LMFDB - Embedded newform 1200.3.bg.d.1057.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,3,Mod(193,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1200.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1200.bg (of order $4$, 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:	$32.6976317232$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1200.1057
Dual form			1200.3.bg.d.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{3} +(-8.89898 - 8.89898i) q^{7} -3.00000i q^{9} +O(q^{10})$	$q+(-1.22474 + 1.22474i) q^{3} +(-8.89898 - 8.89898i) q^{7} -3.00000i q^{9} -5.79796 q^{11} +(6.79796 - 6.79796i) q^{13} +(-6.10102 - 6.10102i) q^{17} -6.20204i q^{19} +21.7980 q^{21} +(-18.6969 + 18.6969i) q^{23} +(3.67423 + 3.67423i) q^{27} -6.20204i q^{29} +0.404082 q^{31} +(7.10102 - 7.10102i) q^{33} +(27.0000 + 27.0000i) q^{37} +16.6515i q^{39} -1.79796 q^{41} +(36.4949 - 36.4949i) q^{43} +(38.6969 + 38.6969i) q^{47} +109.384i q^{49} +14.9444 q^{51} +(-69.0908 + 69.0908i) q^{53} +(7.59592 + 7.59592i) q^{57} -20.0000i q^{59} -63.1918 q^{61} +(-26.6969 + 26.6969i) q^{63} +(40.0908 + 40.0908i) q^{67} -45.7980i q^{69} -25.7980 q^{71} +(56.7980 - 56.7980i) q^{73} +(51.5959 + 51.5959i) q^{77} +139.373i q^{79} -9.00000 q^{81} +(13.7071 - 13.7071i) q^{83} +(7.59592 + 7.59592i) q^{87} +58.6061i q^{89} -120.990 q^{91} +(-0.494897 + 0.494897i) q^{93} +(15.9898 + 15.9898i) q^{97} +17.3939i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{7}+O(q^{10}) $ 4 * q - 16 * q^7	$ 4 q - 16 q^{7} + 16 q^{11} - 12 q^{13} - 44 q^{17} + 48 q^{21} - 16 q^{23} + 80 q^{31} + 48 q^{33} + 108 q^{37} + 32 q^{41} + 48 q^{43} + 96 q^{47} - 48 q^{51} - 100 q^{53} - 48 q^{57} - 96 q^{61} - 48 q^{63} - 16 q^{67} - 64 q^{71} + 188 q^{73} + 128 q^{77} - 36 q^{81} + 192 q^{83} - 48 q^{87} - 288 q^{91} + 96 q^{93} - 132 q^{97}+O(q^{100}) $ 4 * q - 16 * q^7 + 16 * q^11 - 12 * q^13 - 44 * q^17 + 48 * q^21 - 16 * q^23 + 80 * q^31 + 48 * q^33 + 108 * q^37 + 32 * q^41 + 48 * q^43 + 96 * q^47 - 48 * q^51 - 100 * q^53 - 48 * q^57 - 96 * q^61 - 48 * q^63 - 16 * q^67 - 64 * q^71 + 188 * q^73 + 128 * q^77 - 36 * q^81 + 192 * q^83 - 48 * q^87 - 288 * q^91 + 96 * q^93 - 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$.

$n$	$401$	$577$	$751$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−8.89898	−	8.89898i	−1.27128	−	1.27128i	−0.945416	−	0.325867i	$-0.894344\pi$
$7$	−8.89898	−	8.89898i	−1.27128	−	1.27128i	−0.325867	−	0.945416i	$-0.605656\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−5.79796			−0.527087			−0.263544	−	0.964647i	$-0.584891\pi$
$11$	−5.79796			−0.527087			−0.263544	+	0.964647i	$0.584891\pi$
$12$		0			0
$13$	6.79796	−	6.79796i	0.522920	−	0.522920i	−0.395532	−	0.918452i	$-0.629440\pi$
$13$	6.79796	−	6.79796i	0.522920	−	0.522920i	0.918452	+	0.395532i	$0.129440\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.10102	−	6.10102i	−0.358884	−	0.358884i	0.504518	−	0.863401i	$-0.331670\pi$
$17$	−6.10102	−	6.10102i	−0.358884	−	0.358884i	−0.863401	+	0.504518i	$0.831670\pi$
$18$		0			0
$19$		−	6.20204i		−	0.326423i	−0.986591	−	0.163212i	$-0.947815\pi$
$19$		−	6.20204i		−	0.326423i	0.986591	−	0.163212i	$-0.0521853\pi$
$20$		0			0
$21$	21.7980			1.03800
$22$		0			0
$23$	−18.6969	+	18.6969i	−0.812910	+	0.812910i	−0.985069	−	0.172159i	$-0.944926\pi$
$23$	−18.6969	+	18.6969i	−0.812910	+	0.812910i	0.172159	+	0.985069i	$0.444926\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$		0			0
$29$		−	6.20204i		−	0.213863i	−0.994266	−	0.106932i	$-0.965897\pi$
$29$		−	6.20204i		−	0.213863i	0.994266	−	0.106932i	$-0.0341026\pi$
$30$		0			0
$31$	0.404082			0.0130349			0.00651745	−	0.999979i	$-0.497925\pi$
$31$	0.404082			0.0130349			0.00651745	+	0.999979i	$0.497925\pi$
$32$		0			0
$33$	7.10102	−	7.10102i	0.215182	−	0.215182i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	0.970566	−	0.240836i	$-0.0774216\pi$
$37$	27.0000	+	27.0000i	0.729730	+	0.729730i	−0.240836	+	0.970566i	$0.577422\pi$
$38$		0			0
$39$			16.6515i			0.426962i
$40$		0			0
$41$	−1.79796			−0.0438527			−0.0219263	−	0.999760i	$-0.506980\pi$
$41$	−1.79796			−0.0438527			−0.0219263	+	0.999760i	$0.506980\pi$
$42$		0			0
$43$	36.4949	−	36.4949i	0.848719	−	0.848719i	−0.141255	−	0.989973i	$-0.545114\pi$
$43$	36.4949	−	36.4949i	0.848719	−	0.848719i	0.989973	+	0.141255i	$0.0451137\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	38.6969	+	38.6969i	0.823339	+	0.823339i	0.986585	−	0.163246i	$-0.0521965\pi$
$47$	38.6969	+	38.6969i	0.823339	+	0.823339i	−0.163246	+	0.986585i	$0.552197\pi$
$48$		0			0
$49$			109.384i			2.23232i
$50$		0			0
$51$	14.9444			0.293027
$52$		0			0
$53$	−69.0908	+	69.0908i	−1.30360	+	1.30360i	−0.377653	+	0.925947i	$0.623269\pi$
$53$	−69.0908	+	69.0908i	−1.30360	+	1.30360i	−0.925947	+	0.377653i	$0.876731\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	7.59592	+	7.59592i	0.133262	+	0.133262i
$58$		0			0
$59$		−	20.0000i		−	0.338983i	−0.985532	−	0.169492i	$-0.945787\pi$
$59$		−	20.0000i		−	0.338983i	0.985532	−	0.169492i	$-0.0542125\pi$
$60$		0			0
$61$	−63.1918			−1.03593			−0.517966	−	0.855401i	$-0.673311\pi$
$61$	−63.1918			−1.03593			−0.517966	+	0.855401i	$0.673311\pi$
$62$		0			0
$63$	−26.6969	+	26.6969i	−0.423761	+	0.423761i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	40.0908	+	40.0908i	0.598370	+	0.598370i	0.939879	−	0.341508i	$-0.110938\pi$
$67$	40.0908	+	40.0908i	0.598370	+	0.598370i	−0.341508	+	0.939879i	$0.610938\pi$
$68$		0			0
$69$		−	45.7980i		−	0.663739i
$70$		0			0
$71$	−25.7980			−0.363352			−0.181676	−	0.983358i	$-0.558152\pi$
$71$	−25.7980			−0.363352			−0.181676	+	0.983358i	$0.558152\pi$
$72$		0			0
$73$	56.7980	−	56.7980i	0.778054	−	0.778054i	−0.201445	−	0.979500i	$-0.564564\pi$
$73$	56.7980	−	56.7980i	0.778054	−	0.778054i	0.979500	+	0.201445i	$0.0645639\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	51.5959	+	51.5959i	0.670077	+	0.670077i
