LMFDB - Embedded newform 2070.2.j.j.737.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 $ x^20 - 20x^18 + 187x^16 - 1012x^14 + 3533x^12 - 7896x^10 + 10837x^8 - 5668x^6 - 4125x^4 + 8700*x^2 + 3721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.4
Root			$-1.39971 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.j.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.125717 - 2.23253i) q^{5} +(3.50921 + 3.50921i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.125717 - 2.23253i) q^{5} +(3.50921 + 3.50921i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.48974 + 1.66753i) q^{10} +0.764834i q^{11} +(-3.69809 + 3.69809i) q^{13} -4.96277 q^{14} -1.00000 q^{16} +(-0.764834 + 0.764834i) q^{17} +6.41670i q^{19} +(-2.23253 - 0.125717i) q^{20} +(-0.540819 - 0.540819i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-4.96839 - 0.561334i) q^{25} -5.22990i q^{26} +(3.50921 - 3.50921i) q^{28} -1.67897 q^{29} -9.93678 q^{31} +(0.707107 - 0.707107i) q^{32} -1.08164i q^{34} +(8.27559 - 7.39325i) q^{35} +(-8.31090 - 8.31090i) q^{37} +(-4.53730 - 4.53730i) q^{38} +(1.66753 - 1.48974i) q^{40} +10.5906i q^{41} +(2.96839 - 2.96839i) q^{43} +0.764834 q^{44} +1.00000 q^{46} +(2.54798 - 2.54798i) q^{47} +17.6291i q^{49} +(3.91011 - 3.11626i) q^{50} +(3.69809 + 3.69809i) q^{52} +(-9.13318 - 9.13318i) q^{53} +(1.70751 + 0.0961525i) q^{55} +4.96277i q^{56} +(1.18721 - 1.18721i) q^{58} -0.219632 q^{59} -1.82779 q^{61} +(7.02637 - 7.02637i) q^{62} +1.00000i q^{64} +(7.79120 + 8.72102i) q^{65} +(5.38509 + 5.38509i) q^{67} +(0.764834 + 0.764834i) q^{68} +(-0.623904 + 11.0795i) q^{70} -6.14124i q^{71} +(-1.36645 + 1.36645i) q^{73} +11.7534 q^{74} +6.41670 q^{76} +(-2.68396 + 2.68396i) q^{77} -4.66284i q^{79} +(-0.125717 + 2.23253i) q^{80} +(-7.48869 - 7.48869i) q^{82} +(-1.48645 - 1.48645i) q^{83} +(1.61136 + 1.80367i) q^{85} +4.19794i q^{86} +(-0.540819 + 0.540819i) q^{88} +1.81216 q^{89} -25.9548 q^{91} +(-0.707107 + 0.707107i) q^{92} +3.60339i q^{94} +(14.3255 + 0.806688i) q^{95} +(8.54237 + 8.54237i) q^{97} +(-12.4657 - 12.4657i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 16 q^{7}+O(q^{10}) $ 20 * q - 16 * q^7	$ 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) $ 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.125717	−	2.23253i	0.0562223	−	0.998418i
$5$	0.125717	−	2.23253i	0.0562223	−	0.998418i
$6$		0			0
$7$	3.50921	+	3.50921i	1.32636	+	1.32636i	0.908524	+	0.417832i	$0.137210\pi$
$7$	3.50921	+	3.50921i	1.32636	+	1.32636i	0.417832	+	0.908524i	$0.362790\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.48974	+	1.66753i	0.471098	+	0.527320i
$11$			0.764834i			0.230606i	0.993330	+	0.115303i	$0.0367839\pi$
$11$			0.764834i			0.230606i	−0.993330	+	0.115303i	$0.963216\pi$
$12$		0			0
$13$	−3.69809	+	3.69809i	−1.02567	+	1.02567i	−0.0260052	+	0.999662i	$0.508279\pi$
$13$	−3.69809	+	3.69809i	−1.02567	+	1.02567i	−0.999662	+	0.0260052i	$0.991721\pi$
$14$	−4.96277			−1.32636
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.764834	+	0.764834i	−0.185499	+	0.185499i	−0.793747	−	0.608248i	$-0.791873\pi$
$17$	−0.764834	+	0.764834i	−0.185499	+	0.185499i	0.608248	+	0.793747i	$0.291873\pi$
$18$		0			0
$19$			6.41670i			1.47209i	0.676931	+	0.736046i	$0.263310\pi$
$19$			6.41670i			1.47209i	−0.676931	+	0.736046i	$0.736690\pi$
$20$	−2.23253	−	0.125717i	−0.499209	−	0.0281112i
$21$		0			0
$22$	−0.540819	−	0.540819i	−0.115303	−	0.115303i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$		0			0
$25$	−4.96839	−	0.561334i	−0.993678	−	0.112267i
$26$		−	5.22990i		−	1.02567i
$27$		0			0
$28$	3.50921	−	3.50921i	0.663178	−	0.663178i
$29$	−1.67897			−0.311777			−0.155888	−	0.987775i	$-0.549824\pi$
$29$	−1.67897			−0.311777			−0.155888	+	0.987775i	$0.549824\pi$
$30$		0			0
$31$	−9.93678			−1.78470			−0.892349	−	0.451345i	$-0.850944\pi$
$31$	−9.93678			−1.78470			−0.892349	+	0.451345i	$0.850944\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	1.08164i		−	0.185499i
$35$	8.27559	−	7.39325i	1.39883	−	1.24969i
$36$		0			0
$37$	−8.31090	−	8.31090i	−1.36630	−	1.36630i	−0.865644	−	0.500661i	$-0.833090\pi$
$37$	−8.31090	−	8.31090i	−1.36630	−	1.36630i	−0.500661	−	0.865644i	$-0.666910\pi$
$38$	−4.53730	−	4.53730i	−0.736046	−	0.736046i
$39$		0			0
$40$	1.66753	−	1.48974i	0.263660	−	0.235549i
$41$			10.5906i			1.65398i	0.562220	+	0.826988i	$0.309948\pi$
$41$			10.5906i			1.65398i	−0.562220	+	0.826988i	$0.690052\pi$
$42$		0			0
$43$	2.96839	−	2.96839i	0.452675	−	0.452675i	−0.443566	−	0.896242i	$-0.646287\pi$
$43$	2.96839	−	2.96839i	0.452675	−	0.452675i	0.896242	+	0.443566i	$0.146287\pi$
$44$	0.764834			0.115303
$45$		0			0
$46$	1.00000			0.147442
$47$	2.54798	−	2.54798i	0.371661	−	0.371661i	−0.496421	−	0.868082i	$-0.665353\pi$
$47$	2.54798	−	2.54798i	0.371661	−	0.371661i	0.868082	+	0.496421i	$0.165353\pi$
$48$		0			0
$49$			17.6291i			2.51844i
$50$	3.91011	−	3.11626i	0.552972	−	0.440706i
$51$		0			0
$52$	3.69809	+	3.69809i	0.512833	+	0.512833i
$53$	−9.13318	−	9.13318i	−1.25454	−	1.25454i	−0.953664	−	0.300875i	$-0.902721\pi$
$53$	−9.13318	−	9.13318i	−1.25454	−	1.25454i	−0.300875	−	0.953664i	$-0.597279\pi$
$54$		0			0
$55$	1.70751	+	0.0961525i	0.230241	+	0.0129652i
$56$			4.96277i			0.663178i
$57$		0			0
$58$	1.18721	−	1.18721i	0.155888	−	0.155888i
$59$	−0.219632			−0.0285936			−0.0142968	−	0.999898i	$-0.504551\pi$
$59$	−0.219632			−0.0285936			−0.0142968	+	0.999898i	$0.504551\pi$
$60$		0			0
$61$	−1.82779			−0.234024			−0.117012	−	0.993130i	$-0.537332\pi$
$61$	−1.82779			−0.234024			−0.117012	+	0.993130i	$0.537332\pi$
$62$	7.02637	−	7.02637i	0.892349	−	0.892349i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	7.79120	+	8.72102i	0.966379	+	1.08171i
$66$		0			0
$67$	5.38509	+	5.38509i	0.657894	+	0.657894i	0.954881	−	0.296987i	$-0.0959819\pi$
$67$	5.38509	+	5.38509i	0.657894	+	0.657894i	−0.296987	+	0.954881i	$0.595982\pi$
$68$	0.764834	+	0.764834i	0.0927497	+	0.0927497i
$69$		0			0
$70$	−0.623904	+	11.0795i	−0.0745708	+	1.32426i
$71$		−	6.14124i		−	0.728831i	−0.931236	−	0.364416i	$-0.881269\pi$
$71$		−	6.14124i		−	0.728831i	0.931236	−	0.364416i	$-0.118731\pi$
$72$		0			0
$73$	−1.36645	+	1.36645i	−0.159931	+	0.159931i	−0.782536	−	0.622605i	$-0.786074\pi$
$73$	−1.36645	+	1.36645i	−0.159931	+	0.159931i	0.622605	+	0.782536i	$0.286074\pi$
$74$	11.7534			1.36630
$75$		0			0
$76$	6.41670			0.736046
$77$	−2.68396	+	2.68396i	−0.305866	+	0.305866i
$78$		0			0
$79$		−	4.66284i		−	0.524610i	−0.964985	−	0.262305i	$-0.915517\pi$
$79$		−	4.66284i		−	0.524610i	0.964985	−	0.262305i	$-0.0844827\pi$
$80$	−0.125717	+	2.23253i	−0.0140556	+	0.249605i
$81$		0			0
$82$	−7.48869	−	7.48869i	−0.826988	−	0.826988i
$83$	−1.48645	−	1.48645i	−0.163159	−	0.163159i	0.620806	−	0.783964i	$-0.286806\pi$
$83$	−1.48645	−	1.48645i	−0.163159	−	0.163159i	−0.783964	+	0.620806i	$0.786806\pi$
