LMFDB - Embedded newform 1400.2.bh.j.249.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1400.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 15x^{14} + 170x^{12} - 789x^{10} + 2754x^{8} - 960x^{6} + 269x^{4} - 18x^{2} + 1 $ x^16 - 15x^14 + 170x^12 - 789x^10 + 2754x^8 - 960x^6 + 269x^4 - 18*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.5
Root			$-0.462601 - 0.267083i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.j.849.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.403424 + 0.232917i) q^{3} +(2.02469 + 1.70312i) q^{7} +(-1.39150 - 2.41015i) q^{9} +O(q^{10})$	\(q+(0.403424 + 0.232917i) q^{3} +(2.02469 + 1.70312i) q^{7} +(-1.39150 - 2.41015i) q^{9} +(-0.688377 + 1.19230i) q^{11} -5.12091i q^{13} +(-0.292641 - 0.168956i) q^{17} +(2.99649 + 5.19008i) q^{19} +(0.420123 + 1.15867i) q^{21} +(5.67065 - 3.27395i) q^{23} -2.69392i q^{27} +7.99299 q^{29} +(3.62442 - 6.27767i) q^{31} +(-0.555416 + 0.320670i) q^{33} +(-5.24169 + 3.02629i) q^{37} +(1.19275 - 2.06590i) q^{39} +6.68457 q^{41} -5.02949i q^{43} +(-5.75590 + 3.32317i) q^{47} +(1.19875 + 6.89659i) q^{49} +(-0.0787056 - 0.136322i) q^{51} +(-4.21934 - 2.43604i) q^{53} +2.79174i q^{57} +(0.301249 - 0.521778i) q^{59} +(6.54103 + 11.3294i) q^{61} +(1.28742 - 7.24970i) q^{63} +(10.4834 + 6.05258i) q^{67} +3.05024 q^{69} -1.39251 q^{71} +(1.45941 + 0.842589i) q^{73} +(-3.42439 + 1.24166i) q^{77} +(3.80812 + 6.59585i) q^{79} +(-3.54704 + 6.14365i) q^{81} -7.49532i q^{83} +(3.22457 + 1.86170i) q^{87} +(-6.19525 - 10.7305i) q^{89} +(8.72154 - 10.3683i) q^{91} +(2.92436 - 1.68838i) q^{93} -0.691577i q^{97} +3.83151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 20 q^{19} + 50 q^{21} - 8 q^{29} + 28 q^{31} - 20 q^{39} - 16 q^{41} + 26 q^{49} - 10 q^{51} - 2 q^{59} + 50 q^{61} + 64 q^{69} - 80 q^{71} + 4 q^{79} - 48 q^{81} - 38 q^{89} + 34 q^{91} + 204 q^{99}+O(q^{100}) $ 16 * q + 10 * q^9 - 20 * q^19 + 50 * q^21 - 8 * q^29 + 28 * q^31 - 20 * q^39 - 16 * q^41 + 26 * q^49 - 10 * q^51 - 2 * q^59 + 50 * q^61 + 64 * q^69 - 80 * q^71 + 4 * q^79 - 48 * q^81 - 38 * q^89 + 34 * q^91 + 204 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.403424	+	0.232917i	0.232917	+	0.134475i	0.611917	−	0.790922i	$-0.290399\pi$
$3$	0.403424	+	0.232917i	0.232917	+	0.134475i	−0.379000	+	0.925397i	$0.623732\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.02469	+	1.70312i	0.765261	+	0.643720i
$7$	2.02469	+	1.70312i	0.765261	+	0.643720i
$8$		0			0
$9$	−1.39150	−	2.41015i	−0.463833	−	0.803382i
$10$		0			0
$11$	−0.688377	+	1.19230i	−0.207554	+	0.359493i	−0.950943	−	0.309365i	$-0.899883\pi$
$11$	−0.688377	+	1.19230i	−0.207554	+	0.359493i	0.743390	+	0.668858i	$0.233217\pi$
$12$		0			0
$13$		−	5.12091i		−	1.42029i	−0.704058	−	0.710143i	$-0.748630\pi$
$13$		−	5.12091i		−	1.42029i	0.704058	−	0.710143i	$-0.251370\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.292641	−	0.168956i	−0.0709758	−	0.0409779i	0.464092	−	0.885787i	$-0.346381\pi$
$17$	−0.292641	−	0.168956i	−0.0709758	−	0.0409779i	−0.535068	+	0.844809i	$0.679714\pi$
$18$		0			0
$19$	2.99649	+	5.19008i	0.687443	+	1.19069i	0.972662	+	0.232224i	$0.0746002\pi$
$19$	2.99649	+	5.19008i	0.687443	+	1.19069i	−0.285219	+	0.958462i	$0.592066\pi$
$20$		0			0
$21$	0.420123	+	1.15867i	0.0916785	+	0.252842i
$22$		0			0
$23$	5.67065	−	3.27395i	1.18241	−	0.682666i	0.225841	−	0.974164i	$-0.427487\pi$
$23$	5.67065	−	3.27395i	1.18241	−	0.682666i	0.956571	+	0.291498i	$0.0941537\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	2.69392i		−	0.518445i
$28$		0			0
$29$	7.99299			1.48426			0.742130	−	0.670256i	$-0.233816\pi$
$29$	7.99299			1.48426			0.742130	+	0.670256i	$0.233816\pi$
$30$		0			0
$31$	3.62442	−	6.27767i	0.650964	−	1.12750i	−0.331925	−	0.943306i	$-0.607698\pi$
$31$	3.62442	−	6.27767i	0.650964	−	1.12750i	0.982889	−	0.184198i	$-0.0589686\pi$
$32$		0			0
$33$	−0.555416	+	0.320670i	−0.0966856	+	0.0558214i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.24169	+	3.02629i	−0.861728	+	0.497519i	−0.864591	−	0.502477i	$-0.832422\pi$
$37$	−5.24169	+	3.02629i	−0.861728	+	0.497519i	0.00286250	+	0.999996i	$0.499089\pi$
$38$		0			0
$39$	1.19275	−	2.06590i	0.190993	−	0.330809i
$40$		0			0
$41$	6.68457			1.04395			0.521977	−	0.852960i	$-0.325195\pi$
$41$	6.68457			1.04395			0.521977	+	0.852960i	$0.325195\pi$
$42$		0			0
$43$		−	5.02949i		−	0.766990i	−0.923543	−	0.383495i	$-0.874720\pi$
$43$		−	5.02949i		−	0.766990i	0.923543	−	0.383495i	$-0.125280\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.75590	+	3.32317i	−0.839584	+	0.484734i	−0.857123	−	0.515112i	$-0.827750\pi$
$47$	−5.75590	+	3.32317i	−0.839584	+	0.484734i	0.0175390	+	0.999846i	$0.494417\pi$
$48$		0			0
$49$	1.19875	+	6.89659i	0.171250	+	0.985228i
$50$		0			0
$51$	−0.0787056	−	0.136322i	−0.0110210	−	0.0190889i
$52$		0			0
$53$	−4.21934	−	2.43604i	−0.579571	−	0.334616i	0.181392	−	0.983411i	$-0.441940\pi$
$53$	−4.21934	−	2.43604i	−0.579571	−	0.334616i	−0.760963	+	0.648795i	$0.775273\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			2.79174i			0.369775i
$58$		0			0
$59$	0.301249	−	0.521778i	0.0392192	−	0.0679297i	−0.845749	−	0.533580i	$-0.820846\pi$
$59$	0.301249	−	0.521778i	0.0392192	−	0.0679297i	0.884969	+	0.465650i	$0.154180\pi$
$60$		0			0
$61$	6.54103	+	11.3294i	0.837494	+	1.45058i	0.891984	+	0.452067i	$0.149313\pi$
$61$	6.54103	+	11.3294i	0.837494	+	1.45058i	−0.0544903	+	0.998514i	$0.517353\pi$
$62$		0			0
$63$	1.28742	−	7.24970i	0.162199	−	0.913376i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.4834	+	6.05258i	1.28075	+	0.739440i	0.976985	−	0.213307i	$-0.0684236\pi$
$67$	10.4834	+	6.05258i	1.28075	+	0.739440i	0.303763	+	0.952748i	$0.401757\pi$
$68$		0			0
$69$	3.05024			0.367205
$70$		0			0
$71$	−1.39251			−0.165260			−0.0826301	−	0.996580i	$-0.526332\pi$
$71$	−1.39251			−0.165260			−0.0826301	+	0.996580i	$0.526332\pi$
$72$		0			0
$73$	1.45941	+	0.842589i	0.170811	+	0.0986176i	0.582968	−	0.812495i	$-0.301891\pi$
$73$	1.45941	+	0.842589i	0.170811	+	0.0986176i	−0.412157	+	0.911113i	$0.635225\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.42439	+	1.24166i	−0.390246	+	0.141500i
