0.616387	+	1.06761i	0.373753	+	0.927528i	$0.378071\pi$
$89$	−5.81498	+	10.0718i	−0.616387	+	1.06761i	−0.990140	+	0.140084i	$0.955263\pi$
$90$		0			0
$91$	2.81431	−	8.23388i	0.295020	−	0.863145i
$92$	−1.32874			−0.138531
$93$		0			0
$94$	−4.88084	−	8.45386i	−0.503420	−	0.871950i
$95$	8.55698	+	14.8211i	0.877927	+	1.52061i
$96$		0			0
$97$	12.6644			1.28587			0.642936	−	0.765920i	$-0.277716\pi$
$97$	12.6644			1.28587			0.642936	+	0.765920i	$0.277716\pi$
$98$	6.92433	−	2.83415i	0.699463	−	0.286292i
$99$		0			0
$100$	0.963053	−	1.66806i	0.0963053	−	0.166806i
$101$	−2.73842	−	4.74308i	−0.272483	−	0.471954i	0.697014	−	0.717057i	$-0.254511\pi$
$101$	−2.73842	−	4.74308i	−0.272483	−	0.471954i	−0.969497	+	0.245103i	$0.921178\pi$
$102$		0			0
$103$	3.16327	−	5.47894i	0.311686	−	0.539856i	−0.667042	−	0.745021i	$-0.732440\pi$
$103$	3.16327	−	5.47894i	0.311686	−	0.539856i	0.978727	+	0.205165i	$0.0657730\pi$
$104$	10.0452			0.985015
$105$		0			0
$106$	3.79914			0.369005
$107$	−1.75341	+	3.03699i	−0.169508	+	0.293597i	−0.938247	−	0.345966i	$-0.887551\pi$
$107$	−1.75341	+	3.03699i	−0.169508	+	0.293597i	0.768739	+	0.639563i	$0.220885\pi$
$108$		0			0
$109$	−1.90497	−	3.29951i	−0.182463	−	0.316036i	0.760255	−	0.649624i	$-0.225074\pi$
$109$	−1.90497	−	3.29951i	−0.182463	−	0.316036i	−0.942719	+	0.333588i	$0.891740\pi$
$110$	1.43858	−	2.49169i	0.137163	−	0.237573i
$111$		0			0
$112$	2.69642	+	3.08773i	0.254788	+	0.291763i
$113$	−11.1319			−1.04720			−0.523601	−	0.851964i	$-0.675412\pi$
$113$	−11.1319			−1.04720			−0.523601	+	0.851964i	$0.675412\pi$
$114$		0			0
$115$	−2.08538	−	3.61199i	−0.194463	−	0.336820i
$116$	3.67714	+	6.36899i	0.341414	+	0.591346i
$117$		0			0
$118$	1.65608			0.152454
$119$	2.77471	−	0.545871i	0.254357	−	0.0500399i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−6.61048	−	11.4497i	−0.598485	−	1.03661i
$123$		0			0
$124$	1.65408	−	2.86495i	0.148541	−	0.257280i
$125$	−7.41335			−0.663070
$126$		0			0
$127$	12.6951			1.12650			0.563252	−	0.826285i	$-0.309550\pi$
$127$	12.6951			1.12650			0.563252	+	0.826285i	$0.309550\pi$
$128$	0.253106	−	0.438393i	0.0223717	−	0.0387488i
$129$		0			0
$130$	4.73130	+	8.19485i	0.414962	+	0.718736i
$131$	3.27284	−	5.66872i	0.285949	−	0.495278i	−0.686890	−	0.726762i	$-0.741024\pi$
$131$	3.27284	−	5.66872i	0.285949	−	0.495278i	0.972839	+	0.231483i	$0.0743578\pi$
$132$		0			0
$133$	11.0642	+	12.6699i	0.959392	+	1.09862i
$134$	−8.66175			−0.748261
$135$		0			0
$136$	1.63228	+	2.82720i	0.139967	+	0.242430i
$137$	10.7067	+	18.5445i	0.914733	+	1.58436i	0.807292	+	0.590152i	$0.200932\pi$
$137$	10.7067	+	18.5445i	0.914733	+	1.58436i	0.107441	+	0.994211i	$0.465734\pi$
$138$		0			0
$139$	0.850905			0.0721728			0.0360864	−	0.999349i	$-0.488511\pi$
$139$	0.850905			0.0721728			0.0360864	+	0.999349i	$0.488511\pi$
$140$	1.97536	−	5.77933i	0.166948	−	0.488443i
$141$		0			0
$142$	5.57671	−	9.65914i	0.467987	−	0.810577i
$143$	−1.64444	−	2.84825i	−0.137515	−	0.238183i
$144$		0			0
$145$	−11.5421	+	19.9916i	−0.958523	+	1.66021i
$146$	15.2310			1.26053
$147$		0			0
$148$	−6.71441			−0.551921
$149$	−7.89214	+	13.6696i	−0.646550	+	1.11986i	0.337392	+	0.941364i	$0.390455\pi$
$149$	−7.89214	+	13.6696i	−0.646550	+	1.11986i	−0.983941	+	0.178492i	$0.942878\pi$
$150$		0			0
$151$	8.52968	+	14.7738i	0.694136	+	1.20228i	0.970471	+	0.241217i	$0.0775466\pi$
$151$	8.52968	+	14.7738i	0.694136	+	1.20228i	−0.276336	+	0.961061i	$0.589120\pi$
$152$	−9.70919	+	16.8168i	−0.787519	+	1.36402i
$153$		0			0
$154$	0.914616	−	2.67590i	0.0737018	−	0.215630i
$155$	10.3840			0.834060
$156$		0			0
$157$	9.10941	+	15.7780i	0.727010	+	1.25922i	0.958141	+	0.286295i	$0.0924239\pi$
$157$	9.10941	+	15.7780i	0.727010	+	1.25922i	−0.231132	+	0.972922i	$0.574243\pi$
$158$	−5.01683	−	8.68941i	−0.399118	−	0.691292i
$159$		0			0
$160$	11.9855			0.947533
$161$	−2.69642	−	3.08773i	−0.212508	−	0.243347i
$162$		0			0
$163$	−4.95750	+	8.58665i	−0.388302	+	0.672558i	−0.992221	−	0.124487i	$-0.960271\pi$
$163$	−4.95750	+	8.58665i	−0.388302	+	0.672558i	0.603920	+	0.797045i	$0.293605\pi$
$164$	2.94884	+	5.10754i	0.230266	+	0.398832i
$165$		0			0
$166$	1.31957	−	2.28557i	0.102419	−	0.177394i
$167$	0.193790			0.0149960			0.00749798	−	0.999972i	$-0.497613\pi$
$167$	0.193790			0.0149960			0.00749798	+	0.999972i	$0.497613\pi$
$168$		0			0
$169$	−2.18328			−0.167944
$170$	−1.53761	+	2.66322i	−0.117929	+	0.204260i
$171$		0			0
$172$	−1.18590	−	2.05404i	−0.0904243	−	0.156619i
$173$	4.51409	−	7.81863i	0.343200	−	0.594439i	−0.641825	−	0.766851i	$-0.721823\pi$
$173$	4.51409	−	7.81863i	0.343200	−	0.594439i	0.985025	+	0.172411i	$0.0551559\pi$
$174$		0			0
$175$	5.83057	−	1.14705i	0.440750	−	0.0867091i
$176$	1.54941			0.116791
$177$		0			0
$178$	−6.21530	−	10.7652i	−0.465856	−	0.806887i
$179$	6.11215	+	10.5866i	0.456843	+	0.791276i	0.998792	−	0.0491356i	$-0.0156466\pi$
$179$	6.11215	+	10.5866i	0.456843	+	0.791276i	−0.541949	+	0.840412i	$0.682313\pi$
$180$		0			0
$181$	−18.5108			−1.37590			−0.687950	−	0.725758i	$-0.741489\pi$
$181$	−18.5108			−1.37590			−0.687950	+	0.725758i	$0.741489\pi$
$182$	6.11761	+	7.00541i	0.453468	+	0.519276i
$183$		0			0
$184$	2.36619	−	4.09835i	0.174437	−	0.302135i
$185$	−10.5379	−	18.2522i	−0.774762	−	1.34193i
$186$		0			0
$187$	0.534421	−	0.925645i	0.0390808	−	0.0676899i
$188$	−7.83219			−0.571221
$189$		0			0
$190$	−18.2921			−1.32705
$191$	9.23277	−	15.9916i	0.668060	−	1.15711i	−0.310386	−	0.950611i	$-0.600458\pi$
$191$	9.23277	−	15.9916i	0.668060	−	1.15711i	0.978446	−	0.206503i	$-0.0662084\pi$
$192$		0			0
$193$	8.52099	+	14.7588i	0.613354	+	1.06236i	0.990671	+	0.136276i	$0.0435135\pi$
$193$	8.52099	+	14.7588i	0.613354	+	1.06236i	−0.377317	+	0.926084i	$0.623153\pi$
$194$	−6.76811	+	11.7227i	−0.485922	+	0.841641i
$195$		0			0
$196$	0.808534	−	5.94833i	0.0577524	−	0.424881i
$197$	−5.45281			−0.388497			−0.194248	−	0.980952i	$-0.562227\pi$
$197$	−5.45281			−0.388497			−0.194248	+	0.980952i	$0.562227\pi$
$198$		0			0
$199$	−2.16574	−	3.75117i	−0.153525	−	0.265913i	0.778996	−	0.627029i	$-0.215729\pi$
$199$	−2.16574	−	3.75117i	−0.153525	−	0.265913i	−0.932521	+	0.361116i	$0.882396\pi$
$200$	3.42996	+	5.94087i	0.242535	+	0.420083i
$201$		0			0
$202$	5.85387			0.411877
$203$	−7.33825	+	21.4696i	−0.515044	+	1.50687i
