LMFDB - Embedded newform 201.3.b.a.133.14

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			133.14
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.952997i q^{2} -1.73205i q^{3} +3.09180 q^{4} +5.09554i q^{5} +1.65064 q^{6} +5.68326i q^{7} +6.75846i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+0.952997i q^{2} -1.73205i q^{3} +3.09180 q^{4} +5.09554i q^{5} +1.65064 q^{6} +5.68326i q^{7} +6.75846i q^{8} -3.00000 q^{9} -4.85603 q^{10} -14.2586i q^{11} -5.35515i q^{12} +23.0096i q^{13} -5.41613 q^{14} +8.82573 q^{15} +5.92640 q^{16} -18.5259 q^{17} -2.85899i q^{18} +31.3817 q^{19} +15.7544i q^{20} +9.84369 q^{21} +13.5884 q^{22} +2.67603 q^{23} +11.7060 q^{24} -0.964521 q^{25} -21.9281 q^{26} +5.19615i q^{27} +17.5715i q^{28} +17.2640 q^{29} +8.41090i q^{30} -5.03835i q^{31} +32.6817i q^{32} -24.6966 q^{33} -17.6551i q^{34} -28.9593 q^{35} -9.27539 q^{36} -35.1605 q^{37} +29.9067i q^{38} +39.8538 q^{39} -34.4380 q^{40} +10.8485i q^{41} +9.38101i q^{42} -62.7142i q^{43} -44.0846i q^{44} -15.2866i q^{45} +2.55025i q^{46} -4.95729 q^{47} -10.2648i q^{48} +16.7006 q^{49} -0.919186i q^{50} +32.0877i q^{51} +71.1411i q^{52} -77.1120i q^{53} -4.95192 q^{54} +72.6551 q^{55} -38.4101 q^{56} -54.3547i q^{57} +16.4525i q^{58} -36.4059 q^{59} +27.2874 q^{60} -85.7537i q^{61} +4.80153 q^{62} -17.0498i q^{63} -7.43995 q^{64} -117.246 q^{65} -23.5358i q^{66} +(-64.2996 - 18.8298i) q^{67} -57.2782 q^{68} -4.63502i q^{69} -27.5981i q^{70} +110.302 q^{71} -20.2754i q^{72} +70.5667 q^{73} -33.5078i q^{74} +1.67060i q^{75} +97.0258 q^{76} +81.0351 q^{77} +37.9806i q^{78} -28.1669i q^{79} +30.1982i q^{80} +9.00000 q^{81} -10.3386 q^{82} +32.0704 q^{83} +30.4347 q^{84} -94.3992i q^{85} +59.7664 q^{86} -29.9020i q^{87} +96.3660 q^{88} -130.325 q^{89} +14.5681 q^{90} -130.770 q^{91} +8.27374 q^{92} -8.72668 q^{93} -4.72428i q^{94} +159.907i q^{95} +56.6063 q^{96} +73.8503i q^{97} +15.9156i q^{98} +42.7757i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.952997i			0.476498i	0.971204	+	0.238249i	$0.0765735\pi$
$2$			0.952997i			0.476498i	−0.971204	+	0.238249i	$0.923426\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.09180			0.772949
$5$			5.09554i			1.01911i	0.860439	+	0.509554i	$0.170190\pi$
$5$			5.09554i			1.01911i	−0.860439	+	0.509554i	$0.829810\pi$
$6$	1.65064			0.275106
$7$			5.68326i			0.811894i	0.913897	+	0.405947i	$0.133058\pi$
$7$			5.68326i			0.811894i	−0.913897	+	0.405947i	$0.866942\pi$
$8$			6.75846i			0.844808i
$9$	−3.00000			−0.333333
$10$	−4.85603			−0.485603
$11$		−	14.2586i		−	1.29623i	−0.761541	−	0.648117i	$-0.775557\pi$
$11$		−	14.2586i		−	1.29623i	0.761541	−	0.648117i	$-0.224443\pi$
$12$		−	5.35515i		−	0.446262i
$13$			23.0096i			1.76997i	0.465619	+	0.884985i	$0.345832\pi$
$13$			23.0096i			1.76997i	−0.465619	+	0.884985i	$0.654168\pi$
$14$	−5.41613			−0.386866
$15$	8.82573			0.588382
$16$	5.92640			0.370400
$17$	−18.5259			−1.08976			−0.544878	−	0.838515i	$-0.683424\pi$
$17$	−18.5259			−1.08976			−0.544878	+	0.838515i	$0.683424\pi$
$18$		−	2.85899i		−	0.158833i
$19$	31.3817			1.65167			0.825834	−	0.563913i	$-0.190705\pi$
$19$	31.3817			1.65167			0.825834	+	0.563913i	$0.190705\pi$
$20$			15.7544i			0.787719i
$21$	9.84369			0.468747
$22$	13.5884			0.617653
$23$	2.67603			0.116349			0.0581746	−	0.998306i	$-0.481472\pi$
$23$	2.67603			0.116349			0.0581746	+	0.998306i	$0.481472\pi$
$24$	11.7060			0.487750
$25$	−0.964521			−0.0385808
$26$	−21.9281			−0.843388
$27$			5.19615i			0.192450i
$28$			17.5715i			0.627553i
$29$	17.2640			0.595309			0.297654	−	0.954674i	$-0.403796\pi$
$29$	17.2640			0.595309			0.297654	+	0.954674i	$0.403796\pi$
$30$			8.41090i			0.280363i
$31$		−	5.03835i		−	0.162527i	−0.996693	−	0.0812637i	$-0.974104\pi$
$31$		−	5.03835i		−	0.162527i	0.996693	−	0.0812637i	$-0.0258956\pi$
$32$			32.6817i			1.02130i
$33$	−24.6966			−0.748381
$34$		−	17.6551i		−	0.519267i
$35$	−28.9593			−0.827408
$36$	−9.27539			−0.257650
$37$	−35.1605			−0.950283			−0.475141	−	0.879909i	$-0.657603\pi$
$37$	−35.1605			−0.950283			−0.475141	+	0.879909i	$0.657603\pi$
$38$			29.9067i			0.787017i
$39$	39.8538			1.02189
$40$	−34.4380			−0.860950
$41$			10.8485i			0.264598i	0.991210	+	0.132299i	$0.0422359\pi$
$41$			10.8485i			0.264598i	−0.991210	+	0.132299i	$0.957764\pi$
$42$			9.38101i			0.223357i
$43$		−	62.7142i		−	1.45847i	−0.684264	−	0.729234i	$-0.739876\pi$
$43$		−	62.7142i		−	1.45847i	0.684264	−	0.729234i	$-0.260124\pi$
$44$		−	44.0846i		−	1.00192i
$45$		−	15.2866i		−	0.339703i
$46$			2.55025i			0.0554402i
$47$	−4.95729			−0.105474			−0.0527372	−	0.998608i	$-0.516795\pi$
$47$	−4.95729			−0.105474			−0.0527372	+	0.998608i	$0.516795\pi$
$48$		−	10.2648i		−	0.213850i
$49$	16.7006			0.340828
$50$		−	0.919186i		−	0.0183837i
$51$			32.0877i			0.629171i
$52$			71.1411i			1.36810i
$53$		−	77.1120i		−	1.45494i	−0.686138	−	0.727472i	$-0.740695\pi$
$53$		−	77.1120i		−	1.45494i	0.686138	−	0.727472i	$-0.259305\pi$
$54$	−4.95192			−0.0917022
$55$	72.6551			1.32100
$56$	−38.4101			−0.685894
$57$		−	54.3547i		−	0.953591i
$58$			16.4525i			0.283664i
$59$	−36.4059			−0.617049			−0.308525	−	0.951216i	$-0.599835\pi$
$59$	−36.4059			−0.617049			−0.308525	+	0.951216i	$0.599835\pi$
$60$	27.2874			0.454790
$61$		−	85.7537i		−	1.40580i	−0.711289	−	0.702899i	$-0.751888\pi$
$61$		−	85.7537i		−	1.40580i	0.711289	−	0.702899i	$-0.248112\pi$
$62$	4.80153			0.0774441
$63$		−	17.0498i		−	0.270631i
$64$	−7.43995			−0.116249
$65$	−117.246			−1.80379
$66$		−	23.5358i		−	0.356602i
$67$	−64.2996	−	18.8298i	−0.959695	−	0.281042i
$67$	−64.2996	−	18.8298i	−0.959695	−	0.281042i
$68$	−57.2782			−0.842326
$69$		−	4.63502i		−	0.0671742i
$70$		−	27.5981i		−	0.394258i
$71$	110.302			1.55355			0.776775	−	0.629778i	$-0.216854\pi$
$71$	110.302			1.55355			0.776775	+	0.629778i	$0.216854\pi$
$72$		−	20.2754i		−	0.281603i
$73$	70.5667			0.966667			0.483334	−	0.875436i	$-0.339426\pi$
$73$	70.5667			0.966667			0.483334	+	0.875436i	$0.339426\pi$
$74$		−	33.5078i		−	0.452808i
$75$			1.67060i			0.0222747i
$76$	97.0258			1.27666
$77$	81.0351			1.05240
$78$			37.9806i			0.486931i
$79$		−	28.1669i		−	0.356543i	−0.983981	−	0.178272i	$-0.942949\pi$
$79$		−	28.1669i		−	0.356543i	0.983981	−	0.178272i	$-0.0570505\pi$
