LMFDB - Embedded newform 304.6.i.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,6,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("304.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	304.i (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:	$48.7566812231$
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} - 5 x^{17} - 3057 x^{16} + 14564 x^{15} + 3829838 x^{14} - 15907074 x^{13} + \cdots + 66\!\cdots\!83 $ x^18 - 5x^17 - 3057x^16 + 14564x^15 + 3829838x^14 - 15907074x^13 - 2546775754x^12 + 7879525640x^11 + 976140188391x^10 - 1502012839499x^9 - 219575028272723x^8 - 104014033904304x^7 + 28115925509664606x^6 + 76771209356887914x^5 - 1810997176122162810x^4 - 9301294316540690604x^3 + 37701980111568799233x^2 + 354684213311311368351*x + 668276771042404734183
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$26.3623 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	304.49
Dual form			304.6.i.d.273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.4311 + 21.5314i) q^{3} +(-18.0963 + 31.3437i) q^{5} +208.885 q^{7} +(-187.566 - 324.875i) q^{9} +O(q^{10})$	\(q+(-12.4311 + 21.5314i) q^{3} +(-18.0963 + 31.3437i) q^{5} +208.885 q^{7} +(-187.566 - 324.875i) q^{9} +204.444 q^{11} +(-146.736 - 254.155i) q^{13} +(-449.916 - 779.277i) q^{15} +(-850.109 + 1472.43i) q^{17} +(-1329.36 + 841.960i) q^{19} +(-2596.68 + 4497.58i) q^{21} +(1768.22 + 3062.65i) q^{23} +(907.547 + 1571.92i) q^{25} +3285.13 q^{27} +(-3204.96 - 5551.15i) q^{29} +2731.24 q^{31} +(-2541.47 + 4401.96i) q^{33} +(-3780.05 + 6547.24i) q^{35} -5427.82 q^{37} +7296.40 q^{39} +(-3692.75 + 6396.03i) q^{41} +(-7870.13 + 13631.5i) q^{43} +13577.1 q^{45} +(-9723.97 - 16842.4i) q^{47} +26826.0 q^{49} +(-21135.7 - 36608.0i) q^{51} +(-4290.51 - 7431.39i) q^{53} +(-3699.69 + 6408.05i) q^{55} +(-1603.08 - 39089.5i) q^{57} +(-13969.1 + 24195.1i) q^{59} +(-15366.2 - 26615.0i) q^{61} +(-39179.8 - 67861.5i) q^{63} +10621.5 q^{65} +(24126.9 + 41788.9i) q^{67} -87924.1 q^{69} +(3430.92 - 5942.53i) q^{71} +(19300.4 - 33429.3i) q^{73} -45127.4 q^{75} +42705.4 q^{77} +(32155.8 - 55695.5i) q^{79} +(4740.78 - 8211.28i) q^{81} -71525.2 q^{83} +(-30767.7 - 53291.2i) q^{85} +159365. q^{87} +(-23256.6 - 40281.7i) q^{89} +(-30651.0 - 53089.2i) q^{91} +(-33952.4 + 58807.3i) q^{93} +(-2333.64 - 56903.5i) q^{95} +(-45206.3 + 78299.6i) q^{97} +(-38346.9 - 66418.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−12.4311	+	21.5314i	−0.797458	+	1.38124i	0.123809	+	0.992306i	$0.460489\pi$
$3$	−12.4311	+	21.5314i	−0.797458	+	1.38124i	−0.921267	+	0.388932i	$0.872844\pi$
$4$		0			0
$5$	−18.0963	+	31.3437i	−0.323717	+	0.560694i	−0.981252	−	0.192730i	$-0.938266\pi$
$5$	−18.0963	+	31.3437i	−0.323717	+	0.560694i	0.657535	+	0.753424i	$0.271599\pi$
$6$		0			0
$7$	208.885			1.61125			0.805624	−	0.592427i	$-0.201830\pi$
$7$	208.885			1.61125			0.805624	+	0.592427i	$0.201830\pi$
$8$		0			0
$9$	−187.566	−	324.875i	−0.771879	−	1.33693i
$10$		0			0
$11$	204.444			0.509440			0.254720	−	0.967015i	$-0.418017\pi$
$11$	204.444			0.509440			0.254720	+	0.967015i	$0.418017\pi$
$12$		0			0
$13$	−146.736	−	254.155i	−0.240813	−	0.417100i	0.720133	−	0.693836i	$-0.244081\pi$
$13$	−146.736	−	254.155i	−0.240813	−	0.417100i	−0.960946	+	0.276736i	$0.910747\pi$
$14$		0			0
$15$	−449.916	−	779.277i	−0.516301	−	0.894260i
$16$		0			0
$17$	−850.109	+	1472.43i	−0.713432	+	1.23570i	0.250130	+	0.968212i	$0.419527\pi$
$17$	−850.109	+	1472.43i	−0.713432	+	1.23570i	−0.963561	+	0.267488i	$0.913807\pi$
$18$		0			0
$19$	−1329.36	+	841.960i	−0.844810	+	0.535066i
$19$	−1329.36	+	841.960i	−0.844810	+	0.535066i
$20$		0			0
$21$	−2596.68	+	4497.58i	−1.28490	+	2.22552i
$22$		0			0
$23$	1768.22	+	3062.65i	0.696975	+	1.20720i	0.969510	+	0.245051i	$0.0788046\pi$
$23$	1768.22	+	3062.65i	0.696975	+	1.20720i	−0.272535	+	0.962146i	$0.587862\pi$
$24$		0			0
$25$	907.547	+	1571.92i	0.290415	+	0.503013i
$26$		0			0
$27$	3285.13			0.867247
$28$		0			0
$29$	−3204.96	−	5551.15i	−0.707664	−	1.22571i	−0.965722	−	0.259580i	$-0.916416\pi$
$29$	−3204.96	−	5551.15i	−0.707664	−	1.22571i	0.258058	−	0.966130i	$-0.416918\pi$
$30$		0			0
$31$	2731.24			0.510452			0.255226	−	0.966881i	$-0.417850\pi$
$31$	2731.24			0.510452			0.255226	+	0.966881i	$0.417850\pi$
$32$		0			0
$33$	−2541.47	+	4401.96i	−0.406257	+	0.703658i
$34$		0			0
$35$	−3780.05	+	6547.24i	−0.521588	+	0.903417i
$36$		0			0
$37$	−5427.82			−0.651811			−0.325905	−	0.945402i	$-0.605669\pi$
$37$	−5427.82			−0.651811			−0.325905	+	0.945402i	$0.605669\pi$
$38$		0			0
$39$	7296.40			0.768152
$40$		0			0
$41$	−3692.75	+	6396.03i	−0.343076	+	0.594225i	−0.985002	−	0.172541i	$-0.944802\pi$
$41$	−3692.75	+	6396.03i	−0.343076	+	0.594225i	0.641926	+	0.766766i	$0.278135\pi$
$42$		0			0
$43$	−7870.13	+	13631.5i	−0.649099	+	1.12427i	0.334240	+	0.942488i	$0.391520\pi$
$43$	−7870.13	+	13631.5i	−0.649099	+	1.12427i	−0.983339	+	0.181784i	$0.941813\pi$
$44$		0			0
$45$	13577.1			0.999480
$46$		0			0
$47$	−9723.97	−	16842.4i	−0.642094	−	1.11214i	−0.984964	−	0.172757i	$-0.944732\pi$
$47$	−9723.97	−	16842.4i	−0.642094	−	1.11214i	0.342870	−	0.939383i	$-0.388601\pi$
$48$		0			0
$49$	26826.0			1.59612
$50$		0			0
$51$	−21135.7	−	36608.0i	−1.13786	−	1.97084i
$52$		0			0
$53$	−4290.51	−	7431.39i	−0.209807	−	0.363396i	0.741847	−	0.670569i	$-0.233950\pi$
$53$	−4290.51	−	7431.39i	−0.209807	−	0.363396i	−0.951654	+	0.307173i	$0.900617\pi$
$54$		0			0
$55$	−3699.69	+	6408.05i	−0.164914	+	0.285640i
$56$		0			0
$57$	−1603.08	−	39089.5i	−0.0653532	−	1.59358i
$58$		0			0
$59$	−13969.1	+	24195.1i	−0.522441	+	0.904894i	0.477218	+	0.878785i	$0.341645\pi$
$59$	−13969.1	+	24195.1i	−0.522441	+	0.904894i	−0.999659	+	0.0261092i	$0.991688\pi$
$60$		0			0
$61$	−15366.2	−	26615.0i	−0.528739	−	0.915803i	−0.999438	−	0.0335090i	$-0.989332\pi$
$61$	−15366.2	−	26615.0i	−0.528739	−	0.915803i	0.470700	−	0.882294i	$-0.344002\pi$
$62$		0			0
$63$	−39179.8	−	67861.5i	−1.24369	−	2.15413i
$64$		0			0
$65$	10621.5			0.311820
$66$		0			0
$67$	24126.9	+	41788.9i	0.656619	+	1.13730i	0.981485	+	0.191538i	$0.0613475\pi$
$67$	24126.9	+	41788.9i	0.656619	+	1.13730i	−0.324866	+	0.945760i	$0.605319\pi$
$68$		0			0
$69$	−87924.1			−2.22323
$70$		0			0
$71$	3430.92	−	5942.53i	0.0807727	−	0.139902i	−0.822809	−	0.568317i	$-0.807595\pi$
$71$	3430.92	−	5942.53i	0.0807727	−	0.139902i	0.903582	+	0.428415i	$0.140928\pi$
$72$		0			0
$73$	19300.4	−	33429.3i	0.423897	−	0.734210i	−0.572420	−	0.819961i	$-0.693995\pi$
