LMFDB - Embedded newform 624.4.bc.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(31,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("624.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 557 x^{12} + 114776 x^{10} + 11098364 x^{8} + 523047796 x^{6} + 11529575940 x^{4} + \cdots + 338947524864 $ x^14 + 557x^12 + 114776x^10 + 11098364x^8 + 523047796x^6 + 11529575940x^4 + 106577215488x^2 + 338947524864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$10.9706i$ of defining polynomial
Character	$\chi$	$=$	624.31
Dual form			624.4.bc.a.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.00000i q^{3} +(-10.9706 + 10.9706i) q^{5} +(7.36979 - 7.36979i) q^{7} -9.00000 q^{9} +(36.0614 - 36.0614i) q^{11} +(-18.7699 + 42.9498i) q^{13} +(32.9118 + 32.9118i) q^{15} -3.63826i q^{17} +(-67.3749 - 67.3749i) q^{19} +(-22.1094 - 22.1094i) q^{21} +24.5391 q^{23} -115.708i q^{25} +27.0000i q^{27} -82.8379 q^{29} +(102.651 + 102.651i) q^{31} +(-108.184 - 108.184i) q^{33} +161.702i q^{35} +(215.409 + 215.409i) q^{37} +(128.850 + 56.3098i) q^{39} +(-20.3098 + 20.3098i) q^{41} -61.7745 q^{43} +(98.7354 - 98.7354i) q^{45} +(-163.317 + 163.317i) q^{47} +234.372i q^{49} -10.9148 q^{51} -551.555 q^{53} +791.230i q^{55} +(-202.125 + 202.125i) q^{57} +(-541.810 + 541.810i) q^{59} +391.345 q^{61} +(-66.3281 + 66.3281i) q^{63} +(-265.268 - 677.103i) q^{65} +(194.093 + 194.093i) q^{67} -73.6173i q^{69} +(289.844 + 289.844i) q^{71} +(629.772 + 629.772i) q^{73} -347.124 q^{75} -531.530i q^{77} +800.798i q^{79} +81.0000 q^{81} +(-96.9092 - 96.9092i) q^{83} +(39.9139 + 39.9139i) q^{85} +248.514i q^{87} +(444.922 + 444.922i) q^{89} +(178.201 + 454.862i) q^{91} +(307.954 - 307.954i) q^{93} +1478.28 q^{95} +(841.467 - 841.467i) q^{97} +(-324.552 + 324.552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} - 12 q^{7} - 126 q^{9} - 64 q^{11} + 32 q^{13} - 6 q^{15} - 84 q^{19} + 36 q^{21} - 384 q^{23} + 32 q^{29} - 140 q^{31} + 192 q^{33} - 466 q^{37} + 270 q^{39} - 98 q^{41} - 104 q^{43} - 18 q^{45}+ \cdots + 576 q^{99}+O(q^{100}) $ 14 * q + 2 * q^5 - 12 * q^7 - 126 * q^9 - 64 * q^11 + 32 * q^13 - 6 * q^15 - 84 * q^19 + 36 * q^21 - 384 * q^23 + 32 * q^29 - 140 * q^31 + 192 * q^33 - 466 * q^37 + 270 * q^39 - 98 * q^41 - 104 * q^43 - 18 * q^45 + 688 * q^47 + 156 * q^51 - 1612 * q^53 - 252 * q^57 - 1752 * q^59 + 1284 * q^61 + 108 * q^63 + 1566 * q^65 + 1260 * q^67 + 968 * q^71 + 838 * q^73 - 1434 * q^75 + 1134 * q^81 - 1688 * q^83 - 572 * q^85 - 2666 * q^89 - 412 * q^91 - 420 * q^93 - 816 * q^95 + 422 * q^97 + 576 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$		0			0
$5$	−10.9706	+	10.9706i	−0.981240	+	0.981240i	−0.999827	−	0.0185872i	$-0.994083\pi$
$5$	−10.9706	+	10.9706i	−0.981240	+	0.981240i	0.0185872	+	0.999827i	$0.494083\pi$
$6$		0			0
$7$	7.36979	−	7.36979i	0.397931	−	0.397931i	−0.479572	−	0.877503i	$-0.659208\pi$
$7$	7.36979	−	7.36979i	0.397931	−	0.397931i	0.877503	+	0.479572i	$0.159208\pi$
$8$		0			0
$9$	−9.00000			−0.333333
$10$		0			0
$11$	36.0614	−	36.0614i	0.988447	−	0.988447i	−0.0114873	−	0.999934i	$-0.503657\pi$
$11$	36.0614	−	36.0614i	0.988447	−	0.988447i	0.999934	+	0.0114873i	$0.00365660\pi$
$12$		0			0
$13$	−18.7699	+	42.9498i	−0.400450	+	0.916319i
$13$	−18.7699	+	42.9498i	−0.400450	+	0.916319i
$14$		0			0
$15$	32.9118	+	32.9118i	0.566519	+	0.566519i
$16$		0			0
$17$		−	3.63826i		−	0.0519064i	−0.999663	−	0.0259532i	$-0.991738\pi$
$17$		−	3.63826i		−	0.0519064i	0.999663	−	0.0259532i	$-0.00826208\pi$
$18$		0			0
$19$	−67.3749	−	67.3749i	−0.813519	−	0.813519i	0.171641	−	0.985160i	$-0.445093\pi$
$19$	−67.3749	−	67.3749i	−0.813519	−	0.813519i	−0.985160	+	0.171641i	$0.945093\pi$
$20$		0			0
$21$	−22.1094	−	22.1094i	−0.229746	−	0.229746i
$22$		0			0
$23$	24.5391			0.222468			0.111234	−	0.993794i	$-0.464520\pi$
$23$	24.5391			0.222468			0.111234	+	0.993794i	$0.464520\pi$
$24$		0			0
$25$		−	115.708i		−	0.925664i
$26$		0			0
$27$			27.0000i			0.192450i
$28$		0			0
$29$	−82.8379			−0.530435			−0.265218	−	0.964189i	$-0.585444\pi$
$29$	−82.8379			−0.530435			−0.265218	+	0.964189i	$0.585444\pi$
$30$		0			0
$31$	102.651	+	102.651i	0.594734	+	0.594734i	0.938906	−	0.344173i	$-0.111841\pi$
$31$	102.651	+	102.651i	0.594734	+	0.594734i	−0.344173	+	0.938906i	$0.611841\pi$
$32$		0			0
$33$	−108.184	−	108.184i	−0.570680	−	0.570680i
$34$		0			0
$35$			161.702i			0.780932i
$36$		0			0
$37$	215.409	+	215.409i	0.957107	+	0.957107i	0.999117	−	0.0420099i	$-0.0133761\pi$
$37$	215.409	+	215.409i	0.957107	+	0.957107i	−0.0420099	+	0.999117i	$0.513376\pi$
$38$		0			0
$39$	128.850	+	56.3098i	0.529037	+	0.231200i
$40$		0			0
$41$	−20.3098	+	20.3098i	−0.0773625	+	0.0773625i	−0.744729	−	0.667367i	$-0.767421\pi$
$41$	−20.3098	+	20.3098i	−0.0773625	+	0.0773625i	0.667367	+	0.744729i	$0.267421\pi$
$42$		0			0
$43$	−61.7745			−0.219082			−0.109541	−	0.993982i	$-0.534938\pi$
$43$	−61.7745			−0.219082			−0.109541	+	0.993982i	$0.534938\pi$
$44$		0			0
$45$	98.7354	−	98.7354i	0.327080	−	0.327080i
$46$		0			0
$47$	−163.317	+	163.317i	−0.506856	+	0.506856i	−0.913560	−	0.406704i	$-0.866678\pi$
$47$	−163.317	+	163.317i	−0.506856	+	0.506856i	0.406704	+	0.913560i	$0.366678\pi$
$48$		0			0
$49$			234.372i			0.683301i
$50$		0			0
$51$	−10.9148			−0.0299682
$52$		0			0
$53$	−551.555			−1.42947			−0.714735	−	0.699395i	$-0.753453\pi$
$53$	−551.555			−1.42947			−0.714735	+	0.699395i	$0.753453\pi$
$54$		0			0
$55$			791.230i			1.93981i
$56$		0			0
$57$	−202.125	+	202.125i	−0.469685	+	0.469685i
$58$		0			0
$59$	−541.810	+	541.810i	−1.19555	+	1.19555i	−0.220070	+	0.975484i	$0.570629\pi$
$59$	−541.810	+	541.810i	−1.19555	+	1.19555i	−0.975484	+	0.220070i	$0.929371\pi$
$60$		0			0
$61$	391.345			0.821419			0.410709	−	0.911766i	$-0.365281\pi$
$61$	391.345			0.821419			0.410709	+	0.911766i	$0.365281\pi$
$62$		0			0
$63$	−66.3281	+	66.3281i	−0.132644	+	0.132644i
$64$		0			0
$65$	−265.268	−	677.103i	−0.506191	−	1.29207i
$66$		0			0
$67$	194.093	+	194.093i	0.353914	+	0.353914i	0.861563	−	0.507650i	$-0.169486\pi$
$67$	194.093	+	194.093i	0.353914	+	0.353914i	−0.507650	+	0.861563i	$0.669486\pi$
$68$		0			0
$69$		−	73.6173i		−	0.128442i
$70$		0			0
