LMFDB - Embedded newform 1400.2.bh.j.849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(249,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("1400.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.bh (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:	$11.1790562830$
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} - 15x^{14} + 170x^{12} - 789x^{10} + 2754x^{8} - 960x^{6} + 269x^{4} - 18x^{2} + 1 $ x^16 - 15x^14 + 170x^12 - 789x^10 + 2754x^8 - 960x^6 + 269x^4 - 18*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.2
Root			$-2.63854 + 1.52336i$ of defining polynomial
Character	$\chi$	$=$	1400.849
Dual form			1400.2.bh.j.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77252 + 1.02336i) q^{3} +(-1.48827 - 2.18747i) q^{7} +(0.594550 - 1.02979i) q^{9} +O(q^{10})$	$q+(-1.77252 + 1.02336i) q^{3} +(-1.48827 - 2.18747i) q^{7} +(0.594550 - 1.02979i) q^{9} +(1.78203 + 3.08656i) q^{11} -2.90761i q^{13} +(3.22032 - 1.85925i) q^{17} +(-1.78969 + 3.09984i) q^{19} +(4.87658 + 2.35430i) q^{21} +(-2.69230 - 1.55440i) q^{23} -3.70642i q^{27} -1.57939 q^{29} +(0.382085 + 0.661791i) q^{31} +(-6.31735 - 3.64732i) q^{33} +(6.06310 + 3.50053i) q^{37} +(2.97554 + 5.15379i) q^{39} +7.07812 q^{41} +10.9390i q^{43} +(6.38782 + 3.68801i) q^{47} +(-2.57009 + 6.51111i) q^{49} +(-3.80539 + 6.59113i) q^{51} +(-2.88232 + 1.66411i) q^{53} -7.32604i q^{57} +(4.07009 + 7.04961i) q^{59} +(2.96897 - 5.14240i) q^{61} +(-3.13749 + 0.232045i) q^{63} +(-12.1262 + 7.00107i) q^{67} +6.36286 q^{69} -14.5305 q^{71} +(-11.4502 + 6.61078i) q^{73} +(4.09963 - 8.49177i) q^{77} +(1.49233 - 2.58479i) q^{79} +(5.57667 + 9.65908i) q^{81} +10.8923i q^{83} +(2.79950 - 1.61629i) q^{87} +(2.35979 - 4.08727i) q^{89} +(-6.36032 + 4.32731i) q^{91} +(-1.35451 - 0.782025i) q^{93} +10.6575i q^{97} +4.23801 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 20 q^{19} + 50 q^{21} - 8 q^{29} + 28 q^{31} - 20 q^{39} - 16 q^{41} + 26 q^{49} - 10 q^{51} - 2 q^{59} + 50 q^{61} + 64 q^{69} - 80 q^{71} + 4 q^{79} - 48 q^{81} - 38 q^{89} + 34 q^{91} + 204 q^{99}+O(q^{100}) $ 16 * q + 10 * q^9 - 20 * q^19 + 50 * q^21 - 8 * q^29 + 28 * q^31 - 20 * q^39 - 16 * q^41 + 26 * q^49 - 10 * q^51 - 2 * q^59 + 50 * q^61 + 64 * q^69 - 80 * q^71 + 4 * q^79 - 48 * q^81 - 38 * q^89 + 34 * q^91 + 204 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.77252	+	1.02336i	−1.02336	+	0.590840i	−0.915077	−	0.403280i	$-0.867870\pi$
$3$	−1.77252	+	1.02336i	−1.02336	+	0.590840i	−0.108288	+	0.994120i	$0.534537\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.48827	−	2.18747i	−0.562514	−	0.826788i
$7$	−1.48827	−	2.18747i	−0.562514	−	0.826788i
$8$		0			0
$9$	0.594550	−	1.02979i	0.198183	−	0.343264i
$10$		0			0
$11$	1.78203	+	3.08656i	0.537301	+	0.930632i	0.999048	+	0.0436208i	$0.0138893\pi$
$11$	1.78203	+	3.08656i	0.537301	+	0.930632i	−0.461747	+	0.887011i	$0.652777\pi$
$12$		0			0
$13$		−	2.90761i		−	0.806426i	−0.915106	−	0.403213i	$-0.867893\pi$
$13$		−	2.90761i		−	0.806426i	0.915106	−	0.403213i	$-0.132107\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.22032	−	1.85925i	0.781043	−	0.450935i	−0.0557568	−	0.998444i	$-0.517757\pi$
$17$	3.22032	−	1.85925i	0.781043	−	0.450935i	0.836800	+	0.547509i	$0.184424\pi$
$18$		0			0
$19$	−1.78969	+	3.09984i	−0.410584	+	0.711152i	−0.994954	−	0.100335i	$-0.968008\pi$
$19$	−1.78969	+	3.09984i	−0.410584	+	0.711152i	0.584370	+	0.811488i	$0.301342\pi$
$20$		0			0
$21$	4.87658	+	2.35430i	1.06416	+	0.513750i
$22$		0			0
$23$	−2.69230	−	1.55440i	−0.561383	−	0.324114i	0.192318	−	0.981333i	$-0.438400\pi$
$23$	−2.69230	−	1.55440i	−0.561383	−	0.324114i	−0.753700	+	0.657218i	$0.771733\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	3.70642i		−	0.713301i
$28$		0			0
$29$	−1.57939			−0.293285			−0.146642	−	0.989190i	$-0.546847\pi$
$29$	−1.57939			−0.293285			−0.146642	+	0.989190i	$0.546847\pi$
$30$		0			0
$31$	0.382085	+	0.661791i	0.0686245	+	0.118861i	0.898296	−	0.439391i	$-0.144806\pi$
$31$	0.382085	+	0.661791i	0.0686245	+	0.118861i	−0.829672	+	0.558252i	$0.811472\pi$
$32$		0			0
$33$	−6.31735	−	3.64732i	−1.09971	−	0.634917i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.06310	+	3.50053i	0.996768	+	0.575484i	0.907290	−	0.420505i	$-0.138147\pi$
$37$	6.06310	+	3.50053i	0.996768	+	0.575484i	0.0894774	+	0.995989i	$0.471480\pi$
$38$		0			0
$39$	2.97554	+	5.15379i	0.476468	+	0.825267i
$40$		0			0
$41$	7.07812			1.10542			0.552708	−	0.833375i	$-0.313594\pi$
$41$	7.07812			1.10542			0.552708	+	0.833375i	$0.313594\pi$
$42$		0			0
$43$			10.9390i			1.66818i	0.551627	+	0.834091i	$0.314007\pi$
$43$			10.9390i			1.66818i	−0.551627	+	0.834091i	$0.685993\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.38782	+	3.68801i	0.931759	+	0.537951i	0.887367	−	0.461063i	$-0.152532\pi$
$47$	6.38782	+	3.68801i	0.931759	+	0.537951i	0.0443916	+	0.999014i	$0.485865\pi$
$48$		0			0
$49$	−2.57009	+	6.51111i	−0.367156	+	0.930159i
$50$		0			0
$51$	−3.80539	+	6.59113i	−0.532861	+	0.922943i
$52$		0			0
$53$	−2.88232	+	1.66411i	−0.395918	+	0.228583i	−0.684721	−	0.728805i	$-0.740076\pi$
$53$	−2.88232	+	1.66411i	−0.395918	+	0.228583i	0.288803	+	0.957388i	$0.406743\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	7.32604i		−	0.970357i
$58$		0			0
$59$	4.07009	+	7.04961i	0.529881	+	0.917781i	0.999392	+	0.0348545i	$0.0110968\pi$
$59$	4.07009	+	7.04961i	0.529881	+	0.917781i	−0.469511	+	0.882926i	$0.655570\pi$
$60$		0			0
$61$	2.96897	−	5.14240i	0.380137	−	0.658417i	−0.610944	−	0.791674i	$-0.709210\pi$
$61$	2.96897	−	5.14240i	0.380137	−	0.658417i	0.991082	+	0.133257i	$0.0425434\pi$
$62$		0			0
$63$	−3.13749	+	0.232045i	−0.395287	+	0.0292350i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−12.1262	+	7.00107i	−1.48145	+	0.855316i	−0.999779	−	0.0210347i	$-0.993304\pi$
$67$	−12.1262	+	7.00107i	−1.48145	+	0.855316i	−0.481673	+	0.876351i	$0.659971\pi$
$68$		0			0
$69$	6.36286			0.765999
$70$		0			0
$71$	−14.5305			−1.72445			−0.862225	−	0.506525i	$-0.830930\pi$
$71$	−14.5305			−1.72445			−0.862225	+	0.506525i	$0.830930\pi$
$72$		0			0
$73$	−11.4502	+	6.61078i	−1.34015	+	0.773733i	−0.986828	−	0.161771i	$-0.948280\pi$
