LMFDB - Embedded newform 234.8.h.c.55.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,8,Mod(55,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.55"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	234.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-32,0,-256,386] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$73.0980959633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3 x^{7} - 14114 x^{6} + 42351 x^{5} + 205543918 x^{4} + 13390412127 x^{3} + \cdots + 28150431267204 $ x^8 - 3x^7 - 14114x^6 + 42351x^5 + 205543918x^4 + 13390412127x^3 + 374804224653x^2 + 5032619029638*x + 28150431267204
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.2
Root			$-14.5673 + 8.41041i$ of defining polynomial
Character	$\chi$	$=$	234.55
Dual form			234.8.h.c.217.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} -76.2027 q^{5} +(237.214 - 410.867i) q^{7} +512.000 q^{8} +(304.811 + 527.947i) q^{10} +(469.485 + 813.173i) q^{11} +(-6440.26 + 4612.11i) q^{13} -3795.43 q^{14} +(-2048.00 - 3547.24i) q^{16} +(7532.39 - 13046.5i) q^{17} +(13871.3 - 24025.9i) q^{19} +(2438.48 - 4223.58i) q^{20} +(3755.88 - 6505.38i) q^{22} +(47390.7 + 82083.1i) q^{23} -72318.2 q^{25} +(57714.7 + 26171.0i) q^{26} +(15181.7 + 26295.5i) q^{28} +(25004.6 + 43309.3i) q^{29} -253650. q^{31} +(-16384.0 + 28377.9i) q^{32} -120518. q^{34} +(-18076.4 + 31309.2i) q^{35} +(-30321.3 - 52518.1i) q^{37} -221942. q^{38} -39015.8 q^{40} +(312111. + 540592. i) q^{41} +(287232. - 497500. i) q^{43} -60094.1 q^{44} +(379125. - 656664. i) q^{46} +467295. q^{47} +(299230. + 518282. i) q^{49} +(289273. + 501035. i) q^{50} +(-49540.5 - 504543. i) q^{52} +158317. q^{53} +(-35776.0 - 61965.9i) q^{55} +(121454. - 210364. i) q^{56} +(200037. - 346474. i) q^{58} +(128030. - 221754. i) q^{59} +(-190165. + 329375. i) q^{61} +(1.01460e6 + 1.75734e6i) q^{62} +262144. q^{64} +(490765. - 351455. i) q^{65} +(230735. + 399645. i) q^{67} +(482073. + 834975. i) q^{68} +289222. q^{70} +(2.55854e6 - 4.43152e6i) q^{71} -869122. q^{73} +(-242571. + 420145. i) q^{74} +(887766. + 1.53766e6i) q^{76} +445475. q^{77} +3.99615e6 q^{79} +(156063. + 270309. i) q^{80} +(2.49689e6 - 4.32474e6i) q^{82} +1.08553e6 q^{83} +(-573988. + 994177. i) q^{85} -4.59571e6 q^{86} +(240377. + 416344. i) q^{88} +(-4.21989e6 - 7.30906e6i) q^{89} +(367241. + 3.74015e6i) q^{91} -6.06601e6 q^{92} +(-1.86918e6 - 3.23752e6i) q^{94} +(-1.05703e6 + 1.83084e6i) q^{95} +(3.93058e6 - 6.80796e6i) q^{97} +(2.39384e6 - 4.14625e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} - 256 q^{4} + 386 q^{5} + 757 q^{7} + 4096 q^{8} - 1544 q^{10} - 4524 q^{11} + 13272 q^{13} - 12112 q^{14} - 16384 q^{16} + 12775 q^{17} + 38646 q^{19} - 12352 q^{20} - 36192 q^{22} - 24428 q^{23}+ \cdots + 4224696 q^{98}+O(q^{100}) $ 8 * q - 32 * q^2 - 256 * q^4 + 386 * q^5 + 757 * q^7 + 4096 * q^8 - 1544 * q^10 - 4524 * q^11 + 13272 * q^13 - 12112 * q^14 - 16384 * q^16 + 12775 * q^17 + 38646 * q^19 - 12352 * q^20 - 36192 * q^22 - 24428 * q^23 + 305798 * q^25 - 90552 * q^26 + 48448 * q^28 - 22109 * q^29 + 42558 * q^31 - 131072 * q^32 - 204400 * q^34 + 190892 * q^35 + 372411 * q^37 - 618336 * q^38 + 197632 * q^40 - 266009 * q^41 - 399935 * q^43 + 579072 * q^44 - 195424 * q^46 + 487344 * q^47 + 528087 * q^49 - 1223192 * q^50 - 124992 * q^52 - 3351434 * q^53 - 1572842 * q^55 + 387584 * q^56 - 176872 * q^58 - 1025370 * q^59 + 260650 * q^61 - 170232 * q^62 + 2097152 * q^64 + 59673 * q^65 - 2382807 * q^67 + 817600 * q^68 - 3054272 * q^70 - 1773980 * q^71 - 3903260 * q^73 + 2979288 * q^74 + 2473344 * q^76 - 17541708 * q^77 + 11678674 * q^79 - 790528 * q^80 - 2128072 * q^82 + 20314044 * q^83 - 5236237 * q^85 + 6398960 * q^86 - 2316288 * q^88 + 1108942 * q^89 - 29498671 * q^91 + 3126784 * q^92 - 1949376 * q^94 - 10481054 * q^95 - 7003183 * q^97 + 4224696 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−76.2027			−0.272631			−0.136315	−	0.990665i	$-0.543526\pi$
$5$	−76.2027			−0.272631			−0.136315	+	0.990665i	$0.543526\pi$
$6$		0			0
$7$	237.214	−	410.867i	0.261395	−	0.452750i	−0.705218	−	0.708991i	$-0.749151\pi$
$7$	237.214	−	410.867i	0.261395	−	0.452750i	0.966613	+	0.256241i	$0.0824840\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	304.811	+	527.947i	0.0963896	+	0.166952i
$11$	469.485	+	813.173i	0.106353	+	0.184208i	0.914290	−	0.405060i	$-0.132749\pi$
$11$	469.485	+	813.173i	0.106353	+	0.184208i	−0.807937	+	0.589268i	$0.799416\pi$
$12$		0			0
$13$	−6440.26	+	4612.11i	−0.813021	+	0.582234i
$13$	−6440.26	+	4612.11i	−0.813021	+	0.582234i
$14$	−3795.43			−0.369669
$15$		0			0
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	7532.39	−	13046.5i	0.371845	−	0.644054i	−0.618005	−	0.786175i	$-0.712059\pi$
$17$	7532.39	−	13046.5i	0.371845	−	0.644054i	0.989849	+	0.142120i	$0.0453920\pi$
$18$		0			0
$19$	13871.3	−	24025.9i	0.463961	−	0.803603i	−0.535193	−	0.844730i	$-0.679761\pi$
$19$	13871.3	−	24025.9i	0.463961	−	0.803603i	0.999154	+	0.0411263i	$0.0130946\pi$
$20$	2438.48	−	4223.58i	0.0681577	−	0.118053i
$21$		0			0
$22$	3755.88	−	6505.38i	0.0752026	−	0.130255i
$23$	47390.7	+	82083.1i	0.812167	+	1.40671i	0.911344	+	0.411645i	$0.135046\pi$
$23$	47390.7	+	82083.1i	0.812167	+	1.40671i	−0.0991769	+	0.995070i	$0.531621\pi$
$24$		0			0
$25$	−72318.2			−0.925672
$26$	57714.7	+	26171.0i	0.643990	+	0.292021i
$27$		0			0
$28$	15181.7	+	26295.5i	0.130698	+	0.226375i
$29$	25004.6	+	43309.3i	0.190383	+	0.329753i	0.945377	−	0.325979i	$-0.105694\pi$
$29$	25004.6	+	43309.3i	0.190383	+	0.329753i	−0.754994	+	0.655731i	$0.772360\pi$
$30$		0			0
$31$	−253650.			−1.52921			−0.764607	−	0.644497i	$-0.777067\pi$
$31$	−253650.			−1.52921			−0.764607	+	0.644497i	$0.777067\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−120518.			−0.525868
$35$	−18076.4	+	31309.2i	−0.0712645	+	0.123434i
$36$		0			0
$37$	−30321.3	−	52518.1i	−0.0984107	−	0.170452i	0.812616	−	0.582799i	$-0.198043\pi$
$37$	−30321.3	−	52518.1i	−0.0984107	−	0.170452i	−0.911027	+	0.412347i	$0.864709\pi$
$38$	−221942.			−0.656139
$39$		0			0
$40$	−39015.8			−0.0963896
$41$	312111.	+	540592.i	0.707238	+	1.22497i	0.965878	+	0.258998i	$0.0833924\pi$
$41$	312111.	+	540592.i	0.707238	+	1.22497i	−0.258640	+	0.965974i	$0.583274\pi$
$42$		0			0
$43$	287232.	−	497500.i	0.550926	−	0.954231i	−0.447282	−	0.894393i	$-0.647608\pi$
$43$	287232.	−	497500.i	0.550926	−	0.954231i	0.998208	−	0.0598386i	$-0.0190586\pi$
$44$	−60094.1			−0.106353
$45$		0			0
$46$	379125.	−	656664.i	0.574289	−	0.994698i
$47$	467295.			0.656521			0.328261	−	0.944587i	$-0.393538\pi$
$47$	467295.			0.656521			0.328261	+	0.944587i	$0.393538\pi$
$48$		0			0
$49$	299230.	+	518282.i	0.363345	+	0.629332i
$50$	289273.	+	501035.i	0.327275	+	0.566856i
$51$		0			0
$52$	−49540.5	−	504543.i	−0.0488594	−	0.497607i
$53$	158317.			0.146070			0.0730350	−	0.997329i	$-0.476732\pi$
$53$	158317.			0.146070			0.0730350	+	0.997329i	$0.476732\pi$
$54$		0			0
$55$	−35776.0	−	61965.9i	−0.0289950	−	0.0502208i
$56$	121454.	−	210364.i	0.0924172	−	0.160071i
$57$		0			0
$58$	200037.	−	346474.i	0.134621	−	0.233170i
$59$	128030.	−	221754.i	0.0811576	−	0.140569i	−0.822590	−	0.568635i	$-0.807472\pi$
$59$	128030.	−	221754.i	0.0811576	−	0.140569i	0.903747	+	0.428066i	$0.140805\pi$
$60$		0			0
$61$	−190165.	+	329375.i	−0.107269	+	0.185796i	−0.914663	−	0.404217i	$-0.867544\pi$
$61$	−190165.	+	329375.i	−0.107269	+	0.185796i	0.807394	+	0.590013i	$0.200877\pi$
$62$	1.01460e6	+	1.75734e6i	0.540659	+	0.936448i
$63$		0			0
$64$	262144.			0.125000
$65$	490765.	−	351455.i	0.221655	−	0.158735i
$66$		0			0
