LMFDB - Embedded newform 700.2.i.e.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(401,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("700.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			401.1
Root			$-0.956115 + 1.65604i$ of defining polynomial
Character	$\chi$	$=$	700.401
Dual form			700.2.i.e.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28442 - 2.22469i) q^{3} +(-2.58392 - 0.568650i) q^{7} +(-1.79949 + 3.11682i) q^{9} +O(q^{10})$	$q+(-1.28442 - 2.22469i) q^{3} +(-2.58392 - 0.568650i) q^{7} +(-1.79949 + 3.11682i) q^{9} +(0.784425 + 1.35866i) q^{11} -5.56885 q^{13} +(3.58392 + 6.20753i) q^{17} +(-1.58392 + 2.74343i) q^{19} +(2.05378 + 6.47880i) q^{21} +(2.86834 - 4.96812i) q^{23} +1.53871 q^{27} +1.96986 q^{29} +(-0.484931 - 0.839925i) q^{31} +(2.01507 - 3.49020i) q^{33} +(-3.35327 + 5.80804i) q^{37} +(7.15277 + 12.3890i) q^{39} -8.87439 q^{41} +4.59899 q^{43} +(0.200506 - 0.347286i) q^{47} +(6.35327 + 2.93869i) q^{49} +(9.20655 - 15.9462i) q^{51} +(4.76936 + 8.26077i) q^{53} +8.13770 q^{57} +(2.28442 + 3.95674i) q^{59} +(-7.65277 + 13.2550i) q^{61} +(6.42212 - 7.03032i) q^{63} +(0.431150 + 0.746774i) q^{67} -14.7367 q^{69} -12.1377 q^{71} +(2.00000 + 3.46410i) q^{73} +(-1.25429 - 3.95674i) q^{77} +(6.43719 - 11.1495i) q^{79} +(3.42212 + 5.92729i) q^{81} -17.1076 q^{83} +(-2.53014 - 4.38233i) q^{87} +(2.79949 - 4.84887i) q^{89} +(14.3895 + 3.16673i) q^{91} +(-1.24571 + 2.15764i) q^{93} -0.233174 q^{97} -5.64627 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 6 * q + q^3 - 4 * q^7 - 8 * q^9	$ 6 q + q^{3} - 4 q^{7} - 8 q^{9} - 4 q^{11} - 16 q^{13} + 10 q^{17} + 2 q^{19} - 11 q^{21} - 3 q^{23} - 20 q^{27} + 3 q^{31} + 18 q^{33} + 6 q^{37} + 14 q^{39} + 22 q^{41} + 22 q^{43} + 4 q^{47} + 12 q^{49} + 3 q^{51} + 14 q^{53} + 14 q^{57} + 5 q^{59} - 17 q^{61} - 5 q^{63} + 20 q^{67} - 48 q^{69} - 38 q^{71} + 12 q^{73} + 13 q^{77} + q^{79} - 23 q^{81} - 56 q^{83} - 27 q^{87} + 14 q^{89} + 17 q^{91} - 28 q^{93} - 30 q^{97} + 42 q^{99}+O(q^{100}) $ 6 * q + q^3 - 4 * q^7 - 8 * q^9 - 4 * q^11 - 16 * q^13 + 10 * q^17 + 2 * q^19 - 11 * q^21 - 3 * q^23 - 20 * q^27 + 3 * q^31 + 18 * q^33 + 6 * q^37 + 14 * q^39 + 22 * q^41 + 22 * q^43 + 4 * q^47 + 12 * q^49 + 3 * q^51 + 14 * q^53 + 14 * q^57 + 5 * q^59 - 17 * q^61 - 5 * q^63 + 20 * q^67 - 48 * q^69 - 38 * q^71 + 12 * q^73 + 13 * q^77 + q^79 - 23 * q^81 - 56 * q^83 - 27 * q^87 + 14 * q^89 + 17 * q^91 - 28 * q^93 - 30 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.28442	−	2.22469i	−0.741563	−	1.28442i	−0.951783	−	0.306771i	$-0.900751\pi$
$3$	−1.28442	−	2.22469i	−0.741563	−	1.28442i	0.210220	−	0.977654i	$-0.432582\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.58392	−	0.568650i	−0.976630	−	0.214929i
$7$	−2.58392	−	0.568650i	−0.976630	−	0.214929i
$8$		0			0
$9$	−1.79949	+	3.11682i	−0.599831	+	1.03894i
$10$		0			0
$11$	0.784425	+	1.35866i	0.236513	+	0.409652i	0.959711	−	0.280988i	$-0.0906621\pi$
$11$	0.784425	+	1.35866i	0.236513	+	0.409652i	−0.723198	+	0.690640i	$0.757329\pi$
$12$		0			0
$13$	−5.56885			−1.54452			−0.772260	−	0.635306i	$-0.780874\pi$
$13$	−5.56885			−1.54452			−0.772260	+	0.635306i	$0.780874\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.58392	+	6.20753i	0.869228	+	1.50555i	0.862787	+	0.505568i	$0.168717\pi$
$17$	3.58392	+	6.20753i	0.869228	+	1.50555i	0.00644117	+	0.999979i	$0.497950\pi$
$18$		0			0
$19$	−1.58392	+	2.74343i	−0.363376	+	0.629386i	−0.988514	−	0.151129i	$-0.951709\pi$
$19$	−1.58392	+	2.74343i	−0.363376	+	0.629386i	0.625138	+	0.780514i	$0.285043\pi$
$20$		0			0
$21$	2.05378	+	6.47880i	0.448172	+	1.41379i
$22$		0			0
$23$	2.86834	−	4.96812i	0.598091	−	1.03592i	−0.395012	−	0.918676i	$-0.629259\pi$
$23$	2.86834	−	4.96812i	0.598091	−	1.03592i	0.993103	−	0.117248i	$-0.0374072\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.53871			0.296125
$28$		0			0
$29$	1.96986			0.365794			0.182897	−	0.983132i	$-0.441453\pi$
$29$	1.96986			0.365794			0.182897	+	0.983132i	$0.441453\pi$
$30$		0			0
$31$	−0.484931	−	0.839925i	−0.0870961	−	0.150855i	0.819186	−	0.573527i	$-0.194425\pi$
$31$	−0.484931	−	0.839925i	−0.0870961	−	0.150855i	−0.906282	+	0.422673i	$0.861092\pi$
$32$		0			0
$33$	2.01507	−	3.49020i	0.350779	−	0.607566i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.35327	+	5.80804i	−0.551275	+	0.954836i	0.446908	+	0.894580i	$0.352525\pi$
$37$	−3.35327	+	5.80804i	−0.551275	+	0.954836i	−0.998183	+	0.0602563i	$0.980808\pi$
$38$		0			0
$39$	7.15277	+	12.3890i	1.14536	+	1.98382i
$40$		0			0
$41$	−8.87439			−1.38595			−0.692973	−	0.720963i	$-0.743700\pi$
$41$	−8.87439			−1.38595			−0.692973	+	0.720963i	$0.743700\pi$
$42$		0			0
$43$	4.59899			0.701339			0.350670	−	0.936499i	$-0.385954\pi$
$43$	4.59899			0.701339			0.350670	+	0.936499i	$0.385954\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.200506	−	0.347286i	0.0292468	−	0.0506569i	−0.851032	−	0.525115i	$-0.824022\pi$
$47$	0.200506	−	0.347286i	0.0292468	−	0.0506569i	0.880278	+	0.474458i	$0.157356\pi$
$48$		0			0
$49$	6.35327	+	2.93869i	0.907611	+	0.419813i
$50$		0			0
$51$	9.20655	−	15.9462i	1.28917	−	2.23292i
$52$		0			0
$53$	4.76936	+	8.26077i	0.655121	+	1.13470i	0.981863	+	0.189590i	$0.0607158\pi$
$53$	4.76936	+	8.26077i	0.655121	+	1.13470i	−0.326742	+	0.945114i	$0.605951\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	8.13770			1.07786
$58$		0			0
$59$	2.28442	+	3.95674i	0.297407	+	0.515124i	0.975542	−	0.219814i	$-0.0705449\pi$
$59$	2.28442	+	3.95674i	0.297407	+	0.515124i	−0.678135	+	0.734937i	$0.737212\pi$
$60$		0			0
$61$	−7.65277	+	13.2550i	−0.979837	+	1.69713i	−0.316886	+	0.948464i	$0.602637\pi$
$61$	−7.65277	+	13.2550i	−0.979837	+	1.69713i	−0.662951	+	0.748663i	$0.730696\pi$
$62$		0			0
$63$	6.42212	−	7.03032i	0.809112	−	0.885737i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.431150	+	0.746774i	0.0526734	+	0.0912330i	0.891160	−	0.453689i	$-0.149892\pi$
$67$	0.431150	+	0.746774i	0.0526734	+	0.0912330i	−0.838486	+	0.544922i	$0.816559\pi$
$68$		0			0
$69$	−14.7367			−1.77409
$70$		0			0
$71$	−12.1377			−1.44048			−0.720240	−	0.693725i	$-0.755968\pi$
