LMFDB - Embedded newform 1197.2.db.a.647.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(647,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("1197.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.db (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.15
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959209 + 0.553800i) q^{2} +(-0.386612 + 0.669632i) q^{4} +(1.12128 + 1.94211i) q^{5} +(2.59227 + 0.529289i) q^{7} -3.07162i q^{8} +O(q^{10})$	\(q+(-0.959209 + 0.553800i) q^{2} +(-0.386612 + 0.669632i) q^{4} +(1.12128 + 1.94211i) q^{5} +(2.59227 + 0.529289i) q^{7} -3.07162i q^{8} +(-2.15108 - 1.24192i) q^{10} +(-0.163711 - 0.0945186i) q^{11} +6.04921i q^{13} +(-2.77965 + 0.927898i) q^{14} +(0.927838 + 1.60706i) q^{16} +(-1.13951 + 1.97368i) q^{17} +(-0.866025 + 0.500000i) q^{19} -1.73400 q^{20} +0.209377 q^{22} +(2.70313 - 1.56065i) q^{23} +(-0.0145208 + 0.0251507i) q^{25} +(-3.35005 - 5.80246i) q^{26} +(-1.35663 + 1.53124i) q^{28} -2.75914i q^{29} +(4.77099 + 2.75453i) q^{31} +(3.54022 + 2.04395i) q^{32} -2.52423i q^{34} +(1.87871 + 5.62794i) q^{35} +(5.16904 + 8.95303i) q^{37} +(0.553800 - 0.959209i) q^{38} +(5.96542 - 3.44414i) q^{40} -9.88777 q^{41} -0.224395 q^{43} +(0.126585 - 0.0730840i) q^{44} +(-1.72858 + 2.99398i) q^{46} +(-5.66543 - 9.81281i) q^{47} +(6.43971 + 2.74412i) q^{49} -0.0321664i q^{50} +(-4.05075 - 2.33870i) q^{52} +(9.53262 + 5.50366i) q^{53} -0.423926i q^{55} +(1.62577 - 7.96246i) q^{56} +(1.52801 + 2.64659i) q^{58} +(-7.23424 + 12.5301i) q^{59} +(5.34372 - 3.08520i) q^{61} -6.10184 q^{62} -8.23910 q^{64} +(-11.7482 + 6.78284i) q^{65} +(-0.302775 + 0.524421i) q^{67} +(-0.881095 - 1.52610i) q^{68} +(-4.91883 - 4.35794i) q^{70} -12.8617i q^{71} +(-12.2544 - 7.07510i) q^{73} +(-9.91637 - 5.72522i) q^{74} -0.773224i q^{76} +(-0.374355 - 0.331668i) q^{77} +(-3.28382 - 5.68775i) q^{79} +(-2.08073 + 3.60392i) q^{80} +(9.48443 - 5.47584i) q^{82} -2.46084 q^{83} -5.11081 q^{85} +(0.215242 - 0.124270i) q^{86} +(-0.290325 + 0.502858i) q^{88} +(-2.41997 - 4.19150i) q^{89} +(-3.20178 + 15.6812i) q^{91} +2.41347i q^{92} +(10.8687 + 6.27502i) q^{94} +(-1.94211 - 1.12128i) q^{95} +14.1589i q^{97} +(-7.69671 + 0.934126i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) $ 96 * q + 48 * q^4 + 8 * q^7	$ 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.959209	+	0.553800i	−0.678263	+	0.391595i	−0.799200	−	0.601065i	$-0.794743\pi$
$2$	−0.959209	+	0.553800i	−0.678263	+	0.391595i	0.120937	+	0.992660i	$0.461410\pi$
$3$		0			0
$3$		0			0
$4$	−0.386612	+	0.669632i	−0.193306	+	0.334816i
$5$	1.12128	+	1.94211i	0.501450	+	0.868537i	0.999999	+	0.00167510i	$0.000533201\pi$
$5$	1.12128	+	1.94211i	0.501450	+	0.868537i	−0.498549	+	0.866862i	$0.666133\pi$
$6$		0			0
$7$	2.59227	+	0.529289i	0.979785	+	0.200052i
$7$	2.59227	+	0.529289i	0.979785	+	0.200052i
$8$		−	3.07162i		−	1.08598i
$9$		0			0
$10$	−2.15108	−	1.24192i	−0.680230	−	0.392731i
$11$	−0.163711	−	0.0945186i	−0.0493607	−	0.0284984i	0.475117	−	0.879923i	$-0.342406\pi$
$11$	−0.163711	−	0.0945186i	−0.0493607	−	0.0284984i	−0.524477	+	0.851424i	$0.675739\pi$
$12$		0			0
$13$			6.04921i			1.67775i	0.544324	+	0.838875i	$0.316786\pi$
$13$			6.04921i			1.67775i	−0.544324	+	0.838875i	$0.683214\pi$
$14$	−2.77965	+	0.927898i	−0.742892	+	0.247991i
$15$		0			0
$16$	0.927838	+	1.60706i	0.231959	+	0.401766i
$17$	−1.13951	+	1.97368i	−0.276371	+	0.478689i	−0.970480	−	0.241181i	$-0.922465\pi$
$17$	−1.13951	+	1.97368i	−0.276371	+	0.478689i	0.694109	+	0.719870i	$0.255799\pi$
$18$		0			0
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$19$	−0.866025	+	0.500000i	−0.198680	+	0.114708i
$20$	−1.73400			−0.387733
$21$		0			0
$22$	0.209377			0.0446394
$23$	2.70313	−	1.56065i	0.563641	−	0.325419i	−0.190964	−	0.981597i	$-0.561161\pi$
$23$	2.70313	−	1.56065i	0.563641	−	0.325419i	0.754606	+	0.656178i	$0.227828\pi$
$24$		0			0
$25$	−0.0145208	+	0.0251507i	−0.00290416	+	0.00503015i
$26$	−3.35005	−	5.80246i	−0.656999	−	1.13796i
$27$		0			0
$28$	−1.35663	+	1.53124i	−0.256379	+	0.289376i
$29$		−	2.75914i		−	0.512360i	−0.966629	−	0.256180i	$-0.917536\pi$
$29$		−	2.75914i		−	0.512360i	0.966629	−	0.256180i	$-0.0824640\pi$
$30$		0			0
$31$	4.77099	+	2.75453i	0.856895	+	0.494729i	0.862971	−	0.505253i	$-0.168601\pi$
$31$	4.77099	+	2.75453i	0.856895	+	0.494729i	−0.00607621	+	0.999982i	$0.501934\pi$
$32$	3.54022	+	2.04395i	0.625829	+	0.361322i
$33$		0			0
$34$		−	2.52423i		−	0.432903i
$35$	1.87871	+	5.62794i	0.317560	+	0.951296i
$36$		0			0
$37$	5.16904	+	8.95303i	0.849784	+	1.47187i	0.881401	+	0.472370i	$0.156601\pi$
$37$	5.16904	+	8.95303i	0.849784	+	1.47187i	−0.0316161	+	0.999500i	$0.510065\pi$
$38$	0.553800	−	0.959209i	0.0898381	−	0.155604i
$39$		0			0
$40$	5.96542	−	3.44414i	0.943215	−	0.544566i
$41$	−9.88777			−1.54421			−0.772105	−	0.635495i	$-0.780796\pi$
$41$	−9.88777			−1.54421			−0.772105	+	0.635495i	$0.780796\pi$
$42$		0			0
$43$	−0.224395			−0.0342199			−0.0171100	−	0.999854i	$-0.505447\pi$
$43$	−0.224395			−0.0342199			−0.0171100	+	0.999854i	$0.505447\pi$
$44$	0.126585	−	0.0730840i	0.0190834	−	0.0110178i
$45$		0			0
$46$	−1.72858	+	2.99398i	−0.254865	+	0.441439i
$47$	−5.66543	−	9.81281i	−0.826388	−	1.43135i	−0.900854	−	0.434122i	$-0.857059\pi$
$47$	−5.66543	−	9.81281i	−0.826388	−	1.43135i	0.0744661	−	0.997224i	$-0.476275\pi$
$48$		0			0
$49$	6.43971	+	2.74412i	0.919958	+	0.392017i
$50$		−	0.0321664i		−	0.00454902i
$51$		0			0
$52$	−4.05075	−	2.33870i	−0.561737	−	0.324319i
$53$	9.53262	+	5.50366i	1.30941	+	0.755986i	0.981997	−	0.188897i	$-0.0604912\pi$
$53$	9.53262	+	5.50366i	1.30941	+	0.755986i	0.327409	+	0.944883i	$0.393825\pi$
$54$		0			0
$55$		−	0.423926i		−	0.0571621i
$56$	1.62577	−	7.96246i	0.217253	−	1.06403i
$57$		0			0
$58$	1.52801	+	2.64659i	0.200638	+	0.347515i
$59$	−7.23424	+	12.5301i	−0.941817	+	1.63128i	−0.179816	+	0.983700i	$0.557550\pi$
$59$	−7.23424	+	12.5301i	−0.941817	+	1.63128i	−0.762001	+	0.647575i	$0.775783\pi$
$60$		0			0
$61$	5.34372	−	3.08520i	0.684193	−	0.395019i	−0.117240	−	0.993104i	$-0.537405\pi$
$61$	5.34372	−	3.08520i	0.684193	−	0.395019i	0.801433	+	0.598084i	$0.204071\pi$
$62$	−6.10184			−0.774934
$63$		0			0
$64$	−8.23910			−1.02989
$65$	−11.7482	+	6.78284i	−1.45719	+	0.841308i
$66$		0			0
$67$	−0.302775	+	0.524421i	−0.0369898	+	0.0640683i	−0.883928	−	0.467624i	$-0.845110\pi$
$67$	−0.302775	+	0.524421i	−0.0369898	+	0.0640683i	0.846938	+	0.531692i	$0.178444\pi$
$68$	−0.881095	−	1.52610i	−0.106848	−	0.185067i
$69$		0			0
$70$	−4.91883	−	4.35794i	−0.587913	−	0.520874i
$71$		−	12.8617i		−	1.52640i	−0.646163	−	0.763199i	$-0.723627\pi$
$71$		−	12.8617i		−	1.52640i	0.646163	−	0.763199i	$-0.276373\pi$
$72$		0			0
$73$	−12.2544	−	7.07510i	−1.43427	−	0.828078i	−0.436830	−	0.899544i	$-0.643899\pi$
$73$	−12.2544	−	7.07510i	−1.43427	−	0.828078i	−0.997443	+	0.0714658i	$0.977232\pi$
$74$	−9.91637	−	5.72522i	−1.15275	−	0.665543i
$75$		0			0
$76$		−	0.773224i		−	0.0886949i
$77$	−0.374355	−	0.331668i	−0.0426617	−	0.0377971i
$78$		0			0
$79$	−3.28382	−	5.68775i	−0.369459	−	0.639922i	0.620022	−	0.784584i	$-0.287124\pi$
