LMFDB - Embedded newform 930.2.o.d.161.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.7
Character	$\chi$	$=$	930.161
Dual form			930.2.o.d.491.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.761277 - 1.55578i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.55578 - 0.761277i) q^{6} +(-0.777017 - 1.34583i) q^{7} +1.00000i q^{8} +(-1.84092 - 2.36876i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.761277 - 1.55578i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.55578 - 0.761277i) q^{6} +(-0.777017 - 1.34583i) q^{7} +1.00000i q^{8} +(-1.84092 - 2.36876i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.42746 + 2.47243i) q^{11} +(-0.761277 + 1.55578i) q^{12} +(-1.67439 - 0.966709i) q^{13} +(-1.34583 + 0.777017i) q^{14} +(-1.43718 + 0.966709i) q^{15} +1.00000 q^{16} +(-2.05283 - 3.55560i) q^{17} +(-2.36876 + 1.84092i) q^{18} +(2.49986 + 4.32988i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.68535 + 0.184318i) q^{21} +(2.47243 + 1.42746i) q^{22} -8.12291 q^{23} +(1.55578 + 0.761277i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.966709 + 1.67439i) q^{26} +(-5.08672 + 1.06078i) q^{27} +(0.777017 + 1.34583i) q^{28} +1.76088 q^{29} +(0.966709 + 1.43718i) q^{30} +(4.24307 - 3.60505i) q^{31} -1.00000i q^{32} +(2.75988 + 4.10302i) q^{33} +(-3.55560 + 2.05283i) q^{34} +1.55403i q^{35} +(1.84092 + 2.36876i) q^{36} +(-2.22901 + 1.28692i) q^{37} +(4.32988 - 2.49986i) q^{38} +(-2.77866 + 1.86905i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.09028 + 0.629474i) q^{41} +(0.184318 + 2.68535i) q^{42} +(-9.09740 + 5.25239i) q^{43} +(1.42746 - 2.47243i) q^{44} +(0.409900 + 2.97187i) q^{45} +8.12291i q^{46} -4.59744i q^{47} +(0.761277 - 1.55578i) q^{48} +(2.29249 - 3.97071i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-7.09450 + 0.486956i) q^{51} +(1.67439 + 0.966709i) q^{52} +(-5.37194 + 9.30446i) q^{53} +(1.06078 + 5.08672i) q^{54} +(2.47243 - 1.42746i) q^{55} +(1.34583 - 0.777017i) q^{56} +(8.63943 - 0.592997i) q^{57} -1.76088i q^{58} +(11.5208 - 6.65156i) q^{59} +(1.43718 - 0.966709i) q^{60} -4.90931i q^{61} +(-3.60505 - 4.24307i) q^{62} +(-1.75753 + 4.31813i) q^{63} -1.00000 q^{64} +(0.966709 + 1.67439i) q^{65} +(4.10302 - 2.75988i) q^{66} +(0.173499 - 0.300508i) q^{67} +(2.05283 + 3.55560i) q^{68} +(-6.18378 + 12.6375i) q^{69} +1.55403 q^{70} +(-0.0462057 - 0.0266769i) q^{71} +(2.36876 - 1.84092i) q^{72} +(-14.2146 - 8.20680i) q^{73} +(1.28692 + 2.22901i) q^{74} +(1.72799 - 0.118606i) q^{75} +(-2.49986 - 4.32988i) q^{76} +4.43665 q^{77} +(1.86905 + 2.77866i) q^{78} +(-0.174148 + 0.100545i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-2.22206 + 8.72138i) q^{81} +(0.629474 - 1.09028i) q^{82} +(1.60107 - 2.77314i) q^{83} +(2.68535 - 0.184318i) q^{84} +4.10565i q^{85} +(5.25239 + 9.09740i) q^{86} +(1.34052 - 2.73955i) q^{87} +(-2.47243 - 1.42746i) q^{88} -9.22283 q^{89} +(2.97187 - 0.409900i) q^{90} +3.00460i q^{91} +8.12291 q^{92} +(-2.37852 - 9.34573i) q^{93} -4.59744 q^{94} -4.99971i q^{95} +(-1.55578 - 0.761277i) q^{96} +0.201471 q^{97} +(-3.97071 - 2.29249i) q^{98} +(8.48444 - 1.17023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	$ 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.761277	−	1.55578i	0.439523	−	0.898231i
$3$	0.761277	−	1.55578i	0.439523	−	0.898231i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.55578	−	0.761277i	−0.635145	−	0.310790i
$7$	−0.777017	−	1.34583i	−0.293685	−	0.508677i	0.680993	−	0.732290i	$-0.261548\pi$
$7$	−0.777017	−	1.34583i	−0.293685	−	0.508677i	−0.974678	+	0.223613i	$0.928215\pi$
$8$			1.00000i			0.353553i
$9$	−1.84092	−	2.36876i	−0.613639	−	0.789587i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.42746	+	2.47243i	−0.430396	+	0.745467i	−0.996907	−	0.0785866i	$-0.974959\pi$
$11$	−1.42746	+	2.47243i	−0.430396	+	0.745467i	0.566512	+	0.824054i	$0.308293\pi$
$12$	−0.761277	+	1.55578i	−0.219762	+	0.449116i
$13$	−1.67439	−	0.966709i	−0.464392	−	0.268117i	0.249497	−	0.968375i	$-0.419735\pi$
$13$	−1.67439	−	0.966709i	−0.464392	−	0.268117i	−0.713889	+	0.700259i	$0.753068\pi$
$14$	−1.34583	+	0.777017i	−0.359689	+	0.207667i
$15$	−1.43718	+	0.966709i	−0.371077	+	0.249603i
$16$	1.00000			0.250000
$17$	−2.05283	−	3.55560i	−0.497883	−	0.862359i	0.502114	−	0.864802i	$-0.332556\pi$
$17$	−2.05283	−	3.55560i	−0.497883	−	0.862359i	−0.999997	+	0.00244248i	$0.999223\pi$
$18$	−2.36876	+	1.84092i	−0.558322	+	0.433908i
$19$	2.49986	+	4.32988i	0.573506	+	0.993342i	0.996202	+	0.0870705i	$0.0277505\pi$
$19$	2.49986	+	4.32988i	0.573506	+	0.993342i	−0.422696	+	0.906272i	$0.638916\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−2.68535	+	0.184318i	−0.585991	+	0.0402215i
$22$	2.47243	+	1.42746i	0.527125	+	0.304336i
$23$	−8.12291			−1.69374			−0.846871	−	0.531798i	$-0.821517\pi$
$23$	−8.12291			−1.69374			−0.846871	+	0.531798i	$0.821517\pi$
$24$	1.55578	+	0.761277i	0.317573	+	0.155395i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.966709	+	1.67439i	−0.189587	+	0.328375i
$27$	−5.08672	+	1.06078i	−0.978940	+	0.204148i
$28$	0.777017	+	1.34583i	0.146842	+	0.254338i
$29$	1.76088			0.326988			0.163494	−	0.986544i	$-0.447724\pi$
$29$	1.76088			0.326988			0.163494	+	0.986544i	$0.447724\pi$
$30$	0.966709	+	1.43718i	0.176496	+	0.262391i
$31$	4.24307	−	3.60505i	0.762078	−	0.647486i
$31$	4.24307	−	3.60505i	0.762078	−	0.647486i
$32$		−	1.00000i		−	0.176777i
$33$	2.75988	+	4.10302i	0.480433	+	0.714245i
$34$	−3.55560	+	2.05283i	−0.609780	+	0.352057i
$35$			1.55403i			0.262680i
$36$	1.84092	+	2.36876i	0.306819	+	0.394793i
$37$	−2.22901	+	1.28692i	−0.366446	+	0.211568i	−0.671905	−	0.740637i	$-0.734524\pi$
$37$	−2.22901	+	1.28692i	−0.366446	+	0.211568i	0.305458	+	0.952205i	$0.401190\pi$
$38$	4.32988	−	2.49986i	0.702399	−	0.405530i
$39$	−2.77866	+	1.86905i	−0.444942	+	0.299288i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.09028	+	0.629474i	0.170273	+	0.0983074i	0.582715	−	0.812677i	$-0.301990\pi$
$41$	1.09028	+	0.629474i	0.170273	+	0.0983074i	−0.412441	+	0.910984i	$0.635324\pi$
$42$	0.184318	+	2.68535i	0.0284409	+	0.414358i
$43$	−9.09740	+	5.25239i	−1.38734	+	0.800982i	−0.993015	−	0.117989i	$-0.962355\pi$
$43$	−9.09740	+	5.25239i	−1.38734	+	0.800982i	−0.394326	+	0.918971i	$0.629022\pi$
$44$	1.42746	−	2.47243i	0.215198	−	0.372734i
$45$	0.409900	+	2.97187i	0.0611042	+	0.443019i
$46$			8.12291i			1.19766i
$47$		−	4.59744i		−	0.670606i	−0.942110	−	0.335303i	$-0.891161\pi$
$47$		−	4.59744i		−	0.670606i	0.942110	−	0.335303i	$-0.108839\pi$
$48$	0.761277	−	1.55578i	0.109881	−	0.224558i
$49$	2.29249	−	3.97071i	0.327498	−	0.567244i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	−7.09450	+	0.486956i	−0.993429	+	0.0681875i
$52$	1.67439	+	0.966709i	0.232196	+	0.134058i
$53$	−5.37194	+	9.30446i	−0.737892	+	1.27807i	0.215551	+	0.976493i	$0.430845\pi$
$53$	−5.37194	+	9.30446i	−0.737892	+	1.27807i	−0.953443	+	0.301574i	$0.902488\pi$
$54$	1.06078	+	5.08672i	0.144354	+	0.692215i
$55$	2.47243	−	1.42746i	0.333383	−	0.192479i
$56$	1.34583	−	0.777017i	0.179844	−	0.103833i
$57$	8.63943	−	0.592997i	1.14432	−	0.0785444i
$58$		−	1.76088i		−	0.231215i
$59$	11.5208	−	6.65156i	1.49989	−	0.865960i	0.499886	−	0.866091i	$-0.333375\pi$
$59$	11.5208	−	6.65156i	1.49989	−	0.865960i	1.00000		0.000131339i	$4.18066e-5\pi$
$60$	1.43718	−	0.966709i	0.185539	−	0.124802i
$61$		−	4.90931i		−	0.628572i	−0.949328	−	0.314286i	$-0.898235\pi$
$61$		−	4.90931i		−	0.628572i	0.949328	−	0.314286i	$-0.101765\pi$
$62$	−3.60505	−	4.24307i	−0.457841	−	0.538870i
$63$	−1.75753	+	4.31813i	−0.221428	+	0.544034i
$64$	−1.00000			−0.125000
$65$	0.966709	+	1.67439i	0.119905	+	0.207682i
$66$	4.10302	−	2.75988i	0.505047	−	0.339717i
$67$	0.173499	−	0.300508i	0.0211962	−	0.0367129i	−0.855233	−	0.518244i	$-0.826586\pi$
$67$	0.173499	−	0.300508i	0.0211962	−	0.0367129i	0.876429	+	0.481531i	$0.159919\pi$
$68$	2.05283	+	3.55560i	0.248942	+	0.431180i
$69$	−6.18378	+	12.6375i	−0.744439	+	1.52137i
$70$	1.55403			0.185743
$71$	−0.0462057	−	0.0266769i	−0.00548360	−	0.00316596i	0.497256	−	0.867604i	$-0.334341\pi$
$71$	−0.0462057	−	0.0266769i	−0.00548360	−	0.00316596i	−0.502739	+	0.864438i	$0.667674\pi$
$72$	2.36876	−	1.84092i	0.279161	−	0.216954i
$73$	−14.2146	−	8.20680i	−1.66369	−	0.960533i	−0.970929	−	0.239369i	$-0.923060\pi$
$73$	−14.2146	−	8.20680i	−1.66369	−	0.960533i	−0.692764	−	0.721165i	$-0.743607\pi$
$74$	1.28692	+	2.22901i	0.149601	+	0.259117i
$75$	1.72799	−	0.118606i	0.199531	−	0.0136955i
$76$	−2.49986	−	4.32988i	−0.286753	−	0.496671i
$77$	4.43665			0.505603
$78$	1.86905	+	2.77866i	0.211628	+	0.314621i
$79$	−0.174148	+	0.100545i	−0.0195932	+	0.0113121i	−0.509765	−	0.860314i	$-0.670268\pi$
$79$	−0.174148	+	0.100545i	−0.0195932	+	0.0113121i	0.490171	+	0.871626i	$0.336934\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−2.22206	+	8.72138i	−0.246895	+	0.969042i
