LMFDB - Embedded newform 76.5.h.a.65.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(65,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("76.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.85611719437$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.6
Root			$0.500000 - 15.2283i$ of defining polynomial
Character	$\chi$	$=$	76.65
Dual form			76.5.h.a.69.6

$q$-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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	12.4381	+	7.18116i	1.38202	+	0.797907i	0.992398	−	0.123070i	$-0.0392740\pi$
$3$	12.4381	+	7.18116i	1.38202	+	0.797907i	0.389617	+	0.920977i	$0.372607\pi$
$4$		0			0
$5$	−3.11411	+	5.39380i	−0.124564	+	0.215752i	−0.921563	−	0.388230i	$-0.873087\pi$
$5$	−3.11411	+	5.39380i	−0.124564	+	0.215752i	0.796998	+	0.603982i	$0.206420\pi$
$6$		0			0
$7$	49.9415			1.01921			0.509607	−	0.860407i	$-0.329791\pi$
$7$	49.9415			1.01921			0.509607	+	0.860407i	$0.329791\pi$
$8$		0			0
$9$	62.6382	+	108.493i	0.773311	+	1.33941i
$10$		0			0
$11$	1.88575			0.0155847			0.00779237	−	0.999970i	$-0.497520\pi$
$11$	1.88575			0.0155847			0.00779237	+	0.999970i	$0.497520\pi$
$12$		0			0
$13$	−69.0003	+	39.8373i	−0.408286	+	0.235724i	−0.690053	−	0.723759i	$-0.742413\pi$
$13$	−69.0003	+	39.8373i	−0.408286	+	0.235724i	0.281767	+	0.959483i	$0.409079\pi$
$14$		0			0
$15$	−77.4675	+	44.7259i	−0.344300	+	0.198782i
$16$		0			0
$17$	−119.788	+	207.478i	−0.414490	+	0.717918i	−0.995375	−	0.0960680i	$-0.969373\pi$
$17$	−119.788	+	207.478i	−0.414490	+	0.717918i	0.580885	+	0.813986i	$0.302707\pi$
$18$		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	$-0.100342\pi$
$23$	109.429	+	189.537i	0.206861	+	0.358294i	−0.743863	+	0.668332i	$0.767009\pi$
$24$		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	−0.283941	−	0.958842i	$-0.591642\pi$
$29$	340.159	−	196.391i	0.404470	−	0.233521i	0.688411	+	0.725321i	$0.258309\pi$
$30$		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	$-0.639630\pi$
$37$		−	2478.77i		−	1.81064i	0.424727	−	0.905321i	$-0.360370\pi$
$38$		0			0
$39$	−1144.31			−0.752343
$40$		0			0
$41$	−2840.91	−	1640.20i	−1.69001	−	0.975729i	−0.954497	−	0.298222i	$-0.903606\pi$
$41$	−2840.91	−	1640.20i	−1.69001	−	0.975729i	−0.735516	−	0.677507i	$-0.763060\pi$
$42$		0			0
$43$	−162.917	+	282.181i	−0.0881111	+	0.152613i	−0.906713	−	0.421749i	$-0.861416\pi$
$43$	−162.917	+	282.181i	−0.0881111	+	0.152613i	0.818602	+	0.574362i	$0.194750\pi$
$44$		0			0
$45$	−780.249			−0.385308
$46$		0			0
$47$	−969.593	−	1679.39i	−0.438929	−	0.760247i	0.558678	−	0.829384i	$-0.311309\pi$
$47$	−969.593	−	1679.39i	−0.438929	−	0.760247i	−0.997607	+	0.0691376i	$0.977975\pi$
$48$		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	−0.0800686	−	0.996789i	$-0.525514\pi$
$53$	2087.49	−	1205.21i	0.743142	−	0.429053i	0.823211	+	0.567736i	$0.192181\pi$
$54$		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	$-0.164724\pi$
$59$	3046.44	+	1758.86i	0.875163	+	0.505275i	0.00610218	+	0.999981i	$0.498058\pi$
$60$		0			0
$61$	−1039.02	−	1799.64i	−0.279232	−	0.483644i	0.691962	−	0.721934i	$-0.256747\pi$
$61$	−1039.02	−	1799.64i	−0.279232	−	0.483644i	−0.971194	+	0.238290i	$0.923413\pi$
