LMFDB - Embedded newform 208.3.t.c.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,3,Mod(161,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.161"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.t (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,4,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.66758949869$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			177.1
Root			$1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	208.177
Dual form			208.3.t.c.161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.16228 q^{3} +(0.418861 + 0.418861i) q^{5} +(1.41886 - 1.41886i) q^{7} -4.32456 q^{9} +(7.32456 - 7.32456i) q^{11} +(9.90569 - 8.41886i) q^{13} +(-0.905694 - 0.905694i) q^{15} -15.9737i q^{17} +(3.16228 + 3.16228i) q^{19} +(-3.06797 + 3.06797i) q^{21} -27.4868i q^{23} -24.6491i q^{25} +28.8114 q^{27} +25.8114 q^{29} +(-19.4868 - 19.4868i) q^{31} +(-15.8377 + 15.8377i) q^{33} +1.18861 q^{35} +(-4.23025 + 4.23025i) q^{37} +(-21.4189 + 18.2039i) q^{39} +(11.1623 + 11.1623i) q^{41} +11.5132i q^{43} +(-1.81139 - 1.81139i) q^{45} +(-35.3662 + 35.3662i) q^{47} +44.9737i q^{49} +34.5395i q^{51} -4.18861 q^{53} +6.13594 q^{55} +(-6.83772 - 6.83772i) q^{57} +(30.2719 - 30.2719i) q^{59} -67.6754 q^{61} +(-6.13594 + 6.13594i) q^{63} +(7.67544 + 0.622777i) q^{65} +(81.0833 + 81.0833i) q^{67} +59.4342i q^{69} +(-50.4452 - 50.4452i) q^{71} +(-31.6228 + 31.6228i) q^{73} +53.2982i q^{75} -20.7851i q^{77} -50.7851 q^{79} -23.3772 q^{81} +(-18.6228 - 18.6228i) q^{83} +(6.69075 - 6.69075i) q^{85} -55.8114 q^{87} +(91.1096 - 91.1096i) q^{89} +(2.10961 - 26.0000i) q^{91} +(42.1359 + 42.1359i) q^{93} +2.64911i q^{95} +(87.3552 + 87.3552i) q^{97} +(-31.6754 + 31.6754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 8 q^{5} + 12 q^{7} + 8 q^{9} + 4 q^{11} + 8 q^{13} + 28 q^{15} + 32 q^{21} + 52 q^{27} + 40 q^{29} - 40 q^{31} - 76 q^{33} + 68 q^{35} + 40 q^{37} - 92 q^{39} + 32 q^{41} + 56 q^{45} + 4 q^{47}+ \cdots - 152 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 + 8 * q^5 + 12 * q^7 + 8 * q^9 + 4 * q^11 + 8 * q^13 + 28 * q^15 + 32 * q^21 + 52 * q^27 + 40 * q^29 - 40 * q^31 - 76 * q^33 + 68 * q^35 + 40 * q^37 - 92 * q^39 + 32 * q^41 + 56 * q^45 + 4 * q^47 - 80 * q^53 - 64 * q^55 - 40 * q^57 - 56 * q^59 - 296 * q^61 + 64 * q^63 + 56 * q^65 + 84 * q^67 - 284 * q^71 - 64 * q^79 - 220 * q^81 + 52 * q^83 - 144 * q^85 - 160 * q^87 + 200 * q^89 - 156 * q^91 + 80 * q^93 - 68 * q^97 - 152 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.16228			−0.720759			−0.360380	−	0.932806i	$-0.617353\pi$
$3$	−2.16228			−0.720759			−0.360380	+	0.932806i	$0.617353\pi$
$4$		0			0
$5$	0.418861	+	0.418861i	0.0837722	+	0.0837722i	0.747751	−	0.663979i	$-0.231134\pi$
$5$	0.418861	+	0.418861i	0.0837722	+	0.0837722i	−0.663979	+	0.747751i	$0.731134\pi$
$6$		0			0
$7$	1.41886	−	1.41886i	0.202694	−	0.202694i	−0.598459	−	0.801153i	$-0.704220\pi$
$7$	1.41886	−	1.41886i	0.202694	−	0.202694i	0.801153	+	0.598459i	$0.204220\pi$
$8$		0			0
$9$	−4.32456			−0.480506
$10$		0			0
$11$	7.32456	−	7.32456i	0.665869	−	0.665869i	−0.290888	−	0.956757i	$-0.593951\pi$
$11$	7.32456	−	7.32456i	0.665869	−	0.665869i	0.956757	+	0.290888i	$0.0939508\pi$
$12$		0			0
$13$	9.90569	−	8.41886i	0.761976	−	0.647605i
$13$	9.90569	−	8.41886i	0.761976	−	0.647605i
$14$		0			0
$15$	−0.905694	−	0.905694i	−0.0603796	−	0.0603796i
$16$		0			0
$17$		−	15.9737i		−	0.939627i	−0.882766	−	0.469814i	$-0.844321\pi$
$17$		−	15.9737i		−	0.939627i	0.882766	−	0.469814i	$-0.155679\pi$
$18$		0			0
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	0.785411	−	0.618975i	$-0.212452\pi$
$19$	3.16228	+	3.16228i	0.166436	+	0.166436i	−0.618975	+	0.785411i	$0.712452\pi$
$20$		0			0
$21$	−3.06797	+	3.06797i	−0.146094	+	0.146094i
$22$		0			0
$23$		−	27.4868i		−	1.19508i	−0.801839	−	0.597540i	$-0.796145\pi$
$23$		−	27.4868i		−	1.19508i	0.801839	−	0.597540i	$-0.203855\pi$
$24$		0			0
$25$		−	24.6491i		−	0.985964i
$26$		0			0
$27$	28.8114			1.06709
$28$		0			0
$29$	25.8114			0.890048			0.445024	−	0.895519i	$-0.353195\pi$
$29$	25.8114			0.890048			0.445024	+	0.895519i	$0.353195\pi$
$30$		0			0
$31$	−19.4868	−	19.4868i	−0.628608	−	0.628608i	0.319110	−	0.947718i	$-0.396616\pi$
$31$	−19.4868	−	19.4868i	−0.628608	−	0.628608i	−0.947718	+	0.319110i	$0.896616\pi$
$32$		0			0
$33$	−15.8377	+	15.8377i	−0.479931	+	0.479931i
$34$		0			0
$35$	1.18861			0.0339603
$36$		0			0
$37$	−4.23025	+	4.23025i	−0.114331	+	0.114331i	−0.761958	−	0.647627i	$-0.775762\pi$
$37$	−4.23025	+	4.23025i	−0.114331	+	0.114331i	0.647627	+	0.761958i	$0.275762\pi$
$38$		0			0
$39$	−21.4189	+	18.2039i	−0.549202	+	0.466767i
$40$		0			0
$41$	11.1623	+	11.1623i	0.272251	+	0.272251i	0.830006	−	0.557755i	$-0.188337\pi$
$41$	11.1623	+	11.1623i	0.272251	+	0.272251i	−0.557755	+	0.830006i	$0.688337\pi$
$42$		0			0
$43$			11.5132i			0.267748i	0.990998	+	0.133874i	$0.0427418\pi$
$43$			11.5132i			0.267748i	−0.990998	+	0.133874i	$0.957258\pi$
$44$		0			0
$45$	−1.81139	−	1.81139i	−0.0402531	−	0.0402531i
$46$		0			0
$47$	−35.3662	+	35.3662i	−0.752472	+	0.752472i	−0.974940	−	0.222468i	$-0.928589\pi$
$47$	−35.3662	+	35.3662i	−0.752472	+	0.752472i	0.222468	+	0.974940i	$0.428589\pi$
$48$		0			0
$49$			44.9737i			0.917830i
$50$		0			0
$51$			34.5395i			0.677245i
$52$		0			0
$53$	−4.18861			−0.0790304			−0.0395152	−	0.999219i	$-0.512581\pi$
$53$	−4.18861			−0.0790304			−0.0395152	+	0.999219i	$0.512581\pi$
$54$		0			0
$55$	6.13594			0.111563
$56$		0			0
$57$	−6.83772	−	6.83772i	−0.119960	−	0.119960i
$58$		0			0
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	−0.402387	−	0.915470i	$-0.631819\pi$
$59$	30.2719	−	30.2719i	0.513083	−	0.513083i	0.915470	+	0.402387i	$0.131819\pi$
$60$		0			0
$61$	−67.6754			−1.10943			−0.554717	−	0.832039i	$-0.687173\pi$
$61$	−67.6754			−1.10943			−0.554717	+	0.832039i	$0.687173\pi$
$62$		0			0
$63$	−6.13594	+	6.13594i	−0.0973959	+	0.0973959i
$64$		0			0
$65$	7.67544	+	0.622777i	0.118084	+	0.00958118i
$66$		0			0
$67$	81.0833	+	81.0833i	1.21020	+	1.21020i	0.970961	+	0.239237i	$0.0768973\pi$
$67$	81.0833	+	81.0833i	1.21020	+	1.21020i	0.239237	+	0.970961i	$0.423103\pi$
$68$		0			0
$69$			59.4342i			0.861365i
$70$		0			0
$71$	−50.4452	−	50.4452i	−0.710496	−	0.710496i	0.256143	−	0.966639i	$-0.417548\pi$
