LMFDB - Embedded newform 525.3.h.d.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(76,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.h (of order $2$, degree $1$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.1
Root			$1.31896 - 2.28450i$ of defining polynomial
Character	$\chi$	$=$	525.76
Dual form			525.3.h.d.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +6.06857i q^{6} +(6.69736 - 2.03600i) q^{7} -14.9812 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +6.06857i q^{6} +(6.69736 - 2.03600i) q^{7} -14.9812 q^{8} -3.00000 q^{9} -2.03112 q^{11} -14.3342i q^{12} +18.0174i q^{13} +(-23.4655 + 7.13352i) q^{14} +19.3861 q^{16} -1.07289i q^{17} +10.5111 q^{18} +28.7852i q^{19} +(-3.52646 - 11.6002i) q^{21} +7.11640 q^{22} -24.8710 q^{23} +25.9482i q^{24} -63.1275i q^{26} +5.19615i q^{27} +(55.4263 - 16.8496i) q^{28} -38.4300 q^{29} -44.0899i q^{31} -7.99812 q^{32} +3.51800i q^{33} +3.75906i q^{34} -24.8275 q^{36} -37.2832 q^{37} -100.855i q^{38} +31.2071 q^{39} +49.9206i q^{41} +(12.3556 + 40.6434i) q^{42} +9.58871 q^{43} -16.8092 q^{44} +87.1402 q^{46} -55.6978i q^{47} -33.5777i q^{48} +(40.7094 - 27.2717i) q^{49} -1.85829 q^{51} +149.109i q^{52} -57.4656 q^{53} -18.2057i q^{54} +(-100.335 + 30.5018i) q^{56} +49.8575 q^{57} +134.647 q^{58} +101.697i q^{59} -31.9530i q^{61} +154.477i q^{62} +(-20.0921 + 6.10801i) q^{63} -49.5215 q^{64} -12.3260i q^{66} -95.7318 q^{67} -8.87902i q^{68} +43.0778i q^{69} -25.8039 q^{71} +44.9436 q^{72} +95.6803i q^{73} +130.629 q^{74} +238.222i q^{76} +(-13.6031 + 4.13536i) q^{77} -109.340 q^{78} +28.1212 q^{79} +9.00000 q^{81} -174.906i q^{82} +103.374i q^{83} +(-29.1844 - 96.0012i) q^{84} -33.5959 q^{86} +66.5628i q^{87} +30.4286 q^{88} +29.3629i q^{89} +(36.6835 + 120.669i) q^{91} -205.828 q^{92} -76.3659 q^{93} +195.148i q^{94} +13.8531i q^{96} +67.6473i q^{97} +(-142.633 + 95.5515i) q^{98} +6.09335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9	$ 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} - 12 q^{18} + 36 q^{21} + 88 q^{22} + 64 q^{23} - 88 q^{28} + 104 q^{29} + 228 q^{32} - 132 q^{36} - 32 q^{37} - 24 q^{39} + 60 q^{42} - 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 24 q^{51} - 176 q^{53} - 368 q^{56} + 240 q^{57} + 400 q^{58} - 24 q^{63} - 20 q^{64} - 168 q^{67} + 32 q^{71} + 12 q^{72} + 184 q^{74} - 8 q^{77} - 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 400 q^{86} + 536 q^{88} + 24 q^{91} - 192 q^{92} - 48 q^{93} - 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 - 12 * q^18 + 36 * q^21 + 88 * q^22 + 64 * q^23 - 88 * q^28 + 104 * q^29 + 228 * q^32 - 132 * q^36 - 32 * q^37 - 24 * q^39 + 60 * q^42 - 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 24 * q^51 - 176 * q^53 - 368 * q^56 + 240 * q^57 + 400 * q^58 - 24 * q^63 - 20 * q^64 - 168 * q^67 + 32 * q^71 + 12 * q^72 + 184 * q^74 - 8 * q^77 - 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 400 * q^86 + 536 * q^88 + 24 * q^91 - 192 * q^92 - 48 * q^93 - 884 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−3.50369			−1.75184			−0.875922	−	0.482452i	$-0.839746\pi$
$2$	−3.50369			−1.75184			−0.875922	+	0.482452i	$0.839746\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	8.27584			2.06896
$5$		0			0
$5$		0			0
$6$			6.06857i			1.01143i
$7$	6.69736	−	2.03600i	0.956766	−	0.290857i
$7$	6.69736	−	2.03600i	0.956766	−	0.290857i
$8$	−14.9812			−1.87265
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−2.03112			−0.184647			−0.0923235	−	0.995729i	$-0.529429\pi$
$11$	−2.03112			−0.184647			−0.0923235	+	0.995729i	$0.529429\pi$
$12$		−	14.3342i		−	1.19451i
$13$			18.0174i			1.38596i	0.720958	+	0.692978i	$0.243702\pi$
$13$			18.0174i			1.38596i	−0.720958	+	0.692978i	$0.756298\pi$
$14$	−23.4655	+	7.13352i	−1.67611	+	0.509537i
$15$		0			0
$16$	19.3861			1.21163
$17$		−	1.07289i		−	0.0631109i	−0.999502	−	0.0315555i	$-0.989954\pi$
$17$		−	1.07289i		−	0.0631109i	0.999502	−	0.0315555i	$-0.0100461\pi$
$18$	10.5111			0.583948
$19$			28.7852i			1.51501i	0.652828	+	0.757506i	$0.273583\pi$
$19$			28.7852i			1.51501i	−0.652828	+	0.757506i	$0.726417\pi$
$20$		0			0
$21$	−3.52646	−	11.6002i	−0.167927	−	0.552389i
$22$	7.11640			0.323473
$23$	−24.8710			−1.08135			−0.540674	−	0.841232i	$-0.681831\pi$
$23$	−24.8710			−1.08135			−0.540674	+	0.841232i	$0.681831\pi$
$24$			25.9482i			1.08117i
$25$		0			0
$26$		−	63.1275i		−	2.42798i
$27$			5.19615i			0.192450i
$28$	55.4263	−	16.8496i	1.97951	−	0.601772i
$29$	−38.4300			−1.32517			−0.662587	−	0.748985i	$-0.730542\pi$
$29$	−38.4300			−1.32517			−0.662587	+	0.748985i	$0.730542\pi$
$30$		0			0
$31$		−	44.0899i		−	1.42225i	−0.703064	−	0.711127i	$-0.748185\pi$
$31$		−	44.0899i		−	1.42225i	0.703064	−	0.711127i	$-0.251815\pi$
$32$	−7.99812			−0.249941
$33$			3.51800i			0.106606i
$34$			3.75906i			0.110561i
$35$		0			0
$36$	−24.8275			−0.689653
$37$	−37.2832			−1.00765			−0.503827	−	0.863804i	$-0.668075\pi$
$37$	−37.2832			−1.00765			−0.503827	+	0.863804i	$0.668075\pi$
$38$		−	100.855i		−	2.65407i
$39$	31.2071			0.800182
$40$		0			0
$41$			49.9206i			1.21758i	0.793333	+	0.608788i	$0.208344\pi$
$41$			49.9206i			1.21758i	−0.793333	+	0.608788i	$0.791656\pi$
$42$	12.3556	+	40.6434i	0.294181	+	0.967700i
$43$	9.58871			0.222993			0.111497	−	0.993765i	$-0.464436\pi$
$43$	9.58871			0.222993			0.111497	+	0.993765i	$0.464436\pi$
$44$	−16.8092			−0.382027
$45$		0			0
$46$	87.1402			1.89435
$47$		−	55.6978i		−	1.18506i	−0.805549	−	0.592529i	$-0.798129\pi$
$47$		−	55.6978i		−	1.18506i	0.805549	−	0.592529i	$-0.201871\pi$
$48$		−	33.5777i		−	0.699536i
$49$	40.7094	−	27.2717i	0.830804	−	0.556565i
$50$		0			0
$51$	−1.85829			−0.0364371
$52$			149.109i			2.86749i
$53$	−57.4656			−1.08426			−0.542128	−	0.840296i	$-0.682381\pi$
$53$	−57.4656			−1.08426			−0.542128	+	0.840296i	$0.682381\pi$
$54$		−	18.2057i		−	0.337143i
$55$		0			0
$56$	−100.335	+	30.5018i	−1.79169	+	0.544674i
$57$	49.8575			0.874693
$58$	134.647			2.32150
$59$			101.697i			1.72368i	0.507178	+	0.861841i	$0.330689\pi$
$59$			101.697i			1.72368i	−0.507178	+	0.861841i	$0.669311\pi$
$60$		0			0
$61$		−	31.9530i		−	0.523819i	−0.965092	−	0.261910i	$-0.915648\pi$
$61$		−	31.9530i		−	0.523819i	0.965092	−	0.261910i	$-0.0843523\pi$
$62$			154.477i			2.49157i
$63$	−20.0921	+	6.10801i	−0.318922	+	0.0969525i
$64$	−49.5215			−0.773774
$65$		0			0
