LMFDB - Embedded newform 105.2.m.a.97.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.m (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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.6
Root			$1.36166 - 0.381939i$ of defining polynomial
Character	$\chi$	$=$	105.97
Dual form			105.2.m.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540143 + 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(2.57351 + 0.614060i) q^{7} +(1.84539 - 1.84539i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.540143 + 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(2.57351 + 0.614060i) q^{7} +(1.84539 - 1.84539i) q^{8} +1.00000i q^{9} +(-1.63006 + 0.510348i) q^{10} -3.85136 q^{11} +(1.00161 - 1.00161i) q^{12} +(-3.66816 - 3.66816i) q^{13} +(1.05838 + 1.72174i) q^{14} +(-2.13393 + 0.668102i) q^{15} -0.839427 q^{16} +(1.49007 - 1.49007i) q^{17} +(-0.540143 + 0.540143i) q^{18} +0.0697674 q^{19} +(2.80654 + 1.46818i) q^{20} +(1.38554 + 2.25395i) q^{21} +(-2.08029 - 2.08029i) q^{22} +(-0.534176 + 0.534176i) q^{23} +2.60978 q^{24} +(-2.85136 - 4.10728i) q^{25} -3.96267i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.869810 - 3.64535i) q^{28} +2.77107i q^{29} +(-1.51350 - 0.791755i) q^{30} -2.39674i q^{31} +(-4.14420 - 4.14420i) q^{32} +(-2.72332 - 2.72332i) q^{33} +1.60970 q^{34} +(-3.88408 + 4.46250i) q^{35} +1.41649 q^{36} +(6.18757 + 6.18757i) q^{37} +(0.0376844 + 0.0376844i) q^{38} -5.18757i q^{39} +(1.74360 + 5.56908i) q^{40} +8.68077i q^{41} +(-0.469067 + 1.96584i) q^{42} +(-2.77107 + 2.77107i) q^{43} +5.45542i q^{44} +(-1.98133 - 1.03649i) q^{45} -0.577063 q^{46} +(5.49042 - 5.49042i) q^{47} +(-0.593565 - 0.593565i) q^{48} +(6.24586 + 3.16057i) q^{49} +(0.678376 - 3.75866i) q^{50} +2.10728 q^{51} +(-5.19592 + 5.19592i) q^{52} +(6.13823 - 6.13823i) q^{53} -0.763878 q^{54} +(3.99191 - 7.63083i) q^{55} +(5.88231 - 3.61595i) q^{56} +(0.0493330 + 0.0493330i) q^{57} +(-1.49678 + 1.49678i) q^{58} -6.97440 q^{59} +(0.946361 + 3.02269i) q^{60} +14.3107i q^{61} +(1.29458 - 1.29458i) q^{62} +(-0.614060 + 2.57351i) q^{63} -2.79807i q^{64} +(11.0699 - 3.46582i) q^{65} -2.94197i q^{66} +(0.416491 + 0.416491i) q^{67} +(-2.11067 - 2.11067i) q^{68} -0.755439 q^{69} +(-4.50835 + 0.312431i) q^{70} -8.12783 q^{71} +(1.84539 + 1.84539i) q^{72} +(9.55210 + 9.55210i) q^{73} +6.68434i q^{74} +(0.888068 - 4.92050i) q^{75} -0.0988248i q^{76} +(-9.91150 - 2.36497i) q^{77} +(2.80203 - 2.80203i) q^{78} -9.86329i q^{79} +(0.870061 - 1.66319i) q^{80} -1.00000 q^{81} +(-4.68886 + 4.68886i) q^{82} +(1.63570 + 1.63570i) q^{83} +(3.19270 - 1.96260i) q^{84} +(1.40788 + 4.49678i) q^{85} -2.99355 q^{86} +(-1.95945 + 1.95945i) q^{87} +(-7.10728 + 7.10728i) q^{88} -5.05313 q^{89} +(-0.510348 - 1.63006i) q^{90} +(-7.18757 - 11.6925i) q^{91} +(0.756656 + 0.756656i) q^{92} +(1.69475 - 1.69475i) q^{93} +5.93123 q^{94} +(-0.0723134 + 0.138232i) q^{95} -5.86078i q^{96} +(6.85851 - 6.85851i) q^{97} +(1.66650 + 5.08082i) q^{98} -3.85136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 16 * q - 8 * q^7 + 24 * q^8	$ 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.540143	+	0.540143i	0.381939	+	0.381939i	0.871800	−	0.489861i	$-0.162953\pi$
$2$	0.540143	+	0.540143i	0.381939	+	0.381939i	−0.489861	+	0.871800i	$0.662953\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.41649i		−	0.708245i
$5$	−1.03649	+	1.98133i	−0.463534	+	0.886079i
$5$	−1.03649	+	1.98133i	−0.463534	+	0.886079i
$6$			0.763878i			0.311852i
$7$	2.57351	+	0.614060i	0.972694	+	0.232093i
$7$	2.57351	+	0.614060i	0.972694	+	0.232093i
$8$	1.84539	−	1.84539i	0.652445	−	0.652445i
$9$			1.00000i			0.333333i
$10$	−1.63006	+	0.510348i	−0.515470	+	0.161386i
$11$	−3.85136			−1.16123			−0.580615	−	0.814179i	$-0.697188\pi$
$11$	−3.85136			−1.16123			−0.580615	+	0.814179i	$0.697188\pi$
$12$	1.00161	−	1.00161i	0.289140	−	0.289140i
$13$	−3.66816	−	3.66816i	−1.01737	−	1.01737i	−0.999847	−	0.0175187i	$-0.994423\pi$
$13$	−3.66816	−	3.66816i	−1.01737	−	1.01737i	−0.0175187	−	0.999847i	$-0.505577\pi$
$14$	1.05838	+	1.72174i	0.282864	+	0.460155i
$15$	−2.13393	+	0.668102i	−0.550977	+	0.172503i
$16$	−0.839427			−0.209857
$17$	1.49007	−	1.49007i	0.361395	−	0.361395i	−0.502931	−	0.864326i	$-0.667745\pi$
$17$	1.49007	−	1.49007i	0.361395	−	0.361395i	0.864326	+	0.502931i	$0.167745\pi$
$18$	−0.540143	+	0.540143i	−0.127313	+	0.127313i
$19$	0.0697674			0.0160057			0.00800286	−	0.999968i	$-0.497453\pi$
$19$	0.0697674			0.0160057			0.00800286	+	0.999968i	$0.497453\pi$
$20$	2.80654	+	1.46818i	0.627561	+	0.328296i
$21$	1.38554	+	2.25395i	0.302349	+	0.491852i
$22$	−2.08029	−	2.08029i	−0.443519	−	0.443519i
$23$	−0.534176	+	0.534176i	−0.111383	+	0.111383i	−0.760602	−	0.649218i	$-0.775096\pi$
$23$	−0.534176	+	0.534176i	−0.111383	+	0.111383i	0.649218	+	0.760602i	$0.275096\pi$
$24$	2.60978			0.532719
$25$	−2.85136	−	4.10728i	−0.570272	−	0.821456i
$26$		−	3.96267i		−	0.777143i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.869810	−	3.64535i	0.164379	−	0.688906i
$29$			2.77107i			0.514576i	0.966335	+	0.257288i	$0.0828288\pi$
$29$			2.77107i			0.514576i	−0.966335	+	0.257288i	$0.917171\pi$
$30$	−1.51350	−	0.791755i	−0.276325	−	0.144554i
$31$		−	2.39674i		−	0.430467i	−0.976563	−	0.215233i	$-0.930949\pi$
$31$		−	2.39674i		−	0.430467i	0.976563	−	0.215233i	$-0.0690512\pi$
$32$	−4.14420	−	4.14420i	−0.732598	−	0.732598i
$33$	−2.72332	−	2.72332i	−0.474070	−	0.474070i
$34$	1.60970			0.276062
$35$	−3.88408	+	4.46250i	−0.656529	+	0.754301i
$36$	1.41649			0.236082
$37$	6.18757	+	6.18757i	1.01723	+	1.01723i	0.999849	+	0.0173805i	$0.00553267\pi$
$37$	6.18757	+	6.18757i	1.01723	+	1.01723i	0.0173805	+	0.999849i	$0.494467\pi$
$38$	0.0376844	+	0.0376844i	0.00611321	+	0.00611321i
$39$		−	5.18757i		−	0.830675i
$40$	1.74360	+	5.56908i	0.275687	+	0.880549i
$41$			8.68077i			1.35571i	0.735196	+	0.677854i	$0.237090\pi$
$41$			8.68077i			1.35571i	−0.735196	+	0.677854i	$0.762910\pi$
$42$	−0.469067	+	1.96584i	−0.0723786	+	0.303336i
$43$	−2.77107	+	2.77107i	−0.422585	+	0.422585i	−0.886093	−	0.463508i	$-0.846591\pi$
$43$	−2.77107	+	2.77107i	−0.422585	+	0.422585i	0.463508	+	0.886093i	$0.346591\pi$
$44$			5.45542i			0.822435i
$45$	−1.98133	−	1.03649i	−0.295360	−	0.154511i
$46$	−0.577063			−0.0850834
$47$	5.49042	−	5.49042i	0.800860	−	0.800860i	−0.182370	−	0.983230i	$-0.558377\pi$
$47$	5.49042	−	5.49042i	0.800860	−	0.800860i	0.983230	+	0.182370i	$0.0583768\pi$
$48$	−0.593565	−	0.593565i	−0.0856737	−	0.0856737i
$49$	6.24586	+	3.16057i	0.892266	+	0.451510i
$50$	0.678376	−	3.75866i	0.0959368	−	0.531555i
$51$	2.10728			0.295078
$52$	−5.19592	+	5.19592i	−0.720544	+	0.720544i
$53$	6.13823	−	6.13823i	0.843151	−	0.843151i	−0.146116	−	0.989267i	$-0.546677\pi$
$53$	6.13823	−	6.13823i	0.843151	−	0.843151i	0.989267	+	0.146116i	$0.0466774\pi$
$54$	−0.763878			−0.103951
$55$	3.99191	−	7.63083i	0.538269	−	1.02894i
$56$	5.88231	−	3.61595i	0.786057	−	0.483202i
$57$	0.0493330	+	0.0493330i	0.00653431	+	0.00653431i
$58$	−1.49678	+	1.49678i	−0.196536	+	0.196536i
$59$	−6.97440			−0.907990			−0.453995	−	0.891004i	$-0.650002\pi$
$59$	−6.97440			−0.907990			−0.453995	+	0.891004i	$0.650002\pi$
$60$	0.946361	+	3.02269i	0.122175	+	0.390227i
$61$			14.3107i			1.83230i	0.400835	+	0.916150i	$0.368720\pi$
$61$			14.3107i			1.83230i	−0.400835	+	0.916150i	$0.631280\pi$
$62$	1.29458	−	1.29458i	0.164412	−	0.164412i
$63$	−0.614060	+	2.57351i	−0.0773643	+	0.324231i
$64$		−	2.79807i		−	0.349758i
$65$	11.0699	−	3.46582i	1.37305	−	0.429883i
$66$		−	2.94197i		−	0.362131i
$67$	0.416491	+	0.416491i	0.0508824	+	0.0508824i	0.732090	−	0.681208i	$-0.238545\pi$
$67$	0.416491	+	0.416491i	0.0508824	+	0.0508824i	−0.681208	+	0.732090i	$0.738545\pi$
$68$	−2.11067	−	2.11067i	−0.255957	−	0.255957i
$69$	−0.755439			−0.0909442
$70$	−4.50835	+	0.312431i	−0.538851	+	0.0373426i
$71$	−8.12783			−0.964595			−0.482298	−	0.876007i	$-0.660198\pi$
$71$	−8.12783			−0.964595			−0.482298	+	0.876007i	$0.660198\pi$
$72$	1.84539	+	1.84539i	0.217482	+	0.217482i
$73$	9.55210	+	9.55210i	1.11799	+	1.11799i	0.992036	+	0.125953i	$0.0401987\pi$
$73$	9.55210	+	9.55210i	1.11799	+	1.11799i	0.125953	+	0.992036i	$0.459801\pi$
$74$			6.68434i			0.777039i
$75$	0.888068	−	4.92050i	0.102545	−	0.568171i
$76$		−	0.0988248i		−	0.0113360i
$77$	−9.91150	−	2.36497i	−1.12952	−	0.269513i
$78$	2.80203	−	2.80203i	0.317267	−	0.317267i
$79$		−	9.86329i		−	1.10971i	−0.831948	−	0.554854i	$-0.812774\pi$
