LMFDB - Embedded newform 304.5.r.b.145.1

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} + \cdots + 90728724573 $ x^12 - 6x^11 + 631x^10 - 3100x^9 + 142264x^8 - 550522x^7 + 14083117x^6 - 40335478x^5 + 638031136x^4 - 1209472584x^3 + 12784623475x^2 - 12186518934*x + 90728724573
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$0.500000 + 15.2283i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.b.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.4381 + 7.18116i) q^{3} +(-3.11411 - 5.39380i) q^{5} -49.9415 q^{7} +(62.6382 - 108.493i) q^{9} +O(q^{10})$	\(q+(-12.4381 + 7.18116i) q^{3} +(-3.11411 - 5.39380i) q^{5} -49.9415 q^{7} +(62.6382 - 108.493i) q^{9} -1.88575 q^{11} +(-69.0003 - 39.8373i) q^{13} +(77.4675 + 44.7259i) q^{15} +(-119.788 - 207.478i) q^{17} +(-72.4707 - 353.651i) q^{19} +(621.179 - 358.638i) q^{21} +(-109.429 + 189.537i) q^{23} +(293.105 - 507.672i) q^{25} +635.911i q^{27} +(340.159 + 196.391i) q^{29} -580.549i q^{31} +(23.4553 - 13.5419i) q^{33} +(155.523 + 269.374i) q^{35} +2478.77i q^{37} +1144.31 q^{39} +(-2840.91 + 1640.20i) q^{41} +(162.917 + 282.181i) q^{43} -780.249 q^{45} +(969.593 - 1679.39i) q^{47} +93.1537 q^{49} +(2979.87 + 1720.43i) q^{51} +(2087.49 + 1205.21i) q^{53} +(5.87245 + 10.1714i) q^{55} +(3441.03 + 3878.34i) q^{57} +(-3046.44 + 1758.86i) q^{59} +(-1039.02 + 1799.64i) q^{61} +(-3128.24 + 5418.28i) q^{63} +496.232i q^{65} +(4389.01 + 2533.99i) q^{67} -3143.32i q^{69} +(-2994.82 + 1729.06i) q^{71} +(4356.65 + 7545.94i) q^{73} +8419.33i q^{75} +94.1773 q^{77} +(-3640.40 + 2101.79i) q^{79} +(507.109 + 878.339i) q^{81} +11775.2 q^{83} +(-746.064 + 1292.22i) q^{85} -5641.26 q^{87} +(-8212.16 - 4741.29i) q^{89} +(3445.98 + 1989.54i) q^{91} +(4169.02 + 7220.95i) q^{93} +(-1681.84 + 1492.20i) q^{95} +(5045.74 - 2913.16i) q^{97} +(-118.120 + 204.590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 9 q^{5} + 52 q^{7} + 136 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 9 * q^5 + 52 * q^7 + 136 * q^9	$ 12 q + 12 q^{3} + 9 q^{5} + 52 q^{7} + 136 q^{9} - 6 q^{11} - 93 q^{13} + 741 q^{15} - 483 q^{17} + 533 q^{19} + 972 q^{21} - 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} + 1128 q^{35} + 2250 q^{39} - 1692 q^{41} + 63 q^{43} + 7976 q^{45} + 3471 q^{47} + 420 q^{49} - 6741 q^{51} - 3771 q^{53} + 2014 q^{55} + 7617 q^{57} + 9594 q^{59} + 1229 q^{61} - 1514 q^{63} - 7590 q^{67} - 963 q^{71} - 2838 q^{73} - 15408 q^{77} - 11073 q^{79} + 2086 q^{81} + 14202 q^{83} + 9455 q^{85} + 39510 q^{87} + 6525 q^{89} + 7686 q^{91} - 5316 q^{93} - 1521 q^{95} - 34110 q^{97} - 13220 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 9 * q^5 + 52 * q^7 + 136 * q^9 - 6 * q^11 - 93 * q^13 + 741 * q^15 - 483 * q^17 + 533 * q^19 + 972 * q^21 - 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 + 1128 * q^35 + 2250 * q^39 - 1692 * q^41 + 63 * q^43 + 7976 * q^45 + 3471 * q^47 + 420 * q^49 - 6741 * q^51 - 3771 * q^53 + 2014 * q^55 + 7617 * q^57 + 9594 * q^59 + 1229 * q^61 - 1514 * q^63 - 7590 * q^67 - 963 * q^71 - 2838 * q^73 - 15408 * q^77 - 11073 * q^79 + 2086 * q^81 + 14202 * q^83 + 9455 * q^85 + 39510 * q^87 + 6525 * q^89 + 7686 * q^91 - 5316 * q^93 - 1521 * q^95 - 34110 * q^97 - 13220 * 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
$3$	−12.4381	+	7.18116i	−1.38202	+	0.797907i	−0.992398	−	0.123070i	$-0.960726\pi$
$3$	−12.4381	+	7.18116i	−1.38202	+	0.797907i	−0.389617	+	0.920977i	$0.627393\pi$
$4$		0			0
$5$	−3.11411	−	5.39380i	−0.124564	−	0.215752i	0.796998	−	0.603982i	$-0.206420\pi$
$5$	−3.11411	−	5.39380i	−0.124564	−	0.215752i	−0.921563	+	0.388230i	$0.873087\pi$
$6$		0			0
$7$	−49.9415			−1.01921			−0.509607	−	0.860407i	$-0.670209\pi$
$7$	−49.9415			−1.01921			−0.509607	+	0.860407i	$0.670209\pi$
$8$		0			0
$9$	62.6382	−	108.493i	0.773311	−	1.33941i
$10$		0			0
$11$	−1.88575			−0.0155847			−0.00779237	−	0.999970i	$-0.502480\pi$
$11$	−1.88575			−0.0155847			−0.00779237	+	0.999970i	$0.502480\pi$
$12$		0			0
$13$	−69.0003	−	39.8373i	−0.408286	−	0.235724i	0.281767	−	0.959483i	$-0.409079\pi$
$13$	−69.0003	−	39.8373i	−0.408286	−	0.235724i	−0.690053	+	0.723759i	$0.742413\pi$
$14$		0			0
$15$	77.4675	+	44.7259i	0.344300	+	0.198782i
$16$		0			0
$17$	−119.788	−	207.478i	−0.414490	−	0.717918i	0.580885	−	0.813986i	$-0.302707\pi$
$17$	−119.788	−	207.478i	−0.414490	−	0.717918i	−0.995375	+	0.0960680i	$0.969373\pi$
$18$		0			0
$19$	−72.4707	−	353.651i	−0.200750	−	0.979643i
$19$	−72.4707	−	353.651i	−0.200750	−	0.979643i
$20$		0			0
$21$	621.179	−	358.638i	1.40857	−	0.813238i
$22$		0			0
$23$	−109.429	+	189.537i	−0.206861	+	0.358294i	−0.950724	−	0.310038i	$-0.899658\pi$
$23$	−109.429	+	189.537i	−0.206861	+	0.358294i	0.743863	+	0.668332i	$0.232991\pi$
$24$		0			0
$25$	293.105	−	507.672i	0.468967	−	0.812275i
$26$		0			0
$27$			635.911i			0.872306i
$28$		0			0
$29$	340.159	+	196.391i	0.404470	+	0.233521i	0.688411	−	0.725321i	$-0.258309\pi$
$29$	340.159	+	196.391i	0.404470	+	0.233521i	−0.283941	+	0.958842i	$0.591642\pi$
$30$		0			0
$31$		−	580.549i		−	0.604109i	−0.953291	−	0.302055i	$-0.902327\pi$
$31$		−	580.549i		−	0.604109i	0.953291	−	0.302055i	$-0.0976725\pi$
$32$		0			0
$33$	23.4553	−	13.5419i	0.0215383	−	0.0124352i
$34$		0			0
$35$	155.523	+	269.374i	0.126958	+	0.219898i
$36$		0			0
$37$			2478.77i			1.81064i	0.424727	+	0.905321i	$0.360370\pi$
$37$			2478.77i			1.81064i	−0.424727	+	0.905321i	$0.639630\pi$
$38$		0			0
$39$	1144.31			0.752343
$40$		0			0
$41$	−2840.91	+	1640.20i	−1.69001	+	0.975729i	−0.735516	+	0.677507i	$0.763060\pi$
$41$	−2840.91	+	1640.20i	−1.69001	+	0.975729i	−0.954497	+	0.298222i	$0.903606\pi$
$42$		0			0
$43$	162.917	+	282.181i	0.0881111	+	0.152613i	0.906713	−	0.421749i	$-0.138584\pi$
$43$	162.917	+	282.181i	0.0881111	+	0.152613i	−0.818602	+	0.574362i	$0.805250\pi$
$44$		0			0
$45$	−780.249			−0.385308
$46$		0			0
$47$	969.593	−	1679.39i	0.438929	−	0.760247i	−0.558678	−	0.829384i	$-0.688691\pi$
$47$	969.593	−	1679.39i	0.438929	−	0.760247i	0.997607	+	0.0691376i	$0.0220247\pi$
$48$		0			0
$49$	93.1537			0.0387979
$50$		0			0
$51$	2979.87	+	1720.43i	1.14566	+	0.661449i
$52$		0			0
$53$	2087.49	+	1205.21i	0.743142	+	0.429053i	0.823211	−	0.567736i	$-0.192181\pi$
$53$	2087.49	+	1205.21i	0.743142	+	0.429053i	−0.0800686	+	0.996789i	$0.525514\pi$
$54$		0			0
$55$	5.87245	+	10.1714i	0.00194130	+	0.00336244i
$56$		0			0
$57$	3441.03	+	3878.34i	1.05910	+	1.19370i
$58$		0			0
$59$	−3046.44	+	1758.86i	−0.875163	+	0.505275i	−0.869060	−	0.494706i	$-0.835276\pi$
$59$	−3046.44	+	1758.86i	−0.875163	+	0.505275i	−0.00610218	+	0.999981i	$0.501942\pi$
$60$		0			0