$66$		−	12.3260i		−	0.186757i
$67$	−95.7318			−1.42883			−0.714416	−	0.699721i	$-0.753308\pi$
$67$	−95.7318			−1.42883			−0.714416	+	0.699721i	$0.753308\pi$
$68$		−	8.87902i		−	0.130574i
$69$			43.0778i			0.624316i
$70$		0			0
$71$	−25.8039			−0.363435			−0.181718	−	0.983351i	$-0.558166\pi$
$71$	−25.8039			−0.363435			−0.181718	+	0.983351i	$0.558166\pi$
$72$	44.9436			0.624217
$73$			95.6803i			1.31069i	0.755330	+	0.655345i	$0.227477\pi$
$73$			95.6803i			1.31069i	−0.755330	+	0.655345i	$0.772523\pi$
$74$	130.629			1.76525
$75$		0			0
$76$			238.222i			3.13450i
$77$	−13.6031	+	4.13536i	−0.176664	+	0.0537059i
$78$	−109.340			−1.40180
$79$	28.1212			0.355965			0.177982	−	0.984034i	$-0.443043\pi$
$79$	28.1212			0.355965			0.177982	+	0.984034i	$0.443043\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	174.906i		−	2.13301i
$83$			103.374i			1.24547i	0.782435	+	0.622733i	$0.213978\pi$
$83$			103.374i			1.24547i	−0.782435	+	0.622733i	$0.786022\pi$
$84$	−29.1844	−	96.0012i	−0.347433	−	1.14287i
$85$		0			0
$86$	−33.5959			−0.390650
$87$			66.5628i			0.765090i
$88$	30.4286			0.345779
$89$			29.3629i			0.329920i	0.986300	+	0.164960i	$0.0527496\pi$
$89$			29.3629i			0.329920i	−0.986300	+	0.164960i	$0.947250\pi$
$90$		0			0
$91$	36.6835	+	120.669i	0.403116	+	1.32604i
$92$	−205.828			−2.23726
$93$	−76.3659			−0.821138
$94$			195.148i			2.07604i
$95$		0			0
$96$			13.8531i			0.144304i
$97$			67.6473i			0.697395i	0.937235	+	0.348697i	$0.113376\pi$
$97$			67.6473i			0.697395i	−0.937235	+	0.348697i	$0.886624\pi$
$98$	−142.633	+	95.5515i	−1.45544	+	0.975016i
$99$	6.09335			0.0615490
$100$		0			0
$101$			73.3301i			0.726040i	0.931781	+	0.363020i	$0.118254\pi$
$101$			73.3301i			0.726040i	−0.931781	+	0.363020i	$0.881746\pi$
$102$	6.51088			0.0638321
$103$			57.3431i			0.556729i	0.960476	+	0.278365i	$0.0897923\pi$
$103$			57.3431i			0.556729i	−0.960476	+	0.278365i	$0.910208\pi$
$104$		−	269.923i		−	2.59541i
$105$		0			0
$106$	201.342			1.89945
$107$	39.8399			0.372336			0.186168	−	0.982518i	$-0.440393\pi$
$107$	39.8399			0.372336			0.186168	+	0.982518i	$0.440393\pi$
$108$			43.0025i			0.398171i
$109$	−185.052			−1.69773			−0.848863	−	0.528613i	$-0.822712\pi$
$109$	−185.052			−1.69773			−0.848863	+	0.528613i	$0.822712\pi$
$110$		0			0
$111$			64.5764i			0.581770i
$112$	129.836	−	39.4702i	1.15925	−	0.352412i
$113$	120.716			1.06829			0.534143	−	0.845394i	$-0.320634\pi$
$113$	120.716			1.06829			0.534143	+	0.845394i	$0.320634\pi$
$114$	−174.685			−1.53233
$115$		0			0
$116$	−318.041			−2.74173
$117$		−	54.0523i		−	0.461986i
$118$		−	356.316i		−	3.01962i
$119$	−2.18440	−	7.18551i	−0.0183563	−	0.0603824i
$120$		0			0
$121$	−116.875			−0.965906
$122$			111.953i			0.917650i
$123$	86.4651			0.702968
$124$		−	364.880i		−	2.94258i
$125$		0			0
$126$	70.3964	−	21.4006i	0.558702	−	0.169846i
$127$	83.5096			0.657556			0.328778	−	0.944407i	$-0.393363\pi$
$127$	83.5096			0.657556			0.328778	+	0.944407i	$0.393363\pi$
$128$	205.501			1.60547
$129$		−	16.6081i		−	0.128745i
$130$		0			0
$131$		−	198.248i		−	1.51334i	−0.653796	−	0.756671i	$-0.726825\pi$
$131$		−	198.248i		−	1.51334i	0.653796	−	0.756671i	$-0.273175\pi$
$132$			29.1144i			0.220563i
$133$	58.6068	+	192.785i	0.440653	+	1.44951i
$134$	335.414			2.50309
$135$		0			0
$136$			16.0731i			0.118185i
$137$	24.1635			0.176376			0.0881880	−	0.996104i	$-0.471892\pi$
$137$	24.1635			0.176376			0.0881880	+	0.996104i	$0.471892\pi$
$138$		−	150.931i		−	1.09371i
$139$			61.6370i			0.443432i	0.975111	+	0.221716i	$0.0711658\pi$
$139$			61.6370i			0.443432i	−0.975111	+	0.221716i	$0.928834\pi$
$140$		0			0
$141$	−96.4714			−0.684194
$142$	90.4088			0.636682
$143$		−	36.5955i		−	0.255913i
$144$	−58.1583			−0.403877
$145$		0			0
$146$		−	335.234i		−	2.29612i
$147$	−47.2360	−	70.5107i	−0.321333	−	0.479665i
$148$	−308.550			−2.08480
$149$	−28.8271			−0.193470			−0.0967351	−	0.995310i	$-0.530840\pi$
$149$	−28.8271			−0.193470			−0.0967351	+	0.995310i	$0.530840\pi$
$150$		0			0
$151$	248.311			1.64445			0.822223	−	0.569166i	$-0.192734\pi$
$151$	248.311			1.64445			0.822223	+	0.569166i	$0.192734\pi$
$152$		−	431.237i		−	2.83709i
$153$			3.21866i			0.0210370i
$154$	47.6611	−	14.4890i	0.309488	−	0.0940844i
$155$		0			0
$156$	258.265			1.65554
$157$		−	41.3848i		−	0.263597i	−0.991277	−	0.131799i	$-0.957925\pi$
$157$		−	41.3848i		−	0.263597i	0.991277	−	0.131799i	$-0.0420752\pi$
$158$	−98.5280			−0.623595
$159$			99.5334i			0.625996i
$160$		0			0
$161$	−166.570	+	50.6374i	−1.03460	+	0.314518i
$162$	−31.5332			−0.194649
$163$	51.8103			0.317855			0.158927	−	0.987290i	$-0.449196\pi$
$163$	51.8103			0.317855			0.158927	+	0.987290i	$0.449196\pi$
$164$			413.135i			2.51912i
$165$		0			0
$166$		−	362.189i		−	2.18186i
$167$		−	41.9711i		−	0.251324i	−0.992073	−	0.125662i	$-0.959895\pi$
$167$		−	41.9711i		−	0.251324i	0.992073	−	0.125662i	$-0.0401055\pi$
$168$	52.8306	+	173.785i	0.314468	+	1.03443i
$169$	−155.628			−0.920876
$170$		0			0
$171$		−	86.3557i		−	0.505004i
$172$	79.3546			0.461364
$173$			98.0199i			0.566589i	0.959033	+	0.283295i	$0.0914274\pi$
$173$			98.0199i			0.566589i	−0.959033	+	0.283295i	$0.908573\pi$
$174$		−	233.215i		−	1.34032i
$175$		0			0
$176$	−39.3754			−0.223724
$177$	176.145			0.995168
$178$		−	102.879i		−	0.577969i
$179$	68.5830			0.383145			0.191573	−	0.981478i	$-0.438641\pi$
$179$	68.5830			0.383145			0.191573	+	0.981478i	$0.438641\pi$
$180$		0			0
$181$		−	105.124i		−	0.580798i	−0.956906	−	0.290399i	$-0.906212\pi$
$181$		−	105.124i		−	0.580798i	0.956906	−	0.290399i	$-0.0937880\pi$
$182$	−128.528	−	422.788i	−0.706196	−	2.32301i
$183$	−55.3442			−0.302427
$184$	372.597			2.02499
$185$		0			0
$186$	267.562			1.43851
$187$			2.17916i			0.0116532i
$188$		−	460.946i		−	2.45184i
$189$	10.5794	+	34.8005i	0.0559755	+	0.184130i
$190$		0			0
$191$	229.803			1.20316			0.601579	−	0.798813i	$-0.294539\pi$
$191$	229.803			1.20316			0.601579	+	0.798813i	$0.294539\pi$
$192$			85.7738i			0.446739i
$193$	−111.530			−0.577877			−0.288939	−	0.957348i	$-0.593302\pi$
$193$	−111.530			−0.577877			−0.288939	+	0.957348i	$0.593302\pi$
$194$		−	237.015i		−	1.22173i
$195$		0			0
$196$	336.904	−	225.696i	1.71890	−	1.15151i
$197$	172.865			0.877486			0.438743	−	0.898613i	$-0.355424\pi$
$197$	172.865			0.877486			0.438743	+	0.898613i	$0.355424\pi$
$198$	−21.3492			−0.107824
