LMFDB - Embedded newform 92.2.b.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(91,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("92.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.b (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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	92.91
Dual form			92.2.b.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +3.74166i q^{5} +(1.00000 + 1.00000i) q^{6} +3.74166 q^{7} +(2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +3.74166i q^{5} +(1.00000 + 1.00000i) q^{6} +3.74166 q^{7} +(2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +(-3.74166 - 3.74166i) q^{10} -3.74166 q^{11} -2.00000 q^{12} -1.00000 q^{13} +(-3.74166 + 3.74166i) q^{14} +3.74166 q^{15} -4.00000 q^{16} -3.74166i q^{17} +(-2.00000 + 2.00000i) q^{18} +7.48331 q^{20} -3.74166i q^{21} +(3.74166 - 3.74166i) q^{22} +(-3.74166 - 3.00000i) q^{23} +(2.00000 - 2.00000i) q^{24} -9.00000 q^{25} +(1.00000 - 1.00000i) q^{26} -5.00000i q^{27} -7.48331i q^{28} +5.00000 q^{29} +(-3.74166 + 3.74166i) q^{30} +5.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +3.74166i q^{33} +(3.74166 + 3.74166i) q^{34} +14.0000i q^{35} -4.00000i q^{36} -3.74166i q^{37} +1.00000i q^{39} +(-7.48331 + 7.48331i) q^{40} -3.00000 q^{41} +(3.74166 + 3.74166i) q^{42} -7.48331 q^{43} +7.48331i q^{44} +7.48331i q^{45} +(6.74166 - 0.741657i) q^{46} -3.00000i q^{47} +4.00000i q^{48} +7.00000 q^{49} +(9.00000 - 9.00000i) q^{50} -3.74166 q^{51} +2.00000i q^{52} -7.48331i q^{53} +(5.00000 + 5.00000i) q^{54} -14.0000i q^{55} +(7.48331 + 7.48331i) q^{56} +(-5.00000 + 5.00000i) q^{58} +6.00000i q^{59} -7.48331i q^{60} +(-5.00000 - 5.00000i) q^{62} +7.48331 q^{63} +8.00000i q^{64} -3.74166i q^{65} +(-3.74166 - 3.74166i) q^{66} +3.74166 q^{67} -7.48331 q^{68} +(-3.00000 + 3.74166i) q^{69} +(-14.0000 - 14.0000i) q^{70} -5.00000i q^{71} +(4.00000 + 4.00000i) q^{72} -1.00000 q^{73} +(3.74166 + 3.74166i) q^{74} +9.00000i q^{75} -14.0000 q^{77} +(-1.00000 - 1.00000i) q^{78} -14.9666i q^{80} +1.00000 q^{81} +(3.00000 - 3.00000i) q^{82} +11.2250 q^{83} -7.48331 q^{84} +14.0000 q^{85} +(7.48331 - 7.48331i) q^{86} -5.00000i q^{87} +(-7.48331 - 7.48331i) q^{88} +7.48331i q^{89} +(-7.48331 - 7.48331i) q^{90} -3.74166 q^{91} +(-6.00000 + 7.48331i) q^{92} +5.00000 q^{93} +(3.00000 + 3.00000i) q^{94} +(-4.00000 - 4.00000i) q^{96} -3.74166i q^{97} +(-7.00000 + 7.00000i) q^{98} -7.48331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^6 + 8 * q^8 + 8 * q^9	$ 4 q - 4 q^{2} + 4 q^{6} + 8 q^{8} + 8 q^{9} - 8 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{18} + 8 q^{24} - 36 q^{25} + 4 q^{26} + 20 q^{29} + 16 q^{32} - 12 q^{41} + 12 q^{46} + 28 q^{49} + 36 q^{50} + 20 q^{54} - 20 q^{58} - 20 q^{62} - 12 q^{69} - 56 q^{70} + 16 q^{72} - 4 q^{73} - 56 q^{77} - 4 q^{78} + 4 q^{81} + 12 q^{82} + 56 q^{85} - 24 q^{92} + 20 q^{93} + 12 q^{94} - 16 q^{96} - 28 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^6 + 8 * q^8 + 8 * q^9 - 8 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^18 + 8 * q^24 - 36 * q^25 + 4 * q^26 + 20 * q^29 + 16 * q^32 - 12 * q^41 + 12 * q^46 + 28 * q^49 + 36 * q^50 + 20 * q^54 - 20 * q^58 - 20 * q^62 - 12 * q^69 - 56 * q^70 + 16 * q^72 - 4 * q^73 - 56 * q^77 - 4 * q^78 + 4 * q^81 + 12 * q^82 + 56 * q^85 - 24 * q^92 + 20 * q^93 + 12 * q^94 - 16 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$-1$	$-1$

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	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$		−	1.00000i		−	0.577350i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$		−	1.00000i		−	0.577350i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$		−	2.00000i		−	1.00000i
$5$			3.74166i			1.67332i	0.547723	+	0.836660i	$0.315495\pi$
$5$			3.74166i			1.67332i	−0.547723	+	0.836660i	$0.684505\pi$
$6$	1.00000	+	1.00000i	0.408248	+	0.408248i
$7$	3.74166			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$7$	3.74166			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	2.00000			0.666667
$10$	−3.74166	−	3.74166i	−1.18322	−	1.18322i
$11$	−3.74166			−1.12815			−0.564076	−	0.825723i	$-0.690768\pi$
$11$	−3.74166			−1.12815			−0.564076	+	0.825723i	$0.690768\pi$
$12$	−2.00000			−0.577350
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	−3.74166	+	3.74166i	−1.00000	+	1.00000i
$15$	3.74166			0.966092
$16$	−4.00000			−1.00000
$17$		−	3.74166i		−	0.907485i	−0.891133	−	0.453743i	$-0.850089\pi$
$17$		−	3.74166i		−	0.907485i	0.891133	−	0.453743i	$-0.149911\pi$
$18$	−2.00000	+	2.00000i	−0.471405	+	0.471405i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	7.48331			1.67332
$21$		−	3.74166i		−	0.816497i
$22$	3.74166	−	3.74166i	0.797724	−	0.797724i
$23$	−3.74166	−	3.00000i	−0.780189	−	0.625543i
$23$	−3.74166	−	3.00000i	−0.780189	−	0.625543i
$24$	2.00000	−	2.00000i	0.408248	−	0.408248i
$25$	−9.00000			−1.80000
$26$	1.00000	−	1.00000i	0.196116	−	0.196116i
$27$		−	5.00000i		−	0.962250i
$28$		−	7.48331i		−	1.41421i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	−3.74166	+	3.74166i	−0.683130	+	0.683130i
$31$			5.00000i			0.898027i	0.893525	+	0.449013i	$0.148224\pi$
$31$			5.00000i			0.898027i	−0.893525	+	0.449013i	$0.851776\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$			3.74166i			0.651339i
$34$	3.74166	+	3.74166i	0.641689	+	0.641689i
$35$			14.0000i			2.36643i
$36$		−	4.00000i		−	0.666667i
$37$		−	3.74166i		−	0.615125i	−0.951528	−	0.307562i	$-0.900487\pi$
$37$		−	3.74166i		−	0.615125i	0.951528	−	0.307562i	$-0.0995133\pi$
$38$		0			0
$39$			1.00000i			0.160128i
$40$	−7.48331	+	7.48331i	−1.18322	+	1.18322i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	3.74166	+	3.74166i	0.577350	+	0.577350i
$43$	−7.48331			−1.14119			−0.570597	−	0.821230i	$-0.693288\pi$
$43$	−7.48331			−1.14119			−0.570597	+	0.821230i	$0.693288\pi$
$44$			7.48331i			1.12815i
$45$			7.48331i			1.11555i
$46$	6.74166	−	0.741657i	0.994003	−	0.109351i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$			4.00000i			0.577350i
$49$	7.00000			1.00000
$50$	9.00000	−	9.00000i	1.27279	−	1.27279i
$51$	−3.74166			−0.523937
$52$			2.00000i			0.277350i
$53$		−	7.48331i		−	1.02791i	−0.857816	−	0.513956i	$-0.828179\pi$
$53$		−	7.48331i		−	1.02791i	0.857816	−	0.513956i	$-0.171821\pi$
$54$	5.00000	+	5.00000i	0.680414	+	0.680414i
$55$		−	14.0000i		−	1.88776i
$56$	7.48331	+	7.48331i	1.00000	+	1.00000i
$57$		0			0
$58$	−5.00000	+	5.00000i	−0.656532	+	0.656532i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		−	7.48331i		−	0.966092i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−5.00000	−	5.00000i	−0.635001	−	0.635001i
$63$	7.48331			0.942809
$64$			8.00000i			1.00000i
$65$		−	3.74166i		−	0.464095i
$66$	−3.74166	−	3.74166i	−0.460566	−	0.460566i
$67$	3.74166			0.457116			0.228558	−	0.973530i	$-0.426599\pi$
$67$	3.74166			0.457116			0.228558	+	0.973530i	$0.426599\pi$
$68$	−7.48331			−0.907485
$69$	−3.00000	+	3.74166i	−0.361158	+	0.450443i
$70$	−14.0000	−	14.0000i	−1.67332	−	1.67332i
