LMFDB - Embedded newform 112.3.k.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(43,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("112.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.k (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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	112.43
Dual form			112.3.k.a.99.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05702 + 1.69785i) q^{2} +(2.92752 + 2.92752i) q^{3} +(-1.76542 - 3.58933i) q^{4} +(4.98965 + 4.98965i) q^{5} +(-8.06494 + 1.87606i) q^{6} -2.64575 q^{7} +(7.96024 + 0.796563i) q^{8} +8.14073i q^{9} +O(q^{10})$	\(q+(-1.05702 + 1.69785i) q^{2} +(2.92752 + 2.92752i) q^{3} +(-1.76542 - 3.58933i) q^{4} +(4.98965 + 4.98965i) q^{5} +(-8.06494 + 1.87606i) q^{6} -2.64575 q^{7} +(7.96024 + 0.796563i) q^{8} +8.14073i q^{9} +(-13.7459 + 3.19755i) q^{10} +(7.79849 - 7.79849i) q^{11} +(5.33953 - 15.6761i) q^{12} +(-1.45243 + 1.45243i) q^{13} +(2.79661 - 4.49210i) q^{14} +29.2146i q^{15} +(-9.76658 + 12.6734i) q^{16} -29.1121 q^{17} +(-13.8218 - 8.60491i) q^{18} +(-12.6355 - 12.6355i) q^{19} +(9.10067 - 26.7183i) q^{20} +(-7.74549 - 7.74549i) q^{21} +(4.99755 + 21.4838i) q^{22} +26.4489 q^{23} +(20.9718 + 25.6357i) q^{24} +24.7932i q^{25} +(-0.930767 - 4.00126i) q^{26} +(2.51552 - 2.51552i) q^{27} +(4.67086 + 9.49647i) q^{28} +(6.17364 - 6.17364i) q^{29} +(-49.6021 - 30.8804i) q^{30} +1.67856i q^{31} +(-11.1941 - 29.9782i) q^{32} +45.6604 q^{33} +(30.7721 - 49.4282i) q^{34} +(-13.2014 - 13.2014i) q^{35} +(29.2198 - 14.3718i) q^{36} +(40.4014 + 40.4014i) q^{37} +(34.8093 - 8.09729i) q^{38} -8.50402 q^{39} +(35.7443 + 43.6934i) q^{40} -7.61855i q^{41} +(21.3378 - 4.96358i) q^{42} +(56.1470 - 56.1470i) q^{43} +(-41.7590 - 14.2237i) q^{44} +(-40.6194 + 40.6194i) q^{45} +(-27.9570 + 44.9064i) q^{46} -54.4264i q^{47} +(-65.6933 + 8.50964i) q^{48} +7.00000 q^{49} +(-42.0953 - 26.2069i) q^{50} +(-85.2263 - 85.2263i) q^{51} +(7.77739 + 2.64910i) q^{52} +(24.9511 + 24.9511i) q^{53} +(1.61204 + 6.92995i) q^{54} +77.8235 q^{55} +(-21.0608 - 2.10751i) q^{56} -73.9814i q^{57} +(3.95628 + 17.0076i) q^{58} +(-56.7236 + 56.7236i) q^{59} +(104.861 - 51.5761i) q^{60} +(-72.4618 + 72.4618i) q^{61} +(-2.84994 - 1.77427i) q^{62} -21.5384i q^{63} +(62.7310 + 12.6817i) q^{64} -14.4942 q^{65} +(-48.2640 + 77.5248i) q^{66} +(-67.6986 - 67.6986i) q^{67} +(51.3951 + 104.493i) q^{68} +(77.4297 + 77.4297i) q^{69} +(36.3681 - 8.45991i) q^{70} -7.81329 q^{71} +(-6.48461 + 64.8022i) q^{72} +24.4476i q^{73} +(-111.301 + 25.8907i) q^{74} +(-72.5827 + 72.5827i) q^{75} +(-23.0460 + 67.6601i) q^{76} +(-20.6329 + 20.6329i) q^{77} +(8.98891 - 14.4386i) q^{78} +53.2163i q^{79} +(-111.967 + 14.5038i) q^{80} +87.9951 q^{81} +(12.9352 + 8.05295i) q^{82} +(30.7600 + 30.7600i) q^{83} +(-14.1271 + 41.4751i) q^{84} +(-145.259 - 145.259i) q^{85} +(35.9810 + 154.678i) q^{86} +36.1469 q^{87} +(68.2898 - 55.8659i) q^{88} -151.750i q^{89} +(-26.0304 - 111.901i) q^{90} +(3.84276 - 3.84276i) q^{91} +(-46.6935 - 94.9339i) q^{92} +(-4.91400 + 4.91400i) q^{93} +(92.4081 + 57.5297i) q^{94} -126.094i q^{95} +(54.9910 - 120.533i) q^{96} -19.6564 q^{97} +(-7.39913 + 11.8850i) q^{98} +(63.4854 + 63.4854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} + 12 q^{6}+O(q^{10}) $ 48 * q + 6 * q^4 + 12 * q^6	$ 48 q + 6 q^{4} + 12 q^{6} - 40 q^{10} + 16 q^{11} - 108 q^{12} - 14 q^{14} + 66 q^{16} + 30 q^{18} - 64 q^{19} + 84 q^{20} + 94 q^{22} - 64 q^{23} + 40 q^{24} - 196 q^{26} - 96 q^{27} + 16 q^{29} - 72 q^{30} + 160 q^{32} - 28 q^{34} + 64 q^{36} - 48 q^{37} - 224 q^{38} + 384 q^{39} + 180 q^{40} + 176 q^{43} - 114 q^{44} - 256 q^{46} + 52 q^{48} + 336 q^{49} + 6 q^{50} - 192 q^{51} - 48 q^{52} - 80 q^{53} - 288 q^{54} - 512 q^{55} - 98 q^{56} - 50 q^{58} - 288 q^{59} + 512 q^{60} - 64 q^{61} + 156 q^{62} + 126 q^{64} - 32 q^{65} - 116 q^{66} + 80 q^{67} - 32 q^{68} + 192 q^{69} + 168 q^{70} + 26 q^{72} + 330 q^{74} + 608 q^{75} + 672 q^{76} + 112 q^{77} - 352 q^{78} - 980 q^{80} - 432 q^{81} - 76 q^{82} - 160 q^{83} + 320 q^{85} - 542 q^{86} - 896 q^{87} - 214 q^{88} + 1144 q^{90} - 12 q^{92} + 96 q^{93} + 660 q^{94} + 184 q^{96} + 496 q^{99}+O(q^{100}) $ 48 * q + 6 * q^4 + 12 * q^6 - 40 * q^10 + 16 * q^11 - 108 * q^12 - 14 * q^14 + 66 * q^16 + 30 * q^18 - 64 * q^19 + 84 * q^20 + 94 * q^22 - 64 * q^23 + 40 * q^24 - 196 * q^26 - 96 * q^27 + 16 * q^29 - 72 * q^30 + 160 * q^32 - 28 * q^34 + 64 * q^36 - 48 * q^37 - 224 * q^38 + 384 * q^39 + 180 * q^40 + 176 * q^43 - 114 * q^44 - 256 * q^46 + 52 * q^48 + 336 * q^49 + 6 * q^50 - 192 * q^51 - 48 * q^52 - 80 * q^53 - 288 * q^54 - 512 * q^55 - 98 * q^56 - 50 * q^58 - 288 * q^59 + 512 * q^60 - 64 * q^61 + 156 * q^62 + 126 * q^64 - 32 * q^65 - 116 * q^66 + 80 * q^67 - 32 * q^68 + 192 * q^69 + 168 * q^70 + 26 * q^72 + 330 * q^74 + 608 * q^75 + 672 * q^76 + 112 * q^77 - 352 * q^78 - 980 * q^80 - 432 * q^81 - 76 * q^82 - 160 * q^83 + 320 * q^85 - 542 * q^86 - 896 * q^87 - 214 * q^88 + 1144 * q^90 - 12 * q^92 + 96 * q^93 + 660 * q^94 + 184 * q^96 + 496 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.05702	+	1.69785i	−0.528510	+	0.848927i
$2$	−1.05702	+	1.69785i	−0.528510	+	0.848927i
$3$	2.92752	+	2.92752i	0.975840	+	0.975840i	0.999715	−	0.0238754i	$-0.00760049\pi$
$3$	2.92752	+	2.92752i	0.975840	+	0.975840i	−0.0238754	+	0.999715i	$0.507600\pi$
$4$	−1.76542	−	3.58933i	−0.441355	−	0.897333i
$5$	4.98965	+	4.98965i	0.997930	+	0.997930i	0.999998	−	0.00206760i	$-0.000658138\pi$
$5$	4.98965	+	4.98965i	0.997930	+	0.997930i	−0.00206760	+	0.999998i	$0.500658\pi$
$6$	−8.06494	+	1.87606i	−1.34416	+	0.312676i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$	7.96024	+	0.796563i	0.995031	+	0.0995704i
$9$			8.14073i			0.904526i
$10$	−13.7459	+	3.19755i	−1.37459	+	0.319755i
$11$	7.79849	−	7.79849i	0.708953	−	0.708953i	−0.257362	−	0.966315i	$-0.582853\pi$
$11$	7.79849	−	7.79849i	0.708953	−	0.708953i	0.966315	+	0.257362i	$0.0828532\pi$
$12$	5.33953	−	15.6761i	0.444961	−	1.30634i
$13$	−1.45243	+	1.45243i	−0.111725	+	0.111725i	−0.760759	−	0.649034i	$-0.775173\pi$
$13$	−1.45243	+	1.45243i	−0.111725	+	0.111725i	0.649034	+	0.760759i	$0.275173\pi$
$14$	2.79661	−	4.49210i	0.199758	−	0.320864i
$15$			29.2146i			1.94764i
$16$	−9.76658	+	12.6734i	−0.610411	+	0.792085i
$17$	−29.1121			−1.71248			−0.856239	−	0.516580i	$-0.827205\pi$
$17$	−29.1121			−1.71248			−0.856239	+	0.516580i	$0.827205\pi$
$18$	−13.8218	−	8.60491i	−0.767877	−	0.478051i
$19$	−12.6355	−	12.6355i	−0.665027	−	0.665027i	0.291533	−	0.956561i	$-0.405835\pi$
$19$	−12.6355	−	12.6355i	−0.665027	−	0.665027i	−0.956561	+	0.291533i	$0.905835\pi$
$20$	9.10067	−	26.7183i	0.455034	−	1.33592i
$21$	−7.74549	−	7.74549i	−0.368833	−	0.368833i
$22$	4.99755	+	21.4838i	0.227161	+	0.976539i
$23$	26.4489			1.14995			0.574976	−	0.818170i	$-0.305011\pi$
$23$	26.4489			1.14995			0.574976	+	0.818170i	$0.305011\pi$
$24$	20.9718	+	25.6357i	0.873825	+	1.06815i
$25$			24.7932i			0.991730i
$26$	−0.930767	−	4.00126i	−0.0357987	−	0.153894i
$27$	2.51552	−	2.51552i	0.0931675	−	0.0931675i
$28$	4.67086	+	9.49647i	0.166817	+	0.339160i
$29$	6.17364	−	6.17364i	0.212884	−	0.212884i	−0.592607	−	0.805491i	$-0.701901\pi$
$29$	6.17364	−	6.17364i	0.212884	−	0.212884i	0.805491	+	0.592607i	$0.201901\pi$
$30$	−49.6021	−	30.8804i	−1.65340	−	1.02935i
$31$			1.67856i			0.0541469i	0.999633	+	0.0270735i	$0.00861881\pi$
$31$			1.67856i			0.0541469i	−0.999633	+	0.0270735i	$0.991381\pi$
$32$	−11.1941	−	29.9782i	−0.349814	−	0.936819i
$33$	45.6604			1.38365
$34$	30.7721	−	49.4282i	0.905061	−	1.45377i
$35$	−13.2014	−	13.2014i	−0.377182	−	0.377182i
$36$	29.2198	−	14.3718i	0.811660	−	0.399217i
$37$	40.4014	+	40.4014i	1.09193	+	1.09193i	0.995323	+	0.0966077i	$0.0307992\pi$
$37$	40.4014	+	40.4014i	1.09193	+	1.09193i	0.0966077	+	0.995323i	$0.469201\pi$
$38$	34.8093	−	8.09729i	0.916033	−	0.213087i
$39$	−8.50402			−0.218052
$40$	35.7443	+	43.6934i	0.893607	+	1.09234i
$41$		−	7.61855i		−	0.185818i	−0.995675	−	0.0929091i	$-0.970383\pi$
$41$		−	7.61855i		−	0.185818i	0.995675	−	0.0929091i	$-0.0296166\pi$
$42$	21.3378	−	4.96358i	0.508044	−	0.118181i
$43$	56.1470	−	56.1470i	1.30574	−	1.30574i	0.381289	−	0.924456i	$-0.375480\pi$
$43$	56.1470	−	56.1470i	1.30574	−	1.30574i	0.924456	−	0.381289i	$-0.124520\pi$
$44$	−41.7590	−	14.2237i	−0.949067	−	0.323267i
$45$	−40.6194	+	40.6194i	−0.902654	+	0.902654i
$46$	−27.9570	+	44.9064i	−0.607761	+	0.976226i
$47$		−	54.4264i		−	1.15801i	−0.815325	−	0.579004i	$-0.803442\pi$
$47$		−	54.4264i		−	1.15801i	0.815325	−	0.579004i	$-0.196558\pi$
$48$	−65.6933	+	8.50964i	−1.36861	+	0.177284i
$49$	7.00000			0.142857
$50$	−42.0953	−	26.2069i	−0.841906	−	0.524139i
$51$	−85.2263	−	85.2263i	−1.67110	−	1.67110i
$52$	7.77739	+	2.64910i	0.149565	+	0.0509442i
$53$	24.9511	+	24.9511i	0.470775	+	0.470775i	0.902165	−	0.431390i	$-0.141977\pi$
$53$	24.9511	+	24.9511i	0.470775	+	0.470775i	−0.431390	+	0.902165i	$0.641977\pi$
$54$	1.61204	+	6.92995i	0.0298525	+	0.128332i