$73$	19300.4	−	33429.3i	0.423897	−	0.734210i	0.996317	+	0.0857501i	$0.0273287\pi$
$74$		0			0
$75$	−45127.4			−0.926375
$76$		0			0
$77$	42705.4			0.820834
$78$		0			0
$79$	32155.8	−	55695.5i	0.579684	−	1.00404i	−0.415831	−	0.909442i	$-0.636509\pi$
$79$	32155.8	−	55695.5i	0.579684	−	1.00404i	0.995515	−	0.0946008i	$-0.0301575\pi$
$80$		0			0
$81$	4740.78	−	8211.28i	0.0802856	−	0.139059i
$82$		0			0
$83$	−71525.2			−1.13963			−0.569815	−	0.821773i	$-0.692985\pi$
$83$	−71525.2			−1.13963			−0.569815	+	0.821773i	$0.692985\pi$
$84$		0			0
$85$	−30767.7	−	53291.2i	−0.461900	−	0.800034i
$86$		0			0
$87$	159365.			2.25733
$88$		0			0
$89$	−23256.6	−	40281.7i	−0.311223	−	0.539054i	0.667404	−	0.744696i	$-0.267405\pi$
$89$	−23256.6	−	40281.7i	−0.311223	−	0.539054i	−0.978627	+	0.205641i	$0.934072\pi$
$90$		0			0
$91$	−30651.0	−	53089.2i	−0.388009	−	0.672051i
$92$		0			0
$93$	−33952.4	+	58807.3i	−0.407064	+	0.705056i
$94$		0			0
$95$	−2333.64	−	56903.5i	−0.0265292	−	0.646890i
$96$		0			0
$97$	−45206.3	+	78299.6i	−0.487831	+	0.844949i	−0.999902	−	0.0139945i	$-0.995545\pi$
$97$	−45206.3	+	78299.6i	−0.487831	+	0.844949i	0.512071	+	0.858943i	$0.328879\pi$
$98$		0			0
$99$	−38346.9	−	66418.7i	−0.393226	−	0.681087i
$100$		0			0
$101$	73036.4	+	126503.i	0.712420	+	1.23395i	0.963946	+	0.266097i	$0.0857340\pi$
$101$	73036.4	+	126503.i	0.712420	+	1.23395i	−0.251527	+	0.967850i	$0.580933\pi$
$102$		0			0
$103$	85248.6			0.791761			0.395880	−	0.918302i	$-0.370439\pi$
$103$	85248.6			0.791761			0.395880	+	0.918302i	$0.370439\pi$
$104$		0			0
$105$	−93980.7	−	162779.i	−0.831889	−	1.44087i
$106$		0			0
$107$	28226.4			0.238339			0.119170	−	0.992874i	$-0.461977\pi$
$107$	28226.4			0.238339			0.119170	+	0.992874i	$0.461977\pi$
$108$		0			0
$109$	109018.	−	188825.i	0.878888	−	1.52228i	0.0263250	−	0.999653i	$-0.491620\pi$
$109$	109018.	−	188825.i	0.878888	−	1.52228i	0.852563	−	0.522625i	$-0.175047\pi$
$110$		0			0
$111$	67474.0	−	116868.i	0.519792	−	0.900305i
$112$		0			0
$113$	−174546.			−1.28592			−0.642958	−	0.765901i	$-0.722293\pi$
$113$	−174546.			−1.28592			−0.642958	+	0.765901i	$0.722293\pi$
$114$		0			0
$115$	−127993.			−0.902490
$116$		0			0
$117$	−55045.6	+	95341.8i	−0.371756	+	0.643901i
$118$		0			0
$119$	−177575.	+	307569.i	−1.14952	+	1.99102i
$120$		0			0
$121$	−119254.			−0.740471
$122$		0			0
$123$	−91810.2	−	159020.i	−0.547177	−	0.947739i
$124$		0			0
$125$	−178795.			−1.02348
$126$		0			0
$127$	71846.8	+	124442.i	0.395274	+	0.684634i	0.993136	−	0.116965i	$-0.0373164\pi$
$127$	71846.8	+	124442.i	0.395274	+	0.684634i	−0.597862	+	0.801599i	$0.703983\pi$
$128$		0			0
$129$	−195669.	−	338909.i	−1.03526	−	1.79312i
$130$		0			0
$131$	−2867.13	+	4966.01i	−0.0145972	+	0.0252830i	−0.873232	−	0.487305i	$-0.837980\pi$
$131$	−2867.13	+	4966.01i	−0.0145972	+	0.0252830i	0.858635	+	0.512588i	$0.171313\pi$
$132$		0			0
$133$	−277684.	+	175873.i	−1.36120	+	0.862125i
$134$		0			0
$135$	−59448.7	+	102968.i	−0.280742	+	0.486260i
$136$		0			0
$137$	150187.	+	260131.i	0.683645	+	1.18411i	0.973861	+	0.227146i	$0.0729394\pi$
$137$	150187.	+	260131.i	0.683645	+	1.18411i	−0.290216	+	0.956961i	$0.593727\pi$
$138$		0			0
$139$	−218624.	−	378668.i	−0.959757	−	1.66235i	−0.723087	−	0.690757i	$-0.757277\pi$
$139$	−218624.	−	378668.i	−0.959757	−	1.66235i	−0.236670	−	0.971590i	$-0.576056\pi$
$140$		0			0
$141$	483520.			2.04817
$142$		0			0
$143$	−29999.4	−	51960.5i	−0.122680	−	0.212487i
$144$		0			0
$145$	231992.			0.916331
$146$		0			0
$147$	−333478.	+	577600.i	−1.27284	+	2.20462i
$148$		0			0
$149$	4540.46	−	7864.31i	0.0167546	−	0.0290198i	−0.857527	−	0.514440i	$-0.828000\pi$
$149$	4540.46	−	7864.31i	0.0167546	−	0.0290198i	0.874281	+	0.485420i	$0.161333\pi$
$150$		0			0
$151$	−43328.1			−0.154642			−0.0773209	−	0.997006i	$-0.524637\pi$
$151$	−43328.1			−0.154642			−0.0773209	+	0.997006i	$0.524637\pi$
$152$		0			0
$153$	637808.			2.20273
$154$		0			0
$155$	−49425.3	+	85607.2i	−0.165242	+	0.286208i
$156$		0			0
$157$	−50402.1	+	87299.0i	−0.163192	+	0.282657i	−0.936012	−	0.351968i	$-0.885512\pi$
$157$	−50402.1	+	87299.0i	−0.163192	+	0.282657i	0.772820	+	0.634626i	$0.218846\pi$
$158$		0			0
$159$	213344.			0.669248
$160$		0			0
$161$	369355.	+	639742.i	1.12300	+	1.94509i
$162$		0			0
$163$	315707.			0.930712			0.465356	−	0.885124i	$-0.345926\pi$
$163$	315707.			0.930712			0.465356	+	0.885124i	$0.345926\pi$
$164$		0			0
$165$	−91982.7	−	159319.i	−0.263024	−	0.455572i
$166$		0			0
$167$	−280911.	−	486551.i	−0.779430	−	1.35001i	−0.932271	−	0.361761i	$-0.882176\pi$
$167$	−280911.	−	486551.i	−0.779430	−	1.35001i	0.152841	−	0.988251i	$-0.451158\pi$
$168$		0			0
$169$	142583.	−	246962.i	0.384019	−	0.665140i
$170$		0			0
$171$	522875.	+	273952.i	1.36744	+	0.716448i
$172$		0			0
$173$	−323128.	+	559674.i	−0.820842	+	1.42174i	0.0842143	+	0.996448i	$0.473162\pi$
$173$	−323128.	+	559674.i	−0.820842	+	1.42174i	−0.905056	+	0.425292i	$0.860171\pi$
$174$		0			0
$175$	189573.	+	328350.i	0.467930	+	0.810479i
$176$		0			0
$177$	−347303.	−	601546.i	−0.833249	−	1.44323i
$178$		0			0
$179$	−391686.			−0.913704			−0.456852	−	0.889543i	$-0.651023\pi$
$179$	−391686.			−0.913704			−0.456852	+	0.889543i	$0.651023\pi$
$180$		0			0
$181$	−356595.	−	617641.i	−0.809057	−	1.40133i	−0.913518	−	0.406798i	$-0.866645\pi$
$181$	−356595.	−	617641.i	−0.809057	−	1.40133i	0.104461	−	0.994529i	$-0.466688\pi$
$182$		0			0
$183$	764076.			1.68659
$184$		0			0
$185$	98223.6	−	170128.i	0.211002	−	0.365466i
$186$		0			0
$187$	−173800.	+	301030.i	−0.363451	+	0.629515i
$188$		0			0
$189$	686214.			1.39735
$190$		0			0
$191$	−73696.8			−0.146172			−0.0730862	−	0.997326i	$-0.523285\pi$
$191$	−73696.8			−0.146172			−0.0730862	+	0.997326i	$0.523285\pi$
$192$		0			0
$193$	−281706.	+	487929.i	−0.544381	+	0.942896i	0.454264	+	0.890867i	$0.349902\pi$
$193$	−281706.	+	487929.i	−0.544381	+	0.942896i	−0.998646	+	0.0520289i	$0.983431\pi$
$194$		0			0
$195$	−132038.	+	228696.i	−0.248664	+	0.430698i
$196$		0			0
$197$	227957.			0.418491			0.209246	−	0.977863i	$-0.432899\pi$
$197$	227957.			0.418491			0.209246	+	0.977863i	$0.432899\pi$
$198$		0			0
$199$	305231.	+	528676.i	0.546382	+	0.946361i	0.998519	+	0.0544126i	$0.0173286\pi$
$199$	305231.	+	528676.i	0.546382	+	0.946361i	−0.452137	+	0.891949i	$0.649338\pi$
$200$		0			0
$201$	−1.19970e6			−2.09451
$202$		0			0
$203$	−669468.	−	1.15955e6i	−1.14022	−	1.97492i
$204$		0			0
$205$	−133650.	−	231489.i	−0.222119	−	0.384721i
$206$		0			0