$79$		−	9.86329i		−	1.10971i	0.831948	−	0.554854i	$-0.187226\pi$
$80$	0.870061	−	1.66319i	0.0972758	−	0.185950i
$81$	−1.00000			−0.111111
$82$	−4.68886	+	4.68886i	−0.517798	+	0.517798i
$83$	1.63570	+	1.63570i	0.179541	+	0.179541i	0.791156	−	0.611615i	$-0.209480\pi$
$83$	1.63570	+	1.63570i	0.179541	+	0.179541i	−0.611615	+	0.791156i	$0.709480\pi$
$84$	3.19270	−	1.96260i	0.348352	−	0.214137i
$85$	1.40788	+	4.49678i	0.152706	+	0.487744i
$86$	−2.99355			−0.322803
$87$	−1.95945	+	1.95945i	−0.210075	+	0.210075i
$88$	−7.10728	+	7.10728i	−0.757638	+	0.757638i
$89$	−5.05313			−0.535631			−0.267815	−	0.963470i	$-0.586302\pi$
$89$	−5.05313			−0.535631			−0.267815	+	0.963470i	$0.586302\pi$
$90$	−0.510348	−	1.63006i	−0.0537954	−	0.171823i
$91$	−7.18757	−	11.6925i	−0.753462	−	1.22571i
$92$	0.756656	+	0.756656i	0.0788868	+	0.0788868i
$93$	1.69475	−	1.69475i	0.175737	−	0.175737i
$94$	5.93123			0.611759
$95$	−0.0723134	+	0.138232i	−0.00741920	+	0.0141823i
$96$		−	5.86078i		−	0.598164i
$97$	6.85851	−	6.85851i	0.696376	−	0.696376i	−0.267251	−	0.963627i	$-0.586115\pi$
$97$	6.85851	−	6.85851i	0.696376	−	0.696376i	0.963627	+	0.267251i	$0.0861152\pi$
$98$	1.66650	+	5.08082i	0.168342	+	0.513240i
$99$		−	3.85136i		−	0.387076i
$100$	−5.81792	+	4.03893i	−0.581792	+	0.403893i
$101$		−	19.1953i		−	1.91000i	−0.296605	−	0.955000i	$-0.595855\pi$
$101$		−	19.1953i		−	1.91000i	0.296605	−	0.955000i	$-0.404145\pi$
$102$	1.13823	+	1.13823i	0.112702	+	0.112702i
$103$	2.33825	+	2.33825i	0.230394	+	0.230394i	0.812857	−	0.582463i	$-0.197911\pi$
$103$	2.33825	+	2.33825i	0.230394	+	0.230394i	−0.582463	+	0.812857i	$0.697911\pi$
$104$	−13.5384			−1.32755
$105$	−5.90192	+	0.409006i	−0.575969	+	0.0399149i
$106$	6.63105			0.644064
$107$	−6.39747	−	6.39747i	−0.618467	−	0.618467i	0.326671	−	0.945138i	$-0.394073\pi$
$107$	−6.39747	−	6.39747i	−0.618467	−	0.618467i	−0.945138	+	0.326671i	$0.894073\pi$
$108$	1.00161	+	1.00161i	0.0963800	+	0.0963800i
$109$		−	2.16057i		−	0.206945i	−0.994632	−	0.103473i	$-0.967005\pi$
$109$		−	2.16057i		−	0.206945i	0.994632	−	0.103473i	$-0.0329954\pi$
$110$	6.27794	−	1.96554i	0.598578	−	0.187407i
$111$			8.75054i			0.830564i
$112$	−2.16027	−	0.515459i	−0.204126	−	0.0487063i
$113$	−4.13823	+	4.13823i	−0.389292	+	0.389292i	−0.874435	−	0.485143i	$-0.838768\pi$
$113$	−4.13823	+	4.13823i	−0.389292	+	0.389292i	0.485143	+	0.874435i	$0.338768\pi$
$114$			0.0532937i			0.00499142i
$115$	−0.504711	−	1.61205i	−0.0470645	−	0.150325i
$116$	3.92520			0.364446
$117$	3.66816	−	3.66816i	0.339122	−	0.339122i
$118$	−3.76718	−	3.76718i	−0.346797	−	0.346797i
$119$	4.74970	−	2.91971i	0.435404	−	0.267650i
$120$	−2.70502	+	5.17085i	−0.246934	+	0.472032i
$121$	3.83298			0.348453
$122$	−7.72984	+	7.72984i	−0.699827	+	0.699827i
$123$	−6.13823	+	6.13823i	−0.553466	+	0.553466i
$124$	−3.39496			−0.304876
$125$	11.0933	−	1.39233i	0.992215	−	0.124533i
$126$	−1.72174	+	1.05838i	−0.153385	+	0.0942881i
$127$	−4.83298	−	4.83298i	−0.428858	−	0.428858i	0.459381	−	0.888239i	$-0.348071\pi$
$127$	−4.83298	−	4.83298i	−0.428858	−	0.428858i	−0.888239	+	0.459381i	$0.848071\pi$
$128$	−6.77704	+	6.77704i	−0.599011	+	0.599011i
$129$	−3.91889			−0.345039
$130$	7.85136	+	4.10728i	0.688610	+	0.360232i
$131$			0.647499i			0.0565722i	0.999600	+	0.0282861i	$0.00900495\pi$
$131$			0.647499i			0.0565722i	−0.999600	+	0.0282861i	$0.990995\pi$
$132$	−3.85756	+	3.85756i	−0.335758	+	0.335758i
$133$	0.179547	+	0.0428413i	0.0155687	+	0.00371481i
$134$			0.449929i			0.0388680i
$135$	−0.668102	−	2.13393i	−0.0575011	−	0.183659i
$136$		−	5.49954i		−	0.471581i
$137$	10.2369	+	10.2369i	0.874597	+	0.874597i	0.992969	−	0.118372i	$-0.0377676\pi$
$137$	10.2369	+	10.2369i	0.874597	+	0.874597i	−0.118372	+	0.992969i	$0.537768\pi$
$138$	−0.408045	−	0.408045i	−0.0347351	−	0.0347351i
$139$	−22.1663			−1.88012			−0.940060	−	0.341009i	$-0.889231\pi$
$139$	−22.1663			−1.88012			−0.940060	+	0.341009i	$0.889231\pi$
$140$	6.32109	+	5.50176i	0.534230	+	0.464984i
$141$	7.76463			0.653900
$142$	−4.39019	−	4.39019i	−0.368417	−	0.368417i
$143$	14.1274	+	14.1274i	1.18139	+	1.18139i
$144$		−	0.839427i		−	0.0699523i
$145$	−5.49042	−	2.87220i	−0.455955	−	0.238523i
$146$			10.3190i			0.854007i
$147$	2.18163	+	6.65135i	0.179938	+	0.548594i
$148$	8.76463	−	8.76463i	0.720448	−	0.720448i
$149$		−	11.0475i		−	0.905050i	−0.891752	−	0.452525i	$-0.850523\pi$
$149$		−	11.0475i		−	0.905050i	0.891752	−	0.452525i	$-0.149477\pi$
$150$	3.13746	−	2.17809i	0.256172	−	0.177840i
$151$	18.3990			1.49729			0.748645	−	0.662972i	$-0.230705\pi$
$151$	18.3990			1.49729			0.748645	+	0.662972i	$0.230705\pi$
$152$	0.128748	−	0.128748i	0.0104429	−	0.0104429i
$153$	1.49007	+	1.49007i	0.120465	+	0.120465i
$154$	−4.07621	−	6.63105i	−0.328470	−	0.534345i
$155$	4.74873	+	2.48420i	0.381428	+	0.199536i
$156$	−7.34814			−0.588322
$157$	−1.04994	+	1.04994i	−0.0837946	+	0.0837946i	−0.747762	−	0.663967i	$-0.768871\pi$
$157$	−1.04994	+	1.04994i	−0.0837946	+	0.0837946i	0.663967	+	0.747762i	$0.268871\pi$
$158$	5.32759	−	5.32759i	0.423840	−	0.423840i
$159$	8.68077			0.688430
$160$	12.5065	−	3.91560i	0.988724	−	0.309555i
$161$	−1.70272	+	1.04669i	−0.134193	+	0.0824907i
$162$	−0.540143	−	0.540143i	−0.0424377	−	0.0424377i
$163$	5.50539	−	5.50539i	0.431215	−	0.431215i	−0.457826	−	0.889042i	$-0.651372\pi$
$163$	5.50539	−	5.50539i	0.431215	−	0.431215i	0.889042	+	0.457826i	$0.151372\pi$
$164$	12.2962			0.960174
$165$	8.21852	−	2.57310i	0.639811	−	0.200316i
$166$			1.76702i			0.137147i
$167$	1.88968	−	1.88968i	0.146228	−	0.146228i	−0.630203	−	0.776431i	$-0.717028\pi$
$167$	1.88968	−	1.88968i	0.146228	−	0.146228i	0.776431	+	0.630203i	$0.217028\pi$
$168$	6.71629	+	1.60256i	0.518173	+	0.123640i
$169$			13.9108i			1.07006i
$170$	−1.66845	+	3.18936i	−0.127964	+	0.244613i
$171$			0.0697674i			0.00533524i
$172$	3.92520	+	3.92520i	0.299294	+	0.299294i
$173$	−4.90751	−	4.90751i	−0.373111	−	0.373111i	0.495498	−	0.868609i	$-0.334986\pi$
$173$	−4.90751	−	4.90751i	−0.373111	−	0.373111i	−0.868609	+	0.495498i	$0.834986\pi$
$174$	−2.11676			−0.160471
$175$	−4.81588	−	12.3210i	−0.364046	−	0.931381i
$176$	3.23294			0.243692
$177$	−4.93165	−	4.93165i	−0.370685	−	0.370685i
$178$	−2.72941	−	2.72941i	−0.204578	−	0.204578i
$179$			18.5857i			1.38916i	0.719416	+	0.694579i	$0.244409\pi$
$179$			18.5857i			1.38916i	−0.719416	+	0.694579i	$0.755591\pi$
$180$	−1.46818	+	2.80654i	−0.109432	+	0.209187i
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$	2.43331	−	10.1979i	0.180369	−	0.755922i
$183$	−10.1192	+	10.1192i	−0.748034	+	0.748034i
$184$			1.97153i			0.145343i
$185$	−18.6730	+	5.84625i	−1.37287	+	0.429825i
$186$	1.83081			0.134242
$187$	−5.73880	+	5.73880i	−0.419663	+	0.419663i
$188$	−7.77713	−	7.77713i	−0.567206	−	0.567206i
$189$	−2.25395	+	1.38554i	−0.163951	+	0.100783i
$190$	−0.113725	+	0.0356057i	−0.00825047	+	0.00258311i
$191$	−5.39351			−0.390261			−0.195130	−	0.980777i	$-0.562513\pi$
$191$	−5.39351			−0.390261			−0.195130	+	0.980777i	$0.562513\pi$
$192$	1.97853	−	1.97853i	0.142788	−	0.142788i
$193$	−4.80599	+	4.80599i	−0.345943	+	0.345943i	−0.858596	−	0.512653i	$-0.828663\pi$
$193$	−4.80599	+	4.80599i	−0.345943	+	0.345943i	0.512653	+	0.858596i	$0.328663\pi$
$194$	7.40916			0.531946
$195$	10.2783	+	5.37688i	0.736044	+	0.385046i
$196$	4.47692	−	8.84720i	0.319780	−	0.631943i
$197$	12.6739	+	12.6739i	0.902981	+	0.902981i	0.995693	−	0.0927124i	$-0.0295537\pi$
$197$	12.6739	+	12.6739i	0.902981	+	0.902981i	−0.0927124	+	0.995693i	$0.529554\pi$
$198$	2.08029	−	2.08029i	0.147840	−	0.147840i
$199$	−2.67111			−0.189350			−0.0946750	−	0.995508i	$-0.530181\pi$
$199$	−2.67111			−0.189350			−0.0946750	+	0.995508i	$0.530181\pi$
$200$	−12.8414	−	2.31766i	−0.908026	−	0.163884i
$201$			0.589007i			0.0415453i
$202$	10.3682	−	10.3682i	0.729503	−	0.729503i
$203$	−1.70161	+	7.13138i	−0.119429	+	0.500524i
$204$		−	2.98494i		−	0.208988i
$205$	−17.1995	−	8.99757i	−1.20127	−	0.628417i
$206$			2.52597i			0.175993i
$207$	−0.534176	−	0.534176i	−0.0371278	−	0.0371278i
$208$	3.07916	+	3.07916i	0.213501	+	0.213501i
$209$	−0.268699			−0.0185863
$210$	−3.40881	−	2.96696i	−0.235230	−	0.204740i
$211$	−12.0239			−0.827757			−0.413879	−	0.910332i	$-0.635826\pi$
$211$	−12.0239			−0.827757			−0.413879	+	0.910332i	$0.635826\pi$
$212$	−8.69475	−	8.69475i	−0.597158	−	0.597158i
$213$	−5.74724	−	5.74724i	−0.393794	−	0.393794i
$214$		−	6.91110i		−	0.472433i
$215$	−2.61822	−	8.36262i	−0.178561	−	0.570326i
$216$			2.60978i			0.177573i
