LMFDB - Embedded newform 1110.2.o.a.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.1
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.23554 + 0.0484605i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.23554 + 0.0484605i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(2.23554 - 0.0484605i) q^{10} -2.74073i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.09781 q^{13} +(-2.77693 + 2.77693i) q^{14} +(1.54650 - 1.61503i) q^{15} +1.00000 q^{16} +4.54367i q^{17} +1.00000i q^{18} +(-3.00837 - 3.00837i) q^{19} +(-2.23554 + 0.0484605i) q^{20} +3.92718i q^{21} +2.74073i q^{22} -1.09307 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.99530 - 0.216671i) q^{25} +2.09781 q^{26} +(0.707107 + 0.707107i) q^{27} +(2.77693 - 2.77693i) q^{28} +(-3.41798 + 3.41798i) q^{29} +(-1.54650 + 1.61503i) q^{30} +(-0.444286 - 0.444286i) q^{31} -1.00000 q^{32} +(1.93799 + 1.93799i) q^{33} -4.54367i q^{34} +(-6.07338 + 6.34253i) q^{35} -1.00000i q^{36} +(3.14301 + 5.20783i) q^{37} +(3.00837 + 3.00837i) q^{38} +(1.48338 - 1.48338i) q^{39} +(2.23554 - 0.0484605i) q^{40} +3.49239i q^{41} -3.92718i q^{42} -2.64615 q^{43} -2.74073i q^{44} +(0.0484605 + 2.23554i) q^{45} +1.09307 q^{46} +(-4.28090 + 4.28090i) q^{47} +(-0.707107 + 0.707107i) q^{48} -8.42272i q^{49} +(-4.99530 + 0.216671i) q^{50} +(-3.21286 - 3.21286i) q^{51} -2.09781 q^{52} +(-4.10770 - 4.10770i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(0.132817 + 6.12703i) q^{55} +(-2.77693 + 2.77693i) q^{56} +4.25447 q^{57} +(3.41798 - 3.41798i) q^{58} +(-10.1179 - 10.1179i) q^{59} +(1.54650 - 1.61503i) q^{60} +(-4.77382 - 4.77382i) q^{61} +(0.444286 + 0.444286i) q^{62} +(-2.77693 - 2.77693i) q^{63} +1.00000 q^{64} +(4.68975 - 0.101661i) q^{65} +(-1.93799 - 1.93799i) q^{66} +(-3.42538 - 3.42538i) q^{67} +4.54367i q^{68} +(0.772920 - 0.772920i) q^{69} +(6.07338 - 6.34253i) q^{70} +0.512824 q^{71} +1.00000i q^{72} +(-9.57090 + 9.57090i) q^{73} +(-3.14301 - 5.20783i) q^{74} +(-3.37900 + 3.68542i) q^{75} +(-3.00837 - 3.00837i) q^{76} +(-7.61083 - 7.61083i) q^{77} +(-1.48338 + 1.48338i) q^{78} +(-4.84570 - 4.84570i) q^{79} +(-2.23554 + 0.0484605i) q^{80} -1.00000 q^{81} -3.49239i q^{82} +(4.09292 + 4.09292i) q^{83} +3.92718i q^{84} +(-0.220188 - 10.1576i) q^{85} +2.64615 q^{86} -4.83375i q^{87} +2.74073i q^{88} +(-9.59900 + 9.59900i) q^{89} +(-0.0484605 - 2.23554i) q^{90} +(-5.82548 + 5.82548i) q^{91} -1.09307 q^{92} +0.628315 q^{93} +(4.28090 - 4.28090i) q^{94} +(6.87112 + 6.57954i) q^{95} +(0.707107 - 0.707107i) q^{96} +5.08514i q^{97} +8.42272i q^{98} -2.74073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−2.23554	+	0.0484605i	−0.999765	+	0.0216722i
$5$	−2.23554	+	0.0484605i	−0.999765	+	0.0216722i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	2.77693	−	2.77693i	1.04958	−	1.04958i	0.0508772	−	0.998705i	$-0.483798\pi$
$7$	2.77693	−	2.77693i	1.04958	−	1.04958i	0.998705	−	0.0508772i	$-0.0162017\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	2.23554	−	0.0484605i	0.706941	−	0.0153246i
$11$		−	2.74073i		−	0.826362i	−0.910649	−	0.413181i	$-0.864418\pi$
$11$		−	2.74073i		−	0.826362i	0.910649	−	0.413181i	$-0.135582\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−2.09781			−0.581828			−0.290914	−	0.956749i	$-0.593959\pi$
$13$	−2.09781			−0.581828			−0.290914	+	0.956749i	$0.593959\pi$
$14$	−2.77693	+	2.77693i	−0.742167	+	0.742167i
$15$	1.54650	−	1.61503i	0.399305	−	0.417000i
$16$	1.00000			0.250000
$17$			4.54367i			1.10200i	0.834505	+	0.551001i	$0.185754\pi$
$17$			4.54367i			1.10200i	−0.834505	+	0.551001i	$0.814246\pi$
$18$			1.00000i			0.235702i
$19$	−3.00837	−	3.00837i	−0.690166	−	0.690166i	0.272102	−	0.962268i	$-0.412281\pi$
$19$	−3.00837	−	3.00837i	−0.690166	−	0.690166i	−0.962268	+	0.272102i	$0.912281\pi$
$20$	−2.23554	+	0.0484605i	−0.499883	+	0.0108361i
$21$			3.92718i			0.856980i
$22$			2.74073i			0.584326i
$23$	−1.09307			−0.227922			−0.113961	−	0.993485i	$-0.536354\pi$
$23$	−1.09307			−0.227922			−0.113961	+	0.993485i	$0.536354\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	4.99530	−	0.216671i	0.999061	−	0.0433342i
$26$	2.09781			0.411415
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.77693	−	2.77693i	0.524791	−	0.524791i
$29$	−3.41798	+	3.41798i	−0.634703	+	0.634703i	−0.949244	−	0.314541i	$-0.898149\pi$
$29$	−3.41798	+	3.41798i	−0.634703	+	0.634703i	0.314541	+	0.949244i	$0.398149\pi$
$30$	−1.54650	+	1.61503i	−0.282351	+	0.294864i
$31$	−0.444286	−	0.444286i	−0.0797961	−	0.0797961i	0.666082	−	0.745878i	$-0.267970\pi$
$31$	−0.444286	−	0.444286i	−0.0797961	−	0.0797961i	−0.745878	+	0.666082i	$0.767970\pi$
$32$	−1.00000			−0.176777
$33$	1.93799	+	1.93799i	0.337361	+	0.337361i
$34$		−	4.54367i		−	0.779232i
$35$	−6.07338	+	6.34253i	−1.02659	+	1.07208i
$36$		−	1.00000i		−	0.166667i
$37$	3.14301	+	5.20783i	0.516708	+	0.856162i
$37$	3.14301	+	5.20783i	0.516708	+	0.856162i
$38$	3.00837	+	3.00837i	0.488021	+	0.488021i
$39$	1.48338	−	1.48338i	0.237530	−	0.237530i
$40$	2.23554	−	0.0484605i	0.353470	−	0.00766228i
$41$			3.49239i			0.545420i	0.962096	+	0.272710i	$0.0879200\pi$
$41$			3.49239i			0.545420i	−0.962096	+	0.272710i	$0.912080\pi$
$42$		−	3.92718i		−	0.605977i
$43$	−2.64615			−0.403534			−0.201767	−	0.979434i	$-0.564668\pi$
$43$	−2.64615			−0.403534			−0.201767	+	0.979434i	$0.564668\pi$
$44$		−	2.74073i		−	0.413181i
$45$	0.0484605	+	2.23554i	0.00722407	+	0.333255i
$46$	1.09307			0.161165
$47$	−4.28090	+	4.28090i	−0.624434	+	0.624434i	−0.946662	−	0.322228i	$-0.895568\pi$
$47$	−4.28090	+	4.28090i	−0.624434	+	0.624434i	0.322228	+	0.946662i	$0.395568\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	8.42272i		−	1.20325i
$50$	−4.99530	+	0.216671i	−0.706443	+	0.0306419i
$51$	−3.21286	−	3.21286i	−0.449890	−	0.449890i
$52$	−2.09781			−0.290914
$53$	−4.10770	−	4.10770i	−0.564235	−	0.564235i	0.366272	−	0.930508i	$-0.380634\pi$
$53$	−4.10770	−	4.10770i	−0.564235	−	0.564235i	−0.930508	+	0.366272i	$0.880634\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	0.132817	+	6.12703i	0.0179091	+	0.826168i
$56$	−2.77693	+	2.77693i	−0.371083	+	0.371083i
$57$	4.25447			0.563519
$58$	3.41798	−	3.41798i	0.448803	−	0.448803i
$59$	−10.1179	−	10.1179i	−1.31724	−	1.31724i	−0.915954	−	0.401282i	$-0.868565\pi$
$59$	−10.1179	−	10.1179i	−1.31724	−	1.31724i	−0.401282	−	0.915954i	$-0.631435\pi$
$60$	1.54650	−	1.61503i	0.199652	−	0.208500i
$61$	−4.77382	−	4.77382i	−0.611226	−	0.611226i	0.332040	−	0.943265i	$-0.392263\pi$
$61$	−4.77382	−	4.77382i	−0.611226	−	0.611226i	−0.943265	+	0.332040i	$0.892263\pi$
$62$	0.444286	+	0.444286i	0.0564243	+	0.0564243i
$63$	−2.77693	−	2.77693i	−0.349861	−	0.349861i
$64$	1.00000			0.125000
$65$	4.68975	−	0.101661i	0.581692	−	0.0126095i
$66$	−1.93799	−	1.93799i	−0.238550	−	0.238550i
$67$	−3.42538	−	3.42538i	−0.418476	−	0.418476i	0.466202	−	0.884678i	$-0.345622\pi$
$67$	−3.42538	−	3.42538i	−0.418476	−	0.418476i	−0.884678	+	0.466202i	$0.845622\pi$
$68$			4.54367i			0.551001i
$69$	0.772920	−	0.772920i	0.0930486	−	0.0930486i
$70$	6.07338	−	6.34253i	0.725908	−	0.758077i
$71$	0.512824			0.0608611			0.0304305	−	0.999537i	$-0.490312\pi$
$71$	0.512824			0.0608611			0.0304305	+	0.999537i	$0.490312\pi$
$72$			1.00000i			0.117851i
$73$	−9.57090	+	9.57090i	−1.12019	+	1.12019i	−0.128477	+	0.991713i	$0.541009\pi$
$73$	−9.57090	+	9.57090i	−1.12019	+	1.12019i	−0.991713	+	0.128477i	$0.958991\pi$
$74$	−3.14301	−	5.20783i	−0.365368	−	0.605398i
$75$	−3.37900	+	3.68542i	−0.390174	+	0.425556i
$76$	−3.00837	−	3.00837i	−0.345083	−	0.345083i
$77$	−7.61083	−	7.61083i	−0.867335	−	0.867335i
$78$	−1.48338	+	1.48338i	−0.167959	+	0.167959i
$79$	−4.84570	−	4.84570i	−0.545184	−	0.545184i	0.379860	−	0.925044i	$-0.375972\pi$
$79$	−4.84570	−	4.84570i	−0.545184	−	0.545184i	−0.925044	+	0.379860i	$0.875972\pi$
$80$	−2.23554	+	0.0484605i	−0.249941	+	0.00541805i
$81$	−1.00000			−0.111111
$82$		−	3.49239i		−	0.385670i
$83$	4.09292	+	4.09292i	0.449256	+	0.449256i	0.895107	−	0.445851i	$-0.147099\pi$
$83$	4.09292	+	4.09292i	0.449256	+	0.449256i	−0.445851	+	0.895107i	$0.647099\pi$
