LMFDB - Embedded newform 170.2.o.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(3,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([12, 1]))

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

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

chi := DirichletCharacter("170.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.o (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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	170.7
Dual form			170.2.o.a.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 + 0.382683i) q^{2} +(-0.241738 - 1.21530i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.17123 + 1.90479i) q^{5} +(0.688411 + 1.03028i) q^{6} +(-0.590918 + 0.394839i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(1.35312 - 0.560483i) q^{9} +(-1.81101 - 1.31159i) q^{10} +(3.89081 - 2.59976i) q^{11} +(-1.03028 - 0.688411i) q^{12} -0.327094i q^{13} +(0.394839 - 0.590918i) q^{14} +(2.03176 - 1.88385i) q^{15} -1.00000i q^{16} +(4.06450 + 0.692689i) q^{17} +(-1.03564 + 1.03564i) q^{18} +(-0.470758 - 0.194994i) q^{19} +(2.17507 + 0.518705i) q^{20} +(0.622694 + 0.622694i) q^{21} +(-2.59976 + 3.89081i) q^{22} +(-0.729154 - 0.145038i) q^{23} +(1.21530 + 0.241738i) q^{24} +(-2.25644 + 4.46189i) q^{25} +(0.125173 + 0.302195i) q^{26} +(-3.07349 - 4.59980i) q^{27} +(-0.138649 + 0.697035i) q^{28} +(1.37720 + 6.92365i) q^{29} +(-1.15618 + 2.51797i) q^{30} +(-2.70560 - 1.80782i) q^{31} +(0.382683 + 0.923880i) q^{32} +(-4.10004 - 4.10004i) q^{33} +(-4.02019 + 0.915457i) q^{34} +(-1.44419 - 0.663128i) q^{35} +(0.560483 - 1.35312i) q^{36} +(-10.7368 + 2.13568i) q^{37} +0.509545 q^{38} +(-0.397517 + 0.0790710i) q^{39} +(-2.20801 + 0.353144i) q^{40} +(1.39655 - 7.02092i) q^{41} +(-0.813590 - 0.337000i) q^{42} +(-0.310490 - 0.128609i) q^{43} +(0.912914 - 4.58953i) q^{44} +(2.65242 + 1.92096i) q^{45} +(0.729154 - 0.145038i) q^{46} -4.22197 q^{47} +(-1.21530 + 0.241738i) q^{48} +(-2.48550 + 6.00052i) q^{49} +(0.377191 - 4.98575i) q^{50} +(-0.140721 - 5.10703i) q^{51} +(-0.231290 - 0.231290i) q^{52} +(-1.65775 - 4.00217i) q^{53} +(4.59980 + 3.07349i) q^{54} +(9.50903 + 4.36627i) q^{55} +(-0.138649 - 0.697035i) q^{56} +(-0.123176 + 0.619249i) q^{57} +(-3.92193 - 5.86959i) q^{58} +(1.52485 + 3.68132i) q^{59} +(0.104584 - 2.76875i) q^{60} +(-6.63783 - 1.32035i) q^{61} +(3.19147 + 0.634823i) q^{62} +(-0.578286 + 0.865466i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(0.623045 - 0.383102i) q^{65} +(5.35696 + 2.21893i) q^{66} +(0.274816 - 0.274816i) q^{67} +(3.36384 - 2.38423i) q^{68} +0.921201i q^{69} +(1.58802 + 0.0599842i) q^{70} +(-8.70794 + 13.0324i) q^{71} +1.46461i q^{72} +(9.94566 + 6.64548i) q^{73} +(9.10222 - 6.08191i) q^{74} +(5.96800 + 1.66364i) q^{75} +(-0.470758 + 0.194994i) q^{76} +(-1.27267 + 3.07249i) q^{77} +(0.336998 - 0.225175i) q^{78} +(-5.34800 - 8.00385i) q^{79} +(1.90479 - 1.17123i) q^{80} +(-1.74024 + 1.74024i) q^{81} +(1.39655 + 7.02092i) q^{82} +(11.5972 - 4.80373i) q^{83} +0.880623 q^{84} +(3.44104 + 8.55332i) q^{85} +0.336072 q^{86} +(8.08138 - 3.34742i) q^{87} +(0.912914 + 4.58953i) q^{88} +(-0.374770 + 0.374770i) q^{89} +(-3.18564 - 0.759702i) q^{90} +(0.129149 + 0.193286i) q^{91} +(-0.618147 + 0.413033i) q^{92} +(-1.54300 + 3.72513i) q^{93} +(3.90059 - 1.61568i) q^{94} +(-0.179942 - 1.12508i) q^{95} +(1.03028 - 0.688411i) q^{96} +(-8.19271 - 5.47419i) q^{97} -6.49492i q^{98} +(3.80764 - 5.69853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{10} - 40 q^{15} + 16 q^{18} + 8 q^{20} - 8 q^{25} + 8 q^{26} - 72 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 64 q^{33} - 24 q^{34} + 32 q^{35} + 16 q^{37} + 32 q^{39} - 8 q^{40} + 16 q^{41}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^10 - 40 * q^15 + 16 * q^18 + 8 * q^20 - 8 * q^25 + 8 * q^26 - 72 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 - 64 * q^33 - 24 * q^34 + 32 * q^35 + 16 * q^37 + 32 * q^39 - 8 * q^40 + 16 * q^41 - 40 * q^42 + 48 * q^43 + 16 * q^44 + 24 * q^45 - 64 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 16 * q^52 - 24 * q^54 + 8 * q^55 + 8 * q^56 - 8 * q^57 - 16 * q^58 + 64 * q^59 - 48 * q^60 - 24 * q^61 - 24 * q^62 - 24 * q^63 - 16 * q^65 - 16 * q^67 - 16 * q^68 + 24 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 - 8 * q^75 + 40 * q^77 + 48 * q^78 - 72 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 - 8 * q^85 - 64 * q^86 + 24 * q^87 + 16 * q^88 - 16 * q^89 + 48 * q^90 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 + 40 * q^95 + 16 * q^97 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$3$	−0.241738	−	1.21530i	−0.139567	−	0.701653i	−0.985677	−	0.168644i	$-0.946061\pi$
$3$	−0.241738	−	1.21530i	−0.139567	−	0.701653i	0.846110	−	0.533009i	$-0.178939\pi$
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	1.17123	+	1.90479i	0.523790	+	0.851848i
$5$	1.17123	+	1.90479i	0.523790	+	0.851848i
$6$	0.688411	+	1.03028i	0.281043	+	0.420610i
$7$	−0.590918	+	0.394839i	−0.223346	+	0.149235i	−0.662210	−	0.749319i	$-0.730381\pi$
$7$	−0.590918	+	0.394839i	−0.223346	+	0.149235i	0.438864	+	0.898554i	$0.355381\pi$
$8$	−0.382683	+	0.923880i	−0.135299	+	0.326641i
$9$	1.35312	−	0.560483i	0.451042	−	0.186828i
$10$	−1.81101	−	1.31159i	−0.572690	−	0.414760i
$11$	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	$0.0632439\pi$
$12$	−1.03028	−	0.688411i	−0.297416	−	0.198727i
$13$		−	0.327094i		−	0.0907195i	−0.998971	−	0.0453597i	$-0.985557\pi$
$13$		−	0.327094i		−	0.0907195i	0.998971	−	0.0453597i	$-0.0144434\pi$
$14$	0.394839	−	0.590918i	0.105525	−	0.157930i
$15$	2.03176	−	1.88385i	0.524597	−	0.486409i
$16$		−	1.00000i		−	0.250000i
$17$	4.06450	+	0.692689i	0.985787	+	0.168002i
$17$	4.06450	+	0.692689i	0.985787	+	0.168002i
$18$	−1.03564	+	1.03564i	−0.244102	+	0.244102i
$19$	−0.470758	−	0.194994i	−0.107999	−	0.0447348i	0.328030	−	0.944667i	$-0.393615\pi$
$19$	−0.470758	−	0.194994i	−0.107999	−	0.0447348i	−0.436029	+	0.899933i	$0.643615\pi$
$20$	2.17507	+	0.518705i	0.486361	+	0.115986i
$21$	0.622694	+	0.622694i	0.135883	+	0.135883i
$22$	−2.59976	+	3.89081i	−0.554270	+	0.829524i
$23$	−0.729154	−	0.145038i	−0.152039	−	0.0302425i	0.118484	−	0.992956i	$-0.462197\pi$
$23$	−0.729154	−	0.145038i	−0.152039	−	0.0302425i	−0.270523	+	0.962714i	$0.587197\pi$
$24$	1.21530	+	0.241738i	0.248072	+	0.0493445i
$25$	−2.25644	+	4.46189i	−0.451289	+	0.892378i
$26$	0.125173	+	0.302195i	0.0245485	+	0.0592654i
$27$	−3.07349	−	4.59980i	−0.591493	−	0.885232i
$28$	−0.138649	+	0.697035i	−0.0262022	+	0.131727i
$29$	1.37720	+	6.92365i	0.255740	+	1.28569i	0.868606	+	0.495503i	$0.165016\pi$
$29$	1.37720	+	6.92365i	0.255740	+	1.28569i	−0.612867	+	0.790186i	$0.709984\pi$
$30$	−1.15618	+	2.51797i	−0.211089	+	0.459717i
$31$	−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	$0.781893\pi$
$32$	0.382683	+	0.923880i	0.0676495	+	0.163320i
$33$	−4.10004	−	4.10004i	−0.713725	−	0.713725i
$34$	−4.02019	+	0.915457i	−0.689457	+	0.157000i
$35$	−1.44419	−	0.663128i	−0.244112	−	0.112089i
$36$	0.560483	−	1.35312i	0.0934138	−	0.225521i
$37$	−10.7368	+	2.13568i	−1.76512	+	0.351104i	−0.967658	−	0.252265i	$-0.918824\pi$
$37$	−10.7368	+	2.13568i	−1.76512	+	0.351104i	−0.797462	+	0.603369i	$0.793824\pi$
$38$	0.509545			0.0826591
$39$	−0.397517	+	0.0790710i	−0.0636536	+	0.0126615i
$40$	−2.20801	+	0.353144i	−0.349116	+	0.0558369i
$41$	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	$-0.126308\pi$
$42$	−0.813590	−	0.337000i	−0.125540	−	0.0520002i
$43$	−0.310490	−	0.128609i	−0.0473492	−	0.0196127i	0.358883	−	0.933382i	$-0.383158\pi$
$43$	−0.310490	−	0.128609i	−0.0473492	−	0.0196127i	−0.406232	+	0.913770i	$0.633158\pi$
$44$	0.912914	−	4.58953i	0.137627	−	0.691897i
$45$	2.65242	+	1.92096i	0.395400	+	0.286360i
$46$	0.729154	−	0.145038i	0.107508	−	0.0213847i
$47$	−4.22197			−0.615838			−0.307919	−	0.951413i	$-0.599632\pi$
$47$	−4.22197			−0.615838			−0.307919	+	0.951413i	$0.599632\pi$
$48$	−1.21530	+	0.241738i	−0.175413	+	0.0348919i
$49$	−2.48550	+	6.00052i	−0.355071	+	0.857217i
$50$	0.377191	−	4.98575i	0.0533428	−	0.705092i
$51$	−0.140721	−	5.10703i	−0.0197049	−	0.715128i
$52$	−0.231290	−	0.231290i	−0.0320742	−	0.0320742i
$53$	−1.65775	−	4.00217i	−0.227710	−	0.549740i	0.768188	−	0.640224i	$-0.221158\pi$
$53$	−1.65775	−	4.00217i	−0.227710	−	0.549740i	−0.995898	+	0.0904843i	$0.971158\pi$
$54$	4.59980	+	3.07349i	0.625954	+	0.418249i
$55$	9.50903	+	4.36627i	1.28220	+	0.588747i
$56$	−0.138649	−	0.697035i	−0.0185277	−	0.0931453i
$57$	−0.123176	+	0.619249i	−0.0163151	+	0.0820216i
$58$	−3.92193	−	5.86959i	−0.514975	−	0.770714i
$59$	1.52485	+	3.68132i	0.198519	+	0.479267i	0.991520	−	0.129953i	$-0.0414826\pi$
$59$	1.52485	+	3.68132i	0.198519	+	0.479267i	−0.793001	+	0.609220i	$0.791483\pi$
$60$	0.104584	−	2.76875i	0.0135017	−	0.357445i
$61$	−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	$0.705140\pi$
$62$	3.19147	+	0.634823i	0.405317	+	0.0806226i