$79$	−3.28382	−	5.68775i	−0.369459	−	0.639922i	−0.989481	+	0.144663i	$0.953790\pi$
$80$	−2.08073	+	3.60392i	−0.232632	+	0.402931i
$81$		0			0
$82$	9.48443	−	5.47584i	1.04738	−	0.604705i
$83$	−2.46084			−0.270112			−0.135056	−	0.990838i	$-0.543121\pi$
$83$	−2.46084			−0.270112			−0.135056	+	0.990838i	$0.543121\pi$
$84$		0			0
$85$	−5.11081			−0.554345
$86$	0.215242	−	0.124270i	0.0232101	−	0.0134004i
$87$		0			0
$88$	−0.290325	+	0.502858i	−0.0309488	+	0.0536048i
$89$	−2.41997	−	4.19150i	−0.256516	−	0.444299i	0.708790	−	0.705419i	$-0.249241\pi$
$89$	−2.41997	−	4.19150i	−0.256516	−	0.444299i	−0.965306	+	0.261121i	$0.915908\pi$
$90$		0			0
$91$	−3.20178	+	15.6812i	−0.335638	+	1.64383i
$92$			2.41347i			0.251622i
$93$		0			0
$94$	10.8687	+	6.27502i	1.12102	+	0.647219i
$95$	−1.94211	−	1.12128i	−0.199256	−	0.115041i
$96$		0			0
$97$			14.1589i			1.43762i	0.695205	+	0.718812i	$0.255314\pi$
$97$			14.1589i			1.43762i	−0.695205	+	0.718812i	$0.744686\pi$
$98$	−7.69671	+	0.934126i	−0.777486	+	0.0943610i
$99$		0			0
$100$	−0.0112278	−	0.0194472i	−0.00112278	−	0.00194472i
$101$	−7.21039	+	12.4888i	−0.717460	+	1.24268i	0.244543	+	0.969639i	$0.421362\pi$
$101$	−7.21039	+	12.4888i	−0.717460	+	1.24268i	−0.962003	+	0.273039i	$0.911971\pi$
$102$		0			0
$103$	−5.36215	+	3.09584i	−0.528348	+	0.305042i	−0.740343	−	0.672229i	$-0.765337\pi$
$103$	−5.36215	+	3.09584i	−0.528348	+	0.305042i	0.211995	+	0.977271i	$0.432004\pi$
$104$	18.5809			1.82201
$105$		0			0
$106$	−12.1917			−1.18416
$107$	0.601635	−	0.347354i	0.0581623	−	0.0335800i	−0.470637	−	0.882327i	$-0.655976\pi$
$107$	0.601635	−	0.347354i	0.0581623	−	0.0335800i	0.528799	+	0.848747i	$0.322642\pi$
$108$		0			0
$109$	−8.60484	+	14.9040i	−0.824195	+	1.42755i	0.0783387	+	0.996927i	$0.475038\pi$
$109$	−8.60484	+	14.9040i	−0.824195	+	1.42755i	−0.902533	+	0.430620i	$0.858295\pi$
$110$	0.234770	+	0.406633i	0.0223844	+	0.0387710i
$111$		0			0
$112$	1.55460	+	4.65703i	0.146896	+	0.440048i
$113$			12.1051i			1.13875i	0.822078	+	0.569376i	$0.192815\pi$
$113$			12.1051i			1.13875i	−0.822078	+	0.569376i	$0.807185\pi$
$114$		0			0
$115$	6.06191	+	3.49985i	0.565276	+	0.326362i
$116$	1.84761	+	1.06672i	0.171546	+	0.0990423i
$117$		0			0
$118$		−	16.0253i		−	1.47525i
$119$	−3.99856	+	4.51319i	−0.366547	+	0.413724i
$120$		0			0
$121$	−5.48213	−	9.49533i	−0.498376	−	0.863212i
$122$	−3.41716	+	5.91870i	−0.309375	+	0.535854i
$123$		0			0
$124$	−3.68905	+	2.12987i	−0.331286	+	0.191268i
$125$	11.1476			0.997075
$126$		0			0
$127$	12.2139			1.08381			0.541906	−	0.840439i	$-0.317703\pi$
$127$	12.2139			1.08381			0.541906	+	0.840439i	$0.317703\pi$
$128$	0.822575	−	0.474914i	0.0727061	−	0.0419769i
$129$		0			0
$130$	7.51267	−	13.0123i	0.658904	−	1.14126i
$131$	−0.595921	−	1.03217i	−0.0520659	−	0.0901807i	0.838818	−	0.544412i	$-0.183247\pi$
$131$	−0.595921	−	1.03217i	−0.0520659	−	0.0901807i	−0.890884	+	0.454231i	$0.849914\pi$
$132$		0			0
$133$	−2.50961	+	0.837757i	−0.217611	+	0.0726427i
$134$		−	0.670706i		−	0.0579402i
$135$		0			0
$136$	6.06241	+	3.50013i	0.519847	+	0.300134i
$137$	2.81948	+	1.62783i	0.240885	+	0.139075i	0.615583	−	0.788072i	$-0.288920\pi$
$137$	2.81948	+	1.62783i	0.240885	+	0.139075i	−0.374699	+	0.927147i	$0.622254\pi$
$138$		0			0
$139$		−	7.61388i		−	0.645801i	−0.946433	−	0.322900i	$-0.895342\pi$
$139$		−	7.61388i		−	0.645801i	0.946433	−	0.322900i	$-0.104658\pi$
$140$	−4.49498	−	0.917784i	−0.379895	−	0.0775669i
$141$		0			0
$142$	7.12278	+	12.3370i	0.597731	+	1.03530i
$143$	0.571763	−	0.990322i	0.0478132	−	0.0828149i
$144$		0			0
$145$	5.35855	−	3.09376i	0.445004	−	0.256923i
$146$	15.6728			1.29709
$147$		0			0
$148$	−7.99365			−0.657074
$149$	4.88052	−	2.81777i	0.399828	−	0.230841i	−0.286582	−	0.958056i	$-0.592519\pi$
$149$	4.88052	−	2.81777i	0.399828	−	0.230841i	0.686410	+	0.727215i	$0.259186\pi$
$150$		0			0
$151$	−3.30338	+	5.72162i	−0.268825	+	0.465619i	−0.968559	−	0.248785i	$-0.919969\pi$
$151$	−3.30338	+	5.72162i	−0.268825	+	0.465619i	0.699734	+	0.714404i	$0.253302\pi$
$152$	1.53581	+	2.66010i	0.124571	+	0.215763i
$153$		0			0
$154$	0.542762	+	0.110821i	0.0437370	+	0.00893021i
$155$			12.3544i			0.992327i
$156$		0			0
$157$	−11.3226	−	6.53709i	−0.903639	−	0.521716i	−0.0252601	−	0.999681i	$-0.508041\pi$
$157$	−11.3226	−	6.53709i	−0.903639	−	0.521716i	−0.878379	+	0.477965i	$0.841375\pi$
$158$	6.29974	+	3.63716i	0.501181	+	0.289357i
$159$		0			0
$160$			9.16732i			0.724741i
$161$	7.83327	−	2.61489i	0.617348	−	0.206083i
$162$		0			0
$163$	−11.7235	−	20.3057i	−0.918254	−	1.59046i	−0.802066	−	0.597236i	$-0.796266\pi$
$163$	−11.7235	−	20.3057i	−0.918254	−	1.59046i	−0.116188	−	0.993227i	$-0.537068\pi$
$164$	3.82273	−	6.62116i	0.298505	−	0.517026i
$165$		0			0
$166$	2.36046	−	1.36281i	0.183207	−	0.105775i
$167$	−0.109313			−0.00845889			−0.00422944	−	0.999991i	$-0.501346\pi$
$167$	−0.109313			−0.00845889			−0.00422944	+	0.999991i	$0.501346\pi$
$168$		0			0
$169$	−23.5930			−1.81484
$170$	4.90234	−	2.83036i	0.375992	−	0.217079i
$171$		0			0
$172$	0.0867539	−	0.150262i	0.00661492	−	0.0114574i
$173$	1.35490	+	2.34676i	0.103011	+	0.178421i	0.912924	−	0.408130i	$-0.133819\pi$
$173$	1.35490	+	2.34676i	0.103011	+	0.178421i	−0.809913	+	0.586550i	$0.800486\pi$
$174$		0			0
$175$	−0.0509538	+	0.0575118i	−0.00385174	+	0.00434748i
$176$		−	0.350792i		−	0.0264419i
$177$		0			0
$178$	4.64251	+	2.68035i	0.347971	+	0.200901i
$179$	20.3264	+	11.7354i	1.51926	+	0.877147i	0.999743	+	0.0226892i	$0.00722280\pi$
$179$	20.3264	+	11.7354i	1.51926	+	0.877147i	0.519521	+	0.854458i	$0.326111\pi$
$180$		0			0
$181$		−	17.4087i		−	1.29398i	−0.762500	−	0.646988i	$-0.776028\pi$
$181$		−	17.4087i		−	1.29398i	0.762500	−	0.646988i	$-0.223972\pi$
$182$	−5.61305	−	16.8147i	−0.416067	−	1.24639i
$183$		0			0
$184$	−4.79373	−	8.30299i	−0.353399	−	0.612104i
$185$	−11.5918	+	20.0776i	−0.852249	+	1.47614i
$186$		0			0
$187$	0.373100	−	0.215409i	0.0272838	−	0.0157523i
$188$	8.76130			0.638983
$189$		0			0
$190$	2.48385			0.180197
$191$	11.7733	−	6.79732i	0.851887	−	0.491837i	−0.00940041	−	0.999956i	$-0.502992\pi$
$191$	11.7733	−	6.79732i	0.851887	−	0.491837i	0.861287	+	0.508119i	$0.169659\pi$
$192$		0			0
$193$	5.34765	−	9.26240i	0.384932	−	0.666722i	−0.606828	−	0.794833i	$-0.707558\pi$
$193$	5.34765	−	9.26240i	0.384932	−	0.666722i	0.991760	+	0.128112i	$0.0408916\pi$
$194$	−7.84122	−	13.5814i	−0.562967	−	0.975087i
$195$		0			0
$196$	−4.32722	+	3.25132i	−0.309087	+	0.232237i
$197$		−	13.3420i		−	0.950579i	−0.879830	−	0.475289i	$-0.842343\pi$
$197$		−	13.3420i		−	0.950579i	0.879830	−	0.475289i	$-0.157657\pi$
$198$		0			0
$199$	13.2934	+	7.67493i	0.942342	+	0.544061i	0.890694	−	0.454604i	$-0.150219\pi$
$199$	13.2934	+	7.67493i	0.942342	+	0.544061i	0.0516481	+	0.998665i	$0.483553\pi$
$200$	0.0772535	+	0.0446023i	0.00546265	+	0.00315386i
$201$		0			0
$202$		−	15.9724i		−	1.12382i
$203$	1.46038	−	7.15244i	0.102499	−	0.502003i
$204$		0			0
$205$	−11.0869	−	19.2031i	−0.774344	−	1.34120i
$206$	3.42895	−	5.93911i	0.238906	−	0.413797i
$207$		0			0
$208$	−9.72146	+	5.61269i	−0.674062	+	0.389170i