$71$	−12.1377			−1.44048			−0.720240	+	0.693725i	$0.755968\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.25429	−	3.95674i	−0.142939	−	0.450912i
$78$		0			0
$79$	6.43719	−	11.1495i	0.724241	−	1.25442i	−0.235045	−	0.971985i	$-0.575524\pi$
$79$	6.43719	−	11.1495i	0.724241	−	1.25442i	0.959286	−	0.282437i	$-0.0911430\pi$
$80$		0			0
$81$	3.42212	+	5.92729i	0.380236	+	0.658588i
$82$		0			0
$83$	−17.1076			−1.87780			−0.938899	−	0.344192i	$-0.888153\pi$
$83$	−17.1076			−1.87780			−0.938899	+	0.344192i	$0.888153\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.53014	−	4.38233i	−0.271259	−	0.469835i
$88$		0			0
$89$	2.79949	−	4.84887i	0.296746	−	0.513979i	−0.678644	−	0.734468i	$-0.737432\pi$
$89$	2.79949	−	4.84887i	0.296746	−	0.513979i	0.975389	+	0.220489i	$0.0707653\pi$
$90$		0			0
$91$	14.3895	+	3.16673i	1.50842	+	0.331963i
$92$		0			0
$93$	−1.24571	+	2.15764i	−0.129175	+	0.223737i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.233174			−0.0236752			−0.0118376	−	0.999930i	$-0.503768\pi$
$97$	−0.233174			−0.0236752			−0.0118376	+	0.999930i	$0.503768\pi$
$98$		0			0
$99$	−5.64627			−0.567472
$100$		0			0
$101$	−6.25176	−	10.8284i	−0.622073	−	1.07746i	−0.989099	−	0.147251i	$-0.952957\pi$
$101$	−6.25176	−	10.8284i	−0.622073	−	1.07746i	0.367026	−	0.930211i	$-0.380376\pi$
$102$		0			0
$103$	1.68544	−	2.91926i	0.166071	−	0.287643i	−0.770964	−	0.636879i	$-0.780225\pi$
$103$	1.68544	−	2.91926i	0.166071	−	0.287643i	0.937035	+	0.349235i	$0.113559\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.86834	+	15.3604i	−0.857335	+	1.48495i	0.0171265	+	0.999853i	$0.494548\pi$
$107$	−8.86834	+	15.3604i	−0.857335	+	1.48495i	−0.874462	+	0.485095i	$0.838785\pi$
$108$		0			0
$109$	−2.95226	−	5.11347i	−0.282775	−	0.489782i	0.689292	−	0.724484i	$-0.257922\pi$
$109$	−2.95226	−	5.11347i	−0.282775	−	0.489782i	−0.972067	+	0.234702i	$0.924588\pi$
$110$		0			0
$111$	17.2281			1.63522
$112$		0			0
$113$	−15.6412			−1.47140			−0.735701	−	0.677307i	$-0.763147\pi$
$113$	−15.6412			−1.47140			−0.735701	+	0.677307i	$0.763147\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.0211	−	17.3571i	0.926452	−	1.60466i
$118$		0			0
$119$	−5.73064	−	18.0777i	−0.525327	−	1.65718i
$120$		0			0
$121$	4.26936	−	7.39474i	0.388123	−	0.672249i
$122$		0			0
$123$	11.3985	+	19.7428i	1.02777	+	1.78014i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−12.8744			−1.14242			−0.571209	−	0.820805i	$-0.693525\pi$
$127$	−12.8744			−1.14242			−0.571209	+	0.820805i	$0.693525\pi$
$128$		0			0
$129$	−5.90705	−	10.2313i	−0.520087	−	0.900817i
$130$		0			0
$131$	0.114058	−	0.197554i	0.00996526	−	0.0172603i	−0.861000	−	0.508605i	$-0.830161\pi$
$131$	0.114058	−	0.197554i	0.00996526	−	0.0172603i	0.870965	+	0.491345i	$0.163495\pi$
$132$		0			0
$133$	5.65277	−	6.18810i	0.490157	−	0.536576i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.83821	−	8.38002i	−0.413356	−	0.715953i	0.581899	−	0.813261i	$-0.302310\pi$
$137$	−4.83821	−	8.38002i	−0.413356	−	0.715953i	−0.995254	+	0.0973082i	$0.968977\pi$
$138$		0			0
$139$	−12.3709			−1.04928			−0.524642	−	0.851323i	$-0.675801\pi$
$139$	−12.3709			−1.04928			−0.524642	+	0.851323i	$0.675801\pi$
$140$		0			0
$141$	−1.03014			−0.0867533
$142$		0			0
$143$	−4.36834	−	7.56619i	−0.365299	−	0.632717i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.62263	−	17.9086i	−0.133832	−	1.47708i
$148$		0			0
$149$	−5.95479	+	10.3140i	−0.487836	+	0.844956i	−0.999902	−	0.0139898i	$-0.995547\pi$
$149$	−5.95479	+	10.3140i	−0.487836	+	0.844956i	0.512067	+	0.858946i	$0.328880\pi$
$150$		0			0
$151$	−4.98493	−	8.63415i	−0.405668	−	0.702637i	0.588731	−	0.808329i	$-0.299628\pi$
$151$	−4.98493	−	8.63415i	−0.405668	−	0.702637i	−0.994399	+	0.105692i	$0.966294\pi$
$152$		0			0
$153$	−25.7970			−2.08556
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−6.02111	−	10.4289i	−0.480537	−	0.832315i	0.519214	−	0.854645i	$-0.326225\pi$
$157$	−6.02111	−	10.4289i	−0.480537	−	0.832315i	−0.999751	+	0.0223299i	$0.992892\pi$
$158$		0			0
$159$	12.2518	−	21.2207i	0.971628	−	1.68291i
$160$		0			0
$161$	−10.2367	+	11.2061i	−0.806764	+	0.883167i
$162$		0			0
$163$	−8.36834	+	14.4944i	−0.655459	+	1.13529i	0.326319	+	0.945260i	$0.394192\pi$
$163$	−8.36834	+	14.4944i	−0.655459	+	1.13529i	−0.981778	+	0.190029i	$0.939142\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.76683			0.523633			0.261816	−	0.965118i	$-0.415679\pi$
$167$	6.76683			0.523633			0.261816	+	0.965118i	$0.415679\pi$
$168$		0			0
$169$	18.0121			1.38555
$170$		0			0
$171$	−5.70051	−	9.87357i	−0.435929	−	0.755050i
$172$		0			0
$173$	2.34723	−	4.06552i	0.178457	−	0.309096i	−0.762895	−	0.646522i	$-0.776223\pi$
$173$	2.34723	−	4.06552i	0.178457	−	0.309096i	0.941352	+	0.337426i	$0.109556\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.86834	−	10.1643i	0.441092	−	0.763993i
$178$		0			0
$179$	−5.73669	−	9.93623i	−0.428780	−	0.742669i	0.567985	−	0.823039i	$-0.307723\pi$
$179$	−5.73669	−	9.93623i	−0.428780	−	0.742669i	−0.996765	+	0.0803699i	$0.974390\pi$
$180$		0			0
$181$	0.832162			0.0618541			0.0309271	−	0.999522i	$-0.490154\pi$
$181$	0.832162			0.0618541			0.0309271	+	0.999522i	$0.490154\pi$
$182$		0			0
$183$	39.3176			2.90644
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.62263	+	9.73868i	−0.411167	+	0.712163i
$188$		0			0
$189$	−3.97590	−	0.874988i	−0.289204	−	0.0636460i
$190$		0			0
$191$	−3.46986	+	6.00998i	−0.251070	+	0.434867i	−0.963821	−	0.266551i	$-0.914116\pi$
$191$	−3.46986	+	6.00998i	−0.251070	+	0.434867i	0.712750	+	0.701418i	$0.247449\pi$
$192$		0			0
$193$	9.83821	+	17.0403i	0.708169	+	1.22659i	0.965535	+	0.260272i	$0.0838121\pi$
$193$	9.83821	+	17.0403i	0.708169	+	1.22659i	−0.257366	+	0.966314i	$0.582855\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.0422			1.14296			0.571481	−	0.820616i	$-0.306369\pi$
$197$	16.0422			1.14296			0.571481	+	0.820616i	$0.306369\pi$
$198$		0			0
$199$	5.33821	+	9.24604i	0.378415	+	0.655435i	0.990832	−	0.135101i	$-0.0431358\pi$
$199$	5.33821	+	9.24604i	0.378415	+	0.655435i	−0.612417	+	0.790535i	$0.709802\pi$
$200$		0			0
$201$	1.10756	−	1.91835i	0.0781213	−	0.135310i
$202$		0			0
$203$	−5.08996	−	1.12016i	−0.357245	−	0.0786199i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	10.3231	+	17.8802i	0.717508	+	1.24276i