$55$	77.8235			1.41497
$56$	−21.0608	−	2.10751i	−0.376086	−	0.0376341i
$57$		−	73.9814i		−	1.29792i
$58$	3.95628	+	17.0076i	0.0682118	+	0.293234i
$59$	−56.7236	+	56.7236i	−0.961416	+	0.961416i	−0.999283	−	0.0378664i	$-0.987944\pi$
$59$	−56.7236	+	56.7236i	−0.961416	+	0.961416i	0.0378664	+	0.999283i	$0.487944\pi$
$60$	104.861	−	51.5761i	1.74768	−	0.859601i
$61$	−72.4618	+	72.4618i	−1.18790	+	1.18790i	−0.210250	+	0.977648i	$0.567428\pi$
$61$	−72.4618	+	72.4618i	−1.18790	+	1.18790i	−0.977648	+	0.210250i	$0.932572\pi$
$62$	−2.84994	−	1.77427i	−0.0459668	−	0.0286172i
$63$		−	21.5384i		−	0.341879i
$64$	62.7310	+	12.6817i	0.980171	+	0.198151i
$65$	−14.4942			−0.222988
$66$	−48.2640	+	77.5248i	−0.731272	+	1.17462i
$67$	−67.6986	−	67.6986i	−1.01043	−	1.01043i	−0.999945	−	0.0104822i	$-0.996663\pi$
$67$	−67.6986	−	67.6986i	−1.01043	−	1.01043i	−0.0104822	−	0.999945i	$-0.503337\pi$
$68$	51.3951	+	104.493i	0.755811	+	1.53666i
$69$	77.4297	+	77.4297i	1.12217	+	1.12217i
$70$	36.3681	−	8.45991i	0.519545	−	0.120856i
$71$	−7.81329			−0.110046			−0.0550231	−	0.998485i	$-0.517523\pi$
$71$	−7.81329			−0.110046			−0.0550231	+	0.998485i	$0.517523\pi$
$72$	−6.48461	+	64.8022i	−0.0900640	+	0.900031i
$73$			24.4476i			0.334899i	0.985881	+	0.167450i	$0.0535531\pi$
$73$			24.4476i			0.334899i	−0.985881	+	0.167450i	$0.946447\pi$
$74$	−111.301	+	25.8907i	−1.50407	+	0.349874i
$75$	−72.5827	+	72.5827i	−0.967769	+	0.967769i
$76$	−23.0460	+	67.6601i	−0.303237	+	0.890264i
$77$	−20.6329	+	20.6329i	−0.267959	+	0.267959i
$78$	8.98891	−	14.4386i	0.115242	−	0.185110i
$79$			53.2163i			0.673624i	0.941572	+	0.336812i	$0.109349\pi$
$79$			53.2163i			0.673624i	−0.941572	+	0.336812i	$0.890651\pi$
$80$	−111.967	+	14.5038i	−1.39959	+	0.181297i
$81$	87.9951			1.08636
$82$	12.9352	+	8.05295i	0.157746	+	0.0982067i
$83$	30.7600	+	30.7600i	0.370602	+	0.370602i	0.867696	−	0.497095i	$-0.165600\pi$
$83$	30.7600	+	30.7600i	0.370602	+	0.370602i	−0.497095	+	0.867696i	$0.665600\pi$
$84$	−14.1271	+	41.4751i	−0.168179	+	0.493752i
$85$	−145.259	−	145.259i	−1.70893	−	1.70893i
$86$	35.9810	+	154.678i	0.418384	+	1.79858i
$87$	36.1469			0.415481
$88$	68.2898	−	55.8659i	0.776021	−	0.634839i
$89$		−	151.750i		−	1.70506i	−0.522682	−	0.852528i	$-0.675068\pi$
$89$		−	151.750i		−	1.70506i	0.522682	−	0.852528i	$-0.324932\pi$
$90$	−26.0304	−	111.901i	−0.289226	−	1.24335i
$91$	3.84276	−	3.84276i	0.0422282	−	0.0422282i
$92$	−46.6935	−	94.9339i	−0.507538	−	1.03189i
$93$	−4.91400	+	4.91400i	−0.0528387	+	0.0528387i
$94$	92.4081	+	57.5297i	0.983064	+	0.612018i
$95$		−	126.094i		−	1.32730i
$96$	54.9910	−	120.533i	0.572823	−	1.25555i
$97$	−19.6564			−0.202643			−0.101322	−	0.994854i	$-0.532307\pi$
$97$	−19.6564			−0.202643			−0.101322	+	0.994854i	$0.532307\pi$
$98$	−7.39913	+	11.8850i	−0.0755014	+	0.121275i
$99$	63.4854	+	63.4854i	0.641267	+	0.641267i
$100$	88.9911	−	43.7705i	0.889911	−	0.437705i
$101$	−133.783	−	133.783i	−1.32458	−	1.32458i	−0.910023	−	0.414559i	$-0.863936\pi$
$101$	−133.783	−	133.783i	−1.32458	−	1.32458i	−0.414559	−	0.910023i	$-0.636064\pi$
$102$	234.788	−	54.6160i	2.30184	−	0.535451i
$103$	−49.6484			−0.482023			−0.241012	−	0.970522i	$-0.577479\pi$
$103$	−49.6484			−0.482023			−0.241012	+	0.970522i	$0.577479\pi$
$104$	−12.7186	+	10.4047i	−0.122295	+	0.100045i
$105$		−	77.2946i		−	0.736139i
$106$	−68.7371	+	15.9895i	−0.648463	+	0.150845i
$107$	48.0611	−	48.0611i	0.449169	−	0.449169i	−0.445909	−	0.895078i	$-0.647120\pi$
$107$	48.0611	−	48.0611i	0.449169	−	0.449169i	0.895078	+	0.445909i	$0.147120\pi$
$108$	−13.4700	−	4.58809i	−0.124722	−	0.0424823i
$109$	−67.7976	+	67.7976i	−0.621996	+	0.621996i	−0.946042	−	0.324045i	$-0.894957\pi$
$109$	−67.7976	+	67.7976i	−0.621996	+	0.621996i	0.324045	+	0.946042i	$0.394957\pi$
$110$	−82.2609	+	132.133i	−0.747826	+	1.20121i
$111$			236.552i			2.13110i
$112$	25.8399	−	33.5305i	0.230714	−	0.299380i
$113$	−50.7077			−0.448741			−0.224370	−	0.974504i	$-0.572033\pi$
$113$	−50.7077			−0.448741			−0.224370	+	0.974504i	$0.572033\pi$
$114$	125.610	+	78.1998i	1.10184	+	0.685963i
$115$	131.971	+	131.971i	1.14757	+	1.14757i
$116$	−33.0583	−	11.2602i	−0.284985	−	0.0970703i
$117$	−11.8238	−	11.8238i	−0.101058	−	0.101058i
$118$	−36.3505	−	156.266i	−0.308055	−	1.32429i
$119$	77.0234			0.647256
$120$	−23.2713	+	232.555i	−0.193927	+	1.93796i
$121$		−	0.632803i		−	0.00522977i
$122$	−46.4361	−	199.623i	−0.380623	−	1.63625i
$123$	22.3034	−	22.3034i	0.181329	−	0.181329i
$124$	6.02489	−	2.96336i	0.0485878	−	0.0238980i
$125$	1.03166	−	1.03166i	0.00825327	−	0.00825327i
$126$	36.5690	+	22.7665i	0.290230	+	0.180686i
$127$			45.0203i			0.354491i	0.984167	+	0.177245i	$0.0567186\pi$
$127$			45.0203i			0.354491i	−0.984167	+	0.177245i	$0.943281\pi$
$128$	−87.8395	+	93.1033i	−0.686246	+	0.727370i
$129$	328.743			2.54839
$130$	15.3207	−	24.6091i	0.117851	−	0.189301i
$131$	−19.2366	−	19.2366i	−0.146844	−	0.146844i	0.629862	−	0.776707i	$-0.283111\pi$
$131$	−19.2366	−	19.2366i	−0.146844	−	0.146844i	−0.776707	+	0.629862i	$0.783111\pi$
$132$	−80.6099	−	163.890i	−0.610681	−	1.24159i
$133$	33.4304	+	33.4304i	0.251357	+	0.251357i
$134$	186.501	−	43.3837i	1.39180	−	0.323759i
$135$	25.1032			0.185949
$136$	−231.740	−	23.1896i	−1.70397	−	0.170512i
$137$			135.675i			0.990329i	0.868799	+	0.495165i	$0.164892\pi$
$137$			135.675i			0.990329i	−0.868799	+	0.495165i	$0.835108\pi$
$138$	−213.309	+	49.6197i	−1.54572	+	0.359563i
$139$	−90.0083	+	90.0083i	−0.647542	+	0.647542i	−0.952398	−	0.304856i	$-0.901392\pi$
$139$	−90.0083	+	90.0083i	−0.647542	+	0.647542i	0.304856	+	0.952398i	$0.401392\pi$
$140$	−24.0781	+	70.6901i	−0.171987	+	0.504929i
$141$	159.334	−	159.334i	1.13003	−	1.13003i
$142$	8.25879	−	13.2658i	0.0581605	−	0.0934213i
$143$			22.6535i			0.158416i
$144$	−103.170	−	79.5071i	−0.716461	−	0.552133i
$145$	61.6086			0.424887
$146$	−41.5085	−	25.8416i	−0.284305	−	0.176997i
$147$	20.4926	+	20.4926i	0.139406	+	0.139406i
$148$	73.6885	−	216.340i	0.497895	−	1.46175i
$149$	−37.4465	−	37.4465i	−0.251319	−	0.251319i	0.570192	−	0.821511i	$-0.306869\pi$
$149$	−37.4465	−	37.4465i	−0.251319	−	0.251319i	−0.821511	+	0.570192i	$0.806869\pi$
$150$	−46.5135	−	199.956i	−0.310090	−	1.33304i
$151$	−51.3367			−0.339978			−0.169989	−	0.985446i	$-0.554373\pi$
$151$	−51.3367			−0.339978			−0.169989	+	0.985446i	$0.554373\pi$
$152$	−90.5168	−	110.647i	−0.595505	−	0.727940i
$153$		−	236.994i		−	1.54898i
$154$	−13.2223	−	56.8409i	−0.0858589	−	0.369097i
$155$	−8.37541	+	8.37541i	−0.0540349	+	0.0540349i
$156$	15.0132	+	30.5237i	0.0962383	+	0.195665i
$157$	−56.5725	+	56.5725i	−0.360334	+	0.360334i	−0.863936	−	0.503602i	$-0.832008\pi$
$157$	−56.5725	+	56.5725i	−0.360334	+	0.360334i	0.503602	+	0.863936i	$0.332008\pi$
$158$	−90.3535	−	56.2506i	−0.571858	−	0.356017i
$159$			146.090i			0.918802i
$160$	93.7264	−	205.435i	0.585790	−	1.28397i
$161$	−69.9773			−0.434641
$162$	−93.0125	+	149.403i	−0.574151	+	0.922240i
$163$	−185.333	−	185.333i	−1.13701	−	1.13701i	−0.988983	−	0.148032i	$-0.952706\pi$
$163$	−185.333	−	185.333i	−1.13701	−	1.13701i	−0.148032	−	0.988983i	$-0.547294\pi$
$164$	−27.3455	+	13.4499i	−0.166741	+	0.0820118i
$165$	227.830	+	227.830i	1.38079	+	1.38079i
$166$	−84.7398	+	19.7121i	−0.510481	+	0.118747i
$167$	153.619			0.919872			0.459936	−	0.887952i	$-0.347872\pi$
$167$	153.619			0.919872			0.459936	+	0.887952i	$0.347872\pi$
$168$	−55.4862	−	67.8257i	−0.330275	−	0.403725i
$169$			164.781i			0.975035i
$170$	400.171	−	93.0873i	2.35395	−	0.547573i
$171$	102.862	−	102.862i	0.601534	−	0.601534i
$172$	−300.653	−	102.407i	−1.74798	−	0.595390i
$173$	118.910	−	118.910i	0.687343	−	0.687343i	−0.274301	−	0.961644i	$-0.588446\pi$
$173$	118.910	−	118.910i	0.687343	−	0.687343i	0.961644	+	0.274301i	$0.0884464\pi$
$174$	−38.2079	+	61.3721i	−0.219586	+	0.352713i
$175$		−	65.5967i		−	0.374839i
$176$	22.6684	+	174.998i	0.128798	+	0.994304i
$177$	−332.119			−1.87638
$178$	257.649	+	160.403i	1.44747	+	0.901138i
$179$	139.516	+	139.516i	0.779418	+	0.779418i	0.979732	−	0.200313i	$-0.0641960\pi$
$179$	139.516	+	139.516i	0.779418	+	0.779418i	−0.200313	+	0.979732i	$0.564196\pi$
$180$	217.507	+	74.0861i	1.20837	+	0.411590i
$181$	55.8952	+	55.8952i	0.308813	+	0.308813i	0.844449	−	0.535636i	$-0.179928\pi$
$181$	55.8952	+	55.8952i	0.308813	+	0.308813i	−0.535636	+	0.844449i	$0.679928\pi$
$182$	2.46258	+	10.5863i	0.0135307	+	0.0581666i
$183$	−424.266			−2.31840
$184$	210.540	+	21.0682i	1.14424	+	0.114501i
$185$			403.178i			2.17934i
$186$	−3.14907	−	13.5375i	−0.0169305	−	0.0727820i
$187$	−227.031	+	227.031i	−1.21407	+	1.21407i
$188$	−195.354	+	96.0854i	−1.03912	+	0.511093i
$189$	−6.65545	+	6.65545i	−0.0352140	+	0.0352140i
$190$	214.089	+	133.283i	1.12678	+	0.701492i
$191$		−	226.390i		−	1.18529i	−0.805464	−	0.592645i	$-0.798084\pi$
$191$		−	226.390i		−	1.18529i	0.805464	−	0.592645i	$-0.201916\pi$
$192$	146.520	+	220.772i	0.763126	+	1.14985i
$193$	92.1055			0.477231			0.238615	−	0.971114i	$-0.423306\pi$
