LMFDB - Embedded newform 60.4.i.b.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(17,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("60.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.i (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:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.370150560000.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 131x^{4} + 705x^{2} + 1600 $ x^8 + 3x^6 + 131x^4 + 705*x^2 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.3
Root			$-0.593004 - 1.76556i$ of defining polynomial
Character	$\chi$	$=$	60.53
Dual form			60.4.i.b.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18601 + 5.05899i) q^{3} +(-8.06226 + 7.74597i) q^{5} +(-3.75500 + 3.75500i) q^{7} +(-24.1868 + 12.0000i) q^{9} +O(q^{10})$	\(q+(1.18601 + 5.05899i) q^{3} +(-8.06226 + 7.74597i) q^{5} +(-3.75500 + 3.75500i) q^{7} +(-24.1868 + 12.0000i) q^{9} +6.48080i q^{11} +(27.4900 + 27.4900i) q^{13} +(-48.7487 - 31.6001i) q^{15} +(55.8032 + 55.8032i) q^{17} +10.4500i q^{19} +(-23.4500 - 14.5431i) q^{21} +(115.479 - 115.479i) q^{23} +(5.00000 - 124.900i) q^{25} +(-89.3936 - 108.129i) q^{27} +267.791 q^{29} -305.800 q^{31} +(-32.7863 + 7.68628i) q^{33} +(1.18767 - 59.3599i) q^{35} +(187.410 - 187.410i) q^{37} +(-106.468 + 171.675i) q^{39} +374.337i q^{41} +(291.065 + 291.065i) q^{43} +(102.048 - 284.097i) q^{45} +(-230.249 - 230.249i) q^{47} +314.800i q^{49} +(-216.125 + 348.491i) q^{51} +(-178.319 + 178.319i) q^{53} +(-50.2001 - 52.2499i) q^{55} +(-52.8664 + 12.3938i) q^{57} -225.743 q^{59} -315.800 q^{61} +(45.7614 - 135.881i) q^{63} +(-434.568 - 8.69484i) q^{65} +(203.795 - 203.795i) q^{67} +(721.169 + 447.250i) q^{69} -161.400i q^{71} +(300.020 + 300.020i) q^{73} +(637.798 - 122.837i) q^{75} +(-24.3354 - 24.3354i) q^{77} -948.250i q^{79} +(441.000 - 580.483i) q^{81} +(553.837 - 553.837i) q^{83} +(-882.150 - 17.6501i) q^{85} +(317.602 + 1354.75i) q^{87} -577.630 q^{89} -206.450 q^{91} +(-362.681 - 1547.04i) q^{93} +(-80.9452 - 84.2504i) q^{95} +(84.9200 - 84.9200i) q^{97} +(-77.7696 - 156.750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 80 q^{7}+O(q^{10}) $ 8 * q - 80 * q^7	$ 8 q - 80 q^{7} + 120 q^{13} - 120 q^{15} + 312 q^{21} + 40 q^{25} - 448 q^{31} - 600 q^{33} + 600 q^{37} + 480 q^{43} + 1560 q^{45} - 480 q^{51} - 2400 q^{55} - 1560 q^{57} - 528 q^{61} - 960 q^{63} + 2080 q^{67} + 2600 q^{73} + 3120 q^{75} + 3528 q^{81} - 3560 q^{85} - 2400 q^{87} - 1152 q^{91} - 6240 q^{93} - 120 q^{97}+O(q^{100}) $ 8 * q - 80 * q^7 + 120 * q^13 - 120 * q^15 + 312 * q^21 + 40 * q^25 - 448 * q^31 - 600 * q^33 + 600 * q^37 + 480 * q^43 + 1560 * q^45 - 480 * q^51 - 2400 * q^55 - 1560 * q^57 - 528 * q^61 - 960 * q^63 + 2080 * q^67 + 2600 * q^73 + 3120 * q^75 + 3528 * q^81 - 3560 * q^85 - 2400 * q^87 - 1152 * q^91 - 6240 * q^93 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.18601	+	5.05899i	0.228247	+	0.973603i
$3$	1.18601	+	5.05899i	0.228247	+	0.973603i
$4$		0			0
$5$	−8.06226	+	7.74597i	−0.721110	+	0.692820i
$5$	−8.06226	+	7.74597i	−0.721110	+	0.692820i
$6$		0			0
$7$	−3.75500	+	3.75500i	−0.202751	+	0.202751i	−0.801178	−	0.598427i	$-0.795793\pi$
$7$	−3.75500	+	3.75500i	−0.202751	+	0.202751i	0.598427	+	0.801178i	$0.295793\pi$
$8$		0			0
$9$	−24.1868	+	12.0000i	−0.895806	+	0.444444i
$10$		0			0
$11$			6.48080i			0.177640i	0.996048	+	0.0888198i	$0.0283095\pi$
$11$			6.48080i			0.177640i	−0.996048	+	0.0888198i	$0.971690\pi$
$12$		0			0
$13$	27.4900	+	27.4900i	0.586489	+	0.586489i	0.936679	−	0.350190i	$-0.113883\pi$
$13$	27.4900	+	27.4900i	0.586489	+	0.586489i	−0.350190	+	0.936679i	$0.613883\pi$
$14$		0			0
$15$	−48.7487	−	31.6001i	−0.839123	−	0.543941i
$16$		0			0
$17$	55.8032	+	55.8032i	0.796133	+	0.796133i	0.982483	−	0.186350i	$-0.0596658\pi$
$17$	55.8032	+	55.8032i	0.796133	+	0.796133i	−0.186350	+	0.982483i	$0.559666\pi$
$18$		0			0
$19$			10.4500i			0.126178i	0.998008	+	0.0630892i	$0.0200953\pi$
$19$			10.4500i			0.126178i	−0.998008	+	0.0630892i	$0.979905\pi$
$20$		0			0
$21$	−23.4500	−	14.5431i	−0.243676	−	0.151122i
$22$		0			0
$23$	115.479	−	115.479i	1.04692	−	1.04692i	0.0480747	−	0.998844i	$-0.484691\pi$
$23$	115.479	−	115.479i	1.04692	−	1.04692i	0.998844	−	0.0480747i	$-0.0153086\pi$
$24$		0			0
$25$	5.00000	−	124.900i	0.0400000	−	0.999200i
$26$		0			0
$27$	−89.3936	−	108.129i	−0.637178	−	0.770717i
$28$		0			0
$29$	267.791			1.71474			0.857371	−	0.514699i	$-0.172096\pi$
$29$	267.791			1.71474			0.857371	+	0.514699i	$0.172096\pi$
$30$		0			0
$31$	−305.800			−1.77172			−0.885859	−	0.463954i	$-0.846430\pi$
$31$	−305.800			−1.77172			−0.885859	+	0.463954i	$0.846430\pi$
$32$		0			0
$33$	−32.7863	+	7.68628i	−0.172950	+	0.0405457i
$34$		0			0
$35$	1.18767	−	59.3599i	0.00573581	−	0.286676i
$36$		0			0
$37$	187.410	−	187.410i	0.832703	−	0.832703i	−0.155183	−	0.987886i	$-0.549597\pi$
$37$	187.410	−	187.410i	0.832703	−	0.832703i	0.987886	+	0.155183i	$0.0495967\pi$
$38$		0			0
$39$	−106.468	+	171.675i	−0.437143	+	0.704872i
$40$		0			0
$41$			374.337i			1.42589i	0.701219	+	0.712946i	$0.252640\pi$
$41$			374.337i			1.42589i	−0.701219	+	0.712946i	$0.747360\pi$
$42$		0			0
$43$	291.065	+	291.065i	1.03226	+	1.03226i	0.999462	+	0.0327933i	$0.0104403\pi$
$43$	291.065	+	291.065i	1.03226	+	1.03226i	0.0327933	+	0.999462i	$0.489560\pi$
$44$		0			0
$45$	102.048	−	284.097i	0.338055	−	0.941126i
$46$		0			0
$47$	−230.249	−	230.249i	−0.714580	−	0.714580i	0.252910	−	0.967490i	$-0.418612\pi$
$47$	−230.249	−	230.249i	−0.714580	−	0.714580i	−0.967490	+	0.252910i	$0.918612\pi$
$48$		0			0
$49$			314.800i			0.917784i
$50$		0			0
$51$	−216.125	+	348.491i	−0.593403	+	0.956833i
$52$		0			0
$53$	−178.319	+	178.319i	−0.462150	+	0.462150i	−0.899360	−	0.437210i	$-0.855967\pi$
$53$	−178.319	+	178.319i	−0.462150	+	0.462150i	0.437210	+	0.899360i	$0.355967\pi$
$54$		0			0
$55$	−50.2001	−	52.2499i	−0.123072	−	0.128098i
$56$		0			0
$57$	−52.8664	+	12.3938i	−0.122848	+	0.0287999i
$58$		0			0
$59$	−225.743			−0.498123			−0.249062	−	0.968488i	$-0.580122\pi$
$59$	−225.743			−0.498123			−0.249062	+	0.968488i	$0.580122\pi$
$60$		0			0
$61$	−315.800			−0.662853			−0.331427	−	0.943481i	$-0.607530\pi$
$61$	−315.800			−0.662853			−0.331427	+	0.943481i	$0.607530\pi$
$62$		0			0
$63$	45.7614	−	135.881i	0.0915141	−	0.271737i
$64$		0			0
$65$	−434.568	−	8.69484i	−0.829254	−	0.0165917i
$66$		0			0
$67$	203.795	−	203.795i	0.371605	−	0.371605i	−0.496457	−	0.868062i	$-0.665366\pi$
$67$	203.795	−	203.795i	0.371605	−	0.371605i	0.868062	+	0.496457i	$0.165366\pi$
$68$		0			0