$84$			3.92718i			0.428490i
$85$	−0.220188	−	10.1576i	−0.0238828	−	1.10174i
$86$	2.64615			0.285341
$87$		−	4.83375i		−	0.518233i
$88$			2.74073i			0.292163i
$89$	−9.59900	+	9.59900i	−1.01749	+	1.01749i	−0.0176477	+	0.999844i	$0.505618\pi$
$89$	−9.59900	+	9.59900i	−1.01749	+	1.01749i	−0.999844	+	0.0176477i	$0.994382\pi$
$90$	−0.0484605	−	2.23554i	−0.00510819	−	0.235647i
$91$	−5.82548	+	5.82548i	−0.610677	+	0.610677i
$92$	−1.09307			−0.113961
$93$	0.628315			0.0651532
$94$	4.28090	−	4.28090i	0.441541	−	0.441541i
$95$	6.87112	+	6.57954i	0.704962	+	0.675047i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$			5.08514i			0.516318i	0.966102	+	0.258159i	$0.0831158\pi$
$97$			5.08514i			0.516318i	−0.966102	+	0.258159i	$0.916884\pi$
$98$			8.42272i			0.850823i
$99$	−2.74073			−0.275454
$100$	4.99530	−	0.216671i	0.499530	−	0.0216671i
$101$		−	14.3173i		−	1.42463i	−0.701861	−	0.712314i	$-0.747647\pi$
$101$		−	14.3173i		−	1.42463i	0.701861	−	0.712314i	$-0.252353\pi$
$102$	3.21286	+	3.21286i	0.318120	+	0.318120i
$103$			8.41065i			0.828726i	0.910112	+	0.414363i	$0.135996\pi$
$103$			8.41065i			0.828726i	−0.910112	+	0.414363i	$0.864004\pi$
$104$	2.09781			0.205707
$105$	−0.190313	−	8.77937i	−0.0185726	−	0.856779i
$106$	4.10770	+	4.10770i	0.398975	+	0.398975i
$107$	4.88230	−	4.88230i	0.471990	−	0.471990i	−0.430568	−	0.902558i	$-0.641687\pi$
$107$	4.88230	−	4.88230i	0.471990	−	0.471990i	0.902558	+	0.430568i	$0.141687\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	−9.37338	−	9.37338i	−0.897806	−	0.897806i	0.0974354	−	0.995242i	$-0.468936\pi$
$109$	−9.37338	−	9.37338i	−0.897806	−	0.897806i	−0.995242	+	0.0974354i	$0.968936\pi$
$110$	−0.132817	−	6.12703i	−0.0126636	−	0.584189i
$111$	−5.90494	−	1.46004i	−0.560472	−	0.138581i
$112$	2.77693	−	2.77693i	0.262396	−	0.262396i
$113$		−	4.08857i		−	0.384620i	−0.981334	−	0.192310i	$-0.938402\pi$
$113$		−	4.08857i		−	0.384620i	0.981334	−	0.192310i	$-0.0615979\pi$
$114$	−4.25447			−0.398468
$115$	2.44361	−	0.0529709i	0.227868	−	0.00493956i
$116$	−3.41798	+	3.41798i	−0.317352	+	0.317352i
$117$			2.09781i			0.193943i
$118$	10.1179	+	10.1179i	0.931427	+	0.931427i
$119$	12.6175	+	12.6175i	1.15664	+	1.15664i
$120$	−1.54650	+	1.61503i	−0.141176	+	0.147432i
$121$	3.48838			0.317126
$122$	4.77382	+	4.77382i	0.432202	+	0.432202i
$123$	−2.46949	−	2.46949i	−0.222667	−	0.222667i
$124$	−0.444286	−	0.444286i	−0.0398980	−	0.0398980i
$125$	−11.1567	+	0.726452i	−0.997887	+	0.0649759i
$126$	2.77693	+	2.77693i	0.247389	+	0.247389i
$127$	−8.71272	+	8.71272i	−0.773129	+	0.773129i	−0.978652	−	0.205523i	$-0.934110\pi$
$127$	−8.71272	+	8.71272i	−0.773129	+	0.773129i	0.205523	+	0.978652i	$0.434110\pi$
$128$	−1.00000			−0.0883883
$129$	1.87111	−	1.87111i	0.164742	−	0.164742i
$130$	−4.68975	+	0.101661i	−0.411318	+	0.00891626i
$131$	−15.0456	−	15.0456i	−1.31454	−	1.31454i	−0.918032	−	0.396507i	$-0.870222\pi$
$131$	−15.0456	−	15.0456i	−1.31454	−	1.31454i	−0.396507	−	0.918032i	$-0.629778\pi$
$132$	1.93799	+	1.93799i	0.168680	+	0.168680i
$133$	−16.7081			−1.44877
$134$	3.42538	+	3.42538i	0.295908	+	0.295908i
$135$	−1.61503	−	1.54650i	−0.139000	−	0.133102i
$136$		−	4.54367i		−	0.389616i
$137$	7.51357	−	7.51357i	0.641928	−	0.641928i	−0.309101	−	0.951029i	$-0.600028\pi$
$137$	7.51357	−	7.51357i	0.641928	−	0.641928i	0.951029	+	0.309101i	$0.100028\pi$
$138$	−0.772920	+	0.772920i	−0.0657953	+	0.0657953i
$139$	7.58286			0.643170			0.321585	−	0.946881i	$-0.395784\pi$
$139$	7.58286			0.643170			0.321585	+	0.946881i	$0.395784\pi$
$140$	−6.07338	+	6.34253i	−0.513294	+	0.536041i
$141$		−	6.05411i		−	0.509848i
$142$	−0.512824			−0.0430353
$143$			5.74954i			0.480801i
$144$		−	1.00000i		−	0.0833333i
$145$	7.47541	−	7.80668i	0.620799	−	0.648309i
$146$	9.57090	−	9.57090i	0.792093	−	0.792093i
$147$	5.95576	+	5.95576i	0.491223	+	0.491223i
$148$	3.14301	+	5.20783i	0.258354	+	0.428081i
$149$			18.5418i			1.51901i	0.650503	+	0.759504i	$0.274558\pi$
$149$			18.5418i			1.51901i	−0.650503	+	0.759504i	$0.725442\pi$
$150$	3.37900	−	3.68542i	0.275894	−	0.300913i
$151$		−	4.53529i		−	0.369077i	−0.982825	−	0.184538i	$-0.940921\pi$
$151$		−	4.53529i		−	0.369077i	0.982825	−	0.184538i	$-0.0590790\pi$
$152$	3.00837	+	3.00837i	0.244011	+	0.244011i
$153$	4.54367			0.367334
$154$	7.61083	+	7.61083i	0.613298	+	0.613298i
$155$	1.01475	+	0.971689i	0.0815067	+	0.0780480i
$156$	1.48338	−	1.48338i	0.118765	−	0.118765i
$157$	−2.15926	+	2.15926i	−0.172328	+	0.172328i	−0.788001	−	0.615674i	$-0.788884\pi$
$157$	−2.15926	+	2.15926i	−0.172328	+	0.172328i	0.615674	+	0.788001i	$0.288884\pi$
$158$	4.84570	+	4.84570i	0.385503	+	0.385503i
$159$	5.80916			0.460696
$160$	2.23554	−	0.0484605i	0.176735	−	0.00383114i
$161$	−3.03539	+	3.03539i	−0.239222	+	0.239222i
$162$	1.00000			0.0785674
$163$			13.2270i			1.03602i	0.855374	+	0.518011i	$0.173327\pi$
$163$			13.2270i			1.03602i	−0.855374	+	0.518011i	$0.826673\pi$
$164$			3.49239i			0.272710i
$165$	−4.42638	−	4.23855i	−0.344593	−	0.329970i
$166$	−4.09292	−	4.09292i	−0.317672	−	0.317672i
$167$			2.15667i			0.166888i	0.996512	+	0.0834441i	$0.0265920\pi$
$167$			2.15667i			0.166888i	−0.996512	+	0.0834441i	$0.973408\pi$
$168$		−	3.92718i		−	0.302988i
$169$	−8.59918			−0.661476
$170$	0.220188	+	10.1576i	0.0168877	+	0.779049i
$171$	−3.00837	+	3.00837i	−0.230055	+	0.230055i
$172$	−2.64615			−0.201767
$173$	−12.7830	+	12.7830i	−0.971877	+	0.971877i	−0.999615	−	0.0277386i	$-0.991169\pi$
$173$	−12.7830	+	12.7830i	−0.971877	+	0.971877i	0.0277386	+	0.999615i	$0.491169\pi$
$174$			4.83375i			0.366446i
$175$	13.2699	−	14.4733i	1.00311	−	1.09408i
$176$		−	2.74073i		−	0.206591i
$177$	14.3089			1.07552
$178$	9.59900	−	9.59900i	0.719475	−	0.719475i
$179$	8.92829	−	8.92829i	0.667332	−	0.667332i	−0.289766	−	0.957098i	$-0.593577\pi$
$179$	8.92829	−	8.92829i	0.667332	−	0.667332i	0.957098	+	0.289766i	$0.0935774\pi$
$180$	0.0484605	+	2.23554i	0.00361203	+	0.166628i
$181$	8.76543			0.651530			0.325765	−	0.945451i	$-0.394378\pi$
$181$	8.76543			0.651530			0.325765	+	0.945451i	$0.394378\pi$
$182$	5.82548	−	5.82548i	0.431814	−	0.431814i
$183$	6.75121			0.499064
$184$	1.09307			0.0805825
$185$	−7.27871	−	11.4900i	−0.535142	−	0.844762i
$186$	−0.628315			−0.0460703
$187$	12.4530			0.910652
$188$	−4.28090	+	4.28090i	−0.312217	+	0.312217i
$189$	3.92718			0.285660
$190$	−6.87112	−	6.57954i	−0.498483	−	0.477330i
$191$	3.29001	−	3.29001i	0.238057	−	0.238057i	−0.577988	−	0.816045i	$-0.696162\pi$
$191$	3.29001	−	3.29001i	0.238057	−	0.238057i	0.816045	+	0.577988i	$0.196162\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−19.3985			−1.39634			−0.698168	−	0.715934i	$-0.746001\pi$
$193$	−19.3985			−1.39634			−0.698168	+	0.715934i	$0.746001\pi$
$194$		−	5.08514i		−	0.365092i
$195$	−3.24427	+	3.38804i	−0.232327	+	0.242622i
$196$		−	8.42272i		−	0.601623i
$197$	−12.6528	+	12.6528i	−0.901476	+	0.901476i	−0.995564	−	0.0940878i	$-0.970007\pi$
$197$	−12.6528	+	12.6528i	−0.901476	+	0.901476i	0.0940878	+	0.995564i	$0.470007\pi$
$198$	2.74073			0.194775
$199$	3.25794	−	3.25794i	0.230949	−	0.230949i	−0.582140	−	0.813089i	$-0.697784\pi$
$199$	3.25794	−	3.25794i	0.230949	−	0.230949i	0.813089	+	0.582140i	$0.197784\pi$
$200$	−4.99530	+	0.216671i	−0.353221	+	0.0153210i
$201$	4.84421			0.341685
$202$			14.3173i			1.00736i
$203$			18.9830i			1.33235i
$204$	−3.21286	−	3.21286i	−0.224945	−	0.224945i
$205$	−0.169243	−	7.80739i	−0.0118205	−	0.545292i
$206$		−	8.41065i		−	0.585998i
$207$			1.09307i			0.0759739i
$208$	−2.09781			−0.145457
$209$	−8.24513	+	8.24513i	−0.570327	+	0.570327i
$210$	0.190313	+	8.77937i	0.0131328	+	0.605834i
$211$	−1.48256			−0.102064			−0.0510319	−	0.998697i	$-0.516251\pi$
$211$	−1.48256			−0.102064			−0.0510319	+	0.998697i	$0.516251\pi$
$212$	−4.10770	−	4.10770i	−0.282118	−	0.282118i
$213$	−0.362622	+	0.362622i	−0.0248464	+	0.0248464i
$214$	−4.88230	+	4.88230i	−0.333747	+	0.333747i
$215$	5.91557	−	0.128234i	0.403439	−	0.00874546i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−2.46750			−0.167505