$67$	230735.	+	399645.i	0.0937243	+	0.162335i	0.909075	−	0.416631i	$-0.136789\pi$
$67$	230735.	+	399645.i	0.0937243	+	0.162335i	−0.815351	+	0.578967i	$0.803456\pi$
$68$	482073.	+	834975.i	0.185922	+	0.322027i
$69$		0			0
$70$	289222.			0.100783
$71$	2.55854e6	−	4.43152e6i	0.848375	−	1.46943i	−0.0342824	−	0.999412i	$-0.510915\pi$
$71$	2.55854e6	−	4.43152e6i	0.848375	−	1.46943i	0.882658	−	0.470017i	$-0.155752\pi$
$72$		0			0
$73$	−869122.			−0.261487			−0.130744	−	0.991416i	$-0.541737\pi$
$73$	−869122.			−0.261487			−0.130744	+	0.991416i	$0.541737\pi$
$74$	−242571.	+	420145.i	−0.0695869	+	0.120528i
$75$		0			0
$76$	887766.	+	1.53766e6i	0.231980	+	0.401802i
$77$	445475.			0.111200
$78$		0			0
$79$	3.99615e6			0.911899			0.455949	−	0.890006i	$-0.349300\pi$
$79$	3.99615e6			0.911899			0.455949	+	0.890006i	$0.349300\pi$
$80$	156063.	+	270309.i	0.0340789	+	0.0590263i
$81$		0			0
$82$	2.49689e6	−	4.32474e6i	0.500093	−	0.866186i
$83$	1.08553e6			0.208386			0.104193	−	0.994557i	$-0.466774\pi$
$83$	1.08553e6			0.208386			0.104193	+	0.994557i	$0.466774\pi$
$84$		0			0
$85$	−573988.	+	994177.i	−0.101376	+	0.175589i
$86$	−4.59571e6			−0.779127
$87$		0			0
$88$	240377.	+	416344.i	0.0376013	+	0.0651274i
$89$	−4.21989e6	−	7.30906e6i	−0.634506	−	1.09900i	−0.986620	−	0.163040i	$-0.947870\pi$
$89$	−4.21989e6	−	7.30906e6i	−0.634506	−	1.09900i	0.352113	−	0.935957i	$-0.385463\pi$
$90$		0			0
$91$	367241.	+	3.74015e6i	0.0510865	+	0.520289i
$92$	−6.06601e6			−0.812167
$93$		0			0
$94$	−1.86918e6	−	3.23752e6i	−0.232115	−	0.402035i
$95$	−1.05703e6	+	1.83084e6i	−0.126490	+	0.219087i
$96$		0			0
$97$	3.93058e6	−	6.80796e6i	0.437276	−	0.757384i	−0.560203	−	0.828356i	$-0.689277\pi$
$97$	3.93058e6	−	6.80796e6i	0.437276	−	0.757384i	0.997478	+	0.0709720i	$0.0226101\pi$
$98$	2.39384e6	−	4.14625e6i	0.256924	−	0.445005i
$99$		0			0
$100$	2.31418e6	−	4.00828e6i	0.231418	−	0.400828i
$101$	2.83434e6	+	4.90922e6i	0.273733	+	0.474120i	0.969815	−	0.243843i	$-0.0784082\pi$
$101$	2.83434e6	+	4.90922e6i	0.273733	+	0.474120i	−0.696082	+	0.717963i	$0.745075\pi$
$102$		0			0
$103$	1.55693e7			1.40391			0.701955	−	0.712221i	$-0.252311\pi$
$103$	1.55693e7			1.40391			0.701955	+	0.712221i	$0.252311\pi$
$104$	−3.29741e6	+	2.36140e6i	−0.287446	+	0.205851i
$105$		0			0
$106$	−633267.	−	1.09685e6i	−0.0516436	−	0.0894493i
$107$	−8.33480e6	−	1.44363e7i	−0.657737	−	1.13923i	−0.981200	−	0.192992i	$-0.938181\pi$
$107$	−8.33480e6	−	1.44363e7i	−0.657737	−	1.13923i	0.323464	−	0.946241i	$-0.395153\pi$
$108$		0			0
$109$	−9.78699e6			−0.723863			−0.361931	−	0.932205i	$-0.617883\pi$
$109$	−9.78699e6			−0.723863			−0.361931	+	0.932205i	$0.617883\pi$
$110$	−286208.	+	495727.i	−0.0205025	+	0.0355115i
$111$		0			0
$112$	−1.94326e6			−0.130698
$113$	1.19975e7	−	2.07802e7i	0.782196	−	1.35480i	−0.148464	−	0.988918i	$-0.547433\pi$
$113$	1.19975e7	−	2.07802e7i	0.782196	−	1.35480i	0.930660	−	0.365885i	$-0.119234\pi$
$114$		0			0
$115$	−3.61130e6	−	6.25495e6i	−0.221422	−	0.383514i
$116$	−3.20059e6			−0.190383
$117$		0			0
$118$	−2.04848e6			−0.114774
$119$	−3.57358e6	−	6.18963e6i	−0.194397	−	0.336706i
$120$		0			0
$121$	9.30275e6	−	1.61128e7i	0.477378	−	0.826843i
$122$	3.04264e6			0.151702
$123$		0			0
$124$	8.11679e6	−	1.40587e7i	0.382303	−	0.662169i
$125$	1.14642e7			0.524998
$126$		0			0
$127$	−1.75182e7	−	3.03424e7i	−0.758887	−	1.31443i	−0.943419	−	0.331604i	$-0.892410\pi$
$127$	−1.75182e7	−	3.03424e7i	−0.758887	−	1.31443i	0.184532	−	0.982826i	$-0.440923\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−4.39801e6	−	1.99430e6i	−0.175572	−	0.0796139i
$131$	3.05996e7			1.18923			0.594616	−	0.804010i	$-0.297304\pi$
$131$	3.05996e7			1.18923			0.594616	+	0.804010i	$0.297304\pi$
$132$		0			0
$133$	−6.58097e6	−	1.13986e7i	−0.242554	−	0.420116i
$134$	1.84588e6	−	3.19716e6i	0.0662731	−	0.114788i
$135$		0			0
$136$	3.85659e6	−	6.67980e6i	0.131467	−	0.227708i
$137$	−5.06984e6	+	8.78123e6i	−0.168451	+	0.291765i	−0.937875	−	0.346973i	$-0.887210\pi$
$137$	−5.06984e6	+	8.78123e6i	−0.168451	+	0.291765i	0.769425	+	0.638738i	$0.220543\pi$
$138$		0			0
$139$	1.98072e7	−	3.43071e7i	0.625564	−	1.08351i	−0.362867	−	0.931841i	$-0.618202\pi$
$139$	1.98072e7	−	3.43071e7i	0.625564	−	1.08351i	0.988431	−	0.151668i	$-0.0484646\pi$
$140$	−1.15689e6	−	2.00379e6i	−0.0356322	−	0.0617168i
$141$		0			0
$142$	−4.09366e7			−1.19978
$143$	−6.77405e6	−	3.07173e6i	−0.193719	−	0.0878429i
$144$		0			0
$145$	−1.90542e6	−	3.30028e6i	−0.0519042	−	0.0899008i
$146$	3.47649e6	+	6.02146e6i	0.0924498	+	0.160128i
$147$		0			0
$148$	3.88113e6			0.0984107
$149$	−1.46075e7	+	2.53009e7i	−0.361762	+	0.626590i	−0.988251	−	0.152840i	$-0.951158\pi$
$149$	−1.46075e7	+	2.53009e7i	−0.361762	+	0.626590i	0.626489	+	0.779430i	$0.284491\pi$
$150$		0			0
$151$	2.94795e7			0.696788			0.348394	−	0.937348i	$-0.386727\pi$
$151$	2.94795e7			0.696788			0.348394	+	0.937348i	$0.386727\pi$
$152$	7.10213e6	−	1.23012e7i	0.164035	−	0.284117i
$153$		0			0
$154$	−1.78190e6	−	3.08634e6i	−0.0393152	−	0.0680960i
$155$	1.93288e7			0.416911
$156$		0			0
$157$	−3.91044e7			−0.806449			−0.403224	−	0.915101i	$-0.632111\pi$
$157$	−3.91044e7			−0.806449			−0.403224	+	0.915101i	$0.632111\pi$
$158$	−1.59846e7	−	2.76861e7i	−0.322405	−	0.558422i
$159$		0			0
$160$	1.24850e6	−	2.16247e6i	0.0240974	−	0.0417379i
$161$	4.49670e7			0.849187
$162$		0			0
$163$	3.28012e7	−	5.68133e7i	0.593243	−	1.02753i	−0.400549	−	0.916275i	$-0.631181\pi$
$163$	3.28012e7	−	5.68133e7i	0.593243	−	1.02753i	0.993792	−	0.111252i	$-0.0354862\pi$
$164$	−3.99502e7			−0.707238
$165$		0			0
$166$	−4.34212e6	−	7.52077e6i	−0.0736756	−	0.127610i
$167$	−1.69481e7	−	2.93549e7i	−0.281587	−	0.487723i	0.690189	−	0.723629i	$-0.257527\pi$
$167$	−1.69481e7	−	2.93549e7i	−0.281587	−	0.487723i	−0.971776	+	0.235906i	$0.924194\pi$
$168$		0			0
$169$	2.02055e7	−	5.94064e7i	0.322007	−	0.946737i
$170$	9.18381e6			0.143368
$171$		0			0
$172$	1.83828e7	+	3.18400e7i	0.275463	+	0.477116i
$173$	3.20569e6	−	5.55242e6i	0.0470718	−	0.0815307i	−0.841530	−	0.540211i	$-0.818344\pi$
$173$	3.20569e6	−	5.55242e6i	0.0470718	−	0.0815307i	0.888601	+	0.458680i	$0.151678\pi$
$174$		0			0
$175$	−1.71549e7	+	2.97132e7i	−0.241967	+	0.419098i
$176$	1.92301e6	−	3.33076e6i	0.0265881	−	0.0460520i
$177$		0			0
$178$	−3.37591e7	+	5.84725e7i	−0.448664	+	0.777108i
$179$	1.58099e7	+	2.73836e7i	0.206036	+	0.356865i	0.950462	−	0.310840i	$-0.100610\pi$
$179$	1.58099e7	+	2.73836e7i	0.206036	+	0.356865i	−0.744426	+	0.667705i	$0.767277\pi$
$180$		0			0
$181$	1.13389e8			1.42134			0.710669	−	0.703527i	$-0.248392\pi$
$181$	1.13389e8			1.42134			0.710669	+	0.703527i	$0.248392\pi$
$182$	2.44436e7	−	1.75049e7i	0.300549	−	0.215234i
$183$		0			0
$184$	2.42640e7	+	4.20265e7i	0.287144	+	0.497349i
$185$	2.31057e6	+	4.00202e6i	0.0268298	+	0.0464706i
$186$		0			0
$187$	1.41454e7			0.158187
$188$	−1.49534e7	+	2.59001e7i	−0.164130	+	0.284282i
$189$		0			0
$190$	1.69125e7			0.178884
$191$	−1.21920e7	+	2.11172e7i	−0.126607	+	0.219291i	−0.922360	−	0.386331i	$-0.873742\pi$
$191$	−1.21920e7	+	2.11172e7i	−0.126607	+	0.219291i	0.795753	+	0.605622i	$0.207076\pi$
$192$		0			0
$193$	−2.27014e6	−	3.93201e6i	−0.0227302	−	0.0393698i	0.854437	−	0.519556i	$-0.173903\pi$
$193$	−2.27014e6	−	3.93201e6i	−0.0227302	−	0.0393698i	−0.877167	+	0.480186i	$0.840569\pi$
$194$	−6.28892e7			−0.618401
$195$		0			0
$196$	−3.83015e7			−0.363345
$197$	−1.62344e6	−	2.81188e6i	−0.0151288	−	0.0262038i	0.858362	−	0.513045i	$-0.171482\pi$
$197$	−1.62344e6	−	2.81188e6i	−0.0151288	−	0.0262038i	−0.873491	+	0.486841i	$0.838149\pi$
$198$		0			0
$199$	−2.67507e7	+	4.63336e7i	−0.240630	+	0.416784i	−0.960894	−	0.276917i	$-0.910687\pi$