$61$	−1039.02	+	1799.64i	−0.279232	+	0.483644i	−0.971194	−	0.238290i	$-0.923413\pi$
$61$	−1039.02	+	1799.64i	−0.279232	+	0.483644i	0.691962	+	0.721934i	$0.256747\pi$
$62$		0			0
$63$	−3128.24	+	5418.28i	−0.788170	+	1.36515i
$64$		0			0
$65$			496.232i			0.117451i
$66$		0			0
$67$	4389.01	+	2533.99i	0.977725	+	0.564490i	0.901583	−	0.432607i	$-0.142406\pi$
$67$	4389.01	+	2533.99i	0.977725	+	0.564490i	0.0761425	+	0.997097i	$0.475740\pi$
$68$		0			0
$69$		−	3143.32i		−	0.660223i
$70$		0			0
$71$	−2994.82	+	1729.06i	−0.594092	+	0.342999i	−0.766714	−	0.641989i	$-0.778109\pi$
$71$	−2994.82	+	1729.06i	−0.594092	+	0.342999i	0.172622	+	0.984988i	$0.444776\pi$
$72$		0			0
$73$	4356.65	+	7545.94i	0.817536	+	1.41601i	0.907492	+	0.420069i	$0.137994\pi$
$73$	4356.65	+	7545.94i	0.817536	+	1.41601i	−0.0899558	+	0.995946i	$0.528673\pi$
$74$		0			0
$75$			8419.33i			1.49677i
$76$		0			0
$77$	94.1773			0.0158842
$78$		0			0
$79$	−3640.40	+	2101.79i	−0.583304	+	0.336771i	−0.762445	−	0.647053i	$-0.776001\pi$
$79$	−3640.40	+	2101.79i	−0.583304	+	0.336771i	0.179141	+	0.983823i	$0.442668\pi$
$80$		0			0
$81$	507.109	+	878.339i	0.0772915	+	0.133873i
$82$		0			0
$83$	11775.2			1.70927			0.854635	−	0.519229i	$-0.173781\pi$
$83$	11775.2			1.70927			0.854635	+	0.519229i	$0.173781\pi$
$84$		0			0
$85$	−746.064	+	1292.22i	−0.103261	+	0.178854i
$86$		0			0
$87$	−5641.26			−0.745311
$88$		0			0
$89$	−8212.16	−	4741.29i	−1.03676	−	0.598573i	−0.117845	−	0.993032i	$-0.537599\pi$
$89$	−8212.16	−	4741.29i	−1.03676	−	0.598573i	−0.918913	+	0.394460i	$0.870932\pi$
$90$		0			0
$91$	3445.98	+	1989.54i	0.416131	+	0.240253i
$92$		0			0
$93$	4169.02	+	7220.95i	0.482023	+	0.834888i
$94$		0			0
$95$	−1681.84	+	1492.20i	−0.186354	+	0.165341i
$96$		0			0
$97$	5045.74	−	2913.16i	0.536267	−	0.309614i	−0.207297	−	0.978278i	$-0.566467\pi$
$97$	5045.74	−	2913.16i	0.536267	−	0.309614i	0.743565	+	0.668664i	$0.233133\pi$
$98$		0			0
$99$	−118.120	+	204.590i	−0.0120518	+	0.0208744i
$100$		0			0
$101$	9167.14	−	15878.0i	0.898651	−	1.55651i	0.0694313	−	0.997587i	$-0.477882\pi$
$101$	9167.14	−	15878.0i	0.898651	−	1.55651i	0.829220	−	0.558923i	$-0.188785\pi$
$102$		0			0
$103$		−	15685.2i		−	1.47848i	−0.673443	−	0.739239i	$-0.735185\pi$
$103$		−	15685.2i		−	1.47848i	0.673443	−	0.739239i	$-0.264815\pi$
$104$		0			0
$105$	−3868.84	−	2233.68i	−0.350916	−	0.202601i
$106$		0			0
$107$			15464.3i			1.35071i	0.737494	+	0.675354i	$0.236009\pi$
$107$			15464.3i			1.35071i	−0.737494	+	0.675354i	$0.763991\pi$
$108$		0			0
$109$	15286.3	−	8825.56i	1.28662	−	0.742830i	0.308569	−	0.951202i	$-0.400150\pi$
$109$	15286.3	−	8825.56i	1.28662	−	0.742830i	0.978050	+	0.208372i	$0.0668166\pi$
$110$		0			0
$111$	−17800.4	−	30831.3i	−1.44472	−	2.50234i
$112$		0			0
$113$		−	5351.37i		−	0.419090i	−0.977799	−	0.209545i	$-0.932802\pi$
$113$		−	5351.37i		−	0.419090i	0.977799	−	0.209545i	$-0.0671984\pi$
$114$		0			0
$115$	1363.10			0.103070
$116$		0			0
$117$	−8644.10	+	4990.68i	−0.631464	+	0.364576i
$118$		0			0
$119$	5982.37	+	10361.8i	0.422454	+	0.731712i
$120$		0			0
$121$	−14637.4			−0.999757
$122$		0			0
$123$	23557.1	−	40802.1i	1.55708	−	2.69695i
$124$		0			0
$125$	−7543.68			−0.482796
$126$		0			0
$127$	5218.76	+	3013.05i	0.323564	+	0.186810i	0.652980	−	0.757375i	$-0.273519\pi$
$127$	5218.76	+	3013.05i	0.323564	+	0.186810i	−0.329416	+	0.944185i	$0.606852\pi$
$128$		0			0
$129$	−4052.78	−	2339.87i	−0.243542	−	0.140609i
$130$		0			0
$131$	5324.73	+	9222.71i	0.310281	+	0.537423i	0.978423	−	0.206611i	$-0.0662435\pi$
$131$	5324.73	+	9222.71i	0.310281	+	0.537423i	−0.668142	+	0.744034i	$0.732910\pi$
$132$		0			0
$133$	3619.30	+	17661.9i	0.204607	+	0.998466i
$134$		0			0
$135$	3429.98	−	1980.30i	0.188202	−	0.108658i
$136$		0			0
$137$	−4402.76	+	7625.80i	−0.234576	+	0.406298i	−0.959149	−	0.282900i	$-0.908704\pi$
$137$	−4402.76	+	7625.80i	−0.234576	+	0.406298i	0.724573	+	0.689198i	$0.242037\pi$
$138$		0			0
$139$	−3584.83	+	6209.10i	−0.185540	+	0.321366i	−0.943759	−	0.330636i	$-0.892737\pi$
$139$	−3584.83	+	6209.10i	−0.185540	+	0.321366i	0.758218	+	0.652001i	$0.226070\pi$
$140$		0			0
$141$			27851.2i			1.40090i
$142$		0			0
$143$	130.117	+	75.1234i	0.00636302	+	0.00367369i
$144$		0			0
$145$		−	2446.33i		−	0.116354i
$146$		0			0
$147$	−1158.66	+	668.952i	−0.0536192	+	0.0309571i
$148$		0			0
$149$	−8324.08	−	14417.7i	−0.374941	−	0.649418i	0.615377	−	0.788233i	$-0.289004\pi$
$149$	−8324.08	−	14417.7i	−0.374941	−	0.649418i	−0.990318	+	0.138815i	$0.955671\pi$
$150$		0			0
$151$		−	1780.79i		−	0.0781013i	−0.999237	−	0.0390506i	$-0.987567\pi$
$151$		−	1780.79i		−	0.0781013i	0.999237	−	0.0390506i	$-0.0124334\pi$
$152$		0			0
$153$	−30013.1			−1.28212
$154$		0			0
$155$	−3131.37	+	1807.89i	−0.130338	+	0.0752506i
$156$		0			0
$157$	4609.89	+	7984.57i	0.187022	+	0.323931i	0.944256	−	0.329212i	$-0.106783\pi$
$157$	4609.89	+	7984.57i	0.187022	+	0.323931i	−0.757234	+	0.653143i	$0.773450\pi$
$158$		0			0
$159$	−34619.2			−1.36938
$160$		0			0
$161$	5465.07	−	9465.78i	0.210836	−	0.365178i
$162$		0			0
$163$	−29276.2			−1.10189			−0.550947	−	0.834540i	$-0.685733\pi$
$163$	−29276.2			−1.10189			−0.550947	+	0.834540i	$0.685733\pi$
$164$		0			0
$165$	−146.085	−	84.3420i	−0.00536582	−	0.00309796i
$166$		0			0
$167$	37315.4	+	21544.1i	1.33800	+	0.772493i	0.986510	−	0.163700i	$-0.0523428\pi$
$167$	37315.4	+	21544.1i	1.33800	+	0.772493i	0.351487	+	0.936193i	$0.385676\pi$
$168$		0			0
$169$	−11106.5	−	19237.0i	−0.388869	−	0.673540i
$170$		0			0
$171$	−42907.9	−	14289.5i	−1.46739	−	0.488681i
$172$		0			0
$173$	38605.2	−	22288.7i	1.28989	−	0.744721i	0.311259	−	0.950325i	$-0.399249\pi$
$173$	38605.2	−	22288.7i	1.28989	−	0.744721i	0.978635	+	0.205605i	$0.0659161\pi$
$174$		0			0
$175$	−14638.1	+	25353.9i	−0.477978	+	0.827883i
$176$		0			0
$177$	25261.4	−	43754.0i	0.806325	−	1.39660i
$178$		0			0
$179$			18503.2i			0.577486i	0.957407	+	0.288743i	$0.0932373\pi$
$179$			18503.2i			0.577486i	−0.957407	+	0.288743i	$0.906763\pi$
$180$		0			0
$181$	27630.5	+	15952.4i	0.843395	+	0.486934i	0.858417	−	0.512953i	$-0.171448\pi$
$181$	27630.5	+	15952.4i	0.843395	+	0.486934i	−0.0150220	+	0.999887i	$0.504782\pi$
$182$		0			0
$183$		−	29845.6i		−	0.891205i
$184$		0			0
$185$	13370.0	−	7719.17i	0.390650	−	0.225542i
$186$		0			0
$187$	225.890	+	391.253i	0.00645972	+	0.0111886i
$188$		0			0
$189$		−	31758.4i		−	0.889067i
$190$		0			0
$191$	28246.4			0.774276			0.387138	−	0.922022i	$-0.373464\pi$
$191$	28246.4			0.774276			0.387138	+	0.922022i	$0.373464\pi$
$192$		0			0
$193$	−35466.8	+	20476.8i	−0.952154	+	0.549727i	−0.893750	−	0.448566i	$-0.851935\pi$
