LMFDB - Embedded newform 304.5.r.d.145.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.9
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52583 + 1.45829i) q^{3} +(22.1213 + 38.3151i) q^{5} +11.1904 q^{7} +(-36.2468 + 62.7813i) q^{9} +O(q^{10})$	\(q+(-2.52583 + 1.45829i) q^{3} +(22.1213 + 38.3151i) q^{5} +11.1904 q^{7} +(-36.2468 + 62.7813i) q^{9} +221.355 q^{11} +(177.474 + 102.465i) q^{13} +(-111.749 - 64.5183i) q^{15} +(-201.449 - 348.920i) q^{17} +(255.308 + 255.223i) q^{19} +(-28.2649 + 16.3188i) q^{21} +(76.8331 - 133.079i) q^{23} +(-666.200 + 1153.89i) q^{25} -447.676i q^{27} +(510.713 + 294.860i) q^{29} -623.654i q^{31} +(-559.106 + 322.800i) q^{33} +(247.545 + 428.760i) q^{35} +776.955i q^{37} -597.693 q^{39} +(58.6413 - 33.8566i) q^{41} +(-1029.30 - 1782.81i) q^{43} -3207.30 q^{45} +(875.015 - 1515.57i) q^{47} -2275.78 q^{49} +(1017.65 + 587.541i) q^{51} +(3953.72 + 2282.68i) q^{53} +(4896.66 + 8481.26i) q^{55} +(-1017.05 - 272.336i) q^{57} +(-5562.31 + 3211.40i) q^{59} +(286.309 - 495.902i) q^{61} +(-405.615 + 702.545i) q^{63} +9066.61i q^{65} +(4026.32 + 2324.60i) q^{67} +448.179i q^{69} +(-5653.75 + 3264.19i) q^{71} +(5197.73 + 9002.74i) q^{73} -3886.05i q^{75} +2477.05 q^{77} +(1112.57 - 642.341i) q^{79} +(-2283.15 - 3954.53i) q^{81} -4090.86 q^{83} +(8912.61 - 15437.1i) q^{85} -1719.96 q^{87} +(-8249.18 - 4762.66i) q^{89} +(1986.00 + 1146.62i) q^{91} +(909.467 + 1575.24i) q^{93} +(-4131.16 + 15428.0i) q^{95} +(2739.00 - 1581.37i) q^{97} +(-8023.42 + 13897.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−2.52583	+	1.45829i	−0.280648	+	0.162032i	−0.633717	−	0.773565i	$-0.718471\pi$
$3$	−2.52583	+	1.45829i	−0.280648	+	0.162032i	0.353069	+	0.935597i	$0.385138\pi$
$4$		0			0
$5$	22.1213	+	38.3151i	0.884850	+	1.53261i	0.845885	+	0.533365i	$0.179073\pi$
$5$	22.1213	+	38.3151i	0.884850	+	1.53261i	0.0389655	+	0.999241i	$0.487594\pi$
$6$		0			0
$7$	11.1904			0.228375			0.114187	−	0.993459i	$-0.463574\pi$
$7$	11.1904			0.228375			0.114187	+	0.993459i	$0.463574\pi$
$8$		0			0
$9$	−36.2468	+	62.7813i	−0.447491	+	0.775078i
$10$		0			0
$11$	221.355			1.82938			0.914692	−	0.404152i	$-0.132433\pi$
$11$	221.355			1.82938			0.914692	+	0.404152i	$0.132433\pi$
$12$		0			0
$13$	177.474	+	102.465i	1.05014	+	0.606301i	0.922690	−	0.385543i	$-0.125986\pi$
$13$	177.474	+	102.465i	1.05014	+	0.606301i	0.127455	+	0.991844i	$0.459319\pi$
$14$		0			0
$15$	−111.749	−	64.5183i	−0.496662	−	0.286748i
$16$		0			0
$17$	−201.449	−	348.920i	−0.697055	−	1.20733i	−0.969483	−	0.245159i	$-0.921160\pi$
$17$	−201.449	−	348.920i	−0.697055	−	1.20733i	0.272428	−	0.962176i	$-0.412173\pi$
$18$		0			0
$19$	255.308	+	255.223i	0.707225	+	0.706989i
$19$	255.308	+	255.223i	0.707225	+	0.706989i
$20$		0			0
$21$	−28.2649	+	16.3188i	−0.0640928	+	0.0370040i
$22$		0			0
$23$	76.8331	−	133.079i	0.145242	−	0.251567i	−0.784221	−	0.620481i	$-0.786937\pi$
$23$	76.8331	−	133.079i	0.145242	−	0.251567i	0.929463	+	0.368915i	$0.120271\pi$
$24$		0			0
$25$	−666.200	+	1153.89i	−1.06592	+	1.84623i
$26$		0			0
$27$		−	447.676i		−	0.614096i
$28$		0			0
$29$	510.713	+	294.860i	0.607269	+	0.350607i	0.771896	−	0.635749i	$-0.219309\pi$
$29$	510.713	+	294.860i	0.607269	+	0.350607i	−0.164627	+	0.986356i	$0.552642\pi$
$30$		0			0
$31$		−	623.654i		−	0.648964i	−0.945892	−	0.324482i	$-0.894810\pi$
$31$		−	623.654i		−	0.648964i	0.945892	−	0.324482i	$-0.105190\pi$
$32$		0			0
$33$	−559.106	+	322.800i	−0.513412	+	0.296419i
$34$		0			0
$35$	247.545	+	428.760i	0.202077	+	0.350008i
$36$		0			0
$37$			776.955i			0.567535i	0.958893	+	0.283767i	$0.0915844\pi$
$37$			776.955i			0.567535i	−0.958893	+	0.283767i	$0.908416\pi$
$38$		0			0
$39$	−597.693			−0.392961
$40$		0			0
$41$	58.6413	−	33.8566i	0.0348848	−	0.0201407i	−0.482456	−	0.875920i	$-0.660255\pi$
$41$	58.6413	−	33.8566i	0.0348848	−	0.0201407i	0.517341	+	0.855779i	$0.326922\pi$
$42$		0			0
$43$	−1029.30	−	1782.81i	−0.556681	−	0.964200i	−0.997771	−	0.0667366i	$-0.978741\pi$
$43$	−1029.30	−	1782.81i	−0.556681	−	0.964200i	0.441090	−	0.897463i	$-0.354592\pi$
$44$		0			0
$45$	−3207.30			−1.58385
$46$		0			0
$47$	875.015	−	1515.57i	0.396113	−	0.686089i	−0.597129	−	0.802145i	$-0.703692\pi$
$47$	875.015	−	1515.57i	0.396113	−	0.686089i	0.993243	+	0.116056i	$0.0370254\pi$
$48$		0			0
$49$	−2275.78			−0.947845
$50$		0			0
$51$	1017.65	+	587.541i	0.391254	+	0.225890i
$52$		0			0
$53$	3953.72	+	2282.68i	1.40752	+	0.812631i	0.995148	−	0.0983858i	$-0.0313679\pi$
$53$	3953.72	+	2282.68i	1.40752	+	0.812631i	0.412370	+	0.911017i	$0.364701\pi$
$54$		0			0
$55$	4896.66	+	8481.26i	1.61873	+	2.80372i
$56$		0			0
$57$	−1017.05	−	272.336i	−0.313036	−	0.0838216i
$58$		0			0
$59$	−5562.31	+	3211.40i	−1.59791	+	0.922551i	−0.606015	+	0.795453i	$0.707233\pi$
$59$	−5562.31	+	3211.40i	−1.59791	+	0.922551i	−0.991890	+	0.127098i	$0.959434\pi$
$60$		0			0
$61$	286.309	−	495.902i	0.0769441	−	0.133271i	−0.824986	−	0.565153i	$-0.808817\pi$
$61$	286.309	−	495.902i	0.0769441	−	0.133271i	0.901930	+	0.431882i	$0.142150\pi$
$62$		0			0
$63$	−405.615	+	702.545i	−0.102196	+	0.177008i
$64$		0			0
$65$			9066.61i			2.14594i
$66$		0			0
$67$	4026.32	+	2324.60i	0.896930	+	0.517843i	0.876203	−	0.481942i	$-0.160068\pi$
$67$	4026.32	+	2324.60i	0.896930	+	0.517843i	0.0207273	+	0.999785i	$0.493402\pi$
$68$		0			0
$69$			448.179i			0.0941355i
$70$		0			0
$71$	−5653.75	+	3264.19i	−1.12155	+	0.647529i	−0.941797	−	0.336182i	$-0.890864\pi$
$71$	−5653.75	+	3264.19i	−1.12155	+	0.647529i	−0.179756	+	0.983711i	$0.557531\pi$
$72$		0			0
$73$	5197.73	+	9002.74i	0.975368	+	1.68939i	0.678716	+	0.734401i	$0.262537\pi$
$73$	5197.73	+	9002.74i	0.975368	+	1.68939i	0.296652	+	0.954986i	$0.404130\pi$
$74$		0			0
$75$		−	3886.05i		−	0.690853i
$76$		0			0
$77$	2477.05			0.417785
$78$		0			0
$79$	1112.57	−	642.341i	0.178267	−	0.102923i	−0.408211	−	0.912888i	$-0.633847\pi$
$79$	1112.57	−	642.341i	0.178267	−	0.102923i	0.586478	+	0.809965i	$0.300514\pi$
$80$		0			0
$81$	−2283.15	−	3954.53i	−0.347988	−	0.602733i
$82$		0			0
$83$	−4090.86			−0.593824			−0.296912	−	0.954905i	$-0.595957\pi$
$83$	−4090.86			−0.593824			−0.296912	+	0.954905i	$0.595957\pi$
$84$		0			0
$85$	8912.61	−	15437.1i	1.23358	−	2.13662i