$62$		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	$-0.857594\pi$
$67$	−4389.01	+	2533.99i	−0.977725	+	0.564490i	−0.0761425	+	0.997097i	$0.524260\pi$
$68$		0			0
$69$			3143.32i			0.660223i
$70$		0			0
$71$	2994.82	+	1729.06i	0.594092	+	0.342999i	0.766714	−	0.641989i	$-0.221891\pi$
$71$	2994.82	+	1729.06i	0.594092	+	0.342999i	−0.172622	+	0.984988i	$0.555224\pi$
$72$		0			0
$73$	4356.65	−	7545.94i	0.817536	−	1.41601i	−0.0899558	−	0.995946i	$-0.528673\pi$
$73$	4356.65	−	7545.94i	0.817536	−	1.41601i	0.907492	−	0.420069i	$-0.137994\pi$
$74$		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	$-0.223999\pi$
$79$	3640.40	+	2101.79i	0.583304	+	0.336771i	−0.179141	+	0.983823i	$0.557332\pi$
$80$		0			0
$81$	507.109	−	878.339i	0.0772915	−	0.133873i
$82$		0			0
$83$	−11775.2			−1.70927			−0.854635	−	0.519229i	$-0.826219\pi$
$83$	−11775.2			−1.70927			−0.854635	+	0.519229i	$0.826219\pi$
$84$		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	−0.918913	−	0.394460i	$-0.870932\pi$
$89$	−8212.16	+	4741.29i	−1.03676	+	0.598573i	−0.117845	+	0.993032i	$0.537599\pi$
$90$		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	0.743565	−	0.668664i	$-0.233133\pi$
$97$	5045.74	+	2913.16i	0.536267	+	0.309614i	−0.207297	+	0.978278i	$0.566467\pi$
$98$		0			0
$99$	118.120	+	204.590i	0.0120518	+	0.0208744i
$100$		0			0
$101$	9167.14	+	15878.0i	0.898651	+	1.55651i	0.829220	+	0.558923i	$0.188785\pi$
$101$	9167.14	+	15878.0i	0.898651	+	1.55651i	0.0694313	+	0.997587i	$0.477882\pi$
$102$		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	0.978050	−	0.208372i	$-0.0668166\pi$
$109$	15286.3	+	8825.56i	1.28662	+	0.742830i	0.308569	+	0.951202i	$0.400150\pi$
$110$		0			0
$111$	17800.4	−	30831.3i	1.44472	−	2.50234i
$112$		0			0
$113$			5351.37i			0.419090i	0.977799	+	0.209545i	$0.0671984\pi$
$113$			5351.37i			0.419090i	−0.977799	+	0.209545i	$0.932802\pi$
$114$		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	$-0.726481\pi$
$127$	−5218.76	+	3013.05i	−0.323564	+	0.186810i	0.329416	+	0.944185i	$0.393148\pi$
$128$		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	$-0.933757\pi$
$131$	−5324.73	+	9222.71i	−0.310281	+	0.537423i	0.668142	+	0.744034i	$0.267090\pi$
$132$		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	0.724573	−	0.689198i	$-0.242037\pi$
$137$	−4402.76	−	7625.80i	−0.234576	−	0.406298i	−0.959149	+	0.282900i	$0.908704\pi$
$138$		0			0
$139$	3584.83	+	6209.10i	0.185540	+	0.321366i	0.943759	−	0.330636i	$-0.107263\pi$
$139$	3584.83	+	6209.10i	0.185540	+	0.321366i	−0.758218	+	0.652001i	$0.773930\pi$
$140$		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	−0.990318	−	0.138815i	$-0.955671\pi$
$149$	−8324.08	+	14417.7i	−0.374941	+	0.649418i	0.615377	+	0.788233i	$0.289004\pi$
$150$		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	−0.757234	−	0.653143i	$-0.773450\pi$
$157$	4609.89	−	7984.57i	0.187022	−	0.323931i	0.944256	+	0.329212i	$0.106783\pi$
$158$		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	$-0.314267\pi$
$163$	29276.2			1.10189			0.550947	+	0.834540i	$0.314267\pi$
$164$		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	$-0.947657\pi$