$71$		−	5.00000i		−	0.593391i	−0.954972	−	0.296695i	$-0.904115\pi$
$71$		−	5.00000i		−	0.593391i	0.954972	−	0.296695i	$-0.0958846\pi$
$72$	4.00000	+	4.00000i	0.471405	+	0.471405i
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	3.74166	+	3.74166i	0.434959	+	0.434959i
$75$			9.00000i			1.03923i
$76$		0			0
$77$	−14.0000			−1.59545
$78$	−1.00000	−	1.00000i	−0.113228	−	0.113228i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		−	14.9666i		−	1.67332i
$81$	1.00000			0.111111
$82$	3.00000	−	3.00000i	0.331295	−	0.331295i
$83$	11.2250			1.23210			0.616050	−	0.787707i	$-0.288732\pi$
$83$	11.2250			1.23210			0.616050	+	0.787707i	$0.288732\pi$
$84$	−7.48331			−0.816497
$85$	14.0000			1.51851
$86$	7.48331	−	7.48331i	0.806947	−	0.806947i
$87$		−	5.00000i		−	0.536056i
$88$	−7.48331	−	7.48331i	−0.797724	−	0.797724i
$89$			7.48331i			0.793230i	0.917985	+	0.396615i	$0.129815\pi$
$89$			7.48331i			0.793230i	−0.917985	+	0.396615i	$0.870185\pi$
$90$	−7.48331	−	7.48331i	−0.788811	−	0.788811i
$91$	−3.74166			−0.392232
$92$	−6.00000	+	7.48331i	−0.625543	+	0.780189i
$93$	5.00000			0.518476
$94$	3.00000	+	3.00000i	0.309426	+	0.309426i
$95$		0			0
$96$	−4.00000	−	4.00000i	−0.408248	−	0.408248i
$97$		−	3.74166i		−	0.379908i	−0.981793	−	0.189954i	$-0.939166\pi$
$97$		−	3.74166i		−	0.379908i	0.981793	−	0.189954i	$-0.0608338\pi$
$98$	−7.00000	+	7.00000i	−0.707107	+	0.707107i
$99$	−7.48331			−0.752101
$100$			18.0000i			1.80000i
$101$	−8.00000			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$102$	3.74166	−	3.74166i	0.370479	−	0.370479i
$103$	11.2250			1.10603			0.553015	−	0.833172i	$-0.313477\pi$
$103$	11.2250			1.10603			0.553015	+	0.833172i	$0.313477\pi$
$104$	−2.00000	−	2.00000i	−0.196116	−	0.196116i
$105$	14.0000			1.36626
$106$	7.48331	+	7.48331i	0.726844	+	0.726844i
$107$	−14.9666			−1.44688			−0.723439	−	0.690388i	$-0.757440\pi$
$107$	−14.9666			−1.44688			−0.723439	+	0.690388i	$0.757440\pi$
$108$	−10.0000			−0.962250
$109$			7.48331i			0.716772i	0.933574	+	0.358386i	$0.116673\pi$
$109$			7.48331i			0.716772i	−0.933574	+	0.358386i	$0.883327\pi$
$110$	14.0000	+	14.0000i	1.33485	+	1.33485i
$111$	−3.74166			−0.355142
$112$	−14.9666			−1.41421
$113$			11.2250i			1.05596i	0.849258	+	0.527978i	$0.177050\pi$
$113$			11.2250i			1.05596i	−0.849258	+	0.527978i	$0.822950\pi$
$114$		0			0
$115$	11.2250	−	14.0000i	1.04673	−	1.30551i
$116$		−	10.0000i		−	0.928477i
$117$	−2.00000			−0.184900
$118$	−6.00000	−	6.00000i	−0.552345	−	0.552345i
$119$		−	14.0000i		−	1.28338i
$120$	7.48331	+	7.48331i	0.683130	+	0.683130i
$121$	3.00000			0.272727
$122$		0			0
$123$			3.00000i			0.270501i
$124$	10.0000			0.898027
$125$		−	14.9666i		−	1.33866i
$126$	−7.48331	+	7.48331i	−0.666667	+	0.666667i
$127$			17.0000i			1.50851i	0.656584	+	0.754253i	$0.272001\pi$
$127$			17.0000i			1.50851i	−0.656584	+	0.754253i	$0.727999\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$			7.48331i			0.658869i
$130$	3.74166	+	3.74166i	0.328165	+	0.328165i
$131$			5.00000i			0.436852i	0.975854	+	0.218426i	$0.0700922\pi$
$131$			5.00000i			0.436852i	−0.975854	+	0.218426i	$0.929908\pi$
$132$	7.48331			0.651339
$133$		0			0
$134$	−3.74166	+	3.74166i	−0.323230	+	0.323230i
$135$	18.7083			1.61015
$136$	7.48331	−	7.48331i	0.641689	−	0.641689i
$137$		−	22.4499i		−	1.91803i	−0.283358	−	0.959014i	$-0.591449\pi$
$137$		−	22.4499i		−	1.91803i	0.283358	−	0.959014i	$-0.408551\pi$
$138$	−0.741657	−	6.74166i	−0.0631341	−	0.573888i
$139$			1.00000i			0.0848189i	0.999100	+	0.0424094i	$0.0135034\pi$
$139$			1.00000i			0.0848189i	−0.999100	+	0.0424094i	$0.986497\pi$
$140$	28.0000			2.36643
$141$	−3.00000			−0.252646
$142$	5.00000	+	5.00000i	0.419591	+	0.419591i
$143$	3.74166			0.312893
$144$	−8.00000			−0.666667
$145$			18.7083i			1.55364i
$146$	1.00000	−	1.00000i	0.0827606	−	0.0827606i
$147$		−	7.00000i		−	0.577350i
$148$	−7.48331			−0.615125
$149$			7.48331i			0.613057i	0.951861	+	0.306529i	$0.0991675\pi$
$149$			7.48331i			0.613057i	−0.951861	+	0.306529i	$0.900833\pi$
$150$	−9.00000	−	9.00000i	−0.734847	−	0.734847i
$151$			15.0000i			1.22068i	0.792139	+	0.610341i	$0.208968\pi$
$151$			15.0000i			1.22068i	−0.792139	+	0.610341i	$0.791032\pi$
$152$		0			0
$153$		−	7.48331i		−	0.604990i
$154$	14.0000	−	14.0000i	1.12815	−	1.12815i
$155$	−18.7083			−1.50269
$156$	2.00000			0.160128
$157$			14.9666i			1.19447i	0.802067	+	0.597234i	$0.203733\pi$
$157$			14.9666i			1.19447i	−0.802067	+	0.597234i	$0.796267\pi$
$158$		0			0
$159$	−7.48331			−0.593465
$160$	14.9666	+	14.9666i	1.18322	+	1.18322i
$161$	−14.0000	−	11.2250i	−1.10335	−	0.884652i
$162$	−1.00000	+	1.00000i	−0.0785674	+	0.0785674i
$163$		−	21.0000i		−	1.64485i	−0.568876	−	0.822423i	$-0.692621\pi$
$163$		−	21.0000i		−	1.64485i	0.568876	−	0.822423i	$-0.307379\pi$
$164$			6.00000i			0.468521i
$165$	−14.0000			−1.08990
$166$	−11.2250	+	11.2250i	−0.871227	+	0.871227i
$167$			22.0000i			1.70241i	0.524832	+	0.851206i	$0.324128\pi$
$167$			22.0000i			1.70241i	−0.524832	+	0.851206i	$0.675872\pi$
$168$	7.48331	−	7.48331i	0.577350	−	0.577350i
$169$	−12.0000			−0.923077
$170$	−14.0000	+	14.0000i	−1.07375	+	1.07375i
$171$		0			0
$172$			14.9666i			1.14119i
$173$	24.0000			1.82469			0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000			1.82469			0.912343	+	0.409426i	$0.134271\pi$
$174$	5.00000	+	5.00000i	0.379049	+	0.379049i
$175$	−33.6749			−2.54558
$176$	14.9666			1.12815
$177$	6.00000			0.450988
$178$	−7.48331	−	7.48331i	−0.560898	−	0.560898i
$179$			1.00000i			0.0747435i	0.999301	+	0.0373718i	$0.0118986\pi$
$179$			1.00000i			0.0747435i	−0.999301	+	0.0373718i	$0.988101\pi$
$180$	14.9666			1.11555
$181$		−	18.7083i		−	1.39058i	−0.718731	−	0.695288i	$-0.755277\pi$
$181$		−	18.7083i		−	1.39058i	0.718731	−	0.695288i	$-0.244723\pi$
$182$	3.74166	−	3.74166i	0.277350	−	0.277350i
$183$		0			0
$184$	−1.48331	−	13.4833i	−0.109351	−	0.994003i
$185$	14.0000			1.02930
$186$	−5.00000	+	5.00000i	−0.366618	+	0.366618i
$187$			14.0000i			1.02378i
$188$	−6.00000			−0.437595
$189$		−	18.7083i		−	1.36083i
$190$		0			0
$191$	−3.74166			−0.270737			−0.135368	−	0.990795i	$-0.543222\pi$
$191$	−3.74166			−0.270737			−0.135368	+	0.990795i	$0.543222\pi$
$192$	8.00000			0.577350
$193$	−11.0000			−0.791797			−0.395899	−	0.918294i	$-0.629567\pi$
$193$	−11.0000			−0.791797			−0.395899	+	0.918294i	$0.629567\pi$
$194$	3.74166	+	3.74166i	0.268635	+	0.268635i
$195$	−3.74166			−0.267946
$196$		−	14.0000i		−	1.00000i
$197$	−7.00000			−0.498729			−0.249365	−	0.968410i	$-0.580222\pi$
$197$	−7.00000			−0.498729			−0.249365	+	0.968410i	$0.580222\pi$
$198$	7.48331	−	7.48331i	0.531816	−	0.531816i
$199$	18.7083			1.32620			0.663098	−	0.748533i	$-0.269241\pi$
$199$	18.7083			1.32620			0.663098	+	0.748533i	$0.269241\pi$
$200$	−18.0000	−	18.0000i	−1.27279	−	1.27279i
$201$		−	3.74166i		−	0.263916i
$202$	8.00000	−	8.00000i	0.562878	−	0.562878i
$203$	18.7083			1.31306
$204$			7.48331i			0.523937i
$205$		−	11.2250i		−	0.783986i
