LMFDB - Embedded newform 85.2.l.a.26.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			26.6
Character	$\chi$	$=$	85.26
Dual form			85.2.l.a.36.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.66305 - 1.66305i) q^{2} +(-1.44989 - 0.600564i) q^{3} -3.53144i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-3.41000 + 1.41247i) q^{6} +(1.37082 + 3.30945i) q^{7} +(-2.54686 - 2.54686i) q^{8} +(-0.379815 - 0.379815i) q^{9} +(0.900034 + 2.17287i) q^{10} +(2.29362 - 0.950048i) q^{11} +(-2.12086 + 5.12021i) q^{12} -1.25948i q^{13} +(7.78350 + 3.22403i) q^{14} +(1.10970 - 1.10970i) q^{15} -1.40821 q^{16} +(-3.84535 + 1.48772i) q^{17} -1.26330 q^{18} +(-2.56985 + 2.56985i) q^{19} +(3.26263 + 1.35142i) q^{20} -5.62161i q^{21} +(2.23442 - 5.39437i) q^{22} +(-8.16056 + 3.38021i) q^{23} +(2.16312 + 5.22222i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-2.09458 - 2.09458i) q^{26} +(2.12428 + 5.12847i) q^{27} +(11.6871 - 4.84097i) q^{28} +(3.35200 - 8.09244i) q^{29} -3.69096i q^{30} +(2.25799 + 0.935290i) q^{31} +(2.75181 - 2.75181i) q^{32} -3.89606 q^{33} +(-3.92084 + 8.86913i) q^{34} -3.58212 q^{35} +(-1.34129 + 1.34129i) q^{36} +(-4.25128 - 1.76094i) q^{37} +8.54755i q^{38} +(-0.756400 + 1.82611i) q^{39} +(3.32763 - 1.37835i) q^{40} +(-1.65510 - 3.99575i) q^{41} +(-9.34899 - 9.34899i) q^{42} +(5.33668 + 5.33668i) q^{43} +(-3.35504 - 8.09978i) q^{44} +(0.496252 - 0.205554i) q^{45} +(-7.94993 + 19.1928i) q^{46} -11.3322i q^{47} +(2.04175 + 0.845719i) q^{48} +(-4.12357 + 4.12357i) q^{49} -2.35190 q^{50} +(6.46880 + 0.152348i) q^{51} -4.44779 q^{52} +(4.02442 - 4.02442i) q^{53} +(12.0616 + 4.99610i) q^{54} +2.48259i q^{55} +(4.93742 - 11.9200i) q^{56} +(5.26936 - 2.18264i) q^{57} +(-7.88357 - 19.0326i) q^{58} +(3.16077 + 3.16077i) q^{59} +(-3.91884 - 3.91884i) q^{60} +(0.0929426 + 0.224383i) q^{61} +(5.31057 - 2.19971i) q^{62} +(0.736321 - 1.77764i) q^{63} -11.9692i q^{64} +(1.16361 + 0.481983i) q^{65} +(-6.47933 + 6.47933i) q^{66} +7.23278 q^{67} +(5.25380 + 13.5796i) q^{68} +13.8620 q^{69} +(-5.95724 + 5.95724i) q^{70} +(-1.69789 - 0.703290i) q^{71} +1.93467i q^{72} +(-2.09426 + 5.05599i) q^{73} +(-9.99859 + 4.14155i) q^{74} +(0.600564 + 1.44989i) q^{75} +(9.07527 + 9.07527i) q^{76} +(6.28827 + 6.28827i) q^{77} +(1.77898 + 4.29484i) q^{78} +(-8.34789 + 3.45781i) q^{79} +(0.538897 - 1.30101i) q^{80} -7.10006i q^{81} +(-9.39762 - 3.89262i) q^{82} +(-5.17302 + 5.17302i) q^{83} -19.8524 q^{84} +(0.0970771 - 4.12196i) q^{85} +17.7503 q^{86} +(-9.72006 + 9.72006i) q^{87} +(-8.26117 - 3.42189i) q^{88} +2.19350i q^{89} +(0.483443 - 1.16714i) q^{90} +(4.16819 - 1.72652i) q^{91} +(11.9370 + 28.8186i) q^{92} +(-2.71214 - 2.71214i) q^{93} +(-18.8459 - 18.8459i) q^{94} +(-1.39079 - 3.35767i) q^{95} +(-5.64246 + 2.33718i) q^{96} +(-3.75810 + 9.07286i) q^{97} +13.7154i q^{98} +(-1.23199 - 0.510308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	1.66305	−	1.66305i	1.17595	−	1.17595i	0.195185	−	0.980767i	$-0.437469\pi$
$2$	1.66305	−	1.66305i	1.17595	−	1.17595i	0.980767	−	0.195185i	$-0.0625306\pi$
$3$	−1.44989	−	0.600564i	−0.837095	−	0.346736i	−0.0773874	−	0.997001i	$-0.524658\pi$
$3$	−1.44989	−	0.600564i	−0.837095	−	0.346736i	−0.759707	+	0.650265i	$0.774658\pi$
$4$		−	3.53144i		−	1.76572i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$6$	−3.41000	+	1.41247i	−1.39213	+	0.576638i
$7$	1.37082	+	3.30945i	0.518121	+	1.25085i	0.939056	+	0.343764i	$0.111702\pi$
$7$	1.37082	+	3.30945i	0.518121	+	1.25085i	−0.420935	+	0.907091i	$0.638298\pi$
$8$	−2.54686	−	2.54686i	−0.900451	−	0.900451i
$9$	−0.379815	−	0.379815i	−0.126605	−	0.126605i
$10$	0.900034	+	2.17287i	0.284616	+	0.687123i
$11$	2.29362	−	0.950048i	0.691552	−	0.286450i	−0.00909468	−	0.999959i	$-0.502895\pi$
$11$	2.29362	−	0.950048i	0.691552	−	0.286450i	0.700647	+	0.713508i	$0.252895\pi$
$12$	−2.12086	+	5.12021i	−0.612239	+	1.47808i
$13$		−	1.25948i		−	0.349317i	−0.984629	−	0.174659i	$-0.944118\pi$
$13$		−	1.25948i		−	0.349317i	0.984629	−	0.174659i	$-0.0558822\pi$
$14$	7.78350	+	3.22403i	2.08023	+	0.861659i
$15$	1.10970	−	1.10970i	0.286523	−	0.286523i
$16$	−1.40821			−0.352052
$17$	−3.84535	+	1.48772i	−0.932634	+	0.360825i
$17$	−3.84535	+	1.48772i	−0.932634	+	0.360825i
$18$	−1.26330			−0.297762
$19$	−2.56985	+	2.56985i	−0.589563	+	0.589563i	−0.937513	−	0.347950i	$-0.886878\pi$
$19$	−2.56985	+	2.56985i	−0.589563	+	0.589563i	0.347950	+	0.937513i	$0.386878\pi$
$20$	3.26263	+	1.35142i	0.729546	+	0.302188i
$21$		−	5.62161i		−	1.22674i
$22$	2.23442	−	5.39437i	0.476380	−	1.15008i
$23$	−8.16056	+	3.38021i	−1.70159	+	0.704823i	−0.999970	−	0.00772401i	$-0.997541\pi$
$23$	−8.16056	+	3.38021i	−1.70159	+	0.704823i	−0.701624	+	0.712547i	$0.747541\pi$
$24$	2.16312	+	5.22222i	0.441544	+	1.06598i
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	−2.09458	−	2.09458i	−0.410780	−	0.410780i
$27$	2.12428	+	5.12847i	0.408818	+	0.986974i
$28$	11.6871	−	4.84097i	2.20866	−	0.914857i
$29$	3.35200	−	8.09244i	0.622451	−	1.50273i	−0.226367	−	0.974042i	$-0.572685\pi$
$29$	3.35200	−	8.09244i	0.622451	−	1.50273i	0.848817	−	0.528686i	$-0.177315\pi$
$30$		−	3.69096i		−	0.673874i
$31$	2.25799	+	0.935290i	0.405547	+	0.167983i	0.576126	−	0.817361i	$-0.304564\pi$
$31$	2.25799	+	0.935290i	0.405547	+	0.167983i	−0.170579	+	0.985344i	$0.554564\pi$
$32$	2.75181	−	2.75181i	0.486456	−	0.486456i
$33$	−3.89606			−0.678217
$34$	−3.92084	+	8.86913i	−0.672419	+	1.52104i
$35$	−3.58212			−0.605489
$36$	−1.34129	+	1.34129i	−0.223549	+	0.223549i
$37$	−4.25128	−	1.76094i	−0.698906	−	0.289496i	0.00479925	−	0.999988i	$-0.498472\pi$
$37$	−4.25128	−	1.76094i	−0.698906	−	0.289496i	−0.703705	+	0.710492i	$0.748472\pi$
$38$			8.54755i			1.38660i
$39$	−0.756400	+	1.82611i	−0.121121	+	0.292412i
$40$	3.32763	−	1.37835i	0.526145	−	0.217936i
$41$	−1.65510	−	3.99575i	−0.258483	−	0.624032i	0.740356	−	0.672215i	$-0.234657\pi$
$41$	−1.65510	−	3.99575i	−0.258483	−	0.624032i	−0.998839	+	0.0481830i	$0.984657\pi$
$42$	−9.34899	−	9.34899i	−1.44258	−	1.44258i
$43$	5.33668	+	5.33668i	0.813836	+	0.813836i	0.985207	−	0.171371i	$-0.0548196\pi$
$43$	5.33668	+	5.33668i	0.813836	+	0.813836i	−0.171371	+	0.985207i	$0.554820\pi$
$44$	−3.35504	−	8.09978i	−0.505791	−	1.22109i
$45$	0.496252	−	0.205554i	0.0739769	−	0.0306422i
$46$	−7.94993	+	19.1928i	−1.17215	+	2.82983i
$47$		−	11.3322i		−	1.65297i	−0.562961	−	0.826484i	$-0.690338\pi$
$47$		−	11.3322i		−	1.65297i	0.562961	−	0.826484i	$-0.309662\pi$
$48$	2.04175	+	0.845719i	0.294701	+	0.122069i
$49$	−4.12357	+	4.12357i	−0.589081	+	0.589081i
$50$	−2.35190			−0.332609
$51$	6.46880	+	0.152348i	0.905814	+	0.0213330i
$52$	−4.44779			−0.616797
$53$	4.02442	−	4.02442i	0.552797	−	0.552797i	−0.374450	−	0.927247i	$-0.622169\pi$
$53$	4.02442	−	4.02442i	0.552797	−	0.552797i	0.927247	+	0.374450i	$0.122169\pi$
$54$	12.0616	+	4.99610i	1.64138	+	0.679883i
$55$			2.48259i			0.334753i
$56$	4.93742	−	11.9200i	0.659791	−	1.59288i
$57$	5.26936	−	2.18264i	0.697943	−	0.289098i
$58$	−7.88357	−	19.0326i	−1.03516	−	2.49911i
$59$	3.16077	+	3.16077i	0.411497	+	0.411497i	0.882260	−	0.470763i	$-0.156021\pi$
$59$	3.16077	+	3.16077i	0.411497	+	0.411497i	−0.470763	+	0.882260i	$0.656021\pi$
$60$	−3.91884	−	3.91884i	−0.505920	−	0.505920i
$61$	0.0929426	+	0.224383i	0.0119001	+	0.0287293i	0.929718	−	0.368273i	$-0.120051\pi$
$61$	0.0929426	+	0.224383i	0.0119001	+	0.0287293i	−0.917818	+	0.397002i	$0.870051\pi$
$62$	5.31057	−	2.19971i	0.674443	−	0.279364i
$63$	0.736321	−	1.77764i	0.0927677	−	0.223961i
$64$		−	11.9692i		−	1.49615i
$65$	1.16361	+	0.481983i	0.144328	+	0.0597826i
$66$	−6.47933	+	6.47933i	−0.797550	+	0.797550i
$67$	7.23278			0.883625			0.441812	−	0.897108i	$-0.354336\pi$
$67$	7.23278			0.883625			0.441812	+	0.897108i	$0.354336\pi$
$68$	5.25380	+	13.5796i	0.637116	+	1.64677i
$69$	13.8620			1.66878
$70$	−5.95724	+	5.95724i	−0.712026	+	0.712026i
$71$	−1.69789	−	0.703290i	−0.201503	−	0.0834651i	0.279650	−	0.960102i	$-0.409782\pi$
$71$	−1.69789	−	0.703290i	−0.201503	−	0.0834651i	−0.481152	+	0.876637i	$0.659782\pi$
$72$			1.93467i			0.228003i
$73$	−2.09426	+	5.05599i	−0.245114	+	0.591758i	−0.997777	−	0.0666485i	$-0.978769\pi$
$73$	−2.09426	+	5.05599i	−0.245114	+	0.591758i	0.752662	+	0.658407i	$0.228769\pi$
$74$	−9.99859	+	4.14155i	−1.16231	+	0.481446i
$75$	0.600564	+	1.44989i	0.0693472	+	0.167419i
$76$	9.07527	+	9.07527i	1.04100	+	1.04100i
$77$	6.28827	+	6.28827i	0.716615	+	0.716615i
$78$	1.77898	+	4.29484i	0.201430	+	0.486294i
$79$	−8.34789	+	3.45781i	−0.939211	+	0.389034i	−0.799166	−	0.601111i	$-0.794725\pi$
$79$	−8.34789	+	3.45781i	−0.939211	+	0.389034i	−0.140046	+	0.990145i	$0.544725\pi$
$80$	0.538897	−	1.30101i	0.0602505	−	0.145458i
