LMFDB - Embedded newform 300.3.l.g.107.15

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			107.15
Character	$\chi$	$=$	300.107
Dual form			300.3.l.g.143.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07935 + 1.68375i) q^{2} +(-0.130491 + 2.99716i) q^{3} +(-1.67002 + 3.63470i) q^{4} +(-5.18731 + 3.01526i) q^{6} +(1.91561 - 1.91561i) q^{7} +(-7.92245 + 1.11122i) q^{8} +(-8.96594 - 0.782204i) q^{9} +O(q^{10})$	\(q+(1.07935 + 1.68375i) q^{2} +(-0.130491 + 2.99716i) q^{3} +(-1.67002 + 3.63470i) q^{4} +(-5.18731 + 3.01526i) q^{6} +(1.91561 - 1.91561i) q^{7} +(-7.92245 + 1.11122i) q^{8} +(-8.96594 - 0.782204i) q^{9} -6.87236 q^{11} +(-10.6759 - 5.47960i) q^{12} +(-12.2746 + 12.2746i) q^{13} +(5.29303 + 1.15780i) q^{14} +(-10.4221 - 12.1400i) q^{16} +(-9.47120 + 9.47120i) q^{17} +(-8.36034 - 15.9407i) q^{18} +33.2524 q^{19} +(5.49143 + 5.99137i) q^{21} +(-7.41767 - 11.5713i) q^{22} +(-7.20994 + 7.20994i) q^{23} +(-2.29669 - 23.8899i) q^{24} +(-33.9159 - 7.41877i) q^{26} +(3.51436 - 26.7703i) q^{27} +(3.76357 + 10.1618i) q^{28} +2.29155 q^{29} -12.1558i q^{31} +(9.19168 - 30.6515i) q^{32} +(0.896780 - 20.5976i) q^{33} +(-26.1698 - 5.72440i) q^{34} +(17.8164 - 31.2822i) q^{36} +(20.7290 + 20.7290i) q^{37} +(35.8909 + 55.9886i) q^{38} +(-35.1872 - 38.3906i) q^{39} +50.9173i q^{41} +(-4.16080 + 15.7130i) q^{42} +(-15.1975 - 15.1975i) q^{43} +(11.4770 - 24.9790i) q^{44} +(-19.9218 - 4.35769i) q^{46} +(26.7793 + 26.7793i) q^{47} +(37.7456 - 29.6525i) q^{48} +41.6608i q^{49} +(-27.1508 - 29.6226i) q^{51} +(-24.1157 - 65.1132i) q^{52} +(-15.5183 - 15.5183i) q^{53} +(48.8677 - 22.9772i) q^{54} +(-13.0477 + 17.3050i) q^{56} +(-4.33913 + 99.6627i) q^{57} +(2.47338 + 3.85839i) q^{58} +63.0946i q^{59} +28.4752 q^{61} +(20.4672 - 13.1203i) q^{62} +(-18.6737 + 15.6769i) q^{63} +(61.5304 - 17.6071i) q^{64} +(35.6491 - 20.7220i) q^{66} +(-32.4542 + 32.4542i) q^{67} +(-18.6079 - 50.2420i) q^{68} +(-20.6685 - 22.5502i) q^{69} +88.8377 q^{71} +(71.9014 - 3.76614i) q^{72} +(-71.1740 + 71.1740i) q^{73} +(-12.5286 + 57.2763i) q^{74} +(-55.5320 + 120.862i) q^{76} +(-13.1648 + 13.1648i) q^{77} +(26.6609 - 100.683i) q^{78} -75.1410 q^{79} +(79.7763 + 14.0264i) q^{81} +(-85.7318 + 54.9574i) q^{82} +(58.6543 - 58.6543i) q^{83} +(-30.9476 + 9.95402i) q^{84} +(9.18537 - 41.9921i) q^{86} +(-0.299026 + 6.86815i) q^{87} +(54.4459 - 7.63668i) q^{88} -41.1063 q^{89} +47.0267i q^{91} +(-14.1653 - 38.2467i) q^{92} +(36.4327 + 1.58621i) q^{93} +(-16.1854 + 73.9937i) q^{94} +(90.6680 + 31.5487i) q^{96} +(-30.3484 - 30.3484i) q^{97} +(-70.1464 + 44.9665i) q^{98} +(61.6172 + 5.37559i) 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 $

$2$	1.07935	+	1.68375i	0.539674	+	0.841874i
$2$	1.07935	+	1.68375i	0.539674	+	0.841874i
$3$	−0.130491	+	2.99716i	−0.0434969	+	0.999054i
$3$	−0.130491	+	2.99716i	−0.0434969	+	0.999054i
$4$	−1.67002	+	3.63470i	−0.417504	+	0.908675i
$5$		0			0
$5$		0			0
$6$	−5.18731	+	3.01526i	−0.864552	+	0.502544i
$7$	1.91561	−	1.91561i	0.273659	−	0.273659i	−0.556912	−	0.830571i	$-0.688014\pi$
$7$	1.91561	−	1.91561i	0.273659	−	0.273659i	0.830571	+	0.556912i	$0.188014\pi$
$8$	−7.92245	+	1.11122i	−0.990306	+	0.138902i
$9$	−8.96594	−	0.782204i	−0.996216	−	0.0869115i
$10$		0			0
$11$	−6.87236			−0.624760			−0.312380	−	0.949957i	$-0.601126\pi$
$11$	−6.87236			−0.624760			−0.312380	+	0.949957i	$0.601126\pi$
$12$	−10.6759	−	5.47960i	−0.889655	−	0.456634i
$13$	−12.2746	+	12.2746i	−0.944199	+	0.944199i	−0.998523	−	0.0543246i	$-0.982699\pi$
$13$	−12.2746	+	12.2746i	−0.944199	+	0.944199i	0.0543246	+	0.998523i	$0.482699\pi$
$14$	5.29303	+	1.15780i	0.378073	+	0.0826999i
$15$		0			0
$16$	−10.4221	−	12.1400i	−0.651380	−	0.758751i
$17$	−9.47120	+	9.47120i	−0.557129	+	0.557129i	−0.928489	−	0.371360i	$-0.878892\pi$
$17$	−9.47120	+	9.47120i	−0.557129	+	0.557129i	0.371360	+	0.928489i	$0.378892\pi$
$18$	−8.36034	−	15.9407i	−0.464463	−	0.885592i
$19$	33.2524			1.75013			0.875063	−	0.484010i	$-0.160820\pi$
$19$	33.2524			1.75013			0.875063	+	0.484010i	$0.160820\pi$
$20$		0			0
$21$	5.49143	+	5.99137i	0.261497	+	0.285303i
$22$	−7.41767	−	11.5713i	−0.337167	−	0.525969i
$23$	−7.20994	+	7.20994i	−0.313476	+	0.313476i	−0.846255	−	0.532779i	$-0.821148\pi$
$23$	−7.20994	+	7.20994i	−0.313476	+	0.313476i	0.532779	+	0.846255i	$0.321148\pi$
$24$	−2.29669	−	23.8899i	−0.0956954	−	0.995411i
$25$		0			0
$26$	−33.9159	−	7.41877i	−1.30446	−	0.285337i
$27$	3.51436	−	26.7703i	0.130162	−	0.991493i
$28$	3.76357	+	10.1618i	0.134413	+	0.362921i
$29$	2.29155			0.0790190			0.0395095	−	0.999219i	$-0.487420\pi$
$29$	2.29155			0.0790190			0.0395095	+	0.999219i	$0.487420\pi$
$30$		0			0
$31$		−	12.1558i		−	0.392121i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	12.1558i		−	0.392121i	0.980592	−	0.196061i	$-0.0628149\pi$
$32$	9.19168	−	30.6515i	0.287240	−	0.957859i
$33$	0.896780	−	20.5976i	0.0271752	−	0.624169i
$34$	−26.1698	−	5.72440i	−0.769701	−	0.168365i
$35$		0			0
$36$	17.8164	−	31.2822i	0.494899	−	0.868951i
$37$	20.7290	+	20.7290i	0.560244	+	0.560244i	0.929377	−	0.369133i	$-0.120345\pi$
$37$	20.7290	+	20.7290i	0.560244	+	0.560244i	−0.369133	+	0.929377i	$0.620345\pi$
$38$	35.8909	+	55.9886i	0.944497	+	1.47339i
$39$	−35.1872	−	38.3906i	−0.902235	−	0.984375i
$40$		0			0
$41$			50.9173i			1.24188i	0.783856	+	0.620942i	$0.213250\pi$
$41$			50.9173i			1.24188i	−0.783856	+	0.620942i	$0.786750\pi$
$42$	−4.16080	+	15.7130i	−0.0990666	+	0.374118i
$43$	−15.1975	−	15.1975i	−0.353430	−	0.353430i	0.507954	−	0.861384i	$-0.330402\pi$
$43$	−15.1975	−	15.1975i	−0.353430	−	0.353430i	−0.861384	+	0.507954i	$0.830402\pi$
$44$	11.4770	−	24.9790i	0.260840	−	0.567704i
$45$		0			0
$46$	−19.9218	−	4.35769i	−0.433082	−	0.0947325i
$47$	26.7793	+	26.7793i	0.569772	+	0.569772i	0.932064	−	0.362293i	$-0.118006\pi$
$47$	26.7793	+	26.7793i	0.569772	+	0.569772i	−0.362293	+	0.932064i	$0.618006\pi$
$48$	37.7456	−	29.6525i	0.786366	−	0.617761i
$49$			41.6608i			0.850221i
$50$		0			0
$51$	−27.1508	−	29.6226i	−0.532368	−	0.580835i
$52$	−24.1157	−	65.1132i	−0.463763	−	1.25218i
$53$	−15.5183	−	15.5183i	−0.292799	−	0.292799i	0.545386	−	0.838185i	$-0.316383\pi$
$53$	−15.5183	−	15.5183i	−0.292799	−	0.292799i	−0.838185	+	0.545386i	$0.816383\pi$
$54$	48.8677	−	22.9772i	0.904957	−	0.425503i
$55$		0			0
$56$	−13.0477	+	17.3050i	−0.232994	+	0.309018i
$57$	−4.33913	+	99.6627i	−0.0761251	+	1.74847i
$58$	2.47338	+	3.85839i	0.0426445	+	0.0665240i
$59$			63.0946i			1.06940i	0.845042	+	0.534700i	$0.179575\pi$
$59$			63.0946i			1.06940i	−0.845042	+	0.534700i	$0.820425\pi$
$60$		0			0
$61$	28.4752			0.466806			0.233403	−	0.972380i	$-0.425014\pi$
$61$	28.4752			0.466806			0.233403	+	0.972380i	$0.425014\pi$
$62$	20.4672	−	13.1203i	0.330117	−	0.211617i
$63$	−18.6737	+	15.6769i	−0.296408	+	0.248839i
$64$	61.5304	−	17.6071i	0.961412	−	0.275111i
$65$		0			0
$66$	35.6491	−	20.7220i	0.540137	−	0.313970i
$67$	−32.4542	+	32.4542i	−0.484392	+	0.484392i	−0.906531	−	0.422139i	$-0.861279\pi$
$67$	−32.4542	+	32.4542i	−0.484392	+	0.484392i	0.422139	+	0.906531i	$0.361279\pi$
$68$	−18.6079	−	50.2420i	−0.273646	−	0.738853i
$69$	−20.6685	−	22.5502i	−0.299544	−	0.326814i
$70$		0			0
$71$	88.8377			1.25124			0.625618	−	0.780130i	$-0.284847\pi$
$71$	88.8377			1.25124			0.625618	+	0.780130i	$0.284847\pi$
$72$	71.9014	−	3.76614i	0.998631	−	0.0523075i
$73$	−71.1740	+	71.1740i	−0.974987	+	0.974987i	−0.999695	−	0.0247079i	$-0.992134\pi$
$73$	−71.1740	+	71.1740i	−0.974987	+	0.974987i	0.0247079	+	0.999695i	$0.492134\pi$
$74$	−12.5286	+	57.2763i	−0.169306	+	0.774004i
$75$		0			0
$76$	−55.5320	+	120.862i	−0.730685	+	1.59029i
$77$	−13.1648	+	13.1648i	−0.170971	+	0.170971i
$78$	26.6609	−	100.683i	0.341807	−	1.29081i
$79$	−75.1410			−0.951153			−0.475576	−	0.879675i	$-0.657760\pi$
$79$	−75.1410			−0.951153			−0.475576	+	0.879675i	$0.657760\pi$
$80$		0			0
$81$	79.7763	+	14.0264i	0.984893	+	0.173165i
