LMFDB - Embedded newform 201.3.b.a.133.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(133,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("201.133");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			133.11
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.465702i q^{2} +1.73205i q^{3} +3.78312 q^{4} -1.28941i q^{5} +0.806619 q^{6} -11.7488i q^{7} -3.62461i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-0.465702i q^{2} +1.73205i q^{3} +3.78312 q^{4} -1.28941i q^{5} +0.806619 q^{6} -11.7488i q^{7} -3.62461i q^{8} -3.00000 q^{9} -0.600481 q^{10} -17.7054i q^{11} +6.55256i q^{12} +20.8144i q^{13} -5.47144 q^{14} +2.23333 q^{15} +13.4445 q^{16} +17.2487 q^{17} +1.39710i q^{18} +5.65487 q^{19} -4.87800i q^{20} +20.3495 q^{21} -8.24542 q^{22} -14.7294 q^{23} +6.27801 q^{24} +23.3374 q^{25} +9.69332 q^{26} -5.19615i q^{27} -44.4472i q^{28} -51.4696 q^{29} -1.04006i q^{30} +18.2212i q^{31} -20.7596i q^{32} +30.6666 q^{33} -8.03277i q^{34} -15.1491 q^{35} -11.3494 q^{36} +54.4115 q^{37} -2.63348i q^{38} -36.0517 q^{39} -4.67362 q^{40} +64.3042i q^{41} -9.47681i q^{42} -21.7724i q^{43} -66.9816i q^{44} +3.86824i q^{45} +6.85952i q^{46} +12.1180 q^{47} +23.2866i q^{48} -89.0345 q^{49} -10.8683i q^{50} +29.8757i q^{51} +78.7436i q^{52} -1.46702i q^{53} -2.41986 q^{54} -22.8295 q^{55} -42.5849 q^{56} +9.79452i q^{57} +23.9695i q^{58} -7.90335 q^{59} +8.44895 q^{60} +25.0939i q^{61} +8.48565 q^{62} +35.2464i q^{63} +44.1102 q^{64} +26.8384 q^{65} -14.2815i q^{66} +(-47.9500 + 46.7953i) q^{67} +65.2541 q^{68} -25.5121i q^{69} +7.05494i q^{70} -43.8075 q^{71} +10.8738i q^{72} -62.2444 q^{73} -25.3395i q^{74} +40.4216i q^{75} +21.3931 q^{76} -208.017 q^{77} +16.7893i q^{78} +83.6358i q^{79} -17.3355i q^{80} +9.00000 q^{81} +29.9466 q^{82} +106.726 q^{83} +76.9848 q^{84} -22.2408i q^{85} -10.1394 q^{86} -89.1479i q^{87} -64.1751 q^{88} -88.0560 q^{89} +1.80144 q^{90} +244.545 q^{91} -55.7232 q^{92} -31.5601 q^{93} -5.64339i q^{94} -7.29146i q^{95} +35.9566 q^{96} -121.323i q^{97} +41.4635i q^{98} +53.1161i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) $ 22 * q - 52 * q^4 - 66 * q^9	$ 22 q - 52 q^{4} - 66 q^{9} - 36 q^{10} + 72 q^{14} + 12 q^{15} + 116 q^{16} - 14 q^{17} - 26 q^{19} + 48 q^{21} + 32 q^{22} - 82 q^{23} + 36 q^{24} - 62 q^{25} - 100 q^{26} + 102 q^{29} + 36 q^{33} - 180 q^{35} + 156 q^{36} + 106 q^{37} - 72 q^{39} + 76 q^{40} + 154 q^{47} + 146 q^{49} - 224 q^{55} - 452 q^{56} + 370 q^{59} - 24 q^{60} - 300 q^{62} + 148 q^{64} - 284 q^{65} - 134 q^{67} - 116 q^{68} + 160 q^{71} + 218 q^{73} + 480 q^{76} - 396 q^{77} + 198 q^{81} - 68 q^{82} + 128 q^{83} + 20 q^{86} - 856 q^{88} - 118 q^{89} + 108 q^{90} - 400 q^{91} + 804 q^{92} - 72 q^{93} - 144 q^{96}+O(q^{100}) $ 22 * q - 52 * q^4 - 66 * q^9 - 36 * q^10 + 72 * q^14 + 12 * q^15 + 116 * q^16 - 14 * q^17 - 26 * q^19 + 48 * q^21 + 32 * q^22 - 82 * q^23 + 36 * q^24 - 62 * q^25 - 100 * q^26 + 102 * q^29 + 36 * q^33 - 180 * q^35 + 156 * q^36 + 106 * q^37 - 72 * q^39 + 76 * q^40 + 154 * q^47 + 146 * q^49 - 224 * q^55 - 452 * q^56 + 370 * q^59 - 24 * q^60 - 300 * q^62 + 148 * q^64 - 284 * q^65 - 134 * q^67 - 116 * q^68 + 160 * q^71 + 218 * q^73 + 480 * q^76 - 396 * q^77 + 198 * q^81 - 68 * q^82 + 128 * q^83 + 20 * q^86 - 856 * q^88 - 118 * q^89 + 108 * q^90 - 400 * q^91 + 804 * q^92 - 72 * q^93 - 144 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.465702i		−	0.232851i	−0.993199	−	0.116425i	$-0.962856\pi$
$2$		−	0.465702i		−	0.232851i	0.993199	−	0.116425i	$-0.0371436\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.78312			0.945781
$5$		−	1.28941i		−	0.257883i	−0.991652	−	0.128941i	$-0.958842\pi$
$5$		−	1.28941i		−	0.257883i	0.991652	−	0.128941i	$-0.0411579\pi$
$6$	0.806619			0.134436
$7$		−	11.7488i		−	1.67840i	−0.543822	−	0.839201i	$-0.683023\pi$
$7$		−	11.7488i		−	1.67840i	0.543822	−	0.839201i	$-0.316977\pi$
$8$		−	3.62461i		−	0.453077i
$9$	−3.00000			−0.333333
$10$	−0.600481			−0.0600481
$11$		−	17.7054i		−	1.60958i	−0.593560	−	0.804790i	$-0.702278\pi$
$11$		−	17.7054i		−	1.60958i	0.593560	−	0.804790i	$-0.297722\pi$
$12$			6.55256i			0.546047i
$13$			20.8144i			1.60111i	0.599258	+	0.800556i	$0.295462\pi$
$13$			20.8144i			1.60111i	−0.599258	+	0.800556i	$0.704538\pi$
$14$	−5.47144			−0.390817
$15$	2.23333			0.148889
$16$	13.4445			0.840281
$17$	17.2487			1.01463			0.507316	−	0.861760i	$-0.330638\pi$
$17$	17.2487			1.01463			0.507316	+	0.861760i	$0.330638\pi$
$18$			1.39710i			0.0776169i
$19$	5.65487			0.297625			0.148812	−	0.988865i	$-0.452455\pi$
$19$	5.65487			0.297625			0.148812	+	0.988865i	$0.452455\pi$
$20$		−	4.87800i		−	0.243900i
$21$	20.3495			0.969025
$22$	−8.24542			−0.374792
$23$	−14.7294			−0.640410			−0.320205	−	0.947348i	$-0.603752\pi$
$23$	−14.7294			−0.640410			−0.320205	+	0.947348i	$0.603752\pi$
$24$	6.27801			0.261584
$25$	23.3374			0.933497
$26$	9.69332			0.372820
$27$		−	5.19615i		−	0.192450i
$28$		−	44.4472i		−	1.58740i
$29$	−51.4696			−1.77481			−0.887406	−	0.460988i	$-0.847495\pi$
$29$	−51.4696			−1.77481			−0.887406	+	0.460988i	$0.847495\pi$
$30$		−	1.04006i		−	0.0346688i
$31$			18.2212i			0.587782i	0.955839	+	0.293891i	$0.0949502\pi$
$31$			18.2212i			0.587782i	−0.955839	+	0.293891i	$0.905050\pi$
$32$		−	20.7596i		−	0.648737i
$33$	30.6666			0.929291
$34$		−	8.03277i		−	0.236258i
$35$	−15.1491			−0.432830
$36$	−11.3494			−0.315260
$37$	54.4115			1.47058			0.735291	−	0.677752i	$-0.237046\pi$
$37$	54.4115			1.47058			0.735291	+	0.677752i	$0.237046\pi$
$38$		−	2.63348i		−	0.0693021i
$39$	−36.0517			−0.924402
$40$	−4.67362			−0.116841
$41$			64.3042i			1.56840i	0.620511	+	0.784198i	$0.286925\pi$
$41$			64.3042i			1.56840i	−0.620511	+	0.784198i	$0.713075\pi$
$42$		−	9.47681i		−	0.225638i
$43$		−	21.7724i		−	0.506334i	−0.967423	−	0.253167i	$-0.918528\pi$
$43$		−	21.7724i		−	0.506334i	0.967423	−	0.253167i	$-0.0814723\pi$
$44$		−	66.9816i		−	1.52231i
$45$			3.86824i			0.0859608i
$46$			6.85952i			0.149120i
$47$	12.1180			0.257831			0.128915	−	0.991656i	$-0.458850\pi$
$47$	12.1180			0.257831			0.128915	+	0.991656i	$0.458850\pi$
$48$			23.2866i			0.485137i
$49$	−89.0345			−1.81703
$50$		−	10.8683i		−	0.217365i
$51$			29.8757i			0.585798i
$52$			78.7436i			1.51430i
$53$		−	1.46702i		−	0.0276796i	−0.999904	−	0.0138398i	$-0.995595\pi$
$53$		−	1.46702i		−	0.0276796i	0.999904	−	0.0138398i	$-0.00440549\pi$
$54$	−2.41986			−0.0448122
$55$	−22.8295			−0.415082
$56$	−42.5849			−0.760444
$57$			9.79452i			0.171834i
$58$			23.9695i			0.413266i
$59$	−7.90335			−0.133955			−0.0669776	−	0.997754i	$-0.521336\pi$
