LMFDB - Embedded newform 525.3.h.d.76.6

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			76.6
Root			$-1.74681 - 3.02556i$ of defining polynomial
Character	$\chi$	$=$	525.76
Dual form			525.3.h.d.76.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.112974 q^{2} +1.73205i q^{3} -3.98724 q^{4} +0.195676i q^{6} +(6.71303 - 1.98374i) q^{7} -0.902349 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+0.112974 q^{2} +1.73205i q^{3} -3.98724 q^{4} +0.195676i q^{6} +(6.71303 - 1.98374i) q^{7} -0.902349 q^{8} -3.00000 q^{9} -15.8613 q^{11} -6.90610i q^{12} +13.3044i q^{13} +(0.758397 - 0.224110i) q^{14} +15.8470 q^{16} -15.6784i q^{17} -0.338921 q^{18} -30.8816i q^{19} +(3.43593 + 11.6273i) q^{21} -1.79192 q^{22} -3.63638 q^{23} -1.56291i q^{24} +1.50305i q^{26} -5.19615i q^{27} +(-26.7664 + 7.90963i) q^{28} +14.5640 q^{29} -11.3504i q^{31} +5.39969 q^{32} -27.4726i q^{33} -1.77125i q^{34} +11.9617 q^{36} -17.3820 q^{37} -3.48881i q^{38} -23.0439 q^{39} -27.9286i q^{41} +(0.388171 + 1.31358i) q^{42} +12.1944 q^{43} +63.2429 q^{44} -0.410816 q^{46} -80.5893i q^{47} +27.4478i q^{48} +(41.1296 - 26.6338i) q^{49} +27.1557 q^{51} -53.0477i q^{52} +55.9152 q^{53} -0.587029i q^{54} +(-6.05750 + 1.79002i) q^{56} +53.4885 q^{57} +1.64536 q^{58} -79.5439i q^{59} -94.5743i q^{61} -1.28230i q^{62} +(-20.1391 + 5.95121i) q^{63} -62.7780 q^{64} -3.10369i q^{66} +103.457 q^{67} +62.5134i q^{68} -6.29840i q^{69} -113.803 q^{71} +2.70705 q^{72} -20.3444i q^{73} -1.96371 q^{74} +123.132i q^{76} +(-106.478 + 31.4647i) q^{77} -2.60336 q^{78} -1.27532 q^{79} +9.00000 q^{81} -3.15520i q^{82} +19.7667i q^{83} +(-13.6999 - 46.3608i) q^{84} +1.37765 q^{86} +25.2257i q^{87} +14.3125 q^{88} +131.258i q^{89} +(26.3924 + 89.3128i) q^{91} +14.4991 q^{92} +19.6595 q^{93} -9.10448i q^{94} +9.35254i q^{96} +12.4236i q^{97} +(4.64657 - 3.00892i) q^{98} +47.5840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.112974			0.0564869			0.0282435	−	0.999601i	$-0.491009\pi$
$2$	0.112974			0.0564869			0.0282435	+	0.999601i	$0.491009\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.98724			−0.996809
$5$		0			0
$5$		0			0
$6$			0.195676i			0.0326127i
$7$	6.71303	−	1.98374i	0.959004	−	0.283391i
$7$	6.71303	−	1.98374i	0.959004	−	0.283391i
$8$	−0.902349			−0.112794
$9$	−3.00000			−0.333333
$10$		0			0
$11$	−15.8613			−1.44194			−0.720970	−	0.692966i	$-0.756303\pi$
$11$	−15.8613			−1.44194			−0.720970	+	0.692966i	$0.756303\pi$
$12$		−	6.90610i		−	0.575508i
$13$			13.3044i			1.02341i	0.859160	+	0.511707i	$0.170987\pi$
$13$			13.3044i			1.02341i	−0.859160	+	0.511707i	$0.829013\pi$
$14$	0.758397	−	0.224110i	0.0541712	−	0.0160079i
$15$		0			0
$16$	15.8470			0.990438
$17$		−	15.6784i		−	0.922257i	−0.887333	−	0.461129i	$-0.847445\pi$
$17$		−	15.6784i		−	0.922257i	0.887333	−	0.461129i	$-0.152555\pi$
$18$	−0.338921			−0.0188290
$19$		−	30.8816i		−	1.62535i	−0.582719	−	0.812673i	$-0.698011\pi$
$19$		−	30.8816i		−	1.62535i	0.582719	−	0.812673i	$-0.301989\pi$
$20$		0			0
$21$	3.43593	+	11.6273i	0.163616	+	0.553681i
$22$	−1.79192			−0.0814507
$23$	−3.63638			−0.158104			−0.0790518	−	0.996871i	$-0.525189\pi$
$23$	−3.63638			−0.158104			−0.0790518	+	0.996871i	$0.525189\pi$
$24$		−	1.56291i		−	0.0651214i
$25$		0			0
$26$			1.50305i			0.0578095i
$27$		−	5.19615i		−	0.192450i
$28$	−26.7664	+	7.90963i	−0.955944	+	0.282487i
$29$	14.5640			0.502208			0.251104	−	0.967960i	$-0.419206\pi$
$29$	14.5640			0.502208			0.251104	+	0.967960i	$0.419206\pi$
$30$		0			0
$31$		−	11.3504i		−	0.366142i	−0.983100	−	0.183071i	$-0.941396\pi$
$31$		−	11.3504i		−	0.366142i	0.983100	−	0.183071i	$-0.0586038\pi$
$32$	5.39969			0.168740
$33$		−	27.4726i		−	0.832504i
$34$		−	1.77125i		−	0.0520955i
$35$		0			0
$36$	11.9617			0.332270
$37$	−17.3820			−0.469784			−0.234892	−	0.972021i	$-0.575474\pi$
$37$	−17.3820			−0.469784			−0.234892	+	0.972021i	$0.575474\pi$
$38$		−	3.48881i		−	0.0918108i
$39$	−23.0439			−0.590869
$40$		0			0
$41$		−	27.9286i		−	0.681186i	−0.940211	−	0.340593i	$-0.889372\pi$
$41$		−	27.9286i		−	0.681186i	0.940211	−	0.340593i	$-0.110628\pi$
$42$	0.388171	+	1.31358i	0.00924216	+	0.0312758i
$43$	12.1944			0.283591			0.141796	−	0.989896i	$-0.454712\pi$
$43$	12.1944			0.283591			0.141796	+	0.989896i	$0.454712\pi$
$44$	63.2429			1.43734
$45$		0			0
$46$	−0.410816			−0.00893078
$47$		−	80.5893i		−	1.71467i	−0.514762	−	0.857333i	$-0.672120\pi$
$47$		−	80.5893i		−	1.71467i	0.514762	−	0.857333i	$-0.327880\pi$
$48$			27.4478i			0.571830i
$49$	41.1296	−	26.6338i	0.839379	−	0.543546i
$50$		0			0
$51$	27.1557			0.532465
$52$		−	53.0477i		−	1.02015i
$53$	55.9152			1.05500			0.527502	−	0.849554i	$-0.323129\pi$
$53$	55.9152			1.05500			0.527502	+	0.849554i	$0.323129\pi$
$54$		−	0.587029i		−	0.0108709i
$55$		0			0
$56$	−6.05750	+	1.79002i	−0.108170	+	0.0319647i
$57$	53.4885			0.938395
$58$	1.64536			0.0283682
$59$		−	79.5439i		−	1.34820i	−0.738640	−	0.674101i	$-0.764531\pi$
$59$		−	79.5439i		−	1.34820i	0.738640	−	0.674101i	$-0.235469\pi$
$60$		0			0
$61$		−	94.5743i		−	1.55040i	−0.631717	−	0.775199i	$-0.717650\pi$
$61$		−	94.5743i		−	1.55040i	0.631717	−	0.775199i	$-0.282350\pi$
$62$		−	1.28230i		−	0.0206822i
$63$	−20.1391	+	5.95121i	−0.319668	+	0.0944637i
$64$	−62.7780			−0.980906
$65$		0			0
$66$		−	3.10369i		−	0.0470256i
$67$	103.457			1.54414			0.772068	−	0.635540i	$-0.219222\pi$
$67$	103.457			1.54414			0.772068	+	0.635540i	$0.219222\pi$
$68$			62.5134i			0.919314i
$69$		−	6.29840i		−	0.0912811i
$70$		0			0
$71$	−113.803			−1.60286			−0.801431	−	0.598087i	$-0.795928\pi$
$71$	−113.803			−1.60286			−0.801431	+	0.598087i	$0.795928\pi$
$72$	2.70705			0.0375979
$73$		−	20.3444i		−	0.278690i	−0.990244	−	0.139345i	$-0.955500\pi$
$73$		−	20.3444i		−	0.278690i	0.990244	−	0.139345i	$-0.0444998\pi$
$74$	−1.96371			−0.0265367
$75$		0			0
$76$			123.132i			1.62016i
$77$	−106.478	+	31.4647i	−1.38283	+	0.408633i
$78$	−2.60336			−0.0333763
$79$	−1.27532			−0.0161433			−0.00807165	−	0.999967i	$-0.502569\pi$
$79$	−1.27532			−0.0161433			−0.00807165	+	0.999967i	$0.502569\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		−	3.15520i		−	0.0384781i
$83$			19.7667i			0.238153i	0.992885	+	0.119076i	$0.0379934\pi$