$82$	−85.7318	+	54.9574i	−1.04551	+	0.670213i
$83$	58.6543	−	58.6543i	0.706678	−	0.706678i	−0.259157	−	0.965835i	$-0.583445\pi$
$83$	58.6543	−	58.6543i	0.706678	−	0.706678i	0.965835	+	0.259157i	$0.0834448\pi$
$84$	−30.9476	+	9.95402i	−0.368424	+	0.118500i
$85$		0			0
$86$	9.18537	−	41.9921i	0.106807	−	0.488281i
$87$	−0.299026	+	6.86815i	−0.00343708	+	0.0789442i
$88$	54.4459	−	7.63668i	0.618704	−	0.0867805i
$89$	−41.1063			−0.461868			−0.230934	−	0.972969i	$-0.574178\pi$
$89$	−41.1063			−0.461868			−0.230934	+	0.972969i	$0.574178\pi$
$90$		0			0
$91$			47.0267i			0.516777i
$92$	−14.1653	−	38.2467i	−0.153970	−	0.415725i
$93$	36.4327	+	1.58621i	0.391750	+	0.0170561i
$94$	−16.1854	+	73.9937i	−0.172185	+	0.787167i
$95$		0			0
$96$	90.6680	+	31.5487i	0.944458	+	0.328632i
$97$	−30.3484	−	30.3484i	−0.312870	−	0.312870i	0.533150	−	0.846020i	$-0.321008\pi$
$97$	−30.3484	−	30.3484i	−0.312870	−	0.312870i	−0.846020	+	0.533150i	$0.821008\pi$
$98$	−70.1464	+	44.9665i	−0.715779	+	0.458842i
$99$	61.6172	+	5.37559i	0.622396	+	0.0542989i
$100$		0			0
$101$		−	124.297i		−	1.23067i	−0.788267	−	0.615333i	$-0.789022\pi$
$101$		−	124.297i		−	1.23067i	0.788267	−	0.615333i	$-0.210978\pi$
$102$	20.5719	−	77.6882i	0.201685	−	0.761649i
$103$	131.168	+	131.168i	1.27348	+	1.27348i	0.944252	+	0.329223i	$0.106787\pi$
$103$	131.168	+	131.168i	1.27348	+	1.27348i	0.329223	+	0.944252i	$0.393213\pi$
$104$	83.6050	−	110.884i	0.803895	−	1.06620i
$105$		0			0
$106$	9.37929	−	42.8786i	0.0884839	−	0.404516i
$107$	11.4672	+	11.4672i	0.107170	+	0.107170i	0.758659	−	0.651488i	$-0.225855\pi$
$107$	11.4672	+	11.4672i	0.107170	+	0.107170i	−0.651488	+	0.758659i	$0.725855\pi$
$108$	91.4330	+	57.4805i	0.846602	+	0.532227i
$109$			80.0130i			0.734065i	0.930208	+	0.367032i	$0.119626\pi$
$109$			80.0130i			0.734065i	−0.930208	+	0.367032i	$0.880374\pi$
$110$		0			0
$111$	−64.8331	+	59.4232i	−0.584082	+	0.535345i
$112$	−43.2203	−	3.29090i	−0.385895	−	0.0293830i
$113$	−64.8556	−	64.8556i	−0.573943	−	0.573943i	0.359285	−	0.933228i	$-0.383021\pi$
$113$	−64.8556	−	64.8556i	−0.573943	−	0.573943i	−0.933228	+	0.359285i	$0.883021\pi$
$114$	−172.490	+	100.265i	−1.51307	+	0.879515i
$115$		0			0
$116$	−3.82693	+	8.32910i	−0.0329908	+	0.0718026i
$117$	119.654	−	100.452i	1.02269	−	0.858564i
$118$	−106.235	+	68.1010i	−0.900301	+	0.577127i
$119$			36.2863i			0.304927i
$120$		0			0
$121$	−73.7706			−0.609675
$122$	30.7346	+	47.9450i	0.251923	+	0.392992i
$123$	−152.607	−	6.64423i	−1.24071	−	0.0540182i
$124$	44.1825	+	20.3003i	0.356311	+	0.163712i
$125$		0			0
$126$	−46.5513	−	14.5210i	−0.369455	−	0.115246i
$127$	63.5895	−	63.5895i	0.500705	−	0.500705i	−0.410952	−	0.911657i	$-0.634804\pi$
$127$	63.5895	−	63.5895i	0.500705	−	0.500705i	0.911657	+	0.410952i	$0.134804\pi$
$128$	96.0586	+	84.5975i	0.750458	+	0.660918i
$129$	47.5325	−	43.5662i	0.368469	−	0.337722i
$130$		0			0
$131$	144.030			1.09947			0.549734	−	0.835340i	$-0.314729\pi$
$131$	144.030			1.09947			0.549734	+	0.835340i	$0.314729\pi$
$132$	73.3684	+	37.6578i	0.555821	+	0.285287i
$133$	63.6987	−	63.6987i	0.478938	−	0.478938i
$134$	−89.6742	−	19.6154i	−0.669210	−	0.146383i
$135$		0			0
$136$	64.5105	−	85.5596i	0.474342	−	0.629115i
$137$	13.6200	−	13.6200i	0.0994161	−	0.0994161i	−0.655649	−	0.755065i	$-0.727605\pi$
$137$	13.6200	−	13.6200i	0.0994161	−	0.0994161i	0.755065	+	0.655649i	$0.227605\pi$
$138$	15.6603	−	59.1401i	0.113481	−	0.428551i
$139$	62.7261			0.451267			0.225634	−	0.974212i	$-0.427555\pi$
$139$	62.7261			0.451267			0.225634	+	0.974212i	$0.427555\pi$
$140$		0			0
$141$	−83.7563	+	76.7674i	−0.594016	+	0.544449i
$142$	95.8868	+	149.580i	0.675259	+	1.05338i
$143$	84.3554	−	84.3554i	0.589898	−	0.589898i
$144$	83.9479	+	116.999i	0.582971	+	0.812493i
$145$		0			0
$146$	−196.661	−	43.0176i	−1.34699	−	0.294641i
$147$	−124.864	−	5.43636i	−0.849417	−	0.0369820i
$148$	−109.962	+	40.7259i	−0.742983	+	0.275175i
$149$	167.292			1.12277			0.561383	−	0.827556i	$-0.310270\pi$
$149$	167.292			1.12277			0.561383	+	0.827556i	$0.310270\pi$
$150$		0			0
$151$			75.2596i			0.498408i	0.968451	+	0.249204i	$0.0801690\pi$
$151$			75.2596i			0.498408i	−0.968451	+	0.249204i	$0.919831\pi$
$152$	−263.440	+	36.9506i	−1.73316	+	0.243096i
$153$	92.3266	−	77.5098i	0.603442	−	0.506600i
$154$	−36.3756	−	7.95681i	−0.236205	−	0.0516676i
$155$		0			0
$156$	198.302	−	63.7819i	1.27116	−	0.408858i
$157$	−71.6852	−	71.6852i	−0.456593	−	0.456593i	0.440942	−	0.897536i	$-0.354644\pi$
$157$	−71.6852	−	71.6852i	−0.456593	−	0.456593i	−0.897536	+	0.440942i	$0.854644\pi$
$158$	−81.1033	−	126.519i	−0.513312	−	0.800751i
$159$	48.5359	−	44.4859i	0.305258	−	0.279786i
$160$		0			0
$161$			27.6229i			0.171571i
$162$	62.4895	+	149.463i	0.385737	+	0.922609i
$163$	−61.4502	−	61.4502i	−0.376995	−	0.376995i	0.493022	−	0.870017i	$-0.335892\pi$
$163$	−61.4502	−	61.4502i	−0.376995	−	0.376995i	−0.870017	+	0.493022i	$0.835892\pi$
$164$	−185.069	−	85.0327i	−1.12847	−	0.518492i
$165$		0			0
$166$	162.067	+	35.4507i	0.976309	+	0.213558i
$167$	36.7847	+	36.7847i	0.220268	+	0.220268i	0.808611	−	0.588344i	$-0.200220\pi$
$167$	36.7847	+	36.7847i	0.220268	+	0.220268i	−0.588344	+	0.808611i	$0.700220\pi$
$168$	−50.1633	−	41.3642i	−0.298591	−	0.246215i
$169$		−	132.331i		−	0.783022i
$170$		0			0
$171$	−298.139	−	26.0101i	−1.74350	−	0.152106i
$172$	80.6184	−	29.8583i	0.468712	−	0.173595i
$173$	137.897	+	137.897i	0.797091	+	0.797091i	0.982636	−	0.185545i	$-0.0594051\pi$
$173$	137.897	+	137.897i	0.797091	+	0.797091i	−0.185545	+	0.982636i	$0.559405\pi$
$174$	−11.8870	+	6.90963i	−0.0683160	+	0.0397105i
$175$		0			0
$176$	71.6244	+	83.4306i	0.406957	+	0.474038i
$177$	−189.105	−	8.23327i	−1.06839	−	0.0465156i
$178$	−44.3680	−	69.2126i	−0.249258	−	0.388835i
$179$		−	106.971i		−	0.597602i	−0.954315	−	0.298801i	$-0.903413\pi$
$179$		−	106.971i		−	0.597602i	0.954315	−	0.298801i	$-0.0965867\pi$
$180$		0			0
$181$	−11.6057			−0.0641199			−0.0320600	−	0.999486i	$-0.510207\pi$
$181$	−11.6057			−0.0641199			−0.0320600	+	0.999486i	$0.510207\pi$
$182$	−79.1812	+	50.7582i	−0.435061	+	0.278891i
$183$	−3.71575	+	85.3446i	−0.0203046	+	0.466364i
$184$	49.1086	−	65.1322i	0.266895	−	0.353979i
$185$		0			0
$186$	36.6528	+	63.0556i	0.197058	+	0.339009i
$187$	65.0895	−	65.0895i	0.348072	−	0.348072i
$188$	−142.057	+	52.6128i	−0.755620	+	0.279855i
$189$	−44.5494	−	58.0137i	−0.235711	−	0.306951i
$190$		0			0
$191$	135.925			0.711648			0.355824	−	0.934553i	$-0.384200\pi$
$191$	135.925			0.711648			0.355824	+	0.934553i	$0.384200\pi$
$192$	44.7422	+	186.714i	0.233032	+	0.972469i
$193$	62.7362	−	62.7362i	0.325058	−	0.325058i	−0.525646	−	0.850704i	$-0.676176\pi$
$193$	62.7362	−	62.7362i	0.325058	−	0.325058i	0.850704	+	0.525646i	$0.176176\pi$
$194$	18.3426	−	83.8556i	0.0945494	−	0.432245i
$195$		0			0
$196$	−151.425	−	69.5743i	−0.772575	−	0.354971i
$197$	96.9852	−	96.9852i	0.492311	−	0.492311i	−0.416723	−	0.909034i	$-0.636821\pi$
$197$	96.9852	−	96.9852i	0.492311	−	0.492311i	0.909034	+	0.416723i	$0.136821\pi$
$198$	57.4553	+	109.550i	0.290178	+	0.553283i
$199$	−29.0286			−0.145872			−0.0729361	−	0.997337i	$-0.523237\pi$
$199$	−29.0286			−0.145872			−0.0729361	+	0.997337i	$0.523237\pi$
$200$		0			0
$201$	−93.0356	−	101.506i	−0.462864	−	0.505003i
$202$	209.285	−	134.160i	1.03607	−	0.664158i
$203$	4.38973	−	4.38973i	0.0216243	−	0.0216243i
$204$	153.012	−	49.2147i	0.750057	−	0.241249i
$205$		0			0
$206$	−79.2780	+	362.430i	−0.384845	+	1.75937i
$207$	70.2836	−	59.0043i	0.339534	−	0.285045i
$208$	276.940	+	21.0869i	1.33144	+	0.101379i
$209$	−228.522			−1.09341
$210$		0			0
$211$		−	376.951i		−	1.78650i	−0.449561	−	0.893250i	$-0.648420\pi$
$211$		−	376.951i		−	1.78650i	0.449561	−	0.893250i	$-0.351580\pi$
$212$	82.3204	−	30.4886i	0.388304	−	0.143814i
$213$	−11.5925	+	266.261i	−0.0544249	+	1.25005i
$214$	−6.93079	+	31.6850i	−0.0323869	+	0.148061i
$215$		0			0
$216$	1.90525	+	215.992i	0.00882060	+	0.999961i