$73$	−11.4502	+	6.61078i	−1.34015	+	0.773733i	−0.353317	+	0.935504i	$0.614946\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.09963	−	8.49177i	0.467196	−	0.967727i
$78$		0			0
$79$	1.49233	−	2.58479i	0.167900	−	0.290812i	−0.769781	−	0.638308i	$-0.779635\pi$
$79$	1.49233	−	2.58479i	0.167900	−	0.290812i	0.937681	+	0.347496i	$0.112968\pi$
$80$		0			0
$81$	5.57667	+	9.65908i	0.619630	+	1.07323i
$82$		0			0
$83$			10.8923i			1.19558i	0.801652	+	0.597791i	$0.203955\pi$
$83$			10.8923i			1.19558i	−0.801652	+	0.597791i	$0.796045\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.79950	−	1.61629i	0.300137	−	0.173284i
$88$		0			0
$89$	2.35979	−	4.08727i	0.250137	−	0.433250i	−0.713426	−	0.700730i	$-0.752858\pi$
$89$	2.35979	−	4.08727i	0.250137	−	0.433250i	0.963563	+	0.267480i	$0.0861910\pi$
$90$		0			0
$91$	−6.36032	+	4.32731i	−0.666743	+	0.453626i
$92$		0			0
$93$	−1.35451	−	0.782025i	−0.140456	−	0.0810922i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			10.6575i			1.08211i	0.840988	+	0.541053i	$0.181974\pi$
$97$			10.6575i			1.08211i	−0.840988	+	0.541053i	$0.818026\pi$
$98$		0			0
$99$	4.23801			0.425936
$100$		0			0
$101$	4.07776	+	7.06289i	0.405753	+	0.702784i	0.994409	−	0.105599i	$-0.0336761\pi$
$101$	4.07776	+	7.06289i	0.405753	+	0.702784i	−0.588656	+	0.808383i	$0.700343\pi$
$102$		0			0
$103$	−8.09268	−	4.67231i	−0.797396	−	0.460377i	0.0451640	−	0.998980i	$-0.485619\pi$
$103$	−8.09268	−	4.67231i	−0.797396	−	0.460377i	−0.842560	+	0.538603i	$0.818952\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.03239	+	2.90545i	0.486499	+	0.280880i	0.723121	−	0.690721i	$-0.242707\pi$
$107$	5.03239	+	2.90545i	0.486499	+	0.280880i	−0.236622	+	0.971602i	$0.576040\pi$
$108$		0			0
$109$	7.35816	+	12.7447i	0.704784	+	1.22072i	0.966769	+	0.255650i	$0.0822895\pi$
$109$	7.35816	+	12.7447i	0.704784	+	1.22072i	−0.261985	+	0.965072i	$0.584377\pi$
$110$		0			0
$111$	−14.3293			−1.36008
$112$		0			0
$113$		−	0.0164044i		−	0.00154319i	−1.00000		0.000771596i	$-0.999754\pi$
$113$		−	0.0164044i		−	0.00154319i	1.00000		0.000771596i	$-0.000245607\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.99423	−	1.72872i	−0.276817	−	0.159820i
$118$		0			0
$119$	−8.85979	−	4.27730i	−0.812175	−	0.392099i
$120$		0			0
$121$	−0.851227	+	1.47437i	−0.0773843	+	0.134034i
$122$		0			0
$123$	−12.5461	+	7.24350i	−1.13124	+	0.653124i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			15.9044i			1.41128i	0.708569	+	0.705642i	$0.249341\pi$
$127$			15.9044i			1.41128i	−0.708569	+	0.705642i	$0.750659\pi$
$128$		0			0
$129$	−11.1946	−	19.3896i	−0.985628	−	1.70716i
$130$		0			0
$131$	9.12449	−	15.8041i	0.797211	−	1.38081i	−0.124215	−	0.992255i	$-0.539641\pi$
$131$	9.12449	−	15.8041i	0.797211	−	1.38081i	0.921426	−	0.388554i	$-0.127025\pi$
$132$		0			0
$133$	9.44438	−	0.698495i	0.818931	−	0.0605672i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.53435	+	4.34996i	−0.643703	+	0.371642i	−0.786040	−	0.618176i	$-0.787872\pi$
$137$	−7.53435	+	4.34996i	−0.643703	+	0.371642i	0.142336	+	0.989818i	$0.454539\pi$
$138$		0			0
$139$	11.3728			0.964625			0.482313	−	0.875999i	$-0.339797\pi$
$139$	11.3728			0.964625			0.482313	+	0.875999i	$0.339797\pi$
$140$		0			0
$141$	−15.0967			−1.27137
$142$		0			0
$143$	8.97450	−	5.18143i	0.750486	−	0.433293i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.10770	−	14.1712i	−0.173840	−	1.16882i
$148$		0			0
$149$	−8.40047	+	14.5500i	−0.688194	+	1.19199i	0.284228	+	0.958757i	$0.408263\pi$
$149$	−8.40047	+	14.5500i	−0.688194	+	1.19199i	−0.972422	+	0.233230i	$0.925071\pi$
$150$		0			0
$151$	−3.74296	−	6.48301i	−0.304598	−	0.527579i	0.672574	−	0.740030i	$-0.265189\pi$
$151$	−3.74296	−	6.48301i	−0.304598	−	0.527579i	−0.977172	+	0.212451i	$0.931855\pi$
$152$		0			0
$153$		−	4.42168i		−	0.357472i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.7333	−	7.35159i	1.01623	−	0.586720i	0.103220	−	0.994659i	$-0.467085\pi$
$157$	12.7333	−	7.35159i	1.01623	−	0.586720i	0.913010	+	0.407938i	$0.133752\pi$
$158$		0			0
$159$	3.40598	−	5.89934i	0.270112	−	0.467848i
$160$		0			0
$161$	0.606662	+	8.20270i	0.0478117	+	0.646463i
$162$		0			0
$163$	5.53697	+	3.19677i	0.433689	+	0.250390i	0.700917	−	0.713243i	$-0.252774\pi$
$163$	5.53697	+	3.19677i	0.433689	+	0.250390i	−0.267228	+	0.963633i	$0.586108\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			15.8509i			1.22658i	0.789857	+	0.613291i	$0.210155\pi$
$167$			15.8509i			1.22658i	−0.789857	+	0.613291i	$0.789845\pi$
$168$		0			0
$169$	4.54581			0.349678
$170$		0			0
$171$	2.12813	+	3.68602i	0.162742	+	0.281877i
$172$		0			0
$173$	−6.27939	−	3.62541i	−0.477413	−	0.275635i	0.241925	−	0.970295i	$-0.422221\pi$
$173$	−6.27939	−	3.62541i	−0.477413	−	0.275635i	−0.719338	+	0.694660i	$0.755555\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−14.4286	−	8.33038i	−1.08452	−	0.626150i
$178$		0			0
$179$	6.79988	+	11.7777i	0.508247	+	0.880309i	0.999954	+	0.00954899i	$0.00303958\pi$
$179$	6.79988	+	11.7777i	0.508247	+	0.880309i	−0.491708	+	0.870760i	$0.663627\pi$
$180$		0			0
$181$	16.5469			1.22992			0.614960	−	0.788558i	$-0.289172\pi$
$181$	16.5469			1.22992			0.614960	+	0.788558i	$0.289172\pi$
$182$		0			0
$183$			12.1533i			0.898401i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	11.4774	+	6.62648i	0.839310	+	0.484576i
$188$		0			0
$189$	−8.10770	+	5.51616i	−0.589749	+	0.401242i
$190$		0			0
$191$	4.31522	−	7.47418i	0.312238	−	0.540812i	−0.666608	−	0.745408i	$-0.732255\pi$
$191$	4.31522	−	7.47418i	0.312238	−	0.540812i	0.978847	+	0.204596i	$0.0655880\pi$
$192$		0			0
$193$	11.8420	−	6.83696i	0.852403	−	0.492135i	−0.00905815	−	0.999959i	$-0.502883\pi$
$193$	11.8420	−	6.83696i	0.852403	−	0.492135i	0.861461	+	0.507824i	$0.169550\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	26.8922i		−	1.91599i	−0.286783	−	0.957996i	$-0.592586\pi$
$197$		−	26.8922i		−	1.91599i	0.286783	−	0.957996i	$-0.407414\pi$
$198$		0			0
$199$	1.84247	+	3.19125i	0.130609	+	0.226221i	0.923911	−	0.382606i	$-0.124973\pi$
$199$	1.84247	+	3.19125i	0.130609	+	0.226221i	−0.793302	+	0.608828i	$0.791640\pi$
$200$		0			0
$201$	14.3293	−	24.8191i	1.01071	−	1.75060i
