LMFDB - Embedded newform 547.3.b.b.546.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,3,Mod(546,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("547.546");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	547.b (of order $2$, degree $1$, 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:	$14.9046704605$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			546.7
Character	$\chi$	$=$	547.546
Dual form			547.3.b.b.546.82

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.54186i q^{2} -4.64741i q^{3} -8.54479 q^{4} +0.255244i q^{5} -16.4605 q^{6} +11.6148i q^{7} +16.0970i q^{8} -12.5984 q^{9} +O(q^{10})$	\(q-3.54186i q^{2} -4.64741i q^{3} -8.54479 q^{4} +0.255244i q^{5} -16.4605 q^{6} +11.6148i q^{7} +16.0970i q^{8} -12.5984 q^{9} +0.904038 q^{10} -12.4031 q^{11} +39.7112i q^{12} -0.542969 q^{13} +41.1379 q^{14} +1.18622 q^{15} +22.8343 q^{16} -14.5049i q^{17} +44.6219i q^{18} -17.7532 q^{19} -2.18100i q^{20} +53.9786 q^{21} +43.9301i q^{22} +7.49457i q^{23} +74.8095 q^{24} +24.9349 q^{25} +1.92312i q^{26} +16.7234i q^{27} -99.2457i q^{28} +34.3537 q^{29} -4.20144i q^{30} +7.89329i q^{31} -16.4878i q^{32} +57.6423i q^{33} -51.3743 q^{34} -2.96459 q^{35} +107.651 q^{36} +17.1813i q^{37} +62.8794i q^{38} +2.52340i q^{39} -4.10866 q^{40} -36.8465i q^{41} -191.185i q^{42} +41.2589i q^{43} +105.982 q^{44} -3.21567i q^{45} +26.5447 q^{46} -76.1101 q^{47} -106.120i q^{48} -85.9026 q^{49} -88.3158i q^{50} -67.4102 q^{51} +4.63956 q^{52} +18.4763 q^{53} +59.2319 q^{54} -3.16581i q^{55} -186.963 q^{56} +82.5065i q^{57} -121.676i q^{58} +70.5086i q^{59} -10.1360 q^{60} +66.0407i q^{61} +27.9569 q^{62} -146.328i q^{63} +32.9395 q^{64} -0.138590i q^{65} +204.161 q^{66} -20.9057 q^{67} +123.941i q^{68} +34.8304 q^{69} +10.5002i q^{70} +98.2729i q^{71} -202.797i q^{72} -131.826 q^{73} +60.8539 q^{74} -115.882i q^{75} +151.697 q^{76} -144.059i q^{77} +8.93754 q^{78} +79.0613i q^{79} +5.82831i q^{80} -35.6655 q^{81} -130.505 q^{82} -7.11235i q^{83} -461.236 q^{84} +3.70228 q^{85} +146.133 q^{86} -159.656i q^{87} -199.653i q^{88} +77.4494i q^{89} -11.3895 q^{90} -6.30646i q^{91} -64.0396i q^{92} +36.6834 q^{93} +269.571i q^{94} -4.53139i q^{95} -76.6258 q^{96} -175.130 q^{97} +304.255i q^{98} +156.259 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) $ 88 * q - 192 * q^4 - 306 * q^9	$ 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) $ 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	3.54186i		−	1.77093i	−0.464705	−	0.885466i	$-0.653840\pi$
$2$		−	3.54186i		−	1.77093i	0.464705	−	0.885466i	$-0.346160\pi$
$3$		−	4.64741i		−	1.54914i	−0.632490	−	0.774568i	$-0.717967\pi$
$3$		−	4.64741i		−	1.54914i	0.632490	−	0.774568i	$-0.282033\pi$
$4$	−8.54479			−2.13620
$5$			0.255244i			0.0510487i	0.999674	+	0.0255244i	$0.00812554\pi$
$5$			0.255244i			0.0510487i	−0.999674	+	0.0255244i	$0.991874\pi$
$6$	−16.4605			−2.74342
$7$			11.6148i			1.65925i	0.558320	+	0.829626i	$0.311446\pi$
$7$			11.6148i			1.65925i	−0.558320	+	0.829626i	$0.688554\pi$
$8$			16.0970i			2.01213i
$9$	−12.5984			−1.39983
$10$	0.904038			0.0904038
$11$	−12.4031			−1.12755			−0.563777	−	0.825927i	$-0.690652\pi$
$11$	−12.4031			−1.12755			−0.563777	+	0.825927i	$0.690652\pi$
$12$			39.7112i			3.30926i
$13$	−0.542969			−0.0417669			−0.0208834	−	0.999782i	$-0.506648\pi$
$13$	−0.542969			−0.0417669			−0.0208834	+	0.999782i	$0.506648\pi$
$14$	41.1379			2.93842
$15$	1.18622			0.0790815
$16$	22.8343			1.42714
$17$		−	14.5049i		−	0.853229i	−0.904434	−	0.426614i	$-0.859706\pi$
$17$		−	14.5049i		−	0.853229i	0.904434	−	0.426614i	$-0.140294\pi$
$18$			44.6219i			2.47899i
$19$	−17.7532			−0.934379			−0.467190	−	0.884157i	$-0.654733\pi$
$19$	−17.7532			−0.934379			−0.467190	+	0.884157i	$0.654733\pi$
$20$		−	2.18100i		−	0.109050i
$21$	53.9786			2.57041
$22$			43.9301i			1.99682i
$23$			7.49457i			0.325851i	0.986638	+	0.162925i	$0.0520930\pi$
$23$			7.49457i			0.325851i	−0.986638	+	0.162925i	$0.947907\pi$
$24$	74.8095			3.11706
$25$	24.9349			0.997394
$26$			1.92312i			0.0739663i
$27$			16.7234i			0.619384i
$28$		−	99.2457i		−	3.54449i
$29$	34.3537			1.18461			0.592306	−	0.805713i	$-0.298218\pi$
$29$	34.3537			1.18461			0.592306	+	0.805713i	$0.298218\pi$
$30$		−	4.20144i		−	0.140048i
$31$			7.89329i			0.254622i	0.991863	+	0.127311i	$0.0406347\pi$
$31$			7.89329i			0.254622i	−0.991863	+	0.127311i	$0.959365\pi$
$32$		−	16.4878i		−	0.515245i
$33$			57.6423i			1.74674i
$34$	−51.3743			−1.51101
$35$	−2.96459			−0.0847027
$36$	107.651			2.99030
$37$			17.1813i			0.464360i	0.972673	+	0.232180i	$0.0745859\pi$
$37$			17.1813i			0.464360i	−0.972673	+	0.232180i	$0.925414\pi$
$38$			62.8794i			1.65472i
$39$			2.52340i			0.0647026i
$40$	−4.10866			−0.102717
$41$		−	36.8465i		−	0.898694i	−0.893357	−	0.449347i	$-0.851657\pi$
$41$		−	36.8465i		−	0.898694i	0.893357	−	0.449347i	$-0.148343\pi$
$42$		−	191.185i		−	4.55202i
$43$			41.2589i			0.959508i	0.877403	+	0.479754i	$0.159274\pi$
$43$			41.2589i			0.959508i	−0.877403	+	0.479754i	$0.840726\pi$
$44$	105.982			2.40868
$45$		−	3.21567i		−	0.0714593i
$46$	26.5447			0.577060
$47$	−76.1101			−1.61936			−0.809681	−	0.586870i	$-0.800360\pi$
$47$	−76.1101			−1.61936			−0.809681	+	0.586870i	$0.800360\pi$
$48$		−	106.120i		−	2.21084i
$49$	−85.9026			−1.75312
$50$		−	88.3158i		−	1.76632i
$51$	−67.4102			−1.32177
$52$	4.63956			0.0892223
$53$	18.4763			0.348610			0.174305	−	0.984692i	$-0.444232\pi$
$53$	18.4763			0.348610			0.174305	+	0.984692i	$0.444232\pi$
$54$	59.2319			1.09689
$55$		−	3.16581i		−	0.0575602i
$56$	−186.963			−3.33863
$57$			82.5065i			1.44748i
$58$		−	121.676i		−	2.09786i
$59$			70.5086i			1.19506i	0.801846	+	0.597531i	$0.203851\pi$
$59$			70.5086i			1.19506i	−0.801846	+	0.597531i	$0.796149\pi$
$60$	−10.1360			−0.168934
$61$			66.0407i			1.08263i	0.840819	+	0.541317i	$0.182074\pi$
$61$			66.0407i			1.08263i	−0.840819	+	0.541317i	$0.817926\pi$
$62$	27.9569			0.450918
$63$		−	146.328i		−	2.32266i
$64$	32.9395			0.514680
$65$		−	0.138590i		−	0.00213215i
$66$	204.161			3.09335
$67$	−20.9057			−0.312025			−0.156013	−	0.987755i	$-0.549864\pi$
$67$	−20.9057			−0.312025			−0.156013	+	0.987755i	$0.549864\pi$
$68$			123.941i			1.82267i
$69$	34.8304			0.504788
$70$			10.5002i			0.150003i
$71$			98.2729i			1.38413i	0.721837	+	0.692063i	$0.243298\pi$
$71$			98.2729i			1.38413i	−0.721837	+	0.692063i	$0.756702\pi$
