LMFDB - Embedded newform 1800.2.m.d.899.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(899,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1800.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.m (of order $2$, degree $1$, 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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.4
Root			$1.41127 + 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.d.899.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933389 + 1.06244i) q^{2} +(-0.257569 - 1.98335i) q^{4} -1.41421 q^{7} +(2.34760 + 1.57758i) q^{8} +O(q^{10})$	\(q+(-0.933389 + 1.06244i) q^{2} +(-0.257569 - 1.98335i) q^{4} -1.41421 q^{7} +(2.34760 + 1.57758i) q^{8} +2.31934i q^{11} +5.14777 q^{13} +(1.32001 - 1.50252i) q^{14} +(-3.86732 + 1.02170i) q^{16} +5.10495 q^{17} -8.24977 q^{19} +(-2.46417 - 2.16485i) q^{22} +0.969724i q^{23} +(-4.80487 + 5.46921i) q^{26} +(0.364258 + 2.80487i) q^{28} +3.28005 q^{29} -5.10495i q^{31} +(2.52422 - 5.06244i) q^{32} +(-4.76491 + 5.42372i) q^{34} +3.69074 q^{37} +(7.70025 - 8.76491i) q^{38} -4.59587i q^{41} -3.21949i q^{43} +(4.60006 - 0.597391i) q^{44} +(-1.03028 - 0.905130i) q^{46} +9.52982i q^{47} -5.00000 q^{49} +(-1.32591 - 10.2098i) q^{52} +7.21949i q^{53} +(-3.32001 - 2.23104i) q^{56} +(-3.06156 + 3.48486i) q^{58} -0.862313i q^{59} +4.63869i q^{61} +(5.42372 + 4.76491i) q^{62} +(3.02248 + 7.40707i) q^{64} +5.28005i q^{67} +(-1.31488 - 10.1249i) q^{68} +13.2800 q^{71} +12.5601i q^{73} +(-3.44490 + 3.92120i) q^{74} +(2.12489 + 16.3621i) q^{76} -3.28005i q^{77} +8.01901i q^{79} +(4.88285 + 4.28974i) q^{82} +7.38148 q^{83} +(3.42053 + 3.00504i) q^{86} +(-3.65895 + 5.44490i) q^{88} +10.2527i q^{89} -7.28005 q^{91} +(1.92330 - 0.249771i) q^{92} +(-10.1249 - 8.89503i) q^{94} -15.7796i q^{97} +(4.66695 - 5.31221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4}+O(q^{10}) $ 12 * q - 4 * q^4	$ 12 q - 4 q^{4} - 12 q^{16} - 32 q^{19} - 40 q^{26} - 24 q^{29} + 8 q^{34} - 24 q^{44} - 16 q^{46} - 60 q^{49} - 24 q^{56} - 28 q^{64} + 96 q^{71} + 8 q^{74} - 8 q^{76} + 80 q^{86} - 24 q^{91} - 88 q^{94}+O(q^{100}) $ 12 * q - 4 * q^4 - 12 * q^16 - 32 * q^19 - 40 * q^26 - 24 * q^29 + 8 * q^34 - 24 * q^44 - 16 * q^46 - 60 * q^49 - 24 * q^56 - 28 * q^64 + 96 * q^71 + 8 * q^74 - 8 * q^76 + 80 * q^86 - 24 * q^91 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.933389	+	1.06244i	−0.660006	+	0.751260i
$2$	−0.933389	+	1.06244i	−0.660006	+	0.751260i
$3$		0			0
$3$		0			0
$4$	−0.257569	−	1.98335i	−0.128785	−	0.991673i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.41421			−0.534522			−0.267261	−	0.963624i	$-0.586119\pi$
$7$	−1.41421			−0.534522			−0.267261	+	0.963624i	$0.586119\pi$
$8$	2.34760	+	1.57758i	0.830003	+	0.557759i
$9$		0			0
$10$		0			0
$11$			2.31934i			0.699308i	0.936879	+	0.349654i	$0.113701\pi$
$11$			2.31934i			0.699308i	−0.936879	+	0.349654i	$0.886299\pi$
$12$		0			0
$13$	5.14777			1.42773			0.713867	−	0.700281i	$-0.246942\pi$
$13$	5.14777			1.42773			0.713867	+	0.700281i	$0.246942\pi$
$14$	1.32001	−	1.50252i	0.352788	−	0.401566i
$15$		0			0
$16$	−3.86732	+	1.02170i	−0.966829	+	0.255424i
$17$	5.10495			1.23813			0.619067	−	0.785339i	$-0.287511\pi$
$17$	5.10495			1.23813			0.619067	+	0.785339i	$0.287511\pi$
$18$		0			0
$19$	−8.24977			−1.89263			−0.946314	−	0.323250i	$-0.895225\pi$
$19$	−8.24977			−1.89263			−0.946314	+	0.323250i	$0.895225\pi$
$20$		0			0
$21$		0			0
$22$	−2.46417	−	2.16485i	−0.525363	−	0.461548i
$23$			0.969724i			0.202201i	0.994876	+	0.101101i	$0.0322364\pi$
$23$			0.969724i			0.202201i	−0.994876	+	0.101101i	$0.967764\pi$
$24$		0			0
$25$		0			0
$26$	−4.80487	+	5.46921i	−0.942313	+	1.07260i
$27$		0			0
$28$	0.364258	+	2.80487i	0.0688382	+	0.530071i
$29$	3.28005			0.609089			0.304545	−	0.952498i	$-0.401496\pi$
$29$	3.28005			0.609089			0.304545	+	0.952498i	$0.401496\pi$
$30$		0			0
$31$		−	5.10495i		−	0.916877i	−0.888726	−	0.458438i	$-0.848409\pi$
$31$		−	5.10495i		−	0.916877i	0.888726	−	0.458438i	$-0.151591\pi$
$32$	2.52422	−	5.06244i	0.446223	−	0.894922i
$33$		0			0
$34$	−4.76491	+	5.42372i	−0.817175	+	0.930160i
$35$		0			0
$36$		0			0
$37$	3.69074			0.606754			0.303377	−	0.952871i	$-0.401886\pi$
$37$	3.69074			0.606754			0.303377	+	0.952871i	$0.401886\pi$
$38$	7.70025	−	8.76491i	1.24915	−	1.42186i
$39$		0			0
$40$		0			0
$41$		−	4.59587i		−	0.717754i	−0.933385	−	0.358877i	$-0.883160\pi$
$41$		−	4.59587i		−	0.717754i	0.933385	−	0.358877i	$-0.116840\pi$
$42$		0			0
$43$		−	3.21949i		−	0.490968i	−0.969401	−	0.245484i	$-0.921053\pi$
$43$		−	3.21949i		−	0.490968i	0.969401	−	0.245484i	$-0.0789469\pi$
$44$	4.60006	−	0.597391i	0.693485	−	0.0900601i
$45$		0			0
$46$	−1.03028	−	0.905130i	−0.151906	−	0.133454i
$47$			9.52982i			1.39007i	0.718977	+	0.695033i	$0.244610\pi$
$47$			9.52982i			1.39007i	−0.718977	+	0.695033i	$0.755390\pi$
$48$		0			0
$49$	−5.00000			−0.714286
$50$		0			0
$51$		0			0
$52$	−1.32591	−	10.2098i	−0.183870	−	1.41585i
$53$			7.21949i			0.991674i	0.868416	+	0.495837i	$0.165139\pi$
$53$			7.21949i			0.991674i	−0.868416	+	0.495837i	$0.834861\pi$
$54$		0			0
$55$		0			0
$56$	−3.32001	−	2.23104i	−0.443655	−	0.298135i
$57$		0			0
$58$	−3.06156	+	3.48486i	−0.402003	+	0.457585i
$59$		−	0.862313i		−	0.112264i	−0.998423	−	0.0561318i	$-0.982123\pi$
$59$		−	0.862313i		−	0.112264i	0.998423	−	0.0561318i	$-0.0178767\pi$
$60$		0			0
$61$			4.63869i			0.593923i	0.954889	+	0.296961i	$0.0959733\pi$
$61$			4.63869i			0.593923i	−0.954889	+	0.296961i	$0.904027\pi$
$62$	5.42372	+	4.76491i	0.688813	+	0.605144i
$63$		0			0
$64$	3.02248	+	7.40707i	0.377810	+	0.925883i
$65$		0			0
$66$		0			0
$67$			5.28005i			0.645060i	0.946559	+	0.322530i	$0.104533\pi$
$67$			5.28005i			0.645060i	−0.946559	+	0.322530i	$0.895467\pi$
$68$	−1.31488	−	10.1249i	−0.159452	−	1.22782i
$69$		0			0
$70$		0			0
$71$	13.2800			1.57605			0.788026	−	0.615642i	$-0.211103\pi$
$71$	13.2800			1.57605			0.788026	+	0.615642i	$0.211103\pi$
$72$		0			0
$73$			12.5601i			1.47005i	0.678041	+	0.735024i	$0.262829\pi$
$73$			12.5601i			1.47005i	−0.678041	+	0.735024i	$0.737171\pi$
$74$	−3.44490	+	3.92120i	−0.400461	+	0.455830i
$75$		0			0
$76$	2.12489	+	16.3621i	0.243741	+	1.87687i
$77$		−	3.28005i		−	0.373796i
$78$		0			0