$63$	−0.578286	+	0.865466i	−0.0728572	+	0.109038i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	0.623045	−	0.383102i	0.0772792	−	0.0475179i
$66$	5.35696	+	2.21893i	0.659396	+	0.273131i
$67$	0.274816	−	0.274816i	0.0335741	−	0.0335741i	−0.690120	−	0.723695i	$-0.742442\pi$
$67$	0.274816	−	0.274816i	0.0335741	−	0.0335741i	0.723695	+	0.690120i	$0.242442\pi$
$68$	3.36384	−	2.38423i	0.407926	−	0.289131i
$69$			0.921201i			0.110900i
$70$	1.58802	+	0.0599842i	0.189805	+	0.00716948i
$71$	−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	$0.807243\pi$
$72$			1.46461i			0.172606i
$73$	9.94566	+	6.64548i	1.16405	+	0.777795i	0.978784	−	0.204893i	$-0.0656848\pi$
$73$	9.94566	+	6.64548i	1.16405	+	0.777795i	0.185268	+	0.982688i	$0.440685\pi$
$74$	9.10222	−	6.08191i	1.05811	−	0.707008i
$75$	5.96800	+	1.66364i	0.689125	+	0.192101i
$76$	−0.470758	+	0.194994i	−0.0539997	+	0.0223674i
$77$	−1.27267	+	3.07249i	−0.145034	+	0.350143i
$78$	0.336998	−	0.225175i	0.0381575	−	0.0254961i
$79$	−5.34800	−	8.00385i	−0.601697	−	0.900504i	0.398161	−	0.917315i	$-0.369648\pi$
$79$	−5.34800	−	8.00385i	−0.601697	−	0.900504i	−0.999859	+	0.0168118i	$0.994648\pi$
$80$	1.90479	−	1.17123i	0.212962	−	0.130947i
$81$	−1.74024	+	1.74024i	−0.193360	+	0.193360i
$82$	1.39655	+	7.02092i	0.154223	+	0.775331i
$83$	11.5972	−	4.80373i	1.27296	−	0.527278i	0.359098	−	0.933300i	$-0.383084\pi$
$83$	11.5972	−	4.80373i	1.27296	−	0.527278i	0.913863	+	0.406022i	$0.133084\pi$
$84$	0.880623			0.0960838
$85$	3.44104	+	8.55332i	0.373233	+	0.927738i
$86$	0.336072			0.0362395
$87$	8.08138	−	3.34742i	0.866415	−	0.358881i
$88$	0.912914	+	4.58953i	0.0973169	+	0.489245i
$89$	−0.374770	+	0.374770i	−0.0397255	+	0.0397255i	−0.726691	−	0.686965i	$-0.758943\pi$
$89$	−0.374770	+	0.374770i	−0.0397255	+	0.0397255i	0.686965	+	0.726691i	$0.258943\pi$
$90$	−3.18564	−	0.759702i	−0.335796	−	0.0800796i
$91$	0.129149	+	0.193286i	0.0135385	+	0.0202618i
$92$	−0.618147	+	0.413033i	−0.0644463	+	0.0430616i
$93$	−1.54300	+	3.72513i	−0.160002	+	0.386278i
$94$	3.90059	−	1.61568i	0.402315	−	0.166644i
$95$	−0.179942	−	1.12508i	−0.0184617	−	0.115431i
$96$	1.03028	−	0.688411i	0.105153	−	0.0702607i
$97$	−8.19271	−	5.47419i	−0.831844	−	0.555820i	0.0651439	−	0.997876i	$-0.479249\pi$
$97$	−8.19271	−	5.47419i	−0.831844	−	0.555820i	−0.896988	+	0.442056i	$0.854249\pi$
$98$		−	6.49492i		−	0.656086i
$99$	3.80764	−	5.69853i	0.382682	−	0.572724i
$100$	1.55949	+	4.75058i	0.155949	+	0.475058i
$101$		−	14.4498i		−	1.43781i	−0.695108	−	0.718906i	$-0.744643\pi$
$101$		−	14.4498i		−	1.43781i	0.695108	−	0.718906i	$-0.255357\pi$
$102$	2.08439	+	4.66443i	0.206385	+	0.461848i
$103$	8.21768	−	8.21768i	0.809712	−	0.809712i	−0.174878	−	0.984590i	$-0.555953\pi$
$103$	8.21768	−	8.21768i	0.809712	−	0.809712i	0.984590	+	0.174878i	$0.0559531\pi$
$104$	0.302195	+	0.125173i	0.0296327	+	0.0122743i
$105$	−0.456784	+	1.91542i	−0.0445775	+	0.186926i
$106$	3.06313	+	3.06313i	0.297517	+	0.297517i
$107$	5.33929	−	7.99081i	0.516168	−	0.772501i	−0.478226	−	0.878237i	$-0.658720\pi$
$107$	5.33929	−	7.99081i	0.516168	−	0.772501i	0.994394	+	0.105736i	$0.0337200\pi$
$108$	−5.42584	−	1.07927i	−0.522101	−	0.103852i
$109$	−4.69116	−	0.933131i	−0.449332	−	0.0893777i	−0.0347631	−	0.999396i	$-0.511068\pi$
$109$	−4.69116	−	0.933131i	−0.449332	−	0.0893777i	−0.414569	+	0.910018i	$0.636068\pi$
$110$	−10.4561	−	0.394957i	−0.996949	−	0.0376577i
$111$	5.19099	+	12.5321i	0.492707	+	1.18950i
$112$	0.394839	+	0.590918i	0.0373088	+	0.0558365i
$113$	−1.83151	+	9.20761i	−0.172294	+	0.866179i	0.793838	+	0.608130i	$0.208080\pi$
$113$	−1.83151	+	9.20761i	−0.172294	+	0.866179i	−0.966132	+	0.258050i	$0.916920\pi$
$114$	−0.123176	−	0.619249i	−0.0115365	−	0.0579980i
$115$	−0.577740	−	1.55876i	−0.0538746	−	0.145355i
$116$	5.86959	+	3.92193i	0.544977	+	0.364142i
$117$	−0.183330	−	0.442599i	−0.0169489	−	0.0409183i
$118$	−2.81756	−	2.81756i	−0.259377	−	0.259377i
$119$	−2.67529	+	1.19550i	−0.245243	+	0.109591i
$120$	0.962934	+	2.59802i	0.0879034	+	0.237166i
$121$	4.17017	−	10.0677i	0.379106	−	0.915243i
$122$	6.63783	−	1.32035i	0.600961	−	0.119539i
$123$	−8.87012			−0.799792
$124$	−3.19147	+	0.634823i	−0.286603	+	0.0570088i
$125$	−11.1418	+	0.927847i	−0.996550	+	0.0829891i
$126$	0.203067	−	1.02089i	0.0180906	−	0.0909478i
$127$	−0.944755	−	0.391330i	−0.0838334	−	0.0347249i	0.340373	−	0.940291i	$-0.389447\pi$
$127$	−0.944755	−	0.391330i	−0.0838334	−	0.0347249i	−0.424206	+	0.905566i	$0.639447\pi$
$128$	0.923880	+	0.382683i	0.0816602	+	0.0338248i
$129$	−0.0812413	+	0.408427i	−0.00715289	+	0.0359600i
$130$	−0.429011	+	0.592369i	−0.0376268	+	0.0519542i
$131$	−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	$0.776848\pi$
$132$	−5.79833			−0.504680
$133$	0.355171	−	0.0706479i	0.0307972	−	0.00612595i
$134$	−0.148729	+	0.359064i	−0.0128482	+	0.0310184i
$135$	5.16189	−	11.2418i	0.444265	−	0.967538i
$136$	−2.19538	+	3.49003i	−0.188252	+	0.299268i
$137$	12.6973	+	12.6973i	1.08480	+	1.08480i	0.996054	+	0.0887476i	$0.0282864\pi$
$137$	12.6973	+	12.6973i	1.08480	+	1.08480i	0.0887476	+	0.996054i	$0.471714\pi$
$138$	−0.352528	−	0.851079i	−0.0300092	−	0.0724486i
$139$	−13.6528	−	9.12249i	−1.15801	−	0.773759i	−0.180280	−	0.983615i	$-0.557700\pi$
$139$	−13.6528	−	9.12249i	−1.15801	−	0.773759i	−0.977732	+	0.209856i	$0.932700\pi$
$140$	−1.49010	+	0.552291i	−0.125936	+	0.0466771i
$141$	1.02061	+	5.13095i	0.0859509	+	0.432104i
$142$	3.05782	−	15.3727i	0.256607	−	1.29005i
$143$	−0.850365	−	1.27266i	−0.0711111	−	0.106425i
$144$	−0.560483	−	1.35312i	−0.0467069	−	0.112760i
$145$	−11.5751	+	10.7325i	−0.961258	+	0.891282i
$146$	−11.7317	−	2.33358i	−0.970923	−	0.193129i
$147$	7.89327	+	1.57007i	0.651026	+	0.129497i
$148$	−6.08191	+	9.10222i	−0.499930	+	0.748198i
$149$	4.02675	+	4.02675i	0.329884	+	0.329884i	0.852542	−	0.522658i	$-0.175060\pi$
$149$	4.02675	+	4.02675i	0.329884	+	0.329884i	−0.522658	+	0.852542i	$0.675060\pi$
$150$	−6.15036	+	0.746846i	−0.502175	+	0.0609797i
$151$	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
$153$	5.88802	−	1.34079i	0.476018	−	0.108396i
$154$		−	3.32564i		−	0.267987i
$155$	0.274646	−	7.27097i	0.0220601	−	0.584018i
$156$	−0.225175	+	0.336998i	−0.0180284	+	0.0269815i
$157$		−	16.1039i		−	1.28523i	−0.766189	−	0.642616i	$-0.777849\pi$
$157$		−	16.1039i		−	1.28523i	0.766189	−	0.642616i	$-0.222151\pi$
$158$	8.00385	+	5.34800i	0.636752	+	0.425464i
$159$	−4.46309	+	2.98214i	−0.353946	+	0.236499i
$160$	−1.31159	+	1.81101i	−0.103690	+	0.143173i
$161$	0.488137	−	0.202193i	0.0384706	−	0.0159350i
$162$	0.941813	−	2.27374i	0.0739958	−	0.178642i
$163$	−18.2797	+	12.2141i	−1.43178	+	0.956684i	−0.433317	+	0.901242i	$0.642657\pi$
$163$	−18.2797	+	12.2141i	−1.43178	+	0.956684i	−0.998462	+	0.0554422i	$0.982343\pi$
$164$	−3.97703	−	5.95205i	−0.310554	−	0.464777i
$165$	3.00762	−	12.6118i	0.234143	−	0.981827i
$166$	−8.87613	+	8.87613i	−0.688922	+	0.688922i
$167$	3.23562	+	16.2666i	0.250380	+	1.25875i	0.877406	+	0.479748i	$0.159272\pi$
$167$	3.23562	+	16.2666i	0.250380	+	1.25875i	−0.627026	+	0.778998i	$0.715728\pi$
$168$	−0.813590	+	0.337000i	−0.0627698	+	0.0260001i
$169$	12.8930			0.991770
$170$	−6.45232	−	6.58541i	−0.494870	−	0.505078i
$171$	−0.746286			−0.0570699
$172$	−0.310490	+	0.128609i	−0.0236746	+	0.00980635i
$173$	1.67213	+	8.40635i	0.127129	+	0.639123i	0.990830	+	0.135117i	$0.0431410\pi$
$173$	1.67213	+	8.40635i	0.127129	+	0.639123i	−0.863700	+	0.504006i	$0.831859\pi$
$174$	−6.18522	+	6.18522i	−0.468900	+	0.468900i
$175$	−0.428354	−	3.52754i	−0.0323805	−	0.266657i
$176$	−2.59976	−	3.89081i	−0.195964	−	0.293281i
$177$	4.10529	−	2.74307i	0.308572	−	0.206181i
$178$	0.202824	−	0.489660i	0.0152023	−	0.0367016i
$179$	−18.8787	+	7.81980i	−1.41106	+	0.584479i	−0.952597	−	0.304235i	$-0.901599\pi$
$179$	−18.8787	+	7.81980i	−1.41106	+	0.584479i	−0.458461	+	0.888715i	$0.651599\pi$
$180$	3.23387	−	0.517218i	0.241039	−	0.0385512i
$181$	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	$0.261295\pi$
$182$	−0.193286	−	0.129149i	−0.0143273	−	0.00957318i
$183$			8.38613i			0.619920i
$184$	0.413033	−	0.618147i	0.0304492	−	0.0455704i
$185$	−16.6433	−	17.9500i	−1.22364	−	1.31971i
$186$		−	4.03205i		−	0.295644i
$187$	17.6150	−	7.87160i	1.28814	−	0.575629i
$188$	−2.98538	+	2.98538i	−0.217731	+	0.217731i
$189$	3.63236	+	1.50457i	0.264215	+	0.109442i
$190$	0.596794	+	0.970576i	0.0432960	+	0.0704130i
$191$	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	$0.550373\pi$
$192$	−0.688411	+	1.03028i	−0.0496818	+	0.0743541i
$193$	0.0549621	+	0.0109326i	0.00395626	+	0.000786949i	0.197068	−	0.980390i	$-0.436858\pi$
$193$	0.0549621	+	0.0109326i	0.00395626	+	0.000786949i	−0.193112	+	0.981177i	$0.561858\pi$
$194$	9.66396	+	1.92228i	0.693832	+	0.138012i
$195$	−0.616197	−	0.664575i	−0.0441267	−	0.0475912i
$196$	2.48550	+	6.00052i	0.177536	+	0.428609i
$197$	−2.06071	−	3.08408i	−0.146820	−	0.219731i	0.750769	−	0.660565i	$-0.229683\pi$
$197$	−2.06071	−	3.08408i	−0.146820	−	0.219731i	−0.897589	+	0.440833i	$0.854683\pi$
