LMFDB - Embedded newform 850.2.v.c.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			143.2
Character	$\chi$	$=$	850.143
Dual form			850.2.v.c.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 - 0.923880i) q^{2} +(-1.21530 + 0.241738i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(0.688411 + 1.03028i) q^{6} +(-0.394839 - 0.590918i) q^{7} +(0.923880 + 0.382683i) q^{8} +(-1.35312 + 0.560483i) q^{9} +(3.89081 - 2.59976i) q^{11} +(0.688411 - 1.03028i) q^{12} -0.327094 q^{13} +(-0.394839 + 0.590918i) q^{14} -1.00000i q^{16} +(-0.692689 + 4.06450i) q^{17} +(1.03564 + 1.03564i) q^{18} +(0.470758 + 0.194994i) q^{19} +(0.622694 + 0.622694i) q^{21} +(-3.89081 - 2.59976i) q^{22} +(-0.145038 + 0.729154i) q^{23} +(-1.21530 - 0.241738i) q^{24} +(0.125173 + 0.302195i) q^{26} +(4.59980 - 3.07349i) q^{27} +(0.697035 + 0.138649i) q^{28} +(-1.37720 - 6.92365i) q^{29} +(-2.70560 - 1.80782i) q^{31} +(-0.923880 + 0.382683i) q^{32} +(-4.10004 + 4.10004i) q^{33} +(4.02019 - 0.915457i) q^{34} +(0.560483 - 1.35312i) q^{36} +(-2.13568 - 10.7368i) q^{37} -0.509545i q^{38} +(0.397517 - 0.0790710i) q^{39} +(1.39655 - 7.02092i) q^{41} +(0.337000 - 0.813590i) q^{42} +(-0.128609 + 0.310490i) q^{43} +(-0.912914 + 4.58953i) q^{44} +(0.729154 - 0.145038i) q^{46} -4.22197i q^{47} +(0.241738 + 1.21530i) q^{48} +(2.48550 - 6.00052i) q^{49} +(-0.140721 - 5.10703i) q^{51} +(0.231290 - 0.231290i) q^{52} +(-4.00217 + 1.65775i) q^{53} +(-4.59980 - 3.07349i) q^{54} +(-0.138649 - 0.697035i) q^{56} +(-0.619249 - 0.123176i) q^{57} +(-5.86959 + 3.92193i) q^{58} +(-1.52485 - 3.68132i) q^{59} +(-6.63783 - 1.32035i) q^{61} +(-0.634823 + 3.19147i) q^{62} +(0.865466 + 0.578286i) q^{63} +(0.707107 + 0.707107i) q^{64} +(5.35696 + 2.21893i) q^{66} +(0.274816 + 0.274816i) q^{67} +(-2.38423 - 3.36384i) q^{68} -0.921201i q^{69} +(-8.70794 + 13.0324i) q^{71} -1.46461 q^{72} +(6.64548 - 9.94566i) q^{73} +(-9.10222 + 6.08191i) q^{74} +(-0.470758 + 0.194994i) q^{76} +(-3.07249 - 1.27267i) q^{77} +(-0.225175 - 0.336998i) q^{78} +(5.34800 + 8.00385i) q^{79} +(-1.74024 + 1.74024i) q^{81} +(-7.02092 + 1.39655i) q^{82} +(-4.80373 - 11.5972i) q^{83} -0.880623 q^{84} +0.336072 q^{86} +(3.34742 + 8.08138i) q^{87} +(4.58953 - 0.912914i) q^{88} +(0.374770 - 0.374770i) q^{89} +(0.129149 + 0.193286i) q^{91} +(-0.413033 - 0.618147i) q^{92} +(3.72513 + 1.54300i) q^{93} +(-3.90059 + 1.61568i) q^{94} +(1.03028 - 0.688411i) q^{96} +(5.47419 - 8.19271i) q^{97} -6.49492 q^{98} +(-3.80764 + 5.69853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{18} + 8 q^{26} - 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} - 64 q^{33} + 24 q^{34} + 32 q^{37} - 32 q^{39} + 16 q^{41} + 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{49} + 32 q^{51} + 16 q^{52}+ \cdots - 64 q^{99}+O(q^{100}) $ 32 * q - 16 * q^18 + 8 * q^26 - 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 - 64 * q^33 + 24 * q^34 + 32 * q^37 - 32 * q^39 + 16 * q^41 + 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^49 + 32 * q^51 + 16 * q^52 - 16 * q^53 + 24 * q^54 + 8 * q^56 + 24 * q^57 + 16 * q^58 - 64 * q^59 - 24 * q^61 + 40 * q^62 + 24 * q^63 - 16 * q^67 + 8 * q^71 + 16 * q^72 - 32 * q^73 + 8 * q^74 - 24 * q^77 - 32 * q^78 + 72 * q^79 + 48 * q^81 - 48 * q^82 - 16 * q^83 - 64 * q^86 - 40 * q^87 - 32 * q^88 + 16 * q^89 + 48 * q^91 - 24 * q^92 + 8 * q^93 + 8 * q^94 + 48 * q^97 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−0.382683	−	0.923880i	−0.270598	−	0.653281i
$2$	−0.382683	−	0.923880i	−0.270598	−	0.653281i
$3$	−1.21530	+	0.241738i	−0.701653	+	0.139567i	−0.533009	−	0.846110i	$-0.678939\pi$
$3$	−1.21530	+	0.241738i	−0.701653	+	0.139567i	−0.168644	+	0.985677i	$0.553939\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	0.688411	+	1.03028i	0.281043	+	0.420610i
$7$	−0.394839	−	0.590918i	−0.149235	−	0.223346i	0.749319	−	0.662210i	$-0.230381\pi$
$7$	−0.394839	−	0.590918i	−0.149235	−	0.223346i	−0.898554	+	0.438864i	$0.855381\pi$
$8$	0.923880	+	0.382683i	0.326641	+	0.135299i
$9$	−1.35312	+	0.560483i	−0.451042	+	0.186828i
$10$		0			0
$11$	3.89081	−	2.59976i	1.17312	−	0.783857i	0.192798	−	0.981239i	$-0.438244\pi$
$11$	3.89081	−	2.59976i	1.17312	−	0.783857i	0.980327	+	0.197382i	$0.0632439\pi$
$12$	0.688411	−	1.03028i	0.198727	−	0.297416i
$13$	−0.327094			−0.0907195			−0.0453597	−	0.998971i	$-0.514443\pi$
$13$	−0.327094			−0.0907195			−0.0453597	+	0.998971i	$0.514443\pi$
$14$	−0.394839	+	0.590918i	−0.105525	+	0.157930i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	−0.692689	+	4.06450i	−0.168002	+	0.985787i
$17$	−0.692689	+	4.06450i	−0.168002	+	0.985787i
$18$	1.03564	+	1.03564i	0.244102	+	0.244102i
$19$	0.470758	+	0.194994i	0.107999	+	0.0447348i	0.436029	−	0.899933i	$-0.356385\pi$
$19$	0.470758	+	0.194994i	0.107999	+	0.0447348i	−0.328030	+	0.944667i	$0.606385\pi$
$20$		0			0
$21$	0.622694	+	0.622694i	0.135883	+	0.135883i
$22$	−3.89081	−	2.59976i	−0.829524	−	0.554270i
$23$	−0.145038	+	0.729154i	−0.0302425	+	0.152039i	−0.992956	−	0.118484i	$-0.962197\pi$
$23$	−0.145038	+	0.729154i	−0.0302425	+	0.152039i	0.962714	+	0.270523i	$0.0871966\pi$
$24$	−1.21530	−	0.241738i	−0.248072	−	0.0493445i
$25$		0			0
$26$	0.125173	+	0.302195i	0.0245485	+	0.0592654i
$27$	4.59980	−	3.07349i	0.885232	−	0.591493i
$28$	0.697035	+	0.138649i	0.131727	+	0.0262022i
$29$	−1.37720	−	6.92365i	−0.255740	−	1.28569i	−0.868606	−	0.495503i	$-0.834984\pi$
$29$	−1.37720	−	6.92365i	−0.255740	−	1.28569i	0.612867	−	0.790186i	$-0.290016\pi$
$30$		0			0
$31$	−2.70560	−	1.80782i	−0.485940	−	0.324695i	0.288351	−	0.957525i	$-0.406893\pi$
$31$	−2.70560	−	1.80782i	−0.485940	−	0.324695i	−0.774291	+	0.632830i	$0.781893\pi$
$32$	−0.923880	+	0.382683i	−0.163320	+	0.0676495i
$33$	−4.10004	+	4.10004i	−0.713725	+	0.713725i
$34$	4.02019	−	0.915457i	0.689457	−	0.157000i
$35$		0			0
$36$	0.560483	−	1.35312i	0.0934138	−	0.225521i
$37$	−2.13568	−	10.7368i	−0.351104	−	1.76512i	−0.603369	−	0.797462i	$-0.706176\pi$
$37$	−2.13568	−	10.7368i	−0.351104	−	1.76512i	0.252265	−	0.967658i	$-0.418824\pi$
$38$		−	0.509545i		−	0.0826591i
$39$	0.397517	−	0.0790710i	0.0636536	−	0.0126615i
$40$		0			0
$41$	1.39655	−	7.02092i	0.218104	−	1.09648i	−0.704195	−	0.710007i	$-0.748692\pi$
$41$	1.39655	−	7.02092i	0.218104	−	1.09648i	0.922299	−	0.386477i	$-0.126308\pi$
$42$	0.337000	−	0.813590i	0.0520002	−	0.125540i
$43$	−0.128609	+	0.310490i	−0.0196127	+	0.0473492i	−0.933382	−	0.358883i	$-0.883158\pi$
$43$	−0.128609	+	0.310490i	−0.0196127	+	0.0473492i	0.913770	+	0.406232i	$0.133158\pi$
$44$	−0.912914	+	4.58953i	−0.137627	+	0.691897i
$45$		0			0
$46$	0.729154	−	0.145038i	0.107508	−	0.0213847i
$47$		−	4.22197i		−	0.615838i	−0.951413	−	0.307919i	$-0.900368\pi$
$47$		−	4.22197i		−	0.615838i	0.951413	−	0.307919i	$-0.0996325\pi$
$48$	0.241738	+	1.21530i	0.0348919	+	0.175413i
$49$	2.48550	−	6.00052i	0.355071	−	0.857217i
$50$		0			0
$51$	−0.140721	−	5.10703i	−0.0197049	−	0.715128i
$52$	0.231290	−	0.231290i	0.0320742	−	0.0320742i
$53$	−4.00217	+	1.65775i	−0.549740	+	0.227710i	−0.640224	−	0.768188i	$-0.721158\pi$
$53$	−4.00217	+	1.65775i	−0.549740	+	0.227710i	0.0904843	+	0.995898i	$0.471158\pi$
$54$	−4.59980	−	3.07349i	−0.625954	−	0.418249i
$55$		0			0
$56$	−0.138649	−	0.697035i	−0.0185277	−	0.0931453i
$57$	−0.619249	−	0.123176i	−0.0820216	−	0.0163151i
$58$	−5.86959	+	3.92193i	−0.770714	+	0.514975i
$59$	−1.52485	−	3.68132i	−0.198519	−	0.479267i	0.793001	−	0.609220i	$-0.208517\pi$
$59$	−1.52485	−	3.68132i	−0.198519	−	0.479267i	−0.991520	+	0.129953i	$0.958517\pi$
$60$		0			0
$61$	−6.63783	−	1.32035i	−0.849887	−	0.169053i	−0.249116	−	0.968474i	$-0.580140\pi$
$61$	−6.63783	−	1.32035i	−0.849887	−	0.169053i	−0.600772	+	0.799421i	$0.705140\pi$
$62$	−0.634823	+	3.19147i	−0.0806226	+	0.405317i
$63$	0.865466	+	0.578286i	0.109038	+	0.0728572i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	5.35696	+	2.21893i	0.659396	+	0.273131i
$67$	0.274816	+	0.274816i	0.0335741	+	0.0335741i	0.723695	−	0.690120i	$-0.242442\pi$
$67$	0.274816	+	0.274816i	0.0335741	+	0.0335741i	−0.690120	+	0.723695i	$0.742442\pi$
$68$	−2.38423	−	3.36384i	−0.289131	−	0.407926i
$69$		−	0.921201i		−	0.110900i
$70$		0			0
$71$	−8.70794	+	13.0324i	−1.03344	+	1.54666i	−0.211262	+	0.977429i	$0.567757\pi$
$71$	−8.70794	+	13.0324i	−1.03344	+	1.54666i	−0.822180	+	0.569227i	$0.807243\pi$
$72$	−1.46461			−0.172606