$217$	1.47174	−	6.16802i	0.0999082	−	0.418712i
$218$	1.16702	−	1.16702i	0.0790405	−	0.0790405i
$219$			13.5087i			0.912834i
$220$	−10.8090	−	5.65451i	−0.728742	−	0.381227i
$221$	−10.9316			−0.735342
$222$	−4.72654	+	4.72654i	−0.317225	+	0.317225i
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	0.197346	−	0.980334i	$-0.436768\pi$
$223$	−11.6925	−	11.6925i	−0.782988	−	0.782988i	−0.980334	+	0.197346i	$0.936768\pi$
$224$	−8.12033	−	13.2099i	−0.542563	−	0.882624i
$225$	4.10728	−	2.85136i	0.273819	−	0.190091i
$226$	−4.47048			−0.297372
$227$	1.10518	−	1.10518i	0.0733535	−	0.0733535i	−0.669478	−	0.742832i	$-0.733482\pi$
$227$	1.10518	−	1.10518i	0.0733535	−	0.0733535i	0.742832	+	0.669478i	$0.233482\pi$
$228$	0.0698797	−	0.0698797i	0.00462790	−	0.00462790i
$229$	7.83309			0.517625			0.258812	−	0.965928i	$-0.416669\pi$
$229$	7.83309			0.517625			0.258812	+	0.965928i	$0.416669\pi$
$230$	0.598123	−	1.14335i	0.0394390	−	0.0753906i
$231$	−5.33620	−	8.68077i	−0.351096	−	0.571153i
$232$	5.11372	+	5.11372i	0.335732	+	0.335732i
$233$	1.00797	−	1.00797i	0.0660345	−	0.0660345i	−0.673318	−	0.739353i	$-0.735132\pi$
$233$	1.00797	−	1.00797i	0.0660345	−	0.0660345i	0.739353	+	0.673318i	$0.235132\pi$
$234$	3.96267			0.259048
$235$	5.18757	+	16.5691i	0.338399	+	1.08085i
$236$			9.87918i			0.643080i
$237$	6.97440	−	6.97440i	0.453036	−	0.453036i
$238$	4.14258	+	0.988454i	0.268524	+	0.0640720i
$239$		−	20.2805i		−	1.31183i	−0.754833	−	0.655917i	$-0.772282\pi$
$239$		−	20.2805i		−	1.31183i	0.754833	−	0.655917i	$-0.227718\pi$
$240$	1.79128	−	0.560823i	0.115626	−	0.0362010i
$241$			2.76994i			0.178427i	0.996013	+	0.0892136i	$0.0284354\pi$
$241$			2.76994i			0.178427i	−0.996013	+	0.0892136i	$0.971565\pi$
$242$	2.07036	+	2.07036i	0.133088	+	0.133088i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	20.2710			1.29772
$245$	−12.7359	+	9.09922i	−0.813670	+	0.581328i
$246$	−6.63105			−0.422780
$247$	−0.255918	−	0.255918i	−0.0162837	−	0.0162837i
$248$	−4.42292	−	4.42292i	−0.280856	−	0.280856i
$249$			2.31322i			0.146595i
$250$	6.74403	+	5.23992i	0.426530	+	0.331401i
$251$		−	6.09982i		−	0.385017i	−0.981295	−	0.192509i	$-0.938338\pi$
$251$		−	6.09982i		−	0.385017i	0.981295	−	0.192509i	$-0.0616623\pi$
$252$	3.64535	+	0.869810i	0.229635	+	0.0547929i
$253$	2.05731	−	2.05731i	0.129342	−	0.129342i
$254$		−	5.22100i		−	0.327595i
$255$	−2.18418	+	4.17522i	−0.136779	+	0.261463i
$256$	−12.9173			−0.807330
$257$	−2.01843	+	2.01843i	−0.125906	+	0.125906i	−0.767252	−	0.641346i	$-0.778376\pi$
$257$	−2.01843	+	2.01843i	−0.125906	+	0.125906i	0.641346	+	0.767252i	$0.278376\pi$
$258$	−2.11676	−	2.11676i	−0.131784	−	0.131784i
$259$	12.1242	+	19.7233i	0.753361	+	1.22554i
$260$	−4.90931	−	15.6804i	−0.304462	−	0.972456i
$261$	−2.77107			−0.171525
$262$	−0.349742	+	0.349742i	−0.0216071	+	0.0216071i
$263$	16.7686	−	16.7686i	1.03400	−	1.03400i	0.0345941	−	0.999401i	$-0.488986\pi$
$263$	16.7686	−	16.7686i	1.03400	−	1.03400i	0.999401	−	0.0345941i	$-0.0110138\pi$
$264$	−10.0512			−0.618609
$265$	5.79964	+	18.5241i	0.356269	+	1.13793i
$266$	0.0738405	+	0.120121i	0.00452745	+	0.00736511i
$267$	−3.57310	−	3.57310i	−0.218670	−	0.218670i
$268$	0.589955	−	0.589955i	0.0360372	−	0.0360372i
$269$	24.7351			1.50813			0.754064	−	0.656801i	$-0.228091\pi$
$269$	24.7351			1.50813			0.754064	+	0.656801i	$0.228091\pi$
$270$	0.791755	−	1.51350i	0.0481847	−	0.0921085i
$271$			4.13470i			0.251165i	0.992083	+	0.125583i	$0.0400800\pi$
$271$			4.13470i			0.251165i	−0.992083	+	0.125583i	$0.959920\pi$
$272$	−1.25081	+	1.25081i	−0.0758413	+	0.0758413i
$273$	3.18548	−	13.3502i	0.192794	−	0.807993i
$274$			11.0588i			0.668085i
$275$	10.9816	+	15.8186i	0.662217	+	0.953898i
$276$			1.07007i			0.0644108i
$277$	−12.1128	−	12.1128i	−0.727786	−	0.727786i	0.242393	−	0.970178i	$-0.422068\pi$
$277$	−12.1128	−	12.1128i	−0.727786	−	0.727786i	−0.970178	+	0.242393i	$0.922068\pi$
$278$	−11.9730	−	11.9730i	−0.718091	−	0.718091i
$279$	2.39674			0.143489
$280$	1.06742	+	15.4027i	0.0637904	+	0.920489i
$281$	5.25279			0.313355			0.156678	−	0.987650i	$-0.449922\pi$
$281$	5.25279			0.313355			0.156678	+	0.987650i	$0.449922\pi$
$282$	4.19401	+	4.19401i	0.249750	+	0.249750i
$283$	−1.66729	−	1.66729i	−0.0991101	−	0.0991101i	0.655813	−	0.754923i	$-0.272326\pi$
$283$	−1.66729	−	1.66729i	−0.0991101	−	0.0991101i	−0.754923	+	0.655813i	$0.772326\pi$
$284$			11.5130i			0.683170i
$285$	−0.148878	+	0.0466117i	−0.00881879	+	0.00276104i
$286$			15.2617i			0.902441i
$287$	−5.33051	+	22.3400i	−0.314650	+	1.31869i
$288$	4.14420	−	4.14420i	0.244199	−	0.244199i
$289$			12.5594i			0.738787i
$290$	−1.41421	−	4.51701i	−0.0830455	−	0.265248i
$291$	9.69940			0.568589
$292$	13.5305	−	13.5305i	0.791810	−	0.791810i
$293$	−15.2556	−	15.2556i	−0.891240	−	0.891240i	0.103400	−	0.994640i	$-0.467028\pi$
$293$	−15.2556	−	15.2556i	−0.891240	−	0.891240i	−0.994640	+	0.103400i	$0.967028\pi$
$294$	−2.41429	+	4.77107i	−0.140804	+	0.278255i
$295$	7.22893	−	13.8186i	0.420884	−	0.804551i
$296$	22.8370			1.32737
$297$	2.72332	−	2.72332i	0.158023	−	0.158023i
$298$	5.96725	−	5.96725i	0.345674	−	0.345674i
$299$	3.91889			0.226635
$300$	−6.96984	−	1.25794i	−0.402404	−	0.0726272i
$301$	−8.83298	+	5.42977i	−0.509125	+	0.312967i
$302$	9.93809	+	9.93809i	0.571873	+	0.571873i
$303$	13.5731	−	13.5731i	0.779754	−	0.779754i
$304$	−0.0585646			−0.00335891
$305$	−28.3543	−	14.8330i	−1.62356	−	0.849334i
$306$			1.60970i			0.0920206i
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	−0.988114	−	0.153721i	$-0.950874\pi$
$307$	−14.6198	+	14.6198i	−0.834394	+	0.834394i	0.153721	+	0.988114i	$0.450874\pi$
$308$	−3.34995	+	14.0395i	−0.190881	+	0.799977i
$309$			3.30678i			0.188116i
$310$	1.22317	+	3.90682i	0.0694714	+	0.221893i
$311$			2.86218i			0.162299i	0.996702	+	0.0811497i	$0.0258592\pi$
$311$			2.86218i			0.162299i	−0.996702	+	0.0811497i	$0.974141\pi$
$312$	−9.57310	−	9.57310i	−0.541970	−	0.541970i
$313$	−9.41824	−	9.41824i	−0.532350	−	0.532350i	0.388921	−	0.921271i	$-0.372848\pi$
$313$	−9.41824	−	9.41824i	−0.532350	−	0.532350i	−0.921271	+	0.388921i	$0.872848\pi$
$314$	−1.13424			−0.0640088
$315$	−4.46250	−	3.88408i	−0.251434	−	0.218843i
$316$	−13.9713			−0.785945
$317$	7.38310	+	7.38310i	0.414676	+	0.414676i	0.883364	−	0.468688i	$-0.155273\pi$
$317$	7.38310	+	7.38310i	0.414676	+	0.414676i	−0.468688	+	0.883364i	$0.655273\pi$
$318$	4.68886	+	4.68886i	0.262938	+	0.262938i
$319$		−	10.6724i		−	0.597540i
$320$	5.54390	+	2.90018i	0.309914	+	0.162125i
$321$		−	9.04739i		−	0.504976i
$322$	−1.48508	−	0.354351i	−0.0827600	−	0.0197472i
$323$	0.103958	−	0.103958i	0.00578440	−	0.00578440i
$324$			1.41649i			0.0786939i
$325$	−4.60691	+	25.5254i	−0.255545	+	1.41590i
$326$	5.94740			0.329396
$327$	1.52776	−	1.52776i	0.0844851	−	0.0844851i
$328$	16.0194	+	16.0194i	0.884526	+	0.884526i
$329$	17.5011	−	10.7582i	0.964866	−	0.593118i
$330$	5.82902	+	3.04933i	0.320877	+	0.167860i
$331$	23.6200			1.29827			0.649136	−	0.760672i	$-0.275130\pi$
$331$	23.6200			1.29827			0.649136	+	0.760672i	$0.275130\pi$
$332$	2.31695	−	2.31695i	0.127159	−	0.127159i
$333$	−6.18757	+	6.18757i	−0.339076	+	0.339076i
$334$	2.04139			0.111700
$335$	−1.25690	+	0.393517i	−0.0686716	+	0.0215001i
$336$	−1.16306	−	1.89203i	−0.0634500	−	0.103219i
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	0.559700	−	0.828695i	$-0.310916\pi$
$337$	−4.93809	−	4.93809i	−0.268995	−	0.268995i	−0.828695	+	0.559700i	$0.810916\pi$
$338$	−7.51384	+	7.51384i	−0.408699	+	0.408699i
$339$	−5.85234			−0.317856
$340$	6.36964	−	1.99425i	0.345442	−	0.108153i
$341$			9.23070i			0.499870i
$342$	−0.0376844	+	0.0376844i	−0.00203774	+	0.00203774i
$343$	14.1330	+	11.9691i	0.763109	+	0.646270i
$344$			10.2274i			0.551427i
$345$	0.783008	−	1.49678i	0.0421558	−	0.0805838i
$346$		−	5.30151i		−	0.285011i
$347$	5.83694	+	5.83694i	0.313343	+	0.313343i	0.846203	−	0.532860i	$-0.178883\pi$
$347$	5.83694	+	5.83694i	0.313343	+	0.313343i	−0.532860	+	0.846203i	$0.678883\pi$
$348$	2.77554	+	2.77554i	0.148784	+	0.148784i
$349$	−16.9121			−0.905282			−0.452641	−	0.891693i	$-0.649518\pi$
$349$	−16.9121			−0.905282			−0.452641	+	0.891693i	$0.649518\pi$
$350$	4.05385	−	9.25637i	0.216687	−	0.494774i
$351$	5.18757			0.276892
$352$	15.9608	+	15.9608i	0.850714	+	0.850714i
$353$	−11.1265	−	11.1265i	−0.592202	−	0.592202i	0.346024	−	0.938226i	$-0.387532\pi$
$353$	−11.1265	−	11.1265i	−0.592202	−	0.592202i	−0.938226	+	0.346024i	$0.887532\pi$
$354$		−	5.32759i		−	0.283158i