$79$			8.01901i			0.902210i	0.892471	+	0.451105i	$0.148970\pi$
$79$			8.01901i			0.902210i	−0.892471	+	0.451105i	$0.851030\pi$
$80$		0			0
$81$		0			0
$82$	4.88285	+	4.28974i	0.539220	+	0.473722i
$83$	7.38148			0.810223			0.405111	−	0.914267i	$-0.367233\pi$
$83$	7.38148			0.810223			0.405111	+	0.914267i	$0.367233\pi$
$84$		0			0
$85$		0			0
$86$	3.42053	+	3.00504i	0.368845	+	0.324042i
$87$		0			0
$88$	−3.65895	+	5.44490i	−0.390046	+	0.580428i
$89$			10.2527i			1.08679i	0.839478	+	0.543393i	$0.182861\pi$
$89$			10.2527i			1.08679i	−0.839478	+	0.543393i	$0.817139\pi$
$90$		0			0
$91$	−7.28005			−0.763156
$92$	1.92330	−	0.249771i	0.200518	−	0.0260404i
$93$		0			0
$94$	−10.1249	−	8.89503i	−1.04430	−	0.917452i
$95$		0			0
$96$		0			0
$97$		−	15.7796i		−	1.60217i	−0.598548	−	0.801087i	$-0.704255\pi$
$97$		−	15.7796i		−	1.60217i	0.598548	−	0.801087i	$-0.295745\pi$
$98$	4.66695	−	5.31221i	0.471433	−	0.536615i
$99$		0			0
$100$		0			0
$101$	16.4390			1.63574			0.817870	−	0.575403i	$-0.195155\pi$
$101$	16.4390			1.63574			0.817870	+	0.575403i	$0.195155\pi$
$102$		0			0
$103$	15.9096			1.56762			0.783809	−	0.621002i	$-0.213274\pi$
$103$	15.9096			1.56762			0.783809	+	0.621002i	$0.213274\pi$
$104$	12.0849	+	8.12102i	1.18502	+	0.796332i
$105$		0			0
$106$	−7.67030	−	6.73860i	−0.745005	−	0.654511i
$107$	2.82843			0.273434			0.136717	−	0.990610i	$-0.456345\pi$
$107$	2.82843			0.273434			0.136717	+	0.990610i	$0.456345\pi$
$108$		0			0
$109$			10.2955i			0.986134i	0.869991	+	0.493067i	$0.164124\pi$
$109$			10.2955i			0.986134i	−0.869991	+	0.493067i	$0.835876\pi$
$110$		0			0
$111$		0			0
$112$	5.46921	−	1.44490i	0.516792	−	0.136530i
$113$	0.466267			0.0438627			0.0219313	−	0.999759i	$-0.493018\pi$
$113$	0.466267			0.0438627			0.0219313	+	0.999759i	$0.493018\pi$
$114$		0			0
$115$		0			0
$116$	−0.844838	−	6.50547i	−0.0784413	−	0.604017i
$117$		0			0
$118$	0.916158	+	0.804874i	0.0843392	+	0.0740946i
$119$	−7.21949			−0.661810
$120$		0			0
$121$	5.62065			0.510968
$122$	−4.92834	−	4.32970i	−0.446191	−	0.391993i
$123$		0			0
$124$	−10.1249	+	1.31488i	−0.909242	+	0.118080i
$125$		0			0
$126$		0			0
$127$	6.71784			0.596112			0.298056	−	0.954548i	$-0.403662\pi$
$127$	6.71784			0.596112			0.298056	+	0.954548i	$0.403662\pi$
$128$	−10.6907	−	3.70247i	−0.944936	−	0.327255i
$129$		0			0
$130$		0			0
$131$			21.1002i			1.84353i	0.387749	+	0.921765i	$0.373253\pi$
$131$			21.1002i			1.84353i	−0.387749	+	0.921765i	$0.626747\pi$
$132$		0			0
$133$	11.6669			1.01165
$134$	−5.60975	−	4.92834i	−0.484608	−	0.425744i
$135$		0			0
$136$	11.9844	+	8.05348i	1.02765	+	0.690580i
$137$	−21.0573			−1.79905			−0.899525	−	0.436869i	$-0.856087\pi$
$137$	−21.0573			−1.79905			−0.899525	+	0.436869i	$0.856087\pi$
$138$		0			0
$139$	2.90917			0.246753			0.123376	−	0.992360i	$-0.460628\pi$
$139$	2.90917			0.246753			0.123376	+	0.992360i	$0.460628\pi$
$140$		0			0
$141$		0			0
$142$	−12.3955	+	14.1093i	−1.04020	+	1.18403i
$143$			11.9394i			0.998427i
$144$		0			0
$145$		0			0
$146$	−13.3444	−	11.7235i	−1.10439	−	0.970240i
$147$		0			0
$148$	−0.950620	−	7.32001i	−0.0781405	−	0.601701i
$149$	11.2800			0.924097			0.462049	−	0.886855i	$-0.347115\pi$
$149$	11.2800			0.924097			0.462049	+	0.886855i	$0.347115\pi$
$150$		0			0
$151$		−	21.7638i		−	1.77111i	−0.464531	−	0.885557i	$-0.653777\pi$
$151$		−	21.7638i		−	1.77111i	0.464531	−	0.885557i	$-0.346223\pi$
$152$	−19.3672	−	13.0147i	−1.57089	−	1.05563i
$153$		0			0
$154$	3.48486	+	3.06156i	0.280818	+	0.246708i
$155$		0			0
$156$		0			0
$157$	8.32943			0.664761			0.332380	−	0.943145i	$-0.392148\pi$
$157$	8.32943			0.664761			0.332380	+	0.943145i	$0.392148\pi$
$158$	−8.51974	−	7.48486i	−0.677794	−	0.595464i
$159$		0			0
$160$		0			0
$161$		−	1.37140i		−	0.108081i
$162$		0			0
$163$			20.4995i			1.60565i	0.596216	+	0.802824i	$0.296670\pi$
$163$			20.4995i			1.60565i	−0.596216	+	0.802824i	$0.703330\pi$
$164$	−9.11520	+	1.18375i	−0.711777	+	0.0924356i
$165$		0			0
$166$	−6.88979	+	7.84240i	−0.534752	+	0.608688i
$167$			6.90917i			0.534648i	0.963607	+	0.267324i	$0.0861394\pi$
$167$			6.90917i			0.534648i	−0.963607	+	0.267324i	$0.913861\pi$
$168$		0			0
$169$	13.4995			1.03843
$170$		0			0
$171$		0			0
$172$	−6.38537	+	0.829242i	−0.486880	+	0.0632291i
$173$			19.2195i			1.46123i	0.682789	+	0.730616i	$0.260767\pi$
$173$			19.2195i			1.46123i	−0.682789	+	0.730616i	$0.739233\pi$
$174$		0			0
$175$		0			0
$176$	−2.36967	−	8.96963i	−0.178620	−	0.676112i
$177$		0			0
$178$	−10.8929	−	9.56978i	−0.816460	−	0.717286i
$179$			12.5293i			0.936480i	0.883601	+	0.468240i	$0.155112\pi$
$179$			12.5293i			0.936480i	−0.883601	+	0.468240i	$0.844888\pi$
$180$		0			0
$181$			3.53489i			0.262746i	0.991333	+	0.131373i	$0.0419386\pi$
$181$			3.53489i			0.262746i	−0.991333	+	0.131373i	$0.958061\pi$
$182$	6.79512	−	7.73463i	0.503688	−	0.573329i
$183$		0			0
$184$	−1.52982	+	2.27653i	−0.112780	+	0.167828i
$185$		0			0
$186$		0			0
$187$			11.8401i			0.865837i
$188$	18.9009	−	2.45459i	1.37849	−	0.179019i
$189$		0			0
$190$		0			0
$191$	−25.1202			−1.81763			−0.908816	−	0.417196i	$-0.863013\pi$
$191$	−25.1202			−1.81763			−0.908816	+	0.417196i	$0.863013\pi$
$192$		0			0
$193$		−	7.77959i		−	0.559987i	−0.960002	−	0.279994i	$-0.909668\pi$
$193$		−	7.77959i		−	0.559987i	0.960002	−	0.279994i	$-0.0903323\pi$
$194$	16.7649	+	14.7285i	1.20365	+	1.05744i
$195$		0			0
$196$	1.28785	+	9.91673i	0.0919889	+	0.708338i
$197$		−	2.49954i		−	0.178085i	−0.996028	−	0.0890425i	$-0.971619\pi$
$197$		−	2.49954i		−	0.178085i	0.996028	−	0.0890425i	$-0.0283807\pi$
$198$		0			0
$199$		−	21.0573i		−	1.49272i	−0.665545	−	0.746358i	$-0.731801\pi$
$199$		−	21.0573i		−	1.49272i	0.665545	−	0.746358i	$-0.268199\pi$
$200$		0			0
$201$		0			0
$202$	−15.3440	+	17.4655i	−1.07960	+	1.22887i
$203$	−4.63869			−0.325572
$204$		0			0
$205$		0			0
$206$	−14.8498	+	16.9030i	−1.03464	+	1.17769i
$207$		0			0
$208$	−19.9081	+	5.25946i	−1.38038	+	0.364678i
$209$		−	19.1341i		−	1.32353i
$210$		0			0
$211$	−16.0294			−1.10351			−0.551753	−	0.834007i	$-0.686041\pi$
$211$	−16.0294			−1.10351			−0.551753	+	0.834007i	$0.686041\pi$
$212$	14.3188	−	1.85952i	0.983416	−	0.127712i
$213$		0			0
$214$	−2.64002	+	3.00504i	−0.180468	+	0.205420i
$215$		0			0
