LMFDB - Embedded newform 1815.2.c.k.364.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.4
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.k.364.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21395i q^{2} -1.00000i q^{3} -2.90157 q^{4} +(-2.14116 + 0.644543i) q^{5} -2.21395 q^{6} +1.59339i q^{7} +1.99602i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.21395i q^{2} -1.00000i q^{3} -2.90157 q^{4} +(-2.14116 + 0.644543i) q^{5} -2.21395 q^{6} +1.59339i q^{7} +1.99602i q^{8} -1.00000 q^{9} +(1.42699 + 4.74042i) q^{10} +2.90157i q^{12} -0.891576i q^{13} +3.52768 q^{14} +(0.644543 + 2.14116i) q^{15} -1.38404 q^{16} +4.43839i q^{17} +2.21395i q^{18} -5.84384 q^{19} +(6.21272 - 1.87019i) q^{20} +1.59339 q^{21} +3.27284i q^{23} +1.99602 q^{24} +(4.16913 - 2.76014i) q^{25} -1.97390 q^{26} +1.00000i q^{27} -4.62332i q^{28} +5.30235 q^{29} +(4.74042 - 1.42699i) q^{30} +8.91445 q^{31} +7.05624i q^{32} +9.82638 q^{34} +(-1.02701 - 3.41170i) q^{35} +2.90157 q^{36} -5.53121i q^{37} +12.9380i q^{38} -0.891576 q^{39} +(-1.28652 - 4.27381i) q^{40} +4.19014 q^{41} -3.52768i q^{42} -6.39321i q^{43} +(2.14116 - 0.644543i) q^{45} +7.24589 q^{46} +8.47681i q^{47} +1.38404i q^{48} +4.46111 q^{49} +(-6.11081 - 9.23024i) q^{50} +4.43839 q^{51} +2.58697i q^{52} +4.38324i q^{53} +2.21395 q^{54} -3.18044 q^{56} +5.84384i q^{57} -11.7391i q^{58} +7.20613 q^{59} +(-1.87019 - 6.21272i) q^{60} -2.03022 q^{61} -19.7361i q^{62} -1.59339i q^{63} +12.8541 q^{64} +(0.574659 + 1.90901i) q^{65} +13.6199i q^{67} -12.8783i q^{68} +3.27284 q^{69} +(-7.55333 + 2.27374i) q^{70} +1.15336 q^{71} -1.99602i q^{72} -6.66040i q^{73} -12.2458 q^{74} +(-2.76014 - 4.16913i) q^{75} +16.9563 q^{76} +1.97390i q^{78} -4.89466 q^{79} +(2.96345 - 0.892074i) q^{80} +1.00000 q^{81} -9.27676i q^{82} -13.2475i q^{83} -4.62332 q^{84} +(-2.86074 - 9.50331i) q^{85} -14.1542 q^{86} -5.30235i q^{87} +8.06859 q^{89} +(-1.42699 - 4.74042i) q^{90} +1.42063 q^{91} -9.49635i q^{92} -8.91445i q^{93} +18.7672 q^{94} +(12.5126 - 3.76661i) q^{95} +7.05624 q^{96} -10.7654i q^{97} -9.87667i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	2.21395i		−	1.56550i	−0.622338	−	0.782749i	$-0.713817\pi$
$2$		−	2.21395i		−	1.56550i	0.622338	−	0.782749i	$-0.286183\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−2.90157			−1.45078
$5$	−2.14116	+	0.644543i	−0.957556	+	0.288248i
$5$	−2.14116	+	0.644543i	−0.957556	+	0.288248i
$6$	−2.21395			−0.903841
$7$			1.59339i			0.602244i	0.953586	+	0.301122i	$0.0973612\pi$
$7$			1.59339i			0.602244i	−0.953586	+	0.301122i	$0.902639\pi$
$8$			1.99602i			0.705701i
$9$	−1.00000			−0.333333
$10$	1.42699	+	4.74042i	0.451252	+	1.49905i
$11$		0			0
$11$		0			0
$12$			2.90157i			0.837610i
$13$		−	0.891576i		−	0.247279i	−0.992327	−	0.123639i	$-0.960543\pi$
$13$		−	0.891576i		−	0.247279i	0.992327	−	0.123639i	$-0.0394566\pi$
$14$	3.52768			0.942812
$15$	0.644543	+	2.14116i	0.166420	+	0.552845i
$16$	−1.38404			−0.346010
$17$			4.43839i			1.07647i	0.842795	+	0.538234i	$0.180908\pi$
$17$			4.43839i			1.07647i	−0.842795	+	0.538234i	$0.819092\pi$
$18$			2.21395i			0.521833i
$19$	−5.84384			−1.34067			−0.670335	−	0.742059i	$-0.733850\pi$
$19$	−5.84384			−1.34067			−0.670335	+	0.742059i	$0.733850\pi$
$20$	6.21272	−	1.87019i	1.38921	−	0.418186i
$21$	1.59339			0.347706
$22$		0			0
$23$			3.27284i			0.682433i	0.939985	+	0.341217i	$0.110839\pi$
$23$			3.27284i			0.682433i	−0.939985	+	0.341217i	$0.889161\pi$
$24$	1.99602			0.407437
$25$	4.16913	−	2.76014i	0.833826	−	0.552028i
$26$	−1.97390			−0.387114
$27$			1.00000i			0.192450i
$28$		−	4.62332i		−	0.873726i
$29$	5.30235			0.984621			0.492311	−	0.870420i	$-0.336152\pi$
$29$	5.30235			0.984621			0.492311	+	0.870420i	$0.336152\pi$
$30$	4.74042	−	1.42699i	0.865478	−	0.260531i
$31$	8.91445			1.60108			0.800541	−	0.599278i	$-0.204546\pi$
$31$	8.91445			1.60108			0.800541	+	0.599278i	$0.204546\pi$
$32$			7.05624i			1.24738i
$33$		0			0
$34$	9.82638			1.68521
$35$	−1.02701	−	3.41170i	−0.173596	−	0.576682i
$36$	2.90157			0.483595
$37$		−	5.53121i		−	0.909325i	−0.890664	−	0.454663i	$-0.849760\pi$
$37$		−	5.53121i		−	0.909325i	0.890664	−	0.454663i	$-0.150240\pi$
$38$			12.9380i			2.09882i
$39$	−0.891576			−0.142766
$40$	−1.28652	−	4.27381i	−0.203417	−	0.675748i
$41$	4.19014			0.654391			0.327195	−	0.944957i	$-0.393896\pi$
$41$	4.19014			0.654391			0.327195	+	0.944957i	$0.393896\pi$
$42$		−	3.52768i		−	0.544333i
$43$		−	6.39321i		−	0.974955i	−0.873136	−	0.487477i	$-0.837917\pi$
$43$		−	6.39321i		−	0.974955i	0.873136	−	0.487477i	$-0.162083\pi$
$44$		0			0
$45$	2.14116	−	0.644543i	0.319185	−	0.0960828i
$46$	7.24589			1.06835
$47$			8.47681i			1.23647i	0.785993	+	0.618235i	$0.212152\pi$
$47$			8.47681i			1.23647i	−0.785993	+	0.618235i	$0.787848\pi$
$48$			1.38404i			0.199769i
$49$	4.46111			0.637302
$50$	−6.11081	−	9.23024i	−0.864198	−	1.30535i
$51$	4.43839			0.621500
$52$			2.58697i			0.358748i
$53$			4.38324i			0.602084i	0.953611	+	0.301042i	$0.0973345\pi$
$53$			4.38324i			0.602084i	−0.953611	+	0.301042i	$0.902666\pi$
$54$	2.21395			0.301280
$55$		0			0
$56$	−3.18044			−0.425004
$57$			5.84384i			0.774036i
$58$		−	11.7391i		−	1.54142i
$59$	7.20613			0.938159			0.469079	−	0.883156i	$-0.344586\pi$
$59$	7.20613			0.938159			0.469079	+	0.883156i	$0.344586\pi$
$60$	−1.87019	−	6.21272i	−0.241440	−	0.802059i
$61$	−2.03022			−0.259942			−0.129971	−	0.991518i	$-0.541488\pi$
$61$	−2.03022			−0.259942			−0.129971	+	0.991518i	$0.541488\pi$
$62$		−	19.7361i		−	2.50649i
$63$		−	1.59339i		−	0.200748i
$64$	12.8541			1.60676
$65$	0.574659	+	1.90901i	0.0712777	+	0.236783i
$66$		0			0
$67$			13.6199i			1.66393i	0.554825	+	0.831967i	$0.312785\pi$
$67$			13.6199i			1.66393i	−0.554825	+	0.831967i	$0.687215\pi$
$68$		−	12.8783i		−	1.56172i
$69$	3.27284			0.394003
$70$	−7.55333	+	2.27374i	−0.902795	+	0.271764i
$71$	1.15336			0.136879			0.0684394	−	0.997655i	$-0.478198\pi$
$71$	1.15336			0.136879			0.0684394	+	0.997655i	$0.478198\pi$
$72$		−	1.99602i		−	0.235234i
$73$		−	6.66040i		−	0.779541i	−0.920912	−	0.389770i	$-0.872554\pi$
$73$		−	6.66040i		−	0.779541i	0.920912	−	0.389770i	$-0.127446\pi$
$74$	−12.2458			−1.42355
$75$	−2.76014	−	4.16913i	−0.318713	−	0.481409i
$76$	16.9563			1.94502
$77$		0			0
$78$			1.97390i			0.223501i
$79$	−4.89466			−0.550693			−0.275346	−	0.961345i	$-0.588793\pi$
$79$	−4.89466			−0.550693			−0.275346	+	0.961345i	$0.588793\pi$
$80$	2.96345	−	0.892074i	0.331324	−	0.0997369i
$81$	1.00000			0.111111
$82$		−	9.27676i		−	1.02445i
$83$		−	13.2475i		−	1.45410i	−0.686585	−	0.727050i	$-0.740891\pi$
$83$		−	13.2475i		−	1.45410i	0.686585	−	0.727050i	$-0.259109\pi$
$84$	−4.62332			−0.504446
$85$	−2.86074	−	9.50331i	−0.310290	−	1.03078i
$86$	−14.1542			−1.52629