$71$	−50.4452	−	50.4452i	−0.710496	−	0.710496i	−0.966639	+	0.256143i	$0.917548\pi$
$72$		0			0
$73$	−31.6228	+	31.6228i	−0.433189	+	0.433189i	−0.889712	−	0.456523i	$-0.849095\pi$
$73$	−31.6228	+	31.6228i	−0.433189	+	0.433189i	0.456523	+	0.889712i	$0.349095\pi$
$74$		0			0
$75$			53.2982i			0.710643i
$76$		0			0
$77$		−	20.7851i		−	0.269936i
$78$		0			0
$79$	−50.7851			−0.642849			−0.321424	−	0.946935i	$-0.604162\pi$
$79$	−50.7851			−0.642849			−0.321424	+	0.946935i	$0.604162\pi$
$80$		0			0
$81$	−23.3772			−0.288608
$82$		0			0
$83$	−18.6228	−	18.6228i	−0.224371	−	0.224371i	0.585965	−	0.810336i	$-0.300715\pi$
$83$	−18.6228	−	18.6228i	−0.224371	−	0.224371i	−0.810336	+	0.585965i	$0.800715\pi$
$84$		0			0
$85$	6.69075	−	6.69075i	0.0787147	−	0.0787147i
$86$		0			0
$87$	−55.8114			−0.641510
$88$		0			0
$89$	91.1096	−	91.1096i	1.02370	−	1.02370i	0.0239913	−	0.999712i	$-0.492363\pi$
$89$	91.1096	−	91.1096i	1.02370	−	1.02370i	0.999712	−	0.0239913i	$-0.00763740\pi$
$90$		0			0
$91$	2.10961	−	26.0000i	0.0231825	−	0.285714i
$92$		0			0
$93$	42.1359	+	42.1359i	0.453075	+	0.453075i
$94$		0			0
$95$			2.64911i			0.0278854i
$96$		0			0
$97$	87.3552	+	87.3552i	0.900569	+	0.900569i	0.995485	−	0.0949165i	$-0.0302584\pi$
$97$	87.3552	+	87.3552i	0.900569	+	0.900569i	−0.0949165	+	0.995485i	$0.530258\pi$
$98$		0			0
$99$	−31.6754	+	31.6754i	−0.319954	+	0.319954i
$100$		0			0
$101$		−	8.92100i		−	0.0883267i	−0.999024	−	0.0441634i	$-0.985938\pi$
$101$		−	8.92100i		−	0.0883267i	0.999024	−	0.0441634i	$-0.0140622\pi$
$102$		0			0
$103$		−	59.4342i		−	0.577031i	−0.957475	−	0.288515i	$-0.906838\pi$
$103$		−	59.4342i		−	0.577031i	0.957475	−	0.288515i	$-0.0931616\pi$
$104$		0			0
$105$	−2.57011			−0.0244772
$106$		0			0
$107$	143.570			1.34178			0.670888	−	0.741558i	$-0.265913\pi$
$107$	143.570			1.34178			0.670888	+	0.741558i	$0.265913\pi$
$108$		0			0
$109$	−84.7740	−	84.7740i	−0.777743	−	0.777743i	0.201703	−	0.979447i	$-0.435352\pi$
$109$	−84.7740	−	84.7740i	−0.777743	−	0.777743i	−0.979447	+	0.201703i	$0.935352\pi$
$110$		0			0
$111$	9.14697	−	9.14697i	0.0824052	−	0.0824052i
$112$		0			0
$113$	−108.544			−0.960564			−0.480282	−	0.877114i	$-0.659466\pi$
$113$	−108.544			−0.960564			−0.480282	+	0.877114i	$0.659466\pi$
$114$		0			0
$115$	11.5132	−	11.5132i	0.100114	−	0.100114i
$116$		0			0
$117$	−42.8377	+	36.4078i	−0.366134	+	0.311178i
$118$		0			0
$119$	−22.6644	−	22.6644i	−0.190457	−	0.190457i
$120$		0			0
$121$			13.7018i			0.113238i
$122$		0			0
$123$	−24.1359	−	24.1359i	−0.196227	−	0.196227i
$124$		0			0
$125$	20.7961	−	20.7961i	0.166369	−	0.166369i
$126$		0			0
$127$			94.8377i			0.746754i	0.927680	+	0.373377i	$0.121800\pi$
$127$			94.8377i			0.746754i	−0.927680	+	0.373377i	$0.878200\pi$
$128$		0			0
$129$		−	24.8947i		−	0.192982i
$130$		0			0
$131$	112.268			0.857005			0.428502	−	0.903541i	$-0.359041\pi$
$131$	112.268			0.857005			0.428502	+	0.903541i	$0.359041\pi$
$132$		0			0
$133$	8.97367			0.0674712
$134$		0			0
$135$	12.0680	+	12.0680i	0.0893924	+	0.0893924i
$136$		0			0
$137$	86.7281	−	86.7281i	0.633052	−	0.633052i	−0.315780	−	0.948832i	$-0.602266\pi$
$137$	86.7281	−	86.7281i	0.633052	−	0.633052i	0.948832	+	0.315780i	$0.102266\pi$
$138$		0			0
$139$	−78.5395			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$139$	−78.5395			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$140$		0			0
$141$	76.4715	−	76.4715i	0.542351	−	0.542351i
$142$		0			0
$143$	10.8904	−	134.219i	0.0761566	−	0.938596i
$144$		0			0
$145$	10.8114	+	10.8114i	0.0745613	+	0.0745613i
$146$		0			0
$147$		−	97.2456i		−	0.661534i
$148$		0			0
$149$	−128.219	−	128.219i	−0.860532	−	0.860532i	0.130868	−	0.991400i	$-0.458224\pi$
$149$	−128.219	−	128.219i	−0.860532	−	0.860532i	−0.991400	+	0.130868i	$0.958224\pi$
$150$		0			0
$151$	−29.1776	+	29.1776i	−0.193229	+	0.193229i	−0.797090	−	0.603861i	$-0.793628\pi$
$151$	−29.1776	+	29.1776i	−0.193229	+	0.193229i	0.603861	+	0.797090i	$0.293628\pi$
$152$		0			0
$153$			69.0790i			0.451497i
$154$		0			0
$155$		−	16.3246i		−	0.105320i
$156$		0			0
$157$	232.544			1.48117			0.740585	−	0.671962i	$-0.234548\pi$
$157$	232.544			1.48117			0.740585	+	0.671962i	$0.234548\pi$
$158$		0			0
$159$	9.05694			0.0569619
$160$		0			0
$161$	−39.0000	−	39.0000i	−0.242236	−	0.242236i
$162$		0			0
$163$	−11.4605	+	11.4605i	−0.0703098	+	0.0703098i	−0.741387	−	0.671077i	$-0.765832\pi$
$163$	−11.4605	+	11.4605i	−0.0703098	+	0.0703098i	0.671077	+	0.741387i	$0.265832\pi$
$164$		0			0
$165$	−13.2676			−0.0804098
$166$		0			0
$167$	206.785	−	206.785i	1.23823	−	1.23823i	0.277512	−	0.960722i	$-0.410490\pi$
$167$	206.785	−	206.785i	1.23823	−	1.23823i	0.960722	−	0.277512i	$-0.0895097\pi$
$168$		0			0
$169$	27.2456	−	166.789i	0.161216	−	0.986919i
$170$		0			0
$171$	−13.6754	−	13.6754i	−0.0799734	−	0.0799734i
$172$		0			0
$173$		−	91.3815i		−	0.528217i	−0.964493	−	0.264108i	$-0.914922\pi$
$173$		−	91.3815i		−	0.528217i	0.964493	−	0.264108i	$-0.0850777\pi$
$174$		0			0
$175$	−34.9737	−	34.9737i	−0.199850	−	0.199850i
$176$		0			0
$177$	−65.4562	+	65.4562i	−0.369809	+	0.369809i
$178$		0			0
$179$			71.6712i			0.400398i	0.979755	+	0.200199i	$0.0641588\pi$
$179$			71.6712i			0.400398i	−0.979755	+	0.200199i	$0.935841\pi$
$180$		0			0
$181$			274.144i			1.51461i	0.653061	+	0.757305i	$0.273484\pi$
$181$			274.144i			1.51461i	−0.653061	+	0.757305i	$0.726516\pi$
$182$		0			0
$183$	146.333			0.799634
$184$		0			0
$185$	−3.54377			−0.0191555
$186$		0			0
$187$	−117.000	−	117.000i	−0.625668	−	0.625668i
$188$		0			0
$189$	40.8794	−	40.8794i	0.216293	−	0.216293i
$190$		0			0
$191$	−179.706			−0.940869			−0.470435	−	0.882435i	$-0.655903\pi$
$191$	−179.706			−0.940869			−0.470435	+	0.882435i	$0.655903\pi$
$192$		0			0
$193$	−1.13594	+	1.13594i	−0.00588572	+	0.00588572i	−0.710044	−	0.704158i	$-0.751325\pi$
$193$	−1.13594	+	1.13594i	−0.00588572	+	0.00588572i	0.704158	+	0.710044i	$0.251325\pi$
$194$		0			0
$195$	−16.5964	−	1.34662i	−0.0851100	−	0.00690572i
$196$		0			0
$197$	141.906	+	141.906i	0.720333	+	0.720333i	0.968673	−	0.248340i	$-0.0798849\pi$
$197$	141.906	+	141.906i	0.720333	+	0.720333i	−0.248340	+	0.968673i	$0.579885\pi$
$198$		0			0
$199$			259.759i			1.30532i	0.757651	+	0.652660i	$0.226347\pi$
$199$			259.759i			1.30532i	−0.757651	+	0.652660i	$0.773653\pi$
$200$		0			0
$201$	−175.325	−	175.325i	−0.872261	−	0.872261i
$202$		0			0