$84$		0			0
$85$	1.61136	+	1.80367i	0.174777	+	0.195635i
$86$			4.19794i			0.452675i
$87$		0			0
$88$	−0.540819	+	0.540819i	−0.0576515	+	0.0576515i
$89$	1.81216			0.192089			0.0960443	−	0.995377i	$-0.469381\pi$
$89$	1.81216			0.192089			0.0960443	+	0.995377i	$0.469381\pi$
$90$		0			0
$91$	−25.9548			−2.72080
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$		0			0
$94$			3.60339i			0.371661i
$95$	14.3255	+	0.806688i	1.46976	+	0.0827645i
$96$		0			0
$97$	8.54237	+	8.54237i	0.867346	+	0.867346i	0.992178	−	0.124832i	$-0.0398391\pi$
$97$	8.54237	+	8.54237i	0.867346	+	0.867346i	−0.124832	+	0.992178i	$0.539839\pi$
$98$	−12.4657	−	12.4657i	−1.25922	−	1.25922i
$99$		0			0
$100$	−0.561334	+	4.96839i	−0.0561334	+	0.496839i
$101$			7.00584i			0.697107i	0.937289	+	0.348554i	$0.113327\pi$
$101$			7.00584i			0.697107i	−0.937289	+	0.348554i	$0.886673\pi$
$102$		0			0
$103$	0.839077	−	0.839077i	0.0826767	−	0.0826767i	−0.664559	−	0.747236i	$-0.731381\pi$
$103$	0.839077	−	0.839077i	0.0826767	−	0.0826767i	0.747236	+	0.664559i	$0.231381\pi$
$104$	−5.22990			−0.512833
$105$		0			0
$106$	12.9163			1.25454
$107$	−7.70564	+	7.70564i	−0.744933	+	0.744933i	−0.973523	−	0.228590i	$-0.926588\pi$
$107$	−7.70564	+	7.70564i	−0.744933	+	0.744933i	0.228590	+	0.973523i	$0.426588\pi$
$108$		0			0
$109$			2.31665i			0.221895i	0.993826	+	0.110947i	$0.0353885\pi$
$109$			2.31665i			0.221895i	−0.993826	+	0.110947i	$0.964612\pi$
$110$	−1.27539	+	1.13941i	−0.121603	+	0.108638i
$111$		0			0
$112$	−3.50921	−	3.50921i	−0.331589	−	0.331589i
$113$	−4.85580	−	4.85580i	−0.456796	−	0.456796i	0.440807	−	0.897602i	$-0.354692\pi$
$113$	−4.85580	−	4.85580i	−0.456796	−	0.456796i	−0.897602	+	0.440807i	$0.854692\pi$
$114$		0			0
$115$	−1.66753	+	1.48974i	−0.155498	+	0.138919i
$116$			1.67897i			0.155888i
$117$		0			0
$118$	0.155303	−	0.155303i	0.0142968	−	0.0142968i
$119$	−5.36792			−0.492077
$120$		0			0
$121$	10.4150			0.946821
$122$	1.29244	−	1.29244i	0.117012	−	0.117012i
$123$		0			0
$124$			9.93678i			0.892349i
$125$	−1.87781	+	11.0215i	−0.167956	+	0.985794i
$126$		0			0
$127$	4.65707	+	4.65707i	0.413248	+	0.413248i	0.882868	−	0.469621i	$-0.155609\pi$
$127$	4.65707	+	4.65707i	0.413248	+	0.413248i	−0.469621	+	0.882868i	$0.655609\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−11.6759	−	0.657486i	−1.02404	−	0.0576654i
$131$		−	10.2612i		−	0.896527i	−0.893901	−	0.448264i	$-0.852043\pi$
$131$		−	10.2612i		−	0.896527i	0.893901	−	0.448264i	$-0.147957\pi$
$132$		0			0
$133$	−22.5176	+	22.5176i	−1.95252	+	1.95252i
$134$	−7.61567			−0.657894
$135$		0			0
$136$	−1.08164			−0.0927497
$137$	−11.2038	+	11.2038i	−0.957203	+	0.957203i	−0.999121	−	0.0419178i	$-0.986653\pi$
$137$	−11.2038	+	11.2038i	−0.957203	+	0.957203i	0.0419178	+	0.999121i	$0.486653\pi$
$138$		0			0
$139$			11.6073i			0.984521i	0.870448	+	0.492261i	$0.163829\pi$
$139$			11.6073i			0.984521i	−0.870448	+	0.492261i	$0.836171\pi$
$140$	−7.39325	−	8.27559i	−0.624844	−	0.699415i
$141$		0			0
$142$	4.34251	+	4.34251i	0.364416	+	0.364416i
$143$	−2.82843	−	2.82843i	−0.236525	−	0.236525i
$144$		0			0
$145$	−0.211075	+	3.74835i	−0.0175288	+	0.311284i
$146$		−	1.93245i		−	0.159931i
$147$		0			0
$148$	−8.31090	+	8.31090i	−0.683152	+	0.683152i
$149$	−12.9190			−1.05836			−0.529181	−	0.848509i	$-0.677501\pi$
$149$	−12.9190			−1.05836			−0.529181	+	0.848509i	$0.677501\pi$
$150$		0			0
$151$	7.01447			0.570830			0.285415	−	0.958404i	$-0.407869\pi$
$151$	7.01447			0.570830			0.285415	+	0.958404i	$0.407869\pi$
$152$	−4.53730	+	4.53730i	−0.368023	+	0.368023i
$153$		0			0
$154$		−	3.79569i		−	0.305866i
$155$	−1.24922	+	22.1842i	−0.100340	+	1.78188i
$156$		0			0
$157$	4.68533	+	4.68533i	0.373930	+	0.373930i	0.868906	−	0.494977i	$-0.164823\pi$
$157$	4.68533	+	4.68533i	0.373930	+	0.373930i	−0.494977	+	0.868906i	$0.664823\pi$
$158$	3.29712	+	3.29712i	0.262305	+	0.262305i
$159$		0			0
$160$	−1.48974	−	1.66753i	−0.117774	−	0.131830i
$161$		−	4.96277i		−	0.391121i
$162$		0			0
$163$	2.89617	−	2.89617i	0.226846	−	0.226846i	−0.584528	−	0.811374i	$-0.698720\pi$
$163$	2.89617	−	2.89617i	0.226846	−	0.226846i	0.811374	+	0.584528i	$0.198720\pi$
$164$	10.5906			0.826988
$165$		0			0
$166$	2.10215			0.163159
$167$	−1.29908	+	1.29908i	−0.100526	+	0.100526i	−0.755581	−	0.655055i	$-0.772645\pi$
$167$	−1.29908	+	1.29908i	−0.100526	+	0.100526i	0.655055	+	0.755581i	$0.272645\pi$
$168$		0			0
$169$		−	14.3518i		−	1.10399i
$170$	−2.41479	−	0.135980i	−0.185206	−	0.0104292i
$171$		0			0
$172$	−2.96839	−	2.96839i	−0.226338	−	0.226338i
$173$	−15.3651	−	15.3651i	−1.16819	−	1.16819i	−0.982634	−	0.185556i	$-0.940591\pi$
$173$	−15.3651	−	15.3651i	−1.16819	−	1.16819i	−0.185556	−	0.982634i	$-0.559409\pi$
$174$		0			0
$175$	−15.4653	−	19.4050i	−1.16907	−	1.46688i
$176$		−	0.764834i		−	0.0576515i
$177$		0			0
$178$	−1.28139	+	1.28139i	−0.0960443	+	0.0960443i
$179$	−5.04921			−0.377396			−0.188698	−	0.982035i	$-0.560427\pi$
$179$	−5.04921			−0.377396			−0.188698	+	0.982035i	$0.560427\pi$
$180$		0			0
$181$	3.31623			0.246493			0.123247	−	0.992376i	$-0.460669\pi$
$181$	3.31623			0.246493			0.123247	+	0.992376i	$0.460669\pi$
$182$	18.3528	−	18.3528i	1.36040	−	1.36040i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−19.5992	+	17.5095i	−1.44096	+	1.28733i
$186$		0			0
$187$	−0.584970	−	0.584970i	−0.0427773	−	0.0427773i
$188$	−2.54798	−	2.54798i	−0.185831	−	0.185831i
$189$		0			0
$190$	−10.7001	+	9.55924i	−0.776264	+	0.693500i
$191$			9.26011i			0.670038i	0.942211	+	0.335019i	$0.108743\pi$
$191$			9.26011i			0.670038i	−0.942211	+	0.335019i	$0.891257\pi$
$192$		0			0
$193$	10.0816	−	10.0816i	0.725692	−	0.725692i	−0.244066	−	0.969759i	$-0.578481\pi$
$193$	10.0816	−	10.0816i	0.725692	−	0.725692i	0.969759	+	0.244066i	$0.0784815\pi$
$194$	−12.0807			−0.867346
$195$		0			0
$196$	17.6291			1.25922
$197$	19.7516	−	19.7516i	1.40725	−	1.40725i	0.633521	−	0.773726i	$-0.281609\pi$
$197$	19.7516	−	19.7516i	1.40725	−	1.40725i	0.773726	−	0.633521i	$-0.218391\pi$
$198$		0			0
$199$			17.7223i			1.25630i	0.778092	+	0.628150i	$0.216187\pi$
$199$			17.7223i			1.25630i	−0.778092	+	0.628150i	$0.783813\pi$
$200$	−3.11626	−	3.91011i	−0.220353	−	0.276486i
$201$		0			0
$202$	−4.95388	−	4.95388i	−0.348554	−	0.348554i
$203$	−5.89185	−	5.89185i	−0.413527	−	0.413527i
$204$		0			0
$205$	23.6439	+	1.33142i	1.65136	+	0.0929903i
$206$			1.18663i			0.0826767i
$207$		0			0
$208$	3.69809	−	3.69809i	0.256417	−	0.256417i
$209$	−4.90771			−0.339473
$210$		0			0
$211$	23.2846			1.60298			0.801491	−	0.598007i	$-0.204041\pi$
$211$	23.2846			1.60298			0.801491	+	0.598007i	$0.204041\pi$
$212$	−9.13318	+	9.13318i	−0.627269	+	0.627269i
$213$		0			0
$214$		−	10.8974i		−	0.744933i
$215$	−6.25385	−	7.00020i	−0.426509	−	0.477410i
$216$		0			0