$193$	−35466.8	+	20476.8i	−0.952154	+	0.549727i	−0.0584049	+	0.998293i	$0.518601\pi$
$194$		0			0
$195$	−3563.52	−	6172.20i	−0.0937152	−	0.162319i
$196$		0			0
$197$	−22359.6			−0.576144			−0.288072	−	0.957609i	$-0.593014\pi$
$197$	−22359.6			−0.576144			−0.288072	+	0.957609i	$0.593014\pi$
$198$		0			0
$199$	2166.66	−	3752.77i	0.0547123	−	0.0947645i	−0.837372	−	0.546633i	$-0.815909\pi$
$199$	2166.66	−	3752.77i	0.0547123	−	0.0947645i	0.892084	+	0.451869i	$0.149243\pi$
$200$		0			0
$201$	−72788.1			−1.80164
$202$		0			0
$203$	−16988.1	−	9808.06i	−0.412241	−	0.238008i
$204$		0			0
$205$	17693.8	+	10215.5i	0.421031	+	0.243082i
$206$		0			0
$207$	13708.9	+	23744.5i	0.319936	+	0.554145i
$208$		0			0
$209$	136.662	+	666.898i	0.00312863	+	0.0152675i
$210$		0			0
$211$	48243.9	−	27853.6i	1.08362	−	0.625629i	0.151750	−	0.988419i	$-0.451509\pi$
$211$	48243.9	−	27853.6i	1.08362	−	0.625629i	0.931871	+	0.362790i	$0.118176\pi$
$212$		0			0
$213$	24833.3	−	43012.6i	0.547363	−	0.948060i
$214$		0			0
$215$	1014.69	−	1757.49i	0.0219510	−	0.0380203i
$216$		0			0
$217$			28993.5i			0.615717i
$218$		0			0
$219$	−108377.	−	62571.6i	−2.25970	−	1.30464i
$220$		0			0
$221$			19088.1i			0.390821i
$222$		0			0
$223$	23671.3	−	13666.6i	0.476005	−	0.274822i	−0.242745	−	0.970090i	$-0.578048\pi$
$223$	23671.3	−	13666.6i	0.476005	−	0.274822i	0.718750	+	0.695268i	$0.244715\pi$
$224$		0			0
$225$	−36719.1	−	63599.3i	−0.725315	−	1.25628i
$226$		0			0
$227$			42099.3i			0.817003i	0.912758	+	0.408501i	$0.133949\pi$
$227$			42099.3i			0.817003i	−0.912758	+	0.408501i	$0.866051\pi$
$228$		0			0
$229$	12163.3			0.231942			0.115971	−	0.993253i	$-0.463002\pi$
$229$	12163.3			0.231942			0.115971	+	0.993253i	$0.463002\pi$
$230$		0			0
$231$	−1171.39	+	676.303i	−0.0219522	+	0.0126741i
$232$		0			0
$233$	12709.0	+	22012.6i	0.234098	+	0.405470i	0.959010	−	0.283372i	$-0.0914529\pi$
$233$	12709.0	+	22012.6i	0.234098	+	0.405470i	−0.724912	+	0.688841i	$0.758120\pi$
$234$		0			0
$235$	−12077.7			−0.218700
$236$		0			0
$237$	30186.5	−	52284.6i	0.537424	−	0.930845i
$238$		0			0
$239$	86525.4			1.51477			0.757387	−	0.652967i	$-0.226476\pi$
$239$	86525.4			1.51477			0.757387	+	0.652967i	$0.226476\pi$
$240$		0			0
$241$	45400.9	+	26212.2i	0.781682	+	0.451305i	0.837026	−	0.547163i	$-0.184292\pi$
$241$	45400.9	+	26212.2i	0.781682	+	0.451305i	−0.0553438	+	0.998467i	$0.517625\pi$
$242$		0			0
$243$	−57222.9	−	33037.7i	−0.969076	−	0.559496i
$244$		0			0
$245$	−290.091	−	502.452i	−0.00483284	−	0.00837072i
$246$		0			0
$247$	−9088.01	+	27289.1i	−0.148962	+	0.447296i
$248$		0			0
$249$	−146461.	+	84559.4i	−2.36224	+	1.36384i
$250$		0			0
$251$	19639.4	−	34016.4i	0.311732	−	0.539935i	−0.667006	−	0.745053i	$-0.732424\pi$
$251$	19639.4	−	34016.4i	0.311732	−	0.539935i	0.978737	+	0.205118i	$0.0657577\pi$
$252$		0			0
$253$	206.357	−	357.420i	0.00322387	−	0.00558391i
$254$		0			0
$255$		−	21430.4i		−	0.329572i
$256$		0			0
$257$	64968.9	+	37509.8i	0.983646	+	0.567908i	0.903369	−	0.428864i	$-0.141086\pi$
$257$	64968.9	+	37509.8i	0.983646	+	0.567908i	0.0802773	+	0.996773i	$0.474419\pi$
$258$		0			0
$259$		−	123793.i		−	1.84543i
$260$		0			0
$261$	42613.9	−	24603.1i	0.625562	−	0.361168i
$262$		0			0
$263$	14757.8	+	25561.3i	0.213359	+	0.369548i	0.952764	−	0.303713i	$-0.0982264\pi$
$263$	14757.8	+	25561.3i	0.213359	+	0.369548i	−0.739405	+	0.673261i	$0.764893\pi$
$264$		0			0
$265$		−	15012.6i		−	0.213779i
$266$		0			0
$267$	136192.			1.91042
$268$		0			0
$269$	87976.7	−	50793.4i	1.21580	−	0.701944i	0.251785	−	0.967783i	$-0.418982\pi$
$269$	87976.7	−	50793.4i	1.21580	−	0.701944i	0.964017	+	0.265839i	$0.0856490\pi$
$270$		0			0
$271$	−11915.4	−	20638.0i	−0.162244	−	0.281015i	0.773429	−	0.633883i	$-0.218540\pi$
$271$	−11915.4	−	20638.0i	−0.162244	−	0.281015i	−0.935673	+	0.352868i	$0.885207\pi$
$272$		0			0
$273$	−57148.7			−0.766799
$274$		0			0
$275$	−552.723	+	957.344i	−0.00730873	+	0.0126591i
$276$		0			0
$277$	−109790.			−1.43088			−0.715438	−	0.698677i	$-0.753773\pi$
$277$	−109790.			−1.43088			−0.715438	+	0.698677i	$0.753773\pi$
$278$		0			0
$279$	−62985.2	−	36364.5i	−0.809152	−	0.467164i
$280$		0			0
$281$	−52508.2	−	30315.6i	−0.664989	−	0.383932i	0.129186	−	0.991620i	$-0.458764\pi$
$281$	−52508.2	−	30315.6i	−0.664989	−	0.383932i	−0.794175	+	0.607689i	$0.792097\pi$
$282$		0			0
$283$	8384.27	+	14522.0i	0.104687	+	0.181323i	0.913610	−	0.406591i	$-0.133283\pi$
$283$	8384.27	+	14522.0i	0.104687	+	0.181323i	−0.808923	+	0.587914i	$0.799949\pi$
$284$		0			0
$285$	10203.2	−	30637.8i	0.125617	−	0.377196i
$286$		0			0
$287$	141879.	−	81914.1i	1.72249	−	0.994477i
$288$		0			0
$289$	13062.3	−	22624.6i	0.156396	−	0.270886i
$290$		0			0
$291$	−41839.7	+	72468.6i	−0.494087	+	0.855783i
$292$		0			0
$293$			127491.i			1.48506i	0.669813	+	0.742530i	$0.266374\pi$
$293$			127491.i			1.48506i	−0.669813	+	0.742530i	$0.733626\pi$
$294$		0			0
$295$	18973.9	+	10954.6i	0.218028	+	0.125879i
$296$		0			0
$297$		−	1199.17i		−	0.0135947i
$298$		0			0
$299$	15101.3	−	8718.75i	0.168917	−	0.0975241i
$300$		0			0
$301$	−8136.34	−	14092.6i	−0.0898041	−	0.155545i
$302$		0			0
$303$			263323.i			2.86816i
$304$		0			0
$305$	12942.5			0.139130
$306$		0			0
$307$	−94867.2	+	54771.6i	−1.00656	+	0.581137i	−0.910182	−	0.414208i	$-0.864059\pi$
$307$	−94867.2	+	54771.6i	−1.00656	+	0.581137i	−0.0963769	+	0.995345i	$0.530725\pi$
$308$		0			0
$309$	112638.	+	195094.i	1.17969	+	2.04328i
$310$		0			0
$311$	−150216.			−1.55309			−0.776544	−	0.630063i	$-0.783029\pi$
$311$	−150216.			−1.55309			−0.776544	+	0.630063i	$0.783029\pi$
$312$		0			0
$313$	20012.3	−	34662.3i	0.204272	−	0.353809i	−0.745629	−	0.666362i	$-0.767851\pi$
$313$	20012.3	−	34662.3i	0.204272	−	0.353809i	0.949900	+	0.312553i	$0.101184\pi$
$314$		0			0
$315$	38966.8			0.392712
$316$		0			0
$317$	143247.	+	82703.8i	1.42550	+	0.823013i	0.996761	−	0.0804148i	$-0.0256245\pi$
$317$	143247.	+	82703.8i	1.42550	+	0.823013i	0.428739	+	0.903428i	$0.358958\pi$
$318$		0			0
$319$	−641.456	−	370.345i	−0.00630356	−	0.00363936i
$320$		0			0
$321$	−111051.	−	192347.i	−1.07774	−	1.86670i
$322$		0			0
$323$	−64693.8	+	57399.1i	−0.620094	+	0.550174i
$324$		0			0
$325$	−40448.6	+	23353.0i	−0.382945	+	0.221094i
$326$		0			0
$327$	−126756.	+	219547.i	−1.18542	+	2.05320i
$328$		0			0
$329$	−48423.0	+	83871.0i	−0.447362	+	0.774854i
$330$		0			0
$331$			188621.i			1.72161i	0.508935	+	0.860805i	$0.330039\pi$
$331$			188621.i			1.72161i	−0.508935	+	0.860805i	$0.669961\pi$
$332$		0			0
$333$	268928.	+	155266.i	2.42520	+	1.40019i
$334$		0			0
$335$		−	31564.6i		−	0.281262i
$336$		0			0
$337$	31324.9	−	18085.5i	0.275823	−	0.159246i	−0.355708	−	0.934597i	$-0.615760\pi$