$78$		0			0
$79$	3.80812	+	6.59585i	0.428447	+	0.742091i	0.996735	−	0.0807379i	$-0.0257277\pi$
$79$	3.80812	+	6.59585i	0.428447	+	0.742091i	−0.568289	+	0.822829i	$0.692394\pi$
$80$		0			0
$81$	−3.54704	+	6.14365i	−0.394115	+	0.682628i
$82$		0			0
$83$		−	7.49532i		−	0.822719i	−0.911473	−	0.411359i	$-0.865054\pi$
$83$		−	7.49532i		−	0.822719i	0.911473	−	0.411359i	$-0.134946\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.22457	+	1.86170i	0.345710	+	0.199596i
$88$		0			0
$89$	−6.19525	−	10.7305i	−0.656695	−	1.13743i	−0.981466	−	0.191636i	$-0.938621\pi$
$89$	−6.19525	−	10.7305i	−0.656695	−	1.13743i	0.324771	−	0.945793i	$-0.394713\pi$
$90$		0			0
$91$	8.72154	−	10.3683i	0.914265	−	1.08689i
$92$		0			0
$93$	2.92436	−	1.68838i	0.303242	−	0.175077i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	0.691577i		−	0.0702190i	−0.999383	−	0.0351095i	$-0.988822\pi$
$97$		−	0.691577i		−	0.0702190i	0.999383	−	0.0351095i	$-0.0111780\pi$
$98$		0			0
$99$	3.83151			0.385081
$100$		0			0
$101$	−2.00687	+	3.47600i	−0.199691	+	0.345875i	−0.948428	−	0.316992i	$-0.897327\pi$
$101$	−2.00687	+	3.47600i	−0.199691	+	0.345875i	0.748737	+	0.662867i	$0.230660\pi$
$102$		0			0
$103$	5.88615	−	3.39837i	0.579979	−	0.334851i	−0.181146	−	0.983456i	$-0.557981\pi$
$103$	5.88615	−	3.39837i	0.579979	−	0.334851i	0.761125	+	0.648605i	$0.224647\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.47233	−	4.89150i	0.819051	−	0.472879i	−0.0310384	−	0.999518i	$-0.509881\pi$
$107$	8.47233	−	4.89150i	0.819051	−	0.472879i	0.850089	+	0.526639i	$0.176548\pi$
$108$		0			0
$109$	2.29087	−	3.96791i	0.219426	−	0.380057i	−0.735207	−	0.677843i	$-0.762915\pi$
$109$	2.29087	−	3.96791i	0.219426	−	0.380057i	0.954633	+	0.297786i	$0.0962482\pi$
$110$		0			0
$111$	−2.81950			−0.267615
$112$		0			0
$113$		−	17.6688i		−	1.66214i	−0.556166	−	0.831071i	$-0.687728\pi$
$113$		−	17.6688i		−	1.66214i	0.556166	−	0.831071i	$-0.312272\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−12.3421	+	7.12574i	−1.14103	+	0.658775i
$118$		0			0
$119$	−0.304754	−	0.840487i	−0.0279368	−	0.0770473i
$120$		0			0
$121$	4.55227	+	7.88477i	0.413843	+	0.716797i
$122$		0			0
$123$	2.69672	+	1.55695i	0.243155	+	0.140385i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	14.8513i		−	1.31784i	−0.752212	−	0.658921i	$-0.771013\pi$
$127$		−	14.8513i		−	1.31784i	0.752212	−	0.658921i	$-0.228987\pi$
$128$		0			0
$129$	1.17145	−	2.02902i	0.103141	−	0.178645i
$130$		0			0
$131$	0.527297	+	0.913306i	0.0460702	+	0.0797959i	0.888141	−	0.459571i	$-0.151997\pi$
$131$	0.527297	+	0.913306i	0.0460702	+	0.0797959i	−0.842071	+	0.539367i	$0.818664\pi$
$132$		0			0
$133$	−2.77236	+	15.6117i	−0.240394	+	1.35371i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−14.0734	−	8.12528i	−1.20237	−	0.694190i	−0.241290	−	0.970453i	$-0.577570\pi$
$137$	−14.0734	−	8.12528i	−1.20237	−	0.694190i	−0.961082	+	0.276263i	$0.910904\pi$
$138$		0			0
$139$	4.32591			0.366918			0.183459	−	0.983027i	$-0.441270\pi$
$139$	4.32591			0.366918			0.183459	+	0.983027i	$0.441270\pi$
$140$		0			0
$141$	−3.09609			−0.260738
$142$		0			0
$143$	6.10568	+	3.52512i	0.510583	+	0.294785i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.12273	+	3.06146i	−0.0926011	+	0.252505i
$148$		0			0
$149$	3.83908	+	6.64949i	0.314510	+	0.544747i	0.979333	−	0.202253i	$-0.0648265\pi$
$149$	3.83908	+	6.64949i	0.314510	+	0.544747i	−0.664823	+	0.747001i	$0.731493\pi$
$150$		0			0
$151$	−1.46934	+	2.54497i	−0.119573	+	0.207107i	−0.919599	−	0.392859i	$-0.871486\pi$
$151$	−1.46934	+	2.54497i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$152$		0			0
$153$			0.940410i			0.0760276i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	13.2314	+	7.63916i	1.05598	+	0.609671i	0.924318	−	0.381623i	$-0.124635\pi$
$157$	13.2314	+	7.63916i	1.05598	+	0.609671i	0.131664	+	0.991294i	$0.457968\pi$
$158$		0			0
$159$	−1.13479	−	1.96551i	−0.0899947	−	0.155875i
$160$		0			0
$161$	17.0573	+	3.02907i	1.34430	+	0.238724i
$162$		0			0
$163$	−5.35397	+	3.09112i	−0.419355	+	0.242115i	−0.694801	−	0.719202i	$-0.744508\pi$
$163$	−5.35397	+	3.09112i	−0.419355	+	0.242115i	0.275446	+	0.961316i	$0.411174\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			18.1162i			1.40188i	0.713222	+	0.700938i	$0.247235\pi$
$167$			18.1162i			1.40188i	−0.713222	+	0.700938i	$0.752765\pi$
$168$		0			0
$169$	−13.2237			−1.01721
$170$		0			0
$171$	8.33924	−	14.4440i	0.637718	−	1.10456i
$172$		0			0
$173$	−17.8145	+	10.2852i	−1.35441	+	0.781969i	−0.988864	−	0.148825i	$-0.952451\pi$
$173$	−17.8145	+	10.2852i	−1.35441	+	0.781969i	−0.365546	+	0.930793i	$0.619118\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.243062	−	0.140332i	0.0182697	−	0.0105480i
$178$		0			0
$179$	−4.62559	+	8.01175i	−0.345733	+	0.598826i	−0.985487	−	0.169753i	$-0.945703\pi$
$179$	−4.62559	+	8.01175i	−0.345733	+	0.598826i	0.639754	+	0.768580i	$0.279036\pi$
$180$		0			0
$181$	−14.2763			−1.06115			−0.530575	−	0.847638i	$-0.678024\pi$
$181$	−14.2763			−1.06115			−0.530575	+	0.847638i	$0.678024\pi$
$182$		0			0
$183$			6.09408i			0.450487i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.402894	−	0.232611i	0.0294626	−	0.0170102i
$188$		0			0
$189$	4.58807	−	5.45435i	0.333733	−	0.396746i
$190$		0			0
$191$	−11.7418	−	20.3374i	−0.849608	−	1.47156i	−0.881558	−	0.472075i	$-0.843505\pi$
$191$	−11.7418	−	20.3374i	−0.849608	−	1.47156i	0.0319498	−	0.999489i	$-0.489828\pi$
$192$		0			0
$193$	−12.1046	−	6.98862i	−0.871311	−	0.503052i	−0.00352746	−	0.999994i	$-0.501123\pi$
$193$	−12.1046	−	6.98862i	−0.871311	−	0.503052i	−0.867784	+	0.496942i	$0.834456\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	8.69017i		−	0.619149i	−0.950875	−	0.309575i	$-0.899813\pi$
$197$		−	8.69017i		−	0.619149i	0.950875	−	0.309575i	$-0.100187\pi$
$198$		0			0
$199$	−4.28433	+	7.42067i	−0.303708	+	0.526037i	−0.976973	−	0.213364i	$-0.931558\pi$
$199$	−4.28433	+	7.42067i	−0.303708	+	0.526037i	0.673265	+	0.739401i	$0.264891\pi$
$200$		0			0
$201$	2.81950	+	4.88352i	0.198872	+	0.344457i
$202$		0			0
$203$	16.1833	+	13.6130i	1.13585	+	0.955448i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−15.7814	−	9.11140i	−1.09688	−	0.633286i