$59$	−7.90335			−0.133955			−0.0669776	+	0.997754i	$0.521336\pi$
$60$	8.44895			0.140816
$61$			25.0939i			0.411375i	0.978618	+	0.205688i	$0.0659431\pi$
$61$			25.0939i			0.411375i	−0.978618	+	0.205688i	$0.934057\pi$
$62$	8.48565			0.136865
$63$			35.2464i			0.559467i
$64$	44.1102			0.689222
$65$	26.8384			0.412899
$66$		−	14.2815i		−	0.216386i
$67$	−47.9500	+	46.7953i	−0.715671	+	0.698437i
$67$	−47.9500	+	46.7953i	−0.715671	+	0.698437i
$68$	65.2541			0.959619
$69$		−	25.5121i		−	0.369741i
$70$			7.05494i			0.100785i
$71$	−43.8075			−0.617007			−0.308503	−	0.951223i	$-0.599828\pi$
$71$	−43.8075			−0.617007			−0.308503	+	0.951223i	$0.599828\pi$
$72$			10.8738i			0.151026i
$73$	−62.2444			−0.852663			−0.426331	−	0.904567i	$-0.640194\pi$
$73$	−62.2444			−0.852663			−0.426331	+	0.904567i	$0.640194\pi$
$74$		−	25.3395i		−	0.342426i
$75$			40.4216i			0.538955i
$76$	21.3931			0.281488
$77$	−208.017			−2.70152
$78$			16.7893i			0.215248i
$79$			83.6358i			1.05868i	0.848410	+	0.529340i	$0.177561\pi$
$79$			83.6358i			1.05868i	−0.848410	+	0.529340i	$0.822439\pi$
$80$		−	17.3355i		−	0.216694i
$81$	9.00000			0.111111
$82$	29.9466			0.365202
$83$	106.726			1.28585			0.642927	−	0.765927i	$-0.277720\pi$
$83$	106.726			1.28585			0.642927	+	0.765927i	$0.277720\pi$
$84$	76.9848			0.916485
$85$		−	22.2408i		−	0.261656i
$86$	−10.1394			−0.117900
$87$		−	89.1479i		−	1.02469i
$88$	−64.1751			−0.729263
$89$	−88.0560			−0.989393			−0.494697	−	0.869066i	$-0.664721\pi$
$89$	−88.0560			−0.989393			−0.494697	+	0.869066i	$0.664721\pi$
$90$	1.80144			0.0200160
$91$	244.545			2.68731
$92$	−55.7232			−0.605687
$93$	−31.5601			−0.339356
$94$		−	5.64339i		−	0.0600361i
$95$		−	7.29146i		−	0.0767522i
$96$	35.9566			0.374548
$97$		−	121.323i		−	1.25076i	−0.780322	−	0.625378i	$-0.784945\pi$
$97$		−	121.323i		−	1.25076i	0.780322	−	0.625378i	$-0.215055\pi$
$98$			41.4635i			0.423097i
$99$			53.1161i			0.536527i
$100$	88.2883			0.882883
$101$			155.248i			1.53710i	0.639787	+	0.768552i	$0.279022\pi$
$101$			155.248i			1.53710i	−0.639787	+	0.768552i	$0.720978\pi$
$102$	13.9132			0.136404
$103$	−31.6434			−0.307218			−0.153609	−	0.988132i	$-0.549090\pi$
$103$	−31.6434			−0.307218			−0.153609	+	0.988132i	$0.549090\pi$
$104$	75.4443			0.725426
$105$		−	26.2389i		−	0.249895i
$106$	−0.683194			−0.00644522
$107$	81.3288			0.760082			0.380041	−	0.924970i	$-0.375910\pi$
$107$	81.3288			0.760082			0.380041	+	0.924970i	$0.375910\pi$
$108$		−	19.6577i		−	0.182016i
$109$			77.6602i			0.712479i	0.934395	+	0.356239i	$0.115941\pi$
$109$			77.6602i			0.712479i	−0.934395	+	0.356239i	$0.884059\pi$
$110$			10.6318i			0.0966523i
$111$			94.2435i			0.849041i
$112$		−	157.957i		−	1.41033i
$113$		−	171.217i		−	1.51519i	−0.652725	−	0.757595i	$-0.726374\pi$
$113$		−	171.217i		−	1.51519i	0.652725	−	0.757595i	$-0.273626\pi$
$114$	4.56132			0.0400116
$115$			18.9923i			0.165151i
$116$	−194.716			−1.67858
$117$		−	62.4433i		−	0.533704i
$118$			3.68060i			0.0311916i
$119$		−	202.652i		−	1.70296i
$120$		−	8.09495i		−	0.0674579i
$121$	−192.480			−1.59075
$122$	11.6863			0.0957891
$123$	−111.378			−0.905514
$124$			68.9331i			0.555912i
$125$		−	62.3269i		−	0.498615i
$126$	16.4143			0.130272
$127$	−153.030			−1.20496			−0.602481	−	0.798134i	$-0.705821\pi$
$127$	−153.030			−1.20496			−0.602481	+	0.798134i	$0.705821\pi$
$128$		−	103.581i		−	0.809223i
$129$	37.7109			0.292332
$130$		−	12.4987i		−	0.0961438i
$131$	47.6700			0.363893			0.181947	−	0.983308i	$-0.441760\pi$
$131$	47.6700			0.363893			0.181947	+	0.983308i	$0.441760\pi$
$132$	116.016			0.878906
$133$		−	66.4379i		−	0.499533i
$134$	21.7926	+	22.3304i	0.162632	+	0.166645i
$135$	−6.69998			−0.0496295
$136$		−	62.5200i		−	0.459706i
$137$			151.652i			1.10695i	0.832867	+	0.553474i	$0.186698\pi$
$137$			151.652i			1.10695i	−0.832867	+	0.553474i	$0.813302\pi$
$138$	−11.8810			−0.0860945
$139$		−	26.7124i		−	0.192175i	−0.995373	−	0.0960877i	$-0.969367\pi$
$139$		−	26.7124i		−	0.192175i	0.995373	−	0.0960877i	$-0.0306329\pi$
$140$	−57.3107			−0.409362
$141$			20.9891i			0.148859i
$142$			20.4012i			0.143671i
$143$	368.528			2.57712
$144$	−40.3335			−0.280094
$145$			66.3655i			0.457693i
$146$			28.9873i			0.198543i
$147$		−	154.212i		−	1.04906i
$148$	205.845			1.39085
$149$	157.727			1.05857			0.529286	−	0.848443i	$-0.322460\pi$
$149$	157.727			1.05857			0.529286	+	0.848443i	$0.322460\pi$
$150$	18.8244			0.125496
$151$	262.637			1.73932			0.869658	−	0.493654i	$-0.164339\pi$
$151$	262.637			1.73932			0.869658	+	0.493654i	$0.164339\pi$
$152$		−	20.4967i		−	0.134847i
$153$	−51.7462			−0.338211
$154$			96.8739i			0.629051i
$155$	23.4947			0.151579
$156$	−136.388			−0.874282
$157$	50.5428			0.321928			0.160964	−	0.986960i	$-0.448540\pi$
$157$	50.5428			0.321928			0.160964	+	0.986960i	$0.448540\pi$
$158$	38.9493			0.246515
$159$	2.54095			0.0159808
$160$	−26.7677			−0.167298
$161$			173.053i			1.07487i
$162$		−	4.19131i		−	0.0258723i
$163$	−161.214			−0.989040			−0.494520	−	0.869166i	$-0.664656\pi$
$163$	−161.214			−0.989040			−0.494520	+	0.869166i	$0.664656\pi$
$164$			243.271i			1.48336i
$165$		−	39.5419i		−	0.239648i
$166$		−	49.7024i		−	0.299412i
$167$	235.524			1.41033			0.705163	−	0.709045i	$-0.250874\pi$
$167$	235.524			1.41033			0.705163	+	0.709045i	$0.250874\pi$
$168$		−	73.7592i		−	0.439043i
$169$	−264.241			−1.56356
$170$	−10.3576			−0.0609268
$171$	−16.9646			−0.0992082
$172$		−	82.3676i		−	0.478881i
$173$	69.9219			0.404173			0.202086	−	0.979368i	$-0.435228\pi$
$173$	69.9219			0.404173			0.202086	+	0.979368i	$0.435228\pi$
$174$	−41.5163			−0.238599
$175$		−	274.187i		−	1.56678i
$176$		−	238.040i		−	1.35250i
$177$		−	13.6890i		−	0.0773390i
$178$			41.0078i			0.230381i
$179$			58.6614i			0.327717i	0.986484	+	0.163859i	$0.0523941\pi$
$179$			58.6614i			0.327717i	−0.986484	+	0.163859i	$0.947606\pi$
$180$			14.6340i			0.0813001i
$181$	193.658			1.06993			0.534966	−	0.844874i	$-0.320325\pi$
$181$	193.658			1.06993			0.534966	+	0.844874i	$0.320325\pi$
$182$		−	113.885i		−	0.625742i
$183$	−43.4639			−0.237508
$184$			53.3885i			0.290155i
$185$		−	70.1589i		−	0.379237i
$186$			14.6976i			0.0790193i
$187$		−	305.396i		−	1.63313i
$188$	45.8440			0.243851
$189$	−61.0486			−0.323008
$190$	−3.39564			−0.0178718
$191$			105.488i			0.552291i	0.961116	+	0.276146i	$0.0890572\pi$
$191$			105.488i			0.552291i	−0.961116	+	0.276146i	$0.910943\pi$
$192$			76.4012i			0.397923i
$193$	165.424			0.857117			0.428558	−	0.903514i	$-0.359022\pi$
$193$	165.424			0.857117			0.428558	+	0.903514i	$0.359022\pi$
$194$	−56.5005			−0.291240
