LMFDB - Embedded newform 196.6.e.k.165.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,6,Mod(165,196)] 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("196.165"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{109})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 28x^{2} + 27x + 729 $ x^4 - x^3 + 28x^2 + 27x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.2
Root			$-2.36008 - 4.08777i$ of defining polynomial
Character	$\chi$	$=$	196.165
Dual form			196.6.e.k.177.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.2202 - 21.1659i) q^{3} +(41.8209 + 72.4360i) q^{5} +(-177.164 - 306.858i) q^{9} +(-274.623 + 475.661i) q^{11} +823.135 q^{13} +2044.23 q^{15} +(72.7837 - 126.065i) q^{17} +(884.019 + 1531.17i) q^{19} +(761.363 + 1318.72i) q^{23} +(-1935.48 + 3352.35i) q^{25} -2720.90 q^{27} -741.943 q^{29} +(-1602.09 + 2774.90i) q^{31} +(6711.88 + 11625.3i) q^{33} +(1774.77 + 3074.00i) q^{37} +(10058.8 - 17422.4i) q^{39} +6461.29 q^{41} +6716.00 q^{43} +(14818.3 - 25666.1i) q^{45} +(-9588.40 - 16607.6i) q^{47} +(-1778.86 - 3081.07i) q^{51} +(10639.3 - 18427.8i) q^{53} -45940.0 q^{55} +43211.4 q^{57} +(18264.3 - 31634.8i) q^{59} +(21716.9 + 37614.7i) q^{61} +(34424.3 + 59624.6i) q^{65} +(-2514.07 + 4354.50i) q^{67} +37215.9 q^{69} -6311.32 q^{71} +(-21299.0 + 36890.9i) q^{73} +(47303.7 + 81932.4i) q^{75} +(-47534.6 - 82332.3i) q^{79} +(9801.05 - 16975.9i) q^{81} +34978.2 q^{83} +12175.5 q^{85} +(-9066.66 + 15703.9i) q^{87} +(50276.7 + 87081.8i) q^{89} +(39155.5 + 67819.3i) q^{93} +(-73940.9 + 128069. i) q^{95} -76794.5 q^{97} +194614. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 28 q^{3} + 42 q^{5} - 124 q^{9} - 660 q^{11} + 1288 q^{13} + 3792 q^{15} - 210 q^{17} + 3724 q^{19} - 24 q^{23} - 2480 q^{25} - 2072 q^{27} + 11064 q^{29} + 2800 q^{31} + 13818 q^{33} + 13238 q^{37}+ \cdots + 338208 q^{99}+O(q^{100}) $ 4 * q + 28 * q^3 + 42 * q^5 - 124 * q^9 - 660 * q^11 + 1288 * q^13 + 3792 * q^15 - 210 * q^17 + 3724 * q^19 - 24 * q^23 - 2480 * q^25 - 2072 * q^27 + 11064 * q^29 + 2800 * q^31 + 13818 * q^33 + 13238 * q^37 + 19480 * q^39 - 8232 * q^41 + 26864 * q^43 + 39228 * q^45 + 8064 * q^47 - 2292 * q^51 + 53958 * q^53 - 82656 * q^55 + 100348 * q^57 + 36036 * q^59 + 83986 * q^61 + 76308 * q^65 + 2660 * q^67 + 63420 * q^69 + 143136 * q^71 + 31318 * q^73 + 89656 * q^75 - 51136 * q^79 - 30370 * q^81 - 12432 * q^83 + 53964 * q^85 + 4200 * q^87 + 166278 * q^89 + 56938 * q^93 - 66432 * q^95 - 16520 * q^97 + 338208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	12.2202	−	21.1659i	0.783923	−	1.35779i	−0.145717	−	0.989326i	$-0.546549\pi$
$3$	12.2202	−	21.1659i	0.783923	−	1.35779i	0.929640	−	0.368468i	$-0.120118\pi$
$4$		0			0
$5$	41.8209	+	72.4360i	0.748115	+	1.29577i	0.948725	+	0.316103i	$0.102374\pi$
$5$	41.8209	+	72.4360i	0.748115	+	1.29577i	−0.200610	+	0.979671i	$0.564292\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−177.164	−	306.858i	−0.729071	−	1.26279i
$10$		0			0
$11$	−274.623	+	475.661i	−0.684314	+	1.18527i	0.289338	+	0.957227i	$0.406565\pi$
$11$	−274.623	+	475.661i	−0.684314	+	1.18527i	−0.973652	+	0.228040i	$0.926768\pi$
$12$		0			0
$13$	823.135			1.35087			0.675433	−	0.737421i	$-0.263957\pi$
$13$	823.135			1.35087			0.675433	+	0.737421i	$0.263957\pi$
$14$		0			0
$15$	2044.23			2.34586
$16$		0			0
$17$	72.7837	−	126.065i	0.0610818	−	0.105797i	−0.833867	−	0.551965i	$-0.813878\pi$
$17$	72.7837	−	126.065i	0.0610818	−	0.105797i	0.894949	+	0.446168i	$0.147212\pi$
$18$		0			0
$19$	884.019	+	1531.17i	0.561794	+	0.973056i	0.997340	+	0.0728898i	$0.0232221\pi$
$19$	884.019	+	1531.17i	0.561794	+	0.973056i	−0.435546	+	0.900167i	$0.643445\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	761.363	+	1318.72i	0.300104	+	0.519796i	0.976159	−	0.217055i	$-0.0696453\pi$
$23$	761.363	+	1318.72i	0.300104	+	0.519796i	−0.676055	+	0.736851i	$0.736312\pi$
$24$		0			0
$25$	−1935.48	+	3352.35i	−0.619353	+	1.07275i
$26$		0			0
$27$	−2720.90			−0.718297
$28$		0			0
$29$	−741.943			−0.163823			−0.0819116	−	0.996640i	$-0.526103\pi$
$29$	−741.943			−0.163823			−0.0819116	+	0.996640i	$0.526103\pi$
$30$		0			0
$31$	−1602.09	+	2774.90i	−0.299421	+	0.518612i	−0.976004	−	0.217755i	$-0.930127\pi$
$31$	−1602.09	+	2774.90i	−0.299421	+	0.518612i	0.676583	+	0.736367i	$0.263460\pi$
$32$		0			0
$33$	6711.88	+	11625.3i	1.07290	+	1.85832i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1774.77	+	3074.00i	0.213127	+	0.369147i	0.952692	−	0.303939i	$-0.0983018\pi$
$37$	1774.77	+	3074.00i	0.213127	+	0.369147i	−0.739564	+	0.673086i	$0.764968\pi$
$38$		0			0
$39$	10058.8	−	17422.4i	1.05898	−	1.83420i
$40$		0			0
$41$	6461.29			0.600288			0.300144	−	0.953894i	$-0.402965\pi$
$41$	6461.29			0.600288			0.300144	+	0.953894i	$0.402965\pi$
$42$		0			0
$43$	6716.00			0.553910			0.276955	−	0.960883i	$-0.410675\pi$
$43$	6716.00			0.553910			0.276955	+	0.960883i	$0.410675\pi$
$44$		0			0
$45$	14818.3	−	25666.1i	1.09086	−	1.88942i
$46$		0			0
$47$	−9588.40	−	16607.6i	−0.633143	−	1.09664i	−0.986905	−	0.161300i	$-0.948431\pi$
$47$	−9588.40	−	16607.6i	−0.633143	−	1.09664i	0.353763	−	0.935335i	$-0.384902\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1778.86	−	3081.07i	−0.0957669	−	0.165873i
$52$		0			0
$53$	10639.3	−	18427.8i	0.520263	−	0.901123i	−0.479459	−	0.877564i	$-0.659167\pi$
$53$	10639.3	−	18427.8i	0.520263	−	0.901123i	0.999722	−	0.0235583i	$-0.00749954\pi$
$54$		0			0
$55$	−45940.0			−2.04778
$56$		0			0
$57$	43211.4			1.76161
$58$		0			0
$59$	18264.3	−	31634.8i	0.683083	−	1.18314i	−0.290952	−	0.956738i	$-0.593972\pi$
$59$	18264.3	−	31634.8i	0.683083	−	1.18314i	0.974035	−	0.226397i	$-0.0726948\pi$
$60$		0			0
$61$	21716.9	+	37614.7i	0.747262	+	1.29430i	0.949130	+	0.314883i	$0.101965\pi$
$61$	21716.9	+	37614.7i	0.747262	+	1.29430i	−0.201869	+	0.979413i	$0.564701\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	34424.3	+	59624.6i	1.01060	+	1.75042i
$66$		0			0
$67$	−2514.07	+	4354.50i	−0.0684212	+	0.118509i	−0.898207	−	0.439574i	$-0.855130\pi$
$67$	−2514.07	+	4354.50i	−0.0684212	+	0.118509i	0.829785	+	0.558083i	$0.188463\pi$
$68$		0			0
$69$	37215.9			0.941034
$70$		0			0
$71$	−6311.32			−0.148585			−0.0742923	−	0.997237i	$-0.523670\pi$
$71$	−6311.32			−0.148585			−0.0742923	+	0.997237i	$0.523670\pi$
$72$		0			0
$73$	−21299.0	+	36890.9i	−0.467790	+	0.810236i	−0.999323	−	0.0368015i	$-0.988283\pi$
