LMFDB - Embedded newform 105.3.l.a.43.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(22,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("105.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.12
Character	$\chi$	$=$	105.43
Dual form			105.3.l.a.22.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.74240 - 2.74240i) q^{2} +(-1.22474 - 1.22474i) q^{3} -11.0415i q^{4} +(-0.683416 + 4.95307i) q^{5} -6.71747 q^{6} +(1.87083 - 1.87083i) q^{7} +(-19.3105 - 19.3105i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(2.74240 - 2.74240i) q^{2} +(-1.22474 - 1.22474i) q^{3} -11.0415i q^{4} +(-0.683416 + 4.95307i) q^{5} -6.71747 q^{6} +(1.87083 - 1.87083i) q^{7} +(-19.3105 - 19.3105i) q^{8} +3.00000i q^{9} +(11.7091 + 15.4575i) q^{10} +10.9331 q^{11} +(-13.5230 + 13.5230i) q^{12} +(8.10523 + 8.10523i) q^{13} -10.2611i q^{14} +(6.90326 - 5.22924i) q^{15} -61.7483 q^{16} +(-5.51018 + 5.51018i) q^{17} +(8.22719 + 8.22719i) q^{18} -12.1318i q^{19} +(54.6893 + 7.54592i) q^{20} -4.58258 q^{21} +(29.9829 - 29.9829i) q^{22} +(24.3210 + 24.3210i) q^{23} +47.3009i q^{24} +(-24.0659 - 6.77002i) q^{25} +44.4555 q^{26} +(3.67423 - 3.67423i) q^{27} +(-20.6567 - 20.6567i) q^{28} -14.8012i q^{29} +(4.59083 - 33.2721i) q^{30} -8.07276 q^{31} +(-92.0962 + 92.0962i) q^{32} +(-13.3902 - 13.3902i) q^{33} +30.2222i q^{34} +(7.98780 + 10.5449i) q^{35} +33.1244 q^{36} +(-34.6319 + 34.6319i) q^{37} +(-33.2701 - 33.2701i) q^{38} -19.8537i q^{39} +(108.844 - 82.4493i) q^{40} +32.0975 q^{41} +(-12.5672 + 12.5672i) q^{42} +(-13.0663 - 13.0663i) q^{43} -120.717i q^{44} +(-14.8592 - 2.05025i) q^{45} +133.395 q^{46} +(-54.1653 + 54.1653i) q^{47} +(75.6259 + 75.6259i) q^{48} -7.00000i q^{49} +(-84.5643 + 47.4321i) q^{50} +13.4971 q^{51} +(89.4937 - 89.4937i) q^{52} +(6.76541 + 6.76541i) q^{53} -20.1524i q^{54} +(-7.47185 + 54.1524i) q^{55} -72.2534 q^{56} +(-14.8583 + 14.8583i) q^{57} +(-40.5907 - 40.5907i) q^{58} +44.4162i q^{59} +(-57.7385 - 76.2222i) q^{60} -84.4444 q^{61} +(-22.1387 + 22.1387i) q^{62} +(5.61249 + 5.61249i) q^{63} +258.136i q^{64} +(-45.6850 + 34.6066i) q^{65} -73.4427 q^{66} +(0.661895 - 0.661895i) q^{67} +(60.8405 + 60.8405i) q^{68} -59.5739i q^{69} +(50.8240 + 7.01261i) q^{70} +103.429 q^{71} +(57.9316 - 57.9316i) q^{72} +(-55.1974 - 55.1974i) q^{73} +189.949i q^{74} +(21.1830 + 37.7661i) q^{75} -133.952 q^{76} +(20.4539 - 20.4539i) q^{77} +(-54.4467 - 54.4467i) q^{78} -68.8001i q^{79} +(42.1998 - 305.844i) q^{80} -9.00000 q^{81} +(88.0241 - 88.0241i) q^{82} +(-71.4410 - 71.4410i) q^{83} +50.5984i q^{84} +(-23.5266 - 31.0581i) q^{85} -71.6660 q^{86} +(-18.1277 + 18.1277i) q^{87} +(-211.124 - 211.124i) q^{88} -41.6575i q^{89} +(-46.3725 + 35.1273i) q^{90} +30.3270 q^{91} +(268.539 - 268.539i) q^{92} +(9.88708 + 9.88708i) q^{93} +297.086i q^{94} +(60.0895 + 8.29103i) q^{95} +225.589 q^{96} +(25.2508 - 25.2508i) q^{97} +(-19.1968 - 19.1968i) q^{98} +32.7993i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	2.74240	−	2.74240i	1.37120	−	1.37120i	0.512527	−	0.858671i	$-0.328709\pi$
$2$	2.74240	−	2.74240i	1.37120	−	1.37120i	0.858671	−	0.512527i	$-0.171291\pi$
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	11.0415i		−	2.76037i
$5$	−0.683416	+	4.95307i	−0.136683	+	0.990615i
$5$	−0.683416	+	4.95307i	−0.136683	+	0.990615i
$6$	−6.71747			−1.11958
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	−19.3105	−	19.3105i	−2.41382	−	2.41382i
$9$			3.00000i			0.333333i
$10$	11.7091	+	15.4575i	1.17091	+	1.54575i
$11$	10.9331			0.993917			0.496958	−	0.867774i	$-0.334450\pi$
$11$	10.9331			0.993917			0.496958	+	0.867774i	$0.334450\pi$
$12$	−13.5230	+	13.5230i	−1.12692	+	1.12692i
$13$	8.10523	+	8.10523i	0.623479	+	0.623479i	0.946419	−	0.322940i	$-0.104671\pi$
$13$	8.10523	+	8.10523i	0.623479	+	0.623479i	−0.322940	+	0.946419i	$0.604671\pi$
$14$		−	10.2611i		−	0.732936i
$15$	6.90326	−	5.22924i	0.460217	−	0.348616i
$16$	−61.7483			−3.85927
$17$	−5.51018	+	5.51018i	−0.324128	+	0.324128i	−0.850348	−	0.526220i	$-0.823609\pi$
$17$	−5.51018	+	5.51018i	−0.324128	+	0.324128i	0.526220	+	0.850348i	$0.323609\pi$
$18$	8.22719	+	8.22719i	0.457066	+	0.457066i
$19$		−	12.1318i		−	0.638513i	−0.947668	−	0.319257i	$-0.896567\pi$
$19$		−	12.1318i		−	0.638513i	0.947668	−	0.319257i	$-0.103433\pi$
$20$	54.6893	+	7.54592i	2.73446	+	0.377296i
$21$	−4.58258			−0.218218
$22$	29.9829	−	29.9829i	1.36286	−	1.36286i
$23$	24.3210	+	24.3210i	1.05743	+	1.05743i	0.998247	+	0.0591858i	$0.0188504\pi$
$23$	24.3210	+	24.3210i	1.05743	+	1.05743i	0.0591858	+	0.998247i	$0.481150\pi$
$24$			47.3009i			1.97087i
$25$	−24.0659	−	6.77002i	−0.962635	−	0.270801i
$26$	44.4555			1.70983
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−20.6567	−	20.6567i	−0.737740	−	0.737740i
$29$		−	14.8012i		−	0.510385i	−0.966890	−	0.255193i	$-0.917861\pi$
$29$		−	14.8012i		−	0.510385i	0.966890	−	0.255193i	$-0.0821389\pi$
$30$	4.59083	−	33.2721i	0.153028	−	1.10907i
$31$	−8.07276			−0.260412			−0.130206	−	0.991487i	$-0.541564\pi$
$31$	−8.07276			−0.260412			−0.130206	+	0.991487i	$0.541564\pi$
$32$	−92.0962	+	92.0962i	−2.87801	+	2.87801i
$33$	−13.3902	−	13.3902i	−0.405765	−	0.405765i
$34$			30.2222i			0.888888i
$35$	7.98780	+	10.5449i	0.228223	+	0.301283i
$36$	33.1244			0.920123
$37$	−34.6319	+	34.6319i	−0.935998	+	0.935998i	−0.998072	−	0.0620735i	$-0.980229\pi$
$37$	−34.6319	+	34.6319i	−0.935998	+	0.935998i	0.0620735	+	0.998072i	$0.480229\pi$
$38$	−33.2701	−	33.2701i	−0.875528	−	0.875528i
$39$		−	19.8537i		−	0.509069i
$40$	108.844	−	82.4493i	2.72109	−	2.06123i
$41$	32.0975			0.782866			0.391433	−	0.920207i	$-0.371979\pi$
$41$	32.0975			0.782866			0.391433	+	0.920207i	$0.371979\pi$
$42$	−12.5672	+	12.5672i	−0.299220	+	0.299220i
$43$	−13.0663	−	13.0663i	−0.303868	−	0.303868i	0.538657	−	0.842525i	$-0.318932\pi$
$43$	−13.0663	−	13.0663i	−0.303868	−	0.303868i	−0.842525	+	0.538657i	$0.818932\pi$
$44$		−	120.717i		−	2.74358i
$45$	−14.8592	−	2.05025i	−0.330205	−	0.0455611i
$46$	133.395			2.89990
$47$	−54.1653	+	54.1653i	−1.15245	+	1.15245i	−0.166394	+	0.986059i	$0.553212\pi$
$47$	−54.1653	+	54.1653i	−1.15245	+	1.15245i	−0.986059	+	0.166394i	$0.946788\pi$
$48$	75.6259	+	75.6259i	1.57554	+	1.57554i
$49$		−	7.00000i		−	0.142857i
$50$	−84.5643	+	47.4321i	−1.69129	+	0.948642i
$51$	13.4971			0.264649
$52$	89.4937	−	89.4937i	1.72103	−	1.72103i
$53$	6.76541	+	6.76541i	0.127649	+	0.127649i	0.768045	−	0.640396i	$-0.221230\pi$
$53$	6.76541	+	6.76541i	0.127649	+	0.127649i	−0.640396	+	0.768045i	$0.721230\pi$
$54$		−	20.1524i		−	0.373193i
$55$	−7.47185	+	54.1524i	−0.135852	+	0.984589i
$56$	−72.2534			−1.29024
$57$	−14.8583	+	14.8583i	−0.260672	+	0.260672i
$58$	−40.5907	−	40.5907i	−0.699839	−	0.699839i
$59$			44.4162i			0.752816i	0.926454	+	0.376408i	$0.122841\pi$
$59$			44.4162i			0.752816i	−0.926454	+	0.376408i	$0.877159\pi$
$60$	−57.7385	−	76.2222i	−0.962309	−	1.27037i
$61$	−84.4444			−1.38433			−0.692167	−	0.721737i	$-0.743344\pi$
$61$	−84.4444			−1.38433			−0.692167	+	0.721737i	$0.743344\pi$
$62$	−22.1387	+	22.1387i	−0.357076	+	0.357076i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			258.136i			4.03337i
$65$	−45.6850	+	34.6066i	−0.702847	+	0.532409i
$66$	−73.4427			−1.11277
$67$	0.661895	−	0.661895i	0.00987903	−	0.00987903i	−0.702150	−	0.712029i	$-0.747776\pi$
$67$	0.661895	−	0.661895i	0.00987903	−	0.00987903i	0.712029	+	0.702150i	$0.247776\pi$
$68$	60.8405	+	60.8405i	0.894713	+	0.894713i
$69$		−	59.5739i		−	0.863390i
$70$	50.8240	+	7.01261i	0.726058	+	0.100180i
$71$	103.429			1.45675			0.728373	−	0.685181i	$-0.240277\pi$
$71$	103.429			1.45675			0.728373	+	0.685181i	$0.240277\pi$
$72$	57.9316	−	57.9316i	0.804605	−	0.804605i
$73$	−55.1974	−	55.1974i	−0.756129	−	0.756129i	0.219486	−	0.975616i	$-0.429562\pi$
$73$	−55.1974	−	55.1974i	−0.756129	−	0.756129i	−0.975616	+	0.219486i	$0.929562\pi$
$74$			189.949i			2.56688i
$75$	21.1830	+	37.7661i	0.282440	+	0.503548i
$76$	−133.952			−1.76253
$77$	20.4539	−	20.4539i	0.265635	−	0.265635i
$78$	−54.4467	−	54.4467i	−0.698034	−	0.698034i