$73$	6.64548	−	9.94566i	0.777795	−	1.16405i	−0.204893	−	0.978784i	$-0.565685\pi$
$73$	6.64548	−	9.94566i	0.777795	−	1.16405i	0.982688	−	0.185268i	$-0.0593152\pi$
$74$	−9.10222	+	6.08191i	−1.05811	+	0.707008i
$75$		0			0
$76$	−0.470758	+	0.194994i	−0.0539997	+	0.0223674i
$77$	−3.07249	−	1.27267i	−0.350143	−	0.145034i
$78$	−0.225175	−	0.336998i	−0.0254961	−	0.0381575i
$79$	5.34800	+	8.00385i	0.601697	+	0.900504i	0.999859	−	0.0168118i	$-0.00535160\pi$
$79$	5.34800	+	8.00385i	0.601697	+	0.900504i	−0.398161	+	0.917315i	$0.630352\pi$
$80$		0			0
$81$	−1.74024	+	1.74024i	−0.193360	+	0.193360i
$82$	−7.02092	+	1.39655i	−0.775331	+	0.154223i
$83$	−4.80373	−	11.5972i	−0.527278	−	1.27296i	−0.933300	−	0.359098i	$-0.883084\pi$
$83$	−4.80373	−	11.5972i	−0.527278	−	1.27296i	0.406022	−	0.913863i	$-0.366916\pi$
$84$	−0.880623			−0.0960838
$85$		0			0
$86$	0.336072			0.0362395
$87$	3.34742	+	8.08138i	0.358881	+	0.866415i
$88$	4.58953	−	0.912914i	0.489245	−	0.0973169i
$89$	0.374770	−	0.374770i	0.0397255	−	0.0397255i	−0.686965	−	0.726691i	$-0.741057\pi$
$89$	0.374770	−	0.374770i	0.0397255	−	0.0397255i	0.726691	+	0.686965i	$0.241057\pi$
$90$		0			0
$91$	0.129149	+	0.193286i	0.0135385	+	0.0202618i
$92$	−0.413033	−	0.618147i	−0.0430616	−	0.0644463i
$93$	3.72513	+	1.54300i	0.386278	+	0.160002i
$94$	−3.90059	+	1.61568i	−0.402315	+	0.166644i
$95$		0			0
$96$	1.03028	−	0.688411i	0.105153	−	0.0702607i
$97$	5.47419	−	8.19271i	0.555820	−	0.831844i	−0.442056	−	0.896988i	$-0.645751\pi$
$97$	5.47419	−	8.19271i	0.555820	−	0.831844i	0.997876	+	0.0651439i	$0.0207506\pi$
$98$	−6.49492			−0.656086
$99$	−3.80764	+	5.69853i	−0.382682	+	0.572724i
$100$		0			0
$101$		−	14.4498i		−	1.43781i	−0.695108	−	0.718906i	$-0.744643\pi$
$101$		−	14.4498i		−	1.43781i	0.695108	−	0.718906i	$-0.255357\pi$
$102$	−4.66443	+	2.08439i	−0.461848	+	0.206385i
$103$	−8.21768	−	8.21768i	−0.809712	−	0.809712i	0.174878	−	0.984590i	$-0.444047\pi$
$103$	−8.21768	−	8.21768i	−0.809712	−	0.809712i	−0.984590	+	0.174878i	$0.944047\pi$
$104$	−0.302195	−	0.125173i	−0.0296327	−	0.0122743i
$105$		0			0
$106$	3.06313	+	3.06313i	0.297517	+	0.297517i
$107$	7.99081	+	5.33929i	0.772501	+	0.516168i	0.878237	−	0.478226i	$-0.158720\pi$
$107$	7.99081	+	5.33929i	0.772501	+	0.516168i	−0.105736	+	0.994394i	$0.533720\pi$
$108$	−1.07927	+	5.42584i	−0.103852	+	0.522101i
$109$	4.69116	+	0.933131i	0.449332	+	0.0893777i	0.414569	−	0.910018i	$-0.363932\pi$
$109$	4.69116	+	0.933131i	0.449332	+	0.0893777i	0.0347631	+	0.999396i	$0.488932\pi$
$110$		0			0
$111$	5.19099	+	12.5321i	0.492707	+	1.18950i
$112$	−0.590918	+	0.394839i	−0.0558365	+	0.0373088i
$113$	9.20761	+	1.83151i	0.866179	+	0.172294i	0.608130	−	0.793838i	$-0.291920\pi$
$113$	9.20761	+	1.83151i	0.866179	+	0.172294i	0.258050	+	0.966132i	$0.416920\pi$
$114$	0.123176	+	0.619249i	0.0115365	+	0.0579980i
$115$		0			0
$116$	5.86959	+	3.92193i	0.544977	+	0.364142i
$117$	0.442599	−	0.183330i	0.0409183	−	0.0169489i
$118$	−2.81756	+	2.81756i	−0.259377	+	0.259377i
$119$	2.67529	−	1.19550i	0.245243	−	0.109591i
$120$		0			0
$121$	4.17017	−	10.0677i	0.379106	−	0.915243i
$122$	1.32035	+	6.63783i	0.119539	+	0.600961i
$123$			8.87012i			0.799792i
$124$	3.19147	−	0.634823i	0.286603	−	0.0570088i
$125$		0			0
$126$	0.203067	−	1.02089i	0.0180906	−	0.0909478i
$127$	0.391330	−	0.944755i	0.0347249	−	0.0838334i	−0.905566	−	0.424206i	$-0.860553\pi$
$127$	0.391330	−	0.944755i	0.0347249	−	0.0838334i	0.940291	+	0.340373i	$0.110553\pi$
$128$	0.382683	−	0.923880i	0.0338248	−	0.0816602i
$129$	0.0812413	−	0.408427i	0.00715289	−	0.0359600i
$130$		0			0
$131$	−19.6520	+	3.90902i	−1.71700	+	0.341532i	−0.952835	−	0.303489i	$-0.901848\pi$
$131$	−19.6520	+	3.90902i	−1.71700	+	0.341532i	−0.764164	+	0.645022i	$0.776848\pi$
$132$		−	5.79833i		−	0.504680i
$133$	−0.0706479	−	0.355171i	−0.00612595	−	0.0307972i
$134$	0.148729	−	0.359064i	0.0128482	−	0.0310184i
$135$		0			0
$136$	−2.19538	+	3.49003i	−0.188252	+	0.299268i
$137$	−12.6973	+	12.6973i	−1.08480	+	1.08480i	−0.0887476	+	0.996054i	$0.528286\pi$
$137$	−12.6973	+	12.6973i	−1.08480	+	1.08480i	−0.996054	+	0.0887476i	$0.971714\pi$
$138$	−0.851079	+	0.352528i	−0.0724486	+	0.0300092i
$139$	13.6528	+	9.12249i	1.15801	+	0.773759i	0.977732	−	0.209856i	$-0.0672995\pi$
$139$	13.6528	+	9.12249i	1.15801	+	0.773759i	0.180280	+	0.983615i	$0.442300\pi$
$140$		0			0
$141$	1.02061	+	5.13095i	0.0859509	+	0.432104i
$142$	15.3727	+	3.05782i	1.29005	+	0.256607i
$143$	−1.27266	+	0.850365i	−0.106425	+	0.0711111i
$144$	0.560483	+	1.35312i	0.0467069	+	0.112760i
$145$		0			0
$146$	−11.7317	−	2.33358i	−0.970923	−	0.193129i
$147$	−1.57007	+	7.89327i	−0.129497	+	0.651026i
$148$	9.10222	+	6.08191i	0.748198	+	0.499930i
$149$	−4.02675	−	4.02675i	−0.329884	−	0.329884i	0.522658	−	0.852542i	$-0.324940\pi$
$149$	−4.02675	−	4.02675i	−0.329884	−	0.329884i	−0.852542	+	0.522658i	$0.824940\pi$
$150$		0			0
$151$	9.87709	+	4.09122i	0.803786	+	0.332939i	0.746472	−	0.665417i	$-0.231746\pi$
$151$	9.87709	+	4.09122i	0.803786	+	0.332939i	0.0573142	+	0.998356i	$0.481746\pi$
$152$	0.360303	+	0.360303i	0.0292244	+	0.0292244i
$153$	−1.34079	−	5.88802i	−0.108396	−	0.476018i
$154$			3.32564i			0.267987i
$155$		0			0
$156$	−0.225175	+	0.336998i	−0.0180284	+	0.0269815i
$157$	16.1039			1.28523			0.642616	−	0.766189i	$-0.277849\pi$
$157$	16.1039			1.28523			0.642616	+	0.766189i	$0.277849\pi$
$158$	5.34800	−	8.00385i	0.425464	−	0.636752i
$159$	4.46309	−	2.98214i	0.353946	−	0.236499i
$160$		0			0
$161$	0.488137	−	0.202193i	0.0384706	−	0.0159350i
$162$	2.27374	+	0.941813i	0.178642	+	0.0739958i
$163$	12.2141	+	18.2797i	0.956684	+	1.43178i	0.901242	+	0.433317i	$0.142657\pi$
$163$	12.2141	+	18.2797i	0.956684	+	1.43178i	0.0554422	+	0.998462i	$0.482343\pi$
$164$	3.97703	+	5.95205i	0.310554	+	0.464777i
$165$		0			0
$166$	−8.87613	+	8.87613i	−0.688922	+	0.688922i
$167$	−16.2666	+	3.23562i	−1.25875	+	0.250380i	−0.778998	−	0.627026i	$-0.784272\pi$
$167$	−16.2666	+	3.23562i	−1.25875	+	0.250380i	−0.479748	+	0.877406i	$0.659272\pi$
$168$	0.337000	+	0.813590i	0.0260001	+	0.0627698i
$169$	−12.8930			−0.991770
$170$		0			0
$171$	−0.746286			−0.0570699
$172$	−0.128609	−	0.310490i	−0.00980635	−	0.0236746i
$173$	8.40635	−	1.67213i	0.639123	−	0.127129i	0.135117	−	0.990830i	$-0.456859\pi$
$173$	8.40635	−	1.67213i	0.639123	−	0.127129i	0.504006	+	0.863700i	$0.331859\pi$
$174$	6.18522	−	6.18522i	0.468900	−	0.468900i
$175$		0			0
$176$	−2.59976	−	3.89081i	−0.195964	−	0.293281i
$177$	2.74307	+	4.10529i	0.206181	+	0.308572i
$178$	−0.489660	−	0.202824i	−0.0367016	−	0.0152023i
$179$	18.8787	−	7.81980i	1.41106	−	0.584479i	0.458461	−	0.888715i	$-0.348401\pi$
$179$	18.8787	−	7.81980i	1.41106	−	0.584479i	0.952597	+	0.304235i	$0.0984010\pi$
$180$		0			0
$181$	3.58349	−	2.39441i	0.266359	−	0.177975i	−0.415218	−	0.909722i	$-0.636295\pi$
$181$	3.58349	−	2.39441i	0.266359	−	0.177975i	0.681577	+	0.731747i	$0.261295\pi$
$182$	0.129149	−	0.193286i	0.00957318	−	0.0143273i
$183$	8.38613			0.619920
$184$	−0.413033	+	0.618147i	−0.0304492	+	0.0455704i
$185$		0			0
$186$		−	4.03205i		−	0.295644i
$187$	7.87160	+	17.6150i	0.575629	+	1.28814i
$188$	2.98538	+	2.98538i	0.217731	+	0.217731i
$189$	−3.63236	−	1.50457i	−0.264215	−	0.109442i
$190$		0			0
$191$	11.4696	+	11.4696i	0.829911	+	0.829911i	0.987504	−	0.157593i	$-0.0503733\pi$
$191$	11.4696	+	11.4696i	0.829911	+	0.829911i	−0.157593	+	0.987504i	$0.550373\pi$
$192$	−1.03028	−	0.688411i	−0.0743541	−	0.0496818i
$193$	0.0109326	−	0.0549621i	0.000786949	−	0.00395626i	−0.980390	−	0.197068i	$-0.936858\pi$
$193$	0.0109326	−	0.0549621i	0.000786949	−	0.00395626i	0.981177	+	0.193112i	$0.0618580\pi$
$194$	−9.66396	−	1.92228i	−0.693832	−	0.138012i
$195$		0			0
$196$	2.48550	+	6.00052i	0.177536	+	0.428609i
$197$	3.08408	−	2.06071i	0.219731	−	0.146820i	−0.440833	−	0.897589i	$-0.645317\pi$
$197$	3.08408	−	2.06071i	0.219731	−	0.146820i	0.660565	+	0.750769i	$0.270317\pi$
$198$	6.72188	+	1.33706i	0.477703	+	0.0950210i
$199$	−1.29609	−	6.51587i	−0.0918771	−	0.461898i	−0.999145	−	0.0413442i	$-0.986836\pi$
$199$	−1.29609	−	6.51587i	−0.0918771	−	0.461898i	0.907268	−	0.420553i	$-0.138164\pi$
$200$		0			0
$201$	−0.400417	−	0.267550i	−0.0282432	−	0.0188715i
$202$	−13.3499	+	5.52971i	−0.939295	+	0.389069i
$203$	−3.54754	+	3.54754i	−0.248988	+	0.248988i
$204$	3.71072	+	3.51171i	0.259803	+	0.245869i