$69$	721.169	+	447.250i	1.25824	+	0.780327i
$70$		0			0
$71$		−	161.400i		−	0.269784i	−0.990860	−	0.134892i	$-0.956931\pi$
$71$		−	161.400i		−	0.269784i	0.990860	−	0.134892i	$-0.0430688\pi$
$72$		0			0
$73$	300.020	+	300.020i	0.481023	+	0.481023i	0.905458	−	0.424435i	$-0.139527\pi$
$73$	300.020	+	300.020i	0.481023	+	0.481023i	−0.424435	+	0.905458i	$0.639527\pi$
$74$		0			0
$75$	637.798	−	122.837i	0.981954	−	0.189120i
$76$		0			0
$77$	−24.3354	−	24.3354i	−0.0360166	−	0.0360166i
$78$		0			0
$79$		−	948.250i		−	1.35046i	−0.737607	−	0.675231i	$-0.764044\pi$
$79$		−	948.250i		−	1.35046i	0.737607	−	0.675231i	$-0.235956\pi$
$80$		0			0
$81$	441.000	−	580.483i	0.604938	−	0.796272i
$82$		0			0
$83$	553.837	−	553.837i	0.732427	−	0.732427i	−0.238673	−	0.971100i	$-0.576712\pi$
$83$	553.837	−	553.837i	0.732427	−	0.732427i	0.971100	+	0.238673i	$0.0767123\pi$
$84$		0			0
$85$	−882.150	−	17.6501i	−1.12568	−	0.0225226i
$86$		0			0
$87$	317.602	+	1354.75i	0.391385	+	1.66948i
$88$		0			0
$89$	−577.630			−0.687962			−0.343981	−	0.938977i	$-0.611776\pi$
$89$	−577.630			−0.687962			−0.343981	+	0.938977i	$0.611776\pi$
$90$		0			0
$91$	−206.450			−0.237822
$92$		0			0
$93$	−362.681	−	1547.04i	−0.404390	−	1.72495i
$94$		0			0
$95$	−80.9452	−	84.2504i	−0.0874190	−	0.0909885i
$96$		0			0
$97$	84.9200	−	84.9200i	0.0888899	−	0.0888899i	−0.661264	−	0.750154i	$-0.729980\pi$
$97$	84.9200	−	84.9200i	0.0888899	−	0.0888899i	0.750154	+	0.661264i	$0.229980\pi$
$98$		0			0
$99$	−77.7696	−	156.750i	−0.0789509	−	0.159131i
$100$		0			0
$101$		−	1071.47i		−	1.05560i	−0.849369	−	0.527800i	$-0.823017\pi$
$101$		−	1071.47i		−	1.05560i	0.849369	−	0.527800i	$-0.176983\pi$
$102$		0			0
$103$	543.995	+	543.995i	0.520402	+	0.520402i	0.917693	−	0.397291i	$-0.130050\pi$
$103$	543.995	+	543.995i	0.520402	+	0.520402i	−0.397291	+	0.917693i	$0.630050\pi$
$104$		0			0
$105$	301.710	−	64.3929i	0.280418	−	0.0598486i
$106$		0			0
$107$	254.584	+	254.584i	0.230015	+	0.230015i	0.812699	−	0.582684i	$-0.197997\pi$
$107$	254.584	+	254.584i	0.230015	+	0.230015i	−0.582684	+	0.812699i	$0.697997\pi$
$108$		0			0
$109$		−	617.300i		−	0.542446i	−0.962517	−	0.271223i	$-0.912572\pi$
$109$		−	617.300i		−	0.542446i	0.962517	−	0.271223i	$-0.0874281\pi$
$110$		0			0
$111$	1170.37	+	725.836i	1.00078	+	0.620660i
$112$		0			0
$113$	−1369.45	+	1369.45i	−1.14007	+	1.14007i	−0.151628	+	0.988438i	$0.548452\pi$
$113$	−1369.45	+	1369.45i	−1.14007	+	1.14007i	−0.988438	+	0.151628i	$0.951548\pi$
$114$		0			0
$115$	−36.5251	+	1825.52i	−0.0296173	+	1.48027i
$116$		0			0
$117$	−994.774	−	335.014i	−0.786042	−	0.264719i
$118$		0			0
$119$	−419.082			−0.322834
$120$		0			0
$121$	1289.00			0.968444
$122$		0			0
$123$	−1893.77	+	443.966i	−1.38825	+	0.325456i
$124$		0			0
$125$	927.160	+	1045.71i	0.663421	+	0.748246i
$126$		0			0
$127$	−18.2148	+	18.2148i	−0.0127268	+	0.0127268i	−0.713442	−	0.700715i	$-0.752865\pi$
$127$	−18.2148	+	18.2148i	−0.0127268	+	0.0127268i	0.700715	+	0.713442i	$0.252865\pi$
$128$		0			0
$129$	−1127.29	+	1817.70i	−0.769398	+	1.24062i
$130$		0			0
$131$			471.239i			0.314293i	0.987575	+	0.157146i	$0.0502294\pi$
$131$			471.239i			0.314293i	−0.987575	+	0.157146i	$0.949771\pi$
$132$		0			0
$133$	−39.2397	−	39.2397i	−0.0255828	−	0.0255828i
$134$		0			0
$135$	1558.27	+	179.321i	0.993444	+	0.114322i
$136$		0			0
$137$	−282.824	−	282.824i	−0.176375	−	0.176375i	0.613399	−	0.789773i	$-0.289802\pi$
$137$	−282.824	−	282.824i	−0.176375	−	0.176375i	−0.789773	+	0.613399i	$0.789802\pi$
$138$		0			0
$139$		−	2301.75i		−	1.40455i	−0.711908	−	0.702273i	$-0.752169\pi$
$139$		−	2301.75i		−	1.40455i	0.711908	−	0.702273i	$-0.247831\pi$
$140$		0			0
$141$	891.750	−	1437.90i	0.532616	−	0.858818i
$142$		0			0
$143$	−178.157	+	178.157i	−0.104184	+	0.104184i
$144$		0			0
$145$	−2159.00	+	2074.30i	−1.23652	+	1.18801i
$146$		0			0
$147$	−1592.57	+	373.355i	−0.893557	+	0.209482i
$148$		0			0
$149$	1479.98			0.813724			0.406862	−	0.913490i	$-0.366623\pi$
$149$	1479.98			0.813724			0.406862	+	0.913490i	$0.366623\pi$
$150$		0			0
$151$	−166.200			−0.0895707			−0.0447853	−	0.998997i	$-0.514260\pi$
$151$	−166.200			−0.0895707			−0.0447853	+	0.998997i	$0.514260\pi$
$152$		0			0
$153$	−2019.34	−	680.061i	−1.06702	−	0.359344i
$154$		0			0
$155$	2465.44	−	2368.72i	1.27760	−	1.22748i
$156$		0			0
$157$	1012.47	−	1012.47i	0.514675	−	0.514675i	−0.401281	−	0.915955i	$-0.631435\pi$
$157$	1012.47	−	1012.47i	0.514675	−	0.514675i	0.915955	+	0.401281i	$0.131435\pi$
$158$		0			0
$159$	−1113.60	−	690.625i	−0.555435	−	0.344466i
$160$		0			0
$161$			867.251i			0.424528i
$162$		0			0
$163$	−293.835	−	293.835i	−0.141196	−	0.141196i	0.632976	−	0.774172i	$-0.281833\pi$
$163$	−293.835	−	293.835i	−0.141196	−	0.141196i	−0.774172	+	0.632976i	$0.781833\pi$
$164$		0			0
$165$	204.794	−	315.931i	0.0966254	−	0.149062i
$166$		0			0
$167$	1744.84	+	1744.84i	0.808503	+	0.808503i	0.984407	−	0.175904i	$-0.0562849\pi$
$167$	1744.84	+	1744.84i	0.808503	+	0.808503i	−0.175904	+	0.984407i	$0.556285\pi$
$168$		0			0
$169$		−	685.600i		−	0.312062i
$170$		0			0
$171$	−125.400	−	252.751i	−0.0560793	−	0.113031i
$172$		0			0
$173$	2236.23	−	2236.23i	0.982759	−	0.982759i	−0.0170951	−	0.999854i	$-0.505442\pi$
$173$	2236.23	−	2236.23i	0.982759	−	0.982759i	0.999854	+	0.0170951i	$0.00544180\pi$
$174$		0			0
$175$	450.225	+	487.775i	0.194479	+	0.210699i
$176$		0			0
$177$	−267.733	−	1142.03i	−0.113695	−	0.484974i
$178$		0			0
$179$	921.330			0.384712			0.192356	−	0.981325i	$-0.438387\pi$
$179$	921.330			0.384712			0.192356	+	0.981325i	$0.438387\pi$
$180$		0			0
$181$	714.400			0.293375			0.146688	−	0.989183i	$-0.453139\pi$
$181$	714.400			0.293375			0.146688	+	0.989183i	$0.453139\pi$
$182$		0			0
$183$	−374.541	−	1597.63i	−0.151294	−	0.645356i
$184$		0			0
$185$	−59.2761	+	2962.62i	−0.0235571	+	1.17738i
$186$		0			0
$187$	−361.650	+	361.650i	−0.141425	+	0.141425i
$188$		0			0
$189$	741.696	+	70.3499i	0.285452	+	0.0270752i
$190$		0			0
$191$		−	4186.20i		−	1.58588i	−0.609300	−	0.792940i	$-0.708549\pi$
$191$		−	4186.20i		−	1.58588i	0.609300	−	0.792940i	$-0.291451\pi$
$192$		0			0
$193$	1475.44	+	1475.44i	0.550282	+	0.550282i	0.926522	−	0.376240i	$-0.122783\pi$
$193$	1475.44	+	1475.44i	0.550282	+	0.550282i	−0.376240	+	0.926522i	$0.622783\pi$
$194$		0			0
$195$	−471.414	−	2208.79i	−0.173121	−	0.811152i
$196$		0			0
$197$	383.522	+	383.522i	0.138705	+	0.138705i	0.773050	−	0.634345i	$-0.218730\pi$
$197$	383.522	+	383.522i	0.138705	+	0.138705i	−0.634345	+	0.773050i	$0.718730\pi$
$198$		0			0
