LMFDB - Embedded newform 201.3.b.a.133.13

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			133.13
Character	$\chi$	$=$	201.133
Dual form			201.3.b.a.133.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.858352i q^{2} +1.73205i q^{3} +3.26323 q^{4} +8.02842i q^{5} -1.48671 q^{6} -1.82241i q^{7} +6.23441i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+0.858352i q^{2} +1.73205i q^{3} +3.26323 q^{4} +8.02842i q^{5} -1.48671 q^{6} -1.82241i q^{7} +6.23441i q^{8} -3.00000 q^{9} -6.89121 q^{10} +0.484291i q^{11} +5.65208i q^{12} -10.0249i q^{13} +1.56427 q^{14} -13.9056 q^{15} +7.70161 q^{16} -2.19758 q^{17} -2.57506i q^{18} -6.71186 q^{19} +26.1986i q^{20} +3.15650 q^{21} -0.415692 q^{22} +11.9565 q^{23} -10.7983 q^{24} -39.4556 q^{25} +8.60486 q^{26} -5.19615i q^{27} -5.94693i q^{28} +1.08392 q^{29} -11.9359i q^{30} +42.5045i q^{31} +31.5483i q^{32} -0.838817 q^{33} -1.88630i q^{34} +14.6310 q^{35} -9.78969 q^{36} +21.6619 q^{37} -5.76114i q^{38} +17.3636 q^{39} -50.0525 q^{40} -40.8070i q^{41} +2.70939i q^{42} -15.1894i q^{43} +1.58035i q^{44} -24.0853i q^{45} +10.2629i q^{46} -19.5302 q^{47} +13.3396i q^{48} +45.6788 q^{49} -33.8668i q^{50} -3.80632i q^{51} -32.7134i q^{52} +29.3759i q^{53} +4.46013 q^{54} -3.88810 q^{55} +11.3616 q^{56} -11.6253i q^{57} +0.930388i q^{58} +104.153 q^{59} -45.3773 q^{60} -109.511i q^{61} -36.4838 q^{62} +5.46722i q^{63} +3.72684 q^{64} +80.4838 q^{65} -0.720000i q^{66} +(55.3048 - 37.8203i) q^{67} -7.17121 q^{68} +20.7093i q^{69} +12.5586i q^{70} +110.740 q^{71} -18.7032i q^{72} -7.70418 q^{73} +18.5935i q^{74} -68.3391i q^{75} -21.9024 q^{76} +0.882575 q^{77} +14.9041i q^{78} +42.4445i q^{79} +61.8318i q^{80} +9.00000 q^{81} +35.0268 q^{82} -78.6551 q^{83} +10.3004 q^{84} -17.6431i q^{85} +13.0379 q^{86} +1.87741i q^{87} -3.01927 q^{88} -59.7970 q^{89} +20.6736 q^{90} -18.2694 q^{91} +39.0168 q^{92} -73.6199 q^{93} -16.7638i q^{94} -53.8857i q^{95} -54.6433 q^{96} +9.72666i q^{97} +39.2085i q^{98} -1.45287i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.858352i			0.429176i	0.976705	+	0.214588i	$0.0688409\pi$
$2$			0.858352i			0.429176i	−0.976705	+	0.214588i	$0.931159\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.26323			0.815808
$5$			8.02842i			1.60568i	0.596191	+	0.802842i	$0.296680\pi$
$5$			8.02842i			1.60568i	−0.596191	+	0.802842i	$0.703320\pi$
$6$	−1.48671			−0.247785
$7$		−	1.82241i		−	0.260344i	−0.991491	−	0.130172i	$-0.958447\pi$
$7$		−	1.82241i		−	0.260344i	0.991491	−	0.130172i	$-0.0415529\pi$
$8$			6.23441i			0.779301i
$9$	−3.00000			−0.333333
$10$	−6.89121			−0.689121
$11$			0.484291i			0.0440265i	0.999758	+	0.0220132i	$0.00700760\pi$
$11$			0.484291i			0.0440265i	−0.999758	+	0.0220132i	$0.992992\pi$
$12$			5.65208i			0.471007i
$13$		−	10.0249i		−	0.771143i	−0.922678	−	0.385571i	$-0.874004\pi$
$13$		−	10.0249i		−	0.771143i	0.922678	−	0.385571i	$-0.125996\pi$
$14$	1.56427			0.111733
$15$	−13.9056			−0.927042
$16$	7.70161			0.481350
$17$	−2.19758			−0.129269			−0.0646347	−	0.997909i	$-0.520588\pi$
$17$	−2.19758			−0.129269			−0.0646347	+	0.997909i	$0.520588\pi$
$18$		−	2.57506i		−	0.143059i
$19$	−6.71186			−0.353256			−0.176628	−	0.984278i	$-0.556519\pi$
$19$	−6.71186			−0.353256			−0.176628	+	0.984278i	$0.556519\pi$
$20$			26.1986i			1.30993i
$21$	3.15650			0.150309
$22$	−0.415692			−0.0188951
$23$	11.9565			0.519848			0.259924	−	0.965629i	$-0.416303\pi$
$23$	11.9565			0.519848			0.259924	+	0.965629i	$0.416303\pi$
$24$	−10.7983			−0.449930
$25$	−39.4556			−1.57822
$26$	8.60486			0.330956
$27$		−	5.19615i		−	0.192450i
$28$		−	5.94693i		−	0.212390i
$29$	1.08392			0.0373767			0.0186883	−	0.999825i	$-0.494051\pi$
$29$	1.08392			0.0373767			0.0186883	+	0.999825i	$0.494051\pi$
$30$		−	11.9359i		−	0.397864i
$31$			42.5045i			1.37111i	0.728020	+	0.685556i	$0.240441\pi$
$31$			42.5045i			1.37111i	−0.728020	+	0.685556i	$0.759559\pi$
$32$			31.5483i			0.985885i
$33$	−0.838817			−0.0254187
$34$		−	1.88630i		−	0.0554794i
$35$	14.6310			0.418030
$36$	−9.78969			−0.271936
$37$	21.6619			0.585457			0.292728	−	0.956196i	$-0.405437\pi$
$37$	21.6619			0.585457			0.292728	+	0.956196i	$0.405437\pi$
$38$		−	5.76114i		−	0.151609i
$39$	17.3636			0.445220
$40$	−50.0525			−1.25131
$41$		−	40.8070i		−	0.995292i	−0.867380	−	0.497646i	$-0.834198\pi$
$41$		−	40.8070i		−	0.995292i	0.867380	−	0.497646i	$-0.165802\pi$
$42$			2.70939i			0.0645092i
$43$		−	15.1894i		−	0.353243i	−0.984279	−	0.176621i	$-0.943483\pi$
$43$		−	15.1894i		−	0.353243i	0.984279	−	0.176621i	$-0.0565168\pi$
$44$			1.58035i			0.0359171i
$45$		−	24.0853i		−	0.535228i
$46$			10.2629i			0.223106i
$47$	−19.5302			−0.415535			−0.207768	−	0.978178i	$-0.566620\pi$
$47$	−19.5302			−0.415535			−0.207768	+	0.978178i	$0.566620\pi$
$48$			13.3396i			0.277908i
$49$	45.6788			0.932221
$50$		−	33.8668i		−	0.677336i
$51$		−	3.80632i		−	0.0746337i
$52$		−	32.7134i		−	0.629104i
$53$			29.3759i			0.554263i	0.960832	+	0.277132i	$0.0893838\pi$
$53$			29.3759i			0.554263i	−0.960832	+	0.277132i	$0.910616\pi$
$54$	4.46013			0.0825950
$55$	−3.88810			−0.0706926
$56$	11.3616			0.202886
$57$		−	11.6253i		−	0.203952i
$58$			0.930388i			0.0160412i
$59$	104.153			1.76530			0.882652	−	0.470027i	$-0.155756\pi$
$59$	104.153			1.76530			0.882652	+	0.470027i	$0.155756\pi$
$60$	−45.3773			−0.756289
$61$		−	109.511i		−	1.79526i	−0.440754	−	0.897628i	$-0.645289\pi$
$61$		−	109.511i		−	1.79526i	0.440754	−	0.897628i	$-0.354711\pi$
$62$	−36.4838			−0.588449
$63$			5.46722i			0.0867812i
$64$	3.72684			0.0582319
$65$	80.4838			1.23821
$66$		−	0.720000i		−	0.0109091i
$67$	55.3048	−	37.8203i	0.825445	−	0.564482i
$67$	55.3048	−	37.8203i	0.825445	−	0.564482i
$68$	−7.17121			−0.105459
$69$			20.7093i			0.300134i
$70$			12.5586i			0.179408i
$71$	110.740			1.55972			0.779858	−	0.625956i	$-0.215291\pi$
$71$	110.740			1.55972			0.779858	+	0.625956i	$0.215291\pi$
$72$		−	18.7032i		−	0.259767i
$73$	−7.70418			−0.105537			−0.0527683	−	0.998607i	$-0.516804\pi$
$73$	−7.70418			−0.105537			−0.0527683	+	0.998607i	$0.516804\pi$
$74$			18.5935i			0.251264i
$75$		−	68.3391i		−	0.911188i
$76$	−21.9024			−0.288189
$77$	0.882575			0.0114620
$78$			14.9041i			0.191078i
$79$			42.4445i			0.537273i	0.963242	+	0.268636i	$0.0865730\pi$