$216$		0			0
$217$			7.21949i			0.490091i
$218$	−10.9384	−	9.60975i	−0.740843	−	0.650854i
$219$		0			0
$220$		0			0
$221$	26.2791			1.76773
$222$		0			0
$223$	0.310412			0.0207868			0.0103934	−	0.999946i	$-0.496692\pi$
$223$	0.310412			0.0207868			0.0103934	+	0.999946i	$0.496692\pi$
$224$	−3.56978	+	7.15938i	−0.238516	+	0.478356i
$225$		0			0
$226$	−0.435208	+	0.495382i	−0.0289496	+	0.0329523i
$227$	−3.84659			−0.255307			−0.127654	−	0.991819i	$-0.540745\pi$
$227$	−3.84659			−0.255307			−0.127654	+	0.991819i	$0.540745\pi$
$228$		0			0
$229$			6.36331i			0.420500i	0.977648	+	0.210250i	$0.0674277\pi$
$229$			6.36331i			0.420500i	−0.977648	+	0.210250i	$0.932572\pi$
$230$		0			0
$231$		0			0
$232$	7.70025	+	5.17454i	0.505546	+	0.339725i
$233$	1.25836			0.0824379			0.0412189	−	0.999150i	$-0.486876\pi$
$233$	1.25836			0.0824379			0.0412189	+	0.999150i	$0.486876\pi$
$234$		0			0
$235$		0			0
$236$	−1.71026	+	0.222105i	−0.111329	+	0.0144578i
$237$		0			0
$238$	6.73860	−	7.67030i	0.436798	−	0.497192i
$239$	−0.499542			−0.0323127			−0.0161563	−	0.999869i	$-0.505143\pi$
$239$	−0.499542			−0.0323127			−0.0161563	+	0.999869i	$0.505143\pi$
$240$		0			0
$241$	6.06055			0.390394			0.195197	−	0.980764i	$-0.437465\pi$
$241$	6.06055			0.390394			0.195197	+	0.980764i	$0.437465\pi$
$242$	−5.24625	+	5.97161i	−0.337242	+	0.383870i
$243$		0			0
$244$	9.20012	−	1.19478i	0.588977	−	0.0764881i
$245$		0			0
$246$		0			0
$247$	−42.4679			−2.70217
$248$	8.05348	−	11.9844i	0.511396	−	0.761010i
$249$		0			0
$250$		0			0
$251$		−	12.0904i		−	0.763139i	−0.924340	−	0.381569i	$-0.875384\pi$
$251$		−	12.0904i		−	0.763139i	0.924340	−	0.381569i	$-0.124616\pi$
$252$		0			0
$253$	−2.24912			−0.141401
$254$	−6.27036	+	7.13732i	−0.393437	+	0.447835i
$255$		0			0
$256$	13.9123	−	7.90245i	0.869517	−	0.493903i
$257$	−11.5539			−0.720712			−0.360356	−	0.932815i	$-0.617345\pi$
$257$	−11.5539			−0.720712			−0.360356	+	0.932815i	$0.617345\pi$
$258$		0			0
$259$	−5.21949			−0.324324
$260$		0			0
$261$		0			0
$262$	−22.4177	−	19.6947i	−1.38497	−	1.21674i
$263$			7.52982i			0.464308i	0.972679	+	0.232154i	$0.0745774\pi$
$263$			7.52982i			0.464308i	−0.972679	+	0.232154i	$0.925423\pi$
$264$		0			0
$265$		0			0
$266$	−10.8898	+	12.3955i	−0.667696	+	0.760014i
$267$		0			0
$268$	10.4722	−	1.35998i	0.639689	−	0.0830738i
$269$	−25.8401			−1.57550			−0.787751	−	0.615994i	$-0.788754\pi$
$269$	−25.8401			−1.57550			−0.787751	+	0.615994i	$0.788754\pi$
$270$		0			0
$271$		−	23.8001i		−	1.44576i	−0.690976	−	0.722878i	$-0.742819\pi$
$271$		−	23.8001i		−	1.44576i	0.690976	−	0.722878i	$-0.257181\pi$
$272$	−19.7425	+	5.21571i	−1.19706	+	0.316249i
$273$		0			0
$274$	19.6547	−	22.3722i	1.18738	−	1.35156i
$275$		0			0
$276$		0			0
$277$	24.1962			1.45381			0.726904	−	0.686739i	$-0.240958\pi$
$277$	24.1962			1.45381			0.726904	+	0.686739i	$0.240958\pi$
$278$	−2.71539	+	3.09083i	−0.162858	+	0.185376i
$279$		0			0
$280$		0			0
$281$		−	8.96696i		−	0.534924i	−0.963568	−	0.267462i	$-0.913815\pi$
$281$		−	8.96696i		−	0.534924i	0.963568	−	0.267462i	$-0.0861850\pi$
$282$		0			0
$283$		−	14.7200i		−	0.875010i	−0.899216	−	0.437505i	$-0.855862\pi$
$283$		−	14.7200i		−	0.875010i	0.899216	−	0.437505i	$-0.144138\pi$
$284$	−3.42053	−	26.3389i	−0.202971	−	1.56293i
$285$		0			0
$286$	−12.6850	−	11.1442i	−0.750079	−	0.658968i
$287$			6.49954i			0.383656i
$288$		0			0
$289$	9.06055			0.532974
$290$		0			0
$291$		0			0
$292$	24.9110	−	3.23509i	1.45781	−	0.189319i
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		0			0
$295$		0			0
$296$	8.66439	+	5.82244i	0.503608	+	0.338422i
$297$		0			0
$298$	−10.5287	+	11.9844i	−0.609910	+	0.694238i
$299$			4.99192i			0.288690i
$300$		0			0
$301$			4.55305i			0.262434i
$302$	23.1228	+	20.3141i	1.33057	+	1.16895i
$303$		0			0
$304$	31.9045	−	8.42876i	1.82985	−	0.483423i
$305$		0			0
$306$		0			0
$307$			10.0606i			0.574186i	0.957903	+	0.287093i	$0.0926889\pi$
$307$			10.0606i			0.574186i	−0.957903	+	0.287093i	$0.907311\pi$
$308$	−6.50547	+	0.844838i	−0.370683	+	0.0481391i
$309$		0			0
$310$		0			0
$311$	11.5005			0.652131			0.326066	−	0.945347i	$-0.394277\pi$
$311$	11.5005			0.652131			0.326066	+	0.945347i	$0.394277\pi$
$312$		0			0
$313$		−	6.65940i		−	0.376412i	−0.982130	−	0.188206i	$-0.939733\pi$
$313$		−	6.65940i		−	0.376412i	0.982130	−	0.188206i	$-0.0602672\pi$
$314$	−7.77460	+	8.84954i	−0.438746	+	0.499408i
$315$		0			0
$316$	15.9045	−	2.06545i	0.894697	−	0.116191i
$317$			4.06055i			0.228063i	0.993477	+	0.114032i	$0.0363765\pi$
$317$			4.06055i			0.228063i	−0.993477	+	0.114032i	$0.963623\pi$
$318$		0			0
$319$			7.60756i			0.425941i
$320$		0			0
$321$		0			0
$322$	1.45703	+	1.28005i	0.0811971	+	0.0713342i
$323$	−42.1147			−2.34332
$324$		0			0
$325$		0			0
$326$	−21.7796	−	19.1341i	−1.20626	−	1.05974i
$327$		0			0
$328$	7.25036	−	10.7893i	0.400334	−	0.595738i
$329$		−	13.4772i		−	0.743022i
$330$		0			0
$331$	−10.3103			−0.566707			−0.283353	−	0.959016i	$-0.591447\pi$
$331$	−10.3103			−0.566707			−0.283353	+	0.959016i	$0.591447\pi$
$332$	−1.90124	−	14.6400i	−0.104344	−	0.803476i
$333$		0			0
$334$	−7.34060	−	6.44895i	−0.401660	−	0.352871i
$335$		0			0
$336$		0			0
$337$		−	2.12110i		−	0.115544i	−0.998330	−	0.0577720i	$-0.981600\pi$
$337$		−	2.12110i		−	0.115544i	0.998330	−	0.0577720i	$-0.0183996\pi$
$338$	−12.6003	+	14.3425i	−0.685367	+	0.780129i
$339$		0			0
$340$		0			0
$341$	11.8401			0.641180
$342$		0			0
$343$	16.9706			0.916324
$344$	5.07901	−	7.55809i	0.273842	−	0.407505i
$345$		0			0
$346$	−20.4196	−	17.9393i	−1.09777	−	0.964421i
$347$	32.6112			1.75066			0.875332	−	0.483523i	$-0.160643\pi$
$347$	32.6112			1.75066			0.875332	+	0.483523i	$0.160643\pi$
$348$		0			0
$349$		−	7.55275i		−	0.404289i	−0.979356	−	0.202145i	$-0.935209\pi$
$349$		−	7.55275i		−	0.404289i	0.979356	−	0.202145i	$-0.0647911\pi$
$350$		0			0
$351$		0			0
$352$	11.7415	+	5.85453i	0.625826	+	0.312047i
$353$	−8.01901			−0.426809			−0.213405	−	0.976964i	$-0.568455\pi$
$353$	−8.01901			−0.426809			−0.213405	+	0.976964i	$0.568455\pi$
$354$		0			0
$355$		0			0
$356$	20.3347	−	2.64078i	1.07774	−	0.139961i
$357$		0			0
$358$	−13.3116	−	11.6947i	−0.703541	−	0.618082i
$359$	3.71904			0.196283			0.0981416	−	0.995172i	$-0.468710\pi$
