LMFDB - Embedded newform 1155.2.c.e.694.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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, 1, 0, 0]))

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15194x^12 + 40320x^10 + 61593x^8 + 48545x^6 + 15624x^4 + 2116*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.5
Root			$-1.76958i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76958i q^{2} -1.00000i q^{3} -1.13141 q^{4} +(-1.09533 + 1.94942i) q^{5} -1.76958 q^{6} +1.00000i q^{7} -1.53703i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.76958i q^{2} -1.00000i q^{3} -1.13141 q^{4} +(-1.09533 + 1.94942i) q^{5} -1.76958 q^{6} +1.00000i q^{7} -1.53703i q^{8} -1.00000 q^{9} +(3.44966 + 1.93828i) q^{10} -1.00000 q^{11} +1.13141i q^{12} -2.21799i q^{13} +1.76958 q^{14} +(1.94942 + 1.09533i) q^{15} -4.98273 q^{16} +7.13609i q^{17} +1.76958i q^{18} -7.91732 q^{19} +(1.23928 - 2.20560i) q^{20} +1.00000 q^{21} +1.76958i q^{22} +1.96946i q^{23} -1.53703 q^{24} +(-2.60049 - 4.27054i) q^{25} -3.92492 q^{26} +1.00000i q^{27} -1.13141i q^{28} -5.96676 q^{29} +(1.93828 - 3.44966i) q^{30} -1.40203 q^{31} +5.74327i q^{32} +1.00000i q^{33} +12.6279 q^{34} +(-1.94942 - 1.09533i) q^{35} +1.13141 q^{36} +1.37740i q^{37} +14.0103i q^{38} -2.21799 q^{39} +(2.99633 + 1.68357i) q^{40} +4.80897 q^{41} -1.76958i q^{42} +2.34312i q^{43} +1.13141 q^{44} +(1.09533 - 1.94942i) q^{45} +3.48511 q^{46} +9.10681i q^{47} +4.98273i q^{48} -1.00000 q^{49} +(-7.55705 + 4.60177i) q^{50} +7.13609 q^{51} +2.50947i q^{52} +2.65832i q^{53} +1.76958 q^{54} +(1.09533 - 1.94942i) q^{55} +1.53703 q^{56} +7.91732i q^{57} +10.5587i q^{58} -6.97339 q^{59} +(-2.20560 - 1.23928i) q^{60} -1.37707 q^{61} +2.48101i q^{62} -1.00000i q^{63} +0.197717 q^{64} +(4.32380 + 2.42944i) q^{65} +1.76958 q^{66} -12.8612i q^{67} -8.07387i q^{68} +1.96946 q^{69} +(-1.93828 + 3.44966i) q^{70} +1.16523 q^{71} +1.53703i q^{72} +4.94568i q^{73} +2.43742 q^{74} +(-4.27054 + 2.60049i) q^{75} +8.95776 q^{76} -1.00000i q^{77} +3.92492i q^{78} -0.590789 q^{79} +(5.45775 - 9.71344i) q^{80} +1.00000 q^{81} -8.50986i q^{82} +11.2827i q^{83} -1.13141 q^{84} +(-13.9113 - 7.81641i) q^{85} +4.14633 q^{86} +5.96676i q^{87} +1.53703i q^{88} +9.79134 q^{89} +(-3.44966 - 1.93828i) q^{90} +2.21799 q^{91} -2.22827i q^{92} +1.40203i q^{93} +16.1152 q^{94} +(8.67211 - 15.4342i) q^{95} +5.74327 q^{96} -12.8085i q^{97} +1.76958i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * 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 $

$2$		−	1.76958i		−	1.25128i	−0.780111	−	0.625641i	$-0.784838\pi$
$2$		−	1.76958i		−	1.25128i	0.780111	−	0.625641i	$-0.215162\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.13141			−0.565706
$5$	−1.09533	+	1.94942i	−0.489848	+	0.871808i
$5$	−1.09533	+	1.94942i	−0.489848	+	0.871808i
$6$	−1.76958			−0.722428
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.53703i		−	0.543424i
$9$	−1.00000			−0.333333
$10$	3.44966	+	1.93828i	1.09088	+	0.612938i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			1.13141i			0.326611i
$13$		−	2.21799i		−	0.615160i	−0.951522	−	0.307580i	$-0.900481\pi$
$13$		−	2.21799i		−	0.615160i	0.951522	−	0.307580i	$-0.0995192\pi$
$14$	1.76958			0.472940
$15$	1.94942	+	1.09533i	0.503338	+	0.282814i
$16$	−4.98273			−1.24568
$17$			7.13609i			1.73076i	0.501119	+	0.865379i	$0.332922\pi$
$17$			7.13609i			1.73076i	−0.501119	+	0.865379i	$0.667078\pi$
$18$			1.76958i			0.417094i
$19$	−7.91732			−1.81636			−0.908179	−	0.418582i	$-0.862527\pi$
$19$	−7.91732			−1.81636			−0.908179	+	0.418582i	$0.862527\pi$
$20$	1.23928	−	2.20560i	0.277110	−	0.493187i
$21$	1.00000			0.218218
$22$			1.76958i			0.377276i
$23$			1.96946i			0.410660i	0.978693	+	0.205330i	$0.0658268\pi$
$23$			1.96946i			0.410660i	−0.978693	+	0.205330i	$0.934173\pi$
$24$	−1.53703			−0.313746
$25$	−2.60049	−	4.27054i	−0.520097	−	0.854107i
$26$	−3.92492			−0.769739
$27$			1.00000i			0.192450i
$28$		−	1.13141i		−	0.213817i
$29$	−5.96676			−1.10800			−0.554000	−	0.832517i	$-0.686899\pi$
$29$	−5.96676			−1.10800			−0.554000	+	0.832517i	$0.686899\pi$
$30$	1.93828	−	3.44966i	0.353880	−	0.629818i
$31$	−1.40203			−0.251812			−0.125906	−	0.992042i	$-0.540184\pi$
$31$	−1.40203			−0.251812			−0.125906	+	0.992042i	$0.540184\pi$
$32$			5.74327i			1.01528i
$33$			1.00000i			0.174078i
$34$	12.6279			2.16567
$35$	−1.94942	−	1.09533i	−0.329512	−	0.185145i
$36$	1.13141			0.188569
$37$			1.37740i			0.226443i	0.993570	+	0.113221i	$0.0361169\pi$
$37$			1.37740i			0.226443i	−0.993570	+	0.113221i	$0.963883\pi$
$38$			14.0103i			2.27278i
$39$	−2.21799			−0.355163
$40$	2.99633	+	1.68357i	0.473761	+	0.266195i
$41$	4.80897			0.751035			0.375517	−	0.926815i	$-0.377465\pi$
$41$	4.80897			0.751035			0.375517	+	0.926815i	$0.377465\pi$
$42$		−	1.76958i		−	0.273052i
$43$			2.34312i			0.357322i	0.983911	+	0.178661i	$0.0571766\pi$
$43$			2.34312i			0.357322i	−0.983911	+	0.178661i	$0.942823\pi$
$44$	1.13141			0.170567
$45$	1.09533	−	1.94942i	0.163283	−	0.290603i
$46$	3.48511			0.513852
$47$			9.10681i			1.32836i	0.747571	+	0.664182i	$0.231220\pi$
$47$			9.10681i			1.32836i	−0.747571	+	0.664182i	$0.768780\pi$
$48$			4.98273i			0.719195i
$49$	−1.00000			−0.142857
$50$	−7.55705	+	4.60177i	−1.06873	+	0.650788i
$51$	7.13609			0.999253
$52$			2.50947i			0.348000i
$53$			2.65832i			0.365148i	0.983192	+	0.182574i	$0.0584430\pi$
$53$			2.65832i			0.365148i	−0.983192	+	0.182574i	$0.941557\pi$
$54$	1.76958			0.240809
$55$	1.09533	−	1.94942i	0.147695	−	0.262860i
$56$	1.53703			0.205395
$57$			7.91732i			1.04867i
$58$			10.5587i			1.38642i
$59$	−6.97339			−0.907859			−0.453929	−	0.891038i	$-0.649978\pi$
$59$	−6.97339			−0.907859			−0.453929	+	0.891038i	$0.649978\pi$
$60$	−2.20560	−	1.23928i	−0.284742	−	0.159990i
$61$	−1.37707			−0.176316			−0.0881580	−	0.996107i	$-0.528098\pi$
$61$	−1.37707			−0.176316			−0.0881580	+	0.996107i	$0.528098\pi$
$62$			2.48101i			0.315088i
$63$		−	1.00000i		−	0.125988i
$64$	0.197717			0.0247146
$65$	4.32380	+	2.42944i	0.536302	+	0.301335i
$66$	1.76958			0.217820
$67$		−	12.8612i		−	1.57124i	−0.618708	−	0.785621i	$-0.712343\pi$
$67$		−	12.8612i		−	1.57124i	0.618708	−	0.785621i	$-0.287657\pi$
$68$		−	8.07387i		−	0.979101i
$69$	1.96946			0.237095
$70$	−1.93828	+	3.44966i	−0.231669	+	0.412313i
$71$	1.16523			0.138288			0.0691439	−	0.997607i	$-0.477973\pi$
$71$	1.16523			0.138288			0.0691439	+	0.997607i	$0.477973\pi$
$72$			1.53703i			0.181141i
$73$			4.94568i			0.578848i	0.957201	+	0.289424i	$0.0934637\pi$
$73$			4.94568i			0.578848i	−0.957201	+	0.289424i	$0.906536\pi$
$74$	2.43742			0.283344
$75$	−4.27054	+	2.60049i	−0.493119	+	0.300278i
$76$	8.95776			1.02753
$77$		−	1.00000i		−	0.113961i
$78$			3.92492i			0.444409i
$79$	−0.590789			−0.0664690			−0.0332345	−	0.999448i	$-0.510581\pi$