$209$	0.189037			0.0130760
$210$		0			0
$211$	22.4222			1.54361			0.771803	−	0.635862i	$-0.219355\pi$
$211$	22.4222			1.54361			0.771803	+	0.635862i	$0.219355\pi$
$212$	−7.37085	+	4.25556i	−0.506232	+	0.292273i
$213$		0			0
$214$	−0.384729	+	0.666371i	−0.0262995	+	0.0455522i
$215$	−0.251609	−	0.435799i	−0.0171596	−	0.0297213i
$216$		0			0
$217$	10.9097	+	9.66572i	0.740602	+	0.656152i
$218$		−	19.0614i		−	1.29100i
$219$		0			0
$220$	0.283874	+	0.163895i	0.0191388	+	0.0110498i
$221$	−11.9392	−	6.89312i	−0.803120	−	0.463682i
$222$		0			0
$223$		−	9.30010i		−	0.622780i	−0.950282	−	0.311390i	$-0.899205\pi$
$223$		−	9.30010i		−	0.622780i	0.950282	−	0.311390i	$-0.100795\pi$
$224$	8.09537	+	7.17226i	0.540894	+	0.479217i
$225$		0			0
$226$	−6.70379	−	11.6113i	−0.445930	−	0.772373i
$227$	−3.57467	+	6.19151i	−0.237259	+	0.410945i	−0.959927	−	0.280251i	$-0.909582\pi$
$227$	−3.57467	+	6.19151i	−0.237259	+	0.410945i	0.722668	+	0.691196i	$0.242916\pi$
$228$		0			0
$229$	4.98459	−	2.87785i	0.329391	−	0.190174i	−0.326180	−	0.945308i	$-0.605761\pi$
$229$	4.98459	−	2.87785i	0.329391	−	0.190174i	0.655571	+	0.755134i	$0.272428\pi$
$230$	−7.75285			−0.511208
$231$		0			0
$232$	−8.47504			−0.556414
$233$	−9.28065	+	5.35818i	−0.607995	+	0.351026i	−0.772181	−	0.635403i	$-0.780834\pi$
$233$	−9.28065	+	5.35818i	−0.607995	+	0.351026i	0.164185	+	0.986430i	$0.447501\pi$
$234$		0			0
$235$	12.7050	−	22.0057i	0.828784	−	1.43550i
$236$	−5.59369	−	9.68855i	−0.364118	−	0.630671i
$237$		0			0
$238$	1.33605	−	6.54349i	0.0866032	−	0.424152i
$239$			15.2119i			0.983975i	0.870602	+	0.491987i	$0.163729\pi$
$239$			15.2119i			0.983975i	−0.870602	+	0.491987i	$0.836271\pi$
$240$		0			0
$241$	11.5705	+	6.68023i	0.745322	+	0.430312i	0.824001	−	0.566588i	$-0.191737\pi$
$241$	11.5705	+	6.68023i	0.745322	+	0.430312i	−0.0786793	+	0.996900i	$0.525070\pi$
$242$	10.5170	+	6.07200i	0.676060	+	0.390323i
$243$		0			0
$244$			4.77110i			0.305438i
$245$	1.89132	+	15.5835i	0.120832	+	0.995594i
$246$		0			0
$247$	−3.02461	−	5.23877i	−0.192451	−	0.333335i
$248$	8.46088	−	14.6547i	0.537266	−	0.930573i
$249$		0			0
$250$	−10.6929	+	6.17356i	−0.676279	+	0.390450i
$251$	−0.399303			−0.0252038			−0.0126019	−	0.999921i	$-0.504011\pi$
$251$	−0.399303			−0.0252038			−0.0126019	+	0.999921i	$0.504011\pi$
$252$		0			0
$253$	−0.590042			−0.0370957
$254$	−11.7157	+	6.76408i	−0.735110	+	0.424416i
$255$		0			0
$256$	7.71309	−	13.3595i	0.482068	−	0.834966i
$257$	3.08092	+	5.33631i	0.192182	+	0.332870i	0.945973	−	0.324245i	$-0.105110\pi$
$257$	3.08092	+	5.33631i	0.192182	+	0.332870i	−0.753791	+	0.657114i	$0.771777\pi$
$258$		0			0
$259$	8.66079	+	25.9446i	0.538155	+	1.61212i
$260$		−	10.4893i		−	0.650519i
$261$		0			0
$262$	1.14323	+	0.660042i	0.0706287	+	0.0407775i
$263$	9.80617	+	5.66159i	0.604674	+	0.349109i	0.770878	−	0.636983i	$-0.219818\pi$
$263$	9.80617	+	5.66159i	0.604674	+	0.349109i	−0.166204	+	0.986091i	$0.553151\pi$
$264$		0			0
$265$			24.6845i			1.51636i
$266$	1.94330	−	2.19341i	0.119151	−	0.134486i
$267$		0			0
$268$	−0.234113	−	0.405495i	−0.0143007	−	0.0247696i
$269$	7.82711	−	13.5570i	0.477227	−	0.826582i	−0.522432	−	0.852681i	$-0.674975\pi$
$269$	7.82711	−	13.5570i	0.477227	−	0.826582i	0.999659	+	0.0260990i	$0.00830851\pi$
$270$		0			0
$271$	0.118695	−	0.0685286i	0.00721021	−	0.00416282i	−0.496391	−	0.868099i	$-0.665342\pi$
$271$	0.118695	−	0.0685286i	0.00721021	−	0.00416282i	0.503601	+	0.863936i	$0.332008\pi$
$272$	−4.22911			−0.256428
$273$		0			0
$274$	−3.60597			−0.217844
$275$	0.00475442	−	0.00274497i	0.000286702	−	0.000165528i
$276$		0			0
$277$	9.15273	−	15.8530i	0.549934	−	0.952514i	−0.448344	−	0.893861i	$-0.647986\pi$
$277$	9.15273	−	15.8530i	0.549934	−	0.952514i	0.998278	−	0.0586533i	$-0.0186806\pi$
$278$	4.21656	+	7.30330i	0.252893	+	0.438023i
$279$		0			0
$280$	17.2869	−	5.77069i	1.03309	−	0.344865i
$281$		−	8.70405i		−	0.519240i	−0.965711	−	0.259620i	$-0.916403\pi$
$281$		−	8.70405i		−	0.519240i	0.965711	−	0.259620i	$-0.0835974\pi$
$282$		0			0
$283$	16.8812	+	9.74639i	1.00349	+	0.579362i	0.909278	−	0.416190i	$-0.136635\pi$
$283$	16.8812	+	9.74639i	1.00349	+	0.579362i	0.0942076	+	0.995553i	$0.469968\pi$
$284$	8.61258	+	4.97247i	0.511063	+	0.295062i
$285$		0			0
$286$			1.26657i			0.0748937i
$287$	−25.6317	−	5.23348i	−1.51299	−	0.308923i
$288$		0			0
$289$	5.90305	+	10.2244i	0.347238	+	0.601434i
$290$	−3.42665	+	5.93513i	−0.201220	+	0.348523i
$291$		0			0
$292$	9.47543	−	5.47064i	0.554508	−	0.320145i
$293$	6.33097			0.369859			0.184930	−	0.982752i	$-0.440794\pi$
$293$	6.33097			0.369859			0.184930	+	0.982752i	$0.440794\pi$
$294$		0			0
$295$	−32.4463			−1.88910
$296$	27.5003	−	15.8773i	1.59842	−	0.922850i
$297$		0			0
$298$	−3.12096	+	5.40566i	−0.180792	+	0.313141i
$299$	9.44072	+	16.3518i	0.545971	+	0.945649i
$300$		0			0
$301$	−0.581692	−	0.118770i	−0.0335282	−	0.00684578i
$302$		−	7.31764i		−	0.421083i
$303$		0			0
$304$	−1.60706	−	0.927838i	−0.0921713	−	0.0532151i
$305$	11.9836	+	6.91872i	0.686178	+	0.396165i
$306$		0			0
$307$		−	14.5685i		−	0.831467i	−0.909487	−	0.415733i	$-0.863525\pi$
$307$		−	14.5685i		−	0.831467i	0.909487	−	0.415733i	$-0.136475\pi$
$308$	0.366826	−	0.122453i	0.0209018	−	0.00697742i
$309$		0			0
$310$	−6.84184	−	11.8504i	−0.388591	−	0.673059i
$311$	−0.820539	+	1.42122i	−0.0465285	+	0.0805897i	−0.888352	−	0.459164i	$-0.848149\pi$
$311$	−0.820539	+	1.42122i	−0.0465285	+	0.0805897i	0.841823	+	0.539753i	$0.181482\pi$
$312$		0			0
$313$	−1.25211	+	0.722904i	−0.0707732	+	0.0408609i	−0.534969	−	0.844872i	$-0.679677\pi$
$313$	−1.25211	+	0.722904i	−0.0707732	+	0.0408609i	0.464196	+	0.885733i	$0.346343\pi$
$314$	14.4809			0.817207
$315$		0			0
$316$	5.07826			0.285675
$317$	9.30561	−	5.37260i	0.522655	−	0.301755i	−0.215365	−	0.976534i	$-0.569094\pi$
$317$	9.30561	−	5.37260i	0.522655	−	0.301755i	0.738020	+	0.674779i	$0.235761\pi$
$318$		0			0
$319$	−0.260790	+	0.451702i	−0.0146014	+	0.0252905i
$320$	−9.23831	−	16.0012i	−0.516437	−	0.894495i
$321$		0			0
$322$	−6.06562	+	6.84629i	−0.338024	+	0.381529i
$323$		−	2.27901i		−	0.126808i
$324$		0			0
$325$	−0.152142	−	0.0878393i	−0.00843933	−	0.00487245i
$326$	22.4905	+	12.9849i	1.24564	+	0.719168i
$327$		0			0
$328$			30.3715i			1.67698i
$329$	−9.49250	−	28.4361i	−0.523339	−	1.56773i
$330$		0			0
$331$	1.59234	+	2.75801i	0.0875229	+	0.151594i	0.906463	−	0.422284i	$-0.138772\pi$
$331$	1.59234	+	2.75801i	0.0875229	+	0.151594i	−0.818941	+	0.573878i	$0.805438\pi$
$332$	0.951391	−	1.64786i	0.0522144	−	0.0904379i
$333$		0			0
$334$	0.104854	−	0.0605374i	0.00573735	−	0.00331246i
$335$	−1.35798			−0.0741942
$336$		0			0
$337$	4.40125			0.239752			0.119876	−	0.992789i	$-0.461750\pi$
$337$	4.40125			0.239752			0.119876	+	0.992789i	$0.461750\pi$
$338$	22.6306	−	13.0658i	1.23094	−	0.710685i
$339$		0			0
$340$	1.97590	−	3.42236i	0.107158	−	0.185604i
$341$	−0.520709	−	0.901894i	−0.0281980	−	0.0488403i
$342$		0			0
$343$	15.2410	+	10.5219i	0.822938	+	0.568132i
$344$			0.689257i			0.0371622i
$345$		0			0
$346$	−2.59927	−	1.50069i	−0.139737	−	0.0806775i
