LMFDB - Embedded newform 1078.2.i.c.1011.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.4
Root			$-0.186243 + 0.0499037i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.c.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(2.70809 + 1.56352i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.90775 - 1.10144i) q^{5} -3.12703 q^{6} +1.00000i q^{8} +(3.38916 + 5.87020i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(2.70809 + 1.56352i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.90775 - 1.10144i) q^{5} -3.12703 q^{6} +1.00000i q^{8} +(3.38916 + 5.87020i) q^{9} +(-1.10144 + 1.90775i) q^{10} +(3.31114 + 0.190575i) q^{11} +(2.70809 - 1.56352i) q^{12} -1.45937 q^{13} +6.88847 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.80366 - 6.58813i) q^{17} +(-5.87020 - 3.38916i) q^{18} +(0.0903227 + 0.156443i) q^{19} -2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +(-1.14390 - 1.98129i) q^{23} +(-1.56352 + 2.70809i) q^{24} +(-0.0736626 + 0.127587i) q^{25} +(1.26385 - 0.729686i) q^{26} +11.8149i q^{27} +4.45335i q^{29} +(-5.96559 + 3.44423i) q^{30} +(-7.40363 - 4.27449i) q^{31} +(0.866025 + 0.500000i) q^{32} +(8.66891 + 5.69312i) q^{33} +7.60732i q^{34} +6.77832 q^{36} +(-0.754735 - 1.30724i) q^{37} +(-0.156443 - 0.0903227i) q^{38} +(-3.95211 - 2.28175i) q^{39} +(1.10144 + 1.90775i) q^{40} -7.10368 q^{41} +1.58174i q^{43} +(1.82062 - 2.77225i) q^{44} +(12.9313 + 7.46591i) q^{45} +(1.98129 + 1.14390i) q^{46} +(0.472293 - 0.272679i) q^{47} -3.12703i q^{48} -0.147325i q^{50} +(20.6013 - 11.8942i) q^{51} +(-0.729686 + 1.26385i) q^{52} +(-2.41722 + 4.18675i) q^{53} +(-5.90746 - 10.2320i) q^{54} +(6.52674 - 3.28346i) q^{55} +0.564883i q^{57} +(-2.22668 - 3.85672i) q^{58} +(5.36041 + 3.09483i) q^{59} +(3.44423 - 5.96559i) q^{60} +(2.86310 + 4.95904i) q^{61} +8.54897 q^{62} -1.00000 q^{64} +(-2.78412 + 1.60741i) q^{65} +(-10.3541 - 0.595934i) q^{66} +(1.49088 - 2.58228i) q^{67} +(-3.80366 - 6.58813i) q^{68} -7.15399i q^{69} -7.57488 q^{71} +(-5.87020 + 3.38916i) q^{72} +(4.83822 - 8.38004i) q^{73} +(1.30724 + 0.754735i) q^{74} +(-0.398970 + 0.230345i) q^{75} +0.180645 q^{76} +4.56350 q^{78} +(-5.99185 + 3.45939i) q^{79} +(-1.90775 - 1.10144i) q^{80} +(-8.30534 + 14.3853i) q^{81} +(6.15197 - 3.55184i) q^{82} -5.84246 q^{83} -16.7580i q^{85} +(-0.790869 - 1.36983i) q^{86} +(-6.96289 + 12.0601i) q^{87} +(-0.190575 + 3.31114i) q^{88} +(-13.9527 + 8.05557i) q^{89} -14.9318 q^{90} -2.28779 q^{92} +(-13.3665 - 23.1514i) q^{93} +(-0.272679 + 0.472293i) q^{94} +(0.344626 + 0.198970i) q^{95} +(1.56352 + 2.70809i) q^{96} +11.3012i q^{97} +(10.1033 + 20.0830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 32 * q^36 - 16 * q^37 - 12 * q^38 - 8 * q^44 + 108 * q^45 - 24 * q^47 - 28 * q^53 - 12 * q^58 - 60 * q^59 - 4 * q^60 - 16 * q^64 - 48 * q^66 + 12 * q^67 + 8 * q^71 - 60 * q^75 - 16 * q^78 - 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 - 96 * q^89 + 32 * q^92 - 44 * q^93 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	2.70809	+	1.56352i	1.56352	+	0.902696i	0.996897	+	0.0787156i	$0.0250819\pi$
$3$	2.70809	+	1.56352i	1.56352	+	0.902696i	0.566618	+	0.823980i	$0.308251\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.90775	−	1.10144i	0.853171	−	0.492579i	−0.00854833	−	0.999963i	$-0.502721\pi$
$5$	1.90775	−	1.10144i	0.853171	−	0.492579i	0.861720	+	0.507385i	$0.169388\pi$
$6$	−3.12703			−1.27660
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	3.38916	+	5.87020i	1.12972	+	1.95673i
$10$	−1.10144	+	1.90775i	−0.348306	+	0.603283i
$11$	3.31114	+	0.190575i	0.998348	+	0.0574605i
$11$	3.31114	+	0.190575i	0.998348	+	0.0574605i
$12$	2.70809	−	1.56352i	0.781758	−	0.451348i
$13$	−1.45937			−0.404757			−0.202378	−	0.979307i	$-0.564867\pi$
$13$	−1.45937			−0.404757			−0.202378	+	0.979307i	$0.564867\pi$
$14$		0			0
$15$	6.88847			1.77860
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.80366	−	6.58813i	0.922523	−	1.59786i	0.127025	−	0.991899i	$-0.459457\pi$
$17$	3.80366	−	6.58813i	0.922523	−	1.59786i	0.795498	−	0.605957i	$-0.207210\pi$
$18$	−5.87020	−	3.38916i	−1.38362	−	0.798833i
$19$	0.0903227	+	0.156443i	0.0207214	+	0.0358906i	0.876200	−	0.481947i	$-0.160070\pi$
$19$	0.0903227	+	0.156443i	0.0207214	+	0.0358906i	−0.855479	+	0.517838i	$0.826737\pi$
$20$		−	2.20288i		−	0.492579i
$21$		0			0
$22$	−2.96282	+	1.49053i	−0.631676	+	0.317782i
$23$	−1.14390	−	1.98129i	−0.238519	−	0.413127i	0.721771	−	0.692132i	$-0.243329\pi$
$23$	−1.14390	−	1.98129i	−0.238519	−	0.413127i	−0.960289	+	0.279006i	$0.909995\pi$
$24$	−1.56352	+	2.70809i	−0.319151	+	0.552786i
$25$	−0.0736626	+	0.127587i	−0.0147325	+	0.0255175i
$26$	1.26385	−	0.729686i	0.247862	−	0.143103i
$27$			11.8149i			2.27378i
$28$		0			0
$29$			4.45335i			0.826967i	0.910512	+	0.413483i	$0.135688\pi$
$29$			4.45335i			0.826967i	−0.910512	+	0.413483i	$0.864312\pi$
$30$	−5.96559	+	3.44423i	−1.08916	+	0.628828i
$31$	−7.40363	−	4.27449i	−1.32973	−	0.767720i	−0.344473	−	0.938796i	$-0.611942\pi$
$31$	−7.40363	−	4.27449i	−1.32973	−	0.767720i	−0.985258	+	0.171076i	$0.945276\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	8.66891	+	5.69312i	1.50906	+	0.991045i
$34$			7.60732i			1.30464i
$35$		0			0
$36$	6.77832			1.12972
$37$	−0.754735	−	1.30724i	−0.124078	−	0.214909i	0.797294	−	0.603591i	$-0.206264\pi$
$37$	−0.754735	−	1.30724i	−0.124078	−	0.214909i	−0.921372	+	0.388682i	$0.872931\pi$
$38$	−0.156443	−	0.0903227i	−0.0253785	−	0.0146523i
$39$	−3.95211	−	2.28175i	−0.632844	−	0.365373i
$40$	1.10144	+	1.90775i	0.174153	+	0.301642i
$41$	−7.10368			−1.10941			−0.554705	−	0.832047i	$-0.687169\pi$
$41$	−7.10368			−1.10941			−0.554705	+	0.832047i	$0.687169\pi$
$42$		0			0
$43$			1.58174i			0.241213i	0.992700	+	0.120606i	$0.0384839\pi$
$43$			1.58174i			0.241213i	−0.992700	+	0.120606i	$0.961516\pi$
$44$	1.82062	−	2.77225i	0.274468	−	0.417932i
$45$	12.9313	+	7.46591i	1.92769	+	1.11295i
$46$	1.98129	+	1.14390i	0.292125	+	0.168658i
$47$	0.472293	−	0.272679i	0.0688911	−	0.0397743i	−0.465159	−	0.885227i	$-0.654003\pi$
$47$	0.472293	−	0.272679i	0.0688911	−	0.0397743i	0.534050	+	0.845453i	$0.320669\pi$
$48$		−	3.12703i		−	0.451348i
$49$		0			0
$50$		−	0.147325i		−	0.0208349i
$51$	20.6013	−	11.8942i	2.88476	−	1.66552i
$52$	−0.729686	+	1.26385i	−0.101189	+	0.175265i
$53$	−2.41722	+	4.18675i	−0.332031	+	0.575094i	−0.982910	−	0.184087i	$-0.941067\pi$
$53$	−2.41722	+	4.18675i	−0.332031	+	0.575094i	0.650879	+	0.759181i	$0.274400\pi$
$54$	−5.90746	−	10.2320i	−0.803904	−	1.39240i
$55$	6.52674	−	3.28346i	0.880065	−	0.442741i
$56$		0			0
$57$			0.564883i			0.0748206i
$58$	−2.22668	−	3.85672i	−0.292377	−	0.506412i
$59$	5.36041	+	3.09483i	0.697866	+	0.402913i	0.806552	−	0.591163i	$-0.201331\pi$
$59$	5.36041	+	3.09483i	0.697866	+	0.402913i	−0.108686	+	0.994076i	$0.534664\pi$
$60$	3.44423	−	5.96559i	0.444649	−	0.770154i
$61$	2.86310	+	4.95904i	0.366583	+	0.634940i	0.989029	−	0.147723i	$-0.0471943\pi$
$61$	2.86310	+	4.95904i	0.366583	+	0.634940i	−0.622446	+	0.782663i	$0.713861\pi$
$62$	8.54897			1.08572
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.78412	+	1.60741i	−0.345327	+	0.199375i
$66$	−10.3541	−	0.595934i	−1.27450	−	0.0733544i
$67$	1.49088	−	2.58228i	0.182140	−	0.315476i	−0.760469	−	0.649374i	$-0.775031\pi$
$67$	1.49088	−	2.58228i	0.182140	−	0.315476i	0.942609	+	0.333898i	$0.108364\pi$
$68$	−3.80366	−	6.58813i	−0.461261	−	0.798928i
$69$		−	7.15399i		−	0.861240i
$70$		0			0
$71$	−7.57488			−0.898973			−0.449486	−	0.893287i	$-0.648393\pi$
$71$	−7.57488			−0.898973			−0.449486	+	0.893287i	$0.648393\pi$
$72$	−5.87020	+	3.38916i	−0.691809	+	0.399416i
$73$	4.83822	−	8.38004i	0.566271	−	0.980810i	−0.430659	−	0.902515i	$-0.641719\pi$
$73$	4.83822	−	8.38004i	0.566271	−	0.980810i	0.996930	−	0.0782953i	$-0.0249477\pi$
$74$	1.30724	+	0.754735i	0.151964	+	0.0877362i
$75$	−0.398970	+	0.230345i	−0.0460691	+	0.0265980i
$76$	0.180645			0.0207214
$77$		0			0
$78$	4.56350			0.516715
$79$	−5.99185	+	3.45939i	−0.674135	+	0.389212i	−0.797642	−	0.603132i	$-0.793919\pi$