$167$	−37315.4	+	21544.1i	−1.33800	+	0.772493i	−0.351487	+	0.936193i	$0.614324\pi$
$168$		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	0.978635	−	0.205605i	$-0.0659161\pi$
$173$	38605.2	+	22288.7i	1.28989	+	0.744721i	0.311259	+	0.950325i	$0.399249\pi$
$174$		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	−0.0150220	−	0.999887i	$-0.504782\pi$
$181$	27630.5	−	15952.4i	0.843395	−	0.486934i	0.858417	+	0.512953i	$0.171448\pi$
$182$		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	$-0.626536\pi$
$191$	−28246.4			−0.774276			−0.387138	+	0.922022i	$0.626536\pi$
$192$		0			0
$193$	−35466.8	−	20476.8i	−0.952154	−	0.549727i	−0.0584049	−	0.998293i	$-0.518601\pi$
$193$	−35466.8	−	20476.8i	−0.952154	−	0.549727i	−0.893750	+	0.448566i	$0.851935\pi$
$194$		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	$-0.184091\pi$
$199$	−2166.66	−	3752.77i	−0.0547123	−	0.0947645i	−0.892084	+	0.451869i	$0.850757\pi$
$200$		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	$-0.548491\pi$
$211$	−48243.9	−	27853.6i	−1.08362	−	0.625629i	−0.931871	+	0.362790i	$0.881824\pi$
$212$		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	$-0.421952\pi$
$223$	−23671.3	−	13666.6i	−0.476005	−	0.274822i	−0.718750	+	0.695268i	$0.755285\pi$
$224$		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	−0.724912	−	0.688841i	$-0.758120\pi$
$233$	12709.0	−	22012.6i	0.234098	−	0.405470i	0.959010	+	0.283372i	$0.0914529\pi$
$234$		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	$-0.773524\pi$
$239$	−86525.4			−1.51477			−0.757387	+	0.652967i	$0.773524\pi$
$240$		0			0
$241$	45400.9	−	26212.2i	0.781682	−	0.451305i	−0.0553438	−	0.998467i	$-0.517625\pi$
$241$	45400.9	−	26212.2i	0.781682	−	0.451305i	0.837026	+	0.547163i	$0.184292\pi$
$242$		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	$-0.267576\pi$
$251$	−19639.4	−	34016.4i	−0.311732	−	0.539935i	−0.978737	+	0.205118i	$0.934242\pi$
$252$		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	0.0802773	−	0.996773i	$-0.474419\pi$
$257$	64968.9	−	37509.8i	0.983646	−	0.567908i	0.903369	+	0.428864i	$0.141086\pi$
$258$		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	$-0.901774\pi$
$263$	−14757.8	+	25561.3i	−0.213359	+	0.369548i	0.739405	+	0.673261i	$0.235107\pi$
$264$		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	0.964017	−	0.265839i	$-0.0856490\pi$
$269$	87976.7	+	50793.4i	1.21580	+	0.701944i	0.251785	+	0.967783i	$0.418982\pi$
$270$		0			0
$271$	11915.4	−	20638.0i	0.162244	−	0.281015i	−0.773429	−	0.633883i	$-0.781460\pi$
$271$	11915.4	−	20638.0i	0.162244	−	0.281015i	0.935673	+	0.352868i	$0.114793\pi$
$272$		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	−0.794175	−	0.607689i	$-0.792097\pi$
$281$	−52508.2	+	30315.6i	−0.664989	+	0.383932i	0.129186	+	0.991620i	$0.458764\pi$
$282$		0			0
$283$	−8384.27	+	14522.0i	−0.104687	+	0.181323i	−0.913610	−	0.406591i	$-0.866717\pi$
$283$	−8384.27	+	14522.0i	−0.104687	+	0.181323i	0.808923	+	0.587914i	$0.200051\pi$
$284$		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	$-0.733626\pi$
$293$		−	127491.i		−	1.48506i	0.669813	−	0.742530i	$-0.266374\pi$
$294$		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	$-0.135941\pi$