$199$		−	593.650i		−	0.211471i	−0.994394	−	0.105735i	$-0.966280\pi$
$199$		−	593.650i		−	0.211471i	0.994394	−	0.105735i	$-0.0337197\pi$
$200$		0			0
$201$	1272.70	+	789.295i	0.446613	+	0.276978i
$202$		0			0
$203$	−1005.56	+	1005.56i	−0.347666	+	0.347666i
$204$		0			0
$205$	−2899.60	−	3018.00i	−0.987887	−	1.02823i
$206$		0			0
$207$	−1407.32	+	4178.83i	−0.472539	+	1.40313i
$208$		0			0
$209$	−67.7243			−0.0224143
$210$		0			0
$211$	−3984.60			−1.30005			−0.650026	−	0.759912i	$-0.725242\pi$
$211$	−3984.60			−1.30005			−0.650026	+	0.759912i	$0.725242\pi$
$212$		0			0
$213$	816.522	−	191.422i	0.262663	−	0.0615775i
$214$		0			0
$215$	−4601.22	−	92.0612i	−1.45954	−	0.0292024i
$216$		0			0
$217$	1148.28	−	1148.28i	0.359218	−	0.359218i
$218$		0			0
$219$	−1161.97	+	1873.62i	−0.358533	+	0.578118i
$220$		0			0
$221$			3068.06i			0.933847i
$222$		0			0
$223$	2557.01	+	2557.01i	0.767849	+	0.767849i	0.977727	−	0.209878i	$-0.0673068\pi$
$223$	2557.01	+	2557.01i	0.767849	+	0.767849i	−0.209878	+	0.977727i	$0.567307\pi$
$224$		0			0
$225$	1377.87	+	3080.93i	0.408256	+	0.912867i
$226$		0			0
$227$	−1844.44	−	1844.44i	−0.539295	−	0.539295i	0.384027	−	0.923322i	$-0.374537\pi$
$227$	−1844.44	−	1844.44i	−0.539295	−	0.539295i	−0.923322	+	0.384027i	$0.874537\pi$
$228$		0			0
$229$			3060.30i			0.883102i	0.897236	+	0.441551i	$0.145571\pi$
$229$			3060.30i			0.883102i	−0.897236	+	0.441551i	$0.854429\pi$
$230$		0			0
$231$	94.2507	−	151.975i	0.0268452	−	0.0432866i
$232$		0			0
$233$	−1112.42	+	1112.42i	−0.312776	+	0.312776i	−0.845984	−	0.533208i	$-0.820986\pi$
$233$	−1112.42	+	1112.42i	−0.312776	+	0.312776i	0.533208	+	0.845984i	$0.320986\pi$
$234$		0			0
$235$	3639.82	+	72.8256i	1.01037	+	0.0202154i
$236$		0			0
$237$	4797.19	−	1124.63i	1.31481	−	0.308239i
$238$		0			0
$239$	−5653.01			−1.52997			−0.764984	−	0.644049i	$-0.777253\pi$
$239$	−5653.01			−1.52997			−0.764984	+	0.644049i	$0.777253\pi$
$240$		0			0
$241$	1804.60			0.482342			0.241171	−	0.970483i	$-0.422468\pi$
$241$	1804.60			0.482342			0.241171	+	0.970483i	$0.422468\pi$
$242$		0			0
$243$	3459.69	+	1542.56i	0.913329	+	0.407223i
$244$		0			0
$245$	−2438.43	−	2538.00i	−0.635859	−	0.661823i
$246$		0			0
$247$	−287.270	+	287.270i	−0.0740022	+	0.0740022i
$248$		0			0
$249$	3458.71	+	2145.00i	0.880268	+	0.545919i
$250$		0			0
$251$			6484.07i			1.63056i	0.579066	+	0.815281i	$0.303417\pi$
$251$			6484.07i			1.63056i	−0.579066	+	0.815281i	$0.696583\pi$
$252$		0			0
$253$	748.399	+	748.399i	0.185974	+	0.185974i
$254$		0			0
$255$	−956.945	−	4483.72i	−0.235005	−	1.10110i
$256$		0			0
$257$	−2094.74	−	2094.74i	−0.508428	−	0.508428i	0.405616	−	0.914044i	$-0.367057\pi$
$257$	−2094.74	−	2094.74i	−0.508428	−	0.508428i	−0.914044	+	0.405616i	$0.867057\pi$
$258$		0			0
$259$			1407.45i			0.337663i
$260$		0			0
$261$	−6477.00	+	3213.49i	−1.53608	+	0.762108i
$262$		0			0
$263$	1942.24	−	1942.24i	0.455374	−	0.455374i	−0.441759	−	0.897134i	$-0.645645\pi$
$263$	1942.24	−	1942.24i	0.455374	−	0.455374i	0.897134	+	0.441759i	$0.145645\pi$
$264$		0			0
$265$	56.4006	−	2818.90i	0.0130742	−	0.653448i
$266$		0			0
$267$	−685.073	−	2922.22i	−0.157025	−	0.669802i
$268$		0			0
$269$	1778.41			0.403091			0.201546	−	0.979479i	$-0.435404\pi$
$269$	1778.41			0.403091			0.201546	+	0.979479i	$0.435404\pi$
$270$		0			0
$271$	−6555.00			−1.46933			−0.734664	−	0.678431i	$-0.762660\pi$
$271$	−6555.00			−1.46933			−0.734664	+	0.678431i	$0.762660\pi$
$272$		0			0
$273$	−244.851	−	1044.43i	−0.0542823	−	0.231545i
$274$		0			0
$275$	809.452	+	32.4040i	0.177497	+	0.00710558i
$276$		0			0
$277$	325.569	−	325.569i	0.0706193	−	0.0706193i	−0.670915	−	0.741534i	$-0.734098\pi$
$277$	325.569	−	325.569i	0.0706193	−	0.0706193i	0.741534	+	0.670915i	$0.234098\pi$
$278$		0			0
$279$	7396.31	−	3669.60i	1.58712	−	0.787431i
$280$		0			0
$281$		−	7704.29i		−	1.63559i	−0.575513	−	0.817793i	$-0.695198\pi$
$281$		−	7704.29i		−	1.63559i	0.575513	−	0.817793i	$-0.304802\pi$
$282$		0			0
$283$	−1568.53	−	1568.53i	−0.329469	−	0.329469i	0.522916	−	0.852385i	$-0.324844\pi$
$283$	−1568.53	−	1568.53i	−0.329469	−	0.329469i	−0.852385	+	0.522916i	$0.824844\pi$
$284$		0			0
$285$	330.221	−	509.423i	0.0686336	−	0.105879i
$286$		0			0
$287$	−1405.64	−	1405.64i	−0.289101	−	0.289101i
$288$		0			0
$289$			1315.00i			0.267657i
$290$		0			0
$291$	530.325	+	328.894i	0.106832	+	0.0662546i
$292$		0			0
$293$	−527.403	+	527.403i	−0.105158	+	0.105158i	−0.757728	−	0.652570i	$-0.773691\pi$
$293$	−527.403	+	527.403i	−0.105158	+	0.105158i	0.652570	+	0.757728i	$0.273691\pi$
$294$		0			0
$295$	1820.00	−	1748.60i	0.359202	−	0.345110i
$296$		0			0
$297$	700.760	−	579.342i	0.136910	−	0.113188i
$298$		0			0
$299$	6349.06			1.22801
$300$		0			0
$301$	−2185.90			−0.418582
$302$		0			0
$303$	5420.58	−	1270.78i	1.02774	−	0.240938i
$304$		0			0
$305$	2546.06	−	2446.18i	0.477990	−	0.459238i
$306$		0			0
$307$	3963.80	−	3963.80i	0.736892	−	0.736892i	−0.235084	−	0.971975i	$-0.575536\pi$
$307$	3963.80	−	3963.80i	0.736892	−	0.736892i	0.971975	+	0.235084i	$0.0755364\pi$
$308$		0			0
$309$	−2106.88	+	3397.25i	−0.387885	+	0.625446i
$310$		0			0
$311$			8507.88i			1.55125i	0.631196	+	0.775623i	$0.282564\pi$
$311$			8507.88i			1.55125i	−0.631196	+	0.775623i	$0.717436\pi$
$312$		0			0
$313$	−2679.26	−	2679.26i	−0.483836	−	0.483836i	0.422518	−	0.906354i	$-0.361146\pi$
$313$	−2679.26	−	2679.26i	−0.483836	−	0.483836i	−0.906354	+	0.422518i	$0.861146\pi$
$314$		0			0
$315$	683.593	+	1449.98i	0.122273	+	0.259355i
$316$		0			0
$317$	−4481.33	−	4481.33i	−0.793996	−	0.793996i	0.188145	−	0.982141i	$-0.439752\pi$
$317$	−4481.33	−	4481.33i	−0.793996	−	0.793996i	−0.982141	+	0.188145i	$0.939752\pi$
$318$		0			0
$319$			1735.50i			0.304606i
$320$		0			0
$321$	−986.000	+	1589.88i	−0.171443	+	0.276443i
$322$		0			0
$323$	−583.143	+	583.143i	−0.100455	+	0.100455i
$324$		0			0
$325$	3570.95	−	3296.05i	0.609479	−	0.562560i
$326$		0			0
$327$	3122.92	−	732.122i	0.528127	−	0.123812i
$328$		0			0
$329$	1729.17			0.289763
$330$		0			0
$331$	2861.00			0.475090			0.237545	−	0.971377i	$-0.423657\pi$
$331$	2861.00			0.475090			0.237545	+	0.971377i	$0.423657\pi$
$332$		0			0
$333$	−2283.92	+	6781.76i	−0.375850	+	1.11603i
$334$		0			0
$335$	−64.4585	+	3221.64i	−0.0105127	+	0.525423i
$336$		0			0
$337$	−7582.88	+	7582.88i	−1.22571	+	1.22571i	−0.260145	+	0.965570i	$0.583770\pi$
$337$	−7582.88	+	7582.88i	−1.22571	+	1.22571i	−0.965570	+	0.260145i	$0.916230\pi$
$338$		0			0
$339$	−8552.24	−	5303.88i	−1.37019	−	0.849755i
$340$		0			0
$341$		−	1981.83i		−	0.314727i
$342$		0			0