$203$	36.6228	−	36.6228i	0.180408	−	0.180408i
$204$		0			0
$205$			9.35089i			0.0456141i
$206$		0			0
$207$			118.868i			0.574243i
$208$		0			0
$209$	46.3246			0.221649
$210$		0			0
$211$	−325.574			−1.54301			−0.771503	−	0.636225i	$-0.780495\pi$
$211$	−325.574			−1.54301			−0.771503	+	0.636225i	$0.780495\pi$
$212$		0			0
$213$	109.077	+	109.077i	0.512096	+	0.512096i
$214$		0			0
$215$	−4.82242	+	4.82242i	−0.0224299	+	0.0224299i
$216$		0			0
$217$	−55.2982			−0.254831
$218$		0			0
$219$	68.3772	−	68.3772i	0.312225	−	0.312225i
$220$		0			0
$221$	−134.480	−	158.230i	−0.608507	−	0.715974i
$222$		0			0
$223$	243.774	+	243.774i	1.09316	+	1.09316i	0.995190	+	0.0979674i	$0.0312341\pi$
$223$	243.774	+	243.774i	1.09316	+	1.09316i	0.0979674	+	0.995190i	$0.468766\pi$
$224$		0			0
$225$			106.596i			0.473762i
$226$		0			0
$227$	100.732	+	100.732i	0.443755	+	0.443755i	0.893272	−	0.449517i	$-0.148404\pi$
$227$	100.732	+	100.732i	0.443755	+	0.443755i	−0.449517	+	0.893272i	$0.648404\pi$
$228$		0			0
$229$	−240.366	+	240.366i	−1.04963	+	1.04963i	−0.0509319	+	0.998702i	$0.516219\pi$
$229$	−240.366	+	240.366i	−1.04963	+	1.04963i	−0.998702	+	0.0509319i	$0.983781\pi$
$230$		0			0
$231$			44.9431i			0.194559i
$232$		0			0
$233$		−	10.7893i		−	0.0463061i	−0.999732	−	0.0231531i	$-0.992629\pi$
$233$		−	10.7893i		−	0.0463061i	0.999732	−	0.0231531i	$-0.00737051\pi$
$234$		0			0
$235$	−29.6271			−0.126073
$236$		0			0
$237$	109.811			0.463339
$238$		0			0
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	0.881775	−	0.471670i	$-0.156348\pi$
$239$	98.0153	+	98.0153i	0.410106	+	0.410106i	−0.471670	+	0.881775i	$0.656348\pi$
$240$		0			0
$241$	−196.197	+	196.197i	−0.814096	+	0.814096i	−0.985245	−	0.171149i	$-0.945252\pi$
$241$	−196.197	+	196.197i	−0.814096	+	0.814096i	0.171149	+	0.985245i	$0.445252\pi$
$242$		0			0
$243$	−208.754			−0.859072
$244$		0			0
$245$	−18.8377	+	18.8377i	−0.0768887	+	0.0768887i
$246$		0			0
$247$	57.9473	+	4.70178i	0.234605	+	0.0190355i
$248$		0			0
$249$	40.2676	+	40.2676i	0.161717	+	0.161717i
$250$		0			0
$251$			95.8420i			0.381841i	0.981606	+	0.190920i	$0.0611472\pi$
$251$			95.8420i			0.381841i	−0.981606	+	0.190920i	$0.938853\pi$
$252$		0			0
$253$	−201.329	−	201.329i	−0.795766	−	0.795766i
$254$		0			0
$255$	−14.4673	+	14.4673i	−0.0567343	+	0.0567343i
$256$		0			0
$257$			450.579i			1.75322i	0.481198	+	0.876612i	$0.340202\pi$
$257$			450.579i			1.75322i	−0.481198	+	0.876612i	$0.659798\pi$
$258$		0			0
$259$			12.0043i			0.0463485i
$260$		0			0
$261$	−111.623			−0.427673
$262$		0			0
$263$	−166.982			−0.634913			−0.317457	−	0.948273i	$-0.602829\pi$
$263$	−166.982			−0.634913			−0.317457	+	0.948273i	$0.602829\pi$
$264$		0			0
$265$	−1.75445	−	1.75445i	−0.00662055	−	0.00662055i
$266$		0			0
$267$	−197.004	+	197.004i	−0.737844	+	0.737844i
$268$		0			0
$269$	170.061			0.632198			0.316099	−	0.948726i	$-0.397627\pi$
$269$	170.061			0.632198			0.316099	+	0.948726i	$0.397627\pi$
$270$		0			0
$271$	217.072	−	217.072i	0.801005	−	0.801005i	−0.182248	−	0.983253i	$-0.558337\pi$
$271$	217.072	−	217.072i	0.801005	−	0.801005i	0.983253	+	0.182248i	$0.0583374\pi$
$272$		0			0
$273$	−4.56156	+	56.2192i	−0.0167090	+	0.205931i
$274$		0			0
$275$	−180.544	−	180.544i	−0.656523	−	0.656523i
$276$		0			0
$277$			187.947i			0.678510i	0.940694	+	0.339255i	$0.110175\pi$
$277$			187.947i			0.678510i	−0.940694	+	0.339255i	$0.889825\pi$
$278$		0			0
$279$	84.2719	+	84.2719i	0.302050	+	0.302050i
$280$		0			0
$281$	286.846	−	286.846i	1.02081	−	1.02081i	0.0210263	−	0.999779i	$-0.493307\pi$
$281$	286.846	−	286.846i	1.02081	−	1.02081i	0.999779	−	0.0210263i	$-0.00669337\pi$
$282$		0			0
$283$			399.201i			1.41061i	0.708906	+	0.705303i	$0.249189\pi$
$283$			399.201i			1.41061i	−0.708906	+	0.705303i	$0.750811\pi$
$284$		0			0
$285$		−	5.72811i		−	0.0200986i
$286$		0			0
$287$	31.6754			0.110367
$288$		0			0
$289$	33.8420			0.117100
$290$		0			0
$291$	−188.886	−	188.886i	−0.649093	−	0.649093i
$292$		0			0
$293$	136.156	−	136.156i	0.464695	−	0.464695i	−0.435496	−	0.900191i	$-0.643427\pi$
$293$	136.156	−	136.156i	0.464695	−	0.464695i	0.900191	+	0.435496i	$0.143427\pi$
$294$		0			0
$295$	25.3594			0.0859642
$296$		0			0
$297$	211.031	−	211.031i	0.710541	−	0.710541i
$298$		0			0
$299$	−231.408	−	272.276i	−0.773939	−	0.910623i
$300$		0			0
$301$	16.3356	+	16.3356i	0.0542710	+	0.0542710i
$302$		0			0
$303$			19.2897i			0.0636623i
$304$		0			0
$305$	−28.3466	−	28.3466i	−0.0929397	−	0.0929397i
$306$		0			0
$307$	235.684	−	235.684i	0.767700	−	0.767700i	−0.210001	−	0.977701i	$-0.567347\pi$
$307$	235.684	−	235.684i	0.767700	−	0.767700i	0.977701	+	0.210001i	$0.0673467\pi$
$308$		0			0
$309$			128.513i			0.415900i
$310$		0			0
$311$			113.684i			0.365543i	0.983155	+	0.182772i	$0.0585069\pi$
$311$			113.684i			0.365543i	−0.983155	+	0.182772i	$0.941493\pi$
$312$		0			0
$313$	223.483			0.714002			0.357001	−	0.934104i	$-0.383799\pi$
$313$	223.483			0.714002			0.357001	+	0.934104i	$0.383799\pi$
$314$		0			0
$315$	−5.14022			−0.0163181
$316$		0			0
$317$	−125.140	−	125.140i	−0.394764	−	0.394764i	0.481617	−	0.876382i	$-0.340049\pi$
$317$	−125.140	−	125.140i	−0.394764	−	0.394764i	−0.876382	+	0.481617i	$0.840049\pi$
$318$		0			0
$319$	189.057	−	189.057i	0.592655	−	0.592655i
$320$		0			0
$321$	−310.438			−0.967098
$322$		0			0
$323$	50.5132	−	50.5132i	0.156388	−	0.156388i
$324$		0			0
$325$	−207.517	−	244.167i	−0.638515	−	0.751282i
$326$		0			0
$327$	183.305	+	183.305i	0.560566	+	0.560566i
$328$		0			0
$329$			100.359i			0.305044i
$330$		0			0
$331$	−309.982	−	309.982i	−0.936502	−	0.936502i	0.0615988	−	0.998101i	$-0.480380\pi$
$331$	−309.982	−	309.982i	−0.936502	−	0.936502i	−0.998101	+	0.0615988i	$0.980380\pi$
$332$		0			0
$333$	18.2939	−	18.2939i	0.0549368	−	0.0549368i
$334$		0			0
$335$			67.9253i			0.202762i
$336$		0			0
$337$			5.32456i			0.0157999i	0.999969	+	0.00789993i	$0.00251465\pi$
$337$			5.32456i			0.0157999i	−0.999969	+	0.00789993i	$0.997485\pi$
$338$		0			0
$339$	234.702			0.692336
$340$		0			0
$341$	−285.465			−0.837140
$342$		0			0
$343$	133.336	+	133.336i	0.388733	+	0.388733i
$344$		0			0
$345$	−24.8947	+	24.8947i	−0.0721584	+	0.0721584i
$346$		0			0
$347$	47.2413			0.136142			0.0680710	−	0.997680i	$-0.478316\pi$
$347$	47.2413			0.136142			0.0680710	+	0.997680i	$0.478316\pi$
$348$		0			0
