LMFDB - Embedded newform 336.6.q.l.193.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 564x^{8} + 117814x^{6} + 11067780x^{4} + 427918225x^{2} + 3489248448 $ x^10 + 564x^8 + 117814x^6 + 11067780x^4 + 427918225x^2 + 3489248448
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.5
Root			$10.8764i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.6.q.l.289.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 + 7.79423i) q^{3} +(45.8569 + 79.4265i) q^{5} +(-108.828 + 70.4522i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 + 7.79423i) q^{3} +(45.8569 + 79.4265i) q^{5} +(-108.828 + 70.4522i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(-271.590 + 470.408i) q^{11} -28.2573 q^{13} -825.425 q^{15} +(-509.837 + 883.064i) q^{17} +(91.8396 + 159.071i) q^{19} +(-59.3955 - 1165.26i) q^{21} +(-2311.12 - 4002.98i) q^{23} +(-2643.22 + 4578.19i) q^{25} +729.000 q^{27} +3335.60 q^{29} +(-4139.23 + 7169.36i) q^{31} +(-2444.31 - 4233.68i) q^{33} +(-10586.3 - 5413.09i) q^{35} +(-958.872 - 1660.81i) q^{37} +(127.158 - 220.243i) q^{39} +18886.2 q^{41} +1285.40 q^{43} +(3714.41 - 6433.55i) q^{45} +(12651.9 + 21913.7i) q^{47} +(6879.98 - 15334.3i) q^{49} +(-4588.54 - 7947.58i) q^{51} +(2942.99 - 5097.40i) q^{53} -49817.2 q^{55} -1653.11 q^{57} +(18354.7 - 31791.4i) q^{59} +(18278.8 + 31659.8i) q^{61} +(9349.61 + 4780.74i) q^{63} +(-1295.79 - 2244.38i) q^{65} +(13987.2 - 24226.6i) q^{67} +41600.2 q^{69} -33470.8 q^{71} +(-15693.4 + 27181.8i) q^{73} +(-23789.0 - 41203.7i) q^{75} +(-3584.72 - 70327.7i) q^{77} +(-38693.2 - 67018.6i) q^{79} +(-3280.50 + 5681.99i) q^{81} -70029.7 q^{83} -93518.3 q^{85} +(-15010.2 + 25998.4i) q^{87} +(-71716.7 - 124217. i) q^{89} +(3075.17 - 1990.79i) q^{91} +(-37253.1 - 64524.2i) q^{93} +(-8422.97 + 14589.0i) q^{95} -50694.0 q^{97} +43997.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	$ 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) $ 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$		0			0
$5$	45.8569	+	79.4265i	0.820314	+	1.42083i	0.905449	+	0.424456i	$0.139535\pi$
$5$	45.8569	+	79.4265i	0.820314	+	1.42083i	−0.0851348	+	0.996369i	$0.527132\pi$
$6$		0			0
$7$	−108.828	+	70.4522i	−0.839450	+	0.543437i
$7$	−108.828	+	70.4522i	−0.839450	+	0.543437i
$8$		0			0
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$		0			0
$11$	−271.590	+	470.408i	−0.676757	+	1.17218i	0.299195	+	0.954192i	$0.403282\pi$
$11$	−271.590	+	470.408i	−0.676757	+	1.17218i	−0.975952	+	0.217986i	$0.930051\pi$
$12$		0			0
$13$	−28.2573			−0.0463737			−0.0231868	−	0.999731i	$-0.507381\pi$
$13$	−28.2573			−0.0463737			−0.0231868	+	0.999731i	$0.507381\pi$
$14$		0			0
$15$	−825.425			−0.947217
$16$		0			0
$17$	−509.837	+	883.064i	−0.427868	+	0.741088i	−0.996683	−	0.0813766i	$-0.974068\pi$
$17$	−509.837	+	883.064i	−0.427868	+	0.741088i	0.568816	+	0.822465i	$0.307402\pi$
$18$		0			0
$19$	91.8396	+	159.071i	0.0583641	+	0.101090i	0.893731	−	0.448603i	$-0.148078\pi$
$19$	91.8396	+	159.071i	0.0583641	+	0.101090i	−0.835367	+	0.549693i	$0.814745\pi$
$20$		0			0
$21$	−59.3955	−	1165.26i	−0.0293904	−	0.576602i
$22$		0			0
$23$	−2311.12	−	4002.98i	−0.910969	−	1.57784i	−0.812698	−	0.582685i	$-0.802002\pi$
$23$	−2311.12	−	4002.98i	−0.910969	−	1.57784i	−0.0982706	−	0.995160i	$-0.531331\pi$
$24$		0			0
$25$	−2643.22	+	4578.19i	−0.845830	+	1.46502i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	3335.60			0.736510			0.368255	−	0.929725i	$-0.379955\pi$
$29$	3335.60			0.736510			0.368255	+	0.929725i	$0.379955\pi$
$30$		0			0
$31$	−4139.23	+	7169.36i	−0.773598	+	1.33991i	0.161981	+	0.986794i	$0.448212\pi$
$31$	−4139.23	+	7169.36i	−0.773598	+	1.33991i	−0.935579	+	0.353117i	$0.885122\pi$
$32$		0			0
$33$	−2444.31	−	4233.68i	−0.390726	−	0.676757i
$34$		0			0
$35$	−10586.3	−	5413.09i	−1.46074	−	0.746922i
$36$		0			0
$37$	−958.872	−	1660.81i	−0.115148	−	0.199442i	0.802691	−	0.596395i	$-0.203401\pi$
$37$	−958.872	−	1660.81i	−0.115148	−	0.199442i	−0.917839	+	0.396953i	$0.870068\pi$
$38$		0			0
$39$	127.158	−	220.243i	0.0133869	−	0.0231868i
$40$		0			0
$41$	18886.2			1.75462			0.877312	−	0.479921i	$-0.159335\pi$
$41$	18886.2			1.75462			0.877312	+	0.479921i	$0.159335\pi$
$42$		0			0
$43$	1285.40			0.106015			0.0530073	−	0.998594i	$-0.483119\pi$
$43$	1285.40			0.106015			0.0530073	+	0.998594i	$0.483119\pi$
$44$		0			0
$45$	3714.41	−	6433.55i	0.273438	−	0.473608i
$46$		0			0
$47$	12651.9	+	21913.7i	0.835430	+	1.44701i	0.893680	+	0.448705i	$0.148114\pi$
$47$	12651.9	+	21913.7i	0.835430	+	1.44701i	−0.0582505	+	0.998302i	$0.518552\pi$
$48$		0			0
$49$	6879.98	−	15334.3i	0.409352	−	0.912377i
$50$		0			0
$51$	−4588.54	−	7947.58i	−0.247029	−	0.427868i
$52$		0			0
$53$	2942.99	−	5097.40i	0.143912	−	0.249264i	−0.785054	−	0.619427i	$-0.787365\pi$
$53$	2942.99	−	5097.40i	0.143912	−	0.249264i	0.928967	+	0.370163i	$0.120698\pi$
$54$		0			0
$55$	−49817.2			−2.22061
$56$		0			0
$57$	−1653.11			−0.0673931
$58$		0			0
$59$	18354.7	−	31791.4i	0.686465	−	1.18899i	−0.286509	−	0.958078i	$-0.592495\pi$
$59$	18354.7	−	31791.4i	0.686465	−	1.18899i	0.972974	−	0.230915i	$-0.0741718\pi$
$60$		0			0
$61$	18278.8	+	31659.8i	0.628959	+	1.08939i	0.987761	+	0.155976i	$0.0498522\pi$
$61$	18278.8	+	31659.8i	0.628959	+	1.08939i	−0.358802	+	0.933414i	$0.616815\pi$
$62$		0			0
$63$	9349.61	+	4780.74i	0.296785	+	0.151755i
$64$		0			0
$65$	−1295.79	−	2244.38i	−0.0380410	−	0.0658889i
$66$		0			0
$67$	13987.2	−	24226.6i	0.380666	−	0.659333i	−0.610491	−	0.792023i	$-0.709028\pi$
$67$	13987.2	−	24226.6i	0.380666	−	0.659333i	0.991158	+	0.132690i	$0.0423614\pi$
$68$		0			0
$69$	41600.2			1.05190
$70$		0			0
$71$	−33470.8			−0.787989			−0.393995	−	0.919113i	$-0.628907\pi$
$71$	−33470.8			−0.787989			−0.393995	+	0.919113i	$0.628907\pi$
$72$		0			0
$73$	−15693.4	+	27181.8i	−0.344675	+	0.596995i	−0.985295	−	0.170864i	$-0.945344\pi$
$73$	−15693.4	+	27181.8i	−0.344675	+	0.596995i	0.640620	+	0.767858i	$0.278678\pi$
$74$		0			0
$75$	−23789.0	−	41203.7i	−0.488340	−	0.845830i
$76$		0			0
$77$	−3584.72	−	70327.7i	−0.0689015	−	1.35176i
$78$		0			0
$79$	−38693.2	−	67018.6i	−0.697537	−	1.20817i	−0.969318	−	0.245810i	$-0.920946\pi$
$79$	−38693.2	−	67018.6i	−0.697537	−	1.20817i	0.271781	−	0.962359i	$-0.412387\pi$
$80$		0			0
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−70029.7			−1.11580			−0.557901	−	0.829908i	$-0.688393\pi$
$83$	−70029.7			−1.11580			−0.557901	+	0.829908i	$0.688393\pi$
$84$		0			0
$85$	−93518.3			−1.40394
$86$		0			0
$87$	−15010.2	+	25998.4i	−0.212612	+	0.368255i
$88$		0			0
$89$	−71716.7	−	124217.i	−0.959722	−	1.66229i	−0.723172	−	0.690668i	$-0.757317\pi$