$72$		−	202.797i		−	2.81663i
$73$	−131.826			−1.80584			−0.902921	−	0.429807i	$-0.858581\pi$
$73$	−131.826			−1.80584			−0.902921	+	0.429807i	$0.858581\pi$
$74$	60.8539			0.822350
$75$		−	115.882i		−	1.54510i
$76$	151.697			1.99602
$77$		−	144.059i		−	1.87090i
$78$	8.93754			0.114584
$79$			79.0613i			1.00078i	0.865801	+	0.500388i	$0.166809\pi$
$79$			79.0613i			1.00078i	−0.865801	+	0.500388i	$0.833191\pi$
$80$			5.82831i			0.0728539i
$81$	−35.6655			−0.440314
$82$	−130.505			−1.59153
$83$		−	7.11235i		−	0.0856909i	−0.999082	−	0.0428455i	$-0.986358\pi$
$83$		−	7.11235i		−	0.0856909i	0.999082	−	0.0428455i	$-0.0136423\pi$
$84$	−461.236			−5.49090
$85$	3.70228			0.0435563
$86$	146.133			1.69922
$87$		−	159.656i		−	1.83512i
$88$		−	199.653i		−	2.26878i
$89$			77.4494i			0.870218i	0.900378	+	0.435109i	$0.143290\pi$
$89$			77.4494i			0.870218i	−0.900378	+	0.435109i	$0.856710\pi$
$90$	−11.3895			−0.126550
$91$		−	6.30646i		−	0.0693018i
$92$		−	64.0396i		−	0.696082i
$93$	36.6834			0.394445
$94$			269.571i			2.86778i
$95$		−	4.53139i		−	0.0476989i
$96$	−76.6258			−0.798185
$97$	−175.130			−1.80546			−0.902731	−	0.430206i	$-0.858441\pi$
$97$	−175.130			−1.80546			−0.902731	+	0.430206i	$0.858441\pi$
$98$			304.255i			3.10465i
$99$	156.259			1.57838
$100$	−213.063			−2.13063
$101$		−	41.7414i		−	0.413281i	−0.978417	−	0.206640i	$-0.933747\pi$
$101$		−	41.7414i		−	0.413281i	0.978417	−	0.206640i	$-0.0662530\pi$
$102$			238.758i			2.34076i
$103$			158.670i			1.54049i	0.637750	+	0.770243i	$0.279865\pi$
$103$			158.670i			1.54049i	−0.637750	+	0.770243i	$0.720135\pi$
$104$		−	8.74019i		−	0.0840403i
$105$			13.7777i			0.131216i
$106$		−	65.4405i		−	0.617364i
$107$		−	129.023i		−	1.20582i	−0.797810	−	0.602910i	$-0.794008\pi$
$107$		−	129.023i		−	1.20582i	0.797810	−	0.602910i	$-0.205992\pi$
$108$		−	142.898i		−	1.32313i
$109$		−	82.1622i		−	0.753782i	−0.926258	−	0.376891i	$-0.876993\pi$
$109$		−	82.1622i		−	0.753782i	0.926258	−	0.376891i	$-0.123007\pi$
$110$	−11.2129			−0.101935
$111$	79.8487			0.719358
$112$			265.215i			2.36799i
$113$	84.0681			0.743965			0.371983	−	0.928240i	$-0.378678\pi$
$113$	84.0681			0.743965			0.371983	+	0.928240i	$0.378678\pi$
$114$	292.227			2.56339
$115$	−1.91294			−0.0166343
$116$	−293.545			−2.53056
$117$	6.84056			0.0584663
$118$	249.732			2.11637
$119$	168.471			1.41572
$120$			19.0947i			0.159122i
$121$	32.8367			0.271378
$122$	233.907			1.91727
$123$	−171.241			−1.39220
$124$		−	67.4465i		−	0.543923i
$125$			12.7456i			0.101964i
$126$	−518.273			−4.11328
$127$	80.8938			0.636959			0.318480	−	0.947930i	$-0.396828\pi$
$127$	80.8938			0.636959			0.318480	+	0.947930i	$0.396828\pi$
$128$		−	182.619i		−	1.42671i
$129$	191.747			1.48641
$130$	−0.490865			−0.00377588
$131$	51.9527			0.396586			0.198293	−	0.980143i	$-0.436460\pi$
$131$	51.9527			0.396586			0.198293	+	0.980143i	$0.436460\pi$
$132$		−	492.541i		−	3.73137i
$133$		−	206.199i		−	1.55037i
$134$			74.0451i			0.552575i
$135$	−4.26853			−0.0316188
$136$	233.486			1.71681
$137$	−27.8964			−0.203623			−0.101812	−	0.994804i	$-0.532464\pi$
$137$	−27.8964			−0.203623			−0.101812	+	0.994804i	$0.532464\pi$
$138$		−	123.364i		−	0.893945i
$139$	41.2319			0.296632			0.148316	−	0.988940i	$-0.452615\pi$
$139$	41.2319			0.296632			0.148316	+	0.988940i	$0.452615\pi$
$140$	25.3318			0.180942
$141$			353.715i			2.50861i
$142$	348.069			2.45119
$143$	6.73450			0.0470944
$144$	−287.676			−1.99775
$145$			8.76857i			0.0604729i
$146$			466.911i			3.19802i
$147$			399.225i			2.71582i
$148$		−	146.811i		−	0.991965i
$149$	4.00548			0.0268824			0.0134412	−	0.999910i	$-0.495721\pi$
$149$	4.00548			0.0268824			0.0134412	+	0.999910i	$0.495721\pi$
$150$	−410.440			−2.73627
$151$		−	289.948i		−	1.92019i	−0.279678	−	0.960094i	$-0.590228\pi$
$151$		−	289.948i		−	1.92019i	0.279678	−	0.960094i	$-0.409772\pi$
$152$		−	285.774i		−	1.88009i
$153$			182.739i			1.19437i
$154$	−510.237			−3.31323
$155$	−2.01471			−0.0129981
$156$		−	21.5619i		−	0.138218i
$157$	−44.6229			−0.284223			−0.142111	−	0.989851i	$-0.545389\pi$
$157$	−44.6229			−0.284223			−0.142111	+	0.989851i	$0.545389\pi$
$158$	280.024			1.77230
$159$		−	85.8670i		−	0.540044i
$160$	4.20842			0.0263026
$161$	−87.0477			−0.540669
$162$			126.322i			0.779767i
$163$		−	36.5222i		−	0.224062i	−0.993705	−	0.112031i	$-0.964264\pi$
$163$		−	36.5222i		−	0.224062i	0.993705	−	0.112031i	$-0.0357357\pi$
$164$			314.845i			1.91979i
$165$	−14.7128			−0.0891686
$166$	−25.1910			−0.151753
$167$	192.346			1.15177			0.575887	−	0.817529i	$-0.304657\pi$
$167$	192.346			1.15177			0.575887	+	0.817529i	$0.304657\pi$
$168$			868.894i			5.17199i
$169$	−168.705			−0.998256
$170$		−	13.1130i		−	0.0771351i
$171$	223.663			1.30797
$172$		−	352.548i		−	2.04970i
$173$			1.77044i			0.0102338i	0.999987	+	0.00511689i	$0.00162876\pi$
$173$			1.77044i			0.0102338i	−0.999987	+	0.00511689i	$0.998371\pi$
$174$	−565.479			−3.24988
$175$			289.612i			1.65493i
$176$	−283.216			−1.60918
$177$	327.682			1.85131
$178$	274.315			1.54110
$179$	−99.2700			−0.554581			−0.277290	−	0.960786i	$-0.589436\pi$
$179$	−99.2700			−0.554581			−0.277290	+	0.960786i	$0.589436\pi$
$180$			27.4772i			0.152651i
$181$	−316.466			−1.74843			−0.874215	−	0.485539i	$-0.838623\pi$
$181$	−316.466			−1.74843			−0.874215	+	0.485539i	$0.838623\pi$
$182$	−22.3366			−0.122729
$183$	306.918			1.67715
$184$	−120.640			−0.655654
$185$	−4.38542			−0.0237050
$186$		−	129.927i		−	0.698534i
$187$			179.906i			0.962062i
$188$	650.345			3.45928
$189$	−194.238			−1.02771
$190$	−16.0496			−0.0844714
$191$	−255.005			−1.33511			−0.667553	−	0.744562i	$-0.732658\pi$
$191$	−255.005			−1.33511			−0.667553	+	0.744562i	$0.732658\pi$
$192$		−	153.084i		−	0.797310i
$193$	−243.823			−1.26333			−0.631665	−	0.775241i	$-0.717628\pi$
$193$	−243.823			−1.26333			−0.631665	+	0.775241i	$0.717628\pi$
$194$			620.286i			3.19735i
$195$	−0.644082			−0.00330299
$196$	734.020			3.74500
$197$		−	19.5798i		−	0.0993899i	−0.998764	−	0.0496949i	$-0.984175\pi$
$197$		−	19.5798i		−	0.0993899i	0.998764	−	0.0496949i	$-0.0158249\pi$
$198$		−	553.450i		−	2.79520i
$199$	−247.254			−1.24248			−0.621240	−	0.783620i	$-0.713371\pi$
$199$	−247.254			−1.24248			−0.621240	+	0.783620i	$0.713371\pi$
$200$			401.377i			2.00689i
$201$			97.1574i			0.483370i
$202$	−147.842			−0.731892
$203$			399.010i			1.96557i
$204$	576.006			2.82356
$205$	9.40482			0.0458772