$207$	663319.	−	1.14890e6i	1.07596	−	1.86362i
$208$		0			0
$209$	−271780.	+	172134.i	−0.430380	+	0.272584i
$210$		0			0
$211$	340640.	−	590006.i	0.526732	−	0.912327i	−0.472782	−	0.881179i	$-0.656750\pi$
$211$	340640.	−	590006.i	0.526732	−	0.912327i	0.999515	−	0.0311480i	$-0.00991634\pi$
$212$		0			0
$213$	85300.5	+	147745.i	0.128826	+	0.223133i
$214$		0			0
$215$	−284841.	−	493359.i	−0.420248	−	0.727891i
$216$		0			0
$217$	570515.			0.822466
$218$		0			0
$219$	479853.	+	831129.i	0.676079	+	1.17100i
$220$		0			0
$221$	498968.			0.687214
$222$		0			0
$223$	464769.	−	805003.i	0.625856	−	1.08402i	−0.362518	−	0.931977i	$-0.618083\pi$
$223$	464769.	−	805003.i	0.625856	−	1.08402i	0.988375	−	0.152038i	$-0.0485837\pi$
$224$		0			0
$225$	340451.	−	589678.i	0.448330	−	0.776530i
$226$		0			0
$227$	836852.			1.07791			0.538957	−	0.842333i	$-0.318819\pi$
$227$	836852.			1.07791			0.538957	+	0.842333i	$0.318819\pi$
$228$		0			0
$229$	−43953.2			−0.0553862			−0.0276931	−	0.999616i	$-0.508816\pi$
$229$	−43953.2			−0.0553862			−0.0276931	+	0.999616i	$0.508816\pi$
$230$		0			0
$231$	−530876.	+	919505.i	−0.654581	+	1.13377i
$232$		0			0
$233$	19649.6	−	34034.0i	0.0237117	−	0.0410699i	−0.853926	−	0.520394i	$-0.825785\pi$
$233$	19649.6	−	34034.0i	0.0237117	−	0.0410699i	0.877638	+	0.479324i	$0.159118\pi$
$234$		0			0
$235$	703872.			0.831427
$236$		0			0
$237$	799466.	+	1.38472e6i	0.924548	+	1.60136i
$238$		0			0
$239$	−1.14239e6			−1.29365			−0.646827	−	0.762637i	$-0.723904\pi$
$239$	−1.14239e6			−1.29365			−0.646827	+	0.762637i	$0.723904\pi$
$240$		0			0
$241$	−142528.	−	246866.i	−0.158073	−	0.273790i	0.776101	−	0.630609i	$-0.217195\pi$
$241$	−142528.	−	246866.i	−0.158073	−	0.273790i	−0.934174	+	0.356819i	$0.883861\pi$
$242$		0			0
$243$	517010.	+	895487.i	0.561672	+	0.972845i
$244$		0			0
$245$	−485452.	+	840827.i	−0.516691	+	0.894935i
$246$		0			0
$247$	409054.	+	214317.i	0.426617	+	0.223519i
$248$		0			0
$249$	889139.	−	1.54003e6i	0.908806	−	1.57410i
$250$		0			0
$251$	787154.	+	1.36339e6i	0.788634	+	1.36595i	0.926804	+	0.375546i	$0.122545\pi$
$251$	787154.	+	1.36339e6i	0.788634	+	1.36595i	−0.138169	+	0.990409i	$0.544122\pi$
$252$		0			0
$253$	361503.	+	626141.i	0.355067	+	0.614994i
$254$		0			0
$255$	1.52991e6			1.47338
$256$		0			0
$257$	172908.	+	299486.i	0.163299	+	0.282842i	0.936050	−	0.351867i	$-0.114453\pi$
$257$	172908.	+	299486.i	0.163299	+	0.282842i	−0.772751	+	0.634709i	$0.781120\pi$
$258$		0			0
$259$	−1.13379e6			−1.05023
$260$		0			0
$261$	−1.20228e6	+	2.08242e6i	−1.09246	+	1.89220i
$262$		0			0
$263$	−494023.	+	855673.i	−0.440411	+	0.762814i	−0.997720	−	0.0674913i	$-0.978501\pi$
$263$	−494023.	+	855673.i	−0.440411	+	0.762814i	0.557309	+	0.830305i	$0.311834\pi$
$264$		0			0
$265$	310570.			0.271672
$266$		0			0
$267$	1.15643e6			0.992750
$268$		0			0
$269$	418483.	−	724833.i	0.352612	−	0.610741i	−0.634094	−	0.773256i	$-0.718627\pi$
$269$	418483.	−	724833.i	0.352612	−	0.610741i	0.986706	+	0.162514i	$0.0519603\pi$
$270$		0			0
$271$	−1.04254e6	+	1.80574e6i	−0.862325	+	1.49359i	0.00735345	+	0.999973i	$0.497659\pi$
$271$	−1.04254e6	+	1.80574e6i	−0.862325	+	1.49359i	−0.869679	+	0.493618i	$0.835674\pi$
$272$		0			0
$273$	1.52411e6			1.23768
$274$		0			0
$275$	185543.	+	321369.i	0.147949	+	0.256255i
$276$		0			0
$277$	−654742.			−0.512709			−0.256355	−	0.966583i	$-0.582521\pi$
$277$	−654742.			−0.512709			−0.256355	+	0.966583i	$0.582521\pi$
$278$		0			0
$279$	−512289.	−	887310.i	−0.394007	−	0.682441i
$280$		0			0
$281$	432664.	+	749397.i	0.326878	+	0.566169i	0.981891	−	0.189449i	$-0.0606702\pi$
$281$	432664.	+	749397.i	0.326878	+	0.566169i	−0.655013	+	0.755618i	$0.727337\pi$
$282$		0			0
$283$	−840551.	+	1.45588e6i	−0.623876	+	1.08058i	0.364882	+	0.931054i	$0.381109\pi$
$283$	−840551.	+	1.45588e6i	−0.623876	+	1.08058i	−0.988757	+	0.149530i	$0.952224\pi$
$284$		0			0
$285$	1.25422e6	+	657129.i	0.914665	+	0.479224i
$286$		0			0
$287$	−771360.	+	1.33604e6i	−0.552780	+	0.957444i
$288$		0			0
$289$	−735443.	−	1.27382e6i	−0.517970	−	0.897150i
$290$		0			0
$291$	−1.12393e6	−	1.94671e6i	−0.778050	−	1.34762i
$292$		0			0
$293$	495850.			0.337428			0.168714	−	0.985665i	$-0.446039\pi$
$293$	495850.			0.337428			0.168714	+	0.985665i	$0.446039\pi$
$294$		0			0
$295$	−505577.	−	875685.i	−0.338246	−	0.585859i
$296$		0			0
$297$	671625.			0.441810
$298$		0			0
$299$	518925.	−	898805.i	0.335681	−	0.581416i
$300$		0			0
$301$	−1.64395e6	+	2.84741e6i	−1.04586	+	1.81148i
$302$		0			0
$303$	−3.63170e6			−2.27250
$304$		0			0
$305$	1.11228e6			0.684647
$306$		0			0
$307$	−1.22956e6	+	2.12967e6i	−0.744569	+	1.28963i	0.205826	+	0.978589i	$0.434012\pi$
$307$	−1.22956e6	+	2.12967e6i	−0.744569	+	1.28963i	−0.950396	+	0.311043i	$0.899322\pi$
$308$		0			0
$309$	−1.05974e6	+	1.83552e6i	−0.631396	+	1.09361i
$310$		0			0
$311$	−1.82000e6			−1.06702			−0.533508	−	0.845795i	$-0.679127\pi$
$311$	−1.82000e6			−1.06702			−0.533508	+	0.845795i	$0.679127\pi$
$312$		0			0
$313$	−847350.	−	1.46765e6i	−0.488880	−	0.846765i	0.511038	−	0.859558i	$-0.329261\pi$
$313$	−847350.	−	1.46765e6i	−0.488880	−	0.846765i	−0.999918	+	0.0127931i	$0.995928\pi$
$314$		0			0
$315$	2.83604e6			1.61041
$316$		0			0
$317$	−785090.	−	1.35982e6i	−0.438805	−	0.760033i	0.558793	−	0.829307i	$-0.311265\pi$
$317$	−785090.	−	1.35982e6i	−0.438805	−	0.760033i	−0.997598	+	0.0692749i	$0.977931\pi$
$318$		0			0
$319$	−655235.	−	1.13490e6i	−0.360512	−	0.624426i
$320$		0			0
$321$	−350886.	+	607753.i	−0.190066	+	0.329203i
$322$		0			0
$323$	−109627.	−	2.67315e6i	−0.0584671	−	1.42567i
$324$		0			0
$325$	266340.	−	461315.i	0.139871	−	0.242264i
$326$		0			0
$327$	2.71045e6	+	4.69463e6i	1.40175	+	2.42791i
$328$		0			0
$329$	−2.03119e6	−	3.51813e6i	−1.03457	−	1.79193i
$330$		0			0
$331$	1.47267e6			0.738816			0.369408	−	0.929267i	$-0.379560\pi$
$331$	1.47267e6			0.738816			0.369408	+	0.929267i	$0.379560\pi$
$332$		0			0
$333$	1.01808e6	+	1.76336e6i	0.503119	+	0.871427i
$334$		0			0
$335$	−1.74643e6			−0.850235
$336$		0			0
$337$	−1.04852e6	+	1.81609e6i	−0.502922	+	0.871087i	0.497072	+	0.867709i	$0.334409\pi$
$337$	−1.04852e6	+	1.81609e6i	−0.502922	+	0.871087i	−0.999994	+	0.00337788i	$0.998925\pi$
$338$		0			0
$339$	2.16980e6	−	3.75820e6i	1.02546	−	1.77616i
$340$		0			0
$341$	558386.			0.260045
$342$		0			0
$343$	2.09282e6			0.960498
$344$		0			0
$345$	1.59110e6	−	2.75587e6i	0.719698	−	1.24655i
$346$		0			0
$347$	1.08983e6	−	1.88764e6i	0.485887	−	0.841582i	−0.513981	−	0.857802i	$-0.671830\pi$