$343$	−2470.04	−	2470.04i	−0.388833	−	0.388833i
$344$		0			0
$345$	−9278.63	+	1980.31i	−1.44796	+	0.309032i
$346$		0			0
$347$	7580.72	+	7580.72i	1.17278	+	1.17278i	0.981544	+	0.191235i	$0.0612491\pi$
$347$	7580.72	+	7580.72i	1.17278	+	1.17278i	0.191235	+	0.981544i	$0.438751\pi$
$348$		0			0
$349$			4470.50i			0.685675i	0.939395	+	0.342837i	$0.111388\pi$
$349$			4470.50i			0.685675i	−0.939395	+	0.342837i	$0.888612\pi$
$350$		0			0
$351$	515.025	−	5429.88i	0.0783191	−	0.825714i
$352$		0			0
$353$	3156.77	−	3156.77i	0.475972	−	0.475972i	−0.427869	−	0.903841i	$-0.640736\pi$
$353$	3156.77	−	3156.77i	0.475972	−	0.475972i	0.903841	+	0.427869i	$0.140736\pi$
$354$		0			0
$355$	1250.20	+	1301.25i	0.186912	+	0.194544i
$356$		0			0
$357$	−497.035	−	2120.13i	−0.0736859	−	0.314312i
$358$		0			0
$359$	−6798.84			−0.999524			−0.499762	−	0.866163i	$-0.666579\pi$
$359$	−6798.84			−0.999524			−0.499762	+	0.866163i	$0.666579\pi$
$360$		0			0
$361$	6749.80			0.984079
$362$		0			0
$363$	1528.76	+	6521.03i	0.221045	+	0.942880i
$364$		0			0
$365$	−4742.78	−	94.8936i	−0.680133	−	0.0136081i
$366$		0			0
$367$	−340.456	+	340.456i	−0.0484241	+	0.0484241i	−0.730904	−	0.682480i	$-0.760901\pi$
$367$	−340.456	+	340.456i	−0.0484241	+	0.0484241i	0.682480	+	0.730904i	$0.260901\pi$
$368$		0			0
$369$	−4492.04	−	9054.00i	−0.633730	−	1.27732i
$370$		0			0
$371$		−	1339.17i		−	0.187403i
$372$		0			0
$373$	1709.59	+	1709.59i	0.237317	+	0.237317i	0.815738	−	0.578421i	$-0.196331\pi$
$373$	1709.59	+	1709.59i	0.237317	+	0.237317i	−0.578421	+	0.815738i	$0.696331\pi$
$374$		0			0
$375$	−4190.60	+	5930.71i	−0.577071	+	0.816694i
$376$		0			0
$377$	7361.57	+	7361.57i	1.00568	+	1.00568i
$378$		0			0
$379$			6421.85i			0.870365i	0.900342	+	0.435182i	$0.143316\pi$
$379$			6421.85i			0.870365i	−0.900342	+	0.435182i	$0.856684\pi$
$380$		0			0
$381$	−113.751	−	70.5456i	−0.0152957	−	0.00948598i
$382$		0			0
$383$	−2847.22	+	2847.22i	−0.379860	+	0.379860i	−0.871052	−	0.491192i	$-0.836562\pi$
$383$	−2847.22	+	2847.22i	−0.379860	+	0.379860i	0.491192	+	0.871052i	$0.336562\pi$
$384$		0			0
$385$	384.700	+	7.69708i	0.0509250	+	0.00101891i
$386$		0			0
$387$	−10532.7	−	3547.14i	−1.38348	−	0.465921i
$388$		0			0
$389$	−1226.46			−0.159856			−0.0799278	−	0.996801i	$-0.525469\pi$
$389$	−1226.46			−0.159856			−0.0799278	+	0.996801i	$0.525469\pi$
$390$		0			0
$391$	12888.2			1.66697
$392$		0			0
$393$	−2383.99	+	558.893i	−0.305996	+	0.0717364i
$394$		0			0
$395$	7345.11	+	7645.04i	0.935627	+	0.973832i
$396$		0			0
$397$	−6703.53	+	6703.53i	−0.847457	+	0.847457i	−0.989815	−	0.142358i	$-0.954532\pi$
$397$	−6703.53	+	6703.53i	−0.847457	+	0.847457i	0.142358	+	0.989815i	$0.454532\pi$
$398$		0			0
$399$	151.975	−	245.052i	0.0190683	−	0.0307467i
$400$		0			0
$401$		−	7126.29i		−	0.887456i	−0.896161	−	0.443728i	$-0.853656\pi$
$401$		−	7126.29i		−	0.887456i	0.896161	−	0.443728i	$-0.146344\pi$
$402$		0			0
$403$	−8406.44	−	8406.44i	−1.03909	−	1.03909i
$404$		0			0
$405$	940.943	+	8095.97i	0.115446	+	0.993314i
$406$		0			0
$407$	1214.57	+	1214.57i	0.147921	+	0.147921i
$408$		0			0
$409$		−	12924.4i		−	1.56252i	−0.624206	−	0.781260i	$-0.714578\pi$
$409$		−	12924.4i		−	1.56252i	0.624206	−	0.781260i	$-0.285422\pi$
$410$		0			0
$411$	1095.37	−	1766.24i	0.131462	−	0.211976i
$412$		0			0
$413$	847.666	−	847.666i	0.100995	−	0.100995i
$414$		0			0
$415$	−175.174	+	8755.17i	−0.0207203	+	1.03560i
$416$		0			0
$417$	11644.5	−	2729.89i	1.36747	−	0.320584i
$418$		0			0
$419$	7683.45			0.895850			0.447925	−	0.894071i	$-0.352163\pi$
$419$	7683.45			0.895850			0.447925	+	0.894071i	$0.352163\pi$
$420$		0			0
$421$	5173.00			0.598852			0.299426	−	0.954120i	$-0.403205\pi$
$421$	5173.00			0.598852			0.299426	+	0.954120i	$0.403205\pi$
$422$		0			0
$423$	8331.96	+	2805.99i	0.957716	+	0.322534i
$424$		0			0
$425$	7248.84	−	6690.80i	0.827342	−	0.763651i
$426$		0			0
$427$	1185.83	−	1185.83i	0.134394	−	0.134394i
$428$		0			0
$429$	−1112.59	−	690.000i	−0.125213	−	0.0776539i
$430$		0			0
$431$		−	10799.0i		−	1.20689i	−0.797405	−	0.603444i	$-0.793795\pi$
$431$		−	10799.0i		−	1.20689i	0.797405	−	0.603444i	$-0.206205\pi$
$432$		0			0
$433$	−12536.2	−	12536.2i	−1.39134	−	1.39134i	−0.822337	−	0.569001i	$-0.807330\pi$
$433$	−12536.2	−	12536.2i	−1.39134	−	1.39134i	−0.569001	−	0.822337i	$-0.692670\pi$
$434$		0			0
$435$	−13054.5	−	8462.22i	−1.43888	−	0.932719i
$436$		0			0
$437$	1206.76	+	1206.76i	0.132099	+	0.132099i
$438$		0			0
$439$		−	1036.05i		−	0.112638i	−0.998413	−	0.0563189i	$-0.982064\pi$
$439$		−	1036.05i		−	0.112638i	0.998413	−	0.0563189i	$-0.0179364\pi$
$440$		0			0
$441$	−3777.60	−	7613.99i	−0.407904	−	0.822157i
$442$		0			0
$443$	1841.60	−	1841.60i	0.197511	−	0.197511i	−0.601421	−	0.798932i	$-0.705399\pi$
$443$	1841.60	−	1841.60i	0.197511	−	0.197511i	0.798932	+	0.601421i	$0.205399\pi$
$444$		0			0
$445$	4657.00	−	4474.30i	0.496096	−	0.476634i
$446$		0			0
$447$	1755.27	+	7487.22i	0.185730	+	0.792244i
$448$		0			0
$449$	862.292			0.0906326			0.0453163	−	0.998973i	$-0.485570\pi$
$449$	862.292			0.0906326			0.0453163	+	0.998973i	$0.485570\pi$
$450$		0			0
$451$	−2426.00			−0.253295
$452$		0			0
$453$	−197.115	−	840.805i	−0.0204443	−	0.0872063i
$454$		0			0
$455$	1664.45	−	1599.15i	0.171496	−	0.164768i
$456$		0			0
$457$	−11094.5	+	11094.5i	−1.13562	+	1.13562i	−0.146399	+	0.989226i	$0.546768\pi$
$457$	−11094.5	+	11094.5i	−1.13562	+	1.13562i	−0.989226	+	0.146399i	$0.953232\pi$
$458$		0			0
$459$	1045.47	−	11022.4i	0.106315	−	1.12087i
$460$		0			0
$461$			12371.3i			1.24987i	0.780678	+	0.624933i	$0.214874\pi$
$461$			12371.3i			1.24987i	−0.780678	+	0.624933i	$0.785126\pi$
$462$		0			0
$463$	−10729.1	−	10729.1i	−1.07694	−	1.07694i	−0.996782	−	0.0801591i	$-0.974457\pi$
$463$	−10729.1	−	10729.1i	−1.07694	−	1.07694i	−0.0801591	−	0.996782i	$-0.525543\pi$
$464$		0			0
$465$	14907.3	+	9663.31i	1.48669	+	0.963710i
$466$		0			0
$467$	−8748.16	−	8748.16i	−0.866845	−	0.866845i	0.125276	−	0.992122i	$-0.460018\pi$
$467$	−8748.16	−	8748.16i	−0.866845	−	0.866845i	−0.992122	+	0.125276i	$0.960018\pi$
$468$		0			0
$469$			1530.50i			0.150687i
$470$		0			0
$471$	6322.87	+	3921.28i	0.618562	+	0.383616i
$472$		0			0
$473$	−1886.33	+	1886.33i	−0.183369	+	0.183369i
$474$		0			0
$475$	1305.20	+	52.2499i	0.126077	+	0.00504714i
$476$		0			0
$477$	2173.13	−	6452.77i	0.208597	−	0.619397i
$478$		0			0
$479$	−4545.13			−0.433554			−0.216777	−	0.976221i	$-0.569554\pi$
$479$	−4545.13			−0.433554			−0.216777	+	0.976221i	$0.569554\pi$
$480$		0			0
$481$	10303.8			0.976742
$482$		0			0