$217$	−23.2857	−	23.2857i	−0.107307	−	0.107307i
$218$	−134.722	+	86.3619i	−0.617990	+	0.396155i
$219$	−204.032	−	222.608i	−0.931655	−	1.01647i
$220$		0			0
$221$		−	232.510i		−	1.05208i
$222$	−170.031	−	45.0243i	−0.765907	−	0.202812i
$223$	−255.505	−	255.505i	−1.14576	−	1.14576i	−0.987377	−	0.158385i	$-0.949371\pi$
$223$	−255.505	−	255.505i	−1.14576	−	1.14576i	−0.158385	−	0.987377i	$-0.550629\pi$
$224$	−41.1087	−	76.3241i	−0.183521	−	0.340733i
$225$		0			0
$226$	39.1988	−	179.202i	0.173446	−	0.792930i
$227$	−109.045	−	109.045i	−0.480375	−	0.480375i	0.424876	−	0.905251i	$-0.360318\pi$
$227$	−109.045	−	109.045i	−0.480375	−	0.480375i	−0.905251	+	0.424876i	$0.860318\pi$
$228$	−354.998	−	182.210i	−1.55701	−	0.799166i
$229$		−	223.738i		−	0.977023i	−0.872557	−	0.488512i	$-0.837540\pi$
$229$		−	223.738i		−	0.977023i	0.872557	−	0.488512i	$-0.162460\pi$
$230$		0			0
$231$	−37.7391	−	41.1749i	−0.163373	−	0.178246i
$232$	−18.1547	+	2.54641i	−0.0782530	+	0.0109759i
$233$	62.4244	+	62.4244i	0.267916	+	0.267916i	0.828260	−	0.560344i	$-0.189331\pi$
$233$	62.4244	+	62.4244i	0.267916	+	0.267916i	−0.560344	+	0.828260i	$0.689331\pi$
$234$	298.285	+	93.0453i	1.27472	+	0.397630i
$235$		0			0
$236$	−229.330	−	105.369i	−0.971737	−	0.446479i
$237$	9.80522	−	225.210i	0.0413722	−	0.950252i
$238$	−61.0970	+	39.1655i	−0.256710	+	0.164561i
$239$			310.217i			1.29798i	0.760798	+	0.648989i	$0.224808\pi$
$239$			310.217i			1.29798i	−0.760798	+	0.648989i	$0.775192\pi$
$240$		0			0
$241$	−119.905			−0.497529			−0.248765	−	0.968564i	$-0.580025\pi$
$241$	−119.905			−0.497529			−0.248765	+	0.968564i	$0.580025\pi$
$242$	−79.6242	−	124.211i	−0.329026	−	0.513269i
$243$	−52.4494	+	237.272i	−0.215841	+	0.976428i
$244$	−47.5540	+	103.499i	−0.194893	+	0.424175i
$245$		0			0
$246$	−153.529	−	264.124i	−0.624102	−	1.07367i
$247$	−408.159	+	408.159i	−1.65247	+	1.65247i
$248$	13.5077	+	96.3033i	0.0544664	+	0.388320i
$249$	168.142	+	183.450i	0.675271	+	0.736747i
$250$		0			0
$251$	−336.252			−1.33965			−0.669825	−	0.742519i	$-0.733631\pi$
$251$	−336.252			−1.33965			−0.669825	+	0.742519i	$0.733631\pi$
$252$	−25.7954	−	94.0539i	−0.102363	−	0.373230i
$253$	49.5493	−	49.5493i	0.195847	−	0.195847i
$254$	175.704	+	38.4336i	0.691748	+	0.151313i
$255$		0			0
$256$	−38.7602	+	253.049i	−0.151407	+	0.988472i
$257$	199.642	−	199.642i	0.776816	−	0.776816i	−0.202472	−	0.979288i	$-0.564898\pi$
$257$	199.642	−	199.642i	0.776816	−	0.776816i	0.979288	+	0.202472i	$0.0648975\pi$
$258$	124.659	+	33.0096i	0.483173	+	0.127944i
$259$	79.4176			0.306632
$260$		0			0
$261$	−20.5459	−	1.79246i	−0.0787200	−	0.00686766i
$262$	155.459	+	242.511i	0.593354	+	0.925613i
$263$	107.927	−	107.927i	0.410368	−	0.410368i	−0.471499	−	0.881867i	$-0.656287\pi$
$263$	107.927	−	107.927i	0.410368	−	0.410368i	0.881867	+	0.471499i	$0.156287\pi$
$264$	15.7837	+	164.180i	0.0597867	+	0.621893i
$265$		0			0
$266$	176.006	+	38.4995i	0.661675	+	0.144735i
$267$	5.36399	−	123.202i	0.0200899	−	0.461431i
$268$	−63.7623	−	172.161i	−0.237919	−	0.642390i
$269$	279.355			1.03850			0.519248	−	0.854624i	$-0.326212\pi$
$269$	279.355			1.03850			0.519248	+	0.854624i	$0.326212\pi$
$270$		0			0
$271$			353.019i			1.30265i	0.758797	+	0.651327i	$0.225787\pi$
$271$			353.019i			1.30265i	−0.758797	+	0.651327i	$0.774213\pi$
$272$	213.690	+	16.2709i	0.785626	+	0.0598194i
$273$	−140.947	−	6.13656i	−0.516288	−	0.0224782i
$274$	37.6334	+	8.23194i	0.137348	+	0.0300436i
$275$		0			0
$276$	116.480	−	37.4647i	0.422029	−	0.135742i
$277$	−9.06443	−	9.06443i	−0.0327236	−	0.0327236i	0.690556	−	0.723279i	$-0.257366\pi$
$277$	−9.06443	−	9.06443i	−0.0327236	−	0.0327236i	−0.723279	+	0.690556i	$0.757366\pi$
$278$	67.7033	+	105.615i	0.243537	+	0.379910i
$279$	−9.50828	+	108.988i	−0.0340798	+	0.390637i
$280$		0			0
$281$			204.501i			0.727762i	0.931445	+	0.363881i	$0.118549\pi$
$281$			204.501i			0.727762i	−0.931445	+	0.363881i	$0.881451\pi$
$282$	−219.659	−	58.1658i	−0.778933	−	0.206262i
$283$	−4.95961	−	4.95961i	−0.0175251	−	0.0175251i	0.698290	−	0.715815i	$-0.253945\pi$
$283$	−4.95961	−	4.95961i	−0.0175251	−	0.0175251i	−0.715815	+	0.698290i	$0.753945\pi$
$284$	−148.360	+	322.898i	−0.522396	+	1.13697i
$285$		0			0
$286$	233.082	+	50.9844i	0.814972	+	0.178267i
$287$	97.5378	+	97.5378i	0.339853	+	0.339853i
$288$	−106.388	+	267.630i	−0.369402	+	0.929270i
$289$			109.593i			0.379214i
$290$		0			0
$291$	94.9192	−	86.9988i	0.326183	−	0.298965i
$292$	−139.834	−	377.558i	−0.478885	−	1.29301i
$293$	−195.635	−	195.635i	−0.667697	−	0.667697i	0.289485	−	0.957182i	$-0.406516\pi$
$293$	−195.635	−	195.635i	−0.667697	−	0.667697i	−0.957182	+	0.289485i	$0.906516\pi$
$294$	−125.618	−	216.108i	−0.427274	−	0.735060i
$295$		0			0
$296$	−187.259	−	141.190i	−0.632632	−	0.476994i
$297$	−24.1520	+	183.975i	−0.0813198	+	0.619445i
$298$	180.566	+	281.678i	0.605927	+	0.945227i
$299$		−	176.998i		−	0.591967i
$300$		0			0
$301$	−58.2251			−0.193439
$302$	−126.718	+	81.2313i	−0.419597	+	0.268978i
$303$	372.539	+	16.2196i	1.22950	+	0.0535302i
$304$	−346.559	−	403.685i	−1.14000	−	1.32791i
$305$		0			0
$306$	230.160	+	71.7948i	0.752155	+	0.234623i
$307$	323.877	−	323.877i	1.05497	−	1.05497i	0.0565751	−	0.998398i	$-0.481982\pi$
$307$	323.877	−	323.877i	1.05497	−	1.05497i	0.998398	−	0.0565751i	$-0.0180180\pi$
$308$	−25.8646	−	69.8355i	−0.0839761	−	0.226739i
$309$	−410.248	+	376.015i	−1.32766	+	1.21688i
$310$		0			0
$311$	428.968			1.37932			0.689660	−	0.724133i	$-0.257760\pi$
$311$	428.968			1.37932			0.689660	+	0.724133i	$0.257760\pi$
$312$	321.429	+	265.047i	1.03022	+	0.849510i
$313$	144.149	−	144.149i	0.460541	−	0.460541i	−0.438292	−	0.898833i	$-0.644416\pi$
$313$	144.149	−	144.149i	0.460541	−	0.460541i	0.898833	+	0.438292i	$0.144416\pi$
$314$	43.3266	−	198.073i	0.137983	−	0.630806i
$315$		0			0
$316$	125.487	−	273.115i	0.397110	−	0.864288i
$317$	−299.797	+	299.797i	−0.945733	+	0.945733i	−0.998601	−	0.0528685i	$-0.983164\pi$
$317$	−299.797	+	299.797i	−0.945733	+	0.945733i	0.0528685	+	0.998601i	$0.483164\pi$
$318$	127.290	+	33.7065i	0.400284	+	0.105995i
$319$	−15.7484			−0.0493679
$320$		0			0
$321$	−35.8655	+	32.8727i	−0.111730	+	0.102407i
$322$	−46.5101	+	29.8148i	−0.144441	+	0.0925924i
$323$	−314.940	+	314.940i	−0.975046	+	0.975046i
$324$	−184.210	+	266.539i	−0.568548	+	0.822650i
$325$		0			0
$326$	37.1405	−	169.793i	0.113928	−	0.520837i
$327$	−239.812	−	10.4410i	−0.733370	−	0.0319296i
$328$	−56.5801	−	403.389i	−0.172500	−	1.22985i
$329$	102.598			0.311847
$330$		0			0
$331$			89.1276i			0.269268i	0.990895	+	0.134634i	$0.0429858\pi$
$331$			89.1276i			0.269268i	−0.990895	+	0.134634i	$0.957014\pi$
$332$	115.237	+	311.144i	0.347100	+	0.937181i
$333$	−169.641	−	202.070i	−0.509432	−	0.606815i
$334$	−22.2327	+	101.640i	−0.0665649	+	0.304310i
$335$		0			0
$336$	15.5032	−	129.109i	0.0461405	−	0.384252i
$337$	176.973	+	176.973i	0.525141	+	0.525141i	0.919120	−	0.393978i	$-0.128902\pi$
$337$	176.973	+	176.973i	0.525141	+	0.525141i	−0.393978	+	0.919120i	$0.628902\pi$
$338$	222.812	−	142.831i	0.659206	−	0.422577i
$339$	202.846	−	185.920i	0.598365	−	0.548435i
$340$		0			0
$341$			83.5387i			0.244982i
$342$	−278.001	−	530.065i	−0.812869	−	1.54990i
$343$	173.671	+	173.671i	0.506330	+	0.506330i
$344$	137.289	+	103.514i	0.399096	+	0.300912i
$345$		0			0
$346$	−83.3448	+	381.022i	−0.240881	+	1.10122i
$347$	341.548	+	341.548i	0.984288	+	0.984288i	0.999878	−	0.0155906i	$-0.00496283\pi$
$347$	341.548	+	341.548i	0.984288	+	0.984288i	−0.0155906	+	0.999878i	$0.504963\pi$
$348$	−24.4643	−	12.5568i	−0.0702996	−	0.0360827i
$349$		−	190.129i		−	0.544782i	−0.962187	−	0.272391i	$-0.912186\pi$
$349$		−	190.129i		−	0.544782i	0.962187	−	0.272391i	$-0.0878144\pi$
$350$		0			0
$351$	285.457	+	371.732i	0.813268	+	1.05906i
$352$	−63.1686	+	210.648i	−0.179456	+	0.598432i
$353$	−66.4041	−	66.4041i	−0.188114	−	0.188114i	0.606767	−	0.794880i	$-0.292466\pi$