$205$		0			0
$206$	−4.44738	+	10.7369i	−0.309863	+	0.748077i
$207$	−0.212424	−	1.06793i	−0.0147645	−	0.0742261i
$208$			0.327094i			0.0226799i
$209$	2.33857	−	0.465170i	0.161762	−	0.0321765i
$210$		0			0
$211$	3.42608	−	17.2241i	0.235861	−	1.18575i	−0.663373	−	0.748289i	$-0.730876\pi$
$211$	3.42608	−	17.2241i	0.235861	−	1.18575i	0.899235	−	0.437466i	$-0.144124\pi$
$212$	1.65775	−	4.00217i	0.113855	−	0.274870i
$213$	7.43234	−	17.9432i	0.509255	−	1.22945i
$214$	1.87491	−	9.42580i	0.128166	−	0.644334i
$215$		0			0
$216$	5.42584	−	1.07927i	0.369181	−	0.0734348i
$217$			2.31259i			0.156989i
$218$	−0.933131	−	4.69116i	−0.0631996	−	0.317726i
$219$	−5.67200	+	13.6934i	−0.383278	+	0.925315i
$220$		0			0
$221$	0.226574	−	1.32947i	0.0152410	−	0.0894300i
$222$	9.59169	−	9.59169i	0.643752	−	0.643752i
$223$	9.63276	−	3.99002i	0.645058	−	0.267192i	−0.0360779	−	0.999349i	$-0.511486\pi$
$223$	9.63276	−	3.99002i	0.645058	−	0.267192i	0.681136	+	0.732157i	$0.261486\pi$
$224$	0.590918	+	0.394839i	0.0394824	+	0.0263813i
$225$		0			0
$226$	−1.83151	−	9.20761i	−0.121830	−	0.612481i
$227$	12.0404	+	2.39499i	0.799152	+	0.158961i	0.577742	−	0.816220i	$-0.303934\pi$
$227$	12.0404	+	2.39499i	0.799152	+	0.158961i	0.221410	+	0.975181i	$0.428934\pi$
$228$	0.524974	−	0.350776i	0.0347673	−	0.0232307i
$229$	1.03397	+	2.49621i	0.0683263	+	0.164954i	0.954354	−	0.298678i	$-0.0965457\pi$
$229$	1.03397	+	2.49621i	0.0683263	+	0.164954i	−0.886028	+	0.463633i	$0.846546\pi$
$230$		0			0
$231$	4.04164	+	0.803933i	0.265921	+	0.0528949i
$232$	1.37720	−	6.92365i	0.0904176	−	0.454560i
$233$	−16.2429	−	10.8532i	−1.06411	−	0.711014i	−0.105119	−	0.994460i	$-0.533522\pi$
$233$	−16.2429	−	10.8532i	−1.06411	−	0.711014i	−0.958988	+	0.283446i	$0.908522\pi$
$234$	−0.338750	−	0.338750i	−0.0221448	−	0.0221448i
$235$		0			0
$236$	3.68132	+	1.52485i	0.239633	+	0.0992594i
$237$	−8.43425	−	8.43425i	−0.547864	−	0.547864i
$238$	−2.12829	−	2.01415i	−0.137956	−	0.130558i
$239$		−	25.3901i		−	1.64235i	−0.570679	−	0.821173i	$-0.693320\pi$
$239$		−	25.3901i		−	1.64235i	0.570679	−	0.821173i	$-0.306680\pi$
$240$		0			0
$241$	4.45194	−	6.66280i	0.286775	−	0.429189i	−0.659913	−	0.751342i	$-0.729407\pi$
$241$	4.45194	−	6.66280i	0.286775	−	0.429189i	0.946687	+	0.322154i	$0.104407\pi$
$242$	−10.8972			−0.700497
$243$	−7.52624	+	11.2638i	−0.482808	+	0.722574i
$244$	5.62728	−	3.76003i	0.360250	−	0.240711i
$245$		0			0
$246$	8.19492	−	3.39445i	0.522489	−	0.216422i
$247$	−0.153982	−	0.0637814i	−0.00979764	−	0.00405832i
$248$	−1.80782	−	2.70560i	−0.114797	−	0.171806i
$249$	8.64145	+	12.9329i	0.547630	+	0.819586i
$250$		0			0
$251$	−14.7371	+	14.7371i	−0.930197	+	0.930197i	−0.997718	−	0.0675209i	$-0.978491\pi$
$251$	−14.7371	+	14.7371i	−0.930197	+	0.930197i	0.0675209	+	0.997718i	$0.478491\pi$
$252$	−1.02089	+	0.203067i	−0.0643098	+	0.0127920i
$253$	1.33131	+	3.21407i	0.0836987	+	0.202067i
$254$	−1.02260			−0.0641633
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−3.26118	−	7.87318i	−0.203427	−	0.491115i	0.788935	−	0.614476i	$-0.210633\pi$
$257$	−3.26118	−	7.87318i	−0.203427	−	0.491115i	−0.992362	+	0.123361i	$0.960633\pi$
$258$	−0.408427	+	0.0812413i	−0.0254276	+	0.00505786i
$259$	−5.50132	+	5.50132i	−0.341836	+	0.341836i
$260$		0			0
$261$	5.74411	+	8.59667i	0.355551	+	0.532120i
$262$	11.1319	+	16.6601i	0.687733	+	1.02927i
$263$	−20.4534	−	8.47208i	−1.26121	−	0.522411i	−0.350930	−	0.936402i	$-0.614135\pi$
$263$	−20.4534	−	8.47208i	−1.26121	−	0.522411i	−0.910281	+	0.413991i	$0.864135\pi$
$264$	−5.35696	+	2.21893i	−0.329698	+	0.136565i
$265$		0			0
$266$	−0.301099	+	0.201188i	−0.0184616	+	0.0123356i
$267$	−0.364861	+	0.546053i	−0.0223291	+	0.0334179i
$268$	−0.388648			−0.0237405
$269$	−13.2164	+	19.7798i	−0.805819	+	1.20599i	0.169573	+	0.985518i	$0.445761\pi$
$269$	−13.2164	+	19.7798i	−0.805819	+	1.20599i	−0.975392	+	0.220476i	$0.929239\pi$
$270$		0			0
$271$			20.8191i			1.26467i	0.774694	+	0.632336i	$0.217904\pi$
$271$			20.8191i			1.26467i	−0.774694	+	0.632336i	$0.782096\pi$
$272$	4.06450	+	0.692689i	0.246447	+	0.0420004i
$273$	−0.203679	−	0.203679i	−0.0123272	−	0.0123272i
$274$	16.5898	+	6.87172i	1.00223	+	0.415136i
$275$		0			0
$276$	0.651388	+	0.651388i	0.0392089	+	0.0392089i
$277$	3.33059	+	2.22543i	0.200116	+	0.133713i	0.651591	−	0.758571i	$-0.274102\pi$
$277$	3.33059	+	2.22543i	0.200116	+	0.133713i	−0.451475	+	0.892284i	$0.649102\pi$
$278$	3.20339	−	16.1045i	0.192127	−	0.965886i
$279$	4.67427	+	0.929769i	0.279841	+	0.0556638i
$280$		0			0
$281$	5.55980	+	13.4226i	0.331670	+	0.800722i	0.998460	+	0.0554766i	$0.0176678\pi$
$281$	5.55980	+	13.4226i	0.331670	+	0.800722i	−0.666790	+	0.745246i	$0.732332\pi$
$282$	4.34981	−	2.90645i	0.259028	−	0.173077i
$283$	12.4506	+	2.47657i	0.740110	+	0.147217i	0.550726	−	0.834686i	$-0.314351\pi$
$283$	12.4506	+	2.47657i	0.740110	+	0.147217i	0.189384	+	0.981903i	$0.439351\pi$
$284$	−3.05782	−	15.3727i	−0.181448	−	0.912203i
$285$		0			0
$286$	1.27266	+	0.850365i	0.0752540	+	0.0502831i
$287$	−4.70020	+	1.94689i	−0.277444	+	0.114921i
$288$	1.03564	−	1.03564i	0.0610255	−	0.0610255i
$289$	−16.0404	−	5.63087i	−0.943551	−	0.331228i
$290$		0			0
$291$	−4.67229	+	11.2799i	−0.273895	+	0.661240i
$292$	2.33358	+	11.7317i	0.136563	+	0.686546i
$293$			8.34021i			0.487240i	0.969871	+	0.243620i	$0.0783350\pi$
$293$			8.34021i			0.487240i	−0.969871	+	0.243620i	$0.921665\pi$
$294$	7.89327	−	1.57007i	0.460345	−	0.0915682i
$295$		0			0
$296$	2.13568	−	10.7368i	0.124134	−	0.624064i
$297$	9.90664	−	23.9167i	0.574842	−	1.38779i
$298$	−2.17926	+	5.26121i	−0.126241	+	0.304773i
$299$	0.0474409	−	0.238502i	0.00274358	−	0.0137929i
$300$		0			0
$301$	0.234254	−	0.0465960i	0.0135022	−	0.00268575i
$302$		−	10.6909i		−	0.615191i
$303$	3.49307	+	17.5608i	0.200672	+	1.00884i
$304$	0.194994	−	0.470758i	0.0111837	−	0.0269998i
$305$		0			0
$306$	−4.92672	+	3.49198i	−0.281642	+	0.199623i
$307$	−0.0891571	+	0.0891571i	−0.00508847	+	0.00508847i	−0.709646	−	0.704558i	$-0.751145\pi$
$307$	−0.0891571	+	0.0891571i	−0.00508847	+	0.00508847i	0.704558	+	0.709646i	$0.251145\pi$
$308$	3.07249	−	1.27267i	0.175071	−	0.0725169i
$309$	11.9735	+	8.00041i	0.681146	+	0.455128i
$310$		0			0
$311$	−1.86727	−	9.38742i	−0.105883	−	0.532312i	−0.996923	−	0.0783864i	$-0.975023\pi$
$311$	−1.86727	−	9.38742i	−0.105883	−	0.532312i	0.891040	−	0.453926i	$-0.149977\pi$
$312$	0.397517	+	0.0790710i	0.0225049	+	0.00447651i
$313$	14.4669	−	9.66650i	0.817719	−	0.546383i	−0.0749013	−	0.997191i	$-0.523864\pi$
$313$	14.4669	−	9.66650i	0.817719	−	0.546383i	0.892621	+	0.450808i	$0.148864\pi$
$314$	−6.16270	−	14.8781i	−0.347781	−	0.839618i
$315$		0			0
$316$	−9.44119	−	1.87797i	−0.531108	−	0.105644i
$317$	−3.90786	+	19.6461i	−0.219487	+	1.10344i	0.701149	+	0.713015i	$0.252671\pi$
$317$	−3.90786	+	19.6461i	−0.219487	+	1.10344i	−0.920636	+	0.390422i	$0.872329\pi$
$318$	−4.46309	−	2.98214i	−0.250277	−	0.167230i
$319$	−23.3582	−	23.3582i	−1.30781	−	1.30781i
$320$		0			0
$321$	−11.0019	−	4.55715i	−0.614068	−	0.254355i
$322$	−0.373604	−	0.373604i	−0.0208201	−	0.0208201i
$323$	−1.11864	+	1.77833i	−0.0622430	+	0.0989488i
$324$		−	2.46108i		−	0.136726i
$325$		0			0
$326$	12.2141	−	18.2797i	0.676478	−	1.01242i
$327$	−5.92674			−0.327749
$328$	3.97703	−	5.95205i	0.219595	−	0.328647i
$329$	−2.49484	+	1.66700i	−0.137545	+	0.0919045i
$330$		0			0
$331$	13.3662	−	5.53646i	0.734673	−	0.304312i	0.0162023	−	0.999869i	$-0.494842\pi$
$331$	13.3662	−	5.53646i	0.734673	−	0.304312i	0.718471	+	0.695557i	$0.244842\pi$
$332$	11.5972	+	4.80373i	0.636480	+	0.263639i
$333$	8.90764	+	13.3312i	0.488136	+	0.730547i
$334$	9.21428	+	13.7901i	0.504183	+	0.754563i
$335$		0			0
$336$	0.622694	−	0.622694i	0.0339708	−	0.0339708i
$337$	−7.92021	+	1.57543i	−0.431441	+	0.0858190i	−0.406034	−	0.913858i	$-0.633088\pi$
$337$	−7.92021	+	1.57543i	−0.431441	+	0.0858190i	−0.0254078	+	0.999677i	$0.508088\pi$
$338$	4.93394	+	11.9116i	0.268371	+	0.647905i
$339$	−11.6327			−0.631804
$340$		0			0
$341$	−15.2269			−0.824582
$342$	0.285591	+	0.689478i	0.0154430	+	0.0372827i
$343$	−9.40644	+	1.87106i	−0.507900	+	0.101028i
$344$	−0.237639	+	0.237639i	−0.0128126	+	0.0128126i
$345$		0			0
$346$	−4.76181	−	7.12656i	−0.255997	−	0.383126i
$347$	−9.49472	−	14.2098i	−0.509703	−	0.762825i	0.483976	−	0.875081i	$-0.339192\pi$