$347$	15.2499	+	8.80451i	0.818656	+	0.472651i	0.849953	−	0.526859i	$-0.176630\pi$
$347$	15.2499	+	8.80451i	0.818656	+	0.472651i	−0.0312971	+	0.999510i	$0.509964\pi$
$348$		0			0
$349$			18.0696i			0.967245i	0.875277	+	0.483622i	$0.160679\pi$
$349$			18.0696i			0.967245i	−0.875277	+	0.483622i	$0.839321\pi$
$350$	0.0170253	−	0.0833840i	0.000910042	−	0.00445706i
$351$		0			0
$352$	−0.386382	−	0.669233i	−0.0205942	−	0.0356703i
$353$	5.62471	−	9.74228i	0.299373	−	0.518529i	−0.676620	−	0.736333i	$-0.736556\pi$
$353$	5.62471	−	9.74228i	0.299373	−	0.518529i	0.975993	+	0.217803i	$0.0698891\pi$
$354$		0			0
$355$	24.9787	−	14.4215i	1.32573	−	0.765412i
$356$	3.74235			0.198344
$357$		0			0
$358$	−25.9963			−1.37395
$359$	−14.5292	+	8.38846i	−0.766824	+	0.442726i	−0.831740	−	0.555165i	$-0.812655\pi$
$359$	−14.5292	+	8.38846i	−0.766824	+	0.442726i	0.0649165	+	0.997891i	$0.479322\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	9.64091	+	16.6986i	0.506715	+	0.877656i
$363$		0			0
$364$	−9.26277	−	8.20655i	−0.485501	−	0.430140i
$365$		−	31.7326i		−	1.66096i
$366$		0			0
$367$	−2.47646	−	1.42978i	−0.129270	−	0.0746340i	0.433971	−	0.900927i	$-0.357112\pi$
$367$	−2.47646	−	1.42978i	−0.129270	−	0.0746340i	−0.563240	+	0.826293i	$0.690446\pi$
$368$	5.01613	+	2.89606i	0.261484	+	0.150968i
$369$		0			0
$370$		−	25.6782i		−	1.33495i
$371$	21.7981	+	19.3125i	1.13170	+	1.00265i
$372$		0			0
$373$	−12.9240	−	22.3851i	−0.669182	−	1.15906i	−0.978133	−	0.207979i	$-0.933311\pi$
$373$	−12.9240	−	22.3851i	−0.669182	−	1.15906i	0.308952	−	0.951078i	$-0.400022\pi$
$374$	−0.238587	+	0.413245i	−0.0123370	+	0.0213684i
$375$		0			0
$376$	−30.1412	+	17.4021i	−1.55442	+	0.897442i
$377$	16.6906			0.859612
$378$		0			0
$379$	−1.45746			−0.0748647			−0.0374324	−	0.999299i	$-0.511918\pi$
$379$	−1.45746			−0.0748647			−0.0374324	+	0.999299i	$0.511918\pi$
$380$	1.50168	−	0.866998i	0.0770348	−	0.0444761i
$381$		0			0
$382$	−7.52871	+	13.0401i	−0.385202	+	0.667190i
$383$	−9.24968	−	16.0209i	−0.472637	−	0.818631i	0.526873	−	0.849944i	$-0.323364\pi$
$383$	−9.24968	−	16.0209i	−0.472637	−	0.818631i	−0.999510	+	0.0313133i	$0.990031\pi$
$384$		0			0
$385$	0.224379	−	1.09893i	0.0114354	−	0.0560066i
$386$			11.8461i			0.602950i
$387$		0			0
$388$	−9.48128	−	5.47402i	−0.481339	−	0.277901i
$389$	−3.21233	−	1.85464i	−0.162872	−	0.0940340i	0.416349	−	0.909205i	$-0.363310\pi$
$389$	−3.21233	−	1.85464i	−0.162872	−	0.0940340i	−0.579220	+	0.815171i	$0.696643\pi$
$390$		0			0
$391$			7.11350i			0.359745i
$392$	8.42888	−	19.7803i	0.425723	−	0.999058i
$393$		0			0
$394$	7.38880	+	12.7978i	0.372242	+	0.644743i
$395$	7.36414	−	12.7551i	0.370530	−	0.641777i
$396$		0			0
$397$	10.2537	−	5.91998i	0.514619	−	0.297115i	−0.220111	−	0.975475i	$-0.570642\pi$
$397$	10.2537	−	5.91998i	0.514619	−	0.297115i	0.734730	+	0.678359i	$0.237309\pi$
$398$	−17.0015			−0.852208
$399$		0			0
$400$	−0.0538917			−0.00269459
$401$	11.7340	−	6.77463i	0.585968	−	0.338309i	−0.177533	−	0.984115i	$-0.556812\pi$
$401$	11.7340	−	6.77463i	0.585968	−	0.338309i	0.763502	+	0.645806i	$0.223478\pi$
$402$		0			0
$403$	−16.6628	+	28.8607i	−0.830031	+	1.43766i
$404$	−5.57525	−	9.65661i	−0.277379	−	0.480434i
$405$		0			0
$406$	2.56020	+	7.66944i	0.127061	+	0.380628i
$407$		−	1.95428i		−	0.0968700i
$408$		0			0
$409$	11.7717	+	6.79641i	0.582074	+	0.336061i	0.761957	−	0.647627i	$-0.224239\pi$
$409$	11.7717	+	6.79641i	0.582074	+	0.336061i	−0.179883	+	0.983688i	$0.557572\pi$
$410$	21.2693	+	12.2799i	1.05042	+	0.606459i
$411$		0			0
$412$		−	4.78755i		−	0.235866i
$413$	−25.3851	+	28.6523i	−1.24912	+	1.40989i
$414$		0			0
$415$	−2.75928	−	4.77922i	−0.135448	−	0.234603i
$416$	−12.3643	+	21.4156i	−0.606209	+	1.04998i
$417$		0			0
$418$	−0.181326	+	0.104689i	−0.00886895	+	0.00512049i
$419$	−12.0728			−0.589792			−0.294896	−	0.955529i	$-0.595285\pi$
$419$	−12.0728			−0.589792			−0.294896	+	0.955529i	$0.595285\pi$
$420$		0			0
$421$	23.2091			1.13114			0.565571	−	0.824700i	$-0.308656\pi$
$421$	23.2091			1.13114			0.565571	+	0.824700i	$0.308656\pi$
$422$	−21.5075	+	12.4174i	−1.04697	+	0.604469i
$423$		0			0
$424$	16.9052	−	29.2806i	0.820987	−	1.42199i
$425$	−0.0330931	−	0.0573189i	−0.00160525	−	0.00278038i
$426$		0			0
$427$	15.4853	−	5.16929i	0.749387	−	0.250160i
$428$			0.537165i			0.0259649i
$429$		0			0
$430$	0.482691	+	0.278682i	0.0232774	+	0.0134392i
$431$	19.9870	+	11.5395i	0.962741	+	0.555838i	0.897015	−	0.441999i	$-0.145731\pi$
$431$	19.9870	+	11.5395i	0.962741	+	0.555838i	0.0657251	+	0.997838i	$0.479064\pi$
$432$		0			0
$433$			17.6595i			0.848664i	0.905507	+	0.424332i	$0.139491\pi$
$433$			17.6595i			0.848664i	−0.905507	+	0.424332i	$0.860509\pi$
$434$	−15.8176	−	3.22963i	−0.759269	−	0.155027i
$435$		0			0
$436$	−6.65347	−	11.5242i	−0.318644	−	0.551907i
$437$	−1.56065	+	2.70313i	−0.0746561	+	0.129308i
$438$		0			0
$439$	13.1779	−	7.60825i	0.628946	−	0.363122i	−0.151398	−	0.988473i	$-0.548377\pi$
$439$	13.1779	−	7.60825i	0.628946	−	0.363122i	0.780344	+	0.625351i	$0.215044\pi$
$440$	−1.30214			−0.0620770
$441$		0			0
$442$	15.2696			0.726302
$443$	−7.41802	+	4.28279i	−0.352441	+	0.203482i	−0.665760	−	0.746166i	$-0.731892\pi$
$443$	−7.41802	+	4.28279i	−0.352441	+	0.203482i	0.313319	+	0.949648i	$0.398559\pi$
$444$		0			0
$445$	5.42690	−	9.39967i	0.257260	−	0.445587i
$446$	5.15039	+	8.92073i	0.243878	+	0.422409i
$447$		0			0
$448$	−21.3580	−	4.36086i	−1.00907	−	0.206031i
$449$		−	27.7413i		−	1.30919i	−0.755978	−	0.654597i	$-0.772838\pi$
$449$		−	27.7413i		−	1.30919i	0.755978	−	0.654597i	$-0.227162\pi$
$450$		0			0
$451$	1.61874	+	0.934577i	0.0762233	+	0.0440075i
$452$	−8.10596	−	4.67998i	−0.381272	−	0.220128i
$453$		0			0
$454$		−	7.91860i		−	0.371638i
$455$	−34.0446	+	11.3647i	−1.59604	+	0.532787i
$456$		0			0
$457$	−16.8542	−	29.1923i	−0.788407	−	1.36556i	−0.926943	−	0.375203i	$-0.877573\pi$
$457$	−16.8542	−	29.1923i	−0.788407	−	1.36556i	0.138536	−	0.990357i	$-0.455760\pi$
$458$	−3.18751	+	5.52093i	−0.148943	+	0.257976i
$459$		0			0
$460$	−4.68722	+	2.70617i	−0.218543	+	0.126176i
$461$	−9.77973			−0.455487			−0.227744	−	0.973721i	$-0.573135\pi$
$461$	−9.77973			−0.455487			−0.227744	+	0.973721i	$0.573135\pi$
$462$		0			0
$463$	42.1842			1.96046			0.980232	−	0.197850i	$-0.0633958\pi$
$463$	42.1842			1.96046			0.980232	+	0.197850i	$0.0633958\pi$
$464$	4.43411	−	2.56004i	0.205849	−	0.118847i
$465$		0			0
$466$	5.93472	−	10.2792i	0.274921	−	0.476176i
$467$	3.24398	+	5.61873i	0.150113	+	0.260004i	0.931269	−	0.364332i	$-0.118703\pi$
$467$	3.24398	+	5.61873i	0.150113	+	0.260004i	−0.781156	+	0.624336i	$0.785369\pi$
$468$		0			0
$469$	−1.06244	+	1.19919i	−0.0490591	+	0.0553733i
$470$			28.1441i			1.29819i
$471$		0			0
$472$	38.4876	+	22.2208i	1.77154	+	1.02280i
$473$	0.0367359	+	0.0212095i	0.00168912	+	0.000975214i
$474$		0			0
$475$		−	0.0290416i		−	0.00133252i
$476$	−1.47629	−	4.42242i	−0.0676655	−	0.202701i
$477$		0			0
$478$	−8.42433	−	14.5914i	−0.385320	−	0.667394i
$479$	−18.7526	+	32.4805i	−0.856829	+	1.48407i	0.0181081	+	0.999836i	$0.494236\pi$
$479$	−18.7526	+	32.4805i	−0.856829	+	1.48407i	−0.874937	+	0.484236i	$0.839098\pi$
