LMFDB - Embedded newform 1400.2.bh.g.249.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1400.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.3
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.g.849.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.358719 + 0.207107i) q^{3} +(-2.09077 + 1.62132i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q+(0.358719 + 0.207107i) q^{3} +(-2.09077 + 1.62132i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} -2.00000i q^{13} +(6.63103 + 3.82843i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-1.08579 + 0.148586i) q^{21} +(4.83743 - 2.79289i) q^{23} -2.41421i q^{27} +7.82843 q^{29} +(-0.414214 + 0.717439i) q^{31} +(-0.297173 + 0.171573i) q^{33} +(4.89898 - 2.82843i) q^{37} +(0.414214 - 0.717439i) q^{39} +5.82843 q^{41} +6.89949i q^{43} +(10.0951 - 5.82843i) q^{47} +(1.74264 - 6.77962i) q^{49} +(1.58579 + 2.74666i) q^{51} +(-4.89898 - 2.82843i) q^{53} -2.34315i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-3.32843 - 5.76500i) q^{61} +(6.92820 + 2.82843i) q^{63} +(11.1713 + 6.44975i) q^{67} +2.31371 q^{69} -12.0000 q^{71} +(3.16693 + 1.82843i) q^{73} +(-0.297173 - 2.17157i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-3.74264 + 6.48244i) q^{81} +4.75736i q^{83} +(2.80821 + 1.62132i) q^{87} +(-2.67157 - 4.62730i) q^{89} +(3.24264 + 4.18154i) q^{91} +(-0.297173 + 0.171573i) q^{93} +6.00000i q^{97} +2.34315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 8 q^{11} - 20 q^{21} + 40 q^{29} + 8 q^{31} - 8 q^{39} + 24 q^{41} - 20 q^{49} + 24 q^{51} - 16 q^{59} - 4 q^{61} - 72 q^{69} - 96 q^{71} - 16 q^{79} + 4 q^{81} - 44 q^{89} - 8 q^{91} + 64 q^{99}+O(q^{100}) $ 8 * q + 8 * q^11 - 20 * q^21 + 40 * q^29 + 8 * q^31 - 8 * q^39 + 24 * q^41 - 20 * q^49 + 24 * q^51 - 16 * q^59 - 4 * q^61 - 72 * q^69 - 96 * q^71 - 16 * q^79 + 4 * q^81 - 44 * q^89 - 8 * q^91 + 64 * 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
$3$	0.358719	+	0.207107i	0.207107	+	0.119573i	0.599966	−	0.800025i	$-0.295181\pi$
$3$	0.358719	+	0.207107i	0.207107	+	0.119573i	−0.392859	+	0.919599i	$0.628514\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.09077	+	1.62132i	−0.790237	+	0.612801i
$7$	−2.09077	+	1.62132i	−0.790237	+	0.612801i
$8$		0			0
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	−0.414214	+	0.717439i	−0.124890	+	0.216316i	−0.921690	−	0.387927i	$-0.873191\pi$
$11$	−0.414214	+	0.717439i	−0.124890	+	0.216316i	0.796800	+	0.604243i	$0.206524\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.63103	+	3.82843i	1.60826	+	0.928530i	0.989759	+	0.142747i	$0.0455934\pi$
$17$	6.63103	+	3.82843i	1.60826	+	0.928530i	0.618502	+	0.785783i	$0.287740\pi$
$18$		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
$21$	−1.08579	+	0.148586i	−0.236938	+	0.0324242i
$22$		0			0
$23$	4.83743	−	2.79289i	1.00867	−	0.582358i	0.0978712	−	0.995199i	$-0.468797\pi$
$23$	4.83743	−	2.79289i	1.00867	−	0.582358i	0.910803	+	0.412841i	$0.135463\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	2.41421i		−	0.464616i
$28$		0			0
$29$	7.82843			1.45370			0.726851	−	0.686795i	$-0.240983\pi$
$29$	7.82843			1.45370			0.726851	+	0.686795i	$0.240983\pi$
$30$		0			0
$31$	−0.414214	+	0.717439i	−0.0743950	+	0.128856i	−0.900823	−	0.434187i	$-0.857036\pi$
$31$	−0.414214	+	0.717439i	−0.0743950	+	0.128856i	0.826428	+	0.563042i	$0.190369\pi$
$32$		0			0
$33$	−0.297173	+	0.171573i	−0.0517312	+	0.0298670i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.89898	−	2.82843i	0.805387	−	0.464991i	−0.0399642	−	0.999201i	$-0.512724\pi$
$37$	4.89898	−	2.82843i	0.805387	−	0.464991i	0.845351	+	0.534211i	$0.179391\pi$
$38$		0			0
$39$	0.414214	−	0.717439i	0.0663273	−	0.114882i
$40$		0			0
$41$	5.82843			0.910247			0.455124	−	0.890428i	$-0.349595\pi$
$41$	5.82843			0.910247			0.455124	+	0.890428i	$0.349595\pi$
$42$		0			0
$43$			6.89949i			1.05216i	0.850434	+	0.526082i	$0.176339\pi$
$43$			6.89949i			1.05216i	−0.850434	+	0.526082i	$0.823661\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.0951	−	5.82843i	1.47253	−	0.850163i	0.473004	−	0.881060i	$-0.343170\pi$
$47$	10.0951	−	5.82843i	1.47253	−	0.850163i	0.999523	+	0.0308969i	$0.00983637\pi$
$48$		0			0
$49$	1.74264	−	6.77962i	0.248949	−	0.968517i
$50$		0			0
$51$	1.58579	+	2.74666i	0.222055	+	0.384610i
$52$		0			0
$53$	−4.89898	−	2.82843i	−0.672927	−	0.388514i	0.124258	−	0.992250i	$-0.460345\pi$
$53$	−4.89898	−	2.82843i	−0.672927	−	0.388514i	−0.797185	+	0.603736i	$0.793678\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.34315i		−	0.310357i
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−3.32843	−	5.76500i	−0.426161	−	0.738133i	0.570367	−	0.821390i	$-0.306801\pi$
$61$	−3.32843	−	5.76500i	−0.426161	−	0.738133i	−0.996528	+	0.0832569i	$0.973468\pi$
$62$		0			0
$63$	6.92820	+	2.82843i	0.872872	+	0.356348i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	11.1713	+	6.44975i	1.36479	+	0.787962i	0.990257	−	0.139251i	$-0.0444696\pi$
$67$	11.1713	+	6.44975i	1.36479	+	0.787962i	0.374533	+	0.927213i	$0.377803\pi$
$68$		0			0
$69$	2.31371			0.278538
$70$		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
$73$	3.16693	+	1.82843i	0.370661	+	0.214001i	0.673747	−	0.738962i	$-0.264684\pi$
$73$	3.16693	+	1.82843i	0.370661	+	0.214001i	−0.303086	+	0.952963i	$0.598017\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.297173	−	2.17157i	−0.0338660	−	0.247474i
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$			4.75736i			0.522188i	0.965313	+	0.261094i	$0.0840833\pi$
$83$			4.75736i			0.522188i	−0.965313	+	0.261094i	$0.915917\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.80821	+	1.62132i	0.301072	+	0.173824i
$88$		0			0
$89$	−2.67157	−	4.62730i	−0.283186	−	0.490493i	0.688982	−	0.724779i	$-0.258058\pi$
$89$	−2.67157	−	4.62730i	−0.283186	−	0.490493i	−0.972168	+	0.234286i	$0.924725\pi$
$90$		0			0
$91$	3.24264	+	4.18154i	0.339921	+	0.438345i
$92$		0			0
