LMFDB - Embedded newform 201.3.b.a.133.5

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			133.5
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.88392i q^{2} +1.73205i q^{3} -4.31697 q^{4} +1.18875i q^{5} +4.99509 q^{6} -3.84699i q^{7} +0.914116i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-2.88392i q^{2} +1.73205i q^{3} -4.31697 q^{4} +1.18875i q^{5} +4.99509 q^{6} -3.84699i q^{7} +0.914116i q^{8} -3.00000 q^{9} +3.42825 q^{10} -11.0502i q^{11} -7.47721i q^{12} -19.7889i q^{13} -11.0944 q^{14} -2.05897 q^{15} -14.6316 q^{16} +7.89730 q^{17} +8.65175i q^{18} -35.4227 q^{19} -5.13180i q^{20} +6.66318 q^{21} -31.8680 q^{22} +38.7216 q^{23} -1.58330 q^{24} +23.5869 q^{25} -57.0695 q^{26} -5.19615i q^{27} +16.6073i q^{28} -4.14878 q^{29} +5.93791i q^{30} -28.6829i q^{31} +45.8529i q^{32} +19.1396 q^{33} -22.7752i q^{34} +4.57311 q^{35} +12.9509 q^{36} -30.8208 q^{37} +102.156i q^{38} +34.2754 q^{39} -1.08665 q^{40} +64.0233i q^{41} -19.2161i q^{42} +51.4765i q^{43} +47.7036i q^{44} -3.56625i q^{45} -111.670i q^{46} -0.461308 q^{47} -25.3428i q^{48} +34.2007 q^{49} -68.0226i q^{50} +13.6785i q^{51} +85.4281i q^{52} -39.6711i q^{53} -14.9853 q^{54} +13.1360 q^{55} +3.51659 q^{56} -61.3539i q^{57} +11.9647i q^{58} +76.0572 q^{59} +8.88853 q^{60} -60.6401i q^{61} -82.7190 q^{62} +11.5410i q^{63} +73.7093 q^{64} +23.5240 q^{65} -55.1969i q^{66} +(-27.9291 - 60.9013i) q^{67} -34.0924 q^{68} +67.0679i q^{69} -13.1885i q^{70} -38.7507 q^{71} -2.74235i q^{72} +55.4015 q^{73} +88.8847i q^{74} +40.8537i q^{75} +152.919 q^{76} -42.5102 q^{77} -98.8473i q^{78} +25.6418i q^{79} -17.3934i q^{80} +9.00000 q^{81} +184.638 q^{82} +47.9462 q^{83} -28.7648 q^{84} +9.38791i q^{85} +148.454 q^{86} -7.18590i q^{87} +10.1012 q^{88} +71.8386 q^{89} -10.2848 q^{90} -76.1277 q^{91} -167.160 q^{92} +49.6802 q^{93} +1.33037i q^{94} -42.1087i q^{95} -79.4196 q^{96} +96.0761i q^{97} -98.6318i q^{98} +33.1507i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.88392i		−	1.44196i	−0.692957	−	0.720979i	$-0.743692\pi$
$2$		−	2.88392i		−	1.44196i	0.692957	−	0.720979i	$-0.256308\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−4.31697			−1.07924
$5$			1.18875i			0.237750i	0.992909	+	0.118875i	$0.0379288\pi$
$5$			1.18875i			0.237750i	−0.992909	+	0.118875i	$0.962071\pi$
$6$	4.99509			0.832515
$7$		−	3.84699i		−	0.549570i	−0.961506	−	0.274785i	$-0.911393\pi$
$7$		−	3.84699i		−	0.549570i	0.961506	−	0.274785i	$-0.0886067\pi$
$8$			0.914116i			0.114264i
$9$	−3.00000			−0.333333
$10$	3.42825			0.342825
$11$		−	11.0502i		−	1.00457i	−0.864703	−	0.502284i	$-0.832493\pi$
$11$		−	11.0502i		−	1.00457i	0.864703	−	0.502284i	$-0.167507\pi$
$12$		−	7.47721i		−	0.623101i
$13$		−	19.7889i		−	1.52222i	−0.648621	−	0.761112i	$-0.724654\pi$
$13$		−	19.7889i		−	1.52222i	0.648621	−	0.761112i	$-0.275346\pi$
$14$	−11.0944			−0.792457
$15$	−2.05897			−0.137265
$16$	−14.6316			−0.914478
$17$	7.89730			0.464547			0.232274	−	0.972650i	$-0.425384\pi$
$17$	7.89730			0.464547			0.232274	+	0.972650i	$0.425384\pi$
$18$			8.65175i			0.480653i
$19$	−35.4227			−1.86435			−0.932176	−	0.362005i	$-0.882092\pi$
$19$	−35.4227			−1.86435			−0.932176	+	0.362005i	$0.882092\pi$
$20$		−	5.13180i		−	0.256590i
$21$	6.66318			0.317294
$22$	−31.8680			−1.44854
$23$	38.7216			1.68355			0.841775	−	0.539829i	$-0.181511\pi$
$23$	38.7216			1.68355			0.841775	+	0.539829i	$0.181511\pi$
$24$	−1.58330			−0.0659706
$25$	23.5869			0.943475
$26$	−57.0695			−2.19498
$27$		−	5.19615i		−	0.192450i
$28$			16.6073i			0.593119i
$29$	−4.14878			−0.143061			−0.0715307	−	0.997438i	$-0.522788\pi$
$29$	−4.14878			−0.143061			−0.0715307	+	0.997438i	$0.522788\pi$
$30$			5.93791i			0.197930i
$31$		−	28.6829i		−	0.925254i	−0.886553	−	0.462627i	$-0.846907\pi$
$31$		−	28.6829i		−	0.925254i	0.886553	−	0.462627i	$-0.153093\pi$
$32$			45.8529i			1.43290i
$33$	19.1396			0.579987
$34$		−	22.7752i		−	0.669858i
$35$	4.57311			0.130660
$36$	12.9509			0.359748
$37$	−30.8208			−0.832995			−0.416498	−	0.909137i	$-0.636743\pi$
$37$	−30.8208			−0.832995			−0.416498	+	0.909137i	$0.636743\pi$
$38$			102.156i			2.68832i
$39$	34.2754			0.878856
$40$	−1.08665			−0.0271664
$41$			64.0233i			1.56154i	0.624816	+	0.780772i	$0.285174\pi$
$41$			64.0233i			1.56154i	−0.624816	+	0.780772i	$0.714826\pi$
$42$		−	19.2161i		−	0.457525i
$43$			51.4765i			1.19713i	0.801075	+	0.598564i	$0.204262\pi$
$43$			51.4765i			1.19713i	−0.801075	+	0.598564i	$0.795738\pi$
$44$			47.7036i			1.08417i
$45$		−	3.56625i		−	0.0792499i
$46$		−	111.670i		−	2.42761i
$47$	−0.461308			−0.00981506			−0.00490753	−	0.999988i	$-0.501562\pi$
$47$	−0.461308			−0.00981506			−0.00490753	+	0.999988i	$0.501562\pi$
$48$		−	25.3428i		−	0.527974i
$49$	34.2007			0.697973
$50$		−	68.0226i		−	1.36045i
$51$			13.6785i			0.268206i
$52$			85.4281i			1.64285i
$53$		−	39.6711i		−	0.748511i	−0.927326	−	0.374255i	$-0.877898\pi$
$53$		−	39.6711i		−	0.748511i	0.927326	−	0.374255i	$-0.122102\pi$
$54$	−14.9853			−0.277505
$55$	13.1360			0.238836
$56$	3.51659			0.0627963
$57$		−	61.3539i		−	1.07638i
$58$			11.9647i			0.206288i
$59$	76.0572			1.28910			0.644552	−	0.764560i	$-0.277044\pi$
$59$	76.0572			1.28910			0.644552	+	0.764560i	$0.277044\pi$
$60$	8.88853			0.148142
$61$		−	60.6401i		−	0.994099i	−0.867722	−	0.497050i	$-0.834417\pi$
$61$		−	60.6401i		−	0.994099i	0.867722	−	0.497050i	$-0.165583\pi$
$62$	−82.7190			−1.33418
$63$			11.5410i			0.183190i
$64$	73.7093			1.15171
$65$	23.5240			0.361908
$66$		−	55.1969i		−	0.836317i
$67$	−27.9291	−	60.9013i	−0.416853	−	0.908974i
$67$	−27.9291	−	60.9013i	−0.416853	−	0.908974i
$68$	−34.0924			−0.501359
$69$			67.0679i			0.971998i
$70$		−	13.1885i		−	0.188406i
$71$	−38.7507			−0.545785			−0.272892	−	0.962045i	$-0.587980\pi$
$71$	−38.7507			−0.545785			−0.272892	+	0.962045i	$0.587980\pi$
$72$		−	2.74235i		−	0.0380882i
$73$	55.4015			0.758925			0.379462	−	0.925207i	$-0.376109\pi$
$73$	55.4015			0.758925			0.379462	+	0.925207i	$0.376109\pi$
$74$			88.8847i			1.20114i
$75$			40.8537i			0.544716i
$76$	152.919			2.01209
$77$	−42.5102			−0.552080
$78$		−	98.8473i		−	1.26727i
$79$			25.6418i			0.324580i	0.986743	+	0.162290i	$0.0518880\pi$
$79$			25.6418i			0.324580i	−0.986743	+	0.162290i	$0.948112\pi$