$206$	561.988			2.72810
$207$		−	94.4198i		−	0.456134i
$208$	−12.3983			−0.0596073
$209$	220.195			1.05356
$210$	48.7987			0.232375
$211$			95.8966i			0.454486i	0.973838	+	0.227243i	$0.0729712\pi$
$211$			95.8966i			0.454486i	−0.973838	+	0.227243i	$0.927029\pi$
$212$	−157.876			−0.744699
$213$	456.715			2.14420
$214$	−456.981			−2.13542
$215$	−10.5311			−0.0489817
$216$	−269.197			−1.24628
$217$	−91.6787			−0.422482
$218$	−291.007			−1.33490
$219$			612.651i			2.79750i
$220$			27.0512i			0.122960i
$221$			7.87571i			0.0356367i
$222$		−	282.813i		−	1.27393i
$223$		−	227.224i		−	1.01894i	−0.860488	−	0.509470i	$-0.829841\pi$
$223$		−	227.224i		−	1.01894i	0.860488	−	0.509470i	$-0.170159\pi$
$224$	191.502			0.854921
$225$	−314.140			−1.39618
$226$		−	297.758i		−	1.31751i
$227$	−358.894			−1.58103			−0.790516	−	0.612441i	$-0.790188\pi$
$227$	−358.894			−1.58103			−0.790516	+	0.612441i	$0.790188\pi$
$228$		−	705.000i		−	3.09211i
$229$		−	393.051i		−	1.71638i	−0.513332	−	0.858190i	$-0.671589\pi$
$229$		−	393.051i		−	1.71638i	0.513332	−	0.858190i	$-0.328411\pi$
$230$			6.77538i			0.0294582i
$231$	−669.501			−2.89827
$232$			552.993i			2.38359i
$233$	−138.417			−0.594066			−0.297033	−	0.954867i	$-0.595997\pi$
$233$	−138.417			−0.594066			−0.297033	+	0.954867i	$0.595997\pi$
$234$		−	24.2283i		−	0.103540i
$235$		−	19.4266i		−	0.0826664i
$236$		−	602.481i		−	2.55289i
$237$	367.430			1.55034
$238$		−	596.701i		−	2.50715i
$239$	227.485			0.951822			0.475911	−	0.879493i	$-0.342118\pi$
$239$	227.485			0.951822			0.475911	+	0.879493i	$0.342118\pi$
$240$	27.0866			0.112861
$241$			5.68949i			0.0236079i	0.999930	+	0.0118039i	$0.00375740\pi$
$241$			5.68949i			0.0236079i	−0.999930	+	0.0118039i	$0.996243\pi$
$242$		−	116.303i		−	0.480592i
$243$			316.262i			1.30149i
$244$		−	564.304i		−	2.31272i
$245$		−	21.9261i		−	0.0894943i
$246$			606.511i			2.46549i
$247$	9.63945			0.0390261
$248$	−127.058			−0.512333
$249$	−33.0540			−0.132747
$250$	45.1430			0.180572
$251$		−	49.2666i		−	0.196281i	−0.995173	−	0.0981406i	$-0.968711\pi$
$251$		−	49.2666i		−	0.196281i	0.995173	−	0.0981406i	$-0.0312895\pi$
$252$			1250.34i			4.96167i
$253$		−	92.9559i		−	0.367415i
$254$		−	286.515i		−	1.12801i
$255$		−	17.2060i		−	0.0674746i
$256$	−515.052			−2.01192
$257$		−	417.277i		−	1.62365i	−0.583902	−	0.811824i	$-0.698475\pi$
$257$		−	417.277i		−	1.62365i	0.583902	−	0.811824i	$-0.301525\pi$
$258$		−	679.141i		−	2.63233i
$259$	−199.557			−0.770490
$260$			1.18422i			0.00455469i
$261$	−432.803			−1.65825
$262$		−	184.009i		−	0.702326i
$263$	−133.985			−0.509450			−0.254725	−	0.967014i	$-0.581985\pi$
$263$	−133.985			−0.509450			−0.254725	+	0.967014i	$0.581985\pi$
$264$	−927.869			−3.51466
$265$			4.71596i			0.0177961i
$266$	−730.329			−2.74560
$267$	359.939			1.34809
$268$	178.635			0.666548
$269$	223.846			0.832141			0.416070	−	0.909332i	$-0.363407\pi$
$269$	223.846			0.832141			0.416070	+	0.909332i	$0.363407\pi$
$270$			15.1186i			0.0559947i
$271$			212.376i			0.783677i	0.920034	+	0.391838i	$0.128161\pi$
$271$			212.376i			0.783677i	−0.920034	+	0.391838i	$0.871839\pi$
$272$		−	331.209i		−	1.21768i
$273$	−29.3087			−0.107358
$274$			98.8051i			0.360603i
$275$	−309.269			−1.12462
$276$	−297.618			−1.07833
$277$	376.244			1.35828			0.679141	−	0.734008i	$-0.262353\pi$
$277$	376.244			1.35828			0.679141	+	0.734008i	$0.262353\pi$
$278$		−	146.038i		−	0.525315i
$279$		−	99.4430i		−	0.356427i
$280$		−	47.7212i		−	0.170433i
$281$			402.336i			1.43180i	0.698202	+	0.715901i	$0.253984\pi$
$281$			402.336i			1.43180i	−0.698202	+	0.715901i	$0.746016\pi$
$282$	1252.81			4.44258
$283$			33.1549i			0.117155i	0.998283	+	0.0585776i	$0.0186565\pi$
$283$			33.1549i			0.117155i	−0.998283	+	0.0585776i	$0.981343\pi$
$284$		−	839.721i		−	2.95677i
$285$	−21.0592			−0.0738921
$286$		−	23.8527i		−	0.0834010i
$287$	427.963			1.49116
$288$			207.721i			0.721253i
$289$	78.6081			0.272000
$290$	31.0571			0.107093
$291$			813.900i			2.79691i
$292$	1126.43			3.85763
$293$	−527.185			−1.79927			−0.899633	−	0.436646i	$-0.856166\pi$
$293$	−527.185			−1.79927			−0.899633	+	0.436646i	$0.856166\pi$
$294$	1414.00			4.80952
$295$	−17.9969			−0.0610063
$296$	−276.568			−0.934352
$297$		−	207.422i		−	0.698389i
$298$		−	14.1869i		−	0.0476069i
$299$		−	4.06932i		−	0.0136098i
$300$			990.192i			3.30064i
$301$	−479.212			−1.59207
$302$	−1026.96			−3.40052
$303$	−193.989			−0.640229
$304$	−405.382			−1.33349
$305$	−16.8565			−0.0552671
$306$	647.236			2.11515
$307$			454.225i			1.47956i	0.672850	+	0.739779i	$0.265070\pi$
$307$			454.225i			1.47956i	−0.672850	+	0.739779i	$0.734930\pi$
$308$			1230.95i			3.99660i
$309$	737.405			2.38642
$310$			7.13583i			0.0230188i
$311$	−515.653			−1.65805			−0.829025	−	0.559212i	$-0.811104\pi$
$311$	−515.653			−1.65805			−0.829025	+	0.559212i	$0.811104\pi$
$312$	−40.6193			−0.130190
$313$	418.386			1.33670			0.668349	−	0.743848i	$-0.267001\pi$
$313$	418.386			1.33670			0.668349	+	0.743848i	$0.267001\pi$
$314$			158.048i			0.503339i
$315$	37.3492			0.118569
$316$		−	675.562i		−	2.13785i
$317$	287.604			0.907268			0.453634	−	0.891188i	$-0.350127\pi$
$317$	287.604			0.907268			0.453634	+	0.891188i	$0.350127\pi$
$318$	−304.129			−0.956381
$319$	−426.092			−1.33571
$320$			8.40761i			0.0262738i
$321$	−599.621			−1.86798
$322$			308.311i			0.957487i
$323$			257.508i			0.797240i
$324$	304.754			0.940599
$325$	−13.5389			−0.0416580
$326$	−129.357			−0.396799
$327$	−381.842			−1.16771
$328$	593.118			1.80829
$329$		−	884.000i		−	2.68693i
$330$			52.1108i			0.157912i
$331$		−	360.170i		−	1.08813i	−0.839044	−	0.544063i	$-0.816885\pi$
$331$		−	360.170i		−	1.08813i	0.839044	−	0.544063i	$-0.183115\pi$
$332$			60.7735i			0.183053i
$333$		−	216.458i		−	0.650023i
$334$		−	681.264i		−	2.03971i
$335$		−	5.33605i		−	0.0159285i
$336$	1232.56			3.66834
$337$		−	93.6738i		−	0.277964i	−0.990295	−	0.138982i	$-0.955617\pi$
$337$		−	93.6738i		−	0.277964i	0.990295	−	0.138982i	$-0.0443830\pi$
$338$			597.531i			1.76784i
$339$		−	390.699i		−	1.15250i
$340$	−31.6352			−0.0930448
$341$		−	97.9012i		−	0.287100i
$342$		−	792.182i		−	2.31632i
$343$		−	428.615i		−	1.24961i
$344$	−664.145			−1.93065
$345$			8.89023i			0.0257688i
$346$	6.27067			0.0181233
$347$	57.4556			0.165578			0.0827890	−	0.996567i	$-0.473617\pi$
$347$	57.4556			0.165578			0.0827890	+	0.996567i	$0.473617\pi$
$348$			1364.23i			3.92019i