$73$	−21299.0	+	36890.9i	−0.467790	+	0.810236i	0.531532	+	0.847038i	$0.321616\pi$
$74$		0			0
$75$	47303.7	+	81932.4i	0.971051	+	1.68191i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−47534.6	−	82332.3i	−0.856923	−	1.48423i	−0.874850	−	0.484395i	$-0.839040\pi$
$79$	−47534.6	−	82332.3i	−0.856923	−	1.48423i	0.0179267	−	0.999839i	$-0.494293\pi$
$80$		0			0
$81$	9801.05	−	16975.9i	0.165982	−	0.287489i
$82$		0			0
$83$	34978.2			0.557318			0.278659	−	0.960390i	$-0.410110\pi$
$83$	34978.2			0.557318			0.278659	+	0.960390i	$0.410110\pi$
$84$		0			0
$85$	12175.5			0.182785
$86$		0			0
$87$	−9066.66	+	15703.9i	−0.128425	+	0.222438i
$88$		0			0
$89$	50276.7	+	87081.8i	0.672809	+	1.16534i	0.977104	+	0.212762i	$0.0682458\pi$
$89$	50276.7	+	87081.8i	0.672809	+	1.16534i	−0.304295	+	0.952578i	$0.598421\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	39155.5	+	67819.3i	0.469446	+	0.813104i
$94$		0			0
$95$	−73940.9	+	128069.i	−0.840574	+	1.45592i
$96$		0			0
$97$	−76794.5			−0.828707			−0.414353	−	0.910116i	$-0.635992\pi$
$97$	−76794.5			−0.828707			−0.414353	+	0.910116i	$0.635992\pi$
$98$		0			0
$99$	194614.			1.99565
$100$		0			0
$101$	57020.2	−	98761.9i	0.556193	−	0.963355i	−0.441617	−	0.897204i	$-0.645595\pi$
$101$	57020.2	−	98761.9i	0.556193	−	0.963355i	0.997810	−	0.0661508i	$-0.0210718\pi$
$102$		0			0
$103$	−61818.5	−	107073.i	−0.574150	−	0.994457i	−0.996133	−	0.0878533i	$-0.971999\pi$
$103$	−61818.5	−	107073.i	−0.574150	−	0.994457i	0.421983	−	0.906604i	$-0.361334\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11670.1	+	20213.2i	0.0985404	+	0.170677i	0.911081	−	0.412228i	$-0.135249\pi$
$107$	11670.1	+	20213.2i	0.0985404	+	0.170677i	−0.812540	+	0.582905i	$0.801916\pi$
$108$		0			0
$109$	13601.6	−	23558.6i	0.109654	−	0.189926i	−0.805976	−	0.591948i	$-0.798359\pi$
$109$	13601.6	−	23558.6i	0.109654	−	0.189926i	0.915630	+	0.402022i	$0.131692\pi$
$110$		0			0
$111$	86752.1			0.668302
$112$		0			0
$113$	−157394.			−1.15955			−0.579777	−	0.814775i	$-0.696860\pi$
$113$	−157394.			−1.15955			−0.579777	+	0.814775i	$0.696860\pi$
$114$		0			0
$115$	−63681.8	+	110300.i	−0.449025	+	0.777734i
$116$		0			0
$117$	−145830.	−	252585.i	−0.984878	−	1.70586i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−70310.3	−	121781.i	−0.436572	−	0.756165i
$122$		0			0
$123$	78958.0	−	136759.i	0.470580	−	0.815068i
$124$		0			0
$125$	−62393.2			−0.357160
$126$		0			0
$127$	−253263.			−1.39336			−0.696679	−	0.717383i	$-0.745340\pi$
$127$	−253263.			−1.39336			−0.696679	+	0.717383i	$0.745340\pi$
$128$		0			0
$129$	82070.5	−	142150.i	0.434223	−	0.752097i
$130$		0			0
$131$	−57772.6	−	100065.i	−0.294133	−	0.509453i	0.680650	−	0.732609i	$-0.261698\pi$
$131$	−57772.6	−	100065.i	−0.294133	−	0.509453i	−0.974783	+	0.223156i	$0.928364\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−113791.	−	197091.i	−0.537369	−	0.930750i
$136$		0			0
$137$	103904.	−	179967.i	0.472966	−	0.819202i	−0.526555	−	0.850141i	$-0.676517\pi$
$137$	103904.	−	179967.i	0.472966	−	0.819202i	0.999521	+	0.0309393i	$0.00984986\pi$
$138$		0			0
$139$	28993.1			0.127279			0.0636395	−	0.997973i	$-0.479729\pi$
$139$	28993.1			0.127279			0.0636395	+	0.997973i	$0.479729\pi$
$140$		0			0
$141$	−468687.			−1.98534
$142$		0			0
$143$	−226052.	+	391533.i	−0.924417	+	1.60114i
$144$		0			0
$145$	−31028.7	−	53743.4i	−0.122559	−	0.212278i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	165490.	+	286637.i	0.610668	+	1.05771i	0.991128	+	0.132911i	$0.0424325\pi$
$149$	165490.	+	286637.i	0.610668	+	1.05771i	−0.380460	+	0.924798i	$0.624234\pi$
$150$		0			0
$151$	−54428.3	+	94272.6i	−0.194260	+	0.336468i	−0.946658	−	0.322241i	$-0.895564\pi$
$151$	−54428.3	+	94272.6i	−0.194260	+	0.336468i	0.752398	+	0.658709i	$0.228897\pi$
$152$		0			0
$153$	−51578.7			−0.178132
$154$		0			0
$155$	−268003.			−0.896005
$156$		0			0
$157$	−248873.	+	431060.i	−0.805801	+	1.39569i	0.109947	+	0.993937i	$0.464932\pi$
$157$	−248873.	+	431060.i	−0.805801	+	1.39569i	−0.915749	+	0.401752i	$0.868402\pi$
$158$		0			0
$159$	−260028.	−	450381.i	−0.815693	−	1.41282i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	179551.	+	310992.i	0.529321	+	0.916811i	0.999415	+	0.0341950i	$0.0108867\pi$
$163$	179551.	+	310992.i	0.529321	+	0.916811i	−0.470094	+	0.882616i	$0.655780\pi$
$164$		0			0
$165$	−561394.	+	972362.i	−1.60531	+	2.78047i
$166$		0			0
$167$	50645.2			0.140523			0.0702614	−	0.997529i	$-0.477617\pi$
$167$	50645.2			0.140523			0.0702614	+	0.997529i	$0.477617\pi$
$168$		0			0
$169$	306258.			0.824841
$170$		0			0
$171$	313233.	−	542536.i	0.819176	−	1.41885i
$172$		0			0
$173$	151595.	+	262569.i	0.385095	+	0.667005i	0.991782	−	0.127936i	$-0.0408352\pi$
$173$	151595.	+	262569.i	0.385095	+	0.667005i	−0.606687	+	0.794941i	$0.707502\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−446386.	−	773163.i	−1.07097	−	1.85497i
$178$		0			0
$179$	341272.	−	591100.i	0.796100	−	1.37889i	−0.126039	−	0.992025i	$-0.540226\pi$
$179$	341272.	−	591100.i	0.796100	−	1.37889i	0.922138	−	0.386860i	$-0.126440\pi$
$180$		0			0
$181$	−182455.			−0.413961			−0.206980	−	0.978345i	$-0.566364\pi$
$181$	−182455.			−0.413961			−0.206980	+	0.978345i	$0.566364\pi$
$182$		0			0
$183$	1.06153e6			2.34318
$184$		0			0
$185$	−148445.	+	257115.i	−0.318888	+	0.552329i
$186$		0			0
$187$	39976.2	+	69240.8i	0.0835983	+	0.144796i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−341772.	−	591966.i	−0.677879	−	1.17412i	−0.975618	−	0.219474i	$-0.929566\pi$
$191$	−341772.	−	591966.i	−0.677879	−	1.17412i	0.297739	−	0.954647i	$-0.403768\pi$
$192$		0			0
$193$	−473251.	+	819696.i	−0.914532	+	1.58402i	−0.106946	+	0.994265i	$0.534107\pi$
$193$	−473251.	+	819696.i	−0.914532	+	1.58402i	−0.807586	+	0.589750i	$0.799226\pi$
$194$		0			0
$195$	1.68268e6			3.16894
$196$		0			0
$197$	−184209.			−0.338178			−0.169089	−	0.985601i	$-0.554082\pi$
$197$	−184209.			−0.338178			−0.169089	+	0.985601i	$0.554082\pi$
$198$		0			0
$199$	34103.3	−	59068.6i	0.0610469	−	0.105736i	−0.833887	−	0.551936i	$-0.813889\pi$
$199$	34103.3	−	59068.6i	0.0610469	−	0.105736i	0.894934	+	0.446199i	$0.147223\pi$
$200$		0			0
$201$	61444.7	+	106425.i	0.107274	+	0.185804i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	270217.	+	468030.i	0.449085	+	0.777837i
$206$		0			0