$79$	−0.590789			−0.0664690			−0.0332345	+	0.999448i	$0.510581\pi$
$80$	5.45775	−	9.71344i	0.610196	−	1.08600i
$81$	1.00000			0.111111
$82$		−	8.50986i		−	0.939756i
$83$			11.2827i			1.23844i	0.785217	+	0.619221i	$0.212552\pi$
$83$			11.2827i			1.23844i	−0.785217	+	0.619221i	$0.787448\pi$
$84$	−1.13141			−0.123447
$85$	−13.9113	−	7.81641i	−1.50889	−	0.847808i
$86$	4.14633			0.447111
$87$			5.96676i			0.639704i
$88$			1.53703i			0.163848i
$89$	9.79134			1.03788			0.518940	−	0.854811i	$-0.326327\pi$
$89$	9.79134			1.03788			0.518940	+	0.854811i	$0.326327\pi$
$90$	−3.44966	−	1.93828i	−0.363626	−	0.204313i
$91$	2.21799			0.232509
$92$		−	2.22827i		−	0.232313i
$93$			1.40203i			0.145384i
$94$	16.1152			1.66216
$95$	8.67211	−	15.4342i	0.889740	−	1.58351i
$96$	5.74327			0.586170
$97$		−	12.8085i		−	1.30050i	−0.759719	−	0.650252i	$-0.774663\pi$
$97$		−	12.8085i		−	1.30050i	0.759719	−	0.650252i	$-0.225337\pi$
$98$			1.76958i			0.178755i
$99$	1.00000			0.100504
$100$	2.94222	+	4.83174i	0.294222	+	0.483174i
$101$	12.2576			1.21968			0.609840	−	0.792524i	$-0.291234\pi$
$101$	12.2576			1.21968			0.609840	+	0.792524i	$0.291234\pi$
$102$		−	12.6279i		−	1.25035i
$103$		−	2.08029i		−	0.204977i	−0.994734	−	0.102489i	$-0.967319\pi$
$103$		−	2.08029i		−	0.204977i	0.994734	−	0.102489i	$-0.0326805\pi$
$104$	−3.40913			−0.334293
$105$	−1.09533	+	1.94942i	−0.106894	+	0.190244i
$106$	4.70411			0.456903
$107$		−	4.58118i		−	0.442880i	−0.975174	−	0.221440i	$-0.928924\pi$
$107$		−	4.58118i		−	0.442880i	0.975174	−	0.221440i	$-0.0710757\pi$
$108$		−	1.13141i		−	0.108870i
$109$	−17.3946			−1.66610			−0.833049	−	0.553199i	$-0.813407\pi$
$109$	−17.3946			−1.66610			−0.833049	+	0.553199i	$0.813407\pi$
$110$	−3.44966	−	1.93828i	−0.328912	−	0.184808i
$111$	1.37740			0.130737
$112$		−	4.98273i		−	0.470824i
$113$		−	17.4058i		−	1.63740i	−0.574223	−	0.818699i	$-0.694696\pi$
$113$		−	17.4058i		−	1.63740i	0.574223	−	0.818699i	$-0.305304\pi$
$114$	14.0103			1.31219
$115$	−3.83930	−	2.15721i	−0.358017	−	0.201161i
$116$	6.75088			0.626803
$117$			2.21799i			0.205053i
$118$			12.3400i			1.13599i
$119$	−7.13609			−0.654165
$120$	1.68357	−	2.99633i	0.153688	−	0.273526i
$121$	1.00000			0.0909091
$122$			2.43684i			0.220621i
$123$		−	4.80897i		−	0.433610i
$124$	1.58628			0.142452
$125$	11.1735	−	0.391781i	0.999386	−	0.0350420i
$126$	−1.76958			−0.157647
$127$			3.46223i			0.307223i	0.988131	+	0.153612i	$0.0490905\pi$
$127$			3.46223i			0.307223i	−0.988131	+	0.153612i	$0.950910\pi$
$128$			11.1367i			0.984352i
$129$	2.34312			0.206300
$130$	4.29909	−	7.65131i	0.377055	−	0.671065i
$131$	−22.1468			−1.93497			−0.967486	−	0.252926i	$-0.918607\pi$
$131$	−22.1468			−1.93497			−0.967486	+	0.252926i	$0.918607\pi$
$132$		−	1.13141i		−	0.0984769i
$133$		−	7.91732i		−	0.686519i
$134$	−22.7589			−1.96607
$135$	−1.94942	−	1.09533i	−0.167779	−	0.0942713i
$136$	10.9684			0.940534
$137$			1.46064i			0.124791i	0.998052	+	0.0623955i	$0.0198740\pi$
$137$			1.46064i			0.124791i	−0.998052	+	0.0623955i	$0.980126\pi$
$138$		−	3.48511i		−	0.296672i
$139$	−9.36082			−0.793974			−0.396987	−	0.917824i	$-0.629944\pi$
$139$	−9.36082			−0.793974			−0.396987	+	0.917824i	$0.629944\pi$
$140$	2.20560	+	1.23928i	0.186407	+	0.104738i
$141$	9.10681			0.766932
$142$		−	2.06197i		−	0.173037i
$143$			2.21799i			0.185478i
$144$	4.98273			0.415228
$145$	6.53560	−	11.6317i	0.542752	−	0.965963i
$146$	8.75177			0.724302
$147$			1.00000i			0.0824786i
$148$		−	1.55841i		−	0.128100i
$149$	−4.83051			−0.395731			−0.197865	−	0.980229i	$-0.563401\pi$
$149$	−4.83051			−0.395731			−0.197865	+	0.980229i	$0.563401\pi$
$150$	4.60177	+	7.55705i	0.375733	+	0.617031i
$151$	4.20036			0.341820			0.170910	−	0.985287i	$-0.445329\pi$
$151$	4.20036			0.341820			0.170910	+	0.985287i	$0.445329\pi$
$152$			12.1692i			0.987052i
$153$		−	7.13609i		−	0.576919i
$154$	−1.76958			−0.142597
$155$	1.53569	−	2.73315i	0.123350	−	0.219532i
$156$	2.50947			0.200918
$157$		−	15.5645i		−	1.24218i	−0.783740	−	0.621089i	$-0.786690\pi$
$157$		−	15.5645i		−	1.24218i	0.783740	−	0.621089i	$-0.213310\pi$
$158$			1.04545i			0.0831714i
$159$	2.65832			0.210818
$160$	−11.1961	−	6.29080i	−0.885126	−	0.497332i
$161$	−1.96946			−0.155215
$162$		−	1.76958i		−	0.139031i
$163$			13.8852i			1.08757i	0.839224	+	0.543786i	$0.183010\pi$
$163$			13.8852i			1.08757i	−0.839224	+	0.543786i	$0.816990\pi$
$164$	−5.44093			−0.424865
$165$	−1.94942	−	1.09533i	−0.151762	−	0.0852716i
$166$	19.9657			1.54964
$167$		−	0.944301i		−	0.0730722i	−0.999332	−	0.0365361i	$-0.988368\pi$
$167$		−	0.944301i		−	0.0730722i	0.999332	−	0.0365361i	$-0.0116324\pi$
$168$		−	1.53703i		−	0.118585i
$169$	8.08051			0.621578
$170$	−13.8318	+	24.6171i	−1.06085	+	1.88804i
$171$	7.91732			0.605453
$172$		−	2.65103i		−	0.202139i
$173$			18.2684i			1.38892i	0.719533	+	0.694459i	$0.244356\pi$
$173$			18.2684i			1.38892i	−0.719533	+	0.694459i	$0.755644\pi$
$174$	10.5587			0.800451
$175$	4.27054	−	2.60049i	0.322822	−	0.196578i
$176$	4.98273			0.375587
$177$			6.97339i			0.524152i
$178$		−	17.3266i		−	1.29868i
$179$	−22.7304			−1.69895			−0.849475	−	0.527629i	$-0.823081\pi$
$179$	−22.7304			−1.69895			−0.849475	+	0.527629i	$0.823081\pi$
$180$	−1.23928	+	2.20560i	−0.0923701	+	0.164396i
$181$	−0.261264			−0.0194196			−0.00970979	−	0.999953i	$-0.503091\pi$
$181$	−0.261264			−0.0194196			−0.00970979	+	0.999953i	$0.503091\pi$
$182$		−	3.92492i		−	0.290934i
$183$			1.37707i			0.101796i
$184$	3.02712			0.223162
$185$	−2.68513	−	1.50871i	−0.197415	−	0.110923i
$186$	2.48101			0.181916
$187$		−	7.13609i		−	0.521843i
$188$		−	10.3036i		−	0.751464i
$189$	−1.00000			−0.0727393
$190$	−27.3120	−	15.3460i	−1.98142	−	1.11332i
$191$	−10.3563			−0.749353			−0.374676	−	0.927156i	$-0.622246\pi$
$191$	−10.3563			−0.749353			−0.374676	+	0.927156i	$0.622246\pi$
$192$		−	0.197717i		−	0.0142690i
$193$		−	0.379539i		−	0.0273198i	−0.999907	−	0.0136599i	$-0.995652\pi$
$193$		−	0.379539i		−	0.0273198i	0.999907	−	0.0136599i	$-0.00434822\pi$
$194$	−22.6656			−1.62730
$195$	2.42944	−	4.32380i	0.173976	−	0.309634i
$196$	1.13141			0.0808152
$197$			1.99726i			0.142299i	0.997466	+	0.0711496i	$0.0226668\pi$
$197$			1.99726i			0.142299i	−0.997466	+	0.0711496i	$0.977333\pi$
$198$		−	1.76958i		−	0.125759i
$199$	24.8988			1.76503			0.882514	−	0.470285i	$-0.155849\pi$
$199$	24.8988			1.76503			0.882514	+	0.470285i	$0.155849\pi$
$200$	−6.56396	+	3.99704i	−0.464142	+	0.282633i
$201$	−12.8612			−0.907157
$202$		−	21.6909i		−	1.52616i
$203$		−	5.96676i		−	0.418785i
$204$	−8.07387			−0.565284
$205$	−5.26743	+	9.37471i	−0.367893	+	0.654758i
$206$	−3.68124			−0.256484
$207$		−	1.96946i		−	0.136887i
$208$			11.0517i			0.766295i
$209$	7.91732			0.547653
$210$	3.44966	+	1.93828i	0.238049	+	0.133754i