$359$	3.71904			0.196283			0.0981416	+	0.995172i	$0.468710\pi$
$360$		0			0
$361$	49.0587			2.58204
$362$	−3.75561	−	3.29942i	−0.197391	−	0.173414i
$363$		0			0
$364$	1.87511	+	14.4388i	0.0982827	+	0.756801i
$365$		0			0
$366$		0			0
$367$	14.1850			0.740448			0.370224	−	0.928942i	$-0.379281\pi$
$367$	14.1850			0.740448			0.370224	+	0.928942i	$0.379281\pi$
$368$	−0.990764	−	3.75023i	−0.0516471	−	0.195494i
$369$		0			0
$370$		0			0
$371$		−	10.2099i		−	0.530072i
$372$		0			0
$373$	−35.5955			−1.84307			−0.921533	−	0.388299i	$-0.873063\pi$
$373$	−35.5955			−1.84307			−0.921533	+	0.388299i	$0.873063\pi$
$374$	−12.5795	−	11.0515i	−0.650469	−	0.571457i
$375$		0			0
$376$	−15.0341	+	22.3722i	−0.775322	+	1.15376i
$377$	16.8849			0.869618
$378$		0			0
$379$	9.59037			0.492624			0.246312	−	0.969191i	$-0.420781\pi$
$379$	9.59037			0.492624			0.246312	+	0.969191i	$0.420781\pi$
$380$		0			0
$381$		0			0
$382$	23.4469	−	26.6888i	1.19965	−	1.36552i
$383$			19.5904i			1.00102i	0.865730	+	0.500511i	$0.166854\pi$
$383$			19.5904i			1.00102i	−0.865730	+	0.500511i	$0.833146\pi$
$384$		0			0
$385$		0			0
$386$	8.26537	+	7.26138i	0.420696	+	0.369595i
$387$		0			0
$388$	−31.2964	+	4.06433i	−1.58883	+	0.206335i
$389$	−2.12110			−0.107544			−0.0537721	−	0.998553i	$-0.517124\pi$
$389$	−2.12110			−0.107544			−0.0537721	+	0.998553i	$0.517124\pi$
$390$		0			0
$391$			4.95040i			0.250352i
$392$	−11.7380	−	7.88790i	−0.592859	−	0.398399i
$393$		0			0
$394$	2.65562	+	2.33305i	0.133788	+	0.117537i
$395$		0			0
$396$		0			0
$397$	27.3778			1.37405			0.687027	−	0.726632i	$-0.258915\pi$
$397$	27.3778			1.37405			0.687027	+	0.726632i	$0.258915\pi$
$398$	22.3722	+	19.6547i	1.12142	+	0.985201i
$399$		0			0
$400$		0			0
$401$			2.78561i			0.139107i	0.997578	+	0.0695534i	$0.0221574\pi$
$401$			2.78561i			0.139107i	−0.997578	+	0.0695534i	$0.977843\pi$
$402$		0			0
$403$		−	26.2791i		−	1.30906i
$404$	−4.23417	−	32.6042i	−0.210658	−	1.62212i
$405$		0			0
$406$	4.32970	−	4.92834i	0.214879	−	0.244589i
$407$			8.56009i			0.424308i
$408$		0			0
$409$	−12.4390			−0.615068			−0.307534	−	0.951537i	$-0.599504\pi$
$409$	−12.4390			−0.615068			−0.307534	+	0.951537i	$0.599504\pi$
$410$		0			0
$411$		0			0
$412$	−4.09781	−	31.5542i	−0.201885	−	1.55456i
$413$			1.21949i			0.0600074i
$414$		0			0
$415$		0			0
$416$	12.9941	−	26.0603i	0.637088	−	1.27771i
$417$		0			0
$418$	20.3288	+	17.8595i	0.994316	+	0.873538i
$419$		−	9.34759i		−	0.456660i	−0.973584	−	0.228330i	$-0.926674\pi$
$419$		−	9.34759i		−	0.456660i	0.973584	−	0.228330i	$-0.0733265\pi$
$420$		0			0
$421$			23.3339i			1.13722i	0.822606	+	0.568612i	$0.192519\pi$
$421$			23.3339i			1.13722i	−0.822606	+	0.568612i	$0.807481\pi$
$422$	14.9616	−	17.0303i	0.728321	−	0.829021i
$423$		0			0
$424$	−11.3893	+	16.9485i	−0.553115	+	0.823092i
$425$		0			0
$426$		0			0
$427$		−	6.56009i		−	0.317465i
$428$	−0.728515	−	5.60975i	−0.0352141	−	0.271157i
$429$		0			0
$430$		0			0
$431$	−23.7190			−1.14251			−0.571253	−	0.820774i	$-0.693542\pi$
$431$	−23.7190			−1.14251			−0.571253	+	0.820774i	$0.693542\pi$
$432$		0			0
$433$		−	16.5601i		−	0.795827i	−0.917423	−	0.397914i	$-0.869734\pi$
$433$		−	16.5601i		−	0.795827i	0.917423	−	0.397914i	$-0.130266\pi$
$434$	−7.67030	−	6.73860i	−0.368186	−	0.323463i
$435$		0			0
$436$	20.4196	−	2.65181i	0.977922	−	0.126999i
$437$		−	8.00000i		−	0.382692i
$438$		0			0
$439$		−	32.3711i		−	1.54499i	−0.635023	−	0.772493i	$-0.719009\pi$
$439$		−	32.3711i		−	1.54499i	0.635023	−	0.772493i	$-0.280991\pi$
$440$		0			0
$441$		0			0
$442$	−24.5287	+	27.9201i	−1.16671	+	1.32802i
$443$	30.0945			1.42983			0.714917	−	0.699209i	$-0.246464\pi$
$443$	30.0945			1.42983			0.714917	+	0.699209i	$0.246464\pi$
$444$		0			0
$445$		0			0
$446$	−0.289736	+	0.329795i	−0.0137194	+	0.0156163i
$447$		0			0
$448$	−4.27443	−	10.4752i	−0.201948	−	0.494905i
$449$			4.24264i			0.200223i	0.994976	+	0.100111i	$0.0319199\pi$
$449$			4.24264i			0.200223i	−0.994976	+	0.100111i	$0.968080\pi$
$450$		0			0
$451$	10.6594			0.501932
$452$	−0.120096	−	0.924768i	−0.00564884	−	0.0434974i
$453$		0			0
$454$	3.59037	−	4.08679i	0.168504	−	0.191802i
$455$		0			0
$456$		0			0
$457$		−	26.2186i		−	1.22645i	−0.789907	−	0.613227i	$-0.789871\pi$
$457$		−	26.2186i		−	1.22645i	0.789907	−	0.613227i	$-0.210129\pi$
$458$	−6.76066	−	5.93945i	−0.315905	−	0.277532i
$459$		0			0
$460$		0			0
$461$	−15.4012			−0.717303			−0.358652	−	0.933472i	$-0.616763\pi$
$461$	−15.4012			−0.717303			−0.358652	+	0.933472i	$0.616763\pi$
$462$		0			0
$463$	−25.4130			−1.18104			−0.590522	−	0.807022i	$-0.701078\pi$
$463$	−25.4130			−1.18104			−0.590522	+	0.807022i	$0.701078\pi$
$464$	−12.6850	+	3.35121i	−0.588885	+	0.155576i
$465$		0			0
$466$	−1.17454	+	1.33693i	−0.0544095	+	0.0619323i
$467$	26.1623			1.21065			0.605323	−	0.795980i	$-0.293044\pi$
$467$	26.1623			1.21065			0.605323	+	0.795980i	$0.293044\pi$
$468$		0			0
$469$		−	7.46711i		−	0.344799i
$470$		0			0
$471$		0			0
$472$	1.36037	−	2.02437i	0.0626160	−	0.0931791i
$473$	7.46711			0.343338
$474$		0			0
$475$		0			0
$476$	1.85952	+	14.3188i	0.0852309	+	0.656299i
$477$		0			0
$478$	0.466267	−	0.530734i	0.0213265	−	0.0242752i
$479$	−7.84014			−0.358225			−0.179113	−	0.983829i	$-0.557323\pi$
$479$	−7.84014			−0.358225			−0.179113	+	0.983829i	$0.557323\pi$
$480$		0			0
$481$	18.9991			0.866284
$482$	−5.65685	+	6.43899i	−0.257663	+	0.293288i
$483$		0			0
$484$	−1.44770	−	11.1477i	−0.0658047	−	0.506713i
$485$		0			0
$486$		0			0
$487$	−13.1668			−0.596644			−0.298322	−	0.954465i	$-0.596427\pi$
$487$	−13.1668			−0.596644			−0.298322	+	0.954465i	$0.596427\pi$
$488$	−7.31790	+	10.8898i	−0.331266	+	0.492958i
$489$		0			0
$490$		0			0
$491$			12.8825i			0.581378i	0.956818	+	0.290689i	$0.0938845\pi$
$491$			12.8825i			0.581378i	−0.956818	+	0.290689i	$0.906115\pi$
$492$		0			0
$493$	16.7445			0.754134
$494$	39.6391	−	45.1197i	1.78345	−	2.03003i
$495$		0			0
$496$	5.21571	+	19.7425i	0.234192	+	0.886463i
$497$	−18.7808			−0.842435
$498$		0			0
$499$	12.1287			0.542954			0.271477	−	0.962445i	$-0.412488\pi$
$499$	12.1287			0.542954			0.271477	+	0.962445i	$0.412488\pi$
$500$		0			0
$501$		0			0
$502$	12.8453	+	11.2850i	0.573316	+	0.503676i
$503$		−	29.4087i		−	1.31127i	−0.755078	−	0.655635i	$-0.772401\pi$