$337$	31324.9	−	18085.5i	0.275823	−	0.159246i	0.631531	+	0.775351i	$0.282427\pi$
$338$		0			0
$339$	38429.0	+	66561.0i	0.334395	+	0.579189i
$340$		0			0
$341$			1094.77i			0.00941488i
$342$		0			0
$343$	115257.			0.979671
$344$		0			0
$345$	−16954.4	+	9788.65i	−0.142444	+	0.0822403i
$346$		0			0
$347$	90478.1	+	156713.i	0.751423	+	1.30150i	0.947133	+	0.320841i	$0.103965\pi$
$347$	90478.1	+	156713.i	0.751423	+	1.30150i	−0.195710	+	0.980662i	$0.562701\pi$
$348$		0			0
$349$	128784.			1.05733			0.528666	−	0.848830i	$-0.322692\pi$
$349$	128784.			1.05733			0.528666	+	0.848830i	$0.322692\pi$
$350$		0			0
$351$	25333.0	−	43878.1i	0.205623	−	0.356150i
$352$		0			0
$353$	71514.4			0.573910			0.286955	−	0.957944i	$-0.407357\pi$
$353$	71514.4			0.573910			0.286955	+	0.957944i	$0.407357\pi$
$354$		0			0
$355$	18652.4	+	10769.0i	0.148006	+	0.0854510i
$356$		0			0
$357$	−148819.	−	85920.8i	−1.16768	−	0.674158i
$358$		0			0
$359$	−45696.9	−	79149.3i	−0.354566	−	0.614127i	0.632477	−	0.774579i	$-0.282038\pi$
$359$	−45696.9	−	79149.3i	−0.354566	−	0.614127i	−0.987044	+	0.160452i	$0.948705\pi$
$360$		0			0
$361$	−119817.	+	51258.7i	−0.919399	+	0.393326i
$362$		0			0
$363$	182063.	−	105114.i	1.38168	−	0.797713i
$364$		0			0
$365$	27134.2	−	46997.8i	0.203672	−	0.352770i
$366$		0			0
$367$	−103142.	+	178648.i	−0.765781	+	1.32637i	0.174052	+	0.984736i	$0.444314\pi$
$367$	−103142.	+	178648.i	−0.765781	+	1.32637i	−0.939833	+	0.341634i	$0.889020\pi$
$368$		0			0
$369$			410957.i			3.01817i
$370$		0			0
$371$	−104252.	−	60190.0i	−0.757421	−	0.437297i
$372$		0			0
$373$		−	63012.8i		−	0.452909i	−0.974022	−	0.226454i	$-0.927287\pi$
$373$		−	63012.8i		−	0.452909i	0.974022	−	0.226454i	$-0.0727134\pi$
$374$		0			0
$375$	93829.4	−	54172.4i	0.667231	−	0.385226i
$376$		0			0
$377$	−15647.4	−	27102.1i	−0.110093	−	0.190686i
$378$		0			0
$379$		−	74224.9i		−	0.516739i	−0.966046	−	0.258370i	$-0.916815\pi$
$379$		−	74224.9i		−	0.516739i	0.966046	−	0.258370i	$-0.0831852\pi$
$380$		0			0
$381$	−86548.9			−0.596227
$382$		0			0
$383$	191250.	−	110418.i	1.30378	−	0.752738i	0.322731	−	0.946491i	$-0.395399\pi$
$383$	191250.	−	110418.i	1.30378	−	0.752738i	0.981050	+	0.193753i	$0.0620659\pi$
$384$		0			0
$385$	−293.279	−	507.974i	−0.00197861	−	0.00342704i
$386$		0			0
$387$	40819.4			0.272549
$388$		0			0
$389$	−119430.	+	206858.i	−0.789248	+	1.36702i	0.137181	+	0.990546i	$0.456196\pi$
$389$	−119430.	+	206858.i	−0.789248	+	1.36702i	−0.926428	+	0.376471i	$0.877137\pi$
$390$		0			0
$391$	52433.2			0.342967
$392$		0			0
$393$	−132460.	−	76475.6i	−0.857627	−	0.495151i
$394$		0			0
$395$	22673.2	+	13090.4i	0.145318	+	0.0838994i
$396$		0			0
$397$	−121860.	−	211069.i	−0.773182	−	1.33919i	−0.935810	−	0.352504i	$-0.885330\pi$
$397$	−121860.	−	211069.i	−0.773182	−	1.33919i	0.162628	−	0.986687i	$-0.448003\pi$
$398$		0			0
$399$	−171850.	−	193690.i	−1.07945	−	1.21664i
$400$		0			0
$401$	181404.	−	104733.i	1.12812	−	0.651323i	0.184662	−	0.982802i	$-0.440881\pi$
$401$	181404.	−	104733.i	1.12812	−	0.651323i	0.943463	+	0.331479i	$0.107548\pi$
$402$		0			0
$403$	−23127.5	+	40058.1i	−0.142403	+	0.246649i
$404$		0			0
$405$	3158.39	−	5470.49i	0.0192555	−	0.0333516i
$406$		0			0
$407$		−	4674.35i		−	0.0282184i
$408$		0			0
$409$	102139.	+	58969.8i	0.610581	+	0.352519i	0.773193	−	0.634171i	$-0.218658\pi$
$409$	102139.	+	58969.8i	0.610581	+	0.352519i	−0.162612	+	0.986690i	$0.551992\pi$
$410$		0			0
$411$		−	126468.i		−	0.748679i
$412$		0			0
$413$	152144.	−	87840.3i	0.891978	−	0.514984i
$414$		0			0
$415$	−36669.2	−	63512.9i	−0.212914	−	0.368779i
$416$		0			0
$417$		−	102973.i		−	0.592176i
$418$		0			0
$419$	59069.1			0.336459			0.168230	−	0.985748i	$-0.446195\pi$
$419$	59069.1			0.336459			0.168230	+	0.985748i	$0.446195\pi$
$420$		0			0
$421$	45326.1	−	26169.0i	0.255731	−	0.147647i	−0.366654	−	0.930357i	$-0.619497\pi$
$421$	45326.1	−	26169.0i	0.255731	−	0.147647i	0.622386	+	0.782711i	$0.286164\pi$
$422$		0			0
$423$	−121467.	−	210387.i	−0.678857	−	1.17581i
$424$		0			0
$425$	−140441.			−0.777529
$426$		0			0
$427$	51890.4	−	89876.8i	0.284597	−	0.492937i
$428$		0			0
$429$	−2157.89			−0.0117251
$430$		0			0
$431$	−203718.	−	117616.i	−1.09667	−	0.633160i	−0.161322	−	0.986902i	$-0.551576\pi$
$431$	−203718.	−	117616.i	−1.09667	−	0.633160i	−0.935343	+	0.353742i	$0.884909\pi$
$432$		0			0
$433$	−127748.	−	73755.1i	−0.681360	−	0.393384i	0.119007	−	0.992893i	$-0.462029\pi$
$433$	−127748.	−	73755.1i	−0.681360	−	0.393384i	−0.800367	+	0.599510i	$0.795362\pi$
$434$		0			0
$435$	17567.5	+	30427.8i	0.0928393	+	0.160802i
$436$		0			0
$437$	74960.5	+	24963.9i	0.392527	+	0.130722i
$438$		0			0
$439$	7033.58	−	4060.84i	0.0364962	−	0.0210711i	−0.481641	−	0.876369i	$-0.659959\pi$
$439$	7033.58	−	4060.84i	0.0364962	−	0.0210711i	0.518137	+	0.855298i	$0.326626\pi$
$440$		0			0
$441$	5834.98	−	10106.5i	0.0300028	−	0.0519664i
$442$		0			0
$443$	−102446.	+	177441.i	−0.522018	+	0.904162i	0.477654	+	0.878548i	$0.341487\pi$
$443$	−102446.	+	177441.i	−0.522018	+	0.904162i	−0.999672	+	0.0256140i	$0.991846\pi$
$444$		0			0
$445$			59059.7i			0.298244i
$446$		0			0
$447$	207072.	+	119553.i	1.03635	+	0.598337i
$448$		0			0
$449$			114834.i			0.569611i	0.958585	+	0.284806i	$0.0919291\pi$
$449$			114834.i			0.569611i	−0.958585	+	0.284806i	$0.908071\pi$
$450$		0			0
$451$	5357.26	−	3093.01i	0.0263384	−	0.0152065i
$452$		0			0
$453$	12788.1	+	22149.7i	0.0623175	+	0.107937i
$454$		0			0
$455$		−	24782.6i		−	0.119708i
$456$		0			0
$457$	−230282.			−1.10262			−0.551312	−	0.834299i	$-0.685873\pi$
$457$	−230282.			−1.10262			−0.551312	+	0.834299i	$0.685873\pi$
$458$		0			0
$459$	131938.	−	76174.3i	0.626244	−	0.361562i
$460$		0			0
$461$	−52622.7	−	91145.2i	−0.247612	−	0.428876i	0.715251	−	0.698868i	$-0.246312\pi$
$461$	−52622.7	−	91145.2i	−0.247612	−	0.428876i	−0.962863	+	0.269992i	$0.912979\pi$
$462$		0			0
$463$	−103267.			−0.481724			−0.240862	−	0.970559i	$-0.577430\pi$
$463$	−103267.			−0.481724			−0.240862	+	0.970559i	$0.577430\pi$
$464$		0			0
$465$	25965.6	−	44973.7i	0.120086	−	0.207995i
$466$		0			0
$467$	203377.			0.932542			0.466271	−	0.884642i	$-0.345597\pi$
$467$	203377.			0.932542			0.466271	+	0.884642i	$0.345597\pi$
$468$		0			0
$469$	−219194.	−	126552.i	−0.996511	−	0.575336i
$470$		0			0
$471$	−114677.	−	66208.8i	−0.516933	−	0.298452i
$472$		0			0
$473$	−307.222	−	532.124i	−0.00137319	−	0.00237843i
$474$		0			0
$475$	−200780.	−	66865.4i	−0.889885	−	0.296356i
$476$		0			0
$477$	261513.	−	150984.i	1.14936	−	0.663583i
$478$		0			0
$479$	221111.	−	382976.i	0.963697	−	1.66917i	0.250619	−	0.968086i	$-0.419366\pi$