$211$	9.48586			0.653034			0.326517	−	0.945191i	$-0.394125\pi$
$211$	9.48586			0.653034			0.326517	+	0.945191i	$0.394125\pi$
$212$		−	3.00766i		−	0.206567i
$213$		−	1.16523i		−	0.0798405i
$214$	−8.10677			−0.554168
$215$	−4.56772	−	2.56650i	−0.311516	−	0.175034i
$216$	1.53703			0.104582
$217$		−	1.40203i		−	0.0951761i
$218$			30.7811i			2.08476i
$219$	4.94568			0.334198
$220$	−1.23928	+	2.20560i	−0.0835519	+	0.148702i
$221$	15.8278			1.06469
$222$		−	2.43742i		−	0.163589i
$223$		−	7.84249i		−	0.525172i	−0.964909	−	0.262586i	$-0.915425\pi$
$223$		−	7.84249i		−	0.525172i	0.964909	−	0.262586i	$-0.0845753\pi$
$224$	−5.74327			−0.383738
$225$	2.60049	+	4.27054i	0.173366	+	0.284702i
$226$	−30.8009			−2.04885
$227$		−	7.21917i		−	0.479153i	−0.970877	−	0.239577i	$-0.922991\pi$
$227$		−	7.21917i		−	0.479153i	0.970877	−	0.239577i	$-0.0770086\pi$
$228$		−	8.95776i		−	0.593242i
$229$	6.51852			0.430756			0.215378	−	0.976531i	$-0.430902\pi$
$229$	6.51852			0.430756			0.215378	+	0.976531i	$0.430902\pi$
$230$	−3.81736	+	6.79395i	−0.251709	+	0.447980i
$231$	−1.00000			−0.0657952
$232$			9.17112i			0.602114i
$233$		−	6.91090i		−	0.452748i	−0.974040	−	0.226374i	$-0.927313\pi$
$233$		−	6.91090i		−	0.452748i	0.974040	−	0.226374i	$-0.0726871\pi$
$234$	3.92492			0.256580
$235$	−17.7530	−	9.97500i	−1.15808	−	0.650697i
$236$	7.88979			0.513582
$237$			0.590789i			0.0383759i
$238$			12.6279i			0.818544i
$239$	−24.0427			−1.55519			−0.777595	−	0.628765i	$-0.783561\pi$
$239$	−24.0427			−1.55519			−0.777595	+	0.628765i	$0.783561\pi$
$240$	−9.71344	−	5.45775i	−0.627000	−	0.352297i
$241$	−21.8813			−1.40950			−0.704748	−	0.709458i	$-0.748940\pi$
$241$	−21.8813			−1.40950			−0.704748	+	0.709458i	$0.748940\pi$
$242$		−	1.76958i		−	0.113753i
$243$		−	1.00000i		−	0.0641500i
$244$	1.55804			0.0997431
$245$	1.09533	−	1.94942i	0.0699783	−	0.124544i
$246$	−8.50986			−0.542569
$247$			17.5606i			1.11735i
$248$			2.15497i			0.136841i
$249$	11.2827			0.715015
$250$	−0.693288	−	19.7724i	−0.0438474	−	1.25051i
$251$	−0.0191607			−0.00120941			−0.000604705	−	1.00000i	$-0.500192\pi$
$251$	−0.0191607			−0.00120941			−0.000604705		1.00000i	$0.500192\pi$
$252$			1.13141i			0.0712723i
$253$		−	1.96946i		−	0.123819i
$254$	6.12669			0.384423
$255$	−7.81641	+	13.9113i	−0.489482	+	0.871157i
$256$	20.1027			1.25642
$257$			25.0592i			1.56315i	0.623812	+	0.781575i	$0.285583\pi$
$257$			25.0592i			1.56315i	−0.623812	+	0.781575i	$0.714417\pi$
$258$		−	4.14633i		−	0.258140i
$259$	−1.37740			−0.0855874
$260$	−4.89201	−	2.74870i	−0.303389	−	0.170467i
$261$	5.96676			0.369333
$262$			39.1905i			2.42119i
$263$			3.01994i			0.186217i	0.995656	+	0.0931087i	$0.0296804\pi$
$263$			3.01994i			0.186217i	−0.995656	+	0.0931087i	$0.970320\pi$
$264$	1.53703			0.0945979
$265$	−5.18219	−	2.91175i	−0.318339	−	0.178867i
$266$	−14.0103			−0.859029
$267$		−	9.79134i		−	0.599220i
$268$			14.5513i			0.888862i
$269$	−9.10840			−0.555349			−0.277674	−	0.960675i	$-0.589564\pi$
$269$	−9.10840			−0.555349			−0.277674	+	0.960675i	$0.589564\pi$
$270$	−1.93828	+	3.44966i	−0.117960	+	0.209939i
$271$	−8.03162			−0.487886			−0.243943	−	0.969790i	$-0.578441\pi$
$271$	−8.03162			−0.487886			−0.243943	+	0.969790i	$0.578441\pi$
$272$		−	35.5572i		−	2.15597i
$273$		−	2.21799i		−	0.134239i
$274$	2.58472			0.156149
$275$	2.60049	+	4.27054i	0.156815	+	0.257523i
$276$	−2.22827			−0.134126
$277$		−	9.33812i		−	0.561073i	−0.959843	−	0.280537i	$-0.909488\pi$
$277$		−	9.33812i		−	0.561073i	0.959843	−	0.280537i	$-0.0905124\pi$
$278$			16.5647i			0.993485i
$279$	1.40203			0.0839374
$280$	−1.68357	+	2.99633i	−0.100612	+	0.179065i
$281$	12.1258			0.723366			0.361683	−	0.932301i	$-0.382202\pi$
$281$	12.1258			0.723366			0.361683	+	0.932301i	$0.382202\pi$
$282$		−	16.1152i		−	0.959648i
$283$			24.3740i			1.44888i	0.689336	+	0.724442i	$0.257903\pi$
$283$			24.3740i			1.44888i	−0.689336	+	0.724442i	$0.742097\pi$
$284$	−1.31836			−0.0782303
$285$	−15.4342	−	8.67211i	−0.914243	−	0.513692i
$286$	3.92492			0.232085
$287$			4.80897i			0.283864i
$288$		−	5.74327i		−	0.338426i
$289$	−33.9238			−1.99552
$290$	−20.5833	−	11.5653i	−1.20869	−	0.679136i
$291$	−12.8085			−0.750846
$292$		−	5.59561i		−	0.327458i
$293$		−	30.1954i		−	1.76403i	−0.471218	−	0.882017i	$-0.656186\pi$
$293$		−	30.1954i		−	1.76403i	0.471218	−	0.882017i	$-0.343814\pi$
$294$	1.76958			0.103204
$295$	7.63820	−	13.5941i	0.444713	−	0.791478i
$296$	2.11711			0.123054
$297$		−	1.00000i		−	0.0580259i
$298$			8.54797i			0.495171i
$299$	4.36824			0.252622
$300$	4.83174	−	2.94222i	0.278961	−	0.169869i
$301$	−2.34312			−0.135055
$302$		−	7.43287i		−	0.427714i
$303$		−	12.2576i		−	0.704183i
$304$	39.4499			2.26261
$305$	1.50835	−	2.68449i	0.0863681	−	0.153714i
$306$	−12.6279			−0.721888
$307$			11.0606i			0.631263i	0.948882	+	0.315632i	$0.102216\pi$
$307$			11.0606i			0.631263i	−0.948882	+	0.315632i	$0.897784\pi$
$308$			1.13141i			0.0644682i
$309$	−2.08029			−0.118344
$310$	−4.83653	−	2.71753i	−0.274696	−	0.154345i
$311$	14.9280			0.846490			0.423245	−	0.906015i	$-0.360891\pi$
$311$	14.9280			0.846490			0.423245	+	0.906015i	$0.360891\pi$
$312$			3.40913i			0.193004i
$313$		−	5.61520i		−	0.317390i	−0.987328	−	0.158695i	$-0.949271\pi$
$313$		−	5.61520i		−	0.317390i	0.987328	−	0.158695i	$-0.0507287\pi$
$314$	−27.5425			−1.55432
$315$	1.94942	+	1.09533i	0.109837	+	0.0617151i
$316$	0.668426			0.0376019
$317$			5.03635i			0.282870i	0.989948	+	0.141435i	$0.0451716\pi$
$317$			5.03635i			0.282870i	−0.989948	+	0.141435i	$0.954828\pi$
$318$		−	4.70411i		−	0.263793i
$319$	5.96676			0.334075
$320$	−0.216566	+	0.385434i	−0.0121064	+	0.0215464i
$321$	−4.58118			−0.255697
$322$			3.48511i			0.194218i
$323$		−	56.4988i		−	3.14367i
$324$	−1.13141			−0.0628563
$325$	−9.47202	+	5.76786i	−0.525413	+	0.319943i
$326$	24.5709			1.36086
$327$			17.3946i			0.961922i
$328$		−	7.39155i		−	0.408130i
$329$	−9.10681			−0.502075
$330$	−1.93828	+	3.44966i	−0.106699	+	0.189897i
$331$	−14.5088			−0.797474			−0.398737	−	0.917065i	$-0.630551\pi$
$331$	−14.5088			−0.797474			−0.398737	+	0.917065i	$0.630551\pi$
$332$		−	12.7654i		−	0.700595i
$333$		−	1.37740i		−	0.0754810i
$334$	−1.67102			−0.0914339
$335$	25.0718	+	14.0873i	1.36982	+	0.769671i
$336$	−4.98273			−0.271830
$337$		−	11.8934i		−	0.647873i	−0.946079	−	0.323936i	$-0.894994\pi$
$337$		−	11.8934i		−	0.647873i	0.946079	−	0.323936i	$-0.105006\pi$
$338$		−	14.2991i		−	0.777769i
$339$	−17.4058			−0.945352
$340$	15.7394	+	8.84359i	0.853587	+	0.479611i
$341$	1.40203			0.0759242
$342$		−	14.0103i		−	0.757592i
$343$		−	1.00000i		−	0.0539949i
$344$	3.60145			0.194177
$345$	−2.15721	+	3.83930i	−0.116140	+	0.206701i
$346$	32.3273			1.73793
$347$		−	26.7968i		−	1.43853i	−0.694736	−	0.719265i	$-0.744479\pi$