$218$	9.37338	+	9.37338i	0.634845	+	0.634845i
$219$		−	13.5353i		−	0.914631i
$220$	0.132817	+	6.12703i	0.00895454	+	0.413084i
$221$		−	9.53176i		−	0.641175i
$222$	5.90494	+	1.46004i	0.396313	+	0.0979918i
$223$	6.90996	+	6.90996i	0.462725	+	0.462725i	0.899548	−	0.436822i	$-0.143896\pi$
$223$	6.90996	+	6.90996i	0.462725	+	0.462725i	−0.436822	+	0.899548i	$0.643896\pi$
$224$	−2.77693	+	2.77693i	−0.185542	+	0.185542i
$225$	−0.216671	−	4.99530i	−0.0144447	−	0.333020i
$226$			4.08857i			0.271967i
$227$			0.338896i			0.0224933i	0.999937	+	0.0112467i	$0.00358000\pi$
$227$			0.338896i			0.0224933i	−0.999937	+	0.0112467i	$0.996420\pi$
$228$	4.25447			0.281759
$229$			6.86738i			0.453810i	0.973917	+	0.226905i	$0.0728606\pi$
$229$			6.86738i			0.453810i	−0.973917	+	0.226905i	$0.927139\pi$
$230$	−2.44361	+	0.0529709i	−0.161127	+	0.00349280i
$231$	10.7633			0.708176
$232$	3.41798	−	3.41798i	0.224401	−	0.224401i
$233$	11.8523	−	11.8523i	0.776470	−	0.776470i	−0.202758	−	0.979229i	$-0.564991\pi$
$233$	11.8523	−	11.8523i	0.776470	−	0.776470i	0.979229	+	0.202758i	$0.0649906\pi$
$234$		−	2.09781i		−	0.137138i
$235$	9.36269	−	9.77759i	0.610754	−	0.637820i
$236$	−10.1179	−	10.1179i	−0.658618	−	0.658618i
$237$	6.85285			0.445141
$238$	−12.6175	−	12.6175i	−0.817868	−	0.817868i
$239$	11.8453	+	11.8453i	0.766207	+	0.766207i	0.977437	−	0.211229i	$-0.0677467\pi$
$239$	11.8453	+	11.8453i	0.766207	+	0.766207i	−0.211229	+	0.977437i	$0.567747\pi$
$240$	1.54650	−	1.61503i	0.0998262	−	0.104250i
$241$	−1.06176	+	1.06176i	−0.0683939	+	0.0683939i	−0.740476	−	0.672082i	$-0.765400\pi$
$241$	−1.06176	+	1.06176i	−0.0683939	+	0.0683939i	0.672082	+	0.740476i	$0.265400\pi$
$242$	−3.48838			−0.224242
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−4.77382	−	4.77382i	−0.305613	−	0.305613i
$245$	0.408169	+	18.8293i	0.0260770	+	1.20296i
$246$	2.46949	+	2.46949i	0.157449	+	0.157449i
$247$	6.31099	+	6.31099i	0.401558	+	0.401558i
$248$	0.444286	+	0.444286i	0.0282122	+	0.0282122i
$249$	−5.78826			−0.366816
$250$	11.1567	−	0.726452i	0.705613	−	0.0459449i
$251$	10.3290	+	10.3290i	0.651960	+	0.651960i	0.953465	−	0.301505i	$-0.0974890\pi$
$251$	10.3290	+	10.3290i	0.651960	+	0.651960i	−0.301505	+	0.953465i	$0.597489\pi$
$252$	−2.77693	−	2.77693i	−0.174930	−	0.174930i
$253$			2.99582i			0.188346i
$254$	8.71272	−	8.71272i	0.546685	−	0.546685i
$255$	7.33818	+	7.02678i	0.459534	+	0.440034i
$256$	1.00000			0.0625000
$257$		−	28.1460i		−	1.75570i	−0.478939	−	0.877848i	$-0.658978\pi$
$257$		−	28.1460i		−	1.75570i	0.478939	−	0.877848i	$-0.341022\pi$
$258$	−1.87111	+	1.87111i	−0.116490	+	0.116490i
$259$	23.1897	+	5.73385i	1.44094	+	0.356284i
$260$	4.68975	−	0.101661i	0.290846	−	0.00630475i
$261$	3.41798	+	3.41798i	0.211568	+	0.211568i
$262$	15.0456	+	15.0456i	0.929519	+	0.929519i
$263$	−1.14169	+	1.14169i	−0.0703994	+	0.0703994i	−0.741430	−	0.671030i	$-0.765852\pi$
$263$	−1.14169	+	1.14169i	−0.0703994	+	0.0703994i	0.671030	+	0.741430i	$0.265852\pi$
$264$	−1.93799	−	1.93799i	−0.119275	−	0.119275i
$265$	9.38199	+	8.98387i	0.576331	+	0.551875i
$266$	16.7081			1.02444
$267$		−	13.5750i		−	0.830779i
$268$	−3.42538	−	3.42538i	−0.209238	−	0.209238i
$269$			0.755375i			0.0460560i	0.999735	+	0.0230280i	$0.00733069\pi$
$269$			0.755375i			0.0460560i	−0.999735	+	0.0230280i	$0.992669\pi$
$270$	1.61503	+	1.54650i	0.0982879	+	0.0941170i
$271$	13.0803			0.794573			0.397286	−	0.917695i	$-0.369952\pi$
$271$	13.0803			0.794573			0.397286	+	0.917695i	$0.369952\pi$
$272$			4.54367i			0.275500i
$273$		−	8.23848i		−	0.498615i
$274$	−7.51357	+	7.51357i	−0.453912	+	0.453912i
$275$	−0.593838	−	13.6908i	−0.0358097	−	0.825586i
$276$	0.772920	−	0.772920i	0.0465243	−	0.0465243i
$277$	27.8958			1.67610			0.838048	−	0.545597i	$-0.183697\pi$
$277$	27.8958			1.67610			0.838048	+	0.545597i	$0.183697\pi$
$278$	−7.58286			−0.454790
$279$	−0.444286	+	0.444286i	−0.0265987	+	0.0265987i
$280$	6.07338	−	6.34253i	0.362954	−	0.379038i
$281$	3.25168	−	3.25168i	0.193979	−	0.193979i	−0.603434	−	0.797413i	$-0.706201\pi$
$281$	3.25168	−	3.25168i	0.193979	−	0.193979i	0.797413	+	0.603434i	$0.206201\pi$
$282$			6.05411i			0.360517i
$283$		−	12.8597i		−	0.764431i	−0.924073	−	0.382216i	$-0.875161\pi$
$283$		−	12.8597i		−	0.764431i	0.924073	−	0.382216i	$-0.124839\pi$
$284$	0.512824			0.0304305
$285$	−9.51105	+	0.206174i	−0.563386	+	0.0122127i
$286$		−	5.74954i		−	0.339978i
$287$	9.69814	+	9.69814i	0.572463	+	0.572463i
$288$			1.00000i			0.0589256i
$289$	−3.64491			−0.214406
$290$	−7.47541	+	7.80668i	−0.438971	+	0.458424i
$291$	−3.59574	−	3.59574i	−0.210786	−	0.210786i
$292$	−9.57090	+	9.57090i	−0.560095	+	0.560095i
$293$	−8.19264	−	8.19264i	−0.478619	−	0.478619i	0.426071	−	0.904690i	$-0.359897\pi$
$293$	−8.19264	−	8.19264i	−0.478619	−	0.478619i	−0.904690	+	0.426071i	$0.859897\pi$
$294$	−5.95576	−	5.95576i	−0.347347	−	0.347347i
$295$	23.1093	+	22.1287i	1.34547	+	1.28838i
$296$	−3.14301	−	5.20783i	−0.182684	−	0.302699i
$297$	1.93799	−	1.93799i	0.112454	−	0.112454i
$298$		−	18.5418i		−	1.07410i
$299$	2.29306			0.132611
$300$	−3.37900	+	3.68542i	−0.195087	+	0.212778i
$301$	−7.34817	+	7.34817i	−0.423542	+	0.423542i
$302$			4.53529i			0.260977i
$303$	10.1239	+	10.1239i	0.581602	+	0.581602i
$304$	−3.00837	−	3.00837i	−0.172542	−	0.172542i
$305$	10.9034	+	10.4407i	0.624329	+	0.597835i
$306$	−4.54367			−0.259744
$307$	1.93471	+	1.93471i	0.110420	+	0.110420i	0.760158	−	0.649738i	$-0.225121\pi$
$307$	1.93471	+	1.93471i	0.110420	+	0.110420i	−0.649738	+	0.760158i	$0.725121\pi$
$308$	−7.61083	−	7.61083i	−0.433667	−	0.433667i
$309$	−5.94723	−	5.94723i	−0.338326	−	0.338326i
$310$	−1.01475	−	0.971689i	−0.0576339	−	0.0551882i
$311$	−24.0063	−	24.0063i	−1.36127	−	1.36127i	−0.872298	−	0.488974i	$-0.837371\pi$
$311$	−24.0063	−	24.0063i	−1.36127	−	1.36127i	−0.488974	−	0.872298i	$-0.662629\pi$
$312$	−1.48338	+	1.48338i	−0.0839797	+	0.0839797i
$313$	28.6636			1.62016			0.810080	−	0.586319i	$-0.199424\pi$
$313$	28.6636			1.62016			0.810080	+	0.586319i	$0.199424\pi$
$314$	2.15926	−	2.15926i	0.121854	−	0.121854i
$315$	6.34253	+	6.07338i	0.357361	+	0.342196i
$316$	−4.84570	−	4.84570i	−0.272592	−	0.272592i
$317$	−14.0253	−	14.0253i	−0.787739	−	0.787739i	0.193384	−	0.981123i	$-0.438054\pi$
$317$	−14.0253	−	14.0253i	−0.787739	−	0.787739i	−0.981123	+	0.193384i	$0.938054\pi$
$318$	−5.80916			−0.325761
$319$	9.36777	+	9.36777i	0.524495	+	0.524495i
$320$	−2.23554	+	0.0484605i	−0.124971	+	0.00270902i
$321$			6.90462i			0.385378i
$322$	3.03539	−	3.03539i	0.169156	−	0.169156i
$323$	13.6690	−	13.6690i	0.760564	−	0.760564i
$324$	−1.00000			−0.0555556
$325$	−10.4792	+	0.454535i	−0.581282	+	0.0252131i
$326$		−	13.2270i		−	0.732578i
$327$	13.2560			0.733056
$328$		−	3.49239i		−	0.192835i
$329$			23.7756i			1.31079i
$330$	4.42638	+	4.23855i	0.243664	+	0.233324i
$331$	−5.28358	+	5.28358i	−0.290412	+	0.290412i	−0.837243	−	0.546831i	$-0.815834\pi$
$331$	−5.28358	+	5.28358i	−0.290412	+	0.290412i	0.546831	+	0.837243i	$0.315834\pi$
$332$	4.09292	+	4.09292i	0.224628	+	0.224628i
$333$	5.20783	−	3.14301i	0.285387	−	0.172236i
$334$		−	2.15667i		−	0.118008i
$335$	7.82357	+	7.49158i	0.427447	+	0.409309i
$336$			3.92718i			0.214245i
$337$	−15.8649	−	15.8649i	−0.864216	−	0.864216i	0.127609	−	0.991825i	$-0.459270\pi$
$337$	−15.8649	−	15.8649i	−0.864216	−	0.864216i	−0.991825	+	0.127609i	$0.959270\pi$
$338$	8.59918			0.467734
$339$	2.89105	+	2.89105i	0.157020	+	0.157020i
$340$	−0.220188	−	10.1576i	−0.0119414	−	0.550871i
$341$	−1.21767	+	1.21767i	−0.0659404	+	0.0659404i
$342$	3.00837	−	3.00837i	0.162674	−	0.162674i
$343$	−3.95079	−	3.95079i	−0.213323	−	0.213323i
$344$	2.64615			0.142671
$345$	−1.69044	+	1.76535i	−0.0910102	+	0.0950433i
$346$	12.7830	−	12.7830i	0.687221	−	0.687221i
$347$	20.2697			1.08814			0.544068	−	0.839041i	$-0.316884\pi$
$347$	20.2697			1.08814			0.544068	+	0.839041i	$0.316884\pi$
$348$		−	4.83375i		−	0.259116i
$349$			23.3133i			1.24793i	0.781452	+	0.623965i	$0.214479\pi$
$349$			23.3133i			1.24793i	−0.781452	+	0.623965i	$0.785521\pi$