$204$		0			0
$205$	−9.25609	+	16.0320i	−0.646473	+	1.11972i
$206$	3.38103	+	5.85612i	0.235568	+	0.408015i
$207$		0			0
$208$	−2.54792	+	4.41312i	−0.176666	+	0.305995i
$209$	6.35772			0.439773
$210$		0			0
$211$	26.0751			1.79508			0.897542	−	0.440929i	$-0.145351\pi$
$211$	26.0751			1.79508			0.897542	+	0.440929i	$0.145351\pi$
$212$	1.52410	−	2.63982i	0.104676	−	0.181304i
$213$		0			0
$214$	−1.87412	−	3.24607i	−0.128112	−	0.221897i
$215$	3.72242	−	6.44743i	0.253867	−	0.439711i
$216$		0			0
$217$	10.0142	−	1.97011i	0.679811	−	0.133740i
$218$	4.07223			0.275807
$219$		0			0
$220$	−1.15423	−	1.99918i	−0.0778180	−	0.134785i
$221$	1.75765	+	3.04433i	0.118232	+	0.204784i
$222$		0			0
$223$	13.3681			0.895196			0.447598	−	0.894235i	$-0.352280\pi$
$223$	13.3681			0.895196			0.447598	+	0.894235i	$0.352280\pi$
$224$	11.5587	−	2.27395i	0.772298	−	0.151935i
$225$		0			0
$226$	5.94913	−	10.3042i	0.395730	−	0.685425i
$227$	−11.3789	−	19.7089i	−0.755247	−	1.30813i	−0.945252	−	0.326342i	$-0.894184\pi$
$227$	−11.3789	−	19.7089i	−0.755247	−	1.30813i	0.190005	−	0.981783i	$-0.439150\pi$
$228$		0			0
$229$	−12.7815	+	22.1382i	−0.844627	+	1.46294i	0.0413181	+	0.999146i	$0.486844\pi$
$229$	−12.7815	+	22.1382i	−0.844627	+	1.46294i	−0.885945	+	0.463791i	$0.846489\pi$
$230$	4.45790			0.293945
$231$		0			0
$232$	−26.1926			−1.71963
$233$	−11.2338	+	19.4576i	−0.735952	+	1.27471i	0.218352	+	0.975870i	$0.429932\pi$
$233$	−11.2338	+	19.4576i	−0.735952	+	1.27471i	−0.954304	+	0.298837i	$0.903401\pi$
$234$		0			0
$235$	−12.2922	−	21.2907i	−0.801855	−	1.38885i
$236$	0.664369	−	1.15072i	0.0432468	−	0.0749056i
$237$		0			0
$238$	−0.977580	+	2.86012i	−0.0633671	+	0.185394i
$239$	13.1701			0.851900			0.425950	−	0.904747i	$-0.359940\pi$
$239$	13.1701			0.851900			0.425950	+	0.904747i	$0.359940\pi$
$240$		0			0
$241$	−7.27537	−	12.6013i	−0.468648	−	0.811722i	0.530710	−	0.847553i	$-0.321925\pi$
$241$	−7.27537	−	12.6013i	−0.468648	−	0.811722i	−0.999358	+	0.0358316i	$0.988592\pi$
$242$	−0.534421	−	0.925645i	−0.0343539	−	0.0595027i
$243$		0			0
$244$	−10.6077			−0.679089
$245$	17.4387	−	7.13770i	1.11412	−	0.456011i
$246$		0			0
$247$	−10.4549	+	18.1084i	−0.665229	+	1.15221i
$248$	5.89109	+	10.2037i	0.374085	+	0.647934i
$249$		0			0
$250$	3.96185	−	6.86213i	0.250569	−	0.433999i
$251$	5.15996			0.325694			0.162847	−	0.986651i	$-0.447932\pi$
$251$	5.15996			0.325694			0.162847	+	0.986651i	$0.447932\pi$
$252$		0			0
$253$	−1.54941			−0.0974108
$254$	−6.78451	+	11.7511i	−0.425698	+	0.737331i
$255$		0			0
$256$	8.12840	+	14.0788i	0.508025	+	0.879925i
$257$	7.41173	−	12.8375i	0.462331	−	0.800781i	−0.536746	−	0.843744i	$-0.680347\pi$
$257$	7.41173	−	12.8375i	0.462331	−	0.800781i	0.999077	+	0.0429634i	$0.0136799\pi$
$258$		0			0
$259$	−13.6256	−	15.6030i	−0.846654	−	0.969522i
$260$	7.59223			0.470850
$261$		0			0
$262$	3.49815	+	6.05897i	0.216116	+	0.374324i
$263$	7.73443	+	13.3964i	0.476926	+	0.826059i	0.999650	−	0.0264421i	$-0.00841776\pi$
$263$	7.73443	+	13.3964i	0.476926	+	0.826059i	−0.522725	+	0.852502i	$0.675084\pi$
$264$		0			0
$265$	9.56799			0.587757
$266$	−17.6408	+	3.47049i	−1.08163	+	0.212790i
$267$		0			0
$268$	−3.47483	+	6.01859i	−0.212259	+	0.367644i
$269$	−2.95721	−	5.12204i	−0.180304	−	0.312296i	0.761680	−	0.647954i	$-0.224375\pi$
$269$	−2.95721	−	5.12204i	−0.180304	−	0.312296i	−0.941984	+	0.335657i	$0.891042\pi$
$270$		0			0
$271$	4.64510	−	8.04555i	0.282170	−	0.488733i	−0.689749	−	0.724049i	$-0.742279\pi$
$271$	4.64510	−	8.04555i	0.282170	−	0.488733i	0.971919	+	0.235316i	$0.0756125\pi$
$272$	−1.65608			−0.100415
$273$		0			0
$274$	−22.8875			−1.38268
$275$	1.12300	−	1.94508i	0.0677192	−	0.117293i
$276$		0			0
$277$	−4.78333	−	8.28497i	−0.287402	−	0.497796i	0.685787	−	0.727803i	$-0.259458\pi$
$277$	−4.78333	−	8.28497i	−0.287402	−	0.497796i	−0.973189	+	0.230007i	$0.926125\pi$
$278$	−0.454742	+	0.787636i	−0.0272736	+	0.0472393i
$279$		0			0
$280$	14.3081	+	16.3845i	0.855070	+	0.979160i
$281$	13.0057			0.775853			0.387927	−	0.921690i	$-0.373191\pi$
$281$	13.0057			0.775853			0.387927	+	0.921690i	$0.373191\pi$
$282$		0			0
$283$	−12.1118	−	20.9782i	−0.719971	−	1.24703i	−0.961011	−	0.276512i	$-0.910822\pi$
$283$	−12.1118	−	20.9782i	−0.719971	−	1.24703i	0.241039	−	0.970515i	$-0.422512\pi$
$284$	−4.47442	−	7.74992i	−0.265508	−	0.459873i
$285$		0			0
$286$	3.51529			0.207864
$287$	−5.88482	+	17.2173i	−0.347370	+	1.01630i
$288$		0			0
$289$	7.92879	−	13.7331i	0.466399	−	0.807827i
$290$	−12.3367	−	21.3678i	−0.724438	−	1.25476i
$291$		0			0
$292$	6.11023	−	10.5832i	0.357574	−	0.619337i
$293$	−3.05010			−0.178189			−0.0890944	−	0.996023i	$-0.528397\pi$
$293$	−3.05010			−0.178189			−0.0890944	+	0.996023i	$0.528397\pi$
$294$		0			0
$295$	4.17077			0.242832
$296$	11.9568	−	20.7099i	0.694978	−	1.20374i
$297$		0			0
$298$	−8.43546	−	14.6106i	−0.488653	−	0.846372i
$299$	2.54792	−	4.41312i	0.147350	−	0.255217i
$300$		0			0
$301$	2.36664	−	6.92410i	0.136411	−	0.399098i
$302$	−18.2338			−1.04924
$303$		0			0
$304$	−4.92537	−	8.53099i	−0.282489	−	0.489286i
$305$	−16.6482	−	28.8356i	−0.953275	−	1.65112i
$306$		0			0
$307$	20.5254			1.17145			0.585723	−	0.810511i	$-0.300811\pi$
$307$	20.5254			1.17145			0.585723	+	0.810511i	$0.300811\pi$
$308$	−1.49243	−	1.70901i	−0.0850389	−	0.0973799i
$309$		0			0
$310$	−5.54941	+	9.61187i	−0.315185	+	0.545917i
$311$	3.99768	+	6.92418i	0.226687	+	0.392634i	0.956824	−	0.290667i	$-0.0938771\pi$
$311$	3.99768	+	6.92418i	0.226687	+	0.392634i	−0.730137	+	0.683301i	$0.760544\pi$
$312$		0			0
$313$	−7.95736	+	13.7825i	−0.449776	+	0.779036i	−0.998371	−	0.0570527i	$-0.981830\pi$
$313$	−7.95736	+	13.7825i	−0.449776	+	0.779036i	0.548595	+	0.836088i	$0.315163\pi$
$314$	−19.4730			−1.09893
$315$		0			0
$316$	−8.05042			−0.452871
$317$	13.3958	−	23.2022i	0.752381	−	1.30316i	−0.194284	−	0.980945i	$-0.562238\pi$
$317$	13.3958	−	23.2022i	0.752381	−	1.30316i	0.946666	−	0.322218i	$-0.104428\pi$
$318$		0			0
$319$	4.28783	+	7.42674i	0.240072	+	0.415818i
$320$	−10.5761	+	18.3183i	−0.591219	+	1.02402i
$321$		0			0
$322$	4.29917	−	0.845779i	0.239583	−	0.0471334i
$323$	−6.79540			−0.378106
$324$		0			0
$325$	3.69339	+	6.39715i	0.204873	+	0.354850i
$326$	−5.29879	−	9.17778i	−0.293473	−	0.508310i
