LMFDB - Embedded newform 300.3.l.g.107.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,3,Mod(107,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("300.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	300.l (of order $4$, degree $2$, 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:	$8.17440793081$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.13
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.837725 - 1.81610i) q^{2} +(2.69303 - 1.32197i) q^{3} +(-2.59643 - 3.04278i) q^{4} +(-0.144815 - 5.99825i) q^{6} +(3.54241 - 3.54241i) q^{7} +(-7.70110 + 2.16636i) q^{8} +(5.50478 - 7.12021i) q^{9} +O(q^{10})$	\(q+(0.837725 - 1.81610i) q^{2} +(2.69303 - 1.32197i) q^{3} +(-2.59643 - 3.04278i) q^{4} +(-0.144815 - 5.99825i) q^{6} +(3.54241 - 3.54241i) q^{7} +(-7.70110 + 2.16636i) q^{8} +(5.50478 - 7.12021i) q^{9} -16.8337 q^{11} +(-11.0147 - 4.76189i) q^{12} +(8.64592 - 8.64592i) q^{13} +(-3.46580 - 9.40093i) q^{14} +(-2.51707 + 15.8008i) q^{16} +(9.72710 - 9.72710i) q^{17} +(-8.31951 - 15.9620i) q^{18} +4.78419 q^{19} +(4.85684 - 14.2228i) q^{21} +(-14.1020 + 30.5716i) q^{22} +(-13.5716 + 13.5716i) q^{23} +(-17.8754 + 16.0147i) q^{24} +(-8.45895 - 22.9448i) q^{26} +(5.41182 - 26.4521i) q^{27} +(-19.9764 - 1.58116i) q^{28} +14.8741 q^{29} -14.0641i q^{31} +(26.5872 + 17.8080i) q^{32} +(-45.3336 + 22.2536i) q^{33} +(-9.51674 - 25.8140i) q^{34} +(-35.9581 + 1.73727i) q^{36} +(10.1182 + 10.1182i) q^{37} +(4.00784 - 8.68857i) q^{38} +(11.8540 - 34.7134i) q^{39} +6.08509i q^{41} +(-21.7613 - 20.7353i) q^{42} +(57.2366 + 57.2366i) q^{43} +(43.7075 + 51.2213i) q^{44} +(13.2781 + 36.0167i) q^{46} +(-17.6247 - 17.6247i) q^{47} +(14.1096 + 45.8794i) q^{48} +23.9027i q^{49} +(13.3364 - 39.0543i) q^{51} +(-48.7562 - 3.85911i) q^{52} +(16.2015 + 16.2015i) q^{53} +(-43.5060 - 31.9880i) q^{54} +(-19.6063 + 34.9546i) q^{56} +(12.8840 - 6.32456i) q^{57} +(12.4604 - 27.0128i) q^{58} +4.37150i q^{59} +8.52269 q^{61} +(-25.5418 - 11.7818i) q^{62} +(-5.72249 - 44.7229i) q^{63} +(54.6137 - 33.3667i) q^{64} +(2.43777 + 100.973i) q^{66} +(53.9714 - 53.9714i) q^{67} +(-54.8532 - 4.34170i) q^{68} +(-18.6074 + 54.4900i) q^{69} -36.6679 q^{71} +(-26.9679 + 66.7588i) q^{72} +(12.6800 - 12.6800i) q^{73} +(26.8519 - 9.89937i) q^{74} +(-12.4218 - 14.5573i) q^{76} +(-59.6318 + 59.6318i) q^{77} +(-53.1125 - 50.6084i) q^{78} +88.4346 q^{79} +(-20.3947 - 78.3904i) q^{81} +(11.0511 + 5.09763i) q^{82} +(63.7372 - 63.7372i) q^{83} +(-55.8873 + 22.1502i) q^{84} +(151.896 - 55.9988i) q^{86} +(40.0563 - 19.6631i) q^{87} +(129.638 - 36.4679i) q^{88} -115.022 q^{89} -61.2548i q^{91} +(76.5332 + 6.05770i) q^{92} +(-18.5923 - 37.8749i) q^{93} +(-46.7728 + 17.2435i) q^{94} +(95.1415 + 12.8098i) q^{96} +(85.3544 + 85.3544i) q^{97} +(43.4096 + 20.0239i) q^{98} +(-92.6658 + 119.859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.837725	−	1.81610i	0.418863	−	0.908050i
$2$	0.837725	−	1.81610i	0.418863	−	0.908050i
$3$	2.69303	−	1.32197i	0.897676	−	0.440657i
$3$	2.69303	−	1.32197i	0.897676	−	0.440657i
$4$	−2.59643	−	3.04278i	−0.649108	−	0.760696i
$5$		0			0
$5$		0			0
$6$	−0.144815	−	5.99825i	−0.0241358	−	0.999709i
$7$	3.54241	−	3.54241i	0.506059	−	0.506059i	−0.407256	−	0.913314i	$-0.633514\pi$
$7$	3.54241	−	3.54241i	0.506059	−	0.506059i	0.913314	+	0.407256i	$0.133514\pi$
$8$	−7.70110	+	2.16636i	−0.962637	+	0.270795i
$9$	5.50478	−	7.12021i	0.611643	−	0.791134i
$10$		0			0
$11$	−16.8337			−1.53034			−0.765168	−	0.643831i	$-0.777344\pi$
$11$	−16.8337			−1.53034			−0.765168	+	0.643831i	$0.777344\pi$
$12$	−11.0147	−	4.76189i	−0.917895	−	0.396824i
$13$	8.64592	−	8.64592i	0.665071	−	0.665071i	−0.291500	−	0.956571i	$-0.594154\pi$
$13$	8.64592	−	8.64592i	0.665071	−	0.665071i	0.956571	+	0.291500i	$0.0941543\pi$
$14$	−3.46580	−	9.40093i	−0.247557	−	0.671495i
$15$		0			0
$16$	−2.51707	+	15.8008i	−0.157317	+	0.987548i
$17$	9.72710	−	9.72710i	0.572182	−	0.572182i	−0.360556	−	0.932738i	$-0.617413\pi$
$17$	9.72710	−	9.72710i	0.572182	−	0.572182i	0.932738	+	0.360556i	$0.117413\pi$
$18$	−8.31951	−	15.9620i	−0.462195	−	0.886778i
$19$	4.78419			0.251800			0.125900	−	0.992043i	$-0.459818\pi$
$19$	4.78419			0.251800			0.125900	+	0.992043i	$0.459818\pi$
$20$		0			0
$21$	4.85684	−	14.2228i	0.231278	−	0.677275i
$22$	−14.1020	+	30.5716i	−0.641000	+	1.38962i
$23$	−13.5716	+	13.5716i	−0.590070	+	0.590070i	−0.937650	−	0.347580i	$-0.887003\pi$
$23$	−13.5716	+	13.5716i	−0.590070	+	0.590070i	0.347580	+	0.937650i	$0.387003\pi$
$24$	−17.8754	+	16.0147i	−0.744808	+	0.667279i
$25$		0			0
$26$	−8.45895	−	22.9448i	−0.325344	−	0.882491i
$27$	5.41182	−	26.4521i	0.200438	−	0.979706i
$28$	−19.9764	−	1.58116i	−0.713444	−	0.0564699i
$29$	14.8741			0.512899			0.256449	−	0.966558i	$-0.417447\pi$
$29$	14.8741			0.512899			0.256449	+	0.966558i	$0.417447\pi$
$30$		0			0
$31$		−	14.0641i		−	0.453680i	−0.973932	−	0.226840i	$-0.927161\pi$
$31$		−	14.0641i		−	0.453680i	0.973932	−	0.226840i	$-0.0728395\pi$
$32$	26.5872	+	17.8080i	0.830849	+	0.556498i
$33$	−45.3336	+	22.2536i	−1.37374	+	0.674353i
$34$	−9.51674	−	25.8140i	−0.279904	−	0.759235i
$35$		0			0
$36$	−35.9581	+	1.73727i	−0.998835	+	0.0482576i
$37$	10.1182	+	10.1182i	0.273465	+	0.273465i	0.830493	−	0.557029i	$-0.188059\pi$
$37$	10.1182	+	10.1182i	0.273465	+	0.273465i	−0.557029	+	0.830493i	$0.688059\pi$
$38$	4.00784	−	8.68857i	0.105469	−	0.228647i
$39$	11.8540	−	34.7134i	0.303950	−	0.890086i
$40$		0			0
$41$			6.08509i			0.148417i	0.997243	+	0.0742084i	$0.0236430\pi$
$41$			6.08509i			0.148417i	−0.997243	+	0.0742084i	$0.976357\pi$
$42$	−21.7613	−	20.7353i	−0.518125	−	0.493697i
$43$	57.2366	+	57.2366i	1.33108	+	1.33108i	0.904401	+	0.426683i	$0.140318\pi$
$43$	57.2366	+	57.2366i	1.33108	+	1.33108i	0.426683	+	0.904401i	$0.359682\pi$
$44$	43.7075	+	51.2213i	0.993353	+	1.16412i
$45$		0			0
$46$	13.2781	+	36.0167i	0.288654	+	0.782971i
$47$	−17.6247	−	17.6247i	−0.374993	−	0.374993i	0.494299	−	0.869292i	$-0.335425\pi$
$47$	−17.6247	−	17.6247i	−0.374993	−	0.374993i	−0.869292	+	0.494299i	$0.835425\pi$
$48$	14.1096	+	45.8794i	0.293951	+	0.955821i
$49$			23.9027i			0.487809i
$50$		0			0
$51$	13.3364	−	39.0543i	0.261498	−	0.765770i
$52$	−48.7562	−	3.85911i	−0.937620	−	0.0742137i
$53$	16.2015	+	16.2015i	0.305688	+	0.305688i	0.843234	−	0.537546i	$-0.180649\pi$
$53$	16.2015	+	16.2015i	0.305688	+	0.305688i	−0.537546	+	0.843234i	$0.680649\pi$
$54$	−43.5060	−	31.9880i	−0.805666	−	0.592370i
$55$		0			0
$56$	−19.6063	+	34.9546i	−0.350112	+	0.624189i
$57$	12.8840	−	6.32456i	0.226034	−	0.110957i
$58$	12.4604	−	27.0128i	0.214834	−	0.465738i
$59$			4.37150i			0.0740931i	0.999314	+	0.0370466i	$0.0117950\pi$
$59$			4.37150i			0.0740931i	−0.999314	+	0.0370466i	$0.988205\pi$
$60$		0			0
$61$	8.52269			0.139716			0.0698582	−	0.997557i	$-0.477745\pi$
$61$	8.52269			0.139716			0.0698582	+	0.997557i	$0.477745\pi$
$62$	−25.5418	−	11.7818i	−0.411964	−	0.190030i
$63$	−5.72249	−	44.7229i	−0.0908332	−	0.709887i
$64$	54.6137	−	33.3667i	0.853340	−	0.521355i
$65$		0			0
$66$	2.43777	+	100.973i	0.0369359	+	1.52989i
$67$	53.9714	−	53.9714i	0.805543	−	0.805543i	−0.178413	−	0.983956i	$-0.557096\pi$
$67$	53.9714	−	53.9714i	0.805543	−	0.805543i	0.983956	+	0.178413i	$0.0570963\pi$
$68$	−54.8532	−	4.34170i	−0.806665	−	0.0638485i
$69$	−18.6074	+	54.4900i	−0.269673	+	0.789710i
$70$		0			0
$71$	−36.6679			−0.516449			−0.258225	−	0.966085i	$-0.583137\pi$
$71$	−36.6679			−0.516449			−0.258225	+	0.966085i	$0.583137\pi$
$72$	−26.9679	+	66.7588i	−0.374554	+	0.927205i
$73$	12.6800	−	12.6800i	0.173699	−	0.173699i	−0.614903	−	0.788602i	$-0.710805\pi$
$73$	12.6800	−	12.6800i	0.173699	−	0.173699i	0.788602	+	0.614903i	$0.210805\pi$
$74$	26.8519	−	9.89937i	0.362863	−	0.133775i
$75$		0			0
$76$	−12.4218	−	14.5573i	−0.163445	−	0.191543i
$77$	−59.6318	+	59.6318i	−0.774439	+	0.774439i
$78$	−53.1125	−	50.6084i	−0.680929	−	0.648825i
$79$	88.4346			1.11943			0.559713	−	0.828687i	$-0.310912\pi$
$79$	88.4346			1.11943			0.559713	+	0.828687i	$0.310912\pi$
$80$		0			0
