LMFDB - Embedded newform 1110.2.e.c.739.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(739,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1110.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.e (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 $ x^16 - 2x^15 + 2x^14 + 8x^13 + 138x^12 - 220x^11 + 196x^10 + 744x^9 + 4241x^8 - 3018x^7 + 658x^6 - 1584x^5 + 16372x^4 - 18840x^3 + 10952x^2 - 1184*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.15
Root			$-1.32920 - 1.32920i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.c.739.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.32920 + 1.79812i) q^{5} -1.00000i q^{6} +1.87266i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.32920 + 1.79812i) q^{5} -1.00000i q^{6} +1.87266i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-1.32920 - 1.79812i) q^{10} -1.51044 q^{11} +1.00000i q^{12} -4.78011 q^{13} -1.87266i q^{14} +(-1.79812 + 1.32920i) q^{15} +1.00000 q^{16} -3.99190 q^{17} +1.00000 q^{18} -4.68621i q^{19} +(1.32920 + 1.79812i) q^{20} -1.87266 q^{21} +1.51044 q^{22} -6.51179 q^{23} -1.00000i q^{24} +(-1.46648 + 4.78011i) q^{25} +4.78011 q^{26} -1.00000i q^{27} +1.87266i q^{28} -0.200007i q^{29} +(1.79812 - 1.32920i) q^{30} -5.79625i q^{31} -1.00000 q^{32} -1.51044i q^{33} +3.99190 q^{34} +(-3.36727 + 2.48913i) q^{35} -1.00000 q^{36} +(-6.03820 - 0.734967i) q^{37} +4.68621i q^{38} -4.78011i q^{39} +(-1.32920 - 1.79812i) q^{40} +4.10248 q^{41} +1.87266 q^{42} +10.9236 q^{43} -1.51044 q^{44} +(-1.32920 - 1.79812i) q^{45} +6.51179 q^{46} +5.15269i q^{47} +1.00000i q^{48} +3.49314 q^{49} +(1.46648 - 4.78011i) q^{50} -3.99190i q^{51} -4.78011 q^{52} -2.22232i q^{53} +1.00000i q^{54} +(-2.00766 - 2.71595i) q^{55} -1.87266i q^{56} +4.68621 q^{57} +0.200007i q^{58} +13.2646i q^{59} +(-1.79812 + 1.32920i) q^{60} -4.09616i q^{61} +5.79625i q^{62} -1.87266i q^{63} +1.00000 q^{64} +(-6.35370 - 8.59521i) q^{65} +1.51044i q^{66} +5.76584i q^{67} -3.99190 q^{68} -6.51179i q^{69} +(3.36727 - 2.48913i) q^{70} -9.17428 q^{71} +1.00000 q^{72} -14.2905i q^{73} +(6.03820 + 0.734967i) q^{74} +(-4.78011 - 1.46648i) q^{75} -4.68621i q^{76} -2.82853i q^{77} +4.78011i q^{78} +5.95465i q^{79} +(1.32920 + 1.79812i) q^{80} +1.00000 q^{81} -4.10248 q^{82} +9.42048i q^{83} -1.87266 q^{84} +(-5.30602 - 7.17793i) q^{85} -10.9236 q^{86} +0.200007 q^{87} +1.51044 q^{88} +5.47289i q^{89} +(1.32920 + 1.79812i) q^{90} -8.95152i q^{91} -6.51179 q^{92} +5.79625 q^{93} -5.15269i q^{94} +(8.42637 - 6.22888i) q^{95} -1.00000i q^{96} -2.03303 q^{97} -3.49314 q^{98} +1.51044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9	$ 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 + 6 * q^15 + 16 * q^16 - 38 * q^17 + 16 * q^18 - 2 * q^20 + 6 * q^21 - 2 * q^22 - 20 * q^23 - 4 * q^25 - 6 * q^30 - 16 * q^32 + 38 * q^34 - 10 * q^35 - 16 * q^36 - 4 * q^37 + 2 * q^40 - 6 * q^41 - 6 * q^42 - 2 * q^43 + 2 * q^44 + 2 * q^45 + 20 * q^46 - 18 * q^49 + 4 * q^50 + 20 * q^55 + 16 * q^57 + 6 * q^60 + 16 * q^64 + 12 * q^65 - 38 * q^68 + 10 * q^70 - 24 * q^71 + 16 * q^72 + 4 * q^74 - 2 * q^80 + 16 * q^81 + 6 * q^82 + 6 * q^84 + 2 * q^86 + 2 * q^87 - 2 * q^88 - 2 * q^90 - 20 * q^92 + 22 * q^93 - 16 * q^95 + 38 * q^97 + 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$	1.32920	+	1.79812i	0.594434	+	0.804144i
$5$	1.32920	+	1.79812i	0.594434	+	0.804144i
$6$		−	1.00000i		−	0.408248i
$7$			1.87266i			0.707799i	0.935283	+	0.353900i	$0.115145\pi$
$7$			1.87266i			0.707799i	−0.935283	+	0.353900i	$0.884855\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	−1.32920	−	1.79812i	−0.420328	−	0.568616i
$11$	−1.51044			−0.455413			−0.227707	−	0.973730i	$-0.573123\pi$
$11$	−1.51044			−0.455413			−0.227707	+	0.973730i	$0.573123\pi$
$12$			1.00000i			0.288675i
$13$	−4.78011			−1.32576			−0.662882	−	0.748724i	$-0.730667\pi$
$13$	−4.78011			−1.32576			−0.662882	+	0.748724i	$0.730667\pi$
$14$		−	1.87266i		−	0.500490i
$15$	−1.79812	+	1.32920i	−0.464273	+	0.343197i
$16$	1.00000			0.250000
$17$	−3.99190			−0.968179			−0.484089	−	0.875018i	$-0.660849\pi$
$17$	−3.99190			−0.968179			−0.484089	+	0.875018i	$0.660849\pi$
$18$	1.00000			0.235702
$19$		−	4.68621i		−	1.07509i	−0.843235	−	0.537545i	$-0.819352\pi$
$19$		−	4.68621i		−	1.07509i	0.843235	−	0.537545i	$-0.180648\pi$
$20$	1.32920	+	1.79812i	0.297217	+	0.402072i
$21$	−1.87266			−0.408648
$22$	1.51044			0.322026
$23$	−6.51179			−1.35780			−0.678901	−	0.734230i	$-0.737543\pi$
$23$	−6.51179			−1.35780			−0.678901	+	0.734230i	$0.737543\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.46648	+	4.78011i	−0.293296	+	0.956022i
$26$	4.78011			0.937456
$27$		−	1.00000i		−	0.192450i
$28$			1.87266i			0.353900i
$29$		−	0.200007i		−	0.0371403i	−0.999828	−	0.0185702i	$-0.994089\pi$
$29$		−	0.200007i		−	0.0371403i	0.999828	−	0.0185702i	$-0.00591141\pi$
$30$	1.79812	−	1.32920i	0.328291	−	0.242677i
$31$		−	5.79625i		−	1.04104i	−0.853850	−	0.520519i	$-0.825739\pi$
$31$		−	5.79625i		−	1.04104i	0.853850	−	0.520519i	$-0.174261\pi$
$32$	−1.00000			−0.176777
$33$		−	1.51044i		−	0.262933i
$34$	3.99190			0.684606
$35$	−3.36727	+	2.48913i	−0.569173	+	0.420740i
$36$	−1.00000			−0.166667
$37$	−6.03820	−	0.734967i	−0.992673	−	0.120828i
$37$	−6.03820	−	0.734967i	−0.992673	−	0.120828i
$38$			4.68621i			0.760203i
$39$		−	4.78011i		−	0.765430i
$40$	−1.32920	−	1.79812i	−0.210164	−	0.284308i
$41$	4.10248			0.640700			0.320350	−	0.947299i	$-0.396199\pi$
$41$	4.10248			0.640700			0.320350	+	0.947299i	$0.396199\pi$
$42$	1.87266			0.288958
$43$	10.9236			1.66583			0.832916	−	0.553399i	$-0.186670\pi$
$43$	10.9236			1.66583			0.832916	+	0.553399i	$0.186670\pi$
$44$	−1.51044			−0.227707
$45$	−1.32920	−	1.79812i	−0.198145	−	0.268048i
$46$	6.51179			0.960110
$47$			5.15269i			0.751596i	0.926702	+	0.375798i	$0.122631\pi$
$47$			5.15269i			0.751596i	−0.926702	+	0.375798i	$0.877369\pi$
$48$			1.00000i			0.144338i
$49$	3.49314			0.499020
$50$	1.46648	−	4.78011i	0.207392	−	0.676009i
$51$		−	3.99190i		−	0.558978i
$52$	−4.78011			−0.662882
$53$		−	2.22232i		−	0.305259i	−0.988284	−	0.152629i	$-0.951226\pi$
$53$		−	2.22232i		−	0.305259i	0.988284	−	0.152629i	$-0.0487740\pi$
$54$			1.00000i			0.136083i
$55$	−2.00766	−	2.71595i	−0.270713	−	0.366218i
$56$		−	1.87266i		−	0.250245i
$57$	4.68621			0.620703
$58$			0.200007i			0.0262622i
$59$			13.2646i			1.72690i	0.504435	+	0.863450i	$0.331701\pi$
$59$			13.2646i			1.72690i	−0.504435	+	0.863450i	$0.668299\pi$
$60$	−1.79812	+	1.32920i	−0.232136	+	0.171598i
$61$		−	4.09616i		−	0.524459i	−0.965005	−	0.262230i	$-0.915542\pi$
$61$		−	4.09616i		−	0.524459i	0.965005	−	0.262230i	$-0.0844578\pi$
$62$			5.79625i			0.736124i
$63$		−	1.87266i		−	0.235933i
$64$	1.00000			0.125000
$65$	−6.35370	−	8.59521i	−0.788079	−	1.06611i
$66$			1.51044i			0.185922i
$67$			5.76584i			0.704410i	0.935923	+	0.352205i	$0.114568\pi$
$67$			5.76584i			0.704410i	−0.935923	+	0.352205i	$0.885432\pi$
$68$	−3.99190			−0.484089
$69$		−	6.51179i		−	0.783927i
$70$	3.36727	−	2.48913i	0.402466	−	0.297508i
$71$	−9.17428			−1.08879			−0.544393	−	0.838830i	$-0.683240\pi$