$80$			30.1982i			0.377477i
$81$	9.00000			0.111111
$82$	−10.3386			−0.126080
$83$	32.0704			0.386390			0.193195	−	0.981160i	$-0.438115\pi$
$83$	32.0704			0.386390			0.193195	+	0.981160i	$0.438115\pi$
$84$	30.4347			0.362318
$85$		−	94.3992i		−	1.11058i
$86$	59.7664			0.694958
$87$		−	29.9020i		−	0.343702i
$88$	96.3660			1.09507
$89$	−130.325			−1.46433			−0.732165	−	0.681128i	$-0.761490\pi$
$89$	−130.325			−1.46433			−0.732165	+	0.681128i	$0.761490\pi$
$90$	14.5681			0.161868
$91$	−130.770			−1.43703
$92$	8.27374			0.0899320
$93$	−8.72668			−0.0938353
$94$		−	4.72428i		−	0.0502583i
$95$			159.907i			1.68323i
$96$	56.6063			0.589649
$97$			73.8503i			0.761344i	0.924710	+	0.380672i	$0.124307\pi$
$97$			73.8503i			0.761344i	−0.924710	+	0.380672i	$0.875693\pi$
$98$			15.9156i			0.162404i
$99$			42.7757i			0.432078i
$100$	−2.98210			−0.0298210
$101$		−	110.139i		−	1.09049i	−0.838278	−	0.545243i	$-0.816437\pi$
$101$		−	110.139i		−	1.09049i	0.838278	−	0.545243i	$-0.183563\pi$
$102$	−30.5795			−0.299799
$103$	−145.115			−1.40889			−0.704443	−	0.709760i	$-0.748803\pi$
$103$	−145.115			−1.40889			−0.704443	+	0.709760i	$0.748803\pi$
$104$	−155.510			−1.49528
$105$			50.1589i			0.477704i
$106$	73.4875			0.693278
$107$	−142.015			−1.32724			−0.663621	−	0.748069i	$-0.730981\pi$
$107$	−142.015			−1.32724			−0.663621	+	0.748069i	$0.730981\pi$
$108$			16.0654i			0.148754i
$109$			84.7226i			0.777272i	0.921391	+	0.388636i	$0.127054\pi$
$109$			84.7226i			0.777272i	−0.921391	+	0.388636i	$0.872946\pi$
$110$			69.2401i			0.629455i
$111$			60.8997i			0.548646i
$112$			33.6812i			0.300725i
$113$		−	51.5901i		−	0.456550i	−0.973597	−	0.228275i	$-0.926692\pi$
$113$		−	51.5901i		−	0.456550i	0.973597	−	0.228275i	$-0.0733085\pi$
$114$	51.7999			0.454385
$115$			13.6358i			0.118572i
$116$	53.3766			0.460143
$117$		−	69.0289i		−	0.589990i
$118$		−	34.6947i		−	0.294023i
$119$		−	105.287i		−	0.884766i
$120$			59.6484i			0.497070i
$121$	−82.3069			−0.680222
$122$	81.7230			0.669861
$123$	18.7902			0.152766
$124$		−	15.5776i		−	0.125626i
$125$			122.474i			0.979790i
$126$	16.2484			0.128955
$127$	136.554			1.07523			0.537613	−	0.843192i	$-0.319326\pi$
$127$	136.554			1.07523			0.537613	+	0.843192i	$0.319326\pi$
$128$			123.636i			0.965910i
$129$	−108.624			−0.842047
$130$		−	111.735i		−	0.859504i
$131$	53.7590			0.410374			0.205187	−	0.978723i	$-0.434220\pi$
$131$	53.7590			0.410374			0.205187	+	0.978723i	$0.434220\pi$
$132$	−76.3568			−0.578460
$133$			178.350i			1.34098i
$134$	17.9448	−	61.2773i	0.133916	−	0.457293i
$135$	−26.4772			−0.196127
$136$		−	125.206i		−	0.920634i
$137$		−	68.3859i		−	0.499167i	−0.968353	−	0.249584i	$-0.919706\pi$
$137$		−	68.3859i		−	0.499167i	0.968353	−	0.249584i	$-0.0802938\pi$
$138$	4.41716			0.0320084
$139$			12.0448i			0.0866536i	0.999061	+	0.0433268i	$0.0137957\pi$
$139$			12.0448i			0.0866536i	−0.999061	+	0.0433268i	$0.986204\pi$
$140$	−89.5362			−0.639544
$141$			8.58628i			0.0608956i
$142$			105.117i			0.740264i
$143$	328.084			2.29430
$144$	−17.7792			−0.123467
$145$			87.9691i			0.606684i
$146$			67.2499i			0.460615i
$147$		−	28.9262i		−	0.196777i
$148$	−108.709			−0.734520
$149$	−15.6689			−0.105161			−0.0525803	−	0.998617i	$-0.516745\pi$
$149$	−15.6689			−0.105161			−0.0525803	+	0.998617i	$0.516745\pi$
$150$	−1.59208			−0.0106138
$151$	27.8314			0.184314			0.0921571	−	0.995744i	$-0.470624\pi$
$151$	27.8314			0.184314			0.0921571	+	0.995744i	$0.470624\pi$
$152$			212.092i			1.39534i
$153$	55.5776			0.363252
$154$			77.2262i			0.501469i
$155$	25.6731			0.165633
$156$	123.220			0.789872
$157$	14.5749			0.0928336			0.0464168	−	0.998922i	$-0.485220\pi$
$157$	14.5749			0.0928336			0.0464168	+	0.998922i	$0.485220\pi$
$158$	26.8430			0.169892
$159$	−133.562			−0.840012
$160$	−166.531			−1.04082
$161$			15.2086i			0.0944632i
$162$			8.57697i			0.0529443i
$163$	299.006			1.83439			0.917195	−	0.398439i	$-0.130448\pi$
$163$	299.006			1.83439			0.917195	+	0.398439i	$0.130448\pi$
$164$			33.5414i			0.204521i
$165$		−	125.842i		−	0.762681i
$166$			30.5630i			0.184114i
$167$	240.242			1.43858			0.719289	−	0.694711i	$-0.244468\pi$
$167$	240.242			1.43858			0.719289	+	0.694711i	$0.244468\pi$
$168$			66.5282i			0.396001i
$169$	−360.443			−2.13280
$170$	89.9621			0.529189
$171$	−94.1451			−0.550556
$172$		−	193.899i		−	1.12732i
$173$	234.498			1.35548			0.677741	−	0.735301i	$-0.262959\pi$
$173$	234.498			1.35548			0.677741	+	0.735301i	$0.262959\pi$
$174$	28.4966			0.163773
$175$		−	5.48162i		−	0.0313236i
$176$		−	84.5020i		−	0.480125i
$177$			63.0569i			0.356253i
$178$		−	124.200i		−	0.697751i
$179$			280.823i			1.56885i	0.620226	+	0.784423i	$0.287041\pi$
$179$			280.823i			1.56885i	−0.620226	+	0.784423i	$0.712959\pi$
$180$		−	47.2631i		−	0.262573i
$181$	216.689			1.19718			0.598589	−	0.801056i	$-0.295728\pi$
$181$	216.689			1.19718			0.598589	+	0.801056i	$0.295728\pi$
$182$		−	124.623i		−	0.684742i
$183$	−148.530			−0.811638
$184$			18.0858i			0.0982927i
$185$		−	179.162i		−	0.968441i
$186$		−	8.31650i		−	0.0447124i
$187$			264.152i			1.41258i
$188$	−15.3269			−0.0815263
$189$	−29.5311			−0.156249
$190$	−152.391			−0.802056
$191$		−	204.001i		−	1.06807i	−0.845462	−	0.534035i	$-0.820675\pi$
$191$		−	204.001i		−	1.06807i	0.845462	−	0.534035i	$-0.179325\pi$
$192$			12.8864i			0.0671165i
$193$	−75.5947			−0.391682			−0.195841	−	0.980636i	$-0.562744\pi$
$193$	−75.5947			−0.391682			−0.195841	+	0.980636i	$0.562744\pi$
$194$	−70.3791			−0.362779
$195$			203.077i			1.04142i
$196$	51.6348			0.263443
$197$			153.808i			0.780754i	0.920655	+	0.390377i	$0.127655\pi$
$197$			153.808i			0.780754i	−0.920655	+	0.390377i	$0.872345\pi$
$198$	−40.7651			−0.205884
$199$	−11.0070			−0.0553114			−0.0276557	−	0.999618i	$-0.508804\pi$
$199$	−11.0070			−0.0553114			−0.0276557	+	0.999618i	$0.508804\pi$
$200$		−	6.51868i		−	0.0325934i
$201$	−32.6142	+	111.370i	−0.162260	+	0.554080i
$202$	104.962			0.519615
$203$			98.1155i			0.483328i
$204$			99.2087i			0.486317i
$205$	−55.2790			−0.269654
$206$		−	138.294i		−	0.671332i
$207$	−8.02809			−0.0387831
$208$			136.364i			0.655597i
$209$		−	447.458i		−	2.14095i
$210$	−47.8013			−0.227625
$211$	−259.532			−1.23001			−0.615004	−	0.788524i	$-0.710846\pi$