$483$	−4387.41	+	1028.57i	−0.413321	+	0.0968973i
$484$		0			0
$485$	−26.8594	+	1342.43i	−0.00251469	+	0.125684i
$486$		0			0
$487$	8906.45	−	8906.45i	0.828726	−	0.828726i	−0.158615	−	0.987341i	$-0.550703\pi$
$487$	8906.45	−	8906.45i	0.828726	−	0.828726i	0.987341	+	0.158615i	$0.0507027\pi$
$488$		0			0
$489$	1138.02	−	1835.00i	0.105241	−	0.169696i
$490$		0			0
$491$		−	8172.12i		−	0.751126i	−0.926797	−	0.375563i	$-0.877449\pi$
$491$		−	8172.12i		−	0.751126i	0.926797	−	0.375563i	$-0.122551\pi$
$492$		0			0
$493$	14943.6	+	14943.6i	1.36516	+	1.36516i
$494$		0			0
$495$	1841.18	+	661.356i	0.167181	+	0.0600520i
$496$		0			0
$497$	606.058	+	606.058i	0.0546990	+	0.0546990i
$498$		0			0
$499$			16861.2i			1.51265i	0.654195	+	0.756326i	$0.273007\pi$
$499$			16861.2i			1.51265i	−0.654195	+	0.756326i	$0.726993\pi$
$500$		0			0
$501$	−6757.75	+	10896.5i	−0.602623	+	0.971700i
$502$		0			0
$503$	−10794.2	+	10794.2i	−0.956838	+	0.956838i	−0.999106	−	0.0422686i	$-0.986541\pi$
$503$	−10794.2	+	10794.2i	−0.956838	+	0.956838i	0.0422686	+	0.999106i	$0.486541\pi$
$504$		0			0
$505$	8299.60	+	8638.50i	0.731341	+	0.761204i
$506$		0			0
$507$	3468.45	−	813.127i	0.303825	−	0.0712273i
$508$		0			0
$509$	−13820.6			−1.20351			−0.601754	−	0.798681i	$-0.705531\pi$
$509$	−13820.6			−1.20351			−0.601754	+	0.798681i	$0.705531\pi$
$510$		0			0
$511$	−2253.15			−0.195056
$512$		0			0
$513$	1129.94	−	934.161i	0.0972478	−	0.0803981i
$514$		0			0
$515$	−8599.60	−	172.061i	−0.735813	−	0.0147221i
$516$		0			0
$517$	1492.20	−	1492.20i	0.126938	−	0.126938i
$518$		0			0
$519$	13965.2	+	8660.87i	1.18113	+	0.732505i
$520$		0			0
$521$			7894.69i			0.663863i	0.943304	+	0.331931i	$0.107700\pi$
$521$			7894.69i			0.663863i	−0.943304	+	0.331931i	$0.892300\pi$
$522$		0			0
$523$	−2353.74	−	2353.74i	−0.196791	−	0.196791i	0.601832	−	0.798623i	$-0.294438\pi$
$523$	−2353.74	−	2353.74i	−0.196791	−	0.196791i	−0.798623	+	0.601832i	$0.794438\pi$
$524$		0			0
$525$	−1933.68	+	2856.19i	−0.160748	+	0.237437i
$526$		0			0
$527$	−17064.6	−	17064.6i	−1.41052	−	1.41052i
$528$		0			0
$529$		−	14504.0i		−	1.19208i
$530$		0			0
$531$	5460.00	−	2708.92i	0.446222	−	0.221388i
$532$		0			0
$533$	−10290.5	+	10290.5i	−0.836270	+	0.836270i
$534$		0			0
$535$	−4024.52	−	80.5227i	−0.325225	−	0.00650710i
$536$		0			0
$537$	1092.70	+	4661.00i	0.0878095	+	0.374557i
$538$		0			0
$539$	−2040.16			−0.163035
$540$		0			0
$541$	−15636.0			−1.24260			−0.621298	−	0.783575i	$-0.713394\pi$
$541$	−15636.0			−1.24260			−0.621298	+	0.783575i	$0.713394\pi$
$542$		0			0
$543$	847.284	+	3614.14i	0.0669621	+	0.285631i
$544$		0			0
$545$	4781.59	+	4976.83i	0.375818	+	0.391163i
$546$		0			0
$547$	−8705.76	+	8705.76i	−0.680497	+	0.680497i	−0.960112	−	0.279615i	$-0.909793\pi$
$547$	−8705.76	+	8705.76i	−0.680497	+	0.680497i	0.279615	+	0.960112i	$0.409793\pi$
$548$		0			0
$549$	7638.18	−	3789.60i	0.593788	−	0.294601i
$550$		0			0
$551$			2798.41i			0.216363i
$552$		0			0
$553$	3560.68	+	3560.68i	0.273807	+	0.273807i
$554$		0			0
$555$	−15058.2	+	3213.81i	−1.15168	+	0.245799i
$556$		0			0
$557$	2534.96	+	2534.96i	0.192836	+	0.192836i	0.796921	−	0.604084i	$-0.206461\pi$
$557$	2534.96	+	2534.96i	0.192836	+	0.192836i	−0.604084	+	0.796921i	$0.706461\pi$
$558$		0			0
$559$			16002.7i			1.21081i
$560$		0			0
$561$	−2258.50	−	1400.66i	−0.169971	−	0.105412i
$562$		0			0
$563$	8913.28	−	8913.28i	0.667229	−	0.667229i	−0.289845	−	0.957074i	$-0.593604\pi$
$563$	8913.28	−	8913.28i	0.667229	−	0.667229i	0.957074	+	0.289845i	$0.0936036\pi$
$564$		0			0
$565$	433.146	−	21648.6i	0.0322524	−	1.61197i
$566$		0			0
$567$	523.757	+	3835.67i	0.0387932	+	0.284097i
$568$		0			0
$569$	−15177.4			−1.11822			−0.559112	−	0.829092i	$-0.688858\pi$
$569$	−15177.4			−1.11822			−0.559112	+	0.829092i	$0.688858\pi$
$570$		0			0
$571$	842.203			0.0617252			0.0308626	−	0.999524i	$-0.490175\pi$
$571$	842.203			0.0617252			0.0308626	+	0.999524i	$0.490175\pi$
$572$		0			0
$573$	21178.0	−	4964.87i	1.54402	−	0.361973i
$574$		0			0
$575$	−13846.0	−	15000.8i	−1.00420	−	1.08796i
$576$		0			0
$577$	7795.12	−	7795.12i	0.562418	−	0.562418i	−0.367576	−	0.929994i	$-0.619812\pi$
$577$	7795.12	−	7795.12i	0.562418	−	0.562418i	0.929994	+	0.367576i	$0.119812\pi$
$578$		0			0
$579$	−5714.36	+	9214.12i	−0.410156	+	0.661357i
$580$		0			0
$581$			4159.32i			0.297001i
$582$		0			0
$583$	−1155.65	−	1155.65i	−0.0820961	−	0.0820961i
$584$		0			0
$585$	10615.1	−	5004.52i	0.750225	−	0.353694i
$586$		0			0
$587$	17622.8	+	17622.8i	1.23914	+	1.23914i	0.960355	+	0.278781i	$0.0899303\pi$
$587$	17622.8	+	17622.8i	1.23914	+	1.23914i	0.278781	+	0.960355i	$0.410070\pi$
$588$		0			0
$589$		−	3195.60i		−	0.223553i
$590$		0			0
$591$	−1485.37	+	2395.09i	−0.103384	+	0.166702i
$592$		0			0
$593$	16827.1	−	16827.1i	1.16527	−	1.16527i	0.181968	−	0.983304i	$-0.441753\pi$
$593$	16827.1	−	16827.1i	1.16527	−	1.16527i	0.983304	−	0.181968i	$-0.0582467\pi$
$594$		0			0
$595$	3378.75	−	3246.20i	0.232799	−	0.223666i
$596$		0			0
$597$	3003.27	−	704.073i	0.205889	−	0.0482676i
$598$		0			0
$599$	20128.1			1.37297			0.686487	−	0.727142i	$-0.259152\pi$
$599$	20128.1			1.37297			0.686487	+	0.727142i	$0.259152\pi$
$600$		0			0
$601$	5807.00			0.394131			0.197065	−	0.980390i	$-0.436859\pi$
$601$	5807.00			0.394131			0.197065	+	0.980390i	$0.436859\pi$
$602$		0			0
$603$	−2483.60	+	7374.68i	−0.167728	+	0.498044i
$604$		0			0
$605$	−10392.2	+	9984.54i	−0.698355	+	0.670958i
$606$		0			0
$607$	5681.39	−	5681.39i	0.379902	−	0.379902i	−0.491165	−	0.871067i	$-0.663429\pi$
$607$	5681.39	−	5681.39i	0.379902	−	0.379902i	0.871067	+	0.491165i	$0.163429\pi$
$608$		0			0
$609$	−6279.69	−	3894.50i	−0.417842	−	0.259135i
$610$		0			0
$611$		−	12659.1i		−	0.838186i
$612$		0			0
$613$	6004.87	+	6004.87i	0.395651	+	0.395651i	0.876696	−	0.481045i	$-0.159743\pi$
$613$	6004.87	+	6004.87i	0.395651	+	0.395651i	−0.481045	+	0.876696i	$0.659743\pi$
$614$		0			0
$615$	11829.1	−	18248.4i	0.775601	−	1.19650i
$616$		0			0
$617$	−529.923	−	529.923i	−0.0345768	−	0.0345768i	0.689607	−	0.724184i	$-0.257783\pi$
$617$	−529.923	−	529.923i	−0.0345768	−	0.0345768i	−0.724184	+	0.689607i	$0.757783\pi$
$618$		0			0
$619$		−	3022.95i		−	0.196289i	−0.995172	−	0.0981443i	$-0.968709\pi$
$619$		−	3022.95i		−	0.196289i	0.995172	−	0.0981443i	$-0.0312907\pi$
$620$		0			0
$621$	−22809.7	−	2163.51i	−1.47395	−	0.139804i
$622$		0			0
$623$	2169.00	−	2169.00i	0.139485	−	0.139485i
$624$		0			0
$625$	−15575.0	−	1249.00i	−0.996800	−	0.0799360i
$626$		0			0
$627$	−80.3215	−	342.616i	−0.00511600	−	0.0218226i