$217$	−34.8702	−	34.8702i	−2.36715	−	2.36715i
$218$	−1.63812	−	1.63812i	−0.110947	−	0.110947i
$219$		0			0
$220$	0.0961525	−	1.70751i	0.00648260	−	0.115121i
$221$		−	5.65685i		−	0.380521i
$222$		0			0
$223$	6.31235	−	6.31235i	0.422706	−	0.422706i	−0.463428	−	0.886134i	$-0.653381\pi$
$223$	6.31235	−	6.31235i	0.422706	−	0.422706i	0.886134	+	0.463428i	$0.153381\pi$
$224$	4.96277			0.331589
$225$		0			0
$226$	6.86714			0.456796
$227$	−15.5235	+	15.5235i	−1.03033	+	1.03033i	−0.0308046	+	0.999525i	$0.509807\pi$
$227$	−15.5235	+	15.5235i	−1.03033	+	1.03033i	−0.999525	+	0.0308046i	$0.990193\pi$
$228$		0			0
$229$			26.6680i			1.76227i	0.472862	+	0.881137i	$0.343221\pi$
$229$			26.6680i			1.76227i	−0.472862	+	0.881137i	$0.656779\pi$
$230$	0.125717	−	2.23253i	0.00828953	−	0.147209i
$231$		0			0
$232$	−1.18721	−	1.18721i	−0.0779442	−	0.0779442i
$233$	14.3178	+	14.3178i	0.937991	+	0.937991i	0.998187	−	0.0601958i	$-0.0191725\pi$
$233$	14.3178	+	14.3178i	0.937991	+	0.937991i	−0.0601958	+	0.998187i	$0.519173\pi$
$234$		0			0
$235$	−5.36812	−	6.00877i	−0.350178	−	0.391969i
$236$			0.219632i			0.0142968i
$237$		0			0
$238$	3.79569	−	3.79569i	0.246038	−	0.246038i
$239$	8.13112			0.525958			0.262979	−	0.964801i	$-0.415295\pi$
$239$	8.13112			0.525958			0.262979	+	0.964801i	$0.415295\pi$
$240$		0			0
$241$	−1.56965			−0.101110			−0.0505552	−	0.998721i	$-0.516099\pi$
$241$	−1.56965			−0.101110			−0.0505552	+	0.998721i	$0.516099\pi$
$242$	−7.36454	+	7.36454i	−0.473410	+	0.473410i
$243$		0			0
$244$			1.82779i			0.117012i
$245$	39.3575	+	2.21628i	2.51446	+	0.141593i
$246$		0			0
$247$	−23.7296	−	23.7296i	−1.50988	−	1.50988i
$248$	−7.02637	−	7.02637i	−0.446175	−	0.446175i
$249$		0			0
$250$	−6.46558	−	9.12120i	−0.408919	−	0.576875i
$251$		−	23.9786i		−	1.51352i	−0.653695	−	0.756758i	$-0.726782\pi$
$251$		−	23.9786i		−	1.51352i	0.653695	−	0.756758i	$-0.273218\pi$
$252$		0			0
$253$	0.540819	−	0.540819i	0.0340010	−	0.0340010i
$254$	−6.58609			−0.413248
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.5733	−	12.5733i	0.784300	−	0.784300i	−0.196253	−	0.980553i	$-0.562877\pi$
$257$	12.5733	−	12.5733i	0.784300	−	0.784300i	0.980553	+	0.196253i	$0.0628774\pi$
$258$		0			0
$259$		−	58.3294i		−	3.62441i
$260$	8.72102	−	7.79120i	0.540855	−	0.483190i
$261$		0			0
$262$	7.25578	+	7.25578i	0.448264	+	0.448264i
$263$	6.07601	+	6.07601i	0.374663	+	0.374663i	0.869172	−	0.494509i	$-0.164652\pi$
$263$	6.07601	+	6.07601i	0.374663	+	0.374663i	−0.494509	+	0.869172i	$0.664652\pi$
$264$		0			0
$265$	−21.5383	+	19.2419i	−1.32309	+	1.18202i
$266$		−	31.8446i		−	1.95252i
$267$		0			0
$268$	5.38509	−	5.38509i	0.328947	−	0.328947i
$269$	16.4382			1.00225			0.501127	−	0.865374i	$-0.332919\pi$
$269$	16.4382			1.00225			0.501127	+	0.865374i	$0.332919\pi$
$270$		0			0
$271$	1.91878			0.116558			0.0582789	−	0.998300i	$-0.481439\pi$
$271$	1.91878			0.116558			0.0582789	+	0.998300i	$0.481439\pi$
$272$	0.764834	−	0.764834i	0.0463748	−	0.0463748i
$273$		0			0
$274$		−	15.8445i		−	0.957203i
$275$	0.429327	−	3.79999i	0.0258894	−	0.229148i
$276$		0			0
$277$	−11.4499	−	11.4499i	−0.687956	−	0.687956i	0.273824	−	0.961780i	$-0.411711\pi$
$277$	−11.4499	−	11.4499i	−0.687956	−	0.687956i	−0.961780	+	0.273824i	$0.911711\pi$
$278$	−8.20762	−	8.20762i	−0.492261	−	0.492261i
$279$		0			0
$280$	11.0795	+	0.623904i	0.662129	+	0.0372854i
$281$			12.0000i			0.715859i	0.933749	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715859i	−0.933749	+	0.357930i	$0.883483\pi$
$282$		0			0
$283$	2.34054	−	2.34054i	0.139131	−	0.139131i	−0.634111	−	0.773242i	$-0.718634\pi$
$283$	2.34054	−	2.34054i	0.139131	−	0.139131i	0.773242	+	0.634111i	$0.218634\pi$
$284$	−6.14124			−0.364416
$285$		0			0
$286$	4.00000			0.236525
$287$	−37.1647	+	37.1647i	−2.19376	+	2.19376i
$288$		0			0
$289$			15.8301i			0.931180i
$290$	−2.50123	−	2.79974i	−0.146877	−	0.164406i
$291$		0			0
$292$	1.36645	+	1.36645i	0.0799653	+	0.0799653i
$293$	14.0431	+	14.0431i	0.820406	+	0.820406i	0.986166	−	0.165760i	$-0.0530078\pi$
$293$	14.0431	+	14.0431i	0.820406	+	0.820406i	−0.165760	+	0.986166i	$0.553008\pi$
$294$		0			0
$295$	−0.0276114	+	0.490335i	−0.00160760	+	0.0285484i
$296$		−	11.7534i		−	0.683152i
$297$		0			0
$298$	9.13509	−	9.13509i	0.529181	−	0.529181i
$299$	5.22990			0.302453
$300$		0			0
$301$	20.8334			1.20082
$302$	−4.95998	+	4.95998i	−0.285415	+	0.285415i
$303$		0			0
$304$		−	6.41670i		−	0.368023i
$305$	−0.229784	+	4.08060i	−0.0131574	+	0.233654i
$306$		0			0
$307$	5.27394	+	5.27394i	0.301000	+	0.301000i	0.841405	−	0.540405i	$-0.181729\pi$
$307$	5.27394	+	5.27394i	0.301000	+	0.301000i	−0.540405	+	0.841405i	$0.681729\pi$
$308$	2.68396	+	2.68396i	0.152933	+	0.152933i
$309$		0			0
$310$	−14.8032	−	16.5699i	−0.840768	−	0.941108i
$311$			31.5861i			1.79108i	0.444977	+	0.895542i	$0.353212\pi$
$311$			31.5861i			1.79108i	−0.444977	+	0.895542i	$0.646788\pi$
$312$		0			0
$313$	−2.83163	+	2.83163i	−0.160053	+	0.160053i	−0.782590	−	0.622537i	$-0.786102\pi$
$313$	−2.83163	+	2.83163i	−0.160053	+	0.160053i	0.622537	+	0.782590i	$0.286102\pi$
$314$	−6.62605			−0.373930
$315$		0			0
$316$	−4.66284			−0.262305
$317$	−10.6011	+	10.6011i	−0.595420	+	0.595420i	−0.939090	−	0.343671i	$-0.888330\pi$
$317$	−10.6011	+	10.6011i	−0.595420	+	0.595420i	0.343671	+	0.939090i	$0.388330\pi$
$318$		0			0
$319$		−	1.28413i		−	0.0718976i
$320$	2.23253	+	0.125717i	0.124802	+	0.00702779i
$321$		0			0
$322$	3.50921	+	3.50921i	0.195561	+	0.195561i
$323$	−4.90771	−	4.90771i	−0.273072	−	0.273072i
$324$		0			0
$325$	20.4494	−	16.2977i	1.13433	−	0.904035i
$326$			4.09581i			0.226846i
$327$		0			0
$328$	−7.48869	+	7.48869i	−0.413494	+	0.413494i
$329$	17.8828			0.985911
$330$		0			0
$331$	7.81164			0.429367			0.214683	−	0.976684i	$-0.431128\pi$
$331$	7.81164			0.429367			0.214683	+	0.976684i	$0.431128\pi$
$332$	−1.48645	+	1.48645i	−0.0815793	+	0.0815793i
$333$		0			0
$334$		−	1.83718i		−	0.100526i
$335$	12.6994	−	11.3454i	0.693842	−	0.619865i
$336$		0			0
$337$	−15.1462	−	15.1462i	−0.825065	−	0.825065i	0.161764	−	0.986829i	$-0.448282\pi$
$337$	−15.1462	−	15.1462i	−0.825065	−	0.825065i	−0.986829	+	0.161764i	$0.948282\pi$
$338$	10.1483	+	10.1483i	0.551993	+	0.551993i
$339$		0			0
$340$	1.80367	−	1.61136i	0.0978176	−	0.0873884i
$341$		−	7.59998i		−	0.411562i
$342$		0			0
$343$	−37.2998	+	37.2998i	−2.01400	+	2.01400i
$344$	4.19794			0.226338
$345$		0			0
$346$	21.7296			1.16819
$347$	−25.3795	+	25.3795i	−1.36244	+	1.36244i	−0.491649	+	0.870794i	$0.663606\pi$
$347$	−25.3795	+	25.3795i	−1.36244	+	1.36244i	−0.870794	+	0.491649i	$0.836394\pi$
$348$		0			0
$349$			23.9078i			1.27975i	0.768478	+	0.639876i	$0.221014\pi$
$349$			23.9078i			1.27975i	−0.768478	+	0.639876i	$0.778986\pi$
$350$	24.6570	+	2.78577i	1.31797	+	0.148906i
$351$		0			0