$199$	−2.67507e7	+	4.63336e7i	−0.240630	+	0.416784i	0.720264	+	0.693700i	$0.244021\pi$
$200$	−3.70269e7			−0.327275
$201$		0			0
$202$	2.26747e7	−	3.92738e7i	0.193559	−	0.335253i
$203$	2.37258e7			0.199061
$204$		0			0
$205$	−2.37837e7	−	4.11946e7i	−0.192815	−	0.333965i
$206$	−6.22773e7	−	1.07867e8i	−0.496357	−	0.859716i
$207$		0			0
$208$	2.95499e7	+	1.33996e7i	0.227685	+	0.103245i
$209$	2.60496e7			0.197373
$210$		0			0
$211$	9.14497e7	+	1.58396e8i	0.670183	+	1.16079i	0.977852	+	0.209298i	$0.0671179\pi$
$211$	9.14497e7	+	1.58396e8i	0.670183	+	1.16079i	−0.307669	+	0.951494i	$0.599549\pi$
$212$	−5.06614e6	+	8.77480e6i	−0.0365175	+	0.0632502i
$213$		0			0
$214$	−6.66784e7	+	1.15490e8i	−0.465090	+	0.805559i
$215$	−2.18878e7	+	3.79108e7i	−0.150199	+	0.260153i
$216$		0			0
$217$	−6.01693e7	+	1.04216e8i	−0.399729	+	0.692352i
$218$	3.91479e7	+	6.78062e7i	0.255924	+	0.443274i
$219$		0			0
$220$	4.57933e6			0.0289950
$221$	1.16612e7	+	1.18763e8i	0.0726725	+	0.740130i
$222$		0			0
$223$	1.08702e8	+	1.88277e8i	0.656401	+	1.13692i	0.981541	+	0.191254i	$0.0612555\pi$
$223$	1.08702e8	+	1.88277e8i	0.656401	+	1.13692i	−0.325139	+	0.945666i	$0.605411\pi$
$224$	7.77304e6	+	1.34633e7i	0.0462086	+	0.0800357i
$225$		0			0
$226$	−1.91960e8			−1.10619
$227$	3.78670e7	−	6.55876e7i	0.214867	−	0.372161i	−0.738364	−	0.674402i	$-0.764401\pi$
$227$	3.78670e7	−	6.55876e7i	0.214867	−	0.372161i	0.953232	+	0.302241i	$0.0977347\pi$
$228$		0			0
$229$	−4.82050e7			−0.265258			−0.132629	−	0.991166i	$-0.542342\pi$
$229$	−4.82050e7			−0.265258			−0.132629	+	0.991166i	$0.542342\pi$
$230$	−2.88904e7	+	5.00396e7i	−0.156569	+	0.271185i
$231$		0			0
$232$	1.28024e7	+	2.21744e7i	0.0673105	+	0.116585i
$233$	1.71291e8			0.887131			0.443565	−	0.896242i	$-0.353713\pi$
$233$	1.71291e8			0.887131			0.443565	+	0.896242i	$0.353713\pi$
$234$		0			0
$235$	−3.56091e7			−0.178988
$236$	8.19391e6	+	1.41923e7i	0.0405788	+	0.0702845i
$237$		0			0
$238$	−2.85887e7	+	4.95170e7i	−0.137459	+	0.238087i
$239$	−1.06547e7			−0.0504835			−0.0252417	−	0.999681i	$-0.508036\pi$
$239$	−1.06547e7			−0.0504835			−0.0252417	+	0.999681i	$0.508036\pi$
$240$		0			0
$241$	7.07100e7	−	1.22473e8i	0.325403	−	0.563614i	−0.656191	−	0.754595i	$-0.727833\pi$
$241$	7.07100e7	−	1.22473e8i	0.325403	−	0.563614i	0.981594	+	0.190981i	$0.0611668\pi$
$242$	−1.48844e8			−0.675115
$243$		0			0
$244$	−1.21705e7	−	2.10800e7i	−0.0536347	−	0.0928980i
$245$	−2.28021e7	−	3.94944e7i	−0.0990590	−	0.171575i
$246$		0			0
$247$	2.14748e7	+	2.18709e8i	0.0906754	+	0.923480i
$248$	−1.29869e8			−0.540659
$249$		0			0
$250$	−4.58567e7	−	7.94261e7i	−0.185615	−	0.321494i
$251$	2.17755e8	−	3.77162e8i	0.869180	−	1.50546i	0.00634424	−	0.999980i	$-0.497981\pi$
$251$	2.17755e8	−	3.77162e8i	0.869180	−	1.50546i	0.862836	−	0.505484i	$-0.168686\pi$
$252$		0			0
$253$	−4.44985e7	+	7.70736e7i	−0.172752	+	0.299215i
$254$	−1.40146e8	+	2.42740e8i	−0.536614	+	0.929443i
$255$		0			0
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	2.46043e8	+	4.26159e8i	0.904159	+	1.56605i	0.822042	+	0.569427i	$0.192835\pi$
$257$	2.46043e8	+	4.26159e8i	0.904159	+	1.56605i	0.0821171	+	0.996623i	$0.473832\pi$
$258$		0			0
$259$	−2.87706e7			−0.102896
$260$	3.77512e6	+	3.84475e7i	0.0133206	+	0.135663i
$261$		0			0
$262$	−1.22398e8	−	2.12000e8i	−0.420457	−	0.728253i
$263$	1.25783e8	+	2.17862e8i	0.426360	+	0.738478i	0.996546	−	0.0830380i	$-0.0264623\pi$
$263$	1.25783e8	+	2.17862e8i	0.426360	+	0.738478i	−0.570186	+	0.821515i	$0.693129\pi$
$264$		0			0
$265$	−1.20642e7			−0.0398232
$266$	−5.26477e7	+	9.11886e7i	−0.171512	+	0.297067i
$267$		0			0
$268$	−2.95341e7			−0.0937243
$269$	−8.56627e7	+	1.48372e8i	−0.268323	+	0.464750i	−0.968429	−	0.249289i	$-0.919803\pi$
$269$	−8.56627e7	+	1.48372e8i	−0.268323	+	0.464750i	0.700106	+	0.714039i	$0.253136\pi$
$270$		0			0
$271$	−3.33116e7	−	5.76975e7i	−0.101673	−	0.176102i	0.810701	−	0.585460i	$-0.199086\pi$
$271$	−3.33116e7	−	5.76975e7i	−0.101673	−	0.176102i	−0.912374	+	0.409358i	$0.865753\pi$
$272$	−6.17054e7			−0.185922
$273$		0			0
$274$	8.11175e7			0.238225
$275$	−3.39523e7	−	5.88072e7i	−0.0984476	−	0.170516i
$276$		0			0
$277$	−2.12210e8	+	3.67559e8i	−0.599912	+	1.03908i	0.392921	+	0.919572i	$0.371464\pi$
$277$	−2.12210e8	+	3.67559e8i	−0.599912	+	1.03908i	−0.992833	+	0.119506i	$0.961869\pi$
$278$	−3.16916e8			−0.884682
$279$		0			0
$280$	−9.25510e6	+	1.60303e7i	−0.0251958	+	0.0436404i
$281$	8.26544e7			0.222226			0.111113	−	0.993808i	$-0.464559\pi$
$281$	8.26544e7			0.222226			0.111113	+	0.993808i	$0.464559\pi$
$282$		0			0
$283$	−2.13992e7	−	3.70646e7i	−0.0561236	−	0.0972090i	0.836599	−	0.547816i	$-0.184541\pi$
$283$	−2.13992e7	−	3.70646e7i	−0.0561236	−	0.0972090i	−0.892722	+	0.450607i	$0.851207\pi$
$284$	1.63747e8	+	2.83617e8i	0.424188	+	0.734714i
$285$		0			0
$286$	5.81463e6	+	5.92189e7i	0.0146974	+	0.149685i
$287$	2.96149e8			0.739475
$288$		0			0
$289$	9.16955e7	+	1.58821e8i	0.223463	+	0.387049i
$290$	−1.52434e7	+	2.64023e7i	−0.0367018	+	0.0635694i
$291$		0			0
$292$	2.78119e7	−	4.81716e7i	0.0653719	−	0.113227i
$293$	1.08892e7	−	1.88607e7i	0.0252907	−	0.0438047i	−0.853103	−	0.521742i	$-0.825282\pi$
$293$	1.08892e7	−	1.88607e7i	0.0252907	−	0.0438047i	0.878394	+	0.477938i	$0.158616\pi$
$294$		0			0
$295$	−9.75621e6	+	1.68983e7i	−0.0221261	+	0.0383235i
$296$	−1.55245e7	−	2.68893e7i	−0.0347934	−	0.0602640i
$297$		0			0
$298$	2.33719e8			0.511609
$299$	−6.83784e8	−	3.10066e8i	−1.47935	−	0.670818i
$300$		0			0
$301$	−1.36271e8	−	2.36028e8i	−0.288019	−	0.498863i
$302$	−1.17918e8	−	2.04240e8i	−0.246352	−	0.426694i
$303$		0			0
$304$	−1.13634e8			−0.231980
$305$	1.44911e7	−	2.50992e7i	0.0292449	−	0.0506537i
$306$		0			0
$307$	7.22793e7			0.142570			0.0712852	−	0.997456i	$-0.477290\pi$
$307$	7.22793e7			0.142570			0.0712852	+	0.997456i	$0.477290\pi$
$308$	−1.42552e7	+	2.46907e7i	−0.0278001	+	0.0481511i
$309$		0			0
$310$	−7.73151e7	−	1.33914e8i	−0.147400	−	0.255305i
$311$	−3.38264e8			−0.637668			−0.318834	−	0.947811i	$-0.603291\pi$
$311$	−3.38264e8			−0.637668			−0.318834	+	0.947811i	$0.603291\pi$
$312$		0			0
$313$	−3.69419e8			−0.680948			−0.340474	−	0.940254i	$-0.610588\pi$
$313$	−3.69419e8			−0.680948			−0.340474	+	0.940254i	$0.610588\pi$
$314$	1.56418e8	+	2.70923e8i	0.285123	+	0.493847i
$315$		0			0
$316$	−1.27877e8	+	2.21489e8i	−0.227975	+	0.394864i
$317$	1.00099e9			1.76491			0.882455	−	0.470397i	$-0.155889\pi$
$317$	1.00099e9			1.76491			0.882455	+	0.470397i	$0.155889\pi$
$318$		0			0
$319$	−2.34786e7	+	4.06662e7i	−0.0404954	+	0.0701400i
$320$	−1.99761e7			−0.0340789
$321$		0			0
$322$	−1.79868e8	−	3.11541e8i	−0.300233	−	0.520019i
$323$	−2.08969e8	−	3.61945e8i	−0.345043	−	0.597631i
$324$		0			0
$325$	4.65748e8	−	3.33539e8i	0.752591	−	0.538958i
$326$	−5.24819e8			−0.838973
$327$		0			0
$328$	1.59801e8	+	2.76783e8i	0.250046	+	0.433093i
$329$	1.10849e8	−	1.91996e8i	0.171612	−	0.297240i
$330$		0			0
$331$	−3.63874e8	+	6.30248e8i	−0.551510	+	0.955243i	0.446656	+	0.894706i	$0.352615\pi$
$331$	−3.63874e8	+	6.30248e8i	−0.551510	+	0.955243i	−0.998166	+	0.0605370i	$0.980719\pi$
$332$	−3.47370e7	+	6.01662e7i	−0.0520965	+	0.0902338i
$333$		0			0
$334$	−1.35585e8	+	2.34839e8i	−0.199112	+	0.344872i
$335$	−1.75826e7	−	3.04540e7i	−0.0255521	−	0.0442576i
$336$		0			0
$337$	−7.69155e8			−1.09474			−0.547368	−	0.836892i	$-0.684370\pi$
$337$	−7.69155e8			−1.09474			−0.547368	+	0.836892i	$0.684370\pi$
$338$	−4.92401e8	+	9.76379e7i	−0.693602	+	0.137534i
$339$		0			0
$340$	−3.67353e7	−	6.36273e7i	−0.0506882	−	0.0877945i
$341$	−1.19085e8	−	2.06261e8i	−0.162636	−	0.281693i