$80$		−	17.3934i		−	0.217417i
$81$	9.00000			0.111111
$82$	184.638			2.25168
$83$	47.9462			0.577665			0.288832	−	0.957380i	$-0.406733\pi$
$83$	47.9462			0.577665			0.288832	+	0.957380i	$0.406733\pi$
$84$	−28.7648			−0.342438
$85$			9.38791i			0.110446i
$86$	148.454			1.72621
$87$		−	7.18590i		−	0.0825965i
$88$	10.1012			0.114786
$89$	71.8386			0.807176			0.403588	−	0.914941i	$-0.367763\pi$
$89$	71.8386			0.807176			0.403588	+	0.914941i	$0.367763\pi$
$90$	−10.2848			−0.114275
$91$	−76.1277			−0.836568
$92$	−167.160			−1.81696
$93$	49.6802			0.534196
$94$			1.33037i			0.0141529i
$95$		−	42.1087i		−	0.443250i
$96$	−79.4196			−0.827287
$97$			96.0761i			0.990475i	0.868757	+	0.495238i	$0.164919\pi$
$97$			96.0761i			0.990475i	−0.868757	+	0.495238i	$0.835081\pi$
$98$		−	98.6318i		−	1.00645i
$99$			33.1507i			0.334856i
$100$	−101.824			−1.01824
$101$		−	42.5531i		−	0.421318i	−0.977560	−	0.210659i	$-0.932439\pi$
$101$		−	42.5531i		−	0.421318i	0.977560	−	0.210659i	$-0.0675610\pi$
$102$	39.4477			0.386742
$103$	86.1645			0.836549			0.418274	−	0.908321i	$-0.362635\pi$
$103$	86.1645			0.836549			0.418274	+	0.908321i	$0.362635\pi$
$104$	18.0894			0.173936
$105$			7.92085i			0.0754367i
$106$	−114.408			−1.07932
$107$	−75.2351			−0.703132			−0.351566	−	0.936163i	$-0.614351\pi$
$107$	−75.2351			−0.703132			−0.351566	+	0.936163i	$0.614351\pi$
$108$			22.4316i			0.207700i
$109$			197.278i			1.80989i	0.425531	+	0.904944i	$0.360087\pi$
$109$			197.278i			1.80989i	−0.425531	+	0.904944i	$0.639913\pi$
$110$		−	37.8830i		−	0.344391i
$111$		−	53.3832i		−	0.480930i
$112$			56.2878i			0.502570i
$113$			188.474i			1.66791i	0.551830	+	0.833957i	$0.313930\pi$
$113$			188.474i			1.66791i	−0.551830	+	0.833957i	$0.686070\pi$
$114$	−176.940			−1.55210
$115$			46.0303i			0.400264i
$116$	17.9102			0.154398
$117$			59.3667i			0.507408i
$118$		−	219.343i		−	1.85884i
$119$		−	30.3808i		−	0.255301i
$120$		−	1.88214i		−	0.0156845i
$121$	−1.10786			−0.00915590
$122$	−174.881			−1.43345
$123$	−110.892			−0.901558
$124$			123.823i			0.998574i
$125$			57.7576i			0.462061i
$126$	33.2832			0.264152
$127$	−239.879			−1.88881			−0.944404	−	0.328786i	$-0.893360\pi$
$127$	−239.879			−1.88881			−0.944404	+	0.328786i	$0.893360\pi$
$128$		−	29.1599i		−	0.227811i
$129$	−89.1600			−0.691163
$130$		−	67.8414i		−	0.521857i
$131$	123.868			0.945554			0.472777	−	0.881182i	$-0.343252\pi$
$131$	123.868			0.945554			0.472777	+	0.881182i	$0.343252\pi$
$132$	−82.6250			−0.625947
$133$			136.271i			1.02459i
$134$	−175.634	+	80.5453i	−1.31070	+	0.601084i
$135$	6.17692			0.0457550
$136$			7.21905i			0.0530812i
$137$		−	129.766i		−	0.947197i	−0.880741	−	0.473599i	$-0.842955\pi$
$137$		−	129.766i		−	0.947197i	0.880741	−	0.473599i	$-0.157045\pi$
$138$	193.418			1.40158
$139$		−	213.633i		−	1.53693i	−0.639894	−	0.768464i	$-0.721022\pi$
$139$		−	213.633i		−	1.53693i	0.639894	−	0.768464i	$-0.278978\pi$
$140$	−19.7420			−0.141014
$141$		−	0.799009i		−	0.00566673i
$142$			111.754i			0.786999i
$143$	−218.672			−1.52918
$144$	43.8949			0.304826
$145$		−	4.93186i		−	0.0340128i
$146$		−	159.773i		−	1.09434i
$147$			59.2373i			0.402975i
$148$	133.053			0.899004
$149$	36.5031			0.244987			0.122493	−	0.992469i	$-0.460911\pi$
$149$	36.5031			0.244987			0.122493	+	0.992469i	$0.460911\pi$
$150$	117.819			0.785457
$151$	19.4363			0.128717			0.0643587	−	0.997927i	$-0.479500\pi$
$151$	19.4363			0.128717			0.0643587	+	0.997927i	$0.479500\pi$
$152$		−	32.3804i		−	0.213029i
$153$	−23.6919			−0.154849
$154$			122.596i			0.796076i
$155$	34.0967			0.219979
$156$	−147.966			−0.948499
$157$	130.906			0.833795			0.416897	−	0.908954i	$-0.363117\pi$
$157$	130.906			0.833795			0.416897	+	0.908954i	$0.363117\pi$
$158$	73.9488			0.468030
$159$	68.7123			0.432153
$160$	−54.5076			−0.340673
$161$		−	148.962i		−	0.925228i
$162$		−	25.9552i		−	0.160218i
$163$	−96.8692			−0.594289			−0.297145	−	0.954832i	$-0.596034\pi$
$163$	−96.8692			−0.594289			−0.297145	+	0.954832i	$0.596034\pi$
$164$		−	276.387i		−	1.68529i
$165$			22.7522i			0.137892i
$166$		−	138.273i		−	0.832968i
$167$	23.4620			0.140491			0.0702455	−	0.997530i	$-0.477622\pi$
$167$	23.4620			0.140491			0.0702455	+	0.997530i	$0.477622\pi$
$168$			6.09092i			0.0362555i
$169$	−222.601			−1.31716
$170$	27.0739			0.159259
$171$	106.268			0.621451
$172$		−	222.223i		−	1.29199i
$173$	327.279			1.89179			0.945893	−	0.324480i	$-0.105189\pi$
$173$	327.279			1.89179			0.945893	+	0.324480i	$0.105189\pi$
$174$	−20.7235			−0.119101
$175$		−	90.7385i		−	0.518506i
$176$			161.683i			0.918655i
$177$			131.735i			0.744265i
$178$		−	207.177i		−	1.16391i
$179$		−	91.0169i		−	0.508474i	−0.967142	−	0.254237i	$-0.918176\pi$
$179$		−	91.0169i		−	0.508474i	0.967142	−	0.254237i	$-0.0818243\pi$
$180$			15.3954i			0.0855299i
$181$	109.876			0.607049			0.303524	−	0.952824i	$-0.401837\pi$
$181$	109.876			0.607049			0.303524	+	0.952824i	$0.401837\pi$
$182$			219.546i			1.20630i
$183$	105.032			0.573943
$184$			35.3961i			0.192370i
$185$		−	36.6382i		−	0.198045i
$186$		−	143.274i		−	0.770288i
$187$		−	87.2671i		−	0.466669i
$188$	1.99145			0.0105928
$189$	−19.9895			−0.105765
$190$	−121.438			−0.639147
$191$		−	122.760i		−	0.642720i	−0.946957	−	0.321360i	$-0.895860\pi$
$191$		−	122.760i		−	0.642720i	0.946957	−	0.321360i	$-0.104140\pi$
$192$			127.668i			0.664939i
$193$	−100.664			−0.521574			−0.260787	−	0.965396i	$-0.583982\pi$
$193$	−100.664			−0.521574			−0.260787	+	0.965396i	$0.583982\pi$
$194$	277.075			1.42822
$195$			40.7448i			0.208948i
$196$	−147.643			−0.753282
$197$		−	126.794i		−	0.643623i	−0.946804	−	0.321811i	$-0.895708\pi$
$197$		−	126.794i		−	0.643623i	0.946804	−	0.321811i	$-0.104292\pi$
$198$	95.6039			0.482848
$199$	248.677			1.24963			0.624816	−	0.780772i	$-0.285174\pi$
$199$	248.677			1.24963			0.624816	+	0.780772i	$0.285174\pi$
$200$			21.5611i			0.107806i
$201$	105.484	−	48.3747i	0.524796	−	0.240670i
$202$	−122.720			−0.607523
$203$			15.9603i			0.0786222i
$204$		−	59.0498i		−	0.289460i
$205$	−76.1077			−0.371257
$206$		−	248.491i		−	1.20627i
$207$	−116.165			−0.561183
$208$			289.544i			1.39204i
$209$			391.429i			1.87287i
$210$	22.8431			0.108777
$211$	−232.750			−1.10308			−0.551541	−	0.834148i	$-0.685960\pi$