$353$	−66.4041	−	66.4041i	−0.188114	−	0.188114i	−0.794880	+	0.606767i	$0.792466\pi$
$354$	−190.247	−	327.291i	−0.537421	−	0.924552i
$355$		0			0
$356$	68.6482	−	149.409i	0.192832	−	0.419688i
$357$	−108.756	−	4.73503i	−0.304638	−	0.0132634i
$358$	180.112	−	115.459i	0.503106	−	0.322510i
$359$			402.003i			1.11979i	0.828565	+	0.559893i	$0.189158\pi$
$359$			402.003i			1.11979i	−0.828565	+	0.559893i	$0.810842\pi$
$360$		0			0
$361$	744.721			2.06294
$362$	−12.5266	−	19.5411i	−0.0346038	−	0.0539809i
$363$	9.62639	−	221.102i	0.0265190	−	0.609098i
$364$	−170.928	−	78.5354i	−0.469582	−	0.215757i
$365$		0			0
$366$	−147.709	+	85.8602i	−0.403578	+	0.234591i
$367$	183.244	−	183.244i	0.499301	−	0.499301i	−0.411919	−	0.911220i	$-0.635141\pi$
$367$	183.244	−	183.244i	0.499301	−	0.499301i	0.911220	+	0.411919i	$0.135141\pi$
$368$	162.672	+	12.3862i	0.442042	+	0.0336582i
$369$	39.8277	−	456.521i	0.107934	−	1.23719i
$370$		0			0
$371$	−59.4543			−0.160254
$372$	−66.6087	+	129.773i	−0.179056	+	0.348852i
$373$	78.2141	−	78.2141i	0.209689	−	0.209689i	−0.594446	−	0.804135i	$-0.702629\pi$
$373$	78.2141	−	78.2141i	0.209689	−	0.209689i	0.804135	+	0.594446i	$0.202629\pi$
$374$	179.848	+	39.3401i	0.480878	+	0.105187i
$375$		0			0
$376$	−241.915	−	182.400i	−0.643391	−	0.485106i
$377$	−28.1278	+	28.1278i	−0.0746096	+	0.0746096i
$378$	49.5962	−	137.627i	0.131207	−	0.364093i
$379$	−116.155			−0.306478			−0.153239	−	0.988189i	$-0.548970\pi$
$379$	−116.155			−0.306478			−0.153239	+	0.988189i	$0.548970\pi$
$380$		0			0
$381$	182.290	+	198.886i	0.478452	+	0.522010i
$382$	146.710	+	228.863i	0.384058	+	0.599118i
$383$	439.765	−	439.765i	1.14821	−	1.14821i	0.161308	−	0.986904i	$-0.448429\pi$
$383$	439.765	−	439.765i	1.14821	−	1.14821i	0.986904	−	0.161308i	$-0.0515712\pi$
$384$	−266.087	+	276.864i	−0.692935	+	0.721000i
$385$		0			0
$386$	173.346	+	37.9178i	0.449083	+	0.0982326i
$387$	124.372	+	148.147i	0.321376	+	0.382810i
$388$	160.990	−	59.6250i	0.414922	−	0.153673i
$389$	−120.985			−0.311017			−0.155508	−	0.987835i	$-0.549702\pi$
$389$	−120.985			−0.311017			−0.155508	+	0.987835i	$0.549702\pi$
$390$		0			0
$391$		−	136.574i		−	0.349293i
$392$	−46.2942	−	330.056i	−0.118098	−	0.841979i
$393$	−18.7946	+	431.682i	−0.0478235	+	1.09843i
$394$	267.980	+	58.6179i	0.680151	+	0.148776i
$395$		0			0
$396$	−122.440	+	214.983i	−0.309193	+	0.542886i
$397$	549.267	+	549.267i	1.38355	+	1.38355i	0.838233	+	0.545313i	$0.183589\pi$
$397$	549.267	+	549.267i	1.38355	+	1.38355i	0.545313	+	0.838233i	$0.316411\pi$
$398$	−31.3319	−	48.8768i	−0.0787234	−	0.122806i
$399$	182.603	+	199.227i	0.457652	+	0.499317i
$400$		0			0
$401$		−	177.597i		−	0.442885i	−0.975173	−	0.221442i	$-0.928924\pi$
$401$		−	177.597i		−	0.442885i	0.975173	−	0.221442i	$-0.0710765\pi$
$402$	70.4920	−	266.208i	0.175353	−	0.662210i
$403$	149.207	+	149.207i	0.370240	+	0.370240i
$404$	451.783	+	207.578i	1.11827	+	0.513808i
$405$		0			0
$406$	12.1292	+	2.65315i	0.0298750	+	0.00653486i
$407$	−142.457	−	142.457i	−0.350018	−	0.350018i
$408$	248.018	+	204.513i	0.607887	+	0.501258i
$409$			348.822i			0.852865i	0.904519	+	0.426433i	$0.140230\pi$
$409$			348.822i			0.852865i	−0.904519	+	0.426433i	$0.859770\pi$
$410$		0			0
$411$	39.0441	+	42.5986i	0.0949977	+	0.103646i
$412$	−695.809	+	257.703i	−1.68886	+	0.625494i
$413$	120.865	+	120.865i	0.292651	+	0.292651i
$414$	175.209	+	54.6537i	0.423210	+	0.132014i
$415$		0			0
$416$	263.410	+	489.058i	0.633197	+	1.17562i
$417$	−8.18518	+	188.000i	−0.0196287	+	0.450840i
$418$	−246.655	−	384.774i	−0.590084	−	0.920512i
$419$		−	104.631i		−	0.249716i	−0.992175	−	0.124858i	$-0.960152\pi$
$419$		−	104.631i		−	0.249716i	0.992175	−	0.124858i	$-0.0398476\pi$
$420$		0			0
$421$	207.644			0.493217			0.246609	−	0.969115i	$-0.420684\pi$
$421$	207.644			0.493217			0.246609	+	0.969115i	$0.420684\pi$
$422$	634.691	−	406.862i	1.50401	−	0.964127i
$423$	−219.155	−	261.048i	−0.518096	−	0.617136i
$424$	140.187	+	105.699i	0.330631	+	0.249290i
$425$		0			0
$426$	−460.829	+	267.869i	−1.08176	+	0.628801i
$427$	54.5474	−	54.5474i	0.127746	−	0.127746i
$428$	−60.8303	+	22.5294i	−0.142127	+	0.0526389i
$429$	241.819	+	263.834i	0.563681	+	0.614998i
$430$		0			0
$431$	−135.966			−0.315467			−0.157734	−	0.987482i	$-0.550419\pi$
$431$	−135.966			−0.315467			−0.157734	+	0.987482i	$0.550419\pi$
$432$	−361.619	+	236.338i	−0.837081	+	0.547079i
$433$	−426.207	+	426.207i	−0.984312	+	0.984312i	−0.999879	−	0.0155664i	$-0.995045\pi$
$433$	−426.207	+	426.207i	−0.984312	+	0.984312i	0.0155664	+	0.999879i	$0.495045\pi$
$434$	14.0739	−	64.3407i	0.0324284	−	0.148250i
$435$		0			0
$436$	−290.823	−	133.623i	−0.667026	−	0.306475i
$437$	−239.748	+	239.748i	−0.548622	+	0.548622i
$438$	154.593	−	583.810i	0.352952	−	1.33290i
$439$	−408.305			−0.930080			−0.465040	−	0.885290i	$-0.653960\pi$
$439$	−408.305			−0.930080			−0.465040	+	0.885290i	$0.653960\pi$
$440$		0			0
$441$	32.5873	−	373.529i	0.0738940	−	0.847004i
$442$	391.488	−	250.959i	0.885720	−	0.567781i
$443$	−354.483	+	354.483i	−0.800188	+	0.800188i	−0.983125	−	0.182937i	$-0.941440\pi$
$443$	−354.483	+	354.483i	−0.800188	+	0.800188i	0.182937	+	0.983125i	$0.441440\pi$
$444$	−107.713	−	334.887i	−0.242597	−	0.754250i
$445$		0			0
$446$	154.427	−	705.985i	0.346250	−	1.58293i
$447$	−21.8301	+	501.401i	−0.0488368	+	1.12170i
$448$	84.1400	−	151.597i	0.187813	−	0.338386i
$449$	−452.663			−1.00816			−0.504079	−	0.863657i	$-0.668168\pi$
$449$	−452.663			−1.00816			−0.504079	+	0.863657i	$0.668168\pi$
$450$		0			0
$451$		−	349.922i		−	0.775880i
$452$	344.041	−	127.421i	0.761152	−	0.281904i
$453$	−225.565	−	9.82069i	−0.497936	−	0.0216792i
$454$	65.9070	−	301.302i	0.145170	−	0.663661i
$455$		0			0
$456$	−76.3704	−	794.394i	−0.167479	−	1.74209i
$457$	−270.489	−	270.489i	−0.591879	−	0.591879i	0.346260	−	0.938139i	$-0.387452\pi$
$457$	−270.489	−	270.489i	−0.591879	−	0.591879i	−0.938139	+	0.346260i	$0.887452\pi$
$458$	376.719	−	241.491i	0.822531	−	0.527274i
$459$	220.262	+	286.832i	0.479873	+	0.624906i
$460$		0			0
$461$			582.469i			1.26349i	0.775176	+	0.631745i	$0.217661\pi$
$461$			582.469i			1.26349i	−0.775176	+	0.631745i	$0.782339\pi$
$462$	28.5945	−	107.985i	0.0618929	−	0.233734i
$463$	318.146	+	318.146i	0.687140	+	0.687140i	0.961599	−	0.274459i	$-0.0884986\pi$
$463$	318.146	+	318.146i	0.687140	+	0.687140i	−0.274459	+	0.961599i	$0.588499\pi$
$464$	−23.8827	−	27.8195i	−0.0514714	−	0.0599558i
$465$		0			0
$466$	−37.7293	+	172.485i	−0.0809642	+	0.370139i
$467$	−554.211	−	554.211i	−1.18675	−	1.18675i	−0.977961	−	0.208786i	$-0.933049\pi$
$467$	−554.211	−	554.211i	−1.18675	−	1.18675i	−0.208786	−	0.977961i	$-0.566951\pi$
$468$	165.288	+	602.665i	0.353179	+	1.28774i
$469$			124.340i			0.265116i
$470$		0			0
$471$	224.206	−	205.498i	0.476022	−	0.436301i
$472$	−70.1118	−	499.864i	−0.148542	−	1.05903i
$473$	104.443	+	104.443i	0.220809	+	0.220809i
$474$	389.780	−	226.570i	0.822320	−	0.477996i
$475$		0			0
$476$	−131.890	−	60.5987i	−0.277080	−	0.127308i
$477$	126.998	+	151.275i	0.266243	+	0.317138i
$478$	−522.327	+	334.832i	−1.09273	+	0.700485i
$479$		−	857.141i		−	1.78944i	−0.446629	−	0.894719i	$-0.647375\pi$
$479$		−	857.141i		−	1.78944i	0.446629	−	0.894719i	$-0.352625\pi$
$480$		0			0
$481$	−508.880			−1.05796
$482$	−129.419	−	201.889i	−0.268504	−	0.418857i
$483$	−82.7904	−	3.60454i	−0.171409	−	0.00746281i
$484$	123.198	−	268.134i	0.254542	−	0.553996i
$485$		0			0
$486$	−456.118	+	167.787i	−0.938514	+	0.345242i
$487$	97.7824	−	97.7824i	0.200785	−	0.200785i	−0.599551	−	0.800336i	$-0.704654\pi$
$487$	97.7824	−	97.7824i	0.200785	−	0.200785i	0.800336	+	0.599551i	$0.204654\pi$
$488$	−225.593	+	31.6421i	−0.462281	+	0.0648403i
$489$	192.195	−	176.157i	0.393036	−	0.360240i
$490$		0			0
$491$	−770.213			−1.56866			−0.784331	−	0.620342i	$-0.786994\pi$
$491$	−770.213			−1.56866			−0.784331	+	0.620342i	$0.786994\pi$