$87$		−	5.30235i		−	0.568471i
$88$		0			0
$89$	8.06859			0.855268			0.427634	−	0.903952i	$-0.359347\pi$
$89$	8.06859			0.855268			0.427634	+	0.903952i	$0.359347\pi$
$90$	−1.42699	−	4.74042i	−0.150417	−	0.499684i
$91$	1.42063			0.148922
$92$		−	9.49635i		−	0.990063i
$93$		−	8.91445i		−	0.924385i
$94$	18.7672			1.93569
$95$	12.5126	−	3.76661i	1.28377	−	0.386446i
$96$	7.05624			0.720175
$97$		−	10.7654i		−	1.09306i	−0.837441	−	0.546528i	$-0.815949\pi$
$97$		−	10.7654i		−	1.09306i	0.837441	−	0.546528i	$-0.184051\pi$
$98$		−	9.87667i		−	0.997695i
$99$		0			0
$100$	−12.0970	+	8.00873i	−1.20970	+	0.800873i
$101$	−13.3647			−1.32984			−0.664920	−	0.746915i	$-0.731534\pi$
$101$	−13.3647			−1.32984			−0.664920	+	0.746915i	$0.731534\pi$
$102$		−	9.82638i		−	0.972956i
$103$			4.36350i			0.429948i	0.976620	+	0.214974i	$0.0689667\pi$
$103$			4.36350i			0.429948i	−0.976620	+	0.214974i	$0.931033\pi$
$104$	1.77961			0.174505
$105$	−3.41170	+	1.02701i	−0.332948	+	0.100226i
$106$	9.70426			0.942561
$107$			20.6028i			1.99175i	0.0907584	+	0.995873i	$0.471071\pi$
$107$			20.6028i			1.99175i	−0.0907584	+	0.995873i	$0.528929\pi$
$108$		−	2.90157i		−	0.279203i
$109$	−4.83053			−0.462681			−0.231340	−	0.972873i	$-0.574311\pi$
$109$	−4.83053			−0.462681			−0.231340	+	0.972873i	$0.574311\pi$
$110$		0			0
$111$	−5.53121			−0.524999
$112$		−	2.20532i		−	0.208383i
$113$			15.8292i			1.48908i	0.667576	+	0.744542i	$0.267332\pi$
$113$			15.8292i			1.48908i	−0.667576	+	0.744542i	$0.732668\pi$
$114$	12.9380			1.21175
$115$	−2.10948	−	7.00766i	−0.196710	−	0.653468i
$116$	−15.3851			−1.42847
$117$			0.891576i			0.0824263i
$118$		−	15.9540i		−	1.46869i
$119$	−7.07209			−0.648297
$120$	−4.27381	+	1.28652i	−0.390143	+	0.117443i
$121$		0			0
$122$			4.49479i			0.406939i
$123$		−	4.19014i		−	0.377813i
$124$	−25.8659			−2.32282
$125$	−7.14774	+	8.59708i	−0.639313	+	0.768946i
$126$	−3.52768			−0.314271
$127$			9.04884i			0.802955i	0.915869	+	0.401477i	$0.131503\pi$
$127$			9.04884i			0.802955i	−0.915869	+	0.401477i	$0.868497\pi$
$128$		−	14.3458i		−	1.26800i
$129$	−6.39321			−0.562890
$130$	4.22644	−	1.27227i	0.370684	−	0.111585i
$131$	−9.87408			−0.862702			−0.431351	−	0.902184i	$-0.641963\pi$
$131$	−9.87408			−0.862702			−0.431351	+	0.902184i	$0.641963\pi$
$132$		0			0
$133$		−	9.31151i		−	0.807411i
$134$	30.1537			2.60488
$135$	−0.644543	−	2.14116i	−0.0554734	−	0.184282i
$136$	−8.85914			−0.759665
$137$			11.6288i			0.993518i	0.867888	+	0.496759i	$0.165477\pi$
$137$			11.6288i			0.993518i	−0.867888	+	0.496759i	$0.834523\pi$
$138$		−	7.24589i		−	0.616811i
$139$	−1.77693			−0.150717			−0.0753584	−	0.997157i	$-0.524010\pi$
$139$	−1.77693			−0.150717			−0.0753584	+	0.997157i	$0.524010\pi$
$140$	2.97993	+	9.89927i	0.251850	+	0.836641i
$141$	8.47681			0.713876
$142$		−	2.55348i		−	0.214283i
$143$		0			0
$144$	1.38404			0.115337
$145$	−11.3532	+	3.41759i	−0.942830	+	0.283816i
$146$	−14.7458			−1.22037
$147$		−	4.46111i		−	0.367946i
$148$			16.0492i			1.31923i
$149$	21.4976			1.76115			0.880574	−	0.473909i	$-0.157157\pi$
$149$	21.4976			1.76115			0.880574	+	0.473909i	$0.157157\pi$
$150$	−9.23024	+	6.11081i	−0.753646	+	0.498945i
$151$	8.04208			0.654455			0.327228	−	0.944946i	$-0.393886\pi$
$151$	8.04208			0.654455			0.327228	+	0.944946i	$0.393886\pi$
$152$		−	11.6645i		−	0.946112i
$153$		−	4.43839i		−	0.358823i
$154$		0			0
$155$	−19.0873	+	5.74575i	−1.53313	+	0.461509i
$156$	2.58697			0.207123
$157$			17.0621i			1.36170i	0.732421	+	0.680852i	$0.238390\pi$
$157$			17.0621i			1.36170i	−0.732421	+	0.680852i	$0.761610\pi$
$158$			10.8365i			0.862108i
$159$	4.38324			0.347613
$160$	−4.54805	−	15.1085i	−0.359555	−	1.19444i
$161$	−5.21490			−0.410992
$162$		−	2.21395i		−	0.173944i
$163$		−	13.4702i		−	1.05507i	−0.849533	−	0.527535i	$-0.823116\pi$
$163$		−	13.4702i		−	1.05507i	0.849533	−	0.527535i	$-0.176884\pi$
$164$	−12.1580			−0.949379
$165$		0			0
$166$	−29.3292			−2.27639
$167$			6.50196i			0.503136i	0.967840	+	0.251568i	$0.0809463\pi$
$167$			6.50196i			0.503136i	−0.967840	+	0.251568i	$0.919054\pi$
$168$			3.18044i			0.245376i
$169$	12.2051			0.938853
$170$	−21.0398	+	6.33352i	−1.61368	+	0.485759i
$171$	5.84384			0.446890
$172$			18.5503i			1.41445i
$173$			2.47668i			0.188298i	0.995558	+	0.0941491i	$0.0300131\pi$
$173$			2.47668i			0.188298i	−0.995558	+	0.0941491i	$0.969987\pi$
$174$	−11.7391			−0.889941
$175$	4.39797	+	6.64304i	0.332456	+	0.502167i
$176$		0			0
$177$		−	7.20613i		−	0.541646i
$178$		−	17.8634i		−	1.33892i
$179$	11.6127			0.867972			0.433986	−	0.900920i	$-0.357107\pi$
$179$	11.6127			0.867972			0.433986	+	0.900920i	$0.357107\pi$
$180$	−6.21272	+	1.87019i	−0.463069	+	0.139395i
$181$	7.06522			0.525153			0.262577	−	0.964911i	$-0.415428\pi$
$181$	7.06522			0.525153			0.262577	+	0.964911i	$0.415428\pi$
$182$		−	3.14520i		−	0.233137i
$183$			2.03022i			0.150078i
$184$	−6.53266			−0.481594
$185$	3.56510	+	11.8432i	0.262112	+	0.870729i
$186$	−19.7361			−1.44712
$187$		0			0
$188$		−	24.5960i		−	1.79385i
$189$	−1.59339			−0.115902
$190$	−8.33908	−	27.7023i	−0.604980	−	2.00973i
$191$	23.8182			1.72342			0.861712	−	0.507398i	$-0.169393\pi$
$191$	23.8182			1.72342			0.861712	+	0.507398i	$0.169393\pi$
$192$		−	12.8541i		−	0.927663i
$193$			25.1985i			1.81382i	0.421319	+	0.906912i	$0.361567\pi$
$193$			25.1985i			1.81382i	−0.421319	+	0.906912i	$0.638433\pi$
$194$	−23.8339			−1.71118
$195$	1.90901	−	0.574659i	0.136707	−	0.0411522i
$196$	−12.9442			−0.924587
$197$			7.24398i			0.516112i	0.966130	+	0.258056i	$0.0830819\pi$
$197$			7.24398i			0.516112i	−0.966130	+	0.258056i	$0.916918\pi$
$198$		0			0
$199$	13.4111			0.950689			0.475345	−	0.879800i	$-0.342323\pi$
$199$	13.4111			0.950689			0.475345	+	0.879800i	$0.342323\pi$
$200$	5.50930	+	8.32168i	0.389567	+	0.588432i
$201$	13.6199			0.960672
$202$			29.5888i			2.08186i
$203$			8.44870i			0.592983i
$204$	−12.8783			−0.901661
$205$	−8.97177	+	2.70073i	−0.626615	+	0.188627i
$206$	9.66055			0.673083
$207$		−	3.27284i		−	0.227478i
$208$			1.23398i			0.0855610i
$209$		0			0
$210$	2.27374	+	7.55333i	0.156903	+	0.521229i
$211$	−3.11369			−0.214356			−0.107178	−	0.994240i	$-0.534181\pi$
$211$	−3.11369			−0.214356			−0.107178	+	0.994240i	$0.534181\pi$
$212$		−	12.7183i		−	0.873494i
$213$		−	1.15336i		−	0.0790270i
$214$	45.6135			3.11807
$215$	4.12070	+	13.6889i	0.281029	+	0.933573i
$216$	−1.99602			−0.135812
$217$			14.2042i			0.964242i
$218$			10.6945i			0.724326i
$219$	−6.66040			−0.450068
$220$		0			0
$221$	3.95717			0.266188
$222$			12.2458i			0.821885i
$223$		−	12.6942i		−	0.850063i	−0.905178	−	0.425032i	$-0.860263\pi$
$223$		−	12.6942i		−	0.850063i	0.905178	−	0.425032i	$-0.139737\pi$
$224$	−11.2433			−0.751227
$225$	−4.16913	+	2.76014i	−0.277942	+	0.184009i