$355$	8.42444	−	16.1039i	0.447123	−	0.854708i
$356$			7.15771i			0.379358i
$357$	5.42309	+	1.29400i	0.287021	+	0.0684855i
$358$	−10.0389	+	10.0389i	−0.530574	+	0.530574i
$359$		−	8.14864i		−	0.430069i	−0.976606	−	0.215034i	$-0.931014\pi$
$359$		−	8.14864i		−	0.430069i	0.976606	−	0.215034i	$-0.0689864\pi$
$360$	−5.56908	+	1.74360i	−0.293516	+	0.0918958i
$361$	−18.9951			−0.999744
$362$	−4.58327	+	4.58327i	−0.240891	+	0.240891i
$363$	2.71033	+	2.71033i	0.142255	+	0.142255i
$364$	−16.5623	+	10.1811i	−0.868102	+	0.533636i
$365$	−28.8266	+	9.02520i	−1.50885	+	0.472401i
$366$	−10.9316			−0.571406
$367$	14.7480	−	14.7480i	0.769840	−	0.769840i	−0.208238	−	0.978078i	$-0.566773\pi$
$367$	14.7480	−	14.7480i	0.769840	−	0.769840i	0.978078	+	0.208238i	$0.0667728\pi$
$368$	0.448402	−	0.448402i	0.0233746	−	0.0233746i
$369$	−8.68077			−0.451903
$370$	−13.2439	−	6.92828i	−0.688518	−	0.360184i
$371$	19.5660	−	12.0275i	1.01582	−	0.624438i
$372$	−2.40060	−	2.40060i	−0.124465	−	0.124465i
$373$	1.49461	−	1.49461i	0.0773880	−	0.0773880i	−0.667353	−	0.744741i	$-0.732573\pi$
$373$	1.49461	−	1.49461i	0.0773880	−	0.0773880i	0.744741	+	0.667353i	$0.232573\pi$
$374$	−6.19955			−0.320571
$375$	8.82867	+	6.85963i	0.455911	+	0.354230i
$376$		−	20.2640i		−	1.04504i
$377$	10.1648	−	10.1648i	0.523511	−	0.523511i
$378$	−1.96584	−	0.469067i	−0.101112	−	0.0241262i
$379$		−	18.7135i		−	0.961248i	−0.876927	−	0.480624i	$-0.840410\pi$
$379$		−	18.7135i		−	0.961248i	0.876927	−	0.480624i	$-0.159590\pi$
$380$	0.195805	+	0.102431i	0.0100446	+	0.00525461i
$381$		−	6.83487i		−	0.350161i
$382$	−2.91327	−	2.91327i	−0.149056	−	0.149056i
$383$	20.9354	+	20.9354i	1.06975	+	1.06975i	0.997378	+	0.0723706i	$0.0230564\pi$
$383$	20.9354	+	20.9354i	1.06975	+	1.06975i	0.0723706	+	0.997378i	$0.476944\pi$
$384$	−9.58418			−0.489091
$385$	14.9590	−	17.1867i	0.762381	−	0.875916i
$386$	−5.19184			−0.264258
$387$	−2.77107	−	2.77107i	−0.140862	−	0.140862i
$388$	−9.71502	−	9.71502i	−0.493205	−	0.493205i
$389$		−	25.6611i		−	1.30107i	−0.759477	−	0.650535i	$-0.774545\pi$
$389$		−	25.6611i		−	1.30107i	0.759477	−	0.650535i	$-0.225455\pi$
$390$	2.64747	+	8.45604i	0.134060	+	0.428188i
$391$			1.59192i			0.0805069i
$392$	17.3586	−	5.69357i	0.876741	−	0.287569i
$393$	−0.457851	+	0.457851i	−0.0230955	+	0.0230955i
$394$			13.6915i			0.689767i
$395$	19.5425	+	10.2232i	0.983288	+	0.514387i
$396$	−5.45542			−0.274145
$397$	6.73585	−	6.73585i	0.338063	−	0.338063i	−0.517575	−	0.855638i	$-0.673165\pi$
$397$	6.73585	−	6.73585i	0.338063	−	0.338063i	0.855638	+	0.517575i	$0.173165\pi$
$398$	−1.44278	−	1.44278i	−0.0723201	−	0.0723201i
$399$	0.0966653	+	0.157252i	0.00483932	+	0.00787245i
$400$	2.39351	+	3.44776i	0.119676	+	0.172388i
$401$	14.7503			0.736593			0.368296	−	0.929708i	$-0.379941\pi$
$401$	14.7503			0.736593			0.368296	+	0.929708i	$0.379941\pi$
$402$	−0.318148	+	0.318148i	−0.0158678	+	0.0158678i
$403$	−8.79162	+	8.79162i	−0.437942	+	0.437942i
$404$	−27.1899			−1.35275
$405$	1.03649	−	1.98133i	0.0515038	−	0.0984532i
$406$	−4.77107	+	2.93285i	−0.236784	+	0.145555i
$407$	−23.8305	−	23.8305i	−1.18124	−	1.18124i
$408$	3.88876	−	3.88876i	0.192522	−	0.192522i
$409$	10.5604			0.522180			0.261090	−	0.965315i	$-0.415918\pi$
$409$	10.5604			0.522180			0.261090	+	0.965315i	$0.415918\pi$
$410$	−4.43022	−	14.1502i	−0.218793	−	0.698827i
$411$			14.4772i			0.714106i
$412$	3.31210	−	3.31210i	0.163176	−	0.163176i
$413$	−17.9487	−	4.28270i	−0.883196	−	0.210738i
$414$		−	0.577063i		−	0.0283611i
$415$	−4.93625	+	1.54547i	−0.242311	+	0.0758641i
$416$			30.4032i			1.49064i
$417$	−15.6739	−	15.6739i	−0.767556	−	0.767556i
$418$	−0.145136	−	0.145136i	−0.00709884	−	0.00709884i
$419$	15.5472			0.759532			0.379766	−	0.925083i	$-0.376004\pi$
$419$	15.5472			0.759532			0.379766	+	0.925083i	$0.376004\pi$
$420$	0.579354	+	8.36002i	0.0282696	+	0.407927i
$421$	3.29886			0.160776			0.0803882	−	0.996764i	$-0.474384\pi$
$421$	3.29886			0.160776			0.0803882	+	0.996764i	$0.474384\pi$
$422$	−6.49461	−	6.49461i	−0.316153	−	0.316153i
$423$	5.49042	+	5.49042i	0.266953	+	0.266953i
$424$		−	22.6549i		−	1.10022i
$425$	−10.3689	−	1.87141i	−0.502964	−	0.0907766i
$426$		−	6.20867i		−	0.300811i
$427$	−8.78764	+	36.8287i	−0.425264	+	1.78227i
$428$	−9.06196	+	9.06196i	−0.438026	+	0.438026i
$429$			19.9792i			0.964604i
$430$	3.10280	−	5.93123i	0.149630	−	0.286029i
$431$	−14.0911			−0.678743			−0.339371	−	0.940652i	$-0.610214\pi$
$431$	−14.0911			−0.678743			−0.339371	+	0.940652i	$0.610214\pi$
$432$	0.593565	−	0.593565i	0.0285579	−	0.0285579i
$433$	−1.72650	−	1.72650i	−0.0829702	−	0.0829702i	0.664404	−	0.747374i	$-0.268686\pi$
$433$	−1.72650	−	1.72650i	−0.0829702	−	0.0829702i	−0.747374	+	0.664404i	$0.768686\pi$
$434$	4.12656	−	2.53666i	0.198081	−	0.121764i
$435$	−1.85136	−	5.91327i	−0.0887660	−	0.283519i
$436$	−3.06043			−0.146568
$437$	−0.0372681	+	0.0372681i	−0.00178277	+	0.00178277i
$438$	−7.29664	+	7.29664i	−0.348647	+	0.348647i
$439$	−27.1172			−1.29423			−0.647116	−	0.762392i	$-0.724025\pi$
$439$	−27.1172			−1.29423			−0.647116	+	0.762392i	$0.724025\pi$
$440$	−6.71524	−	21.4485i	−0.320136	−	1.02252i
$441$	−3.16057	+	6.24586i	−0.150503	+	0.297422i
$442$	−5.90465	−	5.90465i	−0.280856	−	0.280856i
$443$	−24.1502	+	24.1502i	−1.14741	+	1.14741i	−0.160349	+	0.987060i	$0.551262\pi$
$443$	−24.1502	+	24.1502i	−1.14741	+	1.14741i	−0.987060	+	0.160349i	$0.948738\pi$
$444$	12.3951			0.588243
$445$	5.23754	−	10.0119i	0.248283	−	0.474611i
$446$		−	12.6313i		−	0.598107i
$447$	7.81179	−	7.81179i	0.369485	−	0.369485i
$448$	1.71818	−	7.20084i	0.0811764	−	0.340208i
$449$			9.80267i			0.462617i	0.972881	+	0.231308i	$0.0743006\pi$
$449$			9.80267i			0.462617i	−0.972881	+	0.231308i	$0.925699\pi$
$450$	3.75866	+	0.678376i	0.177185	+	0.0319789i
$451$		−	33.4328i		−	1.57429i
$452$	5.86177	+	5.86177i	0.275714	+	0.275714i
$453$	13.0101	+	13.0101i	0.611266	+	0.611266i
$454$	1.19391			0.0560331
$455$	30.6166	−	2.12175i	1.43533	−	0.0994691i
$456$	0.182078			0.00852656
$457$	0.550071	+	0.550071i	0.0257312	+	0.0257312i	0.719855	−	0.694124i	$-0.244208\pi$
$457$	0.550071	+	0.550071i	0.0257312	+	0.0257312i	−0.694124	+	0.719855i	$0.744208\pi$
$458$	4.23099	+	4.23099i	0.197701	+	0.197701i
$459$			2.10728i			0.0983594i
$460$	−2.28346	+	0.714918i	−0.106467	+	0.0333332i
$461$			0.831786i			0.0387401i	0.999812	+	0.0193701i	$0.00616607\pi$
$461$			0.831786i			0.0387401i	−0.999812	+	0.0193701i	$0.993834\pi$
$462$	1.80655	−	7.57117i	0.0840481	−	0.352243i
$463$	5.45140	−	5.45140i	0.253348	−	0.253348i	−0.568994	−	0.822342i	$-0.692667\pi$
$463$	5.45140	−	5.45140i	0.253348	−	0.253348i	0.822342	+	0.568994i	$0.192667\pi$
$464$		−	2.32612i		−	0.107987i
$465$	1.60127	+	5.11446i	0.0742569	+	0.237177i
$466$	1.08890			0.0504423
$467$	−23.2827	+	23.2827i	−1.07740	+	1.07740i	−0.0806551	+	0.996742i	$0.525701\pi$
$467$	−23.2827	+	23.2827i	−1.07740	+	1.07740i	−0.996742	+	0.0806551i	$0.974299\pi$
$468$	−5.19592	−	5.19592i	−0.240181	−	0.240181i
$469$	0.816091	+	1.32759i	0.0376836	+	0.0613025i
$470$	−6.14768	+	11.7517i	−0.283571	+	0.542067i
$471$	−1.48484			−0.0684180
$472$	−12.8705	+	12.8705i	−0.592414	+	0.592414i
$473$	10.6724	−	10.6724i	0.490718	−	0.490718i
$474$	7.53435			0.346064
$475$	−0.198932	−	0.286554i	−0.00912762	−	0.0131480i
$476$	−4.13575	−	6.72791i	−0.189562	−	0.308373i
$477$	6.13823	+	6.13823i	0.281050	+	0.281050i
$478$	10.9544	−	10.9544i	0.501041	−	0.501041i
$479$	−40.4319			−1.84738			−0.923691	−	0.383138i	$-0.874843\pi$
$479$	−40.4319			−1.84738			−0.923691	+	0.383138i	$0.874843\pi$
$480$	11.6122	+	6.07467i	0.530020	+	0.277269i
$481$		−	45.3940i		−	2.06979i
$482$	−1.49616	+	1.49616i	−0.0681483	+	0.0681483i
$483$	−1.94413	−	0.463885i	−0.0884609	−	0.0211075i
$484$		−	5.42938i		−	0.246790i
$485$	6.48019	+	20.6978i	0.294250	+	0.939839i
$486$		−	0.763878i		−	0.0346502i
$487$	−7.22893	−	7.22893i	−0.327574	−	0.327574i	0.524089	−	0.851663i	$-0.324406\pi$
$487$	−7.22893	−	7.22893i	−0.327574	−	0.327574i	−0.851663	+	0.524089i	$0.824406\pi$
$488$	26.4089	+	26.4089i	1.19548	+	1.19548i
$489$	7.78580			0.352086
$490$	−11.7941	−	1.96435i	−0.532804	−	0.0887404i
$491$	20.1040			0.907279			0.453639	−	0.891185i	$-0.350125\pi$
$491$	20.1040			0.907279			0.453639	+	0.891185i	$0.350125\pi$
$492$	8.69475	+	8.69475i	0.391990	+	0.391990i
$493$	4.12910	+	4.12910i	0.185965	+	0.185965i
$494$		−	0.276465i		−	0.0124387i
$495$	7.63083	+	3.99191i	0.342980	+	0.179423i
$496$			2.01189i			0.0903364i