$71$	289.844	+	289.844i	0.484480	+	0.484480i	0.906559	−	0.422079i	$-0.138699\pi$
$71$	289.844	+	289.844i	0.484480	+	0.484480i	−0.422079	+	0.906559i	$0.638699\pi$
$72$		0			0
$73$	629.772	+	629.772i	1.00972	+	1.00972i	0.999952	+	0.00976281i	$0.00310765\pi$
$73$	629.772	+	629.772i	1.00972	+	1.00972i	0.00976281	+	0.999952i	$0.496892\pi$
$74$		0			0
$75$	−347.124			−0.534432
$76$		0			0
$77$		−	531.530i		−	0.786668i
$78$		0			0
$79$			800.798i			1.14047i	0.821483	+	0.570233i	$0.193147\pi$
$79$			800.798i			1.14047i	−0.821483	+	0.570233i	$0.806853\pi$
$80$		0			0
$81$	81.0000			0.111111
$82$		0			0
$83$	−96.9092	−	96.9092i	−0.128159	−	0.128159i	0.640118	−	0.768277i	$-0.278885\pi$
$83$	−96.9092	−	96.9092i	−0.128159	−	0.128159i	−0.768277	+	0.640118i	$0.778885\pi$
$84$		0			0
$85$	39.9139	+	39.9139i	0.0509326	+	0.0509326i
$86$		0			0
$87$			248.514i			0.306247i
$88$		0			0
$89$	444.922	+	444.922i	0.529906	+	0.529906i	0.920544	−	0.390638i	$-0.127746\pi$
$89$	444.922	+	444.922i	0.529906	+	0.529906i	−0.390638	+	0.920544i	$0.627746\pi$
$90$		0			0
$91$	178.201	+	454.862i	0.205280	+	0.523983i
$92$		0			0
$93$	307.954	−	307.954i	0.343370	−	0.343370i
$94$		0			0
$95$	1478.28			1.59651
$96$		0			0
$97$	841.467	−	841.467i	0.880805	−	0.880805i	−0.112812	−	0.993616i	$-0.535986\pi$
$97$	841.467	−	841.467i	0.880805	−	0.880805i	0.993616	+	0.112812i	$0.0359857\pi$
$98$		0			0
$99$	−324.552	+	324.552i	−0.329482	+	0.329482i
$100$		0			0
$101$			1387.11i			1.36656i	0.730155	+	0.683282i	$0.239448\pi$
$101$			1387.11i			1.36656i	−0.730155	+	0.683282i	$0.760552\pi$
$102$		0			0
$103$	964.726			0.922886			0.461443	−	0.887170i	$-0.347332\pi$
$103$	964.726			0.922886			0.461443	+	0.887170i	$0.347332\pi$
$104$		0			0
$105$	485.106			0.450871
$106$		0			0
$107$			259.962i			0.234873i	0.993080	+	0.117437i	$0.0374677\pi$
$107$			259.962i			0.234873i	−0.993080	+	0.117437i	$0.962532\pi$
$108$		0			0
$109$	−500.506	+	500.506i	−0.439815	+	0.439815i	−0.891950	−	0.452135i	$-0.850663\pi$
$109$	−500.506	+	500.506i	−0.439815	+	0.439815i	0.452135	+	0.891950i	$0.350663\pi$
$110$		0			0
$111$	646.226	−	646.226i	0.552586	−	0.552586i
$112$		0			0
$113$	−1446.07			−1.20385			−0.601924	−	0.798553i	$-0.705599\pi$
$113$	−1446.07			−1.20385			−0.601924	+	0.798553i	$0.705599\pi$
$114$		0			0
$115$	−269.208	+	269.208i	−0.218294	+	0.218294i
$116$		0			0
$117$	168.930	−	386.549i	0.133483	−	0.305440i
$118$		0			0
$119$	−26.8132	−	26.8132i	−0.0206552	−	0.0206552i
$120$		0			0
$121$		−	1269.85i		−	0.954054i
$122$		0			0
$123$	60.9295	+	60.9295i	0.0446652	+	0.0446652i
$124$		0			0
$125$	−101.939	−	101.939i	−0.0729414	−	0.0729414i
$126$		0			0
$127$	−152.628			−0.106642			−0.0533210	−	0.998577i	$-0.516981\pi$
$127$	−152.628			−0.106642			−0.0533210	+	0.998577i	$0.516981\pi$
$128$		0			0
$129$			185.323i			0.126487i
$130$		0			0
$131$			2237.91i			1.49257i	0.665626	+	0.746285i	$0.268164\pi$
$131$			2237.91i			1.49257i	−0.665626	+	0.746285i	$0.731836\pi$
$132$		0			0
$133$	−993.077			−0.647449
$134$		0			0
$135$	−296.206	−	296.206i	−0.188840	−	0.188840i
$136$		0			0
$137$	261.801	+	261.801i	0.163264	+	0.163264i	0.784011	−	0.620747i	$-0.213171\pi$
$137$	261.801	+	261.801i	0.163264	+	0.163264i	−0.620747	+	0.784011i	$0.713171\pi$
$138$		0			0
$139$		−	2681.10i		−	1.63603i	−0.575199	−	0.818014i	$-0.695075\pi$
$139$		−	2681.10i		−	1.63603i	0.575199	−	0.818014i	$-0.304925\pi$
$140$		0			0
$141$	489.951	+	489.951i	0.292633	+	0.292633i
$142$		0			0
$143$	871.960	+	2225.70i	0.509909	+	1.30156i
$144$		0			0
$145$	908.782	−	908.782i	0.520484	−	0.520484i
$146$		0			0
$147$	703.117			0.394504
$148$		0			0
$149$	−593.938	+	593.938i	−0.326559	+	0.326559i	−0.851276	−	0.524718i	$-0.824171\pi$
$149$	−593.938	+	593.938i	−0.326559	+	0.326559i	0.524718	+	0.851276i	$0.324171\pi$
$150$		0			0
$151$	−1760.60	+	1760.60i	−0.948842	+	0.948842i	−0.998754	−	0.0499112i	$-0.984106\pi$
$151$	−1760.60	+	1760.60i	−0.948842	+	0.948842i	0.0499112	+	0.998754i	$0.484106\pi$
$152$		0			0
$153$			32.7444i			0.0173021i
$154$		0			0
$155$	−2252.30			−1.16715
$156$		0			0
$157$	224.026			0.113881			0.0569403	−	0.998378i	$-0.481866\pi$
$157$	224.026			0.113881			0.0569403	+	0.998378i	$0.481866\pi$
$158$		0			0
$159$			1654.67i			0.825305i
$160$		0			0
$161$	180.848	−	180.848i	0.0885268	−	0.0885268i
$162$		0			0
$163$	−1336.85	+	1336.85i	−0.642394	+	0.642394i	−0.951143	−	0.308750i	$-0.900089\pi$
$163$	−1336.85	+	1336.85i	−0.642394	+	0.642394i	0.308750	+	0.951143i	$0.400089\pi$
$164$		0			0
$165$	2373.69			1.11995
$166$		0			0
$167$	1645.17	−	1645.17i	0.762318	−	0.762318i	−0.214423	−	0.976741i	$-0.568787\pi$
$167$	1645.17	−	1645.17i	0.762318	−	0.762318i	0.976741	+	0.214423i	$0.0687870\pi$
$168$		0			0
$169$	−1492.38	−	1612.33i	−0.679280	−	0.733879i
$170$		0			0
$171$	606.374	+	606.374i	0.271173	+	0.271173i
$172$		0			0
$173$		−	495.731i		−	0.217860i	−0.994049	−	0.108930i	$-0.965258\pi$
$173$		−	495.731i		−	0.217860i	0.994049	−	0.108930i	$-0.0347424\pi$
$174$		0			0
$175$	−852.744	−	852.744i	−0.368351	−	0.368351i
$176$		0			0
$177$	1625.43	+	1625.43i	0.690253	+	0.690253i
$178$		0			0
$179$	−19.1300			−0.00798796			−0.00399398	−	0.999992i	$-0.501271\pi$
$179$	−19.1300			−0.00798796			−0.00399398	+	0.999992i	$0.501271\pi$
$180$		0			0
$181$			2416.45i			0.992340i	0.868225	+	0.496170i	$0.165261\pi$
$181$			2416.45i			0.992340i	−0.868225	+	0.496170i	$0.834739\pi$
$182$		0			0
$183$		−	1174.03i		−	0.474246i
$184$		0			0
$185$	−4726.32			−1.87830
$186$		0			0
$187$	−131.201	−	131.201i	−0.0513067	−	0.0513067i
$188$		0			0
$189$	198.984	+	198.984i	0.0765819	+	0.0765819i
$190$		0			0
$191$		−	847.618i		−	0.321107i	−0.987027	−	0.160554i	$-0.948672\pi$
$191$		−	847.618i		−	0.321107i	0.987027	−	0.160554i	$-0.0513279\pi$
$192$		0			0
$193$	−2449.57	−	2449.57i	−0.913594	−	0.913594i	0.0829586	−	0.996553i	$-0.473563\pi$
$193$	−2449.57	−	2449.57i	−0.913594	−	0.913594i	−0.996553	+	0.0829586i	$0.973563\pi$
$194$		0			0
$195$	−2031.31	+	795.804i	−0.745975	+	0.292250i
$196$		0			0
$197$	−1812.44	+	1812.44i	−0.655489	+	0.655489i	−0.954309	−	0.298820i	$-0.903407\pi$
$197$	−1812.44	+	1812.44i	−0.655489	+	0.655489i	0.298820	+	0.954309i	$0.403407\pi$