$199$			117.944i			0.592685i	0.955082	+	0.296343i	$0.0957670\pi$
$199$			117.944i			0.592685i	−0.955082	+	0.296343i	$0.904233\pi$
$200$		0			0
$201$			165.812i			0.824937i
$202$		−	256.926i		−	1.27191i
$203$	−257.380	+	78.2437i	−1.26788	+	0.385437i
$204$	−15.3789			−0.0753869
$205$		0			0
$206$		−	200.912i		−	0.975303i
$207$	74.6130			0.360449
$208$			349.288i			1.67927i
$209$		−	58.4662i		−	0.279742i
$210$		0			0
$211$	−391.940			−1.85754			−0.928769	−	0.370660i	$-0.879131\pi$
$211$	−391.940			−1.85754			−0.928769	+	0.370660i	$0.879131\pi$
$212$	−475.576			−2.24328
$213$			44.6936i			0.209829i
$214$	−139.587			−0.652274
$215$		0			0
$216$		−	77.8446i		−	0.360392i
$217$	−89.7670	−	295.286i	−0.413673	−	1.36076i
$218$	648.365			2.97415
$219$	165.723			0.756727
$220$		0			0
$221$	19.3306			0.0874690
$222$		−	226.256i		−	1.01917i
$223$			96.2512i			0.431620i	0.976435	+	0.215810i	$0.0692391\pi$
$223$			96.2512i			0.431620i	−0.976435	+	0.215810i	$0.930761\pi$
$224$	−53.5663	+	16.2842i	−0.239135	+	0.0726972i
$225$		0			0
$226$	−422.952			−1.87147
$227$			91.6962i			0.403948i	0.979391	+	0.201974i	$0.0647357\pi$
$227$			91.6962i			0.403948i	−0.979391	+	0.201974i	$0.935264\pi$
$228$	412.612			1.80970
$229$		−	323.972i		−	1.41472i	−0.706852	−	0.707361i	$-0.749885\pi$
$229$		−	323.972i		−	1.41472i	0.706852	−	0.707361i	$-0.250115\pi$
$230$		0			0
$231$	7.16265	+	23.5613i	0.0310071	+	0.101997i
$232$	575.728			2.48159
$233$	−182.918			−0.785055			−0.392528	−	0.919740i	$-0.628399\pi$
$233$	−182.918			−0.785055			−0.392528	+	0.919740i	$0.628399\pi$
$234$			189.382i			0.809327i
$235$		0			0
$236$			841.630i			3.56623i
$237$		−	48.7074i		−	0.205516i
$238$	7.65345	+	25.1758i	0.0321573	+	0.105781i
$239$	−42.9240			−0.179598			−0.0897992	−	0.995960i	$-0.528623\pi$
$239$	−42.9240			−0.179598			−0.0897992	+	0.995960i	$0.528623\pi$
$240$		0			0
$241$			99.8942i			0.414499i	0.978288	+	0.207249i	$0.0664511\pi$
$241$			99.8942i			0.414499i	−0.978288	+	0.207249i	$0.933549\pi$
$242$	409.492			1.69212
$243$		−	15.5885i		−	0.0641500i
$244$		−	264.438i		−	1.08376i
$245$		0			0
$246$	−302.947			−1.23149
$247$	−518.636			−2.09974
$248$			660.519i			2.66338i
$249$	179.048			0.719070
$250$		0			0
$251$			404.945i			1.61333i	0.591011	+	0.806663i	$0.298729\pi$
$251$			404.945i			1.61333i	−0.591011	+	0.806663i	$0.701271\pi$
$252$	−166.279	+	50.5489i	−0.659837	+	0.200591i
$253$	50.5159			0.199668
$254$	−292.592			−1.15194
$255$		0			0
$256$	−521.924			−2.03876
$257$			102.697i			0.399600i	0.979837	+	0.199800i	$0.0640292\pi$
$257$			102.697i			0.399600i	−0.979837	+	0.199800i	$0.935971\pi$
$258$			58.1897i			0.225542i
$259$	−249.699	+	75.9087i	−0.964090	+	0.293084i
$260$		0			0
$261$	115.290			0.441725
$262$			694.598i			2.65114i
$263$	−281.479			−1.07026			−0.535132	−	0.844769i	$-0.679738\pi$
$263$	−281.479			−1.07026			−0.535132	+	0.844769i	$0.679738\pi$
$264$		−	52.7038i		−	0.199636i
$265$		0			0
$266$	−205.340	−	675.460i	−0.771955	−	2.53932i
$267$	50.8581			0.190480
$268$	−792.260			−2.95620
$269$			176.412i			0.655808i	0.944711	+	0.327904i	$0.106342\pi$
$269$			176.412i			0.655808i	−0.944711	+	0.327904i	$0.893658\pi$
$270$		0			0
$271$			306.041i			1.12930i	0.825330	+	0.564651i	$0.190989\pi$
$271$			306.041i			1.12930i	−0.825330	+	0.564651i	$0.809011\pi$
$272$		−	20.7991i		−	0.0764672i
$273$	209.005	−	63.5378i	0.765588	−	0.232739i
$274$	−84.6614			−0.308983
$275$		0			0
$276$			356.505i			1.29169i
$277$	−43.7993			−0.158120			−0.0790601	−	0.996870i	$-0.525192\pi$
$277$	−43.7993			−0.158120			−0.0790601	+	0.996870i	$0.525192\pi$
$278$		−	215.957i		−	0.776824i
$279$			132.270i			0.474084i
$280$		0			0
$281$	499.502			1.77759			0.888794	−	0.458307i	$-0.151544\pi$
$281$	499.502			1.77759			0.888794	+	0.458307i	$0.151544\pi$
$282$	338.006			1.19860
$283$		−	122.672i		−	0.433470i	−0.976231	−	0.216735i	$-0.930459\pi$
$283$		−	122.672i		−	0.433470i	0.976231	−	0.216735i	$-0.0695407\pi$
$284$	−213.549			−0.751932
$285$		0			0
$286$			128.219i			0.448319i
$287$	101.639	+	334.337i	0.354141	+	1.16494i
$288$	23.9944			0.0833137
$289$	287.849			0.996017
$290$		0			0
$291$	117.169			0.402641
$292$			791.835i			2.71176i
$293$			123.871i			0.422769i	0.977403	+	0.211385i	$0.0677972\pi$
$293$			123.871i			0.422769i	−0.977403	+	0.211385i	$0.932203\pi$
$294$	165.500	+	247.048i	0.562926	+	0.840298i
$295$		0			0
$296$	558.547			1.88698
$297$		−	10.5540i		−	0.0355353i
$298$	101.001			0.338930
$299$		−	448.112i		−	1.49870i
$300$		0			0
$301$	64.2191	−	19.5226i	0.213352	−	0.0648593i
$302$	−870.006			−2.88081
$303$	127.011			0.419180
$304$			558.034i			1.83564i
$305$		0			0
$306$		−	11.2772i		−	0.0368535i
$307$		−	225.577i		−	0.734778i	−0.930067	−	0.367389i	$-0.880252\pi$
$307$		−	225.577i		−	0.734778i	0.930067	−	0.367389i	$-0.119748\pi$
$308$	−112.577	+	34.2235i	−0.365511	+	0.111115i
$309$	99.3211			0.321428
$310$		0			0
$311$			52.9648i			0.170305i	0.996368	+	0.0851525i	$0.0271377\pi$
$311$			52.9648i			0.170305i	−0.996368	+	0.0851525i	$0.972862\pi$
$312$	−467.520			−1.49846
$313$		−	374.563i		−	1.19669i	−0.801240	−	0.598343i	$-0.795826\pi$
$313$		−	374.563i		−	1.19669i	0.801240	−	0.598343i	$-0.204174\pi$
$314$			144.999i			0.461782i
$315$		0			0
$316$	232.727			0.736477
$317$	−12.0550			−0.0380283			−0.0190142	−	0.999819i	$-0.506053\pi$
$317$	−12.0550			−0.0380283			−0.0190142	+	0.999819i	$0.506053\pi$
$318$		−	348.734i		−	1.09665i
$319$	78.0559			0.244689
$320$		0			0
$321$		−	69.0048i		−	0.214968i
$322$	583.610	−	177.418i	1.81245	−	0.550987i
$323$	30.8833			0.0956138
$324$	74.4825			0.229884
$325$		0			0
$326$	−181.527			−0.556832
$327$			320.520i			0.980183i
$328$		−	747.871i		−	2.28009i
$329$	−113.401	−	373.028i	−0.344683	−	1.13382i
$330$		0			0
$331$	−376.184			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$331$	−376.184			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$332$			855.503i			2.57682i
$333$	111.850			0.335885
$334$			147.054i			0.440281i
$335$		0			0
$336$	−68.3643	−	224.882i	−0.203465	−	0.669293i
$337$	108.973			0.323363			0.161682	−	0.986843i	$-0.448308\pi$
$337$	108.973			0.323363			0.161682	+	0.986843i	$0.448308\pi$
$338$	545.272			1.61323
$339$		−	209.087i		−	0.616775i
$340$		0			0
$341$			89.5516i			0.262615i
$342$			302.564i			0.884689i
$343$	217.120	−	265.533i	0.633004	−	0.774148i
$344$	−143.650			−0.417588