$195$			46.4855i			0.238387i
$196$	−336.828			−1.71851
$197$			323.742i			1.64336i	0.569950	+	0.821680i	$0.306963\pi$
$197$			323.742i			1.64336i	−0.569950	+	0.821680i	$0.693037\pi$
$198$	24.7363			0.124931
$199$	−275.203			−1.38293			−0.691466	−	0.722409i	$-0.743035\pi$
$199$	−275.203			−1.38293			−0.691466	+	0.722409i	$0.743035\pi$
$200$		−	84.5891i		−	0.422945i
$201$	−81.0518	−	83.0518i	−0.403243	−	0.413193i
$202$	72.2990			0.357916
$203$			604.706i			2.97885i
$204$			113.023i			0.554036i
$205$	82.9147			0.404462
$206$			14.7364i			0.0715359i
$207$	44.1883			0.213470
$208$			279.840i			1.34538i
$209$		−	100.122i		−	0.479050i
$210$	−12.2195			−0.0581882
$211$	−32.4268			−0.153681			−0.0768407	−	0.997043i	$-0.524483\pi$
$211$	−32.4268			−0.153681			−0.0768407	+	0.997043i	$0.524483\pi$
$212$		−	5.54992i		−	0.0261788i
$213$		−	75.8768i		−	0.356229i
$214$		−	37.8749i		−	0.176986i
$215$	−28.0736			−0.130575
$216$	−18.8340			−0.0871946
$217$	214.078			0.986533
$218$	36.1665			0.165901
$219$		−	107.810i		−	0.492285i
$220$	−86.3669			−0.392577
$221$			359.023i			1.62454i
$222$	43.8894			0.197700
$223$	−121.416			−0.544464			−0.272232	−	0.962232i	$-0.587762\pi$
$223$	−121.416			−0.544464			−0.272232	+	0.962232i	$0.587762\pi$
$224$	−243.900			−1.08884
$225$	−70.0122			−0.311166
$226$	−79.7358			−0.352813
$227$	−204.570			−0.901191			−0.450595	−	0.892728i	$-0.648788\pi$
$227$	−204.570			−0.901191			−0.450595	+	0.892728i	$0.648788\pi$
$228$			37.0539i			0.162517i
$229$		−	50.6391i		−	0.221131i	−0.993869	−	0.110566i	$-0.964734\pi$
$229$		−	50.6391i		−	0.221131i	0.993869	−	0.110566i	$-0.0352662\pi$
$230$	8.84475			0.0384554
$231$		−	360.296i		−	1.55972i
$232$			186.557i			0.804126i
$233$		−	423.336i		−	1.81689i	−0.418003	−	0.908445i	$-0.637270\pi$
$233$		−	423.336i		−	1.81689i	0.418003	−	0.908445i	$-0.362730\pi$
$234$	−29.0800			−0.124273
$235$		−	15.6252i		−	0.0664900i
$236$	−29.8994			−0.126692
$237$	−144.861			−0.611230
$238$	−94.3755			−0.396536
$239$			229.535i			0.960397i	0.877160	+	0.480198i	$0.159435\pi$
$239$			229.535i			0.960397i	−0.877160	+	0.480198i	$0.840565\pi$
$240$	30.0260			0.125108
$241$	−106.331			−0.441206			−0.220603	−	0.975364i	$-0.570802\pi$
$241$	−106.331			−0.441206			−0.220603	+	0.975364i	$0.570802\pi$
$242$			89.6384i			0.370407i
$243$			15.5885i			0.0641500i
$244$			94.9333i			0.389071i
$245$			114.802i			0.468580i
$246$			51.8690i			0.210850i
$247$			117.703i			0.476530i
$248$	66.0449			0.266310
$249$			184.855i			0.742389i
$250$	−29.0257			−0.116103
$251$		−	137.693i		−	0.548576i	−0.961648	−	0.274288i	$-0.911558\pi$
$251$		−	137.693i		−	0.548576i	0.961648	−	0.274288i	$-0.0884422\pi$
$252$			133.342i			0.529133i
$253$			260.790i			1.03079i
$254$			71.2664i			0.280576i
$255$	38.5221			0.151067
$256$	128.203			0.500794
$257$	−344.181			−1.33923			−0.669613	−	0.742711i	$-0.733540\pi$
$257$	−344.181			−1.33923			−0.669613	+	0.742711i	$0.733540\pi$
$258$		−	17.5620i		−	0.0680698i
$259$		−	639.270i		−	2.46823i
$260$	101.533			0.390511
$261$	154.409			0.591604
$262$		−	22.2000i		−	0.0847328i
$263$	4.25431			0.0161761			0.00808803	−	0.999967i	$-0.497425\pi$
$263$	4.25431			0.0161761			0.00808803	+	0.999967i	$0.497425\pi$
$264$		−	111.155i		−	0.421040i
$265$	−1.89159			−0.00713809
$266$	−30.9403			−0.116317
$267$		−	152.517i		−	0.571226i
$268$	−181.401	+	177.032i	−0.676868	+	0.660568i
$269$	−287.503			−1.06878			−0.534391	−	0.845237i	$-0.679459\pi$
$269$	−287.503			−1.06878			−0.534391	+	0.845237i	$0.679459\pi$
$270$			3.12019i			0.0115563i
$271$			12.6113i			0.0465361i	0.999729	+	0.0232680i	$0.00740712\pi$
$271$			12.6113i			0.0465361i	−0.999729	+	0.0232680i	$0.992593\pi$
$272$	231.901			0.852576
$273$			423.564i			1.55152i
$274$	70.6245			0.257754
$275$		−	413.198i		−	1.50254i
$276$		−	96.5155i		−	0.349694i
$277$	185.618			0.670102			0.335051	−	0.942200i	$-0.391246\pi$
$277$	185.618			0.670102			0.335051	+	0.942200i	$0.391246\pi$
$278$	−12.4400			−0.0447482
$279$		−	54.6637i		−	0.195927i
$280$			54.9095i			0.196105i
$281$			212.365i			0.755746i	0.925857	+	0.377873i	$0.123344\pi$
$281$			212.365i			0.755746i	−0.925857	+	0.377873i	$0.876656\pi$
$282$	9.77464			0.0346619
$283$	45.1317			0.159476			0.0797379	−	0.996816i	$-0.474592\pi$
$283$	45.1317			0.159476			0.0797379	+	0.996816i	$0.474592\pi$
$284$	−165.729			−0.583553
$285$	12.6292			0.0443129
$286$		−	171.624i		−	0.600084i
$287$	755.498			2.63240
$288$			62.2787i			0.216246i
$289$	8.51929			0.0294785
$290$	30.9065			0.106574
$291$	210.138			0.722125
$292$	−235.478			−0.806432
$293$	82.1502			0.280376			0.140188	−	0.990125i	$-0.455229\pi$
$293$	82.1502			0.280376			0.140188	+	0.990125i	$0.455229\pi$
$294$	−71.8169			−0.244275
$295$			10.1907i			0.0345447i
$296$		−	197.221i		−	0.666286i
$297$	−91.9998			−0.309764
$298$		−	73.4538i		−	0.246489i
$299$		−	306.585i		−	1.02537i
$300$			152.920i			0.509733i
$301$	−255.800			−0.849832
$302$		−	122.310i		−	0.405001i
$303$	−268.897			−0.887447
$304$	76.0269			0.250088
$305$	32.3564			0.106087
$306$			24.0983i			0.0787526i
$307$	501.814			1.63457			0.817287	−	0.576231i	$-0.195477\pi$
$307$	501.814			1.63457			0.817287	+	0.576231i	$0.195477\pi$
$308$	−786.954			−2.55505
$309$		−	54.8080i		−	0.177372i
$310$		−	10.9415i		−	0.0352952i
$311$		−	246.858i		−	0.793756i	−0.917871	−	0.396878i	$-0.870094\pi$
$311$		−	246.858i		−	0.793756i	0.917871	−	0.396878i	$-0.129906\pi$
$312$			130.673i			0.418825i
$313$		−	214.238i		−	0.684466i	−0.939615	−	0.342233i	$-0.888817\pi$
$313$		−	214.238i		−	0.684466i	0.939615	−	0.342233i	$-0.111183\pi$
$314$		−	23.5378i		−	0.0749613i
$315$	45.4472			0.144277
$316$			316.404i			1.00128i
$317$	532.500			1.67981			0.839906	−	0.542732i	$-0.182610\pi$
$317$	532.500			1.67981			0.839906	+	0.542732i	$0.182610\pi$
$318$		−	1.18333i		−	0.00372115i
$319$			911.288i			2.85670i
$320$		−	56.8763i		−	0.177738i
$321$			140.866i			0.438834i
$322$	80.5912			0.250283
$323$	97.5394			0.301979
$324$	34.0481			0.105087
$325$			485.755i			1.49463i
$326$			75.0774i			0.230299i
$327$	−134.511			−0.411350
$328$	233.078			0.710603
$329$		−	142.373i		−	0.432743i
$330$	−18.4147			−0.0558022
$331$		−	592.230i		−	1.78921i	−0.446853	−	0.894607i	$-0.647455\pi$
$331$		−	592.230i		−	1.78921i	0.446853	−	0.894607i	$-0.352545\pi$
$332$	403.757			1.21614
$333$	−163.235			−0.490194
$334$		−	109.684i		−	0.328396i
$335$	60.3384	+	61.8273i	0.180115	+	0.184559i
$336$	273.589			0.814254
$337$		−	400.824i		−	1.18939i	−0.803951	−	0.594695i	$-0.797273\pi$
$337$		−	400.824i		−	1.18939i	0.803951	−	0.594695i	$-0.202727\pi$