$89$	−71716.7	−	124217.i	−0.959722	−	1.66229i	−0.236550	−	0.971619i	$-0.576017\pi$
$90$		0			0
$91$	3075.17	−	1990.79i	0.0389284	−	0.0252012i
$92$		0			0
$93$	−37253.1	−	64524.2i	−0.446637	−	0.773598i
$94$		0			0
$95$	−8422.97	+	14589.0i	−0.0957538	+	0.165850i
$96$		0			0
$97$	−50694.0			−0.547051			−0.273525	−	0.961865i	$-0.588190\pi$
$97$	−50694.0			−0.547051			−0.273525	+	0.961865i	$0.588190\pi$
$98$		0			0
$99$	43997.7			0.451171
$100$		0			0
$101$	23915.0	−	41422.0i	0.233275	−	0.404043i	−0.725495	−	0.688227i	$-0.758389\pi$
$101$	23915.0	−	41422.0i	0.233275	−	0.404043i	0.958770	+	0.284184i	$0.0917226\pi$
$102$		0			0
$103$	39537.9	+	68481.7i	0.367215	+	0.636036i	0.989129	−	0.147050i	$-0.0469779\pi$
$103$	39537.9	+	68481.7i	0.367215	+	0.636036i	−0.621914	+	0.783086i	$0.713645\pi$
$104$		0			0
$105$	89829.2	−	58153.0i	0.795141	−	0.514753i
$106$		0			0
$107$	−47288.4	−	81906.0i	−0.399296	−	0.691602i	0.594343	−	0.804212i	$-0.297412\pi$
$107$	−47288.4	−	81906.0i	−0.399296	−	0.691602i	−0.993639	+	0.112610i	$0.964079\pi$
$108$		0			0
$109$	−14426.0	+	24986.5i	−0.116300	+	0.201437i	−0.918299	−	0.395889i	$-0.870437\pi$
$109$	−14426.0	+	24986.5i	−0.116300	+	0.201437i	0.801999	+	0.597326i	$0.203770\pi$
$110$		0			0
$111$	17259.7			0.132961
$112$		0			0
$113$	−54891.9			−0.404401			−0.202200	−	0.979344i	$-0.564809\pi$
$113$	−54891.9			−0.404401			−0.202200	+	0.979344i	$0.564809\pi$
$114$		0			0
$115$	211962.	−	367129.i	1.49456	−	2.58866i
$116$		0			0
$117$	1144.42	+	1982.19i	0.00772895	+	0.0133869i
$118$		0			0
$119$	−6729.34	−	132021.i	−0.0435617	−	0.854626i
$120$		0			0
$121$	−66997.2	−	116043.i	−0.416000	−	0.720533i
$122$		0			0
$123$	−84987.7	+	147203.i	−0.506516	+	0.877312i
$124$		0			0
$125$	−198234.			−1.13476
$126$		0			0
$127$	146580.			0.806426			0.403213	−	0.915106i	$-0.367893\pi$
$127$	146580.			0.806426			0.403213	+	0.915106i	$0.367893\pi$
$128$		0			0
$129$	−5784.28	+	10018.7i	−0.0306038	+	0.0530073i
$130$		0			0
$131$	89310.5	+	154690.i	0.454699	+	0.787562i	0.998671	−	0.0515415i	$-0.0164134\pi$
$131$	89310.5	+	154690.i	0.454699	+	0.787562i	−0.543972	+	0.839104i	$0.683080\pi$
$132$		0			0
$133$	−21201.6	−	10841.0i	−0.103930	−	0.0531424i
$134$		0			0
$135$	33429.7	+	57902.0i	0.157869	+	0.273438i
$136$		0			0
$137$	−160490.	+	277977.i	−0.730545	+	1.26534i	0.226105	+	0.974103i	$0.427401\pi$
$137$	−160490.	+	277977.i	−0.730545	+	1.26534i	−0.956650	+	0.291239i	$0.905933\pi$
$138$		0			0
$139$	199000.			0.873609			0.436804	−	0.899557i	$-0.356110\pi$
$139$	199000.			0.873609			0.436804	+	0.899557i	$0.356110\pi$
$140$		0			0
$141$	−227734.			−0.964671
$142$		0			0
$143$	7674.40	−	13292.5i	0.0313837	−	0.0543582i
$144$		0			0
$145$	152960.	+	264935.i	0.604169	+	1.04645i
$146$		0			0
$147$	88559.3	+	122629.i	0.338019	+	0.468056i
$148$		0			0
$149$	−167594.	−	290282.i	−0.618434	−	1.07116i	−0.989772	−	0.142661i	$-0.954434\pi$
$149$	−167594.	−	290282.i	−0.618434	−	1.07116i	0.371338	−	0.928498i	$-0.378899\pi$
$150$		0			0
$151$	16420.0	−	28440.3i	0.0586045	−	0.101506i	−0.835235	−	0.549894i	$-0.814668\pi$
$151$	16420.0	−	28440.3i	0.0586045	−	0.101506i	0.893839	+	0.448388i	$0.148002\pi$
$152$		0			0
$153$	82593.6			0.285245
$154$		0			0
$155$	−759250.			−2.53837
$156$		0			0
$157$	64878.8	−	112373.i	0.210065	−	0.363843i	−0.741670	−	0.670765i	$-0.765966\pi$
$157$	64878.8	−	112373.i	0.210065	−	0.363843i	0.951735	+	0.306922i	$0.0992991\pi$
$158$		0			0
$159$	26486.9	+	45876.6i	0.0830879	+	0.143912i
$160$		0			0
$161$	533533.	+	272812.i	1.62217	+	0.829467i
$162$		0			0
$163$	−8020.18	−	13891.4i	−0.0236437	−	0.0409521i	0.853961	−	0.520336i	$-0.174193\pi$
$163$	−8020.18	−	13891.4i	−0.0236437	−	0.0409521i	−0.877605	+	0.479384i	$0.840860\pi$
$164$		0			0
$165$	224178.	−	388287.i	0.641036	−	1.11031i
$166$		0			0
$167$	411005.			1.14040			0.570199	−	0.821507i	$-0.306866\pi$
$167$	411005.			1.14040			0.570199	+	0.821507i	$0.306866\pi$
$168$		0			0
$169$	−370495.			−0.997849
$170$		0			0
$171$	7439.01	−	12884.7i	0.0194547	−	0.0336966i
$172$		0			0
$173$	−170401.	−	295143.i	−0.432869	−	0.749752i	0.564250	−	0.825604i	$-0.309166\pi$
$173$	−170401.	−	295143.i	−0.432869	−	0.749752i	−0.997119	+	0.0758523i	$0.975832\pi$
$174$		0			0
$175$	−34887.8	−	684455.i	−0.0861150	−	1.68947i
$176$		0			0
$177$	165193.	+	286122.i	0.396331	+	0.686465i
$178$		0			0
$179$	−336758.	+	583282.i	−0.785570	+	1.36065i	0.143087	+	0.989710i	$0.454297\pi$
$179$	−336758.	+	583282.i	−0.785570	+	1.36065i	−0.928658	+	0.370938i	$0.879036\pi$
$180$		0			0
$181$	−395635.			−0.897631			−0.448815	−	0.893624i	$-0.648154\pi$
$181$	−395635.			−0.897631			−0.448815	+	0.893624i	$0.648154\pi$
$182$		0			0
$183$	−329018.			−0.726260
$184$		0			0
$185$	87941.9	−	152320.i	0.188915	−	0.327210i
$186$		0			0
$187$	−276934.	−	479664.i	−0.579125	−	1.00307i
$188$		0			0
$189$	−79335.5	+	51359.7i	−0.161552	+	0.104585i
$190$		0			0
$191$	150062.	+	259915.i	0.297637	+	0.515522i	0.975595	−	0.219578i	$-0.0704682\pi$
$191$	150062.	+	259915.i	0.297637	+	0.515522i	−0.677958	+	0.735101i	$0.737135\pi$
$192$		0			0
$193$	164830.	−	285494.i	0.318524	−	0.551700i	−0.661656	−	0.749807i	$-0.730146\pi$
$193$	164830.	−	285494.i	0.318524	−	0.551700i	0.980180	+	0.198107i	$0.0634795\pi$
$194$		0			0
$195$	23324.2			0.0439259
$196$		0			0
$197$	−436497.			−0.801338			−0.400669	−	0.916223i	$-0.631222\pi$
$197$	−436497.			−0.801338			−0.400669	+	0.916223i	$0.631222\pi$
$198$		0			0
$199$	217471.	−	376672.i	0.389287	−	0.674264i	−0.603067	−	0.797691i	$-0.706055\pi$
$199$	217471.	−	376672.i	0.389287	−	0.674264i	0.992354	+	0.123426i	$0.0393882\pi$
$200$		0			0
$201$	125885.	+	218039.i	0.219778	+	0.380666i
$202$		0			0
$203$	−363005.	+	235000.i	−0.618263	+	0.400247i
$204$		0			0
$205$	866061.	+	1.50006e6i	1.43934	+	2.49301i
$206$		0			0
$207$	−187201.	+	324242.i	−0.303656	+	0.525948i
$208$		0			0
$209$	−99771.1			−0.157993
$210$		0			0
$211$	416977.			0.644771			0.322386	−	0.946608i	$-0.395515\pi$
$211$	416977.			0.644771			0.322386	+	0.946608i	$0.395515\pi$
$212$		0			0
$213$	150619.	−	260879.i	0.227473	−	0.393995i
$214$		0			0
$215$	58944.3	+	102095.i	0.0869653	+	0.150628i
$216$		0			0
$217$	−54633.7	−	1.07184e6i	−0.0787610	−	1.54519i
$218$		0			0
$219$	−141241.	−	244636.i	−0.198998	−	0.344675i
$220$		0			0
$221$	14406.6	−	24953.0i	0.0198418	−	0.0343670i
$222$		0			0
$223$	661253.			0.890442			0.445221	−	0.895421i	$-0.353125\pi$
$223$	661253.			0.890442			0.445221	+	0.895421i	$0.353125\pi$
$224$		0			0
$225$	428201.			0.563886
$226$		0			0
$227$	−492697.	+	853376.i	−0.634622	+	1.09920i	0.351973	+	0.936010i	$0.385511\pi$