$327$		0			0
$328$	−21.0049			−1.15980
$329$	−15.8939	−	18.2005i	−0.876261	−	1.00343i
$330$		0			0
$331$	5.06134	−	8.76650i	0.278196	−	0.481850i	−0.692740	−	0.721187i	$-0.743597\pi$
$331$	5.06134	−	8.76650i	0.278196	−	0.481850i	0.970937	+	0.239337i	$0.0769300\pi$
$332$	−1.05875	−	1.83380i	−0.0581062	−	0.100643i
$333$		0			0
$334$	−0.103566	+	0.179381i	−0.00566686	+	0.00981530i
$335$	−21.8143			−1.19184
$336$		0			0
$337$	1.36539			0.0743777			0.0371889	−	0.999308i	$-0.488160\pi$
$337$	1.36539			0.0743777			0.0371889	+	0.999308i	$0.488160\pi$
$338$	1.16679	−	2.02094i	0.0634650	−	0.109925i
$339$		0			0
$340$	1.23369	+	2.13681i	0.0669061	+	0.115885i
$341$	1.92879	−	3.34076i	0.104450	−	0.180912i
$342$		0			0
$343$	15.4635	−	10.1921i	0.834952	−	0.550323i
$344$	8.44731			0.455448
$345$		0			0
$346$	4.82485	+	8.35689i	0.259386	+	0.449269i
$347$	−12.6539	−	21.9171i	−0.679295	−	1.17657i	−0.975193	−	0.221355i	$-0.928952\pi$
$347$	−12.6539	−	21.9171i	−0.679295	−	1.17657i	0.295898	−	0.955220i	$-0.404381\pi$
$348$		0			0
$349$	−5.48986			−0.293866			−0.146933	−	0.989146i	$-0.546940\pi$
$349$	−5.48986			−0.293866			−0.146933	+	0.989146i	$0.546940\pi$
$350$	−2.05422	+	6.01005i	−0.109803	+	0.321251i
$351$		0			0
$352$	2.22626	−	3.85599i	0.118660	−	0.205525i
$353$	8.67185	+	15.0201i	0.461556	+	0.799438i	0.999039	−	0.0438363i	$-0.0139580\pi$
$353$	8.67185	+	15.0201i	0.461556	+	0.799438i	−0.537483	+	0.843275i	$0.680625\pi$
$354$		0			0
$355$	14.0447	−	24.3262i	0.745416	−	1.29110i
$356$	−9.97357			−0.528598
$357$		0			0
$358$	−13.0658			−0.690552
$359$	4.77269	−	8.26654i	0.251893	−	0.436292i	−0.712154	−	0.702023i	$-0.752280\pi$
$359$	4.77269	−	8.26654i	0.251893	−	0.436292i	0.964047	+	0.265732i	$0.0856136\pi$
$360$		0			0
$361$	−10.7103	−	18.5508i	−0.563701	−	0.976358i
$362$	9.89259	−	17.1345i	0.519943	−	0.900568i
$363$		0			0
$364$	7.32190	−	1.44044i	0.383772	−	0.0754997i
$365$	38.3587			2.00779
$366$		0			0
$367$	−3.30873	−	5.73088i	−0.172714	−	0.299150i	0.766654	−	0.642061i	$-0.221920\pi$
$367$	−3.30873	−	5.73088i	−0.172714	−	0.299150i	−0.939368	+	0.342911i	$0.888587\pi$
$368$	1.20034	+	2.07905i	0.0625721	+	0.108378i
$369$		0			0
$370$	22.5267			1.17111
$371$	9.22731	−	1.81530i	0.479058	−	0.0942455i
$372$		0			0
$373$	16.3575	−	28.3320i	0.846959	−	1.46698i	−0.0369504	−	0.999317i	$-0.511764\pi$
$373$	16.3575	−	28.3320i	0.846959	−	1.46698i	0.883909	−	0.467659i	$-0.154902\pi$
$374$	0.571212	+	0.989369i	0.0295367	+	0.0511590i
$375$		0			0
$376$	13.9474	−	24.1576i	0.719281	−	1.24583i
$377$	−28.2043			−1.45260
$378$		0			0
$379$	−7.69346			−0.395186			−0.197593	−	0.980284i	$-0.563312\pi$
$379$	−7.69346			−0.395186			−0.197593	+	0.980284i	$0.563312\pi$
$380$	−7.33825	+	12.7102i	−0.376444	+	0.652021i
$381$		0			0
$382$	9.86838	+	17.0925i	0.504910	+	0.874530i
$383$	−3.22903	+	5.59285i	−0.164996	+	0.285781i	−0.936654	−	0.350257i	$-0.886094\pi$
$383$	−3.22903	+	5.59285i	−0.164996	+	0.285781i	0.771658	+	0.636038i	$0.219428\pi$
$384$		0			0
$385$	2.30342	−	6.73915i	0.117393	−	0.343459i
$386$	−18.2152			−0.927129
$387$		0			0
$388$	5.43033	+	9.40560i	0.275683	+	0.477497i
$389$	2.76278	+	4.78527i	0.140078	+	0.242623i	0.927526	−	0.373759i	$-0.121931\pi$
$389$	2.76278	+	4.78527i	0.140078	+	0.242623i	−0.787448	+	0.616382i	$0.788598\pi$
$390$		0			0
$391$	1.65608			0.0837515
$392$	16.9072	+	13.0865i	0.853941	+	0.660967i
$393$		0			0
$394$	2.91410	−	5.04737i	0.146810	−	0.254283i
$395$	−12.6347	−	21.8839i	−0.635721	−	1.10110i
$396$		0			0
$397$	−16.2728	+	28.1853i	−0.816707	+	1.41458i	0.0913884	+	0.995815i	$0.470870\pi$
$397$	−16.2728	+	28.1853i	−0.816707	+	1.41458i	−0.908096	+	0.418763i	$0.862464\pi$
$398$	4.62967			0.232064
$399$		0			0
$400$	−3.47997			−0.173998
$401$	−16.0902	+	27.8691i	−0.803509	+	1.39172i	0.113785	+	0.993505i	$0.463703\pi$
$401$	−16.0902	+	27.8691i	−0.803509	+	1.39172i	−0.917293	+	0.398212i	$0.869631\pi$
$402$		0			0
$403$	6.34355	+	10.9873i	0.315995	+	0.547319i
$404$	2.34840	−	4.06755i	0.116837	−	0.202368i
$405$		0			0
$406$	−15.9515	−	18.2664i	−0.791660	−	0.906547i
$407$	−7.82952			−0.388095
$408$		0			0
$409$	1.09029	+	1.88843i	0.0539112	+	0.0933770i	0.891722	−	0.452584i	$-0.149498\pi$
$409$	1.09029	+	1.88843i	0.0539112	+	0.0933770i	−0.837810	+	0.545961i	$0.816165\pi$
$410$	−9.89330	−	17.1357i	−0.488595	−	0.846272i
$411$		0			0
$412$	5.42548			0.267294
$413$	4.02226	−	0.791304i	0.197923	−	0.0389375i
$414$		0			0
$415$	3.32329	−	5.75611i	0.163134	−	0.282556i
$416$	7.32190	+	12.6819i	0.358985	+	0.621781i
$417$		0			0
$418$	−3.39770	+	5.88499i	−0.166187	+	0.287844i
$419$	36.7377			1.79475			0.897376	−	0.441266i	$-0.145470\pi$
$419$	36.7377			1.79475			0.897376	+	0.441266i	$0.145470\pi$
$420$		0			0
$421$	−36.6439			−1.78591			−0.892957	−	0.450142i	$-0.851373\pi$
$421$	−36.6439			−1.78591			−0.892957	+	0.450142i	$0.851373\pi$
$422$	−13.9351	+	24.1363i	−0.678349	+	1.17494i
$423$		0			0
$424$	5.42817	+	9.40186i	0.263615	+	0.456595i
$425$	−1.20031	+	2.07899i	−0.0582233	+	0.100846i
$426$		0			0
$427$	−21.5263	−	24.6503i	−1.04173	−	1.19291i
$428$	−3.00736			−0.145366
$429$		0			0
$430$	3.97868	+	6.89128i	0.191869	+	0.332327i
$431$	12.9141	+	22.3679i	0.622051	+	1.07742i	0.989103	+	0.147224i	$0.0470337\pi$
$431$	12.9141	+	22.3679i	0.622051	+	1.07742i	−0.367052	+	0.930200i	$0.619633\pi$
$432$		0			0
$433$	−4.81228			−0.231263			−0.115632	−	0.993292i	$-0.536889\pi$
$433$	−4.81228			−0.231263			−0.115632	+	0.993292i	$0.536889\pi$
$434$	−3.52820	+	10.3225i	−0.169359	+	0.495496i
$435$		0			0
$436$	1.63366	−	2.82958i	0.0782381	−	0.135512i
$437$	4.92537	+	8.53099i	0.235612	+	0.408093i
$438$		0			0
$439$	−13.6430	+	23.6304i	−0.651146	+	1.12782i	0.331699	+	0.943385i	$0.392378\pi$
$439$	−13.6430	+	23.6304i	−0.651146	+	1.12782i	−0.982845	+	0.184432i	$0.940955\pi$
$440$	8.22168			0.391953
$441$		0			0
$442$	−3.75730			−0.178716
$443$	−13.5654	+	23.4959i	−0.644510	+	1.11632i	0.339904	+	0.940460i	$0.389605\pi$
$443$	−13.5654	+	23.4959i	−0.644510	+	1.11632i	−0.984414	+	0.175864i	$0.943728\pi$
$444$		0			0
$445$	−15.6530	−	27.1118i	−0.742022	−	1.28522i
$446$	−7.14421	+	12.3741i	−0.338288	+	0.585933i
$447$		0			0
$448$	−6.72403	+	19.6726i	−0.317680	+	0.929442i
$449$	−4.27537			−0.201767			−0.100884	−	0.994898i	$-0.532167\pi$
