LMFDB - Embedded newform 76.6.e.a.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(45,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("76.45");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.e (of order $3$, degree $2$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} + \cdots + 80\!\cdots\!36 $ x^18 - 2x^17 + 1540x^16 - 768x^15 + 1608492x^14 - 1027368x^13 + 897054160x^12 - 1275481376x^11 + 361098181456x^10 - 863969476320x^9 + 79755165392064x^8 - 375077568148992x^7 + 12736924096193536x^6 - 57314532742553600x^5 + 977121800205220864x^4 - 4977732006498379776x^3 + 53672321824823513088x^2 - 185653809995679793152*x + 804303742853852430336
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.1
Root			$14.2764 - 24.7275i$ of defining polynomial
Character	$\chi$	$=$	76.45
Dual form			76.6.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.7764 - 25.5935i) q^{3} +(35.6401 + 61.7304i) q^{5} +252.315 q^{7} +(-315.186 + 545.918i) q^{9} +O(q^{10})$	\(q+(-14.7764 - 25.5935i) q^{3} +(35.6401 + 61.7304i) q^{5} +252.315 q^{7} +(-315.186 + 545.918i) q^{9} +88.0323 q^{11} +(307.862 - 533.232i) q^{13} +(1053.27 - 1824.31i) q^{15} +(285.543 + 494.575i) q^{17} +(361.524 - 1531.47i) q^{19} +(-3728.32 - 6457.64i) q^{21} +(-1214.28 + 2103.20i) q^{23} +(-977.931 + 1693.83i) q^{25} +11447.9 q^{27} +(1142.82 - 1979.43i) q^{29} +3684.20 q^{31} +(-1300.80 - 2253.06i) q^{33} +(8992.54 + 15575.5i) q^{35} +3064.28 q^{37} -18196.4 q^{39} +(-1246.89 - 2159.67i) q^{41} +(-2450.11 - 4243.71i) q^{43} -44933.0 q^{45} +(8786.51 - 15218.7i) q^{47} +46856.0 q^{49} +(8438.61 - 14616.1i) q^{51} +(-12713.9 + 22021.1i) q^{53} +(3137.48 + 5434.27i) q^{55} +(-44537.7 + 13377.0i) q^{57} +(-11756.9 - 20363.5i) q^{59} +(9886.00 - 17123.1i) q^{61} +(-79526.2 + 137743. i) q^{63} +43888.8 q^{65} +(-13694.3 + 23719.2i) q^{67} +71771.0 q^{69} +(-16750.0 - 29011.9i) q^{71} +(-8986.08 - 15564.3i) q^{73} +57801.3 q^{75} +22211.9 q^{77} +(41242.9 + 71434.8i) q^{79} +(-92569.6 - 160335. i) q^{81} +40274.4 q^{83} +(-20353.5 + 35253.4i) q^{85} -67547.4 q^{87} +(-27641.5 + 47876.5i) q^{89} +(77678.2 - 134543. i) q^{91} +(-54439.3 - 94291.7i) q^{93} +(107423. - 32264.7i) q^{95} +(13348.8 + 23120.7i) q^{97} +(-27746.6 + 48058.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9}+O(q^{10}) $ 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9	$ 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99}+O(q^{100}) $ 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9 - 320 * q^11 + 227 * q^13 - 101 * q^15 + 179 * q^17 - 868 * q^19 - 5700 * q^21 - 3425 * q^23 - 7054 * q^25 + 14722 * q^27 - 7349 * q^29 - 9960 * q^31 - 2998 * q^33 + 15888 * q^35 + 26444 * q^37 - 30246 * q^39 - 7311 * q^41 - 8283 * q^43 - 62164 * q^45 + 37603 * q^47 + 124738 * q^49 + 47227 * q^51 - 20337 * q^53 + 716 * q^55 - 57555 * q^57 - 74455 * q^59 - 7569 * q^61 - 52544 * q^63 + 188998 * q^65 - 26177 * q^67 + 116282 * q^69 - 53463 * q^71 - 14103 * q^73 + 120912 * q^75 - 31960 * q^77 + 31825 * q^79 - 21137 * q^81 + 82600 * q^83 - 50787 * q^85 - 339766 * q^87 - 155197 * q^89 - 2800 * q^91 - 46460 * q^93 + 49315 * q^95 + 111241 * q^97 - 193544 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−14.7764	−	25.5935i	−0.947909	−	1.64183i	−0.749820	−	0.661642i	$-0.769860\pi$
$3$	−14.7764	−	25.5935i	−0.947909	−	1.64183i	−0.198088	−	0.980184i	$-0.563473\pi$
$4$		0			0
$5$	35.6401	+	61.7304i	0.637549	+	1.10427i	0.985969	+	0.166929i	$0.0533850\pi$
$5$	35.6401	+	61.7304i	0.637549	+	1.10427i	−0.348420	+	0.937339i	$0.613282\pi$
$6$		0			0
$7$	252.315			1.94625			0.973125	−	0.230279i	$-0.0739637\pi$
$7$	252.315			1.94625			0.973125	+	0.230279i	$0.0739637\pi$
$8$		0			0
$9$	−315.186	+	545.918i	−1.29706	+	2.24658i
$10$		0			0
$11$	88.0323			0.219362			0.109681	−	0.993967i	$-0.465017\pi$
$11$	88.0323			0.219362			0.109681	+	0.993967i	$0.465017\pi$
$12$		0			0
$13$	307.862	−	533.232i	0.505239	−	0.875100i	−0.494742	−	0.869040i	$-0.664738\pi$
$13$	307.862	−	533.232i	0.505239	−	0.875100i	0.999982	−	0.00606030i	$-0.00192907\pi$
$14$		0			0
$15$	1053.27	−	1824.31i	1.20868	−	2.09349i
$16$		0			0
$17$	285.543	+	494.575i	0.239634	+	0.415059i	0.960609	−	0.277902i	$-0.0896391\pi$
$17$	285.543	+	494.575i	0.239634	+	0.415059i	−0.720975	+	0.692961i	$0.756306\pi$
$18$		0			0
$19$	361.524	−	1531.47i	0.229748	−	0.973250i
$19$	361.524	−	1531.47i	0.229748	−	0.973250i
$20$		0			0
$21$	−3728.32	−	6457.64i	−1.84487	−	3.19540i
$22$		0			0
$23$	−1214.28	+	2103.20i	−0.478630	+	0.829011i	−0.999700	−	0.0245027i	$-0.992200\pi$
$23$	−1214.28	+	2103.20i	−0.478630	+	0.829011i	0.521070	+	0.853514i	$0.325533\pi$
$24$		0			0
$25$	−977.931	+	1693.83i	−0.312938	+	0.542024i
$26$		0			0
$27$	11447.9			3.02216
$28$		0			0
$29$	1142.82	−	1979.43i	0.252339	−	0.437064i	−0.711830	−	0.702351i	$-0.752134\pi$
$29$	1142.82	−	1979.43i	0.252339	−	0.437064i	0.964169	+	0.265288i	$0.0854669\pi$
$30$		0			0
$31$	3684.20			0.688555			0.344278	−	0.938868i	$-0.388124\pi$
$31$	3684.20			0.688555			0.344278	+	0.938868i	$0.388124\pi$
$32$		0			0
$33$	−1300.80	−	2253.06i	−0.207935	−	0.360153i
$34$		0			0
$35$	8992.54	+	15575.5i	1.24083	+	2.14918i
$36$		0			0
$37$	3064.28			0.367980			0.183990	−	0.982928i	$-0.441099\pi$
$37$	3064.28			0.367980			0.183990	+	0.982928i	$0.441099\pi$
$38$		0			0
$39$	−18196.4			−1.91568
$40$		0			0
$41$	−1246.89	−	2159.67i	−0.115842	−	0.200645i	0.802274	−	0.596956i	$-0.203623\pi$
$41$	−1246.89	−	2159.67i	−0.115842	−	0.200645i	−0.918116	+	0.396311i	$0.870290\pi$
$42$		0			0
$43$	−2450.11	−	4243.71i	−0.202075	−	0.350005i	0.747122	−	0.664687i	$-0.231435\pi$
$43$	−2450.11	−	4243.71i	−0.202075	−	0.350005i	−0.949197	+	0.314682i	$0.898102\pi$
$44$		0			0
$45$	−44933.0			−3.30776
$46$		0			0
$47$	8786.51	−	15218.7i	0.580192	−	1.00492i	−0.415264	−	0.909701i	$-0.636311\pi$
$47$	8786.51	−	15218.7i	0.580192	−	1.00492i	0.995456	−	0.0952210i	$-0.0303558\pi$
$48$		0			0
$49$	46856.0			2.78789
$50$		0			0
$51$	8438.61	−	14616.1i	0.454303	−	0.786876i
$52$		0			0
$53$	−12713.9	+	22021.1i	−0.621712	+	1.07684i	0.367455	+	0.930041i	$0.380229\pi$
$53$	−12713.9	+	22021.1i	−0.621712	+	1.07684i	−0.989167	+	0.146795i	$0.953104\pi$
$54$		0			0
$55$	3137.48	+	5434.27i	0.139854	+	0.242234i
$56$		0			0
$57$	−44537.7	+	13377.0i	−1.81569	+	0.545345i
$58$		0			0
$59$	−11756.9	−	20363.5i	−0.439706	−	0.761592i	0.557961	−	0.829867i	$-0.311584\pi$
$59$	−11756.9	−	20363.5i	−0.439706	−	0.761592i	−0.997667	+	0.0682748i	$0.978251\pi$
$60$		0			0
$61$	9886.00	−	17123.1i	0.340170	−	0.589192i	−0.644294	−	0.764778i	$-0.722849\pi$
$61$	9886.00	−	17123.1i	0.340170	−	0.589192i	0.984464	+	0.175586i	$0.0561820\pi$
$62$		0			0
$63$	−79526.2	+	137743.i	−2.52440	+	4.37240i
$64$		0			0
$65$	43888.8			1.28846
$66$		0			0