$492$	279.006	−	543.585i	0.567086	−	1.10485i
$493$	−21.7037	+	21.7037i	−0.0440238	+	0.0440238i
$494$	−1127.78	−	246.692i	−2.28296	−	0.499376i
$495$		0			0
$496$	−147.571	+	126.688i	−0.297522	+	0.255420i
$497$	170.179	−	170.179i	0.342412	−	0.342412i
$498$	−127.400	+	481.116i	−0.255823	+	0.966096i
$499$	66.3836			0.133033			0.0665166	−	0.997785i	$-0.478811\pi$
$499$	66.3836			0.133033			0.0665166	+	0.997785i	$0.478811\pi$
$500$		0			0
$501$	−115.050	+	105.450i	−0.229640	+	0.210478i
$502$	−362.933	−	566.164i	−0.722974	−	1.12782i
$503$	−349.224	+	349.224i	−0.694282	+	0.694282i	−0.963171	−	0.268889i	$-0.913344\pi$
$503$	−349.224	+	349.224i	−0.694282	+	0.694282i	0.268889	+	0.963171i	$0.413344\pi$
$504$	130.521	−	144.950i	0.258970	−	0.287599i
$505$		0			0
$506$	136.910	+	29.9477i	0.270572	+	0.0591851i
$507$	396.617	+	17.2680i	0.782281	+	0.0340591i
$508$	124.933	+	337.325i	0.245932	+	0.664025i
$509$	−447.822			−0.879807			−0.439904	−	0.898045i	$-0.644987\pi$
$509$	−447.822			−0.879807			−0.439904	+	0.898045i	$0.644987\pi$
$510$		0			0
$511$			272.684i			0.533628i
$512$	−467.906	+	207.865i	−0.913879	+	0.405987i
$513$	116.861	−	890.176i	0.227799	−	1.73524i
$514$	551.629	+	120.664i	1.07321	+	0.234754i
$515$		0			0
$516$	78.9700	+	245.523i	0.153043	+	0.475819i
$517$	−184.037	−	184.037i	−0.355971	−	0.355971i
$518$	85.7192	+	133.719i	0.165481	+	0.258145i
$519$	−431.293	+	395.304i	−0.831007	+	0.761665i
$520$		0			0
$521$			373.093i			0.716109i	0.933701	+	0.358054i	$0.116560\pi$
$521$			373.093i			0.716109i	−0.933701	+	0.358054i	$0.883440\pi$
$522$	−19.1581	−	36.5288i	−0.0367014	−	0.0699786i
$523$	−593.137	−	593.137i	−1.13411	−	1.13411i	−0.989488	−	0.144618i	$-0.953805\pi$
$523$	−593.137	−	593.137i	−1.13411	−	1.13411i	−0.144618	−	0.989488i	$-0.546195\pi$
$524$	−240.533	+	523.507i	−0.459032	+	0.999058i
$525$		0			0
$526$	298.212	+	65.2311i	0.566943	+	0.124013i
$527$	115.130	+	115.130i	0.218462	+	0.218462i
$528$	−259.401	+	203.783i	−0.491290	+	0.385952i
$529$			425.033i			0.803466i
$530$		0			0
$531$	49.3529	−	565.703i	0.0929432	−	1.06535i
$532$	125.148	+	337.904i	0.235240	+	0.635157i
$533$	−624.988	−	624.988i	−1.17259	−	1.17259i
$534$	213.231	−	123.946i	0.399309	−	0.232109i
$535$		0			0
$536$	221.053	−	293.181i	0.412413	−	0.546979i
$537$	320.609	+	13.9587i	0.597036	+	0.0259939i
$538$	301.522	+	470.364i	0.560449	+	0.874283i
$539$		−	286.308i		−	0.531184i
$540$		0			0
$541$	−46.0398			−0.0851012			−0.0425506	−	0.999094i	$-0.513548\pi$
$541$	−46.0398			−0.0851012			−0.0425506	+	0.999094i	$0.513548\pi$
$542$	−594.395	+	381.030i	−1.09667	+	0.703008i
$543$	1.51444	−	34.7842i	0.00278902	−	0.0640592i
$544$	203.250	+	377.362i	0.373621	+	0.693681i
$545$		0			0
$546$	−141.798	−	243.942i	−0.259703	−	0.446781i
$547$	−586.492	+	586.492i	−1.07220	+	1.07220i	−0.0750146	+	0.997182i	$0.523900\pi$
$547$	−586.492	+	586.492i	−1.07220	+	1.07220i	−0.997182	+	0.0750146i	$0.976100\pi$
$548$	26.7590	+	72.2503i	0.0488303	+	0.131844i
$549$	−255.307	−	22.2734i	−0.465040	−	0.0405708i
$550$		0			0
$551$	76.1995			0.138293
$552$	188.804	+	155.686i	0.342035	+	0.282039i
$553$	−143.941	+	143.941i	−0.260292	+	0.260292i
$554$	5.47855	−	25.0459i	0.00988908	−	0.0452092i
$555$		0			0
$556$	−104.754	+	227.991i	−0.188406	+	0.410055i
$557$	−413.911	+	413.911i	−0.743108	+	0.743108i	−0.973175	−	0.230067i	$-0.926106\pi$
$557$	−413.911	+	413.911i	−0.743108	+	0.743108i	0.230067	+	0.973175i	$0.426106\pi$
$558$	−193.771	+	101.626i	−0.347259	+	0.182126i
$559$	373.086			0.667416
$560$		0			0
$561$	186.590	+	203.577i	0.332603	+	0.362883i
$562$	−344.328	+	220.728i	−0.612684	+	0.392754i
$563$	−185.957	+	185.957i	−0.330296	+	0.330296i	−0.852699	−	0.522403i	$-0.825036\pi$
$563$	−185.957	+	185.957i	−0.330296	+	0.330296i	0.522403	+	0.852699i	$0.325036\pi$
$564$	−139.152	−	432.632i	−0.246723	−	0.767077i
$565$		0			0
$566$	2.99759	−	13.7039i	0.00529610	−	0.0242118i
$567$	179.690	−	125.951i	0.316913	−	0.222137i
$568$	−703.812	+	98.7180i	−1.23911	+	0.173799i
$569$	745.467			1.31014			0.655068	−	0.755570i	$-0.272640\pi$
$569$	745.467			1.31014			0.655068	+	0.755570i	$0.272640\pi$
$570$		0			0
$571$		−	406.663i		−	0.712195i	−0.934449	−	0.356097i	$-0.884107\pi$
$571$		−	406.663i		−	0.712195i	0.934449	−	0.356097i	$-0.115893\pi$
$572$	165.732	+	447.481i	0.289741	+	0.782310i
$573$	−17.7369	+	407.388i	−0.0309545	+	0.710975i
$574$	−58.9519	+	269.506i	−0.102704	+	0.469523i
$575$		0			0
$576$	−565.450	+	109.735i	−0.981685	+	0.190512i
$577$	−73.9694	−	73.9694i	−0.128197	−	0.128197i	0.640097	−	0.768294i	$-0.278894\pi$
$577$	−73.9694	−	73.9694i	−0.128197	−	0.128197i	−0.768294	+	0.640097i	$0.778894\pi$
$578$	−184.527	+	118.289i	−0.319251	+	0.204652i
$579$	179.844	+	196.217i	0.310611	+	0.338889i
$580$		0			0
$581$		−	224.718i		−	0.386778i
$582$	248.935	+	65.9181i	0.427723	+	0.113261i
$583$	106.648	+	106.648i	0.182929	+	0.182929i
$584$	484.783	−	642.962i	0.830108	−	1.10096i
$585$		0			0
$586$	118.242	−	540.559i	0.201778	−	0.922456i
$587$	−422.201	−	422.201i	−0.719251	−	0.719251i	0.249200	−	0.968452i	$-0.419832\pi$
$587$	−422.201	−	422.201i	−0.719251	−	0.719251i	−0.968452	+	0.249200i	$0.919832\pi$
$588$	228.285	−	444.765i	0.388240	−	0.756404i
$589$		−	404.208i		−	0.686261i
$590$		0			0
$591$	278.025	+	303.336i	0.470431	+	0.513259i
$592$	35.6111	−	467.690i	0.0601538	−	0.790017i
$593$	406.869	+	406.869i	0.686119	+	0.686119i	0.961372	−	0.275253i	$-0.0887616\pi$
$593$	406.869	+	406.869i	0.686119	+	0.686119i	−0.275253	+	0.961372i	$0.588762\pi$
$594$	−335.836	+	157.907i	−0.565381	+	0.265837i
$595$		0			0
$596$	−279.381	+	608.056i	−0.468759	+	1.02023i
$597$	3.78796	−	87.0033i	0.00634500	−	0.145734i
$598$	298.020	−	191.043i	0.498362	−	0.319469i
$599$			293.225i			0.489525i	0.969583	+	0.244762i	$0.0787100\pi$
$599$			293.225i			0.489525i	−0.969583	+	0.244762i	$0.921290\pi$
$600$		0			0
$601$	−1087.24			−1.80905			−0.904523	−	0.426424i	$-0.859773\pi$
$601$	−1087.24			−1.80905			−0.904523	+	0.426424i	$0.859773\pi$
$602$	−62.8451	−	98.0363i	−0.104394	−	0.162851i
$603$	316.369	−	265.597i	0.524658	−	0.440459i
$604$	−273.546	−	125.685i	−0.452891	−	0.208087i
$605$		0			0
$606$	374.789	+	644.768i	0.618464	+	1.06397i
$607$	74.9651	−	74.9651i	0.123501	−	0.123501i	−0.642655	−	0.766156i	$-0.722167\pi$
$607$	74.9651	−	74.9651i	0.123501	−	0.123501i	0.766156	+	0.642655i	$0.222167\pi$
$608$	305.645	−	1019.23i	0.502706	−	1.67637i
$609$	12.5839	+	13.7295i	0.0206632	+	0.0225444i
$610$		0			0
$611$	−657.409			−1.07596
$612$	127.538	+	465.022i	0.208395	+	0.759840i
$613$	−22.9005	+	22.9005i	−0.0373581	+	0.0373581i	−0.725539	−	0.688181i	$-0.758410\pi$
$613$	−22.9005	+	22.9005i	−0.0373581	+	0.0373581i	0.688181	+	0.725539i	$0.258410\pi$
$614$	894.903	+	195.751i	1.45750	+	0.318813i
$615$		0			0
$616$	89.6684	−	118.926i	0.145566	−	0.193062i
$617$	115.002	−	115.002i	0.186389	−	0.186389i	−0.607744	−	0.794133i	$-0.707925\pi$
$617$	115.002	−	115.002i	0.186389	−	0.186389i	0.794133	+	0.607744i	$0.207925\pi$
$618$	−1075.91	−	284.903i	−1.74096	−	0.461007i
$619$	710.704			1.14815			0.574074	−	0.818803i	$-0.305362\pi$
$619$	710.704			1.14815			0.574074	+	0.818803i	$0.305362\pi$
$620$		0			0
$621$	167.674	+	218.351i	0.270006	+	0.351612i
$622$	463.006	+	722.275i	0.744383	+	1.16121i
$623$	−78.7438	+	78.7438i	−0.126394	+	0.126394i
$624$	−99.3391	+	827.283i	−0.159197	+	1.32577i
$625$		0			0
$626$	398.299	+	87.1240i	0.636260	+	0.139176i
$627$	29.8201	−	684.918i	0.0475599	−	1.09237i
$628$	380.270	−	140.839i	0.605525	−	0.224265i
$629$	−392.657			−0.624256
$630$		0			0
$631$			209.771i			0.332443i	0.986088	+	0.166221i	$0.0531566\pi$
$631$			209.771i			0.332443i	−0.986088	+	0.166221i	$0.946843\pi$
$632$	595.301	−	83.4980i	0.941932	−	0.132117i
$633$	1129.78	+	49.1887i	1.78481	+	0.0777072i
$634$	−828.369	−	181.198i	−1.30658	−	0.285801i
$635$		0			0
$636$	80.6372	+	250.706i	0.126788	+	0.394192i
$637$	−511.370	−	511.370i	−0.802778	−	0.802778i