$193$	92.1055			0.477231			0.238615	+	0.971114i	$0.423306\pi$
$194$	20.7772	−	33.3737i	0.107099	−	0.172029i
$195$	−42.4321	−	42.4321i	−0.217601	−	0.217601i
$196$	−12.3579	−	25.1253i	−0.0630507	−	0.128190i
$197$	107.014	+	107.014i	0.543217	+	0.543217i	0.924470	−	0.381254i	$-0.124508\pi$
$197$	107.014	+	107.014i	0.543217	+	0.543217i	−0.381254	+	0.924470i	$0.624508\pi$
$198$	−174.894	+	40.6837i	−0.883304	+	0.205473i
$199$	−49.8864			−0.250686			−0.125343	−	0.992113i	$-0.540003\pi$
$199$	−49.8864			−0.250686			−0.125343	+	0.992113i	$0.540003\pi$
$200$	−19.7494	+	197.360i	−0.0987469	+	0.986801i
$201$		−	396.378i		−	1.97203i
$202$	368.554	−	85.7327i	1.82453	−	0.424419i
$203$	−16.3339	+	16.3339i	−0.0804626	+	0.0804626i
$204$	−155.445	+	456.366i	−0.761985	+	2.23709i
$205$	38.0139	−	38.0139i	0.185434	−	0.185434i
$206$	52.4793	−	84.2958i	0.254754	−	0.409203i
$207$			215.314i			1.04016i
$208$	−4.22188	−	32.5924i	−0.0202975	−	0.156694i
$209$	−197.076			−0.942947
$210$	131.235	+	81.7018i	0.624928	+	0.389056i
$211$	−117.499	−	117.499i	−0.556870	−	0.556870i	0.371545	−	0.928415i	$-0.378828\pi$
$211$	−117.499	−	117.499i	−0.556870	−	0.556870i	−0.928415	+	0.371545i	$0.878828\pi$
$212$	45.5085	−	133.607i	0.214663	−	0.630221i
$213$	−22.8735	−	22.8735i	−0.107388	−	0.107388i
$214$	30.7993	+	132.402i	0.143922	+	0.618702i
$215$	560.308			2.60608
$216$	22.0280	−	18.0204i	0.101981	−	0.0834278i
$217$		−	4.44104i		−	0.0204656i
$218$	−43.4471	−	186.774i	−0.199299	−	0.856761i
$219$	−71.5709	+	71.5709i	−0.326808	+	0.326808i
$220$	−137.391	−	279.334i	−0.624505	−	1.26970i
$221$	42.2833	−	42.2833i	0.191327	−	0.191327i
$222$	−401.631	−	250.040i	−1.80915	−	1.12631i
$223$			278.605i			1.24935i	0.780885	+	0.624675i	$0.214769\pi$
$223$			278.605i			1.24935i	−0.780885	+	0.624675i	$0.785231\pi$
$224$	29.6167	+	79.3149i	0.132217	+	0.354084i
$225$	−201.835			−0.897045
$226$	53.5990	−	86.0943i	0.237164	−	0.380948i
$227$	−65.4235	−	65.4235i	−0.288209	−	0.288209i	0.548162	−	0.836372i	$-0.315328\pi$
$227$	−65.4235	−	65.4235i	−0.288209	−	0.288209i	−0.836372	+	0.548162i	$0.815328\pi$
$228$	−265.544	+	130.608i	−1.16467	+	0.572844i
$229$	−223.183	−	223.183i	−0.974600	−	0.974600i	0.0250850	−	0.999685i	$-0.492014\pi$
$229$	−223.183	−	223.183i	−0.974600	−	0.974600i	−0.999685	+	0.0250850i	$0.992014\pi$
$230$	−363.563	+	84.5716i	−1.58071	+	0.367703i
$231$	−120.806			−0.522970
$232$	54.0613	−	44.2260i	0.233023	−	0.190629i
$233$		−	197.395i		−	0.847190i	−0.905852	−	0.423595i	$-0.860768\pi$
$233$		−	197.395i		−	0.847190i	0.905852	−	0.423595i	$-0.139232\pi$
$234$	32.5732	−	7.57713i	0.139202	−	0.0323809i
$235$	271.569	−	271.569i	1.15561	−	1.15561i
$236$	303.741	+	103.459i	1.28704	+	0.438384i
$237$	−155.792	+	155.792i	−0.657349	+	0.657349i
$238$	−81.4153	+	130.775i	−0.342081	+	0.549473i
$239$			286.076i			1.19697i	0.801134	+	0.598485i	$0.204230\pi$
$239$			286.076i			1.19697i	−0.801134	+	0.598485i	$0.795770\pi$
$240$	−370.247	−	285.327i	−1.54270	−	1.18886i
$241$	−92.0870			−0.382104			−0.191052	−	0.981580i	$-0.561190\pi$
$241$	−92.0870			−0.382104			−0.191052	+	0.981580i	$0.561190\pi$
$242$	1.07441	+	0.668885i	0.00443970	+	0.00276399i
$243$	234.968	+	234.968i	0.966944	+	0.966944i
$244$	388.015	+	132.164i	1.59022	+	0.541654i
$245$	34.9276	+	34.9276i	0.142561	+	0.142561i
$246$	14.2928	+	61.4432i	0.0581009	+	0.249769i
$247$	36.7044			0.148601
$248$	−1.33708	+	13.3617i	−0.00539143	+	0.0538779i
$249$			180.101i			0.723296i
$250$	0.661123	+	2.84209i	0.00264449	+	0.0113684i
$251$	14.0544	−	14.0544i	0.0559938	−	0.0559938i	−0.678555	−	0.734549i	$-0.737394\pi$
$251$	14.0544	−	14.0544i	0.0559938	−	0.0559938i	0.734549	+	0.678555i	$0.237394\pi$
$252$	−77.3083	+	38.0243i	−0.306779	+	0.150890i
$253$	206.262	−	206.262i	0.815263	−	0.815263i
$254$	−76.4379	−	47.5873i	−0.300937	−	0.187352i
$255$		−	850.499i		−	3.33529i
$256$	−65.2278	−	247.551i	−0.254796	−	0.966995i
$257$	−220.765			−0.859009			−0.429505	−	0.903065i	$-0.641312\pi$
$257$	−220.765			−0.859009			−0.429505	+	0.903065i	$0.641312\pi$
$258$	−347.488	+	558.158i	−1.34685	+	2.16340i
$259$	−106.892	−	106.892i	−0.412711	−	0.412711i
$260$	25.5884	+	52.0245i	0.0984169	+	0.200094i
$261$	50.2579	+	50.2579i	0.192559	+	0.192559i
$262$	52.9944	−	12.3275i	0.202269	−	0.0470515i
$263$	−265.559			−1.00973			−0.504865	−	0.863198i	$-0.668458\pi$
$263$	−265.559			−1.00973			−0.504865	+	0.863198i	$0.668458\pi$
$264$	363.468	+	36.3714i	1.37677	+	0.137771i
$265$			248.995i			0.939602i
$266$	−92.0966	+	21.4234i	−0.346228	+	0.0805391i
$267$	444.251	−	444.251i	1.66386	−	1.66386i
$268$	−123.476	+	362.509i	−0.460732	+	1.35265i
$269$	230.179	−	230.179i	0.855686	−	0.855686i	−0.135141	−	0.990826i	$-0.543149\pi$
$269$	230.179	−	230.179i	0.855686	−	0.855686i	0.990826	+	0.135141i	$0.0431486\pi$
$270$	−26.5345	+	42.6215i	−0.0982760	+	0.157858i
$271$			87.3827i			0.322445i	0.986918	+	0.161223i	$0.0515437\pi$
$271$			87.3827i			0.322445i	−0.986918	+	0.161223i	$0.948456\pi$
$272$	284.326	−	368.948i	1.04532	−	1.35643i
$273$	22.4995			0.0824158
$274$	−230.357	−	143.411i	−0.840718	−	0.523399i
$275$	193.350	+	193.350i	0.703090	+	0.703090i
$276$	141.225	−	414.617i	0.511684	−	1.50223i
$277$	−196.435	−	196.435i	−0.709150	−	0.709150i	0.257207	−	0.966356i	$-0.417198\pi$
$277$	−196.435	−	196.435i	−0.709150	−	0.709150i	−0.966356	+	0.257207i	$0.917198\pi$
$278$	−57.6805	−	247.962i	−0.207484	−	0.891948i
$279$	−13.6647			−0.0489773
$280$	−94.5704	−	115.602i	−0.337752	−	0.412864i
$281$			176.786i			0.629131i	0.949236	+	0.314565i	$0.101859\pi$
$281$			176.786i			0.629131i	−0.949236	+	0.314565i	$0.898141\pi$
$282$	102.107	+	438.946i	0.362082	+	1.55654i
$283$	−92.3087	+	92.3087i	−0.326179	+	0.326179i	−0.851132	−	0.524952i	$-0.824083\pi$
$283$	−92.3087	+	92.3087i	−0.326179	+	0.326179i	0.524952	+	0.851132i	$0.324083\pi$
$284$	13.7937	+	28.0445i	0.0485695	+	0.0987481i
$285$	369.142	−	369.142i	1.29523	−	1.29523i
$286$	−38.4623	−	23.9452i	−0.134484	−	0.0837244i
$287$			20.1568i			0.0702327i
$288$	244.045	−	91.1278i	0.847377	−	0.316416i
$289$	558.516			1.93258
$290$	−65.1214	+	104.602i	−0.224557	+	0.360698i
$291$	−57.5444	−	57.5444i	−0.197747	−	0.197747i
$292$	87.7506	−	43.1604i	0.300516	−	0.147809i
$293$	39.1464	+	39.1464i	0.133605	+	0.133605i	0.770747	−	0.637141i	$-0.219883\pi$
$293$	39.1464	+	39.1464i	0.133605	+	0.133605i	−0.637141	+	0.770747i	$0.719883\pi$
$294$	−56.4546	+	13.1324i	−0.192022	+	0.0446680i
$295$	−566.062			−1.91885
$296$	289.423	+	353.787i	0.977780	+	1.19523i
$297$		−	39.2345i		−	0.132103i
$298$	103.160	−	23.9971i	0.346176	−	0.0805270i
$299$	−38.4151	+	38.4151i	−0.128479	+	0.128479i
$300$	388.662	+	132.384i	1.29554	+	0.441281i
$301$	−148.551	+	148.551i	−0.493525	+	0.493525i
$302$	54.2639	−	87.1623i	0.179682	−	0.288617i
$303$		−	783.303i		−	2.58516i
$304$	283.540	−	36.7286i	0.932698	−	0.120818i
$305$	−723.118			−2.37088
$306$	402.381	+	250.507i	1.31497	+	0.818651i
$307$	129.660	+	129.660i	0.422346	+	0.422346i	0.886011	−	0.463665i	$-0.153466\pi$
$307$	129.660	+	129.660i	0.422346	+	0.422346i	−0.463665	+	0.886011i	$0.653466\pi$
$308$	110.484	+	37.6325i	0.358714	+	0.122183i
$309$	−145.347	−	145.347i	−0.470377	−	0.470377i
$310$	−5.36726	−	23.0732i	−0.0173137	−	0.0744296i
$311$	−36.3926			−0.117018			−0.0585091	−	0.998287i	$-0.518635\pi$
$311$	−36.3926			−0.117018			−0.0585091	+	0.998287i	$0.518635\pi$
$312$	−67.6941	−	6.77399i	−0.216968	−	0.0217115i
$313$			232.460i			0.742684i	0.928496	+	0.371342i	$0.121102\pi$
$313$			232.460i			0.742684i	−0.928496	+	0.371342i	$0.878898\pi$
$314$	−36.2536	−	155.850i	−0.115457	−	0.496337i
$315$	107.469	−	107.469i	0.341171	−	0.341171i
$316$	191.011	−	93.9491i	0.604465	−	0.297307i
$317$	−354.544	+	354.544i	−1.11844	+	1.11844i	−0.126466	+	0.991971i	$0.540363\pi$
$317$	−354.544	+	354.544i	−1.11844	+	1.11844i	−0.991971	+	0.126466i	$0.959637\pi$
$318$	−248.039	−	154.419i	−0.779996	−	0.485596i
$319$		−	96.2900i		−	0.301850i
$320$	249.729	+	376.283i	0.780402	+	1.17588i
$321$	281.400			0.876634
$322$	73.9673	−	118.811i	0.229712	−	0.368979i
$323$	367.847	+	367.847i	1.13884	+	1.13884i
$324$	−155.348	−	315.843i	−0.479470	−	0.974825i
$325$	−36.0104	−	36.0104i	−0.110801	−	0.110801i
$326$	510.570	−	118.768i	1.56617	−	0.364319i
$327$	−396.958			−1.21394
$328$	6.06865	−	60.6455i	0.0185020	−	0.184895i
$329$			143.999i			0.437686i
$330$	−627.642	+	146.001i	−1.90195	+	0.442428i
$331$	−249.092	+	249.092i	−0.752545	+	0.752545i	−0.974954	−	0.222408i	$-0.928608\pi$
$331$	−249.092	+	249.092i	−0.752545	+	0.752545i	0.222408	+	0.974954i	$0.428608\pi$
$332$	56.1034	−	164.712i	0.168986	−	0.496120i
$333$	−328.897	+	328.897i	−0.987679	+	0.987679i
$334$	−162.378	+	260.822i	−0.486161	+	0.780905i
$335$		−	675.585i		−	2.01667i
$336$	173.808	−	22.5144i	0.517286	−	0.0670071i
$337$	187.353			0.555944			0.277972	−	0.960589i	$-0.410338\pi$
$337$	187.353			0.555944			0.277972	+	0.960589i	$0.410338\pi$
$338$	−279.774	−	174.177i	−0.827734	−	0.515315i
$339$	−148.448	−	148.448i	−0.437899	−	0.437899i