$67$	−13694.3	+	23719.2i	−0.372694	+	0.645525i	−0.989979	−	0.141214i	$-0.954899\pi$
$67$	−13694.3	+	23719.2i	−0.372694	+	0.645525i	0.617285	+	0.786740i	$0.288233\pi$
$68$		0			0
$69$	71771.0			1.81479
$70$		0			0
$71$	−16750.0	−	29011.9i	−0.394339	−	0.683014i	0.598678	−	0.800990i	$-0.295693\pi$
$71$	−16750.0	−	29011.9i	−0.394339	−	0.683014i	−0.993017	+	0.117975i	$0.962360\pi$
$72$		0			0
$73$	−8986.08	−	15564.3i	−0.197362	−	0.341841i	0.750310	−	0.661086i	$-0.229904\pi$
$73$	−8986.08	−	15564.3i	−0.197362	−	0.341841i	−0.947672	+	0.319245i	$0.896571\pi$
$74$		0			0
$75$	57801.3			1.18655
$76$		0			0
$77$	22211.9			0.426932
$78$		0			0
$79$	41242.9	+	71434.8i	0.743501	+	1.28778i	0.950892	+	0.309523i	$0.100169\pi$
$79$	41242.9	+	71434.8i	0.743501	+	1.28778i	−0.207391	+	0.978258i	$0.566497\pi$
$80$		0			0
$81$	−92569.6	−	160335.i	−1.56767	−	2.71529i
$82$		0			0
$83$	40274.4			0.641702			0.320851	−	0.947130i	$-0.396031\pi$
$83$	40274.4			0.641702			0.320851	+	0.947130i	$0.396031\pi$
$84$		0			0
$85$	−20353.5	+	35253.4i	−0.305557	+	0.529241i
$86$		0			0
$87$	−67547.4			−0.956777
$88$		0			0
$89$	−27641.5	+	47876.5i	−0.369902	+	0.640689i	−0.989550	−	0.144191i	$-0.953942\pi$
$89$	−27641.5	+	47876.5i	−0.369902	+	0.640689i	0.619648	+	0.784880i	$0.287275\pi$
$90$		0			0
$91$	77678.2	−	134543.i	0.983322	−	1.70316i
$92$		0			0
$93$	−54439.3	−	94291.7i	−0.652688	−	1.13049i
$94$		0			0
$95$	107423.	−	32264.7i	1.22120	−	0.366791i
$96$		0			0
$97$	13348.8	+	23120.7i	0.144049	+	0.249501i	0.929018	−	0.370035i	$-0.120654\pi$
$97$	13348.8	+	23120.7i	0.144049	+	0.249501i	−0.784968	+	0.619536i	$0.787321\pi$
$98$		0			0
$99$	−27746.6	+	48058.4i	−0.284525	+	0.492812i
$100$		0			0
$101$	−60668.2	+	105080.i	−0.591777	+	1.02499i	0.402216	+	0.915545i	$0.368240\pi$
$101$	−60668.2	+	105080.i	−0.591777	+	1.02499i	−0.993993	+	0.109443i	$0.965093\pi$
$102$		0			0
$103$	−123258.			−1.14478			−0.572392	−	0.819980i	$-0.693985\pi$
$103$	−123258.			−1.14478			−0.572392	+	0.819980i	$0.693985\pi$
$104$		0			0
$105$	265755.	−	460302.i	2.35239	−	4.07445i
$106$		0			0
$107$	225615.			1.90506			0.952529	−	0.304449i	$-0.0984722\pi$
$107$	225615.			1.90506			0.952529	+	0.304449i	$0.0984722\pi$
$108$		0			0
$109$	−25583.8	−	44312.5i	−0.206253	−	0.357240i	0.744279	−	0.667869i	$-0.232793\pi$
$109$	−25583.8	−	44312.5i	−0.206253	−	0.357240i	−0.950531	+	0.310629i	$0.899460\pi$
$110$		0			0
$111$	−45279.2	−	78425.8i	−0.348812	−	0.604160i
$112$		0			0
$113$	−113870.			−0.838909			−0.419454	−	0.907776i	$-0.637779\pi$
$113$	−113870.			−0.838909			−0.419454	+	0.907776i	$0.637779\pi$
$114$		0			0
$115$	−173108.			−1.22060
$116$		0			0
$117$	194067.	+	336134.i	1.31065	+	2.27012i
$118$		0			0
$119$	72046.9	+	124789.i	0.466388	+	0.807808i
$120$		0			0
$121$	−153301.			−0.951881
$122$		0			0
$123$	−36849.1	+	63824.5i	−0.219616	+	0.380386i
$124$		0			0
$125$	83336.4			0.477045
$126$		0			0
$127$	−23234.7	+	40243.6i	−0.127828	+	0.221405i	−0.922835	−	0.385196i	$-0.874134\pi$
$127$	−23234.7	+	40243.6i	−0.127828	+	0.221405i	0.795007	+	0.606601i	$0.207467\pi$
$128$		0			0
$129$	−72407.6	+	125414.i	−0.383098	+	0.663546i
$130$		0			0
$131$	142237.	+	246361.i	0.724157	+	1.25428i	0.959320	+	0.282321i	$0.0911044\pi$
$131$	142237.	+	246361.i	0.724157	+	1.25428i	−0.235163	+	0.971956i	$0.575562\pi$
$132$		0			0
$133$	91217.9	−	386413.i	0.447148	−	1.89419i
$134$		0			0
$135$	408006.	+	706687.i	1.92678	+	3.33728i
$136$		0			0
$137$	−143955.	+	249337.i	−0.655277	+	1.13497i	0.326547	+	0.945181i	$0.394115\pi$
$137$	−143955.	+	249337.i	−0.655277	+	1.13497i	−0.981824	+	0.189792i	$0.939219\pi$
$138$		0			0
$139$	88821.1	−	153843.i	0.389923	−	0.675367i	−0.602515	−	0.798107i	$-0.705835\pi$
$139$	88821.1	−	153843.i	0.389923	−	0.675367i	0.992439	+	0.122740i	$0.0391681\pi$
$140$		0			0
$141$	−519333.			−2.19988
$142$		0			0
$143$	27101.8	−	46941.6i	0.110830	−	0.191963i
$144$		0			0
$145$	162921.			0.643514
$146$		0			0
$147$	−692365.	−	1.19921e6i	−2.64266	−	4.57723i
$148$		0			0
$149$	−81129.1	−	140520.i	−0.299372	−	0.518527i	0.676621	−	0.736332i	$-0.263444\pi$
$149$	−81129.1	−	140520.i	−0.299372	−	0.518527i	−0.975992	+	0.217805i	$0.930110\pi$
$150$		0			0
$151$	−449650.			−1.60484			−0.802420	−	0.596760i	$-0.796455\pi$
$151$	−449650.			−1.60484			−0.802420	+	0.596760i	$0.796455\pi$
$152$		0			0
$153$	−359996.			−1.24328
$154$		0			0
$155$	131305.	+	227427.i	0.438988	+	0.760349i
$156$		0			0
$157$	−27389.5	−	47440.1i	−0.0886820	−	0.153602i	0.818272	−	0.574831i	$-0.194932\pi$
$157$	−27389.5	−	47440.1i	−0.0886820	−	0.153602i	−0.906954	+	0.421229i	$0.861599\pi$
$158$		0			0
$159$	751464.			2.35730
$160$		0			0
$161$	−306382.	+	530669.i	−0.931533	+	1.61346i
$162$		0			0
$163$	207755.			0.612467			0.306233	−	0.951956i	$-0.400931\pi$
$163$	207755.			0.612467			0.306233	+	0.951956i	$0.400931\pi$
$164$		0			0
$165$	92721.5	−	160598.i	0.265137	−	0.459231i
$166$		0			0
$167$	−136696.	+	236765.i	−0.379284	+	0.656940i	−0.990958	−	0.134170i	$-0.957163\pi$
$167$	−136696.	+	236765.i	−0.379284	+	0.656940i	0.611674	+	0.791110i	$0.290496\pi$
$168$		0			0
$169$	−3910.94	−	6773.94i	−0.0105333	−	0.0182442i
$170$		0			0
$171$	722110.	+	680060.i	1.88848	+	1.77851i
$172$		0			0
$173$	−262508.	−	454677.i	−0.666848	−	1.15501i	−0.978781	−	0.204910i	$-0.934310\pi$
$173$	−262508.	−	454677.i	−0.666848	−	1.15501i	0.311933	−	0.950104i	$-0.399024\pi$
$174$		0			0
$175$	−246747.	+	427378.i	−0.609055	+	1.05491i
$176$		0			0
$177$	−347449.	+	601800.i	−0.833601	+	1.44384i
$178$		0			0
$179$	−13590.9			−0.0317041			−0.0158520	−	0.999874i	$-0.505046\pi$
$179$	−13590.9			−0.0317041			−0.0158520	+	0.999874i	$0.505046\pi$
$180$		0			0
$181$	−36970.5	+	64034.9i	−0.0838802	+	0.145285i	−0.904913	−	0.425596i	$-0.860065\pi$
$181$	−36970.5	+	64034.9i	−0.0838802	+	0.145285i	0.821033	+	0.570880i	$0.193398\pi$
$182$		0			0
$183$	−584319.			−1.28980
$184$		0			0
$185$	109211.	+	189160.i	0.234606	+	0.406349i
$186$		0			0
$187$	25137.0	+	43538.6i	0.0525666	+	0.0910480i
$188$		0			0
$189$	2.88849e6			5.88189
$190$		0			0
$191$	−522570.			−1.03648			−0.518240	−	0.855235i	$-0.673413\pi$
$191$	−522570.			−1.03648			−0.518240	+	0.855235i	$0.673413\pi$
$192$		0			0
$193$	12411.0	+	21496.6i	0.0239836	+	0.0415409i	0.877768	−	0.479086i	$-0.159032\pi$
$193$	12411.0	+	21496.6i	0.0239836	+	0.0415409i	−0.853784	+	0.520627i	$0.825698\pi$
$194$		0			0
$195$	−648520.	−	1.12327e6i	−1.22134	−	2.11543i
$196$		0			0
$197$	−363318.			−0.666993			−0.333496	−	0.942751i	$-0.608228\pi$
$197$	−363318.			−0.666993			−0.333496	+	0.942751i	$0.608228\pi$
$198$		0			0
$199$	40673.4	−	70448.5i	0.0728078	−	0.126107i	−0.827323	−	0.561726i	$-0.810137\pi$
$199$	40673.4	−	70448.5i	0.0728078	−	0.126107i	0.900131	+	0.435620i	$0.143471\pi$