$71$	−9.17428			−1.08879			−0.544393	+	0.838830i	$0.683240\pi$
$72$	1.00000			0.117851
$73$		−	14.2905i		−	1.67257i	−0.548294	−	0.836286i	$-0.684722\pi$
$73$		−	14.2905i		−	1.67257i	0.548294	−	0.836286i	$-0.315278\pi$
$74$	6.03820	+	0.734967i	0.701926	+	0.0854382i
$75$	−4.78011	−	1.46648i	−0.551959	−	0.169334i
$76$		−	4.68621i		−	0.537545i
$77$		−	2.82853i		−	0.322341i
$78$			4.78011i			0.541241i
$79$			5.95465i			0.669950i	0.942227	+	0.334975i	$0.108728\pi$
$79$			5.95465i			0.669950i	−0.942227	+	0.334975i	$0.891272\pi$
$80$	1.32920	+	1.79812i	0.148609	+	0.201036i
$81$	1.00000			0.111111
$82$	−4.10248			−0.453044
$83$			9.42048i			1.03403i	0.855976	+	0.517016i	$0.172957\pi$
$83$			9.42048i			1.03403i	−0.855976	+	0.517016i	$0.827043\pi$
$84$	−1.87266			−0.204324
$85$	−5.30602	−	7.17793i	−0.575519	−	0.778556i
$86$	−10.9236			−1.17792
$87$	0.200007			0.0214430
$88$	1.51044			0.161013
$89$			5.47289i			0.580126i	0.957008	+	0.290063i	$0.0936762\pi$
$89$			5.47289i			0.580126i	−0.957008	+	0.290063i	$0.906324\pi$
$90$	1.32920	+	1.79812i	0.140109	+	0.189539i
$91$		−	8.95152i		−	0.938375i
$92$	−6.51179			−0.678901
$93$	5.79625			0.601043
$94$		−	5.15269i		−	0.531459i
$95$	8.42637	−	6.22888i	0.864527	−	0.639070i
$96$		−	1.00000i		−	0.102062i
$97$	−2.03303			−0.206423			−0.103211	−	0.994659i	$-0.532912\pi$
$97$	−2.03303			−0.206423			−0.103211	+	0.994659i	$0.532912\pi$
$98$	−3.49314			−0.352860
$99$	1.51044			0.151804
$100$	−1.46648	+	4.78011i	−0.146648	+	0.478011i
$101$	−9.70730			−0.965913			−0.482956	−	0.875644i	$-0.660437\pi$
$101$	−9.70730			−0.965913			−0.482956	+	0.875644i	$0.660437\pi$
$102$			3.99190i			0.395257i
$103$	2.66390			0.262482			0.131241	−	0.991351i	$-0.458104\pi$
$103$	2.66390			0.262482			0.131241	+	0.991351i	$0.458104\pi$
$104$	4.78011			0.468728
$105$	−2.48913	−	3.36727i	−0.242914	−	0.328612i
$106$			2.22232i			0.215850i
$107$			0.823199i			0.0795816i	0.999208	+	0.0397908i	$0.0126692\pi$
$107$			0.823199i			0.0795816i	−0.999208	+	0.0397908i	$0.987331\pi$
$108$		−	1.00000i		−	0.0962250i
$109$			0.478427i			0.0458250i	0.999737	+	0.0229125i	$0.00729391\pi$
$109$			0.478427i			0.0458250i	−0.999737	+	0.0229125i	$0.992706\pi$
$110$	2.00766	+	2.71595i	0.191423	+	0.258955i
$111$	0.734967	−	6.03820i	0.0697600	−	0.573120i
$112$			1.87266i			0.176950i
$113$	−19.8469			−1.86704			−0.933522	−	0.358521i	$-0.883281\pi$
$113$	−19.8469			−1.86704			−0.933522	+	0.358521i	$0.883281\pi$
$114$	−4.68621			−0.438903
$115$	−8.65543	−	11.7090i	−0.807123	−	1.09187i
$116$		−	0.200007i		−	0.0185702i
$117$	4.78011			0.441921
$118$		−	13.2646i		−	1.22110i
$119$		−	7.47548i		−	0.685277i
$120$	1.79812	−	1.32920i	0.164145	−	0.121338i
$121$	−8.71858			−0.792599
$122$			4.09616i			0.370849i
$123$			4.10248i			0.369909i
$124$		−	5.79625i		−	0.520519i
$125$	−10.5445	+	3.71679i	−0.943124	+	0.332440i
$126$			1.87266i			0.166830i
$127$			6.85655i			0.608420i	0.952605	+	0.304210i	$0.0983925\pi$
$127$			6.85655i			0.608420i	−0.952605	+	0.304210i	$0.901608\pi$
$128$	−1.00000			−0.0883883
$129$			10.9236i			0.961769i
$130$	6.35370	+	8.59521i	0.557256	+	0.753850i
$131$			3.26950i			0.285658i	0.989747	+	0.142829i	$0.0456198\pi$
$131$			3.26950i			0.285658i	−0.989747	+	0.142829i	$0.954380\pi$
$132$		−	1.51044i		−	0.131467i
$133$	8.77568			0.760948
$134$		−	5.76584i		−	0.498093i
$135$	1.79812	−	1.32920i	0.154758	−	0.114399i
$136$	3.99190			0.342303
$137$			2.11793i			0.180947i	0.995899	+	0.0904733i	$0.0288380\pi$
$137$			2.11793i			0.180947i	−0.995899	+	0.0904733i	$0.971162\pi$
$138$			6.51179i			0.554320i
$139$	−15.7132			−1.33277			−0.666387	−	0.745606i	$-0.732160\pi$
$139$	−15.7132			−1.33277			−0.666387	+	0.745606i	$0.732160\pi$
$140$	−3.36727	+	2.48913i	−0.284586	+	0.210370i
$141$	−5.15269			−0.433934
$142$	9.17428			0.769889
$143$	7.22005			0.603771
$144$	−1.00000			−0.0833333
$145$	0.359637	−	0.265848i	0.0298662	−	0.0220775i
$146$			14.2905i			1.18269i
$147$			3.49314i			0.288109i
$148$	−6.03820	−	0.734967i	−0.496337	−	0.0604139i
$149$	−4.47152			−0.366321			−0.183161	−	0.983083i	$-0.558633\pi$
$149$	−4.47152			−0.366321			−0.183161	+	0.983083i	$0.558633\pi$
$150$	4.78011	+	1.46648i	0.390294	+	0.119738i
$151$	3.25118			0.264577			0.132289	−	0.991211i	$-0.457767\pi$
$151$	3.25118			0.264577			0.132289	+	0.991211i	$0.457767\pi$
$152$			4.68621i			0.380101i
$153$	3.99190			0.322726
$154$			2.82853i			0.227930i
$155$	10.4224	−	7.70435i	0.837144	−	0.618828i
$156$		−	4.78011i		−	0.382715i
$157$		−	0.0713960i		−	0.00569802i	−0.999996	−	0.00284901i	$-0.999093\pi$
$157$		−	0.0713960i		−	0.00569802i	0.999996	−	0.00284901i	$-0.000906870\pi$
$158$		−	5.95465i		−	0.473726i
$159$	2.22232			0.176241
$160$	−1.32920	−	1.79812i	−0.105082	−	0.142154i
$161$		−	12.1944i		−	0.961051i
$162$	−1.00000			−0.0785674
$163$	−1.06145			−0.0831389			−0.0415695	−	0.999136i	$-0.513236\pi$
$163$	−1.06145			−0.0831389			−0.0415695	+	0.999136i	$0.513236\pi$
$164$	4.10248			0.320350
$165$	2.71595	−	2.00766i	0.211436	−	0.156296i
$166$		−	9.42048i		−	0.731171i
$167$	20.4097			1.57935			0.789673	−	0.613528i	$-0.210250\pi$
$167$	20.4097			1.57935			0.789673	+	0.613528i	$0.210250\pi$
$168$	1.87266			0.144479
$169$	9.84944			0.757649
$170$	5.30602	+	7.17793i	0.406953	+	0.550522i
$171$			4.68621i			0.358363i
$172$	10.9236			0.832916
$173$		−	16.9195i		−	1.28636i	−0.765713	−	0.643182i	$-0.777614\pi$
$173$		−	16.9195i		−	1.28636i	0.765713	−	0.643182i	$-0.222386\pi$
$174$	−0.200007			−0.0151625
$175$	−8.95152	−	2.74622i	−0.676672	−	0.207595i
$176$	−1.51044			−0.113853
$177$	−13.2646			−0.997026
$178$		−	5.47289i		−	0.410211i
$179$			26.6575i			1.99247i	0.0866723	+	0.996237i	$0.472377\pi$
$179$			26.6575i			1.99247i	−0.0866723	+	0.996237i	$0.527623\pi$
$180$	−1.32920	−	1.79812i	−0.0990724	−	0.134024i
$181$	−13.4428			−0.999196			−0.499598	−	0.866257i	$-0.666519\pi$
$181$	−13.4428			−0.999196			−0.499598	+	0.866257i	$0.666519\pi$
$182$			8.95152i			0.663531i
$183$	4.09616			0.302797
$184$	6.51179			0.480055
$185$	−6.70438	−	11.8343i	−0.492916	−	0.870077i
$186$	−5.79625			−0.425002
$187$	6.02951			0.440922
$188$			5.15269i			0.375798i
$189$	1.87266			0.136216
$190$	−8.42637	+	6.22888i	−0.611313	+	0.451891i
$191$		−	6.76465i		−	0.489473i	−0.969590	−	0.244736i	$-0.921299\pi$
$191$		−	6.76465i		−	0.489473i	0.969590	−	0.244736i	$-0.0787014\pi$
$192$			1.00000i			0.0721688i
$193$	−15.4592			−1.11278			−0.556389	−	0.830922i	$-0.687814\pi$
$193$	−15.4592			−1.11278			−0.556389	+	0.830922i	$0.687814\pi$
$194$	2.03303			0.145963
$195$	8.59521	−	6.35370i	0.615516	−	0.454998i
$196$	3.49314			0.249510
$197$			12.5068i			0.891072i	0.895264	+	0.445536i	$0.146987\pi$
$197$			12.5068i			0.891072i	−0.895264	+	0.445536i	$0.853013\pi$
$198$	−1.51044			−0.107342
$199$			13.4172i			0.951119i	0.879684	+	0.475559i	$0.157754\pi$
$199$			13.4172i			0.951119i	−0.879684	+	0.475559i	$0.842246\pi$
$200$	1.46648	−	4.78011i	0.103696	−	0.338005i
$201$	−5.76584			−0.406691
$202$	9.70730			0.683003
$203$	0.374545			0.0262879
$204$		−	3.99190i		−	0.279489i
$205$	5.45300	+	7.37676i	0.380854	+	0.515216i
$206$	−2.66390			−0.185603
$207$	6.51179			0.452600
