LMFDB - Embedded newform 76.8.i.a.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	76.73
Dual form			76.8.i.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-29.3247 + 10.6733i) q^{3} +(6.78900 - 38.5023i) q^{5} +(-102.056 - 176.766i) q^{7} +(-929.319 + 779.792i) q^{9} +O(q^{10})$	\(q+(-29.3247 + 10.6733i) q^{3} +(6.78900 - 38.5023i) q^{5} +(-102.056 - 176.766i) q^{7} +(-929.319 + 779.792i) q^{9} +(1302.02 - 2255.16i) q^{11} +(-3810.89 - 1387.05i) q^{13} +(211.862 + 1201.53i) q^{15} +(474.035 + 397.763i) q^{17} +(7036.39 - 29057.9i) q^{19} +(4879.45 + 4094.35i) q^{21} +(19463.1 + 110380. i) q^{23} +(71977.1 + 26197.5i) q^{25} +(53053.6 - 91891.6i) q^{27} +(87644.1 - 73542.1i) q^{29} +(118620. + 205455. i) q^{31} +(-14111.3 + 80028.9i) q^{33} +(-7498.77 + 2729.33i) q^{35} +429128. q^{37} +126558. q^{39} +(206837. - 75282.3i) q^{41} +(-66731.4 + 378453. i) q^{43} +(23714.6 + 41075.0i) q^{45} +(169319. - 142076. i) q^{47} +(390941. - 677129. i) q^{49} +(-18146.4 - 6604.75i) q^{51} +(37956.1 + 215260. i) q^{53} +(-77989.6 - 65441.0i) q^{55} +(103804. + 927216. i) q^{57} +(1.51862e6 + 1.27428e6i) q^{59} +(-137234. - 778290. i) q^{61} +(232684. + 84689.9i) q^{63} +(-79276.8 + 137312. i) q^{65} +(-1.47336e6 + 1.23629e6i) q^{67} +(-1.74888e6 - 3.02914e6i) q^{69} +(25177.1 - 142786. i) q^{71} +(1.70223e6 - 619561. i) q^{73} -2.39033e6 q^{75} -531516. q^{77} +(-3.41960e6 + 1.24463e6i) q^{79} +(-114282. + 648123. i) q^{81} +(-2.90828e6 - 5.03728e6i) q^{83} +(18533.0 - 15551.0i) q^{85} +(-1.78520e6 + 3.09206e6i) q^{87} +(-8.57997e6 - 3.12285e6i) q^{89} +(143741. + 815195. i) q^{91} +(-5.67138e6 - 4.75886e6i) q^{93} +(-1.07103e6 - 468191. i) q^{95} +(-5.12899e6 - 4.30374e6i) q^{97} +(548566. + 3.11107e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) $ 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9	$ 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9} - 5793 q^{11} + 22083 q^{13} - 70707 q^{15} + 29409 q^{17} + 12756 q^{19} - 40419 q^{21} - 116796 q^{23} + 26934 q^{25} + 439347 q^{27} - 148005 q^{29} + 141366 q^{31} + 1206654 q^{33} - 531651 q^{35} - 1508004 q^{37} - 2140644 q^{39} + 494157 q^{41} + 923511 q^{43} + 1790028 q^{45} - 662955 q^{47} - 4191369 q^{49} + 3753363 q^{51} - 246513 q^{53} + 2650185 q^{55} + 5831286 q^{57} - 2244432 q^{59} - 10302306 q^{61} - 12102117 q^{63} + 3985635 q^{65} + 11688288 q^{67} + 12632535 q^{69} + 10541736 q^{71} + 560730 q^{73} - 17718750 q^{75} - 22266192 q^{77} + 9424767 q^{79} + 16585437 q^{81} + 2359839 q^{83} - 20859762 q^{85} + 2348574 q^{87} - 4397130 q^{89} - 12653112 q^{91} + 52259766 q^{93} + 46248669 q^{95} - 34112766 q^{97} - 93757926 q^{99}+O(q^{100}) $ 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9 - 5793 * q^11 + 22083 * q^13 - 70707 * q^15 + 29409 * q^17 + 12756 * q^19 - 40419 * q^21 - 116796 * q^23 + 26934 * q^25 + 439347 * q^27 - 148005 * q^29 + 141366 * q^31 + 1206654 * q^33 - 531651 * q^35 - 1508004 * q^37 - 2140644 * q^39 + 494157 * q^41 + 923511 * q^43 + 1790028 * q^45 - 662955 * q^47 - 4191369 * q^49 + 3753363 * q^51 - 246513 * q^53 + 2650185 * q^55 + 5831286 * q^57 - 2244432 * q^59 - 10302306 * q^61 - 12102117 * q^63 + 3985635 * q^65 + 11688288 * q^67 + 12632535 * q^69 + 10541736 * q^71 + 560730 * q^73 - 17718750 * q^75 - 22266192 * q^77 + 9424767 * q^79 + 16585437 * q^81 + 2359839 * q^83 - 20859762 * q^85 + 2348574 * q^87 - 4397130 * q^89 - 12653112 * q^91 + 52259766 * q^93 + 46248669 * q^95 - 34112766 * q^97 - 93757926 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	−29.3247	+	10.6733i	−0.627061	+	0.228231i	−0.635951	−	0.771729i	$-0.719392\pi$
$3$	−29.3247	+	10.6733i	−0.627061	+	0.228231i	0.00889076	+	0.999960i	$0.497170\pi$
$4$		0			0
$5$	6.78900	−	38.5023i	0.0242891	−	0.137750i	−0.970252	−	0.242098i	$-0.922164\pi$
$5$	6.78900	−	38.5023i	0.0242891	−	0.137750i	0.994541	+	0.104348i	$0.0332756\pi$
$6$		0			0
$7$	−102.056	−	176.766i	−0.112459	−	0.194785i	0.804302	−	0.594221i	$-0.202540\pi$
$7$	−102.056	−	176.766i	−0.112459	−	0.194785i	−0.916761	+	0.399435i	$0.869206\pi$
$8$		0			0
$9$	−929.319	+	779.792i	−0.424929	+	0.356558i
$10$		0			0
$11$	1302.02	−	2255.16i	0.294946	−	0.510862i	−0.680026	−	0.733188i	$-0.738032\pi$
$11$	1302.02	−	2255.16i	0.294946	−	0.510862i	0.974972	+	0.222326i	$0.0713649\pi$
$12$		0			0
$13$	−3810.89	−	1387.05i	−0.481088	−	0.175102i	0.0900803	−	0.995935i	$-0.471288\pi$
$13$	−3810.89	−	1387.05i	−0.481088	−	0.175102i	−0.571169	+	0.820833i	$0.693510\pi$
$14$		0			0
$15$	211.862	+	1201.53i	0.0162082	+	0.0919212i
$16$		0			0
$17$	474.035	+	397.763i	0.0234013	+	0.0196360i	0.654413	−	0.756137i	$-0.272916\pi$
$17$	474.035	+	397.763i	0.0234013	+	0.0196360i	−0.631012	+	0.775773i	$0.717360\pi$
$18$		0			0
$19$	7036.39	−	29057.9i	0.235349	−	0.971911i
$19$	7036.39	−	29057.9i	0.235349	−	0.971911i
$20$		0			0
$21$	4879.45	+	4094.35i	0.114975	+	0.0964755i
$22$		0			0
$23$	19463.1	+	110380.i	0.333552	+	1.89167i	0.441083	+	0.897466i	$0.354594\pi$
$23$	19463.1	+	110380.i	0.333552	+	1.89167i	−0.107531	+	0.994202i	$0.534295\pi$
$24$		0			0
$25$	71977.1	+	26197.5i	0.921307	+	0.335329i
$26$		0			0
$27$	53053.6	−	91891.6i	0.518731	−	0.898468i
$28$		0			0
$29$	87644.1	−	73542.1i	0.667313	−	0.559942i	−0.244956	−	0.969534i	$-0.578773\pi$
$29$	87644.1	−	73542.1i	0.667313	−	0.559942i	0.912269	+	0.409592i	$0.134329\pi$
$30$		0			0
$31$	118620.	+	205455.i	0.715140	+	1.23866i	0.962906	+	0.269839i	$0.0869703\pi$
$31$	118620.	+	205455.i	0.715140	+	1.23866i	−0.247766	+	0.968820i	$0.579696\pi$
$32$		0			0
$33$	−14111.3	+	80028.9i	−0.0683545	+	0.387657i
$34$		0			0
$35$	−7498.77	+	2729.33i	−0.0295632	+	0.0107601i
$36$		0			0
$37$	429128.			1.39277			0.696387	−	0.717667i	$-0.254790\pi$
$37$	429128.			1.39277			0.696387	+	0.717667i	$0.254790\pi$
$38$		0			0
$39$	126558.			0.341635
$40$		0			0
$41$	206837.	−	75282.3i	0.468688	−	0.170588i	−0.0968700	−	0.995297i	$-0.530883\pi$
$41$	206837.	−	75282.3i	0.468688	−	0.170588i	0.565558	+	0.824709i	$0.308661\pi$
$42$		0			0
$43$	−66731.4	+	378453.i	−0.127994	+	0.725892i	0.851490	+	0.524371i	$0.175700\pi$
$43$	−66731.4	+	378453.i	−0.127994	+	0.725892i	−0.979484	+	0.201521i	$0.935412\pi$
$44$		0			0
$45$	23714.6	+	41075.0i	0.0387947	+	0.0671944i
$46$		0			0
$47$	169319.	−	142076.i	0.237883	−	0.199608i	−0.516051	−	0.856558i	$-0.672598\pi$
$47$	169319.	−	142076.i	0.237883	−	0.199608i	0.753934	+	0.656950i	$0.228154\pi$
$48$		0			0
$49$	390941.	−	677129.i	0.474706	−	0.822214i
$50$		0			0
$51$	−18146.4	−	6604.75i	−0.0191556	−	0.00697205i
$52$		0			0
$53$	37956.1	+	215260.i	0.0350200	+	0.198608i	0.997298	−	0.0734589i	$-0.0234038\pi$
$53$	37956.1	+	215260.i	0.0350200	+	0.198608i	−0.962278	+	0.272067i	$0.912293\pi$
$54$		0			0
$55$	−77989.6	−	65441.0i	−0.0632073	−	0.0530372i
$56$		0			0
$57$	103804.	+	927216.i	0.0742425	+	0.663161i
$58$		0			0
$59$	1.51862e6	+	1.27428e6i	0.962650	+	0.807759i	0.981382	−	0.192065i	$-0.0615185\pi$
$59$	1.51862e6	+	1.27428e6i	0.962650	+	0.807759i	−0.0187322	+	0.999825i	$0.505963\pi$
$60$		0			0
$61$	−137234.	−	778290.i	−0.0774116	−	0.439023i	−0.998738	−	0.0502320i	$-0.984004\pi$
$61$	−137234.	−	778290.i	−0.0774116	−	0.439023i	0.921326	−	0.388791i	$-0.127107\pi$
$62$		0			0
$63$	232684.	+	84689.9i	0.117240	+	0.0426717i
$64$		0			0
$65$	−79276.8	+	137312.i	−0.0358055	+	0.0620169i
$66$		0			0