$347$	−9.49472	−	14.2098i	−0.509703	−	0.762825i	−0.993679	+	0.112257i	$0.964192\pi$
$348$	−8.08138	−	3.34742i	−0.433207	−	0.179440i
$349$	−24.1690	+	10.0111i	−1.29374	+	0.535884i	−0.920098	−	0.391689i	$-0.871891\pi$
$349$	−24.1690	+	10.0111i	−1.29374	+	0.535884i	−0.373641	+	0.927573i	$0.621891\pi$
$350$		0			0
$351$	−1.50457	+	1.00532i	−0.0803078	+	0.0536600i
$352$	−2.59976	+	3.89081i	−0.138568	+	0.207381i
$353$	−34.0507			−1.81234			−0.906168	−	0.422919i	$-0.861006\pi$
$353$	−34.0507			−1.81234			−0.906168	+	0.422919i	$0.861006\pi$
$354$	2.74307	−	4.10529i	0.145792	−	0.218194i
$355$		0			0
$356$			0.530005i			0.0280902i
$357$	−2.96228	+	2.09961i	−0.156780	+	0.111123i
$358$	−14.4491	−	14.4491i	−0.763659	−	0.763659i
$359$	−1.81224	−	0.750656i	−0.0956465	−	0.0396181i	0.334347	−	0.942450i	$-0.391484\pi$
$359$	−1.81224	−	0.750656i	−0.0956465	−	0.0396181i	−0.429994	+	0.902832i	$0.641484\pi$
$360$		0			0
$361$	−13.2514	−	13.2514i	−0.697444	−	0.697444i
$362$	−3.58349	−	2.39441i	−0.188344	−	0.125847i
$363$	−2.63426	+	13.2433i	−0.138263	+	0.695094i
$364$	−0.227996	−	0.0453512i	−0.0119502	−	0.00237705i
$365$		0			0
$366$	−3.20923	−	7.74777i	−0.167749	−	0.404983i
$367$	13.9565	−	9.32545i	0.728525	−	0.486785i	−0.135156	−	0.990824i	$-0.543153\pi$
$367$	13.9565	−	9.32545i	0.728525	−	0.486785i	0.863681	+	0.504040i	$0.168153\pi$
$368$	0.729154	+	0.145038i	0.0380098	+	0.00756062i
$369$	2.04540	+	10.2829i	0.106479	+	0.535308i
$370$		0			0
$371$	2.55981	+	1.71041i	0.132898	+	0.0887999i
$372$	−3.72513	+	1.54300i	−0.193139	+	0.0800008i
$373$	−5.16638	+	5.16638i	−0.267505	+	0.267505i	−0.828094	−	0.560589i	$-0.810575\pi$
$373$	−5.16638	+	5.16638i	−0.267505	+	0.267505i	0.560589	+	0.828094i	$0.310575\pi$
$374$	13.2618	−	14.0134i	0.685754	−	0.724616i
$375$		0			0
$376$	1.61568	−	3.90059i	0.0833222	−	0.201158i
$377$	0.450473	+	2.26468i	0.0232006	+	0.116637i
$378$			3.93164i			0.202222i
$379$	35.1483	−	6.99144i	1.80545	−	0.359126i	0.826453	−	0.563005i	$-0.190355\pi$
$379$	35.1483	−	6.99144i	1.80545	−	0.359126i	0.978996	+	0.203879i	$0.0653550\pi$
$380$		0			0
$381$	−0.247200	+	1.24276i	−0.0126644	+	0.0636685i
$382$	6.20731	−	14.9858i	0.317593	−	0.766738i
$383$	−6.33151	+	15.2856i	−0.323525	+	0.781058i	0.675519	+	0.737343i	$0.263920\pi$
$383$	−6.33151	+	15.2856i	−0.323525	+	0.781058i	−0.999044	+	0.0437158i	$0.986080\pi$
$384$	−0.241738	+	1.21530i	−0.0123361	+	0.0620179i
$385$		0			0
$386$	−0.0549621	+	0.0109326i	−0.00279750	+	0.000556457i
$387$		−	0.492215i		−	0.0250207i
$388$	1.92228	+	9.66396i	0.0975890	+	0.490613i
$389$	−7.18782	+	17.3529i	−0.364437	+	0.879829i	0.630203	+	0.776430i	$0.282972\pi$
$389$	−7.18782	+	17.3529i	−0.364437	+	0.879829i	−0.994640	+	0.103398i	$0.967028\pi$
$390$		0			0
$391$	−2.86318	−	1.09458i	−0.144797	−	0.0553554i
$392$	4.59260	−	4.59260i	0.231961	−	0.231961i
$393$	22.9380	−	9.50125i	1.15707	−	0.479274i
$394$	−3.08408	−	2.06071i	−0.155373	−	0.103817i
$395$		0			0
$396$	−1.33706	−	6.72188i	−0.0671900	−	0.337787i
$397$	−8.07804	−	1.60682i	−0.405425	−	0.0806440i	−0.0118346	−	0.999930i	$-0.503767\pi$
$397$	−8.07804	−	1.60682i	−0.405425	−	0.0806440i	−0.393590	+	0.919286i	$0.628767\pi$
$398$	−5.52389	+	3.69094i	−0.276887	+	0.185010i
$399$	0.171717	+	0.414560i	0.00859658	+	0.0207540i
$400$		0			0
$401$	−7.93345	−	1.57806i	−0.396178	−	0.0788046i	−0.00701892	−	0.999975i	$-0.502234\pi$
$401$	−7.93345	−	1.57806i	−0.396178	−	0.0788046i	−0.389159	+	0.921171i	$0.627234\pi$
$402$	−0.0939510	+	0.472324i	−0.00468585	+	0.0235574i
$403$	0.884984	+	0.591328i	0.0440842	+	0.0294561i
$404$	10.2176	+	10.2176i	0.508343	+	0.508343i
$405$		0			0
$406$	4.63508	+	1.91991i	0.230035	+	0.0952837i
$407$	−36.2226	−	36.2226i	−1.79549	−	1.79549i
$408$	1.82437	−	4.77214i	0.0903197	−	0.236256i
$409$		−	6.01170i		−	0.297259i	−0.988893	−	0.148630i	$-0.952514\pi$
$409$		−	6.01170i		−	0.297259i	0.988893	−	0.148630i	$-0.0474863\pi$
$410$		0			0
$411$	12.3616	−	18.5004i	0.609751	−	0.912557i
$412$	11.6216			0.572553
$413$	−1.57329	+	2.35459i	−0.0774164	+	0.115862i
$414$	−0.905345	+	0.604932i	−0.0444953	+	0.0297308i
$415$		0			0
$416$	0.302195	−	0.125173i	0.0148163	−	0.00613713i
$417$	−18.7974	−	7.78616i	−0.920515	−	0.381290i
$418$	−1.32469	−	1.98254i	−0.0647929	−	0.0969694i
$419$	−3.45852	−	5.17603i	−0.168960	−	0.252866i	0.737321	−	0.675543i	$-0.236091\pi$
$419$	−3.45852	−	5.17603i	−0.168960	−	0.252866i	−0.906280	+	0.422677i	$0.861091\pi$
$420$		0			0
$421$	18.1423	−	18.1423i	0.884200	−	0.884200i	−0.109759	−	0.993958i	$-0.535008\pi$
$421$	18.1423	−	18.1423i	0.884200	−	0.884200i	0.993958	+	0.109759i	$0.0350078\pi$
$422$	−17.2241	+	3.42608i	−0.838455	+	0.166779i
$423$	2.36634	+	5.71285i	0.115055	+	0.277768i
$424$	−4.33191			−0.210376
$425$		0			0
$426$	−19.4216			−0.940981
$427$	1.84066	+	4.44374i	0.0890757	+	0.215048i
$428$	−9.42580	+	1.87491i	−0.455613	+	0.0906271i
$429$	1.34110	−	1.34110i	0.0647488	−	0.0647488i
$430$		0			0
$431$	20.5669	+	30.7805i	0.990671	+	1.48264i	0.871877	+	0.489725i	$0.162903\pi$
$431$	20.5669	+	30.7805i	0.990671	+	1.48264i	0.118795	+	0.992919i	$0.462097\pi$
$432$	−3.07349	−	4.59980i	−0.147873	−	0.221308i
$433$	−6.74685	−	2.79464i	−0.324233	−	0.134302i	0.214629	−	0.976696i	$-0.431146\pi$
$433$	−6.74685	−	2.79464i	−0.324233	−	0.134302i	−0.538862	+	0.842394i	$0.681146\pi$
$434$	2.13655	−	0.884988i	0.102558	−	0.0424808i
$435$		0			0
$436$	−3.97698	+	2.65733i	−0.190463	+	0.127263i
$437$	−0.210459	+	0.314974i	−0.0100676	+	0.0150672i
$438$	14.8216			0.708206
$439$	−17.4852	+	26.1685i	−0.834523	+	1.24895i	0.131711	+	0.991288i	$0.457953\pi$
$439$	−17.4852	+	26.1685i	−0.834523	+	1.24895i	−0.966235	+	0.257664i	$0.917047\pi$
$440$		0			0
$441$			9.51253i			0.452978i
$442$	−1.31498	+	0.299440i	−0.0625472	+	0.0142429i
$443$	−11.7784	−	11.7784i	−0.559607	−	0.559607i	0.369589	−	0.929195i	$-0.379499\pi$
$443$	−11.7784	−	11.7784i	−0.559607	−	0.559607i	−0.929195	+	0.369589i	$0.879499\pi$
$444$	−12.5321	−	5.19099i	−0.594749	−	0.246353i
$445$		0			0
$446$	−7.37260	−	7.37260i	−0.349103	−	0.349103i
$447$	5.86713	+	3.92029i	0.277506	+	0.185423i
$448$	0.138649	−	0.697035i	0.00655055	−	0.0329318i
$449$	15.7553	+	3.13392i	0.743537	+	0.147899i	0.552300	−	0.833645i	$-0.313750\pi$
$449$	15.7553	+	3.13392i	0.743537	+	0.147899i	0.191237	+	0.981544i	$0.438750\pi$
$450$		0			0
$451$	−12.8190	−	30.9478i	−0.603623	−	1.45727i
$452$	−7.80584	+	5.21569i	−0.367156	+	0.245326i
$453$	−12.9926	−	2.58439i	−0.610446	−	0.121425i
$454$	−2.39499	−	12.0404i	−0.112403	−	0.565086i
$455$		0			0
$456$	−0.524974	−	0.350776i	−0.0245842	−	0.0164266i
$457$	−7.82067	+	3.23943i	−0.365835	+	0.151534i	−0.558026	−	0.829824i	$-0.688441\pi$
$457$	−7.82067	+	3.23943i	−0.365835	+	0.151534i	0.192190	+	0.981358i	$0.438441\pi$
$458$	1.91052	−	1.91052i	0.0892727	−	0.0892727i
$459$	9.30598	+	20.8249i	0.434366	+	0.972022i
$460$		0			0
$461$	12.8444	−	31.0091i	0.598223	−	1.44424i	−0.277168	−	0.960822i	$-0.589396\pi$
$461$	12.8444	−	31.0091i	0.598223	−	1.44424i	0.875391	−	0.483416i	$-0.160604\pi$
$462$	−0.803933	−	4.04164i	−0.0374023	−	0.188034i
$463$		−	5.72199i		−	0.265924i	−0.991121	−	0.132962i	$-0.957551\pi$
$463$		−	5.72199i		−	0.265924i	0.991121	−	0.132962i	$-0.0424488\pi$
$464$	−6.92365	+	1.37720i	−0.321422	+	0.0639349i
$465$		0			0
$466$	−3.81112	+	19.1598i	−0.176547	+	0.887561i
$467$	−14.2144	+	34.3166i	−0.657764	+	1.58798i	0.143485	+	0.989652i	$0.454169\pi$
$467$	−14.2144	+	34.3166i	−0.657764	+	1.58798i	−0.801249	+	0.598330i	$0.795831\pi$
$468$	−0.183330	+	0.442599i	−0.00847445	+	0.0204591i
$469$	0.0538857	−	0.270902i	0.00248821	−	0.0125091i
$470$		0			0
$471$	−19.5711	+	3.89292i	−0.901787	+	0.179377i
$472$		−	3.98463i		−	0.183408i
$473$	0.306804	+	1.54241i	0.0141069	+	0.0709201i
$474$	−4.56459	+	11.0199i	−0.209658	+	0.506160i
$475$		0			0
$476$	−1.04637	+	2.73706i	−0.0479602	+	0.125453i
$477$	4.48629	−	4.48629i	0.205413	−	0.205413i
$478$	−23.4574	+	9.71636i	−1.07291	+	0.444416i
$479$	16.0975	+	10.7560i	0.735513	+	0.491454i	0.866030	−	0.499992i	$-0.166664\pi$
$479$	16.0975	+	10.7560i	0.735513	+	0.491454i	−0.130517	+	0.991446i	$0.541664\pi$
$480$		0			0
$481$	0.698569	+	3.51194i	0.0318520	+	0.160131i
$482$	−7.85931	−	1.56331i	−0.357982	−	0.0712070i
$483$	−0.544354	+	0.363726i	−0.0247690	+	0.0165501i
$484$	4.17017	+	10.0677i	0.189553	+	0.457621i
$485$		0			0