$479$	221111.	−	382976.i	0.963697	−	1.66917i	0.713077	−	0.701086i	$-0.247301\pi$
$480$		0			0
$481$	98747.6	−	171036.i	0.426812	−	0.739260i
$482$		0			0
$483$			156982.i			0.672909i
$484$		0			0
$485$	−31426.0	−	18143.8i	−0.133600	−	0.0771339i
$486$		0			0
$487$			212627.i			0.896519i	0.893903	+	0.448260i	$0.147956\pi$
$487$			212627.i			0.896519i	−0.893903	+	0.448260i	$0.852044\pi$
$488$		0			0
$489$	364141.	−	210237.i	1.52283	−	0.879208i
$490$		0			0
$491$	−216804.	−	375515.i	−0.899298	−	1.55763i	−0.828393	−	0.560147i	$-0.810745\pi$
$491$	−216804.	−	375515.i	−0.899298	−	1.55763i	−0.0709052	−	0.997483i	$-0.522589\pi$
$492$		0			0
$493$		−	94100.8i		−	0.387168i
$494$		0			0
$495$	1471.36			0.00600493
$496$		0			0
$497$	149566.	−	86351.8i	0.605507	−	0.349590i
$498$		0			0
$499$	80809.6	+	139966.i	0.324535	+	0.562111i	0.981418	−	0.191881i	$-0.0614588\pi$
$499$	80809.6	+	139966.i	0.324535	+	0.562111i	−0.656883	+	0.753992i	$0.728125\pi$
$500$		0			0
$501$	−618846.			−2.46551
$502$		0			0
$503$	−27970.9	+	48446.9i	−0.110553	+	0.191483i	−0.915993	−	0.401194i	$-0.868595\pi$
$503$	−27970.9	+	48446.9i	−0.110553	+	0.191483i	0.805440	+	0.592677i	$0.201929\pi$
$504$		0			0
$505$	−114190.			−0.447760
$506$		0			0
$507$	276288.	+	159515.i	1.07484	+	0.620562i
$508$		0			0
$509$	180101.	+	103981.i	0.695152	+	0.401346i	0.805539	−	0.592542i	$-0.201876\pi$
$509$	180101.	+	103981.i	0.695152	+	0.401346i	−0.110387	+	0.993889i	$0.535209\pi$
$510$		0			0
$511$	−217578.	−	376856.i	−0.833245	−	1.44322i
$512$		0			0
$513$	224891.	−	46085.0i	0.854549	−	0.175115i
$514$		0			0
$515$	−84602.7	+	48845.4i	−0.318985	+	0.184166i
$516$		0			0
$517$	−1828.41	+	3166.91i	−0.00684059	+	0.0118482i
$518$		0			0
$519$	−320118.	+	554461.i	−1.18844	+	2.05843i
$520$		0			0
$521$			207601.i			0.764810i	0.923995	+	0.382405i	$0.124904\pi$
$521$			207601.i			0.764810i	−0.923995	+	0.382405i	$0.875096\pi$
$522$		0			0
$523$	35996.4	+	20782.5i	0.131600	+	0.0759792i	0.564355	−	0.825532i	$-0.309125\pi$
$523$	35996.4	+	20782.5i	0.131600	+	0.0759792i	−0.432755	+	0.901512i	$0.642458\pi$
$524$		0			0
$525$		−	420474.i		−	1.52553i
$526$		0			0
$527$	−120451.	+	69542.6i	−0.433701	+	0.250397i
$528$		0			0
$529$	115971.	+	200868.i	0.414417	+	0.717792i
$530$		0			0
$531$			440688.i			1.56294i
$532$		0			0
$533$	261365.			0.920011
$534$		0			0
$535$	83411.1	−	48157.4i	0.291418	−	0.168250i
$536$		0			0
$537$	−132875.	−	230146.i	−0.460780	−	0.798094i
$538$		0			0
$539$	−175.665			−0.000604654
$540$		0			0
$541$	−51917.0	+	89922.8i	−0.177384	+	0.307238i	−0.940984	−	0.338452i	$-0.890097\pi$
$541$	−51917.0	+	89922.8i	−0.177384	+	0.307238i	0.763600	+	0.645690i	$0.223430\pi$
$542$		0			0
$543$	−458229.			−1.55411
$544$		0			0
$545$	−95206.6	−	54967.6i	−0.320534	−	0.185060i
$546$		0			0
$547$	−142979.	−	82548.7i	−0.477855	−	0.275890i	0.241667	−	0.970359i	$-0.422306\pi$
$547$	−142979.	−	82548.7i	−0.477855	−	0.275890i	−0.719522	+	0.694469i	$0.755639\pi$
$548$		0			0
$549$	130165.	+	225452.i	0.431867	+	0.748015i
$550$		0			0
$551$	44802.3	−	134530.i	0.147570	−	0.443115i
$552$		0			0
$553$	181807.	−	104966.i	0.594512	−	0.343242i
$554$		0			0
$555$	−110865.	+	192024.i	−0.359923	+	0.623404i
$556$		0			0
$557$	−30248.0	+	52391.2i	−0.0974960	+	0.168868i	−0.910648	−	0.413184i	$-0.864417\pi$
$557$	−30248.0	+	52391.2i	−0.0974960	+	0.168868i	0.813152	+	0.582052i	$0.197750\pi$
$558$		0			0
$559$		−	25960.8i		−	0.0830796i
$560$		0			0
$561$	−5619.30	−	3244.30i	−0.0178549	−	0.0103085i
$562$		0			0
$563$		−	248939.i		−	0.785374i	−0.919672	−	0.392687i	$-0.871546\pi$
$563$		−	248939.i		−	0.785374i	0.919672	−	0.392687i	$-0.128454\pi$
$564$		0			0
$565$	−28864.2	+	16664.8i	−0.0904196	+	0.0522038i
$566$		0			0
$567$	−25325.8	−	43865.6i	−0.0787766	−	0.136445i
$568$		0			0
$569$			87739.1i			0.270999i	0.990777	+	0.135500i	$0.0432640\pi$
$569$			87739.1i			0.270999i	−0.990777	+	0.135500i	$0.956736\pi$
$570$		0			0
$571$	−130764.			−0.401067			−0.200533	−	0.979687i	$-0.564268\pi$
$571$	−130764.			−0.401067			−0.200533	+	0.979687i	$0.564268\pi$
$572$		0			0
$573$	−351332.	+	202842.i	−1.07006	+	0.617800i
$574$		0			0
$575$	64148.5	+	111108.i	0.194022	+	0.336056i
$576$		0			0
$577$	−572106.			−1.71840			−0.859201	−	0.511639i	$-0.829039\pi$
$577$	−572106.			−1.71840			−0.859201	+	0.511639i	$0.829039\pi$
$578$		0			0
$579$	294094.	−	509386.i	0.877261	−	1.51946i
$580$		0			0
$581$	−588069.			−1.74211
$582$		0			0
$583$	−3936.48	−	2272.73i	−0.0115817	−	0.00668668i
$584$		0			0
$585$	53837.4	+	31083.0i	0.157316	+	0.0908264i
$586$		0			0
$587$	17337.7	+	30029.7i	0.0503169	+	0.0871515i	0.890087	−	0.455791i	$-0.150644\pi$
$587$	17337.7	+	30029.7i	0.0503169	+	0.0871515i	−0.839770	+	0.542942i	$0.817310\pi$
$588$		0			0
$589$	−205312.	+	42072.8i	−0.591811	+	0.121275i
$590$		0			0
$591$	278112.	−	160568.i	0.796240	−	0.459710i
$592$		0			0
$593$	−200472.	+	347228.i	−0.570092	+	0.987429i	0.426463	+	0.904505i	$0.359759\pi$
$593$	−200472.	+	347228.i	−0.570092	+	0.987429i	−0.996556	+	0.0829242i	$0.973574\pi$
$594$		0			0
$595$	37259.6	−	64535.5i	0.105246	−	0.182291i
$596$		0			0
$597$			62236.6i			0.174621i
$598$		0			0
$599$	461443.	+	266414.i	1.28607	+	0.742512i	0.977951	−	0.208836i	$-0.0669676\pi$
$599$	461443.	+	266414.i	1.28607	+	0.742512i	0.308118	+	0.951348i	$0.400301\pi$
$600$		0			0
$601$			169049.i			0.468019i	0.972234	+	0.234009i	$0.0751846\pi$
$601$			169049.i			0.468019i	−0.972234	+	0.234009i	$0.924815\pi$
$602$		0			0
$603$	549839.	−	317450.i	1.51217	−	0.873052i
$604$		0			0
$605$	45582.6	+	78951.4i	0.124534	+	0.215700i
$606$		0			0
$607$		−	527599.i		−	1.43195i	−0.698127	−	0.715974i	$-0.745983\pi$
$607$		−	527599.i		−	1.43195i	0.698127	−	0.715974i	$-0.254017\pi$
$608$		0			0
$609$	281733.			0.759632
$610$		0			0
$611$	−133804.	+	77252.0i	−0.358417	+	0.206932i
$612$		0			0
$613$	144166.	+	249704.i	0.383657	+	0.664513i	0.991582	−	0.129481i	$-0.0413312\pi$
$613$	144166.	+	249704.i	0.383657	+	0.664513i	−0.607925	+	0.793995i	$0.707998\pi$
$614$		0			0
$615$	−293438.			−0.775829
$616$		0			0
$617$	215208.	−	372751.i	0.565311	−	0.979147i	−0.431710	−	0.902013i	$-0.642090\pi$
$617$	215208.	−	372751.i	0.565311	−	0.979147i	0.997021	−	0.0771347i	$-0.0245772\pi$
$618$		0			0
$619$	−490418.			−1.27993			−0.639963	−	0.768405i	$-0.721050\pi$
$619$	−490418.			−1.27993			−0.639963	+	0.768405i	$0.721050\pi$
$620$		0			0
$621$	−120529.	−	69587.4i	−0.312542	−	0.180446i
$622$		0			0
$623$	410128.	+	236787.i	1.05668	+	0.610074i
$624$		0			0
$625$	−159699.	−	276606.i	−0.408828	−	0.708111i
$626$		0			0