$67$	−1.47336e6	+	1.23629e6i	−0.598474	+	0.502180i	−0.890955	−	0.454092i	$-0.849964\pi$
$67$	−1.47336e6	+	1.23629e6i	−0.598474	+	0.502180i	0.292480	+	0.956272i	$0.405519\pi$
$68$		0			0
$69$	−1.74888e6	−	3.02914e6i	−0.640895	−	1.11006i
$70$		0			0
$71$	25177.1	−	142786.i	0.00834837	−	0.0473460i	−0.980349	−	0.197271i	$-0.936792\pi$
$71$	25177.1	−	142786.i	0.00834837	−	0.0473460i	0.988697	+	0.149925i	$0.0479032\pi$
$72$		0			0
$73$	1.70223e6	−	619561.i	0.512139	−	0.186404i	−0.0730066	−	0.997331i	$-0.523259\pi$
$73$	1.70223e6	−	619561.i	0.512139	−	0.186404i	0.585146	+	0.810928i	$0.301037\pi$
$74$		0			0
$75$	−2.39033e6			−0.654248
$76$		0			0
$77$	−531516.			−0.132678
$78$		0			0
$79$	−3.41960e6	+	1.24463e6i	−0.780335	+	0.284019i	−0.701312	−	0.712854i	$-0.747402\pi$
$79$	−3.41960e6	+	1.24463e6i	−0.780335	+	0.284019i	−0.0790227	+	0.996873i	$0.525180\pi$
$80$		0			0
$81$	−114282.	+	648123.i	−0.0238934	+	0.135506i
$82$		0			0
$83$	−2.90828e6	−	5.03728e6i	−0.558293	−	0.966992i	−0.997639	−	0.0686743i	$-0.978123\pi$
$83$	−2.90828e6	−	5.03728e6i	−0.558293	−	0.966992i	0.439346	−	0.898318i	$-0.355210\pi$
$84$		0			0
$85$	18533.0	−	15551.0i	0.00327325	−	0.00274659i
$86$		0			0
$87$	−1.78520e6	+	3.09206e6i	−0.290649	+	0.503419i
$88$		0			0
$89$	−8.57997e6	−	3.12285e6i	−1.29009	−	0.469555i	−0.396335	−	0.918106i	$-0.629718\pi$
$89$	−8.57997e6	−	3.12285e6i	−1.29009	−	0.469555i	−0.893757	+	0.448551i	$0.851940\pi$
$90$		0			0
$91$	143741.	+	815195.i	0.0199956	+	0.113401i
$92$		0			0
$93$	−5.67138e6	−	4.75886e6i	−0.731137	−	0.613497i
$94$		0			0
$95$	−1.07103e6	−	468191.i	−0.128164	−	0.0560262i
$96$		0			0
$97$	−5.12899e6	−	4.30374e6i	−0.570599	−	0.478789i	0.311246	−	0.950329i	$-0.399254\pi$
$97$	−5.12899e6	−	4.30374e6i	−0.570599	−	0.478789i	−0.881845	+	0.471540i	$0.843698\pi$
$98$		0			0
$99$	548566.	+	3.11107e6i	0.0568205	+	0.322245i
$100$		0			0
$101$	1.00304e6	+	365077.i	0.0968711	+	0.0352582i	0.390001	−	0.920814i	$-0.372475\pi$
$101$	1.00304e6	+	365077.i	0.0968711	+	0.0352582i	−0.293130	+	0.956073i	$0.594697\pi$
$102$		0			0
$103$	3.69909e6	−	6.40701e6i	0.333553	−	0.577730i	−0.649653	−	0.760231i	$-0.725086\pi$
$103$	3.69909e6	−	6.40701e6i	0.333553	−	0.577730i	0.983206	+	0.182500i	$0.0584191\pi$
$104$		0			0
$105$	190768.	−	160074.i	0.0160821	−	0.0134945i
$106$		0			0
$107$	4.30511e6	+	7.45667e6i	0.339736	+	0.588440i	0.984383	−	0.176041i	$-0.0563290\pi$
$107$	4.30511e6	+	7.45667e6i	0.339736	+	0.588440i	−0.644647	+	0.764480i	$0.722996\pi$
$108$		0			0
$109$	−573721.	+	3.25374e6i	−0.0424335	+	0.240652i	−0.998646	−	0.0520211i	$-0.983434\pi$
$109$	−573721.	+	3.25374e6i	−0.0424335	+	0.240652i	0.956213	+	0.292673i	$0.0945448\pi$
$110$		0			0
$111$	−1.25841e7	+	4.58022e6i	−0.873354	+	0.317875i
$112$		0			0
$113$	2.46173e7			1.60497			0.802484	−	0.596674i	$-0.203511\pi$
$113$	2.46173e7			1.60497			0.802484	+	0.596674i	$0.203511\pi$
$114$		0			0
$115$	4.38204e6			0.268679
$116$		0			0
$117$	4.62315e6	−	1.68269e6i	0.266862	−	0.0971299i
$118$		0			0
$119$	21932.9	−	124388.i	0.00119311	−	0.00676648i
$120$		0			0
$121$	6.35308e6	+	1.10039e7i	0.326013	+	0.564672i
$122$		0			0
$123$	−5.26191e6	+	4.41527e6i	−0.254962	+	0.213939i
$124$		0			0
$125$	3.02452e6	−	5.23862e6i	0.138507	−	0.239901i
$126$		0			0
$127$	2.84390e7	+	1.03509e7i	1.23197	+	0.448401i	0.874272	−	0.485436i	$-0.161339\pi$
$127$	2.84390e7	+	1.03509e7i	1.23197	+	0.448401i	0.357699	+	0.933837i	$0.383561\pi$
$128$		0			0
$129$	−2.08247e6	−	1.18103e7i	−0.0854112	−	0.484391i
$130$		0			0
$131$	1.72642e7	+	1.44864e7i	0.670962	+	0.563004i	0.913350	−	0.407175i	$-0.133486\pi$
$131$	1.72642e7	+	1.44864e7i	0.670962	+	0.563004i	−0.242388	+	0.970179i	$0.577931\pi$
$132$		0			0
$133$	−5.85456e6	+	1.72174e6i	−0.215781	+	0.0634580i
$134$		0			0
$135$	−3.17786e6	−	2.66654e6i	−0.111165	−	0.0932781i
$136$		0			0
$137$	−3.11260e6	−	1.76524e7i	−0.103419	−	0.586520i	−0.991840	−	0.127490i	$-0.959308\pi$
$137$	−3.11260e6	−	1.76524e7i	−0.103419	−	0.586520i	0.888421	−	0.459030i	$-0.151803\pi$
$138$		0			0
$139$	3.47722e7	+	1.26560e7i	1.09820	+	0.399711i	0.826651	−	0.562715i	$-0.190243\pi$
$139$	3.47722e7	+	1.26560e7i	1.09820	+	0.399711i	0.271545	+	0.962426i	$0.412465\pi$
$140$		0			0
$141$	−3.44882e6	+	5.97353e6i	−0.103611	+	0.179459i
$142$		0			0
$143$	−8.08988e6	+	6.78822e6i	−0.231348	+	0.194124i
$144$		0			0
$145$	−2.23653e6	−	3.87378e6i	−0.0609237	−	0.105523i
$146$		0			0
$147$	−4.23701e6	+	2.40293e7i	−0.110014	+	0.623921i
$148$		0			0
$149$	6.46649e7	−	2.35361e7i	1.60146	−	0.582885i	0.621737	−	0.783226i	$-0.286427\pi$
$149$	6.46649e7	−	2.35361e7i	1.60146	−	0.582885i	0.979726	+	0.200341i	$0.0642052\pi$
$150$		0			0
$151$	−3.58865e7			−0.848227			−0.424113	−	0.905609i	$-0.639414\pi$
$151$	−3.58865e7			−0.848227			−0.424113	+	0.905609i	$0.639414\pi$
$152$		0			0
$153$	−750702.			−0.0169452
$154$		0			0
$155$	8.71582e6	−	3.17230e6i	0.187995	−	0.0684247i
$156$		0			0
$157$	8.47955e6	−	4.80899e7i	0.174874	−	0.991757i	−0.763416	−	0.645907i	$-0.776479\pi$
$157$	8.47955e6	−	4.80899e7i	0.174874	−	0.991757i	0.938290	−	0.345850i	$-0.112410\pi$
$158$		0			0
$159$	−3.41059e6	−	5.90732e6i	−0.0672884	−	0.116547i
$160$		0			0
$161$	1.75252e7	−	1.47054e7i	0.330958	−	0.277707i
$162$		0			0
$163$	−2.36184e7	+	4.09083e7i	−0.427164	+	0.739869i	−0.996620	−	0.0821525i	$-0.973821\pi$
$163$	−2.36184e7	+	4.09083e7i	−0.427164	+	0.739869i	0.569456	+	0.822022i	$0.307154\pi$
$164$		0			0
$165$	2.98550e6	+	1.08663e6i	0.0517396	+	0.0188317i
$166$		0			0
$167$	1.44221e7	+	8.17917e7i	0.239618	+	1.35894i	0.832666	+	0.553776i	$0.186814\pi$
$167$	1.44221e7	+	8.17917e7i	0.239618	+	1.35894i	−0.593047	+	0.805168i	$0.702075\pi$
$168$		0			0
$169$	−3.54692e7	−	2.97622e7i	−0.565259	−	0.474309i
$170$		0			0
$171$	1.61200e7	+	3.24910e7i	0.246536	+	0.496909i
$172$		0			0
$173$	−1.52621e7	−	1.28064e7i	−0.224106	−	0.188047i	0.523821	−	0.851828i	$-0.324506\pi$
$173$	−1.52621e7	−	1.28064e7i	−0.224106	−	0.188047i	−0.747927	+	0.663781i	$0.768950\pi$
$174$		0			0
$175$	−2.71486e6	−	1.53968e7i	−0.0382926	−	0.217168i
$176$		0			0
$177$	−5.81340e7	−	2.11591e7i	−0.787996	−	0.286807i
$178$		0			0
$179$	−2.35010e6	+	4.07049e6i	−0.0306267	+	0.0530470i	−0.880932	−	0.473242i	$-0.843084\pi$
$179$	−2.35010e6	+	4.07049e6i	−0.0306267	+	0.0530470i	0.850306	+	0.526289i	$0.176417\pi$
$180$		0			0
$181$	2.93417e7	−	2.46206e7i	0.367799	−	0.308620i	−0.440091	−	0.897953i	$-0.645054\pi$
$181$	2.93417e7	−	2.46206e7i	0.367799	−	0.308620i	0.807890	+	0.589333i	$0.200609\pi$
$182$		0			0
$183$	1.23313e7	+	2.13584e7i	0.148741	+	0.257626i
$184$		0			0
$185$	2.91335e6	−	1.65224e7i	0.0338292	−	0.191855i
$186$		0			0
$187$	1.51422e6	−	551132.i	0.0169334	−	0.00616325i
$188$		0			0
$189$	−2.16578e7			−0.233345
$190$		0			0
$191$	−7.01288e7			−0.728248			−0.364124	−	0.931350i	$-0.618632\pi$
$191$	−7.01288e7			−0.728248			−0.364124	+	0.931350i	$0.618632\pi$
$192$		0			0
$193$	6.29460e6	−	2.29105e6i	0.0630257	−	0.0229395i	−0.310315	−	0.950634i	$-0.600434\pi$
$193$	6.29460e6	−	2.29105e6i	0.0630257	−	0.0229395i	0.373341	+	0.927694i	$0.378212\pi$
$194$		0			0
$195$	859201.	−	4.87277e6i	0.00829800	−	0.0470603i
$196$		0			0
$197$	−3.83169e7	−	6.63668e7i	−0.357074	−	0.618471i	0.630397	−	0.776273i	$-0.282892\pi$
$197$	−3.83169e7	−	6.63668e7i	−0.357074	−	0.618471i	−0.987471	+	0.157803i	$0.949559\pi$
$198$		0			0