$93$	−0.297173	+	0.171573i	−0.0308154	+	0.0177913i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$		0			0
$99$	2.34315			0.235495
$100$		0			0
$101$	5.74264	−	9.94655i	0.571414	−	0.989718i	−0.425007	−	0.905190i	$-0.639728\pi$
$101$	5.74264	−	9.94655i	0.571414	−	0.989718i	0.996421	−	0.0845282i	$-0.0269383\pi$
$102$		0			0
$103$	−6.56948	+	3.79289i	−0.647310	+	0.373725i	−0.787425	−	0.616410i	$-0.788586\pi$
$103$	−6.56948	+	3.79289i	−0.647310	+	0.373725i	0.140115	+	0.990135i	$0.455253\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.83743	+	2.79289i	−0.467652	+	0.269999i	−0.715256	−	0.698862i	$-0.753690\pi$
$107$	−4.83743	+	2.79289i	−0.467652	+	0.269999i	0.247604	+	0.968861i	$0.420357\pi$
$108$		0			0
$109$	9.15685	−	15.8601i	0.877068	−	1.51913i	0.0225237	−	0.999746i	$-0.492830\pi$
$109$	9.15685	−	15.8601i	0.877068	−	1.51913i	0.854544	−	0.519379i	$-0.173837\pi$
$110$		0			0
$111$	2.34315			0.222402
$112$		0			0
$113$		−	11.3137i		−	1.06430i	−0.846649	−	0.532152i	$-0.821383\pi$
$113$		−	11.3137i		−	1.06430i	0.846649	−	0.532152i	$-0.178617\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.89898	+	2.82843i	−0.452911	+	0.261488i
$118$		0			0
$119$	−20.0711	+	2.74666i	−1.83991	+	0.251786i
$120$		0			0
$121$	5.15685	+	8.93193i	0.468805	+	0.811994i
$122$		0			0
$123$	2.09077	+	1.20711i	0.188518	+	0.108841i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	4.34315i		−	0.385392i	−0.981259	−	0.192696i	$-0.938277\pi$
$127$		−	4.34315i		−	0.385392i	0.981259	−	0.192696i	$-0.0617231\pi$
$128$		0			0
$129$	−1.42893	+	2.47498i	−0.125810	+	0.217910i
$130$		0			0
$131$	−6.82843	−	11.8272i	−0.596602	−	1.03335i	−0.993319	−	0.115404i	$-0.963184\pi$
$131$	−6.82843	−	11.8272i	−0.596602	−	1.03335i	0.396716	−	0.917941i	$-0.370150\pi$
$132$		0			0
$133$	13.8564	+	5.65685i	1.20150	+	0.490511i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	0.640626	−	0.767853i	$-0.278675\pi$
$137$	3.46410	+	2.00000i	0.295958	+	0.170872i	−0.344668	+	0.938725i	$0.612008\pi$
$138$		0			0
$139$	−2.48528			−0.210799			−0.105399	−	0.994430i	$-0.533612\pi$
$139$	−2.48528			−0.210799			−0.105399	+	0.994430i	$0.533612\pi$
$140$		0			0
$141$	4.82843			0.406627
$142$		0			0
$143$	1.43488	+	0.828427i	0.119991	+	0.0692766i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.02922	−	2.07107i	0.167368	−	0.170819i
$148$		0			0
$149$	2.32843	+	4.03295i	0.190752	+	0.330392i	0.945500	−	0.325623i	$-0.105574\pi$
$149$	2.32843	+	4.03295i	0.190752	+	0.330392i	−0.754748	+	0.656015i	$0.772241\pi$
$150$		0			0
$151$	5.58579	−	9.67487i	0.454565	−	0.787329i	−0.544098	−	0.839022i	$-0.683128\pi$
$151$	5.58579	−	9.67487i	0.454565	−	0.787329i	0.998663	+	0.0516921i	$0.0164614\pi$
$152$		0			0
$153$		−	21.6569i		−	1.75085i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.13770	−	0.656854i	−0.0907987	−	0.0524227i	0.453913	−	0.891046i	$-0.350028\pi$
$157$	−1.13770	−	0.656854i	−0.0907987	−	0.0524227i	−0.544712	+	0.838623i	$0.683361\pi$
$158$		0			0
$159$	−1.17157	−	2.02922i	−0.0929118	−	0.160928i
$160$		0			0
$161$	−5.58579	+	13.6823i	−0.440222	+	1.07832i
$162$		0			0
$163$	13.5592	−	7.82843i	1.06204	−	0.613170i	0.136045	−	0.990703i	$-0.456561\pi$
$163$	13.5592	−	7.82843i	1.06204	−	0.613170i	0.925996	+	0.377533i	$0.123227\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			2.07107i			0.160264i	0.996784	+	0.0801320i	$0.0255342\pi$
$167$			2.07107i			0.160264i	−0.996784	+	0.0801320i	$0.974466\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−8.00000	+	13.8564i	−0.611775	+	1.05963i
$172$		0			0
$173$	−8.95743	+	5.17157i	−0.681021	+	0.393187i	−0.800239	−	0.599681i	$-0.795294\pi$
$173$	−8.95743	+	5.17157i	−0.681021	+	0.393187i	0.119219	+	0.992868i	$0.461961\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.43488	+	0.828427i	−0.107852	+	0.0622684i
$178$		0			0
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	−0.961388	−	0.275197i	$-0.911257\pi$
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	0.719022	+	0.694988i	$0.244590\pi$
$180$		0			0
$181$	−4.17157			−0.310071			−0.155035	−	0.987909i	$-0.549549\pi$
$181$	−4.17157			−0.310071			−0.155035	+	0.987909i	$0.549549\pi$
$182$		0			0
$183$		−	2.75736i		−	0.203830i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−5.49333	+	3.17157i	−0.401712	+	0.231928i
$188$		0			0
$189$	3.91421	+	5.04757i	0.284717	+	0.367156i
$190$		0			0
$191$	2.75736	+	4.77589i	0.199516	+	0.345571i	0.948371	−	0.317162i	$-0.102730\pi$
$191$	2.75736	+	4.77589i	0.199516	+	0.345571i	−0.748856	+	0.662733i	$0.769397\pi$
$192$		0			0
$193$	−4.60181	−	2.65685i	−0.331245	−	0.191245i	0.325149	−	0.945663i	$-0.394586\pi$
$193$	−4.60181	−	2.65685i	−0.331245	−	0.191245i	−0.656394	+	0.754418i	$0.727919\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			0.343146i			0.0244481i	0.999925	+	0.0122241i	$0.00389114\pi$
$197$			0.343146i			0.0244481i	−0.999925	+	0.0122241i	$0.996109\pi$
$198$		0			0
$199$	−11.6569	+	20.1903i	−0.826332	+	1.43125i	0.0745642	+	0.997216i	$0.476243\pi$
$199$	−11.6569	+	20.1903i	−0.826332	+	1.43125i	−0.900897	+	0.434034i	$0.857090\pi$
$200$		0			0
$201$	2.67157	+	4.62730i	0.188438	+	0.326385i
$202$		0			0
$203$	−16.3674	+	12.6924i	−1.14877	+	0.890831i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−13.6823	−	7.89949i	−0.950987	−	0.549053i
$208$		0			0
$209$	4.68629			0.324158
$210$		0			0
$211$	26.6274			1.83311			0.916553	−	0.399912i	$-0.130959\pi$
$211$	26.6274			1.83311			0.916553	+	0.399912i	$0.130959\pi$
$212$		0			0
$213$	−4.30463	−	2.48528i	−0.294949	−	0.170289i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.297173	−	2.17157i	−0.0201734	−	0.147416i
$218$		0			0
$219$	0.757359	+	1.31178i	0.0511776	+	0.0886422i
$220$		0			0
$221$	7.65685	−	13.2621i	0.515056	−	0.892103i
$222$		0			0
$223$			14.9706i			1.00250i	0.865302	+	0.501252i	$0.167127\pi$
$223$			14.9706i			1.00250i	−0.865302	+	0.501252i	$0.832873\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	0.0403978	−	0.999184i	$-0.487137\pi$