$342$		0			0
$343$	6.74639e8			0.902698
$344$	1.47063e8	−	2.54720e8i	0.194782	−	0.337372i
$345$		0			0
$346$	−5.12911e7			−0.0665695
$347$	1.28485e8	−	2.22543e8i	0.165082	−	0.285931i	−0.771602	−	0.636105i	$-0.780544\pi$
$347$	1.28485e8	−	2.22543e8i	0.165082	−	0.285931i	0.936684	+	0.350175i	$0.113878\pi$
$348$		0			0
$349$	−1.92351e8	−	3.33161e8i	−0.242217	−	0.419532i	0.719128	−	0.694877i	$-0.244541\pi$
$349$	−1.92351e8	−	3.33161e8i	−0.242217	−	0.419532i	−0.961345	+	0.275345i	$0.911208\pi$
$350$	2.74479e8			0.342192
$351$		0			0
$352$	−3.07682e7			−0.0376013
$353$	−2.99006e8	−	5.17894e8i	−0.361800	−	0.626656i	0.626457	−	0.779456i	$-0.284504\pi$
$353$	−2.99006e8	−	5.17894e8i	−0.361800	−	0.626656i	−0.988257	+	0.152800i	$0.951171\pi$
$354$		0			0
$355$	−1.94968e8	+	3.37694e8i	−0.231293	+	0.400612i
$356$	5.40146e8			0.634506
$357$		0			0
$358$	1.26479e8	−	2.19069e8i	0.145690	−	0.252342i
$359$	−3.63568e8			−0.414720			−0.207360	−	0.978265i	$-0.566487\pi$
$359$	−3.63568e8			−0.414720			−0.207360	+	0.978265i	$0.566487\pi$
$360$		0			0
$361$	6.21073e7	+	1.07573e8i	0.0694812	+	0.120345i
$362$	−4.53557e8	−	7.85584e8i	−0.502519	−	0.870388i
$363$		0			0
$364$	−2.19052e8	−	9.93303e7i	−0.238063	−	0.107951i
$365$	6.62294e7			0.0712896
$366$		0			0
$367$	6.16051e8	+	1.06703e9i	0.650557	+	1.12680i	0.982988	+	0.183670i	$0.0587979\pi$
$367$	6.16051e8	+	1.06703e9i	0.650557	+	1.12680i	−0.332431	+	0.943128i	$0.607869\pi$
$368$	1.94112e8	−	3.36212e8i	0.203042	−	0.351679i
$369$		0			0
$370$	1.84845e7	−	3.20161e7i	0.0189715	−	0.0328596i
$371$	3.75550e7	−	6.50472e7i	0.0381820	−	0.0661332i
$372$		0			0
$373$	6.75250e8	−	1.16957e9i	0.673727	−	1.16693i	−0.303113	−	0.952955i	$-0.598026\pi$
$373$	6.75250e8	−	1.16957e9i	0.673727	−	1.16693i	0.976839	−	0.213974i	$-0.0686408\pi$
$374$	−5.65816e7	−	9.80022e7i	−0.0559274	−	0.0968691i
$375$		0			0
$376$	2.39255e8			0.232115
$377$	−3.60784e8	−	1.63599e8i	−0.346778	−	0.157249i
$378$		0			0
$379$	4.14522e7	+	7.17973e7i	0.0391120	+	0.0677440i	0.884919	−	0.465745i	$-0.154214\pi$
$379$	4.14522e7	+	7.17973e7i	0.0391120	+	0.0677440i	−0.845807	+	0.533489i	$0.820880\pi$
$380$	−6.76501e7	−	1.17173e8i	−0.0632450	−	0.109544i
$381$		0			0
$382$	1.95073e8			0.179050
$383$	−7.16379e8	+	1.24081e9i	−0.651549	+	1.12852i	0.331198	+	0.943561i	$0.392547\pi$
$383$	−7.16379e8	+	1.24081e9i	−0.651549	+	1.12852i	−0.982747	+	0.184955i	$0.940786\pi$
$384$		0			0
$385$	−3.39464e7			−0.0303166
$386$	−1.81612e7	+	3.14560e7i	−0.0160727	+	0.0278387i
$387$		0			0
$388$	2.51557e8	+	4.35709e8i	0.218638	+	0.378692i
$389$	1.19888e9			1.03265			0.516325	−	0.856393i	$-0.327300\pi$
$389$	1.19888e9			1.03265			0.516325	+	0.856393i	$0.327300\pi$
$390$		0			0
$391$	1.42786e9			1.20800
$392$	1.53206e8	+	2.65360e8i	0.128462	+	0.222502i
$393$		0			0
$394$	−1.29875e7	+	2.24950e7i	−0.0106977	+	0.0185289i
$395$	−3.04517e8			−0.248612
$396$		0			0
$397$	8.95994e8	−	1.55191e9i	0.718684	−	1.24480i	−0.242837	−	0.970067i	$-0.578078\pi$
$397$	8.95994e8	−	1.55191e9i	0.718684	−	1.24480i	0.961521	−	0.274731i	$-0.0885888\pi$
$398$	4.28012e8			0.340302
$399$		0			0
$400$	1.48108e8	+	2.56530e8i	0.115709	+	0.200414i
$401$	5.78662e8	+	1.00227e9i	0.448146	+	0.776212i	0.998265	−	0.0588740i	$-0.0187510\pi$
$401$	5.78662e8	+	1.00227e9i	0.448146	+	0.776212i	−0.550119	+	0.835086i	$0.685418\pi$
$402$		0			0
$403$	1.63357e9	−	1.16986e9i	1.24328	−	0.890360i
$404$	−3.62796e8			−0.273733
$405$		0			0
$406$	−9.49034e7	−	1.64377e8i	−0.0703786	−	0.121899i
$407$	2.84708e7	−	4.93130e7i	0.0209324	−	0.0362561i
$408$		0			0
$409$	6.29621e8	−	1.09054e9i	0.455038	−	0.788149i	−0.543652	−	0.839311i	$-0.682959\pi$
$409$	6.29621e8	−	1.09054e9i	0.455038	−	0.788149i	0.998690	+	0.0511614i	$0.0162923\pi$
$410$	−1.90270e8	+	3.29556e8i	−0.136341	+	0.236149i
$411$		0			0
$412$	−4.98218e8	+	8.62939e8i	−0.350977	+	0.607911i
$413$	−6.07410e7	−	1.05207e8i	−0.0424284	−	0.0734882i
$414$		0			0
$415$	−8.27203e7			−0.0568125
$416$	−2.53647e7	−	2.58326e8i	−0.0172744	−	0.175931i
$417$		0			0
$418$	−1.04198e8	−	1.80477e8i	−0.0697821	−	0.120866i
$419$	−6.83207e8	−	1.18335e9i	−0.453736	−	0.785894i	0.544878	−	0.838515i	$-0.316576\pi$
$419$	−6.83207e8	−	1.18335e9i	−0.453736	−	0.785894i	−0.998615	+	0.0526211i	$0.983242\pi$
$420$		0			0
$421$	−1.46622e9			−0.957661			−0.478831	−	0.877907i	$-0.658939\pi$
$421$	−1.46622e9			−0.957661			−0.478831	+	0.877907i	$0.658939\pi$
$422$	7.31598e8	−	1.26716e9i	0.473891	−	0.820804i
$423$		0			0
$424$	8.10582e7			0.0516436
$425$	−5.44729e8	+	9.43498e8i	−0.344206	+	0.596183i
$426$		0			0
$427$	9.02196e7	+	1.56265e8i	0.0560794	+	0.0971324i
$428$	1.06685e9			0.657737
$429$		0			0
$430$	3.50205e8			0.212414
$431$	9.00866e8	+	1.56035e9i	0.541988	+	0.938751i	0.998790	+	0.0491826i	$0.0156616\pi$
$431$	9.00866e8	+	1.56035e9i	0.541988	+	0.938751i	−0.456802	+	0.889569i	$0.651005\pi$
$432$		0			0
$433$	−5.38563e6	+	9.32818e6i	−0.00318808	+	0.00552191i	−0.867615	−	0.497237i	$-0.834348\pi$
$433$	−5.38563e6	+	9.32818e6i	−0.00318808	+	0.00552191i	0.864427	+	0.502758i	$0.167681\pi$
$434$	9.62709e8			0.565303
$435$		0			0
$436$	3.13184e8	−	5.42450e8i	0.180966	−	0.313442i
$437$	2.62949e9			1.50725
$438$		0			0
$439$	−1.72073e9	−	2.98040e9i	−0.970706	−	1.68131i	−0.693434	−	0.720520i	$-0.743903\pi$
$439$	−1.72073e9	−	2.98040e9i	−0.970706	−	1.68131i	−0.277271	−	0.960792i	$-0.589430\pi$
$440$	−1.83173e7	−	3.17266e7i	−0.0102513	−	0.0177557i
$441$		0			0
$442$	7.76169e8	−	5.55843e8i	0.427542	−	0.306178i
$443$	−1.39496e9			−0.762343			−0.381171	−	0.924504i	$-0.624479\pi$
$443$	−1.39496e9			−0.762343			−0.381171	+	0.924504i	$0.624479\pi$
$444$		0			0
$445$	3.21567e8	+	5.56970e8i	0.172986	+	0.299621i
$446$	8.69614e8	−	1.50622e9i	0.464146	−	0.803924i
$447$		0			0
$448$	6.21843e7	−	1.07706e8i	0.0326744	−	0.0565938i
$449$	−1.08348e9	+	1.87664e9i	−0.564883	+	0.978406i	0.432178	+	0.901788i	$0.357745\pi$
$449$	−1.08348e9	+	1.87664e9i	−0.564883	+	0.978406i	−0.997061	+	0.0766173i	$0.975588\pi$
$450$		0			0
$451$	−2.93063e8	+	5.07600e8i	−0.150433	+	0.260558i
$452$	7.67839e8	+	1.32994e9i	0.391098	+	0.677401i
$453$		0			0
$454$	−6.05872e8			−0.303868
$455$	−2.79847e7	−	2.85010e8i	−0.0139278	−	0.141847i
$456$		0			0
$457$	−1.88352e9	−	3.26236e9i	−0.923133	−	1.59891i	−0.794536	−	0.607216i	$-0.792286\pi$
$457$	−1.88352e9	−	3.26236e9i	−0.923133	−	1.59891i	−0.128597	−	0.991697i	$-0.541047\pi$
$458$	1.92820e8	+	3.33974e8i	0.0937827	+	0.162436i
$459$		0			0
$460$	4.62246e8			0.221422
$461$	2.32221e8	−	4.02219e8i	0.110395	−	0.191209i	−0.805535	−	0.592549i	$-0.798122\pi$
$461$	2.32221e8	−	4.02219e8i	0.110395	−	0.191209i	0.915930	+	0.401339i	$0.131455\pi$
$462$		0			0
$463$	−2.90068e9			−1.35821			−0.679104	−	0.734042i	$-0.737631\pi$
$463$	−2.90068e9			−1.35821			−0.679104	+	0.734042i	$0.737631\pi$
$464$	1.02419e8	−	1.77395e8i	0.0475957	−	0.0824382i
$465$		0			0
$466$	−6.85162e8	−	1.18674e9i	−0.313648	−	0.543254i
$467$	3.23507e9			1.46986			0.734928	−	0.678145i	$-0.237216\pi$
$467$	3.23507e9			1.46986			0.734928	+	0.678145i	$0.237216\pi$
$468$		0			0
$469$	2.18935e8			0.0979964
$470$	1.42437e8	+	2.46707e8i	0.0632818	+	0.109607i
$471$		0			0
$472$	6.55513e7	−	1.13538e8i	0.0286935	−	0.0496987i
$473$	5.39405e8			0.234369
$474$		0			0
$475$	−1.00315e9	+	1.73751e9i	−0.429475	+	0.743873i
$476$	4.57419e8			0.194397
$477$		0			0
$478$	4.26189e7	+	7.38181e7i	0.0178486	+	0.0309147i
$479$	−1.29597e9	−	2.24469e9i	−0.538793	−	0.933217i	−0.998969	−	0.0453897i	$-0.985547\pi$
$479$	−1.29597e9	−	2.24469e9i	−0.538793	−	0.933217i	0.460176	−	0.887828i	$-0.347786\pi$
$480$		0			0