$352$	0.540819	+	0.540819i	0.0288258	+	0.0288258i
$353$	16.3729	+	16.3729i	0.871442	+	0.871442i	0.992630	−	0.121187i	$-0.0386702\pi$
$353$	16.3729	+	16.3729i	0.871442	+	0.871442i	−0.121187	+	0.992630i	$0.538670\pi$
$354$		0			0
$355$	−13.7105	−	0.772058i	−0.727679	−	0.0409766i
$356$		−	1.81216i		−	0.0960443i
$357$		0			0
$358$	3.57033	−	3.57033i	0.188698	−	0.188698i
$359$	29.2785			1.54526			0.772630	−	0.634857i	$-0.218941\pi$
$359$	29.2785			1.54526			0.772630	+	0.634857i	$0.218941\pi$
$360$		0			0
$361$	−22.1741			−1.16706
$362$	−2.34493	+	2.34493i	−0.123247	+	0.123247i
$363$		0			0
$364$			25.9548i			1.36040i
$365$	2.87885	+	3.22242i	0.150686	+	0.168669i
$366$		0			0
$367$	−5.86479	−	5.86479i	−0.306140	−	0.306140i	0.537270	−	0.843410i	$-0.319455\pi$
$367$	−5.86479	−	5.86479i	−0.306140	−	0.306140i	−0.843410	+	0.537270i	$0.819455\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$		0			0
$370$	1.47760	−	26.2398i	0.0768168	−	1.36414i
$371$		−	64.1005i		−	3.32793i
$372$		0			0
$373$	−16.0815	+	16.0815i	−0.832669	+	0.832669i	−0.987881	−	0.155212i	$-0.950394\pi$
$373$	−16.0815	+	16.0815i	−0.832669	+	0.832669i	0.155212	+	0.987881i	$0.450394\pi$
$374$	0.827273			0.0427773
$375$		0			0
$376$	3.60339			0.185831
$377$	6.20899	−	6.20899i	0.319779	−	0.319779i
$378$		0			0
$379$			3.82398i			0.196425i	0.995165	+	0.0982124i	$0.0313125\pi$
$379$			3.82398i			0.196425i	−0.995165	+	0.0982124i	$0.968688\pi$
$380$	0.806688	−	14.3255i	0.0413822	−	0.734882i
$381$		0			0
$382$	−6.54789	−	6.54789i	−0.335019	−	0.335019i
$383$	4.12422	+	4.12422i	0.210738	+	0.210738i	0.804581	−	0.593843i	$-0.202390\pi$
$383$	4.12422	+	4.12422i	0.210738	+	0.210738i	−0.593843	+	0.804581i	$0.702390\pi$
$384$		0			0
$385$	5.65461	+	6.32945i	0.288186	+	0.322578i
$386$			14.2576i			0.725692i
$387$		0			0
$388$	8.54237	−	8.54237i	0.433673	−	0.433673i
$389$	34.1969			1.73385			0.866927	−	0.498435i	$-0.166092\pi$
$389$	34.1969			1.73385			0.866927	+	0.498435i	$0.166092\pi$
$390$		0			0
$391$	1.08164			0.0547008
$392$	−12.4657	+	12.4657i	−0.629611	+	0.629611i
$393$		0			0
$394$			27.9330i			1.40725i
$395$	−10.4099	−	0.586197i	−0.523780	−	0.0294948i
$396$		0			0
$397$	0.116895	+	0.116895i	0.00586678	+	0.00586678i	0.710034	−	0.704167i	$-0.248680\pi$
$397$	0.116895	+	0.116895i	0.00586678	+	0.00586678i	−0.704167	+	0.710034i	$0.748680\pi$
$398$	−12.5315	−	12.5315i	−0.628150	−	0.628150i
$399$		0			0
$400$	4.96839	+	0.561334i	0.248420	+	0.0280667i
$401$			5.28905i			0.264123i	0.991242	+	0.132061i	$0.0421596\pi$
$401$			5.28905i			0.264123i	−0.991242	+	0.132061i	$0.957840\pi$
$402$		0			0
$403$	36.7472	−	36.7472i	1.83051	−	1.83051i
$404$	7.00584			0.348554
$405$		0			0
$406$	8.33234			0.413527
$407$	6.35646	−	6.35646i	0.315078	−	0.315078i
$408$		0			0
$409$		−	2.72187i		−	0.134588i	−0.997733	−	0.0672938i	$-0.978564\pi$
$409$		−	2.72187i		−	0.134588i	0.997733	−	0.0672938i	$-0.0214365\pi$
$410$	−17.6602	+	15.7773i	−0.872175	+	0.779185i
$411$		0			0
$412$	−0.839077	−	0.839077i	−0.0413384	−	0.0413384i
$413$	−0.770735	−	0.770735i	−0.0379254	−	0.0379254i
$414$		0			0
$415$	−3.50541	+	3.13167i	−0.172074	+	0.153727i
$416$			5.22990i			0.256417i
$417$		0			0
$418$	3.47028	−	3.47028i	0.169737	−	0.169737i
$419$	7.78582			0.380362			0.190181	−	0.981749i	$-0.439092\pi$
$419$	7.78582			0.380362			0.190181	+	0.981749i	$0.439092\pi$
$420$		0			0
$421$	31.1608			1.51868			0.759341	−	0.650693i	$-0.225521\pi$
$421$	31.1608			1.51868			0.759341	+	0.650693i	$0.225521\pi$
$422$	−16.4647	+	16.4647i	−0.801491	+	0.801491i
$423$		0			0
$424$		−	12.9163i		−	0.627269i
$425$	4.22932	−	3.37067i	0.205152	−	0.163501i
$426$		0			0
$427$	−6.41409	−	6.41409i	−0.310400	−	0.310400i
$428$	7.70564	+	7.70564i	0.372466	+	0.372466i
$429$		0			0
$430$	9.37203	+	0.527752i	0.451959	+	0.0254504i
$431$		−	12.6391i		−	0.608805i	−0.952544	−	0.304402i	$-0.901543\pi$
$431$		−	12.6391i		−	0.608805i	0.952544	−	0.304402i	$-0.0984567\pi$
$432$		0			0
$433$	18.3279	−	18.3279i	0.880782	−	0.880782i	−0.112833	−	0.993614i	$-0.535992\pi$
$433$	18.3279	−	18.3279i	0.880782	−	0.880782i	0.993614	+	0.112833i	$0.0359923\pi$
$434$	49.3140			2.36715
$435$		0			0
$436$	2.31665			0.110947
$437$	4.53730	−	4.53730i	0.217048	−	0.217048i
$438$		0			0
$439$			29.6398i			1.41463i	0.706899	+	0.707315i	$0.250094\pi$
$439$			29.6398i			1.41463i	−0.706899	+	0.707315i	$0.749906\pi$
$440$	1.13941	+	1.27539i	0.0543190	+	0.0608016i
$441$		0			0
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	6.92423	+	6.92423i	0.328980	+	0.328980i	0.852199	−	0.523218i	$-0.175269\pi$
$443$	6.92423	+	6.92423i	0.328980	+	0.328980i	−0.523218	+	0.852199i	$0.675269\pi$
$444$		0			0
$445$	0.227819	−	4.04570i	0.0107997	−	0.191785i
$446$			8.92701i			0.422706i
$447$		0			0
$448$	−3.50921	+	3.50921i	−0.165795	+	0.165795i
$449$	−15.6141			−0.736877			−0.368438	−	0.929652i	$-0.620107\pi$
$449$	−15.6141			−0.736877			−0.368438	+	0.929652i	$0.620107\pi$
$450$		0			0
$451$	−8.10006			−0.381417
$452$	−4.85580	+	4.85580i	−0.228398	+	0.228398i
$453$		0			0
$454$		−	21.9535i		−	1.03033i
$455$	−3.26295	+	57.9449i	−0.152970	+	2.71650i
$456$		0			0
$457$	23.0821	+	23.0821i	1.07974	+	1.07974i	0.996533	+	0.0832035i	$0.0265151\pi$
$457$	23.0821	+	23.0821i	1.07974	+	1.07974i	0.0832035	+	0.996533i	$0.473485\pi$
$458$	−18.8571	−	18.8571i	−0.881137	−	0.881137i
$459$		0			0
$460$	1.48974	+	1.66753i	0.0694596	+	0.0777491i
$461$		−	21.5655i		−	1.00441i	−0.864750	−	0.502203i	$-0.832523\pi$
$461$		−	21.5655i		−	1.00441i	0.864750	−	0.502203i	$-0.167477\pi$
$462$		0			0
$463$	11.0503	−	11.0503i	0.513552	−	0.513552i	−0.402061	−	0.915613i	$-0.631706\pi$
$463$	11.0503	−	11.0503i	0.513552	−	0.513552i	0.915613	+	0.402061i	$0.131706\pi$
$464$	1.67897			0.0779442
$465$		0			0
$466$	−20.2484			−0.937991
$467$	−3.79664	+	3.79664i	−0.175687	+	0.175687i	−0.789473	−	0.613785i	$-0.789646\pi$
$467$	−3.79664	+	3.79664i	−0.175687	+	0.175687i	0.613785	+	0.789473i	$0.289646\pi$
$468$		0			0
$469$			37.7949i			1.74520i
$470$	8.04468	+	0.453007i	0.371073	+	0.0208957i
$471$		0			0
$472$	−0.155303	−	0.155303i	−0.00714841	−	0.00714841i
$473$	2.27032	+	2.27032i	0.104390	+	0.104390i
$474$		0			0
$475$	3.60191	−	31.8807i	0.165267	−	1.46279i
$476$			5.36792i			0.246038i
$477$		0			0
$478$	−5.74957	+	5.74957i	−0.262979	+	0.262979i
$479$	−30.3683			−1.38756			−0.693781	−	0.720186i	$-0.744056\pi$
$479$	−30.3683			−1.38756			−0.693781	+	0.720186i	$0.744056\pi$
$480$		0			0
$481$	61.4690			2.80275
$482$	1.10991	−	1.10991i	0.0505552	−	0.0505552i
$483$		0			0
$484$		−	10.4150i		−	0.473410i
$485$	20.1450	−	17.9972i	0.914739	−	0.817210i
$486$		0			0
$487$	−18.5717	−	18.5717i	−0.841562	−	0.841562i	0.147500	−	0.989062i	$-0.452877\pi$
$487$	−18.5717	−	18.5717i	−0.841562	−	0.841562i	−0.989062	+	0.147500i	$0.952877\pi$