$208$		0			0
$209$	−8.25087			−0.570725
$210$		0			0
$211$	−23.1457			−1.59342			−0.796709	−	0.604363i	$-0.793428\pi$
$211$	−23.1457			−1.59342			−0.796709	+	0.604363i	$0.793428\pi$
$212$		0			0
$213$	−0.561771	−	0.324339i	−0.0384919	−	0.0222233i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	18.0300	−	6.53753i	1.22395	−	0.443796i
$218$		0			0
$219$	0.392507	+	0.679842i	0.0265231	+	0.0459394i
$220$		0			0
$221$	−0.865210	+	1.49859i	−0.0582003	+	0.100806i
$222$		0			0
$223$			2.69158i			0.180241i	0.995931	+	0.0901207i	$0.0287253\pi$
$223$			2.69158i			0.180241i	−0.995931	+	0.0901207i	$0.971275\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.54628	−	5.51155i	−0.633609	−	0.365814i	0.148540	−	0.988906i	$-0.452543\pi$
$227$	−9.54628	−	5.51155i	−0.633609	−	0.365814i	−0.782148	+	0.623092i	$0.785876\pi$
$228$		0			0
$229$	−1.48876	−	2.57861i	−0.0983801	−	0.170399i	0.812634	−	0.582774i	$-0.198033\pi$
$229$	−1.48876	−	2.57861i	−0.0983801	−	0.170399i	−0.911014	+	0.412375i	$0.864699\pi$
$230$		0			0
$231$	−1.67069	−	0.296684i	−0.109923	−	0.0195204i
$232$		0			0
$233$	1.06152	−	0.612871i	0.0695428	−	0.0401505i	−0.464825	−	0.885402i	$-0.653883\pi$
$233$	1.06152	−	0.612871i	0.0695428	−	0.0401505i	0.534368	+	0.845252i	$0.320550\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			3.54790i			0.230461i
$238$		0			0
$239$	17.2381			1.11504			0.557519	−	0.830164i	$-0.311753\pi$
$239$	17.2381			1.11504			0.557519	+	0.830164i	$0.311753\pi$
$240$		0			0
$241$	−2.07200	+	3.58881i	−0.133469	+	0.231176i	−0.925012	−	0.379939i	$-0.875945\pi$
$241$	−2.07200	+	3.58881i	−0.133469	+	0.231176i	0.791542	+	0.611114i	$0.209278\pi$
$242$		0			0
$243$	−9.86093	+	5.69321i	−0.632579	+	0.365220i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	26.5779	−	15.3448i	1.69111	−	0.976365i
$248$		0			0
$249$	1.74579	−	3.02380i	0.110635	−	0.191625i
$250$		0			0
$251$	−18.6481			−1.17706			−0.588528	−	0.808477i	$-0.700292\pi$
$251$	−18.6481			−1.17706			−0.588528	+	0.808477i	$0.700292\pi$
$252$		0			0
$253$			9.01486i			0.566759i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.19333	+	4.73042i	−0.511086	+	0.295075i	−0.733280	−	0.679927i	$-0.762011\pi$
$257$	−8.19333	+	4.73042i	−0.511086	+	0.295075i	0.222194	+	0.975002i	$0.428678\pi$
$258$		0			0
$259$	−15.7669	−	2.79993i	−0.979710	−	0.173979i
$260$		0			0
$261$	−11.1222	−	19.2643i	−0.688449	−	1.19243i
$262$		0			0
$263$	−2.37097	−	1.36888i	−0.146200	−	0.0844087i	0.425116	−	0.905139i	$-0.360233\pi$
$263$	−2.37097	−	1.36888i	−0.146200	−	0.0844087i	−0.571316	+	0.820730i	$0.693567\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	5.77192i		−	0.353235i
$268$		0			0
$269$	−9.14003	+	15.8310i	−0.557277	+	0.965232i	0.440445	+	0.897779i	$0.354821\pi$
$269$	−9.14003	+	15.8310i	−0.557277	+	0.965232i	−0.997722	+	0.0674530i	$0.978513\pi$
$270$		0			0
$271$	15.7087	+	27.2082i	0.954233	+	1.65278i	0.736113	+	0.676859i	$0.236659\pi$
$271$	15.7087	+	27.2082i	0.954233	+	1.65278i	0.218120	+	0.975922i	$0.430007\pi$
$272$		0			0
$273$	5.93343	−	2.15141i	0.359107	−	0.130210i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.81483	+	5.08924i	0.529632	+	0.305783i	0.740866	−	0.671652i	$-0.234415\pi$
$277$	8.81483	+	5.08924i	0.529632	+	0.305783i	−0.211235	+	0.977435i	$0.567748\pi$
$278$		0			0
$279$	−20.1735			−1.20776
$280$		0			0
$281$	−26.4261			−1.57645			−0.788224	−	0.615389i	$-0.788999\pi$
$281$	−26.4261			−1.57645			−0.788224	+	0.615389i	$0.788999\pi$
$282$		0			0
$283$	7.78990	+	4.49750i	0.463062	+	0.267349i	0.713331	−	0.700828i	$-0.247186\pi$
$283$	7.78990	+	4.49750i	0.463062	+	0.267349i	−0.250269	+	0.968176i	$0.580519\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.5342	+	11.3846i	0.798898	+	0.672014i
$288$		0			0
$289$	−8.44291	−	14.6235i	−0.496642	−	0.860209i
$290$		0			0
$291$	0.161080	−	0.278999i	0.00944268	−	0.0163552i
$292$		0			0
$293$			34.1092i			1.99268i	0.0854640	+	0.996341i	$0.472763\pi$
$293$			34.1092i			1.99268i	−0.0854640	+	0.996341i	$0.527237\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.21197	+	1.85443i	0.186377	+	0.107605i
$298$		0			0
$299$	−16.7656	−	29.0389i	−0.969580	−	1.67936i
$300$		0			0
$301$	8.56583	−	10.1832i	0.493726	−	0.586948i
$302$		0			0
$303$	−1.61924	+	0.934868i	−0.0930229	+	0.0537068i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	16.5815i		−	0.946354i	−0.880967	−	0.473177i	$-0.843107\pi$
$307$		−	16.5815i		−	0.946354i	0.880967	−	0.473177i	$-0.156893\pi$
$308$		0			0
$309$	3.16615			0.180116
$310$		0			0
$311$	15.0080	−	25.9947i	0.851028	−	1.47402i	−0.0292538	−	0.999572i	$-0.509313\pi$
$311$	15.0080	−	25.9947i	0.851028	−	1.47402i	0.880282	−	0.474451i	$-0.157354\pi$
$312$		0			0
$313$	−8.31601	+	4.80125i	−0.470048	+	0.271383i	−0.716260	−	0.697833i	$-0.754148\pi$
$313$	−8.31601	+	4.80125i	−0.470048	+	0.271383i	0.246212	+	0.969216i	$0.420814\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.4430	+	12.3801i	−1.20436	+	0.695337i	−0.961521	−	0.274730i	$-0.911411\pi$
$317$	−21.4430	+	12.3801i	−1.20436	+	0.695337i	−0.242837	+	0.970067i	$0.578078\pi$
$318$		0			0
$319$	−5.50219	+	9.53008i	−0.308064	+	0.533582i
$320$		0			0
$321$	4.55726			0.254361
$322$		0			0
$323$		−	2.02511i		−	0.112680i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.84839	−	1.06717i	0.102216	−	0.0590145i
$328$		0			0
$329$	−17.3137	−	3.07460i	−0.954534	−	0.169508i
$330$		0			0
$331$	9.98261	+	17.2904i	0.548694	+	0.950366i	0.998364	+	0.0571715i	$0.0182082\pi$
$331$	9.98261	+	17.2904i	0.548694	+	0.950366i	−0.449670	+	0.893195i	$0.648458\pi$
$332$		0			0
$333$	14.5876	+	8.42216i	0.799396	+	0.461531i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	23.9421i		−	1.30421i	−0.758128	−	0.652106i	$-0.773886\pi$
$337$		−	23.9421i		−	1.30421i	0.758128	−	0.652106i	$-0.226114\pi$
$338$		0			0
$339$	4.11537	−	7.12803i	0.223516	−	0.387141i
$340$		0			0
$341$	4.98993	+	8.64282i	0.270220	+	0.468035i
$342$		0			0
$343$	−9.31864	+	16.0051i	−0.503159	+	0.864194i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.73590	+	1.57957i	0.146871	+	0.0847958i	0.571634	−	0.820508i	$-0.306310\pi$