$481$	4.37496e8	+	1.98385e8i	0.179253	+	0.0812833i
$482$	−1.13136e9			−0.460189
$483$		0			0
$484$	5.95376e8	+	1.03122e9i	0.238689	+	0.413422i
$485$	−2.99520e8	+	5.18785e8i	−0.119215	+	0.206486i
$486$		0			0
$487$	1.71186e9	−	2.96502e9i	0.671609	−	1.16326i	−0.305839	−	0.952083i	$-0.598937\pi$
$487$	1.71186e9	−	2.96502e9i	0.671609	−	1.16326i	0.977448	−	0.211177i	$-0.0677297\pi$
$488$	−9.73644e7	+	1.68640e8i	−0.0379254	+	0.0656888i
$489$		0			0
$490$	−1.82417e8	+	3.15956e8i	−0.0700453	+	0.121322i
$491$	−4.65512e8	−	8.06291e8i	−0.177479	−	0.307402i	0.763538	−	0.645763i	$-0.223461\pi$
$491$	−4.65512e8	−	8.06291e8i	−0.177479	−	0.307402i	−0.941016	+	0.338361i	$0.890127\pi$
$492$		0			0
$493$	7.53379e8			0.283171
$494$	1.42936e9	−	1.02362e9i	0.533455	−	0.382027i
$495$		0			0
$496$	5.19474e8	+	8.99756e8i	0.191152	+	0.331085i
$497$	−1.21385e9	−	2.10244e9i	−0.443523	−	0.768204i
$498$		0			0
$499$	1.19017e9			0.428802			0.214401	−	0.976746i	$-0.431220\pi$
$499$	1.19017e9			0.428802			0.214401	+	0.976746i	$0.431220\pi$
$500$	−3.66853e8	+	6.35409e8i	−0.131249	+	0.227331i
$501$		0			0
$502$	−3.48408e9			−1.22921
$503$	−6.54277e8	+	1.13324e9i	−0.229231	+	0.397040i	−0.957581	−	0.288166i	$-0.906955\pi$
$503$	−6.54277e8	+	1.13324e9i	−0.229231	+	0.397040i	0.728349	+	0.685206i	$0.240288\pi$
$504$		0			0
$505$	−2.15984e8	−	3.74096e8i	−0.0746281	−	0.129260i
$506$	7.11976e8			0.244308
$507$		0			0
$508$	2.24233e9			0.758887
$509$	−1.42276e9	−	2.46429e9i	−0.478210	−	0.828285i	0.521478	−	0.853265i	$-0.325381\pi$
$509$	−1.42276e9	−	2.46429e9i	−0.478210	−	0.828285i	−0.999688	+	0.0249803i	$0.992048\pi$
$510$		0			0
$511$	−2.06168e8	+	3.57094e8i	−0.0683516	+	0.118388i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	1.96834e9	−	3.40927e9i	0.639337	−	1.10736i
$515$	−1.18642e9			−0.382749
$516$		0			0
$517$	2.19388e8	+	3.79992e8i	0.0698227	+	0.120936i
$518$	1.15083e8	+	1.99329e8i	0.0363794	+	0.0630109i
$519$		0			0
$520$	2.51272e8	−	1.79945e8i	0.0783668	−	0.0561213i
$521$	−4.10103e9			−1.27046			−0.635229	−	0.772324i	$-0.719094\pi$
$521$	−4.10103e9			−1.27046			−0.635229	+	0.772324i	$0.719094\pi$
$522$		0			0
$523$	2.74278e9	+	4.75064e9i	0.838370	+	1.45210i	0.891257	+	0.453498i	$0.149824\pi$
$523$	2.74278e9	+	4.75064e9i	0.838370	+	1.45210i	−0.0528876	+	0.998600i	$0.516842\pi$
$524$	−9.79188e8	+	1.69600e9i	−0.297308	+	0.514952i
$525$		0			0
$526$	1.00626e9	−	1.74290e9i	0.301482	−	0.522182i
$527$	−1.91059e9	+	3.30924e9i	−0.568630	+	0.984896i
$528$		0			0
$529$	−2.78934e9	+	4.83128e9i	−0.819231	+	1.41895i
$530$	4.82566e7	+	8.35829e7i	0.0140796	+	0.0243866i
$531$		0			0
$532$	8.42364e8			0.242554
$533$	−4.50335e9	−	2.04207e9i	−1.28822	−	0.584150i
$534$		0			0
$535$	6.35134e8	+	1.10008e9i	0.179319	+	0.310590i
$536$	1.18137e8	+	2.04618e8i	0.0331366	+	0.0573942i
$537$		0			0
$538$	1.37060e9			0.379467
$539$	−2.80968e8	+	4.86652e8i	−0.0772853	+	0.133862i
$540$		0			0
$541$	−2.20052e9			−0.597496			−0.298748	−	0.954332i	$-0.596569\pi$
$541$	−2.20052e9			−0.597496			−0.298748	+	0.954332i	$0.596569\pi$
$542$	−2.66493e8	+	4.61580e8i	−0.0718933	+	0.124523i
$543$		0			0
$544$	2.46821e8	+	4.27507e8i	0.0657335	+	0.113854i
$545$	7.45794e8			0.197347
$546$		0			0
$547$	−2.77848e9			−0.725858			−0.362929	−	0.931817i	$-0.618223\pi$
$547$	−2.77848e9			−0.725858			−0.362929	+	0.931817i	$0.618223\pi$
$548$	−3.24470e8	−	5.61999e8i	−0.0842253	−	0.145883i
$549$		0			0
$550$	−2.71619e8	+	4.70457e8i	−0.0696130	+	0.120573i
$551$	1.38739e9			0.353320
$552$		0			0
$553$	9.47944e8	−	1.64189e9i	0.238366	−	0.412862i
$554$	3.39537e9			0.848404
$555$		0			0
$556$	1.26766e9	+	2.19566e9i	0.312782	+	0.541755i
$557$	−3.77413e9	−	6.53699e9i	−0.925388	−	1.60282i	−0.790935	−	0.611900i	$-0.790406\pi$
$557$	−3.77413e9	−	6.53699e9i	−0.925388	−	1.60282i	−0.134453	−	0.990920i	$-0.542928\pi$
$558$		0			0
$559$	4.44675e8	+	4.52878e9i	0.107672	+	1.09658i
$560$	1.48082e8			0.0356322
$561$		0			0
$562$	−3.30618e8	−	5.72647e8i	−0.0785686	−	0.136085i
$563$	−3.84314e8	+	6.65652e8i	−0.0907626	+	0.157205i	−0.907832	−	0.419334i	$-0.862264\pi$
$563$	−3.84314e8	+	6.65652e8i	−0.0907626	+	0.157205i	0.817070	+	0.576539i	$0.195597\pi$
$564$		0			0
$565$	−9.14240e8	+	1.58351e9i	−0.213251	+	0.369361i
$566$	−1.71194e8	+	2.96516e8i	−0.0396854	+	0.0687371i
$567$		0			0
$568$	1.30997e9	−	2.26894e9i	0.299946	−	0.519522i
$569$	−1.20637e9	−	2.08949e9i	−0.274527	−	0.475496i	0.695488	−	0.718537i	$-0.255188\pi$
$569$	−1.20637e9	−	2.08949e9i	−0.274527	−	0.475496i	−0.970016	+	0.243042i	$0.921855\pi$
$570$		0			0
$571$	−7.10355e9			−1.59680			−0.798398	−	0.602131i	$-0.794319\pi$
$571$	−7.10355e9			−1.59680			−0.798398	+	0.602131i	$0.794319\pi$
$572$	3.87022e8	−	2.77161e8i	0.0864669	−	0.0619221i
$573$		0			0
$574$	−1.18460e9	−	2.05178e9i	−0.261444	−	0.452834i
$575$	−3.42721e9	−	5.93610e9i	−0.751801	−	1.30216i
$576$		0			0
$577$	5.26146e9			1.14023			0.570113	−	0.821566i	$-0.306899\pi$
$577$	5.26146e9			1.14023			0.570113	+	0.821566i	$0.306899\pi$
$578$	7.33564e8	−	1.27057e9i	0.158012	−	0.273685i
$579$		0			0
$580$	2.43894e8			0.0519042
$581$	2.57503e8	−	4.46009e8i	0.0544712	−	0.0943468i
$582$		0			0
$583$	7.43274e7	+	1.28739e8i	0.0155349	+	0.0269073i
$584$	−4.44991e8			−0.0924498
$585$		0			0
$586$	−1.74227e8			−0.0357664
$587$	4.86843e9	+	8.43236e9i	0.993471	+	1.72074i	0.595535	+	0.803329i	$0.296940\pi$
$587$	4.86843e9	+	8.43236e9i	0.993471	+	1.72074i	0.397936	+	0.917413i	$0.369727\pi$
$588$		0			0
$589$	−3.51846e9	+	6.09415e9i	−0.709495	+	1.22888i
$590$	1.56099e8			0.0312910
$591$		0			0
$592$	−1.24196e8	+	2.15114e8i	−0.0246027	+	0.0426131i
$593$	5.73551e9			1.12949			0.564743	−	0.825267i	$-0.308975\pi$
$593$	5.73551e9			1.12949			0.564743	+	0.825267i	$0.308975\pi$
$594$		0			0
$595$	2.72317e8	+	4.71666e8i	0.0529986	+	0.0917963i
$596$	−9.34878e8	−	1.61926e9i	−0.180881	−	0.313295i
$597$		0			0
$598$	5.86939e8	+	5.97766e9i	0.112238	+	1.14308i
$599$	5.85413e9			1.11293			0.556466	−	0.830871i	$-0.312157\pi$
$599$	5.85413e9			1.11293			0.556466	+	0.830871i	$0.312157\pi$
$600$		0			0
$601$	4.46705e9	+	7.73716e9i	0.839383	+	1.45385i	0.890411	+	0.455156i	$0.150417\pi$
$601$	4.46705e9	+	7.73716e9i	0.839383	+	1.45385i	−0.0510287	+	0.998697i	$0.516250\pi$
$602$	−1.09017e9	+	1.88823e9i	−0.203660	+	0.352750i
$603$		0			0
$604$	−9.43344e8	+	1.63392e9i	−0.174197	+	0.301718i
$605$	−7.08894e8	+	1.22784e9i	−0.130148	+	0.225423i
$606$		0			0
$607$	6.59439e8	−	1.14218e9i	0.119678	−	0.207288i	−0.799962	−	0.600050i	$-0.795147\pi$
$607$	6.59439e8	−	1.14218e9i	0.119678	−	0.207288i	0.919640	+	0.392762i	$0.128480\pi$
$608$	4.54536e8	+	7.87280e8i	0.0820174	+	0.142058i
$609$		0			0
$610$	−2.31857e8			−0.0413586
$611$	−3.00950e9	+	2.15521e9i	−0.533766	+	0.382249i
$612$		0			0
$613$	−2.71562e9	−	4.70358e9i	−0.476164	−	0.824740i	0.523463	−	0.852048i	$-0.324640\pi$
$613$	−2.71562e9	−	4.70358e9i	−0.476164	−	0.824740i	−0.999627	+	0.0273080i	$0.991307\pi$
$614$	−2.89117e8	−	5.00766e8i	−0.0504063	−	0.0873062i
$615$		0			0
$616$	2.28083e8			0.0393152
$617$	−4.03201e9	+	6.98365e9i	−0.691073	+	1.19697i	0.280414	+	0.959879i	$0.409528\pi$
$617$	−4.03201e9	+	6.98365e9i	−0.691073	+	1.19697i	−0.971487	+	0.237094i	$0.923805\pi$
$618$		0			0
$619$	−9.26368e9			−1.56988			−0.784940	−	0.619572i	$-0.787306\pi$
$619$	−9.26368e9			−1.56988			−0.784940	+	0.619572i	$0.787306\pi$
$620$	−6.18521e8	+	1.07131e9i	−0.104228	+	0.180528i
$621$		0			0
$622$	1.35306e9	+	2.34356e9i	0.225450	+	0.390490i
$623$	−4.00407e9			−0.663428
$624$		0			0
$625$	4.77626e9			0.782542
$626$	1.47768e9	+	2.55941e9i	0.240751	+	0.416994i
$627$		0			0
