LMFDB - Embedded newform 1155.2.i.d.76.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.7
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.d.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76869i q^{2} -1.00000i q^{3} -5.66565 q^{4} -1.00000i q^{5} -2.76869 q^{6} +(-2.02228 - 1.70599i) q^{7} +10.1491i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.76869i q^{2} -1.00000i q^{3} -5.66565 q^{4} -1.00000i q^{5} -2.76869 q^{6} +(-2.02228 - 1.70599i) q^{7} +10.1491i q^{8} -1.00000 q^{9} -2.76869 q^{10} +(-3.06033 + 1.27843i) q^{11} +5.66565i q^{12} +3.06720 q^{13} +(-4.72335 + 5.59906i) q^{14} -1.00000 q^{15} +16.7683 q^{16} -2.89753 q^{17} +2.76869i q^{18} -5.02294 q^{19} +5.66565i q^{20} +(-1.70599 + 2.02228i) q^{21} +(3.53959 + 8.47311i) q^{22} +6.43703 q^{23} +10.1491 q^{24} -1.00000 q^{25} -8.49212i q^{26} +1.00000i q^{27} +(11.4575 + 9.66554i) q^{28} -3.97972i q^{29} +2.76869i q^{30} +5.54499i q^{31} -26.1282i q^{32} +(1.27843 + 3.06033i) q^{33} +8.02237i q^{34} +(-1.70599 + 2.02228i) q^{35} +5.66565 q^{36} +3.04035 q^{37} +13.9070i q^{38} -3.06720i q^{39} +10.1491 q^{40} -9.03604 q^{41} +(5.59906 + 4.72335i) q^{42} +0.633605i q^{43} +(17.3388 - 7.24316i) q^{44} +1.00000i q^{45} -17.8221i q^{46} -2.57566i q^{47} -16.7683i q^{48} +(1.17921 + 6.89996i) q^{49} +2.76869i q^{50} +2.89753i q^{51} -17.3777 q^{52} +6.66736 q^{53} +2.76869 q^{54} +(1.27843 + 3.06033i) q^{55} +(17.3142 - 20.5242i) q^{56} +5.02294i q^{57} -11.0186 q^{58} +6.56737i q^{59} +5.66565 q^{60} -3.39485 q^{61} +15.3524 q^{62} +(2.02228 + 1.70599i) q^{63} -38.8043 q^{64} -3.06720i q^{65} +(8.47311 - 3.53959i) q^{66} -15.4919 q^{67} +16.4164 q^{68} -6.43703i q^{69} +(5.59906 + 4.72335i) q^{70} +8.52531 q^{71} -10.1491i q^{72} -2.75799 q^{73} -8.41779i q^{74} +1.00000i q^{75} +28.4582 q^{76} +(8.36982 + 2.63554i) q^{77} -8.49212 q^{78} -5.94802i q^{79} -16.7683i q^{80} +1.00000 q^{81} +25.0180i q^{82} -12.6532 q^{83} +(9.66554 - 11.4575i) q^{84} +2.89753i q^{85} +1.75426 q^{86} -3.97972 q^{87} +(-12.9749 - 31.0595i) q^{88} -17.6613i q^{89} +2.76869 q^{90} +(-6.20272 - 5.23260i) q^{91} -36.4700 q^{92} +5.54499 q^{93} -7.13122 q^{94} +5.02294i q^{95} -26.1282 q^{96} +3.11539i q^{97} +(19.1039 - 3.26488i) q^{98} +(3.06033 - 1.27843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 36 * q^4 - 32 * q^9	$ 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) $ 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$-1$

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 $

$2$		−	2.76869i		−	1.95776i	−0.204434	−	0.978880i	$-0.565535\pi$
$2$		−	2.76869i		−	1.95776i	0.204434	−	0.978880i	$-0.434465\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−5.66565			−2.83283
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.76869			−1.13031
$7$	−2.02228	−	1.70599i	−0.764349	−	0.644803i
$7$	−2.02228	−	1.70599i	−0.764349	−	0.644803i
$8$			10.1491i			3.58824i
$9$	−1.00000			−0.333333
$10$	−2.76869			−0.875537
$11$	−3.06033	+	1.27843i	−0.922724	+	0.385462i
$11$	−3.06033	+	1.27843i	−0.922724	+	0.385462i
$12$			5.66565i			1.63553i
$13$	3.06720			0.850687			0.425343	−	0.905032i	$-0.360153\pi$
$13$	3.06720			0.850687			0.425343	+	0.905032i	$0.360153\pi$
$14$	−4.72335	+	5.59906i	−1.26237	+	1.49641i
$15$	−1.00000			−0.258199
$16$	16.7683			4.19208
$17$	−2.89753			−0.702755			−0.351377	−	0.936234i	$-0.614287\pi$
$17$	−2.89753			−0.702755			−0.351377	+	0.936234i	$0.614287\pi$
$18$			2.76869i			0.652587i
$19$	−5.02294			−1.15234			−0.576171	−	0.817329i	$-0.695454\pi$
$19$	−5.02294			−1.15234			−0.576171	+	0.817329i	$0.695454\pi$
$20$			5.66565i			1.26688i
$21$	−1.70599	+	2.02228i	−0.372277	+	0.441297i
$22$	3.53959	+	8.47311i	0.754642	+	1.80647i
$23$	6.43703			1.34221			0.671106	−	0.741361i	$-0.265819\pi$
$23$	6.43703			1.34221			0.671106	+	0.741361i	$0.265819\pi$
$24$	10.1491			2.07167
$25$	−1.00000			−0.200000
$26$		−	8.49212i		−	1.66544i
$27$			1.00000i			0.192450i
$28$	11.4575	+	9.66554i	2.16527	+	1.82661i
$29$		−	3.97972i		−	0.739016i	−0.929228	−	0.369508i	$-0.879526\pi$
$29$		−	3.97972i		−	0.739016i	0.929228	−	0.369508i	$-0.120474\pi$
$30$			2.76869i			0.505492i
$31$			5.54499i			0.995910i	0.867203	+	0.497955i	$0.165916\pi$
$31$			5.54499i			0.995910i	−0.867203	+	0.497955i	$0.834084\pi$
$32$		−	26.1282i		−	4.61886i
$33$	1.27843	+	3.06033i	0.222547	+	0.532735i
$34$			8.02237i			1.37583i
$35$	−1.70599	+	2.02228i	−0.288365	+	0.341827i
$36$	5.66565			0.944276
$37$	3.04035			0.499830			0.249915	−	0.968268i	$-0.419597\pi$
$37$	3.04035			0.499830			0.249915	+	0.968268i	$0.419597\pi$
$38$			13.9070i			2.25601i
$39$		−	3.06720i		−	0.491144i
$40$	10.1491			1.60471
$41$	−9.03604			−1.41119			−0.705596	−	0.708614i	$-0.749321\pi$
$41$	−9.03604			−1.41119			−0.705596	+	0.708614i	$0.749321\pi$
$42$	5.59906	+	4.72335i	0.863954	+	0.728829i
$43$			0.633605i			0.0966239i	0.998832	+	0.0483119i	$0.0153842\pi$
$43$			0.633605i			0.0966239i	−0.998832	+	0.0483119i	$0.984616\pi$
$44$	17.3388	−	7.24316i	2.61392	−	1.09195i
$45$			1.00000i			0.149071i
$46$		−	17.8221i		−	2.62773i
$47$		−	2.57566i		−	0.375699i	−0.982198	−	0.187850i	$-0.939848\pi$
$47$		−	2.57566i		−	0.375699i	0.982198	−	0.187850i	$-0.0601518\pi$
$48$		−	16.7683i		−	2.42030i
$49$	1.17921	+	6.89996i	0.168459	+	0.985709i
$50$			2.76869i			0.391552i
$51$			2.89753i			0.405736i
$52$	−17.3777			−2.40985
$53$	6.66736			0.915832			0.457916	−	0.888995i	$-0.348596\pi$
$53$	6.66736			0.915832			0.457916	+	0.888995i	$0.348596\pi$
$54$	2.76869			0.376771
$55$	1.27843	+	3.06033i	0.172384	+	0.412655i
$56$	17.3142	−	20.5242i	2.31371	−	2.74267i
$57$			5.02294i			0.665305i
$58$	−11.0186			−1.44682
$59$			6.56737i			0.854999i	0.904016	+	0.427499i	$0.140605\pi$
$59$			6.56737i			0.854999i	−0.904016	+	0.427499i	$0.859395\pi$
$60$	5.66565			0.731433
$61$	−3.39485			−0.434666			−0.217333	−	0.976098i	$-0.569736\pi$
$61$	−3.39485			−0.434666			−0.217333	+	0.976098i	$0.569736\pi$
$62$	15.3524			1.94975
$63$	2.02228	+	1.70599i	0.254783	+	0.214934i
$64$	−38.8043			−4.85054
$65$		−	3.06720i		−	0.380439i
$66$	8.47311	−	3.53959i	1.04297	−	0.435693i
$67$	−15.4919			−1.89264			−0.946320	−	0.323231i	$-0.895231\pi$
$67$	−15.4919			−1.89264			−0.946320	+	0.323231i	$0.895231\pi$
$68$	16.4164			1.99078
$69$		−	6.43703i		−	0.774927i
$70$	5.59906	+	4.72335i	0.669216	+	0.564549i
$71$	8.52531			1.01177			0.505884	−	0.862601i	$-0.331166\pi$
$71$	8.52531			1.01177			0.505884	+	0.862601i	$0.331166\pi$
$72$		−	10.1491i		−	1.19608i
$73$	−2.75799			−0.322798			−0.161399	−	0.986889i	$-0.551601\pi$
$73$	−2.75799			−0.322798			−0.161399	+	0.986889i	$0.551601\pi$
$74$		−	8.41779i		−	0.978548i
$75$			1.00000i			0.115470i
$76$	28.4582			3.26438
$77$	8.36982	+	2.63554i	0.953830	+	0.300347i
$78$	−8.49212			−0.961543