$340$	−264.940	+	777.828i	−0.779235	+	2.28773i
$341$	13.0902	+	13.0902i	0.0383877	+	0.0383877i
$342$	65.9179	+	283.373i	0.192742	+	0.828576i
$343$	−18.5203			−0.0539949
$344$	491.669	−	402.219i	1.42927	−	1.16924i
$345$			772.694i			2.23969i
$346$	76.2020	+	327.583i	0.220237	+	0.946772i
$347$	184.141	−	184.141i	0.530666	−	0.530666i	−0.390105	−	0.920771i	$-0.627561\pi$
$347$	184.141	−	184.141i	0.530666	−	0.530666i	0.920771	+	0.390105i	$0.127561\pi$
$348$	−63.8144	−	129.743i	−0.183375	−	0.372825i
$349$	403.609	−	403.609i	1.15647	−	1.15647i	0.171246	−	0.985228i	$-0.445221\pi$
$349$	403.609	−	403.609i	1.15647	−	1.15647i	0.985228	−	0.171246i	$-0.0547792\pi$
$350$	111.374	+	69.3370i	0.318211	+	0.198106i
$351$			7.30723i			0.0208183i
$352$	−321.081	−	146.488i	−0.912163	−	0.416159i
$353$	293.401			0.831164			0.415582	−	0.909556i	$-0.363578\pi$
$353$	293.401			0.831164			0.415582	+	0.909556i	$0.363578\pi$
$354$	351.056	−	563.889i	0.991683	−	1.59291i
$355$	−38.9856	−	38.9856i	−0.109819	−	0.109819i
$356$	−544.681	+	267.903i	−1.53000	+	0.752535i
$357$	225.488	+	225.488i	0.631618	+	0.631618i
$358$	−384.349	+	89.4067i	−1.07360	+	0.249739i
$359$	452.446			1.26030			0.630148	−	0.776475i	$-0.282994\pi$
$359$	452.446			1.26030			0.630148	+	0.776475i	$0.282994\pi$
$360$	−355.696	+	290.985i	−0.988046	+	0.808290i
$361$		−	41.6873i		−	0.115477i
$362$	−153.984	+	35.8196i	−0.425371	+	0.0989492i
$363$	1.85254	−	1.85254i	0.00510342	−	0.00510342i
$364$	−20.5770	−	7.00885i	−0.0565303	−	0.0192551i
$365$	−121.985	+	121.985i	−0.334206	+	0.334206i
$366$	448.458	−	720.343i	1.22529	−	1.96815i
$367$		−	42.0479i		−	0.114572i	−0.998358	−	0.0572860i	$-0.981755\pi$
$367$		−	42.0479i		−	0.114572i	0.998358	−	0.0572860i	$-0.0182447\pi$
$368$	−258.315	+	335.196i	−0.701944	+	0.910860i
$369$	62.0205			0.168077
$370$	−684.538	−	426.167i	−1.85010	−	1.15180i
$371$	−66.0144	−	66.0144i	−0.177936	−	0.177936i
$372$	26.3133	+	8.96269i	0.0707346	+	0.0240933i
$373$	−220.319	−	220.319i	−0.590668	−	0.590668i	0.347144	−	0.937812i	$-0.387152\pi$
$373$	−220.319	−	220.319i	−0.590668	−	0.590668i	−0.937812	+	0.347144i	$0.887152\pi$
$374$	−145.489	−	625.440i	−0.389009	−	1.67230i
$375$	6.04040			0.0161077
$376$	43.3540	−	433.247i	0.115303	−	1.15225i
$377$			17.9335i			0.0475690i
$378$	−4.26505	−	18.3349i	−0.0112832	−	0.0485051i
$379$	−150.622	+	150.622i	−0.397420	+	0.397420i	−0.877322	−	0.479902i	$-0.840672\pi$
$379$	−150.622	+	150.622i	−0.397420	+	0.397420i	0.479902	+	0.877322i	$0.340672\pi$
$380$	−452.592	+	222.608i	−1.19103	+	0.585811i
$381$	−131.798	+	131.798i	−0.345926	+	0.345926i
$382$	384.378	+	239.299i	1.00622	+	0.626437i
$383$			284.514i			0.742856i	0.928462	+	0.371428i	$0.121132\pi$
$383$			284.514i			0.742856i	−0.928462	+	0.371428i	$0.878868\pi$
$384$	−529.713	+	15.4099i	−1.37946	+	0.0401300i
$385$	−205.902			−0.534809
$386$	−97.3573	+	156.382i	−0.252221	+	0.405134i
$387$	457.078	+	457.078i	1.18108	+	1.18108i
$388$	34.7018	+	70.5532i	0.0894375	+	0.181838i
$389$	31.6781	+	31.6781i	0.0814346	+	0.0814346i	0.746651	−	0.665216i	$-0.231661\pi$
$389$	31.6781	+	31.6781i	0.0814346	+	0.0814346i	−0.665216	+	0.746651i	$0.731661\pi$
$390$	116.895	−	27.1920i	0.299731	−	0.0697231i
$391$	−769.984			−1.96927
$392$	55.7217	+	5.57594i	0.142147	+	0.0142243i
$393$		−	112.631i		−	0.286593i
$394$	−294.809	+	68.5782i	−0.748247	+	0.174056i
$395$	−265.531	+	265.531i	−0.672230	+	0.672230i
$396$	115.792	−	339.948i	0.292403	−	0.858456i
$397$	−272.742	+	272.742i	−0.687007	+	0.687007i	−0.961569	−	0.274562i	$-0.911467\pi$
$397$	−272.742	+	272.742i	−0.687007	+	0.687007i	0.274562	+	0.961569i	$0.411467\pi$
$398$	52.7309	−	84.6999i	0.132490	−	0.212814i
$399$			195.736i			0.490568i
$400$	−314.214	−	242.145i	−0.785534	−	0.605363i
$401$	662.577			1.65231			0.826156	−	0.563441i	$-0.190523\pi$
$401$	662.577			1.65231			0.826156	+	0.563441i	$0.190523\pi$
$402$	672.992	+	418.979i	1.67411	+	1.04224i
$403$	−2.43798	−	2.43798i	−0.00604958	−	0.00604958i
$404$	−244.008	+	716.373i	−0.603979	+	1.77320i
$405$	439.065	+	439.065i	1.08411	+	1.08411i
$406$	−10.4673	−	44.9978i	−0.0257816	−	0.110832i
$407$	630.140			1.54826
$408$	−610.534	−	746.310i	−1.49641	−	1.82919i
$409$			791.357i			1.93486i	0.253142	+	0.967429i	$0.418536\pi$
$409$			791.357i			1.93486i	−0.253142	+	0.967429i	$0.581464\pi$
$410$	24.3606	+	104.723i	0.0594162	+	0.255423i
$411$	−397.191	+	397.191i	−0.966403	+	0.966403i
$412$	87.6503	+	178.204i	0.212743	+	0.432535i
$413$	150.076	−	150.076i	0.363381	−	0.363381i
$414$	−365.571	−	227.591i	−0.883022	−	0.549736i
$415$			306.963i			0.739670i
$416$	59.7998	+	27.2826i	0.143749	+	0.0655833i
$417$	−527.002			−1.26379
$418$	208.313	−	334.606i	0.498356	−	0.800493i
$419$	−107.476	−	107.476i	−0.256506	−	0.256506i	0.567126	−	0.823631i	$-0.308055\pi$
$419$	−107.476	−	107.476i	−0.256506	−	0.256506i	−0.823631	+	0.567126i	$0.808055\pi$
$420$	−277.436	+	136.457i	−0.660561	+	0.324899i
$421$	337.169	+	337.169i	0.800876	+	0.800876i	0.983233	−	0.182356i	$-0.0583724\pi$
$421$	337.169	+	337.169i	0.800876	+	0.800876i	−0.182356	+	0.983233i	$0.558372\pi$
$422$	323.696	−	75.2978i	0.767053	−	0.178431i
$423$	443.070			1.04745
$424$	178.742	+	218.492i	0.421561	+	0.515311i
$425$		−	721.784i		−	1.69832i
$426$	63.0137	−	14.6582i	0.147920	−	0.0344089i
$427$	191.716	−	191.716i	0.448983	−	0.448983i
$428$	−257.355	−	87.6591i	−0.601297	−	0.204811i
$429$	−66.3185	+	66.3185i	−0.154589	+	0.154589i
$430$	−592.256	+	951.322i	−1.37734	+	2.21238i
$431$			228.783i			0.530819i	0.964136	+	0.265409i	$0.0855071\pi$
$431$			228.783i			0.530819i	−0.964136	+	0.265409i	$0.914493\pi$
$432$	7.31206	+	56.4482i	0.0169261	+	0.130667i
$433$	−10.5640			−0.0243972			−0.0121986	−	0.999926i	$-0.503883\pi$
$433$	−10.5640			−0.0243972			−0.0121986	+	0.999926i	$0.503883\pi$
$434$	7.54024	+	4.69426i	0.0173738	+	0.0108163i
$435$	180.360	+	180.360i	0.414621	+	0.414621i
$436$	363.039	+	123.657i	0.832659	+	0.283616i
$437$	−334.196	−	334.196i	−0.764750	−	0.764750i
$438$	−45.8652	−	197.169i	−0.104715	−	0.450157i
$439$	−48.5662			−0.110629			−0.0553145	−	0.998469i	$-0.517616\pi$
$439$	−48.5662			−0.110629			−0.0553145	+	0.998469i	$0.517616\pi$
$440$	619.494	+	61.9913i	1.40794	+	0.140889i
$441$			56.9851i			0.129218i
$442$	27.0966	+	116.485i	0.0613046	+	0.263541i
$443$	483.165	−	483.165i	1.09067	−	1.09067i	0.0952080	−	0.995457i	$-0.469648\pi$
$443$	483.165	−	483.165i	1.09067	−	1.09067i	0.995457	−	0.0952080i	$-0.0303516\pi$
$444$	849.063	−	417.613i	1.91230	−	0.940571i
$445$	757.179	−	757.179i	1.70153	−	1.70153i
$446$	−473.031	−	294.491i	−1.06061	−	0.660294i
$447$		−	219.251i		−	0.490494i
$448$	−165.971	−	33.5526i	−0.370470	−	0.0748941i
$449$	123.235			0.274466			0.137233	−	0.990539i	$-0.456179\pi$
$449$	123.235			0.274466			0.137233	+	0.990539i	$0.456179\pi$
$450$	213.344	−	342.687i	0.474097	−	0.761526i
$451$	−59.4131	−	59.4131i	−0.131736	−	0.131736i
$452$	89.5205	+	182.007i	0.198054	+	0.402670i
$453$	−150.289	−	150.289i	−0.331764	−	0.331764i
$454$	180.234	−	41.9257i	0.396990	−	0.0923474i
$455$	38.3481			0.0842815
$456$	58.9309	−	588.910i	0.129234	−	1.29147i
$457$		−	8.18924i		−	0.0179196i	−0.999960	−	0.00895979i	$-0.997148\pi$
$457$		−	8.18924i		−	0.0179196i	0.999960	−	0.00895979i	$-0.00285203\pi$
$458$	614.842	−	143.024i	1.34245	−	0.312279i
$459$	−73.2322	+	73.2322i	−0.159547	+	0.159547i
$460$	240.703	−	706.671i	0.523267	−	1.53624i
$461$	−357.909	+	357.909i	−0.776376	+	0.776376i	−0.979213	−	0.202837i	$-0.934984\pi$
$461$	−357.909	+	357.909i	−0.776376	+	0.776376i	0.202837	+	0.979213i	$0.434984\pi$
$462$	127.694	−	205.111i	0.276395	−	0.443964i
$463$			515.637i			1.11369i	0.830617	+	0.556844i	$0.187988\pi$
$463$			515.637i			1.11369i	−0.830617	+	0.556844i	$0.812012\pi$
$464$	17.9454	+	138.536i	0.0386754	+	0.298569i
$465$	−49.0383			−0.105459
$466$	335.149	+	208.651i	0.719203	+	0.447748i
$467$	14.0668	+	14.0668i	0.0301216	+	0.0301216i	0.722007	−	0.691886i	$-0.243220\pi$
$467$	14.0668	+	14.0668i	0.0301216	+	0.0301216i	−0.691886	+	0.722007i	$0.743220\pi$
$468$	−21.5656	+	63.3136i	−0.0460803	+	0.135286i
$469$	179.114	+	179.114i	0.381906	+	0.381906i
$470$	174.031	+	748.137i	0.370278	+	1.59178i
$471$	−331.234			−0.703257
$472$	−496.717	+	406.350i	−1.05237	+	0.860910i
$473$		−	875.724i		−	1.85142i
$474$	−99.8368	−	429.186i	−0.210626	−	0.905456i
$475$	313.275	−	313.275i	0.659527	−	0.659527i
$476$	−135.979	−	276.463i	−0.285670	−	0.580804i
$477$	−203.120	+	203.120i	−0.425828	+	0.425828i
$478$	−485.715	−	302.388i	−1.01614	−	0.632610i
$479$		−	38.3657i		−	0.0800954i	−0.999198	−	0.0400477i	$-0.987249\pi$
$479$		−	38.3657i		−	0.0800954i	0.999198	−	0.0400477i	$-0.0127510\pi$
$480$	875.801	−	327.030i	1.82459	−	0.681312i
$481$	−117.360			−0.243992
$482$	97.3378	−	156.350i	0.201946	−	0.324378i
$483$	−204.860	−	204.860i	−0.424140	−	0.424140i
$484$	−2.27134	+	1.11716i	−0.00469285	+	0.00230819i
$485$	−98.0784	−	98.0784i	−0.202224	−	0.202224i
$486$	−647.306	+	150.575i	−1.33191	+	0.309826i