$81$		−	7.10006i		−	0.788896i
$82$	−9.39762	−	3.89262i	−1.03779	−	0.429868i
$83$	−5.17302	+	5.17302i	−0.567812	+	0.567812i	−0.931515	−	0.363703i	$-0.881512\pi$
$83$	−5.17302	+	5.17302i	−0.567812	+	0.567812i	0.363703	+	0.931515i	$0.381512\pi$
$84$	−19.8524			−2.16607
$85$	0.0970771	−	4.12196i	0.0105295	−	0.447090i
$86$	17.7503			1.91406
$87$	−9.72006	+	9.72006i	−1.04210	+	1.04210i
$88$	−8.26117	−	3.42189i	−0.880643	−	0.364774i
$89$			2.19350i			0.232510i	0.993219	+	0.116255i	$0.0370890\pi$
$89$			2.19350i			0.232510i	−0.993219	+	0.116255i	$0.962911\pi$
$90$	0.483443	−	1.16714i	0.0509594	−	0.123027i
$91$	4.16819	−	1.72652i	0.436945	−	0.180989i
$92$	11.9370	+	28.8186i	1.24452	+	3.00454i
$93$	−2.71214	−	2.71214i	−0.281235	−	0.281235i
$94$	−18.8459	−	18.8459i	−1.94381	−	1.94381i
$95$	−1.39079	−	3.35767i	−0.142692	−	0.344489i
$96$	−5.64246	+	2.33718i	−0.575882	+	0.238538i
$97$	−3.75810	+	9.07286i	−0.381577	+	0.921209i	0.610084	+	0.792337i	$0.291136\pi$
$97$	−3.75810	+	9.07286i	−0.381577	+	0.921209i	−0.991661	+	0.128872i	$0.958864\pi$
$98$			13.7154i			1.38546i
$99$	−1.23199	−	0.510308i	−0.123820	−	0.0512879i
$100$	−2.49711	+	2.49711i	−0.249711	+	0.249711i
$101$	5.46415			0.543704			0.271852	−	0.962339i	$-0.412364\pi$
$101$	5.46415			0.543704			0.271852	+	0.962339i	$0.412364\pi$
$102$	11.0113	−	10.5046i	1.09028	−	1.04011i
$103$	7.16074			0.705568			0.352784	−	0.935705i	$-0.385235\pi$
$103$	7.16074			0.705568			0.352784	+	0.935705i	$0.385235\pi$
$104$	−3.20773	+	3.20773i	−0.314543	+	0.314543i
$105$	5.19369	+	2.15130i	0.506852	+	0.209945i
$106$		−	13.3856i		−	1.30012i
$107$	−0.238471	+	0.575721i	−0.0230539	+	0.0556570i	−0.934987	−	0.354681i	$-0.884589\pi$
$107$	−0.238471	+	0.575721i	−0.0230539	+	0.0556570i	0.911933	+	0.410338i	$0.134589\pi$
$108$	18.1109	−	7.50177i	1.74272	−	0.721859i
$109$	2.36863	+	5.71837i	0.226873	+	0.547720i	0.995794	−	0.0916242i	$-0.0292058\pi$
$109$	2.36863	+	5.71837i	0.226873	+	0.547720i	−0.768921	+	0.639344i	$0.779206\pi$
$110$	4.12867	+	4.12867i	0.393653	+	0.393653i
$111$	5.10633	+	5.10633i	0.484672	+	0.484672i
$112$	−1.93040	−	4.66039i	−0.182405	−	0.440365i
$113$	14.8371	−	6.14574i	1.39576	−	0.578143i	0.447113	−	0.894478i	$-0.352452\pi$
$113$	14.8371	−	6.14574i	1.39576	−	0.578143i	0.948648	+	0.316335i	$0.102452\pi$
$114$	5.13335	−	12.3930i	0.480782	−	1.16071i
$115$		−	8.83293i		−	0.823675i
$116$	−28.5780	−	11.8374i	−2.65340	−	1.09907i
$117$	−0.478370	+	0.478370i	−0.0442253	+	0.0442253i
$118$	10.5130			0.967801
$119$	−10.1948	−	10.6866i	−0.934557	−	0.979638i
$120$	−5.65249			−0.516000
$121$	−3.42008	+	3.42008i	−0.310916	+	0.310916i
$122$	0.527727	+	0.218592i	0.0477782	+	0.0197904i
$123$			6.78740i			0.611999i
$124$	3.30292	−	7.97396i	0.296611	−	0.716083i
$125$	0.923880	−	0.382683i	0.0826343	−	0.0342282i
$126$	−1.73175	−	4.18082i	−0.154277	−	0.372457i
$127$	4.18456	+	4.18456i	0.371320	+	0.371320i	0.867958	−	0.496638i	$-0.165432\pi$
$127$	4.18456	+	4.18456i	0.371320	+	0.371320i	−0.496638	+	0.867958i	$0.665432\pi$
$128$	−14.4017	−	14.4017i	−1.27294	−	1.27294i
$129$	−4.53258	−	10.9426i	−0.399072	−	0.963444i
$130$	2.73670	−	1.13358i	0.240024	−	0.0994213i
$131$	6.16914	−	14.8936i	0.539000	−	1.30126i	−0.386421	−	0.922322i	$-0.626289\pi$
$131$	6.16914	−	14.8936i	0.539000	−	1.30126i	0.925422	−	0.378939i	$-0.123711\pi$
$132$			13.7587i			1.19754i
$133$	−12.0276	−	4.98198i	−1.04292	−	0.431993i
$134$	12.0284	−	12.0284i	1.03910	−	1.03910i
$135$	−5.55101			−0.477755
$136$	13.5826	+	6.00455i	1.16470	+	0.514886i
$137$	−17.1320			−1.46369			−0.731843	−	0.681473i	$-0.761339\pi$
$137$	−17.1320			−1.46369			−0.731843	+	0.681473i	$0.761339\pi$
$138$	23.0531	−	23.0531i	1.96241	−	1.96241i
$139$	1.97070	+	0.816292i	0.167153	+	0.0692369i	0.464691	−	0.885473i	$-0.346165\pi$
$139$	1.97070	+	0.816292i	0.167153	+	0.0692369i	−0.297538	+	0.954710i	$0.596165\pi$
$140$			12.6501i			1.06913i
$141$	−6.80570	+	16.4304i	−0.573143	+	1.38369i
$142$	−3.99327	+	1.65407i	−0.335108	+	0.138806i
$143$	−1.19657	−	2.88877i	−0.100062	−	0.241571i
$144$	0.534857	+	0.534857i	0.0445715	+	0.0445715i
$145$	6.19369	+	6.19369i	0.514358	+	0.514358i
$146$	4.92549	+	11.8912i	0.407636	+	0.984121i
$147$	8.45519	−	3.50226i	0.697373	−	0.288861i
$148$	−6.21865	+	15.0131i	−0.511170	+	1.23407i
$149$			18.5384i			1.51872i	0.650669	+	0.759362i	$0.274489\pi$
$149$			18.5384i			1.51872i	−0.650669	+	0.759362i	$0.725511\pi$
$150$	3.41000	+	1.41247i	0.278425	+	0.115328i
$151$	−6.30217	+	6.30217i	−0.512863	+	0.512863i	−0.915403	−	0.402539i	$-0.868128\pi$
$151$	−6.30217	+	6.30217i	−0.512863	+	0.512863i	0.402539	+	0.915403i	$0.368128\pi$
$152$	13.0901			1.06175
$153$	2.02558	+	0.895462i	0.163758	+	0.0723938i
$154$	20.9154			1.68541
$155$	−1.72819	+	1.72819i	−0.138812	+	0.138812i
$156$	6.44881	+	2.67118i	0.516318	+	0.213866i
$157$		−	18.2426i		−	1.45592i	−0.685620	−	0.727960i	$-0.740469\pi$
$157$		−	18.2426i		−	1.45592i	0.685620	−	0.727960i	$-0.259531\pi$
$158$	−8.13243	+	19.6334i	−0.646982	+	1.56195i
$159$	−8.25189	+	3.41805i	−0.654418	+	0.271069i
$160$	1.48927	+	3.59541i	0.117737	+	0.284242i
$161$	−22.3733	−	22.3733i	−1.76326	−	1.76326i
$162$	−11.8077	−	11.8077i	−0.927703	−	0.927703i
$163$	−3.58387	−	8.65222i	−0.280710	−	0.677694i	0.719142	−	0.694863i	$-0.244535\pi$
$163$	−3.58387	−	8.65222i	−0.280710	−	0.677694i	−0.999853	+	0.0171684i	$0.994535\pi$
$164$	−14.1108	+	5.84488i	−1.10187	+	0.456408i
$165$	1.49096	−	3.59949i	0.116071	−	0.280220i
$166$			17.2059i			1.33544i
$167$	−8.57484	−	3.55181i	−0.663541	−	0.274848i	0.0253869	−	0.999678i	$-0.491918\pi$
$167$	−8.57484	−	3.55181i	−0.663541	−	0.274848i	−0.688928	+	0.724830i	$0.741918\pi$
$168$	−14.3175	+	14.3175i	−1.10462	+	1.10462i
$169$	11.4137			0.877977
$170$	−6.69357	−	7.01646i	−0.513373	−	0.538138i
$171$	1.95213			0.149283
$172$	18.8462	−	18.8462i	1.43701	−	1.43701i
$173$	−3.97248	−	1.64545i	−0.302022	−	0.125102i	0.226526	−	0.974005i	$-0.427263\pi$
$173$	−3.97248	−	1.64545i	−0.302022	−	0.125102i	−0.528548	+	0.848904i	$0.677263\pi$
$174$			32.3298i			2.45092i
$175$	1.37082	−	3.30945i	0.103624	−	0.250171i
$176$	−3.22989	+	1.33786i	−0.243462	+	0.100845i
$177$	−2.68453	−	6.48102i	−0.201781	−	0.487143i
$178$	3.64789	+	3.64789i	0.273421	+	0.273421i
$179$	−0.0832109	−	0.0832109i	−0.00621948	−	0.00621948i	0.703990	−	0.710210i	$-0.251400\pi$
$179$	−0.0832109	−	0.0832109i	−0.00621948	−	0.00621948i	−0.710210	+	0.703990i	$0.751400\pi$
$180$	−0.725903	−	1.75249i	−0.0541056	−	0.130623i
$181$	−2.14676	+	0.889218i	−0.159568	+	0.0660951i	−0.461038	−	0.887381i	$-0.652523\pi$
$181$	−2.14676	+	0.889218i	−0.159568	+	0.0660951i	0.301470	+	0.953476i	$0.402523\pi$
$182$	4.06061	−	9.80318i	0.300993	−	0.726660i
$183$		−	0.381149i		−	0.0281754i
$184$	29.3927	+	12.1749i	2.16686	+	0.897544i
$185$	3.25379	−	3.25379i	0.239223	−	0.239223i
$186$	−9.02082			−0.661438
$187$	−7.40635	+	7.06552i	−0.541606	+	0.516682i
$188$	−40.0189			−2.91868
$189$	−14.0604	+	14.0604i	−1.02274	+	1.02274i
$190$	−7.89690	−	3.27100i	−0.572902	−	0.237304i
$191$			14.6622i			1.06092i	0.847710	+	0.530461i	$0.177981\pi$
$191$			14.6622i			1.06092i	−0.847710	+	0.530461i	$0.822019\pi$
$192$	−7.18827	+	17.3540i	−0.518768	+	1.25242i
$193$	7.75695	−	3.21303i	0.558357	−	0.231279i	−0.0856146	−	0.996328i	$-0.527285\pi$
$193$	7.75695	−	3.21303i	0.558357	−	0.231279i	0.643972	+	0.765049i	$0.277285\pi$
$194$	8.83869	+	21.3385i	0.634581	+	1.53201i
$195$	−1.39765	−	1.39765i	−0.100087	−	0.100087i
$196$	14.5622	+	14.5622i	1.04015	+	1.04015i
$197$	−2.55690	−	6.17290i	−0.182171	−	0.439801i	0.806242	−	0.591586i	$-0.201498\pi$
$197$	−2.55690	−	6.17290i	−0.182171	−	0.439801i	−0.988414	+	0.151785i	$0.951498\pi$
$198$	−2.89752	+	1.20019i	−0.205918	+	0.0852941i
$199$	7.22192	−	17.4353i	0.511949	−	1.23595i	−0.430800	−	0.902448i	$-0.641768\pi$
$199$	7.22192	−	17.4353i	0.511949	−	1.23595i	0.942748	−	0.333506i	$-0.108232\pi$
$200$			3.60181i			0.254686i
$201$	−10.4867	−	4.34375i	−0.739678	−	0.306384i
$202$	9.08714	−	9.08714i	0.639369	−	0.639369i
$203$	31.3765			2.20220
$204$	0.538009	−	22.8442i	0.0376681	−	1.59942i
$205$	4.32497			0.302069
$206$	11.9086	−	11.9086i	0.829714	−	0.829714i
$207$	4.38336	+	1.81565i	0.304664	+	0.126196i
$208$			1.77361i			0.122978i
$209$	−3.45277	+	8.33572i	−0.238833	+	0.576594i
$210$	12.2150	−	5.05964i	0.842918	−	0.349148i
$211$	2.53326	+	6.11583i	0.174397	+	0.421031i	0.986774	−	0.162101i	$-0.0518270\pi$
$211$	2.53326	+	6.11583i	0.174397	+	0.421031i	−0.812377	+	0.583132i	$0.801827\pi$
$212$	−14.2120	−	14.2120i	−0.976085	−	0.976085i
$213$	2.03939	+	2.03939i	0.139736	+	0.139736i
$214$	0.560861	+	1.35404i	0.0383397	+	0.0925602i