$202$		0			0
$203$	2.35056	+	3.45487i	0.164977	+	0.242484i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.20141	+	1.84833i	−0.222513	+	0.128468i
$208$		0			0
$209$	−12.7571			−0.882428
$210$		0			0
$211$	4.91193			0.338151			0.169075	−	0.985603i	$-0.445922\pi$
$211$	4.91193			0.338151			0.169075	+	0.985603i	$0.445922\pi$
$212$		0			0
$213$	25.7555	−	14.8700i	1.76474	−	1.01887i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.879005	−	1.82073i	0.0596707	−	0.123599i
$218$		0			0
$219$	13.5305	−	23.4355i	0.914305	−	1.58362i
$220$		0			0
$221$	−5.40598	−	9.36344i	−0.363646	−	0.629853i
$222$		0			0
$223$		−	12.6575i		−	0.847609i	−0.905754	−	0.423805i	$-0.860694\pi$
$223$		−	12.6575i		−	0.847609i	0.905754	−	0.423805i	$-0.139306\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.87630	−	3.97003i	0.456396	−	0.263500i	−0.254132	−	0.967170i	$-0.581790\pi$
$227$	6.87630	−	3.97003i	0.456396	−	0.263500i	0.710528	+	0.703669i	$0.248456\pi$
$228$		0			0
$229$	−3.32019	+	5.75074i	−0.219405	+	0.380020i	−0.954626	−	0.297807i	$-0.903745\pi$
$229$	−3.32019	+	5.75074i	−0.219405	+	0.380020i	0.735222	+	0.677827i	$0.237078\pi$
$230$		0			0
$231$	1.42350	+	19.2472i	0.0936597	+	1.26638i
$232$		0			0
$233$	11.8682	+	6.85212i	0.777513	+	0.448897i	0.835548	−	0.549417i	$-0.185150\pi$
$233$	11.8682	+	6.85212i	0.777513	+	0.448897i	−0.0580353	+	0.998315i	$0.518484\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			6.10880i			0.396809i
$238$		0			0
$239$	−28.0010			−1.81124			−0.905618	−	0.424095i	$-0.860592\pi$
$239$	−28.0010			−1.81124			−0.905618	+	0.424095i	$0.860592\pi$
$240$		0			0
$241$	11.4238	+	19.7867i	0.735874	+	1.27457i	0.954339	+	0.298726i	$0.0965618\pi$
$241$	11.4238	+	19.7867i	0.735874	+	1.27457i	−0.218465	+	0.975845i	$0.570105\pi$
$242$		0			0
$243$	−10.1399	−	5.85430i	−0.650478	−	0.375554i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	9.01312	+	5.20373i	0.573491	+	0.331105i
$248$		0			0
$249$	−11.1468	−	19.3068i	−0.706397	−	1.22352i
$250$		0			0
$251$	−3.55973			−0.224688			−0.112344	−	0.993669i	$-0.535836\pi$
$251$	−3.55973			−0.224688			−0.112344	+	0.993669i	$0.535836\pi$
$252$		0			0
$253$		−	11.0799i		−	0.696588i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−23.9230	−	13.8120i	−1.49228	−	0.861567i	−0.492317	−	0.870416i	$-0.663850\pi$
$257$	−23.9230	−	13.8120i	−1.49228	−	0.861567i	−0.999961	+	0.00884937i	$0.997183\pi$
$258$		0			0
$259$	−1.36621	−	18.4726i	−0.0848924	−	1.14783i
$260$		0			0
$261$	−0.939025	+	1.62644i	−0.0581242	+	0.100674i
$262$		0			0
$263$	21.8434	−	12.6113i	1.34692	−	0.777647i	0.359111	−	0.933295i	$-0.383080\pi$
$263$	21.8434	−	12.6113i	1.34692	−	0.777647i	0.987813	+	0.155648i	$0.0497465\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			9.65969i			0.591164i
$268$		0			0
$269$	−8.31946	−	14.4097i	−0.507246	−	0.878577i	−0.999965	−	0.00838779i	$-0.997330\pi$
$269$	−8.31946	−	14.4097i	−0.507246	−	0.878577i	0.492718	−	0.870189i	$-0.336003\pi$
$270$		0			0
$271$	12.2631	−	21.2403i	0.744929	−	1.29025i	−0.205299	−	0.978699i	$-0.565817\pi$
$271$	12.2631	−	21.2403i	0.744929	−	1.29025i	0.950228	−	0.311556i	$-0.100850\pi$
$272$		0			0
$273$	6.84537	−	14.1792i	0.414301	−	0.858163i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−27.3485	+	15.7897i	−1.64321	+	0.948709i	−0.663531	+	0.748148i	$0.730943\pi$
$277$	−27.3485	+	15.7897i	−1.64321	+	0.948709i	−0.979681	+	0.200561i	$0.935724\pi$
$278$		0			0
$279$	0.908675			0.0544010
$280$		0			0
$281$	−28.0413			−1.67280			−0.836402	−	0.548117i	$-0.815345\pi$
$281$	−28.0413			−1.67280			−0.836402	+	0.548117i	$0.815345\pi$
$282$		0			0
$283$	25.6955	−	14.8353i	1.52744	−	0.881869i	0.527974	−	0.849261i	$-0.322952\pi$
$283$	25.6955	−	14.8353i	1.52744	−	0.881869i	0.999468	−	0.0326081i	$-0.0103813\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.5342	−	15.4832i	−0.621812	−	0.913945i
$288$		0			0
$289$	−1.58635	+	2.74764i	−0.0933146	+	0.161626i
$290$		0			0
$291$	−10.9065	−	18.8906i	−0.639351	−	1.10739i
$292$		0			0
$293$			9.43031i			0.550925i	0.961312	+	0.275462i	$0.0888310\pi$
$293$			9.43031i			0.550925i	−0.961312	+	0.275462i	$0.911169\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	11.4401	−	6.60494i	0.663821	−	0.383257i
$298$		0			0
$299$	−4.51958	+	7.82814i	−0.261374	+	0.452713i
$300$		0			0
$301$	23.9288	−	16.2802i	1.37923	−	0.938375i
$302$		0			0
$303$	−14.4558	−	8.34608i	−0.830466	−	0.479470i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	4.59798i		−	0.262420i	−0.991355	−	0.131210i	$-0.958114\pi$
$307$		−	4.59798i		−	0.262420i	0.991355	−	0.131210i	$-0.0418863\pi$
$308$		0			0
$309$	19.1259			1.08804
$310$		0			0
$311$	0.740273	+	1.28219i	0.0419770	+	0.0727063i	0.886251	−	0.463206i	$-0.153301\pi$
$311$	0.740273	+	1.28219i	0.0419770	+	0.0727063i	−0.844274	+	0.535912i	$0.819968\pi$
$312$		0			0
$313$	−14.8438	−	8.57009i	−0.839023	−	0.484410i	0.0179088	−	0.999840i	$-0.494299\pi$
$313$	−14.8438	−	8.57009i	−0.839023	−	0.484410i	−0.856932	+	0.515429i	$0.827632\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.94354	+	3.43151i	0.333823	+	0.192733i	0.657537	−	0.753422i	$-0.271598\pi$
$317$	5.94354	+	3.43151i	0.333823	+	0.192733i	−0.323714	+	0.946155i	$0.604932\pi$
$318$		0			0
$319$	−2.81451	−	4.87487i	−0.157582	−	0.272940i
$320$		0			0
$321$	−11.8933			−0.663821
$322$		0			0
$323$			13.3100i			0.740587i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−26.0850	−	15.0602i	−1.44250	−	0.832829i
$328$		0			0
$329$	−1.43938	−	19.4620i	−0.0793558	−	1.07297i
$330$		0			0
$331$	1.70868	−	2.95952i	0.0939176	−	0.162670i	−0.815239	−	0.579125i	$-0.803394\pi$
$331$	1.70868	−	2.95952i	0.0939176	−	0.162670i	0.909156	+	0.416455i	$0.136728\pi$
$332$		0			0
$333$	7.20964	−	4.16249i	0.395086	−	0.228103i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			26.3574i			1.43578i	0.696156	+	0.717890i	$0.254892\pi$
$337$			26.3574i			1.43578i	−0.696156	+	0.717890i	$0.745108\pi$
$338$		0			0
$339$	0.0167876	+	0.0290771i	0.000911780	+	0.00157925i
$340$		0			0
$341$	−1.36177	+	2.35866i	−0.0737440	+	0.127728i
$342$		0			0