$208$		0			0
$209$	−4.96986			−0.343772
$210$		0			0
$211$	11.3658			0.782455			0.391227	−	0.920294i	$-0.372051\pi$
$211$	11.3658			0.782455			0.391227	+	0.920294i	$0.372051\pi$
$212$		0			0
$213$	15.5900	+	27.0026i	1.06821	+	1.85019i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.775398	+	2.44605i	0.0526375	+	0.166049i
$218$		0			0
$219$	5.13770	−	8.89876i	0.347174	−	0.601322i
$220$		0			0
$221$	−19.9583	−	34.5688i	−1.34254	−	2.32535i
$222$		0			0
$223$	6.04222			0.404617			0.202309	−	0.979322i	$-0.435156\pi$
$223$	6.04222			0.404617			0.202309	+	0.979322i	$0.435156\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.8206	+	18.7418i	0.718189	+	1.24394i	0.961717	+	0.274046i	$0.0883620\pi$
$227$	10.8206	+	18.7418i	0.718189	+	1.24394i	−0.243528	+	0.969894i	$0.578305\pi$
$228$		0			0
$229$	2.71558	−	4.70351i	0.179450	−	0.310817i	−0.762242	−	0.647292i	$-0.775901\pi$
$229$	2.71558	−	4.70351i	0.179450	−	0.310817i	0.941692	+	0.336475i	$0.109235\pi$
$230$		0			0
$231$	−7.19148	+	7.87253i	−0.473165	+	0.517975i
$232$		0			0
$233$	−3.46986	+	6.00998i	−0.227318	+	0.393727i	−0.957012	−	0.290047i	$-0.906329\pi$
$233$	−3.46986	+	6.00998i	−0.227318	+	0.393727i	0.729694	+	0.683774i	$0.239662\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−33.0724			−2.14828
$238$		0			0
$239$	1.69446			0.109606			0.0548028	−	0.998497i	$-0.482547\pi$
$239$	1.69446			0.109606			0.0548028	+	0.998497i	$0.482547\pi$
$240$		0			0
$241$	7.46733	+	12.9338i	0.481013	+	0.833139i	0.999763	−	0.0217871i	$-0.00693559\pi$
$241$	7.46733	+	12.9338i	0.481013	+	0.833139i	−0.518749	+	0.854926i	$0.673602\pi$
$242$		0			0
$243$	11.0990	−	19.2240i	0.712000	−	1.23322i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.82061	−	15.2777i	0.561242	−	0.972099i
$248$		0			0
$249$	21.9734	+	38.0590i	1.39251	+	2.41189i
$250$		0			0
$251$	8.90958			0.562368			0.281184	−	0.959654i	$-0.409273\pi$
$251$	8.90958			0.562368			0.281184	+	0.959654i	$0.409273\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.83216	−	8.36955i	0.301422	−	0.522078i	−0.675036	−	0.737785i	$-0.735872\pi$
$257$	4.83216	−	8.36955i	0.301422	−	0.522078i	0.976458	+	0.215706i	$0.0692054\pi$
$258$		0			0
$259$	11.9673	−	13.1007i	0.743614	−	0.814036i
$260$		0			0
$261$	−3.54475	+	6.13969i	−0.219415	+	0.380038i
$262$		0			0
$263$	−3.05125	−	5.28492i	−0.188148	−	0.325882i	0.756485	−	0.654011i	$-0.226915\pi$
$263$	−3.05125	−	5.28492i	−0.188148	−	0.325882i	−0.944633	+	0.328129i	$0.893582\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−14.3830			−0.880223
$268$		0			0
$269$	−11.2668	−	19.5147i	−0.686951	−	1.18983i	−0.972820	−	0.231565i	$-0.925616\pi$
$269$	−11.2668	−	19.5147i	−0.686951	−	1.18983i	0.285869	−	0.958269i	$-0.407718\pi$
$270$		0			0
$271$	−2.23064	+	3.86359i	−0.135502	+	0.234696i	−0.925789	−	0.378040i	$-0.876598\pi$
$271$	−2.23064	+	3.86359i	−0.135502	+	0.234696i	0.790287	+	0.612737i	$0.209931\pi$
$272$		0			0
$273$	−11.4372	−	36.0795i	−0.692210	−	2.18363i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.25429	+	5.63659i	0.195531	+	0.338670i	0.947074	−	0.321014i	$-0.104024\pi$
$277$	3.25429	+	5.63659i	0.195531	+	0.338670i	−0.751543	+	0.659684i	$0.770690\pi$
$278$		0			0
$279$	3.49052			0.208972
$280$		0			0
$281$	−11.1980			−0.668015			−0.334008	−	0.942570i	$-0.608401\pi$
$281$	−11.1980			−0.668015			−0.334008	+	0.942570i	$0.608401\pi$
$282$		0			0
$283$	−3.82314	−	6.62187i	−0.227262	−	0.393629i	0.729734	−	0.683731i	$-0.239644\pi$
$283$	−3.82314	−	6.62187i	−0.227262	−	0.393629i	−0.956996	+	0.290102i	$0.906311\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	22.9307	+	5.04642i	1.35356	+	0.297881i
$288$		0			0
$289$	−17.1890	+	29.7721i	−1.01111	+	1.75130i
$290$		0			0
$291$	0.299494	+	0.518739i	0.0175567	+	0.0304090i
$292$		0			0
$293$	−6.12561			−0.357862			−0.178931	−	0.983862i	$-0.557264\pi$
$293$	−6.12561			−0.357862			−0.178931	+	0.983862i	$0.557264\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.20700	+	2.09059i	0.0700374	+	0.121308i
$298$		0			0
$299$	−15.9734	+	27.6667i	−0.923764	+	1.60001i
$300$		0			0
$301$	−11.8834	−	2.61521i	−0.684949	−	0.150738i
$302$		0			0
$303$	−16.0598	+	27.8164i	−0.922613	+	1.59801i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−26.4080			−1.50719			−0.753593	−	0.657341i	$-0.771681\pi$
$307$	−26.4080			−1.50719			−0.753593	+	0.657341i	$0.771681\pi$
$308$		0			0
$309$	−8.65927			−0.492608
$310$		0			0
$311$	9.67641	+	16.7600i	0.548699	+	0.950374i	0.998364	+	0.0571771i	$0.0182100\pi$
$311$	9.67641	+	16.7600i	0.548699	+	0.950374i	−0.449665	+	0.893197i	$0.648457\pi$
$312$		0			0
$313$	4.35327	−	7.54009i	0.246062	−	0.426191i	−0.716368	−	0.697723i	$-0.754197\pi$
$313$	4.35327	−	7.54009i	0.246062	−	0.426191i	0.962430	+	0.271531i	$0.0875301\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.63770	−	13.2289i	0.428976	−	0.743008i	−0.567807	−	0.823162i	$-0.692208\pi$
$317$	7.63770	−	13.2289i	0.428976	−	0.743008i	0.996782	+	0.0801539i	$0.0255412\pi$
$318$		0			0
$319$	1.54521	+	2.67638i	0.0865150	+	0.149848i
$320$		0			0
$321$	45.5629			2.54307
$322$		0			0
$323$	−22.7065			−1.26343
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−7.58392	+	13.1357i	−0.419392	+	0.726408i
$328$		0			0
$329$	−0.715575	+	0.783342i	−0.0394509	+	0.0431870i
$330$		0			0
$331$	−8.37439	+	14.5049i	−0.460298	+	0.797259i	−0.998976	−	0.0452526i	$-0.985591\pi$
$331$	−8.37439	+	14.5049i	−0.460298	+	0.797259i	0.538678	+	0.842512i	$0.318924\pi$
$332$		0			0
$333$	−12.0684	−	20.9031i	−0.661344	−	1.14548i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	31.2453			1.70204			0.851019	−	0.525135i	$-0.175985\pi$
$337$	31.2453			1.70204			0.851019	+	0.525135i	$0.175985\pi$
$338$		0			0
$339$	20.0900	+	34.7968i	1.09114	+	1.88990i
$340$		0			0
$341$	0.760783	−	1.31772i	0.0411987	−	0.0713583i
$342$		0			0
$343$	−14.7453	−	11.2061i	−0.796169	−	0.605074i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.05125	+	10.4811i	0.324848	+	0.562654i	0.981482	−	0.191556i	$-0.0613535\pi$
$347$	6.05125	+	10.4811i	0.324848	+	0.562654i	−0.656633	+	0.754210i	$0.728020\pi$
$348$		0			0
$349$	−3.87439			−0.207391			−0.103696	−	0.994609i	$-0.533067\pi$