$307$	94867.2	+	54771.6i	1.00656	+	0.581137i	0.0963769	+	0.995345i	$0.469275\pi$
$308$		0			0
$309$	112638.	−	195094.i	1.17969	−	2.04328i
$310$		0			0
$311$	150216.			1.55309			0.776544	−	0.630063i	$-0.216971\pi$
$311$	150216.			1.55309			0.776544	+	0.630063i	$0.216971\pi$
$312$		0			0
$313$	20012.3	+	34662.3i	0.204272	+	0.353809i	0.949900	−	0.312553i	$-0.101184\pi$
$313$	20012.3	+	34662.3i	0.204272	+	0.353809i	−0.745629	+	0.666362i	$0.767851\pi$
$314$		0			0
$315$	−38966.8			−0.392712
$316$		0			0
$317$	143247.	−	82703.8i	1.42550	−	0.823013i	0.428739	−	0.903428i	$-0.358958\pi$
$317$	143247.	−	82703.8i	1.42550	−	0.823013i	0.996761	+	0.0804148i	$0.0256245\pi$
$318$		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	0.631531	−	0.775351i	$-0.282427\pi$
$337$	31324.9	+	18085.5i	0.275823	+	0.159246i	−0.355708	+	0.934597i	$0.615760\pi$
$338$		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	0.195710	+	0.980662i	$0.437299\pi$
$347$	−90478.1	+	156713.i	−0.751423	+	1.30150i	−0.947133	+	0.320841i	$0.896035\pi$
$348$		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	$-0.717962\pi$
$359$	45696.9	−	79149.3i	0.354566	−	0.614127i	0.987044	+	0.160452i	$0.0512951\pi$
$360$		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	0.939833	+	0.341634i	$0.110980\pi$
$367$	103142.	+	178648.i	0.765781	+	1.32637i	−0.174052	+	0.984736i	$0.555686\pi$
$368$		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	$0.0727134\pi$
$373$			63012.8i			0.452909i	−0.974022	+	0.226454i	$0.927287\pi$
$374$		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	$-0.604601\pi$
$383$	−191250.	−	110418.i	−1.30378	−	0.752738i	−0.981050	+	0.193753i	$0.937934\pi$
$384$		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	−0.926428	−	0.376471i	$-0.877137\pi$
$389$	−119430.	−	206858.i	−0.789248	−	1.36702i	0.137181	−	0.990546i	$-0.456196\pi$
$390$		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	0.162628	+	0.986687i	$0.448003\pi$
$397$	−121860.	+	211069.i	−0.773182	+	1.33919i	−0.935810	+	0.352504i	$0.885330\pi$
$398$		0			0
$399$	171850.	−	193690.i	1.07945	−	1.21664i
$400$		0			0
$401$	181404.	+	104733.i	1.12812	+	0.651323i	0.943463	−	0.331479i	$-0.107548\pi$
$401$	181404.	+	104733.i	1.12812	+	0.651323i	0.184662	+	0.982802i	$0.440881\pi$
$402$		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	−0.162612	−	0.986690i	$-0.551992\pi$
$409$	102139.	−	58969.8i	0.610581	−	0.352519i	0.773193	+	0.634171i	$0.218658\pi$
$410$		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	$-0.553805\pi$
$419$	−59069.1			−0.336459			−0.168230	+	0.985748i	$0.553805\pi$
$420$		0			0
$421$	45326.1	+	26169.0i	0.255731	+	0.147647i	0.622386	−	0.782711i	$-0.286164\pi$
$421$	45326.1	+	26169.0i	0.255731	+	0.147647i	−0.366654	+	0.930357i	$0.619497\pi$
$422$		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	$-0.448424\pi$
$431$	203718.	−	117616.i	1.09667	−	0.633160i	0.935343	+	0.353742i	$0.115091\pi$
$432$		0			0
$433$	−127748.	+	73755.1i	−0.681360	+	0.393384i	−0.800367	−	0.599510i	$-0.795362\pi$
$433$	−127748.	+	73755.1i	−0.681360	+	0.393384i	0.119007	+	0.992893i	$0.462029\pi$
$434$		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	$-0.340041\pi$