$343$	18.0679	−	4.06829i	0.975575	−	0.219667i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.26754	−	4.77326i	0.443825	−	0.256242i	−0.261394	−	0.965232i	$-0.584182\pi$
$347$	8.26754	−	4.77326i	0.443825	−	0.256242i	0.705219	+	0.708990i	$0.250849\pi$
$348$		0			0
$349$	10.8259			0.579496			0.289748	−	0.957103i	$-0.406428\pi$
$349$	10.8259			0.579496			0.289748	+	0.957103i	$0.406428\pi$
$350$		0			0
$351$	−10.7768			−0.575224
$352$		0			0
$353$	−17.8785	+	10.3222i	−0.951576	+	0.549393i	−0.893570	−	0.448923i	$-0.851808\pi$
$353$	−17.8785	+	10.3222i	−0.951576	+	0.549393i	−0.0580059	+	0.998316i	$0.518474\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	20.0814	−	1.48520i	1.06282	−	0.0786049i
$358$		0			0
$359$	10.8430	−	18.7806i	0.572272	−	0.991204i	−0.424061	−	0.905634i	$-0.639396\pi$
$359$	10.8430	−	18.7806i	0.572272	−	0.991204i	0.996332	−	0.0855697i	$-0.0272710\pi$
$360$		0			0
$361$	3.09399	+	5.35895i	0.162842	+	0.282050i
$362$		0			0
$363$		−	3.48446i		−	0.182887i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−16.2916	+	9.40598i	−0.850417	+	0.490988i	−0.860791	−	0.508958i	$-0.830031\pi$
$367$	−16.2916	+	9.40598i	−0.850417	+	0.490988i	0.0103747	+	0.999946i	$0.496698\pi$
$368$		0			0
$369$	4.20830	−	7.28899i	0.219075	−	0.379449i
$370$		0			0
$371$	7.92988	+	3.82836i	0.411699	+	0.198759i
$372$		0			0
$373$	24.4062	+	14.0909i	1.26370	+	0.729600i	0.973789	−	0.227452i	$-0.0730396\pi$
$373$	24.4062	+	14.0909i	1.26370	+	0.729600i	0.289915	+	0.957052i	$0.406373\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			4.59224i			0.236512i
$378$		0			0
$379$	6.93397			0.356174			0.178087	−	0.984015i	$-0.443009\pi$
$379$	6.93397			0.356174			0.178087	+	0.984015i	$0.443009\pi$
$380$		0			0
$381$	−16.2760	−	28.1908i	−0.833843	−	1.44426i
$382$		0			0
$383$	13.1193	+	7.57441i	0.670363	+	0.387034i	0.796214	−	0.605015i	$-0.206833\pi$
$383$	13.1193	+	7.57441i	0.670363	+	0.387034i	−0.125851	+	0.992049i	$0.540166\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	11.2649	+	6.50378i	0.572626	+	0.330606i
$388$		0			0
$389$	13.0803	+	22.6557i	0.663196	+	1.14869i	0.979771	+	0.200122i	$0.0641340\pi$
$389$	13.0803	+	22.6557i	0.663196	+	1.14869i	−0.316574	+	0.948568i	$0.602533\pi$
$390$		0			0
$391$	−11.5601			−0.584619
$392$		0			0
$393$			37.3507i			1.88409i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	17.3691	+	10.0280i	0.871729	+	0.503293i	0.867922	−	0.496700i	$-0.165455\pi$
$397$	17.3691	+	10.0280i	0.871729	+	0.503293i	0.00380651	+	0.999993i	$0.498788\pi$
$398$		0			0
$399$	−16.0255	+	10.9031i	−0.802280	+	0.545839i
$400$		0			0
$401$	−5.72547	+	9.91680i	−0.285916	+	0.495221i	−0.972831	−	0.231517i	$-0.925631\pi$
$401$	−5.72547	+	9.91680i	−0.285916	+	0.495221i	0.686915	+	0.726738i	$0.258965\pi$
$402$		0			0
$403$	1.92423	−	1.11095i	0.0958527	−	0.0553406i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			24.9522i			1.23683i
$408$		0			0
$409$	−13.3109	−	23.0552i	−0.658182	−	1.14000i	−0.981086	−	0.193572i	$-0.937993\pi$
$409$	−13.3109	−	23.0552i	−0.658182	−	1.14000i	0.322904	−	0.946432i	$-0.395341\pi$
$410$		0			0
$411$	8.90319	−	15.4208i	0.439162	−	0.760651i
$412$		0			0
$413$	9.36344	−	19.3950i	0.460745	−	0.954364i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−20.1584	+	11.6385i	−0.987164	+	0.569939i
$418$		0			0
$419$	−26.8944			−1.31388			−0.656939	−	0.753944i	$-0.728149\pi$
$419$	−26.8944			−1.31388			−0.656939	+	0.753944i	$0.728149\pi$
$420$		0			0
$421$	−19.2662			−0.938975			−0.469487	−	0.882939i	$-0.655561\pi$
$421$	−19.2662			−0.938975			−0.469487	+	0.882939i	$0.655561\pi$
$422$		0			0
$423$	7.59576	−	4.38541i	0.369318	−	0.213226i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−15.6675	+	1.15875i	−0.758204	+	0.0560759i
$428$		0			0
$429$	−10.6050	+	18.3684i	−0.512014	+	0.886834i
$430$		0			0
$431$	−10.1177	−	17.5244i	−0.487354	−	0.844123i	0.512540	−	0.858663i	$-0.328705\pi$
$431$	−10.1177	−	17.5244i	−0.487354	−	0.844123i	−0.999894	+	0.0145409i	$0.995371\pi$
$432$		0			0
$433$		−	3.13135i		−	0.150483i	−0.997165	−	0.0752416i	$-0.976027\pi$
$433$		−	3.13135i		−	0.150483i	0.997165	−	0.0752416i	$-0.0239728\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.63677	−	5.56379i	0.460989	−	0.266152i
$438$		0			0
$439$	−8.72923	+	15.1195i	−0.416623	+	0.721613i	−0.995597	−	0.0937332i	$-0.970120\pi$
$439$	−8.72923	+	15.1195i	−0.416623	+	0.721613i	0.578974	+	0.815346i	$0.303453\pi$
$440$		0			0
$441$	5.17704	+	6.51784i	0.246526	+	0.310374i
$442$		0			0
$443$	11.7449	+	6.78093i	0.558018	+	0.322172i	0.752350	−	0.658764i	$-0.228920\pi$
$443$	11.7449	+	6.78093i	0.558018	+	0.322172i	−0.194332	+	0.980936i	$0.562254\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	34.3870i		−	1.62645i
$448$		0			0
$449$	28.7260			1.35566			0.677832	−	0.735216i	$-0.262919\pi$
$449$	28.7260			1.35566			0.677832	+	0.735216i	$0.262919\pi$
$450$		0			0
$451$	12.6134	+	21.8470i	0.593941	+	1.02874i
$452$		0			0
$453$	13.2690	+	7.66083i	0.623430	+	0.359937i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.13495	+	4.11936i	0.333759	+	0.192696i	0.657509	−	0.753447i	$-0.271610\pi$
$457$	7.13495	+	4.11936i	0.333759	+	0.192696i	−0.323750	+	0.946143i	$0.604944\pi$
$458$		0			0
$459$	−6.89118	−	11.9359i	−0.321653	−	0.557119i
$460$		0			0
$461$	−29.8729			−1.39132			−0.695660	−	0.718371i	$-0.744888\pi$
$461$	−29.8729			−1.39132			−0.695660	+	0.718371i	$0.744888\pi$
$462$		0			0
$463$		−	11.4155i		−	0.530525i	−0.964176	−	0.265262i	$-0.914541\pi$
$463$		−	11.4155i		−	0.530525i	0.964176	−	0.265262i	$-0.0854586\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−21.8431	−	12.6111i	−1.01078	−	0.583574i	−0.0993598	−	0.995052i	$-0.531679\pi$
$467$	−21.8431	−	12.6111i	−1.01078	−	0.583574i	−0.911420	+	0.411478i	$0.865013\pi$
$468$		0			0
$469$	33.3617	+	16.1063i	1.54050	+	0.743719i
$470$		0			0
$471$	−15.0467	+	26.0617i	−0.693316	+	1.20086i
$472$		0			0
$473$	−33.7639	+	19.4936i	−1.55246	+	0.896315i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			3.95759i			0.181206i
$478$		0			0
$479$	13.5394	+	23.4510i	0.618632	+	1.07150i	0.989736	+	0.142910i	$0.0456461\pi$
$479$	13.5394	+	23.4510i	0.618632	+	1.07150i	−0.371104	+	0.928591i	$0.621021\pi$