$79$		−	68.8001i		−	0.870887i	−0.900216	−	0.435444i	$-0.856592\pi$
$79$		−	68.8001i		−	0.870887i	0.900216	−	0.435444i	$-0.143408\pi$
$80$	42.1998	−	305.844i	0.527497	−	3.82305i
$81$	−9.00000			−0.111111
$82$	88.0241	−	88.0241i	1.07346	−	1.07346i
$83$	−71.4410	−	71.4410i	−0.860735	−	0.860735i	0.130688	−	0.991423i	$-0.458281\pi$
$83$	−71.4410	−	71.4410i	−0.860735	−	0.860735i	−0.991423	+	0.130688i	$0.958281\pi$
$84$			50.5984i			0.602362i
$85$	−23.5266	−	31.0581i	−0.276783	−	0.365389i
$86$	−71.6660			−0.833326
$87$	−18.1277	+	18.1277i	−0.208364	+	0.208364i
$88$	−211.124	−	211.124i	−2.39913	−	2.39913i
$89$		−	41.6575i		−	0.468062i	−0.972229	−	0.234031i	$-0.924808\pi$
$89$		−	41.6575i		−	0.468062i	0.972229	−	0.234031i	$-0.0751917\pi$
$90$	−46.3725	+	35.1273i	−0.515250	+	0.390303i
$91$	30.3270			0.333264
$92$	268.539	−	268.539i	2.91890	−	2.91890i
$93$	9.88708	+	9.88708i	0.106313	+	0.106313i
$94$			297.086i			3.16048i
$95$	60.0895	+	8.29103i	0.632521	+	0.0872740i
$96$	225.589			2.34988
$97$	25.2508	−	25.2508i	0.260318	−	0.260318i	−0.564865	−	0.825183i	$-0.691072\pi$
$97$	25.2508	−	25.2508i	0.260318	−	0.260318i	0.825183	+	0.564865i	$0.191072\pi$
$98$	−19.1968	−	19.1968i	−0.195885	−	0.195885i
$99$			32.7993i			0.331306i
$100$	−74.7510	+	265.723i	−0.747510	+	2.65723i
$101$	53.7274			0.531955			0.265977	−	0.963979i	$-0.414305\pi$
$101$	53.7274			0.531955			0.265977	+	0.963979i	$0.414305\pi$
$102$	37.0145	−	37.0145i	0.362887	−	0.362887i
$103$	39.6796	+	39.6796i	0.385239	+	0.385239i	0.872985	−	0.487746i	$-0.162181\pi$
$103$	39.6796	+	39.6796i	0.385239	+	0.385239i	−0.487746	+	0.872985i	$0.662181\pi$
$104$		−	313.032i		−	3.00993i
$105$	3.13181	−	22.6978i	0.0298267	−	0.216170i
$106$	37.1069			0.350065
$107$	−68.3716	+	68.3716i	−0.638987	+	0.638987i	−0.950306	−	0.311318i	$-0.899229\pi$
$107$	−68.3716	+	68.3716i	−0.638987	+	0.638987i	0.311318	+	0.950306i	$0.399229\pi$
$108$	−40.5690	−	40.5690i	−0.375639	−	0.375639i
$109$		−	135.475i		−	1.24289i	−0.783458	−	0.621445i	$-0.786546\pi$
$109$		−	135.475i		−	1.24289i	0.783458	−	0.621445i	$-0.213454\pi$
$110$	128.017	+	168.998i	1.16379	+	1.53635i
$111$	84.8306			0.764239
$112$	−115.520	+	115.520i	−1.03143	+	1.03143i
$113$	6.34998	+	6.34998i	0.0561945	+	0.0561945i	0.734646	−	0.678451i	$-0.237348\pi$
$113$	6.34998	+	6.34998i	0.0561945	+	0.0561945i	−0.678451	+	0.734646i	$0.737348\pi$
$114$			81.4947i			0.714866i
$115$	−137.085	+	103.842i	−1.19204	+	0.902975i
$116$	−163.427			−1.40885
$117$	−24.3157	+	24.3157i	−0.207826	+	0.207826i
$118$	121.807	+	121.807i	1.03226	+	1.03226i
$119$			20.6172i			0.173254i
$120$	−234.285	−	32.3262i	−1.95237	−	0.269385i
$121$	−1.46766			−0.0121294
$122$	−231.580	+	231.580i	−1.89820	+	1.89820i
$123$	−39.3113	−	39.3113i	−0.319604	−	0.319604i
$124$			89.1352i			0.718833i
$125$	49.9794	−	114.573i	0.399835	−	0.916587i
$126$	30.7833			0.244312
$127$	20.2819	−	20.2819i	0.159700	−	0.159700i	−0.622734	−	0.782434i	$-0.713978\pi$
$127$	20.2819	−	20.2819i	0.159700	−	0.159700i	0.782434	+	0.622734i	$0.213978\pi$
$128$	339.525	+	339.525i	2.65254	+	2.65254i
$129$			32.0058i			0.248107i
$130$	−30.3816	+	220.191i	−0.233705	+	1.69378i
$131$	77.7144			0.593240			0.296620	−	0.954996i	$-0.404141\pi$
$131$	77.7144			0.593240			0.296620	+	0.954996i	$0.404141\pi$
$132$	−147.848	+	147.848i	−1.12006	+	1.12006i
$133$	−22.6964	−	22.6964i	−0.170650	−	0.170650i
$134$		−	3.63036i		−	0.0270922i
$135$	15.6877	+	20.7098i	0.116205	+	0.153406i
$136$	212.809			1.56477
$137$	146.870	−	146.870i	1.07205	−	1.07205i	0.0748506	−	0.997195i	$-0.476152\pi$
$137$	146.870	−	146.870i	1.07205	−	1.07205i	0.997195	−	0.0748506i	$-0.0238480\pi$
$138$	−163.375	−	163.375i	−1.18388	−	1.18388i
$139$		−	146.322i		−	1.05268i	−0.850275	−	0.526339i	$-0.823564\pi$
$139$		−	146.322i		−	1.05268i	0.850275	−	0.526339i	$-0.176436\pi$
$140$	116.431	−	88.1971i	0.831653	−	0.629979i
$141$	132.677			0.940974
$142$	283.643	−	283.643i	1.99749	−	1.99749i
$143$	88.6152	+	88.6152i	0.619686	+	0.619686i
$144$		−	185.245i		−	1.28642i
$145$	73.3113	+	10.1154i	0.505595	+	0.0697611i
$146$	−302.746			−2.07361
$147$	−8.57321	+	8.57321i	−0.0583212	+	0.0583212i
$148$	382.388	+	382.388i	2.58370	+	2.58370i
$149$			143.223i			0.961228i	0.876932	+	0.480614i	$0.159586\pi$
$149$			143.223i			0.961228i	−0.876932	+	0.480614i	$0.840414\pi$
$150$	161.662	+	45.4774i	1.07775	+	0.303183i
$151$	204.429			1.35384			0.676919	−	0.736058i	$-0.263315\pi$
$151$	204.429			1.35384			0.676919	+	0.736058i	$0.263315\pi$
$152$	−234.270	+	234.270i	−1.54125	+	1.54125i
$153$	−16.5305	−	16.5305i	−0.108043	−	0.108043i
$154$		−	112.186i		−	0.728478i
$155$	5.51706	−	39.9850i	0.0355939	−	0.257968i
$156$	−219.214			−1.40522
$157$	−168.925	+	168.925i	−1.07595	+	1.07595i	−0.0790870	+	0.996868i	$0.525200\pi$
$157$	−168.925	+	168.925i	−1.07595	+	1.07595i	−0.996868	+	0.0790870i	$0.974800\pi$
$158$	−188.677	−	188.677i	−1.19416	−	1.19416i
$159$		−	16.5718i		−	0.104225i
$160$	−393.219	−	519.100i	−2.45762	−	3.24437i
$161$	91.0007			0.565222
$162$	−24.6816	+	24.6816i	−0.152355	+	0.152355i
$163$	167.373	+	167.373i	1.02683	+	1.02683i	0.999630	+	0.0271997i	$0.00865900\pi$
$163$	167.373	+	167.373i	1.02683	+	1.02683i	0.0271997	+	0.999630i	$0.491341\pi$
$164$		−	354.404i		−	2.16100i
$165$	75.4740	−	57.1717i	0.457418	−	0.346495i
$166$	−391.839			−2.36048
$167$	80.3381	−	80.3381i	0.481066	−	0.481066i	−0.424406	−	0.905472i	$-0.639517\pi$
$167$	80.3381	−	80.3381i	0.481066	−	0.481066i	0.905472	+	0.424406i	$0.139517\pi$
$168$	88.4919	+	88.4919i	0.526738	+	0.526738i
$169$		−	37.6105i		−	0.222547i
$170$	−149.693	−	20.6543i	−0.880545	−	0.121496i
$171$	36.3953			0.212838
$172$	−144.271	+	144.271i	−0.838787	+	0.838787i
$173$	−76.0306	−	76.0306i	−0.439483	−	0.439483i	0.452355	−	0.891838i	$-0.350584\pi$
$173$	−76.0306	−	76.0306i	−0.439483	−	0.439483i	−0.891838	+	0.452355i	$0.850584\pi$
$174$			99.4265i			0.571417i
$175$	−57.6887	+	32.3576i	−0.329650	+	0.184901i
$176$	−675.099			−3.83579
$177$	54.3985	−	54.3985i	0.307336	−	0.307336i
$178$	−114.241	−	114.241i	−0.641806	−	0.641806i
$179$			72.8033i			0.406722i	0.979104	+	0.203361i	$0.0651865\pi$
$179$			72.8033i			0.406722i	−0.979104	+	0.203361i	$0.934813\pi$
$180$	−22.6378	+	164.068i	−0.125765	+	0.911488i
$181$	116.021			0.641000			0.320500	−	0.947249i	$-0.396149\pi$
$181$	116.021			0.641000			0.320500	+	0.947249i	$0.396149\pi$
$182$	83.1686	−	83.1686i	0.456971	−	0.456971i
$183$	103.423	+	103.423i	0.565152	+	0.565152i
$184$		−	939.301i		−	5.10489i
$185$	−147.866	−	195.203i	−0.799278	−	1.05515i
$186$	54.2286			0.291551
$187$	−60.2432	+	60.2432i	−0.322156	+	0.322156i
$188$	598.065	+	598.065i	3.18120	+	3.18120i
$189$		−	13.7477i		−	0.0727393i
$190$	187.526	−	142.052i	0.986981	−	0.747641i
$191$	−134.337			−0.703336			−0.351668	−	0.936125i	$-0.614385\pi$
$191$	−134.337			−0.703336			−0.351668	+	0.936125i	$0.614385\pi$
$192$	316.150	−	316.150i	1.64662	−	1.64662i
$193$	−5.00682	−	5.00682i	−0.0259421	−	0.0259421i	0.694017	−	0.719959i	$-0.255839\pi$
$193$	−5.00682	−	5.00682i	−0.0259421	−	0.0259421i	−0.719959	+	0.694017i	$0.755839\pi$
$194$		−	138.495i		−	0.713894i
$195$	98.3367	+	13.5683i	0.504291	+	0.0695811i
$196$	−77.2903			−0.394338
$197$	−207.221	+	207.221i	−1.05188	+	1.05188i	−0.0533056	+	0.998578i	$0.516976\pi$
$197$	−207.221	+	207.221i	−1.05188	+	1.05188i	−0.998578	+	0.0533056i	$0.983024\pi$
$198$	89.9486	+	89.9486i	0.454286	+	0.454286i
$199$		−	115.701i		−	0.581414i	−0.956812	−	0.290707i	$-0.906109\pi$
$199$		−	115.701i		−	0.581414i	0.956812	−	0.290707i	$-0.0938905\pi$
$200$	333.992	+	595.457i	1.66996	+	2.97729i
$201$	−1.62130			−0.00806619
$202$	147.342	−	147.342i	0.729416	−	0.729416i
$203$	−27.6905	−	27.6905i	−0.136406	−	0.136406i
$204$		−	149.028i		−	0.730530i
$205$	−21.9360	+	158.981i	−0.107005	+	0.775519i
$206$	217.634			1.05648
$207$	−72.9629	+	72.9629i	−0.352478	+	0.352478i
$208$	−500.484	−	500.484i	−2.40617	−	2.40617i
$209$		−	132.637i		−	0.634629i
$210$	−53.6578	−	70.8351i	−0.255513	−	0.337310i