$488$	−1.29244	−	1.29244i	−0.0585061	−	0.0585061i
$489$		0			0
$490$	−29.3971	+	26.2628i	−1.32803	+	1.18643i
$491$			44.0696i			1.98883i	0.105520	+	0.994417i	$0.466349\pi$
$491$			44.0696i			1.98883i	−0.105520	+	0.994417i	$0.533651\pi$
$492$		0			0
$493$	1.28413	−	1.28413i	0.0578344	−	0.0578344i
$494$	33.5587			1.50988
$495$		0			0
$496$	9.93678			0.446175
$497$	21.5509	−	21.5509i	0.966690	−	0.966690i
$498$		0			0
$499$		−	8.79482i		−	0.393710i	−0.980433	−	0.196855i	$-0.936927\pi$
$499$		−	8.79482i		−	0.393710i	0.980433	−	0.196855i	$-0.0630728\pi$
$500$	11.0215	+	1.87781i	0.492897	+	0.0839780i
$501$		0			0
$502$	16.9554	+	16.9554i	0.756758	+	0.756758i
$503$	9.97229	+	9.97229i	0.444643	+	0.444643i	0.893569	−	0.448926i	$-0.148193\pi$
$503$	9.97229	+	9.97229i	0.444643	+	0.444643i	−0.448926	+	0.893569i	$0.648193\pi$
$504$		0			0
$505$	15.6408	+	0.880752i	0.696004	+	0.0391930i
$506$			0.764834i			0.0340010i
$507$		0			0
$508$	4.65707	−	4.65707i	0.206624	−	0.206624i
$509$	12.7606			0.565603			0.282801	−	0.959178i	$-0.408736\pi$
$509$	12.7606			0.565603			0.282801	+	0.959178i	$0.408736\pi$
$510$		0			0
$511$	−9.59031			−0.424250
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			17.7813i			0.784300i
$515$	−1.76778	−	1.97875i	−0.0778977	−	0.0871942i
$516$		0			0
$517$	1.94878	+	1.94878i	0.0857073	+	0.0857073i
$518$	41.2451	+	41.2451i	1.81221	+	1.81221i
$519$		0			0
$520$	−0.657486	+	11.6759i	−0.0288327	+	0.512022i
$521$			5.51996i			0.241834i	0.992663	+	0.120917i	$0.0385834\pi$
$521$			5.51996i			0.241834i	−0.992663	+	0.120917i	$0.961417\pi$
$522$		0			0
$523$	28.0942	−	28.0942i	1.22847	−	1.22847i	0.263930	−	0.964542i	$-0.414981\pi$
$523$	28.0942	−	28.0942i	1.22847	−	1.22847i	0.964542	−	0.263930i	$-0.0850188\pi$
$524$	−10.2612			−0.448264
$525$		0			0
$526$	−8.59278			−0.374663
$527$	7.59998	−	7.59998i	0.331060	−	0.331060i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	1.62379	−	28.8360i	0.0705331	−	1.25255i
$531$		0			0
$532$	22.5176	+	22.5176i	0.976260	+	0.976260i
$533$	−39.1651	−	39.1651i	−1.69643	−	1.69643i
$534$		0			0
$535$	16.2344	+	18.1718i	0.701873	+	0.785636i
$536$			7.61567i			0.328947i
$537$		0			0
$538$	−11.6236	+	11.6236i	−0.501127	+	0.501127i
$539$	−13.4833			−0.580768
$540$		0			0
$541$	−27.4184			−1.17881			−0.589405	−	0.807837i	$-0.700638\pi$
$541$	−27.4184			−1.17881			−0.589405	+	0.807837i	$0.700638\pi$
$542$	−1.35678	+	1.35678i	−0.0582789	+	0.0582789i
$543$		0			0
$544$			1.08164i			0.0463748i
$545$	5.17199	+	0.291242i	0.221544	+	0.0124754i
$546$		0			0
$547$	9.37400	+	9.37400i	0.400803	+	0.400803i	0.878516	−	0.477713i	$-0.158534\pi$
$547$	9.37400	+	9.37400i	0.400803	+	0.400803i	−0.477713	+	0.878516i	$0.658534\pi$
$548$	11.2038	+	11.2038i	0.478602	+	0.478602i
$549$		0			0
$550$	2.38342	+	2.99058i	0.101629	+	0.127519i
$551$		−	10.7734i		−	0.458964i
$552$		0			0
$553$	16.3629	−	16.3629i	0.695820	−	0.695820i
$554$	16.1926			0.687956
$555$		0			0
$556$	11.6073			0.492261
$557$	16.9474	−	16.9474i	0.718085	−	0.718085i	−0.250128	−	0.968213i	$-0.580473\pi$
$557$	16.9474	−	16.9474i	0.718085	−	0.718085i	0.968213	+	0.250128i	$0.0804726\pi$
$558$		0			0
$559$			21.9548i			0.928588i
$560$	−8.27559	+	7.39325i	−0.349707	+	0.312422i
$561$		0			0
$562$	−8.48528	−	8.48528i	−0.357930	−	0.357930i
$563$	−18.3096	−	18.3096i	−0.771657	−	0.771657i	0.206739	−	0.978396i	$-0.433715\pi$
$563$	−18.3096	−	18.3096i	−0.771657	−	0.771657i	−0.978396	+	0.206739i	$0.933715\pi$
$564$		0			0
$565$	−11.4512	+	10.2303i	−0.481755	+	0.430391i
$566$			3.31003i			0.139131i
$567$		0			0
$568$	4.34251	−	4.34251i	0.182208	−	0.182208i
$569$	−21.2498			−0.890837			−0.445419	−	0.895322i	$-0.646945\pi$
$569$	−21.2498			−0.890837			−0.445419	+	0.895322i	$0.646945\pi$
$570$		0			0
$571$	−10.4347			−0.436679			−0.218339	−	0.975873i	$-0.570064\pi$
$571$	−10.4347			−0.436679			−0.218339	+	0.975873i	$0.570064\pi$
$572$	−2.82843	+	2.82843i	−0.118262	+	0.118262i
$573$		0			0
$574$		−	52.5588i		−	2.19376i
$575$	3.11626	+	3.91011i	0.129957	+	0.163063i
$576$		0			0
$577$	−2.81127	−	2.81127i	−0.117035	−	0.117035i	0.646164	−	0.763199i	$-0.276372\pi$
$577$	−2.81127	−	2.81127i	−0.117035	−	0.117035i	−0.763199	+	0.646164i	$0.776372\pi$
$578$	−11.1935	−	11.1935i	−0.465590	−	0.465590i
$579$		0			0
$580$	3.74835	+	0.211075i	0.155642	+	0.00876440i
$581$		−	10.4325i		−	0.432813i
$582$		0			0
$583$	6.98536	−	6.98536i	0.289304	−	0.289304i
$584$	−1.93245			−0.0799653
$585$		0			0
$586$	−19.8599			−0.820406
$587$	−14.3854	+	14.3854i	−0.593751	+	0.593751i	−0.938643	−	0.344892i	$-0.887916\pi$
$587$	−14.3854	+	14.3854i	−0.593751	+	0.593751i	0.344892	+	0.938643i	$0.387916\pi$
$588$		0			0
$589$		−	63.7614i		−	2.62724i
$590$	−0.327195	−	0.366244i	−0.0134704	−	0.0150780i
$591$		0			0
$592$	8.31090	+	8.31090i	0.341576	+	0.341576i
$593$	14.6106	+	14.6106i	0.599984	+	0.599984i	0.940308	−	0.340324i	$-0.110537\pi$
$593$	14.6106	+	14.6106i	0.599984	+	0.599984i	−0.340324	+	0.940308i	$0.610537\pi$
$594$		0			0
$595$	−0.674839	+	11.9841i	−0.0276657	+	0.491298i
$596$			12.9190i			0.529181i
$597$		0			0
$598$	−3.69809	+	3.69809i	−0.151226	+	0.151226i
$599$	−40.2853			−1.64601			−0.823007	−	0.568031i	$-0.807705\pi$
$599$	−40.2853			−1.64601			−0.823007	+	0.568031i	$0.807705\pi$
$600$		0			0
$601$	−2.38537			−0.0973013			−0.0486507	−	0.998816i	$-0.515492\pi$
$601$	−2.38537			−0.0973013			−0.0486507	+	0.998816i	$0.515492\pi$
$602$	−14.7314	+	14.7314i	−0.600409	+	0.600409i
$603$		0			0
$604$		−	7.01447i		−	0.285415i
$605$	1.30935	−	23.2519i	0.0532324	−	0.945323i
$606$		0			0
$607$	−24.5540	−	24.5540i	−0.996614	−	0.996614i	0.00338019	−	0.999994i	$-0.498924\pi$
$607$	−24.5540	−	24.5540i	−0.996614	−	0.996614i	−0.999994	+	0.00338019i	$0.998924\pi$
$608$	4.53730	+	4.53730i	0.184012	+	0.184012i
$609$		0			0
$610$	−2.72294	−	3.04790i	−0.110248	−	0.123406i
$611$			18.8454i			0.762401i
$612$		0			0
$613$	15.5537	−	15.5537i	0.628209	−	0.628209i	−0.319408	−	0.947617i	$-0.603484\pi$
$613$	15.5537	−	15.5537i	0.628209	−	0.628209i	0.947617	+	0.319408i	$0.103484\pi$
$614$	−7.45848			−0.301000
$615$		0			0
$616$	−3.79569			−0.152933
$617$	6.57856	−	6.57856i	0.264843	−	0.264843i	−0.562175	−	0.827018i	$-0.690035\pi$
$617$	6.57856	−	6.57856i	0.264843	−	0.264843i	0.827018	+	0.562175i	$0.190035\pi$
$618$		0			0
$619$		−	15.3899i		−	0.618572i	−0.950969	−	0.309286i	$-0.899910\pi$
$619$		−	15.3899i		−	0.618572i	0.950969	−	0.309286i	$-0.100090\pi$
$620$	22.1842	+	1.24922i	0.890938	+	0.0501699i
$621$		0			0
$622$	−22.3347	−	22.3347i	−0.895542	−	0.895542i
$623$	6.35925	+	6.35925i	0.254778	+	0.254778i
$624$		0			0
$625$	24.3698	+	5.57785i	0.974792	+	0.223114i
$626$		−	4.00453i		−	0.160053i
$627$		0			0
$628$	4.68533	−	4.68533i	0.186965	−	0.186965i
$629$	12.7129			0.506897
$630$		0			0
$631$	31.5331			1.25531			0.627656	−	0.778491i	$-0.284014\pi$