$79$	−5.99185	+	3.45939i	−0.674135	+	0.389212i	0.123506	+	0.992344i	$0.460586\pi$
$80$	−1.90775	−	1.10144i	−0.213293	−	0.123145i
$81$	−8.30534	+	14.3853i	−0.922815	+	1.59836i
$82$	6.15197	−	3.55184i	0.679372	−	0.392235i
$83$	−5.84246			−0.641293			−0.320647	−	0.947199i	$-0.603900\pi$
$83$	−5.84246			−0.641293			−0.320647	+	0.947199i	$0.603900\pi$
$84$		0			0
$85$		−	16.7580i		−	1.81766i
$86$	−0.790869	−	1.36983i	−0.0852816	−	0.147712i
$87$	−6.96289	+	12.0601i	−0.746500	+	1.29298i
$88$	−0.190575	+	3.31114i	−0.0203154	+	0.352969i
$89$	−13.9527	+	8.05557i	−1.47898	+	0.853889i	−0.999717	−	0.0237828i	$-0.992429\pi$
$89$	−13.9527	+	8.05557i	−1.47898	+	0.853889i	−0.479262	+	0.877672i	$0.659096\pi$
$90$	−14.9318			−1.57395
$91$		0			0
$92$	−2.28779			−0.238519
$93$	−13.3665	−	23.1514i	−1.38604	−	2.40069i
$94$	−0.272679	+	0.472293i	−0.0281247	+	0.0487133i
$95$	0.344626	+	0.198970i	0.0353579	+	0.0204139i
$96$	1.56352	+	2.70809i	0.159576	+	0.276393i
$97$			11.3012i			1.14746i	0.819045	+	0.573729i	$0.194504\pi$
$97$			11.3012i			1.14746i	−0.819045	+	0.573729i	$0.805496\pi$
$98$		0			0
$99$	10.1033	+	20.0830i	1.01542	+	2.01841i
$100$	0.0736626	+	0.127587i	0.00736626	+	0.0127587i
$101$	0.258858	−	0.448355i	0.0257573	−	0.0446130i	−0.852859	−	0.522141i	$-0.825134\pi$
$101$	0.258858	−	0.448355i	0.0257573	−	0.0446130i	0.878617	+	0.477528i	$0.158467\pi$
$102$	−11.8942	+	20.6013i	−1.17770	+	2.03983i
$103$	2.50035	−	1.44358i	0.246367	−	0.142240i	−0.371733	−	0.928340i	$-0.621236\pi$
$103$	2.50035	−	1.44358i	0.246367	−	0.142240i	0.618100	+	0.786100i	$0.287903\pi$
$104$		−	1.45937i		−	0.143103i
$105$		0			0
$106$		−	4.83444i		−	0.469562i
$107$	−4.52030	+	2.60980i	−0.436994	+	0.252299i	−0.702322	−	0.711860i	$-0.747853\pi$
$107$	−4.52030	+	2.60980i	−0.436994	+	0.252299i	0.265328	+	0.964158i	$0.414520\pi$
$108$	10.2320	+	5.90746i	0.984577	+	0.568446i
$109$	8.70705	+	5.02702i	0.833984	+	0.481501i	0.855215	−	0.518274i	$-0.173425\pi$
$109$	8.70705	+	5.02702i	0.833984	+	0.481501i	−0.0212309	+	0.999775i	$0.506759\pi$
$110$	−4.01059	+	6.10693i	−0.382395	+	0.582273i
$111$		−	4.72016i		−	0.448018i
$112$		0			0
$113$	7.83235			0.736806			0.368403	−	0.929666i	$-0.379905\pi$
$113$	7.83235			0.736806			0.368403	+	0.929666i	$0.379905\pi$
$114$	−0.282442	−	0.489203i	−0.0264531	−	0.0458181i
$115$	−4.36453	−	2.51986i	−0.406995	−	0.234978i
$116$	3.85672	+	2.22668i	0.358087	+	0.206742i
$117$	−4.94605	−	8.56680i	−0.457262	−	0.792001i
$118$	−6.18967			−0.569805
$119$		0			0
$120$			6.88847i			0.628828i
$121$	10.9274	+	1.26204i	0.993397	+	0.114731i
$122$	−4.95904	−	2.86310i	−0.448971	−	0.259213i
$123$	−19.2374	−	11.1067i	−1.73458	−	1.00146i
$124$	−7.40363	+	4.27449i	−0.664865	+	0.383860i
$125$			11.3389i			1.01419i
$126$		0			0
$127$		−	13.4702i		−	1.19529i	−0.801762	−	0.597644i	$-0.796104\pi$
$127$		−	13.4702i		−	1.19529i	0.801762	−	0.597644i	$-0.203896\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.47307	+	4.28348i	−0.217742	+	0.377140i
$130$	1.60741	−	2.78412i	0.140979	−	0.244183i
$131$	1.31231	+	2.27298i	0.114657	+	0.198592i	0.917643	−	0.397407i	$-0.130090\pi$
$131$	1.31231	+	2.27298i	0.114657	+	0.198592i	−0.802986	+	0.595998i	$0.796756\pi$
$132$	9.26484	−	4.66093i	0.806401	−	0.405682i
$133$		0			0
$134$			2.98176i			0.257585i
$135$	13.0134	+	22.5399i	1.12002	+	1.93993i
$136$	6.58813	+	3.80366i	0.564928	+	0.326161i
$137$	4.36145	−	7.55426i	0.372624	−	0.645404i	−0.617344	−	0.786693i	$-0.711791\pi$
$137$	4.36145	−	7.55426i	0.372624	−	0.645404i	0.989968	+	0.141289i	$0.0451247\pi$
$138$	3.57700	+	6.19554i	0.304494	+	0.527399i
$139$	4.09291			0.347156			0.173578	−	0.984820i	$-0.444467\pi$
$139$	4.09291			0.347156			0.173578	+	0.984820i	$0.444467\pi$
$140$		0			0
$141$	1.70535			0.143616
$142$	6.56004	−	3.78744i	0.550506	−	0.317835i
$143$	−4.83219	−	0.278120i	−0.404088	−	0.0232575i
$144$	3.38916	−	5.87020i	0.282430	−	0.489183i
$145$	4.90510	+	8.49588i	0.407346	+	0.705544i
$146$			9.67644i			0.800828i
$147$		0			0
$148$	−1.50947			−0.124078
$149$	−16.1009	+	9.29587i	−1.31904	+	0.761547i	−0.983574	−	0.180506i	$-0.942227\pi$
$149$	−16.1009	+	9.29587i	−1.31904	+	0.761547i	−0.335464	+	0.942053i	$0.608893\pi$
$150$	0.230345	−	0.398970i	0.0188076	−	0.0325757i
$151$	−11.4354	−	6.60225i	−0.930602	−	0.537283i	−0.0435999	−	0.999049i	$-0.513883\pi$
$151$	−11.4354	−	6.60225i	−0.930602	−	0.537283i	−0.887002	+	0.461766i	$0.847216\pi$
$152$	−0.156443	+	0.0903227i	−0.0126892	+	0.00732613i
$153$	51.5648			4.16877
$154$		0			0
$155$	−18.8324			−1.51265
$156$	−3.95211	+	2.28175i	−0.316422	+	0.182686i
$157$	−4.98745	−	2.87951i	−0.398042	−	0.229810i	0.287597	−	0.957752i	$-0.407144\pi$
$157$	−4.98745	−	2.87951i	−0.398042	−	0.229810i	−0.685639	+	0.727942i	$0.740477\pi$
$158$	3.45939	−	5.99185i	0.275215	−	0.476686i
$159$	−13.0921	+	7.55872i	−1.03827	+	0.599445i
$160$	2.20288			0.174153
$161$		0			0
$162$		−	16.6107i		−	1.30506i
$163$	2.65644	+	4.60109i	0.208069	+	0.360386i	0.951106	−	0.308864i	$-0.0999489\pi$
$163$	2.65644	+	4.60109i	0.208069	+	0.360386i	−0.743037	+	0.669250i	$0.766616\pi$
$164$	−3.55184	+	6.15197i	−0.277352	+	0.480388i
$165$	22.8087	+	1.31277i	1.77566	+	0.102199i
$166$	5.05972	−	2.92123i	0.392710	−	0.226731i
$167$	−16.0519			−1.24213			−0.621067	−	0.783757i	$-0.713301\pi$
$167$	−16.0519			−1.24213			−0.621067	+	0.783757i	$0.713301\pi$
$168$		0			0
$169$	−10.8702			−0.836172
$170$	8.37900	+	14.5129i	0.642640	+	1.11308i
$171$	−0.612236	+	1.06042i	−0.0468189	+	0.0810926i
$172$	1.36983	+	0.790869i	0.104448	+	0.0603032i
$173$	3.54738	+	6.14425i	0.269703	+	0.467139i	0.968785	−	0.247903i	$-0.0797413\pi$
$173$	3.54738	+	6.14425i	0.269703	+	0.467139i	−0.699082	+	0.715041i	$0.746408\pi$
$174$		−	13.9258i		−	1.05571i
$175$		0			0
$176$	−1.49053	−	2.96282i	−0.112353	−	0.223331i
$177$	9.67764	+	16.7622i	0.727416	+	1.25992i
$178$	8.05557	−	13.9527i	0.603791	−	1.04580i
$179$	12.4864	−	21.6271i	0.933278	−	1.61648i	0.155602	−	0.987820i	$-0.450268\pi$
$179$	12.4864	−	21.6271i	0.933278	−	1.61648i	0.777676	−	0.628665i	$-0.216398\pi$
$180$	12.9313	−	7.46591i	0.963845	−	0.556476i
$181$		−	19.3579i		−	1.43886i	−0.694566	−	0.719429i	$-0.744404\pi$
$181$		−	19.3579i		−	1.43886i	0.694566	−	0.719429i	$-0.255596\pi$
$182$		0			0
$183$			17.9060i			1.32365i
$184$	1.98129	−	1.14390i	0.146062	−	0.0843291i
$185$	−2.87969	−	1.66259i	−0.211719	−	0.122236i
$186$	23.1514	+	13.3665i	1.69754	+	0.980076i
$187$	13.8500	−	21.0894i	1.01281	−	1.54221i
$188$		−	0.545357i		−	0.0397743i
$189$		0			0
$190$	−0.397940			−0.0288696
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$	−2.70809	−	1.56352i	−0.195439	−	0.112837i
$193$	14.3859	+	8.30569i	1.03552	+	0.597857i	0.918561	−	0.395280i	$-0.129353\pi$
$193$	14.3859	+	8.30569i	1.03552	+	0.597857i	0.116957	+	0.993137i	$0.462686\pi$
$194$	−5.65058	−	9.78709i	−0.405688	−	0.702672i
$195$	−10.0528			−0.719899
$196$		0			0
$197$			20.6396i			1.47051i	0.677790	+	0.735256i	$0.262938\pi$
$197$			20.6396i			1.47051i	−0.677790	+	0.735256i	$0.737062\pi$
$198$	−18.7912	−	12.3407i	−1.33543	−	0.877016i
$199$	−0.628737	−	0.363001i	−0.0445700	−	0.0257325i	0.477549	−	0.878605i	$-0.341525\pi$
$199$	−0.628737	−	0.363001i	−0.0445700	−	0.0257325i	−0.522119	+	0.852872i	$0.674858\pi$
$200$	−0.127587	−	0.0736626i	−0.00902179	−	0.00520873i
$201$	8.07488	−	4.66203i	0.569558	−	0.328834i
$202$			0.517716i			0.0364264i
$203$		0			0
$204$		−	23.7883i		−	1.66552i
$205$	−13.5520	+	7.82428i	−0.946516	+	0.546471i
$206$	−1.44358	+	2.50035i	−0.100579	+	0.174208i
$207$	7.75369	−	13.4298i	0.538919	−	0.933435i
$208$	0.729686	+	1.26385i	0.0505946	+	0.0876325i
$209$	0.269257	+	0.535220i	0.0186249	+	0.0370219i
$210$		0			0
$211$			10.2878i			0.708241i	0.935200	+	0.354120i	$0.115220\pi$
$211$			10.2878i			0.708241i	−0.935200	+	0.354120i	$0.884780\pi$
$212$	2.41722	+	4.18675i	0.166015	+	0.287547i
$213$	−20.5134	−	11.8434i	−1.40556	−	0.811499i
$214$	2.60980	−	4.52030i	0.178402	−	0.309001i
$215$	1.74219	+	3.01756i	0.118816	+	0.205796i
$216$	−11.8149			−0.803904
$217$		0			0
$218$	−10.0540			−0.680945
$219$	26.2046	−	15.1293i	1.77075	−	1.02234i