$350$	−13.2699	+	14.4733i	−0.709308	+	0.773631i
$351$	−1.48338	−	1.48338i	−0.0791768	−	0.0791768i
$352$			2.74073i			0.146082i
$353$			35.1904i			1.87300i	0.350671	+	0.936499i	$0.385953\pi$
$353$			35.1904i			1.87300i	−0.350671	+	0.936499i	$0.614047\pi$
$354$	−14.3089			−0.760507
$355$	−1.14644	+	0.0248517i	−0.0608468	+	0.00131899i
$356$	−9.59900	+	9.59900i	−0.508746	+	0.508746i
$357$	−17.8438			−0.944393
$358$	−8.92829	+	8.92829i	−0.471875	+	0.471875i
$359$		−	34.3706i		−	1.81401i	−0.421118	−	0.907006i	$-0.638362\pi$
$359$		−	34.3706i		−	1.81401i	0.421118	−	0.907006i	$-0.361638\pi$
$360$	−0.0484605	−	2.23554i	−0.00255409	−	0.117823i
$361$		−	0.899470i		−	0.0473405i
$362$	−8.76543			−0.460701
$363$	−2.46666	+	2.46666i	−0.129466	+	0.129466i
$364$	−5.82548	+	5.82548i	−0.305338	+	0.305338i
$365$	20.9323	−	21.8600i	1.09565	−	1.14420i
$366$	−6.75121			−0.352891
$367$	−15.7170	+	15.7170i	−0.820421	+	0.820421i	−0.986168	−	0.165747i	$-0.946996\pi$
$367$	−15.7170	+	15.7170i	−0.820421	+	0.820421i	0.165747	+	0.986168i	$0.446996\pi$
$368$	−1.09307			−0.0569804
$369$	3.49239			0.181807
$370$	7.27871	+	11.4900i	0.378402	+	0.597337i
$371$	−22.8136			−1.18442
$372$	0.628315			0.0325766
$373$	5.59113	−	5.59113i	0.289498	−	0.289498i	−0.547384	−	0.836882i	$-0.684376\pi$
$373$	5.59113	−	5.59113i	0.289498	−	0.289498i	0.836882	+	0.547384i	$0.184376\pi$
$374$	−12.4530			−0.643928
$375$	7.37531	−	8.40267i	0.380859	−	0.433912i
$376$	4.28090	−	4.28090i	0.220771	−	0.220771i
$377$	7.17028	−	7.17028i	0.369288	−	0.369288i
$378$	−3.92718			−0.201992
$379$			20.7595i			1.06634i	0.846007	+	0.533171i	$0.179000\pi$
$379$			20.7595i			1.06634i	−0.846007	+	0.533171i	$0.821000\pi$
$380$	6.87112	+	6.57954i	0.352481	+	0.337523i
$381$		−	12.3216i		−	0.631257i
$382$	−3.29001	+	3.29001i	−0.168331	+	0.168331i
$383$	19.9351			1.01863			0.509317	−	0.860579i	$-0.329898\pi$
$383$	19.9351			1.01863			0.509317	+	0.860579i	$0.329898\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	17.3832	+	16.6455i	0.885928	+	0.848334i
$386$	19.3985			0.987358
$387$			2.64615i			0.134511i
$388$			5.08514i			0.258159i
$389$	2.00735	+	2.00735i	0.101777	+	0.101777i	0.756162	−	0.654385i	$-0.227072\pi$
$389$	2.00735	+	2.00735i	0.101777	+	0.101777i	−0.654385	+	0.756162i	$0.727072\pi$
$390$	3.24427	−	3.38804i	0.164280	−	0.171560i
$391$		−	4.96656i		−	0.251170i
$392$			8.42272i			0.425412i
$393$	21.2777			1.07332
$394$	12.6528	−	12.6528i	0.637440	−	0.637440i
$395$	11.0676	+	10.5979i	0.556871	+	0.533240i
$396$	−2.74073			−0.137727
$397$	−21.4010	−	21.4010i	−1.07408	−	1.07408i	−0.997027	−	0.0770566i	$-0.975448\pi$
$397$	−21.4010	−	21.4010i	−1.07408	−	1.07408i	−0.0770566	−	0.997027i	$-0.524552\pi$
$398$	−3.25794	+	3.25794i	−0.163306	+	0.163306i
$399$	11.8144	−	11.8144i	0.591459	−	0.591459i
$400$	4.99530	−	0.216671i	0.249765	−	0.0108336i
$401$	18.1649	+	18.1649i	0.907111	+	0.907111i	0.996038	−	0.0889270i	$-0.0283438\pi$
$401$	18.1649	+	18.1649i	0.907111	+	0.907111i	−0.0889270	+	0.996038i	$0.528344\pi$
$402$	−4.84421			−0.241607
$403$	0.932028	+	0.932028i	0.0464276	+	0.0464276i
$404$		−	14.3173i		−	0.712314i
$405$	2.23554	−	0.0484605i	0.111085	−	0.00240802i
$406$		−	18.9830i		−	0.942111i
$407$	14.2733	−	8.61416i	0.707499	−	0.426988i
$408$	3.21286	+	3.21286i	0.159060	+	0.159060i
$409$	−20.7880	+	20.7880i	−1.02790	+	1.02790i	−0.0283030	+	0.999599i	$0.509010\pi$
$409$	−20.7880	+	20.7880i	−1.02790	+	1.02790i	−0.999599	+	0.0283030i	$0.990990\pi$
$410$	0.169243	+	7.80739i	0.00835832	+	0.385580i
$411$			10.6258i			0.524132i
$412$			8.41065i			0.414363i
$413$	−56.1934			−2.76510
$414$		−	1.09307i		−	0.0537216i
$415$	−9.34824	−	8.95155i	−0.458887	−	0.439414i
$416$	2.09781			0.102854
$417$	−5.36189	+	5.36189i	−0.262573	+	0.262573i
$418$	8.24513	−	8.24513i	0.403282	−	0.403282i
$419$			6.01083i			0.293648i	0.989163	+	0.146824i	$0.0469051\pi$
$419$			6.01083i			0.293648i	−0.989163	+	0.146824i	$0.953095\pi$
$420$	−0.190313	−	8.77937i	−0.00928632	−	0.428389i
$421$	−14.1798	−	14.1798i	−0.691081	−	0.691081i	0.271389	−	0.962470i	$-0.412517\pi$
$421$	−14.1798	−	14.1798i	−0.691081	−	0.691081i	−0.962470	+	0.271389i	$0.912517\pi$
$422$	1.48256			0.0721700
$423$	4.28090	+	4.28090i	0.208145	+	0.208145i
$424$	4.10770	+	4.10770i	0.199487	+	0.199487i
$425$	0.984481	+	22.6970i	0.0477543	+	1.10097i
$426$	0.362622	−	0.362622i	0.0175691	−	0.0175691i
$427$	−26.5132			−1.28306
$428$	4.88230	−	4.88230i	0.235995	−	0.235995i
$429$	−4.06554	−	4.06554i	−0.196286	−	0.196286i
$430$	−5.91557	+	0.128234i	−0.285274	+	0.00618397i
$431$	19.4897	+	19.4897i	0.938784	+	0.938784i	0.998231	−	0.0594472i	$-0.0189338\pi$
$431$	19.4897	+	19.4897i	0.938784	+	0.938784i	−0.0594472	+	0.998231i	$0.518934\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−27.2929	−	27.2929i	−1.31161	−	1.31161i	−0.920226	−	0.391387i	$-0.871995\pi$
$433$	−27.2929	−	27.2929i	−1.31161	−	1.31161i	−0.391387	−	0.920226i	$-0.628005\pi$
$434$	2.46750			0.118444
$435$	0.234246	+	10.8061i	0.0112312	+	0.518111i
$436$	−9.37338	−	9.37338i	−0.448903	−	0.448903i
$437$	3.28837	+	3.28837i	0.157304	+	0.157304i
$438$			13.5353i			0.646742i
$439$	−27.9211	+	27.9211i	−1.33260	+	1.33260i	−0.429564	+	0.903036i	$0.641333\pi$
$439$	−27.9211	+	27.9211i	−1.33260	+	1.33260i	−0.903036	+	0.429564i	$0.858667\pi$
$440$	−0.132817	−	6.12703i	−0.00633182	−	0.292094i
$441$	−8.42272			−0.401082
$442$			9.53176i			0.453380i
$443$	13.8772	−	13.8772i	0.659326	−	0.659326i	−0.295894	−	0.955221i	$-0.595618\pi$
$443$	13.8772	−	13.8772i	0.659326	−	0.659326i	0.955221	+	0.295894i	$0.0956176\pi$
$444$	−5.90494	−	1.46004i	−0.280236	−	0.0692907i
$445$	20.9938	−	21.9241i	0.995202	−	1.03930i
$446$	−6.90996	−	6.90996i	−0.327196	−	0.327196i
$447$	−13.1111	−	13.1111i	−0.620132	−	0.620132i
$448$	2.77693	−	2.77693i	0.131198	−	0.131198i
$449$	−4.29038	−	4.29038i	−0.202475	−	0.202475i	0.598584	−	0.801060i	$-0.295730\pi$
$449$	−4.29038	−	4.29038i	−0.202475	−	0.202475i	−0.801060	+	0.598584i	$0.795730\pi$
$450$	0.216671	+	4.99530i	0.0102140	+	0.235481i
$451$	9.57172			0.450715
$452$		−	4.08857i		−	0.192310i
$453$	3.20694	+	3.20694i	0.150675	+	0.150675i
$454$		−	0.338896i		−	0.0159052i
$455$	12.7408	−	13.3054i	0.597299	−	0.623768i
$456$	−4.25447			−0.199234
$457$		−	37.1873i		−	1.73955i	−0.493449	−	0.869775i	$-0.664264\pi$
$457$		−	37.1873i		−	1.73955i	0.493449	−	0.869775i	$-0.335736\pi$
$458$		−	6.86738i		−	0.320892i
$459$	−3.21286	+	3.21286i	−0.149963	+	0.149963i
$460$	2.44361	−	0.0529709i	0.113934	−	0.00246978i
$461$	−13.3683	+	13.3683i	−0.622625	+	0.622625i	−0.946202	−	0.323577i	$-0.895115\pi$
$461$	−13.3683	+	13.3683i	−0.622625	+	0.622625i	0.323577	+	0.946202i	$0.395115\pi$
$462$	−10.7633			−0.500756
$463$	−41.3804			−1.92311			−0.961554	−	0.274614i	$-0.911450\pi$
$463$	−41.3804			−1.92311			−0.961554	+	0.274614i	$0.911450\pi$
$464$	−3.41798	+	3.41798i	−0.158676	+	0.158676i
$465$	−1.40462	+	0.0304485i	−0.0651379	+	0.00141201i
$466$	−11.8523	+	11.8523i	−0.549047	+	0.549047i
$467$		−	32.7500i		−	1.51549i	−0.652552	−	0.757744i	$-0.726302\pi$
$467$		−	32.7500i		−	1.51549i	0.652552	−	0.757744i	$-0.273698\pi$
$468$			2.09781i			0.0969714i
$469$	−19.0241			−0.878451
$470$	−9.36269	+	9.77759i	−0.431868	+	0.451007i
$471$		−	3.05366i		−	0.140705i
$472$	10.1179	+	10.1179i	0.465713	+	0.465713i
$473$			7.25238i			0.333465i
$474$	−6.85285			−0.314762
$475$	−15.6795	−	14.3759i	−0.719426	−	0.659610i
$476$	12.6175	+	12.6175i	0.578320	+	0.578320i
$477$	−4.10770	+	4.10770i	−0.188078	+	0.188078i
$478$	−11.8453	−	11.8453i	−0.541790	−	0.541790i
$479$	16.6994	+	16.6994i	0.763017	+	0.763017i	0.976867	−	0.213849i	$-0.0686002\pi$
$479$	16.6994	+	16.6994i	0.763017	+	0.763017i	−0.213849	+	0.976867i	$0.568600\pi$
$480$	−1.54650	+	1.61503i	−0.0705878	+	0.0737159i
$481$	−6.59345	−	10.9250i	−0.300635	−	0.498139i
$482$	1.06176	−	1.06176i	0.0483618	−	0.0483618i
$483$		−	4.29269i		−	0.195324i
$484$	3.48838			0.158563
$485$	−0.246429	−	11.3681i	−0.0111897	−	0.516197i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$		−	0.862986i		−	0.0391056i	−0.999809	−	0.0195528i	$-0.993776\pi$