$349$	−3.87439			−0.207391			−0.103696	+	0.994609i	$0.533067\pi$
$350$		0			0
$351$	−8.56885			−0.457371
$352$		0			0
$353$	−1.28190	−	2.22031i	−0.0682284	−	0.118175i	0.829893	−	0.557922i	$-0.188401\pi$
$353$	−1.28190	−	2.22031i	−0.0682284	−	0.118175i	−0.898122	+	0.439747i	$0.855068\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−32.8568	+	35.9684i	−1.73897	+	1.90365i
$358$		0			0
$359$	−10.4196	+	18.0473i	−0.549925	+	0.952498i	0.448354	+	0.893856i	$0.352010\pi$
$359$	−10.4196	+	18.0473i	−0.549925	+	0.952498i	−0.998279	+	0.0586422i	$0.981323\pi$
$360$		0			0
$361$	4.48240	+	7.76375i	0.235916	+	0.408618i
$362$		0			0
$363$	−21.9347			−1.15127
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.91608	−	13.7111i	−0.413216	−	0.715711i	0.582023	−	0.813172i	$-0.302261\pi$
$367$	−7.91608	−	13.7111i	−0.413216	−	0.715711i	−0.995239	+	0.0974609i	$0.968928\pi$
$368$		0			0
$369$	15.9694	−	27.6598i	0.831334	−	1.43991i
$370$		0			0
$371$	−7.62614	−	24.0572i	−0.395930	−	1.24899i
$372$		0			0
$373$	11.2518	−	19.4886i	0.582594	−	1.00908i	−0.412577	−	0.910923i	$-0.635371\pi$
$373$	11.2518	−	19.4886i	0.582594	−	1.00908i	0.995171	−	0.0981594i	$-0.0312955\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.9699			−0.564977
$378$		0			0
$379$	−7.36581			−0.378356			−0.189178	−	0.981943i	$-0.560582\pi$
$379$	−7.36581			−0.378356			−0.189178	+	0.981943i	$0.560582\pi$
$380$		0			0
$381$	16.5362	+	28.6415i	0.847174	+	1.46735i
$382$		0			0
$383$	16.8266	−	29.1446i	0.859802	−	1.48922i	−0.0123162	−	0.999924i	$-0.503920\pi$
$383$	16.8266	−	29.1446i	0.859802	−	1.48922i	0.872118	−	0.489296i	$-0.162746\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.27585	+	14.3342i	−0.420685	+	0.728648i
$388$		0			0
$389$	−8.74273	−	15.1429i	−0.443274	−	0.767773i	0.554656	−	0.832080i	$-0.312850\pi$
$389$	−8.74273	−	15.1429i	−0.443274	−	0.767773i	−0.997930	+	0.0643065i	$0.979516\pi$
$390$		0			0
$391$	41.1196			2.07951
$392$		0			0
$393$	−0.585994			−0.0295595
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−3.79949	+	6.58092i	−0.190691	+	0.330287i	−0.945479	−	0.325682i	$-0.894406\pi$
$397$	−3.79949	+	6.58092i	−0.190691	+	0.330287i	0.754788	+	0.655968i	$0.227740\pi$
$398$		0			0
$399$	−21.0272	−	4.62750i	−1.05267	−	0.231665i
$400$		0			0
$401$	−5.42212	+	9.39139i	−0.270768	+	0.468984i	−0.969059	−	0.246830i	$-0.920611\pi$
$401$	−5.42212	+	9.39139i	−0.270768	+	0.468984i	0.698291	+	0.715814i	$0.253944\pi$
$402$		0			0
$403$	2.70051	+	4.67741i	0.134522	+	0.232999i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.5216			−0.521535
$408$		0			0
$409$	8.43466	+	14.6093i	0.417067	+	0.722382i	0.995643	−	0.0932469i	$-0.0297246\pi$
$409$	8.43466	+	14.6093i	0.417067	+	0.722382i	−0.578576	+	0.815629i	$0.696391\pi$
$410$		0			0
$411$	−12.4286	+	21.5270i	−0.613059	+	1.06185i
$412$		0			0
$413$	−3.65277	−	11.5229i	−0.179741	−	0.567006i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.8895	+	27.5213i	0.778110	+	1.34773i
$418$		0			0
$419$	−4.03014			−0.196885			−0.0984426	−	0.995143i	$-0.531386\pi$
$419$	−4.03014			−0.196885			−0.0984426	+	0.995143i	$0.531386\pi$
$420$		0			0
$421$	25.1196			1.22426			0.612128	−	0.790758i	$-0.290314\pi$
$421$	25.1196			1.22426			0.612128	+	0.790758i	$0.290314\pi$
$422$		0			0
$423$	0.721618	+	1.24988i	0.0350863	+	0.0607712i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	27.3116	−	29.8981i	1.32170	−	1.44687i
$428$		0			0
$429$	−11.2216	+	19.4364i	−0.541785	+	0.938399i
$430$		0			0
$431$	−15.1201	−	26.1888i	−0.728310	−	1.26147i	−0.957597	−	0.288111i	$-0.906973\pi$
$431$	−15.1201	−	26.1888i	−0.728310	−	1.26147i	0.229288	−	0.973359i	$-0.426360\pi$
$432$		0			0
$433$	22.9769			1.10420			0.552099	−	0.833778i	$-0.313827\pi$
$433$	22.9769			1.10420			0.552099	+	0.833778i	$0.313827\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.08645	+	15.7382i	0.434664	+	0.752860i
$438$		0			0
$439$	−5.97590	+	10.3506i	−0.285214	+	0.494006i	−0.972661	−	0.232229i	$-0.925398\pi$
$439$	−5.97590	+	10.3506i	−0.285214	+	0.494006i	0.687447	+	0.726235i	$0.258731\pi$
$440$		0			0
$441$	−20.5920	+	14.5138i	−0.980573	+	0.691135i
$442$		0			0
$443$	−7.05378	+	12.2175i	−0.335135	+	0.580471i	−0.983511	−	0.180849i	$-0.942115\pi$
$443$	−7.05378	+	12.2175i	−0.335135	+	0.580471i	0.648376	+	0.761321i	$0.275449\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	30.5939			1.44704
$448$		0			0
$449$	37.9468			1.79082			0.895409	−	0.445245i	$-0.146883\pi$
$449$	37.9468			1.79082			0.895409	+	0.445245i	$0.146883\pi$
$450$		0			0
$451$	−6.96129	−	12.0573i	−0.327794	−	0.567756i
$452$		0			0
$453$	−12.8055	+	22.1798i	−0.601657	+	1.04210i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.27287	+	16.0611i	−0.433767	+	0.751306i	−0.997194	−	0.0748598i	$-0.976149\pi$
$457$	−9.27287	+	16.0611i	−0.433767	+	0.751306i	0.563428	+	0.826165i	$0.309482\pi$
$458$		0			0
$459$	5.51462	+	9.55159i	0.257400	+	0.445830i
$460$		0			0
$461$	−23.2453			−1.08264			−0.541320	−	0.840817i	$-0.682075\pi$
$461$	−23.2453			−1.08264			−0.541320	+	0.840817i	$0.682075\pi$
$462$		0			0
$463$	−7.59393			−0.352920			−0.176460	−	0.984308i	$-0.556465\pi$
$463$	−7.59393			−0.352920			−0.176460	+	0.984308i	$0.556465\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.0839	−	24.3941i	0.651726	−	1.12882i	−0.330978	−	0.943639i	$-0.607379\pi$
$467$	14.0839	−	24.3941i	0.651726	−	1.12882i	0.982704	−	0.185184i	$-0.0592881\pi$
$468$		0			0
$469$	−0.689404	−	2.17478i	−0.0318337	−	0.100422i
$470$		0			0
$471$	−15.4673	+	26.7902i	−0.712697	+	1.23443i
$472$		0			0
$473$	3.60756	+	6.24848i	0.165876	+	0.287305i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−34.3297			−1.57185
$478$		0			0
$479$	17.0900	+	29.6007i	0.780860	+	1.35249i	0.931441	+	0.363892i	$0.118552\pi$
$479$	17.0900	+	29.6007i	0.780860	+	1.35249i	−0.150581	+	0.988598i	$0.548114\pi$
$480$		0			0
$481$	18.6739	−	32.3441i	0.851456	−	1.47476i
$482$		0			0
$483$	38.0784	+	8.38002i	1.73263	+	0.381304i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.75176	−	9.96234i	−0.260637	−	0.451436i	0.705774	−	0.708437i	$-0.250599\pi$
$487$	−5.75176	−	9.96234i	−0.260637	−	0.451436i	−0.966411	+	0.257000i	$0.917266\pi$
$488$		0			0