$211$	−259.532			−1.23001			−0.615004	+	0.788524i	$0.710846\pi$
$212$		−	238.415i		−	1.12460i
$213$		−	191.049i		−	0.896942i
$214$		−	135.340i		−	0.632428i
$215$	319.563			1.48634
$216$	−35.1180			−0.162583
$217$	28.6343			0.131955
$218$	−80.7404			−0.370369
$219$		−	122.225i		−	0.558106i
$220$	224.635			1.02107
$221$		−	426.273i		−	1.92884i
$222$	−58.0372			−0.261429
$223$	−254.415			−1.14087			−0.570437	−	0.821342i	$-0.693226\pi$
$223$	−254.415			−1.14087			−0.570437	+	0.821342i	$0.693226\pi$
$224$	−185.738			−0.829189
$225$	2.89356			0.0128603
$226$	49.1652			0.217545
$227$	332.032			1.46270			0.731348	−	0.682004i	$-0.238891\pi$
$227$	332.032			1.46270			0.731348	+	0.682004i	$0.238891\pi$
$228$		−	168.054i		−	0.737078i
$229$		−	29.9512i		−	0.130791i	−0.997859	−	0.0653956i	$-0.979169\pi$
$229$		−	29.9512i		−	0.130791i	0.997859	−	0.0653956i	$-0.0208309\pi$
$230$	−12.9949			−0.0564995
$231$		−	140.357i		−	0.607606i
$232$			116.678i			0.502921i
$233$		−	187.114i		−	0.803065i	−0.915845	−	0.401533i	$-0.868478\pi$
$233$		−	187.114i		−	0.803065i	0.915845	−	0.401533i	$-0.131522\pi$
$234$	65.7843			0.281129
$235$		−	25.2601i		−	0.107490i
$236$	−112.560			−0.476948
$237$	−48.7865			−0.205850
$238$	100.338			0.421590
$239$		−	3.51057i		−	0.0146886i	−0.999973	−	0.00734429i	$-0.997662\pi$
$239$		−	3.51057i		−	0.0146886i	0.999973	−	0.00734429i	$-0.00233778\pi$
$240$	52.3048			0.217937
$241$	−64.2122			−0.266441			−0.133220	−	0.991086i	$-0.542532\pi$
$241$	−64.2122			−0.266441			−0.133220	+	0.991086i	$0.542532\pi$
$242$		−	78.4382i		−	0.324125i
$243$		−	15.5885i		−	0.0641500i
$244$		−	265.133i		−	1.08661i
$245$			85.0984i			0.347341i
$246$			17.9070i			0.0727926i
$247$			722.081i			2.92340i
$248$	34.0515			0.137304
$249$		−	55.5475i		−	0.223082i
$250$	−116.717			−0.466868
$251$			400.408i			1.59525i	0.603154	+	0.797625i	$0.293910\pi$
$251$			400.408i			1.59525i	−0.603154	+	0.797625i	$0.706090\pi$
$252$		−	52.7144i		−	0.209184i
$253$		−	38.1564i		−	0.150816i
$254$			130.135i			0.512343i
$255$	−163.504			−0.641193
$256$	−147.585			−0.576504
$257$	−373.057			−1.45158			−0.725792	−	0.687914i	$-0.758526\pi$
$257$	−373.057			−1.45158			−0.725792	+	0.687914i	$0.758526\pi$
$258$		−	103.518i		−	0.401234i
$259$		−	199.826i		−	0.771529i
$260$	−362.502			−1.39424
$261$	−51.7919			−0.198436
$262$			51.2321i			0.195543i
$263$	−270.224			−1.02747			−0.513733	−	0.857950i	$-0.671738\pi$
$263$	−270.224			−1.02747			−0.513733	+	0.857950i	$0.671738\pi$
$264$		−	166.911i		−	0.632238i
$265$	392.927			1.48274
$266$	−169.967			−0.638975
$267$			225.730i			0.845431i
$268$	−198.801	−	58.2180i	−0.741796	−	0.217231i
$269$	267.076			0.992847			0.496424	−	0.868080i	$-0.334646\pi$
$269$	267.076			0.992847			0.496424	+	0.868080i	$0.334646\pi$
$270$		−	25.2327i		−	0.0934544i
$271$		−	419.522i		−	1.54805i	−0.633153	−	0.774027i	$-0.718240\pi$
$271$		−	419.522i		−	1.54805i	0.633153	−	0.774027i	$-0.281760\pi$
$272$	−109.792			−0.403645
$273$			226.500i			0.829669i
$274$	65.1716			0.237853
$275$			13.7527i			0.0500098i
$276$		−	14.3305i		−	0.0519223i
$277$	−279.225			−1.00803			−0.504016	−	0.863694i	$-0.668145\pi$
$277$	−279.225			−1.00803			−0.504016	+	0.863694i	$0.668145\pi$
$278$	−11.4787			−0.0412903
$279$			15.1151i			0.0541758i
$280$		−	195.720i		−	0.699000i
$281$			318.799i			1.13452i	0.823540	+	0.567258i	$0.191996\pi$
$281$			318.799i			1.13452i	−0.823540	+	0.567258i	$0.808004\pi$
$282$	−8.18270			−0.0290167
$283$	−95.6142			−0.337859			−0.168930	−	0.985628i	$-0.554031\pi$
$283$	−95.6142			−0.337859			−0.168930	+	0.985628i	$0.554031\pi$
$284$	341.031			1.20081
$285$	276.966			0.971812
$286$			312.663i			1.09323i
$287$	−61.6549			−0.214825
$288$		−	98.0450i		−	0.340434i
$289$	54.2072			0.187568
$290$	−83.8343			−0.289084
$291$	127.913			0.439562
$292$	218.178			0.747185
$293$	412.335			1.40729			0.703643	−	0.710553i	$-0.251555\pi$
$293$	412.335			1.40729			0.703643	+	0.710553i	$0.251555\pi$
$294$	27.5666			0.0937640
$295$		−	185.508i		−	0.628840i
$296$		−	237.631i		−	0.802806i
$297$	74.0897			0.249460
$298$		−	14.9324i		−	0.0501089i
$299$			61.5745i			0.205935i
$300$			5.16516i			0.0172172i
$301$	356.421			1.18412
$302$			26.5233i			0.0878254i
$303$	−190.767			−0.629593
$304$	185.980			0.611778
$305$	436.961			1.43266
$306$			52.9652i			0.173089i
$307$	−330.902			−1.07786			−0.538928	−	0.842352i	$-0.681171\pi$
$307$	−330.902			−1.07786			−0.538928	+	0.842352i	$0.681171\pi$
$308$	250.544			0.813455
$309$			251.347i			0.813421i
$310$			24.4664i			0.0789239i
$311$			594.542i			1.91171i	0.293837	+	0.955856i	$0.405068\pi$
$311$			594.542i			1.91171i	−0.293837	+	0.955856i	$0.594932\pi$
$312$			269.351i			0.863303i
$313$		−	541.567i		−	1.73025i	−0.501559	−	0.865123i	$-0.667240\pi$
$313$		−	541.567i		−	1.73025i	0.501559	−	0.865123i	$-0.332760\pi$
$314$			13.8898i			0.0442351i
$315$	86.8778			0.275803
$316$		−	87.0863i		−	0.275590i
$317$	−304.028			−0.959079			−0.479540	−	0.877520i	$-0.659196\pi$
$317$	−304.028			−0.959079			−0.479540	+	0.877520i	$0.659196\pi$
$318$		−	127.284i		−	0.400264i
$319$		−	246.159i		−	0.771659i
$320$		−	37.9106i		−	0.118470i
$321$			245.977i			0.766283i
$322$	−14.4937			−0.0450116
$323$	−581.373			−1.79992
$324$	27.8262			0.0858832
$325$		−	22.1933i		−	0.0682870i
$326$			284.951i			0.874084i
$327$	146.744			0.448758
$328$	−73.3192			−0.223534
$329$		−	28.1736i		−	0.0856340i
$330$	119.927			0.363416
$331$			243.210i			0.734774i	0.930068	+	0.367387i	$0.119748\pi$
$331$			243.210i			0.734774i	−0.930068	+	0.367387i	$0.880252\pi$
$332$	99.1551			0.298660
$333$	105.481			0.316761
$334$			228.950i			0.685480i
$335$	95.9482	−	327.641i	0.286412	−	0.978033i
$336$	58.3376			0.173624
$337$		−	606.610i		−	1.80003i	−0.435860	−	0.900014i	$-0.643556\pi$
$337$		−	606.610i		−	1.80003i	0.435860	−	0.900014i	$-0.356444\pi$
$338$		−	343.501i		−	1.01627i
$339$	−89.3567			−0.263589
$340$		−	291.863i		−	0.858421i
$341$	−71.8397			−0.210674
$342$		−	89.7200i		−	0.262339i
$343$			373.393i			1.08861i
$344$	423.851			1.23213
$345$	23.6179			0.0684578
$346$			223.476i			0.645885i
$347$			37.1962i			0.107194i	0.998563	+	0.0535968i	$0.0170686\pi$
$347$			37.1962i			0.107194i	−0.998563	+	0.0535968i	$0.982931\pi$
$348$		−	92.4510i		−	0.265664i