$631$	31.5331			1.25531			0.627656	+	0.778491i	$0.284014\pi$
$632$	3.29712	−	3.29712i	0.131153	−	0.131153i
$633$		0			0
$634$		−	14.9923i		−	0.595420i
$635$	10.9825	−	9.81157i	0.435828	−	0.389360i
$636$		0			0
$637$	−65.1941	−	65.1941i	−2.58308	−	2.58308i
$638$	0.908018	+	0.908018i	0.0359488	+	0.0359488i
$639$		0			0
$640$	−1.66753	+	1.48974i	−0.0659150	+	0.0588872i
$641$		−	37.5286i		−	1.48229i	−0.671345	−	0.741145i	$-0.734283\pi$
$641$		−	37.5286i		−	1.48229i	0.671345	−	0.741145i	$-0.265717\pi$
$642$		0			0
$643$	−25.9099	+	25.9099i	−1.02179	+	1.02179i	−0.0220314	+	0.999757i	$0.507013\pi$
$643$	−25.9099	+	25.9099i	−1.02179	+	1.02179i	−0.999757	+	0.0220314i	$0.992987\pi$
$644$	−4.96277			−0.195561
$645$		0			0
$646$	6.94055			0.273072
$647$	21.8642	−	21.8642i	0.859570	−	0.859570i	−0.131718	−	0.991287i	$-0.542049\pi$
$647$	21.8642	−	21.8642i	0.859570	−	0.859570i	0.991287	+	0.131718i	$0.0420492\pi$
$648$		0			0
$649$		−	0.167982i		−	0.00659387i
$650$	−2.93572	+	25.9842i	−0.115148	+	1.01918i
$651$		0			0
$652$	−2.89617	−	2.89617i	−0.113423	−	0.113423i
$653$	−27.6181	−	27.6181i	−1.08078	−	1.08078i	−0.996437	−	0.0843434i	$-0.973121\pi$
$653$	−27.6181	−	27.6181i	−1.08078	−	1.08078i	−0.0843434	−	0.996437i	$-0.526879\pi$
$654$		0			0
$655$	−22.9085	−	1.29001i	−0.895109	−	0.0504048i
$656$		−	10.5906i		−	0.413494i
$657$		0			0
$658$	−12.6450	+	12.6450i	−0.492955	+	0.492955i
$659$	−36.9228			−1.43831			−0.719154	−	0.694850i	$-0.755471\pi$
$659$	−36.9228			−1.43831			−0.719154	+	0.694850i	$0.755471\pi$
$660$		0			0
$661$	15.6368			0.608200			0.304100	−	0.952640i	$-0.401644\pi$
$661$	15.6368			0.608200			0.304100	+	0.952640i	$0.401644\pi$
$662$	−5.52366	+	5.52366i	−0.214683	+	0.214683i
$663$		0			0
$664$		−	2.10215i		−	0.0815793i
$665$	47.4403	+	53.1020i	1.83966	+	2.05921i
$666$		0			0
$667$	1.18721	+	1.18721i	0.0459690	+	0.0459690i
$668$	1.29908	+	1.29908i	0.0502630	+	0.0502630i
$669$		0			0
$670$	−0.957419	+	17.0022i	−0.0369883	+	0.656853i
$671$		−	1.39795i		−	0.0539674i
$672$		0			0
$673$	−13.1080	+	13.1080i	−0.505277	+	0.505277i	−0.913073	−	0.407796i	$-0.866298\pi$
$673$	−13.1080	+	13.1080i	−0.505277	+	0.505277i	0.407796	+	0.913073i	$0.366298\pi$
$674$	21.4199			0.825065
$675$		0			0
$676$	−14.3518			−0.551993
$677$	26.1392	−	26.1392i	1.00461	−	1.00461i	0.00462136	−	0.999989i	$-0.498529\pi$
$677$	26.1392	−	26.1392i	1.00461	−	1.00461i	0.999989	−	0.00462136i	$-0.00147103\pi$
$678$		0			0
$679$			59.9539i			2.30082i
$680$	−0.135980	+	2.41479i	−0.00521460	+	0.0926030i
$681$		0			0
$682$	5.37400	+	5.37400i	0.205781	+	0.205781i
$683$	−17.3964	−	17.3964i	−0.665656	−	0.665656i	0.291051	−	0.956707i	$-0.405995\pi$
$683$	−17.3964	−	17.3964i	−0.665656	−	0.665656i	−0.956707	+	0.291051i	$0.905995\pi$
$684$		0			0
$685$	23.6043	+	26.4213i	0.901873	+	1.00951i
$686$		−	52.7498i		−	2.01400i
$687$		0			0
$688$	−2.96839	+	2.96839i	−0.113169	+	0.113169i
$689$	67.5507			2.57348
$690$		0			0
$691$	35.7736			1.36089			0.680447	−	0.732798i	$-0.261786\pi$
$691$	35.7736			1.36089			0.680447	+	0.732798i	$0.261786\pi$
$692$	−15.3651	+	15.3651i	−0.584095	+	0.584095i
$693$		0			0
$694$		−	35.8920i		−	1.36244i
$695$	25.9137	+	1.45924i	0.982964	+	0.0553521i
$696$		0			0
$697$	−8.10006	−	8.10006i	−0.306812	−	0.306812i
$698$	−16.9053	−	16.9053i	−0.639876	−	0.639876i
$699$		0			0
$700$	−19.4050	+	15.4653i	−0.733439	+	0.584533i
$701$		−	13.9819i		−	0.528088i	−0.964511	−	0.264044i	$-0.914944\pi$
$701$		−	13.9819i		−	0.528088i	0.964511	−	0.264044i	$-0.0850565\pi$
$702$		0			0
$703$	53.3286	−	53.3286i	2.01133	−	2.01133i
$704$	−0.764834			−0.0288258
$705$		0			0
$706$	−23.1548			−0.871442
$707$	−24.5850	+	24.5850i	−0.924612	+	0.924612i
$708$		0			0
$709$		−	28.3566i		−	1.06495i	−0.846444	−	0.532477i	$-0.821261\pi$
$709$		−	28.3566i		−	1.06495i	0.846444	−	0.532477i	$-0.178739\pi$
$710$	10.2407	−	9.14887i	0.384328	−	0.343351i
$711$		0			0
$712$	1.28139	+	1.28139i	0.0480221	+	0.0480221i
$713$	7.02637	+	7.02637i	0.263139	+	0.263139i
$714$		0			0
$715$	−6.67013	+	5.95897i	−0.249449	+	0.222853i
$716$			5.04921i			0.188698i
$717$		0			0
$718$	−20.7030	+	20.7030i	−0.772630	+	0.772630i
$719$	2.41743			0.0901550			0.0450775	−	0.998983i	$-0.485647\pi$
$719$	2.41743			0.0901550			0.0450775	+	0.998983i	$0.485647\pi$
$720$		0			0
$721$	5.88899			0.219318
$722$	15.6795	−	15.6795i	0.583529	−	0.583529i
$723$		0			0
$724$		−	3.31623i		−	0.123247i
$725$	8.34177	+	0.942462i	0.309806	+	0.0350022i
$726$		0			0
$727$	−24.9673	−	24.9673i	−0.925987	−	0.925987i	0.0714570	−	0.997444i	$-0.477235\pi$
$727$	−24.9673	−	24.9673i	−0.925987	−	0.925987i	−0.997444	+	0.0714570i	$0.977235\pi$
$728$	−18.3528	−	18.3528i	−0.680200	−	0.680200i
$729$		0			0
$730$	−4.31425	−	0.242942i	−0.159678	−	0.00899167i
$731$			4.54065i			0.167942i
$732$		0			0
$733$	21.9350	−	21.9350i	0.810187	−	0.810187i	−0.174475	−	0.984662i	$-0.555823\pi$
$733$	21.9350	−	21.9350i	0.810187	−	0.810187i	0.984662	+	0.174475i	$0.0558227\pi$
$734$	8.29407			0.306140
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−4.11870	+	4.11870i	−0.151714	+	0.151714i
$738$		0			0
$739$		−	14.1633i		−	0.521005i	−0.965473	−	0.260502i	$-0.916112\pi$
$739$		−	14.1633i		−	0.521005i	0.965473	−	0.260502i	$-0.0838881\pi$
$740$	17.5095	+	19.5992i	0.643663	+	0.720480i
$741$		0			0
$742$	45.3259	+	45.3259i	1.66397	+	1.66397i
$743$	30.7853	+	30.7853i	1.12940	+	1.12940i	0.990274	+	0.139130i	$0.0444306\pi$
$743$	30.7853	+	30.7853i	1.12940	+	1.12940i	0.139130	+	0.990274i	$0.455569\pi$
$744$		0			0
$745$	−1.62413	+	28.8420i	−0.0595036	+	1.05669i
$746$		−	22.7427i		−	0.832669i
$747$		0			0
$748$	−0.584970	+	0.584970i	−0.0213886	+	0.0213886i
$749$	−54.0814			−1.97609
$750$		0			0
$751$	−40.3869			−1.47374			−0.736869	−	0.676036i	$-0.763697\pi$
$751$	−40.3869			−1.47374			−0.736869	+	0.676036i	$0.763697\pi$
$752$	−2.54798	+	2.54798i	−0.0929153	+	0.0929153i
$753$		0			0
$754$			8.78083i			0.319779i
$755$	0.881838	−	15.6600i	0.0320934	−	0.569927i
$756$		0			0
$757$	17.1456	+	17.1456i	0.623166	+	0.623166i	0.946340	−	0.323174i	$-0.104750\pi$
$757$	17.1456	+	17.1456i	0.623166	+	0.623166i	−0.323174	+	0.946340i	$0.604750\pi$
$758$	−2.70397	−	2.70397i	−0.0982124	−	0.0982124i
$759$		0			0
$760$	9.55924	+	10.7001i	0.346750	+	0.388132i
$761$			31.1739i			1.13005i	0.825073	+	0.565026i	$0.191134\pi$
$761$			31.1739i			1.13005i	−0.825073	+	0.565026i	$0.808866\pi$
$762$		0			0
$763$	−8.12960	+	8.12960i	−0.294311	+	0.294311i
$764$	9.26011			0.335019
$765$		0			0
$766$	−5.83253			−0.210738
$767$	0.812220	−	0.812220i	0.0293276	−	0.0293276i
$768$		0			0
$769$		−	7.27059i		−	0.262184i	−0.991370	−	0.131092i	$-0.958152\pi$
$769$		−	7.27059i		−	0.262184i	0.991370	−	0.131092i	$-0.0418484\pi$
$770$	−8.47401	−	0.477183i	−0.305382	−	0.0171965i