$198$		0			0
$199$	3377.35			1.20309			0.601543	−	0.798840i	$-0.294553\pi$
$199$	3377.35			1.20309			0.601543	+	0.798840i	$0.294553\pi$
$200$		0			0
$201$	582.279	−	582.279i	0.204332	−	0.204332i
$202$		0			0
$203$	−610.498	+	610.498i	−0.211077	+	0.211077i
$204$		0			0
$205$		−	445.622i		−	0.151822i
$206$		0			0
$207$	−220.852			−0.0741559
$208$		0			0
$209$	−4859.26			−1.60824
$210$		0			0
$211$			4064.46i			1.32611i	0.748571	+	0.663055i	$0.230741\pi$
$211$			4064.46i			1.32611i	−0.748571	+	0.663055i	$0.769259\pi$
$212$		0			0
$213$	869.531	−	869.531i	0.279715	−	0.279715i
$214$		0			0
$215$	677.703	−	677.703i	0.214972	−	0.214972i
$216$		0			0
$217$	1513.04			0.473326
$218$		0			0
$219$	1889.32	−	1889.32i	0.582959	−	0.582959i
$220$		0			0
$221$	156.263	+	68.2900i	0.0475628	+	0.0207859i
$222$		0			0
$223$	−2441.41	−	2441.41i	−0.733135	−	0.733135i	0.238105	−	0.971240i	$-0.423474\pi$
$223$	−2441.41	−	2441.41i	−0.733135	−	0.733135i	−0.971240	+	0.238105i	$0.923474\pi$
$224$		0			0
$225$			1041.37i			0.308555i
$226$		0			0
$227$	−4148.22	−	4148.22i	−1.21289	−	1.21289i	−0.970070	−	0.242825i	$-0.921926\pi$
$227$	−4148.22	−	4148.22i	−1.21289	−	1.21289i	−0.242825	−	0.970070i	$-0.578074\pi$
$228$		0			0
$229$	191.599	+	191.599i	0.0552890	+	0.0552890i	0.734211	−	0.678922i	$-0.237552\pi$
$229$	191.599	+	191.599i	0.0552890	+	0.0552890i	−0.678922	+	0.734211i	$0.737552\pi$
$230$		0			0
$231$	−1594.59			−0.454183
$232$		0			0
$233$			4035.95i			1.13478i	0.823449	+	0.567390i	$0.192047\pi$
$233$			4035.95i			1.13478i	−0.823449	+	0.567390i	$0.807953\pi$
$234$		0			0
$235$		−	3583.37i		−	0.994694i
$236$		0			0
$237$	2402.39			0.658449
$238$		0			0
$239$	−4449.88	−	4449.88i	−1.20435	−	1.20435i	−0.972831	−	0.231516i	$-0.925631\pi$
$239$	−4449.88	−	4449.88i	−1.20435	−	1.20435i	−0.231516	−	0.972831i	$-0.574369\pi$
$240$		0			0
$241$	4132.19	+	4132.19i	1.10447	+	1.10447i	0.993864	+	0.110609i	$0.0352801\pi$
$241$	4132.19	+	4132.19i	1.10447	+	1.10447i	0.110609	+	0.993864i	$0.464720\pi$
$242$		0			0
$243$		−	243.000i		−	0.0641500i
$244$		0			0
$245$	−2571.20	−	2571.20i	−0.670483	−	0.670483i
$246$		0			0
$247$	4158.36	−	1629.12i	1.07122	−	0.419669i
$248$		0			0
$249$	−290.727	+	290.727i	−0.0739924	+	0.0739924i
$250$		0			0
$251$	7095.04			1.78420			0.892101	−	0.451836i	$-0.149231\pi$
$251$	7095.04			1.78420			0.892101	+	0.451836i	$0.149231\pi$
$252$		0			0
$253$	884.913	−	884.913i	0.219897	−	0.219897i
$254$		0			0
$255$	119.742	−	119.742i	0.0294060	−	0.0294060i
$256$		0			0
$257$		−	2469.31i		−	0.599343i	−0.954043	−	0.299671i	$-0.903123\pi$
$257$		−	2469.31i		−	0.599343i	0.954043	−	0.299671i	$-0.0968770\pi$
$258$		0			0
$259$	3175.03			0.761726
$260$		0			0
$261$	745.541			0.176812
$262$		0			0
$263$		−	5277.61i		−	1.23738i	−0.785635	−	0.618690i	$-0.787664\pi$
$263$		−	5277.61i		−	1.23738i	0.785635	−	0.618690i	$-0.212336\pi$
$264$		0			0
$265$	6050.89	−	6050.89i	1.40265	−	1.40265i
$266$		0			0
$267$	1334.77	−	1334.77i	0.305941	−	0.305941i
$268$		0			0
$269$	3205.60			0.726575			0.363288	−	0.931677i	$-0.381654\pi$
$269$	3205.60			0.726575			0.363288	+	0.931677i	$0.381654\pi$
$270$		0			0
$271$	4988.78	−	4988.78i	1.11825	−	1.11825i	0.126256	−	0.991998i	$-0.459704\pi$
$271$	4988.78	−	4988.78i	1.11825	−	1.11825i	0.991998	−	0.126256i	$-0.0402960\pi$
$272$		0			0
$273$	1364.59	−	534.602i	0.302522	−	0.118519i
$274$		0			0
$275$	−4172.59	−	4172.59i	−0.914970	−	0.914970i
$276$		0			0
$277$			2923.91i			0.634227i	0.948388	+	0.317114i	$0.102714\pi$
$277$			2923.91i			0.634227i	−0.948388	+	0.317114i	$0.897286\pi$
$278$		0			0
$279$	−923.863	−	923.863i	−0.198245	−	0.198245i
$280$		0			0
$281$	−2323.87	−	2323.87i	−0.493347	−	0.493347i	0.416012	−	0.909359i	$-0.363427\pi$
$281$	−2323.87	−	2323.87i	−0.493347	−	0.493347i	−0.909359	+	0.416012i	$0.863427\pi$
$282$		0			0
$283$	−2327.45			−0.488878			−0.244439	−	0.969665i	$-0.578604\pi$
$283$	−2327.45			−0.488878			−0.244439	+	0.969665i	$0.578604\pi$
$284$		0			0
$285$		−	4434.85i		−	0.921748i
$286$		0			0
$287$			299.358i			0.0615699i
$288$		0			0
$289$	4899.76			0.997306
$290$		0			0
$291$	−2524.40	−	2524.40i	−0.508533	−	0.508533i
$292$		0			0
$293$	−5889.56	−	5889.56i	−1.17431	−	1.17431i	−0.981172	−	0.193135i	$-0.938134\pi$
$293$	−5889.56	−	5889.56i	−1.17431	−	1.17431i	−0.193135	−	0.981172i	$-0.561866\pi$
$294$		0			0
$295$		−	11888.0i		−	2.34625i
$296$		0			0
$297$	973.657	+	973.657i	0.190227	+	0.190227i
$298$		0			0
$299$	−460.597	+	1053.95i	−0.0890871	+	0.203851i
$300$		0			0
$301$	−455.265	+	455.265i	−0.0871795	+	0.0871795i
$302$		0			0
$303$	4161.34			0.788986
$304$		0			0
$305$	−4293.29	+	4293.29i	−0.806009	+	0.806009i
$306$		0			0
$307$	−4484.81	+	4484.81i	−0.833750	+	0.833750i	−0.988028	−	0.154277i	$-0.950695\pi$
$307$	−4484.81	+	4484.81i	−0.833750	+	0.833750i	0.154277	+	0.988028i	$0.450695\pi$
$308$		0			0
$309$		−	2894.18i		−	0.532829i
$310$		0			0
$311$	7020.75			1.28010			0.640048	−	0.768335i	$-0.278914\pi$
$311$	7020.75			1.28010			0.640048	+	0.768335i	$0.278914\pi$
$312$		0			0
$313$	5393.47			0.973983			0.486991	−	0.873407i	$-0.338094\pi$
$313$	5393.47			0.973983			0.486991	+	0.873407i	$0.338094\pi$
$314$		0			0
$315$		−	1455.32i		−	0.260311i
$316$		0			0
$317$	−6856.60	+	6856.60i	−1.21484	+	1.21484i	−0.245428	+	0.969415i	$0.578929\pi$
$317$	−6856.60	+	6856.60i	−1.21484	+	1.21484i	−0.969415	+	0.245428i	$0.921071\pi$
$318$		0			0
$319$	−2987.25	+	2987.25i	−0.524307	+	0.524307i
$320$		0			0
$321$	779.886			0.135604
$322$		0			0
$323$	−245.127	+	245.127i	−0.0422268	+	0.0422268i
$324$		0			0
$325$	4969.64	+	2171.83i	0.848203	+	0.370682i
$326$		0			0
$327$	1501.52	+	1501.52i	0.253927	+	0.253927i
$328$		0			0
$329$			2407.22i			0.403387i
$330$		0			0
$331$	−5600.07	−	5600.07i	−0.929932	−	0.929932i	0.0677690	−	0.997701i	$-0.478412\pi$
$331$	−5600.07	−	5600.07i	−0.929932	−	0.929932i	−0.997701	+	0.0677690i	$0.978412\pi$
$332$		0			0
$333$	−1938.68	−	1938.68i	−0.319036	−	0.319036i
$334$		0			0
$335$	−4258.63			−0.694548
$336$		0			0
$337$			7892.56i			1.27577i	0.770131	+	0.637886i	$0.220191\pi$
$337$			7892.56i			1.27577i	−0.770131	+	0.637886i	$0.779809\pi$