$78$		0			0
$79$			139.373i			1.76422i	0.471042	+	0.882111i	$0.343878\pi$
$79$			139.373i			1.76422i	−0.471042	+	0.882111i	$0.656122\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	13.7071	−	13.7071i	0.165146	−	0.165146i	−0.619696	−	0.784842i	$-0.712744\pi$
$83$	13.7071	−	13.7071i	0.165146	−	0.165146i	0.784842	+	0.619696i	$0.212744\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	7.59592	+	7.59592i	0.0873094	+	0.0873094i
$88$		0			0
$89$			58.6061i			0.658496i	0.944244	+	0.329248i	$0.106795\pi$
$89$			58.6061i			0.658496i	−0.944244	+	0.329248i	$0.893205\pi$
$90$		0			0
$91$	−120.990			−1.32956
$92$		0			0
$93$	−0.494897	+	0.494897i	−0.00532148	+	0.00532148i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	15.9898	+	15.9898i	0.164843	+	0.164843i	0.784708	−	0.619865i	$-0.212813\pi$
$97$	15.9898	+	15.9898i	0.164843	+	0.164843i	−0.619865	+	0.784708i	$0.712813\pi$
$98$		0			0
$99$			17.3939i			0.175696i
$100$		0			0
$101$	−128.384			−1.27113			−0.635563	−	0.772049i	$-0.719232\pi$
$101$	−128.384			−1.27113			−0.635563	+	0.772049i	$0.719232\pi$
$102$		0			0
$103$	−32.4949	+	32.4949i	−0.315484	+	0.315484i	−0.847030	−	0.531545i	$-0.821612\pi$
$103$	−32.4949	+	32.4949i	−0.315484	+	0.315484i	0.531545	+	0.847030i	$0.321612\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	24.8990	+	24.8990i	0.232701	+	0.232701i	0.813819	−	0.581118i	$-0.197385\pi$
$107$	24.8990	+	24.8990i	0.232701	+	0.232701i	−0.581118	+	0.813819i	$0.697385\pi$
$108$		0			0
$109$		−	130.000i		−	1.19266i	−0.802739	−	0.596330i	$-0.796625\pi$
$109$		−	130.000i		−	1.19266i	0.802739	−	0.596330i	$-0.203375\pi$
$110$		0			0
$111$	−66.1362			−0.595822
$112$		0			0
$113$	−8.70714	+	8.70714i	−0.0770544	+	0.0770544i	−0.744584	−	0.667529i	$-0.767352\pi$
$113$	−8.70714	+	8.70714i	−0.0770544	+	0.0770544i	0.667529	+	0.744584i	$0.267352\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−20.3939	−	20.3939i	−0.174307	−	0.174307i
$118$		0			0
$119$			108.586i			0.912485i
$120$		0			0
$121$	−87.3837			−0.722179
$122$		0			0
$123$	2.20204	−	2.20204i	0.0179028	−	0.0179028i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−50.2929	−	50.2929i	−0.396007	−	0.396007i	0.480815	−	0.876822i	$-0.340341\pi$
$127$	−50.2929	−	50.2929i	−0.396007	−	0.396007i	−0.876822	+	0.480815i	$0.840341\pi$
$128$		0			0
$129$			89.3939i			0.692976i
$130$		0			0
$131$	114.202			0.871771			0.435886	−	0.900002i	$-0.356435\pi$
$131$	114.202			0.871771			0.435886	+	0.900002i	$0.356435\pi$
$132$		0			0
$133$	−55.1918	+	55.1918i	−0.414976	+	0.414976i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.1010	−	16.1010i	−0.117526	−	0.117526i	0.645898	−	0.763424i	$-0.276483\pi$
$137$	−16.1010	−	16.1010i	−0.117526	−	0.117526i	−0.763424	+	0.645898i	$0.776483\pi$
$138$		0			0
$139$			73.7980i			0.530921i	0.964122	+	0.265460i	$0.0855239\pi$
$139$			73.7980i			0.530921i	−0.964122	+	0.265460i	$0.914476\pi$
$140$		0			0
$141$	−94.7878			−0.672254
$142$		0			0
$143$	−39.4143	+	39.4143i	−0.275624	+	0.275624i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−133.967	−	133.967i	−0.911341	−	0.911341i
$148$		0			0
$149$			270.767i			1.81723i	0.417634	+	0.908615i	$0.362859\pi$
$149$			270.767i			1.81723i	−0.417634	+	0.908615i	$0.637141\pi$
$150$		0			0
$151$	−21.6163			−0.143154			−0.0715772	−	0.997435i	$-0.522803\pi$
$151$	−21.6163			−0.143154			−0.0715772	+	0.997435i	$0.522803\pi$
$152$		0			0
$153$	−18.3031	+	18.3031i	−0.119628	+	0.119628i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	0.196970	−	0.980410i	$-0.436890\pi$
$157$	−123.000	−	123.000i	−0.783439	−	0.783439i	−0.980410	+	0.196970i	$0.936890\pi$
$158$		0			0
$159$		−	169.237i		−	1.06439i
$160$		0			0
$161$	332.767			2.06688
$162$		0			0
$163$	−112.495	+	112.495i	−0.690153	+	0.690153i	−0.962265	−	0.272113i	$-0.912278\pi$
$163$	−112.495	+	112.495i	−0.690153	+	0.690153i	0.272113	+	0.962265i	$0.412278\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	176.677	+	176.677i	1.05794	+	1.05794i	0.998215	+	0.0597286i	$0.0190235\pi$
$167$	176.677	+	176.677i	1.05794	+	1.05794i	0.0597286	+	0.998215i	$0.480976\pi$
$168$		0			0
$169$			76.5755i			0.453110i
$170$		0			0
$171$	−18.6061			−0.108808
$172$		0			0
$173$	−142.889	+	142.889i	−0.825947	+	0.825947i	−0.986953	−	0.161007i	$-0.948526\pi$
$173$	−142.889	+	142.889i	−0.825947	+	0.825947i	0.161007	+	0.986953i	$0.448526\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	24.4949	+	24.4949i	0.138389	+	0.138389i
$178$		0			0
$179$			133.171i			0.743974i	0.928238	+	0.371987i	$0.121323\pi$
$179$			133.171i			0.743974i	−0.928238	+	0.371987i	$0.878677\pi$
$180$		0			0
$181$	137.192			0.757966			0.378983	−	0.925404i	$-0.376274\pi$
$181$	137.192			0.757966			0.378983	+	0.925404i	$0.376274\pi$
$182$		0			0
$183$	77.3939	−	77.3939i	0.422917	−	0.422917i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	35.3735	+	35.3735i	0.189163	+	0.189163i
$188$		0			0
$189$		−	65.3939i		−	0.345999i
$190$		0			0
$191$	266.606			1.39584			0.697922	−	0.716174i	$-0.254108\pi$
$191$	266.606			1.39584			0.697922	+	0.716174i	$0.254108\pi$
$192$		0			0
$193$	−117.384	+	117.384i	−0.608206	+	0.608206i	−0.942477	−	0.334271i	$-0.891510\pi$
$193$	−117.384	+	117.384i	−0.608206	+	0.608206i	0.334271	+	0.942477i	$0.391510\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	246.687	+	246.687i	1.25222	+	1.25222i	0.954724	+	0.297493i	$0.0961505\pi$
$197$	246.687	+	246.687i	1.25222	+	1.25222i	0.297493	+	0.954724i	$0.403850\pi$
$198$		0			0
$199$		−	154.565i		−	0.776710i	−0.921510	−	0.388355i	$-0.873043\pi$
$199$		−	154.565i		−	0.776710i	0.921510	−	0.388355i	$-0.126957\pi$
$200$		0			0
$201$	−98.2020			−0.488567
$202$		0			0
$203$	−55.1918	+	55.1918i	−0.271881	+	0.271881i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	56.0908	+	56.0908i	0.270970	+	0.270970i
$208$		0			0
$209$			35.9592i			0.172053i
$210$		0			0