$79$		−	5.94802i		−	0.669205i	−0.942359	−	0.334602i	$-0.891398\pi$
$79$		−	5.94802i		−	0.669205i	0.942359	−	0.334602i	$-0.108602\pi$
$80$		−	16.7683i		−	1.87476i
$81$	1.00000			0.111111
$82$			25.0180i			2.76278i
$83$	−12.6532			−1.38887			−0.694437	−	0.719553i	$-0.744347\pi$
$83$	−12.6532			−1.38887			−0.694437	+	0.719553i	$0.744347\pi$
$84$	9.66554	−	11.4575i	1.05460	−	1.25012i
$85$			2.89753i			0.314281i
$86$	1.75426			0.189166
$87$	−3.97972			−0.426671
$88$	−12.9749	−	31.0595i	−1.38313	−	3.31095i
$89$		−	17.6613i		−	1.87209i	−0.351877	−	0.936046i	$-0.614457\pi$
$89$		−	17.6613i		−	1.87209i	0.351877	−	0.936046i	$-0.385543\pi$
$90$	2.76869			0.291846
$91$	−6.20272	−	5.23260i	−0.650222	−	0.548525i
$92$	−36.4700			−3.80226
$93$	5.54499			0.574989
$94$	−7.13122			−0.735529
$95$			5.02294i			0.515343i
$96$	−26.1282			−2.66670
$97$			3.11539i			0.316320i	0.987413	+	0.158160i	$0.0505562\pi$
$97$			3.11539i			0.316320i	−0.987413	+	0.158160i	$0.949444\pi$
$98$	19.1039	−	3.26488i	1.92978	−	0.329802i
$99$	3.06033	−	1.27843i	0.307575	−	0.128487i
$100$	5.66565			0.566565
$101$	14.5219			1.44498			0.722491	−	0.691380i	$-0.242997\pi$
$101$	14.5219			1.44498			0.722491	+	0.691380i	$0.242997\pi$
$102$	8.02237			0.794333
$103$			16.1032i			1.58670i	0.608769	+	0.793348i	$0.291664\pi$
$103$			16.1032i			1.58670i	−0.608769	+	0.793348i	$0.708336\pi$
$104$			31.1292i			3.05247i
$105$	2.02228	+	1.70599i	0.197354	+	0.166487i
$106$		−	18.4599i		−	1.79298i
$107$			8.53872i			0.825469i	0.910851	+	0.412735i	$0.135426\pi$
$107$			8.53872i			0.825469i	−0.910851	+	0.412735i	$0.864574\pi$
$108$		−	5.66565i		−	0.545178i
$109$			16.4061i			1.57142i	0.618594	+	0.785711i	$0.287702\pi$
$109$			16.4061i			1.57142i	−0.618594	+	0.785711i	$0.712298\pi$
$110$	8.47311	−	3.53959i	0.807879	−	0.337486i
$111$		−	3.04035i		−	0.288577i
$112$	−33.9102	−	28.6066i	−3.20422	−	2.70307i
$113$	−11.3734			−1.06992			−0.534958	−	0.844879i	$-0.679673\pi$
$113$	−11.3734			−1.06992			−0.534958	+	0.844879i	$0.679673\pi$
$114$	13.9070			1.30251
$115$		−	6.43703i		−	0.600256i
$116$			22.5477i			2.09350i
$117$	−3.06720			−0.283562
$118$	18.1830			1.67388
$119$	5.85961	+	4.94315i	0.537150	+	0.453138i
$120$		−	10.1491i		−	0.926479i
$121$	7.73122	−	7.82485i	0.702838	−	0.711350i
$122$			9.39928i			0.850971i
$123$			9.03604i			0.814752i
$124$		−	31.4160i		−	2.82124i
$125$			1.00000i			0.0894427i
$126$	4.72335	−	5.59906i	0.420790	−	0.498804i
$127$			8.38324i			0.743892i	0.928254	+	0.371946i	$0.121309\pi$
$127$			8.38324i			0.743892i	−0.928254	+	0.371946i	$0.878691\pi$
$128$			55.1807i			4.87734i
$129$	0.633605			0.0557858
$130$	−8.49212			−0.744808
$131$	−13.5257			−1.18175			−0.590874	−	0.806764i	$-0.701217\pi$
$131$	−13.5257			−1.18175			−0.590874	+	0.806764i	$0.701217\pi$
$132$	−7.24316	−	17.3388i	−0.630436	−	1.50915i
$133$	10.1578	+	8.56907i	0.880791	+	0.743033i
$134$			42.8924i			3.70534i
$135$	1.00000			0.0860663
$136$		−	29.4072i		−	2.52165i
$137$	5.67534			0.484877			0.242438	−	0.970167i	$-0.422053\pi$
$137$	5.67534			0.484877			0.242438	+	0.970167i	$0.422053\pi$
$138$	−17.8221			−1.51712
$139$	−12.1380			−1.02953			−0.514767	−	0.857330i	$-0.672122\pi$
$139$	−12.1380			−1.02953			−0.514767	+	0.857330i	$0.672122\pi$
$140$	9.66554	−	11.4575i	0.816887	−	0.968338i
$141$	−2.57566			−0.216910
$142$		−	23.6040i		−	1.98080i
$143$	−9.38662	+	3.92120i	−0.784949	+	0.327907i
$144$	−16.7683			−1.39736
$145$	−3.97972			−0.330498
$146$			7.63602i			0.631962i
$147$	6.89996	−	1.17921i	0.569099	−	0.0972598i
$148$	−17.2256			−1.41593
$149$		−	1.95163i		−	0.159884i	−0.996800	−	0.0799419i	$-0.974527\pi$
$149$		−	1.95163i		−	0.159884i	0.996800	−	0.0799419i	$-0.0254735\pi$
$150$	2.76869			0.226063
$151$			4.47601i			0.364253i	0.983275	+	0.182126i	$0.0582980\pi$
$151$			4.47601i			0.364253i	−0.983275	+	0.182126i	$0.941702\pi$
$152$		−	50.9782i		−	4.13488i
$153$	2.89753			0.234252
$154$	7.29699	−	23.1735i	0.588008	−	1.86737i
$155$	5.54499			0.445385
$156$			17.3777i			1.39133i
$157$			4.65071i			0.371167i	0.982629	+	0.185583i	$0.0594175\pi$
$157$			4.65071i			0.371167i	−0.982629	+	0.185583i	$0.940582\pi$
$158$	−16.4682			−1.31014
$159$		−	6.66736i		−	0.528756i
$160$	−26.1282			−2.06562
$161$	−13.0175	−	10.9815i	−1.02592	−	0.865462i
$162$		−	2.76869i		−	0.217529i
$163$	−11.4617			−0.897746			−0.448873	−	0.893596i	$-0.648174\pi$
$163$	−11.4617			−0.897746			−0.448873	+	0.893596i	$0.648174\pi$
$164$	51.1951			3.99766
$165$	3.06033	−	1.27843i	0.238246	−	0.0995259i
$166$			35.0329i			2.71908i
$167$	−17.8526			−1.38147			−0.690736	−	0.723107i	$-0.742713\pi$
$167$	−17.8526			−1.38147			−0.690736	+	0.723107i	$0.742713\pi$
$168$	−20.5242	−	17.3142i	−1.58348	−	1.33582i
$169$	−3.59231			−0.276332
$170$	8.02237			0.615288
$171$	5.02294			0.384114
$172$		−	3.58979i		−	0.273719i
$173$	−15.0847			−1.14687			−0.573435	−	0.819251i	$-0.694389\pi$
$173$	−15.0847			−1.14687			−0.573435	+	0.819251i	$0.694389\pi$
$174$			11.0186i			0.835320i
$175$	2.02228	+	1.70599i	0.152870	+	0.128961i
$176$	−51.3166	+	21.4372i	−3.86814	+	1.61589i
$177$	6.56737			0.493634
$178$	−48.8987			−3.66511
$179$	19.3721			1.44794			0.723968	−	0.689834i	$-0.242316\pi$
$179$	19.3721			1.44794			0.723968	+	0.689834i	$0.242316\pi$
$180$		−	5.66565i		−	0.422293i
$181$			8.70652i			0.647150i	0.946202	+	0.323575i	$0.104885\pi$
$181$			8.70652i			0.647150i	−0.946202	+	0.323575i	$0.895115\pi$
$182$	−14.4874	+	17.1734i	−1.07388	+	1.27298i
$183$			3.39485i			0.250954i
$184$			65.3298i			4.81618i
$185$		−	3.04035i		−	0.223531i
$186$		−	15.3524i		−	1.12569i
$187$	8.86740	−	3.70430i	0.648448	−	0.270885i
$188$			14.5928i			1.06429i
$189$	1.70599	−	2.02228i	0.124092	−	0.147099i
$190$	13.9070			1.00892
$191$	−1.74411			−0.126199			−0.0630995	−	0.998007i	$-0.520099\pi$
$191$	−1.74411			−0.126199			−0.0630995	+	0.998007i	$0.520099\pi$
$192$			38.8043i			2.80046i
$193$		−	10.8394i		−	0.780236i	−0.920765	−	0.390118i	$-0.872434\pi$
$193$		−	10.8394i		−	0.780236i	0.920765	−	0.390118i	$-0.127566\pi$
$194$	8.62556			0.619279
$195$	−3.06720			−0.219646
$196$	−6.68101	−	39.0928i	−0.477215	−	2.79234i
$197$		−	22.3911i		−	1.59530i	−0.603123	−	0.797649i	$-0.706077\pi$
$197$		−	22.3911i		−	1.59530i	0.603123	−	0.797649i	$-0.293923\pi$
$198$	−3.53959	−	8.47311i	−0.251547	−	0.602157i
$199$		−	10.4984i		−	0.744215i	−0.928190	−	0.372108i	$-0.878635\pi$
$199$		−	10.4984i		−	0.744215i	0.928190	−	0.372108i	$-0.121365\pi$
$200$		−	10.1491i		−	0.717648i
$201$			15.4919i			1.09272i
$202$		−	40.2066i		−	2.82893i
$203$	−6.78936	+	8.04810i	−0.476519	+	0.564866i
$204$		−	16.4164i		−	1.14938i
$205$			9.03604i			0.631104i
$206$	44.5848			3.10637
$207$	−6.43703			−0.447404
$208$	51.4318			3.56615
$209$	15.3718	−	6.42149i	1.06329	−	0.444184i
$210$	4.72335	−	5.59906i	0.325942	−	0.386372i