$206$	−11.2250	+	11.2250i	−0.782081	+	0.782081i
$207$	−7.48331	−	6.00000i	−0.520126	−	0.417029i
$208$	4.00000			0.277350
$209$		0			0
$210$	−14.0000	+	14.0000i	−0.966092	+	0.966092i
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$	−14.9666			−1.02791
$213$	−5.00000			−0.342594
$214$	14.9666	−	14.9666i	1.02310	−	1.02310i
$215$		−	28.0000i		−	1.90958i
$216$	10.0000	−	10.0000i	0.680414	−	0.680414i
$217$			18.7083i			1.27000i
$218$	−7.48331	−	7.48331i	−0.506834	−	0.506834i
$219$			1.00000i			0.0675737i
$220$	−28.0000			−1.88776
$221$			3.74166i			0.251691i
$222$	3.74166	−	3.74166i	0.251124	−	0.251124i
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	14.9666	−	14.9666i	1.00000	−	1.00000i
$225$	−18.0000			−1.20000
$226$	−11.2250	−	11.2250i	−0.746674	−	0.746674i
$227$	3.74166			0.248343			0.124171	−	0.992261i	$-0.460373\pi$
$227$	3.74166			0.248343			0.124171	+	0.992261i	$0.460373\pi$
$228$		0			0
$229$			7.48331i			0.494511i	0.968950	+	0.247256i	$0.0795288\pi$
$229$			7.48331i			0.494511i	−0.968950	+	0.247256i	$0.920471\pi$
$230$	2.77503	+	25.2250i	0.182980	+	1.66329i
$231$			14.0000i			0.921132i
$232$	10.0000	+	10.0000i	0.656532	+	0.656532i
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$	2.00000	−	2.00000i	0.130744	−	0.130744i
$235$	11.2250			0.732236
$236$	12.0000			0.781133
$237$		0			0
$238$	14.0000	+	14.0000i	0.907485	+	0.907485i
$239$			11.0000i			0.711531i	0.934575	+	0.355765i	$0.115780\pi$
$239$			11.0000i			0.711531i	−0.934575	+	0.355765i	$0.884220\pi$
$240$	−14.9666			−0.966092
$241$		−	18.7083i		−	1.20511i	−0.798079	−	0.602553i	$-0.794150\pi$
$241$		−	18.7083i		−	1.20511i	0.798079	−	0.602553i	$-0.205850\pi$
$242$	−3.00000	+	3.00000i	−0.192847	+	0.192847i
$243$		−	16.0000i		−	1.02640i
$244$		0			0
$245$			26.1916i			1.67332i
$246$	−3.00000	−	3.00000i	−0.191273	−	0.191273i
$247$		0			0
$248$	−10.0000	+	10.0000i	−0.635001	+	0.635001i
$249$		−	11.2250i		−	0.711354i
$250$	14.9666	+	14.9666i	0.946573	+	0.946573i
$251$	−3.74166			−0.236171			−0.118086	−	0.993003i	$-0.537676\pi$
$251$	−3.74166			−0.236171			−0.118086	+	0.993003i	$0.537676\pi$
$252$		−	14.9666i		−	0.942809i
$253$	14.0000	+	11.2250i	0.880172	+	0.705708i
$254$	−17.0000	−	17.0000i	−1.06667	−	1.06667i
$255$		−	14.0000i		−	0.876714i
$256$	16.0000			1.00000
$257$	23.0000			1.43470			0.717350	−	0.696713i	$-0.245355\pi$
$257$	23.0000			1.43470			0.717350	+	0.696713i	$0.245355\pi$
$258$	−7.48331	−	7.48331i	−0.465891	−	0.465891i
$259$		−	14.0000i		−	0.869918i
$260$	−7.48331			−0.464095
$261$	10.0000			0.618984
$262$	−5.00000	−	5.00000i	−0.308901	−	0.308901i
$263$	−7.48331			−0.461441			−0.230720	−	0.973020i	$-0.574108\pi$
$263$	−7.48331			−0.461441			−0.230720	+	0.973020i	$0.574108\pi$
$264$	−7.48331	+	7.48331i	−0.460566	+	0.460566i
$265$	28.0000			1.72003
$266$		0			0
$267$	7.48331			0.457971
$268$		−	7.48331i		−	0.457116i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$	−18.7083	+	18.7083i	−1.13855	+	1.13855i
$271$		−	10.0000i		−	0.607457i	−0.952759	−	0.303728i	$-0.901768\pi$
$271$		−	10.0000i		−	0.607457i	0.952759	−	0.303728i	$-0.0982315\pi$
$272$			14.9666i			0.907485i
$273$			3.74166i			0.226455i
$274$	22.4499	+	22.4499i	1.35625	+	1.35625i
$275$	33.6749			2.03067
$276$	7.48331	+	6.00000i	0.450443	+	0.361158i
$277$	13.0000			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$278$	−1.00000	−	1.00000i	−0.0599760	−	0.0599760i
$279$			10.0000i			0.598684i
$280$	−28.0000	+	28.0000i	−1.67332	+	1.67332i
$281$			18.7083i			1.11604i	0.829827	+	0.558021i	$0.188439\pi$
$281$			18.7083i			1.11604i	−0.829827	+	0.558021i	$0.811561\pi$
$282$	3.00000	−	3.00000i	0.178647	−	0.178647i
$283$	11.2250			0.667255			0.333628	−	0.942705i	$-0.391727\pi$
$283$	11.2250			0.667255			0.333628	+	0.942705i	$0.391727\pi$
$284$	−10.0000			−0.593391
$285$		0			0
$286$	−3.74166	+	3.74166i	−0.221249	+	0.221249i
$287$	−11.2250			−0.662589
$288$	8.00000	−	8.00000i	0.471405	−	0.471405i
$289$	3.00000			0.176471
$290$	−18.7083	−	18.7083i	−1.09859	−	1.09859i
$291$	−3.74166			−0.219340
$292$			2.00000i			0.117041i
$293$			29.9333i			1.74872i	0.485278	+	0.874360i	$0.338718\pi$
$293$			29.9333i			1.74872i	−0.485278	+	0.874360i	$0.661282\pi$
$294$	7.00000	+	7.00000i	0.408248	+	0.408248i
$295$	−22.4499			−1.30709
$296$	7.48331	−	7.48331i	0.434959	−	0.434959i
$297$			18.7083i			1.08556i
$298$	−7.48331	−	7.48331i	−0.433497	−	0.433497i
$299$	3.74166	+	3.00000i	0.216386	+	0.173494i
$300$	18.0000			1.03923
$301$	−28.0000			−1.61389
$302$	−15.0000	−	15.0000i	−0.863153	−	0.863153i
$303$			8.00000i			0.459588i
$304$		0			0
$305$		0			0
$306$	7.48331	+	7.48331i	0.427793	+	0.427793i
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$			28.0000i			1.59545i
$309$		−	11.2250i		−	0.638566i
$310$	18.7083	−	18.7083i	1.06256	−	1.06256i
$311$		−	15.0000i		−	0.850572i	−0.905059	−	0.425286i	$-0.860174\pi$
$311$		−	15.0000i		−	0.850572i	0.905059	−	0.425286i	$-0.139826\pi$
$312$	−2.00000	+	2.00000i	−0.113228	+	0.113228i
$313$		−	7.48331i		−	0.422982i	−0.977380	−	0.211491i	$-0.932168\pi$
$313$		−	7.48331i		−	0.422982i	0.977380	−	0.211491i	$-0.0678319\pi$
$314$	−14.9666	−	14.9666i	−0.844616	−	0.844616i
$315$			28.0000i			1.57762i
$316$		0			0
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$	7.48331	−	7.48331i	0.419643	−	0.419643i
$319$	−18.7083			−1.04746
$320$	−29.9333			−1.67332
$321$			14.9666i			0.835356i
$322$	25.2250	−	2.77503i	1.40573	−	0.154646i
$323$		0			0
$324$		−	2.00000i		−	0.111111i
$325$	9.00000			0.499230
$326$	21.0000	+	21.0000i	1.16308	+	1.16308i
$327$	7.48331			0.413828
$328$	−6.00000	−	6.00000i	−0.331295	−	0.331295i
$329$		−	11.2250i		−	0.618853i
$330$	14.0000	−	14.0000i	0.770675	−	0.770675i
$331$			5.00000i			0.274825i	0.990514	+	0.137412i	$0.0438786\pi$
$331$			5.00000i			0.274825i	−0.990514	+	0.137412i	$0.956121\pi$
$332$		−	22.4499i		−	1.23210i
$333$		−	7.48331i		−	0.410083i
$334$	−22.0000	−	22.0000i	−1.20379	−	1.20379i
$335$			14.0000i			0.764902i
$336$			14.9666i			0.816497i
$337$		−	22.4499i		−	1.22293i	−0.791273	−	0.611463i	$-0.790581\pi$
$337$		−	22.4499i		−	1.22293i	0.791273	−	0.611463i	$-0.209419\pi$
$338$	12.0000	−	12.0000i	0.652714	−	0.652714i
$339$	11.2250			0.609657
$340$		−	28.0000i		−	1.51851i
$341$		−	18.7083i		−	1.01311i
$342$		0			0
$343$		0			0
$344$	−14.9666	−	14.9666i	−0.806947	−	0.806947i
$345$	−14.0000	−	11.2250i	−0.753735	−	0.604332i
$346$	−24.0000	+	24.0000i	−1.29025	+	1.29025i
$347$		−	8.00000i		−	0.429463i	−0.976673	−	0.214731i	$-0.931112\pi$
$347$		−	8.00000i		−	0.429463i	0.976673	−	0.214731i	$-0.0688876\pi$
$348$	−10.0000			−0.536056
$349$	−25.0000			−1.33822			−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000			−1.33822			−0.669110	+	0.743164i	$0.733324\pi$
$350$	33.6749	−	33.6749i	1.80000	−	1.80000i
$351$			5.00000i			0.266880i
$352$	−14.9666	+	14.9666i	−0.797724	+	0.797724i
$353$	19.0000			1.01127			0.505634	−	0.862748i	$-0.331259\pi$
$353$	19.0000			1.01127			0.505634	+	0.862748i	$0.331259\pi$