$79$			42.4445i			0.537273i	−0.963242	+	0.268636i	$0.913427\pi$
$80$			61.8318i			0.772897i
$81$	9.00000			0.111111
$82$	35.0268			0.427156
$83$	−78.6551			−0.947651			−0.473826	−	0.880619i	$-0.657127\pi$
$83$	−78.6551			−0.947651			−0.473826	+	0.880619i	$0.657127\pi$
$84$	10.3004			0.122624
$85$		−	17.6431i		−	0.207566i
$86$	13.0379			0.151603
$87$			1.87741i			0.0215794i
$88$	−3.01927			−0.0343099
$89$	−59.7970			−0.671876			−0.335938	−	0.941884i	$-0.609053\pi$
$89$	−59.7970			−0.671876			−0.335938	+	0.941884i	$0.609053\pi$
$90$	20.6736			0.229707
$91$	−18.2694			−0.200762
$92$	39.0168			0.424096
$93$	−73.6199			−0.791612
$94$		−	16.7638i		−	0.178338i
$95$		−	53.8857i		−	0.567218i
$96$	−54.6433			−0.569201
$97$			9.72666i			0.100275i	0.998742	+	0.0501374i	$0.0159659\pi$
$97$			9.72666i			0.100275i	−0.998742	+	0.0501374i	$0.984034\pi$
$98$			39.2085i			0.400087i
$99$		−	1.45287i		−	0.0146755i
$100$	−128.753			−1.28753
$101$			81.6063i			0.807983i	0.914763	+	0.403991i	$0.132377\pi$
$101$			81.6063i			0.807983i	−0.914763	+	0.403991i	$0.867623\pi$
$102$	3.26716			0.0320310
$103$	−40.2157			−0.390444			−0.195222	−	0.980759i	$-0.562543\pi$
$103$	−40.2157			−0.390444			−0.195222	+	0.980759i	$0.562543\pi$
$104$	62.4991			0.600953
$105$			25.3417i			0.241350i
$106$	−25.2149			−0.237876
$107$	−81.3778			−0.760541			−0.380270	−	0.924875i	$-0.624169\pi$
$107$	−81.3778			−0.760541			−0.380270	+	0.924875i	$0.624169\pi$
$108$		−	16.9562i		−	0.157002i
$109$		−	153.719i		−	1.41027i	−0.709073	−	0.705135i	$-0.750886\pi$
$109$		−	153.719i		−	1.41027i	0.709073	−	0.705135i	$-0.249114\pi$
$110$		−	3.33736i		−	0.0303396i
$111$			37.5195i			0.338014i
$112$		−	14.0355i		−	0.125317i
$113$		−	166.349i		−	1.47212i	−0.676917	−	0.736059i	$-0.736684\pi$
$113$		−	166.349i		−	1.47212i	0.676917	−	0.736059i	$-0.263316\pi$
$114$	9.97859			0.0875315
$115$			95.9918i			0.834711i
$116$	3.53709			0.0304922
$117$			30.0746i			0.257048i
$118$			89.3999i			0.757626i
$119$			4.00488i			0.0336545i
$120$		−	86.6935i		−	0.722445i
$121$	120.765			0.998062
$122$	93.9987			0.770481
$123$	70.6798			0.574632
$124$			138.702i			1.11856i
$125$		−	116.055i		−	0.928444i
$126$	−4.69280			−0.0372444
$127$	−157.450			−1.23977			−0.619883	−	0.784694i	$-0.712820\pi$
$127$	−157.450			−1.23977			−0.619883	+	0.784694i	$0.712820\pi$
$128$			129.392i			1.01088i
$129$	26.3089			0.203945
$130$			69.0834i			0.531411i
$131$	−161.155			−1.23019			−0.615095	−	0.788453i	$-0.710882\pi$
$131$	−161.155			−1.23019			−0.615095	+	0.788453i	$0.710882\pi$
$132$	−2.73725			−0.0207368
$133$			12.2317i			0.0919680i
$134$	32.4632	+	47.4710i	0.242262	+	0.354261i
$135$	41.7169			0.309014
$136$		−	13.7006i		−	0.100740i
$137$			164.030i			1.19730i	0.801012	+	0.598648i	$0.204295\pi$
$137$			164.030i			1.19730i	−0.801012	+	0.598648i	$0.795705\pi$
$138$	−17.7758			−0.128810
$139$			152.105i			1.09428i	0.837041	+	0.547140i	$0.184283\pi$
$139$			152.105i			1.09428i	−0.837041	+	0.547140i	$0.815717\pi$
$140$	47.7445			0.341032
$141$		−	33.8272i		−	0.239909i
$142$			95.0538i			0.669393i
$143$	4.85495			0.0339507
$144$	−23.1048			−0.160450
$145$			8.70219i			0.0600151i
$146$		−	6.61290i		−	0.0452938i
$147$			79.1181i			0.538218i
$148$	70.6878			0.477620
$149$	126.451			0.848663			0.424332	−	0.905507i	$-0.360509\pi$
$149$	126.451			0.848663			0.424332	+	0.905507i	$0.360509\pi$
$150$	58.6590			0.391060
$151$	145.917			0.966339			0.483169	−	0.875527i	$-0.339486\pi$
$151$	145.917			0.966339			0.483169	+	0.875527i	$0.339486\pi$
$152$		−	41.8445i		−	0.275293i
$153$	6.59274			0.0430898
$154$			0.757560i			0.00491922i
$155$	−341.244			−2.20157
$156$	56.6613			0.363214
$157$	135.904			0.865631			0.432815	−	0.901483i	$-0.357520\pi$
$157$	135.904			0.865631			0.432815	+	0.901483i	$0.357520\pi$
$158$	−36.4324			−0.230585
$159$	−50.8806			−0.320004
$160$	−253.283			−1.58302
$161$		−	21.7896i		−	0.135339i
$162$			7.72517i			0.0476862i
$163$	−227.905			−1.39819			−0.699095	−	0.715029i	$-0.746413\pi$
$163$	−227.905			−1.39819			−0.699095	+	0.715029i	$0.746413\pi$
$164$		−	133.163i		−	0.811967i
$165$		−	6.73438i		−	0.0408144i
$166$		−	67.5137i		−	0.406709i
$167$	−318.507			−1.90723			−0.953613	−	0.301036i	$-0.902668\pi$
$167$	−318.507			−1.90723			−0.953613	+	0.301036i	$0.902668\pi$
$168$			19.6789i			0.117136i
$169$	68.5023			0.405339
$170$	15.1440			0.0890823
$171$	20.1356			0.117752
$172$		−	49.5666i		−	0.288178i
$173$	−186.601			−1.07862			−0.539310	−	0.842107i	$-0.681315\pi$
$173$	−186.601			−1.07862			−0.539310	+	0.842107i	$0.681315\pi$
$174$	−1.61148			−0.00926137
$175$			71.9041i			0.410880i
$176$			3.72982i			0.0211922i
$177$			180.398i			1.01920i
$178$		−	51.3269i		−	0.288353i
$179$		−	162.498i		−	0.907808i	−0.891051	−	0.453904i	$-0.850031\pi$
$179$		−	162.498i		−	0.907808i	0.891051	−	0.453904i	$-0.149969\pi$
$180$		−	78.5958i		−	0.436643i
$181$	−28.2924			−0.156311			−0.0781557	−	0.996941i	$-0.524903\pi$
$181$	−28.2924			−0.156311			−0.0781557	+	0.996941i	$0.524903\pi$
$182$		−	15.6815i		−	0.0861623i
$183$	189.678			1.03649
$184$			74.5417i			0.405118i
$185$			173.911i			0.940059i
$186$		−	63.1918i		−	0.339741i
$187$		−	1.06427i		−	0.00569128i
$188$	−63.7314			−0.338997
$189$	−9.46950			−0.0501032
$190$	46.2529			0.243436
$191$			9.47516i			0.0496082i	0.999692	+	0.0248041i	$0.00789619\pi$
$191$			9.47516i			0.0496082i	−0.999692	+	0.0248041i	$0.992104\pi$
$192$			6.45508i			0.0336202i
$193$	254.816			1.32029			0.660146	−	0.751137i	$-0.270494\pi$
$193$	254.816			1.32029			0.660146	+	0.751137i	$0.270494\pi$
$194$	−8.34890			−0.0430356
$195$			139.402i			0.714882i
$196$	149.061			0.760513
$197$		−	225.629i		−	1.14533i	−0.819791	−	0.572663i	$-0.805910\pi$
$197$		−	225.629i		−	1.14533i	0.819791	−	0.572663i	$-0.194090\pi$
$198$	1.24708			0.00629837
$199$	170.579			0.857180			0.428590	−	0.903499i	$-0.359010\pi$
$199$	170.579			0.857180			0.428590	+	0.903499i	$0.359010\pi$
$200$		−	245.982i		−	1.22991i
$201$	65.5067	+	95.7908i	0.325904	+	0.476571i
$202$	−70.0469			−0.346767
$203$		−	1.97535i		−	0.00973078i
$204$		−	12.4209i		−	0.0608868i
$205$	327.616			1.59813
$206$		−	34.5192i		−	0.167569i
$207$	−35.8695			−0.173283
$208$		−	77.2075i		−	0.371190i
$209$		−	3.25050i		−	0.0155526i
$210$	−21.7521			−0.103581