$200$		0			0
$201$	809411.			1.41312
$202$		0			0
$203$	288352.	−	499440.i	0.491114	−	0.850635i
$204$		0			0
$205$	88878.3	−	153942.i	0.147710	−	0.255842i
$206$		0			0
$207$	−765449.	−	1.32580e6i	−1.24162	−	2.15056i
$208$		0			0
$209$	31825.8	−	134819.i	0.0503980	−	0.213494i
$210$		0			0
$211$	−235569.	−	408017.i	−0.364260	−	0.630917i	0.624397	−	0.781107i	$-0.285345\pi$
$211$	−235569.	−	408017.i	−0.364260	−	0.630917i	−0.988657	+	0.150190i	$0.952011\pi$
$212$		0			0
$213$	−495011.	+	857384.i	−0.747594	+	1.29487i
$214$		0			0
$215$	174644.	−	302492.i	0.257666	−	0.446291i
$216$		0			0
$217$	929580.			1.34010
$218$		0			0
$219$	−265564.	+	459971.i	−0.374162	+	0.648068i
$220$		0			0
$221$	351631.			0.484291
$222$		0			0
$223$	−650115.	−	1.12603e6i	−0.875443	−	1.51631i	−0.856290	−	0.516495i	$-0.827236\pi$
$223$	−650115.	−	1.12603e6i	−0.875443	−	1.51631i	−0.0191530	−	0.999817i	$-0.506097\pi$
$224$		0			0
$225$	−616460.	−	1.06774e6i	−0.811799	−	1.40608i
$226$		0			0
$227$	−73342.4			−0.0944692			−0.0472346	−	0.998884i	$-0.515041\pi$
$227$	−73342.4			−0.0944692			−0.0472346	+	0.998884i	$0.515041\pi$
$228$		0			0
$229$	−1.25234e6			−1.57809			−0.789046	−	0.614335i	$-0.789424\pi$
$229$	−1.25234e6			−1.57809			−0.789046	+	0.614335i	$0.789424\pi$
$230$		0			0
$231$	−328213.	−	568481.i	−0.404693	−	0.700949i
$232$		0			0
$233$	544644.	+	943351.i	0.657238	+	1.13837i	0.981328	+	0.192344i	$0.0616089\pi$
$233$	544644.	+	943351.i	0.657238	+	1.13837i	−0.324089	+	0.946027i	$0.605058\pi$
$234$		0			0
$235$	1.25261e6			1.47960
$236$		0			0
$237$	1.21885e6	−	2.11110e6i	1.40954	−	2.44140i
$238$		0			0
$239$	928359.			1.05129			0.525644	−	0.850705i	$-0.323825\pi$
$239$	928359.			1.05129			0.525644	+	0.850705i	$0.323825\pi$
$240$		0			0
$241$	−49744.9	+	86160.6i	−0.0551703	+	0.0955578i	−0.892292	−	0.451460i	$-0.850904\pi$
$241$	−49744.9	+	86160.6i	−0.0551703	+	0.0955578i	0.837121	+	0.547017i	$0.184237\pi$
$242$		0			0
$243$	−1.34477e6	+	2.32921e6i	−1.46094	+	2.53043i
$244$		0			0
$245$	1.66995e6	+	2.89244e6i	1.77742	+	3.07857i
$246$		0			0
$247$	−705329.	−	664256.i	−0.735613	−	0.692777i
$248$		0			0
$249$	−595112.	−	1.03076e6i	−0.608275	−	1.05356i
$250$		0			0
$251$	−190030.	+	329141.i	−0.190387	+	0.329760i	−0.945379	−	0.325975i	$-0.894308\pi$
$251$	−190030.	+	329141.i	−0.190387	+	0.329760i	0.754992	+	0.655735i	$0.227641\pi$
$252$		0			0
$253$	−106896.	+	185149.i	−0.104993	+	0.181853i
$254$		0			0
$255$	1.20301e6			1.15856
$256$		0			0
$257$	−552645.	+	957209.i	−0.521931	+	0.904012i	0.477743	+	0.878500i	$0.341455\pi$
$257$	−552645.	+	957209.i	−0.521931	+	0.904012i	−0.999675	+	0.0255121i	$0.991878\pi$
$258$		0			0
$259$	773166.			0.716182
$260$		0			0
$261$	720404.	+	1.24778e6i	0.654598	+	1.13380i
$262$		0			0
$263$	−276003.	−	478051.i	−0.246050	−	0.426172i	0.716376	−	0.697714i	$-0.245800\pi$
$263$	−276003.	−	478051.i	−0.246050	−	0.426172i	−0.962426	+	0.271543i	$0.912466\pi$
$264$		0			0
$265$	−1.81250e6			−1.58549
$266$		0			0
$267$	1.63377e6			1.40253
$268$		0			0
$269$	859906.	+	1.48940e6i	0.724553	+	1.25496i	0.959158	+	0.282872i	$0.0912872\pi$
$269$	859906.	+	1.48940e6i	0.724553	+	1.25496i	−0.234604	+	0.972091i	$0.575379\pi$
$270$		0			0
$271$	451795.	+	782532.i	0.373696	+	0.647260i	0.990131	−	0.140146i	$-0.0447571\pi$
$271$	451795.	+	782532.i	0.373696	+	0.647260i	−0.616435	+	0.787406i	$0.711424\pi$
$272$		0			0
$273$	−4.59123e6			−3.72840
$274$		0			0
$275$	−86089.5	+	149111.i	−0.0686465	+	0.118899i
$276$		0			0
$277$	−1.04518e6			−0.818447			−0.409223	−	0.912434i	$-0.634200\pi$
$277$	−1.04518e6			−0.818447			−0.409223	+	0.912434i	$0.634200\pi$
$278$		0			0
$279$	−1.16121e6	+	2.01127e6i	−0.893099	+	1.54689i
$280$		0			0
$281$	−213159.	+	369202.i	−0.161041	+	0.278932i	−0.935242	−	0.354008i	$-0.884819\pi$
$281$	−213159.	+	369202.i	−0.161041	+	0.278932i	0.774201	+	0.632940i	$0.218152\pi$
$282$		0			0
$283$	−29882.7	−	51758.4i	−0.0221796	−	0.0384162i	0.854723	−	0.519085i	$-0.173727\pi$
$283$	−29882.7	−	51758.4i	−0.0221796	−	0.0384162i	−0.876902	+	0.480669i	$0.840394\pi$
$284$		0			0
$285$	−2.41310e6	−	2.27258e6i	−1.75980	−	1.65732i
$286$		0			0
$287$	−314609.	−	544918.i	−0.225458	−	0.390505i
$288$		0			0
$289$	546859.	−	947188.i	0.385151	−	0.667101i
$290$		0			0
$291$	394494.	−	683284.i	0.273092	−	0.473008i
$292$		0			0
$293$	1.17326e6			0.798410			0.399205	−	0.916862i	$-0.369286\pi$
$293$	1.17326e6			0.798410			0.399205	+	0.916862i	$0.369286\pi$
$294$		0			0
$295$	838032.	−	1.45151e6i	0.560668	−	0.971105i
$296$		0			0
$297$	1.00779e6			0.662947
$298$		0			0
$299$	747661.	+	1.29499e6i	0.483645	+	0.837698i
$300$		0			0
$301$	−618199.	−	1.07075e6i	−0.393289	−	0.681197i
$302$		0			0
$303$	3.58584e6			2.24380
$304$		0			0
$305$	1.40935e6			0.867501
$306$		0			0
$307$	−252040.	−	436545.i	−0.152624	−	0.264353i	0.779567	−	0.626318i	$-0.215439\pi$
$307$	−252040.	−	436545.i	−0.152624	−	0.264353i	−0.932191	+	0.361966i	$0.882106\pi$
$308$		0			0
$309$	1.82132e6	+	3.15462e6i	1.08515	+	1.87954i
$310$		0			0
$311$	2.39525e6			1.40426			0.702132	−	0.712046i	$-0.252231\pi$
$311$	2.39525e6			1.40426			0.702132	+	0.712046i	$0.252231\pi$
$312$		0			0
$313$	−1.06455e6	+	1.84385e6i	−0.614193	+	1.06381i	0.376332	+	0.926485i	$0.377185\pi$
$313$	−1.06455e6	+	1.84385e6i	−0.614193	+	1.06381i	−0.990525	+	0.137329i	$0.956148\pi$
$314$		0			0
$315$	−1.13373e7			−6.43773
$316$		0			0
$317$	−399285.	+	691581.i	−0.223169	+	0.386541i	−0.955769	−	0.294120i	$-0.904974\pi$
$317$	−399285.	+	691581.i	−0.223169	+	0.386541i	0.732599	+	0.680660i	$0.238307\pi$
$318$		0			0
$319$	100605.	−	174254.i	0.0553535	−	0.0958750i
$320$		0			0
$321$	−3.33378e6	−	5.77428e6i	−1.80582	−	3.12777i
$322$		0			0
$323$	860657.	−	258500.i	0.459012	−	0.137865i
$324$		0			0
$325$	602135.	+	1.04293e6i	0.316217	+	0.547704i
$326$		0			0
$327$	−756075.	+	1.30956e6i	−0.391017	+	0.677261i
$328$		0			0
$329$	2.21697e6	−	3.83991e6i	1.12920	−	1.95583i
$330$		0			0
$331$	−224790.			−0.112773			−0.0563867	−	0.998409i	$-0.517958\pi$
$331$	−224790.			−0.112773			−0.0563867	+	0.998409i	$0.517958\pi$
$332$		0			0
$333$	−965819.	+	1.67285e6i	−0.477293	+	0.826696i
$334$		0			0
$335$	−1.95226e6			−0.950444
$336$		0			0
$337$	1.02795e6	+	1.78046e6i	0.493056	+	0.853998i	0.999968	−	0.00799964i	$-0.00254639\pi$
$337$	1.02795e6	+	1.78046e6i	0.493056	+	0.853998i	−0.506912	+	0.861998i	$0.669213\pi$
$338$		0			0
$339$	1.68260e6	+	2.91435e6i	0.795209	+	1.37734i
$340$		0			0
$341$	324329.			0.151043
$342$		0			0
$343$	7.58183e6			3.47967
$344$		0			0
$345$	2.55792e6	+	4.43046e6i	1.15702	+	2.00401i
$346$		0			0
$347$	−1.48248e6	−	2.56773e6i	−0.660946	−	1.14479i	−0.980368	−	0.197179i	$-0.936822\pi$
$347$	−1.48248e6	−	2.56773e6i	−0.660946	−	1.14479i	0.319422	−	0.947613i	$-0.396511\pi$