$83$			19.7667i			0.238153i	−0.992885	+	0.119076i	$0.962007\pi$
$84$	−13.6999	−	46.3608i	−0.163094	−	0.551915i
$85$		0			0
$86$	1.37765			0.0160192
$87$			25.2257i			0.289950i
$88$	14.3125			0.162642
$89$			131.258i			1.47481i	0.675450	+	0.737406i	$0.263949\pi$
$89$			131.258i			1.47481i	−0.675450	+	0.737406i	$0.736051\pi$
$90$		0			0
$91$	26.3924	+	89.3128i	0.290026	+	0.981459i
$92$	14.4991			0.157599
$93$	19.6595			0.211392
$94$		−	9.10448i		−	0.0968562i
$95$		0			0
$96$			9.35254i			0.0974223i
$97$			12.4236i			0.128078i	0.997947	+	0.0640391i	$0.0203982\pi$
$97$			12.4236i			0.128078i	−0.997947	+	0.0640391i	$0.979602\pi$
$98$	4.64657	−	3.00892i	0.0474139	−	0.0307033i
$99$	47.5840			0.480647
$100$		0			0
$101$			15.0668i			0.149176i	0.997214	+	0.0745882i	$0.0237642\pi$
$101$			15.0668i			0.149176i	−0.997214	+	0.0745882i	$0.976236\pi$
$102$	3.06789			0.0300773
$103$			69.5863i			0.675595i	0.941219	+	0.337798i	$0.109682\pi$
$103$			69.5863i			0.675595i	−0.941219	+	0.337798i	$0.890318\pi$
$104$		−	12.0052i		−	0.115435i
$105$		0			0
$106$	6.31696			0.0595939
$107$	−104.493			−0.976569			−0.488285	−	0.872684i	$-0.662377\pi$
$107$	−104.493			−0.976569			−0.488285	+	0.872684i	$0.662377\pi$
$108$			20.7183i			0.191836i
$109$	−19.2137			−0.176273			−0.0881363	−	0.996108i	$-0.528091\pi$
$109$	−19.2137			−0.176273			−0.0881363	+	0.996108i	$0.528091\pi$
$110$		0			0
$111$		−	30.1065i		−	0.271230i
$112$	106.381	−	31.4363i	0.949834	−	0.280681i
$113$	−208.552			−1.84559			−0.922795	−	0.385291i	$-0.874101\pi$
$113$	−208.552			−1.84559			−0.922795	+	0.385291i	$0.874101\pi$
$114$	6.04280			0.0530070
$115$		0			0
$116$	−58.0703			−0.500606
$117$		−	39.9132i		−	0.341138i
$118$		−	8.98637i		−	0.0761557i
$119$	−31.1018	−	105.249i	−0.261359	−	0.884449i
$120$		0			0
$121$	130.582			1.07919
$122$		−	10.6844i		−	0.0875772i
$123$	48.3738			0.393283
$124$			45.2567i			0.364974i
$125$		0			0
$126$	−2.27519	+	0.672331i	−0.0180571	+	0.00533596i
$127$	−65.1002			−0.512600			−0.256300	−	0.966597i	$-0.582504\pi$
$127$	−65.1002			−0.512600			−0.256300	+	0.966597i	$0.582504\pi$
$128$	−28.6910			−0.224149
$129$			21.1213i			0.163731i
$130$		0			0
$131$		−	160.360i		−	1.22412i	−0.790812	−	0.612060i	$-0.790341\pi$
$131$		−	160.360i		−	1.22412i	0.790812	−	0.612060i	$-0.209659\pi$
$132$			109.540i			0.829848i
$133$	−61.2610	−	207.309i	−0.460609	−	1.55871i
$134$	11.6879			0.0872235
$135$		0			0
$136$			14.1474i			0.104025i
$137$	−158.451			−1.15658			−0.578289	−	0.815832i	$-0.696279\pi$
$137$	−158.451			−1.15658			−0.578289	+	0.815832i	$0.696279\pi$
$138$		−	0.711554i		−	0.00515619i
$139$			243.471i			1.75159i	0.482684	+	0.875794i	$0.339662\pi$
$139$			243.471i			1.75159i	−0.482684	+	0.875794i	$0.660338\pi$
$140$		0			0
$141$	139.585			0.989963
$142$	−12.8568			−0.0905408
$143$		−	211.025i		−	1.47570i
$144$	−47.5410			−0.330146
$145$		0			0
$146$		−	2.29838i		−	0.0157424i
$147$	46.1311	+	71.2385i	0.313817	+	0.484616i
$148$	69.3062			0.468285
$149$	−134.390			−0.901948			−0.450974	−	0.892537i	$-0.648923\pi$
$149$	−134.390			−0.901948			−0.450974	+	0.892537i	$0.648923\pi$
$150$		0			0
$151$	1.60056			0.0105997			0.00529987	−	0.999986i	$-0.498313\pi$
$151$	1.60056			0.0105997			0.00529987	+	0.999986i	$0.498313\pi$
$152$			27.8660i			0.183329i
$153$			47.0351i			0.307419i
$154$	−12.0292	+	3.55469i	−0.0781116	+	0.0230824i
$155$		0			0
$156$	91.8814			0.588983
$157$			252.462i			1.60804i	0.594602	+	0.804020i	$0.297310\pi$
$157$			252.462i			1.60804i	−0.594602	+	0.804020i	$0.702690\pi$
$158$	−0.144078			−0.000911885
$159$			96.8480i			0.609107i
$160$		0			0
$161$	−24.4111	+	7.21362i	−0.151622	+	0.0448051i
$162$	1.01676			0.00627632
$163$	239.023			1.46640			0.733199	−	0.680014i	$-0.238026\pi$
$163$	239.023			1.46640			0.733199	+	0.680014i	$0.238026\pi$
$164$			111.358i			0.679013i
$165$		0			0
$166$			2.23312i			0.0134525i
$167$			170.456i			1.02070i	0.859968	+	0.510348i	$0.170483\pi$
$167$			170.456i			1.02070i	−0.859968	+	0.510348i	$0.829517\pi$
$168$	−3.10041	−	10.4919i	−0.0184548	−	0.0624517i
$169$	−8.00675			−0.0473772
$170$		0			0
$171$			92.6448i			0.541782i
$172$	−48.6220			−0.282686
$173$		−	269.554i		−	1.55812i	−0.626952	−	0.779058i	$-0.715698\pi$
$173$		−	269.554i		−	1.55812i	0.626952	−	0.779058i	$-0.284302\pi$
$174$			2.84984i			0.0163784i
$175$		0			0
$176$	−251.355			−1.42815
$177$	137.774			0.778384
$178$			14.8287i			0.0833076i
$179$	132.675			0.741199			0.370599	−	0.928793i	$-0.379152\pi$
$179$	132.675			0.741199			0.370599	+	0.928793i	$0.379152\pi$
$180$		0			0
$181$		−	231.384i		−	1.27836i	−0.769056	−	0.639182i	$-0.779273\pi$
$181$		−	231.384i		−	1.27836i	0.769056	−	0.639182i	$-0.220727\pi$
$182$	2.98165	+	10.0900i	0.0163827	+	0.0554396i
$183$	163.807			0.895123
$184$	3.28128			0.0178331
$185$		0			0
$186$	2.22101			0.0119409
$187$			248.680i			1.32984i
$188$			321.329i			1.70920i
$189$	−10.3078	−	34.8819i	−0.0545386	−	0.184560i
$190$		0			0
$191$	−304.129			−1.59230			−0.796150	−	0.605099i	$-0.793133\pi$
$191$	−304.129			−1.59230			−0.796150	+	0.605099i	$0.793133\pi$
$192$		−	108.735i		−	0.566326i
$193$	−138.227			−0.716202			−0.358101	−	0.933683i	$-0.616576\pi$
$193$	−138.227			−0.716202			−0.358101	+	0.933683i	$0.616576\pi$
$194$			1.40354i			0.00723474i
$195$		0			0
$196$	−163.993	+	106.195i	−0.836701	+	0.541812i
$197$	26.9115			0.136607			0.0683034	−	0.997665i	$-0.478241\pi$
$197$	26.9115			0.136607			0.0683034	+	0.997665i	$0.478241\pi$
$198$	5.37575			0.0271502
$199$		−	251.997i		−	1.26632i	−0.774023	−	0.633158i	$-0.781759\pi$
$199$		−	251.997i		−	1.26632i	0.774023	−	0.633158i	$-0.218241\pi$
$200$		0			0
$201$			179.193i			0.891507i
$202$			1.70216i			0.00842651i
$203$	97.7689	−	28.8912i	0.481620	−	0.142321i
$204$	−108.276			−0.530766
$205$		0			0
$206$			7.86143i			0.0381623i
$207$	10.9091			0.0527012
$208$			210.835i			1.01363i
$209$			489.823i			2.34365i
$210$		0			0
$211$	235.692			1.11702			0.558511	−	0.829497i	$-0.311373\pi$
$211$	235.692			1.11702			0.558511	+	0.829497i	$0.311373\pi$
$212$	−222.947			−1.05164
$213$		−	197.113i		−	0.925413i
$214$	−11.8050			−0.0551634
$215$		0			0