$349$	223.581	−	223.581i	0.640634	−	0.640634i	−0.310078	−	0.950711i	$-0.600355\pi$
$349$	223.581	−	223.581i	0.640634	−	0.640634i	0.950711	+	0.310078i	$0.100355\pi$
$350$		0			0
$351$	285.397	−	242.559i	0.813096	−	0.691052i
$352$		0			0
$353$	110.320	+	110.320i	0.312522	+	0.312522i	0.845886	−	0.533364i	$-0.179072\pi$
$353$	110.320	+	110.320i	0.312522	+	0.312522i	−0.533364	+	0.845886i	$0.679072\pi$
$354$		0			0
$355$		−	42.2591i		−	0.119040i
$356$		0			0
$357$	49.0068	+	49.0068i	0.137274	+	0.137274i
$358$		0			0
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	−0.789647	−	0.613561i	$-0.789736\pi$
$359$	−63.2149	+	63.2149i	−0.176086	+	0.176086i	0.613561	+	0.789647i	$0.289736\pi$
$360$		0			0
$361$		−	341.000i		−	0.944598i
$362$		0			0
$363$		−	29.6271i		−	0.0816172i
$364$		0			0
$365$	−26.4911			−0.0725784
$366$		0			0
$367$	318.416			0.867620			0.433810	−	0.901004i	$-0.357169\pi$
$367$	318.416			0.867620			0.433810	+	0.901004i	$0.357169\pi$
$368$		0			0
$369$	−48.2719	−	48.2719i	−0.130818	−	0.130818i
$370$		0			0
$371$	−5.94306	+	5.94306i	−0.0160190	+	0.0160190i
$372$		0			0
$373$	8.87688			0.0237986			0.0118993	−	0.999929i	$-0.496212\pi$
$373$	8.87688			0.0237986			0.0118993	+	0.999929i	$0.496212\pi$
$374$		0			0
$375$	−44.9669	+	44.9669i	−0.119912	+	0.119912i
$376$		0			0
$377$	255.680	−	217.302i	0.678196	−	0.576399i
$378$		0			0
$379$	144.698	+	144.698i	0.381788	+	0.381788i	0.871746	−	0.489958i	$-0.162988\pi$
$379$	144.698	+	144.698i	0.381788	+	0.381788i	−0.489958	+	0.871746i	$0.662988\pi$
$380$		0			0
$381$		−	205.065i		−	0.538230i
$382$		0			0
$383$	−357.261	−	357.261i	−0.932796	−	0.932796i	0.0650838	−	0.997880i	$-0.479269\pi$
$383$	−357.261	−	357.261i	−0.932796	−	0.932796i	−0.997880	+	0.0650838i	$0.979269\pi$
$384$		0			0
$385$	8.70605	−	8.70605i	0.0226131	−	0.0226131i
$386$		0			0
$387$		−	49.7893i		−	0.128655i
$388$		0			0
$389$			438.342i			1.12684i	0.826170	+	0.563421i	$0.190515\pi$
$389$			438.342i			1.12684i	−0.826170	+	0.563421i	$0.809485\pi$
$390$		0			0
$391$	−439.065			−1.12293
$392$		0			0
$393$	−242.754			−0.617694
$394$		0			0
$395$	−21.2719	−	21.2719i	−0.0538529	−	0.0538529i
$396$		0			0
$397$	250.061	−	250.061i	0.629877	−	0.629877i	−0.318160	−	0.948037i	$-0.603065\pi$
$397$	250.061	−	250.061i	0.629877	−	0.629877i	0.948037	+	0.318160i	$0.103065\pi$
$398$		0			0
$399$	−19.4036			−0.0486305
$400$		0			0
$401$	93.7018	−	93.7018i	0.233670	−	0.233670i	−0.580553	−	0.814223i	$-0.697163\pi$
$401$	93.7018	−	93.7018i	0.233670	−	0.233670i	0.814223	+	0.580553i	$0.197163\pi$
$402$		0			0
$403$	−357.088	−	28.9737i	−0.886073	−	0.0718950i
$404$		0			0
$405$	−9.79181	−	9.79181i	−0.0241773	−	0.0241773i
$406$		0			0
$407$			61.9694i			0.152259i
$408$		0			0
$409$	370.140	+	370.140i	0.904988	+	0.904988i	0.995862	−	0.0908741i	$-0.0289661\pi$
$409$	370.140	+	370.140i	0.904988	+	0.904988i	−0.0908741	+	0.995862i	$0.528966\pi$
$410$		0			0
$411$	−187.530	+	187.530i	−0.456278	+	0.456278i
$412$		0			0
$413$		−	85.9032i		−	0.207998i
$414$		0			0
$415$		−	15.6007i		−	0.0375921i
$416$		0			0
$417$	169.824			0.407252
$418$		0			0
$419$	658.767			1.57224			0.786118	−	0.618076i	$-0.212088\pi$
$419$	658.767			1.57224			0.786118	+	0.618076i	$0.212088\pi$
$420$		0			0
$421$	−80.3135	−	80.3135i	−0.190768	−	0.190768i	0.605260	−	0.796028i	$-0.293069\pi$
$421$	−80.3135	−	80.3135i	−0.190768	−	0.190768i	−0.796028	+	0.605260i	$0.793069\pi$
$422$		0			0
$423$	152.943	−	152.943i	0.361568	−	0.361568i
$424$		0			0
$425$	−393.737			−0.926439
$426$		0			0
$427$	−96.0221	+	96.0221i	−0.224876	+	0.224876i
$428$		0			0
$429$	−23.5480	+	290.219i	−0.0548906	+	0.676502i
$430$		0			0
$431$	−296.037	−	296.037i	−0.686862	−	0.686862i	0.274675	−	0.961537i	$-0.411430\pi$
$431$	−296.037	−	296.037i	−0.686862	−	0.686862i	−0.961537	+	0.274675i	$0.911430\pi$
$432$		0			0
$433$			156.140i			0.360601i	0.983612	+	0.180300i	$0.0577070\pi$
$433$			156.140i			0.360601i	−0.983612	+	0.180300i	$0.942293\pi$
$434$		0			0
$435$	−23.3772	−	23.3772i	−0.0537407	−	0.0537407i
$436$		0			0
$437$	86.9210	−	86.9210i	0.198904	−	0.198904i
$438$		0			0
$439$		−	448.710i		−	1.02212i	−0.859545	−	0.511060i	$-0.829253\pi$
$439$		−	448.710i		−	1.02212i	0.859545	−	0.511060i	$-0.170747\pi$
$440$		0			0
$441$		−	194.491i		−	0.441023i
$442$		0			0
$443$	577.372			1.30332			0.651662	−	0.758510i	$-0.274072\pi$
$443$	577.372			1.30332			0.651662	+	0.758510i	$0.274072\pi$
$444$		0			0
$445$	76.3246			0.171516
$446$		0			0
$447$	277.246	+	277.246i	0.620236	+	0.620236i
$448$		0			0
$449$	−107.127	+	107.127i	−0.238591	+	0.238591i	−0.816267	−	0.577675i	$-0.803960\pi$
$449$	−107.127	+	107.127i	−0.238591	+	0.238591i	0.577675	+	0.816267i	$0.303960\pi$
$450$		0			0
$451$	163.517			0.362566
$452$		0			0
$453$	63.0900	−	63.0900i	0.139272	−	0.139272i
$454$		0			0
$455$	11.7740	−	10.0068i	0.0258770	−	0.0219929i
$456$		0			0
$457$	−356.092	−	356.092i	−0.779194	−	0.779194i	0.200499	−	0.979694i	$-0.435744\pi$
$457$	−356.092	−	356.092i	−0.779194	−	0.779194i	−0.979694	+	0.200499i	$0.935744\pi$
$458$		0			0
$459$		−	460.223i		−	1.00267i
$460$		0			0
$461$	33.7477	+	33.7477i	0.0732054	+	0.0732054i	0.742761	−	0.669556i	$-0.233516\pi$
$461$	33.7477	+	33.7477i	0.0732054	+	0.0732054i	−0.669556	+	0.742761i	$0.733516\pi$
$462$		0			0
$463$	−336.355	+	336.355i	−0.726469	+	0.726469i	−0.969915	−	0.243446i	$-0.921722\pi$
$463$	−336.355	+	336.355i	−0.726469	+	0.726469i	0.243446	+	0.969915i	$0.421722\pi$
$464$		0			0
$465$			35.2982i			0.0759102i
$466$		0			0
$467$			308.263i			0.660093i	0.943965	+	0.330046i	$0.107064\pi$
$467$			308.263i			0.660093i	−0.943965	+	0.330046i	$0.892936\pi$
$468$		0			0
$469$	230.092			0.490601
$470$		0			0
$471$	−502.824			−1.06757
$472$		0			0
$473$	84.3288	+	84.3288i	0.178285	+	0.178285i
$474$		0			0
$475$	77.9473	−	77.9473i	0.164100	−	0.164100i
$476$		0			0
$477$	18.1139			0.0379746
$478$		0			0
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	−0.782569	−	0.622564i	$-0.786091\pi$
$479$	−76.6424	+	76.6424i	−0.160005	+	0.160005i	0.622564	+	0.782569i	$0.286091\pi$
$480$		0			0
$481$	−6.28967	+	77.5174i	−0.0130762	+	0.161159i
$482$		0			0
$483$	84.3288	+	84.3288i	0.174594	+	0.174594i
$484$		0			0
$485$			73.1794i			0.150885i
$486$		0			0
$487$	69.0655	+	69.0655i	0.141818	+	0.141818i	0.774452	−	0.632633i	$-0.218026\pi$