$449$	−4.27537			−0.201767			−0.100884	+	0.994898i	$0.532167\pi$
$450$		0			0
$451$	3.43858	+	5.95579i	0.161916	+	0.280447i
$452$	−4.77323	−	8.26747i	−0.224514	−	0.388869i
$453$		0			0
$454$	24.3246			1.14161
$455$	15.4070	+	17.6429i	0.722290	+	0.827110i
$456$		0			0
$457$	−14.5498	+	25.2009i	−0.680609	+	1.17885i	0.294186	+	0.955748i	$0.404952\pi$
$457$	−14.5498	+	25.2009i	−0.680609	+	1.17885i	−0.974795	+	0.223102i	$0.928382\pi$
$458$	−13.6614	−	23.6623i	−0.638357	−	1.10567i
$459$		0			0
$460$	1.78837	−	3.09756i	0.0833834	−	0.144424i
$461$	2.96972			0.138314			0.0691569	−	0.997606i	$-0.477969\pi$
$461$	2.96972			0.138314			0.0691569	+	0.997606i	$0.477969\pi$
$462$		0			0
$463$	−20.3076			−0.943773			−0.471887	−	0.881659i	$-0.656427\pi$
$463$	−20.3076			−0.943773			−0.471887	+	0.881659i	$0.656427\pi$
$464$	6.64362	−	11.5071i	0.308422	−	0.534203i
$465$		0			0
$466$	−12.0072	−	20.7971i	−0.556222	−	0.963405i
$467$	18.5675	−	32.1598i	0.859200	−	1.48818i	−0.0134931	−	0.999909i	$-0.504295\pi$
$467$	18.5675	−	32.1598i	0.859200	−	1.48818i	0.872693	−	0.488269i	$-0.162372\pi$
$468$		0			0
$469$	−21.0375	+	4.13874i	−0.971424	+	0.191109i
$470$	26.2769			1.21206
$471$		0			0
$472$	2.36619	+	4.09835i	0.108913	+	0.188642i
$473$	−1.38286	−	2.39518i	−0.0635838	−	0.110130i
$474$		0			0
$475$	−14.2794			−0.655183
$476$	1.59517	+	1.82666i	0.0731144	+	0.0837249i
$477$		0			0
$478$	−7.03836	+	12.1908i	−0.321927	+	0.557594i
$479$	9.18431	+	15.9077i	0.419642	+	0.726841i	0.995903	−	0.0904243i	$-0.0288223\pi$
$479$	9.18431	+	15.9077i	0.419642	+	0.726841i	−0.576261	+	0.817265i	$0.695489\pi$
$480$		0			0
$481$	12.8752	−	22.3005i	0.587057	−	1.01681i
$482$	15.5525			0.708395
$483$		0			0
$484$	−0.857576			−0.0389807
$485$	−17.0452	+	29.5232i	−0.773983	+	1.34058i
$486$		0			0
$487$	10.0623	+	17.4285i	0.455968	+	0.789760i	0.998743	−	0.0501182i	$-0.0159598\pi$
$487$	10.0623	+	17.4285i	0.455968	+	0.789760i	−0.542775	+	0.839878i	$0.682626\pi$
$488$	18.8900	−	32.7184i	0.855108	−	1.48109i
$489$		0			0
$490$	−2.71262	+	19.9565i	−0.122544	+	0.901545i
$491$	−15.0288			−0.678238			−0.339119	−	0.940743i	$-0.610129\pi$
$491$	−15.0288			−0.678238			−0.339119	+	0.940743i	$0.610129\pi$
$492$		0			0
$493$	−4.58301	−	7.93801i	−0.206409	−	0.357510i
$494$	−11.1746	−	19.3550i	−0.502770	−	0.870824i
$495$		0			0
$496$	−5.97698			−0.268374
$497$	8.92933	−	26.1247i	0.400535	−	1.17185i
$498$		0			0
$499$	−1.07121	+	1.85539i	−0.0479540	+	0.0830588i	−0.889006	−	0.457895i	$-0.848603\pi$
$499$	−1.07121	+	1.85539i	−0.0479540	+	0.0830588i	0.841052	+	0.540954i	$0.181937\pi$
$500$	−3.17875	−	5.50576i	−0.142158	−	0.246225i
$501$		0			0
$502$	−2.75759	+	4.77629i	−0.123077	+	0.213176i
$503$	−6.30359			−0.281063			−0.140532	−	0.990076i	$-0.544881\pi$
$503$	−6.30359			−0.281063			−0.140532	+	0.990076i	$0.544881\pi$
$504$		0			0
$505$	14.7427			0.656044
$506$	0.828039	−	1.43421i	0.0368108	−	0.0637582i
$507$		0			0
$508$	5.44349	+	9.42840i	0.241516	+	0.418317i
$509$	−12.3517	+	21.3937i	−0.547477	+	0.948259i	0.450969	+	0.892540i	$0.351078\pi$
$509$	−12.3517	+	21.3937i	−0.547477	+	0.948259i	−0.998446	+	0.0557192i	$0.982255\pi$
$510$		0			0
$511$	36.9929	−	7.27765i	1.63647	−	0.321944i
$512$	−16.3635			−0.723173
$513$		0			0
$514$	7.92197	+	13.7213i	0.349423	+	0.605219i
$515$	8.51500	+	14.7484i	0.375216	+	0.649893i
$516$		0			0
$517$	−9.13295			−0.401667
$518$	21.7246	−	4.27391i	0.954525	−	0.187785i
$519$		0			0
$520$	−13.5200	+	23.4174i	−0.592893	+	1.02692i
$521$	1.82659	+	3.16375i	0.0800244	+	0.138606i	0.903260	−	0.429093i	$-0.141167\pi$
$521$	1.82659	+	3.16375i	0.0800244	+	0.138606i	−0.823236	+	0.567700i	$0.807834\pi$
$522$		0			0
$523$	3.83139	−	6.63617i	0.167535	−	0.290179i	−0.770018	−	0.638023i	$-0.779753\pi$
$523$	3.83139	−	6.63617i	0.167535	−	0.290179i	0.937553	+	0.347843i	$0.113086\pi$
$524$	5.61341			0.245223
$525$		0			0
$526$	−16.5338			−0.720907
$527$	−2.06157	+	3.57074i	−0.0898034	+	0.155544i
$528$		0			0
$529$	10.2997	+	17.8395i	0.447811	+	0.775632i
$530$	−5.11334	+	8.85656i	−0.222109	+	0.384704i
$531$		0			0
$532$	−4.66551	+	13.6499i	−0.202275	+	0.591799i
$533$	−22.6181			−0.979699
$534$		0			0
$535$	−4.71989	−	8.17509i	−0.204059	−	0.353440i
$536$	−12.3758	−	21.4355i	−0.534553	−	0.925873i
$537$		0			0
$538$	6.32159			0.272543
$539$	0.942814	−	6.93622i	0.0406099	−	0.298764i
$540$		0			0
$541$	7.24283	−	12.5449i	0.311394	−	0.539349i	−0.667271	−	0.744815i	$-0.732538\pi$
$541$	7.24283	−	12.5449i	0.311394	−	0.539349i	0.978664	+	0.205466i	$0.0658709\pi$
$542$	4.96488	+	8.59943i	0.213260	+	0.369377i
$543$		0			0
$544$	−2.37952	+	4.12145i	−0.102021	+	0.176706i
$545$	10.2558			0.439309
$546$		0			0
$547$	6.15312			0.263089			0.131544	−	0.991310i	$-0.458006\pi$
$547$	6.15312			0.263089			0.131544	+	0.991310i	$0.458006\pi$
$548$	−9.18178	+	15.9033i	−0.392226	+	0.679356i
$549$		0			0
$550$	1.20031	+	2.07899i	0.0511812	+	0.0886484i
$551$	27.2608	−	47.2171i	1.16135	−	2.01152i
$552$		0			0
$553$	−16.3368	−	18.7076i	−0.694710	−	0.795528i
$554$	10.2253			0.434429
$555$		0			0
$556$	0.364858	+	0.631952i	0.0154734	+	0.0268007i
$557$	−9.90091	−	17.1489i	−0.419515	−	0.726621i	0.576376	−	0.817185i	$-0.304467\pi$
$557$	−9.90091	−	17.1489i	−0.419515	−	0.726621i	−0.995891	+	0.0905634i	$0.971133\pi$
$558$		0			0
$559$	9.09609			0.384724
$560$	−10.8273	+	2.13006i	−0.457536	+	0.0900115i
$561$		0			0
$562$	−6.95051	+	12.0386i	−0.293189	+	0.507819i
$563$	2.92208	+	5.06119i	0.123151	+	0.213304i	0.921009	−	0.389542i	$-0.127367\pi$
$563$	2.92208	+	5.06119i	0.123151	+	0.213304i	−0.797858	+	0.602846i	$0.794033\pi$
$564$		0			0
$565$	14.9826	−	25.9507i	0.630325	−	1.09175i
$566$	25.8912			1.08829
$567$		0			0
$568$	31.8717			1.33731
$569$	−17.1742	+	29.7466i	−0.719979	+	1.24704i	0.241028	+	0.970518i	$0.422515\pi$
$569$	−17.1742	+	29.7466i	−0.719979	+	1.24704i	−0.961007	+	0.276522i	$0.910818\pi$
$570$		0			0
$571$	−4.82810	−	8.36252i	−0.202050	−	0.349960i	0.747139	−	0.664668i	$-0.231427\pi$
$571$	−4.82810	−	8.36252i	−0.202050	−	0.349960i	−0.949189	+	0.314707i	$0.898094\pi$
$572$	1.41023	−	2.44259i	0.0589647	−	0.102130i
$573$		0			0
$574$	−12.7921	−	14.6485i	−0.533933	−	0.611418i
$575$	3.47997			0.145125
$576$		0			0