$211$			16.0798i			1.10698i	0.832856	+	0.553490i	$0.186704\pi$
$211$			16.0798i			1.10698i	−0.832856	+	0.553490i	$0.813296\pi$
$212$	−37.7750			−2.59439
$213$		−	8.52531i		−	0.584145i
$214$	23.6411			1.61607
$215$	0.633605			0.0432115
$216$	−10.1491			−0.690557
$217$	9.45969	−	11.2135i	0.642165	−	0.761223i
$218$	45.4235			3.07647
$219$			2.75799i			0.186368i
$220$	−7.24316	−	17.3388i	−0.488334	−	1.16898i
$221$	−8.88729			−0.597824
$222$	−8.41779			−0.564965
$223$			16.8955i			1.13141i	0.824608	+	0.565704i	$0.191395\pi$
$223$			16.8955i			1.13141i	−0.824608	+	0.565704i	$0.808605\pi$
$224$	−44.5744	+	52.8385i	−2.97825	+	3.53042i
$225$	1.00000			0.0666667
$226$			31.4893i			2.09464i
$227$	24.1621			1.60369			0.801846	−	0.597530i	$-0.203851\pi$
$227$	24.1621			1.60369			0.801846	+	0.597530i	$0.203851\pi$
$228$		−	28.4582i		−	1.88469i
$229$			0.806078i			0.0532671i	0.999645	+	0.0266336i	$0.00847873\pi$
$229$			0.806078i			0.0532671i	−0.999645	+	0.0266336i	$0.991521\pi$
$230$	−17.8221			−1.17516
$231$	2.63554	−	8.36982i	0.173406	−	0.550694i
$232$	40.3905			2.65176
$233$			10.0492i			0.658345i	0.944270	+	0.329172i	$0.106770\pi$
$233$			10.0492i			0.658345i	−0.944270	+	0.329172i	$0.893230\pi$
$234$			8.49212i			0.555147i
$235$	−2.57566			−0.168018
$236$		−	37.2085i		−	2.42206i
$237$	−5.94802			−0.386366
$238$	13.6861	−	16.2235i	0.887136	−	1.05161i
$239$			11.9987i			0.776128i	0.921632	+	0.388064i	$0.126856\pi$
$239$			11.9987i			0.776128i	−0.921632	+	0.388064i	$0.873144\pi$
$240$	−16.7683			−1.08239
$241$	0.268330			0.0172847			0.00864234	−	0.999963i	$-0.497249\pi$
$241$	0.268330			0.0172847			0.00864234	+	0.999963i	$0.497249\pi$
$242$	−21.6646	−	21.4054i	−1.39265	−	1.37599i
$243$		−	1.00000i		−	0.0641500i
$244$	19.2340			1.23133
$245$	6.89996	−	1.17921i	0.440822	−	0.0753372i
$246$	25.0180			1.59509
$247$	−15.4063			−0.980282
$248$	−56.2765			−3.57356
$249$			12.6532i			0.801867i
$250$	2.76869			0.175107
$251$		−	11.7091i		−	0.739072i	−0.929216	−	0.369536i	$-0.879517\pi$
$251$		−	11.7091i		−	0.739072i	0.929216	−	0.369536i	$-0.120483\pi$
$252$	−11.4575	−	9.66554i	−0.721756	−	0.608872i
$253$	−19.6994	+	8.22931i	−1.23849	+	0.517372i
$254$	23.2106			1.45636
$255$	2.89753			0.181450
$256$	75.1699			4.69812
$257$			28.6727i			1.78855i	0.447516	+	0.894276i	$0.352309\pi$
$257$			28.6727i			1.78855i	−0.447516	+	0.894276i	$0.647691\pi$
$258$		−	1.75426i		−	0.109215i
$259$	−6.14843	−	5.18680i	−0.382045	−	0.322292i
$260$			17.3777i			1.07772i
$261$			3.97972i			0.246339i
$262$			37.4485i			2.31358i
$263$			9.00084i			0.555016i	0.960723	+	0.277508i	$0.0895084\pi$
$263$			9.00084i			0.555016i	−0.960723	+	0.277508i	$0.910492\pi$
$264$	−31.0595	+	12.9749i	−1.91158	+	0.798550i
$265$		−	6.66736i		−	0.409573i
$266$	23.7251	−	28.1238i	1.45468	−	1.72438i
$267$	−17.6613			−1.08085
$268$	87.7719			5.36152
$269$		−	6.65374i		−	0.405686i	−0.979211	−	0.202843i	$-0.934982\pi$
$269$		−	6.65374i		−	0.405686i	0.979211	−	0.202843i	$-0.0650181\pi$
$270$		−	2.76869i		−	0.168497i
$271$	−15.0988			−0.917188			−0.458594	−	0.888646i	$-0.651647\pi$
$271$	−15.0988			−0.917188			−0.458594	+	0.888646i	$0.651647\pi$
$272$	−48.5868			−2.94601
$273$	−5.23260	+	6.20272i	−0.316691	+	0.375406i
$274$		−	15.7133i		−	0.949273i
$275$	3.06033	−	1.27843i	0.184545	−	0.0770924i
$276$			36.4700i			2.19523i
$277$		−	6.53124i		−	0.392424i	−0.980561	−	0.196212i	$-0.937136\pi$
$277$		−	6.53124i		−	0.392424i	0.980561	−	0.196212i	$-0.0628641\pi$
$278$			33.6065i			2.01558i
$279$		−	5.54499i		−	0.331970i
$280$	−20.5242	−	17.3142i	−1.22656	−	1.03472i
$281$		−	5.05949i		−	0.301824i	−0.988547	−	0.150912i	$-0.951779\pi$
$281$		−	5.05949i		−	0.301824i	0.988547	−	0.150912i	$-0.0482210\pi$
$282$			7.13122i			0.424658i
$283$	−4.57767			−0.272114			−0.136057	−	0.990701i	$-0.543443\pi$
$283$	−4.57767			−0.272114			−0.136057	+	0.990701i	$0.543443\pi$
$284$	−48.3015			−2.86617
$285$	5.02294			0.297533
$286$	10.8566	+	25.9887i	0.641964	+	1.53674i
$287$	18.2734	+	15.4154i	1.07864	+	0.909940i
$288$			26.1282i			1.53962i
$289$	−8.60431			−0.506136
$290$			11.0186i			0.647036i
$291$	3.11539			0.182628
$292$	15.6258			0.914431
$293$	12.9775			0.758155			0.379077	−	0.925365i	$-0.376241\pi$
$293$	12.9775			0.758155			0.379077	+	0.925365i	$0.376241\pi$
$294$	−3.26488	−	19.1039i	−0.190412	−	1.11416i
$295$	6.56737			0.382367
$296$			30.8567i			1.79351i
$297$	−1.27843	−	3.06033i	−0.0741822	−	0.177578i
$298$	−5.40346			−0.313014
$299$	19.7436			1.14180
$300$		−	5.66565i		−	0.327107i
$301$	1.08092	−	1.28133i	0.0623033	−	0.0738544i
$302$	12.3927			0.713120
$303$		−	14.5219i		−	0.834261i
$304$	−84.2263			−4.83071
$305$			3.39485i			0.194388i
$306$		−	8.02237i		−	0.458608i
$307$	1.49201			0.0851537			0.0425768	−	0.999093i	$-0.486443\pi$
$307$	1.49201			0.0851537			0.0425768	+	0.999093i	$0.486443\pi$
$308$	−47.4205	−	14.9320i	−2.70204	−	0.850832i
$309$	16.1032			0.916079
$310$		−	15.3524i		−	0.871956i
$311$		−	18.4951i		−	1.04876i	−0.851484	−	0.524380i	$-0.824297\pi$
$311$		−	18.4951i		−	1.04876i	0.851484	−	0.524380i	$-0.175703\pi$
$312$	31.1292			1.76234
$313$			0.731416i			0.0413421i	0.999786	+	0.0206710i	$0.00658026\pi$
$313$			0.731416i			0.0413421i	−0.999786	+	0.0206710i	$0.993420\pi$
$314$	12.8764			0.726656
$315$	1.70599	−	2.02228i	0.0961215	−	0.113942i
$316$			33.6994i			1.89574i
$317$	4.20879			0.236389			0.118195	−	0.992990i	$-0.462289\pi$
$317$	4.20879			0.236389			0.118195	+	0.992990i	$0.462289\pi$
$318$	−18.4599			−1.03518
$319$	5.08781	+	12.1793i	0.284863	+	0.681907i
$320$			38.8043i			2.16923i
$321$	8.53872			0.476585
$322$	−30.4044	+	36.0413i	−1.69437	+	2.00850i
$323$	14.5541			0.809813
$324$	−5.66565			−0.314759
$325$	−3.06720			−0.170137
$326$			31.7338i			1.75757i
$327$	16.4061			0.907260
$328$		−	91.7074i		−	5.06369i
$329$	−4.39405	+	5.20871i	−0.242252	+	0.287165i
$330$	−3.53959	−	8.47311i	−0.194848	−	0.466429i
$331$	−28.1198			−1.54561			−0.772803	−	0.634646i	$-0.781146\pi$
$331$	−28.1198			−1.54561			−0.772803	+	0.634646i	$0.781146\pi$
$332$	71.6889			3.93444
$333$	−3.04035			−0.166610
$334$			49.4282i			2.70459i
$335$			15.4919i			0.846414i
$336$	−28.6066	+	33.9102i	−1.56062	+	1.84995i
$337$		−	3.00877i		−	0.163898i	−0.996637	−	0.0819491i	$-0.973886\pi$
$337$		−	3.00877i		−	0.163898i	0.996637	−	0.0819491i	$-0.0261145\pi$
$338$			9.94601i			0.540992i
$339$			11.3734i			0.617716i
$340$		−	16.4164i		−	0.890305i
$341$	−7.08890	−	16.9695i	−0.383886	−	0.918950i
$342$		−	13.9070i		−	0.752003i
$343$	9.38655	−	15.9654i	0.506826	−	0.862048i
$344$	−6.43050			−0.346709
$345$	−6.43703			−0.346558
$346$			41.7649i			2.24530i
$347$			34.9667i			1.87711i	0.345126	+	0.938556i	$0.387836\pi$
$347$			34.9667i			1.87711i	−0.345126	+	0.938556i	$0.612164\pi$
$348$	22.5477			1.20869