$207$	269773.	−	467260.i	0.437594	−	0.757936i
$208$		0			0
$209$	−971088.			−1.53778
$210$		0			0
$211$	−1.19270e6			−1.84427			−0.922134	−	0.386871i	$-0.873556\pi$
$211$	−1.19270e6			−1.84427			−0.922134	+	0.386871i	$0.873556\pi$
$212$		0			0
$213$	−77125.2	+	133585.i	−0.116479	+	0.201748i
$214$		0			0
$215$	280869.	+	486480.i	0.414389	+	0.717743i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	520553.	+	901624.i	0.733423	+	1.27033i
$220$		0			0
$221$	59910.8	−	103769.i	0.0825134	−	0.142917i
$222$		0			0
$223$	−200502.			−0.269995			−0.134998	−	0.990846i	$-0.543103\pi$
$223$	−200502.			−0.269995			−0.134998	+	0.990846i	$0.543103\pi$
$224$		0			0
$225$	1.37159e6			1.80621
$226$		0			0
$227$	145384.	−	251813.i	0.187264	−	0.324350i	−0.757073	−	0.653330i	$-0.773371\pi$
$227$	145384.	−	251813.i	0.187264	−	0.324350i	0.944337	+	0.328980i	$0.106705\pi$
$228$		0			0
$229$	472471.	+	818344.i	0.595369	+	1.03121i	0.993495	+	0.113879i	$0.0363276\pi$
$229$	472471.	+	818344.i	0.595369	+	1.03121i	−0.398125	+	0.917331i	$0.630339\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−108192.	−	187394.i	−0.130558	−	0.226134i	0.793334	−	0.608787i	$-0.208344\pi$
$233$	−108192.	−	187394.i	−0.130558	−	0.226134i	−0.923892	+	0.382653i	$0.875010\pi$
$234$		0			0
$235$	801991.	−	1.38909e6i	0.947327	−	1.64082i
$236$		0			0
$237$	−2.32352e6			−2.68705
$238$		0			0
$239$	−668807.			−0.757366			−0.378683	−	0.925526i	$-0.623623\pi$
$239$	−668807.			−0.757366			−0.378683	+	0.925526i	$0.623623\pi$
$240$		0			0
$241$	578006.	−	1.00114e6i	0.641047	−	1.11033i	−0.344152	−	0.938914i	$-0.611834\pi$
$241$	578006.	−	1.00114e6i	0.641047	−	1.11033i	0.985199	−	0.171413i	$-0.0548331\pi$
$242$		0			0
$243$	−570131.	−	987495.i	−0.619382	−	1.07280i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	727666.	+	1.26036e6i	0.758909	+	1.31447i
$248$		0			0
$249$	427439.	−	740347.i	0.436894	−	0.756723i
$250$		0			0
$251$	77574.9			0.0777207			0.0388604	−	0.999245i	$-0.487627\pi$
$251$	77574.9			0.0777207			0.0388604	+	0.999245i	$0.487627\pi$
$252$		0			0
$253$	−836351.			−0.821462
$254$		0			0
$255$	148787.	−	257706.i	0.143289	−	0.248184i
$256$		0			0
$257$	−140101.	−	242662.i	−0.132315	−	0.229176i	0.792254	−	0.610192i	$-0.208908\pi$
$257$	−140101.	−	242662.i	−0.132315	−	0.229176i	−0.924569	+	0.381016i	$0.875574\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	131446.	+	227671.i	0.119439	+	0.206874i
$262$		0			0
$263$	134983.	−	233797.i	0.120334	−	0.208425i	−0.799565	−	0.600579i	$-0.794937\pi$
$263$	134983.	−	233797.i	0.120334	−	0.208425i	0.919900	+	0.392154i	$0.128270\pi$
$264$		0			0
$265$	1.77978e6			1.55687
$266$		0			0
$267$	2.45756e6			2.10972
$268$		0			0
$269$	445133.	−	770994.i	0.375068	−	0.649636i	−0.615270	−	0.788317i	$-0.710953\pi$
$269$	445133.	−	770994.i	0.375068	−	0.649636i	0.990337	+	0.138681i	$0.0442862\pi$
$270$		0			0
$271$	192140.	+	332796.i	0.158926	+	0.275267i	0.934482	−	0.356012i	$-0.115864\pi$
$271$	192140.	+	332796.i	0.158926	+	0.275267i	−0.775556	+	0.631279i	$0.782530\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.06305e6	−	1.84126e6i	−0.847664	−	1.46820i
$276$		0			0
$277$	545967.	−	945642.i	0.427530	−	0.740504i	−0.569123	−	0.822253i	$-0.692717\pi$
$277$	545967.	−	945642.i	0.427530	−	0.740504i	0.996653	+	0.0817484i	$0.0260504\pi$
$278$		0			0
$279$	1.13533e6			0.873196
$280$		0			0
$281$	771640.			0.582974			0.291487	−	0.956575i	$-0.405850\pi$
$281$	771640.			0.582974			0.291487	+	0.956575i	$0.405850\pi$
$282$		0			0
$283$	−270902.	+	469217.i	−0.201070	+	0.348263i	−0.948873	−	0.315657i	$-0.897775\pi$
$283$	−270902.	+	469217.i	−0.201070	+	0.348263i	0.747804	+	0.663920i	$0.231108\pi$
$284$		0			0
$285$	1.80714e6	+	3.13006e6i	1.31789	+	2.28265i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	699334.	+	1.21128e6i	0.492538	+	0.853101i
$290$		0			0
$291$	−938441.	+	1.62543e6i	−0.649643	+	1.12521i
$292$		0			0
$293$	−1.69804e6			−1.15552			−0.577762	−	0.816205i	$-0.696074\pi$
$293$	−1.69804e6			−1.15552			−0.577762	+	0.816205i	$0.696074\pi$
$294$		0			0
$295$	3.05532e6			2.04410
$296$		0			0
$297$	747224.	−	1.29423e6i	0.491541	−	0.851373i
$298$		0			0
$299$	626704.	+	1.08548e6i	0.405401	+	0.702175i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.39359e6	−	2.41377e6i	−0.872025	−	1.51039i
$304$		0			0
$305$	−1.81644e6	+	3.14617e6i	−1.11808	+	1.93656i
$306$		0			0
$307$	288376.			0.174627			0.0873137	−	0.996181i	$-0.472172\pi$
$307$	288376.			0.174627			0.0873137	+	0.996181i	$0.472172\pi$
$308$		0			0
$309$	−3.02173e6			−1.80036
$310$		0			0
$311$	173801.	−	301032.i	0.101894	−	0.176486i	−0.810571	−	0.585641i	$-0.800843\pi$
$311$	173801.	−	301032.i	0.101894	−	0.176486i	0.912465	+	0.409154i	$0.134176\pi$
$312$		0			0
$313$	−385201.	−	667188.i	−0.222242	−	0.384935i	0.733246	−	0.679963i	$-0.238004\pi$
$313$	−385201.	−	667188.i	−0.222242	−	0.384935i	−0.955489	+	0.295028i	$0.904671\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.00876e6	+	1.74722e6i	0.563819	+	0.976564i	0.997158	+	0.0753328i	$0.0240019\pi$
$317$	1.00876e6	+	1.74722e6i	0.563819	+	0.976564i	−0.433339	+	0.901231i	$0.642665\pi$
$318$		0			0
$319$	203755.	−	352914.i	0.112107	−	0.194174i
$320$		0			0
$321$	570441.			0.308993
$322$		0			0
$323$	257369.			0.137262
$324$		0			0
$325$	−1.59316e6	+	2.75943e6i	−0.836664	+	1.44914i
$326$		0			0
$327$	−332427.	−	575780.i	−0.171920	−	0.297775i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−212966.	−	368868.i	−0.106842	−	0.185055i	0.807648	−	0.589666i	$-0.200740\pi$
$331$	−212966.	−	368868.i	−0.106842	−	0.185055i	−0.914489	+	0.404610i	$0.867407\pi$
$332$		0			0
$333$	628853.	−	1.08921e6i	0.310770	−	0.538269i
$334$		0			0
$335$	−420563.			−0.204748
$336$		0			0
$337$	1.15035e6			0.551767			0.275884	−	0.961191i	$-0.411030\pi$
$337$	1.15035e6			0.551767			0.275884	+	0.961191i	$0.411030\pi$
$338$		0			0
$339$	−1.92338e6	+	3.33138e6i	−0.909002	+	1.57444i
$340$		0			0
$341$	−879941.	−	1.52410e6i	−0.409796	−	0.709787i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.55640e6	+	2.69577e6i	0.704002	+	1.21937i
$346$		0			0
$347$	156568.	−	271184.i	0.0698039	−	0.120904i	−0.829011	−	0.559232i	$-0.811096\pi$
$347$	156568.	−	271184.i	0.0698039	−	0.120904i	0.898815	+	0.438328i	$0.144429\pi$
$348$		0			0
$349$	3.01459e6			1.32484			0.662422	−	0.749131i	$-0.269529\pi$