$215$	−6.97271	+	2.88819i	−0.475535	+	0.196973i
$216$	7.65124	−	18.4717i	0.520601	−	1.25684i
$217$			8.75482i			0.594316i
$218$	13.4490	+	5.57077i	0.910884	+	0.377300i
$219$	6.07289	−	6.07289i	0.410368	−	0.410368i
$220$	8.76714			0.591081
$221$	1.87376	+	4.84315i	0.126042	+	0.325785i
$222$	16.9841			1.13990
$223$	2.08077	−	2.08077i	0.139339	−	0.139339i	−0.633997	−	0.773336i	$-0.718587\pi$
$223$	2.08077	−	2.08077i	0.139339	−	0.139339i	0.773336	+	0.633997i	$0.218587\pi$
$224$	12.8792	+	5.33474i	0.860529	+	0.356443i
$225$			0.537139i			0.0358093i
$226$	14.4542	−	34.8955i	0.961478	−	2.32121i
$227$	−19.8871	+	8.23750i	−1.31995	+	0.546742i	−0.927772	−	0.373147i	$-0.878279\pi$
$227$	−19.8871	+	8.23750i	−1.31995	+	0.546742i	−0.392180	+	0.919889i	$0.628279\pi$
$228$	−7.70786	−	18.6084i	−0.510466	−	1.23237i
$229$	8.44347	+	8.44347i	0.557960	+	0.557960i	0.928726	−	0.370766i	$-0.120905\pi$
$229$	8.44347	+	8.44347i	0.557960	+	0.557960i	−0.370766	+	0.928726i	$0.620905\pi$
$230$	−14.6896	−	14.6896i	−0.968601	−	0.968601i
$231$	−5.34080	−	12.8938i	−0.351399	−	0.848351i
$232$	−29.1474	+	12.0732i	−1.91362	+	0.792647i
$233$	−3.85313	+	9.30228i	−0.252427	+	0.609412i	−0.998399	−	0.0565648i	$-0.981985\pi$
$233$	−3.85313	+	9.30228i	−0.252427	+	0.609412i	0.745972	+	0.665977i	$0.231985\pi$
$234$			1.59110i			0.104014i
$235$	10.4696	+	4.33664i	0.682959	+	0.282891i
$236$	11.1621	−	11.1621i	0.726590	−	0.726590i
$237$	14.1802			0.921101
$238$	−34.7267	−	0.817856i	−2.25100	−	0.0530137i
$239$	−16.6253			−1.07540			−0.537701	−	0.843135i	$-0.680707\pi$
$239$	−16.6253			−1.07540			−0.537701	+	0.843135i	$0.680707\pi$
$240$	−1.56268	+	1.56268i	−0.100871	+	0.100871i
$241$	5.47122	+	2.26625i	0.352432	+	0.145982i	0.551874	−	0.833928i	$-0.313913\pi$
$241$	5.47122	+	2.26625i	0.352432	+	0.145982i	−0.199442	+	0.979910i	$0.563913\pi$
$242$			11.3755i			0.731245i
$243$	2.10879	−	5.09108i	0.135279	−	0.326593i
$244$	0.792397	−	0.328221i	0.0507280	−	0.0210122i
$245$	−2.23166	−	5.38770i	−0.142575	−	0.344208i
$246$	11.2878	+	11.2878i	0.719681	+	0.719681i
$247$	3.23668	+	3.23668i	0.205945	+	0.205945i
$248$	−3.36873	−	8.13284i	−0.213915	−	0.516436i
$249$	10.6070	−	4.39358i	0.672194	−	0.278432i
$250$	0.900034	−	2.17287i	0.0569231	−	0.137425i
$251$			7.77270i			0.490608i	0.969446	+	0.245304i	$0.0788878\pi$
$251$			7.77270i			0.490608i	−0.969446	+	0.245304i	$0.921112\pi$
$252$	−6.27762	−	2.60027i	−0.395453	−	0.163802i
$253$	−15.5058	+	15.5058i	−0.974844	+	0.974844i
$254$	13.9182			0.873307
$255$	−2.61626	+	5.91809i	−0.163836	+	0.370605i
$256$	−23.9630			−1.49768
$257$	−5.70344	+	5.70344i	−0.355771	+	0.355771i	−0.862251	−	0.506481i	$-0.830946\pi$
$257$	−5.70344	+	5.70344i	−0.355771	+	0.355771i	0.506481	+	0.862251i	$0.330946\pi$
$258$	−25.7360	−	10.6602i	−1.60225	−	0.663674i
$259$		−	16.4833i		−	1.02422i
$260$	1.70210	−	4.10922i	0.105559	−	0.254843i
$261$	−4.34677	+	1.80049i	−0.269058	+	0.111448i
$262$	−14.5092	−	35.0283i	−0.896382	−	2.16406i
$263$	15.0792	+	15.0792i	0.929822	+	0.929822i	0.997694	−	0.0678724i	$-0.0216211\pi$
$263$	15.0792	+	15.0792i	0.929822	+	0.929822i	−0.0678724	+	0.997694i	$0.521621\pi$
$264$	9.92273	+	9.92273i	0.610702	+	0.610702i
$265$	2.17800	+	5.25816i	0.133794	+	0.323006i
$266$	−28.2877	+	11.7171i	−1.73443	+	0.718424i
$267$	1.31734	−	3.18033i	0.0806197	−	0.194633i
$268$		−	25.5422i		−	1.56024i
$269$	3.88200	+	1.60798i	0.236690	+	0.0980401i	0.497876	−	0.867248i	$-0.334114\pi$
$269$	3.88200	+	1.60798i	0.236690	+	0.0980401i	−0.261186	+	0.965289i	$0.584114\pi$
$270$	−9.23159	+	9.23159i	−0.561816	+	0.561816i
$271$	−24.7136			−1.50124			−0.750621	−	0.660733i	$-0.770245\pi$
$271$	−24.7136			−1.50124			−0.750621	+	0.660733i	$0.770245\pi$
$272$	5.41504	−	2.09502i	0.328335	−	0.127029i
$273$	−7.08031			−0.428520
$274$	−28.4913	+	28.4913i	−1.72122	+	1.72122i
$275$	−2.29362	−	0.950048i	−0.138310	−	0.0572900i
$276$		−	48.9527i		−	2.94661i
$277$	7.67765	−	18.5355i	0.461305	−	1.11369i	−0.506556	−	0.862207i	$-0.669082\pi$
$277$	7.67765	−	18.5355i	0.461305	−	1.11369i	0.967862	−	0.251483i	$-0.0809182\pi$
$278$	4.63490	−	1.91984i	0.277983	−	0.115144i
$279$	−0.502381	−	1.21285i	−0.0300768	−	0.0726117i
$280$	9.12317	+	9.12317i	0.545214	+	0.545214i
$281$	17.8053	+	17.8053i	1.06218	+	1.06218i	0.997934	+	0.0642430i	$0.0204633\pi$
$281$	17.8053	+	17.8053i	1.06218	+	1.06218i	0.0642430	+	0.997934i	$0.479537\pi$
$282$	16.0063	+	38.6427i	0.953164	+	2.30114i
$283$	7.84059	−	3.24768i	0.466075	−	0.193054i	−0.137272	−	0.990533i	$-0.543833\pi$
$283$	7.84059	−	3.24768i	0.466075	−	0.193054i	0.603347	+	0.797479i	$0.293833\pi$
$284$	−2.48363	+	5.99601i	−0.147376	+	0.355798i
$285$			5.70351i			0.337847i
$286$	−6.79411	−	2.81421i	−0.401744	−	0.166408i
$287$	10.9549	−	10.9549i	0.646648	−	0.646648i
$288$	−2.09036			−0.123175
$289$	12.5734	−	11.4416i	0.739611	−	0.673035i
$290$	20.6008			1.20972
$291$	10.8977	−	10.8977i	0.638833	−	0.638833i
$292$	17.8549	+	7.39575i	1.04488	+	0.432804i
$293$		−	25.9873i		−	1.51820i	−0.650977	−	0.759098i	$-0.725640\pi$
$293$		−	25.9873i		−	1.51820i	0.650977	−	0.759098i	$-0.274360\pi$
$294$	8.23696	−	19.8858i	0.480389	−	1.15976i
$295$	−4.12975	+	1.71060i	−0.240443	+	0.0995948i
$296$	6.34255	+	15.3123i	0.368653	+	0.890008i
$297$	9.74457	+	9.74457i	0.565438	+	0.565438i
$298$	30.8302	+	30.8302i	1.78594	+	1.78594i
$299$	4.25732	+	10.2781i	0.246207	+	0.594397i
$300$	5.12021	−	2.12086i	0.295615	−	0.122448i
$301$	−10.3458	+	24.9771i	−0.596325	+	1.43966i
$302$			20.9616i			1.20620i
$303$	−7.92243	−	3.28158i	−0.455132	−	0.188522i
$304$	3.61887	−	3.61887i	0.207557	−	0.207557i
$305$	−0.242871			−0.0139067
$306$	4.85782	−	1.87943i	0.277703	−	0.107440i
$307$	16.9475			0.967245			0.483622	−	0.875277i	$-0.339321\pi$
$307$	16.9475			0.967245			0.483622	+	0.875277i	$0.339321\pi$
$308$	22.2067	−	22.2067i	1.26534	−	1.26534i
$309$	−10.3823	−	4.30048i	−0.590628	−	0.244646i
$310$			5.74812i			0.326471i
$311$	−6.57851	+	15.8819i	−0.373033	+	0.900581i	0.620200	+	0.784444i	$0.287051\pi$
$311$	−6.57851	+	15.8819i	−0.373033	+	0.900581i	−0.993233	+	0.116138i	$0.962949\pi$
$312$	6.57730	−	2.72441i	0.372366	−	0.154239i
$313$	−2.26352	−	5.46463i	−0.127942	−	0.308879i	0.846909	−	0.531738i	$-0.178461\pi$
$313$	−2.26352	−	5.46463i	−0.127942	−	0.308879i	−0.974851	+	0.222859i	$0.928461\pi$
$314$	−30.3383	−	30.3383i	−1.71209	−	1.71209i
$315$	1.36054	+	1.36054i	0.0766579	+	0.0766579i
$316$	12.2111	+	29.4801i	0.686926	+	1.65839i
$317$	−0.591813	+	0.245137i	−0.0332395	+	0.0137683i	−0.399241	−	0.916846i	$-0.630726\pi$
$317$	−0.591813	+	0.245137i	−0.0332395	+	0.0137683i	0.366002	+	0.930614i	$0.380726\pi$
$318$	−8.03891	+	19.4076i	−0.450800	+	1.08833i
$319$		−	21.7455i		−	1.21752i
$320$	11.0581	+	4.58041i	0.618166	+	0.256053i
$321$	0.691515	−	0.691515i	0.0385966	−	0.0385966i
$322$	−74.4157			−4.14702
$323$	6.05874	−	13.7052i	0.337117	−	0.762576i
$324$	−25.0735			−1.39297
$325$	−0.890588	+	0.890588i	−0.0494010	+	0.0494010i
$326$	−20.3492	−	8.42891i	−1.12704	−	0.466834i
$327$		−	9.71352i		−	0.537159i
$328$	−5.96133	+	14.3919i	−0.329160	+	0.794661i
$329$	37.5033	−	15.5344i	2.06762	−	0.856437i
$330$	−3.50659	−	8.46565i	−0.193031	−	0.466019i
$331$	−8.24547	−	8.24547i	−0.453212	−	0.453212i	0.443207	−	0.896419i	$-0.353841\pi$
$331$	−8.24547	−	8.24547i	−0.453212	−	0.453212i	−0.896419	+	0.443207i	$0.853841\pi$
$332$	18.2682	+	18.2682i	1.00260	+	1.00260i
$333$	0.945868	+	2.28353i	0.0518333	+	0.125137i
$334$	−20.1672	+	8.35352i	−1.10350	+	0.457084i
$335$	−2.76786	+	6.68222i	−0.151225	+	0.365088i
$336$			7.91638i			0.431874i
$337$	28.5300	+	11.8175i	1.55413	+	0.643740i	0.984056	−	0.177856i	$-0.0569162\pi$
$337$	28.5300	+	11.8175i	1.55413	+	0.643740i	0.570070	+	0.821596i	$0.306916\pi$
$338$	18.9815	−	18.9815i	1.03246	−	1.03246i
$339$	−25.2031			−1.36885
$340$	−14.5565	−	0.342822i	−0.789436	−	0.0185922i
$341$	6.06754			0.328576
$342$	3.24648	−	3.24648i	0.175550	−	0.175550i
$343$	3.86674	+	1.60166i	0.208784	+	0.0864813i
$344$		−	27.1836i		−	1.46564i
$345$	−5.30474	+	12.8068i	−0.285598	+	0.689494i
$346$	−9.34288	+	3.86995i	−0.502276	+	0.208050i
$347$	−0.00573993	−	0.0138574i	−0.000308135	−	0.000743905i	0.923725	−	0.383055i	$-0.125128\pi$
$347$	−0.00573993	−	0.0138574i	−0.000308135	−	0.000743905i	−0.924034	+	0.382311i	$0.875128\pi$
$348$	34.3259	+	34.3259i	1.84006	+	1.84006i
$349$	−2.58441	−	2.58441i	−0.138340	−	0.138340i	0.634545	−	0.772886i	$-0.281187\pi$
$349$	−2.58441	−	2.58441i	−0.138340	−	0.138340i	−0.772886	+	0.634545i	$0.781187\pi$
$350$	−3.22403	−	7.78350i	−0.172332	−	0.416046i
$351$	6.45921	−	2.67549i	0.344767	−	0.142807i
$352$	3.69725	−	8.92595i	0.197064	−	0.475755i