$349$	8.10030			0.433599			0.216800	−	0.976216i	$-0.430438\pi$
$349$	8.10030			0.433599			0.216800	+	0.976216i	$0.430438\pi$
$350$	4.72335	−	5.59906i	0.252474	−	0.299283i
$351$			3.06720i			0.163715i
$352$	33.4032	+	79.9609i	1.78040	+	4.26193i
$353$		−	4.91000i		−	0.261333i	−0.991426	−	0.130667i	$-0.958288\pi$
$353$		−	4.91000i		−	0.261333i	0.991426	−	0.130667i	$-0.0417117\pi$
$354$		−	18.1830i		−	0.966417i
$355$		−	8.52531i		−	0.452477i
$356$			100.063i			5.30331i
$357$	4.94315	−	5.85961i	0.261619	−	0.310124i
$358$		−	53.6352i		−	2.83471i
$359$		−	35.6577i		−	1.88194i	−0.338488	−	0.940971i	$-0.609915\pi$
$359$		−	35.6577i		−	1.88194i	0.338488	−	0.940971i	$-0.390085\pi$
$360$	−10.1491			−0.534903
$361$	6.22993			0.327891
$362$	24.1057			1.26697
$363$	−7.82485	−	7.73122i	−0.410698	−	0.405784i
$364$	35.1425	+	29.6461i	1.84197	+	1.55388i
$365$			2.75799i			0.144360i
$366$	9.39928			0.491308
$367$		−	0.406243i		−	0.0212057i	−0.999944	−	0.0106029i	$-0.996625\pi$
$367$		−	0.406243i		−	0.0212057i	0.999944	−	0.0106029i	$-0.00337506\pi$
$368$	107.938			5.62667
$369$	9.03604			0.470397
$370$	−8.41779			−0.437620
$371$	−13.4832	−	11.3744i	−0.700015	−	0.590531i
$372$	−31.4160			−1.62884
$373$		−	11.1314i		−	0.576361i	−0.957576	−	0.288180i	$-0.906950\pi$
$373$		−	11.1314i		−	0.576361i	0.957576	−	0.288180i	$-0.0930502\pi$
$374$	−10.2561	−	24.5511i	−0.530328	−	1.26951i
$375$	1.00000			0.0516398
$376$	26.1406			1.34810
$377$		−	12.2066i		−	0.628671i
$378$	−5.59906	−	4.72335i	−0.287985	−	0.242943i
$379$	−1.14600			−0.0588660			−0.0294330	−	0.999567i	$-0.509370\pi$
$379$	−1.14600			−0.0588660			−0.0294330	+	0.999567i	$0.509370\pi$
$380$		−	28.4582i		−	1.45988i
$381$	8.38324			0.429486
$382$			4.82889i			0.247068i
$383$		−	33.0417i		−	1.68835i	−0.536066	−	0.844176i	$-0.680090\pi$
$383$		−	33.0417i		−	1.68835i	0.536066	−	0.844176i	$-0.319910\pi$
$384$	55.1807			2.81593
$385$	2.63554	−	8.36982i	0.134319	−	0.426566i
$386$	−30.0109			−1.52752
$387$		−	0.633605i		−	0.0322080i
$388$		−	17.6507i		−	0.896080i
$389$	−10.9380			−0.554580			−0.277290	−	0.960786i	$-0.589436\pi$
$389$	−10.9380			−0.554580			−0.277290	+	0.960786i	$0.589436\pi$
$390$			8.49212i			0.430015i
$391$	−18.6515			−0.943246
$392$	−70.0282	+	11.9679i	−3.53696	+	0.604471i
$393$			13.5257i			0.682282i
$394$	−61.9940			−3.12321
$395$	−5.94802			−0.299277
$396$	−17.3388	+	7.24316i	−0.871306	+	0.363982i
$397$		−	30.0808i		−	1.50971i	−0.655892	−	0.754855i	$-0.727707\pi$
$397$		−	30.0808i		−	1.50971i	0.655892	−	0.754855i	$-0.272293\pi$
$398$	−29.0670			−1.45700
$399$	8.56907	−	10.1578i	0.428990	−	0.508525i
$400$	−16.7683			−0.838417
$401$	−12.7293			−0.635671			−0.317835	−	0.948146i	$-0.602956\pi$
$401$	−12.7293			−0.635671			−0.317835	+	0.948146i	$0.602956\pi$
$402$	42.8924			2.13928
$403$			17.0076i			0.847208i
$404$	−82.2760			−4.09339
$405$		−	1.00000i		−	0.0496904i
$406$	22.2827	+	18.7976i	1.10587	+	0.932911i
$407$	−9.30446	+	3.88688i	−0.461205	+	0.192666i
$408$	−29.4072			−1.45588
$409$	−20.3823			−1.00784			−0.503920	−	0.863750i	$-0.668109\pi$
$409$	−20.3823			−1.00784			−0.503920	+	0.863750i	$0.668109\pi$
$410$	25.0180			1.23555
$411$		−	5.67534i		−	0.279944i
$412$		−	91.2352i		−	4.49483i
$413$	11.2039	−	13.2810i	0.551306	−	0.653518i
$414$			17.8221i			0.875910i
$415$			12.6532i			0.621124i
$416$		−	80.1403i		−	3.92920i
$417$			12.1380i			0.594402i
$418$	−17.7791	−	42.5599i	−0.869606	−	2.08167i
$419$		−	37.9496i		−	1.85396i	−0.375110	−	0.926980i	$-0.622395\pi$
$419$		−	37.9496i		−	1.85396i	0.375110	−	0.926980i	$-0.377605\pi$
$420$	−11.4575	−	9.66554i	−0.559070	−	0.471630i
$421$	−19.4168			−0.946318			−0.473159	−	0.880977i	$-0.656886\pi$
$421$	−19.4168			−0.946318			−0.473159	+	0.880977i	$0.656886\pi$
$422$	44.5200			2.16720
$423$			2.57566i			0.125233i
$424$			67.6675i			3.28622i
$425$	2.89753			0.140551
$426$	−23.6040			−1.14362
$427$	6.86532	+	5.79157i	0.332236	+	0.280274i
$428$		−	48.3774i		−	2.33841i
$429$	3.92120	+	9.38662i	0.189317	+	0.453190i
$430$		−	1.75426i		−	0.0845978i
$431$		−	1.83030i		−	0.0881623i	−0.999028	−	0.0440812i	$-0.985964\pi$
$431$		−	1.83030i		−	0.0881623i	0.999028	−	0.0440812i	$-0.0140360\pi$
$432$			16.7683i			0.806767i
$433$			39.1465i			1.88126i	0.339430	+	0.940631i	$0.389766\pi$
$433$			39.1465i			1.88126i	−0.339430	+	0.940631i	$0.610234\pi$
$434$	−31.0468	−	26.1910i	−1.49029	−	1.25721i
$435$			3.97972i			0.190813i
$436$		−	92.9514i		−	4.45156i
$437$	−32.3328			−1.54669
$438$	7.63602			0.364863
$439$	−20.9880			−1.00170			−0.500851	−	0.865534i	$-0.666980\pi$
$439$	−20.9880			−1.00170			−0.500851	+	0.865534i	$0.666980\pi$
$440$	−31.0595	+	12.9749i	−1.48070	+	0.618554i
$441$	−1.17921	−	6.89996i	−0.0561530	−	0.328570i
$442$			24.6062i			1.17040i
$443$	−41.7281			−1.98256			−0.991280	−	0.131770i	$-0.957934\pi$
$443$	−41.7281			−1.98256			−0.991280	+	0.131770i	$0.957934\pi$
$444$			17.2256i			0.817489i
$445$	−17.6613			−0.837225
$446$	46.7785			2.21503
$447$	−1.95163			−0.0923090
$448$	78.4731	+	66.1997i	3.70750	+	3.12764i
$449$	5.80523			0.273966			0.136983	−	0.990573i	$-0.456259\pi$
$449$	5.80523			0.273966			0.136983	+	0.990573i	$0.456259\pi$
$450$		−	2.76869i		−	0.130517i
$451$	27.6532	−	11.5520i	1.30214	−	0.543961i
$452$	64.4376			3.03089
$453$	4.47601			0.210301
$454$		−	66.8973i		−	3.13965i
$455$	−5.23260	+	6.20272i	−0.245308	+	0.290788i
$456$	−50.9782			−2.38727
$457$		−	28.0543i		−	1.31233i	−0.754620	−	0.656163i	$-0.772179\pi$
$457$		−	28.0543i		−	1.31233i	0.754620	−	0.656163i	$-0.227821\pi$
$458$	2.23178			0.104284
$459$		−	2.89753i		−	0.135245i
$460$			36.4700i			1.70042i
$461$	−38.4121			−1.78903			−0.894516	−	0.447037i	$-0.852479\pi$
$461$	−38.4121			−1.78903			−0.894516	+	0.447037i	$0.852479\pi$
$462$	−23.1735	−	7.29699i	−1.07813	−	0.339487i
$463$	−33.0290			−1.53499			−0.767493	−	0.641057i	$-0.778496\pi$
$463$	−33.0290			−1.53499			−0.767493	+	0.641057i	$0.778496\pi$
$464$		−	66.7333i		−	3.09802i
$465$		−	5.54499i		−	0.257143i
$466$	27.8231			1.28888
$467$			5.17411i			0.239429i	0.992808	+	0.119715i	$0.0381980\pi$
$467$			5.17411i			0.239429i	−0.992808	+	0.119715i	$0.961802\pi$
$468$	17.3777			0.803283
$469$	31.3290	+	26.4290i	1.44664	+	1.22038i
$470$			7.13122i			0.328939i
$471$	4.65071			0.214293
$472$	−66.6527			−3.06794
$473$	−0.810022	−	1.93904i	−0.0372448	−	0.0891571i
$474$			16.4682i			0.756411i
$475$	5.02294			0.230468
$476$	−33.1985	−	28.0062i	−1.52165	−	1.28366i
$477$	−6.66736			−0.305277
$478$	33.2206			1.51947
$479$	−4.02122			−0.183734			−0.0918672	−	0.995771i	$-0.529284\pi$
$479$	−4.02122			−0.183734			−0.0918672	+	0.995771i	$0.529284\pi$
$480$			26.1282i			1.19258i
$481$	9.32534			0.425199
$482$		−	0.742924i		−	0.0338393i
$483$	−10.9815	+	13.0175i	−0.499675	+	0.592315i
$484$	−43.8024	+	44.3329i	−1.99102	+	2.01513i
