LMFDB - Embedded newform 1400.2.q.h.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(401,1400)]

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, 0, 2]))

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

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

chi := DirichletCharacter("1400.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1400.1201
Dual form			1400.2.q.h.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 + 2.09077i) q^{3} +(2.62132 + 0.358719i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})$	$q+(-1.20711 + 2.09077i) q^{3} +(2.62132 + 0.358719i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(2.41421 - 4.18154i) q^{11} -2.00000 q^{13} +(1.82843 - 3.16693i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-3.91421 + 5.04757i) q^{21} +(-4.20711 - 7.28692i) q^{23} -0.414214 q^{27} -2.17157 q^{29} +(2.41421 - 4.18154i) q^{31} +(5.82843 + 10.0951i) q^{33} +(-2.82843 - 4.89898i) q^{37} +(2.41421 - 4.18154i) q^{39} +0.171573 q^{41} -12.8995 q^{43} +(0.171573 + 0.297173i) q^{47} +(6.74264 + 1.88064i) q^{49} +(4.41421 + 7.64564i) q^{51} +(2.82843 - 4.89898i) q^{53} +13.6569 q^{57} +(2.00000 - 3.46410i) q^{59} +(2.32843 + 4.03295i) q^{61} +(-2.82843 - 6.92820i) q^{63} +(3.44975 - 5.97514i) q^{67} +20.3137 q^{69} -12.0000 q^{71} +(-3.82843 + 6.63103i) q^{73} +(7.82843 - 10.0951i) q^{77} +(2.00000 + 3.46410i) q^{79} +(4.74264 - 8.21449i) q^{81} +13.2426 q^{83} +(2.62132 - 4.54026i) q^{87} +(8.32843 + 14.4253i) q^{89} +(-5.24264 - 0.717439i) q^{91} +(5.82843 + 10.0951i) q^{93} -6.00000 q^{97} -13.6569 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^7	$ 4 q - 2 q^{3} + 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{17} - 10 q^{21} - 14 q^{23} + 4 q^{27} - 20 q^{29} + 4 q^{31} + 12 q^{33} + 4 q^{39} + 12 q^{41} - 12 q^{43} + 12 q^{47} + 10 q^{49} + 12 q^{51} + 32 q^{57} + 8 q^{59} - 2 q^{61} - 6 q^{67} + 36 q^{69} - 48 q^{71} - 4 q^{73} + 20 q^{77} + 8 q^{79} + 2 q^{81} + 36 q^{83} + 2 q^{87} + 22 q^{89} - 4 q^{91} + 12 q^{93} - 24 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^7 + 4 * q^11 - 8 * q^13 - 4 * q^17 - 10 * q^21 - 14 * q^23 + 4 * q^27 - 20 * q^29 + 4 * q^31 + 12 * q^33 + 4 * q^39 + 12 * q^41 - 12 * q^43 + 12 * q^47 + 10 * q^49 + 12 * q^51 + 32 * q^57 + 8 * q^59 - 2 * q^61 - 6 * q^67 + 36 * q^69 - 48 * q^71 - 4 * q^73 + 20 * q^77 + 8 * q^79 + 2 * q^81 + 36 * q^83 + 2 * q^87 + 22 * q^89 - 4 * q^91 + 12 * q^93 - 24 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	0.272605	+	0.962126i	$0.412115\pi$
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	−0.969528	+	0.244981i	$0.921218\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$7$	2.62132	+	0.358719i	0.990766	+	0.135583i
$8$		0			0
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	2.41421	−	4.18154i	0.727913	−	1.26078i	−0.229851	−	0.973226i	$-0.573824\pi$
$11$	2.41421	−	4.18154i	0.727913	−	1.26078i	0.957764	−	0.287556i	$-0.0928428\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.82843	−	3.16693i	0.443459	−	0.768093i	−0.554485	−	0.832194i	$-0.687085\pi$
$17$	1.82843	−	3.16693i	0.443459	−	0.768093i	0.997943	+	0.0641009i	$0.0204179\pi$
$18$		0			0
$19$	−2.82843	−	4.89898i	−0.648886	−	1.12390i	−0.983389	−	0.181509i	$-0.941902\pi$
$19$	−2.82843	−	4.89898i	−0.648886	−	1.12390i	0.334504	−	0.942394i	$-0.391431\pi$
$20$		0			0
$21$	−3.91421	+	5.04757i	−0.854151	+	1.10147i
$22$		0			0
$23$	−4.20711	−	7.28692i	−0.877242	−	1.51943i	−0.854355	−	0.519690i	$-0.826047\pi$
$23$	−4.20711	−	7.28692i	−0.877242	−	1.51943i	−0.0228877	−	0.999738i	$-0.507286\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	−2.17157			−0.403251			−0.201625	−	0.979463i	$-0.564622\pi$
$29$	−2.17157			−0.403251			−0.201625	+	0.979463i	$0.564622\pi$
$30$		0			0
$31$	2.41421	−	4.18154i	0.433606	−	0.751027i	−0.563575	−	0.826065i	$-0.690574\pi$
$31$	2.41421	−	4.18154i	0.433606	−	0.751027i	0.997181	+	0.0750380i	$0.0239078\pi$
$32$		0			0
$33$	5.82843	+	10.0951i	1.01460	+	1.75734i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.82843	−	4.89898i	−0.464991	−	0.805387i	0.534211	−	0.845351i	$-0.320609\pi$
$37$	−2.82843	−	4.89898i	−0.464991	−	0.805387i	−0.999201	+	0.0399642i	$0.987276\pi$
$38$		0			0
$39$	2.41421	−	4.18154i	0.386584	−	0.669582i
$40$		0			0
$41$	0.171573			0.0267952			0.0133976	−	0.999910i	$-0.495735\pi$
$41$	0.171573			0.0267952			0.0133976	+	0.999910i	$0.495735\pi$
$42$		0			0
$43$	−12.8995			−1.96715			−0.983577	−	0.180488i	$-0.942232\pi$
$43$	−12.8995			−1.96715			−0.983577	+	0.180488i	$0.942232\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.171573	+	0.297173i	0.0250265	+	0.0433471i	0.878267	−	0.478170i	$-0.158700\pi$
$47$	0.171573	+	0.297173i	0.0250265	+	0.0433471i	−0.853241	+	0.521517i	$0.825366\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$	4.41421	+	7.64564i	0.618114	+	1.07060i
$52$		0			0
$53$	2.82843	−	4.89898i	0.388514	−	0.672927i	−0.603736	−	0.797185i	$-0.706322\pi$
$53$	2.82843	−	4.89898i	0.388514	−	0.672927i	0.992250	+	0.124258i	$0.0396551\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	13.6569			1.80889
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	2.32843	+	4.03295i	0.298125	+	0.516367i	0.975707	−	0.219080i	$-0.0703056\pi$
$61$	2.32843	+	4.03295i	0.298125	+	0.516367i	−0.677582	+	0.735447i	$0.736972\pi$
$62$		0			0
$63$	−2.82843	−	6.92820i	−0.356348	−	0.872872i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.44975	−	5.97514i	0.421454	−	0.729979i	−0.574628	−	0.818415i	$-0.694853\pi$
$67$	3.44975	−	5.97514i	0.421454	−	0.729979i	0.996082	+	0.0884353i	$0.0281867\pi$
$68$		0			0
$69$	20.3137			2.44548
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−3.82843	+	6.63103i	−0.448084	+	0.776103i	−0.998261	−	0.0589442i	$-0.981227\pi$
$73$	−3.82843	+	6.63103i	−0.448084	+	0.776103i	0.550178	+	0.835048i	$0.314560\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.82843	−	10.0951i	0.892132	−	1.15045i
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$		0			0