$211$	66.2124			0.313803			0.156901	−	0.987614i	$-0.449850\pi$
$211$	66.2124			0.313803			0.156901	+	0.987614i	$0.449850\pi$
$212$	74.7001	−	74.7001i	0.352359	−	0.352359i
$213$	−126.674	−	126.674i	−0.594714	−	0.594714i
$214$			375.004i			1.75236i
$215$	73.6482	−	55.7887i	0.342550	−	0.259482i
$216$	−141.903			−0.656957
$217$	−15.1028	+	15.1028i	−0.0695980	+	0.0695980i
$218$	−371.526	−	371.526i	−1.70425	−	1.70425i
$219$			135.206i			0.617377i
$220$	597.922	+	82.5002i	2.71783	+	0.375001i
$221$	−89.3225			−0.404174
$222$	232.639	−	232.639i	1.04792	−	1.04792i
$223$	−51.3641	−	51.3641i	−0.230332	−	0.230332i	0.582499	−	0.812831i	$-0.302075\pi$
$223$	−51.3641	−	51.3641i	−0.230332	−	0.230332i	−0.812831	+	0.582499i	$0.802075\pi$
$224$			344.593i			1.53836i
$225$	20.3101	−	72.1977i	0.0902670	−	0.320878i
$226$	34.8283			0.154108
$227$	−106.842	+	106.842i	−0.470670	+	0.470670i	−0.902132	−	0.431461i	$-0.857998\pi$
$227$	−106.842	+	106.842i	−0.470670	+	0.470670i	0.431461	+	0.902132i	$0.357998\pi$
$228$	164.058	+	164.058i	0.719551	+	0.719551i
$229$			88.3402i			0.385765i	0.981222	+	0.192883i	$0.0617836\pi$
$229$			88.3402i			0.385765i	−0.981222	+	0.192883i	$0.938216\pi$
$230$	−91.1646	+	660.717i	−0.396368	+	2.87268i
$231$	−50.1017			−0.216890
$232$	−285.818	+	285.818i	−1.23198	+	1.23198i
$233$	−260.550	−	260.550i	−1.11824	−	1.11824i	−0.991999	−	0.126242i	$-0.959708\pi$
$233$	−260.550	−	260.550i	−1.11824	−	1.11824i	−0.126242	−	0.991999i	$-0.540292\pi$
$234$			133.367i			0.569942i
$235$	−231.267	−	305.302i	−0.984116	−	1.29916i
$236$	490.420			2.07805
$237$	−84.2626	+	84.2626i	−0.355538	+	0.355538i
$238$	56.5405	+	56.5405i	0.237565	+	0.237565i
$239$		−	166.308i		−	0.695851i	−0.937522	−	0.347925i	$-0.886886\pi$
$239$		−	166.308i		−	0.695851i	0.937522	−	0.347925i	$-0.113114\pi$
$240$	−426.265	+	322.897i	−1.77610	+	1.34540i
$241$	−309.962			−1.28615			−0.643075	−	0.765804i	$-0.722342\pi$
$241$	−309.962			−1.28615			−0.643075	+	0.765804i	$0.722342\pi$
$242$	−4.02490	+	4.02490i	−0.0166318	+	0.0166318i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			932.391i			3.82127i
$245$	34.6715	+	4.78391i	0.141516	+	0.0195262i
$246$	−215.614			−0.876480
$247$	98.3306	−	98.3306i	0.398100	−	0.398100i
$248$	155.889	+	155.889i	0.628586	+	0.628586i
$249$			174.994i			0.702787i
$250$	−177.142	−	451.269i	−0.708569	−	1.80508i
$251$	−403.709			−1.60840			−0.804201	−	0.594358i	$-0.797406\pi$
$251$	−403.709			−1.60840			−0.804201	+	0.594358i	$0.797406\pi$
$252$	61.9701	−	61.9701i	0.245913	−	0.245913i
$253$	265.903	+	265.903i	1.05100	+	1.05100i
$254$		−	111.242i		−	0.437960i
$255$	−9.22415	+	66.8522i	−0.0361731	+	0.262166i
$256$	829.683			3.24095
$257$	109.310	−	109.310i	0.425332	−	0.425332i	−0.461703	−	0.887035i	$-0.652761\pi$
$257$	109.310	−	109.310i	0.425332	−	0.425332i	0.887035	+	0.461703i	$0.152761\pi$
$258$	87.7726	+	87.7726i	0.340204	+	0.340204i
$259$			129.581i			0.500312i
$260$	382.107	+	504.430i	1.46964	+	1.94012i
$261$	44.4035			0.170128
$262$	213.124	−	213.124i	0.813449	−	0.813449i
$263$	207.442	+	207.442i	0.788754	+	0.788754i	0.981290	−	0.192536i	$-0.0616713\pi$
$263$	207.442	+	207.442i	0.788754	+	0.788754i	−0.192536	+	0.981290i	$0.561671\pi$
$264$			517.145i			1.95888i
$265$	−38.1332	+	28.8860i	−0.143899	+	0.109004i
$266$	−124.485			−0.467989
$267$	−51.0198	+	51.0198i	−0.191086	+	0.191086i
$268$	−7.30830	−	7.30830i	−0.0272698	−	0.0272698i
$269$			31.5174i			0.117165i	0.998283	+	0.0585825i	$0.0186581\pi$
$269$			31.5174i			0.117165i	−0.998283	+	0.0585825i	$0.981342\pi$
$270$	99.8164	+	13.7725i	0.369690	+	0.0510092i
$271$	−92.6505			−0.341884			−0.170942	−	0.985281i	$-0.554681\pi$
$271$	−92.6505			−0.341884			−0.170942	+	0.985281i	$0.554681\pi$
$272$	340.244	−	340.244i	1.25090	−	1.25090i
$273$	−37.1428	−	37.1428i	−0.136054	−	0.136054i
$274$		−	805.553i		−	2.93997i
$275$	−263.114	−	74.0172i	−0.956779	−	0.269154i
$276$	−657.784			−2.38328
$277$	−29.1214	+	29.1214i	−0.105131	+	0.105131i	−0.757716	−	0.652585i	$-0.773685\pi$
$277$	−29.1214	+	29.1214i	−0.105131	+	0.105131i	0.652585	+	0.757716i	$0.273685\pi$
$278$	−401.274	−	401.274i	−1.44343	−	1.44343i
$279$		−	24.2183i		−	0.0868039i
$280$	49.3791	−	357.876i	0.176354	−	1.27813i
$281$	−186.605			−0.664075			−0.332038	−	0.943266i	$-0.607736\pi$
$281$	−186.605			−0.664075			−0.332038	+	0.943266i	$0.607736\pi$
$282$	363.854	−	363.854i	1.29026	−	1.29026i
$283$	199.836	+	199.836i	0.706135	+	0.706135i	0.965720	−	0.259585i	$-0.0835859\pi$
$283$	199.836	+	199.836i	0.706135	+	0.706135i	−0.259585	+	0.965720i	$0.583586\pi$
$284$		−	1142.01i		−	4.02115i
$285$	−63.4399	−	83.7487i	−0.222596	−	0.293855i
$286$	486.036			1.69943
$287$	60.0489	−	60.0489i	0.209230	−	0.209230i
$288$	−276.289	−	276.289i	−0.959336	−	0.959336i
$289$			228.276i			0.789882i
$290$	228.789	−	173.308i	0.788928	−	0.597615i
$291$	−61.8516			−0.212548
$292$	−609.461	+	609.461i	−2.08720	+	2.08720i
$293$	−118.656	−	118.656i	−0.404969	−	0.404969i	0.475011	−	0.879980i	$-0.342444\pi$
$293$	−118.656	−	118.656i	−0.404969	−	0.404969i	−0.879980	+	0.475011i	$0.842444\pi$
$294$			47.0223i			0.159940i
$295$	−219.996	−	30.3547i	−0.745751	−	0.102897i
$296$	1337.52			4.51865
$297$	40.1707	−	40.1707i	0.135255	−	0.135255i
$298$	392.774	+	392.774i	1.31803	+	1.31803i
$299$			394.254i			1.31857i
$300$	416.994	−	233.892i	1.38998	−	0.779639i
$301$	−48.8897			−0.162424
$302$	560.626	−	560.626i	1.85638	−	1.85638i
$303$	−65.8024	−	65.8024i	−0.217170	−	0.217170i
$304$			749.115i			2.46419i
$305$	57.7107	−	418.259i	0.189215	−	1.37134i
$306$	−90.6665			−0.296296
$307$	315.593	−	315.593i	1.02799	−	1.02799i	0.0283934	−	0.999597i	$-0.490961\pi$
$307$	315.593	−	315.593i	1.02799	−	1.02799i	0.999597	−	0.0283934i	$-0.00903913\pi$
$308$	−225.842	−	225.842i	−0.733252	−	0.733252i
$309$		−	97.1948i		−	0.314546i
$310$	−94.5248	−	124.785i	−0.304919	−	0.402531i
$311$	569.702			1.83184			0.915919	−	0.401362i	$-0.131463\pi$
$311$	569.702			1.83184			0.915919	+	0.401362i	$0.131463\pi$
$312$	−383.385	+	383.385i	−1.22880	+	1.22880i
$313$	222.379	+	222.379i	0.710475	+	0.710475i	0.966634	−	0.256160i	$-0.0824574\pi$
$313$	222.379	+	222.379i	0.710475	+	0.710475i	−0.256160	+	0.966634i	$0.582457\pi$
$314$			926.518i			2.95069i
$315$	−31.6347	+	23.9634i	−0.100428	+	0.0760743i
$316$	−759.655			−2.40397
$317$	−183.394	+	183.394i	−0.578530	+	0.578530i	−0.934498	−	0.355968i	$-0.884151\pi$
$317$	−183.394	+	183.394i	−0.578530	+	0.578530i	0.355968	+	0.934498i	$0.384151\pi$
$318$	−45.4464	−	45.4464i	−0.142913	−	0.142913i
$319$		−	161.822i		−	0.507281i
$320$	−1278.56	−	176.414i	−3.99551	−	0.551294i
$321$	167.476			0.521731
$322$	249.560	−	249.560i	0.775031	−	0.775031i
$323$	66.8481	+	66.8481i	0.206960	+	0.206960i
$324$			99.3733i			0.306708i
$325$	−140.187	−	249.932i	−0.431344	−	0.769022i
$326$	918.008			2.81597
$327$	−165.922	+	165.922i	−0.507408	+	0.507408i
$328$	−619.819	−	619.819i	−1.88969	−	1.88969i
$329$			202.668i			0.616012i
$330$	50.1919	−	363.767i	0.152097	−	1.10232i
$331$	−215.246			−0.650291			−0.325146	−	0.945664i	$-0.605413\pi$
$331$	−215.246			−0.650291			−0.325146	+	0.945664i	$0.605413\pi$
$332$	−788.814	+	788.814i	−2.37595	+	2.37595i
$333$	−103.896	−	103.896i	−0.311999	−	0.311999i
$334$		−	440.638i		−	1.31927i
$335$	2.82606	+	3.73076i	0.00843601	+	0.0111366i
$336$	282.966			0.842161
$337$	−401.198	+	401.198i	−1.19050	+	1.19050i	−0.213571	+	0.976927i	$0.568510\pi$
$337$	−401.198	+	401.198i	−1.19050	+	1.19050i	−0.976927	+	0.213571i	$0.931490\pi$
$338$	−103.143	−	103.143i	−0.305157	−	0.305157i
$339$		−	15.5542i		−	0.0458827i
$340$	−342.927	+	259.768i	−1.00861	+	0.764024i
$341$	−88.2602			−0.258828
$342$	99.8102	−	99.8102i	0.291843	−	0.291843i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			504.635i			1.46696i
$345$	295.074	+	40.7138i	0.855287	+	0.118011i
$346$	−417.012			−1.20524
$347$	−122.535	+	122.535i	−0.353126	+	0.353126i	−0.861271	−	0.508145i	$-0.830331\pi$
$347$	−122.535	+	122.535i	−0.353126	+	0.353126i	0.508145	+	0.861271i	$0.330331\pi$
$348$	200.156	+	200.156i	0.575161	+	0.575161i