$216$			4.68874i			0.0217071i
$217$	−22.5162	−	76.1956i	−0.103761	−	0.351132i
$218$	−2.17065			−0.00995709
$219$	35.2375			0.160902
$220$		0			0
$221$	208.591			0.943851
$222$		−	3.40125i		−	0.0153210i
$223$			142.790i			0.640314i	0.947365	+	0.320157i	$0.103736\pi$
$223$			142.790i			0.640314i	−0.947365	+	0.320157i	$0.896264\pi$
$224$	36.2483	−	10.7116i	0.161823	−	0.0478195i
$225$		0			0
$226$	−23.5609			−0.104252
$227$		−	30.6210i		−	0.134894i	−0.997723	−	0.0674472i	$-0.978515\pi$
$227$		−	30.6210i		−	0.134894i	0.997723	−	0.0674472i	$-0.0214854\pi$
$228$	−213.271			−0.935400
$229$		−	210.682i		−	0.920007i	−0.887917	−	0.460004i	$-0.847848\pi$
$229$		−	210.682i		−	0.920007i	0.887917	−	0.460004i	$-0.152152\pi$
$230$		0			0
$231$	−54.4985	−	184.425i	−0.235924	−	0.798375i
$232$	−13.1418			−0.0566459
$233$	182.891			0.784940			0.392470	−	0.919765i	$-0.371621\pi$
$233$	182.891			0.784940			0.392470	+	0.919765i	$0.371621\pi$
$234$		−	4.50914i		−	0.0192698i
$235$		0			0
$236$			317.160i			1.34390i
$237$		−	2.20892i		−	0.00932034i
$238$	−3.51369	−	11.8904i	−0.0147634	−	0.0499598i
$239$	122.511			0.512597			0.256299	−	0.966598i	$-0.417497\pi$
$239$	122.511			0.512597			0.256299	+	0.966598i	$0.417497\pi$
$240$		0			0
$241$			149.941i			0.622160i	0.950384	+	0.311080i	$0.100691\pi$
$241$			149.941i			0.622160i	−0.950384	+	0.311080i	$0.899309\pi$
$242$	14.7524			0.0609601
$243$			15.5885i			0.0641500i
$244$			377.090i			1.54545i
$245$		0			0
$246$	5.46497			0.0222153
$247$	410.861			1.66340
$248$			10.2420i			0.0412985i
$249$	−34.2369			−0.137498
$250$		0			0
$251$		−	229.388i		−	0.913896i	−0.889493	−	0.456948i	$-0.848942\pi$
$251$		−	229.388i		−	0.913896i	0.889493	−	0.456948i	$-0.151058\pi$
$252$	80.2993	−	23.7289i	0.318648	−	0.0941622i
$253$	57.6779			0.227976
$254$	−7.35462			−0.0289552
$255$		0			0
$256$	247.871			0.968245
$257$			48.6524i			0.189309i	0.995510	+	0.0946545i	$0.0301746\pi$
$257$			48.6524i			0.189309i	−0.995510	+	0.0946545i	$0.969825\pi$
$258$			2.38616i			0.00924868i
$259$	−116.686	+	34.4814i	−0.450525	+	0.133133i
$260$		0			0
$261$	−43.6921			−0.167403
$262$		−	18.1164i		−	0.0691467i
$263$	37.6942			0.143324			0.0716620	−	0.997429i	$-0.477170\pi$
$263$	37.6942			0.143324			0.0716620	+	0.997429i	$0.477170\pi$
$264$			24.7899i			0.0939012i
$265$		0			0
$266$	−6.92088	−	23.4205i	−0.0260184	−	0.0880470i
$267$	−227.346			−0.851483
$268$	−412.508			−1.53921
$269$		−	291.724i		−	1.08448i	−0.840225	−	0.542238i	$-0.817577\pi$
$269$		−	291.724i		−	1.08448i	0.840225	−	0.542238i	$-0.182423\pi$
$270$		0			0
$271$		−	102.880i		−	0.379631i	−0.981820	−	0.189815i	$-0.939211\pi$
$271$		−	102.880i		−	0.379631i	0.981820	−	0.189815i	$-0.0607890\pi$
$272$		−	248.455i		−	0.913438i
$273$	−154.694	+	45.7130i	−0.566646	+	0.167447i
$274$	−17.9008			−0.0653316
$275$		0			0
$276$			25.1132i			0.0909898i
$277$	−381.417			−1.37696			−0.688479	−	0.725256i	$-0.741721\pi$
$277$	−381.417			−1.37696			−0.688479	+	0.725256i	$0.741721\pi$
$278$			27.5058i			0.0989418i
$279$			34.0512i			0.122047i
$280$		0			0
$281$	17.4853			0.0622251			0.0311126	−	0.999516i	$-0.490095\pi$
$281$	17.4853			0.0622251			0.0311126	+	0.999516i	$0.490095\pi$
$282$	15.7694			0.0559200
$283$		−	343.358i		−	1.21328i	−0.794977	−	0.606640i	$-0.792517\pi$
$283$		−	343.358i		−	1.21328i	0.794977	−	0.606640i	$-0.207483\pi$
$284$	453.760			1.59775
$285$		0			0
$286$		−	23.8403i		−	0.0833579i
$287$	−55.4031	−	187.486i	−0.193042	−	0.653260i
$288$	−16.1991			−0.0562468
$289$	43.1887			0.149442
$290$		0			0
$291$	−21.5183			−0.0739460
$292$			81.1179i			0.277801i
$293$			244.504i			0.834486i	0.908795	+	0.417243i	$0.137004\pi$
$293$			244.504i			0.834486i	−0.908795	+	0.417243i	$0.862996\pi$
$294$	5.21160	+	8.04809i	0.0177265	+	0.0273744i
$295$		0			0
$296$	15.6846			0.0529887
$297$			82.4179i			0.277501i
$298$	−15.1826			−0.0509482
$299$		−	48.3798i		−	0.161805i
$300$		0			0
$301$	81.8615	−	24.1905i	0.271965	−	0.0803672i
$302$	0.180822			0.000598747
$303$	−26.0965			−0.0861270
$304$		−	489.381i		−	1.60981i
$305$		0			0
$306$			5.31374i			0.0173652i
$307$		−	347.793i		−	1.13287i	−0.824105	−	0.566437i	$-0.808321\pi$
$307$		−	347.793i		−	1.13287i	0.824105	−	0.566437i	$-0.191679\pi$
$308$	424.552	−	125.457i	1.37841	−	0.407329i
$309$	−120.527			−0.390055
$310$		0			0
$311$			105.360i			0.338778i	0.985549	+	0.169389i	$0.0541794\pi$
$311$			105.360i			0.338778i	−0.985549	+	0.169389i	$0.945821\pi$
$312$	20.7936			0.0666462
$313$			165.880i			0.529967i	0.964253	+	0.264984i	$0.0853666\pi$
$313$			165.880i			0.529967i	−0.964253	+	0.264984i	$0.914633\pi$
$314$			28.5216i			0.0908333i
$315$		0			0
$316$	5.08500			0.0160918
$317$	96.7933			0.305342			0.152671	−	0.988277i	$-0.451213\pi$
$317$	96.7933			0.305342			0.152671	+	0.988277i	$0.451213\pi$
$318$			10.9413i			0.0344066i
$319$	−231.005			−0.724154
$320$		0			0
$321$		−	180.987i		−	0.563823i
$322$	−2.75782	+	0.814951i	−0.00856466	+	0.00253090i
$323$	−484.173			−1.49899
$324$	−35.8851			−0.110757
$325$		0			0
$326$	27.0033			0.0828323
$327$		−	33.2791i		−	0.101771i
$328$			25.2014i			0.0768334i
$329$	−159.868	−	540.999i	−0.485921	−	1.64437i
$330$		0			0
$331$	−193.682			−0.585141			−0.292571	−	0.956244i	$-0.594511\pi$
$331$	−193.682			−0.585141			−0.292571	+	0.956244i	$0.594511\pi$
$332$		−	78.8145i		−	0.237393i
$333$	52.1461			0.156595
$334$			19.2571i			0.0576559i
$335$		0			0
$336$	54.4493	+	184.258i	0.162051	+	0.548387i
$337$	238.742			0.708433			0.354216	−	0.935163i	$-0.384748\pi$
$337$	238.742			0.708433			0.354216	+	0.935163i	$0.384748\pi$
$338$	−0.904554			−0.00267619
$339$		−	361.222i		−	1.06555i
$340$		0			0
$341$			180.033i			0.527955i
$342$			10.4664i			0.0306036i
$343$	223.270	−	260.384i	0.650932	−	0.759136i
$344$	−11.0036			−0.0319873
$345$		0			0
$346$		−	30.4526i		−	0.0880132i
$347$	533.787			1.53829			0.769145	−	0.639074i	$-0.220682\pi$
$347$	533.787			1.53829			0.769145	+	0.639074i	$0.220682\pi$
$348$		−	100.581i		−	0.289025i
$349$			230.498i			0.660454i	0.943902	+	0.330227i	$0.107125\pi$
$349$			230.498i			0.660454i	−0.943902	+	0.330227i	$0.892875\pi$
$350$		0			0
$351$	69.1316			0.196956