$199$	−1.40778e8	+	1.18127e8i	−1.26634	+	1.06258i	−0.271362	+	0.962477i	$0.587474\pi$
$199$	−1.40778e8	+	1.18127e8i	−1.26634	+	1.06258i	−0.994977	+	0.100107i	$0.968082\pi$
$200$		0			0
$201$	3.00104e7	−	5.19795e7i	0.260667	−	0.451488i
$202$		0			0
$203$	−2.19444e7	−	7.98710e6i	−0.184114	−	0.0670121i
$204$		0			0
$205$	−1.49433e6	−	8.47478e6i	−0.0121146	−	0.0687052i
$206$		0			0
$207$	−1.04161e8	−	8.74016e7i	−0.816225	−	0.684894i
$208$		0			0
$209$	−5.63688e7	−	5.37021e7i	−0.427097	−	0.406892i
$210$		0			0
$211$	−1.12882e8	−	9.47195e7i	−0.827251	−	0.694146i	0.127407	−	0.991850i	$-0.459334\pi$
$211$	−1.12882e8	−	9.47195e7i	−0.827251	−	0.694146i	−0.954658	+	0.297705i	$0.903779\pi$
$212$		0			0
$213$	785695.	+	4.45590e6i	0.00557090	+	0.0315942i
$214$		0			0
$215$	1.41183e7	+	5.13863e6i	0.0968828	+	0.0352625i
$216$		0			0
$217$	2.42117e7	−	4.19360e7i	0.160848	−	0.278598i
$218$		0			0
$219$	−4.33047e7	+	3.63369e7i	−0.278599	+	0.233773i
$220$		0			0
$221$	−1.25478e6	−	2.17334e6i	−0.00781978	−	0.0135443i
$222$		0			0
$223$	−2.24047e7	+	1.27063e8i	−0.135292	+	0.767279i	0.839364	+	0.543570i	$0.182928\pi$
$223$	−2.24047e7	+	1.27063e8i	−0.135292	+	0.767279i	−0.974656	+	0.223709i	$0.928183\pi$
$224$		0			0
$225$	−8.73184e7	+	3.17813e7i	−0.511054	+	0.186008i
$226$		0			0
$227$	2.82016e8			1.60023			0.800117	−	0.599845i	$-0.204771\pi$
$227$	2.82016e8			1.60023			0.800117	+	0.599845i	$0.204771\pi$
$228$		0			0
$229$	−2.28505e8			−1.25739			−0.628697	−	0.777651i	$-0.716411\pi$
$229$	−2.28505e8			−1.25739			−0.628697	+	0.777651i	$0.716411\pi$
$230$		0			0
$231$	1.55866e7	−	5.67304e6i	0.0831971	−	0.0302813i
$232$		0			0
$233$	3.58878e6	−	2.03530e7i	0.0185867	−	0.105410i	−0.974103	−	0.226104i	$-0.927401\pi$
$233$	3.58878e6	−	2.03530e7i	0.0185867	−	0.105410i	0.992690	+	0.120694i	$0.0385121\pi$
$234$		0			0
$235$	−4.32074e6	−	7.48374e6i	−0.0217180	−	0.0376167i
$236$		0			0
$237$	8.69946e7	−	7.29971e7i	0.424495	−	0.356194i
$238$		0			0
$239$	1.17923e8	−	2.04249e8i	0.558736	−	0.967759i	−0.438867	−	0.898552i	$-0.644620\pi$
$239$	1.17923e8	−	2.04249e8i	0.558736	−	0.967759i	0.997602	−	0.0692065i	$-0.0220467\pi$
$240$		0			0
$241$	1.70680e8	+	6.21223e7i	0.785456	+	0.285883i	0.703446	−	0.710749i	$-0.251644\pi$
$241$	1.70680e8	+	6.21223e7i	0.785456	+	0.285883i	0.0820102	+	0.996631i	$0.473866\pi$
$242$		0			0
$243$	3.67298e7	+	2.08305e8i	0.164209	+	0.931276i
$244$		0			0
$245$	−2.34169e7	−	1.96491e7i	−0.101730	−	0.0853616i
$246$		0			0
$247$	−6.71197e7	+	1.00977e8i	−0.283407	+	0.426365i
$248$		0			0
$249$	1.39049e8	+	1.16676e8i	0.570782	+	0.478943i
$250$		0			0
$251$	1.10196e7	+	6.24951e7i	0.0439852	+	0.249453i	0.998870	−	0.0475235i	$-0.0151329\pi$
$251$	1.10196e7	+	6.24951e7i	0.0439852	+	0.249453i	−0.954885	+	0.296976i	$0.904022\pi$
$252$		0			0
$253$	2.74267e8	+	9.98251e7i	1.06476	+	0.387541i
$254$		0			0
$255$	−377494.	+	653839.i	−0.00142567	+	0.00246934i
$256$		0			0
$257$	−9.22270e7	+	7.73876e7i	−0.338916	+	0.284384i	−0.796321	−	0.604874i	$-0.793223\pi$
$257$	−9.22270e7	+	7.73876e7i	−0.338916	+	0.284384i	0.457405	+	0.889258i	$0.348779\pi$
$258$		0			0
$259$	−4.37951e7	−	7.58554e7i	−0.156631	−	0.271292i
$260$		0			0
$261$	−2.41018e7	+	1.36688e8i	−0.0839089	+	0.475871i
$262$		0			0
$263$	3.85482e8	−	1.40304e8i	1.30665	−	0.475582i	0.407494	−	0.913208i	$-0.366403\pi$
$263$	3.85482e8	−	1.40304e8i	1.30665	−	0.475582i	0.899157	+	0.437626i	$0.144181\pi$
$264$		0			0
$265$	8.54569e6			0.0282089
$266$		0			0
$267$	2.84936e8			0.916133
$268$		0			0
$269$	3.82323e8	−	1.39154e8i	1.19756	−	0.435876i	0.335188	−	0.942151i	$-0.391200\pi$
$269$	3.82323e8	−	1.39154e8i	1.19756	−	0.435876i	0.862372	+	0.506275i	$0.168978\pi$
$270$		0			0
$271$	3.42257e7	−	1.94104e8i	0.104462	−	0.592436i	−0.886971	−	0.461825i	$-0.847195\pi$
$271$	3.42257e7	−	1.94104e8i	0.104462	−	0.592436i	0.991434	−	0.130611i	$-0.0416939\pi$
$272$		0			0
$273$	−1.29160e7	−	2.23712e7i	−0.0384201	−	0.0665456i
$274$		0			0
$275$	1.52795e8	−	1.28210e8i	0.443043	−	0.371757i
$276$		0			0
$277$	−3.20765e8	+	5.55581e8i	−0.906792	+	1.57061i	−0.0882987	+	0.996094i	$0.528143\pi$
$277$	−3.20765e8	+	5.55581e8i	−0.906792	+	1.57061i	−0.818493	+	0.574516i	$0.805190\pi$
$278$		0			0
$279$	−2.70448e8	−	9.84350e7i	−0.745537	−	0.271353i
$280$		0			0
$281$	1.16754e8	+	6.62143e8i	0.313905	+	1.78024i	0.578295	+	0.815828i	$0.303718\pi$
$281$	1.16754e8	+	6.62143e8i	0.313905	+	1.78024i	−0.264389	+	0.964416i	$0.585170\pi$
$282$		0			0
$283$	1.01319e8	+	8.50168e7i	0.265729	+	0.222973i	0.765910	−	0.642948i	$-0.222289\pi$
$283$	1.01319e8	+	8.50168e7i	0.265729	+	0.222973i	−0.500181	+	0.865921i	$0.666733\pi$
$284$		0			0
$285$	3.64047e7	+	2.29817e6i	0.0931538	+	0.00588065i
$286$		0			0
$287$	−3.44163e7	−	2.88787e7i	−0.0859365	−	0.0721093i
$288$		0			0
$289$	−7.11881e7	−	4.03728e8i	−0.173486	−	0.983889i
$290$		0			0
$291$	1.96341e8	+	7.14625e7i	0.467075	+	0.170001i
$292$		0			0
$293$	1.04564e8	−	1.81109e8i	0.242853	−	0.420634i	−0.718673	−	0.695348i	$-0.755250\pi$
$293$	1.04564e8	−	1.81109e8i	0.242853	−	0.420634i	0.961526	+	0.274715i	$0.0885834\pi$
$294$		0			0
$295$	5.93726e7	−	4.98195e7i	0.134651	−	0.112985i
$296$		0			0
$297$	−1.38154e8	−	2.39289e8i	−0.305995	−	0.529999i
$298$		0			0
$299$	7.89318e7	−	4.47644e8i	0.170767	−	0.968465i
$300$		0			0
$301$	7.37081e7	−	2.68275e7i	0.155787	−	0.0567020i
$302$		0			0
$303$	−3.33105e7			−0.0687911
$304$		0			0
$305$	−3.08977e7			−0.0623557
$306$		0			0
$307$	−3.69906e8	+	1.34635e8i	−0.729638	+	0.265566i	−0.680011	−	0.733201i	$-0.738025\pi$
$307$	−3.69906e8	+	1.34635e8i	−0.729638	+	0.265566i	−0.0496262	+	0.998768i	$0.515803\pi$
$308$		0			0
$309$	−4.00907e7	+	2.27365e8i	−0.0773016	+	0.438399i
$310$		0			0
$311$	−1.39739e8	−	2.42034e8i	−0.263424	−	0.456263i	0.703726	−	0.710472i	$-0.251518\pi$
$311$	−1.39739e8	−	2.42034e8i	−0.263424	−	0.456263i	−0.967149	+	0.254208i	$0.918185\pi$
$312$		0			0
$313$	−7.13602e8	+	5.98784e8i	−1.31538	+	1.10373i	−0.328117	+	0.944637i	$0.606414\pi$
$313$	−7.13602e8	+	5.98784e8i	−1.31538	+	1.10373i	−0.987263	+	0.159097i	$0.949142\pi$
$314$		0			0
$315$	4.84045e6	−	8.38390e6i	0.00872567	−	0.0151133i
$316$		0			0
$317$	6.53085e8	+	2.37704e8i	1.15150	+	0.419110i	0.846052	−	0.533100i	$-0.178973\pi$
$317$	6.53085e8	+	2.37704e8i	1.15150	+	0.419110i	0.305444	+	0.952210i	$0.401195\pi$
$318$		0			0
$319$	−5.17352e7	−	2.93405e8i	−0.0892316	−	0.506057i
$320$		0			0
$321$	−2.05834e8	−	1.72715e8i	−0.347335	−	0.291449i
$322$		0			0
$323$	1.48936e7	−	1.09756e7i	0.0245919	−	0.0181226i
$324$		0			0
$325$	−2.37960e8	−	1.99672e8i	−0.384514	−	0.322645i
$326$		0			0
$327$	−1.79040e7	−	1.01538e8i	−0.0283160	−	0.160588i
$328$		0			0
$329$	−4.23943e7	−	1.54303e7i	−0.0656329	−	0.0238884i
$330$		0			0
$331$	2.40864e8	−	4.17188e8i	0.365068	−	0.632315i	−0.623719	−	0.781648i	$-0.714379\pi$
$331$	2.40864e8	−	4.17188e8i	0.365068	−	0.632315i	0.988787	+	0.149333i	$0.0477126\pi$
$332$		0			0
$333$	−3.98797e8	+	3.34630e8i	−0.591830	+	0.496604i
$334$		0			0
$335$	3.75975e7	+	6.51208e7i	0.0546389	+	0.0946374i
$336$		0			0
$337$	−8.58134e7	+	4.86672e8i	−0.122138	+	0.692679i	0.860829	+	0.508895i	$0.169946\pi$
$337$	−8.58134e7	+	4.86672e8i	−0.122138	+	0.692679i	−0.982967	+	0.183784i	$0.941165\pi$
$338$		0			0
$339$	−7.21896e8	+	2.62749e8i	−1.00641	+	0.366304i
$340$		0			0
$341$	6.17780e8			0.843711