$347$	1.08983e6	−	1.88764e6i	0.485887	−	0.841582i	0.999868	+	0.0162199i	$0.00516317\pi$
$348$		0			0
$349$	1.80723e6			0.794238			0.397119	−	0.917767i	$-0.370010\pi$
$349$	1.80723e6			0.794238			0.397119	+	0.917767i	$0.370010\pi$
$350$		0			0
$351$	−482047.	−	834931.i	−0.208844	−	0.361728i
$352$		0			0
$353$	−2.11807e6			−0.904696			−0.452348	−	0.891842i	$-0.649414\pi$
$353$	−2.11807e6			−0.904696			−0.452348	+	0.891842i	$0.649414\pi$
$354$		0			0
$355$	124174.	+	215076.i	0.0522950	+	0.0905775i
$356$		0			0
$357$	−4.41492e6	−	7.64687e6i	−1.83338	−	3.17551i
$358$		0			0
$359$	1.04610e6	−	1.81190e6i	0.428388	−	0.741990i	−0.568342	−	0.822793i	$-0.692415\pi$
$359$	1.04610e6	−	1.81190e6i	0.428388	−	0.741990i	0.996730	+	0.0808022i	$0.0257482\pi$
$360$		0			0
$361$	1.05830e6	−	2.23854e6i	0.427408	−	0.904059i
$362$		0			0
$363$	1.48246e6	−	2.56769e6i	0.590494	−	1.02277i
$364$		0			0
$365$	698534.	+	1.20990e6i	0.274445	+	0.475352i
$366$		0			0
$367$	1.45084e6	+	2.51293e6i	0.562282	+	0.973901i	0.997297	+	0.0734776i	$0.0234098\pi$
$367$	1.45084e6	+	2.51293e6i	0.562282	+	0.973901i	−0.435015	+	0.900423i	$0.643257\pi$
$368$		0			0
$369$	2.77054e6			1.05925
$370$		0			0
$371$	−896224.	−	1.55231e6i	−0.338051	−	0.585521i
$372$		0			0
$373$	−3.15657e6			−1.17474			−0.587372	−	0.809317i	$-0.699837\pi$
$373$	−3.15657e6			−1.17474			−0.587372	+	0.809317i	$0.699837\pi$
$374$		0			0
$375$	2.22263e6	−	3.84970e6i	0.816184	−	1.41367i
$376$		0			0
$377$	−940567.	+	1.62911e6i	−0.340829	+	0.590333i
$378$		0			0
$379$	−3.95334e6			−1.41373			−0.706864	−	0.707350i	$-0.749891\pi$
$379$	−3.95334e6			−1.41373			−0.706864	+	0.707350i	$0.749891\pi$
$380$		0			0
$381$	−3.57255e6			−1.26086
$382$		0			0
$383$	−1.93528e6	+	3.35201e6i	−0.674136	+	1.16764i	0.302584	+	0.953123i	$0.402151\pi$
$383$	−1.93528e6	+	3.35201e6i	−0.674136	+	1.16764i	−0.976720	+	0.214516i	$0.931183\pi$
$384$		0			0
$385$	−772810.	+	1.33855e6i	−0.265718	+	0.460237i
$386$		0			0
$387$	5.90469e6			2.00410
$388$		0			0
$389$	1.11143e6	+	1.92505e6i	0.372399	+	0.645013i	0.989934	−	0.141530i	$-0.0452021\pi$
$389$	1.11143e6	+	1.92505e6i	0.372399	+	0.645013i	−0.617535	+	0.786543i	$0.711869\pi$
$390$		0			0
$391$	−6.01273e6			−1.98898
$392$		0			0
$393$	−71283.3	−	123466.i	−0.0232813	−	0.0403243i
$394$		0			0
$395$	1.16380e6	+	2.01577e6i	0.375307	+	0.650051i
$396$		0			0
$397$	−207721.	+	359784.i	−0.0661462	+	0.114569i	−0.897202	−	0.441621i	$-0.854404\pi$
$397$	−207721.	+	359784.i	−0.0661462	+	0.114569i	0.831056	+	0.556189i	$0.187737\pi$
$398$		0			0
$399$	−334859.	−	8.16521e6i	−0.105300	−	2.56765i
$400$		0			0
$401$	1.50770e6	−	2.61141e6i	0.468224	−	0.810988i	−0.531116	−	0.847299i	$-0.678227\pi$
$401$	1.50770e6	−	2.61141e6i	0.468224	−	0.810988i	0.999341	+	0.0363107i	$0.0115606\pi$
$402$		0			0
$403$	−400772.	−	694157.i	−0.122923	−	0.212910i
$404$		0			0
$405$	171581.	+	297188.i	0.0519796	+	0.0900313i
$406$		0			0
$407$	−1.10969e6			−0.332058
$408$		0			0
$409$	−1.89456e6	−	3.28148e6i	−0.560016	−	0.969976i	−0.997494	−	0.0707474i	$-0.977462\pi$
$409$	−1.89456e6	−	3.28148e6i	−0.560016	−	0.969976i	0.437478	−	0.899229i	$-0.355872\pi$
$410$		0			0
$411$	−7.46797e6			−2.18071
$412$		0			0
$413$	−2.91793e6	+	5.05400e6i	−0.841782	+	1.45801i
$414$		0			0
$415$	1.29434e6	−	2.24187e6i	0.368917	−	0.638983i
$416$		0			0
$417$	1.08710e7			3.06146
$418$		0			0
$419$	−359202.			−0.0999549			−0.0499774	−	0.998750i	$-0.515915\pi$
$419$	−359202.			−0.0999549			−0.0499774	+	0.998750i	$0.515915\pi$
$420$		0			0
$421$	−272896.	+	472669.i	−0.0750398	+	0.129973i	−0.901104	−	0.433604i	$-0.857242\pi$
$421$	−272896.	+	472669.i	−0.0750398	+	0.129973i	0.826064	+	0.563577i	$0.190575\pi$
$422$		0			0
$423$	−3.64778e6	+	6.31814e6i	−0.991238	+	1.71687i
$424$		0			0
$425$	−3.08606e6			−0.828765
$426$		0			0
$427$	−3.20977e6	−	5.55948e6i	−0.851930	−	1.47559i
$428$		0			0
$429$	1.49171e6			0.391327
$430$		0			0
$431$	1.14797e6	+	1.98834e6i	0.297671	+	0.515581i	0.975603	−	0.219544i	$-0.0704569\pi$
$431$	1.14797e6	+	1.98834e6i	0.297671	+	0.515581i	−0.677932	+	0.735125i	$0.737124\pi$
$432$		0			0
$433$	−2.52128e6	−	4.36698e6i	−0.646251	−	1.11934i	−0.984011	−	0.178107i	$-0.943003\pi$
$433$	−2.52128e6	−	4.36698e6i	−0.646251	−	1.11934i	0.337760	−	0.941232i	$-0.390331\pi$
$434$		0			0
$435$	−2.88392e6	+	4.99510e6i	−0.730735	+	1.26567i
$436$		0			0
$437$	−4.92924e6	−	2.58260e6i	−1.23474	−	0.646924i
$438$		0			0
$439$	3.91644e6	−	6.78347e6i	0.969907	−	1.67993i	0.274097	−	0.961702i	$-0.411621\pi$
$439$	3.91644e6	−	6.78347e6i	0.969907	−	1.67993i	0.695810	−	0.718226i	$-0.255045\pi$
$440$		0			0
$441$	−5.03166e6	−	8.71509e6i	−1.23201	−	2.13391i
$442$		0			0
$443$	2.75654e6	+	4.77446e6i	0.667351	+	1.15589i	0.978642	+	0.205571i	$0.0659052\pi$
$443$	2.75654e6	+	4.77446e6i	0.667351	+	1.15589i	−0.311291	+	0.950315i	$0.600761\pi$
$444$		0			0
$445$	1.68344e6			0.402993
$446$		0			0
$447$	112886.	+	195525.i	0.0267222	+	0.0462842i
$448$		0			0
$449$	5.99055e6			1.40233			0.701166	−	0.712998i	$-0.252663\pi$
$449$	5.99055e6			1.40233			0.701166	+	0.712998i	$0.252663\pi$
$450$		0			0
$451$	−754961.	+	1.30763e6i	−0.174777	+	0.302722i
$452$		0			0
$453$	538617.	−	932913.i	0.123320	−	0.213597i
$454$		0			0
$455$	2.21868e6			0.502420
$456$		0			0
$457$	289587.			0.0648617			0.0324308	−	0.999474i	$-0.489675\pi$
$457$	289587.			0.0648617			0.0324308	+	0.999474i	$0.489675\pi$
$458$		0			0
$459$	−2.79272e6	+	4.83713e6i	−0.618721	+	1.07166i
$460$		0			0
$461$	−1.79574e6	+	3.11031e6i	−0.393542	+	0.681635i	−0.992914	−	0.118836i	$-0.962084\pi$
$461$	−1.79574e6	+	3.11031e6i	−0.393542	+	0.681635i	0.599372	+	0.800471i	$0.295417\pi$
$462$		0			0
$463$	−108518.			−0.0235260			−0.0117630	−	0.999931i	$-0.503744\pi$
$463$	−108518.			−0.0235260			−0.0117630	+	0.999931i	$0.503744\pi$
$464$		0			0
$465$	−1.22883e6	−	2.12839e6i	−0.263547	−	0.456477i
$466$		0			0
$467$	4.47855e6			0.950267			0.475133	−	0.879914i	$-0.342400\pi$
$467$	4.47855e6			0.950267			0.475133	+	0.879914i	$0.342400\pi$
$468$		0			0
$469$	5.03974e6	+	8.72909e6i	1.05798	+	1.83247i
$470$		0			0
$471$	−1.25311e6	−	2.17045e6i	−0.260278	−	0.450815i
$472$		0			0
$473$	−1.60900e6	+	2.78687e6i	−0.330677	+	0.572749i
$474$		0			0
$475$	−2.52995e6	−	1.32553e6i	−0.514491	−	0.269560i
$476$		0			0
$477$	−1.60951e6	+	2.78776e6i	−0.323891	+	0.560995i
$478$		0			0
$479$	3.21830e6	+	5.57425e6i	0.640896	+	1.11006i	0.985233	+	0.171218i	$0.0547703\pi$