$497$	−20.9170	−	4.99097i	−0.938256	−	0.223876i
$498$	−1.24947	+	1.24947i	−0.0559902	+	0.0559902i
$499$		−	15.4227i		−	0.690414i	−0.938527	−	0.345207i	$-0.887809\pi$
$499$		−	15.4227i		−	0.690414i	0.938527	−	0.345207i	$-0.112191\pi$
$500$	−1.97222	−	15.7136i	−0.0882002	−	0.702732i
$501$	2.67241			0.119394
$502$	3.29478	−	3.29478i	0.147053	−	0.147053i
$503$	25.9985	+	25.9985i	1.15922	+	1.15922i	0.984644	+	0.174573i	$0.0558546\pi$
$503$	25.9985	+	25.9985i	1.15922	+	1.15922i	0.174573	+	0.984644i	$0.444145\pi$
$504$	3.61595	+	5.88231i	0.161067	+	0.262019i
$505$	38.0322	+	19.8958i	1.69241	+	0.885350i
$506$	2.22248			0.0988013
$507$	−9.83645	+	9.83645i	−0.436852	+	0.436852i
$508$	−6.84587	+	6.84587i	−0.303737	+	0.303737i
$509$	37.1271			1.64563			0.822816	−	0.568309i	$-0.192402\pi$
$509$	37.1271			1.64563			0.822816	+	0.568309i	$0.192402\pi$
$510$	−3.43499	+	1.07545i	−0.152104	+	0.0476216i
$511$	18.7168	+	30.4479i	0.827983	+	1.34694i
$512$	6.57690	+	6.57690i	0.290661	+	0.290661i
$513$	−0.0493330	+	0.0493330i	−0.00217810	+	0.00217810i
$514$	−2.18048			−0.0961768
$515$	−7.05642	+	2.20927i	−0.310943	+	0.0973519i
$516$			5.55107i			0.244372i
$517$	−21.1456	+	21.1456i	−0.929982	+	0.929982i
$518$	−4.10459	+	17.2022i	−0.180345	+	0.755821i
$519$		−	6.94026i		−	0.304644i
$520$	14.0325	−	26.8241i	0.615365	−	1.17631i
$521$		−	2.59132i		−	0.113528i	−0.998388	−	0.0567639i	$-0.981922\pi$
$521$		−	2.59132i		−	0.113528i	0.998388	−	0.0567639i	$-0.0180782\pi$
$522$	−1.49678	−	1.49678i	−0.0655122	−	0.0655122i
$523$	−6.08854	−	6.08854i	−0.266233	−	0.266233i	0.561347	−	0.827581i	$-0.310283\pi$
$523$	−6.08854	−	6.08854i	−0.266233	−	0.266233i	−0.827581	+	0.561347i	$0.810283\pi$
$524$	0.917176			0.0400670
$525$	5.30693	−	12.1176i	0.231613	−	0.528856i
$526$	18.1149			0.789846
$527$	−3.57131	−	3.57131i	−0.155569	−	0.155569i
$528$	2.28603	+	2.28603i	0.0994868	+	0.0994868i
$529$			22.4293i			0.975187i
$530$	−6.87304	+	13.1383i	−0.298546	+	0.570692i
$531$		−	6.97440i		−	0.302663i
$532$	0.0606843	−	0.254326i	0.00263100	−	0.0110264i
$533$	31.8425	−	31.8425i	1.37925	−	1.37925i
$534$		−	3.85997i		−	0.167037i
$535$	19.3065	−	6.04458i	0.834691	−	0.261330i
$536$	1.53718			0.0663960
$537$	−13.1421	+	13.1421i	−0.567122	+	0.567122i
$538$	13.3605	+	13.3605i	0.576013	+	0.576013i
$539$	−24.0551	−	12.1725i	−1.03613	−	0.524307i
$540$	−3.02269	+	0.946361i	−0.130076	+	0.0407249i
$541$	−33.4638			−1.43872			−0.719360	−	0.694638i	$-0.755565\pi$
$541$	−33.4638			−1.43872			−0.719360	+	0.694638i	$0.755565\pi$
$542$	−2.23333	+	2.23333i	−0.0959297	+	0.0959297i
$543$	−6.00000	+	6.00000i	−0.257485	+	0.257485i
$544$	−12.3503			−0.529515
$545$	4.28081	+	2.23942i	0.183370	+	0.0959262i
$546$	8.93165	−	5.49042i	0.382239	−	0.234968i
$547$	−0.828381	−	0.828381i	−0.0354190	−	0.0354190i	0.689175	−	0.724594i	$-0.257973\pi$
$547$	−0.828381	−	0.828381i	−0.0354190	−	0.0354190i	−0.724594	+	0.689175i	$0.757973\pi$
$548$	14.5005	−	14.5005i	0.619429	−	0.619429i
$549$	−14.3107			−0.610767
$550$	−2.61267	+	14.4760i	−0.111405	+	0.617257i
$551$			0.193331i			0.00823616i
$552$	−1.39408	+	1.39408i	−0.0593361	+	0.0593361i
$553$	6.05665	−	25.3832i	0.257555	−	1.07941i
$554$		−	13.0853i		−	0.555939i
$555$	−17.3377	−	9.06988i	−0.735946	−	0.384995i
$556$			31.3983i			1.33159i
$557$	14.7120	+	14.7120i	0.623366	+	0.623366i	0.946391	−	0.323024i	$-0.104700\pi$
$557$	14.7120	+	14.7120i	0.623366	+	0.623366i	−0.323024	+	0.946391i	$0.604700\pi$
$558$	1.29458	+	1.29458i	0.0548040	+	0.0548040i
$559$	20.3295			0.859846
$560$	3.26040	−	3.74595i	0.137777	−	0.158295i
$561$	−8.11589			−0.342653
$562$	2.83726	+	2.83726i	0.119683	+	0.119683i
$563$	−23.9693	−	23.9693i	−1.01019	−	1.01019i	−0.999948	−	0.0102391i	$-0.996741\pi$
$563$	−23.9693	−	23.9693i	−1.01019	−	1.01019i	−0.0102391	−	0.999948i	$-0.503259\pi$
$564$		−	10.9985i		−	0.463121i
$565$	−3.90996	−	12.4885i	−0.164493	−	0.525394i
$566$		−	1.80115i		−	0.0757080i
$567$	−2.57351	−	0.614060i	−0.108077	−	0.0257881i
$568$	−14.9990	+	14.9990i	−0.629346	+	0.629346i
$569$		−	15.6660i		−	0.656751i	−0.944547	−	0.328376i	$-0.893499\pi$
$569$		−	15.6660i		−	0.656751i	0.944547	−	0.328376i	$-0.106501\pi$
$570$	−0.105593	−	0.0552386i	−0.00442279	−	0.00231369i
$571$	36.9887			1.54793			0.773964	−	0.633229i	$-0.218271\pi$
$571$	36.9887			1.54793			0.773964	+	0.633229i	$0.218271\pi$
$572$	20.0114	−	20.0114i	0.836717	−	0.836717i
$573$	−3.81379	−	3.81379i	−0.159323	−	0.159323i
$574$	−14.9460	+	9.18757i	−0.623836	+	0.383482i
$575$	3.71714	+	0.670882i	0.155015	+	0.0279777i
$576$	2.79807			0.116586
$577$	15.5587	−	15.5587i	0.647717	−	0.647717i	−0.304724	−	0.952441i	$-0.598564\pi$
$577$	15.5587	−	15.5587i	0.647717	−	0.647717i	0.952441	+	0.304724i	$0.0985641\pi$
$578$	−6.78386	+	6.78386i	−0.282171	+	0.282171i
$579$	−6.79669			−0.282461
$580$	−4.06845	+	7.77713i	−0.168933	+	0.322928i
$581$	3.20506	+	5.21389i	0.132968	+	0.216309i
$582$	5.23907	+	5.23907i	0.217166	+	0.217166i
$583$	−23.6405	+	23.6405i	−0.979091	+	0.979091i
$584$	35.2548			1.45885
$585$	3.46582	+	11.0699i	0.143294	+	0.457683i
$586$		−	16.4804i		−	0.680798i
$587$	−15.7111	+	15.7111i	−0.648468	+	0.648468i	−0.952623	−	0.304155i	$-0.901626\pi$
$587$	−15.7111	+	15.7111i	−0.648468	+	0.648468i	0.304155	+	0.952623i	$0.401626\pi$
$588$	9.42158	−	3.09026i	0.388539	−	0.127440i
$589$		−	0.167214i		−	0.00688993i
$590$	11.3687	−	3.55938i	0.468041	−	0.146537i
$591$			17.9237i			0.737281i
$592$	−5.19401	−	5.19401i	−0.213473	−	0.213473i
$593$	−1.85199	−	1.85199i	−0.0760523	−	0.0760523i	0.668057	−	0.744110i	$-0.267126\pi$
$593$	−1.85199	−	1.85199i	−0.0760523	−	0.0760523i	−0.744110	+	0.668057i	$0.767126\pi$
$594$	2.94197			0.120710
$595$	0.861891	+	12.4370i	0.0353341	+	0.509867i
$596$	−15.6487			−0.640997
$597$	−1.88876	−	1.88876i	−0.0773018	−	0.0773018i
$598$	2.11676	+	2.11676i	0.0865609	+	0.0865609i
$599$			47.3151i			1.93324i	0.256208	+	0.966622i	$0.417527\pi$
$599$			47.3151i			1.93324i	−0.256208	+	0.966622i	$0.582473\pi$
$600$	−7.44143	−	10.7191i	−0.303795	−	0.437605i
$601$		−	11.0819i		−	0.452041i	−0.974123	−	0.226021i	$-0.927428\pi$
$601$		−	11.0819i		−	0.452041i	0.974123	−	0.226021i	$-0.0725717\pi$
$602$	−7.70393	−	1.83822i	−0.313989	−	0.0749203i
$603$	−0.416491	+	0.416491i	−0.0169608	+	0.0169608i
$604$		−	26.0620i		−	1.06045i
$605$	−3.97286	+	7.59441i	−0.161520	+	0.308757i
$606$	14.6628			0.595637
$607$	7.54653	−	7.54653i	0.306304	−	0.306304i	−0.537170	−	0.843474i	$-0.680507\pi$
$607$	7.54653	−	7.54653i	0.306304	−	0.306304i	0.843474	+	0.537170i	$0.180507\pi$
$608$	−0.289130	−	0.289130i	−0.0117258	−	0.0117258i
$609$	−6.24586	+	3.83943i	−0.253095	+	0.155581i
$610$	−7.30346	−	23.3273i	−0.295708	−	0.944496i
$611$	−40.2795			−1.62953
$612$	2.11067	−	2.11067i	0.0853189	−	0.0853189i
$613$	−2.62487	+	2.62487i	−0.106017	+	0.106017i	−0.758126	−	0.652108i	$-0.773885\pi$
$613$	−2.62487	+	2.62487i	−0.106017	+	0.106017i	0.652108	+	0.758126i	$0.273885\pi$
$614$	−15.7935			−0.637375
$615$	−5.79964	−	18.5241i	−0.233864	−	0.746965i
$616$	−22.6549	+	13.9263i	−0.912793	+	0.561108i
$617$	11.3212	+	11.3212i	0.455774	+	0.455774i	0.897266	−	0.441491i	$-0.145550\pi$
$617$	11.3212	+	11.3212i	0.455774	+	0.455774i	−0.441491	+	0.897266i	$0.645550\pi$
$618$	−1.78613	+	1.78613i	−0.0718488	+	0.0718488i
$619$	−9.06771			−0.364462			−0.182231	−	0.983256i	$-0.558332\pi$
$619$	−9.06771			−0.364462			−0.182231	+	0.983256i	$0.558332\pi$
$620$	3.51885	−	6.72654i	0.141320	−	0.270144i
$621$		−	0.755439i		−	0.0303147i
$622$	−1.54599	+	1.54599i	−0.0619884	+	0.0619884i
$623$	−13.0043	−	3.10292i	−0.521005	−	0.124316i
$624$			4.35458i			0.174323i
$625$	−8.73948	+	23.4227i	−0.349579	+	0.936907i
$626$		−	10.1744i		−	0.406651i
$627$	−0.189999	−	0.189999i	−0.00758783	−	0.00758783i
$628$	1.48723	+	1.48723i	0.0593471	+	0.0593471i
$629$	18.4398			0.735244
$630$	−0.312431	−	4.50835i	−0.0124475	−	0.179617i
$631$	−9.67260			−0.385060			−0.192530	−	0.981291i	$-0.561669\pi$
$631$	−9.67260			−0.385060			−0.192530	+	0.981291i	$0.561669\pi$
$632$	−18.2017	−	18.2017i	−0.724023	−	0.724023i
$633$	−8.50216	−	8.50216i	−0.337930	−	0.337930i
$634$			7.97587i			0.316762i
$635$	14.5851	−	4.56639i	0.578792	−	0.181212i
$636$		−	12.2962i		−	0.487577i
$637$	−11.3173	−	34.5043i	−0.448409	−	1.36711i
$638$	5.76463	−	5.76463i	0.228224	−	0.228224i
$639$		−	8.12783i		−	0.321532i
$640$	−6.40321	−	20.4519i	−0.253109	−	0.808434i
$641$	−40.5847			−1.60300			−0.801500	−	0.597995i	$-0.795964\pi$