$86$		0			0
$87$	−1719.96			−0.227238
$88$		0			0
$89$	−8249.18	−	4762.66i	−1.04143	−	0.601271i	−0.121193	−	0.992629i	$-0.538672\pi$
$89$	−8249.18	−	4762.66i	−1.04143	−	0.601271i	−0.920238	+	0.391358i	$0.872005\pi$
$90$		0			0
$91$	1986.00	+	1146.62i	0.239826	+	0.138464i
$92$		0			0
$93$	909.467	+	1575.24i	0.105153	+	0.182130i
$94$		0			0
$95$	−4131.16	+	15428.0i	−0.457746	+	1.70948i
$96$		0			0
$97$	2739.00	−	1581.37i	0.291105	−	0.168069i	−0.347335	−	0.937741i	$-0.612913\pi$
$97$	2739.00	−	1581.37i	0.291105	−	0.168069i	0.638440	+	0.769672i	$0.279580\pi$
$98$		0			0
$99$	−8023.42	+	13897.0i	−0.818633	+	1.41791i
$100$		0			0
$101$	1856.28	−	3215.18i	0.181971	−	0.315183i	−0.760581	−	0.649243i	$-0.775086\pi$
$101$	1856.28	−	3215.18i	0.181971	−	0.315183i	0.942552	+	0.334061i	$0.108419\pi$
$102$		0			0
$103$		−	8038.53i		−	0.757708i	−0.925456	−	0.378854i	$-0.876318\pi$
$103$		−	8038.53i		−	0.757708i	0.925456	−	0.378854i	$-0.123682\pi$
$104$		0			0
$105$	−1250.51	−	721.983i	−0.113425	−	0.0654860i
$106$		0			0
$107$		−	1587.21i		−	0.138633i	−0.997595	−	0.0693165i	$-0.977918\pi$
$107$		−	1587.21i		−	0.138633i	0.997595	−	0.0693165i	$-0.0220818\pi$
$108$		0			0
$109$	−10631.9	+	6138.33i	−0.894866	+	0.516651i	−0.875531	−	0.483162i	$-0.839488\pi$
$109$	−10631.9	+	6138.33i	−0.894866	+	0.516651i	−0.0193350	+	0.999813i	$0.506155\pi$
$110$		0			0
$111$	−1133.02	−	1962.46i	−0.0919588	−	0.159277i
$112$		0			0
$113$		−	6023.15i		−	0.471701i	−0.971789	−	0.235850i	$-0.924212\pi$
$113$		−	6023.15i		−	0.471701i	0.971789	−	0.235850i	$-0.0757876\pi$
$114$		0			0
$115$	6798.58			0.514070
$116$		0			0
$117$	−12865.8	+	7428.05i	−0.939861	+	0.542629i
$118$		0			0
$119$	−2254.29	−	3904.54i	−0.159190	−	0.275725i
$120$		0			0
$121$	34357.2			2.34664
$122$		0			0
$123$	−98.7453	+	171.032i	−0.00652689	+	0.0113049i
$124$		0			0
$125$	−31297.2			−2.00302
$126$		0			0
$127$	−23397.4	−	13508.5i	−1.45064	−	0.837528i	−0.452123	−	0.891956i	$-0.649333\pi$
$127$	−23397.4	−	13508.5i	−1.45064	−	0.837528i	−0.998518	+	0.0544283i	$0.982666\pi$
$128$		0			0
$129$	5199.69	+	3002.04i	0.312462	+	0.180400i
$130$		0			0
$131$	−2300.77	−	3985.05i	−0.134070	−	0.232215i	0.791172	−	0.611594i	$-0.209471\pi$
$131$	−2300.77	−	3985.05i	−0.134070	−	0.232215i	−0.925242	+	0.379378i	$0.876138\pi$
$132$		0			0
$133$	2856.99	+	2856.04i	0.161512	+	0.161458i
$134$		0			0
$135$	17152.8	−	9903.15i	0.941166	−	0.543383i
$136$		0			0
$137$	11542.5	−	19992.2i	0.614978	−	1.06517i	−0.375411	−	0.926859i	$-0.622498\pi$
$137$	11542.5	−	19992.2i	0.614978	−	1.06517i	0.990388	−	0.138314i	$-0.0441684\pi$
$138$		0			0
$139$	7567.46	−	13107.2i	0.391670	−	0.678392i	−0.601000	−	0.799249i	$-0.705231\pi$
$139$	7567.46	−	13107.2i	0.391670	−	0.678392i	0.992670	+	0.120857i	$0.0385642\pi$
$140$		0			0
$141$			5104.09i			0.256732i
$142$		0			0
$143$	39284.9	+	22681.2i	1.92112	+	1.10916i
$144$		0			0
$145$			26090.7i			1.24094i
$146$		0			0
$147$	5748.22	−	3318.74i	0.266010	−	0.153581i
$148$		0			0
$149$	4060.75	+	7033.42i	0.182908	+	0.316807i	0.942870	−	0.333162i	$-0.108115\pi$
$149$	4060.75	+	7033.42i	0.182908	+	0.316807i	−0.759961	+	0.649968i	$0.774782\pi$
$150$		0			0
$151$		−	23042.0i		−	1.01057i	−0.862953	−	0.505285i	$-0.831387\pi$
$151$		−	23042.0i		−	1.01057i	0.862953	−	0.505285i	$-0.168613\pi$
$152$		0			0
$153$	29207.5			1.24770
$154$		0			0
$155$	23895.4	−	13796.0i	0.994606	−	0.574236i
$156$		0			0
$157$	−13029.0	−	22566.9i	−0.528582	−	0.915532i	−0.999445	−	0.0333248i	$-0.989390\pi$
$157$	−13029.0	−	22566.9i	−0.528582	−	0.915532i	0.470862	−	0.882207i	$-0.343943\pi$
$158$		0			0
$159$	−13315.2			−0.526689
$160$		0			0
$161$	859.790	−	1489.20i	0.0331696	−	0.0574515i
$162$		0			0
$163$	23015.6			0.866259			0.433129	−	0.901332i	$-0.357409\pi$
$163$	23015.6			0.866259			0.433129	+	0.901332i	$0.357409\pi$
$164$		0			0
$165$	−24736.2	−	14281.5i	−0.908586	−	0.524572i
$166$		0			0
$167$	−3242.75	−	1872.20i	−0.116274	−	0.0671306i	0.440735	−	0.897637i	$-0.354718\pi$
$167$	−3242.75	−	1872.20i	−0.116274	−	0.0671306i	−0.557009	+	0.830507i	$0.688051\pi$
$168$		0			0
$169$	6717.61	+	11635.2i	0.235202	+	0.407382i
$170$		0			0
$171$	−25277.3	+	6777.57i	−0.864448	+	0.231783i
$172$		0			0
$173$	−16785.7	+	9691.21i	−0.560850	+	0.323807i	−0.753487	−	0.657463i	$-0.771629\pi$
$173$	−16785.7	+	9691.21i	−0.560850	+	0.323807i	0.192637	+	0.981270i	$0.438296\pi$
$174$		0			0
$175$	−7455.02	+	12912.5i	−0.243429	+	0.421632i
$176$		0			0
$177$	9366.29	−	16222.9i	0.298966	−	0.517823i
$178$		0			0
$179$			13338.3i			0.416287i	0.978098	+	0.208144i	$0.0667421\pi$
$179$			13338.3i			0.416287i	−0.978098	+	0.208144i	$0.933258\pi$
$180$		0			0
$181$	−38421.0	−	22182.4i	−1.17277	−	0.677097i	−0.218436	−	0.975851i	$-0.570096\pi$
$181$	−38421.0	−	22182.4i	−1.17277	−	0.677097i	−0.954330	+	0.298754i	$0.903429\pi$
$182$		0			0
$183$			1670.08i			0.0498696i
$184$		0			0
$185$	−29769.2	+	17187.2i	−0.869807	+	0.502183i
$186$		0			0
$187$	−44591.8	−	77235.3i	−1.27518	−	2.20868i
$188$		0			0
$189$		−	5009.65i		−	0.140244i
$190$		0			0
$191$	18061.2			0.495085			0.247543	−	0.968877i	$-0.420377\pi$
$191$	18061.2			0.495085			0.247543	+	0.968877i	$0.420377\pi$
$192$		0			0
$193$	6610.58	−	3816.62i	0.177470	−	0.102462i	−0.408633	−	0.912699i	$-0.633995\pi$
$193$	6610.58	−	3816.62i	0.177470	−	0.102462i	0.586103	+	0.810236i	$0.300661\pi$
$194$		0			0
$195$	−13221.7	−	22900.7i	−0.347712	−	0.602254i
$196$		0			0
$197$	−2459.86			−0.0633838			−0.0316919	−	0.999498i	$-0.510090\pi$
$197$	−2459.86			−0.0633838			−0.0316919	+	0.999498i	$0.510090\pi$
$198$		0			0
$199$	36261.2	−	62806.2i	0.915663	−	1.58597i	0.109734	−	0.993961i	$-0.465000\pi$
$199$	36261.2	−	62806.2i	0.915663	−	1.58597i	0.805928	−	0.592013i	$-0.201667\pi$
$200$		0			0
$201$	−13559.7			−0.335628
$202$		0			0
$203$	5715.06	+	3299.59i	0.138685	+	0.0800697i
$204$		0			0
$205$	2594.44	+	1497.90i	0.0617356	+	0.0356431i
$206$		0			0
$207$	5569.91	+	9647.36i	0.129989	+	0.225148i
$208$		0			0
$209$	56513.9	+	56495.0i	1.29379	+	1.29335i
$210$		0			0
$211$	−15629.6	+	9023.74i	−0.351061	+	0.202685i	−0.665152	−	0.746708i	$-0.731633\pi$
$211$	−15629.6	+	9023.74i	−0.351061	+	0.202685i	0.314092	+	0.949393i	$0.398300\pi$