$83$	13.2426			1.45357			0.726784	−	0.686866i	$-0.241014\pi$
$83$	13.2426			1.45357			0.726784	+	0.686866i	$0.241014\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.62132	−	4.54026i	0.281035	−	0.486767i
$88$		0			0
$89$	8.32843	+	14.4253i	0.882812	+	1.52907i	0.848202	+	0.529673i	$0.177686\pi$
$89$	8.32843	+	14.4253i	0.882812	+	1.52907i	0.0346099	+	0.999401i	$0.488981\pi$
$90$		0			0
$91$	−5.24264	−	0.717439i	−0.549578	−	0.0752080i
$92$		0			0
$93$	5.82843	+	10.0951i	0.604380	+	1.04682i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$	−13.6569			−1.37257
$100$		0			0
$101$	−2.74264	+	4.75039i	−0.272903	+	0.472682i	−0.969604	−	0.244680i	$-0.921317\pi$
$101$	−2.74264	+	4.75039i	−0.272903	+	0.472682i	0.696701	+	0.717362i	$0.254650\pi$
$102$		0			0
$103$	5.20711	+	9.01897i	0.513071	+	0.888666i	0.999885	+	0.0151600i	$0.00482576\pi$
$103$	5.20711	+	9.01897i	0.513071	+	0.888666i	−0.486814	+	0.873506i	$0.661841\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.20711	−	7.28692i	−0.406716	−	0.704453i	0.587803	−	0.809004i	$-0.299993\pi$
$107$	−4.20711	−	7.28692i	−0.406716	−	0.704453i	−0.994520	+	0.104551i	$0.966660\pi$
$108$		0			0
$109$	2.15685	−	3.73578i	0.206589	−	0.357823i	−0.744049	−	0.668125i	$-0.767097\pi$
$109$	2.15685	−	3.73578i	0.206589	−	0.357823i	0.950638	+	0.310302i	$0.100430\pi$
$110$		0			0
$111$	13.6569			1.29625
$112$		0			0
$113$	11.3137			1.06430			0.532152	−	0.846649i	$-0.321383\pi$
$113$	11.3137			1.06430			0.532152	+	0.846649i	$0.321383\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.82843	+	4.89898i	0.261488	+	0.452911i
$118$		0			0
$119$	5.92893	−	7.64564i	0.543504	−	0.700875i
$120$		0			0
$121$	−6.15685	−	10.6640i	−0.559714	−	0.969453i
$122$		0			0
$123$	−0.207107	+	0.358719i	−0.0186742	+	0.0323446i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	15.6569			1.38932			0.694661	−	0.719338i	$-0.255555\pi$
$127$	15.6569			1.38932			0.694661	+	0.719338i	$0.255555\pi$
$128$		0			0
$129$	15.5711	−	26.9699i	1.37096	−	2.37457i
$130$		0			0
$131$	−1.17157	−	2.02922i	−0.102361	−	0.177294i	0.810296	−	0.586021i	$-0.199306\pi$
$131$	−1.17157	−	2.02922i	−0.102361	−	0.177294i	−0.912657	+	0.408727i	$0.865973\pi$
$132$		0			0
$133$	−5.65685	−	13.8564i	−0.490511	−	1.20150i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$		0			0
$139$	−14.4853			−1.22863			−0.614313	−	0.789063i	$-0.710567\pi$
$139$	−14.4853			−1.22863			−0.614313	+	0.789063i	$0.710567\pi$
$140$		0			0
$141$	−0.828427			−0.0697661
$142$		0			0
$143$	−4.82843	+	8.36308i	−0.403773	+	0.699356i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−12.0711	+	11.8272i	−0.995605	+	0.975490i
$148$		0			0
$149$	3.32843	+	5.76500i	0.272675	+	0.472288i	0.969546	−	0.244909i	$-0.0787582\pi$
$149$	3.32843	+	5.76500i	0.272675	+	0.472288i	−0.696871	+	0.717197i	$0.745425\pi$
$150$		0			0
$151$	8.41421	−	14.5738i	0.684739	−	1.18600i	−0.288780	−	0.957396i	$-0.593250\pi$
$151$	8.41421	−	14.5738i	0.684739	−	1.18600i	0.973519	−	0.228607i	$-0.0734171\pi$
$152$		0			0
$153$	−10.3431			−0.836194
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−10.6569	+	18.4582i	−0.850510	+	1.47313i	0.0302396	+	0.999543i	$0.490373\pi$
$157$	−10.6569	+	18.4582i	−0.850510	+	1.47313i	−0.880749	+	0.473583i	$0.842960\pi$
$158$		0			0
$159$	6.82843	+	11.8272i	0.541529	+	0.937957i
$160$		0			0
$161$	−8.41421	−	20.6105i	−0.663133	−	1.62434i
$162$		0			0
$163$	−2.17157	−	3.76127i	−0.170091	−	0.294606i	0.768361	−	0.640017i	$-0.221073\pi$
$163$	−2.17157	−	3.76127i	−0.170091	−	0.294606i	−0.938451	+	0.345411i	$0.887739\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.0711			0.934087			0.467044	−	0.884234i	$-0.345319\pi$
$167$	12.0711			0.934087			0.467044	+	0.884234i	$0.345319\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−8.00000	+	13.8564i	−0.611775	+	1.05963i
$172$		0			0
$173$	10.8284	+	18.7554i	0.823270	+	1.42595i	0.903234	+	0.429148i	$0.141186\pi$
$173$	10.8284	+	18.7554i	0.823270	+	1.42595i	−0.0799642	+	0.996798i	$0.525481\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.82843	+	8.36308i	0.362927	+	0.628608i
$178$		0			0
$179$	−5.24264	+	9.08052i	−0.391853	+	0.678710i	−0.992694	−	0.120659i	$-0.961499\pi$
$179$	−5.24264	+	9.08052i	−0.391853	+	0.678710i	0.600841	+	0.799369i	$0.294833\pi$
$180$		0			0
$181$	−9.82843			−0.730541			−0.365271	−	0.930901i	$-0.619024\pi$
$181$	−9.82843			−0.730541			−0.365271	+	0.930901i	$0.619024\pi$
$182$		0			0
$183$	−11.2426			−0.831080
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.82843	−	15.2913i	−0.645599	−	1.11821i
$188$		0			0
$189$	−1.08579	−	0.148586i	−0.0789793	−	0.0108081i
$190$		0			0
$191$	11.2426	+	19.4728i	0.813489	+	1.40900i	0.910408	+	0.413712i	$0.135768\pi$
$191$	11.2426	+	19.4728i	0.813489	+	1.40900i	−0.0969189	+	0.995292i	$0.530899\pi$
$192$		0			0
$193$	8.65685	−	14.9941i	0.623134	−	1.07930i	−0.365765	−	0.930707i	$-0.619192\pi$
$193$	8.65685	−	14.9941i	0.623134	−	1.07930i	0.988899	−	0.148592i	$-0.0474742\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.6569			−0.830516			−0.415258	−	0.909704i	$-0.636309\pi$
$197$	−11.6569			−0.830516			−0.415258	+	0.909704i	$0.636309\pi$
$198$		0			0
$199$	0.343146	−	0.594346i	0.0243250	−	0.0421321i	−0.853607	−	0.520918i	$-0.825590\pi$
$199$	0.343146	−	0.594346i	0.0243250	−	0.0421321i	0.877932	+	0.478786i	$0.158923\pi$
$200$		0			0
$201$	8.32843	+	14.4253i	0.587442	+	1.01748i
$202$		0			0
$203$	−5.69239	−	0.778985i	−0.399527	−	0.0546741i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−11.8995	+	20.6105i	−0.827072	+	1.43253i
$208$		0			0
$209$	−27.3137			−1.88933
$210$		0			0
$211$	−18.6274			−1.28236			−0.641182	−	0.767389i	$-0.721556\pi$
$211$	−18.6274			−1.28236			−0.641182	+	0.767389i	$0.721556\pi$
$212$		0			0
$213$	14.4853	−	25.0892i	0.992515	−	1.71909i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	7.82843	−	10.0951i	0.531428	−	0.685302i
$218$		0			0
$219$	−9.24264	−	16.0087i	−0.624560	−	1.08177i
$220$		0			0
$221$	−3.65685	+	6.33386i	−0.245987	+	0.426061i
$222$		0			0