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	−0.845120	+	0.534577i	$0.820471\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$	0.343146	−	0.840532i	0.0225773	−	0.0553029i
$232$		0			0
$233$	−10.0951	+	5.82843i	−0.661354	+	0.381833i	−0.792793	−	0.609491i	$-0.791374\pi$
$233$	−10.0951	+	5.82843i	−0.661354	+	0.381833i	0.131439	+	0.991324i	$0.458040\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	1.65685i		−	0.107624i
$238$		0			0
$239$	30.4853			1.97193			0.985964	−	0.166955i	$-0.0533936\pi$
$239$	30.4853			1.97193			0.985964	+	0.166955i	$0.0533936\pi$
$240$		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
$243$	−8.95743	+	5.17157i	−0.574619	+	0.331757i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.79796	+	5.65685i	−0.623429	+	0.359937i
$248$		0			0
$249$	−0.985281	+	1.70656i	−0.0624397	+	0.108149i
$250$		0			0
$251$	−27.4558			−1.73300			−0.866499	−	0.499179i	$-0.833635\pi$
$251$	−27.4558			−1.73300			−0.866499	+	0.499179i	$0.833635\pi$
$252$		0			0
$253$			4.62742i			0.290923i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.2621	−	7.65685i	0.827265	−	0.477621i	−0.0256506	−	0.999671i	$-0.508166\pi$
$257$	13.2621	−	7.65685i	0.827265	−	0.477621i	0.852915	+	0.522050i	$0.174832\pi$
$258$		0			0
$259$	−5.65685	+	13.8564i	−0.351500	+	0.860995i
$260$		0			0
$261$	−11.0711	−	19.1757i	−0.685282	−	1.18694i
$262$		0			0
$263$	−13.6208	−	7.86396i	−0.839893	−	0.484913i	0.0173347	−	0.999850i	$-0.494482\pi$
$263$	−13.6208	−	7.86396i	−0.839893	−	0.484913i	−0.857228	+	0.514937i	$0.827815\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	2.21320i		−	0.135446i
$268$		0			0
$269$	−3.32843	+	5.76500i	−0.202938	+	0.351499i	−0.949474	−	0.313847i	$-0.898382\pi$
$269$	−3.32843	+	5.76500i	−0.202938	+	0.351499i	0.746536	+	0.665345i	$0.231716\pi$
$270$		0			0
$271$	1.65685	+	2.86976i	0.100647	+	0.174325i	0.911951	−	0.410298i	$-0.134575\pi$
$271$	1.65685	+	2.86976i	0.100647	+	0.174325i	−0.811305	+	0.584624i	$0.801242\pi$
$272$		0			0
$273$	0.297173	+	2.17157i	0.0179857	+	0.131430i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−24.7921	−	14.3137i	−1.48961	−	0.860027i	−0.489682	−	0.871901i	$-0.662887\pi$
$277$	−24.7921	−	14.3137i	−1.48961	−	0.860027i	−0.999930	+	0.0118739i	$0.996220\pi$
$278$		0			0
$279$	2.34315			0.140280
$280$		0			0
$281$	2.68629			0.160251			0.0801254	−	0.996785i	$-0.474468\pi$
$281$	2.68629			0.160251			0.0801254	+	0.996785i	$0.474468\pi$
$282$		0			0
$283$	15.5885	+	9.00000i	0.926638	+	0.534994i	0.885747	−	0.464169i	$-0.153647\pi$
$283$	15.5885	+	9.00000i	0.926638	+	0.534994i	0.0408910	+	0.999164i	$0.486980\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.1859	+	9.44975i	−0.719311	+	0.557801i
$288$		0			0
$289$	20.8137	+	36.0504i	1.22434	+	2.12061i
$290$		0			0
$291$	−1.24264	+	2.15232i	−0.0728449	+	0.126171i
$292$		0			0
$293$		−	16.9706i		−	0.991431i	−0.868485	−	0.495715i	$-0.834906\pi$
$293$		−	16.9706i		−	0.991431i	0.868485	−	0.495715i	$-0.165094\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$		0			0
$299$	−5.58579	−	9.67487i	−0.323034	−	0.559512i
$300$		0			0
$301$	−11.1863	−	14.4253i	−0.644767	−	0.831458i
$302$		0			0
$303$	4.11999	−	2.37868i	0.236687	−	0.136652i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			4.75736i			0.271517i	0.990742	+	0.135758i	$0.0433471\pi$
$307$			4.75736i			0.271517i	−0.990742	+	0.135758i	$0.956653\pi$
$308$		0			0
$309$	−3.14214			−0.178750
$310$		0			0
$311$	−10.8284	+	18.7554i	−0.614024	+	1.06352i	0.376531	+	0.926404i	$0.377117\pi$
$311$	−10.8284	+	18.7554i	−0.614024	+	1.06352i	−0.990555	+	0.137116i	$0.956217\pi$
$312$		0			0
$313$	−18.1610	+	10.4853i	−1.02652	+	0.592663i	−0.915987	−	0.401209i	$-0.868590\pi$
$313$	−18.1610	+	10.4853i	−1.02652	+	0.592663i	−0.110536	+	0.993872i	$0.535257\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−19.0526	+	11.0000i	−1.07010	+	0.617822i	−0.928208	−	0.372061i	$-0.878651\pi$
$317$	−19.0526	+	11.0000i	−1.07010	+	0.617822i	−0.141890	+	0.989882i	$0.545318\pi$
$318$		0			0
$319$	−3.24264	+	5.61642i	−0.181553	+	0.314459i
$320$		0			0
$321$	−2.31371			−0.129139
$322$		0			0
$323$		−	43.3137i		−	2.41004i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.56948	−	3.79289i	0.363293	−	0.209747i
$328$		0			0
$329$	−11.6569	+	28.5533i	−0.642663	+	1.57420i
$330$		0			0
$331$	−13.2426	−	22.9369i	−0.727881	−	1.26073i	−0.957777	−	0.287512i	$-0.907172\pi$
$331$	−13.2426	−	22.9369i	−0.727881	−	1.26073i	0.229896	−	0.973215i	$-0.426162\pi$
$332$		0			0
$333$	−13.8564	−	8.00000i	−0.759326	−	0.438397i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			24.9706i			1.36023i	0.733104	+	0.680117i	$0.238071\pi$
$337$			24.9706i			1.36023i	−0.733104	+	0.680117i	$0.761929\pi$
$338$		0			0
$339$	2.34315	−	4.05845i	0.127262	−	0.220425i
$340$		0			0
$341$	−0.343146	−	0.594346i	−0.0185824	−	0.0321856i
$342$		0			0
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.85951	−	5.69239i	−0.529286	−	0.305583i	0.211440	−	0.977391i	$-0.432185\pi$
$347$	−9.85951	−	5.69239i	−0.529286	−	0.305583i	−0.740726	+	0.671808i	$0.765518\pi$
$348$		0			0
$349$	−9.82843			−0.526104			−0.263052	−	0.964782i	$-0.584729\pi$
$349$	−9.82843			−0.526104			−0.263052	+	0.964782i	$0.584729\pi$
$350$		0			0
$351$	−4.82843			−0.257722
$352$		0			0
$353$	29.1477	+	16.8284i	1.55138	+	0.895687i	0.998030	+	0.0627345i	$0.0199821\pi$
$353$	29.1477	+	16.8284i	1.55138	+	0.895687i	0.553345	+	0.832952i	$0.313351\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.76874	−	3.17157i	−0.411165	−	0.167857i
$358$		0			0
$359$	−3.24264	−	5.61642i	−0.171140	−	0.296423i	0.767679	−	0.640835i	$-0.221412\pi$
$359$	−3.24264	−	5.61642i	−0.171140	−	0.296423i	−0.938819	+	0.344412i	$0.888078\pi$
$360$		0			0
$361$	−6.50000	+	11.2583i	−0.342105	+	0.592544i
$362$		0			0
$363$			4.27208i			0.224226i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−18.6938	−	10.7929i	−0.975810	−	0.563384i	−0.0748078	−	0.997198i	$-0.523834\pi$