$480$		0			0
$481$	10.1782	−	17.6291i	0.464085	−	0.803819i
$482$		0			0
$483$	−9.46967	−	13.9186i	−0.430885	−	0.633318i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	15.8885	−	9.17320i	0.719975	−	0.415678i	−0.0947687	−	0.995499i	$-0.530211\pi$
$487$	15.8885	−	9.17320i	0.719975	−	0.415678i	0.814743	+	0.579822i	$0.196878\pi$
$488$		0			0
$489$	−13.0858			−0.591762
$490$		0			0
$491$	−25.4457			−1.14835			−0.574173	−	0.818734i	$-0.694676\pi$
$491$	−25.4457			−1.14835			−0.574173	+	0.818734i	$0.694676\pi$
$492$		0			0
$493$	−5.08614	+	2.93648i	−0.229068	+	0.132253i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.6253	+	31.7851i	0.970027	+	1.42575i
$498$		0			0
$499$	2.07154	−	3.58802i	0.0927350	−	0.160622i	−0.815926	−	0.578156i	$-0.803772\pi$
$499$	2.07154	−	3.58802i	0.0927350	−	0.160622i	0.908661	+	0.417535i	$0.137106\pi$
$500$		0			0
$501$	−16.2213	−	28.0961i	−0.724713	−	1.25524i
$502$		0			0
$503$			19.0099i			0.847610i	0.905754	+	0.423805i	$0.139306\pi$
$503$			19.0099i			0.847610i	−0.905754	+	0.423805i	$0.860694\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.05754	+	4.65202i	−0.357848	+	0.206604i
$508$		0			0
$509$	−1.92295	+	3.33064i	−0.0852331	+	0.147628i	−0.905491	−	0.424367i	$-0.860497\pi$
$509$	−1.92295	+	3.33064i	−0.0852331	+	0.147628i	0.820257	+	0.571995i	$0.193830\pi$
$510$		0			0
$511$	31.5019	+	15.2084i	1.39356	+	0.672780i
$512$		0			0
$513$	11.4893	+	6.63336i	0.507266	+	0.292870i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			26.2885i			1.15617i
$518$		0			0
$519$	14.8405			0.651424
$520$		0			0
$521$	−6.80772	−	11.7913i	−0.298252	−	0.516587i	0.677484	−	0.735537i	$-0.263070\pi$
$521$	−6.80772	−	11.7913i	−0.298252	−	0.516587i	−0.975736	+	0.218950i	$0.929737\pi$
$522$		0			0
$523$	−19.1974	−	11.0836i	−0.839444	−	0.484653i	0.0176311	−	0.999845i	$-0.494388\pi$
$523$	−19.1974	−	11.0836i	−0.839444	−	0.484653i	−0.857075	+	0.515191i	$0.827721\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.46088	+	1.42079i	0.107197	+	0.0618905i
$528$		0			0
$529$	−6.66769	−	11.5488i	−0.289900	−	0.502121i
$530$		0			0
$531$	9.67950			0.420054
$532$		0			0
$533$		−	20.5804i		−	0.891436i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−24.1058	−	13.9175i	−1.04024	−	0.600585i
$538$		0			0
$539$	−24.6769	+	3.67023i	−1.06291	+	0.158088i
$540$		0			0
$541$	−14.5075	+	25.1277i	−0.623725	+	1.08032i	0.365061	+	0.930984i	$0.381048\pi$
$541$	−14.5075	+	25.1277i	−0.623725	+	1.08032i	−0.988786	+	0.149340i	$0.952285\pi$
$542$		0			0
$543$	−29.3297	+	16.9335i	−1.25866	+	0.726686i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			28.6053i			1.22308i	0.791215	+	0.611538i	$0.209449\pi$
$547$			28.6053i			1.22308i	−0.791215	+	0.611538i	$0.790551\pi$
$548$		0			0
$549$	−3.53040	−	6.11483i	−0.150674	−	0.260975i
$550$		0			0
$551$	2.82662	−	4.89585i	0.120418	−	0.208570i
$552$		0			0
$553$	−7.87517	+	0.582438i	−0.334886	+	0.0247678i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	27.3927	−	15.8152i	1.16067	−	0.670111i	0.209203	−	0.977872i	$-0.432913\pi$
$557$	27.3927	−	15.8152i	1.16067	−	0.670111i	0.951464	+	0.307761i	$0.0995797\pi$
$558$		0			0
$559$	31.8063			1.34526
$560$		0			0
$561$	−27.1252			−1.14523
$562$		0			0
$563$	17.3301	−	10.0055i	0.730375	−	0.421682i	−0.0881846	−	0.996104i	$-0.528107\pi$
$563$	17.3301	−	10.0055i	0.730375	−	0.421682i	0.818559	+	0.574422i	$0.194773\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	12.8294	−	26.5742i	0.538784	−	1.11601i
$568$		0			0
$569$	17.6723	−	30.6093i	0.740861	−	1.28321i	−0.211243	−	0.977434i	$-0.567751\pi$
$569$	17.6723	−	30.6093i	0.740861	−	1.28321i	0.952104	−	0.305775i	$-0.0989155\pi$
$570$		0			0
$571$	7.83533	+	13.5712i	0.327898	+	0.567937i	0.982095	−	0.188388i	$-0.0603263\pi$
$571$	7.83533	+	13.5712i	0.327898	+	0.567937i	−0.654196	+	0.756325i	$0.726993\pi$
$572$		0			0
$573$			17.6642i			0.737931i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−22.4350	+	12.9529i	−0.933982	+	0.539235i	−0.888069	−	0.459711i	$-0.847953\pi$
$577$	−22.4350	+	12.9529i	−0.933982	+	0.539235i	−0.0459132	+	0.998945i	$0.514620\pi$
$578$		0			0
$579$	−13.9934	+	24.2373i	−0.581546	+	1.00727i
$580$		0			0
$581$	23.8266	−	16.2107i	0.988493	−	0.672532i
$582$		0			0
$583$	−10.2727	−	5.93097i	−0.425454	−	0.245636i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	38.2409i		−	1.57837i	−0.614156	−	0.789185i	$-0.710503\pi$
$587$		−	38.2409i		−	1.57837i	0.614156	−	0.789185i	$-0.289497\pi$
$588$		0			0
$589$	−2.73526			−0.112705
$590$		0			0
$591$	27.5205	+	47.6670i	1.13204	+	1.96076i
$592$		0			0
$593$	−40.0707	−	23.1348i	−1.64551	−	0.950034i	−0.978827	−	0.204689i	$-0.934382\pi$
$593$	−40.0707	−	23.1348i	−1.64551	−	0.950034i	−0.666679	−	0.745345i	$-0.732285\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.53162	−	3.77103i	−0.267321	−	0.154338i
$598$		0			0
$599$	−10.5262	−	18.2320i	−0.430090	−	0.744938i	0.566790	−	0.823862i	$-0.308185\pi$
$599$	−10.5262	−	18.2320i	−0.430090	−	0.744938i	−0.996881	+	0.0789240i	$0.974852\pi$
$600$		0			0
$601$	27.5283			1.12290			0.561451	−	0.827510i	$-0.310243\pi$
$601$	27.5283			1.12290			0.561451	+	0.827510i	$0.310243\pi$
$602$		0			0
$603$			16.6499i			0.678038i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.7506	−	10.8257i	−0.761064	−	0.439401i	0.0686134	−	0.997643i	$-0.478143\pi$
$607$	−18.7506	−	10.8257i	−0.761064	−	0.439401i	−0.829678	+	0.558243i	$0.811476\pi$
$608$		0			0
$609$	−7.70200	−	3.71835i	−0.312101	−	0.150675i
$610$		0			0
$611$	10.7233	−	18.5733i	0.433818	−	0.751394i
$612$		0			0
$613$	−22.7190	+	13.1168i	−0.917610	+	0.529782i	−0.882872	−	0.469614i	$-0.844393\pi$
$613$	−22.7190	+	13.1168i	−0.917610	+	0.529782i	−0.0347383	+	0.999396i	$0.511060\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			9.48553i			0.381873i	0.981602	+	0.190937i	$0.0611525\pi$
$617$			9.48553i			0.381873i	−0.981602	+	0.190937i	$0.938848\pi$
$618$		0			0
$619$	3.06971	+	5.31689i	0.123382	+	0.213704i	0.921099	−	0.389328i	$-0.127293\pi$
$619$	3.06971	+	5.31689i	0.123382	+	0.213704i	−0.797717	+	0.603032i	$0.793959\pi$
$620$		0			0
$621$	−5.76125	+	9.97878i	−0.231191	+	0.400435i