$212$		0			0
$213$	9520.27	−	16489.6i	0.209841	−	0.363455i
$214$		0			0
$215$	45539.0	−	78875.8i	0.985159	−	1.70634i
$216$		0			0
$217$		−	6978.92i		−	0.148207i
$218$		0			0
$219$	−26257.2	−	15159.6i	−0.547469	−	0.316082i
$220$		0			0
$221$		−	82565.8i		−	1.69050i
$222$		0			0
$223$	−85957.2	+	49627.4i	−1.72851	+	0.997957i	−0.832315	+	0.554303i	$0.812985\pi$
$223$	−85957.2	+	49627.4i	−1.72851	+	0.997957i	−0.896198	+	0.443654i	$0.853682\pi$
$224$		0			0
$225$	−48295.3	−	83649.8i	−0.953980	−	1.65234i
$226$		0			0
$227$			63251.3i			1.22749i	0.789504	+	0.613745i	$0.210338\pi$
$227$			63251.3i			1.22749i	−0.789504	+	0.613745i	$0.789662\pi$
$228$		0			0
$229$	63678.2			1.21428			0.607141	−	0.794594i	$-0.292316\pi$
$229$	63678.2			1.21428			0.607141	+	0.794594i	$0.292316\pi$
$230$		0			0
$231$	−6256.60	+	3612.25i	−0.117250	+	0.0676945i
$232$		0			0
$233$	−1055.68	−	1828.49i	−0.0194456	−	0.0336807i	0.856139	−	0.516746i	$-0.172857\pi$
$233$	−1055.68	−	1828.49i	−0.0194456	−	0.0336807i	−0.875584	+	0.483065i	$0.839523\pi$
$234$		0			0
$235$	77425.7			1.40200
$236$		0			0
$237$	−1873.44	+	3244.89i	−0.0333536	+	0.0577701i
$238$		0			0
$239$	−45548.2			−0.797399			−0.398700	−	0.917082i	$-0.630538\pi$
$239$	−45548.2			−0.797399			−0.398700	+	0.917082i	$0.630538\pi$
$240$		0			0
$241$	36012.0	+	20791.5i	0.620031	+	0.357975i	0.776881	−	0.629647i	$-0.216801\pi$
$241$	36012.0	+	20791.5i	0.620031	+	0.357975i	−0.156850	+	0.987622i	$0.550134\pi$
$242$		0			0
$243$	42937.3	+	24789.8i	0.727146	+	0.419818i
$244$		0			0
$245$	−50343.0	−	87196.7i	−0.838701	−	1.45267i
$246$		0			0
$247$	19159.3	+	71455.7i	0.314040	+	1.17123i
$248$		0			0
$249$	10332.8	−	5965.65i	0.166655	−	0.0962185i
$250$		0			0
$251$	20807.8	−	36040.1i	0.330277	−	0.572056i	−0.652289	−	0.757970i	$-0.726191\pi$
$251$	20807.8	−	36040.1i	0.330277	−	0.572056i	0.982566	+	0.185914i	$0.0595246\pi$
$252$		0			0
$253$	17007.4	−	29457.7i	0.265704	−	0.460212i
$254$		0			0
$255$			51988.6i			0.799517i
$256$		0			0
$257$	65086.1	+	37577.5i	0.985421	+	0.568933i	0.903902	−	0.427739i	$-0.140690\pi$
$257$	65086.1	+	37577.5i	0.985421	+	0.568933i	0.0815187	+	0.996672i	$0.474023\pi$
$258$		0			0
$259$			8694.41i			0.129611i
$260$		0			0
$261$	−37023.4	+	21375.5i	−0.543495	+	0.313787i
$262$		0			0
$263$	−7457.35	−	12916.5i	−0.107813	−	0.186738i	0.807071	−	0.590455i	$-0.201052\pi$
$263$	−7457.35	−	12916.5i	−0.107813	−	0.186738i	−0.914884	+	0.403716i	$0.867718\pi$
$264$		0			0
$265$			201983.i			2.87623i
$266$		0			0
$267$	27781.3			0.389700
$268$		0			0
$269$	116015.	−	66981.4i	1.60328	−	0.925657i	0.612460	−	0.790502i	$-0.290180\pi$
$269$	116015.	−	66981.4i	1.60328	−	0.925657i	0.990825	−	0.135155i	$-0.0431531\pi$
$270$		0			0
$271$	−14595.7	−	25280.6i	−0.198741	−	0.344230i	0.749379	−	0.662141i	$-0.230352\pi$
$271$	−14595.7	−	25280.6i	−0.198741	−	0.344230i	−0.948120	+	0.317911i	$0.897019\pi$
$272$		0			0
$273$	−6688.40			−0.0897423
$274$		0			0
$275$	−147467.	+	255420.i	−1.94998	+	3.37746i
$276$		0			0
$277$	29098.3			0.379235			0.189617	−	0.981858i	$-0.439275\pi$
$277$	29098.3			0.379235			0.189617	+	0.981858i	$0.439275\pi$
$278$		0			0
$279$	39153.8	+	22605.5i	0.502997	+	0.290406i
$280$		0			0
$281$	15800.9	+	9122.68i	0.200111	+	0.115534i	0.596707	−	0.802459i	$-0.296475\pi$
$281$	15800.9	+	9122.68i	0.200111	+	0.115534i	−0.396596	+	0.917993i	$0.629809\pi$
$282$		0			0
$283$	1760.26	+	3048.86i	0.0219788	+	0.0380684i	0.876806	−	0.480845i	$-0.159670\pi$
$283$	1760.26	+	3048.86i	0.0219788	+	0.0380684i	−0.854827	+	0.518913i	$0.826337\pi$
$284$		0			0
$285$	−12063.9	−	44993.0i	−0.148524	−	0.553930i
$286$		0			0
$287$	656.217	−	378.867i	0.00796680	−	0.00459964i
$288$		0			0
$289$	−39402.8	+	68247.7i	−0.471772	+	0.817132i
$290$		0			0
$291$	−4612.17	+	7988.51i	−0.0544652	+	0.0943366i
$292$		0			0
$293$			93187.0i			1.08548i	0.839902	+	0.542738i	$0.182612\pi$
$293$			93187.0i			1.08548i	−0.839902	+	0.542738i	$0.817388\pi$
$294$		0			0
$295$	−246091.	−	142080.i	−2.82781	−	1.63264i
$296$		0			0
$297$		−	99095.4i		−	1.12342i
$298$		0			0
$299$	27271.8	−	15745.4i	0.305050	−	0.176121i
$300$		0			0
$301$	−11518.3	−	19950.2i	−0.127132	−	0.220199i
$302$		0			0
$303$			10828.0i			0.117940i
$304$		0			0
$305$	25334.1			0.272336
$306$		0			0
$307$	99394.4	−	57385.4i	1.05459	−	0.608870i	0.130662	−	0.991427i	$-0.458290\pi$
$307$	99394.4	−	57385.4i	1.05459	−	0.608870i	0.923932	+	0.382557i	$0.124957\pi$
$308$		0			0
$309$	11722.5	+	20303.9i	0.122773	+	0.212649i
$310$		0			0
$311$	64183.8			0.663598			0.331799	−	0.943350i	$-0.392344\pi$
$311$	64183.8			0.663598			0.331799	+	0.943350i	$0.392344\pi$
$312$		0			0
$313$	−26839.6	+	46487.5i	−0.273960	+	0.474512i	−0.969872	−	0.243615i	$-0.921667\pi$
$313$	−26839.6	+	46487.5i	−0.273960	+	0.474512i	0.695912	+	0.718127i	$0.255000\pi$
$314$		0			0
$315$	−35890.8			−0.361712
$316$		0			0
$317$	−10419.0	−	6015.41i	−0.103683	−	0.0598614i	0.447262	−	0.894403i	$-0.352399\pi$
$317$	−10419.0	−	6015.41i	−0.103683	−	0.0598614i	−0.550945	+	0.834542i	$0.685733\pi$
$318$		0			0
$319$	113049.	+	65268.9i	1.11093	+	0.641394i
$320$		0			0
$321$	2314.61	+	4009.02i	0.0224630	+	0.0389070i
$322$		0			0
$323$	37620.7	−	140496.i	0.360597	−	1.34667i
$324$		0			0
$325$	−236467.	+	136524.i	−2.23874	+	1.29254i
$326$		0			0
$327$	17902.9	−	31008.7i	0.167428	−	0.289994i
$328$		0			0
$329$	9791.73	−	16959.8i	0.0904623	−	0.156685i
$330$		0			0
$331$			153658.i			1.40249i	0.712921	+	0.701244i	$0.247372\pi$
$331$			153658.i			1.40249i	−0.712921	+	0.701244i	$0.752628\pi$
$332$		0			0
$333$	−48778.2	−	28162.1i	−0.439884	−	0.253967i
$334$		0			0
$335$			205692.i			1.83285i
$336$		0			0
$337$	3673.75	−	2121.04i	0.0323482	−	0.0186762i	−0.483739	−	0.875212i	$-0.660721\pi$
$337$	3673.75	−	2121.04i	0.0323482	−	0.0186762i	0.516087	+	0.856536i	$0.327388\pi$
$338$		0			0
$339$	8783.49	+	15213.4i	0.0764306	+	0.132382i
$340$		0			0
$341$		−	138049.i		−	1.18720i
$342$		0			0
$343$	−52334.8			−0.444839
$344$		0			0
$345$	−17172.0	+	9914.29i	−0.144273	+	0.0832958i
$346$		0			0
$347$	−3972.28	−	6880.20i	−0.0329899	−	0.0571402i	0.849059	−	0.528298i	$-0.177170\pi$
$347$	−3972.28	−	6880.20i	−0.0329899	−	0.0571402i	−0.882049	+	0.471158i	$0.843836\pi$