$81$	−20.3947	−	78.3904i	−0.251786	−	0.967783i
$82$	11.0511	+	5.09763i	0.134770	+	0.0621663i
$83$	63.7372	−	63.7372i	0.767918	−	0.767918i	−0.209822	−	0.977740i	$-0.567288\pi$
$83$	63.7372	−	63.7372i	0.767918	−	0.767918i	0.977740	+	0.209822i	$0.0672884\pi$
$84$	−55.8873	+	22.1502i	−0.665325	+	0.263692i
$85$		0			0
$86$	151.896	−	55.9988i	1.76623	−	0.651149i
$87$	40.0563	−	19.6631i	0.460417	−	0.226013i
$88$	129.638	−	36.4679i	1.47316	−	0.414408i
$89$	−115.022			−1.29238			−0.646190	−	0.763177i	$-0.723639\pi$
$89$	−115.022			−1.29238			−0.646190	+	0.763177i	$0.723639\pi$
$90$		0			0
$91$		−	61.2548i		−	0.673130i
$92$	76.5332	+	6.05770i	0.831883	+	0.0658445i
$93$	−18.5923	−	37.8749i	−0.199917	−	0.407258i
$94$	−46.7728	+	17.2435i	−0.497583	+	0.183442i
$95$		0			0
$96$	95.1415	+	12.8098i	0.991057	+	0.133436i
$97$	85.3544	+	85.3544i	0.879942	+	0.879942i	0.993528	−	0.113586i	$-0.0362338\pi$
$97$	85.3544	+	85.3544i	0.879942	+	0.879942i	−0.113586	+	0.993528i	$0.536234\pi$
$98$	43.4096	+	20.0239i	0.442955	+	0.204325i
$99$	−92.6658	+	119.859i	−0.936018	+	1.21070i
$100$		0			0
$101$			158.917i			1.57343i	0.617313	+	0.786717i	$0.288221\pi$
$101$			158.917i			1.57343i	−0.617313	+	0.786717i	$0.711779\pi$
$102$	−59.7542	−	56.9369i	−0.585826	−	0.558205i
$103$	−28.6266	−	28.6266i	−0.277928	−	0.277928i	0.554353	−	0.832282i	$-0.312966\pi$
$103$	−28.6266	−	28.6266i	−0.277928	−	0.277928i	−0.832282	+	0.554353i	$0.812966\pi$
$104$	−47.8529	+	85.3133i	−0.460124	+	0.820320i
$105$		0			0
$106$	42.9959	−	15.8511i	0.405622	−	0.149539i
$107$	28.1808	+	28.1808i	0.263372	+	0.263372i	0.826423	−	0.563050i	$-0.190372\pi$
$107$	28.1808	+	28.1808i	0.263372	+	0.263372i	−0.563050	+	0.826423i	$0.690372\pi$
$108$	−94.5394	+	52.2140i	−0.875365	+	0.483463i
$109$		−	159.944i		−	1.46737i	−0.679489	−	0.733686i	$-0.737798\pi$
$109$		−	159.944i		−	1.46737i	0.679489	−	0.733686i	$-0.262202\pi$
$110$		0			0
$111$	40.6245	+	13.8726i	0.365986	+	0.124978i
$112$	47.0563	+	64.8893i	0.420146	+	0.579369i
$113$	101.260	+	101.260i	0.896110	+	0.896110i	0.995089	−	0.0989792i	$-0.0315577\pi$
$113$	101.260	+	101.260i	0.896110	+	0.896110i	−0.0989792	+	0.995089i	$0.531558\pi$
$114$	−0.692822	−	28.6968i	−0.00607739	−	0.251726i
$115$		0			0
$116$	−38.6195	−	45.2586i	−0.332927	−	0.390160i
$117$	−13.9668	−	109.155i	−0.119375	−	0.932946i
$118$	7.93907	+	3.66211i	0.0672803	+	0.0310348i
$119$		−	68.9147i		−	0.579115i
$120$		0			0
$121$	162.373			1.34193
$122$	7.13968	−	15.4781i	0.0585219	−	0.126869i
$123$	8.04432	+	16.3873i	0.0654009	+	0.133230i
$124$	−42.7940	+	36.5165i	−0.345113	+	0.294488i
$125$		0			0
$126$	−86.0151	−	27.0729i	−0.682659	−	0.214864i
$127$	−94.0845	+	94.0845i	−0.740823	+	0.740823i	−0.972736	−	0.231914i	$-0.925501\pi$
$127$	−94.0845	+	94.0845i	−0.740823	+	0.740823i	0.231914	+	0.972736i	$0.425501\pi$
$128$	−14.8460	−	127.136i	−0.115985	−	0.993251i
$129$	229.805	+	78.4746i	1.78143	+	0.608330i
$130$		0			0
$131$	145.148			1.10800			0.554002	−	0.832515i	$-0.313100\pi$
$131$	145.148			1.10800			0.554002	+	0.832515i	$0.313100\pi$
$132$	185.419	+	80.1601i	1.40469	+	0.607274i
$133$	16.9476	−	16.9476i	0.127425	−	0.127425i
$134$	−52.8042	−	143.231i	−0.394061	−	1.06888i
$135$		0			0
$136$	−53.8369	+	95.9817i	−0.395859	+	0.705748i
$137$	60.1022	−	60.1022i	0.438702	−	0.438702i	−0.452873	−	0.891575i	$-0.649601\pi$
$137$	60.1022	−	60.1022i	0.438702	−	0.438702i	0.891575	+	0.452873i	$0.149601\pi$
$138$	83.3713	+	79.4405i	0.604140	+	0.575656i
$139$	−12.5985			−0.0906366			−0.0453183	−	0.998973i	$-0.514430\pi$
$139$	−12.5985			−0.0906366			−0.0453183	+	0.998973i	$0.514430\pi$
$140$		0			0
$141$	−70.7630	−	24.1644i	−0.501865	−	0.171379i
$142$	−30.7176	+	66.5925i	−0.216321	+	0.468961i
$143$	−145.543	+	145.543i	−1.01778	+	1.01778i
$144$	98.6488	+	104.902i	0.685061	+	0.728485i
$145$		0			0
$146$	−12.4058	−	33.6506i	−0.0849713	−	0.230483i
$147$	31.5986	+	64.3705i	0.214957	+	0.437895i
$148$	4.51626	−	57.0587i	0.0305153	−	0.385531i
$149$	−25.9233			−0.173982			−0.0869911	−	0.996209i	$-0.527725\pi$
$149$	−25.9233			−0.173982			−0.0869911	+	0.996209i	$0.527725\pi$
$150$		0			0
$151$			200.379i			1.32701i	0.748171	+	0.663506i	$0.230932\pi$
$151$			200.379i			1.32701i	−0.748171	+	0.663506i	$0.769068\pi$
$152$	−36.8435	+	10.3643i	−0.242392	+	0.0681862i
$153$	−15.7134	−	122.805i	−0.102702	−	0.802644i
$154$	58.3422	+	158.252i	0.378846	+	1.02761i
$155$		0			0
$156$	−136.403	+	54.0616i	−0.874381	+	0.346549i
$157$	−139.992	−	139.992i	−0.891666	−	0.891666i	0.103014	−	0.994680i	$-0.467151\pi$
$157$	−139.992	−	139.992i	−0.891666	−	0.891666i	−0.994680	+	0.103014i	$0.967151\pi$
$158$	74.0839	−	160.606i	0.468885	−	1.01649i
$159$	65.0489	+	22.2131i	0.409113	+	0.139705i
$160$		0			0
$161$			96.1524i			0.597220i
$162$	−159.450	−	28.6308i	−0.984259	−	0.176733i
$163$	−58.6324	−	58.6324i	−0.359708	−	0.359708i	0.503997	−	0.863705i	$-0.331862\pi$
$163$	−58.6324	−	58.6324i	−0.359708	−	0.359708i	−0.863705	+	0.503997i	$0.831862\pi$
$164$	18.5156	−	15.7995i	0.112900	−	0.0963386i
$165$		0			0
$166$	−62.3588	−	169.147i	−0.375655	−	1.01896i
$167$	−84.2556	−	84.2556i	−0.504524	−	0.504524i	0.408316	−	0.912841i	$-0.366116\pi$
$167$	−84.2556	−	84.2556i	−0.504524	−	0.504524i	−0.912841	+	0.408316i	$0.866116\pi$
$168$	−6.59130	+	120.053i	−0.0392339	+	0.714599i
$169$			19.4961i			0.115361i
$170$		0			0
$171$	26.3359	−	34.0644i	0.154011	−	0.199207i
$172$	25.5476	−	322.770i	0.148533	−	1.87657i
$173$	−51.2341	−	51.2341i	−0.296151	−	0.296151i	0.543353	−	0.839504i	$-0.317154\pi$
$173$	−51.2341	−	51.2341i	−0.296151	−	0.296151i	−0.839504	+	0.543353i	$0.817154\pi$
$174$	−2.15399	−	89.2184i	−0.0123792	−	0.512749i
$175$		0			0
$176$	42.3716	−	265.985i	0.240747	−	1.51128i
$177$	5.77899	+	11.7726i	0.0326497	+	0.0665116i
$178$	−96.3566	+	208.891i	−0.541329	+	1.17354i
$179$		−	27.2276i		−	0.152109i	−0.997104	−	0.0760547i	$-0.975768\pi$
$179$		−	27.2276i		−	0.152109i	0.997104	−	0.0760547i	$-0.0242324\pi$
$180$		0			0
$181$	−276.624			−1.52831			−0.764155	−	0.645033i	$-0.776844\pi$
$181$	−276.624			−1.52831			−0.764155	+	0.645033i	$0.776844\pi$
$182$	−111.245	−	51.3147i	−0.611235	−	0.281949i
$183$	22.9518	−	11.2668i	0.125420	−	0.0615670i
$184$	75.1152	−	133.917i	0.408235	−	0.727811i
$185$		0			0
$186$	−84.3599	+	2.03669i	−0.453548	+	0.0109499i
$187$	−163.743	+	163.743i	−0.875630	+	0.875630i
$188$	−7.86679	+	99.3894i	−0.0418446	+	0.528667i
$189$	−74.5332	−	112.875i	−0.394356	−	0.597222i
$190$		0			0
$191$	−340.010			−1.78016			−0.890078	−	0.455807i	$-0.849351\pi$
$191$	−340.010			−1.78016			−0.890078	+	0.455807i	$0.849351\pi$
$192$	102.966	−	162.055i	0.536283	−	0.844038i
$193$	−100.981	+	100.981i	−0.523220	+	0.523220i	−0.918542	−	0.395322i	$-0.870633\pi$
$193$	−100.981	+	100.981i	−0.523220	+	0.523220i	0.395322	+	0.918542i	$0.370633\pi$
$194$	226.515	−	83.5085i	1.16761	−	0.430456i
$195$		0			0
$196$	72.7306	−	62.0617i	0.371075	−	0.316641i
$197$	−225.584	+	225.584i	−1.14510	+	1.14510i	−0.157595	+	0.987504i	$0.550374\pi$
$197$	−225.584	+	225.584i	−1.14510	+	1.14510i	−0.987504	+	0.157595i	$0.949626\pi$
$198$	140.048	+	268.699i	0.707313	+	1.35707i
$199$	−286.672			−1.44056			−0.720281	−	0.693682i	$-0.755987\pi$
$199$	−286.672			−1.44056			−0.720281	+	0.693682i	$0.755987\pi$
$200$		0			0
$201$	73.9977	−	216.695i	0.368148	−	1.07808i
$202$	288.609	+	133.129i	1.42876	+	0.659053i
$203$	52.6900	−	52.6900i	0.259557	−	0.259557i
$204$	−153.461	+	60.8221i	−0.752259	+	0.298147i
$205$		0			0
$206$	−75.9701	+	28.0076i	−0.368787	+	0.135959i
$207$	21.9239	+	171.341i	0.105912	+	0.827736i
$208$	114.850	+	158.375i	0.552163	+	0.761416i
$209$	−80.5356			−0.385338
$210$		0			0
$211$			183.842i			0.871288i	0.900119	+	0.435644i	$0.143479\pi$
$211$			183.842i			0.871288i	−0.900119	+	0.435644i	$0.856521\pi$
$212$	7.23155	−	91.3637i	0.0341111	−	0.430961i
$213$	−98.7476	+	48.4739i	−0.463604	+	0.227577i
$214$	74.7870	−	27.5714i	0.349472	−	0.128838i
$215$		0			0
$216$	15.6279	+	215.434i	0.0723512	+	0.997379i
$217$	−49.8207	−	49.8207i	−0.229589	−	0.229589i