$439$	−7033.58	−	4060.84i	−0.0364962	−	0.0210711i	−0.518137	+	0.855298i	$0.673374\pi$
$440$		0			0
$441$	5834.98	+	10106.5i	0.0300028	+	0.0519664i
$442$		0			0
$443$	102446.	+	177441.i	0.522018	+	0.904162i	0.999672	+	0.0256140i	$0.00815408\pi$
$443$	102446.	+	177441.i	0.522018	+	0.904162i	−0.477654	+	0.878548i	$0.658513\pi$
$444$		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	$-0.908071\pi$
$449$		−	114834.i		−	0.569611i	0.958585	−	0.284806i	$-0.0919291\pi$
$450$		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	−0.962863	−	0.269992i	$-0.912979\pi$
$461$	−52622.7	+	91145.2i	−0.247612	+	0.428876i	0.715251	+	0.698868i	$0.246312\pi$
$462$		0			0
$463$	103267.			0.481724			0.240862	−	0.970559i	$-0.422570\pi$
$463$	103267.			0.481724			0.240862	+	0.970559i	$0.422570\pi$
$464$		0			0
$465$	25965.6	+	44973.7i	0.120086	+	0.207995i
$466$		0			0
$467$	−203377.			−0.932542			−0.466271	−	0.884642i	$-0.654403\pi$
$467$	−203377.			−0.932542			−0.466271	+	0.884642i	$0.654403\pi$
$468$		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	−0.713077	−	0.701086i	$-0.752699\pi$
$479$	−221111.	−	382976.i	−0.963697	−	1.66917i	−0.250619	−	0.968086i	$-0.580634\pi$
$480$		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	0.0709052	−	0.997483i	$-0.477411\pi$
$491$	216804.	−	375515.i	0.899298	−	1.55763i	0.828393	−	0.560147i	$-0.189255\pi$
$492$		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	$-0.938541\pi$
$499$	−80809.6	+	139966.i	−0.324535	+	0.562111i	0.656883	+	0.753992i	$0.271875\pi$
$500$		0			0
$501$	−618846.			−2.46551
$502$		0			0
$503$	27970.9	+	48446.9i	0.110553	+	0.191483i	0.915993	−	0.401194i	$-0.131405\pi$
$503$	27970.9	+	48446.9i	0.110553	+	0.191483i	−0.805440	+	0.592677i	$0.798071\pi$
$504$		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	−0.110387	−	0.993889i	$-0.535209\pi$
$509$	180101.	−	103981.i	0.695152	−	0.401346i	0.805539	+	0.592542i	$0.201876\pi$
$510$		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	$-0.875096\pi$
$521$		−	207601.i		−	0.764810i	0.923995	−	0.382405i	$-0.124904\pi$
$522$		0			0
$523$	−35996.4	+	20782.5i	−0.131600	+	0.0759792i	−0.564355	−	0.825532i	$-0.690875\pi$
$523$	−35996.4	+	20782.5i	−0.131600	+	0.0759792i	0.432755	+	0.901512i	$0.357542\pi$
$524$		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	0.763600	−	0.645690i	$-0.223430\pi$
$541$	−51917.0	−	89922.8i	−0.177384	−	0.307238i	−0.940984	+	0.338452i	$0.890097\pi$
$542$		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	$-0.577694\pi$
$547$	142979.	−	82548.7i	0.477855	−	0.275890i	0.719522	+	0.694469i	$0.244361\pi$
$548$		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	0.813152	−	0.582052i	$-0.197750\pi$
$557$	−30248.0	−	52391.2i	−0.0974960	−	0.168868i	−0.910648	+	0.413184i	$0.864417\pi$
$558$		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	$-0.956736\pi$
$569$		−	87739.1i		−	0.270999i	0.990777	−	0.135500i	$-0.0432640\pi$
$570$		0			0
$571$	130764.			0.401067			0.200533	−	0.979687i	$-0.435732\pi$
$571$	130764.			0.401067			0.200533	+	0.979687i	$0.435732\pi$
$572$		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	$-0.849356\pi$
$587$	−17337.7	+	30029.7i	−0.0503169	+	0.0871515i	0.839770	+	0.542942i	$0.182690\pi$