$771$		0			0
$772$	−10.0816	−	10.0816i	−0.362846	−	0.362846i
$773$	−8.06437	−	8.06437i	−0.290055	−	0.290055i	0.547047	−	0.837102i	$-0.315752\pi$
$773$	−8.06437	−	8.06437i	−0.290055	−	0.290055i	−0.837102	+	0.547047i	$0.815752\pi$
$774$		0			0
$775$	49.3698	+	5.57785i	1.77342	+	0.200362i
$776$			12.0807i			0.433673i
$777$		0			0
$778$	−24.1809	+	24.1809i	−0.866927	+	0.866927i
$779$	−67.9568			−2.43481
$780$		0			0
$781$	4.69703			0.168073
$782$	−0.764834	+	0.764834i	−0.0273504	+	0.0273504i
$783$		0			0
$784$		−	17.6291i		−	0.629611i
$785$	11.0492	−	9.87111i	0.394361	−	0.352315i
$786$		0			0
$787$	−15.0672	−	15.0672i	−0.537087	−	0.537087i	0.385585	−	0.922672i	$-0.374000\pi$
$787$	−15.0672	−	15.0672i	−0.537087	−	0.537087i	−0.922672	+	0.385585i	$0.874000\pi$
$788$	−19.7516	−	19.7516i	−0.703623	−	0.703623i
$789$		0			0
$790$	7.77544	−	6.94643i	0.276638	−	0.247143i
$791$		−	34.0801i		−	1.21175i
$792$		0			0
$793$	6.75934	−	6.75934i	0.240031	−	0.240031i
$794$	−0.165314			−0.00586678
$795$		0			0
$796$	17.7223			0.628150
$797$	−27.0095	+	27.0095i	−0.956727	+	0.956727i	−0.999102	−	0.0423748i	$-0.986508\pi$
$797$	−27.0095	+	27.0095i	−0.956727	+	0.956727i	0.0423748	+	0.999102i	$0.486508\pi$
$798$		0			0
$799$			3.89756i			0.137886i
$800$	−3.91011	+	3.11626i	−0.138243	+	0.110176i
$801$		0			0
$802$	−3.73992	−	3.73992i	−0.132061	−	0.132061i
$803$	−1.04511	−	1.04511i	−0.0368810	−	0.0368810i
$804$		0			0
$805$	−11.0795	−	0.623904i	−0.390503	−	0.0219897i
$806$			51.9683i			1.83051i
$807$		0			0
$808$	−4.95388	+	4.95388i	−0.174277	+	0.174277i
$809$	25.4136			0.893493			0.446746	−	0.894661i	$-0.352583\pi$
$809$	25.4136			0.893493			0.446746	+	0.894661i	$0.352583\pi$
$810$		0			0
$811$	−15.7740			−0.553899			−0.276949	−	0.960885i	$-0.589323\pi$
$811$	−15.7740			−0.553899			−0.276949	+	0.960885i	$0.589323\pi$
$812$	−5.89185	+	5.89185i	−0.206764	+	0.206764i
$813$		0			0
$814$			8.98939i			0.315078i
$815$	−6.10170	−	6.82989i	−0.213733	−	0.239241i
$816$		0			0
$817$	19.0473	+	19.0473i	0.666380	+	0.666380i
$818$	1.92465	+	1.92465i	0.0672938	+	0.0672938i
$819$		0			0
$820$	1.33142	−	23.6439i	0.0464952	−	0.825680i
$821$		−	23.8083i		−	0.830914i	−0.909613	−	0.415457i	$-0.863622\pi$
$821$		−	23.8083i		−	0.830914i	0.909613	−	0.415457i	$-0.136378\pi$
$822$		0			0
$823$	6.89778	−	6.89778i	0.240441	−	0.240441i	−0.576591	−	0.817033i	$-0.695617\pi$
$823$	6.89778	−	6.89778i	0.240441	−	0.240441i	0.817033	+	0.576591i	$0.195617\pi$
$824$	1.18663			0.0413384
$825$		0			0
$826$	1.08998			0.0379254
$827$	14.3996	−	14.3996i	0.500724	−	0.500724i	−0.410939	−	0.911663i	$-0.634799\pi$
$827$	14.3996	−	14.3996i	0.500724	−	0.500724i	0.911663	+	0.410939i	$0.134799\pi$
$828$		0			0
$829$			34.6696i			1.20412i	0.798449	+	0.602062i	$0.205654\pi$
$829$			34.6696i			1.20412i	−0.798449	+	0.602062i	$0.794346\pi$
$830$	0.264276	−	4.69312i	0.00917316	−	0.162901i
$831$		0			0
$832$	−3.69809	−	3.69809i	−0.128208	−	0.128208i
$833$	−13.4833	−	13.4833i	−0.467170	−	0.467170i
$834$		0			0
$835$	2.73692	+	3.06356i	0.0947152	+	0.106019i
$836$			4.90771i			0.169737i
$837$		0			0
$838$	−5.50541	+	5.50541i	−0.190181	+	0.190181i
$839$	−15.3817			−0.531035			−0.265517	−	0.964106i	$-0.585543\pi$
$839$	−15.3817			−0.531035			−0.265517	+	0.964106i	$0.585543\pi$
$840$		0			0
$841$	−26.1811			−0.902795
$842$	−22.0340	+	22.0340i	−0.759341	+	0.759341i
$843$		0			0
$844$		−	23.2846i		−	0.801491i
$845$	−32.0409	−	1.80426i	−1.10224	−	0.0620686i
$846$		0			0
$847$	36.5485	+	36.5485i	1.25582	+	1.25582i
$848$	9.13318	+	9.13318i	0.313635	+	0.313635i
$849$		0			0
$850$	−0.607160	+	5.37400i	−0.0208254	+	0.184327i
$851$			11.7534i			0.402901i
$852$		0			0
$853$	−24.5725	+	24.5725i	−0.841348	+	0.841348i	−0.989034	−	0.147687i	$-0.952817\pi$
$853$	−24.5725	+	24.5725i	−0.841348	+	0.841348i	0.147687	+	0.989034i	$0.452817\pi$
$854$	9.07090			0.310400
$855$		0			0
$856$	−10.8974			−0.372466
$857$	1.01111	−	1.01111i	0.0345388	−	0.0345388i	−0.689626	−	0.724165i	$-0.742225\pi$
$857$	1.01111	−	1.01111i	0.0345388	−	0.0345388i	0.724165	+	0.689626i	$0.242225\pi$
$858$		0			0
$859$		−	23.4672i		−	0.800691i	−0.916364	−	0.400346i	$-0.868890\pi$
$859$		−	23.4672i		−	0.800691i	0.916364	−	0.400346i	$-0.131110\pi$
$860$	−7.00020	+	6.25385i	−0.238705	+	0.213254i
$861$		0			0
$862$	8.93720	+	8.93720i	0.304402	+	0.304402i
$863$	16.8159	+	16.8159i	0.572421	+	0.572421i	0.932804	−	0.360383i	$-0.117354\pi$
$863$	16.8159	+	16.8159i	0.572421	+	0.572421i	−0.360383	+	0.932804i	$0.617354\pi$
$864$		0			0
$865$	−36.2348	+	32.3715i	−1.23202	+	1.10066i
$866$			25.9195i			0.880782i
$867$		0			0
$868$	−34.8702	+	34.8702i	−1.18357	+	1.18357i
$869$	3.56630			0.120978
$870$		0			0
$871$	−39.8292			−1.34956
$872$	−1.63812	+	1.63812i	−0.0554736	+	0.0554736i
$873$		0			0
$874$			6.41670i			0.217048i
$875$	−45.2664	+	32.0872i	−1.53028	+	1.08475i
$876$		0			0
$877$	11.2750	+	11.2750i	0.380731	+	0.380731i	0.871366	−	0.490634i	$-0.163235\pi$
$877$	11.2750	+	11.2750i	0.380731	+	0.380731i	−0.490634	+	0.871366i	$0.663235\pi$
$878$	−20.9585	−	20.9585i	−0.707315	−	0.707315i
$879$		0			0
$880$	−1.70751	−	0.0961525i	−0.0575603	−	0.00324130i
$881$			1.95840i			0.0659801i	0.999456	+	0.0329901i	$0.0105030\pi$
$881$			1.95840i			0.0659801i	−0.999456	+	0.0329901i	$0.989497\pi$
$882$		0			0
$883$	13.9971	−	13.9971i	0.471040	−	0.471040i	−0.431211	−	0.902251i	$-0.641914\pi$
$883$	13.9971	−	13.9971i	0.471040	−	0.471040i	0.902251	+	0.431211i	$0.141914\pi$
$884$	−5.65685			−0.190261
$885$		0			0
$886$	−9.79234			−0.328980
$887$	−19.7538	+	19.7538i	−0.663269	+	0.663269i	−0.956149	−	0.292880i	$-0.905386\pi$
$887$	−19.7538	+	19.7538i	−0.663269	+	0.663269i	0.292880	+	0.956149i	$0.405386\pi$
$888$		0			0
$889$			32.6852i			1.09623i
$890$	2.69965	+	3.02184i	0.0904925	+	0.101292i
$891$		0			0
$892$	−6.31235	−	6.31235i	−0.211353	−	0.211353i
$893$	16.3496	+	16.3496i	0.547120	+	0.547120i
$894$		0			0
$895$	−0.634771	+	11.2725i	−0.0212181	+	0.376799i
$896$		−	4.96277i		−	0.165795i
$897$		0			0
$898$	11.0409	−	11.0409i	0.368438	−	0.368438i
$899$	16.6835			0.556428
$900$		0			0
$901$	13.9707			0.465432
$902$	5.72761	−	5.72761i	0.190708	−	0.190708i
$903$		0			0
$904$		−	6.86714i		−	0.228398i
$905$	0.416906	−	7.40358i	0.0138584	−	0.246103i
$906$		0			0
$907$	6.93556	+	6.93556i	0.230291	+	0.230291i	0.812814	−	0.582523i	$-0.197934\pi$
$907$	6.93556	+	6.93556i	0.230291	+	0.230291i	−0.582523	+	0.812814i	$0.697934\pi$
$908$	15.5235	+	15.5235i	0.515165	+	0.515165i
$909$		0			0
$910$	−38.6659	−	43.2805i	−1.28176	−	1.43473i
$911$			12.0729i			0.399994i	0.979796	+	0.199997i	$0.0640933\pi$
$911$			12.0729i			0.399994i	−0.979796	+	0.199997i	$0.935907\pi$
$912$		0			0
$913$	1.13688	−	1.13688i	0.0376254	−	0.0376254i
$914$	−32.6430			−1.07974
$915$		0			0
$916$	26.6680			0.881137