$211$	−190.747			−0.904014			−0.452007	−	0.892014i	$-0.649292\pi$
$211$	−190.747			−0.904014			−0.452007	+	0.892014i	$0.649292\pi$
$212$		0			0
$213$	31.5959	−	31.5959i	0.148338	−	0.148338i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.59592	−	3.59592i	−0.0165711	−	0.0165711i
$218$		0			0
$219$			139.126i			0.635279i
$220$		0			0
$221$	−82.9490			−0.375335
$222$		0			0
$223$	−16.6765	+	16.6765i	−0.0747826	+	0.0747826i	−0.743509	−	0.668726i	$-0.766840\pi$
$223$	−16.6765	+	16.6765i	−0.0747826	+	0.0747826i	0.668726	+	0.743509i	$0.266840\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−42.0704	−	42.0704i	−0.185332	−	0.185332i	0.608342	−	0.793675i	$-0.291835\pi$
$227$	−42.0704	−	42.0704i	−0.185332	−	0.185332i	−0.793675	+	0.608342i	$0.791835\pi$
$228$		0			0
$229$		−	173.939i		−	0.759558i	−0.925077	−	0.379779i	$-0.876000\pi$
$229$		−	173.939i		−	0.759558i	0.925077	−	0.379779i	$-0.124000\pi$
$230$		0			0
$231$	−126.384			−0.547115
$232$		0			0
$233$	298.262	−	298.262i	1.28010	−	1.28010i	0.339483	−	0.940612i	$-0.389748\pi$
$233$	298.262	−	298.262i	1.28010	−	1.28010i	0.940612	−	0.339483i	$-0.110252\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−170.697	−	170.697i	−0.720240	−	0.720240i
$238$		0			0
$239$			37.2122i			0.155700i	0.996965	+	0.0778499i	$0.0248055\pi$
$239$			37.2122i			0.155700i	−0.996965	+	0.0778499i	$0.975195\pi$
$240$		0			0
$241$	165.939			0.688543			0.344271	−	0.938870i	$-0.388126\pi$
$241$	165.939			0.688543			0.344271	+	0.938870i	$0.388126\pi$
$242$		0			0
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−42.1612	−	42.1612i	−0.170693	−	0.170693i
$248$		0			0
$249$			33.5755i			0.134841i
$250$		0			0
$251$	−255.414			−1.01759			−0.508793	−	0.860889i	$-0.669908\pi$
$251$	−255.414			−1.01759			−0.508793	+	0.860889i	$0.669908\pi$
$252$		0			0
$253$	108.404	−	108.404i	0.428475	−	0.428475i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	270.485	+	270.485i	1.05247	+	1.05247i	0.998545	+	0.0539246i	$0.0171731\pi$
$257$	270.485	+	270.485i	1.05247	+	1.05247i	0.0539246	+	0.998545i	$0.482827\pi$
$258$		0			0
$259$		−	480.545i		−	1.85539i
$260$		0			0
$261$	−18.6061			−0.0712878
$262$		0			0
$263$	1.30306	−	1.30306i	0.00495461	−	0.00495461i	−0.704625	−	0.709580i	$-0.748885\pi$
$263$	1.30306	−	1.30306i	0.00495461	−	0.00495461i	0.709580	+	0.704625i	$0.248885\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−71.7775	−	71.7775i	−0.268830	−	0.268830i
$268$		0			0
$269$		−	41.1510i		−	0.152978i	−0.997070	−	0.0764889i	$-0.975629\pi$
$269$		−	41.1510i		−	0.152978i	0.997070	−	0.0764889i	$-0.0243710\pi$
$270$		0			0
$271$	484.727			1.78866			0.894329	−	0.447409i	$-0.147653\pi$
$271$	484.727			1.78866			0.894329	+	0.447409i	$0.147653\pi$
$272$		0			0
$273$	148.182	−	148.182i	0.542790	−	0.542790i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−51.9898	−	51.9898i	−0.187689	−	0.187689i	0.607007	−	0.794696i	$-0.292370\pi$
$277$	−51.9898	−	51.9898i	−0.187689	−	0.187689i	−0.794696	+	0.607007i	$0.792370\pi$
$278$		0			0
$279$		−	1.21225i		−	0.00434497i
$280$		0			0
$281$	242.524			0.863076			0.431538	−	0.902095i	$-0.357971\pi$
$281$	242.524			0.863076			0.431538	+	0.902095i	$0.357971\pi$
$282$		0			0
$283$	104.717	−	104.717i	0.370026	−	0.370026i	−0.497461	−	0.867487i	$-0.665734\pi$
$283$	104.717	−	104.717i	0.370026	−	0.370026i	0.867487	+	0.497461i	$0.165734\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.0000	+	16.0000i	0.0557491	+	0.0557491i
$288$		0			0
$289$		−	214.555i		−	0.742405i
$290$		0			0
$291$	−39.1668			−0.134594
$292$		0			0
$293$	60.9092	−	60.9092i	0.207881	−	0.207881i	−0.595485	−	0.803366i	$-0.703040\pi$
$293$	60.9092	−	60.9092i	0.207881	−	0.207881i	0.803366	+	0.595485i	$0.203040\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−21.3031	−	21.3031i	−0.0717275	−	0.0717275i
$298$		0			0
$299$			254.202i			0.850174i
$300$		0			0
$301$	−649.535			−2.15792
$302$		0			0
$303$	157.237	−	157.237i	0.518935	−	0.518935i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−201.303	−	201.303i	−0.655710	−	0.655710i	0.298652	−	0.954362i	$-0.403463\pi$
$307$	−201.303	−	201.303i	−0.655710	−	0.655710i	−0.954362	+	0.298652i	$0.903463\pi$
$308$		0			0
$309$		−	79.5959i		−	0.257592i
$310$		0			0
$311$	−559.737			−1.79980			−0.899898	−	0.436100i	$-0.856359\pi$
$311$	−559.737			−1.79980			−0.899898	+	0.436100i	$0.856359\pi$
$312$		0			0
$313$	93.7673	−	93.7673i	0.299576	−	0.299576i	−0.541272	−	0.840848i	$-0.682057\pi$
$313$	93.7673	−	93.7673i	0.299576	−	0.299576i	0.840848	+	0.541272i	$0.182057\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−362.828	−	362.828i	−1.14457	−	1.14457i	−0.987605	−	0.156962i	$-0.949830\pi$
$317$	−362.828	−	362.828i	−1.14457	−	1.14457i	−0.156962	−	0.987605i	$-0.550170\pi$
$318$		0			0
$319$			35.9592i			0.112725i
$320$		0			0
$321$	−60.9898			−0.189999
$322$		0			0
$323$	−37.8388	+	37.8388i	−0.117148	+	0.117148i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	159.217	+	159.217i	0.486902	+	0.486902i
$328$		0			0
$329$		−	688.727i		−	2.09339i
$330$		0			0
$331$	−14.0204			−0.0423577			−0.0211789	−	0.999776i	$-0.506742\pi$
$331$	−14.0204			−0.0423577			−0.0211789	+	0.999776i	$0.506742\pi$
$332$		0			0
$333$	81.0000	−	81.0000i	0.243243	−	0.243243i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	166.373	+	166.373i	0.493690	+	0.493690i	0.909467	−	0.415777i	$-0.136490\pi$
$337$	166.373	+	166.373i	0.493690	+	0.493690i	−0.415777	+	0.909467i	$0.636490\pi$
$338$		0			0
$339$		−	21.3281i		−	0.0629146i
$340$		0			0
$341$	−2.34285			−0.00687053
$342$		0			0
$343$	537.353	−	537.353i	1.56663	−	1.56663i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	163.505	+	163.505i	0.471196	+	0.471196i	0.902302	−	0.431105i	$-0.141876\pi$
$347$	163.505	+	163.505i	0.471196	+	0.471196i	−0.431105	+	0.902302i	$0.641876\pi$
$348$		0			0
$349$			280.000i			0.802292i	0.916014	+	0.401146i	$0.131388\pi$