$211$	−232.750			−1.10308			−0.551541	+	0.834148i	$0.685960\pi$
$212$			171.259i			0.807825i
$213$		−	67.1182i		−	0.315109i
$214$			216.972i			1.01389i
$215$	−61.1927			−0.284617
$216$	4.74989			0.0219902
$217$	−110.343			−0.508492
$218$	568.932			2.60978
$219$			95.9582i			0.438165i
$220$	−56.7076			−0.257762
$221$		−	156.279i		−	0.707145i
$222$	−153.953			−0.693481
$223$	−229.714			−1.03011			−0.515054	−	0.857158i	$-0.672228\pi$
$223$	−229.714			−1.03011			−0.515054	+	0.857158i	$0.672228\pi$
$224$	176.396			0.787481
$225$	−70.7606			−0.314492
$226$	543.544			2.40506
$227$	−206.866			−0.911304			−0.455652	−	0.890158i	$-0.650594\pi$
$227$	−206.866			−0.911304			−0.455652	+	0.890158i	$0.650594\pi$
$228$			264.863i			1.16168i
$229$		−	116.119i		−	0.507072i	−0.967326	−	0.253536i	$-0.918406\pi$
$229$		−	116.119i		−	0.507072i	0.967326	−	0.253536i	$-0.0815936\pi$
$230$	132.748			0.577163
$231$		−	73.6298i		−	0.318744i
$232$		−	3.79246i		−	0.0163468i
$233$			53.0552i			0.227705i	0.993498	+	0.113852i	$0.0363191\pi$
$233$			53.0552i			0.227705i	−0.993498	+	0.113852i	$0.963681\pi$
$234$	171.209			0.731661
$235$		−	0.548379i		−	0.00233353i
$236$	−328.337			−1.39126
$237$	−44.4129			−0.187396
$238$	−87.6158			−0.368134
$239$		−	381.027i		−	1.59426i	−0.603810	−	0.797128i	$-0.706352\pi$
$239$		−	381.027i		−	1.59426i	0.603810	−	0.797128i	$-0.293648\pi$
$240$	30.1262			0.125526
$241$	−117.922			−0.489303			−0.244651	−	0.969611i	$-0.578673\pi$
$241$	−117.922			−0.489303			−0.244651	+	0.969611i	$0.578673\pi$
$242$			3.19498i			0.0132024i
$243$			15.5885i			0.0641500i
$244$			261.781i			1.07287i
$245$			40.6560i			0.165943i
$246$			319.802i			1.30001i
$247$			700.976i			2.83796i
$248$	26.2195			0.105724
$249$			83.0452i			0.333515i
$250$	166.568			0.666272
$251$		−	101.001i		−	0.402393i	−0.979551	−	0.201196i	$-0.935517\pi$
$251$		−	101.001i		−	0.402393i	0.979551	−	0.201196i	$-0.0644829\pi$
$252$		−	49.8220i		−	0.197706i
$253$		−	427.884i		−	1.69124i
$254$			691.790i			2.72358i
$255$	−16.2603			−0.0637660
$256$	210.743			0.823214
$257$	396.209			1.54167			0.770834	−	0.637036i	$-0.219840\pi$
$257$	396.209			1.54167			0.770834	+	0.637036i	$0.219840\pi$
$258$			257.130i			0.996627i
$259$			118.567i			0.457789i
$260$	−101.553			−0.390587
$261$	12.4463			0.0476871
$262$		−	357.224i		−	1.36345i
$263$	−219.410			−0.834258			−0.417129	−	0.908847i	$-0.636964\pi$
$263$	−219.410			−0.834258			−0.417129	+	0.908847i	$0.636964\pi$
$264$			17.4958i			0.0662719i
$265$	47.1590			0.177958
$266$	392.993			1.47742
$267$			124.428i			0.466023i
$268$	120.569	+	262.909i	0.449885	+	0.981003i
$269$	29.0815			0.108110			0.0540548	−	0.998538i	$-0.482785\pi$
$269$	29.0815			0.108110			0.0540548	+	0.998538i	$0.482785\pi$
$270$		−	17.8137i		−	0.0659768i
$271$		−	73.9552i		−	0.272897i	−0.990647	−	0.136449i	$-0.956431\pi$
$271$		−	73.9552i		−	0.272897i	0.990647	−	0.136449i	$-0.0435689\pi$
$272$	−115.551			−0.424818
$273$		−	131.857i		−	0.482993i
$274$	−374.234			−1.36582
$275$		−	260.641i		−	0.947784i
$276$		−	289.530i		−	1.04902i
$277$	381.738			1.37812			0.689058	−	0.724706i	$-0.258024\pi$
$277$	381.738			1.37812			0.689058	+	0.724706i	$0.258024\pi$
$278$	−616.099			−2.21618
$279$			86.0486i			0.308418i
$280$			4.18035i			0.0149298i
$281$		−	94.7897i		−	0.337330i	−0.985673	−	0.168665i	$-0.946054\pi$
$281$		−	94.7897i		−	0.337330i	0.985673	−	0.168665i	$-0.0539456\pi$
$282$	−2.30427			−0.00817118
$283$	−143.524			−0.507152			−0.253576	−	0.967315i	$-0.581607\pi$
$283$	−143.524			−0.507152			−0.253576	+	0.967315i	$0.581607\pi$
$284$	167.286			0.589034
$285$	72.9344			0.255910
$286$			630.632i			2.20501i
$287$	246.297			0.858178
$288$		−	137.559i		−	0.477634i
$289$	−226.633			−0.784196
$290$	−14.2231			−0.0490450
$291$	−166.409			−0.571851
$292$	−239.167			−0.819064
$293$	−24.2982			−0.0829290			−0.0414645	−	0.999140i	$-0.513202\pi$
$293$	−24.2982			−0.0829290			−0.0414645	+	0.999140i	$0.513202\pi$
$294$	170.835			0.581073
$295$			90.4129i			0.306485i
$296$		−	28.1738i		−	0.0951818i
$297$	−57.4187			−0.193329
$298$		−	105.272i		−	0.353261i
$299$		−	766.259i		−	2.56274i
$300$		−	176.364i		−	0.587880i
$301$	198.030			0.657906
$302$		−	56.0528i		−	0.185605i
$303$	73.7041			0.243248
$304$	518.292			1.70491
$305$	72.0858			0.236347
$306$			68.3255i			0.223286i
$307$	23.2192			0.0756327			0.0378164	−	0.999285i	$-0.487960\pi$
$307$	23.2192			0.0756327			0.0378164	+	0.999285i	$0.487960\pi$
$308$	183.515			0.595828
$309$			149.241i			0.482982i
$310$		−	98.3322i		−	0.317200i
$311$			431.469i			1.38736i	0.720283	+	0.693680i	$0.244012\pi$
$311$			431.469i			1.38736i	−0.720283	+	0.693680i	$0.755988\pi$
$312$			31.3317i			0.100422i
$313$		−	5.31451i		−	0.0169793i	−0.999964	−	0.00848964i	$-0.997298\pi$
$313$		−	5.31451i		−	0.0169793i	0.999964	−	0.00848964i	$-0.00270237\pi$
$314$		−	377.521i		−	1.20230i
$315$	−13.7193			−0.0435534
$316$		−	110.695i		−	0.350300i
$317$	102.127			0.322167			0.161083	−	0.986941i	$-0.448501\pi$
$317$	102.127			0.322167			0.161083	+	0.986941i	$0.448501\pi$
$318$		−	198.161i		−	0.623146i
$319$			45.8450i			0.143715i
$320$			87.6219i			0.273818i
$321$		−	130.311i		−	0.405953i
$322$	−429.593			−1.33414
$323$	−279.744			−0.866080
$324$	−38.8527			−0.119916
$325$		−	466.758i		−	1.43618i
$326$			279.363i			0.856940i
$327$	−341.695			−1.04494
$328$	−58.5247			−0.178429
$329$			1.77465i			0.00539406i
$330$	65.6153			0.198834
$331$		−	215.017i		−	0.649599i	−0.945783	−	0.324799i	$-0.894703\pi$
$331$		−	215.017i		−	0.649599i	0.945783	−	0.324799i	$-0.105297\pi$
$332$	−206.982			−0.623440
$333$	92.4625			0.277665
$334$		−	67.6624i		−	0.202582i
$335$	72.3963	−	33.2008i	0.216108	−	0.0991067i
$336$	−97.4933			−0.290159
$337$		−	87.5452i		−	0.259778i	−0.991529	−	0.129889i	$-0.958538\pi$
$337$		−	87.5452i		−	0.259778i	0.991529	−	0.129889i	$-0.0414621\pi$
$338$			641.962i			1.89930i
$339$	−326.447			−0.962970
$340$		−	40.5273i		−	0.119198i
$341$	−316.953			−0.929480
$342$		−	306.468i		−	0.896106i
$343$		−	320.072i		−	0.933155i
$344$	−47.0555			−0.136789
$345$	−79.7269			−0.231092
$346$		−	943.845i		−	2.72787i
$347$		−	464.703i		−	1.33920i	−0.742721	−	0.669601i	$-0.766465\pi$