$348$		0			0
$349$	2.25013e6			0.988883			0.494441	−	0.869211i	$-0.335373\pi$
$349$	2.25013e6			0.988883			0.494441	+	0.869211i	$0.335373\pi$
$350$		0			0
$351$	3.52438e6	−	6.10441e6i	1.52692	−	2.64470i
$352$		0			0
$353$	−1.72711e6			−0.737706			−0.368853	−	0.929488i	$-0.620249\pi$
$353$	−1.72711e6			−0.737706			−0.368853	+	0.929488i	$0.620249\pi$
$354$		0			0
$355$	1.19394e6	−	2.06797e6i	0.502820	−	0.870910i
$356$		0			0
$357$	2.12919e6	−	3.68787e6i	0.884187	−	1.53146i
$358$		0			0
$359$	−526967.	−	912734.i	−0.215798	−	0.373773i	0.737721	−	0.675106i	$-0.235902\pi$
$359$	−526967.	−	912734.i	−0.215798	−	0.373773i	−0.953519	+	0.301332i	$0.902569\pi$
$360$		0			0
$361$	−2.21470e6	−	1.10732e6i	−0.894431	−	0.447205i
$362$		0			0
$363$	2.26525e6	+	3.92352e6i	0.902296	+	1.56282i
$364$		0			0
$365$	640529.	−	1.10943e6i	0.251656	−	0.435881i
$366$		0			0
$367$	−1.90021e6	+	3.29126e6i	−0.736438	+	1.27555i	0.217651	+	0.976027i	$0.430160\pi$
$367$	−1.90021e6	+	3.29126e6i	−0.736438	+	1.27555i	−0.954089	+	0.299522i	$0.903173\pi$
$368$		0			0
$369$	1.57200e6			0.601018
$370$		0			0
$371$	−3.20791e6	+	5.55627e6i	−1.21001	+	2.09579i
$372$		0			0
$373$	−1.16264e6			−0.432685			−0.216342	−	0.976318i	$-0.569413\pi$
$373$	−1.16264e6			−0.432685			−0.216342	+	0.976318i	$0.569413\pi$
$374$		0			0
$375$	−1.23141e6	−	2.13287e6i	−0.452195	−	0.783225i
$376$		0			0
$377$	−703663.	−	1.21878e6i	−0.254983	−	0.441643i
$378$		0			0
$379$	−1.49509e6			−0.534648			−0.267324	−	0.963607i	$-0.586139\pi$
$379$	−1.49509e6			−0.534648			−0.267324	+	0.963607i	$0.586139\pi$
$380$		0			0
$381$	1.37330e6			0.484678
$382$		0			0
$383$	−2.52086e6	−	4.36626e6i	−0.878115	−	1.52094i	−0.853407	−	0.521246i	$-0.825467\pi$
$383$	−2.52086e6	−	4.36626e6i	−0.878115	−	1.52094i	−0.0247088	−	0.999695i	$-0.507866\pi$
$384$		0			0
$385$	791634.	+	1.37115e6i	0.272190	+	0.471448i
$386$		0			0
$387$	3.08895e6			1.04842
$388$		0			0
$389$	612495.	−	1.06087e6i	0.205224	−	0.355459i	−0.744980	−	0.667087i	$-0.767541\pi$
$389$	612495.	−	1.06087e6i	0.205224	−	0.355459i	0.950204	+	0.311628i	$0.100874\pi$
$390$		0			0
$391$	−1.38692e6			−0.458785
$392$		0			0
$393$	4.20350e6	−	7.28067e6i	1.37287	−	2.37788i
$394$		0			0
$395$	−2.93980e6	+	5.09188e6i	−0.948036	+	1.64205i
$396$		0			0
$397$	−639677.	−	1.10795e6i	−0.203697	−	0.352813i	0.746020	−	0.665924i	$-0.231962\pi$
$397$	−639677.	−	1.10795e6i	−0.203697	−	0.352813i	−0.949717	+	0.313110i	$0.898629\pi$
$398$		0			0
$399$	−1.12376e7	+	3.37522e6i	−3.53378	+	1.06138i
$400$		0			0
$401$	−473386.	−	819928.i	−0.147013	−	0.254633i	0.783109	−	0.621884i	$-0.213632\pi$
$401$	−473386.	−	819928.i	−0.147013	−	0.254633i	−0.930122	+	0.367251i	$0.880299\pi$
$402$		0			0
$403$	1.13422e6	−	1.96453e6i	0.347885	−	0.602555i
$404$		0			0
$405$	6.59838e6	−	1.14287e7i	1.99894	−	3.46226i
$406$		0			0
$407$	269756.			0.0807208
$408$		0			0
$409$	−1.78713e6	+	3.09540e6i	−0.528260	+	0.914974i	0.471197	+	0.882028i	$0.343822\pi$
$409$	−1.78713e6	+	3.09540e6i	−0.528260	+	0.914974i	−0.999457	+	0.0329456i	$0.989511\pi$
$410$		0			0
$411$	8.50856e6			2.48457
$412$		0			0
$413$	−2.96644e6	−	5.13803e6i	−0.855777	−	1.48225i
$414$		0			0
$415$	1.43538e6	+	2.48616e6i	0.409117	+	0.708611i
$416$		0			0
$417$	−5.24984e6			−1.47845
$418$		0			0
$419$	−4.64582e6			−1.29279			−0.646395	−	0.763003i	$-0.723724\pi$
$419$	−4.64582e6			−1.29279			−0.646395	+	0.763003i	$0.723724\pi$
$420$		0			0
$421$	1.59986e6	+	2.77104e6i	0.439923	+	0.761970i	0.997683	−	0.0680329i	$-0.0216723\pi$
$421$	1.59986e6	+	2.77104e6i	0.439923	+	0.761970i	−0.557760	+	0.830002i	$0.688339\pi$
$422$		0			0
$423$	5.53877e6	+	9.59342e6i	1.50509	+	2.60689i
$424$		0			0
$425$	−1.11697e6			−0.299963
$426$		0			0
$427$	2.49439e6	−	4.32041e6i	0.662056	−	1.14671i
$428$		0			0
$429$	−1.60187e6			−0.420227
$430$		0			0
$431$	2.46054e6	−	4.26178e6i	0.638025	−	1.10509i	−0.347841	−	0.937553i	$-0.613085\pi$
$431$	2.46054e6	−	4.26178e6i	0.638025	−	1.10509i	0.985866	−	0.167537i	$-0.0535815\pi$
$432$		0			0
$433$	1.48931e6	−	2.57956e6i	0.381738	−	0.661189i	−0.609573	−	0.792730i	$-0.708659\pi$
$433$	1.48931e6	−	2.57956e6i	0.381738	−	0.661189i	0.991311	+	0.131541i	$0.0419924\pi$
$434$		0			0
$435$	−2.40740e6	−	4.16973e6i	−0.609992	−	1.05654i
$436$		0			0
$437$	2.78199e6	+	2.61999e6i	0.696871	+	0.656291i
$438$		0			0
$439$	1.08758e6	+	1.88374e6i	0.269339	+	0.466509i	0.968691	−	0.248268i	$-0.0798614\pi$
$439$	1.08758e6	+	1.88374e6i	0.269339	+	0.466509i	−0.699352	+	0.714777i	$0.746528\pi$
$440$		0			0
$441$	−1.47684e7	+	2.55795e7i	−3.61606	+	6.26320i
$442$		0			0
$443$	−189407.	+	328062.i	−0.0458549	+	0.0794231i	−0.888042	−	0.459763i	$-0.847935\pi$
$443$	−189407.	+	328062.i	−0.0458549	+	0.0794231i	0.842187	+	0.539186i	$0.181268\pi$
$444$		0			0
$445$	−3.94058e6			−0.943323
$446$		0			0
$447$	−2.39760e6	+	4.15276e6i	−0.567554	+	0.983032i
$448$		0			0
$449$	−5.64067e6			−1.32043			−0.660214	−	0.751077i	$-0.729534\pi$
$449$	−5.64067e6			−1.32043			−0.660214	+	0.751077i	$0.729534\pi$
$450$		0			0
$451$	−109766.	−	190121.i	−0.0254114	−	0.0440138i
$452$		0			0
$453$	6.64422e6	+	1.15081e7i	1.52124	+	2.63487i
$454$		0			0
$455$	1.10738e7			2.50766
$456$		0			0
$457$	−317551.			−0.0711252			−0.0355626	−	0.999367i	$-0.511322\pi$
$457$	−317551.			−0.0711252			−0.0355626	+	0.999367i	$0.511322\pi$
$458$		0			0
$459$	3.26888e6	+	5.66187e6i	0.724215	+	1.25438i
$460$		0			0
$461$	1.63141e6	+	2.82569e6i	0.357529	+	0.619259i	0.987547	−	0.157322i	$-0.0502859\pi$
$461$	1.63141e6	+	2.82569e6i	0.357529	+	0.619259i	−0.630018	+	0.776580i	$0.716953\pi$
$462$		0			0
$463$	−7.65368e6			−1.65927			−0.829636	−	0.558305i	$-0.811452\pi$
$463$	−7.65368e6			−1.65927			−0.829636	+	0.558305i	$0.811452\pi$
$464$		0			0
$465$	3.88044e6	−	6.72113e6i	0.832241	−	1.44148i
$466$		0			0
$467$	885237.			0.187831			0.0939155	−	0.995580i	$-0.470062\pi$
$467$	885237.			0.187831			0.0939155	+	0.995580i	$0.470062\pi$
$468$		0			0
$469$	−3.45528e6	+	5.98472e6i	−0.725356	+	1.25635i
$470$		0			0
$471$	−809439.	+	1.40199e6i	−0.168125	+	0.291201i
$472$		0			0
$473$	−215689.	−	373583.i	−0.0443276	−	0.0767777i
$474$		0			0
$475$	2.24050e6	+	2.11003e6i	0.455628	+	0.429096i
$476$		0			0
$477$	−8.01448e6	−	1.38815e7i	−1.61280	−	2.79345i
$478$		0			0
$479$	2.58332e6	−	4.47445e6i	0.514447	−	0.891047i	−0.485413	−	0.874285i	$-0.661331\pi$
$479$	2.58332e6	−	4.47445e6i	0.514447	−	0.891047i	0.999859	−	0.0167625i	$-0.00533592\pi$
$480$		0			0
$481$	943375.	−	1.63397e6i	0.185918	−	0.322020i
$482$		0			0
$483$	1.81089e7			3.53203
$484$		0			0
$485$	−951502.	+	1.64805e6i	−0.183677	+	0.318138i
$486$		0			0
$487$	−4.53740e6			−0.866931			−0.433465	−	0.901170i	$-0.642709\pi$
$487$	−4.53740e6			−0.866931			−0.433465	+	0.901170i	$0.642709\pi$