$347$	2.73590	+	1.57957i	0.146871	+	0.0847958i	−0.424764	+	0.905304i	$0.639643\pi$
$348$		0			0
$349$	34.6022			1.85221			0.926107	−	0.377261i	$-0.123134\pi$
$349$	34.6022			1.85221			0.926107	+	0.377261i	$0.123134\pi$
$350$		0			0
$351$	−13.7953			−0.736340
$352$		0			0
$353$	9.35078	+	5.39867i	0.497692	+	0.287342i	0.727760	−	0.685832i	$-0.240562\pi$
$353$	9.35078	+	5.39867i	0.497692	+	0.287342i	−0.230068	+	0.973175i	$0.573895\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.0728186	−	0.410055i	0.00385397	−	0.0217024i
$358$		0			0
$359$	−1.81062	−	3.13608i	−0.0955606	−	0.165516i	0.814282	−	0.580470i	$-0.197131\pi$
$359$	−1.81062	−	3.13608i	−0.0955606	−	0.165516i	−0.909842	+	0.414954i	$0.863798\pi$
$360$		0			0
$361$	−8.45796	+	14.6496i	−0.445156	+	0.771032i
$362$		0			0
$363$			4.24121i			0.222606i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−8.42679	−	4.86521i	−0.439875	−	0.253962i	0.263670	−	0.964613i	$-0.415067\pi$
$367$	−8.42679	−	4.86521i	−0.439875	−	0.253962i	−0.703545	+	0.710651i	$0.748400\pi$
$368$		0			0
$369$	−9.30157	−	16.1108i	−0.484220	−	0.838694i
$370$		0			0
$371$	−4.39400	−	12.1183i	−0.228125	−	0.629150i
$372$		0			0
$373$	−4.68250	+	2.70344i	−0.242451	+	0.139979i	−0.616303	−	0.787509i	$-0.711370\pi$
$373$	−4.68250	+	2.70344i	−0.242451	+	0.139979i	0.373852	+	0.927488i	$0.378037\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	40.9314i		−	2.10807i
$378$		0			0
$379$	9.67144			0.496789			0.248394	−	0.968659i	$-0.420097\pi$
$379$	9.67144			0.496789			0.248394	+	0.968659i	$0.420097\pi$
$380$		0			0
$381$	3.45913	−	5.99139i	0.177217	−	0.306948i
$382$		0			0
$383$	−28.1001	+	16.2236i	−1.43585	+	0.828986i	−0.997558	−	0.0698489i	$-0.977748\pi$
$383$	−28.1001	+	16.2236i	−1.43585	+	0.828986i	−0.438288	+	0.898835i	$0.644415\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.1218	+	6.99853i	−0.616186	+	0.355755i
$388$		0			0
$389$	2.67216	−	4.62831i	0.135484	−	0.234665i	−0.790298	−	0.612722i	$-0.790075\pi$
$389$	2.67216	−	4.62831i	0.135484	−	0.234665i	0.925782	+	0.378057i	$0.123408\pi$
$390$		0			0
$391$	−2.21262			−0.111897
$392$		0			0
$393$			0.491266i			0.0247811i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.64112	+	5.56630i	−0.483874	+	0.279365i	−0.722029	−	0.691862i	$-0.756791\pi$
$397$	−9.64112	+	5.56630i	−0.483874	+	0.279365i	0.238156	+	0.971227i	$0.423457\pi$
$398$		0			0
$399$	−4.75467	+	5.65241i	−0.238031	+	0.282975i
$400$		0			0
$401$	−18.0980	−	31.3466i	−0.903770	−	1.56538i	−0.822560	−	0.568679i	$-0.807455\pi$
$401$	−18.0980	−	31.3466i	−0.903770	−	1.56538i	−0.0812106	−	0.996697i	$-0.525879\pi$
$402$		0			0
$403$	−32.1474	−	18.5603i	−1.60138	−	0.924555i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	8.33292i		−	0.413047i
$408$		0			0
$409$	−17.2830	+	29.9350i	−0.854589	+	1.48019i	0.0224363	+	0.999748i	$0.492858\pi$
$409$	−17.2830	+	29.9350i	−0.854589	+	1.48019i	−0.877026	+	0.480444i	$0.840476\pi$
$410$		0			0
$411$	−3.78503	−	6.55587i	−0.186702	−	0.323377i
$412$		0			0
$413$	1.49859	−	0.543376i	0.0737406	−	0.0267378i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.74518	+	1.00758i	0.0854616	+	0.0493413i
$418$		0			0
$419$	2.60984			0.127499			0.0637494	−	0.997966i	$-0.479694\pi$
$419$	2.60984			0.127499			0.0637494	+	0.997966i	$0.479694\pi$
$420$		0			0
$421$	−27.9541			−1.36240			−0.681201	−	0.732097i	$-0.738542\pi$
$421$	−27.9541			−1.36240			−0.681201	+	0.732097i	$0.738542\pi$
$422$		0			0
$423$	16.0186	+	9.24837i	0.778853	+	0.449671i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.05178	+	34.0787i	−0.292866	+	1.64919i
$428$		0			0
$429$	1.64212	+	2.84424i	0.0792824	+	0.137321i
$430$		0			0
$431$	−19.0933	+	33.0706i	−0.919692	+	1.59295i	−0.119810	+	0.992797i	$0.538229\pi$
$431$	−19.0933	+	33.0706i	−0.919692	+	1.59295i	−0.799882	+	0.600157i	$0.795105\pi$
$432$		0			0
$433$		−	13.7257i		−	0.659617i	−0.944048	−	0.329809i	$-0.893016\pi$
$433$		−	13.7257i		−	0.659617i	0.944048	−	0.329809i	$-0.106984\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	33.9841	+	19.6208i	1.62568	+	0.938588i
$438$		0			0
$439$	8.49329	+	14.7108i	0.405363	+	0.702109i	0.994364	−	0.106023i	$-0.0338119\pi$
$439$	8.49329	+	14.7108i	0.405363	+	0.702109i	−0.589001	+	0.808132i	$0.700479\pi$
$440$		0			0
$441$	14.9537	−	12.4858i	0.712083	−	0.594561i
$442$		0			0
$443$	2.20222	−	1.27145i	0.104631	−	0.0604086i	−0.446772	−	0.894648i	$-0.647426\pi$
$443$	2.20222	−	1.27145i	0.104631	−	0.0604086i	0.551402	+	0.834240i	$0.314093\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			3.57675i			0.169175i
$448$		0			0
$449$	−34.5205			−1.62912			−0.814561	−	0.580078i	$-0.803022\pi$
$449$	−34.5205			−1.62912			−0.814561	+	0.580078i	$0.803022\pi$
$450$		0			0
$451$	−4.60150	+	7.97004i	−0.216676	+	0.375294i
$452$		0			0
$453$	−1.18553	+	0.684469i	−0.0557013	+	0.0321591i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.6401	−	9.60719i	0.778393	−	0.449405i	−0.0574676	−	0.998347i	$-0.518303\pi$
$457$	16.6401	−	9.60719i	0.778393	−	0.449405i	0.835860	+	0.548942i	$0.184969\pi$
$458$		0			0
$459$	−0.455154	+	0.788350i	−0.0212448	+	0.0367970i
$460$		0			0
$461$	5.48457			0.255442			0.127721	−	0.991810i	$-0.459234\pi$
$461$	5.48457			0.255442			0.127721	+	0.991810i	$0.459234\pi$
$462$		0			0
$463$		−	2.55056i		−	0.118534i	−0.998242	−	0.0592672i	$-0.981124\pi$
$463$		−	2.55056i		−	0.118534i	0.998242	−	0.0592672i	$-0.0188764\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.7908	+	10.8488i	−0.869532	+	0.502025i	−0.867193	−	0.497973i	$-0.834078\pi$
$467$	−18.7908	+	10.8488i	−0.869532	+	0.502025i	−0.00233950	+	0.999997i	$0.500745\pi$
$468$		0			0
$469$	10.9173	+	30.1091i	0.504115	+	1.39031i
$470$		0			0
$471$	3.55858	+	6.16365i	0.163971	+	0.284006i
$472$		0			0
$473$	5.99668	+	3.46219i	0.275728	+	0.159191i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			13.5590i			0.620823i
$478$		0			0
$479$	19.0337	−	32.9674i	0.869673	−	1.50632i	0.00734135	−	0.999973i	$-0.497663\pi$
$479$	19.0337	−	32.9674i	0.869673	−	1.50632i	0.862331	−	0.506344i	$-0.169004\pi$
$480$		0			0
$481$	15.4974	+	26.8422i	0.706619	+	1.22390i