$487$	69.0655	+	69.0655i	0.141818	+	0.141818i	−0.632633	+	0.774452i	$0.718026\pi$
$488$		0			0
$489$	24.7808	−	24.7808i	0.0506764	−	0.0506764i
$490$		0			0
$491$			685.302i			1.39573i	0.716230	+	0.697864i	$0.245866\pi$
$491$			685.302i			1.39573i	−0.716230	+	0.697864i	$0.754134\pi$
$492$		0			0
$493$		−	412.302i		−	0.836313i
$494$		0			0
$495$	−26.5352			−0.0536065
$496$		0			0
$497$	−143.149			−0.288027
$498$		0			0
$499$	−349.329	−	349.329i	−0.700058	−	0.700058i	0.264365	−	0.964423i	$-0.414838\pi$
$499$	−349.329	−	349.329i	−0.700058	−	0.700058i	−0.964423	+	0.264365i	$0.914838\pi$
$500$		0			0
$501$	−447.127	+	447.127i	−0.892468	+	0.892468i
$502$		0			0
$503$	−42.2719			−0.0840395			−0.0420198	−	0.999117i	$-0.513379\pi$
$503$	−42.2719			−0.0840395			−0.0420198	+	0.999117i	$0.513379\pi$
$504$		0			0
$505$	3.73666	−	3.73666i	0.00739933	−	0.00739933i
$506$		0			0
$507$	−58.9125	+	360.645i	−0.116198	+	0.711331i
$508$		0			0
$509$	184.280	+	184.280i	0.362044	+	0.362044i	0.864565	−	0.502521i	$-0.167594\pi$
$509$	184.280	+	184.280i	0.362044	+	0.362044i	−0.502521	+	0.864565i	$0.667594\pi$
$510$		0			0
$511$			89.7367i			0.175610i
$512$		0			0
$513$	91.1096	+	91.1096i	0.177602	+	0.177602i
$514$		0			0
$515$	24.8947	−	24.8947i	0.0483392	−	0.0483392i
$516$		0			0
$517$			518.083i			1.00210i
$518$		0			0
$519$			197.592i			0.380717i
$520$		0			0
$521$	−757.122			−1.45321			−0.726605	−	0.687055i	$-0.758903\pi$
$521$	−757.122			−1.45321			−0.726605	+	0.687055i	$0.758903\pi$
$522$		0			0
$523$	221.851			0.424188			0.212094	−	0.977249i	$-0.431972\pi$
$523$	221.851			0.424188			0.212094	+	0.977249i	$0.431972\pi$
$524$		0			0
$525$	75.6228	+	75.6228i	0.144043	+	0.144043i
$526$		0			0
$527$	−311.276	+	311.276i	−0.590657	+	0.590657i
$528$		0			0
$529$	−226.526			−0.428215
$530$		0			0
$531$	−130.912	+	130.912i	−0.246539	+	0.246539i
$532$		0			0
$533$	204.544	+	16.5964i	0.383759	+	0.0311378i
$534$		0			0
$535$	60.1359	+	60.1359i	0.112404	+	0.112404i
$536$		0			0
$537$		−	154.973i		−	0.288590i
$538$		0			0
$539$	329.412	+	329.412i	0.611154	+	0.611154i
$540$		0			0
$541$	−243.379	+	243.379i	−0.449869	+	0.449869i	−0.895311	−	0.445442i	$-0.853047\pi$
$541$	−243.379	+	243.379i	−0.449869	+	0.449869i	0.445442	+	0.895311i	$0.353047\pi$
$542$		0			0
$543$		−	592.777i		−	1.09167i
$544$		0			0
$545$		−	71.0171i		−	0.130307i
$546$		0			0
$547$	317.777			0.580944			0.290472	−	0.956883i	$-0.406188\pi$
$547$	317.777			0.580944			0.290472	+	0.956883i	$0.406188\pi$
$548$		0			0
$549$	292.666			0.533090
$550$		0			0
$551$	81.6228	+	81.6228i	0.148136	+	0.148136i
$552$		0			0
$553$	−72.0569	+	72.0569i	−0.130302	+	0.130302i
$554$		0			0
$555$	7.66262			0.0138065
$556$		0			0
$557$	−479.423	+	479.423i	−0.860724	+	0.860724i	−0.991422	−	0.130698i	$-0.958278\pi$
$557$	−479.423	+	479.423i	−0.860724	+	0.860724i	0.130698	+	0.991422i	$0.458278\pi$
$558$		0			0
$559$	96.9278	+	114.046i	0.173395	+	0.204018i
$560$		0			0
$561$	252.986	+	252.986i	0.450956	+	0.450956i
$562$		0			0
$563$			461.671i			0.820020i	0.912081	+	0.410010i	$0.134475\pi$
$563$			461.671i			0.820020i	−0.912081	+	0.410010i	$0.865525\pi$
$564$		0			0
$565$	−45.4648	−	45.4648i	−0.0804686	−	0.0804686i
$566$		0			0
$567$	−33.1690	+	33.1690i	−0.0584992	+	0.0584992i
$568$		0			0
$569$			523.394i			0.919849i	0.887958	+	0.459925i	$0.152124\pi$
$569$			523.394i			0.919849i	−0.887958	+	0.459925i	$0.847876\pi$
$570$		0			0
$571$		−	115.715i		−	0.202654i	−0.994853	−	0.101327i	$-0.967691\pi$
$571$		−	115.715i		−	0.202654i	0.994853	−	0.101327i	$-0.0323088\pi$
$572$		0			0
$573$	388.574			0.678140
$574$		0			0
$575$	−677.526			−1.17831
$576$		0			0
$577$	130.158	+	130.158i	0.225577	+	0.225577i	0.810842	−	0.585265i	$-0.199010\pi$
$577$	130.158	+	130.158i	0.225577	+	0.225577i	−0.585265	+	0.810842i	$0.699010\pi$
$578$		0			0
$579$	2.45623	−	2.45623i	0.00424219	−	0.00424219i
$580$		0			0
$581$	−52.8463			−0.0909574
$582$		0			0
$583$	−30.6797	+	30.6797i	−0.0526239	+	0.0526239i
$584$		0			0
$585$	−33.1929	−	2.69323i	−0.0567400	−	0.00460382i
$586$		0			0
$587$	347.311	+	347.311i	0.591671	+	0.591671i	0.938083	−	0.346411i	$-0.112600\pi$
$587$	347.311	+	347.311i	0.591671	+	0.591671i	−0.346411	+	0.938083i	$0.612600\pi$
$588$		0			0
$589$		−	123.246i		−	0.209245i
$590$		0			0
$591$	−306.840	−	306.840i	−0.519187	−	0.519187i
$592$		0			0
$593$	−240.285	+	240.285i	−0.405202	+	0.405202i	−0.880062	−	0.474860i	$-0.842499\pi$
$593$	−240.285	+	240.285i	−0.405202	+	0.405202i	0.474860	+	0.880062i	$0.342499\pi$
$594$		0			0
$595$		−	18.9865i		−	0.0319101i
$596$		0			0
$597$		−	561.670i		−	0.940822i
$598$		0			0
$599$	−1044.77			−1.74419			−0.872096	−	0.489334i	$-0.837240\pi$
$599$	−1044.77			−1.74419			−0.872096	+	0.489334i	$0.837240\pi$
$600$		0			0
$601$	933.298			1.55291			0.776454	−	0.630174i	$-0.217016\pi$
$601$	933.298			1.55291			0.776454	+	0.630174i	$0.217016\pi$
$602$		0			0
$603$	−350.649	−	350.649i	−0.581508	−	0.581508i
$604$		0			0
$605$	−5.73914	+	5.73914i	−0.00948619	+	0.00948619i
$606$		0			0
$607$	−579.912			−0.955374			−0.477687	−	0.878530i	$-0.658525\pi$
$607$	−579.912			−0.955374			−0.477687	+	0.878530i	$0.658525\pi$
$608$		0			0
$609$	−79.1886	+	79.1886i	−0.130031	+	0.130031i
$610$		0			0
$611$	−52.5836	+	648.070i	−0.0860616	+	1.06067i
$612$		0			0
$613$	−288.460	−	288.460i	−0.470572	−	0.470572i	0.431528	−	0.902100i	$-0.357975\pi$
$613$	−288.460	−	288.460i	−0.470572	−	0.470572i	−0.902100	+	0.431528i	$0.857975\pi$
$614$		0			0
$615$		−	20.2192i		−	0.0328768i
$616$		0			0
$617$	95.4121	+	95.4121i	0.154639	+	0.154639i	0.780186	−	0.625547i	$-0.215124\pi$
$617$	95.4121	+	95.4121i	0.154639	+	0.154639i	−0.625547	+	0.780186i	$0.715124\pi$
$618$		0			0
$619$	544.952	−	544.952i	0.880374	−	0.880374i	−0.113198	−	0.993572i	$-0.536110\pi$
$619$	544.952	−	544.952i	0.880374	−	0.880374i	0.993572	+	0.113198i	$0.0361095\pi$
$620$		0			0
$621$		−	791.934i		−	1.27526i
$622$		0			0
$623$		−	258.544i		−	0.414998i
$624$		0			0
$625$	−598.806			−0.958090
$626$		0			0
$627$	−100.167			−0.159755
$628$		0			0
$629$	67.5726	+	67.5726i	0.107429	+	0.107429i
$630$		0			0
$631$	642.537	−	642.537i	1.01828	−	1.01828i	0.0184540	−	0.999830i	$-0.494126\pi$
$631$	642.537	−	642.537i	1.01828	−	1.01828i	0.999830	−	0.0184540i	$-0.00587442\pi$
$632$		0			0
$633$	703.982			1.11214