$641$	−40.5847			−1.60300			−0.801500	+	0.597995i	$0.795964\pi$
$642$	4.88689	−	4.88689i	0.192870	−	0.192870i
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	0.779733	−	0.626112i	$-0.215355\pi$
$643$	3.89544	+	3.89544i	0.153621	+	0.153621i	−0.626112	+	0.779733i	$0.715355\pi$
$644$	1.48263	+	2.41189i	0.0584236	+	0.0950418i
$645$	4.06191	−	7.76463i	0.159937	−	0.305732i
$646$	0.112305			0.00441857
$647$	16.8414	−	16.8414i	0.662104	−	0.662104i	−0.293772	−	0.955876i	$-0.594911\pi$
$647$	16.8414	−	16.8414i	0.662104	−	0.662104i	0.955876	+	0.293772i	$0.0949106\pi$
$648$	−1.84539	+	1.84539i	−0.0724939	+	0.0724939i
$649$	26.8609			1.05438
$650$	−16.2758	+	11.2990i	−0.638388	+	0.443183i
$651$	5.40212	−	3.32077i	0.211726	−	0.130151i
$652$	−7.79833	−	7.79833i	−0.305406	−	0.305406i
$653$	−22.9951	+	22.9951i	−0.899867	+	0.899867i	−0.995424	−	0.0955569i	$-0.969537\pi$
$653$	−22.9951	+	22.9951i	−0.899867	+	0.899867i	0.0955569	+	0.995424i	$0.469537\pi$
$654$	1.65041			0.0645363
$655$	−1.28291	−	0.671128i	−0.0501275	−	0.0262232i
$656$		−	7.28688i		−	0.284505i
$657$	−9.55210	+	9.55210i	−0.372663	+	0.372663i
$658$	15.2640	+	3.64213i	0.595054	+	0.141985i
$659$			32.7543i			1.27593i	0.770067	+	0.637963i	$0.220223\pi$
$659$			32.7543i			1.27593i	−0.770067	+	0.637963i	$0.779777\pi$
$660$	−3.64478	−	11.6415i	−0.141873	−	0.453143i
$661$			32.5174i			1.26478i	0.774650	+	0.632391i	$0.217926\pi$
$661$			32.5174i			1.26478i	−0.774650	+	0.632391i	$0.782074\pi$
$662$	12.7582	+	12.7582i	0.495861	+	0.495861i
$663$	−7.72984	−	7.72984i	−0.300202	−	0.300202i
$664$	6.03701			0.234281
$665$	−0.270982	+	0.311337i	−0.0105082	+	0.0120731i
$666$	−6.68434			−0.259013
$667$	−1.48024	−	1.48024i	−0.0573152	−	0.0573152i
$668$	−2.67671	−	2.67671i	−0.103565	−	0.103565i
$669$		−	16.5357i		−	0.639307i
$670$	−0.891460	−	0.466349i	−0.0344401	−	0.0180166i
$671$		−	55.1158i		−	2.12772i
$672$	3.59887	−	15.0828i	0.138829	−	0.581830i
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	−0.951974	−	0.306179i	$-0.900950\pi$
$673$	−16.7534	+	16.7534i	−0.645796	+	0.645796i	0.306179	+	0.951974i	$0.400950\pi$
$674$		−	5.33455i		−	0.205479i
$675$	4.92050	+	0.888068i	0.189390	+	0.0341818i
$676$	19.7046			0.757868
$677$	−6.85568	+	6.85568i	−0.263485	+	0.263485i	−0.826468	−	0.562983i	$-0.809654\pi$
$677$	−6.85568	+	6.85568i	−0.263485	+	0.263485i	0.562983	+	0.826468i	$0.309654\pi$
$678$	−3.16110	−	3.16110i	−0.121401	−	0.121401i
$679$	21.8620	−	13.4389i	0.838985	−	0.515737i
$680$	10.8964	+	5.70024i	0.417858	+	0.218594i
$681$	1.56296			0.0598929
$682$	−4.98590	+	4.98590i	−0.190920	+	0.190920i
$683$	23.2345	−	23.2345i	0.889042	−	0.889042i	−0.105389	−	0.994431i	$-0.533609\pi$
$683$	23.2345	−	23.2345i	0.889042	−	0.889042i	0.994431	+	0.105389i	$0.0336088\pi$
$684$	0.0988248			0.00377866
$685$	−30.8932	+	9.67222i	−1.18037	+	0.369557i
$686$	1.16881	+	14.0988i	0.0446255	+	0.538297i
$687$	5.53883	+	5.53883i	0.211319	+	0.211319i
$688$	2.32612	−	2.32612i	0.0886823	−	0.0886823i
$689$	−45.0321			−1.71559
$690$	1.23141	−	0.385537i	0.0468790	−	0.0146772i
$691$			42.4714i			1.61569i	0.589395	+	0.807845i	$0.299366\pi$
$691$			42.4714i			1.61569i	−0.589395	+	0.807845i	$0.700634\pi$
$692$	−6.95144	+	6.95144i	−0.264254	+	0.264254i
$693$	2.36497	−	9.91150i	0.0898376	−	0.376507i
$694$			6.30557i			0.239356i
$695$	22.9752	−	43.9188i	0.871500	−	1.66594i
$696$			7.23190i			0.274124i
$697$	12.9350	+	12.9350i	0.489947	+	0.489947i
$698$	−9.13494	−	9.13494i	−0.345763	−	0.345763i
$699$	1.42549			0.0539169
$700$	−17.4526	+	6.82165i	−0.659646	+	0.257834i
$701$	17.0793			0.645077			0.322539	−	0.946556i	$-0.395464\pi$
$701$	17.0793			0.645077			0.322539	+	0.946556i	$0.395464\pi$
$702$	2.80203	+	2.80203i	0.105756	+	0.105756i
$703$	0.431690	+	0.431690i	0.0162815	+	0.0162815i
$704$			10.7764i			0.406150i
$705$	−8.04799	+	15.3843i	−0.303105	+	0.579407i
$706$		−	12.0198i		−	0.452370i
$707$	11.7870	−	49.3991i	0.443297	−	1.85785i
$708$	−6.98563	+	6.98563i	−0.262536	+	0.262536i
$709$			32.6742i			1.22710i	0.789654	+	0.613552i	$0.210260\pi$
$709$			32.6742i			1.22710i	−0.789654	+	0.613552i	$0.789740\pi$
$710$	13.2488	−	4.14802i	0.497220	−	0.155673i
$711$	9.86329			0.369902
$712$	−9.32502	+	9.32502i	−0.349470	+	0.349470i
$713$	1.28028	+	1.28028i	0.0479469	+	0.0479469i
$714$	2.23030	+	3.62819i	0.0834670	+	0.135782i
$715$	−42.6341	+	13.3481i	−1.59443	+	0.499192i
$716$	26.3264			0.983865
$717$	14.3405	−	14.3405i	0.535554	−	0.535554i
$718$	4.40143	−	4.40143i	0.164260	−	0.164260i
$719$	−19.3248			−0.720693			−0.360346	−	0.932819i	$-0.617341\pi$
$719$	−19.3248			−0.720693			−0.360346	+	0.932819i	$0.617341\pi$
$720$	1.66319	+	0.870061i	0.0619832	+	0.0324253i
$721$	4.58166	+	7.45331i	0.170630	+	0.277576i
$722$	−10.2601	−	10.2601i	−0.381841	−	0.381841i
$723$	−1.95864	+	1.95864i	−0.0728426	+	0.0728426i
$724$	12.0193			0.446695
$725$	11.3816	−	7.90133i	0.422701	−	0.293448i
$726$			2.92793i			0.108666i
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	−0.654907	−	0.755710i	$-0.727292\pi$
$727$	2.71795	−	2.71795i	0.100803	−	0.100803i	0.755710	+	0.654907i	$0.227292\pi$
$728$	−34.8412	−	8.31339i	−1.29130	−	0.308115i
$729$		−	1.00000i		−	0.0370370i
$730$	−20.4454	−	10.6956i	−0.756718	−	0.395861i
$731$			8.25820i			0.305440i
$732$	14.3338	+	14.3338i	0.529791	+	0.529791i
$733$	−2.38437	−	2.38437i	−0.0880686	−	0.0880686i	0.661700	−	0.749769i	$-0.269835\pi$
$733$	−2.38437	−	2.38437i	−0.0880686	−	0.0880686i	−0.749769	+	0.661700i	$0.769835\pi$
$734$	15.9321			0.588064
$735$	−15.4398	−	2.57155i	−0.569505	−	0.0948532i
$736$	4.42747			0.163199
$737$	−1.60406	−	1.60406i	−0.0590862	−	0.0590862i
$738$	−4.68886	−	4.68886i	−0.172599	−	0.172599i
$739$			4.95679i			0.182339i	0.995835	+	0.0911693i	$0.0290605\pi$
$739$			4.95679i			0.182339i	−0.995835	+	0.0911693i	$0.970940\pi$
$740$	8.28116	+	26.4501i	0.304422	+	0.972326i
$741$		−	0.361923i		−	0.0132956i
$742$	17.0650	+	4.07186i	0.626477	+	0.149483i
$743$	15.6556	−	15.6556i	0.574347	−	0.574347i	−0.358993	−	0.933340i	$-0.616880\pi$
$743$	15.6556	−	15.6556i	0.574347	−	0.574347i	0.933340	+	0.358993i	$0.116880\pi$
$744$		−	6.25496i		−	0.229318i
$745$	21.8889	+	11.4507i	0.801946	+	0.419521i
$746$	1.61461			0.0591150
$747$	−1.63570	+	1.63570i	−0.0598470	+	0.0598470i
$748$	8.12896	+	8.12896i	0.297224	+	0.297224i
$749$	−12.5355	−	20.3924i	−0.458037	−	0.745120i
$750$	1.06357	+	8.47393i	0.0388360	+	0.309424i
$751$	−11.1909			−0.408361			−0.204181	−	0.978933i	$-0.565453\pi$
$751$	−11.1909			−0.408361			−0.204181	+	0.978933i	$0.565453\pi$
$752$	−4.60881	+	4.60881i	−0.168066	+	0.168066i
$753$	4.31322	−	4.31322i	0.157183	−	0.157183i
$754$	10.9808			0.399899
$755$	−19.0704	+	36.4545i	−0.694045	+	1.32672i
$756$	1.96260	+	3.19270i	0.0713791	+	0.116117i
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.997189	+	0.0749214i	$0.0238706\pi$
$757$	29.4977	+	29.4977i	1.07211	+	1.07211i	0.0749214	+	0.997189i	$0.476129\pi$
$758$	10.1080	−	10.1080i	0.367138	−	0.367138i
$759$	2.90947			0.105607
$760$	0.121646	+	0.388540i	0.00441258	+	0.0140938i
$761$			28.1175i			1.01926i	0.860395	+	0.509629i	$0.170217\pi$
$761$			28.1175i			1.01926i	−0.860395	+	0.509629i	$0.829783\pi$
$762$	3.69181	−	3.69181i	0.133740	−	0.133740i
$763$	1.32672	−	5.56025i	0.0480305	−	0.201294i
$764$			7.63986i			0.276400i
$765$	−4.49678	+	1.40788i	−0.162581	+	0.0509019i
$766$			22.6162i			0.817157i
$767$	25.5832	+	25.5832i	0.923757	+	0.923757i
$768$	−9.13390	−	9.13390i	−0.329591	−	0.329591i
$769$	6.61248			0.238452			0.119226	−	0.992867i	$-0.461959\pi$
$769$	6.61248			0.238452			0.119226	+	0.992867i	$0.461959\pi$
$770$	17.3633	−	1.20328i	0.625729	−	0.0433634i
$771$	−2.85449			−0.102802
$772$	6.80764	+	6.80764i	0.245012	+	0.245012i
$773$	31.7247	+	31.7247i	1.14106	+	1.14106i	0.988257	+	0.152800i	$0.0488290\pi$
$773$	31.7247	+	31.7247i	1.14106	+	1.14106i	0.152800	+	0.988257i	$0.451171\pi$
$774$		−	2.99355i		−	0.107601i
$775$	−9.84407	+	6.83396i	−0.353609	+	0.245483i
$776$		−	25.3133i		−	0.908695i
$777$	−5.37335	+	22.5196i	−0.192768	+	0.807885i
$778$	13.8607	−	13.8607i	0.496929	−	0.496929i
$779$			0.605634i			0.0216991i
$780$	7.61630	−	14.5591i	0.272707	−	0.521300i
$781$	31.3032			1.12012
$782$	−0.859866	+	0.859866i	−0.0307487	+	0.0307487i
$783$	−1.95945	−	1.95945i	−0.0700249	−	0.0700249i
$784$	−5.24295	−	2.65307i	−0.187248	−	0.0947525i
$785$	−0.992027	−	3.16855i	−0.0354070	−	0.113090i
$786$	−0.494610			−0.0176422