$349$	−45.6213			−0.130720			−0.0653600	−	0.997862i	$-0.520820\pi$
$349$	−45.6213			−0.130720			−0.0653600	+	0.997862i	$0.520820\pi$
$350$	5.22397			0.0149256
$351$	−119.562			−0.340631
$352$	465.994			1.32385
$353$			172.131i			0.487623i	0.969823	+	0.243811i	$0.0783978\pi$
$353$			172.131i			0.487623i	−0.969823	+	0.243811i	$0.921602\pi$
$354$	−60.0930			−0.169754
$355$			562.048i			1.58323i
$356$	−402.939			−1.13185
$357$	−182.363			−0.510820
$358$	−267.624			−0.747553
$359$	−244.241			−0.680338			−0.340169	−	0.940364i	$-0.610484\pi$
$359$	−244.241			−0.680338			−0.340169	+	0.940364i	$0.610484\pi$
$360$	103.314			0.286983
$361$	623.811			1.72801
$362$			206.504i			0.570454i
$363$			142.560i			0.392726i
$364$	−404.313			−1.11075
$365$			359.575i			0.985138i
$366$		−	141.548i		−	0.386744i
$367$			681.787i			1.85773i	0.370417	+	0.928866i	$0.379215\pi$
$367$			681.787i			1.85773i	−0.370417	+	0.928866i	$0.620785\pi$
$368$	15.8592			0.0430957
$369$		−	32.5455i		−	0.0881993i
$370$	170.740			0.461460
$371$	438.248			1.18126
$372$	−26.9811			−0.0725299
$373$		−	77.3969i		−	0.207498i	−0.994603	−	0.103749i	$-0.966916\pi$
$373$		−	77.3969i		−	0.207498i	0.994603	−	0.103749i	$-0.0330839\pi$
$374$	−251.736			−0.673091
$375$	212.131			0.565682
$376$		−	33.5037i		−	0.0891055i
$377$			397.237i			1.05368i
$378$		−	28.1430i		−	0.0744524i
$379$		−	467.387i		−	1.23321i	−0.787273	−	0.616605i	$-0.788508\pi$
$379$		−	467.387i		−	1.23321i	0.787273	−	0.616605i	$-0.211492\pi$
$380$			494.399i			1.30105i
$381$		−	236.518i		−	0.620782i
$382$	194.413			0.508934
$383$		−	396.776i		−	1.03597i	−0.855390	−	0.517984i	$-0.826683\pi$
$383$		−	396.776i		−	1.03597i	0.855390	−	0.517984i	$-0.173317\pi$
$384$	214.145			0.557668
$385$			412.918i			1.07251i
$386$		−	72.0415i		−	0.186636i
$387$			188.142i			0.486156i
$388$			228.330i			0.588480i
$389$	−673.774			−1.73207			−0.866033	−	0.499987i	$-0.833338\pi$
$389$	−673.774			−1.73207			−0.866033	+	0.499987i	$0.833338\pi$
$390$	−193.532			−0.496235
$391$	−49.5758			−0.126792
$392$			112.870i			0.287934i
$393$		−	93.1133i		−	0.236929i
$394$	−146.579			−0.372028
$395$	143.526			0.363356
$396$			132.254i			0.333974i
$397$	−433.713			−1.09248			−0.546238	−	0.837630i	$-0.683941\pi$
$397$	−433.713			−1.09248			−0.546238	+	0.837630i	$0.683941\pi$
$398$		−	10.4896i		−	0.0263558i
$399$	308.912			0.774215
$400$	−5.71614			−0.0142903
$401$		−	101.722i		−	0.253672i	−0.991924	−	0.126836i	$-0.959518\pi$
$401$		−	101.722i		−	0.253672i	0.991924	−	0.126836i	$-0.0404822\pi$
$402$	−106.135	−	31.0813i	−0.264018	−	0.0773166i
$403$	115.931			0.287669
$404$		−	340.528i		−	0.842891i
$405$			45.8599i			0.113234i
$406$	−93.5038			−0.230305
$407$			501.338i			1.23179i
$408$	−216.864			−0.531528
$409$		−	32.9962i		−	0.0806753i	−0.999186	−	0.0403377i	$-0.987157\pi$
$409$		−	32.9962i		−	0.0806753i	0.999186	−	0.0403377i	$-0.0128434\pi$
$410$		−	52.6807i		−	0.128490i
$411$	−118.448			−0.288194
$412$	−448.667			−1.08900
$413$		−	206.904i		−	0.500978i
$414$		−	7.65075i		−	0.0184801i
$415$			163.416i			0.393773i
$416$	−751.993			−1.80768
$417$	20.8623			0.0500295
$418$	426.426			1.02016
$419$	286.814			0.684521			0.342261	−	0.939605i	$-0.388807\pi$
$419$	286.814			0.684521			0.342261	+	0.939605i	$0.388807\pi$
$420$			155.081i			0.369241i
$421$	90.7557			0.215572			0.107786	−	0.994174i	$-0.465624\pi$
$421$	90.7557			0.215572			0.107786	+	0.994174i	$0.465624\pi$
$422$		−	247.333i		−	0.586097i
$423$	14.8719			0.0351581
$424$	521.158			1.22915
$425$	17.8686			0.0420437
$426$	182.069			0.427392
$427$	487.361			1.14136
$428$	−439.081			−1.02589
$429$		−	568.259i		−	1.32461i
$430$			304.542i			0.708237i
$431$	−19.4782			−0.0451930			−0.0225965	−	0.999745i	$-0.507193\pi$
$431$	−19.4782			−0.0451930			−0.0225965	+	0.999745i	$0.507193\pi$
$432$			30.7945i			0.0712835i
$433$			202.571i			0.467830i	0.972257	+	0.233915i	$0.0751538\pi$
$433$			202.571i			0.467830i	−0.972257	+	0.233915i	$0.924846\pi$
$434$			27.2884i			0.0628764i
$435$	152.367			0.350269
$436$			261.945i			0.600792i
$437$	83.9784			0.192170
$438$	116.480			0.265936
$439$	−79.2836			−0.180600			−0.0903002	−	0.995915i	$-0.528783\pi$
$439$	−79.2836			−0.180600			−0.0903002	+	0.995915i	$0.528783\pi$
$440$			491.037i			1.11599i
$441$	−50.1017			−0.113609
$442$	406.237			0.919088
$443$		−	13.2666i		−	0.0299473i	−0.999888	−	0.0149736i	$-0.995234\pi$
$443$		−	13.2666i		−	0.0299473i	0.999888	−	0.0149736i	$-0.00476643\pi$
$444$			188.290i			0.424075i
$445$		−	664.078i		−	1.49231i
$446$		−	242.456i		−	0.543624i
$447$			27.1394i			0.0607145i
$448$		−	42.2832i		−	0.0943821i
$449$	−89.5588			−0.199463			−0.0997314	−	0.995014i	$-0.531798\pi$
$449$	−89.5588			−0.199463			−0.0997314	+	0.995014i	$0.531798\pi$
$450$			2.75756i			0.00612790i
$451$	154.684			0.342981
$452$		−	159.506i		−	0.352890i
$453$		−	48.2055i		−	0.106414i
$454$			316.426i			0.696973i
$455$		−	666.342i		−	1.46449i
$456$	367.354			0.805601
$457$	−718.578			−1.57238			−0.786191	−	0.617984i	$-0.787950\pi$
$457$	−718.578			−1.57238			−0.786191	+	0.617984i	$0.787950\pi$
$458$	28.5434			0.0623218
$459$		−	96.2631i		−	0.209724i
$460$			42.1592i			0.0916504i
$461$	99.7231			0.216319			0.108160	−	0.994134i	$-0.465504\pi$
$461$	99.7231			0.216319			0.108160	+	0.994134i	$0.465504\pi$
$462$	133.760			0.289523
$463$		−	667.866i		−	1.44247i	−0.692688	−	0.721237i	$-0.743574\pi$
$463$		−	667.866i		−	1.44247i	0.692688	−	0.721237i	$-0.256426\pi$
$464$	102.313			0.220502
$465$		−	44.4672i		−	0.0956283i
$466$	178.319			0.382659
$467$	673.910			1.44306			0.721531	−	0.692382i	$-0.243439\pi$
$467$	673.910			1.44306			0.721531	+	0.692382i	$0.243439\pi$
$468$		−	213.423i		−	0.456033i
$469$	107.015	−	365.431i	0.228177	−	0.779171i
$470$	24.0728			0.0512187
$471$		−	25.2444i		−	0.0535975i
$472$		−	246.048i		−	0.521288i
$473$	−894.214			−1.89052
$474$		−	46.4934i		−	0.0980873i
$475$	−30.2683			−0.0637228
$476$		−	325.527i		−	0.683880i
$477$			231.336i			0.484981i
$478$	3.34556			0.00699908
$479$	−303.896			−0.634438			−0.317219	−	0.948352i	$-0.602749\pi$
$479$	−303.896			−0.634438			−0.317219	+	0.948352i	$0.602749\pi$
$480$			288.440i			0.600916i
$481$		−	809.029i		−	1.68197i
$482$		−	61.1940i		−	0.126958i
$483$	26.3420			0.0545384