$223$	−18.9706			−1.27036			−0.635181	−	0.772363i	$-0.719075\pi$
$223$	−18.9706			−1.27036			−0.635181	+	0.772363i	$0.719075\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	−0.534577	−	0.845120i	$-0.679529\pi$
$227$	7.00000	−	12.1244i	0.464606	−	0.804722i	0.999184	+	0.0403978i	$0.0128625\pi$
$228$		0			0
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$	11.6569	+	28.5533i	0.766965	+	1.87867i
$232$		0			0
$233$	0.171573	+	0.297173i	0.0112401	+	0.0194684i	0.871591	−	0.490234i	$-0.163089\pi$
$233$	0.171573	+	0.297173i	0.0112401	+	0.0194684i	−0.860351	+	0.509703i	$0.829755\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.65685			−0.627280
$238$		0			0
$239$	−13.5147			−0.874194			−0.437097	−	0.899414i	$-0.643993\pi$
$239$	−13.5147			−0.874194			−0.437097	+	0.899414i	$0.643993\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$		0			0
$243$	10.8284	+	18.7554i	0.694644	+	1.20316i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.65685	+	9.79796i	0.359937	+	0.623429i
$248$		0			0
$249$	−15.9853	+	27.6873i	−1.01303	+	1.75461i
$250$		0			0
$251$	23.4558			1.48052			0.740260	−	0.672321i	$-0.234702\pi$
$251$	23.4558			1.48052			0.740260	+	0.672321i	$0.234702\pi$
$252$		0			0
$253$	−40.6274			−2.55422
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.65685	−	6.33386i	−0.228108	−	0.395095i	0.729139	−	0.684365i	$-0.239921\pi$
$257$	−3.65685	−	6.33386i	−0.228108	−	0.395095i	−0.957247	+	0.289270i	$0.906587\pi$
$258$		0			0
$259$	−5.65685	−	13.8564i	−0.351500	−	0.860995i
$260$		0			0
$261$	3.07107	+	5.31925i	0.190094	+	0.329253i
$262$		0			0
$263$	4.86396	−	8.42463i	0.299925	−	0.519485i	−0.676194	−	0.736724i	$-0.736372\pi$
$263$	4.86396	−	8.42463i	0.299925	−	0.519485i	0.976118	+	0.217239i	$0.0697051\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−40.2132			−2.46101
$268$		0			0
$269$	−2.32843	+	4.03295i	−0.141967	+	0.245894i	−0.928237	−	0.371989i	$-0.878676\pi$
$269$	−2.32843	+	4.03295i	−0.141967	+	0.245894i	0.786270	+	0.617882i	$0.212009\pi$
$270$		0			0
$271$	−9.65685	−	16.7262i	−0.586612	−	1.01604i	−0.994672	−	0.103087i	$-0.967128\pi$
$271$	−9.65685	−	16.7262i	−0.586612	−	1.01604i	0.408060	−	0.912955i	$-0.366205\pi$
$272$		0			0
$273$	7.82843	−	10.0951i	0.473798	−	0.610985i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−8.31371	+	14.3998i	−0.499522	+	0.865198i	−1.00000		0.000551476i	$-0.999824\pi$
$277$	−8.31371	+	14.3998i	−0.499522	+	0.865198i	0.500478	+	0.865750i	$0.333158\pi$
$278$		0			0
$279$	−13.6569			−0.817614
$280$		0			0
$281$	25.3137			1.51009			0.755045	−	0.655673i	$-0.227615\pi$
$281$	25.3137			1.51009			0.755045	+	0.655673i	$0.227615\pi$
$282$		0			0
$283$	9.00000	−	15.5885i	0.534994	−	0.926638i	−0.464169	−	0.885747i	$-0.653647\pi$
$283$	9.00000	−	15.5885i	0.534994	−	0.926638i	0.999164	−	0.0408910i	$-0.0130196\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.449747	+	0.0615465i	0.0265478	+	0.00363298i
$288$		0			0
$289$	1.81371	+	3.14144i	0.106689	+	0.184790i
$290$		0			0
$291$	7.24264	−	12.5446i	0.424571	−	0.735379i
$292$		0			0
$293$	16.9706			0.991431			0.495715	−	0.868485i	$-0.334906\pi$
$293$	16.9706			0.991431			0.495715	+	0.868485i	$0.334906\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$		0			0
$299$	8.41421	+	14.5738i	0.486607	+	0.842827i
$300$		0			0
$301$	−33.8137	−	4.62730i	−1.94899	−	0.266713i
$302$		0			0
$303$	−6.62132	−	11.4685i	−0.380385	−	0.658846i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−13.2426			−0.755797			−0.377899	−	0.925847i	$-0.623353\pi$
$307$	−13.2426			−0.755797			−0.377899	+	0.925847i	$0.623353\pi$
$308$		0			0
$309$	−25.1421			−1.43029
$310$		0			0
$311$	−5.17157	+	8.95743i	−0.293253	+	0.507929i	−0.974577	−	0.224053i	$-0.928071\pi$
$311$	−5.17157	+	8.95743i	−0.293253	+	0.507929i	0.681324	+	0.731982i	$0.261404\pi$
$312$		0			0
$313$	−6.48528	−	11.2328i	−0.366570	−	0.634917i	0.622457	−	0.782654i	$-0.286135\pi$
$313$	−6.48528	−	11.2328i	−0.366570	−	0.634917i	−0.989027	+	0.147737i	$0.952801\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	−0.989882	−	0.141890i	$-0.954682\pi$
$317$	−11.0000	−	19.0526i	−0.617822	−	1.07010i	0.372061	−	0.928208i	$-0.378651\pi$
$318$		0			0
$319$	−5.24264	+	9.08052i	−0.293532	+	0.508412i
$320$		0			0
$321$	20.3137			1.13380
$322$		0			0
$323$	−20.6863			−1.15102
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.20711	+	9.01897i	0.287954	+	0.498750i
$328$		0			0
$329$	0.343146	+	0.840532i	0.0189182	+	0.0463400i
$330$		0			0
$331$	−4.75736	−	8.23999i	−0.261488	−	0.452911i	0.705149	−	0.709059i	$-0.250880\pi$
$331$	−4.75736	−	8.23999i	−0.261488	−	0.452911i	−0.966638	+	0.256148i	$0.917547\pi$
$332$		0			0
$333$	−8.00000	+	13.8564i	−0.438397	+	0.759326i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.97056			0.488658			0.244329	−	0.969692i	$-0.421432\pi$
$337$	8.97056			0.488658			0.244329	+	0.969692i	$0.421432\pi$
$338$		0			0
$339$	−13.6569	+	23.6544i	−0.741739	+	1.28473i
$340$		0			0
$341$	−11.6569	−	20.1903i	−0.631254	−	1.09336i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.6924	+	21.9839i	−0.681363	+	1.18016i	0.293202	+	0.956051i	$0.405279\pi$
$347$	−12.6924	+	21.9839i	−0.681363	+	1.18016i	−0.974565	+	0.224105i	$0.928054\pi$
$348$		0			0
$349$	4.17157			0.223299			0.111650	−	0.993748i	$-0.464387\pi$
$349$	4.17157			0.223299			0.111650	+	0.993748i	$0.464387\pi$
$350$		0			0
$351$	0.828427			0.0442182
$352$		0			0
$353$	11.1716	−	19.3497i	0.594603	−	1.02988i	−0.399000	−	0.916951i	$-0.630643\pi$
$353$	11.1716	−	19.3497i	0.594603	−	1.02988i	0.993603	−	0.112931i	$-0.0360240\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.82843	+	21.6251i	0.467250	+	1.14452i
$358$		0			0
$359$	−5.24264	−	9.08052i	−0.276696	−	0.479252i	0.693866	−	0.720105i	$-0.255906\pi$
$359$	−5.24264	−	9.08052i	−0.276696	−	0.479252i	−0.970562	+	0.240853i	$0.922573\pi$
$360$		0			0
$361$	−6.50000	+	11.2583i	−0.342105	+	0.592544i
$362$		0			0
$363$	29.7279			1.56031
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.2071	−	21.1433i	0.637206	−	1.10367i	−0.348837	−	0.937183i	$-0.613423\pi$