$338$			123.058i			0.364076i
$339$	296.556			0.874796
$340$		−	84.1395i		−	0.247469i
$341$	322.614			0.946081
$342$			7.90044i			0.0231007i
$343$			470.358i			1.37130i
$344$	−78.9165			−0.229408
$345$	−32.8957			−0.0953497
$346$		−	32.5627i		−	0.0941119i
$347$			193.819i			0.558555i	0.960210	+	0.279277i	$0.0900949\pi$
$347$			193.819i			0.558555i	−0.960210	+	0.279277i	$0.909905\pi$
$348$		−	337.257i		−	0.969130i
$349$	−242.958			−0.696155			−0.348078	−	0.937466i	$-0.613165\pi$
$349$	−242.958			−0.696155			−0.348078	+	0.937466i	$0.613165\pi$
$350$	−127.689			−0.364826
$351$	108.155			0.308134
$352$	−367.556			−1.04419
$353$			104.895i			0.297153i	0.988901	+	0.148576i	$0.0474691\pi$
$353$			104.895i			0.297153i	−0.988901	+	0.148576i	$0.952531\pi$
$354$	−6.37499			−0.0180085
$355$			56.4859i			0.159115i
$356$	−333.127			−0.935749
$357$	351.004			0.983204
$358$	27.3187			0.0763092
$359$	−532.034			−1.48199			−0.740994	−	0.671511i	$-0.765645\pi$
$359$	−532.034			−1.48199			−0.740994	+	0.671511i	$0.765645\pi$
$360$	14.0209			0.0389468
$361$	−329.022			−0.911420
$362$		−	90.1866i		−	0.249134i
$363$		−	333.386i		−	0.918418i
$364$	925.143			2.54160
$365$			80.2587i			0.219887i
$366$			20.2412i			0.0553039i
$367$		−	387.090i		−	1.05474i	−0.849635	−	0.527371i	$-0.823178\pi$
$367$		−	387.090i		−	1.05474i	0.849635	−	0.527371i	$-0.176822\pi$
$368$	−198.030			−0.538125
$369$		−	192.913i		−	0.522799i
$370$	−32.6731			−0.0883057
$371$	−17.2357			−0.0464575
$372$	−119.396			−0.320956
$373$		−	366.130i		−	0.981582i	−0.871277	−	0.490791i	$-0.836708\pi$
$373$		−	366.130i		−	0.981582i	0.871277	−	0.490791i	$-0.163292\pi$
$374$	−142.223			−0.380276
$375$	107.953			0.287875
$376$		−	43.9232i		−	0.116817i
$377$		−	1071.31i		−	2.84167i
$378$			28.4304i			0.0752128i
$379$		−	289.079i		−	0.762743i	−0.924422	−	0.381371i	$-0.875452\pi$
$379$		−	289.079i		−	0.762743i	0.924422	−	0.381371i	$-0.124548\pi$
$380$		−	27.5845i		−	0.0725907i
$381$		−	265.056i		−	0.695685i
$382$	49.1257			0.128601
$383$			43.1117i			0.112563i	0.998415	+	0.0562816i	$0.0179244\pi$
$383$			43.1117i			0.112563i	−0.998415	+	0.0562816i	$0.982076\pi$
$384$	179.407			0.467205
$385$			268.220i			0.696675i
$386$		−	77.0380i		−	0.199580i
$387$			65.3171i			0.168778i
$388$		−	458.981i		−	1.18294i
$389$	−282.892			−0.727230			−0.363615	−	0.931549i	$-0.618458\pi$
$389$	−282.892			−0.727230			−0.363615	+	0.931549i	$0.618458\pi$
$390$	21.6484			0.0555086
$391$	−254.064			−0.649781
$392$			322.716i			0.823254i
$393$			82.5669i			0.210094i
$394$	150.767			0.382658
$395$	107.841			0.273015
$396$			200.945i			0.507436i
$397$	476.452			1.20013			0.600065	−	0.799951i	$-0.295141\pi$
$397$	476.452			1.20013			0.600065	+	0.799951i	$0.295141\pi$
$398$			128.163i			0.322017i
$399$	115.074			0.288406
$400$	313.760			0.784400
$401$			121.337i			0.302586i	0.988489	+	0.151293i	$0.0483437\pi$
$401$			121.337i			0.302586i	−0.988489	+	0.151293i	$0.951656\pi$
$402$	−38.6774	+	37.7460i	−0.0962123	+	0.0938954i
$403$	−379.265			−0.941104
$404$			587.320i			1.45376i
$405$		−	11.6047i		−	0.0286536i
$406$	281.613			0.693627
$407$		−	963.376i		−	2.36702i
$408$	108.288			0.265411
$409$			486.591i			1.18971i	0.803833	+	0.594854i	$0.202790\pi$
$409$			486.591i			1.18971i	−0.803833	+	0.594854i	$0.797210\pi$
$410$		−	38.6135i		−	0.0941793i
$411$	−262.669			−0.639096
$412$	−119.711			−0.290561
$413$			92.8550i			0.224830i
$414$		−	20.5786i		−	0.0497067i
$415$		−	137.614i		−	0.331599i
$416$	432.099			1.03870
$417$	46.2672			0.110953
$418$	−46.6268			−0.111547
$419$	−121.686			−0.290420			−0.145210	−	0.989401i	$-0.546386\pi$
$419$	−121.686			−0.290420			−0.145210	+	0.989401i	$0.546386\pi$
$420$		−	99.2651i		−	0.236346i
$421$	11.4216			0.0271297			0.0135649	−	0.999908i	$-0.495682\pi$
$421$	11.4216			0.0271297			0.0135649	+	0.999908i	$0.495682\pi$
$422$			15.1012i			0.0357849i
$423$	−36.3541			−0.0859436
$424$	−5.31738			−0.0125410
$425$	402.541			0.947156
$426$	−35.3359			−0.0829482
$427$	294.823			0.690453
$428$	307.677			0.718871
$429$			638.309i			1.48790i
$430$			13.0739i			0.0304044i
$431$	10.8807			0.0252452			0.0126226	−	0.999920i	$-0.495982\pi$
$431$	10.8807			0.0252452			0.0126226	+	0.999920i	$0.495982\pi$
$432$		−	69.8597i		−	0.161712i
$433$			111.028i			0.256417i	0.991747	+	0.128208i	$0.0409226\pi$
$433$			111.028i			0.256417i	−0.991747	+	0.128208i	$0.959077\pi$
$434$		−	99.6963i		−	0.229715i
$435$	−114.948			−0.264249
$436$			293.798i			0.673848i
$437$	−83.2930			−0.190602
$438$	−50.2075			−0.114629
$439$	−589.926			−1.34380			−0.671898	−	0.740644i	$-0.734521\pi$
$439$	−589.926			−1.34380			−0.671898	+	0.740644i	$0.734521\pi$
$440$			82.7482i			0.188064i
$441$	267.103			0.605677
$442$	167.198			0.378275
$443$			456.594i			1.03069i	0.856984	+	0.515343i	$0.172336\pi$
$443$			456.594i			1.03069i	−0.856984	+	0.515343i	$0.827664\pi$
$444$			356.535i			0.803006i
$445$			113.540i			0.255147i
$446$			56.5434i			0.126779i
$447$			273.192i			0.611167i
$448$		−	518.243i		−	1.15679i
$449$	−339.671			−0.756505			−0.378253	−	0.925702i	$-0.623475\pi$
$449$	−339.671			−0.756505			−0.378253	+	0.925702i	$0.623475\pi$
$450$			32.6048i			0.0724551i
$451$	1138.53			2.52446
$452$		−	647.733i		−	1.43304i
$453$			454.900i			1.00419i
$454$			95.2687i			0.209843i
$455$		−	315.319i		−	0.693010i
$456$	35.5013			0.0778538
$457$	−637.222			−1.39436			−0.697179	−	0.716897i	$-0.745562\pi$
$457$	−637.222			−1.39436			−0.697179	+	0.716897i	$0.745562\pi$
$458$	−23.5827			−0.0514906
$459$		−	89.6271i		−	0.195266i
$460$			71.8502i			0.156196i
$461$	−691.126			−1.49919			−0.749595	−	0.661897i	$-0.769752\pi$
$461$	−691.126			−1.49919			−0.749595	+	0.661897i	$0.769752\pi$
$462$	−167.790			−0.363183
$463$		−	199.320i		−	0.430497i	−0.976559	−	0.215249i	$-0.930944\pi$
$463$		−	199.320i		−	0.430497i	0.976559	−	0.215249i	$-0.0690562\pi$
$464$	−691.982			−1.49134
$465$			40.6940i			0.0875139i
$466$	−197.148			−0.423065
$467$	−695.153			−1.48855			−0.744275	−	0.667874i	$-0.767205\pi$
$467$	−695.153			−1.48855			−0.744275	+	0.667874i	$0.767205\pi$
$468$		−	236.231i		−	0.504767i
$469$	549.789	+	563.355i	1.17226	+	1.20118i
$470$	−7.27666			−0.0154823
$471$			87.5426i			0.185865i
$472$			28.6466i			0.0606919i
$473$	−385.488			−0.814986
$474$			67.4622i			0.142325i
$475$	131.970			0.277832
$476$		−	766.658i		−	1.61063i
$477$			4.40106i			0.00922654i
$478$	106.895			0.223629
$479$	812.107			1.69542			0.847711	−	0.530458i	$-0.177980\pi$
$479$	812.107			1.69542			0.847711	+	0.530458i	$0.177980\pi$
$480$		−	46.3629i		−	0.0965895i