$488$		0			0
$489$	−3.06988e6	−	5.31719e6i	−0.580563	−	1.00556i
$490$		0			0
$491$	−4.58323e6	−	7.93839e6i	−0.857963	−	1.48603i	−0.873869	−	0.486161i	$-0.838397\pi$
$491$	−4.58323e6	−	7.93839e6i	−0.857963	−	1.48603i	0.0159066	−	0.999873i	$-0.494937\pi$
$492$		0			0
$493$	1.30530e6			0.241876
$494$		0			0
$495$	−3.95556e6			−0.725596
$496$		0			0
$497$	−4.22628e6	−	7.32014e6i	−0.767481	−	1.32932i
$498$		0			0
$499$	−4.86531e6	−	8.42697e6i	−0.874700	−	1.51503i	−0.857081	−	0.515181i	$-0.827725\pi$
$499$	−4.86531e6	−	8.42697e6i	−0.874700	−	1.51503i	−0.0176190	−	0.999845i	$-0.505609\pi$
$500$		0			0
$501$	8.07952e6			1.43811
$502$		0			0
$503$	−5.37084e6	+	9.30257e6i	−0.946503	+	1.63939i	−0.193791	+	0.981043i	$0.562078\pi$
$503$	−5.37084e6	+	9.30257e6i	−0.946503	+	1.63939i	−0.752713	+	0.658349i	$0.771255\pi$
$504$		0			0
$505$	−8.64888e6			−1.50915
$506$		0			0
$507$	−115579.	+	200189.i	−0.0199692	+	0.0345876i
$508$		0			0
$509$	−2.77946e6	+	4.81416e6i	−0.475516	+	0.823618i	−0.999607	−	0.0280444i	$-0.991072\pi$
$509$	−2.77946e6	+	4.81416e6i	−0.475516	+	0.823618i	0.524090	+	0.851663i	$0.324405\pi$
$510$		0			0
$511$	−2.26733e6	−	3.92712e6i	−0.384115	−	0.665307i
$512$		0			0
$513$	4.13870e6	−	1.75322e7i	0.694338	−	2.94132i
$514$		0			0
$515$	−4.39294e6	−	7.60880e6i	−0.729856	−	1.26415i
$516$		0			0
$517$	773497.	−	1.33974e6i	0.127272	−	0.220441i
$518$		0			0
$519$	−7.75785e6	+	1.34370e7i	−1.26422	+	2.18970i
$520$		0			0
$521$	−2.44377e6			−0.394427			−0.197213	−	0.980361i	$-0.563189\pi$
$521$	−2.44377e6			−0.394427			−0.197213	+	0.980361i	$0.563189\pi$
$522$		0			0
$523$	2.06842e6	−	3.58260e6i	0.330662	−	0.572723i	−0.651980	−	0.758236i	$-0.726061\pi$
$523$	2.06842e6	−	3.58260e6i	0.330662	−	0.572723i	0.982642	+	0.185513i	$0.0593948\pi$
$524$		0			0
$525$	1.45842e7			2.30931
$526$		0			0
$527$	1.05200e6	+	1.82211e6i	0.165002	+	0.285791i
$528$		0			0
$529$	269211.	+	466288.i	0.0418268	+	0.0724461i
$530$		0			0
$531$	1.48224e7			2.28130
$532$		0			0
$533$	−1.53547e6			−0.234112
$534$		0			0
$535$	8.04093e6	+	1.39273e7i	1.21457	+	2.10369i
$536$		0			0
$537$	200825.	+	347839.i	0.0300526	+	0.0520526i
$538$		0			0
$539$	4.12485e6			0.611555
$540$		0			0
$541$	332076.	−	575172.i	0.0487803	−	0.0844899i	−0.840604	−	0.541650i	$-0.817800\pi$
$541$	332076.	−	575172.i	0.0487803	−	0.0844899i	0.889385	+	0.457160i	$0.151133\pi$
$542$		0			0
$543$	2.18517e6			0.318043
$544$		0			0
$545$	1.82362e6	−	3.15860e6i	0.262992	−	0.455516i
$546$		0			0
$547$	−2.27290e6	+	3.93678e6i	−0.324797	+	0.562565i	−0.981471	−	0.191609i	$-0.938629\pi$
$547$	−2.27290e6	+	3.93678e6i	−0.324797	+	0.562565i	0.656674	+	0.754174i	$0.271963\pi$
$548$		0			0
$549$	6.23186e6	+	1.07939e7i	0.882443	+	1.52844i
$550$		0			0
$551$	−2.61828e6	−	2.46581e6i	−0.367398	−	0.346004i
$552$		0			0
$553$	1.04062e7	+	1.80241e7i	1.44704	+	2.50634i
$554$		0			0
$555$	3.22751e6	−	5.59021e6i	0.444769	−	0.770363i
$556$		0			0
$557$	4.10469e6	−	7.10954e6i	0.560586	−	0.970964i	−0.436859	−	0.899530i	$-0.643909\pi$
$557$	4.10469e6	−	7.10954e6i	0.560586	−	0.970964i	0.997445	−	0.0714342i	$-0.0227576\pi$
$558$		0			0
$559$	−3.01717e6			−0.408386
$560$		0			0
$561$	742871.	−	1.28669e6i	0.0996566	−	0.172610i
$562$		0			0
$563$	−1.32458e7			−1.76119			−0.880597	−	0.473866i	$-0.842858\pi$
$563$	−1.32458e7			−1.76119			−0.880597	+	0.473866i	$0.842858\pi$
$564$		0			0
$565$	−4.05835e6	−	7.02927e6i	−0.534846	−	0.926380i
$566$		0			0
$567$	−2.33567e7	−	4.04550e7i	−3.05109	−	5.28464i
$568$		0			0
$569$	1.11112e7			1.43873			0.719365	−	0.694632i	$-0.244433\pi$
$569$	1.11112e7			1.43873			0.719365	+	0.694632i	$0.244433\pi$
$570$		0			0
$571$	1.44176e7			1.85055			0.925277	−	0.379291i	$-0.123832\pi$
$571$	1.44176e7			1.85055			0.925277	+	0.379291i	$0.123832\pi$
$572$		0			0
$573$	7.72172e6	+	1.33744e7i	0.982489	+	1.70172i
$574$		0			0
$575$	−2.37497e6	−	4.11356e6i	−0.299563	−	0.518858i
$576$		0			0
$577$	−4.63470e6			−0.579538			−0.289769	−	0.957097i	$-0.593578\pi$
$577$	−4.63470e6			−0.579538			−0.289769	+	0.957097i	$0.593578\pi$
$578$		0			0
$579$	366782.	−	635285.i	0.0454686	−	0.0787539i
$580$		0			0
$581$	1.01618e7			1.24891
$582$		0			0
$583$	−1.11923e6	+	1.93857e6i	−0.136380	+	0.236217i
$584$		0			0
$585$	−1.38331e7	+	2.39597e7i	−1.67121	+	2.89462i
$586$		0			0
$587$	−87378.3	−	151344.i	−0.0104667	−	0.0181288i	0.860745	−	0.509037i	$-0.169998\pi$
$587$	−87378.3	−	151344.i	−0.0104667	−	0.0181288i	−0.871211	+	0.490908i	$0.836665\pi$
$588$		0			0
$589$	1.33193e6	−	5.64224e6i	0.158195	−	0.670137i
$590$		0			0
$591$	5.36854e6	+	9.29858e6i	0.632248	+	1.09509i
$592$		0			0
$593$	63610.1	−	110176.i	0.00742830	−	0.0128662i	−0.862287	−	0.506419i	$-0.830969\pi$
$593$	63610.1	−	110176.i	0.00742830	−	0.0128662i	0.869716	+	0.493553i	$0.164302\pi$
$594$		0			0
$595$	−5.13551e6	+	8.89497e6i	−0.594691	+	1.03003i
$596$		0			0
$597$	−2.40403e6			−0.276061
$598$		0			0
$599$	8.00216e6	−	1.38601e7i	0.911255	−	1.57834i	0.0989618	−	0.995091i	$-0.468448\pi$
$599$	8.00216e6	−	1.38601e7i	0.911255	−	1.57834i	0.812293	−	0.583249i	$-0.198219\pi$
$600$		0			0
$601$	1.52423e7			1.72134			0.860668	−	0.509166i	$-0.170046\pi$
$601$	1.52423e7			1.72134			0.860668	+	0.509166i	$0.170046\pi$
$602$		0			0
$603$	−8.63250e6	−	1.49519e7i	−0.966815	−	1.67457i
$604$		0			0
$605$	−5.46367e6	−	9.46336e6i	−0.606871	−	1.05113i
$606$		0			0
$607$	1.49576e7			1.64774			0.823870	−	0.566778i	$-0.191810\pi$
$607$	1.49576e7			1.64774			0.823870	+	0.566778i	$0.191810\pi$
$608$		0			0
$609$	−1.70432e7			−1.86213
$610$		0			0
$611$	−5.41005e6	−	9.37049e6i	−0.586271	−	1.01545i
$612$		0			0
$613$	889245.	+	1.54022e6i	0.0955807	+	0.165551i	0.909851	−	0.414936i	$-0.136196\pi$
$613$	889245.	+	1.54022e6i	0.0955807	+	0.165551i	−0.814270	+	0.580486i	$0.802863\pi$
$614$		0			0
$615$	−5.25322e6			−0.560064
$616$		0			0
$617$	7.97293e6	−	1.38095e7i	0.843150	−	1.46038i	−0.0440683	−	0.999029i	$-0.514032\pi$
$617$	7.97293e6	−	1.38095e7i	0.843150	−	1.46038i	0.887218	−	0.461350i	$-0.152635\pi$
$618$		0			0
$619$	−1.53524e7			−1.61046			−0.805231	−	0.592962i	$-0.797959\pi$
$619$	−1.53524e7			−1.61046			−0.805231	+	0.592962i	$0.797959\pi$
$620$		0			0
$621$	−1.39010e7	+	2.40773e7i	−1.44650	+	2.50541i
$622$		0			0
$623$	−6.97438e6	+	1.20800e7i	−0.719922	+	1.24694i
$624$		0			0
$625$	6.02615e6	+	1.04376e7i	0.617078	+	1.06881i
$626$		0			0
$627$	−3.92076e6	+	1.17761e6i	−0.398292	+	0.119628i
$628$		0			0
$629$	874985.	+	1.51552e6i	0.0881807	+	0.152734i
$630$		0			0
$631$	1.84277e6	−	3.19177e6i	0.184246	−	0.319123i	−0.759076	−	0.651002i	$-0.774349\pi$
$631$	1.84277e6	−	3.19177e6i	0.184246	−	0.319123i	0.943322	+	0.331879i	$0.107682\pi$
$632$		0			0
$633$	−6.96173e6	+	1.20581e7i	−0.690570	+	1.19610i
$634$		0			0