$353$			3.82333i			0.203495i	0.994810	+	0.101748i	$0.0324434\pi$
$353$			3.82333i			0.203495i	−0.994810	+	0.101748i	$0.967557\pi$
$354$	−15.2427	−	6.31374i	−0.810141	−	0.335572i
$355$	1.29951	−	1.29951i	0.0689708	−	0.0689708i
$356$	7.74622			0.410549
$357$	8.36337	+	21.6170i	0.442637	+	1.14409i
$358$	−0.276767			−0.0146276
$359$	−4.73532	+	4.73532i	−0.249921	+	0.249921i	−0.820938	−	0.571017i	$-0.806549\pi$
$359$	−4.73532	+	4.73532i	−0.249921	+	0.249921i	0.571017	+	0.820938i	$0.306549\pi$
$360$	−1.78740	−	0.740366i	−0.0942044	−	0.0390207i
$361$			5.79178i			0.304830i
$362$	−2.09135	+	5.04897i	−0.109919	+	0.265368i
$363$	7.01272	−	2.90476i	0.368072	−	0.152461i
$364$	−6.09712	−	14.7197i	−0.319576	−	0.771524i
$365$	−3.86968	−	3.86968i	−0.202549	−	0.202549i
$366$	−0.633869	−	0.633869i	−0.0331328	−	0.0331328i
$367$	−8.81227	−	21.2747i	−0.459997	−	1.11053i	−0.968398	−	0.249410i	$-0.919763\pi$
$367$	−8.81227	−	21.2747i	−0.459997	−	1.11053i	0.508401	−	0.861120i	$-0.330237\pi$
$368$	11.4917	−	4.76004i	0.599049	−	0.248134i
$369$	−0.889017	+	2.14628i	−0.0462804	+	0.111731i
$370$		−	10.8224i		−	0.562630i
$371$	18.8354	+	7.80187i	0.977884	+	0.405053i
$372$	−9.57776	+	9.57776i	−0.496584	+	0.496584i
$373$	−23.7303			−1.22871			−0.614355	−	0.789030i	$-0.710584\pi$
$373$	−23.7303			−1.22871			−0.614355	+	0.789030i	$0.710584\pi$
$374$	−0.566816	+	24.0674i	−0.0293094	+	1.24450i
$375$	−1.56935			−0.0810409
$376$	−28.8615	+	28.8615i	−1.48842	+	1.48842i
$377$	−10.1923	−	4.22178i	−0.524929	−	0.217433i
$378$			46.7662i			2.40539i
$379$	1.13970	−	2.75149i	0.0585427	−	0.141335i	−0.891902	−	0.452230i	$-0.850629\pi$
$379$	1.13970	−	2.75149i	0.0585427	−	0.141335i	0.950444	+	0.310895i	$0.100629\pi$
$380$	−11.8574	+	4.91150i	−0.608272	+	0.251955i
$381$	−3.55406	−	8.58025i	−0.182080	−	0.439580i
$382$	24.3839	+	24.3839i	1.24759	+	1.24759i
$383$	−17.2691	−	17.2691i	−0.882408	−	0.882408i	0.111371	−	0.993779i	$-0.464476\pi$
$383$	−17.2691	−	17.2691i	−0.882408	−	0.882408i	−0.993779	+	0.111371i	$0.964476\pi$
$384$	12.2317	+	29.5300i	0.624198	+	1.50695i
$385$	−8.21602	+	3.40319i	−0.418727	+	0.173443i
$386$	7.55674	−	18.2436i	0.384628	−	0.928574i
$387$		−	4.05390i		−	0.206071i
$388$	32.0403	+	13.2715i	1.62660	+	0.673759i
$389$	−1.19407	+	1.19407i	−0.0605418	+	0.0605418i	−0.736729	−	0.676188i	$-0.763631\pi$
$389$	−1.19407	+	1.19407i	−0.0605418	+	0.0605418i	0.676188	+	0.736729i	$0.263631\pi$
$390$	−4.64870			−0.235396
$391$	26.3514	−	25.1387i	1.33265	−	1.27132i
$392$	21.0043			1.06088
$393$	−17.8892	+	17.8892i	−0.902389	+	0.902389i
$394$	−14.5181	−	6.01357i	−0.731409	−	0.302960i
$395$		−	9.03570i		−	0.454635i
$396$	−1.80212	+	4.35071i	−0.0905601	+	0.218631i
$397$	−29.1259	+	12.0643i	−1.46178	+	0.605491i	−0.964969	−	0.262365i	$-0.915498\pi$
$397$	−29.1259	+	12.0643i	−1.46178	+	0.605491i	−0.496816	+	0.867856i	$0.665498\pi$
$398$	−16.9853	−	41.0060i	−0.851394	−	2.05545i
$399$	14.4467	+	14.4467i	0.723238	+	0.723238i
$400$	0.995752	+	0.995752i	0.0497876	+	0.0497876i
$401$	1.93870	+	4.68044i	0.0968141	+	0.233730i	0.964865	−	0.262745i	$-0.0846276\pi$
$401$	1.93870	+	4.68044i	0.0968141	+	0.233730i	−0.868051	+	0.496474i	$0.834628\pi$
$402$	−24.6638	+	10.2161i	−1.23012	+	0.509531i
$403$	1.17798	−	2.84390i	0.0586794	−	0.141665i
$404$		−	19.2964i		−	0.960029i
$405$	6.55960	+	2.71708i	0.325949	+	0.135013i
$406$	52.1806	−	52.1806i	2.58968	−	2.58968i
$407$	−11.4238			−0.566256
$408$	−16.0871	−	16.8632i	−0.796432	−	0.834850i
$409$	−26.1178			−1.29144			−0.645722	−	0.763573i	$-0.723443\pi$
$409$	−26.1178			−1.29144			−0.645722	+	0.763573i	$0.723443\pi$
$410$	7.19263	−	7.19263i	0.355219	−	0.355219i
$411$	24.8395	+	10.2889i	1.22524	+	0.507513i
$412$		−	25.2877i		−	1.24584i
$413$	−6.12757	+	14.7933i	−0.301518	+	0.727929i
$414$	10.3092	−	4.27022i	0.506671	−	0.209870i
$415$	−2.79962	−	6.75887i	−0.137428	−	0.331780i
$416$	−3.46586	−	3.46586i	−0.169928	−	0.169928i
$417$	−2.36707	−	2.36707i	−0.115916	−	0.115916i
$418$	8.12058	+	19.6048i	0.397190	+	0.958903i
$419$	6.74298	−	2.79303i	0.329416	−	0.136449i	−0.211845	−	0.977303i	$-0.567947\pi$
$419$	6.74298	−	2.79303i	0.329416	−	0.136449i	0.541261	+	0.840855i	$0.317947\pi$
$420$	7.59718	−	18.3412i	0.370704	−	0.894960i
$421$		−	21.0644i		−	1.02662i	−0.858204	−	0.513309i	$-0.828420\pi$
$421$		−	21.0644i		−	1.02662i	0.858204	−	0.513309i	$-0.171580\pi$
$422$	14.3838	+	5.95798i	0.700194	+	0.290030i
$423$	−4.30413	+	4.30413i	−0.209274	+	0.209274i
$424$	−20.4993			−0.995533
$425$	3.77105	+	1.66709i	0.182923	+	0.0808660i
$426$	6.78319			0.328646
$427$	−0.615178	+	0.615178i	−0.0297705	+	0.0297705i
$428$	2.03313	+	0.842148i	0.0982749	+	0.0407068i
$429$			4.90702i			0.236913i
$430$	−6.79274	+	16.3991i	−0.327575	+	0.790836i
$431$	−19.4414	+	8.05290i	−0.936460	+	0.387894i	−0.798126	−	0.602491i	$-0.794175\pi$
$431$	−19.4414	+	8.05290i	−0.936460	+	0.387894i	−0.138334	+	0.990386i	$0.544175\pi$
$432$	−2.99142	−	7.22194i	−0.143925	−	0.347466i
$433$	−26.2522	−	26.2522i	−1.26160	−	1.26160i	−0.950318	−	0.311280i	$-0.899242\pi$
$433$	−26.2522	−	26.2522i	−1.26160	−	1.26160i	−0.311280	−	0.950318i	$-0.600758\pi$
$434$	14.5597	+	14.5597i	0.698886	+	0.698886i
$435$	−5.26046	−	12.6999i	−0.252220	−	0.608912i
$436$	20.1941	−	8.36467i	0.967121	−	0.400595i
$437$	12.2848	−	29.6580i	0.587659	−	1.41874i
$438$		−	20.1990i		−	0.965145i
$439$	0.435448	+	0.180369i	0.0207828	+	0.00860852i	0.393051	−	0.919517i	$-0.371420\pi$
$439$	0.435448	+	0.180369i	0.0207828	+	0.00860852i	−0.372268	+	0.928125i	$0.621420\pi$
$440$	6.32282	−	6.32282i	0.301429	−	0.301429i
$441$	3.13238			0.149161
$442$	11.1705	+	4.93823i	0.531327	+	0.234888i
$443$	−11.0249			−0.523808			−0.261904	−	0.965094i	$-0.584350\pi$
$443$	−11.0249			−0.523808			−0.261904	+	0.965094i	$0.584350\pi$
$444$	18.0327	−	18.0327i	0.855795	−	0.855795i
$445$	−2.02653	−	0.839416i	−0.0960667	−	0.0397921i
$446$		−	6.92084i		−	0.327711i
$447$	11.1335	−	26.8786i	0.526596	−	1.27132i
$448$	39.6114	−	16.4076i	1.87146	−	0.775186i
$449$	6.60636	+	15.9492i	0.311773	+	0.752688i	0.999639	+	0.0268500i	$0.00854766\pi$
$449$	6.60636	+	15.9492i	0.311773	+	0.752688i	−0.687866	+	0.725838i	$0.741452\pi$
$450$	0.893287	+	0.893287i	0.0421100	+	0.0421100i
$451$	−7.59232	−	7.59232i	−0.357508	−	0.357508i
$452$	−21.7033	−	52.3965i	−1.02084	−	2.46452i
$453$	12.9223	−	5.35260i	0.607143	−	0.251487i
$454$	−19.3738	+	46.7725i	−0.909257	+	2.19514i
$455$			4.51162i			0.211508i
$456$	−18.9792	−	7.86144i	−0.888782	−	0.368146i
$457$	−7.96742	+	7.96742i	−0.372700	+	0.372700i	−0.868460	−	0.495760i	$-0.834890\pi$
$457$	−7.96742	+	7.96742i	−0.372700	+	0.372700i	0.495760	+	0.868460i	$0.334890\pi$
$458$	28.0837			1.31227
$459$	−15.7983	−	16.5604i	−0.737402	−	0.772973i
$460$	−31.1930			−1.45438
$461$	21.2185	−	21.2185i	0.988244	−	0.988244i	−0.0116873	−	0.999932i	$-0.503720\pi$
$461$	21.2185	−	21.2185i	0.988244	−	0.988244i	0.999932	+	0.0116873i	$0.00372025\pi$
$462$	−30.3250	−	12.5610i	−1.41085	−	0.584392i
$463$			17.1592i			0.797457i	0.917069	+	0.398728i	$0.130548\pi$
$463$			17.1592i			0.797457i	−0.917069	+	0.398728i	$0.869452\pi$
$464$	−4.72031	+	11.3958i	−0.219135	+	0.529038i
$465$	3.54358	−	1.46780i	0.164329	−	0.0680675i
$466$	9.06218	+	21.8780i	0.419798	+	1.01348i
$467$	18.8030	+	18.8030i	0.870099	+	0.870099i	0.992483	−	0.122384i	$-0.0390540\pi$
$467$	18.8030	+	18.8030i	0.870099	+	0.870099i	−0.122384	+	0.992483i	$0.539054\pi$
$468$	1.68934	+	1.68934i	0.0780896	+	0.0780896i
$469$	9.91483	+	23.9365i	0.457824	+	1.10529i
$470$	24.6234	−	10.1993i	1.13579	−	0.470461i
$471$	−10.9559	+	26.4498i	−0.504820	+	1.21874i
$472$		−	16.1001i		−	0.741066i
$473$	17.3104	+	7.17020i	0.795933	+	0.329686i
$474$	23.5823	−	23.5823i	1.08317	−	1.08317i
$475$	3.63431			0.166754
$476$	−37.7391	+	36.0024i	−1.72977	+	1.65017i
$477$	−3.05707			−0.139974
$478$	−27.6487	+	27.6487i	−1.26462	+	1.26462i
$479$	−21.1662	−	8.76732i	−0.967107	−	0.400589i	−0.157473	−	0.987523i	$-0.550335\pi$
$479$	−21.1662	−	8.76732i	−0.967107	−	0.400589i	−0.809635	+	0.586934i	$0.800335\pi$
$480$		−	6.10736i		−	0.278761i
$481$	−2.21787	+	5.35441i	−0.101126	+	0.244140i
$482$	12.8678	−	5.33000i	0.586111	−	0.242775i
$483$	19.0022	+	45.8755i	0.864632	+	2.08741i
$484$	12.0778	+	12.0778i	0.548992	+	0.548992i
$485$	−6.94407	−	6.94407i	−0.315314	−	0.315314i
$486$	−4.95968	−	11.9737i	−0.224975	−	0.543139i
$487$	14.5174	−	6.01330i	0.657846	−	0.272489i	−0.0286857	−	0.999588i	$-0.509132\pi$
$487$	14.5174	−	6.01330i	0.657846	−	0.272489i	0.686532	+	0.727100i	$0.259132\pi$
$488$	0.334761	−	0.808185i	0.0151539	−	0.0365848i
$489$			14.6971i			0.664627i
$490$	−12.6713	−	5.24864i	−0.572433	−	0.237110i