$342$		0			0
$343$	−3.27687e8			−0.438459
$344$		0			0
$345$	−1.28502e8	+	4.67709e7i	−0.168478	+	0.0613210i
$346$		0			0
$347$	8.26656e7	−	4.68820e8i	0.106212	−	0.602355i	−0.884518	−	0.466506i	$-0.845513\pi$
$347$	8.26656e7	−	4.68820e8i	0.106212	−	0.602355i	0.990730	−	0.135849i	$-0.0433763\pi$
$348$		0			0
$349$	−2.19331e8	−	3.79892e8i	−0.276192	−	0.478378i	0.694243	−	0.719740i	$-0.255739\pi$
$349$	−2.19331e8	−	3.79892e8i	−0.276192	−	0.478378i	−0.970435	+	0.241362i	$0.922406\pi$
$350$		0			0
$351$	−3.29640e8	+	2.76601e8i	−0.406879	+	0.341412i
$352$		0			0
$353$	2.44462e8	−	4.23420e8i	0.295801	−	0.512342i	−0.679370	−	0.733796i	$-0.737747\pi$
$353$	2.44462e8	−	4.23420e8i	0.295801	−	0.512342i	0.975171	+	0.221454i	$0.0710801\pi$
$354$		0			0
$355$	−5.32668e6	−	1.93875e6i	−0.00631914	−	0.00229998i
$356$		0			0
$357$	684453.	+	3.88173e6i	0.000796169	+	0.00451530i
$358$		0			0
$359$	−4.28017e8	−	3.59149e8i	−0.488237	−	0.409679i	0.365157	−	0.930946i	$-0.381015\pi$
$359$	−4.28017e8	−	3.59149e8i	−0.488237	−	0.409679i	−0.853394	+	0.521267i	$0.825460\pi$
$360$		0			0
$361$	−7.94850e8	−	4.08925e8i	−0.889222	−	0.457477i
$362$		0			0
$363$	−3.03750e8	−	2.54877e8i	−0.333306	−	0.279677i
$364$		0			0
$365$	−1.22981e7	−	6.97460e7i	−0.0132377	−	0.0750748i
$366$		0			0
$367$	4.49140e8	+	1.63474e8i	0.474297	+	0.172630i	0.568098	−	0.822961i	$-0.307680\pi$
$367$	4.49140e8	+	1.63474e8i	0.474297	+	0.172630i	−0.0938009	+	0.995591i	$0.529902\pi$
$368$		0			0
$369$	−1.33513e8	+	2.31251e8i	−0.138334	+	0.239602i
$370$		0			0
$371$	3.41771e7	−	2.86780e7i	0.0347477	−	0.0291568i
$372$		0			0
$373$	5.32610e8	+	9.22507e8i	0.531408	+	0.920426i	0.999328	+	0.0366549i	$0.0116702\pi$
$373$	5.32610e8	+	9.22507e8i	0.531408	+	0.920426i	−0.467920	+	0.883771i	$0.654996\pi$
$374$		0			0
$375$	−3.27797e7	+	1.85903e8i	−0.0320993	+	0.182044i
$376$		0			0
$377$	−4.36009e8	+	1.58694e8i	−0.419083	+	0.152534i
$378$		0			0
$379$	−1.60479e9			−1.51419			−0.757096	−	0.653303i	$-0.773383\pi$
$379$	−1.60479e9			−1.51419			−0.757096	+	0.653303i	$0.773383\pi$
$380$		0			0
$381$	−9.44443e8			−0.874860
$382$		0			0
$383$	1.26535e9	−	4.60549e8i	1.15084	−	0.418871i	0.305023	−	0.952345i	$-0.401336\pi$
$383$	1.26535e9	−	4.60549e8i	1.15084	−	0.418871i	0.845817	+	0.533474i	$0.179114\pi$
$384$		0			0
$385$	−3.60846e6	+	2.04646e7i	−0.00322262	+	0.0182764i
$386$		0			0
$387$	−2.33099e8	−	4.03740e8i	−0.204434	−	0.354090i
$388$		0			0
$389$	5.12437e8	−	4.29985e8i	0.441384	−	0.370365i	−0.394843	−	0.918749i	$-0.629201\pi$
$389$	5.12437e8	−	4.29985e8i	0.441384	−	0.370365i	0.836227	+	0.548384i	$0.184757\pi$
$390$		0			0
$391$	−3.46791e7	+	6.00659e7i	−0.0293392	+	0.0508170i
$392$		0			0
$393$	−6.60888e8	−	2.40543e8i	−0.549229	−	0.199903i
$394$		0			0
$395$	2.47056e7	+	1.40113e8i	0.0201700	+	0.114390i
$396$		0			0
$397$	8.76536e8	+	7.35501e8i	0.703077	+	0.589951i	0.922647	−	0.385645i	$-0.126021\pi$
$397$	8.76536e8	+	7.35501e8i	0.703077	+	0.589951i	−0.219570	+	0.975597i	$0.570466\pi$
$398$		0			0
$399$	1.53307e8	−	1.12977e8i	0.120825	−	0.0890401i
$400$		0			0
$401$	6.84899e8	+	5.74699e8i	0.530422	+	0.445077i	0.868247	−	0.496132i	$-0.165247\pi$
$401$	6.84899e8	+	5.74699e8i	0.530422	+	0.445077i	−0.337825	+	0.941209i	$0.609691\pi$
$402$		0			0
$403$	−1.67070e8	−	9.47500e8i	−0.127154	−	0.721127i
$404$		0			0
$405$	2.41784e7	+	8.80021e6i	0.0180857	+	0.00658265i
$406$		0			0
$407$	5.58732e8	−	9.67753e8i	0.410793	−	0.711515i
$408$		0			0
$409$	−1.53619e8	+	1.28901e8i	−0.111023	+	0.0931592i	−0.696609	−	0.717451i	$-0.745309\pi$
$409$	−1.53619e8	+	1.28901e8i	−0.111023	+	0.0931592i	0.585586	+	0.810610i	$0.300864\pi$
$410$		0			0
$411$	2.79687e8	+	4.84431e8i	0.198713	+	0.344180i
$412$		0			0
$413$	7.02645e7	−	3.98490e8i	0.0490807	−	0.278350i
$414$		0			0
$415$	−2.13691e8	+	7.77773e7i	−0.146764	+	0.0534176i
$416$		0			0
$417$	−1.15477e9			−0.779863
$418$		0			0
$419$	1.29820e9			0.862167			0.431084	−	0.902312i	$-0.358131\pi$
$419$	1.29820e9			0.862167			0.431084	+	0.902312i	$0.358131\pi$
$420$		0			0
$421$	5.36949e8	−	1.95434e8i	0.350708	−	0.127647i	−0.160658	−	0.987010i	$-0.551362\pi$
$421$	5.36949e8	−	1.95434e8i	0.350708	−	0.127647i	0.511366	+	0.859363i	$0.329139\pi$
$422$		0			0
$423$	−4.65622e7	+	2.64068e8i	−0.0299118	+	0.169638i
$424$		0			0
$425$	2.36993e7	+	4.10484e7i	0.0149752	+	0.0259379i
$426$		0			0
$427$	−1.23570e8	+	1.03688e8i	−0.0768096	+	0.0644509i
$428$		0			0
$429$	1.64781e8	−	2.85408e8i	0.100764	−	0.174529i
$430$		0			0
$431$	2.65679e9	+	9.66991e8i	1.59840	+	0.581771i	0.979100	−	0.203381i	$-0.0651929\pi$
$431$	2.65679e9	+	9.66991e8i	1.59840	+	0.581771i	0.619303	+	0.785152i	$0.287415\pi$
$432$		0			0
$433$	2.84737e8	+	1.61483e9i	0.168553	+	0.955912i	0.945325	+	0.326130i	$0.105745\pi$
$433$	2.84737e8	+	1.61483e9i	0.168553	+	0.955912i	−0.776772	+	0.629782i	$0.783144\pi$
$434$		0			0
$435$	1.06932e8	+	8.97263e7i	0.0622865	+	0.0522645i
$436$		0			0
$437$	3.34437e9	+	2.11125e8i	1.91703	+	0.121019i
$438$		0			0
$439$	1.20609e9	+	1.01203e9i	0.680384	+	0.570910i	0.916119	−	0.400907i	$-0.131305\pi$
$439$	1.20609e9	+	1.01203e9i	0.680384	+	0.570910i	−0.235734	+	0.971818i	$0.575750\pi$
$440$		0			0
$441$	1.64711e8	+	9.34121e8i	0.0914507	+	0.518643i
$442$		0			0
$443$	1.08399e9	+	3.94540e8i	0.592396	+	0.215615i	0.620783	−	0.783983i	$-0.286815\pi$
$443$	1.08399e9	+	3.94540e8i	0.592396	+	0.215615i	−0.0283869	+	0.999597i	$0.509037\pi$
$444$		0			0
$445$	−1.78486e8	+	3.09148e8i	−0.0960164	+	0.166305i
$446$		0			0
$447$	−1.64507e9	+	1.38038e9i	−0.871182	+	0.731008i
$448$		0			0
$449$	−6.63874e8	−	1.14986e9i	−0.346118	−	0.599493i	0.639439	−	0.768842i	$-0.279167\pi$
$449$	−6.63874e8	−	1.14986e9i	−0.346118	−	0.599493i	−0.985556	+	0.169349i	$0.945833\pi$
$450$		0			0
$451$	9.95311e7	−	5.64469e8i	0.0510906	−	0.289749i
$452$		0			0
$453$	1.05236e9	−	3.83028e8i	0.531890	−	0.193592i
$454$		0			0
$455$	3.23627e7			0.0161067
$456$		0			0
$457$	6.15376e8			0.301602			0.150801	−	0.988564i	$-0.451815\pi$
$457$	6.15376e8			0.301602			0.150801	+	0.988564i	$0.451815\pi$
$458$		0			0
$459$	6.17003e7	−	2.24571e7i	0.0297812	−	0.0108395i
$460$		0			0
$461$	−1.85493e8	+	1.05198e9i	−0.0881808	+	0.500098i	0.908444	+	0.418007i	$0.137271\pi$
$461$	−1.85493e8	+	1.05198e9i	−0.0881808	+	0.500098i	−0.996625	+	0.0820915i	$0.973840\pi$
$462$		0			0
$463$	−9.10230e8	−	1.57656e9i	−0.426204	−	0.738207i	0.570328	−	0.821417i	$-0.306816\pi$
$463$	−9.10230e8	−	1.57656e9i	−0.426204	−	0.738207i	−0.996532	+	0.0832098i	$0.973483\pi$
$464$		0			0
$465$	−2.21730e8	+	1.86054e8i	−0.102268	+	0.0858129i
$466$		0			0
$467$	4.79656e8	−	8.30788e8i	0.217932	−	0.377469i	−0.736244	−	0.676716i	$-0.763402\pi$
$467$	4.79656e8	−	8.30788e8i	0.217932	−	0.377469i	0.954175	+	0.299248i	$0.0967357\pi$
$468$		0			0
$469$	3.68900e8	+	1.34269e8i	0.165121	+	0.0600993i
$470$		0			0
$471$	2.64619e8	+	1.50073e9i	0.116694	+	0.661804i
$472$		0			0
$473$	7.66587e8	+	6.43243e8i	0.333079	+	0.279487i
$474$		0			0
$475$	1.26770e9	−	1.90717e9i	0.542738	−	0.816510i
$476$		0			0
$477$	−2.03131e8	−	1.70447e8i	−0.0856964	−	0.0719078i
$478$		0			0
$479$	−3.18444e8	−	1.80599e9i	−0.132391	−	0.750827i	−0.976641	−	0.214877i	$-0.931065\pi$
$479$	−3.18444e8	−	1.80599e9i	−0.132391	−	0.750827i	0.844250	−	0.535950i	$-0.180046\pi$
$480$		0			0
$481$	−1.63536e9	−	5.95222e8i	−0.670047	−	0.243877i
$482$		0			0