$479$	3.21830e6	+	5.57425e6i	0.640896	+	1.11006i	−0.344337	+	0.938846i	$0.611896\pi$
$480$		0			0
$481$	796459.	+	1.37951e6i	0.156964	+	0.271870i
$482$		0			0
$483$	−1.83660e7			−3.58218
$484$		0			0
$485$	−1.63614e6	−	2.83387e6i	−0.315838	−	0.547048i
$486$		0			0
$487$	983792.			0.187967			0.0939833	−	0.995574i	$-0.470040\pi$
$487$	983792.			0.187967			0.0939833	+	0.995574i	$0.470040\pi$
$488$		0			0
$489$	−3.92460e6	+	6.79761e6i	−0.742204	+	1.28553i
$490$		0			0
$491$	−3.28089e6	+	5.68267e6i	−0.614170	+	1.06377i	0.376360	+	0.926474i	$0.377176\pi$
$491$	−3.28089e6	+	5.68267e6i	−0.614170	+	1.06377i	−0.990530	+	0.137300i	$0.956158\pi$
$492$		0			0
$493$	1.08983e7			2.01948
$494$		0			0
$495$	2.77575e6			0.509175
$496$		0			0
$497$	716668.	−	1.24131e6i	0.130145	−	0.225418i
$498$		0			0
$499$	2.23268e6	−	3.86711e6i	0.401398	−	0.695241i	−0.592497	−	0.805572i	$-0.701858\pi$
$499$	2.23268e6	−	3.86711e6i	0.401398	−	0.695241i	0.993895	+	0.110331i	$0.0351912\pi$
$500$		0			0
$501$	1.39682e7			2.48625
$502$		0			0
$503$	1.44875e6	+	2.50931e6i	0.255313	+	0.442215i	0.964981	−	0.262322i	$-0.0844881\pi$
$503$	1.44875e6	+	2.50931e6i	0.255313	+	0.442215i	−0.709667	+	0.704537i	$0.751155\pi$
$504$		0			0
$505$	−5.28676e6			−0.922489
$506$		0			0
$507$	3.54495e6	+	6.14003e6i	0.612477	+	1.06084i
$508$		0			0
$509$	3.19919e6	+	5.54116e6i	0.547325	+	0.947995i	0.998457	+	0.0555374i	$0.0176872\pi$
$509$	3.19919e6	+	5.54116e6i	0.547325	+	0.947995i	−0.451131	+	0.892458i	$0.648979\pi$
$510$		0			0
$511$	4.03157e6	−	6.98289e6i	0.683003	−	1.18300i
$512$		0			0
$513$	−4.36712e6	+	2.76595e6i	−0.732659	+	0.464035i
$514$		0			0
$515$	−1.54269e6	+	2.67201e6i	−0.256306	+	0.443936i
$516$		0			0
$517$	−1.98801e6	−	3.44333e6i	−0.327109	−	0.566569i
$518$		0			0
$519$	−8.03370e6	−	1.39148e7i	−1.30917	−	2.26756i
$520$		0			0
$521$	−1.13178e7			−1.82671			−0.913353	−	0.407168i	$-0.866516\pi$
$521$	−1.13178e7			−1.82671			−0.913353	+	0.407168i	$0.866516\pi$
$522$		0			0
$523$	214962.	+	372326.i	0.0343643	+	0.0595208i	0.882696	−	0.469944i	$-0.155726\pi$
$523$	214962.	+	372326.i	0.0343643	+	0.0595208i	−0.848332	+	0.529465i	$0.822393\pi$
$524$		0			0
$525$	−9.42643e6			−1.49262
$526$		0			0
$527$	−2.32185e6	+	4.02156e6i	−0.364173	+	0.630766i
$528$		0			0
$529$	−3.03505e6	+	5.25687e6i	−0.471549	+	0.816747i
$530$		0			0
$531$	1.04805e7			1.61304
$532$		0			0
$533$	2.16744e6			0.330468
$534$		0			0
$535$	−510794.	+	884721.i	−0.0771545	+	0.133635i
$536$		0			0
$537$	4.86910e6	−	8.43354e6i	0.728641	−	1.26204i
$538$		0			0
$539$	5.48442e6			0.813128
$540$		0			0
$541$	4.05574e6	+	7.02475e6i	0.595768	+	1.03190i	0.993438	+	0.114372i	$0.0364855\pi$
$541$	4.05574e6	+	7.02475e6i	0.595768	+	1.03190i	−0.397670	+	0.917529i	$0.630181\pi$
$542$		0			0
$543$	1.77315e7			2.58075
$544$		0			0
$545$	3.94566e6	+	6.83409e6i	0.569021	+	0.985574i
$546$		0			0
$547$	4.15311e6	+	7.19340e6i	0.593479	+	1.02794i	0.993760	+	0.111543i	$0.0355792\pi$
$547$	4.15311e6	+	7.19340e6i	0.593479	+	1.02794i	−0.400281	+	0.916393i	$0.631087\pi$
$548$		0			0
$549$	−5.76436e6	+	9.98416e6i	−0.816244	+	1.41378i
$550$		0			0
$551$	8.93439e6	+	4.68103e6i	1.25368	+	0.656845i
$552$		0			0
$553$	6.71687e6	−	1.16340e7i	0.934015	−	1.61776i
$554$		0			0
$555$	2.44206e6	+	4.22978e6i	0.336531	+	0.582888i
$556$		0			0
$557$	−1.99228e6	−	3.45072e6i	−0.272089	−	0.471272i	0.697307	−	0.716772i	$-0.254381\pi$
$557$	−1.99228e6	−	3.45072e6i	−0.272089	−	0.471272i	−0.969397	+	0.245500i	$0.921048\pi$
$558$		0			0
$559$	4.61934e6			0.625245
$560$		0			0
$561$	−4.32106e6	−	7.48430e6i	−0.579673	−	1.00402i
$562$		0			0
$563$	−6.11824e6			−0.813496			−0.406748	−	0.913540i	$-0.633337\pi$
$563$	−6.11824e6			−0.813496			−0.406748	+	0.913540i	$0.633337\pi$
$564$		0			0
$565$	3.15863e6	−	5.47091e6i	0.416273	−	0.721005i
$566$		0			0
$567$	990279.	−	1.71521e6i	0.129360	−	0.224058i
$568$		0			0
$569$	908888.			0.117687			0.0588436	−	0.998267i	$-0.481259\pi$
$569$	908888.			0.117687			0.0588436	+	0.998267i	$0.481259\pi$
$570$		0			0
$571$	−1.83881e6			−0.236019			−0.118010	−	0.993012i	$-0.537651\pi$
$571$	−1.83881e6			−0.236019			−0.118010	+	0.993012i	$0.537651\pi$
$572$		0			0
$573$	916135.	−	1.58679e6i	0.116566	−	0.201899i
$574$		0			0
$575$	−3.20949e6	+	5.55900e6i	−0.404824	+	0.701176i
$576$		0			0
$577$	5.44901e6			0.681362			0.340681	−	0.940179i	$-0.389342\pi$
$577$	5.44901e6			0.681362			0.340681	+	0.940179i	$0.389342\pi$
$578$		0			0
$579$	−7.00386e6	−	1.21310e7i	−0.868242	−	1.50384i
$580$		0			0
$581$	−1.49405e7			−1.83623
$582$		0			0
$583$	−877170.	−	1.51930e6i	−0.106884	−	0.185128i
$584$		0			0
$585$	−1.99225e6	−	3.45067e6i	−0.240687	−	0.416883i
$586$		0			0
$587$	1.89239e6	−	3.27772e6i	0.226681	−	0.392623i	−0.730141	−	0.683296i	$-0.760546\pi$
$587$	1.89239e6	−	3.27772e6i	0.226681	−	0.392623i	0.956823	+	0.290673i	$0.0938791\pi$
$588$		0			0
$589$	−3.63080e6	+	2.29959e6i	−0.431235	+	0.273126i
$590$		0			0
$591$	−2.83376e6	+	4.90822e6i	−0.333729	+	0.578036i
$592$		0			0
$593$	5.72339e6	+	9.91320e6i	0.668369	+	1.15765i	0.978360	+	0.206910i	$0.0663408\pi$
$593$	5.72339e6	+	9.91320e6i	0.668369	+	1.15765i	−0.309990	+	0.950740i	$0.600326\pi$
$594$		0			0
$595$	−6.42691e6	−	1.11317e7i	−0.744235	−	1.28905i
$596$		0			0
$597$	−1.51775e7			−1.74287
$598$		0			0
$599$	3.14807e6	+	5.45262e6i	0.358491	+	0.620924i	0.987709	−	0.156305i	$-0.0499582\pi$
$599$	3.14807e6	+	5.45262e6i	0.358491	+	0.620924i	−0.629218	+	0.777229i	$0.716625\pi$
$600$		0			0
$601$	−3.03647e6			−0.342913			−0.171456	−	0.985192i	$-0.554847\pi$
$601$	−3.03647e6			−0.342913			−0.171456	+	0.985192i	$0.554847\pi$
$602$		0			0
$603$	9.05078e6	−	1.56764e7i	1.01366	−	1.75571i
$604$		0			0
$605$	2.15805e6	−	3.73785e6i	0.239703	−	0.415177i
$606$		0			0
$607$	1.08106e7			1.19091			0.595454	−	0.803389i	$-0.296972\pi$
$607$	1.08106e7			1.19091			0.595454	+	0.803389i	$0.296972\pi$
$608$		0			0
$609$	3.32890e7			3.63712
$610$		0			0
$611$	−2.85372e6	+	4.94279e6i	−0.309249	+	0.535635i
$612$		0			0
$613$	4.94957e6	−	8.57291e6i	0.532006	−	0.921461i	−0.467296	−	0.884101i	$-0.654772\pi$
$613$	4.94957e6	−	8.57291e6i	0.532006	−	0.921461i	0.999302	−	0.0373600i	$-0.0118948\pi$
$614$		0			0
$615$	6.64570e6			0.708522
$616$		0			0
$617$	973579.	+	1.68629e6i	0.102958	+	0.178328i	0.912902	−	0.408179i	$-0.133836\pi$
$617$	973579.	+	1.68629e6i	0.102958	+	0.178328i	−0.809944	+	0.586507i	$0.800503\pi$
$618$		0			0
$619$	−3.48976e6			−0.366074			−0.183037	−	0.983106i	$-0.558593\pi$