$487$		−	0.862986i		−	0.0391056i	0.999809	−	0.0195528i	$-0.00622425\pi$
$488$	4.77382	+	4.77382i	0.216101	+	0.216101i
$489$	−9.35293	−	9.35293i	−0.422954	−	0.422954i
$490$	−0.408169	−	18.8293i	−0.0184392	−	0.850623i
$491$	−27.6627			−1.24840			−0.624201	−	0.781264i	$-0.714575\pi$
$491$	−27.6627			−1.24840			−0.624201	+	0.781264i	$0.714575\pi$
$492$	−2.46949	−	2.46949i	−0.111333	−	0.111333i
$493$	−15.5302	−	15.5302i	−0.699443	−	0.699443i
$494$	−6.31099	−	6.31099i	−0.283945	−	0.283945i
$495$	6.12703	−	0.132817i	0.275389	−	0.00596969i
$496$	−0.444286	−	0.444286i	−0.0199490	−	0.0199490i
$497$	1.42408	−	1.42408i	0.0638787	−	0.0638787i
$498$	5.78826			0.259378
$499$	3.33614	−	3.33614i	0.149346	−	0.149346i	−0.628480	−	0.777826i	$-0.716322\pi$
$499$	3.33614	−	3.33614i	0.149346	−	0.149346i	0.777826	+	0.628480i	$0.216322\pi$
$500$	−11.1567	+	0.726452i	−0.498943	+	0.0324879i
$501$	−1.52500	−	1.52500i	−0.0681318	−	0.0681318i
$502$	−10.3290	−	10.3290i	−0.461005	−	0.461005i
$503$	−25.4113			−1.13303			−0.566516	−	0.824050i	$-0.691709\pi$
$503$	−25.4113			−1.13303			−0.566516	+	0.824050i	$0.691709\pi$
$504$	2.77693	+	2.77693i	0.123694	+	0.123694i
$505$	0.693825	+	32.0070i	0.0308748	+	1.42429i
$506$		−	2.99582i		−	0.133181i
$507$	6.08054	−	6.08054i	0.270046	−	0.270046i
$508$	−8.71272	+	8.71272i	−0.386565	+	0.386565i
$509$	−15.9962			−0.709020			−0.354510	−	0.935052i	$-0.615352\pi$
$509$	−15.9962			−0.709020			−0.354510	+	0.935052i	$0.615352\pi$
$510$	−7.33818	−	7.02678i	−0.324940	−	0.311151i
$511$			53.1555i			2.35146i
$512$	−1.00000			−0.0441942
$513$		−	4.25447i		−	0.187840i
$514$			28.1460i			1.24146i
$515$	−0.407584	−	18.8024i	−0.0179603	−	0.828531i
$516$	1.87111	−	1.87111i	0.0823709	−	0.0823709i
$517$	11.7328	+	11.7328i	0.516008	+	0.516008i
$518$	−23.1897	−	5.73385i	−1.01890	−	0.251931i
$519$		−	18.0779i		−	0.793534i
$520$	−4.68975	+	0.101661i	−0.205659	+	0.00445813i
$521$		−	41.9890i		−	1.83957i	−0.392421	−	0.919786i	$-0.628362\pi$
$521$		−	41.9890i		−	1.83957i	0.392421	−	0.919786i	$-0.371638\pi$
$522$	−3.41798	−	3.41798i	−0.149601	−	0.149601i
$523$	−16.7289			−0.731505			−0.365753	−	0.930712i	$-0.619188\pi$
$523$	−16.7289			−0.731505			−0.365753	+	0.930712i	$0.619188\pi$
$524$	−15.0456	−	15.0456i	−0.657269	−	0.657269i
$525$	0.850906	+	19.6174i	0.0371366	+	0.856175i
$526$	1.14169	−	1.14169i	0.0497799	−	0.0497799i
$527$	2.01869	−	2.01869i	0.0879353	−	0.0879353i
$528$	1.93799	+	1.93799i	0.0843402	+	0.0843402i
$529$	−21.8052			−0.948052
$530$	−9.38199	−	8.98387i	−0.407528	−	0.390234i
$531$	−10.1179	+	10.1179i	−0.439079	+	0.439079i
$532$	−16.7081			−0.724386
$533$		−	7.32638i		−	0.317341i
$534$			13.5750i			0.587449i
$535$	−10.6780	+	11.1512i	−0.461650	+	0.482108i
$536$	3.42538	+	3.42538i	0.147954	+	0.147954i
$537$			12.6265i			0.544874i
$538$		−	0.755375i		−	0.0325665i
$539$	−23.0844			−0.994316
$540$	−1.61503	−	1.54650i	−0.0695000	−	0.0665508i
$541$	5.79651	−	5.79651i	0.249212	−	0.249212i	−0.571435	−	0.820647i	$-0.693613\pi$
$541$	5.79651	−	5.79651i	0.249212	−	0.249212i	0.820647	+	0.571435i	$0.193613\pi$
$542$	−13.0803			−0.561848
$543$	−6.19810	+	6.19810i	−0.265986	+	0.265986i
$544$		−	4.54367i		−	0.194808i
$545$	21.4088	+	20.5003i	0.917053	+	0.878138i
$546$			8.23848i			0.352574i
$547$	20.4569			0.874675			0.437337	−	0.899298i	$-0.355922\pi$
$547$	20.4569			0.874675			0.437337	+	0.899298i	$0.355922\pi$
$548$	7.51357	−	7.51357i	0.320964	−	0.320964i
$549$	−4.77382	+	4.77382i	−0.203742	+	0.203742i
$550$	0.593838	+	13.6908i	0.0253213	+	0.583777i
$551$	20.5651			0.876102
$552$	−0.772920	+	0.772920i	−0.0328977	+	0.0328977i
$553$	−26.9124			−1.14443
$554$	−27.8958			−1.18518
$555$	13.2715	+	2.97784i	0.563343	+	0.126402i
$556$	7.58286			0.321585
$557$	5.28270			0.223835			0.111918	−	0.993717i	$-0.464301\pi$
$557$	5.28270			0.223835			0.111918	+	0.993717i	$0.464301\pi$
$558$	0.444286	−	0.444286i	0.0188081	−	0.0188081i
$559$	5.55112			0.234787
$560$	−6.07338	+	6.34253i	−0.256647	+	0.268021i
$561$	−8.80558	+	8.80558i	−0.371772	+	0.371772i
$562$	−3.25168	+	3.25168i	−0.137164	+	0.137164i
$563$	21.9241			0.923990			0.461995	−	0.886882i	$-0.347134\pi$
$563$	21.9241			0.923990			0.461995	+	0.886882i	$0.347134\pi$
$564$		−	6.05411i		−	0.254924i
$565$	0.198134	+	9.14016i	0.00833556	+	0.384530i
$566$			12.8597i			0.540534i
$567$	−2.77693	+	2.77693i	−0.116620	+	0.116620i
$568$	−0.512824			−0.0215176
$569$	13.2365	−	13.2365i	0.554904	−	0.554904i	−0.372948	−	0.927852i	$-0.621653\pi$
$569$	13.2365	−	13.2365i	0.554904	−	0.554904i	0.927852	+	0.372948i	$0.121653\pi$
$570$	9.51105	−	0.206174i	0.398374	−	0.00863567i
$571$	−7.69386			−0.321978			−0.160989	−	0.986956i	$-0.551468\pi$
$571$	−7.69386			−0.321978			−0.160989	+	0.986956i	$0.551468\pi$
$572$			5.74954i			0.240400i
$573$			4.65277i			0.194372i
$574$	−9.69814	−	9.69814i	−0.404793	−	0.404793i
$575$	−5.46023	+	0.236837i	−0.227708	+	0.00987680i
$576$		−	1.00000i		−	0.0416667i
$577$		−	6.45917i		−	0.268899i	−0.990920	−	0.134449i	$-0.957073\pi$
$577$		−	6.45917i		−	0.268899i	0.990920	−	0.134449i	$-0.0429265\pi$
$578$	3.64491			0.151608
$579$	13.7168	−	13.7168i	0.570051	−	0.570051i
$580$	7.47541	−	7.80668i	0.310399	−	0.324155i
$581$	22.7315			0.943062
$582$	3.59574	+	3.59574i	0.149048	+	0.149048i
$583$	−11.2581	+	11.2581i	−0.466263	+	0.466263i
$584$	9.57090	−	9.57090i	0.396047	−	0.396047i
$585$	−0.101661	−	4.68975i	−0.00420317	−	0.193897i
$586$	8.19264	+	8.19264i	0.338435	+	0.338435i
$587$	30.4031			1.25487			0.627435	−	0.778669i	$-0.284105\pi$
$587$	30.4031			1.25487			0.627435	+	0.778669i	$0.284105\pi$
$588$	5.95576	+	5.95576i	0.245611	+	0.245611i
$589$			2.67315i			0.110145i
$590$	−23.1093	−	22.1287i	−0.951394	−	0.911022i
$591$		−	17.8938i		−	0.736052i
$592$	3.14301	+	5.20783i	0.129177	+	0.214040i
$593$	4.55951	+	4.55951i	0.187237	+	0.187237i	0.794500	−	0.607264i	$-0.207733\pi$
$593$	4.55951	+	4.55951i	0.187237	+	0.187237i	−0.607264	+	0.794500i	$0.707733\pi$
$594$	−1.93799	+	1.93799i	−0.0795167	+	0.0795167i
$595$	−28.8183	−	27.5954i	−1.18144	−	1.13130i
$596$			18.5418i			0.759504i
$597$			4.60742i			0.188569i
$598$	−2.29306			−0.0937703
$599$		−	20.9262i		−	0.855023i	−0.904010	−	0.427511i	$-0.859390\pi$
$599$		−	20.9262i		−	0.855023i	0.904010	−	0.427511i	$-0.140610\pi$
$600$	3.37900	−	3.68542i	0.137947	−	0.150457i
$601$	46.3008			1.88865			0.944325	−	0.329013i	$-0.106716\pi$
$601$	46.3008			1.88865			0.944325	+	0.329013i	$0.106716\pi$
$602$	7.34817	−	7.34817i	0.299489	−	0.299489i
$603$	−3.42538	+	3.42538i	−0.139492	+	0.139492i
$604$		−	4.53529i		−	0.184538i
$605$	−7.79843	+	0.169049i	−0.317051	+	0.00687281i
$606$	−10.1239	−	10.1239i	−0.411255	−	0.411255i
$607$	−20.3014			−0.824007			−0.412004	−	0.911182i	$-0.635171\pi$
$607$	−20.3014			−0.824007			−0.412004	+	0.911182i	$0.635171\pi$
$608$	3.00837	+	3.00837i	0.122005	+	0.122005i
$609$	−13.4230	−	13.4230i	−0.543928	−	0.543928i
$610$	−10.9034	−	10.4407i	−0.441467	−	0.422734i
$611$	8.98053	−	8.98053i	0.363313	−	0.363313i
$612$	4.54367			0.183667
$613$	11.6147	−	11.6147i	0.469115	−	0.469115i	−0.432513	−	0.901628i	$-0.642373\pi$
$613$	11.6147	−	11.6147i	0.469115	−	0.469115i	0.901628	+	0.432513i	$0.142373\pi$
$614$	−1.93471	−	1.93471i	−0.0780787	−	0.0780787i
$615$	5.64033	+	5.40099i	0.227440	+	0.217789i
$616$	7.61083	+	7.61083i	0.306649	+	0.306649i
$617$	5.70622	+	5.70622i	0.229724	+	0.229724i	0.812577	−	0.582853i	$-0.198064\pi$
$617$	5.70622	+	5.70622i	0.229724	+	0.229724i	−0.582853	+	0.812577i	$0.698064\pi$
$618$	5.94723	+	5.94723i	0.239233	+	0.239233i
$619$	−10.0488			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$619$	−10.0488			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$620$	1.01475	+	0.971689i	0.0407533	+	0.0390240i
$621$	−0.772920	−	0.772920i	−0.0310162	−	0.0310162i
$622$	24.0063	+	24.0063i	0.962565	+	0.962565i
$623$			53.3116i			2.13588i
$624$	1.48338	−	1.48338i	0.0593826	−	0.0593826i
$625$	24.9061	−	2.16468i	0.996244	−	0.0865870i