$627$	−6488.92	−	7313.58i	−0.0165058	−	0.0186035i
$628$		0			0
$629$	514291.	−	296926.i	1.29989	−	0.750493i
$630$		0			0
$631$	−65005.3	+	112593.i	−0.163264	+	0.282781i	−0.936037	−	0.351901i	$-0.885536\pi$
$631$	−65005.3	+	112593.i	−0.163264	+	0.282781i	0.772774	+	0.634682i	$0.218869\pi$
$632$		0			0
$633$	−400043.	+	692894.i	−0.998387	+	1.72926i
$634$		0			0
$635$		−	37531.9i		−	0.0930794i
$636$		0			0
$637$	−6427.63	−	3710.99i	−0.0158406	−	0.00914558i
$638$		0			0
$639$			433220.i			1.06098i
$640$		0			0
$641$	395283.	−	228217.i	0.962037	−	0.555432i	0.0652376	−	0.997870i	$-0.479219\pi$
$641$	395283.	−	228217.i	0.962037	−	0.555432i	0.896799	+	0.442437i	$0.145886\pi$
$642$		0			0
$643$	−194677.	−	337190.i	−0.470860	−	0.815554i	0.528584	−	0.848881i	$-0.322723\pi$
$643$	−194677.	−	337190.i	−0.470860	−	0.815554i	−0.999445	+	0.0333268i	$0.989390\pi$
$644$		0			0
$645$			29146.5i			0.0700595i
$646$		0			0
$647$	656698.			1.56876			0.784381	−	0.620279i	$-0.212981\pi$
$647$	656698.			1.56876			0.784381	+	0.620279i	$0.212981\pi$
$648$		0			0
$649$	5744.83	−	3316.78i	0.0136392	−	0.00787458i
$650$		0			0
$651$	−208207.	−	360625.i	−0.491285	−	0.850930i
$652$		0			0
$653$	280986.			0.658959			0.329480	−	0.944163i	$-0.393127\pi$
$653$	280986.			0.658959			0.329480	+	0.944163i	$0.393127\pi$
$654$		0			0
$655$	33163.6	−	57441.1i	0.0773000	−	0.133888i
$656$		0			0
$657$	1.09157e6			2.52884
$658$		0			0
$659$	331713.	+	191514.i	0.763820	+	0.440992i	0.830666	−	0.556772i	$-0.187960\pi$
$659$	331713.	+	191514.i	0.763820	+	0.440992i	−0.0668456	+	0.997763i	$0.521293\pi$
$660$		0			0
$661$	−314250.	−	181433.i	−0.719239	−	0.415253i	0.0952338	−	0.995455i	$-0.469640\pi$
$661$	−314250.	−	181433.i	−0.719239	−	0.415253i	−0.814472	+	0.580202i	$0.802973\pi$
$662$		0			0
$663$	−137075.	−	237420.i	−0.311839	−	0.540120i
$664$		0			0
$665$	83993.6	−	74522.8i	0.189934	−	0.168518i
$666$		0			0
$667$	−74446.8	+	42981.9i	−0.167338	+	0.0966126i
$668$		0			0
$669$	−196284.	+	339974.i	−0.438564	+	0.759616i
$670$		0			0
$671$	1959.34	−	3393.68i	0.00435176	−	0.00753747i
$672$		0			0
$673$		−	191020.i		−	0.421744i	−0.977514	−	0.210872i	$-0.932370\pi$
$673$		−	191020.i		−	0.421744i	0.977514	−	0.210872i	$-0.0676304\pi$
$674$		0			0
$675$	322834.	+	186389.i	0.708553	+	0.409083i
$676$		0			0
$677$		−	336677.i		−	0.734575i	−0.930107	−	0.367287i	$-0.880287\pi$
$677$		−	336677.i		−	0.734575i	0.930107	−	0.367287i	$-0.119713\pi$
$678$		0			0
$679$	−251992.	+	145488.i	−0.546571	+	0.315563i
$680$		0			0
$681$	−302322.	−	523637.i	−0.651892	−	1.12911i
$682$		0			0
$683$		−	313252.i		−	0.671509i	−0.941950	−	0.335755i	$-0.891009\pi$
$683$		−	313252.i		−	0.671509i	0.941950	−	0.335755i	$-0.108991\pi$
$684$		0			0
$685$	54842.7			0.116879
$686$		0			0
$687$	−151288.	+	87346.4i	−0.320547	+	0.185068i
$688$		0			0
$689$	−96024.8	−	166320.i	−0.202276	−	0.350353i
$690$		0			0
$691$	−803808.			−1.68344			−0.841718	−	0.539918i	$-0.818455\pi$
$691$	−803808.			−1.68344			−0.841718	+	0.539918i	$0.818455\pi$
$692$		0			0
$693$	5899.10	−	10217.5i	0.0122834	−	0.0212755i
$694$		0			0
$695$	44654.2			0.0924470
$696$		0			0
$697$	680612.	+	392952.i	1.40099	+	0.808860i
$698$		0			0
$699$	−316152.	−	182530.i	−0.647055	−	0.373577i
$700$		0			0
$701$	−247655.	−	428950.i	−0.503977	−	0.872913i	−0.999989	−	0.00459793i	$-0.998536\pi$
$701$	−247655.	−	428950.i	−0.503977	−	0.872913i	0.496013	−	0.868315i	$-0.334797\pi$
$702$		0			0
$703$	876619.	−	179638.i	1.77378	−	0.363486i
$704$		0			0
$705$	150224.	−	86731.9i	0.302246	−	0.174502i
$706$		0			0
$707$	−457821.	+	792969.i	−0.915918	+	1.58642i
$708$		0			0
$709$	−7754.66	+	13431.5i	−0.0154266	+	0.0267197i	−0.873636	−	0.486581i	$-0.838244\pi$
$709$	−7754.66	+	13431.5i	−0.0154266	+	0.0267197i	0.858209	+	0.513300i	$0.171577\pi$
$710$		0			0
$711$			526608.i			1.04171i
$712$		0			0
$713$	110036.	+	63529.1i	0.216448	+	0.124967i
$714$		0			0
$715$		−	935.770i		−	0.00183045i
$716$		0			0
$717$	−1.07621e6	+	621353.i	−2.09344	+	1.20865i
$718$		0			0
$719$	377951.	+	654630.i	0.731102	+	1.26631i	0.956413	+	0.292018i	$0.0943269\pi$
$719$	377951.	+	654630.i	0.731102	+	1.26631i	−0.225311	+	0.974287i	$0.572340\pi$
$720$		0			0
$721$			783342.i			1.50689i
$722$		0			0
$723$	−752937.			−1.44040
$724$		0			0
$725$	199404.	−	115126.i	0.379366	−	0.219027i
$726$		0			0
$727$	326273.	+	565122.i	0.617323	+	1.06923i	0.989972	+	0.141262i	$0.0451162\pi$
$727$	326273.	+	565122.i	0.617323	+	1.06923i	−0.372649	+	0.927972i	$0.621551\pi$
$728$		0			0
$729$	866844.			1.63112
$730$		0			0
$731$	39031.0	−	67603.7i	0.0730424	−	0.126513i
$732$		0			0
$733$	−811947.			−1.51119			−0.755597	−	0.655037i	$-0.772653\pi$
$733$	−811947.			−1.51119			−0.755597	+	0.655037i	$0.772653\pi$
$734$		0			0
$735$	7216.38	+	4166.38i	0.0133581	+	0.00771230i
$736$		0			0
$737$	−8276.58	−	4778.49i	−0.0152376	−	0.00879742i
$738$		0			0
$739$	389853.	+	675246.i	0.713859	+	1.23644i	0.963398	+	0.268075i	$0.0863876\pi$
$739$	389853.	+	675246.i	0.713859	+	1.23644i	−0.249539	+	0.968365i	$0.580279\pi$
$740$		0			0
$741$	−82929.2	−	404688.i	−0.151033	−	0.737027i
$742$		0			0
$743$	497760.	−	287382.i	0.901660	−	0.520574i	0.0239215	−	0.999714i	$-0.492385\pi$
$743$	497760.	−	287382.i	0.901660	−	0.520574i	0.877738	+	0.479140i	$0.159052\pi$
$744$		0			0
$745$	−51844.2	+	89796.8i	−0.0934088	+	0.161789i
$746$		0			0
$747$	737575.	−	1.27752e6i	1.32180	−	2.28942i
$748$		0			0
$749$		−	772308.i		−	1.37666i
$750$		0			0
$751$	−168301.	−	97168.5i	−0.298405	−	0.172284i	0.343321	−	0.939218i	$-0.388448\pi$
$751$	−168301.	−	97168.5i	−0.298405	−	0.172284i	−0.641726	+	0.766934i	$0.721781\pi$
$752$		0			0
$753$			564135.i			0.994931i
$754$		0			0
$755$	−9605.21	+	5545.57i	−0.0168505	+	0.00972864i
$756$		0			0
$757$	−144106.	−	249600.i	−0.251473	−	0.435564i	0.712458	−	0.701714i	$-0.247582\pi$
$757$	−144106.	−	249600.i	−0.251473	−	0.435564i	−0.963932	+	0.266150i	$0.914248\pi$
$758$		0			0
$759$			5927.53i			0.0102894i
$760$		0			0
$761$	660814.			1.14106			0.570532	−	0.821275i	$-0.306737\pi$
$761$	660814.			1.14106			0.570532	+	0.821275i	$0.306737\pi$
$762$		0			0
$763$	−763422.	+	440762.i	−1.31134	+	0.757103i
$764$		0			0
$765$	93464.2	+	161885.i	0.159706	+	0.276620i
$766$		0			0
$767$	280274.			0.476422
$768$		0			0
$769$	367592.	−	636688.i	0.621603	−	1.07665i	−0.367584	−	0.929990i	$-0.619815\pi$
$769$	367592.	−	636688.i	0.621603	−	1.07665i	0.989187	−	0.146658i	$-0.0468516\pi$
$770$		0			0
$771$	−1.07746e6			−1.81255
$772$		0			0
$773$	503015.	+	290416.i	0.841824	+	0.486028i	0.857884	−	0.513843i	$-0.171779\pi$
$773$	503015.	+	290416.i	0.841824	+	0.486028i	−0.0160595	+	0.999871i	$0.505112\pi$