$483$	−3.56967e8	+	6.18285e8i	−0.144149	+	0.249674i
$484$		0			0
$485$	−2.00525e8	+	1.68260e8i	−0.0798126	+	0.0669707i
$486$		0			0
$487$	7.76518e8	+	1.34497e9i	0.304649	+	0.527668i	0.977183	−	0.212398i	$-0.0681274\pi$
$487$	7.76518e8	+	1.34497e9i	0.304649	+	0.527668i	−0.672534	+	0.740066i	$0.734794\pi$
$488$		0			0
$489$	2.55976e8	−	1.45171e9i	0.0989962	−	0.561435i
$490$		0			0
$491$	−3.96169e9	+	1.44194e9i	−1.51041	+	0.549745i	−0.958732	−	0.284310i	$-0.908236\pi$
$491$	−3.96169e9	+	1.44194e9i	−1.51041	+	0.549745i	−0.551681	+	0.834055i	$0.686013\pi$
$492$		0			0
$493$	7.07986e7			0.0266110
$494$		0			0
$495$	1.23508e8			0.0457694
$496$		0			0
$497$	−2.78093e7	+	1.01218e7i	−0.0101612	+	0.00369836i
$498$		0			0
$499$	−2.93130e8	+	1.66242e9i	−0.105611	+	0.598948i	0.885364	+	0.464899i	$0.153909\pi$
$499$	−2.93130e8	+	1.66242e9i	−0.105611	+	0.598948i	−0.990975	+	0.134050i	$0.957202\pi$
$500$		0			0
$501$	−1.29591e9	−	2.24459e9i	−0.460409	−	0.797452i
$502$		0			0
$503$	−5.82528e8	+	4.88799e8i	−0.204093	+	0.171255i	−0.739105	−	0.673590i	$-0.764751\pi$
$503$	−5.82528e8	+	4.88799e8i	−0.204093	+	0.171255i	0.535012	+	0.844844i	$0.320307\pi$
$504$		0			0
$505$	2.08660e7	−	3.61409e7i	0.00720973	−	0.0124876i
$506$		0			0
$507$	1.35778e9	+	4.94193e8i	0.462704	+	0.168410i
$508$		0			0
$509$	−5.72999e8	−	3.24964e9i	−0.192593	−	1.09225i	−0.915804	−	0.401625i	$-0.868446\pi$
$509$	−5.72999e8	−	3.24964e9i	−0.192593	−	1.09225i	0.723211	−	0.690627i	$-0.242665\pi$
$510$		0			0
$511$	−2.83241e8	−	2.37667e8i	−0.0939036	−	0.0787945i
$512$		0			0
$513$	−2.29687e9	−	2.18821e9i	−0.751148	−	0.715613i
$514$		0			0
$515$	−2.21572e8	−	1.85921e8i	−0.0714807	−	0.0599795i
$516$		0			0
$517$	−9.99470e7	−	5.66828e8i	−0.0318092	−	0.180399i
$518$		0			0
$519$	5.84244e8	+	2.12647e8i	0.183446	+	0.0667689i
$520$		0			0
$521$	1.40624e9	−	2.43568e9i	0.435641	−	0.754552i	−0.561707	−	0.827336i	$-0.689855\pi$
$521$	1.40624e9	−	2.43568e9i	0.435641	−	0.754552i	0.997348	+	0.0727845i	$0.0231885\pi$
$522$		0			0
$523$	−3.12105e9	+	2.61887e9i	−0.953993	+	0.800495i	−0.979965	−	0.199167i	$-0.936176\pi$
$523$	−3.12105e9	+	2.61887e9i	−0.953993	+	0.800495i	0.0259723	+	0.999663i	$0.491732\pi$
$524$		0			0
$525$	2.43947e8	+	4.22529e8i	0.0735764	+	0.127438i
$526$		0			0
$527$	−2.54926e7	+	1.44576e8i	−0.00758711	+	0.0430286i
$528$		0			0
$529$	−8.60555e9	+	3.13216e9i	−2.52746	+	0.919919i
$530$		0			0
$531$	−2.40496e9			−0.697071
$532$		0			0
$533$	−8.92652e8			−0.255351
$534$		0			0
$535$	3.16327e8	−	1.15133e8i	0.0893095	−	0.0325060i
$536$		0			0
$537$	2.54703e7	−	1.44449e8i	0.00709781	−	0.0402537i
$538$		0			0
$539$	−1.01802e9	−	1.76327e9i	−0.280025	−	0.485018i
$540$		0			0
$541$	4.16997e9	−	3.49902e9i	1.13225	−	0.950071i	0.133092	−	0.991104i	$-0.457509\pi$
$541$	4.16997e9	−	3.49902e9i	1.13225	−	0.950071i	0.999158	+	0.0410331i	$0.0130649\pi$
$542$		0			0
$543$	−5.97654e8	+	1.03517e9i	−0.160196	+	0.277467i
$544$		0			0
$545$	1.21381e8	+	4.41792e7i	0.0321192	+	0.0116904i
$546$		0			0
$547$	4.41448e8	+	2.50357e9i	0.115325	+	0.654041i	0.986589	+	0.163226i	$0.0521898\pi$
$547$	4.41448e8	+	2.50357e9i	0.115325	+	0.654041i	−0.871264	+	0.490815i	$0.836699\pi$
$548$		0			0
$549$	7.34438e8	+	6.16267e8i	0.189431	+	0.158952i
$550$		0			0
$551$	−1.52028e9	−	3.06422e9i	−0.387162	−	0.780350i
$552$		0			0
$553$	5.69001e8	+	4.77449e8i	0.143079	+	0.120057i
$554$		0			0
$555$	9.09160e7	+	5.15610e8i	0.0225743	+	0.128025i
$556$		0			0
$557$	4.67694e9	+	1.70227e9i	1.14675	+	0.417383i	0.844346	−	0.535798i	$-0.179989\pi$
$557$	4.67694e9	+	1.70227e9i	1.14675	+	0.417383i	0.302403	+	0.953180i	$0.402211\pi$
$558$		0			0
$559$	7.79240e8	−	1.34968e9i	0.188682	−	0.326806i
$560$		0			0
$561$	−3.85217e7	+	3.23236e7i	−0.00921162	+	0.00772946i
$562$		0			0
$563$	9.57030e8	+	1.65762e9i	0.226020	+	0.391478i	0.956625	−	0.291323i	$-0.0940953\pi$
$563$	9.57030e8	+	1.65762e9i	0.226020	+	0.391478i	−0.730605	+	0.682800i	$0.760762\pi$
$564$		0			0
$565$	1.67127e8	−	9.47824e8i	0.0389832	−	0.221084i
$566$		0			0
$567$	1.26229e8	−	4.59438e7i	0.0290817	−	0.0105849i
$568$		0			0
$569$	−6.80779e9			−1.54922			−0.774611	−	0.632438i	$-0.782054\pi$
$569$	−6.80779e9			−1.54922			−0.774611	+	0.632438i	$0.782054\pi$
$570$		0			0
$571$	−2.99970e9			−0.674297			−0.337148	−	0.941452i	$-0.609462\pi$
$571$	−2.99970e9			−0.674297			−0.337148	+	0.941452i	$0.609462\pi$
$572$		0			0
$573$	2.05651e9	−	7.48507e8i	0.456656	−	0.166209i
$574$		0			0
$575$	−1.49080e9	+	8.45476e9i	−0.327026	+	1.85466i
$576$		0			0
$577$	−3.13642e9	−	5.43244e9i	−0.679702	−	1.17728i	−0.975070	−	0.221896i	$-0.928776\pi$
$577$	−3.13642e9	−	5.43244e9i	−0.679702	−	1.17728i	0.295368	−	0.955384i	$-0.404558\pi$
$578$		0			0
$579$	−1.60134e8	+	1.34369e8i	−0.0342854	+	0.0287689i
$580$		0			0
$581$	−5.93615e8	+	1.02817e9i	−0.125571	+	0.217495i
$582$		0			0
$583$	5.34866e8	+	1.94675e8i	0.111790	+	0.0406884i
$584$		0			0
$585$	−3.34009e7	−	1.89426e8i	−0.00689782	−	0.0391195i
$586$		0			0
$587$	3.08415e9	+	2.58791e9i	0.629364	+	0.528099i	0.900731	−	0.434377i	$-0.143031\pi$
$587$	3.08415e9	+	2.58791e9i	0.629364	+	0.528099i	−0.271368	+	0.962476i	$0.587476\pi$
$588$		0			0
$589$	6.80475e9	−	2.00117e9i	1.37217	−	0.403535i
$590$		0			0
$591$	1.83199e9	+	1.53722e9i	0.365062	+	0.306323i
$592$		0			0
$593$	−1.19364e9	−	6.76947e9i	−0.235062	−	1.33310i	−0.842483	−	0.538723i	$-0.818907\pi$
$593$	−1.19364e9	−	6.76947e9i	−0.235062	−	1.33310i	0.607421	−	0.794380i	$-0.292204\pi$
$594$		0			0
$595$	−4.64031e6	−	1.68893e6i	−0.000903103	−	0.000328703i
$596$		0			0
$597$	2.86748e9	−	4.96661e9i	0.551556	−	0.955323i
$598$		0			0
$599$	−4.41659e9	+	3.70596e9i	−0.839641	+	0.704542i	−0.957483	−	0.288490i	$-0.906847\pi$
$599$	−4.41659e9	+	3.70596e9i	−0.839641	+	0.704542i	0.117842	+	0.993032i	$0.462402\pi$
$600$		0			0
$601$	−1.31603e9	−	2.27944e9i	−0.247290	−	0.428319i	0.715483	−	0.698630i	$-0.246207\pi$
$601$	−1.31603e9	−	2.27944e9i	−0.247290	−	0.428319i	−0.962773	+	0.270311i	$0.912873\pi$
$602$		0			0
$603$	4.05168e8	−	2.29782e9i	0.0752531	−	0.426781i
$604$		0			0
$605$	4.66805e8	−	1.69903e8i	0.0857022	−	0.0311930i
$606$		0			0
$607$	−1.88206e9			−0.341565			−0.170782	−	0.985309i	$-0.554630\pi$
$607$	−1.88206e9			−0.341565			−0.170782	+	0.985309i	$0.554630\pi$
$608$		0			0
$609$	7.28762e8			0.130745
$610$		0			0
$611$	−8.42324e8	+	3.06581e8i	−0.149395	+	0.0543752i
$612$		0			0
$613$	1.61879e7	−	9.18062e7i	0.00283844	−	0.0160976i	−0.983356	−	0.181691i	$-0.941843\pi$
$613$	1.61879e7	−	9.18062e7i	0.00283844	−	0.0160976i	0.986194	+	0.165594i	$0.0529540\pi$
$614$		0			0
$615$	1.34275e8	+	2.32571e8i	0.0232773	+	0.0403174i
$616$		0			0
$617$	−7.94881e9	+	6.66984e9i	−1.36240	+	1.14319i	−0.387165	+	0.922011i	$0.626546\pi$
$617$	−7.94881e9	+	6.66984e9i	−1.36240	+	1.14319i	−0.975234	+	0.221178i	$0.929010\pi$
$618$		0			0
$619$	9.45544e8	−	1.63773e9i	0.160238	−	0.277540i	−0.774716	−	0.632309i	$-0.782107\pi$
$619$	9.45544e8	−	1.63773e9i	0.160238	−	0.277540i	0.934954	+	0.354769i	$0.115441\pi$
$620$		0			0
$621$	1.11756e10	+	4.06759e9i	1.87263	+	0.681580i
$622$		0			0
$623$	3.23623e8	+	1.83536e9i	0.0536205	+	0.304097i
$624$		0			0
$625$	4.40292e9	+	3.69449e9i	0.721375	+	0.605305i
$626$		0			0
$627$	2.22618e9	+	9.73158e8i	0.360681	+	0.157669i
$628$		0			0
$629$	2.03422e8	+	1.70691e8i	0.0325927	+	0.0273485i
$630$		0			0