$354$	−6.00000	+	6.00000i	−0.318896	+	0.318896i
$355$	18.7083			0.992933
$356$	14.9666			0.793230
$357$	−14.0000			−0.740959
$358$	−1.00000	−	1.00000i	−0.0528516	−	0.0528516i
$359$	37.4166			1.97477			0.987386	−	0.158334i	$-0.0506123\pi$
$359$	37.4166			1.97477			0.987386	+	0.158334i	$0.0506123\pi$
$360$	−14.9666	+	14.9666i	−0.788811	+	0.788811i
$361$	−19.0000			−1.00000
$362$	18.7083	+	18.7083i	0.983286	+	0.983286i
$363$		−	3.00000i		−	0.157459i
$364$			7.48331i			0.392232i
$365$		−	3.74166i		−	0.195847i
$366$		0			0
$367$	−33.6749			−1.75782			−0.878908	−	0.476991i	$-0.841727\pi$
$367$	−33.6749			−1.75782			−0.878908	+	0.476991i	$0.841727\pi$
$368$	14.9666	+	12.0000i	0.780189	+	0.625543i
$369$	−6.00000			−0.312348
$370$	−14.0000	+	14.0000i	−0.727825	+	0.727825i
$371$		−	28.0000i		−	1.45369i
$372$		−	10.0000i		−	0.518476i
$373$			11.2250i			0.581207i	0.956844	+	0.290604i	$0.0938561\pi$
$373$			11.2250i			0.581207i	−0.956844	+	0.290604i	$0.906144\pi$
$374$	−14.0000	−	14.0000i	−0.723923	−	0.723923i
$375$	−14.9666			−0.772873
$376$	6.00000	−	6.00000i	0.309426	−	0.309426i
$377$	−5.00000			−0.257513
$378$	18.7083	+	18.7083i	0.962250	+	0.962250i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	17.0000			0.870936
$382$	3.74166	−	3.74166i	0.191440	−	0.191440i
$383$	−7.48331			−0.382380			−0.191190	−	0.981553i	$-0.561235\pi$
$383$	−7.48331			−0.382380			−0.191190	+	0.981553i	$0.561235\pi$
$384$	−8.00000	+	8.00000i	−0.408248	+	0.408248i
$385$		−	52.3832i		−	2.66970i
$386$	11.0000	−	11.0000i	0.559885	−	0.559885i
$387$	−14.9666			−0.760797
$388$	−7.48331			−0.379908
$389$		−	29.9333i		−	1.51768i	−0.651279	−	0.758838i	$-0.725767\pi$
$389$		−	29.9333i		−	1.51768i	0.651279	−	0.758838i	$-0.274233\pi$
$390$	3.74166	−	3.74166i	0.189466	−	0.189466i
$391$	−11.2250	+	14.0000i	−0.567671	+	0.708010i
$392$	14.0000	+	14.0000i	0.707107	+	0.707107i
$393$	5.00000			0.252217
$394$	7.00000	−	7.00000i	0.352655	−	0.352655i
$395$		0			0
$396$			14.9666i			0.752101i
$397$	3.00000			0.150566			0.0752828	−	0.997162i	$-0.476014\pi$
$397$	3.00000			0.150566			0.0752828	+	0.997162i	$0.476014\pi$
$398$	−18.7083	+	18.7083i	−0.937762	+	0.937762i
$399$		0			0
$400$	36.0000			1.80000
$401$			18.7083i			0.934247i	0.884192	+	0.467124i	$0.154710\pi$
$401$			18.7083i			0.934247i	−0.884192	+	0.467124i	$0.845290\pi$
$402$	3.74166	+	3.74166i	0.186617	+	0.186617i
$403$		−	5.00000i		−	0.249068i
$404$			16.0000i			0.796030i
$405$			3.74166i			0.185924i
$406$	−18.7083	+	18.7083i	−0.928477	+	0.928477i
$407$			14.0000i			0.693954i
$408$	−7.48331	−	7.48331i	−0.370479	−	0.370479i
$409$	−5.00000			−0.247234			−0.123617	−	0.992330i	$-0.539449\pi$
$409$	−5.00000			−0.247234			−0.123617	+	0.992330i	$0.539449\pi$
$410$	11.2250	+	11.2250i	0.554362	+	0.554362i
$411$	−22.4499			−1.10737
$412$		−	22.4499i		−	1.10603i
$413$			22.4499i			1.10469i
$414$	13.4833	−	1.48331i	0.662669	−	0.0729009i
$415$			42.0000i			2.06170i
$416$	−4.00000	+	4.00000i	−0.196116	+	0.196116i
$417$	1.00000			0.0489702
$418$		0			0
$419$	−37.4166			−1.82792			−0.913960	−	0.405805i	$-0.866991\pi$
$419$	−37.4166			−1.82792			−0.913960	+	0.405805i	$0.866991\pi$
$420$		−	28.0000i		−	1.36626i
$421$		−	18.7083i		−	0.911786i	−0.890035	−	0.455893i	$-0.849320\pi$
$421$		−	18.7083i		−	0.911786i	0.890035	−	0.455893i	$-0.150680\pi$
$422$	−10.0000	−	10.0000i	−0.486792	−	0.486792i
$423$		−	6.00000i		−	0.291730i
$424$	14.9666	−	14.9666i	0.726844	−	0.726844i
$425$			33.6749i			1.63347i
$426$	5.00000	−	5.00000i	0.242251	−	0.242251i
$427$		0			0
$428$			29.9333i			1.44688i
$429$		−	3.74166i		−	0.180649i
$430$	28.0000	+	28.0000i	1.35028	+	1.35028i
$431$	14.9666			0.720917			0.360459	−	0.932775i	$-0.382620\pi$
$431$	14.9666			0.720917			0.360459	+	0.932775i	$0.382620\pi$
$432$			20.0000i			0.962250i
$433$			11.2250i			0.539438i	0.962939	+	0.269719i	$0.0869308\pi$
$433$			11.2250i			0.539438i	−0.962939	+	0.269719i	$0.913069\pi$
$434$	−18.7083	−	18.7083i	−0.898027	−	0.898027i
$435$	18.7083			0.896994
$436$	14.9666			0.716772
$437$		0			0
$438$	−1.00000	−	1.00000i	−0.0477818	−	0.0477818i
$439$			31.0000i			1.47955i	0.672855	+	0.739775i	$0.265068\pi$
$439$			31.0000i			1.47955i	−0.672855	+	0.739775i	$0.734932\pi$
$440$	28.0000	−	28.0000i	1.33485	−	1.33485i
$441$	14.0000			0.666667
$442$	−3.74166	−	3.74166i	−0.177972	−	0.177972i
$443$		−	21.0000i		−	0.997740i	−0.866677	−	0.498870i	$-0.833748\pi$
$443$		−	21.0000i		−	0.997740i	0.866677	−	0.498870i	$-0.166252\pi$
$444$			7.48331i			0.355142i
$445$	−28.0000			−1.32733
$446$	−4.00000	−	4.00000i	−0.189405	−	0.189405i
$447$	7.48331			0.353949
$448$			29.9333i			1.41421i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	18.0000	−	18.0000i	0.848528	−	0.848528i
$451$	11.2250			0.528563
$452$	22.4499			1.05596
$453$	15.0000			0.704761
$454$	−3.74166	+	3.74166i	−0.175605	+	0.175605i
$455$		−	14.0000i		−	0.656330i
$456$		0			0
$457$			33.6749i			1.57525i	0.616157	+	0.787623i	$0.288689\pi$
$457$			33.6749i			1.57525i	−0.616157	+	0.787623i	$0.711311\pi$
$458$	−7.48331	−	7.48331i	−0.349672	−	0.349672i
$459$	−18.7083			−0.873228
$460$	−28.0000	−	22.4499i	−1.30551	−	1.04673i
$461$	−13.0000			−0.605470			−0.302735	−	0.953075i	$-0.597900\pi$
$461$	−13.0000			−0.605470			−0.302735	+	0.953075i	$0.597900\pi$
$462$	−14.0000	−	14.0000i	−0.651339	−	0.651339i
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	−20.0000			−0.928477
$465$			18.7083i			0.867576i
$466$	21.0000	−	21.0000i	0.972806	−	0.972806i
$467$	22.4499			1.03886			0.519430	−	0.854513i	$-0.326144\pi$
$467$	22.4499			1.03886			0.519430	+	0.854513i	$0.326144\pi$
$468$			4.00000i			0.184900i
$469$	14.0000			0.646460
$470$	−11.2250	+	11.2250i	−0.517769	+	0.517769i
$471$	14.9666			0.689626
$472$	−12.0000	+	12.0000i	−0.552345	+	0.552345i
$473$	28.0000			1.28744
$474$		0			0
$475$		0			0
$476$	−28.0000			−1.28338
$477$		−	14.9666i		−	0.685275i
$478$	−11.0000	−	11.0000i	−0.503128	−	0.503128i
$479$	18.7083			0.854803			0.427402	−	0.904062i	$-0.359429\pi$
$479$	18.7083			0.854803			0.427402	+	0.904062i	$0.359429\pi$
$480$	14.9666	−	14.9666i	0.683130	−	0.683130i
$481$			3.74166i			0.170605i
$482$	18.7083	+	18.7083i	0.852139	+	0.852139i
$483$	−11.2250	+	14.0000i	−0.510754	+	0.637022i
$484$		−	6.00000i		−	0.272727i
$485$	14.0000			0.635707
$486$	16.0000	+	16.0000i	0.725775	+	0.725775i
$487$			7.00000i			0.317200i	0.987343	+	0.158600i	$0.0506981\pi$
$487$			7.00000i			0.317200i	−0.987343	+	0.158600i	$0.949302\pi$
$488$		0			0
$489$	−21.0000			−0.949653
$490$	−26.1916	−	26.1916i	−1.18322	−	1.18322i
$491$		−	35.0000i		−	1.57953i	−0.613411	−	0.789764i	$-0.710203\pi$
$491$		−	35.0000i		−	1.57953i	0.613411	−	0.789764i	$-0.289797\pi$
$492$	6.00000			0.270501
$493$		−	18.7083i		−	0.842579i
$494$		0			0
$495$		−	28.0000i		−	1.25851i
$496$		−	20.0000i		−	0.898027i
$497$		−	18.7083i		−	0.839181i
$498$	11.2250	+	11.2250i	0.503003	+	0.503003i
$499$		−	19.0000i		−	0.850557i	−0.905063	−	0.425278i	$-0.860176\pi$