$352$	−85.6463			−0.243313
$353$			12.3883i			0.0350944i	0.999846	+	0.0175472i	$0.00558574\pi$
$353$			12.3883i			0.0350944i	−0.999846	+	0.0175472i	$0.994414\pi$
$354$	15.5649			0.0439685
$355$		0			0
$356$		−	523.358i		−	1.47011i
$357$	182.297	−	53.8698i	0.510637	−	0.150896i
$358$	14.9888			0.0418680
$359$	−442.447			−1.23244			−0.616222	−	0.787572i	$-0.711338\pi$
$359$	−442.447			−1.23244			−0.616222	+	0.787572i	$0.711338\pi$
$360$		0			0
$361$	−592.673			−1.64175
$362$		−	26.1403i		−	0.0722108i
$363$			226.175i			0.623071i
$364$	−105.233	−	356.111i	−0.289101	−	0.978327i
$365$		0			0
$366$	18.5060			0.0505627
$367$		−	567.114i		−	1.54527i	−0.634851	−	0.772635i	$-0.718938\pi$
$367$		−	567.114i		−	1.54527i	0.634851	−	0.772635i	$-0.281062\pi$
$368$	−57.6257			−0.156592
$369$			83.7859i			0.227062i
$370$		0			0
$371$	375.361	−	110.921i	1.01175	−	0.298979i
$372$	−78.3870			−0.210718
$373$	106.146			0.284574			0.142287	−	0.989825i	$-0.454554\pi$
$373$	106.146			0.284574			0.142287	+	0.989825i	$0.454554\pi$
$374$			28.0943i			0.0751185i
$375$		0			0
$376$			72.7197i			0.193403i
$377$			193.766i			0.513967i
$378$	−1.16451	−	3.94075i	−0.00308072	−	0.0104253i
$379$	715.733			1.88848			0.944239	−	0.329262i	$-0.106800\pi$
$379$	715.733			1.88848			0.944239	+	0.329262i	$0.106800\pi$
$380$		0			0
$381$		−	112.757i		−	0.295950i
$382$	−34.3587			−0.0899441
$383$			571.840i			1.49305i	0.665355	+	0.746527i	$0.268280\pi$
$383$			571.840i			1.49305i	−0.665355	+	0.746527i	$0.731720\pi$
$384$		−	49.6943i		−	0.129412i
$385$		0			0
$386$	−15.6160			−0.0404560
$387$	−36.5832			−0.0945304
$388$		−	49.5358i		−	0.127670i
$389$	−12.6584			−0.0325409			−0.0162705	−	0.999868i	$-0.505179\pi$
$389$	−12.6584			−0.0325409			−0.0162705	+	0.999868i	$0.505179\pi$
$390$		0			0
$391$			57.0125i			0.145812i
$392$	−37.1132	+	24.0330i	−0.0946766	+	0.0613086i
$393$	277.751			0.706745
$394$	3.04030			0.00771650
$395$		0			0
$396$	−189.729			−0.479113
$397$			29.1232i			0.0733582i	0.999327	+	0.0366791i	$0.0116779\pi$
$397$			29.1232i			0.0733582i	−0.999327	+	0.0366791i	$0.988322\pi$
$398$		−	28.4690i		−	0.0715302i
$399$	359.070	−	106.107i	0.899925	−	0.265933i
$400$		0			0
$401$	144.012			0.359133			0.179567	−	0.983746i	$-0.442530\pi$
$401$	144.012			0.359133			0.179567	+	0.983746i	$0.442530\pi$
$402$			20.2441i			0.0503585i
$403$	151.010			0.374715
$404$		−	60.0749i		−	0.148700i
$405$		0			0
$406$	11.0453	−	3.26395i	0.0272052	−	0.00803929i
$407$	275.702			0.677401
$408$	−24.5039			−0.0600587
$409$			338.914i			0.828641i	0.910131	+	0.414320i	$0.135981\pi$
$409$			338.914i			0.828641i	−0.910131	+	0.414320i	$0.864019\pi$
$410$		0			0
$411$		−	274.446i		−	0.667751i
$412$		−	277.457i		−	0.673440i
$413$	−157.794	−	533.980i	−0.382068	−	1.29293i
$414$	1.23245			0.00297693
$415$		0			0
$416$			71.8396i			0.172691i
$417$	−421.704			−1.01128
$418$			55.3372i			0.132386i
$419$		−	101.585i		−	0.242446i	−0.992625	−	0.121223i	$-0.961318\pi$
$419$		−	101.585i		−	0.242446i	0.992625	−	0.121223i	$-0.0386816\pi$
$420$		0			0
$421$	−145.700			−0.346081			−0.173041	−	0.984915i	$-0.555359\pi$
$421$	−145.700			−0.346081			−0.173041	+	0.984915i	$0.555359\pi$
$422$	26.6270			0.0630972
$423$			241.768i			0.571555i
$424$	−50.4550			−0.118998
$425$		0			0
$426$		−	22.2686i		−	0.0522737i
$427$	−187.610	−	634.880i	−0.439369	−	1.48684i
$428$	416.638			0.973453
$429$	365.507			0.851997
$430$		0			0
$431$	497.669			1.15468			0.577342	−	0.816502i	$-0.304090\pi$
$431$	497.669			1.15468			0.577342	+	0.816502i	$0.304090\pi$
$432$		−	82.3435i		−	0.190610i
$433$			605.000i			1.39723i	0.715499	+	0.698614i	$0.246199\pi$
$433$			605.000i			1.39723i	−0.715499	+	0.698614i	$0.753801\pi$
$434$	−2.54374	−	8.60811i	−0.00586116	−	0.0198344i
$435$		0			0
$436$	76.6096			0.175710
$437$			112.297i			0.256973i
$438$	3.98092			0.00908886
$439$			211.605i			0.482015i	0.970523	+	0.241008i	$0.0774779\pi$
$439$			211.605i			0.482015i	−0.970523	+	0.241008i	$0.922522\pi$
$440$		0			0
$441$	−123.389	+	79.9013i	−0.279793	+	0.181182i
$442$	23.5653			0.0533152
$443$	−794.013			−1.79235			−0.896177	−	0.443697i	$-0.853666\pi$
$443$	−794.013			−1.79235			−0.896177	+	0.443697i	$0.853666\pi$
$444$			120.042i			0.270365i
$445$		0			0
$446$			16.1315i			0.0361693i
$447$		−	232.771i		−	0.520740i
$448$	−421.431	+	124.535i	−0.940693	+	0.277980i
$449$	−486.171			−1.08279			−0.541393	−	0.840769i	$-0.682103\pi$
$449$	−486.171			−1.08279			−0.541393	+	0.840769i	$0.682103\pi$
$450$		0			0
$451$			442.985i			0.982229i
$452$	831.545			1.83970
$453$			2.77226i			0.00611977i
$454$		−	3.45938i		−	0.00761977i
$455$		0			0
$456$	−48.2653			−0.105845
$457$	−114.609			−0.250786			−0.125393	−	0.992107i	$-0.540019\pi$
$457$	−114.609			−0.250786			−0.125393	+	0.992107i	$0.540019\pi$
$458$		−	23.8015i		−	0.0519684i
$459$	−81.4672			−0.177488
$460$		0			0
$461$			352.184i			0.763957i	0.924171	+	0.381978i	$0.124757\pi$
$461$			352.184i			0.763957i	−0.924171	+	0.381978i	$0.875243\pi$
$462$	−6.15690	−	20.8352i	−0.0133266	−	0.0450978i
$463$	226.624			0.489468			0.244734	−	0.969590i	$-0.421299\pi$
$463$	226.624			0.489468			0.244734	+	0.969590i	$0.421299\pi$
$464$	230.796			0.497406
$465$		0			0
$466$	20.6619			0.0443388
$467$		−	405.655i		−	0.868641i	−0.900758	−	0.434320i	$-0.856989\pi$
$467$		−	405.655i		−	0.868641i	0.900758	−	0.434320i	$-0.143011\pi$
$468$			159.143i			0.340050i
$469$	694.511	−	205.232i	1.48083	−	0.437594i
$470$		0			0
$471$	−437.278			−0.928403
$472$			71.7763i			0.152068i
$473$	−193.420			−0.408921
$474$		−	0.249550i		−	0.000526477i
$475$		0			0
$476$	124.010	+	419.654i	0.260525	+	0.881627i
$477$	−167.746			−0.351668
$478$	13.8405			0.0289550
$479$		−	900.420i		−	1.87979i	−0.341463	−	0.939895i	$-0.610922\pi$
$479$		−	900.420i		−	1.87979i	0.341463	−	0.939895i	$-0.389078\pi$
$480$		0			0
$481$		−	231.257i		−	0.480784i
$482$			16.9394i			0.0351439i
$483$	−12.4944	−	42.2813i	−0.0258682	−	0.0875390i
$484$	−520.661			−1.07575
$485$		0			0
$486$			1.76109i			0.00362364i
$487$	−55.4219			−0.113803			−0.0569014	−	0.998380i	$-0.518122\pi$
$487$	−55.4219			−0.113803			−0.0569014	+	0.998380i	$0.518122\pi$
$488$			85.3390i			0.174875i