$489$	42.9940			1.94426
$490$		0			0
$491$	−25.5337			−1.15232			−0.576159	−	0.817338i	$-0.695449\pi$
$491$	−25.5337			−1.15232			−0.576159	+	0.817338i	$0.695449\pi$
$492$		0			0
$493$	7.05982	+	12.2280i	0.317958	+	0.550720i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	31.3628	+	6.90210i	1.40682	+	0.309602i
$498$		0			0
$499$	5.69798	−	9.86919i	0.255076	−	0.441805i	−0.709840	−	0.704363i	$-0.751233\pi$
$499$	5.69798	−	9.86919i	0.255076	−	0.441805i	0.964916	+	0.262558i	$0.0845660\pi$
$500$		0			0
$501$	−8.69148	−	15.0541i	−0.388307	−	0.672567i
$502$		0			0
$503$	2.49649			0.111313			0.0556564	−	0.998450i	$-0.482275\pi$
$503$	2.49649			0.111313			0.0556564	+	0.998450i	$0.482275\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−23.1352	−	40.0713i	−1.02747	−	1.77963i
$508$		0			0
$509$	−5.77188	+	9.99720i	−0.255834	+	0.443118i	−0.965122	−	0.261801i	$-0.915683\pi$
$509$	−5.77188	+	9.99720i	−0.255834	+	0.443118i	0.709287	+	0.704919i	$0.249017\pi$
$510$		0			0
$511$	−3.19798	−	10.0883i	−0.141470	−	0.446278i
$512$		0			0
$513$	−2.43719	+	4.22134i	−0.107605	+	0.186377i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.629127			0.0276690
$518$		0			0
$519$	−12.0594			−0.529348
$520$		0			0
$521$	−11.8744	−	20.5670i	−0.520226	−	0.901058i	−0.999723	−	0.0235150i	$-0.992514\pi$
$521$	−11.8744	−	20.5670i	−0.520226	−	0.901058i	0.479497	−	0.877543i	$-0.340819\pi$
$522$		0			0
$523$	8.06885	−	13.9757i	0.352826	−	0.611113i	−0.633917	−	0.773401i	$-0.718554\pi$
$523$	8.06885	−	13.9757i	0.352826	−	0.611113i	0.986743	+	0.162288i	$0.0518874\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.47590	−	6.02044i	0.151413	−	0.262255i
$528$		0			0
$529$	−4.95479	−	8.58195i	−0.215426	−	0.373128i
$530$		0			0
$531$	−16.4432			−0.713576
$532$		0			0
$533$	49.4201			2.14062
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−14.7367	+	25.5247i	−0.635935	+	1.10147i
$538$		0			0
$539$	0.990974	+	10.9371i	0.0426843	+	0.471096i
$540$		0			0
$541$	0.769355	−	1.33256i	0.0330772	−	0.0572913i	−0.849013	−	0.528372i	$-0.822803\pi$
$541$	0.769355	−	1.33256i	0.0330772	−	0.0572913i	0.882090	+	0.471081i	$0.156136\pi$
$542$		0			0
$543$	−1.06885	−	1.85130i	−0.0458687	−	0.0794470i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	14.3779			0.614755			0.307377	−	0.951588i	$-0.400549\pi$
$547$	14.3779			0.614755			0.307377	+	0.951588i	$0.400549\pi$
$548$		0			0
$549$	−27.5422	−	47.7045i	−1.17547	−	2.03598i
$550$		0			0
$551$	−3.12010	+	5.40417i	−0.132921	+	0.230226i
$552$		0			0
$553$	−22.9734	+	25.1490i	−0.976927	+	1.06944i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.46733	−	14.6658i	−0.358772	−	0.621412i	0.628984	−	0.777419i	$-0.283471\pi$
$557$	−8.46733	−	14.6658i	−0.358772	−	0.621412i	−0.987756	+	0.156007i	$0.950138\pi$
$558$		0			0
$559$	−25.6111			−1.08323
$560$		0			0
$561$	28.8874			1.21963
$562$		0			0
$563$	0.332162	+	0.575322i	0.0139990	+	0.0242469i	0.872940	−	0.487828i	$-0.162211\pi$
$563$	0.332162	+	0.575322i	0.0139990	+	0.0242469i	−0.858941	+	0.512074i	$0.828877\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−5.47194	−	17.2616i	−0.229800	−	0.724921i
$568$		0			0
$569$	20.5186	−	35.5392i	0.860184	−	1.48988i	−0.0115674	−	0.999933i	$-0.503682\pi$
$569$	20.5186	−	35.5392i	0.860184	−	1.48988i	0.871751	−	0.489949i	$-0.162985\pi$
$570$		0			0
$571$	14.3146	+	24.7936i	0.599046	+	1.03758i	0.992962	+	0.118432i	$0.0377866\pi$
$571$	14.3146	+	24.7936i	0.599046	+	1.03758i	−0.393916	+	0.919146i	$0.628880\pi$
$572$		0			0
$573$	17.8271			0.744738
$574$		0			0
$575$		0			0
$576$		0			0
$577$	15.7302	+	27.2455i	0.654856	+	1.13424i	0.981930	+	0.189246i	$0.0606042\pi$
$577$	15.7302	+	27.2455i	0.654856	+	1.13424i	−0.327073	+	0.944999i	$0.606062\pi$
$578$		0			0
$579$	25.2729	−	43.7739i	1.05030	−	1.81918i
$580$		0			0
$581$	44.2046	+	9.72821i	1.83391	+	0.403594i
$582$		0			0
$583$	−7.48240	+	12.9599i	−0.309889	+	0.536744i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.53871			0.393705			0.196852	−	0.980433i	$-0.436928\pi$
$587$	9.53871			0.393705			0.196852	+	0.980433i	$0.436928\pi$
$588$		0			0
$589$	3.07236			0.126595
$590$		0			0
$591$	−20.6050	−	35.6890i	−0.847578	−	1.46805i
$592$		0			0
$593$	4.96986	−	8.60805i	0.204088	−	0.353490i	−0.745754	−	0.666221i	$-0.767911\pi$
$593$	4.96986	−	8.60805i	0.204088	−	0.353490i	0.949842	+	0.312731i	$0.101244\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	13.7130	−	23.7517i	0.561238	−	0.972092i
$598$		0			0
$599$	−4.70655	−	8.15198i	−0.192304	−	0.333081i	0.753709	−	0.657208i	$-0.228263\pi$
$599$	−4.70655	−	8.15198i	−0.192304	−	0.333081i	−0.946014	+	0.324127i	$0.894929\pi$
$600$		0			0
$601$	−3.00506			−0.122579			−0.0612894	−	0.998120i	$-0.519521\pi$
$601$	−3.00506			−0.122579			−0.0612894	+	0.998120i	$0.519521\pi$
$602$		0			0
$603$	−3.10341			−0.126381
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−9.41608	+	16.3091i	−0.382187	+	0.661967i	−0.991375	−	0.131059i	$-0.958162\pi$
$607$	−9.41608	+	16.3091i	−0.382187	+	0.661967i	0.609188	+	0.793026i	$0.291496\pi$
$608$		0			0
$609$	4.04566	+	12.7623i	0.163939	+	0.517156i
$610$		0			0
$611$	−1.11659	+	1.93399i	−0.0451723	+	0.0782407i
$612$		0			0
$613$	7.91959	+	13.7171i	0.319869	+	0.554030i	0.980461	−	0.196716i	$-0.0630276\pi$
$613$	7.91959	+	13.7171i	0.319869	+	0.554030i	−0.660591	+	0.750746i	$0.729694\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.778912			0.0313578			0.0156789	−	0.999877i	$-0.495009\pi$
$617$	0.778912			0.0313578			0.0156789	+	0.999877i	$0.495009\pi$
$618$		0			0
$619$	−4.97338	−	8.61414i	−0.199897	−	0.346231i	0.748598	−	0.663024i	$-0.230727\pi$
$619$	−4.97338	−	8.61414i	−0.199897	−	0.346231i	−0.948495	+	0.316793i	$0.897394\pi$
$620$		0			0
$621$	4.41355	−	7.64450i	0.177110	−	0.306763i
$622$		0			0
$623$	−9.99097	+	10.9371i	−0.400280	+	0.438187i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.38341	+	11.0564i	0.254929	+	0.441550i
$628$		0			0
$629$	−48.0715			−1.91673
$630$		0			0
$631$	−12.5638			−0.500157			−0.250078	−	0.968226i	$-0.580456\pi$
$631$	−12.5638			−0.500157			−0.250078	+	0.968226i	$0.580456\pi$
$632$		0			0