$482$		0			0
$483$	6.17579	+	5.19493i	0.281008	+	0.236377i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.462071	+	0.266777i	0.0209384	+	0.0120888i	0.510433	−	0.859918i	$-0.329485\pi$
$487$	0.462071	+	0.266777i	0.0209384	+	0.0120888i	−0.489494	+	0.872007i	$0.662819\pi$
$488$		0			0
$489$	−2.87990			−0.130233
$490$		0			0
$491$	22.7255			1.02559			0.512793	−	0.858512i	$-0.328611\pi$
$491$	22.7255			1.02559			0.512793	+	0.858512i	$0.328611\pi$
$492$		0			0
$493$	−2.33907	−	1.35046i	−0.105347	−	0.0608219i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.81940	−	2.37161i	−0.126467	−	0.106381i
$498$		0			0
$499$	7.03285	+	12.1813i	0.314834	+	0.545308i	0.979402	−	0.201919i	$-0.0647179\pi$
$499$	7.03285	+	12.1813i	0.314834	+	0.545308i	−0.664568	+	0.747227i	$0.731385\pi$
$500$		0			0
$501$	−4.21958	+	7.30853i	−0.188517	+	0.326521i
$502$		0			0
$503$		−	15.2757i		−	0.681108i	−0.940225	−	0.340554i	$-0.889385\pi$
$503$		−	15.2757i		−	0.681108i	0.940225	−	0.340554i	$-0.110615\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−5.33477	−	3.08003i	−0.236926	−	0.136789i
$508$		0			0
$509$	10.7371	+	18.5973i	0.475916	+	0.824310i	0.999619	−	0.0275905i	$-0.00878344\pi$
$509$	10.7371	+	18.5973i	0.475916	+	0.824310i	−0.523704	+	0.851900i	$0.675450\pi$
$510$		0			0
$511$	1.51982	+	4.19153i	0.0672327	+	0.185422i
$512$		0			0
$513$	13.9817	−	8.07231i	0.617305	−	0.356401i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	9.15037i		−	0.402433i
$518$		0			0
$519$	−9.58239			−0.420620
$520$		0			0
$521$	19.1514	−	33.1712i	0.839039	−	1.45326i	−0.0516595	−	0.998665i	$-0.516451\pi$
$521$	19.1514	−	33.1712i	0.839039	−	1.45326i	0.890699	−	0.454594i	$-0.150216\pi$
$522$		0			0
$523$	−31.8504	+	18.3889i	−1.39272	+	0.804089i	−0.993616	−	0.112816i	$-0.964013\pi$
$523$	−31.8504	+	18.3889i	−1.39272	+	0.804089i	−0.399106	+	0.916905i	$0.630680\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.12130	+	1.22474i	−0.0924054	+	0.0533503i
$528$		0			0
$529$	9.93752	−	17.2123i	0.432066	−	0.748360i
$530$		0			0
$531$	−1.67675			−0.0727647
$532$		0			0
$533$		−	34.2311i		−	1.48271i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.73215	+	2.15476i	−0.161054	+	0.0929846i
$538$		0			0
$539$	−9.04803	−	3.31818i	−0.389726	−	0.142924i
$540$		0			0
$541$	−8.31686	−	14.4052i	−0.357570	−	0.619329i	0.629985	−	0.776608i	$-0.283061\pi$
$541$	−8.31686	−	14.4052i	−0.357570	−	0.619329i	−0.987554	+	0.157279i	$0.949728\pi$
$542$		0			0
$543$	−5.75941	−	3.32520i	−0.247160	−	0.142698i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	22.0493i		−	0.942761i	−0.881930	−	0.471380i	$-0.843756\pi$
$547$		−	22.0493i		−	0.942761i	0.881930	−	0.471380i	$-0.156244\pi$
$548$		0			0
$549$	18.2037	−	31.5297i	0.776914	−	1.34566i
$550$		0			0
$551$	23.9509	+	41.4843i	1.02034	+	1.76729i
$552$		0			0
$553$	−3.52328	+	19.8403i	−0.149825	+	0.843693i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−28.2923	−	16.3346i	−1.19878	−	0.692118i	−0.238500	−	0.971143i	$-0.576656\pi$
$557$	−28.2923	−	16.3346i	−1.19878	−	0.692118i	−0.960284	+	0.279025i	$0.909989\pi$
$558$		0			0
$559$	−25.7556			−1.08934
$560$		0			0
$561$	0.216717			0.00914978
$562$		0			0
$563$	30.6647	+	17.7043i	1.29236	+	0.746147i	0.979073	−	0.203510i	$-0.0652349\pi$
$563$	30.6647	+	17.7043i	1.29236	+	0.746147i	0.313292	+	0.949657i	$0.398568\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−17.6450	+	6.39796i	−0.741022	+	0.268689i
$568$		0			0
$569$	−6.49112	−	11.2429i	−0.272122	−	0.471329i	0.697283	−	0.716796i	$-0.254392\pi$
$569$	−6.49112	−	11.2429i	−0.272122	−	0.471329i	−0.969405	+	0.245467i	$0.921059\pi$
$570$		0			0
$571$	−2.50250	+	4.33445i	−0.104726	+	0.181391i	−0.913626	−	0.406555i	$-0.866730\pi$
$571$	−2.50250	+	4.33445i	−0.104726	+	0.181391i	0.808900	+	0.587946i	$0.200063\pi$
$572$		0			0
$573$		−	10.9395i		−	0.457004i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	38.8172	+	22.4111i	1.61598	+	0.932986i	0.987946	+	0.154800i	$0.0494733\pi$
$577$	38.8172	+	22.4111i	1.61598	+	0.932986i	0.628034	+	0.778186i	$0.283860\pi$
$578$		0			0
$579$	−3.25554	−	5.63876i	−0.135296	−	0.234339i
$580$		0			0
$581$	12.7654	−	15.1757i	0.529600	−	0.629595i
$582$		0			0
$583$	5.80900	−	3.35383i	0.240584	−	0.138901i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			23.1092i			0.953819i	0.878952	+	0.476910i	$0.158243\pi$
$587$			23.1092i			0.953819i	−0.878952	+	0.476910i	$0.841757\pi$
$588$		0			0
$589$	43.4422			1.79000
$590$		0			0
$591$	2.02409	−	3.50583i	0.0832599	−	0.144210i
$592$		0			0
$593$	35.3551	−	20.4123i	1.45186	−	0.838231i	0.453272	−	0.891372i	$-0.350257\pi$
$593$	35.3551	−	20.4123i	1.45186	−	0.838231i	0.998587	+	0.0531407i	$0.0169232\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.45680	+	1.99579i	−0.141477	+	0.0816821i
$598$		0			0
$599$	19.4893	−	33.7565i	0.796313	−	1.37925i	−0.125689	−	0.992070i	$-0.540114\pi$
$599$	19.4893	−	33.7565i	0.796313	−	1.37925i	0.922002	−	0.387185i	$-0.126552\pi$
$600$		0			0
$601$	8.31217			0.339060			0.169530	−	0.985525i	$-0.445775\pi$
$601$	8.31217			0.339060			0.169530	+	0.985525i	$0.445775\pi$
$602$		0			0
$603$		−	33.6886i		−	1.37191i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.03976	+	0.600305i	−0.0422025	+	0.0243656i	−0.520953	−	0.853585i	$-0.674423\pi$
$607$	−1.03976	+	0.600305i	−0.0422025	+	0.0243656i	0.478750	+	0.877951i	$0.341090\pi$
$608$		0			0
$609$	3.35804	+	9.26121i	0.136075	+	0.375283i
$610$		0			0
$611$	17.0176	+	29.4754i	0.688460	+	1.19245i
$612$		0			0
$613$	16.0342	+	9.25733i	0.647614	+	0.373900i	0.787542	−	0.616262i	$-0.211354\pi$
$613$	16.0342	+	9.25733i	0.647614	+	0.373900i	−0.139927	+	0.990162i	$0.544687\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			2.81137i			0.113181i	0.998397	+	0.0565907i	$0.0180230\pi$
$617$			2.81137i			0.113181i	−0.998397	+	0.0565907i	$0.981977\pi$
$618$		0			0
$619$	−22.4829	+	38.9416i	−0.903665	+	1.56519i	−0.0809667	+	0.996717i	$0.525801\pi$
$619$	−22.4829	+	38.9416i	−0.903665	+	1.56519i	−0.822699	+	0.568478i	$0.807533\pi$
$620$		0			0
$621$	−8.81976	−	15.2763i	−0.353925	−	0.613016i
$622$		0			0