$82$	0.629474	−	1.09028i	0.0695138	−	0.120401i
$83$	1.60107	−	2.77314i	0.175741	−	0.304392i	−0.764677	−	0.644414i	$-0.777101\pi$
$83$	1.60107	−	2.77314i	0.175741	−	0.304392i	0.940417	+	0.340022i	$0.110435\pi$
$84$	2.68535	−	0.184318i	0.292995	−	0.0201108i
$85$			4.10565i			0.445320i
$86$	5.25239	+	9.09740i	0.566380	+	0.980998i
$87$	1.34052	−	2.73955i	0.143719	−	0.293711i
$88$	−2.47243	−	1.42746i	−0.263562	−	0.152168i
$89$	−9.22283			−0.977618			−0.488809	−	0.872391i	$-0.662569\pi$
$89$	−9.22283			−0.977618			−0.488809	+	0.872391i	$0.662569\pi$
$90$	2.97187	−	0.409900i	0.313262	−	0.0432072i
$91$			3.00460i			0.314967i
$92$	8.12291			0.846871
$93$	−2.37852	−	9.34573i	−0.246641	−	0.969107i
$94$	−4.59744			−0.474190
$95$		−	4.99971i		−	0.512960i
$96$	−1.55578	−	0.761277i	−0.158786	−	0.0776975i
$97$	0.201471			0.0204563			0.0102281	−	0.999948i	$-0.496744\pi$
$97$	0.201471			0.0204563			0.0102281	+	0.999948i	$0.496744\pi$
$98$	−3.97071	−	2.29249i	−0.401102	−	0.231576i
$99$	8.48444	−	1.17023i	0.852719	−	0.117613i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$		−	4.45908i		−	0.443695i	−0.975081	−	0.221847i	$-0.928791\pi$
$101$		−	4.45908i		−	0.443695i	0.975081	−	0.221847i	$-0.0712087\pi$
$102$	0.486956	+	7.09450i	0.0482158	+	0.702460i
$103$	5.66980	−	9.82038i	0.558662	−	0.967631i	−0.438947	−	0.898513i	$-0.644648\pi$
$103$	5.66980	−	9.82038i	0.558662	−	0.967631i	0.997609	−	0.0691178i	$-0.0220184\pi$
$104$	0.966709	−	1.67439i	0.0947936	−	0.164187i
$105$	2.41774	+	1.18305i	0.235947	+	0.115454i
$106$	9.30446	+	5.37194i	0.903730	+	0.521768i
$107$	11.6586	−	6.73110i	1.12708	−	0.650720i	0.183881	−	0.982949i	$-0.441134\pi$
$107$	11.6586	−	6.73110i	1.12708	−	0.650720i	0.943199	+	0.332229i	$0.107801\pi$
$108$	5.08672	−	1.06078i	0.489470	−	0.102074i
$109$	−9.48497			−0.908495			−0.454248	−	0.890875i	$-0.650092\pi$
$109$	−9.48497			−0.908495			−0.454248	+	0.890875i	$0.650092\pi$
$110$	−1.42746	−	2.47243i	−0.136103	−	0.235737i
$111$	0.305273	+	4.44755i	0.0289752	+	0.422143i
$112$	−0.777017	−	1.34583i	−0.0734212	−	0.127169i
$113$	7.84056	+	4.52675i	0.737578	+	0.425841i	0.821188	−	0.570658i	$-0.193312\pi$
$113$	7.84056	+	4.52675i	0.737578	+	0.425841i	−0.0836099	+	0.996499i	$0.526645\pi$
$114$	−0.592997	−	8.63943i	−0.0555393	−	0.809157i
$115$	7.03464	+	4.06145i	0.655984	+	0.378732i
$116$	−1.76088			−0.163494
$117$	0.792507	+	5.74586i	0.0732673	+	0.531204i
$118$	−6.65156	−	11.5208i	−0.612326	−	1.06058i
$119$	−3.19016	+	5.52552i	−0.292441	+	0.506523i
$120$	−0.966709	−	1.43718i	−0.0882480	−	0.131196i
$121$	1.42471	+	2.46767i	0.129519	+	0.224334i
$122$	−4.90931			−0.444468
$123$	1.80933	−	1.21704i	0.163142	−	0.109736i
$124$	−4.24307	+	3.60505i	−0.381039	+	0.323743i
$125$		−	1.00000i		−	0.0894427i
$126$	4.31813	+	1.75753i	0.384690	+	0.156573i
$127$	−0.226364	+	0.130691i	−0.0200865	+	0.0115970i	−0.510010	−	0.860169i	$-0.670358\pi$
$127$	−0.226364	+	0.130691i	−0.0200865	+	0.0115970i	0.489923	+	0.871766i	$0.337025\pi$
$128$			1.00000i			0.0883883i
$129$	1.24593	+	18.1521i	0.109698	+	1.59820i
$130$	1.67439	−	0.966709i	0.146854	−	0.0847860i
$131$	3.35950	−	1.93961i	0.293521	−	0.169464i	−0.346008	−	0.938232i	$-0.612463\pi$
$131$	3.35950	−	1.93961i	0.293521	−	0.169464i	0.639529	+	0.768767i	$0.279130\pi$
$132$	−2.75988	−	4.10302i	−0.240217	−	0.357122i
$133$	3.88486	−	6.72878i	0.336860	−	0.583459i
$134$	−0.300508	−	0.173499i	−0.0259600	−	0.0149880i
$135$	4.93562	+	1.62470i	0.424791	+	0.139832i
$136$	3.55560	−	2.05283i	0.304890	−	0.176028i
$137$	7.75654	−	13.4347i	0.662686	−	1.14781i	−0.317221	−	0.948352i	$-0.602750\pi$
$137$	7.75654	−	13.4347i	0.662686	−	1.14781i	0.979907	−	0.199454i	$-0.0639169\pi$
$138$	12.6375	+	6.18378i	1.07577	+	0.526398i
$139$		−	0.991822i		−	0.0841253i	−0.999115	−	0.0420626i	$-0.986607\pi$
$139$		−	0.991822i		−	0.0841253i	0.999115	−	0.0420626i	$-0.0133929\pi$
$140$		−	1.55403i		−	0.131340i
$141$	−7.15262	−	3.49993i	−0.602359	−	0.294747i
$142$	−0.0266769	+	0.0462057i	−0.00223867	+	0.00387749i
$143$	4.78025	−	2.75988i	0.399744	−	0.230793i
$144$	−1.84092	−	2.36876i	−0.153410	−	0.197397i
$145$	−1.52497	−	0.880441i	−0.126642	−	0.0731167i
$146$	−8.20680	+	14.2146i	−0.679200	+	1.17641i
$147$	−4.43234	−	6.58942i	−0.365573	−	0.543486i
$148$	2.22901	−	1.28692i	0.183223	−	0.105784i
$149$	−18.0377	+	10.4141i	−1.47770	+	0.853153i	−0.999683	−	0.0251943i	$-0.991980\pi$
$149$	−18.0377	+	10.4141i	−1.47770	+	0.853153i	−0.478022	+	0.878348i	$0.658646\pi$
$150$	−0.118606	−	1.72799i	−0.00968416	−	0.141089i
$151$		−	12.0232i		−	0.978430i	−0.872163	−	0.489215i	$-0.837283\pi$
$151$		−	12.0232i		−	0.978430i	0.872163	−	0.489215i	$-0.162717\pi$
$152$	−4.32988	+	2.49986i	−0.351199	+	0.202765i
$153$	−4.64328	+	11.4082i	−0.375387	+	0.922299i
$154$		−	4.43665i		−	0.357515i
$155$	−5.47713	+	1.00053i	−0.439934	+	0.0803643i
$156$	2.77866	−	1.86905i	0.222471	−	0.149644i
$157$	−6.19924			−0.494753			−0.247377	−	0.968919i	$-0.579569\pi$
$157$	−6.19924			−0.494753			−0.247377	+	0.968919i	$0.579569\pi$
$158$	0.100545	+	0.174148i	0.00799889	+	0.0138545i
$159$	10.3862	+	15.4408i	0.823679	+	1.22454i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	6.31163	+	10.9321i	0.497427	+	0.861568i
$162$	8.72138	+	2.22206i	0.685216	+	0.174581i
$163$	−22.6517			−1.77422			−0.887111	−	0.461557i	$-0.847291\pi$
$163$	−22.6517			−1.77422			−0.887111	+	0.461557i	$0.847291\pi$
$164$	−1.09028	−	0.629474i	−0.0851367	−	0.0491537i
$165$	−0.338612	−	4.93326i	−0.0263609	−	0.384054i
$166$	−2.77314	−	1.60107i	−0.215237	−	0.124267i
$167$	−5.27565	−	9.13770i	−0.408242	−	0.707096i	0.586451	−	0.809985i	$-0.300525\pi$
$167$	−5.27565	−	9.13770i	−0.408242	−	0.707096i	−0.994693	+	0.102889i	$0.967191\pi$
$168$	−0.184318	−	2.68535i	−0.0142205	−	0.207179i
$169$	−4.63095	−	8.02104i	−0.356227	−	0.617003i
$170$	4.10565			0.314889
$171$	5.65442	−	13.8925i	0.432404	−	1.06239i
$172$	9.09740	−	5.25239i	0.693671	−	0.400491i
$173$	−19.0199	−	10.9812i	−1.44606	−	0.834882i	−0.447815	−	0.894126i	$-0.647798\pi$
$173$	−19.0199	−	10.9812i	−1.44606	−	0.834882i	−0.998244	+	0.0592440i	$0.981131\pi$
$174$	−2.73955	−	1.34052i	−0.207685	−	0.101624i
$175$	0.777017	−	1.34583i	0.0587370	−	0.101735i
$176$	−1.42746	+	2.47243i	−0.107599	+	0.186367i
$177$	−1.57783	−	22.9876i	−0.118597	−	1.72785i
$178$			9.22283i			0.691280i
$179$	3.53636	+	6.12515i	0.264320	+	0.457815i	0.967385	−	0.253310i	$-0.0815193\pi$
$179$	3.53636	+	6.12515i	0.264320	+	0.457815i	−0.703066	+	0.711125i	$0.748186\pi$
$180$	−0.409900	−	2.97187i	−0.0305521	−	0.221510i
$181$	−4.50052	−	2.59838i	−0.334521	−	0.193136i	0.323325	−	0.946288i	$-0.395199\pi$
$181$	−4.50052	−	2.59838i	−0.334521	−	0.193136i	−0.657847	+	0.753152i	$0.728532\pi$
$182$	3.00460			0.222715
$183$	−7.63781	−	3.73734i	−0.564603	−	0.276272i
$184$		−	8.12291i		−	0.598829i
$185$	2.57384			0.189232
$186$	−9.34573	+	2.37852i	−0.685262	+	0.174401i
$187$	11.7213			0.857147
$188$			4.59744i			0.335303i
$189$	5.38010	+	6.02163i	0.391345	+	0.438009i
$190$	−4.99971			−0.362717
$191$	9.46269	+	5.46329i	0.684696	+	0.395310i	0.801622	−	0.597831i	$-0.203971\pi$
$191$	9.46269	+	5.46329i	0.684696	+	0.395310i	−0.116926	+	0.993141i	$0.537304\pi$
$192$	−0.761277	+	1.55578i	−0.0549404	+	0.112279i
$193$	5.55465	+	9.62093i	0.399832	+	0.692530i	0.993705	−	0.112029i	$-0.0357351\pi$
$193$	5.55465	+	9.62093i	0.399832	+	0.692530i	−0.593873	+	0.804559i	$0.702402\pi$
$194$		−	0.201471i		−	0.0144648i
$195$	3.34092	−	0.229315i	0.239248	−	0.0164216i
$196$	−2.29249	+	3.97071i	−0.163749	+	0.283622i
$197$	13.4055	−	23.2190i	0.955100	−	1.65428i	0.220961	−	0.975283i	$-0.429081\pi$
$197$	13.4055	−	23.2190i	0.955100	−	1.65428i	0.734139	−	0.678999i	$-0.237586\pi$
$198$	−1.17023	−	8.48444i	−0.0831647	−	0.602963i
$199$	−13.3931	−	7.73251i	−0.949412	−	0.548143i	−0.0565139	−	0.998402i	$-0.517999\pi$
$199$	−13.3931	−	7.73251i	−0.949412	−	0.548143i	−0.892898	+	0.450258i	$0.851332\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−0.335445	−	0.498696i	−0.0236605	−	0.0351753i
$202$	−4.45908			−0.313739
$203$	−1.36824	−	2.36985i	−0.0960313	−	0.166331i
$204$	7.09450	−	0.486956i	0.496715	−	0.0340937i
$205$	−0.629474	−	1.09028i	−0.0439644	−	0.0761486i
$206$	−9.82038	−	5.66980i	−0.684218	−	0.395034i
$207$	14.9536	+	19.2412i	1.03935	+	1.33736i
$208$	−1.67439	−	0.966709i	−0.116098	−	0.0670292i
$209$	−14.2738			−0.987339
$210$	1.18305	−	2.41774i	0.0816382	−	0.166840i
$211$	−8.68251	−	15.0385i	−0.597728	−	1.03530i	−0.993156	−	0.116799i	$-0.962737\pi$
$211$	−8.68251	−	15.0385i	−0.597728	−	1.03530i	0.395427	−	0.918497i	$-0.370597\pi$
$212$	5.37194	−	9.30446i	0.368946	−	0.639033i
$213$	−0.0766787	+	0.0515775i	−0.00525394	+	0.00353403i
$214$	−6.73110	−	11.6586i	−0.460128	−	0.796966i
$215$	10.5048			0.716420
$216$	−1.06078	−	5.08672i	−0.0721771	−	0.346108i
$217$	−8.14873	−	2.90928i	−0.553172	−	0.197495i