$489$			414.000i			0.846625i
$490$		0			0
$491$	616.592			1.25579			0.627894	−	0.778299i	$-0.283917\pi$
$491$	616.592			1.25579			0.627894	+	0.778299i	$0.283917\pi$
$492$	−192.878			−0.392028
$493$		−	228.340i		−	0.463165i
$494$	46.4165			0.0939605
$495$		0			0
$496$		−	179.870i		−	0.362641i
$497$	−763.965	+	225.756i	−1.53715	+	0.454237i
$498$	−3.86788			−0.00776682
$499$	624.620			1.25174			0.625872	−	0.779926i	$-0.284743\pi$
$499$	624.620			1.25174			0.625872	+	0.779926i	$0.284743\pi$
$500$		0			0
$501$	−295.239			−0.589299
$502$		−	25.9148i		−	0.0516232i
$503$			226.444i			0.450187i	0.974337	+	0.225093i	$0.0722687\pi$
$503$			226.444i			0.450187i	−0.974337	+	0.225093i	$0.927731\pi$
$504$	18.1725	−	5.37007i	0.0360565	−	0.0106549i
$505$		0			0
$506$	6.51609			0.0128776
$507$		−	13.8681i		−	0.0273533i
$508$	259.570			0.510965
$509$			468.169i			0.919781i	0.887976	+	0.459891i	$0.152111\pi$
$509$			468.169i			0.919781i	−0.887976	+	0.459891i	$0.847889\pi$
$510$		0			0
$511$	−40.3579	−	136.573i	−0.0789783	−	0.267265i
$512$	142.767			0.278842
$513$	−160.465			−0.312798
$514$			5.49645i			0.0106935i
$515$		0			0
$516$		−	84.2158i		−	0.163209i
$517$			1278.25i			2.47245i
$518$	−13.1825	+	3.89549i	−0.0254488	+	0.00752025i
$519$	466.881			0.899579
$520$		0			0
$521$			458.100i			0.879271i	0.898176	+	0.439635i	$0.144892\pi$
$521$			458.100i			0.879271i	−0.898176	+	0.439635i	$0.855108\pi$
$522$	−4.93607			−0.00945607
$523$		−	256.863i		−	0.491135i	−0.969380	−	0.245567i	$-0.921026\pi$
$523$		−	256.863i		−	0.491135i	0.969380	−	0.245567i	$-0.0789742\pi$
$524$			639.392i			1.22021i
$525$		0			0
$526$	4.25846			0.00809593
$527$	−177.956			−0.337677
$528$		−	435.359i		−	0.824544i
$529$	−515.777			−0.975003
$530$		0			0
$531$			238.632i			0.449400i
$532$	244.262	+	826.590i	0.459139	+	1.55374i
$533$	371.573			0.697136
$534$	−25.6841			−0.0480976
$535$		0			0
$536$	−93.3544			−0.174169
$537$			229.799i			0.427931i
$538$		−	32.9572i		−	0.0612587i
$539$	−652.370	+	422.447i	−1.21033	+	0.783761i
$540$		0			0
$541$	−57.7912			−0.106823			−0.0534115	−	0.998573i	$-0.517009\pi$
$541$	−57.7912			−0.106823			−0.0534115	+	0.998573i	$0.517009\pi$
$542$		−	11.6227i		−	0.0214442i
$543$	400.768			0.738063
$544$		−	84.6584i		−	0.155622i
$545$		0			0
$546$	−17.4764	+	5.16437i	−0.0320081	+	0.00945856i
$547$	−658.275			−1.20343			−0.601714	−	0.798712i	$-0.705515\pi$
$547$	−658.275			−1.20343			−0.601714	+	0.798712i	$0.705515\pi$
$548$	631.783			1.15289
$549$			283.723i			0.516799i
$550$		0			0
$551$		−	449.761i		−	0.816263i
$552$			5.68335i			0.0102959i
$553$	−8.56126	+	2.52990i	−0.0154815	+	0.00457486i
$554$	−43.0902			−0.0777801
$555$		0			0
$556$		−	970.776i		−	1.74600i
$557$	782.705			1.40521			0.702607	−	0.711578i	$-0.252019\pi$
$557$	782.705			1.40521			0.702607	+	0.711578i	$0.252019\pi$
$558$			3.84690i			0.00689408i
$559$			162.239i			0.290231i
$560$		0			0
$561$	−430.726			−0.767783
$562$	1.97538			0.00351491
$563$		−	632.083i		−	1.12271i	−0.827577	−	0.561353i	$-0.810281\pi$
$563$		−	632.083i		−	1.12271i	0.827577	−	0.561353i	$-0.189719\pi$
$564$	−556.558			−0.986804
$565$		0			0
$566$		−	38.7905i		−	0.0685345i
$567$	60.4173	−	17.8536i	0.106556	−	0.0314879i
$568$	102.690			0.180793
$569$	−603.746			−1.06107			−0.530533	−	0.847665i	$-0.678008\pi$
$569$	−603.746			−1.06107			−0.530533	+	0.847665i	$0.678008\pi$
$570$		0			0
$571$	−638.070			−1.11746			−0.558730	−	0.829349i	$-0.688711\pi$
$571$	−638.070			−1.11746			−0.558730	+	0.829349i	$0.688711\pi$
$572$			841.408i			1.47099i
$573$		−	526.767i		−	0.919315i
$574$	−6.25909	−	21.1810i	−0.0109043	−	0.0369007i
$575$		0			0
$576$	188.334			0.326969
$577$			449.363i			0.778792i	0.921070	+	0.389396i	$0.127316\pi$
$577$			449.363i			0.778792i	−0.921070	+	0.389396i	$0.872684\pi$
$578$	4.87919			0.00844151
$579$		−	239.416i		−	0.413499i
$580$		0			0
$581$	39.2119	+	132.694i	0.0674904	+	0.228390i
$582$	−2.43100			−0.00417698
$583$	−886.890			−1.52125
$584$			18.3577i			0.0314345i
$585$		0			0
$586$			27.6226i			0.0471375i
$587$		−	133.202i		−	0.226920i	−0.993543	−	0.113460i	$-0.963807\pi$
$587$		−	133.202i		−	0.226920i	0.993543	−	0.113460i	$-0.0361935\pi$
$588$	−183.935	−	284.045i	−0.312815	−	0.483069i
$589$	−350.519			−0.595108
$590$		0			0
$591$			46.6122i			0.0788700i
$592$	−275.453			−0.465292
$593$		−	444.341i		−	0.749310i	−0.927164	−	0.374655i	$-0.877761\pi$
$593$		−	444.341i		−	0.749310i	0.927164	−	0.374655i	$-0.122239\pi$
$594$			9.31107i			0.0156752i
$595$		0			0
$596$	535.846			0.899070
$597$	436.471			0.731107
$598$		−	5.46565i		−	0.00913989i
$599$	−230.917			−0.385504			−0.192752	−	0.981247i	$-0.561741\pi$
$599$	−230.917			−0.385504			−0.192752	+	0.981247i	$0.561741\pi$
$600$		0			0
$601$		−	147.957i		−	0.246185i	−0.992395	−	0.123092i	$-0.960719\pi$
$601$		−	147.957i		−	0.246185i	0.992395	−	0.123092i	$-0.0392812\pi$
$602$	9.24821	−	2.73289i	0.0153625	−	0.00453969i
$603$	−310.371			−0.514712
$604$	−6.38182			−0.0105659
$605$		0			0
$606$	−2.94822			−0.00486505
$607$		−	1036.13i		−	1.70697i	−0.521119	−	0.853484i	$-0.674485\pi$
$607$		−	1036.13i		−	1.70697i	0.521119	−	0.853484i	$-0.325515\pi$
$608$		−	166.751i		−	0.274262i
$609$	50.0411	+	169.341i	0.0821692	+	0.278063i
$610$		0			0
$611$	1072.19			1.75481
$612$		−	187.540i		−	0.306438i
$613$	175.987			0.287091			0.143545	−	0.989644i	$-0.454150\pi$
$613$	175.987			0.287091			0.143545	+	0.989644i	$0.454150\pi$
$614$		−	39.2915i		−	0.0639926i
$615$		0			0
$616$	96.0800	−	28.3922i	0.155974	−	0.0460912i
$617$	635.690			1.03029			0.515146	−	0.857103i	$-0.327738\pi$
$617$	635.690			1.03029			0.515146	+	0.857103i	$0.327738\pi$
$618$	−13.6164			−0.0220330
$619$		−	581.258i		−	0.939027i	−0.882925	−	0.469514i	$-0.844429\pi$
$619$		−	581.258i		−	0.939027i	0.882925	−	0.469514i	$-0.155571\pi$
$620$		0			0
$621$			18.8952i			0.0304270i
$622$			11.9029i			0.0191365i
$623$	260.382	+	881.141i	0.417948	+	1.41435i
$624$	−365.176			−0.585219
$625$		0			0
$626$			18.7401i			0.0299362i
$627$	−848.399			−1.35311
$628$		−	1006.63i		−	1.60291i
$629$			272.522i			0.433262i
$630$		0			0
$631$	−550.845			−0.872972			−0.436486	−	0.899711i	$-0.643777\pi$