$628$	1.25134e9	−	2.16739e9i	0.201612	−	0.349203i
$629$	−9.13569e8			−0.146374
$630$		0			0
$631$	−2.00624e9	+	3.47491e9i	−0.317893	+	0.550606i	−0.980048	−	0.198760i	$-0.936308\pi$
$631$	−2.00624e9	+	3.47491e9i	−0.317893	+	0.550606i	0.662156	+	0.749366i	$0.269642\pi$
$632$	2.04603e9			0.322405
$633$		0			0
$634$	−4.00396e9	−	6.93506e9i	−0.623990	−	1.08078i
$635$	1.33493e9	+	2.31217e9i	0.206896	+	0.358354i
$636$		0			0
$637$	−4.31749e9	−	1.95779e9i	−0.661825	−	0.300108i
$638$	3.75658e8			0.0572691
$639$		0			0
$640$	7.99043e7	+	1.38398e8i	0.0120487	+	0.0208690i
$641$	2.37881e9	−	4.12023e9i	0.356745	−	0.617900i	−0.630670	−	0.776051i	$-0.717220\pi$
$641$	2.37881e9	−	4.12023e9i	0.356745	−	0.617900i	0.987415	+	0.158151i	$0.0505533\pi$
$642$		0			0
$643$	4.29324e9	−	7.43611e9i	0.636864	−	1.10308i	−0.349253	−	0.937028i	$-0.613565\pi$
$643$	4.29324e9	−	7.43611e9i	0.636864	−	1.10308i	0.986117	−	0.166052i	$-0.0531020\pi$
$644$	−1.43894e9	+	2.49232e9i	−0.212297	+	0.367709i
$645$		0			0
$646$	−1.67175e9	+	2.89556e9i	−0.243982	+	0.422589i
$647$	2.18039e9	+	3.77654e9i	0.316496	+	0.548187i	0.979754	−	0.200203i	$-0.0641602\pi$
$647$	2.18039e9	+	3.77654e9i	0.316496	+	0.548187i	−0.663258	+	0.748391i	$0.730827\pi$
$648$		0			0
$649$	2.40433e8			0.0345252
$650$	−4.17382e9	−	1.89264e9i	−0.596124	−	0.270316i
$651$		0			0
$652$	2.09928e9	+	3.63605e9i	0.296622	+	0.513764i
$653$	2.68949e9	+	4.65834e9i	0.377985	+	0.654688i	0.990769	−	0.135562i	$-0.0432839\pi$
$653$	2.68949e9	+	4.65834e9i	0.377985	+	0.654688i	−0.612784	+	0.790250i	$0.709951\pi$
$654$		0			0
$655$	−2.33177e9			−0.324221
$656$	1.27841e9	−	2.21427e9i	0.176810	−	0.306243i
$657$		0			0
$658$	−1.77359e9			−0.242695
$659$	−2.78007e9	+	4.81522e9i	−0.378405	+	0.655417i	−0.990830	−	0.135112i	$-0.956861\pi$
$659$	−2.78007e9	+	4.81522e9i	−0.378405	+	0.655417i	0.612425	+	0.790528i	$0.290194\pi$
$660$		0			0
$661$	2.91890e9	+	5.05568e9i	0.393110	+	0.680886i	0.992858	−	0.119303i	$-0.0380660\pi$
$661$	2.91890e9	+	5.05568e9i	0.393110	+	0.680886i	−0.599748	+	0.800189i	$0.704733\pi$
$662$	5.82198e9			0.779952
$663$		0			0
$664$	5.55792e8			0.0736756
$665$	5.01487e8	+	8.68601e8i	0.0661278	+	0.114537i
$666$		0			0
$667$	−2.36997e9	+	4.10492e9i	−0.309245	+	0.535629i
$668$	2.16935e9			0.281587
$669$		0			0
$670$	−1.40661e8	+	2.43632e8i	−0.0180681	+	0.0312949i
$671$	−3.57118e8			−0.0456335
$672$		0			0
$673$	1.56288e8	+	2.70700e8i	0.0197640	+	0.0342322i	0.875738	−	0.482786i	$-0.160375\pi$
$673$	1.56288e8	+	2.70700e8i	0.0197640	+	0.0342322i	−0.855974	+	0.517018i	$0.827042\pi$
$674$	3.07662e9	+	5.32886e9i	0.387048	+	0.670386i
$675$		0			0
$676$	2.64606e9	+	3.02090e9i	0.329448	+	0.376117i
$677$	9.46393e9			1.17223			0.586113	−	0.810229i	$-0.300657\pi$
$677$	9.46393e9			1.17223			0.586113	+	0.810229i	$0.300657\pi$
$678$		0			0
$679$	−1.86478e9	−	3.22989e9i	−0.228604	−	0.395953i
$680$	−2.93882e8	+	5.09019e8i	−0.0358420	+	0.0620801i
$681$		0			0
$682$	−9.52678e8	+	1.65009e9i	−0.115001	+	0.199187i
$683$	−7.62828e9	+	1.32126e10i	−0.916124	+	1.58677i	−0.110876	+	0.993834i	$0.535366\pi$
$683$	−7.62828e9	+	1.32126e10i	−0.916124	+	1.58677i	−0.805248	+	0.592939i	$0.797968\pi$
$684$		0			0
$685$	3.86336e8	−	6.69153e8i	0.0459248	−	0.0795442i
$686$	−2.69856e9	−	4.67404e9i	−0.319152	−	0.552787i
$687$		0			0
$688$	−2.35300e9			−0.275463
$689$	−1.01960e9	+	7.30174e8i	−0.118758	+	0.0850470i
$690$		0			0
$691$	1.44704e8	+	2.50634e8i	0.0166842	+	0.0288980i	0.874247	−	0.485481i	$-0.161356\pi$
$691$	1.44704e8	+	2.50634e8i	0.0166842	+	0.0288980i	−0.857563	+	0.514379i	$0.828022\pi$
$692$	2.05164e8	+	3.55355e8i	0.0235359	+	0.0407653i
$693$		0			0
$694$	−2.05576e9			−0.233461
$695$	−1.50936e9	+	2.61429e9i	−0.170548	+	0.295398i
$696$		0			0
$697$	9.40377e9			1.05193
$698$	−1.53880e9	+	2.66529e9i	−0.171273	+	0.296654i
$699$		0			0
$700$	−1.09791e9	−	1.90164e9i	−0.120983	−	0.209549i
$701$	1.67473e10			1.83625			0.918125	−	0.396291i	$-0.129703\pi$
$701$	1.67473e10			1.83625			0.918125	+	0.396291i	$0.129703\pi$
$702$		0			0
$703$	−1.68239e9			−0.182635
$704$	1.23073e8	+	2.13168e8i	0.0132941	+	0.0230260i
$705$		0			0
$706$	−2.39205e9	+	4.14315e9i	−0.255831	+	0.443113i
$707$	2.68939e9			0.286210
$708$		0			0
$709$	3.83389e9	−	6.64049e9i	0.403996	−	0.699742i	−0.590208	−	0.807251i	$-0.700954\pi$
$709$	3.83389e9	−	6.64049e9i	0.403996	−	0.699742i	0.994204	+	0.107509i	$0.0342875\pi$
$710$	3.11948e9			0.327098
$711$		0			0
$712$	−2.16058e9	−	3.74224e9i	−0.224332	−	0.388554i
$713$	−1.20206e10	−	2.08203e10i	−1.24198	−	2.15117i
$714$		0			0
$715$	5.16201e8	+	2.34074e8i	0.0528138	+	0.0239487i
$716$	−2.02367e9			−0.206036
$717$		0			0
$718$	1.45427e9	+	2.51887e9i	0.146626	+	0.253963i
$719$	−7.06141e9	+	1.22307e10i	−0.708501	+	1.22716i	0.256912	+	0.966435i	$0.417295\pi$
$719$	−7.06141e9	+	1.22307e10i	−0.708501	+	1.22716i	−0.965413	+	0.260725i	$0.916039\pi$
$720$		0			0
$721$	3.69327e9	−	6.39692e9i	0.366976	−	0.635620i
$722$	4.96859e8	−	8.60584e8i	0.0491307	−	0.0850968i
$723$		0			0
$724$	−3.62846e9	+	6.28467e9i	−0.355334	+	0.615457i
$725$	−1.80829e9	−	3.13205e9i	−0.176232	−	0.305243i
$726$		0			0
$727$	−1.28421e9			−0.123956			−0.0619778	−	0.998078i	$-0.519741\pi$
$727$	−1.28421e9			−0.123956			−0.0619778	+	0.998078i	$0.519741\pi$
$728$	1.88027e8	+	1.91496e9i	0.0180618	+	0.183950i
$729$		0			0
$730$	−2.64918e8	−	4.58851e8i	−0.0252047	−	0.0436558i
$731$	−4.32709e9	−	7.49473e9i	−0.409718	−	0.709652i
$732$		0			0
$733$	−9.85736e9			−0.924478			−0.462239	−	0.886755i	$-0.652954\pi$
$733$	−9.85736e9			−0.924478			−0.462239	+	0.886755i	$0.652954\pi$
$734$	4.92841e9	−	8.53625e9i	0.460013	−	0.796767i
$735$		0			0
$736$	−3.10580e9			−0.287144
$737$	−2.16654e8	+	3.75255e8i	−0.0199356	+	0.0345295i
$738$		0			0
$739$	−5.09322e9	−	8.82171e9i	−0.464234	−	0.804076i	0.534933	−	0.844895i	$-0.320337\pi$
$739$	−5.09322e9	−	8.82171e9i	−0.464234	−	0.804076i	−0.999167	+	0.0408181i	$0.987004\pi$
$740$	−2.95752e8			−0.0268298
$741$		0			0
$742$	−6.00880e8			−0.0539976
$743$	1.03270e10	+	1.78869e10i	0.923663	+	1.59983i	0.793697	+	0.608313i	$0.208154\pi$
$743$	1.03270e10	+	1.78869e10i	0.923663	+	1.59983i	0.129966	+	0.991518i	$0.458513\pi$
$744$		0			0
$745$	1.11313e9	−	1.92799e9i	0.0986275	−	0.170828i
$746$	−1.08040e10			−0.952793
$747$		0			0
$748$	−4.52653e8	+	7.84017e8i	−0.0395466	+	0.0684968i
$749$	−7.90854e9			−0.687717
$750$		0			0
$751$	1.16401e8	+	2.01613e8i	0.0100281	+	0.0173692i	0.870996	−	0.491290i	$-0.163475\pi$
$751$	1.16401e8	+	2.01613e8i	0.0100281	+	0.0173692i	−0.860968	+	0.508659i	$0.830141\pi$
$752$	−9.57020e8	−	1.65761e9i	−0.0820651	−	0.142141i
$753$		0			0
$754$	3.09685e8	+	3.15398e9i	0.0263100	+	0.267953i
$755$	−2.24641e9			−0.189966
$756$		0			0
$757$	5.05884e9	+	8.76216e9i	0.423853	+	0.734135i	0.996313	−	0.0857982i	$-0.0273440\pi$
$757$	5.05884e9	+	8.76216e9i	0.423853	+	0.734135i	−0.572460	+	0.819933i	$0.694011\pi$
$758$	3.31617e8	−	5.74378e8i	0.0276564	−	0.0479022i
$759$		0			0
$760$	−5.41201e8	+	9.37388e8i	−0.0447210	+	0.0774590i
$761$	3.28760e9	−	5.69429e9i	0.270416	−	0.468375i	−0.698552	−	0.715559i	$-0.746172\pi$
$761$	3.28760e9	−	5.69429e9i	0.270416	−	0.468375i	0.968968	+	0.247184i	$0.0795054\pi$
$762$		0			0
$763$	−2.32161e9	+	4.02115e9i	−0.189214	+	0.327729i
$764$	−7.80290e8	−	1.35150e9i	−0.0633037	−	0.109645i
$765$		0			0
$766$	1.14621e10			0.921430
$767$	1.98208e8	+	2.01864e9i	0.0158613	+	0.161538i
$768$		0			0
$769$	4.72051e9	+	8.17617e9i	0.374323	+	0.648347i	0.990226	−	0.139476i	$-0.0445417\pi$
$769$	4.72051e9	+	8.17617e9i	0.374323	+	0.648347i	−0.615902	+	0.787823i	$0.711208\pi$
$770$	1.35785e8	+	2.35187e8i	0.0107185	+	0.0185651i