$208$	−4.78011			−0.331441
$209$			7.07821i			0.489610i
$210$	2.48913	+	3.36727i	0.171766	+	0.232364i
$211$	6.46040			0.444752			0.222376	−	0.974961i	$-0.428619\pi$
$211$	6.46040			0.444752			0.222376	+	0.974961i	$0.428619\pi$
$212$		−	2.22232i		−	0.152629i
$213$		−	9.17428i		−	0.628611i
$214$		−	0.823199i		−	0.0562727i
$215$	14.5196	+	19.6419i	0.990228	+	1.33957i
$216$			1.00000i			0.0680414i
$217$	10.8544			0.736845
$218$		−	0.478427i		−	0.0324031i
$219$	14.2905			0.965660
$220$	−2.00766	−	2.71595i	−0.135357	−	0.183109i
$221$	19.0817			1.28358
$222$	−0.734967	+	6.03820i	−0.0493278	+	0.405257i
$223$		−	8.15634i		−	0.546189i	−0.961987	−	0.273095i	$-0.911953\pi$
$223$		−	8.15634i		−	0.546189i	0.961987	−	0.273095i	$-0.0880472\pi$
$224$		−	1.87266i		−	0.125122i
$225$	1.46648	−	4.78011i	0.0977653	−	0.318674i
$226$	19.8469			1.32020
$227$	−13.0456			−0.865866			−0.432933	−	0.901426i	$-0.642521\pi$
$227$	−13.0456			−0.865866			−0.432933	+	0.901426i	$0.642521\pi$
$228$	4.68621			0.310352
$229$	13.3621			0.882995			0.441498	−	0.897262i	$-0.354447\pi$
$229$	13.3621			0.882995			0.441498	+	0.897262i	$0.354447\pi$
$230$	8.65543	+	11.7090i	0.570722	+	0.772067i
$231$	2.82853			0.186104
$232$			0.200007i			0.0131311i
$233$			27.2277i			1.78375i	0.452283	+	0.891875i	$0.350610\pi$
$233$			27.2277i			1.78375i	−0.452283	+	0.891875i	$0.649390\pi$
$234$	−4.78011			−0.312485
$235$	−9.26515	+	6.84893i	−0.604392	+	0.446775i
$236$			13.2646i			0.863450i
$237$	−5.95465			−0.386796
$238$			7.47548i			0.484564i
$239$			10.5417i			0.681888i	0.940084	+	0.340944i	$0.110747\pi$
$239$			10.5417i			0.681888i	−0.940084	+	0.340944i	$0.889253\pi$
$240$	−1.79812	+	1.32920i	−0.116068	+	0.0857992i
$241$			13.3732i			0.861446i	0.902484	+	0.430723i	$0.141741\pi$
$241$			13.3732i			0.861446i	−0.902484	+	0.430723i	$0.858259\pi$
$242$	8.71858			0.560452
$243$			1.00000i			0.0641500i
$244$		−	4.09616i		−	0.262230i
$245$	4.64307	+	6.28109i	0.296635	+	0.401284i
$246$		−	4.10248i		−	0.261565i
$247$			22.4006i			1.42531i
$248$			5.79625i			0.368062i
$249$	−9.42048			−0.596999
$250$	10.5445	−	3.71679i	0.666890	−	0.235070i
$251$			6.68149i			0.421732i	0.977515	+	0.210866i	$0.0676283\pi$
$251$			6.68149i			0.421732i	−0.977515	+	0.210866i	$0.932372\pi$
$252$		−	1.87266i		−	0.117967i
$253$	9.83563			0.618361
$254$		−	6.85655i		−	0.430218i
$255$	7.17793	−	5.30602i	0.449499	−	0.332276i
$256$	1.00000			0.0625000
$257$	4.63516			0.289133			0.144567	−	0.989495i	$-0.453821\pi$
$257$	4.63516			0.289133			0.144567	+	0.989495i	$0.453821\pi$
$258$		−	10.9236i		−	0.680073i
$259$	1.37634	−	11.3075i	0.0855219	−	0.702614i
$260$	−6.35370	−	8.59521i	−0.394040	−	0.533053i
$261$			0.200007i			0.0123801i
$262$		−	3.26950i		−	0.201990i
$263$		−	29.5118i		−	1.81977i	−0.414857	−	0.909887i	$-0.636168\pi$
$263$		−	29.5118i		−	1.81977i	0.414857	−	0.909887i	$-0.363832\pi$
$264$			1.51044i			0.0929609i
$265$	3.99599	−	2.95389i	0.245472	−	0.181456i
$266$	−8.77568			−0.538071
$267$	−5.47289			−0.334936
$268$			5.76584i			0.352205i
$269$	−21.3385			−1.30103			−0.650516	−	0.759493i	$-0.725447\pi$
$269$	−21.3385			−1.30103			−0.650516	+	0.759493i	$0.725447\pi$
$270$	−1.79812	+	1.32920i	−0.109430	+	0.0808923i
$271$	16.5121			1.00304			0.501521	−	0.865146i	$-0.332774\pi$
$271$	16.5121			1.00304			0.501521	+	0.865146i	$0.332774\pi$
$272$	−3.99190			−0.242045
$273$	8.95152			0.541771
$274$		−	2.11793i		−	0.127949i
$275$	2.21502	−	7.22005i	0.133571	−	0.435385i
$276$		−	6.51179i		−	0.391963i
$277$	11.0446			0.663605			0.331802	−	0.943349i	$-0.392343\pi$
$277$	11.0446			0.663605			0.331802	+	0.943349i	$0.392343\pi$
$278$	15.7132			0.942414
$279$			5.79625i			0.347012i
$280$	3.36727	−	2.48913i	0.201233	−	0.148754i
$281$			17.9190i			1.06896i	0.845182	+	0.534478i	$0.179492\pi$
$281$			17.9190i			1.06896i	−0.845182	+	0.534478i	$0.820508\pi$
$282$	5.15269			0.306838
$283$	14.0543			0.835440			0.417720	−	0.908576i	$-0.362829\pi$
$283$	14.0543			0.835440			0.417720	+	0.908576i	$0.362829\pi$
$284$	−9.17428			−0.544393
$285$	6.22888	+	8.42637i	0.368967	+	0.499135i
$286$	−7.22005			−0.426930
$287$			7.68256i			0.453487i
$288$	1.00000			0.0589256
$289$	−1.06470			−0.0626295
$290$	−0.359637	+	0.265848i	−0.0211186	+	0.0156111i
$291$		−	2.03303i		−	0.119178i
$292$		−	14.2905i		−	0.836286i
$293$		−	32.2561i		−	1.88442i	−0.335018	−	0.942212i	$-0.608742\pi$
$293$		−	32.2561i		−	1.88442i	0.335018	−	0.942212i	$-0.391258\pi$
$294$		−	3.49314i		−	0.203724i
$295$	−23.8513	+	17.6312i	−1.38868	+	1.02653i
$296$	6.03820	+	0.734967i	0.350963	+	0.0427191i
$297$			1.51044i			0.0876444i
$298$	4.47152			0.259028
$299$	31.1270			1.80012
$300$	−4.78011	−	1.46648i	−0.275980	−	0.0846672i
$301$			20.4562i			1.17908i
$302$	−3.25118			−0.187084
$303$		−	9.70730i		−	0.557670i
$304$		−	4.68621i		−	0.268772i
$305$	7.36539	−	5.44459i	0.421741	−	0.311757i
$306$	−3.99190			−0.228202
$307$			27.5771i			1.57391i	0.617012	+	0.786953i	$0.288343\pi$
$307$			27.5771i			1.57391i	−0.617012	+	0.786953i	$0.711657\pi$
$308$		−	2.82853i		−	0.161171i
$309$			2.66390i			0.151544i
$310$	−10.4224	+	7.70435i	−0.591950	+	0.437578i
$311$		−	13.8537i		−	0.785570i	−0.919630	−	0.392785i	$-0.871512\pi$
$311$		−	13.8537i		−	0.785570i	0.919630	−	0.392785i	$-0.128488\pi$
$312$			4.78011i			0.270620i
$313$	24.3768			1.37786			0.688930	−	0.724828i	$-0.258081\pi$
$313$	24.3768			1.37786			0.688930	+	0.724828i	$0.258081\pi$
$314$			0.0713960i			0.00402911i
$315$	3.36727	−	2.48913i	0.189724	−	0.140247i
$316$			5.95465i			0.334975i
$317$		−	8.91522i		−	0.500729i	−0.968152	−	0.250364i	$-0.919450\pi$
$317$		−	8.91522i		−	0.500729i	0.968152	−	0.250364i	$-0.0805504\pi$
$318$	−2.22232			−0.124621
$319$			0.302097i			0.0169142i
$320$	1.32920	+	1.79812i	0.0743043	+	0.100518i
$321$	−0.823199			−0.0459465
$322$			12.1944i			0.679566i
$323$			18.7069i			1.04088i
$324$	1.00000			0.0555556
$325$	7.00993	−	22.8494i	0.388841	−	1.26746i
$326$	1.06145			0.0587881
$327$	−0.478427			−0.0264570
$328$	−4.10248			−0.226522
$329$	−9.64923			−0.531979
$330$	−2.71595	+	2.00766i	−0.149508	+	0.110518i
$331$		−	25.6563i		−	1.41020i	−0.709109	−	0.705099i	$-0.750903\pi$
$331$		−	25.6563i		−	1.41020i	0.709109	−	0.705099i	$-0.249097\pi$
$332$			9.42048i			0.517016i
$333$	6.03820	+	0.734967i	0.330891	+	0.0402760i
$334$	−20.4097			−1.11677
$335$	−10.3677	+	7.66393i	−0.566447	+	0.418725i
$336$	−1.87266			−0.102162
$337$			18.5473i			1.01033i	0.863021	+	0.505167i	$0.168569\pi$
$337$			18.5473i			1.01033i	−0.863021	+	0.505167i	$0.831431\pi$
$338$	−9.84944			−0.535739
$339$		−	19.8469i		−	1.07794i
$340$	−5.30602	−	7.17793i	−0.287759	−	0.389278i
$341$			8.75486i			0.474102i
$342$		−	4.68621i		−	0.253401i
$343$			19.6501i			1.06101i
$344$	−10.9236			−0.588961
$345$	11.7090	−	8.65543i	0.630390	−	0.465993i
$346$			16.9195i			0.909597i
$347$	9.07304			0.487066			0.243533	−	0.969893i	$-0.421694\pi$
$347$	9.07304			0.487066			0.243533	+	0.969893i	$0.421694\pi$
$348$	0.200007			0.0107215
$349$	−31.1022			−1.66486			−0.832431	−	0.554129i	$-0.813052\pi$
$349$	−31.1022			−1.66486			−0.832431	+	0.554129i	$0.813052\pi$