$211$	−216.886			−1.02789			−0.513947	−	0.857822i	$-0.671817\pi$
$211$	−216.886			−1.02789			−0.513947	+	0.857822i	$0.671817\pi$
$212$			95.8605i			0.452172i
$213$			191.807i			0.900503i
$214$		−	69.8508i		−	0.326406i
$215$	121.947			0.567196
$216$	32.3949			0.149977
$217$	77.4604			0.356961
$218$	131.945			0.605254
$219$		−	13.3440i		−	0.0609316i
$220$	−12.6878			−0.0576716
$221$			22.0304i			0.0996852i
$222$	−32.2050			−0.145067
$223$	274.408			1.23053			0.615264	−	0.788321i	$-0.289049\pi$
$223$	274.408			1.23053			0.615264	+	0.788321i	$0.289049\pi$
$224$	57.4939			0.256669
$225$	118.367			0.526074
$226$	142.786			0.631798
$227$	−199.016			−0.876723			−0.438361	−	0.898799i	$-0.644441\pi$
$227$	−199.016			−0.876723			−0.438361	+	0.898799i	$0.644441\pi$
$228$		−	37.9360i		−	0.166386i
$229$		−	336.853i		−	1.47098i	−0.677538	−	0.735488i	$-0.736953\pi$
$229$		−	336.853i		−	1.47098i	0.677538	−	0.735488i	$-0.263047\pi$
$230$	−82.3948			−0.358238
$231$			1.52867i			0.00661760i
$232$			6.75762i			0.0291277i
$233$		−	325.037i		−	1.39501i	−0.716581	−	0.697504i	$-0.754294\pi$
$233$		−	325.037i		−	1.39501i	0.716581	−	0.697504i	$-0.245706\pi$
$234$	−25.8146			−0.110319
$235$		−	156.796i		−	0.667218i
$236$	339.875			1.44015
$237$	−73.5161			−0.310195
$238$	−3.43760			−0.0144437
$239$			14.6583i			0.0613316i	0.999530	+	0.0306658i	$0.00976276\pi$
$239$			14.6583i			0.0613316i	−0.999530	+	0.0306658i	$0.990237\pi$
$240$	−107.096			−0.446232
$241$	87.0662			0.361271			0.180635	−	0.983550i	$-0.442185\pi$
$241$	87.0662			0.361271			0.180635	+	0.983550i	$0.442185\pi$
$242$			103.659i			0.428344i
$243$			15.5885i			0.0641500i
$244$		−	357.358i		−	1.46458i
$245$			366.729i			1.49685i
$246$			60.6681i			0.246618i
$247$			67.2855i			0.272411i
$248$	−264.990			−1.06851
$249$		−	136.235i		−	0.547127i
$250$	99.6165			0.398466
$251$		−	91.9893i		−	0.366491i	−0.983067	−	0.183246i	$-0.941340\pi$
$251$		−	91.9893i		−	0.366491i	0.983067	−	0.183246i	$-0.0586603\pi$
$252$			17.8408i			0.0707968i
$253$			5.79043i			0.0228871i
$254$		−	135.148i		−	0.532078i
$255$	30.5588			0.119838
$256$	−96.1568			−0.375612
$257$	−219.195			−0.852898			−0.426449	−	0.904512i	$-0.640236\pi$
$257$	−219.195			−0.852898			−0.426449	+	0.904512i	$0.640236\pi$
$258$			22.5823i			0.0875282i
$259$		−	39.4768i		−	0.152420i
$260$	262.637			1.01014
$261$	−3.25177			−0.0124589
$262$		−	138.328i		−	0.527968i
$263$	−7.87641			−0.0299483			−0.0149742	−	0.999888i	$-0.504767\pi$
$263$	−7.87641			−0.0299483			−0.0149742	+	0.999888i	$0.504767\pi$
$264$		−	5.22953i		−	0.0198088i
$265$	−235.843			−0.889972
$266$	−10.4991			−0.0394705
$267$		−	103.571i		−	0.387908i
$268$	180.472	−	123.416i	0.673405	−	0.460509i
$269$	−311.628			−1.15847			−0.579235	−	0.815161i	$-0.696648\pi$
$269$	−311.628			−1.15847			−0.579235	+	0.815161i	$0.696648\pi$
$270$			35.8078i			0.132621i
$271$			159.485i			0.588505i	0.955728	+	0.294252i	$0.0950706\pi$
$271$			159.485i			0.588505i	−0.955728	+	0.294252i	$0.904929\pi$
$272$	−16.9249			−0.0622239
$273$		−	31.6435i		−	0.115910i
$274$	−140.795			−0.513851
$275$		−	19.1080i		−	0.0694836i
$276$			67.5791i			0.244852i
$277$	−126.187			−0.455548			−0.227774	−	0.973714i	$-0.573145\pi$
$277$	−126.187			−0.455548			−0.227774	+	0.973714i	$0.573145\pi$
$278$	−130.560			−0.469639
$279$		−	127.513i		−	0.457038i
$280$			91.2159i			0.325771i
$281$		−	239.093i		−	0.850863i	−0.904991	−	0.425432i	$-0.860122\pi$
$281$		−	239.093i		−	0.850863i	0.904991	−	0.425432i	$-0.139878\pi$
$282$	29.0357			0.102963
$283$	−201.395			−0.711644			−0.355822	−	0.934554i	$-0.615799\pi$
$283$	−201.395			−0.711644			−0.355822	+	0.934554i	$0.615799\pi$
$284$	361.370			1.27243
$285$	93.3327			0.327483
$286$			4.16726i			0.0145708i
$287$	−74.3669			−0.259118
$288$		−	94.6450i		−	0.328628i
$289$	−284.171			−0.983289
$290$	−7.46955			−0.0257571
$291$	−16.8471			−0.0578937
$292$	−25.1405			−0.0860977
$293$	16.4586			0.0561727			0.0280863	−	0.999606i	$-0.491059\pi$
$293$	16.4586			0.0561727			0.0280863	+	0.999606i	$0.491059\pi$
$294$	−67.9112			−0.230990
$295$			836.184i			2.83452i
$296$			135.049i			0.456247i
$297$	2.51645			0.00847290
$298$			108.539i			0.364226i
$299$		−	119.862i		−	0.400877i
$300$		−	223.006i		−	0.743354i
$301$	−27.6813			−0.0919645
$302$			125.248i			0.414729i
$303$	−141.346			−0.466489
$304$	−51.6921			−0.170040
$305$	879.197			2.88261
$306$			5.65889i			0.0184931i
$307$	−393.009			−1.28016			−0.640080	−	0.768308i	$-0.721099\pi$
$307$	−393.009			−1.28016			−0.640080	+	0.768308i	$0.721099\pi$
$308$	2.88005			0.00935080
$309$		−	69.6556i		−	0.225423i
$310$		−	292.908i		−	0.944863i
$311$		−	52.7513i		−	0.169618i	−0.996397	−	0.0848092i	$-0.972972\pi$
$311$		−	52.7513i		−	0.169618i	0.996397	−	0.0848092i	$-0.0270281\pi$
$312$			108.252i			0.346960i
$313$		−	238.740i		−	0.762747i	−0.924421	−	0.381373i	$-0.875451\pi$
$313$		−	238.740i		−	0.762747i	0.924421	−	0.381373i	$-0.124549\pi$
$314$			116.654i			0.371508i
$315$	−43.8931			−0.139343
$316$			138.506i			0.438311i
$317$	−99.9853			−0.315411			−0.157706	−	0.987486i	$-0.550410\pi$
$317$	−99.9853			−0.315411			−0.157706	+	0.987486i	$0.550410\pi$
$318$		−	43.6735i		−	0.137338i
$319$			0.524935i			0.00164556i
$320$			29.9207i			0.0935021i
$321$		−	140.951i		−	0.439098i
$322$	18.7031			0.0580843
$323$	14.7499			0.0456652
$324$	29.3691			0.0906453
$325$			395.536i			1.21704i
$326$		−	195.623i		−	0.600070i
$327$	266.250			0.814220
$328$	254.407			0.775633
$329$			35.5919i			0.108182i
$330$	5.78047			0.0175166
$331$			491.470i			1.48480i	0.669955	+	0.742402i	$0.266314\pi$
$331$			491.470i			1.48480i	−0.669955	+	0.742402i	$0.733686\pi$
$332$	−256.670			−0.773101
$333$	−64.9857			−0.195152
$334$		−	273.391i		−	0.818536i
$335$	303.638	+	444.010i	0.906381	+	1.32540i
$336$	24.3101			0.0723515
$337$			385.089i			1.14270i	0.820707	+	0.571349i	$0.193580\pi$
$337$			385.089i			1.14270i	−0.820707	+	0.571349i	$0.806420\pi$
$338$			58.7991i			0.173962i
$339$	288.126			0.849928
$340$		−	57.5735i		−	0.169334i
$341$	−20.5846			−0.0603653
$342$			17.2834i			0.0505363i
$343$		−	172.543i		−	0.503042i
$344$	94.6972			0.275283
$345$	−166.263			−0.481921
$346$		−	160.170i		−	0.462918i
$347$			422.486i			1.21754i	0.793347	+	0.608770i	$0.208337\pi$
$347$			422.486i			1.21754i	−0.793347	+	0.608770i	$0.791663\pi$