$198$	−1.33706	+	6.72188i	−0.0950210	+	0.477703i
$199$	1.29609	+	6.51587i	0.0918771	+	0.461898i	0.999145	+	0.0413442i	$0.0131640\pi$
$199$	1.29609	+	6.51587i	0.0918771	+	0.461898i	−0.907268	+	0.420553i	$0.861836\pi$
$200$	−3.25875	−	3.79217i	−0.230428	−	0.268147i
$201$	−0.400417	−	0.267550i	−0.0282432	−	0.0188715i
$202$	5.52971	+	13.3499i	0.389069	+	0.939295i
$203$	−3.54754	−	3.54754i	−0.248988	−	0.248988i
$204$	−3.71072	−	3.51171i	−0.259803	−	0.245869i
$205$	15.0091	−	5.56298i	1.04828	−	0.388535i
$206$	−4.44738	+	10.7369i	−0.309863	+	0.748077i
$207$	−1.06793	+	0.212424i	−0.0742261	+	0.0147645i
$208$	−0.327094			−0.0226799
$209$	−2.33857	+	0.465170i	−0.161762	+	0.0321765i
$210$	−0.310986	−	1.94442i	−0.0214601	−	0.134178i
$211$	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	$-0.144124\pi$
$212$	−4.00217	−	1.65775i	−0.274870	−	0.113855i
$213$	17.9432	+	7.43234i	1.22945	+	0.509255i
$214$	−1.87491	+	9.42580i	−0.128166	+	0.644334i
$215$	−0.118682	−	0.742048i	−0.00809401	−	0.0506073i
$216$	5.42584	−	1.07927i	0.369181	−	0.0734348i
$217$	2.31259			0.156989
$218$	4.69116	−	0.933131i	0.317726	−	0.0631996i
$219$	5.67200	−	13.6934i	0.383278	−	0.925315i
$220$	9.81131	−	3.63648i	0.661479	−	0.245171i
$221$	0.226574	−	1.32947i	0.0152410	−	0.0894300i
$222$	−9.59169	−	9.59169i	−0.643752	−	0.643752i
$223$	3.99002	+	9.63276i	0.267192	+	0.645058i	0.999349	−	0.0360779i	$-0.0114864\pi$
$223$	3.99002	+	9.63276i	0.267192	+	0.645058i	−0.732157	+	0.681136i	$0.761486\pi$
$224$	−0.590918	−	0.394839i	−0.0394824	−	0.0263813i
$225$	−0.552438	+	7.30219i	−0.0368292	+	0.486813i
$226$	−1.83151	−	9.20761i	−0.121830	−	0.612481i
$227$	2.39499	−	12.0404i	0.158961	−	0.799152i	−0.816220	−	0.577742i	$-0.803934\pi$
$227$	2.39499	−	12.0404i	0.158961	−	0.799152i	0.975181	−	0.221410i	$-0.0710659\pi$
$228$	0.350776	+	0.524974i	0.0232307	+	0.0347673i
$229$	−1.03397	−	2.49621i	−0.0683263	−	0.164954i	0.886028	−	0.463633i	$-0.153454\pi$
$229$	−1.03397	−	2.49621i	−0.0683263	−	0.164954i	−0.954354	+	0.298678i	$0.903454\pi$
$230$	1.13027	+	1.21901i	0.0745280	+	0.0803793i
$231$	4.04164	+	0.803933i	0.265921	+	0.0528949i
$232$	−6.92365	−	1.37720i	−0.454560	−	0.0904176i
$233$	10.8532	−	16.2429i	0.711014	−	1.06411i	−0.283446	−	0.958988i	$-0.591478\pi$
$233$	10.8532	−	16.2429i	0.711014	−	1.06411i	0.994460	−	0.105119i	$-0.0335224\pi$
$234$	0.338750	+	0.338750i	0.0221448	+	0.0221448i
$235$	−4.94489	−	8.04196i	−0.322569	−	0.524600i
$236$	3.68132	+	1.52485i	0.239633	+	0.0992594i
$237$	−8.43425	+	8.43425i	−0.547864	+	0.547864i
$238$	2.01415	−	2.12829i	0.130558	−	0.137956i
$239$			25.3901i			1.64235i	0.570679	+	0.821173i	$0.306680\pi$
$239$			25.3901i			1.64235i	−0.570679	+	0.821173i	$0.693320\pi$
$240$	−1.88385	−	2.03176i	−0.121602	−	0.131149i
$241$	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	$0.104407\pi$
$242$			10.8972i			0.700497i
$243$	−11.2638	−	7.52624i	−0.722574	−	0.482808i
$244$	−5.62728	+	3.76003i	−0.360250	+	0.240711i
$245$	−14.3408	+	2.29364i	−0.916201	+	0.146535i
$246$	8.19492	−	3.39445i	0.522489	−	0.216422i
$247$	−0.0637814	+	0.153982i	−0.00405832	+	0.00979764i
$248$	2.70560	−	1.80782i	0.171806	−	0.114797i
$249$	−8.64145	−	12.9329i	−0.547630	−	0.819586i
$250$	9.93858	−	5.12099i	0.628571	−	0.323880i
$251$	−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	$0.478491\pi$
$252$	0.203067	+	1.02089i	0.0127920	+	0.0643098i
$253$	−3.21407	+	1.33131i	−0.202067	+	0.0836987i
$254$	1.02260			0.0641633
$255$	9.56301	−	6.24955i	0.598859	−	0.391362i
$256$	−1.00000			−0.0625000
$257$	−7.87318	+	3.26118i	−0.491115	+	0.203427i	−0.614476	−	0.788935i	$-0.710633\pi$
$257$	−7.87318	+	3.26118i	−0.491115	+	0.203427i	0.123361	+	0.992362i	$0.460633\pi$
$258$	−0.0812413	−	0.408427i	−0.00505786	−	0.0254276i
$259$	5.50132	−	5.50132i	0.341836	−	0.341836i
$260$	0.169665	−	0.711453i	0.0105222	−	0.0441224i
$261$	5.74411	+	8.59667i	0.355551	+	0.532120i
$262$	16.6601	−	11.1319i	1.02927	−	0.687733i
$263$	8.47208	−	20.4534i	0.522411	−	1.26121i	−0.413991	−	0.910281i	$-0.635865\pi$
$263$	8.47208	−	20.4534i	0.522411	−	1.26121i	0.936402	−	0.350930i	$-0.114135\pi$
$264$	5.35696	−	2.21893i	0.329698	−	0.136565i
$265$	5.68168	−	7.84512i	0.349023	−	0.481922i
$266$	−0.301099	+	0.201188i	−0.0184616	+	0.0123356i
$267$	0.546053	+	0.364861i	0.0334179	+	0.0223291i
$268$		−	0.388648i		−	0.0237405i
$269$	13.2164	−	19.7798i	0.805819	−	1.20599i	−0.169573	−	0.985518i	$-0.554239\pi$
$269$	13.2164	−	19.7798i	0.805819	−	1.20599i	0.975392	−	0.220476i	$-0.0707611\pi$
$270$	−0.466926	+	12.3614i	−0.0284162	+	0.752292i
$271$			20.8191i			1.26467i	0.774694	+	0.632336i	$0.217904\pi$
$271$			20.8191i			1.26467i	−0.774694	+	0.632336i	$0.782096\pi$
$272$	0.692689	−	4.06450i	0.0420004	−	0.246447i
$273$	0.203679	−	0.203679i	0.0123272	−	0.0123272i
$274$	−16.5898	−	6.87172i	−1.00223	−	0.415136i
$275$	2.82043	+	23.2266i	0.170079	+	1.40062i
$276$	0.651388	+	0.651388i	0.0392089	+	0.0392089i
$277$	2.22543	−	3.33059i	0.133713	−	0.200116i	−0.758571	−	0.651591i	$-0.774102\pi$
$277$	2.22543	−	3.33059i	0.133713	−	0.200116i	0.892284	+	0.451475i	$0.149102\pi$
$278$	16.1045	+	3.20339i	0.965886	+	0.192127i
$279$	−4.67427	−	0.929769i	−0.279841	−	0.0556638i
$280$	1.16532	−	1.08049i	0.0696409	−	0.0645714i
$281$	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	$0.732332\pi$
$282$	−2.90645	−	4.34981i	−0.173077	−	0.259028i
$283$	−2.47657	+	12.4506i	−0.147217	+	0.740110i	0.834686	+	0.550726i	$0.185649\pi$
$283$	−2.47657	+	12.4506i	−0.147217	+	0.740110i	−0.981903	+	0.189384i	$0.939351\pi$
$284$	3.05782	+	15.3727i	0.181448	+	0.912203i
$285$	−1.32381	+	0.490658i	−0.0784156	+	0.0290641i
$286$	1.27266	+	0.850365i	0.0752540	+	0.0502831i
$287$	1.94689	+	4.70020i	0.114921	+	0.277444i
$288$	1.03564	+	1.03564i	0.0610255	+	0.0610255i
$289$	16.0404	+	5.63087i	0.943551	+	0.331228i
$290$	6.58684	−	14.3451i	0.386793	−	0.842372i
$291$	−4.67229	+	11.2799i	−0.273895	+	0.661240i
$292$	11.7317	−	2.33358i	0.686546	−	0.136563i
$293$	−8.34021			−0.487240			−0.243620	−	0.969871i	$-0.578335\pi$
$293$	−8.34021			−0.487240			−0.243620	+	0.969871i	$0.578335\pi$
$294$	−7.89327	+	1.57007i	−0.460345	+	0.0915682i
$295$	−5.22619	+	7.21619i	−0.304280	+	0.420143i
$296$	2.13568	−	10.7368i	0.124134	−	0.624064i
$297$	−23.9167	−	9.90664i	−1.38779	−	0.574842i
$298$	−5.26121	−	2.17926i	−0.304773	−	0.126241i
$299$	−0.0474409	+	0.238502i	−0.00274358	+	0.0137929i
$300$	5.39639	−	3.04364i	0.311560	−	0.175724i
$301$	0.234254	−	0.0465960i	0.0135022	−	0.00268575i
$302$	−10.6909			−0.615191
$303$	−17.5608	+	3.49307i	−1.00884	+	0.200672i
$304$	−0.194994	+	0.470758i	−0.0111837	+	0.0269998i
$305$	−5.25944	−	14.1901i	−0.301155	−	0.812523i
$306$	−4.92672	+	3.49198i	−0.281642	+	0.199623i
$307$	0.0891571	+	0.0891571i	0.00508847	+	0.00508847i	0.709646	−	0.704558i	$-0.248855\pi$
$307$	0.0891571	+	0.0891571i	0.00508847	+	0.00508847i	−0.704558	+	0.709646i	$0.748855\pi$
$308$	1.27267	+	3.07249i	0.0725169	+	0.175071i
$309$	−11.9735	−	8.00041i	−0.681146	−	0.455128i
$310$	2.52874	+	6.82260i	0.143623	+	0.387498i
$311$	−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	$-0.149977\pi$
$312$	0.0790710	−	0.397517i	0.00447651	−	0.0225049i
$313$	9.66650	+	14.4669i	0.546383	+	0.817719i	0.997191	−	0.0749013i	$-0.0238642\pi$
$313$	9.66650	+	14.4669i	0.546383	+	0.817719i	−0.450808	+	0.892621i	$0.648864\pi$
$314$	6.16270	+	14.8781i	0.347781	+	0.839618i
$315$	−2.32583	−	0.0878535i	−0.131046	−	0.00494999i
$316$	−9.44119	−	1.87797i	−0.531108	−	0.105644i
$317$	19.6461	+	3.90786i	1.10344	+	0.219487i	0.713015	−	0.701149i	$-0.247329\pi$
$317$	19.6461	+	3.90786i	1.10344	+	0.219487i	0.390422	+	0.920636i	$0.372329\pi$
$318$	2.98214	−	4.46309i	0.167230	−	0.250277i
$319$	23.3582	+	23.3582i	1.30781	+	1.30781i
$320$	0.518705	−	2.17507i	0.0289965	−	0.121590i
$321$	−11.0019	−	4.55715i	−0.614068	−	0.254355i
$322$	−0.373604	+	0.373604i	−0.0208201	+	0.0208201i
$323$	−1.77833	−	1.11864i	−0.0989488	−	0.0622430i
$324$			2.46108i			0.136726i
$325$	1.45946	+	0.738069i	0.0809561	+	0.0409407i
$326$	12.2141	−	18.2797i	0.676478	−	1.01242i
$327$			5.92674i			0.327749i
$328$	5.95205	+	3.97703i	0.328647	+	0.219595i
$329$	2.49484	−	1.66700i	0.137545	−	0.0919045i
$330$	2.04764	+	12.8028i	0.112719	+	0.704768i
$331$	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	$0.244842\pi$
$332$	4.80373	−	11.5972i	0.263639	−	0.636480i
$333$	−13.3312	+	8.90764i	−0.730547	+	0.488136i
$334$	−9.21428	−	13.7901i	−0.504183	−	0.754563i
$335$	0.845338	+	0.201594i	0.0461858	+	0.0110142i
$336$	0.622694	−	0.622694i	0.0339708	−	0.0339708i
$337$	1.57543	+	7.92021i	0.0858190	+	0.431441i	0.999677	+	0.0254078i	$0.00808841\pi$
$337$	1.57543	+	7.92021i	0.0858190	+	0.431441i	−0.913858	+	0.406034i	$0.866912\pi$
$338$	−11.9116	+	4.93394i	−0.647905	+	0.268371i
$339$	11.6327			0.631804
$340$	8.48129	+	3.61493i	0.459963	+	0.196047i
$341$	−15.2269			−0.824582