$350$	8.95152	+	2.74622i	0.478479	+	0.146792i
$351$			4.78011i			0.255143i
$352$	1.51044			0.0805065
$353$	16.3289			0.869098			0.434549	−	0.900648i	$-0.356908\pi$
$353$	16.3289			0.869098			0.434549	+	0.900648i	$0.356908\pi$
$354$	13.2646			0.705004
$355$	−12.1944	−	16.4965i	−0.647212	−	0.875542i
$356$			5.47289i			0.290063i
$357$	7.47548			0.395645
$358$		−	26.6575i		−	1.40889i
$359$	17.1135			0.903216			0.451608	−	0.892217i	$-0.350851\pi$
$359$	17.1135			0.903216			0.451608	+	0.892217i	$0.350851\pi$
$360$	1.32920	+	1.79812i	0.0700547	+	0.0947693i
$361$	−2.96053			−0.155817
$362$	13.4428			0.706538
$363$		−	8.71858i		−	0.457607i
$364$		−	8.95152i		−	0.469187i
$365$	25.6960	−	18.9948i	1.34499	−	0.994234i
$366$	−4.09616			−0.214110
$367$			23.2045i			1.21126i	0.795745	+	0.605632i	$0.207080\pi$
$367$			23.2045i			1.21126i	−0.795745	+	0.605632i	$0.792920\pi$
$368$	−6.51179			−0.339450
$369$	−4.10248			−0.213567
$370$	6.70438	+	11.8343i	0.348544	+	0.615237i
$371$	4.16164			0.216062
$372$	5.79625			0.300522
$373$		−	9.69704i		−	0.502094i	−0.967975	−	0.251047i	$-0.919225\pi$
$373$		−	9.69704i		−	0.502094i	0.967975	−	0.251047i	$-0.0807748\pi$
$374$	−6.02951			−0.311779
$375$	−3.71679	−	10.5445i	−0.191934	−	0.544513i
$376$		−	5.15269i		−	0.265729i
$377$			0.956055i			0.0492393i
$378$	−1.87266			−0.0963193
$379$	−9.40066			−0.482880			−0.241440	−	0.970416i	$-0.577620\pi$
$379$	−9.40066			−0.482880			−0.241440	+	0.970416i	$0.577620\pi$
$380$	8.42637	−	6.22888i	0.432263	−	0.319535i
$381$	−6.85655			−0.351272
$382$			6.76465i			0.346109i
$383$	−32.3874			−1.65492			−0.827459	−	0.561526i	$-0.810215\pi$
$383$	−32.3874			−1.65492			−0.827459	+	0.561526i	$0.810215\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	5.08605	−	3.75967i	0.259209	−	0.191611i
$386$	15.4592			0.786853
$387$	−10.9236			−0.555278
$388$	−2.03303			−0.103211
$389$		−	20.8774i		−	1.05853i	−0.848457	−	0.529264i	$-0.822468\pi$
$389$		−	20.8774i		−	1.05853i	0.848457	−	0.529264i	$-0.177532\pi$
$390$	−8.59521	+	6.35370i	−0.435236	+	0.321732i
$391$	25.9944			1.31459
$392$	−3.49314			−0.176430
$393$	−3.26950			−0.164925
$394$		−	12.5068i		−	0.630083i
$395$	−10.7072	+	7.91489i	−0.538737	+	0.398241i
$396$	1.51044			0.0759022
$397$		−	12.2447i		−	0.614546i	−0.951621	−	0.307273i	$-0.900584\pi$
$397$		−	12.2447i		−	0.614546i	0.951621	−	0.307273i	$-0.0994164\pi$
$398$		−	13.4172i		−	0.672543i
$399$			8.77568i			0.439333i
$400$	−1.46648	+	4.78011i	−0.0733240	+	0.239005i
$401$		−	13.7736i		−	0.687820i	−0.939003	−	0.343910i	$-0.888248\pi$
$401$		−	13.7736i		−	0.687820i	0.939003	−	0.343910i	$-0.111752\pi$
$402$	5.76584			0.287574
$403$			27.7067i			1.38017i
$404$	−9.70730			−0.482956
$405$	1.32920	+	1.79812i	0.0660482	+	0.0893494i
$406$	−0.374545			−0.0185884
$407$	9.12031	+	1.11012i	0.452077	+	0.0550266i
$408$			3.99190i			0.197629i
$409$			34.5667i			1.70921i	0.519276	+	0.854606i	$0.326202\pi$
$409$			34.5667i			1.70921i	−0.519276	+	0.854606i	$0.673798\pi$
$410$	−5.45300	−	7.37676i	−0.269305	−	0.364312i
$411$	−2.11793			−0.104470
$412$	2.66390			0.131241
$413$	−24.8400			−1.22230
$414$	−6.51179			−0.320037
$415$	−16.9392	+	12.5217i	−0.831511	+	0.614664i
$416$	4.78011			0.234364
$417$		−	15.7132i		−	0.769478i
$418$		−	7.07821i		−	0.346207i
$419$	22.9413			1.12076			0.560378	−	0.828237i	$-0.310656\pi$
$419$	22.9413			1.12076			0.560378	+	0.828237i	$0.310656\pi$
$420$	−2.48913	−	3.36727i	−0.121457	−	0.164306i
$421$		−	12.1679i		−	0.593026i	−0.955029	−	0.296513i	$-0.904176\pi$
$421$		−	12.1679i		−	0.593026i	0.955029	−	0.296513i	$-0.0958239\pi$
$422$	−6.46040			−0.314487
$423$		−	5.15269i		−	0.250532i
$424$			2.22232i			0.107925i
$425$	5.85405	−	19.0817i	0.283963	−	0.925600i
$426$			9.17428i			0.444495i
$427$	7.67072			0.371212
$428$			0.823199i			0.0397908i
$429$			7.22005i			0.348587i
$430$	−14.5196	−	19.6419i	−0.700197	−	0.947219i
$431$		−	11.2076i		−	0.539853i	−0.962881	−	0.269927i	$-0.913001\pi$
$431$		−	11.2076i		−	0.539853i	0.962881	−	0.269927i	$-0.0869995\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			31.6559i			1.52128i	0.649172	+	0.760642i	$0.275116\pi$
$433$			31.6559i			1.52128i	−0.649172	+	0.760642i	$0.724884\pi$
$434$	−10.8544			−0.521028
$435$	0.265848	+	0.359637i	0.0127464	+	0.0172433i
$436$			0.478427i			0.0229125i
$437$			30.5156i			1.45976i
$438$	−14.2905			−0.682824
$439$			33.9912i			1.62231i	0.584831	+	0.811155i	$0.301161\pi$
$439$			33.9912i			1.62231i	−0.584831	+	0.811155i	$0.698839\pi$
$440$	2.00766	+	2.71595i	0.0957116	+	0.129478i
$441$	−3.49314			−0.166340
$442$	−19.0817			−0.907626
$443$		−	34.9477i		−	1.66042i	−0.557454	−	0.830208i	$-0.688222\pi$
$443$		−	34.9477i		−	1.66042i	0.557454	−	0.830208i	$-0.311778\pi$
$444$	0.734967	−	6.03820i	0.0348800	−	0.286560i
$445$	−9.84093	+	7.27454i	−0.466505	+	0.344846i
$446$			8.15634i			0.386214i
$447$		−	4.47152i		−	0.211496i
$448$			1.87266i			0.0884749i
$449$		−	17.2274i		−	0.813012i	−0.913648	−	0.406506i	$-0.866747\pi$
$449$		−	17.2274i		−	0.813012i	0.913648	−	0.406506i	$-0.133253\pi$
$450$	−1.46648	+	4.78011i	−0.0691305	+	0.225336i
$451$	−6.19654			−0.291784
$452$	−19.8469			−0.933522
$453$			3.25118i			0.152754i
$454$	13.0456			0.612260
$455$	16.0959	−	11.8983i	0.754589	−	0.557802i
$456$	−4.68621			−0.219452
$457$	−24.5044			−1.14627			−0.573133	−	0.819463i	$-0.694272\pi$
$457$	−24.5044			−1.14627			−0.573133	+	0.819463i	$0.694272\pi$
$458$	−13.3621			−0.624372
$459$			3.99190i			0.186326i
$460$	−8.65543	−	11.7090i	−0.403562	−	0.545934i
$461$			9.05274i			0.421628i	0.977526	+	0.210814i	$0.0676115\pi$
$461$			9.05274i			0.421628i	−0.977526	+	0.210814i	$0.932389\pi$
$462$	−2.82853			−0.131595
$463$	2.10640			0.0978927			0.0489463	−	0.998801i	$-0.484414\pi$
$463$	2.10640			0.0978927			0.0489463	+	0.998801i	$0.484414\pi$
$464$		−	0.200007i		−	0.00928509i
$465$	7.70435	+	10.4224i	0.357281	+	0.483325i
$466$		−	27.2277i		−	1.26130i
$467$	−24.0814			−1.11435			−0.557177	−	0.830394i	$-0.688116\pi$
$467$	−24.0814			−1.11435			−0.557177	+	0.830394i	$0.688116\pi$
$468$	4.78011			0.220961
$469$	−10.7975			−0.498581
$470$	9.26515	−	6.84893i	0.427370	−	0.315917i
$471$	0.0713960			0.00328976
$472$		−	13.2646i		−	0.610551i
$473$	−16.4994			−0.758642
$474$	5.95465			0.273506
$475$	22.4006	+	6.87223i	1.02781	+	0.315319i
$476$		−	7.47548i		−	0.342638i
$477$			2.22232i			0.101753i
$478$		−	10.5417i		−	0.482168i
$479$			5.46224i			0.249576i	0.992183	+	0.124788i	$0.0398251\pi$
$479$			5.46224i			0.249576i	−0.992183	+	0.124788i	$0.960175\pi$
$480$	1.79812	−	1.32920i	0.0820726	−	0.0606692i
$481$	28.8632	+	3.51322i	1.31605	+	0.160189i
$482$		−	13.3732i		−	0.609134i
$483$	12.1944			0.554863
$484$	−8.71858			−0.396299
$485$	−2.70229	−	3.65563i	−0.122705	−	0.165994i
$486$		−	1.00000i		−	0.0453609i
$487$	−11.8494			−0.536949			−0.268475	−	0.963287i	$-0.586520\pi$
$487$	−11.8494			−0.536949			−0.268475	+	0.963287i	$0.586520\pi$
$488$			4.09616i			0.185424i
$489$		−	1.06145i		−	0.0480003i
$490$	−4.64307	−	6.28109i	−0.209752	−	0.283751i
$491$	−7.19955			−0.324911			−0.162456	−	0.986716i	$-0.551941\pi$