$220$	0.419814	−	7.29405i	0.0283038	−	0.491765i
$221$	−5.55095	+	9.61453i	−0.373398	+	0.646744i
$222$	2.36008	+	4.08778i	0.158398	+	0.274354i
$223$			0.894768i			0.0599181i	0.999551	+	0.0299590i	$0.00953768\pi$
$223$			0.894768i			0.0599181i	−0.999551	+	0.0299590i	$0.990462\pi$
$224$		0			0
$225$	−0.998618			−0.0665745
$226$	−6.78302	+	3.91618i	−0.451200	+	0.260500i
$227$	−6.74239	+	11.6782i	−0.447508	+	0.775107i	−0.998223	−	0.0595863i	$-0.981022\pi$
$227$	−6.74239	+	11.6782i	−0.447508	+	0.775107i	0.550715	+	0.834693i	$0.314355\pi$
$228$	0.489203	+	0.282442i	0.0323983	+	0.0187052i
$229$	4.23097	−	2.44275i	0.279590	−	0.161422i	−0.353648	−	0.935379i	$-0.615059\pi$
$229$	4.23097	−	2.44275i	0.279590	−	0.161422i	0.633238	+	0.773957i	$0.281725\pi$
$230$	5.03973			0.332310
$231$		0			0
$232$	−4.45335			−0.292377
$233$	19.6247	−	11.3303i	1.28566	−	0.742274i	0.307780	−	0.951458i	$-0.400414\pi$
$233$	19.6247	−	11.3303i	1.28566	−	0.742274i	0.977876	+	0.209184i	$0.0670807\pi$
$234$	8.56680	+	4.94605i	0.560029	+	0.323333i
$235$	0.600678	−	1.04041i	0.0391839	−	0.0678685i
$236$	5.36041	−	3.09483i	0.348933	−	0.201457i
$237$	−21.6353			−1.40536
$238$		0			0
$239$		−	25.2410i		−	1.63270i	−0.577556	−	0.816351i	$-0.695993\pi$
$239$		−	25.2410i		−	1.63270i	0.577556	−	0.816351i	$-0.304007\pi$
$240$	−3.44423	−	5.96559i	−0.222324	−	0.385077i
$241$	7.03345	−	12.1823i	0.453064	−	0.784730i	−0.545510	−	0.838104i	$-0.683664\pi$
$241$	7.03345	−	12.1823i	0.453064	−	0.784730i	0.998575	+	0.0533739i	$0.0169975\pi$
$242$	−10.0944	+	4.37072i	−0.648892	+	0.280961i
$243$	−14.2871	+	8.24865i	−0.916517	+	0.529151i
$244$	5.72621			0.366583
$245$		0			0
$246$	22.2134			1.41628
$247$	−0.131814	−	0.228309i	−0.00838715	−	0.0145270i
$248$	4.27449	−	7.40363i	0.271430	−	0.470131i
$249$	−15.8219	−	9.13478i	−1.00267	−	0.578893i
$250$	−5.66947	−	9.81980i	−0.358569	−	0.621059i
$251$		−	3.03720i		−	0.191706i	−0.995395	−	0.0958532i	$-0.969442\pi$
$251$		−	3.03720i		−	0.191706i	0.995395	−	0.0958532i	$-0.0305579\pi$
$252$		0			0
$253$	−3.41002	−	6.77832i	−0.214386	−	0.426149i
$254$	6.73510	+	11.6655i	0.422598	+	0.731961i
$255$	26.2014	−	45.3821i	1.64079	−	2.84194i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−22.3160	+	12.8842i	−1.39204	+	0.803692i	−0.993541	−	0.113478i	$-0.963801\pi$
$257$	−22.3160	+	12.8842i	−1.39204	+	0.803692i	−0.398496	+	0.917170i	$0.630468\pi$
$258$		−	4.94614i		−	0.307933i
$259$		0			0
$260$			3.21482i			0.199375i
$261$	−26.1421	+	15.0931i	−1.61815	+	0.934241i
$262$	−2.27298	−	1.31231i	−0.140425	−	0.0810747i
$263$	−5.55124	−	3.20501i	−0.342304	−	0.197629i	0.318986	−	0.947759i	$-0.396658\pi$
$263$	−5.55124	−	3.20501i	−0.342304	−	0.197629i	−0.661290	+	0.750130i	$0.729991\pi$
$264$	−5.69312	+	8.66891i	−0.350387	+	0.533534i
$265$			10.6497i			0.654205i
$266$		0			0
$267$	−50.3800			−3.08321
$268$	−1.49088	−	2.58228i	−0.0910701	−	0.157738i
$269$	−2.37423	−	1.37076i	−0.144759	−	0.0835767i	0.425871	−	0.904784i	$-0.359968\pi$
$269$	−2.37423	−	1.37076i	−0.144759	−	0.0835767i	−0.570630	+	0.821207i	$0.693301\pi$
$270$	−22.5399	−	13.0134i	−1.37174	−	0.791972i
$271$	−14.3001	−	24.7685i	−0.868670	−	1.50458i	−0.863357	−	0.504594i	$-0.831642\pi$
$271$	−14.3001	−	24.7685i	−0.868670	−	1.50458i	−0.00531291	−	0.999986i	$-0.501691\pi$
$272$	−7.60732			−0.461261
$273$		0			0
$274$			8.72291i			0.526970i
$275$	−0.268223	+	0.408422i	−0.0161744	+	0.0246288i
$276$	−6.19554	−	3.57700i	−0.372928	−	0.215310i
$277$	−9.32564	−	5.38416i	−0.560324	−	0.323503i	0.192952	−	0.981208i	$-0.438194\pi$
$277$	−9.32564	−	5.38416i	−0.560324	−	0.323503i	−0.753275	+	0.657705i	$0.771527\pi$
$278$	−3.54456	+	2.04645i	−0.212589	+	0.122738i
$279$		−	57.9477i		−	3.46924i
$280$		0			0
$281$		−	19.6289i		−	1.17096i	−0.810686	−	0.585481i	$-0.800906\pi$
$281$		−	19.6289i		−	1.17096i	0.810686	−	0.585481i	$-0.199094\pi$
$282$	−1.47688	+	0.852675i	−0.0879467	+	0.0507760i
$283$	−5.31163	+	9.20001i	−0.315744	+	0.546884i	−0.979595	−	0.200980i	$-0.935587\pi$
$283$	−5.31163	+	9.20001i	−0.315744	+	0.546884i	0.663852	+	0.747864i	$0.268921\pi$
$284$	−3.78744	+	6.56004i	−0.224743	+	0.389267i
$285$	0.622185	+	1.07766i	0.0368551	+	0.0638348i
$286$	4.32386	−	2.17524i	0.255675	−	0.128624i
$287$		0			0
$288$			6.77832i			0.399416i
$289$	−20.4356	−	35.3956i	−1.20210	−	2.08209i
$290$	−8.49588	−	4.90510i	−0.498895	−	0.288037i
$291$	−17.6695	+	30.6045i	−1.03581	+	1.79407i
$292$	−4.83822	−	8.38004i	−0.283135	−	0.490405i
$293$	0.277651			0.0162206			0.00811028	−	0.999967i	$-0.497418\pi$
$293$	0.277651			0.0162206			0.00811028	+	0.999967i	$0.497418\pi$
$294$		0			0
$295$	13.6351			0.793866
$296$	1.30724	−	0.754735i	0.0759818	−	0.0438681i
$297$	−2.25163	+	39.1209i	−0.130653	+	2.27003i
$298$	9.29587	−	16.1009i	0.538495	−	0.932701i
$299$	1.66937	+	2.89143i	0.0965421	+	0.167216i
$300$			0.460691i			0.0265980i
$301$		0			0
$302$	13.2045			0.759833
$303$	1.40202	−	0.809457i	0.0805440	−	0.0465021i
$304$	0.0903227	−	0.156443i	0.00518036	−	0.00897265i
$305$	10.9242	+	6.30707i	0.625516	+	0.361142i
$306$	−44.6565	+	25.7824i	−2.55284	+	1.47388i
$307$	6.41443			0.366091			0.183045	−	0.983104i	$-0.441404\pi$
$307$	6.41443			0.366091			0.183045	+	0.983104i	$0.441404\pi$
$308$		0			0
$309$	9.02823			0.513598
$310$	16.3093	−	9.41618i	0.926306	−	0.534803i
$311$	9.78814	+	5.65119i	0.555035	+	0.320449i	0.751150	−	0.660131i	$-0.229499\pi$
$311$	9.78814	+	5.65119i	0.555035	+	0.320449i	−0.196115	+	0.980581i	$0.562833\pi$
$312$	2.28175	−	3.95211i	0.129179	−	0.223744i
$313$	14.2432	−	8.22333i	0.805075	−	0.464810i	−0.0401677	−	0.999193i	$-0.512789\pi$
$313$	14.2432	−	8.22333i	0.805075	−	0.464810i	0.845243	+	0.534383i	$0.179456\pi$
$314$	5.75901			0.325000
$315$		0			0
$316$			6.91879i			0.389212i
$317$	14.0955	+	24.4141i	0.791683	+	1.37124i	0.924924	+	0.380151i	$0.124128\pi$
$317$	14.0955	+	24.4141i	0.791683	+	1.37124i	−0.133241	+	0.991084i	$0.542539\pi$
$318$	7.55872	−	13.0921i	0.423872	−	0.734168i
$319$	−0.848697	+	14.7457i	−0.0475179	+	0.825601i
$320$	−1.90775	+	1.10144i	−0.106646	+	0.0615723i
$321$	−16.3218			−0.910996
$322$		0			0
$323$	1.37423			0.0764640
$324$	8.30534	+	14.3853i	0.461408	+	0.799181i
$325$	0.107501	−	0.186198i	0.00596309	−	0.0103284i
$326$	−4.60109	−	2.65644i	−0.254831	−	0.147127i
$327$	15.7196	+	27.2272i	0.869298	+	1.50567i
$328$		−	7.10368i		−	0.392235i
$329$		0			0
$330$	−20.4093	+	10.2675i	−1.12350	+	0.565206i
$331$	−9.55629	−	16.5520i	−0.525261	−	0.909779i	−0.999567	−	0.0294190i	$-0.990634\pi$
$331$	−9.55629	−	16.5520i	−0.525261	−	0.909779i	0.474306	−	0.880360i	$-0.342699\pi$
$332$	−2.92123	+	5.05972i	−0.160323	+	0.277688i
$333$	5.11584	−	8.86089i	0.280346	−	0.485574i
$334$	13.9014	−	8.02596i	0.760649	−	0.439161i
$335$		−	6.56846i		−	0.358874i
$336$		0			0
$337$		−	16.0358i		−	0.873525i	−0.899577	−	0.436763i	$-0.856125\pi$
$337$		−	16.0358i		−	0.873525i	0.899577	−	0.436763i	$-0.143875\pi$
$338$	9.41390	−	5.43512i	0.512049	−	0.295631i
$339$	21.2107	+	12.2460i	1.15201	+	0.665112i
$340$	−14.5129	−	8.37900i	−0.787070	−	0.454415i
$341$	−23.6999	−	15.5644i	−1.28342	−	0.842859i
$342$		−	1.22447i		−	0.0662119i
$343$		0			0
$344$	−1.58174			−0.0852816
$345$	−7.87969	−	13.6480i	−0.424228	−	0.734785i
$346$	−6.14425	−	3.54738i	−0.330317	−	0.190708i
$347$	−8.54848	−	4.93547i	−0.458907	−	0.264950i	0.252678	−	0.967550i	$-0.418689\pi$
$347$	−8.54848	−	4.93547i	−0.458907	−	0.264950i	−0.711584	+	0.702601i	$0.752022\pi$
$348$	6.96289	+	12.0601i	0.373250	+	0.646488i
$349$	31.1871			1.66940			0.834702	−	0.550701i	$-0.185640\pi$
$349$	31.1871			1.66940			0.834702	+	0.550701i	$0.185640\pi$
$350$		0			0
$351$		−	17.2424i		−	0.920330i
$352$	2.77225	+	1.82062i	0.147761	+	0.0970391i
$353$	22.4891	+	12.9841i	1.19698	+	0.691075i	0.959880	−	0.280411i	$-0.0904709\pi$
$353$	22.4891	+	12.9841i	1.19698	+	0.691075i	0.237097	+	0.971486i	$0.423804\pi$
$354$	−16.7622	−	9.67764i	−0.890899	−	0.514361i
$355$	−14.4510	+	8.34327i	−0.766978	+	0.442815i
$356$			16.1111i			0.853889i
$357$		0			0
$358$			24.9728i			1.31985i
$359$	−3.47334	+	2.00534i	−0.183316	+	0.105838i	−0.588850	−	0.808243i	$-0.700419\pi$