$342$	0.689478	−	0.285591i	0.0372827	−	0.0154430i
$343$	−1.87106	−	9.40644i	−0.101028	−	0.507900i
$344$	0.237639	−	0.237639i	0.0128126	−	0.0128126i
$345$	−1.75469	+	1.07894i	−0.0944695	+	0.0580881i
$346$	−4.76181	−	7.12656i	−0.255997	−	0.383126i
$347$	−14.2098	+	9.49472i	−0.762825	+	0.509703i	−0.875081	−	0.483976i	$-0.839192\pi$
$347$	−14.2098	+	9.49472i	−0.762825	+	0.509703i	0.112257	+	0.993679i	$0.464192\pi$
$348$	3.34742	−	8.08138i	0.179440	−	0.433207i
$349$	24.1690	−	10.0111i	1.29374	−	0.535884i	0.373641	−	0.927573i	$-0.378109\pi$
$349$	24.1690	−	10.0111i	1.29374	−	0.535884i	0.920098	+	0.391689i	$0.128109\pi$
$350$	1.74568	+	3.09510i	0.0933105	+	0.165440i
$351$	−1.50457	+	1.00532i	−0.0803078	+	0.0536600i
$352$	3.89081	+	2.59976i	0.207381	+	0.138568i
$353$		−	34.0507i		−	1.81234i	−0.422919	−	0.906168i	$-0.638994\pi$
$353$		−	34.0507i		−	1.81234i	0.422919	−	0.906168i	$-0.361006\pi$
$354$	−2.74307	+	4.10529i	−0.145792	+	0.218194i
$355$	−35.0229	−	1.32292i	−1.85882	−	0.0702131i
$356$			0.530005i			0.0280902i
$357$	2.09961	+	2.96228i	0.111123	+	0.156780i
$358$	14.4491	−	14.4491i	0.763659	−	0.763659i
$359$	1.81224	+	0.750656i	0.0956465	+	0.0396181i	0.429994	−	0.902832i	$-0.358516\pi$
$359$	1.81224	+	0.750656i	0.0956465	+	0.0396181i	−0.334347	+	0.942450i	$0.608516\pi$
$360$	−2.78978	+	1.71540i	−0.147034	+	0.0904093i
$361$	−13.2514	−	13.2514i	−0.697444	−	0.697444i
$362$	−2.39441	+	3.58349i	−0.125847	+	0.188344i
$363$	−13.2433	−	2.63426i	−0.695094	−	0.138263i
$364$	0.227996	+	0.0453512i	0.0119502	+	0.00237705i
$365$	−1.00959	+	26.7278i	−0.0528441	+	1.39900i
$366$	−3.20923	−	7.74777i	−0.167749	−	0.404983i
$367$	−9.32545	−	13.9565i	−0.486785	−	0.728525i	0.504040	−	0.863681i	$-0.331847\pi$
$367$	−9.32545	−	13.9565i	−0.486785	−	0.728525i	−0.990824	+	0.135156i	$0.956847\pi$
$368$	−0.145038	+	0.729154i	−0.00756062	+	0.0380098i
$369$	−2.04540	−	10.2829i	−0.106479	−	0.535308i
$370$	22.2456	+	10.2145i	1.15649	+	0.531027i
$371$	2.55981	+	1.71041i	0.132898	+	0.0887999i
$372$	1.54300	+	3.72513i	0.0800008	+	0.193139i
$373$	−5.16638	−	5.16638i	−0.267505	−	0.267505i	0.560589	−	0.828094i	$-0.310575\pi$
$373$	−5.16638	−	5.16638i	−0.267505	−	0.267505i	−0.828094	+	0.560589i	$0.810575\pi$
$374$	−13.2618	+	14.0134i	−0.685754	+	0.724616i
$375$	3.82100	+	13.3163i	0.197316	+	0.687650i
$376$	1.61568	−	3.90059i	0.0833222	−	0.201158i
$377$	2.26468	−	0.450473i	0.116637	−	0.0232006i
$378$	−3.93164			−0.202222
$379$	−35.1483	+	6.99144i	−1.80545	+	0.359126i	−0.978996	−	0.203879i	$-0.934645\pi$
$379$	−35.1483	+	6.99144i	−1.80545	+	0.359126i	−0.826453	+	0.563005i	$0.809645\pi$
$380$	−0.922789	−	0.668312i	−0.0473381	−	0.0342837i
$381$	−0.247200	+	1.24276i	−0.0126644	+	0.0636685i
$382$	−14.9858	−	6.20731i	−0.766738	−	0.317593i
$383$	−15.2856	−	6.33151i	−0.781058	−	0.323525i	−0.0437158	−	0.999044i	$-0.513920\pi$
$383$	−15.2856	−	6.33151i	−0.781058	−	0.323525i	−0.737343	+	0.675519i	$0.763920\pi$
$384$	0.241738	−	1.21530i	0.0123361	−	0.0620179i
$385$	−7.34303	+	1.17443i	−0.374235	+	0.0598544i
$386$	−0.0549621	+	0.0109326i	−0.00279750	+	0.000556457i
$387$	−0.492215			−0.0250207
$388$	−9.66396	+	1.92228i	−0.490613	+	0.0975890i
$389$	7.18782	−	17.3529i	0.364437	−	0.879829i	−0.630203	−	0.776430i	$-0.717028\pi$
$389$	7.18782	−	17.3529i	0.364437	−	0.879829i	0.994640	−	0.103398i	$-0.0329717\pi$
$390$	0.823613	+	0.378179i	0.0417053	+	0.0191498i
$391$	−2.86318	−	1.09458i	−0.144797	−	0.0553554i
$392$	−4.59260	−	4.59260i	−0.231961	−	0.231961i
$393$	9.50125	+	22.9380i	0.479274	+	1.15707i
$394$	3.08408	+	2.06071i	0.155373	+	0.103817i
$395$	8.98191	−	19.5612i	0.451929	−	0.984229i
$396$	−1.33706	−	6.72188i	−0.0671900	−	0.337787i
$397$	−1.60682	+	8.07804i	−0.0806440	+	0.405425i	0.919286	+	0.393590i	$0.128767\pi$
$397$	−1.60682	+	8.07804i	−0.0806440	+	0.405425i	−0.999930	+	0.0118346i	$0.996233\pi$
$398$	−3.69094	−	5.52389i	−0.185010	−	0.276887i
$399$	−0.171717	−	0.414560i	−0.00859658	−	0.0207540i
$400$	4.46189	+	2.25644i	0.223094	+	0.112822i
$401$	−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	$0.627234\pi$
$402$	0.472324	+	0.0939510i	0.0235574	+	0.00468585i
$403$	−0.591328	+	0.884984i	−0.0294561	+	0.0440842i
$404$	−10.2176	−	10.2176i	−0.508343	−	0.508343i
$405$	−5.35302	−	1.27657i	−0.265994	−	0.0634334i
$406$	4.63508	+	1.91991i	0.230035	+	0.0952837i
$407$	−36.2226	+	36.2226i	−1.79549	+	1.79549i
$408$	4.77214	+	1.82437i	0.236256	+	0.0903197i
$409$			6.01170i			0.297259i	0.988893	+	0.148630i	$0.0474863\pi$
$409$			6.01170i			0.297259i	−0.988893	+	0.148630i	$0.952514\pi$
$410$	−11.7377	+	10.8832i	−0.579684	+	0.537485i
$411$	12.3616	−	18.5004i	0.609751	−	0.912557i
$412$		−	11.6216i		−	0.572553i
$413$	−2.35459	−	1.57329i	−0.115862	−	0.0774164i
$414$	0.905345	−	0.604932i	0.0444953	−	0.0297308i
$415$	22.7331	+	16.4640i	1.11592	+	0.808186i
$416$	0.302195	−	0.125173i	0.0148163	−	0.00613713i
$417$	−7.78616	+	18.7974i	−0.381290	+	0.920515i
$418$	1.98254	−	1.32469i	0.0969694	−	0.0647929i
$419$	3.45852	+	5.17603i	0.168960	+	0.252866i	0.906280	−	0.422677i	$-0.138909\pi$
$419$	3.45852	+	5.17603i	0.168960	+	0.252866i	−0.737321	+	0.675543i	$0.763909\pi$
$420$	1.03141	+	1.67740i	0.0503277	+	0.0818488i
$421$	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	$0.0350078\pi$
$422$	3.42608	+	17.2241i	0.166779	+	0.838455i
$423$	−5.71285	+	2.36634i	−0.277768	+	0.115055i
$424$	4.33191			0.210376
$425$	−12.2620	+	16.5724i	−0.594795	+	0.803877i
$426$	−19.4216			−0.940981
$427$	4.44374	−	1.84066i	0.215048	−	0.0890757i
$428$	−1.87491	−	9.42580i	−0.0906271	−	0.455613i
$429$	−1.34110	+	1.34110i	−0.0647488	+	0.0647488i
$430$	0.393617	+	0.640146i	0.0189819	+	0.0308706i
$431$	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	$0.462097\pi$
$432$	−4.59980	+	3.07349i	−0.221308	+	0.147873i
$433$	2.79464	−	6.74685i	0.134302	−	0.324233i	−0.842394	−	0.538862i	$-0.818854\pi$
$433$	2.79464	−	6.74685i	0.134302	−	0.324233i	0.976696	+	0.214629i	$0.0688543\pi$
$434$	−2.13655	+	0.884988i	−0.102558	+	0.0424808i
$435$	15.8413	+	11.4727i	0.759531	+	0.550075i
$436$	−3.97698	+	2.65733i	−0.190463	+	0.127263i
$437$	0.314974	+	0.210459i	0.0150672	+	0.0100676i
$438$			14.8216i			0.708206i
$439$	17.4852	−	26.1685i	0.834523	−	1.24895i	−0.131711	−	0.991288i	$-0.542047\pi$
$439$	17.4852	−	26.1685i	0.834523	−	1.24895i	0.966235	−	0.257664i	$-0.0829528\pi$
$440$	−7.67285	+	7.11430i	−0.365789	+	0.339161i
$441$			9.51253i			0.452978i
$442$	0.299440	+	1.31498i	0.0142429	+	0.0625472i
$443$	11.7784	−	11.7784i	0.559607	−	0.559607i	−0.369589	−	0.929195i	$-0.620501\pi$
$443$	11.7784	−	11.7784i	0.559607	−	0.559607i	0.929195	+	0.369589i	$0.120501\pi$
$444$	12.5321	+	5.19099i	0.594749	+	0.246353i
$445$	−1.15280	−	0.274916i	−0.0546479	−	0.0130323i
$446$	−7.37260	−	7.37260i	−0.349103	−	0.349103i
$447$	3.92029	−	5.86713i	0.185423	−	0.277506i
$448$	0.697035	+	0.138649i	0.0329318	+	0.00655055i
$449$	−15.7553	−	3.13392i	−0.743537	−	0.147899i	−0.191237	−	0.981544i	$-0.561250\pi$
$449$	−15.7553	−	3.13392i	−0.743537	−	0.147899i	−0.552300	+	0.833645i	$0.686250\pi$
$450$	−2.28404	−	6.95776i	−0.107671	−	0.327992i
$451$	−12.8190	−	30.9478i	−0.603623	−	1.45727i
$452$	5.21569	+	7.80584i	0.245326	+	0.367156i
$453$	2.58439	−	12.9926i	0.121425	−	0.610446i
$454$	2.39499	+	12.0404i	0.112403	+	0.565086i
$455$	−0.216905	+	0.472384i	−0.0101687	+	0.0221457i
$456$	−0.524974	−	0.350776i	−0.0245842	−	0.0164266i
$457$	3.23943	+	7.82067i	0.151534	+	0.365835i	0.981358	−	0.192190i	$-0.0615591\pi$
$457$	3.23943	+	7.82067i	0.151534	+	0.365835i	−0.829824	+	0.558026i	$0.811559\pi$
$458$	1.91052	+	1.91052i	0.0892727	+	0.0892727i
$459$	−9.30598	−	20.8249i	−0.434366	−	0.972022i
$460$	−1.51073	−	0.693684i	−0.0704382	−	0.0323432i
$461$	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	$-0.160604\pi$
$462$	−4.04164	+	0.803933i	−0.188034	+	0.0374023i
$463$	5.72199			0.265924			0.132962	−	0.991121i	$-0.457551\pi$
$463$	5.72199			0.265924			0.132962	+	0.991121i	$0.457551\pi$
$464$	6.92365	−	1.37720i	0.321422	−	0.0639349i
$465$	−8.90279	+	1.42389i	−0.412857	+	0.0660314i
$466$	−3.81112	+	19.1598i	−0.176547	+	0.887561i
$467$	34.3166	+	14.2144i	1.58798	+	0.657764i	0.989652	−	0.143485i	$-0.0458310\pi$
$467$	34.3166	+	14.2144i	1.58798	+	0.657764i	0.598330	+	0.801249i	$0.295831\pi$
$468$	−0.442599	−	0.183330i	−0.0204591	−	0.00847445i
$469$	−0.0538857	+	0.270902i	−0.00248821	+	0.0125091i
$470$	7.64601	+	5.53747i	0.352684	+	0.255425i
$471$	−19.5711	+	3.89292i	−0.901787	+	0.179377i
$472$	−3.98463			−0.183408
$473$	−1.54241	+	0.306804i	−0.0709201	+	0.0141069i
$474$	4.56459	−	11.0199i	0.209658	−	0.506160i
$475$	1.93228	−	1.66048i	0.0886592	−	0.0761879i
$476$	−1.04637	+	2.73706i	−0.0479602	+	0.125453i
$477$	−4.48629	−	4.48629i	−0.205413	−	0.205413i
$478$	−9.71636	−	23.4574i	−0.444416	−	1.07291i
$479$	−16.0975	−	10.7560i	−0.735513	−	0.491454i	0.130517	−	0.991446i	$-0.458336\pi$
$479$	−16.0975	−	10.7560i	−0.735513	−	0.491454i	−0.866030	+	0.499992i	$0.833336\pi$