$338$		0			0
$339$			4338.21i			0.695042i
$340$		0			0
$341$	7403.51			1.17573
$342$		0			0
$343$	4255.11	+	4255.11i	0.669838	+	0.669838i
$344$		0			0
$345$	807.625	+	807.625i	0.126032	+	0.126032i
$346$		0			0
$347$		−	439.011i		−	0.0679174i	−0.999423	−	0.0339587i	$-0.989189\pi$
$347$		−	439.011i		−	0.0679174i	0.999423	−	0.0339587i	$-0.0108115\pi$
$348$		0			0
$349$	−2664.52	−	2664.52i	−0.408678	−	0.408678i	0.472599	−	0.881277i	$-0.343316\pi$
$349$	−2664.52	−	2664.52i	−0.408678	−	0.408678i	−0.881277	+	0.472599i	$0.843316\pi$
$350$		0			0
$351$	−1159.65	−	506.789i	−0.176346	−	0.0770666i
$352$		0			0
$353$	−3883.96	+	3883.96i	−0.585615	+	0.585615i	−0.936441	−	0.350826i	$-0.885901\pi$
$353$	−3883.96	+	3883.96i	−0.585615	+	0.585615i	0.350826	+	0.936441i	$0.385901\pi$
$354$		0			0
$355$	−6359.52			−0.950783
$356$		0			0
$357$	−80.4397	+	80.4397i	−0.0119253	+	0.0119253i
$358$		0			0
$359$	−993.863	+	993.863i	−0.146112	+	0.146112i	−0.776379	−	0.630267i	$-0.782945\pi$
$359$	−993.863	+	993.863i	−0.146112	+	0.146112i	0.630267	+	0.776379i	$0.282945\pi$
$360$		0			0
$361$			2219.74i			0.323625i
$362$		0			0
$363$	−3809.54			−0.550823
$364$		0			0
$365$	−13817.9			−1.98155
$366$		0			0
$367$			3038.32i			0.432149i	0.976377	+	0.216075i	$0.0693255\pi$
$367$			3038.32i			0.432149i	−0.976377	+	0.216075i	$0.930675\pi$
$368$		0			0
$369$	182.788	−	182.788i	0.0257875	−	0.0257875i
$370$		0			0
$371$	−4064.85	+	4064.85i	−0.568831	+	0.568831i
$372$		0			0
$373$	4888.47			0.678593			0.339297	−	0.940679i	$-0.389811\pi$
$373$	4888.47			0.678593			0.339297	+	0.940679i	$0.389811\pi$
$374$		0			0
$375$	−305.816	+	305.816i	−0.0421128	+	0.0421128i
$376$		0			0
$377$	1554.86	−	3557.88i	0.212413	−	0.486048i
$378$		0			0
$379$	−6546.84	−	6546.84i	−0.887305	−	0.887305i	0.106958	−	0.994263i	$-0.465889\pi$
$379$	−6546.84	−	6546.84i	−0.887305	−	0.887305i	−0.994263	+	0.106958i	$0.965889\pi$
$380$		0			0
$381$			457.883i			0.0615697i
$382$		0			0
$383$	8521.73	+	8521.73i	1.13692	+	1.13692i	0.988999	+	0.147920i	$0.0472577\pi$
$383$	8521.73	+	8521.73i	1.13692	+	1.13692i	0.147920	+	0.988999i	$0.452742\pi$
$384$		0			0
$385$	5831.20	+	5831.20i	0.771910	+	0.771910i
$386$		0			0
$387$	555.970			0.0730273
$388$		0			0
$389$		−	7276.26i		−	0.948383i	−0.880422	−	0.474191i	$-0.842740\pi$
$389$		−	7276.26i		−	0.948383i	0.880422	−	0.474191i	$-0.157260\pi$
$390$		0			0
$391$		−	89.2796i		−	0.0115475i
$392$		0			0
$393$	6713.72			0.861736
$394$		0			0
$395$	−8785.24	−	8785.24i	−1.11907	−	1.11907i
$396$		0			0
$397$	−3578.87	−	3578.87i	−0.452439	−	0.452439i	0.443724	−	0.896163i	$-0.353657\pi$
$397$	−3578.87	−	3578.87i	−0.452439	−	0.452439i	−0.896163	+	0.443724i	$0.853657\pi$
$398$		0			0
$399$			2979.23i			0.373805i
$400$		0			0
$401$	−9942.14	−	9942.14i	−1.23812	−	1.23812i	−0.960768	−	0.277353i	$-0.910543\pi$
$401$	−9942.14	−	9942.14i	−1.23812	−	1.23812i	−0.277353	−	0.960768i	$-0.589457\pi$
$402$		0			0
$403$	−6335.63	+	2482.10i	−0.783127	+	0.306805i
$404$		0			0
$405$	−888.618	+	888.618i	−0.109027	+	0.109027i
$406$		0			0
$407$	15535.9			1.89210
$408$		0			0
$409$	−1169.15	+	1169.15i	−0.141346	+	0.141346i	−0.774239	−	0.632893i	$-0.781867\pi$
$409$	−1169.15	+	1169.15i	−0.141346	+	0.141346i	0.632893	+	0.774239i	$0.281867\pi$
$410$		0			0
$411$	785.403	−	785.403i	0.0942606	−	0.0942606i
$412$		0			0
$413$			7986.06i			0.951497i
$414$		0			0
$415$	2126.30			0.251509
$416$		0			0
$417$	−8043.30			−0.944561
$418$		0			0
$419$			9436.20i			1.10021i	0.835095	+	0.550105i	$0.185412\pi$
$419$			9436.20i			1.10021i	−0.835095	+	0.550105i	$0.814588\pi$
$420$		0			0
$421$	9925.26	−	9925.26i	1.14900	−	1.14900i	0.162247	−	0.986750i	$-0.448126\pi$
$421$	9925.26	−	9925.26i	1.14900	−	1.14900i	0.986750	−	0.162247i	$-0.0518740\pi$
$422$		0			0
$423$	1469.85	−	1469.85i	0.168952	−	0.168952i
$424$		0			0
$425$	−420.976			−0.0480479
$426$		0			0
$427$	2884.13	−	2884.13i	0.326868	−	0.326868i
$428$		0			0
$429$	6677.10	−	2615.88i	0.751453	−	0.294396i
$430$		0			0
$431$	3896.99	+	3896.99i	0.435526	+	0.435526i	0.890503	−	0.454977i	$-0.150353\pi$
$431$	3896.99	+	3896.99i	0.435526	+	0.435526i	−0.454977	+	0.890503i	$0.650353\pi$
$432$		0			0
$433$		−	1649.61i		−	0.183083i	−0.995801	−	0.0915417i	$-0.970821\pi$
$433$		−	1649.61i		−	0.183083i	0.995801	−	0.0915417i	$-0.0291795\pi$
$434$		0			0
$435$	−2726.34	−	2726.34i	−0.300502	−	0.300502i
$436$		0			0
$437$	−1653.32	−	1653.32i	−0.180981	−	0.180981i
$438$		0			0
$439$	17380.7			1.88960			0.944802	−	0.327643i	$-0.106254\pi$
$439$	17380.7			1.88960			0.944802	+	0.327643i	$0.106254\pi$
$440$		0			0
$441$		−	2109.35i		−	0.227767i
$442$		0			0
$443$		−	11980.0i		−	1.28485i	−0.766349	−	0.642424i	$-0.777929\pi$
$443$		−	11980.0i		−	1.28485i	0.766349	−	0.642424i	$-0.222071\pi$
$444$		0			0
$445$	−9762.12			−1.03993
$446$		0			0
$447$	1781.81	+	1781.81i	0.188539	+	0.188539i
$448$		0			0
$449$	−4541.83	−	4541.83i	−0.477377	−	0.477377i	0.426915	−	0.904292i	$-0.359600\pi$
$449$	−4541.83	−	4541.83i	−0.477377	−	0.477377i	−0.904292	+	0.426915i	$0.859600\pi$
$450$		0			0
$451$			1464.80i			0.152937i
$452$		0			0
$453$	5281.79	+	5281.79i	0.547814	+	0.547814i
$454$		0			0
$455$	−6945.08	−	3035.14i	−0.715583	−	0.312724i
$456$		0			0
$457$	−23.9691	+	23.9691i	−0.00245345	+	0.00245345i	−0.708332	−	0.705879i	$-0.750552\pi$
$457$	−23.9691	+	23.9691i	−0.00245345	+	0.00245345i	0.705879	+	0.708332i	$0.250552\pi$
$458$		0			0
$459$	98.2331			0.00998939
$460$		0			0
$461$	5064.78	−	5064.78i	0.511692	−	0.511692i	−0.403352	−	0.915045i	$-0.632155\pi$
$461$	5064.78	−	5064.78i	0.511692	−	0.511692i	0.915045	+	0.403352i	$0.132155\pi$
$462$		0			0
$463$	−178.036	+	178.036i	−0.0178705	+	0.0178705i	−0.715986	−	0.698115i	$-0.754022\pi$
$463$	−178.036	+	178.036i	−0.0178705	+	0.0178705i	0.698115	+	0.715986i	$0.254022\pi$
$464$		0			0
$465$			6756.89i			0.673856i
$466$		0			0
$467$	111.584			0.0110567			0.00552834	−	0.999985i	$-0.498240\pi$
$467$	111.584			0.0110567			0.00552834	+	0.999985i	$0.498240\pi$
$468$		0			0
$469$	2860.85			0.281667
$470$		0			0
$471$		−	672.079i		−	0.0657490i
$472$		0			0
$473$	−2227.67	+	2227.67i	−0.216551	+	0.216551i
$474$		0			0