$917$	36.0088	−	36.0088i	1.18911	−	1.18911i
$918$		0			0
$919$			46.3777i			1.52986i	0.644113	+	0.764930i	$0.277227\pi$
$919$			46.3777i			1.52986i	−0.644113	+	0.764930i	$0.722773\pi$
$920$	−2.23253	−	0.125717i	−0.0736044	−	0.00414476i
$921$		0			0
$922$	15.2491	+	15.2491i	0.502203	+	0.502203i
$923$	22.7109	+	22.7109i	0.747538	+	0.747538i
$924$		0			0
$925$	36.6266	+	45.9570i	1.20428	+	1.51106i
$926$			15.6275i			0.513552i
$927$		0			0
$928$	−1.18721	+	1.18721i	−0.0389721	+	0.0389721i
$929$	16.9443			0.555924			0.277962	−	0.960592i	$-0.410341\pi$
$929$	16.9443			0.555924			0.277962	+	0.960592i	$0.410341\pi$
$930$		0			0
$931$	−113.121			−3.70738
$932$	14.3178	−	14.3178i	0.468995	−	0.468995i
$933$		0			0
$934$		−	5.36926i		−	0.175687i
$935$	−1.37951	+	1.23242i	−0.0451146	+	0.0403046i
$936$		0			0
$937$	11.8835	+	11.8835i	0.388216	+	0.388216i	0.874051	−	0.485835i	$-0.161484\pi$
$937$	11.8835	+	11.8835i	0.388216	+	0.388216i	−0.485835	+	0.874051i	$0.661484\pi$
$938$	−26.7250	−	26.7250i	−0.872602	−	0.872602i
$939$		0			0
$940$	−6.00877	+	5.36812i	−0.195985	+	0.175089i
$941$		−	23.3437i		−	0.760982i	−0.924785	−	0.380491i	$-0.875755\pi$
$941$		−	23.3437i		−	0.760982i	0.924785	−	0.380491i	$-0.124245\pi$
$942$		0			0
$943$	7.48869	−	7.48869i	0.243865	−	0.243865i
$944$	0.219632			0.00714841
$945$		0			0
$946$	−3.21072			−0.104390
$947$	−36.3518	+	36.3518i	−1.18128	+	1.18128i	−0.201861	+	0.979414i	$0.564699\pi$
$947$	−36.3518	+	36.3518i	−1.18128	+	1.18128i	−0.979414	+	0.201861i	$0.935301\pi$
$948$		0			0
$949$		−	10.1065i		−	0.328071i
$950$	19.9961	+	25.0900i	0.648760	+	0.814027i
$951$		0			0
$952$	−3.79569	−	3.79569i	−0.123019	−	0.123019i
$953$	−11.3056	−	11.3056i	−0.366224	−	0.366224i	0.499874	−	0.866098i	$-0.333380\pi$
$953$	−11.3056	−	11.3056i	−0.366224	−	0.366224i	−0.866098	+	0.499874i	$0.833380\pi$
$954$		0			0
$955$	20.6735	+	1.16415i	0.668978	+	0.0376711i
$956$		−	8.13112i		−	0.262979i
$957$		0			0
$958$	21.4736	−	21.4736i	0.693781	−	0.693781i
$959$	−78.6328			−2.53919
$960$		0			0
$961$	67.7396			2.18515
$962$	−43.4652	+	43.4652i	−1.40137	+	1.40137i
$963$		0			0
$964$			1.56965i			0.0505552i
$965$	−21.2401	−	23.7750i	−0.683744	−	0.765344i
$966$		0			0
$967$	−5.50134	−	5.50134i	−0.176911	−	0.176911i	0.613097	−	0.790008i	$-0.289924\pi$
$967$	−5.50134	−	5.50134i	−0.176911	−	0.176911i	−0.790008	+	0.613097i	$0.789924\pi$
$968$	7.36454	+	7.36454i	0.236705	+	0.236705i
$969$		0			0
$970$	−1.51875	+	26.9706i	−0.0487642	+	0.865974i
$971$		−	55.1034i		−	1.76835i	−0.467154	−	0.884176i	$-0.654721\pi$
$971$		−	55.1034i		−	1.76835i	0.467154	−	0.884176i	$-0.345279\pi$
$972$		0			0
$973$	−40.7326	+	40.7326i	−1.30583	+	1.30583i
$974$	26.2643			0.841562
$975$		0			0
$976$	1.82779			0.0585061
$977$	−24.2198	+	24.2198i	−0.774861	+	0.774861i	−0.978952	−	0.204091i	$-0.934576\pi$
$977$	−24.2198	+	24.2198i	−0.774861	+	0.774861i	0.204091	+	0.978952i	$0.434576\pi$
$978$		0			0
$979$			1.38600i			0.0442968i
$980$	2.21628	−	39.3575i	0.0707963	−	1.25723i
$981$		0			0
$982$	−31.1619	−	31.1619i	−0.994417	−	0.994417i
$983$	11.9012	+	11.9012i	0.379591	+	0.379591i	0.870954	−	0.491364i	$-0.163501\pi$
$983$	11.9012	+	11.9012i	0.379591	+	0.379591i	−0.491364	+	0.870954i	$0.663501\pi$
$984$		0			0
$985$	−41.6130	−	46.5793i	−1.32590	−	1.48414i
$986$			1.81604i			0.0578344i
$987$		0			0
$988$	−23.7296	+	23.7296i	−0.754939	+	0.754939i
$989$	−4.19794			−0.133487
$990$		0			0
$991$	16.7779			0.532969			0.266484	−	0.963839i	$-0.414138\pi$
$991$	16.7779			0.532969			0.266484	+	0.963839i	$0.414138\pi$
$992$	−7.02637	+	7.02637i	−0.223087	+	0.223087i
$993$		0			0
$994$			30.4776i			0.966690i
$995$	39.5656	+	2.22799i	1.25431	+	0.0706321i
$996$		0			0
$997$	−10.1977	−	10.1977i	−0.322963	−	0.322963i	0.526940	−	0.849903i	$-0.323339\pi$
$997$	−10.1977	−	10.1977i	−0.322963	−	0.322963i	−0.849903	+	0.526940i	$0.823339\pi$
$998$	6.21888	+	6.21888i	0.196855	+	0.196855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.j.737.4	yes	20
3.2	odd	2	inner	2070.2.j.j.737.7	yes	20
5.3	odd	4	inner	2070.2.j.j.323.7	yes	20
15.8	even	4	inner	2070.2.j.j.323.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.j.323.4	✓	20	15.8	even	4	inner
2070.2.j.j.323.7	yes	20	5.3	odd	4	inner
2070.2.j.j.737.4	yes	20	1.1	even	1	trivial
2070.2.j.j.737.7	yes	20	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.125717 - 2.23253i) q^{5} +(3.50921 + 3.50921i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.125717 - 2.23253i) q^{5} +(3.50921 + 3.50921i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.48974 + 1.66753i) q^{10} +0.764834i q^{11} +(-3.69809 + 3.69809i) q^{13} -4.96277 q^{14} -1.00000 q^{16} +(-0.764834 + 0.764834i) q^{17} +6.41670i q^{19} +(-2.23253 - 0.125717i) q^{20} +(-0.540819 - 0.540819i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-4.96839 - 0.561334i) q^{25} -5.22990i q^{26} +(3.50921 - 3.50921i) q^{28} -1.67897 q^{29} -9.93678 q^{31} +(0.707107 - 0.707107i) q^{32} -1.08164i q^{34} +(8.27559 - 7.39325i) q^{35} +(-8.31090 - 8.31090i) q^{37} +(-4.53730 - 4.53730i) q^{38} +(1.66753 - 1.48974i) q^{40} +10.5906i q^{41} +(2.96839 - 2.96839i) q^{43} +0.764834 q^{44} +1.00000 q^{46} +(2.54798 - 2.54798i) q^{47} +17.6291i q^{49} +(3.91011 - 3.11626i) q^{50} +(3.69809 + 3.69809i) q^{52} +(-9.13318 - 9.13318i) q^{53} +(1.70751 + 0.0961525i) q^{55} +4.96277i q^{56} +(1.18721 - 1.18721i) q^{58} -0.219632 q^{59} -1.82779 q^{61} +(7.02637 - 7.02637i) q^{62} +1.00000i q^{64} +(7.79120 + 8.72102i) q^{65} +(5.38509 + 5.38509i) q^{67} +(0.764834 + 0.764834i) q^{68} +(-0.623904 + 11.0795i) q^{70} -6.14124i q^{71} +(-1.36645 + 1.36645i) q^{73} +11.7534 q^{74} +6.41670 q^{76} +(-2.68396 + 2.68396i) q^{77} -4.66284i q^{79} +(-0.125717 + 2.23253i) q^{80} +(-7.48869 - 7.48869i) q^{82} +(-1.48645 - 1.48645i) q^{83} +(1.61136 + 1.80367i) q^{85} +4.19794i q^{86} +(-0.540819 + 0.540819i) q^{88} +1.81216 q^{89} -25.9548 q^{91} +(-0.707107 + 0.707107i) q^{92} +3.60339i q^{94} +(14.3255 + 0.806688i) q^{95} +(8.54237 + 8.54237i) q^{97} +(-12.4657 - 12.4657i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 16 q^{7}+O(q^{10}) \) 20 * q - 16 * q^7	\( 20 q - 16 q^{7} + 12 q^{10} - 12 q^{13} - 20 q^{16} - 24 q^{25} - 16 q^{28} - 48 q^{31} - 60 q^{37} - 16 q^{43} + 20 q^{46} + 12 q^{52} - 32 q^{55} + 4 q^{58} + 104 q^{61} - 56 q^{67} - 8 q^{70} - 20 q^{73} + 40 q^{76} - 28 q^{82} - 40 q^{85} - 32 q^{91} - 44 q^{97}+O(q^{100}) \) 20 * q - 16 * q^7 + 12 * q^10 - 12 * q^13 - 20 * q^16 - 24 * q^25 - 16 * q^28 - 48 * q^31 - 60 * q^37 - 16 * q^43 + 20 * q^46 + 12 * q^52 - 32 * q^55 + 4 * q^58 + 104 * q^61 - 56 * q^67 - 8 * q^70 - 20 * q^73 + 40 * q^76 - 28 * q^82 - 40 * q^85 - 32 * q^91 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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