$480$	2.51797	+	1.15618i	0.114929	+	0.0527721i
$481$	0.698569	+	3.51194i	0.0318520	+	0.160131i
$482$	−1.56331	+	7.85931i	−0.0712070	+	0.357982i
$483$	−0.363726	−	0.544354i	−0.0165501	−	0.0247690i
$484$	−4.17017	−	10.0677i	−0.189553	−	0.457621i
$485$	0.831643	−	22.0169i	0.0377630	−	0.999737i
$486$	13.2866	+	2.64286i	0.602691	+	0.119883i
$487$	−1.95796	−	0.389463i	−0.0887238	−	0.0176483i	0.150529	−	0.988606i	$-0.451902\pi$
$487$	−1.95796	−	0.389463i	−0.0887238	−	0.0176483i	−0.239253	+	0.970957i	$0.576902\pi$
$488$	3.76003	−	5.62728i	0.170209	−	0.254735i
$489$	19.2627	+	19.2627i	0.871090	+	0.871090i
$490$	12.3714	−	7.60704i	0.558885	−	0.343651i
$491$	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
$493$	0.801699	+	29.0952i	0.0361067	+	1.31038i
$494$		−	0.166669i		−	0.00749879i
$495$	15.3141	+	0.578459i	0.688318	+	0.0259998i
$496$	−1.80782	+	2.70560i	−0.0811737	+	0.121485i
$497$		−	11.1393i		−	0.499665i
$498$	12.9329	+	8.64145i	0.579535	+	0.387233i
$499$	12.9080	−	8.62482i	0.577840	−	0.386100i	−0.232031	−	0.972708i	$-0.574537\pi$
$499$	12.9080	−	8.62482i	0.577840	−	0.386100i	0.809871	+	0.586608i	$0.199537\pi$
$500$	−7.22234	+	8.53451i	−0.322993	+	0.381675i
$501$	18.9866	−	7.86450i	0.848258	−	0.351360i
$502$	7.97566	−	19.2549i	0.355971	−	0.859390i
$503$	35.9136	−	23.9967i	1.60131	−	1.06996i	0.650808	−	0.759242i	$-0.274430\pi$
$503$	35.9136	−	23.9967i	1.60131	−	1.06996i	0.950502	−	0.310719i	$-0.100570\pi$
$504$	−0.578286	−	0.865466i	−0.0257589	−	0.0385509i
$505$	27.5239	−	16.9241i	1.22480	−	0.753111i
$506$	2.45994	−	2.45994i	0.109358	−	0.109358i
$507$	−3.11673	−	15.6689i	−0.138419	−	0.695878i
$508$	−0.944755	+	0.391330i	−0.0419167	+	0.0173625i
$509$	35.6718			1.58113			0.790563	−	0.612381i	$-0.209788\pi$
$509$	35.6718			1.58113			0.790563	+	0.612381i	$0.209788\pi$
$510$	−6.44347	+	9.43344i	−0.285321	+	0.417720i
$511$	−8.50097			−0.376061
$512$	0.923880	−	0.382683i	0.0408301	−	0.0169124i
$513$	0.549934	+	2.76471i	0.0242802	+	0.122065i
$514$	6.02587	−	6.02587i	0.265790	−	0.265790i
$515$	25.2777	+	6.02816i	1.11387	+	0.265633i
$516$	0.231356	+	0.346248i	0.0101849	+	0.0152427i
$517$	−16.4269	+	10.9761i	−0.722454	+	0.482728i
$518$	−2.97729	+	7.18782i	−0.130815	+	0.315815i
$519$	9.81200	−	4.06426i	0.430699	−	0.178401i
$520$	0.115511	+	0.722225i	0.00506549	+	0.0316717i
$521$	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	$0.259775\pi$
$522$	−8.59667	−	5.74411i	−0.376266	−	0.251413i
$523$		−	17.7492i		−	0.776116i	−0.921635	−	0.388058i	$-0.873146\pi$
$523$		−	17.7492i		−	0.776116i	0.921635	−	0.388058i	$-0.126854\pi$
$524$	−11.1319	+	16.6601i	−0.486301	+	0.727801i
$525$	−4.18347	+	1.37332i	−0.182582	+	0.0599366i
$526$			22.1386i			0.965289i
$527$	−9.74465	−	9.22204i	−0.424484	−	0.401718i
$528$	−4.10004	+	4.10004i	−0.178431	+	0.178431i
$529$	−20.7386	−	8.59021i	−0.901678	−	0.373487i
$530$	−2.24699	+	9.42223i	−0.0976028	+	0.409275i
$531$	4.12663	+	4.12663i	0.179081	+	0.179081i
$532$	0.201188	−	0.301099i	0.00872261	−	0.0130543i
$533$	−2.29650	−	0.456802i	−0.0994725	−	0.0197863i
$534$	−0.644114	−	0.128122i	−0.0278735	−	0.00554439i
$535$	21.4743	+	0.811148i	0.928416	+	0.0350690i
$536$	0.148729	+	0.359064i	0.00642412	+	0.0155092i
$537$	14.0671	+	21.0529i	0.607039	+	0.908499i
$538$	−4.64099	+	23.3318i	−0.200087	+	1.00591i
$539$	5.92930	+	29.8086i	0.255393	+	1.28395i
$540$	−4.29912	−	11.5991i	−0.185005	−	0.499148i
$541$	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	$0.613657\pi$
$542$	−7.96714	−	19.2344i	−0.342218	−	0.826187i
$543$	−3.77619	−	3.77619i	−0.162052	−	0.162052i
$544$	0.915457	+	4.02019i	0.0392499	+	0.172364i
$545$	−3.71701	−	10.0286i	−0.159219	−	0.429578i
$546$	−0.110231	+	0.266120i	−0.00471743	+	0.0113889i
$547$	−13.3586	+	2.65720i	−0.571174	+	0.113614i	−0.472224	−	0.881479i	$-0.656548\pi$
$547$	−13.3586	+	2.65720i	−0.571174	+	0.113614i	−0.0989503	+	0.995092i	$0.531548\pi$
$548$	17.9567			0.767071
$549$	−9.72185	+	1.93380i	−0.414918	+	0.0825324i
$550$	−11.4942	−	20.3792i	−0.490113	−	0.868974i
$551$	0.701745	−	3.52791i	0.0298953	−	0.150294i
$552$	−0.851079	−	0.352528i	−0.0362243	−	0.0150046i
$553$	6.32046	+	2.61802i	0.268773	+	0.111330i
$554$	−0.781467	+	3.92870i	−0.0332013	+	0.166914i
$555$	−17.7913	+	24.5658i	−0.755197	+	1.04276i
$556$	−16.1045	+	3.20339i	−0.682985	+	0.135854i
$557$	−1.23472			−0.0523168			−0.0261584	−	0.999658i	$-0.508327\pi$
$557$	−1.23472			−0.0523168			−0.0261584	+	0.999658i	$0.508327\pi$
$558$	4.67427	−	0.929769i	0.197877	−	0.0393603i
$559$	−0.0420672	+	0.101559i	−0.00177925	+	0.00429550i
$560$	−0.663128	+	1.44419i	−0.0280223	+	0.0610280i
$561$	−13.8246	−	19.5047i	−0.583674	−	0.823488i
$562$	−10.2732	−	10.2732i	−0.433348	−	0.433348i
$563$	8.16721	+	19.7174i	0.344207	+	0.830989i	0.997281	+	0.0736946i	$0.0234790\pi$
$563$	8.16721	+	19.7174i	0.344207	+	0.830989i	−0.653074	+	0.757294i	$0.726521\pi$
$564$	4.34981	+	2.90645i	0.183160	+	0.122384i
$565$	−19.6837	+	7.29559i	−0.828099	+	0.306928i
$566$	−2.47657	−	12.4506i	−0.104098	−	0.523337i
$567$	0.341226	−	1.71546i	0.0143301	−	0.0720424i
$568$	−8.70794	−	13.0324i	−0.365377	−	0.546826i
$569$	12.6066	+	30.4351i	0.528498	+	1.27591i	0.932507	+	0.361152i	$0.117616\pi$
$569$	12.6066	+	30.4351i	0.528498	+	1.27591i	−0.404009	+	0.914755i	$0.632384\pi$
$570$	1.03527	−	0.959908i	0.0433628	−	0.0402061i
$571$	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	$0.206865\pi$
$572$	−1.50121	−	0.298608i	−0.0627685	−	0.0124854i
$573$	11.1664	−	16.7116i	0.466481	−	0.698138i
$574$	−3.59738	−	3.59738i	−0.150152	−	0.150152i
$575$	2.29244	−	2.92614i	0.0956013	−	0.122028i
$576$	−1.35312	−	0.560483i	−0.0563802	−	0.0233534i
$577$	−32.4025	+	32.4025i	−1.34893	+	1.34893i	−0.462109	+	0.886823i	$0.652907\pi$
$577$	−32.4025	+	32.4025i	−1.34893	+	1.34893i	−0.886823	+	0.462109i	$0.847093\pi$
$578$	−16.9742	+	0.936137i	−0.706034	+	0.0389382i
$579$		−	0.0694382i		−	0.00288575i
$580$	−0.595822	+	15.7738i	−0.0247402	+	0.654972i
$581$	−4.95631	+	7.41765i	−0.205622	+	0.307736i
$582$		−	12.2093i		−	0.506091i
$583$	−16.8547	−	11.2619i	−0.698049	−	0.466421i
$584$	−9.94566	+	6.64548i	−0.411554	+	0.274992i
$585$	0.628335	−	0.867590i	0.0259785	−	0.0358704i
$586$	7.70535	−	3.19166i	0.318305	−	0.131846i
$587$	5.23957	−	12.6495i	0.216260	−	0.522099i	−0.778101	−	0.628139i	$-0.783817\pi$
$587$	5.23957	−	12.6495i	0.216260	−	0.522099i	0.994362	+	0.106040i	$0.0338171\pi$
$588$	6.69159	−	4.47118i	0.275956	−	0.184388i
$589$	0.921167	+	1.37862i	0.0379560	+	0.0568052i
$590$	2.06685	−	8.66687i	0.0850908	−	0.356809i
$591$	−3.24992	+	3.24992i	−0.133684	+	0.133684i
$592$	2.13568	+	10.7368i	0.0877760	+	0.441280i
$593$	9.66064	−	4.00157i	0.396715	−	0.164325i	−0.175402	−	0.984497i	$-0.556122\pi$
$593$	9.66064	−	4.00157i	0.396715	−	0.164325i	0.572117	+	0.820172i	$0.306122\pi$
$594$	25.8873			1.06217
$595$	−5.41055	−	3.69565i	−0.221811	−	0.151507i
$596$	5.69469			0.233264
$597$	7.60541	−	3.15026i	0.311269	−	0.128932i
$598$	−0.0474409	−	0.238502i	−0.00194000	−	0.00975306i
$599$	−9.67035	+	9.67035i	−0.395120	+	0.395120i	−0.876508	−	0.481388i	$-0.840133\pi$
$599$	−9.67035	+	9.67035i	−0.395120	+	0.395120i	0.481388	+	0.876508i	$0.340133\pi$
$600$	−3.82086	+	4.87706i	−0.155986	+	0.199105i
$601$	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	$0.702156\pi$
$602$	−0.198591	+	0.132694i	−0.00809396	+	0.00540821i
$603$	0.217831	−	0.525890i	0.00887075	−	0.0214159i
$604$	9.87709	−	4.09122i	0.401893	−	0.166470i
$605$	24.0610	−	3.84826i	0.978219	−	0.156454i
$606$	14.8874	−	9.94742i	0.604758	−	0.404086i
$607$	−8.81933	−	5.89289i	−0.357966	−	0.239185i	0.363563	−	0.931570i	$-0.381560\pi$
$607$	−8.81933	−	5.89289i	−0.357966	−	0.239185i	−0.721529	+	0.692385i	$0.756560\pi$
$608$		−	0.509545i		−	0.0206648i
$609$	−3.45374	+	5.16889i	−0.139953	+	0.209454i
$610$	10.2894	+	11.0972i	0.416606	+	0.449314i
$611$			1.38098i			0.0558685i
$612$	3.21538	−	5.11154i	0.129974	−	0.206622i
$613$	−29.6325	+	29.6325i	−1.19685	+	1.19685i	−0.221742	+	0.975105i	$0.571174\pi$
$613$	−29.6325	+	29.6325i	−1.19685	+	1.19685i	−0.975105	+	0.221742i	$0.928826\pi$
$614$	−0.116489	−	0.0482515i	−0.00470113	−	0.00194727i
$615$	−10.3889	−	16.8957i	−0.418923	−	0.681301i
$616$	−2.35158	−	2.35158i	−0.0947479	−	0.0947479i
$617$	21.3342	−	31.9289i	0.858882	−	1.28541i	−0.0980747	−	0.995179i	$-0.531268\pi$
$617$	21.3342	−	31.9289i	0.858882	−	1.28541i	0.956957	−	0.290229i	$-0.0937316\pi$
$618$	14.1237	+	2.80937i	0.568137	+	0.113009i
$619$	−2.57153	−	0.511509i	−0.103358	−	0.0205593i	0.143140	−	0.989702i	$-0.454280\pi$
$619$	−2.57153	−	0.511509i	−0.103358	−	0.0205593i	−0.246499	+	0.969143i	$0.579280\pi$
$620$	−4.94715	−	5.33556i	−0.198682	−	0.214281i
$621$	1.57390	+	3.79974i	0.0631585	+	0.152478i
$622$	5.31755	+	7.95827i	0.213214	+	0.319098i
$623$	0.0734846	−	0.369432i	0.00294410	−	0.0148010i
$624$	0.0790710	+	0.397517i	0.00316537	+	0.0159134i
$625$	−14.8169	−	20.1360i	−0.592677	−	0.805440i