$349$			280.000i			0.802292i	−0.916014	+	0.401146i	$0.868612\pi$
$350$		0			0
$351$	49.9546			0.142321
$352$		0			0
$353$	−261.495	+	261.495i	−0.740779	+	0.740779i	−0.972728	−	0.231949i	$-0.925490\pi$
$353$	−261.495	+	261.495i	−0.740779	+	0.740779i	0.231949	+	0.972728i	$0.425490\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−132.990	−	132.990i	−0.372520	−	0.372520i
$358$		0			0
$359$		−	425.090i		−	1.18409i	−0.805903	−	0.592047i	$-0.798320\pi$
$359$		−	425.090i		−	1.18409i	0.805903	−	0.592047i	$-0.201680\pi$
$360$		0			0
$361$	322.535			0.893448
$362$		0			0
$363$	107.023	−	107.023i	0.294828	−	0.294828i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−316.495	−	316.495i	−0.862384	−	0.862384i	0.129231	−	0.991615i	$-0.458749\pi$
$367$	−316.495	−	316.495i	−0.862384	−	0.862384i	−0.991615	+	0.129231i	$0.958749\pi$
$368$		0			0
$369$			5.39388i			0.0146176i
$370$		0			0
$371$	1229.68			3.31449
$372$		0			0
$373$	−210.939	+	210.939i	−0.565519	+	0.565519i	−0.930870	−	0.365351i	$-0.880949\pi$
$373$	−210.939	+	210.939i	−0.565519	+	0.565519i	0.365351	+	0.930870i	$0.380949\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−42.1612	−	42.1612i	−0.111833	−	0.111833i
$378$		0			0
$379$		−	344.182i		−	0.908131i	−0.890968	−	0.454065i	$-0.849973\pi$
$379$		−	344.182i		−	0.908131i	0.890968	−	0.454065i	$-0.150027\pi$
$380$		0			0
$381$	123.192			0.323338
$382$		0			0
$383$	−409.707	+	409.707i	−1.06973	+	1.06973i	−0.0723523	+	0.997379i	$0.523051\pi$
$383$	−409.707	+	409.707i	−1.06973	+	1.06973i	−0.997379	+	0.0723523i	$0.976949\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−109.485	−	109.485i	−0.282906	−	0.282906i
$388$		0			0
$389$		−	301.151i		−	0.774167i	−0.922045	−	0.387084i	$-0.873482\pi$
$389$		−	301.151i		−	0.774167i	0.922045	−	0.387084i	$-0.126518\pi$
$390$		0			0
$391$	228.141			0.583480
$392$		0			0
$393$	−139.868	+	139.868i	−0.355899	+	0.355899i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−479.343	−	479.343i	−1.20741	−	1.20741i	−0.971862	−	0.235551i	$-0.924311\pi$
$397$	−479.343	−	479.343i	−1.20741	−	1.20741i	−0.235551	−	0.971862i	$-0.575689\pi$
$398$		0			0
$399$		−	135.192i		−	0.338827i
$400$		0			0
$401$	101.233			0.252451			0.126225	−	0.992002i	$-0.459714\pi$
$401$	101.233			0.252451			0.126225	+	0.992002i	$0.459714\pi$
$402$		0			0
$403$	2.74693	−	2.74693i	0.00681621	−	0.00681621i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−156.545	−	156.545i	−0.384631	−	0.384631i
$408$		0			0
$409$			257.110i			0.628631i	0.949319	+	0.314316i	$0.101775\pi$
$409$			257.110i			0.628631i	−0.949319	+	0.314316i	$0.898225\pi$
$410$		0			0
$411$	39.4393			0.0959593
$412$		0			0
$413$	−177.980	+	177.980i	−0.430943	+	0.430943i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−90.3837	−	90.3837i	−0.216747	−	0.216747i
$418$		0			0
$419$		−	375.959i		−	0.897277i	−0.893713	−	0.448639i	$-0.851909\pi$
$419$		−	375.959i		−	0.897277i	0.893713	−	0.448639i	$-0.148091\pi$
$420$		0			0
$421$	158.829			0.377265			0.188633	−	0.982048i	$-0.439595\pi$
$421$	158.829			0.377265			0.188633	+	0.982048i	$0.439595\pi$
$422$		0			0
$423$	116.091	−	116.091i	0.274446	−	0.274446i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	562.343	+	562.343i	1.31696	+	1.31696i
$428$		0			0
$429$		−	96.5449i		−	0.225046i
$430$		0			0
$431$	152.182			0.353090			0.176545	−	0.984293i	$-0.443508\pi$
$431$	152.182			0.353090			0.176545	+	0.984293i	$0.443508\pi$
$432$		0			0
$433$	254.918	−	254.918i	0.588726	−	0.588726i	−0.348560	−	0.937286i	$-0.613329\pi$
$433$	254.918	−	254.918i	0.588726	−	0.588726i	0.937286	+	0.348560i	$0.113329\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	115.959	+	115.959i	0.265353	+	0.265353i
$438$		0			0
$439$			299.373i			0.681944i	0.940073	+	0.340972i	$0.110756\pi$
$439$			299.373i			0.681944i	−0.940073	+	0.340972i	$0.889244\pi$
$440$		0			0
$441$	328.151			0.744107
$442$		0			0
$443$	144.717	−	144.717i	0.326676	−	0.326676i	−0.524645	−	0.851321i	$-0.675802\pi$
$443$	144.717	−	144.717i	0.326676	−	0.326676i	0.851321	+	0.524645i	$0.175802\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−331.621	−	331.621i	−0.741881	−	0.741881i
$448$		0			0
$449$			846.727i			1.88581i	0.333069	+	0.942903i	$0.391916\pi$
$449$			846.727i			1.88581i	−0.333069	+	0.942903i	$0.608084\pi$
$450$		0			0
$451$	10.4245			0.0231142
$452$		0			0
$453$	26.4745	−	26.4745i	0.0584426	−	0.0584426i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	38.3939	+	38.3939i	0.0840129	+	0.0840129i	0.747864	−	0.663852i	$-0.231079\pi$
$457$	38.3939	+	38.3939i	0.0840129	+	0.0840129i	−0.663852	+	0.747864i	$0.731079\pi$
$458$		0			0
$459$		−	44.8332i		−	0.0976757i
$460$		0			0
$461$	78.7265			0.170773			0.0853867	−	0.996348i	$-0.472787\pi$
$461$	78.7265			0.170773			0.0853867	+	0.996348i	$0.472787\pi$
$462$		0			0
$463$	−461.485	+	461.485i	−0.996727	+	0.996727i	−0.999995	−	0.00326746i	$-0.998960\pi$
$463$	−461.485	+	461.485i	−0.996727	+	0.996727i	0.00326746	+	0.999995i	$0.498960\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.3031	+	17.3031i	0.0370515	+	0.0370515i	0.725390	−	0.688338i	$-0.241660\pi$
$467$	17.3031	+	17.3031i	0.0370515	+	0.0370515i	−0.688338	+	0.725390i	$0.741660\pi$
$468$		0			0
$469$		−	713.535i		−	1.52140i
$470$		0			0
$471$	301.287			0.639676
$472$		0			0
$473$	−211.596	+	211.596i	−0.447349	+	0.447349i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	207.272	+	207.272i	0.434533	+	0.434533i
$478$		0			0
$479$			776.727i			1.62156i	0.585352	+	0.810779i	$0.300956\pi$
$479$			776.727i			1.62156i	−0.585352	+	0.810779i	$0.699044\pi$
$480$		0			0
$481$	367.090			0.763180
$482$		0			0
$483$	−407.555	+	407.555i	−0.843799	+	0.843799i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−439.423	−	439.423i	−0.902307	−	0.902307i	0.0933285	−	0.995635i	$-0.470249\pi$
$487$	−439.423	−	439.423i	−0.902307	−	0.902307i	−0.995635	+	0.0933285i	$0.970249\pi$
$488$		0			0
$489$		−	275.555i		−	0.563507i