$218$	−290.473	−	133.989i	−1.33245	−	0.614627i
$219$	17.3850	−	50.9103i	0.0793836	−	0.232467i
$220$		0			0
$221$		−	168.199i		−	0.761083i
$222$	59.2262	−	62.1567i	0.266785	−	0.279985i
$223$	−7.02165	−	7.02165i	−0.0314872	−	0.0314872i	0.691188	−	0.722675i	$-0.257088\pi$
$223$	−7.02165	−	7.02165i	−0.0314872	−	0.0314872i	−0.722675	+	0.691188i	$0.757088\pi$
$224$	157.266	−	31.0995i	0.702079	−	0.138837i
$225$		0			0
$226$	268.727	−	99.0706i	1.18906	−	0.438366i
$227$	36.6684	+	36.6684i	0.161535	+	0.161535i	0.783246	−	0.621711i	$-0.213562\pi$
$227$	36.6684	+	36.6684i	0.161535	+	0.161535i	−0.621711	+	0.783246i	$0.713562\pi$
$228$	−52.6966	−	22.7818i	−0.231126	−	0.0999201i
$229$			270.126i			1.17959i	0.807554	+	0.589794i	$0.200791\pi$
$229$			270.126i			1.17959i	−0.807554	+	0.589794i	$0.799209\pi$
$230$		0			0
$231$	−81.7585	+	239.422i	−0.353933	+	1.03646i
$232$	−114.547	+	32.2226i	−0.493735	+	0.138891i
$233$	55.2135	+	55.2135i	0.236968	+	0.236968i	0.815593	−	0.578625i	$-0.196411\pi$
$233$	55.2135	+	55.2135i	0.236968	+	0.236968i	−0.578625	+	0.815593i	$0.696411\pi$
$234$	−209.936	−	66.0765i	−0.897163	−	0.282378i
$235$		0			0
$236$	13.3015	−	11.3503i	0.0563624	−	0.0480945i
$237$	238.157	−	116.908i	1.00488	−	0.493283i
$238$	−125.156	−	57.7316i	−0.525865	−	0.242570i
$239$		−	46.1374i		−	0.193044i	−0.995331	−	0.0965218i	$-0.969228\pi$
$239$		−	46.1374i		−	0.193044i	0.995331	−	0.0965218i	$-0.0307718\pi$
$240$		0			0
$241$	−212.165			−0.880351			−0.440176	−	0.897912i	$-0.645084\pi$
$241$	−212.165			−0.880351			−0.440176	+	0.897912i	$0.645084\pi$
$242$	136.024	−	294.885i	0.562082	−	1.21853i
$243$	−158.553	−	184.146i	−0.652483	−	0.757803i
$244$	−22.1286	−	25.9327i	−0.0906910	−	0.106282i
$245$		0			0
$246$	36.4999	−	0.881212i	0.148374	−	0.00358216i
$247$	41.3638	−	41.3638i	0.167465	−	0.167465i
$248$	30.4679	+	108.309i	0.122855	+	0.436729i
$249$	87.3872	−	255.905i	0.350953	−	1.02773i
$250$		0			0
$251$	159.687			0.636203			0.318101	−	0.948057i	$-0.396955\pi$
$251$	159.687			0.636203			0.318101	+	0.948057i	$0.396955\pi$
$252$	−121.224	+	133.532i	−0.481048	+	0.529890i
$253$	228.460	−	228.460i	0.903004	−	0.903004i
$254$	92.0498	+	249.684i	0.362401	+	0.983007i
$255$		0			0
$256$	−243.329	−	79.5433i	−0.950503	−	0.310716i
$257$	98.0877	−	98.0877i	0.381664	−	0.381664i	−0.490037	−	0.871701i	$-0.663017\pi$
$257$	98.0877	−	98.0877i	0.381664	−	0.381664i	0.871701	+	0.490037i	$0.163017\pi$
$258$	335.031	−	351.608i	1.29857	−	1.36282i
$259$	71.6855			0.276778
$260$		0			0
$261$	81.8785	−	105.906i	0.313711	−	0.405772i
$262$	121.595	−	263.604i	0.464101	−	1.00612i
$263$	−141.919	+	141.919i	−0.539614	+	0.539614i	−0.923416	−	0.383802i	$-0.874615\pi$
$263$	−141.919	+	141.919i	−0.539614	+	0.539614i	0.383802	+	0.923416i	$0.374615\pi$
$264$	300.909	−	269.586i	1.13981	−	1.02116i
$265$		0			0
$266$	−16.5811	−	44.9759i	−0.0623348	−	0.169082i
$267$	−309.757	+	152.055i	−1.16014	+	0.569496i
$268$	−304.356	−	24.0902i	−1.13566	−	0.0898887i
$269$	−0.543377			−0.00201999			−0.00100999	−	0.999999i	$-0.500321\pi$
$269$	−0.543377			−0.00201999			−0.00100999	+	0.999999i	$0.500321\pi$
$270$		0			0
$271$		−	362.830i		−	1.33886i	−0.742877	−	0.669428i	$-0.766539\pi$
$271$		−	362.830i		−	1.33886i	0.742877	−	0.669428i	$-0.233461\pi$
$272$	129.212	+	178.179i	0.475044	+	0.655071i
$273$	−80.9771	−	164.961i	−0.296619	−	0.604252i
$274$	−58.8025	−	159.501i	−0.214608	−	0.582120i
$275$		0			0
$276$	214.114	−	84.8612i	0.775776	−	0.307468i
$277$	79.2266	+	79.2266i	0.286016	+	0.286016i	0.835503	−	0.549486i	$-0.185177\pi$
$277$	79.2266	+	79.2266i	0.286016	+	0.286016i	−0.549486	+	0.835503i	$0.685177\pi$
$278$	−10.5541	+	22.8801i	−0.0379643	+	0.0823025i
$279$	−100.139	−	77.4197i	−0.358922	−	0.277490i
$280$		0			0
$281$			318.753i			1.13435i	0.823597	+	0.567176i	$0.191964\pi$
$281$			318.753i			1.13435i	−0.823597	+	0.567176i	$0.808036\pi$
$282$	−103.165	+	108.270i	−0.365833	+	0.383935i
$283$	−223.036	−	223.036i	−0.788112	−	0.788112i	0.193072	−	0.981185i	$-0.438155\pi$
$283$	−223.036	−	223.036i	−0.788112	−	0.788112i	−0.981185	+	0.193072i	$0.938155\pi$
$284$	95.2057	+	111.572i	0.335231	+	0.392861i
$285$		0			0
$286$	142.395	+	386.245i	0.497885	+	1.35051i
$287$	21.5559	+	21.5559i	0.0751076	+	0.0751076i
$288$	273.153	−	91.2771i	0.948447	−	0.316934i
$289$			99.7672i			0.345215i
$290$		0			0
$291$	342.698	+	117.026i	1.17765	+	0.402150i
$292$	−71.5054	−	5.65974i	−0.244881	−	0.0193827i
$293$	−75.3066	−	75.3066i	−0.257019	−	0.257019i	0.566822	−	0.823841i	$-0.308173\pi$
$293$	−75.3066	−	75.3066i	−0.257019	−	0.257019i	−0.823841	+	0.566822i	$0.808173\pi$
$294$	143.374	−	3.46146i	0.487667	−	0.0117737i
$295$		0			0
$296$	−99.8408	−	56.0015i	−0.337300	−	0.189194i
$297$	−91.1009	+	445.286i	−0.306737	+	1.49928i
$298$	−21.7166	+	47.0794i	−0.0728746	+	0.157984i
$299$			234.678i			0.784876i
$300$		0			0
$301$	405.511			1.34721
$302$	363.908	+	167.862i	1.20499	+	0.555836i
$303$	210.084	+	427.967i	0.693345	+	1.41243i
$304$	−12.0421	+	75.5939i	−0.0396123	+	0.248664i
$305$		0			0
$306$	−236.189	−	74.3394i	−0.771858	−	0.242939i
$307$	330.497	−	330.497i	1.07654	−	1.07654i	0.0797218	−	0.996817i	$-0.474597\pi$
$307$	330.497	−	330.497i	1.07654	−	1.07654i	0.996817	−	0.0797218i	$-0.0254032\pi$
$308$	336.277	+	26.6167i	1.09181	+	0.0864179i
$309$	−114.936	−	39.2487i	−0.371961	−	0.127018i
$310$		0			0
$311$	26.5302			0.0853063			0.0426531	−	0.999090i	$-0.486419\pi$
$311$	26.5302			0.0853063			0.0426531	+	0.999090i	$0.486419\pi$
$312$	−16.0873	+	293.011i	−0.0515619	+	0.939138i
$313$	−131.851	+	131.851i	−0.421248	+	0.421248i	−0.885633	−	0.464385i	$-0.846275\pi$
$313$	−131.851	+	131.851i	−0.421248	+	0.421248i	0.464385	+	0.885633i	$0.346275\pi$
$314$	−371.513	+	136.964i	−1.18316	+	0.436191i
$315$		0			0
$316$	−229.614	−	269.087i	−0.726628	−	0.851542i
$317$	66.6091	−	66.6091i	0.210123	−	0.210123i	−0.594197	−	0.804320i	$-0.702530\pi$
$317$	66.6091	−	66.6091i	0.210123	−	0.210123i	0.804320	+	0.594197i	$0.202530\pi$
$318$	94.8344	−	99.5268i	0.298221	−	0.312977i
$319$	−250.385			−0.784907
$320$		0			0
$321$	113.146	+	38.6375i	0.352480	+	0.120366i
$322$	174.622	+	80.5492i	0.542305	+	0.250153i
$323$	46.5363	−	46.5363i	0.144075	−	0.144075i
$324$	−185.572	+	265.592i	−0.572752	+	0.819729i
$325$		0			0
$326$	−155.600	+	57.3644i	−0.477301	+	0.175965i
$327$	−211.441	−	430.732i	−0.646608	−	1.31722i
$328$	−13.1825	−	46.8619i	−0.0401906	−	0.142872i
$329$	−124.868			−0.379537
$330$		0			0
$331$		−	284.948i		−	0.860871i	−0.902621	−	0.430436i	$-0.858360\pi$
$331$		−	284.948i		−	0.860871i	0.902621	−	0.430436i	$-0.141640\pi$
$332$	−359.428	−	28.4491i	−1.08261	−	0.0856902i
$333$	127.742	−	16.3452i	0.383610	−	0.0490845i
$334$	−223.599	+	82.4335i	−0.669460	+	0.246807i
$335$		0			0
$336$	212.506	+	112.542i	0.632457	+	0.334945i
$337$	−294.164	−	294.164i	−0.872889	−	0.872889i	0.119897	−	0.992786i	$-0.461744\pi$
$337$	−294.164	−	294.164i	−0.872889	−	0.872889i	−0.992786	+	0.119897i	$0.961744\pi$
$338$	35.4068	+	16.3324i	0.104754	+	0.0483206i
$339$	406.561	+	138.834i	1.19929	+	0.409539i
$340$		0			0
$341$			236.750i			0.694283i
$342$	−39.8021	−	76.3653i	−0.116380	−	0.223290i
$343$	258.251	+	258.251i	0.752919	+	0.752919i
$344$	−564.780	−	316.789i	−1.64180	−	0.920899i
$345$		0			0
$346$	−135.966	+	50.1262i	−0.392966	+	0.144873i
$347$	274.053	+	274.053i	0.789779	+	0.789779i	0.981458	−	0.191679i	$-0.0613932\pi$
$347$	274.053	+	274.053i	0.789779	+	0.789779i	−0.191679	+	0.981458i	$0.561393\pi$
$348$	−163.834	−	70.8287i	−0.470787	−	0.203531i
$349$		−	129.175i		−	0.370128i	−0.982726	−	0.185064i	$-0.940751\pi$
$349$		−	129.175i		−	0.370128i	0.982726	−	0.185064i	$-0.0592492\pi$
$350$		0			0
$351$	−181.912	−	275.493i	−0.518269	−	0.784880i
$352$	−447.560	−	299.773i	−1.27148	−	0.851629i
$353$	381.746	+	381.746i	1.08143	+	1.08143i	0.996376	+	0.0850569i	$0.0271072\pi$
$353$	381.746	+	381.746i	1.08143	+	1.08143i	0.0850569	+	0.996376i	$0.472893\pi$
$354$	26.2213	−	0.633058i	0.0740716	−	0.00178830i
$355$		0			0
$356$	298.646	+	349.986i	0.838894	+	0.983108i