$367$	−18.6938	−	10.7929i	−0.975810	−	0.563384i	−0.901003	+	0.433814i	$0.857168\pi$
$368$		0			0
$369$	−8.24264	−	14.2767i	−0.429095	−	0.743214i
$370$		0			0
$371$	14.8284	−	2.02922i	0.769854	−	0.105352i
$372$		0			0
$373$	−10.3923	+	6.00000i	−0.538093	+	0.310668i	−0.744306	−	0.667839i	$-0.767219\pi$
$373$	−10.3923	+	6.00000i	−0.538093	+	0.310668i	0.206213	+	0.978507i	$0.433886\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	15.6569i		−	0.806369i
$378$		0			0
$379$	−4.68629			−0.240719			−0.120359	−	0.992730i	$-0.538405\pi$
$379$	−4.68629			−0.240719			−0.120359	+	0.992730i	$0.538405\pi$
$380$		0			0
$381$	0.899495	−	1.55797i	0.0460825	−	0.0798173i
$382$		0			0
$383$	0.778985	−	0.449747i	0.0398043	−	0.0229810i	−0.479966	−	0.877287i	$-0.659351\pi$
$383$	0.778985	−	0.449747i	0.0398043	−	0.0229810i	0.519770	+	0.854306i	$0.326018\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.9002	−	9.75736i	0.859088	−	0.495994i
$388$		0			0
$389$	2.65685	−	4.60181i	0.134708	−	0.233321i	−0.790778	−	0.612103i	$-0.790324\pi$
$389$	2.65685	−	4.60181i	0.134708	−	0.233321i	0.925486	+	0.378782i	$0.123657\pi$
$390$		0			0
$391$	42.7696			2.16295
$392$		0			0
$393$		−	5.65685i		−	0.285351i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−21.3280	+	12.3137i	−1.07042	+	0.618007i	−0.928296	−	0.371842i	$-0.878726\pi$
$397$	−21.3280	+	12.3137i	−1.07042	+	0.618007i	−0.142124	+	0.989849i	$0.545393\pi$
$398$		0			0
$399$	3.79899	+	4.89898i	0.190187	+	0.245256i
$400$		0			0
$401$	16.1569	+	27.9845i	0.806835	+	1.39748i	0.915045	+	0.403351i	$0.132155\pi$
$401$	16.1569	+	27.9845i	0.806835	+	1.39748i	−0.108211	+	0.994128i	$0.534512\pi$
$402$		0			0
$403$	1.43488	+	0.828427i	0.0714764	+	0.0412669i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			4.68629i			0.232291i
$408$		0			0
$409$	−12.5711	+	21.7737i	−0.621599	+	1.07664i	0.367589	+	0.929988i	$0.380183\pi$
$409$	−12.5711	+	21.7737i	−0.621599	+	1.07664i	−0.989188	+	0.146653i	$0.953150\pi$
$410$		0			0
$411$	0.828427	+	1.43488i	0.0408633	+	0.0707773i
$412$		0			0
$413$	−1.43488	−	10.4853i	−0.0706057	−	0.515947i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.891519	−	0.514719i	−0.0436579	−	0.0252059i
$418$		0			0
$419$	15.3137			0.748124			0.374062	−	0.927404i	$-0.377965\pi$
$419$	15.3137			0.748124			0.374062	+	0.927404i	$0.377965\pi$
$420$		0			0
$421$	27.3431			1.33262			0.666312	−	0.745673i	$-0.267872\pi$
$421$	27.3431			1.33262			0.666312	+	0.745673i	$0.267872\pi$
$422$		0			0
$423$	−28.5533	−	16.4853i	−1.38831	−	0.801542i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	16.3059	+	6.65685i	0.789098	+	0.322148i
$428$		0			0
$429$	0.343146	+	0.594346i	0.0165672	+	0.0286953i
$430$		0			0
$431$	0.414214	−	0.717439i	0.0199520	−	0.0345578i	−0.855877	−	0.517179i	$-0.826982\pi$
$431$	0.414214	−	0.717439i	0.0199520	−	0.0345578i	0.875829	+	0.482622i	$0.160315\pi$
$432$		0			0
$433$			19.3137i			0.928158i	0.885794	+	0.464079i	$0.153615\pi$
$433$			19.3137i			0.928158i	−0.885794	+	0.464079i	$0.846385\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−27.3647	−	15.7990i	−1.30903	−	0.755768i
$438$		0			0
$439$	−9.17157	−	15.8856i	−0.437735	−	0.758180i	0.559779	−	0.828642i	$-0.310886\pi$
$439$	−9.17157	−	15.8856i	−0.437735	−	0.758180i	−0.997514	+	0.0704621i	$0.977553\pi$
$440$		0			0
$441$	−19.0711	+	5.31925i	−0.908146	+	0.253297i
$442$		0			0
$443$	13.4977	−	7.79289i	0.641294	−	0.370252i	−0.143819	−	0.989604i	$-0.545938\pi$
$443$	13.4977	−	7.79289i	0.641294	−	0.370252i	0.785113	+	0.619353i	$0.212605\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			1.92893i			0.0912354i
$448$		0			0
$449$	7.48528			0.353252			0.176626	−	0.984278i	$-0.443482\pi$
$449$	7.48528			0.353252			0.176626	+	0.984278i	$0.443482\pi$
$450$		0			0
$451$	−2.41421	+	4.18154i	−0.113681	+	0.196901i
$452$		0			0
$453$	4.00746	−	2.31371i	0.188287	−	0.108708i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	25.0892	−	14.4853i	1.17363	−	0.677593i	0.219094	−	0.975704i	$-0.429690\pi$
$457$	25.0892	−	14.4853i	1.17363	−	0.677593i	0.954531	+	0.298111i	$0.0963565\pi$
$458$		0			0
$459$	9.24264	−	16.0087i	0.431410	−	0.747223i
$460$		0			0
$461$	1.31371			0.0611855			0.0305928	−	0.999532i	$-0.490261\pi$
$461$	1.31371			0.0611855			0.0305928	+	0.999532i	$0.490261\pi$
$462$		0			0
$463$		−	14.8995i		−	0.692438i	−0.938154	−	0.346219i	$-0.887465\pi$
$463$		−	14.8995i		−	0.692438i	0.938154	−	0.346219i	$-0.112535\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−32.7964	+	18.9350i	−1.51764	+	0.876209i	−0.517853	+	0.855470i	$0.673269\pi$
$467$	−32.7964	+	18.9350i	−1.51764	+	0.876209i	−0.999785	+	0.0207390i	$0.993398\pi$
$468$		0			0
$469$	−33.8137	+	4.62730i	−1.56137	+	0.213669i
$470$		0			0
$471$	−0.272078	−	0.471253i	−0.0125367	−	0.0217142i
$472$		0			0
$473$	−4.94997	−	2.85786i	−0.227600	−	0.131405i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			16.0000i			0.732590i
$478$		0			0
$479$	−0.757359	+	1.31178i	−0.0346046	+	0.0599370i	−0.882809	−	0.469732i	$-0.844351\pi$
$479$	−0.757359	+	1.31178i	−0.0346046	+	0.0599370i	0.848204	+	0.529669i	$0.177684\pi$
$480$		0			0
$481$	−5.65685	−	9.79796i	−0.257930	−	0.446748i
$482$		0			0
$483$	−4.83743	+	3.75126i	−0.220111	+	0.170688i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	33.1552	+	19.1421i	1.50240	+	0.867413i	0.999996	+	0.00278182i	$0.000885482\pi$
$487$	33.1552	+	19.1421i	1.50240	+	0.867413i	0.502407	+	0.864631i	$0.332448\pi$
$488$		0			0
$489$	6.48528			0.293275
$490$		0			0
$491$	1.51472			0.0683583			0.0341791	−	0.999416i	$-0.489118\pi$
$491$	1.51472			0.0683583			0.0341791	+	0.999416i	$0.489118\pi$
$492$		0			0
$493$	51.9105	+	29.9706i	2.33793	+	1.34981i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	25.0892	−	19.4558i	1.12541	−	0.872714i
$498$		0			0
$499$	22.0711	+	38.2282i	0.988037	+	1.71133i	0.627576	+	0.778555i	$0.284047\pi$