$348$		0			0
$349$	−147190.			−1.20845			−0.604223	−	0.796815i	$-0.706516\pi$
$349$	−147190.			−1.20845			−0.604223	+	0.796815i	$0.706516\pi$
$350$		0			0
$351$	45871.0	−	79451.0i	0.372327	−	0.644889i
$352$		0			0
$353$	129431.			1.03869			0.519347	−	0.854563i	$-0.326175\pi$
$353$	129431.			1.03869			0.519347	+	0.854563i	$0.326175\pi$
$354$		0			0
$355$	−250136.	−	144416.i	−1.98481	−	1.14593i
$356$		0			0
$357$	11387.9	+	6574.80i	0.0893525	+	0.0515877i
$358$		0			0
$359$	64518.9	+	111750.i	0.500608	+	0.867079i	1.00000		0.000702335i	$0.000223560\pi$
$359$	64518.9	+	111750.i	0.500608	+	0.867079i	−0.499392	+	0.866376i	$0.666443\pi$
$360$		0			0
$361$	43.5891	+	130321.i	0.000334475	+	1.00000i
$362$		0			0
$363$	−86780.4	+	50102.7i	−0.658580	+	0.380231i
$364$		0			0
$365$	−229961.	+	398304.i	−1.72611	+	2.98971i
$366$		0			0
$367$	−39108.3	+	67737.6i	−0.290360	+	0.502919i	−0.973895	−	0.226999i	$-0.927108\pi$
$367$	−39108.3	+	67737.6i	−0.290360	+	0.502919i	0.683535	+	0.729918i	$0.260442\pi$
$368$		0			0
$369$			4908.77i			0.0360512i
$370$		0			0
$371$	44243.5	+	25544.0i	0.321442	+	0.185584i
$372$		0			0
$373$		−	103309.i		−	0.742543i	−0.928524	−	0.371271i	$-0.878922\pi$
$373$		−	103309.i		−	0.742543i	0.928524	−	0.371271i	$-0.121078\pi$
$374$		0			0
$375$	79051.4	−	45640.3i	0.562143	−	0.324553i
$376$		0			0
$377$	60425.7	+	104660.i	0.425147	+	0.736376i
$378$		0			0
$379$		−	132145.i		−	0.919967i	−0.887928	−	0.459983i	$-0.847855\pi$
$379$		−	132145.i		−	0.919967i	0.887928	−	0.459983i	$-0.152145\pi$
$380$		0			0
$381$	78797.0			0.542825
$382$		0			0
$383$	211340.	−	122017.i	1.44073	−	0.831807i	0.442834	−	0.896604i	$-0.353973\pi$
$383$	211340.	−	122017.i	1.44073	−	0.831807i	0.997899	+	0.0647964i	$0.0206398\pi$
$384$		0			0
$385$	54795.4	+	94908.4i	0.369677	+	0.640300i
$386$		0			0
$387$	149236.			0.996439
$388$		0			0
$389$	−26862.4	+	46527.0i	−0.177519	+	0.307472i	−0.941030	−	0.338322i	$-0.890141\pi$
$389$	−26862.4	+	46527.0i	−0.177519	+	0.307472i	0.763511	+	0.645795i	$0.223474\pi$
$390$		0			0
$391$	−61911.8			−0.404967
$392$		0			0
$393$	11622.7	+	6710.36i	0.0752526	+	0.0434471i
$394$		0			0
$395$	49222.8	+	28418.8i	0.315480	+	0.182143i
$396$		0			0
$397$	61663.4	+	106804.i	0.391243	+	0.677652i	0.992614	−	0.121318i	$-0.0387120\pi$
$397$	61663.4	+	106804.i	0.391243	+	0.677652i	−0.601371	+	0.798970i	$0.705379\pi$
$398$		0			0
$399$	−11381.2	−	3047.54i	−0.0714895	−	0.0191427i
$400$		0			0
$401$	−91767.9	+	52982.2i	−0.570692	+	0.329489i	−0.757426	−	0.652921i	$-0.773543\pi$
$401$	−91767.9	+	52982.2i	−0.570692	+	0.329489i	0.186734	+	0.982411i	$0.440210\pi$
$402$		0			0
$403$	63902.7	−	110683.i	0.393468	−	0.681506i
$404$		0			0
$405$	101012.	−	174958.i	0.615835	−	1.06666i
$406$		0			0
$407$			171983.i			1.03824i
$408$		0			0
$409$	24108.7	+	13919.2i	0.144121	+	0.0832084i	0.570327	−	0.821418i	$-0.306817\pi$
$409$	24108.7	+	13919.2i	0.144121	+	0.0832084i	−0.426206	+	0.904626i	$0.640150\pi$
$410$		0			0
$411$			67329.3i			0.398584i
$412$		0			0
$413$	−62244.2	+	35936.7i	−0.364921	+	0.210687i
$414$		0			0
$415$	−90494.9	−	156742.i	−0.525446	−	0.910099i
$416$		0			0
$417$			44142.1i			0.253852i
$418$		0			0
$419$	72955.5			0.415556			0.207778	−	0.978176i	$-0.433377\pi$
$419$	72955.5			0.415556			0.207778	+	0.978176i	$0.433377\pi$
$420$		0			0
$421$	−47674.6	+	27524.9i	−0.268982	+	0.155297i	−0.628425	−	0.777870i	$-0.716300\pi$
$421$	−47674.6	+	27524.9i	−0.268982	+	0.155297i	0.359443	+	0.933167i	$0.382967\pi$
$422$		0			0
$423$	63432.9	+	109869.i	0.354515	+	0.614037i
$424$		0			0
$425$	536821.			2.97202
$426$		0			0
$427$	3203.90	−	5549.32i	0.0175721	−	0.0304358i
$428$		0			0
$429$	−132303.			−0.718876
$430$		0			0
$431$	−52406.2	−	30256.8i	−0.282117	−	0.162880i	0.352265	−	0.935900i	$-0.385412\pi$
$431$	−52406.2	−	30256.8i	−0.282117	−	0.162880i	−0.634381	+	0.773020i	$0.718745\pi$
$432$		0			0
$433$	−208602.	−	120437.i	−1.11261	−	0.642366i	−0.173106	−	0.984903i	$-0.555380\pi$
$433$	−208602.	−	120437.i	−1.11261	−	0.642366i	−0.939504	+	0.342538i	$0.888714\pi$
$434$		0			0
$435$	−38047.8	−	65900.7i	−0.201072	−	0.348266i
$436$		0			0
$437$	53580.9	−	14366.6i	0.280574	−	0.0752298i
$438$		0			0
$439$	72595.1	−	41912.8i	0.376685	−	0.217479i	−0.299690	−	0.954037i	$-0.596883\pi$
$439$	72595.1	−	41912.8i	0.376685	−	0.217479i	0.676375	+	0.736557i	$0.263550\pi$
$440$		0			0
$441$	82489.6	−	142876.i	0.424152	−	0.734653i
$442$		0			0
$443$	−4402.89	+	7626.03i	−0.0224352	+	0.0388589i	−0.877025	−	0.480445i	$-0.840475\pi$
$443$	−4402.89	+	7626.03i	−0.0224352	+	0.0388589i	0.854590	+	0.519304i	$0.173809\pi$
$444$		0			0
$445$		−	421425.i		−	2.12814i
$446$		0			0
$447$	−20513.5	−	11843.5i	−0.102666	−	0.0592740i
$448$		0			0
$449$		−	196528.i		−	0.974839i	−0.873168	−	0.487419i	$-0.837938\pi$
$449$		−	196528.i		−	0.974839i	0.873168	−	0.487419i	$-0.162062\pi$
$450$		0			0
$451$	12980.6	−	7494.34i	0.0638176	−	0.0368451i
$452$		0			0
$453$	33601.9	+	58200.1i	0.163745	+	0.283614i
$454$		0			0
$455$			101459.i			0.490079i
$456$		0			0
$457$	133691.			0.640133			0.320067	−	0.947395i	$-0.396295\pi$
$457$	133691.			0.640133			0.320067	+	0.947395i	$0.396295\pi$
$458$		0			0
$459$	−156203.	+	90183.8i	−0.741419	+	0.428058i
$460$		0			0
$461$	−93635.8	−	162182.i	−0.440595	−	0.763134i	0.557138	−	0.830420i	$-0.311899\pi$
$461$	−93635.8	−	162182.i	−0.440595	−	0.763134i	−0.997734	+	0.0672860i	$0.978566\pi$
$462$		0			0
$463$	−101083.			−0.471539			−0.235770	−	0.971809i	$-0.575761\pi$
$463$	−101083.			−0.471539			−0.235770	+	0.971809i	$0.575761\pi$
$464$		0			0
$465$	−40237.1	+	69692.8i	−0.186089	+	0.322316i
$466$		0			0
$467$	354215.			1.62417			0.812087	−	0.583536i	$-0.198331\pi$
$467$	354215.			1.62417			0.812087	+	0.583536i	$0.198331\pi$
$468$		0			0
$469$	45056.0	+	26013.1i	0.204836	+	0.118262i
$470$		0			0
$471$	65818.2	+	38000.1i	0.296691	+	0.171295i
$472$		0			0
$473$	−227842.	−	394634.i	−1.01838	−	1.76389i
$474$		0			0
$475$	−464586.	+	124569.i	−2.05911	+	0.552106i
$476$		0			0
$477$	−286619.	+	165480.i	−1.25970	+	0.727290i
$478$		0			0
$479$	161353.	−	279472.i	0.703246	−	1.21806i	−0.264075	−	0.964502i	$-0.585067\pi$
$479$	161353.	−	279472.i	0.703246	−	1.21806i	0.967321	−	0.253556i	$-0.0816001\pi$