$480$		0			0
$481$	−54.1588	+	31.2686i	−2.46943	+	1.42573i
$482$	−14.7980			−0.674032
$483$		0			0
$484$	8.47784			0.385356
$485$	−27.4982	+	15.8761i	−1.24863	+	0.720896i
$486$		0			0
$487$	7.77976	−	13.4749i	0.352535	−	0.610608i	−0.634158	−	0.773203i	$-0.718653\pi$
$487$	7.77976	−	13.4749i	0.352535	−	0.610608i	0.986693	+	0.162595i	$0.0519865\pi$
$488$	−9.47656	−	16.4139i	−0.428984	−	0.743022i
$489$		0			0
$490$	−10.4443	−	13.9004i	−0.471826	−	0.627958i
$491$		−	7.87391i		−	0.355345i	−0.984090	−	0.177672i	$-0.943143\pi$
$491$		−	7.87391i		−	0.355345i	0.984090	−	0.177672i	$-0.0568567\pi$
$492$		0			0
$493$	5.44568	+	3.14406i	0.245261	+	0.141602i
$494$	5.80246	+	3.35005i	0.261065	+	0.150726i
$495$		0			0
$496$			10.2230i			0.459028i
$497$	6.80753	−	33.3409i	0.305360	−	1.49554i
$498$		0			0
$499$	11.4325	+	19.8016i	0.511788	+	0.886443i	0.999907	+	0.0136658i	$0.00435010\pi$
$499$	11.4325	+	19.8016i	0.511788	+	0.886443i	−0.488118	+	0.872777i	$0.662317\pi$
$500$	−4.30981	+	7.46481i	−0.192741	+	0.333837i
$501$		0			0
$502$	0.383015	−	0.221134i	0.0170948	−	0.00986969i
$503$	22.7999			1.01660			0.508298	−	0.861181i	$-0.330275\pi$
$503$	22.7999			1.01660			0.508298	+	0.861181i	$0.330275\pi$
$504$		0			0
$505$	−32.3393			−1.43908
$506$	0.565974	−	0.326765i	0.0251606	−	0.0145265i
$507$		0			0
$508$	−4.72206	+	8.17885i	−0.209508	+	0.362878i
$509$	15.3920	+	26.6598i	0.682240	+	1.18167i	0.974296	+	0.225272i	$0.0723272\pi$
$509$	15.3920	+	26.6598i	0.682240	+	1.18167i	−0.292056	+	0.956401i	$0.594339\pi$
$510$		0			0
$511$	−28.0220	−	24.8267i	−1.23962	−	1.09827i
$512$			18.9857i			0.839056i
$513$		0			0
$514$	−5.91049	−	3.41242i	−0.260700	−	0.150515i
$515$	−12.0249	−	6.94258i	−0.529880	−	0.305926i
$516$		0			0
$517$			2.14195i			0.0942030i
$518$	−22.6756	−	20.0899i	−0.996309	−	0.882701i
$519$		0			0
$520$	20.8343	+	36.0861i	0.913645	+	1.58248i
$521$	−17.2662	+	29.9060i	−0.756446	+	1.31020i	0.188206	+	0.982130i	$0.439733\pi$
$521$	−17.2662	+	29.9060i	−0.756446	+	1.31020i	−0.944652	+	0.328074i	$0.893600\pi$
$522$		0			0
$523$	8.99370	−	5.19252i	0.393267	−	0.227053i	−0.290308	−	0.956933i	$-0.593758\pi$
$523$	8.99370	−	5.19252i	0.393267	−	0.227053i	0.683575	+	0.729880i	$0.260424\pi$
$524$	0.921561			0.0402586
$525$		0			0
$526$	−12.5416			−0.546838
$527$	−10.8732	+	6.27762i	−0.473642	+	0.273457i
$528$		0			0
$529$	−6.62873	+	11.4813i	−0.288206	+	0.499187i
$530$	−13.6703	−	23.6776i	−0.593798	−	1.02849i
$531$		0			0
$532$	0.409259	−	2.00440i	0.0177436	−	0.0869020i
$533$		−	59.8132i		−	2.59080i
$534$		0			0
$535$	1.34920	+	0.778960i	0.0583309	+	0.0336774i
$536$	1.61082	+	0.930010i	0.0695770	+	0.0401703i
$537$		0			0
$538$			17.3386i			0.747520i
$539$	−0.794881	−	1.05791i	−0.0342379	−	0.0455676i
$540$		0			0
$541$	4.85067	+	8.40160i	0.208546	+	0.361213i	0.951257	−	0.308400i	$-0.0997934\pi$
$541$	4.85067	+	8.40160i	0.208546	+	0.361213i	−0.742710	+	0.669613i	$0.766460\pi$
$542$	−0.0759023	+	0.131467i	−0.00326028	+	0.00564697i
$543$		0			0
$544$	−8.06822	+	4.65819i	−0.345922	+	0.199718i
$545$	−38.5936			−1.65317
$546$		0			0
$547$	−12.1549			−0.519704			−0.259852	−	0.965648i	$-0.583674\pi$
$547$	−12.1549			−0.519704			−0.259852	+	0.965648i	$0.583674\pi$
$548$	−2.18009	+	1.25868i	−0.0931290	+	0.0537680i
$549$		0			0
$550$	−0.00304032	+	0.00526599i	−0.000129640	+	0.000224543i
$551$	1.37957	+	2.38949i	0.0587717	+	0.101796i
$552$		0			0
$553$	−5.50209	−	16.4823i	−0.233973	−	0.700897i
$554$			20.2751i			0.861407i
$555$		0			0
$556$	5.09850	+	2.94362i	0.216224	+	0.124837i
$557$	−7.68695	−	4.43806i	−0.325707	−	0.188047i	0.328227	−	0.944599i	$-0.393549\pi$
$557$	−7.68695	−	4.43806i	−0.325707	−	0.188047i	−0.653933	+	0.756552i	$0.726882\pi$
$558$		0			0
$559$		−	1.35741i		−	0.0574125i
$560$	−7.30131	+	8.24103i	−0.308537	+	0.348247i
$561$		0			0
$562$	4.82030	+	8.34901i	0.203332	+	0.352182i
$563$	−7.13640	+	12.3606i	−0.300763	+	0.520937i	−0.976309	−	0.216381i	$-0.930575\pi$
$563$	−7.13640	+	12.3606i	−0.300763	+	0.520937i	0.675546	+	0.737318i	$0.263908\pi$
$564$		0			0
$565$	−23.5094	+	13.5732i	−0.989047	+	0.571027i
$566$	−21.5902			−0.907503
$567$		0			0
$568$	−39.5061			−1.65764
$569$	−27.9646	+	16.1454i	−1.17234	+	0.676850i	−0.954230	−	0.299075i	$-0.903322\pi$
$569$	−27.9646	+	16.1454i	−1.17234	+	0.676850i	−0.218108	+	0.975925i	$0.569989\pi$
$570$		0			0
$571$	8.14324	−	14.1045i	0.340784	−	0.590255i	−0.643795	−	0.765198i	$-0.722641\pi$
$571$	8.14324	−	14.1045i	0.340784	−	0.590255i	0.984579	+	0.174943i	$0.0559742\pi$
$572$	0.442101	+	0.765741i	0.0184852	+	0.0320172i
$573$		0			0
$574$	27.4845	−	9.17484i	1.14718	−	0.382951i
$575$			0.0906476i			0.00378027i
$576$		0			0
$577$	36.2057	+	20.9034i	1.50726	+	0.870220i	0.999964	+	0.00845039i	$0.00268988\pi$
$577$	36.2057	+	20.9034i	1.50726	+	0.870220i	0.507300	+	0.861769i	$0.330643\pi$
$578$	−11.3245	−	6.53821i	−0.471037	−	0.271954i
$579$		0			0
$580$			4.78434i			0.198659i
$581$	−6.37916	−	1.30250i	−0.264652	−	0.0540366i
$582$		0			0
$583$	−1.04040	−	1.80202i	−0.0430888	−	0.0746320i
$584$	−21.7320	+	37.6410i	−0.899278	+	1.55759i
$585$		0			0
$586$	−6.07272	+	3.50609i	−0.250862	+	0.144835i
$587$	43.4162			1.79198			0.895989	−	0.444076i	$-0.146468\pi$
$587$	43.4162			1.79198			0.895989	+	0.444076i	$0.146468\pi$
$588$		0			0
$589$	−5.50906			−0.226997
$590$	31.1228	−	17.9688i	1.28131	−	0.739762i
$591$		0			0
$592$	−9.59206	+	16.6139i	−0.394231	+	0.682828i
$593$	−0.899243	−	1.55753i	−0.0369275	−	0.0639603i	0.846971	−	0.531639i	$-0.178424\pi$
$593$	−0.899243	−	1.55753i	−0.0369275	−	0.0639603i	−0.883898	+	0.467679i	$0.845090\pi$
$594$		0			0
$595$	−13.2486	−	2.70509i	−0.543139	−	0.110898i
$596$			4.35753i			0.178492i
$597$		0			0
$598$	−18.1112	−	10.4565i	−0.740624	−	0.427599i
$599$	11.1590	+	6.44266i	0.455945	+	0.263240i	0.710338	−	0.703861i	$-0.248542\pi$
$599$	11.1590	+	6.44266i	0.455945	+	0.263240i	−0.254393	+	0.967101i	$0.581876\pi$
$600$		0			0
$601$		−	24.4615i		−	0.997804i	−0.866658	−	0.498902i	$-0.833737\pi$
$601$		−	24.4615i		−	0.997804i	0.866658	−	0.498902i	$-0.166263\pi$
$602$	0.623739	−	0.208216i	0.0254217	−	0.00848625i
$603$		0			0
$604$	−2.55425	−	4.42410i	−0.103931	−	0.180014i
$605$	12.2940	−	21.2938i	0.499821	−	0.865715i
$606$		0			0
$607$	22.4349	−	12.9528i	0.910606	−	0.525738i	0.0299796	−	0.999551i	$-0.490456\pi$
$607$	22.4349	−	12.9528i	0.910606	−	0.525738i	0.880626	+	0.473812i	$0.157122\pi$
$608$	−4.08790			−0.165786
$609$		0			0
$610$	−15.3263			−0.620545
$611$	59.3598	−	34.2714i	2.40144	−	1.38647i
$612$		0			0
$613$	−18.4006	+	31.8707i	−0.743191	+	1.28725i	0.207844	+	0.978162i	$0.433355\pi$
$613$	−18.4006	+	31.8707i	−0.743191	+	1.28725i	−0.951035	+	0.309083i	$0.899978\pi$
$614$	8.06801	+	13.9742i	0.325599	+	0.563953i
$615$		0			0
$616$	−1.01876	+	1.14988i	−0.0410469	+	0.0463299i
$617$		−	37.3859i		−	1.50510i	−0.658536	−	0.752549i	$-0.728824\pi$
$617$		−	37.3859i		−	1.50510i	0.658536	−	0.752549i	$-0.271176\pi$
$618$		0			0
$619$	−37.2077	−	21.4819i	−1.49550	−	0.863429i	−0.495517	−	0.868598i	$-0.665021\pi$