$499$		−	19.0000i		−	0.850557i	0.905063	−	0.425278i	$-0.139824\pi$
$500$	−29.9333			−1.33866
$501$	22.0000			0.982888
$502$	3.74166	−	3.74166i	0.166998	−	0.166998i
$503$	−7.48331			−0.333665			−0.166832	−	0.985985i	$-0.553354\pi$
$503$	−7.48331			−0.333665			−0.166832	+	0.985985i	$0.553354\pi$
$504$	14.9666	+	14.9666i	0.666667	+	0.666667i
$505$		−	29.9333i		−	1.33201i
$506$	−25.2250	+	2.77503i	−1.12139	+	0.123365i
$507$			12.0000i			0.532939i
$508$	34.0000			1.50851
$509$	25.0000			1.10811			0.554053	−	0.832482i	$-0.313081\pi$
$509$	25.0000			1.10811			0.554053	+	0.832482i	$0.313081\pi$
$510$	14.0000	+	14.0000i	0.619930	+	0.619930i
$511$	−3.74166			−0.165521
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	−23.0000	+	23.0000i	−1.01449	+	1.01449i
$515$			42.0000i			1.85074i
$516$	14.9666			0.658869
$517$			11.2250i			0.493674i
$518$	14.0000	+	14.0000i	0.615125	+	0.615125i
$519$		−	24.0000i		−	1.05348i
$520$	7.48331	−	7.48331i	0.328165	−	0.328165i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−10.0000	+	10.0000i	−0.437688	+	0.437688i
$523$	11.2250			0.490834			0.245417	−	0.969418i	$-0.421075\pi$
$523$	11.2250			0.490834			0.245417	+	0.969418i	$0.421075\pi$
$524$	10.0000			0.436852
$525$			33.6749i			1.46969i
$526$	7.48331	−	7.48331i	0.326288	−	0.326288i
$527$	18.7083			0.814946
$528$		−	14.9666i		−	0.651339i
$529$	5.00000	+	22.4499i	0.217391	+	0.976085i
$530$	−28.0000	+	28.0000i	−1.21624	+	1.21624i
$531$			12.0000i			0.520756i
$532$		0			0
$533$	3.00000			0.129944
$534$	−7.48331	+	7.48331i	−0.323835	+	0.323835i
$535$		−	56.0000i		−	2.42109i
$536$	7.48331	+	7.48331i	0.323230	+	0.323230i
$537$	1.00000			0.0431532
$538$	−15.0000	+	15.0000i	−0.646696	+	0.646696i
$539$	−26.1916			−1.12815
$540$		−	37.4166i		−	1.61015i
$541$	−33.0000			−1.41878			−0.709390	−	0.704816i	$-0.751030\pi$
$541$	−33.0000			−1.41878			−0.709390	+	0.704816i	$0.751030\pi$
$542$	10.0000	+	10.0000i	0.429537	+	0.429537i
$543$	−18.7083			−0.802849
$544$	−14.9666	−	14.9666i	−0.641689	−	0.641689i
$545$	−28.0000			−1.19939
$546$	−3.74166	−	3.74166i	−0.160128	−	0.160128i
$547$		−	3.00000i		−	0.128271i	−0.997941	−	0.0641354i	$-0.979571\pi$
$547$		−	3.00000i		−	0.128271i	0.997941	−	0.0641354i	$-0.0204289\pi$
$548$	−44.8999			−1.91803
$549$		0			0
$550$	−33.6749	+	33.6749i	−1.43590	+	1.43590i
$551$		0			0
$552$	−13.4833	+	1.48331i	−0.573888	+	0.0631341i
$553$		0			0
$554$	−13.0000	+	13.0000i	−0.552317	+	0.552317i
$555$		−	14.0000i		−	0.594267i
$556$	2.00000			0.0848189
$557$		−	22.4499i		−	0.951235i	−0.879652	−	0.475617i	$-0.842225\pi$
$557$		−	22.4499i		−	0.951235i	0.879652	−	0.475617i	$-0.157775\pi$
$558$	−10.0000	−	10.0000i	−0.423334	−	0.423334i
$559$	7.48331			0.316510
$560$		−	56.0000i		−	2.36643i
$561$	14.0000			0.591080
$562$	−18.7083	−	18.7083i	−0.789161	−	0.789161i
$563$	−7.48331			−0.315384			−0.157692	−	0.987488i	$-0.550405\pi$
$563$	−7.48331			−0.315384			−0.157692	+	0.987488i	$0.550405\pi$
$564$			6.00000i			0.252646i
$565$	−42.0000			−1.76695
$566$	−11.2250	+	11.2250i	−0.471821	+	0.471821i
$567$	3.74166			0.157135
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$			26.1916i			1.09801i	0.835819	+	0.549005i	$0.184993\pi$
$569$			26.1916i			1.09801i	−0.835819	+	0.549005i	$0.815007\pi$
$570$		0			0
$571$	33.6749			1.40925			0.704626	−	0.709579i	$-0.251115\pi$
$571$	33.6749			1.40925			0.704626	+	0.709579i	$0.251115\pi$
$572$		−	7.48331i		−	0.312893i
$573$			3.74166i			0.156310i
$574$	11.2250	−	11.2250i	0.468521	−	0.468521i
$575$	33.6749	+	27.0000i	1.40434	+	1.12598i
$576$			16.0000i			0.666667i
$577$	13.0000			0.541197			0.270599	−	0.962692i	$-0.412778\pi$
$577$	13.0000			0.541197			0.270599	+	0.962692i	$0.412778\pi$
$578$	−3.00000	+	3.00000i	−0.124784	+	0.124784i
$579$			11.0000i			0.457144i
$580$	37.4166			1.55364
$581$	42.0000			1.74245
$582$	3.74166	−	3.74166i	0.155097	−	0.155097i
$583$			28.0000i			1.15964i
$584$	−2.00000	−	2.00000i	−0.0827606	−	0.0827606i
$585$		−	7.48331i		−	0.309397i
$586$	−29.9333	−	29.9333i	−1.23653	−	1.23653i
$587$			27.0000i			1.11441i	0.830375	+	0.557205i	$0.188126\pi$
$587$			27.0000i			1.11441i	−0.830375	+	0.557205i	$0.811874\pi$
$588$	−14.0000			−0.577350
$589$		0			0
$590$	22.4499	−	22.4499i	0.924250	−	0.924250i
$591$			7.00000i			0.287942i
$592$			14.9666i			0.615125i
$593$	−16.0000			−0.657041			−0.328521	−	0.944497i	$-0.606550\pi$
$593$	−16.0000			−0.657041			−0.328521	+	0.944497i	$0.606550\pi$
$594$	−18.7083	−	18.7083i	−0.767610	−	0.767610i
$595$	52.3832			2.14750
$596$	14.9666			0.613057
$597$		−	18.7083i		−	0.765679i
$598$	−6.74166	+	0.741657i	−0.275687	+	0.0303286i
$599$		−	34.0000i		−	1.38920i	−0.719395	−	0.694601i	$-0.755581\pi$
$599$		−	34.0000i		−	1.38920i	0.719395	−	0.694601i	$-0.244419\pi$
$600$	−18.0000	+	18.0000i	−0.734847	+	0.734847i
$601$	27.0000			1.10135			0.550676	−	0.834719i	$-0.314370\pi$
$601$	27.0000			1.10135			0.550676	+	0.834719i	$0.314370\pi$
$602$	28.0000	−	28.0000i	1.14119	−	1.14119i
$603$	7.48331			0.304744
$604$	30.0000			1.22068
$605$			11.2250i			0.456360i
$606$	−8.00000	−	8.00000i	−0.324978	−	0.324978i
$607$		−	38.0000i		−	1.54237i	−0.636610	−	0.771186i	$-0.719664\pi$
$607$		−	38.0000i		−	1.54237i	0.636610	−	0.771186i	$-0.280336\pi$
$608$		0			0
$609$		−	18.7083i		−	0.758098i
$610$		0			0
$611$			3.00000i			0.121367i
$612$	−14.9666			−0.604990
$613$			11.2250i			0.453372i	0.973968	+	0.226686i	$0.0727892\pi$
$613$			11.2250i			0.453372i	−0.973968	+	0.226686i	$0.927211\pi$
$614$	18.0000	+	18.0000i	0.726421	+	0.726421i
$615$	−11.2250			−0.452635
$616$	−28.0000	−	28.0000i	−1.12815	−	1.12815i
$617$		−	22.4499i		−	0.903801i	−0.892068	−	0.451900i	$-0.850746\pi$
$617$		−	22.4499i		−	0.903801i	0.892068	−	0.451900i	$-0.149254\pi$
$618$	11.2250	+	11.2250i	0.451535	+	0.451535i
$619$	−37.4166			−1.50390			−0.751950	−	0.659221i	$-0.770886\pi$
$619$	−37.4166			−1.50390			−0.751950	+	0.659221i	$0.770886\pi$
$620$			37.4166i			1.50269i
$621$	−15.0000	+	18.7083i	−0.601929	+	0.750738i
$622$	15.0000	+	15.0000i	0.601445	+	0.601445i
$623$			28.0000i			1.12180i
$624$		−	4.00000i		−	0.160128i
$625$	11.0000			0.440000
$626$	7.48331	+	7.48331i	0.299093	+	0.299093i
$627$		0			0
$628$	29.9333			1.19447
$629$	−14.0000			−0.558217
$630$	−28.0000	−	28.0000i	−1.11555	−	1.11555i
$631$	−22.4499			−0.893718			−0.446859	−	0.894604i	$-0.647457\pi$
$631$	−22.4499			−0.893718			−0.446859	+	0.894604i	$0.647457\pi$
$632$		0			0
$633$	10.0000			0.397464
$634$	12.0000	−	12.0000i	0.476581	−	0.476581i
$635$	−63.6082			−2.52421
$636$			14.9666i			0.593465i
$637$	−7.00000			−0.277350
$638$	18.7083	−	18.7083i	0.740668	−	0.740668i
$639$		−	10.0000i		−	0.395594i
$640$	29.9333	−	29.9333i	1.18322	−	1.18322i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	−14.9666	−	14.9666i	−0.590686	−	0.590686i
$643$	11.2250			0.442670			0.221335	−	0.975198i	$-0.428959\pi$
$643$	11.2250			0.442670			0.221335	+	0.975198i	$0.428959\pi$
$644$	−22.4499	+	28.0000i	−0.884652	+	1.10335i