$631$	−4.58468e8	−	2.60010e9i	−0.0726450	−	0.411991i	−0.999345	−	0.0361884i	$-0.988478\pi$
$631$	−4.58468e8	−	2.60010e9i	−0.0726450	−	0.411991i	0.926700	−	0.375802i	$-0.122633\pi$
$632$		0			0
$633$	4.32121e9	+	1.57279e9i	0.677162	+	0.246467i
$634$		0			0
$635$	5.91607e8	−	1.02469e9i	0.0916907	−	0.158813i
$636$		0			0
$637$	−2.42905e9	+	2.03821e9i	−0.372347	+	0.312436i
$638$		0			0
$639$	8.79461e7	+	1.52327e8i	0.0133341	+	0.0230953i
$640$		0			0
$641$	1.11575e9	−	6.32772e9i	0.167326	−	0.948952i	−0.779308	−	0.626641i	$-0.784429\pi$
$641$	1.11575e9	−	6.32772e9i	0.167326	−	0.948952i	0.946634	−	0.322311i	$-0.104460\pi$
$642$		0			0
$643$	−1.16055e9	+	4.22404e8i	−0.172157	+	0.0626599i	−0.426661	−	0.904412i	$-0.640310\pi$
$643$	−1.16055e9	+	4.22404e8i	−0.172157	+	0.0626599i	0.254504	+	0.967072i	$0.418088\pi$
$644$		0			0
$645$	−4.68861e8			−0.0687994
$646$		0			0
$647$	7.65566e9			1.11126			0.555632	−	0.831428i	$-0.312476\pi$
$647$	7.65566e9			1.11126			0.555632	+	0.831428i	$0.312476\pi$
$648$		0			0
$649$	4.85098e9	−	1.76561e9i	0.696583	−	0.253536i
$650$		0			0
$651$	−2.62406e8	+	1.48818e9i	−0.0372770	+	0.211408i
$652$		0			0
$653$	−6.08052e9	−	1.05318e10i	−0.854564	−	1.48015i	−0.877048	−	0.480402i	$-0.840491\pi$
$653$	−6.08052e9	−	1.05318e10i	−0.854564	−	1.48015i	0.0224840	−	0.999747i	$-0.492843\pi$
$654$		0			0
$655$	6.74968e8	−	5.66365e8i	0.0938509	−	0.0787503i
$656$		0			0
$657$	−1.09879e9	+	1.90315e9i	−0.151159	+	0.261816i
$658$		0			0
$659$	6.76475e9	+	2.46217e9i	0.920774	+	0.335134i	0.758546	−	0.651619i	$-0.225910\pi$
$659$	6.76475e9	+	2.46217e9i	0.920774	+	0.335134i	0.162227	+	0.986753i	$0.448132\pi$
$660$		0			0
$661$	1.97776e9	+	1.12164e10i	0.266360	+	1.51060i	0.765135	+	0.643870i	$0.222672\pi$
$661$	1.97776e9	+	1.12164e10i	0.266360	+	1.51060i	−0.498775	+	0.866732i	$0.666217\pi$
$662$		0			0
$663$	5.99928e7	+	5.03400e7i	0.00799470	+	0.00670835i
$664$		0			0
$665$	2.65443e7	+	2.37103e8i	0.00350022	+	0.0312652i
$666$		0			0
$667$	9.82343e9	+	8.24284e9i	1.28181	+	1.07556i
$668$		0			0
$669$	−6.99177e8	−	3.96523e9i	−0.0902809	−	0.512008i
$670$		0			0
$671$	−1.93385e9	−	7.03865e8i	−0.247112	−	0.0899415i
$672$		0			0
$673$	8.61495e8	−	1.49215e9i	0.108943	−	0.188695i	−0.806399	−	0.591372i	$-0.798587\pi$
$673$	8.61495e8	−	1.49215e9i	0.108943	−	0.188695i	0.915342	+	0.402676i	$0.131920\pi$
$674$		0			0
$675$	6.22598e9	−	5.22422e9i	0.779192	−	0.653820i
$676$		0			0
$677$	7.47294e9	+	1.29435e10i	0.925616	+	1.60321i	0.790567	+	0.612376i	$0.209786\pi$
$677$	7.47294e9	+	1.29435e10i	0.925616	+	1.60321i	0.135049	+	0.990839i	$0.456881\pi$
$678$		0			0
$679$	−2.37311e8	+	1.34586e9i	−0.0290920	+	0.164989i
$680$		0			0
$681$	−8.27004e9	+	3.01005e9i	−1.00344	+	0.365224i
$682$		0			0
$683$	−6.19237e9			−0.743678			−0.371839	−	0.928297i	$-0.621273\pi$
$683$	−6.19237e9			−0.743678			−0.371839	+	0.928297i	$0.621273\pi$
$684$		0			0
$685$	−7.00792e8			−0.0833052
$686$		0			0
$687$	6.70084e9	−	2.43891e9i	0.788462	−	0.286977i
$688$		0			0
$689$	1.53930e8	−	8.72980e8i	0.0179290	−	0.101680i
$690$		0			0
$691$	−2.92216e9	−	5.06134e9i	−0.336924	−	0.583569i	0.646929	−	0.762550i	$-0.276053\pi$
$691$	−2.92216e9	−	5.06134e9i	−0.336924	−	0.583569i	−0.983852	+	0.178982i	$0.942720\pi$
$692$		0			0
$693$	4.93948e8	−	4.14472e8i	0.0563787	−	0.0473073i
$694$		0			0
$695$	7.23355e8	−	1.25289e9i	0.0817344	−	0.141568i
$696$		0			0
$697$	1.27992e8	+	4.65854e7i	0.0143176	+	0.00521116i
$698$		0			0
$699$	1.11994e8	+	6.35150e8i	0.0124030	+	0.0703406i
$700$		0			0
$701$	−8.36475e8	−	7.01886e8i	−0.0917149	−	0.0769579i	0.595777	−	0.803150i	$-0.296844\pi$
$701$	−8.36475e8	−	7.01886e8i	−0.0917149	−	0.0769579i	−0.687492	+	0.726192i	$0.741288\pi$
$702$		0			0
$703$	3.01951e9	−	1.24695e10i	0.327788	−	1.35365i
$704$		0			0
$705$	2.06581e8	+	1.73342e8i	0.0222038	+	0.0186312i
$706$		0			0
$707$	−3.78331e7	−	2.14562e8i	−0.00402628	−	0.0228342i
$708$		0			0
$709$	1.17726e10	+	4.28488e9i	1.24054	+	0.451520i	0.877195	−	0.480134i	$-0.159412\pi$
$709$	1.17726e10	+	4.28488e9i	1.24054	+	0.451520i	0.363347	+	0.931654i	$0.381634\pi$
$710$		0			0
$711$	2.20735e9	−	3.82324e9i	0.230318	−	0.398922i
$712$		0			0
$713$	−2.03696e10	+	1.70921e10i	−2.10459	+	1.76596i
$714$		0			0
$715$	2.06440e8	+	3.57564e8i	0.0211214	+	0.0365833i
$716$		0			0
$717$	−1.27805e9	+	7.24818e9i	−0.129488	+	0.734365i
$718$		0			0
$719$	−1.34670e10	+	4.90159e9i	−1.35120	+	0.491797i	−0.913323	−	0.407237i	$-0.866492\pi$
$719$	−1.34670e10	+	4.90159e9i	−1.35120	+	0.491797i	−0.437879	+	0.899034i	$0.644270\pi$
$720$		0			0
$721$	−1.51006e9			−0.150045
$722$		0			0
$723$	−5.66818e9			−0.557776
$724$		0			0
$725$	8.23499e9	−	2.99729e9i	0.802565	−	0.292110i
$726$		0			0
$727$	1.00018e9	−	5.67232e9i	0.0965405	−	0.547508i	−0.897724	−	0.440558i	$-0.854780\pi$
$727$	1.00018e9	−	5.67232e9i	0.0965405	−	0.547508i	0.994264	−	0.106950i	$-0.0341084\pi$
$728$		0			0
$729$	−4.02006e9	−	6.96295e9i	−0.384314	−	0.665651i
$730$		0			0
$731$	−1.82167e8	+	1.52857e8i	−0.0172488	+	0.0144735i
$732$		0			0
$733$	5.69698e9	−	9.86746e9i	0.534295	−	0.925426i	−0.464902	−	0.885362i	$-0.653911\pi$
$733$	5.69698e9	−	9.86746e9i	0.534295	−	0.925426i	0.999197	−	0.0400638i	$-0.0127561\pi$
$734$		0			0
$735$	8.96417e8	+	3.26269e8i	0.0832731	+	0.0303089i
$736$		0			0
$737$	8.69703e8	+	4.93233e9i	0.0800267	+	0.453854i
$738$		0			0
$739$	−1.09555e10	−	9.19279e9i	−0.998569	−	0.837899i	−0.0117837	−	0.999931i	$-0.503751\pi$
$739$	−1.09555e10	−	9.19279e9i	−0.998569	−	0.837899i	−0.986786	+	0.162031i	$0.948195\pi$
$740$		0			0
$741$	8.90510e8	−	3.67750e9i	0.0804036	−	0.332039i
$742$		0			0
$743$	−1.34003e10	−	1.12442e10i	−1.19855	−	1.00570i	−0.999670	−	0.0256751i	$-0.991826\pi$
$743$	−1.34003e10	−	1.12442e10i	−1.19855	−	1.00570i	−0.198876	−	0.980025i	$-0.563729\pi$
$744$		0			0
$745$	−4.67185e8	−	2.64954e9i	−0.0413944	−	0.234759i
$746$		0			0
$747$	6.63075e9	+	2.41340e9i	0.582023	+	0.211839i
$748$		0			0
$749$	8.78726e8	−	1.52200e9i	0.0764130	−	0.132351i
$750$		0			0
$751$	−4.71242e9	+	3.95419e9i	−0.405979	+	0.340657i	−0.822799	−	0.568332i	$-0.807589\pi$
$751$	−4.71242e9	+	3.95419e9i	−0.405979	+	0.340657i	0.416820	+	0.908989i	$0.363145\pi$
$752$		0			0
$753$	−9.90177e8	−	1.71504e9i	−0.0845144	−	0.146383i
$754$		0			0
$755$	−2.43633e8	+	1.38171e9i	−0.0206026	+	0.116843i
$756$		0			0
$757$	−9.79233e9	+	3.56412e9i	−0.820447	+	0.298618i	−0.717932	−	0.696113i	$-0.754911\pi$
$757$	−9.79233e9	+	3.56412e9i	−0.820447	+	0.298618i	−0.102515	+	0.994731i	$0.532689\pi$
$758$		0			0
$759$	−9.10828e9			−0.756119
$760$		0			0
$761$	−2.19565e10			−1.80599			−0.902997	−	0.429646i	$-0.858638\pi$
$761$	−2.19565e10			−1.80599			−0.902997	+	0.429646i	$0.858638\pi$
$762$		0			0
$763$	6.33703e8	−	2.30649e8i	0.0516476	−	0.0187982i
$764$		0			0
$765$	−5.09651e6	+	2.89038e7i	−0.000411584	+	0.00233421i
$766$		0			0
$767$	−4.01983e9	−	6.96254e9i	−0.321680	−	0.557165i
$768$		0			0
$769$	−8.73320e9	+	7.32802e9i	−0.692518	+	0.581092i	−0.919634	−	0.392776i	$-0.871515\pi$
$769$	−8.73320e9	+	7.32802e9i	−0.692518	+	0.581092i	0.227116	+	0.973868i	$0.427070\pi$
$770$		0			0
$771$	1.87855e9	−	3.25374e9i	0.147615	−	0.255677i
$772$		0			0
$773$	3.10303e9	+	1.12941e9i	0.241633	+	0.0879474i	0.459998	−	0.887920i	$-0.347850\pi$
$773$	3.10303e9	+	1.12941e9i	0.241633	+	0.0879474i	−0.218365	+	0.975867i	$0.570072\pi$
$774$		0			0