$357$	−91.1033	−	185.589i	−0.255191	−	0.519858i
$358$	−49.4480	−	22.8092i	−0.138123	−	0.0637129i
$359$		−	209.720i		−	0.584178i	−0.956391	−	0.292089i	$-0.905650\pi$
$359$		−	209.720i		−	0.584178i	0.956391	−	0.292089i	$-0.0943503\pi$
$360$		0			0
$361$	−338.112			−0.936597
$362$	−231.735	+	502.377i	−0.640151	+	1.38778i
$363$	437.275	−	214.652i	1.20461	−	0.591329i
$364$	−186.385	+	159.044i	−0.512047	+	0.436934i
$365$		0			0
$366$	−1.23421	−	51.1213i	−0.00337217	−	0.139676i
$367$	4.27652	−	4.27652i	0.0116527	−	0.0116527i	−0.701256	−	0.712909i	$-0.747377\pi$
$367$	4.27652	−	4.27652i	0.0116527	−	0.0116527i	0.712909	+	0.701256i	$0.247377\pi$
$368$	−180.281	−	248.602i	−0.489894	−	0.675550i
$369$	43.3271	+	33.4971i	0.117418	+	0.0907781i
$370$		0			0
$371$	114.785			0.309393
$372$	−66.9716	+	154.912i	−0.180031	+	0.416431i
$373$	−363.822	+	363.822i	−0.975394	+	0.975394i	−0.999704	−	0.0243109i	$-0.992261\pi$
$373$	−363.822	+	363.822i	−0.975394	+	0.975394i	0.0243109	+	0.999704i	$0.492261\pi$
$374$	160.202	+	434.545i	0.428347	+	1.16188i
$375$		0			0
$376$	173.911	+	97.5478i	0.462529	+	0.259436i
$377$	128.600	−	128.600i	0.341114	−	0.341114i
$378$	−267.430	+	40.8015i	−0.707488	+	0.107940i
$379$	732.379			1.93240			0.966199	−	0.257796i	$-0.0829962\pi$
$379$	732.379			1.93240			0.966199	+	0.257796i	$0.0829962\pi$
$380$		0			0
$381$	−128.995	+	377.749i	−0.338570	+	0.991467i
$382$	−284.835	+	617.492i	−0.745641	+	1.61647i
$383$	343.246	−	343.246i	0.896203	−	0.896203i	−0.0988948	−	0.995098i	$-0.531531\pi$
$383$	343.246	−	343.246i	0.896203	−	0.896203i	0.995098	+	0.0988948i	$0.0315307\pi$
$384$	−208.051	−	322.755i	−0.541800	−	0.840508i
$385$		0			0
$386$	98.7977	+	267.987i	0.255952	+	0.694267i
$387$	722.612	−	92.4613i	1.86721	−	0.238918i
$388$	38.0980	−	481.332i	0.0981907	−	1.24055i
$389$	600.575			1.54389			0.771947	−	0.635687i	$-0.219283\pi$
$389$	600.575			1.54389			0.771947	+	0.635687i	$0.219283\pi$
$390$		0			0
$391$			264.025i			0.675255i
$392$	−51.7819	−	184.077i	−0.132097	−	0.469583i
$393$	390.889	−	191.882i	0.994628	−	0.488250i
$394$	220.706	+	598.662i	0.560168	+	1.51945i
$395$		0			0
$396$	605.307	−	29.2447i	1.52855	−	0.0738503i
$397$	295.285	+	295.285i	0.743792	+	0.743792i	0.973306	−	0.229513i	$-0.0737135\pi$
$397$	295.285	+	295.285i	0.743792	+	0.743792i	−0.229513	+	0.973306i	$0.573713\pi$
$398$	−240.152	+	520.625i	−0.603398	+	1.30810i
$399$	23.2361	−	68.0445i	0.0582357	−	0.170537i
$400$		0			0
$401$		−	300.412i		−	0.749157i	−0.927195	−	0.374578i	$-0.877787\pi$
$401$		−	300.412i		−	0.749157i	0.927195	−	0.374578i	$-0.122213\pi$
$402$	−331.550	−	315.918i	−0.824751	−	0.785866i
$403$	−121.597	−	121.597i	−0.301729	−	0.301729i
$404$	483.550	−	412.617i	1.19691	−	1.02133i
$405$		0			0
$406$	−51.5506	−	139.830i	−0.126972	−	0.344409i
$407$	−170.326	−	170.326i	−0.418492	−	0.418492i
$408$	−18.0990	+	329.652i	−0.0443604	+	0.807971i
$409$			53.8159i			0.131579i	0.997834	+	0.0657896i	$0.0209566\pi$
$409$			53.8159i			0.131579i	−0.997834	+	0.0657896i	$0.979043\pi$
$410$		0			0
$411$	82.4035	−	241.310i	0.200495	−	0.587130i
$412$	−12.7775	+	161.432i	−0.0310134	+	0.391825i
$413$	15.4856	+	15.4856i	0.0374955	+	0.0374955i
$414$	329.539	+	103.721i	0.795988	+	0.250534i
$415$		0			0
$416$	383.837	−	75.9043i	0.922684	−	0.182462i
$417$	−33.9281	+	16.6548i	−0.0813623	+	0.0399397i
$418$	−67.4667	+	146.261i	−0.161404	+	0.349906i
$419$			582.593i			1.39044i	0.718799	+	0.695218i	$0.244692\pi$
$419$			582.593i			1.39044i	−0.718799	+	0.695218i	$0.755308\pi$
$420$		0			0
$421$	486.678			1.15600			0.578002	−	0.816035i	$-0.303833\pi$
$421$	486.678			1.15600			0.578002	+	0.816035i	$0.303833\pi$
$422$	333.875	+	154.009i	0.791173	+	0.364950i
$423$	−222.511	+	28.4713i	−0.526032	+	0.0673080i
$424$	−159.868	−	89.6709i	−0.377046	−	0.211488i
$425$		0			0
$426$	5.31006	+	219.943i	0.0124649	+	0.516299i
$427$	30.1909	−	30.1909i	0.0707046	−	0.0707046i
$428$	12.5785	−	158.918i	0.0293891	−	0.371304i
$429$	−199.547	+	584.354i	−0.465145	+	1.36213i
$430$		0			0
$431$	−554.639			−1.28686			−0.643432	−	0.765503i	$-0.722490\pi$
$431$	−554.639			−1.28686			−0.643432	+	0.765503i	$0.722490\pi$
$432$	404.341	+	152.093i	0.935975	+	0.352066i
$433$	−152.907	+	152.907i	−0.353135	+	0.353135i	−0.861275	−	0.508140i	$-0.830333\pi$
$433$	−152.907	+	152.907i	−0.353135	+	0.353135i	0.508140	+	0.861275i	$0.330333\pi$
$434$	−132.216	+	48.7433i	−0.304644	+	0.112312i
$435$		0			0
$436$	−486.674	+	415.283i	−1.11622	+	0.952483i
$437$	−64.9292	+	64.9292i	−0.148579	+	0.148579i
$438$	−77.8942	−	74.2217i	−0.177841	−	0.169456i
$439$	−218.824			−0.498461			−0.249231	−	0.968444i	$-0.580178\pi$
$439$	−218.824			−0.498461			−0.249231	+	0.968444i	$0.580178\pi$
$440$		0			0
$441$	170.192	+	131.579i	0.385923	+	0.298365i
$442$	−305.467	−	140.905i	−0.691101	−	0.318789i
$443$	−39.9964	+	39.9964i	−0.0902853	+	0.0902853i	−0.750807	−	0.660522i	$-0.770335\pi$
$443$	−39.9964	+	39.9964i	−0.0902853	+	0.0902853i	0.660522	+	0.750807i	$0.270335\pi$
$444$	−63.2675	−	159.631i	−0.142494	−	0.359529i
$445$		0			0
$446$	−18.6342	+	6.86980i	−0.0417808	+	0.0154031i
$447$	−69.8122	+	34.2699i	−0.156180	+	0.0766665i
$448$	75.2655	−	311.663i	0.168003	−	0.695676i
$449$	−236.471			−0.526660			−0.263330	−	0.964706i	$-0.584821\pi$
$449$	−236.471			−0.526660			−0.263330	+	0.964706i	$0.584821\pi$
$450$		0			0
$451$		−	102.435i		−	0.227128i
$452$	45.1977	−	571.030i	0.0999949	−	1.26334i
$453$	264.895	+	539.626i	0.584757	+	1.19123i
$454$	97.3115	−	35.8754i	0.214343	−	0.0790208i
$455$		0			0
$456$	−85.5193	+	76.6174i	−0.187542	+	0.168021i
$457$	242.806	+	242.806i	0.531304	+	0.531304i	0.920960	−	0.389657i	$-0.127406\pi$
$457$	242.806	+	242.806i	0.531304	+	0.531304i	−0.389657	+	0.920960i	$0.627406\pi$
$458$	490.575	+	226.291i	1.07112	+	0.494085i
$459$	−204.661	−	309.943i	−0.445884	−	0.675257i
$460$		0			0
$461$		−	640.776i		−	1.38997i	−0.719024	−	0.694985i	$-0.755411\pi$
$461$		−	640.776i		−	1.38997i	0.719024	−	0.694985i	$-0.244589\pi$
$462$	366.322	+	349.051i	0.792905	+	0.755522i
$463$	162.780	+	162.780i	0.351577	+	0.351577i	0.860696	−	0.509119i	$-0.170029\pi$
$463$	162.780	+	162.780i	0.351577	+	0.351577i	−0.509119	+	0.860696i	$0.670029\pi$
$464$	−37.4391	+	235.022i	−0.0806876	+	0.506512i
$465$		0			0
$466$	146.527	−	54.0195i	0.314436	−	0.115922i
$467$	−424.962	−	424.962i	−0.909984	−	0.909984i	0.0862867	−	0.996270i	$-0.472500\pi$
$467$	−424.962	−	424.962i	−0.909984	−	0.909984i	−0.996270	+	0.0862867i	$0.972500\pi$
$468$	−295.870	+	325.911i	−0.632201	+	0.696391i
$469$		−	382.377i		−	0.815304i
$470$		0			0
$471$	−562.066	−	191.936i	−1.19335	−	0.407508i
$472$	−9.47025	−	33.6653i	−0.0200641	−	0.0713248i
$473$	−963.503	−	963.503i	−2.03700	−	2.03700i
$474$	−12.8066	−	530.453i	−0.0270182	−	1.11910i
$475$		0			0
$476$	−209.693	+	178.932i	−0.440531	+	0.375909i
$477$	204.544	−	26.1723i	0.428813	−	0.0548685i
$478$	−83.7902	−	38.6505i	−0.175293	−	0.0808588i
$479$		−	439.071i		−	0.916641i	−0.888787	−	0.458321i	$-0.848451\pi$
$479$		−	439.071i		−	0.916641i	0.888787	−	0.458321i	$-0.151549\pi$
$480$		0			0
$481$	174.962			0.363747
$482$	−177.736	+	385.312i	−0.368746	+	0.799403i
$483$	127.111	+	258.941i	0.263169	+	0.536109i
$484$	−421.591	−	494.066i	−0.871055	−	1.02080i
$485$		0			0
$486$	−467.252	+	133.685i	−0.961424	+	0.275071i
$487$	308.231	−	308.231i	0.632918	−	0.632918i	−0.315881	−	0.948799i	$-0.602300\pi$
$487$	308.231	−	308.231i	0.632918	−	0.632918i	0.948799	+	0.315881i	$0.102300\pi$
$488$	−65.6341	+	18.4633i	−0.134496	+	0.0378345i
$489$	−235.409	−	80.3883i	−0.481409	−	0.164393i
$490$		0			0
$491$	751.660			1.53088			0.765438	−	0.643509i	$-0.222522\pi$
$491$	751.660			1.53088			0.765438	+	0.643509i	$0.222522\pi$
$492$	28.9765	−	67.0257i	0.0588954	−	0.136231i
$493$	144.681	−	144.681i	0.293472	−	0.293472i
$494$	−40.4692	−	109.772i	−0.0819215	−	0.222211i
$495$		0			0
$496$	222.223	+	35.4003i	0.448031	+	0.0713715i
$497$	−129.893	+	129.893i	−0.261353	+	0.261353i
$498$	−391.542	−	373.082i	−0.786228	−	0.749160i