$626$	−14.4669	−	9.66650i	−0.578215	−	0.386351i
$627$	1.13064	+	2.72961i	0.0451535	+	0.109010i
$628$	−11.3872	−	11.3872i	−0.454398	−	0.454398i
$629$	−45.1191	+	1.24323i	−1.79902	+	0.0495708i
$630$	2.18241	−	0.808892i	0.0869493	−	0.0322270i
$631$	−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	$0.175641\pi$
$632$	9.44119	−	1.87797i	0.375550	−	0.0747016i
$633$	−21.7606			−0.864907
$634$	−19.6461	+	3.90786i	−0.780247	+	0.155201i
$635$	−0.361123	−	2.25790i	−0.0143307	−	0.0896019i
$636$	−1.04719	+	5.26457i	−0.0415237	+	0.208754i
$637$	1.96273	+	0.812991i	0.0777663	+	0.0322119i
$638$	−30.5190	−	12.6414i	−1.20826	−	0.500477i
$639$	−4.47852	+	22.5151i	−0.177168	+	0.890682i
$640$	0.353144	+	2.20801i	0.0139592	+	0.0872791i
$641$	−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	$0.570764\pi$
$642$	11.9084			0.469987
$643$	−29.8237	+	5.93231i	−1.17613	+	0.233947i	−0.744199	−	0.667958i	$-0.767169\pi$
$643$	−29.8237	+	5.93231i	−1.17613	+	0.233947i	−0.431934	+	0.901905i	$0.642169\pi$
$644$	0.202193	−	0.488137i	0.00796752	−	0.0192353i
$645$	−0.873120	+	0.323615i	−0.0343791	+	0.0127423i
$646$	2.07105	+	0.352956i	0.0814842	+	0.0138869i
$647$	−34.7745	−	34.7745i	−1.36712	−	1.36712i	−0.864511	−	0.502614i	$-0.832372\pi$
$647$	−34.7745	−	34.7745i	−1.36712	−	1.36712i	−0.502614	−	0.864511i	$-0.667628\pi$
$648$	−0.941813	−	2.27374i	−0.0369979	−	0.0893209i
$649$	15.5035	+	10.3591i	0.608564	+	0.406629i
$650$	−1.63081	−	0.123377i	−0.0639656	−	0.00483923i
$651$	−0.559040	−	2.81048i	−0.0219105	−	0.110151i
$652$	−4.28903	+	21.5624i	−0.167971	+	0.844449i
$653$	3.53808	+	5.29511i	0.138456	+	0.207214i	0.894217	−	0.447633i	$-0.147733\pi$
$653$	3.53808	+	5.29511i	0.138456	+	0.207214i	−0.755761	+	0.654847i	$0.772733\pi$
$654$	−2.26806	−	5.47559i	−0.0886884	−	0.214113i
$655$	−30.4628	−	32.8545i	−1.19028	−	1.28373i
$656$	−7.02092	−	1.39655i	−0.274121	−	0.0545261i
$657$	17.1824	+	3.41779i	0.670349	+	0.133341i
$658$	−1.66700	+	2.49484i	−0.0649863	+	0.0972589i
$659$	−19.7490	−	19.7490i	−0.769313	−	0.769313i	0.208672	−	0.977986i	$-0.433086\pi$
$659$	−19.7490	−	19.7490i	−0.769313	−	0.769313i	−0.977986	+	0.208672i	$0.933086\pi$
$660$	−6.79118	−	11.0446i	−0.264346	−	0.429910i
$661$	−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
$663$	−1.67048	+	0.0460290i	−0.0648760	+	0.00178762i
$664$			12.5527i			0.487141i
$665$	0.550556	+	0.593781i	0.0213496	+	0.0230258i
$666$	8.90764	−	13.3312i	0.345164	−	0.516575i
$667$		−	5.24815i		−	0.203209i
$668$	13.7901	+	9.21428i	0.533557	+	0.356511i
$669$	10.7421	−	7.17767i	0.415315	−	0.277505i
$670$	−0.858138	+	0.137249i	−0.0331527	+	0.00530238i
$671$	−29.2592	+	12.1195i	−1.12954	+	0.467870i
$672$	−0.337000	+	0.813590i	−0.0130000	+	0.0313849i
$673$	−9.14587	+	6.11108i	−0.352548	+	0.235565i	−0.719215	−	0.694787i	$-0.755499\pi$
$673$	−9.14587	+	6.11108i	−0.352548	+	0.235565i	0.366668	+	0.930352i	$0.380499\pi$
$674$	−4.48644	−	6.71443i	−0.172811	−	0.258630i
$675$	27.4590	−	3.33438i	1.05690	−	0.128340i
$676$	9.11673	−	9.11673i	0.350644	−	0.350644i
$677$	−1.15687	−	5.81600i	−0.0444623	−	0.223527i	0.952165	−	0.305583i	$-0.0988514\pi$
$677$	−1.15687	−	5.81600i	−0.0444623	−	0.223527i	−0.996628	+	0.0820560i	$0.973851\pi$
$678$	−10.7473	+	4.45166i	−0.412746	+	0.170965i
$679$	7.00265			0.268737
$680$	−9.21906	−	0.0941074i	−0.353535	−	0.00360885i
$681$	−15.2117			−0.582913
$682$	14.0678	−	5.82707i	0.538684	−	0.223130i
$683$	4.12555	+	20.7405i	0.157860	+	0.793615i	0.975860	+	0.218397i	$0.0700828\pi$
$683$	4.12555	+	20.7405i	0.157860	+	0.793615i	−0.818000	+	0.575218i	$0.804917\pi$
$684$	−0.527704	+	0.527704i	−0.0201772	+	0.0201772i
$685$	−9.31421	+	39.0571i	−0.355878	+	1.49229i
$686$	5.32832	+	7.97439i	0.203436	+	0.304464i
$687$	−2.78370	+	1.86001i	−0.106205	+	0.0709637i
$688$	−0.128609	+	0.310490i	−0.00490317	+	0.0118373i
$689$	−1.30908	+	0.542240i	−0.0498721	+	0.0206577i
$690$	1.20823	−	1.66830i	0.0459967	−	0.0635111i
$691$	−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	$0.398232\pi$
$692$	7.12656	+	4.76181i	0.270911	+	0.181017i
$693$			4.87077i			0.185025i
$694$	9.49472	−	14.2098i	0.360415	−	0.539398i
$695$	1.38589	−	36.6902i	0.0525700	−	1.39174i
$696$			8.74722i			0.331563i
$697$	10.5396	−	27.5692i	0.399215	−	1.04426i
$698$	−18.4982	+	18.4982i	−0.700167	+	0.700167i
$699$	−22.3636	−	9.26330i	−0.845868	−	0.350370i
$700$	−2.79724	−	2.19146i	−0.105726	−	0.0828293i
$701$	−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	$-0.533149\pi$
$702$	1.00532	−	1.50457i	0.0379433	−	0.0567862i
$703$	5.47088	+	1.08823i	0.206338	+	0.0410432i
$704$	−4.58953	−	0.912914i	−0.172974	−	0.0344067i
$705$	−8.57802	+	7.95357i	−0.323067	+	0.299549i
$706$	13.0306	+	31.4587i	0.490414	+	1.18397i
$707$	5.70535	+	8.53866i	0.214572	+	0.321129i
$708$	0.963237	−	4.84252i	0.0362006	−	0.181993i
$709$	5.86964	+	29.5087i	0.220439	+	1.10822i	0.919479	+	0.393139i	$0.128611\pi$
$709$	5.86964	+	29.5087i	0.220439	+	1.10822i	−0.699040	+	0.715082i	$0.746389\pi$
$710$	32.8632	−	12.1805i	1.23333	−	0.457125i
$711$	−11.7225	−	7.83275i	−0.439629	−	0.293751i
$712$	−0.202824	−	0.489660i	−0.00760115	−	0.0183508i
$713$	1.71060	+	1.71060i	0.0640623	+	0.0640623i
$714$	−3.07340	−	1.93330i	−0.115019	−	0.0723520i
$715$	1.42818	−	3.11034i	0.0534108	−	0.116320i
$716$	−7.81980	+	18.8787i	−0.292240	+	0.705529i
$717$	30.8565	−	6.13774i	1.15236	−	0.229218i
$718$	−1.96156			−0.0732047
$719$	42.2633	−	8.40669i	1.57616	−	0.313517i	0.671944	−	0.740602i	$-0.265460\pi$
$719$	42.2633	−	8.40669i	1.57616	−	0.313517i	0.904211	+	0.427085i	$0.140460\pi$
$720$	1.92096	−	2.65242i	0.0715901	−	0.0988499i
$721$	−1.61132	+	8.10064i	−0.0600086	+	0.301683i
$722$	17.3138	+	7.17163i	0.644354	+	0.266900i
$723$	−9.17350	−	3.79979i	−0.341166	−	0.141316i
$724$	0.840805	−	4.22701i	0.0312483	−	0.157096i
$725$	−34.0001	−	9.47791i	−1.26273	−	0.352001i
$726$	13.2433	−	2.63426i	0.491505	−	0.0977665i
$727$	22.7691			0.844459			0.422230	−	0.906489i	$-0.361248\pi$
$727$	22.7691			0.844459			0.422230	+	0.906489i	$0.361248\pi$
$728$	−0.227996	+	0.0453512i	−0.00845009	+	0.00168083i
$729$	−9.24917	+	22.3295i	−0.342562	+	0.827018i
$730$	−9.29554	−	25.0796i	−0.344043	−	0.928237i
$731$	−1.17290	−	0.737804i	−0.0433813	−	0.0272887i
$732$	5.92989	+	5.92989i	0.219175	+	0.219175i
$733$	2.78355	+	6.72010i	0.102813	+	0.248212i	0.966912	−	0.255109i	$-0.0821113\pi$
$733$	2.78355	+	6.72010i	0.102813	+	0.248212i	−0.864099	+	0.503321i	$0.832111\pi$
$734$	13.9565	+	9.32545i	0.515145	+	0.344209i
$735$	6.25418	+	16.8739i	0.230689	+	0.622404i
$736$	−0.145038	−	0.729154i	−0.00534616	−	0.0268770i
$737$	0.354802	−	1.78371i	0.0130693	−	0.0657039i
$738$	5.82481	+	8.71745i	0.214414	+	0.320894i
$739$	−19.3452	−	46.7035i	−0.711626	−	1.71802i	−0.695898	−	0.718140i	$-0.744994\pi$
$739$	−19.3452	−	46.7035i	−0.711626	−	1.71802i	−0.0157273	−	0.999876i	$-0.505006\pi$
$740$	−24.4611	−	0.923968i	−0.899209	−	0.0339657i
$741$	0.202553	+	0.0402902i	0.00744095	+	0.00148010i
$742$	−3.01950	−	0.600615i	−0.110849	−	0.0220493i
$743$	−13.1834	+	19.7303i	−0.483651	+	0.723835i	−0.990396	−	0.138261i	$-0.955849\pi$
$743$	−13.1834	+	19.7303i	−0.483651	+	0.723835i	0.506745	+	0.862096i	$0.330849\pi$
$744$	−2.85109	−	2.85109i	−0.104526	−	0.104526i
$745$	−2.95386	+	12.3864i	−0.108221	+	0.453801i
$746$	6.75020	+	2.79603i	0.247143	+	0.102370i
$747$	13.0001	−	13.0001i	0.475648	−	0.475648i
$748$	6.88965	−	18.0218i	0.251911	−	0.658942i
$749$			6.83007i			0.249565i
$750$	−8.62607	−	10.8404i	−0.314979	−	0.395836i
$751$	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	$0.0122457\pi$
$752$			4.22197i			0.153959i
$753$	21.4725	+	14.3475i	0.782501	+	0.522850i
$754$	−1.91990	+	1.28284i	−0.0699188	+	0.0467183i
$755$	3.77542	+	23.6055i	0.137401	+	0.859093i
$756$	3.63236	−	1.50457i	0.132108	−	0.0547208i
$757$	−4.12913	+	9.96860i	−0.150076	+	0.362315i	−0.980982	−	0.194097i	$-0.937822\pi$
$757$	−4.12913	+	9.96860i	−0.150076	+	0.362315i	0.830907	+	0.556412i	$0.187822\pi$
$758$	29.7973	−	19.9099i	1.08229	−	0.723162i
$759$	2.39490	+	3.58422i	0.0869294	+	0.130099i
$760$	1.10830	+	0.264304i	0.0402022	+	0.00958730i
$761$	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	$0.108225\pi$
$762$	−0.247200	−	1.24276i	−0.00895511	−	0.0450204i
$763$	3.14053	−	1.30085i	0.113695	−	0.0470939i
$764$	16.2205			0.586836
$765$	9.45014	+	9.64507i	0.341671	+	0.348718i
$766$	16.5450			0.597796
$767$	1.20414	−	0.498770i	0.0434788	−	0.0180095i
$768$	0.241738	+	1.21530i	0.00872297	+	0.0438533i
$769$	−11.7131	+	11.7131i	−0.422384	+	0.422384i	−0.886024	−	0.463640i	$-0.846543\pi$
$769$	−11.7131	+	11.7131i	−0.422384	+	0.422384i	0.463640	+	0.886024i	$0.346543\pi$
$770$	6.33464	−	3.89508i	0.228285	−	0.140369i
$771$	5.86655	+	8.77991i	0.211279	+	0.316201i
$772$	0.0465946	−	0.0311335i	0.00167698	−	0.00112052i
$773$	−8.01916	+	19.3600i	−0.288429	+	0.696329i	−0.999980	−	0.00630500i	$-0.997993\pi$
$773$	−8.01916	+	19.3600i	−0.288429	+	0.696329i	0.711551	+	0.702634i	$0.247993\pi$