$619$	−3.48976e6			−0.366074			−0.183037	+	0.983106i	$0.558593\pi$
$620$		0			0
$621$	5.80884e6	+	1.00612e7i	0.604450	+	1.04694i
$622$		0			0
$623$	−4.85797e6	−	8.41424e6i	−0.501458	−	0.868550i
$624$		0			0
$625$	399448.	−	691864.i	0.0409034	−	0.0708468i
$626$		0			0
$627$	−327740.	−	7.99162e6i	−0.0332936	−	0.811832i
$628$		0			0
$629$	4.61424e6	−	7.99210e6i	0.465022	−	0.805442i
$630$		0			0
$631$	4.65587e6	+	8.06421e6i	0.465509	+	0.806285i	0.999224	−	0.0393793i	$-0.0125381\pi$
$631$	4.65587e6	+	8.06421e6i	0.465509	+	0.806285i	−0.533716	+	0.845664i	$0.679205\pi$
$632$		0			0
$633$	8.46910e6	+	1.46689e7i	0.840094	+	1.45509i
$634$		0			0
$635$	−5.20065e6			−0.511827
$636$		0			0
$637$	−3.93635e6	−	6.81796e6i	−0.384366	−	0.665741i
$638$		0			0
$639$	−2.57410e6			−0.249387
$640$		0			0
$641$	2.98479e6	−	5.16981e6i	0.286925	−	0.496969i	−0.686149	−	0.727461i	$-0.740700\pi$
$641$	2.98479e6	−	5.16981e6i	0.286925	−	0.496969i	0.973074	+	0.230492i	$0.0740336\pi$
$642$		0			0
$643$	−9.07253e6	+	1.57141e7i	−0.865368	+	1.49886i	0.00131239	+	0.999999i	$0.499582\pi$
$643$	−9.07253e6	+	1.57141e7i	−0.865368	+	1.49886i	−0.866681	+	0.498863i	$0.833751\pi$
$644$		0			0
$645$	1.41636e7			1.34052
$646$		0			0
$647$	−1.03554e7			−0.972537			−0.486269	−	0.873809i	$-0.661642\pi$
$647$	−1.03554e7			−0.972537			−0.486269	+	0.873809i	$0.661642\pi$
$648$		0			0
$649$	−2.85589e6	+	4.94655e6i	−0.266152	+	0.460989i
$650$		0			0
$651$	−7.09215e6	+	1.22840e7i	−0.655882	+	1.13602i
$652$		0			0
$653$	4.38119e6			0.402077			0.201038	−	0.979583i	$-0.435568\pi$
$653$	4.38119e6			0.402077			0.201038	+	0.979583i	$0.435568\pi$
$654$		0			0
$655$	−103769.	−	179733.i	−0.00945069	−	0.0163691i
$656$		0			0
$657$	−1.44805e7			−1.30879
$658$		0			0
$659$	7.34358e6	+	1.27195e7i	0.658710	+	1.14092i	0.980950	+	0.194262i	$0.0622311\pi$
$659$	7.34358e6	+	1.27195e7i	0.658710	+	1.14092i	−0.322239	+	0.946658i	$0.604436\pi$
$660$		0			0
$661$	−1.90277e6	−	3.29569e6i	−0.169388	−	0.293388i	0.768817	−	0.639469i	$-0.220846\pi$
$661$	−1.90277e6	−	3.29569e6i	−0.169388	−	0.293388i	−0.938205	+	0.346081i	$0.887512\pi$
$662$		0			0
$663$	−6.20274e6	+	1.07435e7i	−0.548024	+	0.949205i
$664$		0			0
$665$	−487462.	−	1.18863e7i	−0.0427452	−	1.04230i
$666$		0			0
$667$	1.13342e7	−	1.96313e7i	0.986449	−	1.70858i
$668$		0			0
$669$	1.15552e7	+	2.00142e7i	0.998188	+	1.72891i
$670$		0			0
$671$	−3.14153e6	−	5.44128e6i	−0.269361	−	0.466547i
$672$		0			0
$673$	2.15454e7			1.83365			0.916824	−	0.399291i	$-0.130744\pi$
$673$	2.15454e7			1.83365			0.916824	+	0.399291i	$0.130744\pi$
$674$		0			0
$675$	2.98141e6	+	5.16395e6i	0.251861	+	0.436237i
$676$		0			0
$677$	−182950.			−0.0153412			−0.00767061	−	0.999971i	$-0.502442\pi$
$677$	−182950.			−0.0153412			−0.00767061	+	0.999971i	$0.502442\pi$
$678$		0			0
$679$	−9.44293e6	+	1.63556e7i	−0.786017	+	1.36142i
$680$		0			0
$681$	−1.04030e7	+	1.80186e7i	−0.859591	+	1.48885i
$682$		0			0
$683$	1.90678e7			1.56404			0.782021	−	0.623252i	$-0.214189\pi$
$683$	1.90678e7			1.56404			0.782021	+	0.623252i	$0.214189\pi$
$684$		0			0
$685$	−1.08713e7			−0.885229
$686$		0			0
$687$	546388.	−	946372.i	0.0441682	−	0.0765015i
$688$		0			0
$689$	−1.25915e6	+	2.18091e6i	−0.101048	+	0.175021i
$690$		0			0
$691$	−1.57718e7			−1.25657			−0.628285	−	0.777983i	$-0.716243\pi$
$691$	−1.57718e7			−1.25657			−0.628285	+	0.777983i	$0.716243\pi$
$692$		0			0
$693$	−8.01009e6	−	1.38739e7i	−0.633584	−	1.09740i
$694$		0			0
$695$	1.58252e7			1.24276
$696$		0			0
$697$	−6.27848e6	−	1.08746e7i	−0.489522	−	0.847878i
$698$		0			0
$699$	488533.	+	846164.i	0.0378182	+	0.0655030i
$700$		0			0
$701$	−8.89878e6	+	1.54131e7i	−0.683967	+	1.18467i	0.289793	+	0.957089i	$0.406414\pi$
$701$	−8.89878e6	+	1.54131e7i	−0.683967	+	1.18467i	−0.973760	+	0.227577i	$0.926920\pi$
$702$		0			0
$703$	7.21554e6	−	4.57001e6i	0.550656	−	0.348762i
$704$		0			0
$705$	−8.74993e6	+	1.51553e7i	−0.663028	+	1.14840i
$706$		0			0
$707$	1.52562e7	+	2.64245e7i	1.14788	+	1.98819i
$708$		0			0
$709$	−1.02786e6	−	1.78031e6i	−0.0767924	−	0.133008i	0.825072	−	0.565028i	$-0.191135\pi$
$709$	−1.02786e6	−	1.78031e6i	−0.0767924	−	0.133008i	−0.901864	+	0.432019i	$0.857801\pi$
$710$		0			0
$711$	−2.41254e7			−1.78978
$712$		0			0
$713$	4.82944e6	+	8.36483e6i	0.355773	+	0.616217i
$714$		0			0
$715$	2.17151e6			0.158854
$716$		0			0
$717$	1.42012e7	−	2.45971e7i	1.03163	−	1.78684i
$718$		0			0
$719$	−1.09362e7	+	1.89420e7i	−0.788940	+	1.36648i	0.137676	+	0.990477i	$0.456037\pi$
$719$	−1.09362e7	+	1.89420e7i	−0.788940	+	1.36648i	−0.926617	+	0.376007i	$0.877297\pi$
$720$		0			0
$721$	1.78072e7			1.27572
$722$		0			0
$723$	7.08714e6			0.504226
$724$		0			0
$725$	5.81729e6	−	1.00758e7i	0.411032	−	0.711929i
$726$		0			0
$727$	−1.17837e6	+	2.04099e6i	−0.0826884	+	0.143221i	−0.904404	−	0.426677i	$-0.859684\pi$
$727$	−1.17837e6	+	2.04099e6i	−0.0826884	+	0.143221i	0.821715	+	0.569898i	$0.193017\pi$
$728$		0			0
$729$	−2.34041e7			−1.63107
$730$		0			0
$731$	−1.33809e7	−	2.31765e7i	−0.926175	−	1.60418i
$732$		0			0
$733$	2.16077e7			1.48541			0.742707	−	0.669616i	$-0.233541\pi$
$733$	2.16077e7			1.48541			0.742707	+	0.669616i	$0.233541\pi$
$734$		0			0
$735$	−1.20694e7	−	2.09049e7i	−0.824079	−	1.42735i
$736$		0			0
$737$	4.93260e6	+	8.54351e6i	0.334508	+	0.579385i
$738$		0			0
$739$	2.23082e6	−	3.86389e6i	0.150263	−	0.260264i	−0.781061	−	0.624455i	$-0.785321\pi$
$739$	2.23082e6	−	3.86389e6i	0.150263	−	0.260264i	0.931324	+	0.364191i	$0.118655\pi$
$740$		0			0
$741$	−9.69955e6	+	6.14328e6i	−0.648942	+	0.411012i
$742$		0			0
$743$	7.70913e6	−	1.33526e7i	0.512311	−	0.887348i	−0.487587	−	0.873074i	$-0.662123\pi$
$743$	7.70913e6	−	1.33526e7i	0.512311	−	0.887348i	0.999898	−	0.0142742i	$-0.00454377\pi$
$744$		0			0
$745$	164331.	+	284630.i	0.0108475	+	0.0187884i
$746$		0			0
$747$	1.34157e7	+	2.32367e7i	0.879655	+	1.52361i
$748$		0			0
$749$	5.89607e6			0.384024
$750$		0			0
$751$	1.64269e6	+	2.84522e6i	0.106281	+	0.184084i	0.914261	−	0.405126i	$-0.132772\pi$
$751$	1.64269e6	+	2.84522e6i	0.106281	+	0.184084i	−0.807980	+	0.589210i	$0.799439\pi$
$752$		0			0
$753$	−3.91409e7			−2.51561
$754$		0			0
$755$	784079.	−	1.35806e6i	0.0500602	−	0.0867068i
$756$		0			0
$757$	−5.40092e6	+	9.35466e6i	−0.342553	+	0.593319i	−0.984906	−	0.173090i	$-0.944625\pi$
$757$	−5.40092e6	+	9.35466e6i	−0.342553	+	0.593319i	0.642353	+	0.766409i	$0.277958\pi$
$758$		0			0
$759$	−1.79756e7			−1.13260