$638$	−16.9980	−	26.5163i	−0.0266426	−	0.0415616i
$639$	−796.514	−	69.4892i	−1.24650	−	0.108747i
$640$		0			0
$641$		−	1193.44i		−	1.86184i	−0.365221	−	0.930921i	$-0.619007\pi$
$641$		−	1193.44i		−	1.86184i	0.365221	−	0.930921i	$-0.380993\pi$
$642$	−94.0607	−	24.9073i	−0.146512	−	0.0387964i
$643$	−424.387	−	424.387i	−0.660012	−	0.660012i	0.295371	−	0.955383i	$-0.404557\pi$
$643$	−424.387	−	424.387i	−0.660012	−	0.660012i	−0.955383	+	0.295371i	$0.904557\pi$
$644$	−100.401	−	46.1308i	−0.155902	−	0.0716316i
$645$		0			0
$646$	−870.209	−	190.350i	−1.34707	−	0.294659i
$647$	556.306	+	556.306i	0.859824	+	0.859824i	0.991317	−	0.131493i	$-0.0419772\pi$
$647$	556.306	+	556.306i	0.859824	+	0.859824i	−0.131493	+	0.991317i	$0.541977\pi$
$648$	−647.610	−	22.4746i	−0.999398	−	0.0346830i
$649$		−	433.609i		−	0.668119i
$650$		0			0
$651$	72.8296	−	66.7525i	0.111873	−	0.102538i
$652$	325.976	−	120.730i	0.499963	−	0.185169i
$653$	730.267	+	730.267i	1.11833	+	1.11833i	0.991987	+	0.126340i	$0.0403230\pi$
$653$	730.267	+	730.267i	1.11833	+	1.11833i	0.126340	+	0.991987i	$0.459677\pi$
$654$	−241.261	−	415.052i	−0.368900	−	0.634637i
$655$		0			0
$656$	618.137	−	530.664i	0.942281	−	0.808939i
$657$	693.815	−	582.470i	1.05604	−	0.886560i
$658$	110.738	+	172.748i	0.168295	+	0.262536i
$659$		−	929.519i		−	1.41050i	−0.708959	−	0.705250i	$-0.750835\pi$
$659$		−	929.519i		−	1.41050i	0.708959	−	0.705250i	$-0.249165\pi$
$660$		0			0
$661$	564.895			0.854607			0.427303	−	0.904108i	$-0.359464\pi$
$661$	564.895			0.854607			0.427303	+	0.904108i	$0.359464\pi$
$662$	−150.068	+	96.1997i	−0.226690	+	0.145317i
$663$	696.870	+	30.3404i	1.05109	+	0.0457623i
$664$	−399.508	+	529.863i	−0.601668	+	0.797986i
$665$		0			0
$666$	157.133	−	503.736i	0.235935	−	0.756360i
$667$	−16.5220	+	16.5220i	−0.0247705	+	0.0247705i
$668$	−195.132	+	72.2703i	−0.292114	+	0.108189i
$669$	799.131	−	732.449i	1.19452	−	1.09484i
$670$		0			0
$671$	−195.692			−0.291642
$672$	234.120	−	113.250i	0.348393	−	0.168526i
$673$	−301.487	+	301.487i	−0.447975	+	0.447975i	−0.894681	−	0.446706i	$-0.852597\pi$
$673$	−301.487	+	301.487i	−0.447975	+	0.447975i	0.446706	+	0.894681i	$0.352597\pi$
$674$	−106.962	+	488.992i	−0.158698	+	0.725508i
$675$		0			0
$676$	480.983	+	220.995i	0.711513	+	0.326915i
$677$	530.496	−	530.496i	0.783598	−	0.783598i	−0.196838	−	0.980436i	$-0.563067\pi$
$677$	530.496	−	530.496i	0.783598	−	0.783598i	0.980436	+	0.196838i	$0.0630672\pi$
$678$	531.983	+	140.869i	0.784635	+	0.207772i
$679$	−116.272			−0.171240
$680$		0			0
$681$	341.055	−	312.596i	0.500815	−	0.459026i
$682$	−140.658	+	90.1673i	−0.206244	+	0.132210i
$683$	378.401	−	378.401i	0.554028	−	0.554028i	−0.373573	−	0.927601i	$-0.621867\pi$
$683$	378.401	−	378.401i	0.554028	−	0.554028i	0.927601	+	0.373573i	$0.121867\pi$
$684$	592.436	−	1040.21i	0.866135	−	1.52077i
$685$		0			0
$686$	−104.967	+	479.870i	−0.153013	+	0.699519i
$687$	670.580	+	29.1958i	0.976099	+	0.0424975i
$688$	−26.1083	+	342.887i	−0.0379481	+	0.498383i
$689$	380.962			0.552920
$690$		0			0
$691$			690.583i			0.999396i	0.866200	+	0.499698i	$0.166556\pi$
$691$			690.583i			0.999396i	−0.866200	+	0.499698i	$0.833444\pi$
$692$	−731.503	+	270.923i	−1.05708	+	0.391508i
$693$	128.332	−	107.737i	0.185184	−	0.155465i
$694$	−206.432	+	943.730i	−0.297452	+	1.35984i
$695$		0			0
$696$	−5.26298	−	54.7448i	−0.00756175	−	0.0786563i
$697$	−482.247	−	482.247i	−0.691890	−	0.691890i
$698$	320.129	−	205.215i	0.458638	−	0.294004i
$699$	−195.242	+	178.950i	−0.279316	+	0.256009i
$700$		0			0
$701$		−	129.593i		−	0.184869i	−0.995719	−	0.0924343i	$-0.970535\pi$
$701$		−	129.593i		−	0.184869i	0.995719	−	0.0924343i	$-0.0294648\pi$
$702$	−317.795	+	881.865i	−0.452700	+	1.25622i
$703$	689.289	+	689.289i	0.980496	+	0.980496i
$704$	−422.859	+	121.002i	−0.600652	+	0.171879i
$705$		0			0
$706$	40.1347	−	183.481i	0.0568480	−	0.259888i
$707$	−238.105	−	238.105i	−0.336783	−	0.336783i
$708$	345.734	−	673.589i	0.488324	−	0.951397i
$709$			86.8545i			0.122503i	0.998122	+	0.0612514i	$0.0195091\pi$
$709$			86.8545i			0.122503i	−0.998122	+	0.0612514i	$0.980491\pi$
$710$		0			0
$711$	673.710	+	58.7756i	0.947553	+	0.0826661i
$712$	325.662	−	45.6780i	0.457391	−	0.0641545i
$713$	87.6423	+	87.6423i	0.122920	+	0.122920i
$714$	−109.413	−	188.228i	−0.153239	−	0.263625i
$715$		0			0
$716$	388.807	+	178.643i	0.543026	+	0.249501i
$717$	−929.769	−	40.4804i	−1.29675	−	0.0564581i
$718$	−676.872	+	433.901i	−0.942719	+	0.604319i
$719$		−	104.099i		−	0.144782i	−0.997376	−	0.0723912i	$-0.976937\pi$
$719$		−	104.099i		−	0.144782i	0.997376	−	0.0723912i	$-0.0230630\pi$
$720$		0			0
$721$	502.534			0.696996
$722$	803.812	+	1253.92i	1.11331	+	1.73673i
$723$	15.6464	−	359.373i	0.0216410	−	0.497059i
$724$	19.3817	−	42.1833i	0.0267703	−	0.0582642i
$725$		0			0
$726$	382.671	−	222.438i	0.527095	−	0.306388i
$727$	−252.054	+	252.054i	−0.346704	+	0.346704i	−0.858880	−	0.512176i	$-0.828839\pi$
$727$	−252.054	+	252.054i	−0.346704	+	0.346704i	0.512176	+	0.858880i	$0.328839\pi$
$728$	−52.2569	−	372.567i	−0.0717814	−	0.511768i
$729$	−704.298	−	188.161i	−0.966116	−	0.258109i
$730$		0			0
$731$	287.877			0.393812
$732$	−303.997	−	156.033i	−0.415296	−	0.213159i
$733$	795.114	−	795.114i	1.08474	−	1.08474i	0.0886791	−	0.996060i	$-0.471735\pi$
$733$	795.114	−	795.114i	1.08474	−	1.08474i	0.996060	−	0.0886791i	$-0.0282646\pi$
$734$	506.320	+	110.753i	0.689809	+	0.150889i
$735$		0			0
$736$	154.724	+	287.267i	0.210223	+	0.390308i
$737$	223.037	−	223.037i	0.302629	−	0.302629i
$738$	811.655	−	425.685i	1.09980	−	0.576810i
$739$	622.137			0.841863			0.420931	−	0.907092i	$-0.361703\pi$
$739$	622.137			0.841863			0.420931	+	0.907092i	$0.361703\pi$
$740$		0			0
$741$	−1170.06	−	1276.58i	−1.57902	−	1.72278i
$742$	−64.1718	−	100.106i	−0.0864850	−	0.134914i
$743$	−487.618	+	487.618i	−0.656283	+	0.656283i	−0.954499	−	0.298216i	$-0.903609\pi$
$743$	−487.618	+	487.618i	−0.656283	+	0.656283i	0.298216	+	0.954499i	$0.403609\pi$
$744$	−290.399	+	27.9180i	−0.390321	+	0.0375242i
$745$		0			0
$746$	216.113	+	47.2726i	0.289696	+	0.0633681i
$747$	−571.770	+	480.011i	−0.765422	+	0.642585i
$748$	127.880	+	345.281i	0.170963	+	0.461606i
$749$	43.9335			0.0586562
$750$		0			0
$751$			1089.00i			1.45007i	0.688711	+	0.725036i	$0.258177\pi$
$751$			1089.00i			1.45007i	−0.688711	+	0.725036i	$0.741823\pi$
$752$	46.0050	−	604.197i	0.0611769	−	0.803454i
$753$	43.8778	−	1007.80i	0.0582706	−	1.33838i
$754$	−77.7199	−	17.0005i	−0.103077	−	0.0225470i
$755$		0			0
$756$	285.261	−	65.0398i	0.377329	−	0.0860315i
$757$	628.144	+	628.144i	0.829781	+	0.829781i	0.987486	−	0.157705i	$-0.0504097\pi$
$757$	628.144	+	628.144i	0.829781	+	0.829781i	−0.157705	+	0.987486i	$0.550410\pi$
$758$	−125.372	−	195.576i	−0.165398	−	0.258016i
$759$	142.042	+	154.973i	0.187143	+	0.204181i
$760$		0			0
$761$			723.259i			0.950407i	0.879876	+	0.475203i	$0.157625\pi$
$761$			723.259i			0.950407i	−0.879876	+	0.475203i	$0.842375\pi$
$762$	−138.119	+	521.598i	−0.181259	+	0.684512i
$763$	153.274	+	153.274i	0.200883	+	0.200883i
$764$	−226.997	+	494.046i	−0.297116	+	0.646657i
$765$		0			0
$766$	1215.11	+	265.794i	1.58631	+	0.346990i
$767$	−774.460	−	774.460i	−1.00973	−	1.00973i
$768$	−753.370	−	149.191i	−0.980950	−	0.194259i
$769$			180.270i			0.234421i	0.993107	+	0.117210i	$0.0373952\pi$
$769$			180.270i			0.234421i	−0.993107	+	0.117210i	$0.962605\pi$
$770$		0			0
$771$	572.307	+	624.410i	0.742292	+	0.809870i
$772$	123.257	+	332.798i	0.159659	+	0.431085i
$773$	−482.107	−	482.107i	−0.623683	−	0.623683i	0.322788	−	0.946471i	$-0.395380\pi$
$773$	−482.107	−	482.107i	−0.623683	−	0.623683i	−0.946471	+	0.322788i	$0.895380\pi$
$774$	−115.202	+	369.314i	−0.148840	+	0.477150i
$775$		0			0
$776$	274.157	+	206.710i	0.353296	+	0.266379i
$777$	−10.3633	+	238.027i	−0.0133375	+	0.306341i
$778$	−130.585	−	203.709i	−0.167848	−	0.261837i
$779$			1693.12i			2.17345i