$349$	502.220			1.43903			0.719513	−	0.694479i	$-0.244365\pi$
$349$	502.220			1.43903			0.719513	+	0.694479i	$0.244365\pi$
$350$	1025.77			2.93076
$351$		−	9.08028i		−	0.0258697i
$352$			204.500i			0.580967i
$353$	−428.099			−1.21275			−0.606373	−	0.795180i	$-0.707376\pi$
$353$	−428.099			−1.21275			−0.606373	+	0.795180i	$0.707376\pi$
$354$		−	1160.61i		−	3.27855i
$355$	−25.0835			−0.0706578
$356$		−	661.789i		−	1.85896i
$357$		−	782.953i		−	2.19315i
$358$			351.601i			0.982125i
$359$		−	464.763i		−	1.29460i	−0.762234	−	0.647302i	$-0.775897\pi$
$359$		−	464.763i		−	1.29460i	0.762234	−	0.647302i	$-0.224103\pi$
$360$	51.7627			0.143785
$361$	−45.8236			−0.126935
$362$			1120.88i			3.09635i
$363$		−	152.606i		−	0.420402i
$364$			53.8874i			0.148042i
$365$		−	33.6479i		−	0.0921859i
$366$		−	1087.06i		−	2.97011i
$367$	600.267			1.63560			0.817802	−	0.575500i	$-0.195192\pi$
$367$	600.267			1.63560			0.817802	+	0.575500i	$0.195192\pi$
$368$			171.133i			0.465036i
$369$			464.207i			1.25801i
$370$			15.5326i			0.0419799i
$371$			214.598i			0.578431i
$372$	−313.452			−0.842612
$373$		−	586.860i		−	1.57335i	−0.617366	−	0.786676i	$-0.711800\pi$
$373$		−	586.860i		−	1.57335i	0.617366	−	0.786676i	$-0.288200\pi$
$374$	637.201			1.70375
$375$	59.2338			0.157957
$376$		−	1225.15i		−	3.25837i
$377$	−18.6530			−0.0494775
$378$			687.964i			1.82001i
$379$	−253.570			−0.669049			−0.334525	−	0.942387i	$-0.608576\pi$
$379$	−253.570			−0.669049			−0.334525	+	0.942387i	$0.608576\pi$
$380$			38.7198i			0.101894i
$381$		−	375.947i		−	0.986737i
$382$			903.194i			2.36438i
$383$	−49.1019			−0.128203			−0.0641017	−	0.997943i	$-0.520418\pi$
$383$	−49.1019			−0.128203			−0.0641017	+	0.997943i	$0.520418\pi$
$384$	−848.704			−2.21017
$385$	36.7701			0.0955068
$386$			863.587i			2.23727i
$387$		−	519.797i		−	1.34314i
$388$	1496.45			3.85682
$389$			33.4665i			0.0860320i	0.999074	+	0.0430160i	$0.0136966\pi$
$389$			33.4665i			0.0860320i	−0.999074	+	0.0430160i	$0.986303\pi$
$390$			2.28125i			0.00584936i
$391$	108.708			0.278025
$392$		−	1382.78i		−	3.52749i
$393$		−	241.446i		−	0.614365i
$394$	−69.3490			−0.176013
$395$	−20.1799			−0.0510883
$396$	−1335.20			−3.37173
$397$			734.390i			1.84985i	0.380151	+	0.924925i	$0.375872\pi$
$397$			734.390i			1.84985i	−0.380151	+	0.924925i	$0.624128\pi$
$398$			875.738i			2.20035i
$399$	−958.293			−2.40174
$400$	569.370			1.42342
$401$	469.169			1.17000			0.584999	−	0.811034i	$-0.301095\pi$
$401$	469.169			1.17000			0.584999	+	0.811034i	$0.301095\pi$
$402$	344.118			0.856015
$403$		−	4.28581i		−	0.0106348i
$404$			356.671i			0.882850i
$405$		−	9.10339i		−	0.0224775i
$406$	1413.24			3.48089
$407$		−	213.102i		−	0.523591i
$408$		−	1085.10i		−	2.65957i
$409$	218.153			0.533382			0.266691	−	0.963782i	$-0.414070\pi$
$409$	218.153			0.533382			0.266691	+	0.963782i	$0.414070\pi$
$410$		−	33.3106i		−	0.0812454i
$411$			129.646i			0.315440i
$412$		−	1355.80i		−	3.29078i
$413$	−818.940			−1.98291
$414$	−334.422			−0.807783
$415$	1.81538			0.00437441
$416$			8.95239i			0.0215202i
$417$		−	191.621i		−	0.459524i
$418$		−	779.899i		−	1.86579i
$419$	373.485			0.891373			0.445687	−	0.895189i	$-0.352960\pi$
$419$	373.485			0.891373			0.445687	+	0.895189i	$0.352960\pi$
$420$		−	117.727i		−	0.280303i
$421$		−	419.473i		−	0.996373i	−0.867070	−	0.498187i	$-0.833999\pi$
$421$		−	419.473i		−	0.996373i	0.867070	−	0.498187i	$-0.166001\pi$
$422$	339.653			0.804864
$423$	958.867			2.26683
$424$			297.414i			0.701447i
$425$		−	361.677i		−	0.851005i
$426$		−	1617.62i		−	3.79723i
$427$	−767.046			−1.79636
$428$			1102.47i			2.57587i
$429$		−	31.2980i		−	0.0729557i
$430$			37.2996i			0.0867432i
$431$			299.631i			0.695200i	0.937643	+	0.347600i	$0.113003\pi$
$431$			299.631i			0.695200i	−0.937643	+	0.347600i	$0.886997\pi$
$432$			381.866i			0.883950i
$433$			401.406i			0.927034i	0.886088	+	0.463517i	$0.153413\pi$
$433$			401.406i			0.927034i	−0.886088	+	0.463517i	$0.846587\pi$
$434$			324.713i			0.748187i
$435$	40.7511			0.0936808
$436$			702.059i			1.61023i
$437$		−	133.053i		−	0.304468i
$438$	2169.93			4.95417
$439$	589.716			1.34332			0.671659	−	0.740861i	$-0.265582\pi$
$439$	589.716			1.34332			0.671659	+	0.740861i	$0.265582\pi$
$440$	50.9602			0.115819
$441$	1082.24			2.45405
$442$	27.8947			0.0631102
$443$	824.552			1.86129			0.930646	−	0.365921i	$-0.119246\pi$
$443$	824.552			1.86129			0.930646	+	0.365921i	$0.119246\pi$
$444$	−682.290			−1.53669
$445$	−19.7685			−0.0444235
$446$	−804.796			−1.80447
$447$		−	18.6151i		−	0.0416446i
$448$			382.585i			0.853984i
$449$	253.319			0.564185			0.282093	−	0.959387i	$-0.408971\pi$
$449$	253.319			0.564185			0.282093	+	0.959387i	$0.408971\pi$
$450$			1112.64i			2.47253i
$451$			457.010i			1.01333i
$452$	−718.344			−1.58926
$453$	−1347.51			−2.97463
$454$			1271.15i			2.79990i
$455$	1.60968			0.00353777
$456$	−1328.11			−2.91252
$457$		−	719.122i		−	1.57357i	−0.617227	−	0.786785i	$-0.711744\pi$
$457$		−	719.122i		−	1.57357i	0.617227	−	0.786785i	$-0.288256\pi$
$458$	−1392.13			−3.03959
$459$	242.571			0.528476
$460$	16.3457			0.0355341
$461$			625.434i			1.35669i	0.734744	+	0.678344i	$0.237302\pi$
$461$			625.434i			1.35669i	−0.734744	+	0.678344i	$0.762698\pi$
$462$			2371.28i			5.13264i
$463$		−	59.5483i		−	0.128614i	−0.997930	−	0.0643070i	$-0.979516\pi$
$463$		−	59.5483i		−	0.128614i	0.997930	−	0.0643070i	$-0.0204837\pi$
$464$	784.443			1.69061
$465$			9.36319i			0.0201359i
$466$			490.255i			1.05205i
$467$	151.244			0.323863			0.161932	−	0.986802i	$-0.448228\pi$
$467$	151.244			0.323863			0.161932	+	0.986802i	$0.448228\pi$
$468$	−58.4512			−0.124896
$469$		−	242.815i		−	0.517728i
$470$	−68.8064			−0.146397
$471$			207.381i			0.440300i
$472$	−1134.98			−2.40462
$473$		−	511.738i		−	1.08190i
$474$		−	1301.39i		−	2.74554i
$475$	−442.674			−0.931944
$476$	−1439.55			−3.02426
$477$	−232.772			−0.487992
$478$		−	805.722i		−	1.68561i
$479$	−100.692			−0.210212			−0.105106	−	0.994461i	$-0.533518\pi$
$479$	−100.692			−0.210212			−0.105106	+	0.994461i	$0.533518\pi$
$480$		−	19.5582i		−	0.0407463i
$481$		−	9.32894i		−	0.0193949i
$482$	20.1514			0.0418079
$483$			404.546i			0.837570i
$484$	−280.583			−0.579717
$485$		−	44.7008i		−	0.0921665i
$486$	1120.16			2.30485
$487$		−	281.606i		−	0.578247i	−0.957292	−	0.289124i	$-0.906636\pi$
$487$		−	281.606i		−	0.578247i	0.957292	−	0.289124i	$-0.0933638\pi$