$481$			1132.55i			2.35456i
$482$			49.5183i			0.102735i
$483$	−299.737			−0.620574
$484$	−728.177			−1.50450
$485$	−156.436			−0.322548
$486$	7.25957			0.0149374
$487$			105.689i			0.217021i	0.994095	+	0.108510i	$0.0346081\pi$
$487$			105.689i			0.217021i	−0.994095	+	0.108510i	$0.965392\pi$
$488$	90.9557			0.186385
$489$		−	279.230i		−	0.571023i
$490$	53.4636			0.109109
$491$	−23.8962			−0.0486685			−0.0243343	−	0.999704i	$-0.507747\pi$
$491$	−23.8962			−0.0486685			−0.0243343	+	0.999704i	$0.507747\pi$
$492$	−421.357			−0.856417
$493$	−887.785			−1.80078
$494$	54.8144			0.110960
$495$	68.4886			0.138361
$496$			244.975i			0.493902i
$497$			514.686i			1.03558i
$498$	86.0872			0.172866
$499$		−	50.6547i		−	0.101512i	−0.998711	−	0.0507562i	$-0.983837\pi$
$499$		−	50.6547i		−	0.101512i	0.998711	−	0.0507562i	$-0.0161631\pi$
$500$		−	235.790i		−	0.471580i
$501$			407.940i			0.814252i
$502$	−64.1237			−0.127736
$503$			557.526i			1.10840i	0.832383	+	0.554201i	$0.186976\pi$
$503$			557.526i			1.10840i	−0.832383	+	0.554201i	$0.813024\pi$
$504$	127.755			0.253481
$505$	200.178			0.396392
$506$	121.450			0.240021
$507$		−	457.679i		−	0.902721i
$508$	−578.931			−1.13963
$509$	571.887			1.12355			0.561775	−	0.827290i	$-0.310119\pi$
$509$	571.887			1.12355			0.561775	+	0.827290i	$0.310119\pi$
$510$		−	17.9398i		−	0.0351761i
$511$			731.297i			1.43111i
$512$		−	474.027i		−	0.925833i
$513$		−	29.3836i		−	0.0572779i
$514$			160.286i			0.311840i
$515$			40.8014i			0.0792261i
$516$	142.665			0.276482
$517$		−	214.555i		−	0.414999i
$518$	−297.709			−0.574728
$519$			121.108i			0.233349i
$520$		−	97.2788i		−	0.187075i
$521$		−	923.623i		−	1.77279i	−0.462931	−	0.886394i	$-0.653202\pi$
$521$		−	923.623i		−	1.77279i	0.462931	−	0.886394i	$-0.346798\pi$
$522$		−	71.9084i		−	0.137755i
$523$	−93.8026			−0.179355			−0.0896774	−	0.995971i	$-0.528584\pi$
$523$	−93.8026			−0.179355			−0.0896774	+	0.995971i	$0.528584\pi$
$524$	180.341			0.344163
$525$	474.905			0.904582
$526$		−	1.98124i		−	0.00376661i
$527$			314.293i			0.596382i
$528$	412.297			0.780866
$529$	−312.044			−0.589875
$530$			0.880918i			0.00166211i
$531$	23.7101			0.0446517
$532$		−	251.343i		−	0.472449i
$533$	−1338.46			−2.51118
$534$	−71.0276			−0.133011
$535$		−	104.866i		−	0.196012i
$536$	169.615	+	173.800i	0.316446	+	0.324254i
$537$	−101.604			−0.189208
$538$			133.890i			0.248867i
$539$			1576.39i			2.92466i
$540$	−25.3469			−0.0469386
$541$			66.0761i			0.122137i	0.998134	+	0.0610685i	$0.0194508\pi$
$541$			66.0761i			0.122137i	−0.998134	+	0.0610685i	$0.980549\pi$
$542$	5.87309			0.0108360
$543$			335.425i			0.617725i
$544$		−	358.077i		−	0.658229i
$545$	100.136			0.183736
$546$	197.255			0.361272
$547$		−	479.864i		−	0.877265i	−0.898666	−	0.438633i	$-0.855463\pi$
$547$		−	479.864i		−	0.877265i	0.898666	−	0.438633i	$-0.144537\pi$
$548$			573.717i			1.04693i
$549$		−	75.2817i		−	0.137125i
$550$	−192.427			−0.349867
$551$	−291.053			−0.528228
$552$	−92.4716			−0.167521
$553$	982.621			1.77689
$554$		−	86.4427i		−	0.156034i
$555$	121.519			0.218953
$556$		−	101.056i		−	0.181756i
$557$	−349.316			−0.627139			−0.313569	−	0.949565i	$-0.601525\pi$
$557$	−349.316			−0.627139			−0.313569	+	0.949565i	$0.601525\pi$
$558$	−25.4570			−0.0456218
$559$	453.180			0.810698
$560$	−203.672			−0.363699
$561$	528.961			0.942889
$562$	98.8986			0.175976
$563$		−	358.864i		−	0.637414i	−0.947853	−	0.318707i	$-0.896751\pi$
$563$		−	358.864i		−	0.637414i	0.947853	−	0.318707i	$-0.103249\pi$
$564$			79.4042i			0.140788i
$565$	−220.769			−0.390741
$566$		−	21.0179i		−	0.0371341i
$567$		−	105.739i		−	0.186489i
$568$			158.785i			0.279551i
$569$	−592.221			−1.04081			−0.520405	−	0.853919i	$-0.674219\pi$
$569$	−592.221			−1.04081			−0.520405	+	0.853919i	$0.674219\pi$
$570$		−	5.88143i		−	0.0103183i
$571$	−30.3120			−0.0530859			−0.0265429	−	0.999648i	$-0.508450\pi$
$571$	−30.3120			−0.0530859			−0.0265429	+	0.999648i	$0.508450\pi$
$572$	1394.19			2.43739
$573$	−182.710			−0.318865
$574$		−	351.837i		−	0.612956i
$575$	−343.747			−0.597821
$576$	−132.331			−0.229741
$577$		−	382.551i		−	0.663001i	−0.943455	−	0.331500i	$-0.892445\pi$
$577$		−	382.551i		−	0.663001i	0.943455	−	0.331500i	$-0.107555\pi$
$578$		−	3.96745i		−	0.00686410i
$579$			286.522i			0.494857i
$580$			251.069i			0.432877i
$581$		−	1253.90i		−	2.15818i
$582$		−	97.8617i		−	0.168147i
$583$	−25.9741			−0.0445526
$584$			225.612i			0.386321i
$585$	−80.5152			−0.137633
$586$		−	38.2575i		−	0.0652858i
$587$		−	362.506i		−	0.617558i	−0.951134	−	0.308779i	$-0.900080\pi$
$587$		−	362.506i		−	0.617558i	0.951134	−	0.308779i	$-0.0999203\pi$
$588$		−	583.404i		−	0.992183i
$589$			103.039i			0.174938i
$590$	4.74582			0.00804376
$591$	−560.737			−0.948794
$592$	731.536			1.23570
$593$			631.197i			1.06441i	0.846615	+	0.532206i	$0.178637\pi$
$593$			631.197i			1.06441i	−0.846615	+	0.532206i	$0.821363\pi$
$594$			42.8445i			0.0721287i
$595$	−261.302			−0.439164
$596$	596.701			1.00118
$597$		−	476.666i		−	0.798436i
$598$	−142.777			−0.238758
$599$			178.544i			0.298070i	0.988832	+	0.149035i	$0.0476166\pi$
$599$			178.544i			0.298070i	−0.988832	+	0.149035i	$0.952383\pi$
$600$	146.513			0.244188
$601$	147.267			0.245037			0.122519	−	0.992466i	$-0.460903\pi$
$601$	147.267			0.245037			0.122519	+	0.992466i	$0.460903\pi$
$602$			119.126i			0.197884i
$603$	143.850	−	140.386i	0.238557	−	0.232812i
$604$	993.587			1.64501
$605$			248.187i			0.410226i
$606$			125.226i			0.206643i
$607$	−782.079			−1.28843			−0.644217	−	0.764843i	$-0.722817\pi$
$607$	−782.079			−1.28843			−0.644217	+	0.764843i	$0.722817\pi$
$608$		−	117.393i		−	0.193080i
$609$	−1047.38			−1.71984
$610$		−	15.0684i		−	0.0247023i
$611$			252.230i			0.412816i
$612$	−195.762			−0.319873
$613$	−329.406			−0.537367			−0.268683	−	0.963229i	$-0.586589\pi$
$613$	−329.406			−0.537367			−0.268683	+	0.963229i	$0.586589\pi$
$614$		−	233.696i		−	0.380612i
$615$			143.612i			0.233516i
$616$			753.981i			1.22400i
$617$	−64.1782			−0.104017			−0.0520083	−	0.998647i	$-0.516562\pi$
$617$	−64.1782			−0.104017			−0.0520083	+	0.998647i	$0.516562\pi$
$618$	−25.5242			−0.0413013
$619$	−265.555			−0.429007			−0.214503	−	0.976723i	$-0.568813\pi$
$619$	−265.555			−0.429007			−0.214503	+	0.976723i	$0.568813\pi$
$620$	88.8832			0.143360
$621$			76.5364i			0.123247i
$622$	−114.962			−0.184827
$623$			1034.55i			1.66060i
$624$	−484.697			−0.776758
$625$	503.070			0.804913
$626$	−99.7709			−0.159378
$627$	173.416			0.276580
$628$	191.209			0.304474
$629$	938.531			1.49210
$630$		−	21.1648i		−	0.0335950i