$367$	12.2071	−	21.1433i	0.637206	−	1.10367i	0.986043	−	0.166490i	$-0.0532432\pi$
$368$		0			0
$369$	−0.242641	−	0.420266i	−0.0126314	−	0.0218782i
$370$		0			0
$371$	9.17157	−	11.8272i	0.476164	−	0.614037i
$372$		0			0
$373$	6.00000	+	10.3923i	0.310668	+	0.538093i	0.978507	−	0.206213i	$-0.0661139\pi$
$373$	6.00000	+	10.3923i	0.310668	+	0.538093i	−0.667839	+	0.744306i	$0.732781\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.34315			0.223683
$378$		0			0
$379$	27.3137			1.40301			0.701505	−	0.712664i	$-0.252512\pi$
$379$	27.3137			1.40301			0.701505	+	0.712664i	$0.252512\pi$
$380$		0			0
$381$	−18.8995	+	32.7349i	−0.968250	+	1.67706i
$382$		0			0
$383$	9.44975	+	16.3674i	0.482860	+	0.836337i	0.999806	−	0.0196803i	$-0.00626483\pi$
$383$	9.44975	+	16.3674i	0.482860	+	0.836337i	−0.516947	+	0.856018i	$0.672931\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	18.2426	+	31.5972i	0.927326	+	1.60617i
$388$		0			0
$389$	8.65685	−	14.9941i	0.438920	−	0.760232i	−0.558687	−	0.829379i	$-0.688695\pi$
$389$	8.65685	−	14.9941i	0.438920	−	0.760232i	0.997606	+	0.0691473i	$0.0220278\pi$
$390$		0			0
$391$	−30.7696			−1.55608
$392$		0			0
$393$	5.65685			0.285351
$394$		0			0
$395$		0			0
$396$		0			0
$397$	10.3137	+	17.8639i	0.517630	+	0.896562i	0.999790	+	0.0204787i	$0.00651902\pi$
$397$	10.3137	+	17.8639i	0.517630	+	0.896562i	−0.482160	+	0.876083i	$0.660148\pi$
$398$		0			0
$399$	35.7990	+	4.89898i	1.79219	+	0.245256i
$400$		0			0
$401$	4.84315	+	8.38857i	0.241855	+	0.418905i	0.961243	−	0.275703i	$-0.0889108\pi$
$401$	4.84315	+	8.38857i	0.241855	+	0.418905i	−0.719388	+	0.694609i	$0.755577\pi$
$402$		0			0
$403$	−4.82843	+	8.36308i	−0.240521	+	0.416595i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−27.3137			−1.35389
$408$		0			0
$409$	−1.57107	+	2.72117i	−0.0776843	+	0.134553i	−0.902250	−	0.431212i	$-0.858086\pi$
$409$	−1.57107	+	2.72117i	−0.0776843	+	0.134553i	0.824566	+	0.565766i	$0.191419\pi$
$410$		0			0
$411$	−4.82843	−	8.36308i	−0.238169	−	0.412520i
$412$		0			0
$413$	6.48528	−	8.36308i	0.319120	−	0.411520i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	17.4853	−	30.2854i	0.856258	−	1.48308i
$418$		0			0
$419$	7.31371			0.357298			0.178649	−	0.983913i	$-0.442827\pi$
$419$	7.31371			0.357298			0.178649	+	0.983913i	$0.442827\pi$
$420$		0			0
$421$	38.6569			1.88402			0.942010	−	0.335585i	$-0.108934\pi$
$421$	38.6569			1.88402			0.942010	+	0.335585i	$0.108934\pi$
$422$		0			0
$423$	0.485281	−	0.840532i	0.0235952	−	0.0408681i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.65685	+	11.4069i	0.225361	+	0.552019i
$428$		0			0
$429$	−11.6569	−	20.1903i	−0.562798	−	0.974795i
$430$		0			0
$431$	−2.41421	+	4.18154i	−0.116289	+	0.201418i	−0.918294	−	0.395899i	$-0.870433\pi$
$431$	−2.41421	+	4.18154i	−0.116289	+	0.201418i	0.802006	+	0.597317i	$0.203766\pi$
$432$		0			0
$433$	−3.31371			−0.159247			−0.0796233	−	0.996825i	$-0.525372\pi$
$433$	−3.31371			−0.159247			−0.0796233	+	0.996825i	$0.525372\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.7990	+	41.2211i	−1.13846	+	1.97187i
$438$		0			0
$439$	14.8284	+	25.6836i	0.707722	+	1.22581i	0.965700	+	0.259660i	$0.0836105\pi$
$439$	14.8284	+	25.6836i	0.707722	+	1.22581i	−0.257978	+	0.966151i	$0.583056\pi$
$440$		0			0
$441$	−4.92893	−	19.1757i	−0.234711	−	0.913126i
$442$		0			0
$443$	−9.20711	−	15.9472i	−0.437443	−	0.757673i	0.560049	−	0.828460i	$-0.310782\pi$
$443$	−9.20711	−	15.9472i	−0.437443	−	0.757673i	−0.997491	+	0.0707865i	$0.977449\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−16.0711			−0.760135
$448$		0			0
$449$	9.48528			0.447638			0.223819	−	0.974631i	$-0.428148\pi$
$449$	9.48528			0.447638			0.223819	+	0.974631i	$0.428148\pi$
$450$		0			0
$451$	0.414214	−	0.717439i	0.0195046	−	0.0337829i
$452$		0			0
$453$	20.3137	+	35.1844i	0.954421	+	1.65311i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.48528	−	4.30463i	−0.116257	−	0.201362i	0.802025	−	0.597291i	$-0.203756\pi$
$457$	−2.48528	−	4.30463i	−0.116257	−	0.201362i	−0.918281	+	0.395928i	$0.870423\pi$
$458$		0			0
$459$	−0.757359	+	1.31178i	−0.0353505	+	0.0612289i
$460$		0			0
$461$	−21.3137			−0.992678			−0.496339	−	0.868129i	$-0.665323\pi$
$461$	−21.3137			−0.992678			−0.496339	+	0.868129i	$0.665323\pi$
$462$		0			0
$463$	4.89949			0.227699			0.113849	−	0.993498i	$-0.463682\pi$
$463$	4.89949			0.227699			0.113849	+	0.993498i	$0.463682\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	7.93503	+	13.7439i	0.367189	+	0.635991i	0.989125	−	0.147078i	$-0.0469868\pi$
$467$	7.93503	+	13.7439i	0.367189	+	0.635991i	−0.621936	+	0.783068i	$0.713653\pi$
$468$		0			0
$469$	11.1863	−	14.4253i	0.516535	−	0.666097i
$470$		0			0
$471$	−25.7279	−	44.5621i	−1.18548	−	2.05331i
$472$		0			0
$473$	−31.1421	+	53.9398i	−1.43192	+	2.48015i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−16.0000			−0.732590
$478$		0			0
$479$	9.24264	−	16.0087i	0.422307	−	0.731457i	−0.573858	−	0.818955i	$-0.694554\pi$
$479$	9.24264	−	16.0087i	0.422307	−	0.731457i	0.996165	+	0.0874978i	$0.0278871\pi$
$480$		0			0
$481$	5.65685	+	9.79796i	0.257930	+	0.446748i
$482$		0			0
$483$	53.2487	+	7.28692i	2.42290	+	0.331566i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.14214	−	15.8346i	0.414270	−	0.717536i	−0.581082	−	0.813845i	$-0.697370\pi$
$487$	9.14214	−	15.8346i	0.414270	−	0.717536i	0.995351	+	0.0963090i	$0.0307037\pi$
$488$		0			0
$489$	10.4853			0.474161
$490$		0			0
$491$	18.4853			0.834229			0.417115	−	0.908854i	$-0.363041\pi$
$491$	18.4853			0.834229			0.417115	+	0.908854i	$0.363041\pi$
$492$		0			0
$493$	−3.97056	+	6.87722i	−0.178825	+	0.309734i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−31.4558	−	4.30463i	−1.41099	−	0.193089i
$498$		0			0
$499$	−7.92893	−	13.7333i	−0.354948	−	0.614788i	0.632161	−	0.774837i	$-0.282168\pi$
$499$	−7.92893	−	13.7333i	−0.354948	−	0.614788i	−0.987109	+	0.160049i	$0.948835\pi$
$500$		0			0
$501$	−14.5711	+	25.2378i	−0.650987	+	1.12754i
$502$		0			0