$626$	−28.6636			−1.14563
$627$		−	11.6604i		−	0.465670i
$628$	−2.15926	+	2.15926i	−0.0861639	+	0.0861639i
$629$	−23.6626	+	14.2808i	−0.943491	+	0.569413i
$630$	−6.34253	−	6.07338i	−0.252692	−	0.241969i
$631$	14.4480	+	14.4480i	0.575166	+	0.575166i	0.933568	−	0.358402i	$-0.116678\pi$
$631$	14.4480	+	14.4480i	0.575166	+	0.575166i	−0.358402	+	0.933568i	$0.616678\pi$
$632$	4.84570	+	4.84570i	0.192752	+	0.192752i
$633$	1.04833	−	1.04833i	0.0416674	−	0.0416674i
$634$	14.0253	+	14.0253i	0.557016	+	0.557016i
$635$	19.0554	−	19.8999i	0.756192	−	0.789703i
$636$	5.80916			0.230348
$637$			17.6693i			0.700082i
$638$	−9.36777	−	9.36777i	−0.370874	−	0.370874i
$639$		−	0.512824i		−	0.0202870i
$640$	2.23554	−	0.0484605i	0.0883676	−	0.00191557i
$641$	−37.9442			−1.49870			−0.749352	−	0.662171i	$-0.769635\pi$
$641$	−37.9442			−1.49870			−0.749352	+	0.662171i	$0.769635\pi$
$642$		−	6.90462i		−	0.272504i
$643$		−	27.7110i		−	1.09281i	−0.837520	−	0.546407i	$-0.815995\pi$
$643$		−	27.7110i		−	1.09281i	0.837520	−	0.546407i	$-0.184005\pi$
$644$	−3.03539	+	3.03539i	−0.119611	+	0.119611i
$645$	−4.09227	+	4.27362i	−0.161133	+	0.168273i
$646$	−13.6690	+	13.6690i	−0.537800	+	0.537800i
$647$	13.3729			0.525745			0.262872	−	0.964831i	$-0.415330\pi$
$647$	13.3729			0.525745			0.262872	+	0.964831i	$0.415330\pi$
$648$	1.00000			0.0392837
$649$	−27.7304	+	27.7304i	−1.08851	+	1.08851i
$650$	10.4792	−	0.454535i	0.411028	−	0.0178283i
$651$	1.74479	−	1.74479i	0.0683837	−	0.0683837i
$652$			13.2270i			0.518011i
$653$		−	10.9215i		−	0.427391i	−0.976900	−	0.213695i	$-0.931450\pi$
$653$		−	10.9215i		−	0.427391i	0.976900	−	0.213695i	$-0.0685500\pi$
$654$	−13.2560			−0.518349
$655$	34.3642	+	32.9059i	1.34272	+	1.28574i
$656$			3.49239i			0.136355i
$657$	9.57090	+	9.57090i	0.373396	+	0.373396i
$658$		−	23.7756i		−	0.926868i
$659$	29.6060			1.15329			0.576644	−	0.816996i	$-0.304362\pi$
$659$	29.6060			1.15329			0.576644	+	0.816996i	$0.304362\pi$
$660$	−4.42638	−	4.23855i	−0.172297	−	0.164985i
$661$	31.8938	+	31.8938i	1.24053	+	1.24053i	0.959783	+	0.280744i	$0.0905812\pi$
$661$	31.8938	+	31.8938i	1.24053	+	1.24053i	0.280744	+	0.959783i	$0.409419\pi$
$662$	5.28358	−	5.28358i	0.205352	−	0.205352i
$663$	6.73997	+	6.73997i	0.261759	+	0.261759i
$664$	−4.09292	−	4.09292i	−0.158836	−	0.158836i
$665$	37.3516	−	0.809681i	1.44843	−	0.0313981i
$666$	−5.20783	+	3.14301i	−0.201799	+	0.121789i
$667$	3.73610	−	3.73610i	0.144663	−	0.144663i
$668$			2.15667i			0.0834441i
$669$	−9.77217			−0.377814
$670$	−7.82357	−	7.49158i	−0.302251	−	0.289425i
$671$	−13.0838	+	13.0838i	−0.505094	+	0.505094i
$672$		−	3.92718i		−	0.151494i
$673$	20.0029	+	20.0029i	0.771053	+	0.771053i	0.978291	−	0.207237i	$-0.0664472\pi$
$673$	20.0029	+	20.0029i	0.771053	+	0.771053i	−0.207237	+	0.978291i	$0.566447\pi$
$674$	15.8649	+	15.8649i	0.611093	+	0.611093i
$675$	3.68542	+	3.37900i	0.141852	+	0.130058i
$676$	−8.59918			−0.330738
$677$	4.10184	+	4.10184i	0.157646	+	0.157646i	0.781523	−	0.623876i	$-0.214443\pi$
$677$	4.10184	+	4.10184i	0.157646	+	0.157646i	−0.623876	+	0.781523i	$0.714443\pi$
$678$	−2.89105	−	2.89105i	−0.111030	−	0.111030i
$679$	14.1211	+	14.1211i	0.541918	+	0.541918i
$680$	0.220188	+	10.1576i	0.00844384	+	0.389525i
$681$	−0.239636	−	0.239636i	−0.00918287	−	0.00918287i
$682$	1.21767	−	1.21767i	0.0466269	−	0.0466269i
$683$	26.9295			1.03043			0.515215	−	0.857061i	$-0.327712\pi$
$683$	26.9295			1.03043			0.515215	+	0.857061i	$0.327712\pi$
$684$	−3.00837	+	3.00837i	−0.115028	+	0.115028i
$685$	−16.4328	+	17.1610i	−0.627865	+	0.655689i
$686$	3.95079	+	3.95079i	0.150842	+	0.150842i
$687$	−4.85597	−	4.85597i	−0.185267	−	0.185267i
$688$	−2.64615			−0.100883
$689$	8.61717	+	8.61717i	0.328288	+	0.328288i
$690$	1.69044	−	1.76535i	0.0643539	−	0.0672058i
$691$		−	4.39008i		−	0.167007i	−0.996508	−	0.0835033i	$-0.973389\pi$
$691$		−	4.39008i		−	0.167007i	0.996508	−	0.0835033i	$-0.0266109\pi$
$692$	−12.7830	+	12.7830i	−0.485938	+	0.485938i
$693$	−7.61083	+	7.61083i	−0.289112	+	0.289112i
$694$	−20.2697			−0.769428
$695$	−16.9518	+	0.367469i	−0.643019	+	0.0139389i
$696$			4.83375i			0.183223i
$697$	−15.8683			−0.601054
$698$		−	23.3133i		−	0.882420i
$699$			16.7617i			0.633985i
$700$	13.2699	−	14.4733i	0.501557	−	0.547040i
$701$	7.67375	−	7.67375i	0.289834	−	0.289834i	−0.547181	−	0.837014i	$-0.684299\pi$
$701$	7.67375	−	7.67375i	0.289834	−	0.289834i	0.837014	+	0.547181i	$0.184299\pi$
$702$	1.48338	+	1.48338i	0.0559865	+	0.0559865i
$703$	6.21172	−	25.1224i	0.234279	−	0.947509i
$704$		−	2.74073i		−	0.103295i
$705$	0.293385	+	13.5342i	0.0110495	+	0.509728i
$706$		−	35.1904i		−	1.32441i
$707$	−39.7583	−	39.7583i	−1.49526	−	1.49526i
$708$	14.3089			0.537760
$709$	4.72562	+	4.72562i	0.177474	+	0.177474i	0.790254	−	0.612779i	$-0.209949\pi$
$709$	4.72562	+	4.72562i	0.177474	+	0.177474i	−0.612779	+	0.790254i	$0.709949\pi$
$710$	1.14644	−	0.0248517i	0.0430252	−	0.000932669i
$711$	−4.84570	+	4.84570i	−0.181728	+	0.181728i
$712$	9.59900	−	9.59900i	0.359738	−	0.359738i
$713$	0.485637	+	0.485637i	0.0181872	+	0.0181872i
$714$	17.8438			0.667787
$715$	−0.278626	−	12.8533i	−0.0104200	−	0.480688i
$716$	8.92829	−	8.92829i	0.333666	−	0.333666i
$717$	−16.7517			−0.625606
$718$			34.3706i			1.28270i
$719$		−	48.1348i		−	1.79513i	−0.440887	−	0.897563i	$-0.645336\pi$
$719$		−	48.1348i		−	1.79513i	0.440887	−	0.897563i	$-0.354664\pi$
$720$	0.0484605	+	2.23554i	0.00180602	+	0.0833138i
$721$	23.3558	+	23.3558i	0.869816	+	0.869816i
$722$			0.899470i			0.0334748i
$723$		−	1.50155i		−	0.0558433i
$724$	8.76543			0.325765
$725$	−16.3333	+	17.8144i	−0.606603	+	0.661611i
$726$	2.46666	−	2.46666i	0.0915463	−	0.0915463i
$727$	−30.0659			−1.11508			−0.557541	−	0.830150i	$-0.688255\pi$
$727$	−30.0659			−1.11508			−0.557541	+	0.830150i	$0.688255\pi$
$728$	5.82548	−	5.82548i	0.215907	−	0.215907i
$729$			1.00000i			0.0370370i
$730$	−20.9323	+	21.8600i	−0.774741	+	0.809074i
$731$		−	12.0232i		−	0.444694i
$732$	6.75121			0.249532
$733$	−0.507990	+	0.507990i	−0.0187630	+	0.0187630i	−0.716426	−	0.697663i	$-0.754223\pi$
$733$	−0.507990	+	0.507990i	−0.0187630	+	0.0187630i	0.697663	+	0.716426i	$0.254223\pi$
$734$	15.7170	−	15.7170i	0.580125	−	0.580125i
$735$	−13.6030	−	13.0257i	−0.501753	−	0.480462i
$736$	1.09307			0.0402912
$737$	−9.38804	+	9.38804i	−0.345813	+	0.345813i
$738$	−3.49239			−0.128557
$739$	33.1591			1.21978			0.609889	−	0.792487i	$-0.291214\pi$
$739$	33.1591			1.21978			0.609889	+	0.792487i	$0.291214\pi$
$740$	−7.27871	−	11.4900i	−0.267571	−	0.422381i
$741$	−8.92508			−0.327871
$742$	22.8136			0.837513
$743$	7.44969	−	7.44969i	0.273303	−	0.273303i	−0.557126	−	0.830428i	$-0.688096\pi$
$743$	7.44969	−	7.44969i	0.273303	−	0.273303i	0.830428	+	0.557126i	$0.188096\pi$
$744$	−0.628315			−0.0230351
$745$	−0.898547	−	41.4511i	−0.0329202	−	1.51865i
$746$	−5.59113	+	5.59113i	−0.204706	+	0.204706i
$747$	4.09292	−	4.09292i	0.149752	−	0.149752i
$748$	12.4530			0.455326
$749$		−	27.1157i		−	0.990785i
$750$	−7.37531	+	8.40267i	−0.269308	+	0.306822i
$751$		−	40.2247i		−	1.46782i	−0.679246	−	0.733911i	$-0.737693\pi$
$751$		−	40.2247i		−	1.46782i	0.679246	−	0.733911i	$-0.262307\pi$
$752$	−4.28090	+	4.28090i	−0.156108	+	0.156108i
$753$	−14.6074			−0.532323
$754$	−7.17028	+	7.17028i	−0.261126	+	0.261126i
$755$	0.219783	+	10.1388i	0.00799871	+	0.368990i
$756$	3.92718			0.142830
$757$		−	4.85976i		−	0.176631i	−0.996093	−	0.0883156i	$-0.971852\pi$
$757$		−	4.85976i		−	0.176631i	0.996093	−	0.0883156i	$-0.0281484\pi$
$758$		−	20.7595i		−	0.754018i
$759$	−2.11837	−	2.11837i	−0.0768918	−	0.0768918i
$760$	−6.87112	−	6.57954i	−0.249242	−	0.238665i
$761$			10.4339i			0.378230i	0.981955	+	0.189115i	$0.0605618\pi$
$761$			10.4339i			0.378230i	−0.981955	+	0.189115i	$0.939438\pi$
$762$			12.3216i			0.446366i
$763$	−52.0585			−1.88464
$764$	3.29001	−	3.29001i	0.119028	−	0.119028i
$765$	−10.1576	+	0.220188i	−0.367247	+	0.00796093i
$766$	−19.9351			−0.720284
$767$	21.2254	+	21.2254i	0.766406	+	0.766406i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	29.8513	−	29.8513i	1.07647	−	1.07647i	0.0796432	−	0.996823i	$-0.474622\pi$