$345$		0			0
$346$		−	343.431i		−	0.992576i
$347$	206.351			0.594671			0.297335	−	0.954773i	$-0.403902\pi$
$347$	206.351			0.594671			0.297335	+	0.954773i	$0.403902\pi$
$348$			550.863i			1.58294i
$349$		−	373.475i		−	1.07013i	−0.844811	−	0.535064i	$-0.820287\pi$
$349$		−	373.475i		−	1.07013i	0.844811	−	0.535064i	$-0.179713\pi$
$350$		0			0
$351$	−93.6213			−0.266727
$352$	16.2451			0.0461509
$353$		−	646.142i		−	1.83043i	−0.402964	−	0.915216i	$-0.632020\pi$
$353$		−	646.142i		−	1.83043i	0.402964	−	0.915216i	$-0.367980\pi$
$354$	−617.157			−1.74338
$355$		0			0
$356$			243.003i			0.682592i
$357$	−12.4457	+	3.78349i	−0.0348618	+	0.0105980i
$358$	−240.294			−0.671211
$359$	175.261			0.488192			0.244096	−	0.969751i	$-0.421509\pi$
$359$	175.261			0.488192			0.244096	+	0.969751i	$0.421509\pi$
$360$		0			0
$361$	−467.590			−1.29526
$362$			368.323i			1.01747i
$363$			202.433i			0.557666i
$364$	303.587	+	998.640i	0.834030	+	2.74352i
$365$		0			0
$366$	193.909			0.529805
$367$			106.477i			0.290127i	0.989422	+	0.145063i	$0.0463386\pi$
$367$			106.477i			0.290127i	−0.989422	+	0.145063i	$0.953661\pi$
$368$	−482.152			−1.31020
$369$		−	149.762i		−	0.405859i
$370$		0			0
$371$	−384.868	+	117.000i	−1.03738	+	0.315364i
$372$	−631.991			−1.69890
$373$	−223.324			−0.598723			−0.299362	−	0.954140i	$-0.596774\pi$
$373$	−223.324			−0.598723			−0.299362	+	0.954140i	$0.596774\pi$
$374$		−	7.63508i		−	0.0204147i
$375$		0			0
$376$			834.419i			2.21920i
$377$		−	692.411i		−	1.83663i
$378$	−37.0668	−	121.930i	−0.0980604	−	0.322567i
$379$	119.075			0.314183			0.157092	−	0.987584i	$-0.449788\pi$
$379$	119.075			0.314183			0.157092	+	0.987584i	$0.449788\pi$
$380$		0			0
$381$		−	144.643i		−	0.379640i
$382$	−805.159			−2.10775
$383$		−	494.637i		−	1.29148i	−0.763557	−	0.645740i	$-0.776549\pi$
$383$		−	494.637i		−	1.29148i	0.763557	−	0.645740i	$-0.223451\pi$
$384$		−	355.937i		−	0.926920i
$385$		0			0
$386$	390.767			1.01235
$387$	−28.7661			−0.0743311
$388$			559.838i			1.44288i
$389$	−270.578			−0.695574			−0.347787	−	0.937574i	$-0.613067\pi$
$389$	−270.578			−0.695574			−0.347787	+	0.937574i	$0.613067\pi$
$390$		0			0
$391$			26.6837i			0.0682448i
$392$	−609.875	+	408.563i	−1.55580	+	1.04225i
$393$	−343.375			−0.873728
$394$	−605.664			−1.53722
$395$		0			0
$396$	50.4276			0.127342
$397$			37.1881i			0.0936727i	0.998903	+	0.0468364i	$0.0149139\pi$
$397$			37.1881i			0.0936727i	−0.998903	+	0.0468364i	$0.985086\pi$
$398$		−	413.240i		−	1.03829i
$399$	333.914	−	101.510i	0.836877	−	0.254411i
$400$		0			0
$401$	−36.7102			−0.0915467			−0.0457733	−	0.998952i	$-0.514575\pi$
$401$	−36.7102			−0.0915467			−0.0457733	+	0.998952i	$0.514575\pi$
$402$		−	580.955i		−	1.44516i
$403$	794.386			1.97118
$404$			606.868i			1.50215i
$405$		0			0
$406$	901.780	−	274.141i	2.22113	−	0.675225i
$407$	75.7266			0.186060
$408$	27.8394			0.0682339
$409$		−	495.325i		−	1.21106i	−0.795821	−	0.605532i	$-0.792960\pi$
$409$		−	495.325i		−	1.21106i	0.795821	−	0.605532i	$-0.207040\pi$
$410$		0			0
$411$		−	41.8524i		−	0.101831i
$412$			474.562i			1.15185i
$413$	207.056	+	681.104i	0.501346	+	1.64916i
$414$	−261.421			−0.631451
$415$		0			0
$416$		−	144.106i		−	0.346408i
$417$	106.758			0.256016
$418$			204.847i			0.490065i
$419$			269.297i			0.642713i	0.946958	+	0.321357i	$0.104139\pi$
$419$			269.297i			0.642713i	−0.946958	+	0.321357i	$0.895861\pi$
$420$		0			0
$421$	756.722			1.79744			0.898719	−	0.438524i	$-0.144499\pi$
$421$	756.722			1.79744			0.898719	+	0.438524i	$0.144499\pi$
$422$	1373.24			3.25412
$423$			167.093i			0.395020i
$424$	860.904			2.03043
$425$		0			0
$426$		−	156.593i		−	0.367588i
$427$	−65.0563	−	214.001i	−0.152357	−	0.501173i
$428$	329.709			0.770347
$429$	−63.3853			−0.147751
$430$		0			0
$431$	185.182			0.429657			0.214828	−	0.976652i	$-0.431081\pi$
$431$	185.182			0.429657			0.214828	+	0.976652i	$0.431081\pi$
$432$			100.733i			0.233179i
$433$			642.846i			1.48463i	0.670049	+	0.742317i	$0.266273\pi$
$433$			642.846i			1.48463i	−0.670049	+	0.742317i	$0.733727\pi$
$434$	314.516	+	1034.59i	0.724691	+	2.38385i
$435$		0			0
$436$	−1531.46			−3.51253
$437$		−	715.918i		−	1.63826i
$438$	−580.643			−1.32567
$439$			464.239i			1.05749i	0.848780	+	0.528745i	$0.177337\pi$
$439$			464.239i			1.05749i	−0.848780	+	0.528745i	$0.822663\pi$
$440$		0			0
$441$	−122.128	+	81.8151i	−0.276935	+	0.185522i
$442$	−67.7286			−0.153232
$443$	115.228			0.260109			0.130054	−	0.991507i	$-0.458485\pi$
$443$	115.228			0.260109			0.130054	+	0.991507i	$0.458485\pi$
$444$			534.424i			1.20366i
$445$		0			0
$446$		−	337.234i		−	0.756130i
$447$			49.9299i			0.111700i
$448$	−331.664	+	100.826i	−0.740321	+	0.225058i
$449$	333.955			0.743774			0.371887	−	0.928278i	$-0.378711\pi$
$449$	333.955			0.743774			0.371887	+	0.928278i	$0.378711\pi$
$450$		0			0
$451$		−	101.395i		−	0.224822i
$452$	999.028			2.21024
$453$		−	430.088i		−	0.949421i
$454$		−	321.275i		−	0.707654i
$455$		0			0
$456$	−746.925			−1.63799
$457$	−354.152			−0.774949			−0.387474	−	0.921880i	$-0.626652\pi$
$457$	−354.152			−0.774949			−0.387474	+	0.921880i	$0.626652\pi$
$458$			1135.10i			2.47837i
$459$	5.57488			0.0121457
$460$		0			0
$461$			128.906i			0.279623i	0.990178	+	0.139811i	$0.0446497\pi$
$461$			128.906i			0.279623i	−0.990178	+	0.139811i	$0.955350\pi$
$462$	−25.0957	−	82.5515i	−0.0543197	−	0.178683i
$463$	302.175			0.652645			0.326322	−	0.945259i	$-0.394190\pi$
$463$	302.175			0.652645			0.326322	+	0.945259i	$0.394190\pi$
$464$	−745.009			−1.60562
$465$		0			0
$466$	640.887			1.37530
$467$			808.227i			1.73068i	0.501186	+	0.865339i	$0.332897\pi$
$467$			808.227i			1.73068i	−0.501186	+	0.865339i	$0.667103\pi$
$468$		−	447.328i		−	0.955829i
$469$	−641.151	+	194.910i	−1.36706	+	0.415587i
$470$		0			0
$471$	−71.6805			−0.152188
$472$		−	1523.55i		−	3.22785i
$473$	−19.4758			−0.0411750
$474$			170.656i			0.360033i
$475$		0			0
$476$	−18.0777	−	59.4661i	−0.0379784	−	0.124929i
$477$	172.397			0.361419
$478$	150.392			0.314628
$479$			48.8836i			0.102053i	0.998697	+	0.0510267i	$0.0162494\pi$
$479$			48.8836i			0.102053i	−0.998697	+	0.0510267i	$0.983751\pi$
$480$		0			0
$481$		−	671.748i		−	1.39657i
$482$		−	349.998i		−	0.726137i
$483$	87.7066	+	288.508i	0.181587	+	0.597325i
$484$	−967.235			−1.99842
$485$		0			0
$486$			54.6171i			0.112381i
$487$	−334.433			−0.686720			−0.343360	−	0.939204i	$-0.611565\pi$