$226$	35.0450			2.33116
$227$			2.27677i			0.151114i	0.997141	+	0.0755572i	$0.0240735\pi$
$227$			2.27677i			0.151114i	−0.997141	+	0.0755572i	$0.975926\pi$
$228$		−	16.9563i		−	1.12296i
$229$	−20.1618			−1.33233			−0.666166	−	0.745803i	$-0.732066\pi$
$229$	−20.1618			−1.33233			−0.666166	+	0.745803i	$0.732066\pi$
$230$	−15.5146	+	4.67029i	−1.02300	+	0.307950i
$231$		0			0
$232$			10.5836i			0.694848i
$233$		−	9.85555i		−	0.645659i	−0.946457	−	0.322829i	$-0.895366\pi$
$233$		−	9.85555i		−	0.645659i	0.946457	−	0.322829i	$-0.104634\pi$
$234$	1.97390			0.129038
$235$	−5.46367	−	18.1502i	−0.356410	−	1.18399i
$236$	−20.9091			−1.36107
$237$			4.89466i			0.317942i
$238$			15.6572i			1.01491i
$239$	−9.55913			−0.618328			−0.309164	−	0.951009i	$-0.600049\pi$
$239$	−9.55913			−0.618328			−0.309164	+	0.951009i	$0.600049\pi$
$240$	−0.892074	−	2.96345i	−0.0575831	−	0.191290i
$241$	−4.58482			−0.295334			−0.147667	−	0.989037i	$-0.547176\pi$
$241$	−4.58482			−0.295334			−0.147667	+	0.989037i	$0.547176\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	5.89081			0.377120
$245$	−9.55195	+	2.87538i	−0.610252	+	0.183701i
$246$	−9.27676			−0.591465
$247$			5.21023i			0.331519i
$248$			17.7934i			1.12989i
$249$	−13.2475			−0.839525
$250$	19.0335	+	15.8247i	1.20378	+	1.00084i
$251$	−13.6439			−0.861195			−0.430598	−	0.902544i	$-0.641697\pi$
$251$	−13.6439			−0.861195			−0.430598	+	0.902544i	$0.641697\pi$
$252$			4.62332i			0.291242i
$253$		0			0
$254$	20.0337			1.25702
$255$	−9.50331	+	2.86074i	−0.595120	+	0.179146i
$256$	−6.05265			−0.378291
$257$		−	21.2167i		−	1.32346i	−0.749742	−	0.661731i	$-0.769822\pi$
$257$		−	21.2167i		−	1.32346i	0.749742	−	0.661731i	$-0.230178\pi$
$258$			14.1542i			0.881204i
$259$	8.81336			0.547636
$260$	−1.66741	−	5.53911i	−0.103409	−	0.343521i
$261$	−5.30235			−0.328207
$262$			21.8607i			1.35056i
$263$			15.4054i			0.949936i	0.880003	+	0.474968i	$0.157540\pi$
$263$			15.4054i			0.949936i	−0.880003	+	0.474968i	$0.842460\pi$
$264$		0			0
$265$	−2.82519	−	9.38521i	−0.173550	−	0.576529i
$266$	−20.6152			−1.26400
$267$		−	8.06859i		−	0.493789i
$268$		−	39.5190i		−	2.41401i
$269$	−7.08797			−0.432161			−0.216081	−	0.976376i	$-0.569327\pi$
$269$	−7.08797			−0.432161			−0.216081	+	0.976376i	$0.569327\pi$
$270$	−4.74042	+	1.42699i	−0.288493	+	0.0868435i
$271$	29.1371			1.76996			0.884978	−	0.465633i	$-0.154173\pi$
$271$	29.1371			1.76996			0.884978	+	0.465633i	$0.154173\pi$
$272$		−	6.14292i		−	0.372469i
$273$		−	1.42063i		−	0.0859803i
$274$	25.7456			1.55535
$275$		0			0
$276$	−9.49635			−0.571613
$277$		−	14.1005i		−	0.847218i	−0.905845	−	0.423609i	$-0.860763\pi$
$277$		−	14.1005i		−	0.847218i	0.905845	−	0.423609i	$-0.139237\pi$
$278$			3.93402i			0.235947i
$279$	−8.91445			−0.533694
$280$	6.80983	−	2.04993i	0.406965	−	0.122507i
$281$	−26.2478			−1.56581			−0.782907	−	0.622139i	$-0.786264\pi$
$281$	−26.2478			−1.56581			−0.782907	+	0.622139i	$0.786264\pi$
$282$		−	18.7672i		−	1.11757i
$283$			0.834033i			0.0495781i	0.999693	+	0.0247891i	$0.00789141\pi$
$283$			0.834033i			0.0495781i	−0.999693	+	0.0247891i	$0.992109\pi$
$284$	−3.34655			−0.198581
$285$	−3.76661	−	12.5126i	−0.223115	−	0.741183i
$286$		0			0
$287$			6.67653i			0.394103i
$288$		−	7.05624i		−	0.415793i
$289$	−2.69935			−0.158785
$290$	7.56637	+	25.1353i	0.444313	+	1.47600i
$291$	−10.7654			−0.631077
$292$			19.3256i			1.13095i
$293$			14.2041i			0.829812i	0.909864	+	0.414906i	$0.136186\pi$
$293$			14.2041i			0.829812i	−0.909864	+	0.414906i	$0.863814\pi$
$294$	−9.87667			−0.576019
$295$	−15.4295	+	4.64466i	−0.898339	+	0.270423i
$296$	11.0404			0.641712
$297$		0			0
$298$		−	47.5945i		−	2.75707i
$299$	2.91798			0.168751
$300$	8.00873	+	12.0970i	0.462384	+	0.698421i
$301$	10.1869			0.587161
$302$		−	17.8047i		−	1.02455i
$303$			13.3647i			0.767784i
$304$	8.08812			0.463886
$305$	4.34702	−	1.30856i	0.248909	−	0.0749280i
$306$	−9.82638			−0.561737
$307$			0.166296i			0.00949103i	0.999989	+	0.00474552i	$0.00151055\pi$
$307$			0.166296i			0.00949103i	−0.999989	+	0.00474552i	$0.998489\pi$
$308$		0			0
$309$	4.36350			0.248231
$310$	12.7208	+	42.2582i	0.722492	+	2.40010i
$311$	6.52076			0.369758			0.184879	−	0.982761i	$-0.440811\pi$
$311$	6.52076			0.369758			0.184879	+	0.982761i	$0.440811\pi$
$312$		−	1.77961i		−	0.100750i
$313$		−	0.803861i		−	0.0454369i	−0.999742	−	0.0227185i	$-0.992768\pi$
$313$		−	0.803861i		−	0.0454369i	0.999742	−	0.0227185i	$-0.00723213\pi$
$314$	37.7746			2.13175
$315$	1.02701	+	3.41170i	0.0578653	+	0.192227i
$316$	14.2022			0.798936
$317$			14.4751i			0.813000i	0.913651	+	0.406500i	$0.133251\pi$
$317$			14.4751i			0.813000i	−0.913651	+	0.406500i	$0.866749\pi$
$318$		−	9.70426i		−	0.544188i
$319$		0			0
$320$	−27.5226	+	8.28501i	−1.53856	+	0.463146i
$321$	20.6028			1.14994
$322$			11.5455i			0.643406i
$323$		−	25.9373i		−	1.44319i
$324$	−2.90157			−0.161198
$325$	−2.46087	−	3.71710i	−0.136505	−	0.206187i
$326$	−29.8224			−1.65171
$327$			4.83053i			0.267129i
$328$			8.36363i			0.461804i
$329$	−13.5069			−0.744657
$330$		0			0
$331$	7.41532			0.407583			0.203792	−	0.979014i	$-0.434674\pi$
$331$	7.41532			0.407583			0.203792	+	0.979014i	$0.434674\pi$
$332$			38.4384i			2.10958i
$333$			5.53121i			0.303108i
$334$	14.3950			0.787659
$335$	−8.77860	−	29.1623i	−0.479626	−	1.59331i
$336$	−2.20532			−0.120310
$337$			15.3347i			0.835334i	0.908600	+	0.417667i	$0.137152\pi$
$337$			15.3347i			0.835334i	−0.908600	+	0.417667i	$0.862848\pi$
$338$		−	27.0214i		−	1.46977i
$339$	15.8292			0.859723
$340$	8.30062	+	27.5745i	0.450164	+	1.49544i
$341$		0			0
$342$		−	12.9380i		−	0.699605i
$343$			18.2620i			0.986056i
$344$	12.7610			0.688026
$345$	−7.00766	+	2.10948i	−0.377280	+	0.113571i
$346$	5.48324			0.294781
$347$		−	21.6845i		−	1.16409i	−0.813158	−	0.582043i	$-0.802254\pi$
$347$		−	21.6845i		−	1.16409i	0.813158	−	0.582043i	$-0.197746\pi$
$348$			15.3851i			0.824729i
$349$	−5.85266			−0.313286			−0.156643	−	0.987655i	$-0.550067\pi$
$349$	−5.85266			−0.313286			−0.156643	+	0.987655i	$0.550067\pi$
$350$	14.7074	−	9.73689i	0.786141	−	0.520459i
$351$	0.891576			0.0475888
$352$		0			0
$353$			8.94423i			0.476053i	0.971259	+	0.238027i	$0.0765006\pi$
$353$			8.94423i			0.476053i	−0.971259	+	0.238027i	$0.923499\pi$
$354$	−15.9540			−0.847946
$355$	−2.46953	+	0.743391i	−0.131069	+	0.0394551i
$356$	−23.4115			−1.24081
$357$			7.07209i			0.374295i
$358$		−	25.7099i		−	1.35881i
$359$	5.10770			0.269574			0.134787	−	0.990875i	$-0.456965\pi$
$359$	5.10770			0.269574			0.134787	+	0.990875i	$0.456965\pi$
$360$	1.28652	+	4.27381i	0.0678057	+	0.225249i
$361$	15.1505			0.797395
$362$		−	15.6420i		−	0.822127i
$363$		0			0
$364$	−4.12205			−0.216054
$365$	4.29291	+	14.2610i	0.224701	+	0.746454i
$366$	4.49479			0.234947