$633$	−14.5985	−	25.2854i	−0.580240	−	1.00500i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−35.3804	−	16.3651i	−1.40182	−	0.648410i
$638$		0			0
$639$	21.8417	−	37.8310i	0.864045	−	1.49657i
$640$		0			0
$641$	5.76033	+	9.97718i	0.227519	+	0.394075i	0.957072	−	0.289849i	$-0.0936052\pi$
$641$	5.76033	+	9.97718i	0.227519	+	0.394075i	−0.729553	+	0.683924i	$0.760272\pi$
$642$		0			0
$643$	9.74175			0.384177			0.192088	−	0.981378i	$-0.438474\pi$
$643$	9.74175			0.384177			0.192088	+	0.981378i	$0.438474\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.8769	−	22.3035i	−0.506244	−	0.876840i	−0.999974	−	0.00722479i	$-0.997700\pi$
$647$	−12.8769	−	22.3035i	−0.506244	−	0.876840i	0.493730	−	0.869615i	$-0.335633\pi$
$648$		0			0
$649$	−3.58392	+	6.20753i	−0.140681	+	0.243667i
$650$		0			0
$651$	4.44577	−	4.86679i	0.174243	−	0.190745i
$652$		0			0
$653$	−7.59646	+	13.1575i	−0.297272	+	0.514891i	−0.975511	−	0.219951i	$-0.929410\pi$
$653$	−7.59646	+	13.1575i	−0.297272	+	0.514891i	0.678239	+	0.734842i	$0.262744\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−14.3960			−0.561640
$658$		0			0
$659$	−14.6894			−0.572218			−0.286109	−	0.958197i	$-0.592362\pi$
$659$	−14.6894			−0.572218			−0.286109	+	0.958197i	$0.592362\pi$
$660$		0			0
$661$	−2.16784	−	3.75481i	−0.0843191	−	0.146045i	0.820782	−	0.571242i	$-0.193538\pi$
$661$	−2.16784	−	3.75481i	−0.0843191	−	0.146045i	−0.905101	+	0.425197i	$0.860205\pi$
$662$		0			0
$663$	−51.2699	+	88.8020i	−1.99116	+	3.44879i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.65024	−	9.78650i	0.218778	−	0.378935i
$668$		0			0
$669$	−7.76078	−	13.4421i	−0.300049	−	0.519700i
$670$		0			0
$671$	−24.0121			−0.926976
$672$		0			0
$673$	−34.1971			−1.31820			−0.659100	−	0.752055i	$-0.729063\pi$
$673$	−34.1971			−1.31820			−0.659100	+	0.752055i	$0.729063\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.04521	−	15.6668i	0.347636	−	0.602122i	−0.638193	−	0.769876i	$-0.720318\pi$
$677$	9.04521	−	15.6668i	0.347636	−	0.602122i	0.985829	+	0.167754i	$0.0536513\pi$
$678$		0			0
$679$	0.602502	+	0.132594i	0.0231219	+	0.00508850i
$680$		0			0
$681$	27.7965	−	48.1450i	1.06516	−	1.84492i
$682$		0			0
$683$	−12.0628	−	20.8934i	−0.461570	−	0.799464i	0.537469	−	0.843284i	$-0.319381\pi$
$683$	−12.0628	−	20.8934i	−0.461570	−	0.799464i	−0.999039	+	0.0438200i	$0.986047\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−13.9518			−0.532295
$688$		0			0
$689$	−26.5598	−	46.0030i	−1.01185	−	1.75257i
$690$		0			0
$691$	−8.72415	+	15.1107i	−0.331882	+	0.574837i	−0.982881	−	0.184242i	$-0.941017\pi$
$691$	−8.72415	+	15.1107i	−0.331882	+	0.574837i	0.650999	+	0.759079i	$0.274350\pi$
$692$		0			0
$693$	14.5895	+	3.21075i	0.554210	+	0.121966i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−31.8051	−	55.0880i	−1.20470	−	2.08661i
$698$		0			0
$699$	17.8271			0.674283
$700$		0			0
$701$	20.7015			0.781885			0.390942	−	0.920415i	$-0.372149\pi$
$701$	20.7015			0.781885			0.390942	+	0.920415i	$0.372149\pi$
$702$		0			0
$703$	−10.6226	−	18.3989i	−0.400640	−	0.693929i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.99649	+	31.5347i	0.375957	+	1.18598i
$708$		0			0
$709$	−3.54774	+	6.14486i	−0.133238	+	0.230775i	−0.924923	−	0.380154i	$-0.875871\pi$
$709$	−3.54774	+	6.14486i	−0.133238	+	0.230775i	0.791685	+	0.610930i	$0.209204\pi$
$710$		0			0
$711$	23.1674	+	40.1271i	0.868845	+	1.50488i
$712$		0			0
$713$	−5.56379			−0.208366
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.17641	−	3.76965i	−0.0812795	−	0.140780i
$718$		0			0
$719$	−26.2216	+	45.4172i	−0.977901	+	1.69377i	−0.307893	+	0.951421i	$0.599624\pi$
$719$	−26.2216	+	45.4172i	−0.977901	+	1.69377i	−0.670008	+	0.742354i	$0.733709\pi$
$720$		0			0
$721$	−6.01507	+	6.58471i	−0.224013	+	0.245227i
$722$		0			0
$723$	19.1825	−	33.2250i	0.713403	−	1.23565i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	29.9045			1.10910			0.554549	−	0.832151i	$-0.312891\pi$
$727$	29.9045			1.10910			0.554549	+	0.832151i	$0.312891\pi$
$728$		0			0
$729$	−36.4905			−1.35150
$730$		0			0
$731$	16.4824	+	28.5484i	0.609624	+	1.05590i
$732$		0			0
$733$	2.79047	−	4.83323i	0.103068	−	0.178519i	−0.809879	−	0.586597i	$-0.800467\pi$
$733$	2.79047	−	4.83323i	0.103068	−	0.178519i	0.912947	+	0.408077i	$0.133801\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.676410	+	1.17158i	−0.0249159	+	0.0431556i
$738$		0			0
$739$	−20.3744	−	35.2895i	−0.749484	−	1.29814i	−0.948070	−	0.318061i	$-0.896968\pi$
$739$	−20.3744	−	35.2895i	−0.749484	−	1.29814i	0.198586	−	0.980083i	$-0.436365\pi$
$740$		0			0
$741$	−45.3176			−1.66478
$742$		0			0
$743$	−50.5327			−1.85387			−0.926933	−	0.375226i	$-0.877565\pi$
$743$	−50.5327			−1.85387			−0.926933	+	0.375226i	$0.877565\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	30.7850	−	53.3211i	1.12636	−	1.95092i
$748$		0			0
$749$	31.6498	−	34.6471i	1.15646	−	1.26598i
$750$		0			0
$751$	15.3568	−	26.5987i	0.560377	−	0.970602i	−0.437086	−	0.899420i	$-0.643990\pi$
$751$	15.3568	−	26.5987i	0.560377	−	0.970602i	0.997463	−	0.0711821i	$-0.0226771\pi$
$752$		0			0
$753$	−11.4437	−	19.8211i	−0.417031	−	0.722319i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	20.7116			0.752776			0.376388	−	0.926462i	$-0.377166\pi$
$757$	20.7116			0.752776			0.376388	+	0.926462i	$0.377166\pi$
$758$		0			0
$759$	−11.5598	−	20.0222i	−0.419595	−	0.726760i
$760$		0			0
$761$	17.1764	−	29.7504i	0.622644	−	1.07845i	−0.366347	−	0.930478i	$-0.619392\pi$
$761$	17.1764	−	29.7504i	0.622644	−	1.07845i	0.988991	−	0.147973i	$-0.0472750\pi$
$762$		0			0
$763$	4.72063	+	14.8916i	0.170898	+	0.539112i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.7216	−	22.0345i	−0.459351	−	0.795619i
$768$		0			0
$769$	46.8392			1.68906			0.844532	−	0.535505i	$-0.179879\pi$
$769$	46.8392			1.68906			0.844532	+	0.535505i	$0.179879\pi$
$770$		0			0
$771$	−24.8262			−0.894094
$772$		0			0
$773$	16.6653	+	28.8652i	0.599409	+	1.03821i	0.992908	+	0.118883i	$0.0379312\pi$
$773$	16.6653	+	28.8652i	0.599409	+	1.03821i	−0.393499	+	0.919325i	$0.628735\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−44.5161	−	9.79677i	−1.59700	−	0.351457i
$778$		0			0
$779$	14.0563	−	24.3462i	0.503620	−	0.872295i
$780$		0			0
$781$	−9.52111	−	16.4911i	−0.340692	−	0.590096i