$218$			9.48497i			0.642403i
$219$	−23.5892	+	15.8672i	−1.59401	+	1.07220i
$220$	−2.47243	+	1.42746i	−0.166692	+	0.0962394i
$221$			7.93794i			0.533963i
$222$	4.44755	−	0.305273i	0.298500	−	0.0204886i
$223$	−6.35351	+	3.66820i	−0.425462	+	0.245641i	−0.697412	−	0.716671i	$-0.745665\pi$
$223$	−6.35351	+	3.66820i	−0.425462	+	0.245641i	0.271949	+	0.962312i	$0.412332\pi$
$224$	−1.34583	+	0.777017i	−0.0899222	+	0.0519166i
$225$	1.13095	−	2.77866i	0.0753966	−	0.185244i
$226$	4.52675	−	7.84056i	0.301115	−	0.521547i
$227$	15.2093	+	8.78108i	1.00948	+	0.582821i	0.911038	−	0.412322i	$-0.135282\pi$
$227$	15.2093	+	8.78108i	1.00948	+	0.582821i	0.0984375	+	0.995143i	$0.468616\pi$
$228$	−8.63943	+	0.592997i	−0.572160	+	0.0392722i
$229$	22.7927	−	13.1594i	1.50618	−	0.869595i	0.506208	−	0.862411i	$-0.331047\pi$
$229$	22.7927	−	13.1594i	1.50618	−	0.869595i	0.999974	−	0.00718379i	$-0.00228669\pi$
$230$	4.06145	−	7.03464i	0.267804	−	0.463851i
$231$	3.37751	−	6.90245i	0.222224	−	0.454148i
$232$			1.76088i			0.115608i
$233$			18.6243i			1.22012i	0.792357	+	0.610058i	$0.208854\pi$
$233$			18.6243i			1.22012i	−0.792357	+	0.610058i	$0.791146\pi$
$234$	5.74586	−	0.792507i	0.375618	−	0.0518078i
$235$	−2.29872	+	3.98150i	−0.149952	+	0.259725i
$236$	−11.5208	+	6.65156i	−0.749943	+	0.432980i
$237$	0.0238504	+	0.347479i	0.00154925	+	0.0225712i
$238$	5.52552	+	3.19016i	0.358166	+	0.206787i
$239$	10.6833	−	18.5040i	0.691046	−	1.19693i	−0.280450	−	0.959869i	$-0.590484\pi$
$239$	10.6833	−	18.5040i	0.691046	−	1.19693i	0.971496	−	0.237058i	$-0.0761831\pi$
$240$	−1.43718	+	0.966709i	−0.0927693	+	0.0624008i
$241$	3.82166	−	2.20644i	0.246175	−	0.142129i	−0.371837	−	0.928298i	$-0.621272\pi$
$241$	3.82166	−	2.20644i	0.246175	−	0.142129i	0.618011	+	0.786169i	$0.287939\pi$
$242$	2.46767	−	1.42471i	0.158628	−	0.0915838i
$243$	11.8770	+	10.0964i	0.761908	+	0.647685i
$244$			4.90931i			0.314286i
$245$	−3.97071	+	2.29249i	−0.253679	+	0.146462i
$246$	−1.21704	−	1.80933i	−0.0775954	−	0.115359i
$247$		−	9.66653i		−	0.615067i
$248$	3.60505	+	4.24307i	0.228921	+	0.269435i
$249$	−3.09554	−	4.60205i	−0.196172	−	0.291643i
$250$	−1.00000			−0.0632456
$251$	5.22640	+	9.05239i	0.329887	+	0.571382i	0.982489	−	0.186319i	$-0.0596559\pi$
$251$	5.22640	+	9.05239i	0.329887	+	0.571382i	−0.652602	+	0.757701i	$0.726323\pi$
$252$	1.75753	−	4.31813i	0.110714	−	0.272017i
$253$	11.5951	−	20.0834i	0.728980	−	1.26263i
$254$	0.130691	+	0.226364i	0.00820029	+	0.0142033i
$255$	6.38750	+	3.12554i	0.400001	+	0.195729i
$256$	1.00000			0.0625000
$257$	−15.7852	−	9.11360i	−0.984655	−	0.568491i	−0.0809827	−	0.996716i	$-0.525806\pi$
$257$	−15.7852	−	9.11360i	−0.984655	−	0.568491i	−0.903672	+	0.428225i	$0.859139\pi$
$258$	18.1521	−	1.24593i	1.13010	−	0.0775684i
$259$	3.46395	+	1.99991i	0.215240	+	0.124269i
$260$	−0.966709	−	1.67439i	−0.0599527	−	0.103841i
$261$	−3.24164	−	4.17111i	−0.200652	−	0.258185i
$262$	−1.93961	−	3.35950i	−0.119829	−	0.207551i
$263$	0.603718			0.0372269			0.0186134	−	0.999827i	$-0.494075\pi$
$263$	0.603718			0.0372269			0.0186134	+	0.999827i	$0.494075\pi$
$264$	−4.10302	+	2.75988i	−0.252524	+	0.169859i
$265$	9.30446	−	5.37194i	0.571569	−	0.329995i
$266$	−6.72878	−	3.88486i	−0.412568	−	0.238196i
$267$	−7.02112	+	14.3487i	−0.429686	+	0.878127i
$268$	−0.173499	+	0.300508i	−0.0105981	+	0.0183565i
$269$	−7.01501	+	12.1504i	−0.427713	+	0.740820i	−0.996669	−	0.0815472i	$-0.974014\pi$
$269$	−7.01501	+	12.1504i	−0.427713	+	0.740820i	0.568957	+	0.822367i	$0.307347\pi$
$270$	1.62470	−	4.93562i	0.0988759	−	0.300372i
$271$		−	6.06840i		−	0.368629i	−0.982867	−	0.184314i	$-0.940994\pi$
$271$		−	6.06840i		−	0.368629i	0.982867	−	0.184314i	$-0.0590065\pi$
$272$	−2.05283	−	3.55560i	−0.124471	−	0.215590i
$273$	4.67450	+	2.28733i	0.282913	+	0.138435i
$274$	−13.4347	−	7.75654i	−0.811621	−	0.468590i
$275$	−2.85492			−0.172158
$276$	6.18378	−	12.6375i	0.372220	−	0.760686i
$277$		−	20.8720i		−	1.25408i	−0.778989	−	0.627038i	$-0.784267\pi$
$277$		−	20.8720i		−	1.25408i	0.778989	−	0.627038i	$-0.215733\pi$
$278$	−0.991822			−0.0594856
$279$	−16.3506	−	3.41423i	−0.978887	−	0.204404i
$280$	−1.55403			−0.0928713
$281$			6.41145i			0.382475i	0.981544	+	0.191237i	$0.0612500\pi$
$281$			6.41145i			0.382475i	−0.981544	+	0.191237i	$0.938750\pi$
$282$	−3.49993	+	7.15262i	−0.208418	+	0.425932i
$283$	25.2624			1.50170			0.750848	−	0.660475i	$-0.229645\pi$
$283$	25.2624			1.50170			0.750848	+	0.660475i	$0.229645\pi$
$284$	0.0462057	+	0.0266769i	0.00274180	+	0.00158298i
$285$	−7.77846	−	3.80616i	−0.460756	−	0.225458i
$286$	−2.75988	−	4.78025i	−0.163195	−	0.282662i
$287$		−	1.95645i		−	0.115486i
$288$	−2.36876	+	1.84092i	−0.139581	+	0.108477i
$289$	0.0718170	−	0.124391i	0.00422453	−	0.00731710i
$290$	−0.880441	+	1.52497i	−0.0517013	+	0.0895493i
$291$	0.153375	−	0.313445i	0.00899101	−	0.0183745i
$292$	14.2146	+	8.20680i	0.831846	+	0.480267i
$293$	24.9316	−	14.3942i	1.45652	−	0.840920i	0.457679	−	0.889118i	$-0.348681\pi$
$293$	24.9316	−	14.3942i	1.45652	−	0.840920i	0.998838	+	0.0481971i	$0.0153476\pi$
$294$	−6.58942	+	4.43234i	−0.384303	+	0.258499i
$295$	−13.3031			−0.774538
$296$	−1.28692	−	2.22901i	−0.0748006	−	0.129558i
$297$	4.63838	−	14.0908i	0.269146	−	0.817632i
$298$	10.4141	+	18.0377i	0.603271	+	1.04490i
$299$	13.6009	+	7.85248i	0.786560	+	0.454121i
$300$	−1.72799	+	0.118606i	−0.0997653	+	0.00684774i
$301$	14.1377	+	8.16239i	0.814882	+	0.470472i
$302$	−12.0232			−0.691855
$303$	−6.93735	−	3.39459i	−0.398540	−	0.195014i
$304$	2.49986	+	4.32988i	0.143377	+	0.248336i
$305$	−2.45465	+	4.25158i	−0.140553	+	0.243445i
$306$	11.4082	+	4.64328i	0.652164	+	0.265439i
$307$	9.34924	+	16.1934i	0.533589	+	0.924204i	0.999230	+	0.0392299i	$0.0124905\pi$
$307$	9.34924	+	16.1934i	0.533589	+	0.924204i	−0.465641	+	0.884974i	$0.654176\pi$
$308$	−4.43665			−0.252801
$309$	−10.9621	−	16.2970i	−0.623611	−	0.927104i
$310$	1.00053	+	5.47713i	0.0568262	+	0.311080i
$311$		−	15.0547i		−	0.853673i	−0.904329	−	0.426837i	$-0.859628\pi$
$311$		−	15.0547i		−	0.853673i	0.904329	−	0.426837i	$-0.140372\pi$
$312$	−1.86905	−	2.77866i	−0.105814	−	0.157311i
$313$	−24.9195	+	14.3873i	−1.40853	+	0.813217i	−0.995247	−	0.0973835i	$-0.968953\pi$
$313$	−24.9195	+	14.3873i	−1.40853	+	0.813217i	−0.413287	+	0.910601i	$0.635619\pi$
$314$			6.19924i			0.349844i
$315$	3.68113	−	2.86085i	0.207408	−	0.161190i
$316$	0.174148	−	0.100545i	0.00979660	−	0.00565607i
$317$	0.603634	−	0.348508i	0.0339035	−	0.0195742i	−0.482952	−	0.875647i	$-0.660436\pi$
$317$	0.603634	−	0.348508i	0.0339035	−	0.0195742i	0.516856	+	0.856072i	$0.327102\pi$
$318$	15.4408	−	10.3862i	0.865879	−	0.582429i
$319$	−2.51359	+	4.35367i	−0.140734	+	0.243759i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−1.59670	−	23.2625i	−0.0891192	−	1.29838i
$322$	10.9321	−	6.31163i	0.609221	−	0.351734i
$323$	10.2635	−	17.7770i	0.571078	−	0.989137i
$324$	2.22206	−	8.72138i	0.123448	−	0.484521i
$325$		−	1.93342i		−	0.107247i
$326$			22.6517i			1.25456i
$327$	−7.22068	+	14.7565i	−0.399305	+	0.816039i
$328$	−0.629474	+	1.09028i	−0.0347569	+	0.0602007i
$329$	−6.18739	+	3.57229i	−0.341122	+	0.196947i
$330$	−4.93326	+	0.338612i	−0.271567	+	0.0186400i
$331$	−8.68768	−	5.01584i	−0.477518	−	0.275695i	0.241863	−	0.970310i	$-0.422241\pi$
$331$	−8.68768	−	5.01584i	−0.477518	−	0.275695i	−0.719382	+	0.694615i	$0.755575\pi$
$332$	−1.60107	+	2.77314i	−0.0878703	+	0.152196i
$333$	7.15182	+	2.91088i	0.391917	+	0.159515i
$334$	−9.13770	+	5.27565i	−0.499993	+	0.288671i
$335$	−0.300508	+	0.173499i	−0.0164185	+	0.00947924i
$336$	−2.68535	+	0.184318i	−0.146498	+	0.0100554i
$337$		−	6.20622i		−	0.338074i	−0.985610	−	0.169037i	$-0.945934\pi$
$337$		−	6.20622i		−	0.338074i	0.985610	−	0.169037i	$-0.0540658\pi$
$338$	−8.02104	+	4.63095i	−0.436287	+	0.251890i
$339$	13.0115	−	8.75210i	0.706686	−	0.475349i
$340$		−	4.10565i		−	0.222660i
$341$	2.85643	+	15.6368i	0.154684	+	0.846779i
$342$	−13.8925	−	5.65442i	−0.751221	−	0.305756i
$343$	−18.0034			−0.972095
$344$	−5.25239	−	9.09740i	−0.283190	−	0.490499i
$345$	11.6740	−	7.85248i	0.628509	−	0.422763i
$346$	−10.9812	+	19.0199i	−0.590351	+	1.02252i
$347$	5.21639	+	9.03505i	0.280031	+	0.485027i	0.971392	−	0.237482i	$-0.0763221\pi$
$347$	5.21639	+	9.03505i	0.280031	+	0.485027i	−0.691361	+	0.722509i	$0.742989\pi$
$348$	−1.34052	+	2.73955i	−0.0718594	+	0.146855i
$349$	−1.70719			−0.0913838			−0.0456919	−	0.998956i	$-0.514549\pi$
$349$	−1.70719			−0.0913838			−0.0456919	+	0.998956i	$0.514549\pi$
$350$	−1.34583	−	0.777017i	−0.0719378	−	0.0415333i
$351$	9.54262	+	3.14122i	0.509347	+	0.167666i
$352$	2.47243	+	1.42746i	0.131781	+	0.0760839i
$353$	9.57522	+	16.5848i	0.509638	+	0.882718i	0.999938	+	0.0111645i	$0.00355385\pi$
$353$	9.57522	+	16.5848i	0.509638	+	0.882718i	−0.490300	+	0.871554i	$0.663113\pi$
$354$	−22.9876	+	1.57783i	−1.22178	+	0.0838609i