$499$	22.0711	+	38.2282i	0.988037	+	1.71133i	0.360461	+	0.932774i	$0.382619\pi$
$500$		0			0
$501$	−0.428932	+	0.742932i	−0.0191633	+	0.0331918i
$502$		0			0
$503$			3.92893i			0.175182i	0.996157	+	0.0875912i	$0.0279169\pi$
$503$			3.92893i			0.175182i	−0.996157	+	0.0875912i	$0.972083\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.22848	+	1.86396i	0.143382	+	0.0827814i
$508$		0			0
$509$	−16.7426	−	28.9991i	−0.742105	−	1.28536i	−0.951535	−	0.307539i	$-0.900494\pi$
$509$	−16.7426	−	28.9991i	−0.742105	−	1.28536i	0.209431	−	0.977823i	$-0.432839\pi$
$510$		0			0
$511$	−9.58579	+	1.31178i	−0.424050	+	0.0580299i
$512$		0			0
$513$	−11.8272	+	6.82843i	−0.522183	+	0.301482i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			9.65685i			0.424708i
$518$		0			0
$519$	−4.28427			−0.188059
$520$		0			0
$521$	−18.3137	+	31.7203i	−0.802338	+	1.38969i	0.115735	+	0.993280i	$0.463078\pi$
$521$	−18.3137	+	31.7203i	−0.802338	+	1.38969i	−0.918073	+	0.396410i	$0.870256\pi$
$522$		0			0
$523$	−24.1977	+	13.9706i	−1.05809	+	0.610890i	−0.924904	−	0.380201i	$-0.875855\pi$
$523$	−24.1977	+	13.9706i	−1.05809	+	0.610890i	−0.133189	+	0.991091i	$0.542522\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.49333	+	3.17157i	−0.239293	+	0.138156i
$528$		0			0
$529$	4.10051	−	7.10228i	0.178283	−	0.308795i
$530$		0			0
$531$	11.3137			0.490973
$532$		0			0
$533$		−	11.6569i		−	0.504914i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.32640	+	1.34315i	−0.100391	+	0.0579610i
$538$		0			0
$539$	4.14214	+	4.05845i	0.178414	+	0.174810i
$540$		0			0
$541$	11.7426	+	20.3389i	0.504856	+	0.874435i	0.999984	+	0.00561582i	$0.00178758\pi$
$541$	11.7426	+	20.3389i	0.504856	+	0.874435i	−0.495129	+	0.868820i	$0.664879\pi$
$542$		0			0
$543$	−1.49642	−	0.863961i	−0.0642177	−	0.0370761i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	2.27208i		−	0.0971470i	−0.998820	−	0.0485735i	$-0.984532\pi$
$547$		−	2.27208i		−	0.0971470i	0.998820	−	0.0485735i	$-0.0154675\pi$
$548$		0			0
$549$	−9.41421	+	16.3059i	−0.401789	+	0.695919i
$550$		0			0
$551$	−22.1421	−	38.3513i	−0.943287	−	1.63382i
$552$		0			0
$553$	9.79796	+	4.00000i	0.416652	+	0.170097i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.9941	+	8.65685i	0.635321	+	0.366803i	0.782810	−	0.622261i	$-0.213786\pi$
$557$	14.9941	+	8.65685i	0.635321	+	0.366803i	−0.147489	+	0.989064i	$0.547119\pi$
$558$		0			0
$559$	13.7990			0.583635
$560$		0			0
$561$	−2.62742			−0.110930
$562$		0			0
$563$	−3.52565	−	2.03553i	−0.148588	−	0.0857875i	0.423863	−	0.905727i	$-0.360674\pi$
$563$	−3.52565	−	2.03553i	−0.148588	−	0.0857875i	−0.572451	+	0.819939i	$0.694007\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.68512	−	19.6213i	−0.112764	−	0.824018i
$568$		0			0
$569$	−18.3137	−	31.7203i	−0.767751	−	1.32978i	−0.938780	−	0.344517i	$-0.888043\pi$
$569$	−18.3137	−	31.7203i	−0.767751	−	1.32978i	0.171029	−	0.985266i	$-0.445291\pi$
$570$		0			0
$571$	10.4853	−	18.1610i	0.438795	−	0.760016i	−0.558801	−	0.829301i	$-0.688739\pi$
$571$	10.4853	−	18.1610i	0.438795	−	0.760016i	0.997597	+	0.0692856i	$0.0220720\pi$
$572$		0			0
$573$			2.28427i			0.0954268i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	19.2987	+	11.1421i	0.803417	+	0.463853i	0.844665	−	0.535296i	$-0.179800\pi$
$577$	19.2987	+	11.1421i	0.803417	+	0.463853i	−0.0412474	+	0.999149i	$0.513133\pi$
$578$		0			0
$579$	−1.10051	−	1.90613i	−0.0457354	−	0.0792161i
$580$		0			0
$581$	−7.71320	−	9.94655i	−0.319998	−	0.412652i
$582$		0			0
$583$	4.05845	−	2.34315i	0.168084	−	0.0970432i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	22.6863i		−	0.936363i	−0.883632	−	0.468182i	$-0.844909\pi$
$587$		−	22.6863i		−	0.936363i	0.883632	−	0.468182i	$-0.155091\pi$
$588$		0			0
$589$	4.68629			0.193095
$590$		0			0
$591$	−0.0710678	+	0.123093i	−0.00292334	+	0.00506337i
$592$		0			0
$593$	−25.9298	+	14.9706i	−1.06481	+	0.614767i	−0.926758	−	0.375658i	$-0.877417\pi$
$593$	−25.9298	+	14.9706i	−1.06481	+	0.614767i	−0.138050	+	0.990425i	$0.544083\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.36308	+	4.82843i	−0.342278	+	0.197614i
$598$		0			0
$599$	21.3137	−	36.9164i	0.870855	−	1.50836i	0.00974040	−	0.999953i	$-0.496899\pi$
$599$	21.3137	−	36.9164i	0.870855	−	1.50836i	0.861114	−	0.508412i	$-0.169767\pi$
$600$		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
$603$		−	36.4853i		−	1.48580i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	23.5928	−	13.6213i	0.957603	−	0.552872i	0.0621685	−	0.998066i	$-0.480198\pi$
$607$	23.5928	−	13.6213i	0.957603	−	0.552872i	0.895434	+	0.445193i	$0.146865\pi$
$608$		0			0
$609$	−8.50000	+	1.16320i	−0.344437	+	0.0471352i
$610$		0			0
$611$	−11.6569	−	20.1903i	−0.471586	−	0.816811i
$612$		0			0
$613$	33.7495	+	19.4853i	1.36313	+	0.787003i	0.990039	−	0.140792i	$-0.0449649\pi$
$613$	33.7495	+	19.4853i	1.36313	+	0.787003i	0.373090	+	0.927795i	$0.378298\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	12.6863i		−	0.510731i	−0.966845	−	0.255365i	$-0.917804\pi$
$617$		−	12.6863i		−	0.510731i	0.966845	−	0.255365i	$-0.0821958\pi$
$618$		0			0
$619$	19.7279	−	34.1698i	0.792932	−	1.37340i	−0.131212	−	0.991354i	$-0.541887\pi$
$619$	19.7279	−	34.1698i	0.792932	−	1.37340i	0.924144	−	0.382044i	$-0.124780\pi$
$620$		0			0
$621$	−6.74264	−	11.6786i	−0.270573	−	0.468646i
$622$		0			0
$623$	13.0880	+	5.34315i	0.524359	+	0.214069i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.68106	+	0.970563i	0.0671352	+	0.0387605i
$628$		0			0
$629$	43.3137			1.72703
$630$		0			0
$631$	−1.51472			−0.0603000			−0.0301500	−	0.999545i	$-0.509598\pi$
$631$	−1.51472			−0.0603000			−0.0301500	+	0.999545i	$0.509598\pi$
$632$		0			0
$633$	9.55177	+	5.51472i	0.379649	+	0.219190i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−13.5592	−	3.48528i	−0.537236	−	0.138092i
$638$		0			0
$639$	16.9706	+	29.3939i	0.671345	+	1.16280i
$640$		0			0
$641$	−7.05635	+	12.2220i	−0.278709	+	0.482738i	−0.971064	−	0.238819i	$-0.923240\pi$