$487$	597.632			1.22717			0.613585	−	0.789628i	$-0.289727\pi$
$487$	597.632			1.22717			0.613585	+	0.789628i	$0.289727\pi$
$488$	−634.534	+	519.093i	−1.30027	+	1.06372i
$489$		−	1085.13i		−	2.21909i
$490$	−96.2210	+	22.3828i	−0.196369	+	0.0456792i
$491$	−488.197	+	488.197i	−0.994290	+	0.994290i	−0.999984	−	0.00569345i	$-0.998188\pi$
$491$	−488.197	+	488.197i	−0.994290	+	0.994290i	0.00569345	+	0.999984i	$0.498188\pi$
$492$	−119.429	−	40.6794i	−0.242743	−	0.0826818i
$493$	−179.728	+	179.728i	−0.364559	+	0.364559i
$494$	−38.7972	+	62.3187i	−0.0785369	+	0.126151i
$495$			633.540i			1.27988i
$496$	−21.2729	−	16.3937i	−0.0428890	−	0.0330519i
$497$	20.6720			0.0415936
$498$	−305.785	−	190.370i	−0.614026	−	0.382269i
$499$	−251.045	−	251.045i	−0.503096	−	0.503096i	0.409302	−	0.912399i	$-0.365772\pi$
$499$	−251.045	−	251.045i	−0.503096	−	0.503096i	−0.912399	+	0.409302i	$0.865772\pi$
$500$	−5.52427	−	1.88165i	−0.0110485	−	0.00376330i
$501$	449.722	+	449.722i	0.897648	+	0.897648i
$502$	9.00658	+	38.7182i	0.0179414	+	0.0771279i
$503$	−245.100			−0.487276			−0.243638	−	0.969866i	$-0.578341\pi$
$503$	−245.100			−0.487276			−0.243638	+	0.969866i	$0.578341\pi$
$504$	17.1567	−	171.451i	0.0340410	−	0.340180i
$505$		−	1335.06i		−	2.64368i
$506$	132.180	+	568.224i	0.261225	+	1.12297i
$507$	−482.399	+	482.399i	−0.951478	+	0.951478i
$508$	161.593	−	79.4798i	0.318096	−	0.156456i
$509$	97.1267	−	97.1267i	0.190819	−	0.190819i	−0.605231	−	0.796050i	$-0.706919\pi$
$509$	97.1267	−	97.1267i	0.190819	−	0.190819i	0.796050	+	0.605231i	$0.206919\pi$
$510$	1444.02	+	898.994i	2.83142	+	1.76273i
$511$		−	64.6824i		−	0.126580i
$512$	489.252	+	150.918i	0.955571	+	0.294763i
$513$	−63.5699			−0.123918
$514$	233.353	−	374.828i	0.453995	−	0.729237i
$515$	−247.728	−	247.728i	−0.481026	−	0.481026i
$516$	−580.370	−	1179.97i	−1.12475	−	2.28676i
$517$	−424.443	−	424.443i	−0.820974	−	0.820974i
$518$	294.474	−	68.5002i	0.568483	−	0.132240i
$519$	696.225			1.34147
$520$	−115.378	−	11.5456i	−0.221880	−	0.0222030i
$521$			156.221i			0.299848i	0.988698	+	0.149924i	$0.0479029\pi$
$521$			156.221i			0.299848i	−0.988698	+	0.149924i	$0.952097\pi$
$522$	−138.454	+	32.2070i	−0.265238	+	0.0616993i
$523$	650.513	−	650.513i	1.24381	−	1.24381i	0.285404	−	0.958407i	$-0.407872\pi$
$523$	650.513	−	650.513i	1.24381	−	1.24381i	0.958407	−	0.285404i	$-0.0921277\pi$
$524$	−35.0858	+	103.007i	−0.0669577	+	0.196579i
$525$	192.036	−	192.036i	0.365782	−	0.365782i
$526$	280.701	−	450.881i	0.533652	−	0.857188i
$527$		−	48.8663i		−	0.0927254i
$528$	−445.946	+	578.671i	−0.844595	+	1.09597i
$529$	170.545			0.322391
$530$	−422.756	−	263.192i	−0.797654	−	0.496589i
$531$	−461.771	−	461.771i	−0.869626	−	0.869626i
$532$	60.9741	−	179.012i	0.114613	−	0.336488i
$533$	11.0654	+	11.0654i	0.0207606	+	0.0207606i
$534$	284.692	+	1223.86i	0.533131	+	2.29186i
$535$	479.616			0.896479
$536$	−484.971	−	592.824i	−0.904797	−	1.10601i
$537$			816.871i			1.52117i
$538$	147.507	+	634.115i	0.274177	+	1.17865i
$539$	54.5894	−	54.5894i	0.101279	−	0.101279i
$540$	−44.3176	−	90.1035i	−0.0820697	−	0.166858i
$541$	41.6149	−	41.6149i	0.0769221	−	0.0769221i	−0.667599	−	0.744521i	$-0.732678\pi$
$541$	41.6149	−	41.6149i	0.0769221	−	0.0769221i	0.744521	+	0.667599i	$0.232678\pi$
$542$	−148.363	−	92.3652i	−0.273733	−	0.170415i
$543$			327.269i			0.602704i
$544$	325.883	+	872.729i	0.599049	+	1.60428i
$545$	−676.573			−1.24142
$546$	−23.7824	+	38.2009i	−0.0435576	+	0.0699651i
$547$	−281.326	−	281.326i	−0.514308	−	0.514308i	0.401536	−	0.915843i	$-0.368477\pi$
$547$	−281.326	−	281.326i	−0.514308	−	0.514308i	−0.915843	+	0.401536i	$0.868477\pi$
$548$	486.983	−	239.524i	0.888655	−	0.437087i
$549$	−589.892	−	589.892i	−1.07448	−	1.07448i
$550$	−532.654	+	123.905i	−0.968462	+	0.225282i
$551$	−156.014			−0.283147
$552$	554.682	+	678.037i	1.00486	+	1.22833i
$553$		−	140.797i		−	0.254606i
$554$	541.152	−	125.882i	0.976809	−	0.227224i
$555$	−1180.31	+	1180.31i	−2.12669	+	2.12669i
$556$	481.972	+	164.167i	0.866857	+	0.295264i
$557$	35.2138	−	35.2138i	0.0632204	−	0.0632204i	−0.674790	−	0.738010i	$-0.735766\pi$
$557$	35.2138	−	35.2138i	0.0632204	−	0.0632204i	0.738010	+	0.674790i	$0.235766\pi$
$558$	14.4438	−	23.2006i	0.0258850	−	0.0415782i
$559$			163.099i			0.291769i
$560$	296.238	−	38.3734i	0.528996	−	0.0685240i
$561$	−1329.27			−2.36947
$562$	−300.156	−	186.866i	−0.534086	−	0.332502i
$563$	−173.167	−	173.167i	−0.307578	−	0.307578i	0.536391	−	0.843969i	$-0.319787\pi$
$563$	−173.167	−	173.167i	−0.307578	−	0.307578i	−0.843969	+	0.536391i	$0.819787\pi$
$564$	−853.195	−	290.611i	−1.51276	−	0.515268i
$565$	−253.014	−	253.014i	−0.447812	−	0.447812i
$566$	−59.1547	−	254.299i	−0.104514	−	0.449291i
$567$	−232.813			−0.410605
$568$	−62.1957	−	6.22378i	−0.109499	−	0.0109574i
$569$			730.521i			1.28387i	0.766760	+	0.641934i	$0.221868\pi$
$569$			730.521i			1.28387i	−0.766760	+	0.641934i	$0.778132\pi$
$570$	236.559	+	1016.94i	0.415016	+	1.78410i
$571$	454.187	−	454.187i	0.795425	−	0.795425i	−0.186946	−	0.982370i	$-0.559859\pi$
$571$	454.187	−	454.187i	0.795425	−	0.795425i	0.982370	+	0.186946i	$0.0598588\pi$
$572$	81.3108	−	39.9929i	0.142152	−	0.0699177i
$573$	662.762	−	662.762i	1.15665	−	1.15665i
$574$	−34.2233	−	21.3061i	−0.0596224	−	0.0371186i
$575$			655.754i			1.14044i
$576$	−103.238	+	510.676i	−0.179233	+	0.886590i
$577$	651.335			1.12883			0.564415	−	0.825491i	$-0.309102\pi$
$577$	651.335			1.12883			0.564415	+	0.825491i	$0.309102\pi$
$578$	−590.362	+	948.279i	−1.02139	+	1.64062i
$579$	269.641	+	269.641i	0.465701	+	0.465701i
$580$	−108.765	−	221.133i	−0.187526	−	0.381265i
$581$	−81.3832	−	81.3832i	−0.140074	−	0.140074i
$582$	158.528	−	36.8765i	0.272384	−	0.0633617i
$583$	389.162			0.667516
$584$	−19.4741	+	194.609i	−0.0333460	+	0.333235i
$585$		−	117.994i		−	0.201698i
$586$	−107.843	+	25.0864i	−0.184033	+	0.0428096i
$587$	31.7289	−	31.7289i	0.0540526	−	0.0540526i	−0.679564	−	0.733616i	$-0.737831\pi$
$587$	31.7289	−	31.7289i	0.0540526	−	0.0540526i	0.733616	+	0.679564i	$0.237831\pi$
$588$	37.3767	−	109.733i	0.0635658	−	0.186621i
$589$	21.2094	−	21.2094i	0.0360092	−	0.0360092i
$590$	598.338	−	961.090i	1.01413	−	1.62897i
$591$			626.569i			1.06018i
$592$	−906.605	+	117.438i	−1.53143	+	0.198375i
$593$	605.520			1.02111			0.510556	−	0.859844i	$-0.329439\pi$
$593$	605.520			1.02111			0.510556	+	0.859844i	$0.329439\pi$
$594$	66.6146	+	41.4717i	0.112146	+	0.0698176i
$595$	384.320	+	384.320i	0.645916	+	0.645916i
$596$	−68.2991	+	200.517i	−0.114596	+	0.336438i
$597$	−146.043	−	146.043i	−0.244629	−	0.244629i
$598$	−24.6178	−	105.829i	−0.0411669	−	0.176971i
$599$	−459.683			−0.767418			−0.383709	−	0.923454i	$-0.625353\pi$
$599$	−459.683			−0.767418			−0.383709	+	0.923454i	$0.625353\pi$
$600$	−635.593	+	519.959i	−1.05932	+	0.866599i
$601$			8.05285i			0.0133991i	0.999978	+	0.00669954i	$0.00213255\pi$
$601$			8.05285i			0.0133991i	−0.999978	+	0.00669954i	$0.997867\pi$
$602$	−95.1968	−	409.239i	−0.158134	−	0.679800i
$603$	551.116	−	551.116i	0.913957	−	0.913957i
$604$	90.6309	+	184.264i	0.150051	+	0.305074i
$605$	3.15746	−	3.15746i	0.00521895	−	0.00521895i
$606$	1329.93	+	827.966i	2.19461	+	1.36628i
$607$		−	293.516i		−	0.483552i	−0.970332	−	0.241776i	$-0.922270\pi$
$607$		−	293.516i		−	0.483552i	0.970332	−	0.241776i	$-0.0777300\pi$
$608$	−237.348	+	520.233i	−0.390374	+	0.855646i
$609$	−95.6356			−0.157037
$610$	764.350	−	1227.75i	1.25303	−	2.01270i
$611$	79.0504	+	79.0504i	0.129379	+	0.129379i
$612$	−850.650	+	418.394i	−1.38995	+	0.683651i
$613$	422.169	+	422.169i	0.688693	+	0.688693i	0.961943	−	0.273250i	$-0.0880987\pi$
$613$	422.169	+	422.169i	0.688693	+	0.688693i	−0.273250	+	0.961943i	$0.588099\pi$
$614$	−357.197	+	83.0908i	−0.581755	+	0.135327i
$615$	222.573			0.361907
$616$	−180.678	+	147.807i	−0.293308	+	0.239947i
$617$		−	1040.69i		−	1.68669i	−0.537376	−	0.843343i	$-0.680584\pi$
$617$		−	1040.69i		−	1.68669i	0.537376	−	0.843343i	$-0.319416\pi$
$618$	400.412	−	93.1432i	0.647915	−	0.150717i
$619$	26.3371	−	26.3371i	0.0425479	−	0.0425479i	−0.685513	−	0.728061i	$-0.740422\pi$
$619$	26.3371	−	26.3371i	0.0425479	−	0.0425479i	0.728061	+	0.685513i	$0.240422\pi$
$620$	44.8482	+	15.2760i	0.0723358	+	0.0246387i
$621$	66.5329	−	66.5329i	0.107138	−	0.107138i
$622$	38.4677	−	61.7894i	0.0618452	−	0.0993399i
$623$			401.493i			0.644451i
$624$	83.0552	−	107.774i	0.133101	−	0.172715i
$625$	630.126			1.00820
$626$	−394.684	−	245.715i	−0.630485	−	0.392516i
$627$	−576.943	−	576.943i	−0.920165	−	0.920165i
$628$	302.931	+	103.183i	0.482375	+	0.164304i
$629$	−1176.17	−	1176.17i	−1.86991	−	1.86991i
$630$	68.8699	+	296.063i	0.109317	+	0.469942i
$631$	−707.844			−1.12178			−0.560891	−	0.827890i	$-0.689541\pi$
$631$	−707.844			−1.12178			−0.560891	+	0.827890i	$0.689541\pi$
$632$	−42.3901	+	423.615i	−0.0670730	+	0.670276i
$633$		−	687.964i		−	1.08683i
$634$	−227.205	−	976.725i	−0.358367	−	1.54058i
$635$	−224.636	+	224.636i	−0.353757	+	0.353757i
$636$	524.364	−	257.910i	0.824471	−	0.405518i