$622$		0			0
$623$	−12.4528	+	0.920996i	−0.498911	+	0.0368989i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	22.6122	−	13.0552i	0.903046	−	0.521374i
$628$		0			0
$629$	26.0335			1.03802
$630$		0			0
$631$	36.8070			1.46527			0.732633	−	0.680624i	$-0.238291\pi$
$631$	36.8070			1.46527			0.732633	+	0.680624i	$0.238291\pi$
$632$		0			0
$633$	−8.70648	+	5.02669i	−0.346052	+	0.199793i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	18.9318	+	7.47283i	0.750104	+	0.296084i
$638$		0			0
$639$	−8.63910	+	14.9634i	−0.341757	+	0.591941i
$640$		0			0
$641$	9.82200	+	17.0122i	0.387946	+	0.671942i	0.992173	−	0.124870i	$-0.0398514\pi$
$641$	9.82200	+	17.0122i	0.387946	+	0.671942i	−0.604227	+	0.796812i	$0.706518\pi$
$642$		0			0
$643$		−	17.8590i		−	0.704292i	−0.935945	−	0.352146i	$-0.885452\pi$
$643$		−	17.8590i		−	0.704292i	0.935945	−	0.352146i	$-0.114548\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.2912	−	11.7152i	0.797731	−	0.460570i	−0.0449460	−	0.998989i	$-0.514312\pi$
$647$	20.2912	−	11.7152i	0.797731	−	0.460570i	0.842677	+	0.538419i	$0.180978\pi$
$648$		0			0
$649$	−14.5060	+	25.1252i	−0.569411	+	0.986249i
$650$		0			0
$651$	0.305215	+	4.12682i	0.0119623	+	0.161743i
$652$		0			0
$653$	2.63573	+	1.52174i	0.103144	+	0.0595503i	0.550685	−	0.834713i	$-0.314367\pi$
$653$	2.63573	+	1.52174i	0.103144	+	0.0595503i	−0.447541	+	0.894264i	$0.647700\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			15.7218i			0.613364i
$658$		0			0
$659$	0.576904			0.0224730			0.0112365	−	0.999937i	$-0.496423\pi$
$659$	0.576904			0.0224730			0.0112365	+	0.999937i	$0.496423\pi$
$660$		0			0
$661$	14.0792	+	24.3859i	0.547617	+	0.948500i	0.998437	+	0.0558856i	$0.0177982\pi$
$661$	14.0792	+	24.3859i	0.547617	+	0.948500i	−0.450820	+	0.892615i	$0.648868\pi$
$662$		0			0
$663$	19.1644	+	11.0646i	0.744284	+	0.429713i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.25218	+	2.45500i	0.164645	+	0.0950579i
$668$		0			0
$669$	12.9532	+	22.4357i	0.500801	+	0.867414i
$670$		0			0
$671$	21.1631			0.816992
$672$		0			0
$673$			17.7835i			0.685503i	0.939426	+	0.342751i	$0.111359\pi$
$673$			17.7835i			0.685503i	−0.939426	+	0.342751i	$0.888641\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.2990	−	16.3384i	−1.08762	−	0.627936i	−0.154676	−	0.987965i	$-0.549433\pi$
$677$	−28.2990	−	16.3384i	−1.08762	−	0.627936i	−0.932941	+	0.360029i	$0.882767\pi$
$678$		0			0
$679$	23.3130	−	15.8613i	0.894672	−	0.608700i
$680$		0			0
$681$	−8.12558	+	14.0739i	−0.311373	+	0.539314i
$682$		0			0
$683$	−13.9734	+	8.06755i	−0.534678	+	0.308696i	−0.742919	−	0.669381i	$-0.766559\pi$
$683$	−13.9734	+	8.06755i	−0.534678	+	0.308696i	0.208242	+	0.978077i	$0.433226\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	13.5911i		−	0.518532i
$688$		0			0
$689$	4.83858	+	8.38067i	0.184335	+	0.319278i
$690$		0			0
$691$	−8.09308	+	14.0176i	−0.307875	+	0.533255i	−0.977897	−	0.209086i	$-0.932951\pi$
$691$	−8.09308	+	14.0176i	−0.307875	+	0.533255i	0.670022	+	0.742341i	$0.266285\pi$
$692$		0			0
$693$	−6.30732	−	9.27055i	−0.239595	−	0.352159i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	22.7938	−	13.1600i	0.863378	−	0.498472i
$698$		0			0
$699$	−28.0489			−1.06091
$700$		0			0
$701$	19.8684			0.750419			0.375210	−	0.926940i	$-0.377571\pi$
$701$	19.8684			0.750419			0.375210	+	0.926940i	$0.377571\pi$
$702$		0			0
$703$	−21.7022	+	12.5298i	−0.818514	+	0.472569i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.38108	−	19.4315i	0.352812	−	0.730797i
$708$		0			0
$709$	−12.3833	+	21.4486i	−0.465066	+	0.805517i	−0.999204	−	0.0398795i	$-0.987303\pi$
$709$	−12.3833	+	21.4486i	−0.465066	+	0.805517i	0.534139	+	0.845397i	$0.320636\pi$
$710$		0			0
$711$	−1.77453	−	3.07358i	−0.0665501	−	0.115268i
$712$		0			0
$713$		−	2.37565i		−	0.0889688i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	49.6323	−	28.6552i	1.85355	−	1.07015i
$718$		0			0
$719$	−3.72346	+	6.44922i	−0.138862	+	0.240515i	−0.927066	−	0.374898i	$-0.877678\pi$
$719$	−3.72346	+	6.44922i	−0.138862	+	0.240515i	0.788204	+	0.615414i	$0.211011\pi$
$720$		0			0
$721$	1.82355	+	24.6562i	0.0679124	+	0.918245i
$722$		0			0
$723$	−40.4979	−	23.3815i	−1.50613	−	0.869567i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	2.63572i		−	0.0977534i	−0.998805	−	0.0488767i	$-0.984436\pi$
$727$		−	2.63572i		−	0.0977534i	0.998805	−	0.0488767i	$-0.0155641\pi$
$728$		0			0
$729$	−9.49568			−0.351692
$730$		0			0
$731$	20.3384	+	35.2271i	0.752242	+	1.30292i
$732$		0			0
$733$	10.7223	+	6.19053i	0.396037	+	0.228652i	0.684773	−	0.728757i	$-0.259901\pi$
$733$	10.7223	+	6.19053i	0.396037	+	0.228652i	−0.288735	+	0.957409i	$0.593235\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−43.2184	−	24.9522i	−1.59197	−	0.919124i
$738$		0			0
$739$	3.36512	+	5.82856i	0.123788	+	0.214407i	0.921259	−	0.388951i	$-0.127162\pi$
$739$	3.36512	+	5.82856i	0.123788	+	0.214407i	−0.797471	+	0.603358i	$0.793829\pi$
$740$		0			0
$741$	−21.3012			−0.782521
$742$		0			0
$743$		−	18.6268i		−	0.683352i	−0.939818	−	0.341676i	$-0.889005\pi$
$743$		−	18.6268i		−	0.683352i	0.939818	−	0.341676i	$-0.110995\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	11.2168	+	6.47600i	0.410400	+	0.236944i
$748$		0			0
$749$	−1.13396	−	15.3323i	−0.0414340	−	0.560231i
$750$		0			0
$751$	20.7123	−	35.8747i	0.755801	−	1.30909i	−0.189174	−	0.981944i	$-0.560581\pi$
$751$	20.7123	−	35.8747i	0.755801	−	1.30909i	0.944975	−	0.327143i	$-0.106086\pi$
$752$		0			0
$753$	6.30970	−	3.64290i	0.229938	−	0.132755i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			27.3296i			0.993311i	0.867948	+	0.496655i	$0.165439\pi$
$757$			27.3296i			0.993311i	−0.867948	+	0.496655i	$0.834561\pi$
$758$		0			0
$759$	11.3388	+	19.6393i	0.411572	+	0.712863i
$760$		0			0
$761$	−6.78256	+	11.7477i	−0.245868	+	0.425855i	−0.962375	−	0.271724i	$-0.912406\pi$
$761$	−6.78256	+	11.7477i	−0.245868	+	0.425855i	0.716508	+	0.697579i	$0.245739\pi$
$762$		0			0
$763$	16.9278	−	35.0634i	0.612827	−	1.26938i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	20.4975	−	11.8342i	0.740122	−	0.427310i
$768$		0			0
$769$	33.6618			1.21388			0.606938	−	0.794749i	$-0.292398\pi$