$359$	−3.47334	+	2.00534i	−0.183316	+	0.105838i	0.405534	+	0.914080i	$0.367086\pi$
$360$	−7.46591	+	12.9313i	−0.393488	+	0.681541i
$361$	9.48368	−	16.4262i	0.499141	−	0.864538i
$362$	9.67893	+	16.7644i	0.508713	+	0.881117i
$363$	27.6190	+	20.5028i	1.44962	+	1.07612i
$364$		0			0
$365$		−	21.3160i		−	1.11573i
$366$	−8.95301	−	15.5071i	−0.467982	−	0.810568i
$367$	−16.6148	−	9.59255i	−0.867284	−	0.500727i	−0.000839598	−	1.00000i	$-0.500267\pi$
$367$	−16.6148	−	9.59255i	−0.867284	−	0.500727i	−0.866445	+	0.499273i	$0.833601\pi$
$368$	−1.14390	+	1.98129i	−0.0596297	+	0.103282i
$369$	−24.0755	−	41.7000i	−1.25332	−	2.17082i
$370$	3.32518			0.172868
$371$		0			0
$372$	−26.7329			−1.38604
$373$	18.2116	−	10.5145i	0.942961	−	0.544419i	0.0520734	−	0.998643i	$-0.483417\pi$
$373$	18.2116	−	10.5145i	0.942961	−	0.544419i	0.890887	+	0.454225i	$0.150084\pi$
$374$	−1.44976	+	25.1889i	−0.0749655	+	1.30249i
$375$	−17.7286	+	30.7068i	−0.915501	+	1.58569i
$376$	0.272679	+	0.472293i	0.0140623	+	0.0243567i
$377$		−	6.49910i		−	0.334721i
$378$		0			0
$379$	20.7525			1.06599			0.532993	−	0.846120i	$-0.321067\pi$
$379$	20.7525			1.06599			0.532993	+	0.846120i	$0.321067\pi$
$380$	0.344626	−	0.198970i	0.0176789	−	0.0102069i
$381$	21.0609	−	36.4785i	1.07898	−	1.86885i
$382$	5.19615	+	3.00000i	0.265858	+	0.153493i
$383$	1.08778	−	0.628029i	0.0555829	−	0.0320908i	−0.471951	−	0.881625i	$-0.656450\pi$
$383$	1.08778	−	0.628029i	0.0555829	−	0.0320908i	0.527534	+	0.849534i	$0.323117\pi$
$384$	3.12703			0.159576
$385$		0			0
$386$	−16.6114			−0.845497
$387$	−9.28511	+	5.36076i	−0.471989	+	0.272503i
$388$	9.78709	+	5.65058i	0.496864	+	0.286865i
$389$	8.32393	−	14.4175i	0.422040	−	0.730994i	−0.574099	−	0.818786i	$-0.694648\pi$
$389$	8.32393	−	14.4175i	0.422040	−	0.730994i	0.996139	+	0.0877915i	$0.0279809\pi$
$390$	8.70601	−	5.02642i	0.440846	−	0.254523i
$391$	−17.4040			−0.880156
$392$		0			0
$393$			8.20726i			0.414001i
$394$	−10.3198	−	17.8744i	−0.519904	−	0.900501i
$395$	−7.62062	+	13.1993i	−0.383435	+	0.664129i
$396$	22.4440	+	1.29178i	1.12785	+	0.0649143i
$397$	−12.2752	+	7.08712i	−0.616077	+	0.355692i	−0.775340	−	0.631544i	$-0.782421\pi$
$397$	−12.2752	+	7.08712i	−0.616077	+	0.355692i	0.159263	+	0.987236i	$0.449088\pi$
$398$	0.726003			0.0363912
$399$		0			0
$400$	0.147325			0.00736626
$401$	2.42635	+	4.20256i	0.121166	+	0.209866i	0.920228	−	0.391383i	$-0.128003\pi$
$401$	2.42635	+	4.20256i	0.121166	+	0.209866i	−0.799062	+	0.601249i	$0.794670\pi$
$402$	−4.66203	+	8.07488i	−0.232521	+	0.402738i
$403$	10.8046	+	6.23807i	0.538218	+	0.310740i
$404$	−0.258858	−	0.448355i	−0.0128787	−	0.0223065i
$405$			36.5913i			1.81824i
$406$		0			0
$407$	−2.24991	−	4.47229i	−0.111524	−	0.221683i
$408$	11.8942	+	20.6013i	0.588849	+	1.01992i
$409$	−5.31402	+	9.20415i	−0.262761	+	0.455116i	−0.966975	−	0.254872i	$-0.917967\pi$
$409$	−5.31402	+	9.20415i	−0.262761	+	0.455116i	0.704213	+	0.709988i	$0.251300\pi$
$410$	7.82428	−	13.5520i	0.386414	−	0.669288i
$411$	23.6224	−	13.6384i	1.16521	−	0.672733i
$412$		−	2.88716i		−	0.142240i
$413$		0			0
$414$			15.5074i			0.762146i
$415$	−11.1459	+	6.43512i	−0.547133	+	0.315887i
$416$	−1.26385	−	0.729686i	−0.0619655	−	0.0357758i
$417$	11.0840	+	6.39932i	0.542783	+	0.313376i
$418$	−0.500794	−	0.328886i	−0.0244946	−	0.0160863i
$419$		−	11.3690i		−	0.555410i	−0.960666	−	0.277705i	$-0.910426\pi$
$419$		−	11.3690i		−	0.555410i	0.960666	−	0.277705i	$-0.0895739\pi$
$420$		0			0
$421$	27.2464			1.32791			0.663955	−	0.747772i	$-0.268877\pi$
$421$	27.2464			1.32791			0.663955	+	0.747772i	$0.268877\pi$
$422$	−5.14390	−	8.90949i	−0.250401	−	0.433707i
$423$	3.20136	+	1.84830i	0.155655	+	0.0898676i
$424$	−4.18675	−	2.41722i	−0.203326	−	0.117391i
$425$	0.560375	+	0.970598i	0.0271822	+	0.0470809i
$426$	23.6869			1.14763
$427$		0			0
$428$			5.21959i			0.252299i
$429$	−12.6512	−	8.30838i	−0.610804	−	0.401132i
$430$	−3.01756	−	1.74219i	−0.145520	−	0.0840158i
$431$	−13.1818	−	7.61049i	−0.634943	−	0.366584i	0.147721	−	0.989029i	$-0.452806\pi$
$431$	−13.1818	−	7.61049i	−0.634943	−	0.366584i	−0.782664	+	0.622445i	$0.786140\pi$
$432$	10.2320	−	5.90746i	0.492289	−	0.284223i
$433$		−	1.85534i		−	0.0891619i	−0.999006	−	0.0445810i	$-0.985805\pi$
$433$		−	1.85534i		−	0.0891619i	0.999006	−	0.0445810i	$-0.0141953\pi$
$434$		0			0
$435$			30.6768i			1.47084i
$436$	8.70705	−	5.02702i	0.416992	−	0.240750i
$437$	0.206639	−	0.357910i	0.00988490	−	0.0171212i
$438$	−15.1293	+	26.2046i	−0.722904	+	1.25211i
$439$	16.4702	+	28.5272i	0.786079	+	1.36153i	0.928352	+	0.371701i	$0.121225\pi$
$439$	16.4702	+	28.5272i	0.786079	+	1.36153i	−0.142274	+	0.989827i	$0.545441\pi$
$440$	3.28346	+	6.52674i	0.156533	+	0.311150i
$441$		0			0
$442$		−	11.1019i		−	0.528064i
$443$	16.4306	+	28.4587i	0.780643	+	1.35211i	0.931567	+	0.363569i	$0.118442\pi$
$443$	16.4306	+	28.4587i	0.780643	+	1.35211i	−0.150924	+	0.988545i	$0.548225\pi$
$444$	−4.08778	−	2.36008i	−0.193997	−	0.112004i
$445$	−17.7455	+	30.7360i	−0.841215	+	1.45703i
$446$	−0.447384	−	0.774891i	−0.0211842	−	0.0366922i
$447$	−58.1369			−2.74978
$448$		0			0
$449$	3.62716			0.171176			0.0855880	−	0.996331i	$-0.472723\pi$
$449$	3.62716			0.171176			0.0855880	+	0.996331i	$0.472723\pi$
$450$	0.864828	−	0.499309i	0.0407684	−	0.0235376i
$451$	−23.5213	−	1.35378i	−1.10758	−	0.0637472i
$452$	3.91618	−	6.78302i	0.184201	−	0.319046i
$453$	−20.6454	−	35.7589i	−0.970007	−	1.68010i
$454$		−	13.4848i		−	0.632872i
$455$		0			0
$456$	−0.564883			−0.0264531
$457$	2.36916	−	1.36783i	0.110825	−	0.0639846i	−0.443563	−	0.896243i	$-0.646286\pi$
$457$	2.36916	−	1.36783i	0.110825	−	0.0639846i	0.554388	+	0.832259i	$0.312952\pi$
$458$	−2.44275	+	4.23097i	−0.114142	+	0.197700i
$459$	77.8383	+	44.9399i	3.63318	+	2.09762i
$460$	−4.36453	+	2.51986i	−0.203497	+	0.117489i
$461$	−20.4439			−0.952169			−0.476084	−	0.879400i	$-0.657944\pi$
$461$	−20.4439			−0.952169			−0.476084	+	0.879400i	$0.657944\pi$
$462$		0			0
$463$	30.1701			1.40212			0.701062	−	0.713100i	$-0.252710\pi$
$463$	30.1701			1.40212			0.701062	+	0.713100i	$0.252710\pi$
$464$	3.85672	−	2.22668i	0.179044	−	0.103371i
$465$	−50.9997	−	29.4447i	−2.36505	−	1.36546i
$466$	−11.3303	+	19.6247i	−0.524867	+	0.909096i
$467$	−23.5318	+	13.5861i	−1.08892	+	0.628691i	−0.933290	−	0.359124i	$-0.883075\pi$
$467$	−23.5318	+	13.5861i	−1.08892	+	0.628691i	−0.155634	+	0.987815i	$0.549742\pi$
$468$	−9.89209			−0.457262
$469$		0			0
$470$			1.20136i			0.0554144i
$471$	−9.00431	−	15.5959i	−0.414897	−	0.718622i
$472$	−3.09483	+	5.36041i	−0.142451	+	0.246733i
$473$	−0.301440	+	5.23736i	−0.0138602	+	0.240814i
$474$	18.7367	−	10.8176i	0.860604	−	0.496870i
$475$	−0.0266136			−0.00122112
$476$		0			0
$477$	−32.7694			−1.50041
$478$	12.6205	+	21.8593i	0.577247	+	0.999822i
$479$	10.8092	−	18.7221i	0.493885	−	0.855434i	−0.506090	−	0.862481i	$-0.668910\pi$
$479$	10.8092	−	18.7221i	0.493885	−	0.855434i	0.999975	+	0.00704654i	$0.00224300\pi$
$480$	5.96559	+	3.44423i	0.272291	+	0.157207i
$481$	1.10144	+	1.90775i	0.0502213	+	0.0869859i
$482$			14.0669i			0.640730i
$483$		0			0
$484$	6.55664	−	8.83235i	0.298029	−	0.401471i
$485$	12.4475	+	21.5598i	0.565214	+	0.978979i
$486$	8.24865	−	14.2871i	0.374167	−	0.648075i
$487$	−1.04287	+	1.80630i	−0.0472567	+	0.0818511i	−0.888686	−	0.458516i	$-0.848381\pi$
$487$	−1.04287	+	1.80630i	−0.0472567	+	0.0818511i	0.841429	+	0.540367i	$0.181715\pi$
$488$	−4.95904	+	2.86310i	−0.224485	+	0.129607i
$489$			16.6136i			0.751291i
$490$		0			0
$491$			2.47983i			0.111913i	0.998433	+	0.0559566i	$0.0178208\pi$
$491$			2.47983i			0.111913i	−0.998433	+	0.0559566i	$0.982179\pi$
$492$	−19.2374	+	11.1067i	−0.867289	+	0.500730i
$493$	29.3393	+	16.9390i	1.32137	+	0.762896i
$494$	0.228309	+	0.131814i	0.0102721	+	0.00593061i
$495$	41.3947	+	27.1851i	1.86055	+	1.22188i
$496$			8.54897i			0.383860i
$497$		0			0
$498$	18.2696			0.818678
$499$	−7.69189	−	13.3227i	−0.344336	−	0.596408i	0.640897	−	0.767627i	$-0.278563\pi$
$499$	−7.69189	−	13.3227i	−0.344336	−	0.596408i	−0.985233	+	0.171219i	$0.945229\pi$