$588$		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	−0.996556	−	0.0829242i	$-0.973574\pi$
$593$	−200472.	−	347228.i	−0.570092	−	0.987429i	0.426463	−	0.904505i	$-0.359759\pi$
$594$		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	$-0.933032\pi$
$599$	−461443.	+	266414.i	−1.28607	+	0.742512i	−0.308118	+	0.951348i	$0.599699\pi$
$600$		0			0
$601$		−	169049.i		−	0.468019i	−0.972234	−	0.234009i	$-0.924815\pi$
$601$		−	169049.i		−	0.468019i	0.972234	−	0.234009i	$-0.0751846\pi$
$602$		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	−0.607925	−	0.793995i	$-0.707998\pi$
$613$	144166.	−	249704.i	0.383657	−	0.664513i	0.991582	+	0.129481i	$0.0413312\pi$
$614$		0			0
$615$	293438.			0.775829
$616$		0			0
$617$	215208.	+	372751.i	0.565311	+	0.979147i	0.997021	+	0.0771347i	$0.0245772\pi$
$617$	215208.	+	372751.i	0.565311	+	0.979147i	−0.431710	+	0.902013i	$0.642090\pi$
$618$		0			0
$619$	490418.			1.27993			0.639963	−	0.768405i	$-0.278950\pi$
$619$	490418.			1.27993			0.639963	+	0.768405i	$0.278950\pi$
$620$		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	$-0.114464\pi$
$631$	65005.3	+	112593.i	0.163264	+	0.282781i	−0.772774	+	0.634682i	$0.781131\pi$
$632$		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	0.896799	−	0.442437i	$-0.145886\pi$
$641$	395283.	+	228217.i	0.962037	+	0.555432i	0.0652376	+	0.997870i	$0.479219\pi$
$642$		0			0
$643$	194677.	−	337190.i	0.470860	−	0.815554i	−0.528584	−	0.848881i	$-0.677277\pi$
$643$	194677.	−	337190.i	0.470860	−	0.815554i	0.999445	+	0.0333268i	$0.0106102\pi$
$644$		0			0
$645$		−	29146.5i		−	0.0700595i
$646$		0			0
$647$	−656698.			−1.56876			−0.784381	−	0.620279i	$-0.787019\pi$
$647$	−656698.			−1.56876			−0.784381	+	0.620279i	$0.787019\pi$
$648$		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	$-0.812040\pi$
$659$	−331713.	+	191514.i	−0.763820	+	0.440992i	0.0668456	+	0.997763i	$0.478707\pi$
$660$		0			0
$661$	−314250.	+	181433.i	−0.719239	+	0.415253i	−0.814472	−	0.580202i	$-0.802973\pi$
$661$	−314250.	+	181433.i	−0.719239	+	0.415253i	0.0952338	+	0.995455i	$0.469640\pi$
$662$		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	$0.0676304\pi$
$673$			191020.i			0.421744i	−0.977514	+	0.210872i	$0.932370\pi$
$674$		0			0
$675$	−322834.	+	186389.i	−0.708553	+	0.409083i
$676$		0			0
$677$			336677.i			0.734575i	0.930107	+	0.367287i	$0.119713\pi$
$677$			336677.i			0.734575i	−0.930107	+	0.367287i	$0.880287\pi$
$678$		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	$-0.181545\pi$
$691$	803808.			1.68344			0.841718	+	0.539918i	$0.181545\pi$
$692$		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	0.496013	+	0.868315i	$0.334797\pi$
$701$	−247655.	+	428950.i	−0.503977	+	0.872913i	−0.999989	+	0.00459793i	$0.998536\pi$
$702$		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	0.858209	−	0.513300i	$-0.171577\pi$
$709$	−7754.66	−	13431.5i	−0.0154266	−	0.0267197i	−0.873636	+	0.486581i	$0.838244\pi$
$710$		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	0.225311	+	0.974287i	$0.427660\pi$
$719$	−377951.	+	654630.i	−0.731102	+	1.26631i	−0.956413	+	0.292018i	$0.905673\pi$