$367$			34.0987i			1.77994i	0.456022	+	0.889969i	$0.349274\pi$
$367$			34.0987i			1.77994i	−0.456022	+	0.889969i	$0.650726\pi$
$368$		−	4.52974i		−	0.236129i
$369$	−4.19014			−0.218130
$370$	26.2202	−	7.89295i	1.36313	−	0.410335i
$371$	−6.98420			−0.362602
$372$			25.8659i			1.34108i
$373$		−	26.0424i		−	1.34842i	−0.738538	−	0.674212i	$-0.764483\pi$
$373$		−	26.0424i		−	1.34842i	0.738538	−	0.674212i	$-0.235517\pi$
$374$		0			0
$375$	8.59708	+	7.14774i	0.443951	+	0.369108i
$376$	−16.9199			−0.872578
$377$		−	4.72745i		−	0.243476i
$378$			3.52768i			0.181444i
$379$	1.46216			0.0751060			0.0375530	−	0.999295i	$-0.488044\pi$
$379$	1.46216			0.0751060			0.0375530	+	0.999295i	$0.488044\pi$
$380$	−36.3062	+	10.9291i	−1.86247	+	0.560649i
$381$	9.04884			0.463586
$382$		−	52.7322i		−	2.69802i
$383$		−	3.45296i		−	0.176438i	−0.996101	−	0.0882190i	$-0.971882\pi$
$383$		−	3.45296i		−	0.176438i	0.996101	−	0.0882190i	$-0.0281175\pi$
$384$	−14.3458			−0.732080
$385$		0			0
$386$	55.7881			2.83954
$387$			6.39321i			0.324985i
$388$			31.2364i			1.58579i
$389$	4.09303			0.207525			0.103762	−	0.994602i	$-0.466912\pi$
$389$	4.09303			0.207525			0.103762	+	0.994602i	$0.466912\pi$
$390$	−1.27227	−	4.22644i	−0.0644237	−	0.214014i
$391$	−14.5261			−0.734618
$392$			8.90449i			0.449745i
$393$			9.87408i			0.498082i
$394$	16.0378			0.807972
$395$	10.4803	−	3.15482i	0.527319	−	0.158736i
$396$		0			0
$397$		−	7.10672i		−	0.356676i	−0.983969	−	0.178338i	$-0.942928\pi$
$397$		−	7.10672i		−	0.356676i	0.983969	−	0.178338i	$-0.0570721\pi$
$398$		−	29.6915i		−	1.48830i
$399$	−9.31151			−0.466159
$400$	−5.77025	+	3.82015i	−0.288512	+	0.191007i
$401$	15.6618			0.782113			0.391056	−	0.920367i	$-0.372110\pi$
$401$	15.6618			0.782113			0.391056	+	0.920367i	$0.372110\pi$
$402$		−	30.1537i		−	1.50393i
$403$		−	7.94791i		−	0.395914i
$404$	38.7787			1.92931
$405$	−2.14116	+	0.644543i	−0.106395	+	0.0320276i
$406$	18.7050			0.928313
$407$		0			0
$408$			8.85914i			0.438593i
$409$	−18.5688			−0.918169			−0.459084	−	0.888393i	$-0.651822\pi$
$409$	−18.5688			−0.918169			−0.459084	+	0.888393i	$0.651822\pi$
$410$	5.97927	+	19.8630i	0.295295	+	0.980965i
$411$	11.6288			0.573608
$412$		−	12.6610i		−	0.623761i
$413$			11.4822i			0.565001i
$414$	−7.24589			−0.356116
$415$	8.53857	+	28.3650i	0.419142	+	1.39238i
$416$	6.29118			0.308450
$417$			1.77693i			0.0870164i
$418$		0			0
$419$	−2.39208			−0.116861			−0.0584303	−	0.998291i	$-0.518610\pi$
$419$	−2.39208			−0.116861			−0.0584303	+	0.998291i	$0.518610\pi$
$420$	9.89927	−	2.97993i	0.483035	−	0.145406i
$421$	−16.6767			−0.812770			−0.406385	−	0.913702i	$-0.633211\pi$
$421$	−16.6767			−0.812770			−0.406385	+	0.913702i	$0.633211\pi$
$422$			6.89356i			0.335573i
$423$		−	8.47681i		−	0.412157i
$424$	−8.74905			−0.424891
$425$	12.2506	+	18.5042i	0.594241	+	0.897587i
$426$	−2.55348			−0.123717
$427$		−	3.23492i		−	0.156549i
$428$		−	59.7804i		−	2.88959i
$429$		0			0
$430$	30.3065	−	9.12301i	1.46151	−	0.439951i
$431$	20.3804			0.981690			0.490845	−	0.871247i	$-0.336688\pi$
$431$	20.3804			0.981690			0.490845	+	0.871247i	$0.336688\pi$
$432$		−	1.38404i		−	0.0665897i
$433$		−	13.2139i		−	0.635018i	−0.948255	−	0.317509i	$-0.897154\pi$
$433$		−	13.2139i		−	0.635018i	0.948255	−	0.317509i	$-0.102846\pi$
$434$	31.4473			1.50952
$435$	3.41759	+	11.3532i	0.163861	+	0.544343i
$436$	14.0161			0.671250
$437$		−	19.1259i		−	0.914918i
$438$			14.7458i			0.704581i
$439$	31.6527			1.51070			0.755350	−	0.655321i	$-0.227467\pi$
$439$	31.6527			1.51070			0.755350	+	0.655321i	$0.227467\pi$
$440$		0			0
$441$	−4.46111			−0.212434
$442$		−	8.76097i		−	0.416717i
$443$			23.7672i			1.12921i	0.825361	+	0.564606i	$0.190972\pi$
$443$			23.7672i			1.12921i	−0.825361	+	0.564606i	$0.809028\pi$
$444$	16.0492			0.761660
$445$	−17.2761	+	5.20055i	−0.818967	+	0.246530i
$446$	−28.1042			−1.33077
$447$		−	21.4976i		−	1.01680i
$448$			20.4815i			0.967662i
$449$	14.3253			0.676054			0.338027	−	0.941137i	$-0.390241\pi$
$449$	14.3253			0.676054			0.338027	+	0.941137i	$0.390241\pi$
$450$	6.11081	+	9.23024i	0.288066	+	0.435117i
$451$		0			0
$452$		−	45.9294i		−	2.16034i
$453$		−	8.04208i		−	0.377850i
$454$	5.04065			0.236569
$455$	−3.04179	+	0.915656i	−0.142601	+	0.0429266i
$456$	−11.6645			−0.546238
$457$		−	0.108900i		−	0.00509410i	−0.999997	−	0.00254705i	$-0.999189\pi$
$457$		−	0.108900i		−	0.00509410i	0.999997	−	0.00254705i	$-0.000810753\pi$
$458$			44.6373i			2.08576i
$459$	−4.43839			−0.207167
$460$	6.12081	+	20.3332i	0.285384	+	0.948041i
$461$	8.67446			0.404010			0.202005	−	0.979385i	$-0.435254\pi$
$461$	8.67446			0.404010			0.202005	+	0.979385i	$0.435254\pi$
$462$		0			0
$463$			31.3509i			1.45700i	0.685045	+	0.728501i	$0.259782\pi$
$463$			31.3509i			1.45700i	−0.685045	+	0.728501i	$0.740218\pi$
$464$	−7.33867			−0.340689
$465$	5.74575	+	19.0873i	0.266453	+	0.885150i
$466$	−21.8197			−1.01078
$467$		−	23.6018i		−	1.09216i	−0.837733	−	0.546080i	$-0.816120\pi$
$467$		−	23.6018i		−	1.09216i	0.837733	−	0.546080i	$-0.183880\pi$
$468$		−	2.58697i		−	0.119583i
$469$	−21.7018			−1.00209
$470$	−40.1836	+	12.0963i	−1.85353	+	0.557960i
$471$	17.0621			0.786180
$472$			14.3836i			0.662060i
$473$		0			0
$474$	10.8365			0.497738
$475$	−24.3637	+	16.1298i	−1.11788	+	0.740087i
$476$	20.5201			0.940539
$477$		−	4.38324i		−	0.200695i
$478$			21.1634i			0.967992i
$479$	−24.7008			−1.12861			−0.564304	−	0.825567i	$-0.690855\pi$
$479$	−24.7008			−1.12861			−0.564304	+	0.825567i	$0.690855\pi$
$480$	−15.1085	+	4.54805i	−0.689608	+	0.207589i
$481$	−4.93149			−0.224857
$482$			10.1506i			0.462345i
$483$			5.21490i			0.237286i
$484$		0			0
$485$	6.93874	+	23.0504i	0.315072	+	1.04666i
$486$	−2.21395			−0.100427
$487$			7.73374i			0.350449i	0.984528	+	0.175225i	$0.0560652\pi$
$487$			7.73374i			0.350449i	−0.984528	+	0.175225i	$0.943935\pi$
$488$		−	4.05236i		−	0.183442i
$489$	−13.4702			−0.609145
$490$	6.36594	+	21.1475i	0.287584	+	0.955348i
$491$	−19.4198			−0.876403			−0.438201	−	0.898877i	$-0.644384\pi$
$491$	−19.4198			−0.876403			−0.438201	+	0.898877i	$0.644384\pi$
$492$			12.1580i			0.548124i
$493$			23.5339i			1.05991i
$494$	11.5352			0.518993
$495$		0			0
$496$	−12.3380			−0.553991
$497$			1.83775i			0.0824344i
$498$			29.3292i			1.31427i
$499$	−0.0857258			−0.00383761			−0.00191881	−	0.999998i	$-0.500611\pi$
$499$	−0.0857258			−0.00383761			−0.00191881	+	0.999998i	$0.500611\pi$
$500$	20.7397	−	24.9450i	0.927505	−	1.11557i
$501$	6.50196			0.290486
$502$			30.2069i			1.34820i
$503$		−	13.5923i		−	0.606053i	−0.952982	−	0.303026i	$-0.902003\pi$
$503$		−	13.5923i		−	0.606053i	0.952982	−	0.303026i	$-0.0979971\pi$
$504$	3.18044			0.141668
$505$	28.6160	−	8.61414i	1.27340	−	0.383324i
$506$		0			0
$507$		−	12.2051i		−	0.542047i