$490$		0			0
$491$	−246.080			−0.501180			−0.250590	−	0.968093i	$-0.580625\pi$
$491$	−246.080			−0.501180			−0.250590	+	0.968093i	$0.580625\pi$
$492$		0			0
$493$	−37.8388	+	37.8388i	−0.0767521	+	0.0767521i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	229.576	+	229.576i	0.461923	+	0.461923i
$498$		0			0
$499$			597.839i			1.19807i	0.800721	+	0.599037i	$0.204450\pi$
$499$			597.839i			1.19807i	−0.800721	+	0.599037i	$0.795550\pi$
$500$		0			0
$501$	−432.767			−0.863807
$502$		0			0
$503$	−516.817	+	516.817i	−1.02747	+	1.02747i	−0.0278580	+	0.999612i	$0.508869\pi$
$503$	−516.817	+	516.817i	−1.02747	+	1.02747i	−0.999612	+	0.0278580i	$0.991131\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−93.7855	−	93.7855i	−0.184981	−	0.184981i
$508$		0			0
$509$		−	452.059i		−	0.888132i	−0.895994	−	0.444066i	$-0.853536\pi$
$509$		−	452.059i		−	0.888132i	0.895994	−	0.444066i	$-0.146464\pi$
$510$		0			0
$511$	−1010.89			−1.97825
$512$		0			0
$513$	22.7878	−	22.7878i	0.0444206	−	0.0444206i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−224.363	−	224.363i	−0.433971	−	0.433971i
$518$		0			0
$519$		−	350.005i		−	0.674383i
$520$		0			0
$521$	779.494			1.49615			0.748075	−	0.663614i	$-0.230978\pi$
$521$	779.494			1.49615			0.748075	+	0.663614i	$0.230978\pi$
$522$		0			0
$523$	179.283	−	179.283i	0.342797	−	0.342797i	−0.514621	−	0.857418i	$-0.672067\pi$
$523$	179.283	−	179.283i	0.342797	−	0.342797i	0.857418	+	0.514621i	$0.172067\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.46531	−	2.46531i	−0.00467801	−	0.00467801i
$528$		0			0
$529$		−	170.151i		−	0.321647i
$530$		0			0
$531$	−60.0000			−0.112994
$532$		0			0
$533$	−12.2225	+	12.2225i	−0.0229314	+	0.0229314i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−163.101	−	163.101i	−0.303726	−	0.303726i
$538$		0			0
$539$		−	634.202i		−	1.17663i
$540$		0			0
$541$	−385.110			−0.711849			−0.355924	−	0.934515i	$-0.615834\pi$
$541$	−385.110			−0.711849			−0.355924	+	0.934515i	$0.615834\pi$
$542$		0			0
$543$	−168.025	+	168.025i	−0.309438	+	0.309438i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−504.372	−	504.372i	−0.922070	−	0.922070i	0.0751053	−	0.997176i	$-0.476071\pi$
$547$	−504.372	−	504.372i	−0.922070	−	0.922070i	−0.997176	+	0.0751053i	$0.976071\pi$
$548$		0			0
$549$			189.576i			0.345311i
$550$		0			0
$551$	−38.4653			−0.0698100
$552$		0			0
$553$	1240.28	−	1240.28i	2.24282	−	2.24282i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	130.101	+	130.101i	0.233575	+	0.233575i	0.814183	−	0.580608i	$-0.197185\pi$
$557$	130.101	+	130.101i	0.233575	+	0.233575i	−0.580608	+	0.814183i	$0.697185\pi$
$558$		0			0
$559$		−	496.182i		−	0.887624i
$560$		0			0
$561$	−86.6469			−0.154451
$562$		0			0
$563$	666.879	−	666.879i	1.18451	−	1.18451i	0.205946	−	0.978563i	$-0.433973\pi$
$563$	666.879	−	666.879i	1.18451	−	1.18451i	0.978563	−	0.205946i	$-0.0660270\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	80.0908	+	80.0908i	0.141254	+	0.141254i
$568$		0			0
$569$			987.494i			1.73549i	0.497010	+	0.867745i	$0.334431\pi$
$569$			987.494i			1.73549i	−0.497010	+	0.867745i	$0.665569\pi$
$570$		0			0
$571$	−452.767			−0.792938			−0.396469	−	0.918048i	$-0.629764\pi$
$571$	−452.767			−0.792938			−0.396469	+	0.918048i	$0.629764\pi$
$572$		0			0
$573$	−326.524	+	326.524i	−0.569851	+	0.569851i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−463.000	−	463.000i	−0.802426	−	0.802426i	0.181048	−	0.983474i	$-0.442051\pi$
$577$	−463.000	−	463.000i	−0.802426	−	0.802426i	−0.983474	+	0.181048i	$0.942051\pi$
$578$		0			0
$579$		−	287.530i		−	0.496598i
$580$		0			0
$581$	−243.959			−0.419895
$582$		0			0
$583$	400.586	−	400.586i	0.687111	−	0.687111i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	375.909	+	375.909i	0.640390	+	0.640390i	0.950651	−	0.310261i	$-0.100416\pi$
$587$	375.909	+	375.909i	0.640390	+	0.640390i	−0.310261	+	0.950651i	$0.600416\pi$
$588$		0			0
$589$		−	2.50613i		−	0.00425490i
$590$		0			0
$591$	−604.257			−1.02243
$592$		0			0
$593$	398.646	−	398.646i	0.672253	−	0.672253i	−0.285982	−	0.958235i	$-0.592320\pi$
$593$	398.646	−	398.646i	0.672253	−	0.672253i	0.958235	+	0.285982i	$0.0923198\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	189.303	+	189.303i	0.317091	+	0.317091i
$598$		0			0
$599$		−	509.131i		−	0.849968i	−0.905201	−	0.424984i	$-0.860280\pi$
$599$		−	509.131i		−	0.849968i	0.905201	−	0.424984i	$-0.139720\pi$
$600$		0			0
$601$	−390.302			−0.649421			−0.324711	−	0.945813i	$-0.605267\pi$
$601$	−390.302			−0.649421			−0.324711	+	0.945813i	$0.605267\pi$
$602$		0			0
$603$	120.272	−	120.272i	0.199457	−	0.199457i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	494.030	+	494.030i	0.813887	+	0.813887i	0.985214	−	0.171327i	$-0.0548054\pi$
$607$	494.030	+	494.030i	0.813887	+	0.813887i	−0.171327	+	0.985214i	$0.554805\pi$
$608$		0			0
$609$		−	135.192i		−	0.221990i
$610$		0			0
$611$	526.120			0.861081
$612$		0			0
$613$	−74.1102	+	74.1102i	−0.120898	+	0.120898i	−0.764967	−	0.644069i	$-0.777245\pi$
$613$	−74.1102	+	74.1102i	−0.120898	+	0.120898i	0.644069	+	0.764967i	$0.277245\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	398.221	+	398.221i	0.645416	+	0.645416i	0.951882	−	0.306466i	$-0.0991466\pi$
$617$	398.221	+	398.221i	0.645416	+	0.645416i	−0.306466	+	0.951882i	$0.599147\pi$
$618$		0			0
$619$			838.120i			1.35399i	0.735987	+	0.676995i	$0.236718\pi$
$619$			838.120i			1.35399i	−0.735987	+	0.676995i	$0.763282\pi$
$620$		0			0
$621$	−137.394			−0.221246
$622$		0			0
$623$	521.535	−	521.535i	0.837134	−	0.837134i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−44.0408	−	44.0408i	−0.0702405	−	0.0702405i
$628$		0			0
$629$		−	329.455i		−	0.523776i
$630$		0			0
$631$	−149.980			−0.237686			−0.118843	−	0.992913i	$-0.537918\pi$
$631$	−149.980			−0.237686			−0.118843	+	0.992913i	$0.537918\pi$
$632$		0			0