$486$	13.2866	+	2.64286i	0.602691	+	0.119883i
$487$	0.389463	−	1.95796i	0.0176483	−	0.0887238i	−0.970957	−	0.239253i	$-0.923098\pi$
$487$	0.389463	−	1.95796i	0.0176483	−	0.0887238i	0.988606	+	0.150529i	$0.0480976\pi$
$488$	−5.62728	−	3.76003i	−0.254735	−	0.170209i
$489$	−19.2627	−	19.2627i	−0.871090	−	0.871090i
$490$		0			0
$491$	18.8235	+	7.79693i	0.849491	+	0.351871i	0.764589	−	0.644519i	$-0.222942\pi$
$491$	18.8235	+	7.79693i	0.849491	+	0.351871i	0.0849021	+	0.996389i	$0.472942\pi$
$492$	−6.27212	−	6.27212i	−0.282769	−	0.282769i
$493$	29.0952	−	0.801699i	1.31038	−	0.0361067i
$494$			0.166669i			0.00749879i
$495$		0			0
$496$	−1.80782	+	2.70560i	−0.0811737	+	0.121485i
$497$	11.1393			0.499665
$498$	8.64145	−	12.9329i	0.387233	−	0.579535i
$499$	−12.9080	+	8.62482i	−0.577840	+	0.386100i	−0.809871	−	0.586608i	$-0.800463\pi$
$499$	−12.9080	+	8.62482i	−0.577840	+	0.386100i	0.232031	+	0.972708i	$0.425463\pi$
$500$		0			0
$501$	18.9866	−	7.86450i	0.848258	−	0.351360i
$502$	19.2549	+	7.97566i	0.859390	+	0.355971i
$503$	−23.9967	−	35.9136i	−1.06996	−	1.60131i	−0.759242	−	0.650808i	$-0.774430\pi$
$503$	−23.9967	−	35.9136i	−1.06996	−	1.60131i	−0.310719	−	0.950502i	$-0.600570\pi$
$504$	0.578286	+	0.865466i	0.0257589	+	0.0385509i
$505$		0			0
$506$	2.45994	−	2.45994i	0.109358	−	0.109358i
$507$	15.6689	−	3.11673i	0.695878	−	0.138419i
$508$	0.391330	+	0.944755i	0.0173625	+	0.0419167i
$509$	−35.6718			−1.58113			−0.790563	−	0.612381i	$-0.790212\pi$
$509$	−35.6718			−1.58113			−0.790563	+	0.612381i	$0.790212\pi$
$510$		0			0
$511$	−8.50097			−0.376061
$512$	0.382683	+	0.923880i	0.0169124	+	0.0408301i
$513$	2.76471	−	0.549934i	0.122065	−	0.0242802i
$514$	−6.02587	+	6.02587i	−0.265790	+	0.265790i
$515$		0			0
$516$	0.231356	+	0.346248i	0.0101849	+	0.0152427i
$517$	−10.9761	−	16.4269i	−0.482728	−	0.722454i
$518$	7.18782	+	2.97729i	0.315815	+	0.130815i
$519$	−9.81200	+	4.06426i	−0.430699	+	0.178401i
$520$		0			0
$521$	6.25857	−	4.18185i	0.274193	−	0.183210i	−0.410870	−	0.911694i	$-0.634775\pi$
$521$	6.25857	−	4.18185i	0.274193	−	0.183210i	0.685063	+	0.728484i	$0.259775\pi$
$522$	5.74411	−	8.59667i	0.251413	−	0.376266i
$523$	−17.7492			−0.776116			−0.388058	−	0.921635i	$-0.626854\pi$
$523$	−17.7492			−0.776116			−0.388058	+	0.921635i	$0.626854\pi$
$524$	11.1319	−	16.6601i	0.486301	−	0.727801i
$525$		0			0
$526$			22.1386i			0.965289i
$527$	9.22204	−	9.74465i	0.401718	−	0.424484i
$528$	4.10004	+	4.10004i	0.178431	+	0.178431i
$529$	20.7386	+	8.59021i	0.901678	+	0.373487i
$530$		0			0
$531$	4.12663	+	4.12663i	0.179081	+	0.179081i
$532$	0.301099	+	0.201188i	0.0130543	+	0.00872261i
$533$	−0.456802	+	2.29650i	−0.0197863	+	0.0994725i
$534$	0.644114	+	0.128122i	0.0278735	+	0.00554439i
$535$		0			0
$536$	0.148729	+	0.359064i	0.00642412	+	0.0155092i
$537$	−21.0529	+	14.0671i	−0.908499	+	0.607039i
$538$	23.3318	+	4.64099i	1.00591	+	0.200087i
$539$	−5.92930	−	29.8086i	−0.255393	−	1.28395i
$540$		0			0
$541$	8.89263	+	5.94187i	0.382324	+	0.255461i	0.731850	−	0.681466i	$-0.238657\pi$
$541$	8.89263	+	5.94187i	0.382324	+	0.255461i	−0.349526	+	0.936927i	$0.613657\pi$
$542$	19.2344	−	7.96714i	0.826187	−	0.342218i
$543$	−3.77619	+	3.77619i	−0.162052	+	0.162052i
$544$	−0.915457	−	4.02019i	−0.0392499	−	0.172364i
$545$		0			0
$546$	−0.110231	+	0.266120i	−0.00471743	+	0.0113889i
$547$	−2.65720	−	13.3586i	−0.113614	−	0.571174i	−0.995092	−	0.0989503i	$-0.968452\pi$
$547$	−2.65720	−	13.3586i	−0.113614	−	0.571174i	0.881479	−	0.472224i	$-0.156548\pi$
$548$		−	17.9567i		−	0.767071i
$549$	9.72185	−	1.93380i	0.414918	−	0.0825324i
$550$		0			0
$551$	0.701745	−	3.52791i	0.0298953	−	0.150294i
$552$	0.352528	−	0.851079i	0.0150046	−	0.0362243i
$553$	2.61802	−	6.32046i	0.111330	−	0.268773i
$554$	0.781467	−	3.92870i	0.0332013	−	0.166914i
$555$		0			0
$556$	−16.1045	+	3.20339i	−0.682985	+	0.135854i
$557$		−	1.23472i		−	0.0523168i	−0.999658	−	0.0261584i	$-0.991673\pi$
$557$		−	1.23472i		−	0.0523168i	0.999658	−	0.0261584i	$-0.00832743\pi$
$558$	−0.929769	−	4.67427i	−0.0393603	−	0.197877i
$559$	0.0420672	−	0.101559i	0.00177925	−	0.00429550i
$560$		0			0
$561$	−13.8246	−	19.5047i	−0.583674	−	0.823488i
$562$	10.2732	−	10.2732i	0.433348	−	0.433348i
$563$	19.7174	−	8.16721i	0.830989	−	0.344207i	0.0736946	−	0.997281i	$-0.476521\pi$
$563$	19.7174	−	8.16721i	0.830989	−	0.344207i	0.757294	+	0.653074i	$0.226521\pi$
$564$	−4.34981	−	2.90645i	−0.183160	−	0.122384i
$565$		0			0
$566$	−2.47657	−	12.4506i	−0.104098	−	0.523337i
$567$	1.71546	+	0.341226i	0.0720424	+	0.0143301i
$568$	−13.0324	+	8.70794i	−0.546826	+	0.365377i
$569$	−12.6066	−	30.4351i	−0.528498	−	1.27591i	−0.932507	−	0.361152i	$-0.882384\pi$
$569$	−12.6066	−	30.4351i	−0.528498	−	1.27591i	0.404009	−	0.914755i	$-0.367616\pi$
$570$		0			0
$571$	42.1343	+	8.38102i	1.76326	+	0.350735i	0.967110	−	0.254359i	$-0.0818646\pi$
$571$	42.1343	+	8.38102i	1.76326	+	0.350735i	0.796154	+	0.605094i	$0.206865\pi$
$572$	0.298608	−	1.50121i	0.0124854	−	0.0627685i
$573$	−16.7116	−	11.1664i	−0.698138	−	0.466481i
$574$	3.59738	+	3.59738i	0.150152	+	0.150152i
$575$		0			0
$576$	−1.35312	−	0.560483i	−0.0563802	−	0.0233534i
$577$	−32.4025	−	32.4025i	−1.34893	−	1.34893i	−0.886823	−	0.462109i	$-0.847093\pi$
$577$	−32.4025	−	32.4025i	−1.34893	−	1.34893i	−0.462109	−	0.886823i	$-0.652907\pi$
$578$	0.936137	+	16.9742i	0.0389382	+	0.706034i
$579$			0.0694382i			0.00288575i
$580$		0			0
$581$	−4.95631	+	7.41765i	−0.205622	+	0.307736i
$582$	12.2093			0.506091
$583$	−11.2619	+	16.8547i	−0.466421	+	0.698049i
$584$	9.94566	−	6.64548i	0.411554	−	0.274992i
$585$		0			0
$586$	7.70535	−	3.19166i	0.318305	−	0.131846i
$587$	12.6495	+	5.23957i	0.522099	+	0.216260i	0.628139	−	0.778101i	$-0.283817\pi$
$587$	12.6495	+	5.23957i	0.522099	+	0.216260i	−0.106040	+	0.994362i	$0.533817\pi$
$588$	−4.47118	−	6.69159i	−0.184388	−	0.275956i
$589$	−0.921167	−	1.37862i	−0.0379560	−	0.0568052i
$590$		0			0
$591$	−3.24992	+	3.24992i	−0.133684	+	0.133684i
$592$	−10.7368	+	2.13568i	−0.441280	+	0.0877760i
$593$	−4.00157	−	9.66064i	−0.164325	−	0.396715i	0.820172	−	0.572117i	$-0.193878\pi$
$593$	−4.00157	−	9.66064i	−0.164325	−	0.396715i	−0.984497	+	0.175402i	$0.943878\pi$
$594$	−25.8873			−1.06217
$595$		0			0
$596$	5.69469			0.233264
$597$	3.15026	+	7.60541i	0.128932	+	0.311269i
$598$	−0.238502	+	0.0474409i	−0.00975306	+	0.00194000i
$599$	9.67035	−	9.67035i	0.395120	−	0.395120i	−0.481388	−	0.876508i	$-0.659867\pi$
$599$	9.67035	−	9.67035i	0.395120	−	0.395120i	0.876508	+	0.481388i	$0.159867\pi$
$600$		0			0
$601$	9.25488	+	13.8509i	0.377514	+	0.564990i	0.970766	−	0.240027i	$-0.0771562\pi$
$601$	9.25488	+	13.8509i	0.377514	+	0.564990i	−0.593252	+	0.805017i	$0.702156\pi$
$602$	−0.132694	−	0.198591i	−0.00540821	−	0.00809396i
$603$	−0.525890	−	0.217831i	−0.0214159	−	0.00887075i
$604$	−9.87709	+	4.09122i	−0.401893	+	0.166470i
$605$		0			0
$606$	14.8874	−	9.94742i	0.604758	−	0.404086i
$607$	5.89289	−	8.81933i	0.239185	−	0.357966i	−0.692385	−	0.721529i	$-0.743440\pi$
$607$	5.89289	−	8.81933i	0.239185	−	0.357966i	0.931570	+	0.363563i	$0.118440\pi$
$608$	−0.509545			−0.0206648
$609$	3.45374	−	5.16889i	0.139953	−	0.209454i
$610$		0			0
$611$			1.38098i			0.0558685i
$612$	5.11154	+	3.21538i	0.206622	+	0.129974i
$613$	29.6325	+	29.6325i	1.19685	+	1.19685i	0.975105	+	0.221742i	$0.0711742\pi$
$613$	29.6325	+	29.6325i	1.19685	+	1.19685i	0.221742	+	0.975105i	$0.428826\pi$
$614$	0.116489	+	0.0482515i	0.00470113	+	0.00194727i
$615$		0			0
$616$	−2.35158	−	2.35158i	−0.0947479	−	0.0947479i
$617$	31.9289	+	21.3342i	1.28541	+	0.858882i	0.995179	−	0.0980747i	$-0.0312684\pi$
$617$	31.9289	+	21.3342i	1.28541	+	0.858882i	0.290229	+	0.956957i	$0.406268\pi$
$618$	2.80937	−	14.1237i	0.113009	−	0.568137i
$619$	2.57153	+	0.511509i	0.103358	+	0.0205593i	0.246499	−	0.969143i	$-0.420720\pi$
$619$	2.57153	+	0.511509i	0.103358	+	0.0205593i	−0.143140	+	0.989702i	$0.545720\pi$
$620$		0			0
$621$	1.57390	+	3.79974i	0.0631585	+	0.152478i
$622$	−7.95827	+	5.31755i	−0.319098	+	0.213214i
$623$	−0.369432	−	0.0734846i	−0.0148010	−	0.00294410i
$624$	−0.0790710	−	0.397517i	−0.00316537	−	0.0159134i
$625$		0			0
$626$	−14.4669	−	9.66650i	−0.578215	−	0.386351i
$627$	−2.72961	+	1.13064i	−0.109010	+	0.0451535i
$628$	−11.3872	+	11.3872i	−0.454398	+	0.454398i
$629$	45.1191	−	1.24323i	1.79902	−	0.0495708i
$630$		0			0