$635$	−3.31234e6			−0.325988
$636$		0			0
$637$	1.44252e7	−	2.49851e7i	1.40855	−	2.43968i
$638$		0			0
$639$	2.11175e7			2.04592
$640$		0			0
$641$	2.60486e6	+	4.51176e6i	0.250403	+	0.433711i	0.963637	−	0.267215i	$-0.0861035\pi$
$641$	2.60486e6	+	4.51176e6i	0.250403	+	0.433711i	−0.713234	+	0.700926i	$0.752770\pi$
$642$		0			0
$643$	3.62947e6	+	6.28642e6i	0.346191	+	0.599620i	0.985569	−	0.169272i	$-0.0541417\pi$
$643$	3.62947e6	+	6.28642e6i	0.346191	+	0.599620i	−0.639379	+	0.768892i	$0.720808\pi$
$644$		0			0
$645$	−1.03225e7			−0.976976
$646$		0			0
$647$	−8.49406e6			−0.797728			−0.398864	−	0.917010i	$-0.630595\pi$
$647$	−8.49406e6			−0.797728			−0.398864	+	0.917010i	$0.630595\pi$
$648$		0			0
$649$	−1.03499e6	−	1.79265e6i	−0.0964545	−	0.167064i
$650$		0			0
$651$	−1.37359e7	−	2.37912e7i	−1.27029	−	2.20021i
$652$		0			0
$653$	−1.16393e7			−1.06818			−0.534089	−	0.845428i	$-0.679345\pi$
$653$	−1.16393e7			−1.06818			−0.534089	+	0.845428i	$0.679345\pi$
$654$		0			0
$655$	−1.01386e7	+	1.75606e7i	−0.923372	+	1.59933i
$656$		0			0
$657$	1.13291e7			1.02396
$658$		0			0
$659$	−9.86735e6	+	1.70907e7i	−0.885089	+	1.53302i	−0.0394769	+	0.999220i	$0.512569\pi$
$659$	−9.86735e6	+	1.70907e7i	−0.885089	+	1.53302i	−0.845612	+	0.533798i	$0.820764\pi$
$660$		0			0
$661$	7.97821e6	−	1.38187e7i	0.710235	−	1.23016i	−0.254534	−	0.967064i	$-0.581922\pi$
$661$	7.97821e6	−	1.38187e7i	0.710235	−	1.23016i	0.964769	−	0.263099i	$-0.0847446\pi$
$662$		0			0
$663$	−5.19585e6	−	8.99947e6i	−0.459063	−	0.795121i
$664$		0			0
$665$	2.71045e7	−	8.14088e6i	2.37677	−	0.713867i
$666$		0			0
$667$	2.77542e6	+	4.80717e6i	0.241554	+	0.418384i
$668$		0			0
$669$	−1.92128e7	+	3.32775e7i	−1.65968	+	2.87465i
$670$		0			0
$671$	870288.	−	1.50738e6i	0.0746202	−	0.129246i
$672$		0			0
$673$	1.18685e7			1.01008			0.505041	−	0.863096i	$-0.331477\pi$
$673$	1.18685e7			1.01008			0.505041	+	0.863096i	$0.331477\pi$
$674$		0			0
$675$	−1.11953e7	+	1.93908e7i	−0.945750	+	1.63809i
$676$		0			0
$677$	−1.13643e7			−0.952952			−0.476476	−	0.879188i	$-0.658086\pi$
$677$	−1.13643e7			−0.952952			−0.476476	+	0.879188i	$0.658086\pi$
$678$		0			0
$679$	3.36810e6	+	5.83372e6i	0.280356	+	0.485591i
$680$		0			0
$681$	1.08374e6	+	1.87709e6i	0.0895482	+	0.155102i
$682$		0			0
$683$	1.33134e7			1.09204			0.546018	−	0.837774i	$-0.316143\pi$
$683$	1.33134e7			1.09204			0.546018	+	0.837774i	$0.316143\pi$
$684$		0			0
$685$	−2.05223e7			−1.67109
$686$		0			0
$687$	1.85051e7	+	3.20517e7i	1.49589	+	2.59095i
$688$		0			0
$689$	7.82824e6	+	1.35589e7i	0.628226	+	1.08812i
$690$		0			0
$691$	1.77578e7			1.41480			0.707400	−	0.706813i	$-0.249868\pi$
$691$	1.77578e7			1.41480			0.707400	+	0.706813i	$0.249868\pi$
$692$		0			0
$693$	−7.00088e6	+	1.21259e7i	−0.553757	+	0.959136i
$694$		0			0
$695$	1.26624e7			0.994381
$696$		0			0
$697$	712079.	−	1.23336e6i	0.0555196	−	0.0961628i
$698$		0			0
$699$	1.60958e7	−	2.78787e7i	1.24600	−	2.15814i
$700$		0			0
$701$	2.58452e6	+	4.47652e6i	0.198648	+	0.344069i	0.948090	−	0.318001i	$-0.103012\pi$
$701$	2.58452e6	+	4.47652e6i	0.198648	+	0.344069i	−0.749442	+	0.662070i	$0.769678\pi$
$702$		0			0
$703$	1.10781e6	−	4.69286e6i	0.0845429	−	0.358137i
$704$		0			0
$705$	−1.85091e7	−	3.20586e7i	−1.40253	−	2.42925i
$706$		0			0
$707$	−1.53075e7	+	2.65134e7i	−1.15175	+	1.99488i
$708$		0			0
$709$	6.35081e6	−	1.09999e7i	0.474476	−	0.821816i	−0.525097	−	0.851042i	$-0.675971\pi$
$709$	6.35081e6	−	1.09999e7i	0.474476	−	0.821816i	0.999573	+	0.0292265i	$0.00930441\pi$
$710$		0			0
$711$	−5.19967e7			−3.85746
$712$		0			0
$713$	−4.47366e6	+	7.74860e6i	−0.329563	+	0.570820i
$714$		0			0
$715$	3.86364e6			0.282638
$716$		0			0
$717$	−1.37178e7	−	2.37600e7i	−0.996524	−	1.72603i
$718$		0			0
$719$	1.17643e7	+	2.03763e7i	0.848678	+	1.46995i	0.882388	+	0.470522i	$0.155934\pi$
$719$	1.17643e7	+	2.03763e7i	0.848678	+	1.46995i	−0.0337101	+	0.999432i	$0.510732\pi$
$720$		0			0
$721$	−3.11000e7			−2.22804
$722$		0			0
$723$	2.94021e6			0.209186
$724$		0			0
$725$	2.23520e6	+	3.87149e6i	0.157933	+	0.273548i
$726$		0			0
$727$	1.08765e7	+	1.88387e7i	0.763229	+	1.32195i	0.941178	+	0.337911i	$0.109720\pi$
$727$	1.08765e7	+	1.88387e7i	0.763229	+	1.32195i	−0.177949	+	0.984040i	$0.556946\pi$
$728$		0			0
$729$	3.44949e7			2.40401
$730$		0			0
$731$	1.39922e6	−	2.42352e6i	0.0968485	−	0.167746i
$732$		0			0
$733$	−9.80139e6			−0.673795			−0.336897	−	0.941541i	$-0.609378\pi$
$733$	−9.80139e6			−0.673795			−0.336897	+	0.941541i	$0.609378\pi$
$734$		0			0
$735$	4.93519e7	−	8.54800e7i	3.36965	−	5.83641i
$736$		0			0
$737$	−1.20554e6	+	2.08806e6i	−0.0817548	+	0.141603i
$738$		0			0
$739$	−7.08883e6	−	1.22782e7i	−0.477489	−	0.827035i	0.522178	−	0.852837i	$-0.325120\pi$
$739$	−7.08883e6	−	1.22782e7i	−0.477489	−	0.827035i	−0.999667	+	0.0258011i	$0.991786\pi$
$740$		0			0
$741$	−6.57842e6	+	2.78672e7i	−0.440125	+	1.86444i
$742$		0			0
$743$	−3.04168e6	−	5.26834e6i	−0.202135	−	0.350108i	0.747081	−	0.664733i	$-0.231455\pi$
$743$	−3.04168e6	−	5.26834e6i	−0.202135	−	0.350108i	−0.949216	+	0.314625i	$0.898121\pi$
$744$		0			0
$745$	5.78289e6	−	1.00163e7i	0.381728	−	0.661173i
$746$		0			0
$747$	−1.26939e7	+	2.19865e7i	−0.832327	+	1.44163i
$748$		0			0
$749$	5.69261e7			3.70772
$750$		0			0
$751$	6.05235e6	−	1.04830e7i	0.391584	−	0.678243i	−0.601075	−	0.799193i	$-0.705261\pi$
$751$	6.05235e6	−	1.04830e7i	0.391584	−	0.678243i	0.992659	+	0.120950i	$0.0385941\pi$
$752$		0			0
$753$	1.12318e7			0.721878
$754$		0			0
$755$	−1.60255e7	−	2.77571e7i	−1.02316	−	1.77217i
$756$		0			0
$757$	−837126.	−	1.44994e6i	−0.0530947	−	0.0919627i	0.838257	−	0.545276i	$-0.183575\pi$
$757$	−837126.	−	1.44994e6i	−0.0530947	−	0.0919627i	−0.891351	+	0.453313i	$0.850242\pi$
$758$		0			0
$759$	6.31817e6			0.398095
$760$		0			0
$761$	−1.71108e7			−1.07105			−0.535525	−	0.844520i	$-0.679886\pi$
$761$	−1.71108e7			−1.07105			−0.535525	+	0.844520i	$0.679886\pi$
$762$		0			0
$763$	−6.45519e6	−	1.11807e7i	−0.401419	−	0.695278i
$764$		0			0
$765$	−1.28303e7	−	2.22227e7i	−0.792653	−	1.37292i
$766$		0			0
$767$	−1.44780e7			−0.888626
$768$		0			0
$769$	−4.88795e6	+	8.46617e6i	−0.298065	+	0.516263i	−0.975693	−	0.219141i	$-0.929674\pi$
$769$	−4.88795e6	+	8.46617e6i	−0.298065	+	0.516263i	0.677628	+	0.735404i	$0.263008\pi$
$770$		0			0
$771$	3.26645e7			1.97897
$772$		0			0
$773$	−6.30084e6	+	1.09134e7i	−0.379271	+	0.656916i	−0.990956	−	0.134185i	$-0.957158\pi$
$773$	−6.30084e6	+	1.09134e7i	−0.379271	+	0.656916i	0.611686	+	0.791101i	$0.290492\pi$
$774$		0			0
$775$	−3.60289e6	+	6.24039e6i	−0.215475	+	0.373214i
$776$		0			0
$777$	−1.14246e7	−	1.97880e7i	−0.678875	−	1.17585i
$778$		0			0
$779$	−3.75825e6	+	1.12880e6i	−0.221892	+	0.0666457i
$780$		0			0
$781$	−1.47454e6	−	2.55398e6i	−0.0865027	−	0.149827i