$347$		−	464.703i		−	1.33920i	0.742721	−	0.669601i	$-0.233535\pi$
$348$			31.0213i			0.0891417i
$349$	275.893			0.790525			0.395263	−	0.918568i	$-0.370654\pi$
$349$	275.893			0.790525			0.395263	+	0.918568i	$0.370654\pi$
$350$	−261.682			−0.747663
$351$	−102.826			−0.292952
$352$	506.686			1.43945
$353$			315.923i			0.894967i	0.894292	+	0.447484i	$0.147680\pi$
$353$			315.923i			0.894967i	−0.894292	+	0.447484i	$0.852320\pi$
$354$	379.912			1.07320
$355$		−	46.0649i		−	0.129760i
$356$	−310.125			−0.871139
$357$	52.6212			0.147398
$358$	−262.485			−0.733198
$359$	−503.235			−1.40177			−0.700884	−	0.713276i	$-0.747211\pi$
$359$	−503.235			−1.40177			−0.700884	+	0.713276i	$0.747211\pi$
$360$	3.25996			0.00905545
$361$	893.767			2.47581
$362$		−	316.873i		−	0.875339i
$363$		−	1.91888i		−	0.00528616i
$364$	328.641			0.902860
$365$			65.8585i			0.180434i
$366$		−	302.902i		−	0.827602i
$367$			589.555i			1.60642i	0.595697	+	0.803209i	$0.296876\pi$
$367$			589.555i			1.60642i	−0.595697	+	0.803209i	$0.703124\pi$
$368$	−566.561			−1.53957
$369$		−	192.070i		−	0.520515i
$370$	−105.662			−0.285572
$371$	−152.614			−0.411359
$372$	−214.468			−0.576527
$373$			615.702i			1.65067i	0.564640	+	0.825337i	$0.309015\pi$
$373$			615.702i			1.65067i	−0.564640	+	0.825337i	$0.690985\pi$
$374$	−251.671			−0.672917
$375$	−100.039			−0.266771
$376$		−	0.421689i		−	0.00112151i
$377$			82.0998i			0.217771i
$378$			57.6482i			0.152508i
$379$			278.426i			0.734633i	0.930096	+	0.367316i	$0.119723\pi$
$379$			278.426i			0.734633i	−0.930096	+	0.367316i	$0.880277\pi$
$380$			181.782i			0.478374i
$381$		−	415.482i		−	1.09050i
$382$	−354.028			−0.926775
$383$		−	12.6157i		−	0.0329393i	−0.999864	−	0.0164696i	$-0.994757\pi$
$383$		−	12.6157i		−	0.0329393i	0.999864	−	0.0164696i	$-0.00524268\pi$
$384$	50.5064			0.131527
$385$		−	50.5339i		−	0.131257i
$386$			290.306i			0.752087i
$387$		−	154.430i		−	0.399043i
$388$		−	414.758i		−	1.06896i
$389$	−261.522			−0.672292			−0.336146	−	0.941810i	$-0.609124\pi$
$389$	−261.522			−0.672292			−0.336146	+	0.941810i	$0.609124\pi$
$390$	117.505			0.301294
$391$	305.797			0.782088
$392$			31.2634i			0.0797535i
$393$			214.545i			0.545916i
$394$	−365.662			−0.928077
$395$	−30.4817			−0.0771688
$396$		−	143.111i		−	0.361391i
$397$	−23.9797			−0.0604023			−0.0302012	−	0.999544i	$-0.509615\pi$
$397$	−23.9797			−0.0604023			−0.0302012	+	0.999544i	$0.509615\pi$
$398$		−	717.162i		−	1.80192i
$399$	−236.028			−0.591549
$400$	−345.115			−0.862787
$401$			574.743i			1.43327i	0.697447	+	0.716637i	$0.254319\pi$
$401$			574.743i			1.43327i	−0.697447	+	0.716637i	$0.745681\pi$
$402$	−139.509	−	304.207i	−0.347036	−	0.756734i
$403$	−567.603			−1.40844
$404$			183.701i			0.454704i
$405$			10.6987i			0.0264166i
$406$	46.0282			0.113370
$407$			340.578i			0.836800i
$408$	−12.5038			−0.0306465
$409$			516.008i			1.26163i	0.775932	+	0.630816i	$0.217280\pi$
$409$			516.008i			1.26163i	−0.775932	+	0.630816i	$0.782720\pi$
$410$			219.488i			0.535337i
$411$	224.761			0.546865
$412$	−371.970			−0.902839
$413$		−	292.591i		−	0.708453i
$414$			335.010i			0.809203i
$415$			56.9960i			0.137340i
$416$	907.379			2.18120
$417$	370.023			0.887345
$418$	1128.85			2.70060
$419$	512.788			1.22384			0.611919	−	0.790921i	$-0.290398\pi$
$419$	512.788			1.22384			0.611919	+	0.790921i	$0.290398\pi$
$420$		−	34.1941i		−	0.0814145i
$421$	715.712			1.70003			0.850014	−	0.526760i	$-0.176593\pi$
$421$	715.712			1.70003			0.850014	+	0.526760i	$0.176593\pi$
$422$			671.233i			1.59060i
$423$	1.38392			0.00327169
$424$	36.2640			0.0855282
$425$	186.273			0.438289
$426$	−193.563			−0.454374
$427$	−233.282			−0.546327
$428$	324.788			0.758850
$429$		−	378.751i		−	0.882870i
$430$			176.475i			0.410406i
$431$	194.619			0.451551			0.225776	−	0.974179i	$-0.427508\pi$
$431$	194.619			0.451551			0.225776	+	0.974179i	$0.427508\pi$
$432$			76.0283i			0.175991i
$433$		−	76.8662i		−	0.177520i	−0.996053	−	0.0887601i	$-0.971710\pi$
$433$		−	76.8662i		−	0.177520i	0.996053	−	0.0887601i	$-0.0282904\pi$
$434$			318.219i			0.733224i
$435$	8.54223			0.0196373
$436$		−	851.642i		−	1.95331i
$437$	−1371.63			−3.13873
$438$	276.735			0.631816
$439$	490.223			1.11668			0.558341	−	0.829612i	$-0.311438\pi$
$439$	490.223			1.11668			0.558341	+	0.829612i	$0.311438\pi$
$440$			12.0078i			0.0272904i
$441$	−102.602			−0.232658
$442$	−450.695			−1.01967
$443$			722.105i			1.63003i	0.579437	+	0.815017i	$0.303273\pi$
$443$			722.105i			1.63003i	−0.579437	+	0.815017i	$0.696727\pi$
$444$			230.454i			0.519040i
$445$			85.3981i			0.191906i
$446$			662.476i			1.48537i
$447$			63.2251i			0.141443i
$448$		−	283.559i		−	0.632944i
$449$	−393.619			−0.876658			−0.438329	−	0.898815i	$-0.644429\pi$
$449$	−393.619			−0.876658			−0.438329	+	0.898815i	$0.644429\pi$
$450$			204.068i			0.453484i
$451$	707.473			1.56868
$452$		−	813.638i		−	1.80008i
$453$			33.6647i			0.0743151i
$454$			596.584i			1.31406i
$455$		−	90.4968i		−	0.198894i
$456$	56.0846			0.122992
$457$	−570.819			−1.24906			−0.624529	−	0.781002i	$-0.714709\pi$
$457$	−570.819			−1.24906			−0.624529	+	0.781002i	$0.714709\pi$
$458$	−334.879			−0.731176
$459$		−	41.0356i		−	0.0894022i
$460$		−	198.712i		−	0.431982i
$461$	−408.792			−0.886751			−0.443375	−	0.896336i	$-0.646219\pi$
$461$	−408.792			−0.886751			−0.443375	+	0.896336i	$0.646219\pi$
$462$	−212.342			−0.459615
$463$		−	884.670i		−	1.91073i	−0.295422	−	0.955367i	$-0.595460\pi$
$463$		−	884.670i		−	1.91073i	0.295422	−	0.955367i	$-0.404540\pi$
$464$	60.7035			0.130826
$465$			59.0573i			0.127005i
$466$	153.007			0.328340
$467$	340.158			0.728391			0.364195	−	0.931323i	$-0.381344\pi$
$467$	340.158			0.728391			0.364195	+	0.931323i	$0.381344\pi$
$468$		−	256.284i		−	0.547616i
$469$	−234.287	+	107.443i	−0.499545	+	0.229090i
$470$	−1.58148			−0.00336485
$471$			226.735i			0.481391i
$472$			69.5251i			0.147299i
$473$	568.828			1.20260
$474$			128.083i			0.270217i
$475$	−835.511			−1.75897
$476$			131.153i			0.275532i
$477$			119.013i			0.249504i
$478$	−1098.85			−2.29885
$479$	532.928			1.11258			0.556292	−	0.830987i	$-0.312224\pi$
$479$	532.928			1.11258			0.556292	+	0.830987i	$0.312224\pi$
$480$		−	94.4099i		−	0.196687i
$481$			609.910i			1.26801i
$482$			340.077i			0.705554i