$349$		−	18.8032i		−	0.0538774i	−0.999637	−	0.0269387i	$-0.991424\pi$
$349$		−	18.8032i		−	0.0538774i	0.999637	−	0.0269387i	$-0.00857589\pi$
$350$	−69.4679	+	246.943i	−0.198480	+	0.705550i
$351$	59.5610			0.169690
$352$	−1006.90	+	1006.90i	−2.86050	+	2.86050i
$353$	242.291	+	242.291i	0.686377	+	0.686377i	0.961429	−	0.275052i	$-0.0886951\pi$
$353$	242.291	+	242.291i	0.686377	+	0.686377i	−0.275052	+	0.961429i	$0.588695\pi$
$354$		−	298.364i		−	0.842837i
$355$	−70.6850	+	512.291i	−0.199113	+	1.44307i
$356$	−459.961			−1.29202
$357$	25.2508	−	25.2508i	0.0707305	−	0.0707305i
$358$	199.655	+	199.655i	0.557697	+	0.557697i
$359$		−	228.420i		−	0.636268i	−0.948046	−	0.318134i	$-0.896944\pi$
$359$		−	228.420i		−	0.636268i	0.948046	−	0.318134i	$-0.103056\pi$
$360$	247.348	+	326.531i	0.687078	+	0.907030i
$361$	213.821			0.592301
$362$	318.176	−	318.176i	0.878938	−	0.878938i
$363$	1.79750	+	1.79750i	0.00495180	+	0.00495180i
$364$		−	334.855i		−	0.919931i
$365$	311.120	−	235.674i	0.852383	−	0.645682i
$366$	567.253			1.54987
$367$	490.375	−	490.375i	1.33617	−	1.33617i	0.436437	−	0.899735i	$-0.356240\pi$
$367$	490.375	−	490.375i	1.33617	−	1.33617i	0.899735	−	0.436437i	$-0.143760\pi$
$368$	−1501.78	−	1501.78i	−4.08092	−	4.08092i
$369$			96.2925i			0.260955i
$370$	−940.831	−	129.814i	−2.54279	−	0.350849i
$371$	25.3138			0.0682314
$372$	109.168	−	109.168i	0.293462	−	0.293462i
$373$	282.198	+	282.198i	0.756562	+	0.756562i	0.975695	−	0.219133i	$-0.0703229\pi$
$373$	282.198	+	282.198i	0.756562	+	0.756562i	−0.219133	+	0.975695i	$0.570323\pi$
$374$			330.422i			0.883480i
$375$	−201.535	+	79.1111i	−0.537427	+	0.210963i
$376$	2091.92			5.56362
$377$	119.967	−	119.967i	0.318215	−	0.318215i
$378$	−37.7017	−	37.7017i	−0.0997400	−	0.0997400i
$379$		−	389.970i		−	1.02895i	−0.857507	−	0.514473i	$-0.827988\pi$
$379$		−	389.970i		−	1.02895i	0.857507	−	0.514473i	$-0.172012\pi$
$380$	91.5453	−	663.476i	0.240909	−	1.74599i
$381$	−49.6802			−0.130394
$382$	−368.406	+	368.406i	−0.964412	+	0.964412i
$383$	330.663	+	330.663i	0.863350	+	0.863350i	0.991726	−	0.128376i	$-0.0409764\pi$
$383$	330.663	+	330.663i	0.863350	+	0.863350i	−0.128376	+	0.991726i	$0.540976\pi$
$384$		−	831.663i		−	2.16579i
$385$	87.3313	+	115.288i	0.226834	+	0.299450i
$386$	−27.4614			−0.0711435
$387$	39.1989	−	39.1989i	0.101289	−	0.101289i
$388$	−278.806	−	278.806i	−0.718572	−	0.718572i
$389$			491.789i			1.26424i	0.774871	+	0.632119i	$0.217815\pi$
$389$			491.789i			1.26424i	−0.774871	+	0.632119i	$0.782185\pi$
$390$	306.888	−	232.469i	0.786892	−	0.596073i
$391$	−268.025			−0.685487
$392$	−135.174	+	135.174i	−0.344831	+	0.344831i
$393$	−95.1803	−	95.1803i	−0.242189	−	0.242189i
$394$			1136.56i			2.88468i
$395$	340.772	+	47.0191i	0.862714	+	0.119036i
$396$	362.152			0.914526
$397$	546.007	−	546.007i	1.37533	−	1.37533i	0.523000	−	0.852333i	$-0.324813\pi$
$397$	546.007	−	546.007i	1.37533	−	1.37533i	0.852333	−	0.523000i	$-0.175187\pi$
$398$	−317.299	−	317.299i	−0.797234	−	0.797234i
$399$			55.5947i			0.139335i
$400$	1486.03	+	418.037i	3.71507	+	1.04509i
$401$	−631.914			−1.57585			−0.787923	−	0.615774i	$-0.788843\pi$
$401$	−631.914			−1.57585			−0.787923	+	0.615774i	$0.788843\pi$
$402$	−4.44626	+	4.44626i	−0.0110603	+	0.0110603i
$403$	−65.4316	−	65.4316i	−0.162361	−	0.162361i
$404$		−	593.230i		−	1.46839i
$405$	6.15075	−	44.5777i	0.0151870	−	0.110068i
$406$	−151.876			−0.374080
$407$	−378.634	+	378.634i	−0.930304	+	0.930304i
$408$	−260.636	−	260.636i	−0.638815	−	0.638815i
$409$		−	72.2476i		−	0.176645i	−0.996092	−	0.0883223i	$-0.971849\pi$
$409$		−	72.2476i		−	0.176645i	0.996092	−	0.0883223i	$-0.0281505\pi$
$410$	375.833	+	496.147i	0.916665	+	1.21011i
$411$	−359.757			−0.875321
$412$	438.121	−	438.121i	1.06340	−	1.06340i
$413$	83.0950	+	83.0950i	0.201199	+	0.201199i
$414$			400.186i			0.966633i
$415$	402.677	−	305.029i	0.970305	−	0.735009i
$416$	−1492.92			−3.58876
$417$	−179.207	+	179.207i	−0.429754	+	0.429754i
$418$	−363.744	−	363.744i	−0.870202	−	0.870202i
$419$			334.155i			0.797506i	0.917058	+	0.398753i	$0.130557\pi$
$419$			334.155i			0.797506i	−0.917058	+	0.398753i	$0.869443\pi$
$420$	−250.618	−	34.5798i	−0.596709	−	0.0823328i
$421$	316.485			0.751746			0.375873	−	0.926671i	$-0.377343\pi$
$421$	316.485			0.751746			0.375873	+	0.926671i	$0.377343\pi$
$422$	181.581	−	181.581i	0.430286	−	0.430286i
$423$	−162.496	−	162.496i	−0.384151	−	0.384151i
$424$		−	261.287i		−	0.616243i
$425$	169.911	−	95.3033i	0.399791	−	0.224243i
$426$	−694.781			−1.63094
$427$	−157.981	+	157.981i	−0.369979	+	0.369979i
$428$	754.924	+	754.924i	1.76384	+	1.76384i
$429$		−	217.062i		−	0.505972i
$430$	48.9777	−	354.967i	0.113902	−	0.825505i
$431$	−431.234			−1.00054			−0.500272	−	0.865869i	$-0.666766\pi$
$431$	−431.234			−1.00054			−0.500272	+	0.865869i	$0.666766\pi$
$432$	−226.878	+	226.878i	−0.525180	+	0.525180i
$433$	−13.1404	−	13.1404i	−0.0303474	−	0.0303474i	0.691770	−	0.722118i	$-0.256831\pi$
$433$	−13.1404	−	13.1404i	−0.0303474	−	0.0303474i	−0.722118	+	0.691770i	$0.756831\pi$
$434$			82.8355i			0.190865i
$435$	−77.3989	−	102.176i	−0.177929	−	0.234888i
$436$	−1495.84			−3.43084
$437$	295.056	−	295.056i	0.675185	−	0.675185i
$438$	370.787	+	370.787i	0.846546	+	0.846546i
$439$		−	426.469i		−	0.971457i	−0.874110	−	0.485728i	$-0.838554\pi$
$439$		−	426.469i		−	0.971457i	0.874110	−	0.485728i	$-0.161446\pi$
$440$	1190.00	−	901.425i	2.70454	−	2.04869i
$441$	21.0000			0.0476190
$442$	−244.958	+	244.958i	−0.554203	+	0.554203i
$443$	334.181	+	334.181i	0.754360	+	0.754360i	0.975290	−	0.220930i	$-0.0709093\pi$
$443$	334.181	+	334.181i	0.754360	+	0.754360i	−0.220930	+	0.975290i	$0.570909\pi$
$444$		−	936.655i		−	2.10958i
$445$	206.333	+	28.4694i	0.463669	+	0.0639762i
$446$	−281.721			−0.631662
$447$	175.412	−	175.412i	0.392420	−	0.392420i
$448$	482.927	+	482.927i	1.07796	+	1.07796i
$449$			463.309i			1.03187i	0.856628	+	0.515935i	$0.172555\pi$
$449$			463.309i			1.03187i	−0.856628	+	0.515935i	$0.827445\pi$
$450$	−142.296	−	253.693i	−0.316214	−	0.563762i
$451$	350.925			0.778104
$452$	70.1132	−	70.1132i	0.155118	−	0.155118i
$453$	−250.374	−	250.374i	−0.552702	−	0.552702i
$454$			586.007i			1.29076i
$455$	−20.7260	+	150.212i	−0.0455516	+	0.330136i
$456$	573.843			1.25843
$457$	356.971	−	356.971i	0.781119	−	0.781119i	−0.198901	−	0.980020i	$-0.563737\pi$
$457$	356.971	−	356.971i	0.781119	−	0.781119i	0.980020	+	0.198901i	$0.0637372\pi$
$458$	242.264	+	242.264i	0.528960	+	0.528960i
$459$			40.4914i			0.0882165i
$460$	1146.57	+	1513.62i	2.49255	+	3.29048i
$461$	−126.296			−0.273960			−0.136980	−	0.990574i	$-0.543740\pi$
$461$	−126.296			−0.273960			−0.136980	+	0.990574i	$0.543740\pi$
$462$	−137.399	+	137.399i	−0.297400	+	0.297400i
$463$	−40.0934	−	40.0934i	−0.0865947	−	0.0865947i	0.662483	−	0.749077i	$-0.269503\pi$
$463$	−40.0934	−	40.0934i	−0.0865947	−	0.0865947i	−0.749077	+	0.662483i	$0.769503\pi$
$464$			913.947i			1.96971i
$465$	−55.7284	+	42.2144i	−0.119846	+	0.0907837i
$466$	−1429.06			−3.06666
$467$	494.819	−	494.819i	1.05957	−	1.05957i	0.0614589	−	0.998110i	$-0.480425\pi$
$467$	494.819	−	494.819i	1.05957	−	1.05957i	0.998110	−	0.0614589i	$-0.0195753\pi$
$468$	268.481	+	268.481i	0.573678	+	0.573678i
$469$		−	2.47658i		−	0.00528056i
$470$	−1471.49	−	203.033i	−3.13082	−	0.431985i
$471$	413.780			0.878513
$472$	857.699	−	857.699i	1.81716	−	1.81716i
$473$	−142.855	−	142.855i	−0.302019	−	0.302019i
$474$			462.163i			0.975027i
$475$	−82.1322	+	291.961i	−0.172910	+	0.614655i
$476$	227.644			0.478244
$477$	−20.2962	+	20.2962i	−0.0425497	+	0.0425497i
$478$	−456.083	−	456.083i	−0.954149	−	0.954149i
$479$		−	854.008i		−	1.78290i	−0.453121	−	0.891449i	$-0.649689\pi$
$479$		−	854.008i		−	1.78290i	0.453121	−	0.891449i	$-0.350311\pi$
$480$	−154.171	+	1117.36i	−0.321190	+	2.32783i
$481$	−561.399			−1.16715
$482$	−850.039	+	850.039i	−1.76357	+	1.76357i
$483$	−111.453	−	111.453i	−0.230751	−	0.230751i
$484$			16.2051i			0.0334816i
$485$	107.812	+	142.326i	0.222293	+	0.293455i
$486$	60.4572			0.124398