$631$	−550.845			−0.872972			−0.436486	+	0.899711i	$0.643777\pi$
$632$	1.15078			0.00182086
$633$			408.230i			0.644913i
$634$	10.9351			0.0172478
$635$		0			0
$636$		−	386.156i		−	0.607163i
$637$	354.346	+	547.204i	0.556273	+	0.859033i
$638$	−26.0975			−0.0409052
$639$	341.410			0.534287
$640$		0			0
$641$	−64.8667			−0.101196			−0.0505981	−	0.998719i	$-0.516113\pi$
$641$	−64.8667			−0.101196			−0.0505981	+	0.998719i	$0.516113\pi$
$642$		−	20.4468i		−	0.0318486i
$643$			812.068i			1.26294i	0.775402	+	0.631468i	$0.217547\pi$
$643$			812.068i			1.26294i	−0.775402	+	0.631468i	$0.782453\pi$
$644$	97.3330	−	28.7624i	0.151138	−	0.0446621i
$645$		0			0
$646$	−54.6989			−0.0846732
$647$			618.282i			0.955613i	0.878465	+	0.477807i	$0.158568\pi$
$647$			618.282i			0.955613i	−0.878465	+	0.477807i	$0.841432\pi$
$648$	−8.12114			−0.0125326
$649$			1261.67i			1.94402i
$650$		0			0
$651$	131.975	−	38.9992i	0.202726	−	0.0599066i
$652$	−953.041			−1.46172
$653$	694.281			1.06322			0.531609	−	0.846990i	$-0.321588\pi$
$653$	694.281			1.06322			0.531609	+	0.846990i	$0.321588\pi$
$654$		−	3.75967i		−	0.00574873i
$655$		0			0
$656$		−	442.585i		−	0.674672i
$657$			61.0332i			0.0928968i
$658$	−18.0609	−	61.1187i	−0.0274482	−	0.0928855i
$659$	514.683			0.781007			0.390503	−	0.920601i	$-0.372301\pi$
$659$	514.683			0.781007			0.390503	+	0.920601i	$0.372301\pi$
$660$		0			0
$661$			347.998i			0.526472i	0.964731	+	0.263236i	$0.0847899\pi$
$661$			347.998i			0.526472i	−0.964731	+	0.263236i	$0.915210\pi$
$662$	−21.8810			−0.0330528
$663$			361.290i			0.544933i
$664$		−	17.8364i		−	0.0268621i
$665$		0			0
$666$	5.89114			0.00884556
$667$	−52.9604			−0.0794009
$668$		−	679.649i		−	1.01744i
$669$	−247.319			−0.369685
$670$		0			0
$671$			1500.07i			2.23558i
$672$	18.5530	+	62.7839i	0.0276086	+	0.0934284i
$673$	−478.656			−0.711227			−0.355614	−	0.934633i	$-0.615728\pi$
$673$	−478.656			−0.711227			−0.355614	+	0.934633i	$0.615728\pi$
$674$	26.9716			0.0400172
$675$		0			0
$676$	31.9248			0.0472261
$677$			276.403i			0.408277i	0.978942	+	0.204138i	$0.0654393\pi$
$677$			276.403i			0.408277i	−0.978942	+	0.204138i	$0.934561\pi$
$678$		−	40.8087i		−	0.0601898i
$679$	24.6451	+	83.3999i	0.0362962	+	0.122828i
$680$		0			0
$681$	53.0372			0.0778814
$682$			20.3390i			0.0298225i
$683$	−311.395			−0.455922			−0.227961	−	0.973670i	$-0.573206\pi$
$683$	−311.395			−0.455922			−0.227961	+	0.973670i	$0.573206\pi$
$684$		−	369.397i		−	0.540054i
$685$		0			0
$686$	25.2236	−	29.4165i	0.0367691	−	0.0428812i
$687$	364.911			0.531166
$688$	193.245			0.280879
$689$			743.918i			1.07971i
$690$		0			0
$691$			569.213i			0.823752i	0.911240	+	0.411876i	$0.135126\pi$
$691$			569.213i			0.823752i	−0.911240	+	0.411876i	$0.864874\pi$
$692$			1074.78i			1.55314i
$693$	319.433	−	94.3942i	0.460942	−	0.136211i
$694$	60.3039			0.0868933
$695$		0			0
$696$		−	22.7623i		−	0.0327045i
$697$	−437.875			−0.628229
$698$			26.0403i			0.0373070i
$699$			316.776i			0.453185i
$700$		0			0
$701$	−446.061			−0.636321			−0.318160	−	0.948037i	$-0.603065\pi$
$701$	−446.061			−0.636321			−0.318160	+	0.948037i	$0.603065\pi$
$702$	7.81007			0.0111254
$703$			536.785i			0.763563i
$704$	995.743			1.41441
$705$		0			0
$706$			1.39956i			0.00198238i
$707$	29.8886	+	101.144i	0.0422752	+	0.143061i
$708$	−549.338			−0.775901
$709$	−480.480			−0.677686			−0.338843	−	0.940843i	$-0.610036\pi$
$709$	−480.480			−0.677686			−0.338843	+	0.940843i	$0.610036\pi$
$710$		0			0
$711$	3.82596			0.00538110
$712$		−	118.441i		−	0.166349i
$713$			41.2744i			0.0578883i
$714$	20.5948	−	6.08588i	0.0288443	−	0.00852364i
$715$		0			0
$716$	−529.005			−0.738834
$717$			212.195i			0.295948i
$718$	−49.9850			−0.0696170
$719$		−	330.338i		−	0.459441i	−0.973257	−	0.229721i	$-0.926219\pi$
$719$		−	330.338i		−	0.459441i	0.973257	−	0.229721i	$-0.0737813\pi$
$720$		0			0
$721$	138.041	+	467.135i	0.191458	+	0.647899i
$722$	−66.9565			−0.0927375
$723$	−259.705			−0.359204
$724$			922.582i			1.27428i
$725$		0			0
$726$			25.5518i			0.0351953i
$727$			327.774i			0.450858i	0.974260	+	0.225429i	$0.0723783\pi$
$727$			327.774i			0.450858i	−0.974260	+	0.225429i	$0.927622\pi$
$728$	−23.8152	−	80.5913i	−0.0327131	−	0.110702i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	191.189i		−	0.261544i
$732$	−653.139			−0.892267
$733$			124.845i			0.170320i	0.996367	+	0.0851601i	$0.0271402\pi$
$733$			124.845i			0.170320i	−0.996367	+	0.0851601i	$0.972860\pi$
$734$		−	64.0690i		−	0.0872875i
$735$		0			0
$736$	−19.6353			−0.0266784
$737$	−1640.97			−2.22655
$738$			9.46561i			0.0128260i
$739$	759.049			1.02713			0.513565	−	0.858051i	$-0.328325\pi$
$739$	759.049			1.02713			0.513565	+	0.858051i	$0.328325\pi$
$740$		0			0
$741$			711.632i			0.960367i
$742$	42.4059	−	12.5312i	0.0571508	−	0.0168884i
$743$	−658.165			−0.885820			−0.442910	−	0.896566i	$-0.646054\pi$
$743$	−658.165			−0.885820			−0.442910	+	0.896566i	$0.646054\pi$
$744$	−17.7397			−0.0238437
$745$		0			0
$746$	11.9917			0.0160747
$747$		−	59.3001i		−	0.0793843i
$748$		−	991.546i		−	1.32560i
$749$	−701.464	+	207.286i	−0.936534	+	0.276751i
$750$		0			0
$751$	−15.4050			−0.0205127			−0.0102564	−	0.999947i	$-0.503265\pi$
$751$	−15.4050			−0.0205127			−0.0102564	+	0.999947i	$0.503265\pi$
$752$		−	1277.10i		−	1.69827i
$753$	397.312			0.527638
$754$			21.8904i			0.0290324i
$755$		0			0
$756$	41.0996	+	139.083i	0.0543646	+	0.183972i
$757$	732.280			0.967345			0.483673	−	0.875249i	$-0.339303\pi$
$757$	732.280			0.967345			0.483673	+	0.875249i	$0.339303\pi$
$758$	80.8591			0.106674
$759$			99.9010i			0.131622i
$760$		0			0
$761$		−	969.037i		−	1.27337i	−0.771123	−	0.636686i	$-0.780305\pi$
$761$		−	969.037i		−	1.27337i	0.771123	−	0.636686i	$-0.219695\pi$
$762$		−	12.7386i		−	0.0167173i
$763$	−128.982	+	38.1149i	−0.169046	+	0.0499541i
$764$	1212.64			1.58722
$765$		0			0
$766$			64.6029i			0.0843380i
$767$	1058.28			1.37977
$768$			429.325i			0.559016i
$769$		−	1090.28i		−	1.41778i	−0.705317	−	0.708892i	$-0.749195\pi$
$769$		−	1090.28i		−	1.41778i	0.705317	−	0.708892i	$-0.250805\pi$
$770$		0			0
$771$	−84.2685			−0.109298
$772$	551.144			0.713917
$773$			1490.66i			1.92841i	0.265155	+	0.964206i	$0.414577\pi$