$720$		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	0.372649	+	0.927972i	$0.378449\pi$
$727$	−326273.	+	565122.i	−0.617323	+	1.06923i	−0.989972	+	0.141262i	$0.954884\pi$
$728$		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	0.249539	+	0.968365i	$0.419721\pi$
$739$	−389853.	+	675246.i	−0.713859	+	1.23644i	−0.963398	+	0.268075i	$0.913612\pi$
$740$		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	$-0.507615\pi$
$743$	−497760.	−	287382.i	−0.901660	−	0.520574i	−0.877738	+	0.479140i	$0.840948\pi$
$744$		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	$-0.611552\pi$
$751$	168301.	−	97168.5i	0.298405	−	0.172284i	0.641726	+	0.766934i	$0.278219\pi$
$752$		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	−0.963932	−	0.266150i	$-0.914248\pi$
$757$	−144106.	+	249600.i	−0.251473	+	0.435564i	0.712458	+	0.701714i	$0.247582\pi$
$758$		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	0.989187	+	0.146658i	$0.0468516\pi$
$769$	367592.	+	636688.i	0.621603	+	1.07665i	−0.367584	+	0.929990i	$0.619815\pi$
$770$		0			0
$771$	1.07746e6			1.81255
$772$		0			0
$773$	503015.	−	290416.i	0.841824	−	0.486028i	−0.0160595	−	0.999871i	$-0.505112\pi$
$773$	503015.	−	290416.i	0.841824	−	0.486028i	0.857884	+	0.513843i	$0.171779\pi$
$774$		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	$-0.902159\pi$
$797$		−	384377.i		−	0.605118i	0.953131	−	0.302559i	$-0.0978410\pi$
$798$		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	$-0.686616\pi$
$811$	−71351.1	+	41194.6i	−0.108482	+	0.0626323i	0.444777	+	0.895641i	$0.353283\pi$
$812$		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	0.595615	−	0.803270i	$-0.296908\pi$
$821$	−268164.	−	464473.i	−0.397845	−	0.689087i	−0.993460	+	0.114183i	$0.963575\pi$
$822$		0			0
$823$	−236126.	−	408982.i	−0.348613	−	0.603816i	0.637390	−	0.770541i	$-0.280014\pi$
$823$	−236126.	−	408982.i	−0.348613	−	0.603816i	−0.986003	+	0.166725i	$0.946681\pi$
$824$		0			0
$825$			15876.8i			0.0233268i
$826$		0			0
$827$	−189650.	+	109494.i	−0.277294	+	0.160096i	−0.632198	−	0.774807i	$-0.717847\pi$
$827$	−189650.	+	109494.i	−0.277294	+	0.160096i	0.354903	+	0.934903i	$0.384514\pi$
$828$		0			0
$829$		−	1.15812e6i		−	1.68517i	−0.538561	−	0.842586i	$-0.681032\pi$
$829$		−	1.15812e6i		−	1.68517i	0.538561	−	0.842586i	$-0.318968\pi$
$830$		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	$-0.176583\pi$
$839$	576430.	+	332802.i	0.818885	+	0.472783i	−0.0311469	+	0.999515i	$0.509916\pi$
$840$		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	−0.384792	−	0.923003i	$-0.625727\pi$
$853$	441621.	−	764910.i	0.606949	−	1.05127i	0.991740	−	0.128262i	$-0.0409399\pi$
$854$		0			0
$855$	−56545.2	+	275936.i	−0.0773506	+	0.377464i
$856$		0			0
$857$	−680285.	−	392763.i	−0.926252	−	0.534772i	−0.0406278	−	0.999174i	$-0.512936\pi$
$857$	−680285.	−	392763.i	−0.926252	−	0.534772i	−0.885624	+	0.464403i	$0.846269\pi$
$858$		0			0
$859$	−727091.	−	1.25936e6i	−0.985377	−	1.70672i	−0.640249	−	0.768167i	$-0.721169\pi$
$859$	−727091.	−	1.25936e6i	−0.985377	−	1.70672i	−0.345128	−	0.938556i	$-0.612164\pi$
$860$		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	0.670585	−	0.741833i	$-0.266043\pi$
$877$	279525.	+	161384.i	0.363431	+	0.209827i	−0.307154	+	0.951660i	$0.599377\pi$