$485$	3.11539			0.141463
$486$	−2.76869			−0.125590
$487$	−3.99432			−0.181000			−0.0905000	−	0.995896i	$-0.528847\pi$
$487$	−3.99432			−0.181000			−0.0905000	+	0.995896i	$0.528847\pi$
$488$		−	34.4545i		−	1.55968i
$489$			11.4617i			0.518314i
$490$	−3.26488	−	19.1039i	−0.147492	−	0.863025i
$491$			1.45183i			0.0655200i	0.999463	+	0.0327600i	$0.0104297\pi$
$491$			1.45183i			0.0655200i	−0.999463	+	0.0327600i	$0.989570\pi$
$492$		−	51.1951i		−	2.30805i
$493$			11.5314i			0.519347i
$494$			42.6554i			1.91916i
$495$	−1.27843	−	3.06033i	−0.0574613	−	0.137552i
$496$			92.9803i			4.17494i
$497$	−17.2405	−	14.5441i	−0.773344	−	0.652391i
$498$	35.0329			1.56986
$499$	17.6780			0.791378			0.395689	−	0.918385i	$-0.370506\pi$
$499$	17.6780			0.791378			0.395689	+	0.918385i	$0.370506\pi$
$500$		−	5.66565i		−	0.253376i
$501$			17.8526i			0.797593i
$502$	−32.4189			−1.44693
$503$	33.8070			1.50738			0.753691	−	0.657229i	$-0.228272\pi$
$503$	33.8070			1.50738			0.753691	+	0.657229i	$0.228272\pi$
$504$	−17.3142	+	20.5242i	−0.771235	+	0.914222i
$505$		−	14.5219i		−	0.646216i
$506$	22.7844	+	54.5416i	1.01289	+	2.42467i
$507$			3.59231i			0.159540i
$508$		−	47.4965i		−	2.10732i
$509$		−	9.54760i		−	0.423190i	−0.977357	−	0.211595i	$-0.932134\pi$
$509$		−	9.54760i		−	0.423190i	0.977357	−	0.211595i	$-0.0678658\pi$
$510$		−	8.02237i		−	0.355237i
$511$	5.57742	+	4.70509i	0.246730	+	0.208141i
$512$		−	97.7607i		−	4.32045i
$513$		−	5.02294i		−	0.221768i
$514$	79.3858			3.50156
$515$	16.1032			0.709592
$516$	−3.58979			−0.158032
$517$	3.29281	+	7.88238i	0.144818	+	0.346667i
$518$	−14.3606	+	17.0231i	−0.630970	+	0.747952i
$519$			15.0847i			0.662145i
$520$	31.1292			1.36510
$521$		−	17.0697i		−	0.747838i	−0.927461	−	0.373919i	$-0.878014\pi$
$521$		−	17.0697i		−	0.747838i	0.927461	−	0.373919i	$-0.121986\pi$
$522$	11.0186			0.482272
$523$	−4.45348			−0.194737			−0.0973686	−	0.995248i	$-0.531043\pi$
$523$	−4.45348			−0.194737			−0.0973686	+	0.995248i	$0.531043\pi$
$524$	76.6320			3.34769
$525$	1.70599	−	2.02228i	0.0744554	−	0.0882594i
$526$	24.9206			1.08659
$527$		−	16.0668i		−	0.699880i
$528$	21.4372	+	51.3166i	0.932934	+	2.23327i
$529$	18.4353			0.801535
$530$	−18.4599			−0.801845
$531$		−	6.56737i		−	0.285000i
$532$	−57.5505	−	48.5494i	−2.49513	−	2.10488i
$533$	−27.7153			−1.20048
$534$			48.8987i			2.11605i
$535$	8.53872			0.369161
$536$		−	157.229i		−	6.79124i
$537$		−	19.3721i		−	0.835966i
$538$	−18.4222			−0.794236
$539$	−12.4299	−	19.6086i	−0.535394	−	0.844602i
$540$	−5.66565			−0.243811
$541$		−	27.2822i		−	1.17296i	−0.809965	−	0.586478i	$-0.800514\pi$
$541$		−	27.2822i		−	1.17296i	0.809965	−	0.586478i	$-0.199486\pi$
$542$			41.8040i			1.79564i
$543$	8.70652			0.373632
$544$			75.7073i			3.24592i
$545$	16.4061			0.702761
$546$	17.1734	+	14.4874i	0.734955	+	0.620006i
$547$			9.24749i			0.395394i	0.980263	+	0.197697i	$0.0633462\pi$
$547$			9.24749i			0.395394i	−0.980263	+	0.197697i	$0.936654\pi$
$548$	−32.1545			−1.37357
$549$	3.39485			0.144889
$550$	−3.53959	−	8.47311i	−0.150928	−	0.361294i
$551$			19.9899i			0.851599i
$552$	65.3298			2.78062
$553$	−10.1473	+	12.0286i	−0.431505	+	0.511506i
$554$	−18.0830			−0.768273
$555$	−3.04035			−0.129056
$556$	68.7699			2.91649
$557$		−	20.7279i		−	0.878270i	−0.898421	−	0.439135i	$-0.855285\pi$
$557$		−	20.7279i		−	0.878270i	0.898421	−	0.439135i	$-0.144715\pi$
$558$	−15.3524			−0.649918
$559$			1.94339i			0.0821967i
$560$	−28.6066	+	33.9102i	−1.20885	+	1.43297i
$561$	−3.70430	−	8.86740i	−0.156396	−	0.374382i
$562$	−14.0082			−0.590899
$563$	−8.75854			−0.369128			−0.184564	−	0.982820i	$-0.559087\pi$
$563$	−8.75854			−0.369128			−0.184564	+	0.982820i	$0.559087\pi$
$564$	14.5928			0.614469
$565$			11.3734i			0.478481i
$566$			12.6742i			0.532735i
$567$	−2.02228	−	1.70599i	−0.0849277	−	0.0716447i
$568$			86.5240i			3.63047i
$569$		−	38.8408i		−	1.62829i	−0.580661	−	0.814146i	$-0.697206\pi$
$569$		−	38.8408i		−	1.62829i	0.580661	−	0.814146i	$-0.302794\pi$
$570$		−	13.9070i		−	0.582499i
$571$			12.3624i			0.517349i	0.965965	+	0.258675i	$0.0832857\pi$
$571$			12.3624i			0.517349i	−0.965965	+	0.258675i	$0.916714\pi$
$572$	53.1814	−	22.2162i	2.22362	−	0.928905i
$573$			1.74411i			0.0728610i
$574$	42.6804	−	50.5933i	1.78145	−	2.11173i
$575$	−6.43703			−0.268443
$576$	38.8043			1.61685
$577$		−	4.03645i		−	0.168040i	−0.996464	−	0.0840198i	$-0.973224\pi$
$577$		−	4.03645i		−	0.168040i	0.996464	−	0.0840198i	$-0.0267759\pi$
$578$			23.8227i			0.990893i
$579$	−10.8394			−0.450470
$580$	22.5477			0.936244
$581$	25.5884	+	21.5863i	1.06158	+	0.895550i
$582$		−	8.62556i		−	0.357541i
$583$	−20.4043	+	8.52377i	−0.845060	+	0.353018i
$584$		−	27.9910i		−	1.15828i
$585$			3.06720i			0.126813i
$586$		−	35.9308i		−	1.48429i
$587$		−	19.6929i		−	0.812812i	−0.913693	−	0.406406i	$-0.866782\pi$
$587$		−	19.6929i		−	0.812812i	0.913693	−	0.406406i	$-0.133218\pi$
$588$	−39.0928	+	6.68101i	−1.61216	+	0.275520i
$589$		−	27.8522i		−	1.14763i
$590$		−	18.1830i		−	0.748583i
$591$	−22.3911			−0.921045
$592$	50.9816			2.09533
$593$	28.0963			1.15378			0.576889	−	0.816823i	$-0.304267\pi$
$593$	28.0963			1.15378			0.576889	+	0.816823i	$0.304267\pi$
$594$	−8.47311	+	3.53959i	−0.347656	+	0.145231i
$595$	4.94315	−	5.85961i	0.202649	−	0.240221i
$596$			11.0573i			0.452923i
$597$	−10.4984			−0.429673
$598$		−	54.6640i		−	2.23538i
$599$	−5.60992			−0.229215			−0.114608	−	0.993411i	$-0.536561\pi$
$599$	−5.60992			−0.229215			−0.114608	+	0.993411i	$0.536561\pi$
$600$	−10.1491			−0.414334
$601$	−21.3762			−0.871954			−0.435977	−	0.899958i	$-0.643597\pi$
$601$	−21.3762			−0.871954			−0.435977	+	0.899958i	$0.643597\pi$
$602$	−3.54760	−	2.99274i	−0.144589	−	0.121975i
$603$	15.4919			0.630880
$604$		−	25.3595i		−	1.03187i
$605$	−7.82485	−	7.73122i	−0.318125	−	0.314319i
$606$	−40.2066			−1.63328
$607$	−3.99325			−0.162081			−0.0810406	−	0.996711i	$-0.525824\pi$
$607$	−3.99325			−0.162081			−0.0810406	+	0.996711i	$0.525824\pi$
$608$			131.240i			5.32250i
$609$	8.04810	+	6.78936i	0.326126	+	0.275119i
$610$	9.39928			0.380566
$611$		−	7.90006i		−	0.319602i
$612$	−16.4164			−0.663594
$613$			7.71304i			0.311527i	0.987794	+	0.155763i	$0.0497837\pi$
$613$			7.71304i			0.311527i	−0.987794	+	0.155763i	$0.950216\pi$
$614$		−	4.13092i		−	0.166711i
$615$	9.03604			0.364368
$616$	−26.7482	+	84.9459i	−1.07772	+	3.42257i
$617$	18.4221			0.741645			0.370823	−	0.928704i	$-0.379076\pi$
$617$	18.4221			0.741645			0.370823	+	0.928704i	$0.379076\pi$
$618$		−	44.5848i		−	1.79346i
$619$		−	2.70637i		−	0.108778i	−0.998520	−	0.0543891i	$-0.982679\pi$
$619$		−	2.70637i		−	0.108778i	0.998520	−	0.0543891i	$-0.0173211\pi$
$620$	−31.4160			−1.26170
$621$			6.43703i			0.258309i
$622$	−51.2072			−2.05322
$623$	−30.1299	+	35.7160i	−1.20713	+	1.43093i