$628$		0			0
$629$	20916.2			1.32589
$630$		0			0
$631$	−22001.4			−1.38805			−0.694027	−	0.719949i	$-0.744165\pi$
$631$	−22001.4			−1.38805			−0.694027	+	0.719949i	$0.744165\pi$
$632$		0			0
$633$	−4725.76	−	20158.1i	−0.296733	−	1.26574i
$634$		0			0
$635$	5.76117	−	287.943i	0.000360040	−	0.0179948i
$636$		0			0
$637$	−8653.85	+	8653.85i	−0.538270	+	0.538270i
$638$		0			0
$639$	1936.80	+	3903.75i	0.119904	+	0.241674i
$640$		0			0
$641$			9847.24i			0.606775i	0.952867	+	0.303387i	$0.0981176\pi$
$641$			9847.24i			0.606775i	−0.952867	+	0.303387i	$0.901882\pi$
$642$		0			0
$643$	9848.84	+	9848.84i	0.604044	+	0.604044i	0.941383	−	0.337339i	$-0.109527\pi$
$643$	9848.84	+	9848.84i	0.604044	+	0.604044i	−0.337339	+	0.941383i	$0.609527\pi$
$644$		0			0
$645$	−4991.34	−	23386.7i	−0.304704	−	1.42768i
$646$		0			0
$647$	−3427.13	−	3427.13i	−0.208245	−	0.208245i	0.595276	−	0.803521i	$-0.297043\pi$
$647$	−3427.13	−	3427.13i	−0.208245	−	0.208245i	−0.803521	+	0.595276i	$0.797043\pi$
$648$		0			0
$649$		−	1463.00i		−	0.0884864i
$650$		0			0
$651$	7171.00	+	4447.27i	0.431726	+	0.267745i
$652$		0			0
$653$	14167.1	−	14167.1i	0.849006	−	0.849006i	−0.141004	−	0.990009i	$-0.545033\pi$
$653$	14167.1	−	14167.1i	0.849006	−	0.849006i	0.990009	+	0.141004i	$0.0450329\pi$
$654$		0			0
$655$	−3650.20	−	3799.25i	−0.217748	−	0.226640i
$656$		0			0
$657$	−10856.8	−	3656.28i	−0.644692	−	0.217116i
$658$		0			0
$659$	19499.3			1.15263			0.576315	−	0.817228i	$-0.304490\pi$
$659$	19499.3			1.15263			0.576315	+	0.817228i	$0.304490\pi$
$660$		0			0
$661$	−19567.0			−1.15139			−0.575694	−	0.817665i	$-0.695268\pi$
$661$	−19567.0			−1.15139			−0.575694	+	0.817665i	$0.695268\pi$
$662$		0			0
$663$	−15521.3	+	3638.74i	−0.909196	+	0.213148i
$664$		0			0
$665$	620.310	+	12.4112i	0.0361723	+	0.000723736i
$666$		0			0
$667$	30924.3	−	30924.3i	1.79520	−	1.79520i
$668$		0			0
$669$	−9903.27	+	15968.5i	−0.572321	+	0.922840i
$670$		0			0
$671$		−	2046.64i		−	0.117749i
$672$		0			0
$673$	17216.5	+	17216.5i	0.986104	+	0.986104i	0.999905	−	0.0138008i	$-0.00439308\pi$
$673$	17216.5	+	17216.5i	0.986104	+	0.986104i	−0.0138008	+	0.999905i	$0.504393\pi$
$674$		0			0
$675$	−13952.2	+	10624.6i	−0.795587	+	0.605839i
$676$		0			0
$677$	−1346.41	−	1346.41i	−0.0764355	−	0.0764355i	0.667855	−	0.744291i	$-0.267212\pi$
$677$	−1346.41	−	1346.41i	−0.0764355	−	0.0764355i	−0.744291	+	0.667855i	$0.767212\pi$
$678$		0			0
$679$			637.749i			0.0360450i
$680$		0			0
$681$	7143.50	−	11518.5i	0.401967	−	0.648152i
$682$		0			0
$683$	3975.62	−	3975.62i	0.222727	−	0.222727i	−0.586919	−	0.809646i	$-0.699659\pi$
$683$	3975.62	−	3975.62i	0.222727	−	0.222727i	0.809646	+	0.586919i	$0.199659\pi$
$684$		0			0
$685$	4470.95	+	89.4548i	0.249381	+	0.00498962i
$686$		0			0
$687$	−15482.0	+	3629.54i	−0.859790	+	0.201565i
$688$		0			0
$689$	−9803.95			−0.542091
$690$		0			0
$691$	2341.00			0.128880			0.0644398	−	0.997922i	$-0.479474\pi$
$691$	2341.00			0.128880			0.0644398	+	0.997922i	$0.479474\pi$
$692$		0			0
$693$	880.621	+	296.570i	0.0482713	+	0.0162565i
$694$		0			0
$695$	17829.3	+	18557.3i	0.973098	+	1.01283i
$696$		0			0
$697$	−20889.2	+	20889.2i	−1.13520	+	1.13520i
$698$		0			0
$699$	−6947.05	−	4308.37i	−0.375910	−	0.233130i
$700$		0			0
$701$			19548.5i			1.05326i	0.850093	+	0.526632i	$0.176546\pi$
$701$			19548.5i			1.05326i	−0.850093	+	0.526632i	$0.823454\pi$
$702$		0			0
$703$	1958.43	+	1958.43i	0.105069	+	0.105069i
$704$		0			0
$705$	3948.43	+	18500.2i	0.210931	+	0.988310i
$706$		0			0
$707$	4023.39	+	4023.39i	0.214024	+	0.214024i
$708$		0			0
$709$			5109.49i			0.270650i	0.990801	+	0.135325i	$0.0432079\pi$
$709$			5109.49i			0.270650i	−0.990801	+	0.135325i	$0.956792\pi$
$710$		0			0
$711$	11379.0	+	22935.1i	0.600205	+	1.20975i
$712$		0			0
$713$	−35313.6	+	35313.6i	−1.85485	+	1.85485i
$714$		0			0
$715$	56.3495	−	2816.35i	0.00294735	−	0.147308i
$716$		0			0
$717$	−6704.51	−	28598.5i	−0.349211	−	1.48958i
$718$		0			0
$719$	−4772.86			−0.247563			−0.123781	−	0.992310i	$-0.539502\pi$
$719$	−4772.86			−0.247563			−0.123781	+	0.992310i	$0.539502\pi$
$720$		0			0
$721$	−4085.41			−0.211024
$722$		0			0
$723$	2140.27	+	9129.46i	0.110093	+	0.469610i
$724$		0			0
$725$	1338.95	−	33447.1i	0.0685897	−	1.71337i
$726$		0			0
$727$	20404.6	−	20404.6i	1.04094	−	1.04094i	0.0418187	−	0.999125i	$-0.486685\pi$
$727$	20404.6	−	20404.6i	1.04094	−	1.04094i	0.999125	−	0.0418187i	$-0.0133152\pi$
$728$		0			0
$729$	−3700.58	+	19332.0i	−0.188009	+	0.982167i
$730$		0			0
$731$			32484.7i			1.64363i
$732$		0			0
$733$	6493.97	+	6493.97i	0.327231	+	0.327231i	0.851533	−	0.524302i	$-0.175674\pi$
$733$	6493.97	+	6493.97i	0.327231	+	0.327231i	−0.524302	+	0.851533i	$0.675674\pi$
$734$		0			0
$735$	9947.71	−	15346.1i	0.499220	−	0.770134i
$736$		0			0
$737$	1320.76	+	1320.76i	0.0660117	+	0.0660117i
$738$		0			0
$739$			6049.25i			0.301117i	0.988601	+	0.150558i	$0.0481072\pi$
$739$			6049.25i			0.301117i	−0.988601	+	0.150558i	$0.951893\pi$
$740$		0			0
$741$	−1794.00	−	1112.59i	−0.0889396	−	0.0551580i
$742$		0			0
$743$	5887.26	−	5887.26i	0.290690	−	0.290690i	−0.546663	−	0.837353i	$-0.684102\pi$
$743$	5887.26	−	5887.26i	0.290690	−	0.290690i	0.837353	+	0.546663i	$0.184102\pi$
$744$		0			0
$745$	−11932.0	+	11463.9i	−0.586785	+	0.563765i
$746$		0			0
$747$	−6749.48	+	20041.6i	−0.330590	+	0.981636i
$748$		0			0
$749$	−1911.93			−0.0932715
$750$		0			0
$751$	−7887.00			−0.383224			−0.191612	−	0.981471i	$-0.561371\pi$
$751$	−7887.00			−0.383224			−0.191612	+	0.981471i	$0.561371\pi$
$752$		0			0
$753$	−32802.8	+	7690.15i	−1.58752	+	0.372171i
$754$		0			0
$755$	1339.95	−	1287.38i	0.0645903	−	0.0620564i
$756$		0			0
$757$	12546.0	−	12546.0i	0.602366	−	0.602366i	−0.338574	−	0.940940i	$-0.609945\pi$
$757$	12546.0	−	12546.0i	0.602366	−	0.602366i	0.940940	+	0.338574i	$0.109945\pi$
$758$		0			0
$759$	−2898.54	+	4673.75i	−0.138617	+	0.223513i
$760$		0			0
$761$		−	22737.9i		−	1.08311i	−0.840664	−	0.541556i	$-0.817835\pi$
$761$		−	22737.9i		−	1.08311i	0.840664	−	0.541556i	$-0.182165\pi$
$762$		0			0
$763$	2317.96	+	2317.96i	0.109982	+	0.109982i
$764$		0			0
$765$	21548.2	−	10158.9i	1.01840	−	0.480125i
$766$		0			0
$767$	−6205.68	−	6205.68i	−0.292144	−	0.292144i
$768$		0			0
$769$		−	24928.4i		−	1.16897i	−0.811403	−	0.584487i	$-0.801296\pi$
$769$		−	24928.4i		−	1.16897i	0.811403	−	0.584487i	$-0.198704\pi$
$770$		0			0
$771$	8112.87	−	13081.6i	0.378960	−	0.611054i
$772$		0			0
$773$	17746.9	−	17746.9i	0.825758	−	0.825758i	−0.161169	−	0.986927i	$-0.551526\pi$