$491$	−7.19955			−0.324911			−0.162456	+	0.986716i	$0.551941\pi$
$492$			4.10248i			0.184954i
$493$			0.798408i			0.0359585i
$494$		−	22.4006i		−	1.00785i
$495$	2.00766	+	2.71595i	0.0902378	+	0.122073i
$496$		−	5.79625i		−	0.260259i
$497$		−	17.1803i		−	0.770643i
$498$	9.42048			0.422142
$499$		−	3.32481i		−	0.148839i	−0.997227	−	0.0744194i	$-0.976290\pi$
$499$		−	3.32481i		−	0.148839i	0.997227	−	0.0744194i	$-0.0237104\pi$
$500$	−10.5445	+	3.71679i	−0.471562	+	0.166220i
$501$			20.4097i			0.911836i
$502$		−	6.68149i		−	0.298209i
$503$	9.09539			0.405544			0.202772	−	0.979226i	$-0.435005\pi$
$503$	9.09539			0.405544			0.202772	+	0.979226i	$0.435005\pi$
$504$			1.87266i			0.0834150i
$505$	−12.9029	−	17.4549i	−0.574172	−	0.776733i
$506$	−9.83563			−0.437247
$507$			9.84944i			0.437429i
$508$			6.85655i			0.304210i
$509$	−12.7781			−0.566380			−0.283190	−	0.959064i	$-0.591393\pi$
$509$	−12.7781			−0.566380			−0.283190	+	0.959064i	$0.591393\pi$
$510$	−7.17793	+	5.30602i	−0.317844	+	0.234955i
$511$	26.7612			1.18385
$512$	−1.00000			−0.0441942
$513$	−4.68621			−0.206901
$514$	−4.63516			−0.204448
$515$	3.54084	+	4.79001i	0.156028	+	0.211073i
$516$			10.9236i			0.480884i
$517$		−	7.78280i		−	0.342287i
$518$	−1.37634	+	11.3075i	−0.0604731	+	0.496823i
$519$	16.9195			0.742683
$520$	6.35370	+	8.59521i	0.278628	+	0.376925i
$521$	−37.3185			−1.63495			−0.817476	−	0.575963i	$-0.804627\pi$
$521$	−37.3185			−1.63495			−0.817476	+	0.575963i	$0.804627\pi$
$522$		−	0.200007i		−	0.00875406i
$523$	−1.83536			−0.0802549			−0.0401274	−	0.999195i	$-0.512776\pi$
$523$	−1.83536			−0.0802549			−0.0401274	+	0.999195i	$0.512776\pi$
$524$			3.26950i			0.142829i
$525$	2.74622	−	8.95152i	0.119855	−	0.390677i
$526$			29.5118i			1.28677i
$527$			23.1381i			1.00791i
$528$		−	1.51044i		−	0.0657333i
$529$	19.4034			0.843624
$530$	−3.99599	+	2.95389i	−0.173575	+	0.128309i
$531$		−	13.2646i		−	0.575633i
$532$	8.77568			0.380474
$533$	−19.6103			−0.849417
$534$	5.47289			0.236835
$535$	−1.48021	+	1.09419i	−0.0639951	+	0.0473060i
$536$		−	5.76584i		−	0.249047i
$537$	−26.6575			−1.15036
$538$	21.3385			0.919968
$539$	−5.27616			−0.227260
$540$	1.79812	−	1.32920i	0.0773788	−	0.0571995i
$541$		−	37.3336i		−	1.60510i	−0.596587	−	0.802548i	$-0.703477\pi$
$541$		−	37.3336i		−	1.60510i	0.596587	−	0.802548i	$-0.296523\pi$
$542$	−16.5121			−0.709257
$543$		−	13.4428i		−	0.576886i
$544$	3.99190			0.171151
$545$	−0.860269	+	0.635922i	−0.0368499	+	0.0272399i
$546$	−8.95152			−0.383090
$547$	−17.5386			−0.749897			−0.374949	−	0.927046i	$-0.622340\pi$
$547$	−17.5386			−0.749897			−0.374949	+	0.927046i	$0.622340\pi$
$548$			2.11793i			0.0904733i
$549$			4.09616i			0.174820i
$550$	−2.21502	+	7.22005i	−0.0944489	+	0.307864i
$551$	−0.937273			−0.0399292
$552$			6.51179i			0.277160i
$553$	−11.1510			−0.474191
$554$	−11.0446			−0.469239
$555$	11.8343	−	6.70438i	0.502339	−	0.284585i
$556$	−15.7132			−0.666387
$557$	40.7617			1.72713			0.863565	−	0.504237i	$-0.168226\pi$
$557$	40.7617			1.72713			0.863565	+	0.504237i	$0.168226\pi$
$558$		−	5.79625i		−	0.245375i
$559$	−52.2160			−2.20850
$560$	−3.36727	+	2.48913i	−0.142293	+	0.105185i
$561$			6.02951i			0.254566i
$562$		−	17.9190i		−	0.755867i
$563$	−4.47929			−0.188779			−0.0943897	−	0.995535i	$-0.530090\pi$
$563$	−4.47929			−0.188779			−0.0943897	+	0.995535i	$0.530090\pi$
$564$	−5.15269			−0.216967
$565$	−26.3805	−	35.6872i	−1.10983	−	1.50137i
$566$	−14.0543			−0.590746
$567$			1.87266i			0.0786444i
$568$	9.17428			0.384944
$569$		−	0.243177i		−	0.0101945i	−0.999987	−	0.00509725i	$-0.998377\pi$
$569$		−	0.243177i		−	0.0101945i	0.999987	−	0.00509725i	$-0.00162251\pi$
$570$	−6.22888	−	8.42637i	−0.260899	−	0.352942i
$571$	34.2552			1.43353			0.716767	−	0.697313i	$-0.245621\pi$
$571$	34.2552			1.43353			0.716767	+	0.697313i	$0.245621\pi$
$572$	7.22005			0.301885
$573$	6.76465			0.282597
$574$		−	7.68256i		−	0.320664i
$575$	9.54940	−	31.1270i	0.398238	−	1.29809i
$576$	−1.00000			−0.0416667
$577$	−10.5028			−0.437239			−0.218620	−	0.975810i	$-0.570155\pi$
$577$	−10.5028			−0.437239			−0.218620	+	0.975810i	$0.570155\pi$
$578$	1.06470			0.0442857
$579$		−	15.4592i		−	0.642463i
$580$	0.359637	−	0.265848i	0.0149331	−	0.0110387i
$581$	−17.6414			−0.731887
$582$			2.03303i			0.0842718i
$583$			3.35666i			0.139019i
$584$			14.2905i			0.591343i
$585$	6.35370	+	8.59521i	0.262693	+	0.355368i
$586$			32.2561i			1.33249i
$587$	27.0890			1.11808			0.559042	−	0.829139i	$-0.311169\pi$
$587$	27.0890			1.11808			0.559042	+	0.829139i	$0.311169\pi$
$588$			3.49314i			0.144055i
$589$	−27.1624			−1.11921
$590$	23.8513	−	17.6312i	0.981942	−	0.725865i
$591$	−12.5068			−0.514461
$592$	−6.03820	−	0.734967i	−0.248168	−	0.0302070i
$593$			24.2823i			0.997156i	0.866845	+	0.498578i	$0.166144\pi$
$593$			24.2823i			0.997156i	−0.866845	+	0.498578i	$0.833856\pi$
$594$		−	1.51044i		−	0.0619739i
$595$	13.4418	−	9.93638i	0.551061	−	0.407352i
$596$	−4.47152			−0.183161
$597$	−13.4172			−0.549129
$598$	−31.1270			−1.27288
$599$	−16.0532			−0.655916			−0.327958	−	0.944692i	$-0.606360\pi$
$599$	−16.0532			−0.655916			−0.327958	+	0.944692i	$0.606360\pi$
$600$	4.78011	+	1.46648i	0.195147	+	0.0598688i
$601$	42.5213			1.73448			0.867240	−	0.497891i	$-0.165892\pi$
$601$	42.5213			1.73448			0.867240	+	0.497891i	$0.165892\pi$
$602$		−	20.4562i		−	0.833732i
$603$		−	5.76584i		−	0.234803i
$604$	3.25118			0.132289
$605$	−11.5887	−	15.6771i	−0.471148	−	0.637364i
$606$			9.70730i			0.394332i
$607$	−28.4432			−1.15447			−0.577237	−	0.816577i	$-0.695869\pi$
$607$	−28.4432			−1.15447			−0.577237	+	0.816577i	$0.695869\pi$
$608$			4.68621i			0.190051i
$609$			0.374545i			0.0151773i
$610$	−7.36539	+	5.44459i	−0.298216	+	0.220445i
$611$		−	24.6304i		−	0.996439i
$612$	3.99190			0.161363
$613$		−	20.9056i		−	0.844370i	−0.906510	−	0.422185i	$-0.861263\pi$
$613$		−	20.9056i		−	0.844370i	0.906510	−	0.422185i	$-0.138737\pi$
$614$		−	27.5771i		−	1.11292i
$615$	−7.37676	+	5.45300i	−0.297460	+	0.219886i
$616$			2.82853i			0.113965i
$617$		−	4.08940i		−	0.164633i	−0.996606	−	0.0823165i	$-0.973768\pi$
$617$		−	4.08940i		−	0.164633i	0.996606	−	0.0823165i	$-0.0262318\pi$
$618$		−	2.66390i		−	0.107158i
$619$	11.4039			0.458361			0.229181	−	0.973384i	$-0.426395\pi$
$619$	11.4039			0.458361			0.229181	+	0.973384i	$0.426395\pi$
$620$	10.4224	−	7.70435i	0.418572	−	0.309414i
$621$			6.51179i			0.261309i
$622$			13.8537i			0.555482i
$623$	−10.2489			−0.410613
$624$		−	4.78011i		−	0.191357i
$625$	−20.6989	−	14.0199i	−0.827955	−	0.560795i
$626$	−24.3768			−0.974294
$627$	−7.07821			−0.282677
$628$		−	0.0713960i		−	0.00284901i
$629$	24.1039	+	2.93392i	0.961086	+	0.116983i
$630$	−3.36727	+	2.48913i	−0.134155	+	0.0991694i
$631$			28.1305i			1.11986i	0.828541	+	0.559929i	$0.189171\pi$
$631$			28.1305i			1.11986i	−0.828541	+	0.559929i	$0.810829\pi$
$632$		−	5.95465i		−	0.236863i
$633$			6.46040i			0.256778i
$634$			8.91522i			0.354069i
$635$	−12.3289	+	9.11369i	−0.489258	+	0.361666i
$636$	2.22232			0.0881205
$637$	−16.6976			−0.661583
$638$		−	0.302097i		−	0.0119602i
$639$	9.17428			0.362929
$640$	−1.32920	−	1.79812i	−0.0525411	−	0.0710770i