$633$	233.616	−	233.616i	0.369062	−	0.369062i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	743.586	+	743.586i	1.16732	+	1.16732i
$638$		0			0
$639$			77.3939i			0.121117i
$640$		0			0
$641$	−378.243			−0.590082			−0.295041	−	0.955485i	$-0.595333\pi$
$641$	−378.243			−0.590082			−0.295041	+	0.955485i	$0.595333\pi$
$642$		0			0
$643$	−285.526	+	285.526i	−0.444052	+	0.444052i	−0.893371	−	0.449319i	$-0.851667\pi$
$643$	−285.526	+	285.526i	−0.444052	+	0.444052i	0.449319	+	0.893371i	$0.351667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−360.677	−	360.677i	−0.557460	−	0.557460i	0.371124	−	0.928583i	$-0.378973\pi$
$647$	−360.677	−	360.677i	−0.557460	−	0.557460i	−0.928583	+	0.371124i	$0.878973\pi$
$648$		0			0
$649$			115.959i			0.178674i
$650$		0			0
$651$	8.80816			0.0135302
$652$		0			0
$653$	−547.838	+	547.838i	−0.838955	+	0.838955i	−0.988721	−	0.149766i	$-0.952148\pi$
$653$	−547.838	+	547.838i	−0.838955	+	0.838955i	0.149766	+	0.988721i	$0.452148\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−170.394	−	170.394i	−0.259351	−	0.259351i
$658$		0			0
$659$		−	25.5755i		−	0.0388096i	−0.999812	−	0.0194048i	$-0.993823\pi$
$659$		−	25.5755i		−	0.0388096i	0.999812	−	0.0194048i	$-0.00617712\pi$
$660$		0			0
$661$	−824.727			−1.24770			−0.623848	−	0.781546i	$-0.714431\pi$
$661$	−824.727			−1.24770			−0.623848	+	0.781546i	$0.714431\pi$
$662$		0			0
$663$	101.591	−	101.591i	0.153230	−	0.153230i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	115.959	+	115.959i	0.173852	+	0.173852i
$668$		0			0
$669$		−	40.8490i		−	0.0610598i
$670$		0			0
$671$	366.384			0.546026
$672$		0			0
$673$	−902.857	+	902.857i	−1.34154	+	1.34154i	−0.447014	+	0.894527i	$0.647513\pi$
$673$	−902.857	+	902.857i	−1.34154	+	1.34154i	−0.894527	+	0.447014i	$0.852487\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−688.160	−	688.160i	−1.01648	−	1.01648i	−0.999862	−	0.0166229i	$-0.994709\pi$
$677$	−688.160	−	688.160i	−1.01648	−	1.01648i	−0.0166229	−	0.999862i	$-0.505291\pi$
$678$		0			0
$679$		−	284.586i		−	0.419125i
$680$		0			0
$681$	103.051			0.151323
$682$		0			0
$683$	1.92959	−	1.92959i	0.00282518	−	0.00282518i	−0.705693	−	0.708518i	$-0.749364\pi$
$683$	1.92959	−	1.92959i	0.00282518	−	0.00282518i	0.708518	+	0.705693i	$0.249364\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	213.031	+	213.031i	0.310088	+	0.310088i
$688$		0			0
$689$			939.353i			1.36336i
$690$		0			0
$691$	162.706			0.235465			0.117732	−	0.993045i	$-0.462438\pi$
$691$	162.706			0.235465			0.117732	+	0.993045i	$0.462438\pi$
$692$		0			0
$693$	154.788	−	154.788i	0.223359	−	0.223359i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.9694	+	10.9694i	0.0157380	+	0.0157380i
$698$		0			0
$699$			730.590i			1.04519i
$700$		0			0
$701$	260.222			0.371216			0.185608	−	0.982624i	$-0.440575\pi$
$701$	260.222			0.371216			0.185608	+	0.982624i	$0.440575\pi$
$702$		0			0
$703$	167.455	−	167.455i	0.238201	−	0.238201i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1142.48	+	1142.48i	1.61596	+	1.61596i
$708$		0			0
$709$			151.637i			0.213874i	0.994266	+	0.106937i	$0.0341043\pi$
$709$			151.637i			0.213874i	−0.994266	+	0.106937i	$0.965896\pi$
$710$		0			0
$711$	418.120			0.588074
$712$		0			0
$713$	−7.55510	+	7.55510i	−0.0105962	+	0.0105962i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−45.5755	−	45.5755i	−0.0635642	−	0.0635642i
$718$		0			0
$719$			1281.82i			1.78278i	0.453241	+	0.891388i	$0.350268\pi$
$719$			1281.82i			1.78278i	−0.453241	+	0.891388i	$0.649732\pi$
$720$		0			0
$721$	578.343			0.802140
$722$		0			0
$723$	−203.233	+	203.233i	−0.281096	+	0.281096i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	638.352	+	638.352i	0.878063	+	0.878063i	0.993334	−	0.115271i	$-0.0367736\pi$
$727$	638.352	+	638.352i	0.878063	+	0.878063i	−0.115271	+	0.993334i	$0.536774\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	−445.312			−0.609182
$732$		0			0
$733$	−400.414	+	400.414i	−0.546268	+	0.546268i	−0.925359	−	0.379091i	$-0.876237\pi$
$733$	−400.414	+	400.414i	−0.546268	+	0.546268i	0.379091	+	0.925359i	$0.376237\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−232.445	−	232.445i	−0.315393	−	0.315393i
$738$		0			0
$739$		−	382.647i		−	0.517790i	−0.965905	−	0.258895i	$-0.916642\pi$
$739$		−	382.647i		−	0.517790i	0.965905	−	0.258895i	$-0.0833584\pi$
$740$		0			0
$741$	103.273			0.139370
$742$		0			0
$743$	135.383	−	135.383i	0.182211	−	0.182211i	−0.610108	−	0.792319i	$-0.708874\pi$
$743$	135.383	−	135.383i	0.182211	−	0.182211i	0.792319	+	0.610108i	$0.208874\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−41.1214	−	41.1214i	−0.0550488	−	0.0550488i
$748$		0			0
$749$		−	443.151i		−	0.591657i
$750$		0			0
$751$	571.273			0.760684			0.380342	−	0.924846i	$-0.375806\pi$
$751$	571.273			0.760684			0.380342	+	0.924846i	$0.375806\pi$
$752$		0			0
$753$	312.817	−	312.817i	0.415428	−	0.415428i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	917.908	+	917.908i	1.21256	+	1.21256i	0.970182	+	0.242379i	$0.0779276\pi$
$757$	917.908	+	917.908i	1.21256	+	1.21256i	0.242379	+	0.970182i	$0.422072\pi$
$758$		0			0
$759$			265.535i			0.349848i
$760$		0			0
$761$	−616.261			−0.809804			−0.404902	−	0.914360i	$-0.632694\pi$
$761$	−616.261			−0.809804			−0.404902	+	0.914360i	$0.632694\pi$
$762$		0			0
$763$	−1156.87	+	1156.87i	−1.51621	+	1.51621i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−135.959	−	135.959i	−0.177261	−	0.177261i
$768$		0			0
$769$			154.424i			0.200812i	0.994947	+	0.100406i	$0.0320142\pi$
$769$			154.424i			0.200812i	−0.994947	+	0.100406i	$0.967986\pi$
$770$		0			0
$771$	−662.549			−0.859338
$772$		0			0
$773$	184.323	−	184.323i	0.238452	−	0.238452i	−0.577757	−	0.816209i	$-0.696072\pi$
$773$	184.323	−	184.323i	0.238452	−	0.238452i	0.816209	+	0.577757i	$0.196072\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	588.545	+	588.545i	0.757458	+	0.757458i
$778$		0			0
$779$			11.1510i			0.0143145i