$631$	−3.04583	+	7.35329i	−0.121253	+	0.292730i	−0.972838	−	0.231486i	$-0.925641\pi$
$631$	−3.04583	+	7.35329i	−0.121253	+	0.292730i	0.851586	+	0.524216i	$0.175641\pi$
$632$	1.87797	+	9.44119i	0.0747016	+	0.375550i
$633$			21.7606i			0.864907i
$634$	19.6461	−	3.90786i	0.780247	−	0.155201i
$635$		0			0
$636$	−1.04719	+	5.26457i	−0.0415237	+	0.208754i
$637$	−0.812991	+	1.96273i	−0.0322119	+	0.0777663i
$638$	−12.6414	+	30.5190i	−0.500477	+	1.20826i
$639$	4.47852	−	22.5151i	0.177168	−	0.890682i
$640$		0			0
$641$	−20.1899	+	4.01602i	−0.797453	+	0.158623i	−0.576968	−	0.816767i	$-0.695764\pi$
$641$	−20.1899	+	4.01602i	−0.797453	+	0.158623i	−0.220485	+	0.975390i	$0.570764\pi$
$642$			11.9084i			0.469987i
$643$	5.93231	+	29.8237i	0.233947	+	1.17613i	0.901905	+	0.431934i	$0.142169\pi$
$643$	5.93231	+	29.8237i	0.233947	+	1.17613i	−0.667958	+	0.744199i	$0.732831\pi$
$644$	−0.202193	+	0.488137i	−0.00796752	+	0.0192353i
$645$		0			0
$646$	2.07105	+	0.352956i	0.0814842	+	0.0138869i
$647$	34.7745	−	34.7745i	1.36712	−	1.36712i	0.502614	−	0.864511i	$-0.332372\pi$
$647$	34.7745	−	34.7745i	1.36712	−	1.36712i	0.864511	−	0.502614i	$-0.167628\pi$
$648$	−2.27374	+	0.941813i	−0.0893209	+	0.0369979i
$649$	−15.5035	−	10.3591i	−0.608564	−	0.406629i
$650$		0			0
$651$	−0.559040	−	2.81048i	−0.0219105	−	0.110151i
$652$	−21.5624	−	4.28903i	−0.844449	−	0.167971i
$653$	5.29511	−	3.53808i	0.207214	−	0.138456i	−0.447633	−	0.894217i	$-0.647733\pi$
$653$	5.29511	−	3.53808i	0.207214	−	0.138456i	0.654847	+	0.755761i	$0.272733\pi$
$654$	2.26806	+	5.47559i	0.0886884	+	0.214113i
$655$		0			0
$656$	−7.02092	−	1.39655i	−0.274121	−	0.0545261i
$657$	−3.41779	+	17.1824i	−0.133341	+	0.670349i
$658$	2.49484	+	1.66700i	0.0972589	+	0.0649863i
$659$	19.7490	+	19.7490i	0.769313	+	0.769313i	0.977986	−	0.208672i	$-0.0669142\pi$
$659$	19.7490	+	19.7490i	0.769313	+	0.769313i	−0.208672	+	0.977986i	$0.566914\pi$
$660$		0			0
$661$	−2.39578	−	0.992363i	−0.0931849	−	0.0385984i	0.335604	−	0.942003i	$-0.391060\pi$
$661$	−2.39578	−	0.992363i	−0.0931849	−	0.0385984i	−0.428789	+	0.903405i	$0.641060\pi$
$662$	−10.2301	−	10.2301i	−0.397602	−	0.397602i
$663$	0.0460290	+	1.67048i	0.00178762	+	0.0648760i
$664$		−	12.5527i		−	0.487141i
$665$		0			0
$666$	8.90764	−	13.3312i	0.345164	−	0.516575i
$667$	5.24815			0.203209
$668$	9.21428	−	13.7901i	0.356511	−	0.533557i
$669$	−10.7421	+	7.17767i	−0.415315	+	0.277505i
$670$		0			0
$671$	−29.2592	+	12.1195i	−1.12954	+	0.467870i
$672$	−0.813590	−	0.337000i	−0.0313849	−	0.0130000i
$673$	6.11108	+	9.14587i	0.235565	+	0.352548i	0.930352	−	0.366668i	$-0.119501\pi$
$673$	6.11108	+	9.14587i	0.235565	+	0.352548i	−0.694787	+	0.719215i	$0.744501\pi$
$674$	4.48644	+	6.71443i	0.172811	+	0.258630i
$675$		0			0
$676$	9.11673	−	9.11673i	0.350644	−	0.350644i
$677$	5.81600	−	1.15687i	0.223527	−	0.0444623i	−0.0820560	−	0.996628i	$-0.526149\pi$
$677$	5.81600	−	1.15687i	0.223527	−	0.0444623i	0.305583	+	0.952165i	$0.401149\pi$
$678$	4.45166	+	10.7473i	0.170965	+	0.412746i
$679$	−7.00265			−0.268737
$680$		0			0
$681$	−15.2117			−0.582913
$682$	5.82707	+	14.0678i	0.223130	+	0.538684i
$683$	20.7405	−	4.12555i	0.793615	−	0.157860i	0.218397	−	0.975860i	$-0.429917\pi$
$683$	20.7405	−	4.12555i	0.793615	−	0.157860i	0.575218	+	0.818000i	$0.304917\pi$
$684$	0.527704	−	0.527704i	0.0201772	−	0.0201772i
$685$		0			0
$686$	5.32832	+	7.97439i	0.203436	+	0.304464i
$687$	−1.86001	−	2.78370i	−0.0709637	−	0.106205i
$688$	0.310490	+	0.128609i	0.0118373	+	0.00490317i
$689$	1.30908	−	0.542240i	0.0498721	−	0.0206577i
$690$		0			0
$691$	−11.6317	+	7.77206i	−0.442491	+	0.295663i	−0.756787	−	0.653662i	$-0.773232\pi$
$691$	−11.6317	+	7.77206i	−0.442491	+	0.295663i	0.314295	+	0.949325i	$0.398232\pi$
$692$	−4.76181	+	7.12656i	−0.181017	+	0.270911i
$693$	4.87077			0.185025
$694$	−9.49472	+	14.2098i	−0.360415	+	0.539398i
$695$		0			0
$696$			8.74722i			0.331563i
$697$	27.5692	+	10.5396i	1.04426	+	0.399215i
$698$	18.4982	+	18.4982i	0.700167	+	0.700167i
$699$	22.3636	+	9.26330i	0.845868	+	0.350370i
$700$		0			0
$701$	−29.0853	−	29.0853i	−1.09853	−	1.09853i	−0.994582	−	0.103953i	$-0.966851\pi$
$701$	−29.0853	−	29.0853i	−1.09853	−	1.09853i	−0.103953	−	0.994582i	$-0.533149\pi$
$702$	1.50457	+	1.00532i	0.0567862	+	0.0379433i
$703$	1.08823	−	5.47088i	0.0410432	−	0.206338i
$704$	4.58953	+	0.912914i	0.172974	+	0.0344067i
$705$		0			0
$706$	13.0306	+	31.4587i	0.490414	+	1.18397i
$707$	−8.53866	+	5.70535i	−0.321129	+	0.214572i
$708$	−4.84252	−	0.963237i	−0.181993	−	0.0362006i
$709$	−5.86964	−	29.5087i	−0.220439	−	1.10822i	−0.919479	−	0.393139i	$-0.871389\pi$
$709$	−5.86964	−	29.5087i	−0.220439	−	1.10822i	0.699040	−	0.715082i	$-0.253611\pi$
$710$		0			0
$711$	−11.7225	−	7.83275i	−0.439629	−	0.293751i
$712$	0.489660	−	0.202824i	0.0183508	−	0.00760115i
$713$	1.71060	−	1.71060i	0.0640623	−	0.0640623i
$714$	3.07340	+	1.93330i	0.115019	+	0.0723520i
$715$		0			0
$716$	−7.81980	+	18.8787i	−0.292240	+	0.705529i
$717$	6.13774	+	30.8565i	0.229218	+	1.15236i
$718$			1.96156i			0.0732047i
$719$	−42.2633	+	8.40669i	−1.57616	+	0.313517i	−0.904211	−	0.427085i	$-0.859540\pi$
$719$	−42.2633	+	8.40669i	−1.57616	+	0.313517i	−0.671944	+	0.740602i	$0.734540\pi$
$720$		0			0
$721$	−1.61132	+	8.10064i	−0.0600086	+	0.301683i
$722$	−7.17163	+	17.3138i	−0.266900	+	0.644354i
$723$	−3.79979	+	9.17350i	−0.141316	+	0.341166i
$724$	−0.840805	+	4.22701i	−0.0312483	+	0.157096i
$725$		0			0
$726$	13.2433	−	2.63426i	0.491505	−	0.0977665i
$727$			22.7691i			0.844459i	0.906489	+	0.422230i	$0.138752\pi$
$727$			22.7691i			0.844459i	−0.906489	+	0.422230i	$0.861248\pi$
$728$	0.0453512	+	0.227996i	0.00168083	+	0.00845009i
$729$	9.24917	−	22.3295i	0.342562	−	0.827018i
$730$		0			0
$731$	−1.17290	−	0.737804i	−0.0433813	−	0.0272887i
$732$	−5.92989	+	5.92989i	−0.219175	+	0.219175i
$733$	6.72010	−	2.78355i	0.248212	−	0.102813i	−0.255109	−	0.966912i	$-0.582111\pi$
$733$	6.72010	−	2.78355i	0.248212	−	0.102813i	0.503321	+	0.864099i	$0.332111\pi$
$734$	−13.9565	−	9.32545i	−0.515145	−	0.344209i
$735$		0			0
$736$	−0.145038	−	0.729154i	−0.00534616	−	0.0268770i
$737$	1.78371	+	0.354802i	0.0657039	+	0.0130693i
$738$	8.71745	−	5.82481i	0.320894	−	0.214414i
$739$	19.3452	+	46.7035i	0.711626	+	1.71802i	0.695898	+	0.718140i	$0.255006\pi$
$739$	19.3452	+	46.7035i	0.711626	+	1.71802i	0.0157273	+	0.999876i	$0.494994\pi$
$740$		0			0
$741$	0.202553	+	0.0402902i	0.00744095	+	0.00148010i
$742$	0.600615	−	3.01950i	0.0220493	−	0.110849i
$743$	19.7303	+	13.1834i	0.723835	+	0.483651i	0.862096	−	0.506745i	$-0.169151\pi$
$743$	19.7303	+	13.1834i	0.723835	+	0.483651i	−0.138261	+	0.990396i	$0.544151\pi$
$744$	2.85109	+	2.85109i	0.104526	+	0.104526i
$745$		0			0
$746$	6.75020	+	2.79603i	0.247143	+	0.102370i
$747$	13.0001	+	13.0001i	0.475648	+	0.475648i
$748$	−18.0218	−	6.88965i	−0.658942	−	0.251911i
$749$		−	6.83007i		−	0.249565i
$750$		0			0
$751$	15.9309	−	23.8422i	0.581326	−	0.870016i	−0.417934	−	0.908477i	$-0.637246\pi$
$751$	15.9309	−	23.8422i	0.581326	−	0.870016i	0.999260	+	0.0384614i	$0.0122457\pi$
$752$	−4.22197			−0.153959
$753$	14.3475	−	21.4725i	0.522850	−	0.782501i
$754$	1.91990	−	1.28284i	0.0699188	−	0.0467183i
$755$		0			0
$756$	3.63236	−	1.50457i	0.132108	−	0.0547208i
$757$	−9.96860	−	4.12913i	−0.362315	−	0.150076i	0.194097	−	0.980982i	$-0.437822\pi$
$757$	−9.96860	−	4.12913i	−0.362315	−	0.150076i	−0.556412	+	0.830907i	$0.687822\pi$
$758$	−19.9099	−	29.7973i	−0.723162	−	1.08229i
$759$	−2.39490	−	3.58422i	−0.0869294	−	0.130099i
$760$		0			0
$761$	16.8074	−	16.8074i	0.609267	−	0.609267i	−0.333487	−	0.942755i	$-0.608225\pi$
$761$	16.8074	−	16.8074i	0.609267	−	0.609267i	0.942755	+	0.333487i	$0.108225\pi$
$762$	1.24276	−	0.247200i	0.0450204	−	0.00895511i
$763$	−1.30085	−	3.14053i	−0.0470939	−	0.113695i
$764$	−16.2205			−0.586836
$765$		0			0
$766$	16.5450			0.597796
$767$	0.498770	+	1.20414i	0.0180095	+	0.0434788i
$768$	1.21530	−	0.241738i	0.0438533	−	0.00872297i
$769$	11.7131	−	11.7131i	0.422384	−	0.422384i	−0.463640	−	0.886024i	$-0.653457\pi$
$769$	11.7131	−	11.7131i	0.422384	−	0.422384i	0.886024	+	0.463640i	$0.153457\pi$
$770$		0			0
$771$	5.86655	+	8.77991i	0.211279	+	0.316201i
$772$	0.0311335	+	0.0465946i	0.00112052	+	0.00167698i
$773$	19.3600	+	8.01916i	0.696329	+	0.288429i	0.702634	−	0.711551i	$-0.252007\pi$