$631$		−	1217.29i		−	1.92915i	−0.263813	−	0.964574i	$-0.584980\pi$
$631$		−	1217.29i		−	1.92915i	0.263813	−	0.964574i	$-0.415020\pi$
$632$	303.147			0.479663
$633$		−	56.1649i		−	0.0887281i
$634$		−	247.986i		−	0.391145i
$635$			197.319i			0.310738i
$636$	9.61274			0.0151144
$637$		−	1853.20i		−	2.90927i
$638$	424.388			0.665185
$639$	131.422			0.205669
$640$	−133.558			−0.208684
$641$		−	399.718i		−	0.623585i	−0.950150	−	0.311793i	$-0.899071\pi$
$641$		−	399.718i		−	0.623585i	0.950150	−	0.311793i	$-0.100929\pi$
$642$	65.6013			0.102183
$643$	546.627			0.850119			0.425060	−	0.905165i	$-0.360253\pi$
$643$	546.627			0.850119			0.425060	+	0.905165i	$0.360253\pi$
$644$			654.682i			1.01659i
$645$		−	48.6249i		−	0.0753874i
$646$		−	45.4242i		−	0.0703162i
$647$			535.583i			0.827794i	0.910324	+	0.413897i	$0.135833\pi$
$647$			535.583i			0.827794i	−0.910324	+	0.413897i	$0.864167\pi$
$648$		−	32.6215i		−	0.0503418i
$649$			139.932i			0.215612i
$650$	226.217			0.348026
$651$			370.793i			0.569575i
$652$	−609.891			−0.935415
$653$		−	801.117i		−	1.22683i	−0.789762	−	0.613413i	$-0.789796\pi$
$653$		−	801.117i		−	1.22683i	0.789762	−	0.613413i	$-0.210204\pi$
$654$			62.6422i			0.0957831i
$655$		−	61.4663i		−	0.0938417i
$656$			864.538i			1.31789i
$657$	186.733			0.284221
$658$	−66.3031			−0.100765
$659$	589.533			0.894588			0.447294	−	0.894387i	$-0.352388\pi$
$659$	589.533			0.894588			0.447294	+	0.894387i	$0.352388\pi$
$660$		−	149.592i		−	0.226654i
$661$			506.277i			0.765926i	0.923764	+	0.382963i	$0.125096\pi$
$661$			506.277i			0.765926i	−0.923764	+	0.382963i	$0.874904\pi$
$662$	−275.802			−0.416620
$663$	−621.846			−0.937928
$664$		−	386.840i		−	0.582591i
$665$	−85.6659			−0.128821
$666$			76.0186i			0.114142i
$667$	758.117			1.13661
$668$	891.018			1.33386
$669$		−	210.298i		−	0.314347i
$670$	28.7931	−	28.0997i	0.0429747	−	0.0419399i
$671$	444.297			0.662142
$672$		−	422.448i		−	0.628642i
$673$			660.098i			0.980829i	0.871489	+	0.490415i	$0.163155\pi$
$673$			660.098i			0.980829i	−0.871489	+	0.490415i	$0.836845\pi$
$674$	−186.665			−0.276950
$675$		−	121.265i		−	0.179652i
$676$	−999.657			−1.47878
$677$			915.593i			1.35243i	0.736706	+	0.676213i	$0.236380\pi$
$677$			915.593i			1.35243i	−0.736706	+	0.676213i	$0.763620\pi$
$678$		−	138.106i		−	0.203697i
$679$	−1425.41			−2.09927
$680$	−80.6141			−0.118550
$681$		−	354.326i		−	0.520303i
$682$		−	150.242i		−	0.220296i
$683$		−	259.685i		−	0.380213i	−0.981763	−	0.190106i	$-0.939117\pi$
$683$		−	259.685i		−	0.380213i	0.981763	−	0.190106i	$-0.0608833\pi$
$684$	−64.1792			−0.0938292
$685$	195.542			0.285462
$686$	219.046			0.319309
$687$	87.7094			0.127670
$688$		−	292.719i		−	0.425463i
$689$	30.5352			0.0443182
$690$			15.3196i			0.0222023i
$691$	164.488			0.238044			0.119022	−	0.992892i	$-0.462024\pi$
$691$	164.488			0.238044			0.119022	+	0.992892i	$0.462024\pi$
$692$	264.523			0.382259
$693$	624.051			0.900507
$694$	90.2616			0.130060
$695$	−34.4433			−0.0495587
$696$	−323.127			−0.464262
$697$			1109.17i			1.59134i
$698$			113.146i			0.162100i
$699$	733.239			1.04898
$700$		−	1037.28i		−	1.48183i
$701$		−	1049.36i		−	1.49695i	−0.663162	−	0.748476i	$-0.730786\pi$
$701$		−	1049.36i		−	1.49695i	0.663162	−	0.748476i	$-0.269214\pi$
$702$		−	50.3680i		−	0.0717493i
$703$	307.690			0.437681
$704$		−	780.988i		−	1.10936i
$705$	27.0636			0.0383880
$706$	48.8498			0.0691923
$707$	1823.97			2.57988
$708$		−	51.7872i		−	0.0731458i
$709$	−787.683			−1.11098			−0.555489	−	0.831524i	$-0.687469\pi$
$709$	−787.683			−1.11098			−0.555489	+	0.831524i	$0.687469\pi$
$710$	26.3056			0.0370501
$711$		−	250.907i		−	0.352894i
$712$			319.169i			0.448271i
$713$		−	268.388i		−	0.376421i
$714$		−	163.463i		−	0.228940i
$715$		−	475.184i		−	0.664593i
$716$			221.923i			0.309948i
$717$	−397.566			−0.554485
$718$			247.769i			0.345082i
$719$	136.741			0.190182			0.0950910	−	0.995469i	$-0.469686\pi$
$719$	136.741			0.190182			0.0950910	+	0.995469i	$0.469686\pi$
$720$			52.0065i			0.0722313i
$721$			371.773i			0.515635i
$722$			153.226i			0.212225i
$723$		−	184.170i		−	0.254730i
$724$	732.630			1.01192
$725$	−1201.17			−1.65678
$726$	−155.258			−0.213854
$727$			58.9328i			0.0810629i	0.999178	+	0.0405315i	$0.0129051\pi$
$727$			58.9328i			0.0810629i	−0.999178	+	0.0405315i	$0.987095\pi$
$728$		−	886.381i		−	1.21756i
$729$	−27.0000			−0.0370370
$730$	37.3766			0.0512008
$731$		−	375.546i		−	0.513743i
$732$	−164.429			−0.224630
$733$		−	1067.06i		−	1.45574i	−0.685714	−	0.727871i	$-0.740510\pi$
$733$		−	1067.06i		−	1.45574i	0.685714	−	0.727871i	$-0.259490\pi$
$734$	−180.268			−0.245597
$735$	−198.843			−0.270535
$736$			305.777i			0.415458i
$737$	828.528	+	848.973i	1.12419	+	1.15193i
$738$	−89.8397			−0.121734
$739$			999.902i			1.35305i	0.736421	+	0.676524i	$0.236514\pi$
$739$			999.902i			1.35305i	−0.736421	+	0.676524i	$0.763486\pi$
$740$		−	265.420i		−	0.358675i
$741$	−203.867			−0.275125
$742$			8.02671i			0.0108177i
$743$	768.587			1.03444			0.517219	−	0.855853i	$-0.326967\pi$
$743$	768.587			1.03444			0.517219	+	0.855853i	$0.326967\pi$
$744$			114.393i			0.153754i
$745$		−	203.375i		−	0.272987i
$746$	−170.507			−0.228562
$747$	−320.178			−0.428618
$748$		−	1155.35i		−	1.54458i
$749$		−	955.516i		−	1.27572i
$750$		−	50.2740i		−	0.0670320i
$751$	−873.036			−1.16250			−0.581249	−	0.813726i	$-0.697436\pi$
$751$	−873.036			−1.16250			−0.581249	+	0.813726i	$0.697436\pi$
$752$	162.921			0.216650
$753$	238.491			0.316721
$754$	−498.911			−0.661686
$755$		−	338.647i		−	0.448539i
$756$	−230.954			−0.305495
$757$			336.823i			0.444945i	0.974939	+	0.222472i	$0.0714127\pi$
$757$			336.823i			0.444945i	−0.974939	+	0.222472i	$0.928587\pi$
$758$	−134.625			−0.177605
$759$	−451.702			−0.595128
$760$	−26.4287			−0.0347746
$761$	714.717			0.939182			0.469591	−	0.882884i	$-0.344401\pi$
$761$	714.717			0.939182			0.469591	+	0.882884i	$0.344401\pi$
$762$	−123.437			−0.161991
$763$	912.414			1.19582
$764$			399.072i			0.522346i
$765$			66.7223i			0.0872186i
$766$	20.0772			0.0262104
$767$		−	164.504i		−	0.214477i
$768$			222.055i			0.289134i
$769$		−	568.467i		−	0.739229i	−0.929185	−	0.369615i	$-0.879490\pi$
$769$		−	568.467i		−	0.739229i	0.929185	−	0.369615i	$-0.120510\pi$
$770$	124.910			0.162221
$771$		−	596.139i		−	0.773202i
$772$	625.817			0.810644
$773$	578.184			0.747974			0.373987	−	0.927434i	$-0.377990\pi$
$773$	578.184			0.747974			0.373987	+	0.927434i	$0.377990\pi$
$774$	30.4183			0.0393001
$775$			425.236i			0.548692i
$776$	−439.750			−0.566688
$777$	1107.25			1.42503