$641$	26.3364			1.04023			0.520113	−	0.854098i	$-0.325890\pi$
$641$	26.3364			1.04023			0.520113	+	0.854098i	$0.325890\pi$
$642$	0.823199			0.0324891
$643$	−32.4390			−1.27927			−0.639636	−	0.768678i	$-0.720915\pi$
$643$	−32.4390			−1.27927			−0.639636	+	0.768678i	$0.720915\pi$
$644$		−	12.1944i		−	0.480525i
$645$	−19.6419	+	14.5196i	−0.773401	+	0.571708i
$646$		−	18.7069i		−	0.736013i
$647$	40.5401			1.59380			0.796898	−	0.604114i	$-0.206473\pi$
$647$	40.5401			1.59380			0.796898	+	0.604114i	$0.206473\pi$
$648$	−1.00000			−0.0392837
$649$		−	20.0353i		−	0.786453i
$650$	−7.00993	+	22.8494i	−0.274952	+	0.896229i
$651$			10.8544i			0.425418i
$652$	−1.06145			−0.0415695
$653$	−1.15329			−0.0451319			−0.0225659	−	0.999745i	$-0.507184\pi$
$653$	−1.15329			−0.0451319			−0.0225659	+	0.999745i	$0.507184\pi$
$654$	0.478427			0.0187080
$655$	−5.87896	+	4.34581i	−0.229710	+	0.169805i
$656$	4.10248			0.160175
$657$			14.2905i			0.557524i
$658$	9.64923			0.376166
$659$	46.3614			1.80598			0.902992	−	0.429657i	$-0.141366\pi$
$659$	46.3614			1.80598			0.902992	+	0.429657i	$0.141366\pi$
$660$	2.71595	−	2.00766i	0.105718	−	0.0781482i
$661$			40.8589i			1.58923i	0.607117	+	0.794613i	$0.292326\pi$
$661$			40.8589i			1.58923i	−0.607117	+	0.794613i	$0.707674\pi$
$662$			25.6563i			0.997160i
$663$			19.0817i			0.741073i
$664$		−	9.42048i		−	0.365585i
$665$	11.6646	+	15.7797i	0.452333	+	0.611912i
$666$	−6.03820	−	0.734967i	−0.233975	−	0.0284794i
$667$			1.30240i			0.0504292i
$668$	20.4097			0.789673
$669$	8.15634			0.315342
$670$	10.3677	−	7.66393i	0.400539	−	0.296084i
$671$			6.18698i			0.238846i
$672$	1.87266			0.0722395
$673$		−	31.1524i		−	1.20084i	−0.799686	−	0.600419i	$-0.795001\pi$
$673$		−	31.1524i		−	1.20084i	0.799686	−	0.600419i	$-0.204999\pi$
$674$		−	18.5473i		−	0.714415i
$675$	4.78011	+	1.46648i	0.183986	+	0.0564448i
$676$	9.84944			0.378825
$677$			19.8870i			0.764321i	0.924096	+	0.382160i	$0.124820\pi$
$677$			19.8870i			0.764321i	−0.924096	+	0.382160i	$0.875180\pi$
$678$			19.8469i			0.762217i
$679$		−	3.80718i		−	0.146106i
$680$	5.30602	+	7.17793i	0.203477	+	0.275261i
$681$		−	13.0456i		−	0.499908i
$682$		−	8.75486i		−	0.335241i
$683$	11.3646			0.434855			0.217428	−	0.976076i	$-0.430233\pi$
$683$	11.3646			0.434855			0.217428	+	0.976076i	$0.430233\pi$
$684$			4.68621i			0.179182i
$685$	−3.80829	+	2.81514i	−0.145507	+	0.107561i
$686$		−	19.6501i		−	0.750244i
$687$			13.3621i			0.509798i
$688$	10.9236			0.416458
$689$			10.6229i			0.404701i
$690$	−11.7090	+	8.65543i	−0.445753	+	0.329507i
$691$	−27.8449			−1.05927			−0.529635	−	0.848226i	$-0.677671\pi$
$691$	−27.8449			−1.05927			−0.529635	+	0.848226i	$0.677671\pi$
$692$		−	16.9195i		−	0.643182i
$693$			2.82853i			0.107447i
$694$	−9.07304			−0.344408
$695$	−20.8859	−	28.2542i	−0.792247	−	1.07174i
$696$	−0.200007			−0.00758124
$697$	−16.3767			−0.620313
$698$	31.1022			1.17724
$699$	−27.2277			−1.02985
$700$	−8.95152	−	2.74622i	−0.338336	−	0.103797i
$701$			30.8041i			1.16346i	0.813384	+	0.581728i	$0.197623\pi$
$701$			30.8041i			1.16346i	−0.813384	+	0.581728i	$0.802377\pi$
$702$		−	4.78011i		−	0.180414i
$703$	−3.44421	+	28.2962i	−0.129901	+	1.06721i
$704$	−1.51044			−0.0569267
$705$	−6.84893	−	9.26515i	−0.257945	−	0.348946i
$706$	−16.3289			−0.614545
$707$		−	18.1785i		−	0.683672i
$708$	−13.2646			−0.498513
$709$		−	48.0105i		−	1.80307i	−0.432704	−	0.901536i	$-0.642441\pi$
$709$		−	48.0105i		−	1.80307i	0.432704	−	0.901536i	$-0.357559\pi$
$710$	12.1944	+	16.4965i	0.457648	+	0.619102i
$711$		−	5.95465i		−	0.223317i
$712$		−	5.47289i		−	0.205105i
$713$			37.7439i			1.41352i
$714$	−7.47548			−0.279763
$715$	9.59685	+	12.9825i	0.358902	+	0.485519i
$716$			26.6575i			0.996237i
$717$	−10.5417			−0.393688
$718$	−17.1135			−0.638670
$719$	10.5990			0.395275			0.197638	−	0.980275i	$-0.436673\pi$
$719$	10.5990			0.395275			0.197638	+	0.980275i	$0.436673\pi$
$720$	−1.32920	−	1.79812i	−0.0495362	−	0.0670120i
$721$			4.98858i			0.185784i
$722$	2.96053			0.110179
$723$	−13.3732			−0.497356
$724$	−13.4428			−0.499598
$725$	0.956055	+	0.293306i	0.0355070	+	0.0108931i
$726$			8.71858i			0.323577i
$727$	38.9977			1.44634			0.723172	−	0.690668i	$-0.242683\pi$
$727$	38.9977			1.44634			0.723172	+	0.690668i	$0.242683\pi$
$728$			8.95152i			0.331766i
$729$	−1.00000			−0.0370370
$730$	−25.6960	+	18.9948i	−0.951051	+	0.703029i
$731$	−43.6059			−1.61282
$732$	4.09616			0.151398
$733$		−	16.0616i		−	0.593250i	−0.954994	−	0.296625i	$-0.904139\pi$
$733$		−	16.0616i		−	0.593250i	0.954994	−	0.296625i	$-0.0958611\pi$
$734$		−	23.2045i		−	0.856493i
$735$	−6.28109	+	4.64307i	−0.231681	+	0.171262i
$736$	6.51179			0.240028
$737$		−	8.70894i		−	0.320798i
$738$	4.10248			0.151015
$739$	28.6759			1.05486			0.527430	−	0.849599i	$-0.323156\pi$
$739$	28.6759			1.05486			0.527430	+	0.849599i	$0.323156\pi$
$740$	−6.70438	−	11.8343i	−0.246458	−	0.435038i
$741$	−22.4006			−0.822906
$742$	−4.16164			−0.152779
$743$			23.4444i			0.860090i	0.902807	+	0.430045i	$0.141502\pi$
$743$			23.4444i			0.860090i	−0.902807	+	0.430045i	$0.858498\pi$
$744$	−5.79625			−0.212501
$745$	−5.94353	−	8.04034i	−0.217754	−	0.294575i
$746$			9.69704i			0.355034i
$747$		−	9.42048i		−	0.344677i
$748$	6.02951			0.220461
$749$	−1.54157			−0.0563278
$750$	3.71679	+	10.5445i	0.135718	+	0.385029i
$751$	−20.3229			−0.741592			−0.370796	−	0.928714i	$-0.620915\pi$
$751$	−20.3229			−0.741592			−0.370796	+	0.928714i	$0.620915\pi$
$752$			5.15269i			0.187899i
$753$	−6.68149			−0.243487
$754$		−	0.956055i		−	0.0348175i
$755$	4.32145	+	5.84601i	0.157274	+	0.212758i
$756$	1.87266			0.0681080
$757$	−37.8496			−1.37567			−0.687834	−	0.725868i	$-0.741438\pi$
$757$	−37.8496			−1.37567			−0.687834	+	0.725868i	$0.741438\pi$
$758$	9.40066			0.341448
$759$			9.83563i			0.357011i
$760$	−8.42637	+	6.22888i	−0.305656	+	0.225945i
$761$	−13.4618			−0.487990			−0.243995	−	0.969777i	$-0.578458\pi$
$761$	−13.4618			−0.487990			−0.243995	+	0.969777i	$0.578458\pi$
$762$	6.85655			0.248386
$763$	−0.895931			−0.0324349
$764$		−	6.76465i		−	0.244736i
$765$	5.30602	+	7.17793i	0.191840	+	0.259519i
$766$	32.3874			1.17020
$767$		−	63.4061i		−	2.28946i
$768$			1.00000i			0.0360844i
$769$			19.7800i			0.713285i	0.934241	+	0.356642i	$0.116079\pi$
$769$			19.7800i			0.713285i	−0.934241	+	0.356642i	$0.883921\pi$
$770$	−5.08605	+	3.75967i	−0.183288	+	0.135489i
$771$			4.63516i			0.166931i
$772$	−15.4592			−0.556389
$773$		−	25.4792i		−	0.916423i	−0.888843	−	0.458212i	$-0.848490\pi$
$773$		−	25.4792i		−	0.916423i	0.888843	−	0.458212i	$-0.151510\pi$
$774$	10.9236			0.392640
$775$	27.7067	+	8.50008i	0.995254	+	0.305332i
$776$	2.03303			0.0729815
$777$	11.3075	+	1.37634i	0.405654	+	0.0493761i
$778$			20.8774i			0.748492i
$779$		−	19.2251i		−	0.688810i
$780$	8.59521	−	6.35370i	0.307758	−	0.227499i
$781$	13.8572			0.495848
$782$	−25.9944			−0.929559
$783$	−0.200007			−0.00714766
$784$	3.49314			0.124755
$785$	0.128379	−	0.0948993i	0.00458203	−	0.00338710i
$786$	3.26950			0.116619
$787$		−	50.1801i		−	1.78873i	−0.447339	−	0.894364i	$-0.647628\pi$