$500$	9.81980	+	5.66947i	0.439155	+	0.253546i
$501$	−43.4700	−	25.0974i	−1.94210	−	1.12127i
$502$	1.51860	+	2.63029i	0.0677784	+	0.117396i
$503$	−15.5714			−0.694295			−0.347147	−	0.937811i	$-0.612850\pi$
$503$	−15.5714			−0.694295			−0.347147	+	0.937811i	$0.612850\pi$
$504$		0			0
$505$		−	1.14047i		−	0.0507501i
$506$	6.34233	+	4.16519i	0.281951	+	0.185165i
$507$	−29.4375	−	16.9958i	−1.30737	−	0.754809i
$508$	−11.6655	−	6.73510i	−0.517575	−	0.298822i
$509$	26.6346	−	15.3775i	1.18056	−	0.681595i	0.224414	−	0.974494i	$-0.427953\pi$
$509$	26.6346	−	15.3775i	1.18056	−	0.681595i	0.956144	+	0.292898i	$0.0946198\pi$
$510$			52.4028i			2.32043i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−1.84837	+	1.06716i	−0.0816074	+	0.0471161i
$514$	12.8842	−	22.3160i	0.568296	−	0.984318i
$515$	3.18003	−	5.50797i	0.140129	−	0.242710i
$516$	2.47307	+	4.28348i	0.108871	+	0.188570i
$517$	1.61580	−	0.812872i	0.0710627	−	0.0357500i
$518$		0			0
$519$			22.1856i			0.973838i
$520$	−1.60741	−	2.78412i	−0.0704896	−	0.122092i
$521$	3.19850	+	1.84666i	0.140129	+	0.0809035i	0.568425	−	0.822735i	$-0.307553\pi$
$521$	3.19850	+	1.84666i	0.140129	+	0.0809035i	−0.428296	+	0.903638i	$0.640886\pi$
$522$	15.0931	−	26.1421i	0.660608	−	1.14421i
$523$	14.6007	+	25.2891i	0.638444	+	1.10582i	0.985774	+	0.168074i	$0.0537548\pi$
$523$	14.6007	+	25.2891i	0.638444	+	1.10582i	−0.347331	+	0.937743i	$0.612912\pi$
$524$	2.62462			0.114657
$525$		0			0
$526$	6.41002			0.279490
$527$	−56.3218	+	32.5174i	−2.45341	+	1.41648i
$528$	0.595934	−	10.3541i	0.0259347	−	0.450602i
$529$	8.88301	−	15.3858i	0.386218	−	0.668949i
$530$	−5.32484	−	9.22289i	−0.231296	−	0.400617i
$531$			41.9556i			1.82072i
$532$		0			0
$533$	10.3669			0.449041
$534$	43.6304	−	25.1900i	1.88807	−	1.09008i
$535$	−5.74906	+	9.95767i	−0.248554	+	0.430508i
$536$	2.58228	+	1.49088i	0.111538	+	0.0643963i
$537$	67.6286	−	39.0454i	2.91839	−	1.68493i
$538$	2.74152			0.118195
$539$		0			0
$540$	26.0268			1.12002
$541$	14.0078	−	8.08743i	0.602244	−	0.347706i	−0.167680	−	0.985841i	$-0.553628\pi$
$541$	14.0078	−	8.08743i	0.602244	−	0.347706i	0.769924	+	0.638136i	$0.220294\pi$
$542$	24.7685	+	14.3001i	1.06390	+	0.614242i
$543$	30.2663	−	52.4228i	1.29885	−	2.24968i
$544$	6.58813	−	3.80366i	0.282464	−	0.163081i
$545$	22.1478			0.948708
$546$		0			0
$547$			34.0719i			1.45681i	0.685146	+	0.728405i	$0.259738\pi$
$547$			34.0719i			1.45681i	−0.685146	+	0.728405i	$0.740262\pi$
$548$	−4.36145	−	7.55426i	−0.186312	−	0.322702i
$549$	−19.4070	+	33.6140i	−0.828272	+	1.43461i
$550$	0.0280765	−	0.487815i	0.00119719	−	0.0208005i
$551$	−0.696698	+	0.402239i	−0.0296803	+	0.0171359i
$552$	7.15399			0.304494
$553$		0			0
$554$	10.7683			0.457502
$555$	−5.19897	−	9.00488i	−0.220684	−	0.382236i
$556$	2.04645	−	3.54456i	0.0867889	−	0.150323i
$557$	−22.2451	−	12.8432i	−0.942555	−	0.544185i	−0.0517949	−	0.998658i	$-0.516494\pi$
$557$	−22.2451	−	12.8432i	−0.942555	−	0.544185i	−0.890760	+	0.454473i	$0.849828\pi$
$558$	28.9738	+	50.1842i	1.22656	+	2.12447i
$559$		−	2.30834i		−	0.0976325i
$560$		0			0
$561$	70.4806	−	35.4572i	2.97569	−	1.49700i
$562$	9.81445	+	16.9991i	0.413998	+	0.717065i
$563$	−10.9683	+	18.9976i	−0.462258	+	0.800654i	−0.999073	−	0.0430456i	$-0.986294\pi$
$563$	−10.9683	+	18.9976i	−0.462258	+	0.800654i	0.536815	+	0.843700i	$0.319627\pi$
$564$	0.852675	−	1.47688i	0.0359041	−	0.0621877i
$565$	14.9422	−	8.62686i	0.628621	−	0.362935i
$566$		−	10.6233i		−	0.446529i
$567$		0			0
$568$		−	7.57488i		−	0.317835i
$569$	−2.22306	+	1.28348i	−0.0931956	+	0.0538065i	−0.545873	−	0.837868i	$-0.683802\pi$
$569$	−2.22306	+	1.28348i	−0.0931956	+	0.0538065i	0.452678	+	0.891674i	$0.350469\pi$
$570$	−1.07766	−	0.622185i	−0.0451380	−	0.0260605i
$571$	29.7126	+	17.1546i	1.24343	+	0.717897i	0.969792	−	0.243934i	$-0.0784380\pi$
$571$	29.7126	+	17.1546i	1.24343	+	0.717897i	0.273643	+	0.961831i	$0.411771\pi$
$572$	−2.65696	+	4.04574i	−0.111093	+	0.169161i
$573$		−	18.7622i		−	0.783801i
$574$		0			0
$575$	0.337049			0.0140559
$576$	−3.38916	−	5.87020i	−0.141215	−	0.244592i
$577$	17.9257	+	10.3494i	0.746255	+	0.430851i	0.824339	−	0.566096i	$-0.191547\pi$
$577$	17.9257	+	10.3494i	0.746255	+	0.430851i	−0.0780842	+	0.996947i	$0.524880\pi$
$578$	35.3956	+	20.4356i	1.47226	+	0.850011i
$579$	25.9721	+	44.9851i	1.07937	+	1.86952i
$580$	9.81020			0.407346
$581$		0			0
$582$		−	35.3391i		−	1.46485i
$583$	−8.80165	+	13.4023i	−0.364527	+	0.555065i
$584$	8.38004	+	4.83822i	0.346769	+	0.200207i
$585$	−18.8716	−	10.8955i	−0.780246	−	0.450475i
$586$	−0.240453	+	0.138826i	−0.00993303	+	0.00573484i
$587$			16.0435i			0.662184i	0.943598	+	0.331092i	$0.107417\pi$
$587$			16.0435i			0.662184i	−0.943598	+	0.331092i	$0.892583\pi$
$588$		0			0
$589$		−	1.54433i		−	0.0636331i
$590$	−11.8083	+	6.81755i	−0.486141	+	0.280674i
$591$	−32.2703	+	55.8939i	−1.32742	+	2.29917i
$592$	−0.754735	+	1.30724i	−0.0310194	+	0.0537272i
$593$	−17.7436	−	30.7328i	−0.728641	−	1.26204i	−0.957458	−	0.288574i	$-0.906819\pi$
$593$	−17.7436	−	30.7328i	−0.728641	−	1.26204i	0.228816	−	0.973470i	$-0.426515\pi$
$594$	−17.6105	−	35.0055i	−0.722568	−	1.43629i
$595$		0			0
$596$			18.5917i			0.761547i
$597$	−1.13512	−	1.96608i	−0.0464572	−	0.0804663i
$598$	−2.89143	−	1.66937i	−0.118239	−	0.0682656i
$599$	−0.374693	+	0.648987i	−0.0153095	+	0.0265169i	−0.873579	−	0.486683i	$-0.838207\pi$
$599$	−0.374693	+	0.648987i	−0.0153095	+	0.0265169i	0.858269	+	0.513200i	$0.171540\pi$
$600$	−0.230345	−	0.398970i	−0.00940381	−	0.0162879i
$601$	18.5168			0.755317			0.377658	−	0.925945i	$-0.376729\pi$
$601$	18.5168			0.755317			0.377658	+	0.925945i	$0.376729\pi$
$602$		0			0
$603$	20.2114			0.823070
$604$	−11.4354	+	6.60225i	−0.465301	+	0.268642i
$605$	22.2367	−	9.62817i	0.904052	−	0.391441i
$606$	−0.809457	+	1.40202i	−0.0328820	+	0.0569532i
$607$	−18.4955	−	32.0352i	−0.750710	−	1.30027i	−0.947479	−	0.319817i	$-0.896378\pi$
$607$	−18.4955	−	32.0352i	−0.750710	−	1.30027i	0.196770	−	0.980450i	$-0.436955\pi$
$608$			0.180645i			0.00732613i
$609$		0			0
$610$	−12.6141			−0.510732
$611$	−0.689252	+	0.397940i	−0.0278841	+	0.0160989i
$612$	25.7824	−	44.6565i	1.04219	−	1.80513i
$613$	−2.79338	−	1.61276i	−0.112824	−	0.0651387i	0.442526	−	0.896756i	$-0.354082\pi$
$613$	−2.79338	−	1.61276i	−0.112824	−	0.0651387i	−0.555350	+	0.831617i	$0.687416\pi$
$614$	−5.55506	+	3.20722i	−0.224184	+	0.129433i
$615$	−48.9335			−1.97319
$616$		0			0
$617$	−10.8351			−0.436206			−0.218103	−	0.975926i	$-0.569987\pi$
$617$	−10.8351			−0.436206			−0.218103	+	0.975926i	$0.569987\pi$
$618$	−7.81868	+	4.51412i	−0.314513	+	0.181584i
$619$	−4.44127	−	2.56417i	−0.178510	−	0.103063i	0.408083	−	0.912945i	$-0.366198\pi$
$619$	−4.44127	−	2.56417i	−0.178510	−	0.103063i	−0.586592	+	0.809882i	$0.699531\pi$
$620$	−9.41618	+	16.3093i	−0.378163	+	0.654997i
$621$	23.4087	−	13.5150i	0.939360	−	0.542340i
$622$	−11.3024			−0.453184
$623$		0			0
$624$			4.56350i			0.182686i
$625$	12.1208	+	20.9939i	0.484833	+	0.839756i
$626$	−8.22333	+	14.2432i	−0.328670	+	0.569274i
$627$	−0.107653	+	1.87041i	−0.00429923	+	0.0746970i
$628$	−4.98745	+	2.87951i	−0.199021	+	0.114905i
$629$	−11.4830			−0.457858
$630$		0			0
$631$	−29.9567			−1.19256			−0.596278	−	0.802778i	$-0.703354\pi$
$631$	−29.9567			−1.19256			−0.596278	+	0.802778i	$0.703354\pi$
$632$	−3.45939	−	5.99185i	−0.137607	−	0.238343i
$633$	−16.0851	+	27.8602i	−0.639326	+	1.10735i
$634$	−24.4141	−	14.0955i	−0.969610	−	0.559804i
$635$	−14.8366	−	25.6978i	−0.588773	−	1.01979i
$636$			15.1174i			0.599445i
$637$		0			0
$638$	−6.63786	−	13.1945i	−0.262795	−	0.522375i
$639$	−25.6725	−	44.4660i	−1.01559	−	1.75905i
$640$	1.10144	−	1.90775i	0.0435382	−	0.0754104i
$641$	−4.61345	+	7.99073i	−0.182220	+	0.315615i	−0.942636	−	0.333821i	$-0.891662\pi$
$641$	−4.61345	+	7.99073i	−0.182220	+	0.315615i	0.760416	+	0.649436i	$0.224995\pi$
$642$	14.1351	−	8.16091i	0.557869	−	0.322086i
$643$			1.79941i			0.0709616i	0.999370	+	0.0354808i	$0.0112963\pi$
$643$			1.79941i			0.0709616i	−0.999370	+	0.0354808i	$0.988704\pi$
$644$		0			0
$645$			10.8958i			0.429020i