$508$		−	26.2558i		−	1.16491i
$509$	14.7758			0.654926			0.327463	−	0.944864i	$-0.393806\pi$
$509$	14.7758			0.654926			0.327463	+	0.944864i	$0.393806\pi$
$510$	6.33352	+	21.0398i	0.280453	+	0.931660i
$511$	10.6126			0.469474
$512$		−	15.2913i		−	0.675786i
$513$		−	5.84384i		−	0.258012i
$514$	−46.9727			−2.07188
$515$	−2.81246	−	9.34294i	−0.123932	−	0.411699i
$516$	18.5503			0.816632
$517$		0			0
$518$		−	19.5123i		−	0.857323i
$519$	2.47668			0.108714
$520$	−3.81042	+	1.14703i	−0.167098	+	0.0503008i
$521$	−3.84342			−0.168383			−0.0841916	−	0.996450i	$-0.526831\pi$
$521$	−3.84342			−0.168383			−0.0841916	+	0.996450i	$0.526831\pi$
$522$			11.7391i			0.513808i
$523$			10.4374i			0.456397i	0.973615	+	0.228198i	$0.0732835\pi$
$523$			10.4374i			0.456397i	−0.973615	+	0.228198i	$0.926716\pi$
$524$	28.6503			1.25159
$525$	6.64304	−	4.39797i	0.289926	−	0.191943i
$526$	34.1067			1.48712
$527$			39.5658i			1.72351i
$528$		0			0
$529$	12.2885			0.534285
$530$	−20.7784	+	6.25482i	−0.902555	+	0.271692i
$531$	−7.20613			−0.312720
$532$			27.0180i			1.17138i
$533$		−	3.73583i		−	0.161817i
$534$	−17.8634			−0.773026
$535$	−13.2794	−	44.1138i	−0.574118	−	1.90721i
$536$	−27.1856			−1.17424
$537$		−	11.6127i		−	0.501124i
$538$			15.6924i			0.676547i
$539$		0			0
$540$	1.87019	+	6.21272i	0.0804800	+	0.267353i
$541$	24.0611			1.03447			0.517233	−	0.855845i	$-0.326962\pi$
$541$	24.0611			1.03447			0.517233	+	0.855845i	$0.326962\pi$
$542$		−	64.5081i		−	2.77086i
$543$		−	7.06522i		−	0.303197i
$544$	−31.3184			−1.34277
$545$	10.3429	−	3.11348i	0.443043	−	0.133367i
$546$	−3.14520			−0.134602
$547$			32.0148i			1.36886i	0.729081	+	0.684428i	$0.239948\pi$
$547$			32.0148i			1.36886i	−0.729081	+	0.684428i	$0.760052\pi$
$548$		−	33.7418i		−	1.44138i
$549$	2.03022			0.0866475
$550$		0			0
$551$	−30.9861			−1.32005
$552$			6.53266i			0.278048i
$553$		−	7.79910i		−	0.331651i
$554$	−31.2178			−1.32632
$555$	11.8432	−	3.56510i	0.502716	−	0.151330i
$556$	5.15587			0.218658
$557$			12.3241i			0.522188i	0.965313	+	0.261094i	$0.0840833\pi$
$557$			12.3241i			0.522188i	−0.965313	+	0.261094i	$0.915917\pi$
$558$			19.7361i			0.835497i
$559$	−5.70003			−0.241086
$560$	1.42142	+	4.72193i	0.0600660	+	0.199538i
$561$		0			0
$562$			58.1113i			2.45128i
$563$			27.3735i			1.15366i	0.816865	+	0.576829i	$0.195710\pi$
$563$			27.3735i			1.15366i	−0.816865	+	0.576829i	$0.804290\pi$
$564$	−24.5960			−1.03568
$565$	−10.2026	−	33.8928i	−0.429226	−	1.42588i
$566$	1.84651			0.0776144
$567$			1.59339i			0.0669160i
$568$			2.30214i			0.0965955i
$569$	1.98445			0.0831926			0.0415963	−	0.999135i	$-0.486756\pi$
$569$	1.98445			0.0831926			0.0415963	+	0.999135i	$0.486756\pi$
$570$	−27.7023	+	8.33908i	−1.16032	+	0.349286i
$571$	−27.0887			−1.13363			−0.566813	−	0.823846i	$-0.691824\pi$
$571$	−27.0887			−1.13363			−0.566813	+	0.823846i	$0.691824\pi$
$572$		0			0
$573$		−	23.8182i		−	0.995019i
$574$	14.7815			0.616967
$575$	9.03348	+	13.6449i	0.376722	+	0.569031i
$576$	−12.8541			−0.535587
$577$			7.14188i			0.297320i	0.988888	+	0.148660i	$0.0474960\pi$
$577$			7.14188i			0.297320i	−0.988888	+	0.148660i	$0.952504\pi$
$578$			5.97622i			0.248578i
$579$	25.1985			1.04721
$580$	32.9420	−	9.91637i	1.36784	−	0.411755i
$581$	21.1084			0.875723
$582$			23.8339i			0.987949i
$583$		0			0
$584$	13.2943			0.550123
$585$	−0.574659	−	1.90901i	−0.0237592	−	0.0789277i
$586$	31.4471			1.29907
$587$			44.4172i			1.83329i	0.399699	+	0.916646i	$0.369115\pi$
$587$			44.4172i			1.83329i	−0.399699	+	0.916646i	$0.630885\pi$
$588$			12.9442i			0.533811i
$589$	−52.0946			−2.14652
$590$	10.2830	+	34.1601i	0.423346	+	1.40635i
$591$	7.24398			0.297977
$592$			7.65542i			0.314636i
$593$		−	15.7620i		−	0.647268i	−0.946182	−	0.323634i	$-0.895095\pi$
$593$		−	15.7620i		−	0.647268i	0.946182	−	0.323634i	$-0.104905\pi$
$594$		0			0
$595$	15.1425	−	4.55826i	0.620781	−	0.186871i
$596$	−62.3766			−2.55504
$597$		−	13.4111i		−	0.548881i
$598$		−	6.46026i		−	0.264180i
$599$	−2.03104			−0.0829861			−0.0414930	−	0.999139i	$-0.513211\pi$
$599$	−2.03104			−0.0829861			−0.0414930	+	0.999139i	$0.513211\pi$
$600$	8.32168	−	5.50930i	0.339731	−	0.224916i
$601$	−41.4508			−1.69081			−0.845406	−	0.534124i	$-0.820642\pi$
$601$	−41.4508			−1.69081			−0.845406	+	0.534124i	$0.820642\pi$
$602$		−	22.5532i		−	0.919199i
$603$		−	13.6199i		−	0.554645i
$604$	−23.3346			−0.949473
$605$		0			0
$606$	29.5888			1.20196
$607$		−	6.04010i		−	0.245160i	−0.992459	−	0.122580i	$-0.960883\pi$
$607$		−	6.04010i		−	0.245160i	0.992459	−	0.122580i	$-0.0391168\pi$
$608$		−	41.2356i		−	1.67232i
$609$	8.44870			0.342359
$610$	−2.89709	−	9.62407i	−0.117300	−	0.389667i
$611$	7.55772			0.305753
$612$			12.8783i			0.520574i
$613$		−	30.0199i		−	1.21249i	−0.795278	−	0.606245i	$-0.792675\pi$
$613$		−	30.0199i		−	1.21249i	0.795278	−	0.606245i	$-0.207325\pi$
$614$	0.368171			0.0148582
$615$	2.70073	+	8.97177i	0.108904	+	0.361777i
$616$		0			0
$617$		−	9.99761i		−	0.402488i	−0.979541	−	0.201244i	$-0.935502\pi$
$617$		−	9.99761i		−	0.402488i	0.979541	−	0.201244i	$-0.0644985\pi$
$618$		−	9.66055i		−	0.388604i
$619$	−7.70735			−0.309785			−0.154892	−	0.987931i	$-0.549503\pi$
$619$	−7.70735			−0.309785			−0.154892	+	0.987931i	$0.549503\pi$
$620$	55.3830	−	16.6717i	2.22423	−	0.669550i
$621$	−3.27284			−0.131334
$622$		−	14.4366i		−	0.578856i
$623$			12.8564i			0.515081i
$624$	1.23398			0.0493987
$625$	9.76326	−	23.0147i	0.390531	−	0.920590i
$626$	−1.77971			−0.0711314
$627$		0			0
$628$		−	49.5069i		−	1.97554i
$629$	24.5497			0.978860
$630$	7.55333	−	2.27374i	0.300932	−	0.0905880i
$631$	−12.9428			−0.515244			−0.257622	−	0.966246i	$-0.582939\pi$
$631$	−12.9428			−0.515244			−0.257622	+	0.966246i	$0.582939\pi$
$632$		−	9.76986i		−	0.388624i
$633$			3.11369i			0.123758i
$634$	32.0470			1.27275
$635$	−5.83237	−	19.3750i	−0.231450	−	0.768874i
$636$	−12.7183			−0.504312
$637$		−	3.97742i		−	0.157591i
$638$		0			0
$639$	−1.15336			−0.0456262
$640$	9.24647	+	30.7166i	0.365499	+	1.21418i
$641$	−48.9112			−1.93188			−0.965938	−	0.258775i	$-0.916681\pi$
$641$	−48.9112			−1.93188			−0.965938	+	0.258775i	$0.916681\pi$
$642$		−	45.6135i		−	1.80022i
$643$			46.9790i			1.85267i	0.376700	+	0.926335i	$0.377059\pi$
$643$			46.9790i			1.85267i	−0.376700	+	0.926335i	$0.622941\pi$
$644$	15.1314			0.596260
$645$	13.6889	−	4.12070i	0.538999	−	0.162252i
$646$	−57.4238			−2.25931
$647$			3.87592i			0.152378i	0.997093	+	0.0761891i	$0.0242753\pi$
$647$			3.87592i			0.152378i	−0.997093	+	0.0761891i	$0.975725\pi$
$648$			1.99602i			0.0784112i
$649$		0			0
$650$	−8.22946	+	5.44825i	−0.322786	+	0.213698i
$651$	14.2042			0.556706
$652$			39.0848i			1.53068i
$653$		−	5.57951i		−	0.218343i	−0.994023	−	0.109171i	$-0.965180\pi$