$641$	−7.05635	+	12.2220i	−0.278709	+	0.482738i	0.692355	+	0.721557i	$0.256573\pi$
$642$		0			0
$643$		−	26.0000i		−	1.02534i	−0.858586	−	0.512670i	$-0.828656\pi$
$643$		−	26.0000i		−	1.02534i	0.858586	−	0.512670i	$-0.171344\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.9764	+	10.3787i	0.706725	+	0.408028i	0.809847	−	0.586641i	$-0.199550\pi$
$647$	17.9764	+	10.3787i	0.706725	+	0.408028i	−0.103122	+	0.994669i	$0.532883\pi$
$648$		0			0
$649$	−1.65685	−	2.86976i	−0.0650372	−	0.112648i
$650$		0			0
$651$	0.343146	−	0.840532i	0.0134489	−	0.0329430i
$652$		0			0
$653$	13.5592	−	7.82843i	0.530614	−	0.306350i	−0.210653	−	0.977561i	$-0.567559\pi$
$653$	13.5592	−	7.82843i	0.530614	−	0.306350i	0.741266	+	0.671211i	$0.234226\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	10.3431i		−	0.403525i
$658$		0			0
$659$	−12.6863			−0.494188			−0.247094	−	0.968992i	$-0.579476\pi$
$659$	−12.6863			−0.494188			−0.247094	+	0.968992i	$0.579476\pi$
$660$		0			0
$661$	25.1569	−	43.5729i	0.978488	−	1.69479i	0.310581	−	0.950547i	$-0.399476\pi$
$661$	25.1569	−	43.5729i	0.978488	−	1.69479i	0.667907	−	0.744244i	$-0.267190\pi$
$662$		0			0
$663$	5.49333	−	3.17157i	0.213343	−	0.123174i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	37.8695	−	21.8640i	1.46631	−	0.846576i
$668$		0			0
$669$	−3.10051	+	5.37023i	−0.119872	+	0.207625i
$670$		0			0
$671$	5.51472			0.212893
$672$		0			0
$673$			5.65685i			0.218056i	0.994039	+	0.109028i	$0.0347738\pi$
$673$			5.65685i			0.218056i	−0.994039	+	0.109028i	$0.965226\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.8931	−	11.4853i	0.764554	−	0.441415i	−0.0663747	−	0.997795i	$-0.521143\pi$
$677$	19.8931	−	11.4853i	0.764554	−	0.441415i	0.830928	+	0.556380i	$0.187810\pi$
$678$		0			0
$679$	−9.72792	−	12.5446i	−0.373323	−	0.481418i
$680$		0			0
$681$	−2.89949	−	5.02207i	−0.111109	−	0.192446i
$682$		0			0
$683$	−1.67050	−	0.964466i	−0.0639201	−	0.0369043i	0.467699	−	0.883888i	$-0.345083\pi$
$683$	−1.67050	−	0.964466i	−0.0639201	−	0.0369043i	−0.531619	+	0.846983i	$0.678416\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	5.79899i		−	0.221245i
$688$		0			0
$689$	−5.65685	+	9.79796i	−0.215509	+	0.373273i
$690$		0			0
$691$	21.3848	+	37.0395i	0.813515	+	1.40905i	0.910389	+	0.413753i	$0.135782\pi$
$691$	21.3848	+	37.0395i	0.813515	+	1.40905i	−0.0968739	+	0.995297i	$0.530884\pi$
$692$		0			0
$693$	−4.89898	+	3.79899i	−0.186097	+	0.144312i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	38.6485	+	22.3137i	1.46392	+	0.845192i
$698$		0			0
$699$	−4.82843			−0.182628
$700$		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
$703$	−27.7128	−	16.0000i	−1.04521	−	0.603451i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.11999	+	30.1066i	0.154948	+	1.13228i
$708$		0			0
$709$	−17.7132	−	30.6802i	−0.665233	−	1.15222i	−0.979222	−	0.202791i	$-0.934999\pi$
$709$	−17.7132	−	30.6802i	−0.665233	−	1.15222i	0.313989	−	0.949427i	$-0.398335\pi$
$710$		0			0
$711$	−5.65685	+	9.79796i	−0.212149	+	0.367452i
$712$		0			0
$713$			4.62742i			0.173298i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.9357	+	6.31371i	0.408400	+	0.235790i
$718$		0			0
$719$	−12.8995	−	22.3426i	−0.481070	−	0.833238i	0.518694	−	0.854960i	$-0.326418\pi$
$719$	−12.8995	−	22.3426i	−0.481070	−	0.833238i	−0.999764	+	0.0217223i	$0.993085\pi$
$720$		0			0
$721$	7.58579	−	18.5813i	0.282509	−	0.692004i
$722$		0			0
$723$	3.58719	−	2.07107i	0.133409	−	0.0770238i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			38.0711i			1.41198i	0.708223	+	0.705989i	$0.249497\pi$
$727$			38.0711i			1.41198i	−0.708223	+	0.705989i	$0.750503\pi$
$728$		0			0
$729$	18.1716			0.673021
$730$		0			0
$731$	−26.4142	+	45.7508i	−0.976965	+	1.69215i
$732$		0			0
$733$	−6.63103	+	3.82843i	−0.244923	+	0.141406i	−0.617437	−	0.786620i	$-0.711829\pi$
$733$	−6.63103	+	3.82843i	−0.244923	+	0.141406i	0.372514	+	0.928026i	$0.378496\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.25460	+	5.34315i	−0.340898	+	0.196817i
$738$		0			0
$739$	8.41421	−	14.5738i	0.309522	−	0.536108i	−0.668736	−	0.743500i	$-0.733164\pi$
$739$	8.41421	−	14.5738i	0.309522	−	0.536108i	0.978258	+	0.207392i	$0.0664977\pi$
$740$		0			0
$741$	−4.68629			−0.172155
$742$		0			0
$743$			10.7574i			0.394649i	0.980338	+	0.197325i	$0.0632253\pi$
$743$			10.7574i			0.394649i	−0.980338	+	0.197325i	$0.936775\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	11.6531	−	6.72792i	0.426365	−	0.246162i
$748$		0			0
$749$	5.58579	−	13.6823i	0.204100	−	0.499941i
$750$		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
$753$	−9.84895	−	5.68629i	−0.358916	−	0.207220i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			6.00000i			0.218074i	0.994038	+	0.109037i	$0.0347767\pi$
$757$			6.00000i			0.218074i	−0.994038	+	0.109037i	$0.965223\pi$
$758$		0			0
$759$	−0.958369	+	1.65994i	−0.0347866	+	0.0602522i
$760$		0			0
$761$	21.9706	+	38.0541i	0.796432	+	1.37946i	0.921926	+	0.387367i	$0.126615\pi$
$761$	21.9706	+	38.0541i	0.796432	+	1.37946i	−0.125493	+	0.992094i	$0.540051\pi$
$762$		0			0
$763$	6.56948	+	48.0061i	0.237831	+	1.73794i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.92820	+	4.00000i	0.250163	+	0.144432i
$768$		0			0
$769$	−43.2548			−1.55981			−0.779905	−	0.625898i	$-0.784732\pi$
$769$	−43.2548			−1.55981			−0.779905	+	0.625898i	$0.784732\pi$
$770$		0			0
$771$	6.34315			0.228443
$772$		0			0
$773$	21.0818	+	12.1716i	0.758259	+	0.437781i	0.828670	−	0.559737i	$-0.189098\pi$
$773$	21.0818	+	12.1716i	0.758259	+	0.437781i	−0.0704113	+	0.997518i	$0.522431\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.89898	+	3.79899i	−0.175750	+	0.136288i
$778$		0			0
$779$	−16.4853	−	28.5533i	−0.590647	−	1.02303i
$780$		0			0
$781$	4.97056	−	8.60927i	0.177861	−	0.308064i
$782$		0			0
$783$		−	18.8995i		−	0.675413i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	1.37333	+	0.792893i	0.0489540	+	0.0282636i	0.524277	−	0.851548i	$-0.324336\pi$