$878$		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	0.977225	+	0.212205i	$0.0680646\pi$
$883$	524253.	+	908034.i	0.672388	+	1.16461i	−0.304837	+	0.952404i	$0.598602\pi$
$884$		0			0
$885$	−314667.			−0.401758
$886$		0			0
$887$	318039.	−	183620.i	0.404234	−	0.233385i	−0.284075	−	0.958802i	$-0.591687\pi$
$887$	318039.	−	183620.i	0.404234	−	0.233385i	0.688309	+	0.725417i	$0.258353\pi$
$888$		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	$-0.303802\pi$
$907$	132002.	+	76211.4i	0.160460	+	0.0926415i	−0.417620	+	0.908622i	$0.637136\pi$
$908$		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	$-0.526319\pi$
$919$	−139504.			−0.165180			−0.0825898	+	0.996584i	$0.526319\pi$
$920$		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	−0.731803	−	0.681516i	$-0.761321\pi$
$929$	193588.	−	335304.i	0.224309	−	0.388515i	0.956112	+	0.293002i	$0.0946541\pi$
$930$		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	0.883590	−	0.468261i	$-0.155119\pi$
$937$	31843.4	+	55154.4i	0.0362694	+	0.0628205i	−0.847321	+	0.531081i	$0.821786\pi$
$938$		0			0
$939$			574846.i			0.651959i
$940$		0			0
$941$	−783860.	+	452562.i	−0.885237	+	0.511092i	−0.872381	−	0.488826i	$-0.837425\pi$
$941$	−783860.	+	452562.i	−0.885237	+	0.511092i	−0.0128552	+	0.999917i	$0.504092\pi$
$942$		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	$-0.802583\pi$
$947$	86501.2	−	149824.i	0.0964544	−	0.167064i	0.910215	+	0.414137i	$0.135916\pi$
$948$		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	0.869620	−	0.493722i	$-0.164364\pi$
$953$	796366.	+	459782.i	0.876853	+	0.506251i	0.00723358	+	0.999974i	$0.497697\pi$
$954$		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	$-0.850876\pi$
$967$	−51509.8	+	89217.7i	−0.0550855	+	0.0954109i	0.837168	+	0.546946i	$0.184210\pi$
$968$		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	$-0.364176\pi$
$971$	−157988.	−	91214.6i	−0.167566	−	0.0967445i	−0.581438	+	0.813591i	$0.697510\pi$
$972$		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	$-0.926511\pi$
$977$		−	436847.i		−	0.457657i	0.973467	−	0.228828i	$-0.0734895\pi$
$978$		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	$-0.221241\pi$
$983$	577269.	+	333286.i	0.597408	+	0.344914i	−0.170613	+	0.985338i	$0.554575\pi$
$984$		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	$-0.469589\pi$
$991$	−706100.	−	407667.i	−0.718984	−	0.415105i	−0.814378	+	0.580334i	$0.802922\pi$
$992$		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	−0.958981	−	0.283470i	$-0.908514\pi$
$997$	−720639.	−	1.24818e6i	−0.724983	−	1.25571i	0.233999	−	0.972237i	$-0.424819\pi$
$998$		0			0
$999$	1.57628e6			1.57944

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.h.a.65.6	✓	12	1.1	even	1	trivial
76.5.h.a.69.6	yes	12	19.12	odd	6	inner
304.5.r.b.65.1		12	4.3	odd	2
304.5.r.b.145.1		12	76.31	even	6
684.5.y.c.145.4		12	57.50	even	6
684.5.y.c.217.4		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.h (of order \(6\), degree \(2\), 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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Database

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