$483$	258.009			0.534181
$484$	4.78261			0.00988143
$485$	−114.210			−0.235485
$486$	44.9558			0.0925016
$487$			342.212i			0.702695i	0.936245	+	0.351347i	$0.114276\pi$
$487$			342.212i			0.702695i	−0.936245	+	0.351347i	$0.885724\pi$
$488$	55.4320			0.113590
$489$		−	167.782i		−	0.343113i
$490$	117.249			0.239283
$491$	−903.284			−1.83968			−0.919841	−	0.392291i	$-0.871683\pi$
$491$	−903.284			−1.83968			−0.919841	+	0.392291i	$0.871683\pi$
$492$	478.716			0.973000
$493$	−32.7642			−0.0664587
$494$	2021.56			4.09222
$495$	−39.4079			−0.0796119
$496$			419.678i			0.846125i
$497$			149.074i			0.299947i
$498$	239.495			0.480914
$499$			216.413i			0.433694i	0.976206	+	0.216847i	$0.0695772\pi$
$499$			216.413i			0.433694i	−0.976206	+	0.216847i	$0.930423\pi$
$500$		−	249.338i		−	0.498676i
$501$			40.6374i			0.0811125i
$502$	−291.277			−0.580233
$503$			158.448i			0.315007i	0.987518	+	0.157503i	$0.0503445\pi$
$503$			158.448i			0.315007i	−0.987518	+	0.157503i	$0.949655\pi$
$504$	−10.5498			−0.0209321
$505$	50.5850			0.100168
$506$	−1233.98			−2.43870
$507$		−	385.556i		−	0.760465i
$508$	1035.55			2.03848
$509$	367.320			0.721649			0.360825	−	0.932634i	$-0.382495\pi$
$509$	367.320			0.721649			0.360825	+	0.932634i	$0.382495\pi$
$510$			46.8935i			0.0919479i
$511$		−	213.129i		−	0.417082i
$512$		−	724.404i		−	1.41485i
$513$			184.062i			0.358795i
$514$		−	1142.63i		−	2.22302i
$515$			102.428i			0.198889i
$516$	384.901			0.745932
$517$			5.09756i			0.00985989i
$518$	341.938			0.660113
$519$			566.864i			1.09222i
$520$			21.5037i			0.0413533i
$521$		−	446.330i		−	0.856679i	−0.903618	−	0.428340i	$-0.859099\pi$
$521$		−	446.330i		−	0.856679i	0.903618	−	0.428340i	$-0.140901\pi$
$522$		−	35.8942i		−	0.0687628i
$523$	−195.714			−0.374214			−0.187107	−	0.982340i	$-0.559911\pi$
$523$	−195.714			−0.374214			−0.187107	+	0.982340i	$0.559911\pi$
$524$	−534.733			−1.02048
$525$	157.164			0.299359
$526$			632.760i			1.20297i
$527$		−	226.517i		−	0.429824i
$528$	−280.044			−0.530386
$529$	970.366			1.83434
$530$		−	136.002i		−	0.256608i
$531$	−228.172			−0.429702
$532$		−	588.277i		−	1.10578i
$533$	1266.95			2.37702
$534$	358.840			0.671986
$535$		−	89.4357i		−	0.167169i
$536$	55.6708	−	25.5305i	0.103863	−	0.0476315i
$537$	157.646			0.293568
$538$		−	83.8685i		−	0.155889i
$539$		−	377.926i		−	0.701161i
$540$	−26.6656			−0.0493807
$541$		−	637.640i		−	1.17863i	−0.807903	−	0.589316i	$-0.799397\pi$
$541$		−	637.640i		−	1.17863i	0.807903	−	0.589316i	$-0.200603\pi$
$542$	−213.280			−0.393506
$543$			190.311i			0.350480i
$544$			362.114i			0.665651i
$545$	−234.514			−0.430301
$546$	−380.265			−0.696456
$547$		−	177.450i		−	0.324406i	−0.986757	−	0.162203i	$-0.948140\pi$
$547$		−	177.450i		−	0.324406i	0.986757	−	0.162203i	$-0.0518599\pi$
$548$			560.196i			1.02226i
$549$			181.920i			0.331366i
$550$	−751.666			−1.36667
$551$	146.961			0.266717
$552$	−61.3078			−0.111065
$553$	98.6438			0.178379
$554$		−	1100.90i		−	1.98719i
$555$	63.4593			0.114341
$556$			922.247i			1.65872i
$557$	844.756			1.51662			0.758309	−	0.651896i	$-0.226026\pi$
$557$	844.756			1.51662			0.758309	+	0.651896i	$0.226026\pi$
$558$	248.157			0.444726
$559$	1018.66			1.82230
$560$	−66.9121			−0.119486
$561$	151.151			0.269431
$562$	−273.366			−0.486416
$563$			712.278i			1.26515i	0.774500	+	0.632574i	$0.218002\pi$
$563$			712.278i			1.26515i	−0.774500	+	0.632574i	$0.781998\pi$
$564$			3.44930i			0.00611577i
$565$	−224.049			−0.396546
$566$			413.911i			0.731292i
$567$		−	34.6229i		−	0.0610633i
$568$		−	35.4226i		−	0.0623638i
$569$	129.562			0.227702			0.113851	−	0.993498i	$-0.463681\pi$
$569$	129.562			0.227702			0.113851	+	0.993498i	$0.463681\pi$
$570$		−	210.337i		−	0.369012i
$571$	−141.029			−0.246986			−0.123493	−	0.992345i	$-0.539410\pi$
$571$	−141.029			−0.246986			−0.123493	+	0.992345i	$0.539410\pi$
$572$	944.001			1.65035
$573$	212.626			0.371075
$574$		−	710.300i		−	1.23746i
$575$	913.323			1.58839
$576$	−221.128			−0.383903
$577$		−	806.938i		−	1.39851i	−0.714874	−	0.699253i	$-0.753516\pi$
$577$		−	806.938i		−	1.39851i	0.714874	−	0.699253i	$-0.246484\pi$
$578$			653.589i			1.13078i
$579$		−	174.355i		−	0.301131i
$580$			21.2907i			0.0367081i
$581$		−	184.448i		−	0.317467i
$582$			479.909i			0.824585i
$583$	−438.375			−0.751930
$584$			50.6434i			0.0867181i
$585$	−70.5721			−0.120636
$586$			70.0739i			0.119580i
$587$			272.521i			0.464260i	0.972685	+	0.232130i	$0.0745695\pi$
$587$			272.521i			0.464260i	−0.972685	+	0.232130i	$0.925431\pi$
$588$		−	255.726i		−	0.434908i
$589$			1016.02i			1.72500i
$590$	260.743			0.441938
$591$	219.613			0.371596
$592$	450.960			0.761756
$593$			961.908i			1.62211i	0.584973	+	0.811053i	$0.301105\pi$
$593$			961.908i			1.62211i	−0.584973	+	0.811053i	$0.698895\pi$
$594$			165.591i			0.278772i
$595$	36.1152			0.0606978
$596$	−157.583			−0.264400
$597$			430.721i			0.721475i
$598$	−2209.83			−3.69536
$599$		−	666.088i		−	1.11200i	−0.831182	−	0.556000i	$-0.812335\pi$
$599$		−	666.088i		−	1.11200i	0.831182	−	0.556000i	$-0.187665\pi$
$600$	−37.3450			−0.0622416
$601$	−6.77582			−0.0112742			−0.00563712	−	0.999984i	$-0.501794\pi$
$601$	−6.77582			−0.0112742			−0.00563712	+	0.999984i	$0.501794\pi$
$602$		−	571.101i		−	0.948673i
$603$	83.7874	+	182.704i	0.138951	+	0.302991i
$604$	−83.9061			−0.138917
$605$		−	1.31697i		−	0.00217681i
$606$		−	212.557i		−	0.350753i
$607$	−508.888			−0.838366			−0.419183	−	0.907902i	$-0.637683\pi$
$607$	−508.888			−0.838366			−0.419183	+	0.907902i	$0.637683\pi$
$608$		−	1624.23i		−	2.67144i
$609$	−27.6441			−0.0453926
$610$		−	207.889i		−	0.340802i
$611$			9.12878i			0.0149407i
$612$	102.277			0.167120
$613$	−820.999			−1.33931			−0.669656	−	0.742671i	$-0.733559\pi$
$613$	−820.999			−1.33931			−0.669656	+	0.742671i	$0.733559\pi$
$614$		−	66.9624i		−	0.109059i
$615$		−	131.822i		−	0.214345i
$616$		−	38.8592i		−	0.0630832i
$617$	−824.130			−1.33571			−0.667853	−	0.744293i	$-0.732786\pi$
$617$	−824.130			−1.33571			−0.667853	+	0.744293i	$0.732786\pi$
$618$	430.399			0.696439
$619$	−186.609			−0.301468			−0.150734	−	0.988574i	$-0.548164\pi$
$619$	−186.609			−0.301468			−0.150734	+	0.988574i	$0.548164\pi$
$620$	−147.195			−0.237411