$645$	−28.0000			−1.10250
$646$		0			0
$647$		−	33.0000i		−	1.29736i	−0.761060	−	0.648682i	$-0.775321\pi$
$647$		−	33.0000i		−	1.29736i	0.761060	−	0.648682i	$-0.224679\pi$
$648$	2.00000	+	2.00000i	0.0785674	+	0.0785674i
$649$		−	22.4499i		−	0.881237i
$650$	−9.00000	+	9.00000i	−0.353009	+	0.353009i
$651$	18.7083			0.733236
$652$	−42.0000			−1.64485
$653$	9.00000			0.352197			0.176099	−	0.984373i	$-0.443652\pi$
$653$	9.00000			0.352197			0.176099	+	0.984373i	$0.443652\pi$
$654$	−7.48331	+	7.48331i	−0.292621	+	0.292621i
$655$	−18.7083			−0.730993
$656$	12.0000			0.468521
$657$	−2.00000			−0.0780274
$658$	11.2250	+	11.2250i	0.437595	+	0.437595i
$659$	18.7083			0.728771			0.364386	−	0.931248i	$-0.381279\pi$
$659$	18.7083			0.728771			0.364386	+	0.931248i	$0.381279\pi$
$660$			28.0000i			1.08990i
$661$			37.4166i			1.45534i	0.685929	+	0.727668i	$0.259396\pi$
$661$			37.4166i			1.45534i	−0.685929	+	0.727668i	$0.740604\pi$
$662$	−5.00000	−	5.00000i	−0.194331	−	0.194331i
$663$	3.74166			0.145314
$664$	22.4499	+	22.4499i	0.871227	+	0.871227i
$665$		0			0
$666$	7.48331	+	7.48331i	0.289973	+	0.289973i
$667$	−18.7083	−	15.0000i	−0.724388	−	0.580802i
$668$	44.0000			1.70241
$669$	4.00000			0.154649
$670$	−14.0000	−	14.0000i	−0.540867	−	0.540867i
$671$		0			0
$672$	−14.9666	−	14.9666i	−0.577350	−	0.577350i
$673$	−21.0000			−0.809491			−0.404745	−	0.914429i	$-0.632640\pi$
$673$	−21.0000			−0.809491			−0.404745	+	0.914429i	$0.632640\pi$
$674$	22.4499	+	22.4499i	0.864740	+	0.864740i
$675$			45.0000i			1.73205i
$676$			24.0000i			0.923077i
$677$			14.9666i			0.575214i	0.957748	+	0.287607i	$0.0928597\pi$
$677$			14.9666i			0.575214i	−0.957748	+	0.287607i	$0.907140\pi$
$678$	−11.2250	+	11.2250i	−0.431092	+	0.431092i
$679$		−	14.0000i		−	0.537271i
$680$	28.0000	+	28.0000i	1.07375	+	1.07375i
$681$		−	3.74166i		−	0.143381i
$682$	18.7083	+	18.7083i	0.716377	+	0.716377i
$683$		−	11.0000i		−	0.420903i	−0.977604	−	0.210452i	$-0.932507\pi$
$683$		−	11.0000i		−	0.420903i	0.977604	−	0.210452i	$-0.0674935\pi$
$684$		0			0
$685$	84.0000			3.20948
$686$		0			0
$687$	7.48331			0.285506
$688$	29.9333			1.14119
$689$			7.48331i			0.285092i
$690$	25.2250	−	2.77503i	0.960298	−	0.105644i
$691$			10.0000i			0.380418i	0.981744	+	0.190209i	$0.0609166\pi$
$691$			10.0000i			0.380418i	−0.981744	+	0.190209i	$0.939083\pi$
$692$		−	48.0000i		−	1.82469i
$693$	−28.0000			−1.06363
$694$	8.00000	+	8.00000i	0.303676	+	0.303676i
$695$	−3.74166			−0.141929
$696$	10.0000	−	10.0000i	0.379049	−	0.379049i
$697$			11.2250i			0.425176i
$698$	25.0000	−	25.0000i	0.946264	−	0.946264i
$699$			21.0000i			0.794293i
$700$			67.3498i			2.54558i
$701$		−	18.7083i		−	0.706602i	−0.935510	−	0.353301i	$-0.885059\pi$
$701$		−	18.7083i		−	0.706602i	0.935510	−	0.353301i	$-0.114941\pi$
$702$	−5.00000	−	5.00000i	−0.188713	−	0.188713i
$703$		0			0
$704$		−	29.9333i		−	1.12815i
$705$		−	11.2250i		−	0.422757i
$706$	−19.0000	+	19.0000i	−0.715074	+	0.715074i
$707$	−29.9333			−1.12576
$708$		−	12.0000i		−	0.450988i
$709$		−	11.2250i		−	0.421563i	−0.977533	−	0.210781i	$-0.932399\pi$
$709$		−	11.2250i		−	0.421563i	0.977533	−	0.210781i	$-0.0676008\pi$
$710$	−18.7083	+	18.7083i	−0.702109	+	0.702109i
$711$		0			0
$712$	−14.9666	+	14.9666i	−0.560898	+	0.560898i
$713$	15.0000	−	18.7083i	0.561754	−	0.700631i
$714$	14.0000	−	14.0000i	0.523937	−	0.523937i
$715$			14.0000i			0.523570i
$716$	2.00000			0.0747435
$717$	11.0000			0.410803
$718$	−37.4166	+	37.4166i	−1.39637	+	1.39637i
$719$			26.0000i			0.969636i	0.874615	+	0.484818i	$0.161114\pi$
$719$			26.0000i			0.969636i	−0.874615	+	0.484818i	$0.838886\pi$
$720$		−	29.9333i		−	1.11555i
$721$	42.0000			1.56416
$722$	19.0000	−	19.0000i	0.707107	−	0.707107i
$723$	−18.7083			−0.695769
$724$	−37.4166			−1.39058
$725$	−45.0000			−1.67126
$726$	3.00000	+	3.00000i	0.111340	+	0.111340i
$727$	41.1582			1.52647			0.763237	−	0.646118i	$-0.223609\pi$
$727$	41.1582			1.52647			0.763237	+	0.646118i	$0.223609\pi$
$728$	−7.48331	−	7.48331i	−0.277350	−	0.277350i
$729$	−13.0000			−0.481481
$730$	3.74166	+	3.74166i	0.138485	+	0.138485i
$731$			28.0000i			1.03562i
$732$		0			0
$733$		−	26.1916i		−	0.967409i	−0.875231	−	0.483704i	$-0.839291\pi$
$733$		−	26.1916i		−	0.967409i	0.875231	−	0.483704i	$-0.160709\pi$
$734$	33.6749	−	33.6749i	1.24296	−	1.24296i
$735$	26.1916			0.966092
$736$	−26.9666	+	2.96663i	−0.994003	+	0.109351i
$737$	−14.0000			−0.515697
$738$	6.00000	−	6.00000i	0.220863	−	0.220863i
$739$			31.0000i			1.14035i	0.821522	+	0.570177i	$0.193125\pi$
$739$			31.0000i			1.14035i	−0.821522	+	0.570177i	$0.806875\pi$
$740$		−	28.0000i		−	1.02930i
$741$		0			0
$742$	28.0000	+	28.0000i	1.02791	+	1.02791i
$743$	−26.1916			−0.960877			−0.480438	−	0.877029i	$-0.659522\pi$
$743$	−26.1916			−0.960877			−0.480438	+	0.877029i	$0.659522\pi$
$744$	10.0000	+	10.0000i	0.366618	+	0.366618i
$745$	−28.0000			−1.02584
$746$	−11.2250	−	11.2250i	−0.410975	−	0.410975i
$747$	22.4499			0.821401
$748$	28.0000			1.02378
$749$	−56.0000			−2.04620
$750$	14.9666	−	14.9666i	0.546504	−	0.546504i
$751$	−22.4499			−0.819210			−0.409605	−	0.912263i	$-0.634333\pi$
$751$	−22.4499			−0.819210			−0.409605	+	0.912263i	$0.634333\pi$
$752$			12.0000i			0.437595i
$753$			3.74166i			0.136354i
$754$	5.00000	−	5.00000i	0.182089	−	0.182089i
$755$	−56.1249			−2.04259
$756$	−37.4166			−1.36083
$757$			33.6749i			1.22394i	0.790883	+	0.611968i	$0.209622\pi$
$757$			33.6749i			1.22394i	−0.790883	+	0.611968i	$0.790378\pi$
$758$		0			0
$759$	11.2250	−	14.0000i	0.407441	−	0.508168i
$760$		0			0
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$	−17.0000	+	17.0000i	−0.615845	+	0.615845i
$763$			28.0000i			1.01367i
$764$			7.48331i			0.270737i
$765$	28.0000			1.01234
$766$	7.48331	−	7.48331i	0.270383	−	0.270383i
$767$		−	6.00000i		−	0.216647i
$768$		−	16.0000i		−	0.577350i
$769$		−	11.2250i		−	0.404783i	−0.979305	−	0.202391i	$-0.935129\pi$
$769$		−	11.2250i		−	0.404783i	0.979305	−	0.202391i	$-0.0648713\pi$
$770$	52.3832	+	52.3832i	1.88776	+	1.88776i
$771$		−	23.0000i		−	0.828325i
$772$			22.0000i			0.791797i
$773$		−	7.48331i		−	0.269156i	−0.990903	−	0.134578i	$-0.957032\pi$
$773$		−	7.48331i		−	0.269156i	0.990903	−	0.134578i	$-0.0429679\pi$
$774$	14.9666	−	14.9666i	0.537964	−	0.537964i
$775$		−	45.0000i		−	1.61645i
$776$	7.48331	−	7.48331i	0.268635	−	0.268635i
$777$	−14.0000			−0.502247
$778$	29.9333	+	29.9333i	1.07316	+	1.07316i
$779$		0			0
$780$			7.48331i			0.267946i
$781$			18.7083i			0.669435i
$782$	−2.77503	−	25.2250i	−0.0992348	−	0.902043i
$783$		−	25.0000i		−	0.893427i
$784$	−28.0000			−1.00000
$785$	−56.0000			−1.99873
$786$	−5.00000	+	5.00000i	−0.178344	+	0.178344i
$787$	22.4499			0.800254			0.400127	−	0.916460i	$-0.368966\pi$
$787$	22.4499			0.800254			0.400127	+	0.916460i	$0.368966\pi$
$788$			14.0000i			0.498729i
$789$			7.48331i			0.266413i
$790$		0			0
$791$			42.0000i			1.49335i
$792$	−14.9666	−	14.9666i	−0.531816	−	0.531816i
$793$		0			0
$794$	−3.00000	+	3.00000i	−0.106466	+	0.106466i