$499$	−304.485			−0.610191			−0.305096	−	0.952322i	$-0.598688\pi$
$499$	−304.485			−0.610191			−0.305096	+	0.952322i	$0.598688\pi$
$500$		0			0
$501$	−338.286	−	115.519i	−0.675221	−	0.230577i
$502$	133.774	−	290.007i	0.266481	−	0.577704i
$503$	−230.058	+	230.058i	−0.457372	+	0.457372i	−0.897792	−	0.440420i	$-0.854830\pi$
$503$	−230.058	+	230.058i	−0.457372	+	0.457372i	0.440420	+	0.897792i	$0.354830\pi$
$504$	140.955	+	332.018i	0.279674	+	0.658766i
$505$		0			0
$506$	−223.519	−	606.293i	−0.441738	−	1.19821i
$507$	25.7733	+	52.5035i	0.0508348	+	0.103557i
$508$	530.563	+	41.9947i	1.04442	+	0.0826667i
$509$	−98.9386			−0.194378			−0.0971892	−	0.995266i	$-0.530985\pi$
$509$	−98.9386			−0.194378			−0.0971892	+	0.995266i	$0.530985\pi$
$510$		0			0
$511$		−	89.8357i		−	0.175804i
$512$	−348.301	+	375.274i	−0.680276	+	0.732956i
$513$	25.8912	−	126.552i	0.0504702	−	0.246690i
$514$	−95.9665	−	260.307i	−0.186705	−	0.506435i
$515$		0			0
$516$	−357.892	−	903.001i	−0.693589	−	1.75000i
$517$	296.688	+	296.688i	0.573865	+	0.573865i
$518$	60.0528	−	130.188i	0.115932	−	0.251328i
$519$	−205.705	−	70.2448i	−0.396349	−	0.135346i
$520$		0			0
$521$		−	485.997i		−	0.932816i	−0.884570	−	0.466408i	$-0.845548\pi$
$521$		−	485.997i		−	0.932816i	0.884570	−	0.466408i	$-0.154452\pi$
$522$	−123.745	−	237.420i	−0.237059	−	0.454828i
$523$	303.922	+	303.922i	0.581112	+	0.581112i	0.935209	−	0.354096i	$-0.115212\pi$
$523$	303.922	+	303.922i	0.581112	+	0.581112i	−0.354096	+	0.935209i	$0.615212\pi$
$524$	−376.868	−	441.655i	−0.719214	−	0.842854i
$525$		0			0
$526$	138.849	+	376.627i	0.263972	+	0.716021i
$527$	−136.803	−	136.803i	−0.259588	−	0.259588i
$528$	−237.517	−	772.319i	−0.449843	−	1.46273i
$529$			160.623i			0.303636i
$530$		0			0
$531$	31.1260	+	24.0641i	0.0586176	+	0.0453185i
$532$	−95.5710	−	7.56456i	−0.179645	−	0.0142191i
$533$	52.6112	+	52.6112i	0.0987077	+	0.0987077i
$534$	16.6569	+	689.930i	0.0311926	+	1.29200i
$535$		0			0
$536$	−298.717	+	532.560i	−0.557308	+	0.993583i
$537$	−35.9941	−	73.3246i	−0.0670281	−	0.136545i
$538$	−0.455200	+	0.986826i	−0.000846097	+	0.00183425i
$539$		−	402.370i		−	0.746512i
$540$		0			0
$541$	−388.275			−0.717700			−0.358850	−	0.933395i	$-0.616831\pi$
$541$	−388.275			−0.717700			−0.358850	+	0.933395i	$0.616831\pi$
$542$	−658.936	−	303.952i	−1.21575	−	0.560797i
$543$	−744.956	+	365.689i	−1.37193	+	0.673460i
$544$	431.835	−	85.3962i	0.793815	−	0.156978i
$545$		0			0
$546$	−367.422	+	8.87061i	−0.672934	+	0.0162465i
$547$	−169.325	+	169.325i	−0.309551	+	0.309551i	−0.844735	−	0.535184i	$-0.820242\pi$
$547$	−169.325	+	169.325i	−0.309551	+	0.309551i	0.535184	+	0.844735i	$0.320242\pi$
$548$	−338.929	−	26.8267i	−0.618484	−	0.0489538i
$549$	46.9156	−	60.6834i	0.0854565	−	0.110534i
$550$		0			0
$551$	71.1604			0.129148
$552$	25.2524	−	459.943i	0.0457472	−	0.833230i
$553$	313.272	−	313.272i	0.566495	−	0.566495i
$554$	210.253	−	77.5132i	0.379519	−	0.139916i
$555$		0			0
$556$	32.7111	+	38.3345i	0.0588330	+	0.0689469i
$557$	310.481	−	310.481i	0.557417	−	0.557417i	−0.371155	−	0.928571i	$-0.621038\pi$
$557$	310.481	−	310.481i	0.557417	−	0.557417i	0.928571	+	0.371155i	$0.121038\pi$
$558$	−224.491	+	117.006i	−0.402314	+	0.209689i
$559$	989.727			1.77053
$560$		0			0
$561$	−224.501	+	657.427i	−0.400179	+	1.17188i
$562$	578.887	+	267.027i	1.03005	+	0.475137i
$563$	234.187	−	234.187i	0.415962	−	0.415962i	−0.467847	−	0.883809i	$-0.654970\pi$
$563$	234.187	−	234.187i	0.415962	−	0.415962i	0.883809	+	0.467847i	$0.154970\pi$
$564$	110.204	+	278.058i	0.195398	+	0.493010i
$565$		0			0
$566$	−591.898	+	218.212i	−1.04576	+	0.385534i
$567$	−349.937	−	205.445i	−0.617173	−	0.362336i
$568$	282.383	−	79.4360i	0.497153	−	0.139852i
$569$	386.708			0.679627			0.339813	−	0.940493i	$-0.389636\pi$
$569$	386.708			0.679627			0.339813	+	0.940493i	$0.389636\pi$
$570$		0			0
$571$		−	556.152i		−	0.973996i	−0.873403	−	0.486998i	$-0.838092\pi$
$571$		−	556.152i		−	0.973996i	0.873403	−	0.486998i	$-0.161908\pi$
$572$	820.747	+	64.9631i	1.43487	+	0.113572i
$573$	−915.656	+	449.483i	−1.59800	+	0.784439i
$574$	57.2055	−	21.0897i	0.0996612	−	0.0367417i
$575$		0			0
$576$	63.0587	−	572.538i	0.109477	−	0.993989i
$577$	−695.792	−	695.792i	−1.20588	−	1.20588i	−0.972350	−	0.233530i	$-0.924972\pi$
$577$	−695.792	−	695.792i	−1.20588	−	1.20588i	−0.233530	−	0.972350i	$-0.575028\pi$
$578$	181.187	+	83.5775i	0.313473	+	0.144598i
$579$	−138.451	+	405.440i	−0.239121	+	0.700242i
$580$		0			0
$581$		−	451.566i		−	0.777223i
$582$	499.616	−	524.338i	0.858447	−	0.900924i
$583$	−272.731	−	272.731i	−0.467806	−	0.467806i
$584$	−70.1805	+	125.120i	−0.120172	+	0.214246i
$585$		0			0
$586$	−199.850	+	73.6780i	−0.341042	+	0.125730i
$587$	241.691	+	241.691i	0.411740	+	0.411740i	0.882344	−	0.470604i	$-0.155964\pi$
$587$	241.691	+	241.691i	0.411740	+	0.411740i	−0.470604	+	0.882344i	$0.655964\pi$
$588$	113.822	−	263.282i	0.193575	−	0.447758i
$589$		−	67.2853i		−	0.114236i
$590$		0			0
$591$	−309.289	+	905.721i	−0.523331	+	1.53252i
$592$	−185.343	+	134.407i	−0.313080	+	0.227039i
$593$	−109.471	−	109.471i	−0.184605	−	0.184605i	0.608754	−	0.793359i	$-0.291670\pi$
$593$	−109.471	−	109.471i	−0.184605	−	0.184605i	−0.793359	+	0.608754i	$0.791670\pi$
$594$	732.366	+	538.475i	1.23294	+	0.906524i
$595$		0			0
$596$	67.3082	+	78.8791i	0.112933	+	0.132348i
$597$	−772.015	+	378.972i	−1.29316	+	0.634794i
$598$	426.199	+	196.596i	0.712707	+	0.328755i
$599$		−	527.412i		−	0.880487i	−0.897878	−	0.440243i	$-0.854892\pi$
$599$		−	527.412i		−	0.880487i	0.897878	−	0.440243i	$-0.145108\pi$
$600$		0			0
$601$	−133.338			−0.221861			−0.110930	−	0.993828i	$-0.535383\pi$
$601$	−133.338			−0.221861			−0.110930	+	0.993828i	$0.535383\pi$
$602$	339.707	−	736.448i	0.564297	−	1.22334i
$603$	−87.1866	−	681.388i	−0.144588	−	1.13000i
$604$	609.710	−	520.270i	1.00945	−	0.861375i
$605$		0			0
$606$	953.224	−	23.0135i	1.57298	−	0.0379761i
$607$	−401.515	+	401.515i	−0.661475	+	0.661475i	−0.955728	−	0.294253i	$-0.904929\pi$
$607$	−401.515	+	401.515i	−0.661475	+	0.661475i	0.294253	+	0.955728i	$0.404929\pi$
$608$	127.198	+	85.1967i	0.209207	+	0.140126i
$609$	72.2410	−	211.550i	0.118622	−	0.347373i
$610$		0			0
$611$	−304.763			−0.498794
$612$	−332.869	+	366.666i	−0.543903	+	0.599128i
$613$	604.618	−	604.618i	0.986326	−	0.986326i	−0.0135821	−	0.999908i	$-0.504323\pi$
$613$	604.618	−	604.618i	0.986326	−	0.986326i	0.999908	+	0.0135821i	$0.00432346\pi$
$614$	−323.350	−	877.082i	−0.526629	−	1.42847i
$615$		0			0
$616$	330.046	−	588.414i	0.535789	−	0.955218i
$617$	51.5846	−	51.5846i	0.0836055	−	0.0836055i	−0.664067	−	0.747673i	$-0.731171\pi$
$617$	51.5846	−	51.5846i	0.0836055	−	0.0836055i	0.747673	+	0.664067i	$0.231171\pi$
$618$	−167.564	+	175.855i	−0.271139	+	0.284556i
$619$	−1063.63			−1.71831			−0.859155	−	0.511716i	$-0.829010\pi$
$619$	−1063.63			−1.71831			−0.859155	+	0.511716i	$0.829010\pi$
$620$		0			0
$621$	285.550	+	432.444i	0.459823	+	0.696367i
$622$	22.2251	−	48.1816i	0.0357316	−	0.0774623i
$623$	−407.454	+	407.454i	−0.654020	+	0.654020i
$624$	518.660	+	274.679i	0.831186	+	0.440190i
$625$		0			0
$626$	128.999	+	349.908i	0.206069	+	0.558959i
$627$	−216.884	+	106.466i	−0.345908	+	0.169802i
$628$	−62.4854	+	789.443i	−0.0994990	+	1.25707i
$629$	196.841			0.312943
$630$		0			0
$631$			834.260i			1.32212i	0.750331	+	0.661062i	$0.229894\pi$
$631$			834.260i			1.32212i	−0.750331	+	0.661062i	$0.770106\pi$
$632$	−681.043	+	191.581i	−1.07760	+	0.303135i
$633$	243.034	+	495.091i	0.383939	+	0.782134i
$634$	−65.1686	−	176.769i	−0.102790	−	0.278815i
$635$		0			0
$636$	−101.305	−	255.605i	−0.159285	−	0.401894i
$637$	206.661	+	206.661i	0.324428	+	0.324428i
$638$	−209.754	+	454.725i	−0.328768	+	0.712735i
$639$	−201.849	+	261.083i	−0.315882	+	0.408581i
$640$		0			0
$641$			104.566i			0.163130i	0.996668	+	0.0815648i	$0.0259918\pi$
$641$			104.566i			0.163130i	−0.996668	+	0.0815648i	$0.974008\pi$
$642$	164.955	−	173.117i	0.256939	−	0.269652i
$643$	357.160	+	357.160i	0.555459	+	0.555459i	0.928011	−	0.372552i	$-0.121517\pi$