$778$			131.743i			0.169336i
$779$			363.632i			0.466793i
$780$			175.860i			0.225462i
$781$			775.628i			0.993122i
$782$			118.318i			0.151302i
$783$			267.444i			0.341563i
$784$	−1197.02			−1.52682
$785$		−	65.1705i		−	0.0830197i
$786$	38.4515			0.0489205
$787$		−	846.832i		−	1.07603i	−0.842937	−	0.538013i	$-0.819175\pi$
$787$		−	846.832i		−	1.07603i	0.842937	−	0.538013i	$-0.180825\pi$
$788$			1224.75i			1.55426i
$789$			7.36867i			0.00933926i
$790$		−	50.2217i		−	0.0635718i
$791$	−2011.59			−2.54310
$792$	192.525			0.243088
$793$	−522.316			−0.658658
$794$		−	221.884i		−	0.279451i
$795$		−	3.27634i		−	0.00412118i
$796$	−1041.13			−1.30795
$797$	−134.701			−0.169010			−0.0845048	−	0.996423i	$-0.526931\pi$
$797$	−134.701			−0.169010			−0.0845048	+	0.996423i	$0.526931\pi$
$798$		−	53.5901i		−	0.0671555i
$799$	209.021			0.261603
$800$		−	484.475i		−	0.605594i
$801$	264.168			0.329798
$802$	56.5068			0.0704574
$803$			1102.06i			1.37243i
$804$	−306.629	−	314.195i	−0.381379	−	0.390790i
$805$	223.137			0.277189
$806$			176.624i			0.219137i
$807$		−	497.969i		−	0.617062i
$808$	562.712			0.696426
$809$		−	980.745i		−	1.21229i	−0.795353	−	0.606146i	$-0.792715\pi$
$809$		−	980.745i		−	1.21229i	0.795353	−	0.606146i	$-0.207285\pi$
$810$	−5.40433			−0.00667202
$811$		−	291.228i		−	0.359097i	−0.983749	−	0.179549i	$-0.942536\pi$
$811$		−	291.228i		−	0.359097i	0.983749	−	0.179549i	$-0.0574637\pi$
$812$			2287.68i			2.81734i
$813$	−21.8434			−0.0268676
$814$	−448.646			−0.551162
$815$			207.871i			0.255056i
$816$			401.664i			0.492235i
$817$		−	123.120i		−	0.150698i
$818$	226.606			0.277025
$819$	−733.635			−0.895769
$820$	313.676			0.382532
$821$	−523.509			−0.637648			−0.318824	−	0.947814i	$-0.603288\pi$
$821$	−523.509			−0.637648			−0.318824	+	0.947814i	$0.603288\pi$
$822$			122.325i			0.148814i
$823$	267.819			0.325418			0.162709	−	0.986674i	$-0.447977\pi$
$823$	267.819			0.325418			0.162709	+	0.986674i	$0.447977\pi$
$824$			114.695i			0.139193i
$825$	715.679			0.867490
$826$	43.2427			0.0523520
$827$	824.495			0.996970			0.498485	−	0.866898i	$-0.333890\pi$
$827$	824.495			0.996970			0.498485	+	0.866898i	$0.333890\pi$
$828$	167.170			0.201896
$829$	1348.34			1.62647			0.813235	−	0.581936i	$-0.197704\pi$
$829$	1348.34			1.62647			0.813235	+	0.581936i	$0.197704\pi$
$830$	−64.0870			−0.0772132
$831$			321.500i			0.386884i
$832$			918.130i			1.10352i
$833$	−1535.73			−1.84362
$834$		−	21.5467i		−	0.0258354i
$835$		−	303.688i		−	0.363698i
$836$		−	378.772i		−	0.453077i
$837$	94.6803			0.113119
$838$			56.6694i			0.0676246i
$839$	−401.409			−0.478438			−0.239219	−	0.970966i	$-0.576891\pi$
$839$	−401.409			−0.478438			−0.239219	+	0.970966i	$0.576891\pi$
$840$	−95.1060			−0.113221
$841$	1808.12			2.14996
$842$		−	5.31906i		−	0.00631718i
$843$	−367.827			−0.436330
$844$	−122.675			−0.145349
$845$			340.716i			0.403214i
$846$			16.9302i			0.0200120i
$847$			2261.42i			2.66991i
$848$		−	19.7234i		−	0.0232587i
$849$			78.1704i			0.0920734i
$850$		−	187.464i		−	0.220546i
$851$	−801.451			−0.941775
$852$		−	287.051i		−	0.336914i
$853$	−903.281			−1.05895			−0.529473	−	0.848327i	$-0.677610\pi$
$853$	−903.281			−1.05895			−0.529473	+	0.848327i	$0.677610\pi$
$854$		−	137.300i		−	0.160773i
$855$			21.8744i			0.0255841i
$856$		−	294.785i		−	0.344375i
$857$			1177.61i			1.37411i	0.726605	+	0.687056i	$0.241097\pi$
$857$			1177.61i			1.37411i	−0.726605	+	0.687056i	$0.758903\pi$
$858$	297.261			0.346458
$859$	−298.428			−0.347413			−0.173707	−	0.984797i	$-0.555574\pi$
$859$	−298.428			−0.347413			−0.173707	+	0.984797i	$0.555574\pi$
$860$	−106.206			−0.123495
$861$			1308.56i			1.51982i
$862$		−	5.06716i		−	0.00587837i
$863$	−526.939			−0.610590			−0.305295	−	0.952258i	$-0.598755\pi$
$863$	−526.939			−0.610590			−0.305295	+	0.952258i	$0.598755\pi$
$864$	−107.870			−0.124849
$865$		−	90.1581i		−	0.104229i
$866$	51.7061			0.0597068
$867$			14.7558i			0.0170194i
$868$	809.882			0.933044
$869$	1480.80			1.70403
$870$			53.5317i			0.0615306i
$871$	−974.018	−	998.052i	−1.11828	−	1.14587i
$872$	281.488			0.322807
$873$			363.970i			0.416919i
$874$			38.7897i			0.0443818i
$875$	−732.266			−0.836876
$876$		−	407.860i		−	0.465594i
$877$	−523.750			−0.597207			−0.298603	−	0.954377i	$-0.596521\pi$
$877$	−523.750			−0.597207			−0.298603	+	0.954377i	$0.596521\pi$
$878$			274.730i			0.312904i
$879$			142.288i			0.161875i
$880$	−306.932			−0.348786
$881$	−425.864			−0.483387			−0.241693	−	0.970353i	$-0.577703\pi$
$881$	−425.864			−0.483387			−0.241693	+	0.970353i	$0.577703\pi$
$882$		−	124.391i		−	0.141032i
$883$			582.486i			0.659667i	0.944039	+	0.329833i	$0.106993\pi$
$883$			582.486i			0.659667i	−0.944039	+	0.329833i	$0.893007\pi$
$884$			1358.23i			1.53646i
$885$	−17.6508			−0.0199444
$886$	212.637			0.239996
$887$	−385.892			−0.435053			−0.217527	−	0.976054i	$-0.569799\pi$
$887$	−385.892			−0.435053			−0.217527	+	0.976054i	$0.569799\pi$
$888$	341.596			0.384680
$889$			1797.92i			2.02241i
$890$	52.8760			0.0594112
$891$		−	159.348i		−	0.178842i
$892$	−459.330			−0.514944
$893$	68.5259			0.0767368
$894$	127.226			0.142311
$895$	75.6387			0.0845125
$896$	−1216.95			−1.35820
$897$	531.021			0.591997
$898$			158.185i			0.176153i
$899$		−	937.838i		−	1.04320i
$900$	−264.865			−0.294294
$901$		−	25.3043i		−	0.0280846i
$902$		−	530.216i		−	0.587822i
$903$		−	443.058i		−	0.490651i
$904$	−620.594			−0.686497
$905$		−	249.705i		−	0.275917i
$906$	211.848			0.233828
$907$	−1084.15			−1.19531			−0.597656	−	0.801752i	$-0.703901\pi$
$907$	−1084.15			−1.19531			−0.597656	+	0.801752i	$0.703901\pi$
$908$	−773.915			−0.852329
$909$		−	465.743i		−	0.512368i
$910$	−146.845			−0.161368
$911$	−447.254			−0.490948			−0.245474	−	0.969403i	$-0.578944\pi$
$911$	−447.254			−0.490948			−0.245474	+	0.969403i	$0.578944\pi$
$912$			131.682i			0.144389i
$913$		−	1889.62i		−	2.06969i
$914$			296.755i			0.324678i
$915$			56.0429i			0.0612491i
$916$		−	191.574i		−	0.209142i
$917$		−	560.066i		−	0.610759i
$918$	−41.7395			−0.0454679
$919$			1027.84i			1.11843i	0.829021	+	0.559217i	$0.188898\pi$
$919$			1027.84i			1.11843i	−0.829021	+	0.559217i	$0.811102\pi$
$920$	68.8398			0.0748259
$921$			869.167i			0.943721i
$922$			321.859i			0.349087i
$923$		−	911.829i		−	0.987897i
$924$		−	1363.04i		−	1.47516i
$925$	1269.82			1.37278
$926$	−92.8238			−0.100242
$927$	94.9303			0.102406
$928$			1068.49i			1.15139i
$929$			10.8638i			0.0116941i	0.999983	+	0.00584707i	$0.00186119\pi$
$929$			10.8638i			0.0116941i	−0.999983	+	0.00584707i	$0.998139\pi$
$930$	18.9513			0.0203777
$931$	−503.478			−0.540793