$619$	−37.2077	−	21.4819i	−1.49550	−	0.863429i	−0.999987	+	0.00516920i	$0.998355\pi$
$620$	−8.27288	−	4.77635i	−0.332247	−	0.191823i
$621$		0			0
$622$		−	1.81766i		−	0.0728814i
$623$	−4.05468	−	12.1464i	−0.162448	−	0.486634i
$624$		0			0
$625$	12.5722	+	21.7757i	0.502887	+	0.871026i
$626$	0.800688	−	1.38683i	0.0320019	−	0.0554289i
$627$		0			0
$628$	8.75488	−	5.05463i	0.349358	−	0.201702i
$629$	−23.5606			−0.939424
$630$		0			0
$631$	45.3472			1.80524			0.902622	−	0.430434i	$-0.141639\pi$
$631$	45.3472			1.80524			0.902622	+	0.430434i	$0.141639\pi$
$632$	−17.4706	+	10.0867i	−0.694943	+	0.401226i
$633$		0			0
$634$	−5.95068	+	10.3069i	−0.236332	+	0.409339i
$635$	13.6952	+	23.7208i	0.543478	+	0.941331i
$636$		0			0
$637$	−16.5997	+	38.9552i	−0.657706	+	1.54346i
$638$		−	0.577702i		−	0.0228714i
$639$		0			0
$640$	1.84467	+	1.06502i	0.0729169	+	0.0420986i
$641$	−39.1440	−	22.5998i	−1.54610	−	0.892639i	−0.998434	−	0.0559399i	$-0.982184\pi$
$641$	−39.1440	−	22.5998i	−1.54610	−	0.892639i	−0.547662	−	0.836699i	$-0.684482\pi$
$642$		0			0
$643$		−	11.4541i		−	0.451704i	−0.974162	−	0.225852i	$-0.927483\pi$
$643$		−	11.4541i		−	0.451704i	0.974162	−	0.225852i	$-0.0725166\pi$
$644$	−1.27742	+	6.25636i	−0.0503375	+	0.246535i
$645$		0			0
$646$	1.26212	+	2.18605i	0.0496573	+	0.0860090i
$647$	5.47205	−	9.47787i	0.215128	−	0.372613i	−0.738184	−	0.674600i	$-0.764316\pi$
$647$	5.47205	−	9.47787i	0.215128	−	0.372613i	0.953312	+	0.301986i	$0.0976496\pi$
$648$		0			0
$649$	2.36865	−	1.36754i	0.0929775	−	0.0536806i
$650$	0.194581			0.00763211
$651$		0			0
$652$	18.1298			0.710016
$653$	30.3385	−	17.5159i	1.18724	−	0.685451i	0.229558	−	0.973295i	$-0.426272\pi$
$653$	30.3385	−	17.5159i	1.18724	−	0.685451i	0.957677	+	0.287844i	$0.0929386\pi$
$654$		0			0
$655$	1.33638	−	2.31469i	0.0522169	−	0.0904422i
$656$	−9.17424	−	15.8903i	−0.358194	−	0.620410i
$657$		0			0
$658$	24.8532	+	22.0192i	0.968878	+	0.858398i
$659$			39.7257i			1.54749i	0.633494	+	0.773747i	$0.281620\pi$
$659$			39.7257i			1.54749i	−0.633494	+	0.773747i	$0.718380\pi$
$660$		0			0
$661$	−32.3406	−	18.6719i	−1.25790	−	0.726251i	−0.285237	−	0.958457i	$-0.592072\pi$
$661$	−32.3406	−	18.6719i	−1.25790	−	0.726251i	−0.972667	+	0.232206i	$0.925406\pi$
$662$	−3.05477	−	1.76367i	−0.118727	−	0.0685471i
$663$		0			0
$664$			7.55877i			0.293337i
$665$	−4.44098	−	3.93458i	−0.172214	−	0.152577i
$666$		0			0
$667$	−4.30606	−	7.45832i	−0.166731	−	0.288787i
$668$	0.0422617	−	0.0731994i	0.00163515	−	0.00283217i
$669$		0			0
$670$	1.30258	−	0.752047i	0.0503232	−	0.0290541i
$671$	−1.16643			−0.0450297
$672$		0			0
$673$	3.11633			0.120126			0.0600628	−	0.998195i	$-0.480870\pi$
$673$	3.11633			0.120126			0.0600628	+	0.998195i	$0.480870\pi$
$674$	−4.22172	+	2.43741i	−0.162615	+	0.0938856i
$675$		0			0
$676$	9.12133	−	15.7986i	0.350820	−	0.607639i
$677$	−1.88444	−	3.26395i	−0.0724250	−	0.125444i	0.827539	−	0.561409i	$-0.189740\pi$
$677$	−1.88444	−	3.26395i	−0.0724250	−	0.125444i	−0.899964	+	0.435965i	$0.856407\pi$
$678$		0			0
$679$	−7.49417	+	36.7038i	−0.287600	+	1.40856i
$680$			15.6985i			0.602009i
$681$		0			0
$682$	0.998937	+	0.576737i	0.0382513	+	0.0220844i
$683$	−6.88838	−	3.97701i	−0.263577	−	0.152176i	0.362388	−	0.932027i	$-0.381961\pi$
$683$	−6.88838	−	3.97701i	−0.263577	−	0.152176i	−0.625965	+	0.779851i	$0.715295\pi$
$684$		0			0
$685$			7.30099i			0.278956i
$686$	−20.4464	−	1.65228i	−0.780646	−	0.0630843i
$687$		0			0
$688$	−0.208202	−	0.360617i	−0.00793764	−	0.0137484i
$689$	−33.2928	+	57.6648i	−1.26835	+	2.19686i
$690$		0			0
$691$	−1.51324	+	0.873668i	−0.0575663	+	0.0332359i	−0.528507	−	0.848929i	$-0.677248\pi$
$691$	−1.51324	+	0.873668i	−0.0575663	+	0.0332359i	0.470941	+	0.882165i	$0.343915\pi$
$692$	−2.09529			−0.0796508
$693$		0			0
$694$	−19.5037			−0.740352
$695$	14.7870	−	8.53726i	0.560902	−	0.323837i
$696$		0			0
$697$	11.2672	−	19.5153i	0.426775	−	0.739196i
$698$	−10.0070	−	17.3325i	−0.378769	−	0.656047i
$699$		0			0
$700$	−0.0188124	−	0.0563550i	−0.000711041	−	0.00213002i
$701$		−	0.796826i		−	0.0300957i	−0.999887	−	0.0150479i	$-0.995210\pi$
$701$		−	0.796826i		−	0.0300957i	0.999887	−	0.0150479i	$-0.00479006\pi$
$702$		0			0
$703$	−8.95303	−	5.16904i	−0.337670	−	0.194954i
$704$	1.34883	+	0.778748i	0.0508360	+	0.0293502i
$705$		0			0
$706$			12.4598i			0.468933i
$707$	−25.3014	+	28.5578i	−0.951557	+	1.07403i
$708$		0			0
$709$	14.3197	+	24.8024i	0.537788	+	0.931475i	0.999023	+	0.0441975i	$0.0140731\pi$
$709$	14.3197	+	24.8024i	0.537788	+	0.931475i	−0.461235	+	0.887278i	$0.652594\pi$
$710$	−15.9732	+	27.6664i	−0.599464	+	1.03830i
$711$		0			0
$712$	−12.8747	+	7.43322i	−0.482500	+	0.278572i
$713$	17.1955			0.643975
$714$		0			0
$715$	2.56442			0.0959037
$716$	−15.7168	+	9.07412i	−0.587366	+	0.339116i
$717$		0			0
$718$	9.29105	−	16.0926i	0.346739	−	0.600569i
$719$	16.4544	+	28.4998i	0.613644	+	1.06286i	0.990621	+	0.136640i	$0.0436303\pi$
$719$	16.4544	+	28.4998i	0.613644	+	1.06286i	−0.376977	+	0.926223i	$0.623036\pi$
$720$		0			0
$721$	−15.5387	+	5.18712i	−0.578692	+	0.193178i
$722$			1.10760i			0.0412206i
$723$		0			0
$724$	11.6574	+	6.73040i	0.433244	+	0.250133i
$725$	0.0693945	+	0.0400649i	0.00257725	+	0.00148797i
$726$		0			0
$727$		−	33.9908i		−	1.26065i	−0.776331	−	0.630325i	$-0.782922\pi$
$727$		−	33.9908i		−	1.26065i	0.776331	−	0.630325i	$-0.217078\pi$
$728$	48.1666	+	9.83465i	1.78517	+	0.364496i
$729$		0			0
$730$	17.5735	+	30.4382i	0.650424	+	1.12657i
$731$	0.255700	−	0.442885i	0.00945740	−	0.0163807i
$732$		0			0
$733$	20.2767	−	11.7067i	0.748936	−	0.432398i	−0.0763733	−	0.997079i	$-0.524334\pi$
$733$	20.2767	−	11.7067i	0.748936	−	0.432398i	0.825309	+	0.564681i	$0.191001\pi$
$734$	3.16725			0.116905
$735$		0			0
$736$	12.7596			0.470324
$737$	0.0991351	−	0.0572357i	0.00365169	−	0.00210830i
$738$		0			0
$739$	−11.5954	+	20.0839i	−0.426545	+	0.738798i	−0.996563	−	0.0828340i	$-0.973603\pi$
$739$	−11.5954	+	20.0839i	−0.426545	+	0.738798i	0.570018	+	0.821632i	$0.306936\pi$
$740$	−8.96309	−	15.5245i	−0.329490	−	0.570693i
$741$		0			0
$742$	−31.6041	−	6.45293i	−1.16022	−	0.236894i
$743$			13.6450i			0.500586i	0.968170	+	0.250293i	$0.0805269\pi$
$743$			13.6450i			0.500586i	−0.968170	+	0.250293i	$0.919473\pi$
$744$		0			0
$745$	10.9448	+	6.31899i	0.400987	+	0.231510i
$746$	24.7937	+	14.3147i	0.907763	+	0.524097i
$747$		0			0
$748$			0.333119i			0.0121800i
$749$	1.74345	−	0.581997i	0.0637043	−	0.0212657i
$750$		0			0
$751$	−20.6047	−	35.6884i	−0.751876	−	1.30229i	−0.946912	−	0.321492i	$-0.895816\pi$
$751$	−20.6047	−	35.6884i	−0.751876	−	1.30229i	0.195036	−	0.980796i	$-0.437518\pi$
$752$	10.5132	−	18.2094i	0.383377	−	0.664028i
$753$		0			0
$754$	−16.0098	+	9.24327i	−0.583043	+	0.336620i
$755$	−14.8160			−0.539210
$756$		0			0
$757$	−6.08509			−0.221166			−0.110583	−	0.993867i	$-0.535272\pi$
$757$	−6.08509			−0.221166			−0.110583	+	0.993867i	$0.535272\pi$
$758$	1.39801	−	0.807141i	0.0507780	−	0.0293167i
$759$		0			0
$760$	−3.44414	+	5.96542i	−0.124932	+	0.216388i
$761$	−6.07657	−	10.5249i	−0.220276	−	0.381529i	0.734616	−	0.678483i	$-0.237362\pi$