$769$	33.6618			1.21388			0.606938	+	0.794749i	$0.292398\pi$
$770$		0			0
$771$	56.5387			2.03619
$772$		0			0
$773$	−0.918853	+	0.530500i	−0.0330488	+	0.0190808i	−0.516433	−	0.856327i	$-0.672741\pi$
$773$	−0.918853	+	0.530500i	−0.0330488	+	0.0190808i	0.483385	+	0.875408i	$0.339407\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	21.3259	+	31.3450i	0.765062	+	1.12449i
$778$		0			0
$779$	−12.6677	+	21.9410i	−0.453866	+	0.786120i
$780$		0			0
$781$	−25.8937	−	44.8492i	−0.926548	−	1.60483i
$782$		0			0
$783$			5.85388i			0.209200i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−34.9667	+	20.1880i	−1.24643	+	0.719625i	−0.970395	−	0.241524i	$-0.922353\pi$
$787$	−34.9667	+	20.1880i	−1.24643	+	0.719625i	−0.276032	+	0.961149i	$0.589020\pi$
$788$		0			0
$789$	−25.8119	+	44.7076i	−0.918929	+	1.59163i
$790$		0			0
$791$	−0.0358841	+	0.0244142i	−0.00127589	+	0.000868067i
$792$		0			0
$793$	−14.9521	−	8.63259i	−0.530964	−	0.306552i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	6.16436i		−	0.218353i	−0.994022	−	0.109176i	$-0.965179\pi$
$797$		−	6.16436i		−	0.218353i	0.994022	−	0.109176i	$-0.0348214\pi$
$798$		0			0
$799$	27.4278			0.970325
$800$		0			0
$801$	−2.80602	−	4.86018i	−0.0991460	−	0.171726i
$802$		0			0
$803$	−40.8091	−	23.5611i	−1.44012	−	0.831455i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	29.4928	+	17.0277i	1.03820	+	0.599403i
$808$		0			0
$809$	−14.0383	−	24.3151i	−0.493561	−	0.854873i	0.506411	−	0.862292i	$-0.330972\pi$
$809$	−14.0383	−	24.3151i	−0.493561	−	0.854873i	−0.999972	+	0.00741889i	$0.997638\pi$
$810$		0			0
$811$	−40.3175			−1.41574			−0.707869	−	0.706343i	$-0.750344\pi$
$811$	−40.3175			−1.41574			−0.707869	+	0.706343i	$0.750344\pi$
$812$		0			0
$813$			50.1984i			1.76053i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−33.9092	−	19.5775i	−1.18633	−	0.684929i
$818$		0			0
$819$	0.674697	+	9.12261i	0.0235758	+	0.318770i
$820$		0			0
$821$	−27.3300	+	47.3369i	−0.953823	+	1.65207i	−0.216786	+	0.976219i	$0.569557\pi$
$821$	−27.3300	+	47.3369i	−0.953823	+	1.65207i	−0.737038	+	0.675851i	$0.763776\pi$
$822$		0			0
$823$	−21.7097	+	12.5341i	−0.756752	+	0.436911i	−0.828128	−	0.560539i	$-0.810594\pi$
$823$	−21.7097	+	12.5341i	−0.756752	+	0.436911i	0.0713767	+	0.997449i	$0.477261\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			19.8101i			0.688866i	0.938811	+	0.344433i	$0.111929\pi$
$827$			19.8101i			0.688866i	−0.938811	+	0.344433i	$0.888071\pi$
$828$		0			0
$829$	10.1347	+	17.5537i	0.351991	+	0.609666i	0.986598	−	0.163169i	$-0.0521714\pi$
$829$	10.1347	+	17.5537i	0.351991	+	0.609666i	−0.634607	+	0.772835i	$0.718838\pi$
$830$		0			0
$831$	32.3172	−	55.9750i	1.12107	−	1.94175i
$832$		0			0
$833$	3.82929	+	25.7463i	0.132677	+	0.892058i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.45288	−	1.41617i	0.0847838	−	0.0489500i
$838$		0			0
$839$	−54.3873			−1.87766			−0.938829	−	0.344384i	$-0.888088\pi$
$839$	−54.3873			−1.87766			−0.938829	+	0.344384i	$0.888088\pi$
$840$		0			0
$841$	−26.5055			−0.913984
$842$		0			0
$843$	49.7037	−	28.6965i	1.71189	−	0.988359i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	4.49200	−	0.332223i	0.154347	−	0.0114153i
$848$		0			0
$849$	−30.3639	+	52.5918i	−1.04209	+	1.80495i
$850$		0			0
$851$	−10.8824	−	18.8489i	−0.373045	−	0.646134i
$852$		0			0
$853$			3.88160i			0.132903i	0.997790	+	0.0664517i	$0.0211678\pi$
$853$			3.88160i			0.132903i	−0.997790	+	0.0664517i	$0.978832\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	24.4068	−	14.0913i	0.833722	−	0.481350i	−0.0214033	−	0.999771i	$-0.506813\pi$
$857$	24.4068	−	14.0913i	0.833722	−	0.481350i	0.855125	+	0.518421i	$0.173480\pi$
$858$		0			0
$859$	9.25043	−	16.0222i	0.315621	−	0.546671i	−0.663949	−	0.747778i	$-0.731121\pi$
$859$	9.25043	−	16.0222i	0.315621	−	0.546671i	0.979569	+	0.201107i	$0.0644539\pi$
$860$		0			0
$861$	34.5170	+	16.6640i	1.17634	+	0.567908i
$862$		0			0
$863$	12.1809	+	7.03263i	0.414642	+	0.239394i	0.692782	−	0.721147i	$-0.256385\pi$
$863$	12.1809	+	7.03263i	0.414642	+	0.239394i	−0.278140	+	0.960540i	$0.589718\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	6.49365i		−	0.220536i
$868$		0			0
$869$	10.6375			0.360852
$870$		0			0
$871$	20.3564	+	35.2583i	0.689749	+	1.19468i
$872$		0			0
$873$	10.9750	+	6.33642i	0.371448	+	0.214455i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.7499	−	6.78383i	−0.396767	−	0.229074i	0.288321	−	0.957534i	$-0.406903\pi$
$877$	−11.7499	−	6.78383i	−0.396767	−	0.229074i	−0.685088	+	0.728460i	$0.740236\pi$
$878$		0			0
$879$	−9.65065	−	16.7154i	−0.325508	−	0.563797i
$880$		0			0
$881$	9.90324			0.333649			0.166824	−	0.985987i	$-0.446649\pi$
$881$	9.90324			0.333649			0.166824	+	0.985987i	$0.446649\pi$
$882$		0			0
$883$		−	27.4705i		−	0.924456i	−0.886761	−	0.462228i	$-0.847050\pi$
$883$		−	27.4705i		−	0.924456i	0.886761	−	0.462228i	$-0.152950\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	31.0434	+	17.9229i	1.04234	+	0.601793i	0.920494	−	0.390757i	$-0.127787\pi$
$887$	31.0434	+	17.9229i	1.04234	+	0.601793i	0.121842	+	0.992550i	$0.461120\pi$
$888$		0			0
$889$	34.7904	−	23.6700i	1.16683	−	0.793867i
$890$		0			0
$891$	−19.8755	+	34.4254i	−0.665855	+	1.15330i
$892$		0			0
$893$	−22.8645	+	13.2008i	−0.765131	+	0.441748i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	18.5007i		−	0.617721i
$898$		0			0
$899$	−0.603461	−	1.04522i	−0.0201265	−	0.0348602i
$900$		0			0
$901$	−6.18801	+	10.7179i	−0.206152	+	0.357067i
$902$		0			0
$903$	−25.7537	+	53.3449i	−0.857028	+	1.77521i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.53533	−	2.61847i	0.150593	−	0.0869450i	−0.422810	−	0.906218i	$-0.638956\pi$
$907$	4.53533	−	2.61847i	0.150593	−	0.0869450i	0.573403	+	0.819273i	$0.305623\pi$
$908$		0			0
$909$	9.69774			0.321654
$910$		0			0
$911$	−13.2519			−0.439054			−0.219527	−	0.975606i	$-0.570451\pi$
$911$	−13.2519			−0.439054			−0.219527	+	0.975606i	$0.570451\pi$
$912$		0			0
$913$	−33.6196	+	19.4103i	−1.11265	+	0.642387i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−48.1508	+	3.56117i	−1.59008	+	0.117600i
$918$		0			0