$347$		−	26.7968i		−	1.43853i	0.694736	−	0.719265i	$-0.255521\pi$
$348$		−	6.75088i		−	0.361885i
$349$	28.8650			1.54511			0.772555	−	0.634948i	$-0.218978\pi$
$349$	28.8650			1.54511			0.772555	+	0.634948i	$0.218978\pi$
$350$	−4.60177	−	7.55705i	−0.245975	−	0.403941i
$351$	2.21799			0.118388
$352$		−	5.74327i		−	0.306117i
$353$			7.28455i			0.387717i	0.981029	+	0.193859i	$0.0621003\pi$
$353$			7.28455i			0.387717i	−0.981029	+	0.193859i	$0.937900\pi$
$354$	12.3400			0.655862
$355$	−1.27632	+	2.27153i	−0.0677401	+	0.120560i
$356$	−11.0781			−0.587136
$357$			7.13609i			0.377682i
$358$			40.2233i			2.12587i
$359$	1.98422			0.104723			0.0523615	−	0.998628i	$-0.483325\pi$
$359$	1.98422			0.104723			0.0523615	+	0.998628i	$0.483325\pi$
$360$	−2.99633	−	1.68357i	−0.157920	−	0.0887317i
$361$	43.6840			2.29916
$362$			0.462327i			0.0242994i
$363$		−	1.00000i		−	0.0524864i
$364$	−2.50947			−0.131532
$365$	−9.64121	−	5.41717i	−0.504644	−	0.283548i
$366$	2.43684			0.127376
$367$		−	19.8366i		−	1.03546i	−0.855543	−	0.517732i	$-0.826776\pi$
$367$		−	19.8366i		−	1.03546i	0.855543	−	0.517732i	$-0.173224\pi$
$368$		−	9.81327i		−	0.511552i
$369$	−4.80897			−0.250345
$370$	−2.66979	+	4.75155i	−0.138796	+	0.247021i
$371$	−2.65832			−0.138013
$372$		−	1.58628i		−	0.0822446i
$373$			14.3441i			0.742708i	0.928491	+	0.371354i	$0.121106\pi$
$373$			14.3441i			0.742708i	−0.928491	+	0.371354i	$0.878894\pi$
$374$	−12.6279			−0.652973
$375$	−0.391781	−	11.1735i	−0.0202315	−	0.576996i
$376$	13.9975			0.721865
$377$			13.2342i			0.681598i
$378$			1.76958i			0.0910174i
$379$	−28.9764			−1.48842			−0.744209	−	0.667947i	$-0.767173\pi$
$379$	−28.9764			−1.48842			−0.744209	+	0.667947i	$0.767173\pi$
$380$	−9.81174	+	17.4624i	−0.503332	+	0.895805i
$381$	3.46223			0.177375
$382$			18.3262i			0.937652i
$383$			24.7933i			1.26688i	0.773792	+	0.633440i	$0.218358\pi$
$383$			24.7933i			1.26688i	−0.773792	+	0.633440i	$0.781642\pi$
$384$	11.1367			0.568316
$385$	1.94942	+	1.09533i	0.0993517	+	0.0558234i
$386$	−0.671625			−0.0341848
$387$		−	2.34312i		−	0.119107i
$388$			14.4917i			0.735703i
$389$	−8.85937			−0.449188			−0.224594	−	0.974452i	$-0.572106\pi$
$389$	−8.85937			−0.449188			−0.224594	+	0.974452i	$0.572106\pi$
$390$	−7.65131	−	4.29909i	−0.387439	−	0.217693i
$391$	−14.0542			−0.710753
$392$			1.53703i			0.0776319i
$393$			22.1468i			1.11716i
$394$	3.53432			0.178056
$395$	0.647111	−	1.15170i	0.0325597	−	0.0579481i
$396$	−1.13141			−0.0568556
$397$			14.7265i			0.739103i	0.929210	+	0.369552i	$0.120489\pi$
$397$			14.7265i			0.739103i	−0.929210	+	0.369552i	$0.879511\pi$
$398$		−	44.0604i		−	2.20855i
$399$	−7.91732			−0.396362
$400$	12.9575	+	21.2789i	0.647876	+	1.06395i
$401$	28.4932			1.42288			0.711441	−	0.702746i	$-0.248043\pi$
$401$	28.4932			1.42288			0.711441	+	0.702746i	$0.248043\pi$
$402$			22.7589i			1.13511i
$403$			3.10969i			0.154905i
$404$	−13.8685			−0.689981
$405$	−1.09533	+	1.94942i	−0.0544276	+	0.0968675i
$406$	−10.5587			−0.524018
$407$		−	1.37740i		−	0.0682751i
$408$		−	10.9684i		−	0.543018i
$409$	−25.4674			−1.25928			−0.629642	−	0.776886i	$-0.716798\pi$
$409$	−25.4674			−1.25928			−0.629642	+	0.776886i	$0.716798\pi$
$410$	16.5893	+	9.32113i	0.819287	+	0.460338i
$411$	1.46064			0.0720482
$412$			2.35367i			0.115957i
$413$		−	6.97339i		−	0.343138i
$414$	−3.48511			−0.171284
$415$	−21.9948	−	12.3584i	−1.07968	−	0.606649i
$416$	12.7385			0.624558
$417$			9.36082i			0.458401i
$418$		−	14.0103i		−	0.685268i
$419$	12.2976			0.600779			0.300389	−	0.953817i	$-0.402883\pi$
$419$	12.2976			0.600779			0.300389	+	0.953817i	$0.402883\pi$
$420$	1.23928	−	2.20560i	0.0604704	−	0.107622i
$421$	16.5454			0.806371			0.403186	−	0.915118i	$-0.367903\pi$
$421$	16.5454			0.806371			0.403186	+	0.915118i	$0.367903\pi$
$422$		−	16.7860i		−	0.817129i
$423$		−	9.10681i		−	0.442788i
$424$	4.08593			0.198430
$425$	30.4749	−	18.5573i	1.47825	−	0.900162i
$426$	−2.06197			−0.0999030
$427$		−	1.37707i		−	0.0666412i
$428$			5.18321i			0.250540i
$429$	2.21799			0.107086
$430$	−4.54162	+	8.08295i	−0.219016	+	0.389795i
$431$	−38.6855			−1.86341			−0.931706	−	0.363212i	$-0.881680\pi$
$431$	−38.6855			−1.86341			−0.931706	+	0.363212i	$0.881680\pi$
$432$		−	4.98273i		−	0.239732i
$433$			22.2802i			1.07072i	0.844625	+	0.535358i	$0.179823\pi$
$433$			22.2802i			1.07072i	−0.844625	+	0.535358i	$0.820177\pi$
$434$	−2.48101			−0.119092
$435$	−11.6317	−	6.53560i	−0.557699	−	0.313358i
$436$	19.6804			0.942522
$437$		−	15.5928i		−	0.745906i
$438$		−	8.75177i		−	0.418176i
$439$	20.7467			0.990187			0.495094	−	0.868840i	$-0.335134\pi$
$439$	20.7467			0.990187			0.495094	+	0.868840i	$0.335134\pi$
$440$	−2.99633	−	1.68357i	−0.142844	−	0.0802609i
$441$	1.00000			0.0476190
$442$		−	28.0086i		−	1.33223i
$443$			18.3531i			0.871982i	0.899951	+	0.435991i	$0.143602\pi$
$443$			18.3531i			0.871982i	−0.899951	+	0.435991i	$0.856398\pi$
$444$	−1.55841			−0.0739587
$445$	−10.7248	+	19.0875i	−0.508404	+	0.904832i
$446$	−13.8779			−0.657138
$447$			4.83051i			0.228475i
$448$			0.197717i			0.00934125i
$449$	−17.3259			−0.817660			−0.408830	−	0.912611i	$-0.634063\pi$
$449$	−17.3259			−0.817660			−0.408830	+	0.912611i	$0.634063\pi$
$450$	7.55705	−	4.60177i	0.356243	−	0.216929i
$451$	−4.80897			−0.226446
$452$			19.6931i			0.926287i
$453$		−	4.20036i		−	0.197350i
$454$	−12.7749			−0.599556
$455$	−2.42944	+	4.32380i	−0.113894	+	0.202703i
$456$	12.1692			0.569875
$457$		−	24.7408i		−	1.15733i	−0.815567	−	0.578663i	$-0.803575\pi$
$457$		−	24.7408i		−	1.15733i	0.815567	−	0.578663i	$-0.196425\pi$
$458$		−	11.5350i		−	0.538997i
$459$	−7.13609			−0.333084
$460$	4.34383	+	2.44070i	0.202532	+	0.113798i
$461$	−16.6240			−0.774256			−0.387128	−	0.922026i	$-0.626533\pi$
$461$	−16.6240			−0.774256			−0.387128	+	0.922026i	$0.626533\pi$
$462$			1.76958i			0.0823283i
$463$		−	2.97360i		−	0.138195i	−0.997610	−	0.0690973i	$-0.977988\pi$
$463$		−	2.97360i		−	0.138195i	0.997610	−	0.0690973i	$-0.0220119\pi$
$464$	29.7308			1.38022
$465$	−2.73315	−	1.53569i	−0.126747	−	0.0712160i
$466$	−12.2294			−0.566515
$467$			5.72027i			0.264702i	0.991203	+	0.132351i	$0.0422527\pi$
$467$			5.72027i			0.264702i	−0.991203	+	0.132351i	$0.957747\pi$
$468$		−	2.50947i		−	0.116000i
$469$	12.8612			0.593874
$470$	−17.6516	+	31.4154i	−0.814205	+	1.44908i
$471$	−15.5645			−0.717172
$472$			10.7183i			0.493352i
$473$		−	2.34312i		−	0.107737i
$474$	1.04545			0.0480190
$475$	20.5889	+	33.8112i	0.944683	+	1.55136i
$476$	8.07387			0.370065
$477$		−	2.65832i		−	0.121716i
$478$			42.5454i			1.94598i
$479$	−39.5973			−1.80925			−0.904624	−	0.426210i	$-0.859849\pi$
$479$	−39.5973			−1.80925			−0.904624	+	0.426210i	$0.859849\pi$
$480$	−6.29080	+	11.1961i	−0.287134	+	0.511028i
$481$	3.05506			0.139299
$482$			38.7206i			1.76368i