$782$		0			0
$783$	3.03105			0.108321
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.20402	+	7.28158i	0.149857	+	0.259560i	0.931175	−	0.364574i	$-0.118785\pi$
$787$	4.20402	+	7.28158i	0.149857	+	0.259560i	−0.781317	+	0.624134i	$0.785452\pi$
$788$		0			0
$789$	−7.83821	+	13.5762i	−0.279047	+	0.483324i
$790$		0			0
$791$	40.4156	+	8.89438i	1.43701	+	0.316248i
$792$		0			0
$793$	42.6171	−	73.8150i	1.51338	−	2.62125i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.2935			−0.577144			−0.288572	−	0.957458i	$-0.593180\pi$
$797$	−16.2935			−0.577144			−0.288572	+	0.957458i	$0.593180\pi$
$798$		0			0
$799$	2.87439			0.101688
$800$		0			0
$801$	10.0753	+	17.4510i	0.355995	+	0.616601i
$802$		0			0
$803$	−3.13770	+	5.43465i	−0.110727	+	0.191785i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.9428	+	50.1304i	−1.01883	+	1.76467i
$808$		0			0
$809$	7.75176	+	13.4264i	0.272537	+	0.472048i	0.969511	−	0.245048i	$-0.0788039\pi$
$809$	7.75176	+	13.4264i	0.272537	+	0.472048i	−0.696974	+	0.717097i	$0.745471\pi$
$810$		0			0
$811$	−36.6232			−1.28601			−0.643007	−	0.765861i	$-0.722313\pi$
$811$	−36.6232			−1.28601			−0.643007	+	0.765861i	$0.722313\pi$
$812$		0			0
$813$	11.4604			0.401933
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.28442	+	12.6170i	−0.254850	+	0.441413i
$818$		0			0
$819$	−35.7638	+	39.1508i	−1.24969	+	1.36804i
$820$		0			0
$821$	21.6649	−	37.5246i	0.756109	−	1.30962i	−0.188713	−	0.982032i	$-0.560431\pi$
$821$	21.6649	−	37.5246i	0.756109	−	1.30962i	0.944821	−	0.327586i	$-0.106235\pi$
$822$		0			0
$823$	20.5272	+	35.5541i	0.715532	+	1.23934i	0.962754	+	0.270378i	$0.0871488\pi$
$823$	20.5272	+	35.5541i	0.715532	+	1.23934i	−0.247222	+	0.968959i	$0.579518\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0473			−1.04485			−0.522423	−	0.852686i	$-0.674972\pi$
$827$	−30.0473			−1.04485			−0.522423	+	0.852686i	$0.674972\pi$
$828$		0			0
$829$	21.0146	+	36.3984i	0.729868	+	1.26417i	0.956939	+	0.290290i	$0.0937517\pi$
$829$	21.0146	+	36.3984i	0.729868	+	1.26417i	−0.227071	+	0.973878i	$0.572915\pi$
$830$		0			0
$831$	8.35977	−	14.4795i	0.289997	−	0.502290i
$832$		0			0
$833$	4.52761	+	49.9702i	0.156872	+	1.73136i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.746168	−	1.29240i	−0.0257913	−	0.0446719i
$838$		0			0
$839$	3.38893			0.116999			0.0584994	−	0.998287i	$-0.481368\pi$
$839$	3.38893			0.116999			0.0584994	+	0.998287i	$0.481368\pi$
$840$		0			0
$841$	−25.1196			−0.866195
$842$		0			0
$843$	14.3830	+	24.9120i	0.495375	+	0.858015i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−15.2367	+	16.6796i	−0.523539	+	0.573119i
$848$		0			0
$849$	−9.82106	+	17.0106i	−0.337058	+	0.583801i
$850$		0			0
$851$	19.2367	+	33.3189i	0.659425	+	1.14216i
$852$		0			0
$853$	−25.1267			−0.860321			−0.430160	−	0.902752i	$-0.641543\pi$
$853$	−25.1267			−0.860321			−0.430160	+	0.902752i	$0.641543\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.8683	+	41.3412i	0.815327	+	1.41219i	0.909093	+	0.416594i	$0.136776\pi$
$857$	23.8683	+	41.3412i	0.815327	+	1.41219i	−0.0937657	+	0.995594i	$0.529890\pi$
$858$		0			0
$859$	20.5211	−	35.5436i	0.700171	−	1.21273i	−0.268235	−	0.963354i	$-0.586440\pi$
$859$	20.5211	−	35.5436i	0.700171	−	1.21273i	0.968406	−	0.249379i	$-0.0802264\pi$
$860$		0			0
$861$	−18.2260	−	57.4954i	−0.621142	−	1.95944i
$862$		0			0
$863$	15.5663	−	26.9617i	0.529884	−	0.917786i	−0.469509	−	0.882928i	$-0.655569\pi$
$863$	15.5663	−	26.9617i	0.529884	−	0.917786i	0.999392	−	0.0348576i	$-0.0110978\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	88.3117			2.99922
$868$		0			0
$869$	20.1980			0.685169
$870$		0			0
$871$	−2.40101	−	4.15867i	−0.0813552	−	0.140911i
$872$		0			0
$873$	0.419595	−	0.726760i	0.0142011	−	0.0245971i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.96986	−	6.87600i	0.134053	−	0.232186i	−0.791182	−	0.611580i	$-0.790534\pi$
$877$	3.96986	−	6.87600i	0.134053	−	0.232186i	0.925235	+	0.379394i	$0.123868\pi$
$878$		0			0
$879$	7.86789	+	13.6276i	0.265377	+	0.459647i
$880$		0			0
$881$	−29.3709			−0.989530			−0.494765	−	0.869027i	$-0.664746\pi$
$881$	−29.3709			−0.989530			−0.494765	+	0.869027i	$0.664746\pi$
$882$		0			0
$883$	26.9718			0.907674			0.453837	−	0.891085i	$-0.350055\pi$
$883$	26.9718			0.907674			0.453837	+	0.891085i	$0.350055\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.7427	+	20.3390i	−0.394282	+	0.682917i	−0.993009	−	0.118036i	$-0.962340\pi$
$887$	−11.7427	+	20.3390i	−0.394282	+	0.682917i	0.598727	+	0.800953i	$0.295673\pi$
$888$		0			0
$889$	33.2664	+	7.32102i	1.11572	+	0.245539i
$890$		0			0
$891$	−5.36880	+	9.29903i	−0.179861	+	0.311529i
$892$		0			0
$893$	0.635170	+	1.10015i	0.0212552	+	0.0368150i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	82.0664			2.74012
$898$		0			0
$899$	−0.955246	−	1.65453i	−0.0318592	−	0.0551818i
$900$		0			0
$901$	−34.1860	+	59.2118i	−1.13890	+	1.97263i
$902$		0			0
$903$	9.44531	+	29.7959i	0.314320	+	0.991547i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.79345	+	8.30250i	0.159164	+	0.275680i	0.934567	−	0.355786i	$-0.115787\pi$
$907$	4.79345	+	8.30250i	0.159164	+	0.275680i	−0.775403	+	0.631466i	$0.782453\pi$
$908$		0			0
$909$	45.0000			1.49256
$910$		0			0
$911$	−3.78994			−0.125566			−0.0627831	−	0.998027i	$-0.519998\pi$
$911$	−3.78994			−0.125566			−0.0627831	+	0.998027i	$0.519998\pi$
$912$		0			0
$913$	−13.4196	−	23.2434i	−0.444124	−	0.769245i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.407055	+	0.445604i	−0.0134421	+	0.0147151i
$918$		0			0
$919$	−11.6950	+	20.2563i	−0.385782	+	0.668194i	−0.991877	−	0.127198i	$-0.959402\pi$
$919$	−11.6950	+	20.2563i	−0.385782	+	0.668194i	0.606095	+	0.795392i	$0.292735\pi$
$920$		0			0
$921$	33.9191	+	58.7497i	1.11767	+	1.93587i
$922$		0			0
$923$	67.5930			2.22485
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.06587	+	10.5064i	0.199229	+	0.345075i
$928$		0			0
$929$	−25.1287	+	43.5241i	−0.824445	+	1.42798i	0.0778977	+	0.996961i	$0.475179\pi$
$929$	−25.1287	+	43.5241i	−0.824445	+	1.42798i	−0.902343	+	0.431019i	$0.858154\pi$
$930$		0			0
$931$	−18.1252	+	12.7751i	−0.594028	+	0.418687i
$932$		0			0