$760$		0			0
$761$	−9.38280e6			−0.587315			−0.293657	−	0.955911i	$-0.594872\pi$
$761$	−9.38280e6			−0.587315			−0.293657	+	0.955911i	$0.594872\pi$
$762$		0			0
$763$	2.27723e7	−	3.94428e7i	1.41611	−	2.45277i
$764$		0			0
$765$	−1.15420e7	+	1.99913e7i	−0.713061	+	1.23506i
$766$		0			0
$767$	8.19907e6			0.503241
$768$		0			0
$769$	2.58311e6	+	4.47407e6i	0.157517	+	0.272827i	0.933973	−	0.357345i	$-0.116318\pi$
$769$	2.58311e6	+	4.47407e6i	0.157517	+	0.272827i	−0.776456	+	0.630172i	$0.782985\pi$
$770$		0			0
$771$	−8.59780e6			−0.520896
$772$		0			0
$773$	2.46904e6	+	4.27650e6i	0.148621	+	0.257419i	0.930718	−	0.365738i	$-0.119183\pi$
$773$	2.46904e6	+	4.27650e6i	0.148621	+	0.257419i	−0.782097	+	0.623156i	$0.785850\pi$
$774$		0			0
$775$	2.47873e6	+	4.29328e6i	0.148243	+	0.256764i
$776$		0			0
$777$	1.40943e7	−	2.44121e7i	0.837513	−	1.45062i
$778$		0			0
$779$	−476204.	−	1.16118e7i	−0.0281157	−	0.685575i
$780$		0			0
$781$	701432.	−	1.21492e6i	0.0411489	−	0.0712719i
$782$		0			0
$783$	−1.05287e7	−	1.82362e7i	−0.613719	−	1.06299i
$784$		0			0
$785$	−1.82419e6	−	3.15958e6i	−0.105656	−	0.183002i
$786$		0			0
$787$	7.65272e6			0.440432			0.220216	−	0.975451i	$-0.429324\pi$
$787$	7.65272e6			0.440432			0.220216	+	0.975451i	$0.429324\pi$
$788$		0			0
$789$	−1.22825e7	−	2.12740e7i	−0.702418	−	1.21662i
$790$		0			0
$791$	−3.64600e7			−2.07193
$792$		0			0
$793$	−4.50955e6	+	7.81077e6i	−0.254654	+	0.441074i
$794$		0			0
$795$	−3.86074e6	+	6.68699e6i	−0.216647	+	0.375243i
$796$		0			0
$797$	−1.09086e7			−0.608306			−0.304153	−	0.952623i	$-0.598373\pi$
$797$	−1.09086e7			−0.608306			−0.304153	+	0.952623i	$0.598373\pi$
$798$		0			0
$799$	3.30657e7			1.83236
$800$		0			0
$801$	−8.72433e6	+	1.51110e7i	−0.480453	+	0.832169i
$802$		0			0
$803$	3.94586e6	−	6.83443e6i	0.215950	−	0.374036i
$804$		0			0
$805$	−2.67359e7			−1.45414
$806$		0			0
$807$	1.04044e7	+	1.80210e7i	0.562386	+	0.974081i
$808$		0			0
$809$	2.87426e7			1.54403			0.772013	−	0.635606i	$-0.219250\pi$
$809$	2.87426e7			1.54403			0.772013	+	0.635606i	$0.219250\pi$
$810$		0			0
$811$	9.14408e6	+	1.58380e7i	0.488189	+	0.845568i	0.999908	−	0.0135852i	$-0.00432444\pi$
$811$	9.14408e6	+	1.58380e7i	0.488189	+	0.845568i	−0.511719	+	0.859153i	$0.670991\pi$
$812$		0			0
$813$	−2.59200e7	−	4.48948e7i	−1.37534	−	2.38215i
$814$		0			0
$815$	−5.71314e6	+	9.89544e6i	−0.301287	+	0.521845i
$816$		0			0
$817$	−1.01490e6	−	2.47475e7i	−0.0531949	−	1.29711i
$818$		0			0
$819$	−1.14982e7	+	1.99155e7i	−0.598991	+	1.03748i
$820$		0			0
$821$	7.63449e6	+	1.32233e7i	0.395296	+	0.684672i	0.993139	−	0.116941i	$-0.0373088\pi$
$821$	7.63449e6	+	1.32233e7i	0.395296	+	0.684672i	−0.597843	+	0.801613i	$0.703975\pi$
$822$		0			0
$823$	−3.66967e6	−	6.35605e6i	−0.188854	−	0.327105i	0.756014	−	0.654555i	$-0.227144\pi$
$823$	−3.66967e6	−	6.35605e6i	−0.188854	−	0.327105i	−0.944869	+	0.327450i	$0.893811\pi$
$824$		0			0
$825$	−9.22603e6			−0.471932
$826$		0			0
$827$	−9.35237e6	−	1.61988e7i	−0.475508	−	0.823605i	0.524098	−	0.851658i	$-0.324403\pi$
$827$	−9.35237e6	−	1.61988e7i	−0.475508	−	0.823605i	−0.999606	+	0.0280533i	$0.991069\pi$
$828$		0			0
$829$	1.92855e7			0.974641			0.487320	−	0.873223i	$-0.337974\pi$
$829$	1.92855e7			0.974641			0.487320	+	0.873223i	$0.337974\pi$
$830$		0			0
$831$	8.13919e6	−	1.40975e7i	0.408864	−	0.708173i
$832$		0			0
$833$	−2.28050e7	+	3.94995e7i	−1.13872	+	1.97233i
$834$		0			0
$835$	2.03338e7			1.00926
$836$		0			0
$837$	8.97246e6			0.442688
$838$		0			0
$839$	−6.24428e6	+	1.08154e7i	−0.306251	+	0.530442i	−0.977539	−	0.210754i	$-0.932408\pi$
$839$	−6.24428e6	+	1.08154e7i	−0.306251	+	0.530442i	0.671288	+	0.741196i	$0.265741\pi$
$840$		0			0
$841$	−1.02879e7	+	1.78192e7i	−0.501576	+	0.868756i
$842$		0			0
$843$	−2.15140e7			−1.04268
$844$		0			0
$845$	5.16047e6	+	8.93819e6i	0.248626	+	0.430634i
$846$		0			0
$847$	−2.49103e7			−1.19308
$848$		0			0
$849$	−2.08980e7	−	3.61964e7i	−0.995029	−	1.72344i
$850$		0			0
$851$	−9.59760e6	−	1.66235e7i	−0.454296	−	0.786864i
$852$		0			0
$853$	3.42614e6	−	5.93425e6i	0.161225	−	0.279250i	−0.774083	−	0.633084i	$-0.781789\pi$
$853$	3.42614e6	−	5.93425e6i	0.161225	−	0.279250i	0.935308	+	0.353834i	$0.115122\pi$
$854$		0			0
$855$	−1.80488e7	+	1.14313e7i	−0.844371	+	0.534788i
$856$		0			0
$857$	−5.61768e6	+	9.73011e6i	−0.261279	+	0.452549i	−0.966582	−	0.256357i	$-0.917478\pi$
$857$	−5.61768e6	+	9.73011e6i	−0.261279	+	0.452549i	0.705303	+	0.708906i	$0.250811\pi$
$858$		0			0
$859$	−1.89450e6	−	3.28138e6i	−0.0876017	−	0.151731i	0.818895	−	0.573943i	$-0.194587\pi$
$859$	−1.89450e6	−	3.28138e6i	−0.0876017	−	0.151731i	−0.906497	+	0.422212i	$0.861254\pi$
$860$		0			0
$861$	−1.91778e7	−	3.32169e7i	−0.881638	−	1.52704i
$862$		0			0
$863$	3.08965e7			1.41215			0.706077	−	0.708135i	$-0.250463\pi$
$863$	3.08965e7			1.41215			0.706077	+	0.708135i	$0.250463\pi$
$864$		0			0
$865$	−1.16949e7	−	2.02561e7i	−0.531441	−	0.920482i
$866$		0			0
$867$	3.65696e7			1.65224
$868$		0			0
$869$	6.57407e6	−	1.13866e7i	0.295314	−	0.511500i
$870$		0			0
$871$	7.08057e6	−	1.22639e7i	0.316244	−	0.547752i
$872$		0			0
$873$	3.39168e7			1.50619
$874$		0			0
$875$	−3.73476e7			−1.64908
$876$		0			0
$877$	1.06989e7	−	1.85310e7i	0.469719	−	0.813577i	−0.529682	−	0.848197i	$-0.677689\pi$
$877$	1.06989e7	−	1.85310e7i	0.469719	−	0.813577i	0.999401	+	0.0346194i	$0.0110219\pi$
$878$		0			0
$879$	−6.16398e6	+	1.06763e7i	−0.269085	+	0.466068i
$880$		0			0
$881$	3.47758e6			0.150951			0.0754756	−	0.997148i	$-0.475952\pi$
$881$	3.47758e6			0.150951			0.0754756	+	0.997148i	$0.475952\pi$
$882$		0			0
$883$	7.52985e6	+	1.30421e7i	0.325001	+	0.562918i	0.981513	−	0.191398i	$-0.0613020\pi$
$883$	7.52985e6	+	1.30421e7i	0.325001	+	0.562918i	−0.656512	+	0.754316i	$0.727969\pi$
$884$		0			0
$885$	2.51396e7			1.07895
$886$		0			0
$887$	−1.37599e7	−	2.38328e7i	−0.587225	−	1.01710i	−0.994594	−	0.103840i	$-0.966887\pi$
$887$	−1.37599e7	−	2.38328e7i	−0.587225	−	1.01710i	0.407369	−	0.913264i	$-0.366446\pi$
$888$		0			0
$889$	1.50077e7	+	2.59941e7i	0.636884	+	1.10312i
$890$		0			0
$891$	969226.	−	1.67875e6i	0.0409007	−	0.0708421i
$892$		0			0
$893$	2.71073e7	+	1.42025e7i	1.13752	+	0.595984i
$894$		0			0
$895$	7.08807e6	−	1.22769e7i	0.295781	−	0.512308i
$896$		0			0
$897$	1.29017e7	+	2.23463e7i	0.535383	+	0.927310i
$898$		0			0
$899$	−8.75350e6	−	1.51615e7i	−0.361229	−	0.625667i
$900$		0			0
$901$	1.45896e7			0.598731
$902$		0			0
$903$	−4.08724e7	−	7.07931e7i	−1.66806	−	2.88916i