$483$			1.96946i			0.0896134i
$484$	−1.13141			−0.0514279
$485$	24.9691	+	14.0296i	1.13379	+	0.637049i
$486$	−1.76958			−0.0802698
$487$		−	38.9282i		−	1.76401i	−0.471244	−	0.882003i	$-0.656195\pi$
$487$		−	38.9282i		−	1.76401i	0.471244	−	0.882003i	$-0.343805\pi$
$488$			2.11661i			0.0958143i
$489$	13.8852			0.627910
$490$	−3.44966	−	1.93828i	−0.155840	−	0.0875626i
$491$	3.98865			0.180005			0.0900027	−	0.995942i	$-0.471312\pi$
$491$	3.98865			0.180005			0.0900027	+	0.995942i	$0.471312\pi$
$492$			5.44093i			0.245296i
$493$		−	42.5794i		−	1.91768i
$494$	31.0748			1.39812
$495$	−1.09533	+	1.94942i	−0.0492316	+	0.0876200i
$496$	6.98594			0.313678
$497$			1.16523i			0.0522679i
$498$		−	19.9657i		−	0.894685i
$499$	−0.0121357			−0.000543266			−0.000271633	−	1.00000i	$-0.500086\pi$
$499$	−0.0121357			−0.000543266			−0.000271633		1.00000i	$0.500086\pi$
$500$	−12.6418	+	0.443266i	−0.565359	+	0.0198235i
$501$	−0.944301			−0.0421883
$502$			0.0339063i			0.00151331i
$503$		−	40.7776i		−	1.81818i	−0.416595	−	0.909092i	$-0.636777\pi$
$503$		−	40.7776i		−	1.81818i	0.416595	−	0.909092i	$-0.363223\pi$
$504$	−1.53703			−0.0684649
$505$	−13.4262	+	23.8953i	−0.597458	+	1.06333i
$506$	−3.48511			−0.154932
$507$		−	8.08051i		−	0.358868i
$508$		−	3.91721i		−	0.173798i
$509$	31.8460			1.41155			0.705775	−	0.708436i	$-0.250599\pi$
$509$	31.8460			1.41155			0.705775	+	0.708436i	$0.250599\pi$
$510$	24.6171	+	13.8318i	1.09006	+	0.612481i
$511$	−4.94568			−0.218784
$512$		−	13.2999i		−	0.587779i
$513$		−	7.91732i		−	0.349558i
$514$	44.3442			1.95594
$515$	4.05537	+	2.27861i	0.178701	+	0.100408i
$516$	−2.65103			−0.116705
$517$		−	9.10681i		−	0.400517i
$518$			2.43742i			0.107094i
$519$	18.2684			0.801892
$520$	3.73414	−	6.64583i	0.163753	−	0.291439i
$521$	34.7276			1.52145			0.760723	−	0.649077i	$-0.224845\pi$
$521$	34.7276			1.52145			0.760723	+	0.649077i	$0.224845\pi$
$522$		−	10.5587i		−	0.462140i
$523$		−	37.2612i		−	1.62932i	−0.579939	−	0.814660i	$-0.696924\pi$
$523$		−	37.2612i		−	1.62932i	0.579939	−	0.814660i	$-0.303076\pi$
$524$	25.0571			1.09463
$525$	−2.60049	−	4.27054i	−0.113495	−	0.186381i
$526$	5.34402			0.233010
$527$		−	10.0050i		−	0.435826i
$528$		−	4.98273i		−	0.216846i
$529$	19.1212			0.831358
$530$	−5.15257	+	9.17029i	−0.223813	+	0.398332i
$531$	6.97339			0.302620
$532$			8.95776i			0.388368i
$533$		−	10.6663i		−	0.462007i
$534$	−17.3266			−0.749794
$535$	8.93066	+	5.01793i	0.386106	+	0.216944i
$536$	−19.7681			−0.853850
$537$			22.7304i			0.980889i
$538$			16.1180i			0.694898i
$539$	1.00000			0.0430730
$540$	2.20560	+	1.23928i	0.0949139	+	0.0533299i
$541$	−22.3089			−0.959132			−0.479566	−	0.877506i	$-0.659206\pi$
$541$	−22.3089			−0.959132			−0.479566	+	0.877506i	$0.659206\pi$
$542$			14.2126i			0.610483i
$543$			0.261264i			0.0112119i
$544$	−40.9845			−1.75720
$545$	19.0529	−	33.9093i	0.816135	−	1.45252i
$546$	−3.92492			−0.167971
$547$			32.2667i			1.37962i	0.723989	+	0.689812i	$0.242307\pi$
$547$			32.2667i			1.37962i	−0.723989	+	0.689812i	$0.757693\pi$
$548$		−	1.65259i		−	0.0705951i
$549$	1.37707			0.0587720
$550$	7.55705	−	4.60177i	0.322234	−	0.196220i
$551$	47.2408			2.01253
$552$		−	3.02712i		−	0.128843i
$553$		−	0.590789i		−	0.0251229i
$554$	−16.5246			−0.702061
$555$	−1.50871	+	2.68513i	−0.0640412	+	0.113977i
$556$	10.5909			0.449156
$557$			38.4999i			1.63129i	0.578550	+	0.815647i	$0.303619\pi$
$557$			38.4999i			1.63129i	−0.578550	+	0.815647i	$0.696381\pi$
$558$		−	2.48101i		−	0.105029i
$559$	5.19702			0.219810
$560$	9.71344	+	5.45775i	0.410468	+	0.230632i
$561$	−7.13609			−0.301286
$562$		−	21.4576i		−	0.905135i
$563$		−	37.1076i		−	1.56390i	−0.623342	−	0.781949i	$-0.714226\pi$
$563$		−	37.1076i		−	1.56390i	0.623342	−	0.781949i	$-0.285774\pi$
$564$	−10.3036			−0.433858
$565$	33.9312	+	19.0651i	1.42750	+	0.802077i
$566$	43.1318			1.81296
$567$			1.00000i			0.0419961i
$568$		−	1.79100i		−	0.0751489i
$569$	0.784309			0.0328799			0.0164400	−	0.999865i	$-0.494767\pi$
$569$	0.784309			0.0328799			0.0164400	+	0.999865i	$0.494767\pi$
$570$	−15.3460	+	27.3120i	−0.642773	+	1.14398i
$571$	−1.36653			−0.0571877			−0.0285938	−	0.999591i	$-0.509103\pi$
$571$	−1.36653			−0.0571877			−0.0285938	+	0.999591i	$0.509103\pi$
$572$		−	2.50947i		−	0.104926i
$573$			10.3563i			0.432639i
$574$	8.50986			0.355194
$575$	8.41063	−	5.12154i	0.350748	−	0.213583i
$576$	−0.197717			−0.00823820
$577$			37.8759i			1.57680i	0.615166	+	0.788398i	$0.289089\pi$
$577$			37.8759i			1.57680i	−0.615166	+	0.788398i	$0.710911\pi$
$578$			60.0310i			2.49696i
$579$	−0.379539			−0.0157731
$580$	−7.39446	+	13.1603i	−0.307038	+	0.546452i
$581$	−11.2827			−0.468087
$582$			22.6656i			0.939520i
$583$		−	2.65832i		−	0.110096i
$584$	7.60168			0.314560
$585$	−4.32380	−	2.42944i	−0.178767	−	0.100445i
$586$	−53.4331			−2.20730
$587$			20.6247i			0.851273i	0.904894	+	0.425636i	$0.139950\pi$
$587$			20.6247i			0.851273i	−0.904894	+	0.425636i	$0.860050\pi$
$588$		−	1.13141i		−	0.0466587i
$589$	11.1003			0.457381
$590$	−24.0558	−	13.5164i	−0.990362	−	0.556461i
$591$	1.99726			0.0821565
$592$		−	6.86320i		−	0.282076i
$593$			18.6126i			0.764328i	0.924095	+	0.382164i	$0.124821\pi$
$593$			18.6126i			0.764328i	−0.924095	+	0.382164i	$0.875179\pi$
$594$	−1.76958			−0.0726067
$595$	7.81641	−	13.9113i	0.320441	−	0.570306i
$596$	5.46530			0.223867
$597$		−	24.8988i		−	1.01904i
$598$		−	7.72995i		−	0.316101i
$599$	31.5650			1.28971			0.644855	−	0.764305i	$-0.276918\pi$
$599$	31.5650			1.28971			0.644855	+	0.764305i	$0.276918\pi$
$600$	3.99704	+	6.56396i	0.163178	+	0.267972i
$601$	14.8343			0.605102			0.302551	−	0.953133i	$-0.402162\pi$
$601$	14.8343			0.605102			0.302551	+	0.953133i	$0.402162\pi$
$602$			4.14633i			0.168992i
$603$			12.8612i			0.523748i
$604$	−4.75234			−0.193370
$605$	−1.09533	+	1.94942i	−0.0445317	+	0.0792552i
$606$	−21.6909			−0.881131
$607$			45.2317i			1.83590i	0.396697	+	0.917950i	$0.370156\pi$
$607$			45.2317i			1.83590i	−0.396697	+	0.917950i	$0.629844\pi$
$608$		−	45.4713i		−	1.84411i
$609$	−5.96676			−0.241786
$610$	−4.75043	−	2.66915i	−0.192339	−	0.108071i
$611$	20.1988			0.817157
$612$			8.07387i			0.326367i
$613$			21.6441i			0.874196i	0.899414	+	0.437098i	$0.143994\pi$
$613$			21.6441i			0.874196i	−0.899414	+	0.437098i	$0.856006\pi$
$614$	19.5727			0.789888
$615$	9.37471	+	5.26743i	0.378025	+	0.212403i
$616$	−1.53703			−0.0619289
$617$			31.9140i			1.28481i	0.766365	+	0.642405i	$0.222063\pi$
$617$			31.9140i			1.28481i	−0.766365	+	0.642405i	$0.777937\pi$
$618$			3.68124i			0.148081i
$619$	−39.5115			−1.58810			−0.794051	−	0.607851i	$-0.792032\pi$
$619$	−39.5115			−1.58810			−0.794051	+	0.607851i	$0.792032\pi$
$620$	−1.73750	+	3.09232i	−0.0697798	+	0.124191i
$621$	−1.96946			−0.0790316
$622$		−	26.4163i		−	1.05920i