$503$	18.0711			0.805749			0.402875	−	0.915255i	$-0.368011\pi$
$503$	18.0711			0.805749			0.402875	+	0.915255i	$0.368011\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	10.8640	−	18.8169i	0.482485	−	0.835689i
$508$		0			0
$509$	8.25736	+	14.3022i	0.366001	+	0.633932i	0.988936	−	0.148341i	$-0.0473933\pi$
$509$	8.25736	+	14.3022i	0.366001	+	0.633932i	−0.622935	+	0.782273i	$0.714060\pi$
$510$		0			0
$511$	−12.4142	+	16.0087i	−0.549172	+	0.708184i
$512$		0			0
$513$	1.17157	+	2.02922i	0.0517262	+	0.0895924i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.65685			0.0728684
$518$		0			0
$519$	−52.2843			−2.29502
$520$		0			0
$521$	4.31371	−	7.47156i	0.188987	−	0.327335i	−0.755926	−	0.654657i	$-0.772813\pi$
$521$	4.31371	−	7.47156i	0.188987	−	0.327335i	0.944913	+	0.327322i	$0.106146\pi$
$522$		0			0
$523$	−19.9706	−	34.5900i	−0.873252	−	1.51252i	−0.858613	−	0.512624i	$-0.828674\pi$
$523$	−19.9706	−	34.5900i	−0.873252	−	1.51252i	−0.0146382	−	0.999893i	$-0.504660\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.82843	−	15.2913i	−0.384572	−	0.666099i
$528$		0			0
$529$	−23.8995	+	41.3951i	−1.03911	+	1.79979i
$530$		0			0
$531$	−11.3137			−0.490973
$532$		0			0
$533$	−0.343146			−0.0148633
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−12.6569	−	21.9223i	−0.546184	−	0.946018i
$538$		0			0
$539$	24.1421	−	23.6544i	1.03988	−	1.01887i
$540$		0			0
$541$	3.25736	+	5.64191i	0.140045	+	0.242565i	0.927513	−	0.373790i	$-0.121942\pi$
$541$	3.25736	+	5.64191i	0.140045	+	0.242565i	−0.787468	+	0.616355i	$0.788609\pi$
$542$		0			0
$543$	11.8640	−	20.5490i	0.509131	−	0.881841i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	27.7279			1.18556			0.592780	−	0.805364i	$-0.298030\pi$
$547$	27.7279			1.18556			0.592780	+	0.805364i	$0.298030\pi$
$548$		0			0
$549$	6.58579	−	11.4069i	0.281075	−	0.486835i
$550$		0			0
$551$	6.14214	+	10.6385i	0.261664	+	0.453215i
$552$		0			0
$553$	4.00000	+	9.79796i	0.170097	+	0.416652i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.65685	−	4.60181i	0.112575	−	0.194985i	−0.804233	−	0.594314i	$-0.797424\pi$
$557$	2.65685	−	4.60181i	0.112575	−	0.194985i	0.916808	+	0.399329i	$0.130757\pi$
$558$		0			0
$559$	25.7990			1.09118
$560$		0			0
$561$	42.6274			1.79973
$562$		0			0
$563$	5.03553	−	8.72180i	0.212222	−	0.367580i	−0.740187	−	0.672401i	$-0.765263\pi$
$563$	5.03553	−	8.72180i	0.212222	−	0.367580i	0.952410	+	0.304821i	$0.0985965\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	15.3787	−	19.8315i	0.645844	−	0.832847i
$568$		0			0
$569$	−4.31371	−	7.47156i	−0.180840	−	0.313224i	0.761327	−	0.648368i	$-0.224548\pi$
$569$	−4.31371	−	7.47156i	−0.180840	−	0.313224i	−0.942167	+	0.335144i	$0.891215\pi$
$570$		0			0
$571$	−6.48528	+	11.2328i	−0.271401	+	0.470080i	−0.969221	−	0.246193i	$-0.920820\pi$
$571$	−6.48528	+	11.2328i	−0.271401	+	0.470080i	0.697820	+	0.716273i	$0.254153\pi$
$572$		0			0
$573$	−54.2843			−2.26776
$574$		0			0
$575$		0			0
$576$		0			0
$577$	17.1421	−	29.6910i	0.713636	−	1.23605i	−0.249847	−	0.968285i	$-0.580380\pi$
$577$	17.1421	−	29.6910i	0.713636	−	1.23605i	0.963483	−	0.267769i	$-0.0862865\pi$
$578$		0			0
$579$	20.8995	+	36.1990i	0.868553	+	1.50438i
$580$		0			0
$581$	34.7132	+	4.75039i	1.44015	+	0.197080i
$582$		0			0
$583$	−13.6569	−	23.6544i	−0.565609	−	0.979664i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	45.3137			1.87030			0.935148	−	0.354256i	$-0.115266\pi$
$587$	45.3137			1.87030			0.935148	+	0.354256i	$0.115266\pi$
$588$		0			0
$589$	−27.3137			−1.12544
$590$		0			0
$591$	14.0711	−	24.3718i	0.578806	−	1.00252i
$592$		0			0
$593$	−18.9706	−	32.8580i	−0.779028	−	1.34932i	−0.932503	−	0.361163i	$-0.882380\pi$
$593$	−18.9706	−	32.8580i	−0.779028	−	1.34932i	0.153475	−	0.988153i	$-0.450954\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.828427	+	1.43488i	0.0339053	+	0.0587256i
$598$		0			0
$599$	1.31371	−	2.27541i	0.0536767	−	0.0929707i	−0.837939	−	0.545765i	$-0.816239\pi$
$599$	1.31371	−	2.27541i	0.0536767	−	0.0929707i	0.891615	+	0.452794i	$0.149573\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$		0			0
$603$	−19.5147			−0.794701
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.37868	+	16.2443i	0.380669	+	0.659338i	0.991158	−	0.132687i	$-0.0423604\pi$
$607$	9.37868	+	16.2443i	0.380669	+	0.659338i	−0.610489	+	0.792025i	$0.709027\pi$
$608$		0			0
$609$	8.50000	−	10.9612i	0.344437	−	0.444169i
$610$		0			0
$611$	−0.343146	−	0.594346i	−0.0138822	−	0.0240447i
$612$		0			0
$613$	2.51472	−	4.35562i	0.101569	−	0.175922i	−0.810763	−	0.585375i	$-0.800947\pi$
$613$	2.51472	−	4.35562i	0.101569	−	0.175922i	0.912331	+	0.409453i	$0.134281\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	35.3137			1.42168			0.710838	−	0.703356i	$-0.248316\pi$
$617$	35.3137			1.42168			0.710838	+	0.703356i	$0.248316\pi$
$618$		0			0
$619$	5.72792	−	9.92105i	0.230225	−	0.398761i	−0.727649	−	0.685949i	$-0.759387\pi$
$619$	5.72792	−	9.92105i	0.230225	−	0.398761i	0.957874	+	0.287188i	$0.0927206\pi$
$620$		0			0
$621$	1.74264	+	3.01834i	0.0699298	+	0.121122i
$622$		0			0
$623$	16.6569	+	40.8008i	0.667343	+	1.63465i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	32.9706	−	57.1067i	1.31672	−	2.28062i
$628$		0			0
$629$	−20.6863			−0.824816
$630$		0			0
$631$	−18.4853			−0.735887			−0.367944	−	0.929848i	$-0.619938\pi$
$631$	−18.4853			−0.735887			−0.367944	+	0.929848i	$0.619938\pi$
$632$		0			0
$633$	22.4853	−	38.9456i	0.893710	−	1.54795i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−13.4853	−	3.76127i	−0.534306	−	0.149027i
$638$		0			0
$639$	16.9706	+	29.3939i	0.671345	+	1.16280i
$640$		0			0
$641$	24.0563	−	41.6668i	0.950169	−	1.64574i	0.205113	−	0.978738i	$-0.434244\pi$
$641$	24.0563	−	41.6668i	0.950169	−	1.64574i	0.745056	−	0.667002i	$-0.232423\pi$
$642$		0			0
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.6213	+	25.3249i	−0.574823	+	0.995623i	0.421237	+	0.906950i	$0.361596\pi$
$647$	−14.6213	+	25.3249i	−0.574823	+	0.995623i	−0.996061	+	0.0886729i	$0.971737\pi$