$480$		0			0
$481$	−79610.6	+	137890.i	−0.344097	+	0.595994i
$482$		0			0
$483$			5015.29i			0.0214982i
$484$		0			0
$485$	121180.	+	69963.6i	0.515168	+	0.297433i
$486$		0			0
$487$		−	226388.i		−	0.954541i	−0.878756	−	0.477271i	$-0.841626\pi$
$487$		−	226388.i		−	0.954541i	0.878756	−	0.477271i	$-0.158374\pi$
$488$		0			0
$489$	−58133.5	+	33563.4i	−0.243113	+	0.140362i
$490$		0			0
$491$	105334.	+	182444.i	0.436925	+	0.756776i	0.997451	−	0.0713612i	$-0.0227343\pi$
$491$	105334.	+	182444.i	0.436925	+	0.756776i	−0.560526	+	0.828137i	$0.689401\pi$
$492$		0			0
$493$		−	237597.i		−	0.977569i
$494$		0			0
$495$	−709953.			−2.89747
$496$		0			0
$497$	−63267.5	+	36527.5i	−0.256134	+	0.147879i
$498$		0			0
$499$	−204860.	−	354827.i	−0.822727	−	1.42500i	−0.903644	−	0.428283i	$-0.859118\pi$
$499$	−204860.	−	354827.i	−0.822727	−	1.42500i	0.0809178	−	0.996721i	$-0.474215\pi$
$500$		0			0
$501$	10920.8			0.0435092
$502$		0			0
$503$	−4726.10	+	8185.85i	−0.0186796	+	0.0323540i	−0.875214	−	0.483736i	$-0.839280\pi$
$503$	−4726.10	+	8185.85i	−0.0186796	+	0.0323540i	0.856535	+	0.516090i	$0.172613\pi$
$504$		0			0
$505$	164253.			0.644068
$506$		0			0
$507$	−33935.1	−	19592.4i	−0.132018	−	0.0762206i
$508$		0			0
$509$	309090.	+	178453.i	1.19303	+	0.688794i	0.958992	−	0.283434i	$-0.0914738\pi$
$509$	309090.	+	178453.i	1.19303	+	0.688794i	0.234035	+	0.972228i	$0.424807\pi$
$510$		0			0
$511$	58164.5	+	100744.i	0.222749	+	0.385813i
$512$		0			0
$513$	114257.	−	114295.i	0.434158	−	0.434304i
$514$		0			0
$515$	307997.	−	177822.i	1.16127	−	0.670459i
$516$		0			0
$517$	193689.	−	335480.i	0.724643	−	1.25512i
$518$		0			0
$519$	28265.2	−	48956.7i	0.104934	−	0.181751i
$520$		0			0
$521$		−	421163.i		−	1.55158i	−0.630989	−	0.775792i	$-0.717351\pi$
$521$		−	421163.i		−	1.55158i	0.630989	−	0.775792i	$-0.282649\pi$
$522$		0			0
$523$	216003.	+	124709.i	0.789689	+	0.455927i	0.839853	−	0.542814i	$-0.182641\pi$
$523$	216003.	+	124709.i	0.789689	+	0.455927i	−0.0501642	+	0.998741i	$0.515974\pi$
$524$		0			0
$525$		−	43486.3i		−	0.157773i
$526$		0			0
$527$	−217605.	+	125634.i	−0.783517	+	0.452364i
$528$		0			0
$529$	128114.	+	221900.i	0.457809	+	0.792949i
$530$		0			0
$531$		−	465612.i		−	1.65133i
$532$		0			0
$533$	13876.4			0.0488454
$534$		0			0
$535$	60814.2	−	35111.1i	0.212470	−	0.122670i
$536$		0			0
$537$	−19451.0	−	33690.1i	−0.0674518	−	0.116830i
$538$		0			0
$539$	−503755.			−1.73397
$540$		0			0
$541$	271554.	−	470345.i	0.927815	−	1.60702i	0.140846	−	0.990032i	$-0.455018\pi$
$541$	271554.	−	470345.i	0.927815	−	1.60702i	0.786970	−	0.616992i	$-0.211649\pi$
$542$		0			0
$543$	129393.			0.438845
$544$		0			0
$545$	−470382.	−	271575.i	−1.58365	−	0.914318i
$546$		0			0
$547$	190356.	+	109902.i	0.636196	+	0.367308i	0.783148	−	0.621836i	$-0.213613\pi$
$547$	190356.	+	109902.i	0.636196	+	0.367308i	−0.146951	+	0.989144i	$0.546946\pi$
$548$		0			0
$549$	20755.6	+	35949.7i	0.0688636	+	0.119275i
$550$		0			0
$551$	55134.2	+	205626.i	0.181601	+	0.677290i
$552$		0			0
$553$	12450.0	−	7188.03i	0.0407118	−	0.0235050i
$554$		0			0
$555$	50127.9	−	86824.0i	0.162740	−	0.281873i
$556$		0			0
$557$	−123540.	+	213978.i	−0.398197	+	0.689698i	−0.993504	−	0.113801i	$-0.963697\pi$
$557$	−123540.	+	213978.i	−0.398197	+	0.689698i	0.595306	+	0.803499i	$0.297031\pi$
$558$		0			0
$559$		−	421870.i		−	1.35007i
$560$		0			0
$561$	225263.	+	130055.i	0.715753	+	0.413240i
$562$		0			0
$563$			523710.i			1.65224i	0.563492	+	0.826122i	$0.309458\pi$
$563$			523710.i			1.65224i	−0.563492	+	0.826122i	$0.690542\pi$
$564$		0			0
$565$	230778.	−	133240.i	0.722932	−	0.417385i
$566$		0			0
$567$	−25549.3	−	44252.6i	−0.0794717	−	0.137649i
$568$		0			0
$569$			451709.i			1.39519i	0.716491	+	0.697596i	$0.245747\pi$
$569$			451709.i			1.39519i	−0.716491	+	0.697596i	$0.754253\pi$
$570$		0			0
$571$	−278663.			−0.854686			−0.427343	−	0.904089i	$-0.640550\pi$
$571$	−278663.			−0.854686			−0.427343	+	0.904089i	$0.640550\pi$
$572$		0			0
$573$	−45619.5	+	26338.4i	−0.138944	+	0.0802196i
$574$		0			0
$575$	102372.	+	177314.i	0.309633	+	0.536300i
$576$		0			0
$577$	−224889.			−0.675486			−0.337743	−	0.941238i	$-0.609663\pi$
$577$	−224889.			−0.675486			−0.337743	+	0.941238i	$0.609663\pi$
$578$		0			0
$579$	−11131.5	+	19280.3i	−0.0332044	+	0.0575117i
$580$		0			0
$581$	−45778.2			−0.135614
$582$		0			0
$583$	875177.	+	505284.i	2.57489	+	1.48661i
$584$		0			0
$585$	−569214.	−	328636.i	−1.66327	−	0.960291i
$586$		0			0
$587$	248603.	+	430593.i	0.721490	+	1.24966i	0.960402	+	0.278617i	$0.0898759\pi$
$587$	248603.	+	430593.i	0.721490	+	1.24966i	−0.238912	+	0.971041i	$0.576791\pi$
$588$		0			0
$589$	159171.	−	159224.i	0.458810	−	0.458963i
$590$		0			0
$591$	6213.19	−	3587.19i	0.0177885	−	0.0102702i
$592$		0			0
$593$	130268.	−	225630.i	0.370448	−	0.641635i	−0.619186	−	0.785244i	$-0.712537\pi$
$593$	130268.	−	225630.i	0.370448	−	0.641635i	0.989634	+	0.143609i	$0.0458708\pi$
$594$		0			0
$595$	99735.3	−	172747.i	0.281718	−	0.487950i
$596$		0			0
$597$			211517.i			0.593466i
$598$		0			0
$599$	−219983.	−	127007.i	−0.613106	−	0.353977i	0.161074	−	0.986942i	$-0.448504\pi$
$599$	−219983.	−	127007.i	−0.613106	−	0.353977i	−0.774180	+	0.632965i	$0.781838\pi$
$600$		0			0
$601$			160041.i			0.443080i	0.975151	+	0.221540i	$0.0711083\pi$
$601$			160041.i			0.443080i	−0.975151	+	0.221540i	$0.928892\pi$
$602$		0			0
$603$	−291882.	+	168518.i	−0.802737	+	0.463460i
$604$		0			0
$605$	760025.	+	1.31640e6i	2.07643	+	3.59648i
$606$		0			0
$607$			115052.i			0.312261i	0.987736	+	0.156130i	$0.0499020\pi$
$607$			115052.i			0.312261i	−0.987736	+	0.156130i	$0.950098\pi$
$608$		0			0
$609$	−19247.0			−0.0518954
$610$		0			0
$611$	310585.	−	179317.i	0.831953	−	0.480328i
$612$		0			0
$613$	280434.	+	485727.i	0.746295	+	1.29262i	0.949587	+	0.313502i	$0.101502\pi$
$613$	280434.	+	485727.i	0.746295	+	1.29262i	−0.203293	+	0.979118i	$0.565164\pi$
$614$		0			0
$615$	−8737.48			−0.0231013
$616$		0			0
$617$	166816.	−	288933.i	0.438194	−	0.758975i	−0.559356	−	0.828927i	$-0.688952\pi$
$617$	166816.	−	288933.i	0.438194	−	0.758975i	0.997550	+	0.0699528i	$0.0222849\pi$
$618$		0			0
$619$	351705.			0.917905			0.458952	−	0.888461i	$-0.348225\pi$