$227$	−492697.	+	853376.i	−0.634622	+	1.09920i	−0.986595	+	0.163188i	$0.947822\pi$
$228$		0			0
$229$	456147.	+	790070.i	0.574799	+	0.995581i	0.996063	+	0.0886435i	$0.0282532\pi$
$229$	456147.	+	790070.i	0.574799	+	0.995581i	−0.421264	+	0.906938i	$0.638413\pi$
$230$		0			0
$231$	564281.	+	288534.i	0.695770	+	0.355769i
$232$		0			0
$233$	168915.	+	292569.i	0.203834	+	0.353052i	0.949761	−	0.312977i	$-0.101326\pi$
$233$	168915.	+	292569.i	0.203834	+	0.353052i	−0.745926	+	0.666028i	$0.767993\pi$
$234$		0			0
$235$	−1.16035e6	+	2.00979e6i	−1.37063	+	2.37400i
$236$		0			0
$237$	696478.			0.805446
$238$		0			0
$239$	−483102.			−0.547071			−0.273536	−	0.961862i	$-0.588193\pi$
$239$	−483102.			−0.547071			−0.273536	+	0.961862i	$0.588193\pi$
$240$		0			0
$241$	−640764.	+	1.10984e6i	−0.710650	+	1.23088i	0.253964	+	0.967214i	$0.418266\pi$
$241$	−640764.	+	1.10984e6i	−0.710650	+	1.23088i	−0.964614	+	0.263668i	$0.915068\pi$
$242$		0			0
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	1.53345e6	−	156732.i	1.63212	−	0.166818i
$246$		0			0
$247$	−2595.14	−	4494.91i	−0.00270656	−	0.00468790i
$248$		0			0
$249$	315134.	−	545827.i	0.322104	−	0.557901i
$250$		0			0
$251$	215401.			0.215806			0.107903	−	0.994161i	$-0.465586\pi$
$251$	215401.			0.215806			0.107903	+	0.994161i	$0.465586\pi$
$252$		0			0
$253$	2.51072e6			2.46602
$254$		0			0
$255$	420832.	−	728903.i	0.405283	−	0.701971i
$256$		0			0
$257$	−284938.	−	493527.i	−0.269102	−	0.466099i	0.699528	−	0.714605i	$-0.253394\pi$
$257$	−284938.	−	493527.i	−0.269102	−	0.466099i	−0.968630	+	0.248507i	$0.920060\pi$
$258$		0			0
$259$	221360.	+	113188.i	0.205045	+	0.104846i
$260$		0			0
$261$	−135092.	−	233986.i	−0.122752	−	0.212612i
$262$		0			0
$263$	1.05525e6	−	1.82774e6i	0.940731	−	1.62939i	0.176649	−	0.984274i	$-0.443474\pi$
$263$	1.05525e6	−	1.82774e6i	0.940731	−	1.62939i	0.764081	−	0.645120i	$-0.223193\pi$
$264$		0			0
$265$	539825.			0.472214
$266$		0			0
$267$	1.29090e6			1.10819
$268$		0			0
$269$	−320637.	+	555360.i	−0.270168	+	0.467944i	−0.968905	−	0.247435i	$-0.920412\pi$
$269$	−320637.	+	555360.i	−0.270168	+	0.467944i	0.698737	+	0.715379i	$0.253746\pi$
$270$		0			0
$271$	1.02062e6	+	1.76777e6i	0.844191	+	1.46218i	0.886322	+	0.463070i	$0.153252\pi$
$271$	1.02062e6	+	1.76777e6i	0.844191	+	1.46218i	−0.0421304	+	0.999112i	$0.513414\pi$
$272$		0			0
$273$	1678.35	+	32927.1i	0.00136294	+	0.0267391i
$274$		0			0
$275$	−1.43575e6	−	2.48678e6i	−1.14484	−	1.98293i
$276$		0			0
$277$	−792401.	+	1.37248e6i	−0.620505	+	1.07475i	0.368886	+	0.929475i	$0.379739\pi$
$277$	−792401.	+	1.37248e6i	−0.620505	+	1.07475i	−0.989392	+	0.145272i	$0.953594\pi$
$278$		0			0
$279$	670555.			0.515732
$280$		0			0
$281$	−37483.9			−0.0283191			−0.0141595	−	0.999900i	$-0.504507\pi$
$281$	−37483.9			−0.0283191			−0.0141595	+	0.999900i	$0.504507\pi$
$282$		0			0
$283$	−565224.	+	978997.i	−0.419522	+	0.726633i	−0.995891	−	0.0905559i	$-0.971136\pi$
$283$	−565224.	+	978997.i	−0.419522	+	0.726633i	0.576369	+	0.817189i	$0.304469\pi$
$284$		0			0
$285$	−75806.7	−	131301.i	−0.0552835	−	0.0957538i
$286$		0			0
$287$	−2.05534e6	+	1.33057e6i	−1.47292	+	0.953528i
$288$		0			0
$289$	190060.	+	329194.i	0.133859	+	0.231850i
$290$		0			0
$291$	228123.	−	395121.i	0.157920	−	0.273525i
$292$		0			0
$293$	−2.70066e6			−1.83781			−0.918906	−	0.394477i	$-0.870926\pi$
$293$	−2.70066e6			−1.83781			−0.918906	+	0.394477i	$0.870926\pi$
$294$		0			0
$295$	3.36677e6			2.25247
$296$		0			0
$297$	−197989.	+	342928.i	−0.130242	+	0.225586i
$298$		0			0
$299$	65306.0	+	113113.i	0.0422450	+	0.0731705i
$300$		0			0
$301$	−139887.	+	90559.0i	−0.0889940	+	0.0576123i
$302$		0			0
$303$	215235.	+	372798.i	0.134681	+	0.233275i
$304$		0			0
$305$	−1.67642e6	+	2.90364e6i	−1.03189	+	1.78728i
$306$		0			0
$307$	−568937.			−0.344523			−0.172262	−	0.985051i	$-0.555107\pi$
$307$	−568937.			−0.344523			−0.172262	+	0.985051i	$0.555107\pi$
$308$		0			0
$309$	−711683.			−0.424024
$310$		0			0
$311$	−392425.	+	679701.i	−0.230068	+	0.398489i	−0.957828	−	0.287343i	$-0.907228\pi$
$311$	−392425.	+	679701.i	−0.230068	+	0.398489i	0.727760	+	0.685832i	$0.240562\pi$
$312$		0			0
$313$	−1.71402e6	−	2.96877e6i	−0.988905	−	1.71283i	−0.623099	−	0.782143i	$-0.714126\pi$
$313$	−1.71402e6	−	2.96877e6i	−0.988905	−	1.71283i	−0.365807	−	0.930691i	$-0.619207\pi$
$314$		0			0
$315$	49026.5	+	961838.i	0.0278391	+	0.546167i
$316$		0			0
$317$	1.40936e6	+	2.44108e6i	0.787723	+	1.36438i	0.927359	+	0.374173i	$0.122074\pi$
$317$	1.40936e6	+	2.44108e6i	0.787723	+	1.36438i	−0.139636	+	0.990203i	$0.544593\pi$
$318$		0			0
$319$	−905916.	+	1.56909e6i	−0.498438	+	0.863320i
$320$		0			0
$321$	851192.			0.461068
$322$		0			0
$323$	−187293.			−0.0998885
$324$		0			0
$325$	74690.1	−	129367.i	0.0392242	−	0.0679384i
$326$		0			0
$327$	−129834.	−	224878.i	−0.0671456	−	0.116300i
$328$		0			0
$329$	−2.92074e6	−	1.49346e6i	−1.48766	−	0.760686i
$330$		0			0
$331$	−1.10243e6	−	1.90947e6i	−0.553072	−	0.957949i	−0.998051	−	0.0624078i	$-0.980122\pi$
$331$	−1.10243e6	−	1.90947e6i	−0.553072	−	0.957949i	0.444979	−	0.895541i	$-0.353211\pi$
$332$		0			0
$333$	−77668.6	+	134526.i	−0.0383827	+	0.0664807i
$334$		0			0
$335$	2.56564e6			1.24906
$336$		0			0
$337$	998199.			0.478787			0.239393	−	0.970923i	$-0.423051\pi$
$337$	998199.			0.478787			0.239393	+	0.970923i	$0.423051\pi$
$338$		0			0
$339$	247013.	−	427840.i	0.116740	−	0.202200i
$340$		0			0
$341$	−2.24835e6	−	3.89426e6i	−1.04708	−	1.81359i
$342$		0			0
$343$	331603.	+	2.15351e6i	0.152189	+	0.988351i
$344$		0			0
$345$	1.90766e6	+	3.30416e6i	0.862885	+	1.49456i
$346$		0			0
$347$	−1.48383e6	+	2.57007e6i	−0.661548	+	1.14583i	0.318661	+	0.947869i	$0.396767\pi$
$347$	−1.48383e6	+	2.57007e6i	−0.661548	+	1.14583i	−0.980209	+	0.197966i	$0.936567\pi$
$348$		0			0
$349$	−2.12310e6			−0.933055			−0.466528	−	0.884507i	$-0.654495\pi$
$349$	−2.12310e6			−0.933055			−0.466528	+	0.884507i	$0.654495\pi$
$350$		0			0
$351$	−20599.5			−0.00892462
$352$		0			0
$353$	−731166.	+	1.26642e6i	−0.312305	+	0.540929i	−0.978861	−	0.204527i	$-0.934435\pi$
$353$	−731166.	+	1.26642e6i	−0.312305	+	0.540929i	0.666556	+	0.745455i	$0.267768\pi$
$354$		0			0
$355$	−1.53487e6	−	2.65847e6i	−0.646398	−	1.11959i
$356$		0			0
$357$	1.05928e6	+	541645.i	0.439888	+	0.224928i
$358$		0			0
$359$	827058.	+	1.43251e6i	0.338688	+	0.586625i	0.984186	−	0.177137i	$-0.0566835\pi$
$359$	827058.	+	1.43251e6i	0.338688	+	0.586625i	−0.645498	+	0.763762i	$0.723350\pi$
$360$		0			0
$361$	1.22118e6	−	2.11515e6i	0.493187	−	0.854225i
$362$		0			0
$363$	1.20595e6			0.480356
$364$		0			0
$365$	−2.87860e6			−1.13097
$366$		0			0