$773$			1490.66i			1.92841i	−0.265155	+	0.964206i	$0.585423\pi$
$774$	−4.13295			−0.00533973
$775$		0			0
$776$		−	11.2104i		−	0.0144464i
$777$	−59.7235	−	202.106i	−0.0768642	−	0.260111i
$778$	−1.43007			−0.00183814
$779$	−862.481			−1.10716
$780$		0			0
$781$	1805.07			2.31123
$782$			6.44092i			0.00823647i
$783$		−	75.6770i		−	0.0966500i
$784$	651.781	−	422.066i	0.831353	−	0.538349i
$785$		0			0
$786$	31.3786			0.0399219
$787$		−	290.045i		−	0.368545i	−0.982875	−	0.184272i	$-0.941007\pi$
$787$		−	290.045i		−	0.368545i	0.982875	−	0.184272i	$-0.0589928\pi$
$788$	−107.303			−0.136171
$789$			65.2883i			0.0827481i
$790$		0			0
$791$	−1400.01	+	413.712i	−1.76993	+	0.523024i
$792$	−42.9374			−0.0542139
$793$	1258.25			1.58670
$794$			3.29016i			0.00414378i
$795$		0			0
$796$			1004.77i			1.26227i
$797$		−	1089.39i		−	1.36686i	−0.730016	−	0.683430i	$-0.760488\pi$
$797$		−	1089.39i		−	1.36686i	0.730016	−	0.683430i	$-0.239512\pi$
$798$	40.5655	−	11.9873i	0.0508340	−	0.0150217i
$799$	−1263.51			−1.58136
$800$		0			0
$801$		−	393.775i		−	0.491604i
$802$	16.2696			0.0202863
$803$			322.689i			0.401855i
$804$		−	714.485i		−	0.888663i
$805$		0			0
$806$	17.0602			0.0211665
$807$	505.281			0.626123
$808$		−	13.5955i		−	0.0168261i
$809$	1396.14			1.72576			0.862880	−	0.505408i	$-0.168658\pi$
$809$	1396.14			1.72576			0.862880	+	0.505408i	$0.168658\pi$
$810$		0			0
$811$		−	1199.88i		−	1.47950i	−0.672881	−	0.739751i	$-0.734943\pi$
$811$		−	1199.88i		−	1.47950i	0.672881	−	0.739751i	$-0.265057\pi$
$812$	−389.828	+	115.196i	−0.480083	+	0.141867i
$813$	178.193			0.219180
$814$	31.1471			0.0382643
$815$		0			0
$816$	430.337			0.527374
$817$		−	376.583i		−	0.460934i
$818$			38.2884i			0.0468073i
$819$	−79.1772	−	267.938i	−0.0966755	−	0.327153i
$820$		0			0
$821$	−720.125			−0.877131			−0.438565	−	0.898699i	$-0.644513\pi$
$821$	−720.125			−0.877131			−0.438565	+	0.898699i	$0.644513\pi$
$822$		−	31.0052i		−	0.0377192i
$823$	136.641			0.166027			0.0830137	−	0.996548i	$-0.473545\pi$
$823$	136.641			0.166027			0.0830137	+	0.996548i	$0.473545\pi$
$824$		−	62.7911i		−	0.0762028i
$825$		0			0
$826$	−17.8266	−	60.3258i	−0.0215818	−	0.0730337i
$827$	732.193			0.885360			0.442680	−	0.896680i	$-0.354028\pi$
$827$	732.193			0.885360			0.442680	+	0.896680i	$0.354028\pi$
$828$	−43.4973			−0.0525330
$829$			478.689i			0.577430i	0.957415	+	0.288715i	$0.0932280\pi$
$829$			478.689i			0.577430i	−0.957415	+	0.288715i	$0.906772\pi$
$830$		0			0
$831$		−	660.634i		−	0.794987i
$832$		−	835.223i		−	1.00387i
$833$	−417.574	−	644.845i	−0.501290	−	0.774123i
$834$	−47.6415			−0.0571241
$835$		0			0
$836$		−	1953.04i		−	2.33617i
$837$	−58.9784			−0.0704641
$838$		−	11.4764i		−	0.0136950i
$839$		−	1156.58i		−	1.37852i	−0.724516	−	0.689258i	$-0.757936\pi$
$839$		−	1156.58i		−	1.37852i	0.724516	−	0.689258i	$-0.242064\pi$
$840$		0			0
$841$	−628.889			−0.747787
$842$	−16.4603			−0.0195491
$843$			30.2854i			0.0359257i
$844$	−939.759			−1.11346
$845$		0			0
$846$			27.3135i			0.0322854i
$847$	876.601	−	259.040i	1.03495	−	0.305833i
$848$	886.089			1.04492
$849$	594.714			0.700488
$850$		0			0
$851$	63.2077			0.0742746
$852$			785.936i			0.922460i
$853$		−	338.541i		−	0.396883i	−0.980113	−	0.198441i	$-0.936412\pi$
$853$		−	338.541i		−	0.396883i	0.980113	−	0.198441i	$-0.0635880\pi$
$854$	−21.1951	−	71.7248i	−0.0248186	−	0.0839869i
$855$		0			0
$856$	94.2890			0.110151
$857$			884.607i			1.03221i	0.856524	+	0.516107i	$0.172619\pi$
$857$			884.607i			1.03221i	−0.856524	+	0.516107i	$0.827381\pi$
$858$	41.2927			0.0481267
$859$			87.7088i			0.102106i	0.998696	+	0.0510528i	$0.0162577\pi$
$859$			87.7088i			0.102106i	−0.998696	+	0.0510528i	$0.983742\pi$
$860$		0			0
$861$	324.735	−	95.9609i	0.377160	−	0.111453i
$862$	56.2236			0.0652246
$863$	1419.95			1.64537			0.822683	−	0.568501i	$-0.192476\pi$
$863$	1419.95			1.64537			0.822683	+	0.568501i	$0.192476\pi$
$864$		−	28.0576i		−	0.0324741i
$865$		0			0
$866$			68.3491i			0.0789251i
$867$			74.8050i			0.0862803i
$868$	89.7775	+	303.810i	0.103430	+	0.350011i
$869$	20.2283			0.0232777
$870$		0			0
$871$			1376.43i			1.58029i
$872$	17.3375			0.0198824
$873$		−	37.2708i		−	0.0426927i
$874$			12.6866i			0.0145156i
$875$		0			0
$876$	−140.500			−0.160389
$877$	831.389			0.947992			0.473996	−	0.880527i	$-0.342811\pi$
$877$	831.389			0.947992			0.473996	+	0.880527i	$0.342811\pi$
$878$			23.9058i			0.0272276i
$879$	−423.494			−0.481791
$880$		0			0
$881$		−	782.236i		−	0.887895i	−0.896053	−	0.443948i	$-0.853578\pi$
$881$		−	782.236i		−	0.887895i	0.896053	−	0.443948i	$-0.146422\pi$
$882$	−13.9397	+	9.02676i	−0.0158046	+	0.0102344i
$883$	−10.4243			−0.0118056			−0.00590278	−	0.999983i	$-0.501879\pi$
$883$	−10.4243			−0.0118056			−0.00590278	+	0.999983i	$0.501879\pi$
$884$	−831.702			−0.940840
$885$		0			0
$886$	−89.7026			−0.101245
$887$		−	691.076i		−	0.779116i	−0.921002	−	0.389558i	$-0.872628\pi$
$887$		−	691.076i		−	0.779116i	0.921002	−	0.389558i	$-0.127372\pi$
$888$			27.1666i			0.0305930i
$889$	−437.020	+	129.142i	−0.491586	+	0.145266i
$890$		0			0
$891$	−142.752			−0.160216
$892$		−	569.337i		−	0.638271i
$893$	−2488.73			−2.78693
$894$		−	26.2970i		−	0.0294150i
$895$		0			0
$896$	−192.604	+	56.9155i	−0.214960	+	0.0635217i
$897$	83.7963			0.0934184
$898$	−54.9246			−0.0611633
$899$		−	165.308i		−	0.183880i
$900$		0			0
$901$		−	876.660i		−	0.972985i
$902$			50.0458i			0.0554831i
$903$	41.8992	+	141.788i	0.0464000	+	0.157019i
$904$	188.186			0.208171
$905$		0			0
$906$			0.313192i			0.000345687i
$907$	−704.064			−0.776256			−0.388128	−	0.921606i	$-0.626878\pi$
$907$	−704.064			−0.776256			−0.388128	+	0.921606i	$0.626878\pi$
$908$			122.093i			0.134464i
$909$		−	45.2004i		−	0.0497255i
$910$		0			0
$911$	1359.34			1.49214			0.746071	−	0.665867i	$-0.231938\pi$
$911$	1359.34			1.49214			0.746071	+	0.665867i	$0.231938\pi$
$912$	847.632			0.929421
$913$		−	313.526i		−	0.343402i
$914$	−12.9479			−0.0141662
$915$		0			0
$916$			840.038i			0.917072i
$917$	−318.111	−	1076.50i	−0.346904	−	1.17394i
$918$	−9.20366			−0.0100258
$919$	1475.83			1.60591			0.802953	−	0.596043i	$-0.203261\pi$