$348$			6.12642i			0.0176047i
$349$	159.657			0.457469			0.228734	−	0.973489i	$-0.426541\pi$
$349$	159.657			0.457469			0.228734	+	0.973489i	$0.426541\pi$
$350$	−61.7190			−0.176340
$351$	−52.0907			−0.148407
$352$	−15.2786			−0.0434051
$353$		−	406.964i		−	1.15287i	−0.817142	−	0.576437i	$-0.804443\pi$
$353$		−	406.964i		−	1.15287i	0.817142	−	0.576437i	$-0.195557\pi$
$354$	−154.845			−0.437416
$355$			889.067i			2.50441i
$356$	−195.131			−0.548122
$357$	−6.93666			−0.0194304
$358$	139.480			0.389609
$359$	−252.187			−0.702470			−0.351235	−	0.936287i	$-0.614238\pi$
$359$	−252.187			−0.702470			−0.351235	+	0.936287i	$0.614238\pi$
$360$	150.157			0.417104
$361$	−315.951			−0.875210
$362$		−	24.2848i		−	0.0670851i
$363$			209.172i			0.576231i
$364$	−59.6171			−0.163783
$365$		−	61.8524i		−	0.169459i
$366$			162.810i			0.444837i
$367$			330.938i			0.901738i	0.892590	+	0.450869i	$0.148886\pi$
$367$			330.938i			0.901738i	−0.892590	+	0.450869i	$0.851114\pi$
$368$	92.0842			0.250229
$369$			122.421i			0.331764i
$370$	−149.277			−0.403451
$371$	53.5349			0.144299
$372$	−240.239			−0.645803
$373$		−	661.975i		−	1.77473i	−0.461066	−	0.887366i	$-0.652533\pi$
$373$		−	661.975i		−	1.77473i	0.461066	−	0.887366i	$-0.347467\pi$
$374$	0.913518			0.00244256
$375$	201.014			0.536037
$376$		−	121.759i		−	0.323827i
$377$		−	10.8662i		−	0.0288227i
$378$		−	8.12816i		−	0.0215031i
$379$		−	435.877i		−	1.15007i	−0.818128	−	0.575036i	$-0.804988\pi$
$379$		−	435.877i		−	1.15007i	0.818128	−	0.575036i	$-0.195012\pi$
$380$		−	175.841i		−	0.462741i
$381$		−	272.712i		−	0.715779i
$382$	−8.13302			−0.0212906
$383$			205.665i			0.536984i	0.963282	+	0.268492i	$0.0865253\pi$
$383$			205.665i			0.536984i	−0.963282	+	0.268492i	$0.913475\pi$
$384$	−224.114			−0.583630
$385$			7.08569i			0.0184044i
$386$			218.722i			0.566638i
$387$			45.5683i			0.117748i
$388$			31.7403i			0.0818050i
$389$	539.491			1.38687			0.693433	−	0.720521i	$-0.256097\pi$
$389$	539.491			1.38687			0.693433	+	0.720521i	$0.256097\pi$
$390$	−119.656			−0.306810
$391$	−26.2754			−0.0672004
$392$			284.781i			0.726481i
$393$		−	279.129i		−	0.710251i
$394$	193.669			0.491546
$395$	−340.763			−0.862690
$396$		−	4.74106i		−	0.0119724i
$397$	−360.077			−0.906995			−0.453498	−	0.891257i	$-0.649824\pi$
$397$	−360.077			−0.906995			−0.453498	+	0.891257i	$0.649824\pi$
$398$			146.417i			0.367881i
$399$	−21.1860			−0.0530977
$400$	−303.871			−0.759678
$401$			612.829i			1.52825i	0.645068	+	0.764126i	$0.276829\pi$
$401$			612.829i			1.52825i	−0.645068	+	0.764126i	$0.723171\pi$
$402$	−82.2222	+	56.2278i	−0.204533	+	0.139870i
$403$	426.101			1.05732
$404$			266.300i			0.659159i
$405$			72.2558i			0.178409i
$406$	1.69554			0.00417622
$407$			10.4907i			0.0257756i
$408$	23.7302			0.0581622
$409$			346.344i			0.846806i	0.905941	+	0.423403i	$0.139165\pi$
$409$			346.344i			0.846806i	−0.905941	+	0.423403i	$0.860835\pi$
$410$			281.210i			0.685877i
$411$	−284.108			−0.691259
$412$	−131.233			−0.318527
$413$		−	189.809i		−	0.459586i
$414$		−	30.7886i		−	0.0743687i
$415$		−	631.476i		−	1.52163i
$416$	316.268			0.760258
$417$	−263.453			−0.631782
$418$	2.79007			0.00667481
$419$	−409.264			−0.976764			−0.488382	−	0.872630i	$-0.662413\pi$
$419$	−409.264			−0.976764			−0.488382	+	0.872630i	$0.662413\pi$
$420$			82.6959i			0.196895i
$421$	−392.331			−0.931903			−0.465952	−	0.884810i	$-0.654288\pi$
$421$	−392.331			−0.931903			−0.465952	+	0.884810i	$0.654288\pi$
$422$		−	186.164i		−	0.441147i
$423$	58.5905			0.138512
$424$	−183.142			−0.431938
$425$	86.7068			0.204016
$426$	−164.638			−0.386474
$427$	−199.573			−0.467383
$428$	−265.555			−0.620455
$429$			8.40902i			0.0196014i
$430$			104.674i			0.243427i
$431$	86.3386			0.200322			0.100161	−	0.994971i	$-0.468064\pi$
$431$	86.3386			0.200322			0.100161	+	0.994971i	$0.468064\pi$
$432$		−	40.0187i		−	0.0926359i
$433$		−	228.984i		−	0.528831i	−0.964409	−	0.264415i	$-0.914821\pi$
$433$		−	228.984i		−	0.528831i	0.964409	−	0.264415i	$-0.0851790\pi$
$434$			66.4883i			0.153199i
$435$	−15.0726			−0.0346498
$436$		−	501.622i		−	1.15051i
$437$	−80.2504			−0.183639
$438$	11.4539			0.0261504
$439$	639.389			1.45647			0.728233	−	0.685329i	$-0.240342\pi$
$439$	639.389			1.45647			0.728233	+	0.685329i	$0.240342\pi$
$440$		−	24.2400i		−	0.0550909i
$441$	−137.037			−0.310740
$442$	−18.9099			−0.0427825
$443$			2.41341i			0.00544787i	0.999996	+	0.00272394i	$0.000867057\pi$
$443$			2.41341i			0.00544787i	−0.999996	+	0.00272394i	$0.999133\pi$
$444$			122.435i			0.275754i
$445$		−	480.075i		−	1.07882i
$446$			235.539i			0.528113i
$447$			219.019i			0.489976i
$448$		−	6.79182i		−	0.0151603i
$449$	887.102			1.97573			0.987864	−	0.155320i	$-0.0496408\pi$
$449$	887.102			1.97573			0.987864	+	0.155320i	$0.0496408\pi$
$450$			101.600i			0.225779i
$451$	19.7625			0.0438192
$452$		−	542.837i		−	1.20097i
$453$			252.736i			0.557916i
$454$		−	170.826i		−	0.376268i
$455$		−	146.674i		−	0.322361i
$456$	72.4768			0.158940
$457$	203.749			0.445841			0.222921	−	0.974837i	$-0.428441\pi$
$457$	203.749			0.445841			0.222921	+	0.974837i	$0.428441\pi$
$458$	289.139			0.631307
$459$			11.4190i			0.0248779i
$460$			313.243i			0.680964i
$461$	−503.081			−1.09128			−0.545641	−	0.838019i	$-0.683714\pi$
$461$	−503.081			−1.09128			−0.545641	+	0.838019i	$0.683714\pi$
$462$	−1.31213			−0.00284011
$463$		−	585.201i		−	1.26393i	−0.774996	−	0.631966i	$-0.782248\pi$
$463$		−	585.201i		−	1.26393i	0.774996	−	0.631966i	$-0.217752\pi$
$464$	8.34795			0.0179913
$465$		−	591.052i		−	1.27108i
$466$	278.996			0.598704
$467$	83.3835			0.178551			0.0892757	−	0.996007i	$-0.471545\pi$
$467$	83.3835			0.178551			0.0892757	+	0.996007i	$0.471545\pi$
$468$			98.1403i			0.209701i
$469$	−68.9240	−	100.788i	−0.146959	−	0.214899i
$470$	134.586			0.286354
$471$			235.393i			0.499772i
$472$			649.332i			1.37570i
$473$	7.35611			0.0155520
$474$		−	63.1027i		−	0.133128i
$475$	264.820			0.557517
$476$			13.0689i			0.0274556i
$477$		−	88.1278i		−	0.184754i
$478$	−12.5820			−0.0263221
$479$	292.164			0.609947			0.304973	−	0.952361i	$-0.401352\pi$
$479$	292.164			0.609947			0.304973	+	0.952361i	$0.401352\pi$
$480$		−	438.700i		−	0.913958i
$481$		−	217.157i		−	0.451471i
$482$			74.7335i			0.155049i