$621$		−	201.204i		−	0.323999i
$622$	1244.32			2.00051
$623$		−	276.363i		−	0.443600i
$624$	−501.505			−0.803695
$625$	521.013			0.833620
$626$	−15.3266			−0.0244834
$627$	−677.976			−1.08130
$628$	−565.116			−0.899867
$629$	−243.401			−0.386966
$630$			39.5654i			0.0628022i
$631$			752.448i			1.19247i	0.802810	+	0.596234i	$0.203337\pi$
$631$			752.448i			1.19247i	−0.802810	+	0.596234i	$0.796663\pi$
$632$	−23.4396			−0.0370879
$633$		−	403.136i		−	0.636865i
$634$		−	294.525i		−	0.464551i
$635$		−	285.156i		−	0.449064i
$636$	−296.629			−0.466398
$637$		−	676.794i		−	1.06247i
$638$	132.213			0.207231
$639$	116.252			0.181928
$640$	34.6638			0.0541621
$641$			497.911i			0.776772i	0.921497	+	0.388386i	$0.126967\pi$
$641$			497.911i			0.776772i	−0.921497	+	0.388386i	$0.873033\pi$
$642$	−375.806			−0.585368
$643$	−490.064			−0.762153			−0.381076	−	0.924544i	$-0.624446\pi$
$643$	−490.064			−0.762153			−0.381076	+	0.924544i	$0.624446\pi$
$644$			643.064i			0.998546i
$645$		−	105.989i		−	0.164324i
$646$			806.757i			1.24885i
$647$		−	330.797i		−	0.511278i	−0.966772	−	0.255639i	$-0.917714\pi$
$647$		−	330.797i		−	0.511278i	0.966772	−	0.255639i	$-0.0822859\pi$
$648$			8.22704i			0.0126961i
$649$		−	840.450i		−	1.29499i
$650$	−1346.09			−2.07091
$651$		−	191.119i		−	0.293578i
$652$	418.181			0.641382
$653$			556.627i			0.852416i	0.904625	+	0.426208i	$0.140151\pi$
$653$			556.627i			0.852416i	−0.904625	+	0.426208i	$0.859849\pi$
$654$			985.420i			1.50676i
$655$			147.248i			0.224805i
$656$		−	936.767i		−	1.42800i
$657$	−166.205			−0.252975
$658$	5.11793			0.00777801
$659$	866.468			1.31482			0.657411	−	0.753532i	$-0.271651\pi$
$659$	866.468			1.31482			0.657411	+	0.753532i	$0.271651\pi$
$660$		−	98.2204i		−	0.148819i
$661$		−	482.717i		−	0.730282i	−0.930952	−	0.365141i	$-0.881021\pi$
$661$		−	482.717i		−	0.730282i	0.930952	−	0.365141i	$-0.118979\pi$
$662$	−620.091			−0.936694
$663$	270.683			0.408270
$664$			43.8283i			0.0660065i
$665$	−161.992			−0.243597
$666$		−	266.654i		−	0.400381i
$667$	−160.648			−0.240851
$668$	−101.285			−0.151624
$669$		−	397.876i		−	0.594733i
$670$	−95.7482	−	208.785i	−0.142908	−	0.311619i
$671$	−670.087			−0.998640
$672$			305.526i			0.454652i
$673$			332.676i			0.494318i	0.968975	+	0.247159i	$0.0794971\pi$
$673$			332.676i			0.494318i	−0.968975	+	0.247159i	$0.920503\pi$
$674$	−252.473			−0.374589
$675$		−	122.561i		−	0.181572i
$676$	960.961			1.42154
$677$			725.816i			1.07211i	0.844184	+	0.536053i	$0.180085\pi$
$677$			725.816i			1.07211i	−0.844184	+	0.536053i	$0.819915\pi$
$678$			941.446i			1.38856i
$679$	369.604			0.544336
$680$	−8.58164			−0.0126201
$681$		−	358.302i		−	0.526141i
$682$			914.065i			1.34027i
$683$			971.321i			1.42214i	0.703122	+	0.711070i	$0.251789\pi$
$683$			971.321i			1.42214i	−0.703122	+	0.711070i	$0.748211\pi$
$684$	−458.756			−0.670696
$685$	154.259			0.225196
$686$	−923.061			−1.34557
$687$	201.125			0.292758
$688$		−	753.187i		−	1.09475i
$689$	−785.047			−1.13940
$690$			229.926i			0.333225i
$691$	−673.821			−0.975139			−0.487569	−	0.873084i	$-0.662116\pi$
$691$	−673.821			−0.975139			−0.487569	+	0.873084i	$0.662116\pi$
$692$	−1412.85			−2.04170
$693$	127.531			0.184027
$694$	−1340.16			−1.93107
$695$	253.956			0.365404
$696$	6.56874			0.00943785
$697$			505.612i			0.725411i
$698$		−	795.653i		−	1.13990i
$699$	−91.8943			−0.131465
$700$			391.715i			0.559593i
$701$			929.041i			1.32531i	0.748926	+	0.662654i	$0.230570\pi$
$701$			929.041i			1.32531i	−0.748926	+	0.662654i	$0.769430\pi$
$702$			296.542i			0.422425i
$703$	1091.76			1.55300
$704$		−	814.506i		−	1.15697i
$705$	0.949821			0.00134726
$706$	911.096			1.29050
$707$	−163.701			−0.231544
$708$		−	568.696i		−	0.803243i
$709$	−12.9589			−0.0182778			−0.00913889	−	0.999958i	$-0.502909\pi$
$709$	−12.9589			−0.0182778			−0.00913889	+	0.999958i	$0.502909\pi$
$710$	−132.847			−0.187109
$711$		−	76.9254i		−	0.108193i
$712$			65.6688i			0.0922315i
$713$		−	1110.65i		−	1.55771i
$714$		−	151.755i		−	0.212542i
$715$		−	259.946i		−	0.363561i
$716$			392.917i			0.548767i
$717$	659.959			0.920444
$718$			1451.29i			2.02129i
$719$	975.493			1.35674			0.678368	−	0.734722i	$-0.262688\pi$
$719$	975.493			1.35674			0.678368	+	0.734722i	$0.262688\pi$
$720$			52.1801i			0.0724723i
$721$		−	331.474i		−	0.459742i
$722$		−	2577.55i		−	3.57001i
$723$		−	204.247i		−	0.282499i
$724$	−474.331			−0.655153
$725$	−97.8567			−0.134975
$726$	−5.53388			−0.00762242
$727$			437.218i			0.601401i	0.953719	+	0.300700i	$0.0972204\pi$
$727$			437.218i			0.601401i	−0.953719	+	0.300700i	$0.902780\pi$
$728$		−	69.5896i		−	0.0955900i
$729$	−27.0000			−0.0370370
$730$	189.930			0.260179
$731$			406.526i			0.556123i
$732$	−453.419			−0.619424
$733$			203.838i			0.278088i	0.990286	+	0.139044i	$0.0444029\pi$
$733$			203.838i			0.278088i	−0.990286	+	0.139044i	$0.955597\pi$
$734$	1700.23			2.31639
$735$	−70.4183			−0.0958072
$736$			1775.50i			2.41236i
$737$	−672.974	+	308.624i	−0.913126	+	0.418757i
$738$	−553.914			−0.750561
$739$		−	2.02543i		−	0.00274076i	−0.999999	−	0.00137038i	$-0.999564\pi$
$739$		−	2.02543i		−	0.00274076i	0.999999	−	0.00137038i	$-0.000436206\pi$
$740$			158.166i			0.213738i
$741$	−1214.13			−1.63850
$742$			440.127i			0.593163i
$743$	−387.113			−0.521013			−0.260507	−	0.965472i	$-0.583890\pi$
$743$	−387.113			−0.521013			−0.260507	+	0.965472i	$0.583890\pi$
$744$			45.4135i			0.0610396i
$745$			43.3930i			0.0582456i
$746$	1775.63			2.38020
$747$	−143.838			−0.192555
$748$			376.730i			0.503649i
$749$			289.429i			0.386420i
$750$			288.504i			0.384673i
$751$	518.746			0.690740			0.345370	−	0.938467i	$-0.387753\pi$
$751$	518.746			0.690740			0.345370	+	0.938467i	$0.387753\pi$
$752$	6.74969			0.00897566
$753$	174.938			0.232321
$754$	236.769			0.314017
$755$			23.1049i			0.0306026i
$756$	86.2943			0.114146
$757$			495.963i			0.655169i	0.944822	+	0.327584i	$0.106235\pi$
$757$			495.963i			0.655169i	−0.944822	+	0.327584i	$0.893765\pi$
$758$	802.957			1.05931
$759$	741.116			0.976438
$760$	38.4922			0.0506477
$761$	−1062.55			−1.39625			−0.698127	−	0.715974i	$-0.745983\pi$
$761$	−1062.55			−1.39625			−0.698127	+	0.715974i	$0.745983\pi$
$762$	−1198.22			−1.57246
$763$	758.926			0.994660