$577$	17.3262	+	30.0099i	0.721299	+	1.24933i	0.960479	+	0.278351i	$0.0897880\pi$
$577$	17.3262	+	30.0099i	0.721299	+	1.24933i	−0.239180	+	0.970975i	$0.576879\pi$
$578$	8.47463	+	14.6785i	0.352498	+	0.610544i
$579$		0			0
$580$	−19.7965			−0.822006
$581$	2.11288	−	6.18167i	0.0876569	−	0.256459i
$582$		0			0
$583$	1.77722	−	3.07824i	0.0736050	−	0.127488i
$584$	21.7619	+	37.6927i	0.900514	+	1.55974i
$585$		0			0
$586$	1.63004	−	2.82331i	0.0673363	−	0.116630i
$587$	15.4442			0.637451			0.318726	−	0.947847i	$-0.396745\pi$
$587$	15.4442			0.637451			0.318726	+	0.947847i	$0.396745\pi$
$588$		0			0
$589$	−24.5254			−1.01055
$590$	−2.22895	+	3.86065i	−0.0917643	+	0.158940i
$591$		0			0
$592$	6.06558	+	10.5059i	0.249294	+	0.431790i
$593$	−2.78395	+	4.82194i	−0.114323	+	0.198013i	−0.917509	−	0.397715i	$-0.869803\pi$
$593$	−2.78395	+	4.82194i	−0.114323	+	0.198013i	0.803186	+	0.595728i	$0.203137\pi$
$594$		0			0
$595$	−2.46200	+	7.20309i	−0.100932	+	0.295298i
$596$	−13.5362			−0.554465
$597$		0			0
$598$	2.72332	+	4.71693i	0.111365	+	0.192890i
$599$	13.7745	+	23.8581i	0.562810	+	0.974816i	0.997250	+	0.0741146i	$0.0236131\pi$
$599$	13.7745	+	23.8581i	0.562810	+	0.974816i	−0.434440	+	0.900701i	$0.643054\pi$
$600$		0			0
$601$	15.6408			0.638000			0.319000	−	0.947755i	$-0.396653\pi$
$601$	15.6408			0.638000			0.319000	+	0.947755i	$0.396653\pi$
$602$	5.14448	+	5.89105i	0.209673	+	0.240101i
$603$		0			0
$604$	−7.31485	+	12.6697i	−0.297637	+	0.515522i
$605$	−1.34592	−	2.33120i	−0.0547194	−	0.0947768i
$606$		0			0
$607$	−5.72550	+	9.91685i	−0.232391	+	0.402513i	−0.958511	−	0.285055i	$-0.907988\pi$
$607$	−5.72550	+	9.91685i	−0.232391	+	0.402513i	0.726120	+	0.687568i	$0.241321\pi$
$608$	−28.3079			−1.14804
$609$		0			0
$610$	35.5887			1.44094
$611$	15.0186	−	26.0129i	0.607587	−	1.05237i
$612$		0			0
$613$	−7.45755	−	12.9169i	−0.301208	−	0.521707i	0.675202	−	0.737633i	$-0.264056\pi$
$613$	−7.45755	−	12.9169i	−0.301208	−	0.521707i	−0.976410	+	0.215926i	$0.930723\pi$
$614$	−10.9692	+	18.9992i	−0.442681	+	0.766746i
$615$		0			0
$616$	7.92893	−	1.55987i	0.319466	−	0.0628488i
$617$	−27.8601			−1.12161			−0.560803	−	0.827949i	$-0.689507\pi$
$617$	−27.8601			−1.12161			−0.560803	+	0.827949i	$0.689507\pi$
$618$		0			0
$619$	−0.648970	−	1.12405i	−0.0260843	−	0.0451793i	0.852689	−	0.522420i	$-0.174970\pi$
$619$	−0.648970	−	1.12405i	−0.0260843	−	0.0451793i	−0.878773	+	0.477240i	$0.841637\pi$
$620$	4.45252	+	7.71199i	0.178817	+	0.309721i
$621$		0			0
$622$	−8.54577			−0.342654
$623$	−20.2394	−	23.1766i	−0.810876	−	0.928552i
$624$		0			0
$625$	15.5927	−	27.0074i	0.623710	−	1.08030i
$626$	−8.50516	−	14.7314i	−0.339935	−	0.588784i
$627$		0			0
$628$	−7.81200	+	13.5308i	−0.311733	+	0.539937i
$629$	8.36853			0.333675
$630$		0			0
$631$	45.9952			1.83104			0.915519	−	0.402274i	$-0.131780\pi$
$631$	45.9952			1.83104			0.915519	+	0.402274i	$0.131780\pi$
$632$	14.3360	−	24.8306i	0.570255	−	0.987710i
$633$		0			0
$634$	14.3180	+	24.7995i	0.568639	+	0.984912i
$635$	−17.0865	+	29.5947i	−0.678058	+	1.17443i
$636$		0			0
$637$	18.2057	+	14.0916i	0.721336	+	0.558328i
$638$	−9.16603			−0.362887
$639$		0			0
$640$	0.681321	+	1.18008i	0.0269316	+	0.0466469i
$641$	−1.26224	−	2.18626i	−0.0498555	−	0.0863522i	0.840021	−	0.542554i	$-0.182543\pi$
$641$	−1.26224	−	2.18626i	−0.0498555	−	0.0863522i	−0.889876	+	0.456202i	$0.849209\pi$
$642$		0			0
$643$	22.1800			0.874692			0.437346	−	0.899293i	$-0.355919\pi$
$643$	22.1800			0.874692			0.437346	+	0.899293i	$0.355919\pi$
$644$	1.13701	−	3.32657i	0.0448045	−	0.131085i
$645$		0			0
$646$	3.63161	−	6.29013i	0.142884	−	0.247482i
$647$	11.6482	+	20.1753i	0.457940	+	0.793175i	0.998852	−	0.0479044i	$-0.0152543\pi$
$647$	11.6482	+	20.1753i	0.457940	+	0.793175i	−0.540912	+	0.841079i	$0.681921\pi$
$648$		0			0
$649$	0.774707	−	1.34183i	0.0304099	−	0.0526715i
$650$	−7.89532			−0.309680
$651$		0			0
$652$	−8.50287			−0.332998
$653$	18.6188	−	32.2488i	0.728611	−	1.26199i	−0.228859	−	0.973460i	$-0.573499\pi$
$653$	18.6188	−	32.2488i	0.728611	−	1.26199i	0.957470	−	0.288532i	$-0.0931673\pi$
$654$		0			0
$655$	8.80995	+	15.2593i	0.344233	+	0.596229i
$656$	5.32777	−	9.22798i	0.208015	−	0.360292i
$657$		0			0
$658$	25.3412	−	4.98541i	0.987905	−	0.194351i
$659$	13.8016			0.537632			0.268816	−	0.963192i	$-0.413368\pi$
$659$	13.8016			0.537632			0.268816	+	0.963192i	$0.413368\pi$
$660$		0			0
$661$	−13.4675	−	23.3264i	−0.523825	−	0.907292i	−0.999615	−	0.0277328i	$-0.991171\pi$
$661$	−13.4675	−	23.3264i	−0.523825	−	0.907292i	0.475790	−	0.879559i	$-0.342162\pi$
$662$	5.40978	+	9.37001i	0.210257	+	0.364176i
$663$		0			0
$664$	7.54155			0.292669
$665$	−44.4277	+	8.74030i	−1.72283	+	0.338934i
$666$		0			0
$667$	−6.64362	+	11.5071i	−0.257242	+	0.445556i
$668$	0.0830950	+	0.143925i	0.00321504	+	0.00556861i
$669$		0			0
$670$	11.6580	−	20.1923i	0.450388	−	0.780095i
$671$	−12.3694			−0.477516
$672$		0			0
$673$	24.7186			0.952832			0.476416	−	0.879220i	$-0.341936\pi$
$673$	24.7186			0.952832			0.476416	+	0.879220i	$0.341936\pi$
$674$	−0.729695	+	1.26387i	−0.0281068	+	0.0486824i
$675$		0			0
$676$	−0.936162	−	1.62148i	−0.0360062	−	0.0623646i
$677$	−12.4334	+	21.5353i	−0.477854	+	0.827667i	−0.999678	−	0.0253859i	$-0.991919\pi$
$677$	−12.4334	+	21.5353i	−0.477854	+	0.827667i	0.521824	+	0.853053i	$0.325252\pi$
$678$		0			0
$679$	−10.8370	+	31.7059i	−0.415885	+	1.21676i
$680$	−8.78768			−0.336992
$681$		0			0
$682$	2.06157	+	3.57074i	0.0789416	+	0.136731i
$683$	3.06026	+	5.30053i	0.117098	+	0.202819i	0.918616	−	0.395151i	$-0.129308\pi$
$683$	3.06026	+	5.30053i	0.117098	+	0.202819i	−0.801519	+	0.597970i	$0.795974\pi$
$684$		0			0
$685$	−57.6413			−2.20236
$686$	1.17024	+	19.7606i	0.0446801	+	0.754464i
$687$		0			0
$688$	−2.14261	+	3.71112i	−0.0816864	+	0.141485i
$689$	5.84507	+	10.1240i	0.222679	+	0.385692i
$690$		0			0
$691$	−6.24162	+	10.8108i	−0.237443	+	0.411263i	−0.959980	−	0.280070i	$-0.909642\pi$
$691$	−6.24162	+	10.8108i	−0.237443	+	0.411263i	0.722537	+	0.691332i	$0.242976\pi$
$692$	7.74234			0.294320
$693$		0			0
$694$	27.0500			1.02680
$695$	−1.14525	+	1.98363i	−0.0434418	+	0.0752434i
$696$		0			0
$697$	−3.67530	−	6.36580i	−0.139212	−	0.241122i
$698$	2.93390	−	5.08166i	0.111050	−	0.192344i
$699$		0			0
$700$	3.35197	+	3.83842i	0.126693	+	0.145079i