$503$		−	29.4087i		−	1.31127i	0.755078	−	0.655635i	$-0.227599\pi$
$504$		0			0
$505$		0			0
$506$	2.09931	−	2.38956i	0.0933256	−	0.106229i
$507$		0			0
$508$	−1.73031	−	13.3238i	−0.0767700	−	0.591148i
$509$	25.5592			1.13289			0.566445	−	0.824099i	$-0.308318\pi$
$509$	25.5592			1.13289			0.566445	+	0.824099i	$0.308318\pi$
$510$		0			0
$511$		−	17.7627i		−	0.785774i
$512$	−4.58967	+	22.1571i	−0.202837	+	0.979213i
$513$		0			0
$514$	10.7843	−	12.2754i	0.475674	−	0.541443i
$515$		0			0
$516$		0			0
$517$	−22.1029			−0.972085
$518$	4.87182	−	5.54541i	0.214055	−	0.243652i
$519$		0			0
$520$		0			0
$521$		−	19.0912i		−	0.836402i	−0.908354	−	0.418201i	$-0.862661\pi$
$521$		−	19.0912i		−	0.836402i	0.908354	−	0.418201i	$-0.137339\pi$
$522$		0			0
$523$		−	8.12110i		−	0.355111i	−0.984111	−	0.177556i	$-0.943181\pi$
$523$		−	8.12110i		−	0.355111i	0.984111	−	0.177556i	$-0.0568189\pi$
$524$	41.8489	−	5.43475i	1.82818	−	0.237418i
$525$		0			0
$526$	−8.00000	−	7.02825i	−0.348817	−	0.306446i
$527$		−	26.0606i		−	1.13522i
$528$		0			0
$529$	22.0596			0.959115
$530$		0			0
$531$		0			0
$532$	−3.00504	−	23.1396i	−0.130285	−	1.00323i
$533$		−	23.6585i		−	1.02476i
$534$		0			0
$535$		0			0
$536$	−8.32970	+	12.3955i	−0.359788	+	0.535402i
$537$		0			0
$538$	24.1189	−	27.4537i	1.03984	−	1.18361i
$539$		−	11.5967i		−	0.499506i
$540$		0			0
$541$			17.5914i			0.756313i	0.925742	+	0.378156i	$0.123442\pi$
$541$			17.5914i			0.756313i	−0.925742	+	0.378156i	$0.876558\pi$
$542$	25.2863	+	22.2148i	1.08614	+	0.954207i
$543$		0			0
$544$	12.8860	−	25.8435i	0.552483	−	1.10803i
$545$		0			0
$546$		0			0
$547$			20.3397i			0.869662i	0.900512	+	0.434831i	$0.143192\pi$
$547$			20.3397i			0.869662i	−0.900512	+	0.434831i	$0.856808\pi$
$548$	5.42372	+	41.7640i	0.231690	+	1.78407i
$549$		0			0
$550$		0			0
$551$	−27.0596			−1.15278
$552$		0			0
$553$		−	11.3406i		−	0.482251i
$554$	−22.5845	+	25.7071i	−0.959522	+	1.09219i
$555$		0			0
$556$	−0.749313	−	5.76989i	−0.0317779	−	0.244698i
$557$		−	25.7796i		−	1.09232i	−0.837682	−	0.546158i	$-0.816090\pi$
$557$		−	25.7796i		−	1.09232i	0.837682	−	0.546158i	$-0.183910\pi$
$558$		0			0
$559$		−	16.5732i		−	0.700973i
$560$		0			0
$561$		0			0
$562$	9.52688	+	8.36967i	0.401867	+	0.353053i
$563$	−2.03633			−0.0858213			−0.0429106	−	0.999079i	$-0.513663\pi$
$563$	−2.03633			−0.0858213			−0.0429106	+	0.999079i	$0.513663\pi$
$564$		0			0
$565$		0			0
$566$	15.6391	+	13.7394i	0.657361	+	0.577512i
$567$		0			0
$568$	31.1763	+	20.9503i	1.30813	+	0.879057i
$569$		−	34.6904i		−	1.45430i	−0.686480	−	0.727149i	$-0.740845\pi$
$569$		−	34.6904i		−	1.45430i	0.686480	−	0.727149i	$-0.259155\pi$
$570$		0			0
$571$	−35.3094			−1.47765			−0.738826	−	0.673896i	$-0.764620\pi$
$571$	−35.3094			−1.47765			−0.738826	+	0.673896i	$0.764620\pi$
$572$	23.6800	−	3.07523i	0.990112	−	0.128582i
$573$		0			0
$574$	−6.90539	−	6.06660i	−0.288225	−	0.253215i
$575$		0			0
$576$		0			0
$577$		−	1.21949i		−	0.0507682i	−0.999678	−	0.0253841i	$-0.991919\pi$
$577$		−	1.21949i		−	0.0507682i	0.999678	−	0.0253841i	$-0.00808088\pi$
$578$	−8.45702	+	9.62632i	−0.351766	+	0.400402i
$579$		0			0
$580$		0			0
$581$	−10.4390			−0.433082
$582$		0			0
$583$	−16.7445			−0.693486
$584$	−19.8146	+	29.4861i	−0.819932	+	1.22014i
$585$		0			0
$586$	6.37466	+	5.60034i	0.263335	+	0.231348i
$587$	−24.1260			−0.995785			−0.497893	−	0.867239i	$-0.665893\pi$
$587$	−24.1260			−0.995785			−0.497893	+	0.867239i	$0.665893\pi$
$588$		0			0
$589$			42.1147i			1.73531i
$590$		0			0
$591$		0			0
$592$	−14.2733	+	3.77082i	−0.586627	+	0.154980i
$593$	8.10465			0.332818			0.166409	−	0.986057i	$-0.446783\pi$
$593$	8.10465			0.332818			0.166409	+	0.986057i	$0.446783\pi$
$594$		0			0
$595$		0			0
$596$	−2.90539	−	22.3722i	−0.119009	−	0.916402i
$597$		0			0
$598$	−5.30362	−	4.65940i	−0.216881	−	0.190537i
$599$	−31.7190			−1.29600			−0.648002	−	0.761638i	$-0.724395\pi$
$599$	−31.7190			−1.29600			−0.648002	+	0.761638i	$0.724395\pi$
$600$		0			0
$601$	−39.4381			−1.60871			−0.804356	−	0.594147i	$-0.797490\pi$
$601$	−39.4381			−1.60871			−0.804356	+	0.594147i	$0.797490\pi$
$602$	−4.83736	−	4.24977i	−0.197156	−	0.173208i
$603$		0			0
$604$	−43.1651	+	5.60568i	−1.75636	+	0.228092i
$605$		0			0
$606$		0			0
$607$	−10.5203			−0.427007			−0.213503	−	0.976942i	$-0.568487\pi$
$607$	−10.5203			−0.427007			−0.213503	+	0.976942i	$0.568487\pi$
$608$	−20.8242	+	41.7640i	−0.844533	+	1.69375i
$609$		0			0
$610$		0			0
$611$			49.0573i			1.98465i
$612$		0			0
$613$	6.25157			0.252499			0.126249	−	0.991999i	$-0.459706\pi$
$613$	6.25157			0.252499			0.126249	+	0.991999i	$0.459706\pi$
$614$	−10.6888	−	9.39041i	−0.431363	−	0.378966i
$615$		0			0
$616$	5.17454	−	7.70025i	0.208488	−	0.310252i
$617$	11.6395			0.468590			0.234295	−	0.972166i	$-0.424722\pi$
$617$	11.6395			0.468590			0.234295	+	0.972166i	$0.424722\pi$
$618$		0			0
$619$	−33.0284			−1.32753			−0.663763	−	0.747943i	$-0.731041\pi$
$619$	−33.0284			−1.32753			−0.663763	+	0.747943i	$0.731041\pi$
$620$		0			0
$621$		0			0
$622$	−10.7344	+	12.2186i	−0.430410	+	0.489920i
$623$		−	14.4995i		−	0.580912i
$624$		0			0
$625$		0			0
$626$	7.07523	+	6.21581i	0.282783	+	0.248434i
$627$		0			0
$628$	−2.14540	−	16.5201i	−0.0856109	−	0.659225i
$629$	18.8411			0.751242
$630$		0			0
$631$			39.7525i			1.58252i	0.611478	+	0.791262i	$0.290575\pi$
$631$			39.7525i			1.58252i	−0.611478	+	0.791262i	$0.709425\pi$
$632$	−12.6506	+	18.8255i	−0.503216	+	0.748837i
$633$		0			0
$634$	−4.31410	−	3.79008i	−0.171335	−	0.150523i
$635$		0			0
$636$		0			0
$637$	−25.7389			−1.01981
$638$	−8.08259	−	7.10081i	−0.319993	−	0.281124i
$639$		0			0
$640$		0			0
$641$		−	37.9577i		−	1.49924i	−0.661869	−	0.749619i	$-0.730237\pi$
$641$		−	37.9577i		−	1.49924i	0.661869	−	0.749619i	$-0.269763\pi$
$642$		0			0
$643$			32.4995i			1.28166i	0.767684	+	0.640828i	$0.221409\pi$
$643$			32.4995i			1.28166i	−0.767684	+	0.640828i	$0.778591\pi$
$644$	−2.71995	+	0.353229i	−0.107181	+	0.0139192i
$645$		0			0
$646$	39.3094	−	44.7445i	1.54661	−	1.76045i
$647$			36.0899i			1.41884i	0.704786	+	0.709420i	$0.251043\pi$
$647$			36.0899i			1.41884i	−0.704786	+	0.709420i	$0.748957\pi$
$648$		0			0
$649$	2.00000			0.0785069
$650$		0			0
$651$		0			0