$637$	−10.1670	+	10.1670i	−0.0159607	+	0.0159607i
$638$	163.486	+	101.780i	0.256248	+	0.159530i
$639$		−	63.6059i		−	0.0995397i
$640$	−902.841	+	26.2646i	−1.41069	+	0.0410384i
$641$	340.563			0.531299			0.265649	−	0.964070i	$-0.414414\pi$
$641$	340.563			0.531299			0.265649	+	0.964070i	$0.414414\pi$
$642$	−297.445	+	477.776i	−0.463310	+	0.744199i
$643$	198.835	+	198.835i	0.309231	+	0.309231i	0.844611	−	0.535380i	$-0.179832\pi$
$643$	198.835	+	198.835i	0.309231	+	0.309231i	−0.535380	+	0.844611i	$0.679832\pi$
$644$	123.539	+	251.171i	0.191831	+	0.390018i
$645$	1640.31	+	1640.31i	2.54312	+	2.54312i
$646$	−1013.37	+	235.729i	−1.56869	+	0.364906i
$647$	441.888			0.682979			0.341490	−	0.939886i	$-0.389069\pi$
$647$	441.888			0.682979			0.341490	+	0.939886i	$0.389069\pi$
$648$	700.462	+	70.0936i	1.08096	+	0.108169i
$649$			884.716i			1.36320i
$650$	99.2041	−	23.0767i	0.152622	−	0.0355027i
$651$	13.0012	−	13.0012i	0.0199712	−	0.0199712i
$652$	−338.031	+	992.414i	−0.518453	+	1.52211i
$653$	−681.938	+	681.938i	−1.04432	+	1.04432i	−0.0453447	+	0.998971i	$0.514439\pi$
$653$	−681.938	+	681.938i	−1.04432	+	1.04432i	−0.998971	+	0.0453447i	$0.985561\pi$
$654$	419.592	−	673.976i	0.641578	−	1.03054i
$655$		−	191.968i		−	0.293081i
$656$	96.5525	+	74.4071i	0.147184	+	0.113426i
$657$	−199.022			−0.302925
$658$	−244.489	−	152.209i	−0.371563	−	0.231321i
$659$	−638.128	−	638.128i	−0.968328	−	0.968328i	0.0311860	−	0.999514i	$-0.490072\pi$
$659$	−638.128	−	638.128i	−0.968328	−	0.968328i	−0.999514	+	0.0311860i	$0.990072\pi$
$660$	415.541	−	1219.97i	0.629607	−	1.84844i
$661$	−122.066	−	122.066i	−0.184669	−	0.184669i	0.608718	−	0.793387i	$-0.291684\pi$
$661$	−122.066	−	122.066i	−0.184669	−	0.184669i	−0.793387	+	0.608718i	$0.791684\pi$
$662$	−159.627	−	686.218i	−0.241129	−	1.03658i
$663$	247.570			0.373409
$664$	220.354	+	269.359i	0.331859	+	0.405661i
$665$			333.612i			0.501673i
$666$	−210.769	−	906.070i	−0.316470	−	1.36047i
$667$	163.286	−	163.286i	0.244807	−	0.244807i
$668$	−271.202	−	551.388i	−0.405990	−	0.825431i
$669$	−815.622	+	815.622i	−1.21917	+	1.21917i
$670$	1147.05	+	714.106i	1.71201	+	1.06583i
$671$			1130.18i			1.68433i
$672$	−145.492	+	318.899i	−0.216507	+	0.474552i
$673$	834.099			1.23937			0.619687	−	0.784849i	$-0.287260\pi$
$673$	834.099			1.23937			0.619687	+	0.784849i	$0.287260\pi$
$674$	−198.036	+	318.099i	−0.293822	+	0.471956i
$675$	62.3680	+	62.3680i	0.0923970	+	0.0923970i
$676$	591.453	−	290.908i	0.874931	−	0.430337i
$677$	743.024	+	743.024i	1.09752	+	1.09752i	0.994700	+	0.102824i	$0.0327880\pi$
$677$	743.024	+	743.024i	1.09752	+	1.09752i	0.102824	+	0.994700i	$0.467212\pi$
$678$	408.955	−	95.1306i	0.603178	−	0.140311i
$679$	52.0059			0.0765919
$680$	−1040.59	−	1272.01i	−1.53028	−	1.87060i
$681$		−	383.057i		−	0.562492i
$682$	−36.0618	+	8.38866i	−0.0528766	+	0.0123001i
$683$	512.204	−	512.204i	0.749933	−	0.749933i	−0.224533	−	0.974466i	$-0.572086\pi$
$683$	512.204	−	512.204i	0.749933	−	0.749933i	0.974466	+	0.224533i	$0.0720858\pi$
$684$	−550.802	−	187.612i	−0.805267	−	0.274286i
$685$	−676.972	+	676.972i	−0.988280	+	0.988280i
$686$	19.5763	−	31.4447i	0.0285368	−	0.0458378i
$687$		−	1306.75i		−	1.90211i
$688$	163.207	+	1259.94i	0.237219	+	1.83130i
$689$	−72.4793			−0.105195
$690$	−1311.92	−	816.753i	−1.90134	−	1.18370i
$691$	238.624	+	238.624i	0.345332	+	0.345332i	0.858367	−	0.513035i	$-0.171479\pi$
$691$	238.624	+	238.624i	0.345332	+	0.345332i	−0.513035	+	0.858367i	$0.671479\pi$
$692$	−636.735	−	216.882i	−0.920138	−	0.313413i
$693$	−167.967	−	167.967i	−0.242376	−	0.242376i
$694$	118.004	+	507.285i	0.170035	+	0.730959i
$695$	−898.220			−1.29240
$696$	287.738	+	28.7933i	0.413416	+	0.0413696i
$697$			221.792i			0.318210i
$698$	258.647	+	1111.89i	0.370555	+	1.59297i
$699$	577.879	−	577.879i	0.826722	−	0.826722i
$700$	−235.448	+	115.806i	−0.336355	+	0.165437i
$701$	−271.291	+	271.291i	−0.387005	+	0.387005i	−0.873618	−	0.486612i	$-0.838232\pi$
$701$	−271.291	+	271.291i	−0.387005	+	0.387005i	0.486612	+	0.873618i	$0.338232\pi$
$702$	−12.4066	−	7.72389i	−0.0176732	−	0.0110027i
$703$		−	1020.99i		−	1.45233i
$704$	588.105	−	390.309i	0.835376	−	0.554416i
$705$	1590.04			2.25538
$706$	−310.130	+	498.152i	−0.439278	+	0.705598i
$707$	353.956	+	353.956i	0.500645	+	0.500645i
$708$	586.329	+	1192.08i	0.828148	+	1.68373i
$709$	−503.533	−	503.533i	−0.710201	−	0.710201i	0.256376	−	0.966577i	$-0.417472\pi$
$709$	−503.533	−	503.533i	−0.710201	−	0.710201i	−0.966577	+	0.256376i	$0.917472\pi$
$710$	107.400	−	24.9833i	0.151268	−	0.0351878i
$711$	−433.219			−0.609310
$712$	120.878	−	1207.97i	0.169773	−	1.69658i
$713$			44.3960i			0.0622664i
$714$	−621.190	+	144.500i	−0.870014	+	0.202382i
$715$	−113.033	+	113.033i	−0.158088	+	0.158088i
$716$	254.464	−	747.073i	0.355397	−	1.04340i
$717$	−837.492	+	837.492i	−1.16805	+	1.16805i
$718$	−478.244	+	768.188i	−0.666078	+	1.06990i
$719$		−	1097.27i		−	1.52611i	−0.646332	−	0.763056i	$-0.723698\pi$
$719$		−	1097.27i		−	1.52611i	0.646332	−	0.763056i	$-0.276302\pi$
$720$	−118.071	−	911.497i	−0.163988	−	1.26597i
$721$	131.357			0.182188
$722$	70.7790	+	44.0643i	0.0980318	+	0.0610309i
$723$	−269.586	−	269.586i	−0.372872	−	0.372872i
$724$	101.948	−	299.305i	0.140812	−	0.413405i
$725$	153.064	+	153.064i	0.211123	+	0.211123i
$726$	1.18717	+	5.10352i	0.00163523	+	0.00702964i
$727$	−59.1604			−0.0813761			−0.0406881	−	0.999172i	$-0.512955\pi$
$727$	−59.1604			−0.0813761			−0.0406881	+	0.999172i	$0.512955\pi$
$728$	33.6503	−	27.5283i	0.0462230	−	0.0378136i
$729$			583.788i			0.800807i
$730$	−78.1724	−	336.054i	−0.107085	−	0.460348i
$731$	−1634.56	+	1634.56i	−2.23606	+	2.23606i
$732$	749.009	+	1522.83i	1.02324	+	2.08037i
$733$	76.3792	−	76.3792i	0.104201	−	0.104201i	−0.653084	−	0.757285i	$-0.726525\pi$
$733$	76.3792	−	76.3792i	0.104201	−	0.104201i	0.757285	+	0.653084i	$0.226525\pi$
$734$	71.3912	+	44.4455i	0.0972633	+	0.0605524i
$735$			204.502i			0.278234i
$736$	−296.071	−	792.891i	−0.402270	−	1.07730i
$737$	−1055.89			−1.43269
$738$	−65.5569	+	105.302i	−0.0888305	+	0.142685i
$739$	−736.537	−	736.537i	−0.996667	−	0.996667i	0.00332794	−	0.999994i	$-0.498941\pi$
$739$	−736.537	−	736.537i	−0.996667	−	0.996667i	−0.999994	+	0.00332794i	$0.998941\pi$
$740$	1447.14	−	711.779i	1.95559	−	0.961863i
$741$	107.453	+	107.453i	0.145010	+	0.145010i
$742$	181.861	−	42.3044i	0.245096	−	0.0570140i
$743$	813.679			1.09513			0.547563	−	0.836764i	$-0.315556\pi$
$743$	813.679			1.09513			0.547563	+	0.836764i	$0.315556\pi$
$744$	−43.0310	+	35.2023i	−0.0578373	+	0.0473150i
$745$		−	373.690i		−	0.501598i
$746$	606.952	−	141.188i	0.813608	−	0.189261i
$747$	−250.409	+	250.409i	−0.335219	+	0.335219i
$748$	1215.69	+	414.083i	1.62526	+	0.553587i
$749$	−127.158	+	127.158i	−0.169770	+	0.169770i
$750$	−6.38482	+	10.2557i	−0.00851309	+	0.0136743i
$751$			5.65571i			0.00753090i	0.999993	+	0.00376545i	$0.00119858\pi$
$751$			5.65571i			0.00753090i	−0.999993	+	0.00376545i	$0.998801\pi$
$752$	689.765	+	531.559i	0.917240	+	0.706861i
$753$	82.2892			0.109282
$754$	−30.4485	−	18.9561i	−0.0403826	−	0.0251407i
$755$	−256.152	−	256.152i	−0.339275	−	0.339275i
$756$	35.6383	+	12.1389i	0.0471406	+	0.0160568i
$757$	62.6860	+	62.6860i	0.0828085	+	0.0828085i	0.747298	−	0.664489i	$-0.231351\pi$
$757$	62.6860	+	62.6860i	0.0828085	+	0.0828085i	−0.664489	+	0.747298i	$0.731351\pi$
$758$	−96.5240	−	414.945i	−0.127340	−	0.547421i
$759$	1207.67			1.59113
$760$	100.442	−	1003.74i	0.132160	−	1.32071i
$761$			867.427i			1.13985i	0.821696	+	0.569926i	$0.193028\pi$
$761$			867.427i			1.13985i	−0.821696	+	0.569926i	$0.806972\pi$
$762$	−84.4607	−	363.086i	−0.110841	−	0.476491i
$763$	179.376	−	179.376i	0.235093	−	0.235093i
$764$	−812.589	+	399.674i	−1.06360	+	0.523133i
$765$	1182.52	−	1182.52i	1.54577	−	1.54577i
$766$	−483.063	−	300.736i	−0.630630	−	0.392606i
$767$		−	164.774i		−	0.214829i
$768$	533.753	−	915.665i	0.694992	−	1.19227i
$769$	680.441			0.884839			0.442420	−	0.896808i	$-0.354120\pi$
$769$	680.441			0.884839			0.442420	+	0.896808i	$0.354120\pi$
$770$	217.642	−	349.591i	0.282652	−	0.454014i
$771$	−646.295	−	646.295i	−0.838255	−	0.838255i
$772$	−162.605	−	330.597i	−0.210628	−	0.428235i
$773$	869.214	+	869.214i	1.12447	+	1.12447i	0.991061	+	0.133406i	$0.0425915\pi$
$773$	869.214	+	869.214i	1.12447	+	1.12447i	0.133406	+	0.991061i	$0.457408\pi$
$774$	−1259.19	+	292.912i	−1.62686	+	0.378439i
$775$	−41.6168			−0.0536991
$776$	−156.470	−	15.6575i	−0.201636	−	0.0201772i
$777$		−	625.857i		−	0.805479i
$778$	−87.2691	+	20.3004i	−0.112171	+	0.0260931i
$779$	−96.2643	+	96.2643i	−0.123574	+	0.123574i
$780$	−77.3923	+	227.213i	−0.0992209	+	0.291299i
$781$	−60.9318	+	60.9318i	−0.0780177	+	0.0780177i
$782$	813.888	−	1307.32i	1.04078	−	1.67177i
$783$		−	31.0598i		−	0.0396677i
$784$	−68.3661	+	88.7135i	−0.0872016	+	0.113155i
$785$	−564.554			−0.719177
$786$	191.231	+	119.053i	0.243297	+	0.151467i
$787$	676.477	+	676.477i	0.859564	+	0.859564i	0.991287	−	0.131723i	$-0.0420509\pi$