$787$	1.37333	+	0.792893i	0.0489540	+	0.0282636i	−0.475323	+	0.879811i	$0.657669\pi$
$788$		0			0
$789$	−3.25736	−	5.64191i	−0.115965	−	0.200857i
$790$		0			0
$791$	18.3431	+	23.6544i	0.652207	+	0.841052i
$792$		0			0
$793$	−11.5300	+	6.65685i	−0.409443	+	0.236392i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	35.3137i		−	1.25088i	−0.780274	−	0.625438i	$-0.784920\pi$
$797$		−	35.3137i		−	1.25088i	0.780274	−	0.625438i	$-0.215080\pi$
$798$		0			0
$799$	89.2548			3.15761
$800$		0			0
$801$	−7.55635	+	13.0880i	−0.266990	+	0.462441i
$802$		0			0
$803$	−2.62357	+	1.51472i	−0.0925838	+	0.0534533i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.38794	+	1.37868i	−0.0840596	+	0.0485318i
$808$		0			0
$809$	−17.9853	+	31.1514i	−0.632329	+	1.09523i	0.354746	+	0.934963i	$0.384567\pi$
$809$	−17.9853	+	31.1514i	−0.632329	+	1.09523i	−0.987074	+	0.160263i	$0.948766\pi$
$810$		0			0
$811$	52.1421			1.83096			0.915479	−	0.402366i	$-0.131812\pi$
$811$	52.1421			1.83096			0.915479	+	0.402366i	$0.131812\pi$
$812$		0			0
$813$			1.37258i			0.0481386i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	33.8005	−	19.5147i	1.18253	−	0.682734i
$818$		0			0
$819$	5.65685	−	13.8564i	0.197666	−	0.484182i
$820$		0			0
$821$	16.3137	+	28.2562i	0.569352	+	0.986147i	0.996630	+	0.0820268i	$0.0261393\pi$
$821$	16.3137	+	28.2562i	0.569352	+	0.986147i	−0.427278	+	0.904120i	$0.640527\pi$
$822$		0			0
$823$	25.9913	+	15.0061i	0.906001	+	0.523080i	0.879142	−	0.476560i	$-0.158116\pi$
$823$	25.9913	+	15.0061i	0.906001	+	0.523080i	0.0268584	+	0.999639i	$0.491450\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.5269i			0.470377i	0.971950	+	0.235188i	$0.0755707\pi$
$827$			13.5269i			0.470377i	−0.971950	+	0.235188i	$0.924429\pi$
$828$		0			0
$829$	2.65685	−	4.60181i	0.0922764	−	0.159827i	−0.816192	−	0.577780i	$-0.803919\pi$
$829$	2.65685	−	4.60181i	0.0922764	−	0.159827i	0.908469	+	0.417953i	$0.137252\pi$
$830$		0			0
$831$	−5.92893	−	10.2692i	−0.205672	−	0.356235i
$832$		0			0
$833$	37.5108	−	38.2843i	1.29967	−	1.32647i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.73205	+	1.00000i	0.0598684	+	0.0345651i
$838$		0			0
$839$	−20.1421			−0.695384			−0.347692	−	0.937609i	$-0.613034\pi$
$839$	−20.1421			−0.695384			−0.347692	+	0.937609i	$0.613034\pi$
$840$		0			0
$841$	32.2843			1.11325
$842$		0			0
$843$	0.963625	+	0.556349i	0.0331890	+	0.0191617i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−25.2633	−	10.3137i	−0.868058	−	0.354383i
$848$		0			0
$849$	3.72792	+	6.45695i	0.127942	+	0.221602i
$850$		0			0
$851$	15.7990	−	27.3647i	0.541582	−	0.938048i
$852$		0			0
$853$		−	12.6863i		−	0.434370i	−0.976130	−	0.217185i	$-0.930312\pi$
$853$		−	12.6863i		−	0.434370i	0.976130	−	0.217185i	$-0.0696875\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.4290	+	9.48528i	0.561204	+	0.324011i	0.753628	−	0.657301i	$-0.228302\pi$
$857$	16.4290	+	9.48528i	0.561204	+	0.324011i	−0.192425	+	0.981312i	$0.561635\pi$
$858$		0			0
$859$	−15.3137	−	26.5241i	−0.522497	−	0.904991i	−0.999657	−	0.0261751i	$-0.991667\pi$
$859$	−15.3137	−	26.5241i	−0.522497	−	0.904991i	0.477160	−	0.878816i	$-0.341666\pi$
$860$		0			0
$861$	−6.32843	+	0.866025i	−0.215672	+	0.0295141i
$862$		0			0
$863$	48.5080	−	28.0061i	1.65123	−	0.953339i	0.674664	−	0.738125i	$-0.264289\pi$
$863$	48.5080	−	28.0061i	1.65123	−	0.953339i	0.976567	−	0.215214i	$-0.0690448\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			17.2426i			0.585591i
$868$		0			0
$869$	3.31371			0.112410
$870$		0			0
$871$	12.8995	−	22.3426i	0.437083	−	0.757049i
$872$		0			0
$873$	14.6969	−	8.48528i	0.497416	−	0.287183i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−24.4949	+	14.1421i	−0.827134	+	0.477546i	−0.852870	−	0.522123i	$-0.825140\pi$
$877$	−24.4949	+	14.1421i	−0.827134	+	0.477546i	0.0257364	+	0.999669i	$0.491807\pi$
$878$		0			0
$879$	3.51472	−	6.08767i	0.118549	−	0.205332i
$880$		0			0
$881$	−26.4558			−0.891320			−0.445660	−	0.895202i	$-0.647031\pi$
$881$	−26.4558			−0.891320			−0.445660	+	0.895202i	$0.647031\pi$
$882$		0			0
$883$		−	6.68629i		−	0.225012i	−0.993651	−	0.112506i	$-0.964112\pi$
$883$		−	6.68629i		−	0.225012i	0.993651	−	0.112506i	$-0.0358877\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.2297	−	8.79289i	0.511365	−	0.295236i	−0.222030	−	0.975040i	$-0.571268\pi$
$887$	15.2297	−	8.79289i	0.511365	−	0.295236i	0.733394	+	0.679803i	$0.237935\pi$
$888$		0			0
$889$	7.04163	+	9.08052i	0.236169	+	0.304551i
$890$		0			0
$891$	−3.10051	−	5.37023i	−0.103871	−	0.179910i
$892$		0			0
$893$	−57.1067	−	32.9706i	−1.91100	−	1.10332i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	4.62742i		−	0.154505i
$898$		0			0
$899$	−3.24264	+	5.61642i	−0.108148	+	0.187318i
$900$		0			0
$901$	−21.6569	−	37.5108i	−0.721494	−	1.24966i
$902$		0			0
$903$	−1.02517	−	7.49138i	−0.0341156	−	0.249297i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−40.0218	−	23.1066i	−1.32890	−	0.767242i	−0.343772	−	0.939053i	$-0.611705\pi$
$907$	−40.0218	−	23.1066i	−1.32890	−	0.767242i	−0.985130	+	0.171811i	$0.945038\pi$
$908$		0			0
$909$	−32.4853			−1.07747
$910$		0			0
$911$	−18.4853			−0.612445			−0.306222	−	0.951960i	$-0.599065\pi$
$911$	−18.4853			−0.612445			−0.306222	+	0.951960i	$0.599065\pi$
$912$		0			0
$913$	−3.41311	−	1.97056i	−0.112958	−	0.0652161i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	33.4523	+	13.6569i	1.10469	+	0.450989i
$918$		0			0
$919$	−16.6274	−	28.7995i	−0.548488	−	0.950009i	−0.998378	−	0.0569252i	$-0.981870\pi$
$919$	−16.6274	−	28.7995i	−0.548488	−	0.950009i	0.449891	−	0.893084i	$-0.351463\pi$
$920$		0			0
$921$	−0.985281	+	1.70656i	−0.0324661	+	0.0562330i
$922$		0			0
$923$			24.0000i			0.789970i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	18.5813	+	10.7279i	0.610290	+	0.352351i
$928$		0			0
$929$	4.60051	+	7.96831i	0.150938	+	0.261432i	0.931572	−	0.363556i	$-0.118437\pi$