$780$		0			0
$781$	149.576			0.191518
$782$		0			0
$783$	22.7878	−	22.7878i	0.0291031	−	0.0291031i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−784.858	−	784.858i	−0.997278	−	0.997278i	0.00271783	−	0.999996i	$-0.499135\pi$
$787$	−784.858	−	784.858i	−0.997278	−	0.997278i	−0.999996	+	0.00271783i	$0.999135\pi$
$788$		0			0
$789$			3.19184i			0.00404542i
$790$		0			0
$791$	154.969			0.195916
$792$		0			0
$793$	−429.576	+	429.576i	−0.541709	+	0.541709i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	485.191	+	485.191i	0.608771	+	0.608771i	0.942625	−	0.333854i	$-0.108349\pi$
$797$	485.191	+	485.191i	0.608771	+	0.608771i	−0.333854	+	0.942625i	$0.608349\pi$
$798$		0			0
$799$		−	472.182i		−	0.590966i
$800$		0			0
$801$	175.818			0.219499
$802$		0			0
$803$	−329.312	+	329.312i	−0.410102	+	0.410102i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	50.3995	+	50.3995i	0.0624529	+	0.0624529i
$808$		0			0
$809$		−	397.839i		−	0.491766i	−0.969300	−	0.245883i	$-0.920922\pi$
$809$		−	397.839i		−	0.491766i	0.969300	−	0.245883i	$-0.0790779\pi$
$810$		0			0
$811$	1005.49			1.23982			0.619910	−	0.784673i	$-0.287169\pi$
$811$	1005.49			1.23982			0.619910	+	0.784673i	$0.287169\pi$
$812$		0			0
$813$	−593.666	+	593.666i	−0.730217	+	0.730217i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−226.343	−	226.343i	−0.277041	−	0.277041i
$818$		0			0
$819$			362.969i			0.443186i
$820$		0			0
$821$	−101.312			−0.123401			−0.0617005	−	0.998095i	$-0.519652\pi$
$821$	−101.312			−0.123401			−0.0617005	+	0.998095i	$0.519652\pi$
$822$		0			0
$823$	68.2724	−	68.2724i	0.0829556	−	0.0829556i	−0.664411	−	0.747367i	$-0.731318\pi$
$823$	68.2724	−	68.2724i	0.0829556	−	0.0829556i	0.747367	+	0.664411i	$0.231318\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−363.464	−	363.464i	−0.439497	−	0.439497i	0.452345	−	0.891843i	$-0.350587\pi$
$827$	−363.464	−	363.464i	−0.439497	−	0.439497i	−0.891843	+	0.452345i	$0.850587\pi$
$828$		0			0
$829$			891.535i			1.07543i	0.843125	+	0.537717i	$0.180713\pi$
$829$			891.535i			1.07543i	−0.843125	+	0.537717i	$0.819287\pi$
$830$		0			0
$831$	127.348			0.153247
$832$		0			0
$833$	667.352	−	667.352i	0.801143	−	0.801143i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.48469	+	1.48469i	0.00177383	+	0.00177383i
$838$		0			0
$839$			705.090i			0.840393i	0.907433	+	0.420197i	$0.138039\pi$
$839$			705.090i			0.840393i	−0.907433	+	0.420197i	$0.861961\pi$
$840$		0			0
$841$	802.535			0.954262
$842$		0			0
$843$	−297.031	+	297.031i	−0.352349	+	0.352349i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	777.626	+	777.626i	0.918094	+	0.918094i
$848$		0			0
$849$			256.504i			0.302125i
$850$		0			0
$851$	−1009.63			−1.18641
$852$		0			0
$853$	−450.555	+	450.555i	−0.528201	+	0.528201i	−0.920036	−	0.391835i	$-0.871840\pi$
$853$	−450.555	+	450.555i	−0.528201	+	0.528201i	0.391835	+	0.920036i	$0.371840\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−63.5561	−	63.5561i	−0.0741612	−	0.0741612i	0.669053	−	0.743214i	$-0.266700\pi$
$857$	−63.5561	−	63.5561i	−0.0741612	−	0.0741612i	−0.743214	+	0.669053i	$0.766700\pi$
$858$		0			0
$859$			1467.53i			1.70842i	0.519928	+	0.854210i	$0.325959\pi$
$859$			1467.53i			1.70842i	−0.519928	+	0.854210i	$0.674041\pi$
$860$		0			0
$861$	−39.1918			−0.0455190
$862$		0			0
$863$	−294.797	+	294.797i	−0.341596	+	0.341596i	−0.856967	−	0.515371i	$-0.827654\pi$
$863$	−294.797	+	294.797i	−0.341596	+	0.341596i	0.515371	+	0.856967i	$0.327654\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	262.775	+	262.775i	0.303086	+	0.303086i
$868$		0			0
$869$		−	808.082i		−	0.929898i
$870$		0			0
$871$	545.071			0.625800
$872$		0			0
$873$	47.9694	−	47.9694i	0.0549477	−	0.0549477i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−113.102	−	113.102i	−0.128965	−	0.128965i	0.639678	−	0.768643i	$-0.279068\pi$
$877$	−113.102	−	113.102i	−0.128965	−	0.128965i	−0.768643	+	0.639678i	$0.779068\pi$
$878$		0			0
$879$			149.196i			0.169734i
$880$		0			0
$881$	−1370.44			−1.55555			−0.777777	−	0.628540i	$-0.783653\pi$
$881$	−1370.44			−1.55555			−0.777777	+	0.628540i	$0.783653\pi$
$882$		0			0
$883$	175.587	−	175.587i	0.198852	−	0.198852i	−0.600655	−	0.799508i	$-0.705094\pi$
$883$	175.587	−	175.587i	0.198852	−	0.198852i	0.799508	+	0.600655i	$0.205094\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−512.313	−	512.313i	−0.577580	−	0.577580i	0.356656	−	0.934236i	$-0.383917\pi$
$887$	−512.313	−	512.313i	−0.577580	−	0.577580i	−0.934236	+	0.356656i	$0.883917\pi$
$888$		0			0
$889$			895.110i			1.00687i
$890$		0			0
$891$	52.1816			0.0585652
$892$		0			0
$893$	240.000	−	240.000i	0.268757	−	0.268757i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−311.333	−	311.333i	−0.347082	−	0.347082i
$898$		0			0
$899$		−	2.50613i		−	0.00278769i
$900$		0			0
$901$	843.049			0.935681
$902$		0			0
$903$	795.514	−	795.514i	0.880968	−	0.880968i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−922.697	−	922.697i	−1.01731	−	1.01731i	−0.999848	−	0.0174589i	$-0.994442\pi$
$907$	−922.697	−	922.697i	−1.01731	−	1.01731i	−0.0174589	−	0.999848i	$-0.505558\pi$
$908$		0			0
$909$			385.151i			0.423708i
$910$		0			0
$911$	−1338.97			−1.46978			−0.734890	−	0.678186i	$-0.762766\pi$
$911$	−1338.97			−1.46978			−0.734890	+	0.678186i	$0.762766\pi$
$912$		0			0
$913$	−79.4735	+	79.4735i	−0.0870465	+	0.0870465i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1016.28	−	1016.28i	−1.10827	−	1.10827i
$918$		0			0
$919$		−	1371.57i		−	1.49246i	−0.665687	−	0.746231i	$-0.731861\pi$
$919$		−	1371.57i		−	1.49246i	0.665687	−	0.746231i	$-0.268139\pi$
$920$		0			0
$921$	493.090			0.535385
$922$		0			0
$923$	−175.373	+	175.373i	−0.190004	+	0.190004i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	97.4847	+	97.4847i	0.105161	+	0.105161i
$928$		0			0
$929$			218.645i			0.235355i	0.993052	+	0.117678i	$0.0375449\pi$
$929$			218.645i			0.235355i	−0.993052	+	0.117678i	$0.962455\pi$