$483$	37.7407			0.0781380
$484$	394.086			0.814227
$485$	−78.0897			−0.161010
$486$	−13.3804			−0.0275317
$487$			125.844i			0.258407i	0.991618	+	0.129203i	$0.0412420\pi$
$487$			125.844i			0.258407i	−0.991618	+	0.129203i	$0.958758\pi$
$488$	682.734			1.39905
$489$		−	394.743i		−	0.807245i
$490$	−314.783			−0.642414
$491$	558.781			1.13805			0.569023	−	0.822322i	$-0.307322\pi$
$491$	558.781			1.13805			0.569023	+	0.822322i	$0.307322\pi$
$492$	230.644			0.468790
$493$	−2.38201			−0.00483166
$494$	−57.7546			−0.116912
$495$	11.6643			0.0235642
$496$			327.353i			0.659986i
$497$		−	201.813i		−	0.406062i
$498$	116.937			0.234814
$499$		−	362.983i		−	0.727421i	−0.931512	−	0.363710i	$-0.881510\pi$
$499$		−	362.983i		−	0.727421i	0.931512	−	0.363710i	$-0.118490\pi$
$500$		−	378.716i		−	0.757432i
$501$		−	551.670i		−	1.10114i
$502$	78.9592			0.157289
$503$		−	480.564i		−	0.955396i	−0.878524	−	0.477698i	$-0.841471\pi$
$503$		−	480.564i		−	0.955396i	0.878524	−	0.477698i	$-0.158529\pi$
$504$	−34.0849			−0.0676287
$505$	−655.170			−1.29737
$506$	−4.97022			−0.00982258
$507$			118.649i			0.234022i
$508$	−513.797			−1.01141
$509$	−140.767			−0.276556			−0.138278	−	0.990393i	$-0.544157\pi$
$509$	−140.767			−0.276556			−0.138278	+	0.990393i	$0.544157\pi$
$510$			26.2302i			0.0514317i
$511$			14.0401i			0.0274758i
$512$			435.033i			0.849673i
$513$			34.8759i			0.0679841i
$514$		−	188.146i		−	0.366043i
$515$		−	322.869i		−	0.626929i
$516$	85.8520			0.166380
$517$		−	9.45828i		−	0.0182946i
$518$	33.8850			0.0654150
$519$		−	323.203i		−	0.622742i
$520$			501.769i			0.964940i
$521$			54.1161i			0.103870i	0.998650	+	0.0519349i	$0.0165388\pi$
$521$			54.1161i			0.103870i	−0.998650	+	0.0519349i	$0.983461\pi$
$522$		−	2.79116i		−	0.00534706i
$523$	146.612			0.280330			0.140165	−	0.990128i	$-0.455237\pi$
$523$	146.612			0.280330			0.140165	+	0.990128i	$0.455237\pi$
$524$	−525.886			−1.00360
$525$	−124.542			−0.237222
$526$		−	6.76073i		−	0.0128531i
$527$		−	93.4070i		−	0.177243i
$528$	−6.46024			−0.0122353
$529$	−386.042			−0.729759
$530$		−	202.436i		−	0.381955i
$531$	−312.459			−0.588435
$532$			39.9150i			0.0750282i
$533$	−409.084			−0.767512
$534$	88.9008			0.166481
$535$		−	653.336i		−	1.22119i
$536$	235.787	+	344.793i	0.439902	+	0.643270i
$537$	281.454			0.524123
$538$		−	267.487i		−	0.497187i
$539$			22.1219i			0.0410424i
$540$	136.132			0.252096
$541$		−	953.817i		−	1.76306i	−0.472125	−	0.881531i	$-0.656513\pi$
$541$		−	953.817i		−	1.76306i	0.472125	−	0.881531i	$-0.343487\pi$
$542$	−136.894			−0.252572
$543$		−	49.0038i		−	0.0902464i
$544$		−	69.3300i		−	0.127445i
$545$	1234.12			2.26445
$546$	27.1612			0.0497458
$547$			880.448i			1.60960i	0.593549	+	0.804798i	$0.297726\pi$
$547$			880.448i			1.60960i	−0.593549	+	0.804798i	$0.702274\pi$
$548$			535.266i			0.976764i
$549$			328.532i			0.598419i
$550$	16.4014			0.0298207
$551$	−7.27515			−0.0132035
$552$	−129.110			−0.233895
$553$	77.3512			0.139876
$554$		−	108.313i		−	0.195510i
$555$	−301.223			−0.542743
$556$			496.353i			0.892722i
$557$	243.499			0.437162			0.218581	−	0.975819i	$-0.429857\pi$
$557$	243.499			0.437162			0.218581	+	0.975819i	$0.429857\pi$
$558$	109.451			0.196150
$559$	−152.272			−0.272401
$560$	112.683			0.201219
$561$	1.84337			0.00328586
$562$	205.226			0.365170
$563$		−	241.358i		−	0.428700i	−0.976757	−	0.214350i	$-0.931237\pi$
$563$		−	241.358i		−	0.428700i	0.976757	−	0.214350i	$-0.0687633\pi$
$564$		−	110.386i		−	0.195720i
$565$	1335.52			2.36376
$566$		−	172.868i		−	0.305421i
$567$		−	16.4017i		−	0.0289271i
$568$			690.398i			1.21549i
$569$	556.193			0.977492			0.488746	−	0.872426i	$-0.337454\pi$
$569$	556.193			0.977492			0.488746	+	0.872426i	$0.337454\pi$
$570$			80.1124i			0.140548i
$571$	−385.003			−0.674262			−0.337131	−	0.941458i	$-0.609456\pi$
$571$	−385.003			−0.674262			−0.337131	+	0.941458i	$0.609456\pi$
$572$	15.8428			0.0276973
$573$	−16.4115			−0.0286413
$574$		−	63.8330i		−	0.111207i
$575$	−471.750			−0.820435
$576$	−11.1805			−0.0194106
$577$			282.772i			0.490072i	0.969514	+	0.245036i	$0.0787999\pi$
$577$			282.772i			0.490072i	−0.969514	+	0.245036i	$0.921200\pi$
$578$		−	243.918i		−	0.422004i
$579$			441.355i			0.762271i
$580$			28.3973i			0.0489608i
$581$			143.341i			0.246715i
$582$		−	14.4607i		−	0.0248466i
$583$	−14.2265			−0.0244023
$584$		−	48.0310i		−	0.0822449i
$585$	−241.451			−0.412737
$586$			14.1273i			0.0241080i
$587$			1042.24i			1.77554i	0.460290	+	0.887769i	$0.347745\pi$
$587$			1042.24i			1.77554i	−0.460290	+	0.887769i	$0.652255\pi$
$588$			258.181i			0.439083i
$589$		−	285.284i		−	0.484354i
$590$	−717.740			−1.21651
$591$	390.801			0.661254
$592$	166.831			0.281810
$593$			185.863i			0.313429i	0.987644	+	0.156714i	$0.0500902\pi$
$593$			185.863i			0.313429i	−0.987644	+	0.156714i	$0.949910\pi$
$594$			2.16000i			0.00363637i
$595$	−32.1529			−0.0540385
$596$	412.638			0.692346
$597$			295.451i			0.494893i
$598$	102.884			0.172047
$599$		−	921.879i		−	1.53903i	−0.638629	−	0.769515i	$-0.720498\pi$
$599$		−	921.879i		−	1.53903i	0.638629	−	0.769515i	$-0.279502\pi$
$600$	426.054			0.710090
$601$	−657.867			−1.09462			−0.547310	−	0.836930i	$-0.684348\pi$
$601$	−657.867			−1.09462			−0.547310	+	0.836930i	$0.684348\pi$
$602$		−	23.7603i		−	0.0394690i
$603$	−165.914	+	113.461i	−0.275148	+	0.188161i
$604$	476.161			0.788347
$605$			969.556i			1.60257i
$606$		−	121.325i		−	0.200206i
$607$	591.641			0.974697			0.487348	−	0.873208i	$-0.337964\pi$
$607$	591.641			0.974697			0.487348	+	0.873208i	$0.337964\pi$
$608$		−	211.748i		−	0.348270i
$609$	3.42140			0.00561807
$610$			754.661i			1.23715i
$611$			195.787i			0.320437i
$612$	21.5136			0.0351530
$613$	654.685			1.06800			0.534000	−	0.845484i	$-0.320688\pi$
$613$	654.685			1.06800			0.534000	+	0.845484i	$0.320688\pi$
$614$		−	337.340i		−	0.549414i
$615$			567.447i			0.922678i
$616$			5.50234i			0.00893236i
$617$	−885.383			−1.43498			−0.717490	−	0.696569i	$-0.754709\pi$
$617$	−885.383			−1.43498			−0.717490	+	0.696569i	$0.754709\pi$
$618$	59.7891			0.0967461
$619$	−214.765			−0.346954			−0.173477	−	0.984838i	$-0.555500\pi$
$619$	−214.765			−0.346954			−0.173477	+	0.984838i	$0.555500\pi$
$620$	−1113.56			−1.79606
$621$		−	62.1278i		−	0.100045i
$622$	45.2792			0.0727962
$623$			108.974i			0.174919i