$634$		0			0
$635$	−39.7238	+	39.7238i	−0.0625572	+	0.0625572i
$636$		0			0
$637$	378.627	+	445.495i	0.594391	+	0.699365i
$638$		0			0
$639$	218.153	+	218.153i	0.341398	+	0.341398i
$640$		0			0
$641$		−	487.290i		−	0.760202i	−0.924945	−	0.380101i	$-0.875889\pi$
$641$		−	487.290i		−	0.760202i	0.924945	−	0.380101i	$-0.124111\pi$
$642$		0			0
$643$	797.688	+	797.688i	1.24057	+	1.24057i	0.959764	+	0.280809i	$0.0906028\pi$
$643$	797.688	+	797.688i	1.24057	+	1.24057i	0.280809	+	0.959764i	$0.409397\pi$
$644$		0			0
$645$	10.4274	−	10.4274i	0.0161665	−	0.0161665i
$646$		0			0
$647$		−	989.526i		−	1.52941i	−0.644383	−	0.764703i	$-0.722886\pi$
$647$		−	989.526i		−	1.52941i	0.644383	−	0.764703i	$-0.277114\pi$
$648$		0			0
$649$		−	443.456i		−	0.683292i
$650$		0			0
$651$	119.570			0.183671
$652$		0			0
$653$	−86.3075			−0.132171			−0.0660853	−	0.997814i	$-0.521051\pi$
$653$	−86.3075			−0.132171			−0.0660853	+	0.997814i	$0.521051\pi$
$654$		0			0
$655$	47.0245	+	47.0245i	0.0717932	+	0.0717932i
$656$		0			0
$657$	136.754	−	136.754i	0.208150	−	0.208150i
$658$		0			0
$659$	1184.99			1.79817			0.899083	−	0.437779i	$-0.144235\pi$
$659$	1184.99			1.79817			0.899083	+	0.437779i	$0.144235\pi$
$660$		0			0
$661$	−194.408	+	194.408i	−0.294112	+	0.294112i	−0.838702	−	0.544590i	$-0.816685\pi$
$661$	−194.408	+	194.408i	−0.294112	+	0.294112i	0.544590	+	0.838702i	$0.316685\pi$
$662$		0			0
$663$	290.783	+	342.138i	0.438587	+	0.516045i
$664$		0			0
$665$	3.75872	+	3.75872i	0.00565221	+	0.00565221i
$666$		0			0
$667$		−	709.473i		−	1.06368i
$668$		0			0
$669$	−527.107	−	527.107i	−0.787903	−	0.787903i
$670$		0			0
$671$	−495.693	+	495.693i	−0.738737	+	0.738737i
$672$		0			0
$673$		−	615.500i		−	0.914561i	−0.889322	−	0.457281i	$-0.848824\pi$
$673$		−	615.500i		−	0.914561i	0.889322	−	0.457281i	$-0.151176\pi$
$674$		0			0
$675$		−	710.175i		−	1.05211i
$676$		0			0
$677$	−412.031			−0.608612			−0.304306	−	0.952574i	$-0.598425\pi$
$677$	−412.031			−0.608612			−0.304306	+	0.952574i	$0.598425\pi$
$678$		0			0
$679$	247.890			0.365081
$680$		0			0
$681$	−217.811	−	217.811i	−0.319841	−	0.319841i
$682$		0			0
$683$	−129.044	+	129.044i	−0.188937	+	0.188937i	−0.795237	−	0.606299i	$-0.792653\pi$
$683$	−129.044	+	129.044i	−0.188937	+	0.188937i	0.606299	+	0.795237i	$0.292653\pi$
$684$		0			0
$685$	72.6541			0.106064
$686$		0			0
$687$	519.738	−	519.738i	0.756533	−	0.756533i
$688$		0			0
$689$	−41.4911	+	35.2633i	−0.0602193	+	0.0511805i
$690$		0			0
$691$	−727.105	−	727.105i	−1.05225	−	1.05225i	−0.998558	−	0.0536923i	$-0.982901\pi$
$691$	−727.105	−	727.105i	−1.05225	−	1.05225i	−0.0536923	−	0.998558i	$-0.517099\pi$
$692$		0			0
$693$			89.8861i			0.129706i
$694$		0			0
$695$	−32.8971	−	32.8971i	−0.0473340	−	0.0473340i
$696$		0			0
$697$	178.302	−	178.302i	0.255814	−	0.255814i
$698$		0			0
$699$			23.3295i			0.0333756i
$700$		0			0
$701$			635.934i			0.907181i	0.891210	+	0.453590i	$0.149857\pi$
$701$			635.934i			0.907181i	−0.891210	+	0.453590i	$0.850143\pi$
$702$		0			0
$703$	−26.7544			−0.0380575
$704$		0			0
$705$	64.0619			0.0908680
$706$		0			0
$707$	−12.6577	−	12.6577i	−0.0179033	−	0.0179033i
$708$		0			0
$709$	695.315	−	695.315i	0.980699	−	0.980699i	−0.0191186	−	0.999817i	$-0.506086\pi$
$709$	695.315	−	695.315i	0.980699	−	0.980699i	0.999817	+	0.0191186i	$0.00608601\pi$
$710$		0			0
$711$	219.623			0.308893
$712$		0			0
$713$	−535.631	+	535.631i	−0.751236	+	0.751236i
$714$		0			0
$715$	60.7808	−	51.6577i	0.0850081	−	0.0722485i
$716$		0			0
$717$	−211.936	−	211.936i	−0.295588	−	0.295588i
$718$		0			0
$719$			859.565i			1.19550i	0.801682	+	0.597750i	$0.203939\pi$
$719$			859.565i			1.19550i	−0.801682	+	0.597750i	$0.796061\pi$
$720$		0			0
$721$	−84.3288	−	84.3288i	−0.116961	−	0.116961i
$722$		0			0
$723$	424.233	−	424.233i	0.586767	−	0.586767i
$724$		0			0
$725$		−	636.228i		−	0.877556i
$726$		0			0
$727$		−	437.337i		−	0.601564i	−0.953693	−	0.300782i	$-0.902752\pi$
$727$		−	437.337i		−	0.601564i	0.953693	−	0.300782i	$-0.0972477\pi$
$728$		0			0
$729$	661.780			0.907792
$730$		0			0
$731$	183.907			0.251583
$732$		0			0
$733$	39.5591	+	39.5591i	0.0539687	+	0.0539687i	0.733576	−	0.679607i	$-0.237850\pi$
$733$	39.5591	+	39.5591i	0.0539687	+	0.0539687i	−0.679607	+	0.733576i	$0.737850\pi$
$734$		0			0
$735$	40.7324	−	40.7324i	0.0554182	−	0.0554182i
$736$		0			0
$737$	1187.80			1.61167
$738$		0			0
$739$	−919.732	+	919.732i	−1.24456	+	1.24456i	−0.286475	+	0.958088i	$0.592483\pi$
$739$	−919.732	+	919.732i	−1.24456	+	1.24456i	−0.958088	+	0.286475i	$0.907517\pi$
$740$		0			0
$741$	−125.298	−	10.1666i	−0.169093	−	0.0137200i
$742$		0			0
$743$	−730.642	−	730.642i	−0.983368	−	0.983368i	0.0164960	−	0.999864i	$-0.494749\pi$
$743$	−730.642	−	730.642i	−0.983368	−	0.983368i	−0.999864	+	0.0164960i	$0.994749\pi$
$744$		0			0
$745$		−	107.412i		−	0.144177i
$746$		0			0
$747$	80.5352	+	80.5352i	0.107812	+	0.107812i
$748$		0			0
$749$	203.706	−	203.706i	0.271971	−	0.271971i
$750$		0			0
$751$		−	199.764i		−	0.265997i	−0.991116	−	0.132998i	$-0.957539\pi$
$751$		−	199.764i		−	0.265997i	0.991116	−	0.132998i	$-0.0424605\pi$
$752$		0			0
$753$		−	207.237i		−	0.275215i
$754$		0			0
$755$	−24.4427			−0.0323745
$756$		0			0
$757$	124.549			0.164529			0.0822647	−	0.996611i	$-0.473785\pi$
$757$	124.549			0.164529			0.0822647	+	0.996611i	$0.473785\pi$
$758$		0			0
$759$	435.329	+	435.329i	0.573556	+	0.573556i
$760$		0			0
$761$	161.412	−	161.412i	0.212105	−	0.212105i	−0.593056	−	0.805161i	$-0.702079\pi$
$761$	161.412	−	161.412i	0.212105	−	0.212105i	0.805161	+	0.593056i	$0.202079\pi$
$762$		0			0
$763$	−240.565			−0.315289
$764$		0			0
$765$	−28.9345	+	28.9345i	−0.0378229	+	0.0378229i
$766$		0			0
$767$	45.0092	−	554.719i	0.0586822	−	0.723232i
$768$		0			0
$769$	137.947	+	137.947i	0.179385	+	0.179385i	0.791088	−	0.611703i	$-0.209515\pi$
$769$	137.947	+	137.947i	0.179385	+	0.179385i	−0.611703	+	0.791088i	$0.709515\pi$
$770$		0			0
$771$		−	974.276i		−	1.26365i
$772$		0			0
$773$	550.813	+	550.813i	0.712566	+	0.712566i	0.967071	−	0.254506i	$-0.0819128\pi$
$773$	550.813	+	550.813i	0.712566	+	0.712566i	−0.254506	+	0.967071i	$0.581913\pi$
$774$		0			0
$775$	−480.333	+	480.333i	−0.619785	+	0.619785i
$776$		0			0
$777$		−	25.9566i		−	0.0334061i
$778$		0			0
$779$			70.5964i			0.0906244i
$780$		0			0
$781$	−738.977			−0.946194