$764$			529.949i			0.693651i
$765$		−	28.1637i		−	0.0368153i
$766$	−36.3827			−0.0474970
$767$		−	1505.09i		−	1.96231i
$768$			365.017i			0.475283i
$769$		−	1359.43i		−	1.76779i	−0.467682	−	0.883897i	$-0.654911\pi$
$769$		−	1359.43i		−	1.76779i	0.467682	−	0.883897i	$-0.345089\pi$
$770$	−145.736			−0.189267
$771$			686.254i			0.890082i
$772$	434.562			0.562904
$773$	590.537			0.763954			0.381977	−	0.924172i	$-0.375243\pi$
$773$	590.537			0.763954			0.381977	+	0.924172i	$0.375243\pi$
$774$	−445.362			−0.575403
$775$		−	676.539i		−	0.872954i
$776$	−87.8247			−0.113176
$777$	−205.365			−0.264305
$778$			754.206i			0.969417i
$779$		−	2267.88i		−	2.91127i
$780$		−	175.894i		−	0.225505i
$781$			428.205i			0.548278i
$782$		−	881.891i		−	1.12774i
$783$			21.5577i			0.0275322i
$784$	−500.412			−0.638281
$785$			155.614i			0.198235i
$786$	618.730			0.787188
$787$		−	1162.99i		−	1.47775i	−0.673843	−	0.738874i	$-0.735358\pi$
$787$		−	1162.99i		−	1.47775i	0.673843	−	0.738874i	$-0.264642\pi$
$788$			547.365i			0.694625i
$789$		−	380.029i		−	0.481659i
$790$			87.9066i			0.111274i
$791$	725.058			0.916635
$792$	−30.3036			−0.0382621
$793$	−1200.00			−1.51324
$794$			69.1555i			0.0870976i
$795$			81.6817i			0.102744i
$796$	−1073.53			−1.34866
$797$	−1263.93			−1.58586			−0.792929	−	0.609315i	$-0.791445\pi$
$797$	−1263.93			−1.58586			−0.792929	+	0.609315i	$0.791445\pi$
$798$			680.685i			0.852988i
$799$	−3.64309			−0.00455956
$800$			1081.53i			1.35191i
$801$	−215.516			−0.269059
$802$	1657.51			2.06672
$803$		−	612.200i		−	0.762391i
$804$	−455.372	+	208.832i	−0.566383	+	0.259742i
$805$	177.078			0.219973
$806$			1636.92i			2.03092i
$807$			50.3706i			0.0624171i
$808$	38.8985			0.0481417
$809$		−	323.619i		−	0.400024i	−0.979793	−	0.200012i	$-0.935902\pi$
$809$		−	323.619i		−	0.400024i	0.979793	−	0.200012i	$-0.0640981\pi$
$810$	30.8543			0.0380917
$811$			1000.39i			1.23353i	0.787148	+	0.616764i	$0.211557\pi$
$811$			1000.39i			1.23353i	−0.787148	+	0.616764i	$0.788443\pi$
$812$		−	68.9002i		−	0.0848524i
$813$	128.094			0.157557
$814$	982.197			1.20663
$815$		−	115.153i		−	0.141292i
$816$		−	200.139i		−	0.245269i
$817$		−	1823.44i		−	2.23187i
$818$	1488.12			1.81922
$819$	228.383			0.278856
$820$	328.555			0.400676
$821$	531.672			0.647591			0.323795	−	0.946127i	$-0.395041\pi$
$821$	531.672			0.647591			0.323795	+	0.946127i	$0.395041\pi$
$822$		−	648.193i		−	0.788556i
$823$	298.971			0.363270			0.181635	−	0.983366i	$-0.441861\pi$
$823$	298.971			0.363270			0.181635	+	0.983366i	$0.441861\pi$
$824$			78.7643i			0.0955878i
$825$	451.443			0.547204
$826$	−843.809			−1.02156
$827$	785.602			0.949942			0.474971	−	0.880001i	$-0.342459\pi$
$827$	785.602			0.949942			0.474971	+	0.880001i	$0.342459\pi$
$828$	501.481			0.605653
$829$	233.270			0.281387			0.140694	−	0.990053i	$-0.455067\pi$
$829$	233.270			0.281387			0.140694	+	0.990053i	$0.455067\pi$
$830$	164.372			0.198038
$831$			661.190i			0.795656i
$832$		−	1458.63i		−	1.75316i
$833$	270.093			0.324241
$834$		−	1067.12i		−	1.27951i
$835$			27.8904i			0.0334017i
$836$		−	1689.79i		−	2.02128i
$837$	−149.041			−0.178065
$838$		−	1478.84i		−	1.76472i
$839$	−1495.89			−1.78295			−0.891473	−	0.453074i	$-0.850328\pi$
$839$	−1495.89			−1.78295			−0.891473	+	0.453074i	$0.850328\pi$
$840$	−7.24058			−0.00861973
$841$	−823.788			−0.979533
$842$		−	2064.05i		−	2.45137i
$843$	164.181			0.194758
$844$	1004.78			1.19049
$845$		−	264.617i		−	0.313156i
$846$		−	3.99112i		−	0.00471763i
$847$			4.26194i			0.00503181i
$848$			580.453i			0.684497i
$849$		−	248.591i		−	0.292804i
$850$		−	537.195i		−	0.631994i
$851$	−1193.43			−1.40239
$852$			289.747i			0.340079i
$853$	614.726			0.720663			0.360332	−	0.932824i	$-0.382664\pi$
$853$	614.726			0.720663			0.360332	+	0.932824i	$0.382664\pi$
$854$			672.765i			0.787781i
$855$			126.326i			0.147750i
$856$		−	68.7736i		−	0.0803430i
$857$			1493.92i			1.74320i	0.490220	+	0.871599i	$0.336917\pi$
$857$			1493.92i			1.74320i	−0.490220	+	0.871599i	$0.663083\pi$
$858$	−1092.29			−1.27306
$859$	249.864			0.290878			0.145439	−	0.989367i	$-0.453541\pi$
$859$	249.864			0.290878			0.145439	+	0.989367i	$0.453541\pi$
$860$	264.167			0.307171
$861$			426.599i			0.495469i
$862$		−	561.264i		−	0.651118i
$863$	1390.20			1.61089			0.805446	−	0.592669i	$-0.201926\pi$
$863$	1390.20			1.61089			0.805446	+	0.592669i	$0.201926\pi$
$864$	238.259			0.275762
$865$			389.052i			0.449772i
$866$	−221.676			−0.255977
$867$		−	392.539i		−	0.452756i
$868$	476.346			0.548786
$869$	283.348			0.326062
$870$		−	24.6351i		−	0.0283162i
$871$	−1205.17	+	552.687i	−1.38366	+	0.634543i
$872$	−180.335			−0.206806
$873$		−	288.228i		−	0.330158i
$874$			3955.65i			4.52592i
$875$	222.193			0.253935
$876$		−	414.249i		−	0.472887i
$877$	−256.726			−0.292733			−0.146366	−	0.989230i	$-0.546758\pi$
$877$	−256.726			−0.292733			−0.146366	+	0.989230i	$0.546758\pi$
$878$		−	1413.76i		−	1.61021i
$879$		−	42.0857i		−	0.0478791i
$880$	−192.201			−0.218410
$881$	33.9608			0.0385480			0.0192740	−	0.999814i	$-0.493865\pi$
$881$	33.9608			0.0385480			0.0192740	+	0.999814i	$0.493865\pi$
$882$			295.896i			0.335482i
$883$			715.749i			0.810588i	0.914186	+	0.405294i	$0.132831\pi$
$883$			715.749i			0.810588i	−0.914186	+	0.405294i	$0.867169\pi$
$884$			674.652i			0.763181i
$885$	−156.600			−0.176949
$886$	2082.49			2.35044
$887$	1140.31			1.28558			0.642790	−	0.766042i	$-0.277777\pi$
$887$	1140.31			1.28558			0.642790	+	0.766042i	$0.277777\pi$
$888$	48.7985			0.0549532
$889$			922.811i			1.03803i
$890$	246.281			0.276720
$891$		−	99.4522i		−	0.111619i
$892$	991.668			1.11174
$893$	16.3408			0.0182987
$894$	182.336			0.203955
$895$	108.196			0.120890
$896$	−112.178			−0.125198
$897$	1327.20			1.47960
$898$			1135.16i			1.26410i
$899$			118.999i			0.132368i
$900$	305.472			0.339413
$901$		−	313.295i		−	0.347719i
$902$		−	2040.29i		−	2.26197i
$903$			342.998i			0.379842i
$904$	−172.287			−0.190583
$905$			130.615i			0.144326i
$906$	97.0862			0.107159
$907$	15.9333			0.0175670			0.00878352	−	0.999961i	$-0.497204\pi$
$907$	15.9333			0.0175670			0.00878352	+	0.999961i	$0.497204\pi$
$908$	893.034			0.983518
$909$			127.659i			0.140439i
$910$	−260.985			−0.286797