$491$	0.607534	−	0.607534i	0.0274176	−	0.0274176i	−0.693265	−	0.720683i	$-0.743828\pi$
$491$	0.607534	−	0.607534i	0.0274176	−	0.0274176i	0.720683	+	0.693265i	$0.243828\pi$
$492$	23.9693			1.08062
$493$	−0.850318	+	36.1051i	−0.0382964	+	1.62609i
$494$	10.7655			0.484362
$495$	0.942926	−	0.942926i	0.0423814	−	0.0423814i
$496$	−3.17972	−	1.31708i	−0.142773	−	0.0591387i
$497$		−	6.58317i		−	0.295296i
$498$	10.3333	−	24.9467i	0.463045	−	1.11789i
$499$	−20.9163	+	8.66380i	−0.936340	+	0.387845i	−0.798080	−	0.602551i	$-0.794151\pi$
$499$	−20.9163	+	8.66380i	−0.936340	+	0.387845i	−0.138260	+	0.990396i	$0.544151\pi$
$500$	−1.35142	−	3.26263i	−0.0604376	−	0.145909i
$501$	10.2995	+	10.2995i	0.460147	+	0.460147i
$502$	12.9264	+	12.9264i	0.576931	+	0.576931i
$503$	6.54963	+	15.8122i	0.292034	+	0.705032i	0.999999	−	0.00121517i	$-0.000386801\pi$
$503$	6.54963	+	15.8122i	0.292034	+	0.705032i	−0.707966	+	0.706247i	$0.750387\pi$
$504$	−6.40270	+	2.65208i	−0.285199	+	0.118133i
$505$	−2.09104	+	5.04822i	−0.0930501	+	0.224643i
$506$			51.5739i			2.29274i
$507$	−16.5486	−	6.85467i	−0.734950	−	0.304426i
$508$	14.7775	−	14.7775i	0.655647	−	0.655647i
$509$	29.7081			1.31679			0.658393	−	0.752674i	$-0.271236\pi$
$509$	29.7081			1.31679			0.658393	+	0.752674i	$0.271236\pi$
$510$	5.49111	+	14.1930i	0.243150	+	0.628477i
$511$	−19.6034			−0.867203
$512$	−11.0481	+	11.0481i	−0.488263	+	0.488263i
$513$	−18.6384	−	7.72030i	−0.822907	−	0.340859i
$514$			18.9701i			0.836737i
$515$	−2.74030	+	6.61566i	−0.120752	+	0.291521i
$516$	−38.6432	+	16.0066i	−1.70117	+	0.704649i
$517$	−10.7661	−	25.9917i	−0.473493	−	1.14311i
$518$	−27.4125	−	27.4125i	−1.20444	−	1.20444i
$519$	4.77146	+	4.77146i	0.209444	+	0.209444i
$520$	−1.73601	−	4.19110i	−0.0761290	−	0.183792i
$521$	−35.7139	+	14.7932i	−1.56465	+	0.648101i	−0.985890	−	0.167395i	$-0.946465\pi$
$521$	−35.7139	+	14.7932i	−1.56465	+	0.648101i	−0.578764	+	0.815495i	$0.696465\pi$
$522$	−4.23458	+	10.2232i	−0.185342	+	0.447456i
$523$			0.599508i			0.0262147i	0.999914	+	0.0131073i	$0.00417231\pi$
$523$			0.599508i			0.0262147i	−0.999914	+	0.0131073i	$0.995828\pi$
$524$	−52.5960	−	21.7860i	−2.29767	−	0.951724i
$525$	−3.97508	+	3.97508i	−0.173487	+	0.173487i
$526$	50.1547			2.18685
$527$	−10.0742	−	0.237259i	−0.438839	−	0.0103352i
$528$	5.48646			0.238767
$529$	38.9054	−	38.9054i	1.69154	−	1.69154i
$530$	12.3667	+	5.12244i	0.537174	+	0.222505i
$531$		−	2.40101i		−	0.104195i
$532$	−17.5936	+	42.4747i	−0.762779	+	1.84151i
$533$	−5.03258	+	2.08456i	−0.217985	+	0.0902925i
$534$	−3.09825	−	7.47983i	−0.134074	−	0.323684i
$535$	−0.440638	−	0.440638i	−0.0190504	−	0.0190504i
$536$	−18.4209	−	18.4209i	−0.795661	−	0.795661i
$537$	0.0706732	+	0.170620i	0.00304977	+	0.00736281i
$538$	9.13009	−	3.78181i	0.393626	−	0.163045i
$539$	−5.54031	+	13.3755i	−0.238638	+	0.576123i
$540$			19.6031i			0.843582i
$541$	36.6847	+	15.1953i	1.57720	+	0.653297i	0.987966	−	0.154668i	$-0.0494308\pi$
$541$	36.6847	+	15.1953i	1.57720	+	0.653297i	0.589231	+	0.807965i	$0.299431\pi$
$542$	−41.0998	+	41.0998i	−1.76539	+	1.76539i
$543$	3.64660			0.156491
$544$	−6.48774	+	14.6756i	−0.278160	+	0.629211i
$545$	−6.18952			−0.265130
$546$	−11.7749	+	11.7749i	−0.503919	+	0.503919i
$547$	−3.73035	−	1.54516i	−0.159498	−	0.0660663i	0.301506	−	0.953464i	$-0.402511\pi$
$547$	−3.73035	−	1.54516i	−0.159498	−	0.0660663i	−0.461004	+	0.887398i	$0.652511\pi$
$548$			60.5007i			2.58446i
$549$	0.0499231	−	0.120525i	0.00213067	−	0.00514388i
$550$	−5.39437	+	2.23442i	−0.230017	+	0.0952760i
$551$	12.1822	+	29.4105i	0.518980	+	1.25293i
$552$	−35.3045	−	35.3045i	−1.50266	−	1.50266i
$553$	−22.8869	−	22.8869i	−0.973250	−	0.973250i
$554$	−18.0571	−	43.5937i	−0.767172	−	1.85212i
$555$	−6.67175	+	2.76353i	−0.283200	+	0.117305i
$556$	2.88269	−	6.95942i	0.122253	−	0.295145i
$557$			5.42781i			0.229984i	0.993366	+	0.114992i	$0.0366842\pi$
$557$			5.42781i			0.229984i	−0.993366	+	0.114992i	$0.963316\pi$
$558$	−2.85252	−	1.18155i	−0.120757	−	0.0500190i
$559$	6.72145	−	6.72145i	0.284287	−	0.284287i
$560$	5.04437			0.213163
$561$	14.9817	−	5.79624i	0.632528	−	0.244718i
$562$	59.2222			2.49814
$563$	−3.66888	+	3.66888i	−0.154625	+	0.154625i	−0.780180	−	0.625555i	$-0.784873\pi$
$563$	−3.66888	+	3.66888i	−0.154625	+	0.154625i	0.625555	+	0.780180i	$0.284873\pi$
$564$	58.0231	+	24.0339i	2.44321	+	1.01201i
$565$			16.0596i			0.675632i
$566$	7.63822	−	18.4403i	0.321058	−	0.775104i
$567$	23.4973	−	9.73290i	0.986794	−	0.408744i
$568$	2.53311	+	6.11547i	0.106287	+	0.256600i
$569$	8.48266	+	8.48266i	0.355611	+	0.355611i	0.862192	−	0.506581i	$-0.169091\pi$
$569$	8.48266	+	8.48266i	0.355611	+	0.355611i	−0.506581	+	0.862192i	$0.669091\pi$
$570$	9.48520	+	9.48520i	0.397291	+	0.397291i
$571$	−16.6512	−	40.1996i	−0.696833	−	1.68230i	−0.730539	−	0.682871i	$-0.760731\pi$
$571$	−16.6512	−	40.1996i	−0.696833	−	1.68230i	0.0337061	−	0.999432i	$-0.489269\pi$
$572$	−10.2015	+	4.22561i	−0.426548	+	0.176682i
$573$	8.80561	−	21.2586i	0.367860	−	0.888092i
$574$		−	36.4371i		−	1.52085i
$575$	8.16056	+	3.38021i	0.340319	+	0.140965i
$576$	−4.54607	+	4.54607i	−0.189420	+	0.189420i
$577$	27.7097			1.15357			0.576784	−	0.816897i	$-0.304307\pi$
$577$	27.7097			1.15357			0.576784	+	0.816897i	$0.304307\pi$
$578$	1.88222	−	39.9380i	0.0782900	−	1.66120i
$579$	−13.1764			−0.547591
$580$	21.8727	−	21.8727i	0.908212	−	0.908212i
$581$	−24.2111	−	10.0286i	−1.00445	−	0.416055i
$582$		−	36.2467i		−	1.50247i
$583$	5.40709	−	13.0539i	0.223939	−	0.540636i
$584$	18.2107	−	7.54311i	0.753563	−	0.312136i
$585$	−0.258892	−	0.625020i	−0.0107039	−	0.0258414i
$586$	−43.2181	−	43.2181i	−1.78532	−	1.78532i
$587$	3.09653	+	3.09653i	0.127808	+	0.127808i	0.768117	−	0.640309i	$-0.221194\pi$
$587$	3.09653	+	3.09653i	0.127808	+	0.127808i	−0.640309	+	0.768117i	$0.721194\pi$
$588$	−12.3680	−	29.8590i	−0.510048	−	1.23137i
$589$	−8.20624	+	3.39914i	−0.338132	+	0.140059i
$590$	−4.02316	+	9.71276i	−0.165631	+	0.399868i
$591$			10.4856i			0.431320i
$592$	5.98668	+	2.47976i	0.246051	+	0.101918i
$593$	25.3698	−	25.3698i	1.04181	−	1.04181i	0.0427255	−	0.999087i	$-0.486396\pi$
$593$	25.3698	−	25.3698i	1.04181	−	1.04181i	0.999087	−	0.0427255i	$-0.0136041\pi$
$594$	32.4114			1.32985
$595$	13.7745	−	5.32919i	0.564700	−	0.218476i
$596$	65.4673			2.68164
$597$	−20.9420	+	20.9420i	−0.857099	+	0.857099i
$598$	24.1730	+	10.0128i	0.988509	+	0.409454i
$599$		−	11.1415i		−	0.455230i	−0.973751	−	0.227615i	$-0.926907\pi$
$599$		−	11.1415i		−	0.455230i	0.973751	−	0.227615i	$-0.0730928\pi$
$600$	2.16312	−	5.22222i	0.0883088	−	0.213196i
$601$	18.8938	−	7.82606i	0.770693	−	0.319232i	0.0375402	−	0.999295i	$-0.488048\pi$
$601$	18.8938	−	7.82606i	0.770693	−	0.319232i	0.733153	+	0.680063i	$0.238048\pi$
$602$	24.3324	+	58.7437i	0.991716	+	2.39421i
$603$	−2.74712	−	2.74712i	−0.111871	−	0.111871i
$604$	22.2558	+	22.2558i	0.905574	+	0.905574i
$605$	−1.85093	−	4.46855i	−0.0752512	−	0.181672i
$606$	−18.6328	+	7.71795i	−0.756905	+	0.313520i
$607$	0.602934	−	1.45561i	0.0244723	−	0.0590814i	−0.911171	−	0.412028i	$-0.864820\pi$
$607$	0.602934	−	1.45561i	0.0244723	−	0.0590814i	0.935643	+	0.352947i	$0.114820\pi$
$608$			14.1435i			0.573593i
$609$	−45.4925	−	18.8436i	−1.84345	−	0.763582i
$610$	−0.403905	+	0.403905i	−0.0163536	+	0.0163536i
$611$	−14.2727			−0.577410
$612$	3.16227	−	7.15321i	0.127827	−	0.289151i
$613$	−22.4800			−0.907959			−0.453980	−	0.891012i	$-0.649996\pi$
$613$	−22.4800			−0.907959			−0.453980	+	0.891012i	$0.649996\pi$
$614$	28.1845	−	28.1845i	1.13743	−	1.13743i
$615$	−6.27074	−	2.59743i	−0.252861	−	0.104738i
$616$		−	32.0307i		−	1.29055i
$617$	10.4081	−	25.1273i	0.419013	−	1.01159i	−0.563621	−	0.826034i	$-0.690592\pi$
$617$	10.4081	−	25.1273i	0.419013	−	1.01159i	0.982634	−	0.185554i	$-0.0594079\pi$
$618$	−24.4181	+	10.1143i	−0.982241	+	0.406858i
$619$	5.49924	+	13.2763i	0.221033	+	0.533621i	0.995031	−	0.0995671i	$-0.0317458\pi$
$619$	5.49924	+	13.2763i	0.221033	+	0.533621i	−0.773998	+	0.633188i	$0.781746\pi$
$620$	6.10301	+	6.10301i	0.245103	+	0.245103i
$621$	−34.6706	−	34.6706i	−1.39128	−	1.39128i
$622$	15.4720	+	37.3527i	0.620371	+	1.49771i
$623$	−7.25927	+	3.00689i	−0.290837	+	0.120469i
$624$	1.06517	−	2.57154i	0.0426408	−	0.102944i
$625$			1.00000i			0.0400000i
$626$	−12.8523	−	5.32358i	−0.513680	−	0.212773i
$627$	10.0123	−	10.0123i	0.399852	−	0.399852i
$628$	−64.4228			−2.57075
$629$	18.9674	+	0.446705i	0.756280	+	0.0178113i
$630$	4.52529			0.180292
$631$	−16.4538	+	16.4538i	−0.655014	+	0.655014i	−0.954196	−	0.299182i	$-0.903286\pi$
$631$	−16.4538	+	16.4538i	−0.655014	+	0.655014i	0.299182	+	0.954196i	$0.403286\pi$
$632$	30.0675	+	12.4544i	1.19602	+	0.495408i
$633$		−	10.3887i		−	0.412913i