$349$	3.01459e6			1.32484			0.662422	+	0.749131i	$0.269529\pi$
$350$		0			0
$351$	−2.23967e6			−0.970323
$352$		0			0
$353$	2.19230e6	−	3.79717e6i	0.936404	−	1.62190i	0.164292	−	0.986412i	$-0.447466\pi$
$353$	2.19230e6	−	3.79717e6i	0.936404	−	1.62190i	0.772111	−	0.635487i	$-0.219201\pi$
$354$		0			0
$355$	−263945.	−	457166.i	−0.111158	−	0.192532i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	96327.8	+	166845.i	0.0394471	+	0.0683244i	0.885075	−	0.465449i	$-0.154107\pi$
$359$	96327.8	+	166845.i	0.0394471	+	0.0683244i	−0.845628	+	0.533773i	$0.820774\pi$
$360$		0			0
$361$	−324928.	+	562792.i	−0.131226	+	0.227290i
$362$		0			0
$363$	−3.43681e6			−1.36896
$364$		0			0
$365$	−3.56297e6			−1.39984
$366$		0			0
$367$	−1.16991e6	+	2.02634e6i	−0.453405	+	0.785320i	−0.998595	−	0.0529924i	$-0.983124\pi$
$367$	−1.16991e6	+	2.02634e6i	−0.453405	+	0.785320i	0.545190	+	0.838312i	$0.316457\pi$
$368$		0			0
$369$	−1.14471e6	−	1.98270e6i	−0.437653	−	0.758037i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.96217e6	−	3.39857e6i	−0.730237	−	1.26481i	−0.956782	−	0.290806i	$-0.906077\pi$
$373$	−1.96217e6	−	3.39857e6i	−0.730237	−	1.26481i	0.226545	−	0.974001i	$-0.427257\pi$
$374$		0			0
$375$	−762455.	+	1.32061e6i	−0.279986	+	0.484950i
$376$		0			0
$377$	−610719.			−0.221303
$378$		0			0
$379$	−3.26556e6			−1.16778			−0.583889	−	0.811834i	$-0.698470\pi$
$379$	−3.26556e6			−1.16778			−0.583889	+	0.811834i	$0.698470\pi$
$380$		0			0
$381$	−3.09492e6	+	5.36055e6i	−1.09229	+	1.89190i
$382$		0			0
$383$	−2.21488e6	−	3.83628e6i	−0.771529	−	1.33633i	−0.936725	−	0.350067i	$-0.886159\pi$
$383$	−2.21488e6	−	3.83628e6i	−0.771529	−	1.33633i	0.165195	−	0.986261i	$-0.447175\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.18984e6	−	2.06086e6i	−0.403840	−	0.699472i
$388$		0			0
$389$	2.55733e6	−	4.42943e6i	0.856867	−	1.48414i	−0.0180345	−	0.999837i	$-0.505741\pi$
$389$	2.55733e6	−	4.42943e6i	0.856867	−	1.48414i	0.874902	−	0.484300i	$-0.160926\pi$
$390$		0			0
$391$	221659.			0.0733236
$392$		0			0
$393$	−2.82396e6			−0.922311
$394$		0			0
$395$	3.97588e6	−	6.88642e6i	1.28215	−	2.22076i
$396$		0			0
$397$	−770944.	−	1.33531e6i	−0.245497	−	0.425214i	0.716774	−	0.697306i	$-0.245618\pi$
$397$	−770944.	−	1.33531e6i	−0.245497	−	0.425214i	−0.962271	+	0.272092i	$0.912285\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.72114e6	−	4.71315e6i	−0.845064	−	1.46369i	−0.885566	−	0.464514i	$-0.846229\pi$
$401$	−2.72114e6	−	4.71315e6i	−0.845064	−	1.46369i	0.0405025	−	0.999179i	$-0.487104\pi$
$402$		0			0
$403$	−1.31873e6	+	2.28411e6i	−0.404478	+	0.700576i
$404$		0			0
$405$	1.63956e6			0.496694
$406$		0			0
$407$	−1.94958e6			−0.583384
$408$		0			0
$409$	2.59241e6	−	4.49019e6i	0.766294	−	1.32726i	−0.173265	−	0.984875i	$-0.555432\pi$
$409$	2.59241e6	−	4.49019e6i	0.766294	−	1.32726i	0.939560	−	0.342385i	$-0.111235\pi$
$410$		0			0
$411$	−2.53944e6	−	4.39844e6i	−0.741539	−	1.28438i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.46282e6	+	2.53368e6i	0.416938	+	0.722157i
$416$		0			0
$417$	354300.	−	613665.i	0.0997770	−	0.172819i
$418$		0			0
$419$	2.17093e6			0.604102			0.302051	−	0.953292i	$-0.402329\pi$
$419$	2.17093e6			0.604102			0.302051	+	0.953292i	$0.402329\pi$
$420$		0			0
$421$	6.61967e6			1.82025			0.910125	−	0.414334i	$-0.135986\pi$
$421$	6.61967e6			1.82025			0.910125	+	0.414334i	$0.135986\pi$
$422$		0			0
$423$	−3.39744e6	+	5.88455e6i	−0.923212	+	1.59905i
$424$		0			0
$425$	281743.	+	487992.i	0.0756624	+	0.131051i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	5.52478e6	+	9.56920e6i	1.44934	+	2.51034i
$430$		0			0
$431$	1.44992e6	−	2.51134e6i	0.375968	−	0.651196i	−0.614503	−	0.788914i	$-0.710643\pi$
$431$	1.44992e6	−	2.51134e6i	0.375968	−	0.651196i	0.990471	+	0.137718i	$0.0439768\pi$
$432$		0			0
$433$	−4.71803e6			−1.20932			−0.604659	−	0.796484i	$-0.706691\pi$
$433$	−4.71803e6			−1.20932			−0.604659	+	0.796484i	$0.706691\pi$
$434$		0			0
$435$	−1.51670e6			−0.384306
$436$		0			0
$437$	−1.34612e6	+	2.33154e6i	−0.337194	+	0.584036i
$438$		0			0
$439$	−1.73850e6	−	3.01117e6i	−0.430540	−	0.745718i	0.566379	−	0.824145i	$-0.308344\pi$
$439$	−1.73850e6	−	3.01117e6i	−0.430540	−	0.745718i	−0.996920	+	0.0784267i	$0.975010\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.64829e6	−	6.31902e6i	−0.883243	−	1.52982i	−0.847715	−	0.530452i	$-0.822022\pi$
$443$	−3.64829e6	−	6.31902e6i	−0.883243	−	1.52982i	−0.0355278	−	0.999369i	$-0.511311\pi$
$444$		0			0
$445$	−4.20524e6	+	7.28368e6i	−1.00668	+	1.74362i
$446$		0			0
$447$	8.08924e6			1.91487
$448$		0			0
$449$	3.65867e6			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$449$	3.65867e6			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$450$		0			0
$451$	−1.77442e6	+	3.07339e6i	−0.410786	+	0.711501i
$452$		0			0
$453$	1.33025e6	+	2.30405e6i	0.304569	+	0.527530i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.22031e6	−	5.57774e6i	−0.721286	−	1.24930i	−0.960485	−	0.278333i	$-0.910218\pi$
$457$	−3.22031e6	−	5.57774e6i	−0.721286	−	1.24930i	0.239199	−	0.970971i	$-0.423115\pi$
$458$		0			0
$459$	−198037.	+	343011.i	−0.0438748	+	0.0759935i
$460$		0			0
$461$	−4.47898e6			−0.981583			−0.490791	−	0.871277i	$-0.663292\pi$
$461$	−4.47898e6			−0.981583			−0.490791	+	0.871277i	$0.663292\pi$
$462$		0			0
$463$	−2.11214e6			−0.457899			−0.228949	−	0.973438i	$-0.573529\pi$
$463$	−2.11214e6			−0.457899			−0.228949	+	0.973438i	$0.573529\pi$
$464$		0			0
$465$	−3.27504e6	+	5.67253e6i	−0.702399	+	1.21659i
$466$		0			0
$467$	3.92919e6	+	6.80556e6i	0.833702	+	1.44401i	0.895083	+	0.445900i	$0.147116\pi$
$467$	3.92919e6	+	6.80556e6i	0.833702	+	1.44401i	−0.0613806	+	0.998114i	$0.519550\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	6.08252e6	+	1.05352e7i	1.26337	+	2.18823i
$472$		0			0
$473$	−1.84437e6	+	3.19454e6i	−0.379049	+	0.656532i
$474$		0			0
$475$	−6.84400e6			−1.39180
$476$		0			0
$477$	−7.53961e6			−1.51724
$478$		0			0
$479$	4.24373e6	−	7.35035e6i	0.845101	−	1.46376i	−0.0404324	−	0.999182i	$-0.512874\pi$
$479$	4.24373e6	−	7.35035e6i	0.845101	−	1.46376i	0.885533	−	0.464576i	$-0.153793\pi$
$480$		0			0
$481$	1.46088e6	+	2.53032e6i	0.287907	+	0.498669i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.21162e6	−	5.56269e6i	−0.619968	−	1.07382i
$486$		0			0
$487$	−1.37808e6	+	2.38691e6i	−0.263301	+	0.456051i	−0.967117	−	0.254331i	$-0.918145\pi$