$771$		0			0
$772$	2.90578e8			0.0227302
$773$	1.04407e10	−	1.80837e10i	0.813017	−	1.40819i	−0.0977268	−	0.995213i	$-0.531157\pi$
$773$	1.04407e10	−	1.80837e10i	0.813017	−	1.40819i	0.910743	−	0.412973i	$-0.135510\pi$
$774$		0			0
$775$	1.83435e10			1.41555
$776$	2.01246e9	−	3.48568e9i	0.154600	−	0.267776i
$777$		0			0
$778$	−4.79553e9	−	8.30610e9i	−0.365097	−	0.632366i
$779$	1.73176e10			1.31252
$780$		0			0
$781$	4.80479e9			0.360907
$782$	−5.71144e9	−	9.89251e9i	−0.427093	−	0.739746i
$783$		0			0
$784$	1.22565e9	−	2.12288e9i	0.0908362	−	0.157333i
$785$	2.97986e9			0.219863
$786$		0			0
$787$	9.17201e9	−	1.58864e10i	0.670738	−	1.16175i	−0.306957	−	0.951723i	$-0.599311\pi$
$787$	9.17201e9	−	1.58864e10i	0.670738	−	1.16175i	0.977695	−	0.210029i	$-0.0673558\pi$
$788$	2.07800e8			0.0151288
$789$		0			0
$790$	1.21807e9	+	2.10976e9i	0.0878975	+	0.152243i
$791$	−5.69195e9	−	9.85875e9i	−0.408925	−	0.708278i
$792$		0			0
$793$	−2.94402e8	−	2.99832e9i	−0.0209645	−	0.213512i
$794$	−1.43359e10			−1.01637
$795$		0			0
$796$	−1.71205e9	−	2.96535e9i	−0.120315	−	0.208392i
$797$	4.35075e9	−	7.53572e9i	0.304411	−	0.527255i	−0.672719	−	0.739898i	$-0.734874\pi$
$797$	4.35075e9	−	7.53572e9i	0.304411	−	0.527255i	0.977130	+	0.212643i	$0.0682071\pi$
$798$		0			0
$799$	3.51985e9	−	6.09656e9i	0.244124	−	0.422835i
$800$	1.18486e9	−	2.05224e9i	0.0818187	−	0.141714i
$801$		0			0
$802$	4.62930e9	−	8.01818e9i	0.316887	−	0.548865i
$803$	−4.08040e8	−	7.06747e8i	−0.0278099	−	0.0481681i
$804$		0			0
$805$	−3.42661e9			−0.231515
$806$	−1.46393e10	−	6.63827e9i	−0.984799	−	0.446562i
$807$		0			0
$808$	1.45118e9	+	2.51352e9i	0.0967793	+	0.167627i
$809$	−2.27116e9	−	3.93376e9i	−0.150809	−	0.261209i	0.780716	−	0.624886i	$-0.214855\pi$
$809$	−2.27116e9	−	3.93376e9i	−0.150809	−	0.261209i	−0.931525	+	0.363677i	$0.881521\pi$
$810$		0			0
$811$	1.79325e10			1.18051			0.590253	−	0.807219i	$-0.299028\pi$
$811$	1.79325e10			1.18051			0.590253	+	0.807219i	$0.299028\pi$
$812$	−7.59227e8	+	1.31502e9i	−0.0497652	+	0.0861958i
$813$		0			0
$814$	−4.55534e8			−0.0296029
$815$	−2.49954e9	+	4.32933e9i	−0.161736	+	0.280136i
$816$		0			0
$817$	−7.96859e9	−	1.38020e10i	−0.511216	−	0.885451i
$818$	−1.00739e10			−0.643521
$819$		0			0
$820$	3.04431e9			0.192815
$821$	−9.03896e9	−	1.56559e10i	−0.570056	−	0.987366i	−0.996560	−	0.0828798i	$-0.973588\pi$
$821$	−9.03896e9	−	1.56559e10i	−0.570056	−	0.987366i	0.426504	−	0.904486i	$-0.359745\pi$
$822$		0			0
$823$	−6.89144e9	+	1.19363e10i	−0.430934	+	0.746399i	−0.996954	−	0.0779924i	$-0.975149\pi$
$823$	−6.89144e9	+	1.19363e10i	−0.430934	+	0.746399i	0.566020	+	0.824391i	$0.308482\pi$
$824$	7.97149e9			0.496357
$825$		0			0
$826$	−4.85928e8	+	8.41652e8i	−0.0300014	+	0.0519640i
$827$	−3.70262e9			−0.227636			−0.113818	−	0.993502i	$-0.536308\pi$
$827$	−3.70262e9			−0.227636			−0.113818	+	0.993502i	$0.536308\pi$
$828$		0			0
$829$	−5.58069e9	−	9.66604e9i	−0.340210	−	0.589261i	0.644261	−	0.764805i	$-0.277165\pi$
$829$	−5.58069e9	−	9.66604e9i	−0.340210	−	0.589261i	−0.984472	+	0.175544i	$0.943832\pi$
$830$	3.30881e8	+	5.73103e8i	0.0200862	+	0.0347904i
$831$		0			0
$832$	−1.68828e9	+	1.20904e9i	−0.101628	+	0.0727793i
$833$	9.01568e9			0.540432
$834$		0			0
$835$	1.29149e9	+	2.23692e9i	0.0767693	+	0.132968i
$836$	−8.33587e8	+	1.44381e9i	−0.0493434	+	0.0854652i
$837$		0			0
$838$	−5.46566e9	+	9.46680e9i	−0.320840	+	0.555711i
$839$	1.40162e10	−	2.42768e10i	0.819339	−	1.41914i	−0.0868313	−	0.996223i	$-0.527674\pi$
$839$	1.40162e10	−	2.42768e10i	0.819339	−	1.41914i	0.906170	−	0.422913i	$-0.138993\pi$
$840$		0			0
$841$	7.37447e9	−	1.27730e10i	0.427509	−	0.740467i
$842$	5.86488e9	+	1.01583e10i	0.338584	+	0.586445i
$843$		0			0
$844$	−1.17056e10			−0.670183
$845$	−1.53971e9	+	4.52692e9i	−0.0877891	+	0.258110i
$846$		0			0
$847$	−4.41349e9	−	7.64440e9i	−0.249569	−	0.432266i
$848$	−3.24233e8	−	5.61587e8i	−0.0182588	−	0.0316251i
$849$		0			0
$850$	8.71566e9			0.486781
$851$	2.87390e9	−	4.97773e9i	0.159852	−	0.276872i
$852$		0			0
$853$	2.14218e10			1.18177			0.590887	−	0.806754i	$-0.298778\pi$
$853$	2.14218e10			1.18177			0.590887	+	0.806754i	$0.298778\pi$
$854$	7.21757e8	−	1.25012e9i	0.0396541	−	0.0686830i
$855$		0			0
$856$	−4.26742e9	−	7.39138e9i	−0.232545	−	0.402780i
$857$	−1.22735e10			−0.666093			−0.333047	−	0.942910i	$-0.608077\pi$
$857$	−1.22735e10			−0.666093			−0.333047	+	0.942910i	$0.608077\pi$
$858$		0			0
$859$	5.90261e9			0.317737			0.158869	−	0.987300i	$-0.449215\pi$
$859$	5.90261e9			0.317737			0.158869	+	0.987300i	$0.449215\pi$
$860$	−1.40082e9	−	2.42629e9i	−0.0750997	−	0.130076i
$861$		0			0
$862$	7.20693e9	−	1.24828e10i	0.383244	−	0.663797i
$863$	1.69052e10			0.895329			0.447664	−	0.894202i	$-0.352256\pi$
$863$	1.69052e10			0.895329			0.447664	+	0.894202i	$0.352256\pi$
$864$		0			0
$865$	−2.44282e8	+	4.23109e8i	−0.0128332	+	0.0222278i
$866$	8.61700e7			0.00450862
$867$		0			0
$868$	−3.85084e9	−	6.66985e9i	−0.199865	−	0.346176i
$869$	1.87613e9	+	3.24956e9i	0.0969827	+	0.167979i
$870$		0			0
$871$	−3.32920e9	−	1.50965e9i	−0.170717	−	0.0774126i
$872$	−5.01094e9			−0.255924
$873$		0			0
$874$	−1.05180e10	−	1.82176e10i	−0.532895	−	0.923001i
$875$	2.71947e9	−	4.71025e9i	0.137232	−	0.237693i
$876$		0			0
$877$	9.59918e9	−	1.66263e10i	0.480547	−	0.832331i	−0.519204	−	0.854650i	$-0.673772\pi$
$877$	9.59918e9	−	1.66263e10i	0.480547	−	0.832331i	0.999751	+	0.0223189i	$0.00710490\pi$
$878$	−1.37659e10	+	2.38432e10i	−0.686393	+	1.18887i
$879$		0			0
$880$	−1.46539e8	+	2.53812e8i	−0.00724875	+	0.0125552i
$881$	−9.77828e9	−	1.69365e10i	−0.481778	−	0.834464i	0.518003	−	0.855379i	$-0.326675\pi$
$881$	−9.77828e9	−	1.69365e10i	−0.481778	−	0.834464i	−0.999781	+	0.0209149i	$0.993342\pi$
$882$		0			0
$883$	−2.35704e10			−1.15214			−0.576069	−	0.817401i	$-0.695414\pi$
$883$	−2.35704e10			−1.15214			−0.576069	+	0.817401i	$0.695414\pi$
$884$	−6.95567e9	−	3.15409e9i	−0.338654	−	0.153564i
$885$		0			0
$886$	5.57986e9	+	9.66460e9i	0.269529	+	0.466838i
$887$	1.57524e10	+	2.72840e10i	0.757906	+	1.31273i	0.943917	+	0.330183i	$0.107111\pi$
$887$	1.57524e10	+	2.72840e10i	0.757906	+	1.31273i	−0.186011	+	0.982548i	$0.559556\pi$
$888$		0			0
$889$	−1.66223e10			−0.793478
$890$	2.57253e9	−	4.45576e9i	0.122320	−	0.211864i
$891$		0			0
$892$	−1.39138e10			−0.656401
$893$	6.48201e9	−	1.12272e10i	0.304600	−	0.527583i
$894$		0			0
$895$	−1.20476e9	−	2.08670e9i	−0.0561719	−	0.0972925i
$896$	−9.94949e8			−0.0462086
$897$		0			0
$898$	1.73357e10			0.798865
$899$	−6.34242e9	−	1.09854e10i	−0.291136	−	0.504262i
$900$		0			0
$901$	1.19250e9	−	2.06548e9i	0.0543154	−	0.0940770i
$902$	4.68901e9			0.212745
$903$		0			0
$904$	6.14271e9	−	1.06395e10i	0.276548	−	0.478995i
$905$	−8.64057e9			−0.387501
$906$		0			0
$907$	−9.02228e9	−	1.56270e10i	−0.401505	−	0.695427i	0.592403	−	0.805642i	$-0.298179\pi$
$907$	−9.02228e9	−	1.56270e10i	−0.401505	−	0.695427i	−0.993908	+	0.110215i	$0.964846\pi$
$908$	2.42349e9	+	4.19761e9i	0.107434	+	0.186081i
$909$		0			0
$910$	−1.86267e9	+	1.33392e9i	−0.0819389	+	0.0586794i
$911$	−9.87521e9			−0.432745			−0.216373	−	0.976311i	$-0.569423\pi$
$911$	−9.87521e9			−0.432745			−0.216373	+	0.976311i	$0.569423\pi$
$912$		0			0
$913$	5.09641e8	+	8.82724e8i	0.0221624	+	0.0383864i
$914$	−1.50682e10	+	2.60989e10i	−0.652754	+	1.13060i
$915$		0			0
$916$	1.54256e9	−	2.67179e9i	0.0663144	−	0.114860i
$917$	7.25867e9	−	1.25724e10i	0.310860	−	0.538425i
$918$		0			0
$919$	−8.87371e9	+	1.53697e10i	−0.377139	+	0.653223i	−0.990645	−	0.136467i	$-0.956425\pi$
$919$	−8.87371e9	+	1.53697e10i	−0.377139	+	0.653223i	0.613506	+	0.789690i	$0.289759\pi$