$769$	29.8513	−	29.8513i	1.07647	−	1.07647i	0.996823	−	0.0796432i	$-0.0253781\pi$
$770$	−17.3832	−	16.6455i	−0.626446	−	0.599863i
$771$	19.9022	+	19.9022i	0.716760	+	0.716760i
$772$	−19.3985			−0.698168
$773$	−31.7498	−	31.7498i	−1.14196	−	1.14196i	−0.988091	−	0.153868i	$-0.950827\pi$
$773$	−31.7498	−	31.7498i	−1.14196	−	1.14196i	−0.153868	−	0.988091i	$-0.549173\pi$
$774$		−	2.64615i		−	0.0951138i
$775$	−2.31561	−	2.12308i	−0.0831790	−	0.0762632i
$776$		−	5.08514i		−	0.182546i
$777$	−20.4521	+	12.3432i	−0.733714	+	0.442809i
$778$	−2.00735	−	2.00735i	−0.0719671	−	0.0719671i
$779$	10.5064	−	10.5064i	0.376431	−	0.376431i
$780$	−3.24427	+	3.38804i	−0.116163	+	0.121311i
$781$		−	1.40551i		−	0.0502933i
$782$			4.96656i			0.177604i
$783$	−4.83375			−0.172744
$784$		−	8.42272i		−	0.300811i
$785$	4.72248	−	4.93176i	0.168553	−	0.176022i
$786$	−21.2777			−0.758949
$787$	−26.3501	+	26.3501i	−0.939280	+	0.939280i	−0.998259	−	0.0589790i	$-0.981215\pi$
$787$	−26.3501	+	26.3501i	−0.939280	+	0.939280i	0.0589790	+	0.998259i	$0.481215\pi$
$788$	−12.6528	+	12.6528i	−0.450738	+	0.450738i
$789$		−	1.61459i		−	0.0574808i
$790$	−11.0676	−	10.5979i	−0.393767	−	0.377058i
$791$	−11.3537	−	11.3537i	−0.403690	−	0.403690i
$792$	2.74073			0.0973877
$793$	10.0146	+	10.0146i	0.355628	+	0.355628i
$794$	21.4010	+	21.4010i	0.759492	+	0.759492i
$795$	−12.9866	+	0.281515i	−0.460588	+	0.00998430i
$796$	3.25794	−	3.25794i	0.115474	−	0.115474i
$797$	−18.4042			−0.651912			−0.325956	−	0.945385i	$-0.605686\pi$
$797$	−18.4042			−0.651912			−0.325956	+	0.945385i	$0.605686\pi$
$798$	−11.8144	+	11.8144i	−0.418225	+	0.418225i
$799$	−19.4510	−	19.4510i	−0.688127	−	0.688127i
$800$	−4.99530	+	0.216671i	−0.176611	+	0.00766048i
$801$	9.59900	+	9.59900i	0.339164	+	0.339164i
$802$	−18.1649	−	18.1649i	−0.641424	−	0.641424i
$803$	26.2313	+	26.2313i	0.925682	+	0.925682i
$804$	4.84421			0.170842
$805$	6.63865	−	6.93285i	0.233982	−	0.244351i
$806$	−0.932028	−	0.932028i	−0.0328293	−	0.0328293i
$807$	−0.534131	−	0.534131i	−0.0188023	−	0.0188023i
$808$			14.3173i			0.503682i
$809$	32.1862	−	32.1862i	1.13161	−	1.13161i	0.141697	−	0.989910i	$-0.454744\pi$
$809$	32.1862	−	32.1862i	1.13161	−	1.13161i	0.989910	−	0.141697i	$-0.0452560\pi$
$810$	−2.23554	+	0.0484605i	−0.0785490	+	0.00170273i
$811$	−39.7904			−1.39723			−0.698616	−	0.715497i	$-0.746200\pi$
$811$	−39.7904			−1.39723			−0.698616	+	0.715497i	$0.746200\pi$
$812$			18.9830i			0.666173i
$813$	−9.24918	+	9.24918i	−0.324383	+	0.324383i
$814$	−14.2733	+	8.61416i	−0.500278	+	0.301926i
$815$	−0.640989	−	29.5696i	−0.0224529	−	1.03578i
$816$	−3.21286	−	3.21286i	−0.112473	−	0.112473i
$817$	7.96058	+	7.96058i	0.278505	+	0.278505i
$818$	20.7880	−	20.7880i	0.726837	−	0.726837i
$819$	5.82548	+	5.82548i	0.203559	+	0.203559i
$820$	−0.169243	−	7.80739i	−0.00591023	−	0.272646i
$821$	−10.6472			−0.371591			−0.185796	−	0.982588i	$-0.559486\pi$
$821$	−10.6472			−0.371591			−0.185796	+	0.982588i	$0.559486\pi$
$822$		−	10.6258i		−	0.370617i
$823$	−23.8488	−	23.8488i	−0.831316	−	0.831316i	0.156381	−	0.987697i	$-0.450017\pi$
$823$	−23.8488	−	23.8488i	−0.831316	−	0.831316i	−0.987697	+	0.156381i	$0.950017\pi$
$824$		−	8.41065i		−	0.292999i
$825$	10.1008	+	9.26094i	0.351663	+	0.322425i
$826$	56.1934			1.95522
$827$		−	9.17793i		−	0.319148i	−0.987186	−	0.159574i	$-0.948988\pi$
$827$		−	9.17793i		−	0.319148i	0.987186	−	0.159574i	$-0.0510120\pi$
$828$			1.09307i			0.0379869i
$829$	38.2927	−	38.2927i	1.32996	−	1.32996i	0.424564	−	0.905398i	$-0.360428\pi$
$829$	38.2927	−	38.2927i	1.32996	−	1.32996i	0.905398	−	0.424564i	$-0.139572\pi$
$830$	9.34824	+	8.95155i	0.324482	+	0.310713i
$831$	−19.7253	+	19.7253i	−0.684263	+	0.684263i
$832$	−2.09781			−0.0727285
$833$	38.2700			1.32598
$834$	5.36189	−	5.36189i	0.185667	−	0.185667i
$835$	−0.104513	−	4.82133i	−0.00361683	−	0.166849i
$836$	−8.24513	+	8.24513i	−0.285164	+	0.285164i
$837$		−	0.628315i		−	0.0217177i
$838$		−	6.01083i		−	0.207641i
$839$	−8.64494			−0.298457			−0.149228	−	0.988803i	$-0.547679\pi$
$839$	−8.64494			−0.298457			−0.149228	+	0.988803i	$0.547679\pi$
$840$	0.190313	+	8.77937i	0.00656642	+	0.302917i
$841$			5.63482i			0.194304i
$842$	14.1798	+	14.1798i	0.488668	+	0.488668i
$843$			4.59858i			0.158383i
$844$	−1.48256			−0.0510319
$845$	19.2238	−	0.416721i	0.661320	−	0.0143356i
$846$	−4.28090	−	4.28090i	−0.147180	−	0.147180i
$847$	9.68701	−	9.68701i	0.332850	−	0.332850i
$848$	−4.10770	−	4.10770i	−0.141059	−	0.141059i
$849$	9.09320	+	9.09320i	0.312078	+	0.312078i
$850$	−0.984481	−	22.6970i	−0.0337674	−	0.778500i
$851$	−3.43554	−	5.69254i	−0.117769	−	0.195138i
$852$	−0.362622	+	0.362622i	−0.0124232	+	0.0124232i
$853$			37.4151i			1.28107i	0.767929	+	0.640535i	$0.221287\pi$
$853$			37.4151i			1.28107i	−0.767929	+	0.640535i	$0.778713\pi$
$854$	26.5132			0.907263
$855$	6.57954	−	6.87112i	0.225016	−	0.234987i
$856$	−4.88230	+	4.88230i	−0.166874	+	0.166874i
$857$		−	37.7547i		−	1.28967i	−0.764320	−	0.644837i	$-0.776925\pi$
$857$		−	37.7547i		−	1.28967i	0.764320	−	0.644837i	$-0.223075\pi$
$858$	4.06554	+	4.06554i	0.138795	+	0.138795i
$859$	9.37733	+	9.37733i	0.319950	+	0.319950i	0.848748	−	0.528798i	$-0.177357\pi$
$859$	9.37733	+	9.37733i	0.319950	+	0.319950i	−0.528798	+	0.848748i	$0.677357\pi$
$860$	5.91557	−	0.128234i	0.201719	−	0.00437273i
$861$	−13.7152			−0.467414
$862$	−19.4897	−	19.4897i	−0.663821	−	0.663821i
$863$	−31.0440	−	31.0440i	−1.05675	−	1.05675i	−0.998290	−	0.0584611i	$-0.981381\pi$
$863$	−31.0440	−	31.0440i	−1.05675	−	1.05675i	−0.0584611	−	0.998290i	$-0.518619\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	27.9576	−	29.1965i	0.950586	−	0.992711i
$866$	27.2929	+	27.2929i	0.927451	+	0.927451i
$867$	2.57734	−	2.57734i	0.0875310	−	0.0875310i
$868$	−2.46750			−0.0837525
$869$	−13.2808	+	13.2808i	−0.450519	+	0.450519i
$870$	−0.234246	−	10.8061i	−0.00794169	−	0.366360i
$871$	7.18580	+	7.18580i	0.243481	+	0.243481i
$872$	9.37338	+	9.37338i	0.317423	+	0.317423i
$873$	5.08514			0.172106
$874$	−3.28837	−	3.28837i	−0.111231	−	0.111231i
$875$	−28.9641	+	32.9988i	−0.979167	+	1.11556i
$876$		−	13.5353i		−	0.457315i
$877$	−13.1731	+	13.1731i	−0.444825	+	0.444825i	−0.893630	−	0.448805i	$-0.851850\pi$
$877$	−13.1731	+	13.1731i	−0.444825	+	0.444825i	0.448805	+	0.893630i	$0.351850\pi$
$878$	27.9211	−	27.9211i	0.942291	−	0.942291i
$879$	11.5861			0.390791
$880$	0.132817	+	6.12703i	0.00447727	+	0.206542i
$881$		−	19.6288i		−	0.661311i	−0.943752	−	0.330655i	$-0.892730\pi$
$881$		−	19.6288i		−	0.661311i	0.943752	−	0.330655i	$-0.107270\pi$
$882$	8.42272			0.283608
$883$			14.8323i			0.499145i	0.968356	+	0.249573i	$0.0802902\pi$
$883$			14.8323i			0.499145i	−0.968356	+	0.249573i	$0.919710\pi$
$884$		−	9.53176i		−	0.320588i
$885$	−31.9881	+	0.693414i	−1.07527	+	0.0233089i
$886$	−13.8772	+	13.8772i	−0.466214	+	0.466214i
$887$	22.6343	+	22.6343i	0.759985	+	0.759985i	0.976319	−	0.216335i	$-0.0694102\pi$
$887$	22.6343	+	22.6343i	0.759985	+	0.759985i	−0.216335	+	0.976319i	$0.569410\pi$
$888$	5.90494	+	1.46004i	0.198157	+	0.0489959i
$889$			48.3893i			1.62292i
$890$	−20.9938	+	21.9241i	−0.703714	+	0.734899i
$891$			2.74073i			0.0918180i
$892$	6.90996	+	6.90996i	0.231363	+	0.231363i
$893$	25.7570			0.861926
$894$	13.1111	+	13.1111i	0.438500	+	0.438500i
$895$	−19.5269	+	20.3922i	−0.652712	+	0.681637i
$896$	−2.77693	+	2.77693i	−0.0927708	+	0.0927708i
$897$	−1.62144	+	1.62144i	−0.0541383	+	0.0541383i
$898$	4.29038	+	4.29038i	0.143172	+	0.143172i
$899$	3.03712			0.101294
$900$	−0.216671	−	4.99530i	−0.00722237	−	0.166510i
$901$	18.6640	−	18.6640i	0.621788	−	0.621788i
$902$	−9.57172			−0.318703
$903$		−	10.3919i		−	0.345820i
$904$			4.08857i			0.135984i
$905$	−19.5955	+	0.424777i	−0.651377	+	0.0141201i
$906$	−3.20694	−	3.20694i	−0.106543	−	0.106543i
$907$			45.0345i			1.49535i	0.664067	+	0.747673i	$0.268829\pi$
$907$			45.0345i			1.49535i	−0.664067	+	0.747673i	$0.731171\pi$
$908$			0.338896i			0.0112467i
$909$	−14.3173			−0.474876