$487$	−334.433			−0.686720			−0.343360	+	0.939204i	$0.611565\pi$
$488$			478.694i			0.980930i
$489$		−	89.7381i		−	0.183514i
$490$		0			0
$491$	−549.151			−1.11843			−0.559217	−	0.829021i	$-0.688898\pi$
$491$	−549.151			−1.11843			−0.559217	+	0.829021i	$0.688898\pi$
$492$	715.571			1.45441
$493$			41.2310i			0.0836329i
$494$	1817.14			3.67842
$495$		0			0
$496$		−	854.731i		−	1.72325i
$497$	−172.818	+	52.5368i	−0.347722	+	0.105708i
$498$	−627.330			−1.25970
$499$	−462.450			−0.926754			−0.463377	−	0.886161i	$-0.653362\pi$
$499$	−462.450			−0.926754			−0.463377	+	0.886161i	$0.653362\pi$
$500$		0			0
$501$	−72.6961			−0.145102
$502$		−	1418.80i		−	2.82630i
$503$		−	676.817i		−	1.34556i	−0.739842	−	0.672781i	$-0.765100\pi$
$503$		−	676.817i		−	1.34556i	0.739842	−	0.672781i	$-0.234900\pi$
$504$	301.004	−	91.5053i	0.597229	−	0.181558i
$505$		0			0
$506$	−176.992			−0.349786
$507$			269.556i			0.531668i
$508$	691.112			1.36046
$509$			31.5959i			0.0620744i	0.999518	+	0.0310372i	$0.00988104\pi$
$509$			31.5959i			0.0620744i	−0.999518	+	0.0310372i	$0.990119\pi$
$510$		0			0
$511$	194.805	+	640.806i	0.381224	+	1.25402i
$512$	1006.66			1.96613
$513$	−149.572			−0.291564
$514$		−	359.819i		−	0.700036i
$515$		0			0
$516$		−	137.446i		−	0.266369i
$517$			113.129i			0.218817i
$518$	874.869	−	265.961i	1.68894	−	0.513437i
$519$	169.775			0.327120
$520$		0			0
$521$		−	793.420i		−	1.52288i	−0.648236	−	0.761440i	$-0.724493\pi$
$521$		−	793.420i		−	1.52288i	0.648236	−	0.761440i	$-0.275507\pi$
$522$	−403.941			−0.773833
$523$		−	593.508i		−	1.13481i	−0.823438	−	0.567407i	$-0.807947\pi$
$523$		−	593.508i		−	1.13481i	0.823438	−	0.567407i	$-0.192053\pi$
$524$		−	1640.67i		−	3.13104i
$525$		0			0
$526$	986.216			1.87494
$527$	−47.3034			−0.0897597
$528$			68.2003i			0.129167i
$529$	89.5666			0.169313
$530$		0			0
$531$		−	305.092i		−	0.574561i
$532$	485.020	+	1595.46i	0.911692	+	2.99898i
$533$	−899.442			−1.68751
$534$	−178.191			−0.333691
$535$		0			0
$536$	1434.18			2.67570
$537$		−	118.789i		−	0.221209i
$538$		−	618.094i		−	1.14887i
$539$	−82.6855	+	55.3920i	−0.153405	+	0.102768i
$540$		0			0
$541$	217.690			0.402385			0.201192	−	0.979552i	$-0.435518\pi$
$541$	217.690			0.402385			0.201192	+	0.979552i	$0.435518\pi$
$542$		−	1072.27i		−	1.97836i
$543$	−182.081			−0.335324
$544$			8.58106i			0.0157740i
$545$		0			0
$546$	−732.290	+	222.617i	−1.34119	+	0.407723i
$547$	137.891			0.252085			0.126043	−	0.992025i	$-0.459772\pi$
$547$	137.891			0.252085			0.126043	+	0.992025i	$0.459772\pi$
$548$	199.973			0.364915
$549$			95.8589i			0.174606i
$550$		0			0
$551$		−	1106.22i		−	2.00766i
$552$		−	645.358i		−	1.16913i
$553$	188.338	−	57.2549i	0.340575	−	0.103535i
$554$	153.459			0.277002
$555$		0			0
$556$			510.098i			0.917442i
$557$	316.337			0.567930			0.283965	−	0.958835i	$-0.408350\pi$
$557$	316.337			0.567930			0.283965	+	0.958835i	$0.408350\pi$
$558$		−	463.431i		−	0.830522i
$559$			172.764i			0.309059i
$560$		0			0
$561$	3.77441			0.00672800
$562$	−1750.10			−3.11406
$563$			151.482i			0.269063i	0.990909	+	0.134531i	$0.0429529\pi$
$563$			151.482i			0.269063i	−0.990909	+	0.134531i	$0.957047\pi$
$564$	−798.381			−1.41557
$565$		0			0
$566$			429.804i			0.759371i
$567$	60.2763	−	18.3240i	0.106307	−	0.0323175i
$568$	386.573			0.680586
$569$	−213.993			−0.376086			−0.188043	−	0.982161i	$-0.560214\pi$
$569$	−213.993			−0.376086			−0.188043	+	0.982161i	$0.560214\pi$
$570$		0			0
$571$	−204.492			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$571$	−204.492			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$572$		−	302.858i		−	0.529473i
$573$		−	398.031i		−	0.694643i
$574$	−356.110	−	1171.41i	−0.620400	−	2.04079i
$575$		0			0
$576$	148.565			0.257925
$577$		−	957.823i		−	1.66001i	−0.557759	−	0.830003i	$-0.688339\pi$
$577$		−	957.823i		−	1.66001i	0.557759	−	0.830003i	$-0.311661\pi$
$578$	−1008.53			−1.74487
$579$			193.176i			0.333638i
$580$		0			0
$581$	210.469	+	692.331i	0.362253	+	1.19162i
$582$	−410.522			−0.705364
$583$	116.719			0.200205
$584$		−	1433.41i		−	2.45446i
$585$		0			0
$586$		−	434.007i		−	0.740626i
$587$			981.279i			1.67168i	0.548969	+	0.835842i	$0.315020\pi$
$587$			981.279i			1.67168i	−0.548969	+	0.835842i	$0.684980\pi$
$588$	−390.917	−	583.535i	−0.664825	−	0.992407i
$589$	1269.14			2.15473
$590$		0			0
$591$		−	299.410i		−	0.506617i
$592$	−722.777			−1.22091
$593$		−	708.384i		−	1.19458i	−0.802026	−	0.597288i	$-0.796245\pi$
$593$		−	708.384i		−	1.19458i	0.802026	−	0.597288i	$-0.203755\pi$
$594$			36.9779i			0.0622523i
$595$		0			0
$596$	−238.568			−0.400282
$597$	204.286			0.342187
$598$			1570.04i			2.62549i
$599$	−928.994			−1.55091			−0.775454	−	0.631404i	$-0.782479\pi$
$599$	−928.994			−1.55091			−0.775454	+	0.631404i	$0.782479\pi$
$600$		0			0
$601$			466.882i			0.776842i	0.921482	+	0.388421i	$0.126979\pi$
$601$			466.882i			0.776842i	−0.921482	+	0.388421i	$0.873021\pi$
$602$	−225.004	+	68.4012i	−0.373760	+	0.113623i
$603$	287.195			0.476277
$604$	2054.98			3.40229
$605$		0			0
$606$	−445.009			−0.734338
$607$			988.757i			1.62892i	0.580216	+	0.814462i	$0.302968\pi$
$607$			988.757i			1.62892i	−0.580216	+	0.814462i	$0.697032\pi$
$608$		−	230.228i		−	0.378664i
$609$	135.522	+	445.795i	0.222532	+	0.732012i
$610$		0			0
$611$	1003.53			1.64244
$612$			26.6371i			0.0435246i
$613$	−469.962			−0.766660			−0.383330	−	0.923612i	$-0.625223\pi$
$613$	−469.962			−0.766660			−0.383330	+	0.923612i	$0.625223\pi$
$614$			790.351i			1.28722i
$615$		0			0
$616$	203.791	−	61.9526i	0.330830	−	0.100572i
$617$	−1081.72			−1.75320			−0.876598	−	0.481223i	$-0.840193\pi$
$617$	−1081.72			−1.75320			−0.876598	+	0.481223i	$0.840193\pi$
$618$	−347.990			−0.563091
$619$			553.956i			0.894921i	0.894304	+	0.447461i	$0.147672\pi$
$619$			553.956i			0.894921i	−0.894304	+	0.447461i	$0.852328\pi$
$620$		0			0
$621$		−	129.234i		−	0.208105i
$622$		−	185.572i		−	0.298348i
$623$	59.7829	+	196.654i	0.0959598	+	0.315657i
$624$	604.985			0.969527
$625$		0			0
$626$			1312.35i			2.09641i
$627$	−101.266			−0.161509
$628$		−	342.494i		−	0.545372i
$629$			40.0006i			0.0635940i
$630$		0			0
$631$	−77.8822			−0.123427			−0.0617133	−	0.998094i	$-0.519656\pi$
$631$	−77.8822			−0.123427			−0.0617133	+	0.998094i	$0.519656\pi$
$632$	−421.290			−0.666597
$633$			678.861i			1.07245i