$367$	−83460.8	+	144558.i	−0.0323458	+	0.0560245i	−0.881745	−	0.471726i	$-0.843631\pi$
$367$	−83460.8	+	144558.i	−0.0323458	+	0.0560245i	0.849399	+	0.527751i	$0.176964\pi$
$368$		0			0
$369$	−764889.	−	1.32483e6i	−0.292437	−	0.506516i
$370$		0			0
$371$	38844.4	+	762079.i	0.0146519	+	0.287452i
$372$		0			0
$373$	−1.06059e6	−	1.83699e6i	−0.394707	−	0.683652i	0.598357	−	0.801230i	$-0.295820\pi$
$373$	−1.06059e6	−	1.83699e6i	−0.394707	−	0.683652i	−0.993064	+	0.117578i	$0.962487\pi$
$374$		0			0
$375$	892051.	−	1.54508e6i	0.327576	−	0.567378i
$376$		0			0
$377$	−94254.8			−0.0341547
$378$		0			0
$379$	2.85242e6			1.02004			0.510018	−	0.860164i	$-0.329639\pi$
$379$	2.85242e6			1.02004			0.510018	+	0.860164i	$0.329639\pi$
$380$		0			0
$381$	−659609.	+	1.14248e6i	−0.232795	+	0.403213i
$382$		0			0
$383$	−1.46122e6	−	2.53091e6i	−0.509002	−	0.881617i	−0.999946	−	0.0104256i	$-0.996681\pi$
$383$	−1.46122e6	−	2.53091e6i	−0.509002	−	0.881617i	0.490944	−	0.871191i	$-0.336652\pi$
$384$		0			0
$385$	5.42150e6	−	3.50973e6i	1.86409	−	1.20676i
$386$		0			0
$387$	−52058.5	−	90168.1i	−0.0176691	−	0.0306038i
$388$		0			0
$389$	1.61135e6	−	2.79095e6i	0.539904	−	0.935142i	−0.459004	−	0.888434i	$-0.651794\pi$
$389$	1.61135e6	−	2.79095e6i	0.539904	−	0.935142i	0.998909	−	0.0467079i	$-0.0148730\pi$
$390$		0			0
$391$	4.71319e6			1.55910
$392$		0			0
$393$	−1.60759e6			−0.525041
$394$		0			0
$395$	3.54871e6	−	6.14654e6i	1.14440	−	1.98216i
$396$		0			0
$397$	323031.	+	559505.i	0.102865	+	0.178167i	0.912864	−	0.408264i	$-0.133866\pi$
$397$	323031.	+	559505.i	0.102865	+	0.178167i	−0.809999	+	0.586431i	$0.800532\pi$
$398$		0			0
$399$	179905.	−	116465.i	0.0565731	−	0.0366239i
$400$		0			0
$401$	2.22390e6	+	3.85190e6i	0.690643	+	1.19623i	0.971627	+	0.236517i	$0.0760057\pi$
$401$	2.22390e6	+	3.85190e6i	0.690643	+	1.19623i	−0.280984	+	0.959712i	$0.590661\pi$
$402$		0			0
$403$	116963.	−	202586.i	0.0358746	−	0.0621366i
$404$		0			0
$405$	−601735.			−0.182292
$406$		0			0
$407$	1.04168e6			0.311709
$408$		0			0
$409$	−68279.3	+	118263.i	−0.0201828	+	0.0349576i	−0.875940	−	0.482419i	$-0.839758\pi$
$409$	−68279.3	+	118263.i	−0.0201828	+	0.0349576i	0.855758	+	0.517377i	$0.173091\pi$
$410$		0			0
$411$	−1.44441e6	−	2.50180e6i	−0.421781	−	0.730545i
$412$		0			0
$413$	242264.	+	4.75291e6i	0.0698898	+	1.37115i
$414$		0			0
$415$	−3.21135e6	−	5.56222e6i	−0.915308	−	1.58536i
$416$		0			0
$417$	−895502.	+	1.55105e6i	−0.252189	+	0.436804i
$418$		0			0
$419$	−5.72474e6			−1.59302			−0.796509	−	0.604626i	$-0.793323\pi$
$419$	−5.72474e6			−1.59302			−0.796509	+	0.604626i	$0.793323\pi$
$420$		0			0
$421$	6.80110e6			1.87014			0.935070	−	0.354463i	$-0.115336\pi$
$421$	6.80110e6			1.87014			0.935070	+	0.354463i	$0.115336\pi$
$422$		0			0
$423$	1.02480e6	−	1.77501e6i	0.278477	−	0.482336i
$424$		0			0
$425$	−2.69522e6	−	4.66826e6i	−0.723806	−	1.25367i
$426$		0			0
$427$	−4.21974e6	−	2.15768e6i	−1.11999	−	0.572688i
$428$		0			0
$429$	69069.6	+	119632.i	0.0181194	+	0.0313837i
$430$		0			0
$431$	−2.85483e6	+	4.94471e6i	−0.740265	+	1.28218i	0.212110	+	0.977246i	$0.431967\pi$
$431$	−2.85483e6	+	4.94471e6i	−0.740265	+	1.28218i	−0.952375	+	0.304930i	$0.901367\pi$
$432$		0			0
$433$	−3.13874e6			−0.804519			−0.402259	−	0.915526i	$-0.631775\pi$
$433$	−3.13874e6			−0.804519			−0.402259	+	0.915526i	$0.631775\pi$
$434$		0			0
$435$	−2.75328e6			−0.697634
$436$		0			0
$437$	424505.	−	735265.i	0.106336	−	0.184179i
$438$		0			0
$439$	−206778.	−	358150.i	−0.0512086	−	0.0886959i	0.839285	−	0.543692i	$-0.182974\pi$
$439$	−206778.	−	358150.i	−0.0512086	−	0.0886959i	−0.890493	+	0.454996i	$0.849641\pi$
$440$		0			0
$441$	−1.35431e6	+	138423.i	−0.331606	+	0.0338931i
$442$		0			0
$443$	−1.22503e6	−	2.12181e6i	−0.296577	−	0.513687i	0.678773	−	0.734348i	$-0.262512\pi$
$443$	−1.22503e6	−	2.12181e6i	−0.296577	−	0.513687i	−0.975351	+	0.220661i	$0.929178\pi$
$444$		0			0
$445$	6.57742e6	−	1.13924e7i	1.57455	−	2.72719i
$446$		0			0
$447$	3.01670e6			0.714106
$448$		0			0
$449$	−902207.			−0.211198			−0.105599	−	0.994409i	$-0.533676\pi$
$449$	−902207.			−0.211198			−0.105599	+	0.994409i	$0.533676\pi$
$450$		0			0
$451$	−5.12930e6	+	8.88421e6i	−1.18745	+	2.05673i
$452$		0			0
$453$	147780.	+	255963.i	0.0338353	+	0.0586045i
$454$		0			0
$455$	299139.	+	152959.i	0.0677400	+	0.0346375i
$456$		0			0
$457$	−2.63007e6	−	4.55541e6i	−0.589083	−	1.02032i	−0.994353	−	0.106124i	$-0.966156\pi$
$457$	−2.63007e6	−	4.55541e6i	−0.589083	−	1.02032i	0.405270	−	0.914197i	$-0.367177\pi$
$458$		0			0
$459$	−371671.	+	643754.i	−0.0823431	+	0.142623i
$460$		0			0
$461$	−2.79974e6			−0.613573			−0.306786	−	0.951778i	$-0.599254\pi$
$461$	−2.79974e6			−0.613573			−0.306786	+	0.951778i	$0.599254\pi$
$462$		0			0
$463$	1.54186e6			0.334266			0.167133	−	0.985934i	$-0.446549\pi$
$463$	1.54186e6			0.334266			0.167133	+	0.985934i	$0.446549\pi$
$464$		0			0
$465$	3.41662e6	−	5.91777e6i	0.732765	−	1.26919i
$466$		0			0
$467$	−3.65218e6	−	6.32577e6i	−0.774926	−	1.34221i	−0.934836	−	0.355080i	$-0.884454\pi$
$467$	−3.65218e6	−	6.32577e6i	−0.774926	−	1.34221i	0.159910	−	0.987132i	$-0.448880\pi$
$468$		0			0
$469$	184617.	+	3.62195e6i	0.0387561	+	0.760345i
$470$		0			0
$471$	583909.	+	1.01136e6i	0.121281	+	0.210065i
$472$		0			0
$473$	−349101.	+	604661.i	−0.0717462	+	0.124268i
$474$		0			0
$475$	−971008.			−0.197464
$476$		0			0
$477$	−476764.			−0.0959416
$478$		0			0
$479$	3.69966e6	−	6.40801e6i	0.736756	−	1.27610i	−0.217193	−	0.976129i	$-0.569690\pi$
$479$	3.69966e6	−	6.40801e6i	0.736756	−	1.27610i	0.953949	−	0.299970i	$-0.0969766\pi$
$480$		0			0
$481$	27095.1	+	46930.1i	0.00533983	+	0.00924887i
$482$		0			0
$483$	−4.52726e6	+	2.93083e6i	−0.883014	+	0.571640i
$484$		0			0
$485$	−2.32467e6	−	4.02645e6i	−0.448753	−	0.777263i
$486$		0			0
$487$	−2.25178e6	+	3.90020e6i	−0.430234	+	0.745187i	−0.996893	−	0.0787655i	$-0.974902\pi$
$487$	−2.25178e6	+	3.90020e6i	−0.430234	+	0.745187i	0.566660	+	0.823952i	$0.308236\pi$
$488$		0			0
$489$	144363.			0.0273014
$490$		0			0
$491$	−8.10273e6			−1.51680			−0.758399	−	0.651791i	$-0.774018\pi$
$491$	−8.10273e6			−1.51680			−0.758399	+	0.651791i	$0.774018\pi$
$492$		0			0
$493$	−1.70061e6	+	2.94554e6i	−0.315128	+	0.545819i
$494$		0			0
$495$	2.01760e6	+	3.49458e6i	0.370102	+	0.641036i
$496$		0			0
$497$	3.64255e6	−	2.35809e6i	0.661477	−	0.428223i
$498$		0			0
$499$	635251.	+	1.10029e6i	0.114207	+	0.197813i	0.917463	−	0.397822i	$-0.130234\pi$
$499$	635251.	+	1.10029e6i	0.114207	+	0.197813i	−0.803255	+	0.595635i	$0.796901\pi$
$500$		0			0
$501$	−1.84952e6	+	3.20347e6i	−0.329205	+	0.570199i
$502$		0			0