$484$	−254.476			−0.525777
$485$	−376.307			−0.775891
$486$	14.8558			0.0305674
$487$		−	478.159i		−	0.981847i	−0.871203	−	0.490923i	$-0.836660\pi$
$487$		−	478.159i		−	0.981847i	0.871203	−	0.490923i	$-0.163340\pi$
$488$	579.563			1.18763
$489$		−	517.893i		−	1.05909i
$490$	−81.0985			−0.165507
$491$	−225.597			−0.459465			−0.229732	−	0.973254i	$-0.573785\pi$
$491$	−225.597			−0.459465			−0.229732	+	0.973254i	$0.573785\pi$
$492$	58.0954			0.118080
$493$	−319.829			−0.648741
$494$	−688.141			−1.39300
$495$	−217.965			−0.440334
$496$		−	29.8593i		−	0.0602001i
$497$			626.875i			1.26132i
$498$	52.9366			0.106298
$499$			501.899i			1.00581i	0.864342	+	0.502905i	$0.167735\pi$
$499$			501.899i			1.00581i	−0.864342	+	0.502905i	$0.832265\pi$
$500$			378.664i			0.757328i
$501$		−	416.112i		−	0.830563i
$502$	−381.587			−0.760134
$503$			228.581i			0.454435i	0.973844	+	0.227217i	$0.0729628\pi$
$503$			228.581i			0.454435i	−0.973844	+	0.227217i	$0.927037\pi$
$504$	115.230			0.228631
$505$	561.218			1.11132
$506$	36.3629			0.0718635
$507$			624.305i			1.23137i
$508$	422.196			0.831095
$509$	−507.229			−0.996521			−0.498261	−	0.867027i	$-0.666028\pi$
$509$	−507.229			−0.996521			−0.498261	+	0.867027i	$0.666028\pi$
$510$		−	155.819i		−	0.305527i
$511$			401.049i			0.784831i
$512$			353.898i			0.691207i
$513$			163.064i			0.317864i
$514$		−	355.522i		−	0.691677i
$515$		−	739.441i		−	1.43581i
$516$	−335.844			−0.650860
$517$			70.6839i			0.136719i
$518$	190.434			0.367632
$519$		−	406.163i		−	0.782588i
$520$		−	792.405i		−	1.52386i
$521$			178.388i			0.342396i	0.985237	+	0.171198i	$0.0547638\pi$
$521$			178.388i			0.342396i	−0.985237	+	0.171198i	$0.945236\pi$
$522$		−	49.3575i		−	0.0945545i
$523$	−372.700			−0.712619			−0.356310	−	0.934368i	$-0.615965\pi$
$523$	−372.700			−0.712619			−0.356310	+	0.934368i	$0.615965\pi$
$524$	166.212			0.317198
$525$	−9.49445			−0.0180847
$526$		−	257.522i		−	0.489586i
$527$			93.3398i			0.177115i
$528$	−146.362			−0.277200
$529$	−521.839			−0.986463
$530$			374.458i			0.706525i
$531$	109.218			0.205683
$532$			551.423i			1.03651i
$533$	−249.620			−0.468330
$534$	−215.120			−0.402847
$535$		−	723.642i		−	1.35260i
$536$	127.261	−	434.566i	0.237427	−	0.810758i
$537$	486.401			0.905774
$538$			254.523i			0.473090i
$539$		−	238.126i		−	0.441793i
$540$	−81.8621			−0.151597
$541$			118.286i			0.218643i	0.994006	+	0.109321i	$0.0348678\pi$
$541$			118.286i			0.218643i	−0.994006	+	0.109321i	$0.965132\pi$
$542$	399.804			0.737645
$543$		−	375.317i		−	0.691192i
$544$		−	605.456i		−	1.11297i
$545$	−431.708			−0.792124
$546$	−215.853			−0.395336
$547$			820.295i			1.49962i	0.661651	+	0.749812i	$0.269856\pi$
$547$			820.295i			1.49962i	−0.661651	+	0.749812i	$0.730144\pi$
$548$		−	211.435i		−	0.385831i
$549$			257.261i			0.468600i
$550$	−13.1063			−0.0238296
$551$	541.772			0.983252
$552$	31.3256			0.0567493
$553$	160.080			0.289475
$554$		−	266.100i		−	0.480325i
$555$	−310.317			−0.559129
$556$			37.2402i			0.0669788i
$557$	−258.250			−0.463644			−0.231822	−	0.972758i	$-0.574469\pi$
$557$	−258.250			−0.463644			−0.231822	+	0.972758i	$0.574469\pi$
$558$	−14.4046			−0.0258147
$559$	1443.03			2.58145
$560$	−171.624			−0.306472
$561$	457.525			0.815553
$562$	−303.814			−0.540595
$563$		−	519.585i		−	0.922887i	−0.887170	−	0.461443i	$-0.847332\pi$
$563$		−	519.585i		−	0.922887i	0.887170	−	0.461443i	$-0.152668\pi$
$564$			26.5470i			0.0470692i
$565$	262.879			0.465273
$566$		−	91.1200i		−	0.160989i
$567$			51.1493i			0.0902105i
$568$			745.472i			1.31245i
$569$	−588.892			−1.03496			−0.517480	−	0.855695i	$-0.673130\pi$
$569$	−588.892			−1.03496			−0.517480	+	0.855695i	$0.673130\pi$
$570$			263.948i			0.463067i
$571$	−138.088			−0.241835			−0.120918	−	0.992663i	$-0.538584\pi$
$571$	−138.088			−0.241835			−0.120918	+	0.992663i	$0.538584\pi$
$572$	1014.37			1.77337
$573$	−353.341			−0.616651
$574$		−	58.7569i		−	0.102364i
$575$	−2.58109			−0.00448885
$576$	22.3199			0.0387497
$577$		−	93.9797i		−	0.162876i	−0.996678	−	0.0814382i	$-0.974049\pi$
$577$		−	93.9797i		−	0.162876i	0.996678	−	0.0814382i	$-0.0259513\pi$
$578$			51.6593i			0.0893759i
$579$			130.934i			0.226138i
$580$			271.983i			0.468936i
$581$			182.264i			0.313708i
$582$			121.900i			0.209451i
$583$	−1099.51			−1.88595
$584$			476.922i			0.816648i
$585$	351.739			0.601264
$586$			392.954i			0.670570i
$587$		−	391.440i		−	0.666848i	−0.942777	−	0.333424i	$-0.891796\pi$
$587$		−	391.440i		−	0.666848i	0.942777	−	0.333424i	$-0.108204\pi$
$588$		−	89.4341i		−	0.152099i
$589$		−	158.112i		−	0.268442i
$590$	176.788			0.299641
$591$	266.404			0.450768
$592$	−208.375			−0.351985
$593$		−	1072.87i		−	1.80922i	−0.426241	−	0.904609i	$-0.640163\pi$
$593$		−	1072.87i		−	1.80922i	0.426241	−	0.904609i	$-0.359837\pi$
$594$			70.6073i			0.118867i
$595$	536.495			0.901672
$596$	−48.4452			−0.0812839
$597$			19.0646i			0.0319340i
$598$	−58.6803			−0.0981275
$599$		−	257.125i		−	0.429257i	−0.976696	−	0.214628i	$-0.931146\pi$
$599$		−	257.125i		−	0.429257i	0.976696	−	0.214628i	$-0.0688540\pi$
$600$	−11.2907			−0.0188178
$601$	−338.421			−0.563096			−0.281548	−	0.959547i	$-0.590848\pi$
$601$	−338.421			−0.563096			−0.281548	+	0.959547i	$0.590848\pi$
$602$			339.668i			0.564232i
$603$	192.899	+	56.4895i	0.319898	+	0.0936808i
$604$	86.0492			0.142466
$605$		−	419.398i		−	0.693220i
$606$		−	181.800i		−	0.300000i
$607$	641.521			1.05687			0.528436	−	0.848973i	$-0.322779\pi$
$607$	641.521			1.05687			0.528436	+	0.848973i	$0.322779\pi$
$608$			1025.61i			1.68685i
$609$	169.941			0.279049
$610$			416.423i			0.682660i
$611$		−	114.065i		−	0.186686i
$612$	171.835			0.280775
$613$	1095.72			1.78747			0.893733	−	0.448600i	$-0.148077\pi$
$613$	1095.72			1.78747			0.893733	+	0.448600i	$0.148077\pi$
$614$		−	315.348i		−	0.513597i
$615$			95.7461i			0.155685i
$616$			547.673i			0.889079i
$617$	602.283			0.976148			0.488074	−	0.872802i	$-0.337700\pi$
$617$	602.283			0.976148			0.488074	+	0.872802i	$0.337700\pi$
$618$	−239.533			−0.387594
$619$	−433.711			−0.700664			−0.350332	−	0.936626i	$-0.613931\pi$
$619$	−433.711			−0.700664			−0.350332	+	0.936626i	$0.613931\pi$
$620$	79.3761			0.128026
$621$			13.9051i			0.0223914i
$622$	−566.597			−0.910927
$623$		−	740.672i		−	1.18888i