$780$		0			0
$781$	−610.525			−0.781722
$782$	229.956	−	147.410i	0.294061	−	0.188504i
$783$	8.05334	−	61.3455i	0.0102852	−	0.0783468i
$784$	505.764	−	434.193i	0.645107	−	0.553818i
$785$		0			0
$786$	−747.129	+	434.289i	−0.950546	+	0.552531i
$787$	279.225	−	279.225i	0.354797	−	0.354797i	−0.507094	−	0.861891i	$-0.669280\pi$
$787$	279.225	−	279.225i	0.354797	−	0.354797i	0.861891	+	0.507094i	$0.169280\pi$
$788$	190.545	+	514.479i	0.241809	+	0.652892i
$789$	309.391	+	337.558i	0.392130	+	0.427830i
$790$		0			0
$791$	−248.477			−0.314130
$792$	−494.133	+	25.8823i	−0.623905	+	0.0326796i
$793$	−349.521	+	349.521i	−0.440758	+	0.440758i
$794$	−331.978	+	1517.68i	−0.418108	+	1.91143i
$795$		0			0
$796$	48.4782	−	105.510i	0.0609023	−	0.132550i
$797$	861.626	−	861.626i	1.08109	−	1.08109i	0.0846783	−	0.996408i	$-0.473014\pi$
$797$	861.626	−	861.626i	1.08109	−	1.08109i	0.996408	−	0.0846783i	$-0.0269863\pi$
$798$	−138.356	+	522.493i	−0.173379	+	0.654754i
$799$	−507.264			−0.634873
$800$		0			0
$801$	368.557	+	32.1535i	0.460121	+	0.0401417i
$802$	299.028	−	191.689i	0.372853	−	0.239013i
$803$	489.134	−	489.134i	0.609133	−	0.609133i
$804$	524.313	−	168.640i	0.652131	−	0.209752i
$805$		0			0
$806$	−90.1807	+	412.273i	−0.111887	+	0.511505i
$807$	−36.4533	+	837.273i	−0.0451714	+	1.03751i
$808$	138.121	+	984.738i	0.170942	+	1.21874i
$809$	430.022			0.531548			0.265774	−	0.964035i	$-0.414373\pi$
$809$	430.022			0.531548			0.265774	+	0.964035i	$0.414373\pi$
$810$		0			0
$811$		−	1351.37i		−	1.66630i	−0.553047	−	0.833150i	$-0.686535\pi$
$811$		−	1351.37i		−	1.66630i	0.553047	−	0.833150i	$-0.313465\pi$
$812$	8.62442	+	23.2863i	0.0106212	+	0.0286777i
$813$	−1058.06	−	46.0658i	−1.30142	−	0.0566614i
$814$	86.1013	−	393.623i	0.105776	−	0.483567i
$815$		0			0
$816$	−76.6511	+	638.341i	−0.0939351	+	0.782280i
$817$	−505.353	−	505.353i	−0.618547	−	0.618547i
$818$	−587.328	+	376.500i	−0.718005	+	0.460269i
$819$	36.7845	−	421.639i	0.0449139	−	0.514822i
$820$		0			0
$821$			901.925i			1.09857i	0.835636	+	0.549284i	$0.185100\pi$
$821$			901.925i			1.09857i	−0.835636	+	0.549284i	$0.814900\pi$
$822$	−29.5833	+	111.719i	−0.0359894	+	0.135911i
$823$	−512.252	−	512.252i	−0.622421	−	0.622421i	0.323729	−	0.946150i	$-0.395063\pi$
$823$	−512.252	−	512.252i	−0.622421	−	0.622421i	−0.946150	+	0.323729i	$0.895063\pi$
$824$	−1184.93	−	893.415i	−1.43802	−	1.08424i
$825$		0			0
$826$	−73.0508	+	333.961i	−0.0884393	+	0.404312i
$827$	683.717	+	683.717i	0.826744	+	0.826744i	0.987065	−	0.160321i	$-0.0512530\pi$
$827$	683.717	+	683.717i	0.826744	+	0.826744i	−0.160321	+	0.987065i	$0.551253\pi$
$828$	97.0882	+	353.998i	0.117256	+	0.427534i
$829$			1001.78i			1.20842i	0.796827	+	0.604208i	$0.206510\pi$
$829$			1001.78i			1.20842i	−0.796827	+	0.604208i	$0.793490\pi$
$830$		0			0
$831$	28.3504	−	25.9847i	0.0341160	−	0.0312692i
$832$	−539.140	+	971.380i	−0.648005	+	1.16752i
$833$	−394.578	−	394.578i	−0.473683	−	0.473683i
$834$	−325.380	+	189.136i	−0.390144	+	0.226782i
$835$		0			0
$836$	381.636	−	830.610i	0.456503	−	0.993553i
$837$	−325.413	−	42.7197i	−0.388785	−	0.0510391i
$838$	176.173	−	112.933i	0.210230	−	0.134765i
$839$		−	189.192i		−	0.225497i	−0.993624	−	0.112749i	$-0.964035\pi$
$839$		−	189.192i		−	0.225497i	0.993624	−	0.112749i	$-0.0359654\pi$
$840$		0			0
$841$	−835.749			−0.993756
$842$	224.120	+	349.621i	0.266176	+	0.415227i
$843$	−612.923	−	26.6855i	−0.727073	−	0.0316554i
$844$	1370.10	+	629.515i	1.62335	+	0.745871i
$845$		0			0
$846$	202.996	−	650.763i	0.239948	−	0.769224i
$847$	−141.316	+	141.316i	−0.166843	+	0.166843i
$848$	−26.6595	+	350.126i	−0.0314381	+	0.412885i
$849$	15.5119	−	14.2176i	0.0182708	−	0.0167462i
$850$		0			0
$851$	−298.910			−0.351246
$852$	−948.419	−	486.795i	−1.11317	−	0.571356i
$853$	430.775	−	430.775i	0.505011	−	0.505011i	−0.407980	−	0.912991i	$-0.633767\pi$
$853$	430.775	−	430.775i	0.505011	−	0.505011i	0.912991	+	0.407980i	$0.133767\pi$
$854$	150.720	+	32.9685i	0.176487	+	0.0386048i
$855$		0			0
$856$	−103.591	−	78.1059i	−0.121018	−	0.0912452i
$857$	−684.012	+	684.012i	−0.798147	+	0.798147i	−0.982803	−	0.184656i	$-0.940883\pi$
$857$	−684.012	+	684.012i	−0.798147	+	0.798147i	0.184656	+	0.982803i	$0.440883\pi$
$858$	−183.224	+	691.931i	−0.213547	+	0.806447i
$859$	−1397.70			−1.62712			−0.813560	−	0.581481i	$-0.802473\pi$
$859$	−1397.70			−1.62712			−0.813560	+	0.581481i	$0.802473\pi$
$860$		0			0
$861$	−305.064	+	279.609i	−0.354314	+	0.324749i
$862$	−146.755	−	228.933i	−0.170249	−	0.265584i
$863$	−90.1987	+	90.1987i	−0.104518	+	0.104518i	−0.757432	−	0.652914i	$-0.773546\pi$
$863$	−90.1987	+	90.1987i	−0.104518	+	0.104518i	0.652914	+	0.757432i	$0.273546\pi$
$864$	−788.246	−	353.785i	−0.912322	−	0.409473i
$865$		0			0
$866$	−1177.65	−	257.600i	−1.35987	−	0.297459i
$867$	−328.468	−	14.3009i	−0.378855	−	0.0164947i
$868$	123.524	−	45.7491i	0.142309	−	0.0527063i
$869$	516.396			0.594242
$870$		0			0
$871$		−	796.724i		−	0.914724i
$872$	−88.9118	−	633.899i	−0.101963	−	0.726949i
$873$	248.363	+	295.841i	0.284494	+	0.338878i
$874$	−662.446	−	144.904i	−0.757948	−	0.165794i
$875$		0			0
$876$	1149.85	−	369.838i	1.31261	−	0.422190i
$877$	−19.3296	−	19.3296i	−0.0220406	−	0.0220406i	0.696001	−	0.718041i	$-0.254961\pi$
$877$	−19.3296	−	19.3296i	−0.0220406	−	0.0220406i	−0.718041	+	0.696001i	$0.754961\pi$
$878$	−440.703	−	687.483i	−0.501940	−	0.783010i
$879$	611.879	−	560.822i	0.696108	−	0.638022i
$880$		0			0
$881$		−	721.297i		−	0.818725i	−0.912372	−	0.409363i	$-0.865751\pi$
$881$		−	721.297i		−	0.818725i	0.912372	−	0.409363i	$-0.134249\pi$
$882$	664.102	−	348.299i	0.752950	−	0.394897i
$883$	941.983	+	941.983i	1.06680	+	1.06680i	0.997603	+	0.0691949i	$0.0220430\pi$
$883$	941.983	+	941.983i	1.06680	+	1.06680i	0.0691949	+	0.997603i	$0.477957\pi$
$884$	845.104	+	388.296i	0.956000	+	0.439248i
$885$		0			0
$886$	−979.471	−	214.250i	−1.10550	−	0.241817i
$887$	489.902	+	489.902i	0.552313	+	0.552313i	0.927108	−	0.374795i	$-0.122287\pi$
$887$	489.902	+	489.902i	0.552313	+	0.552313i	−0.374795	+	0.927108i	$0.622287\pi$
$888$	447.605	−	542.821i	0.504060	−	0.611285i
$889$		−	243.626i		−	0.274045i
$890$		0			0
$891$	−548.252	−	96.3944i	−0.615322	−	0.108187i
$892$	1355.38	−	501.986i	1.51949	−	0.562765i
$893$	890.475	+	890.475i	0.997172	+	0.997172i
$894$	−867.795	+	504.430i	−0.970688	+	0.564239i
$895$		0			0
$896$	346.067	−	21.9551i	0.386236	−	0.0245035i
$897$	530.492	+	23.0966i	0.591407	+	0.0257487i
$898$	−488.581	−	762.171i	−0.544077	−	0.848743i
$899$		−	27.8555i		−	0.0309850i
$900$		0			0
$901$	293.954			0.326253
$902$	589.180	−	377.687i	0.653193	−	0.418722i
$903$	7.59784	−	174.510i	0.00841399	−	0.193256i
$904$	585.884	+	441.746i	0.648101	+	0.488658i
$905$		0			0
$906$	−226.928	−	390.395i	−0.250472	−	0.430899i
$907$	−193.827	+	193.827i	−0.213701	+	0.213701i	−0.805838	−	0.592137i	$-0.798285\pi$
$907$	−193.827	+	193.827i	−0.213701	+	0.213701i	0.592137	+	0.805838i	$0.298285\pi$
$908$	578.454	−	214.239i	0.637064	−	0.235946i
$909$	−97.2258	+	1114.44i	−0.106959	+	1.22601i
$910$		0			0
$911$	830.304			0.911421			0.455710	−	0.890128i	$-0.349385\pi$
$911$	830.304			0.911421			0.455710	+	0.890128i	$0.349385\pi$
$912$	1255.13	−	986.016i	1.37624	−	1.08116i
$913$	−403.093	+	403.093i	−0.441504	+	0.441504i
$914$	163.484	−	747.386i	0.178866	−	0.817709i
$915$		0			0
$916$	813.222	+	373.647i	0.887797	+	0.407911i
$917$	275.906	−	275.906i	0.300879	−	0.300879i
$918$	−245.214	+	680.457i	−0.267118	+	0.741238i
$919$	−1072.00			−1.16649			−0.583245	−	0.812296i	$-0.698217\pi$
$919$	−1072.00			−1.16649			−0.583245	+	0.812296i	$0.698217\pi$
$920$		0			0
$921$	928.448	+	1012.97i	1.00809	+	1.09986i
$922$	−980.731	+	628.687i	−1.06370	+	0.681873i
$923$	−1090.45	+	1090.45i	−1.18141	+	1.18141i
$924$	212.683	−	68.4076i	0.230177	−	0.0740342i
$925$		0			0
$926$	−192.288	+	879.068i	−0.207654	+	0.949317i
$927$	−1073.44	−	1278.64i	−1.15798	−	1.37934i