$775$	3.15548e9	+	1.78956e10i	0.243506	+	1.38099i
$776$		0			0
$777$	2.09391e9	+	1.75700e9i	0.160134	+	0.134369i
$778$		0			0
$779$	−7.32163e8	−	6.53995e9i	−0.0554915	−	0.495671i
$780$		0			0
$781$	−2.89226e8	−	2.42689e8i	−0.0217249	−	0.0182294i
$782$		0			0
$783$	−2.10806e9	−	1.19554e10i	−0.156934	−	0.890018i
$784$		0			0
$785$	−1.79401e9	−	6.52965e8i	−0.132367	−	0.0481777i
$786$		0			0
$787$	1.30255e10	−	2.25608e10i	0.952540	−	1.64985i	0.212639	−	0.977131i	$-0.431794\pi$
$787$	1.30255e10	−	2.25608e10i	0.952540	−	1.64985i	0.739901	−	0.672716i	$-0.234873\pi$
$788$		0			0
$789$	−9.80666e9	+	8.22876e9i	−0.710807	+	0.596437i
$790$		0			0
$791$	−2.51235e9	−	4.35152e9i	−0.180494	−	0.312624i
$792$		0			0
$793$	−5.56546e8	+	3.15633e9i	−0.0396319	+	0.224764i
$794$		0			0
$795$	−2.50600e8	+	9.12110e7i	−0.0176887	+	0.00643817i
$796$		0			0
$797$	−4.32943e9			−0.302919			−0.151460	−	0.988463i	$-0.548397\pi$
$797$	−4.32943e9			−0.302919			−0.151460	+	0.988463i	$0.548397\pi$
$798$		0			0
$799$	1.36776e8			0.00948626
$800$		0			0
$801$	1.04087e10	−	3.78846e9i	0.715621	−	0.260465i
$802$		0			0
$803$	8.19125e8	−	4.64549e9i	0.0558272	−	0.316612i
$804$		0			0
$805$	−4.47214e8	−	7.74597e8i	−0.0302155	−	0.0523348i
$806$		0			0
$807$	−9.72627e9	+	8.16131e9i	−0.651462	+	0.546641i
$808$		0			0
$809$	−7.52645e9	+	1.30362e10i	−0.499770	+	0.865628i	−1.00000		0.000264987i	$-0.999916\pi$
$809$	−7.52645e9	+	1.30362e10i	−0.499770	+	0.865628i	0.500229	+	0.865893i	$0.333249\pi$
$810$		0			0
$811$	1.92455e10	+	7.00479e9i	1.26694	+	0.461129i	0.886092	−	0.463509i	$-0.153410\pi$
$811$	1.92455e10	+	7.00479e9i	1.26694	+	0.461129i	0.380848	+	0.924638i	$0.375632\pi$
$812$		0			0
$813$	1.06807e9	+	6.05734e9i	0.0697082	+	0.395335i
$814$		0			0
$815$	1.41472e9	+	1.18709e9i	0.0915417	+	0.0768126i
$816$		0			0
$817$	1.05275e10	+	4.60202e9i	0.675379	+	0.295237i
$818$		0			0
$819$	−7.69263e8	−	6.45488e8i	−0.0489307	−	0.0410577i
$820$		0			0
$821$	−8.96521e8	−	5.08442e9i	−0.0565404	−	0.320657i	0.943399	−	0.331660i	$-0.107609\pi$
$821$	−8.96521e8	−	5.08442e9i	−0.0565404	−	0.320657i	−0.999939	+	0.0110031i	$0.996498\pi$
$822$		0			0
$823$	8.89095e9	+	3.23604e9i	0.555967	+	0.202355i	0.604696	−	0.796457i	$-0.293295\pi$
$823$	8.89095e9	+	3.23604e9i	0.555967	+	0.202355i	−0.0487287	+	0.998812i	$0.515517\pi$
$824$		0			0
$825$	−3.11225e9	+	5.39057e9i	−0.192968	+	0.334230i
$826$		0			0
$827$	−1.13133e10	+	9.49301e9i	−0.695539	+	0.583626i	−0.920501	−	0.390741i	$-0.872219\pi$
$827$	−1.13133e10	+	9.49301e9i	−0.695539	+	0.583626i	0.224962	+	0.974368i	$0.427774\pi$
$828$		0			0
$829$	−1.61548e9	−	2.79810e9i	−0.0984832	−	0.170578i	0.812574	−	0.582858i	$-0.198066\pi$
$829$	−1.61548e9	−	2.79810e9i	−0.0984832	−	0.170578i	−0.911057	+	0.412280i	$0.864732\pi$
$830$		0			0
$831$	3.47644e9	−	1.97159e10i	0.210151	−	1.19183i
$832$		0			0
$833$	4.54656e8	−	1.65481e8i	0.0272537	−	0.00991954i
$834$		0			0
$835$	3.24708e9			0.193015
$836$		0			0
$837$	2.51728e10			1.48386
$838$		0			0
$839$	−1.02254e9	+	3.72175e8i	−0.0597742	+	0.0217560i	−0.371734	−	0.928339i	$-0.621237\pi$
$839$	−1.02254e9	+	3.72175e8i	−0.0597742	+	0.0217560i	0.311960	+	0.950095i	$0.399015\pi$
$840$		0			0
$841$	−7.22369e8	+	4.09676e9i	−0.0418768	+	0.237495i
$842$		0			0
$843$	−1.04910e10	−	1.81710e10i	−0.603145	−	1.04468i
$844$		0			0
$845$	−1.38671e9	+	1.16359e9i	−0.0790657	+	0.0663440i
$846$		0			0
$847$	1.29674e9	−	2.24602e9i	0.0733266	−	0.127005i
$848$		0			0
$849$	−3.87857e9	−	1.41168e9i	−0.217518	−	0.0791700i
$850$		0			0
$851$	8.35214e9	+	4.73673e10i	0.464563	+	2.63467i
$852$		0			0
$853$	5.94741e9	+	4.99047e9i	0.328100	+	0.275309i	0.791925	−	0.610618i	$-0.209079\pi$
$853$	5.94741e9	+	4.99047e9i	0.328100	+	0.275309i	−0.463825	+	0.885927i	$0.653523\pi$
$854$		0			0
$855$	1.36042e9	−	4.00078e8i	0.0744373	−	0.0218909i
$856$		0			0
$857$	1.24459e10	+	1.04433e10i	0.675448	+	0.566768i	0.914672	−	0.404196i	$-0.132449\pi$
$857$	1.24459e10	+	1.04433e10i	0.675448	+	0.566768i	−0.239224	+	0.970964i	$0.576893\pi$
$858$		0			0
$859$	−6.25946e9	−	3.54992e10i	−0.336946	−	1.91092i	−0.407104	−	0.913382i	$-0.633461\pi$
$859$	−6.25946e9	−	3.54992e10i	−0.336946	−	1.91092i	0.0701573	−	0.997536i	$-0.477650\pi$
$860$		0			0
$861$	1.31748e9	+	4.79524e8i	0.0703450	+	0.0256035i
$862$		0			0
$863$	2.78286e9	−	4.82005e9i	0.147385	−	0.255278i	−0.782875	−	0.622179i	$-0.786248\pi$
$863$	2.78286e9	−	4.82005e9i	0.147385	−	0.255278i	0.930260	+	0.366901i	$0.119581\pi$
$864$		0			0
$865$	−5.96691e8	+	5.00683e8i	−0.0313468	+	0.0263031i
$866$		0			0
$867$	6.39669e9	+	1.10794e10i	0.333341	+	0.577363i
$868$		0			0
$869$	−1.64554e9	+	9.33230e9i	−0.0850625	+	0.482414i
$870$		0			0
$871$	7.32960e9	−	2.66776e9i	0.375852	−	0.136799i
$872$		0			0
$873$	8.12249e9			0.413180
$874$		0			0
$875$	−1.23468e9			−0.0623056
$876$		0			0
$877$	2.03303e10	−	7.39962e9i	1.01776	−	0.370434i	0.221351	−	0.975194i	$-0.428953\pi$
$877$	2.03303e10	−	7.39962e9i	1.01776	−	0.370434i	0.796407	+	0.604760i	$0.206731\pi$
$878$		0			0
$879$	−1.13326e9	+	6.42702e9i	−0.0562818	+	0.319190i
$880$		0			0
$881$	−1.64963e10	−	2.85724e10i	−0.812774	−	1.40777i	−0.910915	−	0.412594i	$-0.864623\pi$
$881$	−1.64963e10	−	2.85724e10i	−0.812774	−	1.40777i	0.0981408	−	0.995173i	$-0.468710\pi$
$882$		0			0
$883$	−9.92651e9	+	8.32933e9i	−0.485215	+	0.407144i	−0.852308	−	0.523041i	$-0.824798\pi$
$883$	−9.92651e9	+	8.32933e9i	−0.485215	+	0.407144i	0.367093	+	0.930184i	$0.380353\pi$
$884$		0			0
$885$	−1.20934e9	+	2.09465e9i	−0.0586474	+	0.101580i
$886$		0			0
$887$	2.88490e10	+	1.05002e10i	1.38803	+	0.505200i	0.924601	−	0.380936i	$-0.124398\pi$
$887$	2.88490e10	+	1.05002e10i	1.38803	+	0.505200i	0.463424	+	0.886136i	$0.346621\pi$
$888$		0			0
$889$	−1.07267e9	−	6.08343e9i	−0.0512048	−	0.290397i
$890$		0			0
$891$	1.31283e9	+	1.10159e9i	0.0621778	+	0.0521733i
$892$		0			0
$893$	−2.93702e9	−	5.91976e9i	−0.138015	−	0.278179i
$894$		0			0
$895$	1.40768e8	+	1.18119e8i	0.00656333	+	0.00550729i
$896$		0			0
$897$	2.46320e9	+	1.39695e10i	0.113953	+	0.646261i
$898$		0			0
$899$	2.55059e10	+	9.28340e9i	1.17080	+	0.426136i
$900$		0			0
$901$	−6.76298e7	+	1.17138e8i	−0.00308036	+	0.00533534i
$902$		0			0
$903$	−1.87513e9	+	1.57342e9i	−0.0847470	+	0.0711112i
$904$		0			0
$905$	−7.48751e8	−	1.29687e9i	−0.0335790	−	0.0581605i
$906$		0			0
$907$	−1.66054e9	+	9.41737e9i	−0.0738963	+	0.419087i	0.925309	+	0.379215i	$0.123806\pi$
$907$	−1.66054e9	+	9.41737e9i	−0.0738963	+	0.419087i	−0.999205	+	0.0398716i	$0.987305\pi$
$908$		0			0
$909$	−1.21683e9	+	4.42890e8i	−0.0537349	+	0.0195579i
$910$		0			0
$911$	−5.27753e9			−0.231269			−0.115634	−	0.993292i	$-0.536890\pi$
$911$	−5.27753e9			−0.231269			−0.115634	+	0.993292i	$0.536890\pi$
$912$		0			0
$913$	−1.51465e10			−0.658666
$914$		0			0
$915$	9.06066e8	−	3.29781e8i	0.0391008	−	0.0142315i
$916$		0			0
$917$	7.98791e8	−	4.53017e9i	0.0342090	−	0.194009i
$918$		0			0
$919$	−1.05883e10	−	1.83395e10i	−0.450011	−	0.779442i	0.548375	−	0.836232i	$-0.315247\pi$
$919$	−1.05883e10	−	1.83395e10i	−0.450011	−	0.779442i	−0.998386	+	0.0567908i	$0.981913\pi$
$920$		0			0
$921$	9.41040e9	−	7.89626e9i	0.396917	−	0.333053i
$922$		0			0
$923$	−2.93999e8	+	5.09222e8i	−0.0123067	+	0.0213158i
$924$		0			0
$925$	3.08874e10	+	1.12421e10i	1.28317	+	0.467037i
$926$		0			0
$927$	1.55850e9	+	8.83868e9i	0.0642580	+	0.364425i