$773$	17746.9	−	17746.9i	0.825758	−	0.825758i	0.986927	+	0.161169i	$0.0515264\pi$
$774$		0			0
$775$	−1529.00	+	38194.4i	−0.0708688	+	1.77030i
$776$		0			0
$777$	−7120.27	+	1669.25i	−0.328750	+	0.0770706i
$778$		0			0
$779$	−3911.81			−0.179917
$780$		0			0
$781$	1046.00			0.0479243
$782$		0			0
$783$	−23938.8	−	28955.9i	−1.09260	−	1.32158i
$784$		0			0
$785$	−320.235	+	16005.4i	−0.0145601	+	0.727714i
$786$		0			0
$787$	−14743.4	+	14743.4i	−0.667783	+	0.667783i	−0.957202	−	0.289419i	$-0.906538\pi$
$787$	−14743.4	+	14743.4i	−0.667783	+	0.667783i	0.289419	+	0.957202i	$0.406538\pi$
$788$		0			0
$789$	12129.3	+	7522.25i	0.547292	+	0.339416i
$790$		0			0
$791$		−	10284.6i		−	0.462299i
$792$		0			0
$793$	−8681.34	−	8681.34i	−0.388756	−	0.388756i
$794$		0			0
$795$	14327.7	−	3057.91i	0.639183	−	0.136419i
$796$		0			0
$797$	1013.66	+	1013.66i	0.0450509	+	0.0450509i	0.729273	−	0.684222i	$-0.239858\pi$
$797$	1013.66	+	1013.66i	0.0450509	+	0.0450509i	−0.684222	+	0.729273i	$0.739858\pi$
$798$		0			0
$799$		−	25697.2i		−	1.13780i
$800$		0			0
$801$	13971.0	−	6931.56i	0.616281	−	0.305761i
$802$		0			0
$803$	−1944.37	+	1944.37i	−0.0854487	+	0.0854487i
$804$		0			0
$805$	−6717.70	−	6992.00i	−0.294121	−	0.306131i
$806$		0			0
$807$	2109.21	+	8996.96i	0.0920044	+	0.392451i
$808$		0			0
$809$	11575.8			0.503069			0.251535	−	0.967848i	$-0.419065\pi$
$809$	11575.8			0.503069			0.251535	+	0.967848i	$0.419065\pi$
$810$		0			0
$811$	−93.0028			−0.00402684			−0.00201342	−	0.999998i	$-0.500641\pi$
$811$	−93.0028			−0.00402684			−0.00201342	+	0.999998i	$0.500641\pi$
$812$		0			0
$813$	−7774.28	−	33161.7i	−0.335370	−	1.43054i
$814$		0			0
$815$	4645.01	+	92.9374i	0.199641	+	0.00399442i
$816$		0			0
$817$	−3041.62	+	3041.62i	−0.130248	+	0.130248i
$818$		0			0
$819$	4993.36	−	2477.40i	0.213043	−	0.105699i
$820$		0			0
$821$		−	11528.0i		−	0.490047i	−0.969517	−	0.245024i	$-0.921204\pi$
$821$		−	11528.0i		−	0.490047i	0.969517	−	0.245024i	$-0.0787957\pi$
$822$		0			0
$823$	18047.3	+	18047.3i	0.764386	+	0.764386i	0.977112	−	0.212726i	$-0.0682341\pi$
$823$	18047.3	+	18047.3i	0.764386	+	0.764386i	−0.212726	+	0.977112i	$0.568234\pi$
$824$		0			0
$825$	796.084	+	4133.44i	0.0335953	+	0.174434i
$826$		0			0
$827$	−9065.11	−	9065.11i	−0.381166	−	0.381166i	0.490356	−	0.871522i	$-0.336867\pi$
$827$	−9065.11	−	9065.11i	−0.381166	−	0.381166i	−0.871522	+	0.490356i	$0.836867\pi$
$828$		0			0
$829$		−	17884.5i		−	0.749282i	−0.927170	−	0.374641i	$-0.877766\pi$
$829$		−	17884.5i		−	0.749282i	0.927170	−	0.374641i	$-0.122234\pi$
$830$		0			0
$831$	2033.18	+	1260.92i	0.0848739	+	0.0526366i
$832$		0			0
$833$	−17566.8	+	17566.8i	−0.730679	+	0.730679i
$834$		0			0
$835$	−27582.9	−	551.878i	−1.14317	−	0.0228725i
$836$		0			0
$837$	27336.5	+	33065.7i	1.12890	+	1.36549i
$838$		0			0
$839$	−8050.59			−0.331272			−0.165636	−	0.986187i	$-0.552968\pi$
$839$	−8050.59			−0.331272			−0.165636	+	0.986187i	$0.552968\pi$
$840$		0			0
$841$	47323.0			1.94034
$842$		0			0
$843$	38975.9	−	9137.35i	1.59241	−	0.373318i
$844$		0			0
$845$	5310.64	+	5527.49i	0.216203	+	0.225031i
$846$		0			0
$847$	−4840.19	+	4840.19i	−0.196353	+	0.196353i
$848$		0			0
$849$	6074.91	−	9795.50i	0.245572	−	0.395972i
$850$		0			0
$851$		−	43284.0i		−	1.74354i
$852$		0			0
$853$	−5649.81	−	5649.81i	−0.226783	−	0.226783i	0.584564	−	0.811347i	$-0.301265\pi$
$853$	−5649.81	−	5649.81i	−0.226783	−	0.226783i	−0.811347	+	0.584564i	$0.801265\pi$
$854$		0			0
$855$	2968.81	+	1066.40i	0.118750	+	0.0426552i
$856$		0			0
$857$	12835.0	+	12835.0i	0.511592	+	0.511592i	0.915014	−	0.403422i	$-0.132179\pi$
$857$	12835.0	+	12835.0i	0.511592	+	0.511592i	−0.403422	+	0.915014i	$0.632179\pi$
$858$		0			0
$859$		−	28819.7i		−	1.14472i	−0.820001	−	0.572361i	$-0.806027\pi$
$859$		−	28819.7i		−	1.14472i	0.820001	−	0.572361i	$-0.193973\pi$
$860$		0			0
$861$	5444.00	−	8778.19i	0.215483	−	0.347456i
$862$		0			0
$863$	−7024.37	+	7024.37i	−0.277071	+	0.277071i	−0.831939	−	0.554868i	$-0.812769\pi$
$863$	−7024.37	+	7024.37i	−0.277071	+	0.277071i	0.554868	+	0.831939i	$0.312769\pi$
$864$		0			0
$865$	−707.299	+	35350.8i	−0.0278022	+	1.38955i
$866$		0			0
$867$	−6652.57	+	1559.60i	−0.260592	+	0.0610920i
$868$		0			0
$869$	6145.42			0.239895
$870$		0			0
$871$	11204.6			0.435884
$872$		0			0
$873$	−1034.90	+	3072.98i	−0.0401215	+	0.119135i
$874$		0			0
$875$	−7408.11	−	445.140i	−0.286217	−	0.0171983i
$876$		0			0
$877$	17443.1	−	17443.1i	0.671620	−	0.671620i	−0.286470	−	0.958089i	$-0.592482\pi$
$877$	17443.1	−	17443.1i	0.671620	−	0.671620i	0.958089	+	0.286470i	$0.0924818\pi$
$878$		0			0
$879$	−3293.63	−	2042.62i	−0.126384	−	0.0783799i
$880$		0			0
$881$		−	28660.3i		−	1.09602i	−0.836473	−	0.548009i	$-0.815386\pi$
$881$		−	28660.3i		−	1.09602i	0.836473	−	0.548009i	$-0.184614\pi$
$882$		0			0
$883$	−32185.6	−	32185.6i	−1.22665	−	1.22665i	−0.965223	−	0.261428i	$-0.915807\pi$
$883$	−32185.6	−	32185.6i	−1.22665	−	1.22665i	−0.261428	−	0.965223i	$-0.584193\pi$
$884$		0			0
$885$	11004.7	+	7133.51i	0.417987	+	0.270950i
$886$		0			0
$887$	3001.76	+	3001.76i	0.113629	+	0.113629i	0.761635	−	0.648006i	$-0.224397\pi$
$887$	3001.76	+	3001.76i	0.113629	+	0.113629i	−0.648006	+	0.761635i	$0.724397\pi$
$888$		0			0
$889$		−	136.793i		−	0.00516074i
$890$		0			0
$891$	3761.99	+	2858.03i	0.141449	+	0.107461i
$892$		0			0
$893$	2406.10	−	2406.10i	0.0901645	−	0.0901645i
$894$		0			0
$895$	−7428.00	+	7136.59i	−0.277420	+	0.266536i
$896$		0			0
$897$	7530.03	+	32119.8i	0.280290	+	1.19560i
$898$		0			0
$899$	−81890.4			−3.03804
$900$		0			0
$901$	−19901.5			−0.735866
$902$		0			0
$903$	−2592.49	−	11058.4i	−0.0955401	−	0.407533i
$904$		0			0
$905$	−5759.68	+	5533.72i	−0.211556	+	0.203256i
$906$		0			0
$907$	−33321.1	+	33321.1i	−1.21985	+	1.21985i	−0.252172	+	0.967683i	$0.581145\pi$
$907$	−33321.1	+	33321.1i	−1.21985	+	1.21985i	−0.967683	+	0.252172i	$0.918855\pi$
$908$		0			0
$909$	12857.7	+	25915.5i	0.469156	+	0.945613i
$910$		0			0
$911$			21453.3i			0.780217i	0.920769	+	0.390109i	$0.127563\pi$
$911$			21453.3i			0.780217i	−0.920769	+	0.390109i	$0.872437\pi$
$912$		0			0
$913$	3589.31	+	3589.31i	0.130108	+	0.130108i
$914$		0			0
$915$	15394.8	+	9979.31i	0.556216	+	0.360553i
$916$		0			0
$917$	−1769.50	−	1769.50i	−0.0637231	−	0.0637231i
$918$		0			0
$919$		−	3357.65i		−	0.120521i	−0.998183	−	0.0602604i	$-0.980807\pi$
$919$		−	3357.65i		−	0.120521i	0.998183	−	0.0602604i	$-0.0191931\pi$
$920$		0			0
$921$	24753.9	+	15351.7i	0.885634	+	0.549247i
$922$		0			0
$923$	4436.89	−	4436.89i	0.158225	−	0.158225i
$924$		0			0