$930$		0			0
$931$	678.402			0.728681
$932$		0			0
$933$	685.535	−	685.535i	0.734764	−	0.734764i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1127.38	+	1127.38i	1.20318	+	1.20318i	0.973193	+	0.229992i	$0.0738699\pi$
$937$	1127.38	+	1127.38i	1.20318	+	1.20318i	0.229992	+	0.973193i	$0.426130\pi$
$938$		0			0
$939$			229.682i			0.244603i
$940$		0			0
$941$	−588.384			−0.625275			−0.312637	−	0.949873i	$-0.601212\pi$
$941$	−588.384			−0.625275			−0.312637	+	0.949873i	$0.601212\pi$
$942$		0			0
$943$	33.6163	−	33.6163i	0.0356483	−	0.0356483i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−926.879	−	926.879i	−0.978752	−	0.978752i	0.0210265	−	0.999779i	$-0.493307\pi$
$947$	−926.879	−	926.879i	−0.978752	−	0.978752i	−0.999779	+	0.0210265i	$0.993307\pi$
$948$		0			0
$949$		−	772.220i		−	0.813720i
$950$		0			0
$951$	888.742			0.934535
$952$		0			0
$953$	−1271.29	+	1271.29i	−1.33399	+	1.33399i	−0.432220	+	0.901768i	$0.642270\pi$
$953$	−1271.29	+	1271.29i	−1.33399	+	1.33399i	−0.901768	+	0.432220i	$0.857730\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−44.0408	−	44.0408i	−0.0460197	−	0.0460197i
$958$		0			0
$959$			286.565i			0.298817i
$960$		0			0
$961$	−960.837			−0.999830
$962$		0			0
$963$	74.6969	−	74.6969i	0.0775669	−	0.0775669i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	753.121	+	753.121i	0.778823	+	0.778823i	0.979631	−	0.200808i	$-0.0643567\pi$
$967$	753.121	+	753.121i	0.778823	+	0.778823i	−0.200808	+	0.979631i	$0.564357\pi$
$968$		0			0
$969$		−	92.6857i		−	0.0956509i
$970$		0			0
$971$	−1803.86			−1.85773			−0.928865	−	0.370419i	$-0.879214\pi$
$971$	−1803.86			−1.85773			−0.928865	+	0.370419i	$0.879214\pi$
$972$		0			0
$973$	656.727	−	656.727i	0.674950	−	0.674950i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−223.838	−	223.838i	−0.229107	−	0.229107i	0.583212	−	0.812320i	$-0.301796\pi$
$977$	−223.838	−	223.838i	−0.229107	−	0.229107i	−0.812320	+	0.583212i	$0.801796\pi$
$978$		0			0
$979$		−	339.796i		−	0.347085i
$980$		0			0
$981$	−390.000			−0.397554
$982$		0			0
$983$	−976.536	+	976.536i	−0.993424	+	0.993424i	−0.999979	−	0.00655459i	$-0.997914\pi$
$983$	−976.536	+	976.536i	−0.993424	+	0.993424i	0.00655459	+	0.999979i	$0.497914\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	843.514	+	843.514i	0.854624	+	0.854624i
$988$		0			0
$989$			1364.69i			1.37986i
$990$		0			0
$991$	−1331.03			−1.34312			−0.671558	−	0.740952i	$-0.734375\pi$
$991$	−1331.03			−1.34312			−0.671558	+	0.740952i	$0.734375\pi$
$992$		0			0
$993$	17.1714	−	17.1714i	0.0172925	−	0.0172925i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−852.616	−	852.616i	−0.855182	−	0.855182i	0.135584	−	0.990766i	$-0.456709\pi$
$997$	−852.616	−	852.616i	−0.855182	−	0.855182i	−0.990766	+	0.135584i	$0.956709\pi$
$998$		0			0
$999$			198.409i			0.198607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.3.bg.d.1057.1		4
4.3	odd	2		150.3.f.b.7.2		4
5.2	odd	4		240.3.bg.b.193.2		4
5.3	odd	4	inner	1200.3.bg.d.193.1		4
5.4	even	2		240.3.bg.b.97.2		4
12.11	even	2		450.3.g.j.307.2		4
15.2	even	4		720.3.bh.i.433.1		4
15.14	odd	2		720.3.bh.i.577.1		4
20.3	even	4		150.3.f.b.43.2		4
20.7	even	4		30.3.f.a.13.1	yes	4
20.19	odd	2		30.3.f.a.7.1	✓	4
40.19	odd	2		960.3.bg.e.577.2		4
40.27	even	4		960.3.bg.e.193.2		4
40.29	even	2		960.3.bg.g.577.1		4
40.37	odd	4		960.3.bg.g.193.1		4
60.23	odd	4		450.3.g.j.343.2		4
60.47	odd	4		90.3.g.d.73.1		4
60.59	even	2		90.3.g.d.37.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.1	✓	4	20.19	odd	2
30.3.f.a.13.1	yes	4	20.7	even	4
90.3.g.d.37.1		4	60.59	even	2
90.3.g.d.73.1		4	60.47	odd	4
150.3.f.b.7.2		4	4.3	odd	2
150.3.f.b.43.2		4	20.3	even	4
240.3.bg.b.97.2		4	5.4	even	2
240.3.bg.b.193.2		4	5.2	odd	4
450.3.g.j.307.2		4	12.11	even	2
450.3.g.j.343.2		4	60.23	odd	4
720.3.bh.i.433.1		4	15.2	even	4
720.3.bh.i.577.1		4	15.14	odd	2
960.3.bg.e.193.2		4	40.27	even	4
960.3.bg.e.577.2		4	40.19	odd	2
960.3.bg.g.193.1		4	40.37	odd	4
960.3.bg.g.577.1		4	40.29	even	2
1200.3.bg.d.193.1		4	5.3	odd	4	inner
1200.3.bg.d.1057.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{3} +(-8.89898 - 8.89898i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{3} +(-8.89898 - 8.89898i) q^{7} -3.00000i q^{9} -5.79796 q^{11} +(6.79796 - 6.79796i) q^{13} +(-6.10102 - 6.10102i) q^{17} -6.20204i q^{19} +21.7980 q^{21} +(-18.6969 + 18.6969i) q^{23} +(3.67423 + 3.67423i) q^{27} -6.20204i q^{29} +0.404082 q^{31} +(7.10102 - 7.10102i) q^{33} +(27.0000 + 27.0000i) q^{37} +16.6515i q^{39} -1.79796 q^{41} +(36.4949 - 36.4949i) q^{43} +(38.6969 + 38.6969i) q^{47} +109.384i q^{49} +14.9444 q^{51} +(-69.0908 + 69.0908i) q^{53} +(7.59592 + 7.59592i) q^{57} -20.0000i q^{59} -63.1918 q^{61} +(-26.6969 + 26.6969i) q^{63} +(40.0908 + 40.0908i) q^{67} -45.7980i q^{69} -25.7980 q^{71} +(56.7980 - 56.7980i) q^{73} +(51.5959 + 51.5959i) q^{77} +139.373i q^{79} -9.00000 q^{81} +(13.7071 - 13.7071i) q^{83} +(7.59592 + 7.59592i) q^{87} +58.6061i q^{89} -120.990 q^{91} +(-0.494897 + 0.494897i) q^{93} +(15.9898 + 15.9898i) q^{97} +17.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{7}+O(q^{10}) \) 4 * q - 16 * q^7	\( 4 q - 16 q^{7} + 16 q^{11} - 12 q^{13} - 44 q^{17} + 48 q^{21} - 16 q^{23} + 80 q^{31} + 48 q^{33} + 108 q^{37} + 32 q^{41} + 48 q^{43} + 96 q^{47} - 48 q^{51} - 100 q^{53} - 48 q^{57} - 96 q^{61} - 48 q^{63} - 16 q^{67} - 64 q^{71} + 188 q^{73} + 128 q^{77} - 36 q^{81} + 192 q^{83} - 48 q^{87} - 288 q^{91} + 96 q^{93} - 132 q^{97}+O(q^{100}) \) 4 * q - 16 * q^7 + 16 * q^11 - 12 * q^13 - 44 * q^17 + 48 * q^21 - 16 * q^23 + 80 * q^31 + 48 * q^33 + 108 * q^37 + 32 * q^41 + 48 * q^43 + 96 * q^47 - 48 * q^51 - 100 * q^53 - 48 * q^57 - 96 * q^61 - 48 * q^63 - 16 * q^67 - 64 * q^71 + 188 * q^73 + 128 * q^77 - 36 * q^81 + 192 * q^83 - 48 * q^87 - 288 * q^91 + 96 * q^93 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more