$761$	−6.07657	−	10.5249i	−0.220276	−	0.381529i	−0.954892	+	0.296955i	$0.904029\pi$
$762$		0			0
$763$	−30.1946	+	34.0808i	−1.09312	+	1.23381i
$764$			10.5117i			0.380300i
$765$		0			0
$766$	17.7448	+	10.2449i	0.641144	+	0.370165i
$767$	−75.7970	−	43.7614i	−2.73687	−	1.58013i
$768$		0			0
$769$		−	22.4599i		−	0.809926i	−0.914333	−	0.404963i	$-0.867284\pi$
$769$		−	22.4599i		−	0.809926i	0.914333	−	0.404963i	$-0.132716\pi$
$770$	0.393360	+	1.17836i	0.0141757	+	0.0424653i
$771$		0			0
$772$	4.13493	+	7.16191i	0.148819	+	0.257763i
$773$	4.73757	−	8.20572i	0.170399	−	0.295139i	−0.768161	−	0.640257i	$-0.778828\pi$
$773$	4.73757	−	8.20572i	0.170399	−	0.295139i	0.938559	+	0.345118i	$0.112161\pi$
$774$		0			0
$775$	−0.138557	+	0.0799959i	−0.00497712	+	0.00287354i
$776$	43.4909			1.56123
$777$		0			0
$778$	4.10840			0.147293
$779$	8.56306	−	4.94388i	0.306803	−	0.177133i
$780$		0			0
$781$	−1.21567	+	2.10559i	−0.0434999	+	0.0753441i
$782$	−3.93945	−	6.82333i	−0.140875	−	0.244002i
$783$		0			0
$784$	1.56504	+	12.8951i	0.0558942	+	0.460539i
$785$		−	29.3195i		−	1.04646i
$786$		0			0
$787$	−32.1802	−	18.5793i	−1.14710	−	0.662279i	−0.198922	−	0.980015i	$-0.563744\pi$
$787$	−32.1802	−	18.5793i	−1.14710	−	0.662279i	−0.948179	+	0.317736i	$0.897077\pi$
$788$	8.93423	+	5.15818i	0.318269	+	0.183753i
$789$		0			0
$790$			16.3130i			0.580392i
$791$	−6.40709	+	31.3796i	−0.227810	+	1.11573i
$792$		0			0
$793$	18.6630	+	32.3253i	0.662743	+	1.14791i
$794$	−6.55697	+	11.3570i	−0.232698	+	0.403045i
$795$		0			0
$796$	−10.2788	+	5.93444i	−0.364321	+	0.210341i
$797$	−44.4280			−1.57372			−0.786860	−	0.617132i	$-0.788294\pi$
$797$	−44.4280			−1.57372			−0.786860	+	0.617132i	$0.788294\pi$
$798$		0			0
$799$	25.8232			0.913559
$800$	−0.102814	+	0.0593595i	−0.00363501	+	0.00209867i
$801$		0			0
$802$	−7.50358	+	12.9966i	−0.264960	+	0.458925i
$803$	1.33746	+	2.31654i	0.0471978	+	0.0817490i
$804$		0			0
$805$	13.8617	+	12.2810i	0.488560	+	0.432850i
$806$		−	36.9113i		−	1.30014i
$807$		0			0
$808$	38.3607	+	22.1476i	1.34953	+	0.779149i
$809$	−26.5681	−	15.3391i	−0.934084	−	0.539294i	−0.0459830	−	0.998942i	$-0.514642\pi$
$809$	−26.5681	−	15.3391i	−0.934084	−	0.539294i	−0.888101	+	0.459649i	$0.847975\pi$
$810$		0			0
$811$		−	4.03238i		−	0.141596i	−0.997491	−	0.0707981i	$-0.977445\pi$
$811$		−	4.03238i		−	0.141596i	0.997491	−	0.0707981i	$-0.0225546\pi$
$812$	4.22490	+	3.74314i	0.148265	+	0.131358i
$813$		0			0
$814$	1.08228	+	1.87456i	0.0379339	+	0.0657034i
$815$	26.2905	−	45.5365i	0.920917	−	1.59508i
$816$		0			0
$817$	0.194332	−	0.112198i	0.00679881	−	0.00392530i
$818$	−15.0554			−0.526399
$819$		0			0
$820$	17.1453			0.598741
$821$	18.8478	−	10.8818i	0.657794	−	0.379778i	−0.133642	−	0.991030i	$-0.542667\pi$
$821$	18.8478	−	10.8818i	0.657794	−	0.379778i	0.791436	+	0.611252i	$0.209334\pi$
$822$		0			0
$823$	22.0381	−	38.1710i	0.768198	−	1.33056i	−0.170341	−	0.985385i	$-0.554487\pi$
$823$	22.0381	−	38.1710i	0.768198	−	1.33056i	0.938539	−	0.345173i	$-0.112180\pi$
$824$	9.50924	+	16.4705i	0.331270	+	0.573776i
$825$		0			0
$826$	8.48199	−	41.5418i	0.295126	−	1.44542i
$827$		−	37.1790i		−	1.29284i	−0.762982	−	0.646420i	$-0.776265\pi$
$827$		−	37.1790i		−	1.29284i	0.762982	−	0.646420i	$-0.223735\pi$
$828$		0			0
$829$	13.3974	+	7.73501i	0.465312	+	0.268648i	0.714275	−	0.699865i	$-0.246756\pi$
$829$	13.3974	+	7.73501i	0.465312	+	0.268648i	−0.248963	+	0.968513i	$0.580090\pi$
$830$	5.29346	+	3.05618i	0.183739	+	0.106082i
$831$		0			0
$832$		−	49.8401i		−	1.72789i
$833$	−12.7541	+	9.58301i	−0.441904	+	0.332032i
$834$		0			0
$835$	−0.122570	−	0.212297i	−0.00424171	−	0.00734686i
$836$	−0.0730840	+	0.126585i	−0.00252766	+	0.00437804i
$837$		0			0
$838$	11.5803	−	6.68588i	0.400035	−	0.230960i
$839$	−5.13650			−0.177332			−0.0886658	−	0.996061i	$-0.528260\pi$
$839$	−5.13650			−0.177332			−0.0886658	+	0.996061i	$0.528260\pi$
$840$		0			0
$841$	21.3871			0.737487
$842$	−22.2624	+	12.8532i	−0.767212	+	0.442950i
$843$		0			0
$844$	−8.66868	+	15.0146i	−0.298388	+	0.516824i
$845$	−26.4542	−	45.8201i	−0.910054	−	1.57626i
$846$		0			0
$847$	−9.18539	−	27.5161i	−0.315614	−	0.945464i
$848$			20.4260i			0.701432i
$849$		0			0
$850$	0.0634864	+	0.0366539i	0.00217756	+	0.00125722i
$851$	27.9452	+	16.1341i	0.957947	+	0.553071i
$852$		0			0
$853$			16.1569i			0.553203i	0.960985	+	0.276602i	$0.0892082\pi$
$853$			16.1569i			0.553203i	−0.960985	+	0.276602i	$0.910792\pi$
$854$	−11.9909	+	13.5342i	−0.410320	+	0.463131i
$855$		0			0
$856$	−1.06694	−	1.84800i	−0.0364673	−	0.0631632i
$857$	6.62075	−	11.4675i	0.226160	−	0.391721i	−0.730507	−	0.682906i	$-0.760716\pi$
$857$	6.62075	−	11.4675i	0.226160	−	0.391721i	0.956667	+	0.291184i	$0.0940493\pi$
$858$		0			0
$859$	−0.893535	+	0.515883i	−0.0304870	+	0.0176017i	−0.515166	−	0.857090i	$-0.672270\pi$
$859$	−0.893535	+	0.515883i	−0.0304870	+	0.0176017i	0.484679	+	0.874692i	$0.338936\pi$
$860$	0.389100			0.0132682
$861$		0			0
$862$	−25.5623			−0.870655
$863$	6.44951	−	3.72362i	0.219544	−	0.126754i	−0.386195	−	0.922417i	$-0.626211\pi$
$863$	6.44951	−	3.72362i	0.219544	−	0.126754i	0.605739	+	0.795663i	$0.292878\pi$
$864$		0			0
$865$	−3.03844	+	5.26273i	−0.103310	+	0.178938i
$866$	−9.77985	−	16.9392i	−0.332333	−	0.575617i
$867$		0			0
$868$	−10.6903	+	3.56863i	−0.362853	+	0.121127i
$869$			1.24153i			0.0421160i
$870$		0			0
$871$	−3.17234	−	1.83155i	−0.107491	−	0.0620597i
$872$	45.7795	+	26.4308i	1.55029	+	0.895060i
$873$		0			0
$874$		−	3.45715i		−	0.116940i
$875$	28.8977	+	5.90032i	0.976919	+	0.199467i
$876$		0			0
$877$	−5.30281	−	9.18474i	−0.179063	−	0.310147i	0.762497	−	0.646992i	$-0.223973\pi$
$877$	−5.30281	−	9.18474i	−0.179063	−	0.310147i	−0.941560	+	0.336846i	$0.890640\pi$
$878$	−8.42690	+	14.5958i	−0.284394	+	0.492585i
$879$		0			0
$880$	0.681275	−	0.393334i	0.0229658	−	0.0132593i
$881$	−18.6715			−0.629058			−0.314529	−	0.949248i	$-0.601847\pi$
$881$	−18.6715			−0.629058			−0.314529	+	0.949248i	$0.601847\pi$
$882$		0			0
$883$	−20.4810			−0.689241			−0.344621	−	0.938742i	$-0.611992\pi$
$883$	−20.4810			−0.689241			−0.344621	+	0.938742i	$0.611992\pi$
$884$	9.23171	−	5.32993i	0.310496	−	0.179265i
$885$		0			0
$886$	4.74362	−	8.21619i	0.159365	−	0.276028i
$887$	−14.6632	−	25.3975i	−0.492343	−	0.852763i	0.507618	−	0.861582i	$-0.330526\pi$
$887$	−14.6632	−	25.3975i	−0.492343	−	0.852763i	−0.999961	+	0.00881916i	$0.997193\pi$
$888$		0			0
$889$	31.6618	+	6.46470i	1.06190	+	0.216819i
$890$			12.0217i			0.402967i
$891$		0			0
$892$	6.22764	+	3.59553i	0.208517	+	0.120387i
$893$	9.81281	+	5.66543i	0.328373	+	0.189586i
$894$		0			0
$895$			52.6346i			1.75938i
$896$	2.38370	−	0.795725i	0.0796339	−	0.0265833i
$897$		0			0
$898$	15.3631	+	26.6097i	0.512674	+	0.887978i
$899$	7.60015	−	13.1638i	0.253479	−	0.439039i
$900$		0			0
$901$	−21.7250	+	12.5429i	−0.723764	+	0.417865i
$902$	−2.07027			−0.0689326
$903$		0			0
$904$	37.1822			1.23666
$905$	33.8095	−	19.5199i	1.12387	−	0.648864i
$906$		0			0
$907$	5.42003	−	9.38777i	0.179969	−	0.311716i	−0.761901	−	0.647694i	$-0.775734\pi$