$634$	42.2369			0.0666197
$635$		0			0
$636$			823.722i			1.29516i
$637$	491.366	+	733.479i	0.771375	+	1.15146i
$638$	−273.484			−0.428658
$639$	77.4117			0.121145
$640$		0			0
$641$	−360.619			−0.562589			−0.281294	−	0.959622i	$-0.590764\pi$
$641$	−360.619			−0.562589			−0.281294	+	0.959622i	$0.590764\pi$
$642$			241.771i			0.376591i
$643$			793.158i			1.23353i	0.787148	+	0.616764i	$0.211557\pi$
$643$			793.158i			1.23353i	−0.787148	+	0.616764i	$0.788443\pi$
$644$	−1378.51	+	419.067i	−2.14054	+	0.650725i
$645$		0			0
$646$	−108.205			−0.167501
$647$		−	405.244i		−	0.626344i	−0.949696	−	0.313172i	$-0.898608\pi$
$647$		−	405.244i		−	0.626344i	0.949696	−	0.313172i	$-0.101392\pi$
$648$	−134.831			−0.208072
$649$		−	206.559i		−	0.318273i
$650$		0			0
$651$	−511.450	+	155.481i	−0.785638	+	0.238834i
$652$	428.774			0.657629
$653$	−493.508			−0.755755			−0.377877	−	0.925856i	$-0.623346\pi$
$653$	−493.508			−0.755755			−0.377877	+	0.925856i	$0.623346\pi$
$654$		−	1123.00i		−	1.71713i
$655$		0			0
$656$			967.767i			1.47526i
$657$		−	287.041i		−	0.436896i
$658$	397.321	+	1306.97i	0.603831	+	1.98628i
$659$	−1120.88			−1.70088			−0.850441	−	0.526070i	$-0.823665\pi$
$659$	−1120.88			−1.70088			−0.850441	+	0.526070i	$0.823665\pi$
$660$		0			0
$661$		−	1134.48i		−	1.71631i	−0.513393	−	0.858154i	$-0.671612\pi$
$661$		−	1134.48i		−	1.71631i	0.513393	−	0.858154i	$-0.328388\pi$
$662$	1318.03			1.99098
$663$		−	33.4817i		−	0.0505002i
$664$		−	1548.66i		−	2.33232i
$665$		0			0
$666$	−391.887			−0.588418
$667$	955.794			1.43297
$668$		−	347.346i		−	0.519979i
$669$	166.712			0.249196
$670$		0			0
$671$			64.9002i			0.0967216i
$672$	28.2050	+	92.7796i	0.0419718	+	0.138065i
$673$	763.267			1.13413			0.567063	−	0.823674i	$-0.308080\pi$
$673$	763.267			1.13413			0.567063	+	0.823674i	$0.308080\pi$
$674$	−381.809			−0.566482
$675$		0			0
$676$	−1287.95			−1.90525
$677$		−	456.611i		−	0.674463i	−0.941422	−	0.337232i	$-0.890509\pi$
$677$		−	456.611i		−	0.674463i	0.941422	−	0.337232i	$-0.109491\pi$
$678$			732.575i			1.08049i
$679$	137.730	+	453.058i	0.202842	+	0.667244i
$680$		0			0
$681$	158.822			0.233219
$682$		−	313.761i		−	0.460060i
$683$	219.276			0.321049			0.160524	−	0.987032i	$-0.448681\pi$
$683$	219.276			0.321049			0.160524	+	0.987032i	$0.448681\pi$
$684$		−	714.666i		−	1.04483i
$685$		0			0
$686$	−760.722	+	930.345i	−1.10892	+	1.35619i
$687$	−561.135			−0.816791
$688$	185.888			0.270186
$689$		−	1035.38i		−	1.50273i
$690$		0			0
$691$		−	396.801i		−	0.574242i	−0.957894	−	0.287121i	$-0.907302\pi$
$691$		−	396.801i		−	0.574242i	0.957894	−	0.287121i	$-0.0926982\pi$
$692$			811.197i			1.17225i
$693$	40.8094	−	12.4061i	0.0588880	−	0.0179020i
$694$	−722.989			−1.04177
$695$		0			0
$696$		−	997.190i		−	1.43274i
$697$	53.5591			0.0768424
$698$			1308.54i			1.87470i
$699$			316.823i			0.453252i
$700$		0			0
$701$	−493.156			−0.703503			−0.351752	−	0.936093i	$-0.614414\pi$
$701$	−493.156			−0.703503			−0.351752	+	0.936093i	$0.614414\pi$
$702$	328.020			0.467265
$703$		−	1073.21i		−	1.52661i
$704$	100.584			0.142875
$705$		0			0
$706$			2263.88i			3.20663i
$707$	149.300	+	491.118i	0.211174	+	0.694651i
$708$	1457.75			2.05896
$709$	859.326			1.21202			0.606012	−	0.795455i	$-0.292768\pi$
$709$	859.326			1.21202			0.606012	+	0.795455i	$0.292768\pi$
$710$		0			0
$711$	−84.3637			−0.118655
$712$		−	439.892i		−	0.617825i
$713$			1096.56i			1.53795i
$714$	43.6057	−	13.2562i	0.0610724	−	0.0185661i
$715$		0			0
$716$	567.582			0.792712
$717$			74.3466i			0.103691i
$718$	−614.060			−0.855237
$719$			385.539i			0.536216i	0.963389	+	0.268108i	$0.0863983\pi$
$719$			385.539i			0.536216i	−0.963389	+	0.268108i	$0.913602\pi$
$720$		0			0
$721$	116.751	+	384.048i	0.161929	+	0.532660i
$722$	1638.29			2.26910
$723$	173.022			0.239311
$724$		−	869.992i		−	1.20165i
$725$		0			0
$726$		−	709.261i		−	0.976944i
$727$		−	114.722i		−	0.157802i	−0.996882	−	0.0789012i	$-0.974859\pi$
$727$		−	114.722i		−	0.157802i	0.996882	−	0.0789012i	$-0.0251412\pi$
$728$	−549.563	−	1807.77i	−0.754895	−	2.48320i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	10.2876i		−	0.0140733i
$732$	−458.019			−0.625710
$733$		−	140.433i		−	0.191586i	−0.995401	−	0.0957932i	$-0.969461\pi$
$733$		−	140.433i		−	0.191586i	0.995401	−	0.0957932i	$-0.0305388\pi$
$734$		−	373.061i		−	0.508257i
$735$		0			0
$736$	198.921			0.270273
$737$	194.442			0.263830
$738$			524.719i			0.711002i
$739$	−50.8609			−0.0688239			−0.0344120	−	0.999408i	$-0.510956\pi$
$739$	−50.8609			−0.0688239			−0.0344120	+	0.999408i	$0.510956\pi$
$740$		0			0
$741$			898.304i			1.21229i
$742$	1348.46	−	409.932i	1.81733	−	0.552469i
$743$	−930.694			−1.25262			−0.626309	−	0.779575i	$-0.715435\pi$
$743$	−930.694			−1.25262			−0.626309	+	0.779575i	$0.715435\pi$
$744$	1144.05			1.53770
$745$		0			0
$746$	782.457			1.04887
$747$		−	310.121i		−	0.415155i
$748$			18.0343i			0.0241101i
$749$	266.822	−	81.1142i	0.356238	−	0.108297i
$750$		0			0
$751$	−446.702			−0.594809			−0.297404	−	0.954752i	$-0.596121\pi$
$751$	−446.702			−0.594809			−0.297404	+	0.954752i	$0.596121\pi$
$752$		−	1079.76i		−	1.43586i
$753$	701.385			0.931455
$754$			2425.99i			3.21750i
$755$		0			0
$756$	87.5532	+	288.003i	0.115811	+	0.380957i
$757$	−27.2042			−0.0359369			−0.0179684	−	0.999839i	$-0.505720\pi$
$757$	−27.2042			−0.0359369			−0.0179684	+	0.999839i	$0.505720\pi$
$758$	−417.203			−0.550400
$759$		−	87.4961i		−	0.115278i
$760$		0			0
$761$		−	333.536i		−	0.438287i	−0.975693	−	0.219143i	$-0.929674\pi$
$761$		−	333.536i		−	0.438287i	0.975693	−	0.219143i	$-0.0703262\pi$
$762$			506.784i			0.665070i
$763$	−1239.36	+	376.767i	−1.62433	+	0.493796i
$764$	1901.81			2.48928
$765$		0			0
$766$			1733.05i			2.26247i
$767$	−1832.32			−2.38895
$768$			903.998i			1.17708i
$769$			56.3903i			0.0733294i	0.999328	+	0.0366647i	$0.0116734\pi$
$769$			56.3903i			0.0733294i	−0.999328	+	0.0366647i	$0.988327\pi$
$770$		0			0
$771$	177.877			0.230709
$772$	−923.006			−1.19560
$773$		−	296.398i		−	0.383438i	−0.981450	−	0.191719i	$-0.938594\pi$
$773$		−	296.398i		−	0.383438i	0.981450	−	0.191719i	$-0.0614063\pi$
$774$	100.788			0.130217
$775$		0			0
$776$		−	1013.44i		−	1.30598i
$777$	131.478	+	432.492i	0.169212	+	0.556618i
$778$	948.022			1.21854
$779$	−1436.98			−1.84464
$780$		0			0
$781$	52.4107			0.0671072
$782$		−	93.4915i		−	0.119554i