$355$	0.0266769	+	0.0462057i	0.00141586	+	0.00245234i
$356$	9.22283			0.488809
$357$	6.16791	+	9.16964i	0.326440	+	0.485309i
$358$	6.12515	−	3.53636i	0.323724	−	0.186902i
$359$	−7.48207	−	4.31978i	−0.394889	−	0.227989i	0.289387	−	0.957212i	$-0.406548\pi$
$359$	−7.48207	−	4.31978i	−0.394889	−	0.227989i	−0.684276	+	0.729223i	$0.739882\pi$
$360$	−2.97187	+	0.409900i	−0.156631	+	0.0216036i
$361$	−2.99856	+	5.19366i	−0.157819	+	0.273350i
$362$	−2.59838	+	4.50052i	−0.136568	+	0.236542i
$363$	4.92376	−	0.337959i	0.258430	−	0.0177383i
$364$		−	3.00460i		−	0.157484i
$365$	8.20680	+	14.2146i	0.429564	+	0.744026i
$366$	−3.73734	+	7.63781i	−0.195354	+	0.399235i
$367$	23.8989	+	13.7980i	1.24751	+	0.720251i	0.970612	−	0.240648i	$-0.0773601\pi$
$367$	23.8989	+	13.7980i	1.24751	+	0.720251i	0.276898	+	0.960899i	$0.410693\pi$
$368$	−8.12291			−0.423436
$369$	−0.516043	−	3.74143i	−0.0268641	−	0.194771i
$370$		−	2.57384i		−	0.133807i
$371$	16.6963			0.866831
$372$	2.37852	+	9.34573i	0.123320	+	0.484553i
$373$	0.897873			0.0464901			0.0232450	−	0.999730i	$-0.492600\pi$
$373$	0.897873			0.0464901			0.0232450	+	0.999730i	$0.492600\pi$
$374$		−	11.7213i		−	0.606095i
$375$	−1.55578	−	0.761277i	−0.0803402	−	0.0393122i
$376$	4.59744			0.237095
$377$	−2.94840	−	1.70226i	−0.151850	−	0.0876709i
$378$	6.02163	−	5.38010i	0.309719	−	0.276723i
$379$	17.1241	+	29.6599i	0.879608	+	1.52353i	0.851771	+	0.523914i	$0.175529\pi$
$379$	17.1241	+	29.6599i	0.879608	+	1.52353i	0.0278370	+	0.999612i	$0.491138\pi$
$380$			4.99971i			0.256480i
$381$	0.0310016	+	0.451664i	0.00158826	+	0.0231395i
$382$	5.46329	−	9.46269i	0.279526	−	0.484153i
$383$	2.51506	−	4.35622i	0.128514	−	0.222592i	−0.794587	−	0.607150i	$-0.792313\pi$
$383$	2.51506	−	4.35622i	0.128514	−	0.222592i	0.923101	+	0.384558i	$0.125646\pi$
$384$	1.55578	+	0.761277i	0.0793932	+	0.0388487i
$385$	−3.84225	−	2.21832i	−0.195819	−	0.113056i
$386$	9.62093	−	5.55465i	0.489692	−	0.282724i
$387$	29.1892	+	11.8804i	1.48377	+	0.603913i
$388$	−0.201471			−0.0102281
$389$	3.61715	+	6.26508i	0.183397	+	0.317652i	0.943035	−	0.332693i	$-0.107957\pi$
$389$	3.61715	+	6.26508i	0.183397	+	0.317652i	−0.759638	+	0.650346i	$0.774624\pi$
$390$	−0.229315	−	3.34092i	−0.0116118	−	0.169174i
$391$	16.6749	+	28.8818i	0.843286	+	1.46061i
$392$	3.97071	+	2.29249i	0.200551	+	0.115788i
$393$	−0.460099	−	6.70323i	−0.0232089	−	0.338133i
$394$	−23.2190	−	13.4055i	−1.16975	−	0.675358i
$395$	0.201089			0.0101179
$396$	−8.48444	+	1.17023i	−0.426359	+	0.0588064i
$397$	1.66235	+	2.87927i	0.0834309	+	0.144507i	0.904722	−	0.426004i	$-0.140079\pi$
$397$	1.66235	+	2.87927i	0.0834309	+	0.144507i	−0.821291	+	0.570510i	$0.806746\pi$
$398$	−7.73251	+	13.3931i	−0.387596	+	0.671336i
$399$	−7.51106	−	11.1665i	−0.376023	−	0.559022i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−14.3510			−0.716655			−0.358327	−	0.933596i	$-0.616653\pi$
$401$	−14.3510			−0.716655			−0.358327	+	0.933596i	$0.616653\pi$
$402$	−0.498696	+	0.335445i	−0.0248727	+	0.0167305i
$403$	−10.5896	+	1.93444i	−0.527504	+	0.0963612i
$404$			4.45908i			0.221847i
$405$	6.28505	−	6.44191i	0.312306	−	0.320101i
$406$	−2.36985	+	1.36824i	−0.117614	+	0.0679044i
$407$		−	7.34810i		−	0.364232i
$408$	−0.486956	−	7.09450i	−0.0241079	−	0.351230i
$409$	−4.25426	+	2.45620i	−0.210360	+	0.121451i	−0.601479	−	0.798889i	$-0.705421\pi$
$409$	−4.25426	+	2.45620i	−0.210360	+	0.121451i	0.391119	+	0.920340i	$0.372088\pi$
$410$	−1.09028	+	0.629474i	−0.0538452	+	0.0310875i
$411$	−14.9966	−	22.2950i	−0.739729	−	1.09973i
$412$	−5.66980	+	9.82038i	−0.279331	+	0.483815i
$413$	−17.9038	−	10.3368i	−0.880988	−	0.508638i
$414$	19.2412	−	14.9536i	0.945654	−	0.734929i
$415$	−2.77314	+	1.60107i	−0.136128	+	0.0785936i
$416$	−0.966709	+	1.67439i	−0.0473968	+	0.0820936i
$417$	−1.54306	−	0.755051i	−0.0755640	−	0.0369750i
$418$			14.2738i			0.698154i
$419$		−	2.63538i		−	0.128747i	−0.997926	−	0.0643734i	$-0.979495\pi$
$419$		−	2.63538i		−	0.128747i	0.997926	−	0.0643734i	$-0.0205049\pi$
$420$	−2.41774	−	1.18305i	−0.117974	−	0.0577269i
$421$	−15.7175	+	27.2236i	−0.766026	+	1.32680i	0.173677	+	0.984803i	$0.444435\pi$
$421$	−15.7175	+	27.2236i	−0.766026	+	1.32680i	−0.939703	+	0.341993i	$0.888898\pi$
$422$	−15.0385	+	8.68251i	−0.732065	+	0.422658i
$423$	−10.8902	+	8.46351i	−0.529502	+	0.411510i
$424$	−9.30446	−	5.37194i	−0.451865	−	0.260884i
$425$	2.05283	−	3.55560i	0.0995767	−	0.172472i
$426$	0.0515775	+	0.0766787i	0.00249894	+	0.00371509i
$427$	−6.60710	+	3.81461i	−0.319740	+	0.184602i
$428$	−11.6586	+	6.73110i	−0.563540	+	0.325360i
$429$	−0.654678	−	9.53805i	−0.0316081	−	0.460502i
$430$		−	10.5048i		−	0.506585i
$431$	−3.70070	+	2.13660i	−0.178257	+	0.102916i	−0.586473	−	0.809969i	$-0.699484\pi$
$431$	−3.70070	+	2.13660i	−0.178257	+	0.102916i	0.408217	+	0.912885i	$0.366151\pi$
$432$	−5.08672	+	1.06078i	−0.244735	+	0.0510369i
$433$			7.77289i			0.373541i	0.982404	+	0.186771i	$0.0598021\pi$
$433$			7.77289i			0.373541i	−0.982404	+	0.186771i	$0.940198\pi$
$434$	−2.90928	+	8.14873i	−0.139650	+	0.391151i
$435$	−2.53070	+	1.70226i	−0.121338	+	0.0816172i
$436$	9.48497			0.454248
$437$	−20.3061	−	35.1712i	−0.971372	−	1.68247i
$438$	15.8672	+	23.5892i	0.758163	+	1.12714i
$439$	−3.32138	+	5.75280i	−0.158521	+	0.274566i	−0.934336	−	0.356395i	$-0.884006\pi$
$439$	−3.32138	+	5.75280i	−0.158521	+	0.274566i	0.775815	+	0.630961i	$0.217339\pi$
$440$	1.42746	+	2.47243i	0.0680515	+	0.117869i
$441$	−13.6259	+	1.87938i	−0.648854	+	0.0894944i
$442$	7.93794			0.377569
$443$	26.5577	+	15.3331i	1.26179	+	0.728496i	0.973421	−	0.229022i	$-0.0735529\pi$
$443$	26.5577	+	15.3331i	1.26179	+	0.728496i	0.288371	+	0.957519i	$0.406886\pi$
$444$	−0.305273	−	4.44755i	−0.0144876	−	0.211071i
$445$	7.98720	+	4.61141i	0.378630	+	0.218602i
$446$	3.66820	+	6.35351i	0.173694	+	0.300847i
$447$	2.47035	+	35.9907i	0.116843	+	1.70230i
$448$	0.777017	+	1.34583i	0.0367106	+	0.0635846i
$449$	−18.1493			−0.856518			−0.428259	−	0.903656i	$-0.640873\pi$
$449$	−18.1493			−0.856518			−0.428259	+	0.903656i	$0.640873\pi$
$450$	−2.77866	−	1.13095i	−0.130987	−	0.0533134i
$451$	−3.11267	+	1.79710i	−0.146570	+	0.0846221i
$452$	−7.84056	−	4.52675i	−0.368789	−	0.212920i
$453$	−18.7054	−	9.15294i	−0.878857	−	0.430043i
$454$	8.78108	−	15.2093i	0.412117	−	0.713807i
$455$	1.50230	−	2.60206i	0.0704288	−	0.121986i
$456$	0.592997	+	8.63943i	0.0277696	+	0.404578i
$457$			37.2797i			1.74387i	0.489621	+	0.871936i	$0.337135\pi$
$457$			37.2797i			1.74387i	−0.489621	+	0.871936i	$0.662865\pi$
$458$	−13.1594	−	22.7927i	−0.614896	−	1.06503i
$459$	14.2139	+	15.9087i	0.663446	+	0.742556i
$460$	−7.03464	−	4.06145i	−0.327992	−	0.189366i
$461$	−11.8080			−0.549954			−0.274977	−	0.961451i	$-0.588670\pi$
$461$	−11.8080			−0.549954			−0.274977	+	0.961451i	$0.588670\pi$
$462$	−6.90245	−	3.37751i	−0.321131	−	0.157136i
$463$			32.6600i			1.51784i	0.651184	+	0.758920i	$0.274273\pi$
$463$			32.6600i			1.51784i	−0.651184	+	0.758920i	$0.725727\pi$
$464$	1.76088			0.0817469
$465$	−2.61301	+	9.28290i	−0.121175	+	0.430484i
$466$	18.6243			0.862753
$467$		−	9.64118i		−	0.446141i	−0.974802	−	0.223070i	$-0.928392\pi$
$467$		−	9.64118i		−	0.446141i	0.974802	−	0.223070i	$-0.0716080\pi$
$468$	−0.792507	−	5.74586i	−0.0366337	−	0.265602i
$469$	−0.539245			−0.0249000
$470$	3.98150	+	2.29872i	0.183653	+	0.106032i
$471$	−4.71934	+	9.64467i	−0.217456	+	0.444403i
$472$	6.65156	+	11.5208i	0.306163	+	0.530290i
$473$		−	29.9903i		−	1.37896i
$474$	0.347479	−	0.0238504i	0.0159602	−	0.00109549i
$475$	−2.49986	+	4.32988i	−0.114701	+	0.198668i
$476$	3.19016	−	5.52552i	0.146221	−	0.253262i
$477$	31.9293	−	4.40391i	1.46194	−	0.201641i
$478$	−18.5040	−	10.6833i	−0.846355	−	0.488643i
$479$	18.8130	−	10.8617i	0.859590	−	0.496284i	−0.00428514	−	0.999991i	$-0.501364\pi$
$479$	18.8130	−	10.8617i	0.859590	−	0.496284i	0.863875	+	0.503706i	$0.168031\pi$
$480$	0.966709	+	1.43718i	0.0441240	+	0.0655978i
$481$	4.97630			0.226900
$482$	−2.20644	−	3.82166i	−0.100500	−	0.174072i
$483$	21.8128	−	1.49720i	0.992518	−	0.0681249i
$484$	−1.42471	−	2.46767i	−0.0647596	−	0.112167i
$485$	−0.174479	−	0.100735i	−0.00792268	−	0.00457416i
$486$	10.0964	−	11.8770i	0.457983	−	0.538750i
$487$	18.4054	+	10.6263i	0.834027	+	0.481526i	0.855229	−	0.518250i	$-0.173416\pi$
$487$	18.4054	+	10.6263i	0.834027	+	0.481526i	−0.0212027	+	0.999775i	$0.506750\pi$
$488$	4.90931			0.222234
$489$	−17.2442	+	35.2412i	−0.779811	+	1.59366i
$490$	2.29249	+	3.97071i	0.103564	+	0.179378i
$491$	4.47943	−	7.75860i	0.202154	−	0.350141i	−0.747068	−	0.664747i	$-0.768539\pi$
$491$	4.47943	−	7.75860i	0.202154	−	0.350141i	0.949222	+	0.314607i	$0.101873\pi$
$492$	−1.80933	+	1.21704i	−0.0815709	+	0.0548682i
$493$	−3.61479	−	6.26099i	−0.162802	−	0.281981i
$494$	−9.66653			−0.434918
$495$	−7.93286	−	3.22877i	−0.356555	−	0.145122i
$496$	4.24307	−	3.60505i	0.190519	−	0.161871i