$503$	−2.90365e6			−0.511710			−0.255855	−	0.966715i	$-0.582357\pi$
$503$	−2.90365e6			−0.511710			−0.255855	+	0.966715i	$0.582357\pi$
$504$		0			0
$505$	4.38668e6			0.765433
$506$		0			0
$507$	1.66723e6	−	2.88772e6i	0.288054	−	0.498925i
$508$		0			0
$509$	4.46536e6	+	7.73423e6i	0.763945	+	1.32319i	0.940803	+	0.338955i	$0.110073\pi$
$509$	4.46536e6	+	7.73423e6i	0.763945	+	1.32319i	−0.176858	+	0.984236i	$0.556593\pi$
$510$		0			0
$511$	−207137.	−	4.06377e6i	−0.0350918	−	0.688456i
$512$		0			0
$513$	66951.1	+	115963.i	0.0112322	+	0.0194547i
$514$		0			0
$515$	−3.62618e6	+	6.28072e6i	−0.602464	+	1.04350i
$516$		0			0
$517$	−1.37445e7			−2.26153
$518$		0			0
$519$	3.06722e6			0.499835
$520$		0			0
$521$	−262540.	+	454732.i	−0.0423741	+	0.0733942i	−0.886435	−	0.462854i	$-0.846825\pi$
$521$	−262540.	+	454732.i	−0.0423741	+	0.0733942i	0.844060	+	0.536248i	$0.180159\pi$
$522$		0			0
$523$	1.36105e6	+	2.35741e6i	0.217581	+	0.376861i	0.954068	−	0.299590i	$-0.0968500\pi$
$523$	1.36105e6	+	2.35741e6i	0.217581	+	0.376861i	−0.736487	+	0.676452i	$0.763517\pi$
$524$		0			0
$525$	5.49179e6	+	2.80812e6i	0.869592	+	0.444649i
$526$		0			0
$527$	−4.22067e6	−	7.31041e6i	−0.661995	−	1.14661i
$528$		0			0
$529$	−7.46441e6	+	1.29287e7i	−1.15973	+	2.00871i
$530$		0			0
$531$	−2.97347e6			−0.457643
$532$		0			0
$533$	−533671.			−0.0813683
$534$		0			0
$535$	4.33701e6	−	7.51191e6i	0.655097	−	1.13466i
$536$		0			0
$537$	−3.03082e6	−	5.24953e6i	−0.453549	−	0.785570i
$538$		0			0
$539$	5.34485e6	+	7.40105e6i	0.792436	+	1.09729i
$540$		0			0
$541$	−922098.	−	1.59712e6i	−0.135451	−	0.234609i	0.790318	−	0.612696i	$-0.209915\pi$
$541$	−922098.	−	1.59712e6i	−0.135451	−	0.234609i	−0.925770	+	0.378088i	$0.876582\pi$
$542$		0			0
$543$	1.78036e6	−	3.08367e6i	0.259124	−	0.448815i
$544$		0			0
$545$	−2.64612e6			−0.381609
$546$		0			0
$547$	−7.41792e6			−1.06002			−0.530010	−	0.847992i	$-0.677812\pi$
$547$	−7.41792e6			−1.06002			−0.530010	+	0.847992i	$0.677812\pi$
$548$		0			0
$549$	1.48058e6	−	2.56444e6i	0.209653	−	0.363130i
$550$		0			0
$551$	306340.	+	530596.i	0.0429857	+	0.0744535i
$552$		0			0
$553$	8.93251e6	+	4.56747e6i	1.24211	+	0.635130i
$554$		0			0
$555$	791477.	+	1.37088e6i	0.109070	+	0.188915i
$556$		0			0
$557$	3.81148e6	−	6.60168e6i	0.520542	−	0.901606i	−0.479172	−	0.877721i	$-0.659063\pi$
$557$	3.81148e6	−	6.60168e6i	0.520542	−	0.901606i	0.999715	−	0.0238850i	$-0.00760354\pi$
$558$		0			0
$559$	−36321.8			−0.00491629
$560$		0			0
$561$	4.98481e6			0.668716
$562$		0			0
$563$	−1.19628e6	+	2.07201e6i	−0.159060	+	0.275500i	−0.934530	−	0.355885i	$-0.884180\pi$
$563$	−1.19628e6	+	2.07201e6i	−0.159060	+	0.275500i	0.775470	+	0.631384i	$0.217513\pi$
$564$		0			0
$565$	−2.51717e6	−	4.35987e6i	−0.331735	−	0.574583i
$566$		0			0
$567$	−43299.3	−	849477.i	−0.00565618	−	0.110967i
$568$		0			0
$569$	2.40156e6	+	4.15963e6i	0.310966	+	0.538609i	0.978572	−	0.205906i	$-0.0660141\pi$
$569$	2.40156e6	+	4.15963e6i	0.310966	+	0.538609i	−0.667606	+	0.744515i	$0.732681\pi$
$570$		0			0
$571$	−2.10893e6	+	3.65278e6i	−0.270690	+	0.468849i	−0.969039	−	0.246909i	$-0.920585\pi$
$571$	−2.10893e6	+	3.65278e6i	−0.270690	+	0.468849i	0.698349	+	0.715758i	$0.253919\pi$
$572$		0			0
$573$	−2.70111e6			−0.343681
$574$		0			0
$575$	2.44352e7			3.08210
$576$		0			0
$577$	−4.24750e6	+	7.35688e6i	−0.531121	+	0.919929i	0.468219	+	0.883612i	$0.344896\pi$
$577$	−4.24750e6	+	7.35688e6i	−0.531121	+	0.919929i	−0.999340	+	0.0363167i	$0.988437\pi$
$578$		0			0
$579$	1.48347e6	+	2.56944e6i	0.183900	+	0.318524i
$580$		0			0
$581$	7.62118e6	−	4.93375e6i	0.936659	−	0.606368i
$582$		0			0
$583$	1.59857e6	+	2.76881e6i	0.194788	+	0.337382i
$584$		0			0
$585$	−104959.	+	181794.i	−0.0126803	+	0.0219630i
$586$		0			0
$587$	1.35441e6			0.162238			0.0811192	−	0.996704i	$-0.474151\pi$
$587$	1.35441e6			0.162238			0.0811192	+	0.996704i	$0.474151\pi$
$588$		0			0
$589$	−1.52058e6			−0.180602
$590$		0			0
$591$	1.96424e6	−	3.40216e6i	0.231326	−	0.400669i
$592$		0			0
$593$	−2.20201e6	−	3.81399e6i	−0.257147	−	0.445392i	0.708329	−	0.705882i	$-0.249449\pi$
$593$	−2.20201e6	−	3.81399e6i	−0.257147	−	0.445392i	−0.965476	+	0.260490i	$0.916116\pi$
$594$		0			0
$595$	1.01774e7	−	6.58857e6i	1.17854	−	0.762955i
$596$		0			0
$597$	1.95724e6	+	3.39004e6i	0.224755	+	0.389287i
$598$		0			0
$599$	−2.40934e6	+	4.17309e6i	−0.274366	+	0.475216i	−0.969975	−	0.243205i	$-0.921801\pi$
$599$	−2.40934e6	+	4.17309e6i	−0.274366	+	0.475216i	0.695609	+	0.718421i	$0.255135\pi$
$600$		0			0
$601$	8.64290e6			0.976053			0.488027	−	0.872829i	$-0.337717\pi$
$601$	8.64290e6			0.976053			0.488027	+	0.872829i	$0.337717\pi$
$602$		0			0
$603$	−2.26593e6			−0.253777
$604$		0			0
$605$	6.14458e6	−	1.06427e7i	0.682501	−	1.18213i
$606$		0			0
$607$	125066.	+	216621.i	0.0137775	+	0.0238633i	0.872832	−	0.488021i	$-0.162281\pi$
$607$	125066.	+	216621.i	0.0137775	+	0.0238633i	−0.859054	+	0.511884i	$0.828948\pi$
$608$		0			0
$609$	−198119.	−	3.88685e6i	−0.0216463	−	0.424673i
$610$		0			0
$611$	−357507.	−	619220.i	−0.0387419	−	0.0671030i
$612$		0			0
$613$	−7.05759e6	+	1.22241e7i	−0.758587	+	1.31391i	0.184985	+	0.982741i	$0.440776\pi$
$613$	−7.05759e6	+	1.22241e7i	−0.758587	+	1.31391i	−0.943571	+	0.331169i	$0.892557\pi$
$614$		0			0
$615$	−1.55891e7			−1.66201
$616$		0			0
$617$	−1.14663e7			−1.21258			−0.606291	−	0.795243i	$-0.707343\pi$
$617$	−1.14663e7			−1.21258			−0.606291	+	0.795243i	$0.707343\pi$
$618$		0			0
$619$	−322987.	+	559430.i	−0.0338812	+	0.0586839i	−0.882469	−	0.470371i	$-0.844120\pi$
$619$	−322987.	+	559430.i	−0.0338812	+	0.0586839i	0.848588	+	0.529055i	$0.177453\pi$
$620$		0			0
$621$	−1.68481e6	−	2.91817e6i	−0.175316	−	0.303656i
$622$		0			0
$623$	1.65561e7	+	8.46566e6i	1.70899	+	0.873858i
$624$		0			0
$625$	−830333.	−	1.43818e6i	−0.0850260	−	0.147269i
$626$		0			0
$627$	448970.	−	777638.i	0.0456088	−	0.0789967i
$628$		0			0
$629$	1.95547e6			0.197072
$630$		0			0
$631$	1.83763e7			1.83732			0.918658	−	0.395053i	$-0.129274\pi$
$631$	1.83763e7			1.83732			0.918658	+	0.395053i	$0.129274\pi$
$632$		0			0
$633$	−1.87639e6	+	3.25001e6i	−0.186129	+	0.322386i
$634$		0			0
$635$	6.72170e6	+	1.16423e7i	0.661523	+	1.14579i
$636$		0			0
$637$	−194409.	+	433306.i	−0.0189832	+	0.0423103i
$638$		0			0
$639$	1.35557e6	+	2.34791e6i	0.131332	+	0.227473i
$640$		0			0
$641$	−5.57166e6	+	9.65039e6i	−0.535599	+	0.927684i	0.463536	+	0.886078i	$0.346581\pi$
$641$	−5.57166e6	+	9.65039e6i	−0.535599	+	0.927684i	−0.999134	+	0.0416055i	$0.986753\pi$
$642$		0			0
$643$	323686.			0.0308743			0.0154371	−	0.999881i	$-0.495086\pi$
$643$	323686.			0.0308743			0.0154371	+	0.999881i	$0.495086\pi$