$643$	357.160	+	357.160i	0.555459	+	0.555459i	−0.372552	+	0.928011i	$0.621517\pi$
$644$	292.571	−	249.653i	0.454303	−	0.387660i
$645$		0			0
$646$	−45.5299	−	123.499i	−0.0704797	−	0.191175i
$647$	428.808	+	428.808i	0.662764	+	0.662764i	0.956031	−	0.293266i	$-0.0947423\pi$
$647$	428.808	+	428.808i	0.662764	+	0.662764i	−0.293266	+	0.956031i	$0.594742\pi$
$648$	326.884	+	559.510i	0.504450	+	0.863441i
$649$		−	73.5884i		−	0.113387i
$650$		0			0
$651$	−200.030	−	68.3070i	−0.307266	−	0.104926i
$652$	−26.1706	+	330.641i	−0.0401390	+	0.507118i
$653$	216.356	+	216.356i	0.331327	+	0.331327i	0.853090	−	0.521763i	$-0.174726\pi$
$653$	216.356	+	216.356i	0.331327	+	0.331327i	−0.521763	+	0.853090i	$0.674726\pi$
$654$	−959.382	+	23.1622i	−1.46694	+	0.0354162i
$655$		0			0
$656$	−96.1491	−	15.3166i	−0.146569	−	0.0233485i
$657$	−20.4836	−	160.085i	−0.0311775	−	0.243661i
$658$	−104.605	+	226.772i	−0.158974	+	0.344638i
$659$			862.678i			1.30907i	0.756031	+	0.654535i	$0.227136\pi$
$659$			862.678i			1.30907i	−0.756031	+	0.654535i	$0.772864\pi$
$660$		0			0
$661$	56.1770			0.0849879			0.0424939	−	0.999097i	$-0.486470\pi$
$661$	56.1770			0.0849879			0.0424939	+	0.999097i	$0.486470\pi$
$662$	−517.494	−	238.708i	−0.781714	−	0.360587i
$663$	−222.355	−	452.966i	−0.335377	−	0.683206i
$664$	−352.768	+	628.924i	−0.531277	+	0.947175i
$665$		0			0
$666$	77.3283	−	245.685i	0.116109	−	0.368896i
$667$	−201.865	+	201.865i	−0.302646	+	0.302646i
$668$	−37.6075	+	475.135i	−0.0562987	+	0.711281i
$669$	−28.1919	−	9.62707i	−0.0421404	−	0.0143902i
$670$		0			0
$671$	−143.468			−0.213813
$672$	382.408	−	291.653i	0.569059	−	0.434007i
$673$	−236.472	+	236.472i	−0.351371	+	0.351371i	−0.860619	−	0.509249i	$-0.829923\pi$
$673$	−236.472	+	236.472i	−0.351371	+	0.351371i	0.509249	+	0.860619i	$0.329923\pi$
$674$	−780.659	+	287.802i	−1.15825	+	0.427006i
$675$		0			0
$676$	59.3223	−	50.6203i	0.0877550	−	0.0748820i
$677$	754.987	−	754.987i	1.11520	−	1.11520i	0.122759	−	0.992437i	$-0.460826\pi$
$677$	754.987	−	754.987i	1.11520	−	1.11520i	0.992437	−	0.122759i	$-0.0391742\pi$
$678$	592.722	−	622.050i	0.874221	−	0.917478i
$679$	604.720			0.890604
$680$		0			0
$681$	147.224	+	50.2744i	0.216187	+	0.0738244i
$682$	429.962	+	198.332i	0.630443	+	0.290809i
$683$	848.561	−	848.561i	1.24240	−	1.24240i	0.283401	−	0.959002i	$-0.408537\pi$
$683$	848.561	−	848.561i	1.24240	−	1.24240i	0.959002	−	0.283401i	$-0.0914626\pi$
$684$	−172.030	+	8.31145i	−0.251506	+	0.0121512i
$685$		0			0
$686$	685.353	−	252.666i	0.999057	−	0.368318i
$687$	357.098	+	727.455i	0.519794	+	1.05889i
$688$	−1048.45	+	760.314i	−1.52391	+	1.10511i
$689$	280.154			0.406609
$690$		0			0
$691$			973.366i			1.40863i	0.709886	+	0.704317i	$0.248747\pi$
$691$			973.366i			1.40863i	−0.709886	+	0.704317i	$0.751253\pi$
$692$	−22.8684	+	288.920i	−0.0330468	+	0.417515i
$693$	96.3306	+	752.851i	0.139005	+	1.08637i
$694$	727.289	−	268.127i	1.04797	−	0.386350i
$695$		0			0
$696$	−265.880	+	238.204i	−0.382011	+	0.342247i
$697$	59.1903	+	59.1903i	0.0849215	+	0.0849215i
$698$	−234.594	−	108.213i	−0.336094	−	0.155033i
$699$	221.682	+	75.7008i	0.317142	+	0.108299i
$700$		0			0
$701$		−	8.02635i		−	0.0114499i	−0.999984	−	0.00572493i	$-0.998178\pi$
$701$		−	8.02635i		−	0.0114499i	0.999984	−	0.00572493i	$-0.00182231\pi$
$702$	−652.715	+	99.5837i	−0.929793	+	0.141857i
$703$	48.4074	+	48.4074i	0.0688583	+	0.0688583i
$704$	−919.350	+	561.685i	−1.30590	+	0.797848i
$705$		0			0
$706$	1013.09	−	373.490i	1.43497	−	0.529023i
$707$	562.949	+	562.949i	0.796250	+	0.796250i
$708$	20.8166	−	48.1509i	0.0294019	−	0.0680097i
$709$			378.225i			0.533463i	0.963771	+	0.266731i	$0.0859437\pi$
$709$			378.225i			0.533463i	−0.963771	+	0.266731i	$0.914056\pi$
$710$		0			0
$711$	486.813	−	629.673i	0.684688	−	0.885615i
$712$	885.794	−	249.179i	1.24409	−	0.349970i
$713$	190.872	+	190.872i	0.267703	+	0.267703i
$714$	−413.368	+	9.97988i	−0.578947	+	0.0139774i
$715$		0			0
$716$	−82.8476	+	70.6946i	−0.115709	+	0.0987354i
$717$	−60.9924	−	124.249i	−0.0850660	−	0.173291i
$718$	−380.872	−	175.688i	−0.530463	−	0.244690i
$719$			901.949i			1.25445i	0.778838	+	0.627225i	$0.215809\pi$
$719$			901.949i			1.25445i	−0.778838	+	0.627225i	$0.784191\pi$
$720$		0			0
$721$	−202.815			−0.281296
$722$	−283.245	+	614.044i	−0.392305	+	0.850477i
$723$	−571.365	+	280.476i	−0.790270	+	0.387933i
$724$	718.236	+	841.707i	0.992038	+	1.16258i
$725$		0			0
$726$	−23.5140	−	973.954i	−0.0323885	−	1.34153i
$727$	−647.476	+	647.476i	−0.890613	+	0.890613i	−0.994581	−	0.103967i	$-0.966846\pi$
$727$	−647.476	+	647.476i	−0.890613	+	0.890613i	0.103967	+	0.994581i	$0.466846\pi$
$728$	132.700	+	471.729i	0.182280	+	0.647979i
$729$	−670.424	−	286.308i	−0.919649	−	0.392740i
$730$		0			0
$731$	1113.49			1.52325
$732$	−93.8752	−	40.5841i	−0.128245	−	0.0554428i
$733$	664.993	−	664.993i	0.907221	−	0.907221i	−0.0888262	−	0.996047i	$-0.528312\pi$
$733$	664.993	−	664.993i	0.907221	−	0.907221i	0.996047	+	0.0888262i	$0.0283116\pi$
$734$	−4.18404	−	11.3491i	−0.00570033	−	0.0154620i
$735$		0			0
$736$	−602.513	+	119.148i	−0.818631	+	0.161886i
$737$	−908.537	+	908.537i	−1.23275	+	1.23275i
$738$	97.1303	−	50.6250i	0.131613	−	0.0685975i
$739$	−605.307			−0.819090			−0.409545	−	0.912290i	$-0.634313\pi$
$739$	−605.307			−0.819090			−0.409545	+	0.912290i	$0.634313\pi$
$740$		0			0
$741$	56.7120	−	166.075i	0.0765344	−	0.224123i
$742$	96.1580	−	208.460i	0.129593	−	0.280944i
$743$	−149.548	+	149.548i	−0.201275	+	0.201275i	−0.800546	−	0.599271i	$-0.795457\pi$
$743$	−149.548	+	149.548i	−0.201275	+	0.201275i	0.599271	+	0.800546i	$0.295457\pi$
$744$	225.232	+	251.401i	0.302731	+	0.337904i
$745$		0			0
$746$	355.954	+	965.519i	0.477150	+	1.29426i
$747$	−102.963	−	804.681i	−0.137835	−	1.07722i
$748$	923.382	+	73.0868i	1.23447	+	0.0977096i
$749$	199.656			0.266564
$750$		0			0
$751$			988.027i			1.31562i	0.753186	+	0.657808i	$0.228516\pi$
$751$			988.027i			1.31562i	−0.753186	+	0.657808i	$0.771484\pi$
$752$	322.846	−	234.121i	0.429316	−	0.311331i
$753$	430.041	−	211.101i	0.571103	−	0.280347i
$754$	−125.819	−	341.282i	−0.166869	−	0.452629i
$755$		0			0
$756$	−149.934	+	519.861i	−0.198325	+	0.687646i
$757$	−590.607	−	590.607i	−0.780195	−	0.780195i	0.199669	−	0.979863i	$-0.436013\pi$
$757$	−590.607	−	590.607i	−0.780195	−	0.780195i	−0.979863	+	0.199669i	$0.936013\pi$
$758$	613.532	−	1330.07i	0.809410	−	1.75471i
$759$	313.231	−	917.267i	0.412690	−	1.20852i
$760$		0			0
$761$			354.692i			0.466087i	0.972466	+	0.233043i	$0.0748684\pi$
$761$			354.692i			0.466087i	−0.972466	+	0.233043i	$0.925132\pi$
$762$	577.967	+	550.718i	0.758487	+	0.722727i
$763$	−566.586	−	566.586i	−0.742576	−	0.742576i
$764$	882.813	+	1034.58i	1.15551	+	1.35416i
$765$		0			0
$766$	−335.823	−	910.914i	−0.438411	−	1.18918i
$767$	37.7956	+	37.7956i	0.0492772	+	0.0492772i
$768$	−760.445	+	107.461i	−0.990162	+	0.139924i
$769$		−	262.078i		−	0.340804i	−0.985375	−	0.170402i	$-0.945493\pi$
$769$		−	262.078i		−	0.340804i	0.985375	−	0.170402i	$-0.0545067\pi$
$770$		0			0
$771$	134.484	−	393.822i	0.174428	−	0.510794i
$772$	569.456	+	45.0732i	0.737638	+	0.0583849i
$773$	−616.984	−	616.984i	−0.798168	−	0.798168i	0.184639	−	0.982806i	$-0.440888\pi$
$773$	−616.984	−	616.984i	−0.798168	−	0.798168i	−0.982806	+	0.184639i	$0.940888\pi$
$774$	437.431	−	1389.79i	0.565156	−	1.79560i
$775$		0			0
$776$	−842.231	−	472.413i	−1.08535	−	0.608780i
$777$	193.051	−	94.7662i	0.248457	−	0.121964i
$778$	503.117	−	1090.70i	0.646679	−	1.40193i
$779$			29.1122i			0.0373713i
$780$		0			0
$781$	617.256			0.790340
$782$	479.495	+	221.180i	0.613165	+	0.282839i
$783$	80.4958	−	393.450i	0.102804	−	0.502490i
$784$	−377.681	−	60.1647i	−0.481735	−	0.0767407i
$785$		0			0
$786$	−21.0197	−	870.637i	−0.0267426	−	1.10768i
$787$	−471.258	+	471.258i	−0.598803	+	0.598803i	−0.939994	−	0.341191i	$-0.889170\pi$
$787$	−471.258	+	471.258i	−0.598803	+	0.598803i	0.341191	+	0.939994i	$0.389170\pi$
$788$	1272.12	+	100.690i	1.61437	+	0.127779i
$789$	−194.578	+	569.802i	−0.246614	+	0.722183i