$497$			0.0829135i			0.00371918i
$498$	−4.60205	+	3.09554i	−0.206223	+	0.138715i
$499$	18.7295	−	10.8135i	0.838449	−	0.484079i	−0.0182876	−	0.999833i	$-0.505821\pi$
$499$	18.7295	−	10.8135i	0.838449	−	0.484079i	0.856737	+	0.515754i	$0.172488\pi$
$500$			1.00000i			0.0447214i
$501$	−18.2325	+	1.25145i	−0.814568	+	0.0559107i
$502$	9.05239	−	5.22640i	0.404028	−	0.233266i
$503$	−2.66578	+	1.53909i	−0.118861	+	0.0686245i	−0.558252	−	0.829672i	$-0.688528\pi$
$503$	−2.66578	+	1.53909i	−0.118861	+	0.0686245i	0.439391	+	0.898296i	$0.355194\pi$
$504$	−4.31813	−	1.75753i	−0.192345	−	0.0782867i
$505$	−2.22954	+	3.86167i	−0.0992131	+	0.171842i
$506$	−20.0834	−	11.5951i	−0.892814	−	0.515466i
$507$	−16.0044	+	1.09852i	−0.710781	+	0.0487869i
$508$	0.226364	−	0.130691i	0.0100433	−	0.00579848i
$509$	−12.3130	+	21.3267i	−0.545762	+	0.945288i	0.452796	+	0.891614i	$0.350427\pi$
$509$	−12.3130	+	21.3267i	−0.545762	+	0.945288i	−0.998559	+	0.0536741i	$0.982907\pi$
$510$	3.12554	−	6.38750i	0.138401	−	0.282843i
$511$			25.5073i			1.12838i
$512$		−	1.00000i		−	0.0441942i
$513$	−17.3091	−	19.3731i	−0.764217	−	0.855342i
$514$	−9.11360	+	15.7852i	−0.401984	+	0.696256i
$515$	−9.82038	+	5.66980i	−0.432738	+	0.249841i
$516$	−1.24593	−	18.1521i	−0.0548491	−	0.799102i
$517$	11.3669	+	6.56267i	0.499915	+	0.288626i
$518$	1.99991	−	3.46395i	0.0878712	−	0.152197i
$519$	−31.5637	+	21.2312i	−1.38549	+	0.931945i
$520$	−1.67439	+	0.966709i	−0.0734268	+	0.0423930i
$521$	−13.5385	+	7.81648i	−0.593134	+	0.342446i	−0.766336	−	0.642440i	$-0.777922\pi$
$521$	−13.5385	+	7.81648i	−0.593134	+	0.342446i	0.173202	+	0.984886i	$0.444589\pi$
$522$	−4.17111	+	3.24164i	−0.182565	+	0.141883i
$523$			14.4895i			0.633582i	0.948495	+	0.316791i	$0.102605\pi$
$523$			14.4895i			0.633582i	−0.948495	+	0.316791i	$0.897395\pi$
$524$	−3.35950	+	1.93961i	−0.146760	+	0.0847322i
$525$	−1.50230	−	2.23342i	−0.0655657	−	0.0974744i
$526$		−	0.603718i		−	0.0263234i
$527$	−21.5284	−	7.68611i	−0.937791	−	0.334812i
$528$	2.75988	+	4.10302i	0.120108	+	0.178561i
$529$	42.9816			1.86876
$530$	−5.37194	−	9.30446i	−0.233342	−	0.404160i
$531$	−36.9649	−	15.0452i	−1.60414	−	0.652904i
$532$	−3.88486	+	6.72878i	−0.168430	+	0.291729i
$533$	−1.21704	−	2.10797i	−0.0527157	−	0.0913063i
$534$	14.3487	+	7.02112i	0.620930	+	0.303834i
$535$	−13.4622			−0.582022
$536$	0.300508	+	0.173499i	0.0129800	+	0.00749399i
$537$	12.2215	−	0.838868i	0.527398	−	0.0361998i
$538$	12.1504	+	7.01501i	0.523839	+	0.302439i
$539$	6.54488	+	11.3361i	0.281908	+	0.488279i
$540$	−4.93562	−	1.62470i	−0.212395	−	0.0699158i
$541$	−8.39607	−	14.5424i	−0.360975	−	0.625228i	0.627146	−	0.778901i	$-0.284223\pi$
$541$	−8.39607	−	14.5424i	−0.360975	−	0.625228i	−0.988122	+	0.153674i	$0.950889\pi$
$542$	−6.06840			−0.260660
$543$	−7.46865	+	5.02375i	−0.320510	+	0.215590i
$544$	−3.55560	+	2.05283i	−0.152445	+	0.0880142i
$545$	8.21422	+	4.74248i	0.351859	+	0.203146i
$546$	2.28733	−	4.67450i	0.0978886	−	0.200050i
$547$	−12.1551	+	21.0532i	−0.519714	+	0.900172i	0.480023	+	0.877256i	$0.340628\pi$
$547$	−12.1551	+	21.0532i	−0.519714	+	0.900172i	−0.999737	+	0.0229158i	$0.992705\pi$
$548$	−7.75654	+	13.4347i	−0.331343	+	0.573903i
$549$	−11.6290	+	9.03762i	−0.496312	+	0.385716i
$550$			2.85492i			0.121734i
$551$	4.40195	+	7.62441i	0.187530	+	0.324811i
$552$	−12.6375	−	6.18378i	−0.537886	−	0.263199i
$553$	0.270632	+	0.156250i	0.0115085	+	0.00664441i
$554$	−20.8720			−0.886765
$555$	1.95940	−	4.00433i	0.0831719	−	0.169974i
$556$			0.991822i			0.0420626i
$557$	6.43986			0.272866			0.136433	−	0.990649i	$-0.456436\pi$
$557$	6.43986			0.272866			0.136433	+	0.990649i	$0.456436\pi$
$558$	−3.41423	+	16.3506i	−0.144536	+	0.692177i
$559$	20.3101			0.859026
$560$			1.55403i			0.0656699i
$561$	8.92316	−	18.2358i	0.376736	−	0.769916i
$562$	6.41145			0.270451
$563$	9.10584	+	5.25726i	0.383765	+	0.221567i	0.679455	−	0.733717i	$-0.262216\pi$
$563$	9.10584	+	5.25726i	0.383765	+	0.221567i	−0.295690	+	0.955284i	$0.595550\pi$
$564$	7.15262	+	3.49993i	0.301180	+	0.147373i
$565$	−4.52675	−	7.84056i	−0.190442	−	0.329855i
$566$		−	25.2624i		−	1.06186i
$567$	13.4641	−	3.78614i	0.565439	−	0.159003i
$568$	0.0266769	−	0.0462057i	0.00111934	−	0.00193875i
$569$	−0.144125	+	0.249631i	−0.00604202	+	0.0104651i	−0.869031	−	0.494758i	$-0.835257\pi$
$569$	−0.144125	+	0.249631i	−0.00604202	+	0.0104651i	0.862989	+	0.505223i	$0.168590\pi$
$570$	−3.80616	+	7.77846i	−0.159423	+	0.325804i
$571$	20.5493	+	11.8641i	0.859961	+	0.496499i	0.863999	−	0.503493i	$-0.167952\pi$
$571$	20.5493	+	11.8641i	0.859961	+	0.496499i	−0.00403816	+	0.999992i	$0.501285\pi$
$572$	−4.78025	+	2.75988i	−0.199872	+	0.115396i
$573$	15.7034	−	10.5628i	0.656019	−	0.441268i
$574$	−1.95645			−0.0816606
$575$	−4.06145	−	7.03464i	−0.169374	−	0.293365i
$576$	1.84092	+	2.36876i	0.0767048	+	0.0986984i
$577$	−4.90598	−	8.49741i	−0.204239	−	0.353752i	0.745651	−	0.666336i	$-0.232139\pi$
$577$	−4.90598	−	8.49741i	−0.204239	−	0.353752i	−0.949890	+	0.312585i	$0.898805\pi$
$578$	−0.124391	−	0.0718170i	−0.00517397	−	0.00298719i
$579$	19.1967	−	1.31763i	0.797787	−	0.0547589i
$580$	1.52497	+	0.880441i	0.0633209	+	0.0365583i
$581$	−4.97624			−0.206449
$582$	−0.313445	−	0.153375i	−0.0129927	−	0.00635760i
$583$	−15.3365	−	26.5635i	−0.635171	−	1.10015i
$584$	8.20680	−	14.2146i	0.339600	−	0.588204i
$585$	2.18660	−	5.37231i	0.0904046	−	0.222118i
$586$	−14.3942	−	24.9316i	−0.594621	−	1.02991i
$587$	8.89476			0.367126			0.183563	−	0.983008i	$-0.441237\pi$
$587$	8.89476			0.367126			0.183563	+	0.983008i	$0.441237\pi$
$588$	4.43234	+	6.58942i	0.182787	+	0.271743i
$589$	26.2165	+	9.35987i	1.08023	+	0.385667i
$590$			13.3031i			0.547681i
$591$	−25.9184	−	38.5320i	−1.06614	−	1.58500i
$592$	−2.22901	+	1.28692i	−0.0916116	+	0.0528920i
$593$			22.2477i			0.913605i	0.889568	+	0.456802i	$0.151005\pi$
$593$			22.2477i			0.913605i	−0.889568	+	0.456802i	$0.848995\pi$
$594$	−14.0908	−	4.63838i	−0.578153	−	0.190315i
$595$	5.52552	−	3.19016i	0.226524	−	0.130784i
$596$	18.0377	−	10.4141i	0.738852	−	0.426577i
$597$	−22.2260	+	14.9502i	−0.909648	+	0.611870i
$598$	7.85248	−	13.6009i	0.321112	−	0.556182i
$599$	29.1896	+	16.8526i	1.19265	+	0.688579i	0.958908	−	0.283718i	$-0.0915680\pi$
$599$	29.1896	+	16.8526i	1.19265	+	0.688579i	0.233747	+	0.972298i	$0.424901\pi$
$600$	0.118606	+	1.72799i	0.00484208	+	0.0705447i
$601$	16.0624	−	9.27365i	0.655200	−	0.378280i	−0.135245	−	0.990812i	$-0.543182\pi$
$601$	16.0624	−	9.27365i	0.655200	−	0.378280i	0.790446	+	0.612532i	$0.209849\pi$
$602$	8.16239	−	14.1377i	0.332674	−	0.576209i
$603$	−1.03123	+	0.142234i	−0.0419949	+	0.00579222i
$604$			12.0232i			0.489215i
$605$		−	2.84942i		−	0.115845i
$606$	−3.39459	+	6.93735i	−0.137896	+	0.281811i
$607$	−24.0780	+	41.7043i	−0.977294	+	1.69272i	−0.305149	+	0.952305i	$0.598706\pi$
$607$	−24.0780	+	41.7043i	−0.977294	+	1.69272i	−0.672146	+	0.740419i	$0.734627\pi$
$608$	4.32988	−	2.49986i	0.175600	−	0.101383i
$609$	−4.72858	+	0.324563i	−0.191612	+	0.0131519i
$610$	4.25158	+	2.45465i	0.172142	+	0.0993860i
$611$	−4.44439	+	7.69790i	−0.179801	+	0.311424i
$612$	4.64328	−	11.4082i	0.187694	−	0.461150i
$613$	12.7085	−	7.33723i	0.513290	−	0.296348i	−0.220895	−	0.975298i	$-0.570898\pi$
$613$	12.7085	−	7.33723i	0.513290	−	0.296348i	0.734185	+	0.678949i	$0.237564\pi$
$614$	16.1934	−	9.34924i	0.653511	−	0.377305i
$615$	−2.17544	+	0.149319i	−0.0877224	+	0.00602113i
$616$			4.43665i			0.178758i
$617$	−3.80291	+	2.19561i	−0.153099	+	0.0883919i	−0.574593	−	0.818440i	$-0.694839\pi$
$617$	−3.80291	+	2.19561i	−0.153099	+	0.0883919i	0.421493	+	0.906832i	$0.361506\pi$
$618$	−16.2970	+	10.9621i	−0.655561	+	0.440960i
$619$			32.1026i			1.29031i	0.764051	+	0.645156i	$0.223207\pi$
$619$			32.1026i			1.29031i	−0.764051	+	0.645156i	$0.776793\pi$
$620$	5.47713	−	1.00053i	0.219967	−	0.0401822i
$621$	41.3190	−	8.61664i	1.65807	−	0.345774i
$622$	−15.0547			−0.603638
$623$	7.16629	+	12.4124i	0.287112	+	0.497292i
$624$	−2.77866	+	1.86905i	−0.111235	+	0.0748219i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.3873	+	24.9195i	0.575032	+	0.995984i
$627$	−10.8663	+	22.2069i	−0.433958	+	0.886858i
$628$	6.19924			0.247377
$629$	9.15152	+	5.28363i	0.364895	+	0.210672i
$630$	−2.86085	−	3.68113i	−0.113979	−	0.146660i
$631$	−15.8729	−	9.16424i	−0.631891	−	0.364823i	0.149593	−	0.988748i	$-0.452204\pi$
$631$	−15.8729	−	9.16424i	−0.631891	−	0.364823i	−0.781484	+	0.623925i	$0.785537\pi$
$632$	−0.100545	−	0.174148i	−0.00399945	−	0.00692724i
$633$	−30.0065	+	2.05960i	−1.19265	+	0.0818617i
$634$	−0.348508	−	0.603634i	−0.0138410	−	0.0239734i
$635$	0.261382			0.0103726
$636$	−10.3862	−	15.4408i	−0.411839	−	0.612269i
$637$	−7.67704	+	4.43234i	−0.304175	+	0.175616i
$638$	4.35367	+	2.51359i	0.172363	+	0.0995141i