$475$	−7795.81	+	7795.81i	−0.753045	+	0.753045i
$476$		0			0
$477$	4964.00			0.476490
$478$		0			0
$479$	−3259.16	+	3259.16i	−0.310887	+	0.310887i	−0.845253	−	0.534366i	$-0.820550\pi$
$479$	−3259.16	+	3259.16i	−0.310887	+	0.310887i	0.534366	+	0.845253i	$0.320550\pi$
$480$		0			0
$481$	−13295.0	+	5208.56i	−1.26029	+	0.493742i
$482$		0			0
$483$	−542.544	−	542.544i	−0.0511110	−	0.0511110i
$484$		0			0
$485$			18462.8i			1.72856i
$486$		0			0
$487$	12524.9	+	12524.9i	1.16541	+	1.16541i	0.983272	+	0.182141i	$0.0583028\pi$
$487$	12524.9	+	12524.9i	1.16541	+	1.16541i	0.182141	+	0.983272i	$0.441697\pi$
$488$		0			0
$489$	4010.55	+	4010.55i	0.370886	+	0.370886i
$490$		0			0
$491$	−261.811			−0.0240638			−0.0120319	−	0.999928i	$-0.503830\pi$
$491$	−261.811			−0.0240638			−0.0120319	+	0.999928i	$0.503830\pi$
$492$		0			0
$493$			301.386i			0.0275330i
$494$		0			0
$495$		−	7121.07i		−	0.646602i
$496$		0			0
$497$	4272.17			0.385580
$498$		0			0
$499$	6817.56	+	6817.56i	0.611615	+	0.611615i	0.943367	−	0.331751i	$-0.107640\pi$
$499$	6817.56	+	6817.56i	0.611615	+	0.611615i	−0.331751	+	0.943367i	$0.607640\pi$
$500$		0			0
$501$	−4935.51	−	4935.51i	−0.440125	−	0.440125i
$502$		0			0
$503$			6873.42i			0.609286i	0.952467	+	0.304643i	$0.0985371\pi$
$503$			6873.42i			0.609286i	−0.952467	+	0.304643i	$0.901463\pi$
$504$		0			0
$505$	−15217.5	−	15217.5i	−1.34093	−	1.34093i
$506$		0			0
$507$	−4837.00	+	4477.13i	−0.423705	+	0.392182i
$508$		0			0
$509$	−8261.33	+	8261.33i	−0.719405	+	0.719405i	−0.968483	−	0.249078i	$-0.919872\pi$
$509$	−8261.33	+	8261.33i	−0.719405	+	0.719405i	0.249078	+	0.968483i	$0.419872\pi$
$510$		0			0
$511$	9282.57			0.803595
$512$		0			0
$513$	1819.12	−	1819.12i	0.156562	−	0.156562i
$514$		0			0
$515$	−10583.6	+	10583.6i	−0.905573	+	0.905573i
$516$		0			0
$517$			11778.9i			1.00200i
$518$		0			0
$519$	−1487.19			−0.125781
$520$		0			0
$521$	19121.9			1.60796			0.803978	−	0.594660i	$-0.202713\pi$
$521$	19121.9			1.60796			0.803978	+	0.594660i	$0.202713\pi$
$522$		0			0
$523$			13346.3i			1.11585i	0.829890	+	0.557927i	$0.188403\pi$
$523$			13346.3i			1.11585i	−0.829890	+	0.557927i	$0.811597\pi$
$524$		0			0
$525$	−2558.23	+	2558.23i	−0.212667	+	0.212667i
$526$		0			0
$527$	373.473	−	373.473i	0.0308705	−	0.0308705i
$528$		0			0
$529$	−11564.8			−0.950508
$530$		0			0
$531$	4876.29	−	4876.29i	0.398518	−	0.398518i
$532$		0			0
$533$	−491.089	−	1253.52i	−0.0399089	−	0.101868i
$534$		0			0
$535$	−2851.94	−	2851.94i	−0.230467	−	0.230467i
$536$		0			0
$537$			57.3900i			0.00461185i
$538$		0			0
$539$	8451.79	+	8451.79i	0.675407	+	0.675407i
$540$		0			0
$541$	−8318.38	−	8318.38i	−0.661063	−	0.661063i	0.294568	−	0.955631i	$-0.404824\pi$
$541$	−8318.38	−	8318.38i	−0.661063	−	0.661063i	−0.955631	+	0.294568i	$0.904824\pi$
$542$		0			0
$543$	7249.36			0.572928
$544$		0			0
$545$		−	10981.7i		−	0.863127i
$546$		0			0
$547$		−	5413.15i		−	0.423125i	−0.977364	−	0.211563i	$-0.932145\pi$
$547$		−	5413.15i		−	0.423125i	0.977364	−	0.211563i	$-0.0678553\pi$
$548$		0			0
$549$	−3522.10			−0.273806
$550$		0			0
$551$	5581.19	+	5581.19i	0.431519	+	0.431519i
$552$		0			0
$553$	5901.72	+	5901.72i	0.453827	+	0.453827i
$554$		0			0
$555$			14179.0i			1.08444i
$556$		0			0
$557$	18416.6	+	18416.6i	1.40096	+	1.40096i	0.797050	+	0.603913i	$0.206393\pi$
$557$	18416.6	+	18416.6i	1.40096	+	1.40096i	0.603913	+	0.797050i	$0.293607\pi$
$558$		0			0
$559$	1159.50	−	2653.20i	0.0877313	−	0.200749i
$560$		0			0
$561$	−393.602	+	393.602i	−0.0296219	+	0.0296219i
$562$		0			0
$563$	−14219.0			−1.06441			−0.532204	−	0.846616i	$-0.678636\pi$
$563$	−14219.0			−1.06441			−0.532204	+	0.846616i	$0.678636\pi$
$564$		0			0
$565$	15864.3	−	15864.3i	1.18126	−	1.18126i
$566$		0			0
$567$	596.953	−	596.953i	0.0442146	−	0.0442146i
$568$		0			0
$569$		−	2144.88i		−	0.158028i	−0.996874	−	0.0790140i	$-0.974823\pi$
$569$		−	2144.88i		−	0.158028i	0.996874	−	0.0790140i	$-0.0251772\pi$
$570$		0			0
$571$	1393.24			0.102111			0.0510555	−	0.998696i	$-0.483741\pi$
$571$	1393.24			0.102111			0.0510555	+	0.998696i	$0.483741\pi$
$572$		0			0
$573$	−2542.85			−0.185391
$574$		0			0
$575$		−	2839.37i		−	0.205930i
$576$		0			0
$577$	5614.68	−	5614.68i	0.405099	−	0.405099i	−0.474926	−	0.880026i	$-0.657525\pi$
$577$	5614.68	−	5614.68i	0.405099	−	0.405099i	0.880026	+	0.474926i	$0.157525\pi$
$578$		0			0
$579$	−7348.70	+	7348.70i	−0.527464	+	0.527464i
$580$		0			0
$581$	−1428.40			−0.101997
$582$		0			0
$583$	−19889.8	+	19889.8i	−1.41296	+	1.41296i
$584$		0			0
$585$	2387.41	+	6093.93i	0.168730	+	0.430689i
$586$		0			0
$587$	10456.4	+	10456.4i	0.735230	+	0.735230i	0.971651	−	0.236421i	$-0.0759743\pi$
$587$	10456.4	+	10456.4i	0.735230	+	0.735230i	−0.236421	+	0.971651i	$0.575974\pi$
$588$		0			0
$589$		−	13832.3i		−	0.967654i
$590$		0			0
$591$	5437.33	+	5437.33i	0.378447	+	0.378447i
$592$		0			0
$593$	5623.39	+	5623.39i	0.389418	+	0.389418i	0.874480	−	0.485062i	$-0.161203\pi$
$593$	5623.39	+	5623.39i	0.389418	+	0.389418i	−0.485062	+	0.874480i	$0.661203\pi$
$594$		0			0
$595$	588.314			0.0405354
$596$		0			0
$597$		−	10132.1i		−	0.694602i
$598$		0			0
$599$			5680.38i			0.387469i	0.981054	+	0.193735i	$0.0620601\pi$
$599$			5680.38i			0.387469i	−0.981054	+	0.193735i	$0.937940\pi$
$600$		0			0
$601$	−23639.4			−1.60444			−0.802221	−	0.597027i	$-0.796349\pi$
$601$	−23639.4			−1.60444			−0.802221	+	0.597027i	$0.796349\pi$
$602$		0			0
$603$	−1746.84	−	1746.84i	−0.117971	−	0.117971i
$604$		0			0
$605$	13931.0	+	13931.0i	0.936156	+	0.936156i
$606$		0			0
$607$			20622.5i			1.37898i	0.724293	+	0.689492i	$0.242166\pi$
$607$			20622.5i			1.37898i	−0.724293	+	0.689492i	$0.757834\pi$
$608$		0			0
$609$	1831.49	+	1831.49i	0.121865	+	0.121865i
$610$		0			0
$611$	−3948.99	−	10079.9i	−0.261471	−	0.667412i
$612$		0			0
$613$	4785.20	−	4785.20i	0.315289	−	0.315289i	−0.531665	−	0.846955i	$-0.678434\pi$
$613$	4785.20	−	4785.20i	0.315289	−	0.315289i	0.846955	+	0.531665i	$0.178434\pi$
$614$		0			0
$615$	−1336.87			−0.0876547
$616$		0			0
$617$	12088.8	−	12088.8i	0.788780	−	0.788780i	−0.192514	−	0.981294i	$-0.561664\pi$
$617$	12088.8	−	12088.8i	0.788780	−	0.788780i	0.981294	+	0.192514i	$0.0616642\pi$