$487$	401.669	−	401.669i	0.824782	−	0.824782i	−0.162007	−	0.986790i	$-0.551797\pi$
$487$	401.669	−	401.669i	0.824782	−	0.824782i	0.986790	+	0.162007i	$0.0517968\pi$
$488$	1630.66	+	1630.66i	3.34153	+	3.34153i
$489$		−	409.979i		−	0.838403i
$490$	108.202	−	81.9637i	0.220821	−	0.167273i
$491$	−250.314			−0.509805			−0.254903	−	0.966967i	$-0.582043\pi$
$491$	−250.314			−0.509805			−0.254903	+	0.966967i	$0.582043\pi$
$492$	−434.054	+	434.054i	−0.882224	+	0.882224i
$493$	81.5571	+	81.5571i	0.165430	+	0.165430i
$494$		−	539.323i		−	1.09175i
$495$	−162.457	−	22.4155i	−0.328196	−	0.0452839i
$496$	498.480			1.00500
$497$	193.498	−	193.498i	0.389332	−	0.389332i
$498$	479.903	+	479.903i	0.963661	+	0.963661i
$499$		−	293.789i		−	0.588756i	−0.955689	−	0.294378i	$-0.904888\pi$
$499$		−	293.789i		−	0.588756i	0.955689	−	0.294378i	$-0.0951125\pi$
$500$	−1265.06	−	551.847i	−2.53012	−	1.10369i
$501$	−196.787			−0.392789
$502$	−1107.13	+	1107.13i	−2.20544	+	2.20544i
$503$	−301.845	−	301.845i	−0.600090	−	0.600090i	0.340246	−	0.940336i	$-0.389490\pi$
$503$	−301.845	−	301.845i	−0.600090	−	0.600090i	−0.940336	+	0.340246i	$0.889490\pi$
$504$		−	216.760i		−	0.430079i
$505$	−36.7182	+	266.116i	−0.0727093	+	0.526962i
$506$	1458.42			2.88226
$507$	−46.0633	+	46.0633i	−0.0908546	+	0.0908546i
$508$	−223.942	−	223.942i	−0.440830	−	0.440830i
$509$			495.550i			0.973575i	0.873520	+	0.486787i	$0.161831\pi$
$509$			495.550i			0.973575i	−0.873520	+	0.486787i	$0.838169\pi$
$510$	158.039	+	208.632i	0.309881	+	0.409082i
$511$	−206.530			−0.404168
$512$	917.219	−	917.219i	1.79144	−	1.79144i
$513$	−44.5749	−	44.5749i	−0.0868906	−	0.0868906i
$514$		−	599.544i		−	1.16643i
$515$	−223.654	+	169.418i	−0.434279	+	0.328968i
$516$	353.391			0.684867
$517$	−592.194	+	592.194i	−1.14544	+	1.14544i
$518$	355.362	+	355.362i	0.686027	+	0.686027i
$519$			186.236i			0.358837i
$520$	1550.47	+	213.931i	2.98168	+	0.411407i
$521$	375.437			0.720609			0.360304	−	0.932835i	$-0.382673\pi$
$521$	375.437			0.720609			0.360304	+	0.932835i	$0.382673\pi$
$522$	121.772	−	121.772i	0.233280	−	0.233280i
$523$	−671.097	−	671.097i	−1.28317	−	1.28317i	−0.938855	−	0.344314i	$-0.888111\pi$
$523$	−671.097	−	671.097i	−1.28317	−	1.28317i	−0.344314	−	0.938855i	$-0.611889\pi$
$524$		−	858.082i		−	1.63756i
$525$	110.284	+	31.0241i	0.210064	+	0.0590936i
$526$	1137.78			2.16308
$527$	44.4824	−	44.4824i	0.0844068	−	0.0844068i
$528$	826.825	+	826.825i	1.56596	+	1.56596i
$529$			654.018i			1.23633i
$530$	−25.3594	+	183.793i	−0.0478480	+	0.346779i
$531$	−133.248			−0.250939
$532$	−250.602	+	250.602i	−0.471057	+	0.471057i
$533$	260.158	+	260.158i	0.488101	+	0.488101i
$534$			279.833i			0.524032i
$535$	−291.924	−	385.376i	−0.545651	−	0.720329i
$536$	−25.5631			−0.0476923
$537$	89.1654	−	89.1654i	0.166044	−	0.166044i
$538$	86.4331	+	86.4331i	0.160656	+	0.160656i
$539$		−	76.5316i		−	0.141988i
$540$	228.667	−	173.216i	0.423457	−	0.320770i
$541$	557.721			1.03091			0.515454	−	0.856917i	$-0.327623\pi$
$541$	557.721			1.03091			0.515454	+	0.856917i	$0.327623\pi$
$542$	−254.084	+	254.084i	−0.468790	+	0.468790i
$543$	−142.096	−	142.096i	−0.261687	−	0.261687i
$544$		−	1014.93i		−	1.86569i
$545$	671.018	+	92.5858i	1.23123	+	0.169882i
$546$	−203.721			−0.373115
$547$	−656.108	+	656.108i	−1.19947	+	1.19947i	−0.225141	+	0.974326i	$0.572284\pi$
$547$	−656.108	+	656.108i	−1.19947	+	1.19947i	−0.974326	+	0.225141i	$0.927716\pi$
$548$	−1621.66	−	1621.66i	−2.95924	−	2.95924i
$549$		−	253.333i		−	0.461445i
$550$	−924.548	+	518.579i	−1.68100	+	0.942871i
$551$	−179.564			−0.325888
$552$	−1150.40	+	1150.40i	−2.08406	+	2.08406i
$553$	−128.713	−	128.713i	−0.232754	−	0.232754i
$554$			159.725i			0.288312i
$555$	−57.9746	+	420.172i	−0.104459	+	0.757067i
$556$	−1615.61			−2.90578
$557$	77.0795	−	77.0795i	0.138383	−	0.138383i	−0.634522	−	0.772905i	$-0.718803\pi$
$557$	77.0795	−	77.0795i	0.138383	−	0.138383i	0.772905	+	0.634522i	$0.218803\pi$
$558$	−66.4162	−	66.4162i	−0.119025	−	0.119025i
$559$		−	211.811i		−	0.378910i
$560$	−493.233	−	651.130i	−0.880773	−	1.16273i
$561$	147.565			0.263040
$562$	−511.745	+	511.745i	−0.910579	+	0.910579i
$563$	100.072	+	100.072i	0.177747	+	0.177747i	0.790373	−	0.612626i	$-0.209887\pi$
$563$	100.072	+	100.072i	0.177747	+	0.177747i	−0.612626	+	0.790373i	$0.709887\pi$
$564$		−	1464.95i		−	2.59744i
$565$	−35.7916	+	27.1123i	−0.0633480	+	0.0479863i
$566$	1096.06			1.93650
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	−1997.27	−	1997.27i	−3.51631	−	3.51631i
$569$		−	73.3966i		−	0.128992i	−0.997918	−	0.0644961i	$-0.979456\pi$
$569$		−	73.3966i		−	0.128992i	0.997918	−	0.0644961i	$-0.0205440\pi$
$570$	−403.649	−	55.6948i	−0.708157	−	0.0977102i
$571$	−131.618			−0.230504			−0.115252	−	0.993336i	$-0.536768\pi$
$571$	−131.618			−0.230504			−0.115252	+	0.993336i	$0.536768\pi$
$572$	978.442	−	978.442i	1.71056	−	1.71056i
$573$	164.529	+	164.529i	0.287136	+	0.287136i
$574$		−	329.356i		−	0.573791i
$575$	−420.652	−	749.959i	−0.731568	−	1.30428i
$576$	−774.407			−1.34446
$577$	−614.754	+	614.754i	−1.06543	+	1.06543i	−0.0677285	+	0.997704i	$0.521575\pi$
$577$	−614.754	+	614.754i	−1.06543	+	1.06543i	−0.997704	+	0.0677285i	$0.978425\pi$
$578$	626.023	+	626.023i	1.08308	+	1.08308i
$579$			12.2642i			0.0211816i
$580$	111.689	−	809.465i	0.192566	−	1.39563i
$581$	−267.308			−0.460082
$582$	−169.622	+	169.622i	−0.291446	+	0.291446i
$583$	73.9668	+	73.9668i	0.126873	+	0.126873i
$584$			2131.78i			3.65031i
$585$	−103.820	−	137.055i	−0.177470	−	0.234282i
$586$	−650.803			−1.11059
$587$	−328.506	+	328.506i	−0.559636	+	0.559636i	−0.929204	−	0.369568i	$-0.879506\pi$
$587$	−328.506	+	328.506i	−0.559636	+	0.559636i	0.369568	+	0.929204i	$0.379506\pi$
$588$	94.6609	+	94.6609i	0.160988	+	0.160988i
$589$			97.9368i			0.166276i
$590$	−686.562	+	520.073i	−1.16366	+	0.881480i
$591$	507.586			0.858860
$592$	2138.46	−	2138.46i	3.61227	−	3.61227i
$593$	−46.4495	−	46.4495i	−0.0783298	−	0.0783298i	0.666856	−	0.745186i	$-0.267639\pi$
$593$	−46.4495	−	46.4495i	−0.0783298	−	0.0783298i	−0.745186	+	0.666856i	$0.767639\pi$
$594$		−	220.328i		−	0.370923i
$595$	−102.118	−	14.0901i	−0.171628	−	0.0236809i
$596$	1581.39			2.65334
$597$	−141.705	+	141.705i	−0.237361	+	0.237361i
$598$	1081.20	+	1081.20i	1.80803	+	1.80803i
$599$		−	256.090i		−	0.427529i	−0.976885	−	0.213764i	$-0.931428\pi$
$599$		−	256.090i		−	0.427529i	0.976885	−	0.213764i	$-0.0685724\pi$
$600$	320.228	−	1138.34i	0.533714	−	1.89723i
$601$	433.545			0.721372			0.360686	−	0.932687i	$-0.382543\pi$
$601$	433.545			0.721372			0.360686	+	0.932687i	$0.382543\pi$
$602$	−134.075	+	134.075i	−0.222716	+	0.222716i
$603$	1.98568	+	1.98568i	0.00329301	+	0.00329301i
$604$		−	2257.20i		−	3.73709i
$605$	1.00302	−	7.26941i	0.00165788	−	0.0120156i
$606$	−360.913			−0.595565
$607$	788.344	−	788.344i	1.29875	−	1.29875i	0.369540	−	0.929215i	$-0.379515\pi$
$607$	788.344	−	788.344i	1.29875	−	1.29875i	0.929215	−	0.369540i	$-0.120485\pi$
$608$	1117.29	+	1117.29i	1.83765	+	1.83765i
$609$			67.8275i			0.111375i
$610$	−988.767	−	1305.30i	−1.62093	−	2.13983i
$611$	−878.045			−1.43706
$612$	−182.521	+	182.521i	−0.298238	+	0.298238i
$613$	143.879	+	143.879i	0.234712	+	0.234712i	0.814656	−	0.579944i	$-0.196926\pi$
$613$	143.879	+	143.879i	0.234712	+	0.234712i	−0.579944	+	0.814656i	$0.696926\pi$
$614$		−	1730.96i		−	2.81916i
$615$	221.577	−	167.846i	0.360289	−	0.272920i
$616$	−789.952			−1.28239
$617$	−280.216	+	280.216i	−0.454159	+	0.454159i	−0.896732	−	0.442573i	$-0.854066\pi$
$617$	−280.216	+	280.216i	−0.454159	+	0.454159i	0.442573	+	0.896732i	$0.354066\pi$
$618$	−266.547	−	266.547i	−0.431305	−	0.431305i
$619$			438.884i			0.709020i	0.935052	+	0.354510i	$0.115352\pi$
$619$			438.884i			0.709020i	−0.935052	+	0.354510i	$0.884648\pi$
$620$	−441.493	−	60.9165i	−0.712086	−	0.0982524i
$621$	178.722			0.287797
$622$	1562.35	−	1562.35i	2.51181	−	2.51181i
$623$	−77.9341	−	77.9341i	−0.125095	−	0.125095i
$624$			1225.93i			1.96463i
$625$	533.334	+	325.853i	0.853334	+	0.521365i
$626$	1219.70			1.94840