$904$		0			0
$905$	2.58122e7			1.04762
$906$		0			0
$907$	1.31824e7	−	2.28326e7i	0.532079	−	0.921588i	−0.467219	−	0.884141i	$-0.654744\pi$
$907$	1.31824e7	−	2.28326e7i	0.532079	−	0.921588i	0.999299	−	0.0374469i	$-0.0119225\pi$
$908$		0			0
$909$	2.73984e7	−	4.74553e7i	1.09980	−	1.90491i
$910$		0			0
$911$	6.00749e6			0.239827			0.119913	−	0.992784i	$-0.461738\pi$
$911$	6.00749e6			0.239827			0.119913	+	0.992784i	$0.461738\pi$
$912$		0			0
$913$	−1.46229e7			−0.580573
$914$		0			0
$915$	−1.38270e7	+	2.39490e7i	−0.545977	+	0.945660i
$916$		0			0
$917$	−598900.	+	1.03733e6i	−0.0235197	+	0.0407372i
$918$		0			0
$919$	−1.21396e7			−0.474150			−0.237075	−	0.971491i	$-0.576189\pi$
$919$	−1.21396e7			−0.474150			−0.237075	+	0.971491i	$0.576189\pi$
$920$		0			0
$921$	−3.05698e7	−	5.29484e7i	−1.18753	−	2.05685i
$922$		0			0
$923$	−2.01376e6			−0.0778044
$924$		0			0
$925$	−4.92600e6	−	8.53209e6i	−0.189296	−	0.327869i
$926$		0			0
$927$	−1.59898e7	−	2.76951e7i	−0.611143	−	1.05853i
$928$		0			0
$929$	−4.94616e6	+	8.56699e6i	−0.188031	+	0.325679i	−0.944594	−	0.328242i	$-0.893544\pi$
$929$	−4.94616e6	+	8.56699e6i	−0.188031	+	0.325679i	0.756563	+	0.653921i	$0.226877\pi$
$930$		0			0
$931$	−3.56614e7	+	2.25864e7i	−1.34842	+	0.854030i
$932$		0			0
$933$	2.26247e7	−	3.91871e7i	0.850901	−	1.47380i
$934$		0			0
$935$	−6.29028e6	−	1.08951e7i	−0.235310	−	0.407569i
$936$		0			0
$937$	−1.02564e7	−	1.77646e7i	−0.381632	−	0.661007i	0.609663	−	0.792660i	$-0.291305\pi$
$937$	−1.02564e7	−	1.77646e7i	−0.381632	−	0.661007i	−0.991296	+	0.131654i	$0.957971\pi$
$938$		0			0
$939$	4.21341e7			1.55944
$940$		0			0
$941$	2.28320e7	+	3.95462e7i	0.840562	+	1.45590i	0.889420	+	0.457090i	$0.151108\pi$
$941$	2.28320e7	+	3.95462e7i	0.840562	+	1.45590i	−0.0488582	+	0.998806i	$0.515558\pi$
$942$		0			0
$943$	−2.61184e7			−0.956462
$944$		0			0
$945$	−1.24179e7	+	2.15085e7i	−0.452346	+	0.783486i
$946$		0			0
$947$	5.04770e6	−	8.74287e6i	0.182902	−	0.316796i	−0.759966	−	0.649963i	$-0.774784\pi$
$947$	5.04770e6	−	8.74287e6i	0.182902	−	0.316796i	0.942868	+	0.333168i	$0.108118\pi$
$948$		0			0
$949$	−1.13283e7			−0.408319
$950$		0			0
$951$	3.90383e7			1.39971
$952$		0			0
$953$	−1.33676e7	+	2.31533e7i	−0.476782	+	0.825811i	−0.999646	−	0.0266050i	$-0.991530\pi$
$953$	−1.33676e7	+	2.31533e7i	−0.476782	+	0.825811i	0.522864	+	0.852416i	$0.324864\pi$
$954$		0			0
$955$	1.33364e6	−	2.30993e6i	0.0473184	−	0.0819579i
$956$		0			0
$957$	3.25813e7			1.14997
$958$		0			0
$959$	3.13718e7	+	5.43375e7i	1.10152	+	1.90789i
$960$		0			0
$961$	−2.11695e7			−0.739438
$962$		0			0
$963$	−5.29433e6	−	9.17004e6i	−0.183969	−	0.318644i
$964$		0			0
$965$	−1.01957e7	−	1.76594e7i	−0.352451	−	0.610462i
$966$		0			0
$967$	−4.40549e6	+	7.63054e6i	−0.151505	+	0.262415i	−0.931781	−	0.363021i	$-0.881745\pi$
$967$	−4.40549e6	+	7.63054e6i	−0.151505	+	0.262415i	0.780276	+	0.625436i	$0.215079\pi$
$968$		0			0
$969$	5.89194e7	+	3.08699e7i	2.01581	+	1.05615i
$970$		0			0
$971$	−1.90262e7	+	3.29543e7i	−0.647594	+	1.12167i	0.336102	+	0.941826i	$0.390891\pi$
$971$	−1.90262e7	+	3.29543e7i	−0.647594	+	1.12167i	−0.983696	+	0.179840i	$0.942442\pi$
$972$		0			0
$973$	−4.56673e7	−	7.90981e7i	−1.54641	−	2.67845i
$974$		0			0
$975$	6.62182e6	+	1.14693e7i	0.223083	+	0.386391i
$976$		0			0
$977$	−4.16722e7			−1.39672			−0.698361	−	0.715746i	$-0.746087\pi$
$977$	−4.16722e7			−1.39672			−0.698361	+	0.715746i	$0.746087\pi$
$978$		0			0
$979$	−4.75469e6	−	8.23536e6i	−0.158550	−	0.274616i
$980$		0			0
$981$	−8.17928e7			−2.71358
$982$		0			0
$983$	−2.16371e7	+	3.74766e7i	−0.714194	+	1.23702i	0.249076	+	0.968484i	$0.419873\pi$
$983$	−2.16371e7	+	3.74766e7i	−0.714194	+	1.23702i	−0.963270	+	0.268536i	$0.913460\pi$
$984$		0			0
$985$	−4.12517e6	+	7.14501e6i	−0.135473	+	0.234646i
$986$		0			0
$987$	1.01000e8			3.30012
$988$		0			0
$989$	−5.56646e7			−1.80962
$990$		0			0
$991$	−1.59147e7	+	2.75651e7i	−0.514772	+	0.891611i	0.485081	+	0.874469i	$0.338790\pi$
$991$	−1.59147e7	+	2.75651e7i	−0.514772	+	0.891611i	−0.999853	+	0.0171418i	$0.994543\pi$
$992$		0			0
$993$	−1.83070e7	+	3.17087e7i	−0.589175	+	1.02048i
$994$		0			0
$995$	−2.20942e7			−0.707492
$996$		0			0
$997$	2.67257e7	+	4.62903e7i	0.851514	+	1.47487i	0.879841	+	0.475267i	$0.157649\pi$
$997$	2.67257e7	+	4.62903e7i	0.851514	+	1.47487i	−0.0283272	+	0.999599i	$0.509018\pi$
$998$		0			0
$999$	−1.78311e7			−0.565281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.6.i.d.49.1		18
4.3	odd	2		76.6.e.a.49.9	yes	18
12.11	even	2		684.6.k.f.505.6		18
19.7	even	3	inner	304.6.i.d.273.1		18
76.7	odd	6		76.6.e.a.45.9	✓	18
228.83	even	6		684.6.k.f.577.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.e.a.45.9	✓	18	76.7	odd	6
76.6.e.a.49.9	yes	18	4.3	odd	2
304.6.i.d.49.1		18	1.1	even	1	trivial
304.6.i.d.273.1		18	19.7	even	3	inner
684.6.k.f.505.6		18	12.11	even	2
684.6.k.f.577.6		18	228.83	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-12.4311 + 21.5314i) q^{3} +(-18.0963 + 31.3437i) q^{5} +208.885 q^{7} +(-187.566 - 324.875i) q^{9} +O(q^{10})\)	\(q+(-12.4311 + 21.5314i) q^{3} +(-18.0963 + 31.3437i) q^{5} +208.885 q^{7} +(-187.566 - 324.875i) q^{9} +204.444 q^{11} +(-146.736 - 254.155i) q^{13} +(-449.916 - 779.277i) q^{15} +(-850.109 + 1472.43i) q^{17} +(-1329.36 + 841.960i) q^{19} +(-2596.68 + 4497.58i) q^{21} +(1768.22 + 3062.65i) q^{23} +(907.547 + 1571.92i) q^{25} +3285.13 q^{27} +(-3204.96 - 5551.15i) q^{29} +2731.24 q^{31} +(-2541.47 + 4401.96i) q^{33} +(-3780.05 + 6547.24i) q^{35} -5427.82 q^{37} +7296.40 q^{39} +(-3692.75 + 6396.03i) q^{41} +(-7870.13 + 13631.5i) q^{43} +13577.1 q^{45} +(-9723.97 - 16842.4i) q^{47} +26826.0 q^{49} +(-21135.7 - 36608.0i) q^{51} +(-4290.51 - 7431.39i) q^{53} +(-3699.69 + 6408.05i) q^{55} +(-1603.08 - 39089.5i) q^{57} +(-13969.1 + 24195.1i) q^{59} +(-15366.2 - 26615.0i) q^{61} +(-39179.8 - 67861.5i) q^{63} +10621.5 q^{65} +(24126.9 + 41788.9i) q^{67} -87924.1 q^{69} +(3430.92 - 5942.53i) q^{71} +(19300.4 - 33429.3i) q^{73} -45127.4 q^{75} +42705.4 q^{77} +(32155.8 - 55695.5i) q^{79} +(4740.78 - 8211.28i) q^{81} -71525.2 q^{83} +(-30767.7 - 53291.2i) q^{85} +159365. q^{87} +(-23256.6 - 40281.7i) q^{89} +(-30651.0 - 53089.2i) q^{91} +(-33952.4 + 58807.3i) q^{93} +(-2333.64 - 56903.5i) q^{95} +(-45206.3 + 78299.6i) q^{97} +(-38346.9 - 66418.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} + 11 q^{5} - 336 q^{7} - 902 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more