$487$	−1.37808e6	+	2.38691e6i	−0.263301	+	0.456051i	0.703816	+	0.710382i	$0.251478\pi$
$488$		0			0
$489$	8.77658e6			1.65979
$490$		0			0
$491$	2.45533e6			0.459628			0.229814	−	0.973235i	$-0.426188\pi$
$491$	2.45533e6			0.459628			0.229814	+	0.973235i	$0.426188\pi$
$492$		0			0
$493$	−54001.3	+	93533.1i	−0.0100066	+	0.0173320i
$494$		0			0
$495$	8.13892e6	+	1.40970e7i	1.49298	+	2.58592i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.22925e6	+	3.86117e6i	0.400781	+	0.694172i	0.993820	−	0.111001i	$-0.0354056\pi$
$499$	2.22925e6	+	3.86117e6i	0.400781	+	0.694172i	−0.593040	+	0.805173i	$0.702072\pi$
$500$		0			0
$501$	618892.	−	1.07195e6i	0.110159	−	0.190801i
$502$		0			0
$503$	−2.64080e6			−0.465389			−0.232694	−	0.972550i	$-0.574754\pi$
$503$	−2.64080e6			−0.465389			−0.232694	+	0.972550i	$0.574754\pi$
$504$		0			0
$505$	9.53856e6			1.66439
$506$		0			0
$507$	3.74252e6	−	6.48223e6i	0.646612	−	1.11997i
$508$		0			0
$509$	2.35520e6	+	4.07933e6i	0.402934	+	0.697902i	0.994079	−	0.108663i	$-0.0346571\pi$
$509$	2.35520e6	+	4.07933e6i	0.402934	+	0.697902i	−0.591145	+	0.806566i	$0.701324\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.40533e6	−	4.16615e6i	−0.403535	−	0.698943i
$514$		0			0
$515$	5.17061e6	−	8.95576e6i	0.859061	−	1.48794i
$516$		0			0
$517$	1.05328e7			1.73307
$518$		0			0
$519$	7.41003e6			1.20754
$520$		0			0
$521$	−1.40134e6	+	2.42720e6i	−0.226178	+	0.391752i	−0.956672	−	0.291167i	$-0.905956\pi$
$521$	−1.40134e6	+	2.42720e6i	−0.226178	+	0.391752i	0.730494	+	0.682919i	$0.239290\pi$
$522$		0			0
$523$	−1.49878e6	−	2.59596e6i	−0.239598	−	0.414995i	0.721001	−	0.692934i	$-0.243682\pi$
$523$	−1.49878e6	−	2.59596e6i	−0.239598	−	0.414995i	−0.960599	+	0.277939i	$0.910349\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	233212.	+	403934.i	0.0365783	+	0.0633555i
$528$		0			0
$529$	2.05883e6	−	3.56599e6i	0.319875	−	0.554040i
$530$		0			0
$531$	−1.29431e7			−1.99207
$532$		0			0
$533$	5.31851e6			0.810909
$534$		0			0
$535$	−976107.	+	1.69067e6i	−0.147439	+	0.255372i
$536$		0			0
$537$	−8.34078e6	−	1.44467e7i	−1.24816	−	2.16188i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.65252e6	−	2.86225e6i	−0.242747	−	0.420450i	0.718749	−	0.695270i	$-0.244715\pi$
$541$	−1.65252e6	−	2.86225e6i	−0.242747	−	0.420450i	−0.961496	+	0.274820i	$0.911382\pi$
$542$		0			0
$543$	−2.22963e6	+	3.86183e6i	−0.324514	+	0.562074i
$544$		0			0
$545$	2.27532e6			0.328135
$546$		0			0
$547$	3.51435e6			0.502201			0.251100	−	0.967961i	$-0.419208\pi$
$547$	3.51435e6			0.502201			0.251100	+	0.967961i	$0.419208\pi$
$548$		0			0
$549$	7.69491e6	−	1.33280e7i	1.08961	−	1.88727i
$550$		0			0
$551$	−655891.	−	1.13604e6i	−0.0920350	−	0.159409i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.62805e6	+	6.28397e6i	0.499967	+	0.865968i
$556$		0			0
$557$	2.99093e6	−	5.18045e6i	0.408478	−	0.707505i	−0.586241	−	0.810137i	$-0.699393\pi$
$557$	2.99093e6	−	5.18045e6i	0.408478	−	0.707505i	0.994719	+	0.102632i	$0.0327263\pi$
$558$		0			0
$559$	5.52817e6			0.748259
$560$		0			0
$561$	1.95406e6			0.262138
$562$		0			0
$563$	5.36921e6	−	9.29974e6i	0.713903	−	1.23652i	−0.249478	−	0.968380i	$-0.580259\pi$
$563$	5.36921e6	−	9.29974e6i	0.713903	−	1.23652i	0.963381	−	0.268136i	$-0.0864075\pi$
$564$		0			0
$565$	−6.58235e6	−	1.14010e7i	−0.867481	−	1.50252i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.29774e6	+	5.71186e6i	0.427008	+	0.739600i	0.996606	−	0.0823241i	$-0.0262343\pi$
$569$	3.29774e6	+	5.71186e6i	0.427008	+	0.739600i	−0.569598	+	0.821924i	$0.692901\pi$
$570$		0			0
$571$	1.30789e6	−	2.26533e6i	0.167873	−	0.290764i	−0.769799	−	0.638286i	$-0.779644\pi$
$571$	1.30789e6	−	2.26533e6i	0.167873	−	0.290764i	0.937672	+	0.347522i	$0.112977\pi$
$572$		0			0
$573$	−1.67060e7			−2.12562
$574$		0			0
$575$	−5.89440e6			−0.743482
$576$		0			0
$577$	−619490.	+	1.07299e6i	−0.0774630	+	0.134170i	−0.902155	−	0.431413i	$-0.858015\pi$
$577$	−619490.	+	1.07299e6i	−0.0774630	+	0.134170i	0.824692	+	0.565583i	$0.191349\pi$
$578$		0			0
$579$	1.15664e7	+	2.00336e7i	1.43385	+	2.48349i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	5.84360e6	+	1.01214e7i	0.712047	+	1.23330i
$584$		0			0
$585$	1.21975e7	−	2.11267e7i	1.47360	−	2.55236i
$586$		0			0
$587$	−1.02896e7			−1.23254			−0.616270	−	0.787535i	$-0.711357\pi$
$587$	−1.02896e7			−1.23254			−0.616270	+	0.787535i	$0.711357\pi$
$588$		0			0
$589$	−5.66510e6			−0.672852
$590$		0			0
$591$	−2.25106e6	+	3.89895e6i	−0.265105	+	0.459176i
$592$		0			0
$593$	7.65889e6	+	1.32656e7i	0.894394	+	1.54914i	0.834553	+	0.550928i	$0.185726\pi$
$593$	7.65889e6	+	1.32656e7i	0.894394	+	1.54914i	0.0598415	+	0.998208i	$0.480940\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−833495.	−	1.44366e6i	−0.0957122	−	0.165778i
$598$		0			0
$599$	−1.34748e6	+	2.33391e6i	−0.153446	+	0.265776i	−0.932492	−	0.361190i	$-0.882370\pi$
$599$	−1.34748e6	+	2.33391e6i	−0.153446	+	0.265776i	0.779046	+	0.626967i	$0.215704\pi$
$600$		0			0
$601$	−1.54704e6			−0.174709			−0.0873547	−	0.996177i	$-0.527841\pi$
$601$	−1.54704e6			−0.174709			−0.0873547	+	0.996177i	$0.527841\pi$
$602$		0			0
$603$	1.78162e6			0.199536
$604$		0			0
$605$	5.88088e6	−	1.01860e7i	0.653212	−	1.13140i
$606$		0			0
$607$	1.89569e6	+	3.28343e6i	0.208831	+	0.361706i	0.951347	−	0.308123i	$-0.0997008\pi$
$607$	1.89569e6	+	3.28343e6i	0.208831	+	0.361706i	−0.742516	+	0.669829i	$0.766367\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.89255e6	−	1.36703e7i	−0.855291	−	1.48141i
$612$		0			0
$613$	−3.09603e6	+	5.36249e6i	−0.332778	+	0.576388i	−0.983055	−	0.183308i	$-0.941319\pi$
$613$	−3.09603e6	+	5.36249e6i	−0.332778	+	0.576388i	0.650277	+	0.759697i	$0.274653\pi$
$614$		0			0
$615$	1.32084e7			1.40819
$616$		0			0
$617$	−1.59349e7			−1.68514			−0.842571	−	0.538585i	$-0.818959\pi$
$617$	−1.59349e7			−1.68514			−0.842571	+	0.538585i	$0.818959\pi$
$618$		0			0
$619$	−5.78660e6	+	1.00227e7i	−0.607011	+	1.05137i	0.384719	+	0.923034i	$0.374298\pi$
$619$	−5.78660e6	+	1.00227e7i	−0.607011	+	1.05137i	−0.991730	+	0.128341i	$0.959035\pi$
$620$		0			0
$621$	−2.07159e6	−	3.58811e6i	−0.215564	−	0.373367i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	3.43903e6	+	5.95657e6i	0.352156	+	0.609953i
$626$		0			0
$627$	−1.18668e7	+	2.05540e7i	−1.20550	+	2.08798i
$628$		0			0
$629$	516699.			0.0520728
$630$		0			0