$648$		0			0
$649$	−9.65685	−	16.7262i	−0.379065	−	0.656559i
$650$		0			0
$651$	11.6569	+	28.5533i	0.456868	+	1.11909i
$652$		0			0
$653$	−2.17157	−	3.76127i	−0.0849802	−	0.147190i	0.820403	−	0.571786i	$-0.193749\pi$
$653$	−2.17157	−	3.76127i	−0.0849802	−	0.147190i	−0.905383	+	0.424596i	$0.860416\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	21.6569			0.844914
$658$		0			0
$659$	35.3137			1.37563			0.687813	−	0.725888i	$-0.258571\pi$
$659$	35.3137			1.37563			0.687813	+	0.725888i	$0.258571\pi$
$660$		0			0
$661$	13.8431	−	23.9770i	0.538436	−	0.932598i	−0.460553	−	0.887632i	$-0.652349\pi$
$661$	13.8431	−	23.9770i	0.538436	−	0.932598i	0.998989	−	0.0449660i	$-0.0143180\pi$
$662$		0			0
$663$	−8.82843	−	15.2913i	−0.342868	−	0.593864i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.13604	+	15.8241i	0.353749	+	0.612711i
$668$		0			0
$669$	22.8995	−	39.6631i	0.885346	−	1.53346i
$670$		0			0
$671$	22.4853			0.868035
$672$		0			0
$673$	−5.65685			−0.218056			−0.109028	−	0.994039i	$-0.534774\pi$
$673$	−5.65685			−0.218056			−0.109028	+	0.994039i	$0.534774\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.48528	−	9.50079i	−0.210816	−	0.365145i	0.741154	−	0.671335i	$-0.234279\pi$
$677$	−5.48528	−	9.50079i	−0.210816	−	0.365145i	−0.951970	+	0.306190i	$0.900946\pi$
$678$		0			0
$679$	−15.7279	−	2.15232i	−0.603582	−	0.0825983i
$680$		0			0
$681$	16.8995	+	29.2708i	0.647590	+	1.12166i
$682$		0			0
$683$	−8.03553	+	13.9180i	−0.307471	+	0.532556i	−0.977808	−	0.209501i	$-0.932816\pi$
$683$	−8.03553	+	13.9180i	−0.307471	+	0.532556i	0.670337	+	0.742057i	$0.266149\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−33.7990			−1.28951
$688$		0			0
$689$	−5.65685	+	9.79796i	−0.215509	+	0.373273i
$690$		0			0
$691$	−15.3848	−	26.6472i	−0.585264	−	1.01371i	−0.994842	−	0.101433i	$-0.967657\pi$
$691$	−15.3848	−	26.6472i	−0.585264	−	1.01371i	0.409578	−	0.912275i	$-0.365676\pi$
$692$		0			0
$693$	−35.7990	−	4.89898i	−1.35989	−	0.186097i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.313708	−	0.543359i	0.0118826	−	0.0205812i
$698$		0			0
$699$	−0.828427			−0.0313340
$700$		0			0
$701$	−11.0000			−0.415464			−0.207732	−	0.978186i	$-0.566608\pi$
$701$	−11.0000			−0.415464			−0.207732	+	0.978186i	$0.566608\pi$
$702$		0			0
$703$	−16.0000	+	27.7128i	−0.603451	+	1.04521i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.89340	+	11.4685i	−0.334471	+	0.431316i
$708$		0			0
$709$	−24.7132	−	42.8045i	−0.928124	−	1.60756i	−0.786459	−	0.617643i	$-0.788088\pi$
$709$	−24.7132	−	42.8045i	−0.928124	−	1.60756i	−0.141665	−	0.989915i	$-0.545246\pi$
$710$		0			0
$711$	5.65685	−	9.79796i	0.212149	−	0.367452i
$712$		0			0
$713$	−40.6274			−1.52151
$714$		0			0
$715$		0			0
$716$		0			0
$717$	16.3137	−	28.2562i	0.609247	−	1.05525i
$718$		0			0
$719$	−6.89949	−	11.9503i	−0.257308	−	0.445670i	0.708212	−	0.706000i	$-0.249502\pi$
$719$	−6.89949	−	11.9503i	−0.257308	−	0.445670i	−0.965520	+	0.260330i	$0.916169\pi$
$720$		0			0
$721$	10.4142	+	25.5095i	0.387846	+	0.950024i
$722$		0			0
$723$	12.0711	+	20.9077i	0.448928	+	0.777566i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−23.9289			−0.887475			−0.443737	−	0.896157i	$-0.646348\pi$
$727$	−23.9289			−0.887475			−0.443737	+	0.896157i	$0.646348\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−23.5858	+	40.8518i	−0.872352	+	1.51096i
$732$		0			0
$733$	−1.82843	−	3.16693i	−0.0675345	−	0.116973i	0.830281	−	0.557345i	$-0.188180\pi$
$733$	−1.82843	−	3.16693i	−0.0675345	−	0.116973i	−0.897815	+	0.440372i	$0.854847\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.6569	−	28.8505i	−0.613563	−	1.06272i
$738$		0			0
$739$	−5.58579	+	9.67487i	−0.205476	+	0.355896i	−0.950284	−	0.311383i	$-0.899208\pi$
$739$	−5.58579	+	9.67487i	−0.205476	+	0.355896i	0.744808	+	0.667279i	$0.232541\pi$
$740$		0			0
$741$	−27.3137			−1.00339
$742$		0			0
$743$	19.2426			0.705944			0.352972	−	0.935634i	$-0.385171\pi$
$743$	19.2426			0.705944			0.352972	+	0.935634i	$0.385171\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−18.7279	−	32.4377i	−0.685219	−	1.18683i
$748$		0			0
$749$	−8.41421	−	20.6105i	−0.307449	−	0.753092i
$750$		0			0
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	0.954485	−	0.298259i	$-0.0964058\pi$
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	−0.735542	+	0.677479i	$0.763072\pi$
$752$		0			0
$753$	−28.3137	+	49.0408i	−1.03181	+	1.78715i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−6.00000			−0.218074			−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000			−0.218074			−0.109037	+	0.994038i	$0.534777\pi$
$758$		0			0
$759$	49.0416	−	84.9426i	1.78010	−	3.08322i
$760$		0			0
$761$	−11.9706	−	20.7336i	−0.433933	−	0.751593i	0.563275	−	0.826269i	$-0.309541\pi$
$761$	−11.9706	−	20.7336i	−0.433933	−	0.751593i	−0.997208	+	0.0746761i	$0.976208\pi$
$762$		0			0
$763$	6.99390	−	9.01897i	0.253196	−	0.326509i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.00000	+	6.92820i	−0.144432	+	0.250163i
$768$		0			0
$769$	−47.2548			−1.70405			−0.852026	−	0.523499i	$-0.824626\pi$
$769$	−47.2548			−1.70405			−0.852026	+	0.523499i	$0.824626\pi$
$770$		0			0
$771$	17.6569			0.635896
$772$		0			0
$773$	17.8284	−	30.8797i	0.641244	−	1.11067i	−0.343911	−	0.939002i	$-0.611752\pi$
$773$	17.8284	−	30.8797i	0.641244	−	1.11067i	0.985155	−	0.171665i	$-0.0549147\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	35.7990	+	4.89898i	1.28428	+	0.175750i
$778$		0			0
$779$	−0.485281	−	0.840532i	−0.0173870	−	0.0301152i
$780$		0			0
$781$	−28.9706	+	50.1785i	−1.03665	+	1.79553i
$782$		0			0
$783$	0.899495			0.0321453
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−2.20711	+	3.82282i	−0.0786749	+	0.136269i	−0.902678	−	0.430316i	$-0.858402\pi$
$787$	−2.20711	+	3.82282i	−0.0786749	+	0.136269i	0.824004	+	0.566585i	$0.191736\pi$
$788$		0			0
$789$	11.7426	+	20.3389i	0.418049	+	0.724082i
$790$		0			0
$791$	29.6569	+	4.05845i	1.05448	+	0.144302i
$792$		0			0