$782$		0			0
$783$	743.662			0.949760
$784$		0			0
$785$	97.4036	+	97.4036i	0.124081	+	0.124081i
$786$		0			0
$787$	−729.434	+	729.434i	−0.926854	+	0.926854i	−0.997501	−	0.0706473i	$-0.977494\pi$
$787$	−729.434	+	729.434i	−0.926854	+	0.926854i	0.0706473	+	0.997501i	$0.477494\pi$
$788$		0			0
$789$	361.062			0.457620
$790$		0			0
$791$	−154.009	+	154.009i	−0.194701	+	0.194701i
$792$		0			0
$793$	−670.372	+	569.750i	−0.845362	+	0.718474i
$794$		0			0
$795$	3.79360	+	3.79360i	0.00477183	+	0.00477183i
$796$		0			0
$797$			444.974i			0.558311i	0.960246	+	0.279155i	$0.0900545\pi$
$797$			444.974i			0.558311i	−0.960246	+	0.279155i	$0.909946\pi$
$798$		0			0
$799$	564.928	+	564.928i	0.707043	+	0.707043i
$800$		0			0
$801$	−394.009	+	394.009i	−0.491896	+	0.491896i
$802$		0			0
$803$			463.246i			0.576894i
$804$		0			0
$805$		−	32.6712i		−	0.0405853i
$806$		0			0
$807$	−367.720			−0.455662
$808$		0			0
$809$	−1090.36			−1.34779			−0.673893	−	0.738829i	$-0.735379\pi$
$809$	−1090.36			−1.34779			−0.673893	+	0.738829i	$0.735379\pi$
$810$		0			0
$811$	−445.614	−	445.614i	−0.549463	−	0.549463i	0.376823	−	0.926285i	$-0.377017\pi$
$811$	−445.614	−	445.614i	−0.549463	−	0.549463i	−0.926285	+	0.376823i	$0.877017\pi$
$812$		0			0
$813$	−469.370	+	469.370i	−0.577331	+	0.577331i
$814$		0			0
$815$	−9.60072			−0.0117800
$816$		0			0
$817$	−36.4078	+	36.4078i	−0.0445628	+	0.0445628i
$818$		0			0
$819$	−9.12312	+	112.438i	−0.0111393	+	0.137287i
$820$		0			0
$821$	−242.186	−	242.186i	−0.294989	−	0.294989i	0.544058	−	0.839047i	$-0.316887\pi$
$821$	−242.186	−	242.186i	−0.294989	−	0.294989i	−0.839047	+	0.544058i	$0.816887\pi$
$822$		0			0
$823$		−	99.5787i		−	0.120995i	−0.998168	−	0.0604974i	$-0.980731\pi$
$823$		−	99.5787i		−	0.120995i	0.998168	−	0.0604974i	$-0.0192687\pi$
$824$		0			0
$825$	390.386	+	390.386i	0.473195	+	0.473195i
$826$		0			0
$827$	899.548	−	899.548i	1.08772	−	1.08772i	0.0919618	−	0.995763i	$-0.470686\pi$
$827$	899.548	−	899.548i	1.08772	−	1.08772i	0.995763	−	0.0919618i	$-0.0293138\pi$
$828$		0			0
$829$		−	32.1103i		−	0.0387338i	−0.999812	−	0.0193669i	$-0.993835\pi$
$829$		−	32.1103i		−	0.0387338i	0.999812	−	0.0193669i	$-0.00616506\pi$
$830$		0			0
$831$		−	406.394i		−	0.489042i
$832$		0			0
$833$	718.394			0.862418
$834$		0			0
$835$	173.228			0.207459
$836$		0			0
$837$	−561.443	−	561.443i	−0.670780	−	0.670780i
$838$		0			0
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	−0.907434	−	0.420195i	$-0.861962\pi$
$839$	−408.794	+	408.794i	−0.487239	+	0.487239i	0.420195	+	0.907434i	$0.361962\pi$
$840$		0			0
$841$	−174.772			−0.207815
$842$		0			0
$843$	−620.241	+	620.241i	−0.735755	+	0.735755i
$844$		0			0
$845$	81.2737	−	58.4495i	0.0961819	−	0.0691710i
$846$		0			0
$847$	19.4409	+	19.4409i	0.0229527	+	0.0229527i
$848$		0			0
$849$		−	863.184i		−	1.01671i
$850$		0			0
$851$	116.276	+	116.276i	0.136635	+	0.136635i
$852$		0			0
$853$	529.546	−	529.546i	0.620804	−	0.620804i	−0.324933	−	0.945737i	$-0.605342\pi$
$853$	529.546	−	529.546i	0.620804	−	0.620804i	0.945737	+	0.324933i	$0.105342\pi$
$854$		0			0
$855$		−	11.4562i		−	0.0133991i
$856$		0			0
$857$			1586.76i			1.85153i	0.378097	+	0.925766i	$0.376579\pi$
$857$			1586.76i			1.85153i	−0.378097	+	0.925766i	$0.623421\pi$
$858$		0			0
$859$	−145.062			−0.168873			−0.0844365	−	0.996429i	$-0.526909\pi$
$859$	−145.062			−0.168873			−0.0844365	+	0.996429i	$0.526909\pi$
$860$		0			0
$861$	−68.4911			−0.0795483
$862$		0			0
$863$	1005.80	+	1005.80i	1.16547	+	1.16547i	0.983258	+	0.182216i	$0.0583271\pi$
$863$	1005.80	+	1005.80i	1.16547	+	1.16547i	0.182216	+	0.983258i	$0.441673\pi$
$864$		0			0
$865$	38.2762	−	38.2762i	0.0442499	−	0.0442499i
$866$		0			0
$867$	−73.1758			−0.0844011
$868$		0			0
$869$	−371.978	+	371.978i	−0.428053	+	0.428053i
$870$		0			0
$871$	1485.81	+	120.557i	1.70587	+	0.138413i
$872$		0			0
$873$	−377.772	−	377.772i	−0.432729	−	0.432729i
$874$		0			0
$875$		−	59.0135i		−	0.0674440i
$876$		0			0
$877$	689.532	+	689.532i	0.786240	+	0.786240i	0.980876	−	0.194636i	$-0.0623526\pi$
$877$	689.532	+	689.532i	0.786240	+	0.786240i	−0.194636	+	0.980876i	$0.562353\pi$
$878$		0			0
$879$	−294.406	+	294.406i	−0.334933	+	0.334933i
$880$		0			0
$881$		−	1607.31i		−	1.82442i	−0.409722	−	0.912210i	$-0.634374\pi$
$881$		−	1607.31i		−	1.82442i	0.409722	−	0.912210i	$-0.365626\pi$
$882$		0			0
$883$			153.969i			0.174370i	0.996192	+	0.0871850i	$0.0277871\pi$
$883$			153.969i			0.174370i	−0.996192	+	0.0871850i	$0.972213\pi$
$884$		0			0
$885$	−54.8341			−0.0619595
$886$		0			0
$887$	−125.273			−0.141232			−0.0706159	−	0.997504i	$-0.522496\pi$
$887$	−125.273			−0.141232			−0.0706159	+	0.997504i	$0.522496\pi$
$888$		0			0
$889$	134.562	+	134.562i	0.151363	+	0.151363i
$890$		0			0
$891$	−171.228	+	171.228i	−0.192175	+	0.192175i
$892$		0			0
$893$	−223.675			−0.250476
$894$		0			0
$895$	−30.0203	+	30.0203i	−0.0335422	+	0.0335422i
$896$		0			0
$897$	500.368	+	588.737i	0.557824	+	0.656340i
$898$		0			0
$899$	−502.982	−	502.982i	−0.559491	−	0.559491i
$900$		0			0
$901$			66.9075i			0.0742591i
$902$		0			0
$903$	−35.3221	−	35.3221i	−0.0391164	−	0.0391164i
$904$		0			0
$905$	−114.828	+	114.828i	−0.126882	+	0.126882i
$906$		0			0
$907$			354.574i			0.390930i	0.980711	+	0.195465i	$0.0626216\pi$
$907$			354.574i			0.390930i	−0.980711	+	0.195465i	$0.937378\pi$
$908$		0			0
$909$			38.5793i			0.0424415i
$910$		0			0
$911$	−1040.31			−1.14194			−0.570972	−	0.820970i	$-0.693434\pi$
$911$	−1040.31			−1.14194			−0.570972	+	0.820970i	$0.693434\pi$
$912$		0			0
$913$	−272.807			−0.298803
$914$		0			0
$915$	61.2933	+	61.2933i	0.0669872	+	0.0669872i
$916$		0			0
$917$	159.292	−	159.292i	0.173710	−	0.173710i
$918$		0			0
$919$	416.201			0.452884			0.226442	−	0.974025i	$-0.427291\pi$
$919$	416.201			0.452884			0.226442	+	0.974025i	$0.427291\pi$
$920$		0			0
$921$	−509.614	+	509.614i	−0.553327	+	0.553327i
$922$		0			0
$923$	−924.386	−	75.0036i	−1.00150	−	0.0812606i
$924$		0			0
$925$	104.272	+	104.272i	0.112726	+	0.112726i
$926$		0			0
$927$			257.026i			0.277267i
$928$		0			0
$929$	−428.403	−	428.403i	−0.461144	−	0.461144i	0.437886	−	0.899030i	$-0.355727\pi$
$929$	−428.403	−	428.403i	−0.461144	−	0.461144i	−0.899030	+	0.437886i	$0.855727\pi$
$930$		0			0
$931$	−142.219	+	142.219i	−0.152760	+	0.152760i
$932$		0			0
$933$		−	245.816i		−	0.263469i