$933$	24.8572	−	43.0540i	0.813790	−	1.40952i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	2.43621			0.0795875			0.0397937	−	0.999208i	$-0.487330\pi$
$937$	2.43621			0.0795875			0.0397937	+	0.999208i	$0.487330\pi$
$938$		0			0
$939$	−22.3658			−0.729881
$940$		0			0
$941$	11.9824	+	20.7541i	0.390615	+	0.676565i	0.992531	−	0.121994i	$-0.0389290\pi$
$941$	11.9824	+	20.7541i	0.390615	+	0.676565i	−0.601916	+	0.798560i	$0.705596\pi$
$942$		0			0
$943$	−25.4548	+	44.0890i	−0.828922	+	1.43574i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.5809	+	44.3075i	−0.831269	+	1.43980i	0.0657639	+	0.997835i	$0.479052\pi$
$947$	−25.5809	+	44.3075i	−0.831269	+	1.43980i	−0.897033	+	0.441964i	$0.854282\pi$
$948$		0			0
$949$	−11.1377	−	19.2911i	−0.361545	−	0.626214i
$950$		0			0
$951$	−39.2402			−1.27245
$952$		0			0
$953$	−33.3306			−1.07968			−0.539842	−	0.841766i	$-0.681516\pi$
$953$	−33.3306			−1.07968			−0.539842	+	0.841766i	$0.681516\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	3.96941	−	6.87521i	0.128313	−	0.222244i
$958$		0			0
$959$	7.73623	+	24.4045i	0.249816	+	0.788063i
$960$		0			0
$961$	15.0297	−	26.0322i	0.484829	−	0.839748i
$962$		0			0
$963$	−31.9171	−	55.2820i	−1.02851	−	1.78144i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	31.8392			1.02388			0.511940	−	0.859021i	$-0.328927\pi$
$967$	31.8392			1.02388			0.511940	+	0.859021i	$0.328927\pi$
$968$		0			0
$969$	29.1649	+	50.5150i	0.936910	+	1.62278i
$970$		0			0
$971$	−0.973375	+	1.68594i	−0.0312371	+	0.0541042i	−0.881221	−	0.472704i	$-0.843278\pi$
$971$	−0.973375	+	1.68594i	−0.0312371	+	0.0541042i	0.849984	+	0.526808i	$0.176611\pi$
$972$		0			0
$973$	31.9653	+	7.03470i	1.02476	+	0.225522i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.0598	−	43.4049i	−0.801735	−	1.38865i	−0.918473	−	0.395483i	$-0.870577\pi$
$977$	−25.0598	−	43.4049i	−0.801735	−	1.38865i	0.116739	−	0.993163i	$-0.462756\pi$
$978$		0			0
$979$	8.78397			0.280737
$980$		0			0
$981$	21.2503			0.678470
$982$		0			0
$983$	−23.9608	−	41.5014i	−0.764232	−	1.32369i	−0.940652	−	0.339374i	$-0.889785\pi$
$983$	−23.9608	−	41.5014i	−0.764232	−	1.32369i	0.176420	−	0.984315i	$-0.443548\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.66179	+	0.585788i	0.0847259	+	0.0186458i
$988$		0			0
$989$	13.1915	−	22.8483i	0.419465	−	0.726534i
$990$		0			0
$991$	−4.43466	−	7.68106i	−0.140872	−	0.243997i	0.786953	−	0.617012i	$-0.211657\pi$
$991$	−4.43466	−	7.68106i	−0.140872	−	0.243997i	−0.927825	+	0.373015i	$0.878324\pi$
$992$		0			0
$993$	43.0251			1.36536
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.10503	+	10.5742i	0.193348	+	0.334889i	0.946358	−	0.323121i	$-0.104732\pi$
$997$	6.10503	+	10.5742i	0.193348	+	0.334889i	−0.753010	+	0.658010i	$0.771399\pi$
$998$		0			0
$999$	−5.15972	+	8.93690i	−0.163246	+	0.282751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.i.e.401.1	yes	6
5.2	odd	4		700.2.r.d.149.2		12
5.3	odd	4		700.2.r.d.149.5		12
5.4	even	2		700.2.i.d.401.3	✓	6
7.2	even	3		4900.2.a.ba.1.3		3
7.4	even	3	inner	700.2.i.e.501.1	yes	6
7.5	odd	6		4900.2.a.bd.1.1		3
35.2	odd	12		4900.2.e.t.2549.2		6
35.4	even	6		700.2.i.d.501.3	yes	6
35.9	even	6		4900.2.a.bc.1.1		3
35.12	even	12		4900.2.e.s.2549.5		6
35.18	odd	12		700.2.r.d.249.2		12
35.19	odd	6		4900.2.a.bb.1.3		3
35.23	odd	12		4900.2.e.t.2549.5		6
35.32	odd	12		700.2.r.d.249.5		12
35.33	even	12		4900.2.e.s.2549.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.i.d.401.3	✓	6	5.4	even	2
700.2.i.d.501.3	yes	6	35.4	even	6
700.2.i.e.401.1	yes	6	1.1	even	1	trivial
700.2.i.e.501.1	yes	6	7.4	even	3	inner
700.2.r.d.149.2		12	5.2	odd	4
700.2.r.d.149.5		12	5.3	odd	4
700.2.r.d.249.2		12	35.18	odd	12
700.2.r.d.249.5		12	35.32	odd	12
4900.2.a.ba.1.3		3	7.2	even	3
4900.2.a.bb.1.3		3	35.19	odd	6
4900.2.a.bc.1.1		3	35.9	even	6
4900.2.a.bd.1.1		3	7.5	odd	6
4900.2.e.s.2549.2		6	35.33	even	12
4900.2.e.s.2549.5		6	35.12	even	12
4900.2.e.t.2549.2		6	35.2	odd	12
4900.2.e.t.2549.5		6	35.23	odd	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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28442 - 2.22469i) q^{3} +(-2.58392 - 0.568650i) q^{7} +(-1.79949 + 3.11682i) q^{9} +O(q^{10})\)	\(q+(-1.28442 - 2.22469i) q^{3} +(-2.58392 - 0.568650i) q^{7} +(-1.79949 + 3.11682i) q^{9} +(0.784425 + 1.35866i) q^{11} -5.56885 q^{13} +(3.58392 + 6.20753i) q^{17} +(-1.58392 + 2.74343i) q^{19} +(2.05378 + 6.47880i) q^{21} +(2.86834 - 4.96812i) q^{23} +1.53871 q^{27} +1.96986 q^{29} +(-0.484931 - 0.839925i) q^{31} +(2.01507 - 3.49020i) q^{33} +(-3.35327 + 5.80804i) q^{37} +(7.15277 + 12.3890i) q^{39} -8.87439 q^{41} +4.59899 q^{43} +(0.200506 - 0.347286i) q^{47} +(6.35327 + 2.93869i) q^{49} +(9.20655 - 15.9462i) q^{51} +(4.76936 + 8.26077i) q^{53} +8.13770 q^{57} +(2.28442 + 3.95674i) q^{59} +(-7.65277 + 13.2550i) q^{61} +(6.42212 - 7.03032i) q^{63} +(0.431150 + 0.746774i) q^{67} -14.7367 q^{69} -12.1377 q^{71} +(2.00000 + 3.46410i) q^{73} +(-1.25429 - 3.95674i) q^{77} +(6.43719 - 11.1495i) q^{79} +(3.42212 + 5.92729i) q^{81} -17.1076 q^{83} +(-2.53014 - 4.38233i) q^{87} +(2.79949 - 4.84887i) q^{89} +(14.3895 + 3.16673i) q^{91} +(-1.24571 + 2.15764i) q^{93} -0.233174 q^{97} -5.64627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 6 * q + q^3 - 4 * q^7 - 8 * q^9	\( 6 q + q^{3} - 4 q^{7} - 8 q^{9} - 4 q^{11} - 16 q^{13} + 10 q^{17} + 2 q^{19} - 11 q^{21} - 3 q^{23} - 20 q^{27} + 3 q^{31} + 18 q^{33} + 6 q^{37} + 14 q^{39} + 22 q^{41} + 22 q^{43} + 4 q^{47} + 12 q^{49} + 3 q^{51} + 14 q^{53} + 14 q^{57} + 5 q^{59} - 17 q^{61} - 5 q^{63} + 20 q^{67} - 48 q^{69} - 38 q^{71} + 12 q^{73} + 13 q^{77} + q^{79} - 23 q^{81} - 56 q^{83} - 27 q^{87} + 14 q^{89} + 17 q^{91} - 28 q^{93} - 30 q^{97} + 42 q^{99}+O(q^{100}) \) 6 * q + q^3 - 4 * q^7 - 8 * q^9 - 4 * q^11 - 16 * q^13 + 10 * q^17 + 2 * q^19 - 11 * q^21 - 3 * q^23 - 20 * q^27 + 3 * q^31 + 18 * q^33 + 6 * q^37 + 14 * q^39 + 22 * q^41 + 22 * q^43 + 4 * q^47 + 12 * q^49 + 3 * q^51 + 14 * q^53 + 14 * q^57 + 5 * q^59 - 17 * q^61 - 5 * q^63 + 20 * q^67 - 48 * q^69 - 38 * q^71 + 12 * q^73 + 13 * q^77 + q^79 - 23 * q^81 - 56 * q^83 - 27 * q^87 + 14 * q^89 + 17 * q^91 - 28 * q^93 - 30 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more