$634$	−0.576538	+	1.39189i	−0.0228972	+	0.0552788i
$635$	−5.46739	+	2.26467i	−0.216967	+	0.0898706i
$636$	12.0706	+	29.1411i	0.478632	+	1.15552i
$637$	5.19356	+	5.19356i	0.205776	+	0.205776i
$638$	−36.1638	−	36.1638i	−1.43174	−	1.43174i
$639$	0.377764	+	0.912004i	0.0149441	+	0.0360783i
$640$	18.8167	−	7.79414i	0.743796	−	0.308090i
$641$	−2.06038	+	4.97419i	−0.0813800	+	0.196469i	−0.959332	−	0.282280i	$-0.908909\pi$
$641$	−2.06038	+	4.97419i	−0.0813800	+	0.196469i	0.877952	+	0.478748i	$0.158909\pi$
$642$		−	2.30004i		−	0.0907754i
$643$	14.9568	+	6.19532i	0.589839	+	0.244319i	0.657582	−	0.753383i	$-0.271580\pi$
$643$	14.9568	+	6.19532i	0.589839	+	0.244319i	−0.0677421	+	0.997703i	$0.521580\pi$
$644$	−79.0101	+	79.0101i	−3.11343	+	3.11343i
$645$	11.8442			0.466365
$646$	−12.7163	−	32.8683i	−0.500318	−	1.29319i
$647$	−25.8383			−1.01581			−0.507904	−	0.861413i	$-0.669580\pi$
$647$	−25.8383			−1.01581			−0.507904	+	0.861413i	$0.669580\pi$
$648$	−18.0829	+	18.0829i	−0.710362	+	0.710362i
$649$	10.2525	+	4.24672i	0.402445	+	0.166698i
$650$			2.96218i			0.116186i
$651$	5.25783	−	12.6935i	0.206071	−	0.497499i
$652$	−30.5548	+	12.6562i	−1.19662	+	0.495656i
$653$	−4.77529	−	11.5286i	−0.186872	−	0.451148i	0.802483	−	0.596675i	$-0.203512\pi$
$653$	−4.77529	−	11.5286i	−0.186872	−	0.451148i	−0.989354	+	0.145528i	$0.953512\pi$
$654$	−16.1540	−	16.1540i	−0.631672	−	0.631672i
$655$	11.3991	+	11.3991i	0.445399	+	0.445399i
$656$	2.33072	+	5.62685i	0.0909992	+	0.219691i
$657$	2.71577	−	1.12491i	0.105952	−	0.0438868i
$658$	36.5353	−	88.2040i	1.42429	−	3.43855i
$659$			41.7109i			1.62483i	0.583082	+	0.812413i	$0.301847\pi$
$659$			41.7109i			1.62483i	−0.583082	+	0.812413i	$0.698153\pi$
$660$	−12.7114	−	5.26523i	−0.494791	−	0.204949i
$661$	−12.8495	+	12.8495i	−0.499789	+	0.499789i	−0.911372	−	0.411583i	$-0.864976\pi$
$661$	−12.8495	+	12.8495i	−0.499789	+	0.499789i	0.411583	+	0.911372i	$0.364976\pi$
$662$	−27.4252			−1.06591
$663$	0.191880	−	8.14734i	0.00745199	−	0.316417i
$664$	26.3499			1.02257
$665$	9.20551	−	9.20551i	0.356974	−	0.356974i
$666$	5.37063	+	2.22459i	0.208108	+	0.0862011i
$667$			77.3693i			2.99575i
$668$	−12.5430	+	30.2815i	−0.485304	+	1.17163i
$669$	−4.26653	+	1.76726i	−0.164954	+	0.0683260i
$670$	6.50975	+	15.7159i	0.251493	+	0.607159i
$671$	0.426350	+	0.426350i	0.0164590	+	0.0164590i
$672$	−15.4696	−	15.4696i	−0.596753	−	0.596753i
$673$	2.44794	+	5.90984i	0.0943610	+	0.227808i	0.964012	−	0.265860i	$-0.0856559\pi$
$673$	2.44794	+	5.90984i	0.0943610	+	0.227808i	−0.869651	+	0.493668i	$0.835656\pi$
$674$	67.0997	−	27.7936i	2.58458	−	1.07057i
$675$	2.12428	−	5.12847i	0.0817636	−	0.197395i
$676$		−	40.3069i		−	1.55026i
$677$	−38.7001	−	16.0301i	−1.48737	−	0.616087i	−0.516624	−	0.856212i	$-0.672811\pi$
$677$	−38.7001	−	16.0301i	−1.48737	−	0.616087i	−0.970742	+	0.240125i	$0.922811\pi$
$678$	−41.9140	+	41.9140i	−1.60970	+	1.60970i
$679$	−35.1779			−1.35000
$680$	−10.7453	+	10.2508i	−0.412064	+	0.393101i
$681$	33.7812			1.29450
$682$	10.0906	−	10.0906i	0.386389	−	0.386389i
$683$	27.9994	+	11.5977i	1.07137	+	0.443775i	0.847473	−	0.530838i	$-0.178123\pi$
$683$	27.9994	+	11.5977i	1.07137	+	0.443775i	0.223895	+	0.974613i	$0.428123\pi$
$684$		−	6.89384i		−	0.263593i
$685$	6.55613	−	15.8279i	0.250497	−	0.604753i
$686$	9.09419	−	3.76694i	0.347218	−	0.143822i
$687$	−7.17126	−	17.3130i	−0.273601	−	0.660530i
$688$	−7.51514	−	7.51514i	−0.286512	−	0.286512i
$689$	−5.06869	−	5.06869i	−0.193102	−	0.193102i
$690$	12.4762	+	30.1203i	0.474962	+	1.14666i
$691$	5.35185	−	2.21681i	0.203594	−	0.0843314i	−0.278556	−	0.960420i	$-0.589856\pi$
$691$	5.35185	−	2.21681i	0.203594	−	0.0843314i	0.482150	+	0.876088i	$0.339856\pi$
$692$	−5.81083	+	14.0286i	−0.220895	+	0.533287i
$693$		−	4.77676i		−	0.181454i
$694$	−0.0325913	−	0.0134997i	−0.00123715	−	0.000512443i
$695$	−1.50831	+	1.50831i	−0.0572135	+	0.0572135i
$696$	49.5113			1.87672
$697$	12.3090	+	12.9027i	0.466236	+	0.488726i
$698$	−8.59600			−0.325363
$699$	11.1732	−	11.1732i	0.422611	−	0.422611i
$700$	−11.6871	−	4.84097i	−0.441732	−	0.182971i
$701$		−	5.24783i		−	0.198208i	−0.995077	−	0.0991039i	$-0.968402\pi$
$701$		−	5.24783i		−	0.198208i	0.995077	−	0.0991039i	$-0.0315976\pi$
$702$	6.29250	−	15.1914i	0.237495	−	0.573364i
$703$	15.4505	−	6.39979i	0.582726	−	0.241373i
$704$	−11.3713	−	27.4527i	−0.428572	−	1.03466i
$705$	−12.5753	−	12.5753i	−0.473613	−	0.473613i
$706$	6.35837	+	6.35837i	0.239300	+	0.239300i
$707$	7.49037	+	18.0833i	0.281704	+	0.680094i
$708$	−22.8873	+	9.48025i	−0.860159	+	0.356290i
$709$	15.9798	−	38.5786i	0.600134	−	1.44885i	−0.273310	−	0.961926i	$-0.588118\pi$
$709$	15.9798	−	38.5786i	0.600134	−	1.44885i	0.873444	−	0.486925i	$-0.161882\pi$
$710$		−	4.32229i		−	0.162213i
$711$	4.48398	+	1.85733i	0.168162	+	0.0696551i
$712$	5.58654	−	5.58654i	0.209364	−	0.209364i
$713$	−21.5879			−0.808475
$714$	49.8588	+	22.0414i	1.86592	+	0.824880i
$715$	3.12678			0.116935
$716$	−0.293855	+	0.293855i	−0.0109819	+	0.0109819i
$717$	24.1049	+	9.98458i	0.900214	+	0.372881i
$718$			15.7501i			0.587789i
$719$	3.89643	−	9.40681i	0.145312	−	0.350815i	−0.834419	−	0.551130i	$-0.814197\pi$
$719$	3.89643	−	9.40681i	0.145312	−	0.350815i	0.979731	+	0.200316i	$0.0641967\pi$
$720$	−0.698825	+	0.289463i	−0.0260437	+	0.0107876i
$721$	9.81608	+	23.6981i	0.365570	+	0.882564i
$722$	9.63199	+	9.63199i	0.358465	+	0.358465i
$723$	−6.57164	−	6.57164i	−0.244402	−	0.244402i
$724$	3.14022	+	7.58117i	0.116705	+	0.281752i
$725$	−8.09244	+	3.35200i	−0.300546	+	0.124490i
$726$	6.83172	−	16.4932i	0.253549	−	0.612121i
$727$			46.0182i			1.70672i	0.521321	+	0.853361i	$0.325439\pi$
$727$			46.0182i			1.70672i	−0.521321	+	0.853361i	$0.674561\pi$
$728$	−15.0130	−	6.21860i	−0.556420	−	0.230477i
$729$	−21.1766	+	21.1766i	−0.784317	+	0.784317i
$730$	−12.8709			−0.476374
$731$	−28.4609	−	12.5819i	−1.05266	−	0.465358i
$732$	−1.34601			−0.0497498
$733$	−1.80962	+	1.80962i	−0.0668398	+	0.0668398i	−0.739736	−	0.672897i	$-0.765050\pi$
$733$	−1.80962	+	1.80962i	−0.0668398	+	0.0668398i	0.672897	+	0.739736i	$0.265050\pi$
$734$	−50.0360	−	20.7256i	−1.84686	−	0.764996i
$735$			9.15184i			0.337571i
$736$	−13.1546	+	31.7580i	−0.484885	+	1.17062i
$737$	16.5892	−	6.87149i	0.611072	−	0.253114i
$738$	2.09088	+	5.04783i	0.0769664	+	0.185813i
$739$	1.75127	+	1.75127i	0.0644215	+	0.0644215i	0.738583	−	0.674162i	$-0.235495\pi$
$739$	1.75127	+	1.75127i	0.0644215	+	0.0644215i	−0.674162	+	0.738583i	$0.735495\pi$
$740$	−11.4906	−	11.4906i	−0.422402	−	0.422402i
$741$	−2.74899	−	6.63666i	−0.100987	−	0.243804i
$742$	44.2989	−	18.3492i	1.62627	−	0.673621i
$743$	0.610291	−	1.47337i	0.0223894	−	0.0540528i	−0.912289	−	0.409546i	$-0.865687\pi$
$743$	0.610291	−	1.47337i	0.0223894	−	0.0540528i	0.934679	+	0.355493i	$0.115687\pi$
$744$			13.8149i			0.506478i
$745$	−17.1272	−	7.09433i	−0.627493	−	0.259916i
$746$	−39.4646	+	39.4646i	−1.44490	+	1.44490i
$747$	3.92957			0.143776
$748$	24.9515	+	26.1551i	0.912317	+	0.956326i
$749$	−2.23222			−0.0815636
$750$	−2.60990	+	2.60990i	−0.0953001	+	0.0953001i
$751$	11.7741	+	4.87697i	0.429641	+	0.177963i	0.587015	−	0.809576i	$-0.300303\pi$
$751$	11.7741	+	4.87697i	0.429641	+	0.177963i	−0.157374	+	0.987539i	$0.550303\pi$
$752$			15.9580i			0.581930i
$753$	4.66801	−	11.2696i	0.170112	−	0.410686i
$754$	−23.9713	+	9.92922i	−0.872982	+	0.361601i
$755$	−3.41071	−	8.23418i	−0.124128	−	0.299672i
$756$	49.6535	+	49.6535i	1.80588	+	1.80588i
$757$	−32.5674	−	32.5674i	−1.18368	−	1.18368i	−0.978783	−	0.204901i	$-0.934313\pi$
$757$	−32.5674	−	32.5674i	−1.18368	−	1.18368i	−0.204901	−	0.978783i	$-0.565687\pi$
$758$	−2.68047	−	6.47123i	−0.0973592	−	0.235046i
$759$	31.7940	−	13.1695i	1.15405	−	0.478023i
$760$	−5.00936	+	12.0937i	−0.181709	+	0.438683i
$761$		−	29.7003i		−	1.07664i	−0.842742	−	0.538318i	$-0.819060\pi$
$761$		−	29.7003i		−	1.07664i	0.842742	−	0.538318i	$-0.180940\pi$
$762$	−20.1799	−	8.35879i	−0.731041	−	0.302807i
$763$	−15.6777	+	15.6777i	−0.567571	+	0.567571i
$764$	51.7788			1.87329
$765$	−1.60245	+	1.52871i	−0.0579368	+	0.0552706i
$766$	−57.4385			−2.07534
$767$	3.98093	−	3.98093i	0.143743	−	0.143743i
$768$	34.7437	+	14.3913i	1.25370	+	0.519301i
$769$		−	43.8299i		−	1.58055i	−0.612755	−	0.790273i	$-0.709939\pi$
$769$		−	43.8299i		−	1.58055i	0.612755	−	0.790273i	$-0.290061\pi$
$770$	−8.00397	+	19.3233i	−0.288443	+	0.696363i
$771$	11.6946	−	4.84408i	0.421172	−	0.174455i
$772$	−11.3466	−	27.3932i	−0.408375	−	0.985904i
$773$	19.7369	+	19.7369i	0.709887	+	0.709887i	0.966511	−	0.256624i	$-0.0826103\pi$
$773$	19.7369	+	19.7369i	0.709887	+	0.709887i	−0.256624	+	0.966511i	$0.582610\pi$
$774$	−6.74182	−	6.74182i	−0.242330	−	0.242330i