$911$	1026.51			1.12680			0.563398	−	0.826186i	$-0.309494\pi$
$911$	1026.51			1.12680			0.563398	+	0.826186i	$0.309494\pi$
$912$			897.709i			0.984330i
$913$		−	529.817i		−	0.580303i
$914$			1646.20i			1.80109i
$915$			124.856i			0.136455i
$916$			501.284i			0.547254i
$917$		−	476.517i		−	0.519648i
$918$	−118.343			−0.128914
$919$		−	1328.74i		−	1.44585i	−0.690924	−	0.722927i	$-0.742796\pi$
$919$		−	1328.74i		−	1.44585i	0.690924	−	0.722927i	$-0.257204\pi$
$920$	−42.0770			−0.0457359
$921$			40.2169i			0.0436666i
$922$			1178.92i			1.27866i
$923$			766.834i			0.830806i
$924$			317.858i			0.344002i
$925$	−726.967			−0.785910
$926$	−2551.31			−2.75520
$927$	−258.494			−0.278850
$928$		−	190.234i		−	0.204993i
$929$			653.379i			0.703314i	0.936129	+	0.351657i	$0.114382\pi$
$929$			653.379i			0.703314i	−0.936129	+	0.351657i	$0.885618\pi$
$930$	170.316			0.183136
$931$	−1211.48			−1.30127
$932$		−	229.038i		−	0.245749i
$933$	−747.326			−0.800993
$934$		−	980.988i		−	1.05031i
$935$	103.739			0.110950
$936$	−54.2681			−0.0579787
$937$		−	476.531i		−	0.508570i	−0.967129	−	0.254285i	$-0.918160\pi$
$937$		−	476.531i		−	0.508570i	0.967129	−	0.254285i	$-0.0818402\pi$
$938$	309.857	+	675.663i	0.330338	+	0.720323i
$939$	9.20501			0.00980299
$940$			2.36734i			0.00251844i
$941$			317.921i			0.337855i	0.985629	+	0.168927i	$0.0540303\pi$
$941$			317.921i			0.337855i	−0.985629	+	0.168927i	$0.945970\pi$
$942$	653.886			0.694146
$943$			2479.09i			2.62894i
$944$	−1112.84			−1.17886
$945$		−	23.7626i		−	0.0251456i
$946$		−	1640.45i		−	1.73409i
$947$	−1457.11			−1.53866			−0.769330	−	0.638851i	$-0.779410\pi$
$947$	−1457.11			−1.53866			−0.769330	+	0.638851i	$0.779410\pi$
$948$	191.729			0.202246
$949$		−	1096.34i		−	1.15525i
$950$			2409.54i			2.53636i
$951$			176.889i			0.186003i
$952$	27.7716			0.0291719
$953$	−957.078			−1.00428			−0.502139	−	0.864787i	$-0.667454\pi$
$953$	−957.078			−1.00428			−0.502139	+	0.864787i	$0.667454\pi$
$954$	343.224			0.359774
$955$	145.930			0.152807
$956$			1644.88i			1.72059i
$957$	−79.4059			−0.0829738
$958$		−	1536.92i		−	1.60430i
$959$	−499.209			−0.520551
$960$	−151.766			−0.158089
$961$	138.293			0.143905
$962$	1758.93			1.82841
$963$	225.705			0.234377
$964$	509.065			0.528076
$965$		−	119.664i		−	0.124004i
$966$		−	744.077i		−	0.770266i
$967$	−150.097			−0.155219			−0.0776097	−	0.996984i	$-0.524729\pi$
$967$	−150.097			−0.155219			−0.0776097	+	0.996984i	$0.524729\pi$
$968$		−	1.01272i		−	0.00104619i
$969$		−	484.530i		−	0.500031i
$970$			329.373i			0.339560i
$971$	−1386.06			−1.42746			−0.713730	−	0.700421i	$-0.752996\pi$
$971$	−1386.06			−1.42746			−0.713730	+	0.700421i	$0.752996\pi$
$972$		−	67.2949i		−	0.0692334i
$973$	−821.844			−0.844649
$974$	986.912			1.01326
$975$	808.449			0.829179
$976$			887.264i			0.909082i
$977$	1419.92			1.45334			0.726671	−	0.686985i	$-0.241066\pi$
$977$	1419.92			1.45334			0.726671	+	0.686985i	$0.241066\pi$
$978$	−483.870			−0.494755
$979$		−	793.834i		−	0.810863i
$980$		−	175.511i		−	0.179093i
$981$		−	591.833i		−	0.603296i
$982$			2605.00i			2.65274i
$983$			870.191i			0.885240i	0.896709	+	0.442620i	$0.145951\pi$
$983$			870.191i			0.885240i	−0.896709	+	0.442620i	$0.854049\pi$
$984$		−	101.368i		−	0.103016i
$985$	150.726			0.153021
$986$			94.4891i			0.0958307i
$987$	−3.07378			−0.00311426
$988$		−	3026.09i		−	3.06285i
$989$			1993.26i			2.01543i
$990$			113.649i			0.114797i
$991$		−	836.325i		−	0.843920i	−0.906614	−	0.421960i	$-0.861342\pi$
$991$		−	836.325i		−	0.843920i	0.906614	−	0.421960i	$-0.138658\pi$
$992$	1315.19			1.32580
$993$	372.421			0.375046
$994$	429.916			0.432511
$995$			295.614i			0.297100i
$996$		−	358.504i		−	0.359943i
$997$	−1087.41			−1.09068			−0.545342	−	0.838214i	$-0.683600\pi$
$997$	−1087.41			−1.09068			−0.545342	+	0.838214i	$0.683600\pi$
$998$	624.117			0.625368
$999$			160.150i			0.160310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.5	✓	22
3.2	odd	2		603.3.b.e.334.18		22
67.66	odd	2	inner	201.3.b.a.133.18	yes	22
201.200	even	2		603.3.b.e.334.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.5	✓	22	1.1	even	1	trivial
201.3.b.a.133.18	yes	22	67.66	odd	2	inner
603.3.b.e.334.5		22	201.200	even	2
603.3.b.e.334.18		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)

\(f(q)\)	\(=\)	\(q-2.88392i q^{2} +1.73205i q^{3} -4.31697 q^{4} +1.18875i q^{5} +4.99509 q^{6} -3.84699i q^{7} +0.914116i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-2.88392i q^{2} +1.73205i q^{3} -4.31697 q^{4} +1.18875i q^{5} +4.99509 q^{6} -3.84699i q^{7} +0.914116i q^{8} -3.00000 q^{9} +3.42825 q^{10} -11.0502i q^{11} -7.47721i q^{12} -19.7889i q^{13} -11.0944 q^{14} -2.05897 q^{15} -14.6316 q^{16} +7.89730 q^{17} +8.65175i q^{18} -35.4227 q^{19} -5.13180i q^{20} +6.66318 q^{21} -31.8680 q^{22} +38.7216 q^{23} -1.58330 q^{24} +23.5869 q^{25} -57.0695 q^{26} -5.19615i q^{27} +16.6073i q^{28} -4.14878 q^{29} +5.93791i q^{30} -28.6829i q^{31} +45.8529i q^{32} +19.1396 q^{33} -22.7752i q^{34} +4.57311 q^{35} +12.9509 q^{36} -30.8208 q^{37} +102.156i q^{38} +34.2754 q^{39} -1.08665 q^{40} +64.0233i q^{41} -19.2161i q^{42} +51.4765i q^{43} +47.7036i q^{44} -3.56625i q^{45} -111.670i q^{46} -0.461308 q^{47} -25.3428i q^{48} +34.2007 q^{49} -68.0226i q^{50} +13.6785i q^{51} +85.4281i q^{52} -39.6711i q^{53} -14.9853 q^{54} +13.1360 q^{55} +3.51659 q^{56} -61.3539i q^{57} +11.9647i q^{58} +76.0572 q^{59} +8.88853 q^{60} -60.6401i q^{61} -82.7190 q^{62} +11.5410i q^{63} +73.7093 q^{64} +23.5240 q^{65} -55.1969i q^{66} +(-27.9291 - 60.9013i) q^{67} -34.0924 q^{68} +67.0679i q^{69} -13.1885i q^{70} -38.7507 q^{71} -2.74235i q^{72} +55.4015 q^{73} +88.8847i q^{74} +40.8537i q^{75} +152.919 q^{76} -42.5102 q^{77} -98.8473i q^{78} +25.6418i q^{79} -17.3934i q^{80} +9.00000 q^{81} +184.638 q^{82} +47.9462 q^{83} -28.7648 q^{84} +9.38791i q^{85} +148.454 q^{86} -7.18590i q^{87} +10.1012 q^{88} +71.8386 q^{89} -10.2848 q^{90} -76.1277 q^{91} -167.160 q^{92} +49.6802 q^{93} +1.33037i q^{94} -42.1087i q^{95} -79.4196 q^{96} +96.0761i q^{97} -98.6318i q^{98} +33.1507i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 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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