$624$	133.727			0.214307
$625$	−54.6468			−0.0874350
$626$	204.923			0.327353
$627$	5.63003			0.00897931
$628$	443.486			0.706188
$629$	−47.6038			−0.0756817
$630$		−	37.6758i		−	0.0598028i
$631$		−	985.057i		−	1.56110i	−0.625091	−	0.780552i	$-0.714938\pi$
$631$		−	985.057i		−	1.56110i	0.625091	−	0.780552i	$-0.285062\pi$
$632$	−264.617			−0.418697
$633$		−	375.657i		−	0.593455i
$634$		−	85.8226i		−	0.135367i
$635$		−	1264.08i		−	1.99067i
$636$	−166.035			−0.261062
$637$		−	457.924i		−	0.718876i
$638$	−0.450579			−0.000706236
$639$	−332.220			−0.519906
$640$	−1038.82			−1.62315
$641$			360.413i			0.562267i	0.959669	+	0.281134i	$0.0907104\pi$
$641$			360.413i			0.562267i	−0.959669	+	0.281134i	$0.909290\pi$
$642$	120.985			0.188450
$643$	1081.75			1.68234			0.841172	−	0.540768i	$-0.181866\pi$
$643$	1081.75			1.68234			0.841172	+	0.540768i	$0.181866\pi$
$644$		−	71.1044i		−	0.110411i
$645$			211.219i			0.327471i
$646$			12.6606i			0.0195984i
$647$		−	72.9948i		−	0.112820i	−0.998408	−	0.0564102i	$-0.982035\pi$
$647$		−	72.9948i		−	0.112820i	0.998408	−	0.0564102i	$-0.0179655\pi$
$648$			56.1097i			0.0865890i
$649$			50.4404i			0.0777201i
$650$	−339.510			−0.522322
$651$			134.165i			0.206091i
$652$	−743.707			−1.14065
$653$		−	391.601i		−	0.599695i	−0.953987	−	0.299848i	$-0.903064\pi$
$653$		−	391.601i		−	0.599695i	0.953987	−	0.299848i	$-0.0969359\pi$
$654$			228.536i			0.349444i
$655$		−	1293.82i		−	1.97530i
$656$		−	314.279i		−	0.479084i
$657$	23.1125			0.0351789
$658$	−30.5504			−0.0464291
$659$	−1137.91			−1.72673			−0.863363	−	0.504583i	$-0.831646\pi$
$659$	−1137.91			−1.72673			−0.863363	+	0.504583i	$0.831646\pi$
$660$		−	21.9758i		−	0.0332967i
$661$			1133.56i			1.71492i	0.514553	+	0.857459i	$0.327958\pi$
$661$			1133.56i			1.71492i	−0.514553	+	0.857459i	$0.672042\pi$
$662$	−421.854			−0.637242
$663$	−38.1578			−0.0575533
$664$		−	490.368i		−	0.738506i
$665$	−98.2016			−0.147672
$666$		−	55.7806i		−	0.0837547i
$667$	12.9599			0.0194302
$668$	−1039.36			−1.55593
$669$			475.288i			0.710446i
$670$	−381.117	+	260.628i	−0.568832	+	0.388997i
$671$	53.0350			0.0790388
$672$			99.5823i			0.148188i
$673$			1145.47i			1.70203i	0.525141	+	0.851015i	$0.324013\pi$
$673$			1145.47i			1.70203i	−0.525141	+	0.851015i	$0.675987\pi$
$674$	−330.542			−0.490418
$675$			205.017i			0.303729i
$676$	223.539			0.330679
$677$		−	662.472i		−	0.978541i	−0.872132	−	0.489270i	$-0.837263\pi$
$677$		−	662.472i		−	0.978541i	0.872132	−	0.489270i	$-0.162737\pi$
$678$			247.313i			0.364769i
$679$	17.7259			0.0261059
$680$	109.994			0.161756
$681$		−	344.706i		−	0.506176i
$682$		−	17.6688i		−	0.0259073i
$683$			1073.18i			1.57127i	0.618691	+	0.785634i	$0.287663\pi$
$683$			1073.18i			1.57127i	−0.618691	+	0.785634i	$0.712337\pi$
$684$	65.7071			0.0960630
$685$	−1316.90			−1.92248
$686$	148.103			0.215893
$687$	583.447			0.849268
$688$		−	116.983i		−	0.170034i
$689$	294.490			0.427416
$690$		−	142.712i		−	0.206829i
$691$	996.055			1.44147			0.720734	−	0.693211i	$-0.243805\pi$
$691$	996.055			1.44147			0.720734	+	0.693211i	$0.243805\pi$
$692$	−608.923			−0.879947
$693$	−2.64773			−0.00382067
$694$	−362.642			−0.522539
$695$	−1221.16			−1.75707
$696$	−11.7045			−0.0168169
$697$			89.6766i			0.128661i
$698$			137.042i			0.196335i
$699$	562.980			0.805408
$700$			234.640i			0.335199i
$701$		−	149.187i		−	0.212820i	−0.994322	−	0.106410i	$-0.966064\pi$
$701$		−	149.187i		−	0.212820i	0.994322	−	0.106410i	$-0.0339356\pi$
$702$		−	44.7122i		−	0.0636925i
$703$	−145.392			−0.206816
$704$			1.80488i			0.00256375i
$705$	271.579			0.385219
$706$	349.319			0.494786
$707$	148.720			0.210353
$708$			588.681i			0.831470i
$709$	1282.28			1.80858			0.904290	−	0.426918i	$-0.140401\pi$
$709$	1282.28			1.80858			0.904290	+	0.426918i	$0.140401\pi$
$710$	−763.132			−1.07483
$711$		−	127.334i		−	0.179091i
$712$		−	372.799i		−	0.523594i
$713$			508.205i			0.712769i
$714$		−	5.95410i		−	0.00833907i
$715$			38.9776i			0.0545141i
$716$		−	530.267i		−	0.740597i
$717$	−25.3889			−0.0354098
$718$		−	216.465i		−	0.301483i
$719$	−203.704			−0.283315			−0.141658	−	0.989916i	$-0.545243\pi$
$719$	−203.704			−0.283315			−0.141658	+	0.989916i	$0.545243\pi$
$720$		−	185.495i		−	0.257632i
$721$			73.2893i			0.101650i
$722$		−	271.197i		−	0.375619i
$723$			150.803i			0.208580i
$724$	−92.3245			−0.127520
$725$	−42.7668			−0.0589887
$726$	−179.543			−0.247305
$727$			1288.60i			1.77249i	0.463213	+	0.886247i	$0.346696\pi$
$727$			1288.60i			1.77249i	−0.463213	+	0.886247i	$0.653304\pi$
$728$		−	113.899i		−	0.156454i
$729$	−27.0000			−0.0370370
$730$	53.0911			0.0727276
$731$			33.3800i			0.0456635i
$732$	618.963			0.845578
$733$		−	234.758i		−	0.320271i	−0.987095	−	0.160135i	$-0.948807\pi$
$733$		−	234.758i		−	0.320271i	0.987095	−	0.160135i	$-0.0511931\pi$
$734$	−284.061			−0.387004
$735$	−635.193			−0.864209
$736$			377.207i			0.512510i
$737$	18.3161	+	26.7836i	0.0248522	+	0.0363414i
$738$	−105.080			−0.142385
$739$			314.604i			0.425716i	0.977083	+	0.212858i	$0.0682772\pi$
$739$			314.604i			0.425716i	−0.977083	+	0.212858i	$0.931723\pi$
$740$			567.512i			0.766908i
$741$	−116.542			−0.157276
$742$			45.9518i			0.0619296i
$743$	1151.64			1.54998			0.774992	−	0.631970i	$-0.217754\pi$
$743$	1151.64			1.54998			0.774992	+	0.631970i	$0.217754\pi$
$744$		−	458.977i		−	0.616904i
$745$			1015.20i			1.36269i
$746$	568.208			0.761672
$747$	235.965			0.315884
$748$		−	3.47296i		−	0.00464299i
$749$			148.303i			0.198002i
$750$			172.541i			0.230054i
$751$	−1418.44			−1.88873			−0.944367	−	0.328892i	$-0.893325\pi$
$751$	−1418.44			−1.88873			−0.944367	+	0.328892i	$0.893325\pi$
$752$	−150.414			−0.200018
$753$	159.330			0.211594
$754$	9.32701			0.0123700
$755$			1171.48i			1.55164i
$756$	−30.9012			−0.0408746
$757$			933.164i			1.23271i	0.787467	+	0.616357i	$0.211392\pi$
$757$			933.164i			1.23271i	−0.787467	+	0.616357i	$0.788608\pi$
$758$	374.136			0.493583
$759$	−10.0293			−0.0132138
$760$	335.945			0.442034
$761$	547.932			0.720016			0.360008	−	0.932949i	$-0.382774\pi$
$761$	547.932			0.720016			0.360008	+	0.932949i	$0.382774\pi$
$762$	234.083			0.307195
$763$	−280.139			−0.367155
$764$			30.9196i			0.0404707i
$765$			52.9293i			0.0691887i
$766$	−176.533			−0.230461