$790$		0			0
$791$	717.412			0.906969
$792$	453.969	−	1123.80i	0.573194	−	1.41893i
$793$	73.6865	−	73.6865i	0.0929212	−	0.0929212i
$794$	783.636	−	288.900i	0.986947	−	0.363853i
$795$		0			0
$796$	744.324	+	872.281i	0.935081	+	1.09583i
$797$	−485.701	+	485.701i	−0.609411	+	0.609411i	−0.942792	−	0.333381i	$-0.891811\pi$
$797$	−485.701	+	485.701i	−0.609411	+	0.609411i	0.333381	+	0.942792i	$0.391811\pi$
$798$	−104.110	−	99.2015i	−0.130464	−	0.124313i
$799$	−342.874			−0.429129
$800$		0			0
$801$	−633.170	+	818.979i	−0.790474	+	1.02245i
$802$	−545.578	−	251.663i	−0.680271	−	0.313794i
$803$	−213.451	+	213.451i	−0.265818	+	0.265818i
$804$	−851.486	+	337.475i	−1.05906	+	0.419745i
$805$		0			0
$806$	−322.697	+	118.967i	−0.400368	+	0.147602i
$807$	−1.46333	+	0.718328i	−0.00181329	+	0.000890122i
$808$	−344.272	−	1223.83i	−0.426079	−	1.51465i
$809$	183.688			0.227056			0.113528	−	0.993535i	$-0.463785\pi$
$809$	183.688			0.227056			0.113528	+	0.993535i	$0.463785\pi$
$810$		0			0
$811$		−	1332.68i		−	1.64325i	−0.570027	−	0.821626i	$-0.693067\pi$
$811$		−	1332.68i		−	1.64325i	0.570027	−	0.821626i	$-0.306933\pi$
$812$	−297.131	−	23.5182i	−0.365924	−	0.0289634i
$813$	−479.651	−	977.111i	−0.589977	−	1.20186i
$814$	−452.016	+	166.643i	−0.555303	+	0.204721i
$815$		0			0
$816$	583.519	+	309.028i	0.715097	+	0.378710i
$817$	273.831	+	273.831i	0.335166	+	0.335166i
$818$	97.7350	+	45.0829i	0.119480	+	0.0551136i
$819$	−436.147	−	337.194i	−0.532536	−	0.411715i
$820$		0			0
$821$			1157.86i			1.41030i	0.709057	+	0.705152i	$0.249121\pi$
$821$			1157.86i			1.41030i	−0.709057	+	0.705152i	$0.750879\pi$
$822$	−369.212	−	351.805i	−0.449163	−	0.427986i
$823$	−420.085	−	420.085i	−0.510432	−	0.510432i	0.404227	−	0.914659i	$-0.367541\pi$
$823$	−420.085	−	420.085i	−0.510432	−	0.510432i	−0.914659	+	0.404227i	$0.867541\pi$
$824$	282.472	+	158.441i	0.342806	+	0.192282i
$825$		0			0
$826$	41.0961	−	15.1507i	0.0497532	−	0.0183423i
$827$	−450.627	−	450.627i	−0.544893	−	0.544893i	0.380066	−	0.924959i	$-0.375901\pi$
$827$	−450.627	−	450.627i	−0.544893	−	0.544893i	−0.924959	+	0.380066i	$0.875901\pi$
$828$	464.431	−	511.586i	0.560907	−	0.617858i
$829$		−	1059.56i		−	1.27812i	−0.769155	−	0.639062i	$-0.779323\pi$
$829$		−	1059.56i		−	1.27812i	0.769155	−	0.639062i	$-0.220677\pi$
$830$		0			0
$831$	318.094	+	108.624i	0.382785	+	0.130715i
$832$	183.700	−	760.672i	0.220793	−	0.914270i
$833$	232.504	+	232.504i	0.279116	+	0.279116i
$834$	1.82445	+	75.5689i	0.00218759	+	0.0906102i
$835$		0			0
$836$	209.105	+	245.052i	0.250126	+	0.293125i
$837$	−372.024	−	76.1123i	−0.444473	−	0.0909346i
$838$	1058.05	+	488.053i	1.26259	+	0.582402i
$839$			425.692i			0.507380i	0.967286	+	0.253690i	$0.0816443\pi$
$839$			425.692i			0.507380i	−0.967286	+	0.253690i	$0.918356\pi$
$840$		0			0
$841$	−619.762			−0.736935
$842$	407.702	−	883.855i	0.484207	−	1.04971i
$843$	421.382	+	858.410i	0.499860	+	1.01828i
$844$	559.391	−	477.333i	0.662786	−	0.565560i
$845$		0			0
$846$	−134.697	+	427.954i	−0.159216	+	0.505856i
$847$	575.192	−	575.192i	0.679093	−	0.679093i
$848$	−296.776	+	215.216i	−0.349972	+	0.253792i
$849$	−895.488	−	305.794i	−1.05476	−	0.360182i
$850$		0			0
$851$	−274.640			−0.322726
$852$	403.887	+	174.608i	0.474046	+	0.204939i
$853$	−533.860	+	533.860i	−0.625861	+	0.625861i	−0.947024	−	0.321163i	$-0.895926\pi$
$853$	−533.860	+	533.860i	−0.625861	+	0.625861i	0.321163	+	0.947024i	$0.395926\pi$
$854$	−29.5380	−	80.1213i	−0.0345878	−	0.0938188i
$855$		0			0
$856$	−278.073	−	155.973i	−0.324852	−	0.182212i
$857$	575.339	−	575.339i	0.671340	−	0.671340i	−0.286685	−	0.958025i	$-0.592553\pi$
$857$	575.339	−	575.339i	0.671340	−	0.671340i	0.958025	+	0.286685i	$0.0925532\pi$
$858$	894.079	+	851.925i	1.04205	+	0.992920i
$859$	730.948			0.850929			0.425465	−	0.904975i	$-0.360111\pi$
$859$	730.948			0.850929			0.425465	+	0.904975i	$0.360111\pi$
$860$		0			0
$861$	86.5468	+	29.5543i	0.100519	+	0.0343256i
$862$	−464.635	+	1007.28i	−0.539019	+	1.16854i
$863$	−503.710	+	503.710i	−0.583673	+	0.583673i	−0.935911	−	0.352238i	$-0.885421\pi$
$863$	−503.710	+	503.710i	−0.583673	+	0.583673i	0.352238	+	0.935911i	$0.385421\pi$
$864$	614.942	−	606.912i	0.711739	−	0.702444i
$865$		0			0
$866$	149.601	+	405.789i	0.172749	+	0.468579i
$867$	131.889	+	268.676i	0.152122	+	0.309891i
$868$	−22.2375	+	280.950i	−0.0256193	+	0.323675i
$869$	−1488.68			−1.71310
$870$		0			0
$871$		−	933.264i		−	1.07149i
$872$	346.496	+	1231.74i	0.397358	+	1.41255i
$873$	1077.60	−	137.883i	1.23436	−	0.157942i
$874$	63.5250	+	172.311i	0.0726831	+	0.197152i
$875$		0			0
$876$	−200.048	+	79.2862i	−0.228365	+	0.0905094i
$877$	1002.77	+	1002.77i	1.14341	+	1.14341i	0.987822	+	0.155586i	$0.0497266\pi$
$877$	1002.77	+	1002.77i	1.14341	+	1.14341i	0.155586	+	0.987822i	$0.450273\pi$
$878$	−183.315	+	397.407i	−0.208787	+	0.452627i
$879$	−302.356	−	103.249i	−0.343977	−	0.117462i
$880$		0			0
$881$		−	1337.17i		−	1.51779i	−0.651213	−	0.758895i	$-0.725739\pi$
$881$		−	1337.17i		−	1.51779i	0.651213	−	0.758895i	$-0.274261\pi$
$882$	381.535	−	198.858i	0.432579	−	0.225463i
$883$	29.5709	+	29.5709i	0.0334891	+	0.0334891i	0.723653	−	0.690164i	$-0.242462\pi$
$883$	29.5709	+	29.5709i	0.0334891	+	0.0334891i	−0.690164	+	0.723653i	$0.742462\pi$
$884$	−511.795	+	436.719i	−0.578953	+	0.494026i
$885$		0			0
$886$	39.1314	+	106.143i	0.0441664	+	0.119801i
$887$	−815.068	−	815.068i	−0.918904	−	0.918904i	0.0780457	−	0.996950i	$-0.475132\pi$
$887$	−815.068	−	815.068i	−0.918904	−	0.918904i	−0.996950	+	0.0780457i	$0.975132\pi$
$888$	−342.906	−	18.8267i	−0.386156	−	0.0212013i
$889$			666.572i			0.749799i
$890$		0			0
$891$	343.318	+	1319.60i	0.385318	+	1.48103i
$892$	−3.13412	+	39.5966i	−0.00351359	+	0.0443908i
$893$	−84.3198	−	84.3198i	−0.0944231	−	0.0944231i
$894$	3.75409	+	155.495i	0.00419920	+	0.173931i
$895$		0			0
$896$	−502.959	−	397.778i	−0.561338	−	0.443948i
$897$	310.238	+	631.994i	0.345861	+	0.704564i
$898$	−198.097	+	429.454i	−0.220598	+	0.478234i
$899$		−	209.190i		−	0.232692i
$900$		0			0
$901$	315.187			0.349819
$902$	−186.031	−	85.8120i	−0.206243	−	0.0951352i
$903$	1092.05	−	536.074i	1.20936	−	0.593659i
$904$	−999.183	−	560.449i	−1.10529	−	0.619966i
$905$		0			0
$906$	1201.92	−	29.0178i	1.32663	−	0.0320285i
$907$	551.789	−	551.789i	0.608367	−	0.608367i	−0.334152	−	0.942519i	$-0.608450\pi$
$907$	551.789	−	551.789i	0.608367	−	0.608367i	0.942519	+	0.334152i	$0.108450\pi$
$908$	16.3670	−	206.781i	0.0180253	−	0.227733i
$909$	1131.52	+	874.803i	1.24480	+	0.962380i
$910$		0			0
$911$	−1547.30			−1.69846			−0.849231	−	0.528022i	$-0.822934\pi$
$911$	−1547.30			−1.69846			−0.849231	+	0.528022i	$0.822934\pi$
$912$	67.5032	+	219.496i	0.0740166	+	0.240675i
$913$	−1072.93	+	1072.93i	−1.17517	+	1.17517i
$914$	644.364	−	237.555i	0.704993	−	0.259907i
$915$		0			0
$916$	821.934	−	701.363i	0.897307	−	0.765680i
$917$	514.175	−	514.175i	0.560715	−	0.560715i
$918$	−734.337	+	112.037i	−0.799931	+	0.122044i
$919$	−1012.94			−1.10222			−0.551109	−	0.834433i	$-0.685795\pi$
$919$	−1012.94			−1.10222			−0.551109	+	0.834433i	$0.685795\pi$
$920$		0			0
$921$	453.130	−	1326.95i	0.491998	−	1.44077i
$922$	−1163.71	−	536.794i	−1.26216	−	0.582207i
$923$	−317.028	+	317.028i	−0.343475	+	0.343475i
$924$	940.789	−	372.869i	1.01817	−	0.403538i
$925$		0			0
$926$	431.990	−	159.260i	0.466512	−	0.171987i
$927$	−361.411	+	46.2441i	−0.389872	+	0.0498858i
$928$	395.459	+	264.877i	0.426141	+	0.285427i
$929$	1529.05			1.64591			0.822955	−	0.568106i	$-0.192324\pi$
$929$	1529.05			1.64591			0.822955	+	0.568106i	$0.192324\pi$
$930$		0			0
$931$			114.355i			0.122830i
$932$	24.6446	−	311.361i	0.0264427	−	0.334079i
$933$	71.4467	−	35.0722i	0.0765773	−	0.0375908i
$934$	−1127.78	+	415.772i	−1.20747	+	0.445152i
$935$		0			0
$936$	344.029	+	810.353i	0.367552	+	0.865762i
$937$	−662.561	−	662.561i	−0.707109	−	0.707109i	0.258818	−	0.965926i	$-0.416667\pi$
$937$	−662.561	−	662.561i	−0.707109	−	0.707109i	−0.965926	+	0.258818i	$0.916667\pi$
$938$	−694.435	−	320.327i	−0.740336	−	0.341500i