$919$	22.3200	−	38.6593i	0.736268	−	1.27525i	−0.217897	−	0.975972i	$-0.569920\pi$
$919$	22.3200	−	38.6593i	0.736268	−	1.27525i	0.954165	−	0.299282i	$-0.0967470\pi$
$920$		0			0
$921$	4.70541	+	8.15000i	0.155048	+	0.268552i
$922$		0			0
$923$			42.2489i			1.39064i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−9.62301	+	5.55585i	−0.316061	+	0.182478i
$928$		0			0
$929$	4.18107	−	7.24183i	0.137177	−	0.237597i	−0.789250	−	0.614072i	$-0.789531\pi$
$929$	4.18107	−	7.24183i	0.137177	−	0.237597i	0.926427	+	0.376475i	$0.122864\pi$
$930$		0			0
$931$	−15.5837	−	19.6198i	−0.510736	−	0.643012i
$932$		0			0
$933$	−2.62430	−	1.51514i	−0.0859156	−	0.0496034i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	2.76234i		−	0.0902416i	−0.998982	−	0.0451208i	$-0.985633\pi$
$937$		−	2.76234i		−	0.0902416i	0.998982	−	0.0451208i	$-0.0143673\pi$
$938$		0			0
$939$	35.0813			1.14484
$940$		0			0
$941$	7.86121	+	13.6160i	0.256268	+	0.443870i	0.965239	−	0.261368i	$-0.0841736\pi$
$941$	7.86121	+	13.6160i	0.256268	+	0.443870i	−0.708971	+	0.705238i	$0.750840\pi$
$942$		0			0
$943$	−19.0564	−	11.0022i	−0.620562	−	0.358281i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.1266	−	5.84661i	−0.329071	−	0.189989i	0.326358	−	0.945246i	$-0.394179\pi$
$947$	−10.1266	−	5.84661i	−0.329071	−	0.189989i	−0.655429	+	0.755257i	$0.727512\pi$
$948$		0			0
$949$	19.2216	+	33.2927i	0.623958	+	1.08073i
$950$		0			0
$951$	−14.0467			−0.455496
$952$		0			0
$953$			3.83507i			0.124230i	0.998069	+	0.0621151i	$0.0197846\pi$
$953$			3.83507i			0.124230i	−0.998069	+	0.0621151i	$0.980215\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	9.97754	+	5.76054i	0.322528	+	0.186212i
$958$		0			0
$959$	20.7286	+	10.0073i	0.669361	+	0.323152i
$960$		0			0
$961$	15.2080	−	26.3411i	0.490581	−	0.849712i
$962$		0			0
$963$	5.98401	−	3.45487i	0.192832	−	0.111332i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			37.3745i			1.20188i	0.799292	+	0.600942i	$0.205208\pi$
$967$			37.3745i			1.20188i	−0.799292	+	0.600942i	$0.794792\pi$
$968$		0			0
$969$	−13.6210	−	23.5922i	−0.437568	−	0.757891i
$970$		0			0
$971$	−22.2891	+	38.6059i	−0.715292	+	1.23892i	0.247554	+	0.968874i	$0.420373\pi$
$971$	−22.2891	+	38.6059i	−0.715292	+	1.23892i	−0.962847	+	0.270049i	$0.912960\pi$
$972$		0			0
$973$	−16.9258	−	24.8776i	−0.542615	−	0.797541i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.0560	+	6.38318i	−0.353712	+	0.204216i	−0.666319	−	0.745667i	$-0.732131\pi$
$977$	−11.0560	+	6.38318i	−0.353712	+	0.204216i	0.312607	+	0.949883i	$0.398798\pi$
$978$		0			0
$979$	16.8208			0.537595
$980$		0			0
$981$	17.4992			0.558706
$982$		0			0
$983$	−13.6521	+	7.88206i	−0.435435	+	0.251399i	−0.701659	−	0.712512i	$-0.747557\pi$
$983$	−13.6521	+	7.88206i	−0.435435	+	0.251399i	0.266224	+	0.963911i	$0.414224\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	22.4680	+	33.0237i	0.715165	+	1.05116i
$988$		0			0
$989$	17.0036	−	29.4510i	0.540682	−	0.936488i
$990$		0			0
$991$	0.785809	+	1.36106i	0.0249620	+	0.0432355i	0.878237	−	0.478226i	$-0.158720\pi$
$991$	0.785809	+	1.36106i	0.0249620	+	0.0432355i	−0.853275	+	0.521462i	$0.825387\pi$
$992$		0			0
$993$			6.99441i			0.221961i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	19.6906	−	11.3683i	0.623606	−	0.360039i	−0.154665	−	0.987967i	$-0.549430\pi$
$997$	19.6906	−	11.3683i	0.623606	−	0.360039i	0.778272	+	0.627928i	$0.216097\pi$
$998$		0			0
$999$	12.9745	−	22.4724i	0.410493	−	0.710996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.j.849.2		16
5.2	odd	4		1400.2.q.l.401.4	✓	8
5.3	odd	4		1400.2.q.m.401.1	yes	8
5.4	even	2	inner	1400.2.bh.j.849.7		16
7.4	even	3	inner	1400.2.bh.j.249.7		16
35.2	odd	12		9800.2.a.ct.1.1		4
35.4	even	6	inner	1400.2.bh.j.249.2		16
35.12	even	12		9800.2.a.ck.1.4		4
35.18	odd	12		1400.2.q.m.1201.1	yes	8
35.23	odd	12		9800.2.a.cj.1.4		4
35.32	odd	12		1400.2.q.l.1201.4	yes	8
35.33	even	12		9800.2.a.cu.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.l.401.4	✓	8	5.2	odd	4
1400.2.q.l.1201.4	yes	8	35.32	odd	12
1400.2.q.m.401.1	yes	8	5.3	odd	4
1400.2.q.m.1201.1	yes	8	35.18	odd	12
1400.2.bh.j.249.2		16	35.4	even	6	inner
1400.2.bh.j.249.7		16	7.4	even	3	inner
1400.2.bh.j.849.2		16	1.1	even	1	trivial
1400.2.bh.j.849.7		16	5.4	even	2	inner
9800.2.a.cj.1.4		4	35.23	odd	12
9800.2.a.ck.1.4		4	35.12	even	12
9800.2.a.ct.1.1		4	35.2	odd	12
9800.2.a.cu.1.1		4	35.33	even	12

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.77252 + 1.02336i) q^{3} +(-1.48827 - 2.18747i) q^{7} +(0.594550 - 1.02979i) q^{9} +O(q^{10})\)	\(q+(-1.77252 + 1.02336i) q^{3} +(-1.48827 - 2.18747i) q^{7} +(0.594550 - 1.02979i) q^{9} +(1.78203 + 3.08656i) q^{11} -2.90761i q^{13} +(3.22032 - 1.85925i) q^{17} +(-1.78969 + 3.09984i) q^{19} +(4.87658 + 2.35430i) q^{21} +(-2.69230 - 1.55440i) q^{23} -3.70642i q^{27} -1.57939 q^{29} +(0.382085 + 0.661791i) q^{31} +(-6.31735 - 3.64732i) q^{33} +(6.06310 + 3.50053i) q^{37} +(2.97554 + 5.15379i) q^{39} +7.07812 q^{41} +10.9390i q^{43} +(6.38782 + 3.68801i) q^{47} +(-2.57009 + 6.51111i) q^{49} +(-3.80539 + 6.59113i) q^{51} +(-2.88232 + 1.66411i) q^{53} -7.32604i q^{57} +(4.07009 + 7.04961i) q^{59} +(2.96897 - 5.14240i) q^{61} +(-3.13749 + 0.232045i) q^{63} +(-12.1262 + 7.00107i) q^{67} +6.36286 q^{69} -14.5305 q^{71} +(-11.4502 + 6.61078i) q^{73} +(4.09963 - 8.49177i) q^{77} +(1.49233 - 2.58479i) q^{79} +(5.57667 + 9.65908i) q^{81} +10.8923i q^{83} +(2.79950 - 1.61629i) q^{87} +(2.35979 - 4.08727i) q^{89} +(-6.36032 + 4.32731i) q^{91} +(-1.35451 - 0.782025i) q^{93} +10.6575i q^{97} +4.23801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 20 q^{19} + 50 q^{21} - 8 q^{29} + 28 q^{31} - 20 q^{39} - 16 q^{41} + 26 q^{49} - 10 q^{51} - 2 q^{59} + 50 q^{61} + 64 q^{69} - 80 q^{71} + 4 q^{79} - 48 q^{81} - 38 q^{89} + 34 q^{91} + 204 q^{99}+O(q^{100}) \) 16 * q + 10 * q^9 - 20 * q^19 + 50 * q^21 - 8 * q^29 + 28 * q^31 - 20 * q^39 - 16 * q^41 + 26 * q^49 - 10 * q^51 - 2 * q^59 + 50 * q^61 + 64 * q^69 - 80 * q^71 + 4 * q^79 - 48 * q^81 - 38 * q^89 + 34 * q^91 + 204 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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