$925$	−22470.4	−	24344.5i	−0.798728	−	0.865345i
$926$		0			0
$927$	−19685.4	−	6629.54i	−0.697470	−	0.234890i
$928$		0			0
$929$	−35509.7			−1.25407			−0.627037	−	0.778990i	$-0.715732\pi$
$929$	−35509.7			−1.25407			−0.627037	+	0.778990i	$0.715732\pi$
$930$		0			0
$931$	−3289.65			−0.115805
$932$		0			0
$933$	−43041.3	+	10090.4i	−1.51030	+	0.354068i
$934$		0			0
$935$	114.387	−	5717.04i	0.00400090	−	0.199965i
$936$		0			0
$937$	15084.4	−	15084.4i	0.525920	−	0.525920i	−0.393434	−	0.919353i	$-0.628713\pi$
$937$	15084.4	−	15084.4i	0.525920	−	0.525920i	0.919353	+	0.393434i	$0.128713\pi$
$938$		0			0
$939$	10376.7	−	16732.0i	0.360630	−	0.581499i
$940$		0			0
$941$			16515.8i			0.572156i	0.958206	+	0.286078i	$0.0923517\pi$
$941$			16515.8i			0.572156i	−0.958206	+	0.286078i	$0.907648\pi$
$942$		0			0
$943$	43228.2	+	43228.2i	1.49279	+	1.49279i
$944$		0			0
$945$	−6524.67	+	5177.97i	−0.224601	+	0.178243i
$946$		0			0
$947$	14453.8	+	14453.8i	0.495973	+	0.495973i	0.910182	−	0.414209i	$-0.135942\pi$
$947$	14453.8	+	14453.8i	0.495973	+	0.495973i	−0.414209	+	0.910182i	$0.635942\pi$
$948$		0			0
$949$			16495.1i			0.564229i
$950$		0			0
$951$	17356.1	−	27985.9i	0.591809	−	0.954264i
$952$		0			0
$953$	−23545.5	+	23545.5i	−0.800329	+	0.800329i	−0.983147	−	0.182818i	$-0.941478\pi$
$953$	−23545.5	+	23545.5i	−0.800329	+	0.800329i	0.182818	+	0.983147i	$0.441478\pi$
$954$		0			0
$955$	32426.2	+	33750.2i	1.09873	+	1.14359i
$956$		0			0
$957$	−8779.88	+	2058.32i	−0.296566	+	0.0695255i
$958$		0			0
$959$	2124.01			0.0715202
$960$		0			0
$961$	63722.6			2.13899
$962$		0			0
$963$	−9212.58	−	3102.56i	−0.308278	−	0.103820i
$964$		0			0
$965$	−23324.1	−	466.669i	−0.778061	−	0.0155675i
$966$		0			0
$967$	14544.1	−	14544.1i	0.483667	−	0.483667i	−0.422634	−	0.906301i	$-0.638894\pi$
$967$	14544.1	−	14544.1i	0.483667	−	0.483667i	0.906301	+	0.422634i	$0.138894\pi$
$968$		0			0
$969$	−3641.72	−	2258.50i	−0.120732	−	0.0748746i
$970$		0			0
$971$			6384.10i			0.210994i	0.994420	+	0.105497i	$0.0336434\pi$
$971$			6384.10i			0.210994i	−0.994420	+	0.105497i	$0.966357\pi$
$972$		0			0
$973$	8643.07	+	8643.07i	0.284773	+	0.284773i
$974$		0			0
$975$	20909.9	+	14156.3i	0.686822	+	0.464988i
$976$		0			0
$977$	−24367.0	−	24367.0i	−0.797920	−	0.797920i	0.184847	−	0.982767i	$-0.440821\pi$
$977$	−24367.0	−	24367.0i	−0.797920	−	0.797920i	−0.982767	+	0.184847i	$0.940821\pi$
$978$		0			0
$979$		−	3743.50i		−	0.122209i
$980$		0			0
$981$	7407.60	+	14930.5i	0.241087	+	0.485927i
$982$		0			0
$983$	−11902.9	+	11902.9i	−0.386209	+	0.386209i	−0.873333	−	0.487124i	$-0.838046\pi$
$983$	−11902.9	+	11902.9i	−0.386209	+	0.386209i	0.487124	+	0.873333i	$0.338046\pi$
$984$		0			0
$985$	−6062.80	−	121.305i	−0.196119	−	0.00392394i
$986$		0			0
$987$	2050.81	+	8747.85i	0.0661377	+	0.282115i
$988$		0			0
$989$	67224.0			2.16137
$990$		0			0
$991$	−44162.6			−1.41561			−0.707806	−	0.706407i	$-0.750315\pi$
$991$	−44162.6			−1.41561			−0.707806	+	0.706407i	$0.750315\pi$
$992$		0			0
$993$	3393.17	+	14473.8i	0.108438	+	0.462549i
$994$		0			0
$995$	4598.39	+	4786.16i	0.146511	+	0.152494i
$996$		0			0
$997$	−18948.4	+	18948.4i	−0.601907	+	0.601907i	−0.940818	−	0.338911i	$-0.889941\pi$
$997$	−18948.4	+	18948.4i	−0.601907	+	0.601907i	0.338911	+	0.940818i	$0.389941\pi$
$998$		0			0
$999$	−37017.6	−	3511.12i	−1.17236	−	0.111198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.i.b.53.3	yes	8
3.2	odd	2	inner	60.4.i.b.53.4	yes	8
4.3	odd	2		240.4.v.b.113.2		8
5.2	odd	4	inner	60.4.i.b.17.4	yes	8
5.3	odd	4		300.4.i.f.257.1		8
5.4	even	2		300.4.i.f.293.2		8
12.11	even	2		240.4.v.b.113.1		8
15.2	even	4	inner	60.4.i.b.17.3	✓	8
15.8	even	4		300.4.i.f.257.2		8
15.14	odd	2		300.4.i.f.293.1		8
20.7	even	4		240.4.v.b.17.1		8
60.47	odd	4		240.4.v.b.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.i.b.17.3	✓	8	15.2	even	4	inner
60.4.i.b.17.4	yes	8	5.2	odd	4	inner
60.4.i.b.53.3	yes	8	1.1	even	1	trivial
60.4.i.b.53.4	yes	8	3.2	odd	2	inner
240.4.v.b.17.1		8	20.7	even	4
240.4.v.b.17.2		8	60.47	odd	4
240.4.v.b.113.1		8	12.11	even	2
240.4.v.b.113.2		8	4.3	odd	2
300.4.i.f.257.1		8	5.3	odd	4
300.4.i.f.257.2		8	15.8	even	4
300.4.i.f.293.1		8	15.14	odd	2
300.4.i.f.293.2		8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18601 + 5.05899i) q^{3} +(-8.06226 + 7.74597i) q^{5} +(-3.75500 + 3.75500i) q^{7} +(-24.1868 + 12.0000i) q^{9} +O(q^{10})\)	\(q+(1.18601 + 5.05899i) q^{3} +(-8.06226 + 7.74597i) q^{5} +(-3.75500 + 3.75500i) q^{7} +(-24.1868 + 12.0000i) q^{9} +6.48080i q^{11} +(27.4900 + 27.4900i) q^{13} +(-48.7487 - 31.6001i) q^{15} +(55.8032 + 55.8032i) q^{17} +10.4500i q^{19} +(-23.4500 - 14.5431i) q^{21} +(115.479 - 115.479i) q^{23} +(5.00000 - 124.900i) q^{25} +(-89.3936 - 108.129i) q^{27} +267.791 q^{29} -305.800 q^{31} +(-32.7863 + 7.68628i) q^{33} +(1.18767 - 59.3599i) q^{35} +(187.410 - 187.410i) q^{37} +(-106.468 + 171.675i) q^{39} +374.337i q^{41} +(291.065 + 291.065i) q^{43} +(102.048 - 284.097i) q^{45} +(-230.249 - 230.249i) q^{47} +314.800i q^{49} +(-216.125 + 348.491i) q^{51} +(-178.319 + 178.319i) q^{53} +(-50.2001 - 52.2499i) q^{55} +(-52.8664 + 12.3938i) q^{57} -225.743 q^{59} -315.800 q^{61} +(45.7614 - 135.881i) q^{63} +(-434.568 - 8.69484i) q^{65} +(203.795 - 203.795i) q^{67} +(721.169 + 447.250i) q^{69} -161.400i q^{71} +(300.020 + 300.020i) q^{73} +(637.798 - 122.837i) q^{75} +(-24.3354 - 24.3354i) q^{77} -948.250i q^{79} +(441.000 - 580.483i) q^{81} +(553.837 - 553.837i) q^{83} +(-882.150 - 17.6501i) q^{85} +(317.602 + 1354.75i) q^{87} -577.630 q^{89} -206.450 q^{91} +(-362.681 - 1547.04i) q^{93} +(-80.9452 - 84.2504i) q^{95} +(84.9200 - 84.9200i) q^{97} +(-77.7696 - 156.750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 80 q^{7}+O(q^{10}) \) 8 * q - 80 * q^7	\( 8 q - 80 q^{7} + 120 q^{13} - 120 q^{15} + 312 q^{21} + 40 q^{25} - 448 q^{31} - 600 q^{33} + 600 q^{37} + 480 q^{43} + 1560 q^{45} - 480 q^{51} - 2400 q^{55} - 1560 q^{57} - 528 q^{61} - 960 q^{63} + 2080 q^{67} + 2600 q^{73} + 3120 q^{75} + 3528 q^{81} - 3560 q^{85} - 2400 q^{87} - 1152 q^{91} - 6240 q^{93} - 120 q^{97}+O(q^{100}) \) 8 * q - 80 * q^7 + 120 * q^13 - 120 * q^15 + 312 * q^21 + 40 * q^25 - 448 * q^31 - 600 * q^33 + 600 * q^37 + 480 * q^43 + 1560 * q^45 - 480 * q^51 - 2400 * q^55 - 1560 * q^57 - 528 * q^61 - 960 * q^63 + 2080 * q^67 + 2600 * q^73 + 3120 * q^75 + 3528 * q^81 - 3560 * q^85 - 2400 * q^87 - 1152 * q^91 - 6240 * q^93 - 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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