$488$	−1063.06			−2.17840
$489$	−169.734			−0.347103
$490$	−77.6593			−0.158488
$491$			619.633i			1.26198i	0.775790	+	0.630991i	$0.217352\pi$
$491$			619.633i			1.26198i	−0.775790	+	0.630991i	$0.782648\pi$
$492$	1463.22			2.97402
$493$		−	498.297i		−	1.01074i
$494$		−	34.1416i		−	0.0691126i
$495$			39.8842i			0.0805742i
$496$			180.238i			0.363382i
$497$	−1141.42			−2.29661
$498$			117.073i			0.235086i
$499$	309.127			0.619493			0.309747	−	0.950819i	$-0.399756\pi$
$499$	309.127			0.619493			0.309747	+	0.950819i	$0.399756\pi$
$500$		−	108.908i		−	0.217816i
$501$		−	893.912i		−	1.78426i
$502$	−174.495			−0.347600
$503$			607.853i			1.20846i	0.796812	+	0.604228i	$0.206518\pi$
$503$			607.853i			1.20846i	−0.796812	+	0.604228i	$0.793482\pi$
$504$	2355.44			4.67349
$505$	10.6542			0.0210975
$506$	−329.237			−0.650666
$507$			784.042i			1.54643i
$508$	−691.221			−1.36067
$509$	−225.459			−0.442945			−0.221472	−	0.975167i	$-0.571086\pi$
$509$	−225.459			−0.442945			−0.221472	+	0.975167i	$0.571086\pi$
$510$	−60.9414			−0.119493
$511$		−	1531.13i		−	2.99634i
$512$			1093.77i			2.13627i
$513$		−	296.893i		−	0.578740i
$514$	−1477.94			−2.87537
$515$	−40.4995			−0.0786399
$516$	−1638.44			−3.17527
$517$	944.000			1.82592
$518$			706.803i			1.36449i
$519$	8.22798			0.0158535
$520$	2.23088			0.00429015
$521$	−429.749			−0.824853			−0.412427	−	0.910991i	$-0.635319\pi$
$521$	−429.749			−0.824853			−0.412427	+	0.910991i	$0.635319\pi$
$522$			1532.93i			2.93664i
$523$			541.704i			1.03576i	0.855452	+	0.517881i	$0.173279\pi$
$523$			541.704i			1.03576i	−0.855452	+	0.517881i	$0.826721\pi$
$524$	−443.925			−0.847185
$525$	1345.95			2.56371
$526$			474.557i			0.902200i
$527$	114.491			0.217251
$528$			1316.22i			2.49284i
$529$	472.831			0.893821
$530$	16.7033			0.0315156
$531$		−	888.297i		−	1.67288i
$532$			1761.93i			3.31190i
$533$			20.0065i			0.0375356i
$534$		−	1274.85i		−	2.38737i
$535$	32.9322			0.0615555
$536$		−	336.520i		−	0.627835i
$537$			461.348i			0.859122i
$538$		−	792.831i		−	1.47366i
$539$	1065.46			1.97673
$540$	36.4737			0.0675440
$541$			512.004i			0.946404i	0.880954	+	0.473202i	$0.156902\pi$
$541$			512.004i			0.946404i	−0.880954	+	0.473202i	$0.843098\pi$
$542$	752.208			1.38784
$543$			1470.75i			2.70856i
$544$	−239.154			−0.439622
$545$	20.9714			0.0384796
$546$			103.807i			0.190123i
$547$	−479.375	−	263.456i	−0.876370	−	0.481638i
$547$	−479.375	−	263.456i	−0.876370	−	0.481638i
$548$	238.369			0.434979
$549$		−	832.008i		−	1.51550i
$550$			1095.39i			1.99162i
$551$	−609.889			−1.10688
$552$			560.665i			1.01570i
$553$	−918.278			−1.66054
$554$		−	1332.60i		−	2.40542i
$555$			20.3809i			0.0367223i
$556$	−352.318			−0.633665
$557$	−169.655			−0.304587			−0.152294	−	0.988335i	$-0.548666\pi$
$557$	−169.655			−0.304587			−0.152294	+	0.988335i	$0.548666\pi$
$558$	−352.214			−0.631207
$559$		−	22.4023i		−	0.0400757i
$560$	−67.6944			−0.120883
$561$	836.095			1.49037
$562$	1425.02			2.53562
$563$	−644.735			−1.14518			−0.572589	−	0.819843i	$-0.694061\pi$
$563$	−644.735			−1.14518			−0.572589	+	0.819843i	$0.694061\pi$
$564$		−	3022.42i		−	5.35890i
$565$			21.4578i			0.0379785i
$566$	117.430			0.207474
$567$		−	414.246i		−	0.730592i
$568$	−1581.90			−2.78504
$569$			217.226i			0.381769i	0.981613	+	0.190884i	$0.0611355\pi$
$569$			217.226i			0.381769i	−0.981613	+	0.190884i	$0.938864\pi$
$570$			74.5890i			0.130858i
$571$	198.700			0.347986			0.173993	−	0.984747i	$-0.444333\pi$
$571$	198.700			0.347986			0.173993	+	0.984747i	$0.444333\pi$
$572$	−57.5449			−0.100603
$573$			1185.11i			2.06826i
$574$		−	1515.79i		−	2.64074i
$575$			186.876i			0.325002i
$576$	−414.986			−0.720462
$577$		−	317.108i		−	0.549580i	−0.961504	−	0.274790i	$-0.911392\pi$
$577$		−	317.108i		−	0.549580i	0.961504	−	0.274790i	$-0.0886083\pi$
$578$		−	278.419i		−	0.481694i
$579$			1133.14i			1.95707i
$580$		−	74.9256i		−	0.129182i
$581$	82.6082			0.142183
$582$	2882.72			4.95313
$583$	−229.163			−0.393076
$584$		−	2122.01i		−	3.63358i
$585$			1.74601i			0.00298463i
$586$			1867.22i			3.18638i
$587$	624.463			1.06382			0.531910	−	0.846801i	$-0.321474\pi$
$587$	624.463			1.06382			0.531910	+	0.846801i	$0.321474\pi$
$588$		−	3411.29i		−	5.80152i
$589$		−	140.131i		−	0.237914i
$590$			63.7425i			0.108038i
$591$	−90.9954			−0.153968
$592$			392.324i			0.662709i
$593$	−59.5932			−0.100494			−0.0502472	−	0.998737i	$-0.516001\pi$
$593$	−59.5932			−0.100494			−0.0502472	+	0.998737i	$0.516001\pi$
$594$	−734.659			−1.23680
$595$			43.0011i			0.0722708i
$596$	−34.2260			−0.0574262
$597$			1149.09i			1.92477i
$598$	−14.4130			−0.0241020
$599$	−15.7219			−0.0262468			−0.0131234	−	0.999914i	$-0.504177\pi$
$599$	−15.7219			−0.0262468			−0.0131234	+	0.999914i	$0.504177\pi$
$600$	1865.36			3.10894
$601$	−355.166			−0.590958			−0.295479	−	0.955349i	$-0.595479\pi$
$601$	−355.166			−0.590958			−0.295479	+	0.955349i	$0.595479\pi$
$602$			1697.30i			2.81944i
$603$	263.379			0.436781
$604$			2477.55i			4.10190i
$605$			8.38137i			0.0138535i
$606$			687.084i			1.13380i
$607$	−667.380			−1.09947			−0.549736	−	0.835338i	$-0.685272\pi$
$607$	−667.380			−1.09947			−0.549736	+	0.835338i	$0.685272\pi$
$608$			292.712i			0.481434i
$609$	1854.36			3.04493
$610$			59.7033i			0.0978742i
$611$	41.3254			0.0676357
$612$		−	1561.47i		−	2.55141i
$613$	133.226			0.217334			0.108667	−	0.994078i	$-0.465342\pi$
$613$	133.226			0.217334			0.108667	+	0.994078i	$0.465342\pi$
$614$	1608.80			2.62020
$615$		−	43.7081i		−	0.0710701i
$616$	2318.92			3.76448
$617$		−	300.628i		−	0.487242i	−0.969871	−	0.243621i	$-0.921665\pi$
$617$		−	300.628i		−	0.487242i	0.969871	−	0.243621i	$-0.0783352\pi$
$618$		−	2611.79i		−	4.22619i
$619$		−	323.248i		−	0.522209i	−0.965310	−	0.261105i	$-0.915913\pi$
$619$		−	323.248i		−	0.522209i	0.965310	−	0.261105i	$-0.0840868\pi$
$620$	17.2153			0.0277666
$621$	−125.335			−0.201827
$622$			1826.37i			2.93629i
$623$	−899.556			−1.44391
$624$			57.6201i			0.0923399i
$625$	620.118			0.992189
$626$		−	1481.87i		−	2.36720i
$627$		−	1023.34i		−	1.63211i
$628$	381.294			0.607156
$629$	249.213			0.396206
$630$		−	132.286i		−	0.209977i
$631$	−1002.85			−1.58930			−0.794651	−	0.607067i	$-0.792346\pi$
$631$	−1002.85			−1.58930			−0.794651	+	0.607067i	$0.792346\pi$
$632$	−1272.65			−2.01369
$633$	445.671			0.704062
$634$		−	1018.65i		−	1.60671i
$635$			20.6476i			0.0325160i