$639$	0.0218697	+	0.158560i	0.000865151	+	0.00627254i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−4.23839	+	7.34111i	−0.167406	+	0.289957i	−0.937507	−	0.347966i	$-0.886873\pi$
$641$	−4.23839	+	7.34111i	−0.167406	+	0.289957i	0.770101	+	0.637922i	$0.220206\pi$
$642$	−23.2625	+	1.59670i	−0.918097	+	0.0630168i
$643$		−	31.8317i		−	1.25532i	−0.778487	−	0.627660i	$-0.784013\pi$
$643$		−	31.8317i		−	1.25532i	0.778487	−	0.627660i	$-0.215987\pi$
$644$	−6.31163	−	10.9321i	−0.248713	−	0.430784i
$645$	7.99704	−	16.3431i	0.314883	−	0.643511i
$646$	−17.7770	−	10.2635i	−0.699425	−	0.403813i
$647$	33.3977			1.31300			0.656499	−	0.754327i	$-0.272037\pi$
$647$	33.3977			1.31300			0.656499	+	0.754327i	$0.272037\pi$
$648$	−8.72138	−	2.22206i	−0.342608	−	0.0872906i
$649$			37.9794i			1.49082i
$650$	−1.93342			−0.0758349
$651$	−10.7296	+	10.4629i	−0.420528	+	0.410073i
$652$	22.6517			0.887111
$653$		−	28.5453i		−	1.11706i	−0.829483	−	0.558532i	$-0.811365\pi$
$653$		−	28.5453i		−	1.11706i	0.829483	−	0.558532i	$-0.188635\pi$
$654$	14.7565	+	7.22068i	0.577027	+	0.282351i
$655$	−3.87922			−0.151574
$656$	1.09028	+	0.629474i	0.0425683	+	0.0245768i
$657$	6.72793	+	48.7790i	0.262482	+	1.90305i
$658$	3.57229	+	6.18739i	0.139262	+	0.241210i
$659$		−	33.8844i		−	1.31995i	−0.751288	−	0.659974i	$-0.770567\pi$
$659$		−	33.8844i		−	1.31995i	0.751288	−	0.659974i	$-0.229433\pi$
$660$	0.338612	+	4.93326i	0.0131804	+	0.192027i
$661$	16.8559	−	29.1953i	0.655619	−	1.13557i	−0.326119	−	0.945329i	$-0.605741\pi$
$661$	16.8559	−	29.1953i	0.655619	−	1.13557i	0.981738	−	0.190237i	$-0.0609255\pi$
$662$	−5.01584	+	8.68768i	−0.194946	+	0.337656i
$663$	12.3497	+	6.04296i	0.479623	+	0.234689i
$664$	2.77314	+	1.60107i	0.107619	+	0.0621337i
$665$	−6.72878	+	3.88486i	−0.260931	+	0.150648i
$666$	2.91088	−	7.15182i	0.112794	−	0.277127i
$667$	−14.3035			−0.553833
$668$	5.27565	+	9.13770i	0.204121	+	0.353548i
$669$	0.870143	+	12.6772i	0.0336417	+	0.490128i
$670$	0.173499	+	0.300508i	0.00670283	+	0.0116096i
$671$	12.1379	+	7.00784i	0.468580	+	0.270535i
$672$	0.184318	+	2.68535i	0.00711023	+	0.103590i
$673$	22.3053	+	12.8779i	0.859805	+	0.496408i	0.863947	−	0.503583i	$-0.167985\pi$
$673$	22.3053	+	12.8779i	0.859805	+	0.496408i	−0.00414230	+	0.999991i	$0.501319\pi$
$674$	−6.20622			−0.239055
$675$	−3.46203	−	3.87484i	−0.133253	−	0.149143i
$676$	4.63095	+	8.02104i	0.178113	+	0.308501i
$677$	−11.9502	+	20.6983i	−0.459282	+	0.795499i	−0.998923	−	0.0463959i	$-0.985226\pi$
$677$	−11.9502	+	20.6983i	−0.459282	+	0.795499i	0.539642	+	0.841895i	$0.318560\pi$
$678$	−8.75210	−	13.0115i	−0.336122	−	0.499703i
$679$	−0.156546	−	0.271146i	−0.00600770	−	0.0104056i
$680$	−4.10565			−0.157445
$681$	25.2399	−	16.9775i	0.967196	−	0.650579i
$682$	15.6368	−	2.85643i	0.598763	−	0.109378i
$683$		−	40.5270i		−	1.55072i	−0.631517	−	0.775362i	$-0.717568\pi$
$683$		−	40.5270i		−	1.55072i	0.631517	−	0.775362i	$-0.282432\pi$
$684$	−5.65442	+	13.8925i	−0.216202	+	0.531193i
$685$	−13.4347	+	7.75654i	−0.513314	+	0.296362i
$686$			18.0034i			0.687375i
$687$	−3.12156	−	45.4784i	−0.119095	−	1.73511i
$688$	−9.09740	+	5.25239i	−0.346835	+	0.200245i
$689$	17.9894	−	10.3862i	0.685342	−	0.395682i
$690$	−7.85248	−	11.6740i	−0.298939	−	0.444423i
$691$	15.2363	−	26.3900i	0.579616	−	1.00392i	−0.415907	−	0.909407i	$-0.636536\pi$
$691$	15.2363	−	26.3900i	0.579616	−	1.00392i	0.995523	−	0.0945172i	$-0.0301307\pi$
$692$	19.0199	+	10.9812i	0.723029	+	0.417441i
$693$	−8.16749	−	10.5094i	−0.310257	−	0.399217i
$694$	9.03505	−	5.21639i	0.342966	−	0.198011i
$695$	−0.495911	+	0.858943i	−0.0188110	+	0.0325816i
$696$	2.73955	+	1.34052i	0.103842	+	0.0508122i
$697$		−	5.16880i		−	0.195782i
$698$			1.70719i			0.0646181i
$699$	28.9753	+	14.1782i	1.09595	+	0.536269i
$700$	−0.777017	+	1.34583i	−0.0293685	+	0.0508677i
$701$	−13.3658	+	7.71673i	−0.504818	+	0.291457i	−0.730701	−	0.682698i	$-0.760807\pi$
$701$	−13.3658	+	7.71673i	−0.504818	+	0.291457i	0.225883	+	0.974154i	$0.427473\pi$
$702$	3.14122	−	9.54262i	0.118558	−	0.360163i
$703$	−11.1444	−	6.43422i	−0.420319	−	0.242671i
$704$	1.42746	−	2.47243i	0.0537995	−	0.0931834i
$705$	4.44439	+	6.60733i	0.167385	+	0.248847i
$706$	16.5848	−	9.57522i	0.624176	−	0.360368i
$707$	−6.00117	+	3.46478i	−0.225697	+	0.130306i
$708$	1.57783	+	22.9876i	0.0592986	+	0.863927i
$709$		−	46.2651i		−	1.73752i	−0.495233	−	0.868760i	$-0.664917\pi$
$709$		−	46.2651i		−	1.73752i	0.495233	−	0.868760i	$-0.335083\pi$
$710$	0.0462057	−	0.0266769i	0.00173407	−	0.00100116i
$711$	0.558758	+	0.227421i	0.0209551	+	0.00852897i
$712$		−	9.22283i		−	0.345640i
$713$	−34.4660	+	29.2835i	−1.29076	+	1.09667i
$714$	9.16964	−	6.16791i	0.343165	−	0.230828i
$715$	−5.51976			−0.206427
$716$	−3.53636	−	6.12515i	−0.132160	−	0.228907i
$717$	−20.6553	−	30.7076i	−0.771386	−	1.14680i
$718$	−4.31978	+	7.48207i	−0.161213	+	0.279228i
$719$	−7.49210	−	12.9767i	−0.279408	−	0.483949i	0.691830	−	0.722061i	$-0.256805\pi$
$719$	−7.49210	−	12.9767i	−0.279408	−	0.483949i	−0.971238	+	0.238112i	$0.923472\pi$
$720$	0.409900	+	2.97187i	0.0152761	+	0.110755i
$721$	−17.6221			−0.656282
$722$	5.19366	+	2.99856i	0.193288	+	0.111595i
$723$	−0.523394	−	7.62538i	−0.0194652	−	0.283591i
$724$	4.50052	+	2.59838i	0.167261	+	0.0965679i
$725$	0.880441	+	1.52497i	0.0326988	+	0.0566359i
$726$	−0.337959	−	4.92376i	−0.0125428	−	0.182738i
$727$	−23.8686	−	41.3415i	−0.885236	−	1.53327i	−0.845443	−	0.534065i	$-0.820664\pi$
$727$	−23.8686	−	41.3415i	−0.885236	−	1.53327i	−0.0397921	−	0.999208i	$-0.512670\pi$
$728$	−3.00460			−0.111358
$729$	24.7495	−	10.7918i	0.916647	−	0.399697i
$730$	14.2146	−	8.20680i	0.526106	−	0.303747i
$731$	37.3508	+	21.5645i	1.38147	+	0.797591i
$732$	7.63781	+	3.73734i	0.282302	+	0.138136i
$733$	−0.0886488	+	0.153544i	−0.00327432	+	0.00567128i	−0.867658	−	0.497162i	$-0.834376\pi$
$733$	−0.0886488	+	0.153544i	−0.00327432	+	0.00567128i	0.864384	+	0.502833i	$0.167709\pi$
$734$	13.7980	−	23.8989i	0.509294	−	0.882123i
$735$	0.543807	+	7.92278i	0.0200586	+	0.292236i
$736$			8.12291i			0.299414i
$737$	0.495325	+	0.857928i	0.0182455	+	0.0316022i
$738$	−3.74143	+	0.516043i	−0.137724	+	0.0189958i
$739$	−2.80530	−	1.61964i	−0.103195	−	0.0595795i	0.447514	−	0.894277i	$-0.352309\pi$
$739$	−2.80530	−	1.61964i	−0.103195	−	0.0595795i	−0.550709	+	0.834697i	$0.685643\pi$
$740$	−2.57384			−0.0946161
$741$	−15.0390	−	7.35890i	−0.552472	−	0.270336i
$742$		−	16.6963i		−	0.612942i
$743$	−27.0340			−0.991782			−0.495891	−	0.868385i	$-0.665158\pi$
$743$	−27.0340			−0.991782			−0.495891	+	0.868385i	$0.665158\pi$
$744$	9.34573	−	2.37852i	0.342631	−	0.0872007i
$745$	20.8281			0.763084
$746$		−	0.897873i		−	0.0328734i
$747$	−9.51635	+	1.31256i	−0.348185	+	0.0480240i
$748$	−11.7213			−0.428574
$749$	−18.1179	−	10.4604i	−0.662012	−	0.382213i
$750$	−0.761277	+	1.55578i	−0.0277979	+	0.0568091i
$751$	−15.7188	−	27.2257i	−0.573587	−	0.993481i	−0.996194	−	0.0871680i	$-0.972218\pi$
$751$	−15.7188	−	27.2257i	−0.573587	−	0.993481i	0.422607	−	0.906313i	$-0.361115\pi$
$752$		−	4.59744i		−	0.167651i
$753$	18.0623	−	1.23977i	0.658226	−	0.0451796i
$754$	−1.70226	+	2.94840i	−0.0619927	+	0.107374i
$755$	−6.01158	+	10.4124i	−0.218784	+	0.378944i
$756$	−5.38010	−	6.02163i	−0.195673	−	0.219005i
$757$	−40.7429	−	23.5229i	−1.48083	−	0.854955i	−0.481062	−	0.876687i	$-0.659749\pi$
$757$	−40.7429	−	23.5229i	−1.48083	−	0.854955i	−0.999764	+	0.0217312i	$0.993082\pi$
$758$	29.6599	−	17.1241i	1.07730	−	0.621977i
$759$	−22.4182	−	33.3285i	−0.813730	−	1.20975i
$760$	4.99971			0.181359
$761$	−8.90549	−	15.4248i	−0.322824	−	0.559147i	0.658246	−	0.752803i	$-0.271299\pi$
$761$	−8.90549	−	15.4248i	−0.322824	−	0.559147i	−0.981070	+	0.193656i	$0.937965\pi$
$762$	0.451664	−	0.0310016i	0.0163621	−	0.00112307i
$763$	7.36998	+	12.7652i	0.266811	+	0.462131i
$764$	−9.46269	−	5.46329i	−0.342348	−	0.197655i
$765$	9.72530	−	7.55816i	0.351619	−	0.273266i
$766$	−4.35622	−	2.51506i	−0.157397	−	0.0908729i
$767$	−25.7205			−0.928713
$768$	0.761277	−	1.55578i	0.0274702	−	0.0561395i
$769$	9.81860	+	17.0063i	0.354068	+	0.613264i	0.986958	−	0.160978i	$-0.0514648\pi$
$769$	9.81860	+	17.0063i	0.354068	+	0.613264i	−0.632890	+	0.774242i	$0.718131\pi$
$770$	−2.21832	+	3.84225i	−0.0799428	+	0.138465i
$771$	−26.1957	+	17.6204i	−0.943415	+	0.634583i
$772$	−5.55465	−	9.62093i	−0.199916	−	0.346265i
$773$	13.9046			0.500114			0.250057	−	0.968231i	$-0.419551\pi$
$773$	13.9046			0.500114			0.250057	+	0.968231i	$0.419551\pi$
$774$	11.8804	−	29.1892i	0.427031	−	1.04918i
$775$	5.24360	+	1.87208i	0.188356	+	0.0672472i
$776$			0.201471i			0.00723238i
$777$	5.74846	−	3.86667i	0.206225	−	0.138716i
$778$	6.26508	−	3.61715i	0.224614	−	0.129681i
$779$			6.29438i			0.225520i
$780$	−3.34092	+	0.229315i	−0.119624	+	0.00821081i
$781$	0.131914	−	0.0761603i	0.00472024	−	0.00272523i
$782$	28.8818	−	16.6749i	1.03281	−	0.596293i
$783$	−8.95712	+	1.86791i	−0.320101	+	0.0667538i