$787$	22.4472	−	22.4472i	0.800155	−	0.800155i	−0.182964	−	0.983120i	$-0.558569\pi$
$787$	22.4472	−	22.4472i	0.800155	−	0.800155i	0.983120	+	0.182964i	$0.0585693\pi$
$788$	17.9525	−	17.9525i	0.639532	−	0.639532i
$789$	23.7144			0.844254
$790$	5.03372	+	16.0777i	0.179092	+	0.572021i
$791$	−13.1909	+	8.10864i	−0.469014	+	0.288310i
$792$	−7.10728	−	7.10728i	−0.252546	−	0.252546i
$793$	52.4941	−	52.4941i	1.86412	−	1.86412i
$794$	7.27665			0.258239
$795$	−8.99757	+	17.1995i	−0.319111	+	0.610003i
$796$			3.78360i			0.134106i
$797$	5.14677	−	5.14677i	0.182308	−	0.182308i	−0.610053	−	0.792361i	$-0.708852\pi$
$797$	5.14677	−	5.14677i	0.182308	−	0.182308i	0.792361	+	0.610053i	$0.208852\pi$
$798$	−0.0327255	+	0.137152i	−0.00115847	+	0.00485512i
$799$		−	16.3622i		−	0.578854i
$800$	−5.20477	+	28.8380i	−0.184017	+	1.01958i
$801$		−	5.05313i		−	0.178544i
$802$	7.96725	+	7.96725i	0.281333	+	0.281333i
$803$	−36.7886	−	36.7886i	−1.29824	−	1.29824i
$804$	0.834323			0.0294243
$805$	−0.308980	−	4.45855i	−0.0108901	−	0.157143i
$806$	−9.49747			−0.334534
$807$	17.4904	+	17.4904i	0.615691	+	0.615691i
$808$	−35.4228	−	35.4228i	−1.24617	−	1.24617i
$809$			22.5215i			0.791815i	0.918290	+	0.395907i	$0.129570\pi$
$809$			22.5215i			0.791815i	−0.918290	+	0.395907i	$0.870430\pi$
$810$	1.63006	−	0.510348i	0.0572744	−	0.0179318i
$811$		−	34.9145i		−	1.22602i	−0.790077	−	0.613008i	$-0.789960\pi$
$811$		−	34.9145i		−	1.22602i	0.790077	−	0.613008i	$-0.210040\pi$
$812$	10.1015	+	2.41031i	0.354494	+	0.0845852i
$813$	−2.92367	+	2.92367i	−0.102538	+	0.102538i
$814$		−	25.7438i		−	0.902320i
$815$	5.20171	+	16.6143i	0.182208	+	0.581974i
$816$	−1.76891			−0.0619241
$817$	−0.193331	+	0.193331i	−0.00676378	+	0.00676378i
$818$	5.70414	+	5.70414i	0.199441	+	0.199441i
$819$	11.6925	−	7.18757i	0.408569	−	0.251154i
$820$	−12.7450	+	24.3629i	−0.445074	+	0.850790i
$821$	8.52640			0.297573			0.148787	−	0.988869i	$-0.452463\pi$
$821$	8.52640			0.297573			0.148787	+	0.988869i	$0.452463\pi$
$822$	−7.81974	+	7.81974i	−0.272745	+	0.272745i
$823$	−33.9044	+	33.9044i	−1.18183	+	1.18183i	−0.202564	+	0.979269i	$0.564927\pi$
$823$	−33.9044	+	33.9044i	−1.18183	+	1.18183i	−0.979269	+	0.202564i	$0.935073\pi$
$824$	8.62997			0.300639
$825$	−3.42027	+	18.9506i	−0.119079	+	0.659776i
$826$	−7.38158	−	12.0081i	−0.256838	−	0.417816i
$827$	−37.8440	−	37.8440i	−1.31597	−	1.31597i	−0.916940	−	0.399025i	$-0.869349\pi$
$827$	−37.8440	−	37.8440i	−1.31597	−	1.31597i	−0.399025	−	0.916940i	$-0.630651\pi$
$828$	−0.756656	+	0.756656i	−0.0262956	+	0.0262956i
$829$	−33.7140			−1.17094			−0.585469	−	0.810695i	$-0.699089\pi$
$829$	−33.7140			−1.17094			−0.585469	+	0.810695i	$0.699089\pi$
$830$	−3.50106	−	1.83151i	−0.121523	−	0.0635725i
$831$		−	17.1300i		−	0.594234i
$832$	−10.2638	+	10.2638i	−0.355832	+	0.355832i
$833$	14.0163	−	4.59730i	0.485635	−	0.159287i
$834$		−	16.9323i		−	0.586319i
$835$	1.78544	+	5.70272i	0.0617878	+	0.197351i
$836$			0.380610i			0.0131637i
$837$	1.69475	+	1.69475i	0.0585791	+	0.0585791i
$838$	8.39773	+	8.39773i	0.290095	+	0.290095i
$839$	−16.0665			−0.554679			−0.277339	−	0.960772i	$-0.589453\pi$
$839$	−16.0665			−0.554679			−0.277339	+	0.960772i	$0.589453\pi$
$840$	−10.1366	+	11.6462i	−0.349746	+	0.401831i
$841$	21.3211			0.735212
$842$	1.78185	+	1.78185i	0.0614068	+	0.0614068i
$843$	3.71429	+	3.71429i	0.127927	+	0.127927i
$844$			17.0317i			0.586255i
$845$	−27.5620	−	14.4185i	−0.948161	−	0.496011i
$846$			5.93123i			0.203920i
$847$	9.86420	+	2.35368i	0.338938	+	0.0808734i
$848$	−5.15260	+	5.15260i	−0.176941	+	0.176941i
$849$		−	2.35790i		−	0.0809231i
$850$	−4.58985	−	6.61150i	−0.157430	−	0.226773i
$851$	−6.61050			−0.226605
$852$	−8.14091	+	8.14091i	−0.278903	+	0.278903i
$853$	5.14393	+	5.14393i	0.176125	+	0.176125i	0.789664	−	0.613539i	$-0.210255\pi$
$853$	5.14393	+	5.14393i	0.176125	+	0.176125i	−0.613539	+	0.789664i	$0.710255\pi$
$854$	−24.6394	+	15.1462i	−0.843142	+	0.518292i
$855$	−0.138232	−	0.0723134i	−0.00472745	−	0.00247307i
$856$	−23.6117			−0.807032
$857$	−5.65076	+	5.65076i	−0.193026	+	0.193026i	−0.797002	−	0.603976i	$-0.793582\pi$
$857$	−5.65076	+	5.65076i	−0.193026	+	0.193026i	0.603976	+	0.797002i	$0.293582\pi$
$858$	−10.7916	+	10.7916i	−0.368420	+	0.368420i
$859$	42.0801			1.43575			0.717877	−	0.696170i	$-0.245114\pi$
$859$	42.0801			1.43575			0.717877	+	0.696170i	$0.245114\pi$
$860$	−11.8456	+	3.70868i	−0.403931	+	0.126465i
$861$	−19.5660	+	12.0275i	−0.666808	+	0.409897i
$862$	−7.61119	−	7.61119i	−0.259238	−	0.259238i
$863$	−11.9777	+	11.9777i	−0.407724	+	0.407724i	−0.880944	−	0.473220i	$-0.843092\pi$
$863$	−11.9777	+	11.9777i	−0.407724	+	0.407724i	0.473220	+	0.880944i	$0.343092\pi$
$864$	5.86078			0.199388
$865$	14.8100	−	4.63680i	0.503555	−	0.157656i
$866$		−	1.86511i		−	0.0633791i
$867$	−8.88082	+	8.88082i	−0.301608	+	0.301608i
$868$	−8.73694	−	2.08471i	−0.296551	−	0.0707595i
$869$			37.9871i			1.28862i
$870$	2.19401	−	4.19401i	0.0743839	−	0.142190i
$871$		−	3.05551i		−	0.103532i
$872$	−3.98711	−	3.98711i	−0.135021	−	0.135021i
$873$	6.85851	+	6.85851i	0.232125	+	0.232125i
$874$	−0.0402602			−0.00136182
$875$	29.4037	+	3.22879i	0.994025	+	0.109153i
$876$	19.1350			0.646510
$877$	−11.5817	−	11.5817i	−0.391085	−	0.391085i	0.483989	−	0.875074i	$-0.339187\pi$
$877$	−11.5817	−	11.5817i	−0.391085	−	0.391085i	−0.875074	+	0.483989i	$0.839187\pi$
$878$	−14.6471	−	14.6471i	−0.494317	−	0.494317i
$879$		−	21.5746i		−	0.727694i
$880$	−3.35092	+	6.40553i	−0.112959	+	0.215930i
$881$			8.72058i			0.293804i	0.989151	+	0.146902i	$0.0469301\pi$
$881$			8.72058i			0.293804i	−0.989151	+	0.146902i	$0.953070\pi$
$882$	−5.08082	+	1.66650i	−0.171080	+	0.0561139i
$883$	17.0876	−	17.0876i	0.575044	−	0.575044i	−0.358490	−	0.933534i	$-0.616708\pi$
$883$	17.0876	−	17.0876i	0.575044	−	0.575044i	0.933534	+	0.358490i	$0.116708\pi$
$884$			15.4846i			0.520803i
$885$	14.8829	−	4.65961i	0.500282	−	0.156631i
$886$	−26.0891			−0.876480
$887$	26.4024	−	26.4024i	0.886507	−	0.886507i	−0.107679	−	0.994186i	$-0.534342\pi$
$887$	26.4024	−	26.4024i	0.886507	−	0.886507i	0.994186	+	0.107679i	$0.0343419\pi$
$888$	16.1482	+	16.1482i	0.541898	+	0.541898i
$889$	−9.46996	−	15.4054i	−0.317612	−	0.516682i
$890$	8.23690	−	2.57886i	0.276101	−	0.0864435i
$891$	3.85136			0.129025
$892$	−16.5623	+	16.5623i	−0.554548	+	0.554548i
$893$	0.383052	−	0.383052i	0.0128184	−	0.0128184i
$894$	8.43897			0.282241
$895$	−36.8244	−	19.2639i	−1.23090	−	0.643922i
$896$	−21.6023	+	13.2792i	−0.721681	+	0.443628i
$897$	2.77107	+	2.77107i	0.0925235	+	0.0925235i
$898$	−5.29484	+	5.29484i	−0.176691	+	0.176691i
$899$	6.64154			0.221508
$900$	−4.03893	−	5.81792i	−0.134631	−	0.193931i
$901$		−	18.2928i		−	0.609422i
$902$	18.0585	−	18.0585i	0.601282	−	0.601282i
$903$	−10.0853	−	2.40643i	−0.335617	−	0.0800811i
$904$			15.2733i			0.507984i
$905$	−16.8122	−	8.79494i	−0.558855	−	0.292354i
$906$			14.0546i			0.466932i
$907$	−23.6454	−	23.6454i	−0.785133	−	0.785133i	0.195559	−	0.980692i	$-0.437348\pi$
$907$	−23.6454	−	23.6454i	−0.785133	−	0.785133i	−0.980692	+	0.195559i	$0.937348\pi$
$908$	−1.56548	−	1.56548i	−0.0519523	−	0.0519523i
$909$	19.1953			0.636667
$910$	17.6834	+	15.3913i	0.586199	+	0.510217i
$911$	−17.8226			−0.590490			−0.295245	−	0.955422i	$-0.595401\pi$
$911$	−17.8226			−0.590490			−0.295245	+	0.955422i	$0.595401\pi$
$912$	−0.0414114	−	0.0414114i	−0.00137127	−	0.00137127i
$913$	−6.29966	−	6.29966i	−0.208488	−	0.208488i
$914$			0.594234i			0.0196555i
$915$	−9.56103	−	30.5380i	−0.316078	−	1.00956i
$916$		−	11.0955i		−	0.366605i
$917$	−0.397603	+	1.66634i	−0.0131300	+	0.0550274i
$918$	−1.13823	+	1.13823i	−0.0375673	+	0.0375673i
$919$			21.5752i			0.711701i	0.934543	+	0.355850i	$0.115809\pi$
$919$			21.5752i			0.711701i	−0.934543	+	0.355850i	$0.884191\pi$
$920$	−3.90626	−	2.04348i	−0.128786	−	0.0673716i
$921$	−20.6755			−0.681280
$922$	−0.449284	+	0.449284i	−0.0147964	+	0.0147964i
$923$	29.8142	+	29.8142i	0.981346	+	0.981346i
$924$	−12.2962	+	7.55868i	−0.404516	+	0.248662i
$925$	7.77107	−	43.0570i	0.255511	−	1.41571i
$926$	5.88908			0.193527
$927$	−2.33825	+	2.33825i	−0.0767980	+	0.0767980i
$928$	11.4839	−	11.4839i	0.376977	−	0.376977i
$929$	38.3070			1.25681			0.628405	−	0.777886i	$-0.283708\pi$
$929$	38.3070			1.25681			0.628405	+	0.777886i	$0.283708\pi$
$930$	−1.89763	+	3.62745i	−0.0622257	+	0.118949i
$931$	0.435757	+	0.220505i	0.0142814	+	0.00722675i
$932$	−1.42778	−	1.42778i	−0.0467686	−	0.0467686i
$933$	−2.02387	+	2.02387i	−0.0662584	+	0.0662584i