$773$	19.3600	+	8.01916i	0.696329	+	0.288429i	−0.00630500	+	0.999980i	$0.502007\pi$
$774$	−0.454747	+	0.188362i	−0.0163455	+	0.00677054i
$775$		0			0
$776$	8.19271	−	5.47419i	0.294101	−	0.196512i
$777$	5.35587	−	8.01563i	0.192141	−	0.287559i
$778$	18.7827			0.673392
$779$	2.02648	−	3.03284i	0.0726061	−	0.108663i
$780$		0			0
$781$			73.3450i			2.62449i
$782$	0.0844297	+	3.06411i	0.00301920	+	0.109573i
$783$	−27.6146	−	27.6146i	−0.986866	−	0.986866i
$784$	−6.00052	−	2.48550i	−0.214304	−	0.0887678i
$785$		0			0
$786$	−17.5560	−	17.5560i	−0.626202	−	0.626202i
$787$	−10.9455	−	7.31354i	−0.390164	−	0.260700i	0.344980	−	0.938610i	$-0.387886\pi$
$787$	−10.9455	−	7.31354i	−0.390164	−	0.260700i	−0.735144	+	0.677910i	$0.762886\pi$
$788$	−0.723626	+	3.63792i	−0.0257781	+	0.129595i
$789$	26.9050	+	5.35174i	0.957844	+	0.190527i
$790$		0			0
$791$	−2.55325	−	6.16410i	−0.0907832	−	0.219170i
$792$	−5.69853	+	3.80764i	−0.202488	+	0.135298i
$793$	2.17119	+	0.431877i	0.0771013	+	0.0153364i
$794$	1.60682	+	8.07804i	0.0570240	+	0.286679i
$795$		0			0
$796$	5.52389	+	3.69094i	0.195789	+	0.130822i
$797$	15.4224	−	6.38819i	0.546291	−	0.226281i	−0.0924305	−	0.995719i	$-0.529464\pi$
$797$	15.4224	−	6.38819i	0.546291	−	0.226281i	0.638722	+	0.769438i	$0.279464\pi$
$798$	0.317291	−	0.317291i	0.0112320	−	0.0112320i
$799$	17.1602	+	2.92451i	0.607084	+	0.103462i
$800$		0			0
$801$	−0.297058	+	0.717163i	−0.0104960	+	0.0253397i
$802$	1.57806	+	7.93345i	0.0557233	+	0.280140i
$803$		−	55.9734i		−	1.97526i
$804$	0.472324	−	0.0939510i	0.0166576	−	0.00331340i
$805$		0			0
$806$	0.207647	−	1.04391i	0.00731404	−	0.0367702i
$807$	11.2804	−	27.2332i	0.397088	−	0.958655i
$808$	5.52971	−	13.3499i	0.194534	−	0.469648i
$809$	−1.40383	+	7.05754i	−0.0493561	+	0.248130i	−0.997585	−	0.0694582i	$-0.977873\pi$
$809$	−1.40383	+	7.05754i	−0.0493561	+	0.248130i	0.948229	+	0.317588i	$0.102873\pi$
$810$		0			0
$811$	−10.1395	+	2.01688i	−0.356048	+	0.0708223i	−0.369873	−	0.929082i	$-0.620599\pi$
$811$	−10.1395	+	2.01688i	−0.356048	+	0.0708223i	0.0138259	+	0.999904i	$0.495599\pi$
$812$		−	5.01698i		−	0.176061i
$813$	−5.03278	−	25.3015i	−0.176507	−	0.887362i
$814$	−19.6036	+	47.3272i	−0.687104	+	1.65882i
$815$		0			0
$816$	−5.10703	+	0.140721i	−0.178782	+	0.00492622i
$817$	−0.121087	+	0.121087i	−0.00423632	+	0.00423632i
$818$	−5.55409	+	2.30058i	−0.194194	+	0.0804378i
$819$	−0.283088	−	0.189154i	−0.00989191	−	0.00660956i
$820$		0			0
$821$	7.89804	+	39.7061i	0.275643	+	1.38575i	0.831984	+	0.554799i	$0.187205\pi$
$821$	7.89804	+	39.7061i	0.275643	+	1.38575i	−0.556341	+	0.830954i	$0.687795\pi$
$822$	−21.8227	−	4.34081i	−0.761154	−	0.151403i
$823$	33.6500	−	22.4842i	1.17297	−	0.783751i	0.192666	−	0.981264i	$-0.438287\pi$
$823$	33.6500	−	22.4842i	1.17297	−	0.783751i	0.980300	+	0.197514i	$0.0632867\pi$
$824$	−4.44738	−	10.7369i	−0.154932	−	0.374038i
$825$		0			0
$826$	2.77743	+	0.552465i	0.0966391	+	0.0192227i
$827$	−8.79987	+	44.2399i	−0.306001	+	1.53837i	0.455515	+	0.890228i	$0.349455\pi$
$827$	−8.79987	+	44.2399i	−0.306001	+	1.53837i	−0.761517	+	0.648145i	$0.775545\pi$
$828$	0.905345	+	0.604932i	0.0314629	+	0.0210229i
$829$	−3.20565	−	3.20565i	−0.111337	−	0.111337i	0.649244	−	0.760580i	$-0.275086\pi$
$829$	−3.20565	−	3.20565i	−0.111337	−	0.111337i	−0.760580	+	0.649244i	$0.775086\pi$
$830$		0			0
$831$	−4.58563	−	1.89943i	−0.159074	−	0.0658905i
$832$	−0.231290	−	0.231290i	−0.00801854	−	0.00801854i
$833$	22.6675	+	14.2588i	0.785381	+	0.494038i
$834$			20.3462i			0.704531i
$835$		0			0
$836$	−1.32469	+	1.98254i	−0.0458155	+	0.0685677i
$837$	−18.0015			−0.622224
$838$	−3.45852	+	5.17603i	−0.119472	+	0.178803i
$839$	−5.29222	+	3.53615i	−0.182708	+	0.122081i	−0.643561	−	0.765395i	$-0.722544\pi$
$839$	−5.29222	+	3.53615i	−0.182708	+	0.122081i	0.460853	+	0.887477i	$0.347544\pi$
$840$		0			0
$841$	−19.2477	+	7.97267i	−0.663715	+	0.274920i
$842$	−23.7040	−	9.81852i	−0.816894	−	0.338369i
$843$	−10.0016	−	14.9684i	−0.344472	−	0.515539i
$844$	9.75666	+	14.6019i	0.335838	+	0.502617i
$845$		0			0
$846$	4.37243	−	4.37243i	0.150327	−	0.150327i
$847$	−7.59571	+	1.51088i	−0.260992	+	0.0519145i
$848$	1.65775	+	4.00217i	0.0569274	+	0.137435i
$849$	−15.7299			−0.539847
$850$		0			0
$851$	8.13854			0.278986
$852$	7.43234	+	17.9432i	0.254628	+	0.614726i
$853$	−24.6319	+	4.89959i	−0.843381	+	0.167759i	−0.597828	−	0.801624i	$-0.703969\pi$
$853$	−24.6319	+	4.89959i	−0.843381	+	0.167759i	−0.245553	+	0.969383i	$0.578969\pi$
$854$	3.40109	−	3.40109i	0.116383	−	0.116383i
$855$		0			0
$856$	5.33929	+	7.99081i	0.182493	+	0.273120i
$857$	19.7655	+	29.5811i	0.675175	+	1.01047i	0.997950	+	0.0639953i	$0.0203843\pi$
$857$	19.7655	+	29.5811i	0.675175	+	1.01047i	−0.322775	+	0.946476i	$0.604616\pi$
$858$	−1.75223	−	0.725797i	−0.0598201	−	0.0247783i
$859$	21.0814	−	8.73222i	0.719289	−	0.297939i	0.00714690	−	0.999974i	$-0.497725\pi$
$859$	21.0814	−	8.73222i	0.719289	−	0.297939i	0.712142	+	0.702035i	$0.247725\pi$
$860$		0			0
$861$	5.24151	−	3.50227i	0.178630	−	0.119357i
$862$	20.5669	−	30.7805i	0.700510	−	1.04839i
$863$	−25.2963			−0.861095			−0.430548	−	0.902568i	$-0.641680\pi$
$863$	−25.2963			−0.861095			−0.430548	+	0.902568i	$0.641680\pi$
$864$	−3.07349	+	4.59980i	−0.104562	+	0.156488i
$865$		0			0
$866$			7.30274i			0.248157i
$867$	20.8550	+	2.96562i	0.708274	+	0.100718i
$868$	−1.63525	−	1.63525i	−0.0555038	−	0.0555038i
$869$	41.6162	+	17.2380i	1.41173	+	0.584758i
$870$		0			0
$871$	−0.0898905	−	0.0898905i	−0.00304582	−	0.00304582i
$872$	3.97698	+	2.65733i	0.134677	+	0.0899886i
$873$	−2.81540	+	14.1540i	−0.0952867	+	0.479039i
$874$	0.371537	+	0.0739032i	0.0125674	+	0.00249981i
$875$		0			0
$876$	−5.67200	−	13.6934i	−0.191639	−	0.462658i
$877$	−10.7855	+	7.20665i	−0.364201	+	0.243351i	−0.724183	−	0.689608i	$-0.757783\pi$
$877$	−10.7855	+	7.20665i	−0.364201	+	0.243351i	0.359982	+	0.932959i	$0.382783\pi$
$878$	30.8678	+	6.13999i	1.04174	+	0.207214i
$879$	−2.01615	−	10.1358i	−0.0680029	−	0.341874i
$880$		0			0
$881$	11.7274	+	7.83599i	0.395106	+	0.264001i	0.737214	−	0.675659i	$-0.236141\pi$
$881$	11.7274	+	7.83599i	0.395106	+	0.264001i	−0.342108	+	0.939661i	$0.611141\pi$
$882$	8.78844	−	3.64029i	0.295922	−	0.122575i
$883$	2.99147	−	2.99147i	0.100671	−	0.100671i	−0.654977	−	0.755648i	$-0.727322\pi$
$883$	2.99147	−	2.99147i	0.100671	−	0.100671i	0.755648	+	0.654977i	$0.227322\pi$
$884$	0.779867	+	1.10029i	0.0262298	+	0.0370068i
$885$		0			0
$886$	−6.37440	+	15.3892i	−0.214152	+	0.517009i
$887$	7.78099	+	39.1177i	0.261260	+	1.31344i	0.859092	+	0.511822i	$0.171029\pi$
$887$	7.78099	+	39.1177i	0.261260	+	1.31344i	−0.597831	+	0.801622i	$0.703971\pi$
$888$			13.5647i			0.455202i
$889$	−0.712785	+	0.141782i	−0.0239060	+	0.00475521i
$890$		0			0
$891$	−2.24675	+	11.2952i	−0.0752690	+	0.378403i
$892$	−3.99002	+	9.63276i	−0.133596	+	0.322529i
$893$	0.823260	−	1.98753i	0.0275494	−	0.0665100i
$894$	1.37662	−	6.92075i	0.0460411	−	0.231464i
$895$		0			0
$896$	−0.697035	+	0.138649i	−0.0232863	+	0.00463194i
$897$			0.301319i			0.0100608i
$898$	−3.13392	−	15.7553i	−0.104580	−	0.525760i
$899$	−8.79058	+	21.2223i	−0.293182	+	0.707805i
$900$		0			0
$901$	−3.96568	−	17.4151i	−0.132116	−	0.580182i
$902$	−23.6864	+	23.6864i	−0.788671	+	0.788671i
$903$	−0.273424	+	0.113256i	−0.00909899	+	0.00376893i
$904$	7.80584	+	5.21569i	0.259618	+	0.173471i
$905$		0			0
$906$	2.58439	+	12.9926i	0.0858607	+	0.431651i
$907$	−3.80511	−	0.756884i	−0.126347	−	0.0251319i	0.131512	−	0.991315i	$-0.458017\pi$
$907$	−3.80511	−	0.756884i	−0.126347	−	0.0251319i	−0.257859	+	0.966183i	$0.583017\pi$
$908$	−10.2074	+	6.82036i	−0.338744	+	0.226342i
$909$	8.09888	+	19.5524i	0.268623	+	0.648513i
$910$		0			0
$911$	−21.2127	−	4.21946i	−0.702807	−	0.139797i	−0.169265	−	0.985571i	$-0.554139\pi$
$911$	−21.2127	−	4.21946i	−0.702807	−	0.139797i	−0.533542	+	0.845773i	$0.679139\pi$
$912$	−0.123176	+	0.619249i	−0.00407878	+	0.0205054i
$913$	−48.8404	−	32.6341i	−1.61638	−	1.08003i
$914$	5.98568	+	5.98568i	0.197989	+	0.197989i
$915$		0			0
$916$	−2.49621	−	1.03397i	−0.0824772	−	0.0341632i
$917$	10.0693	+	10.0693i	0.332516	+	0.332516i
$918$	15.6784	−	16.5669i	0.517466	−	0.546790i
$919$		−	21.0567i		−	0.694597i	−0.937755	−	0.347298i	$-0.887099\pi$
$919$		−	21.0567i		−	0.694597i	0.937755	−	0.347298i	$-0.112901\pi$
$920$		0			0
$921$	0.0867999	−	0.129905i	0.00286015	−	0.00428052i