$795$		−	28.0000i		−	0.993058i
$796$		−	37.4166i		−	1.32620i
$797$		−	22.4499i		−	0.795218i	−0.917555	−	0.397609i	$-0.869840\pi$
$797$		−	22.4499i		−	0.795218i	0.917555	−	0.397609i	$-0.130160\pi$
$798$		0			0
$799$	−11.2250			−0.397111
$800$	−36.0000	+	36.0000i	−1.27279	+	1.27279i
$801$			14.9666i			0.528820i
$802$	−18.7083	−	18.7083i	−0.660613	−	0.660613i
$803$	3.74166			0.132040
$804$	−7.48331			−0.263916
$805$	42.0000	−	52.3832i	1.48031	−	1.84627i
$806$	5.00000	+	5.00000i	0.176117	+	0.176117i
$807$		−	15.0000i		−	0.528025i
$808$	−16.0000	−	16.0000i	−0.562878	−	0.562878i
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$	−3.74166	−	3.74166i	−0.131468	−	0.131468i
$811$		−	45.0000i		−	1.58016i	−0.613001	−	0.790082i	$-0.710038\pi$
$811$		−	45.0000i		−	1.58016i	0.613001	−	0.790082i	$-0.289962\pi$
$812$		−	37.4166i		−	1.31306i
$813$	−10.0000			−0.350715
$814$	−14.0000	−	14.0000i	−0.490700	−	0.490700i
$815$	78.5748			2.75236
$816$	14.9666			0.523937
$817$		0			0
$818$	5.00000	−	5.00000i	0.174821	−	0.174821i
$819$	−7.48331			−0.261488
$820$	−22.4499			−0.783986
$821$	12.0000			0.418803			0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000			0.418803			0.209401	+	0.977830i	$0.432848\pi$
$822$	22.4499	−	22.4499i	0.783032	−	0.783032i
$823$			39.0000i			1.35945i	0.733465	+	0.679727i	$0.237902\pi$
$823$			39.0000i			1.35945i	−0.733465	+	0.679727i	$0.762098\pi$
$824$	22.4499	+	22.4499i	0.782081	+	0.782081i
$825$		−	33.6749i		−	1.17241i
$826$	−22.4499	−	22.4499i	−0.781133	−	0.781133i
$827$	−14.9666			−0.520441			−0.260220	−	0.965549i	$-0.583795\pi$
$827$	−14.9666			−0.520441			−0.260220	+	0.965549i	$0.583795\pi$
$828$	−12.0000	+	14.9666i	−0.417029	+	0.520126i
$829$	40.0000			1.38926			0.694629	−	0.719368i	$-0.255569\pi$
$829$	40.0000			1.38926			0.694629	+	0.719368i	$0.255569\pi$
$830$	−42.0000	−	42.0000i	−1.45784	−	1.45784i
$831$		−	13.0000i		−	0.450965i
$832$		−	8.00000i		−	0.277350i
$833$		−	26.1916i		−	0.907485i
$834$	−1.00000	+	1.00000i	−0.0346272	+	0.0346272i
$835$	−82.3165			−2.84868
$836$		0			0
$837$	25.0000			0.864126
$838$	37.4166	−	37.4166i	1.29253	−	1.29253i
$839$	18.7083			0.645882			0.322941	−	0.946419i	$-0.395328\pi$
$839$	18.7083			0.645882			0.322941	+	0.946419i	$0.395328\pi$
$840$	28.0000	+	28.0000i	0.966092	+	0.966092i
$841$	−4.00000			−0.137931
$842$	18.7083	+	18.7083i	0.644730	+	0.644730i
$843$	18.7083			0.644348
$844$	20.0000			0.688428
$845$		−	44.8999i		−	1.54460i
$846$	6.00000	+	6.00000i	0.206284	+	0.206284i
$847$	11.2250			0.385695
$848$			29.9333i			1.02791i
$849$		−	11.2250i		−	0.385240i
$850$	−33.6749	−	33.6749i	−1.15504	−	1.15504i
$851$	−11.2250	+	14.0000i	−0.384787	+	0.479914i
$852$			10.0000i			0.342594i
$853$	4.00000			0.136957			0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000			0.136957			0.0684787	+	0.997653i	$0.478185\pi$
$854$		0			0
$855$		0			0
$856$	−29.9333	−	29.9333i	−1.02310	−	1.02310i
$857$	−37.0000			−1.26390			−0.631948	−	0.775011i	$-0.717744\pi$
$857$	−37.0000			−1.26390			−0.631948	+	0.775011i	$0.717744\pi$
$858$	3.74166	+	3.74166i	0.127738	+	0.127738i
$859$			51.0000i			1.74010i	0.492966	+	0.870049i	$0.335913\pi$
$859$			51.0000i			1.74010i	−0.492966	+	0.870049i	$0.664087\pi$
$860$	−56.0000			−1.90958
$861$			11.2250i			0.382546i
$862$	−14.9666	+	14.9666i	−0.509765	+	0.509765i
$863$		−	21.0000i		−	0.714848i	−0.933942	−	0.357424i	$-0.883655\pi$
$863$		−	21.0000i		−	0.714848i	0.933942	−	0.357424i	$-0.116345\pi$
$864$	−20.0000	−	20.0000i	−0.680414	−	0.680414i
$865$			89.7998i			3.05328i
$866$	−11.2250	−	11.2250i	−0.381440	−	0.381440i
$867$		−	3.00000i		−	0.101885i
$868$	37.4166			1.27000
$869$		0			0
$870$	−18.7083	+	18.7083i	−0.634270	+	0.634270i
$871$	−3.74166			−0.126781
$872$	−14.9666	+	14.9666i	−0.506834	+	0.506834i
$873$		−	7.48331i		−	0.253272i
$874$		0			0
$875$		−	56.0000i		−	1.89315i
$876$	2.00000			0.0675737
$877$	28.0000			0.945493			0.472746	−	0.881199i	$-0.343263\pi$
$877$	28.0000			0.945493			0.472746	+	0.881199i	$0.343263\pi$
$878$	−31.0000	−	31.0000i	−1.04620	−	1.04620i
$879$	29.9333			1.00962
$880$			56.0000i			1.88776i
$881$			18.7083i			0.630298i	0.949042	+	0.315149i	$0.102055\pi$
$881$			18.7083i			0.630298i	−0.949042	+	0.315149i	$0.897945\pi$
$882$	−14.0000	+	14.0000i	−0.471405	+	0.471405i
$883$		−	46.0000i		−	1.54802i	−0.633171	−	0.774012i	$-0.718247\pi$
$883$		−	46.0000i		−	1.54802i	0.633171	−	0.774012i	$-0.281753\pi$
$884$	7.48331			0.251691
$885$			22.4499i			0.754647i
$886$	21.0000	+	21.0000i	0.705509	+	0.705509i
$887$			47.0000i			1.57811i	0.614325	+	0.789053i	$0.289428\pi$
$887$			47.0000i			1.57811i	−0.614325	+	0.789053i	$0.710572\pi$
$888$	−7.48331	−	7.48331i	−0.251124	−	0.251124i
$889$			63.6082i			2.13335i
$890$	28.0000	−	28.0000i	0.938562	−	0.938562i
$891$	−3.74166			−0.125350
$892$	8.00000			0.267860
$893$		0			0
$894$	−7.48331	+	7.48331i	−0.250279	+	0.250279i
$895$	−3.74166			−0.125070
$896$	−29.9333	−	29.9333i	−1.00000	−	1.00000i
$897$	3.00000	−	3.74166i	0.100167	−	0.124930i
$898$	10.0000	−	10.0000i	0.333704	−	0.333704i
$899$			25.0000i			0.833797i
$900$			36.0000i			1.20000i
$901$	−28.0000			−0.932815
$902$	−11.2250	+	11.2250i	−0.373751	+	0.373751i
$903$			28.0000i			0.931782i
$904$	−22.4499	+	22.4499i	−0.746674	+	0.746674i
$905$	70.0000			2.32688
$906$	−15.0000	+	15.0000i	−0.498342	+	0.498342i
$907$	22.4499			0.745438			0.372719	−	0.927944i	$-0.378426\pi$
$907$	22.4499			0.745438			0.372719	+	0.927944i	$0.378426\pi$
$908$		−	7.48331i		−	0.248343i
$909$	−16.0000			−0.530687
$910$	14.0000	+	14.0000i	0.464095	+	0.464095i
$911$	14.9666			0.495867			0.247933	−	0.968777i	$-0.420249\pi$
$911$	14.9666			0.495867			0.247933	+	0.968777i	$0.420249\pi$
$912$		0			0
$913$	−42.0000			−1.39000
$914$	−33.6749	−	33.6749i	−1.11387	−	1.11387i
$915$		0			0
$916$	14.9666			0.494511
$917$			18.7083i			0.617802i
$918$	18.7083	−	18.7083i	0.617465	−	0.617465i
$919$	56.1249			1.85139			0.925694	−	0.378273i	$-0.123482\pi$
$919$	56.1249			1.85139			0.925694	+	0.378273i	$0.123482\pi$
$920$	50.4499	−	5.55006i	1.66329	−	0.182980i
$921$	−18.0000			−0.593120
$922$	13.0000	−	13.0000i	0.428132	−	0.428132i
$923$			5.00000i			0.164577i
$924$	28.0000			0.921132
$925$			33.6749i			1.10722i
$926$	−4.00000	−	4.00000i	−0.131448	−	0.131448i
$927$	22.4499			0.737353
$928$	20.0000	−	20.0000i	0.656532	−	0.656532i
$929$	45.0000			1.47640			0.738201	−	0.674581i	$-0.235676\pi$
$929$	45.0000			1.47640			0.738201	+	0.674581i	$0.235676\pi$
$930$	−18.7083	−	18.7083i	−0.613469	−	0.613469i
$931$		0			0
$932$			42.0000i			1.37576i
$933$	−15.0000			−0.491078
$934$	−22.4499	+	22.4499i	−0.734585	+	0.734585i
$935$	−52.3832			−1.71311
$936$	−4.00000	−	4.00000i	−0.130744	−	0.130744i
$937$			33.6749i			1.10011i	0.835128	+	0.550056i	$0.185394\pi$
$937$			33.6749i			1.10011i	−0.835128	+	0.550056i	$0.814606\pi$
$938$	−14.0000	+	14.0000i	−0.457116	+	0.457116i
$939$	−7.48331			−0.244209
$940$		−	22.4499i		−	0.732236i