$784$	2.29249	−	3.97071i	0.0818746	−	0.141811i
$785$	5.36870	+	3.09962i	0.191617	+	0.110630i
$786$	−6.70323	+	0.460099i	−0.239096	+	0.0164112i
$787$	34.8718	−	20.1332i	1.24305	−	0.717672i	0.273332	−	0.961920i	$-0.411874\pi$
$787$	34.8718	−	20.1332i	1.24305	−	0.717672i	0.969713	+	0.244247i	$0.0785409\pi$
$788$	−13.4055	+	23.2190i	−0.477550	+	0.827141i
$789$	0.459597	−	0.939254i	0.0163621	−	0.0334383i
$790$		−	0.201089i		−	0.00715443i
$791$		−	14.0694i		−	0.500252i
$792$	1.17023	+	8.48444i	0.0415824	+	0.301482i
$793$	−4.74587	+	8.22008i	−0.168531	+	0.291904i
$794$	2.87927	−	1.66235i	0.102182	−	0.0589946i
$795$	−1.27429	−	18.5652i	−0.0451944	−	0.658441i
$796$	13.3931	+	7.73251i	0.474706	+	0.274072i
$797$	22.2254	−	38.4955i	0.787263	−	1.36358i	−0.140374	−	0.990098i	$-0.544831\pi$
$797$	22.2254	−	38.4955i	0.787263	−	1.36358i	0.927638	−	0.373481i	$-0.121836\pi$
$798$	−11.1665	+	7.51106i	−0.395288	+	0.265889i
$799$	−16.3467	+	9.43775i	−0.578303	+	0.333883i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	16.9785	+	21.8467i	0.599904	+	0.771914i
$802$			14.3510i			0.506752i
$803$	40.5816	−	23.4298i	1.43209	−	0.826819i
$804$	0.335445	+	0.498696i	0.0118302	+	0.0175876i
$805$		−	12.6233i		−	0.444912i
$806$	1.93444	+	10.5896i	0.0681377	+	0.373002i
$807$	13.5629	+	20.1636i	0.477438	+	0.709793i
$808$	4.45908			0.156870
$809$	−6.16309	−	10.6748i	−0.216683	−	0.375306i	0.737109	−	0.675774i	$-0.236190\pi$
$809$	−6.16309	−	10.6748i	−0.216683	−	0.375306i	−0.953792	+	0.300468i	$0.902857\pi$
$810$	−6.44191	−	6.28505i	−0.226346	−	0.220834i
$811$	−20.9582	+	36.3007i	−0.735944	+	1.27469i	0.218364	+	0.975867i	$0.429928\pi$
$811$	−20.9582	+	36.3007i	−0.735944	+	1.27469i	−0.954308	+	0.298824i	$0.903405\pi$
$812$	1.36824	+	2.36985i	0.0480157	+	0.0831656i
$813$	−9.44110	−	4.61973i	−0.331114	−	0.162021i
$814$	−7.34810			−0.257551
$815$	19.6170	+	11.3259i	0.687153	+	0.396728i
$816$	−7.09450	+	0.486956i	−0.248357	+	0.0170469i
$817$	−45.4844	−	26.2604i	−1.59130	−	0.918736i
$818$	2.45620	+	4.25426i	0.0858790	+	0.148747i
$819$	7.11717	−	5.53121i	0.248694	−	0.193276i
$820$	0.629474	+	1.09028i	0.0219822	+	0.0380743i
$821$	−24.8966			−0.868896			−0.434448	−	0.900697i	$-0.643057\pi$
$821$	−24.8966			−0.868896			−0.434448	+	0.900697i	$0.643057\pi$
$822$	−22.2950	+	14.9966i	−0.777628	+	0.523067i
$823$	40.7705	−	23.5389i	1.42117	−	0.820513i	0.424772	−	0.905300i	$-0.360354\pi$
$823$	40.7705	−	23.5389i	1.42117	−	0.820513i	0.996399	+	0.0847870i	$0.0270210\pi$
$824$	9.82038	+	5.66980i	0.342109	+	0.197517i
$825$	−2.17339	+	4.44164i	−0.0756676	+	0.154638i
$826$	−10.3368	+	17.9038i	−0.359662	+	0.622952i
$827$	−11.9045	+	20.6191i	−0.413959	+	0.716997i	−0.995319	−	0.0966492i	$-0.969188\pi$
$827$	−11.9045	+	20.6191i	−0.413959	+	0.716997i	0.581360	+	0.813647i	$0.302521\pi$
$828$	−14.9536	−	19.2412i	−0.519673	−	0.668679i
$829$		−	11.0697i		−	0.384468i	−0.981349	−	0.192234i	$-0.938427\pi$
$829$		−	11.0697i		−	0.384468i	0.981349	−	0.192234i	$-0.0615732\pi$
$830$	1.60107	+	2.77314i	0.0555741	+	0.0962571i
$831$	−32.4722	−	15.8893i	−1.12645	−	0.551195i
$832$	1.67439	+	0.966709i	0.0580490	+	0.0335146i
$833$	−18.8243			−0.652224
$834$	−0.755051	+	1.54306i	−0.0261453	+	0.0534318i
$835$			10.5513i			0.365143i
$836$	14.2738			0.493669
$837$	−17.7591	+	22.8388i	−0.613846	+	0.789426i
$838$	−2.63538			−0.0910377
$839$			18.6812i			0.644948i	0.946578	+	0.322474i	$0.104515\pi$
$839$			18.6812i			0.644948i	−0.946578	+	0.322474i	$0.895485\pi$
$840$	−1.18305	+	2.41774i	−0.0408191	+	0.0834199i
$841$	−25.8993			−0.893079
$842$	27.2236	+	15.7175i	0.938186	+	0.541662i
$843$	9.97481	+	4.88088i	0.343551	+	0.168107i
$844$	8.68251	+	15.0385i	0.298864	+	0.517648i
$845$			9.26190i			0.318619i
$846$	8.46351	+	10.8902i	0.290981	+	0.374414i
$847$	2.21405	−	3.83484i	0.0760756	−	0.131767i
$848$	−5.37194	+	9.30446i	−0.184473	+	0.319517i
$849$	19.2317	−	39.3029i	0.660031	−	1.34887i
$850$	−3.55560	−	2.05283i	−0.121956	−	0.0704113i
$851$	18.1060	−	10.4535i	0.620666	−	0.358342i
$852$	0.0766787	−	0.0515775i	0.00262697	−	0.00176702i
$853$	−31.4348			−1.07631			−0.538153	−	0.842847i	$-0.680878\pi$
$853$	−31.4348			−1.07631			−0.538153	+	0.842847i	$0.680878\pi$
$854$	3.81461	+	6.60710i	0.130533	+	0.226090i
$855$	−11.8431	+	9.20405i	−0.405026	+	0.314772i
$856$	6.73110	+	11.6586i	0.230064	+	0.398483i
$857$	16.7355	+	9.66227i	0.571675	+	0.330057i	0.757818	−	0.652466i	$-0.226265\pi$
$857$	16.7355	+	9.66227i	0.571675	+	0.330057i	−0.186143	+	0.982523i	$0.559599\pi$
$858$	−9.53805	+	0.654678i	−0.325624	+	0.0223503i
$859$	42.3828	+	24.4697i	1.44608	+	0.834897i	0.998245	−	0.0592180i	$-0.0188607\pi$
$859$	42.3828	+	24.4697i	1.44608	+	0.834897i	0.447838	+	0.894115i	$0.352194\pi$
$860$	−10.5048			−0.358210
$861$	−3.04381	−	1.48940i	−0.103733	−	0.0507586i
$862$	2.13660	+	3.70070i	0.0727729	+	0.126046i
$863$	20.8558	−	36.1233i	0.709940	−	1.22965i	−0.254938	−	0.966957i	$-0.582055\pi$
$863$	20.8558	−	36.1233i	0.709940	−	1.22965i	0.964879	−	0.262695i	$-0.0846114\pi$
$864$	1.06078	+	5.08672i	0.0360886	+	0.173054i
$865$	10.9812	+	19.0199i	0.373371	+	0.646697i
$866$	7.77289			0.264134
$867$	−0.138852	−	0.206427i	−0.00471567	−	0.00701064i
$868$	8.14873	+	2.90928i	0.276586	+	0.0987474i
$869$		−	0.574093i		−	0.0194748i
$870$	1.70226	+	2.53070i	0.0577120	+	0.0857987i
$871$	−0.581008	+	0.335445i	−0.0196867	+	0.0113661i
$872$		−	9.48497i		−	0.321202i
$873$	−0.370891	−	0.477236i	−0.0125528	−	0.0161520i
$874$	−35.1712	+	20.3061i	−1.18968	+	0.686864i
$875$	−1.34583	+	0.777017i	−0.0454975	+	0.0262680i
$876$	23.5892	−	15.8672i	0.797006	−	0.536102i
$877$	4.61705	−	7.99697i	0.155907	−	0.270038i	−0.777482	−	0.628905i	$-0.783503\pi$
$877$	4.61705	−	7.99697i	0.155907	−	0.270038i	0.933389	+	0.358867i	$0.116837\pi$
$878$	5.75280	+	3.32138i	0.194148	+	0.112091i
$879$	−3.41449	−	49.7461i	−0.115168	−	1.67789i
$880$	2.47243	−	1.42746i	0.0833458	−	0.0481197i
$881$	11.1066	−	19.2371i	0.374190	−	0.648116i	−0.616016	−	0.787734i	$-0.711254\pi$
$881$	11.1066	−	19.2371i	0.374190	−	0.648116i	0.990205	+	0.139618i	$0.0445876\pi$
$882$	1.87938	+	13.6259i	0.0632821	+	0.458809i
$883$			26.8831i			0.904689i	0.891843	+	0.452345i	$0.149412\pi$
$883$			26.8831i			0.904689i	−0.891843	+	0.452345i	$0.850588\pi$
$884$		−	7.93794i		−	0.266982i
$885$	−10.1274	+	20.6968i	−0.340427	+	0.695714i
$886$	15.3331	−	26.5577i	0.515125	−	0.892222i
$887$	−49.1942	+	28.4023i	−1.65178	+	0.953655i	−0.675439	+	0.737415i	$0.736046\pi$
$887$	−49.1942	+	28.4023i	−1.65178	+	0.953655i	−0.976340	+	0.216240i	$0.930621\pi$
$888$	−4.44755	+	0.305273i	−0.149250	+	0.0102443i
$889$	0.351777	+	0.203098i	0.0117982	+	0.00681170i
$890$	4.61141	−	7.98720i	0.154575	−	0.267732i
$891$	−18.3911	−	17.9433i	−0.616127	−	0.601124i
$892$	6.35351	−	3.66820i	0.212731	−	0.122820i
$893$	19.9064	−	11.4929i	0.666141	−	0.384597i
$894$	35.9907	−	2.47035i	1.20371	−	0.0826207i
$895$		−	7.07271i		−	0.236415i
$896$	1.34583	−	0.777017i	0.0449611	−	0.0259583i
$897$	22.5708	−	15.1821i	0.753617	−	0.506916i
$898$			18.1493i			0.605649i
$899$	7.47155	−	6.34807i	0.249190	−	0.211720i
$900$	−1.13095	+	2.77866i	−0.0376983	+	0.0926220i
$901$	44.1106			1.46954
$902$	1.79710	+	3.11267i	0.0598369	+	0.103641i
$903$	23.4616	−	15.7813i	0.780752	−	0.525169i
$904$	−4.52675	+	7.84056i	−0.150558	+	0.260773i
$905$	2.59838	+	4.50052i	0.0863730	+	0.149602i
$906$	−9.15294	+	18.7054i	−0.304086	+	0.621446i
$907$	24.9536			0.828571			0.414285	−	0.910147i	$-0.364032\pi$
$907$	24.9536			0.828571			0.414285	+	0.910147i	$0.364032\pi$
$908$	−15.2093	−	8.78108i	−0.504738	−	0.291411i
$909$	−10.5625	+	8.20878i	−0.350335	+	0.272268i
$910$	−2.60206	−	1.50230i	−0.0862573	−	0.0498007i
$911$	13.0194	+	22.5502i	0.431351	+	0.747123i	0.996990	−	0.0775307i	$-0.0247036\pi$
$911$	13.0194	+	22.5502i	0.431351	+	0.747123i	−0.565639	+	0.824653i	$0.691370\pi$
$912$	8.63943	−	0.592997i	0.286080	−	0.0196361i
$913$	4.57094	+	7.91710i	0.151276	+	0.262018i
$914$	37.2797			1.23310
$915$	4.74587	+	7.05554i	0.156894	+	0.233249i
$916$	−22.7927	+	13.1594i	−0.753091	+	0.434797i
$917$	−5.22078	−	3.01422i	−0.172405	−	0.0995382i
$918$	15.9087	−	14.2139i	0.525067	−	0.469128i
$919$	12.2534	−	21.2236i	0.404204	−	0.700101i	−0.590025	−	0.807385i	$-0.700882\pi$
$919$	12.2534	−	21.2236i	0.404204	−	0.700101i	0.994228	+	0.107284i	$0.0342154\pi$
$920$	−4.06145	+	7.03464i	−0.133902	+	0.231925i
$921$	32.3107	−	2.21776i	1.06467	−	0.0730776i
$922$			11.8080i			0.388876i
$923$	0.0515775	+	0.0893348i	0.00169769	+	0.00294049i
$924$	−3.37751	+	6.90245i	−0.111112	+	0.227074i
$925$	−2.22901	−	1.28692i	−0.0732893	−	0.0423136i
$926$	32.6600			1.07328
$927$	−33.6998	+	4.64810i	−1.10685	+	0.152664i
$928$		−	1.76088i		−	0.0578038i
$929$	−0.658797			−0.0216144			−0.0108072	−	0.999942i	$-0.503440\pi$
$929$	−0.658797			−0.0216144			−0.0108072	+	0.999942i	$0.503440\pi$