$939$	−180.774	+	529.380i	−0.192518	+	0.563769i
$940$		0			0
$941$		−	961.186i		−	1.02145i	−0.859744	−	0.510726i	$-0.829377\pi$
$941$		−	961.186i		−	1.02145i	0.859744	−	0.510726i	$-0.170623\pi$
$942$	−819.432	+	859.978i	−0.869885	+	0.912927i
$943$	−82.5844	−	82.5844i	−0.0875763	−	0.0875763i
$944$	−69.0730	−	11.0034i	−0.0731706	−	0.0116561i
$945$		0			0
$946$	−2556.97	+	942.667i	−2.70293	+	0.996476i
$947$	1259.29	+	1259.29i	1.32977	+	1.32977i	0.905568	+	0.424202i	$0.139445\pi$
$947$	1259.29	+	1259.29i	1.32977	+	1.32977i	0.424202	+	0.905568i	$0.360555\pi$
$948$	−974.084	−	421.116i	−1.02751	−	0.444215i
$949$		−	219.261i		−	0.231044i
$950$		0			0
$951$	91.3247	−	267.435i	0.0960302	−	0.281215i
$952$	149.294	+	530.719i	0.156822	+	0.557478i
$953$	−62.1880	−	62.1880i	−0.0652550	−	0.0652550i	0.673726	−	0.738981i	$-0.264693\pi$
$953$	−62.1880	−	62.1880i	−0.0652550	−	0.0652550i	−0.738981	+	0.673726i	$0.764693\pi$
$954$	123.820	−	393.397i	0.129790	−	0.412366i
$955$		0			0
$956$	−140.386	+	119.793i	−0.146848	+	0.125306i
$957$	−674.295	+	331.002i	−0.704592	+	0.345875i
$958$	−797.397	−	367.821i	−0.832356	−	0.383947i
$959$		−	425.813i		−	0.444018i
$960$		0			0
$961$	763.202			0.794174
$962$	146.570	−	317.749i	0.152360	−	0.330300i
$963$	355.783	−	45.5240i	0.369453	−	0.0472731i
$964$	550.871	+	645.571i	0.571443	+	0.669680i
$965$		0			0
$966$	576.746	−	13.9243i	0.597046	−	0.0144144i
$967$	−1.17333	+	1.17333i	−0.00121337	+	0.00121337i	−0.707713	−	0.706500i	$-0.750273\pi$
$967$	−1.17333	+	1.17333i	−0.00121337	+	0.00121337i	0.706500	+	0.707713i	$0.250273\pi$
$968$	−1250.45	+	351.759i	−1.29179	+	0.363387i
$969$	63.8038	−	186.843i	0.0658450	−	0.192821i
$970$		0			0
$971$	−570.125			−0.587153			−0.293576	−	0.955936i	$-0.594846\pi$
$971$	−570.125			−0.587153			−0.293576	+	0.955936i	$0.594846\pi$
$972$	−148.644	+	960.567i	−0.152926	+	0.988238i
$973$	−44.6290	+	44.6290i	−0.0458674	+	0.0458674i
$974$	−301.565	−	817.991i	−0.309615	−	0.839827i
$975$		0			0
$976$	−21.4522	+	134.665i	−0.0219797	+	0.137977i
$977$	−430.216	+	430.216i	−0.440344	+	0.440344i	−0.892128	−	0.451784i	$-0.850788\pi$
$977$	−430.216	+	430.216i	−0.440344	+	0.440344i	0.451784	+	0.892128i	$0.350788\pi$
$978$	−343.201	+	360.183i	−0.350921	+	0.368285i
$979$	1936.24			1.97777
$980$		0			0
$981$	−1138.83	−	880.455i	−1.16089	−	0.897507i
$982$	629.685	−	1365.09i	0.641227	−	1.39011i
$983$	876.585	−	876.585i	0.891745	−	0.891745i	−0.102942	−	0.994687i	$-0.532826\pi$
$983$	876.585	−	876.585i	0.891745	−	0.891745i	0.994687	+	0.102942i	$0.0328257\pi$
$984$	−97.4509	−	108.773i	−0.0990355	−	0.110542i
$985$		0			0
$986$	−141.553	−	383.959i	−0.143563	−	0.389411i
$987$	−336.272	+	165.071i	−0.340701	+	0.167246i
$988$	−233.259	−	18.4627i	−0.236092	−	0.0186870i
$989$	−1553.59			−1.57086
$990$		0			0
$991$		−	183.991i		−	0.185662i	−0.995682	−	0.0928310i	$-0.970408\pi$
$991$		−	183.991i		−	0.185662i	0.995682	−	0.0928310i	$-0.0295916\pi$
$992$	250.453	−	373.924i	0.252472	−	0.376939i
$993$	−376.693	−	767.373i	−0.379349	−	0.772783i
$994$	127.084	+	344.712i	0.127851	+	0.346793i
$995$		0			0
$996$	−1005.56	+	398.539i	−1.00960	+	0.400139i
$997$	−276.341	−	276.341i	−0.277172	−	0.277172i	0.554807	−	0.831979i	$-0.312792\pi$
$997$	−276.341	−	276.341i	−0.277172	−	0.277172i	−0.831979	+	0.554807i	$0.812792\pi$
$998$	−255.075	+	552.976i	−0.255586	+	0.554084i
$999$	322.405	−	212.889i	0.322728	−	0.213102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.13		40
3.2	odd	2	inner	300.3.l.g.107.8		40
4.3	odd	2	inner	300.3.l.g.107.18		40
5.2	odd	4		60.3.l.a.23.18	yes	40
5.3	odd	4	inner	300.3.l.g.143.3		40
5.4	even	2		60.3.l.a.47.8	yes	40
12.11	even	2	inner	300.3.l.g.107.3		40
15.2	even	4		60.3.l.a.23.3	✓	40
15.8	even	4	inner	300.3.l.g.143.18		40
15.14	odd	2		60.3.l.a.47.13	yes	40
20.3	even	4	inner	300.3.l.g.143.8		40
20.7	even	4		60.3.l.a.23.13	yes	40
20.19	odd	2		60.3.l.a.47.3	yes	40
60.23	odd	4	inner	300.3.l.g.143.13		40
60.47	odd	4		60.3.l.a.23.8	yes	40
60.59	even	2		60.3.l.a.47.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.3	✓	40	15.2	even	4
60.3.l.a.23.8	yes	40	60.47	odd	4
60.3.l.a.23.13	yes	40	20.7	even	4
60.3.l.a.23.18	yes	40	5.2	odd	4
60.3.l.a.47.3	yes	40	20.19	odd	2
60.3.l.a.47.8	yes	40	5.4	even	2
60.3.l.a.47.13	yes	40	15.14	odd	2
60.3.l.a.47.18	yes	40	60.59	even	2
300.3.l.g.107.3		40	12.11	even	2	inner
300.3.l.g.107.8		40	3.2	odd	2	inner
300.3.l.g.107.13		40	1.1	even	1	trivial
300.3.l.g.107.18		40	4.3	odd	2	inner
300.3.l.g.143.3		40	5.3	odd	4	inner
300.3.l.g.143.8		40	20.3	even	4	inner
300.3.l.g.143.13		40	60.23	odd	4	inner
300.3.l.g.143.18		40	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	300.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.837725 - 1.81610i) q^{2} +(2.69303 - 1.32197i) q^{3} +(-2.59643 - 3.04278i) q^{4} +(-0.144815 - 5.99825i) q^{6} +(3.54241 - 3.54241i) q^{7} +(-7.70110 + 2.16636i) q^{8} +(5.50478 - 7.12021i) q^{9} +O(q^{10})\)	\(q+(0.837725 - 1.81610i) q^{2} +(2.69303 - 1.32197i) q^{3} +(-2.59643 - 3.04278i) q^{4} +(-0.144815 - 5.99825i) q^{6} +(3.54241 - 3.54241i) q^{7} +(-7.70110 + 2.16636i) q^{8} +(5.50478 - 7.12021i) q^{9} -16.8337 q^{11} +(-11.0147 - 4.76189i) q^{12} +(8.64592 - 8.64592i) q^{13} +(-3.46580 - 9.40093i) q^{14} +(-2.51707 + 15.8008i) q^{16} +(9.72710 - 9.72710i) q^{17} +(-8.31951 - 15.9620i) q^{18} +4.78419 q^{19} +(4.85684 - 14.2228i) q^{21} +(-14.1020 + 30.5716i) q^{22} +(-13.5716 + 13.5716i) q^{23} +(-17.8754 + 16.0147i) q^{24} +(-8.45895 - 22.9448i) q^{26} +(5.41182 - 26.4521i) q^{27} +(-19.9764 - 1.58116i) q^{28} +14.8741 q^{29} -14.0641i q^{31} +(26.5872 + 17.8080i) q^{32} +(-45.3336 + 22.2536i) q^{33} +(-9.51674 - 25.8140i) q^{34} +(-35.9581 + 1.73727i) q^{36} +(10.1182 + 10.1182i) q^{37} +(4.00784 - 8.68857i) q^{38} +(11.8540 - 34.7134i) q^{39} +6.08509i q^{41} +(-21.7613 - 20.7353i) q^{42} +(57.2366 + 57.2366i) q^{43} +(43.7075 + 51.2213i) q^{44} +(13.2781 + 36.0167i) q^{46} +(-17.6247 - 17.6247i) q^{47} +(14.1096 + 45.8794i) q^{48} +23.9027i q^{49} +(13.3364 - 39.0543i) q^{51} +(-48.7562 - 3.85911i) q^{52} +(16.2015 + 16.2015i) q^{53} +(-43.5060 - 31.9880i) q^{54} +(-19.6063 + 34.9546i) q^{56} +(12.8840 - 6.32456i) q^{57} +(12.4604 - 27.0128i) q^{58} +4.37150i q^{59} +8.52269 q^{61} +(-25.5418 - 11.7818i) q^{62} +(-5.72249 - 44.7229i) q^{63} +(54.6137 - 33.3667i) q^{64} +(2.43777 + 100.973i) q^{66} +(53.9714 - 53.9714i) q^{67} +(-54.8532 - 4.34170i) q^{68} +(-18.6074 + 54.4900i) q^{69} -36.6679 q^{71} +(-26.9679 + 66.7588i) q^{72} +(12.6800 - 12.6800i) q^{73} +(26.8519 - 9.89937i) q^{74} +(-12.4218 - 14.5573i) q^{76} +(-59.6318 + 59.6318i) q^{77} +(-53.1125 - 50.6084i) q^{78} +88.4346 q^{79} +(-20.3947 - 78.3904i) q^{81} +(11.0511 + 5.09763i) q^{82} +(63.7372 - 63.7372i) q^{83} +(-55.8873 + 22.1502i) q^{84} +(151.896 - 55.9988i) q^{86} +(40.0563 - 19.6631i) q^{87} +(129.638 - 36.4679i) q^{88} -115.022 q^{89} -61.2548i q^{91} +(76.5332 + 6.05770i) q^{92} +(-18.5923 - 37.8749i) q^{93} +(-46.7728 + 17.2435i) q^{94} +(95.1415 + 12.8098i) q^{96} +(85.3544 + 85.3544i) q^{97} +(43.4096 + 20.0239i) q^{98} +(-92.6658 + 119.859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} + 20 q^{12} + 8 q^{13} - 36 q^{16} + 24 q^{18} - 24 q^{21} + 76 q^{22} + 84 q^{28} + 40 q^{33} + 172 q^{36} + 40 q^{37} - 236 q^{42} + 240 q^{46} - 196 q^{48} - 304 q^{52} + 72 q^{57} - 180 q^{58} + 48 q^{61} - 552 q^{66} + 600 q^{72} - 104 q^{73} - 736 q^{76} + 408 q^{78} + 72 q^{81} + 720 q^{82} + 580 q^{88} - 368 q^{93} + 884 q^{96} - 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 + 20 * q^12 + 8 * q^13 - 36 * q^16 + 24 * q^18 - 24 * q^21 + 76 * q^22 + 84 * q^28 + 40 * q^33 + 172 * q^36 + 40 * q^37 - 236 * q^42 + 240 * q^46 - 196 * q^48 - 304 * q^52 + 72 * q^57 - 180 * q^58 + 48 * q^61 - 552 * q^66 + 600 * q^72 - 104 * q^73 - 736 * q^76 + 408 * q^78 + 72 * q^81 + 720 * q^82 + 580 * q^88 - 368 * q^93 + 884 * q^96 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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