$929$	4.60051	+	7.96831i	0.150938	+	0.261432i	−0.780635	+	0.624988i	$0.785104\pi$
$930$		0			0
$931$	−38.1421	+	10.6385i	−1.25006	+	0.348662i
$932$		0			0
$933$	−7.76874	+	4.48528i	−0.254337	+	0.146842i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			18.6274i			0.608531i	0.952587	+	0.304266i	$0.0984110\pi$
$937$			18.6274i			0.608531i	−0.952587	+	0.304266i	$0.901589\pi$
$938$		0			0
$939$	−8.68629			−0.283466
$940$		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
$943$	28.1946	−	16.2782i	0.918143	−	0.530090i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.61332	−	5.55025i	0.312391	−	0.180359i	−0.335605	−	0.942003i	$-0.608941\pi$
$947$	9.61332	−	5.55025i	0.312391	−	0.180359i	0.647996	+	0.761644i	$0.275607\pi$
$948$		0			0
$949$	3.65685	−	6.33386i	0.118707	−	0.205606i
$950$		0			0
$951$	−9.11270			−0.295499
$952$		0			0
$953$			54.6274i			1.76956i	0.466013	+	0.884778i	$0.345690\pi$
$953$			54.6274i			1.76956i	−0.466013	+	0.884778i	$0.654310\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.32640	+	1.34315i	−0.0752017	+	0.0434177i
$958$		0			0
$959$	−10.4853	+	1.43488i	−0.338587	+	0.0463346i
$960$		0			0
$961$	15.1569	+	26.2524i	0.488931	+	0.846853i
$962$		0			0
$963$	13.6823	+	7.89949i	0.440907	+	0.254558i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	24.7574i		−	0.796143i	−0.917354	−	0.398072i	$-0.869680\pi$
$967$		−	24.7574i		−	0.796143i	0.917354	−	0.398072i	$-0.130320\pi$
$968$		0			0
$969$	8.97056	−	15.5375i	0.288176	−	0.499135i
$970$		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
$973$	5.19615	−	4.02944i	0.166581	−	0.129178i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.2269	−	15.1421i	−0.839074	−	0.484440i	0.0178751	−	0.999840i	$-0.494310\pi$
$977$	−26.2269	−	15.1421i	−0.839074	−	0.484440i	−0.856949	+	0.515400i	$0.827643\pi$
$978$		0			0
$979$	4.42641			0.141469
$980$		0			0
$981$	−51.7990			−1.65381
$982$		0			0
$983$	−35.8403	−	20.6924i	−1.14313	−	0.659985i	−0.195924	−	0.980619i	$-0.562771\pi$
$983$	−35.8403	−	20.6924i	−1.14313	−	0.659985i	−0.947203	+	0.320634i	$0.896104\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−10.0951	+	7.82843i	−0.321332	+	0.249182i
$988$		0			0
$989$	19.2696	+	33.3758i	0.612736	+	1.06129i
$990$		0			0
$991$	−2.41421	+	4.18154i	−0.0766900	+	0.132831i	−0.901820	−	0.432112i	$-0.857769\pi$
$991$	−2.41421	+	4.18154i	−0.0766900	+	0.132831i	0.825130	+	0.564943i	$0.191102\pi$
$992$		0			0
$993$		−	10.9706i		−	0.348140i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	12.4215	+	7.17157i	0.393394	+	0.227126i	0.683630	−	0.729829i	$-0.260400\pi$
$997$	12.4215	+	7.17157i	0.393394	+	0.227126i	−0.290236	+	0.956955i	$0.593734\pi$
$998$		0			0
$999$	−6.82843	−	11.8272i	−0.216042	−	0.374196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.g.249.3		8
5.2	odd	4		1400.2.q.h.1201.2		4
5.3	odd	4		280.2.q.d.81.1	✓	4
5.4	even	2	inner	1400.2.bh.g.249.2		8
7.2	even	3	inner	1400.2.bh.g.849.2		8
15.8	even	4		2520.2.bi.k.361.2		4
20.3	even	4		560.2.q.j.81.2		4
35.2	odd	12		1400.2.q.h.401.2		4
35.3	even	12		1960.2.a.t.1.1		2
35.9	even	6	inner	1400.2.bh.g.849.3		8
35.13	even	4		1960.2.q.q.361.2		4
35.17	even	12		9800.2.a.br.1.2		2
35.18	odd	12		1960.2.a.p.1.2		2
35.23	odd	12		280.2.q.d.121.1	yes	4
35.32	odd	12		9800.2.a.bz.1.1		2
35.33	even	12		1960.2.q.q.961.2		4
105.23	even	12		2520.2.bi.k.1801.2		4
140.3	odd	12		3920.2.a.bp.1.2		2
140.23	even	12		560.2.q.j.401.2		4
140.123	even	12		3920.2.a.bz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.d.81.1	✓	4	5.3	odd	4
280.2.q.d.121.1	yes	4	35.23	odd	12
560.2.q.j.81.2		4	20.3	even	4
560.2.q.j.401.2		4	140.23	even	12
1400.2.q.h.401.2		4	35.2	odd	12
1400.2.q.h.1201.2		4	5.2	odd	4
1400.2.bh.g.249.2		8	5.4	even	2	inner
1400.2.bh.g.249.3		8	1.1	even	1	trivial
1400.2.bh.g.849.2		8	7.2	even	3	inner
1400.2.bh.g.849.3		8	35.9	even	6	inner
1960.2.a.p.1.2		2	35.18	odd	12
1960.2.a.t.1.1		2	35.3	even	12
1960.2.q.q.361.2		4	35.13	even	4
1960.2.q.q.961.2		4	35.33	even	12
2520.2.bi.k.361.2		4	15.8	even	4
2520.2.bi.k.1801.2		4	105.23	even	12
3920.2.a.bp.1.2		2	140.3	odd	12
3920.2.a.bz.1.1		2	140.123	even	12
9800.2.a.br.1.2		2	35.17	even	12
9800.2.a.bz.1.1		2	35.32	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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.358719 + 0.207107i) q^{3} +(-2.09077 + 1.62132i) q^{7} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.358719 + 0.207107i) q^{3} +(-2.09077 + 1.62132i) q^{7} +(-1.41421 - 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} -2.00000i q^{13} +(6.63103 + 3.82843i) q^{17} +(-2.82843 - 4.89898i) q^{19} +(-1.08579 + 0.148586i) q^{21} +(4.83743 - 2.79289i) q^{23} -2.41421i q^{27} +7.82843 q^{29} +(-0.414214 + 0.717439i) q^{31} +(-0.297173 + 0.171573i) q^{33} +(4.89898 - 2.82843i) q^{37} +(0.414214 - 0.717439i) q^{39} +5.82843 q^{41} +6.89949i q^{43} +(10.0951 - 5.82843i) q^{47} +(1.74264 - 6.77962i) q^{49} +(1.58579 + 2.74666i) q^{51} +(-4.89898 - 2.82843i) q^{53} -2.34315i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-3.32843 - 5.76500i) q^{61} +(6.92820 + 2.82843i) q^{63} +(11.1713 + 6.44975i) q^{67} +2.31371 q^{69} -12.0000 q^{71} +(3.16693 + 1.82843i) q^{73} +(-0.297173 - 2.17157i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(-3.74264 + 6.48244i) q^{81} +4.75736i q^{83} +(2.80821 + 1.62132i) q^{87} +(-2.67157 - 4.62730i) q^{89} +(3.24264 + 4.18154i) q^{91} +(-0.297173 + 0.171573i) q^{93} +6.00000i q^{97} +2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 8 q^{11} - 20 q^{21} + 40 q^{29} + 8 q^{31} - 8 q^{39} + 24 q^{41} - 20 q^{49} + 24 q^{51} - 16 q^{59} - 4 q^{61} - 72 q^{69} - 96 q^{71} - 16 q^{79} + 4 q^{81} - 44 q^{89} - 8 q^{91} + 64 q^{99}+O(q^{100}) \) 8 * q + 8 * q^11 - 20 * q^21 + 40 * q^29 + 8 * q^31 - 8 * q^39 + 24 * q^41 - 20 * q^49 + 24 * q^51 - 16 * q^59 - 4 * q^61 - 72 * q^69 - 96 * q^71 - 16 * q^79 + 4 * q^81 - 44 * q^89 - 8 * q^91 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more