$618$		0			0
$619$	9308.41	−	9308.41i	0.604421	−	0.604421i	−0.337062	−	0.941483i	$-0.609433\pi$
$619$	9308.41	−	9308.41i	0.604421	−	0.604421i	0.941483	+	0.337062i	$0.109433\pi$
$620$		0			0
$621$			662.555i			0.0428139i
$622$		0			0
$623$	6557.97			0.421732
$624$		0			0
$625$	16700.2			1.06881
$626$		0			0
$627$			14577.8i			0.928517i
$628$		0			0
$629$	783.713	−	783.713i	0.0496800	−	0.0496800i
$630$		0			0
$631$	−22247.7	+	22247.7i	−1.40359	+	1.40359i	−0.615298	+	0.788295i	$0.710964\pi$
$631$	−22247.7	+	22247.7i	−1.40359	+	1.40359i	−0.788295	+	0.615298i	$0.789036\pi$
$632$		0			0
$633$	12193.4			0.765630
$634$		0			0
$635$	1674.42	−	1674.42i	0.104641	−	0.104641i
$636$		0			0
$637$	−10066.3	−	4399.16i	−0.626122	−	0.273628i
$638$		0			0
$639$	−2608.59	−	2608.59i	−0.161493	−	0.161493i
$640$		0			0
$641$		−	16079.9i		−	0.990825i	−0.868658	−	0.495413i	$-0.835017\pi$
$641$		−	16079.9i		−	0.990825i	0.868658	−	0.495413i	$-0.164983\pi$
$642$		0			0
$643$	15703.6	+	15703.6i	0.963125	+	0.963125i	0.999344	−	0.0362193i	$-0.0115315\pi$
$643$	15703.6	+	15703.6i	0.963125	+	0.963125i	−0.0362193	+	0.999344i	$0.511531\pi$
$644$		0			0
$645$	−2033.11	−	2033.11i	−0.124114	−	0.124114i
$646$		0			0
$647$	−25336.7			−1.53955			−0.769774	−	0.638316i	$-0.779631\pi$
$647$	−25336.7			−1.53955			−0.769774	+	0.638316i	$0.779631\pi$
$648$		0			0
$649$			39076.8i			2.36348i
$650$		0			0
$651$		−	4539.12i		−	0.273275i
$652$		0			0
$653$	4028.17			0.241400			0.120700	−	0.992689i	$-0.461486\pi$
$653$	4028.17			0.241400			0.120700	+	0.992689i	$0.461486\pi$
$654$		0			0
$655$	−24551.2	−	24551.2i	−1.46457	−	1.46457i
$656$		0			0
$657$	−5667.95	−	5667.95i	−0.336572	−	0.336572i
$658$		0			0
$659$			14725.1i			0.870423i	0.900328	+	0.435212i	$0.143326\pi$
$659$			14725.1i			0.870423i	−0.900328	+	0.435212i	$0.856674\pi$
$660$		0			0
$661$	−13921.2	−	13921.2i	−0.819168	−	0.819168i	0.166820	−	0.985987i	$-0.446650\pi$
$661$	−13921.2	−	13921.2i	−0.819168	−	0.819168i	−0.985987	+	0.166820i	$0.946650\pi$
$662$		0			0
$663$	204.870	−	468.788i	0.0120007	−	0.0274604i
$664$		0			0
$665$	10894.6	−	10894.6i	0.635303	−	0.635303i
$666$		0			0
$667$	−2032.77			−0.118005
$668$		0			0
$669$	−7324.24	+	7324.24i	−0.423276	+	0.423276i
$670$		0			0
$671$	14112.4	−	14112.4i	0.811929	−	0.811929i
$672$		0			0
$673$			20696.7i			1.18544i	0.805409	+	0.592720i	$0.201946\pi$
$673$			20696.7i			1.18544i	−0.805409	+	0.592720i	$0.798054\pi$
$674$		0			0
$675$	3124.12			0.178144
$676$		0			0
$677$	−12720.7			−0.722149			−0.361075	−	0.932537i	$-0.617590\pi$
$677$	−12720.7			−0.722149			−0.361075	+	0.932537i	$0.617590\pi$
$678$		0			0
$679$		−	12402.9i		−	0.700999i
$680$		0			0
$681$	−12444.7	+	12444.7i	−0.700265	+	0.700265i
$682$		0			0
$683$	−14912.0	+	14912.0i	−0.835421	+	0.835421i	−0.988252	−	0.152832i	$-0.951161\pi$
$683$	−14912.0	+	14912.0i	−0.835421	+	0.835421i	0.152832	+	0.988252i	$0.451161\pi$
$684$		0			0
$685$	−5744.23			−0.320403
$686$		0			0
$687$	574.796	−	574.796i	0.0319211	−	0.0319211i
$688$		0			0
$689$	10352.7	−	23689.2i	0.572431	−	1.30985i
$690$		0			0
$691$	10432.9	+	10432.9i	0.574366	+	0.574366i	0.933346	−	0.358979i	$-0.116875\pi$
$691$	10432.9	+	10432.9i	0.574366	+	0.574366i	−0.358979	+	0.933346i	$0.616875\pi$
$692$		0			0
$693$			4783.77i			0.262223i
$694$		0			0
$695$	29413.2	+	29413.2i	1.60534	+	1.60534i
$696$		0			0
$697$	73.8925	+	73.8925i	0.00401561	+	0.00401561i
$698$		0			0
$699$	12107.8			0.655165
$700$		0			0
$701$		−	1078.91i		−	0.0581311i	−0.999578	−	0.0290655i	$-0.990747\pi$
$701$		−	1078.91i		−	0.0581311i	0.999578	−	0.0290655i	$-0.00925315\pi$
$702$		0			0
$703$		−	29026.3i		−	1.55725i
$704$		0			0
$705$	−10750.1			−0.574287
$706$		0			0
$707$	10222.7	+	10222.7i	0.543799	+	0.543799i
$708$		0			0
$709$	19584.2	+	19584.2i	1.03737	+	1.03737i	0.999274	+	0.0381009i	$0.0121308\pi$
$709$	19584.2	+	19584.2i	1.03737	+	1.03737i	0.0381009	+	0.999274i	$0.487869\pi$
$710$		0			0
$711$		−	7207.18i		−	0.380155i
$712$		0			0
$713$	2518.97	+	2518.97i	0.132309	+	0.132309i
$714$		0			0
$715$	−33983.2	−	14851.3i	−1.77748	−	0.776795i
$716$		0			0
$717$	−13349.7	+	13349.7i	−0.695330	+	0.695330i
$718$		0			0
$719$	7040.96			0.365206			0.182603	−	0.983187i	$-0.441548\pi$
$719$	7040.96			0.365206			0.182603	+	0.983187i	$0.441548\pi$
$720$		0			0
$721$	7109.83	−	7109.83i	0.367245	−	0.367245i
$722$		0			0
$723$	12396.6	−	12396.6i	0.637668	−	0.637668i
$724$		0			0
$725$			9585.01i			0.491005i
$726$		0			0
$727$	10443.8			0.532793			0.266397	−	0.963864i	$-0.414167\pi$
$727$	10443.8			0.532793			0.266397	+	0.963864i	$0.414167\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$			224.752i			0.0113717i
$732$		0			0
$733$	−1106.47	+	1106.47i	−0.0557550	+	0.0557550i	−0.734435	−	0.678680i	$-0.762553\pi$
$733$	−1106.47	+	1106.47i	−0.0557550	+	0.0557550i	0.678680	+	0.734435i	$0.262553\pi$
$734$		0			0
$735$	−7713.61	+	7713.61i	−0.387103	+	0.387103i
$736$		0			0
$737$	13998.5			0.699650
$738$		0			0
$739$	23725.4	−	23725.4i	1.18099	−	1.18099i	0.201504	−	0.979488i	$-0.435417\pi$
$739$	23725.4	−	23725.4i	1.18099	−	1.18099i	0.979488	−	0.201504i	$-0.0645828\pi$
$740$		0			0
$741$	−4887.35	−	12475.1i	−0.242296	−	0.618467i
$742$		0			0
$743$	−17110.9	−	17110.9i	−0.844867	−	0.844867i	0.144620	−	0.989487i	$-0.453804\pi$
$743$	−17110.9	−	17110.9i	−0.844867	−	0.844867i	−0.989487	+	0.144620i	$0.953804\pi$
$744$		0			0
$745$		−	13031.7i		−	0.640865i
$746$		0			0
$747$	872.182	+	872.182i	0.0427195	+	0.0427195i
$748$		0			0
$749$	1915.86	+	1915.86i	0.0934635	+	0.0934635i
$750$		0			0
$751$	18833.9			0.915124			0.457562	−	0.889178i	$-0.348723\pi$
$751$	18833.9			0.915124			0.457562	+	0.889178i	$0.348723\pi$
$752$		0			0
$753$		−	21285.1i		−	1.03011i
$754$		0			0
$755$		−	38629.6i		−	1.86208i
$756$		0			0
$757$	−13709.0			−0.658208			−0.329104	−	0.944294i	$-0.606747\pi$
$757$	−13709.0			−0.658208			−0.329104	+	0.944294i	$0.606747\pi$
$758$		0			0
$759$	−2654.74	−	2654.74i	−0.126958	−	0.126958i
$760$		0			0
$761$	−12656.7	−	12656.7i	−0.602899	−	0.602899i	0.338181	−	0.941081i	$-0.390188\pi$
$761$	−12656.7	−	12656.7i	−0.602899	−	0.602899i	−0.941081	+	0.338181i	$0.890188\pi$