$653$		−	5.57951i		−	0.218343i	0.994023	−	0.109171i	$-0.0348198\pi$
$654$	10.6945			0.418190
$655$	21.1420	−	6.36427i	0.826086	−	0.248673i
$656$	−5.79933			−0.226426
$657$			6.66040i			0.259847i
$658$			29.9035i			1.16576i
$659$	−5.45979			−0.212683			−0.106342	−	0.994330i	$-0.533914\pi$
$659$	−5.45979			−0.212683			−0.106342	+	0.994330i	$0.533914\pi$
$660$		0			0
$661$	32.1316			1.24977			0.624887	−	0.780715i	$-0.285145\pi$
$661$	32.1316			1.24977			0.624887	+	0.780715i	$0.285145\pi$
$662$		−	16.4171i		−	0.638070i
$663$		−	3.95717i		−	0.153684i
$664$	26.4423			1.02616
$665$	6.00167	+	19.9374i	0.232735	+	0.773141i
$666$	12.2458			0.474516
$667$			17.3537i			0.671938i
$668$		−	18.8659i		−	0.729942i
$669$	−12.6942			−0.490784
$670$	−64.5639	+	19.4354i	−2.49432	+	0.750854i
$671$		0			0
$672$			11.2433i			0.433721i
$673$			1.58054i			0.0609254i	0.999536	+	0.0304627i	$0.00969808\pi$
$673$			1.58054i			0.0609254i	−0.999536	+	0.0304627i	$0.990302\pi$
$674$	33.9502			1.30771
$675$	2.76014	+	4.16913i	0.106238	+	0.160470i
$676$	−35.4139			−1.36207
$677$		−	1.81064i		−	0.0695887i	−0.999394	−	0.0347944i	$-0.988922\pi$
$677$		−	1.81064i		−	0.0695887i	0.999394	−	0.0347944i	$-0.0110776\pi$
$678$		−	35.0450i		−	1.34589i
$679$	17.1534			0.658287
$680$	18.9688	−	5.71010i	0.727422	−	0.218972i
$681$	2.27677			0.0872459
$682$		0			0
$683$			11.3990i			0.436170i	0.975930	+	0.218085i	$0.0699810\pi$
$683$			11.3990i			0.436170i	−0.975930	+	0.218085i	$0.930019\pi$
$684$	−16.9563			−0.648341
$685$	−7.49528	−	24.8992i	−0.286380	−	0.951349i
$686$	40.4311			1.54367
$687$			20.1618i			0.769222i
$688$			8.84846i			0.337344i
$689$	3.90799			0.148883
$690$	4.67029	+	15.5146i	0.177795	+	0.590631i
$691$	9.31126			0.354217			0.177108	−	0.984191i	$-0.443326\pi$
$691$	9.31126			0.354217			0.177108	+	0.984191i	$0.443326\pi$
$692$		−	7.18625i		−	0.273180i
$693$		0			0
$694$	−48.0084			−1.82237
$695$	3.80468	−	1.14530i	0.144320	−	0.0434439i
$696$	10.5836			0.401171
$697$			18.5975i			0.704431i
$698$			12.9575i			0.490448i
$699$	−9.85555			−0.372771
$700$	−12.7610	−	19.2752i	−0.482321	−	0.728535i
$701$	22.6245			0.854515			0.427258	−	0.904130i	$-0.359480\pi$
$701$	22.6245			0.854515			0.427258	+	0.904130i	$0.359480\pi$
$702$		−	1.97390i		−	0.0745002i
$703$			32.3235i			1.21910i
$704$		0			0
$705$	−18.1502	+	5.46367i	−0.683576	+	0.205774i
$706$	19.8021			0.745261
$707$		−	21.2952i		−	0.800889i
$708$			20.9091i			0.785812i
$709$	−17.0391			−0.639918			−0.319959	−	0.947431i	$-0.603669\pi$
$709$	−17.0391			−0.639918			−0.319959	+	0.947431i	$0.603669\pi$
$710$	1.64583	+	5.46741i	0.0617668	+	0.205188i
$711$	4.89466			0.183564
$712$			16.1051i			0.603564i
$713$			29.1755i			1.09263i
$714$	15.6572			0.585957
$715$		0			0
$716$	−33.6950			−1.25924
$717$			9.55913i			0.356992i
$718$		−	11.3082i		−	0.422018i
$719$	−38.3908			−1.43173			−0.715867	−	0.698236i	$-0.753969\pi$
$719$	−38.3908			−1.43173			−0.715867	+	0.698236i	$0.753969\pi$
$720$	−2.96345	+	0.892074i	−0.110441	+	0.0332456i
$721$	−6.95274			−0.258934
$722$		−	33.5425i		−	1.24832i
$723$			4.58482i			0.170511i
$724$	−20.5002			−0.761884
$725$	22.1062	−	14.6352i	0.821003	−	0.543538i
$726$		0			0
$727$		−	35.5819i		−	1.31966i	−0.751416	−	0.659829i	$-0.770629\pi$
$727$		−	35.5819i		−	1.31966i	0.751416	−	0.659829i	$-0.229371\pi$
$728$			2.83561i			0.105095i
$729$	−1.00000			−0.0370370
$730$	31.5731	−	9.50429i	1.16857	−	0.351770i
$731$	28.3756			1.04951
$732$		−	5.89081i		−	0.217730i
$733$		−	43.3052i		−	1.59951i	−0.600324	−	0.799757i	$-0.704962\pi$
$733$		−	43.3052i		−	1.59951i	0.600324	−	0.799757i	$-0.295038\pi$
$734$	75.4928			2.78649
$735$	2.87538	+	9.55195i	0.106060	+	0.352329i
$736$	−23.0939			−0.851253
$737$		0			0
$738$			9.27676i			0.341482i
$739$	2.05329			0.0755314			0.0377657	−	0.999287i	$-0.487976\pi$
$739$	2.05329			0.0755314			0.0377657	+	0.999287i	$0.487976\pi$
$740$	−10.3444	−	34.3638i	−0.380267	−	1.26324i
$741$	5.21023			0.191403
$742$			15.4627i			0.567652i
$743$			5.12186i			0.187903i	0.995577	+	0.0939515i	$0.0299499\pi$
$743$			5.12186i			0.187903i	−0.995577	+	0.0939515i	$0.970050\pi$
$744$	17.7934			0.652339
$745$	−46.0297	+	13.8561i	−1.68640	+	0.507648i
$746$	−57.6565			−2.11096
$747$			13.2475i			0.484700i
$748$		0			0
$749$	−32.8282			−1.19952
$750$	15.8247	−	19.0335i	0.577837	−	0.695005i
$751$	−22.7758			−0.831101			−0.415551	−	0.909570i	$-0.636411\pi$
$751$	−22.7758			−0.831101			−0.415551	+	0.909570i	$0.636411\pi$
$752$		−	11.7323i		−	0.427831i
$753$			13.6439i			0.497211i
$754$	−10.4663			−0.381161
$755$	−17.2194	+	5.18347i	−0.626677	+	0.188646i
$756$	4.62332			0.168149
$757$		−	23.3537i		−	0.848806i	−0.905474	−	0.424403i	$-0.860484\pi$
$757$		−	23.3537i		−	0.848806i	0.905474	−	0.424403i	$-0.139516\pi$
$758$		−	3.23714i		−	0.117578i
$759$		0			0
$760$	7.51824	+	24.9755i	0.272715	+	0.905955i
$761$	12.3032			0.445990			0.222995	−	0.974820i	$-0.428417\pi$
$761$	12.3032			0.445990			0.222995	+	0.974820i	$0.428417\pi$
$762$		−	20.0337i		−	0.725743i
$763$		−	7.69691i		−	0.278647i
$764$	−69.1101			−2.50031
$765$	2.86074	+	9.50331i	0.103430	+	0.343593i
$766$	−7.64467			−0.276213
$767$		−	6.42482i		−	0.231987i
$768$			6.05265i			0.218406i
$769$	6.67277			0.240626			0.120313	−	0.992736i	$-0.461610\pi$
$769$	6.67277			0.240626			0.120313	+	0.992736i	$0.461610\pi$
$770$		0			0
$771$	−21.2167			−0.764101
$772$		−	73.1150i		−	2.63147i
$773$		−	4.51340i		−	0.162336i	−0.996700	−	0.0811678i	$-0.974135\pi$
$773$		−	4.51340i		−	0.162336i	0.996700	−	0.0811678i	$-0.0258650\pi$
$774$	14.1542			0.508763
$775$	37.1655	−	24.6051i	1.33502	−	0.883842i
$776$	21.4879			0.771371
$777$		−	8.81336i		−	0.316178i
$778$		−	9.06176i		−	0.324880i
$779$	−24.4866			−0.877322
$780$	−5.53911	+	1.66741i	−0.198332	+	0.0597030i
$781$		0			0
$782$			32.1601i			1.15004i
$783$			5.30235i			0.189490i
$784$	−6.17437			−0.220513
$785$	−10.9973	−	36.5327i	−0.392509	−	1.30391i
$786$	21.8607			0.779746
$787$			19.7596i			0.704355i	0.935933	+	0.352178i	$0.114559\pi$
$787$			19.7596i			0.704355i	−0.935933	+	0.352178i	$0.885441\pi$
$788$		−	21.0189i		−	0.748767i
$789$	15.4054			0.548446
$790$	−6.98461	−	23.2027i	−0.248501	−	0.825516i
$791$	−25.2220			−0.896792
$792$		0			0
$793$			1.81009i			0.0642783i
$794$	−15.7339			−0.558376
$795$	−9.38521	+	2.82519i	−0.332859	+	0.100199i
$796$	−38.9133			−1.37924
$797$			7.73449i			0.273970i	0.990573	+	0.136985i	$0.0437412\pi$
$797$			7.73449i			0.273970i	−0.990573	+	0.136985i	$0.956259\pi$
$798$			20.6152i			0.729771i
$799$	−37.6234			−1.33102
$800$	19.4762	+	29.4184i	0.688588	+	1.04010i
$801$	−8.06859			−0.285089
$802$		−	34.6744i		−	1.22440i
$803$		0			0
$804$	−39.5190			−1.39373
$805$	11.1659	−	3.36123i	0.393547	−	0.118468i