$624$	236.190			0.378509
$625$	−648.183			−1.03709
$626$	516.112			0.824460
$627$	−775.020			−1.23608
$628$	45.0626			0.0717557
$629$	651.377			1.03558
$630$			82.7943i			0.131419i
$631$		−	404.297i		−	0.640724i	−0.947295	−	0.320362i	$-0.896195\pi$
$631$		−	404.297i		−	0.640724i	0.947295	−	0.320362i	$-0.103805\pi$
$632$	190.365			0.301210
$633$			449.522i			0.710146i
$634$		−	289.738i		−	0.457000i
$635$			695.814i			1.09577i
$636$	−412.946			−0.649287
$637$			384.274i			0.603256i
$638$	234.589			0.367694
$639$	−330.906			−0.517850
$640$	−629.994			−0.984366
$641$			421.399i			0.657408i	0.944433	+	0.328704i	$0.106612\pi$
$641$			421.399i			0.657408i	−0.944433	+	0.328704i	$0.893388\pi$
$642$	−234.415			−0.365133
$643$	−269.779			−0.419564			−0.209782	−	0.977748i	$-0.567275\pi$
$643$	−269.779			−0.419564			−0.209782	+	0.977748i	$0.567275\pi$
$644$			47.0218i			0.0730153i
$645$		−	553.498i		−	0.858137i
$646$		−	554.046i		−	0.857657i
$647$		−	221.211i		−	0.341902i	−0.985280	−	0.170951i	$-0.945316\pi$
$647$		−	221.211i		−	0.341902i	0.985280	−	0.170951i	$-0.0546840\pi$
$648$			60.8261i			0.0938675i
$649$			519.096i			0.799840i
$650$	21.1501			0.0325386
$651$		−	49.5960i		−	0.0761843i
$652$	924.465			1.41789
$653$			442.396i			0.677482i	0.940880	+	0.338741i	$0.110001\pi$
$653$			442.396i			0.677482i	−0.940880	+	0.338741i	$0.889999\pi$
$654$			139.846i			0.213833i
$655$			273.931i			0.418215i
$656$			64.2926i			0.0980070i
$657$	−211.700			−0.322222
$658$	26.8493			0.0408044
$659$	398.787			0.605140			0.302570	−	0.953127i	$-0.402155\pi$
$659$	398.787			0.605140			0.302570	+	0.953127i	$0.402155\pi$
$660$		−	389.079i		−	0.589514i
$661$			1059.55i			1.60295i	0.598030	+	0.801474i	$0.295950\pi$
$661$			1059.55i			1.60295i	−0.598030	+	0.801474i	$0.704050\pi$
$662$	−231.779			−0.350119
$663$	−738.326			−1.11361
$664$			216.746i			0.326425i
$665$	−908.791			−1.36660
$666$			100.523i			0.150936i
$667$	46.1989			0.0692637
$668$	742.781			1.11195
$669$			440.659i			0.658684i
$670$	312.241	+	91.4383i	0.466031	+	0.136475i
$671$	−1222.73			−1.82224
$672$			321.708i			0.478733i
$673$			265.324i			0.394240i	0.980379	+	0.197120i	$0.0631589\pi$
$673$			265.324i			0.394240i	−0.980379	+	0.197120i	$0.936841\pi$
$674$	578.097			0.857711
$675$		−	5.01180i		−	0.00742489i
$676$	−1114.42			−1.64854
$677$			8.67329i			0.0128114i	0.999979	+	0.00640568i	$0.00203900\pi$
$677$			8.67329i			0.0128114i	−0.999979	+	0.00640568i	$0.997961\pi$
$678$		−	85.1567i		−	0.125600i
$679$	−419.711			−0.618130
$680$	637.993			0.938225
$681$		−	575.097i		−	0.844488i
$682$		−	68.4630i		−	0.100386i
$683$		−	433.375i		−	0.634517i	−0.948339	−	0.317259i	$-0.897238\pi$
$683$		−	433.375i		−	0.634517i	0.948339	−	0.317259i	$-0.102762\pi$
$684$	−291.078			−0.425552
$685$	348.463			0.508705
$686$	−355.843			−0.518721
$687$	−51.8770			−0.0755123
$688$		−	371.669i		−	0.540217i
$689$	1774.32			2.57521
$690$			22.5078i			0.0326200i
$691$	−264.772			−0.383172			−0.191586	−	0.981476i	$-0.561363\pi$
$691$	−264.772			−0.383172			−0.191586	+	0.981476i	$0.561363\pi$
$692$	725.021			1.04772
$693$	−243.105			−0.350802
$694$	−35.4478			−0.0510776
$695$	−61.3750			−0.0883094
$696$	202.092			0.290362
$697$		−	200.978i		−	0.288347i
$698$		−	43.4769i		−	0.0622879i
$699$	−324.091			−0.463650
$700$		−	16.9481i		−	0.0242115i
$701$			1044.23i			1.48962i	0.667275	+	0.744811i	$0.267460\pi$
$701$			1044.23i			1.48962i	−0.667275	+	0.744811i	$0.732540\pi$
$702$		−	113.942i		−	0.162310i
$703$	−1103.39			−1.56955
$704$			106.083i			0.150686i
$705$	−43.7517			−0.0620592
$706$	−164.040			−0.232352
$707$	625.949			0.885359
$708$			194.959i			0.275366i
$709$	531.335			0.749415			0.374707	−	0.927143i	$-0.377743\pi$
$709$	531.335			0.749415			0.374707	+	0.927143i	$0.377743\pi$
$710$	−535.630			−0.754409
$711$			84.5007i			0.118848i
$712$		−	880.799i		−	1.23708i
$713$		−	13.4828i		−	0.0189099i
$714$		−	173.791i		−	0.243405i
$715$			1671.77i			2.33814i
$716$			868.249i			1.21264i
$717$	−6.08048			−0.00848045
$718$		−	232.761i		−	0.324180i
$719$	1087.85			1.51300			0.756502	−	0.653991i	$-0.226907\pi$
$719$	1087.85			1.51300			0.756502	+	0.653991i	$0.226907\pi$
$720$		−	90.5946i		−	0.125826i
$721$		−	824.728i		−	1.14387i
$722$			594.490i			0.823393i
$723$			111.219i			0.153829i
$724$	669.960			0.925359
$725$	−16.6514			−0.0229675
$726$	−135.859			−0.187134
$727$		−	204.959i		−	0.281924i	−0.990015	−	0.140962i	$-0.954980\pi$
$727$		−	204.959i		−	0.281924i	0.990015	−	0.140962i	$-0.0450196\pi$
$728$		−	883.801i		−	1.21401i
$729$	−27.0000			−0.0370370
$730$	−342.674			−0.469417
$731$			1161.83i			1.58938i
$732$	−459.224			−0.627355
$733$			1374.00i			1.87449i	0.348673	+	0.937244i	$0.386632\pi$
$733$			1374.00i			1.87449i	−0.348673	+	0.937244i	$0.613368\pi$
$734$	−649.741			−0.885206
$735$	147.395			0.200537
$736$			87.4572i			0.118828i
$737$	−268.487	+	916.820i	−0.364297	+	1.24399i
$738$	31.0158			0.0420268
$739$		−	679.479i		−	0.919458i	−0.888059	−	0.459729i	$-0.847947\pi$
$739$		−	679.479i		−	0.919458i	0.888059	−	0.459729i	$-0.152053\pi$
$740$		−	553.931i		−	0.748555i
$741$	1250.68			1.68783
$742$			417.648i			0.562869i
$743$	855.242			1.15107			0.575533	−	0.817779i	$-0.304795\pi$
$743$	855.242			1.15107			0.575533	+	0.817779i	$0.304795\pi$
$744$		−	58.9789i		−	0.0792728i
$745$		−	79.8417i		−	0.107170i
$746$	73.7590			0.0988727
$747$	−96.2111			−0.128797
$748$			816.705i			1.09185i
$749$		−	807.107i		−	1.07758i
$750$			202.160i			0.269547i
$751$	−20.4023			−0.0271668			−0.0135834	−	0.999908i	$-0.504324\pi$
$751$	−20.4023			−0.0271668			−0.0135834	+	0.999908i	$0.504324\pi$
$752$	−29.3789			−0.0390677
$753$	693.526			0.921018
$754$	−378.566			−0.502076
$755$			141.816i			0.187836i
$756$	−91.3041			−0.120773
$757$			420.243i			0.555143i	0.960705	+	0.277571i	$0.0895295\pi$
$757$			420.243i			0.555143i	−0.960705	+	0.277571i	$0.910470\pi$
$758$	445.418			0.587623
$759$	−66.0888			−0.0870735
$760$	−1080.72			−1.42200
$761$	−967.358			−1.27117			−0.635583	−	0.772032i	$-0.719240\pi$
$761$	−967.358			−1.27117			−0.635583	+	0.772032i	$0.719240\pi$
$762$	225.401			0.295801
$763$	−481.501			−0.631062
$764$		−	630.731i		−	0.825564i
$765$			283.198i			0.370193i
$766$	378.126			0.493637