$631$	900933.			0.0900781			0.0450390	−	0.998985i	$-0.485659\pi$
$631$	900933.			0.0900781			0.0450390	+	0.998985i	$0.485659\pi$
$632$		0			0
$633$	−1.45749e7	+	2.52445e7i	−1.44576	+	2.50414i
$634$		0			0
$635$	−1.05917e7	−	1.83454e7i	−1.04239	−	1.80548i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.11814e6	+	1.93667e6i	0.108329	+	0.187631i
$640$		0			0
$641$	424385.	−	735057.i	0.0407958	−	0.0706604i	−0.844907	−	0.534914i	$-0.820344\pi$
$641$	424385.	−	735057.i	0.0407958	−	0.0706604i	0.885702	+	0.464254i	$0.153677\pi$
$642$		0			0
$643$	1.37977e7			1.31607			0.658036	−	0.752986i	$-0.271387\pi$
$643$	1.37977e7			1.31607			0.658036	+	0.752986i	$0.271387\pi$
$644$		0			0
$645$	1.37291e7			1.29940
$646$		0			0
$647$	−1.82675e6	+	3.16402e6i	−0.171561	+	0.297152i	−0.938966	−	0.344011i	$-0.888214\pi$
$647$	−1.82675e6	+	3.16402e6i	−0.171561	+	0.297152i	0.767405	+	0.641163i	$0.221548\pi$
$648$		0			0
$649$	1.00316e7	+	1.73753e7i	0.934887	+	1.61927i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.89558e6	−	1.02115e7i	−0.541058	−	0.937140i	−0.998844	−	0.0480774i	$-0.984691\pi$
$653$	−5.89558e6	−	1.02115e7i	−0.541058	−	0.937140i	0.457786	−	0.889063i	$-0.348643\pi$
$654$		0			0
$655$	4.83221e6	−	8.36963e6i	0.440091	−	0.762260i
$656$		0			0
$657$	1.50937e7			1.36421
$658$		0			0
$659$	−1.15208e7			−1.03340			−0.516700	−	0.856166i	$-0.672840\pi$
$659$	−1.15208e7			−1.03340			−0.516700	+	0.856166i	$0.672840\pi$
$660$		0			0
$661$	2.68607e6	−	4.65241e6i	0.239119	−	0.414166i	−0.721343	−	0.692578i	$-0.756475\pi$
$661$	2.68607e6	−	4.65241e6i	0.239119	−	0.414166i	0.960462	+	0.278412i	$0.0898081\pi$
$662$		0			0
$663$	−1.46424e6	−	2.53613e6i	−0.129368	−	0.224072i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−564888.	−	978414.i	−0.0491640	−	0.0851546i
$668$		0			0
$669$	−2.45016e6	+	4.24381e6i	−0.211655	+	0.366598i
$670$		0			0
$671$	−2.38558e7			−2.04545
$672$		0			0
$673$	1.48042e7			1.25993			0.629966	−	0.776623i	$-0.283069\pi$
$673$	1.48042e7			1.25993			0.629966	+	0.776623i	$0.283069\pi$
$674$		0			0
$675$	5.26625e6	−	9.12142e6i	0.444879	−	0.770554i
$676$		0			0
$677$	−2.95353e6	−	5.11567e6i	−0.247668	−	0.428974i	0.715210	−	0.698909i	$-0.246331\pi$
$677$	−2.95353e6	−	5.11567e6i	−0.247668	−	0.428974i	−0.962878	+	0.269935i	$0.912998\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.55324e6	−	6.15439e6i	−0.293601	−	0.508531i
$682$		0			0
$683$	−1.10080e7	+	1.90663e7i	−0.902932	+	1.56392i	−0.0792618	+	0.996854i	$0.525256\pi$
$683$	−1.10080e7	+	1.90663e7i	−0.902932	+	1.56392i	−0.823670	+	0.567070i	$0.808077\pi$
$684$		0			0
$685$	1.73814e7			1.41533
$686$		0			0
$687$	2.30947e7			1.86690
$688$		0			0
$689$	8.75757e6	−	1.51686e7i	0.702806	−	1.21730i
$690$		0			0
$691$	6.53254e6	+	1.13147e7i	0.520460	+	0.901463i	0.999717	+	0.0237881i	$0.00757271\pi$
$691$	6.53254e6	+	1.13147e7i	0.520460	+	0.901463i	−0.479257	+	0.877674i	$0.659094\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.21252e6	+	2.10014e6i	0.0952194	+	0.164925i
$696$		0			0
$697$	470276.	−	814543.i	0.0366667	−	0.0635085i
$698$		0			0
$699$	−5.28848e6			−0.409391
$700$		0			0
$701$	1.20043e7			0.922658			0.461329	−	0.887229i	$-0.347373\pi$
$701$	1.20043e7			0.922658			0.461329	+	0.887229i	$0.347373\pi$
$702$		0			0
$703$	−3.13787e6	+	5.43495e6i	−0.239467	+	0.414770i
$704$		0			0
$705$	−1.96009e7	−	3.39498e7i	−1.48526	−	2.57255i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	8.23972e6	+	1.42716e7i	0.615597	+	1.06625i	0.990279	+	0.139093i	$0.0444185\pi$
$709$	8.23972e6	+	1.42716e7i	0.615597	+	1.06625i	−0.374682	+	0.927153i	$0.622248\pi$
$710$		0			0
$711$	−1.68429e7	+	2.91727e7i	−1.24952	+	2.16422i
$712$		0			0
$713$	−4.87908e6			−0.359430
$714$		0			0
$715$	−3.78148e7			−2.76628
$716$		0			0
$717$	−8.17292e6	+	1.41559e7i	−0.593717	+	1.02835i
$718$		0			0
$719$	−3.66177e6	−	6.34237e6i	−0.264161	−	0.457540i	0.703183	−	0.711009i	$-0.251762\pi$
$719$	−3.66177e6	−	6.34237e6i	−0.264161	−	0.457540i	−0.967343	+	0.253469i	$0.918428\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.41267e7	−	2.44681e7i	−1.00506	−	1.74082i
$724$		0			0
$725$	1.43601e6	−	2.48725e6i	0.101464	−	0.175742i
$726$		0			0
$727$	−1.83777e7			−1.28960			−0.644798	−	0.764353i	$-0.723059\pi$
$727$	−1.83777e7			−1.28960			−0.644798	+	0.764353i	$0.723059\pi$
$728$		0			0
$729$	−2.31050e7			−1.61023
$730$		0			0
$731$	488815.	−	846653.i	0.0338338	−	0.0586019i
$732$		0			0
$733$	−5.92488e6	−	1.02622e7i	−0.407305	−	0.705472i	0.587282	−	0.809382i	$-0.300198\pi$
$733$	−5.92488e6	−	1.02622e7i	−0.407305	−	0.705472i	−0.994587	+	0.103910i	$0.966865\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.38085e6	−	2.39170e6i	−0.0936432	−	0.162195i
$738$		0			0
$739$	1.04756e7	−	1.81442e7i	0.705613	−	1.22216i	−0.260857	−	0.965377i	$-0.584005\pi$
$739$	1.04756e7	−	1.81442e7i	0.705613	−	1.22216i	0.966470	−	0.256780i	$-0.0826616\pi$
$740$		0			0
$741$	3.55688e7			2.37971
$742$		0			0
$743$	−1.42524e7			−0.947141			−0.473570	−	0.880756i	$-0.657035\pi$
$743$	−1.42524e7			−0.947141			−0.473570	+	0.880756i	$0.657035\pi$
$744$		0			0
$745$	−1.38419e7	+	2.39748e7i	−0.913701	+	1.58258i
$746$		0			0
$747$	−6.19689e6	−	1.07333e7i	−0.406324	−	0.703774i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−659846.	−	1.14289e6i	−0.0426916	−	0.0739441i	0.843890	−	0.536516i	$-0.180260\pi$
$751$	−659846.	−	1.14289e6i	−0.0426916	−	0.0739441i	−0.886582	+	0.462572i	$0.846927\pi$
$752$		0			0
$753$	947977.	−	1.64194e6i	0.0609271	−	0.105529i
$754$		0			0
$755$	−9.10497e6			−0.581315
$756$		0			0
$757$	102138.			0.00647812			0.00323906	−	0.999995i	$-0.498969\pi$
$757$	102138.			0.00647812			0.00323906	+	0.999995i	$0.498969\pi$
$758$		0			0
$759$	−1.02203e7	+	1.77022e7i	−0.643963	+	1.11538i
$760$		0			0
$761$	1.09596e7	+	1.89826e7i	0.686016	+	1.18821i	0.973116	+	0.230314i	$0.0739754\pi$
$761$	1.09596e7	+	1.89826e7i	0.686016	+	1.18821i	−0.287100	+	0.957901i	$0.592691\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−2.15707e6	−	3.73615e6i	−0.133263	−	0.230819i
$766$		0			0
$767$	1.50340e7	−	2.60397e7i	0.922755	−	1.59826i
$768$		0			0
$769$	−6.44098e6			−0.392768			−0.196384	−	0.980527i	$-0.562920\pi$
$769$	−6.44098e6			−0.392768			−0.196384	+	0.980527i	$0.562920\pi$
$770$		0			0
$771$	−6.84823e6			−0.414899
$772$		0			0