$652$	40.6577	−	5.28005i	1.59228	−	0.206783i
$653$			4.18166i			0.163641i	0.996647	+	0.0818204i	$0.0260734\pi$
$653$			4.18166i			0.163641i	−0.996647	+	0.0818204i	$0.973927\pi$
$654$		0			0
$655$		0			0
$656$	4.69558	+	17.7737i	0.183332	+	0.693946i
$657$		0			0
$658$	14.3188	+	12.5795i	0.558203	+	0.490399i
$659$		−	16.6434i		−	0.648336i	−0.945999	−	0.324168i	$-0.894916\pi$
$659$		−	16.6434i		−	0.648336i	0.945999	−	0.324168i	$-0.105084\pi$
$660$		0			0
$661$		−	19.7990i		−	0.770091i	−0.922897	−	0.385046i	$-0.874186\pi$
$661$		−	19.7990i		−	0.770091i	0.922897	−	0.385046i	$-0.125814\pi$
$662$	9.62354	−	10.9541i	0.374030	−	0.425744i
$663$		0			0
$664$	17.3288	+	11.6449i	0.672487	+	0.451909i
$665$		0			0
$666$		0			0
$667$			3.18074i			0.123159i
$668$	13.7033	−	1.77959i	0.530196	−	0.0688544i
$669$		0			0
$670$		0			0
$671$	−10.7587			−0.415335
$672$		0			0
$673$			43.9982i			1.69600i	0.529992	+	0.848002i	$0.322195\pi$
$673$			43.9982i			1.69600i	−0.529992	+	0.848002i	$0.677805\pi$
$674$	2.25355	+	1.97982i	0.0868036	+	0.0762597i
$675$		0			0
$676$	−3.47706	−	26.7743i	−0.133733	−	1.02978i
$677$		−	2.49954i		−	0.0960652i	−0.998846	−	0.0480326i	$-0.984705\pi$
$677$		−	2.49954i		−	0.0960652i	0.998846	−	0.0480326i	$-0.0152951\pi$
$678$		0			0
$679$			22.3157i			0.856398i
$680$		0			0
$681$		0			0
$682$	−11.0515	+	12.5795i	−0.423182	+	0.481693i
$683$	23.6456			0.904773			0.452387	−	0.891822i	$-0.350573\pi$
$683$	23.6456			0.904773			0.452387	+	0.891822i	$0.350573\pi$
$684$		0			0
$685$		0			0
$686$	−15.8401	+	18.0303i	−0.604779	+	0.688398i
$687$		0			0
$688$	3.28935	+	12.4508i	0.125405	+	0.474682i
$689$			37.1643i			1.41585i
$690$		0			0
$691$	14.6888			0.558787			0.279393	−	0.960177i	$-0.409867\pi$
$691$	14.6888			0.558787			0.279393	+	0.960177i	$0.409867\pi$
$692$	38.1189	−	4.95035i	1.44906	−	0.188184i
$693$		0			0
$694$	−30.4390	+	34.6476i	−1.15545	+	1.31520i
$695$		0			0
$696$		0			0
$697$		−	23.4617i		−	0.888675i
$698$	8.02436	+	7.04965i	0.303727	+	0.266833i
$699$		0			0
$700$		0			0
$701$	−8.43899			−0.318736			−0.159368	−	0.987219i	$-0.550946\pi$
$701$	−8.43899			−0.318736			−0.159368	+	0.987219i	$0.550946\pi$
$702$		0			0
$703$	−30.4478			−1.14836
$704$	−17.1795	+	7.01016i	−0.647478	+	0.264206i
$705$		0			0
$706$	7.48486	−	8.51974i	0.281696	−	0.320645i
$707$	−23.2482			−0.874340
$708$		0			0
$709$		−	37.3904i		−	1.40423i	−0.712066	−	0.702113i	$-0.752240\pi$
$709$		−	37.3904i		−	1.40423i	0.712066	−	0.702113i	$-0.247760\pi$
$710$		0			0
$711$		0			0
$712$	−16.1745	+	24.0693i	−0.606165	+	0.902036i
$713$	4.95040			0.185394
$714$		0			0
$715$		0			0
$716$	24.8498	−	3.22715i	0.928682	−	0.120604i
$717$		0			0
$718$	−3.47131	+	3.95126i	−0.129548	+	0.147460i
$719$	40.3397			1.50442			0.752208	−	0.658926i	$-0.228989\pi$
$719$	40.3397			1.50442			0.752208	+	0.658926i	$0.228989\pi$
$720$		0			0
$721$	−22.4995			−0.837927
$722$	−45.7909	+	52.1221i	−1.70416	+	1.93978i
$723$		0			0
$724$	7.01090	−	0.910477i	0.260558	−	0.0338376i
$725$		0			0
$726$		0			0
$727$	11.1305			0.412806			0.206403	−	0.978467i	$-0.433824\pi$
$727$	11.1305			0.412806			0.206403	+	0.978467i	$0.433824\pi$
$728$	−17.0907	−	11.4849i	−0.633422	−	0.425657i
$729$		0			0
$730$		0			0
$731$		−	16.4354i		−	0.607884i
$732$		0			0
$733$	−29.8530			−1.10265			−0.551324	−	0.834291i	$-0.685877\pi$
$733$	−29.8530			−1.10265			−0.551324	+	0.834291i	$0.685877\pi$
$734$	−13.2401	+	15.0707i	−0.488700	+	0.556270i
$735$		0			0
$736$	4.90917	+	2.44779i	0.180954	+	0.0902269i
$737$	−12.2462			−0.451096
$738$		0			0
$739$	16.7493			0.616133			0.308067	−	0.951365i	$-0.400318\pi$
$739$	16.7493			0.616133			0.308067	+	0.951365i	$0.400318\pi$
$740$		0			0
$741$		0			0
$742$	10.8474	+	9.52982i	0.398222	+	0.349851i
$743$		−	44.0899i		−	1.61750i	−0.588151	−	0.808751i	$-0.700144\pi$
$743$		−	44.0899i		−	1.61750i	0.588151	−	0.808751i	$-0.299856\pi$
$744$		0			0
$745$		0			0
$746$	33.2245	−	37.8182i	1.21643	−	1.38462i
$747$		0			0
$748$	23.4831	−	3.04965i	0.858627	−	0.111506i
$749$	−4.00000			−0.146157
$750$		0			0
$751$		−	24.9896i		−	0.911883i	−0.890010	−	0.455941i	$-0.849303\pi$
$751$		−	24.9896i		−	0.911883i	0.890010	−	0.455941i	$-0.150697\pi$
$752$	−9.73658	−	36.8548i	−0.355057	−	1.34396i
$753$		0			0
$754$	−15.7602	+	17.9393i	−0.573953	+	0.653310i
$755$		0			0
$756$		0			0
$757$	22.7833			0.828072			0.414036	−	0.910260i	$-0.364119\pi$
$757$	22.7833			0.828072			0.414036	+	0.910260i	$0.364119\pi$
$758$	−8.95155	+	10.1892i	−0.325135	+	0.370089i
$759$		0			0
$760$		0			0
$761$			30.4049i			1.10218i	0.834446	+	0.551089i	$0.185788\pi$
$761$			30.4049i			1.10218i	−0.834446	+	0.551089i	$0.814212\pi$
$762$		0			0
$763$		−	14.5601i		−	0.527111i
$764$	6.47018	+	49.8220i	0.234083	+	1.80250i
$765$		0			0
$766$	−20.8136	−	18.2854i	−0.752028	−	0.660680i
$767$		−	4.43899i		−	0.160283i
$768$		0			0
$769$	10.3179			0.372072			0.186036	−	0.982543i	$-0.440436\pi$
$769$	10.3179			0.372072			0.186036	+	0.982543i	$0.440436\pi$
$770$		0			0
$771$		0			0
$772$	−15.4296	+	2.00378i	−0.555324	+	0.0721177i
$773$		−	2.94036i		−	0.105758i	−0.998601	−	0.0528788i	$-0.983160\pi$
$773$		−	2.94036i		−	0.105758i	0.998601	−	0.0528788i	$-0.0168397\pi$
$774$		0			0
$775$		0			0
$776$	24.8936	−	37.0442i	0.893627	−	1.32981i
$777$		0			0
$778$	1.97982	−	2.25355i	0.0709798	−	0.0807937i
$779$			37.9149i			1.35844i
$780$		0			0
$781$			30.8010i			1.10215i
$782$	−5.25951	−	4.62065i	−0.188080	−	0.165234i
$783$		0			0
$784$	19.3366	−	5.10848i	0.690592	−	0.182446i
$785$		0			0
$786$		0			0
$787$		−	25.2413i		−	0.899755i	−0.893090	−	0.449877i	$-0.851468\pi$
$787$		−	25.2413i		−	0.899755i	0.893090	−	0.449877i	$-0.148532\pi$
$788$	−4.95745	+	0.643805i	−0.176602	+	0.0229346i
$789$		0			0
$790$		0			0
$791$	−0.659401			−0.0234456
$792$		0			0
$793$			23.8789i			0.847964i
$794$	−25.5542	+	29.0874i	−0.906884	+	1.03227i
$795$		0			0
$796$	−41.7640	+	5.42372i	−1.48029	+	0.192239i
$797$		−	13.7796i		−	0.488098i	−0.969763	−	0.244049i	$-0.921524\pi$
$797$		−	13.7796i		−	0.488098i	0.969763	−	0.244049i	$-0.0784758\pi$
$798$		0			0
$799$			48.6493i			1.72109i
$800$		0			0
$801$		0			0
$802$	−2.95955	−	2.60006i	−0.104505	−	0.0918113i
$803$	−29.1312			−1.02802
$804$		0			0
$805$		0			0