$636$			733.715i			1.15364i
$637$	46.6425			0.0732221
$638$			1509.16i			2.36546i
$639$		−	1238.08i		−	1.93753i
$640$	46.6123			0.0728317
$641$			156.581i			0.244276i	0.992513	+	0.122138i	$0.0389751\pi$
$641$			156.581i			0.244276i	−0.992513	+	0.122138i	$0.961025\pi$
$642$			2123.78i			3.30806i
$643$	833.845			1.29680			0.648402	−	0.761298i	$-0.275437\pi$
$643$	833.845			1.29680			0.648402	+	0.761298i	$0.275437\pi$
$644$	743.804			1.15498
$645$			48.9422i			0.0758793i
$646$	912.059			1.41186
$647$	−256.406			−0.396300			−0.198150	−	0.980172i	$-0.563493\pi$
$647$	−256.406			−0.396300			−0.198150	+	0.980172i	$0.563493\pi$
$648$		−	574.108i		−	0.885969i
$649$		−	874.525i		−	1.34750i
$650$			47.9528i			0.0737735i
$651$			426.068i			0.654483i
$652$			312.074i			0.478642i
$653$		−	169.705i		−	0.259886i	−0.991521	−	0.129943i	$-0.958521\pi$
$653$		−	169.705i		−	0.259886i	0.991521	−	0.129943i	$-0.0414794\pi$
$654$			1352.43i			2.06794i
$655$			13.2606i			0.0202452i
$656$		−	841.363i		−	1.28257i
$657$	1660.81			2.52786
$658$	−3131.01			−4.75837
$659$			277.218i			0.420665i	0.977630	+	0.210332i	$0.0674546\pi$
$659$			277.218i			0.420665i	−0.977630	+	0.210332i	$0.932545\pi$
$660$	125.718			0.190482
$661$	−1064.31			−1.61015			−0.805076	−	0.593171i	$-0.797876\pi$
$661$	−1064.31			−1.61015			−0.805076	+	0.593171i	$0.797876\pi$
$662$	−1275.67			−1.92700
$663$	36.6017			0.0552061
$664$	114.488			0.172421
$665$	52.6310			0.0791444
$666$	−766.663			−1.15115
$667$			257.466i			0.386007i
$668$	−1643.56			−2.46042
$669$	−1056.00			−1.57848
$670$	−18.8995			−0.0282083
$671$		−	819.109i		−	1.22073i
$672$		−	889.990i		−	1.32439i
$673$	271.445			0.403336			0.201668	−	0.979454i	$-0.435364\pi$
$673$	271.445			0.403336			0.201668	+	0.979454i	$0.435364\pi$
$674$	−331.780			−0.492255
$675$			416.995i			0.617770i
$676$	1441.55			2.13247
$677$	614.055			0.907024			0.453512	−	0.891250i	$-0.350171\pi$
$677$	614.055			0.907024			0.453512	+	0.891250i	$0.350171\pi$
$678$	−1383.80			−2.04101
$679$		−	2034.09i		−	2.99571i
$680$			59.5957i			0.0876408i
$681$			1667.93i			2.44924i
$682$	−346.753			−0.508435
$683$	−1246.05			−1.82438			−0.912189	−	0.409769i	$-0.865609\pi$
$683$	−1246.05			−1.82438			−0.912189	+	0.409769i	$0.865609\pi$
$684$	−1911.15			−2.79408
$685$		−	7.12037i		−	0.0103947i
$686$	−1518.10			−2.21297
$687$	−1826.67			−2.65891
$688$			942.117i			1.36936i
$689$	−10.0321			−0.0145603
$690$	31.4880			0.0456347
$691$	262.717			0.380199			0.190099	−	0.981765i	$-0.439119\pi$
$691$	262.717			0.380199			0.190099	+	0.981765i	$0.439119\pi$
$692$		−	15.1281i		−	0.0218614i
$693$			1814.92i			2.61893i
$694$		−	203.500i		−	0.293227i
$695$			10.5242i			0.0151427i
$696$	2569.98			3.69251
$697$	−534.454			−0.766792
$698$		−	1778.79i		−	2.54842i
$699$			643.282i			0.920289i
$700$		−	2474.68i		−	3.53525i
$701$	101.129			0.144265			0.0721323	−	0.997395i	$-0.477020\pi$
$701$	101.129			0.144265			0.0721323	+	0.997395i	$0.477020\pi$
$702$	−32.1611			−0.0458135
$703$		−	305.024i		−	0.433889i
$704$	−408.552			−0.580330
$705$	−90.2834			−0.128062
$706$			1516.27i			2.14769i
$707$	484.816			0.685737
$708$	−2799.98			−3.95477
$709$			1084.25i			1.52926i	0.644469	+	0.764631i	$0.277079\pi$
$709$			1084.25i			1.52926i	−0.644469	+	0.764631i	$0.722921\pi$
$710$			88.8424i			0.125130i
$711$		−	996.048i		−	1.40091i
$712$	−1246.70			−1.75099
$713$	−59.1568			−0.0829689
$714$	−2773.11			−3.88391
$715$			1.71894i			0.00240411i
$716$	848.241			1.18469
$717$		−	1057.22i		−	1.47450i
$718$	−1646.13			−2.29265
$719$			921.048i			1.28101i	0.767953	+	0.640506i	$0.221275\pi$
$719$			921.048i			1.28101i	−0.767953	+	0.640506i	$0.778725\pi$
$720$		−	73.4275i		−	0.101983i
$721$	−1842.92			−2.55605
$722$			162.301i			0.224794i
$723$	26.4414			0.0365718
$724$	2704.14			3.73499
$725$	856.605			1.18152
$726$	−540.509			−0.744503
$727$			317.777i			0.437107i	0.975825	+	0.218554i	$0.0701339\pi$
$727$			317.777i			0.437107i	−0.975825	+	0.218554i	$0.929866\pi$
$728$	101.515			0.139444
$729$	1148.81			1.57587
$730$	−119.176			−0.163255
$731$	598.455			0.818680
$732$	−2622.55			−3.58272
$733$			954.872i			1.30269i	0.758782	+	0.651345i	$0.225795\pi$
$733$			954.872i			1.30269i	−0.758782	+	0.651345i	$0.774205\pi$
$734$		−	2126.06i		−	2.89654i
$735$	−101.900			−0.138639
$736$	123.569			0.167893
$737$	259.295			0.351825
$738$	1644.16			2.22786
$739$			294.178i			0.398076i	0.979992	+	0.199038i	$0.0637817\pi$
$739$			294.178i			0.398076i	−0.979992	+	0.199038i	$0.936218\pi$
$740$	37.4725			0.0506386
$741$		−	44.7985i		−	0.0604568i
$742$	760.076			1.02436
$743$	651.313			0.876599			0.438300	−	0.898829i	$-0.355581\pi$
$743$	651.313			0.876599			0.438300	+	0.898829i	$0.355581\pi$
$744$			590.493i			0.793673i
$745$			1.02237i			0.00137231i
$746$	−2078.58			−2.78630
$747$			89.6044i			0.119952i
$748$		−	1537.26i		−	2.05515i
$749$	1498.57			2.00076
$750$		−	209.798i		−	0.279731i
$751$	−1363.63			−1.81575			−0.907875	−	0.419242i	$-0.862296\pi$
$751$	−1363.63			−1.81575			−0.907875	+	0.419242i	$0.862296\pi$
$752$	−1737.92			−2.31106
$753$	−228.962			−0.304066
$754$			66.0664i			0.0876213i
$755$	74.0075			0.0980231
$756$	1659.72			2.19540
$757$	223.801			0.295642			0.147821	−	0.989014i	$-0.452774\pi$
$757$	223.801			0.295642			0.147821	+	0.989014i	$0.452774\pi$
$758$			898.109i			1.18484i
$759$	−432.004			−0.569176
$760$	72.9420			0.0959763
$761$	−128.112			−0.168346			−0.0841732	−	0.996451i	$-0.526825\pi$
$761$	−128.112			−0.168346			−0.0841732	+	0.996451i	$0.526825\pi$
$762$	−1331.55			−1.74744
$763$	954.295			1.25071
$764$	2178.97			2.85205
$765$	−46.6429			−0.0609711
$766$			173.912i			0.227039i
$767$		−	38.2840i		−	0.0499140i
$768$			2393.66i			3.11674i
$769$		−	1352.44i		−	1.75870i	−0.476179	−	0.879348i	$-0.657979\pi$
$769$		−	1352.44i		−	1.75870i	0.476179	−	0.879348i	$-0.342021\pi$
$770$		−	130.235i		−	0.169136i
$771$	−1939.26			−2.51525
$772$	2083.41			2.69872
$773$			1389.13i			1.79707i	0.438905	+	0.898534i	$0.355367\pi$
$773$			1389.13i			1.79707i	−0.438905	+	0.898534i	$0.644633\pi$
$774$	−1841.05			−2.37862
$775$			196.818i			0.253959i
$776$		−	2819.07i		−	3.63282i
$777$			927.423i			1.19359i
$778$	118.534			0.152357
$779$			654.143i			0.839721i
$780$	5.50355			0.00705583
$781$		−	1218.89i		−	1.56068i
$782$		−	385.029i		−	0.492364i
$783$			574.510i			0.733729i
$784$	−1961.53			−2.50195