$928$	21.0632	−	70.2394i	0.0226974	−	0.0756890i
$929$	−1289.64			−1.38821			−0.694103	−	0.719876i	$-0.744199\pi$
$929$	−1289.64			−1.38821			−0.694103	+	0.719876i	$0.744199\pi$
$930$		0			0
$931$			1385.32i			1.48799i
$932$	−331.144	+	122.644i	−0.355304	+	0.131592i
$933$	−55.9764	+	1285.69i	−0.0599962	+	1.37801i
$934$	334.966	−	1531.34i	0.358636	−	1.63955i
$935$		0			0
$936$	−836.332	+	928.788i	−0.893517	+	0.992295i
$937$	507.002	+	507.002i	0.541091	+	0.541091i	0.923849	−	0.382758i	$-0.125026\pi$
$937$	507.002	+	507.002i	0.541091	+	0.541091i	−0.382758	+	0.923849i	$0.625026\pi$
$938$	−209.357	+	134.206i	−0.223195	+	0.143076i
$939$	413.229	+	450.849i	0.440073	+	0.480138i
$940$		0			0
$941$		−	707.695i		−	0.752067i	−0.926606	−	0.376033i	$-0.877288\pi$
$941$		−	707.695i		−	0.752067i	0.926606	−	0.376033i	$-0.122712\pi$
$942$	588.003	+	155.703i	0.624207	+	0.165290i
$943$	−367.111	−	367.111i	−0.389301	−	0.389301i
$944$	765.970	−	657.578i	0.811409	−	0.696586i
$945$		0			0
$946$	−63.1252	+	288.585i	−0.0667286	+	0.305058i
$947$	233.033	+	233.033i	0.246075	+	0.246075i	0.819358	−	0.573283i	$-0.194330\pi$
$947$	233.033	+	233.033i	0.246075	+	0.246075i	−0.573283	+	0.819358i	$0.694330\pi$
$948$	802.195	+	411.743i	0.846197	+	0.434328i
$949$		−	1747.26i		−	1.84116i
$950$		0			0
$951$	−859.420	−	937.662i	−0.903701	−	0.985974i
$952$	−40.3220	−	287.476i	−0.0423550	−	0.301971i
$953$	−414.033	−	414.033i	−0.434452	−	0.434452i	0.455688	−	0.890140i	$-0.349393\pi$
$953$	−414.033	−	414.033i	−0.434452	−	0.434452i	−0.890140	+	0.455688i	$0.849393\pi$
$954$	−117.634	+	377.111i	−0.123306	+	0.395295i
$955$		0			0
$956$	−1127.54	−	518.067i	−1.17944	−	0.541911i
$957$	2.05502	−	47.2004i	0.00214735	−	0.0493212i
$958$	1443.21	−	925.153i	1.50648	−	0.965713i
$959$		−	52.1813i		−	0.0544122i
$960$		0			0
$961$	813.238			0.846241
$962$	−549.259	−	856.826i	−0.570955	−	0.890671i
$963$	−93.8447	−	111.784i	−0.0974504	−	0.116079i
$964$	200.243	−	435.817i	0.207721	−	0.452093i
$965$		0			0
$966$	−83.2905	−	143.289i	−0.0862220	−	0.148332i
$967$	534.588	−	534.588i	0.552831	−	0.552831i	−0.374426	−	0.927257i	$-0.622160\pi$
$967$	534.588	−	534.588i	0.552831	−	0.552831i	0.927257	+	0.374426i	$0.122160\pi$
$968$	584.444	−	81.9752i	0.603765	−	0.0846851i
$969$	−902.828	−	985.022i	−0.931711	−	1.01653i
$970$		0			0
$971$	438.396			0.451490			0.225745	−	0.974186i	$-0.427518\pi$
$971$	438.396			0.451490			0.225745	+	0.974186i	$0.427518\pi$
$972$	−774.822	−	586.886i	−0.797141	−	0.603793i
$973$	120.159	−	120.159i	0.123493	−	0.123493i
$974$	270.182	+	59.0997i	0.277394	+	0.0606773i
$975$		0			0
$976$	−296.771	−	345.689i	−0.304068	−	0.354190i
$977$	−1230.19	+	1230.19i	−1.25915	+	1.25915i	−0.307644	+	0.951501i	$0.599541\pi$
$977$	−1230.19	+	1230.19i	−1.25915	+	1.25915i	−0.951501	+	0.307644i	$0.900459\pi$
$978$	504.050	+	133.472i	0.515388	+	0.136475i
$979$	282.497			0.288557
$980$		0			0
$981$	62.5865	−	717.392i	0.0637987	−	0.731287i
$982$	−831.328	−	1296.85i	−0.846566	−	1.32062i
$983$	1245.00	−	1245.00i	1.26653	−	1.26653i	0.318665	−	0.947867i	$-0.396765\pi$
$983$	1245.00	−	1245.00i	1.26653	−	1.26653i	0.947867	−	0.318665i	$-0.103235\pi$
$984$	1216.41	−	116.941i	1.23618	−	0.118843i
$985$		0			0
$986$	−59.9695	−	13.1177i	−0.0608210	−	0.0133040i
$987$	−13.3880	+	307.501i	−0.0135644	+	0.311551i
$988$	−801.903	−	2165.17i	−0.811643	−	2.19147i
$989$	219.146			0.221584
$990$		0			0
$991$		−	1328.35i		−	1.34041i	−0.742176	−	0.670205i	$-0.766206\pi$
$991$		−	1328.35i		−	1.34041i	0.742176	−	0.670205i	$-0.233794\pi$
$992$	−372.592	−	111.732i	−0.375597	−	0.112633i
$993$	−267.130	−	11.6303i	−0.269013	−	0.0117123i
$994$	470.220	+	102.856i	0.473059	+	0.103477i
$995$		0			0
$996$	−947.587	+	304.782i	−0.951392	+	0.306006i
$997$	553.349	+	553.349i	0.555014	+	0.555014i	0.927884	−	0.372870i	$-0.121626\pi$
$997$	553.349	+	553.349i	0.555014	+	0.555014i	−0.372870	+	0.927884i	$0.621626\pi$
$998$	71.6510	+	111.773i	0.0717945	+	0.111997i
$999$	627.771	−	482.073i	0.628400	−	0.482555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.3.l.g.107.15		40
3.2	odd	2	inner	300.3.l.g.107.6		40
4.3	odd	2	inner	300.3.l.g.107.5		40
5.2	odd	4		60.3.l.a.23.5	✓	40
5.3	odd	4	inner	300.3.l.g.143.16		40
5.4	even	2		60.3.l.a.47.6	yes	40
12.11	even	2	inner	300.3.l.g.107.16		40
15.2	even	4		60.3.l.a.23.16	yes	40
15.8	even	4	inner	300.3.l.g.143.5		40
15.14	odd	2		60.3.l.a.47.15	yes	40
20.3	even	4	inner	300.3.l.g.143.6		40
20.7	even	4		60.3.l.a.23.15	yes	40
20.19	odd	2		60.3.l.a.47.16	yes	40
60.23	odd	4	inner	300.3.l.g.143.15		40
60.47	odd	4		60.3.l.a.23.6	yes	40
60.59	even	2		60.3.l.a.47.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.5	✓	40	5.2	odd	4
60.3.l.a.23.6	yes	40	60.47	odd	4
60.3.l.a.23.15	yes	40	20.7	even	4
60.3.l.a.23.16	yes	40	15.2	even	4
60.3.l.a.47.5	yes	40	60.59	even	2
60.3.l.a.47.6	yes	40	5.4	even	2
60.3.l.a.47.15	yes	40	15.14	odd	2
60.3.l.a.47.16	yes	40	20.19	odd	2
300.3.l.g.107.5		40	4.3	odd	2	inner
300.3.l.g.107.6		40	3.2	odd	2	inner
300.3.l.g.107.15		40	1.1	even	1	trivial
300.3.l.g.107.16		40	12.11	even	2	inner
300.3.l.g.143.5		40	15.8	even	4	inner
300.3.l.g.143.6		40	20.3	even	4	inner
300.3.l.g.143.15		40	60.23	odd	4	inner
300.3.l.g.143.16		40	5.3	odd	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)

\(f(q)\)	\(=\)	\(q+(1.07935 + 1.68375i) q^{2} +(-0.130491 + 2.99716i) q^{3} +(-1.67002 + 3.63470i) q^{4} +(-5.18731 + 3.01526i) q^{6} +(1.91561 - 1.91561i) q^{7} +(-7.92245 + 1.11122i) q^{8} +(-8.96594 - 0.782204i) q^{9} +O(q^{10})\)	\(q+(1.07935 + 1.68375i) q^{2} +(-0.130491 + 2.99716i) q^{3} +(-1.67002 + 3.63470i) q^{4} +(-5.18731 + 3.01526i) q^{6} +(1.91561 - 1.91561i) q^{7} +(-7.92245 + 1.11122i) q^{8} +(-8.96594 - 0.782204i) q^{9} -6.87236 q^{11} +(-10.6759 - 5.47960i) q^{12} +(-12.2746 + 12.2746i) q^{13} +(5.29303 + 1.15780i) q^{14} +(-10.4221 - 12.1400i) q^{16} +(-9.47120 + 9.47120i) q^{17} +(-8.36034 - 15.9407i) q^{18} +33.2524 q^{19} +(5.49143 + 5.99137i) q^{21} +(-7.41767 - 11.5713i) q^{22} +(-7.20994 + 7.20994i) q^{23} +(-2.29669 - 23.8899i) q^{24} +(-33.9159 - 7.41877i) q^{26} +(3.51436 - 26.7703i) q^{27} +(3.76357 + 10.1618i) q^{28} +2.29155 q^{29} -12.1558i q^{31} +(9.19168 - 30.6515i) q^{32} +(0.896780 - 20.5976i) q^{33} +(-26.1698 - 5.72440i) q^{34} +(17.8164 - 31.2822i) q^{36} +(20.7290 + 20.7290i) q^{37} +(35.8909 + 55.9886i) q^{38} +(-35.1872 - 38.3906i) q^{39} +50.9173i q^{41} +(-4.16080 + 15.7130i) q^{42} +(-15.1975 - 15.1975i) q^{43} +(11.4770 - 24.9790i) q^{44} +(-19.9218 - 4.35769i) q^{46} +(26.7793 + 26.7793i) q^{47} +(37.7456 - 29.6525i) q^{48} +41.6608i q^{49} +(-27.1508 - 29.6226i) q^{51} +(-24.1157 - 65.1132i) q^{52} +(-15.5183 - 15.5183i) q^{53} +(48.8677 - 22.9772i) q^{54} +(-13.0477 + 17.3050i) q^{56} +(-4.33913 + 99.6627i) q^{57} +(2.47338 + 3.85839i) q^{58} +63.0946i q^{59} +28.4752 q^{61} +(20.4672 - 13.1203i) q^{62} +(-18.6737 + 15.6769i) q^{63} +(61.5304 - 17.6071i) q^{64} +(35.6491 - 20.7220i) q^{66} +(-32.4542 + 32.4542i) q^{67} +(-18.6079 - 50.2420i) q^{68} +(-20.6685 - 22.5502i) q^{69} +88.8377 q^{71} +(71.9014 - 3.76614i) q^{72} +(-71.1740 + 71.1740i) q^{73} +(-12.5286 + 57.2763i) q^{74} +(-55.5320 + 120.862i) q^{76} +(-13.1648 + 13.1648i) q^{77} +(26.6609 - 100.683i) q^{78} -75.1410 q^{79} +(79.7763 + 14.0264i) q^{81} +(-85.7318 + 54.9574i) q^{82} +(58.6543 - 58.6543i) q^{83} +(-30.9476 + 9.95402i) q^{84} +(9.18537 - 41.9921i) q^{86} +(-0.299026 + 6.86815i) q^{87} +(54.4459 - 7.63668i) q^{88} -41.1063 q^{89} +47.0267i q^{91} +(-14.1653 - 38.2467i) q^{92} +(36.4327 + 1.58621i) q^{93} +(-16.1854 + 73.9937i) q^{94} +(90.6680 + 31.5487i) q^{96} +(-30.3484 - 30.3484i) q^{97} +(-70.1464 + 44.9665i) q^{98} +(61.6172 + 5.37559i) 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

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Database

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