$922$	−33.5640			−1.10537
$923$	2.84831	−	4.26280i	0.0937534	−	0.140312i
$924$	−3.42634	+	2.28941i	−0.112718	+	0.0753159i
$925$		0			0
$926$	−5.28643	+	2.18971i	−0.173723	+	0.0719584i
$927$	15.7254	+	6.51368i	0.516491	+	0.213937i
$928$	3.92193	+	5.86959i	0.128744	+	0.192679i
$929$	15.1360	+	22.6526i	0.496595	+	0.743207i	0.992107	−	0.125394i	$-0.0400196\pi$
$929$	15.1360	+	22.6526i	0.496595	+	0.743207i	−0.495512	+	0.868601i	$0.665020\pi$
$930$		0			0
$931$	2.34014	−	2.34014i	0.0766949	−	0.0766949i
$932$	19.1598	−	3.81112i	0.627600	−	0.124837i
$933$	4.53859	+	10.9571i	0.148587	+	0.358720i
$934$	37.1440			1.21539
$935$		0			0
$936$	0.479065			0.0156587
$937$	−6.54003	−	15.7890i	−0.213653	−	0.515805i	0.780326	−	0.625373i	$-0.215053\pi$
$937$	−6.54003	−	15.7890i	−0.213653	−	0.515805i	−0.993979	+	0.109568i	$0.965053\pi$
$938$	−0.270902	+	0.0538857i	−0.00884525	+	0.00175943i
$939$	−15.2449	+	15.2449i	−0.497498	+	0.497498i
$940$		0			0
$941$	−3.01100	−	4.50628i	−0.0981558	−	0.146900i	0.779141	−	0.626849i	$-0.215656\pi$
$941$	−3.01100	−	4.50628i	−0.0981558	−	0.146900i	−0.877297	+	0.479948i	$0.840656\pi$
$942$	11.0861	+	16.5915i	0.361205	+	0.540582i
$943$	4.91678	+	2.03660i	0.160112	+	0.0663208i
$944$	−3.68132	+	1.52485i	−0.119817	+	0.0496297i
$945$		0			0
$946$	1.30759	−	0.873705i	0.0425135	−	0.0284066i
$947$	−3.28837	+	4.92140i	−0.106858	+	0.159924i	−0.881045	−	0.473033i	$-0.843159\pi$
$947$	−3.28837	+	4.92140i	−0.106858	+	0.159924i	0.774187	+	0.632957i	$0.218159\pi$
$948$	11.9278			0.387398
$949$	−2.17369	+	3.25316i	−0.0705611	+	0.105602i
$950$		0			0
$951$		−	24.8206i		−	0.804863i
$952$	2.92914	−	0.0807107i	0.0949341	−	0.00261585i
$953$	15.4098	+	15.4098i	0.499172	+	0.499172i	0.911180	−	0.412008i	$-0.135173\pi$
$953$	15.4098	+	15.4098i	0.499172	+	0.499172i	−0.412008	+	0.911180i	$0.635173\pi$
$954$	−5.86162	−	2.42796i	−0.189777	−	0.0786082i
$955$		0			0
$956$	17.9535	+	17.9535i	0.580657	+	0.580657i
$957$	34.0338	+	22.7407i	1.10016	+	0.735101i
$958$	3.77700	−	18.9883i	0.122029	−	0.613484i
$959$	12.5164	+	2.48967i	0.404177	+	0.0803957i
$960$		0			0
$961$	−7.81115	−	18.8578i	−0.251973	−	0.608315i
$962$	2.97728	−	1.98935i	0.0959914	−	0.0641394i
$963$	−13.8051	−	2.74601i	−0.444864	−	0.0884890i
$964$	1.56331	+	7.85931i	0.0503510	+	0.253131i
$965$		0			0
$966$	0.544354	+	0.363726i	0.0175143	+	0.0117027i
$967$	−42.9099	+	17.7739i	−1.37989	+	0.571569i	−0.944452	−	0.328649i	$-0.893407\pi$
$967$	−42.9099	+	17.7739i	−1.37989	+	0.571569i	−0.435438	+	0.900219i	$0.643407\pi$
$968$	7.70546	−	7.70546i	0.247663	−	0.247663i
$969$	0.929597	−	2.43162i	0.0298630	−	0.0781148i
$970$		0			0
$971$	−6.91456	+	16.6932i	−0.221899	+	0.535711i	−0.995148	−	0.0983915i	$-0.968630\pi$
$971$	−6.91456	+	16.6932i	−0.221899	+	0.535711i	0.773249	+	0.634102i	$0.218630\pi$
$972$	−2.64286	−	13.2866i	−0.0847699	−	0.426167i
$973$		−	11.6696i		−	0.374110i
$974$	−1.95796	+	0.389463i	−0.0627372	+	0.0124792i
$975$		0			0
$976$	−1.32035	+	6.63783i	−0.0422633	+	0.212472i
$977$	−4.78935	+	11.5625i	−0.153225	+	0.369917i	−0.981788	−	0.189978i	$-0.939158\pi$
$977$	−4.78935	+	11.5625i	−0.153225	+	0.369917i	0.828564	+	0.559895i	$0.189158\pi$
$978$	−10.4249	+	25.1679i	−0.333352	+	0.804782i
$979$	0.483849	−	2.43247i	0.0154639	−	0.0777421i
$980$		0			0
$981$	−6.87074	+	1.36667i	−0.219366	+	0.0436346i
$982$		−	20.3744i		−	0.650172i
$983$	10.4133	+	52.3512i	0.332132	+	1.66974i	0.680779	+	0.732489i	$0.261641\pi$
$983$	10.4133	+	52.3512i	0.332132	+	1.66974i	−0.348647	+	0.937254i	$0.613359\pi$
$984$	−3.39445	+	8.19492i	−0.108211	+	0.261245i
$985$		0			0
$986$	−11.8749	−	26.5736i	−0.378174	−	0.846277i
$987$	2.62900	−	2.62900i	0.0836819	−	0.0836819i
$988$	0.153982	−	0.0637814i	0.00489882	−	0.00202916i
$989$	−0.207742	−	0.138809i	−0.00660580	−	0.00441385i
$990$		0			0
$991$	−5.61025	−	28.2046i	−0.178216	−	0.895950i	−0.961609	−	0.274424i	$-0.911513\pi$
$991$	−5.61025	−	28.2046i	−0.178216	−	0.895950i	0.783393	−	0.621526i	$-0.213487\pi$
$992$	3.19147	+	0.634823i	0.101329	+	0.0201557i
$993$	−14.9056	+	9.95958i	−0.473014	+	0.316058i
$994$	−4.26282	−	10.2914i	−0.135209	−	0.326422i
$995$		0			0
$996$	−15.2553	−	3.03448i	−0.483384	−	0.0961510i
$997$	4.14662	−	20.8465i	0.131325	−	0.660215i	−0.857901	−	0.513815i	$-0.828232\pi$
$997$	4.14662	−	20.8465i	0.131325	−	0.660215i	0.989226	−	0.146399i	$-0.0467684\pi$
$998$	12.9080	+	8.62482i	0.408594	+	0.273014i
$999$	−42.8232	−	42.8232i	−1.35487	−	1.35487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.c.143.2		32
5.2	odd	4		850.2.s.c.7.3		32
5.3	odd	4		170.2.o.a.7.2	✓	32
5.4	even	2		170.2.r.a.143.3	yes	32
17.5	odd	16		850.2.s.c.243.3		32
85.22	even	16	inner	850.2.v.c.107.2		32
85.39	odd	16		170.2.o.a.73.2	yes	32
85.73	even	16		170.2.r.a.107.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.a.7.2	✓	32	5.3	odd	4
170.2.o.a.73.2	yes	32	85.39	odd	16
170.2.r.a.107.3	yes	32	85.73	even	16
170.2.r.a.143.3	yes	32	5.4	even	2
850.2.s.c.7.3		32	5.2	odd	4
850.2.s.c.243.3		32	17.5	odd	16
850.2.v.c.107.2		32	85.22	even	16	inner
850.2.v.c.143.2		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{2} +(-1.21530 + 0.241738i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(0.688411 + 1.03028i) q^{6} +(-0.394839 - 0.590918i) q^{7} +(0.923880 + 0.382683i) q^{8} +(-1.35312 + 0.560483i) q^{9} +(3.89081 - 2.59976i) q^{11} +(0.688411 - 1.03028i) q^{12} -0.327094 q^{13} +(-0.394839 + 0.590918i) q^{14} -1.00000i q^{16} +(-0.692689 + 4.06450i) q^{17} +(1.03564 + 1.03564i) q^{18} +(0.470758 + 0.194994i) q^{19} +(0.622694 + 0.622694i) q^{21} +(-3.89081 - 2.59976i) q^{22} +(-0.145038 + 0.729154i) q^{23} +(-1.21530 - 0.241738i) q^{24} +(0.125173 + 0.302195i) q^{26} +(4.59980 - 3.07349i) q^{27} +(0.697035 + 0.138649i) q^{28} +(-1.37720 - 6.92365i) q^{29} +(-2.70560 - 1.80782i) q^{31} +(-0.923880 + 0.382683i) q^{32} +(-4.10004 + 4.10004i) q^{33} +(4.02019 - 0.915457i) q^{34} +(0.560483 - 1.35312i) q^{36} +(-2.13568 - 10.7368i) q^{37} -0.509545i q^{38} +(0.397517 - 0.0790710i) q^{39} +(1.39655 - 7.02092i) q^{41} +(0.337000 - 0.813590i) q^{42} +(-0.128609 + 0.310490i) q^{43} +(-0.912914 + 4.58953i) q^{44} +(0.729154 - 0.145038i) q^{46} -4.22197i q^{47} +(0.241738 + 1.21530i) q^{48} +(2.48550 - 6.00052i) q^{49} +(-0.140721 - 5.10703i) q^{51} +(0.231290 - 0.231290i) q^{52} +(-4.00217 + 1.65775i) q^{53} +(-4.59980 - 3.07349i) q^{54} +(-0.138649 - 0.697035i) q^{56} +(-0.619249 - 0.123176i) q^{57} +(-5.86959 + 3.92193i) q^{58} +(-1.52485 - 3.68132i) q^{59} +(-6.63783 - 1.32035i) q^{61} +(-0.634823 + 3.19147i) q^{62} +(0.865466 + 0.578286i) q^{63} +(0.707107 + 0.707107i) q^{64} +(5.35696 + 2.21893i) q^{66} +(0.274816 + 0.274816i) q^{67} +(-2.38423 - 3.36384i) q^{68} -0.921201i q^{69} +(-8.70794 + 13.0324i) q^{71} -1.46461 q^{72} +(6.64548 - 9.94566i) q^{73} +(-9.10222 + 6.08191i) q^{74} +(-0.470758 + 0.194994i) q^{76} +(-3.07249 - 1.27267i) q^{77} +(-0.225175 - 0.336998i) q^{78} +(5.34800 + 8.00385i) q^{79} +(-1.74024 + 1.74024i) q^{81} +(-7.02092 + 1.39655i) q^{82} +(-4.80373 - 11.5972i) q^{83} -0.880623 q^{84} +0.336072 q^{86} +(3.34742 + 8.08138i) q^{87} +(4.58953 - 0.912914i) q^{88} +(0.374770 - 0.374770i) q^{89} +(0.129149 + 0.193286i) q^{91} +(-0.413033 - 0.618147i) q^{92} +(3.72513 + 1.54300i) q^{93} +(-3.90059 + 1.61568i) q^{94} +(1.03028 - 0.688411i) q^{96} +(5.47419 - 8.19271i) q^{97} -6.49492 q^{98} +(-3.80764 + 5.69853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{18} + 8 q^{26} - 24 q^{27} + 8 q^{28} - 8 q^{29} - 16 q^{31} - 64 q^{33} + 24 q^{34} + 32 q^{37} - 32 q^{39} + 16 q^{41} + 24 q^{42} + 16 q^{43} - 16 q^{44} - 16 q^{49} + 32 q^{51} + 16 q^{52}+ \cdots - 64 q^{99}+O(q^{100}) \) 32 * q - 16 * q^18 + 8 * q^26 - 24 * q^27 + 8 * q^28 - 8 * q^29 - 16 * q^31 - 64 * q^33 + 24 * q^34 + 32 * q^37 - 32 * q^39 + 16 * q^41 + 24 * q^42 + 16 * q^43 - 16 * q^44 - 16 * q^49 + 32 * q^51 + 16 * q^52 - 16 * q^53 + 24 * q^54 + 8 * q^56 + 24 * q^57 + 16 * q^58 - 64 * q^59 - 24 * q^61 + 40 * q^62 + 24 * q^63 - 16 * q^67 + 8 * q^71 + 16 * q^72 - 32 * q^73 + 8 * q^74 - 24 * q^77 - 32 * q^78 + 72 * q^79 + 48 * q^81 - 48 * q^82 - 16 * q^83 - 64 * q^86 - 40 * q^87 - 32 * q^88 + 16 * q^89 + 48 * q^91 - 24 * q^92 + 8 * q^93 + 8 * q^94 + 48 * q^97 - 64 * q^99

Introduction

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