$785$		−	11.3897i		−	0.0145092i
$786$	−855.167			−1.08800
$787$	−30.2894			−0.0384872			−0.0192436	−	0.999815i	$-0.506126\pi$
$787$	−30.2894			−0.0384872			−0.0192436	+	0.999815i	$0.506126\pi$
$788$			167.305i			0.212316i
$789$			622.684i			0.789207i
$790$			71.4744i			0.0904739i
$791$			976.431i			1.23443i
$792$			2515.31i			3.17590i
$793$		−	35.8581i		−	0.0452182i
$794$	2601.11			3.27596
$795$	21.9170			0.0275686
$796$	2112.73			2.65418
$797$	890.874			1.11778			0.558892	−	0.829240i	$-0.311226\pi$
$797$	890.874			1.11778			0.558892	+	0.829240i	$0.311226\pi$
$798$			3394.14i			4.25331i
$799$			1103.97i			1.38169i
$800$		−	411.122i		−	0.513902i
$801$		−	975.740i		−	1.21815i
$802$		−	1661.73i		−	2.07199i
$803$	1635.06			2.03618
$804$		−	830.189i		−	1.03257i
$805$		−	22.2184i		−	0.0276005i
$806$	−15.1798			−0.0188335
$807$		−	1040.30i		−	1.28910i
$808$	671.912			0.831574
$809$		−	1161.66i		−	1.43592i	−0.696087	−	0.717958i	$-0.745077\pi$
$809$		−	1161.66i		−	1.43592i	0.696087	−	0.717958i	$-0.254923\pi$
$810$	−32.2429			−0.0398061
$811$	−554.698			−0.683968			−0.341984	−	0.939706i	$-0.611099\pi$
$811$	−554.698			−0.683968			−0.341984	+	0.939706i	$0.611099\pi$
$812$		−	3409.46i		−	4.19884i
$813$	987.001			1.21402
$814$	−754.777			−0.927244
$815$	9.32206			0.0114381
$816$	−1539.26			−1.88635
$817$		−	732.477i		−	0.896545i
$818$		−	772.669i		−	0.944583i
$819$			79.4515i			0.0970103i
$820$	−80.3623			−0.0980028
$821$			63.0516i			0.0767986i	0.999262	+	0.0383993i	$0.0122259\pi$
$821$			63.0516i			0.0767986i	−0.999262	+	0.0383993i	$0.987774\pi$
$822$	459.188			0.558623
$823$	564.309			0.685674			0.342837	−	0.939395i	$-0.388612\pi$
$823$	564.309			0.685674			0.342837	+	0.939395i	$0.388612\pi$
$824$	−2554.12			−3.09966
$825$			1437.30i			1.74218i
$826$			2900.57i			3.51159i
$827$		−	528.866i		−	0.639500i	−0.947502	−	0.319750i	$-0.896401\pi$
$827$		−	528.866i		−	0.639500i	0.947502	−	0.319750i	$-0.103599\pi$
$828$			806.798i			0.974393i
$829$	752.658			0.907911			0.453955	−	0.891024i	$-0.350013\pi$
$829$	752.658			0.907911			0.453955	+	0.891024i	$0.350013\pi$
$830$		−	6.42983i		−	0.00774678i
$831$		−	1748.56i		−	2.10416i
$832$	−17.8852			−0.0214966
$833$			1246.01i			1.49581i
$834$	−678.697			−0.813785
$835$			49.0952i			0.0587966i
$836$	−1881.52			−2.25062
$837$	−132.002			−0.157709
$838$		−	1322.83i		−	1.57856i
$839$	777.430			0.926615			0.463307	−	0.886198i	$-0.346663\pi$
$839$	777.430			0.926615			0.463307	+	0.886198i	$0.346663\pi$
$840$	−221.780			−0.264024
$841$	339.178			0.403303
$842$	−1485.72			−1.76451
$843$	1869.82			2.21806
$844$		−	819.417i		−	0.970873i
$845$		−	43.0609i		−	0.0509597i
$846$		−	3396.18i		−	4.01439i
$847$			381.391i			0.450284i
$848$	421.893			0.497516
$849$	154.085			0.181489
$850$	−1281.01			−1.50707
$851$	−128.767			−0.151312
$852$	−3902.53			−4.58044
$853$	−980.119			−1.14903			−0.574513	−	0.818495i	$-0.694809\pi$
$853$	−980.119			−1.14903			−0.574513	+	0.818495i	$0.694809\pi$
$854$			2716.77i			3.18123i
$855$			57.0884i			0.0667701i
$856$	2076.88			2.42626
$857$		−	860.179i		−	1.00371i	−0.864952	−	0.501855i	$-0.832651\pi$
$857$		−	860.179i		−	1.00371i	0.864952	−	0.501855i	$-0.167349\pi$
$858$	−110.853			−0.129200
$859$	−1528.17			−1.77901			−0.889507	−	0.456921i	$-0.848952\pi$
$859$	−1528.17			−1.77901			−0.889507	+	0.456921i	$0.848952\pi$
$860$	89.9857			0.104635
$861$		−	1988.92i		−	2.31001i
$862$	1061.25			1.23115
$863$		−	1544.20i		−	1.78934i	−0.446730	−	0.894669i	$-0.647412\pi$
$863$		−	1544.20i		−	1.78934i	0.446730	−	0.894669i	$-0.352588\pi$
$864$	275.732			0.319135
$865$	−0.451895			−0.000522422
$866$	1421.72			1.64171
$867$		−	365.324i		−	0.421366i
$868$	783.375			0.902506
$869$		−	980.604i		−	1.12843i
$870$		−	144.335i		−	0.165902i
$871$	11.3512			0.0130323
$872$	1322.57			1.51671
$873$	2206.36			2.52733
$874$	−471.254			−0.539193
$875$	−148.037			−0.169185
$876$		−	5234.98i		−	5.97600i
$877$			747.733i			0.852604i	0.904581	+	0.426302i	$0.140184\pi$
$877$			747.733i			0.852604i	−0.904581	+	0.426302i	$0.859816\pi$
$878$		−	2088.69i		−	2.37892i
$879$			2450.05i			2.78731i
$880$		−	72.2891i		−	0.0821467i
$881$			1354.18i			1.53709i	0.639793	+	0.768547i	$0.279020\pi$
$881$			1354.18i			1.53709i	−0.639793	+	0.768547i	$0.720980\pi$
$882$		−	3833.14i		−	4.34596i
$883$	1072.25			1.21433			0.607166	−	0.794575i	$-0.292306\pi$
$883$	1072.25			1.21433			0.607166	+	0.794575i	$0.292306\pi$
$884$		−	67.2963i		−	0.0761271i
$885$			83.6389i			0.0945072i
$886$		−	2920.45i		−	3.29622i
$887$	−4.66772			−0.00526236			−0.00263118	−	0.999997i	$-0.500838\pi$
$887$	−4.66772			−0.00526236			−0.00263118	+	0.999997i	$0.500838\pi$
$888$			1285.33i			1.44744i
$889$			939.562i			1.05688i
$890$			70.0172i			0.0786710i
$891$	442.362			0.496478
$892$			1941.58i			2.17666i
$893$	1351.20			1.51310
$894$	−65.9322			−0.0737497
$895$		−	25.3380i		−	0.0283107i
$896$	2121.07			2.36727
$897$	−18.9118			−0.0210834
$898$		−	897.222i		−	0.999133i
$899$			271.164i			0.301628i
$900$	2684.26			2.98251
$901$		−	267.997i		−	0.297444i
$902$	1618.67			1.79453
$903$			2227.09i			2.46633i
$904$			1353.25i			1.49695i
$905$		−	80.7759i		−	0.0892552i
$906$			4772.69i			5.26787i
$907$	311.899			0.343880			0.171940	−	0.985107i	$-0.444996\pi$
$907$	311.899			0.343880			0.171940	+	0.985107i	$0.444996\pi$
$908$	3066.68			3.37740
$909$			525.876i			0.578521i
$910$		−	5.70128i		−	0.00626514i
$911$		−	1303.70i		−	1.43107i	−0.698578	−	0.715533i	$-0.746184\pi$
$911$		−	1303.70i		−	1.43107i	0.698578	−	0.715533i	$-0.253816\pi$
$912$			1883.98i			2.06576i
$913$			88.2151i			0.0966211i
$914$	−2547.03			−2.78668
$915$			78.3389i			0.0856163i
$916$			3358.54i			3.66653i
$917$			603.418i			0.658035i
$918$		−	859.152i		−	0.935896i
$919$	−252.898			−0.275188			−0.137594	−	0.990489i	$-0.543937\pi$
$919$	−252.898			−0.275188			−0.137594	+	0.990489i	$0.543937\pi$
$920$		−	30.7927i		−	0.0334703i
$921$	2110.97			2.29204
$922$	2215.20			2.40260
$923$		−	53.3592i		−	0.0578106i
$924$	5720.75			6.19129
$925$			428.414i			0.463150i
$926$	−210.912			−0.227767
$927$		−	1998.99i		−	2.15641i
$928$		−	566.419i		−	0.610365i
$929$		−	1526.00i		−	1.64263i	−0.570475	−	0.821315i	$-0.693241\pi$
$929$		−	1526.00i		−	1.64263i	0.570475	−	0.821315i	$-0.306759\pi$
$930$	33.1631			0.0356593
$931$	1525.05			1.63807
$932$	1182.75			1.26904
$933$			2396.45i			2.56855i