$793$	−4.65685	−	8.06591i	−0.165370	−	0.286429i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.6863			0.449372			0.224686	−	0.974431i	$-0.427864\pi$
$797$	12.6863			0.449372			0.224686	+	0.974431i	$0.427864\pi$
$798$		0			0
$799$	1.25483			0.0443928
$800$		0			0
$801$	23.5563	−	40.8008i	0.832323	−	1.44163i
$802$		0			0
$803$	18.4853	+	32.0174i	0.652331	+	1.12987i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.62132	−	9.73641i	−0.197880	−	0.342738i
$808$		0			0
$809$	1.01472	−	1.75754i	0.0356756	−	0.0617920i	−0.847636	−	0.530578i	$-0.821975\pi$
$809$	1.01472	−	1.75754i	0.0356756	−	0.0617920i	0.883312	+	0.468786i	$0.155308\pi$
$810$		0			0
$811$	23.8579			0.837763			0.418881	−	0.908041i	$-0.362422\pi$
$811$	23.8579			0.837763			0.418881	+	0.908041i	$0.362422\pi$
$812$		0			0
$813$	46.6274			1.63529
$814$		0			0
$815$		0			0
$816$		0			0
$817$	36.4853	+	63.1944i	1.27646	+	2.21089i
$818$		0			0
$819$	5.65685	+	13.8564i	0.197666	+	0.484182i
$820$		0			0
$821$	−6.31371	−	10.9357i	−0.220350	−	0.381657i	0.734564	−	0.678539i	$-0.237387\pi$
$821$	−6.31371	−	10.9357i	−0.220350	−	0.381657i	−0.954914	+	0.296882i	$0.904053\pi$
$822$		0			0
$823$	−26.0061	+	45.0439i	−0.906516	+	1.57013i	−0.0876457	+	0.996152i	$0.527934\pi$
$823$	−26.0061	+	45.0439i	−0.906516	+	1.57013i	−0.818870	+	0.573979i	$0.805399\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	51.5269			1.79177			0.895883	−	0.444290i	$-0.146544\pi$
$827$	51.5269			1.79177			0.895883	+	0.444290i	$0.146544\pi$
$828$		0			0
$829$	8.65685	−	14.9941i	0.300665	−	0.520767i	−0.675622	−	0.737248i	$-0.736125\pi$
$829$	8.65685	−	14.9941i	0.300665	−	0.520767i	0.976287	+	0.216481i	$0.0694581\pi$
$830$		0			0
$831$	−20.0711	−	34.7641i	−0.696258	−	1.20595i
$832$		0			0
$833$	18.2843	−	17.9149i	0.633512	−	0.620713i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.00000	+	1.73205i	−0.0345651	+	0.0598684i
$838$		0			0
$839$	−8.14214			−0.281098			−0.140549	−	0.990074i	$-0.544887\pi$
$839$	−8.14214			−0.281098			−0.140549	+	0.990074i	$0.544887\pi$
$840$		0			0
$841$	−24.2843			−0.837389
$842$		0			0
$843$	−30.5563	+	52.9251i	−1.05242	+	1.82284i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.3137	−	30.1623i	−0.423104	−	1.03639i
$848$		0			0
$849$	21.7279	+	37.6339i	0.745700	+	1.29159i
$850$		0			0
$851$	−23.7990	+	41.2211i	−0.815819	+	1.41304i
$852$		0			0
$853$	−35.3137			−1.20912			−0.604559	−	0.796560i	$-0.706651\pi$
$853$	−35.3137			−1.20912			−0.604559	+	0.796560i	$0.706651\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.48528	−	12.9649i	0.255692	−	0.442872i	−0.709391	−	0.704815i	$-0.751030\pi$
$857$	7.48528	−	12.9649i	0.255692	−	0.442872i	0.965083	+	0.261943i	$0.0843633\pi$
$858$		0			0
$859$	−7.31371	−	12.6677i	−0.249541	−	0.432217i	0.713858	−	0.700291i	$-0.246946\pi$
$859$	−7.31371	−	12.6677i	−0.249541	−	0.432217i	−0.963398	+	0.268074i	$0.913613\pi$
$860$		0			0
$861$	−0.671573	+	0.866025i	−0.0228871	+	0.0295141i
$862$		0			0
$863$	13.0061	+	22.5272i	0.442733	+	0.766835i	0.997891	−	0.0649091i	$-0.0206757\pi$
$863$	13.0061	+	22.5272i	0.442733	+	0.766835i	−0.555159	+	0.831745i	$0.687342\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−8.75736			−0.297416
$868$		0			0
$869$	19.3137			0.655173
$870$		0			0
$871$	−6.89949	+	11.9503i	−0.233780	+	0.404920i
$872$		0			0
$873$	8.48528	+	14.6969i	0.287183	+	0.497416i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14.1421	+	24.4949i	0.477546	+	0.827134i	0.999669	−	0.0257364i	$-0.00819306\pi$
$877$	14.1421	+	24.4949i	0.477546	+	0.827134i	−0.522123	+	0.852870i	$0.674860\pi$
$878$		0			0
$879$	−20.4853	+	35.4815i	−0.690951	+	1.19676i
$880$		0			0
$881$	24.4558			0.823938			0.411969	−	0.911198i	$-0.364841\pi$
$881$	24.4558			0.823938			0.411969	+	0.911198i	$0.364841\pi$
$882$		0			0
$883$	−29.3137			−0.986485			−0.493242	−	0.869892i	$-0.664188\pi$
$883$	−29.3137			−0.986485			−0.493242	+	0.869892i	$0.664188\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.2071	+	17.6792i	0.342721	+	0.593610i	0.984937	−	0.172913i	$-0.0553181\pi$
$887$	10.2071	+	17.6792i	0.342721	+	0.593610i	−0.642216	+	0.766524i	$0.721985\pi$
$888$		0			0
$889$	41.0416	+	5.61642i	1.37649	+	0.188369i
$890$		0			0
$891$	−22.8995	−	39.6631i	−0.767162	−	1.32876i
$892$		0			0
$893$	0.970563	−	1.68106i	0.0324786	−	0.0562547i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−40.6274			−1.35651
$898$		0			0
$899$	−5.24264	+	9.08052i	−0.174852	+	0.302852i
$900$		0			0
$901$	−10.3431	−	17.9149i	−0.344580	−	0.596830i
$902$		0			0
$903$	50.4914	−	65.1111i	1.68025	−	2.16676i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.89340	−	3.27946i	0.0628693	−	0.108893i	−0.832878	−	0.553457i	$-0.813308\pi$
$907$	1.89340	−	3.27946i	0.0628693	−	0.108893i	0.895747	+	0.444565i	$0.146642\pi$
$908$		0			0
$909$	15.5147			0.514591
$910$		0			0
$911$	−1.51472			−0.0501849			−0.0250924	−	0.999685i	$-0.507988\pi$
$911$	−1.51472			−0.0501849			−0.0250924	+	0.999685i	$0.507988\pi$
$912$		0			0
$913$	31.9706	−	55.3746i	1.05807	−	1.83263i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.34315	−	5.73951i	−0.0773775	−	0.189535i
$918$		0			0
$919$	−28.6274	−	49.5841i	−0.944331	−	1.63563i	−0.757084	−	0.653317i	$-0.773377\pi$
$919$	−28.6274	−	49.5841i	−0.944331	−	1.63563i	−0.187247	−	0.982313i	$-0.559956\pi$
$920$		0			0
$921$	15.9853	−	27.6873i	0.526733	−	0.912328i
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$		0			0
$926$		0			0
$927$	14.7279	−	25.5095i	0.483728	−	0.837842i
$928$		0			0
$929$	−24.3995	−	42.2612i	−0.800521	−	1.38654i	−0.919273	−	0.393620i	$-0.871223\pi$
$929$	−24.3995	−	42.2612i	−0.800521	−	1.38654i	0.118752	−	0.992924i	$-0.462111\pi$
$930$		0			0
$931$	−9.85786	−	38.3513i	−0.323078	−	1.25691i
$932$		0			0
$933$	−12.4853	−	21.6251i	−0.408750	−	0.707975i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	26.6274			0.869880			0.434940	−	0.900459i	$-0.356770\pi$
$937$	26.6274			0.869880			0.434940	+	0.900459i	$0.356770\pi$
$938$		0			0
$939$	31.3137			1.02188
$940$		0			0