$623$	5.73186	−	32.2772i	0.229642	−	1.29316i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−3.32860	−	1.92177i	−0.132932	−	0.0767481i
$628$		0			0
$629$	2.04524			0.0815491
$630$		0			0
$631$	−9.37270			−0.373121			−0.186561	−	0.982443i	$-0.559734\pi$
$631$	−9.37270			−0.373121			−0.186561	+	0.982443i	$0.559734\pi$
$632$		0			0
$633$	−9.33755	−	5.39104i	−0.371134	−	0.214274i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	35.3168	−	6.13870i	1.39930	−	0.243224i
$638$		0			0
$639$	1.93767	+	3.35615i	0.0766531	+	0.132767i
$640$		0			0
$641$	22.4118	−	38.8184i	0.885213	−	1.53323i	0.0397433	−	0.999210i	$-0.487346\pi$
$641$	22.4118	−	38.8184i	0.885213	−	1.53323i	0.845470	−	0.534024i	$-0.179321\pi$
$642$		0			0
$643$		−	18.1709i		−	0.716589i	−0.933609	−	0.358294i	$-0.883358\pi$
$643$		−	18.1709i		−	0.716589i	0.933609	−	0.358294i	$-0.116642\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.4151	−	10.0546i	−0.684658	−	0.395288i	0.116949	−	0.993138i	$-0.462688\pi$
$647$	−17.4151	−	10.0546i	−0.684658	−	0.395288i	−0.801608	+	0.597850i	$0.796022\pi$
$648$		0			0
$649$	0.414745	+	0.718360i	0.0162802	+	0.0281981i
$650$		0			0
$651$	8.79643	+	1.56209i	0.344759	+	0.0612231i
$652$		0			0
$653$	6.50074	−	3.75320i	0.254394	−	0.146874i	−0.367381	−	0.930071i	$-0.619745\pi$
$653$	6.50074	−	3.75320i	0.254394	−	0.146874i	0.621774	+	0.783196i	$0.286412\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	4.68985i		−	0.182968i
$658$		0			0
$659$	41.5476			1.61847			0.809233	−	0.587488i	$-0.199883\pi$
$659$	41.5476			1.61847			0.809233	+	0.587488i	$0.199883\pi$
$660$		0			0
$661$	0.631987	−	1.09463i	0.0245814	−	0.0425763i	−0.853473	−	0.521137i	$-0.825508\pi$
$661$	0.631987	−	1.09463i	0.0245814	−	0.0425763i	0.878054	+	0.478561i	$0.158841\pi$
$662$		0			0
$663$	−0.698093	+	0.403044i	−0.0271117	+	0.0156529i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	45.3254	−	26.1687i	1.75501	−	1.01325i
$668$		0			0
$669$	−0.626914	+	1.08585i	−0.0242379	+	0.0419813i
$670$		0			0
$671$	−18.0108			−0.695299
$672$		0			0
$673$		−	24.0432i		−	0.926798i	−0.886150	−	0.463399i	$-0.846630\pi$
$673$		−	24.0432i		−	0.926798i	0.886150	−	0.463399i	$-0.153370\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.4734	+	11.2430i	−0.748424	+	0.432103i	−0.825124	−	0.564951i	$-0.808895\pi$
$677$	−19.4734	+	11.2430i	−0.748424	+	0.432103i	0.0766999	+	0.997054i	$0.475562\pi$
$678$		0			0
$679$	1.17784	−	1.40023i	0.0452013	−	0.0537359i
$680$		0			0
$681$	−2.56747	−	4.44698i	−0.0983855	−	0.170409i
$682$		0			0
$683$	12.9393	+	7.47052i	0.495110	+	0.285852i	0.726692	−	0.686964i	$-0.241057\pi$
$683$	12.9393	+	7.47052i	0.495110	+	0.285852i	−0.231582	+	0.972815i	$0.574390\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	1.38703i		−	0.0529186i
$688$		0			0
$689$	−12.4747	+	21.6069i	−0.475250	+	0.823157i
$690$		0			0
$691$	18.7159	+	32.4168i	0.711985	+	1.23319i	0.964111	+	0.265499i	$0.0855367\pi$
$691$	18.7159	+	32.4168i	0.711985	+	1.23319i	−0.252127	+	0.967694i	$0.581130\pi$
$692$		0			0
$693$	7.75762	+	6.52552i	0.294688	+	0.247884i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.95618	−	1.12940i	−0.0740954	−	0.0427790i
$698$		0			0
$699$	0.570993			0.0215969
$700$		0			0
$701$	−44.8376			−1.69349			−0.846747	−	0.531996i	$-0.821442\pi$
$701$	−44.8376			−1.69349			−0.846747	+	0.531996i	$0.821442\pi$
$702$		0			0
$703$	−31.4134	−	18.1365i	−1.18478	−	0.684032i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.98334	+	3.61988i	−0.375462	+	0.136140i
$708$		0			0
$709$	9.64589	+	16.7072i	0.362259	+	0.627451i	0.988332	−	0.152313i	$-0.0486723\pi$
$709$	9.64589	+	16.7072i	0.362259	+	0.627451i	−0.626073	+	0.779764i	$0.715339\pi$
$710$		0			0
$711$	10.5980	−	18.3562i	0.397455	−	0.688413i
$712$		0			0
$713$		−	47.4647i		−	1.77757i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.95426	+	4.01504i	0.259712	+	0.149945i
$718$		0			0
$719$	2.20008	+	3.81065i	0.0820491	+	0.142113i	0.904130	−	0.427258i	$-0.140520\pi$
$719$	2.20008	+	3.81065i	0.0820491	+	0.142113i	−0.822081	+	0.569371i	$0.807187\pi$
$720$		0			0
$721$	17.7055	+	3.14418i	0.659386	+	0.117095i
$722$		0			0
$723$	−1.67179	+	0.965209i	−0.0621746	+	0.0358965i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			43.4378i			1.61102i	0.592583	+	0.805509i	$0.298108\pi$
$727$			43.4378i			1.61102i	−0.592583	+	0.805509i	$0.701892\pi$
$728$		0			0
$729$	15.9780			0.591779
$730$		0			0
$731$	−0.849763	+	1.47183i	−0.0314296	+	0.0544377i
$732$		0			0
$733$	−8.90992	+	5.14414i	−0.329095	+	0.190003i	−0.655439	−	0.755248i	$-0.727517\pi$
$733$	−8.90992	+	5.14414i	−0.329095	+	0.190003i	0.326344	+	0.945251i	$0.394183\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−14.4330	+	8.33292i	−0.531648	+	0.306947i
$738$		0			0
$739$	14.7268	−	25.5075i	0.541733	−	0.938309i	−0.457072	−	0.889430i	$-0.651102\pi$
$739$	14.7268	−	25.5075i	0.541733	−	0.938309i	0.998805	−	0.0488793i	$-0.0155650\pi$
$740$		0			0
$741$	14.2962			0.525186
$742$		0			0
$743$			17.9240i			0.657569i	0.944405	+	0.328785i	$0.106639\pi$
$743$			17.9240i			0.657569i	−0.944405	+	0.328785i	$0.893361\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−18.0648	+	10.4297i	−0.660958	+	0.381604i
$748$		0			0
$749$	25.4847	+	4.52563i	0.931189	+	0.165363i
$750$		0			0
$751$	11.6091	+	20.1075i	0.423621	+	0.733732i	0.996291	−	0.0860536i	$-0.0274256\pi$
$751$	11.6091	+	20.1075i	0.423621	+	0.733732i	−0.572670	+	0.819786i	$0.694092\pi$
$752$		0			0
$753$	−7.52308	−	4.34345i	−0.274156	−	0.158284i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			40.8014i			1.48295i	0.670978	+	0.741477i	$0.265874\pi$
$757$			40.8014i			1.48295i	−0.670978	+	0.741477i	$0.734126\pi$
$758$		0			0
$759$	−2.09971	+	3.63681i	−0.0762148	+	0.132008i
$760$		0			0
$761$	2.21467	+	3.83592i	0.0802816	+	0.139052i	0.903371	−	0.428860i	$-0.141085\pi$
$761$	2.21467	+	3.83592i	0.0802816	+	0.139052i	−0.823089	+	0.567912i	$0.807751\pi$
$762$		0			0
$763$	11.3962	−	4.13216i	0.412568	−	0.149594i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.67198	−	1.54267i	−0.0964795	−	0.0557025i
$768$		0			0
$769$	3.66676			0.132227			0.0661133	−	0.997812i	$-0.478940\pi$