$774$		0			0
$775$	−294729.	−	170162.i	−0.490703	−	0.283308i
$776$		0			0
$777$	888981.	+	1.53976e6i	1.47248	+	2.55042i
$778$		0			0
$779$	785942.	+	885824.i	1.29514	+	1.45973i
$780$		0			0
$781$	5647.49	−	3260.58i	0.00925877	−	0.00534555i
$782$		0			0
$783$	−124887.	+	216311.i	−0.203702	+	0.352822i
$784$		0			0
$785$	28711.5	−	49729.7i	0.0465925	−	0.0807006i
$786$		0			0
$787$			209530.i			0.338296i	0.985591	+	0.169148i	$0.0541015\pi$
$787$			209530.i			0.338296i	−0.985591	+	0.169148i	$0.945898\pi$
$788$		0			0
$789$	−367119.	−	211956.i	−0.589730	−	0.340481i
$790$		0			0
$791$			267255.i			0.427143i
$792$		0			0
$793$	143386.	−	82783.8i	0.228013	−	0.131643i
$794$		0			0
$795$	107808.	+	186729.i	0.170576	+	0.295446i
$796$		0			0
$797$			384377.i			0.605118i	0.953131	+	0.302559i	$0.0978410\pi$
$797$			384377.i			0.605118i	−0.953131	+	0.302559i	$0.902159\pi$
$798$		0			0
$799$	−464581.			−0.727726
$800$		0			0
$801$	−1.02879e6	+	593972.i	−1.60347	+	0.925765i
$802$		0			0
$803$	−8215.57	−	14229.8i	−0.0127411	−	0.0220682i
$804$		0			0
$805$	−68075.3			−0.105050
$806$		0			0
$807$	−729511.	+	1.26355e6i	−1.12017	+	1.94019i
$808$		0			0
$809$	−133009.			−0.203228			−0.101614	−	0.994824i	$-0.532401\pi$
$809$	−133009.			−0.203228			−0.101614	+	0.994824i	$0.532401\pi$
$810$		0			0
$811$	71351.1	+	41194.6i	0.108482	+	0.0626323i	0.553259	−	0.833009i	$-0.313384\pi$
$811$	71351.1	+	41194.6i	0.108482	+	0.0626323i	−0.444777	+	0.895641i	$0.646717\pi$
$812$		0			0
$813$	296410.	+	171132.i	0.448448	+	0.258911i
$814$		0			0
$815$	91169.4	+	157910.i	0.137257	+	0.237736i
$816$		0			0
$817$	87986.9	−	78065.8i	0.131818	−	0.116954i
$818$		0			0
$819$	431700.	−	249242.i	0.643597	−	0.371581i
$820$		0			0
$821$	−268164.	+	464473.i	−0.397845	+	0.689087i	−0.993460	−	0.114183i	$-0.963575\pi$
$821$	−268164.	+	464473.i	−0.397845	+	0.689087i	0.595615	+	0.803270i	$0.296908\pi$
$822$		0			0
$823$	236126.	−	408982.i	0.348613	−	0.603816i	−0.637390	−	0.770541i	$-0.719986\pi$
$823$	236126.	−	408982.i	0.348613	−	0.603816i	0.986003	+	0.166725i	$0.0533193\pi$
$824$		0			0
$825$		−	15876.8i		−	0.0233268i
$826$		0			0
$827$	189650.	+	109494.i	0.277294	+	0.160096i	0.632198	−	0.774807i	$-0.282153\pi$
$827$	189650.	+	109494.i	0.277294	+	0.160096i	−0.354903	+	0.934903i	$0.615486\pi$
$828$		0			0
$829$			1.15812e6i			1.68517i	0.538561	+	0.842586i	$0.318968\pi$
$829$			1.15812e6i			1.68517i	−0.538561	+	0.842586i	$0.681032\pi$
$830$		0			0
$831$	1.36558e6	−	788417.i	1.97749	−	1.14171i
$832$		0			0
$833$	−11158.7	−	19327.4i	−0.0160813	−	0.0278537i
$834$		0			0
$835$		−	268362.i		−	0.384901i
$836$		0			0
$837$	369178.			0.526969
$838$		0			0
$839$	−576430.	+	332802.i	−0.818885	+	0.472783i	−0.850032	−	0.526731i	$-0.823417\pi$
$839$	−576430.	+	332802.i	−0.818885	+	0.472783i	0.0311469	+	0.999515i	$0.490084\pi$
$840$		0			0
$841$	−276502.	−	478915.i	−0.390936	−	0.677121i
$842$		0			0
$843$	870806.			1.22537
$844$		0			0
$845$	−69173.6	+	119812.i	−0.0968784	+	0.167798i
$846$		0			0
$847$	731016.			1.01897
$848$		0			0
$849$	−208569.	−	120418.i	−0.289358	−	0.167061i
$850$		0			0
$851$	−469819.	−	271250.i	−0.648742	−	0.374551i
$852$		0			0
$853$	441621.	+	764910.i	0.606949	+	1.05127i	0.991740	+	0.128262i	$0.0409399\pi$
$853$	441621.	+	764910.i	0.606949	+	1.05127i	−0.384792	+	0.923003i	$0.625727\pi$
$854$		0			0
$855$	56545.2	+	275936.i	0.0773506	+	0.377464i
$856$		0			0
$857$	−680285.	+	392763.i	−0.926252	+	0.534772i	−0.885624	−	0.464403i	$-0.846269\pi$
$857$	−680285.	+	392763.i	−0.926252	+	0.534772i	−0.0406278	+	0.999174i	$0.512936\pi$
$858$		0			0
$859$	727091.	−	1.25936e6i	0.985377	−	1.70672i	0.345128	−	0.938556i	$-0.387836\pi$
$859$	727091.	−	1.25936e6i	0.985377	−	1.70672i	0.640249	−	0.768167i	$-0.278831\pi$
$860$		0			0
$861$	−1.17648e6	+	2.03772e6i	−1.58700	+	2.74877i
$862$		0			0
$863$			899567.i			1.20785i	0.797042	+	0.603924i	$0.206397\pi$
$863$			899567.i			1.20785i	−0.797042	+	0.603924i	$0.793603\pi$
$864$		0			0
$865$	−240442.	−	138819.i	−0.321350	−	0.185531i
$866$		0			0
$867$			375211.i			0.499158i
$868$		0			0
$869$	6864.90	−	3963.45i	0.00909064	−	0.00524848i
$870$		0			0
$871$	−201895.	−	349693.i	−0.266127	−	0.460946i
$872$		0			0
$873$		−	729900.i		−	0.957712i
$874$		0			0
$875$	376743.			0.492072
$876$		0			0
$877$	279525.	−	161384.i	0.363431	−	0.209827i	−0.307154	−	0.951660i	$-0.599377\pi$
$877$	279525.	−	161384.i	0.363431	−	0.209827i	0.670585	+	0.741833i	$0.266043\pi$
$878$		0			0
$879$	−915533.	−	1.58575e6i	−1.18494	−	2.05238i
$880$		0			0
$881$	547085.			0.704860			0.352430	−	0.935838i	$-0.385355\pi$
$881$	547085.			0.704860			0.352430	+	0.935838i	$0.385355\pi$
$882$		0			0
$883$	−524253.	+	908034.i	−0.672388	+	1.16461i	0.304837	+	0.952404i	$0.401398\pi$
$883$	−524253.	+	908034.i	−0.672388	+	1.16461i	−0.977225	+	0.212205i	$0.931935\pi$
$884$		0			0
$885$	−314667.			−0.401758
$886$		0			0
$887$	−318039.	−	183620.i	−0.404234	−	0.233385i	0.284075	−	0.958802i	$-0.408313\pi$
$887$	−318039.	−	183620.i	−0.404234	−	0.233385i	−0.688309	+	0.725417i	$0.741647\pi$
$888$		0			0
$889$	−260633.	−	150476.i	−0.329781	−	0.190399i
$890$		0			0
$891$	−956.283	−	1656.33i	−0.00120457	−	0.00208637i
$892$		0			0
$893$	−664183.	−	221191.i	−0.832885	−	0.277374i
$894$		0			0
$895$	99802.7	−	57621.1i	0.124594	−	0.0719342i
$896$		0			0
$897$	−125222.	+	216890.i	−0.155630	+	0.269560i
$898$		0			0
$899$	114015.	−	197479.i	0.141072	−	0.244344i
$900$		0			0
$901$		−	577477.i		−	0.711353i
$902$		0			0
$903$	202402.	+	116857.i	0.248221	+	0.143311i
$904$		0			0
$905$		−	198711.i		−	0.242619i
$906$		0			0
$907$	−132002.	+	76211.4i	−0.160460	+	0.0926415i	−0.578080	−	0.815980i	$-0.696198\pi$
$907$	−132002.	+	76211.4i	−0.160460	+	0.0926415i	0.417620	+	0.908622i	$0.362864\pi$
$908$		0			0
$909$	−1.14843e6	−	1.98913e6i	−1.38987	−	2.40733i
$910$		0			0
$911$		−	826053.i		−	0.995339i	−0.867367	−	0.497669i	$-0.834189\pi$
$911$		−	826053.i		−	0.995339i	0.867367	−	0.497669i	$-0.165811\pi$
$912$		0			0
$913$	−22205.0			−0.0266385
$914$		0			0
$915$	−160981.	+	92942.5i	−0.192279	+	0.111013i
$916$		0			0
$917$	−265925.	−	460596.i	−0.316243	−	0.547749i
$918$		0			0
$919$	139504.			0.165180			0.0825898	−	0.996584i	$-0.473681\pi$
$919$	139504.			0.165180			0.0825898	+	0.996584i	$0.473681\pi$
$920$		0			0
$921$	786648.	−	1.36251e6i	0.927387	−	1.60628i
$922$		0			0
$923$	275524.			0.323412
$924$		0			0
$925$	1.25840e6	+	726539.i	1.47074	+	0.849132i
$926$		0			0
$927$	−1.70172e6	−	982491.i	−1.98029	−	1.14332i
$928$		0			0
$929$	193588.	+	335304.i	0.224309	+	0.388515i	0.956112	−	0.293002i	$-0.0946541\pi$