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	−0.772946	−	0.634472i	$-0.781218\pi$
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	0.935942	+	0.352155i	$0.114551\pi$
$942$		0			0
$943$	−0.721825	−	1.25024i	−0.0235059	−	0.0407134i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.4497	+	26.7597i	0.502049	+	0.869575i	0.999997	+	0.00236799i	$0.000753754\pi$
$947$	15.4497	+	26.7597i	0.502049	+	0.869575i	−0.497948	+	0.867207i	$0.665913\pi$
$948$		0			0
$949$	7.65685	−	13.2621i	0.248552	−	0.430505i
$950$		0			0
$951$	53.1127			1.72230
$952$		0			0
$953$	9.37258			0.303608			0.151804	−	0.988411i	$-0.451492\pi$
$953$	9.37258			0.303608			0.151804	+	0.988411i	$0.451492\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−12.6569	−	21.9223i	−0.409138	−	0.708648i
$958$		0			0
$959$	−6.48528	+	8.36308i	−0.209421	+	0.270058i
$960$		0			0
$961$	3.84315	+	6.65652i	0.123972	+	0.214727i
$962$		0			0
$963$	−11.8995	+	20.6105i	−0.383456	+	0.664165i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	33.2426			1.06901			0.534506	−	0.845165i	$-0.320498\pi$
$967$	33.2426			1.06901			0.534506	+	0.845165i	$0.320498\pi$
$968$		0			0
$969$	24.9706	−	43.2503i	0.802170	−	1.38940i
$970$		0			0
$971$	−4.00000	−	6.92820i	−0.128366	−	0.222337i	0.794678	−	0.607032i	$-0.207640\pi$
$971$	−4.00000	−	6.92820i	−0.128366	−	0.222337i	−0.923044	+	0.384695i	$0.874307\pi$
$972$		0			0
$973$	−37.9706	−	5.19615i	−1.21728	−	0.166581i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−13.1421	+	22.7628i	−0.420454	+	0.728248i	−0.995984	−	0.0895329i	$-0.971463\pi$
$977$	−13.1421	+	22.7628i	−0.420454	+	0.728248i	0.575530	+	0.817781i	$0.304796\pi$
$978$		0			0
$979$	80.4264			2.57044
$980$		0			0
$981$	−12.2010			−0.389548
$982$		0			0
$983$	−2.30761	+	3.99690i	−0.0736014	+	0.127481i	−0.900477	−	0.434903i	$-0.856783\pi$
$983$	−2.30761	+	3.99690i	−0.0736014	+	0.127481i	0.826876	+	0.562385i	$0.190116\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.17157	−	0.297173i	−0.0691219	−	0.00945912i
$988$		0			0
$989$	54.2696	+	93.9976i	1.72567	+	2.98895i
$990$		0			0
$991$	0.414214	−	0.717439i	0.0131579	−	0.0227902i	−0.859371	−	0.511352i	$-0.829145\pi$
$991$	0.414214	−	0.717439i	0.0131579	−	0.0227902i	0.872529	+	0.488562i	$0.162478\pi$
$992$		0			0
$993$	22.9706			0.728949
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−12.8284	+	22.2195i	−0.406280	+	0.703698i	−0.994470	−	0.105025i	$-0.966508\pi$
$997$	−12.8284	+	22.2195i	−0.406280	+	0.703698i	0.588189	+	0.808723i	$0.299841\pi$
$998$		0			0
$999$	1.17157	+	2.02922i	0.0370669	+	0.0642018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.q.h.1201.1		4
5.2	odd	4		1400.2.bh.g.249.4		8
5.3	odd	4		1400.2.bh.g.249.1		8
5.4	even	2		280.2.q.d.81.2	✓	4
7.2	even	3	inner	1400.2.q.h.401.1		4
7.3	odd	6		9800.2.a.br.1.1		2
7.4	even	3		9800.2.a.bz.1.2		2
15.14	odd	2		2520.2.bi.k.361.1		4
20.19	odd	2		560.2.q.j.81.1		4
35.2	odd	12		1400.2.bh.g.849.1		8
35.4	even	6		1960.2.a.p.1.1		2
35.9	even	6		280.2.q.d.121.2	yes	4
35.19	odd	6		1960.2.q.q.961.1		4
35.23	odd	12		1400.2.bh.g.849.4		8
35.24	odd	6		1960.2.a.t.1.2		2
35.34	odd	2		1960.2.q.q.361.1		4
105.44	odd	6		2520.2.bi.k.1801.1		4
140.39	odd	6		3920.2.a.bz.1.2		2
140.59	even	6		3920.2.a.bp.1.1		2
140.79	odd	6		560.2.q.j.401.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.d.81.2	✓	4	5.4	even	2
280.2.q.d.121.2	yes	4	35.9	even	6
560.2.q.j.81.1		4	20.19	odd	2
560.2.q.j.401.1		4	140.79	odd	6
1400.2.q.h.401.1		4	7.2	even	3	inner
1400.2.q.h.1201.1		4	1.1	even	1	trivial
1400.2.bh.g.249.1		8	5.3	odd	4
1400.2.bh.g.249.4		8	5.2	odd	4
1400.2.bh.g.849.1		8	35.2	odd	12
1400.2.bh.g.849.4		8	35.23	odd	12
1960.2.a.p.1.1		2	35.4	even	6
1960.2.a.t.1.2		2	35.24	odd	6
1960.2.q.q.361.1		4	35.34	odd	2
1960.2.q.q.961.1		4	35.19	odd	6
2520.2.bi.k.361.1		4	15.14	odd	2
2520.2.bi.k.1801.1		4	105.44	odd	6
3920.2.a.bp.1.1		2	140.59	even	6
3920.2.a.bz.1.2		2	140.39	odd	6
9800.2.a.br.1.1		2	7.3	odd	6
9800.2.a.bz.1.2		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{3} +(2.62132 + 0.358719i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(-1.20711 + 2.09077i) q^{3} +(2.62132 + 0.358719i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(2.41421 - 4.18154i) q^{11} -2.00000 q^{13} +(1.82843 - 3.16693i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-3.91421 + 5.04757i) q^{21} +(-4.20711 - 7.28692i) q^{23} -0.414214 q^{27} -2.17157 q^{29} +(2.41421 - 4.18154i) q^{31} +(5.82843 + 10.0951i) q^{33} +(-2.82843 - 4.89898i) q^{37} +(2.41421 - 4.18154i) q^{39} +0.171573 q^{41} -12.8995 q^{43} +(0.171573 + 0.297173i) q^{47} +(6.74264 + 1.88064i) q^{49} +(4.41421 + 7.64564i) q^{51} +(2.82843 - 4.89898i) q^{53} +13.6569 q^{57} +(2.00000 - 3.46410i) q^{59} +(2.32843 + 4.03295i) q^{61} +(-2.82843 - 6.92820i) q^{63} +(3.44975 - 5.97514i) q^{67} +20.3137 q^{69} -12.0000 q^{71} +(-3.82843 + 6.63103i) q^{73} +(7.82843 - 10.0951i) q^{77} +(2.00000 + 3.46410i) q^{79} +(4.74264 - 8.21449i) q^{81} +13.2426 q^{83} +(2.62132 - 4.54026i) q^{87} +(8.32843 + 14.4253i) q^{89} +(-5.24264 - 0.717439i) q^{91} +(5.82843 + 10.0951i) q^{93} -6.00000 q^{97} -13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^7	\( 4 q - 2 q^{3} + 2 q^{7} + 4 q^{11} - 8 q^{13} - 4 q^{17} - 10 q^{21} - 14 q^{23} + 4 q^{27} - 20 q^{29} + 4 q^{31} + 12 q^{33} + 4 q^{39} + 12 q^{41} - 12 q^{43} + 12 q^{47} + 10 q^{49} + 12 q^{51} + 32 q^{57} + 8 q^{59} - 2 q^{61} - 6 q^{67} + 36 q^{69} - 48 q^{71} - 4 q^{73} + 20 q^{77} + 8 q^{79} + 2 q^{81} + 36 q^{83} + 2 q^{87} + 22 q^{89} - 4 q^{91} + 12 q^{93} - 24 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^7 + 4 * q^11 - 8 * q^13 - 4 * q^17 - 10 * q^21 - 14 * q^23 + 4 * q^27 - 20 * q^29 + 4 * q^31 + 12 * q^33 + 4 * q^39 + 12 * q^41 - 12 * q^43 + 12 * q^47 + 10 * q^49 + 12 * q^51 + 32 * q^57 + 8 * q^59 - 2 * q^61 - 6 * q^67 + 36 * q^69 - 48 * q^71 - 4 * q^73 + 20 * q^77 + 8 * q^79 + 2 * q^81 + 36 * q^83 + 2 * q^87 + 22 * q^89 - 4 * q^91 + 12 * q^93 - 24 * q^97 - 32 * q^99

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