$783$		−	199.688i		−	0.255030i
$784$	789.197	−	528.692i	1.00663	−	0.674352i
$785$		0			0
$786$	1203.08			1.53064
$787$			226.427i			0.287709i	0.989599	+	0.143854i	$0.0459497\pi$
$787$			226.427i			0.287709i	−0.989599	+	0.143854i	$0.954050\pi$
$788$	1430.60			1.81548
$789$			487.537i			0.617917i
$790$		0			0
$791$	808.481	−	245.779i	1.02210	−	0.310719i
$792$	−91.2857			−0.115260
$793$	575.711			0.725991
$794$		−	130.295i		−	0.164100i
$795$		0			0
$796$			976.088i			1.22624i
$797$		−	305.282i		−	0.383038i	−0.981489	−	0.191519i	$-0.938659\pi$
$797$		−	305.282i		−	0.383038i	0.981489	−	0.191519i	$-0.0613414\pi$
$798$	−1169.93	+	355.659i	−1.46608	+	0.445688i
$799$	−59.7573			−0.0747901
$800$		0			0
$801$		−	88.0887i		−	0.109973i
$802$	128.621			0.160375
$803$		−	194.338i		−	0.242015i
$804$			1372.24i			1.70676i
$805$		0			0
$806$	−2783.28			−3.45320
$807$	305.555			0.378631
$808$		−	1098.57i		−	1.35962i
$809$	592.651			0.732573			0.366286	−	0.930502i	$-0.380629\pi$
$809$	592.651			0.732573			0.366286	+	0.930502i	$0.380629\pi$
$810$		0			0
$811$		−	731.348i		−	0.901785i	−0.892578	−	0.450893i	$-0.851106\pi$
$811$		−	731.348i		−	0.901785i	0.892578	−	0.450893i	$-0.148894\pi$
$812$	−2130.04	+	647.532i	−2.62320	+	0.797453i
$813$	530.078			0.652003
$814$	−265.322			−0.325949
$815$		0			0
$816$	−36.0251			−0.0441484
$817$			276.013i			0.337838i
$818$			1735.47i			2.12160i
$819$	−110.051	−	362.008i	−0.134372	−	0.442012i
$820$		0			0
$821$	268.560			0.327114			0.163557	−	0.986534i	$-0.447703\pi$
$821$	268.560			0.327114			0.163557	+	0.986534i	$0.447703\pi$
$822$			146.638i			0.178392i
$823$	−1213.35			−1.47430			−0.737151	−	0.675728i	$-0.763830\pi$
$823$	−1213.35			−1.47430			−0.737151	+	0.675728i	$0.763830\pi$
$824$		−	859.068i		−	1.04256i
$825$		0			0
$826$	−725.459	−	2386.37i	−0.878280	−	2.88907i
$827$	1238.49			1.49757			0.748785	−	0.662813i	$-0.230637\pi$
$827$	1238.49			1.49757			0.748785	+	0.662813i	$0.230637\pi$
$828$	617.485			0.745755
$829$			873.056i			1.05314i	0.850131	+	0.526572i	$0.176523\pi$
$829$			873.056i			1.05314i	−0.850131	+	0.526572i	$0.823477\pi$
$830$		0			0
$831$			75.8626i			0.0912908i
$832$		−	892.251i		−	1.07242i
$833$	−29.2594	−	43.6765i	−0.0351253	−	0.0524328i
$834$	−374.048			−0.448499
$835$		0			0
$836$		−	483.856i		−	0.578776i
$837$	229.098			0.273713
$838$		−	943.532i		−	1.12593i
$839$			100.572i			0.119871i	0.998202	+	0.0599355i	$0.0190895\pi$
$839$			100.572i			0.119871i	−0.998202	+	0.0599355i	$0.980910\pi$
$840$		0			0
$841$	635.869			0.756086
$842$	−2651.32			−3.14883
$843$		−	865.163i		−	1.02629i
$844$	−3243.63			−3.84317
$845$		0			0
$846$		−	585.443i		−	0.692013i
$847$	−782.752	+	237.957i	−0.924146	+	0.280941i
$848$	−1114.03			−1.31372
$849$	−212.474			−0.250264
$850$		0			0
$851$	927.271			1.08963
$852$			369.877i			0.434128i
$853$			1162.30i			1.36260i	0.732003	+	0.681302i	$0.238586\pi$
$853$			1162.30i			1.36260i	−0.732003	+	0.681302i	$0.761414\pi$
$854$	227.937	+	749.792i	0.266905	+	0.877977i
$855$		0			0
$856$	−596.850			−0.697254
$857$		−	87.8213i		−	0.102475i	−0.998686	−	0.0512376i	$-0.983683\pi$
$857$		−	87.8213i		−	0.102475i	0.998686	−	0.0512376i	$-0.0163166\pi$
$858$	222.082			0.258837
$859$			200.580i			0.233504i	0.993161	+	0.116752i	$0.0372482\pi$
$859$			200.580i			0.233504i	−0.993161	+	0.116752i	$0.962752\pi$
$860$		0			0
$861$	579.088	−	176.043i	0.672576	−	0.204464i
$862$	−648.820			−0.752691
$863$	617.914			0.716007			0.358004	−	0.933720i	$-0.383458\pi$
$863$	617.914			0.716007			0.358004	+	0.933720i	$0.383458\pi$
$864$		−	41.5594i		−	0.0481012i
$865$		0			0
$866$		−	2252.33i		−	2.60085i
$867$		−	498.569i		−	0.575051i
$868$	−742.897	−	2443.74i	−0.855872	−	2.81537i
$869$	−57.1175			−0.0657278
$870$		0			0
$871$		−	1724.84i		−	1.98030i
$872$	2772.30			3.17925
$873$		−	202.942i		−	0.232465i
$874$			2508.35i			2.86997i
$875$		0			0
$876$	1371.50			1.56564
$877$	638.649			0.728220			0.364110	−	0.931356i	$-0.381373\pi$
$877$	638.649			0.728220			0.364110	+	0.931356i	$0.381373\pi$
$878$		−	1626.55i		−	1.85256i
$879$	214.551			0.244086
$880$		0			0
$881$		−	148.009i		−	0.168001i	−0.996466	−	0.0840003i	$-0.973230\pi$
$881$		−	148.009i		−	0.168001i	0.996466	−	0.0840003i	$-0.0267697\pi$
$882$	427.899	−	286.655i	0.485146	−	0.325005i
$883$	784.505			0.888454			0.444227	−	0.895914i	$-0.353478\pi$
$883$	784.505			0.888454			0.444227	+	0.895914i	$0.353478\pi$
$884$	159.977			0.180970
$885$		0			0
$886$	−403.724			−0.455670
$887$			1466.40i			1.65321i	0.562783	+	0.826605i	$0.309731\pi$
$887$			1466.40i			1.65321i	−0.562783	+	0.826605i	$0.690269\pi$
$888$		−	967.433i		−	1.08945i
$889$	559.294	−	170.026i	0.629127	−	0.191255i
$890$		0			0
$891$	−18.2800			−0.0205163
$892$			796.559i			0.893003i
$893$	1603.27			1.79538
$894$		−	174.939i		−	0.195681i
$895$		0			0
$896$	1376.31	−	418.400i	1.53606	−	0.466964i
$897$	−776.152			−0.865276
$898$	−1170.07			−1.30298
$899$			1694.38i			1.88473i
$900$		0			0
$901$			61.6540i			0.0684284i
$902$			355.255i			0.393853i
$903$	−33.8142	−	111.231i	−0.0374465	−	0.123179i
$904$	−1808.48			−2.00053
$905$		0			0
$906$			1506.89i			1.66324i
$907$	−488.454			−0.538538			−0.269269	−	0.963065i	$-0.586782\pi$
$907$	−488.454			−0.538538			−0.269269	+	0.963065i	$0.586782\pi$
$908$			758.863i			0.835752i
$909$		−	219.990i		−	0.242013i
$910$		0			0
$911$	1329.44			1.45932			0.729658	−	0.683812i	$-0.239679\pi$
$911$	1329.44			1.45932			0.729658	+	0.683812i	$0.239679\pi$
$912$	966.543			1.05981
$913$		−	209.964i		−	0.229971i
$914$	1240.84			1.35759
$915$		0			0
$916$		−	2681.14i		−	2.92700i
$917$	−403.633	−	1327.74i	−0.440167	−	1.44791i
$918$	−19.5326			−0.0212774
$919$	1369.52			1.49023			0.745113	−	0.666938i	$-0.232395\pi$
$919$	1369.52			1.49023			0.745113	+	0.666938i	$0.232395\pi$
$920$		0			0
$921$	−390.710			−0.424224
$922$		−	451.647i		−	0.489856i
$923$		−	464.920i		−	0.503705i
$924$	59.2769	+	194.989i	0.0641525	+	0.211028i
$925$		0			0
$926$	−1058.73			−1.14333
$927$		−	172.029i		−	0.185576i
$928$	307.368			0.331216
$929$		−	909.289i		−	0.978783i	−0.872064	−	0.489391i	$-0.837219\pi$
$929$		−	909.289i		−	0.978783i	0.872064	−	0.489391i	$-0.162781\pi$
$930$		0			0
$931$	785.022	+	1171.83i	0.843203	+	1.25868i
$932$	−1513.80			−1.62425
$933$	91.7378			0.0983256
$934$		−	2831.78i		−	3.03188i
$935$		0			0
$936$			809.768i			0.865137i