$787$		−	50.1801i		−	1.78873i	0.447339	−	0.894364i	$-0.352372\pi$
$788$			12.5068i			0.445536i
$789$	29.5118			1.05065
$790$	10.7072	−	7.91489i	0.380944	−	0.281599i
$791$		−	37.1666i		−	1.32149i
$792$	−1.51044			−0.0536710
$793$			19.5801i			0.695309i
$794$			12.2447i			0.434549i
$795$	2.95389	+	3.99599i	0.104764	+	0.141723i
$796$			13.4172i			0.475559i
$797$	26.4099			0.935485			0.467743	−	0.883865i	$-0.345067\pi$
$797$	26.4099			0.935485			0.467743	+	0.883865i	$0.345067\pi$
$798$		−	8.77568i		−	0.310656i
$799$		−	20.5690i		−	0.727680i
$800$	1.46648	−	4.78011i	0.0518479	−	0.169002i
$801$		−	5.47289i		−	0.193375i
$802$			13.7736i			0.486362i
$803$			21.5848i			0.761711i
$804$	−5.76584			−0.203346
$805$	21.9270	−	16.2087i	0.772823	−	0.571282i
$806$		−	27.7067i		−	0.975927i
$807$		−	21.3385i		−	0.751151i
$808$	9.70730			0.341502
$809$		−	8.11189i		−	0.285199i	−0.989780	−	0.142599i	$-0.954454\pi$
$809$		−	8.11189i		−	0.285199i	0.989780	−	0.142599i	$-0.0455461\pi$
$810$	−1.32920	−	1.79812i	−0.0467032	−	0.0631795i
$811$	27.0320			0.949223			0.474611	−	0.880195i	$-0.342589\pi$
$811$	27.0320			0.949223			0.474611	+	0.880195i	$0.342589\pi$
$812$	0.374545			0.0131440
$813$			16.5121i			0.579106i
$814$	−9.12031	−	1.11012i	−0.319667	−	0.0389097i
$815$	−1.41087	−	1.90861i	−0.0494206	−	0.0668557i
$816$		−	3.99190i		−	0.139745i
$817$		−	51.1902i		−	1.79092i
$818$		−	34.5667i		−	1.20860i
$819$			8.95152i			0.312792i
$820$	5.45300	+	7.37676i	0.190427	+	0.257608i
$821$	−19.7666			−0.689859			−0.344930	−	0.938629i	$-0.612097\pi$
$821$	−19.7666			−0.689859			−0.344930	+	0.938629i	$0.612097\pi$
$822$	2.11793			0.0738711
$823$			41.4991i			1.44657i	0.690550	+	0.723285i	$0.257368\pi$
$823$			41.4991i			1.44657i	−0.690550	+	0.723285i	$0.742632\pi$
$824$	−2.66390			−0.0928013
$825$	7.22005	+	2.21502i	0.251370	+	0.0771172i
$826$	24.8400			0.864295
$827$	39.6665			1.37934			0.689671	−	0.724123i	$-0.257755\pi$
$827$	39.6665			1.37934			0.689671	+	0.724123i	$0.257755\pi$
$828$	6.51179			0.226300
$829$			27.0227i			0.938538i	0.883055	+	0.469269i	$0.155483\pi$
$829$			27.0227i			0.938538i	−0.883055	+	0.469269i	$0.844517\pi$
$830$	16.9392	−	12.5217i	0.587967	−	0.434633i
$831$			11.0446i			0.383132i
$832$	−4.78011			−0.165720
$833$	−13.9443			−0.483141
$834$			15.7132i			0.544103i
$835$	27.1284	+	36.6990i	0.938818	+	1.27002i
$836$			7.07821i			0.244805i
$837$	−5.79625			−0.200348
$838$	−22.9413			−0.792495
$839$	6.29148			0.217206			0.108603	−	0.994085i	$-0.465362\pi$
$839$	6.29148			0.217206			0.108603	+	0.994085i	$0.465362\pi$
$840$	2.48913	+	3.36727i	0.0858832	+	0.116182i
$841$	28.9600			0.998621
$842$			12.1679i			0.419333i
$843$	−17.9190			−0.617162
$844$	6.46040			0.222376
$845$	13.0918	+	17.7105i	0.450373	+	0.609259i
$846$			5.15269i			0.177153i
$847$		−	16.3270i		−	0.561001i
$848$		−	2.22232i		−	0.0763146i
$849$			14.0543i			0.482342i
$850$	−5.85405	+	19.0817i	−0.200792	+	0.654498i
$851$	39.3194	+	4.78595i	1.34785	+	0.164060i
$852$		−	9.17428i		−	0.314306i
$853$	−1.33464			−0.0456971			−0.0228486	−	0.999739i	$-0.507274\pi$
$853$	−1.33464			−0.0456971			−0.0228486	+	0.999739i	$0.507274\pi$
$854$	−7.67072			−0.262487
$855$	−8.42637	+	6.22888i	−0.288176	+	0.213023i
$856$		−	0.823199i		−	0.0281364i
$857$	22.7053			0.775597			0.387799	−	0.921744i	$-0.373236\pi$
$857$	22.7053			0.775597			0.387799	+	0.921744i	$0.373236\pi$
$858$		−	7.22005i		−	0.246488i
$859$			8.92509i			0.304520i	0.988340	+	0.152260i	$0.0486551\pi$
$859$			8.92509i			0.304520i	−0.988340	+	0.152260i	$0.951345\pi$
$860$	14.5196	+	19.6419i	0.495114	+	0.669785i
$861$	−7.68256			−0.261821
$862$			11.2076i			0.381734i
$863$			8.98998i			0.306022i	0.988224	+	0.153011i	$0.0488971\pi$
$863$			8.98998i			0.306022i	−0.988224	+	0.153011i	$0.951103\pi$
$864$			1.00000i			0.0340207i
$865$	30.4233	−	22.4893i	1.03442	−	0.764659i
$866$		−	31.6559i		−	1.07571i
$867$		−	1.06470i		−	0.0361591i
$868$	10.8544			0.368423
$869$		−	8.99411i		−	0.305104i
$870$	−0.265848	−	0.359637i	−0.00901310	−	0.0121928i
$871$		−	27.5614i		−	0.933881i
$872$		−	0.478427i		−	0.0162016i
$873$	2.03303			0.0688076
$874$		−	30.5156i		−	1.03220i
$875$	−6.96029	−	19.7462i	−0.235301	−	0.667543i
$876$	14.2905			0.482830
$877$			9.40084i			0.317444i	0.987323	+	0.158722i	$0.0507373\pi$
$877$			9.40084i			0.317444i	−0.987323	+	0.158722i	$0.949263\pi$
$878$		−	33.9912i		−	1.14715i
$879$	32.2561			1.08797
$880$	−2.00766	−	2.71595i	−0.0676783	−	0.0915545i
$881$	−19.9044			−0.670596			−0.335298	−	0.942112i	$-0.608837\pi$
$881$	−19.9044			−0.670596			−0.335298	+	0.942112i	$0.608837\pi$
$882$	3.49314			0.117620
$883$	48.8646			1.64442			0.822212	−	0.569181i	$-0.192740\pi$
$883$	48.8646			1.64442			0.822212	+	0.569181i	$0.192740\pi$
$884$	19.0817			0.641788
$885$	−17.6312	−	23.8513i	−0.592666	−	0.801752i
$886$			34.9477i			1.17409i
$887$		−	32.4651i		−	1.09007i	−0.838413	−	0.545036i	$-0.816516\pi$
$887$		−	32.4651i		−	1.09007i	0.838413	−	0.545036i	$-0.183484\pi$
$888$	−0.734967	+	6.03820i	−0.0246639	+	0.202629i
$889$	−12.8400			−0.430639
$890$	9.84093	−	7.27454i	0.329869	−	0.243843i
$891$	−1.51044			−0.0506015
$892$		−	8.15634i		−	0.273095i
$893$	24.1465			0.808033
$894$			4.47152i			0.149550i
$895$	−47.9334	+	35.4330i	−1.60224	+	1.18439i
$896$		−	1.87266i		−	0.0625612i
$897$			31.1270i			1.03930i
$898$			17.2274i			0.574886i
$899$	−1.15929			−0.0386645
$900$	1.46648	−	4.78011i	0.0488827	−	0.159337i
$901$			8.87127i			0.295545i
$902$	6.19654			0.206322
$903$	−20.4562			−0.680739
$904$	19.8469			0.660099
$905$	−17.8681	−	24.1718i	−0.593956	−	0.803497i
$906$		−	3.25118i		−	0.108013i
$907$	−6.47916			−0.215137			−0.107568	−	0.994198i	$-0.534306\pi$
$907$	−6.47916			−0.215137			−0.107568	+	0.994198i	$0.534306\pi$
$908$	−13.0456			−0.432933
$909$	9.70730			0.321971
$910$	−16.0959	+	11.8983i	−0.533575	+	0.394426i
$911$		−	17.1972i		−	0.569767i	−0.958562	−	0.284884i	$-0.908045\pi$
$911$		−	17.1972i		−	0.569767i	0.958562	−	0.284884i	$-0.0919550\pi$
$912$	4.68621			0.155176
$913$		−	14.2290i		−	0.470912i
$914$	24.5044			0.810532
$915$	5.44459	+	7.36539i	0.179993	+	0.243492i
$916$	13.3621			0.441498
$917$	−6.12267			−0.202188
$918$		−	3.99190i		−	0.131752i
$919$			39.5341i			1.30411i	0.758172	+	0.652054i	$0.226093\pi$
$919$			39.5341i			1.30411i	−0.758172	+	0.652054i	$0.773907\pi$
$920$	8.65543	+	11.7090i	0.285361	+	0.386034i
$921$	−27.5771			−0.908695
$922$		−	9.05274i		−	0.298136i
$923$	43.8541			1.44347
$924$	2.82853			0.0930519
$925$	12.3681	−	27.7854i	0.406661	−	0.913579i
$926$	−2.10640			−0.0692206
$927$	−2.66390			−0.0874939
$928$			0.200007i			0.00656555i
$929$	53.4172			1.75256			0.876281	−	0.481800i	$-0.160017\pi$
$929$	53.4172			1.75256			0.876281	+	0.481800i	$0.160017\pi$
$930$	−7.70435	−	10.4224i	−0.252636	−	0.341763i
$931$		−	16.3696i		−	0.536491i
$932$			27.2277i			0.891875i
$933$	13.8537			0.453549
$934$	24.0814			0.787967
$935$	8.01440	+	10.8418i	0.262099	+	0.354565i
$936$	−4.78011			−0.156243
$937$			15.1507i			0.494953i	0.968894	+	0.247477i	$0.0796013\pi$
$937$			15.1507i			0.494953i	−0.968894	+	0.247477i	$0.920399\pi$
$938$	10.7975			0.352550