$787$	676.477	+	676.477i	0.859564	+	0.859564i	−0.131723	+	0.991287i	$0.542051\pi$
$788$	195.183	−	573.032i	0.247694	−	0.727197i
$789$	−777.429	−	777.429i	−0.985335	−	0.985335i
$790$	−170.161	−	731.504i	−0.215394	−	0.925954i
$791$	134.160			0.169608
$792$	454.789	+	555.929i	0.574229	+	0.701931i
$793$		−	210.491i		−	0.265436i
$794$	−174.783	−	751.369i	−0.220129	−	0.946309i
$795$	−728.936	+	728.936i	−0.916901	+	0.916901i
$796$	88.0706	+	179.059i	0.110641	+	0.224948i
$797$	−31.7443	+	31.7443i	−0.0398297	+	0.0398297i	−0.726741	−	0.686911i	$-0.758966\pi$
$797$	−31.7443	+	31.7443i	−0.0398297	+	0.0398297i	0.686911	+	0.726741i	$0.258966\pi$
$798$	−332.332	−	206.897i	−0.416456	−	0.259270i
$799$			1584.47i			1.98306i
$800$	743.257	−	277.537i	0.929071	−	0.346921i
$801$	1235.36			1.54227
$802$	−700.357	+	1124.96i	−0.873263	+	1.40269i
$803$	190.655	+	190.655i	0.237428	+	0.237428i
$804$	−1422.73	+	699.774i	−1.76957	+	0.870366i
$805$	−349.162	−	349.162i	−0.433742	−	0.433742i
$806$	6.71633	−	1.56234i	0.00833292	−	0.00193839i
$807$	1347.71			1.67002
$808$	−958.377	−	1171.51i	−1.18611	−	1.44989i
$809$		−	966.134i		−	1.19423i	−0.802155	−	0.597116i	$-0.796313\pi$
$809$		−	966.134i		−	1.19423i	0.802155	−	0.597116i	$-0.203687\pi$
$810$	−1209.57	+	281.368i	−1.49329	+	0.347368i
$811$	789.583	−	789.583i	0.973592	−	0.973592i	−0.0260681	−	0.999660i	$-0.508299\pi$
$811$	789.583	−	789.583i	0.973592	−	0.973592i	0.999660	+	0.0260681i	$0.00829866\pi$
$812$	87.4640	+	29.7916i	0.107714	+	0.0366891i
$813$	−255.814	+	255.814i	−0.314655	+	0.314655i
$814$	−666.070	+	1069.89i	−0.818268	+	1.31436i
$815$		−	1849.50i		−	2.26932i
$816$	1912.47	−	247.734i	2.34372	−	0.303595i
$817$	−1418.89			−1.73671
$818$	−1343.61	−	836.480i	−1.64255	−	1.02259i
$819$	31.2829	+	31.2829i	0.0381965	+	0.0381965i
$820$	−203.555	−	69.3339i	−0.248238	−	0.0845535i
$821$	528.527	+	528.527i	0.643761	+	0.643761i	0.951478	−	0.307717i	$-0.0995651\pi$
$821$	528.527	+	528.527i	0.643761	+	0.643761i	−0.307717	+	0.951478i	$0.599565\pi$
$822$	−254.534	−	1094.21i	−0.309652	−	1.33116i
$823$	−143.296			−0.174114			−0.0870569	−	0.996203i	$-0.527746\pi$
$823$	−143.296			−0.174114			−0.0870569	+	0.996203i	$0.527746\pi$
$824$	−395.213	−	39.5481i	−0.479628	−	0.0479952i
$825$			1132.07i			1.37221i
$826$	96.1743	+	413.442i	0.116434	+	0.500535i
$827$	593.412	−	593.412i	0.717547	−	0.717547i	−0.250555	−	0.968102i	$-0.580613\pi$
$827$	593.412	−	593.412i	0.717547	−	0.717547i	0.968102	+	0.250555i	$0.0806131\pi$
$828$	772.831	−	380.119i	0.933371	−	0.459081i
$829$	−62.1034	+	62.1034i	−0.0749136	+	0.0749136i	−0.743571	−	0.668657i	$-0.766869\pi$
$829$	−62.1034	+	62.1034i	−0.0749136	+	0.0749136i	0.668657	+	0.743571i	$0.266869\pi$
$830$	−521.178	−	324.466i	−0.627926	−	0.390922i
$831$		−	1150.13i		−	1.38403i
$832$	−109.531	+	72.6930i	−0.131648	+	0.0873714i
$833$	−203.785			−0.244640
$834$	557.051	−	894.773i	0.667927	−	1.07287i
$835$	766.504	+	766.504i	0.917968	+	0.917968i
$836$	347.922	+	707.370i	0.416174	+	0.846137i
$837$	4.22244	+	4.22244i	0.00504474	+	0.00504474i
$838$	296.082	−	68.8743i	0.353320	−	0.0821889i
$839$	668.680			0.796996			0.398498	−	0.917169i	$-0.369532\pi$
$839$	668.680			0.796996			0.398498	+	0.917169i	$0.369532\pi$
$840$	61.5700	−	615.284i	0.0732976	−	0.732480i
$841$			764.772i			0.909361i
$842$	−928.858	+	216.070i	−1.10316	+	0.256615i
$843$	−517.543	+	517.543i	−0.613930	+	0.613930i
$844$	−214.308	+	629.180i	−0.253920	+	0.745474i
$845$	−822.199	+	822.199i	−0.973017	+	0.973017i
$846$	−468.334	+	752.269i	−0.553586	+	0.889207i
$847$			1.67424i			0.00197667i
$848$	−559.901	+	72.5272i	−0.660260	+	0.0855274i
$849$	−540.471			−0.636597
$850$	1225.48	+	762.939i	1.44175	+	0.897576i
$851$	1068.57	+	1068.57i	1.25567	+	1.25567i
$852$	−41.7193	+	122.482i	−0.0489663	+	0.143758i
$853$	1179.37	+	1179.37i	1.38262	+	1.38262i	0.839946	+	0.542671i	$0.182587\pi$
$853$	1179.37	+	1179.37i	1.38262	+	1.38262i	0.542671	+	0.839946i	$0.317413\pi$
$854$	122.858	+	528.153i	0.143862	+	0.618446i
$855$	1026.49			1.20058
$856$	420.862	−	344.294i	0.491661	−	0.402213i
$857$		−	1092.29i		−	1.27455i	−0.770637	−	0.637274i	$-0.780062\pi$
$857$		−	1092.29i		−	1.27455i	0.770637	−	0.637274i	$-0.219938\pi$
$858$	−42.4992	−	182.699i	−0.0495329	−	0.212936i
$859$	452.662	−	452.662i	0.526964	−	0.526964i	−0.392702	−	0.919666i	$-0.628459\pi$
$859$	452.662	−	452.662i	0.526964	−	0.526964i	0.919666	+	0.392702i	$0.128459\pi$
$860$	−989.180	−	2011.13i	−1.15021	−	2.33852i
$861$	−59.0093	+	59.0093i	−0.0685358	+	0.0685358i
$862$	−388.440	−	241.828i	−0.450627	−	0.280543i
$863$			926.770i			1.07389i	0.843616	+	0.536947i	$0.180422\pi$
$863$			926.770i			1.07389i	−0.843616	+	0.536947i	$0.819578\pi$
$864$	−103.570	−	47.2520i	−0.119872	−	0.0546898i
$865$	1186.64			1.37184
$866$	11.1664	−	17.9361i	0.0128942	−	0.0207115i
$867$	1635.07	+	1635.07i	1.88589	+	1.88589i
$868$	−15.9404	+	7.84030i	−0.0183645	+	0.00903261i
$869$	415.006	+	415.006i	0.477568	+	0.477568i
$870$	−496.870	+	115.581i	−0.571115	+	0.132852i
$871$	196.655			0.225780
$872$	−593.691	+	485.680i	−0.680838	+	0.556973i
$873$		−	160.017i		−	0.183296i
$874$	920.667	−	214.164i	1.05339	−	0.245039i
$875$	−2.72951	+	2.72951i	−0.00311944	+	0.00311944i
$876$	383.244	+	130.539i	0.437494	+	0.149017i
$877$	216.549	−	216.549i	0.246921	−	0.246921i	−0.572785	−	0.819706i	$-0.694137\pi$
$877$	216.549	−	216.549i	0.246921	−	0.246921i	0.819706	+	0.572785i	$0.194137\pi$
$878$	51.3354	−	82.4583i	0.0584685	−	0.0939160i
$879$			229.204i			0.260755i
$880$	−760.069	+	986.284i	−0.863715	+	1.12078i
$881$	−739.217			−0.839066			−0.419533	−	0.907740i	$-0.637806\pi$
$881$	−739.217			−0.839066			−0.419533	+	0.907740i	$0.637806\pi$
$882$	−96.7525	−	60.2344i	−0.109697	−	0.0682929i
$883$	220.078	+	220.078i	0.249238	+	0.249238i	0.820658	−	0.571420i	$-0.193607\pi$
$883$	220.078	+	220.078i	0.249238	+	0.249238i	−0.571420	+	0.820658i	$0.693607\pi$
$884$	−226.416	−	77.1208i	−0.256127	−	0.0872408i
$885$	−1657.16	−	1657.16i	−1.87249	−	1.87249i
$886$	309.629	+	1331.06i	0.349468	+	1.50232i
$887$	−271.194			−0.305743			−0.152872	−	0.988246i	$-0.548852\pi$
$887$	−271.194			−0.305743			−0.152872	+	0.988246i	$0.548852\pi$
$888$	−188.428	+	1883.01i	−0.212194	+	2.12051i
$889$		−	119.113i		−	0.133985i
$890$	485.227	+	2085.93i	0.545199	+	2.34375i
$891$	686.228	−	686.228i	0.770178	−	0.770178i
$892$	1000.01	−	491.855i	1.12108	−	0.551407i
$893$	−687.705	+	687.705i	−0.770107	+	0.770107i
$894$	372.256	+	231.752i	0.416394	+	0.259231i
$895$			1392.27i			1.55561i
$896$	232.401	−	246.328i	0.259377	−	0.274920i
$897$	−224.922			−0.250749
$898$	−130.262	+	209.235i	−0.145058	+	0.233001i
$899$	10.3628	+	10.3628i	0.0115270	+	0.0115270i
$900$	356.324	+	724.453i	0.395915	+	0.804948i
$901$	−726.379	−	726.379i	−0.806192	−	0.806192i
$902$	163.676	−	38.0740i	0.181459	−	0.0422107i
$903$	−869.772			−0.963203
$904$	−403.646	−	40.3919i	−0.446511	−	0.0446813i
$905$			557.795i			0.616348i
$906$	414.028	−	96.3107i	0.456984	−	0.106303i
$907$	−1022.54	+	1022.54i	−1.12739	+	1.12739i	−0.136793	+	0.990600i	$0.543679\pi$
$907$	−1022.54	+	1022.54i	−1.12739	+	1.12739i	−0.990600	+	0.136793i	$0.956321\pi$
$908$	−119.327	+	350.327i	−0.131417	+	0.385822i
$909$	1089.09	−	1089.09i	1.19812	−	1.19812i
$910$	−40.5347	+	65.1095i	−0.0445436	+	0.0715489i
$911$		−	990.220i		−	1.08696i	−0.839422	−	0.543480i	$-0.817107\pi$
$911$		−	990.220i		−	1.08696i	0.839422	−	0.543480i	$-0.182893\pi$
$912$	937.593	+	722.546i	1.02806	+	0.792265i
$913$	479.762			0.525479
$914$	13.9041	+	8.65619i	0.0152124	+	0.00947067i
$915$	−2116.94	−	2116.94i	−2.31360	−	2.31360i
$916$	−407.066	+	1195.09i	−0.444396	+	1.30469i
$917$	50.8953	+	50.8953i	0.0555019	+	0.0555019i
$918$	−46.9298	−	201.746i	−0.0511218	−	0.219766i
$919$	−1390.65			−1.51322			−0.756612	−	0.653864i	$-0.773147\pi$
$919$	−1390.65			−1.51322			−0.756612	+	0.653864i	$0.773147\pi$
$920$	945.397	+	1155.64i	1.02761	+	1.25613i
$921$			759.165i			0.824284i
$922$	−229.361	−	985.995i	−0.248765	−	1.06941i
$923$	11.3482	−	11.3482i	0.0122949	−	0.0122949i
$924$	213.274	+	433.613i	0.230816	+	0.469278i
$925$	−1001.68	+	1001.68i	−1.08290	+	1.08290i
$926$	−875.477	−	545.038i	−0.945439	−	0.588594i
$927$		−	404.174i		−	0.436002i
$928$	−254.183	−	115.967i	−0.273904	−	0.124964i
$929$	−957.170			−1.03032			−0.515161	−	0.857093i	$-0.672268\pi$
$929$	−957.170			−1.03032			−0.515161	+	0.857093i	$0.672268\pi$
$930$	51.8344	−	83.2599i	0.0557360	−	0.0895268i
$931$	−88.4486	−	88.4486i	−0.0950039	−	0.0950039i
$932$	−708.517	+	348.486i	−0.760211	+	0.373912i
$933$	−106.540	−	106.540i	−0.114191	−	0.114191i
$934$	−38.7522	+	9.01448i	−0.0414905	+	0.00965148i
$935$	−2265.61			−2.42311
$936$	−84.7021	−	103.539i	−0.0904937	−	0.110619i
$937$			43.3847i			0.0463017i	0.999732	+	0.0231508i	$0.00736980\pi$
$937$			43.3847i			0.0463017i	−0.999732	+	0.0231508i	$0.992630\pi$
$938$	−493.436	+	114.782i	−0.526051	+	0.122369i
$939$	−680.532	+	680.532i	−0.724741	+	0.724741i