$619$	351705.			0.917905			0.458952	+	0.888461i	$0.348225\pi$
$620$		0			0
$621$	−59576.1	−	34396.3i	−0.154486	−	0.0891925i
$622$		0			0
$623$	−92311.3	−	53295.9i	−0.237837	−	0.137315i
$624$		0			0
$625$	−275958.	−	477974.i	−0.706453	−	1.22361i
$626$		0			0
$627$	−225130.	−	60283.1i	−0.572662	−	0.153342i
$628$		0			0
$629$	271095.	−	156517.i	0.685205	−	0.395603i
$630$		0			0
$631$	225790.	−	391081.i	0.567083	−	0.982217i	−0.429769	−	0.902939i	$-0.641405\pi$
$631$	225790.	−	391081.i	0.567083	−	0.982217i	0.996853	−	0.0792785i	$-0.0252616\pi$
$632$		0			0
$633$	26318.4	−	45584.8i	0.0656829	−	0.113766i
$634$		0			0
$635$		−	1.19530e6i		−	2.96435i
$636$		0			0
$637$	−403892.	−	233187.i	−0.995374	−	0.574680i
$638$		0			0
$639$		−	473266.i		−	1.15905i
$640$		0			0
$641$	−245997.	+	142027.i	−0.598707	+	0.345664i	−0.768533	−	0.639810i	$-0.779013\pi$
$641$	−245997.	+	142027.i	−0.598707	+	0.345664i	0.169826	+	0.985474i	$0.445680\pi$
$642$		0			0
$643$	−28334.8	−	49077.3i	−0.0685328	−	0.118702i	0.829723	−	0.558176i	$-0.188498\pi$
$643$	−28334.8	−	49077.3i	−0.0685328	−	0.118702i	−0.898256	+	0.439473i	$0.855165\pi$
$644$		0			0
$645$			265636.i			0.638509i
$646$		0			0
$647$	−763633.			−1.82422			−0.912108	−	0.409949i	$-0.865546\pi$
$647$	−763633.			−1.82422			−0.912108	+	0.409949i	$0.865546\pi$
$648$		0			0
$649$	−1.23125e6	+	710861.i	−2.92318	+	1.68770i
$650$		0			0
$651$	10177.3	+	17627.5i	0.0240143	+	0.0415939i
$652$		0			0
$653$	−95023.7			−0.222846			−0.111423	−	0.993773i	$-0.535541\pi$
$653$	−95023.7			−0.222846			−0.111423	+	0.993773i	$0.535541\pi$
$654$		0			0
$655$	101792.	−	176309.i	0.237263	−	0.410952i
$656$		0			0
$657$	−753605.			−1.74587
$658$		0			0
$659$	−539553.	−	311511.i	−1.24241	−	0.717304i	−0.272823	−	0.962064i	$-0.587957\pi$
$659$	−539553.	−	311511.i	−1.24241	−	0.717304i	−0.969584	+	0.244761i	$0.921291\pi$
$660$		0			0
$661$	−201737.	−	116473.i	−0.461724	−	0.266577i	0.251045	−	0.967975i	$-0.419226\pi$
$661$	−201737.	−	116473.i	−0.461724	−	0.266577i	−0.712769	+	0.701399i	$0.752559\pi$
$662$		0			0
$663$	120405.	+	208547.i	0.273915	+	0.474435i
$664$		0			0
$665$	−46229.2	+	172645.i	−0.104538	+	0.390401i
$666$		0			0
$667$	78479.3	−	45310.1i	0.176402	−	0.101846i
$668$		0			0
$669$	144742.	−	250701.i	0.323402	−	0.560149i
$670$		0			0
$671$	63376.0	−	109771.i	0.140760	−	0.243804i
$672$		0			0
$673$		−	651134.i		−	1.43761i	−0.695213	−	0.718804i	$-0.744690\pi$
$673$		−	651134.i		−	1.43761i	0.695213	−	0.718804i	$-0.255310\pi$
$674$		0			0
$675$	516570.	+	298242.i	1.13376	+	0.654577i
$676$		0			0
$677$			113702.i			0.248080i	0.992277	+	0.124040i	$0.0395851\pi$
$677$			113702.i			0.248080i	−0.992277	+	0.124040i	$0.960415\pi$
$678$		0			0
$679$	30650.5	−	17696.0i	0.0664810	−	0.0383828i
$680$		0			0
$681$	−92238.6	−	159762.i	−0.198893	−	0.344492i
$682$		0			0
$683$			50549.5i			0.108362i	0.998531	+	0.0541808i	$0.0172547\pi$
$683$			50549.5i			0.108362i	−0.998531	+	0.0541808i	$0.982745\pi$
$684$		0			0
$685$	1.02134e6			2.17665
$686$		0			0
$687$	−160840.	+	92861.1i	−0.340786	+	0.196753i
$688$		0			0
$689$	467789.	+	810235.i	0.985398	+	1.70676i
$690$		0			0
$691$	54349.0			0.113824			0.0569122	−	0.998379i	$-0.481874\pi$
$691$	54349.0			0.113824			0.0569122	+	0.998379i	$0.481874\pi$
$692$		0			0
$693$	−89785.0	+	155512.i	−0.186955	+	0.323816i
$694$		0			0
$695$	669607.			1.38628
$696$		0			0
$697$	−23626.5	−	13640.7i	−0.0486332	−	0.0280784i
$698$		0			0
$699$	5332.94	+	3078.97i	0.0109147	+	0.00630161i
$700$		0			0
$701$	−199780.	−	346029.i	−0.406552	−	0.704169i	0.587949	−	0.808898i	$-0.299936\pi$
$701$	−199780.	−	346029.i	−0.406552	−	0.704169i	−0.994501	+	0.104729i	$0.966602\pi$
$702$		0			0
$703$	−198297.	+	198363.i	−0.401241	+	0.401375i
$704$		0			0
$705$	−195564.	+	112909.i	−0.393469	+	0.227170i
$706$		0			0
$707$	20772.5	−	35979.0i	0.0415575	−	0.0719798i
$708$		0			0
$709$	−121200.	+	209925.i	−0.241107	+	0.417610i	−0.961030	−	0.276444i	$-0.910844\pi$
$709$	−121200.	+	209925.i	−0.241107	+	0.417610i	0.719923	+	0.694054i	$0.244177\pi$
$710$		0			0
$711$			93131.2i			0.184228i
$712$		0			0
$713$	−82995.2	−	47917.3i	−0.163258	−	0.0942569i
$714$		0			0
$715$			2.00694e6i			3.92575i
$716$		0			0
$717$	115047.	−	66422.5i	0.223788	−	0.129204i
$718$		0			0
$719$	70745.7	+	122535.i	0.136849	+	0.237030i	0.926302	−	0.376781i	$-0.122969\pi$
$719$	70745.7	+	122535.i	0.136849	+	0.237030i	−0.789453	+	0.613811i	$0.789636\pi$
$720$		0			0
$721$		−	89954.0i		−	0.173041i
$722$		0			0
$723$	−121280.			−0.232014
$724$		0			0
$725$	−680474.	+	392872.i	−1.29460	+	0.747438i
$726$		0			0
$727$	−33668.0	−	58314.8i	−0.0637014	−	0.110334i	0.832416	−	0.554152i	$-0.186957\pi$
$727$	−33668.0	−	58314.8i	−0.0637014	−	0.110334i	−0.896117	+	0.443817i	$0.853624\pi$
$728$		0			0
$729$	225267.			0.423880
$730$		0			0
$731$	−414704.	+	718288.i	−0.776075	+	1.34420i
$732$		0			0
$733$	140696.			0.261863			0.130931	−	0.991391i	$-0.458203\pi$
$733$	140696.			0.261863			0.130931	+	0.991391i	$0.458203\pi$
$734$		0			0
$735$	254316.	+	146829.i	0.470759	+	0.271793i
$736$		0			0
$737$	891248.	+	514562.i	1.64083	+	0.947333i
$738$		0			0
$739$	56940.8	+	98624.4i	0.104264	+	0.180591i	0.913437	−	0.406979i	$-0.133418\pi$
$739$	56940.8	+	98624.4i	0.104264	+	0.180591i	−0.809173	+	0.587570i	$0.800085\pi$
$740$		0			0
$741$	−152596.	−	152545.i	−0.277912	−	0.277819i
$742$		0			0
$743$	−74898.0	+	43242.4i	−0.135673	+	0.0783307i	−0.566300	−	0.824199i	$-0.691626\pi$
$743$	−74898.0	+	43242.4i	−0.135673	+	0.0783307i	0.430627	+	0.902530i	$0.358292\pi$
$744$		0			0
$745$	−179658.	+	311176.i	−0.323693	+	0.560653i
$746$		0			0
$747$	148280.	−	256829.i	0.265731	−	0.460260i
$748$		0			0
$749$		−	17761.5i		−	0.0316603i
$750$		0			0
$751$	−678055.	−	391475.i	−1.20222	−	0.694104i	−0.241174	−	0.970482i	$-0.577533\pi$
$751$	−678055.	−	391475.i	−1.20222	−	0.694104i	−0.961049	+	0.276378i	$0.910866\pi$
$752$		0			0
$753$			121375.i			0.214062i
$754$		0			0
$755$	882858.	−	509718.i	1.54881	−	0.894203i
$756$		0			0
$757$	−142305.	−	246479.i	−0.248329	−	0.430118i	0.714733	−	0.699397i	$-0.246548\pi$
$757$	−142305.	−	246479.i	−0.248329	−	0.430118i	−0.963062	+	0.269279i	$0.913215\pi$