$932$		−	1601.53i		−	1.71838i
$933$	427.571			0.458275
$934$			323.734i			0.346610i
$935$	−393.781			−0.421156
$936$	−226.333			−0.241809
$937$		−	27.7906i		−	0.0296591i	−0.999890	−	0.0148295i	$-0.995279\pi$
$937$		−	27.7906i		−	0.0296591i	0.999890	−	0.0148295i	$-0.00472056\pi$
$938$	262.355	−	256.038i	0.279697	−	0.272961i
$939$	371.071			0.395176
$940$		−	59.1119i		−	0.0628850i
$941$		−	705.210i		−	0.749426i	−0.927141	−	0.374713i	$-0.877741\pi$
$941$		−	705.210i		−	0.749426i	0.927141	−	0.374713i	$-0.122259\pi$
$942$	40.7687			0.0432789
$943$		−	947.165i		−	1.00442i
$944$	−106.257			−0.112560
$945$			78.7168i			0.0832982i
$946$			179.522i			0.189770i
$947$	1172.66			1.23829			0.619147	−	0.785275i	$-0.287478\pi$
$947$	1172.66			1.23829			0.619147	+	0.785275i	$0.287478\pi$
$948$	−548.028			−0.578089
$949$		−	1295.58i		−	1.36521i
$950$		−	61.4586i		−	0.0646933i
$951$			922.317i			0.969840i
$952$	−734.536			−0.771571
$953$	739.206			0.775662			0.387831	−	0.921731i	$-0.373224\pi$
$953$	739.206			0.775662			0.387831	+	0.921731i	$0.373224\pi$
$954$	2.04958			0.00214841
$955$	136.017			0.142426
$956$			868.358i			0.908325i
$957$	−1578.40			−1.64932
$958$		−	378.200i		−	0.394780i
$959$	1781.73			1.85790
$960$	98.5126			0.102617
$961$	628.987			0.654513
$962$	527.428			0.548262
$963$	−243.986			−0.253361
$964$	−402.261			−0.417284
$965$		−	213.299i		−	0.221035i
$966$			139.588i			0.144501i
$967$	−586.617			−0.606636			−0.303318	−	0.952889i	$-0.598094\pi$
$967$	−586.617			−0.606636			−0.303318	+	0.952889i	$0.598094\pi$
$968$			697.667i			0.720730i
$969$			168.943i			0.174348i
$970$			72.8524i			0.0751056i
$971$	856.679			0.882264			0.441132	−	0.897442i	$-0.354577\pi$
$971$	856.679			0.882264			0.441132	+	0.897442i	$0.354577\pi$
$972$			58.9730i			0.0606718i
$973$	−313.839			−0.322548
$974$	49.2196			0.0505335
$975$	−841.353			−0.862926
$976$			337.375i			0.345671i
$977$	−1046.96			−1.07161			−0.535805	−	0.844342i	$-0.679992\pi$
$977$	−1046.96			−1.07161			−0.535805	+	0.844342i	$0.679992\pi$
$978$	−130.038			−0.132963
$979$			1559.06i			1.59251i
$980$			434.311i			0.443174i
$981$		−	232.980i		−	0.237493i
$982$			11.1285i			0.0113325i
$983$		−	395.357i		−	0.402194i	−0.979571	−	0.201097i	$-0.935549\pi$
$983$		−	395.357i		−	0.402194i	0.979571	−	0.201097i	$-0.0644507\pi$
$984$			403.703i			0.410267i
$985$	417.437			0.423794
$986$			413.443i			0.419313i
$987$	246.597			0.249845
$988$			445.285i			0.450693i
$989$			320.695i			0.324262i
$990$		−	31.8953i		−	0.0322174i
$991$		−	62.9130i		−	0.0634844i	−0.999496	−	0.0317422i	$-0.989894\pi$
$991$		−	62.9130i		−	0.0634844i	0.999496	−	0.0317422i	$-0.0101055\pi$
$992$	378.265			0.381315
$993$	1025.77			1.03300
$994$	239.690			0.241137
$995$			354.851i			0.356634i
$996$			699.328i			0.702137i
$997$	1508.36			1.51289			0.756447	−	0.654055i	$-0.226933\pi$
$997$	1508.36			1.51289			0.756447	+	0.654055i	$0.226933\pi$
$998$	−23.5900			−0.0236372
$999$		−	282.731i		−	0.283014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.11	✓	22
3.2	odd	2		603.3.b.e.334.12		22
67.66	odd	2	inner	201.3.b.a.133.12	yes	22
201.200	even	2		603.3.b.e.334.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.11	✓	22	1.1	even	1	trivial
201.3.b.a.133.12	yes	22	67.66	odd	2	inner
603.3.b.e.334.11		22	201.200	even	2
603.3.b.e.334.12		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.465702i q^{2} +1.73205i q^{3} +3.78312 q^{4} -1.28941i q^{5} +0.806619 q^{6} -11.7488i q^{7} -3.62461i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-0.465702i q^{2} +1.73205i q^{3} +3.78312 q^{4} -1.28941i q^{5} +0.806619 q^{6} -11.7488i q^{7} -3.62461i q^{8} -3.00000 q^{9} -0.600481 q^{10} -17.7054i q^{11} +6.55256i q^{12} +20.8144i q^{13} -5.47144 q^{14} +2.23333 q^{15} +13.4445 q^{16} +17.2487 q^{17} +1.39710i q^{18} +5.65487 q^{19} -4.87800i q^{20} +20.3495 q^{21} -8.24542 q^{22} -14.7294 q^{23} +6.27801 q^{24} +23.3374 q^{25} +9.69332 q^{26} -5.19615i q^{27} -44.4472i q^{28} -51.4696 q^{29} -1.04006i q^{30} +18.2212i q^{31} -20.7596i q^{32} +30.6666 q^{33} -8.03277i q^{34} -15.1491 q^{35} -11.3494 q^{36} +54.4115 q^{37} -2.63348i q^{38} -36.0517 q^{39} -4.67362 q^{40} +64.3042i q^{41} -9.47681i q^{42} -21.7724i q^{43} -66.9816i q^{44} +3.86824i q^{45} +6.85952i q^{46} +12.1180 q^{47} +23.2866i q^{48} -89.0345 q^{49} -10.8683i q^{50} +29.8757i q^{51} +78.7436i q^{52} -1.46702i q^{53} -2.41986 q^{54} -22.8295 q^{55} -42.5849 q^{56} +9.79452i q^{57} +23.9695i q^{58} -7.90335 q^{59} +8.44895 q^{60} +25.0939i q^{61} +8.48565 q^{62} +35.2464i q^{63} +44.1102 q^{64} +26.8384 q^{65} -14.2815i q^{66} +(-47.9500 + 46.7953i) q^{67} +65.2541 q^{68} -25.5121i q^{69} +7.05494i q^{70} -43.8075 q^{71} +10.8738i q^{72} -62.2444 q^{73} -25.3395i q^{74} +40.4216i q^{75} +21.3931 q^{76} -208.017 q^{77} +16.7893i q^{78} +83.6358i q^{79} -17.3355i q^{80} +9.00000 q^{81} +29.9466 q^{82} +106.726 q^{83} +76.9848 q^{84} -22.2408i q^{85} -10.1394 q^{86} -89.1479i q^{87} -64.1751 q^{88} -88.0560 q^{89} +1.80144 q^{90} +244.545 q^{91} -55.7232 q^{92} -31.5601 q^{93} -5.64339i q^{94} -7.29146i q^{95} +35.9566 q^{96} -121.323i q^{97} +41.4635i q^{98} +53.1161i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 22 * q - 52 * q^4 - 66 * q^9	\( 22 q - 52 q^{4} - 66 q^{9} - 36 q^{10} + 72 q^{14} + 12 q^{15} + 116 q^{16} - 14 q^{17} - 26 q^{19} + 48 q^{21} + 32 q^{22} - 82 q^{23} + 36 q^{24} - 62 q^{25} - 100 q^{26} + 102 q^{29} + 36 q^{33} - 180 q^{35} + 156 q^{36} + 106 q^{37} - 72 q^{39} + 76 q^{40} + 154 q^{47} + 146 q^{49} - 224 q^{55} - 452 q^{56} + 370 q^{59} - 24 q^{60} - 300 q^{62} + 148 q^{64} - 284 q^{65} - 134 q^{67} - 116 q^{68} + 160 q^{71} + 218 q^{73} + 480 q^{76} - 396 q^{77} + 198 q^{81} - 68 q^{82} + 128 q^{83} + 20 q^{86} - 856 q^{88} - 118 q^{89} + 108 q^{90} - 400 q^{91} + 804 q^{92} - 72 q^{93} - 144 q^{96}+O(q^{100}) \) 22 * q - 52 * q^4 - 66 * q^9 - 36 * q^10 + 72 * q^14 + 12 * q^15 + 116 * q^16 - 14 * q^17 - 26 * q^19 + 48 * q^21 + 32 * q^22 - 82 * q^23 + 36 * q^24 - 62 * q^25 - 100 * q^26 + 102 * q^29 + 36 * q^33 - 180 * q^35 + 156 * q^36 + 106 * q^37 - 72 * q^39 + 76 * q^40 + 154 * q^47 + 146 * q^49 - 224 * q^55 - 452 * q^56 + 370 * q^59 - 24 * q^60 - 300 * q^62 + 148 * q^64 - 284 * q^65 - 134 * q^67 - 116 * q^68 + 160 * q^71 + 218 * q^73 + 480 * q^76 - 396 * q^77 + 198 * q^81 - 68 * q^82 + 128 * q^83 + 20 * q^86 - 856 * q^88 - 118 * q^89 + 108 * q^90 - 400 * q^91 + 804 * q^92 - 72 * q^93 - 144 * q^96

Introduction

L-functions

Modular forms

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