$769$	3.66676			0.132227			0.0661133	+	0.997812i	$0.478940\pi$
$770$		0			0
$771$	−4.40718			−0.158721
$772$		0			0
$773$	−6.03664	−	3.48526i	−0.217123	−	0.125356i	0.387495	−	0.921872i	$-0.373341\pi$
$773$	−6.03664	−	3.48526i	−0.217123	−	0.125356i	−0.604617	+	0.796516i	$0.706674\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.70862	−	4.80195i	−0.204795	−	0.172269i
$778$		0			0
$779$	20.0303	+	34.6934i	0.717659	+	1.24302i
$780$		0			0
$781$	0.958570	−	1.66029i	0.0343003	−	0.0594099i
$782$		0			0
$783$		−	21.5325i		−	0.769507i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.8229	−	13.1768i	−0.813550	−	0.469703i	0.0346371	−	0.999400i	$-0.488972\pi$
$787$	−22.8229	−	13.1768i	−0.813550	−	0.469703i	−0.848187	+	0.529697i	$0.822306\pi$
$788$		0			0
$789$	−0.637671	−	1.10448i	−0.0227017	−	0.0393204i
$790$		0			0
$791$	30.0921	−	35.7739i	1.06995	−	1.27197i
$792$		0			0
$793$	58.0169	−	33.4961i	2.06024	−	1.18948i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			3.31451i			0.117406i	0.998275	+	0.0587030i	$0.0186965\pi$
$797$			3.31451i			0.117406i	−0.998275	+	0.0587030i	$0.981304\pi$
$798$		0			0
$799$	2.24588			0.0794535
$800$		0			0
$801$	−17.2414	+	29.8629i	−0.609193	+	1.05515i
$802$		0			0
$803$	−2.00924	+	1.16004i	−0.0709047	+	0.0409369i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−7.37462	+	4.25774i	−0.259599	+	0.149879i
$808$		0			0
$809$	−16.4935	+	28.5677i	−0.579882	+	1.00439i	0.415610	+	0.909543i	$0.363568\pi$
$809$	−16.4935	+	28.5677i	−0.579882	+	1.00439i	−0.995492	+	0.0948426i	$0.969765\pi$
$810$		0			0
$811$	30.1575			1.05897			0.529486	−	0.848319i	$-0.322385\pi$
$811$	30.1575			1.05897			0.529486	+	0.848319i	$0.322385\pi$
$812$		0			0
$813$			14.6353i			0.513281i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	26.1035	−	15.0708i	0.913244	−	0.527262i
$818$		0			0
$819$	−37.1251	−	6.59275i	−1.29725	−	0.230369i
$820$		0			0
$821$	2.92451	+	5.06541i	0.102066	+	0.176784i	0.912536	−	0.408997i	$-0.134121\pi$
$821$	2.92451	+	5.06541i	0.102066	+	0.176784i	−0.810470	+	0.585781i	$0.800788\pi$
$822$		0			0
$823$	3.27063	+	1.88830i	0.114007	+	0.0658220i	0.555919	−	0.831236i	$-0.312366\pi$
$823$	3.27063	+	1.88830i	0.114007	+	0.0658220i	−0.441912	+	0.897058i	$0.645700\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			19.7854i			0.688005i	0.938969	+	0.344002i	$0.111783\pi$
$827$			19.7854i			0.688005i	−0.938969	+	0.344002i	$0.888217\pi$
$828$		0			0
$829$	−21.1945	+	36.7100i	−0.736117	+	1.27499i	0.218115	+	0.975923i	$0.430009\pi$
$829$	−21.1945	+	36.7100i	−0.736117	+	1.27499i	−0.954232	+	0.299069i	$0.903324\pi$
$830$		0			0
$831$	2.37074	+	4.10625i	0.0822402	+	0.142444i
$832$		0			0
$833$	0.814419	−	2.22076i	0.0282179	−	0.0769448i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−16.9115	−	9.76388i	−0.584548	−	0.337489i
$838$		0			0
$839$	33.0442			1.14081			0.570406	−	0.821363i	$-0.306786\pi$
$839$	33.0442			1.14081			0.570406	+	0.821363i	$0.306786\pi$
$840$		0			0
$841$	34.8879			1.20303
$842$		0			0
$843$	−10.6609	−	6.15508i	−0.367182	−	0.211992i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−4.21177	+	23.7173i	−0.144718	+	0.814936i
$848$		0			0
$849$	2.09509	+	3.62880i	0.0719033	+	0.124540i
$850$		0			0
$851$	−19.8159	+	34.3221i	−0.679279	+	1.17655i
$852$		0			0
$853$			39.3487i			1.34727i	0.739062	+	0.673637i	$0.235269\pi$
$853$			39.3487i			1.34727i	−0.739062	+	0.673637i	$0.764731\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.0488	+	19.0807i	1.12893	+	0.651786i	0.943665	−	0.330904i	$-0.107353\pi$
$857$	33.0488	+	19.0807i	1.12893	+	0.651786i	0.185261	+	0.982689i	$0.440687\pi$
$858$		0			0
$859$	0.786198	+	1.36173i	0.0268247	+	0.0464618i	0.879126	−	0.476589i	$-0.158127\pi$
$859$	0.786198	+	1.36173i	0.0268247	+	0.0464618i	−0.852301	+	0.523051i	$0.824794\pi$
$860$		0			0
$861$	2.80834	+	7.74518i	0.0957081	+	0.263955i
$862$		0			0
$863$	−27.9205	+	16.1199i	−0.950425	+	0.548728i	−0.893213	−	0.449634i	$-0.851554\pi$
$863$	−27.9205	+	16.1199i	−0.950425	+	0.548728i	−0.0572118	+	0.998362i	$0.518221\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	7.86599i		−	0.267143i
$868$		0			0
$869$	−10.4857			−0.355703
$870$		0			0
$871$	30.9947	−	53.6844i	1.05022	−	1.81903i
$872$		0			0
$873$	−1.66680	+	0.962329i	−0.0564127	+	0.0325699i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.7319	−	11.3922i	0.666299	−	0.384688i	−0.128374	−	0.991726i	$-0.540976\pi$
$877$	19.7319	−	11.3922i	0.666299	−	0.384688i	0.794673	+	0.607038i	$0.207642\pi$
$878$		0			0
$879$	−7.94462	+	13.7605i	−0.267966	+	0.464130i
$880$		0			0
$881$	−10.2816			−0.346396			−0.173198	−	0.984887i	$-0.555410\pi$
$881$	−10.2816			−0.346396			−0.173198	+	0.984887i	$0.555410\pi$
$882$		0			0
$883$		−	36.8161i		−	1.23896i	−0.785013	−	0.619480i	$-0.787344\pi$
$883$		−	36.8161i		−	1.23896i	0.785013	−	0.619480i	$-0.212656\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.7579	+	10.8299i	−0.629830	+	0.363632i	−0.780686	−	0.624923i	$-0.785130\pi$
$887$	−18.7579	+	10.8299i	−0.629830	+	0.363632i	0.150857	+	0.988556i	$0.451797\pi$
$888$		0			0
$889$	25.2936	−	30.0694i	0.848321	−	1.00849i
$890$		0			0
$891$	−4.88340	−	8.45830i	−0.163600	−	0.283364i
$892$		0			0
$893$	−34.4950	−	19.9157i	−1.15433	−	0.666454i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	15.6200i		−	0.521536i
$898$		0			0
$899$	28.9699	−	50.1774i	0.966201	−	1.67351i
$900$		0			0
$901$	0.823168	+	1.42577i	0.0274237	+	0.0474992i
$902$		0			0
$903$	5.82750	−	2.11301i	0.193927	−	0.0703165i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	15.4881	+	8.94204i	0.514273	+	0.296916i	0.734588	−	0.678513i	$-0.237375\pi$
$907$	15.4881	+	8.94204i	0.514273	+	0.296916i	−0.220315	+	0.975429i	$0.570709\pi$
$908$		0			0
$909$	11.1702			0.370493
$910$		0			0
$911$	−13.5178			−0.447865			−0.223932	−	0.974605i	$-0.571889\pi$
$911$	−13.5178			−0.447865			−0.223932	+	0.974605i	$0.571889\pi$
$912$		0			0
$913$	8.93671	+	5.15961i	0.295762	+	0.170758i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.487857	+	2.74721i	−0.0161104	+	0.0907210i
$918$		0			0
$919$	0.520988	+	0.902377i	0.0171858	+	0.0297667i	0.874490	−	0.485043i	$-0.161196\pi$