$774$	0.454747	−	0.188362i	0.0163455	−	0.00677054i
$775$	14.1713	−	7.99283i	0.509050	−	0.287111i
$776$	8.19271	−	5.47419i	0.294101	−	0.196512i
$777$	−8.01563	−	5.35587i	−0.287559	−	0.192141i
$778$			18.7827i			0.673392i
$779$	−2.02648	+	3.03284i	−0.0726061	+	0.108663i
$780$	−0.905642	−	0.0342087i	−0.0324272	−	0.00122487i
$781$			73.3450i			2.62449i
$782$	3.06411	−	0.0844297i	0.109573	−	0.00301920i
$783$	27.6146	−	27.6146i	0.986866	−	0.986866i
$784$	6.00052	+	2.48550i	0.214304	+	0.0887678i
$785$	30.6745	−	18.8614i	1.09482	−	0.673191i
$786$	−17.5560	−	17.5560i	−0.626202	−	0.626202i
$787$	−7.31354	+	10.9455i	−0.260700	+	0.390164i	−0.938610	−	0.344980i	$-0.887886\pi$
$787$	−7.31354	+	10.9455i	−0.260700	+	0.390164i	0.677910	+	0.735144i	$0.262886\pi$
$788$	−3.63792	−	0.723626i	−0.129595	−	0.0257781i
$789$	−26.9050	−	5.35174i	−0.957844	−	0.190527i
$790$	−0.812472	+	21.5094i	−0.0289065	+	0.765270i
$791$	−2.55325	−	6.16410i	−0.0907832	−	0.219170i
$792$	3.80764	+	5.69853i	0.135298	+	0.202488i
$793$	−0.431877	+	2.17119i	−0.0153364	+	0.0771013i
$794$	−1.60682	−	8.07804i	−0.0570240	−	0.286679i
$795$	−10.9076	−	5.00847i	−0.386854	−	0.177632i
$796$	5.52389	+	3.69094i	0.195789	+	0.130822i
$797$	−6.38819	−	15.4224i	−0.226281	−	0.546291i	0.769438	−	0.638722i	$-0.220536\pi$
$797$	−6.38819	−	15.4224i	−0.226281	−	0.546291i	−0.995719	+	0.0924305i	$0.970536\pi$
$798$	0.317291	+	0.317291i	0.0112320	+	0.0112320i
$799$	−17.1602	−	2.92451i	−0.607084	−	0.103462i
$800$	−4.98575	−	0.377191i	−0.176273	−	0.0133357i
$801$	−0.297058	+	0.717163i	−0.0104960	+	0.0253397i
$802$	7.93345	−	1.57806i	0.280140	−	0.0557233i
$803$	55.9734			1.97526
$804$	−0.472324	+	0.0939510i	−0.0166576	+	0.00331340i
$805$	0.956855	+	0.692984i	0.0337247	+	0.0244245i
$806$	0.207647	−	1.04391i	0.00731404	−	0.0367702i
$807$	−27.2332	−	11.2804i	−0.958655	−	0.397088i
$808$	13.3499	+	5.52971i	0.469648	+	0.194534i
$809$	1.40383	−	7.05754i	0.0493561	−	0.248130i	−0.948229	−	0.317588i	$-0.897127\pi$
$809$	1.40383	−	7.05754i	0.0493561	−	0.248130i	0.997585	+	0.0694582i	$0.0221271\pi$
$810$	5.43407	−	0.869113i	0.190934	−	0.0305375i
$811$	−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	$0.495599\pi$
$812$	−5.01698			−0.176061
$813$	25.3015	−	5.03278i	0.887362	−	0.176507i
$814$	19.6036	−	47.3272i	0.687104	−	1.65882i
$815$	−44.6751	−	20.5135i	−1.56490	−	0.718556i
$816$	−5.10703	+	0.140721i	−0.178782	+	0.00492622i
$817$	0.121087	+	0.121087i	0.00423632	+	0.00423632i
$818$	−2.30058	−	5.55409i	−0.0804378	−	0.194194i
$819$	0.283088	+	0.189154i	0.00989191	+	0.00660956i
$820$	6.67939	−	14.5466i	0.233254	−	0.507990i
$821$	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	$0.687795\pi$
$822$	−4.34081	+	21.8227i	−0.151403	+	0.761154i
$823$	22.4842	+	33.6500i	0.783751	+	1.17297i	0.981264	+	0.192666i	$0.0617133\pi$
$823$	22.4842	+	33.6500i	0.783751	+	1.17297i	−0.197514	+	0.980300i	$0.563287\pi$
$824$	4.44738	+	10.7369i	0.154932	+	0.374038i
$825$	27.5454	−	9.04242i	0.959009	−	0.314817i
$826$	2.77743	+	0.552465i	0.0966391	+	0.0192227i
$827$	44.2399	+	8.79987i	1.53837	+	0.306001i	0.890228	−	0.455515i	$-0.150545\pi$
$827$	44.2399	+	8.79987i	1.53837	+	0.306001i	0.648145	+	0.761517i	$0.275545\pi$
$828$	−0.604932	+	0.905345i	−0.0210229	+	0.0314629i
$829$	3.20565	+	3.20565i	0.111337	+	0.111337i	0.760580	−	0.649244i	$-0.224914\pi$
$829$	3.20565	+	3.20565i	0.111337	+	0.111337i	−0.649244	+	0.760580i	$0.724914\pi$
$830$	−27.3031	−	6.51117i	−0.947706	−	0.226006i
$831$	−4.58563	−	1.89943i	−0.159074	−	0.0658905i
$832$	−0.231290	+	0.231290i	−0.00801854	+	0.00801854i
$833$	−14.2588	+	22.6675i	−0.494038	+	0.785381i
$834$		−	20.3462i		−	0.704531i
$835$	−27.1948	+	25.2151i	−0.941113	+	0.872604i
$836$	−1.32469	+	1.98254i	−0.0458155	+	0.0685677i
$837$			18.0015i			0.622224i
$838$	−5.17603	−	3.45852i	−0.178803	−	0.119472i
$839$	5.29222	−	3.53615i	0.182708	−	0.122081i	−0.460853	−	0.887477i	$-0.652456\pi$
$839$	5.29222	−	3.53615i	0.182708	−	0.122081i	0.643561	+	0.765395i	$0.277456\pi$
$840$	−1.59481	−	1.15501i	−0.0550263	−	0.0398517i
$841$	−19.2477	+	7.97267i	−0.663715	+	0.274920i
$842$	−9.81852	+	23.7040i	−0.338369	+	0.816894i
$843$	14.9684	−	10.0016i	0.515539	−	0.344472i
$844$	−9.75666	−	14.6019i	−0.335838	−	0.502617i
$845$	15.1007	+	24.5585i	0.519479	+	0.844837i
$846$	4.37243	−	4.37243i	0.150327	−	0.150327i
$847$	1.51088	+	7.59571i	0.0519145	+	0.260992i
$848$	−4.00217	+	1.65775i	−0.137435	+	0.0569274i
$849$	15.7299			0.539847
$850$	4.98667	−	20.0033i	0.171041	−	0.686109i
$851$	8.13854			0.278986
$852$	17.9432	−	7.43234i	0.614726	−	0.254628i
$853$	−4.89959	−	24.6319i	−0.167759	−	0.843381i	−0.969383	−	0.245553i	$-0.921031\pi$
$853$	−4.89959	−	24.6319i	−0.167759	−	0.843381i	0.801624	−	0.597828i	$-0.203969\pi$
$854$	−3.40109	+	3.40109i	−0.116383	+	0.116383i
$855$	−0.874071	−	1.42152i	−0.0298926	−	0.0486148i
$856$	5.33929	+	7.99081i	0.182493	+	0.273120i
$857$	29.5811	−	19.7655i	1.01047	−	0.675175i	0.0639953	−	0.997950i	$-0.479616\pi$
$857$	29.5811	−	19.7655i	1.01047	−	0.675175i	0.946476	+	0.322775i	$0.104616\pi$
$858$	0.725797	−	1.75223i	0.0247783	−	0.0598201i
$859$	−21.0814	+	8.73222i	−0.719289	+	0.297939i	−0.712142	−	0.702035i	$-0.752275\pi$
$859$	−21.0814	+	8.73222i	−0.719289	+	0.297939i	−0.00714690	+	0.999974i	$0.502275\pi$
$860$	−0.608628	−	0.440787i	−0.0207540	−	0.0150307i
$861$	5.24151	−	3.50227i	0.178630	−	0.119357i
$862$	−30.7805	−	20.5669i	−1.04839	−	0.700510i
$863$		−	25.2963i		−	0.861095i	−0.902568	−	0.430548i	$-0.858320\pi$
$863$		−	25.2963i		−	0.861095i	0.902568	−	0.430548i	$-0.141680\pi$
$864$	3.07349	−	4.59980i	0.104562	−	0.156488i
$865$	−14.0539	+	13.0308i	−0.477846	+	0.443061i
$866$			7.30274i			0.248157i
$867$	2.96562	−	20.8550i	0.100718	−	0.708274i
$868$	1.63525	−	1.63525i	0.0555038	−	0.0555038i
$869$	−41.6162	−	17.2380i	−1.41173	−	0.584758i
$870$	−19.0259	−	4.53723i	−0.645037	−	0.153826i
$871$	−0.0898905	−	0.0898905i	−0.00304582	−	0.00304582i
$872$	2.65733	−	3.97698i	0.0899886	−	0.134677i
$873$	−14.1540	−	2.81540i	−0.479039	−	0.0952867i
$874$	−0.371537	−	0.0739032i	−0.0125674	−	0.00249981i
$875$	6.21753	−	4.94749i	0.210191	−	0.167256i
$876$	−5.67200	−	13.6934i	−0.191639	−	0.462658i
$877$	7.20665	+	10.7855i	0.243351	+	0.364201i	0.932959	−	0.359982i	$-0.117217\pi$
$877$	7.20665	+	10.7855i	0.243351	+	0.364201i	−0.689608	+	0.724183i	$0.742217\pi$
$878$	−6.13999	+	30.8678i	−0.207214	+	1.04174i
$879$	2.01615	+	10.1358i	0.0680029	+	0.341874i
$880$	4.36627	−	9.50903i	0.147187	−	0.320549i
$881$	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	$0.611141\pi$
$882$	−3.64029	−	8.78844i	−0.122575	−	0.295922i
$883$	2.99147	+	2.99147i	0.100671	+	0.100671i	0.755648	−	0.654977i	$-0.227322\pi$
$883$	2.99147	+	2.99147i	0.100671	+	0.100671i	−0.654977	+	0.755648i	$0.727322\pi$
$884$	−0.779867	−	1.10029i	−0.0262298	−	0.0370068i
$885$	10.0332	+	4.60695i	0.337262	+	0.154861i
$886$	−6.37440	+	15.3892i	−0.214152	+	0.517009i
$887$	39.1177	−	7.78099i	1.31344	−	0.261260i	0.511822	−	0.859092i	$-0.328971\pi$
$887$	39.1177	−	7.78099i	1.31344	−	0.261260i	0.801622	+	0.597831i	$0.203971\pi$
$888$	−13.5647			−0.455202
$889$	0.712785	−	0.141782i	0.0239060	−	0.00475521i
$890$	1.17025	−	0.187168i	0.0392270	−	0.00627388i
$891$	−2.24675	+	11.2952i	−0.0752690	+	0.378403i
$892$	9.63276	+	3.99002i	0.322529	+	0.133596i
$893$	1.98753	+	0.823260i	0.0665100	+	0.0275494i
$894$	−1.37662	+	6.92075i	−0.0460411	+	0.231464i
$895$	−37.0063	−	26.8011i	−1.23698	−	0.895862i
$896$	−0.697035	+	0.138649i	−0.0232863	+	0.00463194i
$897$	0.301319			0.0100608
$898$	15.7553	−	3.13392i	0.525760	−	0.104580i
$899$	8.79058	−	21.2223i	0.293182	−	0.707805i
$900$	4.77280	+	5.55406i	0.159093	+	0.185135i
$901$	−3.96568	−	17.4151i	−0.132116	−	0.580182i
$902$	23.6864	+	23.6864i	0.788671	+	0.788671i
$903$	−0.113256	−	0.273424i	−0.00376893	−	0.00909899i
$904$	−7.80584	−	5.21569i	−0.259618	−	0.173471i
$905$	8.75794	+	4.02139i	0.291124	+	0.133675i
$906$	2.58439	+	12.9926i	0.0858607	+	0.431651i
$907$	−0.756884	+	3.80511i	−0.0251319	+	0.126347i	−0.991315	−	0.131512i	$-0.958017\pi$
$907$	−0.756884	+	3.80511i	−0.0251319	+	0.126347i	0.966183	+	0.257859i	$0.0830169\pi$
$908$	−6.82036	−	10.2074i	−0.226342	−	0.338744i
$909$	−8.09888	−	19.5524i	−0.268623	−	0.648513i
$910$	0.0196204	−	0.519432i	0.000650411	−	0.0172190i
$911$	−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	$0.679139\pi$
$912$	0.619249	+	0.123176i	0.0205054	+	0.00407878i
$913$	32.6341	−	48.8404i	1.08003	−	1.61638i
$914$	−5.98568	−	5.98568i	−0.197989	−	0.197989i
$915$	−15.9738	+	9.82208i	−0.528078	+	0.324708i
$916$	−2.49621	−	1.03397i	−0.0824772	−	0.0341632i
$917$	10.0693	−	10.0693i	0.332516	−	0.332516i
$918$	16.5669	+	15.6784i	0.546790	+	0.517466i
$919$			21.0567i			0.694597i	0.937755	+	0.347298i	$0.112901\pi$
$919$			21.0567i			0.694597i	−0.937755	+	0.347298i	$0.887099\pi$
$920$	1.66120	+	0.0627482i	0.0547680	+	0.00206875i