$624$		−	51.4318i		−	2.05892i
$625$	1.00000			0.0400000
$626$	2.02506			0.0809379
$627$	−6.42149	−	15.3718i	−0.256450	−	0.613892i
$628$		−	26.3493i		−	1.05145i
$629$	−8.80950			−0.351258
$630$	−5.59906	−	4.72335i	−0.223072	−	0.188183i
$631$	−18.9646			−0.754968			−0.377484	−	0.926016i	$-0.623211\pi$
$631$	−18.9646			−0.754968			−0.377484	+	0.926016i	$0.623211\pi$
$632$	60.3669			2.40127
$633$	16.0798			0.639115
$634$		−	11.6528i		−	0.462793i
$635$	8.38324			0.332679
$636$			37.7750i			1.49787i
$637$	3.61688	+	21.1635i	0.143306	+	0.838529i
$638$	33.7206	−	14.0866i	1.33501	−	0.557693i
$639$	−8.52531			−0.337256
$640$	55.1807			2.18121
$641$	−40.0747			−1.58285			−0.791427	−	0.611263i	$-0.790662\pi$
$641$	−40.0747			−1.58285			−0.791427	+	0.611263i	$0.790662\pi$
$642$		−	23.6411i		−	0.933039i
$643$		−	16.8813i		−	0.665732i	−0.942974	−	0.332866i	$-0.891984\pi$
$643$		−	16.8813i		−	0.665732i	0.942974	−	0.332866i	$-0.108016\pi$
$644$	73.7524	+	62.2173i	2.90625	+	2.45171i
$645$		−	0.633605i		−	0.0249482i
$646$		−	40.2959i		−	1.58542i
$647$			26.8210i			1.05444i	0.849728	+	0.527221i	$0.176766\pi$
$647$			26.8210i			1.05444i	−0.849728	+	0.527221i	$0.823234\pi$
$648$			10.1491i			0.398693i
$649$	−8.39594	−	20.0983i	−0.329570	−	0.788928i
$650$			8.49212i			0.333088i
$651$	−11.2135	−	9.45969i	−0.439492	−	0.370754i
$652$	64.9378			2.54316
$653$	4.70331			0.184055			0.0920274	−	0.995756i	$-0.470665\pi$
$653$	4.70331			0.184055			0.0920274	+	0.995756i	$0.470665\pi$
$654$		−	45.4235i		−	1.77620i
$655$			13.5257i			0.528493i
$656$	−151.519			−5.91583
$657$	2.75799			0.107599
$658$	14.4213	+	12.1658i	0.562201	+	0.474271i
$659$			10.6253i			0.413901i	0.978351	+	0.206951i	$0.0663539\pi$
$659$			10.6253i			0.413901i	−0.978351	+	0.206951i	$0.933646\pi$
$660$	−17.3388	+	7.24316i	−0.674910	+	0.281940i
$661$		−	2.15842i		−	0.0839530i	−0.999119	−	0.0419765i	$-0.986635\pi$
$661$		−	2.15842i		−	0.0839530i	0.999119	−	0.0419765i	$-0.0133655\pi$
$662$			77.8552i			3.02593i
$663$			8.88729i			0.345154i
$664$		−	128.419i		−	4.98361i
$665$	8.56907	−	10.1578i	0.332294	−	0.393902i
$666$			8.41779i			0.326183i
$667$		−	25.6176i		−	0.991916i
$668$	101.146			3.91347
$669$	16.8955			0.653219
$670$	42.8924			1.65708
$671$	10.3893	−	4.34008i	0.401076	−	0.167547i
$672$	52.8385	+	44.5744i	2.03829	+	1.71950i
$673$			1.84197i			0.0710029i	0.999370	+	0.0355014i	$0.0113028\pi$
$673$			1.84197i			0.0710029i	−0.999370	+	0.0355014i	$0.988697\pi$
$674$	−8.33036			−0.320873
$675$		−	1.00000i		−	0.0384900i
$676$	20.3528			0.782800
$677$	25.5724			0.982829			0.491415	−	0.870926i	$-0.336480\pi$
$677$	25.5724			0.982829			0.491415	+	0.870926i	$0.336480\pi$
$678$	31.4893			1.20934
$679$	5.31482	−	6.30019i	0.203964	−	0.241779i
$680$	−29.4072			−1.12772
$681$		−	24.1621i		−	0.925892i
$682$	−46.9833	+	19.6270i	−1.79908	+	0.751556i
$683$	−43.0692			−1.64800			−0.823999	−	0.566592i	$-0.808262\pi$
$683$	−43.0692			−1.64800			−0.823999	+	0.566592i	$0.808262\pi$
$684$	−28.4582			−1.08813
$685$		−	5.67534i		−	0.216843i
$686$	−44.2032	−	25.9885i	−1.68768	−	0.992244i
$687$	0.806078			0.0307538
$688$			10.6245i			0.405055i
$689$	20.4501			0.779086
$690$			17.8221i			0.678477i
$691$			38.4696i			1.46345i	0.681599	+	0.731726i	$0.261285\pi$
$691$			38.4696i			1.46345i	−0.681599	+	0.731726i	$0.738715\pi$
$692$	85.4648			3.24888
$693$	−8.36982	−	2.63554i	−0.317943	−	0.100116i
$694$	96.8121			3.67494
$695$			12.1380i			0.460422i
$696$		−	40.3905i		−	1.53100i
$697$	26.1822			0.991721
$698$		−	22.4272i		−	0.848884i
$699$	10.0492			0.380096
$700$	−11.4575	−	9.66554i	−0.433054	−	0.365323i
$701$		−	40.2754i		−	1.52118i	−0.649231	−	0.760591i	$-0.724909\pi$
$701$		−	40.2754i		−	1.52118i	0.649231	−	0.760591i	$-0.275091\pi$
$702$	8.49212			0.320514
$703$	−15.2715			−0.575975
$704$	118.754	−	49.6087i	4.47571	−	1.86970i
$705$			2.57566i			0.0970051i
$706$	−13.5943			−0.511628
$707$	−29.3673	−	24.7742i	−1.10447	−	0.931728i
$708$	−37.2085			−1.39838
$709$	39.2756			1.47503			0.737513	−	0.675333i	$-0.236000\pi$
$709$	39.2756			1.47503			0.737513	+	0.675333i	$0.236000\pi$
$710$	−23.6040			−0.885841
$711$			5.94802i			0.223068i
$712$	179.246			6.71751
$713$			35.6933i			1.33672i
$714$	−16.2235	−	13.6861i	−0.607148	−	0.512188i
$715$	3.92120	+	9.38662i	0.146645	+	0.351040i
$716$	−109.755			−4.10175
$717$	11.9987			0.448098
$718$	−98.7252			−3.68439
$719$		−	25.4918i		−	0.950682i	−0.879802	−	0.475341i	$-0.842325\pi$
$719$		−	25.4918i		−	0.950682i	0.879802	−	0.475341i	$-0.157675\pi$
$720$			16.7683i			0.624919i
$721$	27.4719	−	32.5651i	1.02311	−	1.21279i
$722$		−	17.2488i		−	0.641932i
$723$		−	0.268330i		−	0.00997931i
$724$		−	49.3281i		−	1.83327i
$725$			3.97972i			0.147803i
$726$	−21.4054	+	21.6646i	−0.794428	+	0.804049i
$727$		−	21.7928i		−	0.808250i	−0.914704	−	0.404125i	$-0.867576\pi$
$727$		−	21.7928i		−	0.808250i	0.914704	−	0.404125i	$-0.132424\pi$
$728$	53.1060	−	62.9518i	1.96824	−	2.33315i
$729$	−1.00000			−0.0370370
$730$	7.63602			0.282622
$731$		−	1.83589i		−	0.0679029i
$732$		−	19.2340i		−	0.710910i
$733$	35.7601			1.32083			0.660414	−	0.750901i	$-0.270381\pi$
$733$	35.7601			1.32083			0.660414	+	0.750901i	$0.270381\pi$
$734$	−1.12476			−0.0415157
$735$	−1.17921	−	6.89996i	−0.0434959	−	0.254509i
$736$		−	168.188i		−	6.19949i
$737$	47.4104	−	19.8054i	1.74638	−	0.729541i
$738$		−	25.0180i		−	0.920925i
$739$			28.8289i			1.06049i	0.847845	+	0.530244i	$0.177900\pi$
$739$			28.8289i			1.06049i	−0.847845	+	0.530244i	$0.822100\pi$
$740$			17.2256i			0.633224i
$741$			15.4063i			0.565966i
$742$	−31.4923	+	37.3310i	−1.15612	+	1.37046i
$743$		−	36.8388i		−	1.35149i	−0.737137	−	0.675743i	$-0.763823\pi$
$743$		−	36.8388i		−	1.35149i	0.737137	−	0.675743i	$-0.236177\pi$
$744$			56.2765i			2.06320i
$745$	−1.95163			−0.0715022
$746$	−30.8193			−1.12838
$747$	12.6532			0.462958
$748$	−50.2396	+	20.9873i	−1.83694	+	0.767371i
$749$	14.5670	−	17.2677i	0.532265	−	0.630947i
$750$		−	2.76869i		−	0.101098i
$751$	18.5200			0.675804			0.337902	−	0.941181i	$-0.390283\pi$
$751$	18.5200			0.675804			0.337902	+	0.941181i	$0.390283\pi$
$752$		−	43.1896i		−	1.57496i
$753$	−11.7091			−0.426703
$754$	−33.7963			−1.23079
$755$	4.47601			0.162899
$756$	−9.66554	+	11.4575i	−0.351532	+	0.416706i
$757$	−25.4733			−0.925844			−0.462922	−	0.886399i	$-0.653199\pi$
$757$	−25.4733			−0.925844			−0.462922	+	0.886399i	$0.653199\pi$
$758$			3.17292i			0.115246i
$759$	8.22931	+	19.6994i	0.298705	+	0.715043i
$760$	−50.9782			−1.84917
$761$	17.8374			0.646607			0.323303	−	0.946295i	$-0.395207\pi$
$761$	17.8374			0.646607			0.323303	+	0.946295i	$0.395207\pi$
$762$		−	23.2106i		−	0.840831i
$763$	27.9886	−	33.1777i	1.01326	−	1.20111i
$764$	9.88150			0.357500
$765$		−	2.89753i		−	0.104760i
$766$	−91.4823			−3.30539