$806$	−17.5963			−0.619802
$807$			7.08797i			0.249508i
$808$		−	26.6763i		−	0.938469i
$809$	47.2899			1.66263			0.831313	−	0.555805i	$-0.187590\pi$
$809$	47.2899			1.66263			0.831313	+	0.555805i	$0.187590\pi$
$810$	1.42699	+	4.74042i	0.0501391	+	0.166561i
$811$	30.8261			1.08245			0.541226	−	0.840877i	$-0.317960\pi$
$811$	30.8261			1.08245			0.541226	+	0.840877i	$0.317960\pi$
$812$		−	24.5145i		−	0.860289i
$813$		−	29.1371i		−	1.02188i
$814$		0			0
$815$	8.68215	+	28.8419i	0.304122	+	1.01029i
$816$	−6.14292			−0.215045
$817$			37.3609i			1.30709i
$818$			41.1104i			1.43739i
$819$	−1.42063			−0.0496407
$820$	26.0322	−	7.83635i	0.909084	−	0.273657i
$821$	−2.64720			−0.0923877			−0.0461939	−	0.998932i	$-0.514709\pi$
$821$	−2.64720			−0.0923877			−0.0461939	+	0.998932i	$0.514709\pi$
$822$		−	25.7456i		−	0.897982i
$823$		−	6.44694i		−	0.224726i	−0.993667	−	0.112363i	$-0.964158\pi$
$823$		−	6.44694i		−	0.224726i	0.993667	−	0.112363i	$-0.0358420\pi$
$824$	−8.70964			−0.303415
$825$		0			0
$826$	25.4209			0.884508
$827$			26.9646i			0.937652i	0.883291	+	0.468826i	$0.155323\pi$
$827$			26.9646i			0.937652i	−0.883291	+	0.468826i	$0.844677\pi$
$828$			9.49635i			0.330021i
$829$	−34.6453			−1.20328			−0.601640	−	0.798767i	$-0.705486\pi$
$829$	−34.6453			−1.20328			−0.601640	+	0.798767i	$0.705486\pi$
$830$	62.7985	−	18.9039i	2.17977	−	0.656166i
$831$	−14.1005			−0.489142
$832$		−	11.4604i		−	0.397318i
$833$			19.8002i			0.686036i
$834$	3.93402			0.136224
$835$	−4.19079	−	13.9217i	−0.145028	−	0.481781i
$836$		0			0
$837$			8.91445i			0.308128i
$838$			5.29594i			0.182945i
$839$	−15.1597			−0.523372			−0.261686	−	0.965153i	$-0.584278\pi$
$839$	−15.1597			−0.523372			−0.261686	+	0.965153i	$0.584278\pi$
$840$	−2.04993	−	6.80983i	−0.0707294	−	0.234962i
$841$	−0.885106			−0.0305209
$842$			36.9213i			1.27239i
$843$			26.2478i			0.904023i
$844$	9.03459			0.310984
$845$	−26.1330	+	7.86671i	−0.899004	+	0.270623i
$846$	−18.7672			−0.645230
$847$		0			0
$848$		−	6.06658i		−	0.208327i
$849$	0.834033			0.0286239
$850$	40.9674	−	27.1222i	1.40517	−	0.930283i
$851$	18.1027			0.620554
$852$			3.34655i			0.114651i
$853$		−	44.4195i		−	1.52090i	−0.649399	−	0.760448i	$-0.724980\pi$
$853$		−	44.4195i		−	1.52090i	0.649399	−	0.760448i	$-0.275020\pi$
$854$	−7.16195			−0.245077
$855$	−12.5126	+	3.76661i	−0.427922	+	0.128815i
$856$	−41.1236			−1.40558
$857$		−	13.7395i		−	0.469333i	−0.972076	−	0.234667i	$-0.924600\pi$
$857$		−	13.7395i		−	0.469333i	0.972076	−	0.234667i	$-0.0753998\pi$
$858$		0			0
$859$	−54.6076			−1.86319			−0.931594	−	0.363499i	$-0.881582\pi$
$859$	−54.6076			−1.86319			−0.931594	+	0.363499i	$0.881582\pi$
$860$	−11.9565	−	39.7192i	−0.407713	−	1.35441i
$861$	6.67653			0.227535
$862$		−	45.1212i		−	1.53683i
$863$		−	42.3365i		−	1.44115i	−0.693377	−	0.720575i	$-0.743878\pi$
$863$		−	42.3365i		−	1.44115i	0.693377	−	0.720575i	$-0.256122\pi$
$864$	−7.05624			−0.240058
$865$	−1.59633	−	5.30296i	−0.0542767	−	0.180306i
$866$	−29.2548			−0.994119
$867$			2.69935i			0.0916747i
$868$		−	41.2144i		−	1.39891i
$869$		0			0
$870$	25.1353	−	7.56637i	0.852168	−	0.256524i
$871$	12.1432			0.411455
$872$		−	9.64185i		−	0.326514i
$873$			10.7654i			0.364352i
$874$	−42.3438			−1.43230
$875$	−13.6985	−	11.3891i	−0.463093	−	0.385023i
$876$	19.3256			0.652952
$877$			2.33065i			0.0787006i	0.999225	+	0.0393503i	$0.0125288\pi$
$877$			2.33065i			0.0787006i	−0.999225	+	0.0393503i	$0.987471\pi$
$878$		−	70.0774i		−	2.36500i
$879$	14.2041			0.479092
$880$		0			0
$881$	−21.4550			−0.722837			−0.361419	−	0.932404i	$-0.617707\pi$
$881$	−21.4550			−0.722837			−0.361419	+	0.932404i	$0.617707\pi$
$882$			9.87667i			0.332565i
$883$			10.1555i			0.341761i	0.985292	+	0.170880i	$0.0546611\pi$
$883$			10.1555i			0.341761i	−0.985292	+	0.170880i	$0.945339\pi$
$884$	−11.4820			−0.386181
$885$	4.64466	+	15.4295i	0.156129	+	0.518656i
$886$	52.6193			1.76778
$887$		−	17.2592i		−	0.579509i	−0.957101	−	0.289754i	$-0.906426\pi$
$887$		−	17.2592i		−	0.579509i	0.957101	−	0.289754i	$-0.0935736\pi$
$888$		−	11.0404i		−	0.370492i
$889$	−14.4183			−0.483575
$890$	11.5138	+	38.2485i	0.385942	+	1.28209i
$891$		0			0
$892$			36.8329i			1.23326i
$893$		−	49.5372i		−	1.65770i
$894$	−47.5945			−1.59180
$895$	−24.8646	+	7.48487i	−0.831132	+	0.250192i
$896$	22.8584			0.763645
$897$		−	2.91798i		−	0.0974286i
$898$		−	31.7155i		−	1.05836i
$899$	47.2675			1.57646
$900$	12.0970	−	8.00873i	0.403234	−	0.266958i
$901$	−19.4545			−0.648125
$902$		0			0
$903$		−	10.1869i		−	0.338997i
$904$	−31.5954			−1.05085
$905$	−15.1278	+	4.55384i	−0.502864	+	0.151375i
$906$	−17.8047			−0.591523
$907$		−	56.3356i		−	1.87059i	−0.353865	−	0.935297i	$-0.615133\pi$
$907$		−	56.3356i		−	1.87059i	0.353865	−	0.935297i	$-0.384867\pi$
$908$		−	6.60620i		−	0.219234i
$909$	13.3647			0.443280
$910$	2.02721	+	6.73437i	0.0672015	+	0.223242i
$911$	55.8484			1.85034			0.925170	−	0.379554i	$-0.123923\pi$
$911$	55.8484			1.85034			0.925170	+	0.379554i	$0.123923\pi$
$912$		−	8.08812i		−	0.267824i
$913$		0			0
$914$	−0.241098			−0.00797481
$915$	−1.30856	−	4.34702i	−0.0432597	−	0.143708i
$916$	58.5010			1.93293
$917$		−	15.7332i		−	0.519558i
$918$			9.82638i			0.324319i
$919$	7.07031			0.233228			0.116614	−	0.993177i	$-0.462796\pi$
$919$	7.07031			0.233228			0.116614	+	0.993177i	$0.462796\pi$
$920$	13.9875	−	4.21058i	0.461153	−	0.138819i
$921$	0.166296			0.00547965
$922$		−	19.2048i		−	0.632476i
$923$		−	1.02831i		−	0.0338472i
$924$		0			0
$925$	−15.2669	−	23.0603i	−0.501973	−	0.758219i
$926$	69.4093			2.28093
$927$		−	4.36350i		−	0.143316i
$928$			37.4147i			1.22820i
$929$	−33.6177			−1.10296			−0.551480	−	0.834188i	$-0.685937\pi$
$929$	−33.6177			−1.10296			−0.551480	+	0.834188i	$0.685937\pi$
$930$	42.2582	−	12.7208i	1.38570	−	0.417131i
$931$	−26.0700			−0.854411
$932$			28.5965i			0.936711i
$933$		−	6.52076i		−	0.213480i
$934$	−52.2531			−1.70977
$935$		0			0
$936$	−1.77961			−0.0581683
$937$		−	55.2419i		−	1.80467i	−0.431032	−	0.902337i	$-0.641850\pi$
$937$		−	55.2419i		−	1.80467i	0.431032	−	0.902337i	$-0.358150\pi$
$938$			48.0466i			1.56878i
$939$	−0.803861			−0.0262330
$940$	15.8532	+	52.6640i	0.517074	+	1.71771i
$941$	47.9312			1.56251			0.781256	−	0.624211i	$-0.214579\pi$
$941$	47.9312			1.56251			0.781256	+	0.624211i	$0.214579\pi$
$942$		−	37.7746i		−	1.23076i
$943$			13.7137i			0.446578i
$944$	−9.97359			−0.324613
$945$	3.41170	−	1.02701i	0.110983	−	0.0334086i
$946$		0			0
$947$			42.2493i			1.37292i	0.727168	+	0.686459i	$0.240836\pi$
$947$			42.2493i			1.37292i	−0.727168	+	0.686459i	$0.759164\pi$
$948$		−	14.2022i		−	0.461266i
$949$	−5.93826			−0.192764
$950$	35.7106	+	53.9401i	1.15860	+	1.75005i
$951$	14.4751			0.469386
$952$		−	14.1161i		−	0.457504i