$934$		0			0
$935$		−	98.0135i		−	0.104827i
$936$		0			0
$937$	−990.702			−1.05731			−0.528656	−	0.848836i	$-0.677304\pi$
$937$	−990.702			−1.05731			−0.528656	+	0.848836i	$0.677304\pi$
$938$		0			0
$939$	−483.231			−0.514623
$940$		0			0
$941$	974.392	+	974.392i	1.03549	+	1.03549i	0.999347	+	0.0361387i	$0.0115058\pi$
$941$	974.392	+	974.392i	1.03549	+	1.03549i	0.0361387	+	0.999347i	$0.488494\pi$
$942$		0			0
$943$	306.816	−	306.816i	0.325361	−	0.325361i
$944$		0			0
$945$	34.2456			0.0362387
$946$		0			0
$947$	−897.569	+	897.569i	−0.947803	+	0.947803i	−0.998704	−	0.0509007i	$-0.983791\pi$
$947$	−897.569	+	897.569i	−0.947803	+	0.947803i	0.0509007	+	0.998704i	$0.483791\pi$
$948$		0			0
$949$	−47.0178	+	579.473i	−0.0495446	+	0.610615i
$950$		0			0
$951$	270.588	+	270.588i	0.284530	+	0.284530i
$952$		0			0
$953$			1111.71i			1.16654i	0.812279	+	0.583269i	$0.198227\pi$
$953$			1111.71i			1.16654i	−0.812279	+	0.583269i	$0.801773\pi$
$954$		0			0
$955$	−75.2719	−	75.2719i	−0.0788187	−	0.0788187i
$956$		0			0
$957$	−408.794	+	408.794i	−0.427162	+	0.427162i
$958$		0			0
$959$		−	246.110i		−	0.256632i
$960$		0			0
$961$		−	201.527i		−	0.209705i
$962$		0			0
$963$	−620.877			−0.644732
$964$		0			0
$965$	−0.951605			−0.000986120
$966$		0			0
$967$	1333.92	+	1333.92i	1.37944	+	1.37944i	0.845561	+	0.533879i	$0.179266\pi$
$967$	1333.92	+	1333.92i	1.37944	+	1.37944i	0.533879	+	0.845561i	$0.320734\pi$
$968$		0			0
$969$	−109.223	+	109.223i	−0.112718	+	0.112718i
$970$		0			0
$971$	556.110			0.572718			0.286359	−	0.958122i	$-0.407555\pi$
$971$	556.110			0.572718			0.286359	+	0.958122i	$0.407555\pi$
$972$		0			0
$973$	−111.437	+	111.437i	−0.114529	+	0.114529i
$974$		0			0
$975$	448.710	+	527.956i	0.460216	+	0.541493i
$976$		0			0
$977$	−1103.56	−	1103.56i	−1.12954	−	1.12954i	−0.990252	−	0.139288i	$-0.955518\pi$
$977$	−1103.56	−	1103.56i	−1.12954	−	1.12954i	−0.139288	−	0.990252i	$-0.544482\pi$
$978$		0			0
$979$		−	1334.67i		−	1.36330i
$980$		0			0
$981$	366.610	+	366.610i	0.373710	+	0.373710i
$982$		0			0
$983$	901.475	−	901.475i	0.917065	−	0.917065i	−0.0797497	−	0.996815i	$-0.525412\pi$
$983$	901.475	−	901.475i	0.917065	−	0.917065i	0.996815	+	0.0797497i	$0.0254121\pi$
$984$		0			0
$985$			118.878i			0.120688i
$986$		0			0
$987$		−	217.005i		−	0.219863i
$988$		0			0
$989$	316.460			0.319980
$990$		0			0
$991$	−765.341			−0.772292			−0.386146	−	0.922438i	$-0.626194\pi$
$991$	−765.341			−0.772292			−0.386146	+	0.922438i	$0.626194\pi$
$992$		0			0
$993$	670.268	+	670.268i	0.674993	+	0.674993i
$994$		0			0
$995$	−108.803	+	108.803i	−0.109350	+	0.109350i
$996$		0			0
$997$	1075.40			1.07863			0.539317	−	0.842103i	$-0.318682\pi$
$997$	1075.40			1.07863			0.539317	+	0.842103i	$0.318682\pi$
$998$		0			0
$999$	−121.879	+	121.879i	−0.122001	+	0.122001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.t.c.177.1		4
4.3	odd	2		13.3.d.a.8.1	yes	4
12.11	even	2		117.3.j.a.73.2		4
13.5	odd	4	inner	208.3.t.c.161.1		4
20.3	even	4		325.3.g.a.99.1		4
20.7	even	4		325.3.g.b.99.2		4
20.19	odd	2		325.3.j.a.151.2		4
52.3	odd	6		169.3.f.f.150.2		8
52.7	even	12		169.3.f.d.80.1		8
52.11	even	12		169.3.f.d.19.2		8
52.15	even	12		169.3.f.f.19.1		8
52.19	even	12		169.3.f.f.80.2		8
52.23	odd	6		169.3.f.d.150.1		8
52.31	even	4		13.3.d.a.5.1	✓	4
52.35	odd	6		169.3.f.f.89.1		8
52.43	odd	6		169.3.f.d.89.2		8
52.47	even	4		169.3.d.d.70.2		4
52.51	odd	2		169.3.d.d.99.2		4
156.83	odd	4		117.3.j.a.109.2		4
260.83	odd	4		325.3.g.b.174.2		4
260.187	odd	4		325.3.g.a.174.1		4
260.239	even	4		325.3.j.a.226.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.1	✓	4	52.31	even	4
13.3.d.a.8.1	yes	4	4.3	odd	2
117.3.j.a.73.2		4	12.11	even	2
117.3.j.a.109.2		4	156.83	odd	4
169.3.d.d.70.2		4	52.47	even	4
169.3.d.d.99.2		4	52.51	odd	2
169.3.f.d.19.2		8	52.11	even	12
169.3.f.d.80.1		8	52.7	even	12
169.3.f.d.89.2		8	52.43	odd	6
169.3.f.d.150.1		8	52.23	odd	6
169.3.f.f.19.1		8	52.15	even	12
169.3.f.f.80.2		8	52.19	even	12
169.3.f.f.89.1		8	52.35	odd	6
169.3.f.f.150.2		8	52.3	odd	6
208.3.t.c.161.1		4	13.5	odd	4	inner
208.3.t.c.177.1		4	1.1	even	1	trivial
325.3.g.a.99.1		4	20.3	even	4
325.3.g.a.174.1		4	260.187	odd	4
325.3.g.b.99.2		4	20.7	even	4
325.3.g.b.174.2		4	260.83	odd	4
325.3.j.a.151.2		4	20.19	odd	2
325.3.j.a.226.2		4	260.239	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.16228 q^{3} +(0.418861 + 0.418861i) q^{5} +(1.41886 - 1.41886i) q^{7} -4.32456 q^{9} +(7.32456 - 7.32456i) q^{11} +(9.90569 - 8.41886i) q^{13} +(-0.905694 - 0.905694i) q^{15} -15.9737i q^{17} +(3.16228 + 3.16228i) q^{19} +(-3.06797 + 3.06797i) q^{21} -27.4868i q^{23} -24.6491i q^{25} +28.8114 q^{27} +25.8114 q^{29} +(-19.4868 - 19.4868i) q^{31} +(-15.8377 + 15.8377i) q^{33} +1.18861 q^{35} +(-4.23025 + 4.23025i) q^{37} +(-21.4189 + 18.2039i) q^{39} +(11.1623 + 11.1623i) q^{41} +11.5132i q^{43} +(-1.81139 - 1.81139i) q^{45} +(-35.3662 + 35.3662i) q^{47} +44.9737i q^{49} +34.5395i q^{51} -4.18861 q^{53} +6.13594 q^{55} +(-6.83772 - 6.83772i) q^{57} +(30.2719 - 30.2719i) q^{59} -67.6754 q^{61} +(-6.13594 + 6.13594i) q^{63} +(7.67544 + 0.622777i) q^{65} +(81.0833 + 81.0833i) q^{67} +59.4342i q^{69} +(-50.4452 - 50.4452i) q^{71} +(-31.6228 + 31.6228i) q^{73} +53.2982i q^{75} -20.7851i q^{77} -50.7851 q^{79} -23.3772 q^{81} +(-18.6228 - 18.6228i) q^{83} +(6.69075 - 6.69075i) q^{85} -55.8114 q^{87} +(91.1096 - 91.1096i) q^{89} +(2.10961 - 26.0000i) q^{91} +(42.1359 + 42.1359i) q^{93} +2.64911i q^{95} +(87.3552 + 87.3552i) q^{97} +(-31.6754 + 31.6754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 8 q^{5} + 12 q^{7} + 8 q^{9} + 4 q^{11} + 8 q^{13} + 28 q^{15} + 32 q^{21} + 52 q^{27} + 40 q^{29} - 40 q^{31} - 76 q^{33} + 68 q^{35} + 40 q^{37} - 92 q^{39} + 32 q^{41} + 56 q^{45} + 4 q^{47}+ \cdots - 152 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 + 8 * q^5 + 12 * q^7 + 8 * q^9 + 4 * q^11 + 8 * q^13 + 28 * q^15 + 32 * q^21 + 52 * q^27 + 40 * q^29 - 40 * q^31 - 76 * q^33 + 68 * q^35 + 40 * q^37 - 92 * q^39 + 32 * q^41 + 56 * q^45 + 4 * q^47 - 80 * q^53 - 64 * q^55 - 40 * q^57 - 56 * q^59 - 296 * q^61 + 64 * q^63 + 56 * q^65 + 84 * q^67 - 284 * q^71 - 64 * q^79 - 220 * q^81 + 52 * q^83 - 144 * q^85 - 160 * q^87 + 200 * q^89 - 156 * q^91 + 80 * q^93 - 68 * q^97 - 152 * q^99

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