$806$	27.9201	+	24.5287i	0.983443	+	0.863985i
$807$		0			0
$808$	38.5922	+	25.9338i	1.35767	+	0.912349i
$809$			32.3865i			1.13865i	0.822113	+	0.569324i	$0.192795\pi$
$809$			32.3865i			1.13865i	−0.822113	+	0.569324i	$0.807205\pi$
$810$		0			0
$811$	−12.4702			−0.437887			−0.218944	−	0.975738i	$-0.570261\pi$
$811$	−12.4702			−0.437887			−0.218944	+	0.975738i	$0.570261\pi$
$812$	1.19478	+	9.20012i	0.0419286	+	0.322861i
$813$		0			0
$814$	−9.09461	−	7.98990i	−0.318766	−	0.280046i
$815$		0			0
$816$		0			0
$817$			26.5601i			0.929220i
$818$	11.6104	−	13.2157i	0.405949	−	0.462077i
$819$		0			0
$820$		0			0
$821$	−41.8401			−1.46023			−0.730115	−	0.683324i	$-0.760534\pi$
$821$	−41.8401			−1.46023			−0.730115	+	0.683324i	$0.760534\pi$
$822$		0			0
$823$	3.39574			0.118368			0.0591840	−	0.998247i	$-0.481150\pi$
$823$	3.39574			0.118368			0.0591840	+	0.998247i	$0.481150\pi$
$824$	37.3494	+	25.0986i	1.30113	+	0.874353i
$825$		0			0
$826$	−1.29564	−	1.13826i	−0.0450812	−	0.0396052i
$827$	−4.38179			−0.152370			−0.0761848	−	0.997094i	$-0.524274\pi$
$827$	−4.38179			−0.152370			−0.0761848	+	0.997094i	$0.524274\pi$
$828$		0			0
$829$		−	45.8757i		−	1.59333i	−0.604423	−	0.796664i	$-0.706596\pi$
$829$		−	45.8757i		−	1.59333i	0.604423	−	0.796664i	$-0.293404\pi$
$830$		0			0
$831$		0			0
$832$	15.5590	+	38.1299i	0.539412	+	1.32192i
$833$	−25.5248			−0.884381
$834$		0			0
$835$		0			0
$836$	−37.9494	+	4.92834i	−1.31251	+	0.170450i
$837$		0			0
$838$	9.93128	+	8.72494i	0.343070	+	0.301398i
$839$	−24.8392			−0.857545			−0.428773	−	0.903412i	$-0.641054\pi$
$839$	−24.8392			−0.857545			−0.428773	+	0.903412i	$0.641054\pi$
$840$		0			0
$841$	−18.2413			−0.629010
$842$	−24.7909	−	21.7796i	−0.854351	−	0.750574i
$843$		0			0
$844$	4.12867	+	31.7918i	0.142115	+	1.09432i
$845$		0			0
$846$		0			0
$847$	−7.94879			−0.273124
$848$	−7.37613	−	27.9201i	−0.253297	−	0.958779i
$849$		0			0
$850$		0			0
$851$			3.57900i			0.122687i
$852$		0			0
$853$	−10.0125			−0.342823			−0.171411	−	0.985200i	$-0.554833\pi$
$853$	−10.0125			−0.342823			−0.171411	+	0.985200i	$0.554833\pi$
$854$	6.96972	+	6.12312i	0.238499	+	0.209529i
$855$		0			0
$856$	6.64002	+	4.46207i	0.226951	+	0.152510i
$857$	26.6286			0.909615			0.454807	−	0.890590i	$-0.349708\pi$
$857$	26.6286			0.909615			0.454807	+	0.890590i	$0.349708\pi$
$858$		0			0
$859$	−14.4096			−0.491650			−0.245825	−	0.969314i	$-0.579059\pi$
$859$	−14.4096			−0.491650			−0.245825	+	0.969314i	$0.579059\pi$
$860$		0			0
$861$		0			0
$862$	22.1391	−	25.2001i	0.754061	−	0.858319i
$863$		−	49.5280i		−	1.68595i	−0.537951	−	0.842976i	$-0.680801\pi$
$863$		−	49.5280i		−	1.68595i	0.537951	−	0.842976i	$-0.319199\pi$
$864$		0			0
$865$		0			0
$866$	17.5942	+	15.4570i	0.597874	+	0.525251i
$867$		0			0
$868$	14.3188	−	1.85952i	0.486010	−	0.0631162i
$869$	−18.5988			−0.630923
$870$		0			0
$871$			27.1805i			0.920975i
$872$	−16.2420	+	24.1698i	−0.550025	+	0.818494i
$873$		0			0
$874$	8.49954	+	7.46711i	0.287501	+	0.252579i
$875$		0			0
$876$		0			0
$877$	−23.0924			−0.779775			−0.389887	−	0.920863i	$-0.627486\pi$
$877$	−23.0924			−0.779775			−0.389887	+	0.920863i	$0.627486\pi$
$878$	34.3924	+	30.2148i	1.16069	+	1.01970i
$879$		0			0
$880$		0			0
$881$			24.3092i			0.818999i	0.912310	+	0.409499i	$0.134297\pi$
$881$			24.3092i			0.818999i	−0.912310	+	0.409499i	$0.865703\pi$
$882$		0			0
$883$			14.0606i			0.473175i	0.971610	+	0.236588i	$0.0760290\pi$
$883$			14.0606i			0.473175i	−0.971610	+	0.236588i	$0.923971\pi$
$884$	−6.76869	−	52.1206i	−0.227656	−	1.75301i
$885$		0			0
$886$	−28.0899	+	31.9737i	−0.943699	+	1.07418i
$887$		−	5.96881i		−	0.200413i	−0.994967	−	0.100206i	$-0.968050\pi$
$887$		−	5.96881i		−	0.200413i	0.994967	−	0.100206i	$-0.0319503\pi$
$888$		0			0
$889$	−9.50046			−0.318635
$890$		0			0
$891$		0			0
$892$	−0.0799526	−	0.615655i	−0.00267701	−	0.0206137i
$893$		−	78.6188i		−	2.63088i
$894$		0			0
$895$		0			0
$896$	15.1190	+	5.23608i	0.505090	+	0.174925i
$897$		0			0
$898$	−4.50756	−	3.96004i	−0.150419	−	0.132148i
$899$		−	16.7445i		−	0.558460i
$900$		0			0
$901$			36.8552i			1.22782i
$902$	−9.94937	+	11.3250i	−0.331278	+	0.377081i
$903$		0			0
$904$	1.09461	+	0.735574i	0.0364062	+	0.0244648i
$905$		0			0
$906$		0			0
$907$		−	7.96125i		−	0.264349i	−0.991226	−	0.132174i	$-0.957804\pi$
$907$		−	7.96125i		−	0.264349i	0.991226	−	0.132174i	$-0.0421959\pi$
$908$	0.990764	+	7.62912i	0.0328796	+	0.253181i
$909$		0			0
$910$		0			0
$911$	40.4995			1.34181			0.670905	−	0.741543i	$-0.265906\pi$
$911$	40.4995			1.34181			0.670905	+	0.741543i	$0.265906\pi$
$912$		0			0
$913$			17.1202i			0.566596i
$914$	27.8557	+	24.4721i	0.921386	+	0.809466i
$915$		0			0
$916$	12.6206	−	1.63899i	0.416998	−	0.0541538i
$917$		−	29.8401i		−	0.985408i
$918$		0			0
$919$			11.6395i			0.383953i	0.981400	+	0.191976i	$0.0614897\pi$
$919$			11.6395i			0.383953i	−0.981400	+	0.191976i	$0.938510\pi$
$920$		0			0
$921$		0			0
$922$	14.3753	−	16.3628i	0.473424	−	0.538881i
$923$	68.3626			2.25018
$924$		0			0
$925$		0			0
$926$	23.7202	−	26.9999i	0.779496	−	0.887271i
$927$		0			0
$928$	8.27955	−	16.6050i	0.271790	−	0.545087i
$929$			23.9560i			0.785971i	0.919545	+	0.392985i	$0.128558\pi$
$929$			23.9560i			0.785971i	−0.919545	+	0.392985i	$0.871442\pi$
$930$		0			0
$931$	41.2489			1.35188
$932$	−0.324114	−	2.49576i	−0.0106167	−	0.0817514i
$933$		0			0
$934$	−24.4196	+	27.7959i	−0.799034	+	0.909511i
$935$		0			0
$936$		0			0
$937$			10.1211i			0.330642i	0.986240	+	0.165321i	$0.0528660\pi$
$937$			10.1211i			0.330642i	−0.986240	+	0.165321i	$0.947134\pi$
$938$	7.93338	+	6.96972i	0.259034	+	0.227570i
$939$		0			0
$940$		0			0
$941$	−28.3179			−0.923137			−0.461568	−	0.887105i	$-0.652713\pi$
$941$	−28.3179			−0.923137			−0.461568	+	0.887105i	$0.652713\pi$
$942$		0			0
$943$	4.45673			0.145131
$944$	0.881022	+	3.33484i	0.0286748	+	0.108540i
$945$		0			0
$946$	−6.96972	+	7.93338i	−0.226605	+	0.257936i
$947$	−53.4284			−1.73619			−0.868095	−	0.496398i	$-0.834656\pi$
$947$	−53.4284			−1.73619			−0.868095	+	0.496398i	$0.834656\pi$
$948$		0			0
$949$			64.6565i			2.09884i
$950$		0			0
$951$		0			0
$952$	−16.9485	−	11.3893i	−0.549304	−	0.369130i
$953$	4.48413			0.145255			0.0726276	−	0.997359i	$-0.476862\pi$