$767$		−	837.686i		−	1.09216i
$768$			255.625i			0.332845i
$769$		−	545.842i		−	0.709808i	−0.934903	−	0.354904i	$-0.884514\pi$
$769$		−	545.842i		−	0.709808i	0.934903	−	0.354904i	$-0.115486\pi$
$770$	−393.509			−0.511051
$771$			646.154i			0.838072i
$772$	−233.723			−0.302751
$773$	−865.419			−1.11956			−0.559779	−	0.828642i	$-0.689114\pi$
$773$	−865.419			−1.11956			−0.559779	+	0.828642i	$0.689114\pi$
$774$	−179.299			−0.231653
$775$			4.85960i			0.00627045i
$776$	−499.115			−0.643189
$777$	−346.109			−0.445442
$778$		−	642.104i		−	0.825327i
$779$			340.445i			0.437028i
$780$			627.872i			0.804964i
$781$		−	1572.75i		−	2.01376i
$782$		−	47.2455i		−	0.0604163i
$783$			89.7061i			0.114567i
$784$	98.9742			0.126243
$785$			74.2669i			0.0946075i
$786$	88.7367			0.112897
$787$		−	165.192i		−	0.209900i	−0.994477	−	0.104950i	$-0.966532\pi$
$787$		−	165.192i		−	0.209900i	0.994477	−	0.104950i	$-0.0334683\pi$
$788$			475.544i			0.603483i
$789$			468.041i			0.593208i
$790$			136.779i			0.173138i
$791$	293.200			0.370670
$792$	−289.098			−0.365023
$793$	1973.16			2.48822
$794$		−	413.327i		−	0.520563i
$795$		−	680.570i		−	0.856063i
$796$	−34.0313			−0.0427529
$797$	1385.68			1.73862			0.869311	−	0.494266i	$-0.164563\pi$
$797$	1385.68			1.73862			0.869311	+	0.494266i	$0.164563\pi$
$798$			294.392i			0.368912i
$799$	91.8381			0.114941
$800$		−	31.5222i		−	0.0394027i
$801$	390.976			0.488110
$802$	96.9412			0.120874
$803$		−	1006.18i		−	1.25303i
$804$	−100.837	+	344.334i	−0.125419	+	0.428276i
$805$	−77.4959			−0.0962682
$806$			110.481i			0.137074i
$807$		−	462.589i		−	0.573221i
$808$	744.371			0.921251
$809$			93.9009i			0.116070i	0.998315	+	0.0580352i	$0.0184835\pi$
$809$			93.9009i			0.116070i	−0.998315	+	0.0580352i	$0.981516\pi$
$810$	−43.7043			−0.0539559
$811$		−	1102.59i		−	1.35954i	−0.733426	−	0.679769i	$-0.762080\pi$
$811$		−	1102.59i		−	1.35954i	0.733426	−	0.679769i	$-0.237920\pi$
$812$			303.353i			0.373588i
$813$	−726.634			−0.893769
$814$	−477.773			−0.586945
$815$			1523.59i			1.86944i
$816$			190.165i			0.233045i
$817$		−	1968.08i		−	2.40891i
$818$	31.4453			0.0384417
$819$	392.309			0.479010
$820$	−170.911			−0.208429
$821$	−304.199			−0.370523			−0.185262	−	0.982689i	$-0.559313\pi$
$821$	−304.199			−0.370523			−0.185262	+	0.982689i	$0.559313\pi$
$822$		−	112.880i		−	0.137324i
$823$	−259.291			−0.315055			−0.157528	−	0.987515i	$-0.550352\pi$
$823$	−259.291			−0.315055			−0.157528	+	0.987515i	$0.550352\pi$
$824$		−	980.756i		−	1.19024i
$825$	23.8204			0.0288732
$826$	197.179			0.238715
$827$	1117.45			1.35121			0.675607	−	0.737262i	$-0.263882\pi$
$827$	1117.45			1.35121			0.675607	+	0.737262i	$0.263882\pi$
$828$	−24.8212			−0.0299773
$829$	−255.108			−0.307729			−0.153865	−	0.988092i	$-0.549172\pi$
$829$	−255.108			−0.307729			−0.153865	+	0.988092i	$0.549172\pi$
$830$	−155.735			−0.187632
$831$			483.631i			0.581987i
$832$		−	171.190i		−	0.205758i
$833$	−309.392			−0.371419
$834$			19.8817i			0.0238390i
$835$			1224.17i			1.46607i
$836$		−	1383.45i		−	1.65484i
$837$	26.1800			0.0312784
$838$			273.333i			0.326173i
$839$	−161.873			−0.192936			−0.0964681	−	0.995336i	$-0.530755\pi$
$839$	−161.873			−0.192936			−0.0964681	+	0.995336i	$0.530755\pi$
$840$	−338.997			−0.403568
$841$	−542.956			−0.645608
$842$			86.4899i			0.102720i
$843$	552.176			0.655013
$844$	−802.420			−0.950734
$845$		−	1836.65i		−	2.17355i
$846$			14.1729i			0.0167528i
$847$		−	467.771i		−	0.552268i
$848$		−	456.996i		−	0.538911i
$849$			165.609i			0.195063i
$850$			17.0287i			0.0200338i
$851$	−94.0905			−0.110565
$852$		−	590.684i		−	0.693291i
$853$	556.768			0.652718			0.326359	−	0.945246i	$-0.394178\pi$
$853$	556.768			0.652718			0.326359	+	0.945246i	$0.394178\pi$
$854$			464.453i			0.543856i
$855$		−	479.720i		−	0.561076i
$856$		−	959.802i		−	1.12126i
$857$			1291.48i			1.50697i	0.657463	+	0.753486i	$0.271629\pi$
$857$			1291.48i			1.50697i	−0.657463	+	0.753486i	$0.728371\pi$
$858$	541.549			0.631176
$859$	1017.18			1.18414			0.592072	−	0.805885i	$-0.298310\pi$
$859$	1017.18			1.18414			0.592072	+	0.805885i	$0.298310\pi$
$860$	988.022			1.14886
$861$			106.789i			0.124030i
$862$		−	18.5627i		−	0.0215344i
$863$	−102.454			−0.118719			−0.0593594	−	0.998237i	$-0.518906\pi$
$863$	−102.454			−0.118719			−0.0593594	+	0.998237i	$0.518906\pi$
$864$	−169.819			−0.196550
$865$			1194.90i			1.38138i
$866$	−193.049			−0.222920
$867$		−	93.8896i		−	0.108292i
$868$	88.5313			0.101995
$869$	−401.620			−0.462163
$870$			145.205i			0.166903i
$871$	433.267	−	1479.51i	0.497437	−	1.69863i
$872$	−572.595			−0.656645
$873$		−	221.551i		−	0.253781i
$874$			80.0311i			0.0915688i
$875$	−696.050			−0.795486
$876$		−	377.895i		−	0.431387i
$877$	−786.415			−0.896711			−0.448355	−	0.893855i	$-0.647990\pi$
$877$	−786.415			−0.896711			−0.448355	+	0.893855i	$0.647990\pi$
$878$		−	75.5570i		−	0.0860558i
$879$		−	714.185i		−	0.812497i
$880$	430.583			0.489299
$881$	−699.602			−0.794100			−0.397050	−	0.917797i	$-0.629966\pi$
$881$	−699.602			−0.794100			−0.397050	+	0.917797i	$0.629966\pi$
$882$		−	47.7468i		−	0.0541347i
$883$		−	474.681i		−	0.537578i	−0.963199	−	0.268789i	$-0.913377\pi$
$883$		−	474.681i		−	0.537578i	0.963199	−	0.268789i	$-0.0866234\pi$
$884$		−	1317.95i		−	1.49089i
$885$	−321.309			−0.363061
$886$	12.6431			0.0142698
$887$	−394.466			−0.444719			−0.222360	−	0.974965i	$-0.571376\pi$
$887$	−394.466			−0.444719			−0.222360	+	0.974965i	$0.571376\pi$
$888$	−411.588			−0.463500
$889$			776.070i			0.872969i
$890$	632.864			0.711083
$891$		−	128.327i		−	0.144026i
$892$	−786.599			−0.881837
$893$	−155.568			−0.174209
$894$	−25.8638			−0.0289304
$895$	−1430.95			−1.59882
$896$	−702.658			−0.784216
$897$	106.650			0.118896
$898$		−	85.3492i		−	0.0950437i
$899$		−	86.9819i		−	0.0967540i
$900$	8.94631			0.00994035
$901$			1428.57i			1.58553i
$902$			147.414i			0.163430i
$903$		−	617.339i		−	0.683653i
$904$	348.670			0.385697
$905$			1104.15i			1.22005i
$906$	45.9397			0.0507060
$907$	−356.078			−0.392589			−0.196294	−	0.980545i	$-0.562891\pi$
$907$	−356.078			−0.392589			−0.196294	+	0.980545i	$0.562891\pi$
$908$	1026.58			1.13059
$909$			330.417i			0.363495i
$910$	635.022			0.697826
$911$	−785.723			−0.862484			−0.431242	−	0.902236i	$-0.641924\pi$