$910$	−12.7408	+	13.3054i	−0.422354	+	0.441071i
$911$	−18.3283	+	18.3283i	−0.607244	+	0.607244i	−0.942225	−	0.334981i	$-0.891270\pi$
$911$	−18.3283	+	18.3283i	−0.607244	+	0.607244i	0.334981	+	0.942225i	$0.391270\pi$
$912$	4.25447			0.140880
$913$	11.2176	−	11.2176i	0.371248	−	0.371248i
$914$			37.1873i			1.23005i
$915$	−15.0926	+	0.327167i	−0.498946	+	0.0108158i
$916$			6.86738i			0.226905i
$917$	−83.5612			−2.75943
$918$	3.21286	−	3.21286i	0.106040	−	0.106040i
$919$	24.5868	−	24.5868i	0.811045	−	0.811045i	−0.173746	−	0.984791i	$-0.555587\pi$
$919$	24.5868	−	24.5868i	0.811045	−	0.811045i	0.984791	+	0.173746i	$0.0555872\pi$
$920$	−2.44361	+	0.0529709i	−0.0805635	+	0.00174640i
$921$	−2.73610			−0.0901575
$922$	13.3683	−	13.3683i	0.440262	−	0.440262i
$923$	−1.07581			−0.0354107
$924$	10.7633			0.354088
$925$	16.8287	+	25.3337i	0.553324	+	0.832966i
$926$	41.3804			1.35984
$927$	8.41065			0.276242
$928$	3.41798	−	3.41798i	0.112201	−	0.112201i
$929$	56.6055			1.85717			0.928583	−	0.371124i	$-0.121028\pi$
$929$	56.6055			1.85717			0.928583	+	0.371124i	$0.121028\pi$
$930$	1.40462	−	0.0304485i	0.0460595	−	0.000998444i
$931$	−25.3386	+	25.3386i	−0.830440	+	0.830440i
$932$	11.8523	−	11.8523i	0.388235	−	0.388235i
$933$	33.9500			1.11147
$934$			32.7500i			1.07161i
$935$	−27.8392	+	0.603478i	−0.910438	+	0.0197358i
$936$		−	2.09781i		−	0.0685691i
$937$	−3.72209	+	3.72209i	−0.121596	+	0.121596i	−0.765286	−	0.643690i	$-0.777402\pi$
$937$	−3.72209	+	3.72209i	−0.121596	+	0.121596i	0.643690	+	0.765286i	$0.277402\pi$
$938$	19.0241			0.621159
$939$	−20.2682	+	20.2682i	−0.661428	+	0.661428i
$940$	9.36269	−	9.77759i	0.305377	−	0.318910i
$941$	−12.1814			−0.397102			−0.198551	−	0.980091i	$-0.563624\pi$
$941$	−12.1814			−0.397102			−0.198551	+	0.980091i	$0.563624\pi$
$942$			3.05366i			0.0994935i
$943$		−	3.81744i		−	0.124313i
$944$	−10.1179	−	10.1179i	−0.329309	−	0.329309i
$945$	−8.77937	+	0.190313i	−0.285593	+	0.00619088i
$946$		−	7.25238i		−	0.235795i
$947$		−	10.2614i		−	0.333450i	−0.986003	−	0.166725i	$-0.946681\pi$
$947$		−	10.2614i		−	0.333450i	0.986003	−	0.166725i	$-0.0533191\pi$
$948$	6.85285			0.222570
$949$	20.0780	−	20.0780i	0.651758	−	0.651758i
$950$	15.6795	+	14.3759i	0.508711	+	0.466415i
$951$	19.8348			0.643186
$952$	−12.6175	−	12.6175i	−0.408934	−	0.408934i
$953$	−21.4108	+	21.4108i	−0.693564	+	0.693564i	−0.963014	−	0.269451i	$-0.913158\pi$
$953$	−21.4108	+	21.4108i	−0.693564	+	0.693564i	0.269451	+	0.963014i	$0.413158\pi$
$954$	4.10770	−	4.10770i	0.132992	−	0.132992i
$955$	−7.19552	+	7.51439i	−0.232841	+	0.243160i
$956$	11.8453	+	11.8453i	0.383104	+	0.383104i
$957$	−13.2480			−0.428248
$958$	−16.6994	−	16.6994i	−0.539535	−	0.539535i
$959$		−	41.7294i		−	1.34751i
$960$	1.54650	−	1.61503i	0.0499131	−	0.0521250i
$961$		−	30.6052i		−	0.987265i
$962$	6.59345	+	10.9250i	0.212581	+	0.352238i
$963$	−4.88230	−	4.88230i	−0.157330	−	0.157330i
$964$	−1.06176	+	1.06176i	−0.0341969	+	0.0341969i
$965$	43.3662	−	0.940061i	1.39601	−	0.0302616i
$966$			4.29269i			0.138115i
$967$		−	4.67326i		−	0.150282i	−0.997173	−	0.0751409i	$-0.976059\pi$
$967$		−	4.67326i		−	0.150282i	0.997173	−	0.0751409i	$-0.0239407\pi$
$968$	−3.48838			−0.112121
$969$			19.3309i			0.620998i
$970$	0.246429	+	11.3681i	0.00791234	+	0.365006i
$971$	−17.6883			−0.567643			−0.283822	−	0.958877i	$-0.591602\pi$
$971$	−17.6883			−0.567643			−0.283822	+	0.958877i	$0.591602\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	21.0571	−	21.0571i	0.675060	−	0.675060i
$974$			0.862986i			0.0276519i
$975$	7.08851	−	7.73132i	0.227014	−	0.247601i
$976$	−4.77382	−	4.77382i	−0.152806	−	0.152806i
$977$	17.8116			0.569845			0.284922	−	0.958551i	$-0.408032\pi$
$977$	17.8116			0.569845			0.284922	+	0.958551i	$0.408032\pi$
$978$	9.35293	+	9.35293i	0.299074	+	0.299074i
$979$	26.3083	+	26.3083i	0.840817	+	0.840817i
$980$	0.408169	+	18.8293i	0.0130385	+	0.601481i
$981$	−9.37338	+	9.37338i	−0.299269	+	0.299269i
$982$	27.6627			0.882754
$983$	12.7706	−	12.7706i	0.407318	−	0.407318i	−0.473484	−	0.880802i	$-0.657004\pi$
$983$	12.7706	−	12.7706i	0.407318	−	0.407318i	0.880802	+	0.473484i	$0.157004\pi$
$984$	2.46949	+	2.46949i	0.0787246	+	0.0787246i
$985$	27.6728	−	28.8991i	0.881727	−	0.920801i
$986$	15.5302	+	15.5302i	0.494581	+	0.494581i
$987$	−16.8119	−	16.8119i	−0.535127	−	0.535127i
$988$	6.31099	+	6.31099i	0.200779	+	0.200779i
$989$	2.89243			0.0919740
$990$	−6.12703	+	0.132817i	−0.194730	+	0.00422121i
$991$	−24.4516	−	24.4516i	−0.776731	−	0.776731i	0.202543	−	0.979273i	$-0.435079\pi$
$991$	−24.4516	−	24.4516i	−0.776731	−	0.776731i	−0.979273	+	0.202543i	$0.935079\pi$
$992$	0.444286	+	0.444286i	0.0141061	+	0.0141061i
$993$		−	7.47211i		−	0.237120i
$994$	−1.42408	+	1.42408i	−0.0451691	+	0.0451691i
$995$	−7.12537	+	7.44114i	−0.225890	+	0.235900i
$996$	−5.78826			−0.183408
$997$			12.2888i			0.389189i	0.980884	+	0.194594i	$0.0623391\pi$
$997$			12.2888i			0.389189i	−0.980884	+	0.194594i	$0.937661\pi$
$998$	−3.33614	+	3.33614i	−0.105604	+	0.105604i
$999$	−1.46004	+	5.90494i	−0.0461938	+	0.186824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.1	yes	36
5.2	odd	4		1110.2.l.a.697.17	yes	36
37.6	odd	4		1110.2.l.a.43.17	✓	36
185.117	even	4	inner	1110.2.o.a.487.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.17	✓	36	37.6	odd	4
1110.2.l.a.697.17	yes	36	5.2	odd	4
1110.2.o.a.253.1	yes	36	1.1	even	1	trivial
1110.2.o.a.487.1	yes	36	185.117	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.23554 + 0.0484605i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.23554 + 0.0484605i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(2.23554 - 0.0484605i) q^{10} -2.74073i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.09781 q^{13} +(-2.77693 + 2.77693i) q^{14} +(1.54650 - 1.61503i) q^{15} +1.00000 q^{16} +4.54367i q^{17} +1.00000i q^{18} +(-3.00837 - 3.00837i) q^{19} +(-2.23554 + 0.0484605i) q^{20} +3.92718i q^{21} +2.74073i q^{22} -1.09307 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.99530 - 0.216671i) q^{25} +2.09781 q^{26} +(0.707107 + 0.707107i) q^{27} +(2.77693 - 2.77693i) q^{28} +(-3.41798 + 3.41798i) q^{29} +(-1.54650 + 1.61503i) q^{30} +(-0.444286 - 0.444286i) q^{31} -1.00000 q^{32} +(1.93799 + 1.93799i) q^{33} -4.54367i q^{34} +(-6.07338 + 6.34253i) q^{35} -1.00000i q^{36} +(3.14301 + 5.20783i) q^{37} +(3.00837 + 3.00837i) q^{38} +(1.48338 - 1.48338i) q^{39} +(2.23554 - 0.0484605i) q^{40} +3.49239i q^{41} -3.92718i q^{42} -2.64615 q^{43} -2.74073i q^{44} +(0.0484605 + 2.23554i) q^{45} +1.09307 q^{46} +(-4.28090 + 4.28090i) q^{47} +(-0.707107 + 0.707107i) q^{48} -8.42272i q^{49} +(-4.99530 + 0.216671i) q^{50} +(-3.21286 - 3.21286i) q^{51} -2.09781 q^{52} +(-4.10770 - 4.10770i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(0.132817 + 6.12703i) q^{55} +(-2.77693 + 2.77693i) q^{56} +4.25447 q^{57} +(3.41798 - 3.41798i) q^{58} +(-10.1179 - 10.1179i) q^{59} +(1.54650 - 1.61503i) q^{60} +(-4.77382 - 4.77382i) q^{61} +(0.444286 + 0.444286i) q^{62} +(-2.77693 - 2.77693i) q^{63} +1.00000 q^{64} +(4.68975 - 0.101661i) q^{65} +(-1.93799 - 1.93799i) q^{66} +(-3.42538 - 3.42538i) q^{67} +4.54367i q^{68} +(0.772920 - 0.772920i) q^{69} +(6.07338 - 6.34253i) q^{70} +0.512824 q^{71} +1.00000i q^{72} +(-9.57090 + 9.57090i) q^{73} +(-3.14301 - 5.20783i) q^{74} +(-3.37900 + 3.68542i) q^{75} +(-3.00837 - 3.00837i) q^{76} +(-7.61083 - 7.61083i) q^{77} +(-1.48338 + 1.48338i) q^{78} +(-4.84570 - 4.84570i) q^{79} +(-2.23554 + 0.0484605i) q^{80} -1.00000 q^{81} -3.49239i q^{82} +(4.09292 + 4.09292i) q^{83} +3.92718i q^{84} +(-0.220188 - 10.1576i) q^{85} +2.64615 q^{86} -4.83375i q^{87} +2.74073i q^{88} +(-9.59900 + 9.59900i) q^{89} +(-0.0484605 - 2.23554i) q^{90} +(-5.82548 + 5.82548i) q^{91} -1.09307 q^{92} +0.628315 q^{93} +(4.28090 - 4.28090i) q^{94} +(6.87112 + 6.57954i) q^{95} +(0.707107 - 0.707107i) q^{96} +5.08514i q^{97} +8.42272i q^{98} -2.74073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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