$627$	−162.447	+	162.447i	−0.259086	+	0.259086i
$628$	1865.18	+	1865.18i	2.97003	+	2.97003i
$629$		−	381.656i		−	0.606766i
$630$	−21.0378	+	152.472i	−0.0333934	+	0.242019i
$631$	601.250			0.952852			0.476426	−	0.879215i	$-0.341932\pi$
$631$	601.250			0.952852			0.476426	+	0.879215i	$0.341932\pi$
$632$	−1328.57	+	1328.57i	−2.10216	+	2.10216i
$633$	−81.0933	−	81.0933i	−0.128109	−	0.128109i
$634$			1005.88i			1.58656i
$635$	86.5966	+	114.319i	0.136373	+	0.180029i
$636$	−182.977			−0.287700
$637$	56.7366	−	56.7366i	0.0890685	−	0.0890685i
$638$	−443.781	−	443.781i	−0.695582	−	0.695582i
$639$			310.287i			0.485582i
$640$	−1913.73	+	1449.66i	−2.99020	+	2.26509i
$641$	803.007			1.25274			0.626371	−	0.779525i	$-0.284540\pi$
$641$	803.007			1.25274			0.626371	+	0.779525i	$0.284540\pi$
$642$	459.285	−	459.285i	0.715397	−	0.715397i
$643$	−164.070	−	164.070i	−0.255163	−	0.255163i	0.567920	−	0.823084i	$-0.307748\pi$
$643$	−164.070	−	164.070i	−0.255163	−	0.255163i	−0.823084	+	0.567920i	$0.807748\pi$
$644$		−	1004.78i		−	1.56022i
$645$	−158.527	−	21.8733i	−0.245778	−	0.0339121i
$646$	366.648			0.567566
$647$	495.936	−	495.936i	0.766517	−	0.766517i	−0.210975	−	0.977491i	$-0.567664\pi$
$647$	495.936	−	495.936i	0.766517	−	0.766517i	0.977491	+	0.210975i	$0.0676638\pi$
$648$	173.795	+	173.795i	0.268202	+	0.268202i
$649$			485.606i			0.748237i
$650$	−1069.86	−	300.965i	−1.64594	−	0.463023i
$651$	36.9941			0.0568265
$652$	1848.05	−	1848.05i	2.83443	−	2.83443i
$653$	−812.931	−	812.931i	−1.24492	−	1.24492i	−0.957936	−	0.286982i	$-0.907348\pi$
$653$	−812.931	−	812.931i	−1.24492	−	1.24492i	−0.286982	−	0.957936i	$-0.592652\pi$
$654$			910.050i			1.39151i
$655$	−53.1113	+	384.925i	−0.0810859	+	0.587672i
$656$	−1981.97			−3.02129
$657$	165.592	−	165.592i	0.252043	−	0.252043i
$658$	555.796	+	555.796i	0.844675	+	0.844675i
$659$		−	135.081i		−	0.204979i	−0.994734	−	0.102490i	$-0.967319\pi$
$659$		−	135.081i		−	0.204979i	0.994734	−	0.102490i	$-0.0326808\pi$
$660$	−631.260	−	833.344i	−0.956455	−	1.26264i
$661$	−128.892			−0.194996			−0.0974980	−	0.995236i	$-0.531084\pi$
$661$	−128.892			−0.194996			−0.0974980	+	0.995236i	$0.531084\pi$
$662$	−590.291	+	590.291i	−0.891678	+	0.891678i
$663$	109.397	+	109.397i	0.165003	+	0.165003i
$664$			2759.13i			4.15531i
$665$	127.928	−	96.9060i	0.192373	−	0.145723i
$666$	−569.847			−0.855626
$667$	359.979	−	359.979i	0.539698	−	0.539698i
$668$	−887.051	−	887.051i	−1.32792	−	1.32792i
$669$			125.816i			0.188065i
$670$	17.9814	+	2.48104i	0.0268379	+	0.00370305i
$671$	−923.237			−1.37591
$672$	422.038	−	422.038i	0.628033	−	0.628033i
$673$	−217.545	−	217.545i	−0.323246	−	0.323246i	0.526765	−	0.850011i	$-0.323405\pi$
$673$	−217.545	−	217.545i	−0.323246	−	0.323246i	−0.850011	+	0.526765i	$0.823405\pi$
$674$			2200.49i			3.26482i
$675$	−113.298	+	63.5491i	−0.167849	+	0.0941468i
$676$	−415.276			−0.614313
$677$	−601.143	+	601.143i	−0.887952	+	0.887952i	−0.994326	−	0.106374i	$-0.966076\pi$
$677$	−601.143	+	601.143i	−0.887952	+	0.887952i	0.106374	+	0.994326i	$0.466076\pi$
$678$	−42.6558	−	42.6558i	−0.0629142	−	0.0629142i
$679$		−	94.4798i		−	0.139146i
$680$	−145.437	+	1054.06i	−0.213878	+	1.55008i
$681$	261.709			0.384301
$682$	−242.045	+	242.045i	−0.354904	+	0.354904i
$683$	−16.6370	−	16.6370i	−0.0243587	−	0.0243587i	0.694823	−	0.719181i	$-0.255483\pi$
$683$	−16.6370	−	16.6370i	−0.0243587	−	0.0243587i	−0.719181	+	0.694823i	$0.755483\pi$
$684$		−	401.857i		−	0.587511i
$685$	627.086	+	827.833i	0.915453	+	1.20851i
$686$	−71.8278			−0.104705
$687$	108.194	−	108.194i	0.157488	−	0.157488i
$688$	806.823	+	806.823i	1.17271	+	1.17271i
$689$			109.670i			0.159173i
$690$	920.863	−	697.557i	1.33458	−	1.01095i
$691$	333.673			0.482884			0.241442	−	0.970415i	$-0.422380\pi$
$691$	333.673			0.482884			0.241442	+	0.970415i	$0.422380\pi$
$692$	−839.490	+	839.490i	−1.21314	+	1.21314i
$693$	61.3618	+	61.3618i	0.0885451	+	0.0885451i
$694$			672.077i			0.968411i
$695$	724.745	+	99.9990i	1.04280	+	0.143883i
$696$	700.109			1.00590
$697$	−176.863	+	176.863i	−0.253749	+	0.253749i
$698$	−51.5659	−	51.5659i	−0.0738766	−	0.0738766i
$699$			638.215i			0.913040i
$700$	357.276	+	636.968i	0.510394	+	0.909955i
$701$	978.544			1.39593			0.697963	−	0.716134i	$-0.254090\pi$
$701$	978.544			1.39593			0.697963	+	0.716134i	$0.254090\pi$
$702$	163.340	−	163.340i	0.232678	−	0.232678i
$703$	420.146	+	420.146i	0.597647	+	0.597647i
$704$			2822.22i			4.00883i
$705$	−90.6739	+	657.161i	−0.128615	+	0.932143i
$706$	1328.92			1.88232
$707$	100.515	−	100.515i	0.142171	−	0.142171i
$708$	−600.639	−	600.639i	−0.848361	−	0.848361i
$709$		−	775.664i		−	1.09402i	−0.837125	−	0.547012i	$-0.815765\pi$
$709$		−	775.664i		−	1.09402i	0.837125	−	0.547012i	$-0.184235\pi$
$710$	1211.06	+	1598.75i	1.70572	+	2.25176i
$711$	206.400			0.290296
$712$	−804.428	+	804.428i	−1.12982	+	1.12982i
$713$	−196.337	−	196.337i	−0.275368	−	0.275368i
$714$		−	138.495i		−	0.193971i
$715$	−499.478	+	378.356i	−0.698571	+	0.529170i
$716$	803.856			1.12270
$717$	−203.685	+	203.685i	−0.284080	+	0.284080i
$718$	−626.419	−	626.419i	−0.872450	−	0.872450i
$719$			195.183i			0.271464i	0.990746	+	0.135732i	$0.0433386\pi$
$719$			195.183i			0.271464i	−0.990746	+	0.135732i	$0.956661\pi$
$720$	917.532	+	126.599i	1.27435	+	0.175832i
$721$	148.467			0.205919
$722$	586.381	−	586.381i	0.812162	−	0.812162i
$723$	379.624	+	379.624i	0.525068	+	0.525068i
$724$		−	1281.04i		−	1.76940i
$725$	−100.204	+	356.203i	−0.138213	+	0.491315i
$726$	9.85894			0.0135798
$727$	−127.418	+	127.418i	−0.175265	+	0.175265i	−0.789288	−	0.614023i	$-0.789550\pi$
$727$	−127.418	+	127.418i	−0.175265	+	0.175265i	0.614023	+	0.789288i	$0.289550\pi$
$728$	−585.630	−	585.630i	−0.804437	−	0.804437i
$729$		−	27.0000i		−	0.0370370i
$730$	206.902	−	1499.53i	0.283427	−	2.05414i
$731$	143.995			0.196984
$732$	1141.94	−	1141.94i	1.56003	−	1.56003i
$733$	−657.079	−	657.079i	−0.896425	−	0.896425i	0.0986932	−	0.995118i	$-0.468534\pi$
$733$	−657.079	−	657.079i	−0.896425	−	0.896425i	−0.995118	+	0.0986932i	$0.968534\pi$
$734$		−	2689.61i		−	3.66431i
$735$	−36.6047	−	48.3228i	−0.0498023	−	0.0657454i
$736$	−4479.74			−6.08660
$737$	7.23655	−	7.23655i	0.00981893	−	0.00981893i
$738$	264.072	+	264.072i	0.357821	+	0.357821i
$739$		−	1191.53i		−	1.61235i	−0.591676	−	0.806176i	$-0.701534\pi$
$739$		−	1191.53i		−	1.61235i	0.591676	−	0.806176i	$-0.298466\pi$
$740$	−2155.32	+	1632.66i	−2.91260	+	2.20630i
$741$	−240.860			−0.325047
$742$	69.4206	−	69.4206i	0.0935588	−	0.0935588i
$743$	115.268	+	115.268i	0.155138	+	0.155138i	0.780408	−	0.625270i	$-0.215011\pi$
$743$	115.268	+	115.268i	0.155138	+	0.155138i	−0.625270	+	0.780408i	$0.715011\pi$
$744$		−	381.849i		−	0.513238i
$745$	−709.394	−	97.8809i	−0.952207	−	0.131384i
$746$	1547.79			2.07479
$747$	214.323	−	214.323i	0.286912	−	0.286912i
$748$	665.174	+	665.174i	0.889270	+	0.889270i
$749$			255.823i			0.341553i
$750$	−335.735	+	769.643i	−0.447647	+	1.02619i
$751$	−627.744			−0.835878			−0.417939	−	0.908475i	$-0.637247\pi$
$751$	−627.744			−0.835878			−0.417939	+	0.908475i	$0.637247\pi$
$752$	3344.62	−	3344.62i	4.44763	−	4.44763i
$753$	494.440	+	494.440i	0.656627	+	0.656627i
$754$		−	657.994i		−	0.872671i
$755$	−139.710	+	1012.55i	−0.185047	+	1.34113i
$756$	−151.795			−0.200787
$757$	117.159	−	117.159i	0.154767	−	0.154767i	−0.625476	−	0.780243i	$-0.715095\pi$
$757$	117.159	−	117.159i	0.154767	−	0.154767i	0.780243	+	0.625476i	$0.215095\pi$
$758$	−1069.45	−	1069.45i	−1.41089	−	1.41089i
$759$		−	651.327i		−	0.858138i
$760$	−1000.25	−	1320.46i	−1.31612	−	1.73745i
$761$	1272.61			1.67229			0.836145	−	0.548509i	$-0.184804\pi$
$761$	1272.61			1.67229			0.836145	+	0.548509i	$0.184804\pi$
$762$	−136.243	+	136.243i	−0.178796	+	0.178796i
$763$	−253.451	−	253.451i	−0.332176	−	0.332176i
$764$			1483.28i			1.94147i
$765$	93.1742	−	70.5797i	0.121796	−	0.0922610i
$766$	1813.62			2.36765
$767$	−360.003	+	360.003i	−0.469365	+	0.469365i
$768$	−1016.15	−	1016.15i	−1.32311	−	1.32311i
$769$			1506.02i			1.95842i	0.202857	+	0.979208i	$0.434978\pi$