$934$	−25.1520			−0.823000
$935$	−5.42225	−	17.3187i	−0.177326	−	0.566382i
$936$		−	13.5384i		−	0.442517i
$937$	13.2317	−	13.2317i	0.432262	−	0.432262i	−0.457135	−	0.889397i	$-0.651125\pi$
$937$	13.2317	−	13.2317i	0.432262	−	0.432262i	0.889397	+	0.457135i	$0.151125\pi$
$938$	−0.276283	+	1.15790i	−0.00902097	+	0.0378066i
$939$		−	13.3194i		−	0.434662i
$940$	23.4700	−	7.34814i	0.765508	−	0.239670i
$941$		−	2.58095i		−	0.0841366i	−0.999115	−	0.0420683i	$-0.986605\pi$
$941$		−	2.58095i		−	0.0841366i	0.999115	−	0.0420683i	$-0.0133947\pi$
$942$	−0.802028	−	0.802028i	−0.0261315	−	0.0261315i
$943$	−4.63706	−	4.63706i	−0.151004	−	0.151004i
$944$	5.85450			0.190548
$945$	−0.409006	−	5.90192i	−0.0133050	−	0.191990i
$946$	11.5293			0.374848
$947$	4.94205	+	4.94205i	0.160595	+	0.160595i	0.782830	−	0.622235i	$-0.213775\pi$
$947$	4.94205	+	4.94205i	0.160595	+	0.160595i	−0.622235	+	0.782830i	$0.713775\pi$
$948$	−9.87918	−	9.87918i	−0.320861	−	0.320861i
$949$		−	70.0773i		−	2.27481i
$950$	0.0473285	−	0.262232i	0.00153554	−	0.00850793i
$951$			10.4413i			0.338582i
$952$	3.37705	−	14.1531i	0.109451	−	0.458704i
$953$	−16.3558	+	16.3558i	−0.529818	+	0.529818i	−0.920518	−	0.390700i	$-0.872233\pi$
$953$	−16.3558	+	16.3558i	−0.529818	+	0.529818i	0.390700	+	0.920518i	$0.372233\pi$
$954$			6.63105i			0.214688i
$955$	5.59034	−	10.6863i	0.180899	−	0.345802i
$956$	−28.7271			−0.929101
$957$	7.54653	−	7.54653i	0.243945	−	0.243945i
$958$	−21.8390	−	21.8390i	−0.705587	−	0.705587i
$959$	20.0586	+	32.6308i	0.647727	+	1.05370i
$960$	1.86939	+	5.97087i	0.0603345	+	0.192709i
$961$	25.2557			0.814698
$962$	24.5193	−	24.5193i	0.790533	−	0.790533i
$963$	6.39747	−	6.39747i	0.206156	−	0.206156i
$964$	3.92359			0.126370
$965$	−4.54089	−	14.5036i	−0.146176	−	0.466889i
$966$	−0.799543	−	1.30067i	−0.0257249	−	0.0418484i
$967$	8.66781	+	8.66781i	0.278738	+	0.278738i	0.832605	−	0.553867i	$-0.186848\pi$
$967$	8.66781	+	8.66781i	0.278738	+	0.278738i	−0.553867	+	0.832605i	$0.686848\pi$
$968$	7.07336	−	7.07336i	0.227346	−	0.227346i
$969$	0.147019			0.00472294
$970$	−7.67955	+	14.6800i	−0.246575	+	0.471347i
$971$		−	13.1861i		−	0.423163i	−0.977360	−	0.211582i	$-0.932139\pi$
$971$		−	13.1861i		−	0.423163i	0.977360	−	0.211582i	$-0.0678614\pi$
$972$	−1.00161	+	1.00161i	−0.0321267	+	0.0321267i
$973$	−57.0451	−	13.6114i	−1.82878	−	0.436362i
$974$		−	7.80931i		−	0.250226i
$975$	−21.3068	+	14.7916i	−0.682363	+	0.473711i
$976$		−	12.0128i		−	0.384521i
$977$	−24.4925	−	24.4925i	−0.783586	−	0.783586i	0.196848	−	0.980434i	$-0.436929\pi$
$977$	−24.4925	−	24.4925i	−0.783586	−	0.783586i	−0.980434	+	0.196848i	$0.936929\pi$
$978$	4.20545	+	4.20545i	0.134475	+	0.134475i
$979$	19.4614			0.621990
$980$	12.8890	+	18.0403i	0.411723	+	0.576278i
$981$	2.16057			0.0689818
$982$	10.8590	+	10.8590i	0.346525	+	0.346525i
$983$	15.7362	+	15.7362i	0.501907	+	0.501907i	0.912030	−	0.410123i	$-0.134514\pi$
$983$	15.7362	+	15.7362i	0.501907	+	0.501907i	−0.410123	+	0.912030i	$0.634514\pi$
$984$			22.6549i			0.722212i
$985$	−38.2477	+	11.9748i	−1.21867	+	0.381550i
$986$			4.46061i			0.142055i
$987$	19.9823	+	4.76795i	0.636044	+	0.151765i
$988$	−0.362505	+	0.362505i	−0.0115328	+	0.0115328i
$989$		−	2.96048i		−	0.0941379i
$990$	1.96554	+	6.27794i	0.0624688	+	0.199526i
$991$	−30.1031			−0.956257			−0.478128	−	0.878290i	$-0.658685\pi$
$991$	−30.1031			−0.956257			−0.478128	+	0.878290i	$0.658685\pi$
$992$	−9.93256	+	9.93256i	−0.315359	+	0.315359i
$993$	16.7019	+	16.7019i	0.530018	+	0.530018i
$994$	−8.60234	−	13.9940i	−0.272850	−	0.443863i
$995$	2.76859	−	5.29236i	0.0877702	−	0.167779i
$996$	3.27666			0.103825
$997$	−22.8721	+	22.8721i	−0.724367	+	0.724367i	−0.969491	−	0.245125i	$-0.921171\pi$
$997$	−22.8721	+	22.8721i	−0.724367	+	0.724367i	0.245125	+	0.969491i	$0.421171\pi$
$998$	8.33045	−	8.33045i	0.263696	−	0.263696i
$999$	−8.75054			−0.276855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.m.a.97.6	yes	16
3.2	odd	2		315.2.p.e.307.4		16
4.3	odd	2		1680.2.cz.d.97.2		16
5.2	odd	4		525.2.m.b.118.4		16
5.3	odd	4	inner	105.2.m.a.13.5	✓	16
5.4	even	2		525.2.m.b.307.3		16
7.2	even	3		735.2.v.a.472.5		32
7.3	odd	6		735.2.v.a.607.3		32
7.4	even	3		735.2.v.a.607.4		32
7.5	odd	6		735.2.v.a.472.6		32
7.6	odd	2	inner	105.2.m.a.97.5	yes	16
15.8	even	4		315.2.p.e.118.3		16
20.3	even	4		1680.2.cz.d.433.7		16
21.20	even	2		315.2.p.e.307.3		16
28.27	even	2		1680.2.cz.d.97.7		16
35.3	even	12		735.2.v.a.313.5		32
35.13	even	4	inner	105.2.m.a.13.6	yes	16
35.18	odd	12		735.2.v.a.313.6		32
35.23	odd	12		735.2.v.a.178.3		32
35.27	even	4		525.2.m.b.118.3		16
35.33	even	12		735.2.v.a.178.4		32
35.34	odd	2		525.2.m.b.307.4		16
105.83	odd	4		315.2.p.e.118.4		16
140.83	odd	4		1680.2.cz.d.433.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.5	✓	16	5.3	odd	4	inner
105.2.m.a.13.6	yes	16	35.13	even	4	inner
105.2.m.a.97.5	yes	16	7.6	odd	2	inner
105.2.m.a.97.6	yes	16	1.1	even	1	trivial
315.2.p.e.118.3		16	15.8	even	4
315.2.p.e.118.4		16	105.83	odd	4
315.2.p.e.307.3		16	21.20	even	2
315.2.p.e.307.4		16	3.2	odd	2
525.2.m.b.118.3		16	35.27	even	4
525.2.m.b.118.4		16	5.2	odd	4
525.2.m.b.307.3		16	5.4	even	2
525.2.m.b.307.4		16	35.34	odd	2
735.2.v.a.178.3		32	35.23	odd	12
735.2.v.a.178.4		32	35.33	even	12
735.2.v.a.313.5		32	35.3	even	12
735.2.v.a.313.6		32	35.18	odd	12
735.2.v.a.472.5		32	7.2	even	3
735.2.v.a.472.6		32	7.5	odd	6
735.2.v.a.607.3		32	7.3	odd	6
735.2.v.a.607.4		32	7.4	even	3
1680.2.cz.d.97.2		16	4.3	odd	2
1680.2.cz.d.97.7		16	28.27	even	2
1680.2.cz.d.433.2		16	140.83	odd	4
1680.2.cz.d.433.7		16	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540143 + 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(2.57351 + 0.614060i) q^{7} +(1.84539 - 1.84539i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.540143 + 0.540143i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +0.763878i q^{6} +(2.57351 + 0.614060i) q^{7} +(1.84539 - 1.84539i) q^{8} +1.00000i q^{9} +(-1.63006 + 0.510348i) q^{10} -3.85136 q^{11} +(1.00161 - 1.00161i) q^{12} +(-3.66816 - 3.66816i) q^{13} +(1.05838 + 1.72174i) q^{14} +(-2.13393 + 0.668102i) q^{15} -0.839427 q^{16} +(1.49007 - 1.49007i) q^{17} +(-0.540143 + 0.540143i) q^{18} +0.0697674 q^{19} +(2.80654 + 1.46818i) q^{20} +(1.38554 + 2.25395i) q^{21} +(-2.08029 - 2.08029i) q^{22} +(-0.534176 + 0.534176i) q^{23} +2.60978 q^{24} +(-2.85136 - 4.10728i) q^{25} -3.96267i q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.869810 - 3.64535i) q^{28} +2.77107i q^{29} +(-1.51350 - 0.791755i) q^{30} -2.39674i q^{31} +(-4.14420 - 4.14420i) q^{32} +(-2.72332 - 2.72332i) q^{33} +1.60970 q^{34} +(-3.88408 + 4.46250i) q^{35} +1.41649 q^{36} +(6.18757 + 6.18757i) q^{37} +(0.0376844 + 0.0376844i) q^{38} -5.18757i q^{39} +(1.74360 + 5.56908i) q^{40} +8.68077i q^{41} +(-0.469067 + 1.96584i) q^{42} +(-2.77107 + 2.77107i) q^{43} +5.45542i q^{44} +(-1.98133 - 1.03649i) q^{45} -0.577063 q^{46} +(5.49042 - 5.49042i) q^{47} +(-0.593565 - 0.593565i) q^{48} +(6.24586 + 3.16057i) q^{49} +(0.678376 - 3.75866i) q^{50} +2.10728 q^{51} +(-5.19592 + 5.19592i) q^{52} +(6.13823 - 6.13823i) q^{53} -0.763878 q^{54} +(3.99191 - 7.63083i) q^{55} +(5.88231 - 3.61595i) q^{56} +(0.0493330 + 0.0493330i) q^{57} +(-1.49678 + 1.49678i) q^{58} -6.97440 q^{59} +(0.946361 + 3.02269i) q^{60} +14.3107i q^{61} +(1.29458 - 1.29458i) q^{62} +(-0.614060 + 2.57351i) q^{63} -2.79807i q^{64} +(11.0699 - 3.46582i) q^{65} -2.94197i q^{66} +(0.416491 + 0.416491i) q^{67} +(-2.11067 - 2.11067i) q^{68} -0.755439 q^{69} +(-4.50835 + 0.312431i) q^{70} -8.12783 q^{71} +(1.84539 + 1.84539i) q^{72} +(9.55210 + 9.55210i) q^{73} +6.68434i q^{74} +(0.888068 - 4.92050i) q^{75} -0.0988248i q^{76} +(-9.91150 - 2.36497i) q^{77} +(2.80203 - 2.80203i) q^{78} -9.86329i q^{79} +(0.870061 - 1.66319i) q^{80} -1.00000 q^{81} +(-4.68886 + 4.68886i) q^{82} +(1.63570 + 1.63570i) q^{83} +(3.19270 - 1.96260i) q^{84} +(1.40788 + 4.49678i) q^{85} -2.99355 q^{86} +(-1.95945 + 1.95945i) q^{87} +(-7.10728 + 7.10728i) q^{88} -5.05313 q^{89} +(-0.510348 - 1.63006i) q^{90} +(-7.18757 - 11.6925i) q^{91} +(0.756656 + 0.756656i) q^{92} +(1.69475 - 1.69475i) q^{93} +5.93123 q^{94} +(-0.0723134 + 0.138232i) q^{95} -5.86078i q^{96} +(6.85851 - 6.85851i) q^{97} +(1.66650 + 5.08082i) q^{98} -3.85136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 + 24 * q^8	\( 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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