$767$		−	1044.12i		−	1.36130i
$768$		−	166.548i		−	0.216860i
$769$			1154.35i			1.50111i	0.660807	+	0.750556i	$0.270214\pi$
$769$			1154.35i			1.50111i	−0.660807	+	0.750556i	$0.729786\pi$
$770$	−6.08202			−0.00789872
$771$		−	379.656i		−	0.492421i
$772$	831.525			1.07710
$773$	1283.57			1.66050			0.830252	−	0.557389i	$-0.188197\pi$
$773$	1283.57			1.66050			0.830252	+	0.557389i	$0.188197\pi$
$774$	−39.1137			−0.0505344
$775$		−	1677.04i		−	2.16392i
$776$	−60.6400			−0.0781443
$777$	68.3758			0.0879997
$778$			463.073i			0.595210i
$779$			273.891i			0.351593i
$780$			454.901i			0.583206i
$781$			53.6304i			0.0686688i
$782$		−	22.5535i		−	0.0288408i
$783$		−	5.63223i		−	0.00719314i
$784$	351.800			0.448725
$785$			1091.09i			1.38993i
$786$	239.591			0.304823
$787$			765.804i			0.973068i	0.873662	+	0.486534i	$0.161739\pi$
$787$			765.804i			0.973068i	−0.873662	+	0.486534i	$0.838261\pi$
$788$		−	736.280i		−	0.934366i
$789$		−	13.6423i		−	0.0172907i
$790$		−	292.494i		−	0.370246i
$791$	−303.156			−0.383257
$792$	9.05781			0.0114366
$793$	−1097.83			−1.38440
$794$		−	309.073i		−	0.389261i
$795$		−	408.491i		−	0.513825i
$796$	556.638			0.699295
$797$	1056.70			1.32584			0.662922	−	0.748688i	$-0.269316\pi$
$797$	1056.70			1.32584			0.662922	+	0.748688i	$0.269316\pi$
$798$		−	18.1850i		−	0.0227883i
$799$	42.9191			0.0537160
$800$		−	1244.76i		−	1.55595i
$801$	179.391			0.223959
$802$	−526.023			−0.655889
$803$		−	3.73107i		−	0.00464641i
$804$	213.764	+	312.587i	0.265875	+	0.388790i
$805$	174.936			0.217312
$806$			365.745i			0.453778i
$807$		−	539.756i		−	0.668842i
$808$	−508.767			−0.629662
$809$		−	1507.68i		−	1.86363i	−0.362935	−	0.931814i	$-0.618225\pi$
$809$		−	1507.68i		−	1.86363i	0.362935	−	0.931814i	$-0.381775\pi$
$810$	−62.0209			−0.0765691
$811$			1241.66i			1.53102i	0.643425	+	0.765509i	$0.277513\pi$
$811$			1241.66i			1.53102i	−0.643425	+	0.765509i	$0.722487\pi$
$812$		−	6.44602i		−	0.00793845i
$813$	−276.236			−0.339773
$814$	−9.00469			−0.0110623
$815$		−	1829.72i		−	2.24505i
$816$		−	29.3148i		−	0.0359250i
$817$			101.949i			0.124785i
$818$	−297.285			−0.363429
$819$	54.8081			0.0669207
$820$	1069.09			1.30376
$821$	244.688			0.298037			0.149018	−	0.988834i	$-0.452389\pi$
$821$	244.688			0.298037			0.149018	+	0.988834i	$0.452389\pi$
$822$		−	243.864i		−	0.296672i
$823$	616.466			0.749048			0.374524	−	0.927217i	$-0.377806\pi$
$823$	616.466			0.749048			0.374524	+	0.927217i	$0.377806\pi$
$824$		−	250.721i		−	0.304273i
$825$	33.0960			0.0401164
$826$	162.923			0.197243
$827$	−962.213			−1.16350			−0.581749	−	0.813368i	$-0.697631\pi$
$827$	−962.213			−1.16350			−0.581749	+	0.813368i	$0.697631\pi$
$828$	−117.050			−0.141365
$829$	−133.378			−0.160890			−0.0804450	−	0.996759i	$-0.525634\pi$
$829$	−133.378			−0.160890			−0.0804450	+	0.996759i	$0.525634\pi$
$830$	542.029			0.653047
$831$		−	218.562i		−	0.263011i
$832$		−	37.3611i		−	0.0449051i
$833$	−100.383			−0.120508
$834$		−	226.136i		−	0.271146i
$835$		−	2557.11i		−	3.06240i
$836$		−	10.6071i		−	0.0126879i
$837$	220.860			0.263871
$838$		−	351.293i		−	0.419204i
$839$	−575.860			−0.686365			−0.343183	−	0.939269i	$-0.611505\pi$
$839$	−575.860			−0.686365			−0.343183	+	0.939269i	$0.611505\pi$
$840$	−157.991			−0.188084
$841$	−839.825			−0.998603
$842$		−	336.758i		−	0.399951i
$843$	414.120			0.491246
$844$	−707.748			−0.838564
$845$			549.965i			0.650846i
$846$			50.2913i			0.0594459i
$847$		−	220.084i		−	0.259839i
$848$			226.242i			0.266795i
$849$		−	348.827i		−	0.410868i
$850$			74.4250i			0.0875588i
$851$	259.000			0.304348
$852$			625.911i			0.734637i
$853$	−178.625			−0.209408			−0.104704	−	0.994503i	$-0.533389\pi$
$853$	−178.625			−0.209408			−0.104704	+	0.994503i	$0.533389\pi$
$854$		−	171.304i		−	0.200590i
$855$			161.657i			0.189073i
$856$		−	507.343i		−	0.592690i
$857$			1266.31i			1.47761i	0.673918	+	0.738806i	$0.264610\pi$
$857$			1266.31i			1.47761i	−0.673918	+	0.738806i	$0.735390\pi$
$858$	−7.21790			−0.00841247
$859$	−116.665			−0.135815			−0.0679076	−	0.997692i	$-0.521632\pi$
$859$	−116.665			−0.135815			−0.0679076	+	0.997692i	$0.521632\pi$
$860$	397.942			0.462723
$861$		−	128.807i		−	0.149602i
$862$			74.1089i			0.0859733i
$863$	−820.416			−0.950656			−0.475328	−	0.879809i	$-0.657671\pi$
$863$	−820.416			−0.950656			−0.475328	+	0.879809i	$0.657671\pi$
$864$	163.930			0.189734
$865$		−	1498.11i		−	1.73192i
$866$	196.549			0.226962
$867$		−	492.198i		−	0.567702i
$868$	252.771			0.291211
$869$	−20.5555			−0.0236542
$870$		−	12.9376i		−	0.0148708i
$871$	−379.143	−	554.423i	−0.435297	−	0.636536i
$872$	958.350			1.09903
$873$		−	29.1800i		−	0.0334249i
$874$		−	68.8831i		−	0.0788136i
$875$	−211.500			−0.241715
$876$		−	43.5446i		−	0.0497085i
$877$	−157.796			−0.179927			−0.0899637	−	0.995945i	$-0.528675\pi$
$877$	−157.796			−0.179927			−0.0899637	+	0.995945i	$0.528675\pi$
$878$			548.821i			0.625081i
$879$			28.5071i			0.0324313i
$880$	−29.9446			−0.0340279
$881$	1255.19			1.42474			0.712368	−	0.701807i	$-0.247623\pi$
$881$	1255.19			1.42474			0.712368	+	0.701807i	$0.247623\pi$
$882$		−	117.626i		−	0.133362i
$883$		−	91.7520i		−	0.103909i	−0.998649	−	0.0519547i	$-0.983455\pi$
$883$		−	91.7520i		−	0.103909i	0.998649	−	0.0519547i	$-0.0165451\pi$
$884$			71.8904i			0.0813240i
$885$	−1448.31			−1.63651
$886$	−2.07155			−0.00233810
$887$	−953.087			−1.07451			−0.537253	−	0.843421i	$-0.680538\pi$
$887$	−953.087			−1.07451			−0.537253	+	0.843421i	$0.680538\pi$
$888$	−233.912			−0.263415
$889$			286.938i			0.322765i
$890$	412.074			0.463004
$891$			4.35862i			0.00489183i
$892$	895.456			1.00387
$893$	131.084			0.146790
$894$	−187.996			−0.210286
$895$	1304.60			1.45765
$896$	235.805			0.263175
$897$	207.607			0.231446
$898$			761.446i			0.847935i
$899$			46.0716i			0.0512476i
$900$	386.258			0.429176
$901$		−	64.5560i		−	0.0716493i
$902$			16.9632i			0.0188062i
$903$		−	47.9454i		−	0.0530957i
$904$	1037.09			1.14722
$905$		−	227.143i		−	0.250987i
$906$	−216.936			−0.239444
$907$	−161.062			−0.177577			−0.0887885	−	0.996051i	$-0.528300\pi$
$907$	−161.062			−0.177577			−0.0887885	+	0.996051i	$0.528300\pi$
$908$	−649.436			−0.715237
$909$		−	244.819i		−	0.269328i
$910$	125.898			0.138350
$911$	345.660			0.379429			0.189715	−	0.981839i	$-0.439244\pi$