$769$			1506.02i			1.95842i	−0.202857	+	0.979208i	$0.565022\pi$
$770$	555.663	+	76.6694i	0.721641	+	0.0995707i
$771$	−267.754			−0.347282
$772$	−55.2827	+	55.2827i	−0.0716097	+	0.0716097i
$773$	−580.116	−	580.116i	−0.750474	−	0.750474i	0.224094	−	0.974568i	$-0.428058\pi$
$773$	−580.116	−	580.116i	−0.750474	−	0.750474i	−0.974568	+	0.224094i	$0.928058\pi$
$774$		−	214.998i		−	0.277775i
$775$	194.278	+	54.6528i	0.250682	+	0.0705197i
$776$	−975.212			−1.25672
$777$	158.703	−	158.703i	0.204252	−	0.204252i
$778$	1348.68	+	1348.68i	1.73352	+	1.73352i
$779$		−	389.399i		−	0.499870i
$780$	149.814	−	1085.78i	0.192070	−	1.39203i
$781$	1130.80			1.44788
$782$	−735.032	+	735.032i	−0.939939	+	0.939939i
$783$	−54.3830	−	54.3830i	−0.0694546	−	0.0694546i
$784$			432.238i			0.551324i
$785$	−721.251	−	952.144i	−0.918792	−	1.21292i
$786$	−522.044			−0.664179
$787$	−138.491	+	138.491i	−0.175973	+	0.175973i	−0.789598	−	0.613625i	$-0.789711\pi$
$787$	−138.491	+	138.491i	−0.175973	+	0.175973i	0.613625	+	0.789598i	$0.289711\pi$
$788$	2288.03	+	2288.03i	2.90359	+	2.90359i
$789$		−	508.128i		−	0.644015i
$790$	1063.48	−	805.587i	1.34617	−	1.01973i
$791$	23.7595			0.0300372
$792$	633.371	−	633.371i	0.799710	−	0.799710i
$793$	−684.441	−	684.441i	−0.863103	−	0.863103i
$794$		−	2994.74i		−	3.77171i
$795$	82.0814	+	11.3254i	0.103247	+	0.0142458i
$796$	−1277.51			−1.60492
$797$	1122.40	−	1122.40i	1.40829	−	1.40829i	0.639475	−	0.768811i	$-0.279152\pi$
$797$	1122.40	−	1122.40i	1.40829	−	1.40829i	0.768811	−	0.639475i	$-0.220848\pi$
$798$	152.463	+	152.463i	0.191056	+	0.191056i
$799$		−	596.921i		−	0.747085i
$800$	2839.87	−	1592.88i	3.54984	−	1.99110i
$801$	124.973			0.156021
$802$	−1732.96	+	1732.96i	−2.16080	+	2.16080i
$803$	−603.478	−	603.478i	−0.751529	−	0.751529i
$804$			17.9016i			0.0222657i
$805$	−62.1913	+	450.733i	−0.0772563	+	0.559917i
$806$	−358.879			−0.445259
$807$	38.6007	−	38.6007i	0.0478324	−	0.0478324i
$808$	−1037.50	−	1037.50i	−1.28404	−	1.28404i
$809$		−	30.2805i		−	0.0374295i	−0.999825	−	0.0187147i	$-0.994043\pi$
$809$		−	30.2805i		−	0.0374295i	0.999825	−	0.0187147i	$-0.00595744\pi$
$810$	−105.382	−	139.117i	−0.130101	−	0.171750i
$811$	−1118.58			−1.37926			−0.689629	−	0.724163i	$-0.742226\pi$
$811$	−1118.58			−1.37926			−0.689629	+	0.724163i	$0.742226\pi$
$812$	−305.744	+	305.744i	−0.376532	+	0.376532i
$813$	113.473	+	113.473i	0.139573	+	0.139573i
$814$			2076.73i			2.55126i
$815$	−943.398	+	714.626i	−1.15754	+	0.876842i
$816$	−833.424			−1.02135
$817$	−158.517	+	158.517i	−0.194024	+	0.194024i
$818$	−198.132	−	198.132i	−0.242215	−	0.242215i
$819$			90.9810i			0.111088i
$820$	1755.39	+	242.205i	2.14072	+	0.295372i
$821$	−923.859			−1.12528			−0.562642	−	0.826700i	$-0.690215\pi$
$821$	−923.859			−1.12528			−0.562642	+	0.826700i	$0.690215\pi$
$822$	−986.597	+	986.597i	−1.20024	+	1.20024i
$823$	−186.823	−	186.823i	−0.227002	−	0.227002i	0.584437	−	0.811439i	$-0.301315\pi$
$823$	−186.823	−	186.823i	−0.227002	−	0.227002i	−0.811439	+	0.584437i	$0.801315\pi$
$824$		−	1532.47i		−	1.85979i
$825$	231.596	+	412.900i	0.280722	+	0.500485i
$826$	455.759			0.551766
$827$	59.3982	−	59.3982i	0.0718237	−	0.0718237i	−0.670282	−	0.742106i	$-0.733827\pi$
$827$	59.3982	−	59.3982i	0.0718237	−	0.0718237i	0.742106	+	0.670282i	$0.233827\pi$
$828$	805.618	+	805.618i	0.972968	+	0.972968i
$829$			1486.79i			1.79347i	0.442564	+	0.896737i	$0.354069\pi$
$829$			1486.79i			1.79347i	−0.442564	+	0.896737i	$0.645931\pi$
$830$	267.789	−	1940.81i	0.322638	−	2.33832i
$831$	71.3326			0.0858394
$832$	−2092.25	+	2092.25i	−2.51472	+	2.51472i
$833$	38.5712	+	38.5712i	0.0463040	+	0.0463040i
$834$			982.916i			1.17856i
$835$	343.016	+	452.825i	0.410798	+	0.542305i
$836$	−1464.51			−1.75181
$837$	−29.6612	+	29.6612i	−0.0354376	+	0.0354376i
$838$	916.386	+	916.386i	1.09354	+	1.09354i
$839$			453.536i			0.540568i	0.962781	+	0.270284i	$0.0871176\pi$
$839$			453.536i			0.540568i	−0.962781	+	0.270284i	$0.912882\pi$
$840$	−498.784	+	377.830i	−0.593790	+	0.449798i
$841$	621.925			0.739507
$842$	867.927	−	867.927i	1.03079	−	1.03079i
$843$	228.544	+	228.544i	0.271108	+	0.271108i
$844$		−	731.082i		−	0.866211i
$845$	186.288	+	25.7036i	0.220459	+	0.0304185i
$846$	−891.257			−1.05349
$847$	−2.74573	+	2.74573i	−0.00324172	+	0.00324172i
$848$	−417.753	−	417.753i	−0.492633	−	0.492633i
$849$		−	489.497i		−	0.576557i
$850$	204.605	−	727.323i	0.240712	−	0.855675i
$851$	−1684.56			−1.97951
$852$	−1398.67	+	1398.67i	−1.64163	+	1.64163i
$853$	−827.180	−	827.180i	−0.969730	−	0.969730i	0.0298251	−	0.999555i	$-0.490505\pi$
$853$	−827.180	−	827.180i	−0.969730	−	0.969730i	−0.999555	+	0.0298251i	$0.990505\pi$
$854$			866.493i			1.01463i
$855$	−24.8731	+	180.268i	−0.0290913	+	0.210840i
$856$	2640.58			3.08479
$857$	−264.140	+	264.140i	−0.308215	+	0.308215i	−0.844217	−	0.536002i	$-0.819934\pi$
$857$	−264.140	+	264.140i	−0.308215	+	0.308215i	0.536002	+	0.844217i	$0.319934\pi$
$858$	−595.270	−	595.270i	−0.693788	−	0.693788i
$859$			710.066i			0.826619i	0.910591	+	0.413310i	$0.135627\pi$
$859$			710.066i			0.826619i	−0.910591	+	0.413310i	$0.864373\pi$
$860$	−615.990	−	813.184i	−0.716267	−	0.945563i
$861$	−147.089			−0.170835
$862$	−1182.61	+	1182.61i	−1.37194	+	1.37194i
$863$	966.508	+	966.508i	1.11994	+	1.11994i	0.991750	+	0.128190i	$0.0409167\pi$
$863$	966.508	+	966.508i	1.11994	+	1.11994i	0.128190	+	0.991750i	$0.459083\pi$
$864$			676.766i			0.783294i
$865$	428.546	−	324.625i	0.495429	−	0.375289i
$866$	−72.0725			−0.0832246
$867$	279.580	−	279.580i	0.322468	−	0.322468i
$868$	166.757	+	166.757i	0.192116	+	0.192116i
$869$		−	752.197i		−	0.865590i
$870$	−492.467	−	67.9497i	−0.566054	−	0.0781031i
$871$	10.7296			0.0123187
$872$	−2616.09	+	2616.09i	−3.00011	+	3.00011i
$873$	75.7524	+	75.7524i	0.0867725	+	0.0867725i
$874$		−	1618.32i		−	1.85162i
$875$	−120.844	−	307.850i	−0.138108	−	0.351829i
$876$	1492.87			1.70419
$877$	−1016.78	+	1016.78i	−1.15939	+	1.15939i	−0.174779	+	0.984608i	$0.555921\pi$
$877$	−1016.78	+	1016.78i	−1.15939	+	1.15939i	−0.984608	+	0.174779i	$0.944079\pi$
$878$	−1169.55	−	1169.55i	−1.33206	−	1.33206i
$879$			290.646i			0.330656i
$880$	461.374	−	3343.82i	0.524288	−	3.79979i
$881$	615.784			0.698961			0.349480	−	0.936944i	$-0.386358\pi$
$881$	615.784			0.698961			0.349480	+	0.936944i	$0.386358\pi$
$882$	57.5903	−	57.5903i	0.0652952	−	0.0652952i
$883$	−393.825	−	393.825i	−0.446008	−	0.446008i	0.448017	−	0.894025i	$-0.352130\pi$
$883$	−393.825	−	393.825i	−0.446008	−	0.446008i	−0.894025	+	0.448017i	$0.852130\pi$
$884$			986.252i			1.11567i
$885$	232.263	+	306.616i	0.262444	+	0.346459i
$886$	1832.92			2.06875
$887$	1046.82	−	1046.82i	1.18018	−	1.18018i	0.200486	−	0.979697i	$-0.435748\pi$
$887$	1046.82	−	1046.82i	1.18018	−	1.18018i	0.979697	−	0.200486i	$-0.0642520\pi$
$888$	−1638.12	−	1638.12i	−1.84473	−	1.84473i
$889$		−	75.8878i		−	0.0853631i
$890$	643.921	−	487.772i	0.723506	−	0.548058i
$891$	−98.3978			−0.110435
$892$	−567.135	+	567.135i	−0.635802	+	0.635802i
$893$	657.120	+	657.120i	0.735857	+	0.735857i
$894$		−	962.096i		−	1.07617i
$895$	−360.600	−	49.7549i	−0.402905	−	0.0555921i
$896$	1270.39			1.41784
$897$	482.860	−	482.860i	0.538306	−	0.538306i
$898$	1270.58	+	1270.58i	1.41490	+	1.41490i
$899$			119.486i			0.132910i
$900$	−797.169	−	224.253i	−0.885743	−	0.249170i
$901$	−74.5572			−0.0827494
$902$	962.375	−	962.375i	1.06693	−	1.06693i
$903$	59.8774	+	59.8774i	0.0663094	+	0.0663094i
$904$		−	245.243i		−	0.271286i
$905$	−79.2906	+	574.661i	−0.0876140	+	0.634984i
$906$	−1373.25			−1.51573
$907$	−343.564	+	343.564i	−0.378791	+	0.378791i	−0.870666	−	0.491875i	$-0.836312\pi$
$907$	−343.564	+	343.564i	−0.378791	+	0.378791i	0.491875	+	0.870666i	$0.336312\pi$
$908$	1179.70	+	1179.70i	1.29922	+	1.29922i
$909$			161.182i			0.177318i
$910$	355.102	+	468.779i	0.390222	+	0.515142i
$911$	313.466			0.344090			0.172045	−	0.985089i	$-0.444963\pi$
$911$	313.466			0.344090			0.172045	+	0.985089i	$0.444963\pi$
$912$	917.475	−	917.475i	1.00600	−	1.00600i