$911$	−785.723			−0.862484			−0.431242	+	0.902236i	$0.641924\pi$
$912$		−	322.127i		−	0.353210i
$913$		−	457.278i		−	0.500852i
$914$		−	684.803i		−	0.749237i
$915$		−	756.839i		−	0.827147i
$916$		−	92.6030i		−	0.101095i
$917$			305.526i			0.333180i
$918$	91.7385			0.0999330
$919$		−	1455.71i		−	1.58401i	−0.610513	−	0.792006i	$-0.709037\pi$
$919$		−	1455.71i		−	1.58401i	0.610513	−	0.792006i	$-0.290963\pi$
$920$	−92.1572			−0.100171
$921$			573.139i			0.622300i
$922$			95.0358i			0.103076i
$923$			2538.01i			2.74974i
$924$		−	433.955i		−	0.469649i
$925$	33.9130			0.0366627
$926$	636.474			0.687337
$927$	435.346			0.469629
$928$			564.215i			0.607990i
$929$		−	1214.54i		−	1.30737i	−0.756768	−	0.653683i	$-0.773223\pi$
$929$		−	1214.54i		−	1.30737i	0.756768	−	0.653683i	$-0.226777\pi$
$930$	42.3771			0.0455667
$931$	524.092			0.562935
$932$		−	578.519i		−	0.620729i
$933$	1029.78			1.10373
$934$			642.234i			0.687617i
$935$	−1346.00			−1.43957
$936$	466.529			0.498428
$937$			131.498i			0.140339i	0.997535	+	0.0701695i	$0.0223540\pi$
$937$			131.498i			0.140339i	−0.997535	+	0.0701695i	$0.977646\pi$
$938$	348.255	+	101.985i	0.371274	+	0.108726i
$939$	−938.022			−0.998958
$940$		−	78.0990i		−	0.0830841i
$941$		−	809.742i		−	0.860512i	−0.902707	−	0.430256i	$-0.858423\pi$
$941$		−	809.742i		−	0.860512i	0.902707	−	0.430256i	$-0.141577\pi$
$942$	24.0579			0.0255391
$943$			29.0310i			0.0307857i
$944$	−215.756			−0.228555
$945$		−	150.477i		−	0.159235i
$946$		−	852.184i		−	0.900828i
$947$	248.706			0.262625			0.131312	−	0.991341i	$-0.458081\pi$
$947$	248.706			0.262625			0.131312	+	0.991341i	$0.458081\pi$
$948$	−150.838			−0.159112
$949$			1623.71i			1.71097i
$950$		−	28.8456i		−	0.0303638i
$951$			526.592i			0.553725i
$952$	711.579			0.747457
$953$	−998.053			−1.04727			−0.523637	−	0.851941i	$-0.675425\pi$
$953$	−998.053			−1.04727			−0.523637	+	0.851941i	$0.675425\pi$
$954$	−220.463			−0.231093
$955$	1039.50			1.08848
$956$		−	10.8540i		−	0.0113535i
$957$	−426.360			−0.445518
$958$		−	289.612i		−	0.302309i
$959$	388.655			0.405271
$960$	−65.6630			−0.0683990
$961$	935.615			0.973585
$962$	771.002			0.801457
$963$	426.044			0.442414
$964$	−198.531			−0.205945
$965$		−	385.196i		−	0.399167i
$966$			25.1039i			0.0259874i
$967$	−229.940			−0.237787			−0.118894	−	0.992907i	$-0.537935\pi$
$967$	−229.940			−0.237787			−0.118894	+	0.992907i	$0.537935\pi$
$968$		−	556.268i		−	0.574657i
$969$			1006.97i			1.03918i
$970$		−	358.620i		−	0.369711i
$971$	−1127.08			−1.16075			−0.580373	−	0.814351i	$-0.697093\pi$
$971$	−1127.08			−1.16075			−0.580373	+	0.814351i	$0.697093\pi$
$972$		−	48.1963i		−	0.0495847i
$973$	−68.4540			−0.0703535
$974$	455.684			0.467848
$975$	−38.4399			−0.0394255
$976$		−	508.211i		−	0.520708i
$977$	−206.527			−0.211389			−0.105694	−	0.994399i	$-0.533707\pi$
$977$	−206.527			−0.211389			−0.105694	+	0.994399i	$0.533707\pi$
$978$	493.550			0.504653
$979$			1858.25i			1.89811i
$980$			263.107i			0.268477i
$981$		−	254.168i		−	0.259091i
$982$		−	214.993i		−	0.218934i
$983$			333.715i			0.339486i	0.985488	+	0.169743i	$0.0542938\pi$
$983$			333.715i			0.339486i	−0.985488	+	0.169743i	$0.945706\pi$
$984$			126.993i			0.129058i
$985$	−783.737			−0.795672
$986$		−	304.796i		−	0.309124i
$987$	−48.7981			−0.0494408
$988$			2232.53i			2.25964i
$989$		−	167.825i		−	0.169692i
$990$		−	207.720i		−	0.209818i
$991$		−	575.470i		−	0.580696i	−0.956921	−	0.290348i	$-0.906229\pi$
$991$		−	575.470i		−	0.580696i	0.956921	−	0.290348i	$-0.0937711\pi$
$992$	164.662			0.165990
$993$	421.252			0.424222
$994$	−597.410			−0.601016
$995$		−	56.0864i		−	0.0563682i
$996$		−	171.742i		−	0.172431i
$997$	−25.3362			−0.0254125			−0.0127062	−	0.999919i	$-0.504045\pi$
$997$	−25.3362			−0.0254125			−0.0127062	+	0.999919i	$0.504045\pi$
$998$	−478.308			−0.479267
$999$		−	182.699i		−	0.182882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.14	yes	22
3.2	odd	2		603.3.b.e.334.9		22
67.66	odd	2	inner	201.3.b.a.133.9	✓	22
201.200	even	2		603.3.b.e.334.14		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.9	✓	22	67.66	odd	2	inner
201.3.b.a.133.14	yes	22	1.1	even	1	trivial
603.3.b.e.334.9		22	3.2	odd	2
603.3.b.e.334.14		22	201.200	even	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)

\(f(q)\)	\(=\)	\(q+0.952997i q^{2} -1.73205i q^{3} +3.09180 q^{4} +5.09554i q^{5} +1.65064 q^{6} +5.68326i q^{7} +6.75846i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+0.952997i q^{2} -1.73205i q^{3} +3.09180 q^{4} +5.09554i q^{5} +1.65064 q^{6} +5.68326i q^{7} +6.75846i q^{8} -3.00000 q^{9} -4.85603 q^{10} -14.2586i q^{11} -5.35515i q^{12} +23.0096i q^{13} -5.41613 q^{14} +8.82573 q^{15} +5.92640 q^{16} -18.5259 q^{17} -2.85899i q^{18} +31.3817 q^{19} +15.7544i q^{20} +9.84369 q^{21} +13.5884 q^{22} +2.67603 q^{23} +11.7060 q^{24} -0.964521 q^{25} -21.9281 q^{26} +5.19615i q^{27} +17.5715i q^{28} +17.2640 q^{29} +8.41090i q^{30} -5.03835i q^{31} +32.6817i q^{32} -24.6966 q^{33} -17.6551i q^{34} -28.9593 q^{35} -9.27539 q^{36} -35.1605 q^{37} +29.9067i q^{38} +39.8538 q^{39} -34.4380 q^{40} +10.8485i q^{41} +9.38101i q^{42} -62.7142i q^{43} -44.0846i q^{44} -15.2866i q^{45} +2.55025i q^{46} -4.95729 q^{47} -10.2648i q^{48} +16.7006 q^{49} -0.919186i q^{50} +32.0877i q^{51} +71.1411i q^{52} -77.1120i q^{53} -4.95192 q^{54} +72.6551 q^{55} -38.4101 q^{56} -54.3547i q^{57} +16.4525i q^{58} -36.4059 q^{59} +27.2874 q^{60} -85.7537i q^{61} +4.80153 q^{62} -17.0498i q^{63} -7.43995 q^{64} -117.246 q^{65} -23.5358i q^{66} +(-64.2996 - 18.8298i) q^{67} -57.2782 q^{68} -4.63502i q^{69} -27.5981i q^{70} +110.302 q^{71} -20.2754i q^{72} +70.5667 q^{73} -33.5078i q^{74} +1.67060i q^{75} +97.0258 q^{76} +81.0351 q^{77} +37.9806i q^{78} -28.1669i q^{79} +30.1982i q^{80} +9.00000 q^{81} -10.3386 q^{82} +32.0704 q^{83} +30.4347 q^{84} -94.3992i q^{85} +59.7664 q^{86} -29.9020i q^{87} +96.3660 q^{88} -130.325 q^{89} +14.5681 q^{90} -130.770 q^{91} +8.27374 q^{92} -8.72668 q^{93} -4.72428i q^{94} +159.907i q^{95} +56.6063 q^{96} +73.8503i q^{97} +15.9156i q^{98} +42.7757i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 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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