$773$	1.45580e6	−	2.52152e6i	0.0876302	−	0.151780i	−0.818879	−	0.573966i	$-0.805404\pi$
$773$	1.45580e6	−	2.52152e6i	0.0876302	−	0.151780i	0.906509	+	0.422187i	$0.138737\pi$
$774$		0			0
$775$	−6.20161e6	−	1.07415e7i	−0.370894	−	0.642408i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.71190e6	+	9.89330e6i	0.337238	+	0.584114i
$780$		0			0
$781$	1.73323e6	−	3.00205e6i	0.101679	−	0.176113i
$782$		0			0
$783$	2.01876e6			0.117674
$784$		0			0
$785$	−4.16323e7			−2.41133
$786$		0			0
$787$	1.27290e7	−	2.20472e7i	0.732582	−	1.26887i	−0.223195	−	0.974774i	$-0.571649\pi$
$787$	1.27290e7	−	2.20472e7i	0.732582	−	1.26887i	0.955776	−	0.294095i	$-0.0950181\pi$
$788$		0			0
$789$	−3.29902e6	−	5.71408e6i	−0.188666	−	0.326779i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.78759e7	+	3.09620e7i	1.00945	+	1.74842i
$794$		0			0
$795$	2.17492e7	−	3.76707e7i	1.22046	−	2.11391i
$796$		0			0
$797$	2.04344e7			1.13950			0.569752	−	0.821817i	$-0.307039\pi$
$797$	2.04344e7			1.13950			0.569752	+	0.821817i	$0.307039\pi$
$798$		0			0
$799$	−2.79152e6			−0.154694
$800$		0			0
$801$	1.78145e7	−	3.08556e7i	0.981051	−	1.69923i
$802$		0			0
$803$	−1.16984e7	−	2.02622e7i	−0.640231	−	1.10891i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.08792e7	−	1.88433e7i	−0.588048	−	1.01853i
$808$		0			0
$809$	−1.41416e7	+	2.44939e7i	−0.759672	+	1.31579i	0.183345	+	0.983049i	$0.441307\pi$
$809$	−1.41416e7	+	2.44939e7i	−0.759672	+	1.31579i	−0.943018	+	0.332743i	$0.892026\pi$
$810$		0			0
$811$	−1.58852e7			−0.848087			−0.424043	−	0.905642i	$-0.639390\pi$
$811$	−1.58852e7			−0.848087			−0.424043	+	0.905642i	$0.639390\pi$
$812$		0			0
$813$	9.39191e6			0.498342
$814$		0			0
$815$	−1.50180e7	+	2.60119e7i	−0.791987	+	1.37176i
$816$		0			0
$817$	5.93707e6	+	1.02833e7i	0.311184	+	0.538986i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.72198e6	−	1.33749e7i	−0.399826	−	0.692519i	0.593878	−	0.804555i	$-0.297596\pi$
$821$	−7.72198e6	−	1.33749e7i	−0.399826	−	0.692519i	−0.993704	+	0.112036i	$0.964263\pi$
$822$		0			0
$823$	−1.48943e7	+	2.57977e7i	−0.766516	+	1.32764i	0.172926	+	0.984935i	$0.444678\pi$
$823$	−1.48943e7	+	2.57977e7i	−0.766516	+	1.32764i	−0.939441	+	0.342710i	$0.888655\pi$
$824$		0			0
$825$	−5.19628e7			−2.65801
$826$		0			0
$827$	1.66831e7			0.848230			0.424115	−	0.905608i	$-0.360585\pi$
$827$	1.66831e7			0.848230			0.424115	+	0.905608i	$0.360585\pi$
$828$		0			0
$829$	−1.10568e7	+	1.91510e7i	−0.558785	+	0.967844i	0.438813	+	0.898578i	$0.355399\pi$
$829$	−1.10568e7	+	1.91510e7i	−0.558785	+	0.967844i	−0.997598	+	0.0692656i	$0.977934\pi$
$830$		0			0
$831$	−1.33436e7	−	2.31118e7i	−0.670302	−	1.16100i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.11803e6	+	3.66853e6i	0.105127	+	0.182086i
$836$		0			0
$837$	4.35913e6	−	7.55023e6i	0.215073	−	0.372517i
$838$		0			0
$839$	−539166.			−0.0264434			−0.0132217	−	0.999913i	$-0.504209\pi$
$839$	−539166.			−0.0264434			−0.0132217	+	0.999913i	$0.504209\pi$
$840$		0			0
$841$	−1.99607e7			−0.973162
$842$		0			0
$843$	9.42956e6	−	1.63325e7i	0.457007	−	0.791559i
$844$		0			0
$845$	1.28080e7	+	2.21841e7i	0.617076	+	1.06881i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6.62094e6	+	1.14678e7i	0.315247	+	0.546023i
$850$		0			0
$851$	−2.70249e6	+	4.68086e6i	−0.127921	+	0.221565i
$852$		0			0
$853$	−2.55452e6			−0.120209			−0.0601044	−	0.998192i	$-0.519143\pi$
$853$	−2.55452e6			−0.120209			−0.0601044	+	0.998192i	$0.519143\pi$
$854$		0			0
$855$	5.23988e7			2.45135
$856$		0			0
$857$	120039.	−	207913.i	0.00558303	−	0.00967008i	−0.863220	−	0.504827i	$-0.831556\pi$
$857$	120039.	−	207913.i	0.00558303	−	0.00967008i	0.868803	+	0.495157i	$0.164890\pi$
$858$		0			0
$859$	3.33955e6	+	5.78428e6i	0.154421	+	0.267464i	0.932848	−	0.360270i	$-0.117316\pi$
$859$	3.33955e6	+	5.78428e6i	0.154421	+	0.267464i	−0.778427	+	0.627735i	$0.783982\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.02530e7	+	1.77587e7i	0.468622	+	0.811678i	0.999357	−	0.0358604i	$-0.0114172\pi$
$863$	1.02530e7	+	1.77587e7i	0.468622	+	0.811678i	−0.530734	+	0.847538i	$0.678084\pi$
$864$		0			0
$865$	−1.26796e7	+	2.19618e7i	−0.576192	+	0.997993i
$866$		0			0
$867$	3.41839e7			1.54445
$868$		0			0
$869$	5.22164e7			2.34562
$870$		0			0
$871$	−2.06942e6	+	3.58434e6i	−0.0924280	+	0.160090i
$872$		0			0
$873$	1.36052e7	+	2.35650e7i	0.604186	+	1.04648i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.26387e7	−	2.18909e7i	−0.554888	−	0.961093i	−0.997912	−	0.0645840i	$-0.979428\pi$
$877$	−1.26387e7	−	2.18909e7i	−0.554888	−	0.961093i	0.443025	−	0.896509i	$-0.353905\pi$
$878$		0			0
$879$	−2.07503e7	+	3.59406e7i	−0.905842	+	1.56896i
$880$		0			0
$881$	2.45932e7			1.06752			0.533759	−	0.845637i	$-0.320779\pi$
$881$	2.45932e7			1.06752			0.533759	+	0.845637i	$0.320779\pi$
$882$		0			0
$883$	2.78301e7			1.20120			0.600598	−	0.799551i	$-0.294929\pi$
$883$	2.78301e7			1.20120			0.600598	+	0.799551i	$0.294929\pi$
$884$		0			0
$885$	3.73365e7	−	6.46688e7i	1.60242	−	2.77547i
$886$		0			0
$887$	1.74928e7	+	3.02984e7i	0.746534	+	1.29304i	0.949474	+	0.313844i	$0.101617\pi$
$887$	1.74928e7	+	3.02984e7i	0.746534	+	1.29304i	−0.202940	+	0.979191i	$0.565050\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.38319e6	+	9.32396e6i	0.227167	+	0.393465i
$892$		0			0
$893$	1.69526e7	−	2.93629e7i	0.711392	−	1.23217i
$894$		0			0
$895$	5.70892e7			2.38230
$896$		0			0
$897$	3.06337e7			1.27121
$898$		0			0
$899$	1.18866e6	−	2.05882e6i	0.0490521	−	0.0849607i
$900$		0			0
$901$	−1.54873e6	−	2.68249e6i	−0.0635572	−	0.110084i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.63044e6	−	1.32163e7i	−0.309691	−	0.536400i
$906$		0			0
$907$	2.03300e7	−	3.52127e7i	0.820578	−	1.42128i	−0.0846741	−	0.996409i	$-0.526985\pi$
$907$	2.03300e7	−	3.52127e7i	0.820578	−	1.42128i	0.905252	−	0.424874i	$-0.139682\pi$
$908$		0			0
$909$	−4.04078e7			−1.62202
$910$		0			0
$911$	−2.87014e7			−1.14579			−0.572897	−	0.819627i	$-0.694180\pi$
$911$	−2.87014e7			−1.14579			−0.572897	+	0.819627i	$0.694180\pi$
$912$		0			0
$913$	−9.60584e6	+	1.66378e7i	−0.381380	+	0.660570i
$914$		0			0
$915$	4.43943e7	+	7.68933e7i	1.75297	+	3.03624i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.47415e7	−	2.55330e7i	−0.575773	−	0.997269i	−0.995957	−	0.0898297i	$-0.971368\pi$
$919$	−1.47415e7	−	2.55330e7i	−0.575773	−	0.997269i	0.420184	−	0.907439i	$-0.361966\pi$
$920$		0			0