$762$		0			0
$763$			7377.25i			0.350032i
$764$		0			0
$765$	−359.225	−	359.225i	−0.0169775	−	0.0169775i
$766$		0			0
$767$	−13100.9	−	33440.4i	−0.616749	−	1.57427i
$768$		0			0
$769$	−18582.2	+	18582.2i	−0.871378	+	0.871378i	−0.992623	−	0.121245i	$-0.961311\pi$
$769$	−18582.2	+	18582.2i	−0.871378	+	0.871378i	0.121245	+	0.992623i	$0.461311\pi$
$770$		0			0
$771$	−7407.92			−0.346031
$772$		0			0
$773$	−494.241	+	494.241i	−0.0229969	+	0.0229969i	−0.718512	−	0.695515i	$-0.755176\pi$
$773$	−494.241	+	494.241i	−0.0229969	+	0.0229969i	0.695515	+	0.718512i	$0.255176\pi$
$774$		0			0
$775$	11877.6	−	11877.6i	0.550524	−	0.550524i
$776$		0			0
$777$		−	9525.10i		−	0.439783i
$778$		0			0
$779$	2736.74			0.125872
$780$		0			0
$781$	20904.3			0.957766
$782$		0			0
$783$		−	2236.62i		−	0.102082i
$784$		0			0
$785$	−2457.70	+	2457.70i	−0.111744	+	0.111744i
$786$		0			0
$787$	7208.46	−	7208.46i	0.326498	−	0.326498i	−0.524755	−	0.851253i	$-0.675843\pi$
$787$	7208.46	−	7208.46i	0.326498	−	0.326498i	0.851253	+	0.524755i	$0.175843\pi$
$788$		0			0
$789$	−15832.8			−0.714402
$790$		0			0
$791$	−10657.2	+	10657.2i	−0.479049	+	0.479049i
$792$		0			0
$793$	−7345.52	+	16808.2i	−0.328937	+	0.752682i
$794$		0			0
$795$	−18152.7	−	18152.7i	−0.809823	−	0.809823i
$796$		0			0
$797$			5869.01i			0.260842i	0.991459	+	0.130421i	$0.0416328\pi$
$797$			5869.01i			0.260842i	−0.991459	+	0.130421i	$0.958367\pi$
$798$		0			0
$799$	594.190	+	594.190i	0.0263090	+	0.0263090i
$800$		0			0
$801$	−4004.30	−	4004.30i	−0.176635	−	0.176635i
$802$		0			0
$803$	45420.9			1.99610
$804$		0			0
$805$			3968.02i			0.173732i
$806$		0			0
$807$		−	9616.80i		−	0.419489i
$808$		0			0
$809$	11522.9			0.500771			0.250386	−	0.968146i	$-0.419443\pi$
$809$	11522.9			0.500771			0.250386	+	0.968146i	$0.419443\pi$
$810$		0			0
$811$	1281.18	+	1281.18i	0.0554728	+	0.0554728i	0.734299	−	0.678826i	$-0.237511\pi$
$811$	1281.18	+	1281.18i	0.0554728	+	0.0554728i	−0.678826	+	0.734299i	$0.737511\pi$
$812$		0			0
$813$	−14966.3	−	14966.3i	−0.645624	−	0.645624i
$814$		0			0
$815$		−	29332.1i		−	1.26068i
$816$		0			0
$817$	4162.05	+	4162.05i	0.178227	+	0.178227i
$818$		0			0
$819$	−1603.81	−	4093.76i	−0.0684268	−	0.174661i
$820$		0			0
$821$	54.1554	−	54.1554i	0.00230211	−	0.00230211i	−0.705955	−	0.708257i	$-0.749482\pi$
$821$	54.1554	−	54.1554i	0.00230211	−	0.00230211i	0.708257	+	0.705955i	$0.249482\pi$
$822$		0			0
$823$	1414.64			0.0599166			0.0299583	−	0.999551i	$-0.490463\pi$
$823$	1414.64			0.0599166			0.0299583	+	0.999551i	$0.490463\pi$
$824$		0			0
$825$	−12517.8	+	12517.8i	−0.528258	+	0.528258i
$826$		0			0
$827$	17163.5	−	17163.5i	0.721686	−	0.721686i	−0.247262	−	0.968949i	$-0.579531\pi$
$827$	17163.5	−	17163.5i	0.721686	−	0.721686i	0.968949	+	0.247262i	$0.0795309\pi$
$828$		0			0
$829$		−	32076.3i		−	1.34385i	−0.740617	−	0.671927i	$-0.765467\pi$
$829$		−	32076.3i		−	1.34385i	0.740617	−	0.671927i	$-0.234533\pi$
$830$		0			0
$831$	8771.74			0.366171
$832$		0			0
$833$	852.708			0.0354677
$834$		0			0
$835$			36097.0i			1.49603i
$836$		0			0
$837$	−2771.59	+	2771.59i	−0.114457	+	0.114457i
$838$		0			0
$839$	−25536.5	+	25536.5i	−1.05080	+	1.05080i	−0.0521563	+	0.998639i	$0.516609\pi$
$839$	−25536.5	+	25536.5i	−1.05080	+	1.05080i	−0.998639	+	0.0521563i	$0.983391\pi$
$840$		0			0
$841$	−17526.9			−0.718639
$842$		0			0
$843$	−6971.61	+	6971.61i	−0.284834	+	0.284834i
$844$		0			0
$845$	34060.5	+	1315.97i	1.38665	+	0.0535749i
$846$		0			0
$847$	−9358.50	−	9358.50i	−0.379648	−	0.379648i
$848$		0			0
$849$			6982.35i			0.282254i
$850$		0			0
$851$	5285.93	+	5285.93i	0.212925	+	0.212925i
$852$		0			0
$853$	10542.2	+	10542.2i	0.423163	+	0.423163i	0.886291	−	0.463128i	$-0.153273\pi$
$853$	10542.2	+	10542.2i	0.423163	+	0.423163i	−0.463128	+	0.886291i	$0.653273\pi$
$854$		0			0
$855$	−13304.6			−0.532171
$856$		0			0
$857$		−	14583.2i		−	0.581275i	−0.956833	−	0.290638i	$-0.906133\pi$
$857$		−	14583.2i		−	0.581275i	0.956833	−	0.290638i	$-0.0938674\pi$
$858$		0			0
$859$		−	48275.6i		−	1.91751i	−0.284232	−	0.958756i	$-0.591738\pi$
$859$		−	48275.6i		−	1.91751i	0.284232	−	0.958756i	$-0.408262\pi$
$860$		0			0
$861$	898.075			0.0355474
$862$		0			0
$863$	−33892.6	−	33892.6i	−1.33687	−	1.33687i	−0.899077	−	0.437791i	$-0.855761\pi$
$863$	−33892.6	−	33892.6i	−1.33687	−	1.33687i	−0.437791	−	0.899077i	$-0.644239\pi$
$864$		0			0
$865$	5438.46	+	5438.46i	0.213772	+	0.213772i
$866$		0			0
$867$		−	14699.3i		−	0.575795i
$868$		0			0
$869$	28877.9	+	28877.9i	1.12729	+	1.12729i
$870$		0			0
$871$	−11979.4	+	4693.14i	−0.466022	+	0.182573i
$872$		0			0
$873$	−7573.20	+	7573.20i	−0.293602	+	0.293602i
$874$		0			0
$875$	−1502.53			−0.0580514
$876$		0			0
$877$	−33797.2	+	33797.2i	−1.30131	+	1.30131i	−0.373807	+	0.927507i	$0.621948\pi$
$877$	−33797.2	+	33797.2i	−1.30131	+	1.30131i	−0.927507	+	0.373807i	$0.878052\pi$
$878$		0			0
$879$	−17668.7	+	17668.7i	−0.677987	+	0.677987i
$880$		0			0
$881$		−	10799.2i		−	0.412977i	−0.978449	−	0.206489i	$-0.933796\pi$
$881$		−	10799.2i		−	0.412977i	0.978449	−	0.206489i	$-0.0662037\pi$
$882$		0			0
$883$	−32825.4			−1.25103			−0.625517	−	0.780210i	$-0.715112\pi$
$883$	−32825.4			−1.25103			−0.625517	+	0.780210i	$0.715112\pi$
$884$		0			0
$885$	−35663.9			−1.35461
$886$		0			0
$887$			13074.6i			0.494929i	0.968897	+	0.247464i	$0.0795973\pi$
$887$			13074.6i			0.494929i	−0.968897	+	0.247464i	$0.920403\pi$
$888$		0			0
$889$	−1124.83	+	1124.83i	−0.0424362	+	0.0424362i
$890$		0			0
$891$	2920.97	−	2920.97i	0.109827	−	0.109827i
$892$		0			0
$893$	22006.9			0.824673
$894$		0			0
$895$	209.868	−	209.868i	0.00783810	−	0.00783810i
$896$		0			0
$897$	3161.85	+	1381.79i	0.117694	+	0.0514344i
$898$		0			0
$899$	−8503.43	−	8503.43i	−0.315468	−	0.315468i
$900$		0			0
$901$			2006.70i			0.0741986i
$902$		0			0
$903$	1365.79	+	1365.79i	0.0503331	+	0.0503331i
$904$		0			0
$905$	−26509.9	−	26509.9i	−0.973724	−	0.973724i
$906$		0			0
$907$	−2492.74			−0.0912570			−0.0456285	−	0.998958i	$-0.514529\pi$
$907$	−2492.74			−0.0912570			−0.0456285	+	0.998958i	$0.514529\pi$
$908$		0			0
$909$		−	12484.0i		−	0.455521i
$910$		0			0
$911$		−	35909.3i		−	1.30596i	−0.757376	−	0.652979i	$-0.773519\pi$