$701$	28.0867			1.06082			0.530409	−	0.847742i	$-0.322038\pi$
$701$	28.0867			1.06082			0.530409	+	0.847742i	$0.322038\pi$
$702$		0			0
$703$	24.8890	+	43.1089i	0.938705	+	1.62588i
$704$	3.92893	+	6.80511i	0.148077	+	0.256477i
$705$		0			0
$706$	−18.5377			−0.697675
$707$	14.2178	−	2.79708i	0.534716	−	0.105195i
$708$		0			0
$709$	6.88131	−	11.9188i	0.258433	−	0.447619i	−0.707389	−	0.706824i	$-0.750127\pi$
$709$	6.88131	−	11.9188i	0.258433	−	0.447619i	0.965822	+	0.259205i	$0.0834606\pi$
$710$	15.0116	+	26.0008i	0.563375	+	0.975794i
$711$		0			0
$712$	17.7607	−	30.7624i	0.665610	−	1.15287i
$713$	5.97698			0.223840
$714$		0			0
$715$	8.85313			0.331088
$716$	−5.24163	+	9.07877i	−0.195889	+	0.339289i
$717$		0			0
$718$	5.10126	+	8.83563i	0.190377	+	0.329743i
$719$	15.3224	−	26.5392i	0.571430	−	0.989745i	−0.424990	−	0.905198i	$-0.639722\pi$
$719$	15.3224	−	26.5392i	0.571430	−	0.989745i	0.996419	−	0.0845470i	$-0.0269443\pi$
$720$		0			0
$721$	11.0100	+	12.6078i	0.410033	+	0.469538i
$722$	22.8953			0.852074
$723$		0			0
$724$	−7.93722	−	13.7477i	−0.294985	−	0.510928i
$725$	−9.63042	−	16.6804i	−0.357665	−	0.619494i
$726$		0			0
$727$	28.8508			1.07002			0.535009	−	0.844846i	$-0.320308\pi$
$727$	28.8508			1.07002			0.535009	+	0.844846i	$0.320308\pi$
$728$	−8.59576	+	25.1487i	−0.318580	+	0.932073i
$729$		0			0
$730$	−20.4997	+	35.5066i	−0.758729	+	1.31416i
$731$	1.47806	+	2.56007i	0.0546678	+	0.0946875i
$732$		0			0
$733$	−4.02618	+	6.97355i	−0.148710	+	0.257574i	−0.930751	−	0.365653i	$-0.880846\pi$
$733$	−4.02618	+	6.97355i	−0.148710	+	0.257574i	0.782041	+	0.623227i	$0.214179\pi$
$734$	7.07301			0.261070
$735$		0			0
$736$	6.89879			0.254293
$737$	−4.05193	+	7.01815i	−0.149255	+	0.258517i
$738$		0			0
$739$	7.72812	+	13.3855i	0.284283	+	0.492393i	0.972435	−	0.233173i	$-0.0749110\pi$
$739$	7.72812	+	13.3855i	0.284283	+	0.492393i	−0.688152	+	0.725567i	$0.741578\pi$
$740$	9.03705	−	15.6526i	0.332208	−	0.575402i
$741$		0			0
$742$	−3.25095	+	9.51134i	−0.119346	+	0.349172i
$743$	−14.1256			−0.518216			−0.259108	−	0.965848i	$-0.583429\pi$
$743$	−14.1256			−0.518216			−0.259108	+	0.965848i	$0.583429\pi$
$744$		0			0
$745$	−21.2444	−	36.7963i	−0.778333	−	1.34811i
$746$	17.4836	+	30.2825i	0.640119	+	1.10872i
$747$		0			0
$748$	0.916613			0.0335147
$749$	−6.10286	−	6.98852i	−0.222994	−	0.255355i
$750$		0			0
$751$	−0.935267	+	1.61993i	−0.0341284	+	0.0591121i	−0.882585	−	0.470153i	$-0.844199\pi$
$751$	−0.935267	+	1.61993i	−0.0341284	+	0.0591121i	0.848457	+	0.529265i	$0.177532\pi$
$752$	7.07535	+	12.2549i	0.258012	+	0.446889i
$753$		0			0
$754$	15.0730	−	26.1072i	0.548926	−	0.950767i
$755$	−45.9210			−1.67124
$756$		0			0
$757$	2.68353			0.0975345			0.0487672	−	0.998810i	$-0.484471\pi$
$757$	2.68353			0.0975345			0.0487672	+	0.998810i	$0.484471\pi$
$758$	4.11155	−	7.12141i	0.149338	−	0.258661i
$759$		0			0
$760$	−26.1356	−	45.2681i	−0.948036	−	1.64205i
$761$	13.1029	−	22.6950i	0.474981	−	0.822692i	−0.524608	−	0.851344i	$-0.675788\pi$
$761$	13.1029	−	22.6950i	0.474981	−	0.822692i	0.999589	+	0.0286520i	$0.00912147\pi$
$762$		0			0
$763$	9.89059	−	1.94579i	0.358063	−	0.0704422i
$764$	15.8356			0.572912
$765$		0			0
$766$	−3.45133	−	5.97787i	−0.124701	−	0.215989i
$767$	2.54792	+	4.41312i	0.0919999	+	0.159349i
$768$		0			0
$769$	−14.9106			−0.537689			−0.268844	−	0.963184i	$-0.586642\pi$
$769$	−14.9106			−0.537689			−0.268844	+	0.963184i	$0.586642\pi$
$770$	5.00706	+	5.73370i	0.180442	+	0.206628i
$771$		0			0
$772$	−7.30739	+	12.6568i	−0.262999	+	0.455527i
$773$	5.50652	+	9.53758i	0.198056	+	0.343043i	0.947898	−	0.318574i	$-0.103204\pi$
$773$	5.50652	+	9.53758i	0.198056	+	0.343043i	−0.749842	+	0.661617i	$0.769871\pi$
$774$		0			0
$775$	−4.33204	+	7.50331i	−0.155611	+	0.269527i
$776$	−38.6808			−1.38856
$777$		0			0
$778$	−5.90595			−0.211739
$779$	21.8615	−	37.8652i	0.783270	−	1.35666i
$780$		0			0
$781$	−5.21752	−	9.03701i	−0.186698	−	0.323370i
$782$	−0.885044	+	1.53294i	−0.0316491	+	0.0548179i
$783$		0			0
$784$	−10.0376	+	4.10844i	−0.358487	+	0.146730i
$785$	−49.0421			−1.75039
$786$		0			0
$787$	20.5926	+	35.6674i	0.734046	+	1.27141i	0.955141	+	0.296153i	$0.0957038\pi$
$787$	20.5926	+	35.6674i	0.734046	+	1.27141i	−0.221094	+	0.975252i	$0.570963\pi$
$788$	−2.33810	−	4.04970i	−0.0832913	−	0.144265i
$789$		0			0
$790$	27.0090			0.960937
$791$	9.52565	−	27.8693i	0.338693	−	0.990918i
$792$		0			0
$793$	20.3408	−	35.2312i	0.722322	−	1.25110i
$794$	−17.3930	−	30.1256i	−0.617256	−	1.06912i
$795$		0			0
$796$	1.85728	−	3.21691i	0.0658297	−	0.114020i
$797$	21.5389			0.762947			0.381473	−	0.924380i	$-0.375417\pi$
$797$	21.5389			0.762947			0.381473	+	0.924380i	$0.375417\pi$
$798$		0			0
$799$	9.76168			0.345343
$800$	−5.00016	+	8.66052i	−0.176782	+	0.306196i
$801$		0			0
$802$	−17.1979	−	29.7877i	−0.607280	−	1.05184i
$803$	7.12501	−	12.3409i	0.251436	−	0.435500i
$804$		0			0
$805$	10.8273	−	2.13006i	0.381612	−	0.0750748i
$806$	−13.5605			−0.477649
$807$		0			0
$808$	8.36394	+	14.4868i	0.294242	+	0.509643i
$809$	−14.4335	−	24.9996i	−0.507456	−	0.878940i	−0.999963	−	0.00863141i	$-0.997253\pi$
$809$	−14.4335	−	24.9996i	−0.507456	−	0.878940i	0.492506	−	0.870309i	$-0.336081\pi$
$810$		0			0
$811$	−19.7341			−0.692959			−0.346480	−	0.938057i	$-0.612623\pi$
$811$	−19.7341			−0.692959			−0.346480	+	0.938057i	$0.612623\pi$
$812$	−19.0916	+	3.75592i	−0.669985	+	0.131807i
$813$		0			0
$814$	4.18426	−	7.24736i	0.146658	−	0.254020i
$815$	−13.3448	−	23.1139i	−0.467448	−	0.809643i
$816$		0			0
$817$	−8.79181	+	15.2279i	−0.307587	+	0.532756i
$818$	−2.33069			−0.0814907
$819$		0			0
$820$	−15.8756			−0.554400
$821$	−1.16927	+	2.02524i	−0.0408079	+	0.0706813i	−0.885708	−	0.464243i	$-0.846326\pi$
$821$	−1.16927	+	2.02524i	−0.0408079	+	0.0706813i	0.844900	+	0.534924i	$0.179660\pi$
$822$		0			0
$823$	−19.7444	−	34.1984i	−0.688248	−	1.19208i	−0.972404	−	0.233302i	$-0.925047\pi$
$823$	−19.7444	−	34.1984i	−0.688248	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$824$	−9.66156	+	16.7343i	−0.336576	+	0.582968i
$825$		0			0
$826$	−1.41712	+	4.14608i	−0.0493078	+	0.144260i
$827$	8.04663			0.279809			0.139904	−	0.990165i	$-0.455321\pi$
$827$	8.04663			0.279809			0.139904	+	0.990165i	$0.455321\pi$
$828$		0			0