$953$		−	24.5617i		−	0.795631i	−0.917465	−	0.397815i	$-0.869768\pi$
$953$		−	24.5617i		−	0.795631i	0.917465	−	0.397815i	$-0.130232\pi$
$954$	−9.70426			−0.314187
$955$	−50.9985	+	15.3518i	−1.65027	+	0.496774i
$956$	27.7365			0.897061
$957$		0			0
$958$			54.6863i			1.76683i
$959$	−18.5292			−0.598341
$960$	8.28501	+	27.5226i	0.267397	+	0.888289i
$961$	48.4674			1.56346
$962$			10.9181i			0.352013i
$963$		−	20.6028i		−	0.663915i
$964$	13.3032			0.428466
$965$	−16.2415	−	53.9539i	−0.522832	−	1.73684i
$966$	11.5455			0.371471
$967$		−	6.41686i		−	0.206352i	−0.994663	−	0.103176i	$-0.967099\pi$
$967$		−	6.41686i		−	0.206352i	0.994663	−	0.103176i	$-0.0329006\pi$
$968$		0			0
$969$	−25.9373			−0.833226
$970$	51.0323	−	15.3620i	1.63855	−	0.493244i
$971$	4.82827			0.154946			0.0774732	−	0.996994i	$-0.475315\pi$
$971$	4.82827			0.154946			0.0774732	+	0.996994i	$0.475315\pi$
$972$			2.90157i			0.0930678i
$973$		−	2.83133i		−	0.0907683i
$974$	17.1221			0.548628
$975$	−3.71710	+	2.46087i	−0.119042	+	0.0788111i
$976$	2.80990			0.0899428
$977$		−	42.7689i		−	1.36830i	−0.729343	−	0.684149i	$-0.760174\pi$
$977$		−	42.7689i		−	1.36830i	0.729343	−	0.684149i	$-0.239826\pi$
$978$			29.8224i			0.953616i
$979$		0			0
$980$	27.7156	−	8.34311i	0.885344	−	0.266511i
$981$	4.83053			0.154227
$982$			42.9944i			1.37201i
$983$			4.63530i			0.147843i	0.997264	+	0.0739215i	$0.0235514\pi$
$983$			4.63530i			0.147843i	−0.997264	+	0.0739215i	$0.976449\pi$
$984$	8.36363			0.266623
$985$	−4.66905	−	15.5105i	−0.148768	−	0.494206i
$986$	52.1029			1.65929
$987$			13.5069i			0.429928i
$988$		−	15.1178i		−	0.480963i
$989$	20.9239			0.665342
$990$		0			0
$991$	17.0726			0.542330			0.271165	−	0.962533i	$-0.412591\pi$
$991$	17.0726			0.542330			0.271165	+	0.962533i	$0.412591\pi$
$992$			62.9025i			1.99716i
$993$		−	7.41532i		−	0.235318i
$994$	4.06869			0.129051
$995$	−28.7154	+	8.64405i	−0.910338	+	0.274035i
$996$	38.4384			1.21797
$997$		−	6.59685i		−	0.208924i	−0.994529	−	0.104462i	$-0.966688\pi$
$997$		−	6.59685i		−	0.208924i	0.994529	−	0.104462i	$-0.0333121\pi$
$998$			0.189792i			0.00600777i
$999$	5.53121			0.175000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.k.364.4		24
5.2	odd	4		9075.2.a.dx.1.11		12
5.3	odd	4		9075.2.a.ea.1.2		12
5.4	even	2	inner	1815.2.c.k.364.21		24
11.7	odd	10		165.2.s.a.49.2	✓	48
11.8	odd	10		165.2.s.a.64.11	yes	48
11.10	odd	2		1815.2.c.j.364.21		24
33.8	even	10		495.2.ba.c.64.2		48
33.29	even	10		495.2.ba.c.379.11		48
55.7	even	20		825.2.n.o.676.1		24
55.8	even	20		825.2.n.p.526.6		24
55.18	even	20		825.2.n.p.676.6		24
55.19	odd	10		165.2.s.a.64.2	yes	48
55.29	odd	10		165.2.s.a.49.11	yes	48
55.32	even	4		9075.2.a.dz.1.2		12
55.43	even	4		9075.2.a.dy.1.11		12
55.52	even	20		825.2.n.o.526.1		24
55.54	odd	2		1815.2.c.j.364.4		24
165.29	even	10		495.2.ba.c.379.2		48
165.74	even	10		495.2.ba.c.64.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.2	✓	48	11.7	odd	10
165.2.s.a.49.11	yes	48	55.29	odd	10
165.2.s.a.64.2	yes	48	55.19	odd	10
165.2.s.a.64.11	yes	48	11.8	odd	10
495.2.ba.c.64.2		48	33.8	even	10
495.2.ba.c.64.11		48	165.74	even	10
495.2.ba.c.379.2		48	165.29	even	10
495.2.ba.c.379.11		48	33.29	even	10
825.2.n.o.526.1		24	55.52	even	20
825.2.n.o.676.1		24	55.7	even	20
825.2.n.p.526.6		24	55.8	even	20
825.2.n.p.676.6		24	55.18	even	20
1815.2.c.j.364.4		24	55.54	odd	2
1815.2.c.j.364.21		24	11.10	odd	2
1815.2.c.k.364.4		24	1.1	even	1	trivial
1815.2.c.k.364.21		24	5.4	even	2	inner
9075.2.a.dx.1.11		12	5.2	odd	4
9075.2.a.dy.1.11		12	55.43	even	4
9075.2.a.dz.1.2		12	55.32	even	4
9075.2.a.ea.1.2		12	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.21395i q^{2} -1.00000i q^{3} -2.90157 q^{4} +(-2.14116 + 0.644543i) q^{5} -2.21395 q^{6} +1.59339i q^{7} +1.99602i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.21395i q^{2} -1.00000i q^{3} -2.90157 q^{4} +(-2.14116 + 0.644543i) q^{5} -2.21395 q^{6} +1.59339i q^{7} +1.99602i q^{8} -1.00000 q^{9} +(1.42699 + 4.74042i) q^{10} +2.90157i q^{12} -0.891576i q^{13} +3.52768 q^{14} +(0.644543 + 2.14116i) q^{15} -1.38404 q^{16} +4.43839i q^{17} +2.21395i q^{18} -5.84384 q^{19} +(6.21272 - 1.87019i) q^{20} +1.59339 q^{21} +3.27284i q^{23} +1.99602 q^{24} +(4.16913 - 2.76014i) q^{25} -1.97390 q^{26} +1.00000i q^{27} -4.62332i q^{28} +5.30235 q^{29} +(4.74042 - 1.42699i) q^{30} +8.91445 q^{31} +7.05624i q^{32} +9.82638 q^{34} +(-1.02701 - 3.41170i) q^{35} +2.90157 q^{36} -5.53121i q^{37} +12.9380i q^{38} -0.891576 q^{39} +(-1.28652 - 4.27381i) q^{40} +4.19014 q^{41} -3.52768i q^{42} -6.39321i q^{43} +(2.14116 - 0.644543i) q^{45} +7.24589 q^{46} +8.47681i q^{47} +1.38404i q^{48} +4.46111 q^{49} +(-6.11081 - 9.23024i) q^{50} +4.43839 q^{51} +2.58697i q^{52} +4.38324i q^{53} +2.21395 q^{54} -3.18044 q^{56} +5.84384i q^{57} -11.7391i q^{58} +7.20613 q^{59} +(-1.87019 - 6.21272i) q^{60} -2.03022 q^{61} -19.7361i q^{62} -1.59339i q^{63} +12.8541 q^{64} +(0.574659 + 1.90901i) q^{65} +13.6199i q^{67} -12.8783i q^{68} +3.27284 q^{69} +(-7.55333 + 2.27374i) q^{70} +1.15336 q^{71} -1.99602i q^{72} -6.66040i q^{73} -12.2458 q^{74} +(-2.76014 - 4.16913i) q^{75} +16.9563 q^{76} +1.97390i q^{78} -4.89466 q^{79} +(2.96345 - 0.892074i) q^{80} +1.00000 q^{81} -9.27676i q^{82} -13.2475i q^{83} -4.62332 q^{84} +(-2.86074 - 9.50331i) q^{85} -14.1542 q^{86} -5.30235i q^{87} +8.06859 q^{89} +(-1.42699 - 4.74042i) q^{90} +1.42063 q^{91} -9.49635i q^{92} -8.91445i q^{93} +18.7672 q^{94} +(12.5126 - 3.76661i) q^{95} +7.05624 q^{96} -10.7654i q^{97} -9.87667i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} - 2 q^{5} + 8 q^{6} - 24 q^{9} + 6 q^{10} - 12 q^{14} + 48 q^{16} - 32 q^{19} - 2 q^{20} + 16 q^{21} - 24 q^{24} + 2 q^{25} + 32 q^{26} + 8 q^{30} - 12 q^{34} - 10 q^{35} + 24 q^{36} - 36 q^{39} - 34 q^{40} + 2 q^{45} + 56 q^{46} - 24 q^{49} - 46 q^{50} + 36 q^{51} - 8 q^{54} + 12 q^{56} - 40 q^{59} - 26 q^{60} + 40 q^{61} + 12 q^{64} - 10 q^{65} - 2 q^{70} + 64 q^{71} + 136 q^{74} + 20 q^{75} + 68 q^{76} - 64 q^{79} + 76 q^{80} + 24 q^{81} - 60 q^{84} - 72 q^{86} + 20 q^{89} - 6 q^{90} + 4 q^{94} - 64 q^{95} + 56 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 - 2 * q^5 + 8 * q^6 - 24 * q^9 + 6 * q^10 - 12 * q^14 + 48 * q^16 - 32 * q^19 - 2 * q^20 + 16 * q^21 - 24 * q^24 + 2 * q^25 + 32 * q^26 + 8 * q^30 - 12 * q^34 - 10 * q^35 + 24 * q^36 - 36 * q^39 - 34 * q^40 + 2 * q^45 + 56 * q^46 - 24 * q^49 - 46 * q^50 + 36 * q^51 - 8 * q^54 + 12 * q^56 - 40 * q^59 - 26 * q^60 + 40 * q^61 + 12 * q^64 - 10 * q^65 - 2 * q^70 + 64 * q^71 + 136 * q^74 + 20 * q^75 + 68 * q^76 - 64 * q^79 + 76 * q^80 + 24 * q^81 - 60 * q^84 - 72 * q^86 + 20 * q^89 - 6 * q^90 + 4 * q^94 - 64 * q^95 + 56 * q^96

Introduction

L-functions

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