$928$		0			0
$929$	−2.09266e10	−	1.75595e10i	−0.856335	−	0.718550i	0.104841	−	0.994489i	$-0.466567\pi$
$929$	−2.09266e10	−	1.75595e10i	−0.856335	−	0.718550i	−0.961175	+	0.275939i	$0.911011\pi$
$930$		0			0
$931$	−1.69251e10	−	1.61245e10i	−0.687398	−	0.654879i
$932$		0			0
$933$	6.68111e9	+	5.60612e9i	0.269316	+	0.225983i
$934$		0			0
$935$	−1.09398e7	−	6.20427e7i	−0.000437692	−	0.00248228i
$936$		0			0
$937$	4.54995e10	+	1.65605e10i	1.80683	+	0.657634i	0.997530	+	0.0702429i	$0.0223774\pi$
$937$	4.54995e10	+	1.65605e10i	1.80683	+	0.657634i	0.809304	+	0.587391i	$0.199845\pi$
$938$		0			0
$939$	1.45352e10	−	2.51757e10i	0.572916	−	0.992320i
$940$		0			0
$941$	9.63933e9	−	8.08836e9i	0.377123	−	0.316444i	−0.434449	−	0.900697i	$-0.643057\pi$
$941$	9.63933e9	−	8.08836e9i	0.377123	−	0.316444i	0.811572	+	0.584253i	$0.198612\pi$
$942$		0			0
$943$	1.23354e10	+	2.13655e10i	0.479028	+	0.829702i
$944$		0			0
$945$	−1.47035e8	+	8.33875e8i	−0.00566772	+	0.0321432i
$946$		0			0
$947$	−1.98936e10	+	7.24067e9i	−0.761181	+	0.277047i	−0.693303	−	0.720646i	$-0.743845\pi$
$947$	−1.98936e10	+	7.24067e9i	−0.761181	+	0.277047i	−0.0678782	+	0.997694i	$0.521623\pi$
$948$		0			0
$949$	−7.34638e9			−0.279024
$950$		0			0
$951$	−2.16886e10			−0.817712
$952$		0			0
$953$	2.09354e9	−	7.61986e8i	0.0783530	−	0.0285182i	−0.302546	−	0.953135i	$-0.597837\pi$
$953$	2.09354e9	−	7.61986e8i	0.0783530	−	0.0285182i	0.380899	+	0.924617i	$0.375614\pi$
$954$		0			0
$955$	−4.76104e8	+	2.70012e9i	−0.0176885	+	0.100316i
$956$		0			0
$957$	4.64873e9	+	8.05183e9i	0.171452	+	0.296963i
$958$		0			0
$959$	−2.80270e9	+	2.35174e9i	−0.102615	+	0.0861043i
$960$		0			0
$961$	−1.43850e10	+	2.49155e10i	−0.522850	+	0.905603i
$962$		0			0
$963$	−9.81548e9	−	3.57254e9i	−0.354176	−	0.128910i
$964$		0			0
$965$	−4.54766e7	−	2.57911e8i	−0.00162908	−	0.00923898i
$966$		0			0
$967$	1.70109e10	+	1.42739e10i	0.604972	+	0.507632i	0.893039	−	0.449978i	$-0.148568\pi$
$967$	1.70109e10	+	1.42739e10i	0.604972	+	0.507632i	−0.288068	+	0.957610i	$0.593013\pi$
$968$		0			0
$969$	−3.19605e8	+	4.80822e8i	−0.0112845	+	0.0169766i
$970$		0			0
$971$	1.36616e9	+	1.14634e9i	0.0478888	+	0.0401835i	0.666418	−	0.745578i	$-0.267827\pi$
$971$	1.36616e9	+	1.14634e9i	0.0478888	+	0.0401835i	−0.618529	+	0.785762i	$0.712271\pi$
$972$		0			0
$973$	−1.31155e9	−	7.43818e9i	−0.0456447	−	0.258864i
$974$		0			0
$975$	9.10927e9	+	3.31550e9i	0.314751	+	0.114560i
$976$		0			0
$977$	1.62123e10	−	2.80805e10i	0.556176	−	0.963326i	−0.441635	−	0.897195i	$-0.645601\pi$
$977$	1.62123e10	−	2.80805e10i	0.556176	−	0.963326i	0.997811	−	0.0661307i	$-0.0210654\pi$
$978$		0			0
$979$	−1.82138e10	+	1.52832e10i	−0.620386	+	0.520565i
$980$		0			0
$981$	−2.00407e9	−	3.47114e9i	−0.0677751	−	0.117390i
$982$		0			0
$983$	−1.34373e9	+	7.62065e9i	−0.0451204	+	0.255891i	−0.999021	−	0.0442311i	$-0.985916\pi$
$983$	−1.34373e9	+	7.62065e9i	−0.0451204	+	0.255891i	0.953901	+	0.300122i	$0.0970273\pi$
$984$		0			0
$985$	−2.81541e9	+	1.02473e9i	−0.0938674	+	0.0341649i
$986$		0			0
$987$	1.40789e9			0.0466079
$988$		0			0
$989$	−4.30726e10			−1.41584
$990$		0			0
$991$	1.05104e10	−	3.82546e9i	0.343052	−	0.124861i	−0.164748	−	0.986336i	$-0.552681\pi$
$991$	1.05104e10	−	3.82546e9i	0.343052	−	0.124861i	0.507800	+	0.861475i	$0.330459\pi$
$992$		0			0
$993$	−2.61048e9	+	1.48047e10i	−0.0846052	+	0.479820i
$994$		0			0
$995$	3.59242e9	+	6.22225e9i	0.115613	+	0.200247i
$996$		0			0
$997$	−2.66832e10	+	2.23898e10i	−0.852716	+	0.715514i	−0.960386	−	0.278673i	$-0.910105\pi$
$997$	−2.66832e10	+	2.23898e10i	−0.852716	+	0.715514i	0.107670	+	0.994187i	$0.465661\pi$
$998$		0			0
$999$	2.27668e10	−	3.94332e10i	0.722474	−	1.25136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.i.a.73.5	yes	72
19.6	even	9	inner	76.8.i.a.25.5	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.i.a.25.5	✓	72	19.6	even	9	inner
76.8.i.a.73.5	yes	72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-29.3247 + 10.6733i) q^{3} +(6.78900 - 38.5023i) q^{5} +(-102.056 - 176.766i) q^{7} +(-929.319 + 779.792i) q^{9} +O(q^{10})\)	\(q+(-29.3247 + 10.6733i) q^{3} +(6.78900 - 38.5023i) q^{5} +(-102.056 - 176.766i) q^{7} +(-929.319 + 779.792i) q^{9} +(1302.02 - 2255.16i) q^{11} +(-3810.89 - 1387.05i) q^{13} +(211.862 + 1201.53i) q^{15} +(474.035 + 397.763i) q^{17} +(7036.39 - 29057.9i) q^{19} +(4879.45 + 4094.35i) q^{21} +(19463.1 + 110380. i) q^{23} +(71977.1 + 26197.5i) q^{25} +(53053.6 - 91891.6i) q^{27} +(87644.1 - 73542.1i) q^{29} +(118620. + 205455. i) q^{31} +(-14111.3 + 80028.9i) q^{33} +(-7498.77 + 2729.33i) q^{35} +429128. q^{37} +126558. q^{39} +(206837. - 75282.3i) q^{41} +(-66731.4 + 378453. i) q^{43} +(23714.6 + 41075.0i) q^{45} +(169319. - 142076. i) q^{47} +(390941. - 677129. i) q^{49} +(-18146.4 - 6604.75i) q^{51} +(37956.1 + 215260. i) q^{53} +(-77989.6 - 65441.0i) q^{55} +(103804. + 927216. i) q^{57} +(1.51862e6 + 1.27428e6i) q^{59} +(-137234. - 778290. i) q^{61} +(232684. + 84689.9i) q^{63} +(-79276.8 + 137312. i) q^{65} +(-1.47336e6 + 1.23629e6i) q^{67} +(-1.74888e6 - 3.02914e6i) q^{69} +(25177.1 - 142786. i) q^{71} +(1.70223e6 - 619561. i) q^{73} -2.39033e6 q^{75} -531516. q^{77} +(-3.41960e6 + 1.24463e6i) q^{79} +(-114282. + 648123. i) q^{81} +(-2.90828e6 - 5.03728e6i) q^{83} +(18533.0 - 15551.0i) q^{85} +(-1.78520e6 + 3.09206e6i) q^{87} +(-8.57997e6 - 3.12285e6i) q^{89} +(143741. + 815195. i) q^{91} +(-5.67138e6 - 4.75886e6i) q^{93} +(-1.07103e6 - 468191. i) q^{95} +(-5.12899e6 - 4.30374e6i) q^{97} +(548566. + 3.11107e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9}+O(q^{10}) \) 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9	\( 72 q - 39 q^{3} + 591 q^{7} - 1677 q^{9} - 5793 q^{11} + 22083 q^{13} - 70707 q^{15} + 29409 q^{17} + 12756 q^{19} - 40419 q^{21} - 116796 q^{23} + 26934 q^{25} + 439347 q^{27} - 148005 q^{29} + 141366 q^{31} + 1206654 q^{33} - 531651 q^{35} - 1508004 q^{37} - 2140644 q^{39} + 494157 q^{41} + 923511 q^{43} + 1790028 q^{45} - 662955 q^{47} - 4191369 q^{49} + 3753363 q^{51} - 246513 q^{53} + 2650185 q^{55} + 5831286 q^{57} - 2244432 q^{59} - 10302306 q^{61} - 12102117 q^{63} + 3985635 q^{65} + 11688288 q^{67} + 12632535 q^{69} + 10541736 q^{71} + 560730 q^{73} - 17718750 q^{75} - 22266192 q^{77} + 9424767 q^{79} + 16585437 q^{81} + 2359839 q^{83} - 20859762 q^{85} + 2348574 q^{87} - 4397130 q^{89} - 12653112 q^{91} + 52259766 q^{93} + 46248669 q^{95} - 34112766 q^{97} - 93757926 q^{99}+O(q^{100}) \) 72 * q - 39 * q^3 + 591 * q^7 - 1677 * q^9 - 5793 * q^11 + 22083 * q^13 - 70707 * q^15 + 29409 * q^17 + 12756 * q^19 - 40419 * q^21 - 116796 * q^23 + 26934 * q^25 + 439347 * q^27 - 148005 * q^29 + 141366 * q^31 + 1206654 * q^33 - 531651 * q^35 - 1508004 * q^37 - 2140644 * q^39 + 494157 * q^41 + 923511 * q^43 + 1790028 * q^45 - 662955 * q^47 - 4191369 * q^49 + 3753363 * q^51 - 246513 * q^53 + 2650185 * q^55 + 5831286 * q^57 - 2244432 * q^59 - 10302306 * q^61 - 12102117 * q^63 + 3985635 * q^65 + 11688288 * q^67 + 12632535 * q^69 + 10541736 * q^71 + 560730 * q^73 - 17718750 * q^75 - 22266192 * q^77 + 9424767 * q^79 + 16585437 * q^81 + 2359839 * q^83 - 20859762 * q^85 + 2348574 * q^87 - 4397130 * q^89 - 12653112 * q^91 + 52259766 * q^93 + 46248669 * q^95 - 34112766 * q^97 - 93757926 * q^99

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