$940$	−1454.18	−	495.317i	−1.54700	−	0.526932i
$941$	839.813	−	839.813i	0.892468	−	0.892468i	−0.102287	−	0.994755i	$-0.532616\pi$
$941$	839.813	−	839.813i	0.892468	−	0.892468i	0.994755	+	0.102287i	$0.0326159\pi$
$942$	350.121	−	562.387i	0.371678	−	0.597014i
$943$		−	201.502i		−	0.213682i
$944$	−164.883	−	1272.87i	−0.174664	−	1.34838i
$945$	−66.4167			−0.0702823
$946$	1486.85	+	925.657i	1.57172	+	0.978496i
$947$	−1139.80	−	1139.80i	−1.20359	−	1.20359i	−0.973066	−	0.230525i	$-0.925956\pi$
$947$	−1139.80	−	1139.80i	−1.20359	−	1.20359i	−0.230525	−	0.973066i	$-0.574044\pi$
$948$	834.225	+	284.150i	0.879985	+	0.299736i
$949$	−35.5084	−	35.5084i	−0.0374167	−	0.0374167i
$950$	200.758	+	863.034i	0.211324	+	0.908457i
$951$	−2075.87			−2.18283
$952$	613.125	+	61.3540i	0.644039	+	0.0644475i
$953$		−	157.577i		−	0.165349i	−0.996577	−	0.0826744i	$-0.973654\pi$
$953$		−	157.577i		−	0.165349i	0.996577	−	0.0826744i	$-0.0263462\pi$
$954$	−130.167	−	559.570i	−0.136443	−	0.586552i
$955$	1129.61	−	1129.61i	1.18284	−	1.18284i
$956$	1026.82	−	505.044i	1.07408	−	0.528289i
$957$	281.891	−	281.891i	0.294557	−	0.294557i
$958$	65.1394	+	40.5533i	0.0679952	+	0.0423312i
$959$		−	358.963i		−	0.374309i
$960$	−370.490	+	1832.66i	−0.385927	+	1.90902i
$961$	958.182			0.997068
$962$	124.052	−	199.261i	0.128952	−	0.207132i
$963$	391.253	+	391.253i	0.406285	+	0.406285i
$964$	162.572	+	330.531i	0.168644	+	0.342874i
$965$	459.574	+	459.574i	0.476243	+	0.476243i
$966$	564.363	−	131.281i	0.584226	−	0.135902i
$967$	−1293.51			−1.33766			−0.668828	−	0.743418i	$-0.733204\pi$
$967$	−1293.51			−1.33766			−0.668828	+	0.743418i	$0.733204\pi$
$968$	0.504067	−	5.03726i	0.000520731	−	0.00520379i
$969$			2153.76i			2.22266i
$970$	270.194	−	62.8521i	0.278550	−	0.0647960i
$971$	1276.10	−	1276.10i	1.31421	−	1.31421i	0.395924	−	0.918283i	$-0.370424\pi$
$971$	1276.10	−	1276.10i	1.31421	−	1.31421i	0.918283	−	0.395924i	$-0.129576\pi$
$972$	428.559	−	1258.19i	0.440905	−	1.29444i
$973$	238.140	−	238.140i	0.244748	−	0.244748i
$974$	−631.709	+	1014.69i	−0.648571	+	1.04178i
$975$		−	210.842i		−	0.216248i
$976$	−210.630	−	1626.04i	−0.215809	−	1.66602i
$977$	−1734.87			−1.77571			−0.887855	−	0.460123i	$-0.847805\pi$
$977$	−1734.87			−1.77571			−0.887855	+	0.460123i	$0.847805\pi$
$978$	1842.40	+	1147.01i	1.88384	+	1.17281i
$979$	−1183.42	−	1183.42i	−1.20881	−	1.20881i
$980$	63.7047	−	187.028i	0.0650048	−	0.190845i
$981$	−551.922	−	551.922i	−0.562612	−	0.562612i
$982$	−312.854	−	1344.92i	−0.318588	−	1.36957i
$983$	−1138.16			−1.15784			−0.578921	−	0.815384i	$-0.696526\pi$
$983$	−1138.16			−1.15784			−0.578921	+	0.815384i	$0.696526\pi$
$984$	195.307	−	159.775i	0.198483	−	0.162373i
$985$			1067.92i			1.08418i
$986$	−115.176	−	495.127i	−0.116811	−	0.502157i
$987$	−421.559	+	421.559i	−0.427111	+	0.427111i
$988$	−64.7986	−	131.744i	−0.0655857	−	0.133344i
$989$	1485.03	−	1485.03i	1.50154	−	1.50154i
$990$	−1075.66	−	669.664i	−1.08652	−	0.676428i
$991$			232.522i			0.234633i	0.993095	+	0.117317i	$0.0374292\pi$
$991$			232.522i			0.234633i	−0.993095	+	0.117317i	$0.962571\pi$
$992$	50.3201	−	18.7898i	0.0507259	−	0.0189414i
$993$	−1458.45			−1.46873
$994$	−21.8507	+	35.0981i	−0.0219826	+	0.0353099i
$995$	−248.916	−	248.916i	−0.250167	−	0.250167i
$996$	646.441	−	317.953i	0.649037	−	0.319230i
$997$	−446.136	−	446.136i	−0.447479	−	0.447479i	0.447037	−	0.894516i	$-0.352479\pi$
$997$	−446.136	−	446.136i	−0.447479	−	0.447479i	−0.894516	+	0.447037i	$0.852479\pi$
$998$	691.598	−	160.879i	0.692984	−	0.161201i
$999$	203.261			0.203465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.k.a.43.8	✓	48
4.3	odd	2		448.3.k.a.15.4		48
8.3	odd	2		896.3.k.b.799.21		48
8.5	even	2		896.3.k.a.799.4		48
16.3	odd	4	inner	112.3.k.a.99.8	yes	48
16.5	even	4		896.3.k.b.351.21		48
16.11	odd	4		896.3.k.a.351.4		48
16.13	even	4		448.3.k.a.239.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.k.a.43.8	✓	48	1.1	even	1	trivial
112.3.k.a.99.8	yes	48	16.3	odd	4	inner
448.3.k.a.15.4		48	4.3	odd	2
448.3.k.a.239.4		48	16.13	even	4
896.3.k.a.351.4		48	16.11	odd	4
896.3.k.a.799.4		48	8.5	even	2
896.3.k.b.351.21		48	16.5	even	4
896.3.k.b.799.21		48	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05702 + 1.69785i) q^{2} +(2.92752 + 2.92752i) q^{3} +(-1.76542 - 3.58933i) q^{4} +(4.98965 + 4.98965i) q^{5} +(-8.06494 + 1.87606i) q^{6} -2.64575 q^{7} +(7.96024 + 0.796563i) q^{8} +8.14073i q^{9} +O(q^{10})\)	\(q+(-1.05702 + 1.69785i) q^{2} +(2.92752 + 2.92752i) q^{3} +(-1.76542 - 3.58933i) q^{4} +(4.98965 + 4.98965i) q^{5} +(-8.06494 + 1.87606i) q^{6} -2.64575 q^{7} +(7.96024 + 0.796563i) q^{8} +8.14073i q^{9} +(-13.7459 + 3.19755i) q^{10} +(7.79849 - 7.79849i) q^{11} +(5.33953 - 15.6761i) q^{12} +(-1.45243 + 1.45243i) q^{13} +(2.79661 - 4.49210i) q^{14} +29.2146i q^{15} +(-9.76658 + 12.6734i) q^{16} -29.1121 q^{17} +(-13.8218 - 8.60491i) q^{18} +(-12.6355 - 12.6355i) q^{19} +(9.10067 - 26.7183i) q^{20} +(-7.74549 - 7.74549i) q^{21} +(4.99755 + 21.4838i) q^{22} +26.4489 q^{23} +(20.9718 + 25.6357i) q^{24} +24.7932i q^{25} +(-0.930767 - 4.00126i) q^{26} +(2.51552 - 2.51552i) q^{27} +(4.67086 + 9.49647i) q^{28} +(6.17364 - 6.17364i) q^{29} +(-49.6021 - 30.8804i) q^{30} +1.67856i q^{31} +(-11.1941 - 29.9782i) q^{32} +45.6604 q^{33} +(30.7721 - 49.4282i) q^{34} +(-13.2014 - 13.2014i) q^{35} +(29.2198 - 14.3718i) q^{36} +(40.4014 + 40.4014i) q^{37} +(34.8093 - 8.09729i) q^{38} -8.50402 q^{39} +(35.7443 + 43.6934i) q^{40} -7.61855i q^{41} +(21.3378 - 4.96358i) q^{42} +(56.1470 - 56.1470i) q^{43} +(-41.7590 - 14.2237i) q^{44} +(-40.6194 + 40.6194i) q^{45} +(-27.9570 + 44.9064i) q^{46} -54.4264i q^{47} +(-65.6933 + 8.50964i) q^{48} +7.00000 q^{49} +(-42.0953 - 26.2069i) q^{50} +(-85.2263 - 85.2263i) q^{51} +(7.77739 + 2.64910i) q^{52} +(24.9511 + 24.9511i) q^{53} +(1.61204 + 6.92995i) q^{54} +77.8235 q^{55} +(-21.0608 - 2.10751i) q^{56} -73.9814i q^{57} +(3.95628 + 17.0076i) q^{58} +(-56.7236 + 56.7236i) q^{59} +(104.861 - 51.5761i) q^{60} +(-72.4618 + 72.4618i) q^{61} +(-2.84994 - 1.77427i) q^{62} -21.5384i q^{63} +(62.7310 + 12.6817i) q^{64} -14.4942 q^{65} +(-48.2640 + 77.5248i) q^{66} +(-67.6986 - 67.6986i) q^{67} +(51.3951 + 104.493i) q^{68} +(77.4297 + 77.4297i) q^{69} +(36.3681 - 8.45991i) q^{70} -7.81329 q^{71} +(-6.48461 + 64.8022i) q^{72} +24.4476i q^{73} +(-111.301 + 25.8907i) q^{74} +(-72.5827 + 72.5827i) q^{75} +(-23.0460 + 67.6601i) q^{76} +(-20.6329 + 20.6329i) q^{77} +(8.98891 - 14.4386i) q^{78} +53.2163i q^{79} +(-111.967 + 14.5038i) q^{80} +87.9951 q^{81} +(12.9352 + 8.05295i) q^{82} +(30.7600 + 30.7600i) q^{83} +(-14.1271 + 41.4751i) q^{84} +(-145.259 - 145.259i) q^{85} +(35.9810 + 154.678i) q^{86} +36.1469 q^{87} +(68.2898 - 55.8659i) q^{88} -151.750i q^{89} +(-26.0304 - 111.901i) q^{90} +(3.84276 - 3.84276i) q^{91} +(-46.6935 - 94.9339i) q^{92} +(-4.91400 + 4.91400i) q^{93} +(92.4081 + 57.5297i) q^{94} -126.094i q^{95} +(54.9910 - 120.533i) q^{96} -19.6564 q^{97} +(-7.39913 + 11.8850i) q^{98} +(63.4854 + 63.4854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} + 12 q^{6}+O(q^{10}) \) 48 * q + 6 * q^4 + 12 * q^6	\( 48 q + 6 q^{4} + 12 q^{6} - 40 q^{10} + 16 q^{11} - 108 q^{12} - 14 q^{14} + 66 q^{16} + 30 q^{18} - 64 q^{19} + 84 q^{20} + 94 q^{22} - 64 q^{23} + 40 q^{24} - 196 q^{26} - 96 q^{27} + 16 q^{29} - 72 q^{30} + 160 q^{32} - 28 q^{34} + 64 q^{36} - 48 q^{37} - 224 q^{38} + 384 q^{39} + 180 q^{40} + 176 q^{43} - 114 q^{44} - 256 q^{46} + 52 q^{48} + 336 q^{49} + 6 q^{50} - 192 q^{51} - 48 q^{52} - 80 q^{53} - 288 q^{54} - 512 q^{55} - 98 q^{56} - 50 q^{58} - 288 q^{59} + 512 q^{60} - 64 q^{61} + 156 q^{62} + 126 q^{64} - 32 q^{65} - 116 q^{66} + 80 q^{67} - 32 q^{68} + 192 q^{69} + 168 q^{70} + 26 q^{72} + 330 q^{74} + 608 q^{75} + 672 q^{76} + 112 q^{77} - 352 q^{78} - 980 q^{80} - 432 q^{81} - 76 q^{82} - 160 q^{83} + 320 q^{85} - 542 q^{86} - 896 q^{87} - 214 q^{88} + 1144 q^{90} - 12 q^{92} + 96 q^{93} + 660 q^{94} + 184 q^{96} + 496 q^{99}+O(q^{100}) \) 48 * q + 6 * q^4 + 12 * q^6 - 40 * q^10 + 16 * q^11 - 108 * q^12 - 14 * q^14 + 66 * q^16 + 30 * q^18 - 64 * q^19 + 84 * q^20 + 94 * q^22 - 64 * q^23 + 40 * q^24 - 196 * q^26 - 96 * q^27 + 16 * q^29 - 72 * q^30 + 160 * q^32 - 28 * q^34 + 64 * q^36 - 48 * q^37 - 224 * q^38 + 384 * q^39 + 180 * q^40 + 176 * q^43 - 114 * q^44 - 256 * q^46 + 52 * q^48 + 336 * q^49 + 6 * q^50 - 192 * q^51 - 48 * q^52 - 80 * q^53 - 288 * q^54 - 512 * q^55 - 98 * q^56 - 50 * q^58 - 288 * q^59 + 512 * q^60 - 64 * q^61 + 156 * q^62 + 126 * q^64 - 32 * q^65 - 116 * q^66 + 80 * q^67 - 32 * q^68 + 192 * q^69 + 168 * q^70 + 26 * q^72 + 330 * q^74 + 608 * q^75 + 672 * q^76 + 112 * q^77 - 352 * q^78 - 980 * q^80 - 432 * q^81 - 76 * q^82 - 160 * q^83 + 320 * q^85 - 542 * q^86 - 896 * q^87 - 214 * q^88 + 1144 * q^90 - 12 * q^92 + 96 * q^93 + 660 * q^94 + 184 * q^96 + 496 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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