$782$		0			0
$783$	1.30830e7	−	2.26604e7i	0.762610	−	1.32088i
$784$		0			0
$785$	1.95233e6	−	3.38154e6i	0.113078	−	0.195857i
$786$		0			0
$787$	−1.91406e7			−1.10159			−0.550795	−	0.834641i	$-0.685675\pi$
$787$	−1.91406e7			−1.10159			−0.550795	+	0.834641i	$0.685675\pi$
$788$		0			0
$789$	−8.15667e6	+	1.41278e7i	−0.466466	+	0.807944i
$790$		0			0
$791$	−2.87312e7			−1.63273
$792$		0			0
$793$	−6.08704e6	−	1.05431e7i	−0.343735	−	0.595366i
$794$		0			0
$795$	2.67823e7	+	4.63882e7i	1.50290	+	2.60309i
$796$		0			0
$797$	−1.28733e6			−0.0717865			−0.0358932	−	0.999356i	$-0.511428\pi$
$797$	−1.28733e6			−0.0717865			−0.0358932	+	0.999356i	$0.511428\pi$
$798$		0			0
$799$	1.00357e7			0.556136
$800$		0			0
$801$	−1.74244e7	−	3.01800e7i	−0.959572	−	1.66203i
$802$		0			0
$803$	−791066.	−	1.37017e6i	−0.0432936	−	0.0749867i
$804$		0			0
$805$	−4.36779e7			−2.37559
$806$		0			0
$807$	2.54127e7	−	4.40161e7i	1.37362	−	2.37918i
$808$		0			0
$809$	2.73676e7			1.47016			0.735082	−	0.677978i	$-0.237144\pi$
$809$	2.73676e7			1.47016			0.735082	+	0.677978i	$0.237144\pi$
$810$		0			0
$811$	−3.68597e6	+	6.38429e6i	−0.196789	+	0.340848i	−0.947485	−	0.319799i	$-0.896385\pi$
$811$	−3.68597e6	+	6.38429e6i	−0.196789	+	0.340848i	0.750697	+	0.660647i	$0.229718\pi$
$812$		0			0
$813$	1.33518e7	−	2.31260e7i	0.708459	−	1.22709i
$814$		0			0
$815$	7.40441e6	+	1.28248e7i	0.390478	+	0.676327i
$816$		0			0
$817$	−7.38488e6	+	2.21806e6i	−0.387069	+	0.116257i
$818$		0			0
$819$	4.89661e7	+	8.48118e7i	2.55086	+	4.41821i
$820$		0			0
$821$	1.13053e7	−	1.95813e7i	0.585360	−	1.01387i	−0.409471	−	0.912323i	$-0.634287\pi$
$821$	1.13053e7	−	1.95813e7i	0.585360	−	1.01387i	0.994830	−	0.101550i	$-0.0323800\pi$
$822$		0			0
$823$	1.42337e7	−	2.46536e7i	0.732520	−	1.26876i	−0.223283	−	0.974754i	$-0.571677\pi$
$823$	1.42337e7	−	2.46536e7i	0.732520	−	1.26876i	0.955803	−	0.294008i	$-0.0949893\pi$
$824$		0			0
$825$	5.08839e6			0.260283
$826$		0			0
$827$	−5.08685e6	+	8.81069e6i	−0.258634	+	0.447967i	−0.965876	−	0.259004i	$-0.916606\pi$
$827$	−5.08685e6	+	8.81069e6i	−0.258634	+	0.447967i	0.707242	+	0.706971i	$0.249939\pi$
$828$		0			0
$829$	4.96805e6			0.251073			0.125536	−	0.992089i	$-0.459935\pi$
$829$	4.96805e6			0.251073			0.125536	+	0.992089i	$0.459935\pi$
$830$		0			0
$831$	1.54440e7	+	2.67498e7i	0.775813	+	1.34375i
$832$		0			0
$833$	1.33794e7	+	2.31738e7i	0.668074	+	1.15714i
$834$		0			0
$835$	−1.94874e7			−0.967250
$836$		0			0
$837$	4.21765e7			2.08093
$838$		0			0
$839$	−5.19839e6	−	9.00387e6i	−0.254955	−	0.441595i	0.709928	−	0.704274i	$-0.248727\pi$
$839$	−5.19839e6	−	9.00387e6i	−0.254955	−	0.441595i	−0.964883	+	0.262679i	$0.915394\pi$
$840$		0			0
$841$	7.64348e6	+	1.32389e7i	0.372650	+	0.645449i
$842$		0			0
$843$	1.25989e7			0.610610
$844$		0			0
$845$	278772.	−	482847.i	0.0134310	−	0.0232631i
$846$		0			0
$847$	−3.86803e7			−1.85260
$848$		0			0
$849$	−883119.	+	1.52961e6i	−0.0420485	+	0.0728301i
$850$		0			0
$851$	−3.72090e6	+	6.44479e6i	−0.176126	+	0.305060i
$852$		0			0
$853$	1.62456e6	+	2.81382e6i	0.0764475	+	0.132411i	0.901715	−	0.432331i	$-0.142309\pi$
$853$	1.62456e6	+	2.81382e6i	0.0764475	+	0.132411i	−0.825267	+	0.564742i	$0.808976\pi$
$854$		0			0
$855$	−1.62443e7	+	6.88135e7i	−0.759953	+	3.21928i
$856$		0			0
$857$	−1.16911e7	−	2.02495e7i	−0.543754	−	0.941810i	−0.998684	−	0.0512826i	$-0.983669\pi$
$857$	−1.16911e7	−	2.02495e7i	−0.543754	−	0.941810i	0.454930	−	0.890527i	$-0.349664\pi$
$858$		0			0
$859$	469598.	−	813368.i	0.0217142	−	0.0376101i	−0.854964	−	0.518687i	$-0.826421\pi$
$859$	469598.	−	813368.i	0.0217142	−	0.0376101i	0.876678	+	0.481077i	$0.159754\pi$
$860$		0			0
$861$	−9.29758e6	+	1.61039e7i	−0.427427	+	0.740326i
$862$		0			0
$863$	−3.88566e7			−1.77598			−0.887989	−	0.459864i	$-0.847898\pi$
$863$	−3.88566e7			−1.77598			−0.887989	+	0.459864i	$0.847898\pi$
$864$		0			0
$865$	1.87116e7	−	3.24094e7i	0.850296	−	1.47276i
$866$		0			0
$867$	−3.23225e7			−1.46035
$868$		0			0
$869$	3.63071e6	+	6.28857e6i	0.163095	+	0.282490i
$870$		0			0
$871$	8.43189e6	+	1.46045e7i	0.376599	+	0.652289i
$872$		0			0
$873$	−1.68294e7			−0.747364
$874$		0			0
$875$	2.10270e7			0.928449
$876$		0			0
$877$	6.05008e6	+	1.04790e7i	0.265621	+	0.460069i	0.967726	−	0.252004i	$-0.0810897\pi$
$877$	6.05008e6	+	1.04790e7i	0.265621	+	0.460069i	−0.702105	+	0.712073i	$0.747756\pi$
$878$		0			0
$879$	−1.73366e7	−	3.00279e7i	−0.756819	−	1.31085i
$880$		0			0
$881$	1.25012e7			0.542642			0.271321	−	0.962489i	$-0.412539\pi$
$881$	1.25012e7			0.542642			0.271321	+	0.962489i	$0.412539\pi$
$882$		0			0
$883$	−1.22509e7	+	2.12191e7i	−0.528767	+	0.915852i	0.470670	+	0.882309i	$0.344012\pi$
$883$	−1.22509e7	+	2.12191e7i	−0.528767	+	0.915852i	−0.999437	+	0.0335424i	$0.989321\pi$
$884$		0			0
$885$	−4.95325e7			−2.12585
$886$		0			0
$887$	3.48831e6	−	6.04194e6i	0.148870	−	0.257850i	−0.781940	−	0.623353i	$-0.785770\pi$
$887$	3.48831e6	−	6.04194e6i	0.148870	−	0.257850i	0.930810	+	0.365503i	$0.119103\pi$
$888$		0			0
$889$	−5.86246e6	+	1.01541e7i	−0.248786	+	0.430910i
$890$		0			0
$891$	−8.14912e6	−	1.41147e7i	−0.343888	−	0.595631i
$892$		0			0
$893$	−2.01304e7	−	1.89582e7i	−0.844742	−	0.795551i
$894$		0			0
$895$	−484380.	−	838971.i	−0.0202129	−	0.0350098i
$896$		0			0
$897$	2.20955e7	−	3.82706e7i	0.916903	−	1.58812i
$898$		0			0
$899$	4.21039e6	−	7.29261e6i	0.173749	−	0.300943i
$900$		0			0
$901$	−1.45215e7			−0.595934
$902$		0			0
$903$	−1.82696e7	+	3.16438e7i	−0.745605	+	1.29143i
$904$		0			0
$905$	−5.27053e6			−0.213911
$906$		0			0
$907$	1.41679e7	+	2.45394e7i	0.571855	+	0.990482i	0.996376	+	0.0850637i	$0.0271094\pi$
$907$	1.41679e7	+	2.45394e7i	0.571855	+	0.990482i	−0.424520	+	0.905418i	$0.639557\pi$
$908$		0			0
$909$	−3.82435e7	−	6.62398e7i	−1.53514	−	2.65894i
$910$		0			0
$911$	−7.34867e6			−0.293368			−0.146684	−	0.989183i	$-0.546860\pi$
$911$	−7.34867e6			−0.293368			−0.146684	+	0.989183i	$0.546860\pi$
$912$		0			0
$913$	3.54545e6			0.140765
$914$		0			0
$915$	−2.08252e7	−	3.60703e7i	−0.822311	−	1.42428i
$916$		0			0
$917$	3.58885e7	+	6.21606e7i	1.40939	+	2.44114i
$918$		0			0
$919$	−1.01362e7			−0.395899			−0.197949	−	0.980212i	$-0.563428\pi$
$919$	−1.01362e7			−0.395899			−0.197949	+	0.980212i	$0.563428\pi$
$920$		0			0
$921$	−7.44849e6	+	1.29012e7i	−0.289347	+	0.501164i
$922$		0			0
$923$	−2.06267e7			−0.796941
$924$		0			0
$925$	−2.99666e6	+	5.19036e6i	−0.115155	+	0.199454i
$926$		0			0
$927$	3.88493e7	−	6.72890e7i	1.48486	−	2.57185i
$928$		0			0
$929$	1.13628e7	+	1.96809e7i	0.431961	+	0.748179i	0.997042	−	0.0768569i	$-0.0244885\pi$
$929$	1.13628e7	+	1.96809e7i	0.431961	+	0.748179i	−0.565081	+	0.825035i	$0.691155\pi$
$930$		0			0
$931$	1.69396e7	−	7.17586e7i	0.640513	−	2.71331i
$932$		0			0