$646$	−1.19011	+	0.687113i	−0.0468244	+	0.0270341i
$647$	35.2683	+	20.3622i	1.38654	+	0.800520i	0.992924	−	0.118754i	$-0.0378899\pi$
$647$	35.2683	+	20.3622i	1.38654	+	0.800520i	0.393618	+	0.919274i	$0.371223\pi$
$648$	−14.3853	−	8.30534i	−0.565107	−	0.326264i
$649$	17.1593	+	11.2690i	0.673561	+	0.442347i
$650$			0.215002i			0.00843309i
$651$		0			0
$652$	5.31289			0.208069
$653$	18.8692	+	32.6824i	0.738408	+	1.27896i	0.953212	+	0.302304i	$0.0977557\pi$
$653$	18.8692	+	32.6824i	0.738408	+	1.27896i	−0.214803	+	0.976657i	$0.568911\pi$
$654$	−27.2272	−	15.7196i	−1.06467	−	0.614686i
$655$	5.00711	+	2.89086i	0.195644	+	0.112955i
$656$	3.55184	+	6.15197i	0.138676	+	0.240194i
$657$	65.5900			2.55891
$658$		0			0
$659$			32.5997i			1.26991i	0.772551	+	0.634953i	$0.218981\pi$
$659$			32.5997i			1.26991i	−0.772551	+	0.634953i	$0.781019\pi$
$660$	12.5413	−	19.0965i	0.488168	−	0.743332i
$661$	−10.9747	−	6.33624i	−0.426866	−	0.246451i	0.271145	−	0.962539i	$-0.412598\pi$
$661$	−10.9747	−	6.33624i	−0.426866	−	0.246451i	−0.698011	+	0.716087i	$0.745931\pi$
$662$	16.5520	+	9.55629i	0.643311	+	0.371416i
$663$	−30.0649	+	17.3580i	−1.16763	+	0.674129i
$664$		−	5.84246i		−	0.226731i
$665$		0			0
$666$			10.2317i			0.396469i
$667$	8.82336	−	5.09417i	0.341642	−	0.197247i
$668$	−8.02596	+	13.9014i	−0.310534	+	0.537860i
$669$	−1.39898	+	2.42311i	−0.0540878	+	0.0936828i
$670$	3.28423	+	5.68846i	0.126881	+	0.219764i
$671$	8.53508	+	16.9657i	0.329493	+	0.654955i
$672$		0			0
$673$			1.20344i			0.0463893i	0.999731	+	0.0231947i	$0.00738375\pi$
$673$			1.20344i			0.0463893i	−0.999731	+	0.0231947i	$0.992616\pi$
$674$	8.01790	+	13.8874i	0.308838	+	0.534923i
$675$	−1.50744	−	0.870318i	−0.0580212	−	0.0334986i
$676$	−5.43512	+	9.41390i	−0.209043	+	0.362073i
$677$	13.1579	+	22.7902i	0.505701	+	0.875900i	0.999978	+	0.00659557i	$0.00209945\pi$
$677$	13.1579	+	22.7902i	0.505701	+	0.875900i	−0.494277	+	0.869304i	$0.664567\pi$
$678$	−24.4920			−0.940610
$679$		0			0
$680$	16.7580			0.642640
$681$	−36.5180	+	21.0837i	−1.39937	+	0.807928i
$682$	28.3069	+	1.62922i	1.08393	+	0.0623861i
$683$	−16.4637	+	28.5160i	−0.629966	+	1.09113i	0.357592	+	0.933878i	$0.383598\pi$
$683$	−16.4637	+	28.5160i	−0.629966	+	1.09113i	−0.987558	+	0.157255i	$0.949735\pi$
$684$	0.612236	+	1.06042i	0.0234094	+	0.0405463i
$685$		−	19.2155i		−	0.734187i
$686$		0			0
$687$	15.2771			0.582858
$688$	1.36983	−	0.790869i	0.0522241	−	0.0301516i
$689$	3.52762	−	6.11002i	0.134392	−	0.232773i
$690$	13.6480	+	7.87969i	0.519571	+	0.299975i
$691$	−24.4510	+	14.1168i	−0.930159	+	0.537028i	−0.886862	−	0.462034i	$-0.847120\pi$
$691$	−24.4510	+	14.1168i	−0.930159	+	0.537028i	−0.0432974	+	0.999062i	$0.513786\pi$
$692$	7.09477			0.269703
$693$		0			0
$694$	9.87094			0.374696
$695$	7.80824	−	4.50809i	0.296183	−	0.171002i
$696$	−12.0601	−	6.96289i	−0.457136	−	0.263927i
$697$	−27.0200	+	46.8000i	−1.02346	+	1.77268i
$698$	−27.0088	+	15.5935i	−1.02230	+	0.590224i
$699$	70.8605			2.68019
$700$		0			0
$701$			24.2464i			0.915775i	0.889010	+	0.457888i	$0.151394\pi$
$701$			24.2464i			0.915775i	−0.889010	+	0.457888i	$0.848606\pi$
$702$	8.62119	+	14.9323i	0.325386	+	0.563585i
$703$	0.136339	−	0.236147i	0.00514214	−	0.00890644i
$704$	−3.31114	−	0.190575i	−0.124793	−	0.00718256i
$705$	3.25338	−	1.87834i	0.122529	−	0.0707423i
$706$	−25.9682			−0.977327
$707$		0			0
$708$	19.3553			0.727416
$709$	−21.6350	−	37.4729i	−0.812518	−	1.40732i	−0.911096	−	0.412193i	$-0.864763\pi$
$709$	−21.6350	−	37.4729i	−0.812518	−	1.40732i	0.0985783	−	0.995129i	$-0.468571\pi$
$710$	8.34327	−	14.4510i	0.313117	−	0.542335i
$711$	−40.6147	−	23.4489i	−1.52317	−	0.879402i
$712$	−8.05557	−	13.9527i	−0.301895	−	0.522898i
$713$			19.5583i			0.732463i
$714$		0			0
$715$	−9.52494	+	4.79178i	−0.356213	+	0.179203i
$716$	−12.4864	−	21.6271i	−0.466639	−	0.808242i
$717$	39.4646	−	68.3548i	1.47383	−	2.55276i
$718$	2.00534	−	3.47334i	0.0748385	−	0.129624i
$719$	−19.9268	+	11.5048i	−0.743145	+	0.429055i	−0.823212	−	0.567735i	$-0.807820\pi$
$719$	−19.9268	+	11.5048i	−0.743145	+	0.429055i	0.0800668	+	0.996790i	$0.474487\pi$
$720$		−	14.9318i		−	0.556476i
$721$		0			0
$722$			18.9674i			0.705892i
$723$	38.0944	−	21.9938i	1.41675	−	0.817958i
$724$	−16.7644	−	9.67893i	−0.623044	−	0.359714i
$725$	−0.568192	−	0.328046i	−0.0211021	−	0.0121833i
$726$	−34.1702	−	3.94645i	−1.26817	−	0.146466i
$727$			39.3745i			1.46032i	0.683276	+	0.730160i	$0.260555\pi$
$727$			39.3745i			1.46032i	−0.683276	+	0.730160i	$0.739445\pi$
$728$		0			0
$729$	−1.75557			−0.0650210
$730$	10.6580	+	18.4602i	0.394471	+	0.683243i
$731$	10.4207	+	6.01639i	0.385423	+	0.222524i
$732$	15.5071	+	8.95301i	0.573158	+	0.330913i
$733$	4.09264	+	7.08867i	0.151165	+	0.261826i	0.931656	−	0.363341i	$-0.118364\pi$
$733$	4.09264	+	7.08867i	0.151165	+	0.261826i	−0.780491	+	0.625167i	$0.785031\pi$
$734$	19.1851			0.708135
$735$		0			0
$736$		−	2.28779i		−	0.0843291i
$737$	5.42864	−	8.26619i	0.199967	−	0.304489i
$738$	41.7000	+	24.0755i	1.53500	+	0.886232i
$739$	−33.0756	−	19.0962i	−1.21671	−	0.702466i	−0.252494	−	0.967598i	$-0.581251\pi$
$739$	−33.0756	−	19.0962i	−1.21671	−	0.702466i	−0.964212	+	0.265133i	$0.914584\pi$
$740$	−2.87969	+	1.66259i	−0.105860	+	0.0611180i
$741$		−	0.824375i		−	0.0302842i
$742$		0			0
$743$			27.3005i			1.00156i	0.865575	+	0.500779i	$0.166953\pi$
$743$			27.3005i			1.00156i	−0.865575	+	0.500779i	$0.833047\pi$
$744$	23.1514	−	13.3665i	0.848771	−	0.490038i
$745$	−20.4777	+	35.4684i	−0.750244	+	1.29946i
$746$	−10.5145	+	18.2116i	−0.384962	+	0.666774i
$747$	−19.8010	−	34.2964i	−0.724482	−	1.25484i
$748$	−11.3389	−	22.5391i	−0.414592	−	0.824112i
$749$		0			0
$750$		−	35.4572i		−	1.29471i
$751$	1.11584	+	1.93269i	0.0407175	+	0.0705247i	0.885666	−	0.464323i	$-0.153702\pi$
$751$	1.11584	+	1.93269i	0.0407175	+	0.0705247i	−0.844948	+	0.534848i	$0.820369\pi$
$752$	−0.472293	−	0.272679i	−0.0172228	−	0.00994357i
$753$	4.74871	−	8.22500i	0.173053	−	0.299736i
$754$	3.24955	+	5.62838i	0.118342	+	0.204974i
$755$	−29.0879			−1.05862
$756$		0			0
$757$	−16.6709			−0.605913			−0.302956	−	0.953004i	$-0.597974\pi$
$757$	−16.6709			−0.605913			−0.302956	+	0.953004i	$0.597974\pi$
$758$	−17.9722	+	10.3763i	−0.652780	+	0.376883i
$759$	1.36337	−	23.6879i	0.0494873	−	0.859817i
$760$	−0.198970	+	0.344626i	−0.00721740	+	0.0125009i
$761$	−22.8160	−	39.5185i	−0.827081	−	1.43255i	−0.900318	−	0.435232i	$-0.856666\pi$
$761$	−22.8160	−	39.5185i	−0.827081	−	1.43255i	0.0732375	−	0.997315i	$-0.476667\pi$
$762$			42.1218i			1.52591i
$763$		0			0
$764$	−6.00000			−0.217072
$765$	98.3728	−	56.7955i	3.55668	−	2.05345i
$766$	−0.628029	+	1.08778i	−0.0226916	+	0.0393030i
$767$	−7.82283	−	4.51652i	−0.282466	−	0.163082i
$768$	−2.70809	+	1.56352i	−0.0977197	+	0.0564185i
$769$	−51.3570			−1.85198			−0.925991	−	0.377546i	$-0.876768\pi$
$769$	−51.3570			−1.85198			−0.925991	+	0.377546i	$0.876768\pi$
$770$		0			0
$771$	−80.5784			−2.90196
$772$	14.3859	−	8.30569i	0.517759	−	0.298928i
$773$	18.9208	+	10.9239i	0.680533	+	0.392906i	0.800056	−	0.599926i	$-0.204803\pi$
$773$	18.9208	+	10.9239i	0.680533	+	0.392906i	−0.119523	+	0.992831i	$0.538137\pi$
$774$	5.36076	−	9.28511i	0.192689	−	0.333747i
$775$	1.09074	−	0.629740i	0.0391806	−	0.0226209i
$776$	−11.3012			−0.405688
$777$		0			0
$778$			16.6479i			0.596854i
$779$	−0.641624	−	1.11132i	−0.0229886	−	0.0398173i
$780$	−5.02642	+	8.70601i	−0.179975	+	0.311725i
$781$	−25.0815	−	1.44358i	−0.897487	−	0.0516554i
$782$	15.0723	−	8.70198i	0.538983	−	0.311182i
$783$	−52.6160			−1.88034
$784$		0			0
$785$	−12.6864			−0.452797
$786$	−4.10363	−	7.10769i	−0.146372	−	0.253523i
$787$	−10.2201	+	17.7017i	−0.364307	+	0.630998i	−0.988665	−	0.150141i	$-0.952027\pi$
$787$	−10.2201	+	17.7017i	−0.364307	+	0.630998i	0.624358	+	0.781138i	$0.285361\pi$
$788$	17.8744	+	10.3198i	0.636750	+	0.367628i
$789$	−10.0222	−	17.3589i	−0.356799	−	0.617993i
$790$		−	15.2412i		−	0.542259i
$791$		0			0
$792$	−20.0830	+	10.1033i	−0.713617	+	0.359005i
$793$	−4.17833	−	7.23709i	−0.148377	−	0.256996i
$794$	7.08712	−	12.2752i	0.251512	−	0.435632i
$795$	−16.6509	+	28.8403i	−0.590548	+	1.02286i