$921$	3.52399e6	−	6.10374e6i	0.136895	−	0.237108i
$922$		0			0
$923$	−5.19506e6			−0.200718
$924$		0			0
$925$	−1.37402e7			−0.528004
$926$		0			0
$927$	−2.19041e7	+	3.79389e7i	−0.837192	+	1.45006i
$928$		0			0
$929$	−7.94112e6	−	1.37544e7i	−0.301886	−	0.522881i	0.674677	−	0.738113i	$-0.264283\pi$
$929$	−7.94112e6	−	1.37544e7i	−0.301886	−	0.522881i	−0.976563	+	0.215231i	$0.930949\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.24774e6	−	7.35731e6i	−0.159755	−	0.276704i
$934$		0			0
$935$	−3.34368e6	+	5.79143e6i	−0.125082	+	0.216649i
$936$		0			0
$937$	−1.04452e7			−0.388656			−0.194328	−	0.980937i	$-0.562253\pi$
$937$	−1.04452e7			−0.388656			−0.194328	+	0.980937i	$0.562253\pi$
$938$		0			0
$939$	−1.88289e7			−0.696884
$940$		0			0
$941$	−1.34241e7	+	2.32513e7i	−0.494211	+	0.855998i	−0.999978	−	0.00667223i	$-0.997876\pi$
$941$	−1.34241e7	+	2.32513e7i	−0.494211	+	0.855998i	0.505767	+	0.862670i	$0.331209\pi$
$942$		0			0
$943$	4.91938e6	+	8.52062e6i	0.180149	+	0.312027i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.62047e6	+	1.31990e7i	0.276126	+	0.478264i	0.970418	−	0.241429i	$-0.0776161\pi$
$947$	7.62047e6	+	1.31990e7i	0.276126	+	0.478264i	−0.694293	+	0.719693i	$0.744283\pi$
$948$		0			0
$949$	−1.75319e7	+	3.03662e7i	−0.631922	+	1.09452i
$950$		0			0
$951$	4.93088e7			1.76796
$952$		0			0
$953$	−1.29112e7			−0.460504			−0.230252	−	0.973131i	$-0.573955\pi$
$953$	−1.29112e7			−0.460504			−0.230252	+	0.973131i	$0.573955\pi$
$954$		0			0
$955$	2.85864e7	−	4.95131e7i	1.01426	−	1.75676i
$956$		0			0
$957$	−4.97983e6	−	8.62532e6i	−0.175766	−	0.304435i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	9.18121e6	+	1.59023e7i	0.320694	+	0.555459i
$962$		0			0
$963$	4.13504e6	−	7.16211e6i	0.143686	−	0.248871i
$964$		0			0
$965$	−7.91672e7			−2.73670
$966$		0			0
$967$	4.60406e7			1.58334			0.791671	−	0.610948i	$-0.209211\pi$
$967$	4.60406e7			1.58334			0.791671	+	0.610948i	$0.209211\pi$
$968$		0			0
$969$	3.14508e6	−	5.44744e6i	0.107603	−	0.186373i
$970$		0			0
$971$	9.36580e6	+	1.62220e7i	0.318784	+	0.552150i	0.980235	−	0.197839i	$-0.0633922\pi$
$971$	9.36580e6	+	1.62220e7i	0.318784	+	0.552150i	−0.661451	+	0.749989i	$0.730059\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.89373e7	+	6.74414e7i	1.31176	+	2.27204i
$976$		0			0
$977$	1.44602e7	−	2.50458e7i	0.484660	−	0.839456i	−0.515184	−	0.857079i	$-0.672277\pi$
$977$	1.44602e7	−	2.50458e7i	0.484660	−	0.839456i	0.999845	+	0.0176231i	$0.00560991\pi$
$978$		0			0
$979$	−5.52286e7			−1.84165
$980$		0			0
$981$	−9.63886e6			−0.319781
$982$		0			0
$983$	1.08834e7	−	1.88505e7i	0.359235	−	0.622214i	−0.628598	−	0.777730i	$-0.716371\pi$
$983$	1.08834e7	−	1.88505e7i	0.359235	−	0.622214i	0.987833	+	0.155517i	$0.0497042\pi$
$984$		0			0
$985$	−7.70379e6	−	1.33433e7i	−0.252996	−	0.438202i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.11331e6	+	8.85651e6i	0.166231	+	0.287920i
$990$		0			0
$991$	9.39333e6	−	1.62697e7i	0.303833	−	0.526255i	−0.673168	−	0.739490i	$-0.735067\pi$
$991$	9.39333e6	−	1.62697e7i	0.303833	−	0.526255i	0.977001	+	0.213235i	$0.0684001\pi$
$992$		0			0
$993$	−1.04099e7			−0.335023
$994$		0			0
$995$	5.70492e6			0.182680
$996$		0			0
$997$	−7.38382e6	+	1.27891e7i	−0.235257	+	0.407477i	−0.959347	−	0.282228i	$-0.908927\pi$
$997$	−7.38382e6	+	1.27891e7i	−0.235257	+	0.407477i	0.724090	+	0.689705i	$0.242260\pi$
$998$		0			0
$999$	−4.82899e6	−	8.36406e6i	−0.153089	−	0.265157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.e.k.165.2		4
7.2	even	3	inner	196.6.e.k.177.2		4
7.3	odd	6		196.6.a.j.1.2		2
7.4	even	3		196.6.a.h.1.1		2
7.5	odd	6		28.6.e.b.9.1	✓	4
7.6	odd	2		28.6.e.b.25.1	yes	4
21.5	even	6		252.6.k.d.37.2		4
21.20	even	2		252.6.k.d.109.2		4
28.3	even	6		784.6.a.o.1.1		2
28.11	odd	6		784.6.a.bd.1.2		2
28.19	even	6		112.6.i.e.65.2		4
28.27	even	2		112.6.i.e.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.e.b.9.1	✓	4	7.5	odd	6
28.6.e.b.25.1	yes	4	7.6	odd	2
112.6.i.e.65.2		4	28.19	even	6
112.6.i.e.81.2		4	28.27	even	2
196.6.a.h.1.1		2	7.4	even	3
196.6.a.j.1.2		2	7.3	odd	6
196.6.e.k.165.2		4	1.1	even	1	trivial
196.6.e.k.177.2		4	7.2	even	3	inner
252.6.k.d.37.2		4	21.5	even	6
252.6.k.d.109.2		4	21.20	even	2
784.6.a.o.1.1		2	28.3	even	6
784.6.a.bd.1.2		2	28.11	odd	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.2202 - 21.1659i) q^{3} +(41.8209 + 72.4360i) q^{5} +(-177.164 - 306.858i) q^{9} +(-274.623 + 475.661i) q^{11} +823.135 q^{13} +2044.23 q^{15} +(72.7837 - 126.065i) q^{17} +(884.019 + 1531.17i) q^{19} +(761.363 + 1318.72i) q^{23} +(-1935.48 + 3352.35i) q^{25} -2720.90 q^{27} -741.943 q^{29} +(-1602.09 + 2774.90i) q^{31} +(6711.88 + 11625.3i) q^{33} +(1774.77 + 3074.00i) q^{37} +(10058.8 - 17422.4i) q^{39} +6461.29 q^{41} +6716.00 q^{43} +(14818.3 - 25666.1i) q^{45} +(-9588.40 - 16607.6i) q^{47} +(-1778.86 - 3081.07i) q^{51} +(10639.3 - 18427.8i) q^{53} -45940.0 q^{55} +43211.4 q^{57} +(18264.3 - 31634.8i) q^{59} +(21716.9 + 37614.7i) q^{61} +(34424.3 + 59624.6i) q^{65} +(-2514.07 + 4354.50i) q^{67} +37215.9 q^{69} -6311.32 q^{71} +(-21299.0 + 36890.9i) q^{73} +(47303.7 + 81932.4i) q^{75} +(-47534.6 - 82332.3i) q^{79} +(9801.05 - 16975.9i) q^{81} +34978.2 q^{83} +12175.5 q^{85} +(-9066.66 + 15703.9i) q^{87} +(50276.7 + 87081.8i) q^{89} +(39155.5 + 67819.3i) q^{93} +(-73940.9 + 128069. i) q^{95} -76794.5 q^{97} +194614. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 28 q^{3} + 42 q^{5} - 124 q^{9} - 660 q^{11} + 1288 q^{13} + 3792 q^{15} - 210 q^{17} + 3724 q^{19} - 24 q^{23} - 2480 q^{25} - 2072 q^{27} + 11064 q^{29} + 2800 q^{31} + 13818 q^{33} + 13238 q^{37}+ \cdots + 338208 q^{99}+O(q^{100}) \) 4 * q + 28 * q^3 + 42 * q^5 - 124 * q^9 - 660 * q^11 + 1288 * q^13 + 3792 * q^15 - 210 * q^17 + 3724 * q^19 - 24 * q^23 - 2480 * q^25 - 2072 * q^27 + 11064 * q^29 + 2800 * q^31 + 13818 * q^33 + 13238 * q^37 + 19480 * q^39 - 8232 * q^41 + 26864 * q^43 + 39228 * q^45 + 8064 * q^47 - 2292 * q^51 + 53958 * q^53 - 82656 * q^55 + 100348 * q^57 + 36036 * q^59 + 83986 * q^61 + 76308 * q^65 + 2660 * q^67 + 63420 * q^69 + 143136 * q^71 + 31318 * q^73 + 89656 * q^75 - 51136 * q^79 - 30370 * q^81 - 12432 * q^83 + 53964 * q^85 + 4200 * q^87 + 166278 * q^89 + 56938 * q^93 - 66432 * q^95 - 16520 * q^97 + 338208 * q^99

Introduction

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