$623$			9.79134i			0.392282i
$624$	11.0517			0.442420
$625$	−11.4749	+	22.2109i	−0.458998	+	0.888438i
$626$	−9.93655			−0.397144
$627$		−	7.91732i		−	0.316187i
$628$			17.6098i			0.702708i
$629$	−9.82924			−0.391918
$630$	1.93828	−	3.44966i	0.0772230	−	0.137438i
$631$	11.3107			0.450273			0.225136	−	0.974327i	$-0.427717\pi$
$631$	11.3107			0.450273			0.225136	+	0.974327i	$0.427717\pi$
$632$			0.908063i			0.0361208i
$633$		−	9.48586i		−	0.377029i
$634$	8.91223			0.353950
$635$	−6.74935	−	3.79230i	−0.267840	−	0.150493i
$636$	−3.00766			−0.119261
$637$			2.21799i			0.0878801i
$638$		−	10.5587i		−	0.418022i
$639$	−1.16523			−0.0460959
$640$	−21.7101	−	12.1984i	−0.858165	−	0.482183i
$641$	40.8060			1.61174			0.805871	−	0.592091i	$-0.201698\pi$
$641$	40.8060			1.61174			0.805871	+	0.592091i	$0.201698\pi$
$642$			8.10677i			0.319949i
$643$		−	24.1200i		−	0.951200i	−0.879662	−	0.475600i	$-0.842231\pi$
$643$		−	24.1200i		−	0.951200i	0.879662	−	0.475600i	$-0.157769\pi$
$644$	2.22827			0.0878061
$645$	−2.56650	+	4.56772i	−0.101056	+	0.179854i
$646$	−99.9791			−3.93362
$647$		−	15.4220i		−	0.606301i	−0.952943	−	0.303151i	$-0.901961\pi$
$647$		−	15.4220i		−	0.606301i	0.952943	−	0.303151i	$-0.0980385\pi$
$648$		−	1.53703i		−	0.0603804i
$649$	6.97339			0.273730
$650$	10.2067	+	16.7615i	0.400339	+	0.657440i
$651$	−1.40203			−0.0549499
$652$		−	15.7099i		−	0.615246i
$653$		−	29.7746i		−	1.16517i	−0.812769	−	0.582586i	$-0.802041\pi$
$653$		−	29.7746i		−	1.16517i	0.812769	−	0.582586i	$-0.197959\pi$
$654$	30.7811			1.20364
$655$	24.2581	−	43.1734i	0.947842	−	1.68692i
$656$	−23.9618			−0.935551
$657$		−	4.94568i		−	0.192949i
$658$			16.1152i			0.628237i
$659$	41.5065			1.61686			0.808432	−	0.588589i	$-0.200316\pi$
$659$	41.5065			1.61686			0.808432	+	0.588589i	$0.200316\pi$
$660$	2.20560	+	1.23928i	0.0858529	+	0.0482387i
$661$	19.5684			0.761124			0.380562	−	0.924755i	$-0.375731\pi$
$661$	19.5684			0.761124			0.380562	+	0.924755i	$0.375731\pi$
$662$			25.6744i			0.997865i
$663$		−	15.8278i		−	0.614701i
$664$	17.3420			0.672999
$665$	15.4342	+	8.67211i	0.598512	+	0.336290i
$666$	−2.43742			−0.0944480
$667$		−	11.7513i		−	0.455012i
$668$			1.06839i			0.0413374i
$669$	−7.84249			−0.303208
$670$	24.9286	−	44.3666i	0.963075	−	1.71403i
$671$	1.37707			0.0531613
$672$			5.74327i			0.221552i
$673$			35.7976i			1.37990i	0.723859	+	0.689948i	$0.242367\pi$
$673$			35.7976i			1.37990i	−0.723859	+	0.689948i	$0.757633\pi$
$674$	−21.0463			−0.810672
$675$	4.27054	−	2.60049i	0.164373	−	0.100093i
$676$	−9.14239			−0.351630
$677$		−	0.241869i		−	0.00929579i	−0.999989	−	0.00464789i	$-0.998521\pi$
$677$		−	0.241869i		−	0.00929579i	0.999989	−	0.00464789i	$-0.00147948\pi$
$678$			30.8009i			1.18290i
$679$	12.8085			0.491544
$680$	−12.0141	+	21.3821i	−0.460719	+	0.819965i
$681$	−7.21917			−0.276639
$682$		−	2.48101i		−	0.0950026i
$683$			22.0987i			0.845582i	0.906227	+	0.422791i	$0.138949\pi$
$683$			22.0987i			0.845582i	−0.906227	+	0.422791i	$0.861051\pi$
$684$	−8.95776			−0.342509
$685$	−2.84741	−	1.59989i	−0.108794	−	0.0611287i
$686$	−1.76958			−0.0675629
$687$		−	6.51852i		−	0.248697i
$688$		−	11.6751i		−	0.445110i
$689$	5.89613			0.224625
$690$	6.79395	+	3.81736i	0.258641	+	0.145324i
$691$	13.6138			0.517893			0.258946	−	0.965892i	$-0.416625\pi$
$691$	13.6138			0.517893			0.258946	+	0.965892i	$0.416625\pi$
$692$		−	20.6691i		−	0.785719i
$693$			1.00000i			0.0379869i
$694$	−47.4191			−1.80001
$695$	10.2532	−	18.2482i	0.388927	−	0.692193i
$696$	9.17112			0.347630
$697$			34.3173i			1.29986i
$698$		−	51.0790i		−	1.93337i
$699$	−6.91090			−0.261394
$700$	−4.83174	+	2.94222i	−0.182623	+	0.111206i
$701$	27.2209			1.02812			0.514060	−	0.857754i	$-0.328141\pi$
$701$	27.2209			1.02812			0.514060	+	0.857754i	$0.328141\pi$
$702$		−	3.92492i		−	0.148136i
$703$		−	10.9053i		−	0.411301i
$704$	−0.197717			−0.00745174
$705$	−9.97500	+	17.7530i	−0.375680	+	0.668617i
$706$	12.8906			0.485144
$707$			12.2576i			0.460996i
$708$		−	7.88979i		−	0.296516i
$709$	0.0718130			0.00269699			0.00134850	−	0.999999i	$-0.499571\pi$
$709$	0.0718130			0.00269699			0.00134850	+	0.999999i	$0.499571\pi$
$710$	4.01966	+	2.25855i	0.150855	+	0.0847619i
$711$	0.590789			0.0221563
$712$		−	15.0496i		−	0.564009i
$713$		−	2.76124i		−	0.103409i
$714$	12.6279			0.472587
$715$	−4.32380	−	2.42944i	−0.161701	−	0.0908560i
$716$	25.7175			0.961107
$717$			24.0427i			0.897890i
$718$		−	3.51123i		−	0.131038i
$719$	−10.0867			−0.376171			−0.188085	−	0.982153i	$-0.560228\pi$
$719$	−10.0867			−0.376171			−0.188085	+	0.982153i	$0.560228\pi$
$720$	−5.45775	+	9.71344i	−0.203399	+	0.361999i
$721$	2.08029			0.0774741
$722$		−	77.3023i		−	2.87689i
$723$			21.8813i			0.813773i
$724$	0.295597			0.0109858
$725$	15.5165	+	25.4813i	0.576268	+	0.946351i
$726$	−1.76958			−0.0656753
$727$			29.2620i			1.08527i	0.839969	+	0.542634i	$0.182573\pi$
$727$			29.2620i			1.08527i	−0.839969	+	0.542634i	$0.817427\pi$
$728$		−	3.40913i		−	0.126351i
$729$	−1.00000			−0.0370370
$730$	−9.58612	+	17.0609i	−0.354798	+	0.631452i
$731$	−16.7207			−0.618438
$732$		−	1.55804i		−	0.0575867i
$733$		−	2.30063i		−	0.0849758i	−0.999097	−	0.0424879i	$-0.986472\pi$
$733$		−	2.30063i		−	0.0849758i	0.999097	−	0.0424879i	$-0.0135284\pi$
$734$	−35.1025			−1.29566
$735$	−1.94942	−	1.09533i	−0.0719055	−	0.0404020i
$736$	−11.3111			−0.416934
$737$			12.8612i			0.473747i
$738$			8.50986i			0.313252i
$739$	−14.2355			−0.523662			−0.261831	−	0.965114i	$-0.584326\pi$
$739$	−14.2355			−0.523662			−0.261831	+	0.965114i	$0.584326\pi$
$740$	3.03799	+	1.70698i	0.111679	+	0.0627497i
$741$	17.5606			0.645103
$742$			4.70411i			0.172693i
$743$		−	6.68593i		−	0.245283i	−0.992451	−	0.122642i	$-0.960863\pi$
$743$		−	6.68593i		−	0.245283i	0.992451	−	0.122642i	$-0.0391366\pi$
$744$	2.15497			0.0790050
$745$	5.29102	−	9.41670i	0.193848	−	0.345001i
$746$	25.3830			0.929337
$747$		−	11.2827i		−	0.412814i
$748$			8.07387i			0.295210i
$749$	4.58118			0.167393
$750$	−19.7724	+	0.693288i	−0.721984	+	0.0253153i
$751$	−28.6928			−1.04702			−0.523508	−	0.852021i	$-0.675377\pi$
$751$	−28.6928			−1.04702			−0.523508	+	0.852021i	$0.675377\pi$
$752$		−	45.3768i		−	1.65472i
$753$			0.0191607i			0.000698253i
$754$	23.4190			0.852871
$755$	−4.60080	+	8.18827i	−0.167440	+	0.298002i
$756$	1.13141			0.0411491
$757$			10.4635i			0.380302i	0.981755	+	0.190151i	$0.0608977\pi$
$757$			10.4635i			0.380302i	−0.981755	+	0.190151i	$0.939102\pi$
$758$			51.2761i			1.86243i
$759$	−1.96946			−0.0714867
$760$	−23.7229	−	13.3293i	−0.860519	−	0.483506i
$761$	−41.8218			−1.51604			−0.758019	−	0.652232i	$-0.773833\pi$
$761$	−41.8218			−1.51604			−0.758019	+	0.652232i	$0.773833\pi$
$762$		−	6.12669i		−	0.221947i
$763$		−	17.3946i		−	0.629726i
$764$	11.7172			0.423914