$941$			18.7083i			0.609873i	0.952373	+	0.304936i	$0.0986352\pi$
$941$			18.7083i			0.609873i	−0.952373	+	0.304936i	$0.901365\pi$
$942$	−14.9666	+	14.9666i	−0.487639	+	0.487639i
$943$	11.2250	+	9.00000i	0.365535	+	0.293080i
$944$		−	24.0000i		−	0.781133i
$945$	70.0000			2.27710
$946$	−28.0000	+	28.0000i	−0.910359	+	0.910359i
$947$		−	23.0000i		−	0.747400i	−0.927550	−	0.373700i	$-0.878089\pi$
$947$		−	23.0000i		−	0.747400i	0.927550	−	0.373700i	$-0.121911\pi$
$948$		0			0
$949$	1.00000			0.0324614
$950$		0			0
$951$			12.0000i			0.389127i
$952$	28.0000	−	28.0000i	0.907485	−	0.907485i
$953$		−	7.48331i		−	0.242408i	−0.992628	−	0.121204i	$-0.961324\pi$
$953$		−	7.48331i		−	0.242408i	0.992628	−	0.121204i	$-0.0386756\pi$
$954$	14.9666	+	14.9666i	0.484563	+	0.484563i
$955$		−	14.0000i		−	0.453029i
$956$	22.0000			0.711531
$957$			18.7083i			0.604753i
$958$	−18.7083	+	18.7083i	−0.604437	+	0.604437i
$959$		−	84.0000i		−	2.71250i
$960$			29.9333i			0.966092i
$961$	6.00000			0.193548
$962$	−3.74166	−	3.74166i	−0.120636	−	0.120636i
$963$	−29.9333			−0.964586
$964$	−37.4166			−1.20511
$965$		−	41.1582i		−	1.32493i
$966$	−2.77503	−	25.2250i	−0.0892851	−	0.811600i
$967$		−	23.0000i		−	0.739630i	−0.929105	−	0.369815i	$-0.879421\pi$
$967$		−	23.0000i		−	0.739630i	0.929105	−	0.369815i	$-0.120579\pi$
$968$	6.00000	+	6.00000i	0.192847	+	0.192847i
$969$		0			0
$970$	−14.0000	+	14.0000i	−0.449513	+	0.449513i
$971$	52.3832			1.68106			0.840528	−	0.541767i	$-0.182245\pi$
$971$	52.3832			1.68106			0.840528	+	0.541767i	$0.182245\pi$
$972$	−32.0000			−1.02640
$973$			3.74166i			0.119952i
$974$	−7.00000	−	7.00000i	−0.224294	−	0.224294i
$975$		−	9.00000i		−	0.288231i
$976$		0			0
$977$		−	41.1582i		−	1.31677i	−0.752682	−	0.658384i	$-0.771240\pi$
$977$		−	41.1582i		−	1.31677i	0.752682	−	0.658384i	$-0.228760\pi$
$978$	21.0000	−	21.0000i	0.671506	−	0.671506i
$979$		−	28.0000i		−	0.894884i
$980$	52.3832			1.67332
$981$			14.9666i			0.477848i
$982$	35.0000	+	35.0000i	1.11689	+	1.11689i
$983$	−7.48331			−0.238681			−0.119340	−	0.992853i	$-0.538078\pi$
$983$	−7.48331			−0.238681			−0.119340	+	0.992853i	$0.538078\pi$
$984$	−6.00000	+	6.00000i	−0.191273	+	0.191273i
$985$		−	26.1916i		−	0.834534i
$986$	18.7083	+	18.7083i	0.595793	+	0.595793i
$987$	−11.2250			−0.357295
$988$		0			0
$989$	28.0000	+	22.4499i	0.890348	+	0.713867i
$990$	28.0000	+	28.0000i	0.889898	+	0.889898i
$991$		−	10.0000i		−	0.317660i	−0.987306	−	0.158830i	$-0.949228\pi$
$991$		−	10.0000i		−	0.317660i	0.987306	−	0.158830i	$-0.0507723\pi$
$992$	20.0000	+	20.0000i	0.635001	+	0.635001i
$993$	5.00000			0.158670
$994$	18.7083	+	18.7083i	0.593391	+	0.593391i
$995$			70.0000i			2.21915i
$996$	−22.4499			−0.711354
$997$	−12.0000			−0.380044			−0.190022	−	0.981780i	$-0.560856\pi$
$997$	−12.0000			−0.380044			−0.190022	+	0.981780i	$0.560856\pi$
$998$	19.0000	+	19.0000i	0.601434	+	0.601434i
$999$	−18.7083			−0.591904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.b.a.91.4	yes	4
3.2	odd	2		828.2.e.a.91.1		4
4.3	odd	2	inner	92.2.b.a.91.2	yes	4
8.3	odd	2		1472.2.c.b.1471.1		4
8.5	even	2		1472.2.c.b.1471.3		4
12.11	even	2		828.2.e.a.91.3		4
23.22	odd	2	inner	92.2.b.a.91.3	yes	4
69.68	even	2		828.2.e.a.91.2		4
92.91	even	2	inner	92.2.b.a.91.1	✓	4
184.45	odd	2		1472.2.c.b.1471.4		4
184.91	even	2		1472.2.c.b.1471.2		4
276.275	odd	2		828.2.e.a.91.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.b.a.91.1	✓	4	92.91	even	2	inner
92.2.b.a.91.2	yes	4	4.3	odd	2	inner
92.2.b.a.91.3	yes	4	23.22	odd	2	inner
92.2.b.a.91.4	yes	4	1.1	even	1	trivial
828.2.e.a.91.1		4	3.2	odd	2
828.2.e.a.91.2		4	69.68	even	2
828.2.e.a.91.3		4	12.11	even	2
828.2.e.a.91.4		4	276.275	odd	2
1472.2.c.b.1471.1		4	8.3	odd	2
1472.2.c.b.1471.2		4	184.91	even	2
1472.2.c.b.1471.3		4	8.5	even	2
1472.2.c.b.1471.4		4	184.45	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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +3.74166i q^{5} +(1.00000 + 1.00000i) q^{6} +3.74166 q^{7} +(2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -1.00000i q^{3} -2.00000i q^{4} +3.74166i q^{5} +(1.00000 + 1.00000i) q^{6} +3.74166 q^{7} +(2.00000 + 2.00000i) q^{8} +2.00000 q^{9} +(-3.74166 - 3.74166i) q^{10} -3.74166 q^{11} -2.00000 q^{12} -1.00000 q^{13} +(-3.74166 + 3.74166i) q^{14} +3.74166 q^{15} -4.00000 q^{16} -3.74166i q^{17} +(-2.00000 + 2.00000i) q^{18} +7.48331 q^{20} -3.74166i q^{21} +(3.74166 - 3.74166i) q^{22} +(-3.74166 - 3.00000i) q^{23} +(2.00000 - 2.00000i) q^{24} -9.00000 q^{25} +(1.00000 - 1.00000i) q^{26} -5.00000i q^{27} -7.48331i q^{28} +5.00000 q^{29} +(-3.74166 + 3.74166i) q^{30} +5.00000i q^{31} +(4.00000 - 4.00000i) q^{32} +3.74166i q^{33} +(3.74166 + 3.74166i) q^{34} +14.0000i q^{35} -4.00000i q^{36} -3.74166i q^{37} +1.00000i q^{39} +(-7.48331 + 7.48331i) q^{40} -3.00000 q^{41} +(3.74166 + 3.74166i) q^{42} -7.48331 q^{43} +7.48331i q^{44} +7.48331i q^{45} +(6.74166 - 0.741657i) q^{46} -3.00000i q^{47} +4.00000i q^{48} +7.00000 q^{49} +(9.00000 - 9.00000i) q^{50} -3.74166 q^{51} +2.00000i q^{52} -7.48331i q^{53} +(5.00000 + 5.00000i) q^{54} -14.0000i q^{55} +(7.48331 + 7.48331i) q^{56} +(-5.00000 + 5.00000i) q^{58} +6.00000i q^{59} -7.48331i q^{60} +(-5.00000 - 5.00000i) q^{62} +7.48331 q^{63} +8.00000i q^{64} -3.74166i q^{65} +(-3.74166 - 3.74166i) q^{66} +3.74166 q^{67} -7.48331 q^{68} +(-3.00000 + 3.74166i) q^{69} +(-14.0000 - 14.0000i) q^{70} -5.00000i q^{71} +(4.00000 + 4.00000i) q^{72} -1.00000 q^{73} +(3.74166 + 3.74166i) q^{74} +9.00000i q^{75} -14.0000 q^{77} +(-1.00000 - 1.00000i) q^{78} -14.9666i q^{80} +1.00000 q^{81} +(3.00000 - 3.00000i) q^{82} +11.2250 q^{83} -7.48331 q^{84} +14.0000 q^{85} +(7.48331 - 7.48331i) q^{86} -5.00000i q^{87} +(-7.48331 - 7.48331i) q^{88} +7.48331i q^{89} +(-7.48331 - 7.48331i) q^{90} -3.74166 q^{91} +(-6.00000 + 7.48331i) q^{92} +5.00000 q^{93} +(3.00000 + 3.00000i) q^{94} +(-4.00000 - 4.00000i) q^{96} -3.74166i q^{97} +(-7.00000 + 7.00000i) q^{98} -7.48331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^6 + 8 * q^8 + 8 * q^9	\( 4 q - 4 q^{2} + 4 q^{6} + 8 q^{8} + 8 q^{9} - 8 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{18} + 8 q^{24} - 36 q^{25} + 4 q^{26} + 20 q^{29} + 16 q^{32} - 12 q^{41} + 12 q^{46} + 28 q^{49} + 36 q^{50} + 20 q^{54} - 20 q^{58} - 20 q^{62} - 12 q^{69} - 56 q^{70} + 16 q^{72} - 4 q^{73} - 56 q^{77} - 4 q^{78} + 4 q^{81} + 12 q^{82} + 56 q^{85} - 24 q^{92} + 20 q^{93} + 12 q^{94} - 16 q^{96} - 28 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^6 + 8 * q^8 + 8 * q^9 - 8 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^18 + 8 * q^24 - 36 * q^25 + 4 * q^26 + 20 * q^29 + 16 * q^32 - 12 * q^41 + 12 * q^46 + 28 * q^49 + 36 * q^50 + 20 * q^54 - 20 * q^58 - 20 * q^62 - 12 * q^69 - 56 * q^70 + 16 * q^72 - 4 * q^73 - 56 * q^77 - 4 * q^78 + 4 * q^81 + 12 * q^82 + 56 * q^85 - 24 * q^92 + 20 * q^93 + 12 * q^94 - 16 * q^96 - 28 * q^98

Introduction

L-functions

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