$775$	−0.935290	−	2.25799i	−0.0335966	−	0.0811094i
$776$	32.6787	−	13.5359i	1.17310	−	0.485912i
$777$	−9.89930	+	23.8990i	−0.355135	+	0.857372i
$778$			3.97159i			0.142388i
$779$	14.5218	+	6.01513i	0.520298	+	0.215515i
$780$	−4.93571	+	4.93571i	−0.176727	+	0.176727i
$781$	−4.56247			−0.163258
$782$	2.01670	−	85.6304i	0.0721170	−	3.06214i
$783$	48.6224			1.73762
$784$	5.80684	−	5.80684i	0.207387	−	0.207387i
$785$	16.8540	+	6.98115i	0.601545	+	0.249168i
$786$			59.5010i			2.12233i
$787$	11.4892	−	27.7373i	0.409544	−	0.988728i	−0.575713	−	0.817652i	$-0.695276\pi$
$787$	11.4892	−	27.7373i	0.409544	−	0.988728i	0.985258	−	0.171076i	$-0.0547244\pi$
$788$	−21.7992	+	9.02954i	−0.776566	+	0.321664i
$789$	−12.8071	−	30.9192i	−0.455946	−	1.10075i
$790$	−15.0268	−	15.0268i	−0.534629	−	0.534629i
$791$	40.6781	+	40.6781i	1.44635	+	1.44635i
$792$	1.83803	+	4.43740i	0.0653115	+	0.157676i
$793$	0.282607	−	0.117060i	0.0100357	−	0.00415691i
$794$	−28.3741	+	68.5012i	−1.00696	+	2.43102i
$795$		−	8.93178i		−	0.316778i
$796$	−61.5717	−	25.5038i	−2.18235	−	0.903959i
$797$	3.65013	−	3.65013i	0.129294	−	0.129294i	−0.639498	−	0.768793i	$-0.720858\pi$
$797$	3.65013	−	3.65013i	0.129294	−	0.129294i	0.768793	+	0.639498i	$0.220858\pi$
$798$	48.0509			1.70099
$799$	16.8591	+	43.5761i	0.596432	+	1.54161i
$800$	−3.89165			−0.137591
$801$	0.833123	−	0.833123i	0.0294370	−	0.0294370i
$802$	11.0079	+	4.55963i	0.388704	+	0.161006i
$803$			13.5861i			0.479445i
$804$	−15.3397	+	37.0333i	−0.540990	+	1.30606i
$805$	29.2321	−	12.1083i	1.03030	−	0.426763i
$806$	−2.77050	−	6.68857i	−0.0975866	−	0.235595i
$807$	−4.66278	−	4.66278i	−0.164138	−	0.164138i
$808$	−13.9164	−	13.9164i	−0.489579	−	0.489579i
$809$	8.50871	+	20.5418i	0.299150	+	0.722213i	0.999961	+	0.00886509i	$0.00282188\pi$
$809$	8.50871	+	20.5418i	0.299150	+	0.722213i	−0.700810	+	0.713348i	$0.747178\pi$
$810$	15.4275	−	6.39030i	0.542069	−	0.224532i
$811$	−5.99450	+	14.4720i	−0.210495	+	0.508181i	−0.993500	−	0.113836i	$-0.963686\pi$
$811$	−5.99450	+	14.4720i	−0.210495	+	0.508181i	0.783004	+	0.622016i	$0.213686\pi$
$812$		−	110.804i		−	3.88847i
$813$	35.8320	+	14.8421i	1.25668	+	0.520535i
$814$	−18.9983	+	18.9983i	−0.665889	+	0.665889i
$815$	9.36510			0.328045
$816$	−9.10941	−	0.214537i	−0.318893	−	0.00751031i
$817$	−27.4289			−0.959615
$818$	−43.4351	+	43.4351i	−1.51867	+	1.51867i
$819$	−2.23890	−	0.927383i	−0.0782335	−	0.0324054i
$820$		−	15.2734i		−	0.533370i
$821$	13.3707	−	32.2797i	0.466640	−	1.12657i	−0.498981	−	0.866613i	$-0.666292\pi$
$821$	13.3707	−	32.2797i	0.466640	−	1.12657i	0.965621	−	0.259955i	$-0.0837077\pi$
$822$	58.4201	−	24.1984i	2.03764	−	0.844017i
$823$	0.935339	+	2.25811i	0.0326039	+	0.0787127i	0.939343	−	0.342980i	$-0.111436\pi$
$823$	0.935339	+	2.25811i	0.0326039	+	0.0787127i	−0.906739	+	0.421692i	$0.861436\pi$
$824$	−18.2374	−	18.2374i	−0.635330	−	0.635330i
$825$	2.75493	+	2.75493i	0.0959144	+	0.0959144i
$826$	14.4114	+	34.7923i	0.501438	+	1.21058i
$827$	−46.9533	+	19.4487i	−1.63273	+	0.676298i	−0.995534	−	0.0944054i	$-0.969905\pi$
$827$	−46.9533	+	19.4487i	−1.63273	+	0.676298i	−0.637194	+	0.770703i	$0.719905\pi$
$828$	6.41185	−	15.4796i	0.222827	−	0.537952i
$829$			41.5846i			1.44429i	0.691740	+	0.722147i	$0.256844\pi$
$829$			41.5846i			1.44429i	−0.691740	+	0.722147i	$0.743156\pi$
$830$	−15.8962	−	6.58442i	−0.551765	−	0.228549i
$831$	−22.2635	+	22.2635i	−0.772313	+	0.772313i
$832$	−15.0750			−0.522631
$833$	9.72184	−	21.9913i	0.336842	−	0.761952i
$834$	−7.87308			−0.272623
$835$	6.56289	−	6.56289i	0.227118	−	0.227118i
$836$	29.4371	+	12.1933i	1.01810	+	0.421713i
$837$			13.5668i			0.468939i
$838$	6.56894	−	15.8588i	0.226920	−	0.547834i
$839$	4.10912	−	1.70205i	0.141863	−	0.0587614i	−0.310623	−	0.950533i	$-0.600538\pi$
$839$	4.10912	−	1.70205i	0.141863	−	0.0587614i	0.452485	+	0.891772i	$0.350538\pi$
$840$	−7.74855	−	18.7067i	−0.267350	−	0.645441i
$841$	−33.7456	−	33.7456i	−1.16364	−	1.16364i
$842$	−35.0311	−	35.0311i	−1.20725	−	1.20725i
$843$	−15.1225	−	36.5090i	−0.520848	−	1.25744i
$844$	21.5977	−	8.94607i	0.743424	−	0.307936i
$845$	−4.36784	+	10.5449i	−0.150258	+	0.362755i
$846$			14.3159i			0.492191i
$847$	−16.0069	−	6.63027i	−0.550004	−	0.227819i
$848$	−5.66721	+	5.66721i	−0.194613	+	0.194613i
$849$	−13.3184			−0.457088
$850$	9.04388	−	3.49897i	0.310202	−	0.120014i
$851$	40.6451			1.39330
$852$	7.20198	−	7.20198i	0.246736	−	0.246736i
$853$	16.5251	+	6.84491i	0.565808	+	0.234365i	0.647204	−	0.762317i	$-0.275938\pi$
$853$	16.5251	+	6.84491i	0.565808	+	0.234365i	−0.0813967	+	0.996682i	$0.525938\pi$
$854$			2.04614i			0.0700174i
$855$	−0.747048	+	1.80353i	−0.0255485	+	0.0616796i
$856$	2.07363	−	0.858928i	0.0708754	−	0.0293575i
$857$	14.7557	+	35.6234i	0.504045	+	1.21687i	0.947263	+	0.320458i	$0.103837\pi$
$857$	14.7557	+	35.6234i	0.504045	+	1.21687i	−0.443218	+	0.896414i	$0.646163\pi$
$858$	8.16060	+	8.16060i	0.278598	+	0.278598i
$859$	2.48184	+	2.48184i	0.0846792	+	0.0846792i	0.748178	−	0.663498i	$-0.230929\pi$
$859$	2.48184	+	2.48184i	0.0846792	+	0.0846792i	−0.663498	+	0.748178i	$0.730929\pi$
$860$	10.1995	+	24.6237i	0.347799	+	0.839662i
$861$	−22.4626	+	9.30430i	−0.765522	+	0.317090i
$862$	−18.9396	+	45.7243i	−0.645086	+	1.55738i
$863$		−	21.9552i		−	0.747365i	−0.927557	−	0.373683i	$-0.878095\pi$
$863$		−	21.9552i		−	0.747365i	0.927557	−	0.373683i	$-0.121905\pi$
$864$	19.9582	+	8.26695i	0.678991	+	0.281247i
$865$	3.04040	−	3.04040i	0.103377	−	0.103377i
$866$	−87.3171			−2.96715
$867$	−25.1014	+	9.03793i	−0.852490	+	0.306944i
$868$	30.9171			1.04940
$869$	−15.8618	+	15.8618i	−0.538075	+	0.538075i
$870$	−29.8689	−	12.3721i	−1.01265	−	0.419453i
$871$		−	9.10956i		−	0.308666i
$872$	8.53133	−	20.5964i	0.288907	−	0.697484i
$873$	4.87339	−	2.01862i	0.164939	−	0.0683200i
$874$	−28.8925	−	69.7528i	−0.977305	−	2.35942i
$875$	2.53294	+	2.53294i	0.0856291	+	0.0856291i
$876$	−21.4461	−	21.4461i	−0.724596	−	0.724596i
$877$	2.16444	+	5.22542i	0.0730879	+	0.176450i	0.956201	−	0.292710i	$-0.0945569\pi$
$877$	2.16444	+	5.22542i	0.0730879	+	0.176450i	−0.883113	+	0.469159i	$0.844557\pi$
$878$	1.02413	−	0.424209i	0.0345628	−	0.0143164i
$879$	−15.6071	+	37.6788i	−0.526413	+	1.27087i
$880$		−	3.49601i		−	0.117850i
$881$	31.7736	+	13.1611i	1.07048	+	0.443407i	0.847160	−	0.531338i	$-0.178311\pi$
$881$	31.7736	+	13.1611i	1.07048	+	0.443407i	0.223320	+	0.974745i	$0.428311\pi$
$882$	5.20930	−	5.20930i	0.175406	−	0.175406i
$883$	−58.3115			−1.96234			−0.981170	−	0.193148i	$-0.938130\pi$
$883$	−58.3115			−1.96234			−0.981170	+	0.193148i	$0.938130\pi$
$884$	17.1033	−	6.61706i	0.575246	−	0.222556i
$885$	7.01500			0.235807
$886$	−18.3349	+	18.3349i	−0.615973	+	0.615973i
$887$	41.1137	+	17.0299i	1.38046	+	0.571807i	0.944605	−	0.328208i	$-0.106445\pi$
$887$	41.1137	+	17.0299i	1.38046	+	0.571807i	0.435859	+	0.900015i	$0.356445\pi$
$888$		−	26.0102i		−	0.872846i
$889$	−8.11232	+	19.5849i	−0.272078	+	0.656855i
$890$	−4.76620	+	1.97422i	−0.159763	+	0.0661761i
$891$	−6.74540	−	16.2848i	−0.225979	−	0.545563i
$892$	−7.34813	−	7.34813i	−0.246034	−	0.246034i
$893$	29.1220	+	29.1220i	0.974529	+	0.974529i
$894$	−26.1849	−	63.2159i	−0.875754	−	2.11426i
$895$	0.108720	−	0.0450334i	0.00363412	−	0.00150530i
$896$	27.9196	−	67.4038i	0.932727	−	2.25180i
$897$		−	17.4589i		−	0.582935i
$898$	37.5109	+	15.5375i	1.25175	+	0.518494i
$899$	15.1376	−	15.1376i	0.504866	−	0.504866i
$900$	1.89688			0.0632292
$901$	−9.48808	+	21.4625i	−0.316094	+	0.715019i
$902$	−25.2527			−0.840824
$903$	30.0007	−	30.0007i	0.998361	−	0.998361i
$904$	−53.4405	−	22.1358i	−1.77740	−	0.736225i
$905$		−	2.32364i		−	0.0772404i
$906$	12.5888	−	30.3920i	0.418234	−	1.00971i
$907$	−32.6800	+	13.5365i	−1.08512	+	0.449472i	−0.852303	−	0.523048i	$-0.824795\pi$
$907$	−32.6800	+	13.5365i	−1.08512	+	0.449472i	−0.232819	+	0.972520i	$0.574795\pi$
$908$	29.0903	+	70.2301i	0.965394	+	2.33067i
$909$	−2.07537	−	2.07537i	−0.0688355	−	0.0688355i
$910$	7.50303	+	7.50303i	0.248723	+	0.248723i
$911$	−18.8207	−	45.4373i	−0.623559	−	1.50540i	−0.847496	−	0.530801i	$-0.821891\pi$
$911$	−18.8207	−	45.4373i	−0.623559	−	1.50540i	0.223937	−	0.974604i	$-0.428109\pi$
$912$	−7.42034	+	3.07361i	−0.245712	+	0.101777i
$913$	−6.95031	+	16.7795i	−0.230022	+	0.555322i
$914$			26.5004i			0.876554i
$915$	0.352136	+	0.145859i	0.0116413	+	0.00482197i
$916$	29.8176	−	29.8176i	0.985202	−	0.985202i
$917$	57.7465			1.90696
$918$	−53.8140	−	1.26738i	−1.77613	−	0.0418299i
$919$	49.6635			1.63825			0.819123	−	0.573618i	$-0.194460\pi$
$919$	49.6635			1.63825			0.819123	+	0.573618i	$0.194460\pi$
$920$	−22.4962	+	22.4962i	−0.741679	+	0.741679i
$921$	−24.5720	−	10.1781i	−0.809676	−	0.335379i