$829$	−3.50513	−	6.07107i	−0.121738	−	0.210857i	0.798715	−	0.601710i	$-0.205514\pi$
$829$	−3.50513	−	6.07107i	−0.121738	−	0.210857i	−0.920453	+	0.390853i	$0.872180\pi$
$830$	3.55207	+	6.15237i	0.123294	+	0.213552i
$831$		0			0
$832$	−25.8436			−0.895965
$833$	−1.00772	+	7.41372i	−0.0349154	+	0.256870i
$834$		0			0
$835$	−0.260826	+	0.451764i	−0.00902626	+	0.0156339i
$836$	2.72611	+	4.72177i	0.0942846	+	0.163306i
$837$		0			0
$838$	−19.6334	+	34.0060i	−0.678224	+	1.17472i
$839$	−22.4205			−0.774043			−0.387021	−	0.922071i	$-0.626496\pi$
$839$	−22.4205			−0.774043			−0.387021	+	0.922071i	$0.626496\pi$
$840$		0			0
$841$	44.5419			1.53593
$842$	19.5833	−	33.9192i	0.674884	−	1.16893i
$843$		0			0
$844$	11.1807	+	19.3655i	0.384855	+	0.666588i
$845$	2.93851	−	5.08965i	0.101088	−	0.175089i
$846$		0			0
$847$	−1.74029	−	1.99284i	−0.0597969	−	0.0684748i
$848$	−5.50730			−0.189122
$849$		0			0
$850$	−1.28294	−	2.22211i	−0.0440044	−	0.0762178i
$851$	−6.06558	−	10.5059i	−0.207926	−	0.360138i
$852$		0			0
$853$	−36.0726			−1.23510			−0.617551	−	0.786531i	$-0.711875\pi$
$853$	−36.0726			−1.23510			−0.617551	+	0.786531i	$0.711875\pi$
$854$	34.3215	−	6.75210i	1.17446	−	0.231052i
$855$		0			0
$856$	5.35543	−	9.27588i	0.183045	−	0.317043i
$857$	14.4568	+	25.0399i	0.493835	+	0.855347i	0.999975	−	0.00710463i	$-0.00226149\pi$
$857$	14.4568	+	25.0399i	0.493835	+	0.855347i	−0.506140	+	0.862451i	$0.668928\pi$
$858$		0			0
$859$	14.5667	−	25.2302i	0.497008	−	0.860843i	−0.502986	−	0.864295i	$-0.667765\pi$
$859$	14.5667	−	25.2302i	0.497008	−	0.860843i	0.999994	+	0.00345141i	$0.00109862\pi$
$860$	6.38452			0.217710
$861$		0			0
$862$	−27.6063			−0.940275
$863$	24.3239	−	42.1302i	0.827995	−	1.43413i	−0.0716137	−	0.997432i	$-0.522815\pi$
$863$	24.3239	−	42.1302i	0.827995	−	1.43413i	0.899609	−	0.436697i	$-0.143852\pi$
$864$		0			0
$865$	12.1512	+	21.0465i	0.413153	+	0.715602i
$866$	2.57178	−	4.45446i	0.0873927	−	0.151369i
$867$		0			0
$868$	5.75715	+	6.59263i	0.195410	+	0.223769i
$869$	−9.38741			−0.318446
$870$		0			0
$871$	−13.3263	−	23.0818i	−0.451545	−	0.782098i
$872$	5.81836	+	10.0777i	0.197034	+	0.341274i
$873$		0			0
$874$	−10.5289			−0.356145
$875$	6.34365	−	18.5597i	0.214454	−	0.627432i
$876$		0			0
$877$	−5.25459	+	9.10122i	−0.177435	+	0.307326i	−0.941001	−	0.338403i	$-0.890113\pi$
$877$	−5.25459	+	9.10122i	−0.177435	+	0.307326i	0.763566	+	0.645729i	$0.223447\pi$
$878$	−14.5822	−	25.2572i	−0.492127	−	0.852388i
$879$		0			0
$880$	−2.08538	+	3.61199i	−0.0702983	+	0.121760i
$881$	18.6650			0.628841			0.314420	−	0.949284i	$-0.398190\pi$
$881$	18.6650			0.628841			0.314420	+	0.949284i	$0.398190\pi$
$882$		0			0
$883$	26.2974			0.884980			0.442490	−	0.896774i	$-0.354095\pi$
$883$	26.2974			0.884980			0.442490	+	0.896774i	$0.354095\pi$
$884$	−1.50731	+	2.61075i	−0.0506965	+	0.0878089i
$885$		0			0
$886$	−14.4992	−	25.1134i	−0.487112	−	0.843702i
$887$	−23.3883	+	40.5097i	−0.785302	+	1.36018i	0.143516	+	0.989648i	$0.454159\pi$
$887$	−23.3883	+	40.5097i	−0.785302	+	1.36018i	−0.928818	+	0.370536i	$0.879174\pi$
$888$		0			0
$889$	−10.8632	+	31.7827i	−0.364342	+	1.06596i
$890$	33.4611			1.12162
$891$		0			0
$892$	5.73209	+	9.92827i	0.191925	+	0.332423i
$893$	29.0324	+	50.2855i	0.971531	+	1.68274i
$894$		0			0
$895$	−32.9058			−1.09992
$896$	0.880955	+	1.00880i	0.0294306	+	0.0337017i
$897$		0			0
$898$	2.28485	−	3.95747i	0.0762464	−	0.132063i
$899$	−16.5406	−	28.6492i	−0.551661	−	0.955504i
$900$		0			0
$901$	−1.89957	+	3.29015i	−0.0632839	+	0.109611i
$902$	−7.35059			−0.244748
$903$		0			0
$904$	34.0002			1.13083
$905$	24.9141	−	43.1525i	0.828173	−	1.43444i
$906$		0			0
$907$	−20.3777	−	35.2951i	−0.676629	−	1.17196i	−0.975990	−	0.217816i	$-0.930107\pi$
$907$	−20.3777	−	35.2951i	−0.676629	−	1.17196i	0.299361	−	0.954140i	$-0.403227\pi$
$908$	9.75830	−	16.9019i	0.323840	−	0.560908i
$909$		0			0
$910$	−24.5648	+	4.83266i	−0.814316	+	0.160201i
$911$	14.9736			0.496099			0.248050	−	0.968747i	$-0.420210\pi$
$911$	14.9736			0.496099			0.248050	+	0.968747i	$0.420210\pi$
$912$		0			0
$913$	−1.23458	−	2.13836i	−0.0408586	−	0.0707693i
$914$	−15.5514	−	26.9358i	−0.514395	−	0.890958i
$915$		0			0
$916$	−21.9222			−0.724331
$917$	11.3913	+	13.0445i	0.376175	+	0.430767i
$918$		0			0
$919$	16.9907	−	29.4288i	0.560473	−	0.970767i	−0.436982	−	0.899470i	$-0.643953\pi$
$919$	16.9907	−	29.4288i	0.560473	−	0.970767i	0.997455	−	0.0712972i	$-0.0227139\pi$
$920$	6.36939	+	11.0321i	0.209992	+	0.363718i
$921$		0			0
$922$	−1.58708	+	2.74891i	−0.0522678	+	0.0905305i
$923$	34.3196			1.12964
$924$		0			0
$925$	17.5850			0.578192
$926$	10.8528	−	18.7976i	0.356645	−	0.617728i
$927$		0			0
$928$	−19.0916	−	33.0677i	−0.626714	−	1.08550i
$929$	−26.0368	+	45.0971i	−0.854241	+	1.47959i	0.0231073	+	0.999733i	$0.492644\pi$
$929$	−26.0368	+	45.0971i	−0.854241	+	1.47959i	−0.877348	+	0.479855i	$0.840689\pi$
$930$		0			0
$931$	−41.1875	+	16.8582i	−1.34987	+	0.552505i
$932$	−19.2677			−0.631135
$933$		0			0
$934$	19.8457	+	34.3738i	0.649371	+	1.12474i
$935$	1.43858	+	2.49169i	0.0470464	+	0.0814868i
$936$		0			0
$937$	−50.0381			−1.63467			−0.817336	−	0.576161i	$-0.804550\pi$
$937$	−50.0381			−1.63467			−0.817336	+	0.576161i	$0.804550\pi$
$938$	7.41191	−	21.6851i	0.242008	−	0.708044i
$939$		0			0
$940$	10.5415	−	18.2584i	0.343826	−	0.595523i
$941$	12.7152	+	22.0234i	0.414504	+	0.717941i	0.995376	−	0.0960531i	$-0.0306219\pi$
$941$	12.7152	+	22.0234i	0.414504	+	0.717941i	−0.580873	+	0.813995i	$0.697289\pi$
$942$		0			0
$943$	−5.32777	+	9.22798i	−0.173496	+	0.300504i
$944$	−2.40068			−0.0781355
$945$		0			0
$946$	2.95611			0.0961114
$947$	10.3518	−	17.9298i	0.336387	−	0.582639i	−0.647363	−	0.762182i	$-0.724128\pi$
$947$	10.3518	−	17.9298i	0.336387	−	0.582639i	0.983750	+	0.179542i	$0.0574617\pi$
$948$		0			0
$949$	23.4333	+	40.5877i	0.760677	+	1.31753i
$950$	7.63120	−	13.2176i	0.247589	−	0.428837i
$951$		0			0
$952$	−8.47478	+	1.66725i	−0.274669	+	0.0540359i
$953$	4.08220			0.132235			0.0661177	−	0.997812i	$-0.478939\pi$
$953$	4.08220			0.132235			0.0661177	+	0.997812i	$0.478939\pi$
$954$		0			0
$955$	24.8531	+	43.0469i	0.804228	+	1.39296i
$956$	5.64716	+	9.78117i	0.182642	+	0.316346i
$957$		0			0
$958$	−19.6332			−0.634319
$959$	−55.5889	+	10.9360i	−1.79506	+	0.353143i