$765$	13.9113	+	7.81641i	0.502962	+	0.282603i
$766$	43.8738			1.58522
$767$			15.4669i			0.558479i
$768$		−	20.1027i		−	0.725392i
$769$	−8.55949			−0.308663			−0.154332	−	0.988019i	$-0.549322\pi$
$769$	−8.55949			−0.308663			−0.154332	+	0.988019i	$0.549322\pi$
$770$	1.93828	−	3.44966i	0.0698508	−	0.124317i
$771$	25.0592			0.902485
$772$			0.429416i			0.0154550i
$773$			52.3119i			1.88153i	0.339061	+	0.940764i	$0.389891\pi$
$773$			52.3119i			1.88153i	−0.339061	+	0.940764i	$0.610109\pi$
$774$	−4.14633			−0.149037
$775$	3.64596	+	5.98742i	0.130967	+	0.215075i
$776$	−19.6871			−0.706724
$777$			1.37740i			0.0494139i
$778$			15.6774i			0.562061i
$779$	−38.0742			−1.36415
$780$	−2.74870	+	4.89201i	−0.0984194	+	0.175162i
$781$	−1.16523			−0.0416954
$782$			24.8701i			0.889352i
$783$		−	5.96676i		−	0.213235i
$784$	4.98273			0.177955
$785$	30.3417	+	17.0483i	1.08294	+	0.608479i
$786$	39.1905			1.39788
$787$			20.2837i			0.723037i	0.932365	+	0.361519i	$0.117742\pi$
$787$			20.2837i			0.723037i	−0.932365	+	0.361519i	$0.882258\pi$
$788$		−	2.25973i		−	0.0804996i
$789$	3.01994			0.107513
$790$	−2.03802	−	1.14512i	−0.0725095	−	0.0407414i
$791$	17.4058			0.618878
$792$		−	1.53703i		−	0.0546161i
$793$			3.05434i			0.108463i
$794$	26.0598			0.924827
$795$	−2.91175	+	5.18219i	−0.103269	+	0.183793i
$796$	−28.1708			−0.998488
$797$		−	40.1164i		−	1.42099i	−0.703700	−	0.710497i	$-0.748470\pi$
$797$		−	40.1164i		−	1.42099i	0.703700	−	0.710497i	$-0.251530\pi$
$798$			14.0103i			0.495960i
$799$	−64.9870			−2.29908
$800$	24.5268	−	14.9353i	0.867155	−	0.528043i
$801$	−9.79134			−0.345960
$802$		−	50.4210i		−	1.78043i
$803$		−	4.94568i		−	0.174529i
$804$	14.5513			0.513185
$805$	2.15721	−	3.83930i	0.0760318	−	0.135318i
$806$	5.50285			0.193830
$807$			9.10840i			0.320631i
$808$		−	18.8404i		−	0.662803i
$809$	14.8891			0.523474			0.261737	−	0.965139i	$-0.415705\pi$
$809$	14.8891			0.523474			0.261737	+	0.965139i	$0.415705\pi$
$810$	3.44966	+	1.93828i	0.121209	+	0.0681043i
$811$	13.9262			0.489015			0.244508	−	0.969647i	$-0.421374\pi$
$811$	13.9262			0.489015			0.244508	+	0.969647i	$0.421374\pi$
$812$			6.75088i			0.236909i
$813$			8.03162i			0.281681i
$814$	−2.43742			−0.0854314
$815$	−27.0681	−	15.2089i	−0.948153	−	0.532745i
$816$	−35.5572			−1.24475
$817$		−	18.5512i		−	0.649025i
$818$			45.0667i			1.57572i
$819$	−2.21799			−0.0775029
$820$	5.95964	−	10.6067i	0.208120	−	0.370401i
$821$	−12.8248			−0.447588			−0.223794	−	0.974636i	$-0.571844\pi$
$821$	−12.8248			−0.447588			−0.223794	+	0.974636i	$0.571844\pi$
$822$		−	2.58472i		−	0.0901526i
$823$		−	45.9807i		−	1.60279i	−0.598139	−	0.801393i	$-0.704093\pi$
$823$		−	45.9807i		−	1.60279i	0.598139	−	0.801393i	$-0.295907\pi$
$824$	−3.19748			−0.111389
$825$	4.27054	−	2.60049i	0.148681	−	0.0905373i
$826$	−12.3400			−0.429363
$827$			45.5710i			1.58466i	0.610093	+	0.792330i	$0.291132\pi$
$827$			45.5710i			1.58466i	−0.610093	+	0.792330i	$0.708868\pi$
$828$			2.22827i			0.0774377i
$829$	−28.6693			−0.995727			−0.497864	−	0.867255i	$-0.665882\pi$
$829$	−28.6693			−0.995727			−0.497864	+	0.867255i	$0.665882\pi$
$830$	−21.8691	+	38.9216i	−0.759089	+	1.35099i
$831$	−9.33812			−0.323936
$832$		−	0.438535i		−	0.0152035i
$833$		−	7.13609i		−	0.247251i
$834$	16.5647			0.573589
$835$	1.84084	+	1.03432i	0.0637049	+	0.0357943i
$836$	−8.95776			−0.309811
$837$		−	1.40203i		−	0.0484613i
$838$		−	21.7617i		−	0.751744i
$839$	39.6335			1.36830			0.684150	−	0.729341i	$-0.260173\pi$
$839$	39.6335			1.36830			0.684150	+	0.729341i	$0.260173\pi$
$840$	2.99633	+	1.68357i	0.103383	+	0.0580885i
$841$	6.60228			0.227665
$842$		−	29.2783i		−	1.00900i
$843$		−	12.1258i		−	0.417635i
$844$	−10.7324			−0.369425
$845$	−8.85086	+	15.7523i	−0.304479	+	0.541896i
$846$	−16.1152			−0.554053
$847$			1.00000i			0.0343604i
$848$		−	13.2457i		−	0.454859i
$849$	24.3740			0.836514
$850$	−32.8387	−	53.9278i	−1.12636	−	1.84971i
$851$	−2.71273			−0.0929910
$852$			1.31836i			0.0451663i
$853$			10.6005i			0.362954i	0.983395	+	0.181477i	$0.0580877\pi$
$853$			10.6005i			0.362954i	−0.983395	+	0.181477i	$0.941912\pi$
$854$	−2.43684			−0.0833869
$855$	−8.67211	+	15.4342i	−0.296580	+	0.527838i
$856$	−7.04144			−0.240671
$857$			45.6115i			1.55806i	0.626987	+	0.779030i	$0.284288\pi$
$857$			45.6115i			1.55806i	−0.626987	+	0.779030i	$0.715712\pi$
$858$		−	3.92492i		−	0.133994i
$859$	22.7318			0.775599			0.387800	−	0.921744i	$-0.373235\pi$
$859$	22.7318			0.775599			0.387800	+	0.921744i	$0.373235\pi$
$860$	5.16798	+	2.90377i	0.176227	+	0.0990177i
$861$	4.80897			0.163889
$862$			68.4570i			2.33165i
$863$		−	23.2087i		−	0.790034i	−0.918674	−	0.395017i	$-0.870739\pi$
$863$		−	23.2087i		−	0.790034i	0.918674	−	0.395017i	$-0.129261\pi$
$864$	−5.74327			−0.195390
$865$	−35.6127	−	20.0099i	−1.21087	−	0.680359i
$866$	39.4265			1.33977
$867$			33.9238i			1.15211i
$868$			1.58628i			0.0538417i
$869$	0.590789			0.0200411
$870$	−11.5653	+	20.5833i	−0.392099	+	0.697839i
$871$	−28.5260			−0.966566
$872$			26.7360i			0.905397i
$873$			12.8085i			0.433501i
$874$	−27.5927			−0.933338
$875$	0.391781	+	11.1735i	0.0132446	+	0.377732i
$876$	−5.59561			−0.189058
$877$		−	33.6558i		−	1.13648i	−0.822864	−	0.568238i	$-0.807625\pi$
$877$		−	33.6558i		−	1.13648i	0.822864	−	0.568238i	$-0.192375\pi$
$878$		−	36.7130i		−	1.23900i
$879$	−30.1954			−1.01846
$880$	−5.45775	+	9.71344i	−0.183981	+	0.327440i
$881$	−20.3345			−0.685085			−0.342543	−	0.939502i	$-0.611288\pi$
$881$	−20.3345			−0.685085			−0.342543	+	0.939502i	$0.611288\pi$
$882$		−	1.76958i		−	0.0595849i
$883$			20.4887i			0.689499i	0.938695	+	0.344749i	$0.112036\pi$
$883$			20.4887i			0.689499i	−0.938695	+	0.344749i	$0.887964\pi$
$884$	−17.9078			−0.602304
$885$	−13.5941	−	7.63820i	−0.456960	−	0.256755i
$886$	32.4773			1.09110
$887$		−	33.7448i		−	1.13304i	−0.824048	−	0.566520i	$-0.808289\pi$
$887$		−	33.7448i		−	1.13304i	0.824048	−	0.566520i	$-0.191711\pi$
$888$		−	2.11711i		−	0.0710455i
$889$	−3.46223			−0.116120
$890$	33.7768	+	18.9784i	1.13220	+	0.636157i
$891$	−1.00000			−0.0335013
$892$			8.87310i			0.297093i
$893$		−	72.1015i		−	2.41279i
$894$	8.54797			0.285887
$895$	24.8974	−	44.3111i	0.832228	−	1.48116i
$896$	−11.1367			−0.372050
$897$		−	4.36824i		−	0.145851i
$898$			30.6596i			1.02312i
$899$	8.36559			0.279008
$900$	−2.94222	−	4.83174i	−0.0980741	−	0.161058i
$901$	−18.9700			−0.631983
$902$			8.50986i			0.283347i
$903$			2.34312i			0.0779741i
$904$	−26.7533			−0.889801
$905$	0.286171	−	0.509313i	0.00951265	−	0.0169301i
$906$	−7.43287			−0.246941
$907$			31.2353i			1.03715i	0.855031	+	0.518576i	$0.173538\pi$
$907$			31.2353i			1.03715i	−0.855031	+	0.518576i	$0.826462\pi$
$908$			8.16787i			0.271060i
$909$	−12.2576			−0.406560
$910$	7.65131	+	4.29909i	0.253639	+	0.142514i