$920$	−1.84898e9	−	3.20253e9i	−0.0782845	−	0.135593i
$921$		0			0
$922$	−3.71554e9			−0.156122
$923$	3.96098e9	+	4.03404e10i	0.165805	+	1.68863i
$924$		0			0
$925$	2.19278e9	+	3.79801e9i	0.0910960	+	0.157783i
$926$	1.16027e10	+	2.00965e10i	0.480199	+	0.831729i
$927$		0			0
$928$	−1.63870e9			−0.0673105
$929$	4.97128e9	−	8.61051e9i	0.203429	−	0.352350i	−0.746202	−	0.665720i	$-0.768125\pi$
$929$	4.97128e9	−	8.61051e9i	0.203429	−	0.352350i	0.949631	+	0.313370i	$0.101458\pi$
$930$		0			0
$931$	1.66029e10			0.674311
$932$	−5.48130e9	+	9.49388e9i	−0.221783	+	0.384139i
$933$		0			0
$934$	−1.29403e10	−	2.24132e10i	−0.519672	−	0.900099i
$935$	−1.07792e9			−0.0431265
$936$		0			0
$937$	−2.07532e10			−0.824133			−0.412067	−	0.911154i	$-0.635193\pi$
$937$	−2.07532e10			−0.824133			−0.412067	+	0.911154i	$0.635193\pi$
$938$	−8.75740e8	−	1.51683e9i	−0.0346470	−	0.0600103i
$939$		0			0
$940$	1.13949e9	−	1.97366e9i	0.0447470	−	0.0775041i
$941$	3.69570e10			1.44588			0.722942	−	0.690909i	$-0.242790\pi$
$941$	3.69570e10			1.44588			0.722942	+	0.690909i	$0.242790\pi$
$942$		0			0
$943$	−2.95823e10	+	5.12381e10i	−1.14879	+	1.98976i
$944$	−1.04882e9			−0.0405788
$945$		0			0
$946$	−2.15762e9	−	3.73711e9i	−0.0828621	−	0.143521i
$947$	2.82048e9	+	4.88521e9i	0.107919	+	0.186921i	0.914927	−	0.403619i	$-0.132248\pi$
$947$	2.82048e9	+	4.88521e9i	0.107919	+	0.186921i	−0.807008	+	0.590540i	$0.798915\pi$
$948$		0			0
$949$	5.59738e9	−	4.00848e9i	0.212595	−	0.152247i
$950$	1.60504e10			0.607370
$951$		0			0
$952$	−1.82968e9	−	3.16909e9i	−0.0687297	−	0.119043i
$953$	8.70405e9	−	1.50759e10i	0.325759	−	0.564231i	−0.655907	−	0.754842i	$-0.727714\pi$
$953$	8.70405e9	−	1.50759e10i	0.325759	−	0.564231i	0.981666	+	0.190611i	$0.0610469\pi$
$954$		0			0
$955$	9.29065e8	−	1.60919e9i	0.0345171	−	0.0597854i
$956$	3.40951e8	−	5.90545e8i	0.0126209	−	0.0218600i
$957$		0			0
$958$	−1.03678e10	+	1.79576e10i	−0.380984	+	0.659884i
$959$	2.40528e9	+	4.16607e9i	0.0880644	+	0.152532i
$960$		0			0
$961$	3.68255e10			1.33849
$962$	−3.75533e8	−	3.82460e9i	−0.0135999	−	0.138508i
$963$		0			0
$964$	4.52544e9	+	7.83829e9i	0.162701	+	0.281807i
$965$	1.72991e8	+	2.99629e8i	0.00619695	+	0.0107334i
$966$		0			0
$967$	3.44861e8			0.0122646			0.00613228	−	0.999981i	$-0.498048\pi$
$967$	3.44861e8			0.0122646			0.00613228	+	0.999981i	$0.498048\pi$
$968$	4.76301e9	−	8.24977e9i	0.168779	−	0.292333i
$969$		0			0
$970$	4.79233e9			0.168595
$971$	−5.91506e9	+	1.02452e10i	−0.207344	+	0.359131i	−0.950877	−	0.309569i	$-0.899815\pi$
$971$	−5.91506e9	+	1.02452e10i	−0.207344	+	0.359131i	0.743533	+	0.668699i	$0.233149\pi$
$972$		0			0
$973$	−9.39712e9	−	1.62763e10i	−0.327039	−	0.566449i
$974$	−2.73897e10			−0.949798
$975$		0			0
$976$	1.55783e9			0.0536347
$977$	2.35225e10	+	4.07422e10i	0.806961	+	1.39770i	0.914959	+	0.403547i	$0.132223\pi$
$977$	2.35225e10	+	4.07422e10i	0.806961	+	1.39770i	−0.107998	+	0.994151i	$0.534444\pi$
$978$		0			0
$979$	3.96235e9	−	6.86300e9i	0.134963	−	0.233762i
$980$	2.91867e9			0.0990590
$981$		0			0
$982$	−3.72410e9	+	6.45033e9i	−0.125496	+	0.217366i
$983$	−6.84160e9			−0.229731			−0.114866	−	0.993381i	$-0.536644\pi$
$983$	−6.84160e9			−0.229731			−0.114866	+	0.993381i	$0.536644\pi$
$984$		0			0
$985$	1.23710e8	+	2.14273e8i	0.00412458	+	0.00714398i
$986$	−3.01352e9	−	5.21956e9i	−0.100116	−	0.173406i
$987$		0			0
$988$	−1.28093e10	−	5.80844e9i	−0.422547	−	0.191606i
$989$	5.44485e10			1.78978
$990$		0			0
$991$	1.06550e10	+	1.84550e10i	0.347774	+	0.602362i	0.985854	−	0.167608i	$-0.0536044\pi$
$991$	1.06550e10	+	1.84550e10i	0.347774	+	0.602362i	−0.638080	+	0.769970i	$0.720271\pi$
$992$	4.15579e9	−	7.19805e9i	0.135165	−	0.234112i
$993$		0			0
$994$	−9.71076e9	+	1.68195e10i	−0.313618	+	0.543202i
$995$	2.03848e9	−	3.53075e9i	0.0656032	−	0.113628i
$996$		0			0
$997$	−5.83424e9	+	1.01052e10i	−0.186445	+	0.322932i	−0.944063	−	0.329766i	$-0.893030\pi$
$997$	−5.83424e9	+	1.01052e10i	−0.186445	+	0.322932i	0.757617	+	0.652699i	$0.226363\pi$
$998$	−4.76068e9	−	8.24574e9i	−0.151605	−	0.262587i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.8.h.c.55.2		8
3.2	odd	2		78.8.e.a.55.3	✓	8
13.9	even	3	inner	234.8.h.c.217.2		8
39.35	odd	6		78.8.e.a.61.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.8.e.a.55.3	✓	8	3.2	odd	2
78.8.e.a.61.3	yes	8	39.35	odd	6
234.8.h.c.55.2		8	1.1	even	1	trivial
234.8.h.c.217.2		8	13.9	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	234.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} -76.2027 q^{5} +(237.214 - 410.867i) q^{7} +512.000 q^{8} +(304.811 + 527.947i) q^{10} +(469.485 + 813.173i) q^{11} +(-6440.26 + 4612.11i) q^{13} -3795.43 q^{14} +(-2048.00 - 3547.24i) q^{16} +(7532.39 - 13046.5i) q^{17} +(13871.3 - 24025.9i) q^{19} +(2438.48 - 4223.58i) q^{20} +(3755.88 - 6505.38i) q^{22} +(47390.7 + 82083.1i) q^{23} -72318.2 q^{25} +(57714.7 + 26171.0i) q^{26} +(15181.7 + 26295.5i) q^{28} +(25004.6 + 43309.3i) q^{29} -253650. q^{31} +(-16384.0 + 28377.9i) q^{32} -120518. q^{34} +(-18076.4 + 31309.2i) q^{35} +(-30321.3 - 52518.1i) q^{37} -221942. q^{38} -39015.8 q^{40} +(312111. + 540592. i) q^{41} +(287232. - 497500. i) q^{43} -60094.1 q^{44} +(379125. - 656664. i) q^{46} +467295. q^{47} +(299230. + 518282. i) q^{49} +(289273. + 501035. i) q^{50} +(-49540.5 - 504543. i) q^{52} +158317. q^{53} +(-35776.0 - 61965.9i) q^{55} +(121454. - 210364. i) q^{56} +(200037. - 346474. i) q^{58} +(128030. - 221754. i) q^{59} +(-190165. + 329375. i) q^{61} +(1.01460e6 + 1.75734e6i) q^{62} +262144. q^{64} +(490765. - 351455. i) q^{65} +(230735. + 399645. i) q^{67} +(482073. + 834975. i) q^{68} +289222. q^{70} +(2.55854e6 - 4.43152e6i) q^{71} -869122. q^{73} +(-242571. + 420145. i) q^{74} +(887766. + 1.53766e6i) q^{76} +445475. q^{77} +3.99615e6 q^{79} +(156063. + 270309. i) q^{80} +(2.49689e6 - 4.32474e6i) q^{82} +1.08553e6 q^{83} +(-573988. + 994177. i) q^{85} -4.59571e6 q^{86} +(240377. + 416344. i) q^{88} +(-4.21989e6 - 7.30906e6i) q^{89} +(367241. + 3.74015e6i) q^{91} -6.06601e6 q^{92} +(-1.86918e6 - 3.23752e6i) q^{94} +(-1.05703e6 + 1.83084e6i) q^{95} +(3.93058e6 - 6.80796e6i) q^{97} +(2.39384e6 - 4.14625e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} - 256 q^{4} + 386 q^{5} + 757 q^{7} + 4096 q^{8} - 1544 q^{10} - 4524 q^{11} + 13272 q^{13} - 12112 q^{14} - 16384 q^{16} + 12775 q^{17} + 38646 q^{19} - 12352 q^{20} - 36192 q^{22} - 24428 q^{23}+ \cdots + 4224696 q^{98}+O(q^{100}) \) 8 * q - 32 * q^2 - 256 * q^4 + 386 * q^5 + 757 * q^7 + 4096 * q^8 - 1544 * q^10 - 4524 * q^11 + 13272 * q^13 - 12112 * q^14 - 16384 * q^16 + 12775 * q^17 + 38646 * q^19 - 12352 * q^20 - 36192 * q^22 - 24428 * q^23 + 305798 * q^25 - 90552 * q^26 + 48448 * q^28 - 22109 * q^29 + 42558 * q^31 - 131072 * q^32 - 204400 * q^34 + 190892 * q^35 + 372411 * q^37 - 618336 * q^38 + 197632 * q^40 - 266009 * q^41 - 399935 * q^43 + 579072 * q^44 - 195424 * q^46 + 487344 * q^47 + 528087 * q^49 - 1223192 * q^50 - 124992 * q^52 - 3351434 * q^53 - 1572842 * q^55 + 387584 * q^56 - 176872 * q^58 - 1025370 * q^59 + 260650 * q^61 - 170232 * q^62 + 2097152 * q^64 + 59673 * q^65 - 2382807 * q^67 + 817600 * q^68 - 3054272 * q^70 - 1773980 * q^71 - 3903260 * q^73 + 2979288 * q^74 + 2473344 * q^76 - 17541708 * q^77 + 11678674 * q^79 - 790528 * q^80 - 2128072 * q^82 + 20314044 * q^83 - 5236237 * q^85 + 6398960 * q^86 - 2316288 * q^88 + 1108942 * q^89 - 29498671 * q^91 + 3126784 * q^92 - 1949376 * q^94 - 10481054 * q^95 - 7003183 * q^97 + 4224696 * q^98

Introduction

L-functions

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