$644$		0			0
$645$	−1.06100e6			−0.100419
$646$		0			0
$647$	4.31428e6	−	7.47256e6i	0.405180	−	0.701792i	−0.589162	−	0.808015i	$-0.700542\pi$
$647$	4.31428e6	−	7.47256e6i	0.405180	−	0.701792i	0.994342	+	0.106222i	$0.0338755\pi$
$648$		0			0
$649$	9.96995e6	+	1.72685e7i	0.929140	+	1.60932i
$650$		0			0
$651$	8.60004e6	+	4.39747e6i	0.795331	+	0.406678i
$652$		0			0
$653$	−4.60795e6	−	7.98120e6i	−0.422887	−	0.732462i	0.573333	−	0.819322i	$-0.305650\pi$
$653$	−4.60795e6	−	7.98120e6i	−0.422887	−	0.732462i	−0.996221	+	0.0868600i	$0.972317\pi$
$654$		0			0
$655$	−8.19101e6	+	1.41872e7i	−0.745992	+	1.29210i
$656$		0			0
$657$	2.54233e6			0.229783
$658$		0			0
$659$	8.19016e6			0.734647			0.367324	−	0.930093i	$-0.380274\pi$
$659$	8.19016e6			0.734647			0.367324	+	0.930093i	$0.380274\pi$
$660$		0			0
$661$	−2.60129e6	+	4.50557e6i	−0.231572	+	0.401094i	−0.958271	−	0.285862i	$-0.907720\pi$
$661$	−2.60129e6	+	4.50557e6i	−0.231572	+	0.401094i	0.726699	+	0.686956i	$0.241054\pi$
$662$		0			0
$663$	129659.	+	224577.i	0.0114557	+	0.0198418i
$664$		0			0
$665$	−111175.	−	2.18111e6i	−0.00974881	−	0.191259i
$666$		0			0
$667$	−7.70897e6	−	1.33523e7i	−0.670937	−	1.16210i
$668$		0			0
$669$	−2.97564e6	+	5.15396e6i	−0.257048	+	0.445221i
$670$		0			0
$671$	−1.98574e7			−1.70261
$672$		0			0
$673$	−1.57148e6			−0.133743			−0.0668715	−	0.997762i	$-0.521302\pi$
$673$	−1.57148e6			−0.133743			−0.0668715	+	0.997762i	$0.521302\pi$
$674$		0			0
$675$	−1.92691e6	+	3.33750e6i	−0.162780	+	0.281943i
$676$		0			0
$677$	9.71371e6	+	1.68246e7i	0.814542	+	1.41083i	0.909656	+	0.415361i	$0.136345\pi$
$677$	9.71371e6	+	1.68246e7i	0.814542	+	1.41083i	−0.0951147	+	0.995466i	$0.530322\pi$
$678$		0			0
$679$	5.51692e6	−	3.57151e6i	0.459221	−	0.297288i
$680$		0			0
$681$	−4.43427e6	−	7.68039e6i	−0.366399	−	0.634622i
$682$		0			0
$683$	6.08715e6	−	1.05433e7i	0.499301	−	0.864814i	−0.500699	−	0.865622i	$-0.666924\pi$
$683$	6.08715e6	−	1.05433e7i	0.499301	−	0.864814i	1.00000		0.000807242i	$0.000256953\pi$
$684$		0			0
$685$	−2.94384e7			−2.39711
$686$		0			0
$687$	−8.21065e6			−0.663721
$688$		0			0
$689$	−83160.7	+	144039.i	−0.00667375	+	0.0115593i
$690$		0			0
$691$	831962.	+	1.44100e6i	0.0662839	+	0.114807i	0.897263	−	0.441497i	$-0.145552\pi$
$691$	831962.	+	1.44100e6i	0.0662839	+	0.114807i	−0.830979	+	0.556304i	$0.812219\pi$
$692$		0			0
$693$	−4.78817e6	+	3.09973e6i	−0.378736	+	0.245183i
$694$		0			0
$695$	9.12555e6	+	1.58059e7i	0.716633	+	1.24125i
$696$		0			0
$697$	−9.62887e6	+	1.66777e7i	−0.750746	+	1.30033i
$698$		0			0
$699$	−3.04046e6			−0.235368
$700$		0			0
$701$	1.62394e7			1.24817			0.624087	−	0.781355i	$-0.285471\pi$
$701$	1.62394e7			1.24817			0.624087	+	0.781355i	$0.285471\pi$
$702$		0			0
$703$	176125.	−	305057.i	0.0134410	−	0.0232805i
$704$		0			0
$705$	−1.04432e7	−	1.80881e7i	−0.791333	−	1.37063i
$706$		0			0
$707$	315654.	+	6.19273e6i	0.0237500	+	0.465944i
$708$		0			0
$709$	−5.31112e6	−	9.19913e6i	−0.396799	−	0.687276i	0.596530	−	0.802591i	$-0.296546\pi$
$709$	−5.31112e6	−	9.19913e6i	−0.396799	−	0.687276i	−0.993329	+	0.115315i	$0.963212\pi$
$710$		0			0
$711$	−3.13415e6	+	5.42851e6i	−0.232512	+	0.402723i
$712$		0			0
$713$	3.82651e7			2.81890
$714$		0			0
$715$	1.40770e6			0.102978
$716$		0			0
$717$	2.17396e6	−	3.76541e6i	0.157926	−	0.273536i
$718$		0			0
$719$	4.18925e6	+	7.25599e6i	0.302214	+	0.523449i	0.976637	−	0.214895i	$-0.0689411\pi$
$719$	4.18925e6	+	7.25599e6i	0.302214	+	0.523449i	−0.674423	+	0.738345i	$0.735608\pi$
$720$		0			0
$721$	−9.12751e6	−	4.66718e6i	−0.653904	−	0.334361i
$722$		0			0
$723$	−5.76688e6	−	9.98853e6i	−0.410294	−	0.710650i
$724$		0			0
$725$	−8.81671e6	+	1.52710e7i	−0.622962	+	1.07900i
$726$		0			0
$727$	7.58477e6			0.532239			0.266119	−	0.963940i	$-0.414258\pi$
$727$	7.58477e6			0.532239			0.266119	+	0.963940i	$0.414258\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−655343.	+	1.13509e6i	−0.0453602	+	0.0785662i
$732$		0			0
$733$	−5.11733e6	−	8.86347e6i	−0.351790	−	0.609318i	0.634773	−	0.772699i	$-0.281094\pi$
$733$	−5.11733e6	−	8.86347e6i	−0.351790	−	0.609318i	−0.986563	+	0.163380i	$0.947760\pi$
$734$		0			0
$735$	−5.67890e6	+	1.26573e7i	−0.387745	+	0.864219i
$736$		0			0
$737$	7.59759e6	+	1.31594e7i	0.515237	+	0.892417i
$738$		0			0
$739$	9.49404e6	−	1.64442e7i	0.639499	−	1.10764i	−0.346044	−	0.938218i	$-0.612475\pi$
$739$	9.49404e6	−	1.64442e7i	0.639499	−	1.10764i	0.985543	−	0.169427i	$-0.0541916\pi$
$740$		0			0
$741$	46712.4			0.00312527
$742$		0			0
$743$	−2.42011e7			−1.60829			−0.804143	−	0.594436i	$-0.797375\pi$
$743$	−2.42011e7			−1.60829			−0.804143	+	0.594436i	$0.797375\pi$
$744$		0			0
$745$	1.53707e7	−	2.66229e7i	1.01462	−	1.75737i
$746$		0			0
$747$	2.83620e6	+	4.91245e6i	0.185967	+	0.322104i
$748$		0			0
$749$	1.09168e7	+	5.58207e6i	0.711032	+	0.363572i
$750$		0			0
$751$	3.98715e6	+	6.90594e6i	0.257966	+	0.446810i	0.965697	−	0.259672i	$-0.0836144\pi$
$751$	3.98715e6	+	6.90594e6i	0.257966	+	0.446810i	−0.707731	+	0.706482i	$0.750281\pi$
$752$		0			0
$753$	−969305.	+	1.67889e6i	−0.0622978	+	0.107903i
$754$		0			0
$755$	3.01188e6			0.192296
$756$		0			0
$757$	3.00632e7			1.90676			0.953378	−	0.301778i	$-0.0975800\pi$
$757$	3.00632e7			1.90676			0.953378	+	0.301778i	$0.0975800\pi$
$758$		0			0
$759$	−1.12982e7	+	1.95691e7i	−0.711878	+	1.23301i
$760$		0			0
$761$	−3.23479e6	−	5.60282e6i	−0.202481	−	0.350708i	0.746846	−	0.664997i	$-0.231567\pi$
$761$	−3.23479e6	−	5.60282e6i	−0.202481	−	0.350708i	−0.949327	+	0.314289i	$0.898234\pi$
$762$		0			0
$763$	−190408.	−	3.73556e6i	−0.0118406	−	0.232298i
$764$		0			0
$765$	3.78749e6	+	6.56013e6i	0.233990	+	0.405283i
$766$		0			0
$767$	−518655.	+	898336.i	−0.0318339	+	0.0551379i
$768$		0			0
$769$	3.52170e6			0.214752			0.107376	−	0.994219i	$-0.465755\pi$
$769$	3.52170e6			0.214752			0.107376	+	0.994219i	$0.465755\pi$
$770$		0			0
$771$	5.12888e6			0.310732
$772$		0			0
$773$	1.22474e7	−	2.12131e7i	0.737216	−	1.27690i	−0.216528	−	0.976276i	$-0.569473\pi$
$773$	1.22474e7	−	2.12131e7i	0.737216	−	1.27690i	0.953744	−	0.300619i	$-0.0971934\pi$
$774$		0			0
$775$	−2.18818e7	−	3.79004e7i	−1.30866	−	2.26667i
$776$		0			0
$777$	−1.87833e6	+	1.21598e6i	−0.111614	+	0.0722562i
$778$		0			0
$779$	1.73450e6	+	3.00424e6i	0.102407	+	0.177374i
$780$		0			0
$781$	9.09035e6	−	1.57449e7i	0.533277	−	0.923663i
$782$		0			0
$783$	2.43165e6			0.141741
$784$		0			0
$785$	1.19006e7			0.689277
$786$		0			0
$787$	4.91530e6	−	8.51356e6i	0.282887	−	0.489975i	−0.689207	−	0.724564i	$-0.742041\pi$
$787$	4.91530e6	−	8.51356e6i	0.282887	−	0.489975i	0.972095	+	0.234589i	$0.0753744\pi$