$922$		−	70.5747i		−	2.32425i
$923$	−0.885781	+	2.13846i	−0.0291558	+	0.0703884i
$924$	−45.5338	+	18.8607i	−1.49795	+	0.620472i
$925$	1.76094	+	4.25128i	0.0578993	+	0.139781i
$926$	28.5366	+	28.5366i	0.937770	+	0.937770i
$927$	−2.71975	−	2.71975i	−0.0893284	−	0.0893284i
$928$	−13.0448	−	31.4929i	−0.428216	−	1.03381i
$929$	−31.5196	+	13.0558i	−1.03412	+	0.428348i	−0.834199	−	0.551463i	$-0.814070\pi$
$929$	−31.5196	+	13.0558i	−1.03412	+	0.428348i	−0.199924	+	0.979811i	$0.564070\pi$
$930$	3.45212	−	8.33415i	0.113199	−	0.273287i
$931$		−	21.1939i		−	0.694601i
$932$	32.8505	+	13.6071i	1.07605	+	0.445716i
$933$	19.0762	−	19.0762i	0.624528	−	0.624528i
$934$	62.5405			2.04639
$935$	−3.69340	−	9.54644i	−0.120787	−	0.312202i
$936$	2.43668			0.0796455
$937$	−27.2430	+	27.2430i	−0.889991	+	0.889991i	−0.994522	−	0.104530i	$-0.966666\pi$
$937$	−27.2430	+	27.2430i	−0.889991	+	0.889991i	0.104530	+	0.994522i	$0.466666\pi$
$938$	56.2964	+	23.3187i	1.83814	+	0.761383i
$939$			9.28250i			0.302923i
$940$	15.3146	−	36.9727i	0.499507	−	1.20592i
$941$	34.3095	−	14.2115i	1.11846	−	0.463280i	0.254615	−	0.967043i	$-0.418051\pi$
$941$	34.3095	−	14.2115i	1.11846	−	0.463280i	0.863842	+	0.503762i	$0.168051\pi$
$942$	25.7671	+	62.2074i	0.839539	+	2.02683i
$943$	27.0130	+	27.0130i	0.879665	+	0.879665i
$944$	−4.45102	−	4.45102i	−0.144868	−	0.144868i
$945$	−7.60943	−	18.3708i	−0.247535	−	0.597602i
$946$	40.7124	−	16.8636i	1.32367	−	0.548283i
$947$	−0.853817	+	2.06130i	−0.0277453	+	0.0669832i	−0.937145	−	0.348940i	$-0.886542\pi$
$947$	−0.853817	+	2.06130i	−0.0277453	+	0.0669832i	0.909400	+	0.415923i	$0.136542\pi$
$948$		−	50.0765i		−	1.62641i
$949$	6.36792	+	2.63768i	0.206712	+	0.0856227i
$950$	6.04403	−	6.04403i	0.196094	−	0.196094i
$951$	1.00528			0.0325986
$952$	−1.25250	+	53.1820i	−0.0405938	+	1.72364i
$953$	25.8280			0.836651			0.418326	−	0.908297i	$-0.362617\pi$
$953$	25.8280			0.836651			0.418326	+	0.908297i	$0.362617\pi$
$954$	−5.08404	+	5.08404i	−0.164602	+	0.164602i
$955$	−13.5461	−	5.61099i	−0.438342	−	0.181567i
$956$			58.7114i			1.89886i
$957$	−13.0596	+	31.5286i	−0.422157	+	1.01918i
$958$	−49.7808	+	20.6199i	−1.60834	+	0.666198i
$959$	−23.4849	−	56.6975i	−0.758366	−	1.83086i
$960$	−13.2822	−	13.2822i	−0.428681	−	0.428681i
$961$	−17.6966	−	17.6966i	−0.570857	−	0.570857i
$962$	5.21621	+	12.5930i	0.168177	+	0.406016i
$963$	0.309242	−	0.128092i	0.00996519	−	0.00412772i
$964$	8.00314	−	19.3213i	0.257764	−	0.622297i
$965$			8.39606i			0.270279i
$966$	107.895	+	44.6914i	3.47145	+	1.43792i
$967$	22.2041	−	22.2041i	0.714035	−	0.714035i	−0.253341	−	0.967377i	$-0.581530\pi$
$967$	22.2041	−	22.2041i	0.714035	−	0.714035i	0.967377	+	0.253341i	$0.0815296\pi$
$968$	17.4209			0.559930
$969$	−17.0153	+	16.2323i	−0.546612	+	0.521457i
$970$	−23.0966			−0.741587
$971$	29.0808	−	29.0808i	0.933248	−	0.933248i	−0.0646590	−	0.997907i	$-0.520596\pi$
$971$	29.0808	−	29.0808i	0.933248	−	0.933248i	0.997907	+	0.0646590i	$0.0205960\pi$
$972$	−17.9789	−	7.44709i	−0.576672	−	0.238865i
$973$			7.64093i			0.244957i
$974$	14.1427	−	34.1435i	0.453161	−	1.09403i
$975$	1.82611	−	0.756400i	0.0584824	−	0.0242242i
$976$	−0.130882	−	0.315978i	−0.00418944	−	0.0101142i
$977$	−19.7205	−	19.7205i	−0.630916	−	0.630916i	0.317382	−	0.948298i	$-0.397196\pi$
$977$	−19.7205	−	19.7205i	−0.630916	−	0.630916i	−0.948298	+	0.317382i	$0.897196\pi$
$978$	24.4420	+	24.4420i	0.781569	+	0.781569i
$979$	2.08393	+	5.03105i	0.0666026	+	0.160793i
$980$	−19.0264	+	7.88098i	−0.607775	+	0.251749i
$981$	1.27228	−	3.07156i	0.0406208	−	0.0980673i
$982$		−	2.02071i		−	0.0644836i
$983$	−52.3778	−	21.6956i	−1.67059	−	0.691982i	−0.671782	−	0.740749i	$-0.734471\pi$
$983$	−52.3778	−	21.6956i	−1.67059	−	0.691982i	−0.998810	+	0.0487673i	$0.984471\pi$
$984$	17.2866	−	17.2866i	0.551075	−	0.551075i
$985$	6.68150			0.212890
$986$	58.6303	+	61.4585i	1.86717	+	1.95724i
$987$	−63.7050			−2.02775
$988$	11.4301	−	11.4301i	0.363641	−	0.363641i
$989$	−61.5894	−	25.5112i	−1.95843	−	0.811208i
$990$		−	3.13626i		−	0.0996768i
$991$	−13.7333	+	33.1551i	−0.436252	+	1.05321i	0.540980	+	0.841035i	$0.318053\pi$
$991$	−13.7333	+	33.1551i	−0.436252	+	1.05321i	−0.977233	+	0.212171i	$0.931947\pi$
$992$	8.78730	−	3.63982i	0.278997	−	0.115564i
$993$	7.00310	+	16.9070i	0.222237	+	0.536526i
$994$	−10.9481	−	10.9481i	−0.347253	−	0.347253i
$995$	13.3444	+	13.3444i	0.423045	+	0.423045i
$996$	−15.5157	−	37.4581i	−0.491633	−	1.18691i
$997$	30.4465	−	12.6113i	0.964249	−	0.399405i	0.155681	−	0.987807i	$-0.450243\pi$
$997$	30.4465	−	12.6113i	0.964249	−	0.399405i	0.808568	+	0.588402i	$0.200243\pi$
$998$	−20.3764	+	49.1930i	−0.645004	+	1.55718i
$999$		−	25.5433i		−	0.808153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.26.6	✓	24
3.2	odd	2		765.2.be.b.451.1		24
5.2	odd	4		425.2.n.f.349.6		24
5.3	odd	4		425.2.n.c.349.1		24
5.4	even	2		425.2.m.b.26.1		24
17.2	even	8	inner	85.2.l.a.36.6	yes	24
17.6	odd	16		1445.2.a.p.1.12		12
17.7	odd	16		1445.2.d.j.866.1		24
17.10	odd	16		1445.2.d.j.866.2		24
17.11	odd	16		1445.2.a.q.1.12		12
51.2	odd	8		765.2.be.b.631.1		24
85.2	odd	8		425.2.n.c.274.1		24
85.19	even	8		425.2.m.b.376.1		24
85.53	odd	8		425.2.n.f.274.6		24
85.74	odd	16		7225.2.a.bs.1.1		12
85.79	odd	16		7225.2.a.bq.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.6	✓	24	1.1	even	1	trivial
85.2.l.a.36.6	yes	24	17.2	even	8	inner
425.2.m.b.26.1		24	5.4	even	2
425.2.m.b.376.1		24	85.19	even	8
425.2.n.c.274.1		24	85.2	odd	8
425.2.n.c.349.1		24	5.3	odd	4
425.2.n.f.274.6		24	85.53	odd	8
425.2.n.f.349.6		24	5.2	odd	4
765.2.be.b.451.1		24	3.2	odd	2
765.2.be.b.631.1		24	51.2	odd	8
1445.2.a.p.1.12		12	17.6	odd	16
1445.2.a.q.1.12		12	17.11	odd	16
1445.2.d.j.866.1		24	17.7	odd	16
1445.2.d.j.866.2		24	17.10	odd	16
7225.2.a.bq.1.1		12	85.79	odd	16
7225.2.a.bs.1.1		12	85.74	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66305 - 1.66305i) q^{2} +(-1.44989 - 0.600564i) q^{3} -3.53144i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-3.41000 + 1.41247i) q^{6} +(1.37082 + 3.30945i) q^{7} +(-2.54686 - 2.54686i) q^{8} +(-0.379815 - 0.379815i) q^{9} +(0.900034 + 2.17287i) q^{10} +(2.29362 - 0.950048i) q^{11} +(-2.12086 + 5.12021i) q^{12} -1.25948i q^{13} +(7.78350 + 3.22403i) q^{14} +(1.10970 - 1.10970i) q^{15} -1.40821 q^{16} +(-3.84535 + 1.48772i) q^{17} -1.26330 q^{18} +(-2.56985 + 2.56985i) q^{19} +(3.26263 + 1.35142i) q^{20} -5.62161i q^{21} +(2.23442 - 5.39437i) q^{22} +(-8.16056 + 3.38021i) q^{23} +(2.16312 + 5.22222i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(-2.09458 - 2.09458i) q^{26} +(2.12428 + 5.12847i) q^{27} +(11.6871 - 4.84097i) q^{28} +(3.35200 - 8.09244i) q^{29} -3.69096i q^{30} +(2.25799 + 0.935290i) q^{31} +(2.75181 - 2.75181i) q^{32} -3.89606 q^{33} +(-3.92084 + 8.86913i) q^{34} -3.58212 q^{35} +(-1.34129 + 1.34129i) q^{36} +(-4.25128 - 1.76094i) q^{37} +8.54755i q^{38} +(-0.756400 + 1.82611i) q^{39} +(3.32763 - 1.37835i) q^{40} +(-1.65510 - 3.99575i) q^{41} +(-9.34899 - 9.34899i) q^{42} +(5.33668 + 5.33668i) q^{43} +(-3.35504 - 8.09978i) q^{44} +(0.496252 - 0.205554i) q^{45} +(-7.94993 + 19.1928i) q^{46} -11.3322i q^{47} +(2.04175 + 0.845719i) q^{48} +(-4.12357 + 4.12357i) q^{49} -2.35190 q^{50} +(6.46880 + 0.152348i) q^{51} -4.44779 q^{52} +(4.02442 - 4.02442i) q^{53} +(12.0616 + 4.99610i) q^{54} +2.48259i q^{55} +(4.93742 - 11.9200i) q^{56} +(5.26936 - 2.18264i) q^{57} +(-7.88357 - 19.0326i) q^{58} +(3.16077 + 3.16077i) q^{59} +(-3.91884 - 3.91884i) q^{60} +(0.0929426 + 0.224383i) q^{61} +(5.31057 - 2.19971i) q^{62} +(0.736321 - 1.77764i) q^{63} -11.9692i q^{64} +(1.16361 + 0.481983i) q^{65} +(-6.47933 + 6.47933i) q^{66} +7.23278 q^{67} +(5.25380 + 13.5796i) q^{68} +13.8620 q^{69} +(-5.95724 + 5.95724i) q^{70} +(-1.69789 - 0.703290i) q^{71} +1.93467i q^{72} +(-2.09426 + 5.05599i) q^{73} +(-9.99859 + 4.14155i) q^{74} +(0.600564 + 1.44989i) q^{75} +(9.07527 + 9.07527i) q^{76} +(6.28827 + 6.28827i) q^{77} +(1.77898 + 4.29484i) q^{78} +(-8.34789 + 3.45781i) q^{79} +(0.538897 - 1.30101i) q^{80} -7.10006i q^{81} +(-9.39762 - 3.89262i) q^{82} +(-5.17302 + 5.17302i) q^{83} -19.8524 q^{84} +(0.0970771 - 4.12196i) q^{85} +17.7503 q^{86} +(-9.72006 + 9.72006i) q^{87} +(-8.26117 - 3.42189i) q^{88} +2.19350i q^{89} +(0.483443 - 1.16714i) q^{90} +(4.16819 - 1.72652i) q^{91} +(11.9370 + 28.8186i) q^{92} +(-2.71214 - 2.71214i) q^{93} +(-18.8459 - 18.8459i) q^{94} +(-1.39079 - 3.35767i) q^{95} +(-5.64246 + 2.33718i) q^{96} +(-3.75810 + 9.07286i) q^{97} +13.7154i q^{98} +(-1.23199 - 0.510308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Introduction

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