$911$	345.660			0.379429			0.189715	+	0.981839i	$0.439244\pi$
$912$		−	89.5334i		−	0.0981726i
$913$		−	38.0920i		−	0.0417217i
$914$			174.889i			0.191344i
$915$			1522.81i			1.66428i
$916$		−	1099.23i		−	1.20003i
$917$			293.690i			0.320272i
$918$	−9.80149			−0.0106770
$919$			1647.79i			1.79302i	0.443020	+	0.896512i	$0.353907\pi$
$919$			1647.79i			1.79302i	−0.443020	+	0.896512i	$0.646093\pi$
$920$	−598.452			−0.650492
$921$		−	680.712i		−	0.739101i
$922$		−	431.821i		−	0.468353i
$923$		−	1110.15i		−	1.20276i
$924$			4.98839i			0.00539869i
$925$	−854.683			−0.923982
$926$	502.308			0.542449
$927$	120.647			0.130148
$928$			34.1960i			0.0368491i
$929$		−	850.797i		−	0.915821i	−0.888998	−	0.457910i	$-0.848598\pi$
$929$		−	850.797i		−	0.915821i	0.888998	−	0.457910i	$-0.151402\pi$
$930$	507.331			0.545517
$931$	−306.590			−0.329313
$932$		−	1060.67i		−	1.13806i
$933$	91.3680			0.0979293
$934$			71.5724i			0.0766300i
$935$	8.54440			0.00913840
$936$	−187.497			−0.200318
$937$		−	627.669i		−	0.669871i	−0.942241	−	0.334935i	$-0.891285\pi$
$937$		−	627.669i		−	0.669871i	0.942241	−	0.334935i	$-0.108715\pi$
$938$	86.5114	−	59.1610i	0.0922297	−	0.0630715i
$939$	413.509			0.440372
$940$		−	511.663i		−	0.544322i
$941$			248.878i			0.264482i	0.991218	+	0.132241i	$0.0422173\pi$
$941$			248.878i			0.264482i	−0.991218	+	0.132241i	$0.957783\pi$
$942$	−202.050			−0.214490
$943$		−	487.908i		−	0.517400i
$944$	802.145			0.849730
$945$		−	76.0251i		−	0.0804499i
$946$			6.31413i			0.00667456i
$947$	247.947			0.261824			0.130912	−	0.991394i	$-0.458210\pi$
$947$	247.947			0.261824			0.130912	+	0.991394i	$0.458210\pi$
$948$	−239.900			−0.253059
$949$			77.2333i			0.0813838i
$950$			227.309i			0.239273i
$951$		−	173.180i		−	0.182103i
$952$	−24.9681			−0.0262270
$953$	−721.778			−0.757375			−0.378687	−	0.925525i	$-0.623624\pi$
$953$	−721.778			−0.757375			−0.378687	+	0.925525i	$0.623624\pi$
$954$	75.6447			0.0792922
$955$	−76.0706			−0.0796551
$956$			47.8333i			0.0500348i
$957$	−0.909213			−0.000950066
$958$			250.780i			0.261775i
$959$	298.928			0.311708
$960$	−51.8241			−0.0539835
$961$	−845.632			−0.879950
$962$	186.398			0.193760
$963$	244.134			0.253514
$964$	284.117			0.294727
$965$			2045.77i			2.11997i
$966$			32.3948i			0.0335350i
$967$	528.165			0.546190			0.273095	−	0.961987i	$-0.411953\pi$
$967$	528.165			0.546190			0.273095	+	0.961987i	$0.411953\pi$
$968$			752.901i			0.777791i
$969$			25.5475i			0.0263648i
$970$		−	67.0285i		−	0.0691015i
$971$	−167.452			−0.172454			−0.0862268	−	0.996276i	$-0.527481\pi$
$971$	−167.452			−0.172454			−0.0862268	+	0.996276i	$0.527481\pi$
$972$			50.8687i			0.0523341i
$973$	277.197			0.284889
$974$	−108.019			−0.110902
$975$	−685.089			−0.702656
$976$		−	843.407i		−	0.864147i
$977$	−1.54853			−0.00158499			−0.000792493	−	1.00000i	$-0.500252\pi$
$977$	−1.54853			−0.00158499			−0.000792493		1.00000i	$0.500252\pi$
$978$	338.828			0.346450
$979$		−	28.9592i		−	0.0295803i
$980$			1196.72i			1.22114i
$981$			461.158i			0.470090i
$982$			479.631i			0.488422i
$983$		−	257.390i		−	0.261842i	−0.991393	−	0.130921i	$-0.958207\pi$
$983$		−	257.390i		−	0.261842i	0.991393	−	0.130921i	$-0.0417934\pi$
$984$			440.647i			0.447812i
$985$	1811.45			1.83903
$986$		−	2.04460i		−	0.00207363i
$987$	−61.6469			−0.0624589
$988$			219.568i			0.222235i
$989$		−	181.612i		−	0.183632i
$990$			10.0121i			0.0101132i
$991$			192.643i			0.194392i	0.995265	+	0.0971961i	$0.0309874\pi$
$991$			192.643i			0.194392i	−0.995265	+	0.0971961i	$0.969013\pi$
$992$	−1340.95			−1.35176
$993$	−851.251			−0.857252
$994$	173.227			0.174272
$995$			1369.48i			1.37636i
$996$		−	444.565i		−	0.446350i
$997$	−1386.10			−1.39027			−0.695133	−	0.718881i	$-0.744655\pi$
$997$	−1386.10			−1.39027			−0.695133	+	0.718881i	$0.744655\pi$
$998$	311.567			0.312192
$999$		−	112.559i		−	0.112671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.b.a.133.13	yes	22
3.2	odd	2		603.3.b.e.334.10		22
67.66	odd	2	inner	201.3.b.a.133.10	✓	22
201.200	even	2		603.3.b.e.334.13		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.b.a.133.10	✓	22	67.66	odd	2	inner
201.3.b.a.133.13	yes	22	1.1	even	1	trivial
603.3.b.e.334.10		22	3.2	odd	2
603.3.b.e.334.13		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)

\(f(q)\)	\(=\)	\(q+0.858352i q^{2} +1.73205i q^{3} +3.26323 q^{4} +8.02842i q^{5} -1.48671 q^{6} -1.82241i q^{7} +6.23441i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+0.858352i q^{2} +1.73205i q^{3} +3.26323 q^{4} +8.02842i q^{5} -1.48671 q^{6} -1.82241i q^{7} +6.23441i q^{8} -3.00000 q^{9} -6.89121 q^{10} +0.484291i q^{11} +5.65208i q^{12} -10.0249i q^{13} +1.56427 q^{14} -13.9056 q^{15} +7.70161 q^{16} -2.19758 q^{17} -2.57506i q^{18} -6.71186 q^{19} +26.1986i q^{20} +3.15650 q^{21} -0.415692 q^{22} +11.9565 q^{23} -10.7983 q^{24} -39.4556 q^{25} +8.60486 q^{26} -5.19615i q^{27} -5.94693i q^{28} +1.08392 q^{29} -11.9359i q^{30} +42.5045i q^{31} +31.5483i q^{32} -0.838817 q^{33} -1.88630i q^{34} +14.6310 q^{35} -9.78969 q^{36} +21.6619 q^{37} -5.76114i q^{38} +17.3636 q^{39} -50.0525 q^{40} -40.8070i q^{41} +2.70939i q^{42} -15.1894i q^{43} +1.58035i q^{44} -24.0853i q^{45} +10.2629i q^{46} -19.5302 q^{47} +13.3396i q^{48} +45.6788 q^{49} -33.8668i q^{50} -3.80632i q^{51} -32.7134i q^{52} +29.3759i q^{53} +4.46013 q^{54} -3.88810 q^{55} +11.3616 q^{56} -11.6253i q^{57} +0.930388i q^{58} +104.153 q^{59} -45.3773 q^{60} -109.511i q^{61} -36.4838 q^{62} +5.46722i q^{63} +3.72684 q^{64} +80.4838 q^{65} -0.720000i q^{66} +(55.3048 - 37.8203i) q^{67} -7.17121 q^{68} +20.7093i q^{69} +12.5586i q^{70} +110.740 q^{71} -18.7032i q^{72} -7.70418 q^{73} +18.5935i q^{74} -68.3391i q^{75} -21.9024 q^{76} +0.882575 q^{77} +14.9041i q^{78} +42.4445i q^{79} +61.8318i q^{80} +9.00000 q^{81} +35.0268 q^{82} -78.6551 q^{83} +10.3004 q^{84} -17.6431i q^{85} +13.0379 q^{86} +1.87741i q^{87} -3.01927 q^{88} -59.7970 q^{89} +20.6736 q^{90} -18.2694 q^{91} +39.0168 q^{92} -73.6199 q^{93} -16.7638i q^{94} -53.8857i q^{95} -54.6433 q^{96} +9.72666i q^{97} +39.2085i q^{98} -1.45287i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 52 q^{4} - 66 q^{9}+O(q^{10}) \) 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

Varieties

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