$913$	−781.071	−	781.071i	−0.855499	−	0.855499i
$914$		−	1957.91i		−	2.14214i
$915$	−582.942	+	441.580i	−0.637095	+	0.482601i
$916$	975.406			1.06485
$917$	145.390	−	145.390i	0.158550	−	0.158550i
$918$	111.043	+	111.043i	0.120962	+	0.120962i
$919$			229.218i			0.249422i	0.992193	+	0.124711i	$0.0398003\pi$
$919$			229.218i			0.249422i	−0.992193	+	0.124711i	$0.960200\pi$
$920$	4652.43	+	641.933i	5.05698	+	0.697753i
$921$	−773.042			−0.839351
$922$	−346.352	+	346.352i	−0.375653	+	0.375653i
$923$	838.315	+	838.315i	0.908250	+	0.908250i
$924$			553.197i			0.598698i
$925$	1067.91	−	598.989i	1.15449	−	0.647556i
$926$	−219.904			−0.237477
$927$	−119.039	+	119.039i	−0.128413	+	0.128413i
$928$	1363.13	+	1363.13i	1.46889	+	1.46889i
$929$			1037.08i			1.11634i	0.829728	+	0.558168i	$0.188495\pi$
$929$			1037.08i			1.11634i	−0.829728	+	0.558168i	$0.811505\pi$
$930$	−37.0607	+	268.598i	−0.0398502	+	0.288815i
$931$	−84.9223			−0.0912162
$932$	−2876.86	+	2876.86i	−3.08676	+	3.08676i
$933$	−697.739	−	697.739i	−0.747845	−	0.747845i
$934$		−	2713.98i		−	2.90576i
$935$	−257.218	−	339.560i	−0.275099	−	0.363166i
$936$	939.097			1.00331
$937$	−147.149	+	147.149i	−0.157043	+	0.157043i	−0.781255	−	0.624212i	$-0.785420\pi$
$937$	−147.149	+	147.149i	−0.157043	+	0.157043i	0.624212	+	0.781255i	$0.285420\pi$
$938$	−6.79177	−	6.79177i	−0.00724070	−	0.00724070i
$939$		−	544.714i		−	0.580100i
$940$	−3370.99	+	2553.53i	−3.58616	+	2.71652i
$941$	−1810.77			−1.92431			−0.962154	−	0.272505i	$-0.912148\pi$
$941$	−1810.77			−1.92431			−0.962154	+	0.272505i	$0.912148\pi$
$942$	1134.75	−	1134.75i	1.20462	−	1.20462i
$943$	780.642	+	780.642i	0.827828	+	0.827828i
$944$		−	2742.62i		−	2.90532i
$945$	68.0935	+	9.39542i	0.0720566	+	0.00994224i
$946$	−783.531			−0.828257
$947$	147.333	−	147.333i	0.155579	−	0.155579i	−0.625026	−	0.780604i	$-0.714911\pi$
$947$	147.333	−	147.333i	0.155579	−	0.155579i	0.780604	+	0.625026i	$0.214911\pi$
$948$	930.383	+	930.383i	0.981417	+	0.981417i
$949$		−	894.776i		−	0.942861i
$950$	575.435	+	1025.91i	0.605721	+	1.07991i
$951$	449.222			0.472368
$952$	398.129	−	398.129i	0.418202	−	0.418202i
$953$	85.4967	+	85.4967i	0.0897132	+	0.0897132i	0.750539	−	0.660826i	$-0.229794\pi$
$953$	85.4967	+	85.4967i	0.0897132	+	0.0897132i	−0.660826	+	0.750539i	$0.729794\pi$
$954$			111.321i			0.116688i
$955$	91.8081	−	665.382i	0.0961342	−	0.696735i
$956$	−1836.29			−1.92081
$957$	−198.191	+	198.191i	−0.207096	+	0.207096i
$958$	−2342.03	−	2342.03i	−2.44471	−	2.44471i
$959$		−	549.538i		−	0.573032i
$960$	1349.85	+	1781.98i	1.40610	+	1.85623i
$961$	−895.830			−0.932186
$962$	−1539.58	+	1539.58i	−1.60039	+	1.60039i
$963$	−205.115	−	205.115i	−0.212996	−	0.212996i
$964$			3422.44i			3.55025i
$965$	28.2209	−	21.3774i	0.0292444	−	0.0221528i
$966$	−611.295			−0.632810
$967$	−322.508	+	322.508i	−0.333514	+	0.333514i	−0.853919	−	0.520406i	$-0.825781\pi$
$967$	−322.508	+	322.508i	−0.333514	+	0.333514i	0.520406	+	0.853919i	$0.325781\pi$
$968$	28.3412	+	28.3412i	0.0292781	+	0.0292781i
$969$		−	163.744i		−	0.168982i
$970$	685.978	+	94.6500i	0.707194	+	0.0975773i
$971$	−1373.43			−1.41445			−0.707223	−	0.706991i	$-0.750052\pi$
$971$	−1373.43			−1.41445			−0.707223	+	0.706991i	$0.750052\pi$
$972$	121.707	−	121.707i	0.125213	−	0.125213i
$973$	−273.744	−	273.744i	−0.281340	−	0.281340i
$974$		−	2203.07i		−	2.26188i
$975$	−134.410	+	477.796i	−0.137856	+	0.490047i
$976$	5214.30			5.34252
$977$	40.3145	−	40.3145i	0.0412635	−	0.0412635i	−0.686174	−	0.727437i	$-0.740711\pi$
$977$	40.3145	−	40.3145i	0.0412635	−	0.0412635i	0.727437	+	0.686174i	$0.240711\pi$
$978$	−1124.33	−	1124.33i	−1.14962	−	1.14962i
$979$		−	455.445i		−	0.465215i
$980$	52.8215	−	382.825i	0.0538995	−	0.390638i
$981$	406.425			0.414297
$982$	−686.461	+	686.461i	−0.699044	+	0.699044i
$983$	1061.02	+	1061.02i	1.07937	+	1.07937i	0.996566	+	0.0828047i	$0.0263878\pi$
$983$	1061.02	+	1061.02i	1.07937	+	1.07937i	0.0828047	+	0.996566i	$0.473612\pi$
$984$			1518.24i			1.54293i
$985$	−884.763	−	1168.00i	−0.898237	−	1.18579i
$986$	447.324			0.453675
$987$	248.217	−	248.217i	0.251486	−	0.251486i
$988$	−1085.72	−	1085.72i	−1.09890	−	1.09890i
$989$		−	635.570i		−	0.642640i
$990$	−506.994	+	384.050i	−0.512115	+	0.387929i
$991$	1624.85			1.63960			0.819802	−	0.572647i	$-0.194083\pi$
$991$	1624.85			1.63960			0.819802	+	0.572647i	$0.194083\pi$
$992$	743.471	−	743.471i	0.749467	−	0.749467i
$993$	263.622	+	263.622i	0.265480	+	0.265480i
$994$		−	1061.30i		−	1.06770i
$995$	573.078	+	79.0722i	0.575957	+	0.0794696i
$996$	1932.19			1.93995
$997$	−273.633	+	273.633i	−0.274456	+	0.274456i	−0.830891	−	0.556435i	$-0.812169\pi$
$997$	−273.633	+	273.633i	−0.274456	+	0.274456i	0.556435	+	0.830891i	$0.312169\pi$
$998$	−805.687	−	805.687i	−0.807301	−	0.807301i
$999$			254.492i			0.254746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.43.12	yes	24
3.2	odd	2		315.3.o.b.253.1		24
5.2	odd	4	inner	105.3.l.a.22.12	✓	24
5.3	odd	4		525.3.l.e.232.1		24
5.4	even	2		525.3.l.e.43.1		24
15.2	even	4		315.3.o.b.127.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.12	✓	24	5.2	odd	4	inner
105.3.l.a.43.12	yes	24	1.1	even	1	trivial
315.3.o.b.127.1		24	15.2	even	4
315.3.o.b.253.1		24	3.2	odd	2
525.3.l.e.43.1		24	5.4	even	2
525.3.l.e.232.1		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.74240 - 2.74240i) q^{2} +(-1.22474 - 1.22474i) q^{3} -11.0415i q^{4} +(-0.683416 + 4.95307i) q^{5} -6.71747 q^{6} +(1.87083 - 1.87083i) q^{7} +(-19.3105 - 19.3105i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(2.74240 - 2.74240i) q^{2} +(-1.22474 - 1.22474i) q^{3} -11.0415i q^{4} +(-0.683416 + 4.95307i) q^{5} -6.71747 q^{6} +(1.87083 - 1.87083i) q^{7} +(-19.3105 - 19.3105i) q^{8} +3.00000i q^{9} +(11.7091 + 15.4575i) q^{10} +10.9331 q^{11} +(-13.5230 + 13.5230i) q^{12} +(8.10523 + 8.10523i) q^{13} -10.2611i q^{14} +(6.90326 - 5.22924i) q^{15} -61.7483 q^{16} +(-5.51018 + 5.51018i) q^{17} +(8.22719 + 8.22719i) q^{18} -12.1318i q^{19} +(54.6893 + 7.54592i) q^{20} -4.58258 q^{21} +(29.9829 - 29.9829i) q^{22} +(24.3210 + 24.3210i) q^{23} +47.3009i q^{24} +(-24.0659 - 6.77002i) q^{25} +44.4555 q^{26} +(3.67423 - 3.67423i) q^{27} +(-20.6567 - 20.6567i) q^{28} -14.8012i q^{29} +(4.59083 - 33.2721i) q^{30} -8.07276 q^{31} +(-92.0962 + 92.0962i) q^{32} +(-13.3902 - 13.3902i) q^{33} +30.2222i q^{34} +(7.98780 + 10.5449i) q^{35} +33.1244 q^{36} +(-34.6319 + 34.6319i) q^{37} +(-33.2701 - 33.2701i) q^{38} -19.8537i q^{39} +(108.844 - 82.4493i) q^{40} +32.0975 q^{41} +(-12.5672 + 12.5672i) q^{42} +(-13.0663 - 13.0663i) q^{43} -120.717i q^{44} +(-14.8592 - 2.05025i) q^{45} +133.395 q^{46} +(-54.1653 + 54.1653i) q^{47} +(75.6259 + 75.6259i) q^{48} -7.00000i q^{49} +(-84.5643 + 47.4321i) q^{50} +13.4971 q^{51} +(89.4937 - 89.4937i) q^{52} +(6.76541 + 6.76541i) q^{53} -20.1524i q^{54} +(-7.47185 + 54.1524i) q^{55} -72.2534 q^{56} +(-14.8583 + 14.8583i) q^{57} +(-40.5907 - 40.5907i) q^{58} +44.4162i q^{59} +(-57.7385 - 76.2222i) q^{60} -84.4444 q^{61} +(-22.1387 + 22.1387i) q^{62} +(5.61249 + 5.61249i) q^{63} +258.136i q^{64} +(-45.6850 + 34.6066i) q^{65} -73.4427 q^{66} +(0.661895 - 0.661895i) q^{67} +(60.8405 + 60.8405i) q^{68} -59.5739i q^{69} +(50.8240 + 7.01261i) q^{70} +103.429 q^{71} +(57.9316 - 57.9316i) q^{72} +(-55.1974 - 55.1974i) q^{73} +189.949i q^{74} +(21.1830 + 37.7661i) q^{75} -133.952 q^{76} +(20.4539 - 20.4539i) q^{77} +(-54.4467 - 54.4467i) q^{78} -68.8001i q^{79} +(42.1998 - 305.844i) q^{80} -9.00000 q^{81} +(88.0241 - 88.0241i) q^{82} +(-71.4410 - 71.4410i) q^{83} +50.5984i q^{84} +(-23.5266 - 31.0581i) q^{85} -71.6660 q^{86} +(-18.1277 + 18.1277i) q^{87} +(-211.124 - 211.124i) q^{88} -41.6575i q^{89} +(-46.3725 + 35.1273i) q^{90} +30.3270 q^{91} +(268.539 - 268.539i) q^{92} +(9.88708 + 9.88708i) q^{93} +297.086i q^{94} +(60.0895 + 8.29103i) q^{95} +225.589 q^{96} +(25.2508 - 25.2508i) q^{97} +(-19.1968 - 19.1968i) q^{98} +32.7993i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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