$953$	4.48413			0.145255			0.0726276	+	0.997359i	$0.476862\pi$
$954$		0			0
$955$		0			0
$956$	0.128666	+	0.990764i	0.00416137	+	0.0320436i
$957$		0			0
$958$	7.31790	−	8.32970i	0.236431	−	0.269120i
$959$	29.7796			0.961633
$960$		0			0
$961$	4.93945			0.159337
$962$	−17.7335	+	20.1854i	−0.571752	+	0.650805i
$963$		0			0
$964$	−1.56101	−	12.0202i	−0.0502768	−	0.387144i
$965$		0			0
$966$		0			0
$967$	−13.5748			−0.436537			−0.218268	−	0.975889i	$-0.570041\pi$
$967$	−13.5748			−0.436537			−0.218268	+	0.975889i	$0.570041\pi$
$968$	13.1950	+	8.86702i	0.424105	+	0.284997i
$969$		0			0
$970$		0			0
$971$		−	54.2907i		−	1.74227i	−0.491042	−	0.871136i	$-0.663384\pi$
$971$		−	54.2907i		−	1.74227i	0.491042	−	0.871136i	$-0.336616\pi$
$972$		0			0
$973$	−4.11419			−0.131895
$974$	12.2897	−	13.9890i	0.393789	−	0.448235i
$975$		0			0
$976$	−4.73933	−	17.9393i	−0.151702	−	0.574222i
$977$	15.7122			0.502678			0.251339	−	0.967899i	$-0.419129\pi$
$977$	15.7122			0.502678			0.251339	+	0.967899i	$0.419129\pi$
$978$		0			0
$979$	−23.7796			−0.759999
$980$		0			0
$981$		0			0
$982$	−13.6869	−	12.0244i	−0.436766	−	0.383713i
$983$			13.4087i			0.427672i	0.976870	+	0.213836i	$0.0685957\pi$
$983$			13.4087i			0.427672i	−0.976870	+	0.213836i	$0.931404\pi$
$984$		0			0
$985$		0			0
$986$	−15.6291	+	17.7901i	−0.497733	+	0.566551i
$987$		0			0
$988$	10.9384	+	84.2286i	0.347998	+	2.67967i
$989$	3.12202			0.0992745
$990$		0			0
$991$			18.1433i			0.576341i	0.957579	+	0.288170i	$0.0930469\pi$
$991$			18.1433i			0.576341i	−0.957579	+	0.288170i	$0.906953\pi$
$992$	−25.8435	−	12.8860i	−0.820533	−	0.409131i
$993$		0			0
$994$	17.5298	−	19.9535i	0.556012	−	0.632888i
$995$		0			0
$996$		0			0
$997$	−28.7385			−0.910159			−0.455079	−	0.890451i	$-0.650389\pi$
$997$	−28.7385			−0.910159			−0.455079	+	0.890451i	$0.650389\pi$
$998$	−11.3208	+	12.8860i	−0.358353	+	0.407900i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.m.d.899.4		12
3.2	odd	2		1800.2.m.e.899.9		12
4.3	odd	2		7200.2.m.d.3599.8		12
5.2	odd	4		1800.2.b.e.251.1		6
5.3	odd	4		360.2.b.c.251.6	yes	6
5.4	even	2	inner	1800.2.m.d.899.9		12
8.3	odd	2		1800.2.m.e.899.3		12
8.5	even	2		7200.2.m.e.3599.2		12
12.11	even	2		7200.2.m.e.3599.11		12
15.2	even	4		1800.2.b.d.251.6		6
15.8	even	4		360.2.b.d.251.1	yes	6
15.14	odd	2		1800.2.m.e.899.4		12
20.3	even	4		1440.2.b.c.431.1		6
20.7	even	4		7200.2.b.d.4751.4		6
20.19	odd	2		7200.2.m.d.3599.2		12
24.5	odd	2		7200.2.m.d.3599.5		12
24.11	even	2	inner	1800.2.m.d.899.10		12
40.3	even	4		360.2.b.d.251.2	yes	6
40.13	odd	4		1440.2.b.d.431.4		6
40.19	odd	2		1800.2.m.e.899.10		12
40.27	even	4		1800.2.b.d.251.5		6
40.29	even	2		7200.2.m.e.3599.8		12
40.37	odd	4		7200.2.b.e.4751.1		6
60.23	odd	4		1440.2.b.d.431.3		6
60.47	odd	4		7200.2.b.e.4751.6		6
60.59	even	2		7200.2.m.e.3599.5		12
120.29	odd	2		7200.2.m.d.3599.11		12
120.53	even	4		1440.2.b.c.431.6		6
120.59	even	2	inner	1800.2.m.d.899.3		12
120.77	even	4		7200.2.b.d.4751.3		6
120.83	odd	4		360.2.b.c.251.5	✓	6
120.107	odd	4		1800.2.b.e.251.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.b.c.251.5	✓	6	120.83	odd	4
360.2.b.c.251.6	yes	6	5.3	odd	4
360.2.b.d.251.1	yes	6	15.8	even	4
360.2.b.d.251.2	yes	6	40.3	even	4
1440.2.b.c.431.1		6	20.3	even	4
1440.2.b.c.431.6		6	120.53	even	4
1440.2.b.d.431.3		6	60.23	odd	4
1440.2.b.d.431.4		6	40.13	odd	4
1800.2.b.d.251.5		6	40.27	even	4
1800.2.b.d.251.6		6	15.2	even	4
1800.2.b.e.251.1		6	5.2	odd	4
1800.2.b.e.251.2		6	120.107	odd	4
1800.2.m.d.899.3		12	120.59	even	2	inner
1800.2.m.d.899.4		12	1.1	even	1	trivial
1800.2.m.d.899.9		12	5.4	even	2	inner
1800.2.m.d.899.10		12	24.11	even	2	inner
1800.2.m.e.899.3		12	8.3	odd	2
1800.2.m.e.899.4		12	15.14	odd	2
1800.2.m.e.899.9		12	3.2	odd	2
1800.2.m.e.899.10		12	40.19	odd	2
7200.2.b.d.4751.3		6	120.77	even	4
7200.2.b.d.4751.4		6	20.7	even	4
7200.2.b.e.4751.1		6	40.37	odd	4
7200.2.b.e.4751.6		6	60.47	odd	4
7200.2.m.d.3599.2		12	20.19	odd	2
7200.2.m.d.3599.5		12	24.5	odd	2
7200.2.m.d.3599.8		12	4.3	odd	2
7200.2.m.d.3599.11		12	120.29	odd	2
7200.2.m.e.3599.2		12	8.5	even	2
7200.2.m.e.3599.5		12	60.59	even	2
7200.2.m.e.3599.8		12	40.29	even	2
7200.2.m.e.3599.11		12	12.11	even	2

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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.933389 + 1.06244i) q^{2} +(-0.257569 - 1.98335i) q^{4} -1.41421 q^{7} +(2.34760 + 1.57758i) q^{8} +O(q^{10})\)	\(q+(-0.933389 + 1.06244i) q^{2} +(-0.257569 - 1.98335i) q^{4} -1.41421 q^{7} +(2.34760 + 1.57758i) q^{8} +2.31934i q^{11} +5.14777 q^{13} +(1.32001 - 1.50252i) q^{14} +(-3.86732 + 1.02170i) q^{16} +5.10495 q^{17} -8.24977 q^{19} +(-2.46417 - 2.16485i) q^{22} +0.969724i q^{23} +(-4.80487 + 5.46921i) q^{26} +(0.364258 + 2.80487i) q^{28} +3.28005 q^{29} -5.10495i q^{31} +(2.52422 - 5.06244i) q^{32} +(-4.76491 + 5.42372i) q^{34} +3.69074 q^{37} +(7.70025 - 8.76491i) q^{38} -4.59587i q^{41} -3.21949i q^{43} +(4.60006 - 0.597391i) q^{44} +(-1.03028 - 0.905130i) q^{46} +9.52982i q^{47} -5.00000 q^{49} +(-1.32591 - 10.2098i) q^{52} +7.21949i q^{53} +(-3.32001 - 2.23104i) q^{56} +(-3.06156 + 3.48486i) q^{58} -0.862313i q^{59} +4.63869i q^{61} +(5.42372 + 4.76491i) q^{62} +(3.02248 + 7.40707i) q^{64} +5.28005i q^{67} +(-1.31488 - 10.1249i) q^{68} +13.2800 q^{71} +12.5601i q^{73} +(-3.44490 + 3.92120i) q^{74} +(2.12489 + 16.3621i) q^{76} -3.28005i q^{77} +8.01901i q^{79} +(4.88285 + 4.28974i) q^{82} +7.38148 q^{83} +(3.42053 + 3.00504i) q^{86} +(-3.65895 + 5.44490i) q^{88} +10.2527i q^{89} -7.28005 q^{91} +(1.92330 - 0.249771i) q^{92} +(-10.1249 - 8.89503i) q^{94} -15.7796i q^{97} +(4.66695 - 5.31221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4}+O(q^{10}) \) 12 * q - 4 * q^4	\( 12 q - 4 q^{4} - 12 q^{16} - 32 q^{19} - 40 q^{26} - 24 q^{29} + 8 q^{34} - 24 q^{44} - 16 q^{46} - 60 q^{49} - 24 q^{56} - 28 q^{64} + 96 q^{71} + 8 q^{74} - 8 q^{76} + 80 q^{86} - 24 q^{91} - 88 q^{94}+O(q^{100}) \) 12 * q - 4 * q^4 - 12 * q^16 - 32 * q^19 - 40 * q^26 - 24 * q^29 + 8 * q^34 - 24 * q^44 - 16 * q^46 - 60 * q^49 - 24 * q^56 - 28 * q^64 + 96 * q^71 + 8 * q^74 - 8 * q^76 + 80 * q^86 - 24 * q^91 - 88 * q^94

Introduction

L-functions

Modular forms

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