$919$	1475.83			1.60591			0.802953	+	0.596043i	$0.203261\pi$
$920$		0			0
$921$	602.394			0.654065
$922$			39.7876i			0.0431536i
$923$		−	1514.08i		−	1.64039i
$924$	217.298	+	735.345i	0.235171	+	0.795828i
$925$		0			0
$926$	25.6025			0.0276485
$927$		−	208.759i		−	0.225198i
$928$	78.6413			0.0847428
$929$		−	795.306i		−	0.856088i	−0.903758	−	0.428044i	$-0.859203\pi$
$929$		−	795.306i		−	0.856088i	0.903758	−	0.428044i	$-0.140797\pi$
$930$		0			0
$931$	−822.493	−	1270.15i	−0.883452	−	1.36428i
$932$	−729.229			−0.782435
$933$	−182.489			−0.195594
$934$		−	45.8284i		−	0.0490668i
$935$		0			0
$936$			36.0156i			0.0384782i
$937$		−	199.954i		−	0.213398i	−0.994291	−	0.106699i	$-0.965972\pi$
$937$		−	199.954i		−	0.213398i	0.994291	−	0.106699i	$-0.0340281\pi$
$938$	78.4616	−	23.1858i	0.0836477	−	0.0247183i
$939$	−287.312			−0.305977
$940$		0			0
$941$			1488.22i			1.58153i	0.612119	+	0.790765i	$0.290317\pi$
$941$			1488.22i			1.58153i	−0.612119	+	0.790765i	$0.709683\pi$
$942$	−49.4009			−0.0524426
$943$			101.559i			0.107698i
$944$		−	1260.53i		−	1.33531i
$945$		0			0
$946$	−21.8514			−0.0230987
$947$	−1232.27			−1.30124			−0.650620	−	0.759404i	$-0.725491\pi$
$947$	−1232.27			−1.30124			−0.650620	+	0.759404i	$0.725491\pi$
$948$			8.80749i			0.00929060i
$949$	270.670			0.285216
$950$		0			0
$951$			167.651i			0.176289i
$952$	28.0646	+	94.9717i	0.0294797	+	0.0997601i
$953$	2.73670			0.00287167			0.00143584	−	0.999999i	$-0.499543\pi$
$953$	2.73670			0.00287167			0.00143584	+	0.999999i	$0.499543\pi$
$954$	−18.9509			−0.0198646
$955$		0			0
$956$	−488.479			−0.510961
$957$		−	400.113i		−	0.418091i
$958$		−	101.724i		−	0.106184i
$959$	−1063.69	+	314.326i	−1.10916	+	0.327764i
$960$		0			0
$961$	832.168			0.865940
$962$		−	26.1260i		−	0.0271580i
$963$	313.479			0.325523
$964$		−	597.849i		−	0.620175i
$965$		0			0
$966$	−1.41154	−	4.77668i	−0.00146122	−	0.00494481i
$967$	−831.688			−0.860070			−0.430035	−	0.902812i	$-0.641499\pi$
$967$	−831.688			−0.860070			−0.430035	+	0.902812i	$0.641499\pi$
$968$	−117.831			−0.121726
$969$		−	838.612i		−	0.865441i
$970$		0			0
$971$			1800.97i			1.85476i	0.374118	+	0.927381i	$0.377945\pi$
$971$			1800.97i			1.85476i	−0.374118	+	0.927381i	$0.622055\pi$
$972$		−	62.1549i		−	0.0639453i
$973$	482.982	+	1634.43i	0.496384	+	1.67978i
$974$	−6.26123			−0.00642837
$975$		0			0
$976$		−	1498.72i		−	1.53557i
$977$	681.141			0.697176			0.348588	−	0.937276i	$-0.386661\pi$
$977$	681.141			0.697176			0.348588	+	0.937276i	$0.386661\pi$
$978$			46.7711i			0.0478233i
$979$		−	2081.93i		−	2.12659i
$980$		0			0
$981$	57.6411			0.0587575
$982$	69.6587			0.0709356
$983$			1188.81i			1.20937i	0.796465	+	0.604684i	$0.206701\pi$
$983$			1188.81i			1.20937i	−0.796465	+	0.604684i	$0.793299\pi$
$984$	−43.6500			−0.0443598
$985$		0			0
$986$		−	25.7965i		−	0.0261628i
$987$	937.037	−	276.900i	0.949379	−	0.280547i
$988$	−1638.20			−1.65810
$989$	−44.3435			−0.0448367
$990$		0			0
$991$	−325.271			−0.328225			−0.164113	−	0.986442i	$-0.552476\pi$
$991$	−325.271			−0.328225			−0.164113	+	0.986442i	$0.552476\pi$
$992$		−	61.2887i		−	0.0617829i
$993$		−	335.467i		−	0.337831i
$994$	−86.3080	+	25.5045i	−0.0868290	+	0.0256584i
$995$		0			0
$996$	136.511			0.137059
$997$			17.2566i			0.0173085i	0.999963	+	0.00865426i	$0.00275477\pi$
$997$			17.2566i			0.0173085i	−0.999963	+	0.00865426i	$0.997245\pi$
$998$	70.5657			0.0707071
$999$			90.3196i			0.0904100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.h.d.76.6		12
5.2	odd	4		525.3.e.c.349.18		24
5.3	odd	4		525.3.e.c.349.5		24
5.4	even	2		105.3.h.a.76.7	✓	12
7.6	odd	2	inner	525.3.h.d.76.5		12
15.14	odd	2		315.3.h.d.181.6		12
20.19	odd	2		1680.3.s.c.1441.9		12
35.13	even	4		525.3.e.c.349.17		24
35.27	even	4		525.3.e.c.349.6		24
35.34	odd	2		105.3.h.a.76.8	yes	12
105.104	even	2		315.3.h.d.181.5		12
140.139	even	2		1680.3.s.c.1441.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.7	✓	12	5.4	even	2
105.3.h.a.76.8	yes	12	35.34	odd	2
315.3.h.d.181.5		12	105.104	even	2
315.3.h.d.181.6		12	15.14	odd	2
525.3.e.c.349.5		24	5.3	odd	4
525.3.e.c.349.6		24	35.27	even	4
525.3.e.c.349.17		24	35.13	even	4
525.3.e.c.349.18		24	5.2	odd	4
525.3.h.d.76.5		12	7.6	odd	2	inner
525.3.h.d.76.6		12	1.1	even	1	trivial
1680.3.s.c.1441.6		12	140.139	even	2
1680.3.s.c.1441.9		12	20.19	odd	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)

\(f(q)\)	\(=\)	\(q+0.112974 q^{2} +1.73205i q^{3} -3.98724 q^{4} +0.195676i q^{6} +(6.71303 - 1.98374i) q^{7} -0.902349 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+0.112974 q^{2} +1.73205i q^{3} -3.98724 q^{4} +0.195676i q^{6} +(6.71303 - 1.98374i) q^{7} -0.902349 q^{8} -3.00000 q^{9} -15.8613 q^{11} -6.90610i q^{12} +13.3044i q^{13} +(0.758397 - 0.224110i) q^{14} +15.8470 q^{16} -15.6784i q^{17} -0.338921 q^{18} -30.8816i q^{19} +(3.43593 + 11.6273i) q^{21} -1.79192 q^{22} -3.63638 q^{23} -1.56291i q^{24} +1.50305i q^{26} -5.19615i q^{27} +(-26.7664 + 7.90963i) q^{28} +14.5640 q^{29} -11.3504i q^{31} +5.39969 q^{32} -27.4726i q^{33} -1.77125i q^{34} +11.9617 q^{36} -17.3820 q^{37} -3.48881i q^{38} -23.0439 q^{39} -27.9286i q^{41} +(0.388171 + 1.31358i) q^{42} +12.1944 q^{43} +63.2429 q^{44} -0.410816 q^{46} -80.5893i q^{47} +27.4478i q^{48} +(41.1296 - 26.6338i) q^{49} +27.1557 q^{51} -53.0477i q^{52} +55.9152 q^{53} -0.587029i q^{54} +(-6.05750 + 1.79002i) q^{56} +53.4885 q^{57} +1.64536 q^{58} -79.5439i q^{59} -94.5743i q^{61} -1.28230i q^{62} +(-20.1391 + 5.95121i) q^{63} -62.7780 q^{64} -3.10369i q^{66} +103.457 q^{67} +62.5134i q^{68} -6.29840i q^{69} -113.803 q^{71} +2.70705 q^{72} -20.3444i q^{73} -1.96371 q^{74} +123.132i q^{76} +(-106.478 + 31.4647i) q^{77} -2.60336 q^{78} -1.27532 q^{79} +9.00000 q^{81} -3.15520i q^{82} +19.7667i q^{83} +(-13.6999 - 46.3608i) q^{84} +1.37765 q^{86} +25.2257i q^{87} +14.3125 q^{88} +131.258i q^{89} +(26.3924 + 89.3128i) q^{91} +14.4991 q^{92} +19.6595 q^{93} -9.10448i q^{94} +9.35254i q^{96} +12.4236i q^{97} +(4.64657 - 3.00892i) q^{98} +47.5840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) \) 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

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