$933$	−3.53932e7	−	6.13028e7i	−1.33111	−	2.30556i
$934$		0			0
$935$	−1.79177e6	+	3.10344e6i	−0.0670275	+	0.116095i
$936$		0			0
$937$	−1.38676e6	+	2.40195e6i	−0.0516005	+	0.0893747i	−0.890672	−	0.454647i	$-0.849766\pi$
$937$	−1.38676e6	+	2.40195e6i	−0.0516005	+	0.0893747i	0.839071	+	0.544021i	$0.183099\pi$
$938$		0			0
$939$	6.29210e7			2.32880
$940$		0			0
$941$	−1.59541e7	+	2.76333e7i	−0.587351	+	1.01732i	0.407227	+	0.913327i	$0.366496\pi$
$941$	−1.59541e7	+	2.76333e7i	−0.587351	+	1.01732i	−0.994578	+	0.103994i	$0.966838\pi$
$942$		0			0
$943$	6.05629e6			0.221782
$944$		0			0
$945$	1.02946e8	+	1.78308e8i	3.74999	+	6.49518i
$946$		0			0
$947$	7.89457e6	+	1.36738e7i	0.286058	+	0.495466i	0.972865	−	0.231373i	$-0.0743218\pi$
$947$	7.89457e6	+	1.36738e7i	0.286058	+	0.495466i	−0.686808	+	0.726839i	$0.740988\pi$
$948$		0			0
$949$	−1.10659e7			−0.398860
$950$		0			0
$951$	2.36000e7			0.846176
$952$		0			0
$953$	8.02282e6	+	1.38959e7i	0.286151	+	0.495628i	0.972888	−	0.231278i	$-0.0742909\pi$
$953$	8.02282e6	+	1.38959e7i	0.286151	+	0.495628i	−0.686737	+	0.726906i	$0.740958\pi$
$954$		0			0
$955$	−1.86244e7	−	3.22585e7i	−0.660808	−	1.14455i
$956$		0			0
$957$	−5.94636e6			−0.209880
$958$		0			0
$959$	−3.63220e7	+	6.29116e7i	−1.27533	+	2.20894i
$960$		0			0
$961$	−1.50558e7			−0.525891
$962$		0			0
$963$	−7.11106e7	+	1.23167e8i	−2.47098	+	4.27986i
$964$		0			0
$965$	−884662.	+	1.53228e6i	−0.0305815	+	0.0529687i
$966$		0			0
$967$	3.12207e6	+	5.40759e6i	0.107368	+	0.185968i	0.914703	−	0.404126i	$-0.132424\pi$
$967$	3.12207e6	+	5.40759e6i	0.107368	+	0.185968i	−0.807335	+	0.590093i	$0.799091\pi$
$968$		0			0
$969$	−1.93334e7	−	1.82075e7i	−0.661451	−	0.622934i
$970$		0			0
$971$	−1.44348e7	−	2.50019e7i	−0.491319	−	0.850990i	0.508631	−	0.860985i	$-0.330152\pi$
$971$	−1.44348e7	−	2.50019e7i	−0.491319	−	0.850990i	−0.999950	+	0.00999502i	$0.996818\pi$
$972$		0			0
$973$	2.24109e7	−	3.88169e7i	0.758888	−	1.31443i
$974$		0			0
$975$	1.77948e7	−	3.08215e7i	0.599490	−	1.03835i
$976$		0			0
$977$	1.53409e6			0.0514179			0.0257089	−	0.999669i	$-0.491816\pi$
$977$	1.53409e6			0.0514179			0.0257089	+	0.999669i	$0.491816\pi$
$978$		0			0
$979$	−2.43335e6	+	4.21468e6i	−0.0811423	+	0.140543i
$980$		0			0
$981$	3.22546e7			1.07009
$982$		0			0
$983$	1.37733e7	+	2.38561e7i	0.454627	+	0.787437i	0.998667	−	0.0516223i	$-0.0164392\pi$
$983$	1.37733e7	+	2.38561e7i	0.454627	+	0.787437i	−0.544040	+	0.839060i	$0.683106\pi$
$984$		0			0
$985$	−1.29487e7	−	2.24278e7i	−0.425241	−	0.736538i
$986$		0			0
$987$	−1.31036e8			−4.28151
$988$		0			0
$989$	1.19005e7			0.386878
$990$		0			0
$991$	1.81799e7	+	3.14885e7i	0.588040	+	1.01851i	0.994489	+	0.104841i	$0.0334334\pi$
$991$	1.81799e7	+	3.14885e7i	0.588040	+	1.01851i	−0.406449	+	0.913673i	$0.633233\pi$
$992$		0			0
$993$	3.32159e6	+	5.75316e6i	0.106899	+	0.185154i
$994$		0			0
$995$	5.79842e6			0.185674
$996$		0			0
$997$	1.15365e7	−	1.99819e7i	0.367568	−	0.636646i	−0.621617	−	0.783322i	$-0.713524\pi$
$997$	1.15365e7	−	1.99819e7i	0.367568	−	0.636646i	0.989185	+	0.146675i	$0.0468572\pi$
$998$		0			0
$999$	3.50798e7			1.11210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.e.a.45.1	✓	18
3.2	odd	2		684.6.k.f.577.2		18
4.3	odd	2		304.6.i.d.273.9		18
19.11	even	3	inner	76.6.e.a.49.1	yes	18
57.11	odd	6		684.6.k.f.505.2		18
76.11	odd	6		304.6.i.d.49.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.e.a.45.1	✓	18	1.1	even	1	trivial
76.6.e.a.49.1	yes	18	19.11	even	3	inner
304.6.i.d.49.9		18	76.11	odd	6
304.6.i.d.273.9		18	4.3	odd	2
684.6.k.f.505.2		18	57.11	odd	6
684.6.k.f.577.2		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.7764 - 25.5935i) q^{3} +(35.6401 + 61.7304i) q^{5} +252.315 q^{7} +(-315.186 + 545.918i) q^{9} +O(q^{10})\)	\(q+(-14.7764 - 25.5935i) q^{3} +(35.6401 + 61.7304i) q^{5} +252.315 q^{7} +(-315.186 + 545.918i) q^{9} +88.0323 q^{11} +(307.862 - 533.232i) q^{13} +(1053.27 - 1824.31i) q^{15} +(285.543 + 494.575i) q^{17} +(361.524 - 1531.47i) q^{19} +(-3728.32 - 6457.64i) q^{21} +(-1214.28 + 2103.20i) q^{23} +(-977.931 + 1693.83i) q^{25} +11447.9 q^{27} +(1142.82 - 1979.43i) q^{29} +3684.20 q^{31} +(-1300.80 - 2253.06i) q^{33} +(8992.54 + 15575.5i) q^{35} +3064.28 q^{37} -18196.4 q^{39} +(-1246.89 - 2159.67i) q^{41} +(-2450.11 - 4243.71i) q^{43} -44933.0 q^{45} +(8786.51 - 15218.7i) q^{47} +46856.0 q^{49} +(8438.61 - 14616.1i) q^{51} +(-12713.9 + 22021.1i) q^{53} +(3137.48 + 5434.27i) q^{55} +(-44537.7 + 13377.0i) q^{57} +(-11756.9 - 20363.5i) q^{59} +(9886.00 - 17123.1i) q^{61} +(-79526.2 + 137743. i) q^{63} +43888.8 q^{65} +(-13694.3 + 23719.2i) q^{67} +71771.0 q^{69} +(-16750.0 - 29011.9i) q^{71} +(-8986.08 - 15564.3i) q^{73} +57801.3 q^{75} +22211.9 q^{77} +(41242.9 + 71434.8i) q^{79} +(-92569.6 - 160335. i) q^{81} +40274.4 q^{83} +(-20353.5 + 35253.4i) q^{85} -67547.4 q^{87} +(-27641.5 + 47876.5i) q^{89} +(77678.2 - 134543. i) q^{91} +(-54439.3 - 94291.7i) q^{93} +(107423. - 32264.7i) q^{95} +(13348.8 + 23120.7i) q^{97} +(-27746.6 + 48058.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9}+O(q^{10}) \) 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9	\( 18 q - 11 q^{3} + 11 q^{5} + 336 q^{7} - 902 q^{9} - 320 q^{11} + 227 q^{13} - 101 q^{15} + 179 q^{17} - 868 q^{19} - 5700 q^{21} - 3425 q^{23} - 7054 q^{25} + 14722 q^{27} - 7349 q^{29} - 9960 q^{31} - 2998 q^{33} + 15888 q^{35} + 26444 q^{37} - 30246 q^{39} - 7311 q^{41} - 8283 q^{43} - 62164 q^{45} + 37603 q^{47} + 124738 q^{49} + 47227 q^{51} - 20337 q^{53} + 716 q^{55} - 57555 q^{57} - 74455 q^{59} - 7569 q^{61} - 52544 q^{63} + 188998 q^{65} - 26177 q^{67} + 116282 q^{69} - 53463 q^{71} - 14103 q^{73} + 120912 q^{75} - 31960 q^{77} + 31825 q^{79} - 21137 q^{81} + 82600 q^{83} - 50787 q^{85} - 339766 q^{87} - 155197 q^{89} - 2800 q^{91} - 46460 q^{93} + 49315 q^{95} + 111241 q^{97} - 193544 q^{99}+O(q^{100}) \) 18 * q - 11 * q^3 + 11 * q^5 + 336 * q^7 - 902 * q^9 - 320 * q^11 + 227 * q^13 - 101 * q^15 + 179 * q^17 - 868 * q^19 - 5700 * q^21 - 3425 * q^23 - 7054 * q^25 + 14722 * q^27 - 7349 * q^29 - 9960 * q^31 - 2998 * q^33 + 15888 * q^35 + 26444 * q^37 - 30246 * q^39 - 7311 * q^41 - 8283 * q^43 - 62164 * q^45 + 37603 * q^47 + 124738 * q^49 + 47227 * q^51 - 20337 * q^53 + 716 * q^55 - 57555 * q^57 - 74455 * q^59 - 7569 * q^61 - 52544 * q^63 + 188998 * q^65 - 26177 * q^67 + 116282 * q^69 - 53463 * q^71 - 14103 * q^73 + 120912 * q^75 - 31960 * q^77 + 31825 * q^79 - 21137 * q^81 + 82600 * q^83 - 50787 * q^85 - 339766 * q^87 - 155197 * q^89 - 2800 * q^91 - 46460 * q^93 + 49315 * q^95 + 111241 * q^97 - 193544 * q^99

Introduction

L-functions

Modular forms

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Database

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