$911$		−	35909.3i		−	1.30596i	0.757376	−	0.652979i	$-0.226481\pi$
$912$		0			0
$913$	−6989.36			−0.253356
$914$		0			0
$915$	12879.9	+	12879.9i	0.465350	+	0.465350i
$916$		0			0
$917$	16492.9	+	16492.9i	0.593940	+	0.593940i
$918$		0			0
$919$			32386.7i			1.16250i	0.813725	+	0.581250i	$0.197436\pi$
$919$			32386.7i			1.16250i	−0.813725	+	0.581250i	$0.802564\pi$
$920$		0			0
$921$	13454.4	+	13454.4i	0.481366	+	0.481366i
$922$		0			0
$923$	−17889.1	+	7008.39i	−0.637949	+	0.249928i
$924$		0			0
$925$	24924.5	−	24924.5i	0.885960	−	0.885960i
$926$		0			0
$927$	−8682.53			−0.307629
$928$		0			0
$929$	−17.3090	+	17.3090i	−0.000611290	+	0.000611290i	−0.707412	−	0.706801i	$-0.750138\pi$
$929$	−17.3090	+	17.3090i	−0.000611290	+	0.000611290i	0.706801	+	0.707412i	$0.250138\pi$
$930$		0			0
$931$	15790.8	−	15790.8i	0.555878	−	0.555878i
$932$		0			0
$933$		−	21062.2i		−	0.739064i
$934$		0			0
$935$	2878.70			0.100688
$936$		0			0
$937$	−6915.56			−0.241112			−0.120556	−	0.992707i	$-0.538468\pi$
$937$	−6915.56			−0.241112			−0.120556	+	0.992707i	$0.538468\pi$
$938$		0			0
$939$		−	16180.4i		−	0.562329i
$940$		0			0
$941$	−1197.33	+	1197.33i	−0.0414790	+	0.0414790i	−0.727542	−	0.686063i	$-0.759337\pi$
$941$	−1197.33	+	1197.33i	−0.0414790	+	0.0414790i	0.686063	+	0.727542i	$0.259337\pi$
$942$		0			0
$943$	−498.385	+	498.385i	−0.0172106	+	0.0172106i
$944$		0			0
$945$	−4365.95			−0.150290
$946$		0			0
$947$	16390.6	−	16390.6i	0.562432	−	0.562432i	−0.367566	−	0.929998i	$-0.619809\pi$
$947$	16390.6	−	16390.6i	0.562432	−	0.562432i	0.929998	+	0.367566i	$0.119809\pi$
$948$		0			0
$949$	−38869.4	+	15227.8i	−1.32956	+	0.520881i
$950$		0			0
$951$	20569.8	+	20569.8i	0.701390	+	0.701390i
$952$		0			0
$953$		−	6451.51i		−	0.219292i	−0.993971	−	0.109646i	$-0.965028\pi$
$953$		−	6451.51i		−	0.219292i	0.993971	−	0.109646i	$-0.0349717\pi$
$954$		0			0
$955$	9298.87	+	9298.87i	0.315083	+	0.315083i
$956$		0			0
$957$	8961.75	+	8961.75i	0.302709	+	0.302709i
$958$		0			0
$959$	3858.84			0.129936
$960$		0			0
$961$		−	8716.35i		−	0.292583i
$962$		0			0
$963$		−	2339.66i		−	0.0782912i
$964$		0			0
$965$	53746.4			1.79291
$966$		0			0
$967$	−29010.0	−	29010.0i	−0.964735	−	0.964735i	0.0346639	−	0.999399i	$-0.488964\pi$
$967$	−29010.0	−	29010.0i	−0.964735	−	0.964735i	−0.999399	+	0.0346639i	$0.988964\pi$
$968$		0			0
$969$	735.382	+	735.382i	0.0243796	+	0.0243796i
$970$		0			0
$971$		−	8585.89i		−	0.283764i	−0.989884	−	0.141882i	$-0.954685\pi$
$971$		−	8585.89i		−	0.283764i	0.989884	−	0.141882i	$-0.0453153\pi$
$972$		0			0
$973$	−19759.1	−	19759.1i	−0.651026	−	0.651026i
$974$		0			0
$975$	6515.50	−	14908.9i	0.214013	−	0.489710i
$976$		0			0
$977$	34810.6	−	34810.6i	1.13991	−	1.13991i	0.151442	−	0.988466i	$-0.451608\pi$
$977$	34810.6	−	34810.6i	1.13991	−	1.13991i	0.988466	−	0.151442i	$-0.0483918\pi$
$978$		0			0
$979$	32089.0			1.04757
$980$		0			0
$981$	4504.56	−	4504.56i	0.146605	−	0.146605i
$982$		0			0
$983$	−19086.5	+	19086.5i	−0.619291	+	0.619291i	−0.945350	−	0.326058i	$-0.894279\pi$
$983$	−19086.5	+	19086.5i	−0.619291	+	0.619291i	0.326058	+	0.945350i	$0.394279\pi$
$984$		0			0
$985$		−	39767.2i		−	1.28638i
$986$		0			0
$987$	7221.67			0.232896
$988$		0			0
$989$	−1515.89			−0.0487386
$990$		0			0
$991$		−	43302.0i		−	1.38802i	−0.719963	−	0.694012i	$-0.755841\pi$
$991$		−	43302.0i		−	1.38802i	0.719963	−	0.694012i	$-0.244159\pi$
$992$		0			0
$993$	−16800.2	+	16800.2i	−0.536897	+	0.536897i
$994$		0			0
$995$	−37051.6	+	37051.6i	−1.18052	+	1.18052i
$996$		0			0
$997$	8852.23			0.281197			0.140598	−	0.990067i	$-0.455097\pi$
$997$	8852.23			0.281197			0.140598	+	0.990067i	$0.455097\pi$
$998$		0			0
$999$	−5816.03	+	5816.03i	−0.184195	+	0.184195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bc.a.31.1	✓	14
4.3	odd	2		624.4.bc.b.31.1	yes	14
13.8	odd	4		624.4.bc.b.463.1	yes	14
52.47	even	4	inner	624.4.bc.a.463.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.4.bc.a.31.1	✓	14	1.1	even	1	trivial
624.4.bc.a.463.1	yes	14	52.47	even	4	inner
624.4.bc.b.31.1	yes	14	4.3	odd	2
624.4.bc.b.463.1	yes	14	13.8	odd	4

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.00000i q^{3} +(-10.9706 + 10.9706i) q^{5} +(7.36979 - 7.36979i) q^{7} -9.00000 q^{9} +(36.0614 - 36.0614i) q^{11} +(-18.7699 + 42.9498i) q^{13} +(32.9118 + 32.9118i) q^{15} -3.63826i q^{17} +(-67.3749 - 67.3749i) q^{19} +(-22.1094 - 22.1094i) q^{21} +24.5391 q^{23} -115.708i q^{25} +27.0000i q^{27} -82.8379 q^{29} +(102.651 + 102.651i) q^{31} +(-108.184 - 108.184i) q^{33} +161.702i q^{35} +(215.409 + 215.409i) q^{37} +(128.850 + 56.3098i) q^{39} +(-20.3098 + 20.3098i) q^{41} -61.7745 q^{43} +(98.7354 - 98.7354i) q^{45} +(-163.317 + 163.317i) q^{47} +234.372i q^{49} -10.9148 q^{51} -551.555 q^{53} +791.230i q^{55} +(-202.125 + 202.125i) q^{57} +(-541.810 + 541.810i) q^{59} +391.345 q^{61} +(-66.3281 + 66.3281i) q^{63} +(-265.268 - 677.103i) q^{65} +(194.093 + 194.093i) q^{67} -73.6173i q^{69} +(289.844 + 289.844i) q^{71} +(629.772 + 629.772i) q^{73} -347.124 q^{75} -531.530i q^{77} +800.798i q^{79} +81.0000 q^{81} +(-96.9092 - 96.9092i) q^{83} +(39.9139 + 39.9139i) q^{85} +248.514i q^{87} +(444.922 + 444.922i) q^{89} +(178.201 + 454.862i) q^{91} +(307.954 - 307.954i) q^{93} +1478.28 q^{95} +(841.467 - 841.467i) q^{97} +(-324.552 + 324.552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} - 12 q^{7} - 126 q^{9} - 64 q^{11} + 32 q^{13} - 6 q^{15} - 84 q^{19} + 36 q^{21} - 384 q^{23} + 32 q^{29} - 140 q^{31} + 192 q^{33} - 466 q^{37} + 270 q^{39} - 98 q^{41} - 104 q^{43} - 18 q^{45}+ \cdots + 576 q^{99}+O(q^{100}) \) 14 * q + 2 * q^5 - 12 * q^7 - 126 * q^9 - 64 * q^11 + 32 * q^13 - 6 * q^15 - 84 * q^19 + 36 * q^21 - 384 * q^23 + 32 * q^29 - 140 * q^31 + 192 * q^33 - 466 * q^37 + 270 * q^39 - 98 * q^41 - 104 * q^43 - 18 * q^45 + 688 * q^47 + 156 * q^51 - 1612 * q^53 - 252 * q^57 - 1752 * q^59 + 1284 * q^61 + 108 * q^63 + 1566 * q^65 + 1260 * q^67 + 968 * q^71 + 838 * q^73 - 1434 * q^75 + 1134 * q^81 - 1688 * q^83 - 572 * q^85 - 2666 * q^89 - 412 * q^91 - 420 * q^93 - 816 * q^95 + 422 * q^97 + 576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more