$796$	−0.628737	+	0.363001i	−0.0222850	+	0.0128662i
$797$			6.09214i			0.215795i	0.994162	+	0.107897i	$0.0344118\pi$
$797$			6.09214i			0.215795i	−0.994162	+	0.107897i	$0.965588\pi$
$798$		0			0
$799$		−	4.14871i		−	0.146771i
$800$	−0.127587	+	0.0736626i	−0.00451090	+	0.00260437i
$801$	−94.5756	−	54.6033i	−3.34167	−	1.92931i
$802$	−4.20256	−	2.42635i	−0.148398	−	0.0856774i
$803$	17.6171	−	26.8255i	0.621693	−	0.946651i
$804$		−	9.32407i		−	0.328834i
$805$		0			0
$806$	−12.4761			−0.439453
$807$	−4.28641	−	7.42428i	−0.150889	−	0.261347i
$808$	0.448355	+	0.258858i	0.0157731	+	0.00910660i
$809$	30.1186	+	17.3890i	1.05891	+	0.611364i	0.925132	−	0.379646i	$-0.123954\pi$
$809$	30.1186	+	17.3890i	1.05891	+	0.611364i	0.133783	+	0.991011i	$0.457288\pi$
$810$	−18.2956	−	31.6890i	−0.642844	−	1.11344i
$811$	26.6602			0.936167			0.468083	−	0.883684i	$-0.344945\pi$
$811$	26.6602			0.936167			0.468083	+	0.883684i	$0.344945\pi$
$812$		0			0
$813$		−	89.4337i		−	3.13658i
$814$	4.18463	+	2.74816i	0.146671	+	0.0963231i
$815$	10.1357	+	5.85182i	0.355036	+	0.204980i
$816$	−20.6013	−	11.8942i	−0.721189	−	0.416379i
$817$	−0.247452	+	0.142867i	−0.00865727	+	0.00499827i
$818$		−	10.6280i		−	0.371601i
$819$		0			0
$820$			15.6486i			0.546471i
$821$	−11.0422	+	6.37522i	−0.385375	+	0.222497i	−0.680154	−	0.733069i	$-0.738087\pi$
$821$	−11.0422	+	6.37522i	−0.385375	+	0.222497i	0.294779	+	0.955565i	$0.404754\pi$
$822$	−13.6384	+	23.6224i	−0.475694	+	0.823926i
$823$	7.93819	−	13.7494i	0.276708	−	0.479272i	−0.693857	−	0.720113i	$-0.744090\pi$
$823$	7.93819	−	13.7494i	0.276708	−	0.479272i	0.970565	+	0.240841i	$0.0774232\pi$
$824$	1.44358	+	2.50035i	0.0502895	+	0.0871039i
$825$	−1.36494	+	0.686673i	−0.0475213	+	0.0239069i
$826$		0			0
$827$		−	35.9639i		−	1.25059i	−0.780390	−	0.625293i	$-0.784979\pi$
$827$		−	35.9639i		−	1.25059i	0.780390	−	0.625293i	$-0.215021\pi$
$828$	−7.75369	−	13.4298i	−0.269459	−	0.466717i
$829$	31.0966	+	17.9536i	1.08003	+	0.623555i	0.930904	−	0.365264i	$-0.119021\pi$
$829$	31.0966	+	17.9536i	1.08003	+	0.623555i	0.149124	+	0.988818i	$0.452355\pi$
$830$	6.43512	−	11.1459i	0.223366	−	0.386882i
$831$	−16.8364	−	29.1616i	−0.584050	−	1.01160i
$832$	1.45937			0.0505946
$833$		0			0
$834$	−12.7986			−0.443181
$835$	−30.6230	+	17.6802i	−1.05975	+	0.611849i
$836$	0.598143	+	0.0344265i	0.0206872	+	0.00119066i
$837$	50.5027	−	87.4733i	1.74563	−	3.02352i
$838$	5.68448	+	9.84582i	0.196367	+	0.340118i
$839$		−	39.5137i		−	1.36416i	−0.731276	−	0.682081i	$-0.761075\pi$
$839$		−	39.5137i		−	1.36416i	0.731276	−	0.682081i	$-0.238925\pi$
$840$		0			0
$841$	9.16765			0.316126
$842$	−23.5961	+	13.6232i	−0.813176	+	0.469487i
$843$	30.6901	−	53.1568i	1.05702	−	1.83082i
$844$	8.90949	+	5.14390i	0.306677	+	0.177060i
$845$	−20.7377	+	11.9729i	−0.713398	+	0.411880i
$846$	−3.69661			−0.127092
$847$		0			0
$848$	4.83444			0.166015
$849$	−28.7687	+	16.6096i	−0.987340	+	0.570041i
$850$	−0.970598	−	0.560375i	−0.0332912	−	0.0192207i
$851$	−1.72668	+	2.99069i	−0.0591897	+	0.102520i
$852$	−20.5134	+	11.8434i	−0.702779	+	0.405750i
$853$	−8.92246			−0.305499			−0.152750	−	0.988265i	$-0.548813\pi$
$853$	−8.92246			−0.305499			−0.152750	+	0.988265i	$0.548813\pi$
$854$		0			0
$855$			2.69736i			0.0922479i
$856$	−2.60980	−	4.52030i	−0.0892010	−	0.154501i
$857$	−4.37047	+	7.56987i	−0.149292	+	0.258582i	−0.930966	−	0.365106i	$-0.881033\pi$
$857$	−4.37047	+	7.56987i	−0.149292	+	0.258582i	0.781674	+	0.623687i	$0.214366\pi$
$858$	15.1104	+	0.869689i	0.515861	+	0.0296907i
$859$	−25.7825	+	14.8855i	−0.879688	+	0.507888i	−0.870556	−	0.492070i	$-0.836240\pi$
$859$	−25.7825	+	14.8855i	−0.879688	+	0.507888i	−0.00913247	+	0.999958i	$0.502907\pi$
$860$	3.48438			0.118816
$861$		0			0
$862$	15.2210			0.518428
$863$	−11.4864	−	19.8951i	−0.391002	−	0.677236i	0.601580	−	0.798813i	$-0.294538\pi$
$863$	−11.4864	−	19.8951i	−0.391002	−	0.677236i	−0.992582	+	0.121577i	$0.961205\pi$
$864$	−5.90746	+	10.2320i	−0.200976	+	0.348101i
$865$	13.5350	+	7.81445i	0.460205	+	0.265699i
$866$	0.927669	+	1.60677i	0.0315235	+	0.0546003i
$867$		−	127.806i		−	4.34051i
$868$		0			0
$869$	−20.4991	+	10.3127i	−0.695386	+	0.349833i
$870$	−15.3384	−	26.5669i	−0.520020	−	0.900701i
$871$	−2.17575	+	3.76851i	−0.0737225	+	0.127691i
$872$	−5.02702	+	8.70705i	−0.170236	+	0.294858i
$873$	−66.3400	+	38.3014i	−2.24527	+	1.29631i
$874$			0.413279i			0.0139794i
$875$		0			0
$876$		−	30.2585i		−	1.02234i
$877$	28.7911	−	16.6225i	0.972205	−	0.561303i	0.0722974	−	0.997383i	$-0.476967\pi$
$877$	28.7911	−	16.6225i	0.972205	−	0.561303i	0.899908	+	0.436080i	$0.143634\pi$
$878$	−28.5272	−	16.4702i	−0.962746	−	0.555842i
$879$	0.751904	+	0.434112i	0.0253611	+	0.0146422i
$880$	−6.10693	−	4.01059i	−0.205864	−	0.135197i
$881$		−	2.73248i		−	0.0920594i	−0.998940	−	0.0460297i	$-0.985343\pi$
$881$		−	2.73248i		−	0.0920594i	0.998940	−	0.0460297i	$-0.0146569\pi$
$882$		0			0
$883$	−19.7473			−0.664550			−0.332275	−	0.943183i	$-0.607816\pi$
$883$	−19.7473			−0.664550			−0.332275	+	0.943183i	$0.607816\pi$
$884$	5.55095	+	9.61453i	0.186699	+	0.323372i
$885$	36.9250	+	21.3187i	1.24122	+	0.716619i
$886$	−28.4587	−	16.4306i	−0.956089	−	0.551998i
$887$	12.2310	+	21.1847i	0.410676	+	0.711312i	0.994964	−	0.100235i	$-0.0319593\pi$
$887$	12.2310	+	21.1847i	0.410676	+	0.711312i	−0.584288	+	0.811547i	$0.698626\pi$
$888$	4.72016			0.158398
$889$		0			0
$890$		−	35.4909i		−	1.18966i
$891$	−30.2416	+	46.0489i	−1.01313	+	1.54270i
$892$	0.774891	+	0.447384i	0.0259453	+	0.0149795i
$893$	0.0853176	+	0.0492581i	0.00285504	+	0.00164836i
$894$	50.3480	−	29.0685i	1.68389	−	0.972195i
$895$		−	55.0121i		−	1.83885i
$896$		0			0
$897$			10.4403i			0.348593i
$898$	−3.14121	+	1.81358i	−0.104824	+	0.0605199i
$899$	19.0358	−	32.9710i	0.634879	−	1.09964i
$900$	−0.499309	+	0.864828i	−0.0166436	+	0.0288276i
$901$	18.3886	+	31.8499i	0.612612	+	1.06107i
$902$	21.0470	−	10.5883i	0.700787	−	0.352550i
$903$		0			0
$904$			7.83235i			0.260500i
$905$	−21.3215	−	36.9299i	−0.708751	−	1.22759i
$906$	35.7589	+	20.6454i	1.18801	+	0.685898i
$907$	22.3109	−	38.6436i	0.740820	−	1.28314i	−0.211302	−	0.977421i	$-0.567770\pi$
$907$	22.3109	−	38.6436i	0.740820	−	1.28314i	0.952122	−	0.305718i	$-0.0988964\pi$
$908$	6.74239	+	11.6782i	0.223754	+	0.387554i
$909$	3.50925			0.116394
$910$		0			0
$911$	37.0868			1.22874			0.614370	−	0.789018i	$-0.289410\pi$
$911$	37.0868			1.22874			0.614370	+	0.789018i	$0.289410\pi$
$912$	0.489203	−	0.282442i	0.0161991	−	0.00935258i
$913$	−19.3452	−	1.11343i	−0.640234	−	0.0368490i
$914$	−1.36783	+	2.36916i	−0.0452439	+	0.0783648i
$915$	19.7224	+	34.1602i	0.652003	+	1.12930i
$916$		−	4.88550i		−	0.161422i
$917$		0			0
$918$	−89.8799			−2.96648
$919$	−44.1563	+	25.4937i	−1.45658	+	0.840958i	−0.998841	−	0.0481269i	$-0.984675\pi$
$919$	−44.1563	+	25.4937i	−1.45658	+	0.840958i	−0.457741	+	0.889085i	$0.651341\pi$
$920$	2.51986	−	4.36453i	0.0830774	−	0.143894i
$921$	17.3708	+	10.0291i	0.572389	+	0.330469i
$922$	17.7050	−	10.2220i	0.583082	−	0.336642i
$923$	11.0546			0.363865
$924$		0			0
$925$	0.222383			0.00731191
$926$	−26.1281	+	15.0851i	−0.858622	+	0.495726i
$927$	16.9482	+	9.78504i	0.556652	+	0.321383i
$928$	−2.22668	+	3.85672i	−0.0730942	+	0.126603i
$929$	−10.5567	+	6.09489i	−0.346353	+	0.199967i	−0.663078	−	0.748551i	$-0.730750\pi$
$929$	−10.5567	+	6.09489i	−0.346353	+	0.199967i	0.316725	+	0.948517i	$0.397417\pi$
$930$	58.8893			1.93106
$931$		0			0
$932$		−	22.6606i		−	0.742274i
$933$	17.6714	+	30.6078i	0.578537	+	1.00206i
$934$	13.5861	−	23.5318i	0.444551	−	0.769986i
$935$	3.19365	−	55.4882i	0.104444	−	1.81466i
$936$	8.56680	−	4.94605i	0.280015	−	0.161667i
$937$	17.0188			0.555979			0.277990	−	0.960584i	$-0.410332\pi$
$937$	17.0188			0.555979			0.277990	+	0.960584i	$0.410332\pi$
$938$		0			0
$939$	51.4292			1.67833
$940$	−0.600678	−	1.04041i	−0.0195920	−	0.0339343i
$941$	−6.79916	+	11.7765i	−0.221646	+	0.383902i	−0.955308	−	0.295612i	$-0.904476\pi$
$941$	−6.79916	+	11.7765i	−0.221646	+	0.383902i	0.733662	+	0.679515i	$0.237810\pi$
$942$	15.5959	+	9.00431i	0.508142	+	0.293376i