$937$			184.883i			0.197313i	0.995122	+	0.0986566i	$0.0314545\pi$
$937$			184.883i			0.197313i	−0.995122	+	0.0986566i	$0.968545\pi$
$938$	2246.39	−	682.904i	2.39487	−	0.728043i
$939$	−648.762			−0.690907
$940$		0			0
$941$		−	884.454i		−	0.939909i	−0.882691	−	0.469955i	$-0.844270\pi$
$941$		−	884.454i		−	0.939909i	0.882691	−	0.469955i	$-0.155730\pi$
$942$	251.146			0.266610
$943$		−	1241.58i		−	1.31662i
$944$			1971.51i			2.08847i
$945$		0			0
$946$	68.2371			0.0721322
$947$	651.331			0.687784			0.343892	−	0.939009i	$-0.388255\pi$
$947$	651.331			0.687784			0.343892	+	0.939009i	$0.388255\pi$
$948$		−	403.094i		−	0.425205i
$949$	−1723.91			−1.81656
$950$		0			0
$951$			20.8798i			0.0219557i
$952$	32.7249	+	107.647i	0.0343749	+	0.113075i
$953$	−1622.61			−1.70263			−0.851316	−	0.524654i	$-0.824195\pi$
$953$	−1622.61			−1.70263			−0.851316	+	0.524654i	$0.824195\pi$
$954$	−604.025			−0.633150
$955$		0			0
$956$	−355.232			−0.371582
$957$		−	135.197i		−	0.141271i
$958$		−	171.273i		−	0.178782i
$959$	161.832	−	49.1970i	0.168751	−	0.0513003i
$960$		0			0
$961$	−982.915			−1.02280
$962$			2353.60i			2.44657i
$963$	−119.520			−0.124112
$964$			826.708i			0.857581i
$965$		0			0
$966$	−307.297	−	1010.84i	−0.318112	−	1.04642i
$967$	1491.24			1.54213			0.771067	−	0.636754i	$-0.219724\pi$
$967$	1491.24			1.54213			0.771067	+	0.636754i	$0.219724\pi$
$968$	1750.92			1.80880
$969$		−	53.4914i		−	0.0552027i
$970$		0			0
$971$			1739.36i			1.79130i	0.444756	+	0.895652i	$0.353291\pi$
$971$			1739.36i			1.79130i	−0.444756	+	0.895652i	$0.646709\pi$
$972$		−	129.008i		−	0.132724i
$973$	125.493	+	412.806i	0.128975	+	0.424261i
$974$	1171.75			1.20303
$975$		0			0
$976$		−	619.444i		−	0.634676i
$977$	62.8973			0.0643780			0.0321890	−	0.999482i	$-0.489752\pi$
$977$	62.8973			0.0643780			0.0321890	+	0.999482i	$0.489752\pi$
$978$			314.414i			0.321487i
$979$		−	59.6395i		−	0.0609188i
$980$		0			0
$981$	555.156			0.565909
$982$	1924.06			1.95932
$983$			1214.68i			1.23569i	0.786299	+	0.617846i	$0.211994\pi$
$983$			1214.68i			1.23569i	−0.786299	+	0.617846i	$0.788006\pi$
$984$	−1295.35			−1.31641
$985$		0			0
$986$		−	144.461i		−	0.146512i
$987$	−646.104	+	196.416i	−0.654614	+	0.199003i
$988$	−4292.15			−4.34428
$989$	−238.481			−0.241133
$990$		0			0
$991$	114.216			0.115253			0.0576266	−	0.998338i	$-0.481647\pi$
$991$	114.216			0.115253			0.0576266	+	0.998338i	$0.481647\pi$
$992$			352.636i			0.355480i
$993$			651.570i			0.656163i
$994$	605.501	−	184.072i	0.609156	−	0.185184i
$995$		0			0
$996$	1481.78			1.48773
$997$		−	178.000i		−	0.178536i	−0.996008	−	0.0892678i	$-0.971547\pi$
$997$		−	178.000i		−	0.178536i	0.996008	−	0.0892678i	$-0.0284527\pi$
$998$	1620.28			1.62353
$999$		−	193.729i		−	0.193923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.h.d.76.1		12
5.2	odd	4		525.3.e.c.349.9		24
5.3	odd	4		525.3.e.c.349.24		24
5.4	even	2		105.3.h.a.76.12	yes	12
7.6	odd	2	inner	525.3.h.d.76.2		12
15.14	odd	2		315.3.h.d.181.2		12
20.19	odd	2		1680.3.s.c.1441.3		12
35.13	even	4		525.3.e.c.349.10		24
35.27	even	4		525.3.e.c.349.23		24
35.34	odd	2		105.3.h.a.76.11	✓	12
105.104	even	2		315.3.h.d.181.1		12
140.139	even	2		1680.3.s.c.1441.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.11	✓	12	35.34	odd	2
105.3.h.a.76.12	yes	12	5.4	even	2
315.3.h.d.181.1		12	105.104	even	2
315.3.h.d.181.2		12	15.14	odd	2
525.3.e.c.349.9		24	5.2	odd	4
525.3.e.c.349.10		24	35.13	even	4
525.3.e.c.349.23		24	35.27	even	4
525.3.e.c.349.24		24	5.3	odd	4
525.3.h.d.76.1		12	1.1	even	1	trivial
525.3.h.d.76.2		12	7.6	odd	2	inner
1680.3.s.c.1441.3		12	20.19	odd	2
1680.3.s.c.1441.12		12	140.139	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +6.06857i q^{6} +(6.69736 - 2.03600i) q^{7} -14.9812 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.50369 q^{2} -1.73205i q^{3} +8.27584 q^{4} +6.06857i q^{6} +(6.69736 - 2.03600i) q^{7} -14.9812 q^{8} -3.00000 q^{9} -2.03112 q^{11} -14.3342i q^{12} +18.0174i q^{13} +(-23.4655 + 7.13352i) q^{14} +19.3861 q^{16} -1.07289i q^{17} +10.5111 q^{18} +28.7852i q^{19} +(-3.52646 - 11.6002i) q^{21} +7.11640 q^{22} -24.8710 q^{23} +25.9482i q^{24} -63.1275i q^{26} +5.19615i q^{27} +(55.4263 - 16.8496i) q^{28} -38.4300 q^{29} -44.0899i q^{31} -7.99812 q^{32} +3.51800i q^{33} +3.75906i q^{34} -24.8275 q^{36} -37.2832 q^{37} -100.855i q^{38} +31.2071 q^{39} +49.9206i q^{41} +(12.3556 + 40.6434i) q^{42} +9.58871 q^{43} -16.8092 q^{44} +87.1402 q^{46} -55.6978i q^{47} -33.5777i q^{48} +(40.7094 - 27.2717i) q^{49} -1.85829 q^{51} +149.109i q^{52} -57.4656 q^{53} -18.2057i q^{54} +(-100.335 + 30.5018i) q^{56} +49.8575 q^{57} +134.647 q^{58} +101.697i q^{59} -31.9530i q^{61} +154.477i q^{62} +(-20.0921 + 6.10801i) q^{63} -49.5215 q^{64} -12.3260i q^{66} -95.7318 q^{67} -8.87902i q^{68} +43.0778i q^{69} -25.8039 q^{71} +44.9436 q^{72} +95.6803i q^{73} +130.629 q^{74} +238.222i q^{76} +(-13.6031 + 4.13536i) q^{77} -109.340 q^{78} +28.1212 q^{79} +9.00000 q^{81} -174.906i q^{82} +103.374i q^{83} +(-29.1844 - 96.0012i) q^{84} -33.5959 q^{86} +66.5628i q^{87} +30.4286 q^{88} +29.3629i q^{89} +(36.6835 + 120.669i) q^{91} -205.828 q^{92} -76.3659 q^{93} +195.148i q^{94} +13.8531i q^{96} +67.6473i q^{97} +(-142.633 + 95.5515i) q^{98} +6.09335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} - 12 q^{18} + 36 q^{21} + 88 q^{22} + 64 q^{23} - 88 q^{28} + 104 q^{29} + 228 q^{32} - 132 q^{36} - 32 q^{37} - 24 q^{39} + 60 q^{42} - 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 24 q^{51} - 176 q^{53} - 368 q^{56} + 240 q^{57} + 400 q^{58} - 24 q^{63} - 20 q^{64} - 168 q^{67} + 32 q^{71} + 12 q^{72} + 184 q^{74} - 8 q^{77} - 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 400 q^{86} + 536 q^{88} + 24 q^{91} - 192 q^{92} - 48 q^{93} - 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 - 12 * q^18 + 36 * q^21 + 88 * q^22 + 64 * q^23 - 88 * q^28 + 104 * q^29 + 228 * q^32 - 132 * q^36 - 32 * q^37 - 24 * q^39 + 60 * q^42 - 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 24 * q^51 - 176 * q^53 - 368 * q^56 + 240 * q^57 + 400 * q^58 - 24 * q^63 - 20 * q^64 - 168 * q^67 + 32 * q^71 + 12 * q^72 + 184 * q^74 - 8 * q^77 - 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 400 * q^86 + 536 * q^88 + 24 * q^91 - 192 * q^92 - 48 * q^93 - 884 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more