$939$			24.3768i			0.795508i
$940$	−9.26515	+	6.84893i	−0.302196	+	0.223387i
$941$	24.9479			0.813279			0.406639	−	0.913589i	$-0.366701\pi$
$941$	24.9479			0.813279			0.406639	+	0.913589i	$0.366701\pi$
$942$	−0.0713960			−0.00232621
$943$	−26.7145			−0.869944
$944$			13.2646i			0.431725i
$945$	2.48913	+	3.36727i	0.0809715	+	0.109537i
$946$	16.4994			0.536441
$947$	−3.44085			−0.111813			−0.0559063	−	0.998436i	$-0.517805\pi$
$947$	−3.44085			−0.111813			−0.0559063	+	0.998436i	$0.517805\pi$
$948$	−5.95465			−0.193398
$949$			68.3099i			2.21743i
$950$	−22.4006	−	6.87223i	−0.726771	−	0.222964i
$951$	8.91522			0.289096
$952$			7.47548i			0.242282i
$953$			16.3551i			0.529794i	0.964277	+	0.264897i	$0.0853380\pi$
$953$			16.3551i			0.529794i	−0.964277	+	0.264897i	$0.914662\pi$
$954$		−	2.22232i		−	0.0719501i
$955$	12.1637	−	8.99153i	0.393607	−	0.290959i
$956$			10.5417i			0.340944i
$957$	−0.302097			−0.00976542
$958$		−	5.46224i		−	0.176477i
$959$	−3.96616			−0.128074
$960$	−1.79812	+	1.32920i	−0.0580341	+	0.0428996i
$961$	−2.59651			−0.0837582
$962$	−28.8632	−	3.51322i	−0.930588	−	0.113271i
$963$		−	0.823199i		−	0.0265272i
$964$			13.3732i			0.430723i
$965$	−20.5483	−	27.7975i	−0.661473	−	0.894834i
$966$	−12.1944			−0.392347
$967$	40.2993			1.29594			0.647968	−	0.761667i	$-0.275619\pi$
$967$	40.2993			1.29594			0.647968	+	0.761667i	$0.275619\pi$
$968$	8.71858			0.280226
$969$	−18.7069			−0.600952
$970$	2.70229	+	3.65563i	0.0867654	+	0.117375i
$971$	−45.6611			−1.46533			−0.732667	−	0.680587i	$-0.761725\pi$
$971$	−45.6611			−1.46533			−0.732667	+	0.680587i	$0.761725\pi$
$972$			1.00000i			0.0320750i
$973$		−	29.4255i		−	0.943337i
$974$	11.8494			0.379681
$975$	22.8494	+	7.00993i	0.731768	+	0.224497i
$976$		−	4.09616i		−	0.131115i
$977$	−4.88784			−0.156376			−0.0781879	−	0.996939i	$-0.524913\pi$
$977$	−4.88784			−0.156376			−0.0781879	+	0.996939i	$0.524913\pi$
$978$			1.06145i			0.0339413i
$979$		−	8.26645i		−	0.264197i
$980$	4.64307	+	6.28109i	0.148317	+	0.200642i
$981$		−	0.478427i		−	0.0152750i
$982$	7.19955			0.229747
$983$			0.259395i			0.00827341i	0.999991	+	0.00413670i	$0.00131676\pi$
$983$			0.259395i			0.00827341i	−0.999991	+	0.00413670i	$0.998683\pi$
$984$		−	4.10248i		−	0.130782i
$985$	−22.4887	+	16.6240i	−0.716550	+	0.529684i
$986$		−	0.798408i		−	0.0254265i
$987$		−	9.64923i		−	0.307139i
$988$			22.4006i			0.712657i
$989$	−71.1321			−2.26187
$990$	−2.00766	−	2.71595i	−0.0638077	−	0.0863184i
$991$		−	29.6464i		−	0.941750i	−0.882200	−	0.470875i	$-0.843938\pi$
$991$		−	29.6464i		−	0.941750i	0.882200	−	0.470875i	$-0.156062\pi$
$992$			5.79625i			0.184031i
$993$	25.6563			0.814178
$994$			17.1803i			0.544927i
$995$	−24.1257	+	17.8341i	−0.764837	+	0.565378i
$996$	−9.42048			−0.298499
$997$	33.3064			1.05482			0.527411	−	0.849610i	$-0.323163\pi$
$997$	33.3064			1.05482			0.527411	+	0.849610i	$0.323163\pi$
$998$			3.32481i			0.105245i
$999$	−0.734967	+	6.03820i	−0.0232533	+	0.191040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.c.739.15	yes	16
3.2	odd	2		3330.2.e.f.739.3		16
5.4	even	2		1110.2.e.d.739.2	yes	16
15.14	odd	2		3330.2.e.e.739.13		16
37.36	even	2		1110.2.e.d.739.10	yes	16
111.110	odd	2		3330.2.e.e.739.14		16
185.184	even	2	inner	1110.2.e.c.739.7	✓	16
555.554	odd	2		3330.2.e.f.739.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.c.739.7	✓	16	185.184	even	2	inner
1110.2.e.c.739.15	yes	16	1.1	even	1	trivial
1110.2.e.d.739.2	yes	16	5.4	even	2
1110.2.e.d.739.10	yes	16	37.36	even	2
3330.2.e.e.739.13		16	15.14	odd	2
3330.2.e.e.739.14		16	111.110	odd	2
3330.2.e.f.739.3		16	3.2	odd	2
3330.2.e.f.739.4		16	555.554	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.32920 + 1.79812i) q^{5} -1.00000i q^{6} +1.87266i q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(1.32920 + 1.79812i) q^{5} -1.00000i q^{6} +1.87266i q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-1.32920 - 1.79812i) q^{10} -1.51044 q^{11} +1.00000i q^{12} -4.78011 q^{13} -1.87266i q^{14} +(-1.79812 + 1.32920i) q^{15} +1.00000 q^{16} -3.99190 q^{17} +1.00000 q^{18} -4.68621i q^{19} +(1.32920 + 1.79812i) q^{20} -1.87266 q^{21} +1.51044 q^{22} -6.51179 q^{23} -1.00000i q^{24} +(-1.46648 + 4.78011i) q^{25} +4.78011 q^{26} -1.00000i q^{27} +1.87266i q^{28} -0.200007i q^{29} +(1.79812 - 1.32920i) q^{30} -5.79625i q^{31} -1.00000 q^{32} -1.51044i q^{33} +3.99190 q^{34} +(-3.36727 + 2.48913i) q^{35} -1.00000 q^{36} +(-6.03820 - 0.734967i) q^{37} +4.68621i q^{38} -4.78011i q^{39} +(-1.32920 - 1.79812i) q^{40} +4.10248 q^{41} +1.87266 q^{42} +10.9236 q^{43} -1.51044 q^{44} +(-1.32920 - 1.79812i) q^{45} +6.51179 q^{46} +5.15269i q^{47} +1.00000i q^{48} +3.49314 q^{49} +(1.46648 - 4.78011i) q^{50} -3.99190i q^{51} -4.78011 q^{52} -2.22232i q^{53} +1.00000i q^{54} +(-2.00766 - 2.71595i) q^{55} -1.87266i q^{56} +4.68621 q^{57} +0.200007i q^{58} +13.2646i q^{59} +(-1.79812 + 1.32920i) q^{60} -4.09616i q^{61} +5.79625i q^{62} -1.87266i q^{63} +1.00000 q^{64} +(-6.35370 - 8.59521i) q^{65} +1.51044i q^{66} +5.76584i q^{67} -3.99190 q^{68} -6.51179i q^{69} +(3.36727 - 2.48913i) q^{70} -9.17428 q^{71} +1.00000 q^{72} -14.2905i q^{73} +(6.03820 + 0.734967i) q^{74} +(-4.78011 - 1.46648i) q^{75} -4.68621i q^{76} -2.82853i q^{77} +4.78011i q^{78} +5.95465i q^{79} +(1.32920 + 1.79812i) q^{80} +1.00000 q^{81} -4.10248 q^{82} +9.42048i q^{83} -1.87266 q^{84} +(-5.30602 - 7.17793i) q^{85} -10.9236 q^{86} +0.200007 q^{87} +1.51044 q^{88} +5.47289i q^{89} +(1.32920 + 1.79812i) q^{90} -8.95152i q^{91} -6.51179 q^{92} +5.79625 q^{93} -5.15269i q^{94} +(8.42637 - 6.22888i) q^{95} -1.00000i q^{96} -2.03303 q^{97} -3.49314 q^{98} +1.51044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9	\( 16 q - 16 q^{2} + 16 q^{4} - 2 q^{5} - 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} + 6 q^{15} + 16 q^{16} - 38 q^{17} + 16 q^{18} - 2 q^{20} + 6 q^{21} - 2 q^{22} - 20 q^{23} - 4 q^{25} - 6 q^{30} - 16 q^{32} + 38 q^{34} - 10 q^{35} - 16 q^{36} - 4 q^{37} + 2 q^{40} - 6 q^{41} - 6 q^{42} - 2 q^{43} + 2 q^{44} + 2 q^{45} + 20 q^{46} - 18 q^{49} + 4 q^{50} + 20 q^{55} + 16 q^{57} + 6 q^{60} + 16 q^{64} + 12 q^{65} - 38 q^{68} + 10 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{74} - 2 q^{80} + 16 q^{81} + 6 q^{82} + 6 q^{84} + 2 q^{86} + 2 q^{87} - 2 q^{88} - 2 q^{90} - 20 q^{92} + 22 q^{93} - 16 q^{95} + 38 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 2 * q^5 - 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 + 6 * q^15 + 16 * q^16 - 38 * q^17 + 16 * q^18 - 2 * q^20 + 6 * q^21 - 2 * q^22 - 20 * q^23 - 4 * q^25 - 6 * q^30 - 16 * q^32 + 38 * q^34 - 10 * q^35 - 16 * q^36 - 4 * q^37 + 2 * q^40 - 6 * q^41 - 6 * q^42 - 2 * q^43 + 2 * q^44 + 2 * q^45 + 20 * q^46 - 18 * q^49 + 4 * q^50 + 20 * q^55 + 16 * q^57 + 6 * q^60 + 16 * q^64 + 12 * q^65 - 38 * q^68 + 10 * q^70 - 24 * q^71 + 16 * q^72 + 4 * q^74 - 2 * q^80 + 16 * q^81 + 6 * q^82 + 6 * q^84 + 2 * q^86 + 2 * q^87 - 2 * q^88 - 2 * q^90 - 20 * q^92 + 22 * q^93 - 16 * q^95 + 38 * q^97 + 18 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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