$921$	0.0867999	−	0.129905i	0.00286015	−	0.00428052i
$922$			33.5640i			1.10537i
$923$	4.26280	+	2.84831i	0.140312	+	0.0937534i
$924$	3.42634	−	2.28941i	0.112718	−	0.0753159i
$925$	14.6978	−	52.7255i	0.483261	−	1.73360i
$926$	−5.28643	+	2.18971i	−0.173723	+	0.0719584i
$927$	6.51368	−	15.7254i	0.213937	−	0.516491i
$928$	−5.86959	+	3.92193i	−0.192679	+	0.128744i
$929$	−15.1360	−	22.6526i	−0.496595	−	0.743207i	0.495512	−	0.868601i	$-0.334980\pi$
$929$	−15.1360	−	22.6526i	−0.496595	−	0.743207i	−0.992107	+	0.125394i	$0.959980\pi$
$930$	7.68021	−	4.72246i	0.251844	−	0.154855i
$931$	2.34014	−	2.34014i	0.0766949	−	0.0766949i
$932$	−3.81112	−	19.1598i	−0.124837	−	0.627600i
$933$	−10.9571	+	4.53859i	−0.358720	+	0.148587i
$934$	−37.1440			−1.21539
$935$	35.6250	+	24.3335i	1.16506	+	0.795790i
$936$	0.479065			0.0156587
$937$	−15.7890	+	6.54003i	−0.515805	+	0.213653i	−0.625373	−	0.780326i	$-0.715053\pi$
$937$	−15.7890	+	6.54003i	−0.515805	+	0.213653i	0.109568	+	0.993979i	$0.465053\pi$
$938$	−0.0538857	−	0.270902i	−0.00175943	−	0.00884525i
$939$	15.2449	−	15.2449i	0.497498	−	0.497498i
$940$	−9.18309	−	2.18996i	−0.299519	−	0.0714285i
$941$	−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	$0.840656\pi$
$942$	16.5915	−	11.0861i	0.540582	−	0.361205i
$943$	−2.03660	+	4.91678i	−0.0663208	+	0.160112i
$944$	3.68132	−	1.52485i	0.119817	−	0.0496297i
$945$	1.38843	+	8.68108i	0.0451657	+	0.282396i
$946$	1.30759	−	0.873705i	0.0425135	−	0.0284066i
$947$	4.92140	+	3.28837i	0.159924	+	0.106858i	0.632957	−	0.774187i	$-0.281841\pi$
$947$	4.92140	+	3.28837i	0.159924	+	0.106858i	−0.473033	+	0.881045i	$0.656841\pi$
$948$			11.9278i			0.387398i
$949$	2.17369	−	3.25316i	0.0705611	−	0.105602i
$950$	−1.14976	+	2.27353i	−0.0373031	+	0.0737632i
$951$		−	24.8206i		−	0.804863i
$952$	−0.0807107	−	2.92914i	−0.00261585	−	0.0949341i
$953$	−15.4098	+	15.4098i	−0.499172	+	0.499172i	−0.911180	−	0.412008i	$-0.864827\pi$
$953$	−15.4098	+	15.4098i	−0.499172	+	0.499172i	0.412008	+	0.911180i	$0.364827\pi$
$954$	5.86162	+	2.42796i	0.189777	+	0.0786082i
$955$	−8.41364	+	35.2807i	−0.272259	+	1.14166i
$956$	17.9535	+	17.9535i	0.580657	+	0.580657i
$957$	22.7407	−	34.0338i	0.735101	−	1.10016i
$958$	18.9883	+	3.77700i	0.613484	+	0.122029i
$959$	−12.5164	−	2.48967i	−0.404177	−	0.0803957i
$960$	−2.76875	−	0.104584i	−0.0893612	−	0.00337543i
$961$	−7.81115	−	18.8578i	−0.251973	−	0.608315i
$962$	−1.98935	−	2.97728i	−0.0641394	−	0.0959914i
$963$	2.74601	−	13.8051i	0.0884890	−	0.444864i
$964$	−1.56331	−	7.85931i	−0.0503510	−	0.253131i
$965$	0.0435488	+	0.117496i	0.00140189	+	0.00378233i
$966$	0.544354	+	0.363726i	0.0175143	+	0.0117027i
$967$	17.7739	+	42.9099i	0.571569	+	1.37989i	0.900219	+	0.435438i	$0.143407\pi$
$967$	17.7739	+	42.9099i	0.571569	+	1.37989i	−0.328649	+	0.944452i	$0.606593\pi$
$968$	7.70546	+	7.70546i	0.247663	+	0.247663i
$969$	−0.929597	+	2.43162i	−0.0298630	+	0.0781148i
$970$	7.65717	+	20.6592i	0.245857	+	0.663328i
$971$	−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	$0.218630\pi$
$972$	−13.2866	+	2.64286i	−0.426167	+	0.0847699i
$973$	11.6696			0.374110
$974$	1.95796	−	0.389463i	0.0627372	−	0.0124792i
$975$	0.544168	−	1.95209i	0.0174273	−	0.0625170i
$976$	−1.32035	+	6.63783i	−0.0422633	+	0.212472i
$977$	11.5625	+	4.78935i	0.369917	+	0.153225i	0.559895	−	0.828564i	$-0.310842\pi$
$977$	11.5625	+	4.78935i	0.369917	+	0.153225i	−0.189978	+	0.981788i	$0.560842\pi$
$978$	−25.1679	−	10.4249i	−0.804782	−	0.333352i
$979$	−0.483849	+	2.43247i	−0.0154639	+	0.0777421i
$980$	−8.51864	+	11.7623i	−0.272118	+	0.375734i
$981$	−6.87074	+	1.36667i	−0.219366	+	0.0436346i
$982$	−20.3744			−0.650172
$983$	−52.3512	+	10.4133i	−1.66974	+	0.332132i	−0.937254	−	0.348647i	$-0.886641\pi$
$983$	−52.3512	+	10.4133i	−1.66974	+	0.332132i	−0.732489	+	0.680779i	$0.761641\pi$
$984$	3.39445	−	8.19492i	0.108211	−	0.261245i
$985$	3.46095	−	7.53738i	0.110275	−	0.240161i
$986$	−11.8749	−	26.5736i	−0.378174	−	0.846277i
$987$	−2.62900	−	2.62900i	−0.0836819	−	0.0836819i
$988$	0.0637814	+	0.153982i	0.00202916	+	0.00489882i
$989$	0.207742	+	0.138809i	0.00660580	+	0.00441385i
$990$	−14.3698	+	5.32603i	−0.456701	+	0.169272i
$991$	−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	$-0.213487\pi$
$992$	0.634823	−	3.19147i	0.0201557	−	0.101329i
$993$	−9.95958	−	14.9056i	−0.316058	−	0.473014i
$994$	4.26282	+	10.2914i	0.135209	+	0.326422i
$995$	−10.8933	+	10.1003i	−0.345342	+	0.320202i
$996$	−15.2553	−	3.03448i	−0.483384	−	0.0961510i
$997$	−20.8465	−	4.14662i	−0.660215	−	0.131325i	−0.146399	−	0.989226i	$-0.546768\pi$
$997$	−20.8465	−	4.14662i	−0.660215	−	0.131325i	−0.513815	+	0.857901i	$0.671768\pi$
$998$	−8.62482	+	12.9080i	−0.273014	+	0.408594i
$999$	42.8232	+	42.8232i	1.35487	+	1.35487i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.o (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(-0.241738 - 1.21530i) q^{3} +(0.707107 - 0.707107i) q^{4} +(1.17123 + 1.90479i) q^{5} +(0.688411 + 1.03028i) q^{6} +(-0.590918 + 0.394839i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(1.35312 - 0.560483i) q^{9} +(-1.81101 - 1.31159i) q^{10} +(3.89081 - 2.59976i) q^{11} +(-1.03028 - 0.688411i) q^{12} -0.327094i q^{13} +(0.394839 - 0.590918i) q^{14} +(2.03176 - 1.88385i) q^{15} -1.00000i q^{16} +(4.06450 + 0.692689i) q^{17} +(-1.03564 + 1.03564i) q^{18} +(-0.470758 - 0.194994i) q^{19} +(2.17507 + 0.518705i) q^{20} +(0.622694 + 0.622694i) q^{21} +(-2.59976 + 3.89081i) q^{22} +(-0.729154 - 0.145038i) q^{23} +(1.21530 + 0.241738i) q^{24} +(-2.25644 + 4.46189i) q^{25} +(0.125173 + 0.302195i) q^{26} +(-3.07349 - 4.59980i) q^{27} +(-0.138649 + 0.697035i) q^{28} +(1.37720 + 6.92365i) q^{29} +(-1.15618 + 2.51797i) q^{30} +(-2.70560 - 1.80782i) q^{31} +(0.382683 + 0.923880i) q^{32} +(-4.10004 - 4.10004i) q^{33} +(-4.02019 + 0.915457i) q^{34} +(-1.44419 - 0.663128i) q^{35} +(0.560483 - 1.35312i) q^{36} +(-10.7368 + 2.13568i) q^{37} +0.509545 q^{38} +(-0.397517 + 0.0790710i) q^{39} +(-2.20801 + 0.353144i) q^{40} +(1.39655 - 7.02092i) q^{41} +(-0.813590 - 0.337000i) q^{42} +(-0.310490 - 0.128609i) q^{43} +(0.912914 - 4.58953i) q^{44} +(2.65242 + 1.92096i) q^{45} +(0.729154 - 0.145038i) q^{46} -4.22197 q^{47} +(-1.21530 + 0.241738i) q^{48} +(-2.48550 + 6.00052i) q^{49} +(0.377191 - 4.98575i) q^{50} +(-0.140721 - 5.10703i) q^{51} +(-0.231290 - 0.231290i) q^{52} +(-1.65775 - 4.00217i) q^{53} +(4.59980 + 3.07349i) q^{54} +(9.50903 + 4.36627i) q^{55} +(-0.138649 - 0.697035i) q^{56} +(-0.123176 + 0.619249i) q^{57} +(-3.92193 - 5.86959i) q^{58} +(1.52485 + 3.68132i) q^{59} +(0.104584 - 2.76875i) q^{60} +(-6.63783 - 1.32035i) q^{61} +(3.19147 + 0.634823i) q^{62} +(-0.578286 + 0.865466i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(0.623045 - 0.383102i) q^{65} +(5.35696 + 2.21893i) q^{66} +(0.274816 - 0.274816i) q^{67} +(3.36384 - 2.38423i) q^{68} +0.921201i q^{69} +(1.58802 + 0.0599842i) q^{70} +(-8.70794 + 13.0324i) q^{71} +1.46461i q^{72} +(9.94566 + 6.64548i) q^{73} +(9.10222 - 6.08191i) q^{74} +(5.96800 + 1.66364i) q^{75} +(-0.470758 + 0.194994i) q^{76} +(-1.27267 + 3.07249i) q^{77} +(0.336998 - 0.225175i) q^{78} +(-5.34800 - 8.00385i) q^{79} +(1.90479 - 1.17123i) q^{80} +(-1.74024 + 1.74024i) q^{81} +(1.39655 + 7.02092i) q^{82} +(11.5972 - 4.80373i) q^{83} +0.880623 q^{84} +(3.44104 + 8.55332i) q^{85} +0.336072 q^{86} +(8.08138 - 3.34742i) q^{87} +(0.912914 + 4.58953i) q^{88} +(-0.374770 + 0.374770i) q^{89} +(-3.18564 - 0.759702i) q^{90} +(0.129149 + 0.193286i) q^{91} +(-0.618147 + 0.413033i) q^{92} +(-1.54300 + 3.72513i) q^{93} +(3.90059 - 1.61568i) q^{94} +(-0.179942 - 1.12508i) q^{95} +(1.03028 - 0.688411i) q^{96} +(-8.19271 - 5.47419i) q^{97} -6.49492i q^{98} +(3.80764 - 5.69853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{10} - 40 q^{15} + 16 q^{18} + 8 q^{20} - 8 q^{25} + 8 q^{26} - 72 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} - 64 q^{33} - 24 q^{34} + 32 q^{35} + 16 q^{37} + 32 q^{39} - 8 q^{40} + 16 q^{41}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^10 - 40 * q^15 + 16 * q^18 + 8 * q^20 - 8 * q^25 + 8 * q^26 - 72 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 - 64 * q^33 - 24 * q^34 + 32 * q^35 + 16 * q^37 + 32 * q^39 - 8 * q^40 + 16 * q^41 - 40 * q^42 + 48 * q^43 + 16 * q^44 + 24 * q^45 - 64 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 16 * q^52 - 24 * q^54 + 8 * q^55 + 8 * q^56 - 8 * q^57 - 16 * q^58 + 64 * q^59 - 48 * q^60 - 24 * q^61 - 24 * q^62 - 24 * q^63 - 16 * q^65 - 16 * q^67 - 16 * q^68 + 24 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 - 8 * q^75 + 40 * q^77 + 48 * q^78 - 72 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 - 8 * q^85 - 64 * q^86 + 24 * q^87 + 16 * q^88 - 16 * q^89 + 48 * q^90 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 + 40 * q^95 + 16 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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