$930$	9.28290	+	2.61301i	0.304398	+	0.0856839i
$931$	22.9236			0.751290
$932$		−	18.6243i		−	0.610058i
$933$	−23.4218	−	11.4608i	−0.766796	−	0.375209i
$934$	−9.64118			−0.315469
$935$	−10.1510	−	5.86066i	−0.331972	−	0.191664i
$936$	−5.74586	+	0.792507i	−0.187809	+	0.0259039i
$937$	−25.9755	−	44.9909i	−0.848583	−	1.46979i	−0.882473	−	0.470363i	$-0.844123\pi$
$937$	−25.9755	−	44.9909i	−0.848583	−	1.46979i	0.0338898	−	0.999426i	$-0.489210\pi$
$938$			0.539245i			0.0176070i
$939$	3.41284	+	49.7220i	0.111374	+	1.62262i
$940$	2.29872	−	3.98150i	0.0749760	−	0.129862i
$941$	−19.6663	+	34.0630i	−0.641103	+	1.11042i	0.344084	+	0.938939i	$0.388190\pi$
$941$	−19.6663	+	34.0630i	−0.641103	+	1.11042i	−0.985187	+	0.171484i	$0.945144\pi$
$942$	9.64467	+	4.71934i	0.314240	+	0.153764i
$943$	−8.85625	−	5.11316i	−0.288399	−	0.166507i
$944$	11.5208	−	6.65156i	0.374972	−	0.216490i
$945$	−1.64849	−	7.90494i	−0.0536254	−	0.257148i
$946$	−29.9903			−0.975069
$947$	−14.3298	−	24.8199i	−0.465656	−	0.806540i	0.533575	−	0.845753i	$-0.320848\pi$
$947$	−14.3298	−	24.8199i	−0.465656	−	0.806540i	−0.999231	+	0.0392131i	$0.987515\pi$
$948$	−0.0238504	−	0.347479i	−0.000774626	−	0.0112856i
$949$	15.8672	+	27.4827i	0.515070	+	0.892128i
$950$	4.32988	+	2.49986i	0.140480	+	0.0811060i
$951$	−0.0826705	−	1.20443i	−0.00268077	−	0.0390564i
$952$	−5.52552	−	3.19016i	−0.179083	−	0.103394i
$953$	−35.8318			−1.16071			−0.580353	−	0.814365i	$-0.697085\pi$
$953$	−35.8318			−1.16071			−0.580353	+	0.814365i	$0.697085\pi$
$954$	−4.40391	−	31.9293i	−0.142582	−	1.03375i
$955$	−5.46329	−	9.46269i	−0.176788	−	0.306206i
$956$	−10.6833	+	18.5040i	−0.345523	+	0.598463i
$957$	4.85982	+	7.22495i	0.157096	+	0.233549i
$958$	−10.8617	−	18.8130i	−0.350926	−	0.607822i
$959$	−24.1078			−0.778483
$960$	1.43718	−	0.966709i	0.0463847	−	0.0312004i
$961$	5.00727	−	30.5929i	0.161525	−	0.986869i
$962$		−	4.97630i		−	0.160442i
$963$	−37.4069	−	15.2251i	−1.20542	−	0.490621i
$964$	−3.82166	+	2.20644i	−0.123087	+	0.0710645i
$965$		−	11.1093i		−	0.357621i
$966$	−1.49720	−	21.8128i	−0.0481716	−	0.701816i
$967$	−4.92891	+	2.84571i	−0.158503	+	0.0915118i	−0.577154	−	0.816636i	$-0.695837\pi$
$967$	−4.92891	+	2.84571i	−0.158503	+	0.0915118i	0.418650	+	0.908147i	$0.362503\pi$
$968$	−2.46767	+	1.42471i	−0.0793139	+	0.0457919i
$969$	−19.8437	−	29.5010i	−0.637471	−	0.947709i
$970$	−0.100735	+	0.174479i	−0.00323442	+	0.00560218i
$971$	5.37649	+	3.10412i	0.172540	+	0.0996159i	0.583783	−	0.811910i	$-0.301572\pi$
$971$	5.37649	+	3.10412i	0.172540	+	0.0996159i	−0.411243	+	0.911526i	$0.634905\pi$
$972$	−11.8770	−	10.0964i	−0.380954	−	0.323843i
$973$	−1.33483	+	0.770663i	−0.0427926	+	0.0247063i
$974$	10.6263	−	18.4054i	0.340490	−	0.589746i
$975$	−3.00798	−	1.47187i	−0.0963323	−	0.0471374i
$976$		−	4.90931i		−	0.157143i
$977$			30.8123i			0.985772i	0.870094	+	0.492886i	$0.164058\pi$
$977$			30.8123i			0.985772i	−0.870094	+	0.492886i	$0.835942\pi$
$978$	35.2412	+	17.2442i	1.12689	+	0.551410i
$979$	13.1652	−	22.8028i	0.420763	−	0.728782i
$980$	3.97071	−	2.29249i	0.126840	−	0.0732309i
$981$	17.4610	+	22.4676i	0.557488	+	0.717336i
$982$	−7.75860	−	4.47943i	−0.247587	−	0.142944i
$983$	−2.26966	+	3.93116i	−0.0723908	+	0.125385i	−0.899949	−	0.435996i	$-0.856396\pi$
$983$	−2.26966	+	3.93116i	−0.0723908	+	0.125385i	0.827558	+	0.561380i	$0.189730\pi$
$984$	1.21704	+	1.80933i	0.0387977	+	0.0576794i
$985$	−23.2190	+	13.4055i	−0.739817	+	0.427134i
$986$	−6.26099	+	3.61479i	−0.199391	+	0.115118i
$987$	0.847392	+	12.3457i	0.0269728	+	0.392969i
$988$			9.66653i			0.307533i
$989$	73.8974	−	42.6647i	2.34980	−	1.35666i
$990$	−3.22877	+	7.93286i	−0.102617	+	0.252123i
$991$		−	23.7517i		−	0.754499i	−0.926112	−	0.377249i	$-0.876870\pi$
$991$		−	23.7517i		−	0.754499i	0.926112	−	0.377249i	$-0.123130\pi$
$992$	−3.60505	−	4.24307i	−0.114460	−	0.134718i
$993$	−14.4173	+	9.69770i	−0.457518	+	0.307747i
$994$	0.0829135			0.00262986
$995$	7.73251	+	13.3931i	0.245137	+	0.424590i
$996$	3.09554	+	4.60205i	0.0980860	+	0.145821i
$997$	11.3190	−	19.6052i	0.358478	−	0.620902i	−0.629229	−	0.777220i	$-0.716629\pi$
$997$	11.3190	−	19.6052i	0.358478	−	0.620902i	0.987707	+	0.156318i	$0.0499626\pi$
$998$	−10.8135	−	18.7295i	−0.342295	−	0.592873i
$999$	9.97320	−	8.91068i	0.315538	−	0.281922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.d.161.7	✓	36
3.2	odd	2	inner	930.2.o.d.161.18	yes	36
31.26	odd	6	inner	930.2.o.d.491.9	yes	36
93.26	even	6	inner	930.2.o.d.491.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.d.161.7	✓	36	1.1	even	1	trivial
930.2.o.d.161.18	yes	36	3.2	odd	2	inner
930.2.o.d.491.9	yes	36	31.26	odd	6	inner
930.2.o.d.491.16	yes	36	93.26	even	6	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.761277 - 1.55578i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.55578 - 0.761277i) q^{6} +(-0.777017 - 1.34583i) q^{7} +1.00000i q^{8} +(-1.84092 - 2.36876i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.761277 - 1.55578i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.55578 - 0.761277i) q^{6} +(-0.777017 - 1.34583i) q^{7} +1.00000i q^{8} +(-1.84092 - 2.36876i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.42746 + 2.47243i) q^{11} +(-0.761277 + 1.55578i) q^{12} +(-1.67439 - 0.966709i) q^{13} +(-1.34583 + 0.777017i) q^{14} +(-1.43718 + 0.966709i) q^{15} +1.00000 q^{16} +(-2.05283 - 3.55560i) q^{17} +(-2.36876 + 1.84092i) q^{18} +(2.49986 + 4.32988i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-2.68535 + 0.184318i) q^{21} +(2.47243 + 1.42746i) q^{22} -8.12291 q^{23} +(1.55578 + 0.761277i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.966709 + 1.67439i) q^{26} +(-5.08672 + 1.06078i) q^{27} +(0.777017 + 1.34583i) q^{28} +1.76088 q^{29} +(0.966709 + 1.43718i) q^{30} +(4.24307 - 3.60505i) q^{31} -1.00000i q^{32} +(2.75988 + 4.10302i) q^{33} +(-3.55560 + 2.05283i) q^{34} +1.55403i q^{35} +(1.84092 + 2.36876i) q^{36} +(-2.22901 + 1.28692i) q^{37} +(4.32988 - 2.49986i) q^{38} +(-2.77866 + 1.86905i) q^{39} +(0.500000 - 0.866025i) q^{40} +(1.09028 + 0.629474i) q^{41} +(0.184318 + 2.68535i) q^{42} +(-9.09740 + 5.25239i) q^{43} +(1.42746 - 2.47243i) q^{44} +(0.409900 + 2.97187i) q^{45} +8.12291i q^{46} -4.59744i q^{47} +(0.761277 - 1.55578i) q^{48} +(2.29249 - 3.97071i) q^{49} +(0.866025 - 0.500000i) q^{50} +(-7.09450 + 0.486956i) q^{51} +(1.67439 + 0.966709i) q^{52} +(-5.37194 + 9.30446i) q^{53} +(1.06078 + 5.08672i) q^{54} +(2.47243 - 1.42746i) q^{55} +(1.34583 - 0.777017i) q^{56} +(8.63943 - 0.592997i) q^{57} -1.76088i q^{58} +(11.5208 - 6.65156i) q^{59} +(1.43718 - 0.966709i) q^{60} -4.90931i q^{61} +(-3.60505 - 4.24307i) q^{62} +(-1.75753 + 4.31813i) q^{63} -1.00000 q^{64} +(0.966709 + 1.67439i) q^{65} +(4.10302 - 2.75988i) q^{66} +(0.173499 - 0.300508i) q^{67} +(2.05283 + 3.55560i) q^{68} +(-6.18378 + 12.6375i) q^{69} +1.55403 q^{70} +(-0.0462057 - 0.0266769i) q^{71} +(2.36876 - 1.84092i) q^{72} +(-14.2146 - 8.20680i) q^{73} +(1.28692 + 2.22901i) q^{74} +(1.72799 - 0.118606i) q^{75} +(-2.49986 - 4.32988i) q^{76} +4.43665 q^{77} +(1.86905 + 2.77866i) q^{78} +(-0.174148 + 0.100545i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-2.22206 + 8.72138i) q^{81} +(0.629474 - 1.09028i) q^{82} +(1.60107 - 2.77314i) q^{83} +(2.68535 - 0.184318i) q^{84} +4.10565i q^{85} +(5.25239 + 9.09740i) q^{86} +(1.34052 - 2.73955i) q^{87} +(-2.47243 - 1.42746i) q^{88} -9.22283 q^{89} +(2.97187 - 0.409900i) q^{90} +3.00460i q^{91} +8.12291 q^{92} +(-2.37852 - 9.34573i) q^{93} -4.59744 q^{94} -4.99971i q^{95} +(-1.55578 - 0.761277i) q^{96} +0.201471 q^{97} +(-3.97071 - 2.29249i) q^{98} +(8.48444 - 1.17023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9	\( 36 q - 36 q^{4} - 8 q^{7} + 8 q^{9} - 18 q^{10} + 36 q^{16} - 4 q^{18} - 4 q^{19} + 72 q^{21} - 18 q^{22} + 18 q^{25} + 8 q^{28} + 52 q^{31} - 36 q^{33} + 18 q^{34} - 8 q^{36} - 54 q^{37} - 8 q^{39} + 18 q^{40} + 12 q^{42} - 18 q^{43} + 4 q^{45} - 62 q^{49} - 10 q^{51} - 18 q^{55} + 12 q^{57} + 88 q^{63} - 36 q^{64} - 4 q^{66} + 10 q^{67} + 46 q^{69} + 16 q^{70} + 4 q^{72} + 24 q^{73} + 4 q^{76} + 92 q^{78} + 42 q^{79} + 4 q^{81} - 12 q^{82} - 72 q^{84} - 16 q^{87} + 18 q^{88} + 8 q^{90} + 48 q^{93} - 92 q^{94} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 - 8 * q^7 + 8 * q^9 - 18 * q^10 + 36 * q^16 - 4 * q^18 - 4 * q^19 + 72 * q^21 - 18 * q^22 + 18 * q^25 + 8 * q^28 + 52 * q^31 - 36 * q^33 + 18 * q^34 - 8 * q^36 - 54 * q^37 - 8 * q^39 + 18 * q^40 + 12 * q^42 - 18 * q^43 + 4 * q^45 - 62 * q^49 - 10 * q^51 - 18 * q^55 + 12 * q^57 + 88 * q^63 - 36 * q^64 - 4 * q^66 + 10 * q^67 + 46 * q^69 + 16 * q^70 + 4 * q^72 + 24 * q^73 + 4 * q^76 + 92 * q^78 + 42 * q^79 + 4 * q^81 - 12 * q^82 - 72 * q^84 - 16 * q^87 + 18 * q^88 + 8 * q^90 + 48 * q^93 - 92 * q^94 - 80 * q^97 - 18 * q^99

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