$788$		0			0
$789$	9.49724e6	+	1.64497e7i	0.543131	+	0.940731i
$790$		0			0
$791$	5.97376e6	−	3.86725e6i	0.339474	−	0.219766i
$792$		0			0
$793$	−516508.	−	894618.i	−0.0291672	−	0.0505190i
$794$		0			0
$795$	−2.42921e6	+	4.20752e6i	−0.136316	+	0.236107i
$796$		0			0
$797$	2.59743e6			0.144843			0.0724215	−	0.997374i	$-0.476927\pi$
$797$	2.59743e6			0.144843			0.0724215	+	0.997374i	$0.476927\pi$
$798$		0			0
$799$	−2.58016e7			−1.42981
$800$		0			0
$801$	−5.80906e6	+	1.00616e7i	−0.319907	+	0.554096i
$802$		0			0
$803$	−8.52435e6	−	1.47646e7i	−0.466522	−	0.808041i
$804$		0			0
$805$	2.79769e6	+	5.48870e7i	0.152163	+	2.98525i
$806$		0			0
$807$	−2.88574e6	−	4.99824e6i	−0.155981	−	0.270168i
$808$		0			0
$809$	−1.45127e7	+	2.51368e7i	−0.779611	+	1.35033i	0.152555	+	0.988295i	$0.451250\pi$
$809$	−1.45127e7	+	2.51368e7i	−0.779611	+	1.35033i	−0.932166	+	0.362031i	$0.882083\pi$
$810$		0			0
$811$	−196756.			−0.0105045			−0.00525227	−	0.999986i	$-0.501672\pi$
$811$	−196756.			−0.0105045			−0.00525227	+	0.999986i	$0.501672\pi$
$812$		0			0
$813$	−1.83712e7			−0.974788
$814$		0			0
$815$	735562.	−	1.27403e6i	0.0387905	−	0.0671871i
$816$		0			0
$817$	118050.	+	204469.i	0.00618745	+	0.0107170i
$818$		0			0
$819$	−264194.	−	135091.i	−0.0137630	−	0.00703746i
$820$		0			0
$821$	−6.64732e6	−	1.15135e7i	−0.344183	−	0.596142i	0.641022	−	0.767522i	$-0.278511\pi$
$821$	−6.64732e6	−	1.15135e7i	−0.344183	−	0.596142i	−0.985205	+	0.171381i	$0.945177\pi$
$822$		0			0
$823$	−1.66709e7	+	2.88749e7i	−0.857946	+	1.48601i	0.0159382	+	0.999873i	$0.494927\pi$
$823$	−1.66709e7	+	2.88749e7i	−0.857946	+	1.48601i	−0.873884	+	0.486134i	$0.838407\pi$
$824$		0			0
$825$	2.58434e7			1.32195
$826$		0			0
$827$	2.68644e7			1.36588			0.682942	−	0.730473i	$-0.260700\pi$
$827$	2.68644e7			1.36588			0.682942	+	0.730473i	$0.260700\pi$
$828$		0			0
$829$	6.28567e6	−	1.08871e7i	0.317662	−	0.550206i	−0.662338	−	0.749205i	$-0.730436\pi$
$829$	6.28567e6	−	1.08871e7i	0.317662	−	0.550206i	0.980000	+	0.198999i	$0.0637690\pi$
$830$		0			0
$831$	−7.13161e6	−	1.23523e7i	−0.358249	−	0.620505i
$832$		0			0
$833$	1.00335e7	+	1.38935e7i	0.501003	+	0.693742i
$834$		0			0
$835$	1.88475e7	+	3.26447e7i	0.935484	+	1.62031i
$836$		0			0
$837$	−3.01750e6	+	5.22646e6i	−0.148879	+	0.257866i
$838$		0			0
$839$	−1.61488e6			−0.0792018			−0.0396009	−	0.999216i	$-0.512609\pi$
$839$	−1.61488e6			−0.0792018			−0.0396009	+	0.999216i	$0.512609\pi$
$840$		0			0
$841$	−9.38495e6			−0.457554
$842$		0			0
$843$	168677.	−	292158.i	0.00817501	−	0.0141595i
$844$		0			0
$845$	−1.69897e7	−	2.94271e7i	−0.818550	−	1.41777i
$846$		0			0
$847$	1.54666e7	+	7.90856e6i	0.740776	+	0.378782i
$848$		0			0
$849$	−5.08702e6	−	8.81097e6i	−0.242211	−	0.419522i
$850$		0			0
$851$	−4.43214e6	+	7.67670e6i	−0.209792	+	0.363371i
$852$		0			0
$853$	−1.64014e7			−0.771807			−0.385903	−	0.922539i	$-0.626110\pi$
$853$	−1.64014e7			−0.771807			−0.385903	+	0.922539i	$0.626110\pi$
$854$		0			0
$855$	1.36452e6			0.0638359
$856$		0			0
$857$	1.87706e6	−	3.25116e6i	0.0873022	−	0.151212i	−0.819068	−	0.573697i	$-0.805509\pi$
$857$	1.87706e6	−	3.25116e6i	0.0873022	−	0.151212i	0.906370	+	0.422485i	$0.138842\pi$
$858$		0			0
$859$	−1.63044e7	−	2.82401e7i	−0.753916	−	1.30582i	−0.945912	−	0.324425i	$-0.894829\pi$
$859$	−1.63044e7	−	2.82401e7i	−0.753916	−	1.30582i	0.191996	−	0.981396i	$-0.438504\pi$
$860$		0			0
$861$	−1.12175e6	−	2.20073e7i	−0.0515690	−	1.01172i
$862$		0			0
$863$	3.43895e6	+	5.95644e6i	0.157181	+	0.272245i	0.933851	−	0.357662i	$-0.116426\pi$
$863$	3.43895e6	+	5.95644e6i	0.157181	+	0.272245i	−0.776670	+	0.629907i	$0.783093\pi$
$864$		0			0
$865$	1.56281e7	−	2.70687e7i	0.710178	−	1.23006i
$866$		0			0
$867$	−3.42109e6			−0.154567
$868$		0			0
$869$	4.20348e7			1.88825
$870$		0			0
$871$	−395240.	+	684576.i	−0.0176529	+	0.0305757i
$872$		0			0
$873$	2.05311e6	+	3.55609e6i	0.0911751	+	0.157920i
$874$		0			0
$875$	2.15733e7	−	1.39660e7i	0.952570	−	0.616668i
$876$		0			0
$877$	329879.	+	571367.i	0.0144829	+	0.0250851i	0.873176	−	0.487405i	$-0.162056\pi$
$877$	329879.	+	571367.i	0.0144829	+	0.0250851i	−0.858693	+	0.512490i	$0.828723\pi$
$878$		0			0
$879$	1.21530e7	−	2.10496e7i	0.530531	−	0.918906i
$880$		0			0
$881$	−3.91651e7			−1.70004			−0.850022	−	0.526748i	$-0.823411\pi$
$881$	−3.91651e7			−1.70004			−0.850022	+	0.526748i	$0.823411\pi$
$882$		0			0
$883$	−1.30226e7			−0.562078			−0.281039	−	0.959696i	$-0.590679\pi$
$883$	−1.30226e7			−0.562078			−0.281039	+	0.959696i	$0.590679\pi$
$884$		0			0
$885$	−1.51505e7	+	2.62414e7i	−0.650231	+	1.12623i
$886$		0			0
$887$	4.10805e6	+	7.11535e6i	0.175318	+	0.303660i	0.940271	−	0.340426i	$-0.110571\pi$
$887$	4.10805e6	+	7.11535e6i	0.175318	+	0.303660i	−0.764953	+	0.644086i	$0.777238\pi$
$888$		0			0
$889$	−1.59519e7	+	1.03269e7i	−0.676954	+	0.438242i
$890$		0			0
$891$	−1.78190e6	−	3.08635e6i	−0.0751952	−	0.130242i
$892$		0			0
$893$	−2.32388e6	+	4.02509e6i	−0.0975183	+	0.168907i
$894$		0			0
$895$	−6.17707e7			−2.57766
$896$		0			0
$897$	−1.17551e6			−0.0487803
$898$		0			0
$899$	−1.38068e7	+	2.39141e7i	−0.569762	+	0.986857i
$900$		0			0
$901$	3.00089e6	+	5.19769e6i	0.123151	+	0.213304i
$902$		0			0
$903$	−76346.7	−	1.49783e6i	−0.00311581	−	0.0611282i
$904$		0			0
$905$	−1.81426e7	−	3.14239e7i	−0.736339	−	1.27538i
$906$		0			0
$907$	−1.40624e7	+	2.43567e7i	−0.567597	+	0.983107i	0.429205	+	0.903207i	$0.358794\pi$
$907$	−1.40624e7	+	2.43567e7i	−0.567597	+	0.983107i	−0.996803	+	0.0799006i	$0.974540\pi$
$908$		0			0
$909$	−3.87423e6			−0.155516
$910$		0			0
$911$	−2.65678e7			−1.06062			−0.530310	−	0.847804i	$-0.677925\pi$
$911$	−2.65678e7			−1.06062			−0.530310	+	0.847804i	$0.677925\pi$
$912$		0			0
$913$	1.90194e7	−	3.29426e7i	0.755127	−	1.30792i
$914$		0			0
$915$	−1.50878e7	−	2.61328e7i	−0.595761	−	1.03189i
$916$		0			0
$917$	−2.06177e7	−	1.05425e7i	−0.809688	−	0.414018i
$918$		0			0
$919$	1.86095e7	+	3.22326e7i	0.726851	+	1.25894i	0.958208	+	0.286074i	$0.0923503\pi$
$919$	1.86095e7	+	3.22326e7i	0.726851	+	1.25894i	−0.231356	+	0.972869i	$0.574316\pi$
$920$		0			0
$921$	2.56022e6	−	4.43443e6i	0.0994552	−	0.172262i
$922$		0			0
$923$	945793.			0.0365420
$924$		0			0
$925$	1.01380e7			0.389582
$926$		0			0
$927$	3.20257e6	−	5.54702e6i	0.122405	−	0.212012i
$928$		0			0
$929$	−1.45083e7	−	2.51291e7i	−0.551539	−	0.955294i	−0.998164	−	0.0605722i	$-0.980707\pi$
$929$	−1.45083e7	−	2.51291e7i	−0.551539	−	0.955294i	0.446625	−	0.894721i	$-0.352626\pi$
$930$		0			0
$931$	3.07110e6	−	313894.i	0.116123	−	0.0118688i
$932$		0			0
$933$	−3.53183e6	−	6.11731e6i	−0.132830	−	0.230068i
$934$		0			0