$907$	5.42003	−	9.38777i	0.179969	−	0.311716i	0.941870	+	0.335978i	$0.109067\pi$
$908$	−2.76402	−	4.78743i	−0.0917273	−	0.158876i
$909$		0			0
$910$	26.3621	−	29.7550i	0.873896	−	0.986370i
$911$			55.9935i			1.85515i	0.373640	+	0.927574i	$0.378109\pi$
$911$			55.9935i			1.85515i	−0.373640	+	0.927574i	$0.621891\pi$
$912$		0			0
$913$	0.402867	+	0.232595i	0.0133329	+	0.00769778i
$914$	32.3334	+	18.6677i	1.06949	+	0.617473i
$915$		0			0
$916$			4.45045i			0.147047i
$917$	−0.998474	−	2.99106i	−0.0329725	−	0.0987736i
$918$		0			0
$919$	9.81094	+	16.9930i	0.323633	+	0.560549i	0.981235	−	0.192817i	$-0.0617623\pi$
$919$	9.81094	+	16.9930i	0.323633	+	0.560549i	−0.657602	+	0.753366i	$0.728429\pi$
$920$	10.7502	−	18.6199i	0.354423	−	0.613880i
$921$		0			0
$922$	9.38080	−	5.41601i	0.308940	−	0.178367i
$923$	77.8029			2.56091
$924$		0			0
$925$	−0.300234			−0.00987163
$926$	−40.4634	+	23.3616i	−1.32971	+	0.767709i
$927$		0			0
$928$	5.63955	−	9.76798i	0.185127	−	0.320650i
$929$	9.80629	+	16.9850i	0.321734	+	0.557260i	0.980846	−	0.194785i	$-0.0624010\pi$
$929$	9.80629	+	16.9850i	0.321734	+	0.557260i	−0.659112	+	0.752045i	$0.729068\pi$
$930$		0			0
$931$	−6.94901	+	0.843379i	−0.227745	+	0.0276406i
$932$		−	8.28616i		−	0.271422i
$933$		0			0
$934$	−6.22330	−	3.59303i	−0.203633	−	0.117567i
$935$	0.836696	+	0.483066i	0.0273629	+	0.0157980i
$936$		0			0
$937$			0.431335i			0.0140911i	0.999975	+	0.00704555i	$0.00224269\pi$
$937$			0.431335i			0.0140911i	−0.999975	+	0.00704555i	$0.997757\pi$
$938$	0.354997	−	1.73865i	0.0115911	−	0.0567690i
$939$		0			0
$940$	9.82383	+	17.0154i	0.320418	+	0.554980i
$941$	16.3672	−	28.3488i	0.533555	−	0.924145i	−0.465676	−	0.884955i	$-0.654189\pi$
$941$	16.3672	−	28.3488i	0.533555	−	0.924145i	0.999232	−	0.0391898i	$-0.0124777\pi$
$942$		0			0
$943$	−26.7279	+	15.4314i	−0.870381	+	0.502514i
$944$	−26.8488			−0.873854
$945$		0			0
$946$	−0.0469833			−0.00152756
$947$	28.2420	−	16.3055i	0.917742	−	0.529859i	0.0348282	−	0.999393i	$-0.488912\pi$
$947$	28.2420	−	16.3055i	0.917742	−	0.529859i	0.882914	+	0.469535i	$0.155578\pi$
$948$		0			0
$949$	42.7988	−	74.1297i	1.38931	−	2.40635i
$950$	0.0160832	+	0.0278569i	0.000521808	+	0.000903798i
$951$		0			0
$952$	13.8628	+	12.2821i	0.449296	+	0.398064i
$953$		−	26.6295i		−	0.862614i	−0.902205	−	0.431307i	$-0.858053\pi$
$953$		−	26.6295i		−	0.862614i	0.902205	−	0.431307i	$-0.141947\pi$
$954$		0			0
$955$	26.4023	+	15.2433i	0.854357	+	0.493263i
$956$	−10.1864	−	5.88110i	−0.329450	−	0.190208i
$957$		0			0
$958$		−	41.5408i		−	1.34212i
$959$	6.44727	+	5.71209i	0.208193	+	0.184453i
$960$		0			0
$961$	−0.325103	−	0.563094i	−0.0104872	−	0.0181643i
$962$	34.6331	−	59.9862i	1.11662	−	1.93403i
$963$		0			0
$964$	−8.94660	+	5.16532i	−0.288150	+	0.166364i
$965$	23.9848			0.772097
$966$		0			0
$967$	−22.8749			−0.735607			−0.367803	−	0.929904i	$-0.619890\pi$
$967$	−22.8749			−0.735607			−0.367803	+	0.929904i	$0.619890\pi$
$968$	−29.1661	+	16.8390i	−0.937433	+	0.541227i
$969$		0			0
$970$	17.5843	−	30.4570i	0.564599	−	0.977915i
$971$	15.1948	+	26.3182i	0.487624	+	0.844590i	0.999899	−	0.0142317i	$-0.00453024\pi$
$971$	15.1948	+	26.3182i	0.487624	+	0.844590i	−0.512274	+	0.858822i	$0.671197\pi$
$972$		0			0
$973$	4.02994	−	19.7372i	0.129194	−	0.632746i
$974$			17.2337i			0.552204i
$975$		0			0
$976$	9.91621	+	5.72513i	0.317410	+	0.183257i
$977$	−29.1104	−	16.8069i	−0.931325	−	0.537701i	−0.0440947	−	0.999027i	$-0.514040\pi$
$977$	−29.1104	−	16.8069i	−0.931325	−	0.537701i	−0.887230	+	0.461327i	$0.847374\pi$
$978$		0			0
$979$			0.914927i			0.0292412i
$980$	−11.1664	−	4.75829i	−0.356698	−	0.151998i
$981$		0			0
$982$	4.36057	+	7.55273i	0.139151	+	0.241017i
$983$	6.55347	−	11.3509i	0.209023	−	0.362039i	−0.742384	−	0.669975i	$-0.766305\pi$
$983$	6.55347	−	11.3509i	0.209023	−	0.362039i	0.951407	+	0.307936i	$0.0996382\pi$
$984$		0			0
$985$	25.9116	−	14.9601i	0.825613	−	0.476668i
$986$	−6.96472			−0.221802
$987$		0			0
$988$	4.67740			0.148808
$989$	−0.606569	+	0.350203i	−0.0192878	+	0.0111358i
$990$		0			0
$991$	−3.02016	+	5.23107i	−0.0959386	+	0.166170i	−0.910000	−	0.414608i	$-0.863919\pi$
$991$	−3.02016	+	5.23107i	−0.0959386	+	0.166170i	0.814061	+	0.580779i	$0.197252\pi$
$992$	11.2602	+	19.5033i	0.357513	+	0.619231i
$993$		0			0
$994$	11.9343	+	35.7509i	0.378534	+	1.13395i
$995$			34.4229i			1.09128i
$996$		0			0
$997$	−45.8727	−	26.4846i	−1.45280	−	0.838777i	−0.454164	−	0.890918i	$-0.650062\pi$
$997$	−45.8727	−	26.4846i	−1.45280	−	0.838777i	−0.998640	+	0.0521412i	$0.983395\pi$
$998$	−21.9323	−	12.6626i	−0.694254	−	0.400828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.db.a.647.15	✓	96
3.2	odd	2	inner	1197.2.db.a.647.34	yes	96
7.5	odd	6	inner	1197.2.db.a.1160.34	yes	96
21.5	even	6	inner	1197.2.db.a.1160.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.db.a.647.15	✓	96	1.1	even	1	trivial
1197.2.db.a.647.34	yes	96	3.2	odd	2	inner
1197.2.db.a.1160.15	yes	96	21.5	even	6	inner
1197.2.db.a.1160.34	yes	96	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959209 + 0.553800i) q^{2} +(-0.386612 + 0.669632i) q^{4} +(1.12128 + 1.94211i) q^{5} +(2.59227 + 0.529289i) q^{7} -3.07162i q^{8} +O(q^{10})\)	\(q+(-0.959209 + 0.553800i) q^{2} +(-0.386612 + 0.669632i) q^{4} +(1.12128 + 1.94211i) q^{5} +(2.59227 + 0.529289i) q^{7} -3.07162i q^{8} +(-2.15108 - 1.24192i) q^{10} +(-0.163711 - 0.0945186i) q^{11} +6.04921i q^{13} +(-2.77965 + 0.927898i) q^{14} +(0.927838 + 1.60706i) q^{16} +(-1.13951 + 1.97368i) q^{17} +(-0.866025 + 0.500000i) q^{19} -1.73400 q^{20} +0.209377 q^{22} +(2.70313 - 1.56065i) q^{23} +(-0.0145208 + 0.0251507i) q^{25} +(-3.35005 - 5.80246i) q^{26} +(-1.35663 + 1.53124i) q^{28} -2.75914i q^{29} +(4.77099 + 2.75453i) q^{31} +(3.54022 + 2.04395i) q^{32} -2.52423i q^{34} +(1.87871 + 5.62794i) q^{35} +(5.16904 + 8.95303i) q^{37} +(0.553800 - 0.959209i) q^{38} +(5.96542 - 3.44414i) q^{40} -9.88777 q^{41} -0.224395 q^{43} +(0.126585 - 0.0730840i) q^{44} +(-1.72858 + 2.99398i) q^{46} +(-5.66543 - 9.81281i) q^{47} +(6.43971 + 2.74412i) q^{49} -0.0321664i q^{50} +(-4.05075 - 2.33870i) q^{52} +(9.53262 + 5.50366i) q^{53} -0.423926i q^{55} +(1.62577 - 7.96246i) q^{56} +(1.52801 + 2.64659i) q^{58} +(-7.23424 + 12.5301i) q^{59} +(5.34372 - 3.08520i) q^{61} -6.10184 q^{62} -8.23910 q^{64} +(-11.7482 + 6.78284i) q^{65} +(-0.302775 + 0.524421i) q^{67} +(-0.881095 - 1.52610i) q^{68} +(-4.91883 - 4.35794i) q^{70} -12.8617i q^{71} +(-12.2544 - 7.07510i) q^{73} +(-9.91637 - 5.72522i) q^{74} -0.773224i q^{76} +(-0.374355 - 0.331668i) q^{77} +(-3.28382 - 5.68775i) q^{79} +(-2.08073 + 3.60392i) q^{80} +(9.48443 - 5.47584i) q^{82} -2.46084 q^{83} -5.11081 q^{85} +(0.215242 - 0.124270i) q^{86} +(-0.290325 + 0.502858i) q^{88} +(-2.41997 - 4.19150i) q^{89} +(-3.20178 + 15.6812i) q^{91} +2.41347i q^{92} +(10.8687 + 6.27502i) q^{94} +(-1.94211 - 1.12128i) q^{95} +14.1589i q^{97} +(-7.69671 + 0.934126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) \) 96 * q + 48 * q^4 + 8 * q^7	\( 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

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