$960$		0			0
$961$	8.05956	−	13.9596i	0.259986	−	0.450308i
$962$	13.7615	+	23.8357i	0.443690	+	0.768493i
$963$		0			0
$964$	6.23918	−	10.8066i	0.200950	−	0.348056i
$965$	−45.8742			−1.47674
$966$		0			0
$967$	−20.6016			−0.662503			−0.331251	−	0.943543i	$-0.607471\pi$
$967$	−20.6016			−0.662503			−0.331251	+	0.943543i	$0.607471\pi$
$968$	1.52715	−	2.64510i	0.0490844	−	0.0850167i
$969$		0			0
$970$	−18.2186	−	31.5556i	−0.584966	−	1.01319i
$971$	−13.1401	+	22.7593i	−0.421685	+	0.730380i	−0.996104	−	0.0881812i	$-0.971895\pi$
$971$	−13.1401	+	22.7593i	−0.421685	+	0.730380i	0.574419	+	0.818561i	$0.305228\pi$
$972$		0			0
$973$	−0.728125	+	2.13028i	−0.0233426	+	0.0682938i
$974$	−21.5101			−0.689228
$975$		0			0
$976$	9.58267	+	16.5977i	0.306734	+	0.531279i
$977$	14.5896	+	25.2699i	0.466761	+	0.808454i	0.999279	−	0.0379644i	$-0.0120874\pi$
$977$	14.5896	+	25.2699i	0.466761	+	0.808454i	−0.532518	+	0.846419i	$0.678754\pi$
$978$		0			0
$979$	−11.6300			−0.371695
$980$	12.7785	+	9.89082i	0.408195	+	0.315951i
$981$		0			0
$982$	8.03169	−	13.9113i	0.256302	−	0.443927i
$983$	23.1034	+	40.0162i	0.736883	+	1.27632i	0.953892	+	0.300150i	$0.0970366\pi$
$983$	23.1034	+	40.0162i	0.736883	+	1.27632i	−0.217009	+	0.976170i	$0.569630\pi$
$984$		0			0
$985$	7.33904	−	12.7116i	0.233841	−	0.405025i
$986$	9.79704			0.312001
$987$		0			0
$988$	−17.9317			−0.570484
$989$	2.14261	−	3.71112i	0.0681312	−	0.118007i
$990$		0			0
$991$	15.7825	+	27.3361i	0.501348	+	0.868361i	0.999999	+	0.00155771i	$0.000495834\pi$
$991$	15.7825	+	27.3361i	0.501348	+	0.868361i	−0.498650	+	0.866803i	$0.666171\pi$
$992$	−8.58796	+	14.8748i	−0.272668	+	0.472275i
$993$		0			0
$994$	19.4101	+	22.2270i	0.615652	+	0.704996i
$995$	11.6596			0.369635
$996$		0			0
$997$	−9.04177	−	15.6608i	−0.286356	−	0.495982i	0.686581	−	0.727053i	$-0.259111\pi$
$997$	−9.04177	−	15.6608i	−0.286356	−	0.495982i	−0.972937	+	0.231070i	$0.925777\pi$
$998$	−1.14496	−	1.98312i	−0.0362430	−	0.0627747i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.i.j.100.2		10
3.2	odd	2		231.2.i.f.100.4	yes	10
7.2	even	3		4851.2.a.ca.1.4		5
7.4	even	3	inner	693.2.i.j.298.2		10
7.5	odd	6		4851.2.a.bz.1.4		5
21.2	odd	6		1617.2.a.ba.1.2		5
21.5	even	6		1617.2.a.bb.1.2		5
21.11	odd	6		231.2.i.f.67.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.f.67.4	✓	10	21.11	odd	6
231.2.i.f.100.4	yes	10	3.2	odd	2
693.2.i.j.100.2		10	1.1	even	1	trivial
693.2.i.j.298.2		10	7.4	even	3	inner
1617.2.a.ba.1.2		5	21.2	odd	6
1617.2.a.bb.1.2		5	21.5	even	6
4851.2.a.bz.1.4		5	7.5	odd	6
4851.2.a.ca.1.4		5	7.2	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.534421 + 0.925645i) q^{2} +(0.428788 + 0.742682i) q^{4} +(-1.34592 + 2.33120i) q^{5} +(-0.855706 + 2.50355i) q^{7} -3.05430 q^{8} +O(q^{10})\)	\(q+(-0.534421 + 0.925645i) q^{2} +(0.428788 + 0.742682i) q^{4} +(-1.34592 + 2.33120i) q^{5} +(-0.855706 + 2.50355i) q^{7} -3.05430 q^{8} +(-1.43858 - 2.49169i) q^{10} +(0.500000 + 0.866025i) q^{11} -3.28888 q^{13} +(-1.86009 - 2.13003i) q^{14} +(0.774707 - 1.34183i) q^{16} +(-0.534421 - 0.925645i) q^{17} +(3.17886 - 5.50595i) q^{19} -2.30845 q^{20} -1.06884 q^{22} +(-0.774707 + 1.34183i) q^{23} +(-1.12300 - 1.94508i) q^{25} +(1.75765 - 3.04433i) q^{26} +(-2.22626 + 0.437974i) q^{28} +8.57566 q^{29} +(-1.92879 - 3.34076i) q^{31} +(-2.22626 - 3.85599i) q^{32} +1.14242 q^{34} +(-4.68457 - 5.36440i) q^{35} +(-3.91476 + 6.78057i) q^{37} +(3.39770 + 5.88499i) q^{38} +(4.11084 - 7.12018i) q^{40} +6.87715 q^{41} -2.76571 q^{43} +(-0.428788 + 0.742682i) q^{44} +(-0.828039 - 1.43421i) q^{46} +(-4.56647 + 7.90936i) q^{47} +(-5.53553 - 4.28461i) q^{49} +2.40061 q^{50} +(-1.41023 - 2.44259i) q^{52} +(-1.77722 - 3.07824i) q^{53} -2.69184 q^{55} +(2.61358 - 7.64659i) q^{56} +(-4.58301 + 7.93801i) q^{58} +(-0.774707 - 1.34183i) q^{59} +(-6.18471 + 10.7122i) q^{61} +4.12314 q^{62} +7.85787 q^{64} +(4.42656 - 7.66703i) q^{65} +(4.05193 + 7.01815i) q^{67} +(0.458307 - 0.793810i) q^{68} +(7.46906 - 1.46939i) q^{70} -10.4350 q^{71} +(-7.12501 - 12.3409i) q^{73} +(-4.18426 - 7.24736i) q^{74} +5.45223 q^{76} +(-2.59599 + 0.510712i) q^{77} +(-4.69371 + 8.12974i) q^{79} +(2.08538 + 3.61199i) q^{80} +(-3.67530 + 6.36580i) q^{82} -2.46916 q^{83} +2.87715 q^{85} +(1.47806 - 2.56007i) q^{86} +(-1.52715 - 2.64510i) q^{88} +(-5.81498 + 10.0718i) q^{89} +(2.81431 - 8.23388i) q^{91} -1.32874 q^{92} +(-4.88084 - 8.45386i) q^{94} +(8.55698 + 14.8211i) q^{95} +12.6644 q^{97} +(6.92433 - 2.83415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 10 q^{4} - 4 q^{5} - q^{7} - 12 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 - 10 * q^4 - 4 * q^5 - q^7 - 12 * q^8	\( 10 q + 2 q^{2} - 10 q^{4} - 4 q^{5} - q^{7} - 12 q^{8} - 2 q^{10} + 5 q^{11} + 10 q^{13} + 10 q^{14} - 16 q^{16} + 2 q^{17} + 3 q^{19} + 16 q^{20} + 4 q^{22} + 16 q^{23} - 7 q^{25} - 10 q^{26} + 4 q^{28} - 5 q^{31} + 4 q^{32} + 40 q^{34} - 26 q^{35} - 15 q^{37} + 6 q^{38} + 6 q^{40} + 44 q^{41} + 6 q^{43} + 10 q^{44} - 16 q^{46} - 2 q^{47} + 31 q^{49} - 68 q^{50} - 40 q^{52} + 6 q^{53} - 8 q^{55} + 12 q^{56} - 12 q^{58} + 16 q^{59} - 12 q^{61} + 8 q^{62} - 8 q^{64} - 28 q^{65} - 7 q^{67} + 10 q^{68} + 32 q^{70} - 48 q^{71} - 17 q^{73} - 36 q^{74} + 60 q^{76} - 2 q^{77} - 7 q^{79} + 16 q^{80} - 8 q^{82} + 24 q^{83} + 4 q^{85} - 18 q^{86} - 6 q^{88} - 6 q^{89} + 11 q^{91} - 136 q^{92} - 82 q^{94} - 18 q^{95} - 28 q^{97} + 38 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 10 * q^4 - 4 * q^5 - q^7 - 12 * q^8 - 2 * q^10 + 5 * q^11 + 10 * q^13 + 10 * q^14 - 16 * q^16 + 2 * q^17 + 3 * q^19 + 16 * q^20 + 4 * q^22 + 16 * q^23 - 7 * q^25 - 10 * q^26 + 4 * q^28 - 5 * q^31 + 4 * q^32 + 40 * q^34 - 26 * q^35 - 15 * q^37 + 6 * q^38 + 6 * q^40 + 44 * q^41 + 6 * q^43 + 10 * q^44 - 16 * q^46 - 2 * q^47 + 31 * q^49 - 68 * q^50 - 40 * q^52 + 6 * q^53 - 8 * q^55 + 12 * q^56 - 12 * q^58 + 16 * q^59 - 12 * q^61 + 8 * q^62 - 8 * q^64 - 28 * q^65 - 7 * q^67 + 10 * q^68 + 32 * q^70 - 48 * q^71 - 17 * q^73 - 36 * q^74 + 60 * q^76 - 2 * q^77 - 7 * q^79 + 16 * q^80 - 8 * q^82 + 24 * q^83 + 4 * q^85 - 18 * q^86 - 6 * q^88 - 6 * q^89 + 11 * q^91 - 136 * q^92 - 82 * q^94 - 18 * q^95 - 28 * q^97 + 38 * q^98

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