$911$	7.49166			0.248210			0.124105	−	0.992269i	$-0.460394\pi$
$911$	7.49166			0.248210			0.124105	+	0.992269i	$0.460394\pi$
$912$		−	39.4499i		−	1.30632i
$913$		−	11.2827i		−	0.373404i
$914$	−43.7808			−1.44814
$915$	−2.68449	−	1.50835i	−0.0887466	−	0.0498646i
$916$	−7.37514			−0.243681
$917$		−	22.1468i		−	0.731350i
$918$			12.6279i			0.416782i
$919$	32.1890			1.06182			0.530908	−	0.847430i	$-0.321851\pi$
$919$	32.1890			1.06182			0.530908	+	0.847430i	$0.321851\pi$
$920$	−3.31571	+	5.90114i	−0.109316	+	0.194555i
$921$	11.0606			0.364460
$922$			29.4175i			0.968813i
$923$		−	2.58448i		−	0.0850692i
$924$	1.13141			0.0372208
$925$	5.88223	−	3.58191i	0.193406	−	0.117772i
$926$	−5.26201			−0.172921
$927$			2.08029i			0.0683258i
$928$		−	34.2688i		−	1.12493i
$929$	−40.1476			−1.31720			−0.658600	−	0.752493i	$-0.728851\pi$
$929$	−40.1476			−1.31720			−0.658600	+	0.752493i	$0.728851\pi$
$930$	−2.71753	+	4.83653i	−0.0891113	+	0.158596i
$931$	7.91732			0.259480
$932$			7.81908i			0.256122i
$933$		−	14.9280i		−	0.488721i
$934$	10.1225			0.331217
$935$	13.9113	+	7.81641i	0.454947	+	0.255624i
$936$	3.40913			0.111431
$937$			53.1660i			1.73686i	0.495813	+	0.868429i	$0.334870\pi$
$937$			53.1660i			1.73686i	−0.495813	+	0.868429i	$0.665130\pi$
$938$		−	22.7589i		−	0.743104i
$939$	−5.61520			−0.183245
$940$	20.0860	+	11.2858i	0.655132	+	0.368104i
$941$	11.8219			0.385384			0.192692	−	0.981259i	$-0.438278\pi$
$941$	11.8219			0.385384			0.192692	+	0.981259i	$0.438278\pi$
$942$			27.5425i			0.897384i
$943$			9.47106i			0.308420i
$944$	34.7465			1.13090
$945$	1.09533	−	1.94942i	0.0356312	−	0.0634147i
$946$	−4.14633			−0.134809
$947$		−	23.7292i		−	0.771094i	−0.922688	−	0.385547i	$-0.874013\pi$
$947$		−	23.7292i		−	0.771094i	0.922688	−	0.385547i	$-0.125987\pi$
$948$		−	0.668426i		−	0.0217095i
$949$	10.9695			0.356084
$950$	59.8316	−	36.4337i	1.94119	−	1.18206i
$951$	5.03635			0.163315
$952$			10.9684i			0.355489i
$953$			16.3012i			0.528049i	0.964516	+	0.264025i	$0.0850500\pi$
$953$			16.3012i			0.528049i	−0.964516	+	0.264025i	$0.914950\pi$
$954$	−4.70411			−0.152301
$955$	11.3436	−	20.1887i	0.367069	−	0.653292i
$956$	27.2022			0.879781
$957$		−	5.96676i		−	0.192878i
$958$			70.0707i			2.26388i
$959$	−1.46064			−0.0471666
$960$	0.385434	+	0.216566i	0.0124398	+	0.00698964i
$961$	−29.0343			−0.936591
$962$		−	5.40617i		−	0.174302i
$963$			4.58118i			0.147627i
$964$	24.7567			0.797361
$965$	0.739882	+	0.415722i	0.0238176	+	0.0133826i
$966$	3.48511			0.112132
$967$		−	26.5737i		−	0.854551i	−0.904121	−	0.427276i	$-0.859473\pi$
$967$		−	26.5737i		−	0.854551i	0.904121	−	0.427276i	$-0.140527\pi$
$968$		−	1.53703i		−	0.0494021i
$969$	−56.4988			−1.81500
$970$	24.8264	−	44.1848i	0.797129	−	1.41869i
$971$	−25.2387			−0.809950			−0.404975	−	0.914328i	$-0.632720\pi$
$971$	−25.2387			−0.809950			−0.404975	+	0.914328i	$0.632720\pi$
$972$			1.13141i			0.0362901i
$973$		−	9.36082i		−	0.300094i
$974$	−68.8866			−2.20727
$975$	5.76786	+	9.47202i	0.184719	+	0.303347i
$976$	6.86158			0.219634
$977$		−	15.4121i		−	0.493077i	−0.969133	−	0.246539i	$-0.920707\pi$
$977$		−	15.4121i		−	0.493077i	0.969133	−	0.246539i	$-0.0792932\pi$
$978$		−	24.5709i		−	0.785692i
$979$	−9.79134			−0.312933
$980$	−1.23928	+	2.20560i	−0.0395872	+	0.0704553i
$981$	17.3946			0.555366
$982$		−	7.05824i		−	0.225238i
$983$		−	41.0989i		−	1.31085i	−0.755259	−	0.655426i	$-0.772489\pi$
$983$		−	41.0989i		−	1.31085i	0.755259	−	0.655426i	$-0.227511\pi$
$984$	−7.39155			−0.235634
$985$	−3.89351	−	2.18767i	−0.124058	−	0.0697050i
$986$	−75.3476			−2.39956
$987$			9.10681i			0.289873i
$988$		−	19.8682i		−	0.632093i
$989$	−4.61467			−0.146738
$990$	3.44966	+	1.93828i	0.109637	+	0.0616026i
$991$	6.66344			0.211671			0.105836	−	0.994384i	$-0.466248\pi$
$991$	6.66344			0.211671			0.105836	+	0.994384i	$0.466248\pi$
$992$		−	8.05225i		−	0.255659i
$993$			14.5088i			0.460422i
$994$	2.06197			0.0654019
$995$	−27.2725	+	48.5382i	−0.864596	+	1.53877i
$996$	−12.7654			−0.404489
$997$		−	34.1288i		−	1.08087i	−0.841386	−	0.540435i	$-0.818260\pi$
$997$		−	34.1288i		−	1.08087i	0.841386	−	0.540435i	$-0.181740\pi$
$998$			0.0214750i			0.000679779i
$999$	−1.37740			−0.0435790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.5	✓	20
5.2	odd	4		5775.2.a.cm.1.9		10
5.3	odd	4		5775.2.a.cp.1.2		10
5.4	even	2	inner	1155.2.c.e.694.16	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.5	✓	20	1.1	even	1	trivial
1155.2.c.e.694.16	yes	20	5.4	even	2	inner
5775.2.a.cm.1.9		10	5.2	odd	4
5775.2.a.cp.1.2		10	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.76958i q^{2} -1.00000i q^{3} -1.13141 q^{4} +(-1.09533 + 1.94942i) q^{5} -1.76958 q^{6} +1.00000i q^{7} -1.53703i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.76958i q^{2} -1.00000i q^{3} -1.13141 q^{4} +(-1.09533 + 1.94942i) q^{5} -1.76958 q^{6} +1.00000i q^{7} -1.53703i q^{8} -1.00000 q^{9} +(3.44966 + 1.93828i) q^{10} -1.00000 q^{11} +1.13141i q^{12} -2.21799i q^{13} +1.76958 q^{14} +(1.94942 + 1.09533i) q^{15} -4.98273 q^{16} +7.13609i q^{17} +1.76958i q^{18} -7.91732 q^{19} +(1.23928 - 2.20560i) q^{20} +1.00000 q^{21} +1.76958i q^{22} +1.96946i q^{23} -1.53703 q^{24} +(-2.60049 - 4.27054i) q^{25} -3.92492 q^{26} +1.00000i q^{27} -1.13141i q^{28} -5.96676 q^{29} +(1.93828 - 3.44966i) q^{30} -1.40203 q^{31} +5.74327i q^{32} +1.00000i q^{33} +12.6279 q^{34} +(-1.94942 - 1.09533i) q^{35} +1.13141 q^{36} +1.37740i q^{37} +14.0103i q^{38} -2.21799 q^{39} +(2.99633 + 1.68357i) q^{40} +4.80897 q^{41} -1.76958i q^{42} +2.34312i q^{43} +1.13141 q^{44} +(1.09533 - 1.94942i) q^{45} +3.48511 q^{46} +9.10681i q^{47} +4.98273i q^{48} -1.00000 q^{49} +(-7.55705 + 4.60177i) q^{50} +7.13609 q^{51} +2.50947i q^{52} +2.65832i q^{53} +1.76958 q^{54} +(1.09533 - 1.94942i) q^{55} +1.53703 q^{56} +7.91732i q^{57} +10.5587i q^{58} -6.97339 q^{59} +(-2.20560 - 1.23928i) q^{60} -1.37707 q^{61} +2.48101i q^{62} -1.00000i q^{63} +0.197717 q^{64} +(4.32380 + 2.42944i) q^{65} +1.76958 q^{66} -12.8612i q^{67} -8.07387i q^{68} +1.96946 q^{69} +(-1.93828 + 3.44966i) q^{70} +1.16523 q^{71} +1.53703i q^{72} +4.94568i q^{73} +2.43742 q^{74} +(-4.27054 + 2.60049i) q^{75} +8.95776 q^{76} -1.00000i q^{77} +3.92492i q^{78} -0.590789 q^{79} +(5.45775 - 9.71344i) q^{80} +1.00000 q^{81} -8.50986i q^{82} +11.2827i q^{83} -1.13141 q^{84} +(-13.9113 - 7.81641i) q^{85} +4.14633 q^{86} +5.96676i q^{87} +1.53703i q^{88} +9.79134 q^{89} +(-3.44966 - 1.93828i) q^{90} +2.21799 q^{91} -2.22827i q^{92} +1.40203i q^{93} +16.1152 q^{94} +(8.67211 - 15.4342i) q^{95} +5.74327 q^{96} -12.8085i q^{97} +1.76958i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

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Database

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