$934$		−	535.686i		−	0.573540i
$935$	−45.9198			−0.0491120
$936$			110.113i			0.117642i
$937$			1244.90i			1.32861i	0.747463	+	0.664303i	$0.231272\pi$
$937$			1244.90i			1.32861i	−0.747463	+	0.664303i	$0.768728\pi$
$938$	−860.016			−0.916862
$939$		−	1944.41i		−	2.07073i
$940$			165.996i			0.176592i
$941$	231.711			0.246239			0.123119	−	0.992392i	$-0.460710\pi$
$941$	231.711			0.246239			0.123119	+	0.992392i	$0.460710\pi$
$942$	734.515			0.779740
$943$	276.148			0.292840
$944$			1610.01i			1.70552i
$945$		−	49.5780i		−	0.0524635i
$946$	−1812.50			−1.91597
$947$	70.5104			0.0744566			0.0372283	−	0.999307i	$-0.488147\pi$
$947$	70.5104			0.0744566			0.0372283	+	0.999307i	$0.488147\pi$
$948$	−3139.61			−3.31183
$949$	71.5777			0.0754244
$950$			1567.89i			1.65041i
$951$		−	1336.61i		−	1.40548i
$952$			2711.88i			2.84861i
$953$	1259.93			1.32207			0.661033	−	0.750357i	$-0.270118\pi$
$953$	1259.93			1.32207			0.661033	+	0.750357i	$0.270118\pi$
$954$			824.448i			0.864201i
$955$		−	65.0885i		−	0.0681555i
$956$	−1943.82			−2.03328
$957$			1980.23i			2.06920i
$958$			356.636i			0.372272i
$959$		−	324.010i		−	0.337862i
$960$	39.0736			0.0407017
$961$	898.696			0.935168
$962$	−33.0418			−0.0343470
$963$			1625.48i			1.68794i
$964$		−	48.6155i		−	0.0504311i
$965$		−	62.2342i		−	0.0644914i
$966$	1432.85			1.48328
$967$		−	636.274i		−	0.657988i	−0.944332	−	0.328994i	$-0.893290\pi$
$967$		−	636.274i		−	0.657988i	0.944332	−	0.328994i	$-0.106710\pi$
$968$			528.574i			0.546048i
$969$	1196.75			1.23503
$970$	−158.324			−0.163221
$971$			241.411i			0.248621i	0.992243	+	0.124310i	$0.0396719\pi$
$971$			241.411i			0.248621i	−0.992243	+	0.124310i	$0.960328\pi$
$972$		−	2702.40i		−	2.78024i
$973$			478.898i			0.492187i
$974$	−997.411			−1.02404
$975$			62.9207i			0.0645340i
$976$			1507.99i			1.54507i
$977$			961.791i			0.984432i	0.870473	+	0.492216i	$0.163813\pi$
$977$			961.791i			0.984432i	−0.870473	+	0.492216i	$0.836187\pi$
$978$			601.173i			0.614696i
$979$		−	960.612i		−	0.981217i
$980$			187.354i			0.191178i
$981$			1035.11i			1.05516i
$982$	2194.66			2.23488
$983$		−	565.487i		−	0.575267i	−0.957741	−	0.287633i	$-0.907132\pi$
$983$		−	565.487i		−	0.575267i	0.957741	−	0.287633i	$-0.0928685\pi$
$984$		−	2756.47i		−	2.80129i
$985$	4.99762			0.00507373
$986$	−1764.90			−1.78996
$987$	−4108.31			−4.16242
$988$	−82.3671			−0.0833675
$989$	−309.218			−0.312657
$990$	141.265			0.142691
$991$	1502.89			1.51654			0.758270	−	0.651941i	$-0.226045\pi$
$991$	1502.89			1.51654			0.758270	+	0.651941i	$0.226045\pi$
$992$	130.143			0.131193
$993$	−1673.86			−1.68566
$994$			4042.74i			4.06714i
$995$		−	63.1099i		−	0.0634271i
$996$	282.439			0.283574
$997$		−	816.091i		−	0.818546i	−0.912412	−	0.409273i	$-0.865782\pi$
$997$		−	816.091i		−	0.818546i	0.912412	−	0.409273i	$-0.134218\pi$
$998$		−	1094.89i		−	1.09708i
$999$	−287.330			−0.287617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.3.b.b.546.7	✓	88
547.546	odd	2	inner	547.3.b.b.546.82	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.3.b.b.546.7	✓	88	1.1	even	1	trivial
547.3.b.b.546.82	yes	88	547.546	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	547.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.54186i q^{2} -4.64741i q^{3} -8.54479 q^{4} +0.255244i q^{5} -16.4605 q^{6} +11.6148i q^{7} +16.0970i q^{8} -12.5984 q^{9} +O(q^{10})\)	\(q-3.54186i q^{2} -4.64741i q^{3} -8.54479 q^{4} +0.255244i q^{5} -16.4605 q^{6} +11.6148i q^{7} +16.0970i q^{8} -12.5984 q^{9} +0.904038 q^{10} -12.4031 q^{11} +39.7112i q^{12} -0.542969 q^{13} +41.1379 q^{14} +1.18622 q^{15} +22.8343 q^{16} -14.5049i q^{17} +44.6219i q^{18} -17.7532 q^{19} -2.18100i q^{20} +53.9786 q^{21} +43.9301i q^{22} +7.49457i q^{23} +74.8095 q^{24} +24.9349 q^{25} +1.92312i q^{26} +16.7234i q^{27} -99.2457i q^{28} +34.3537 q^{29} -4.20144i q^{30} +7.89329i q^{31} -16.4878i q^{32} +57.6423i q^{33} -51.3743 q^{34} -2.96459 q^{35} +107.651 q^{36} +17.1813i q^{37} +62.8794i q^{38} +2.52340i q^{39} -4.10866 q^{40} -36.8465i q^{41} -191.185i q^{42} +41.2589i q^{43} +105.982 q^{44} -3.21567i q^{45} +26.5447 q^{46} -76.1101 q^{47} -106.120i q^{48} -85.9026 q^{49} -88.3158i q^{50} -67.4102 q^{51} +4.63956 q^{52} +18.4763 q^{53} +59.2319 q^{54} -3.16581i q^{55} -186.963 q^{56} +82.5065i q^{57} -121.676i q^{58} +70.5086i q^{59} -10.1360 q^{60} +66.0407i q^{61} +27.9569 q^{62} -146.328i q^{63} +32.9395 q^{64} -0.138590i q^{65} +204.161 q^{66} -20.9057 q^{67} +123.941i q^{68} +34.8304 q^{69} +10.5002i q^{70} +98.2729i q^{71} -202.797i q^{72} -131.826 q^{73} +60.8539 q^{74} -115.882i q^{75} +151.697 q^{76} -144.059i q^{77} +8.93754 q^{78} +79.0613i q^{79} +5.82831i q^{80} -35.6655 q^{81} -130.505 q^{82} -7.11235i q^{83} -461.236 q^{84} +3.70228 q^{85} +146.133 q^{86} -159.656i q^{87} -199.653i q^{88} +77.4494i q^{89} -11.3895 q^{90} -6.30646i q^{91} -64.0396i q^{92} +36.6834 q^{93} +269.571i q^{94} -4.53139i q^{95} -76.6258 q^{96} -175.130 q^{97} +304.255i q^{98} +156.259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 192 q^{4} - 306 q^{9}+O(q^{10}) \) 88 * q - 192 * q^4 - 306 * q^9	\( 88 q - 192 q^{4} - 306 q^{9} - 4 q^{10} - 32 q^{11} + 26 q^{13} - 26 q^{14} + 22 q^{15} + 236 q^{16} - 12 q^{19} - 16 q^{21} - 2 q^{24} - 544 q^{25} - 96 q^{29} + 26 q^{34} + 10 q^{35} + 364 q^{36} + 44 q^{40} + 124 q^{44} - 288 q^{46} - 310 q^{47} - 694 q^{49} + 86 q^{51} - 316 q^{52} + 24 q^{53} - 266 q^{54} + 158 q^{56} - 80 q^{60} + 40 q^{62} - 652 q^{64} + 528 q^{66} + 28 q^{67} + 16 q^{69} + 94 q^{73} - 614 q^{74} - 28 q^{76} - 98 q^{78} + 928 q^{81} - 772 q^{82} + 358 q^{84} + 74 q^{85} - 410 q^{86} - 214 q^{90} + 656 q^{93} - 724 q^{96} + 346 q^{97} + 50 q^{99}+O(q^{100}) \) 88 * q - 192 * q^4 - 306 * q^9 - 4 * q^10 - 32 * q^11 + 26 * q^13 - 26 * q^14 + 22 * q^15 + 236 * q^16 - 12 * q^19 - 16 * q^21 - 2 * q^24 - 544 * q^25 - 96 * q^29 + 26 * q^34 + 10 * q^35 + 364 * q^36 + 44 * q^40 + 124 * q^44 - 288 * q^46 - 310 * q^47 - 694 * q^49 + 86 * q^51 - 316 * q^52 + 24 * q^53 - 266 * q^54 + 158 * q^56 - 80 * q^60 + 40 * q^62 - 652 * q^64 + 528 * q^66 + 28 * q^67 + 16 * q^69 + 94 * q^73 - 614 * q^74 - 28 * q^76 - 98 * q^78 + 928 * q^81 - 772 * q^82 + 358 * q^84 + 74 * q^85 - 410 * q^86 - 214 * q^90 + 656 * q^93 - 724 * q^96 + 346 * q^97 + 50 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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