$943$	8.12587	+	14.0744i	0.264615	+	0.458326i
$944$		−	6.18967i		−	0.201457i
$945$		0			0
$946$	−2.35763	−	4.68641i	−0.0766531	−	0.152368i
$947$	16.5425	+	28.6524i	0.537558	+	0.931078i	0.999035	+	0.0439257i	$0.0139865\pi$
$947$	16.5425	+	28.6524i	0.537558	+	0.931078i	−0.461477	+	0.887152i	$0.652680\pi$
$948$	−10.8176	+	18.7367i	−0.351340	+	0.608539i
$949$	−7.06076	+	12.2296i	−0.229202	+	0.396990i
$950$	0.0230481	−	0.0133068i	0.000747778	−	0.000431730i
$951$			88.1542i			2.85860i
$952$		0			0
$953$		−	0.427553i		−	0.0138498i	−0.999976	−	0.00692490i	$-0.997796\pi$
$953$		−	0.427553i		−	0.0138498i	0.999976	−	0.00692490i	$-0.00220428\pi$
$954$	28.3791	−	16.3847i	0.918808	−	0.530474i
$955$	−11.4465	−	6.60864i	−0.370400	−	0.213850i
$956$	−21.8593	−	12.6205i	−0.706981	−	0.408176i
$957$	−25.3535	+	38.6057i	−0.819561	+	1.24794i
$958$			21.6184i			0.698459i
$959$		0			0
$960$	−6.88847			−0.222324
$961$	21.0425	+	36.4466i	0.678790	+	1.17570i
$962$	−1.90775	−	1.10144i	−0.0615083	−	0.0355118i
$963$	−30.6400	−	17.6900i	−0.987362	−	0.570053i
$964$	−7.03345	−	12.1823i	−0.226532	−	0.392365i
$965$	36.5928			1.17797
$966$		0			0
$967$		−	6.75935i		−	0.217366i	−0.994076	−	0.108683i	$-0.965337\pi$
$967$		−	6.75935i		−	0.217366i	0.994076	−	0.108683i	$-0.0346634\pi$
$968$	−1.26204	+	10.9274i	−0.0405636	+	0.351219i
$969$	3.72153	+	2.14862i	0.119553	+	0.0690237i
$970$	−21.5598	−	12.4475i	−0.692242	−	0.399666i
$971$	−18.6089	+	10.7439i	−0.597189	+	0.344787i	−0.767935	−	0.640528i	$-0.778716\pi$
$971$	−18.6089	+	10.7439i	−0.597189	+	0.344787i	0.170746	+	0.985315i	$0.445382\pi$
$972$			16.4973i			0.529151i
$973$		0			0
$974$		−	2.08573i		−	0.0668311i
$975$	0.582245	−	0.336159i	0.0186468	−	0.0107657i
$976$	2.86310	−	4.95904i	0.0916457	−	0.158735i
$977$	−21.6466	+	37.4931i	−0.692537	+	1.19951i	0.278467	+	0.960446i	$0.410174\pi$
$977$	−21.6466	+	37.4931i	−0.692537	+	1.19951i	−0.971004	+	0.239064i	$0.923160\pi$
$978$	−8.30678	−	14.3878i	−0.265622	−	0.460070i
$979$	−47.7345	+	24.0141i	−1.52560	+	0.767495i
$980$		0			0
$981$			68.1495i			2.17584i
$982$	−1.23992	−	2.14760i	−0.0395673	−	0.0685326i
$983$	−18.1526	−	10.4804i	−0.578977	−	0.334273i	0.181750	−	0.983345i	$-0.441824\pi$
$983$	−18.1526	−	10.4804i	−0.578977	−	0.334273i	−0.760727	+	0.649072i	$0.775157\pi$
$984$	11.1067	−	19.2374i	0.354069	−	0.613266i
$985$	22.7333	+	39.3752i	0.724342	+	1.25460i
$986$	−33.8781			−1.07890
$987$		0			0
$988$	−0.263629			−0.00838715
$989$	3.13387	−	1.80934i	0.0996514	−	0.0575338i
$990$	−49.4414	−	2.84563i	−1.57135	−	0.0904401i
$991$	−19.2702	+	33.3770i	−0.612138	+	1.06025i	0.378742	+	0.925502i	$0.376357\pi$
$991$	−19.2702	+	33.3770i	−0.612138	+	1.06025i	−0.990879	+	0.134751i	$0.956976\pi$
$992$	−4.27449	−	7.40363i	−0.135715	−	0.235065i
$993$		−	59.7656i		−	1.89660i
$994$		0			0
$995$	−1.59930			−0.0507011
$996$	−15.8219	+	9.13478i	−0.501336	+	0.289447i
$997$	9.72323	−	16.8411i	0.307938	−	0.533364i	−0.669973	−	0.742385i	$-0.733694\pi$
$997$	9.72323	−	16.8411i	0.307938	−	0.533364i	0.977911	+	0.209021i	$0.0670278\pi$
$998$	13.3227	+	7.69189i	0.421724	+	0.243482i
$999$	15.4449	−	8.91714i	0.488656	−	0.282126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.c.1011.4		16
7.2	even	3		154.2.i.a.131.5	yes	16
7.3	odd	6		1078.2.c.b.1077.8		16
7.4	even	3		1078.2.c.b.1077.1		16
7.5	odd	6	inner	1078.2.i.c.901.8		16
7.6	odd	2		154.2.i.a.87.1	✓	16
11.10	odd	2	inner	1078.2.i.c.1011.8		16
21.2	odd	6		1386.2.bk.c.901.3		16
21.20	even	2		1386.2.bk.c.703.7		16
28.23	odd	6		1232.2.bn.b.593.8		16
28.27	even	2		1232.2.bn.b.241.7		16
77.10	even	6		1078.2.c.b.1077.16		16
77.32	odd	6		1078.2.c.b.1077.9		16
77.54	even	6	inner	1078.2.i.c.901.4		16
77.65	odd	6		154.2.i.a.131.1	yes	16
77.76	even	2		154.2.i.a.87.5	yes	16
231.65	even	6		1386.2.bk.c.901.7		16
231.230	odd	2		1386.2.bk.c.703.3		16
308.219	even	6		1232.2.bn.b.593.7		16
308.307	odd	2		1232.2.bn.b.241.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.i.a.87.1	✓	16	7.6	odd	2
154.2.i.a.87.5	yes	16	77.76	even	2
154.2.i.a.131.1	yes	16	77.65	odd	6
154.2.i.a.131.5	yes	16	7.2	even	3
1078.2.c.b.1077.1		16	7.4	even	3
1078.2.c.b.1077.8		16	7.3	odd	6
1078.2.c.b.1077.9		16	77.32	odd	6
1078.2.c.b.1077.16		16	77.10	even	6
1078.2.i.c.901.4		16	77.54	even	6	inner
1078.2.i.c.901.8		16	7.5	odd	6	inner
1078.2.i.c.1011.4		16	1.1	even	1	trivial
1078.2.i.c.1011.8		16	11.10	odd	2	inner
1232.2.bn.b.241.7		16	28.27	even	2
1232.2.bn.b.241.8		16	308.307	odd	2
1232.2.bn.b.593.7		16	308.219	even	6
1232.2.bn.b.593.8		16	28.23	odd	6
1386.2.bk.c.703.3		16	231.230	odd	2
1386.2.bk.c.703.7		16	21.20	even	2
1386.2.bk.c.901.3		16	21.2	odd	6
1386.2.bk.c.901.7		16	231.65	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(2.70809 + 1.56352i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.90775 - 1.10144i) q^{5} -3.12703 q^{6} +1.00000i q^{8} +(3.38916 + 5.87020i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(2.70809 + 1.56352i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.90775 - 1.10144i) q^{5} -3.12703 q^{6} +1.00000i q^{8} +(3.38916 + 5.87020i) q^{9} +(-1.10144 + 1.90775i) q^{10} +(3.31114 + 0.190575i) q^{11} +(2.70809 - 1.56352i) q^{12} -1.45937 q^{13} +6.88847 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.80366 - 6.58813i) q^{17} +(-5.87020 - 3.38916i) q^{18} +(0.0903227 + 0.156443i) q^{19} -2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +(-1.14390 - 1.98129i) q^{23} +(-1.56352 + 2.70809i) q^{24} +(-0.0736626 + 0.127587i) q^{25} +(1.26385 - 0.729686i) q^{26} +11.8149i q^{27} +4.45335i q^{29} +(-5.96559 + 3.44423i) q^{30} +(-7.40363 - 4.27449i) q^{31} +(0.866025 + 0.500000i) q^{32} +(8.66891 + 5.69312i) q^{33} +7.60732i q^{34} +6.77832 q^{36} +(-0.754735 - 1.30724i) q^{37} +(-0.156443 - 0.0903227i) q^{38} +(-3.95211 - 2.28175i) q^{39} +(1.10144 + 1.90775i) q^{40} -7.10368 q^{41} +1.58174i q^{43} +(1.82062 - 2.77225i) q^{44} +(12.9313 + 7.46591i) q^{45} +(1.98129 + 1.14390i) q^{46} +(0.472293 - 0.272679i) q^{47} -3.12703i q^{48} -0.147325i q^{50} +(20.6013 - 11.8942i) q^{51} +(-0.729686 + 1.26385i) q^{52} +(-2.41722 + 4.18675i) q^{53} +(-5.90746 - 10.2320i) q^{54} +(6.52674 - 3.28346i) q^{55} +0.564883i q^{57} +(-2.22668 - 3.85672i) q^{58} +(5.36041 + 3.09483i) q^{59} +(3.44423 - 5.96559i) q^{60} +(2.86310 + 4.95904i) q^{61} +8.54897 q^{62} -1.00000 q^{64} +(-2.78412 + 1.60741i) q^{65} +(-10.3541 - 0.595934i) q^{66} +(1.49088 - 2.58228i) q^{67} +(-3.80366 - 6.58813i) q^{68} -7.15399i q^{69} -7.57488 q^{71} +(-5.87020 + 3.38916i) q^{72} +(4.83822 - 8.38004i) q^{73} +(1.30724 + 0.754735i) q^{74} +(-0.398970 + 0.230345i) q^{75} +0.180645 q^{76} +4.56350 q^{78} +(-5.99185 + 3.45939i) q^{79} +(-1.90775 - 1.10144i) q^{80} +(-8.30534 + 14.3853i) q^{81} +(6.15197 - 3.55184i) q^{82} -5.84246 q^{83} -16.7580i q^{85} +(-0.790869 - 1.36983i) q^{86} +(-6.96289 + 12.0601i) q^{87} +(-0.190575 + 3.31114i) q^{88} +(-13.9527 + 8.05557i) q^{89} -14.9318 q^{90} -2.28779 q^{92} +(-13.3665 - 23.1514i) q^{93} +(-0.272679 + 0.472293i) q^{94} +(0.344626 + 0.198970i) q^{95} +(1.56352 + 2.70809i) q^{96} +11.3012i q^{97} +(10.1033 + 20.0830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{9} + 8 q^{11} - 8 q^{15} - 8 q^{16} - 8 q^{22} + 16 q^{23} + 36 q^{26} + 12 q^{31} + 24 q^{33} + 32 q^{36} - 16 q^{37} - 12 q^{38} - 8 q^{44} + 108 q^{45} - 24 q^{47} - 28 q^{53} - 12 q^{58} - 60 q^{59} - 4 q^{60} - 16 q^{64} - 48 q^{66} + 12 q^{67} + 8 q^{71} - 60 q^{75} - 16 q^{78} - 12 q^{80} - 8 q^{81} + 20 q^{86} - 4 q^{88} - 96 q^{89} + 32 q^{92} - 44 q^{93} + 56 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^9 + 8 * q^11 - 8 * q^15 - 8 * q^16 - 8 * q^22 + 16 * q^23 + 36 * q^26 + 12 * q^31 + 24 * q^33 + 32 * q^36 - 16 * q^37 - 12 * q^38 - 8 * q^44 + 108 * q^45 - 24 * q^47 - 28 * q^53 - 12 * q^58 - 60 * q^59 - 4 * q^60 - 16 * q^64 - 48 * q^66 + 12 * q^67 + 8 * q^71 - 60 * q^75 - 16 * q^78 - 12 * q^80 - 8 * q^81 + 20 * q^86 - 4 * q^88 - 96 * q^89 + 32 * q^92 - 44 * q^93 + 56 * q^99

Introduction

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