$919$	0.520988	+	0.902377i	0.0171858	+	0.0297667i	−0.857305	+	0.514809i	$0.827863\pi$
$920$		0			0
$921$	3.86211	−	6.68937i	0.127261	−	0.220422i
$922$		0			0
$923$			7.13090i			0.234717i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−16.3811	−	9.45765i	−0.538027	−	0.310630i
$928$		0			0
$929$	−3.16632	−	5.48422i	−0.103883	−	0.179931i	0.809398	−	0.587260i	$-0.199794\pi$
$929$	−3.16632	−	5.48422i	−0.103883	−	0.179931i	−0.913281	+	0.407329i	$0.866460\pi$
$930$		0			0
$931$	−32.2018	+	26.8872i	−1.05537	+	0.881193i
$932$		0			0
$933$	12.1092	−	6.99126i	0.396438	−	0.228884i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	21.2670i		−	0.694761i	−0.937724	−	0.347381i	$-0.887071\pi$
$937$		−	21.2670i		−	0.694761i	0.937724	−	0.347381i	$-0.112929\pi$
$938$		0			0
$939$	−4.47317			−0.145976
$940$		0			0
$941$	−8.05639	+	13.9541i	−0.262631	+	0.454890i	−0.966940	−	0.255003i	$-0.917923\pi$
$941$	−8.05639	+	13.9541i	−0.262631	+	0.454890i	0.704309	+	0.709893i	$0.251257\pi$
$942$		0			0
$943$	37.9058	−	21.8849i	1.23438	−	0.712672i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0148	−	8.09142i	0.455418	−	0.262936i	−0.254698	−	0.967021i	$-0.581976\pi$
$947$	14.0148	−	8.09142i	0.455418	−	0.262936i	0.710116	+	0.704085i	$0.248643\pi$
$948$		0			0
$949$	4.31482	−	7.47349i	0.140065	−	0.242600i
$950$		0			0
$951$	−11.5342			−0.374021
$952$		0			0
$953$		−	12.4950i		−	0.404753i	−0.979308	−	0.202377i	$-0.935134\pi$
$953$		−	12.4950i		−	0.404753i	0.979308	−	0.202377i	$-0.0648665\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.43944	+	2.56311i	−0.143507	+	0.0828536i
$958$		0			0
$959$	−14.6559	−	40.4199i	−0.473265	−	1.30523i
$960$		0			0
$961$	−10.7728	−	18.6590i	−0.347509	−	0.601904i
$962$		0			0
$963$	−23.5785	−	13.6130i	−0.759806	−	0.438674i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	28.6562i		−	0.921521i	−0.887524	−	0.460761i	$-0.847577\pi$
$967$		−	28.6562i		−	0.921521i	0.887524	−	0.460761i	$-0.152423\pi$
$968$		0			0
$969$	0.471682	−	0.816977i	0.0151526	−	0.0262451i
$970$		0			0
$971$	−7.93705	−	13.7474i	−0.254712	−	0.441174i	0.710105	−	0.704096i	$-0.248647\pi$
$971$	−7.93705	−	13.7474i	−0.254712	−	0.441174i	−0.964817	+	0.262921i	$0.915314\pi$
$972$		0			0
$973$	8.75862	+	7.36754i	0.280789	+	0.236193i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.9357	−	12.6646i	−0.701785	−	0.405176i	0.106227	−	0.994342i	$-0.466123\pi$
$977$	−21.9357	−	12.6646i	−0.701785	−	0.405176i	−0.808012	+	0.589166i	$0.799456\pi$
$978$		0			0
$979$	17.0587			0.545197
$980$		0			0
$981$	−12.7510			−0.407108
$982$		0			0
$983$	8.60540	+	4.96833i	0.274470	+	0.158465i	0.630917	−	0.775850i	$-0.282679\pi$
$983$	8.60540	+	4.96833i	0.274470	+	0.158465i	−0.356447	+	0.934315i	$0.616012\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.26863	−	5.27302i	−0.199533	−	0.167842i
$988$		0			0
$989$	−16.4663	−	28.5205i	−0.523598	−	0.906898i
$990$		0			0
$991$	−15.1869	+	26.3045i	−0.482428	+	0.835590i	−0.999797	−	0.0201729i	$-0.993578\pi$
$991$	−15.1869	+	26.3045i	−0.482428	+	0.835590i	0.517368	+	0.855763i	$0.326912\pi$
$992$		0			0
$993$			9.30049i			0.295142i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.585811	−	0.338218i	−0.0185528	−	0.0107115i	0.490695	−	0.871331i	$-0.336743\pi$
$997$	−0.585811	−	0.338218i	−0.0185528	−	0.0107115i	−0.509248	+	0.860620i	$0.670076\pi$
$998$		0			0
$999$	8.15258	+	14.1207i	0.257936	+	0.446759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.j.249.5		16
5.2	odd	4		1400.2.q.m.1201.2	yes	8
5.3	odd	4		1400.2.q.l.1201.3	yes	8
5.4	even	2	inner	1400.2.bh.j.249.4		16
7.2	even	3	inner	1400.2.bh.j.849.4		16
35.2	odd	12		1400.2.q.m.401.2	yes	8
35.3	even	12		9800.2.a.ck.1.3		4
35.9	even	6	inner	1400.2.bh.j.849.5		16
35.17	even	12		9800.2.a.cu.1.2		4
35.18	odd	12		9800.2.a.ct.1.2		4
35.23	odd	12		1400.2.q.l.401.3	✓	8
35.32	odd	12		9800.2.a.cj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.l.401.3	✓	8	35.23	odd	12
1400.2.q.l.1201.3	yes	8	5.3	odd	4
1400.2.q.m.401.2	yes	8	35.2	odd	12
1400.2.q.m.1201.2	yes	8	5.2	odd	4
1400.2.bh.j.249.4		16	5.4	even	2	inner
1400.2.bh.j.249.5		16	1.1	even	1	trivial
1400.2.bh.j.849.4		16	7.2	even	3	inner
1400.2.bh.j.849.5		16	35.9	even	6	inner
9800.2.a.cj.1.3		4	35.32	odd	12
9800.2.a.ck.1.3		4	35.3	even	12
9800.2.a.ct.1.2		4	35.18	odd	12
9800.2.a.cu.1.2		4	35.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.403424 + 0.232917i) q^{3} +(2.02469 + 1.70312i) q^{7} +(-1.39150 - 2.41015i) q^{9} +O(q^{10})\)	\(q+(0.403424 + 0.232917i) q^{3} +(2.02469 + 1.70312i) q^{7} +(-1.39150 - 2.41015i) q^{9} +(-0.688377 + 1.19230i) q^{11} -5.12091i q^{13} +(-0.292641 - 0.168956i) q^{17} +(2.99649 + 5.19008i) q^{19} +(0.420123 + 1.15867i) q^{21} +(5.67065 - 3.27395i) q^{23} -2.69392i q^{27} +7.99299 q^{29} +(3.62442 - 6.27767i) q^{31} +(-0.555416 + 0.320670i) q^{33} +(-5.24169 + 3.02629i) q^{37} +(1.19275 - 2.06590i) q^{39} +6.68457 q^{41} -5.02949i q^{43} +(-5.75590 + 3.32317i) q^{47} +(1.19875 + 6.89659i) q^{49} +(-0.0787056 - 0.136322i) q^{51} +(-4.21934 - 2.43604i) q^{53} +2.79174i q^{57} +(0.301249 - 0.521778i) q^{59} +(6.54103 + 11.3294i) q^{61} +(1.28742 - 7.24970i) q^{63} +(10.4834 + 6.05258i) q^{67} +3.05024 q^{69} -1.39251 q^{71} +(1.45941 + 0.842589i) q^{73} +(-3.42439 + 1.24166i) q^{77} +(3.80812 + 6.59585i) q^{79} +(-3.54704 + 6.14365i) q^{81} -7.49532i q^{83} +(3.22457 + 1.86170i) q^{87} +(-6.19525 - 10.7305i) q^{89} +(8.72154 - 10.3683i) q^{91} +(2.92436 - 1.68838i) q^{93} -0.691577i q^{97} +3.83151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 20 q^{19} + 50 q^{21} - 8 q^{29} + 28 q^{31} - 20 q^{39} - 16 q^{41} + 26 q^{49} - 10 q^{51} - 2 q^{59} + 50 q^{61} + 64 q^{69} - 80 q^{71} + 4 q^{79} - 48 q^{81} - 38 q^{89} + 34 q^{91} + 204 q^{99}+O(q^{100}) \) 16 * q + 10 * q^9 - 20 * q^19 + 50 * q^21 - 8 * q^29 + 28 * q^31 - 20 * q^39 - 16 * q^41 + 26 * q^49 - 10 * q^51 - 2 * q^59 + 50 * q^61 + 64 * q^69 - 80 * q^71 + 4 * q^79 - 48 * q^81 - 38 * q^89 + 34 * q^91 + 204 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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