$767$			20.1434i			0.727336i
$768$		−	75.1699i		−	2.71246i
$769$	8.27910			0.298552			0.149276	−	0.988796i	$-0.452306\pi$
$769$	8.27910			0.298552			0.149276	+	0.988796i	$0.452306\pi$
$770$	−23.1735	−	7.29699i	−0.835114	−	0.262965i
$771$	28.6727			1.03262
$772$			61.4122i			2.21027i
$773$		−	8.18156i		−	0.294270i	−0.989116	−	0.147135i	$-0.952995\pi$
$773$		−	8.18156i		−	0.294270i	0.989116	−	0.147135i	$-0.0470052\pi$
$774$	−1.75426			−0.0630555
$775$		−	5.54499i		−	0.199182i
$776$	−31.6183			−1.13503
$777$	−5.18680	+	6.14843i	−0.186075	+	0.220574i
$778$			30.2840i			1.08573i
$779$	45.3875			1.62617
$780$	17.3777			0.622220
$781$	−26.0903	+	10.8990i	−0.933583	+	0.389998i
$782$			51.6402i			1.84665i
$783$	3.97972			0.142224
$784$	19.7734	+	115.701i	0.706194	+	4.13217i
$785$	4.65071			0.165991
$786$	37.4485			1.33575
$787$	36.2400			1.29182			0.645908	−	0.763415i	$-0.276479\pi$
$787$	36.2400			1.29182			0.645908	+	0.763415i	$0.276479\pi$
$788$			126.860i			4.51920i
$789$	9.00084			0.320438
$790$			16.4682i			0.585914i
$791$	23.0001	+	19.4028i	0.817790	+	0.689885i
$792$	12.9749	+	31.0595i	0.461043	+	1.10365i
$793$	−10.4127			−0.369764
$794$	−83.2844			−2.95565
$795$	−6.66736			−0.236467
$796$			59.4806i			2.10823i
$797$			31.9640i			1.13222i	0.824328	+	0.566112i	$0.191553\pi$
$797$			31.9640i			1.13222i	−0.824328	+	0.566112i	$0.808447\pi$
$798$	−28.1238	−	23.7251i	−0.995570	−	0.839860i
$799$			7.46307i			0.264024i
$800$			26.1282i			0.923772i
$801$			17.6613i			0.624031i
$802$			35.2435i			1.24449i
$803$	8.44035	−	3.52590i	0.297854	−	0.124426i
$804$		−	87.7719i		−	3.09548i
$805$	−10.9815	+	13.0175i	−0.387047	+	0.458805i
$806$	47.0887			1.65863
$807$	−6.65374			−0.234223
$808$			147.384i			5.18494i
$809$			4.83423i			0.169963i	0.996383	+	0.0849813i	$0.0270831\pi$
$809$			4.83423i			0.169963i	−0.996383	+	0.0849813i	$0.972917\pi$
$810$	−2.76869			−0.0972819
$811$	−53.1939			−1.86789			−0.933945	−	0.357417i	$-0.883658\pi$
$811$	−53.1939			−1.86789			−0.933945	+	0.357417i	$0.883658\pi$
$812$	38.4662	−	45.5978i	1.34990	−	1.60017i
$813$			15.0988i			0.529539i
$814$	10.7616	+	25.7612i	0.377193	+	0.902929i
$815$			11.4617i			0.401484i
$816$			48.5868i			1.70088i
$817$		−	3.18256i		−	0.111344i
$818$			56.4323i			1.97311i
$819$	6.20272	+	5.23260i	0.216741	+	0.182842i
$820$		−	51.1951i		−	1.78781i
$821$		−	4.38062i		−	0.152885i	−0.997074	−	0.0764423i	$-0.975644\pi$
$821$		−	4.38062i		−	0.152885i	0.997074	−	0.0764423i	$-0.0243561\pi$
$822$	−15.7133			−0.548063
$823$	−32.8113			−1.14373			−0.571866	−	0.820347i	$-0.693780\pi$
$823$	−32.8113			−1.14373			−0.571866	+	0.820347i	$0.693780\pi$
$824$	−163.432			−5.69344
$825$	−1.27843	−	3.06033i	−0.0445093	−	0.106547i
$826$	−36.7711	−	31.0200i	−1.27943	−	1.07932i
$827$			25.5192i			0.887391i	0.896178	+	0.443695i	$0.146333\pi$
$827$			25.5192i			0.887391i	−0.896178	+	0.443695i	$0.853667\pi$
$828$	36.4700			1.26742
$829$			42.7654i			1.48530i	0.669678	+	0.742651i	$0.266432\pi$
$829$			42.7654i			1.48530i	−0.669678	+	0.742651i	$0.733568\pi$
$830$	35.0329			1.21601
$831$	−6.53124			−0.226566
$832$	−119.020			−4.12629
$833$	−3.41681	−	19.9929i	−0.118385	−	0.692711i
$834$	33.6065			1.16370
$835$			17.8526i			0.617813i
$836$	−87.0916	+	36.3820i	−3.01213	+	1.25830i
$837$	−5.54499			−0.191663
$838$	−105.071			−3.62961
$839$		−	35.6166i		−	1.22962i	−0.788675	−	0.614810i	$-0.789233\pi$
$839$		−	35.6166i		−	1.22962i	0.788675	−	0.614810i	$-0.210767\pi$
$840$	−17.3142	+	20.5242i	−0.597396	+	0.708153i
$841$	13.1618			0.453855
$842$			53.7592i			1.85266i
$843$	−5.05949			−0.174258
$844$		−	91.1026i		−	3.13588i
$845$			3.59231i			0.123579i
$846$	7.13122			0.245176
$847$	−28.9838	+	2.63465i	−0.995894	+	0.0905277i
$848$	111.800			3.83924
$849$			4.57767i			0.157105i
$850$		−	8.02237i		−	0.275165i
$851$	19.5708			0.670878
$852$			48.3015i			1.65478i
$853$	42.3298			1.44934			0.724672	−	0.689094i	$-0.241991\pi$
$853$	42.3298			1.44934			0.724672	+	0.689094i	$0.241991\pi$
$854$	16.0351	−	19.0080i	0.548708	−	0.650439i
$855$		−	5.02294i		−	0.171781i
$856$	−86.6601			−2.96198
$857$	−13.1663			−0.449751			−0.224876	−	0.974387i	$-0.572198\pi$
$857$	−13.1663			−0.449751			−0.224876	+	0.974387i	$0.572198\pi$
$858$	25.9887	−	10.8566i	0.887239	−	0.370638i
$859$		−	18.7858i		−	0.640964i	−0.947255	−	0.320482i	$-0.896155\pi$
$859$		−	18.7858i		−	0.640964i	0.947255	−	0.320482i	$-0.103845\pi$
$860$	−3.58979			−0.122411
$861$	15.4154	−	18.2734i	0.525354	−	0.622755i
$862$	−5.06753			−0.172601
$863$	1.15095			0.0391789			0.0195895	−	0.999808i	$-0.493764\pi$
$863$	1.15095			0.0391789			0.0195895	+	0.999808i	$0.493764\pi$
$864$	26.1282			0.888900
$865$			15.0847i			0.512896i
$866$	108.385			3.68306
$867$			8.60431i			0.292218i
$868$	−53.5953	+	63.5319i	−1.81914	+	2.15641i
$869$	7.60415	+	18.2029i	0.257953	+	0.617491i
$870$	11.0186			0.373566
$871$	−47.5168			−1.61004
$872$	−166.507			−5.63863
$873$		−	3.11539i		−	0.105440i
$874$			89.5195i			3.02804i
$875$	1.70599	−	2.02228i	0.0576729	−	0.0683655i
$876$		−	15.6258i		−	0.527947i
$877$			20.4094i			0.689177i	0.938754	+	0.344589i	$0.111982\pi$
$877$			20.4094i			0.689177i	−0.938754	+	0.344589i	$0.888018\pi$
$878$			58.1093i			1.96109i
$879$		−	12.9775i		−	0.437721i
$880$	21.4372	+	51.3166i	0.722648	+	1.72988i
$881$			16.3256i			0.550024i	0.961441	+	0.275012i	$0.0886818\pi$
$881$			16.3256i			0.550024i	−0.961441	+	0.275012i	$0.911318\pi$
$882$	−19.1039	+	3.26488i	−0.643261	+	0.109934i
$883$	−7.74921			−0.260782			−0.130391	−	0.991463i	$-0.541623\pi$
$883$	−7.74921			−0.260782			−0.130391	+	0.991463i	$0.541623\pi$
$884$	50.3523			1.69353
$885$		−	6.56737i		−	0.220760i
$886$			115.532i			3.88138i
$887$	−55.3198			−1.85746			−0.928729	−	0.370760i	$-0.879097\pi$
$887$	−55.3198			−1.85746			−0.928729	+	0.370760i	$0.879097\pi$
$888$	30.8567			1.03548
$889$	14.3017	−	16.9532i	0.479664	−	0.568593i
$890$			48.8987i			1.63909i
$891$	−3.06033	+	1.27843i	−0.102525	+	0.0428291i
$892$		−	95.7242i		−	3.20508i
$893$			12.9374i			0.432934i
$894$			5.40346i			0.180719i
$895$		−	19.3721i		−	0.647536i
$896$	94.1377	−	111.591i	3.14492	−	3.72799i
$897$		−	19.7436i		−	0.659220i
$898$		−	16.0729i		−	0.536359i
$899$	22.0675			0.735993
$900$	−5.66565			−0.188855
$901$	−19.3189			−0.643605
$902$	−31.9838	−	76.5633i	−1.06495	−	2.54928i
$903$	−1.28133	−	1.08092i	−0.0426398	−	0.0359708i
$904$		−	115.429i		−	3.83911i
$905$	8.70652			0.289414
$906$		−	12.3927i		−	0.411720i
$907$	−8.76349			−0.290987			−0.145493	−	0.989359i	$-0.546477\pi$
$907$	−8.76349			−0.290987			−0.145493	+	0.989359i	$0.546477\pi$
$908$	−136.894			−4.54298
$909$	−14.5219			−0.481661
$910$	17.1734	+	14.4874i	0.569293	+	0.480254i
$911$	24.4122			0.808811			0.404405	−	0.914580i	$-0.367478\pi$