$758$		0			0
$759$			99206.8i			0.172210i
$760$		0			0
$761$	−406541.			−0.701997			−0.350999	−	0.936376i	$-0.614158\pi$
$761$	−406541.			−0.701997			−0.350999	+	0.936376i	$0.614158\pi$
$762$		0			0
$763$	−118975.	+	68690.2i	−0.204365	+	0.117990i
$764$		0			0
$765$	646107.	+	1.11909e6i	1.10403	+	1.91224i
$766$		0			0
$767$	−1.31622e6			−2.23738
$768$		0			0
$769$	224297.	−	388494.i	0.379290	−	0.656949i	−0.611669	−	0.791114i	$-0.709502\pi$
$769$	224297.	−	388494.i	0.379290	−	0.656949i	0.990959	+	0.134164i	$0.0428350\pi$
$770$		0			0
$771$	−219195.			−0.368741
$772$		0			0
$773$	709142.	+	409423.i	1.18679	+	0.685194i	0.957576	−	0.288182i	$-0.0930508\pi$
$773$	709142.	+	409423.i	1.18679	+	0.685194i	0.229215	+	0.973376i	$0.426384\pi$
$774$		0			0
$775$	719630.	+	415479.i	1.19814	+	0.691744i
$776$		0			0
$777$	−12679.0	−	21960.6i	−0.0210011	−	0.0363749i
$778$		0			0
$779$	23612.6	+	6322.74i	0.0389107	+	0.0104191i
$780$		0			0
$781$	−1.25149e6	+	722547.i	−2.05175	+	1.18458i
$782$		0			0
$783$	132002.	−	228634.i	0.215306	−	0.372921i
$784$		0			0
$785$	576437.	−	998418.i	0.935433	−	1.62022i
$786$		0			0
$787$		−	138682.i		−	0.223908i	−0.993713	−	0.111954i	$-0.964289\pi$
$787$		−	138682.i		−	0.223908i	0.993713	−	0.111954i	$-0.0357109\pi$
$788$		0			0
$789$	37672.0	+	21749.9i	0.0605152	+	0.0349385i
$790$		0			0
$791$		−	67401.2i		−	0.107725i
$792$		0			0
$793$	101625.	−	58673.3i	0.161605	−	0.0933026i
$794$		0			0
$795$	−294549.	−	510175.i	−0.466041	−	0.807206i
$796$		0			0
$797$		−	278675.i		−	0.438714i	−0.975645	−	0.219357i	$-0.929604\pi$
$797$		−	278675.i		−	0.438714i	0.975645	−	0.219357i	$-0.0703959\pi$
$798$		0			0
$799$	−705083.			−1.10445
$800$		0			0
$801$	598012.	−	345263.i	0.932063	−	0.538127i
$802$		0			0
$803$	1.15055e6	+	1.99281e6i	1.78432	+	3.09054i
$804$		0			0
$805$	76078.6			0.117401
$806$		0			0
$807$	−195356.	+	338367.i	−0.299972	+	0.519567i
$808$		0			0
$809$	782908.			1.19623			0.598114	−	0.801411i	$-0.295917\pi$
$809$	782908.			1.19623			0.598114	+	0.801411i	$0.295917\pi$
$810$		0			0
$811$	−992129.	−	572806.i	−1.50843	−	0.870895i	−0.999952	−	0.00982200i	$-0.996874\pi$
$811$	−992129.	−	572806.i	−1.50843	−	0.870895i	−0.508482	−	0.861073i	$-0.669793\pi$
$812$		0			0
$813$	73732.7	+	42569.6i	0.111552	+	0.0644048i
$814$		0			0
$815$	509135.	+	881847.i	0.766509	+	1.32763i
$816$		0			0
$817$	192223.	−	717866.i	0.287979	−	1.07547i
$818$		0			0
$819$	−143972.	+	83122.5i	−0.214641	+	0.123923i
$820$		0			0
$821$	−442362.	+	766194.i	−0.656284	+	1.13672i	0.325287	+	0.945615i	$0.394539\pi$
$821$	−442362.	+	766194.i	−0.656284	+	1.13672i	−0.981570	+	0.191101i	$0.938794\pi$
$822$		0			0
$823$	−351695.	+	609153.i	−0.519238	+	0.899346i	0.480512	+	0.876988i	$0.340451\pi$
$823$	−351695.	+	609153.i	−0.519238	+	0.899346i	−0.999750	+	0.0223580i	$0.992883\pi$
$824$		0			0
$825$		−	860198.i		−	1.26383i
$826$		0			0
$827$	−249371.	−	143974.i	−0.364615	−	0.210510i	0.306488	−	0.951874i	$-0.400846\pi$
$827$	−249371.	−	143974.i	−0.364615	−	0.210510i	−0.671103	+	0.741364i	$0.734179\pi$
$828$		0			0
$829$		−	25717.1i		−	0.0374207i	−0.999825	−	0.0187104i	$-0.994044\pi$
$829$		−	25717.1i		−	0.0374207i	0.999825	−	0.0187104i	$-0.00595604\pi$
$830$		0			0
$831$	−73497.4	+	42433.7i	−0.106431	+	0.0614482i
$832$		0			0
$833$	458453.	+	794063.i	0.660700	+	1.14437i
$834$		0			0
$835$		−	165662.i		−	0.237602i
$836$		0			0
$837$	−279195.			−0.398526
$838$		0			0
$839$	1.01375e6	−	585291.i	1.44015	−	0.831472i	0.442293	−	0.896871i	$-0.354165\pi$
$839$	1.01375e6	−	585291.i	1.44015	−	0.831472i	0.997859	+	0.0653988i	$0.0208319\pi$
$840$		0			0
$841$	−179755.	−	311345.i	−0.254150	−	0.440200i
$842$		0			0
$843$	−53214.0			−0.0748808
$844$		0			0
$845$	−297204.	+	514773.i	−0.416238	+	0.720945i
$846$		0			0
$847$	384470.			0.535914
$848$		0			0
$849$	−8892.22	−	5133.93i	−0.0123366	−	0.00712253i
$850$		0			0
$851$	103396.	+	59695.9i	0.142773	+	0.0824300i
$852$		0			0
$853$	−99339.2	−	172061.i	−0.136528	−	0.236474i	0.789652	−	0.613555i	$-0.210261\pi$
$853$	−99339.2	−	172061.i	−0.136528	−	0.236474i	−0.926180	+	0.377081i	$0.876928\pi$
$854$		0			0
$855$	−818850.	−	818576.i	−1.12014	−	1.11976i
$856$		0			0
$857$	−854393.	+	493284.i	−1.16331	+	0.671638i	−0.952095	−	0.305801i	$-0.901076\pi$
$857$	−854393.	+	493284.i	−1.16331	+	0.671638i	−0.211216	+	0.977439i	$0.567742\pi$
$858$		0			0
$859$	−537820.	+	931532.i	−0.728871	+	1.26244i	0.228489	+	0.973546i	$0.426621\pi$
$859$	−537820.	+	931532.i	−0.728871	+	1.26244i	−0.957361	+	0.288896i	$0.906712\pi$
$860$		0			0
$861$	−1105.00	+	1913.91i	−0.00149058	+	0.00258175i
$862$		0			0
$863$			1.03208e6i			1.38577i	0.721047	+	0.692886i	$0.243661\pi$
$863$			1.03208e6i			1.38577i	−0.721047	+	0.692886i	$0.756339\pi$
$864$		0			0
$865$	−742641.	−	428764.i	−0.992537	−	0.573041i
$866$		0			0
$867$		−	229843.i		−	0.305768i
$868$		0			0
$869$	246273.	−	142186.i	0.326120	−	0.188285i
$870$		0			0
$871$	476379.	+	825113.i	0.627938	+	1.08762i
$872$		0			0
$873$			229278.i			0.300838i
$874$		0			0
$875$	−350227.			−0.457439
$876$		0			0
$877$	833629.	−	481296.i	1.08386	−	0.625767i	0.151926	−	0.988392i	$-0.451453\pi$
$877$	833629.	−	481296.i	1.08386	−	0.625767i	0.931935	+	0.362624i	$0.118119\pi$
$878$		0			0
$879$	−135893.	−	235374.i	−0.175882	−	0.304636i
$880$		0			0
$881$	−664094.			−0.855613			−0.427807	−	0.903870i	$-0.640714\pi$
$881$	−664094.			−0.855613			−0.427807	+	0.903870i	$0.640714\pi$
$882$		0			0
$883$	438947.	−	760279.i	0.562977	−	0.975105i	−0.434257	−	0.900789i	$-0.642989\pi$
$883$	438947.	−	760279.i	0.562977	−	0.975105i	0.997235	−	0.0743165i	$-0.0236775\pi$
$884$		0			0
$885$	828777.			1.05816
$886$		0			0
$887$	179230.	+	103479.i	0.227806	+	0.131524i	0.609559	−	0.792740i	$-0.291346\pi$
$887$	179230.	+	103479.i	0.227806	+	0.131524i	−0.381754	+	0.924264i	$0.624680\pi$
$888$		0			0
$889$	−261825.	−	151165.i	−0.331290	−	0.191270i
$890$		0			0
$891$	−505388.	−	875357.i	−0.636604	−	1.10263i
$892$		0			0
$893$	610206.	−	163614.i	0.765198	−	0.205171i
$894$		0			0
$895$	−511057.	+	295059.i	−0.638004	+	0.368352i
$896$		0			0
$897$	−45922.6	+	79540.3i	−0.0570745	+	0.0988559i
$898$		0			0
$899$	183891.	−	318508.i	0.227531	−	0.394095i
$900$		0			0