$935$	2.53987e7	−	4.39918e7i	0.950128	−	1.64567i
$936$		0			0
$937$	−4.84662e7			−1.80339			−0.901696	−	0.432370i	$-0.857677\pi$
$937$	−4.84662e7			−1.80339			−0.901696	+	0.432370i	$0.857677\pi$
$938$		0			0
$939$	3.08523e7			1.14189
$940$		0			0
$941$	1.46201e7	−	2.53227e7i	0.538239	−	0.932258i	−0.460759	−	0.887525i	$-0.652423\pi$
$941$	1.46201e7	−	2.53227e7i	0.538239	−	0.932258i	0.998999	−	0.0447331i	$-0.0142437\pi$
$942$		0			0
$943$	−4.36482e7	−	7.56010e7i	−1.59841	−	2.76852i
$944$		0			0
$945$	−7.71740e6	−	3.94615e6i	−0.281120	−	0.143745i
$946$		0			0
$947$	−1.60062e7	−	2.77236e7i	−0.579982	−	1.00456i	−0.995481	−	0.0949641i	$-0.969726\pi$
$947$	−1.60062e7	−	2.77236e7i	−0.579982	−	1.00456i	0.415499	−	0.909594i	$-0.363607\pi$
$948$		0			0
$949$	443452.	−	768082.i	0.0159838	−	0.0276848i
$950$		0			0
$951$	−2.53685e7			−0.909584
$952$		0			0
$953$	1.89025e7			0.674196			0.337098	−	0.941470i	$-0.390555\pi$
$953$	1.89025e7			0.674196			0.337098	+	0.941470i	$0.390555\pi$
$954$		0			0
$955$	−1.37627e7	+	2.38378e7i	−0.488311	+	0.845780i
$956$		0			0
$957$	−8.15324e6	−	1.41218e7i	−0.287773	−	0.498438i
$958$		0			0
$959$	−2.11831e6	−	4.15585e7i	−0.0743777	−	1.45920i
$960$		0			0
$961$	−1.99519e7	−	3.45577e7i	−0.696908	−	1.20708i
$962$		0			0
$963$	−3.83036e6	+	6.63438e6i	−0.133099	+	0.230534i
$964$		0			0
$965$	3.02344e7			1.04516
$966$		0			0
$967$	5.66513e7			1.94825			0.974123	−	0.226017i	$-0.0725705\pi$
$967$	5.66513e7			1.94825			0.974123	+	0.226017i	$0.0725705\pi$
$968$		0			0
$969$	842819.	−	1.45980e6i	0.0288353	−	0.0499442i
$970$		0			0
$971$	−6.72939e6	−	1.16556e7i	−0.229049	−	0.396724i	0.728478	−	0.685069i	$-0.240228\pi$
$971$	−6.72939e6	−	1.16556e7i	−0.229049	−	0.396724i	−0.957526	+	0.288346i	$0.906895\pi$
$972$		0			0
$973$	−2.16568e7	+	1.40200e7i	−0.733351	+	0.474752i
$974$		0			0
$975$	672211.	+	1.16430e6i	0.0226461	+	0.0392242i
$976$		0			0
$977$	−2.86448e7	+	4.96142e7i	−0.960084	+	1.66291i	−0.237804	+	0.971313i	$0.576428\pi$
$977$	−2.86448e7	+	4.96142e7i	−0.960084	+	1.66291i	−0.722280	+	0.691601i	$0.756906\pi$
$978$		0			0
$979$	7.79103e7			2.59799
$980$		0			0
$981$	2.33700e6			0.0775331
$982$		0			0
$983$	9.74148e6	−	1.68727e7i	0.321544	−	0.556931i	−0.659262	−	0.751913i	$-0.729131\pi$
$983$	9.74148e6	−	1.68727e7i	0.321544	−	0.556931i	0.980807	+	0.194982i	$0.0624647\pi$
$984$		0			0
$985$	−2.00164e7	−	3.46695e7i	−0.657349	−	1.13856i
$986$		0			0
$987$	2.47837e7	−	1.60443e7i	0.809793	−	0.524238i
$988$		0			0
$989$	−2.97071e6	−	5.14542e6i	−0.0965761	−	0.167275i
$990$		0			0
$991$	−2.03075e7	+	3.51736e7i	−0.656859	+	1.13771i	0.324566	+	0.945863i	$0.394782\pi$
$991$	−2.03075e7	+	3.51736e7i	−0.656859	+	1.13771i	−0.981424	+	0.191849i	$0.938552\pi$
$992$		0			0
$993$	1.98438e7			0.638633
$994$		0			0
$995$	3.98903e7			1.27735
$996$		0			0
$997$	−2.66000e7	+	4.60725e7i	−0.847506	+	1.46792i	0.0359201	+	0.999355i	$0.488564\pi$
$997$	−2.66000e7	+	4.60725e7i	−0.847506	+	1.46792i	−0.883427	+	0.468570i	$0.844770\pi$
$998$		0			0
$999$	−699018.	−	1.21073e6i	−0.0221602	−	0.0383827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.l.193.5		10
4.3	odd	2		168.6.q.c.25.5	✓	10
7.2	even	3	inner	336.6.q.l.289.5		10
12.11	even	2		504.6.s.c.361.1		10
28.23	odd	6		168.6.q.c.121.5	yes	10
84.23	even	6		504.6.s.c.289.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.c.25.5	✓	10	4.3	odd	2
168.6.q.c.121.5	yes	10	28.23	odd	6
336.6.q.l.193.5		10	1.1	even	1	trivial
336.6.q.l.289.5		10	7.2	even	3	inner
504.6.s.c.289.1		10	84.23	even	6
504.6.s.c.361.1		10	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 + 7.79423i) q^{3} +(45.8569 + 79.4265i) q^{5} +(-108.828 + 70.4522i) q^{7} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 + 7.79423i) q^{3} +(45.8569 + 79.4265i) q^{5} +(-108.828 + 70.4522i) q^{7} +(-40.5000 - 70.1481i) q^{9} +(-271.590 + 470.408i) q^{11} -28.2573 q^{13} -825.425 q^{15} +(-509.837 + 883.064i) q^{17} +(91.8396 + 159.071i) q^{19} +(-59.3955 - 1165.26i) q^{21} +(-2311.12 - 4002.98i) q^{23} +(-2643.22 + 4578.19i) q^{25} +729.000 q^{27} +3335.60 q^{29} +(-4139.23 + 7169.36i) q^{31} +(-2444.31 - 4233.68i) q^{33} +(-10586.3 - 5413.09i) q^{35} +(-958.872 - 1660.81i) q^{37} +(127.158 - 220.243i) q^{39} +18886.2 q^{41} +1285.40 q^{43} +(3714.41 - 6433.55i) q^{45} +(12651.9 + 21913.7i) q^{47} +(6879.98 - 15334.3i) q^{49} +(-4588.54 - 7947.58i) q^{51} +(2942.99 - 5097.40i) q^{53} -49817.2 q^{55} -1653.11 q^{57} +(18354.7 - 31791.4i) q^{59} +(18278.8 + 31659.8i) q^{61} +(9349.61 + 4780.74i) q^{63} +(-1295.79 - 2244.38i) q^{65} +(13987.2 - 24226.6i) q^{67} +41600.2 q^{69} -33470.8 q^{71} +(-15693.4 + 27181.8i) q^{73} +(-23789.0 - 41203.7i) q^{75} +(-3584.72 - 70327.7i) q^{77} +(-38693.2 - 67018.6i) q^{79} +(-3280.50 + 5681.99i) q^{81} -70029.7 q^{83} -93518.3 q^{85} +(-15010.2 + 25998.4i) q^{87} +(-71716.7 - 124217. i) q^{89} +(3075.17 - 1990.79i) q^{91} +(-37253.1 - 64524.2i) q^{93} +(-8422.97 + 14589.0i) q^{95} -50694.0 q^{97} +43997.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9}+O(q^{10}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9	\( 10 q - 45 q^{3} - 6 q^{5} + 97 q^{7} - 405 q^{9} - 424 q^{11} + 374 q^{13} + 108 q^{15} - 952 q^{17} - 139 q^{19} - 1044 q^{21} - 4288 q^{23} - 5605 q^{25} + 7290 q^{27} - 4216 q^{29} - 8131 q^{31} - 3816 q^{33} - 20106 q^{35} - 5425 q^{37} - 1683 q^{39} + 29364 q^{41} + 46862 q^{43} - 486 q^{45} + 17190 q^{47} + 23255 q^{49} - 8568 q^{51} + 15064 q^{53} + 1176 q^{55} + 2502 q^{57} + 83242 q^{59} + 14954 q^{61} + 1539 q^{63} - 23250 q^{65} - 39501 q^{67} + 77184 q^{69} + 56020 q^{71} - 90395 q^{73} - 50445 q^{75} + 63448 q^{77} + 43067 q^{79} - 32805 q^{81} + 75672 q^{83} - 75272 q^{85} + 18972 q^{87} - 72608 q^{89} - 288287 q^{91} - 73179 q^{93} - 190138 q^{95} + 183000 q^{97} + 68688 q^{99}+O(q^{100}) \) 10 * q - 45 * q^3 - 6 * q^5 + 97 * q^7 - 405 * q^9 - 424 * q^11 + 374 * q^13 + 108 * q^15 - 952 * q^17 - 139 * q^19 - 1044 * q^21 - 4288 * q^23 - 5605 * q^25 + 7290 * q^27 - 4216 * q^29 - 8131 * q^31 - 3816 * q^33 - 20106 * q^35 - 5425 * q^37 - 1683 * q^39 + 29364 * q^41 + 46862 * q^43 - 486 * q^45 + 17190 * q^47 + 23255 * q^49 - 8568 * q^51 + 15064 * q^53 + 1176 * q^55 + 2502 * q^57 + 83242 * q^59 + 14954 * q^61 + 1539 * q^63 - 23250 * q^65 - 39501 * q^67 + 77184 * q^69 + 56020 * q^71 - 90395 * q^73 - 50445 * q^75 + 63448 * q^77 + 43067 * q^79 - 32805 * q^81 + 75672 * q^83 - 75272 * q^85 + 18972 * q^87 - 72608 * q^89 - 288287 * q^91 - 73179 * q^93 - 190138 * q^95 + 183000 * q^97 + 68688 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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