$911$	24.4122			0.808811			0.404405	+	0.914580i	$0.367478\pi$
$912$			84.2263i			2.78901i
$913$	38.7231	−	16.1763i	1.28155	−	0.535358i
$914$	−77.6737			−2.56922
$915$	3.39485			0.112230
$916$		−	4.56696i		−	0.150897i
$917$	27.3528	+	23.0747i	0.903267	+	0.761994i
$918$	−8.02237			−0.264778
$919$		−	18.1362i		−	0.598259i	−0.954212	−	0.299130i	$-0.903304\pi$
$919$		−	18.1362i		−	0.598259i	0.954212	−	0.299130i	$-0.0966963\pi$
$920$	65.3298			2.15386
$921$		−	1.49201i		−	0.0491635i
$922$			106.351i			3.50249i
$923$	26.1488			0.860698
$924$	−14.9320	+	47.4205i	−0.491228	+	1.56002i
$925$	−3.04035			−0.0999660
$926$			91.4471i			3.00514i
$927$		−	16.1032i		−	0.528898i
$928$	−103.983			−3.41341
$929$			21.0860i			0.691811i	0.938269	+	0.345905i	$0.112428\pi$
$929$			21.0860i			0.691811i	−0.938269	+	0.345905i	$0.887572\pi$
$930$	−15.3524			−0.503424
$931$	−5.92312	−	34.6581i	−0.194122	−	1.13587i
$932$		−	56.9353i		−	1.86498i
$933$	−18.4951			−0.605502
$934$	14.3255			0.468745
$935$	−3.70430	−	8.86740i	−0.121144	−	0.289995i
$936$		−	31.1292i		−	1.01749i
$937$	35.8456			1.17102			0.585512	−	0.810664i	$-0.300894\pi$
$937$	35.8456			1.17102			0.585512	+	0.810664i	$0.300894\pi$
$938$	73.1739	−	86.7403i	2.38921	−	2.83217i
$939$	0.731416			0.0238688
$940$	14.5928			0.475965
$941$	11.0154			0.359093			0.179547	−	0.983749i	$-0.442537\pi$
$941$	11.0154			0.359093			0.179547	+	0.983749i	$0.442537\pi$
$942$		−	12.8764i		−	0.419535i
$943$	−58.1652			−1.89412
$944$			110.124i			3.58423i
$945$	−2.02228	−	1.70599i	−0.0657847	−	0.0554958i
$946$	−5.36860	+	2.24270i	−0.174548	+	0.0729165i
$947$	−56.8250			−1.84657			−0.923283	−	0.384121i	$-0.874504\pi$
$947$	−56.8250			−1.84657			−0.923283	+	0.384121i	$0.874504\pi$
$948$	33.6994			1.09451
$949$	−8.45929			−0.274600
$950$		−	13.9070i		−	0.451202i
$951$		−	4.20879i		−	0.136479i
$952$	−50.1684	+	59.4696i	−1.62597	+	1.92742i
$953$		−	8.77039i		−	0.284101i	−0.989859	−	0.142050i	$-0.954630\pi$
$953$		−	8.77039i		−	0.284101i	0.989859	−	0.142050i	$-0.0453695\pi$
$954$			18.4599i			0.597660i
$955$			1.74411i			0.0564379i
$956$		−	67.9802i		−	2.19864i
$957$	12.1793	−	5.08781i	0.393699	−	0.164465i
$958$			11.1335i			0.359708i
$959$	−11.4771	−	9.68205i	−0.370615	−	0.312650i
$960$	38.8043			1.25240
$961$	0.253057			0.00816313
$962$		−	25.8190i		−	0.832438i
$963$		−	8.53872i		−	0.275156i
$964$	−1.52027			−0.0489645
$965$	−10.8394			−0.348932
$966$	36.0413	+	30.4044i	1.15961	+	0.978244i
$967$			10.8083i			0.347572i	0.984783	+	0.173786i	$0.0556001\pi$
$967$			10.8083i			0.347572i	−0.984783	+	0.173786i	$0.944400\pi$
$968$	79.4149	+	78.4647i	2.55249	+	2.52195i
$969$		−	14.5541i		−	0.467546i
$970$		−	8.62556i		−	0.276950i
$971$			5.94385i			0.190747i	0.995442	+	0.0953737i	$0.0304046\pi$
$971$			5.94385i			0.190747i	−0.995442	+	0.0953737i	$0.969595\pi$
$972$			5.66565i			0.181726i
$973$	24.5465	+	20.7073i	0.786924	+	0.663846i
$974$			11.0591i			0.354355i
$975$			3.06720i			0.0982289i
$976$	−56.9259			−1.82215
$977$	30.2436			0.967578			0.483789	−	0.875185i	$-0.339260\pi$
$977$	30.2436			0.967578			0.483789	+	0.875185i	$0.339260\pi$
$978$	31.7338			1.01473
$979$	22.5788	+	54.0493i	0.721620	+	1.72742i
$980$	−39.0928	+	6.68101i	−1.24877	+	0.213417i
$981$		−	16.4061i		−	0.523807i
$982$	4.01966			0.128272
$983$			28.2528i			0.901123i	0.892745	+	0.450562i	$0.148776\pi$
$983$			28.2528i			0.901123i	−0.892745	+	0.450562i	$0.851224\pi$
$984$	−91.7074			−2.92352
$985$	−22.3911			−0.713439
$986$	31.9268			1.01676
$987$	5.20871	+	4.39405i	0.165795	+	0.139864i
$988$	87.2870			2.77697
$989$			4.07853i			0.129690i
$990$	−8.47311	+	3.53959i	−0.269293	+	0.112495i
$991$	30.2532			0.961026			0.480513	−	0.876988i	$-0.340451\pi$
$991$	30.2532			0.961026			0.480513	+	0.876988i	$0.340451\pi$
$992$	144.881			4.59997
$993$			28.1198i			0.892356i
$994$	−40.2681	+	47.7338i	−1.27723	+	1.51402i
$995$	−10.4984			−0.332823
$996$		−	71.6889i		−	2.27155i
$997$	−10.8175			−0.342593			−0.171296	−	0.985220i	$-0.554796\pi$
$997$	−10.8175			−0.342593			−0.171296	+	0.985220i	$0.554796\pi$
$998$		−	48.9450i		−	1.54933i
$999$			3.04035i			0.0961923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.d.76.7	✓	32
7.6	odd	2	inner	1155.2.i.d.76.25	yes	32
11.10	odd	2	inner	1155.2.i.d.76.26	yes	32
77.76	even	2	inner	1155.2.i.d.76.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.d.76.7	✓	32	1.1	even	1	trivial
1155.2.i.d.76.8	yes	32	77.76	even	2	inner
1155.2.i.d.76.25	yes	32	7.6	odd	2	inner
1155.2.i.d.76.26	yes	32	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.76869i q^{2} -1.00000i q^{3} -5.66565 q^{4} -1.00000i q^{5} -2.76869 q^{6} +(-2.02228 - 1.70599i) q^{7} +10.1491i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.76869i q^{2} -1.00000i q^{3} -5.66565 q^{4} -1.00000i q^{5} -2.76869 q^{6} +(-2.02228 - 1.70599i) q^{7} +10.1491i q^{8} -1.00000 q^{9} -2.76869 q^{10} +(-3.06033 + 1.27843i) q^{11} +5.66565i q^{12} +3.06720 q^{13} +(-4.72335 + 5.59906i) q^{14} -1.00000 q^{15} +16.7683 q^{16} -2.89753 q^{17} +2.76869i q^{18} -5.02294 q^{19} +5.66565i q^{20} +(-1.70599 + 2.02228i) q^{21} +(3.53959 + 8.47311i) q^{22} +6.43703 q^{23} +10.1491 q^{24} -1.00000 q^{25} -8.49212i q^{26} +1.00000i q^{27} +(11.4575 + 9.66554i) q^{28} -3.97972i q^{29} +2.76869i q^{30} +5.54499i q^{31} -26.1282i q^{32} +(1.27843 + 3.06033i) q^{33} +8.02237i q^{34} +(-1.70599 + 2.02228i) q^{35} +5.66565 q^{36} +3.04035 q^{37} +13.9070i q^{38} -3.06720i q^{39} +10.1491 q^{40} -9.03604 q^{41} +(5.59906 + 4.72335i) q^{42} +0.633605i q^{43} +(17.3388 - 7.24316i) q^{44} +1.00000i q^{45} -17.8221i q^{46} -2.57566i q^{47} -16.7683i q^{48} +(1.17921 + 6.89996i) q^{49} +2.76869i q^{50} +2.89753i q^{51} -17.3777 q^{52} +6.66736 q^{53} +2.76869 q^{54} +(1.27843 + 3.06033i) q^{55} +(17.3142 - 20.5242i) q^{56} +5.02294i q^{57} -11.0186 q^{58} +6.56737i q^{59} +5.66565 q^{60} -3.39485 q^{61} +15.3524 q^{62} +(2.02228 + 1.70599i) q^{63} -38.8043 q^{64} -3.06720i q^{65} +(8.47311 - 3.53959i) q^{66} -15.4919 q^{67} +16.4164 q^{68} -6.43703i q^{69} +(5.59906 + 4.72335i) q^{70} +8.52531 q^{71} -10.1491i q^{72} -2.75799 q^{73} -8.41779i q^{74} +1.00000i q^{75} +28.4582 q^{76} +(8.36982 + 2.63554i) q^{77} -8.49212 q^{78} -5.94802i q^{79} -16.7683i q^{80} +1.00000 q^{81} +25.0180i q^{82} -12.6532 q^{83} +(9.66554 - 11.4575i) q^{84} +2.89753i q^{85} +1.75426 q^{86} -3.97972 q^{87} +(-12.9749 - 31.0595i) q^{88} -17.6613i q^{89} +2.76869 q^{90} +(-6.20272 - 5.23260i) q^{91} -36.4700 q^{92} +5.54499 q^{93} -7.13122 q^{94} +5.02294i q^{95} -26.1282 q^{96} +3.11539i q^{97} +(19.1039 - 3.26488i) q^{98} +(3.06033 - 1.27843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 36 * q^4 - 32 * q^9	\( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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