$929$	193588.	+	335304.i	0.224309	+	0.388515i	−0.731803	+	0.681516i	$0.761321\pi$
$930$		0			0
$931$	−6750.91	−	32943.9i	−0.00778867	−	0.0380080i
$932$		0			0
$933$	1.86841e6	−	1.07873e6i	2.14639	−	1.23922i
$934$		0			0
$935$	1406.89	−	2436.81i	0.00160930	−	0.00278739i
$936$		0			0
$937$	31843.4	−	55154.4i	0.0362694	−	0.0628205i	−0.847321	−	0.531081i	$-0.821786\pi$
$937$	31843.4	−	55154.4i	0.0362694	−	0.0628205i	0.883590	+	0.468261i	$0.155119\pi$
$938$		0			0
$939$			574846.i			0.651959i
$940$		0			0
$941$	−783860.	−	452562.i	−0.885237	−	0.511092i	−0.0128552	−	0.999917i	$-0.504092\pi$
$941$	−783860.	−	452562.i	−0.885237	−	0.511092i	−0.872381	+	0.488826i	$0.837425\pi$
$942$		0			0
$943$		−	717945.i		−	0.807361i
$944$		0			0
$945$	−171298.	+	98899.1i	−0.191818	+	0.110746i
$946$		0			0
$947$	−86501.2	−	149824.i	−0.0964544	−	0.167064i	0.813760	−	0.581201i	$-0.197417\pi$
$947$	−86501.2	−	149824.i	−0.0964544	−	0.167064i	−0.910215	+	0.414137i	$0.864084\pi$
$948$		0			0
$949$		−	694230.i		−	0.770851i
$950$		0			0
$951$	−2.37564e6			−2.62675
$952$		0			0
$953$	796366.	−	459782.i	0.876853	−	0.506251i	0.00723358	−	0.999974i	$-0.497697\pi$
$953$	796366.	−	459782.i	0.876853	−	0.506251i	0.869620	+	0.493722i	$0.164364\pi$
$954$		0			0
$955$	−87962.4	−	152355.i	−0.0964473	−	0.167052i
$956$		0			0
$957$	10638.0			0.0116155
$958$		0			0
$959$	219880.	−	380844.i	0.239083	−	0.414104i
$960$		0			0
$961$	586484.			0.635052
$962$		0			0
$963$	1.67776e6	+	968653.i	1.80916	+	1.04452i
$964$		0			0
$965$	220895.	+	127534.i	0.237209	+	0.136953i
$966$		0			0
$967$	51509.8	+	89217.7i	0.0550855	+	0.0954109i	0.892253	−	0.451535i	$-0.149124\pi$
$967$	51509.8	+	89217.7i	0.0550855	+	0.0954109i	−0.837168	+	0.546946i	$0.815790\pi$
$968$		0			0
$969$	392478.	−	1.17851e6i	0.417992	−	1.25513i
$970$		0			0
$971$	157988.	−	91214.6i	0.167566	−	0.0967445i	−0.413871	−	0.910335i	$-0.635824\pi$
$971$	157988.	−	91214.6i	0.167566	−	0.0967445i	0.581438	+	0.813591i	$0.302490\pi$
$972$		0			0
$973$	179032.	−	310092.i	0.189105	−	0.327540i
$974$		0			0
$975$	335404.	−	580936.i	0.352824	−	0.611110i
$976$		0			0
$977$			436847.i			0.457657i	0.973467	+	0.228828i	$0.0734895\pi$
$977$			436847.i			0.457657i	−0.973467	+	0.228828i	$0.926511\pi$
$978$		0			0
$979$	15486.1	+	8940.91i	0.0161576	+	0.00932859i
$980$		0			0
$981$		−	2.21127e6i		−	2.29775i
$982$		0			0
$983$	−577269.	+	333286.i	−0.597408	+	0.344914i	−0.768021	−	0.640424i	$-0.778759\pi$
$983$	−577269.	+	333286.i	−0.597408	+	0.344914i	0.170613	+	0.985338i	$0.445425\pi$
$984$		0			0
$985$	69630.3	+	120603.i	0.0717671	+	0.124304i
$986$		0			0
$987$		−	1.39093e6i		−	1.42781i
$988$		0			0
$989$	−71311.8			−0.0729070
$990$		0			0
$991$	706100.	−	407667.i	0.718984	−	0.415105i	−0.0953949	−	0.995440i	$-0.530411\pi$
$991$	706100.	−	407667.i	0.718984	−	0.415105i	0.814378	+	0.580334i	$0.197078\pi$
$992$		0			0
$993$	−1.35452e6	−	2.34610e6i	−1.37368	−	2.37929i
$994$		0			0
$995$	−26988.9			−0.0272608
$996$		0			0
$997$	−720639.	+	1.24818e6i	−0.724983	+	1.25571i	0.233999	+	0.972237i	$0.424819\pi$
$997$	−720639.	+	1.24818e6i	−0.724983	+	1.25571i	−0.958981	+	0.283470i	$0.908514\pi$
$998$		0			0
$999$	−1.57628e6			−1.57944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.b.145.1		12
4.3	odd	2		76.5.h.a.69.6	yes	12
12.11	even	2		684.5.y.c.145.4		12
19.8	odd	6	inner	304.5.r.b.65.1		12
76.27	even	6		76.5.h.a.65.6	✓	12
228.179	odd	6		684.5.y.c.217.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.6	✓	12	76.27	even	6
76.5.h.a.69.6	yes	12	4.3	odd	2
304.5.r.b.65.1		12	19.8	odd	6	inner
304.5.r.b.145.1		12	1.1	even	1	trivial
684.5.y.c.145.4		12	12.11	even	2
684.5.y.c.217.4		12	228.179	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-12.4381 + 7.18116i) q^{3} +(-3.11411 - 5.39380i) q^{5} -49.9415 q^{7} +(62.6382 - 108.493i) q^{9} +O(q^{10})\)	\(q+(-12.4381 + 7.18116i) q^{3} +(-3.11411 - 5.39380i) q^{5} -49.9415 q^{7} +(62.6382 - 108.493i) q^{9} -1.88575 q^{11} +(-69.0003 - 39.8373i) q^{13} +(77.4675 + 44.7259i) q^{15} +(-119.788 - 207.478i) q^{17} +(-72.4707 - 353.651i) q^{19} +(621.179 - 358.638i) q^{21} +(-109.429 + 189.537i) q^{23} +(293.105 - 507.672i) q^{25} +635.911i q^{27} +(340.159 + 196.391i) q^{29} -580.549i q^{31} +(23.4553 - 13.5419i) q^{33} +(155.523 + 269.374i) q^{35} +2478.77i q^{37} +1144.31 q^{39} +(-2840.91 + 1640.20i) q^{41} +(162.917 + 282.181i) q^{43} -780.249 q^{45} +(969.593 - 1679.39i) q^{47} +93.1537 q^{49} +(2979.87 + 1720.43i) q^{51} +(2087.49 + 1205.21i) q^{53} +(5.87245 + 10.1714i) q^{55} +(3441.03 + 3878.34i) q^{57} +(-3046.44 + 1758.86i) q^{59} +(-1039.02 + 1799.64i) q^{61} +(-3128.24 + 5418.28i) q^{63} +496.232i q^{65} +(4389.01 + 2533.99i) q^{67} -3143.32i q^{69} +(-2994.82 + 1729.06i) q^{71} +(4356.65 + 7545.94i) q^{73} +8419.33i q^{75} +94.1773 q^{77} +(-3640.40 + 2101.79i) q^{79} +(507.109 + 878.339i) q^{81} +11775.2 q^{83} +(-746.064 + 1292.22i) q^{85} -5641.26 q^{87} +(-8212.16 - 4741.29i) q^{89} +(3445.98 + 1989.54i) q^{91} +(4169.02 + 7220.95i) q^{93} +(-1681.84 + 1492.20i) q^{95} +(5045.74 - 2913.16i) q^{97} +(-118.120 + 204.590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 9 q^{5} + 52 q^{7} + 136 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 9 * q^5 + 52 * q^7 + 136 * q^9	\( 12 q + 12 q^{3} + 9 q^{5} + 52 q^{7} + 136 q^{9} - 6 q^{11} - 93 q^{13} + 741 q^{15} - 483 q^{17} + 533 q^{19} + 972 q^{21} - 531 q^{23} - 217 q^{25} + 2025 q^{29} - 75 q^{33} + 1128 q^{35} + 2250 q^{39} - 1692 q^{41} + 63 q^{43} + 7976 q^{45} + 3471 q^{47} + 420 q^{49} - 6741 q^{51} - 3771 q^{53} + 2014 q^{55} + 7617 q^{57} + 9594 q^{59} + 1229 q^{61} - 1514 q^{63} - 7590 q^{67} - 963 q^{71} - 2838 q^{73} - 15408 q^{77} - 11073 q^{79} + 2086 q^{81} + 14202 q^{83} + 9455 q^{85} + 39510 q^{87} + 6525 q^{89} + 7686 q^{91} - 5316 q^{93} - 1521 q^{95} - 34110 q^{97} - 13220 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 9 * q^5 + 52 * q^7 + 136 * q^9 - 6 * q^11 - 93 * q^13 + 741 * q^15 - 483 * q^17 + 533 * q^19 + 972 * q^21 - 531 * q^23 - 217 * q^25 + 2025 * q^29 - 75 * q^33 + 1128 * q^35 + 2250 * q^39 - 1692 * q^41 + 63 * q^43 + 7976 * q^45 + 3471 * q^47 + 420 * q^49 - 6741 * q^51 - 3771 * q^53 + 2014 * q^55 + 7617 * q^57 + 9594 * q^59 + 1229 * q^61 - 1514 * q^63 - 7590 * q^67 - 963 * q^71 - 2838 * q^73 - 15408 * q^77 - 11073 * q^79 + 2086 * q^81 + 14202 * q^83 + 9455 * q^85 + 39510 * q^87 + 6525 * q^89 + 7686 * q^91 - 5316 * q^93 - 1521 * q^95 - 34110 * q^97 - 13220 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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