$901$		−	1.83937e6i		−	2.26579i
$902$		0			0
$903$	58186.4	+	33593.9i	0.0713585	+	0.0411989i
$904$		0			0
$905$		−	1.96281e6i		−	2.39652i
$906$		0			0
$907$	624129.	−	360341.i	0.758682	−	0.438025i	−0.0701405	−	0.997537i	$-0.522345\pi$
$907$	624129.	−	360341.i	0.758682	−	0.438025i	0.828822	+	0.559512i	$0.189011\pi$
$908$		0			0
$909$	134569.	+	233080.i	0.162861	+	0.282083i
$910$		0			0
$911$			633956.i			0.763875i	0.924188	+	0.381937i	$0.124743\pi$
$911$			633956.i			0.763875i	−0.924188	+	0.381937i	$0.875257\pi$
$912$		0			0
$913$	−905533.			−1.08633
$914$		0			0
$915$	−63989.5	+	36944.4i	−0.0764305	+	0.0441272i
$916$		0			0
$917$	−25746.4	−	44594.1i	−0.0306181	−	0.0530321i
$918$		0			0
$919$	−495095.			−0.586216			−0.293108	−	0.956079i	$-0.594690\pi$
$919$	−495095.			−0.586216			−0.293108	+	0.956079i	$0.594690\pi$
$920$		0			0
$921$	−167369.	+	289891.i	−0.197313	+	0.341756i
$922$		0			0
$923$	−1.33786e6			−1.57039
$924$		0			0
$925$	−896523.	−	517608.i	−1.04780	−	0.604947i
$926$		0			0
$927$	504669.	+	291371.i	0.587283	+	0.339068i
$928$		0			0
$929$	4581.26	+	7934.97i	0.00530827	+	0.00919420i	0.868667	−	0.495396i	$-0.164977\pi$
$929$	4581.26	+	7934.97i	0.00530827	+	0.00919420i	−0.863359	+	0.504590i	$0.831644\pi$
$930$		0			0
$931$	−581024.	−	580830.i	−0.670340	−	0.670116i
$932$		0			0
$933$	−162117.	+	93598.5i	−0.186237	+	0.107524i
$934$		0			0
$935$	1.97285e6	−	3.41708e6i	2.25669	−	3.90870i
$936$		0			0
$937$	63459.9	−	109916.i	0.0722804	−	0.125193i	−0.827620	−	0.561289i	$-0.810306\pi$
$937$	63459.9	−	109916.i	0.0722804	−	0.125193i	0.899900	+	0.436096i	$0.143639\pi$
$938$		0			0
$939$		−	156559.i		−	0.177561i
$940$		0			0
$941$	1.13668e6	+	656265.i	1.28369	+	0.741140i	0.977521	−	0.210837i	$-0.0676188\pi$
$941$	1.13668e6	+	656265.i	1.28369	+	0.741140i	0.306171	+	0.951977i	$0.400952\pi$
$942$		0			0
$943$		−	10405.2i		−	0.0117011i
$944$		0			0
$945$	191946.	−	110820.i	0.214939	−	0.124095i
$946$		0			0
$947$	−577514.	−	1.00028e6i	−0.643966	−	1.11538i	−0.984539	−	0.175164i	$-0.943954\pi$
$947$	−577514.	−	1.00028e6i	−0.643966	−	1.11538i	0.340573	−	0.940218i	$-0.389379\pi$
$948$		0			0
$949$			2.13034e6i			2.36547i
$950$		0			0
$951$	35088.8			0.0387978
$952$		0			0
$953$	−248222.	+	143311.i	−0.273309	+	0.157795i	−0.630390	−	0.776278i	$-0.717105\pi$
$953$	−248222.	+	143311.i	−0.273309	+	0.157795i	0.357082	+	0.934073i	$0.383772\pi$
$954$		0			0
$955$	399537.	+	692018.i	0.438076	+	0.758770i
$956$		0			0
$957$	−380723.			−0.415705
$958$		0			0
$959$	129165.	−	223720.i	0.140445	−	0.243259i
$960$		0			0
$961$	534576.			0.578846
$962$		0			0
$963$	99647.1	+	57531.3i	0.107451	+	0.0620371i
$964$		0			0
$965$	292469.	+	168857.i	0.314069	+	0.181328i
$966$		0			0
$967$	−740794.	−	1.28309e6i	−0.792217	−	1.37216i	−0.924591	−	0.380961i	$-0.875593\pi$
$967$	−740794.	−	1.28309e6i	−0.792217	−	1.37216i	0.132374	−	0.991200i	$-0.457740\pi$
$968$		0			0
$969$	109861.	+	409732.i	0.117002	+	0.436367i
$970$		0			0
$971$	350559.	−	202395.i	0.371811	−	0.214665i	−0.302438	−	0.953169i	$-0.597801\pi$
$971$	350559.	−	202395.i	0.371811	−	0.214665i	0.674249	+	0.738504i	$0.264467\pi$
$972$		0			0
$973$	84682.6	−	146675.i	0.0894475	−	0.154928i
$974$		0			0
$975$	398184.	−	689674.i	0.418865	−	0.725495i
$976$		0			0
$977$			1.28905e6i			1.35046i	0.737608	+	0.675229i	$0.235955\pi$
$977$			1.28905e6i			1.35046i	−0.737608	+	0.675229i	$0.764045\pi$
$978$		0			0
$979$	−1.82600e6	−	1.05424e6i	−1.90518	−	1.09995i
$980$		0			0
$981$		−	889979.i		−	0.924787i
$982$		0			0
$983$	537947.	−	310584.i	0.556714	−	0.321419i	−0.195112	−	0.980781i	$-0.562507\pi$
$983$	537947.	−	310584.i	0.556714	−	0.321419i	0.751826	+	0.659362i	$0.229174\pi$
$984$		0			0
$985$	−54415.2	−	94249.9i	−0.0560852	−	0.0971424i
$986$		0			0
$987$			57116.6i			0.0586311i
$988$		0			0
$989$	−316338.			−0.323414
$990$		0			0
$991$	−1.37552e6	+	794156.i	−1.40062	+	0.808647i	−0.994456	−	0.105155i	$-0.966466\pi$
$991$	−1.37552e6	+	794156.i	−1.40062	+	0.808647i	−0.406161	+	0.913801i	$0.633133\pi$
$992$		0			0
$993$	−224078.	−	388114.i	−0.227248	−	0.393605i
$994$		0			0
$995$	3.20857e6			3.24090
$996$		0			0
$997$	564046.	−	976956.i	0.567445	−	0.982844i	−0.429372	−	0.903128i	$-0.641265\pi$
$997$	564046.	−	976956.i	0.567445	−	0.982844i	0.996818	−	0.0797166i	$-0.0254015\pi$
$998$		0			0
$999$	347824.			0.348521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.9		40
4.3	odd	2		152.5.n.a.145.12	yes	40
19.8	odd	6	inner	304.5.r.d.65.9		40
76.27	even	6		152.5.n.a.65.12	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.12	✓	40	76.27	even	6
152.5.n.a.145.12	yes	40	4.3	odd	2
304.5.r.d.65.9		40	19.8	odd	6	inner
304.5.r.d.145.9		40	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.52583 + 1.45829i) q^{3} +(22.1213 + 38.3151i) q^{5} +11.1904 q^{7} +(-36.2468 + 62.7813i) q^{9} +O(q^{10})\)	\(q+(-2.52583 + 1.45829i) q^{3} +(22.1213 + 38.3151i) q^{5} +11.1904 q^{7} +(-36.2468 + 62.7813i) q^{9} +221.355 q^{11} +(177.474 + 102.465i) q^{13} +(-111.749 - 64.5183i) q^{15} +(-201.449 - 348.920i) q^{17} +(255.308 + 255.223i) q^{19} +(-28.2649 + 16.3188i) q^{21} +(76.8331 - 133.079i) q^{23} +(-666.200 + 1153.89i) q^{25} -447.676i q^{27} +(510.713 + 294.860i) q^{29} -623.654i q^{31} +(-559.106 + 322.800i) q^{33} +(247.545 + 428.760i) q^{35} +776.955i q^{37} -597.693 q^{39} +(58.6413 - 33.8566i) q^{41} +(-1029.30 - 1782.81i) q^{43} -3207.30 q^{45} +(875.015 - 1515.57i) q^{47} -2275.78 q^{49} +(1017.65 + 587.541i) q^{51} +(3953.72 + 2282.68i) q^{53} +(4896.66 + 8481.26i) q^{55} +(-1017.05 - 272.336i) q^{57} +(-5562.31 + 3211.40i) q^{59} +(286.309 - 495.902i) q^{61} +(-405.615 + 702.545i) q^{63} +9066.61i q^{65} +(4026.32 + 2324.60i) q^{67} +448.179i q^{69} +(-5653.75 + 3264.19i) q^{71} +(5197.73 + 9002.74i) q^{73} -3886.05i q^{75} +2477.05 q^{77} +(1112.57 - 642.341i) q^{79} +(-2283.15 - 3954.53i) q^{81} -4090.86 q^{83} +(8912.61 - 15437.1i) q^{85} -1719.96 q^{87} +(-8249.18 - 4762.66i) q^{89} +(1986.00 + 1146.62i) q^{91} +(909.467 + 1575.24i) q^{93} +(-4131.16 + 15428.0i) q^{95} +(2739.00 - 1581.37i) q^{97} +(-8023.42 + 13897.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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